LMFDB - Embedded newform 5.16.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,16,Mod(1,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	5.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:	$7.13467525500$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 1972x + 21070 $ x^3 - x^2 - 1972*x + 21070
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$38.1900$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-125.613 q^{2} +4146.67 q^{3} -16989.4 q^{4} -78125.0 q^{5} -520875. q^{6} +4.19779e6 q^{7} +6.25017e6 q^{8} +2.84597e6 q^{9} +O(q^{10})$	\(q-125.613 q^{2} +4146.67 q^{3} -16989.4 q^{4} -78125.0 q^{5} -520875. q^{6} +4.19779e6 q^{7} +6.25017e6 q^{8} +2.84597e6 q^{9} +9.81350e6 q^{10} +5.50890e7 q^{11} -7.04495e7 q^{12} +3.01999e8 q^{13} -5.27296e8 q^{14} -3.23959e8 q^{15} -2.28392e8 q^{16} -2.80735e8 q^{17} -3.57490e8 q^{18} -4.05216e9 q^{19} +1.32730e9 q^{20} +1.74068e10 q^{21} -6.91988e9 q^{22} +4.20462e9 q^{23} +2.59174e10 q^{24} +6.10352e9 q^{25} -3.79349e10 q^{26} -4.76989e10 q^{27} -7.13180e10 q^{28} +1.40692e9 q^{29} +4.06934e10 q^{30} +1.19322e11 q^{31} -1.76117e11 q^{32} +2.28436e11 q^{33} +3.52640e10 q^{34} -3.27952e11 q^{35} -4.83513e10 q^{36} +3.56966e11 q^{37} +5.09003e11 q^{38} +1.25229e12 q^{39} -4.88295e11 q^{40} -5.16564e11 q^{41} -2.18652e12 q^{42} +5.03673e11 q^{43} -9.35930e11 q^{44} -2.22341e11 q^{45} -5.28155e11 q^{46} -4.20204e12 q^{47} -9.47067e11 q^{48} +1.28739e13 q^{49} -7.66680e11 q^{50} -1.16412e12 q^{51} -5.13078e12 q^{52} +6.08126e12 q^{53} +5.99159e12 q^{54} -4.30383e12 q^{55} +2.62369e13 q^{56} -1.68030e13 q^{57} -1.76728e11 q^{58} -3.64636e13 q^{59} +5.50387e12 q^{60} -1.45163e13 q^{61} -1.49884e13 q^{62} +1.19468e13 q^{63} +2.96065e13 q^{64} -2.35936e13 q^{65} -2.86945e13 q^{66} +6.54964e13 q^{67} +4.76953e12 q^{68} +1.74352e13 q^{69} +4.11950e13 q^{70} -2.67606e13 q^{71} +1.77878e13 q^{72} -5.52031e13 q^{73} -4.48396e13 q^{74} +2.53093e13 q^{75} +6.88439e13 q^{76} +2.31252e14 q^{77} -1.57303e14 q^{78} -6.24509e13 q^{79} +1.78431e13 q^{80} -2.38628e14 q^{81} +6.48871e13 q^{82} -5.20704e13 q^{83} -2.95732e14 q^{84} +2.19325e13 q^{85} -6.32678e13 q^{86} +5.83405e12 q^{87} +3.44316e14 q^{88} -5.44067e14 q^{89} +2.79289e13 q^{90} +1.26773e15 q^{91} -7.14341e13 q^{92} +4.94790e14 q^{93} +5.27830e14 q^{94} +3.16575e14 q^{95} -7.30297e14 q^{96} -1.36596e14 q^{97} -1.61712e15 q^{98} +1.56782e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 4 q^{2} + 3518 q^{3} + 20384 q^{4} - 234375 q^{5} + 2075176 q^{6} - 905206 q^{7} + 16674720 q^{8} + 47911531 q^{9}+O(q^{10}) $ 3 * q + 4 * q^2 + 3518 * q^3 + 20384 * q^4 - 234375 * q^5 + 2075176 * q^6 - 905206 * q^7 + 16674720 * q^8 + 47911531 * q^9	\( 3 q + 4 q^{2} + 3518 q^{3} + 20384 q^{4} - 234375 q^{5} + 2075176 q^{6} - 905206 q^{7} + 16674720 q^{8} + 47911531 q^{9} - 312500 q^{10} + 122875456 q^{11} + 259564864 q^{12} - 90911522 q^{13} - 1195428552 q^{14} - 274843750 q^{15} - 1314428032 q^{16} - 3868973426 q^{17} + 905373668 q^{18} + 3670884220 q^{19} - 1592500000 q^{20} + 9596808996 q^{21} + 20569860608 q^{22} + 26698058238 q^{23} + 7659524160 q^{24} + 18310546875 q^{25} - 27015047384 q^{26} - 99092472220 q^{27} - 210410855488 q^{28} + 145544932730 q^{29} - 162123125000 q^{30} - 25873382644 q^{31} - 531675479296 q^{32} + 851520900736 q^{33} + 208184081768 q^{34} + 70719218750 q^{35} + 578919966368 q^{36} + 419480249934 q^{37} + 205247686480 q^{38} + 2390867460332 q^{39} - 1302712500000 q^{40} + 274005770306 q^{41} - 9314366945232 q^{42} + 2350065869158 q^{43} + 3324410490368 q^{44} - 3743088359375 q^{45} - 2445701814744 q^{46} - 8891070209486 q^{47} + 968269957888 q^{48} + 17603715811879 q^{49} + 24414062500 q^{50} + 11276036492236 q^{51} - 7757281361856 q^{52} + 8749242811318 q^{53} + 24761205955120 q^{54} - 9599645000000 q^{55} + 1555780658880 q^{56} - 41669191785640 q^{57} + 53844260003320 q^{58} - 14173516437140 q^{59} - 20278505000000 q^{60} - 38066837721794 q^{61} - 53610636798192 q^{62} - 97119517183302 q^{63} + 12081926129664 q^{64} + 7102462656250 q^{65} + 93794721354752 q^{66} + 144391638065474 q^{67} - 9729892224448 q^{68} - 83804251999188 q^{69} + 93392855625000 q^{70} - 126512337318844 q^{71} + 262100048315040 q^{72} + 199804772078038 q^{73} - 103551095018392 q^{74} + 21472167968750 q^{75} + 108919950456960 q^{76} - 24166822365312 q^{77} - 612963962524784 q^{78} - 73797562093720 q^{79} + 102689690000000 q^{80} - 252524358845777 q^{81} + 452714654584408 q^{82} - 219109046205402 q^{83} - 12\!\cdots\!12 q^{84}+ \cdots + 12\!\cdots\!12 q^{99}+O(q^{100}) \) 3 * q + 4 * q^2 + 3518 * q^3 + 20384 * q^4 - 234375 * q^5 + 2075176 * q^6 - 905206 * q^7 + 16674720 * q^8 + 47911531 * q^9 - 312500 * q^10 + 122875456 * q^11 + 259564864 * q^12 - 90911522 * q^13 - 1195428552 * q^14 - 274843750 * q^15 - 1314428032 * q^16 - 3868973426 * q^17 + 905373668 * q^18 + 3670884220 * q^19 - 1592500000 * q^20 + 9596808996 * q^21 + 20569860608 * q^22 + 26698058238 * q^23 + 7659524160 * q^24 + 18310546875 * q^25 - 27015047384 * q^26 - 99092472220 * q^27 - 210410855488 * q^28 + 145544932730 * q^29 - 162123125000 * q^30 - 25873382644 * q^31 - 531675479296 * q^32 + 851520900736 * q^33 + 208184081768 * q^34 + 70719218750 * q^35 + 578919966368 * q^36 + 419480249934 * q^37 + 205247686480 * q^38 + 2390867460332 * q^39 - 1302712500000 * q^40 + 274005770306 * q^41 - 9314366945232 * q^42 + 2350065869158 * q^43 + 3324410490368 * q^44 - 3743088359375 * q^45 - 2445701814744 * q^46 - 8891070209486 * q^47 + 968269957888 * q^48 + 17603715811879 * q^49 + 24414062500 * q^50 + 11276036492236 * q^51 - 7757281361856 * q^52 + 8749242811318 * q^53 + 24761205955120 * q^54 - 9599645000000 * q^55 + 1555780658880 * q^56 - 41669191785640 * q^57 + 53844260003320 * q^58 - 14173516437140 * q^59 - 20278505000000 * q^60 - 38066837721794 * q^61 - 53610636798192 * q^62 - 97119517183302 * q^63 + 12081926129664 * q^64 + 7102462656250 * q^65 + 93794721354752 * q^66 + 144391638065474 * q^67 - 9729892224448 * q^68 - 83804251999188 * q^69 + 93392855625000 * q^70 - 126512337318844 * q^71 + 262100048315040 * q^72 + 199804772078038 * q^73 - 103551095018392 * q^74 + 21472167968750 * q^75 + 108919950456960 * q^76 - 24166822365312 * q^77 - 612963962524784 * q^78 - 73797562093720 * q^79 + 102689690000000 * q^80 - 252524358845777 * q^81 + 452714654584408 * q^82 - 219109046205402 * q^83 - 1299933721590912 * q^84 + 302263548906250 * q^85 - 630643429487864 * q^86 + 1207083364260740 * q^87 + 566411960125440 * q^88 - 360765737744610 * q^89 - 70732317812500 * q^90 + 2140337559198436 * q^91 - 88583572138176 * q^92 - 274593012441864 * q^93 + 1632141806127128 * q^94 - 286787829687500 * q^95 - 1457456297665024 * q^96 - 509209931654586 * q^97 + 411284837393972 * q^98 + 1279088372251712 * 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 $

$2$	−125.613	−0.693919	−0.346960	−	0.937880i	$-0.612786\pi$
$2$	−125.613	−0.693919	−0.346960	+	0.937880i	$0.612786\pi$
$3$	4146.67	1.09469	0.547344	−	0.836908i	$-0.315639\pi$
$3$	4146.67	1.09469	0.547344	+	0.836908i	$0.315639\pi$
$4$	−16989.4	−0.518476
$5$	−78125.0	−0.447214
$5$	−78125.0	−0.447214
$6$	−520875.	−0.759625
$7$	4.19779e6	1.92657	0.963286	−	0.268478i	$-0.0865206\pi$
$7$	4.19779e6	1.92657	0.963286	+	0.268478i	$0.0865206\pi$
$8$	6.25017e6	1.05370
$9$	2.84597e6	0.198340
$10$	9.81350e6	0.310330
$11$	5.50890e7	0.852353	0.426177	−	0.904640i	$-0.359860\pi$
$11$	5.50890e7	0.852353	0.426177	+	0.904640i	$0.359860\pi$
$12$	−7.04495e7	−0.567569
$13$	3.01999e8	1.33484	0.667421	−	0.744681i	$-0.267398\pi$
$13$	3.01999e8	1.33484	0.667421	+	0.744681i	$0.267398\pi$
$14$	−5.27296e8	−1.33689
$15$	−3.23959e8	−0.489559
$16$	−2.28392e8	−0.212707
$17$	−2.80735e8	−0.165932	−0.0829660	−	0.996552i	$-0.526439\pi$
$17$	−2.80735e8	−0.165932	−0.0829660	+	0.996552i	$0.526439\pi$
$18$	−3.57490e8	−0.137632
$19$	−4.05216e9	−1.04000	−0.520002	−	0.854165i	$-0.674069\pi$
$19$	−4.05216e9	−1.04000	−0.520002	+	0.854165i	$0.674069\pi$
$20$	1.32730e9	0.231869
$21$	1.74068e10	2.10899
$22$	−6.91988e9	−0.591465
$23$	4.20462e9	0.257495	0.128747	−	0.991677i	$-0.458904\pi$
$23$	4.20462e9	0.257495	0.128747	+	0.991677i	$0.458904\pi$
$24$	2.59174e10	1.15347
$25$	6.10352e9	0.200000
$26$	−3.79349e10	−0.926272
$27$	−4.76989e10	−0.877567
$28$	−7.13180e10	−0.998881
$29$	1.40692e9	0.0151456	0.00757279	−	0.999971i	$-0.497589\pi$
$29$	1.40692e9	0.0151456	0.00757279	+	0.999971i	$0.497589\pi$
$30$	4.06934e10	0.339715
$31$	1.19322e11	0.778949	0.389474	−	0.921037i	$-0.372657\pi$
$31$	1.19322e11	0.778949	0.389474	+	0.921037i	$0.372657\pi$
$32$	−1.76117e11	−0.906098
$33$	2.28436e11	0.933061
$34$	3.52640e10	0.115143
$35$	−3.27952e11	−0.861589
$36$	−4.83513e10	−0.102835
$37$	3.56966e11	0.618179	0.309090	−	0.951033i	$-0.399976\pi$
$37$	3.56966e11	0.618179	0.309090	+	0.951033i	$0.399976\pi$
$38$	5.09003e11	0.721679
$39$	1.25229e12	1.46123
$40$	−4.88295e11	−0.471229
$41$	−5.16564e11	−0.414234	−0.207117	−	0.978316i	$-0.566408\pi$
$41$	−5.16564e11	−0.414234	−0.207117	+	0.978316i	$0.566408\pi$
$42$	−2.18652e12	−1.46347
$43$	5.03673e11	0.282576	0.141288	−	0.989969i	$-0.454876\pi$
$43$	5.03673e11	0.282576	0.141288	+	0.989969i	$0.454876\pi$
$44$	−9.35930e11	−0.441925
$45$	−2.22341e11	−0.0887005
$46$	−5.28155e11	−0.178681
$47$	−4.20204e12	−1.20983	−0.604917	−	0.796288i	$-0.706794\pi$
$47$	−4.20204e12	−1.20983	−0.604917	+	0.796288i	$0.706794\pi$
$48$	−9.47067e11	−0.232847
$49$	1.28739e13	2.71168
$50$	−7.66680e11	−0.138784
$51$	−1.16412e12	−0.181644
$52$	−5.13078e12	−0.692083
$53$	6.08126e12	0.711090	0.355545	−	0.934659i	$-0.384295\pi$
$53$	6.08126e12	0.711090	0.355545	+	0.934659i	$0.384295\pi$
$54$	5.99159e12	0.608960
$55$	−4.30383e12	−0.381184
$56$	2.62369e13	2.03003
$57$	−1.68030e13	−1.13848
$58$	−1.76728e11	−0.0105098
$59$	−3.64636e13	−1.90752	−0.953761	−	0.300565i	$-0.902825\pi$
$59$	−3.64636e13	−1.90752	−0.953761	+	0.300565i	$0.902825\pi$
$60$	5.50387e12	0.253825
$61$	−1.45163e13	−0.591400	−0.295700	−	0.955281i	$-0.595553\pi$
$61$	−1.45163e13	−0.591400	−0.295700	+	0.955281i	$0.595553\pi$
$62$	−1.49884e13	−0.540528
$63$	1.19468e13	0.382117
$64$	2.96065e13	0.841466
$65$	−2.35936e13	−0.596959
$66$	−2.86945e13	−0.647469
$67$	6.54964e13	1.32025	0.660126	−	0.751155i	$-0.270503\pi$
$67$	6.54964e13	1.32025	0.660126	+	0.751155i	$0.270503\pi$
$68$	4.76953e12	0.0860318
$69$	1.74352e13	0.281876
$70$	4.11950e13	0.597873
$71$	−2.67606e13	−0.349187	−0.174593	−	0.984641i	$-0.555861\pi$
$71$	−2.67606e13	−0.349187	−0.174593	+	0.984641i	$0.555861\pi$
$72$	1.77878e13	0.208991
$73$	−5.52031e13	−0.584847	−0.292423	−	0.956289i	$-0.594462\pi$
$73$	−5.52031e13	−0.584847	−0.292423	+	0.956289i	$0.594462\pi$
$74$	−4.48396e13	−0.428967
$75$	2.53093e13	0.218937
$76$	6.88439e13	0.539217
$77$	2.31252e14	1.64212
$78$	−1.57303e14	−1.01398
$79$	−6.24509e13	−0.365878	−0.182939	−	0.983124i	$-0.558561\pi$
$79$	−6.24509e13	−0.365878	−0.182939	+	0.983124i	$0.558561\pi$
$80$	1.78431e13	0.0951254
$81$	−2.38628e14	−1.15900
$82$	6.48871e13	0.287445
$83$	−5.20704e13	−0.210623	−0.105311	−	0.994439i	$-0.533584\pi$
$83$	−5.20704e13	−0.210623	−0.105311	+	0.994439i	$0.533584\pi$
$84$	−2.95732e14	−1.09346
$85$	2.19325e13	0.0742071
$86$	−6.32678e13	−0.196085
$87$	5.83405e12	0.0165797
$88$	3.44316e14	0.898125
$89$	−5.44067e14	−1.30385	−0.651925	−	0.758284i	$-0.726038\pi$
$89$	−5.44067e14	−1.30385	−0.651925	+	0.758284i	$0.726038\pi$
$90$	2.79289e13	0.0615510
$91$	1.26773e15	2.57167
$92$	−7.14341e13	−0.133505
$93$	4.94790e14	0.852706
$94$	5.27830e14	0.839527
$95$	3.16575e14	0.465104
$96$	−7.30297e14	−0.991895
$97$	−1.36596e14	−0.171653	−0.0858264	−	0.996310i	$-0.527353\pi$
$97$	−1.36596e14	−0.171653	−0.0858264	+	0.996310i	$0.527353\pi$
$98$	−1.61712e15	−1.88169
$99$	1.56782e14	0.169056
$100$	−1.03695e14	−0.103695
$101$	−6.70123e14	−0.621934	−0.310967	−	0.950421i	$-0.600653\pi$
$101$	−6.70123e14	−0.621934	−0.310967	+	0.950421i	$0.600653\pi$
$102$	1.46228e14	0.126046
$103$	4.19247e14	0.335885	0.167943	−	0.985797i	$-0.446288\pi$
$103$	4.19247e14	0.335885	0.167943	+	0.985797i	$0.446288\pi$
$104$	1.88754e15	1.40652
$105$	−1.35991e15	−0.943171
$106$	−7.63884e14	−0.493439
$107$	−2.46627e15	−1.48478	−0.742391	−	0.669967i	$-0.766308\pi$
$107$	−2.46627e15	−1.48478	−0.742391	+	0.669967i	$0.766308\pi$
$108$	8.10376e14	0.454997
$109$	3.14733e14	0.164909	0.0824544	−	0.996595i	$-0.473724\pi$
$109$	3.14733e14	0.164909	0.0824544	+	0.996595i	$0.473724\pi$
$110$	5.40616e14	0.264511
$111$	1.48022e15	0.676713
$112$	−9.58742e14	−0.409795
$113$	8.32852e14	0.333027	0.166514	−	0.986039i	$-0.446749\pi$
$113$	8.32852e14	0.333027	0.166514	+	0.986039i	$0.446749\pi$
$114$	2.11067e15	0.790012
$115$	−3.28486e14	−0.115155
$116$	−2.39028e13	−0.00785262
$117$	8.59478e14	0.264753
$118$	4.58030e15	1.32367
$119$	−1.17847e15	−0.319680
$120$	−2.02480e15	−0.515848
$121$	−1.14245e15	−0.273494
$122$	1.82343e15	0.410384
$123$	−2.14202e15	−0.453457
$124$	−2.02722e15	−0.403866
$125$	−4.76837e14	−0.0894427
$126$	−1.50067e15	−0.265158
$127$	−6.94245e15	−1.15607	−0.578036	−	0.816011i	$-0.696181\pi$
$127$	−6.94245e15	−1.15607	−0.578036	+	0.816011i	$0.696181\pi$
$128$	2.05204e15	0.322189
$129$	2.08857e15	0.309333
$130$	2.96366e15	0.414242
$131$	1.22378e16	1.61498	0.807492	−	0.589878i	$-0.200824\pi$
$131$	1.22378e16	1.61498	0.807492	+	0.589878i	$0.200824\pi$
$132$	−3.88099e15	−0.483769
$133$	−1.70101e16	−2.00364
$134$	−8.22719e15	−0.916148
$135$	3.72648e15	0.392460
$136$	−1.75464e15	−0.174843
$137$	1.18593e16	1.11855	0.559275	−	0.828982i	$-0.311079\pi$
$137$	1.18593e16	1.11855	0.559275	+	0.828982i	$0.311079\pi$
$138$	−2.19008e15	−0.195599
$139$	7.62510e15	0.645111	0.322555	−	0.946551i	$-0.395458\pi$
$139$	7.62510e15	0.645111	0.322555	+	0.946551i	$0.395458\pi$
$140$	5.57172e15	0.446713
$141$	−1.74245e16	−1.32439
$142$	3.36147e15	0.242307
$143$	1.66368e16	1.13776
$144$	−6.49997e14	−0.0421884
$145$	−1.09916e14	−0.00677331
$146$	6.93422e15	0.405836
$147$	5.33837e16	2.96844
$148$	−6.06465e15	−0.320511
$149$	−2.87463e16	−1.44439	−0.722197	−	0.691688i	$-0.756867\pi$
$149$	−2.87463e16	−1.44439	−0.722197	+	0.691688i	$0.756867\pi$
$150$	−3.17917e15	−0.151925
$151$	−7.88575e14	−0.0358522	−0.0179261	−	0.999839i	$-0.505706\pi$
$151$	−7.88575e14	−0.0358522	−0.0179261	+	0.999839i	$0.505706\pi$
$152$	−2.53267e16	−1.09585
$153$	−7.98964e14	−0.0329110
$154$	−2.90482e16	−1.13950
$155$	−9.32206e15	−0.348357
$156$	−2.12757e16	−0.757615
$157$	−2.49202e16	−0.845872	−0.422936	−	0.906160i	$-0.639000\pi$
$157$	−2.49202e16	−0.845872	−0.422936	+	0.906160i	$0.639000\pi$
$158$	7.84464e15	0.253890
$159$	2.52170e16	0.778421
$160$	1.37591e16	0.405220
$161$	1.76501e16	0.496082
$162$	2.99748e16	0.804254
$163$	−6.09828e16	−1.56243	−0.781214	−	0.624263i	$-0.785399\pi$
$163$	−6.09828e16	−1.56243	−0.781214	+	0.624263i	$0.785399\pi$
$164$	8.77613e15	0.214770
$165$	−1.78466e16	−0.417277
$166$	6.54071e15	0.146155
$167$	2.22250e16	0.474753	0.237377	−	0.971418i	$-0.423712\pi$
$167$	2.22250e16	0.474753	0.237377	+	0.971418i	$0.423712\pi$
$168$	1.08796e17	2.22225
$169$	4.00172e16	0.781802
$170$	−2.75500e15	−0.0514937
$171$	−1.15323e16	−0.206275
$172$	−8.55712e15	−0.146509
$173$	−8.38350e16	−1.37429	−0.687147	−	0.726519i	$-0.741137\pi$
$173$	−8.38350e16	−1.37429	−0.687147	+	0.726519i	$0.741137\pi$
$174$	−7.32832e14	−0.0115050
$175$	2.56213e16	0.385314
$176$	−1.25819e16	−0.181301
$177$	−1.51203e17	−2.08814
$178$	6.83418e16	0.904766
$179$	1.29982e17	1.65000	0.825002	−	0.565131i	$-0.191174\pi$
$179$	1.29982e17	1.65000	0.825002	+	0.565131i	$0.191174\pi$
$180$	3.77745e15	0.0459891
$181$	1.36711e17	1.59667	0.798333	−	0.602216i	$-0.205716\pi$
$181$	1.36711e17	1.59667	0.798333	+	0.602216i	$0.205716\pi$
$182$	−1.59243e17	−1.78453
$183$	−6.01942e16	−0.647399
$184$	2.62796e16	0.271322
$185$	−2.78880e16	−0.276458
$186$	−6.21520e16	−0.591709
$187$	−1.54654e16	−0.141433
$188$	7.13902e16	0.627270
$189$	−2.00230e17	−1.69070
$190$	−3.97659e16	−0.322744
$191$	3.03201e16	0.236581	0.118291	−	0.992979i	$-0.462259\pi$
$191$	3.03201e16	0.236581	0.118291	+	0.992979i	$0.462259\pi$
$192$	1.22768e17	0.921142
$193$	8.54661e16	0.616757	0.308378	−	0.951264i	$-0.400214\pi$
$193$	8.54661e16	0.616757	0.308378	+	0.951264i	$0.400214\pi$
$194$	1.71583e16	0.119113
$195$	−9.78350e16	−0.653484
$196$	−2.18719e17	−1.40594
$197$	1.12516e17	0.696172	0.348086	−	0.937463i	$-0.386832\pi$
$197$	1.12516e17	0.696172	0.348086	+	0.937463i	$0.386832\pi$
$198$	−1.96938e16	−0.117311
$199$	1.43182e17	0.821279	0.410639	−	0.911798i	$-0.365306\pi$
$199$	1.43182e17	0.821279	0.410639	+	0.911798i	$0.365306\pi$
$200$	3.81480e16	0.210740
$201$	2.71592e17	1.44526
$202$	8.41760e16	0.431572
$203$	5.90597e15	0.0291790
$204$	1.97777e16	0.0941779
$205$	4.03566e16	0.185251
$206$	−5.26629e16	−0.233077
$207$	1.19662e16	0.0510716
$208$	−6.89741e16	−0.283930
$209$	−2.23230e17	−0.886451
$210$	1.70822e17	0.654484
$211$	−1.49191e17	−0.551600	−0.275800	−	0.961215i	$-0.588943\pi$
$211$	−1.49191e17	−0.551600	−0.275800	+	0.961215i	$0.588943\pi$
$212$	−1.03317e17	−0.368683
$213$	−1.10967e17	−0.382250
$214$	3.09795e17	1.03032
$215$	−3.93495e16	−0.126372
$216$	−2.98126e17	−0.924692
$217$	5.00890e17	1.50070
$218$	−3.95345e16	−0.114433
$219$	−2.28909e17	−0.640224
$220$	7.31195e16	0.197635
$221$	−8.47817e16	−0.221493
$222$	−1.85935e17	−0.469584
$223$	−6.17427e17	−1.50764	−0.753822	−	0.657078i	$-0.771792\pi$
$223$	−6.17427e17	−1.50764	−0.753822	+	0.657078i	$0.771792\pi$
$224$	−7.39300e17	−1.74566
$225$	1.73704e16	0.0396681
$226$	−1.04617e17	−0.231094
$227$	5.03881e17	1.07680	0.538399	−	0.842690i	$-0.319029\pi$
$227$	5.03881e17	1.07680	0.538399	+	0.842690i	$0.319029\pi$
$228$	2.85473e17	0.590274
$229$	1.04953e17	0.210005	0.105002	−	0.994472i	$-0.466515\pi$
$229$	1.04953e17	0.210005	0.105002	+	0.994472i	$0.466515\pi$
$230$	4.12621e16	0.0799084
$231$	9.58926e17	1.79761
$232$	8.79352e15	0.0159589
$233$	3.35151e17	0.588939	0.294470	−	0.955661i	$-0.404857\pi$
$233$	3.35151e17	0.588939	0.294470	+	0.955661i	$0.404857\pi$
$234$	−1.07962e17	−0.183717
$235$	3.28284e17	0.541054
$236$	6.19496e17	0.989004
$237$	−2.58963e17	−0.400522
$238$	1.48031e17	0.221832
$239$	−1.87821e17	−0.272747	−0.136374	−	0.990657i	$-0.543545\pi$
$239$	−1.87821e17	−0.272747	−0.136374	+	0.990657i	$0.543545\pi$
$240$	7.39896e16	0.104133
$241$	−1.85398e17	−0.252917	−0.126459	−	0.991972i	$-0.540361\pi$
$241$	−1.85398e17	−0.252917	−0.126459	+	0.991972i	$0.540361\pi$
$242$	1.43506e17	0.189782
$243$	−3.05085e17	−0.391178
$244$	2.46623e17	0.306627
$245$	−1.00577e18	−1.21270
$246$	2.69065e17	0.314662
$247$	−1.22375e18	−1.38824
$248$	7.45785e17	0.820778
$249$	−2.15919e17	−0.230566
$250$	5.98969e16	0.0620660
$251$	−1.77717e18	−1.78721	−0.893607	−	0.448851i	$-0.851834\pi$
$251$	−1.77717e18	−1.78721	−0.893607	+	0.448851i	$0.851834\pi$
$252$	−2.02969e17	−0.198118
$253$	2.31628e17	0.219476
$254$	8.72060e17	0.802220
$255$	9.09466e16	0.0812335
$256$	−1.22791e18	−1.06504
$257$	1.63048e18	1.37346	0.686731	−	0.726911i	$-0.259045\pi$
$257$	1.63048e18	1.37346	0.686731	+	0.726911i	$0.259045\pi$
$258$	−2.62351e17	−0.214652
$259$	1.49847e18	1.19097
$260$	4.00842e17	0.309509
$261$	4.00406e15	0.00300398
$262$	−1.53722e18	−1.12067
$263$	−1.43533e18	−1.01691	−0.508456	−	0.861088i	$-0.669783\pi$
$263$	−1.43533e18	−1.01691	−0.508456	+	0.861088i	$0.669783\pi$
$264$	1.42776e18	0.983166
$265$	−4.75098e17	−0.318009
$266$	2.13669e18	1.39037
$267$	−2.25607e18	−1.42731
$268$	−1.11275e18	−0.684519
$269$	8.66872e17	0.518577	0.259288	−	0.965800i	$-0.416512\pi$
$269$	8.66872e17	0.518577	0.259288	+	0.965800i	$0.416512\pi$
$270$	−4.68093e17	−0.272335
$271$	3.59143e17	0.203235	0.101617	−	0.994824i	$-0.467598\pi$
$271$	3.59143e17	0.203235	0.101617	+	0.994824i	$0.467598\pi$
$272$	6.41178e16	0.0352949
$273$	5.25684e18	2.81517
$274$	−1.48968e18	−0.776184
$275$	3.36237e17	0.170471
$276$	−2.96214e17	−0.146146
$277$	5.91709e17	0.284125	0.142063	−	0.989858i	$-0.454627\pi$
$277$	5.91709e17	0.284125	0.142063	+	0.989858i	$0.454627\pi$
$278$	−9.57810e17	−0.447655
$279$	3.39588e17	0.154497
$280$	−2.04976e18	−0.907856
$281$	1.62393e18	0.700277	0.350138	−	0.936698i	$-0.386135\pi$
$281$	1.62393e18	0.700277	0.350138	+	0.936698i	$0.386135\pi$
$282$	2.18874e18	0.919020
$283$	−3.93791e17	−0.161015	−0.0805077	−	0.996754i	$-0.525654\pi$
$283$	−3.93791e17	−0.161015	−0.0805077	+	0.996754i	$0.525654\pi$
$284$	4.54646e17	0.181045
$285$	1.31273e18	0.509143
$286$	−2.08980e18	−0.789512
$287$	−2.16843e18	−0.798051
$288$	−5.01222e17	−0.179716
$289$	−2.78361e18	−0.972467
$290$	1.38069e16	0.00470013
$291$	−5.66420e17	−0.187906
$292$	9.37869e17	0.303229
$293$	−2.71560e18	−0.855774	−0.427887	−	0.903832i	$-0.640742\pi$
$293$	−2.71560e18	−0.855774	−0.427887	+	0.903832i	$0.640742\pi$
$294$	−6.70567e18	−2.05986
$295$	2.84872e18	0.853070
$296$	2.23110e18	0.651375
$297$	−2.62768e18	−0.747997
$298$	3.61091e18	1.00229
$299$	1.26979e18	0.343715
$300$	−4.29990e17	−0.113514
$301$	2.11431e18	0.544403
$302$	9.90552e16	0.0248785
$303$	−2.77878e18	−0.680823
$304$	9.25482e17	0.221216
$305$	1.13408e18	0.264482
$306$	1.00360e17	0.0228376
$307$	7.69847e18	1.70949	0.854745	−	0.519048i	$-0.173713\pi$
$307$	7.69847e18	1.70949	0.854745	+	0.519048i	$0.173713\pi$
$308$	−3.92884e18	−0.851400
$309$	1.73848e18	0.367690
$310$	1.17097e18	0.241731
$311$	−5.38963e18	−1.08607	−0.543033	−	0.839711i	$-0.682724\pi$
$311$	−5.38963e18	−1.08607	−0.543033	+	0.839711i	$0.682724\pi$
$312$	7.82702e18	1.53970
$313$	2.19015e18	0.420622	0.210311	−	0.977635i	$-0.432552\pi$
$313$	2.19015e18	0.420622	0.210311	+	0.977635i	$0.432552\pi$
$314$	3.13030e18	0.586967
$315$	−9.33342e17	−0.170888
$316$	1.06101e18	0.189699
$317$	1.25112e18	0.218452	0.109226	−	0.994017i	$-0.465163\pi$
$317$	1.25112e18	0.218452	0.109226	+	0.994017i	$0.465163\pi$
$318$	−3.16757e18	−0.540161
$319$	7.75061e16	0.0129094
$320$	−2.31300e18	−0.376315
$321$	−1.02268e19	−1.62537
$322$	−2.21708e18	−0.344241
$323$	1.13759e18	0.172570
$324$	4.05415e18	0.600914
$325$	1.84325e18	0.266968
$326$	7.66022e18	1.08420
$327$	1.30509e18	0.180524
$328$	−3.22862e18	−0.436478
$329$	−1.76393e19	−2.33083
$330$	2.24176e18	0.289557
$331$	−5.36688e16	−0.00677661	−0.00338830	−	0.999994i	$-0.501079\pi$
$331$	−5.36688e16	−0.00677661	−0.00338830	+	0.999994i	$0.501079\pi$
$332$	8.84646e17	0.109203
$333$	1.01592e18	0.122610
$334$	−2.79174e18	−0.329441
$335$	−5.11691e18	−0.590434
$336$	−3.97559e18	−0.448597
$337$	−1.22272e19	−1.34928	−0.674639	−	0.738148i	$-0.735701\pi$
$337$	−1.22272e19	−1.34928	−0.674639	+	0.738148i	$0.735701\pi$
$338$	−5.02668e18	−0.542508
$339$	3.45356e18	0.364561
$340$	−3.72620e17	−0.0384746
$341$	6.57335e18	0.663940
$342$	1.44861e18	0.143138
$343$	3.41125e19	3.29767
$344$	3.14804e18	0.297751
$345$	−1.36212e18	−0.126059
$346$	1.05308e19	0.953649
$347$	−3.31677e18	−0.293930	−0.146965	−	0.989142i	$-0.546950\pi$
$347$	−3.31677e18	−0.293930	−0.146965	+	0.989142i	$0.546950\pi$
$348$	−9.91172e16	−0.00859616
$349$	7.89861e18	0.670440	0.335220	−	0.942140i	$-0.391189\pi$
$349$	7.89861e18	0.670440	0.335220	+	0.942140i	$0.391189\pi$
$350$	−3.21836e18	−0.267377
$351$	−1.44050e19	−1.17141
$352$	−9.70209e18	−0.772316
$353$	−9.10780e18	−0.709746	−0.354873	−	0.934914i	$-0.615476\pi$
$353$	−9.10780e18	−0.709746	−0.354873	+	0.934914i	$0.615476\pi$
$354$	1.89930e19	1.44900
$355$	2.09067e18	0.156161
$356$	9.24339e18	0.676015
$357$	−4.88672e18	−0.349950
$358$	−1.63274e19	−1.14497
$359$	2.25275e19	1.54705	0.773527	−	0.633763i	$-0.218491\pi$
$359$	2.25275e19	1.54705	0.773527	+	0.633763i	$0.218491\pi$
$360$	−1.38967e18	−0.0934637
$361$	1.23889e18	0.0816072
$362$	−1.71727e19	−1.10796
$363$	−4.73736e18	−0.299390
$364$	−2.15379e19	−1.33335
$365$	4.31274e18	0.261551
$366$	7.56117e18	0.449242
$367$	3.97552e18	0.231419	0.115709	−	0.993283i	$-0.463086\pi$
$367$	3.97552e18	0.231419	0.115709	+	0.993283i	$0.463086\pi$
$368$	−9.60303e17	−0.0547709
$369$	−1.47013e18	−0.0821593
$370$	3.50309e18	0.191840
$371$	2.55278e19	1.36997
$372$	−8.40620e18	−0.442107
$373$	4.08251e18	0.210432	0.105216	−	0.994449i	$-0.466447\pi$
$373$	4.08251e18	0.210432	0.105216	+	0.994449i	$0.466447\pi$
$374$	1.94266e18	0.0981429
$375$	−1.97729e18	−0.0979118
$376$	−2.62634e19	−1.27480
$377$	4.24889e17	0.0202169
$378$	2.51514e19	1.17321
$379$	−1.30460e19	−0.596601	−0.298300	−	0.954472i	$-0.596420\pi$
$379$	−1.30460e19	−0.596601	−0.298300	+	0.954472i	$0.596420\pi$
$380$	−5.37843e18	−0.241145
$381$	−2.87880e19	−1.26554
$382$	−3.80859e18	−0.164168
$383$	−3.37280e19	−1.42561	−0.712804	−	0.701363i	$-0.752575\pi$
$383$	−3.37280e19	−1.42561	−0.712804	+	0.701363i	$0.752575\pi$
$384$	8.50912e18	0.352696
$385$	−1.80666e19	−0.734378
$386$	−1.07356e19	−0.427979
$387$	1.43344e18	0.0560463
$388$	2.32069e18	0.0889979
$389$	2.63035e19	0.989443	0.494722	−	0.869051i	$-0.335270\pi$
$389$	2.63035e19	0.989443	0.494722	+	0.869051i	$0.335270\pi$
$390$	1.22893e19	0.453465
$391$	−1.18039e18	−0.0427266
$392$	8.04638e19	2.85730
$393$	5.07461e19	1.76790
$394$	−1.41334e19	−0.483087
$395$	4.87898e18	0.163625
$396$	−2.66363e18	−0.0876515
$397$	2.34982e19	0.758763	0.379382	−	0.925240i	$-0.376137\pi$
$397$	2.34982e19	0.758763	0.379382	+	0.925240i	$0.376137\pi$
$398$	−1.79855e19	−0.569901
$399$	−7.05353e19	−2.19336
$400$	−1.39400e18	−0.0425414
$401$	3.78904e19	1.13487	0.567435	−	0.823418i	$-0.307936\pi$
$401$	3.78904e19	1.13487	0.567435	+	0.823418i	$0.307936\pi$
$402$	−3.41155e19	−1.00290
$403$	3.60352e19	1.03977
$404$	1.13850e19	0.322458
$405$	1.86428e19	0.518321
$406$	−7.41866e17	−0.0202479
$407$	1.96649e19	0.526907
$408$	−7.27593e18	−0.191398
$409$	−3.27125e19	−0.844868	−0.422434	−	0.906394i	$-0.638824\pi$
$409$	−3.27125e19	−0.844868	−0.422434	+	0.906394i	$0.638824\pi$
$410$	−5.06931e18	−0.128549
$411$	4.91767e19	1.22446
$412$	−7.12277e18	−0.174149
$413$	−1.53067e20	−3.67498
$414$	−1.50311e18	−0.0354396
$415$	4.06800e18	0.0941934
$416$	−5.31870e19	−1.20950
$417$	3.16188e19	0.706195
$418$	2.80405e19	0.615125
$419$	−1.57334e19	−0.339013	−0.169507	−	0.985529i	$-0.554217\pi$
$419$	−1.57334e19	−0.339013	−0.169507	+	0.985529i	$0.554217\pi$
$420$	2.31041e19	0.489011
$421$	−8.37806e19	−1.74192	−0.870959	−	0.491355i	$-0.836502\pi$
$421$	−8.37806e19	−1.74192	−0.870959	+	0.491355i	$0.836502\pi$
$422$	1.87403e19	0.382766
$423$	−1.19589e19	−0.239959
$424$	3.80089e19	0.749275
$425$	−1.71347e18	−0.0331864
$426$	1.39389e19	0.265251
$427$	−6.09363e19	−1.13938
$428$	4.19005e19	0.769824
$429$	6.89873e19	1.24549
$430$	4.94280e18	0.0876919
$431$	7.92401e19	1.38155	0.690773	−	0.723072i	$-0.257270\pi$
$431$	7.92401e19	1.38155	0.690773	+	0.723072i	$0.257270\pi$
$432$	1.08941e19	0.186664
$433$	−3.05656e19	−0.514723	−0.257361	−	0.966315i	$-0.582853\pi$
$433$	−3.05656e19	−0.514723	−0.257361	+	0.966315i	$0.582853\pi$
$434$	−6.29182e19	−1.04137
$435$	−4.55785e17	−0.00741466
$436$	−5.34713e18	−0.0855012
$437$	−1.70378e19	−0.267795
$438$	2.87539e19	0.444264
$439$	3.65740e19	0.555506	0.277753	−	0.960652i	$-0.410410\pi$
$439$	3.65740e19	0.555506	0.277753	+	0.960652i	$0.410410\pi$
$440$	−2.68997e19	−0.401654
$441$	3.66386e19	0.537836
$442$	1.06497e19	0.153698
$443$	3.29525e19	0.467585	0.233793	−	0.972287i	$-0.424886\pi$
$443$	3.29525e19	0.467585	0.233793	+	0.972287i	$0.424886\pi$
$444$	−2.51481e19	−0.350859
$445$	4.25053e19	0.583099
$446$	7.75567e19	1.04618
$447$	−1.19202e20	−1.58116
$448$	1.24282e20	1.62114
$449$	2.50194e19	0.320944	0.160472	−	0.987040i	$-0.448698\pi$
$449$	2.50194e19	0.320944	0.160472	+	0.987040i	$0.448698\pi$
$450$	−2.18195e18	−0.0275265
$451$	−2.84570e19	−0.353074
$452$	−1.41497e19	−0.172667
$453$	−3.26996e18	−0.0392470
$454$	−6.32939e19	−0.747211
$455$	−9.90411e19	−1.15008
$456$	−1.05021e20	−1.19961
$457$	1.47649e20	1.65904	0.829522	−	0.558474i	$-0.188613\pi$
$457$	1.47649e20	1.65904	0.829522	+	0.558474i	$0.188613\pi$
$458$	−1.31834e19	−0.145726
$459$	1.33908e19	0.145616
$460$	5.58079e18	0.0597052
$461$	1.64671e19	0.173324	0.0866621	−	0.996238i	$-0.472380\pi$
$461$	1.64671e19	0.173324	0.0866621	+	0.996238i	$0.472380\pi$
$462$	−1.20453e20	−1.24740
$463$	−7.83287e19	−0.798112	−0.399056	−	0.916927i	$-0.630662\pi$
$463$	−7.83287e19	−0.798112	−0.399056	+	0.916927i	$0.630662\pi$
$464$	−3.21331e17	−0.00322157
$465$	−3.86555e19	−0.381342
$466$	−4.20992e19	−0.408676
$467$	8.15432e19	0.778953	0.389477	−	0.921036i	$-0.372656\pi$
$467$	8.15432e19	0.778953	0.389477	+	0.921036i	$0.372656\pi$
$468$	−1.46020e19	−0.137268
$469$	2.74940e20	2.54356
$470$	−4.12367e19	−0.375448
$471$	−1.03336e20	−0.925965
$472$	−2.27904e20	−2.00996
$473$	2.77469e19	0.240855
$474$	3.25291e19	0.277930
$475$	−2.47324e19	−0.208001
$476$	2.00215e19	0.165746
$477$	1.73071e19	0.141038
$478$	2.35928e19	0.189265
$479$	−3.32359e17	−0.00262477	−0.00131238	−	0.999999i	$-0.500418\pi$
$479$	−3.32359e17	−0.00262477	−0.00131238	+	0.999999i	$0.500418\pi$
$480$	5.70545e19	0.443589
$481$	1.07803e20	0.825171
$482$	2.32884e19	0.175504
$483$	7.31892e19	0.543055
$484$	1.94096e19	0.141800
$485$	1.06716e19	0.0767655
$486$	3.83226e19	0.271446
$487$	4.68937e18	0.0327075	0.0163538	−	0.999866i	$-0.494794\pi$
$487$	4.68937e18	0.0327075	0.0163538	+	0.999866i	$0.494794\pi$
$488$	−9.07292e19	−0.623158
$489$	−2.52875e20	−1.71037
$490$	1.26338e20	0.841516
$491$	2.58089e19	0.169301	0.0846504	−	0.996411i	$-0.473023\pi$
$491$	2.58089e19	0.169301	0.0846504	+	0.996411i	$0.473023\pi$
$492$	3.63917e19	0.235106
$493$	−3.94974e17	−0.00251314
$494$	1.53718e20	0.963327
$495$	−1.22486e19	−0.0756042
$496$	−2.72523e19	−0.165688
$497$	−1.12335e20	−0.672733
$498$	2.71222e19	0.159994
$499$	3.93466e19	0.228641	0.114320	−	0.993444i	$-0.463531\pi$
$499$	3.93466e19	0.228641	0.114320	+	0.993444i	$0.463531\pi$
$500$	8.10119e18	0.0463739
$501$	9.21597e19	0.519707
$502$	2.23236e20	1.24018
$503$	−2.37117e20	−1.29778	−0.648891	−	0.760881i	$-0.724767\pi$
$503$	−2.37117e20	−1.29778	−0.648891	+	0.760881i	$0.724767\pi$
$504$	7.46694e19	0.402637
$505$	5.23534e19	0.278137
$506$	−2.90955e19	−0.152299
$507$	1.65938e20	0.855829
$508$	1.17948e20	0.599395
$509$	−2.61373e20	−1.30881	−0.654405	−	0.756144i	$-0.727081\pi$
$509$	−2.61373e20	−1.30881	−0.654405	+	0.756144i	$0.727081\pi$
$510$	−1.14241e19	−0.0563695
$511$	−2.31731e20	−1.12675
$512$	8.69996e19	0.416862
$513$	1.93284e20	0.912672
$514$	−2.04809e20	−0.953073
$515$	−3.27537e19	−0.150213
$516$	−3.54836e19	−0.160382
$517$	−2.31486e20	−1.03121
$518$	−1.88227e20	−0.826435
$519$	−3.47636e20	−1.50442
$520$	−1.47464e20	−0.629016
$521$	2.97998e20	1.25294	0.626470	−	0.779446i	$-0.284499\pi$
$521$	2.97998e20	1.25294	0.626470	+	0.779446i	$0.284499\pi$
$522$	−5.02962e17	−0.00208452
$523$	−4.33854e18	−0.0177248	−0.00886238	−	0.999961i	$-0.502821\pi$
$523$	−4.33854e18	−0.0177248	−0.00886238	+	0.999961i	$0.502821\pi$
$524$	−2.07913e20	−0.837331
$525$	1.06243e20	0.421799
$526$	1.80296e20	0.705654
$527$	−3.34980e19	−0.129253
$528$	−5.21730e19	−0.198468
$529$	−2.48956e20	−0.933696
$530$	5.96784e19	0.220673
$531$	−1.03774e20	−0.378339
$532$	2.88992e20	1.03884
$533$	−1.56002e20	−0.552937
$534$	2.83391e20	0.990436
$535$	1.92678e20	0.664015
$536$	4.09364e20	1.39115
$537$	5.38992e20	1.80624
$538$	−1.08890e20	−0.359850
$539$	7.09208e20	2.31131
$540$	−6.33107e19	−0.203481
$541$	−4.72884e20	−1.49891	−0.749454	−	0.662056i	$-0.769684\pi$
$541$	−4.72884e20	−1.49891	−0.749454	+	0.662056i	$0.769684\pi$
$542$	−4.51130e19	−0.141029
$543$	5.66895e20	1.74785
$544$	4.94422e19	0.150351
$545$	−2.45885e19	−0.0737495
$546$	−6.60327e20	−1.95350
$547$	−1.45807e20	−0.425475	−0.212738	−	0.977109i	$-0.568238\pi$
$547$	−1.45807e20	−0.425475	−0.212738	+	0.977109i	$0.568238\pi$
$548$	−2.01483e20	−0.579942
$549$	−4.13129e19	−0.117299
$550$	−4.22356e19	−0.118293
$551$	−5.70109e18	−0.0157515
$552$	1.08973e20	0.297013
$553$	−2.62156e20	−0.704889
$554$	−7.43262e19	−0.197160
$555$	−1.15642e20	−0.302635
$556$	−1.29546e20	−0.334474
$557$	1.88400e20	0.479917	0.239959	−	0.970783i	$-0.422866\pi$
$557$	1.88400e20	0.479917	0.239959	+	0.970783i	$0.422866\pi$
$558$	−4.26566e19	−0.107209
$559$	1.52109e20	0.377195
$560$	7.49017e19	0.183266
$561$	−6.41300e19	−0.154825
$562$	−2.03986e20	−0.485936
$563$	2.59992e20	0.611148	0.305574	−	0.952168i	$-0.401152\pi$
$563$	2.59992e20	0.611148	0.305574	+	0.952168i	$0.401152\pi$
$564$	2.96031e20	0.686665
$565$	−6.50666e19	−0.148934
$566$	4.94652e19	0.111732
$567$	−1.00171e21	−2.23290
$568$	−1.67258e20	−0.367938
$569$	−3.48598e20	−0.756804	−0.378402	−	0.925641i	$-0.623526\pi$
$569$	−3.48598e20	−0.756804	−0.378402	+	0.925641i	$0.623526\pi$
$570$	−1.64896e20	−0.353304
$571$	8.88533e20	1.87890	0.939448	−	0.342693i	$-0.111339\pi$
$571$	8.88533e20	1.87890	0.939448	+	0.342693i	$0.111339\pi$
$572$	−2.82650e20	−0.589900
$573$	1.25728e20	0.258983
$574$	2.72382e20	0.553783
$575$	2.56630e19	0.0514989
$576$	8.42590e19	0.166897
$577$	−8.07920e20	−1.57961	−0.789805	−	0.613358i	$-0.789818\pi$
$577$	−8.07920e20	−1.57961	−0.789805	+	0.613358i	$0.789818\pi$
$578$	3.49657e20	0.674813
$579$	3.54400e20	0.675156
$580$	1.86741e18	0.00351180
$581$	−2.18581e20	−0.405780
$582$	7.11496e19	0.130392
$583$	3.35010e20	0.606100
$584$	−3.45029e20	−0.616253
$585$	−6.71467e19	−0.118401
$586$	3.41115e20	0.593838
$587$	6.01086e20	1.03312	0.516560	−	0.856251i	$-0.327212\pi$
$587$	6.01086e20	1.03312	0.516560	+	0.856251i	$0.327212\pi$
$588$	−9.06957e20	−1.53906
$589$	−4.83513e20	−0.810110
$590$	−3.57836e20	−0.591962
$591$	4.66565e20	0.762090
$592$	−8.15283e19	−0.131491
$593$	1.01135e21	1.61061	0.805307	−	0.592857i	$-0.202000\pi$
$593$	1.01135e21	1.61061	0.805307	+	0.592857i	$0.202000\pi$
$594$	3.30071e20	0.519050
$595$	9.20678e19	0.142965
$596$	4.88383e20	0.748883
$597$	5.93729e20	0.899043
$598$	−1.59502e20	−0.238510
$599$	6.06762e20	0.896019	0.448010	−	0.894029i	$-0.352133\pi$
$599$	6.06762e20	0.896019	0.448010	+	0.894029i	$0.352133\pi$
$600$	1.58187e20	0.230694
$601$	−1.05915e21	−1.52545	−0.762727	−	0.646721i	$-0.776140\pi$
$601$	−1.05915e21	−1.52545	−0.762727	+	0.646721i	$0.776140\pi$
$602$	−2.65585e20	−0.377772
$603$	1.86401e20	0.261859
$604$	1.33974e19	0.0185885
$605$	8.92539e19	0.122310
$606$	3.49050e20	0.472436
$607$	−1.05893e21	−1.41564	−0.707818	−	0.706395i	$-0.750320\pi$
$607$	−1.05893e21	−1.41564	−0.707818	+	0.706395i	$0.750320\pi$
$608$	7.13653e20	0.942346
$609$	2.44901e19	0.0319419
$610$	−1.42456e20	−0.183529
$611$	−1.26901e21	−1.61494
$612$	1.35739e19	0.0170636
$613$	−2.18287e20	−0.271065	−0.135532	−	0.990773i	$-0.543275\pi$
$613$	−2.18287e20	−0.271065	−0.135532	+	0.990773i	$0.543275\pi$
$614$	−9.67026e20	−1.18625
$615$	1.67345e20	0.202792
$616$	1.44536e21	1.73030
$617$	1.57542e20	0.186319	0.0931594	−	0.995651i	$-0.470303\pi$
$617$	1.57542e20	0.186319	0.0931594	+	0.995651i	$0.470303\pi$
$618$	−2.18375e20	−0.255147
$619$	1.15824e21	1.33696	0.668479	−	0.743731i	$-0.266946\pi$
$619$	1.15824e21	1.33696	0.668479	+	0.743731i	$0.266946\pi$
$620$	1.58376e20	0.180614
$621$	−2.00556e20	−0.225969
$622$	6.77007e20	0.753642
$623$	−2.28388e21	−2.51196
$624$	−2.86013e20	−0.310814
$625$	3.72529e19	0.0400000
$626$	−2.75111e20	−0.291878
$627$	−9.25659e20	−0.970386
$628$	4.23380e20	0.438564
$629$	−1.00213e20	−0.102576
$630$	1.17240e20	0.118582
$631$	−1.32229e21	−1.32162	−0.660808	−	0.750555i	$-0.729786\pi$
$631$	−1.32229e21	−1.32162	−0.660808	+	0.750555i	$0.729786\pi$
$632$	−3.90329e20	−0.385525
$633$	−6.18646e20	−0.603830
$634$	−1.57157e20	−0.151588
$635$	5.42379e20	0.517011
$636$	−4.28422e20	−0.403592
$637$	3.88789e21	3.61966
$638$	−9.73576e18	−0.00895807
$639$	−7.61597e19	−0.0692578
$640$	−1.60315e20	−0.144087
$641$	−9.88407e20	−0.878013	−0.439006	−	0.898484i	$-0.644669\pi$
$641$	−9.88407e20	−0.878013	−0.439006	+	0.898484i	$0.644669\pi$
$642$	1.28462e21	1.12788
$643$	1.21948e21	1.05826	0.529131	−	0.848540i	$-0.322518\pi$
$643$	1.21948e21	1.05826	0.529131	+	0.848540i	$0.322518\pi$
$644$	−2.99865e20	−0.257207
$645$	−1.63169e20	−0.138338
$646$	−1.42895e20	−0.119750
$647$	−1.99384e20	−0.165162	−0.0825808	−	0.996584i	$-0.526316\pi$
$647$	−1.99384e20	−0.165162	−0.0825808	+	0.996584i	$0.526316\pi$
$648$	−1.49147e21	−1.22124
$649$	−2.00874e21	−1.62588
$650$	−2.31536e20	−0.185254
$651$	2.07702e21	1.64280
$652$	1.03606e21	0.810081
$653$	1.18511e21	0.916032	0.458016	−	0.888944i	$-0.348560\pi$
$653$	1.18511e21	0.916032	0.458016	+	0.888944i	$0.348560\pi$
$654$	−1.63937e20	−0.125269
$655$	−9.56077e20	−0.722243
$656$	1.17979e20	0.0881104
$657$	−1.57106e20	−0.115999
$658$	2.21572e21	1.61741
$659$	7.64112e20	0.551463	0.275732	−	0.961235i	$-0.411080\pi$
$659$	7.64112e20	0.551463	0.275732	+	0.961235i	$0.411080\pi$
$660$	3.03203e20	0.216348
$661$	2.03884e21	1.43838	0.719189	−	0.694814i	$-0.244514\pi$
$661$	2.03884e21	1.43838	0.719189	+	0.694814i	$0.244514\pi$
$662$	6.74149e18	0.00470242
$663$	−3.51562e20	−0.242466
$664$	−3.25449e20	−0.221933
$665$	1.32892e21	0.896056
$666$	−1.27612e20	−0.0850814
$667$	5.91559e18	0.00389991
$668$	−3.77590e20	−0.246148
$669$	−2.56027e21	−1.65040
$670$	6.42749e20	0.409714
$671$	−7.99687e20	−0.504082
$672$	−3.06563e21	−1.91096
$673$	−2.72310e21	−1.67861	−0.839307	−	0.543657i	$-0.817039\pi$
$673$	−2.72310e21	−1.67861	−0.839307	+	0.543657i	$0.817039\pi$
$674$	1.53589e21	0.936290
$675$	−2.91131e20	−0.175513
$676$	−6.79870e20	−0.405346
$677$	−1.77793e21	−1.04834	−0.524168	−	0.851615i	$-0.675623\pi$
$677$	−1.77793e21	−1.04834	−0.524168	+	0.851615i	$0.675623\pi$
$678$	−4.33812e20	−0.252976
$679$	−5.73402e20	−0.330702
$680$	1.37082e20	0.0781920
$681$	2.08943e21	1.17876
$682$	−8.25697e20	−0.460721
$683$	2.10572e21	1.16210	0.581052	−	0.813866i	$-0.302641\pi$
$683$	2.10572e21	1.16210	0.581052	+	0.813866i	$0.302641\pi$
$684$	1.95927e20	0.106948
$685$	−9.26510e20	−0.500231
$686$	−4.28497e21	−2.28832
$687$	4.35206e20	0.229889
$688$	−1.15035e20	−0.0601059
$689$	1.83653e21	0.949192
$690$	1.71100e20	0.0874747
$691$	7.20890e20	0.364573	0.182286	−	0.983246i	$-0.441650\pi$
$691$	7.20890e20	0.364573	0.182286	+	0.983246i	$0.441650\pi$
$692$	1.42431e21	0.712538
$693$	6.58136e20	0.325699
$694$	4.16628e20	0.203964
$695$	−5.95711e20	−0.288502
$696$	3.64638e19	0.0174700
$697$	1.45018e20	0.0687347
$698$	−9.92167e20	−0.465231
$699$	1.38976e21	0.644704
$700$	−4.35290e20	−0.199776
$701$	2.35289e21	1.06836	0.534178	−	0.845372i	$-0.320621\pi$
$701$	2.35289e21	1.06836	0.534178	+	0.845372i	$0.320621\pi$
$702$	1.80945e21	0.812866
$703$	−1.44649e21	−0.642908
$704$	1.63099e21	0.717227
$705$	1.36129e21	0.592285
$706$	1.14406e21	0.492507
$707$	−2.81303e21	−1.19820
$708$	2.56884e21	1.08265
$709$	2.59176e21	1.08080	0.540402	−	0.841407i	$-0.318272\pi$
$709$	2.59176e21	1.08080	0.540402	+	0.841407i	$0.318272\pi$
$710$	−2.62615e20	−0.108363
$711$	−1.77733e20	−0.0725683
$712$	−3.40051e21	−1.37387
$713$	5.01705e20	0.200575
$714$	6.13834e20	0.242837
$715$	−1.29975e21	−0.508820
$716$	−2.20831e21	−0.855487
$717$	−7.78833e20	−0.298573
$718$	−2.82975e21	−1.07353
$719$	3.14455e20	0.118057	0.0590286	−	0.998256i	$-0.481200\pi$
$719$	3.14455e20	0.118057	0.0590286	+	0.998256i	$0.481200\pi$
$720$	5.07810e19	0.0188672
$721$	1.75991e21	0.647107
$722$	−1.55620e20	−0.0566288
$723$	−7.68786e20	−0.276865
$724$	−2.32264e21	−0.827833
$725$	8.58719e18	0.00302912
$726$	5.95074e20	0.207752
$727$	−6.36621e20	−0.219975	−0.109987	−	0.993933i	$-0.535081\pi$
$727$	−6.36621e20	−0.219975	−0.109987	+	0.993933i	$0.535081\pi$
$728$	7.92350e21	2.70977
$729$	2.15897e21	0.730784
$730$	−5.41736e20	−0.181496
$731$	−1.41399e20	−0.0468885
$732$	1.02266e21	0.335661
$733$	−2.18932e21	−0.711262	−0.355631	−	0.934626i	$-0.615734\pi$
$733$	−2.18932e21	−0.711262	−0.355631	+	0.934626i	$0.615734\pi$
$734$	−4.99377e20	−0.160586
$735$	−4.17060e21	−1.32753
$736$	−7.40504e20	−0.233316
$737$	3.60813e21	1.12532
$738$	1.84667e20	0.0570119
$739$	−1.92313e21	−0.587726	−0.293863	−	0.955848i	$-0.594941\pi$
$739$	−1.92313e21	−0.587726	−0.293863	+	0.955848i	$0.594941\pi$
$740$	4.73801e20	0.143337
$741$	−5.07448e21	−1.51969
$742$	−3.20662e21	−0.950645
$743$	3.52612e21	1.03486	0.517429	−	0.855726i	$-0.326889\pi$
$743$	3.52612e21	1.03486	0.517429	+	0.855726i	$0.326889\pi$
$744$	3.09252e21	0.898496
$745$	2.24581e21	0.645952
$746$	−5.12816e20	−0.146023
$747$	−1.48191e20	−0.0417750
$748$	2.62749e20	0.0733295
$749$	−1.03529e22	−2.86054
$750$	2.48373e20	0.0679429
$751$	−3.88437e21	−1.05201	−0.526007	−	0.850480i	$-0.676311\pi$
$751$	−3.88437e21	−1.05201	−0.526007	+	0.850480i	$0.676311\pi$
$752$	9.59712e20	0.257340
$753$	−7.36934e21	−1.95644
$754$	−5.33715e19	−0.0140289
$755$	6.16074e19	0.0160336
$756$	3.40179e21	0.876585
$757$	7.50772e21	1.91553	0.957765	−	0.287552i	$-0.0928414\pi$
$757$	7.50772e21	1.91553	0.957765	+	0.287552i	$0.0928414\pi$
$758$	1.63875e21	0.413993
$759$	9.60487e20	0.240258
$760$	1.97865e21	0.490080
$761$	2.31317e21	0.567312	0.283656	−	0.958926i	$-0.408453\pi$
$761$	2.31317e21	0.567312	0.283656	+	0.958926i	$0.408453\pi$
$762$	3.61615e21	0.878181
$763$	1.32118e21	0.317709
$764$	−5.15121e20	−0.122662
$765$	6.24191e19	0.0147183
$766$	4.23667e21	0.989257
$767$	−1.10120e22	−2.54624
$768$	−5.09172e21	−1.16588
$769$	6.52589e21	1.47976	0.739881	−	0.672737i	$-0.234882\pi$
$769$	6.52589e21	1.47976	0.739881	+	0.672737i	$0.234882\pi$
$770$	2.26939e21	0.509599
$771$	6.76106e21	1.50351
$772$	−1.45202e21	−0.319773
$773$	1.01984e21	0.222427	0.111213	−	0.993797i	$-0.464526\pi$
$773$	1.01984e21	0.222427	0.111213	+	0.993797i	$0.464526\pi$
$774$	−1.80058e20	−0.0388916
$775$	7.28286e20	0.155790
$776$	−8.53750e20	−0.180871
$777$	6.21366e21	1.30374
$778$	−3.30405e21	−0.686594
$779$	2.09320e21	0.430805
$780$	1.66216e21	0.338816
$781$	−1.47421e21	−0.297630
$782$	1.48272e20	0.0296488
$783$	−6.71088e19	−0.0132913
$784$	−2.94029e21	−0.576793
$785$	1.94689e21	0.378285
$786$	−6.37436e21	−1.22678
$787$	2.82373e21	0.538285	0.269142	−	0.963100i	$-0.413260\pi$
$787$	2.82373e21	0.538285	0.269142	+	0.963100i	$0.413260\pi$
$788$	−1.91158e21	−0.360948
$789$	−5.95183e21	−1.11320
$790$	−6.12862e20	−0.113543
$791$	3.49614e21	0.641601
$792$	9.79911e20	0.178134
$793$	−4.38390e21	−0.789426
$794$	−2.95168e21	−0.526520
$795$	−1.97008e21	−0.348120
$796$	−2.43258e21	−0.425813
$797$	8.17576e21	1.41772	0.708861	−	0.705348i	$-0.249209\pi$
$797$	8.17576e21	1.41772	0.708861	+	0.705348i	$0.249209\pi$
$798$	8.86014e21	1.52202
$799$	1.17966e21	0.200750
$800$	−1.07493e21	−0.181220
$801$	−1.54840e21	−0.258606
$802$	−4.75952e21	−0.787508
$803$	−3.04108e21	−0.498496
$804$	−4.61419e21	−0.749334
$805$	−1.37892e21	−0.221855
$806$	−4.52648e21	−0.721519
$807$	3.59463e21	0.567679
$808$	−4.18838e21	−0.655332
$809$	−5.68336e21	−0.881032	−0.440516	−	0.897745i	$-0.645204\pi$
$809$	−5.68336e21	−0.881032	−0.440516	+	0.897745i	$0.645204\pi$
$810$	−2.34178e21	−0.359673
$811$	1.98915e21	0.302700	0.151350	−	0.988480i	$-0.451638\pi$
$811$	1.98915e21	0.302700	0.151350	+	0.988480i	$0.451638\pi$
$812$	−1.00339e20	−0.0151286
$813$	1.48925e21	0.222478
$814$	−2.47017e21	−0.365631
$815$	4.76428e21	0.698739
$816$	2.65875e20	0.0386369
$817$	−2.04097e21	−0.293880
$818$	4.10911e21	0.586270
$819$	3.60791e21	0.510066
$820$	−6.85635e20	−0.0960482
$821$	−1.37149e22	−1.90379	−0.951895	−	0.306425i	$-0.900867\pi$
$821$	−1.37149e22	−1.90379	−0.951895	+	0.306425i	$0.900867\pi$
$822$	−6.17723e21	−0.849679
$823$	1.13143e22	1.54216	0.771080	−	0.636739i	$-0.219717\pi$
$823$	1.13143e22	1.54216	0.771080	+	0.636739i	$0.219717\pi$
$824$	2.62037e21	0.353922
$825$	1.39426e21	0.186612
$826$	1.92271e22	2.55014
$827$	−6.39375e21	−0.840358	−0.420179	−	0.907441i	$-0.638033\pi$
$827$	−6.39375e21	−0.840358	−0.420179	+	0.907441i	$0.638033\pi$
$828$	−2.03299e20	−0.0264794
$829$	1.23621e22	1.59563	0.797816	−	0.602901i	$-0.205989\pi$
$829$	1.23621e22	1.59563	0.797816	+	0.602901i	$0.205989\pi$
$830$	−5.10993e20	−0.0653626
$831$	2.45362e21	0.311028
$832$	8.94111e21	1.12322
$833$	−3.61415e21	−0.449954
$834$	−3.97172e21	−0.490042
$835$	−1.73633e21	−0.212316
$836$	3.79254e21	0.459603
$837$	−5.69154e21	−0.683580
$838$	1.97631e21	0.235248
$839$	8.00216e21	0.944045	0.472023	−	0.881586i	$-0.343524\pi$
$839$	8.00216e21	0.944045	0.472023	+	0.881586i	$0.343524\pi$
$840$	−8.49967e21	−0.993819
$841$	−8.62721e21	−0.999771
$842$	1.05239e22	1.20875
$843$	6.73390e21	0.766584
$844$	2.53467e21	0.285991
$845$	−3.12635e21	−0.349633
$846$	1.50219e21	0.166512
$847$	−4.79576e21	−0.526905
$848$	−1.38891e21	−0.151254
$849$	−1.63292e21	−0.176261
$850$	2.15234e20	0.0230287
$851$	1.50091e21	0.159178
$852$	1.88527e21	0.198188
$853$	−4.09809e21	−0.427035	−0.213518	−	0.976939i	$-0.568492\pi$
$853$	−4.09809e21	−0.427035	−0.213518	+	0.976939i	$0.568492\pi$
$854$	7.65438e21	0.790635
$855$	9.00963e20	0.0922489
$856$	−1.54146e22	−1.56451
$857$	−1.55610e22	−1.56560	−0.782801	−	0.622272i	$-0.786210\pi$
$857$	−1.55610e22	−1.56560	−0.782801	+	0.622272i	$0.786210\pi$
$858$	−8.66569e21	−0.864268
$859$	7.94903e21	0.785897	0.392948	−	0.919561i	$-0.371455\pi$
$859$	7.94903e21	0.785897	0.392948	+	0.919561i	$0.371455\pi$
$860$	6.68525e20	0.0655208
$861$	−8.99176e21	−0.873617
$862$	−9.95357e21	−0.958682
$863$	−7.80107e19	−0.00744858	−0.00372429	−	0.999993i	$-0.501185\pi$
$863$	−7.80107e19	−0.00744858	−0.00372429	+	0.999993i	$0.501185\pi$
$864$	8.40057e21	0.795162
$865$	6.54961e21	0.614603
$866$	3.83943e21	0.357176
$867$	−1.15427e22	−1.06455
$868$	−8.50983e21	−0.778077
$869$	−3.44036e21	−0.311857
$870$	5.72525e19	0.00514517
$871$	1.97798e22	1.76233
$872$	1.96714e21	0.173764
$873$	−3.88749e20	−0.0340457
$874$	2.14017e21	0.185828
$875$	−2.00166e21	−0.172318
$876$	3.88903e21	0.331941
$877$	3.67778e21	0.311236	0.155618	−	0.987817i	$-0.450263\pi$
$877$	3.67778e21	0.311236	0.155618	+	0.987817i	$0.450263\pi$
$878$	−4.59417e21	−0.385477
$879$	−1.12607e22	−0.936805
$880$	9.82961e20	0.0810804
$881$	1.68275e22	1.37626	0.688129	−	0.725588i	$-0.258432\pi$
$881$	1.68275e22	1.37626	0.688129	+	0.725588i	$0.258432\pi$
$882$	−4.60228e21	−0.373214
$883$	1.10385e22	0.887571	0.443785	−	0.896133i	$-0.353635\pi$
$883$	1.10385e22	0.887571	0.443785	+	0.896133i	$0.353635\pi$
$884$	1.44039e21	0.114839
$885$	1.18127e22	0.933845
$886$	−4.13926e21	−0.324466
$887$	−1.41379e22	−1.09890	−0.549451	−	0.835526i	$-0.685163\pi$
$887$	−1.41379e22	−1.09890	−0.549451	+	0.835526i	$0.685163\pi$
$888$	9.25164e21	0.713052
$889$	−2.91429e22	−2.22725
$890$	−5.33920e21	−0.404624
$891$	−1.31458e22	−0.987879
$892$	1.04897e22	0.781678
$893$	1.70273e22	1.25823
$894$	1.49732e22	1.09720
$895$	−1.01548e22	−0.737904
$896$	8.61402e21	0.620720
$897$	5.26540e21	0.376260
$898$	−3.14275e21	−0.222709
$899$	1.67878e20	0.0117976
$900$	−2.95113e20	−0.0205669
$901$	−1.70722e21	−0.117993
$902$	3.57457e21	0.245005
$903$	8.76737e21	0.595952
$904$	5.20547e21	0.350911
$905$	−1.06805e22	−0.714051
$906$	4.10749e20	0.0272342
$907$	4.78820e21	0.314860	0.157430	−	0.987530i	$-0.449679\pi$
$907$	4.78820e21	0.314860	0.157430	+	0.987530i	$0.449679\pi$
$908$	−8.56065e21	−0.558294
$909$	−1.90715e21	−0.123355
$910$	1.24408e22	0.798066
$911$	−2.12528e22	−1.35216	−0.676081	−	0.736827i	$-0.736323\pi$
$911$	−2.12528e22	−1.35216	−0.676081	+	0.736827i	$0.736323\pi$
$912$	3.83767e21	0.242162
$913$	−2.86851e21	−0.179525
$914$	−1.85466e22	−1.15124
$915$	4.70267e21	0.289525
$916$	−1.78309e21	−0.108882
$917$	5.13717e22	3.11138
$918$	−1.68205e21	−0.101046
$919$	1.67526e22	0.998196	0.499098	−	0.866545i	$-0.333665\pi$
$919$	1.67526e22	0.998196	0.499098	+	0.866545i	$0.333665\pi$
$920$	−2.05309e21	−0.121339
$921$	3.19230e22	1.87136
$922$	−2.06847e21	−0.120273
$923$	−8.08165e21	−0.466109
$924$	−1.62916e22	−0.932017
$925$	2.17875e21	0.123636
$926$	9.83909e21	0.553825
$927$	1.19316e21	0.0666197
$928$	−2.47783e20	−0.0137234
$929$	−1.80581e22	−0.992098	−0.496049	−	0.868294i	$-0.665216\pi$
$929$	−1.80581e22	−0.992098	−0.496049	+	0.868294i	$0.665216\pi$
$930$	4.85563e21	0.264620
$931$	−5.21670e22	−2.82016
$932$	−5.69401e21	−0.305351
$933$	−2.23490e22	−1.18890
$934$	−1.02429e22	−0.540531
$935$	1.20824e21	0.0632506
$936$	5.37189e21	0.278970
$937$	−1.56638e22	−0.806957	−0.403478	−	0.914989i	$-0.632199\pi$
$937$	−1.56638e22	−0.806957	−0.403478	+	0.914989i	$0.632199\pi$
$938$	−3.45360e22	−1.76503
$939$	9.08185e21	0.460450
$940$	−5.57736e21	−0.280524
$941$	−8.59709e21	−0.428972	−0.214486	−	0.976727i	$-0.568808\pi$
$941$	−8.59709e21	−0.428972	−0.214486	+	0.976727i	$0.568808\pi$
$942$	1.29803e22	0.642545
$943$	−2.17196e21	−0.106663
$944$	8.32801e21	0.405743
$945$	1.56430e22	0.756102
$946$	−3.48536e21	−0.167134
$947$	1.67394e22	0.796370	0.398185	−	0.917305i	$-0.369640\pi$
$947$	1.67394e22	0.796370	0.398185	+	0.917305i	$0.369640\pi$
$948$	4.39964e21	0.207661
$949$	−1.66713e22	−0.780678
$950$	3.10671e21	0.144336
$951$	5.18800e21	0.239137
$952$	−7.36562e21	−0.336847
$953$	3.69735e22	1.67762	0.838811	−	0.544422i	$-0.183251\pi$
$953$	3.69735e22	1.67762	0.838811	+	0.544422i	$0.183251\pi$
$954$	−2.17399e21	−0.0978689
$955$	−2.36876e21	−0.105802
$956$	3.19098e21	0.141413
$957$	3.21392e20	0.0141317
$958$	4.17485e19	0.00182138
$959$	4.97829e22	2.15497
$960$	−9.59127e21	−0.411947
$961$	−9.22745e21	−0.393239
$962$	−1.35415e22	−0.572602
$963$	−7.01893e21	−0.294492
$964$	3.14981e21	0.131131
$965$	−6.67704e21	−0.275822
$966$	−9.19350e21	−0.376836
$967$	3.20861e22	1.30502	0.652511	−	0.757779i	$-0.273716\pi$
$967$	3.20861e22	1.30502	0.652511	+	0.757779i	$0.273716\pi$
$968$	−7.14051e21	−0.288180
$969$	4.71719e21	0.188910
$970$	−1.34049e21	−0.0532691
$971$	2.32064e22	0.915089	0.457544	−	0.889187i	$-0.348729\pi$
$971$	2.32064e22	0.915089	0.457544	+	0.889187i	$0.348729\pi$
$972$	5.18322e21	0.202816
$973$	3.20085e22	1.24285
$974$	−5.89046e20	−0.0226964
$975$	7.64336e21	0.292247
$976$	3.31541e21	0.125795
$977$	3.13190e21	0.117923	0.0589614	−	0.998260i	$-0.481221\pi$
$977$	3.13190e21	0.117923	0.0589614	+	0.998260i	$0.481221\pi$
$978$	3.17644e22	1.18686
$979$	−2.99721e22	−1.11134
$980$	1.70875e22	0.628756
$981$	8.95721e20	0.0327081
$982$	−3.24193e21	−0.117481
$983$	−5.05135e22	−1.81659	−0.908293	−	0.418336i	$-0.862614\pi$
$983$	−5.05135e22	−1.81659	−0.908293	+	0.418336i	$0.862614\pi$
$984$	−1.33880e22	−0.477807
$985$	−8.79029e21	−0.311337
$986$	4.96137e19	0.00174391
$987$	−7.31442e22	−2.55153
$988$	2.07908e22	0.719769
$989$	2.11776e21	0.0727619
$990$	1.53858e21	0.0524632
$991$	2.46682e22	0.834804	0.417402	−	0.908722i	$-0.362941\pi$
$991$	2.46682e22	0.834804	0.417402	+	0.908722i	$0.362941\pi$
$992$	−2.10146e22	−0.705804
$993$	−2.22547e20	−0.00741826
$994$	1.41107e22	0.466823
$995$	−1.11861e22	−0.367287
$996$	3.66834e21	0.119543
$997$	−8.13282e21	−0.263043	−0.131522	−	0.991313i	$-0.541986\pi$
$997$	−8.13282e21	−0.263043	−0.131522	+	0.991313i	$0.541986\pi$
$998$	−4.94244e21	−0.158658
$999$	−1.70269e22	−0.542493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.16.a.b.1.2	✓	3
3.2	odd	2		45.16.a.f.1.2		3
4.3	odd	2		80.16.a.g.1.2		3
5.2	odd	4		25.16.b.c.24.3		6
5.3	odd	4		25.16.b.c.24.4		6
5.4	even	2		25.16.a.c.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.16.a.b.1.2	✓	3	1.1	even	1	trivial
25.16.a.c.1.2		3	5.4	even	2
25.16.b.c.24.3		6	5.2	odd	4
25.16.b.c.24.4		6	5.3	odd	4
45.16.a.f.1.2		3	3.2	odd	2
80.16.a.g.1.2		3	4.3	odd	2

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q-125.613 q^{2} +4146.67 q^{3} -16989.4 q^{4} -78125.0 q^{5} -520875. q^{6} +4.19779e6 q^{7} +6.25017e6 q^{8} +2.84597e6 q^{9} +O(q^{10})\)	\(q-125.613 q^{2} +4146.67 q^{3} -16989.4 q^{4} -78125.0 q^{5} -520875. q^{6} +4.19779e6 q^{7} +6.25017e6 q^{8} +2.84597e6 q^{9} +9.81350e6 q^{10} +5.50890e7 q^{11} -7.04495e7 q^{12} +3.01999e8 q^{13} -5.27296e8 q^{14} -3.23959e8 q^{15} -2.28392e8 q^{16} -2.80735e8 q^{17} -3.57490e8 q^{18} -4.05216e9 q^{19} +1.32730e9 q^{20} +1.74068e10 q^{21} -6.91988e9 q^{22} +4.20462e9 q^{23} +2.59174e10 q^{24} +6.10352e9 q^{25} -3.79349e10 q^{26} -4.76989e10 q^{27} -7.13180e10 q^{28} +1.40692e9 q^{29} +4.06934e10 q^{30} +1.19322e11 q^{31} -1.76117e11 q^{32} +2.28436e11 q^{33} +3.52640e10 q^{34} -3.27952e11 q^{35} -4.83513e10 q^{36} +3.56966e11 q^{37} +5.09003e11 q^{38} +1.25229e12 q^{39} -4.88295e11 q^{40} -5.16564e11 q^{41} -2.18652e12 q^{42} +5.03673e11 q^{43} -9.35930e11 q^{44} -2.22341e11 q^{45} -5.28155e11 q^{46} -4.20204e12 q^{47} -9.47067e11 q^{48} +1.28739e13 q^{49} -7.66680e11 q^{50} -1.16412e12 q^{51} -5.13078e12 q^{52} +6.08126e12 q^{53} +5.99159e12 q^{54} -4.30383e12 q^{55} +2.62369e13 q^{56} -1.68030e13 q^{57} -1.76728e11 q^{58} -3.64636e13 q^{59} +5.50387e12 q^{60} -1.45163e13 q^{61} -1.49884e13 q^{62} +1.19468e13 q^{63} +2.96065e13 q^{64} -2.35936e13 q^{65} -2.86945e13 q^{66} +6.54964e13 q^{67} +4.76953e12 q^{68} +1.74352e13 q^{69} +4.11950e13 q^{70} -2.67606e13 q^{71} +1.77878e13 q^{72} -5.52031e13 q^{73} -4.48396e13 q^{74} +2.53093e13 q^{75} +6.88439e13 q^{76} +2.31252e14 q^{77} -1.57303e14 q^{78} -6.24509e13 q^{79} +1.78431e13 q^{80} -2.38628e14 q^{81} +6.48871e13 q^{82} -5.20704e13 q^{83} -2.95732e14 q^{84} +2.19325e13 q^{85} -6.32678e13 q^{86} +5.83405e12 q^{87} +3.44316e14 q^{88} -5.44067e14 q^{89} +2.79289e13 q^{90} +1.26773e15 q^{91} -7.14341e13 q^{92} +4.94790e14 q^{93} +5.27830e14 q^{94} +3.16575e14 q^{95} -7.30297e14 q^{96} -1.36596e14 q^{97} -1.61712e15 q^{98} +1.56782e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 4 q^{2} + 3518 q^{3} + 20384 q^{4} - 234375 q^{5} + 2075176 q^{6} - 905206 q^{7} + 16674720 q^{8} + 47911531 q^{9}+O(q^{10}) \) 3 * q + 4 * q^2 + 3518 * q^3 + 20384 * q^4 - 234375 * q^5 + 2075176 * q^6 - 905206 * q^7 + 16674720 * q^8 + 47911531 * q^9	\( 3 q + 4 q^{2} + 3518 q^{3} + 20384 q^{4} - 234375 q^{5} + 2075176 q^{6} - 905206 q^{7} + 16674720 q^{8} + 47911531 q^{9} - 312500 q^{10} + 122875456 q^{11} + 259564864 q^{12} - 90911522 q^{13} - 1195428552 q^{14} - 274843750 q^{15} - 1314428032 q^{16} - 3868973426 q^{17} + 905373668 q^{18} + 3670884220 q^{19} - 1592500000 q^{20} + 9596808996 q^{21} + 20569860608 q^{22} + 26698058238 q^{23} + 7659524160 q^{24} + 18310546875 q^{25} - 27015047384 q^{26} - 99092472220 q^{27} - 210410855488 q^{28} + 145544932730 q^{29} - 162123125000 q^{30} - 25873382644 q^{31} - 531675479296 q^{32} + 851520900736 q^{33} + 208184081768 q^{34} + 70719218750 q^{35} + 578919966368 q^{36} + 419480249934 q^{37} + 205247686480 q^{38} + 2390867460332 q^{39} - 1302712500000 q^{40} + 274005770306 q^{41} - 9314366945232 q^{42} + 2350065869158 q^{43} + 3324410490368 q^{44} - 3743088359375 q^{45} - 2445701814744 q^{46} - 8891070209486 q^{47} + 968269957888 q^{48} + 17603715811879 q^{49} + 24414062500 q^{50} + 11276036492236 q^{51} - 7757281361856 q^{52} + 8749242811318 q^{53} + 24761205955120 q^{54} - 9599645000000 q^{55} + 1555780658880 q^{56} - 41669191785640 q^{57} + 53844260003320 q^{58} - 14173516437140 q^{59} - 20278505000000 q^{60} - 38066837721794 q^{61} - 53610636798192 q^{62} - 97119517183302 q^{63} + 12081926129664 q^{64} + 7102462656250 q^{65} + 93794721354752 q^{66} + 144391638065474 q^{67} - 9729892224448 q^{68} - 83804251999188 q^{69} + 93392855625000 q^{70} - 126512337318844 q^{71} + 262100048315040 q^{72} + 199804772078038 q^{73} - 103551095018392 q^{74} + 21472167968750 q^{75} + 108919950456960 q^{76} - 24166822365312 q^{77} - 612963962524784 q^{78} - 73797562093720 q^{79} + 102689690000000 q^{80} - 252524358845777 q^{81} + 452714654584408 q^{82} - 219109046205402 q^{83} - 12\!\cdots\!12 q^{84}+ \cdots + 12\!\cdots\!12 q^{99}+O(q^{100}) \) 3 * q + 4 * q^2 + 3518 * q^3 + 20384 * q^4 - 234375 * q^5 + 2075176 * q^6 - 905206 * q^7 + 16674720 * q^8 + 47911531 * q^9 - 312500 * q^10 + 122875456 * q^11 + 259564864 * q^12 - 90911522 * q^13 - 1195428552 * q^14 - 274843750 * q^15 - 1314428032 * q^16 - 3868973426 * q^17 + 905373668 * q^18 + 3670884220 * q^19 - 1592500000 * q^20 + 9596808996 * q^21 + 20569860608 * q^22 + 26698058238 * q^23 + 7659524160 * q^24 + 18310546875 * q^25 - 27015047384 * q^26 - 99092472220 * q^27 - 210410855488 * q^28 + 145544932730 * q^29 - 162123125000 * q^30 - 25873382644 * q^31 - 531675479296 * q^32 + 851520900736 * q^33 + 208184081768 * q^34 + 70719218750 * q^35 + 578919966368 * q^36 + 419480249934 * q^37 + 205247686480 * q^38 + 2390867460332 * q^39 - 1302712500000 * q^40 + 274005770306 * q^41 - 9314366945232 * q^42 + 2350065869158 * q^43 + 3324410490368 * q^44 - 3743088359375 * q^45 - 2445701814744 * q^46 - 8891070209486 * q^47 + 968269957888 * q^48 + 17603715811879 * q^49 + 24414062500 * q^50 + 11276036492236 * q^51 - 7757281361856 * q^52 + 8749242811318 * q^53 + 24761205955120 * q^54 - 9599645000000 * q^55 + 1555780658880 * q^56 - 41669191785640 * q^57 + 53844260003320 * q^58 - 14173516437140 * q^59 - 20278505000000 * q^60 - 38066837721794 * q^61 - 53610636798192 * q^62 - 97119517183302 * q^63 + 12081926129664 * q^64 + 7102462656250 * q^65 + 93794721354752 * q^66 + 144391638065474 * q^67 - 9729892224448 * q^68 - 83804251999188 * q^69 + 93392855625000 * q^70 - 126512337318844 * q^71 + 262100048315040 * q^72 + 199804772078038 * q^73 - 103551095018392 * q^74 + 21472167968750 * q^75 + 108919950456960 * q^76 - 24166822365312 * q^77 - 612963962524784 * q^78 - 73797562093720 * q^79 + 102689690000000 * q^80 - 252524358845777 * q^81 + 452714654584408 * q^82 - 219109046205402 * q^83 - 1299933721590912 * q^84 + 302263548906250 * q^85 - 630643429487864 * q^86 + 1207083364260740 * q^87 + 566411960125440 * q^88 - 360765737744610 * q^89 - 70732317812500 * q^90 + 2140337559198436 * q^91 - 88583572138176 * q^92 - 274593012441864 * q^93 + 1632141806127128 * q^94 - 286787829687500 * q^95 - 1457456297665024 * q^96 - 509209931654586 * q^97 + 411284837393972 * q^98 + 1279088372251712 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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