LMFDB - Embedded newform 471.8.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,8,Mod(1,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("471.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	471.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:	$147.133347003$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0952 q^{2} -27.0000 q^{3} +131.055 q^{4} +414.780 q^{5} +434.570 q^{6} +1067.44 q^{7} -49.1712 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-16.0952 q^{2} -27.0000 q^{3} +131.055 q^{4} +414.780 q^{5} +434.570 q^{6} +1067.44 q^{7} -49.1712 q^{8} +729.000 q^{9} -6675.96 q^{10} +5970.09 q^{11} -3538.49 q^{12} +4926.04 q^{13} -17180.7 q^{14} -11199.0 q^{15} -15983.6 q^{16} -12203.1 q^{17} -11733.4 q^{18} +25487.3 q^{19} +54359.0 q^{20} -28820.9 q^{21} -96089.8 q^{22} +84625.9 q^{23} +1327.62 q^{24} +93917.1 q^{25} -79285.5 q^{26} -19683.0 q^{27} +139894. q^{28} -113169. q^{29} +180251. q^{30} +273215. q^{31} +263553. q^{32} -161193. q^{33} +196411. q^{34} +442753. q^{35} +95539.1 q^{36} +58799.6 q^{37} -410223. q^{38} -133003. q^{39} -20395.2 q^{40} +56316.0 q^{41} +463879. q^{42} +888119. q^{43} +782411. q^{44} +302374. q^{45} -1.36207e6 q^{46} +797873. q^{47} +431558. q^{48} +315891. q^{49} -1.51161e6 q^{50} +329484. q^{51} +645582. q^{52} +205221. q^{53} +316802. q^{54} +2.47627e6 q^{55} -52487.4 q^{56} -688157. q^{57} +1.82148e6 q^{58} -330888. q^{59} -1.46769e6 q^{60} -313051. q^{61} -4.39744e6 q^{62} +778166. q^{63} -2.19604e6 q^{64} +2.04322e6 q^{65} +2.59442e6 q^{66} +740624. q^{67} -1.59928e6 q^{68} -2.28490e6 q^{69} -7.12620e6 q^{70} +2.40101e6 q^{71} -35845.8 q^{72} +1.54776e6 q^{73} -946391. q^{74} -2.53576e6 q^{75} +3.34024e6 q^{76} +6.37273e6 q^{77} +2.14071e6 q^{78} +550911. q^{79} -6.62968e6 q^{80} +531441. q^{81} -906416. q^{82} -1.73074e6 q^{83} -3.77713e6 q^{84} -5.06160e6 q^{85} -1.42944e7 q^{86} +3.05557e6 q^{87} -293556. q^{88} +7.79544e6 q^{89} -4.86677e6 q^{90} +5.25826e6 q^{91} +1.10907e7 q^{92} -7.37680e6 q^{93} -1.28419e7 q^{94} +1.05716e7 q^{95} -7.11594e6 q^{96} -1.54929e7 q^{97} -5.08432e6 q^{98} +4.35220e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{2} - 1296 q^{3} + 3214 q^{4} + 428 q^{5} - 54 q^{6} - 680 q^{7} + 2355 q^{8} + 34992 q^{9}+O(q^{10}) $ 48 * q + 2 * q^2 - 1296 * q^3 + 3214 * q^4 + 428 * q^5 - 54 * q^6 - 680 * q^7 + 2355 * q^8 + 34992 * q^9	\( 48 q + 2 q^{2} - 1296 q^{3} + 3214 q^{4} + 428 q^{5} - 54 q^{6} - 680 q^{7} + 2355 q^{8} + 34992 q^{9} + 6185 q^{10} + 11989 q^{11} - 86778 q^{12} - 2393 q^{13} + 18201 q^{14} - 11556 q^{15} + 208150 q^{16} + 62538 q^{17} + 1458 q^{18} - 39882 q^{19} + 113423 q^{20} + 18360 q^{21} - 93716 q^{22} + 195618 q^{23} - 63585 q^{24} + 886490 q^{25} + 294399 q^{26} - 944784 q^{27} - 60819 q^{28} + 421501 q^{29} - 166995 q^{30} + 392689 q^{31} - 341578 q^{32} - 323703 q^{33} + 50837 q^{34} + 697874 q^{35} + 2343006 q^{36} - 410396 q^{37} + 677216 q^{38} + 64611 q^{39} + 3232376 q^{40} + 3832958 q^{41} - 491427 q^{42} - 1751932 q^{43} + 4888297 q^{44} + 312012 q^{45} + 1163150 q^{46} + 106461 q^{47} - 5620050 q^{48} + 8202048 q^{49} - 2159111 q^{50} - 1688526 q^{51} - 3605030 q^{52} + 1755534 q^{53} - 39366 q^{54} - 1220729 q^{55} - 4430622 q^{56} + 1076814 q^{57} - 10000202 q^{58} - 2037752 q^{59} - 3062421 q^{60} + 1274098 q^{61} + 97748 q^{62} - 495720 q^{63} + 15135201 q^{64} + 6139645 q^{65} + 2530332 q^{66} - 7751257 q^{67} + 1700631 q^{68} - 5281686 q^{69} - 20935703 q^{70} - 12592217 q^{71} + 1716795 q^{72} + 12508355 q^{73} - 14999956 q^{74} - 23935230 q^{75} - 23946874 q^{76} + 1874177 q^{77} - 7948773 q^{78} - 5103480 q^{79} + 3128449 q^{80} + 25509168 q^{81} + 11622426 q^{82} + 3040643 q^{83} + 1642113 q^{84} - 13756076 q^{85} + 964635 q^{86} - 11380527 q^{87} - 29653500 q^{88} + 28462995 q^{89} + 4508865 q^{90} + 3016621 q^{91} + 22938254 q^{92} - 10602603 q^{93} - 10070348 q^{94} - 2579984 q^{95} + 9222606 q^{96} + 16208760 q^{97} + 6323227 q^{98} + 8739981 q^{99}+O(q^{100}) \) 48 * q + 2 * q^2 - 1296 * q^3 + 3214 * q^4 + 428 * q^5 - 54 * q^6 - 680 * q^7 + 2355 * q^8 + 34992 * q^9 + 6185 * q^10 + 11989 * q^11 - 86778 * q^12 - 2393 * q^13 + 18201 * q^14 - 11556 * q^15 + 208150 * q^16 + 62538 * q^17 + 1458 * q^18 - 39882 * q^19 + 113423 * q^20 + 18360 * q^21 - 93716 * q^22 + 195618 * q^23 - 63585 * q^24 + 886490 * q^25 + 294399 * q^26 - 944784 * q^27 - 60819 * q^28 + 421501 * q^29 - 166995 * q^30 + 392689 * q^31 - 341578 * q^32 - 323703 * q^33 + 50837 * q^34 + 697874 * q^35 + 2343006 * q^36 - 410396 * q^37 + 677216 * q^38 + 64611 * q^39 + 3232376 * q^40 + 3832958 * q^41 - 491427 * q^42 - 1751932 * q^43 + 4888297 * q^44 + 312012 * q^45 + 1163150 * q^46 + 106461 * q^47 - 5620050 * q^48 + 8202048 * q^49 - 2159111 * q^50 - 1688526 * q^51 - 3605030 * q^52 + 1755534 * q^53 - 39366 * q^54 - 1220729 * q^55 - 4430622 * q^56 + 1076814 * q^57 - 10000202 * q^58 - 2037752 * q^59 - 3062421 * q^60 + 1274098 * q^61 + 97748 * q^62 - 495720 * q^63 + 15135201 * q^64 + 6139645 * q^65 + 2530332 * q^66 - 7751257 * q^67 + 1700631 * q^68 - 5281686 * q^69 - 20935703 * q^70 - 12592217 * q^71 + 1716795 * q^72 + 12508355 * q^73 - 14999956 * q^74 - 23935230 * q^75 - 23946874 * q^76 + 1874177 * q^77 - 7948773 * q^78 - 5103480 * q^79 + 3128449 * q^80 + 25509168 * q^81 + 11622426 * q^82 + 3040643 * q^83 + 1642113 * q^84 - 13756076 * q^85 + 964635 * q^86 - 11380527 * q^87 - 29653500 * q^88 + 28462995 * q^89 + 4508865 * q^90 + 3016621 * q^91 + 22938254 * q^92 - 10602603 * q^93 - 10070348 * q^94 - 2579984 * q^95 + 9222606 * q^96 + 16208760 * q^97 + 6323227 * q^98 + 8739981 * 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 $

$2$	−16.0952	−1.42263	−0.711313	−	0.702875i	$-0.751899\pi$
$2$	−16.0952	−1.42263	−0.711313	+	0.702875i	$0.751899\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	131.055	1.02387
$5$	414.780	1.48396	0.741980	−	0.670422i	$-0.233887\pi$
$5$	414.780	1.48396	0.741980	+	0.670422i	$0.233887\pi$
$6$	434.570	0.821354
$7$	1067.44	1.17625	0.588127	−	0.808768i	$-0.299865\pi$
$7$	1067.44	1.17625	0.588127	+	0.808768i	$0.299865\pi$
$8$	−49.1712	−0.0339544
$9$	729.000	0.333333
$10$	−6675.96	−2.11112
$11$	5970.09	1.35240	0.676202	−	0.736716i	$-0.263624\pi$
$11$	5970.09	1.35240	0.676202	+	0.736716i	$0.263624\pi$
$12$	−3538.49	−0.591130
$13$	4926.04	0.621865	0.310932	−	0.950432i	$-0.399359\pi$
$13$	4926.04	0.621865	0.310932	+	0.950432i	$0.399359\pi$
$14$	−17180.7	−1.67337
$15$	−11199.0	−0.856765
$16$	−15983.6	−0.975563
$17$	−12203.1	−0.602420	−0.301210	−	0.953558i	$-0.597391\pi$
$17$	−12203.1	−0.602420	−0.301210	+	0.953558i	$0.597391\pi$
$18$	−11733.4	−0.474209
$19$	25487.3	0.852484	0.426242	−	0.904609i	$-0.359837\pi$
$19$	25487.3	0.852484	0.426242	+	0.904609i	$0.359837\pi$
$20$	54359.0	1.51938
$21$	−28820.9	−0.679111
$22$	−96089.8	−1.92397
$23$	84625.9	1.45029	0.725147	−	0.688594i	$-0.241772\pi$
$23$	84625.9	1.45029	0.725147	+	0.688594i	$0.241772\pi$
$24$	1327.62	0.0196036
$25$	93917.1	1.20214
$26$	−79285.5	−0.884681
$27$	−19683.0	−0.192450
$28$	139894.	1.20433
$29$	−113169.	−0.861660	−0.430830	−	0.902433i	$-0.641779\pi$
$29$	−113169.	−0.861660	−0.430830	+	0.902433i	$0.641779\pi$
$30$	180251.	1.21886
$31$	273215.	1.64717	0.823585	−	0.567193i	$-0.191971\pi$
$31$	273215.	1.64717	0.823585	+	0.567193i	$0.191971\pi$
$32$	263553.	1.42182
$33$	−161193.	−0.780811
$34$	196411.	0.857019
$35$	442753.	1.74552
$36$	95539.1	0.341289
$37$	58799.6	0.190840	0.0954198	−	0.995437i	$-0.469581\pi$
$37$	58799.6	0.190840	0.0954198	+	0.995437i	$0.469581\pi$
$38$	−410223.	−1.21277
$39$	−133003.	−0.359034
$40$	−20395.2	−0.0503869
$41$	56316.0	0.127611	0.0638055	−	0.997962i	$-0.479676\pi$
$41$	56316.0	0.127611	0.0638055	+	0.997962i	$0.479676\pi$
$42$	463879.	0.966122
$43$	888119.	1.70346	0.851729	−	0.523982i	$-0.175554\pi$
$43$	888119.	1.70346	0.851729	+	0.523982i	$0.175554\pi$
$44$	782411.	1.38468
$45$	302374.	0.494654
$46$	−1.36207e6	−2.06323
$47$	797873.	1.12096	0.560482	−	0.828167i	$-0.310616\pi$
$47$	797873.	1.12096	0.560482	+	0.828167i	$0.310616\pi$
$48$	431558.	0.563242
$49$	315891.	0.383575
$50$	−1.51161e6	−1.71020
$51$	329484.	0.347808
$52$	645582.	0.636707
$53$	205221.	0.189346	0.0946731	−	0.995508i	$-0.469819\pi$
$53$	205221.	0.189346	0.0946731	+	0.995508i	$0.469819\pi$
$54$	316802.	0.273785
$55$	2.47627e6	2.00692
$56$	−52487.4	−0.0399390
$57$	−688157.	−0.492182
$58$	1.82148e6	1.22582
$59$	−330888.	−0.209748	−0.104874	−	0.994485i	$-0.533444\pi$
$59$	−330888.	−0.209748	−0.104874	+	0.994485i	$0.533444\pi$
$60$	−1.46769e6	−0.877214
$61$	−313051.	−0.176588	−0.0882940	−	0.996094i	$-0.528141\pi$
$61$	−313051.	−0.176588	−0.0882940	+	0.996094i	$0.528141\pi$
$62$	−4.39744e6	−2.34331
$63$	778166.	0.392085
$64$	−2.19604e6	−1.04715
$65$	2.04322e6	0.922822
$66$	2.59442e6	1.11080
$67$	740624.	0.300840	0.150420	−	0.988622i	$-0.451937\pi$
$67$	740624.	0.300840	0.150420	+	0.988622i	$0.451937\pi$
$68$	−1.59928e6	−0.616799
$69$	−2.28490e6	−0.837328
$70$	−7.12620e6	−2.48322
$71$	2.40101e6	0.796140	0.398070	−	0.917355i	$-0.369680\pi$
$71$	2.40101e6	0.796140	0.398070	+	0.917355i	$0.369680\pi$
$72$	−35845.8	−0.0113181
$73$	1.54776e6	0.465666	0.232833	−	0.972517i	$-0.425200\pi$
$73$	1.54776e6	0.465666	0.232833	+	0.972517i	$0.425200\pi$
$74$	−946391.	−0.271494
$75$	−2.53576e6	−0.694055
$76$	3.34024e6	0.872830
$77$	6.37273e6	1.59077
$78$	2.14071e6	0.510771
$79$	550911.	0.125715	0.0628574	−	0.998023i	$-0.479979\pi$
$79$	550911.	0.125715	0.0628574	+	0.998023i	$0.479979\pi$
$80$	−6.62968e6	−1.44770
$81$	531441.	0.111111
$82$	−906416.	−0.181543
$83$	−1.73074e6	−0.332246	−0.166123	−	0.986105i	$-0.553125\pi$
$83$	−1.73074e6	−0.332246	−0.166123	+	0.986105i	$0.553125\pi$
$84$	−3.77713e6	−0.695320
$85$	−5.06160e6	−0.893968
$86$	−1.42944e7	−2.42339
$87$	3.05557e6	0.497479
$88$	−293556.	−0.0459200
$89$	7.79544e6	1.17213	0.586065	−	0.810264i	$-0.300676\pi$
$89$	7.79544e6	1.17213	0.586065	+	0.810264i	$0.300676\pi$
$90$	−4.86677e6	−0.703707
$91$	5.25826e6	0.731471
$92$	1.10907e7	1.48491
$93$	−7.37680e6	−0.950994
$94$	−1.28419e7	−1.59471
$95$	1.05716e7	1.26505
$96$	−7.11594e6	−0.820886
$97$	−1.54929e7	−1.72358	−0.861791	−	0.507264i	$-0.830657\pi$
$97$	−1.54929e7	−1.72358	−0.861791	+	0.507264i	$0.830657\pi$
$98$	−5.08432e6	−0.545684
$99$	4.35220e6	0.450802
$100$	1.23083e7	1.23083
$101$	−1.44872e7	−1.39914	−0.699568	−	0.714566i	$-0.746624\pi$
$101$	−1.44872e7	−1.39914	−0.699568	+	0.714566i	$0.746624\pi$
$102$	−5.30311e6	−0.494800
$103$	−5.17014e6	−0.466200	−0.233100	−	0.972453i	$-0.574887\pi$
$103$	−5.17014e6	−0.466200	−0.233100	+	0.972453i	$0.574887\pi$
$104$	−242219.	−0.0211150
$105$	−1.19543e7	−1.00777
$106$	−3.30307e6	−0.269369
$107$	−1.08892e7	−0.859314	−0.429657	−	0.902992i	$-0.641366\pi$
$107$	−1.08892e7	−0.859314	−0.429657	+	0.902992i	$0.641366\pi$
$108$	−2.57956e6	−0.197043
$109$	−2.33501e7	−1.72701	−0.863507	−	0.504337i	$-0.831737\pi$
$109$	−2.33501e7	−1.72701	−0.863507	+	0.504337i	$0.831737\pi$
$110$	−3.98561e7	−2.85509
$111$	−1.58759e6	−0.110181
$112$	−1.70616e7	−1.14751
$113$	−1.31695e7	−0.858611	−0.429305	−	0.903159i	$-0.641242\pi$
$113$	−1.31695e7	−0.858611	−0.429305	+	0.903159i	$0.641242\pi$
$114$	1.10760e7	0.700191
$115$	3.51011e7	2.15218
$116$	−1.48314e7	−0.882225
$117$	3.59108e6	0.207288
$118$	5.32570e6	0.298394
$119$	−1.30261e7	−0.708600
$120$	550670.	0.0290909
$121$	1.61548e7	0.828999
$122$	5.03862e6	0.251219
$123$	−1.52053e6	−0.0736762
$124$	3.58062e7	1.68648
$125$	6.55025e6	0.299967
$126$	−1.25247e7	−0.557791
$127$	2.48979e7	1.07857	0.539286	−	0.842123i	$-0.318694\pi$
$127$	2.48979e7	1.07857	0.539286	+	0.842123i	$0.318694\pi$
$128$	1.61078e6	0.0678894
$129$	−2.39792e7	−0.983492
$130$	−3.28860e7	−1.31283
$131$	3.63919e7	1.41434	0.707172	−	0.707042i	$-0.249971\pi$
$131$	3.63919e7	1.41434	0.707172	+	0.707042i	$0.249971\pi$
$132$	−2.11251e7	−0.799447
$133$	2.72062e7	1.00274
$134$	−1.19205e7	−0.427983
$135$	−8.16411e6	−0.285588
$136$	600042.	0.0204548
$137$	3.35973e7	1.11630	0.558151	−	0.829739i	$-0.311511\pi$
$137$	3.35973e7	1.11630	0.558151	+	0.829739i	$0.311511\pi$
$138$	3.67759e7	1.19120
$139$	6.53684e6	0.206450	0.103225	−	0.994658i	$-0.467084\pi$
$139$	6.53684e6	0.206450	0.103225	+	0.994658i	$0.467084\pi$
$140$	5.80251e7	1.78718
$141$	−2.15426e7	−0.647189
$142$	−3.86447e7	−1.13261
$143$	2.94089e7	0.841013
$144$	−1.16521e7	−0.325188
$145$	−4.69403e7	−1.27867
$146$	−2.49115e7	−0.662469
$147$	−8.52905e6	−0.221457
$148$	7.70599e6	0.195395
$149$	−1.06584e7	−0.263962	−0.131981	−	0.991252i	$-0.542134\pi$
$149$	−1.06584e7	−0.263962	−0.131981	+	0.991252i	$0.542134\pi$
$150$	4.08136e7	0.987382
$151$	−1.02159e7	−0.241467	−0.120734	−	0.992685i	$-0.538525\pi$
$151$	−1.02159e7	−0.241467	−0.120734	+	0.992685i	$0.538525\pi$
$152$	−1.25324e6	−0.0289455
$153$	−8.89607e6	−0.200807
$154$	−1.02570e8	−2.26308
$155$	1.13324e8	2.44434
$156$	−1.74307e7	−0.367603
$157$	−3.86989e6	−0.0798087
$157$	−3.86989e6	−0.0798087
$158$	−8.86701e6	−0.178845
$159$	−5.54097e6	−0.109319
$160$	1.09317e8	2.10992
$161$	9.03333e7	1.70591
$162$	−8.55364e6	−0.158070
$163$	−9.41360e7	−1.70255	−0.851273	−	0.524723i	$-0.824169\pi$
$163$	−9.41360e7	−1.70255	−0.851273	+	0.524723i	$0.824169\pi$
$164$	7.38049e6	0.130657
$165$	−6.68594e7	−1.15869
$166$	2.78567e7	0.472662
$167$	−1.10794e7	−0.184081	−0.0920407	−	0.995755i	$-0.529339\pi$
$167$	−1.10794e7	−0.184081	−0.0920407	+	0.995755i	$0.529339\pi$
$168$	1.41716e6	0.0230588
$169$	−3.84827e7	−0.613285
$170$	8.14675e7	1.27178
$171$	1.85802e7	0.284161
$172$	1.16392e8	1.74412
$173$	8.79525e7	1.29148	0.645739	−	0.763558i	$-0.276550\pi$
$173$	8.79525e7	1.29148	0.645739	+	0.763558i	$0.276550\pi$
$174$	−4.91800e7	−0.707728
$175$	1.00251e8	1.41402
$176$	−9.54237e7	−1.31936
$177$	8.93397e6	0.121098
$178$	−1.25469e8	−1.66750
$179$	−7.03922e7	−0.917358	−0.458679	−	0.888602i	$-0.651677\pi$
$179$	−7.03922e7	−0.917358	−0.458679	+	0.888602i	$0.651677\pi$
$180$	3.96277e7	0.506460
$181$	−4.32326e7	−0.541921	−0.270961	−	0.962590i	$-0.587341\pi$
$181$	−4.32326e7	−0.541921	−0.270961	+	0.962590i	$0.587341\pi$
$182$	−8.46327e7	−1.04061
$183$	8.45238e6	0.101953
$184$	−4.16116e6	−0.0492438
$185$	2.43889e7	0.283199
$186$	1.18731e8	1.35291
$187$	−7.28538e7	−0.814716
$188$	1.04565e8	1.14772
$189$	−2.10105e7	−0.226370
$190$	−1.70152e8	−1.79970
$191$	−4.97837e7	−0.516976	−0.258488	−	0.966014i	$-0.583224\pi$
$191$	−4.97837e7	−0.516976	−0.258488	+	0.966014i	$0.583224\pi$
$192$	5.92930e7	0.604573
$193$	−1.16484e8	−1.16631	−0.583157	−	0.812360i	$-0.698183\pi$
$193$	−1.16484e8	−1.16631	−0.583157	+	0.812360i	$0.698183\pi$
$194$	2.49361e8	2.45201
$195$	−5.51669e7	−0.532792
$196$	4.13991e7	0.392730
$197$	4.67288e7	0.435465	0.217732	−	0.976009i	$-0.430134\pi$
$197$	4.67288e7	0.435465	0.217732	+	0.976009i	$0.430134\pi$
$198$	−7.00494e7	−0.641322
$199$	−1.57824e8	−1.41967	−0.709837	−	0.704366i	$-0.751231\pi$
$199$	−1.57824e8	−1.41967	−0.709837	+	0.704366i	$0.751231\pi$
$200$	−4.61801e6	−0.0408179
$201$	−1.99968e7	−0.173690
$202$	2.33174e8	1.99045
$203$	−1.20802e8	−1.01353
$204$	4.31806e7	0.356109
$205$	2.33587e7	0.189370
$206$	8.32144e7	0.663229
$207$	6.16923e7	0.483431
$208$	−7.87359e7	−0.606668
$209$	1.52162e8	1.15290
$210$	1.92407e8	1.43369
$211$	2.00968e8	1.47278	0.736390	−	0.676557i	$-0.236529\pi$
$211$	2.00968e8	1.47278	0.736390	+	0.676557i	$0.236529\pi$
$212$	2.68953e7	0.193865
$213$	−6.48273e7	−0.459652
$214$	1.75263e8	1.22248
$215$	3.68374e8	2.52787
$216$	967836.	0.00653452
$217$	2.91641e8	1.93749
$218$	3.75824e8	2.45690
$219$	−4.17896e7	−0.268852
$220$	3.24528e8	2.05482
$221$	−6.01130e7	−0.374624
$222$	2.55526e7	0.156747
$223$	−2.34937e7	−0.141868	−0.0709340	−	0.997481i	$-0.522598\pi$
$223$	−2.34937e7	−0.141868	−0.0709340	+	0.997481i	$0.522598\pi$
$224$	2.81328e8	1.67242
$225$	6.84656e7	0.400713
$226$	2.11966e8	1.22148
$227$	−2.82387e8	−1.60234	−0.801170	−	0.598437i	$-0.795789\pi$
$227$	−2.82387e8	−1.60234	−0.801170	+	0.598437i	$0.795789\pi$
$228$	−9.01864e7	−0.503929
$229$	−1.09908e8	−0.604791	−0.302396	−	0.953182i	$-0.597786\pi$
$229$	−1.09908e8	−0.604791	−0.302396	+	0.953182i	$0.597786\pi$
$230$	−5.64959e8	−3.06175
$231$	−1.72064e8	−0.918433
$232$	5.56467e6	0.0292571
$233$	−1.61875e8	−0.838369	−0.419185	−	0.907901i	$-0.637684\pi$
$233$	−1.61875e8	−0.838369	−0.419185	+	0.907901i	$0.637684\pi$
$234$	−5.77991e7	−0.294894
$235$	3.30942e8	1.66347
$236$	−4.33645e7	−0.214755
$237$	−1.48746e7	−0.0725815
$238$	2.09658e8	1.00807
$239$	2.19234e8	1.03876	0.519380	−	0.854543i	$-0.326163\pi$
$239$	2.19234e8	1.03876	0.519380	+	0.854543i	$0.326163\pi$
$240$	1.79001e8	0.835828
$241$	−6.46409e7	−0.297473	−0.148737	−	0.988877i	$-0.547521\pi$
$241$	−6.46409e7	−0.297473	−0.148737	+	0.988877i	$0.547521\pi$
$242$	−2.60015e8	−1.17936
$243$	−1.43489e7	−0.0641500
$244$	−4.10269e7	−0.180803
$245$	1.31025e8	0.569210
$246$	2.44732e7	0.104814
$247$	1.25551e8	0.530129
$248$	−1.34343e7	−0.0559286
$249$	4.67301e7	0.191822
$250$	−1.05428e8	−0.426741
$251$	−5.46136e7	−0.217993	−0.108997	−	0.994042i	$-0.534764\pi$
$251$	−5.46136e7	−0.217993	−0.108997	+	0.994042i	$0.534764\pi$
$252$	1.01983e8	0.401443
$253$	5.05225e8	1.96138
$254$	−4.00736e8	−1.53440
$255$	1.36663e8	0.516133
$256$	2.55167e8	0.950570
$257$	1.19147e8	0.437842	0.218921	−	0.975743i	$-0.429746\pi$
$257$	1.19147e8	0.437842	0.218921	+	0.975743i	$0.429746\pi$
$258$	3.85950e8	1.39914
$259$	6.27652e7	0.224476
$260$	2.67774e8	0.944848
$261$	−8.25005e7	−0.287220
$262$	−5.85734e8	−2.01208
$263$	1.85809e8	0.629828	0.314914	−	0.949120i	$-0.398024\pi$
$263$	1.85809e8	0.629828	0.314914	+	0.949120i	$0.398024\pi$
$264$	7.92602e6	0.0265119
$265$	8.51216e7	0.280982
$266$	−4.37889e8	−1.42652
$267$	−2.10477e8	−0.676729
$268$	9.70625e7	0.308020
$269$	−4.92791e8	−1.54358	−0.771791	−	0.635876i	$-0.780639\pi$
$269$	−4.92791e8	−1.54358	−0.771791	+	0.635876i	$0.780639\pi$
$270$	1.31403e8	0.406286
$271$	2.42765e8	0.740956	0.370478	−	0.928841i	$-0.379194\pi$
$271$	2.42765e8	0.740956	0.370478	+	0.928841i	$0.379194\pi$
$272$	1.95050e8	0.587699
$273$	−1.41973e8	−0.422315
$274$	−5.40754e8	−1.58808
$275$	5.60694e8	1.62578
$276$	−2.99448e8	−0.857312
$277$	−2.73740e8	−0.773855	−0.386927	−	0.922110i	$-0.626464\pi$
$277$	−2.73740e8	−0.773855	−0.386927	+	0.922110i	$0.626464\pi$
$278$	−1.05212e8	−0.293702
$279$	1.99174e8	0.549057
$280$	−2.17707e7	−0.0592679
$281$	4.23743e8	1.13928	0.569640	−	0.821894i	$-0.307083\pi$
$281$	4.23743e8	1.13928	0.569640	+	0.821894i	$0.307083\pi$
$282$	3.46732e8	0.920708
$283$	−6.48911e8	−1.70189	−0.850947	−	0.525251i	$-0.823971\pi$
$283$	−6.48911e8	−1.70189	−0.850947	+	0.525251i	$0.823971\pi$
$284$	3.14664e8	0.815142
$285$	−2.85433e8	−0.730378
$286$	−4.73342e8	−1.19645
$287$	6.01141e7	0.150103
$288$	1.92130e8	0.473939
$289$	−2.61423e8	−0.637090
$290$	7.55513e8	1.81907
$291$	4.18308e8	0.995110
$292$	2.02842e8	0.476780
$293$	4.26772e8	0.991195	0.495597	−	0.868552i	$-0.334949\pi$
$293$	4.26772e8	0.991195	0.495597	+	0.868552i	$0.334949\pi$
$294$	1.37277e8	0.315051
$295$	−1.37245e8	−0.311258
$296$	−2.89125e6	−0.00647984
$297$	−1.17509e8	−0.260270
$298$	1.71549e8	0.375519
$299$	4.16870e8	0.901886
$300$	−3.32324e8	−0.710621
$301$	9.48016e8	2.00370
$302$	1.64427e8	0.343518
$303$	3.91155e8	0.807792
$304$	−4.07379e8	−0.831652
$305$	−1.29847e8	−0.262050
$306$	1.43184e8	0.285673
$307$	−5.71023e8	−1.12634	−0.563169	−	0.826341i	$-0.690418\pi$
$307$	−5.71023e8	−1.12634	−0.563169	+	0.826341i	$0.690418\pi$
$308$	8.35178e8	1.62874
$309$	1.39594e8	0.269161
$310$	−1.82397e9	−3.47738
$311$	5.81749e8	1.09667	0.548333	−	0.836260i	$-0.315263\pi$
$311$	5.81749e8	1.09667	0.548333	+	0.836260i	$0.315263\pi$
$312$	6.53991e6	0.0121908
$313$	8.66056e8	1.59640	0.798199	−	0.602394i	$-0.205786\pi$
$313$	8.66056e8	1.59640	0.798199	+	0.602394i	$0.205786\pi$
$314$	6.22866e7	0.113538
$315$	3.22767e8	0.581839
$316$	7.21996e7	0.128715
$317$	−7.29293e8	−1.28586	−0.642932	−	0.765924i	$-0.722282\pi$
$317$	−7.29293e8	−1.28586	−0.642932	+	0.765924i	$0.722282\pi$
$318$	8.91830e7	0.155520
$319$	−6.75631e8	−1.16531
$320$	−9.10871e8	−1.55393
$321$	2.94008e8	0.496125
$322$	−1.45393e9	−2.42688
$323$	−3.11025e8	−0.513554
$324$	6.96480e7	0.113763
$325$	4.62639e8	0.747568
$326$	1.51514e9	2.42209
$327$	6.30452e8	0.997092
$328$	−2.76912e6	−0.00433295
$329$	8.51684e8	1.31854
$330$	1.07611e9	1.64839
$331$	−7.50917e8	−1.13813	−0.569067	−	0.822291i	$-0.692696\pi$
$331$	−7.50917e8	−1.13813	−0.569067	+	0.822291i	$0.692696\pi$
$332$	−2.26823e8	−0.340176
$333$	4.28649e7	0.0636132
$334$	1.78325e8	0.261879
$335$	3.07196e8	0.446435
$336$	4.60663e8	0.662516
$337$	−3.34070e8	−0.475481	−0.237740	−	0.971329i	$-0.576407\pi$
$337$	−3.34070e8	−0.475481	−0.237740	+	0.971329i	$0.576407\pi$
$338$	6.19386e8	0.872475
$339$	3.55578e8	0.495719
$340$	−6.63349e8	−0.915305
$341$	1.63112e9	2.22764
$342$	−2.99052e8	−0.404256
$343$	−5.41890e8	−0.725073
$344$	−4.36698e7	−0.0578398
$345$	−9.47730e8	−1.24256
$346$	−1.41561e9	−1.83729
$347$	−5.37925e8	−0.691144	−0.345572	−	0.938392i	$-0.612315\pi$
$347$	−5.37925e8	−0.691144	−0.345572	+	0.938392i	$0.612315\pi$
$348$	4.00448e8	0.509353
$349$	−1.31336e9	−1.65385	−0.826925	−	0.562312i	$-0.809912\pi$
$349$	−1.31336e9	−1.65385	−0.826925	+	0.562312i	$0.809912\pi$
$350$	−1.61356e9	−2.01163
$351$	−9.69591e7	−0.119678
$352$	1.57344e9	1.92287
$353$	1.47490e7	0.0178465	0.00892323	−	0.999960i	$-0.497160\pi$
$353$	1.47490e7	0.0178465	0.00892323	+	0.999960i	$0.497160\pi$
$354$	−1.43794e8	−0.172278
$355$	9.95890e8	1.18144
$356$	1.02163e9	1.20011
$357$	3.51705e8	0.409110
$358$	1.13298e9	1.30506
$359$	−1.23279e9	−1.40624	−0.703118	−	0.711073i	$-0.748209\pi$
$359$	−1.23279e9	−1.40624	−0.703118	+	0.711073i	$0.748209\pi$
$360$	−1.48681e7	−0.0167956
$361$	−2.44269e8	−0.273271
$362$	6.95836e8	0.770952
$363$	−4.36181e8	−0.478623
$364$	6.89121e8	0.748929
$365$	6.41980e8	0.691030
$366$	−1.36043e8	−0.145041
$367$	−1.83439e8	−0.193714	−0.0968568	−	0.995298i	$-0.530879\pi$
$367$	−1.83439e8	−0.193714	−0.0968568	+	0.995298i	$0.530879\pi$
$368$	−1.35263e9	−1.41485
$369$	4.10543e7	0.0425370
$370$	−3.92544e8	−0.402886
$371$	2.19062e8	0.222719
$372$	−9.66767e8	−0.973692
$373$	7.58723e8	0.757011	0.378506	−	0.925599i	$-0.376438\pi$
$373$	7.58723e8	0.757011	0.378506	+	0.925599i	$0.376438\pi$
$374$	1.17259e9	1.15904
$375$	−1.76857e8	−0.173186
$376$	−3.92324e7	−0.0380616
$377$	−5.57476e8	−0.535836
$378$	3.38167e8	0.322041
$379$	−1.43259e9	−1.35172	−0.675859	−	0.737031i	$-0.736227\pi$
$379$	−1.43259e9	−1.35172	−0.675859	+	0.737031i	$0.736227\pi$
$380$	1.38546e9	1.29525
$381$	−6.72242e8	−0.622714
$382$	8.01278e8	0.735464
$383$	3.12885e8	0.284570	0.142285	−	0.989826i	$-0.454555\pi$
$383$	3.12885e8	0.284570	0.142285	+	0.989826i	$0.454555\pi$
$384$	−4.34911e7	−0.0391960
$385$	2.64328e9	2.36064
$386$	1.87483e9	1.65923
$387$	6.47439e8	0.567819
$388$	−2.03042e9	−1.76472
$389$	5.77188e7	0.0497157	0.0248579	−	0.999691i	$-0.492087\pi$
$389$	5.77188e7	0.0497157	0.0248579	+	0.999691i	$0.492087\pi$
$390$	8.87922e8	0.757964
$391$	−1.03270e9	−0.873686
$392$	−1.55327e7	−0.0130241
$393$	−9.82580e8	−0.816571
$394$	−7.52109e8	−0.619504
$395$	2.28507e8	0.186556
$396$	5.70377e8	0.461561
$397$	−2.11451e9	−1.69607	−0.848033	−	0.529944i	$-0.822213\pi$
$397$	−2.11451e9	−1.69607	−0.848033	+	0.529944i	$0.822213\pi$
$398$	2.54021e9	2.01967
$399$	−7.34568e8	−0.578931
$400$	−1.50114e9	−1.17276
$401$	−3.80744e8	−0.294868	−0.147434	−	0.989072i	$-0.547101\pi$
$401$	−3.80744e8	−0.294868	−0.147434	+	0.989072i	$0.547101\pi$
$402$	3.21853e8	0.247096
$403$	1.34587e9	1.02432
$404$	−1.89862e9	−1.43253
$405$	2.20431e8	0.164885
$406$	1.94433e9	1.44188
$407$	3.51039e8	0.258092
$408$	−1.62011e7	−0.0118096
$409$	−1.38472e9	−1.00076	−0.500381	−	0.865805i	$-0.666807\pi$
$409$	−1.38472e9	−1.00076	−0.500381	+	0.865805i	$0.666807\pi$
$410$	−3.75963e8	−0.269402
$411$	−9.07126e8	−0.644498
$412$	−6.77573e8	−0.477327
$413$	−3.53204e8	−0.246718
$414$	−9.92949e8	−0.687742
$415$	−7.17877e8	−0.493040
$416$	1.29827e9	0.884177
$417$	−1.76495e8	−0.119194
$418$	−2.44907e9	−1.64015
$419$	2.60043e9	1.72701	0.863506	−	0.504338i	$-0.168263\pi$
$419$	2.60043e9	1.72701	0.863506	+	0.504338i	$0.168263\pi$
$420$	−1.56668e9	−1.03183
$421$	−1.39526e9	−0.911310	−0.455655	−	0.890156i	$-0.650595\pi$
$421$	−1.39526e9	−0.911310	−0.455655	+	0.890156i	$0.650595\pi$
$422$	−3.23462e9	−2.09522
$423$	5.81650e8	0.373654
$424$	−1.00910e7	−0.00642913
$425$	−1.14608e9	−0.724193
$426$	1.04341e9	0.653913
$427$	−3.34164e8	−0.207712
$428$	−1.42708e9	−0.879824
$429$	−7.94040e8	−0.485559
$430$	−5.92904e9	−3.59621
$431$	8.16468e8	0.491212	0.245606	−	0.969370i	$-0.421013\pi$
$431$	8.16468e8	0.491212	0.245606	+	0.969370i	$0.421013\pi$
$432$	3.14606e8	0.187747
$433$	−2.35389e9	−1.39341	−0.696704	−	0.717359i	$-0.745351\pi$
$433$	−2.35389e9	−1.39341	−0.696704	+	0.717359i	$0.745351\pi$
$434$	−4.69402e9	−2.75633
$435$	1.26739e9	0.738240
$436$	−3.06015e9	−1.76823
$437$	2.15689e9	1.23635
$438$	6.72611e8	0.382476
$439$	−5.99798e8	−0.338360	−0.169180	−	0.985585i	$-0.554112\pi$
$439$	−5.99798e8	−0.338360	−0.169180	+	0.985585i	$0.554112\pi$
$440$	−1.21761e8	−0.0681435
$441$	2.30284e8	0.127858
$442$	9.67530e8	0.532950
$443$	1.57295e9	0.859609	0.429805	−	0.902922i	$-0.358582\pi$
$443$	1.57295e9	0.859609	0.429805	+	0.902922i	$0.358582\pi$
$444$	−2.08062e8	−0.112811
$445$	3.23339e9	1.73939
$446$	3.78136e8	0.201825
$447$	2.87778e8	0.152398
$448$	−2.34414e9	−1.23172
$449$	−1.36431e9	−0.711298	−0.355649	−	0.934620i	$-0.615740\pi$
$449$	−1.36431e9	−0.711298	−0.355649	+	0.934620i	$0.615740\pi$
$450$	−1.10197e9	−0.570065
$451$	3.36212e8	0.172582
$452$	−1.72594e9	−0.879103
$453$	2.75830e8	0.139411
$454$	4.54507e9	2.27953
$455$	2.18102e9	1.08547
$456$	3.38375e7	0.0167117
$457$	3.08483e9	1.51190	0.755951	−	0.654628i	$-0.227175\pi$
$457$	3.08483e9	1.51190	0.755951	+	0.654628i	$0.227175\pi$
$458$	1.76899e9	0.860393
$459$	2.40194e8	0.115936
$460$	4.60018e9	2.20355
$461$	−2.86228e9	−1.36069	−0.680344	−	0.732893i	$-0.738170\pi$
$461$	−2.86228e9	−1.36069	−0.680344	+	0.732893i	$0.738170\pi$
$462$	2.76940e9	1.30659
$463$	−3.01265e9	−1.41064	−0.705318	−	0.708891i	$-0.749196\pi$
$463$	−3.01265e9	−1.41064	−0.705318	+	0.708891i	$0.749196\pi$
$464$	1.80886e9	0.840603
$465$	−3.05975e9	−1.41124
$466$	2.60542e9	1.19269
$467$	5.39952e8	0.245327	0.122664	−	0.992448i	$-0.460856\pi$
$467$	5.39952e8	0.245327	0.122664	+	0.992448i	$0.460856\pi$
$468$	4.70629e8	0.212236
$469$	7.90573e8	0.353865
$470$	−5.32657e9	−2.36649
$471$	1.04487e8	0.0460776
$472$	1.62701e7	0.00712187
$473$	5.30215e9	2.30377
$474$	2.39409e8	0.103256
$475$	2.39369e9	1.02480
$476$	−1.70714e9	−0.725512
$477$	1.49606e8	0.0631154
$478$	−3.52861e9	−1.47777
$479$	−2.33669e9	−0.971465	−0.485733	−	0.874107i	$-0.661447\pi$
$479$	−2.33669e9	−0.971465	−0.485733	+	0.874107i	$0.661447\pi$
$480$	−2.95155e9	−1.21816
$481$	2.89649e8	0.118676
$482$	1.04041e9	0.423194
$483$	−2.43900e9	−0.984910
$484$	2.11717e9	0.848785
$485$	−6.42614e9	−2.55773
$486$	2.30948e8	0.0912616
$487$	2.52088e9	0.989010	0.494505	−	0.869175i	$-0.335349\pi$
$487$	2.52088e9	0.989010	0.494505	+	0.869175i	$0.335349\pi$
$488$	1.53931e7	0.00599593
$489$	2.54167e9	0.982966
$490$	−2.10887e9	−0.809774
$491$	2.41256e9	0.919799	0.459900	−	0.887971i	$-0.347885\pi$
$491$	2.41256e9	0.919799	0.459900	+	0.887971i	$0.347885\pi$
$492$	−1.99273e8	−0.0754347
$493$	1.38102e9	0.519081
$494$	−2.02077e9	−0.754176
$495$	1.80520e9	0.668972
$496$	−4.36696e9	−1.60692
$497$	2.56294e9	0.936464
$498$	−7.52130e8	−0.272891
$499$	1.63154e9	0.587821	0.293910	−	0.955833i	$-0.405043\pi$
$499$	1.63154e9	0.587821	0.293910	+	0.955833i	$0.405043\pi$
$500$	8.58443e8	0.307126
$501$	2.99145e8	0.106279
$502$	8.79016e8	0.310123
$503$	−3.36342e9	−1.17840	−0.589200	−	0.807987i	$-0.700557\pi$
$503$	−3.36342e9	−1.17840	−0.589200	+	0.807987i	$0.700557\pi$
$504$	−3.82633e7	−0.0133130
$505$	−6.00900e9	−2.07626
$506$	−8.13168e9	−2.79032
$507$	1.03903e9	0.354080
$508$	3.26299e9	1.10431
$509$	1.77894e9	0.597927	0.298964	−	0.954265i	$-0.403359\pi$
$509$	1.77894e9	0.597927	0.298964	+	0.954265i	$0.403359\pi$
$510$	−2.19962e9	−0.734264
$511$	1.65215e9	0.547742
$512$	−4.31314e9	−1.42020
$513$	−5.01666e8	−0.164061
$514$	−1.91769e9	−0.622886
$515$	−2.14447e9	−0.691823
$516$	−3.14260e9	−1.00697
$517$	4.76338e9	1.51600
$518$	−1.01022e9	−0.319346
$519$	−2.37472e9	−0.745635
$520$	−1.00467e8	−0.0313338
$521$	−2.74764e9	−0.851193	−0.425597	−	0.904913i	$-0.639936\pi$
$521$	−2.74764e9	−0.851193	−0.425597	+	0.904913i	$0.639936\pi$
$522$	1.32786e9	0.408607
$523$	−5.86194e9	−1.79178	−0.895892	−	0.444272i	$-0.853462\pi$
$523$	−5.86194e9	−1.79178	−0.895892	+	0.444272i	$0.853462\pi$
$524$	4.76934e9	1.44810
$525$	−2.70678e9	−0.816386
$526$	−2.99063e9	−0.896010
$527$	−3.33407e9	−0.992289
$528$	2.57644e9	0.761731
$529$	3.75672e9	1.10335
$530$	−1.37005e9	−0.399733
$531$	−2.41217e8	−0.0699161
$532$	3.56551e9	1.02667
$533$	2.77414e8	0.0793567
$534$	3.38766e9	0.962733
$535$	−4.51661e9	−1.27519
$536$	−3.64173e7	−0.0102148
$537$	1.90059e9	0.529637
$538$	7.93156e9	2.19594
$539$	1.88590e9	0.518749
$540$	−1.06995e9	−0.292405
$541$	−5.81634e8	−0.157928	−0.0789641	−	0.996877i	$-0.525161\pi$
$541$	−5.81634e8	−0.157928	−0.0789641	+	0.996877i	$0.525161\pi$
$542$	−3.90734e9	−1.05410
$543$	1.16728e9	0.312878
$544$	−3.21617e9	−0.856531
$545$	−9.68514e9	−2.56282
$546$	2.28508e9	0.600797
$547$	−2.70943e9	−0.707819	−0.353909	−	0.935280i	$-0.615148\pi$
$547$	−2.70943e9	−0.707819	−0.353909	+	0.935280i	$0.615148\pi$
$548$	4.40309e9	1.14295
$549$	−2.28214e8	−0.0588627
$550$	−9.02447e9	−2.31288
$551$	−2.88438e9	−0.734551
$552$	1.12351e8	0.0284309
$553$	5.88065e8	0.147873
$554$	4.40590e9	1.10091
$555$	−6.58500e8	−0.163505
$556$	8.56685e8	0.211378
$557$	−3.35145e8	−0.0821750	−0.0410875	−	0.999156i	$-0.513082\pi$
$557$	−3.35145e8	−0.0821750	−0.0410875	+	0.999156i	$0.513082\pi$
$558$	−3.20574e9	−0.781103
$559$	4.37490e9	1.05932
$560$	−7.07680e9	−1.70286
$561$	1.96705e9	0.470377
$562$	−6.82023e9	−1.62077
$563$	1.55417e9	0.367046	0.183523	−	0.983015i	$-0.441250\pi$
$563$	1.55417e9	0.367046	0.183523	+	0.983015i	$0.441250\pi$
$564$	−2.82326e9	−0.662635
$565$	−5.46246e9	−1.27414
$566$	1.04443e10	2.42116
$567$	5.67283e8	0.130695
$568$	−1.18060e8	−0.0270324
$569$	6.33378e9	1.44135	0.720676	−	0.693272i	$-0.243831\pi$
$569$	6.33378e9	1.44135	0.720676	+	0.693272i	$0.243831\pi$
$570$	4.59411e9	1.03906
$571$	2.76964e9	0.622582	0.311291	−	0.950315i	$-0.399239\pi$
$571$	2.76964e9	0.622582	0.311291	+	0.950315i	$0.399239\pi$
$572$	3.85418e9	0.861085
$573$	1.34416e9	0.298476
$574$	−9.67547e8	−0.213541
$575$	7.94782e9	1.74345
$576$	−1.60091e9	−0.349050
$577$	7.07967e9	1.53426	0.767128	−	0.641494i	$-0.221685\pi$
$577$	7.07967e9	1.53426	0.767128	+	0.641494i	$0.221685\pi$
$578$	4.20764e9	0.906341
$579$	3.14507e9	0.673371
$580$	−6.15177e9	−1.30919
$581$	−1.84747e9	−0.390806
$582$	−6.73275e9	−1.41567
$583$	1.22519e9	0.256073
$584$	−7.61053e7	−0.0158114
$585$	1.48951e9	0.307607
$586$	−6.86897e9	−1.41010
$587$	−5.37462e9	−1.09677	−0.548384	−	0.836227i	$-0.684757\pi$
$587$	−5.37462e9	−1.09677	−0.548384	+	0.836227i	$0.684757\pi$
$588$	−1.11777e9	−0.226743
$589$	6.96351e9	1.40419
$590$	2.20899e9	0.442805
$591$	−1.26168e9	−0.251416
$592$	−9.39831e8	−0.186176
$593$	2.07195e9	0.408026	0.204013	−	0.978968i	$-0.434602\pi$
$593$	2.07195e9	0.408026	0.204013	+	0.978968i	$0.434602\pi$
$594$	1.89133e9	0.370268
$595$	−5.40297e9	−1.05153
$596$	−1.39684e9	−0.270262
$597$	4.26126e9	0.819649
$598$	−6.70960e9	−1.28305
$599$	4.69320e8	0.0892227	0.0446114	−	0.999004i	$-0.485795\pi$
$599$	4.69320e8	0.0892227	0.0446114	+	0.999004i	$0.485795\pi$
$600$	1.24686e8	0.0235662
$601$	9.30362e9	1.74820	0.874101	−	0.485745i	$-0.161452\pi$
$601$	9.30362e9	1.74820	0.874101	+	0.485745i	$0.161452\pi$
$602$	−1.52585e10	−2.85052
$603$	5.39915e8	0.100280
$604$	−1.33885e9	−0.247231
$605$	6.70070e9	1.23020
$606$	−6.29571e9	−1.14919
$607$	−6.64544e9	−1.20604	−0.603022	−	0.797724i	$-0.706037\pi$
$607$	−6.64544e9	−1.20604	−0.603022	+	0.797724i	$0.706037\pi$
$608$	6.71726e9	1.21208
$609$	3.26165e9	0.585163
$610$	2.08992e9	0.372799
$611$	3.93035e9	0.697087
$612$	−1.16588e9	−0.205600
$613$	1.33822e9	0.234648	0.117324	−	0.993094i	$-0.462568\pi$
$613$	1.33822e9	0.234648	0.117324	+	0.993094i	$0.462568\pi$
$614$	9.19072e9	1.60236
$615$	−6.30685e8	−0.109333
$616$	−3.13355e8	−0.0540137
$617$	7.78957e9	1.33511	0.667553	−	0.744562i	$-0.267342\pi$
$617$	7.78957e9	1.33511	0.667553	+	0.744562i	$0.267342\pi$
$618$	−2.24679e9	−0.382915
$619$	7.80159e9	1.32210	0.661052	−	0.750340i	$-0.270110\pi$
$619$	7.80159e9	1.32210	0.661052	+	0.750340i	$0.270110\pi$
$620$	1.48517e10	2.50268
$621$	−1.66569e9	−0.279109
$622$	−9.36337e9	−1.56015
$623$	8.32118e9	1.37872
$624$	2.12587e9	0.350260
$625$	−4.62036e9	−0.757001
$626$	−1.39393e10	−2.27108
$627$	−4.10836e9	−0.665629
$628$	−5.07169e8	−0.0817135
$629$	−7.17539e8	−0.114966
$630$	−5.19500e9	−0.827739
$631$	5.05900e8	0.0801609	0.0400804	−	0.999196i	$-0.487239\pi$
$631$	5.05900e8	0.0801609	0.0400804	+	0.999196i	$0.487239\pi$
$632$	−2.70889e7	−0.00426857
$633$	−5.42613e9	−0.850310
$634$	1.17381e10	1.82930
$635$	1.03271e10	1.60056
$636$	−7.26172e8	−0.111928
$637$	1.55609e9	0.238532
$638$	1.08744e10	1.65781
$639$	1.75034e9	0.265380
$640$	6.68119e8	0.100745
$641$	−5.05684e9	−0.758361	−0.379180	−	0.925323i	$-0.623794\pi$
$641$	−5.05684e9	−0.758361	−0.379180	+	0.925323i	$0.623794\pi$
$642$	−4.73211e9	−0.705801
$643$	4.35184e9	0.645558	0.322779	−	0.946474i	$-0.395383\pi$
$643$	4.35184e9	0.645558	0.322779	+	0.946474i	$0.395383\pi$
$644$	1.18386e10	1.74663
$645$	−9.94609e9	−1.45946
$646$	5.00600e9	0.730595
$647$	1.13708e10	1.65054	0.825268	−	0.564741i	$-0.191024\pi$
$647$	1.13708e10	1.65054	0.825268	+	0.564741i	$0.191024\pi$
$648$	−2.61316e7	−0.00377271
$649$	−1.97543e9	−0.283665
$650$	−7.44626e9	−1.06351
$651$	−7.87431e9	−1.11861
$652$	−1.23370e10	−1.74318
$653$	−5.18608e9	−0.728859	−0.364429	−	0.931231i	$-0.618736\pi$
$653$	−5.18608e9	−0.728859	−0.364429	+	0.931231i	$0.618736\pi$
$654$	−1.01472e10	−1.41849
$655$	1.50946e10	2.09883
$656$	−9.00133e8	−0.124493
$657$	1.12832e9	0.155222
$658$	−1.37080e10	−1.87579
$659$	9.23927e9	1.25759	0.628794	−	0.777572i	$-0.283549\pi$
$659$	9.23927e9	1.25759	0.628794	+	0.777572i	$0.283549\pi$
$660$	−8.76226e9	−1.18635
$661$	−1.96244e9	−0.264297	−0.132148	−	0.991230i	$-0.542187\pi$
$661$	−1.96244e9	−0.264297	−0.132148	+	0.991230i	$0.542187\pi$
$662$	1.20861e10	1.61914
$663$	1.62305e9	0.216289
$664$	8.51027e7	0.0112812
$665$	1.12846e10	1.48802
$666$	−6.89919e8	−0.0904979
$667$	−9.57706e9	−1.24966
$668$	−1.45201e9	−0.188475
$669$	6.34330e8	0.0819075
$670$	−4.94437e9	−0.635110
$671$	−1.86895e9	−0.238818
$672$	−7.59586e9	−0.965571
$673$	4.32129e9	0.546462	0.273231	−	0.961948i	$-0.411908\pi$
$673$	4.32129e9	0.546462	0.273231	+	0.961948i	$0.411908\pi$
$674$	5.37692e9	0.676432
$675$	−1.84857e9	−0.231352
$676$	−5.04335e9	−0.627922
$677$	6.79696e9	0.841889	0.420944	−	0.907086i	$-0.361699\pi$
$677$	6.79696e9	0.841889	0.420944	+	0.907086i	$0.361699\pi$
$678$	−5.72309e9	−0.705223
$679$	−1.65378e10	−2.02737
$680$	2.48885e8	0.0303541
$681$	7.62445e9	0.925111
$682$	−2.62531e10	−3.16910
$683$	2.25158e9	0.270405	0.135203	−	0.990818i	$-0.456831\pi$
$683$	2.25158e9	0.270405	0.135203	+	0.990818i	$0.456831\pi$
$684$	2.43503e9	0.290943
$685$	1.39355e10	1.65655
$686$	8.72182e9	1.03151
$687$	2.96752e9	0.349177
$688$	−1.41954e10	−1.66183
$689$	1.01093e9	0.117748
$690$	1.52539e10	1.76770
$691$	1.18370e10	1.36480	0.682400	−	0.730979i	$-0.260936\pi$
$691$	1.18370e10	1.36480	0.682400	+	0.730979i	$0.260936\pi$
$692$	1.15266e10	1.32230
$693$	4.64572e9	0.530258
$694$	8.65800e9	0.983240
$695$	2.71135e9	0.306364
$696$	−1.50246e8	−0.0168916
$697$	−6.87231e8	−0.0768755
$698$	2.11388e10	2.35281
$699$	4.37064e9	0.484033
$700$	1.31384e10	1.44777
$701$	3.94080e9	0.432087	0.216043	−	0.976384i	$-0.430685\pi$
$701$	3.94080e9	0.432087	0.216043	+	0.976384i	$0.430685\pi$
$702$	1.56058e9	0.170257
$703$	1.49864e9	0.162688
$704$	−1.31105e10	−1.41617
$705$	−8.93542e9	−0.960402
$706$	−2.37388e8	−0.0253888
$707$	−1.54643e10	−1.64574
$708$	1.17084e9	0.123989
$709$	1.19473e10	1.25895	0.629473	−	0.777022i	$-0.283271\pi$
$709$	1.19473e10	1.25895	0.629473	+	0.777022i	$0.283271\pi$
$710$	−1.60290e10	−1.68075
$711$	4.01614e8	0.0419049
$712$	−3.83311e8	−0.0397989
$713$	2.31211e10	2.38888
$714$	−5.66077e9	−0.582011
$715$	1.21982e10	1.24803
$716$	−9.22525e9	−0.939253
$717$	−5.91932e9	−0.599729
$718$	1.98420e10	2.00055
$719$	2.85691e9	0.286646	0.143323	−	0.989676i	$-0.454221\pi$
$719$	2.85691e9	0.286646	0.143323	+	0.989676i	$0.454221\pi$
$720$	−4.83304e9	−0.482566
$721$	−5.51883e9	−0.548370
$722$	3.93156e9	0.388763
$723$	1.74531e9	0.171746
$724$	−5.66585e9	−0.554855
$725$	−1.06285e10	−1.03583
$726$	7.02041e9	0.680901
$727$	5.55420e9	0.536107	0.268053	−	0.963404i	$-0.413620\pi$
$727$	5.55420e9	0.536107	0.268053	+	0.963404i	$0.413620\pi$
$728$	−2.58555e8	−0.0248366
$729$	3.87420e8	0.0370370
$730$	−1.03328e10	−0.983077
$731$	−1.08378e10	−1.02620
$732$	1.10773e9	0.104386
$733$	−4.51120e9	−0.423085	−0.211543	−	0.977369i	$-0.567849\pi$
$733$	−4.51120e9	−0.423085	−0.211543	+	0.977369i	$0.567849\pi$
$734$	2.95248e9	0.275582
$735$	−3.53768e9	−0.328634
$736$	2.23034e10	2.06205
$737$	4.42159e9	0.406858
$738$	−6.60777e8	−0.0605143
$739$	1.28425e10	1.17056	0.585279	−	0.810832i	$-0.300985\pi$
$739$	1.28425e10	1.17056	0.585279	+	0.810832i	$0.300985\pi$
$740$	3.19629e9	0.289958
$741$	−3.38989e9	−0.306070
$742$	−3.52584e9	−0.316847
$743$	−1.06496e10	−0.952513	−0.476256	−	0.879306i	$-0.658007\pi$
$743$	−1.06496e10	−0.952513	−0.476256	+	0.879306i	$0.658007\pi$
$744$	3.62726e8	0.0322904
$745$	−4.42090e9	−0.391709
$746$	−1.22118e10	−1.07694
$747$	−1.26171e9	−0.110749
$748$	−9.54785e9	−0.834161
$749$	−1.16236e10	−1.01077
$750$	2.84654e9	0.246379
$751$	1.67590e10	1.44380	0.721901	−	0.691996i	$-0.243268\pi$
$751$	1.67590e10	1.44380	0.721901	+	0.691996i	$0.243268\pi$
$752$	−1.27529e10	−1.09357
$753$	1.47457e9	0.125858
$754$	8.97268e9	0.762294
$755$	−4.23736e9	−0.358328
$756$	−2.75353e9	−0.231773
$757$	3.16467e9	0.265150	0.132575	−	0.991173i	$-0.457675\pi$
$757$	3.16467e9	0.265150	0.132575	+	0.991173i	$0.457675\pi$
$758$	2.30579e10	1.92299
$759$	−1.36411e10	−1.13241
$760$	−5.19818e8	−0.0429541
$761$	1.58706e10	1.30541	0.652704	−	0.757613i	$-0.273634\pi$
$761$	1.58706e10	1.30541	0.652704	+	0.757613i	$0.273634\pi$
$762$	1.08199e10	0.885889
$763$	−2.49249e10	−2.03141
$764$	−6.52440e9	−0.529315
$765$	−3.68991e9	−0.297989
$766$	−5.03595e9	−0.404837
$767$	−1.62996e9	−0.130435
$768$	−6.88950e9	−0.548812
$769$	−4.66639e9	−0.370032	−0.185016	−	0.982736i	$-0.559234\pi$
$769$	−4.66639e9	−0.370032	−0.185016	+	0.982736i	$0.559234\pi$
$770$	−4.25441e10	−3.35832
$771$	−3.21697e9	−0.252788
$772$	−1.52658e10	−1.19415
$773$	−2.12683e10	−1.65617	−0.828083	−	0.560605i	$-0.810569\pi$
$773$	−2.12683e10	−1.65617	−0.828083	+	0.560605i	$0.810569\pi$
$774$	−1.04206e10	−0.807795
$775$	2.56596e10	1.98013
$776$	7.61804e8	0.0585231
$777$	−1.69466e9	−0.129601
$778$	−9.28995e8	−0.0707270
$779$	1.43534e9	0.108786
$780$	−7.22990e9	−0.545508
$781$	1.43343e10	1.07670
$782$	1.66215e10	1.24293
$783$	2.22751e9	0.165826
$784$	−5.04908e9	−0.374202
$785$	−1.60515e9	−0.118433
$786$	1.58148e10	1.16168
$787$	1.87369e10	1.37020	0.685102	−	0.728447i	$-0.259757\pi$
$787$	1.87369e10	1.37020	0.685102	+	0.728447i	$0.259757\pi$
$788$	6.12404e9	0.445858
$789$	−5.01685e9	−0.363631
$790$	−3.67785e9	−0.265399
$791$	−1.40577e10	−1.00994
$792$	−2.14003e8	−0.0153067
$793$	−1.54210e9	−0.109814
$794$	3.40334e10	2.41287
$795$	−2.29828e9	−0.162225
$796$	−2.06837e10	−1.45356
$797$	2.14453e10	1.50047	0.750237	−	0.661169i	$-0.229939\pi$
$797$	2.14453e10	1.50047	0.750237	+	0.661169i	$0.229939\pi$
$798$	1.18230e10	0.823603
$799$	−9.73654e9	−0.675291
$800$	2.47522e10	1.70922
$801$	5.68288e9	0.390710
$802$	6.12815e9	0.419487
$803$	9.24029e9	0.629769
$804$	−2.62069e9	−0.177836
$805$	3.74684e10	2.53151
$806$	−2.16620e10	−1.45722
$807$	1.33054e10	0.891187
$808$	7.12353e8	0.0475068
$809$	−1.87172e10	−1.24285	−0.621427	−	0.783472i	$-0.713447\pi$
$809$	−1.87172e10	−1.24285	−0.621427	+	0.783472i	$0.713447\pi$
$810$	−3.54788e9	−0.234569
$811$	−1.88761e10	−1.24262	−0.621310	−	0.783565i	$-0.713399\pi$
$811$	−1.88761e10	−1.24262	−0.621310	+	0.783565i	$0.713399\pi$
$812$	−1.58317e10	−1.03772
$813$	−6.55464e9	−0.427791
$814$	−5.65004e9	−0.367169
$815$	−3.90457e10	−2.52651
$816$	−5.26635e9	−0.339308
$817$	2.26357e10	1.45217
$818$	2.22874e10	1.42371
$819$	3.83327e9	0.243824
$820$	3.06128e9	0.193889
$821$	−1.32165e10	−0.833519	−0.416760	−	0.909017i	$-0.636834\pi$
$821$	−1.32165e10	−0.833519	−0.416760	+	0.909017i	$0.636834\pi$
$822$	1.46004e10	0.916880
$823$	4.50534e9	0.281727	0.140863	−	0.990029i	$-0.455012\pi$
$823$	4.50534e9	0.281727	0.140863	+	0.990029i	$0.455012\pi$
$824$	2.54222e8	0.0158295
$825$	−1.51387e10	−0.938644
$826$	5.68488e9	0.350987
$827$	−6.31004e8	−0.0387939	−0.0193969	−	0.999812i	$-0.506175\pi$
$827$	−6.31004e8	−0.0387939	−0.0193969	+	0.999812i	$0.506175\pi$
$828$	8.08509e9	0.494969
$829$	2.01240e10	1.22680	0.613401	−	0.789772i	$-0.289801\pi$
$829$	2.01240e10	1.22680	0.613401	+	0.789772i	$0.289801\pi$
$830$	1.15544e10	0.701412
$831$	7.39099e9	0.446785
$832$	−1.08177e10	−0.651186
$833$	−3.85485e9	−0.231073
$834$	2.84071e9	0.169569
$835$	−4.59552e9	−0.273169
$836$	1.99415e10	1.18042
$837$	−5.37769e9	−0.316998
$838$	−4.18544e10	−2.45690
$839$	1.04279e10	0.609579	0.304790	−	0.952420i	$-0.401414\pi$
$839$	1.04279e10	0.609579	0.304790	+	0.952420i	$0.401414\pi$
$840$	5.87809e8	0.0342183
$841$	−4.44258e9	−0.257542
$842$	2.24569e10	1.29645
$843$	−1.14411e10	−0.657764
$844$	2.63379e10	1.50793
$845$	−1.59618e10	−0.910090
$846$	−9.36176e9	−0.531571
$847$	1.72444e10	0.975114
$848$	−3.28018e9	−0.184719
$849$	1.75206e10	0.982589
$850$	1.84464e10	1.03026
$851$	4.97597e9	0.276774
$852$	−8.49594e9	−0.470623
$853$	−1.99395e10	−1.10000	−0.550001	−	0.835164i	$-0.685373\pi$
$853$	−1.99395e10	−1.10000	−0.550001	+	0.835164i	$0.685373\pi$
$854$	5.37844e9	0.295497
$855$	7.70670e9	0.421684
$856$	5.35434e8	0.0291775
$857$	−4.09849e9	−0.222429	−0.111214	−	0.993796i	$-0.535474\pi$
$857$	−4.09849e9	−0.222429	−0.111214	+	0.993796i	$0.535474\pi$
$858$	1.27802e10	0.690769
$859$	1.64253e10	0.884174	0.442087	−	0.896972i	$-0.354238\pi$
$859$	1.64253e10	0.884174	0.442087	+	0.896972i	$0.354238\pi$
$860$	4.82772e10	2.58820
$861$	−1.62308e9	−0.0866620
$862$	−1.31412e10	−0.698811
$863$	−5.86196e8	−0.0310460	−0.0155230	−	0.999880i	$-0.504941\pi$
$863$	−5.86196e8	−0.0310460	−0.0155230	+	0.999880i	$0.504941\pi$
$864$	−5.18752e9	−0.273629
$865$	3.64809e10	1.91650
$866$	3.78863e10	1.98230
$867$	7.05841e9	0.367824
$868$	3.82210e10	1.98373
$869$	3.28899e9	0.170017
$870$	−2.03989e10	−1.05024
$871$	3.64834e9	0.187082
$872$	1.14815e9	0.0586397
$873$	−1.12943e10	−0.574527
$874$	−3.47155e10	−1.75887
$875$	6.99202e9	0.352837
$876$	−5.47674e9	−0.275269
$877$	6.07367e8	0.0304056	0.0152028	−	0.999884i	$-0.495161\pi$
$877$	6.07367e8	0.0304056	0.0152028	+	0.999884i	$0.495161\pi$
$878$	9.65386e9	0.481360
$879$	−1.15228e10	−0.572267
$880$	−3.95798e10	−1.95787
$881$	−1.25671e9	−0.0619186	−0.0309593	−	0.999521i	$-0.509856\pi$
$881$	−1.25671e9	−0.0619186	−0.0309593	+	0.999521i	$0.509856\pi$
$882$	−3.70647e9	−0.181895
$883$	−3.35352e10	−1.63923	−0.819613	−	0.572917i	$-0.805812\pi$
$883$	−3.35352e10	−1.63923	−0.819613	+	0.572917i	$0.805812\pi$
$884$	−7.87811e9	−0.383565
$885$	3.70563e9	0.179705
$886$	−2.53169e10	−1.22290
$887$	−1.14756e10	−0.552132	−0.276066	−	0.961139i	$-0.589031\pi$
$887$	−1.14756e10	−0.552132	−0.276066	+	0.961139i	$0.589031\pi$
$888$	7.80637e7	0.00374114
$889$	2.65770e10	1.26867
$890$	−5.20420e10	−2.47451
$891$	3.17275e9	0.150267
$892$	−3.07897e9	−0.145254
$893$	2.03356e10	0.955603
$894$	−4.63183e9	−0.216806
$895$	−2.91972e10	−1.36132
$896$	1.71942e9	0.0798552
$897$	−1.12555e10	−0.520704
$898$	2.19589e10	1.01191
$899$	−3.09195e10	−1.41930
$900$	8.97276e9	0.410277
$901$	−2.50434e9	−0.114066
$902$	−5.41139e9	−0.245519
$903$	−2.55964e10	−1.15684
$904$	6.47562e8	0.0291536
$905$	−1.79320e10	−0.804190
$906$	−4.43954e9	−0.198330
$907$	−3.61389e10	−1.60824	−0.804118	−	0.594470i	$-0.797362\pi$
$907$	−3.61389e10	−1.60824	−0.804118	+	0.594470i	$0.797362\pi$
$908$	−3.70083e10	−1.64058
$909$	−1.05612e10	−0.466379
$910$	−3.51039e10	−1.54422
$911$	−3.20052e10	−1.40251	−0.701255	−	0.712910i	$-0.747377\pi$
$911$	−3.20052e10	−1.40251	−0.701255	+	0.712910i	$0.747377\pi$
$912$	1.09992e10	0.480154
$913$	−1.03327e10	−0.449331
$914$	−4.96508e10	−2.15087
$915$	3.50588e9	0.151294
$916$	−1.44040e10	−0.619226
$917$	3.88462e10	1.66363
$918$	−3.86597e9	−0.164933
$919$	1.22766e10	0.521763	0.260882	−	0.965371i	$-0.415987\pi$
$919$	1.22766e10	0.521763	0.260882	+	0.965371i	$0.415987\pi$
$920$	−1.72596e9	−0.0730759
$921$	1.54176e10	0.650292
$922$	4.60689e10	1.93575
$923$	1.18275e10	0.495091
$924$	−2.25498e10	−0.940354
$925$	5.52229e9	0.229416
$926$	4.84891e10	2.00681
$927$	−3.76904e9	−0.155400
$928$	−2.98262e10	−1.22512
$929$	−3.42700e10	−1.40236	−0.701180	−	0.712985i	$-0.747343\pi$
$929$	−3.42700e10	−1.40236	−0.701180	+	0.712985i	$0.747343\pi$
$930$	4.92472e10	2.00766
$931$	8.05120e9	0.326992
$932$	−2.12146e10	−0.858379
$933$	−1.57072e10	−0.633161
$934$	−8.69062e9	−0.349009
$935$	−3.02183e10	−1.20901
$936$	−1.76578e8	−0.00703834
$937$	−2.38537e10	−0.947256	−0.473628	−	0.880725i	$-0.657056\pi$
$937$	−2.38537e10	−0.947256	−0.473628	+	0.880725i	$0.657056\pi$
$938$	−1.27244e10	−0.503417
$939$	−2.33835e10	−0.921681
$940$	4.33716e10	1.70317
$941$	3.39564e10	1.32849	0.664245	−	0.747515i	$-0.268753\pi$
$941$	3.39564e10	1.32849	0.664245	+	0.747515i	$0.268753\pi$
$942$	−1.68174e9	−0.0655512
$943$	4.76579e9	0.185073
$944$	5.28879e9	0.204623
$945$	−8.71472e9	−0.335925
$946$	−8.53391e10	−3.27740
$947$	2.97399e10	1.13793	0.568964	−	0.822362i	$-0.307344\pi$
$947$	2.97399e10	1.13793	0.568964	+	0.822362i	$0.307344\pi$
$948$	−1.94939e9	−0.0743138
$949$	7.62433e9	0.289581
$950$	−3.85269e10	−1.45791
$951$	1.96909e10	0.742393
$952$	6.40510e8	0.0240601
$953$	1.94919e10	0.729506	0.364753	−	0.931104i	$-0.381153\pi$
$953$	1.94919e10	0.729506	0.364753	+	0.931104i	$0.381153\pi$
$954$	−2.40794e9	−0.0897897
$955$	−2.06493e10	−0.767172
$956$	2.87317e10	1.06355
$957$	1.82421e10	0.672794
$958$	3.76095e10	1.38203
$959$	3.58632e10	1.31306
$960$	2.45935e10	0.897163
$961$	4.71337e10	1.71317
$962$	−4.66196e9	−0.168832
$963$	−7.93821e9	−0.286438
$964$	−8.47152e9	−0.304573
$965$	−4.83151e10	−1.73076
$966$	3.92562e10	1.40116
$967$	3.11971e10	1.10949	0.554743	−	0.832022i	$-0.312817\pi$
$967$	3.11971e10	1.10949	0.554743	+	0.832022i	$0.312817\pi$
$968$	−7.94352e8	−0.0281481
$969$	8.39766e9	0.296500
$970$	1.03430e11	3.63869
$971$	9.42674e9	0.330441	0.165221	−	0.986257i	$-0.447166\pi$
$971$	9.42674e9	0.330441	0.165221	+	0.986257i	$0.447166\pi$
$972$	−1.88050e9	−0.0656811
$973$	6.97770e9	0.242838
$974$	−4.05740e10	−1.40699
$975$	−1.24913e10	−0.431608
$976$	5.00369e9	0.172273
$977$	−2.74415e10	−0.941407	−0.470703	−	0.882292i	$-0.656000\pi$
$977$	−2.74415e10	−0.941407	−0.470703	+	0.882292i	$0.656000\pi$
$978$	−4.09087e10	−1.39839
$979$	4.65395e10	1.58519
$980$	1.71715e10	0.582796
$981$	−1.70222e10	−0.575671
$982$	−3.88306e10	−1.30853
$983$	−2.40805e10	−0.808590	−0.404295	−	0.914629i	$-0.632483\pi$
$983$	−2.40805e10	−0.808590	−0.404295	+	0.914629i	$0.632483\pi$
$984$	7.47663e7	0.00250163
$985$	1.93822e10	0.646212
$986$	−2.22278e10	−0.738459
$987$	−2.29955e10	−0.761259
$988$	1.64541e10	0.542782
$989$	7.51579e10	2.47052
$990$	−2.90551e10	−0.951697
$991$	−4.29758e10	−1.40271	−0.701353	−	0.712815i	$-0.747420\pi$
$991$	−4.29758e10	−1.40271	−0.701353	+	0.712815i	$0.747420\pi$
$992$	7.20067e10	2.34197
$993$	2.02748e10	0.657103
$994$	−4.12510e10	−1.33224
$995$	−6.54623e10	−2.10674
$996$	6.12421e9	0.196401
$997$	−2.12859e10	−0.680235	−0.340118	−	0.940383i	$-0.610467\pi$
$997$	−2.12859e10	−0.680235	−0.340118	+	0.940383i	$0.610467\pi$
$998$	−2.62599e10	−0.836250
$999$	−1.15735e9	−0.0367271

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.8.a.c.1.9	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.8.a.c.1.9	✓	48	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	471.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0952 q^{2} -27.0000 q^{3} +131.055 q^{4} +414.780 q^{5} +434.570 q^{6} +1067.44 q^{7} -49.1712 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-16.0952 q^{2} -27.0000 q^{3} +131.055 q^{4} +414.780 q^{5} +434.570 q^{6} +1067.44 q^{7} -49.1712 q^{8} +729.000 q^{9} -6675.96 q^{10} +5970.09 q^{11} -3538.49 q^{12} +4926.04 q^{13} -17180.7 q^{14} -11199.0 q^{15} -15983.6 q^{16} -12203.1 q^{17} -11733.4 q^{18} +25487.3 q^{19} +54359.0 q^{20} -28820.9 q^{21} -96089.8 q^{22} +84625.9 q^{23} +1327.62 q^{24} +93917.1 q^{25} -79285.5 q^{26} -19683.0 q^{27} +139894. q^{28} -113169. q^{29} +180251. q^{30} +273215. q^{31} +263553. q^{32} -161193. q^{33} +196411. q^{34} +442753. q^{35} +95539.1 q^{36} +58799.6 q^{37} -410223. q^{38} -133003. q^{39} -20395.2 q^{40} +56316.0 q^{41} +463879. q^{42} +888119. q^{43} +782411. q^{44} +302374. q^{45} -1.36207e6 q^{46} +797873. q^{47} +431558. q^{48} +315891. q^{49} -1.51161e6 q^{50} +329484. q^{51} +645582. q^{52} +205221. q^{53} +316802. q^{54} +2.47627e6 q^{55} -52487.4 q^{56} -688157. q^{57} +1.82148e6 q^{58} -330888. q^{59} -1.46769e6 q^{60} -313051. q^{61} -4.39744e6 q^{62} +778166. q^{63} -2.19604e6 q^{64} +2.04322e6 q^{65} +2.59442e6 q^{66} +740624. q^{67} -1.59928e6 q^{68} -2.28490e6 q^{69} -7.12620e6 q^{70} +2.40101e6 q^{71} -35845.8 q^{72} +1.54776e6 q^{73} -946391. q^{74} -2.53576e6 q^{75} +3.34024e6 q^{76} +6.37273e6 q^{77} +2.14071e6 q^{78} +550911. q^{79} -6.62968e6 q^{80} +531441. q^{81} -906416. q^{82} -1.73074e6 q^{83} -3.77713e6 q^{84} -5.06160e6 q^{85} -1.42944e7 q^{86} +3.05557e6 q^{87} -293556. q^{88} +7.79544e6 q^{89} -4.86677e6 q^{90} +5.25826e6 q^{91} +1.10907e7 q^{92} -7.37680e6 q^{93} -1.28419e7 q^{94} +1.05716e7 q^{95} -7.11594e6 q^{96} -1.54929e7 q^{97} -5.08432e6 q^{98} +4.35220e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 1296 q^{3} + 3214 q^{4} + 428 q^{5} - 54 q^{6} - 680 q^{7} + 2355 q^{8} + 34992 q^{9}+O(q^{10}) \) 48 * q + 2 * q^2 - 1296 * q^3 + 3214 * q^4 + 428 * q^5 - 54 * q^6 - 680 * q^7 + 2355 * q^8 + 34992 * q^9	\( 48 q + 2 q^{2} - 1296 q^{3} + 3214 q^{4} + 428 q^{5} - 54 q^{6} - 680 q^{7} + 2355 q^{8} + 34992 q^{9} + 6185 q^{10} + 11989 q^{11} - 86778 q^{12} - 2393 q^{13} + 18201 q^{14} - 11556 q^{15} + 208150 q^{16} + 62538 q^{17} + 1458 q^{18} - 39882 q^{19} + 113423 q^{20} + 18360 q^{21} - 93716 q^{22} + 195618 q^{23} - 63585 q^{24} + 886490 q^{25} + 294399 q^{26} - 944784 q^{27} - 60819 q^{28} + 421501 q^{29} - 166995 q^{30} + 392689 q^{31} - 341578 q^{32} - 323703 q^{33} + 50837 q^{34} + 697874 q^{35} + 2343006 q^{36} - 410396 q^{37} + 677216 q^{38} + 64611 q^{39} + 3232376 q^{40} + 3832958 q^{41} - 491427 q^{42} - 1751932 q^{43} + 4888297 q^{44} + 312012 q^{45} + 1163150 q^{46} + 106461 q^{47} - 5620050 q^{48} + 8202048 q^{49} - 2159111 q^{50} - 1688526 q^{51} - 3605030 q^{52} + 1755534 q^{53} - 39366 q^{54} - 1220729 q^{55} - 4430622 q^{56} + 1076814 q^{57} - 10000202 q^{58} - 2037752 q^{59} - 3062421 q^{60} + 1274098 q^{61} + 97748 q^{62} - 495720 q^{63} + 15135201 q^{64} + 6139645 q^{65} + 2530332 q^{66} - 7751257 q^{67} + 1700631 q^{68} - 5281686 q^{69} - 20935703 q^{70} - 12592217 q^{71} + 1716795 q^{72} + 12508355 q^{73} - 14999956 q^{74} - 23935230 q^{75} - 23946874 q^{76} + 1874177 q^{77} - 7948773 q^{78} - 5103480 q^{79} + 3128449 q^{80} + 25509168 q^{81} + 11622426 q^{82} + 3040643 q^{83} + 1642113 q^{84} - 13756076 q^{85} + 964635 q^{86} - 11380527 q^{87} - 29653500 q^{88} + 28462995 q^{89} + 4508865 q^{90} + 3016621 q^{91} + 22938254 q^{92} - 10602603 q^{93} - 10070348 q^{94} - 2579984 q^{95} + 9222606 q^{96} + 16208760 q^{97} + 6323227 q^{98} + 8739981 q^{99}+O(q^{100}) \) 48 * q + 2 * q^2 - 1296 * q^3 + 3214 * q^4 + 428 * q^5 - 54 * q^6 - 680 * q^7 + 2355 * q^8 + 34992 * q^9 + 6185 * q^10 + 11989 * q^11 - 86778 * q^12 - 2393 * q^13 + 18201 * q^14 - 11556 * q^15 + 208150 * q^16 + 62538 * q^17 + 1458 * q^18 - 39882 * q^19 + 113423 * q^20 + 18360 * q^21 - 93716 * q^22 + 195618 * q^23 - 63585 * q^24 + 886490 * q^25 + 294399 * q^26 - 944784 * q^27 - 60819 * q^28 + 421501 * q^29 - 166995 * q^30 + 392689 * q^31 - 341578 * q^32 - 323703 * q^33 + 50837 * q^34 + 697874 * q^35 + 2343006 * q^36 - 410396 * q^37 + 677216 * q^38 + 64611 * q^39 + 3232376 * q^40 + 3832958 * q^41 - 491427 * q^42 - 1751932 * q^43 + 4888297 * q^44 + 312012 * q^45 + 1163150 * q^46 + 106461 * q^47 - 5620050 * q^48 + 8202048 * q^49 - 2159111 * q^50 - 1688526 * q^51 - 3605030 * q^52 + 1755534 * q^53 - 39366 * q^54 - 1220729 * q^55 - 4430622 * q^56 + 1076814 * q^57 - 10000202 * q^58 - 2037752 * q^59 - 3062421 * q^60 + 1274098 * q^61 + 97748 * q^62 - 495720 * q^63 + 15135201 * q^64 + 6139645 * q^65 + 2530332 * q^66 - 7751257 * q^67 + 1700631 * q^68 - 5281686 * q^69 - 20935703 * q^70 - 12592217 * q^71 + 1716795 * q^72 + 12508355 * q^73 - 14999956 * q^74 - 23935230 * q^75 - 23946874 * q^76 + 1874177 * q^77 - 7948773 * q^78 - 5103480 * q^79 + 3128449 * q^80 + 25509168 * q^81 + 11622426 * q^82 + 3040643 * q^83 + 1642113 * q^84 - 13756076 * q^85 + 964635 * q^86 - 11380527 * q^87 - 29653500 * q^88 + 28462995 * q^89 + 4508865 * q^90 + 3016621 * q^91 + 22938254 * q^92 - 10602603 * q^93 - 10070348 * q^94 - 2579984 * q^95 + 9222606 * q^96 + 16208760 * q^97 + 6323227 * q^98 + 8739981 * q^99

Introduction

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