LMFDB - Embedded newform 5.16.a.b.1.1

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			1.1
Root			$11.3631$ 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)

$f(q)$	$=$	$q-152.575 q^{2} -6379.22 q^{3} -9488.76 q^{4} -78125.0 q^{5} +973313. q^{6} -1.77538e6 q^{7} +6.44734e6 q^{8} +2.63456e7 q^{9} +O(q^{10})$	\(q-152.575 q^{2} -6379.22 q^{3} -9488.76 q^{4} -78125.0 q^{5} +973313. q^{6} -1.77538e6 q^{7} +6.44734e6 q^{8} +2.63456e7 q^{9} +1.19200e7 q^{10} -1.92316e7 q^{11} +6.05309e7 q^{12} -2.80139e8 q^{13} +2.70880e8 q^{14} +4.98377e8 q^{15} -6.72778e8 q^{16} -2.72672e9 q^{17} -4.01969e9 q^{18} +5.71140e9 q^{19} +7.41309e8 q^{20} +1.13256e10 q^{21} +2.93427e9 q^{22} +1.90102e10 q^{23} -4.11290e10 q^{24} +6.10352e9 q^{25} +4.27424e10 q^{26} -7.65296e10 q^{27} +1.68462e10 q^{28} -3.06993e10 q^{29} -7.60400e10 q^{30} -5.40590e9 q^{31} -1.08617e11 q^{32} +1.22683e11 q^{33} +4.16030e11 q^{34} +1.38702e11 q^{35} -2.49987e11 q^{36} +1.75618e11 q^{37} -8.71419e11 q^{38} +1.78707e12 q^{39} -5.03698e11 q^{40} -3.78914e11 q^{41} -1.72800e12 q^{42} +2.50344e12 q^{43} +1.82484e11 q^{44} -2.05825e12 q^{45} -2.90048e12 q^{46} -5.58350e12 q^{47} +4.29180e12 q^{48} -1.59558e12 q^{49} -9.31246e11 q^{50} +1.73944e13 q^{51} +2.65818e12 q^{52} -6.97257e11 q^{53} +1.16765e13 q^{54} +1.50247e12 q^{55} -1.14465e13 q^{56} -3.64343e13 q^{57} +4.68396e12 q^{58} +1.01247e13 q^{59} -4.72898e12 q^{60} +4.63960e12 q^{61} +8.24807e11 q^{62} -4.67735e13 q^{63} +3.86179e13 q^{64} +2.18859e13 q^{65} -1.87184e13 q^{66} +3.14445e13 q^{67} +2.58732e13 q^{68} -1.21270e14 q^{69} -2.11625e13 q^{70} -5.42430e12 q^{71} +1.69859e14 q^{72} +1.79595e14 q^{73} -2.67950e13 q^{74} -3.89357e13 q^{75} -5.41941e13 q^{76} +3.41435e13 q^{77} -2.72663e14 q^{78} -1.08215e14 q^{79} +5.25608e13 q^{80} +1.10169e14 q^{81} +5.78129e13 q^{82} -1.53722e14 q^{83} -1.07466e14 q^{84} +2.13025e14 q^{85} -3.81964e14 q^{86} +1.95838e14 q^{87} -1.23993e14 q^{88} -1.41514e14 q^{89} +3.14038e14 q^{90} +4.97355e14 q^{91} -1.80383e14 q^{92} +3.44855e13 q^{93} +8.51904e14 q^{94} -4.46203e14 q^{95} +6.92893e14 q^{96} +2.50467e14 q^{97} +2.43445e14 q^{98} -5.06669e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−152.575	−0.842868	−0.421434	−	0.906859i	$-0.638473\pi$
$2$	−152.575	−0.842868	−0.421434	+	0.906859i	$0.638473\pi$
$3$	−6379.22	−1.68406	−0.842032	−	0.539428i	$-0.818641\pi$
$3$	−6379.22	−1.68406	−0.842032	+	0.539428i	$0.818641\pi$
$4$	−9488.76	−0.289574
$5$	−78125.0	−0.447214
$5$	−78125.0	−0.447214
$6$	973313.	1.41944
$7$	−1.77538e6	−0.814811	−0.407405	−	0.913247i	$-0.633566\pi$
$7$	−1.77538e6	−0.814811	−0.407405	+	0.913247i	$0.633566\pi$
$8$	6.44734e6	1.08694
$9$	2.63456e7	1.83607
$10$	1.19200e7	0.376942
$11$	−1.92316e7	−0.297557	−0.148779	−	0.988871i	$-0.547534\pi$
$11$	−1.92316e7	−0.297557	−0.148779	+	0.988871i	$0.547534\pi$
$12$	6.05309e7	0.487661
$13$	−2.80139e8	−1.23822	−0.619112	−	0.785303i	$-0.712507\pi$
$13$	−2.80139e8	−1.23822	−0.619112	+	0.785303i	$0.712507\pi$
$14$	2.70880e8	0.686778
$15$	4.98377e8	0.753136
$16$	−6.72778e8	−0.626573
$17$	−2.72672e9	−1.61166	−0.805830	−	0.592146i	$-0.798281\pi$
$17$	−2.72672e9	−1.61166	−0.805830	+	0.592146i	$0.798281\pi$
$18$	−4.01969e9	−1.54756
$19$	5.71140e9	1.46585	0.732927	−	0.680308i	$-0.238154\pi$
$19$	5.71140e9	1.46585	0.732927	+	0.680308i	$0.238154\pi$
$20$	7.41309e8	0.129501
$21$	1.13256e10	1.37219
$22$	2.93427e9	0.250802
$23$	1.90102e10	1.16420	0.582100	−	0.813118i	$-0.302231\pi$
$23$	1.90102e10	1.16420	0.582100	+	0.813118i	$0.302231\pi$
$24$	−4.11290e10	−1.83048
$25$	6.10352e9	0.200000
$26$	4.27424e10	1.04366
$27$	−7.65296e10	−1.40799
$28$	1.68462e10	0.235948
$29$	−3.06993e10	−0.330479	−0.165239	−	0.986253i	$-0.552840\pi$
$29$	−3.06993e10	−0.330479	−0.165239	+	0.986253i	$0.552840\pi$
$30$	−7.60400e10	−0.634794
$31$	−5.40590e9	−0.0352903	−0.0176452	−	0.999844i	$-0.505617\pi$
$31$	−5.40590e9	−0.0352903	−0.0176452	+	0.999844i	$0.505617\pi$
$32$	−1.08617e11	−0.558822
$33$	1.22683e11	0.501106
$34$	4.16030e11	1.35842
$35$	1.38702e11	0.364395
$36$	−2.49987e11	−0.531678
$37$	1.75618e11	0.304127	0.152064	−	0.988371i	$-0.451408\pi$
$37$	1.75618e11	0.304127	0.152064	+	0.988371i	$0.451408\pi$
$38$	−8.71419e11	−1.23552
$39$	1.78707e12	2.08525
$40$	−5.03698e11	−0.486094
$41$	−3.78914e11	−0.303852	−0.151926	−	0.988392i	$-0.548547\pi$
$41$	−3.78914e11	−0.303852	−0.151926	+	0.988392i	$0.548547\pi$
$42$	−1.72800e12	−1.15658
$43$	2.50344e12	1.40451	0.702254	−	0.711926i	$-0.252177\pi$
$43$	2.50344e12	1.40451	0.702254	+	0.711926i	$0.252177\pi$
$44$	1.82484e11	0.0861648
$45$	−2.05825e12	−0.821115
$46$	−2.90048e12	−0.981266
$47$	−5.58350e12	−1.60758	−0.803790	−	0.594913i	$-0.797186\pi$
$47$	−5.58350e12	−1.60758	−0.803790	+	0.594913i	$0.797186\pi$
$48$	4.29180e12	1.05519
$49$	−1.59558e12	−0.336083
$50$	−9.31246e11	−0.168574
$51$	1.73944e13	2.71414
$52$	2.65818e12	0.358557
$53$	−6.97257e11	−0.0815312	−0.0407656	−	0.999169i	$-0.512980\pi$
$53$	−6.97257e11	−0.0815312	−0.0407656	+	0.999169i	$0.512980\pi$
$54$	1.16765e13	1.18675
$55$	1.50247e12	0.133072
$56$	−1.14465e13	−0.885651
$57$	−3.64343e13	−2.46859
$58$	4.68396e12	0.278550
$59$	1.01247e13	0.529653	0.264826	−	0.964296i	$-0.414685\pi$
$59$	1.01247e13	0.529653	0.264826	+	0.964296i	$0.414685\pi$
$60$	−4.72898e12	−0.218089
$61$	4.63960e12	0.189019	0.0945097	−	0.995524i	$-0.469872\pi$
$61$	4.63960e12	0.189019	0.0945097	+	0.995524i	$0.469872\pi$
$62$	8.24807e11	0.0297451
$63$	−4.67735e13	−1.49605
$64$	3.86179e13	1.09759
$65$	2.18859e13	0.553751
$66$	−1.87184e13	−0.422366
$67$	3.14445e13	0.633846	0.316923	−	0.948451i	$-0.397350\pi$
$67$	3.14445e13	0.633846	0.316923	+	0.948451i	$0.397350\pi$
$68$	2.58732e13	0.466695
$69$	−1.21270e14	−1.96059
$70$	−2.11625e13	−0.307136
$71$	−5.42430e12	−0.0707793	−0.0353897	−	0.999374i	$-0.511267\pi$
$71$	−5.42430e12	−0.0707793	−0.0353897	+	0.999374i	$0.511267\pi$
$72$	1.69859e14	1.99570
$73$	1.79595e14	1.90271	0.951355	−	0.308096i	$-0.0996917\pi$
$73$	1.79595e14	1.90271	0.951355	+	0.308096i	$0.0996917\pi$
$74$	−2.67950e13	−0.256339
$75$	−3.89357e13	−0.336813
$76$	−5.41941e13	−0.424473
$77$	3.41435e13	0.242453
$78$	−2.72663e14	−1.75759
$79$	−1.08215e14	−0.633991	−0.316996	−	0.948427i	$-0.602674\pi$
$79$	−1.08215e14	−0.633991	−0.316996	+	0.948427i	$0.602674\pi$
$80$	5.25608e13	0.280212
$81$	1.10169e14	0.535083
$82$	5.78129e13	0.256107
$83$	−1.53722e14	−0.621799	−0.310900	−	0.950443i	$-0.600630\pi$
$83$	−1.53722e14	−0.621799	−0.310900	+	0.950443i	$0.600630\pi$
$84$	−1.07466e14	−0.397351
$85$	2.13025e14	0.720757
$86$	−3.81964e14	−1.18381
$87$	1.95838e14	0.556547
$88$	−1.23993e14	−0.323427
$89$	−1.41514e14	−0.339135	−0.169568	−	0.985519i	$-0.554237\pi$
$89$	−1.41514e14	−0.339135	−0.169568	+	0.985519i	$0.554237\pi$
$90$	3.14038e14	0.692092
$91$	4.97355e14	1.00892
$92$	−1.80383e14	−0.337122
$93$	3.44855e13	0.0594311
$94$	8.51904e14	1.35498
$95$	−4.46203e14	−0.655550
$96$	6.92893e14	0.941092
$97$	2.50467e14	0.314748	0.157374	−	0.987539i	$-0.449697\pi$
$97$	2.50467e14	0.314748	0.157374	+	0.987539i	$0.449697\pi$
$98$	2.43445e14	0.283274
$99$	−5.06669e14	−0.546336
$100$	−5.79148e13	−0.0579148
$101$	−7.99545e14	−0.742049	−0.371024	−	0.928623i	$-0.620993\pi$
$101$	−7.99545e14	−0.742049	−0.371024	+	0.928623i	$0.620993\pi$
$102$	−2.65395e15	−2.28766
$103$	9.82312e14	0.786992	0.393496	−	0.919326i	$-0.371265\pi$
$103$	9.82312e14	0.786992	0.393496	+	0.919326i	$0.371265\pi$
$104$	−1.80615e15	−1.34588
$105$	−8.84810e14	−0.613664
$106$	1.06384e14	0.0687200
$107$	2.09434e15	1.26087	0.630434	−	0.776243i	$-0.282877\pi$
$107$	2.09434e15	1.26087	0.630434	+	0.776243i	$0.282877\pi$
$108$	7.26171e14	0.407719
$109$	1.78299e15	0.934222	0.467111	−	0.884199i	$-0.345295\pi$
$109$	1.78299e15	0.934222	0.467111	+	0.884199i	$0.345295\pi$
$110$	−2.29240e14	−0.112162
$111$	−1.12031e15	−0.512170
$112$	1.19444e15	0.510539
$113$	−1.84008e14	−0.0735780	−0.0367890	−	0.999323i	$-0.511713\pi$
$113$	−1.84008e14	−0.0735780	−0.0367890	+	0.999323i	$0.511713\pi$
$114$	5.55898e15	2.08070
$115$	−1.48517e15	−0.520646
$116$	2.91298e14	0.0956981
$117$	−7.38044e15	−2.27347
$118$	−1.54478e15	−0.446427
$119$	4.84097e15	1.31320
$120$	3.21321e15	0.818614
$121$	−3.80739e15	−0.911460
$122$	−7.07888e14	−0.159318
$123$	2.41718e15	0.511706
$124$	5.12953e13	0.0102192
$125$	−4.76837e14	−0.0894427
$126$	7.13649e15	1.26097
$127$	2.91225e15	0.484955	0.242478	−	0.970157i	$-0.422040\pi$
$127$	2.91225e15	0.484955	0.242478	+	0.970157i	$0.422040\pi$
$128$	−2.33297e15	−0.366298
$129$	−1.59700e16	−2.36528
$130$	−3.33925e15	−0.466738
$131$	6.70705e15	0.885109	0.442554	−	0.896742i	$-0.354072\pi$
$131$	6.70705e15	0.885109	0.442554	+	0.896742i	$0.354072\pi$
$132$	−1.16411e15	−0.145107
$133$	−1.01399e16	−1.19439
$134$	−4.79765e15	−0.534248
$135$	5.97887e15	0.629675
$136$	−1.75801e16	−1.75178
$137$	9.82925e15	0.927077	0.463539	−	0.886077i	$-0.346579\pi$
$137$	9.82925e15	0.927077	0.463539	+	0.886077i	$0.346579\pi$
$138$	1.85028e16	1.65251
$139$	3.36972e14	0.0285091	0.0142545	−	0.999898i	$-0.495462\pi$
$139$	3.36972e14	0.0285091	0.0142545	+	0.999898i	$0.495462\pi$
$140$	−1.31611e15	−0.105519
$141$	3.56184e16	2.70727
$142$	8.27615e14	0.0596576
$143$	5.38754e15	0.368443
$144$	−1.77247e16	−1.15043
$145$	2.39838e15	0.147795
$146$	−2.74018e16	−1.60373
$147$	1.01785e16	0.565985
$148$	−1.66639e15	−0.0880674
$149$	2.15942e16	1.08503	0.542513	−	0.840048i	$-0.317473\pi$
$149$	2.15942e16	1.08503	0.542513	+	0.840048i	$0.317473\pi$
$150$	5.94063e15	0.283889
$151$	−1.62387e16	−0.738285	−0.369142	−	0.929373i	$-0.620348\pi$
$151$	−1.62387e16	−0.738285	−0.369142	+	0.929373i	$0.620348\pi$
$152$	3.68233e16	1.59329
$153$	−7.18371e16	−2.95912
$154$	−5.20946e15	−0.204356
$155$	4.22336e14	0.0157823
$156$	−1.69571e16	−0.603833
$157$	3.09113e15	0.104923	0.0524614	−	0.998623i	$-0.483293\pi$
$157$	3.09113e15	0.104923	0.0524614	+	0.998623i	$0.483293\pi$
$158$	1.65109e16	0.534371
$159$	4.44796e15	0.137304
$160$	8.48571e15	0.249913
$161$	−3.37503e16	−0.948602
$162$	−1.68091e16	−0.451004
$163$	6.77281e15	0.173525	0.0867624	−	0.996229i	$-0.472348\pi$
$163$	6.77281e15	0.173525	0.0867624	+	0.996229i	$0.472348\pi$
$164$	3.59542e15	0.0879875
$165$	−9.58460e15	−0.224101
$166$	2.34542e16	0.524094
$167$	−2.86471e16	−0.611939	−0.305969	−	0.952041i	$-0.598980\pi$
$167$	−2.86471e16	−0.611939	−0.305969	+	0.952041i	$0.598980\pi$
$168$	7.30198e16	1.49149
$169$	2.72922e16	0.533198
$170$	−3.25024e16	−0.607503
$171$	1.50470e17	2.69141
$172$	−2.37546e16	−0.406709
$173$	2.35612e16	0.386235	0.193118	−	0.981176i	$-0.438140\pi$
$173$	2.35612e16	0.386235	0.193118	+	0.981176i	$0.438140\pi$
$174$	−2.98800e16	−0.469096
$175$	−1.08361e16	−0.162962
$176$	1.29386e16	0.186441
$177$	−6.45876e16	−0.891969
$178$	2.15915e16	0.285846
$179$	−8.06231e16	−1.02344	−0.511719	−	0.859153i	$-0.670991\pi$
$179$	−8.06231e16	−1.02344	−0.511719	+	0.859153i	$0.670991\pi$
$180$	1.95302e16	0.237774
$181$	−1.35199e17	−1.57901	−0.789505	−	0.613744i	$-0.789663\pi$
$181$	−1.35199e17	−1.57901	−0.789505	+	0.613744i	$0.789663\pi$
$182$	−7.58841e16	−0.850385
$183$	−2.95970e16	−0.318321
$184$	1.22565e17	1.26541
$185$	−1.37201e16	−0.136010
$186$	−5.26163e15	−0.0500926
$187$	5.24392e16	0.479562
$188$	5.29805e16	0.465513
$189$	1.35869e17	1.14725
$190$	6.80796e16	0.552542
$191$	1.10510e17	0.862288	0.431144	−	0.902283i	$-0.358110\pi$
$191$	1.10510e17	0.862288	0.431144	+	0.902283i	$0.358110\pi$
$192$	−2.46352e17	−1.84840
$193$	−2.53257e17	−1.82760	−0.913800	−	0.406164i	$-0.866866\pi$
$193$	−2.53257e17	−1.82760	−0.913800	+	0.406164i	$0.866866\pi$
$194$	−3.82151e16	−0.265291
$195$	−1.39615e17	−0.932551
$196$	1.51400e16	0.0973209
$197$	8.37243e16	0.518030	0.259015	−	0.965873i	$-0.416602\pi$
$197$	8.37243e16	0.518030	0.259015	+	0.965873i	$0.416602\pi$
$198$	7.73051e16	0.460489
$199$	3.13095e17	1.79589	0.897943	−	0.440113i	$-0.145062\pi$
$199$	3.13095e17	1.79589	0.897943	+	0.440113i	$0.145062\pi$
$200$	3.93514e16	0.217388
$201$	−2.00591e17	−1.06744
$202$	1.21991e17	0.625449
$203$	5.45031e16	0.269278
$204$	−1.65051e17	−0.785944
$205$	2.96027e16	0.135887
$206$	−1.49877e17	−0.663330
$207$	5.00834e17	2.13755
$208$	1.88472e17	0.775838
$209$	−1.09839e17	−0.436175
$210$	1.35000e17	0.517237
$211$	2.30962e17	0.853929	0.426965	−	0.904268i	$-0.359583\pi$
$211$	2.30962e17	0.853929	0.426965	+	0.904268i	$0.359583\pi$
$212$	6.61610e15	0.0236093
$213$	3.46028e16	0.119197
$214$	−3.19545e17	−1.06274
$215$	−1.95581e17	−0.628115
$216$	−4.93412e17	−1.53041
$217$	9.59755e15	0.0287549
$218$	−2.72040e17	−0.787425
$219$	−1.14568e18	−3.20429
$220$	−1.42566e16	−0.0385341
$221$	7.63862e17	1.99560
$222$	1.70931e17	0.431692
$223$	−1.38177e17	−0.337404	−0.168702	−	0.985667i	$-0.553958\pi$
$223$	−1.38177e17	−0.337404	−0.168702	+	0.985667i	$0.553958\pi$
$224$	1.92837e17	0.455334
$225$	1.60801e17	0.367214
$226$	2.80751e16	0.0620166
$227$	−3.05757e17	−0.653405	−0.326703	−	0.945127i	$-0.605938\pi$
$227$	−3.05757e17	−0.653405	−0.326703	+	0.945127i	$0.605938\pi$
$228$	3.45716e17	0.714839
$229$	6.37765e17	1.27613	0.638065	−	0.769983i	$-0.279735\pi$
$229$	6.37765e17	1.27613	0.638065	+	0.769983i	$0.279735\pi$
$230$	2.26600e17	0.438835
$231$	−2.17809e17	−0.408306
$232$	−1.97929e17	−0.359211
$233$	−4.47532e17	−0.786420	−0.393210	−	0.919449i	$-0.628635\pi$
$233$	−4.47532e17	−0.786420	−0.393210	+	0.919449i	$0.628635\pi$
$234$	1.12607e18	1.91623
$235$	4.36211e17	0.718932
$236$	−9.60707e16	−0.153374
$237$	6.90326e17	1.06768
$238$	−7.38613e17	−1.10685
$239$	−1.09889e18	−1.59576	−0.797882	−	0.602814i	$-0.794046\pi$
$239$	−1.09889e18	−1.59576	−0.797882	+	0.602814i	$0.794046\pi$
$240$	−3.35297e17	−0.471895
$241$	5.16725e17	0.704906	0.352453	−	0.935829i	$-0.385348\pi$
$241$	5.16725e17	0.704906	0.352453	+	0.935829i	$0.385348\pi$
$242$	5.80914e17	0.768240
$243$	3.95324e17	0.506881
$244$	−4.40240e16	−0.0547351
$245$	1.24654e17	0.150301
$246$	−3.68802e17	−0.431300
$247$	−1.59999e18	−1.81505
$248$	−3.48537e16	−0.0383585
$249$	9.80627e17	1.04715
$250$	7.27536e16	0.0753884
$251$	1.64940e17	0.165872	0.0829358	−	0.996555i	$-0.473570\pi$
$251$	1.64940e17	0.165872	0.0829358	+	0.996555i	$0.473570\pi$
$252$	4.43823e17	0.433217
$253$	−3.65596e17	−0.346416
$254$	−4.44338e17	−0.408753
$255$	−1.35893e18	−1.21380
$256$	−9.09477e17	−0.788845
$257$	−1.52442e18	−1.28412	−0.642059	−	0.766655i	$-0.721920\pi$
$257$	−1.52442e18	−1.28412	−0.642059	+	0.766655i	$0.721920\pi$
$258$	2.43663e18	1.99362
$259$	−3.11789e17	−0.247806
$260$	−2.07670e17	−0.160352
$261$	−8.08792e17	−0.606782
$262$	−1.02333e18	−0.746030
$263$	1.92306e18	1.36246	0.681232	−	0.732068i	$-0.261444\pi$
$263$	1.92306e18	1.36246	0.681232	+	0.732068i	$0.261444\pi$
$264$	7.90978e17	0.544672
$265$	5.44732e16	0.0364618
$266$	1.54710e18	1.00672
$267$	9.02747e17	0.571125
$268$	−2.98369e17	−0.183545
$269$	2.50005e18	1.49557	0.747785	−	0.663941i	$-0.231117\pi$
$269$	2.50005e18	1.49557	0.747785	+	0.663941i	$0.231117\pi$
$270$	−9.12229e17	−0.530732
$271$	−5.29175e17	−0.299454	−0.149727	−	0.988727i	$-0.547839\pi$
$271$	−5.29175e17	−0.299454	−0.149727	+	0.988727i	$0.547839\pi$
$272$	1.83448e18	1.00982
$273$	−3.17274e18	−1.69908
$274$	−1.49970e18	−0.781404
$275$	−1.17380e17	−0.0595115
$276$	1.15070e18	0.567734
$277$	8.25807e17	0.396534	0.198267	−	0.980148i	$-0.436469\pi$
$277$	8.25807e17	0.396534	0.198267	+	0.980148i	$0.436469\pi$
$278$	−5.14137e16	−0.0240294
$279$	−1.42422e17	−0.0647955
$280$	8.94258e17	0.396075
$281$	7.90010e17	0.340671	0.170336	−	0.985386i	$-0.445515\pi$
$281$	7.90010e17	0.340671	0.170336	+	0.985386i	$0.445515\pi$
$282$	−5.43449e18	−2.28187
$283$	2.51021e18	1.02639	0.513195	−	0.858272i	$-0.328462\pi$
$283$	2.51021e18	1.02639	0.513195	+	0.858272i	$0.328462\pi$
$284$	5.14699e16	0.0204958
$285$	2.84643e18	1.10399
$286$	−8.22005e17	−0.310548
$287$	6.72718e17	0.247582
$288$	−2.86158e18	−1.02604
$289$	4.57258e18	1.59745
$290$	−3.65934e17	−0.124571
$291$	−1.59779e18	−0.530056
$292$	−1.70413e18	−0.550975
$293$	−2.43217e18	−0.766456	−0.383228	−	0.923654i	$-0.625188\pi$
$293$	−2.43217e18	−0.766456	−0.383228	+	0.923654i	$0.625188\pi$
$294$	−1.55299e18	−0.477051
$295$	−7.90991e17	−0.236868
$296$	1.13227e18	0.330568
$297$	1.47179e18	0.418959
$298$	−3.29474e18	−0.914533
$299$	−5.32550e18	−1.44154
$300$	3.69451e17	0.0975322
$301$	−4.44457e18	−1.14441
$302$	2.47762e18	0.622276
$303$	5.10048e18	1.24966
$304$	−3.84250e18	−0.918464
$305$	−3.62468e17	−0.0845321
$306$	1.09606e19	2.49415
$307$	5.22033e18	1.15920	0.579602	−	0.814900i	$-0.303208\pi$
$307$	5.22033e18	1.15920	0.579602	+	0.814900i	$0.303208\pi$
$308$	−3.23979e17	−0.0702081
$309$	−6.26639e18	−1.32534
$310$	−6.44381e16	−0.0133024
$311$	−1.83561e18	−0.369893	−0.184947	−	0.982749i	$-0.559211\pi$
$311$	−1.83561e18	−0.369893	−0.184947	+	0.982749i	$0.559211\pi$
$312$	1.15219e19	2.26654
$313$	1.03258e19	1.98308	0.991541	−	0.129795i	$-0.0414320\pi$
$313$	1.03258e19	1.98308	0.991541	+	0.129795i	$0.0414320\pi$
$314$	−4.71630e17	−0.0884360
$315$	3.65418e18	0.669054
$316$	1.02682e18	0.183587
$317$	−3.88933e18	−0.679095	−0.339548	−	0.940589i	$-0.610274\pi$
$317$	−3.88933e18	−0.679095	−0.339548	+	0.940589i	$0.610274\pi$
$318$	−6.78649e17	−0.115729
$319$	5.90398e17	0.0983364
$320$	−3.01702e18	−0.490855
$321$	−1.33603e19	−2.12338
$322$	5.14947e18	0.799546
$323$	−1.55734e19	−2.36246
$324$	−1.04537e18	−0.154946
$325$	−1.70984e18	−0.247645
$326$	−1.03336e18	−0.146258
$327$	−1.13741e19	−1.57329
$328$	−2.44299e18	−0.330269
$329$	9.91285e18	1.30987
$330$	1.46237e18	0.188888
$331$	5.74090e18	0.724887	0.362443	−	0.932006i	$-0.381943\pi$
$331$	5.74090e18	0.724887	0.362443	+	0.932006i	$0.381943\pi$
$332$	1.45863e18	0.180057
$333$	4.62676e18	0.558399
$334$	4.37085e18	0.515783
$335$	−2.45660e18	−0.283464
$336$	−7.61959e18	−0.859780
$337$	7.96430e18	0.878867	0.439433	−	0.898275i	$-0.355179\pi$
$337$	7.96430e18	0.878867	0.439433	+	0.898275i	$0.355179\pi$
$338$	−4.16412e18	−0.449416
$339$	1.17383e18	0.123910
$340$	−2.02134e18	−0.208712
$341$	1.03964e17	0.0105009
$342$	−2.29580e19	−2.26850
$343$	1.12615e19	1.08866
$344$	1.61405e19	1.52662
$345$	9.47423e18	0.876800
$346$	−3.59486e18	−0.325545
$347$	5.40771e18	0.479228	0.239614	−	0.970868i	$-0.422979\pi$
$347$	5.40771e18	0.479228	0.239614	+	0.970868i	$0.422979\pi$
$348$	−1.85826e18	−0.161162
$349$	−1.88921e19	−1.60358	−0.801790	−	0.597606i	$-0.796119\pi$
$349$	−1.88921e19	−1.60358	−0.801790	+	0.597606i	$0.796119\pi$
$350$	1.65332e18	0.137356
$351$	2.14390e19	1.74341
$352$	2.08888e18	0.166282
$353$	−9.30204e18	−0.724883	−0.362441	−	0.932007i	$-0.618057\pi$
$353$	−9.30204e18	−0.724883	−0.362441	+	0.932007i	$0.618057\pi$
$354$	9.85448e18	0.751812
$355$	4.23774e17	0.0316535
$356$	1.34279e18	0.0982047
$357$	−3.08817e19	−2.21151
$358$	1.23011e19	0.862623
$359$	5.37619e18	0.369204	0.184602	−	0.982813i	$-0.440900\pi$
$359$	5.37619e18	0.369204	0.184602	+	0.982813i	$0.440900\pi$
$360$	−1.32702e19	−0.892503
$361$	1.74390e19	1.14873
$362$	2.06281e19	1.33090
$363$	2.42882e19	1.53496
$364$	−4.71928e18	−0.292156
$365$	−1.40309e19	−0.850918
$366$	4.51578e18	0.268302
$367$	−3.22779e19	−1.87893	−0.939464	−	0.342646i	$-0.888677\pi$
$367$	−3.22779e19	−1.87893	−0.939464	+	0.342646i	$0.888677\pi$
$368$	−1.27896e19	−0.729456
$369$	−9.98271e18	−0.557893
$370$	2.09336e18	0.114638
$371$	1.23790e18	0.0664325
$372$	−3.27224e17	−0.0172097
$373$	1.61690e19	0.833425	0.416713	−	0.909038i	$-0.363182\pi$
$373$	1.61690e19	0.833425	0.416713	+	0.909038i	$0.363182\pi$
$374$	−8.00094e18	−0.404207
$375$	3.04185e18	0.150627
$376$	−3.59987e19	−1.74734
$377$	8.60009e18	0.409207
$378$	−2.07303e19	−0.966980
$379$	8.16512e18	0.373395	0.186697	−	0.982417i	$-0.440222\pi$
$379$	8.16512e18	0.373395	0.186697	+	0.982417i	$0.440222\pi$
$380$	4.23391e18	0.189830
$381$	−1.85779e19	−0.816695
$382$	−1.68611e19	−0.726795
$383$	1.24415e19	0.525873	0.262937	−	0.964813i	$-0.415309\pi$
$383$	1.24415e19	0.525873	0.262937	+	0.964813i	$0.415309\pi$
$384$	1.48825e19	0.616869
$385$	−2.66746e18	−0.108428
$386$	3.86407e19	1.54043
$387$	6.59547e19	2.57878
$388$	−2.37662e18	−0.0911428
$389$	−3.49556e18	−0.131490	−0.0657452	−	0.997836i	$-0.520942\pi$
$389$	−3.49556e18	−0.131490	−0.0657452	+	0.997836i	$0.520942\pi$
$390$	2.13018e19	0.786017
$391$	−5.18354e19	−1.87629
$392$	−1.02872e19	−0.365302
$393$	−4.27858e19	−1.49058
$394$	−1.27743e19	−0.436631
$395$	8.45427e18	0.283529
$396$	4.80765e18	0.158205
$397$	3.40726e19	1.10021	0.550106	−	0.835095i	$-0.314587\pi$
$397$	3.40726e19	1.10021	0.550106	+	0.835095i	$0.314587\pi$
$398$	−4.77706e19	−1.51369
$399$	6.46848e19	2.01143
$400$	−4.10631e18	−0.125315
$401$	2.58719e19	0.774898	0.387449	−	0.921891i	$-0.373356\pi$
$401$	2.58719e19	0.774898	0.387449	+	0.921891i	$0.373356\pi$
$402$	3.06053e19	0.899708
$403$	1.51441e18	0.0436973
$404$	7.58669e18	0.214878
$405$	−8.60694e18	−0.239296
$406$	−8.31582e18	−0.226966
$407$	−3.37741e18	−0.0904954
$408$	1.12147e20	2.95011
$409$	−6.63572e19	−1.71381	−0.856907	−	0.515472i	$-0.827617\pi$
$409$	−6.63572e19	−1.71381	−0.856907	+	0.515472i	$0.827617\pi$
$410$	−4.51664e18	−0.114534
$411$	−6.27030e19	−1.56126
$412$	−9.32092e18	−0.227892
$413$	−1.79752e19	−0.431567
$414$	−7.64150e19	−1.80167
$415$	1.20095e19	0.278077
$416$	3.04279e19	0.691947
$417$	−2.14962e18	−0.0480111
$418$	1.67588e19	0.367638
$419$	−4.44876e19	−0.958593	−0.479296	−	0.877653i	$-0.659108\pi$
$419$	−4.44876e19	−0.958593	−0.479296	+	0.877653i	$0.659108\pi$
$420$	8.39575e18	0.177701
$421$	7.76044e19	1.61351	0.806753	−	0.590889i	$-0.201223\pi$
$421$	7.76044e19	1.61351	0.806753	+	0.590889i	$0.201223\pi$
$422$	−3.52391e19	−0.719749
$423$	−1.47101e20	−2.95163
$424$	−4.49545e18	−0.0886195
$425$	−1.66426e19	−0.322332
$426$	−5.27954e18	−0.100467
$427$	−8.23706e18	−0.154015
$428$	−1.98727e19	−0.365114
$429$	−3.43683e19	−0.620481
$430$	2.98409e19	0.529418
$431$	6.49591e19	1.13256	0.566279	−	0.824214i	$-0.308383\pi$
$431$	6.49591e19	1.13256	0.566279	+	0.824214i	$0.308383\pi$
$432$	5.14874e19	0.882212
$433$	1.05280e20	1.77292	0.886459	−	0.462807i	$-0.153158\pi$
$433$	1.05280e20	1.77292	0.886459	+	0.462807i	$0.153158\pi$
$434$	−1.46435e18	−0.0242366
$435$	−1.52998e19	−0.248896
$436$	−1.69183e19	−0.270526
$437$	1.08575e20	1.70654
$438$	1.74802e20	2.70079
$439$	8.36657e19	1.27076	0.635380	−	0.772199i	$-0.280843\pi$
$439$	8.36657e19	1.27076	0.635380	+	0.772199i	$0.280843\pi$
$440$	9.68694e18	0.144641
$441$	−4.20364e19	−0.617072
$442$	−1.16547e20	−1.68202
$443$	−1.16185e20	−1.64862	−0.824309	−	0.566140i	$-0.808436\pi$
$443$	−1.16185e20	−1.64862	−0.824309	+	0.566140i	$0.808436\pi$
$444$	1.06303e19	0.148311
$445$	1.10557e19	0.151666
$446$	2.10825e19	0.284387
$447$	−1.37754e20	−1.82725
$448$	−6.85615e19	−0.894325
$449$	9.33272e19	1.19718	0.598591	−	0.801054i	$-0.295727\pi$
$449$	9.33272e19	1.19718	0.598591	+	0.801054i	$0.295727\pi$
$450$	−2.45342e19	−0.309513
$451$	7.28713e18	0.0904133
$452$	1.74601e18	0.0213063
$453$	1.03590e20	1.24332
$454$	4.66510e19	0.550734
$455$	−3.88559e19	−0.451202
$456$	−2.34904e20	−2.68321
$457$	−5.58697e19	−0.627777	−0.313888	−	0.949460i	$-0.601632\pi$
$457$	−5.58697e19	−0.627777	−0.313888	+	0.949460i	$0.601632\pi$
$458$	−9.73073e19	−1.07561
$459$	2.08675e20	2.26921
$460$	1.40924e19	0.150765
$461$	1.07509e20	1.13159	0.565794	−	0.824546i	$-0.308570\pi$
$461$	1.07509e20	1.13159	0.565794	+	0.824546i	$0.308570\pi$
$462$	3.32323e19	0.344148
$463$	−1.19309e20	−1.21567	−0.607834	−	0.794064i	$-0.707961\pi$
$463$	−1.19309e20	−1.21567	−0.607834	+	0.794064i	$0.707961\pi$
$464$	2.06538e19	0.207069
$465$	−2.69418e18	−0.0265784
$466$	6.82823e19	0.662848
$467$	−2.61708e19	−0.250001	−0.125000	−	0.992157i	$-0.539893\pi$
$467$	−2.61708e19	−0.250001	−0.125000	+	0.992157i	$0.539893\pi$
$468$	7.00312e19	0.658336
$469$	−5.58260e19	−0.516464
$470$	−6.65550e19	−0.605964
$471$	−1.97190e19	−0.176697
$472$	6.52773e19	0.575701
$473$	−4.81453e19	−0.417922
$474$	−1.05327e20	−0.899914
$475$	3.48596e19	0.293171
$476$	−4.59348e19	−0.380268
$477$	−1.83696e19	−0.149697
$478$	1.67663e20	1.34502
$479$	−2.01169e20	−1.58871	−0.794355	−	0.607453i	$-0.792191\pi$
$479$	−2.01169e20	−1.58871	−0.794355	+	0.607453i	$0.792191\pi$
$480$	−5.41323e19	−0.420869
$481$	−4.91975e19	−0.376578
$482$	−7.88395e19	−0.594143
$483$	2.15301e20	1.59751
$484$	3.61274e19	0.263935
$485$	−1.95678e19	−0.140760
$486$	−6.03167e19	−0.427234
$487$	1.08004e20	0.753306	0.376653	−	0.926354i	$-0.377075\pi$
$487$	1.08004e20	0.753306	0.376653	+	0.926354i	$0.377075\pi$
$488$	2.99131e19	0.205453
$489$	−4.32052e19	−0.292227
$490$	−1.90192e19	−0.126684
$491$	2.64208e20	1.73314	0.866572	−	0.499053i	$-0.166319\pi$
$491$	2.64208e20	1.73314	0.866572	+	0.499053i	$0.166319\pi$
$492$	−2.29360e19	−0.148177
$493$	8.37084e19	0.532620
$494$	2.44119e20	1.52985
$495$	3.95835e19	0.244329
$496$	3.63697e18	0.0221120
$497$	9.63022e18	0.0576718
$498$	−1.49619e20	−0.882608
$499$	7.30868e19	0.424702	0.212351	−	0.977193i	$-0.431888\pi$
$499$	7.30868e19	0.424702	0.212351	+	0.977193i	$0.431888\pi$
$500$	4.52459e18	0.0259003
$501$	1.82747e20	1.03054
$502$	−2.51657e19	−0.139808
$503$	−1.47007e20	−0.804597	−0.402298	−	0.915509i	$-0.631789\pi$
$503$	−1.47007e20	−0.804597	−0.402298	+	0.915509i	$0.631789\pi$
$504$	−3.01565e20	−1.62612
$505$	6.24644e19	0.331854
$506$	5.57810e19	0.291983
$507$	−1.74103e20	−0.897940
$508$	−2.76337e19	−0.140430
$509$	−2.51908e20	−1.26142	−0.630708	−	0.776020i	$-0.717235\pi$
$509$	−2.51908e20	−1.26142	−0.630708	+	0.776020i	$0.717235\pi$
$510$	2.07340e20	1.02307
$511$	−3.18850e20	−1.55035
$512$	2.15211e20	1.03119
$513$	−4.37091e20	−2.06391
$514$	2.32588e20	1.08234
$515$	−7.67432e19	−0.351954
$516$	1.51536e20	0.684924
$517$	1.07380e20	0.478347
$518$	4.75713e19	0.208868
$519$	−1.50302e20	−0.650444
$520$	1.41106e20	0.601894
$521$	−2.63260e20	−1.10688	−0.553441	−	0.832889i	$-0.686685\pi$
$521$	−2.63260e20	−1.10688	−0.553441	+	0.832889i	$0.686685\pi$
$522$	1.23402e20	0.511437
$523$	−1.15808e19	−0.0473126	−0.0236563	−	0.999720i	$-0.507531\pi$
$523$	−1.15808e19	−0.0473126	−0.0236563	+	0.999720i	$0.507531\pi$
$524$	−6.36415e19	−0.256304
$525$	6.91258e19	0.274439
$526$	−2.93412e20	−1.14838
$527$	1.47404e19	0.0568760
$528$	−8.25383e19	−0.313979
$529$	9.47513e19	0.355359
$530$	−8.31126e18	−0.0307325
$531$	2.66741e20	0.972480
$532$	9.62153e19	0.345865
$533$	1.06149e20	0.376236
$534$	−1.37737e20	−0.481383
$535$	−1.63621e20	−0.563877
$536$	2.02733e20	0.688952
$537$	5.14313e20	1.72354
$538$	−3.81446e20	−1.26057
$539$	3.06855e19	0.100004
$540$	−5.67321e19	−0.182337
$541$	−3.38984e20	−1.07448	−0.537242	−	0.843428i	$-0.680534\pi$
$541$	−3.38984e20	−1.07448	−0.537242	+	0.843428i	$0.680534\pi$
$542$	8.07391e19	0.252400
$543$	8.62466e20	2.65915
$544$	2.96169e20	0.900632
$545$	−1.39296e20	−0.417797
$546$	4.84082e20	1.43210
$547$	−1.40713e20	−0.410609	−0.205304	−	0.978698i	$-0.565818\pi$
$547$	−1.40713e20	−0.410609	−0.205304	+	0.978698i	$0.565818\pi$
$548$	−9.32673e19	−0.268457
$549$	1.22233e20	0.347053
$550$	1.79094e19	0.0501603
$551$	−1.75336e20	−0.484434
$552$	−7.81870e20	−2.13104
$553$	1.92123e20	0.516583
$554$	−1.25998e20	−0.334226
$555$	8.75239e19	0.229049
$556$	−3.19745e18	−0.00825548
$557$	5.58454e20	1.42257	0.711284	−	0.702904i	$-0.248114\pi$
$557$	5.58454e20	1.42257	0.711284	+	0.702904i	$0.248114\pi$
$558$	2.17300e19	0.0546140
$559$	−7.01313e20	−1.73910
$560$	−9.33155e19	−0.228320
$561$	−3.34522e20	−0.807612
$562$	−1.20536e20	−0.287141
$563$	5.80160e20	1.36375	0.681875	−	0.731469i	$-0.261165\pi$
$563$	5.80160e20	1.36375	0.681875	+	0.731469i	$0.261165\pi$
$564$	−3.37974e20	−0.783954
$565$	1.43756e19	0.0329051
$566$	−3.82997e20	−0.865111
$567$	−1.95592e20	−0.435992
$568$	−3.49723e19	−0.0769329
$569$	2.45839e20	0.533713	0.266857	−	0.963736i	$-0.414015\pi$
$569$	2.45839e20	0.533713	0.266857	+	0.963736i	$0.414015\pi$
$570$	−4.34295e20	−0.930515
$571$	−2.19147e20	−0.463409	−0.231704	−	0.972786i	$-0.574430\pi$
$571$	−2.19147e20	−0.463409	−0.231704	+	0.972786i	$0.574430\pi$
$572$	−5.11210e19	−0.106691
$573$	−7.04970e20	−1.45215
$574$	−1.02640e20	−0.208679
$575$	1.16029e20	0.232840
$576$	1.01741e21	2.01525
$577$	−6.00374e20	−1.17382	−0.586912	−	0.809650i	$-0.699657\pi$
$577$	−6.00374e20	−1.17382	−0.586912	+	0.809650i	$0.699657\pi$
$578$	−6.97663e20	−1.34644
$579$	1.61558e21	3.07780
$580$	−2.27577e19	−0.0427975
$581$	2.72915e20	0.506649
$582$	2.43783e20	0.446767
$583$	1.34094e19	0.0242602
$584$	1.15791e21	2.06813
$585$	5.76597e20	1.01672
$586$	3.71090e20	0.646021
$587$	−7.97376e20	−1.37050	−0.685248	−	0.728310i	$-0.740306\pi$
$587$	−7.97376e20	−1.37050	−0.685248	+	0.728310i	$0.740306\pi$
$588$	−9.65816e19	−0.163895
$589$	−3.08753e19	−0.0517304
$590$	1.20686e20	0.199648
$591$	−5.34096e20	−0.872395
$592$	−1.18152e20	−0.190558
$593$	2.71947e20	0.433086	0.216543	−	0.976273i	$-0.430522\pi$
$593$	2.71947e20	0.433086	0.216543	+	0.976273i	$0.430522\pi$
$594$	−2.24559e20	−0.353127
$595$	−3.78201e20	−0.587280
$596$	−2.04902e20	−0.314195
$597$	−1.99731e21	−3.02438
$598$	8.12540e20	1.21503
$599$	−2.75976e20	−0.407540	−0.203770	−	0.979019i	$-0.565319\pi$
$599$	−2.75976e20	−0.407540	−0.203770	+	0.979019i	$0.565319\pi$
$600$	−2.51032e20	−0.366095
$601$	6.55872e20	0.944627	0.472313	−	0.881431i	$-0.343419\pi$
$601$	6.55872e20	0.944627	0.472313	+	0.881431i	$0.343419\pi$
$602$	6.78132e20	0.964585
$603$	8.28424e20	1.16378
$604$	1.54085e20	0.213788
$605$	2.97453e20	0.407617
$606$	−7.78207e20	−1.05330
$607$	1.01588e21	1.35808	0.679040	−	0.734101i	$-0.262396\pi$
$607$	1.01588e21	1.35808	0.679040	+	0.734101i	$0.262396\pi$
$608$	−6.20356e20	−0.819151
$609$	−3.47687e20	−0.453481
$610$	5.53038e19	0.0712494
$611$	1.56416e21	1.99054
$612$	6.81644e20	0.856884
$613$	−1.00413e21	−1.24691	−0.623457	−	0.781857i	$-0.714272\pi$
$613$	−1.00413e21	−1.24691	−0.623457	+	0.781857i	$0.714272\pi$
$614$	−7.96494e20	−0.977056
$615$	−1.88842e20	−0.228842
$616$	2.20135e20	0.263532
$617$	5.42581e20	0.641691	0.320845	−	0.947132i	$-0.396033\pi$
$617$	5.42581e20	0.641691	0.320845	+	0.947132i	$0.396033\pi$
$618$	9.56097e20	1.11709
$619$	−5.11954e20	−0.590951	−0.295475	−	0.955350i	$-0.595478\pi$
$619$	−5.11954e20	−0.590951	−0.295475	+	0.955350i	$0.595478\pi$
$620$	−4.00744e18	−0.00457014
$621$	−1.45484e21	−1.63919
$622$	2.80068e20	0.311771
$623$	2.51241e20	0.276331
$624$	−1.20230e21	−1.30656
$625$	3.72529e19	0.0400000
$626$	−1.57546e21	−1.67148
$627$	7.00691e20	0.734547
$628$	−2.93310e19	−0.0303829
$629$	−4.78861e20	−0.490150
$630$	−5.57538e20	−0.563924
$631$	5.87018e20	0.586720	0.293360	−	0.956002i	$-0.405227\pi$
$631$	5.87018e20	0.586720	0.293360	+	0.956002i	$0.405227\pi$
$632$	−6.97697e20	−0.689110
$633$	−1.47336e21	−1.43807
$634$	5.93417e20	0.572388
$635$	−2.27520e20	−0.216878
$636$	−4.22056e19	−0.0397595
$637$	4.46984e20	0.416146
$638$	−9.00801e19	−0.0828846
$639$	−1.42906e20	−0.129956
$640$	1.82263e20	0.163813
$641$	−1.38747e21	−1.23250	−0.616251	−	0.787550i	$-0.711349\pi$
$641$	−1.38747e21	−1.23250	−0.616251	+	0.787550i	$0.711349\pi$
$642$	2.03845e21	1.78973
$643$	1.51156e21	1.31172	0.655862	−	0.754881i	$-0.272305\pi$
$643$	1.51156e21	1.31172	0.655862	+	0.754881i	$0.272305\pi$
$644$	3.20249e20	0.274690
$645$	1.24766e21	1.05779
$646$	2.37612e21	1.99124
$647$	−2.03681e21	−1.68721	−0.843605	−	0.536963i	$-0.819571\pi$
$647$	−2.03681e21	−1.68721	−0.843605	+	0.536963i	$0.819571\pi$
$648$	7.10296e20	0.581603
$649$	−1.94714e20	−0.157602
$650$	2.60879e20	0.208732
$651$	−6.12249e19	−0.0484251
$652$	−6.42655e19	−0.0502483
$653$	−1.74934e18	−0.00135215	−0.000676074	−	1.00000i	$-0.500215\pi$
$653$	−1.74934e18	−0.00135215	−0.000676074		1.00000i	$0.500215\pi$
$654$	1.73541e21	1.32607
$655$	−5.23988e20	−0.395833
$656$	2.54925e20	0.190385
$657$	4.73154e21	3.49351
$658$	−1.51246e21	−1.10405
$659$	2.70541e19	0.0195251	0.00976254	−	0.999952i	$-0.496892\pi$
$659$	2.70541e19	0.0195251	0.00976254	+	0.999952i	$0.496892\pi$
$660$	9.09459e19	0.0648939
$661$	−9.20381e20	−0.649317	−0.324658	−	0.945831i	$-0.605249\pi$
$661$	−9.20381e20	−0.649317	−0.324658	+	0.945831i	$0.605249\pi$
$662$	−8.75920e20	−0.610984
$663$	−4.87285e21	−3.36071
$664$	−9.91098e20	−0.675859
$665$	7.92182e20	0.534149
$666$	−7.05929e20	−0.470657
$667$	−5.83599e20	−0.384743
$668$	2.71826e20	0.177201
$669$	8.81465e20	0.568210
$670$	3.74817e20	0.238923
$671$	−8.92270e19	−0.0562441
$672$	−1.23015e21	−0.766812
$673$	2.16186e21	1.33264	0.666322	−	0.745664i	$-0.267868\pi$
$673$	2.16186e21	1.33264	0.666322	+	0.745664i	$0.267868\pi$
$674$	−1.21516e21	−0.740769
$675$	−4.67100e20	−0.281599
$676$	−2.58969e20	−0.154400
$677$	−8.23757e20	−0.485718	−0.242859	−	0.970062i	$-0.578085\pi$
$677$	−8.23757e20	−0.485718	−0.242859	+	0.970062i	$0.578085\pi$
$678$	−1.79097e20	−0.104440
$679$	−4.44676e20	−0.256460
$680$	1.37344e21	0.783419
$681$	1.95049e21	1.10038
$682$	−1.58624e19	−0.00885086
$683$	3.06571e21	1.69191	0.845953	−	0.533258i	$-0.179032\pi$
$683$	3.06571e21	1.69191	0.845953	+	0.533258i	$0.179032\pi$
$684$	−1.42778e21	−0.779362
$685$	−7.67910e20	−0.414602
$686$	−1.71823e21	−0.917592
$687$	−4.06845e21	−2.14908
$688$	−1.68426e21	−0.880027
$689$	1.95329e20	0.100954
$690$	−1.44553e21	−0.739027
$691$	1.48009e21	0.748518	0.374259	−	0.927324i	$-0.377897\pi$
$691$	1.48009e21	0.748518	0.374259	+	0.927324i	$0.377897\pi$
$692$	−2.23567e20	−0.111844
$693$	8.99531e20	0.445161
$694$	−8.25083e20	−0.403926
$695$	−2.63260e19	−0.0127496
$696$	1.26263e21	0.604934
$697$	1.03319e21	0.489706
$698$	2.88248e21	1.35161
$699$	2.85491e21	1.32438
$700$	1.02821e20	0.0471896
$701$	3.21111e21	1.45804	0.729021	−	0.684491i	$-0.239976\pi$
$701$	3.21111e21	1.45804	0.729021	+	0.684491i	$0.239976\pi$
$702$	−3.27106e21	−1.46947
$703$	1.00302e21	0.445806
$704$	−7.42684e20	−0.326595
$705$	−2.78269e21	−1.21073
$706$	1.41926e21	0.610980
$707$	1.41950e21	0.604630
$708$	6.12856e20	0.258291
$709$	−1.88743e21	−0.787088	−0.393544	−	0.919306i	$-0.628751\pi$
$709$	−1.88743e21	−0.787088	−0.393544	+	0.919306i	$0.628751\pi$
$710$	−6.46574e19	−0.0266797
$711$	−2.85098e21	−1.16405
$712$	−9.12386e20	−0.368620
$713$	−1.02767e20	−0.0410849
$714$	4.71178e21	1.86401
$715$	−4.20901e20	−0.164773
$716$	7.65013e20	0.296361
$717$	7.01004e21	2.68737
$718$	−8.20274e20	−0.311190
$719$	3.21535e21	1.20715	0.603575	−	0.797306i	$-0.293742\pi$
$719$	3.21535e21	1.20715	0.603575	+	0.797306i	$0.293742\pi$
$720$	1.38474e21	0.514489
$721$	−1.74398e21	−0.641250
$722$	−2.66075e21	−0.968224
$723$	−3.29630e21	−1.18711
$724$	1.28287e21	0.457240
$725$	−1.87374e20	−0.0660958
$726$	−3.70578e21	−1.29376
$727$	−3.25204e21	−1.12369	−0.561846	−	0.827242i	$-0.689909\pi$
$727$	−3.25204e21	−1.12369	−0.561846	+	0.827242i	$0.689909\pi$
$728$	3.20662e21	1.09663
$729$	−4.10266e21	−1.38870
$730$	2.14076e21	0.717211
$731$	−6.82619e21	−2.26359
$732$	2.80839e20	0.0921774
$733$	−4.86758e21	−1.58137	−0.790684	−	0.612225i	$-0.790275\pi$
$733$	−4.86758e21	−1.58137	−0.790684	+	0.612225i	$0.790275\pi$
$734$	4.92482e21	1.58369
$735$	−7.95198e20	−0.253116
$736$	−2.06483e21	−0.650580
$737$	−6.04728e20	−0.188605
$738$	1.52312e21	0.470230
$739$	1.77704e21	0.543079	0.271540	−	0.962427i	$-0.412467\pi$
$739$	1.77704e21	0.543079	0.271540	+	0.962427i	$0.412467\pi$
$740$	1.30187e20	0.0393849
$741$	1.02067e22	3.05667
$742$	−1.88873e20	−0.0559938
$743$	6.57112e20	0.192852	0.0964258	−	0.995340i	$-0.469259\pi$
$743$	6.57112e20	0.192852	0.0964258	+	0.995340i	$0.469259\pi$
$744$	2.22340e20	0.0645981
$745$	−1.68705e21	−0.485238
$746$	−2.46699e21	−0.702467
$747$	−4.04990e21	−1.14167
$748$	−4.97583e20	−0.138869
$749$	−3.71826e21	−1.02737
$750$	−4.64112e20	−0.126959
$751$	4.84975e21	1.31347	0.656735	−	0.754122i	$-0.271937\pi$
$751$	4.84975e21	1.31347	0.656735	+	0.754122i	$0.271937\pi$
$752$	3.75645e21	1.00727
$753$	−1.05219e21	−0.279338
$754$	−1.31216e21	−0.344907
$755$	1.26865e21	0.330171
$756$	−1.28923e21	−0.332214
$757$	1.09290e21	0.278843	0.139422	−	0.990233i	$-0.455476\pi$
$757$	1.09290e21	0.278843	0.139422	+	0.990233i	$0.455476\pi$
$758$	−1.24580e21	−0.314723
$759$	2.33222e21	0.583387
$760$	−2.87682e21	−0.712543
$761$	−6.24209e21	−1.53089	−0.765447	−	0.643499i	$-0.777482\pi$
$761$	−6.24209e21	−1.53089	−0.765447	+	0.643499i	$0.777482\pi$
$762$	2.83453e21	0.688366
$763$	−3.16549e21	−0.761214
$764$	−1.04861e21	−0.249696
$765$	5.61227e21	1.32336
$766$	−1.89826e21	−0.443242
$767$	−2.83632e21	−0.655829
$768$	5.80176e21	1.32847
$769$	−2.55765e21	−0.579955	−0.289977	−	0.957033i	$-0.593648\pi$
$769$	−2.55765e21	−0.579955	−0.289977	+	0.957033i	$0.593648\pi$
$770$	4.06989e20	0.0913907
$771$	9.72459e21	2.16254
$772$	2.40309e21	0.529225
$773$	2.88678e21	0.629603	0.314802	−	0.949157i	$-0.398062\pi$
$773$	2.88678e21	0.629603	0.314802	+	0.949157i	$0.398062\pi$
$774$	−1.00631e22	−2.17357
$775$	−3.29950e19	−0.00705806
$776$	1.61485e21	0.342112
$777$	1.98897e21	0.417322
$778$	5.33336e20	0.110829
$779$	−2.16413e21	−0.445402
$780$	1.32477e21	0.270042
$781$	1.04318e20	0.0210609
$782$	7.90881e21	1.58147
$783$	2.34941e21	0.465313
$784$	1.07347e21	0.210581
$785$	−2.41494e20	−0.0469229
$786$	6.52805e21	1.25636
$787$	8.82064e21	1.68147	0.840736	−	0.541445i	$-0.182123\pi$
$787$	8.82064e21	1.68147	0.840736	+	0.541445i	$0.182123\pi$
$788$	−7.94439e20	−0.150008
$789$	−1.22676e22	−2.29448
$790$	−1.28991e21	−0.238978
$791$	3.26685e20	0.0599522
$792$	−3.26666e21	−0.593835
$793$	−1.29973e21	−0.234048
$794$	−5.19864e21	−0.927334
$795$	−3.47497e20	−0.0614041
$796$	−2.97089e21	−0.520041
$797$	−4.69302e21	−0.813795	−0.406898	−	0.913474i	$-0.633389\pi$
$797$	−4.69302e21	−0.813795	−0.406898	+	0.913474i	$0.633389\pi$
$798$	−9.86931e21	−1.69537
$799$	1.52246e22	2.59087
$800$	−6.62946e20	−0.111764
$801$	−3.72826e21	−0.622676
$802$	−3.94741e21	−0.653137
$803$	−3.45390e21	−0.566166
$804$	1.90336e21	0.309102
$805$	2.63675e21	0.424228
$806$	−2.31061e20	−0.0368310
$807$	−1.59484e22	−2.51863
$808$	−5.15494e21	−0.806563
$809$	−3.07141e21	−0.476128	−0.238064	−	0.971249i	$-0.576513\pi$
$809$	−3.07141e21	−0.476128	−0.238064	+	0.971249i	$0.576513\pi$
$810$	1.31321e21	0.201695
$811$	−5.92007e21	−0.900888	−0.450444	−	0.892805i	$-0.648734\pi$
$811$	−5.92007e21	−0.900888	−0.450444	+	0.892805i	$0.648734\pi$
$812$	−5.17166e20	−0.0779758
$813$	3.37573e21	0.504299
$814$	5.15310e20	0.0762756
$815$	−5.29125e20	−0.0776027
$816$	−1.17025e22	−1.70061
$817$	1.42982e22	2.05880
$818$	1.01245e22	1.44452
$819$	1.31031e22	1.85244
$820$	−2.80892e20	−0.0393492
$821$	2.74036e21	0.380395	0.190197	−	0.981746i	$-0.439087\pi$
$821$	2.74036e21	0.380395	0.190197	+	0.981746i	$0.439087\pi$
$822$	9.56693e21	1.31593
$823$	−2.39952e21	−0.327059	−0.163529	−	0.986538i	$-0.552288\pi$
$823$	−2.39952e21	−0.327059	−0.163529	+	0.986538i	$0.552288\pi$
$824$	6.33330e21	0.855414
$825$	7.48797e20	0.100221
$826$	2.74257e21	0.363754
$827$	7.90681e21	1.03923	0.519613	−	0.854402i	$-0.326076\pi$
$827$	7.90681e21	1.03923	0.519613	+	0.854402i	$0.326076\pi$
$828$	−4.75229e21	−0.618979
$829$	1.05463e22	1.36125	0.680627	−	0.732630i	$-0.261707\pi$
$829$	1.05463e22	1.36125	0.680627	+	0.732630i	$0.261707\pi$
$830$	−1.83236e21	−0.234382
$831$	−5.26801e21	−0.667788
$832$	−1.08184e22	−1.35906
$833$	4.35069e21	0.541652
$834$	3.27979e20	0.0404670
$835$	2.23806e21	0.273667
$836$	1.04224e21	0.126305
$837$	4.13711e20	0.0496886
$838$	6.78772e21	0.807967
$839$	−7.09568e21	−0.837104	−0.418552	−	0.908193i	$-0.637462\pi$
$839$	−7.09568e21	−0.837104	−0.418552	+	0.908193i	$0.637462\pi$
$840$	−5.70467e21	−0.667016
$841$	−7.68674e21	−0.890784
$842$	−1.18405e22	−1.35997
$843$	−5.03965e21	−0.573712
$844$	−2.19154e21	−0.247276
$845$	−2.13221e21	−0.238453
$846$	2.24439e22	2.48783
$847$	6.75958e21	0.742667
$848$	4.69099e20	0.0510852
$849$	−1.60132e22	−1.72851
$850$	2.53925e21	0.271683
$851$	3.33852e21	0.354065
$852$	−3.28338e20	−0.0345163
$853$	3.95136e19	0.00411745	0.00205873	−	0.999998i	$-0.499345\pi$
$853$	3.95136e19	0.00411745	0.00205873	+	0.999998i	$0.499345\pi$
$854$	1.25677e21	0.129814
$855$	−1.17555e22	−1.20363
$856$	1.35029e22	1.37049
$857$	−4.90383e21	−0.493377	−0.246689	−	0.969095i	$-0.579342\pi$
$857$	−4.90383e21	−0.493377	−0.246689	+	0.969095i	$0.579342\pi$
$858$	5.24376e21	0.522983
$859$	7.26851e21	0.718616	0.359308	−	0.933219i	$-0.383013\pi$
$859$	7.26851e21	0.718616	0.359308	+	0.933219i	$0.383013\pi$
$860$	1.85583e21	0.181886
$861$	−4.29142e21	−0.416943
$862$	−9.91115e21	−0.954596
$863$	1.58838e22	1.51661	0.758304	−	0.651901i	$-0.226028\pi$
$863$	1.58838e22	1.51661	0.758304	+	0.651901i	$0.226028\pi$
$864$	8.31242e21	0.786819
$865$	−1.84072e21	−0.172730
$866$	−1.60632e22	−1.49434
$867$	−2.91695e22	−2.69021
$868$	−9.10688e19	−0.00832668
$869$	2.08114e21	0.188649
$870$	2.33438e21	0.209786
$871$	−8.80884e21	−0.784843
$872$	1.14955e22	1.01544
$873$	6.59871e21	0.577900
$874$	−1.65658e22	−1.43839
$875$	8.46569e20	0.0728789
$876$	1.08710e22	0.927877
$877$	−1.52887e22	−1.29382	−0.646909	−	0.762567i	$-0.723939\pi$
$877$	−1.52887e22	−1.29382	−0.646909	+	0.762567i	$0.723939\pi$
$878$	−1.27653e22	−1.07108
$879$	1.55154e22	1.29076
$880$	−1.01083e21	−0.0833792
$881$	−2.32377e21	−0.190052	−0.0950262	−	0.995475i	$-0.530293\pi$
$881$	−2.32377e21	−0.190052	−0.0950262	+	0.995475i	$0.530293\pi$
$882$	6.41372e21	0.520110
$883$	1.26708e22	1.01882	0.509411	−	0.860524i	$-0.329863\pi$
$883$	1.26708e22	1.01882	0.509411	+	0.860524i	$0.329863\pi$
$884$	−7.24810e21	−0.577873
$885$	5.04591e21	0.398901
$886$	1.77269e22	1.38957
$887$	−8.27482e20	−0.0643179	−0.0321589	−	0.999483i	$-0.510238\pi$
$887$	−8.27482e20	−0.0643179	−0.0321589	+	0.999483i	$0.510238\pi$
$888$	−7.22299e21	−0.556698
$889$	−5.17037e21	−0.395147
$890$	−1.68683e21	−0.127834
$891$	−2.11873e21	−0.159218
$892$	1.31113e21	0.0977035
$893$	−3.18896e22	−2.35648
$894$	2.10179e22	1.54013
$895$	6.29868e21	0.457696
$896$	4.14192e21	0.298464
$897$	3.39726e22	2.42764
$898$	−1.42394e22	−1.00907
$899$	1.65957e20	0.0116627
$900$	−1.52580e21	−0.106336
$901$	1.90122e21	0.131401
$902$	−1.11184e21	−0.0762065
$903$	2.83529e22	1.92726
$904$	−1.18636e21	−0.0799749
$905$	1.05624e22	0.706155
$906$	−1.58053e22	−1.04795
$907$	−8.89980e21	−0.585229	−0.292614	−	0.956231i	$-0.594525\pi$
$907$	−8.89980e21	−0.585229	−0.292614	+	0.956231i	$0.594525\pi$
$908$	2.90125e21	0.189209
$909$	−2.10645e22	−1.36245
$910$	5.92845e21	0.380304
$911$	1.24256e22	0.790553	0.395276	−	0.918562i	$-0.370649\pi$
$911$	1.24256e22	0.790553	0.395276	+	0.918562i	$0.370649\pi$
$912$	2.45122e22	1.54675
$913$	2.95632e21	0.185021
$914$	8.52435e21	0.529133
$915$	2.31227e21	0.142357
$916$	−6.05160e21	−0.369534
$917$	−1.19076e22	−0.721196
$918$	−3.18386e22	−1.91264
$919$	−1.08612e21	−0.0647157	−0.0323578	−	0.999476i	$-0.510302\pi$
$919$	−1.08612e21	−0.0647157	−0.0323578	+	0.999476i	$0.510302\pi$
$920$	−9.57539e21	−0.565911
$921$	−3.33016e22	−1.95217
$922$	−1.64033e22	−0.953780
$923$	1.51956e21	0.0876406
$924$	2.06674e21	0.118235
$925$	1.07189e21	0.0608255
$926$	1.82036e22	1.02465
$927$	2.58796e22	1.44497
$928$	3.33447e21	0.184679
$929$	2.81840e22	1.54841	0.774203	−	0.632938i	$-0.218151\pi$
$929$	2.81840e22	1.54841	0.774203	+	0.632938i	$0.218151\pi$
$930$	4.11065e20	0.0224021
$931$	−9.11297e21	−0.492648
$932$	4.24652e21	0.227727
$933$	1.17097e22	0.622924
$934$	3.99303e21	0.210717
$935$	−4.09682e21	−0.214466
$936$	−4.75842e22	−2.47112
$937$	2.89583e22	1.49185	0.745927	−	0.666028i	$-0.232007\pi$
$937$	2.89583e22	1.49185	0.745927	+	0.666028i	$0.232007\pi$
$938$	8.51768e21	0.435311
$939$	−6.58705e22	−3.33964
$940$	−4.13910e21	−0.208184
$941$	3.43007e22	1.71152	0.855758	−	0.517377i	$-0.173091\pi$
$941$	3.43007e22	1.71152	0.855758	+	0.517377i	$0.173091\pi$
$942$	3.00864e21	0.148932
$943$	−7.20322e21	−0.353744
$944$	−6.81166e21	−0.331866
$945$	−1.06148e22	−0.513066
$946$	7.34578e21	0.352253
$947$	−1.30591e22	−0.621282	−0.310641	−	0.950527i	$-0.600544\pi$
$947$	−1.30591e22	−0.621282	−0.310641	+	0.950527i	$0.600544\pi$
$948$	−6.55033e21	−0.309173
$949$	−5.03116e22	−2.35598
$950$	−5.31872e21	−0.247104
$951$	2.48109e22	1.14364
$952$	3.12114e22	1.42737
$953$	−2.43409e22	−1.10443	−0.552217	−	0.833700i	$-0.686218\pi$
$953$	−2.43409e22	−1.10443	−0.552217	+	0.833700i	$0.686218\pi$
$954$	2.80275e21	0.126175
$955$	−8.63361e21	−0.385627
$956$	1.04271e22	0.462091
$957$	−3.76628e21	−0.165605
$958$	3.06934e22	1.33907
$959$	−1.74507e22	−0.755393
$960$	1.92463e22	0.826632
$961$	−2.34360e22	−0.998755
$962$	7.50632e21	0.317405
$963$	5.51767e22	2.31504
$964$	−4.90307e21	−0.204122
$965$	1.97857e22	0.817328
$966$	−3.28496e22	−1.34649
$967$	−1.92293e22	−0.782105	−0.391053	−	0.920368i	$-0.627889\pi$
$967$	−1.92293e22	−0.782105	−0.391053	+	0.920368i	$0.627889\pi$
$968$	−2.45476e22	−0.990702
$969$	9.93461e22	3.97853
$970$	2.98556e21	0.118642
$971$	3.35657e22	1.32359	0.661793	−	0.749687i	$-0.269796\pi$
$971$	3.35657e22	1.32359	0.661793	+	0.749687i	$0.269796\pi$
$972$	−3.75113e21	−0.146780
$973$	−5.98255e20	−0.0232295
$974$	−1.64787e22	−0.634937
$975$	1.09074e22	0.417050
$976$	−3.12142e21	−0.118434
$977$	3.13279e22	1.17957	0.589783	−	0.807562i	$-0.299213\pi$
$977$	3.13279e22	1.17957	0.589783	+	0.807562i	$0.299213\pi$
$978$	6.59206e21	0.246309
$979$	2.72154e21	0.100912
$980$	−1.18281e21	−0.0435232
$981$	4.69739e22	1.71530
$982$	−4.03116e22	−1.46081
$983$	−4.17174e22	−1.50026	−0.750129	−	0.661291i	$-0.770009\pi$
$983$	−4.17174e22	−1.50026	−0.750129	+	0.661291i	$0.770009\pi$
$984$	1.55844e22	0.556193
$985$	−6.54096e21	−0.231670
$986$	−1.27718e22	−0.448928
$987$	−6.32363e22	−2.20591
$988$	1.51819e22	0.525592
$989$	4.75909e22	1.63513
$990$	−6.03946e21	−0.205937
$991$	−2.20929e21	−0.0747654	−0.0373827	−	0.999301i	$-0.511902\pi$
$991$	−2.20929e21	−0.0747654	−0.0373827	+	0.999301i	$0.511902\pi$
$992$	5.87174e20	0.0197210
$993$	−3.66225e22	−1.22076
$994$	−1.46933e21	−0.0486097
$995$	−2.44606e22	−0.803144
$996$	−9.30493e21	−0.303227
$997$	−3.00907e22	−0.973236	−0.486618	−	0.873615i	$-0.661770\pi$
$997$	−3.00907e22	−0.973236	−0.486618	+	0.873615i	$0.661770\pi$
$998$	−1.11512e22	−0.357968
$999$	−1.34400e22	−0.428210

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.16.a.b.1.1	✓	3
3.2	odd	2		45.16.a.f.1.3		3
4.3	odd	2		80.16.a.g.1.3		3
5.2	odd	4		25.16.b.c.24.2		6
5.3	odd	4		25.16.b.c.24.5		6
5.4	even	2		25.16.a.c.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.16.a.b.1.1	✓	3	1.1	even	1	trivial
25.16.a.c.1.3		3	5.4	even	2
25.16.b.c.24.2		6	5.2	odd	4
25.16.b.c.24.5		6	5.3	odd	4
45.16.a.f.1.3		3	3.2	odd	2
80.16.a.g.1.3		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)

\(f(q)\)	\(=\)	\(q-152.575 q^{2} -6379.22 q^{3} -9488.76 q^{4} -78125.0 q^{5} +973313. q^{6} -1.77538e6 q^{7} +6.44734e6 q^{8} +2.63456e7 q^{9} +O(q^{10})\)	\(q-152.575 q^{2} -6379.22 q^{3} -9488.76 q^{4} -78125.0 q^{5} +973313. q^{6} -1.77538e6 q^{7} +6.44734e6 q^{8} +2.63456e7 q^{9} +1.19200e7 q^{10} -1.92316e7 q^{11} +6.05309e7 q^{12} -2.80139e8 q^{13} +2.70880e8 q^{14} +4.98377e8 q^{15} -6.72778e8 q^{16} -2.72672e9 q^{17} -4.01969e9 q^{18} +5.71140e9 q^{19} +7.41309e8 q^{20} +1.13256e10 q^{21} +2.93427e9 q^{22} +1.90102e10 q^{23} -4.11290e10 q^{24} +6.10352e9 q^{25} +4.27424e10 q^{26} -7.65296e10 q^{27} +1.68462e10 q^{28} -3.06993e10 q^{29} -7.60400e10 q^{30} -5.40590e9 q^{31} -1.08617e11 q^{32} +1.22683e11 q^{33} +4.16030e11 q^{34} +1.38702e11 q^{35} -2.49987e11 q^{36} +1.75618e11 q^{37} -8.71419e11 q^{38} +1.78707e12 q^{39} -5.03698e11 q^{40} -3.78914e11 q^{41} -1.72800e12 q^{42} +2.50344e12 q^{43} +1.82484e11 q^{44} -2.05825e12 q^{45} -2.90048e12 q^{46} -5.58350e12 q^{47} +4.29180e12 q^{48} -1.59558e12 q^{49} -9.31246e11 q^{50} +1.73944e13 q^{51} +2.65818e12 q^{52} -6.97257e11 q^{53} +1.16765e13 q^{54} +1.50247e12 q^{55} -1.14465e13 q^{56} -3.64343e13 q^{57} +4.68396e12 q^{58} +1.01247e13 q^{59} -4.72898e12 q^{60} +4.63960e12 q^{61} +8.24807e11 q^{62} -4.67735e13 q^{63} +3.86179e13 q^{64} +2.18859e13 q^{65} -1.87184e13 q^{66} +3.14445e13 q^{67} +2.58732e13 q^{68} -1.21270e14 q^{69} -2.11625e13 q^{70} -5.42430e12 q^{71} +1.69859e14 q^{72} +1.79595e14 q^{73} -2.67950e13 q^{74} -3.89357e13 q^{75} -5.41941e13 q^{76} +3.41435e13 q^{77} -2.72663e14 q^{78} -1.08215e14 q^{79} +5.25608e13 q^{80} +1.10169e14 q^{81} +5.78129e13 q^{82} -1.53722e14 q^{83} -1.07466e14 q^{84} +2.13025e14 q^{85} -3.81964e14 q^{86} +1.95838e14 q^{87} -1.23993e14 q^{88} -1.41514e14 q^{89} +3.14038e14 q^{90} +4.97355e14 q^{91} -1.80383e14 q^{92} +3.44855e13 q^{93} +8.51904e14 q^{94} -4.46203e14 q^{95} +6.92893e14 q^{96} +2.50467e14 q^{97} +2.43445e14 q^{98} -5.06669e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 4 q^{2} + 3518 q^{3} + 20384 q^{4} - 234375 q^{5} + 2075176 q^{6} - 905206 q^{7} + 16674720 q^{8} + 47911531 q^{9}+O(q^{10}) \) 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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