LMFDB - Embedded newform 547.8.a.b.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,8,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	547.a (trivial)

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:	yes
Analytic conductor:	$170.874608940$
Analytic rank:	$0$
Dimension:	$162$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-19.0596 q^{2} -63.9317 q^{3} +235.270 q^{4} -257.662 q^{5} +1218.51 q^{6} +712.325 q^{7} -2044.53 q^{8} +1900.26 q^{9} +O(q^{10})$	\(q-19.0596 q^{2} -63.9317 q^{3} +235.270 q^{4} -257.662 q^{5} +1218.51 q^{6} +712.325 q^{7} -2044.53 q^{8} +1900.26 q^{9} +4910.95 q^{10} +747.391 q^{11} -15041.2 q^{12} -8700.23 q^{13} -13576.7 q^{14} +16472.8 q^{15} +8853.40 q^{16} -10608.4 q^{17} -36218.2 q^{18} -21633.5 q^{19} -60620.2 q^{20} -45540.1 q^{21} -14245.0 q^{22} -46696.5 q^{23} +130710. q^{24} -11735.0 q^{25} +165823. q^{26} +18332.0 q^{27} +167589. q^{28} +85633.0 q^{29} -313965. q^{30} +243736. q^{31} +92956.8 q^{32} -47781.9 q^{33} +202192. q^{34} -183539. q^{35} +447073. q^{36} -200607. q^{37} +412327. q^{38} +556220. q^{39} +526798. q^{40} -713952. q^{41} +867979. q^{42} -393315. q^{43} +175839. q^{44} -489625. q^{45} +890018. q^{46} +587162. q^{47} -566013. q^{48} -316136. q^{49} +223666. q^{50} +678212. q^{51} -2.04690e6 q^{52} +1.63327e6 q^{53} -349401. q^{54} -192575. q^{55} -1.45637e6 q^{56} +1.38306e6 q^{57} -1.63214e6 q^{58} +2.31149e6 q^{59} +3.87555e6 q^{60} -2.97105e6 q^{61} -4.64552e6 q^{62} +1.35360e6 q^{63} -2.90496e6 q^{64} +2.24172e6 q^{65} +910707. q^{66} +1.42002e6 q^{67} -2.49584e6 q^{68} +2.98538e6 q^{69} +3.49820e6 q^{70} -3.64051e6 q^{71} -3.88513e6 q^{72} +6.29974e6 q^{73} +3.82349e6 q^{74} +750241. q^{75} -5.08971e6 q^{76} +532385. q^{77} -1.06014e7 q^{78} +2.98121e6 q^{79} -2.28119e6 q^{80} -5.32785e6 q^{81} +1.36077e7 q^{82} -736516. q^{83} -1.07142e7 q^{84} +2.73339e6 q^{85} +7.49645e6 q^{86} -5.47466e6 q^{87} -1.52806e6 q^{88} -1.27479e7 q^{89} +9.33208e6 q^{90} -6.19739e6 q^{91} -1.09863e7 q^{92} -1.55824e7 q^{93} -1.11911e7 q^{94} +5.57414e6 q^{95} -5.94288e6 q^{96} -1.30250e7 q^{97} +6.02544e6 q^{98} +1.42023e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 48 q^{2} + 310 q^{3} + 10650 q^{4} + 3999 q^{5} + 1998 q^{6} + 4301 q^{7} + 9216 q^{8} + 124464 q^{9}+O(q^{10}) $ 162 * q + 48 * q^2 + 310 * q^3 + 10650 * q^4 + 3999 * q^5 + 1998 * q^6 + 4301 * q^7 + 9216 * q^8 + 124464 * q^9	\( 162 q + 48 q^{2} + 310 q^{3} + 10650 q^{4} + 3999 q^{5} + 1998 q^{6} + 4301 q^{7} + 9216 q^{8} + 124464 q^{9} + 7430 q^{10} + 19840 q^{11} + 55737 q^{12} + 51223 q^{13} + 75679 q^{14} + 44609 q^{15} + 709506 q^{16} + 258906 q^{17} + 135171 q^{18} + 80362 q^{19} + 506432 q^{20} + 138572 q^{21} + 158320 q^{22} + 571410 q^{23} + 325871 q^{24} + 2732541 q^{25} + 488640 q^{26} + 772231 q^{27} + 699304 q^{28} + 968170 q^{29} + 301526 q^{30} + 348203 q^{31} + 1078196 q^{32} + 1536618 q^{33} + 870073 q^{34} + 1089291 q^{35} + 8775356 q^{36} + 2226256 q^{37} + 3884597 q^{38} + 923555 q^{39} + 2518352 q^{40} + 1825935 q^{41} + 3419892 q^{42} + 1582376 q^{43} + 4352040 q^{44} + 9457186 q^{45} + 1012278 q^{46} + 4801410 q^{47} + 9073674 q^{48} + 21448221 q^{49} + 2366848 q^{50} + 3749747 q^{51} + 7035334 q^{52} + 17191348 q^{53} + 5748697 q^{54} + 5271331 q^{55} + 14854657 q^{56} + 5393884 q^{57} + 4036260 q^{58} + 8263804 q^{59} + 10193498 q^{60} + 12366404 q^{61} + 18470554 q^{62} + 15526895 q^{63} + 49399626 q^{64} + 17325330 q^{65} + 11279868 q^{66} + 5477434 q^{67} + 44562265 q^{68} + 26851278 q^{69} + 9428823 q^{70} + 12108395 q^{71} + 22153063 q^{72} + 13995388 q^{73} + 13478769 q^{74} + 24654171 q^{75} + 8225460 q^{76} + 61240119 q^{77} + 17624449 q^{78} + 8215066 q^{79} + 65708461 q^{80} + 112675190 q^{81} + 29179962 q^{82} + 33597369 q^{83} + 13895447 q^{84} + 24308391 q^{85} + 22043075 q^{86} + 25661967 q^{87} + 32743591 q^{88} + 47538968 q^{89} + 46132321 q^{90} + 24574095 q^{91} + 108017386 q^{92} + 63765304 q^{93} + 41203657 q^{94} + 38032578 q^{95} + 41465754 q^{96} + 45954628 q^{97} + 37164970 q^{98} + 43882333 q^{99}+O(q^{100}) \) 162 * q + 48 * q^2 + 310 * q^3 + 10650 * q^4 + 3999 * q^5 + 1998 * q^6 + 4301 * q^7 + 9216 * q^8 + 124464 * q^9 + 7430 * q^10 + 19840 * q^11 + 55737 * q^12 + 51223 * q^13 + 75679 * q^14 + 44609 * q^15 + 709506 * q^16 + 258906 * q^17 + 135171 * q^18 + 80362 * q^19 + 506432 * q^20 + 138572 * q^21 + 158320 * q^22 + 571410 * q^23 + 325871 * q^24 + 2732541 * q^25 + 488640 * q^26 + 772231 * q^27 + 699304 * q^28 + 968170 * q^29 + 301526 * q^30 + 348203 * q^31 + 1078196 * q^32 + 1536618 * q^33 + 870073 * q^34 + 1089291 * q^35 + 8775356 * q^36 + 2226256 * q^37 + 3884597 * q^38 + 923555 * q^39 + 2518352 * q^40 + 1825935 * q^41 + 3419892 * q^42 + 1582376 * q^43 + 4352040 * q^44 + 9457186 * q^45 + 1012278 * q^46 + 4801410 * q^47 + 9073674 * q^48 + 21448221 * q^49 + 2366848 * q^50 + 3749747 * q^51 + 7035334 * q^52 + 17191348 * q^53 + 5748697 * q^54 + 5271331 * q^55 + 14854657 * q^56 + 5393884 * q^57 + 4036260 * q^58 + 8263804 * q^59 + 10193498 * q^60 + 12366404 * q^61 + 18470554 * q^62 + 15526895 * q^63 + 49399626 * q^64 + 17325330 * q^65 + 11279868 * q^66 + 5477434 * q^67 + 44562265 * q^68 + 26851278 * q^69 + 9428823 * q^70 + 12108395 * q^71 + 22153063 * q^72 + 13995388 * q^73 + 13478769 * q^74 + 24654171 * q^75 + 8225460 * q^76 + 61240119 * q^77 + 17624449 * q^78 + 8215066 * q^79 + 65708461 * q^80 + 112675190 * q^81 + 29179962 * q^82 + 33597369 * q^83 + 13895447 * q^84 + 24308391 * q^85 + 22043075 * q^86 + 25661967 * q^87 + 32743591 * q^88 + 47538968 * q^89 + 46132321 * q^90 + 24574095 * q^91 + 108017386 * q^92 + 63765304 * q^93 + 41203657 * q^94 + 38032578 * q^95 + 41465754 * q^96 + 45954628 * q^97 + 37164970 * q^98 + 43882333 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−19.0596	−1.68465	−0.842325	−	0.538970i	$-0.818814\pi$
$2$	−19.0596	−1.68465	−0.842325	+	0.538970i	$0.818814\pi$
$3$	−63.9317	−1.36707	−0.683536	−	0.729917i	$-0.739559\pi$
$3$	−63.9317	−1.36707	−0.683536	+	0.729917i	$0.739559\pi$
$4$	235.270	1.83805
$5$	−257.662	−0.921841	−0.460921	−	0.887441i	$-0.652481\pi$
$5$	−257.662	−0.921841	−0.460921	+	0.887441i	$0.652481\pi$
$6$	1218.51	2.30304
$7$	712.325	0.784938	0.392469	−	0.919765i	$-0.371621\pi$
$7$	712.325	0.784938	0.392469	+	0.919765i	$0.371621\pi$
$8$	−2044.53	−1.41182
$9$	1900.26	0.868887
$10$	4910.95	1.55298
$11$	747.391	0.169306	0.0846532	−	0.996410i	$-0.473022\pi$
$11$	747.391	0.169306	0.0846532	+	0.996410i	$0.473022\pi$
$12$	−15041.2	−2.51274
$13$	−8700.23	−1.09832	−0.549160	−	0.835717i	$-0.685052\pi$
$13$	−8700.23	−1.09832	−0.549160	+	0.835717i	$0.685052\pi$
$14$	−13576.7	−1.32235
$15$	16472.8	1.26022
$16$	8853.40	0.540369
$17$	−10608.4	−0.523695	−0.261848	−	0.965109i	$-0.584332\pi$
$17$	−10608.4	−0.523695	−0.261848	+	0.965109i	$0.584332\pi$
$18$	−36218.2	−1.46377
$19$	−21633.5	−0.723584	−0.361792	−	0.932259i	$-0.617835\pi$
$19$	−21633.5	−0.723584	−0.361792	+	0.932259i	$0.617835\pi$
$20$	−60620.2	−1.69439
$21$	−45540.1	−1.07307
$22$	−14245.0	−0.285222
$23$	−46696.5	−0.800270	−0.400135	−	0.916456i	$-0.631037\pi$
$23$	−46696.5	−0.800270	−0.400135	+	0.916456i	$0.631037\pi$
$24$	130710.	1.93005
$25$	−11735.0	−0.150209
$26$	165823.	1.85029
$27$	18332.0	0.179240
$28$	167589.	1.44275
$29$	85633.0	0.652001	0.326001	−	0.945370i	$-0.394299\pi$
$29$	85633.0	0.652001	0.326001	+	0.945370i	$0.394299\pi$
$30$	−313965.	−2.12304
$31$	243736.	1.46944	0.734722	−	0.678368i	$-0.237312\pi$
$31$	243736.	1.46944	0.734722	+	0.678368i	$0.237312\pi$
$32$	92956.8	0.501483
$33$	−47781.9	−0.231454
$34$	202192.	0.882243
$35$	−183539.	−0.723588
$36$	447073.	1.59706
$37$	−200607.	−0.651087	−0.325544	−	0.945527i	$-0.605547\pi$
$37$	−200607.	−0.651087	−0.325544	+	0.945527i	$0.605547\pi$
$38$	412327.	1.21899
$39$	556220.	1.50148
$40$	526798.	1.30147
$41$	−713952.	−1.61780	−0.808901	−	0.587945i	$-0.799937\pi$
$41$	−713952.	−1.61780	−0.808901	+	0.587945i	$0.799937\pi$
$42$	867979.	1.80774
$43$	−393315.	−0.754399	−0.377200	−	0.926132i	$-0.623113\pi$
$43$	−393315.	−0.754399	−0.377200	+	0.926132i	$0.623113\pi$
$44$	175839.	0.311193
$45$	−489625.	−0.800976
$46$	890018.	1.34817
$47$	587162.	0.824927	0.412464	−	0.910974i	$-0.364668\pi$
$47$	587162.	0.824927	0.412464	+	0.910974i	$0.364668\pi$
$48$	−566013.	−0.738723
$49$	−316136.	−0.383873
$50$	223666.	0.253049
$51$	678212.	0.715929
$52$	−2.04690e6	−2.01876
$53$	1.63327e6	1.50693	0.753464	−	0.657489i	$-0.228381\pi$
$53$	1.63327e6	1.50693	0.753464	+	0.657489i	$0.228381\pi$
$54$	−349401.	−0.301957
$55$	−192575.	−0.156074
$56$	−1.45637e6	−1.10819
$57$	1.38306e6	0.989192
$58$	−1.63214e6	−1.09839
$59$	2.31149e6	1.46524	0.732622	−	0.680636i	$-0.238297\pi$
$59$	2.31149e6	1.46524	0.732622	+	0.680636i	$0.238297\pi$
$60$	3.87555e6	2.31635
$61$	−2.97105e6	−1.67593	−0.837966	−	0.545723i	$-0.816255\pi$
$61$	−2.97105e6	−1.67593	−0.837966	+	0.545723i	$0.816255\pi$
$62$	−4.64552e6	−2.47550
$63$	1.35360e6	0.682022
$64$	−2.90496e6	−1.38519
$65$	2.24172e6	1.01248
$66$	910707.	0.389919
$67$	1.42002e6	0.576811	0.288405	−	0.957508i	$-0.406875\pi$
$67$	1.42002e6	0.576811	0.288405	+	0.957508i	$0.406875\pi$
$68$	−2.49584e6	−0.962576
$69$	2.98538e6	1.09403
$70$	3.49820e6	1.21899
$71$	−3.64051e6	−1.20714	−0.603570	−	0.797310i	$-0.706256\pi$
$71$	−3.64051e6	−1.20714	−0.603570	+	0.797310i	$0.706256\pi$
$72$	−3.88513e6	−1.22671
$73$	6.29974e6	1.89536	0.947682	−	0.319216i	$-0.103419\pi$
$73$	6.29974e6	1.89536	0.947682	+	0.319216i	$0.103419\pi$
$74$	3.82349e6	1.09685
$75$	750241.	0.205346
$76$	−5.08971e6	−1.32998
$77$	532385.	0.132895
$78$	−1.06014e7	−2.52948
$79$	2.98121e6	0.680295	0.340148	−	0.940372i	$-0.389523\pi$
$79$	2.98121e6	0.680295	0.340148	+	0.940372i	$0.389523\pi$
$80$	−2.28119e6	−0.498134
$81$	−5.32785e6	−1.11392
$82$	1.36077e7	2.72543
$83$	−736516.	−0.141387	−0.0706934	−	0.997498i	$-0.522521\pi$
$83$	−736516.	−0.141387	−0.0706934	+	0.997498i	$0.522521\pi$
$84$	−1.07142e7	−1.97235
$85$	2.73339e6	0.482764
$86$	7.49645e6	1.27090
$87$	−5.47466e6	−0.891333
$88$	−1.52806e6	−0.239029
$89$	−1.27479e7	−1.91678	−0.958392	−	0.285454i	$-0.907856\pi$
$89$	−1.27479e7	−1.91678	−0.958392	+	0.285454i	$0.907856\pi$
$90$	9.33208e6	1.34937
$91$	−6.19739e6	−0.862113
$92$	−1.09863e7	−1.47093
$93$	−1.55824e7	−2.00884
$94$	−1.11911e7	−1.38971
$95$	5.57414e6	0.667030
$96$	−5.94288e6	−0.685564
$97$	−1.30250e7	−1.44902	−0.724511	−	0.689263i	$-0.757935\pi$
$97$	−1.30250e7	−1.44902	−0.724511	+	0.689263i	$0.757935\pi$
$98$	6.02544e6	0.646692
$99$	1.42023e6	0.147108
$100$	−2.76090e6	−0.276090
$101$	−5.46856e6	−0.528139	−0.264069	−	0.964504i	$-0.585065\pi$
$101$	−5.46856e6	−0.528139	−0.264069	+	0.964504i	$0.585065\pi$
$102$	−1.29265e7	−1.20609
$103$	−1.65204e7	−1.48967	−0.744835	−	0.667249i	$-0.767472\pi$
$103$	−1.65204e7	−1.48967	−0.744835	+	0.667249i	$0.767472\pi$
$104$	1.77879e7	1.55063
$105$	1.17340e7	0.989197
$106$	−3.11296e7	−2.53865
$107$	1.24896e7	0.985610	0.492805	−	0.870140i	$-0.335972\pi$
$107$	1.24896e7	0.985610	0.492805	+	0.870140i	$0.335972\pi$
$108$	4.31296e6	0.329452
$109$	−5.80692e6	−0.429490	−0.214745	−	0.976670i	$-0.568892\pi$
$109$	−5.80692e6	−0.429490	−0.214745	+	0.976670i	$0.568892\pi$
$110$	3.67040e6	0.262929
$111$	1.28251e7	0.890083
$112$	6.30650e6	0.424156
$113$	7.76904e6	0.506515	0.253258	−	0.967399i	$-0.418498\pi$
$113$	7.76904e6	0.506515	0.253258	+	0.967399i	$0.418498\pi$
$114$	−2.63607e7	−1.66644
$115$	1.20319e7	0.737722
$116$	2.01469e7	1.19841
$117$	−1.65327e7	−0.954317
$118$	−4.40561e7	−2.46842
$119$	−7.55663e6	−0.411068
$120$	−3.36791e7	−1.77920
$121$	−1.89286e7	−0.971335
$122$	5.66272e7	2.82336
$123$	4.56441e7	2.21165
$124$	5.73437e7	2.70091
$125$	2.31536e7	1.06031
$126$	−2.57991e7	−1.14897
$127$	−3.90644e6	−0.169226	−0.0846132	−	0.996414i	$-0.526965\pi$
$127$	−3.90644e6	−0.169226	−0.0846132	+	0.996414i	$0.526965\pi$
$128$	4.34690e7	1.83208
$129$	2.51453e7	1.03132
$130$	−4.27265e7	−1.70567
$131$	−1.31960e7	−0.512852	−0.256426	−	0.966564i	$-0.582545\pi$
$131$	−1.31960e7	−0.512852	−0.256426	+	0.966564i	$0.582545\pi$
$132$	−1.12417e7	−0.425424
$133$	−1.54101e7	−0.567968
$134$	−2.70651e7	−0.971724
$135$	−4.72346e6	−0.165231
$136$	2.16892e7	0.739361
$137$	−4.61243e7	−1.53252	−0.766262	−	0.642528i	$-0.777886\pi$
$137$	−4.61243e7	−1.53252	−0.766262	+	0.642528i	$0.777886\pi$
$138$	−5.69003e7	−1.84305
$139$	−5.40135e7	−1.70589	−0.852943	−	0.522003i	$-0.825185\pi$
$139$	−5.40135e7	−1.70589	−0.852943	+	0.522003i	$0.825185\pi$
$140$	−4.31813e7	−1.32999
$141$	−3.75383e7	−1.12774
$142$	6.93868e7	2.03361
$143$	−6.50247e6	−0.185953
$144$	1.68237e7	0.469520
$145$	−2.20644e7	−0.601042
$146$	−1.20071e8	−3.19303
$147$	2.02111e7	0.524782
$148$	−4.71967e7	−1.19673
$149$	−1.45373e7	−0.360025	−0.180012	−	0.983664i	$-0.557614\pi$
$149$	−1.45373e7	−0.360025	−0.180012	+	0.983664i	$0.557614\pi$
$150$	−1.42993e7	−0.345936
$151$	5.76150e7	1.36181	0.680905	−	0.732372i	$-0.261587\pi$
$151$	5.76150e7	1.36181	0.680905	+	0.732372i	$0.261587\pi$
$152$	4.42303e7	1.02157
$153$	−2.01587e7	−0.455032
$154$	−1.01471e7	−0.223882
$155$	−6.28015e7	−1.35459
$156$	1.30862e8	2.75980
$157$	−7.79992e7	−1.60858	−0.804288	−	0.594240i	$-0.797453\pi$
$157$	−7.79992e7	−1.60858	−0.804288	+	0.594240i	$0.797453\pi$
$158$	−5.68208e7	−1.14606
$159$	−1.04418e8	−2.06008
$160$	−2.39515e7	−0.462288
$161$	−3.32631e7	−0.628162
$162$	1.01547e8	1.87657
$163$	−1.71645e7	−0.310438	−0.155219	−	0.987880i	$-0.549608\pi$
$163$	−1.71645e7	−0.310438	−0.155219	+	0.987880i	$0.549608\pi$
$164$	−1.67971e8	−2.97359
$165$	1.23116e7	0.213364
$166$	1.40377e7	0.238187
$167$	3.78331e7	0.628585	0.314293	−	0.949326i	$-0.398233\pi$
$167$	3.78331e7	0.628585	0.314293	+	0.949326i	$0.398233\pi$
$168$	9.31080e7	1.51497
$169$	1.29455e7	0.206308
$170$	−5.20974e7	−0.813288
$171$	−4.11092e7	−0.628713
$172$	−9.25353e7	−1.38662
$173$	1.87502e7	0.275324	0.137662	−	0.990479i	$-0.456041\pi$
$173$	1.87502e7	0.275324	0.137662	+	0.990479i	$0.456041\pi$
$174$	1.04345e8	1.50158
$175$	−8.35917e6	−0.117904
$176$	6.61695e6	0.0914879
$177$	−1.47777e8	−2.00309
$178$	2.42970e8	3.22911
$179$	5.93554e7	0.773526	0.386763	−	0.922179i	$-0.373593\pi$
$179$	5.93554e7	0.773526	0.386763	+	0.922179i	$0.373593\pi$
$180$	−1.15194e8	−1.47223
$181$	−9.76119e7	−1.22357	−0.611784	−	0.791025i	$-0.709548\pi$
$181$	−9.76119e7	−1.22357	−0.611784	+	0.791025i	$0.709548\pi$
$182$	1.18120e8	1.45236
$183$	1.89944e8	2.29112
$184$	9.54722e7	1.12983
$185$	5.16888e7	0.600199
$186$	2.96996e8	3.38419
$187$	−7.92862e6	−0.0886649
$188$	1.38142e8	1.51625
$189$	1.30583e7	0.140692
$190$	−1.06241e8	−1.12371
$191$	−4.07543e7	−0.423210	−0.211605	−	0.977355i	$-0.567869\pi$
$191$	−4.07543e7	−0.423210	−0.211605	+	0.977355i	$0.567869\pi$
$192$	1.85719e8	1.89366
$193$	−1.40187e8	−1.40364	−0.701822	−	0.712352i	$-0.747630\pi$
$193$	−1.40187e8	−1.40364	−0.701822	+	0.712352i	$0.747630\pi$
$194$	2.48251e8	2.44110
$195$	−1.43317e8	−1.38413
$196$	−7.43773e7	−0.705576
$197$	−8.53805e7	−0.795659	−0.397829	−	0.917459i	$-0.630236\pi$
$197$	−8.53805e7	−0.795659	−0.397829	+	0.917459i	$0.630236\pi$
$198$	−2.70692e7	−0.247826
$199$	9.31957e7	0.838321	0.419160	−	0.907912i	$-0.362325\pi$
$199$	9.31957e7	0.838321	0.419160	+	0.907912i	$0.362325\pi$
$200$	2.39926e7	0.212067
$201$	−9.07844e7	−0.788542
$202$	1.04229e8	0.889729
$203$	6.09986e7	0.511780
$204$	1.59563e8	1.31591
$205$	1.83959e8	1.49136
$206$	3.14873e8	2.50957
$207$	−8.87353e7	−0.695344
$208$	−7.70267e7	−0.593498
$209$	−1.61687e7	−0.122507
$210$	−2.23646e8	−1.66645
$211$	−2.27844e8	−1.66974	−0.834871	−	0.550446i	$-0.814458\pi$
$211$	−2.27844e8	−1.66974	−0.834871	+	0.550446i	$0.814458\pi$
$212$	3.84260e8	2.76980
$213$	2.32744e8	1.65025
$214$	−2.38047e8	−1.66041
$215$	1.01343e8	0.695436
$216$	−3.74802e7	−0.253054
$217$	1.73619e8	1.15342
$218$	1.10678e8	0.723541
$219$	−4.02753e8	−2.59110
$220$	−4.53070e7	−0.286871
$221$	9.22955e7	0.575185
$222$	−2.44442e8	−1.49948
$223$	1.37493e8	0.830258	0.415129	−	0.909763i	$-0.363736\pi$
$223$	1.37493e8	0.830258	0.415129	+	0.909763i	$0.363736\pi$
$224$	6.62155e7	0.393633
$225$	−2.22996e7	−0.130514
$226$	−1.48075e8	−0.853301
$227$	−6.43979e7	−0.365411	−0.182705	−	0.983168i	$-0.558485\pi$
$227$	−6.43979e7	−0.365411	−0.182705	+	0.983168i	$0.558485\pi$
$228$	3.25394e8	1.81818
$229$	3.02401e8	1.66402	0.832010	−	0.554761i	$-0.187190\pi$
$229$	3.02401e8	1.66402	0.832010	+	0.554761i	$0.187190\pi$
$230$	−2.29324e8	−1.24280
$231$	−3.40363e7	−0.181677
$232$	−1.75079e8	−0.920505
$233$	−2.34746e8	−1.21577	−0.607887	−	0.794023i	$-0.707983\pi$
$233$	−2.34746e8	−1.21577	−0.607887	+	0.794023i	$0.707983\pi$
$234$	3.15107e8	1.60769
$235$	−1.51290e8	−0.760452
$236$	5.43824e8	2.69319
$237$	−1.90594e8	−0.930013
$238$	1.44027e8	0.692506
$239$	−1.92016e8	−0.909798	−0.454899	−	0.890543i	$-0.650325\pi$
$239$	−1.92016e8	−0.909798	−0.454899	+	0.890543i	$0.650325\pi$
$240$	1.45840e8	0.680986
$241$	2.47335e8	1.13822	0.569109	−	0.822262i	$-0.307288\pi$
$241$	2.47335e8	1.13822	0.569109	+	0.822262i	$0.307288\pi$
$242$	3.60772e8	1.63636
$243$	3.00527e8	1.34357
$244$	−6.99000e8	−3.08044
$245$	8.14564e7	0.353870
$246$	−8.69960e8	−3.72586
$247$	1.88216e8	0.794727
$248$	−4.98324e8	−2.07458
$249$	4.70867e7	0.193286
$250$	−4.41299e8	−1.78625
$251$	1.25987e8	0.502883	0.251442	−	0.967872i	$-0.419095\pi$
$251$	1.25987e8	0.502883	0.251442	+	0.967872i	$0.419095\pi$
$252$	3.18462e8	1.25359
$253$	−3.49005e7	−0.135491
$254$	7.44553e7	0.285087
$255$	−1.74750e8	−0.659973
$256$	−4.56669e8	−1.70122
$257$	4.20152e8	1.54398	0.771989	−	0.635636i	$-0.219262\pi$
$257$	4.20152e8	1.54398	0.771989	+	0.635636i	$0.219262\pi$
$258$	−4.79260e8	−1.73741
$259$	−1.42897e8	−0.511063
$260$	5.27410e8	1.86098
$261$	1.62725e8	0.566516
$262$	2.51511e8	0.863977
$263$	−3.89517e7	−0.132033	−0.0660163	−	0.997819i	$-0.521029\pi$
$263$	−3.89517e7	−0.132033	−0.0660163	+	0.997819i	$0.521029\pi$
$264$	9.76915e7	0.326771
$265$	−4.20833e8	−1.38915
$266$	2.93711e8	0.956828
$267$	8.14994e8	2.62038
$268$	3.34089e8	1.06020
$269$	−5.92509e8	−1.85593	−0.927967	−	0.372664i	$-0.878445\pi$
$269$	−5.92509e8	−1.85593	−0.927967	+	0.372664i	$0.878445\pi$
$270$	9.00274e7	0.278357
$271$	−1.67605e8	−0.511556	−0.255778	−	0.966736i	$-0.582332\pi$
$271$	−1.67605e8	−0.511556	−0.255778	+	0.966736i	$0.582332\pi$
$272$	−9.39204e7	−0.282989
$273$	3.96210e8	1.17857
$274$	8.79112e8	2.58177
$275$	−8.77067e6	−0.0254313
$276$	7.02371e8	2.01087
$277$	−6.95993e8	−1.96755	−0.983775	−	0.179405i	$-0.942583\pi$
$277$	−6.95993e8	−1.96755	−0.983775	+	0.179405i	$0.942583\pi$
$278$	1.02948e9	2.87382
$279$	4.63160e8	1.27678
$280$	3.75251e8	1.02157
$281$	−2.49579e8	−0.671020	−0.335510	−	0.942037i	$-0.608909\pi$
$281$	−2.49579e8	−0.671020	−0.335510	+	0.942037i	$0.608909\pi$
$282$	7.15466e8	1.89984
$283$	1.31963e8	0.346098	0.173049	−	0.984913i	$-0.444638\pi$
$283$	1.31963e8	0.346098	0.173049	+	0.984913i	$0.444638\pi$
$284$	−8.56502e8	−2.21878
$285$	−3.56364e8	−0.911878
$286$	1.23935e8	0.313265
$287$	−5.08566e8	−1.26987
$288$	1.76642e8	0.435732
$289$	−2.97801e8	−0.725743
$290$	4.20540e8	1.01254
$291$	8.32707e8	1.98092
$292$	1.48214e9	3.48377
$293$	5.52597e8	1.28343	0.641714	−	0.766944i	$-0.278224\pi$
$293$	5.52597e8	1.28343	0.641714	+	0.766944i	$0.278224\pi$
$294$	−3.85216e8	−0.884074
$295$	−5.95584e8	−1.35072
$296$	4.10146e8	0.919215
$297$	1.37011e7	0.0303465
$298$	2.77076e8	0.606516
$299$	4.06270e8	0.878953
$300$	1.76509e8	0.377436
$301$	−2.80168e8	−0.592156
$302$	−1.09812e9	−2.29417
$303$	3.49614e8	0.722004
$304$	−1.91530e8	−0.391002
$305$	7.65529e8	1.54494
$306$	3.84217e8	0.766570
$307$	−3.01926e8	−0.595547	−0.297774	−	0.954637i	$-0.596244\pi$
$307$	−3.01926e8	−0.595547	−0.297774	+	0.954637i	$0.596244\pi$
$308$	1.25254e8	0.244267
$309$	1.05618e9	2.03649
$310$	1.19698e9	2.28202
$311$	1.03652e9	1.95397	0.976983	−	0.213316i	$-0.0684264\pi$
$311$	1.03652e9	1.95397	0.976983	+	0.213316i	$0.0684264\pi$
$312$	−1.13721e9	−2.11982
$313$	−4.16176e8	−0.767135	−0.383568	−	0.923513i	$-0.625305\pi$
$313$	−4.16176e8	−0.767135	−0.383568	+	0.923513i	$0.625305\pi$
$314$	1.48664e9	2.70989
$315$	−3.48772e8	−0.628716
$316$	7.01389e8	1.25041
$317$	−6.50043e8	−1.14613	−0.573066	−	0.819509i	$-0.694246\pi$
$317$	−6.50043e8	−1.14613	−0.573066	+	0.819509i	$0.694246\pi$
$318$	1.99016e9	3.47052
$319$	6.40013e7	0.110388
$320$	7.48499e8	1.27693
$321$	−7.98480e8	−1.34740
$322$	6.33982e8	1.05823
$323$	2.29497e8	0.378937
$324$	−1.25348e9	−2.04744
$325$	1.02098e8	0.164977
$326$	3.27149e8	0.522979
$327$	3.71246e8	0.587144
$328$	1.45969e9	2.28404
$329$	4.18250e8	0.647516
$330$	−2.34655e8	−0.359444
$331$	−4.25921e8	−0.645551	−0.322776	−	0.946476i	$-0.604616\pi$
$331$	−4.25921e8	−0.645551	−0.322776	+	0.946476i	$0.604616\pi$
$332$	−1.73280e8	−0.259875
$333$	−3.81204e8	−0.565721
$334$	−7.21085e8	−1.05895
$335$	−3.65886e8	−0.531728
$336$	−4.03185e8	−0.579852
$337$	1.49967e8	0.213447	0.106723	−	0.994289i	$-0.465964\pi$
$337$	1.49967e8	0.213447	0.106723	+	0.994289i	$0.465964\pi$
$338$	−2.46737e8	−0.347557
$339$	−4.96687e8	−0.692443
$340$	6.43084e8	0.887342
$341$	1.82166e8	0.248786
$342$	7.83526e8	1.05916
$343$	−8.11822e8	−1.08625
$344$	8.04144e8	1.06507
$345$	−7.69221e8	−1.00852
$346$	−3.57372e8	−0.463825
$347$	9.92881e8	1.27569	0.637844	−	0.770166i	$-0.279827\pi$
$347$	9.92881e8	1.27569	0.637844	+	0.770166i	$0.279827\pi$
$348$	−1.28802e9	−1.63831
$349$	−3.94569e8	−0.496860	−0.248430	−	0.968650i	$-0.579915\pi$
$349$	−3.94569e8	−0.496860	−0.248430	+	0.968650i	$0.579915\pi$
$350$	1.59323e8	0.198628
$351$	−1.59492e8	−0.196863
$352$	6.94751e7	0.0849043
$353$	1.44525e9	1.74876	0.874382	−	0.485238i	$-0.161267\pi$
$353$	1.44525e9	1.74876	0.874382	+	0.485238i	$0.161267\pi$
$354$	2.81658e9	3.37451
$355$	9.38022e8	1.11279
$356$	−2.99920e9	−3.52314
$357$	4.83108e8	0.561960
$358$	−1.13129e9	−1.30312
$359$	−1.26816e9	−1.44659	−0.723294	−	0.690541i	$-0.757373\pi$
$359$	−1.26816e9	−1.44659	−0.723294	+	0.690541i	$0.757373\pi$
$360$	1.00105e9	1.13083
$361$	−4.25864e8	−0.476426
$362$	1.86045e9	2.06128
$363$	1.21014e9	1.32789
$364$	−1.45806e9	−1.58460
$365$	−1.62321e9	−1.74722
$366$	−3.62027e9	−3.85974
$367$	−1.61345e8	−0.170383	−0.0851913	−	0.996365i	$-0.527150\pi$
$367$	−1.61345e8	−0.170383	−0.0851913	+	0.996365i	$0.527150\pi$
$368$	−4.13423e8	−0.432441
$369$	−1.35669e9	−1.40569
$370$	−9.85170e8	−1.01113
$371$	1.16342e9	1.18284
$372$	−3.66608e9	−3.69234
$373$	−1.82506e9	−1.82094	−0.910470	−	0.413574i	$-0.864280\pi$
$373$	−1.82506e9	−1.82094	−0.910470	+	0.413574i	$0.864280\pi$
$374$	1.51117e8	0.149369
$375$	−1.48025e9	−1.44952
$376$	−1.20047e9	−1.16465
$377$	−7.45027e8	−0.716106
$378$	−2.48887e8	−0.237018
$379$	1.60699e9	1.51627	0.758134	−	0.652099i	$-0.226111\pi$
$379$	1.60699e9	1.51627	0.758134	+	0.652099i	$0.226111\pi$
$380$	1.31143e9	1.22603
$381$	2.49745e8	0.231345
$382$	7.76762e8	0.712961
$383$	1.40920e8	0.128167	0.0640837	−	0.997945i	$-0.479588\pi$
$383$	1.40920e8	0.128167	0.0640837	+	0.997945i	$0.479588\pi$
$384$	−2.77905e9	−2.50459
$385$	−1.37176e8	−0.122508
$386$	2.67191e9	2.36465
$387$	−7.47400e8	−0.655488
$388$	−3.06438e9	−2.66337
$389$	−2.31189e9	−1.99133	−0.995666	−	0.0930008i	$-0.970354\pi$
$389$	−2.31189e9	−1.99133	−0.995666	+	0.0930008i	$0.970354\pi$
$390$	2.73157e9	2.33178
$391$	4.95375e8	0.419097
$392$	6.46348e8	0.541958
$393$	8.43641e8	0.701106
$394$	1.62732e9	1.34041
$395$	−7.68145e8	−0.627124
$396$	3.34139e8	0.270392
$397$	8.90051e8	0.713917	0.356959	−	0.934120i	$-0.383814\pi$
$397$	8.90051e8	0.713917	0.356959	+	0.934120i	$0.383814\pi$
$398$	−1.77628e9	−1.41228
$399$	9.85192e8	0.776454
$400$	−1.03895e8	−0.0811681
$401$	−1.20190e9	−0.930815	−0.465408	−	0.885096i	$-0.654092\pi$
$401$	−1.20190e9	−0.930815	−0.465408	+	0.885096i	$0.654092\pi$
$402$	1.73032e9	1.32842
$403$	−2.12056e9	−1.61392
$404$	−1.28659e9	−0.970744
$405$	1.37279e9	1.02686
$406$	−1.16261e9	−0.862171
$407$	−1.49931e8	−0.110233
$408$	−1.38662e9	−1.01076
$409$	−2.37000e9	−1.71284	−0.856421	−	0.516278i	$-0.827317\pi$
$409$	−2.37000e9	−1.71284	−0.856421	+	0.516278i	$0.827317\pi$
$410$	−3.50618e9	−2.51241
$411$	2.94880e9	2.09507
$412$	−3.88675e9	−2.73808
$413$	1.64653e9	1.15012
$414$	1.69126e9	1.17141
$415$	1.89772e8	0.130336
$416$	−8.08746e8	−0.550789
$417$	3.45317e9	2.33207
$418$	3.08169e8	0.206382
$419$	1.69206e7	0.0112374	0.00561871	−	0.999984i	$-0.498212\pi$
$419$	1.69206e7	0.0112374	0.00561871	+	0.999984i	$0.498212\pi$
$420$	2.76065e9	1.81819
$421$	2.46434e8	0.160958	0.0804792	−	0.996756i	$-0.474355\pi$
$421$	2.46434e8	0.160958	0.0804792	+	0.996756i	$0.474355\pi$
$422$	4.34263e9	2.81293
$423$	1.11576e9	0.716769
$424$	−3.33927e9	−2.12751
$425$	1.24490e8	0.0786635
$426$	−4.43601e9	−2.78009
$427$	−2.11636e9	−1.31550
$428$	2.93843e9	1.81160
$429$	4.15714e8	0.254211
$430$	−1.93155e9	−1.17157
$431$	2.07895e8	0.125076	0.0625381	−	0.998043i	$-0.480081\pi$
$431$	2.07895e8	0.125076	0.0625381	+	0.998043i	$0.480081\pi$
$432$	1.62300e8	0.0968559
$433$	−1.64520e9	−0.973890	−0.486945	−	0.873433i	$-0.661889\pi$
$433$	−1.64520e9	−0.973890	−0.486945	+	0.873433i	$0.661889\pi$
$434$	−3.30912e9	−1.94311
$435$	1.41061e9	0.821667
$436$	−1.36619e9	−0.789423
$437$	1.01021e9	0.579063
$438$	7.67633e9	4.36510
$439$	−9.07981e8	−0.512213	−0.256107	−	0.966649i	$-0.582440\pi$
$439$	−9.07981e8	−0.512213	−0.256107	+	0.966649i	$0.582440\pi$
$440$	3.93724e8	0.220347
$441$	−6.00739e8	−0.333542
$442$	−1.75912e9	−0.968986
$443$	3.18601e9	1.74114	0.870571	−	0.492042i	$-0.163749\pi$
$443$	3.18601e9	1.74114	0.870571	+	0.492042i	$0.163749\pi$
$444$	3.01736e9	1.63601
$445$	3.28465e9	1.76697
$446$	−2.62056e9	−1.39869
$447$	9.29395e8	0.492180
$448$	−2.06928e9	−1.08729
$449$	1.40051e9	0.730172	0.365086	−	0.930974i	$-0.381040\pi$
$449$	1.40051e9	0.730172	0.365086	+	0.930974i	$0.381040\pi$
$450$	4.25022e8	0.219871
$451$	−5.33601e8	−0.273904
$452$	1.82782e9	0.930999
$453$	−3.68342e9	−1.86169
$454$	1.22740e9	0.615589
$455$	1.59684e9	0.794732
$456$	−2.82771e9	−1.39656
$457$	−6.01066e8	−0.294588	−0.147294	−	0.989093i	$-0.547056\pi$
$457$	−6.01066e8	−0.294588	−0.147294	+	0.989093i	$0.547056\pi$
$458$	−5.76365e9	−2.80329
$459$	−1.94473e8	−0.0938673
$460$	2.83075e9	1.35597
$461$	1.35049e8	0.0642004	0.0321002	−	0.999485i	$-0.489780\pi$
$461$	1.35049e8	0.0642004	0.0321002	+	0.999485i	$0.489780\pi$
$462$	6.48719e8	0.306062
$463$	−1.19396e9	−0.559058	−0.279529	−	0.960137i	$-0.590178\pi$
$463$	−1.19396e9	−0.559058	−0.279529	+	0.960137i	$0.590178\pi$
$464$	7.58144e8	0.352321
$465$	4.01501e9	1.85183
$466$	4.47418e9	2.04815
$467$	−1.63567e9	−0.743168	−0.371584	−	0.928399i	$-0.621185\pi$
$467$	−1.63567e9	−0.743168	−0.371584	+	0.928399i	$0.621185\pi$
$468$	−3.88964e9	−1.75408
$469$	1.01152e9	0.452760
$470$	2.88353e9	1.28110
$471$	4.98662e9	2.19904
$472$	−4.72590e9	−2.06865
$473$	−2.93960e8	−0.127725
$474$	3.63265e9	1.56675
$475$	2.53870e8	0.108689
$476$	−1.77785e9	−0.755562
$477$	3.10363e9	1.30935
$478$	3.65976e9	1.53269
$479$	−1.93350e9	−0.803839	−0.401919	−	0.915675i	$-0.631657\pi$
$479$	−1.93350e9	−0.803839	−0.401919	+	0.915675i	$0.631657\pi$
$480$	1.53126e9	0.631981
$481$	1.74532e9	0.715102
$482$	−4.71411e9	−1.91750
$483$	2.12656e9	0.858743
$484$	−4.45333e9	−1.78536
$485$	3.35604e9	1.33577
$486$	−5.72793e9	−2.26345
$487$	−3.97846e9	−1.56086	−0.780429	−	0.625245i	$-0.784999\pi$
$487$	−3.97846e9	−1.56086	−0.780429	+	0.625245i	$0.784999\pi$
$488$	6.07440e9	2.36611
$489$	1.09736e9	0.424391
$490$	−1.55253e9	−0.596147
$491$	3.47679e9	1.32554	0.662771	−	0.748822i	$-0.269380\pi$
$491$	3.47679e9	1.32554	0.662771	+	0.748822i	$0.269380\pi$
$492$	1.07387e10	4.06512
$493$	−9.08429e8	−0.341450
$494$	−3.58734e9	−1.33884
$495$	−3.65941e8	−0.135610
$496$	2.15789e9	0.794042
$497$	−2.59322e9	−0.947530
$498$	−8.97455e8	−0.325619
$499$	6.97641e8	0.251351	0.125675	−	0.992071i	$-0.459890\pi$
$499$	6.97641e8	0.251351	0.125675	+	0.992071i	$0.459890\pi$
$500$	5.44734e9	1.94890
$501$	−2.41873e9	−0.859322
$502$	−2.40126e9	−0.847182
$503$	−8.72825e8	−0.305801	−0.152901	−	0.988242i	$-0.548861\pi$
$503$	−8.72825e8	−0.305801	−0.152901	+	0.988242i	$0.548861\pi$
$504$	−2.76747e9	−0.962890
$505$	1.40904e9	0.486860
$506$	6.65191e8	0.228255
$507$	−8.27630e8	−0.282038
$508$	−9.19068e8	−0.311046
$509$	−9.53472e8	−0.320476	−0.160238	−	0.987078i	$-0.551226\pi$
$509$	−9.53472e8	−0.320476	−0.160238	+	0.987078i	$0.551226\pi$
$510$	3.33067e9	1.11182
$511$	4.48746e9	1.48774
$512$	3.13992e9	1.03389
$513$	−3.96584e8	−0.129695
$514$	−8.00796e9	−2.60106
$515$	4.25668e9	1.37324
$516$	5.91593e9	1.89561
$517$	4.38840e8	0.139665
$518$	2.72357e9	0.860962
$519$	−1.19873e9	−0.376388
$520$	−4.58327e9	−1.42943
$521$	1.43078e9	0.443241	0.221620	−	0.975133i	$-0.428865\pi$
$521$	1.43078e9	0.443241	0.221620	+	0.975133i	$0.428865\pi$
$522$	−3.10148e9	−0.954381
$523$	1.19130e9	0.364136	0.182068	−	0.983286i	$-0.441721\pi$
$523$	1.19130e9	0.364136	0.182068	+	0.983286i	$0.441721\pi$
$524$	−3.10462e9	−0.942647
$525$	5.34416e8	0.161184
$526$	7.42405e8	0.222429
$527$	−2.58565e9	−0.769541
$528$	−4.23033e8	−0.125071
$529$	−1.22427e9	−0.359568
$530$	8.02092e9	2.34023
$531$	4.39242e9	1.27313
$532$	−3.62553e9	−1.04395
$533$	6.21154e9	1.77686
$534$	−1.55335e10	−4.41443
$535$	−3.21810e9	−0.908576
$536$	−2.90327e9	−0.814350
$537$	−3.79469e9	−1.05747
$538$	1.12930e10	3.12660
$539$	−2.36277e8	−0.0649921
$540$	−1.11129e9	−0.303703
$541$	9.32571e8	0.253216	0.126608	−	0.991953i	$-0.459591\pi$
$541$	9.32571e8	0.253216	0.126608	+	0.991953i	$0.459591\pi$
$542$	3.19448e9	0.861793
$543$	6.24049e9	1.67271
$544$	−9.86123e8	−0.262624
$545$	1.49623e9	0.395922
$546$	−7.55162e9	−1.98548
$547$	−1.63667e8	−0.0427569
$547$	−1.63667e8	−0.0427569
$548$	−1.08517e10	−2.81685
$549$	−5.64577e9	−1.45620
$550$	1.67166e8	0.0428428
$551$	−1.85254e9	−0.471778
$552$	−6.10369e9	−1.54456
$553$	2.12359e9	0.533989
$554$	1.32654e10	3.31463
$555$	−3.30455e9	−0.820515
$556$	−1.27077e10	−3.13550
$557$	−1.98827e9	−0.487509	−0.243754	−	0.969837i	$-0.578379\pi$
$557$	−1.98827e9	−0.487509	−0.243754	+	0.969837i	$0.578379\pi$
$558$	−8.82767e9	−2.15093
$559$	3.42193e9	0.828572
$560$	−1.62495e9	−0.391004
$561$	5.06890e8	0.121211
$562$	4.75688e9	1.13043
$563$	−5.95731e9	−1.40693	−0.703463	−	0.710732i	$-0.748364\pi$
$563$	−5.95731e9	−1.40693	−0.703463	+	0.710732i	$0.748364\pi$
$564$	−8.83162e9	−2.07283
$565$	−2.00179e9	−0.466927
$566$	−2.51517e9	−0.583055
$567$	−3.79516e9	−0.874359
$568$	7.44312e9	1.70426
$569$	−1.58947e8	−0.0361710	−0.0180855	−	0.999836i	$-0.505757\pi$
$569$	−1.58947e8	−0.0361710	−0.0180855	+	0.999836i	$0.505757\pi$
$570$	6.79217e9	1.53620
$571$	−2.60451e8	−0.0585463	−0.0292731	−	0.999571i	$-0.509319\pi$
$571$	−2.60451e8	−0.0585463	−0.0292731	+	0.999571i	$0.509319\pi$
$572$	−1.52984e9	−0.341790
$573$	2.60549e9	0.578559
$574$	9.69308e9	2.13929
$575$	5.47985e8	0.120207
$576$	−5.52017e9	−1.20358
$577$	6.49576e8	0.140771	0.0703857	−	0.997520i	$-0.477577\pi$
$577$	6.49576e8	0.140771	0.0703857	+	0.997520i	$0.477577\pi$
$578$	5.67597e9	1.22262
$579$	8.96239e9	1.91888
$580$	−5.19110e9	−1.10474
$581$	−5.24639e8	−0.110980
$582$	−1.58711e10	−3.33716
$583$	1.22069e9	0.255133
$584$	−1.28800e10	−2.67590
$585$	4.25985e9	0.879729
$586$	−1.05323e10	−2.16213
$587$	3.20653e9	0.654338	0.327169	−	0.944966i	$-0.393905\pi$
$587$	3.20653e9	0.654338	0.327169	+	0.944966i	$0.393905\pi$
$588$	4.75506e9	0.964574
$589$	−5.27285e9	−1.06327
$590$	1.13516e10	2.27549
$591$	5.45851e9	1.08772
$592$	−1.77605e9	−0.351827
$593$	−1.56314e9	−0.307828	−0.153914	−	0.988084i	$-0.549188\pi$
$593$	−1.56314e9	−0.307828	−0.153914	+	0.988084i	$0.549188\pi$
$594$	−2.61139e8	−0.0511233
$595$	1.94706e9	0.378939
$596$	−3.42019e9	−0.661742
$597$	−5.95816e9	−1.14605
$598$	−7.74336e9	−1.48073
$599$	−7.06390e9	−1.34292	−0.671461	−	0.741040i	$-0.734333\pi$
$599$	−7.06390e9	−1.34292	−0.671461	+	0.741040i	$0.734333\pi$
$600$	−1.53389e9	−0.289911
$601$	4.33702e9	0.814950	0.407475	−	0.913216i	$-0.366409\pi$
$601$	4.33702e9	0.814950	0.407475	+	0.913216i	$0.366409\pi$
$602$	5.33991e9	0.997576
$603$	2.69841e9	0.501184
$604$	1.35551e10	2.50307
$605$	4.87718e9	0.895417
$606$	−6.66352e9	−1.21632
$607$	−4.49334e9	−0.815472	−0.407736	−	0.913100i	$-0.633682\pi$
$607$	−4.49334e9	−0.815472	−0.407736	+	0.913100i	$0.633682\pi$
$608$	−2.01098e9	−0.362865
$609$	−3.89974e9	−0.699641
$610$	−1.45907e10	−2.60269
$611$	−5.10845e9	−0.906035
$612$	−4.74273e9	−0.836370
$613$	4.20936e9	0.738082	0.369041	−	0.929413i	$-0.379686\pi$
$613$	4.20936e9	0.738082	0.369041	+	0.929413i	$0.379686\pi$
$614$	5.75460e9	1.00329
$615$	−1.17608e10	−2.03879
$616$	−1.08848e9	−0.187623
$617$	1.00087e10	1.71546	0.857732	−	0.514098i	$-0.171873\pi$
$617$	1.00087e10	1.71546	0.857732	+	0.514098i	$0.171873\pi$
$618$	−2.01303e10	−3.43077
$619$	−3.91122e9	−0.662820	−0.331410	−	0.943487i	$-0.607524\pi$
$619$	−3.91122e9	−0.662820	−0.331410	+	0.943487i	$0.607524\pi$
$620$	−1.47753e10	−2.48981
$621$	−8.56038e8	−0.143441
$622$	−1.97557e10	−3.29175
$623$	−9.08064e9	−1.50456
$624$	4.92444e9	0.811355
$625$	−5.04900e9	−0.827229
$626$	7.93217e9	1.29235
$627$	1.03369e9	0.167477
$628$	−1.83509e10	−2.95664
$629$	2.12811e9	0.340971
$630$	6.64747e9	1.05917
$631$	6.38807e9	1.01220	0.506100	−	0.862475i	$-0.331087\pi$
$631$	6.38807e9	1.01220	0.506100	+	0.862475i	$0.331087\pi$
$632$	−6.09516e9	−0.960451
$633$	1.45665e10	2.28266
$634$	1.23896e10	1.93083
$635$	1.00654e9	0.156000
$636$	−2.45664e10	−3.78652
$637$	2.75046e9	0.421616
$638$	−1.21984e9	−0.185965
$639$	−6.91790e9	−1.04887
$640$	−1.12003e10	−1.68889
$641$	−1.91278e9	−0.286855	−0.143428	−	0.989661i	$-0.545812\pi$
$641$	−1.91278e9	−0.286855	−0.143428	+	0.989661i	$0.545812\pi$
$642$	1.52187e10	2.26990
$643$	1.21149e10	1.79714	0.898571	−	0.438828i	$-0.144606\pi$
$643$	1.21149e10	1.79714	0.898571	+	0.438828i	$0.144606\pi$
$644$	−7.82580e9	−1.15459
$645$	−6.47900e9	−0.950712
$646$	−4.37412e9	−0.638377
$647$	1.59475e9	0.231488	0.115744	−	0.993279i	$-0.463075\pi$
$647$	1.59475e9	0.231488	0.115744	+	0.993279i	$0.463075\pi$
$648$	1.08929e10	1.57265
$649$	1.72759e9	0.248075
$650$	−1.94594e9	−0.277929
$651$	−1.10998e10	−1.57681
$652$	−4.03829e9	−0.570599
$653$	−5.02648e9	−0.706428	−0.353214	−	0.935543i	$-0.614911\pi$
$653$	−5.02648e9	−0.706428	−0.353214	+	0.935543i	$0.614911\pi$
$654$	−7.07582e9	−0.989133
$655$	3.40011e9	0.472768
$656$	−6.32090e9	−0.874210
$657$	1.19711e10	1.64686
$658$	−7.97170e9	−1.09084
$659$	5.27501e9	0.717999	0.359000	−	0.933338i	$-0.383118\pi$
$659$	5.27501e9	0.717999	0.359000	+	0.933338i	$0.383118\pi$
$660$	2.89655e9	0.392173
$661$	7.79954e9	1.05042	0.525211	−	0.850972i	$-0.323986\pi$
$661$	7.79954e9	1.05042	0.525211	+	0.850972i	$0.323986\pi$
$662$	8.11789e9	1.08753
$663$	−5.90061e9	−0.786320
$664$	1.50583e9	0.199612
$665$	3.97060e9	0.523577
$666$	7.26561e9	0.953043
$667$	−3.99876e9	−0.521777
$668$	8.90099e9	1.15537
$669$	−8.79014e9	−1.13502
$670$	6.97366e9	0.895776
$671$	−2.22054e9	−0.283746
$672$	−4.23326e9	−0.538125
$673$	−4.16138e9	−0.526240	−0.263120	−	0.964763i	$-0.584752\pi$
$673$	−4.16138e9	−0.526240	−0.263120	+	0.964763i	$0.584752\pi$
$674$	−2.85831e9	−0.359583
$675$	−2.15126e8	−0.0269234
$676$	3.04570e9	0.379204
$677$	6.27538e9	0.777284	0.388642	−	0.921389i	$-0.372944\pi$
$677$	6.27538e9	0.777284	0.388642	+	0.921389i	$0.372944\pi$
$678$	9.46669e9	1.16652
$679$	−9.27800e9	−1.13739
$680$	−5.58848e9	−0.681573
$681$	4.11706e9	0.499543
$682$	−3.47202e9	−0.419118
$683$	1.36494e10	1.63923	0.819616	−	0.572913i	$-0.194187\pi$
$683$	1.36494e10	1.63923	0.819616	+	0.572913i	$0.194187\pi$
$684$	−9.67176e9	−1.15560
$685$	1.18845e10	1.41274
$686$	1.54730e10	1.82996
$687$	−1.93330e10	−2.27484
$688$	−3.48218e9	−0.407654
$689$	−1.42098e10	−1.65509
$690$	1.46611e10	1.69900
$691$	7.32536e9	0.844609	0.422304	−	0.906454i	$-0.361221\pi$
$691$	7.32536e9	0.844609	0.422304	+	0.906454i	$0.361221\pi$
$692$	4.41136e9	0.506059
$693$	1.01167e9	0.115471
$694$	−1.89240e10	−2.14909
$695$	1.39172e10	1.57256
$696$	1.11931e10	1.25840
$697$	7.57388e9	0.847235
$698$	7.52035e9	0.837036
$699$	1.50077e10	1.66205
$700$	−1.96666e9	−0.216714
$701$	−8.10980e9	−0.889196	−0.444598	−	0.895730i	$-0.646653\pi$
$701$	−8.10980e9	−0.889196	−0.444598	+	0.895730i	$0.646653\pi$
$702$	3.03987e9	0.331646
$703$	4.33982e9	0.471116
$704$	−2.17114e9	−0.234522
$705$	9.67220e9	1.03959
$706$	−2.75459e10	−2.94606
$707$	−3.89539e9	−0.414556
$708$	−3.47676e10	−3.68178
$709$	2.16804e9	0.228458	0.114229	−	0.993454i	$-0.463560\pi$
$709$	2.16804e9	0.228458	0.114229	+	0.993454i	$0.463560\pi$
$710$	−1.78784e10	−1.87466
$711$	5.66506e9	0.591100
$712$	2.60634e10	2.70615
$713$	−1.13816e10	−1.17595
$714$	−9.20786e9	−0.946706
$715$	1.67544e9	0.171419
$716$	1.39646e10	1.42178
$717$	1.22759e10	1.24376
$718$	2.41707e10	2.43699
$719$	−9.10026e9	−0.913067	−0.456533	−	0.889706i	$-0.650909\pi$
$719$	−9.10026e9	−0.913067	−0.456533	+	0.889706i	$0.650909\pi$
$720$	−4.33485e9	−0.432823
$721$	−1.17679e10	−1.16930
$722$	8.11681e9	0.802611
$723$	−1.58125e10	−1.55603
$724$	−2.29652e10	−2.24897
$725$	−1.00491e9	−0.0979362
$726$	−2.30647e10	−2.23702
$727$	1.45842e10	1.40771	0.703854	−	0.710345i	$-0.251461\pi$
$727$	1.45842e10	1.40771	0.703854	+	0.710345i	$0.251461\pi$
$728$	1.26707e10	1.21714
$729$	−7.56114e9	−0.722838
$730$	3.09377e10	2.94346
$731$	4.17244e9	0.395075
$732$	4.46882e10	4.21118
$733$	1.66000e10	1.55684	0.778422	−	0.627741i	$-0.216020\pi$
$733$	1.66000e10	1.55684	0.778422	+	0.627741i	$0.216020\pi$
$734$	3.07518e9	0.287035
$735$	−5.20764e9	−0.483766
$736$	−4.34075e9	−0.401322
$737$	1.06131e9	0.0976577
$738$	2.58581e10	2.36809
$739$	5.79345e9	0.528058	0.264029	−	0.964515i	$-0.414948\pi$
$739$	5.79345e9	0.528058	0.264029	+	0.964515i	$0.414948\pi$
$740$	1.21608e10	1.10319
$741$	−1.20330e10	−1.08645
$742$	−2.21744e10	−1.99268
$743$	−6.03748e9	−0.540001	−0.270001	−	0.962860i	$-0.587024\pi$
$743$	−6.03748e9	−0.540001	−0.270001	+	0.962860i	$0.587024\pi$
$744$	3.18587e10	2.83611
$745$	3.74572e9	0.331886
$746$	3.47850e10	3.06765
$747$	−1.39957e9	−0.122849
$748$	−1.86537e9	−0.162970
$749$	8.89665e9	0.773642
$750$	2.82130e10	2.44194
$751$	1.40216e10	1.20798	0.603989	−	0.796993i	$-0.293577\pi$
$751$	1.40216e10	1.20798	0.603989	+	0.796993i	$0.293577\pi$
$752$	5.19838e9	0.445765
$753$	−8.05455e9	−0.687478
$754$	1.42000e10	1.20639
$755$	−1.48452e10	−1.25537
$756$	3.07223e9	0.258599
$757$	−1.97804e10	−1.65730	−0.828649	−	0.559769i	$-0.810890\pi$
$757$	−1.97804e10	−1.65730	−0.828649	+	0.559769i	$0.810890\pi$
$758$	−3.06287e10	−2.55438
$759$	2.23125e9	0.185226
$760$	−1.13965e10	−0.941723
$761$	−9.38231e9	−0.771727	−0.385863	−	0.922556i	$-0.626096\pi$
$761$	−9.38231e9	−0.771727	−0.385863	+	0.922556i	$0.626096\pi$
$762$	−4.76005e9	−0.389735
$763$	−4.13642e9	−0.337123
$764$	−9.58825e9	−0.777880
$765$	5.19414e9	0.419467
$766$	−2.68589e9	−0.215917
$767$	−2.01105e10	−1.60931
$768$	2.91956e10	2.32570
$769$	−6.76952e9	−0.536804	−0.268402	−	0.963307i	$-0.586496\pi$
$769$	−6.76952e9	−0.536804	−0.268402	+	0.963307i	$0.586496\pi$
$770$	2.61452e9	0.206383
$771$	−2.68610e10	−2.11073
$772$	−3.29818e10	−2.57996
$773$	−9.00138e9	−0.700940	−0.350470	−	0.936574i	$-0.613978\pi$
$773$	−9.00138e9	−0.700940	−0.350470	+	0.936574i	$0.613978\pi$
$774$	1.42452e10	1.10427
$775$	−2.86025e9	−0.220723
$776$	2.66299e10	2.04575
$777$	9.13565e9	0.698660
$778$	4.40638e10	3.35470
$779$	1.54453e10	1.17062
$780$	−3.37182e10	−2.54410
$781$	−2.72088e9	−0.204377
$782$	−9.44166e9	−0.706033
$783$	1.56982e9	0.116865
$784$	−2.79888e9	−0.207433
$785$	2.00975e10	1.48285
$786$	−1.60795e10	−1.18112
$787$	1.41668e10	1.03600	0.518001	−	0.855380i	$-0.326676\pi$
$787$	1.41668e10	1.03600	0.518001	+	0.855380i	$0.326676\pi$
$788$	−2.00875e10	−1.46246
$789$	2.49025e9	0.180498
$790$	1.46406e10	1.05649
$791$	5.53408e9	0.397583
$792$	−2.90371e9	−0.207690
$793$	2.58489e10	1.84071
$794$	−1.69640e10	−1.20270
$795$	2.69045e10	1.89907
$796$	2.19262e10	1.54087
$797$	1.29798e10	0.908166	0.454083	−	0.890959i	$-0.349967\pi$
$797$	1.29798e10	0.908166	0.454083	+	0.890959i	$0.349967\pi$
$798$	−1.87774e10	−1.30805
$799$	−6.22885e9	−0.432010
$800$	−1.09085e9	−0.0753271
$801$	−2.42243e10	−1.66547
$802$	2.29078e10	1.56810
$803$	4.70837e9	0.320897
$804$	−2.13588e10	−1.44938
$805$	8.57064e9	0.579066
$806$	4.04171e10	2.71889
$807$	3.78801e10	2.53720
$808$	1.11806e10	0.745635
$809$	2.62536e10	1.74329	0.871645	−	0.490137i	$-0.163053\pi$
$809$	2.62536e10	1.74329	0.871645	+	0.490137i	$0.163053\pi$
$810$	−2.61649e10	−1.72990
$811$	1.23622e9	0.0813811	0.0406906	−	0.999172i	$-0.487044\pi$
$811$	1.23622e9	0.0813811	0.0406906	+	0.999172i	$0.487044\pi$
$812$	1.43511e10	0.940676
$813$	1.07152e10	0.699334
$814$	2.85764e9	0.185704
$815$	4.42265e9	0.286175
$816$	6.00449e9	0.386866
$817$	8.50878e9	0.545871
$818$	4.51714e10	2.88554
$819$	−1.17766e10	−0.749079
$820$	4.32799e10	2.74118
$821$	−2.34666e10	−1.47996	−0.739979	−	0.672630i	$-0.765164\pi$
$821$	−2.34666e10	−1.47996	−0.739979	+	0.672630i	$0.765164\pi$
$822$	−5.62031e10	−3.52946
$823$	1.53592e10	0.960438	0.480219	−	0.877149i	$-0.340557\pi$
$823$	1.53592e10	0.960438	0.480219	+	0.877149i	$0.340557\pi$
$824$	3.37764e10	2.10314
$825$	5.60723e8	0.0347664
$826$	−3.13823e10	−1.93756
$827$	2.07216e10	1.27396	0.636978	−	0.770882i	$-0.280184\pi$
$827$	2.07216e10	1.27396	0.636978	+	0.770882i	$0.280184\pi$
$828$	−2.08767e10	−1.27808
$829$	2.01259e10	1.22691	0.613456	−	0.789729i	$-0.289779\pi$
$829$	2.01259e10	1.22691	0.613456	+	0.789729i	$0.289779\pi$
$830$	−3.61700e9	−0.219571
$831$	4.44960e10	2.68978
$832$	2.52738e10	1.52139
$833$	3.35370e9	0.201032
$834$	−6.58162e10	−3.92872
$835$	−9.74817e9	−0.579456
$836$	−3.80400e9	−0.225174
$837$	4.46815e9	0.263384
$838$	−3.22500e8	−0.0189311
$839$	6.61009e9	0.386403	0.193202	−	0.981159i	$-0.438113\pi$
$839$	6.61009e9	0.386403	0.193202	+	0.981159i	$0.438113\pi$
$840$	−2.39904e10	−1.39656
$841$	−9.91686e9	−0.574895
$842$	−4.69695e9	−0.271159
$843$	1.59560e10	0.917333
$844$	−5.36049e10	−3.06906
$845$	−3.33558e9	−0.190183
$846$	−2.12660e10	−1.20750
$847$	−1.34833e10	−0.762438
$848$	1.44600e10	0.814297
$849$	−8.43661e9	−0.473142
$850$	−2.37274e9	−0.132521
$851$	9.36761e9	0.521045
$852$	5.47576e10	3.03323
$853$	7.65957e9	0.422555	0.211277	−	0.977426i	$-0.432238\pi$
$853$	7.65957e9	0.422555	0.211277	+	0.977426i	$0.432238\pi$
$854$	4.03370e10	2.21616
$855$	1.05923e10	0.579574
$856$	−2.55353e10	−1.39150
$857$	−1.21457e10	−0.659156	−0.329578	−	0.944128i	$-0.606907\pi$
$857$	−1.21457e10	−0.659156	−0.329578	+	0.944128i	$0.606907\pi$
$858$	−7.92336e9	−0.428256
$859$	−1.46787e10	−0.790153	−0.395076	−	0.918648i	$-0.629282\pi$
$859$	−1.46787e10	−0.790153	−0.395076	+	0.918648i	$0.629282\pi$
$860$	2.38429e10	1.27824
$861$	3.25134e10	1.73601
$862$	−3.96241e9	−0.210710
$863$	1.93580e10	1.02524	0.512618	−	0.858617i	$-0.328676\pi$
$863$	1.93580e10	1.02524	0.512618	+	0.858617i	$0.328676\pi$
$864$	1.70408e9	0.0898860
$865$	−4.83123e9	−0.253805
$866$	3.13568e10	1.64066
$867$	1.90389e10	0.992144
$868$	4.08474e10	2.12004
$869$	2.22813e9	0.115178
$870$	−2.68858e10	−1.38422
$871$	−1.23545e10	−0.633523
$872$	1.18724e10	0.606361
$873$	−2.47508e10	−1.25904
$874$	−1.92542e10	−0.975518
$875$	1.64929e10	0.832277
$876$	−9.47557e10	−4.76256
$877$	3.91845e10	1.96163	0.980813	−	0.194950i	$-0.0624546\pi$
$877$	3.91845e10	1.96163	0.980813	+	0.194950i	$0.0624546\pi$
$878$	1.73058e10	0.862900
$879$	−3.53284e10	−1.75454
$880$	−1.70494e9	−0.0843373
$881$	−3.35415e10	−1.65260	−0.826298	−	0.563234i	$-0.809557\pi$
$881$	−3.35415e10	−1.65260	−0.826298	+	0.563234i	$0.809557\pi$
$882$	1.14499e10	0.561902
$883$	−3.37446e10	−1.64946	−0.824730	−	0.565527i	$-0.808673\pi$
$883$	−3.37446e10	−1.64946	−0.824730	+	0.565527i	$0.808673\pi$
$884$	2.17144e10	1.05722
$885$	3.80767e10	1.84653
$886$	−6.07242e10	−2.93322
$887$	2.50492e10	1.20521	0.602604	−	0.798041i	$-0.294130\pi$
$887$	2.50492e10	1.20521	0.602604	+	0.798041i	$0.294130\pi$
$888$	−2.62213e10	−1.25663
$889$	−2.78265e9	−0.132832
$890$	−6.26043e10	−2.97673
$891$	−3.98199e9	−0.188594
$892$	3.23479e10	1.52605
$893$	−1.27024e10	−0.596904
$894$	−1.77139e10	−0.829151
$895$	−1.52937e10	−0.713068
$896$	3.09641e10	1.43807
$897$	−2.59735e10	−1.20159
$898$	−2.66933e10	−1.23008
$899$	2.08718e10	0.958080
$900$	−5.24643e9	−0.239891
$901$	−1.73264e10	−0.789171
$902$	1.01702e10	0.461433
$903$	1.79116e10	0.809521
$904$	−1.58840e10	−0.715106
$905$	2.51509e10	1.12794
$906$	7.02047e10	3.13630
$907$	2.23230e10	0.993408	0.496704	−	0.867920i	$-0.334543\pi$
$907$	2.23230e10	0.993408	0.496704	+	0.867920i	$0.334543\pi$
$908$	−1.51509e10	−0.671642
$909$	−1.03917e10	−0.458893
$910$	−3.04351e10	−1.33884
$911$	−1.47386e10	−0.645866	−0.322933	−	0.946422i	$-0.604669\pi$
$911$	−1.47386e10	−0.645866	−0.322933	+	0.946422i	$0.604669\pi$
$912$	1.22448e10	0.534529
$913$	−5.50465e8	−0.0239377
$914$	1.14561e10	0.496279
$915$	−4.89416e10	−2.11205
$916$	7.11458e10	3.05855
$917$	−9.39983e9	−0.402557
$918$	3.70658e9	0.158134
$919$	−1.51595e10	−0.644291	−0.322145	−	0.946690i	$-0.604404\pi$
$919$	−1.51595e10	−0.644291	−0.322145	+	0.946690i	$0.604404\pi$
$920$	−2.45996e10	−1.04153
$921$	1.93026e10	0.814156
$922$	−2.57398e9	−0.108155
$923$	3.16733e10	1.32583
$924$	−8.00771e9	−0.333931
$925$	2.35413e9	0.0977989
$926$	2.27565e10	0.941817
$927$	−3.13930e10	−1.29436
$928$	7.96017e9	0.326967
$929$	−3.57224e10	−1.46179	−0.730895	−	0.682489i	$-0.760897\pi$
$929$	−3.57224e10	−1.46179	−0.730895	+	0.682489i	$0.760897\pi$
$930$	−7.65246e10	−3.11969
$931$	6.83912e9	0.277764
$932$	−5.52287e10	−2.23465
$933$	−6.62666e10	−2.67121
$934$	3.11753e10	1.25198
$935$	2.04291e9	0.0817350
$936$	3.38015e10	1.34732
$937$	2.18976e10	0.869576	0.434788	−	0.900533i	$-0.356823\pi$
$937$	2.18976e10	0.869576	0.434788	+	0.900533i	$0.356823\pi$
$938$	−1.92792e10	−0.762743
$939$	2.66068e10	1.04873
$940$	−3.55939e10	−1.39775
$941$	2.60977e10	1.02103	0.510514	−	0.859869i	$-0.329455\pi$
$941$	2.60977e10	1.02103	0.510514	+	0.859869i	$0.329455\pi$
$942$	−9.50432e10	−3.70461
$943$	3.33390e10	1.29468
$944$	2.04645e10	0.791772
$945$	−3.36464e9	−0.129696
$946$	5.60278e9	0.215171
$947$	5.08414e10	1.94533	0.972663	−	0.232220i	$-0.0745990\pi$
$947$	5.08414e10	1.94533	0.972663	+	0.232220i	$0.0745990\pi$
$948$	−4.48409e10	−1.70941
$949$	−5.48092e10	−2.08172
$950$	−4.83867e9	−0.183102
$951$	4.15583e10	1.56685
$952$	1.54497e10	0.580352
$953$	3.93473e10	1.47262	0.736309	−	0.676646i	$-0.236567\pi$
$953$	3.93473e10	1.47262	0.736309	+	0.676646i	$0.236567\pi$
$954$	−5.91542e10	−2.20580
$955$	1.05008e10	0.390133
$956$	−4.51756e10	−1.67225
$957$	−4.09171e9	−0.150908
$958$	3.68517e10	1.35419
$959$	−3.28555e10	−1.20294
$960$	−4.78528e10	−1.74565
$961$	3.18945e10	1.15927
$962$	−3.32652e10	−1.20470
$963$	2.37334e10	0.856384
$964$	5.81905e10	2.09210
$965$	3.61209e10	1.29394
$966$	−4.05315e10	−1.44668
$967$	−3.29998e10	−1.17359	−0.586797	−	0.809734i	$-0.699611\pi$
$967$	−3.29998e10	−1.17359	−0.586797	+	0.809734i	$0.699611\pi$
$968$	3.87000e10	1.37135
$969$	−1.46721e10	−0.518035
$970$	−6.39650e10	−2.25030
$971$	−3.97458e10	−1.39324	−0.696618	−	0.717443i	$-0.745313\pi$
$971$	−3.97458e10	−1.39324	−0.696618	+	0.717443i	$0.745313\pi$
$972$	7.07049e10	2.46955
$973$	−3.84751e10	−1.33901
$974$	7.58280e10	2.62950
$975$	−6.52727e9	−0.225536
$976$	−2.63039e10	−0.905621
$977$	−4.34211e10	−1.48960	−0.744800	−	0.667287i	$-0.767455\pi$
$977$	−4.34211e10	−1.48960	−0.744800	+	0.667287i	$0.767455\pi$
$978$	−2.09152e10	−0.714951
$979$	−9.52766e9	−0.324524
$980$	1.91642e10	0.650429
$981$	−1.10346e10	−0.373179
$982$	−6.62664e10	−2.23308
$983$	1.55122e10	0.520877	0.260438	−	0.965490i	$-0.416133\pi$
$983$	1.55122e10	0.520877	0.260438	+	0.965490i	$0.416133\pi$
$984$	−9.33206e10	−3.12245
$985$	2.19993e10	0.733471
$986$	1.73143e10	0.575224
$987$	−2.67394e10	−0.885202
$988$	4.42817e10	1.46075
$989$	1.83664e10	0.603723
$990$	6.97471e9	0.228456
$991$	−4.02243e10	−1.31290	−0.656448	−	0.754371i	$-0.727942\pi$
$991$	−4.02243e10	−1.31290	−0.656448	+	0.754371i	$0.727942\pi$
$992$	2.26569e10	0.736902
$993$	2.72298e10	0.882515
$994$	4.94259e10	1.59626
$995$	−2.40130e10	−0.772799
$996$	1.10781e10	0.355269
$997$	−1.01823e9	−0.0325398	−0.0162699	−	0.999868i	$-0.505179\pi$
$997$	−1.01823e9	−0.0325398	−0.0162699	+	0.999868i	$0.505179\pi$
$998$	−1.32968e10	−0.423438
$999$	−3.67751e9	−0.116701

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.8.a.b.1.16	✓	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.8.a.b.1.16	✓	162	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-19.0596 q^{2} -63.9317 q^{3} +235.270 q^{4} -257.662 q^{5} +1218.51 q^{6} +712.325 q^{7} -2044.53 q^{8} +1900.26 q^{9} +O(q^{10})\)	\(q-19.0596 q^{2} -63.9317 q^{3} +235.270 q^{4} -257.662 q^{5} +1218.51 q^{6} +712.325 q^{7} -2044.53 q^{8} +1900.26 q^{9} +4910.95 q^{10} +747.391 q^{11} -15041.2 q^{12} -8700.23 q^{13} -13576.7 q^{14} +16472.8 q^{15} +8853.40 q^{16} -10608.4 q^{17} -36218.2 q^{18} -21633.5 q^{19} -60620.2 q^{20} -45540.1 q^{21} -14245.0 q^{22} -46696.5 q^{23} +130710. q^{24} -11735.0 q^{25} +165823. q^{26} +18332.0 q^{27} +167589. q^{28} +85633.0 q^{29} -313965. q^{30} +243736. q^{31} +92956.8 q^{32} -47781.9 q^{33} +202192. q^{34} -183539. q^{35} +447073. q^{36} -200607. q^{37} +412327. q^{38} +556220. q^{39} +526798. q^{40} -713952. q^{41} +867979. q^{42} -393315. q^{43} +175839. q^{44} -489625. q^{45} +890018. q^{46} +587162. q^{47} -566013. q^{48} -316136. q^{49} +223666. q^{50} +678212. q^{51} -2.04690e6 q^{52} +1.63327e6 q^{53} -349401. q^{54} -192575. q^{55} -1.45637e6 q^{56} +1.38306e6 q^{57} -1.63214e6 q^{58} +2.31149e6 q^{59} +3.87555e6 q^{60} -2.97105e6 q^{61} -4.64552e6 q^{62} +1.35360e6 q^{63} -2.90496e6 q^{64} +2.24172e6 q^{65} +910707. q^{66} +1.42002e6 q^{67} -2.49584e6 q^{68} +2.98538e6 q^{69} +3.49820e6 q^{70} -3.64051e6 q^{71} -3.88513e6 q^{72} +6.29974e6 q^{73} +3.82349e6 q^{74} +750241. q^{75} -5.08971e6 q^{76} +532385. q^{77} -1.06014e7 q^{78} +2.98121e6 q^{79} -2.28119e6 q^{80} -5.32785e6 q^{81} +1.36077e7 q^{82} -736516. q^{83} -1.07142e7 q^{84} +2.73339e6 q^{85} +7.49645e6 q^{86} -5.47466e6 q^{87} -1.52806e6 q^{88} -1.27479e7 q^{89} +9.33208e6 q^{90} -6.19739e6 q^{91} -1.09863e7 q^{92} -1.55824e7 q^{93} -1.11911e7 q^{94} +5.57414e6 q^{95} -5.94288e6 q^{96} -1.30250e7 q^{97} +6.02544e6 q^{98} +1.42023e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 48 q^{2} + 310 q^{3} + 10650 q^{4} + 3999 q^{5} + 1998 q^{6} + 4301 q^{7} + 9216 q^{8} + 124464 q^{9}+O(q^{10}) \) 162 * q + 48 * q^2 + 310 * q^3 + 10650 * q^4 + 3999 * q^5 + 1998 * q^6 + 4301 * q^7 + 9216 * q^8 + 124464 * q^9	\( 162 q + 48 q^{2} + 310 q^{3} + 10650 q^{4} + 3999 q^{5} + 1998 q^{6} + 4301 q^{7} + 9216 q^{8} + 124464 q^{9} + 7430 q^{10} + 19840 q^{11} + 55737 q^{12} + 51223 q^{13} + 75679 q^{14} + 44609 q^{15} + 709506 q^{16} + 258906 q^{17} + 135171 q^{18} + 80362 q^{19} + 506432 q^{20} + 138572 q^{21} + 158320 q^{22} + 571410 q^{23} + 325871 q^{24} + 2732541 q^{25} + 488640 q^{26} + 772231 q^{27} + 699304 q^{28} + 968170 q^{29} + 301526 q^{30} + 348203 q^{31} + 1078196 q^{32} + 1536618 q^{33} + 870073 q^{34} + 1089291 q^{35} + 8775356 q^{36} + 2226256 q^{37} + 3884597 q^{38} + 923555 q^{39} + 2518352 q^{40} + 1825935 q^{41} + 3419892 q^{42} + 1582376 q^{43} + 4352040 q^{44} + 9457186 q^{45} + 1012278 q^{46} + 4801410 q^{47} + 9073674 q^{48} + 21448221 q^{49} + 2366848 q^{50} + 3749747 q^{51} + 7035334 q^{52} + 17191348 q^{53} + 5748697 q^{54} + 5271331 q^{55} + 14854657 q^{56} + 5393884 q^{57} + 4036260 q^{58} + 8263804 q^{59} + 10193498 q^{60} + 12366404 q^{61} + 18470554 q^{62} + 15526895 q^{63} + 49399626 q^{64} + 17325330 q^{65} + 11279868 q^{66} + 5477434 q^{67} + 44562265 q^{68} + 26851278 q^{69} + 9428823 q^{70} + 12108395 q^{71} + 22153063 q^{72} + 13995388 q^{73} + 13478769 q^{74} + 24654171 q^{75} + 8225460 q^{76} + 61240119 q^{77} + 17624449 q^{78} + 8215066 q^{79} + 65708461 q^{80} + 112675190 q^{81} + 29179962 q^{82} + 33597369 q^{83} + 13895447 q^{84} + 24308391 q^{85} + 22043075 q^{86} + 25661967 q^{87} + 32743591 q^{88} + 47538968 q^{89} + 46132321 q^{90} + 24574095 q^{91} + 108017386 q^{92} + 63765304 q^{93} + 41203657 q^{94} + 38032578 q^{95} + 41465754 q^{96} + 45954628 q^{97} + 37164970 q^{98} + 43882333 q^{99}+O(q^{100}) \) 162 * q + 48 * q^2 + 310 * q^3 + 10650 * q^4 + 3999 * q^5 + 1998 * q^6 + 4301 * q^7 + 9216 * q^8 + 124464 * q^9 + 7430 * q^10 + 19840 * q^11 + 55737 * q^12 + 51223 * q^13 + 75679 * q^14 + 44609 * q^15 + 709506 * q^16 + 258906 * q^17 + 135171 * q^18 + 80362 * q^19 + 506432 * q^20 + 138572 * q^21 + 158320 * q^22 + 571410 * q^23 + 325871 * q^24 + 2732541 * q^25 + 488640 * q^26 + 772231 * q^27 + 699304 * q^28 + 968170 * q^29 + 301526 * q^30 + 348203 * q^31 + 1078196 * q^32 + 1536618 * q^33 + 870073 * q^34 + 1089291 * q^35 + 8775356 * q^36 + 2226256 * q^37 + 3884597 * q^38 + 923555 * q^39 + 2518352 * q^40 + 1825935 * q^41 + 3419892 * q^42 + 1582376 * q^43 + 4352040 * q^44 + 9457186 * q^45 + 1012278 * q^46 + 4801410 * q^47 + 9073674 * q^48 + 21448221 * q^49 + 2366848 * q^50 + 3749747 * q^51 + 7035334 * q^52 + 17191348 * q^53 + 5748697 * q^54 + 5271331 * q^55 + 14854657 * q^56 + 5393884 * q^57 + 4036260 * q^58 + 8263804 * q^59 + 10193498 * q^60 + 12366404 * q^61 + 18470554 * q^62 + 15526895 * q^63 + 49399626 * q^64 + 17325330 * q^65 + 11279868 * q^66 + 5477434 * q^67 + 44562265 * q^68 + 26851278 * q^69 + 9428823 * q^70 + 12108395 * q^71 + 22153063 * q^72 + 13995388 * q^73 + 13478769 * q^74 + 24654171 * q^75 + 8225460 * q^76 + 61240119 * q^77 + 17624449 * q^78 + 8215066 * q^79 + 65708461 * q^80 + 112675190 * q^81 + 29179962 * q^82 + 33597369 * q^83 + 13895447 * q^84 + 24308391 * q^85 + 22043075 * q^86 + 25661967 * q^87 + 32743591 * q^88 + 47538968 * q^89 + 46132321 * q^90 + 24574095 * q^91 + 108017386 * q^92 + 63765304 * q^93 + 41203657 * q^94 + 38032578 * q^95 + 41465754 * q^96 + 45954628 * q^97 + 37164970 * q^98 + 43882333 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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