LMFDB - Embedded newform 10.34.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,34,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 34, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 34 $
Character orbit:	$[\chi]$	$=$	10.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:	$68.9828288810$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3937184160 $ x^2 - x - 3937184160
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-62746.5$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+65536.0 q^{2} -3.44083e6 q^{3} +4.29497e9 q^{4} +1.52588e11 q^{5} -2.25498e11 q^{6} +9.65954e13 q^{7} +2.81475e14 q^{8} -5.54722e15 q^{9} +1.00000e16 q^{10} -1.25630e17 q^{11} -1.47783e16 q^{12} -3.83776e18 q^{13} +6.33048e18 q^{14} -5.25030e17 q^{15} +1.84467e19 q^{16} -1.12561e19 q^{17} -3.63543e20 q^{18} -1.21644e21 q^{19} +6.55360e20 q^{20} -3.32369e20 q^{21} -8.23330e21 q^{22} +3.30661e22 q^{23} -9.68509e20 q^{24} +2.32831e22 q^{25} -2.51511e23 q^{26} +3.82149e22 q^{27} +4.14874e23 q^{28} +5.37492e23 q^{29} -3.44083e22 q^{30} -4.22167e24 q^{31} +1.20893e24 q^{32} +4.32273e23 q^{33} -7.37680e23 q^{34} +1.47393e25 q^{35} -2.38251e25 q^{36} -1.37889e26 q^{37} -7.97206e25 q^{38} +1.32051e25 q^{39} +4.29497e25 q^{40} +4.39352e26 q^{41} -2.17821e25 q^{42} -1.20456e27 q^{43} -5.39577e26 q^{44} -8.46439e26 q^{45} +2.16702e27 q^{46} -3.56629e27 q^{47} -6.34722e25 q^{48} +1.59968e27 q^{49} +1.52588e27 q^{50} +3.87304e25 q^{51} -1.64830e28 q^{52} +3.20094e28 q^{53} +2.50445e27 q^{54} -1.91696e28 q^{55} +2.71892e28 q^{56} +4.18557e27 q^{57} +3.52251e28 q^{58} +2.08570e29 q^{59} -2.25498e27 q^{60} -1.84408e29 q^{61} -2.76671e29 q^{62} -5.35836e29 q^{63} +7.92282e28 q^{64} -5.85595e29 q^{65} +2.83294e28 q^{66} -3.61772e29 q^{67} -4.83446e28 q^{68} -1.13775e29 q^{69} +9.65954e29 q^{70} -5.64849e30 q^{71} -1.56140e30 q^{72} -6.52836e29 q^{73} -9.03671e30 q^{74} -8.01132e28 q^{75} -5.22457e30 q^{76} -1.21353e31 q^{77} +8.65408e29 q^{78} -2.61534e31 q^{79} +2.81475e30 q^{80} +3.07058e31 q^{81} +2.87934e31 q^{82} -7.88667e31 q^{83} -1.42751e30 q^{84} -1.71755e30 q^{85} -7.89424e31 q^{86} -1.84942e30 q^{87} -3.53617e31 q^{88} +6.51043e31 q^{89} -5.54722e31 q^{90} -3.70710e32 q^{91} +1.42018e32 q^{92} +1.45261e31 q^{93} -2.33721e32 q^{94} -1.85614e32 q^{95} -4.15971e30 q^{96} -7.62730e32 q^{97} +1.04837e32 q^{98} +6.96898e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 131072 q^{2} - 74648412 q^{3} + 8589934592 q^{4} + 305175781250 q^{5} - 4892158328832 q^{6} + 20327789415556 q^{7} + 562949953421312 q^{8} - 60\!\cdots\!74 q^{9} + 20\!\cdots\!00 q^{10} - 11\!\cdots\!76 q^{11}+ \cdots + 64\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q + 131072 * q^2 - 74648412 * q^3 + 8589934592 * q^4 + 305175781250 * q^5 - 4892158328832 * q^6 + 20327789415556 * q^7 + 562949953421312 * q^8 - 6035762623792374 * q^9 + 20000000000000000 * q^10 - 11282427183095376 * q^11 - 320612488238333952 * q^12 + 80760781784046988 * q^13 + 1332202007137878016 * q^14 - 11390443725585937500 * q^15 + 36893488147419103232 * q^16 - 205963221786194409324 * q^17 - 395559739312857022464 * q^18 - 2435166480698605800200 * q^19 + 1310720000000000000000 * q^20 + 5098464356293085660064 * q^21 - 739405147871338561536 * q^22 + 29028845471264700782748 * q^23 - 21011660029187453878272 * q^24 + 46566128730773925781250 * q^25 + 5292738594999303405568 * q^26 + 468849960215466385570920 * q^27 + 87307190739787973656576 * q^28 + 669911834369977099655580 * q^29 - 746484120000000000000000 * q^30 + 337264281536360263914904 * q^31 + 2417851639229258349412352 * q^32 - 7710152394128777821944144 * q^33 - 13498005702980036809457664 * q^34 + 3101774507988891601562500 * q^35 - 25923403075607397824200704 * q^36 - 184139192244080353693197524 * q^37 - 159591070479063829721907200 * q^38 - 265823042069990418214193928 * q^39 + 85899345920000000000000000 * q^40 + 14298843461054952714348324 * q^41 + 334132960054023661817954304 * q^42 - 608685062932886434615318652 * q^43 - 48457655770896043968823296 * q^44 - 920984287077693786621093750 * q^45 + 1902434416804803430498172928 * q^46 - 6646835622774856917274050444 * q^47 - 1377020151672828977366433792 * q^48 - 314561308595229853488986046 * q^49 + 3051757812500000000000000000 * q^50 + 13903352393449636924474059144 * q^51 + 346864916561874347987304448 * q^52 - 23551888524780401802822701892 * q^53 + 30726550992680805044775813120 * q^54 - 1721561764998684082031250000 * q^55 + 5721764052322744641557364736 * q^56 + 90968097453666874117923963600 * q^57 + 43903341977270819203028090880 * q^58 + 22604203336846958159402367960 * q^59 - 48921583288320000000000000000 * q^60 - 339703294897757897934093836996 * q^61 + 22102951954766906255927148544 * q^62 - 498576262245539929538020028172 * q^63 + 158456325028528675187087900672 * q^64 + 12323117337653654174804687500 * q^65 - 505292547301623583338931421184 * q^66 - 2526076586974742197515421878164 * q^67 - 884605301750499692344617467904 * q^68 + 173707302971204205114453695712 * q^69 + 203277894155560000000000000000 * q^70 - 8757591773294778824971571836536 * q^71 - 1698916143963006423806817337344 * q^72 - 8032530857221267753332158819132 * q^73 - 12067746102908050059637392932864 * q^74 - 1738043781369924545288085937500 * q^75 - 10458960394915927144654910259200 * q^76 - 20856327865334287425485502151728 * q^77 - 17420978885098892048085413265408 * q^78 - 19259566961569543032032618239280 * q^79 + 5629499534213120000000000000000 * q^80 + 2757197276039678745749615255682 * q^81 + 937089005063697381087531761664 * q^82 - 27953508025018595447820979950492 * q^83 + 21897737670100494700901453266944 * q^84 - 31427493558684449664916992187500 * q^85 - 39890784284369645378949523177472 * q^86 - 11278711205229412420659895252680 * q^87 - 3175720928601443137540803526656 * q^88 - 151408466968396001182516810504620 * q^89 - 60357626237923740000000000000000 * q^90 - 669565717488479778480411355776136 * q^91 + 124677941939719597621128261009408 * q^92 - 310104499419190165213555069751424 * q^93 - 435607019374173022930472169897984 * q^94 - 371576916610505035430908203125000 * q^95 - 90244392660030519860686604992512 * q^96 - 616001214102537194391941400541484 * q^97 - 20615089920096983678254189510656 * q^98 + 641034674983890137043915947758512 * q^99

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 $

$2$	65536.0	0.707107
$2$	65536.0	0.707107
$3$	−3.44083e6	−0.0461491	−0.0230745	−	0.999734i	$-0.507346\pi$
$3$	−3.44083e6	−0.0461491	−0.0230745	+	0.999734i	$0.507346\pi$
$4$	4.29497e9	0.500000
$5$	1.52588e11	0.447214
$5$	1.52588e11	0.447214
$6$	−2.25498e11	−0.0326323
$7$	9.65954e13	1.09860	0.549299	−	0.835626i	$-0.314895\pi$
$7$	9.65954e13	1.09860	0.549299	+	0.835626i	$0.314895\pi$
$8$	2.81475e14	0.353553
$9$	−5.54722e15	−0.997870
$10$	1.00000e16	0.316228
$11$	−1.25630e17	−0.824356	−0.412178	−	0.911103i	$-0.635232\pi$
$11$	−1.25630e17	−0.824356	−0.412178	+	0.911103i	$0.635232\pi$
$12$	−1.47783e16	−0.0230745
$13$	−3.83776e18	−1.59960	−0.799801	−	0.600265i	$-0.795062\pi$
$13$	−3.83776e18	−1.59960	−0.799801	+	0.600265i	$0.795062\pi$
$14$	6.33048e18	0.776826
$15$	−5.25030e17	−0.0206385
$16$	1.84467e19	0.250000
$17$	−1.12561e19	−0.0561023	−0.0280512	−	0.999606i	$-0.508930\pi$
$17$	−1.12561e19	−0.0561023	−0.0280512	+	0.999606i	$0.508930\pi$
$18$	−3.63543e20	−0.705601
$19$	−1.21644e21	−0.967512	−0.483756	−	0.875203i	$-0.660728\pi$
$19$	−1.21644e21	−0.967512	−0.483756	+	0.875203i	$0.660728\pi$
$20$	6.55360e20	0.223607
$21$	−3.32369e20	−0.0506993
$22$	−8.23330e21	−0.582907
$23$	3.30661e22	1.12428	0.562139	−	0.827043i	$-0.309979\pi$
$23$	3.30661e22	1.12428	0.562139	+	0.827043i	$0.309979\pi$
$24$	−9.68509e20	−0.0163162
$25$	2.32831e22	0.200000
$26$	−2.51511e23	−1.13109
$27$	3.82149e22	0.0921999
$28$	4.14874e23	0.549299
$29$	5.37492e23	0.398846	0.199423	−	0.979914i	$-0.436093\pi$
$29$	5.37492e23	0.398846	0.199423	+	0.979914i	$0.436093\pi$
$30$	−3.44083e22	−0.0145936
$31$	−4.22167e24	−1.04236	−0.521178	−	0.853448i	$-0.674507\pi$
$31$	−4.22167e24	−1.04236	−0.521178	+	0.853448i	$0.674507\pi$
$32$	1.20893e24	0.176777
$33$	4.32273e23	0.0380432
$34$	−7.37680e23	−0.0396704
$35$	1.47393e25	0.491308
$36$	−2.38251e25	−0.498935
$37$	−1.37889e26	−1.83739	−0.918696	−	0.394966i	$-0.870756\pi$
$37$	−1.37889e26	−1.83739	−0.918696	+	0.394966i	$0.870756\pi$
$38$	−7.97206e25	−0.684134
$39$	1.32051e25	0.0738202
$40$	4.29497e25	0.158114
$41$	4.39352e26	1.07617	0.538083	−	0.842892i	$-0.319149\pi$
$41$	4.39352e26	1.07617	0.538083	+	0.842892i	$0.319149\pi$
$42$	−2.17821e25	−0.0358498
$43$	−1.20456e27	−1.34462	−0.672312	−	0.740268i	$-0.734699\pi$
$43$	−1.20456e27	−1.34462	−0.672312	+	0.740268i	$0.734699\pi$
$44$	−5.39577e26	−0.412178
$45$	−8.46439e26	−0.446261
$46$	2.16702e27	0.794984
$47$	−3.56629e27	−0.917493	−0.458746	−	0.888567i	$-0.651701\pi$
$47$	−3.56629e27	−0.917493	−0.458746	+	0.888567i	$0.651701\pi$
$48$	−6.34722e25	−0.0115373
$49$	1.59968e27	0.206918
$50$	1.52588e27	0.141421
$51$	3.87304e25	0.00258907
$52$	−1.64830e28	−0.799801
$53$	3.20094e28	1.13429	0.567147	−	0.823617i	$-0.308047\pi$
$53$	3.20094e28	1.13429	0.567147	+	0.823617i	$0.308047\pi$
$54$	2.50445e27	0.0651952
$55$	−1.91696e28	−0.368663
$56$	2.71892e28	0.388413
$57$	4.18557e27	0.0446498
$58$	3.52251e28	0.282027
$59$	2.08570e29	1.25949	0.629744	−	0.776803i	$-0.283160\pi$
$59$	2.08570e29	1.25949	0.629744	+	0.776803i	$0.283160\pi$
$60$	−2.25498e27	−0.0103192
$61$	−1.84408e29	−0.642448	−0.321224	−	0.947003i	$-0.604094\pi$
$61$	−1.84408e29	−0.642448	−0.321224	+	0.947003i	$0.604094\pi$
$62$	−2.76671e29	−0.737057
$63$	−5.35836e29	−1.09626
$64$	7.92282e28	0.125000
$65$	−5.85595e29	−0.715364
$66$	2.83294e28	0.0269006
$67$	−3.61772e29	−0.268040	−0.134020	−	0.990979i	$-0.542789\pi$
$67$	−3.61772e29	−0.268040	−0.134020	+	0.990979i	$0.542789\pi$
$68$	−4.83446e28	−0.0280512
$69$	−1.13775e29	−0.0518844
$70$	9.65954e29	0.347407
$71$	−5.64849e30	−1.60757	−0.803784	−	0.594921i	$-0.797183\pi$
$71$	−5.64849e30	−1.60757	−0.803784	+	0.594921i	$0.797183\pi$
$72$	−1.56140e30	−0.352800
$73$	−6.52836e29	−0.117484	−0.0587418	−	0.998273i	$-0.518709\pi$
$73$	−6.52836e29	−0.117484	−0.0587418	+	0.998273i	$0.518709\pi$
$74$	−9.03671e30	−1.29923
$75$	−8.01132e28	−0.00922982
$76$	−5.22457e30	−0.483756
$77$	−1.21353e31	−0.905636
$78$	8.65408e29	0.0521988
$79$	−2.61534e31	−1.27844	−0.639221	−	0.769023i	$-0.720743\pi$
$79$	−2.61534e31	−1.27844	−0.639221	+	0.769023i	$0.720743\pi$
$80$	2.81475e30	0.111803
$81$	3.07058e31	0.993615
$82$	2.87934e31	0.760965
$83$	−7.88667e31	−1.70650	−0.853248	−	0.521505i	$-0.825371\pi$
$83$	−7.88667e31	−1.70650	−0.853248	+	0.521505i	$0.825371\pi$
$84$	−1.42751e30	−0.0253496
$85$	−1.71755e30	−0.0250897
$86$	−7.89424e31	−0.950792
$87$	−1.84942e30	−0.0184064
$88$	−3.53617e31	−0.291454
$89$	6.51043e31	0.445323	0.222661	−	0.974896i	$-0.428526\pi$
$89$	6.51043e31	0.445323	0.222661	+	0.974896i	$0.428526\pi$
$90$	−5.54722e31	−0.315554
$91$	−3.70710e32	−1.75732
$92$	1.42018e32	0.562139
$93$	1.45261e31	0.0481038
$94$	−2.33721e32	−0.648765
$95$	−1.85614e32	−0.432685
$96$	−4.15971e30	−0.00815808
$97$	−7.62730e32	−1.26077	−0.630387	−	0.776281i	$-0.717104\pi$
$97$	−7.62730e32	−1.26077	−0.630387	+	0.776281i	$0.717104\pi$
$98$	1.04837e32	0.146313
$99$	6.96898e32	0.822600
$100$	1.00000e32	0.100000
$101$	−3.89030e32	−0.330127	−0.165063	−	0.986283i	$-0.552783\pi$
$101$	−3.89030e32	−0.330127	−0.165063	+	0.986283i	$0.552783\pi$
$102$	2.53824e30	0.00183075
$103$	1.75553e33	1.07794	0.538970	−	0.842325i	$-0.318814\pi$
$103$	1.75553e33	1.07794	0.538970	+	0.842325i	$0.318814\pi$
$104$	−1.08023e33	−0.565545
$105$	−5.07155e31	−0.0226734
$106$	2.09777e33	0.802067
$107$	2.84461e33	0.931517	0.465759	−	0.884912i	$-0.345781\pi$
$107$	2.84461e33	0.931517	0.465759	+	0.884912i	$0.345781\pi$
$108$	1.64132e32	0.0460999
$109$	7.03753e33	1.69779	0.848894	−	0.528564i	$-0.177269\pi$
$109$	7.03753e33	1.69779	0.848894	+	0.528564i	$0.177269\pi$
$110$	−1.25630e33	−0.260684
$111$	4.74454e32	0.0847939
$112$	1.78187e33	0.274650
$113$	−3.22217e33	−0.428898	−0.214449	−	0.976735i	$-0.568796\pi$
$113$	−3.22217e33	−0.428898	−0.214449	+	0.976735i	$0.568796\pi$
$114$	2.74305e32	0.0315722
$115$	5.04548e33	0.502792
$116$	2.30851e33	0.199423
$117$	2.12889e34	1.59620
$118$	1.36689e34	0.890593
$119$	−1.08729e33	−0.0616339
$120$	−1.47783e32	−0.00729681
$121$	−7.44222e33	−0.320438
$122$	−1.20854e34	−0.454279
$123$	−1.51174e33	−0.0496641
$124$	−1.81319e34	−0.521178
$125$	3.55271e33	0.0894427
$126$	−3.51166e34	−0.775172
$127$	−2.14069e33	−0.0414756	−0.0207378	−	0.999785i	$-0.506602\pi$
$127$	−2.14069e33	−0.0414756	−0.0207378	+	0.999785i	$0.506602\pi$
$128$	5.19230e33	0.0883883
$129$	4.14471e33	0.0620531
$130$	−3.83776e34	−0.505839
$131$	7.71149e34	0.895699	0.447850	−	0.894109i	$-0.352190\pi$
$131$	7.71149e34	0.895699	0.447850	+	0.894109i	$0.352190\pi$
$132$	1.85660e33	0.0190216
$133$	−1.17503e35	−1.06291
$134$	−2.37091e34	−0.189533
$135$	5.83113e33	0.0412330
$136$	−3.16831e33	−0.0198352
$137$	−2.86481e35	−1.58930	−0.794650	−	0.607068i	$-0.792345\pi$
$137$	−2.86481e35	−1.58930	−0.794650	+	0.607068i	$0.792345\pi$
$138$	−7.45635e33	−0.0366878
$139$	4.17053e34	0.182158	0.0910788	−	0.995844i	$-0.470968\pi$
$139$	4.17053e34	0.182158	0.0910788	+	0.995844i	$0.470968\pi$
$140$	6.33048e34	0.245654
$141$	1.22710e34	0.0423414
$142$	−3.70179e35	−1.13672
$143$	4.82138e35	1.31864
$144$	−1.02328e35	−0.249468
$145$	8.20148e34	0.178369
$146$	−4.27843e34	−0.0830734
$147$	−5.50424e33	−0.00954907
$148$	−5.92230e35	−0.918696
$149$	2.17706e35	0.302201	0.151101	−	0.988518i	$-0.451718\pi$
$149$	2.17706e35	0.302201	0.151101	+	0.988518i	$0.451718\pi$
$150$	−5.25030e33	−0.00652646
$151$	−3.80622e35	−0.424008	−0.212004	−	0.977269i	$-0.567999\pi$
$151$	−3.80622e35	−0.424008	−0.212004	+	0.977269i	$0.567999\pi$
$152$	−3.42398e35	−0.342067
$153$	6.24401e34	0.0559829
$154$	−7.95299e35	−0.640381
$155$	−6.44175e35	−0.466156
$156$	5.67154e34	0.0369101
$157$	1.98603e36	1.16316	0.581582	−	0.813488i	$-0.302434\pi$
$157$	1.98603e36	1.16316	0.581582	+	0.813488i	$0.302434\pi$
$158$	−1.71399e36	−0.903995
$159$	−1.10139e35	−0.0523466
$160$	1.84467e35	0.0790569
$161$	3.19403e36	1.23513
$162$	2.01234e36	0.702592
$163$	4.49451e36	1.41771	0.708854	−	0.705355i	$-0.249212\pi$
$163$	4.49451e36	1.41771	0.708854	+	0.705355i	$0.249212\pi$
$164$	1.88700e36	0.538083
$165$	6.59596e34	0.0170135
$166$	−5.16861e36	−1.20668
$167$	−1.58924e36	−0.336023	−0.168012	−	0.985785i	$-0.553735\pi$
$167$	−1.58924e36	−0.336023	−0.168012	+	0.985785i	$0.553735\pi$
$168$	−9.35535e34	−0.0179249
$169$	8.97224e36	1.55873
$170$	−1.12561e35	−0.0177411
$171$	6.74786e36	0.965452
$172$	−5.17357e36	−0.672312
$173$	6.81608e36	0.804960	0.402480	−	0.915429i	$-0.368148\pi$
$173$	6.81608e36	0.804960	0.402480	+	0.915429i	$0.368148\pi$
$174$	−1.21204e35	−0.0130153
$175$	2.24904e36	0.219720
$176$	−2.31747e36	−0.206089
$177$	−7.17655e35	−0.0581242
$178$	4.26668e36	0.314891
$179$	7.04020e36	0.473707	0.236853	−	0.971545i	$-0.423884\pi$
$179$	7.04020e36	0.473707	0.236853	+	0.971545i	$0.423884\pi$
$180$	−3.63543e36	−0.223131
$181$	1.81472e36	0.101651	0.0508257	−	0.998708i	$-0.483815\pi$
$181$	1.81472e36	0.101651	0.0508257	+	0.998708i	$0.483815\pi$
$182$	−2.42948e37	−1.24261
$183$	6.34518e35	0.0296484
$184$	9.30728e36	0.397492
$185$	−2.10402e37	−0.821707
$186$	9.51980e35	0.0340145
$187$	1.41411e36	0.0462483
$188$	−1.53171e37	−0.458746
$189$	3.69138e36	0.101291
$190$	−1.21644e37	−0.305954
$191$	−5.47196e37	−1.26209	−0.631047	−	0.775744i	$-0.717375\pi$
$191$	−5.47196e37	−1.26209	−0.631047	+	0.775744i	$0.717375\pi$
$192$	−2.72611e35	−0.00576863
$193$	−4.57793e37	−0.889148	−0.444574	−	0.895742i	$-0.646645\pi$
$193$	−4.57793e37	−0.889148	−0.444574	+	0.895742i	$0.646645\pi$
$194$	−4.99863e37	−0.891502
$195$	2.01494e36	0.0330134
$196$	6.87058e36	0.103459
$197$	−7.48669e37	−1.03657	−0.518284	−	0.855209i	$-0.673429\pi$
$197$	−7.48669e37	−1.03657	−0.518284	+	0.855209i	$0.673429\pi$
$198$	4.56719e37	0.581666
$199$	3.94421e37	0.462258	0.231129	−	0.972923i	$-0.425758\pi$
$199$	3.94421e37	0.462258	0.231129	+	0.972923i	$0.425758\pi$
$200$	6.55360e36	0.0707107
$201$	1.24480e36	0.0123698
$202$	−2.54955e37	−0.233435
$203$	5.19193e37	0.438171
$204$	1.66346e35	0.00129454
$205$	6.70399e37	0.481276
$206$	1.15051e38	0.762219
$207$	−1.83425e38	−1.12188
$208$	−7.07941e37	−0.399901
$209$	1.52822e38	0.797574
$210$	−3.32369e36	−0.0160325
$211$	2.10514e38	0.938905	0.469452	−	0.882958i	$-0.344451\pi$
$211$	2.10514e38	0.938905	0.469452	+	0.882958i	$0.344451\pi$
$212$	1.37479e38	0.567147
$213$	1.94355e37	0.0741878
$214$	1.86425e38	0.658682
$215$	−1.83802e38	−0.601334
$216$	1.07565e37	0.0325976
$217$	−4.07794e38	−1.14513
$218$	4.61212e38	1.20052
$219$	2.24630e36	0.00542176
$220$	−8.23330e37	−0.184332
$221$	4.31982e37	0.0897415
$222$	3.10938e37	0.0599584
$223$	2.49660e38	0.447012	0.223506	−	0.974703i	$-0.428250\pi$
$223$	2.49660e38	0.447012	0.223506	+	0.974703i	$0.428250\pi$
$224$	1.16777e38	0.194207
$225$	−1.29156e38	−0.199574
$226$	−2.11168e38	−0.303276
$227$	−3.49100e38	−0.466147	−0.233073	−	0.972459i	$-0.574878\pi$
$227$	−3.49100e38	−0.466147	−0.233073	+	0.972459i	$0.574878\pi$
$228$	1.79769e37	0.0223249
$229$	8.78358e38	1.01481	0.507406	−	0.861707i	$-0.330604\pi$
$229$	8.78358e38	1.01481	0.507406	+	0.861707i	$0.330604\pi$
$230$	3.30661e38	0.355528
$231$	4.17555e37	0.0417942
$232$	1.51291e38	0.141013
$233$	1.89180e38	0.164249	0.0821245	−	0.996622i	$-0.473829\pi$
$233$	1.89180e38	0.164249	0.0821245	+	0.996622i	$0.473829\pi$
$234$	1.39519e39	1.12868
$235$	−5.44173e38	−0.410315
$236$	8.95802e38	0.629744
$237$	8.99895e37	0.0589989
$238$	−7.12565e37	−0.0435818
$239$	−2.46744e39	−1.40825	−0.704126	−	0.710075i	$-0.748661\pi$
$239$	−2.46744e39	−1.40825	−0.704126	+	0.710075i	$0.748661\pi$
$240$	−9.68509e36	−0.00515962
$241$	−3.30287e39	−1.64289	−0.821447	−	0.570284i	$-0.806833\pi$
$241$	−3.30287e39	−1.64289	−0.821447	+	0.570284i	$0.806833\pi$
$242$	−4.87733e38	−0.226584
$243$	−3.18093e38	−0.138054
$244$	−7.92027e38	−0.321224
$245$	2.44092e38	0.0925365
$246$	−9.90733e37	−0.0351178
$247$	4.66840e39	1.54764
$248$	−1.18829e39	−0.368529
$249$	2.71367e38	0.0787532
$250$	2.32831e38	0.0632456
$251$	2.80676e39	0.713820	0.356910	−	0.934139i	$-0.383830\pi$
$251$	2.80676e39	0.713820	0.356910	+	0.934139i	$0.383830\pi$
$252$	−2.30140e39	−0.548129
$253$	−4.15410e39	−0.926804
$254$	−1.40292e38	−0.0293277
$255$	5.90979e36	0.00115787
$256$	3.40282e38	0.0625000
$257$	−7.29261e39	−1.25599	−0.627996	−	0.778217i	$-0.716124\pi$
$257$	−7.29261e39	−1.25599	−0.627996	+	0.778217i	$0.716124\pi$
$258$	2.71628e38	0.0438782
$259$	−1.33195e40	−2.01856
$260$	−2.51511e39	−0.357682
$261$	−2.98159e39	−0.397996
$262$	5.05380e39	0.633355
$263$	8.76662e39	1.03172	0.515861	−	0.856673i	$-0.327472\pi$
$263$	8.76662e39	1.03172	0.515861	+	0.856673i	$0.327472\pi$
$264$	1.21674e38	0.0134503
$265$	4.88425e39	0.507272
$266$	−7.70065e39	−0.751589
$267$	−2.24013e38	−0.0205512
$268$	−1.55380e39	−0.134020
$269$	2.09117e40	1.69620	0.848098	−	0.529839i	$-0.177748\pi$
$269$	2.09117e40	1.69620	0.848098	+	0.529839i	$0.177748\pi$
$270$	3.82149e38	0.0291562
$271$	1.15067e39	0.0825958	0.0412979	−	0.999147i	$-0.486851\pi$
$271$	1.15067e39	0.0825958	0.0412979	+	0.999147i	$0.486851\pi$
$272$	−2.07639e38	−0.0140256
$273$	1.27555e39	0.0810987
$274$	−1.87748e40	−1.12380
$275$	−2.92506e39	−0.164871
$276$	−4.88660e38	−0.0259422
$277$	2.78662e40	1.39367	0.696837	−	0.717229i	$-0.254590\pi$
$277$	2.78662e40	1.39367	0.696837	+	0.717229i	$0.254590\pi$
$278$	2.73320e39	0.128805
$279$	2.34185e40	1.04014
$280$	4.14874e39	0.173704
$281$	4.93528e40	1.94831	0.974153	−	0.225888i	$-0.0725283\pi$
$281$	4.93528e40	1.94831	0.974153	+	0.225888i	$0.0725283\pi$
$282$	8.04194e38	0.0299399
$283$	−1.57701e40	−0.553806	−0.276903	−	0.960898i	$-0.589308\pi$
$283$	−1.57701e40	−0.553806	−0.276903	+	0.960898i	$0.589308\pi$
$284$	−2.42601e40	−0.803784
$285$	6.38667e38	0.0199680
$286$	3.15974e40	0.932420
$287$	4.24394e40	1.18227
$288$	−6.70618e39	−0.176400
$289$	−4.01278e40	−0.996853
$290$	5.37492e39	0.126126
$291$	2.62443e39	0.0581836
$292$	−2.80391e39	−0.0587418
$293$	3.85942e40	0.764199	0.382100	−	0.924121i	$-0.375201\pi$
$293$	3.85942e40	0.764199	0.382100	+	0.924121i	$0.375201\pi$
$294$	−3.60726e38	−0.00675221
$295$	3.18253e40	0.563260
$296$	−3.88124e40	−0.649616
$297$	−4.80094e39	−0.0760055
$298$	1.42676e40	0.213689
$299$	−1.26900e41	−1.79840
$300$	−3.44083e38	−0.00461491
$301$	−1.16355e41	−1.47720
$302$	−2.49444e40	−0.299819
$303$	1.33859e39	0.0152351
$304$	−2.24394e40	−0.241878
$305$	−2.81385e40	−0.287311
$306$	4.09208e39	0.0395859
$307$	8.29043e40	0.759965	0.379983	−	0.924994i	$-0.375930\pi$
$307$	8.29043e40	0.759965	0.379983	+	0.924994i	$0.375930\pi$
$308$	−5.21207e40	−0.452818
$309$	−6.04050e39	−0.0497460
$310$	−4.22167e40	−0.329622
$311$	1.68520e40	0.124769	0.0623844	−	0.998052i	$-0.480130\pi$
$311$	1.68520e40	0.124769	0.0623844	+	0.998052i	$0.480130\pi$
$312$	3.71690e39	0.0260994
$313$	−5.51347e39	−0.0367235	−0.0183617	−	0.999831i	$-0.505845\pi$
$313$	−5.51347e39	−0.0367235	−0.0183617	+	0.999831i	$0.505845\pi$
$314$	1.30156e41	0.822482
$315$	−8.17621e40	−0.490262
$316$	−1.12328e41	−0.639221
$317$	−2.09450e41	−1.13136	−0.565682	−	0.824624i	$-0.691387\pi$
$317$	−2.09450e41	−1.13136	−0.565682	+	0.824624i	$0.691387\pi$
$318$	−7.21807e39	−0.0370147
$319$	−6.75252e40	−0.328791
$320$	1.20893e40	0.0559017
$321$	−9.78784e39	−0.0429887
$322$	2.09324e41	0.873368
$323$	1.36924e40	0.0542797
$324$	1.31881e41	0.496808
$325$	−8.93547e40	−0.319921
$326$	2.94552e41	1.00247
$327$	−2.42150e40	−0.0783513
$328$	1.23667e41	0.380482
$329$	−3.44488e41	−1.00796
$330$	4.32273e39	0.0120303
$331$	1.39181e41	0.368485	0.184242	−	0.982881i	$-0.441017\pi$
$331$	1.39181e41	0.368485	0.184242	+	0.982881i	$0.441017\pi$
$332$	−3.38730e41	−0.853248
$333$	7.64902e41	1.83348
$334$	−1.04153e41	−0.237604
$335$	−5.52020e40	−0.119871
$336$	−6.13112e39	−0.0126748
$337$	−4.64639e41	−0.914582	−0.457291	−	0.889317i	$-0.651180\pi$
$337$	−4.64639e41	−0.914582	−0.457291	+	0.889317i	$0.651180\pi$
$338$	5.88005e41	1.10219
$339$	1.10869e40	0.0197932
$340$	−7.37680e39	−0.0125449
$341$	5.30369e41	0.859272
$342$	4.42228e41	0.682677
$343$	−5.92257e41	−0.871279
$344$	−3.39055e41	−0.475396
$345$	−1.73607e40	−0.0232034
$346$	4.46699e41	0.569192
$347$	3.74401e41	0.454884	0.227442	−	0.973792i	$-0.426964\pi$
$347$	3.74401e41	0.454884	0.227442	+	0.973792i	$0.426964\pi$
$348$	−7.94320e39	−0.00920318
$349$	−3.17132e41	−0.350446	−0.175223	−	0.984529i	$-0.556065\pi$
$349$	−3.17132e41	−0.350446	−0.175223	+	0.984529i	$0.556065\pi$
$350$	1.47393e41	0.155365
$351$	−1.46659e41	−0.147483
$352$	−1.51878e41	−0.145727
$353$	1.29547e42	1.18616	0.593080	−	0.805144i	$-0.297912\pi$
$353$	1.29547e42	1.18616	0.593080	+	0.805144i	$0.297912\pi$
$354$	−4.70323e40	−0.0411000
$355$	−8.61891e41	−0.718926
$356$	2.79621e41	0.222661
$357$	3.74118e39	0.00284435
$358$	4.61386e41	0.334961
$359$	1.19616e42	0.829338	0.414669	−	0.909972i	$-0.363897\pi$
$359$	1.19616e42	0.829338	0.414669	+	0.909972i	$0.363897\pi$
$360$	−2.38251e41	−0.157777
$361$	−1.01043e41	−0.0639202
$362$	1.18930e41	0.0718784
$363$	2.56074e40	0.0147879
$364$	−1.59219e42	−0.878660
$365$	−9.96149e40	−0.0525402
$366$	4.15838e40	0.0209646
$367$	−2.24871e42	−1.08378	−0.541892	−	0.840448i	$-0.682292\pi$
$367$	−2.24871e42	−1.08378	−0.541892	+	0.840448i	$0.682292\pi$
$368$	6.09962e41	0.281069
$369$	−2.43719e42	−1.07387
$370$	−1.37889e42	−0.581034
$371$	3.09196e42	1.24613
$372$	6.23890e40	0.0240519
$373$	4.82851e42	1.78081	0.890404	−	0.455171i	$-0.150422\pi$
$373$	4.82851e42	1.78081	0.890404	+	0.455171i	$0.150422\pi$
$374$	9.26749e40	0.0327025
$375$	−1.22243e40	−0.00412770
$376$	−1.00382e42	−0.324383
$377$	−2.06276e42	−0.637995
$378$	2.41918e41	0.0716233
$379$	−4.26076e42	−1.20765	−0.603823	−	0.797118i	$-0.706357\pi$
$379$	−4.26076e42	−1.20765	−0.603823	+	0.797118i	$0.706357\pi$
$380$	−7.97206e41	−0.216342
$381$	7.36576e39	0.00191406
$382$	−3.58610e42	−0.892436
$383$	8.60164e41	0.205023	0.102511	−	0.994732i	$-0.467312\pi$
$383$	8.60164e41	0.205023	0.102511	+	0.994732i	$0.467312\pi$
$384$	−1.78658e40	−0.00407904
$385$	−1.85170e42	−0.405013
$386$	−3.00020e42	−0.628722
$387$	6.68199e42	1.34176
$388$	−3.27590e42	−0.630387
$389$	−1.00931e43	−1.86148	−0.930739	−	0.365685i	$-0.880835\pi$
$389$	−1.00931e43	−1.86148	−0.930739	+	0.365685i	$0.880835\pi$
$390$	1.32051e41	0.0233440
$391$	−3.72195e41	−0.0630746
$392$	4.50270e41	0.0731565
$393$	−2.65340e41	−0.0413357
$394$	−4.90648e42	−0.732964
$395$	−3.99069e42	−0.571737
$396$	2.99316e42	0.411300
$397$	8.51038e42	1.12177	0.560887	−	0.827892i	$-0.310460\pi$
$397$	8.51038e42	1.12177	0.560887	+	0.827892i	$0.310460\pi$
$398$	2.58488e42	0.326866
$399$	4.04307e41	0.0490522
$400$	4.29497e41	0.0500000
$401$	5.69759e42	0.636516	0.318258	−	0.948004i	$-0.396902\pi$
$401$	5.69759e42	0.636516	0.318258	+	0.948004i	$0.396902\pi$
$402$	8.15789e40	0.00874678
$403$	1.62017e43	1.66736
$404$	−1.67087e42	−0.165063
$405$	4.68534e42	0.444358
$406$	3.40258e42	0.309834
$407$	1.73230e43	1.51466
$408$	1.09016e40	0.000915375 0
$409$	−1.52688e43	−1.23132	−0.615660	−	0.788012i	$-0.711111\pi$
$409$	−1.52688e43	−1.23132	−0.615660	+	0.788012i	$0.711111\pi$
$410$	4.39352e42	0.340314
$411$	9.85732e41	0.0733447
$412$	7.53996e42	0.538970
$413$	2.01469e43	1.38367
$414$	−1.20209e43	−0.793291
$415$	−1.20341e43	−0.763168
$416$	−4.63956e42	−0.282772
$417$	−1.43501e41	−0.00840640
$418$	1.00153e43	0.563970
$419$	−2.95628e43	−1.60035	−0.800173	−	0.599769i	$-0.795259\pi$
$419$	−2.95628e43	−1.60035	−0.800173	+	0.599769i	$0.795259\pi$
$420$	−2.17821e41	−0.0113367
$421$	2.45835e43	1.23024	0.615119	−	0.788434i	$-0.289108\pi$
$421$	2.45835e43	1.23024	0.615119	+	0.788434i	$0.289108\pi$
$422$	1.37963e43	0.663906
$423$	1.97830e43	0.915539
$424$	9.00985e42	0.401034
$425$	−2.62077e41	−0.0112205
$426$	1.27373e42	0.0524587
$427$	−1.78130e43	−0.705792
$428$	1.22175e43	0.465759
$429$	−1.65896e42	−0.0608541
$430$	−1.20456e43	−0.425207
$431$	1.54742e43	0.525693	0.262846	−	0.964838i	$-0.415339\pi$
$431$	1.54742e43	0.525693	0.262846	+	0.964838i	$0.415339\pi$
$432$	7.04940e41	0.0230500
$433$	−4.36385e43	−1.37347	−0.686735	−	0.726907i	$-0.740957\pi$
$433$	−4.36385e43	−1.37347	−0.686735	+	0.726907i	$0.740957\pi$
$434$	−2.67252e43	−0.809730
$435$	−2.82199e41	−0.00823158
$436$	3.02260e43	0.848894
$437$	−4.02229e43	−1.08775
$438$	1.47214e41	0.00383376
$439$	−6.44930e43	−1.61751	−0.808757	−	0.588144i	$-0.799859\pi$
$439$	−6.44930e43	−1.61751	−0.808757	+	0.588144i	$0.799859\pi$
$440$	−5.39577e42	−0.130342
$441$	−8.87379e42	−0.206477
$442$	2.83104e42	0.0634568
$443$	3.04125e43	0.656736	0.328368	−	0.944550i	$-0.393501\pi$
$443$	3.04125e43	0.656736	0.328368	+	0.944550i	$0.393501\pi$
$444$	2.03776e42	0.0423970
$445$	9.93413e42	0.199154
$446$	1.63617e43	0.316085
$447$	−7.49089e41	−0.0139463
$448$	7.65308e42	0.137325
$449$	−6.70336e43	−1.15939	−0.579693	−	0.814835i	$-0.696827\pi$
$449$	−6.70336e43	−1.15939	−0.579693	+	0.814835i	$0.696827\pi$
$450$	−8.46439e42	−0.141120
$451$	−5.51959e43	−0.887144
$452$	−1.38391e43	−0.214449
$453$	1.30966e42	0.0195676
$454$	−2.28786e43	−0.329616
$455$	−5.65658e43	−0.785898
$456$	1.17813e42	0.0157861
$457$	5.09970e43	0.659064	0.329532	−	0.944144i	$-0.393109\pi$
$457$	5.09970e43	0.659064	0.329532	+	0.944144i	$0.393109\pi$
$458$	5.75640e43	0.717581
$459$	−4.30151e41	−0.00517263
$460$	2.16702e43	0.251396
$461$	−7.70670e43	−0.862588	−0.431294	−	0.902211i	$-0.641943\pi$
$461$	−7.70670e43	−0.862588	−0.431294	+	0.902211i	$0.641943\pi$
$462$	2.73649e42	0.0295530
$463$	4.19125e43	0.436774	0.218387	−	0.975862i	$-0.429921\pi$
$463$	4.19125e43	0.436774	0.218387	+	0.975862i	$0.429921\pi$
$464$	9.91498e42	0.0997115
$465$	2.21650e42	0.0215127
$466$	1.23981e43	0.116142
$467$	1.16618e44	1.05448	0.527238	−	0.849717i	$-0.323227\pi$
$467$	1.16618e44	1.05448	0.527238	+	0.849717i	$0.323227\pi$
$468$	9.14351e43	0.798098
$469$	−3.49455e43	−0.294469
$470$	−3.56629e43	−0.290137
$471$	−6.83359e42	−0.0536790
$472$	5.87073e43	0.445296
$473$	1.51330e44	1.10845
$474$	5.89755e42	0.0417185
$475$	−2.83225e43	−0.193502
$476$	−4.66987e42	−0.0308170
$477$	−1.77563e44	−1.13188
$478$	−1.61706e44	−0.995785
$479$	1.47459e44	0.877276	0.438638	−	0.898664i	$-0.355461\pi$
$479$	1.47459e44	0.877276	0.438638	+	0.898664i	$0.355461\pi$
$480$	−6.34722e41	−0.00364840
$481$	5.29185e44	2.93910
$482$	−2.16457e44	−1.16170
$483$	−1.09901e43	−0.0570001
$484$	−3.19641e43	−0.160219
$485$	−1.16383e44	−0.563835
$486$	−2.08465e43	−0.0976191
$487$	1.46242e44	0.661979	0.330990	−	0.943634i	$-0.392618\pi$
$487$	1.46242e44	0.661979	0.330990	+	0.943634i	$0.392618\pi$
$488$	−5.19063e43	−0.227140
$489$	−1.54649e43	−0.0654260
$490$	1.59968e43	0.0654332
$491$	−1.96551e44	−0.777374	−0.388687	−	0.921370i	$-0.627071\pi$
$491$	−1.96551e44	−0.777374	−0.388687	+	0.921370i	$0.627071\pi$
$492$	−6.49287e42	−0.0248320
$493$	−6.05007e42	−0.0223762
$494$	3.05948e44	1.09434
$495$	1.06338e44	0.367878
$496$	−7.78760e43	−0.260589
$497$	−5.45618e44	−1.76607
$498$	1.77843e43	0.0556869
$499$	5.06608e44	1.53466	0.767332	−	0.641250i	$-0.221584\pi$
$499$	5.06608e44	1.53466	0.767332	+	0.641250i	$0.221584\pi$
$500$	1.52588e43	0.0447214
$501$	5.46833e42	0.0155072
$502$	1.83944e44	0.504747
$503$	6.45463e44	1.71395	0.856977	−	0.515354i	$-0.172340\pi$
$503$	6.45463e44	1.71395	0.856977	+	0.515354i	$0.172340\pi$
$504$	−1.50824e44	−0.387586
$505$	−5.93613e43	−0.147637
$506$	−2.72243e44	−0.655350
$507$	−3.08720e43	−0.0719339
$508$	−9.19419e42	−0.0207378
$509$	−1.22512e44	−0.267507	−0.133753	−	0.991015i	$-0.542703\pi$
$509$	−1.22512e44	−0.267507	−0.133753	+	0.991015i	$0.542703\pi$
$510$	3.87304e41	0.000818736 0
$511$	−6.30610e43	−0.129067
$512$	2.23007e43	0.0441942
$513$	−4.64861e43	−0.0892045
$514$	−4.77929e44	−0.888120
$515$	2.67873e44	0.482070
$516$	1.78014e43	0.0310266
$517$	4.48034e44	0.756340
$518$	−8.72904e44	−1.42733
$519$	−2.34530e43	−0.0371481
$520$	−1.64830e44	−0.252919
$521$	4.86872e43	0.0723757	0.0361878	−	0.999345i	$-0.488479\pi$
$521$	4.86872e43	0.0723757	0.0361878	+	0.999345i	$0.488479\pi$
$522$	−1.95401e44	−0.281426
$523$	−1.13407e45	−1.58257	−0.791283	−	0.611450i	$-0.790587\pi$
$523$	−1.13407e45	−1.58257	−0.791283	+	0.611450i	$0.790587\pi$
$524$	3.31206e44	0.447850
$525$	−7.73856e42	−0.0101399
$526$	5.74529e44	0.729537
$527$	4.75196e43	0.0584786
$528$	7.97402e42	0.00951081
$529$	2.28361e44	0.264000
$530$	3.20094e44	0.358695
$531$	−1.15699e45	−1.25681
$532$	−5.04670e44	−0.531454
$533$	−1.68613e45	−1.72144
$534$	−1.46809e43	−0.0145319
$535$	4.34054e44	0.416587
$536$	−1.01830e44	−0.0947666
$537$	−2.42241e43	−0.0218611
$538$	1.37047e45	1.19939
$539$	−2.00968e44	−0.170574
$540$	2.50445e43	0.0206165
$541$	−6.78227e44	−0.541527	−0.270763	−	0.962646i	$-0.587276\pi$
$541$	−6.78227e44	−0.541527	−0.270763	+	0.962646i	$0.587276\pi$
$542$	7.54104e43	0.0584041
$543$	−6.24415e42	−0.00469112
$544$	−1.36078e43	−0.00991759
$545$	1.07384e45	0.759273
$546$	8.35945e43	0.0573455
$547$	6.38198e44	0.424780	0.212390	−	0.977185i	$-0.431875\pi$
$547$	6.38198e44	0.424780	0.212390	+	0.977185i	$0.431875\pi$
$548$	−1.23042e45	−0.794650
$549$	1.02295e45	0.641080
$550$	−1.91696e44	−0.116581
$551$	−6.53827e44	−0.385888
$552$	−3.20248e43	−0.0183439
$553$	−2.52630e45	−1.40449
$554$	1.82624e45	0.985477
$555$	7.23959e43	0.0379210
$556$	1.79123e44	0.0910788
$557$	−1.02802e45	−0.507447	−0.253724	−	0.967277i	$-0.581655\pi$
$557$	−1.02802e45	−0.507447	−0.253724	+	0.967277i	$0.581655\pi$
$558$	1.53476e45	0.735487
$559$	4.62283e45	2.15086
$560$	2.71892e44	0.122827
$561$	−4.86571e42	−0.00213432
$562$	3.23438e45	1.37766
$563$	1.16743e45	0.482885	0.241442	−	0.970415i	$-0.422380\pi$
$563$	1.16743e45	0.482885	0.241442	+	0.970415i	$0.422380\pi$
$564$	5.27037e43	0.0211707
$565$	−4.91664e44	−0.191809
$566$	−1.03351e45	−0.391600
$567$	2.96604e45	1.09158
$568$	−1.58991e45	−0.568361
$569$	−1.70096e45	−0.590666	−0.295333	−	0.955394i	$-0.595431\pi$
$569$	−1.70096e45	−0.590666	−0.295333	+	0.955394i	$0.595431\pi$
$570$	4.18557e43	0.0141195
$571$	2.65488e45	0.870060	0.435030	−	0.900416i	$-0.356738\pi$
$571$	2.65488e45	0.870060	0.435030	+	0.900416i	$0.356738\pi$
$572$	2.07077e45	0.659321
$573$	1.88281e44	0.0582445
$574$	2.78131e45	0.835994
$575$	7.69880e44	0.224855
$576$	−4.39496e44	−0.124734
$577$	−2.36511e45	−0.652304	−0.326152	−	0.945317i	$-0.605752\pi$
$577$	−2.36511e45	−0.652304	−0.326152	+	0.945317i	$0.605752\pi$
$578$	−2.62982e45	−0.704881
$579$	1.57519e44	0.0410334
$580$	3.52251e44	0.0891846
$581$	−7.61817e45	−1.87475
$582$	1.71994e44	0.0411420
$583$	−4.02135e45	−0.935062
$584$	−1.83757e44	−0.0415367
$585$	3.24843e45	0.713840
$586$	2.52931e45	0.540370
$587$	−1.20601e45	−0.250508	−0.125254	−	0.992125i	$-0.539975\pi$
$587$	−1.20601e45	−0.250508	−0.125254	+	0.992125i	$0.539975\pi$
$588$	−2.36405e43	−0.00477454
$589$	5.13541e45	1.00849
$590$	2.08570e45	0.398285
$591$	2.57605e44	0.0478366
$592$	−2.54361e45	−0.459348
$593$	−2.17738e45	−0.382413	−0.191206	−	0.981550i	$-0.561240\pi$
$593$	−2.17738e45	−0.382413	−0.191206	+	0.981550i	$0.561240\pi$
$594$	−3.14634e44	−0.0537440
$595$	−1.65907e44	−0.0275635
$596$	9.35039e44	0.151101
$597$	−1.35714e44	−0.0213328
$598$	−8.31649e45	−1.27166
$599$	−4.67713e45	−0.695724	−0.347862	−	0.937546i	$-0.613092\pi$
$599$	−4.67713e45	−0.695724	−0.347862	+	0.937546i	$0.613092\pi$
$600$	−2.25498e43	−0.00326323
$601$	−1.01814e46	−1.43344	−0.716722	−	0.697359i	$-0.754358\pi$
$601$	−1.01814e46	−1.43344	−0.716722	+	0.697359i	$0.754358\pi$
$602$	−7.62547e45	−1.04454
$603$	2.00683e45	0.267470
$604$	−1.63476e45	−0.212004
$605$	−1.13559e45	−0.143304
$606$	8.77258e43	0.0107728
$607$	−8.73331e45	−1.04368	−0.521838	−	0.853045i	$-0.674753\pi$
$607$	−8.73331e45	−1.04368	−0.521838	+	0.853045i	$0.674753\pi$
$608$	−1.47059e45	−0.171034
$609$	−1.78646e44	−0.0202212
$610$	−1.84408e45	−0.203160
$611$	1.36866e46	1.46762
$612$	2.68178e44	0.0279914
$613$	−8.45222e44	−0.0858763	−0.0429381	−	0.999078i	$-0.513672\pi$
$613$	−8.45222e44	−0.0858763	−0.0429381	+	0.999078i	$0.513672\pi$
$614$	5.43321e45	0.537377
$615$	−2.30673e44	−0.0222105
$616$	−3.41578e45	−0.320191
$617$	−6.99843e44	−0.0638698	−0.0319349	−	0.999490i	$-0.510167\pi$
$617$	−6.99843e44	−0.0638698	−0.0319349	+	0.999490i	$0.510167\pi$
$618$	−3.95870e44	−0.0351757
$619$	1.82399e46	1.57807	0.789037	−	0.614345i	$-0.210580\pi$
$619$	1.82399e46	1.57807	0.789037	+	0.614345i	$0.210580\pi$
$620$	−2.76671e45	−0.233078
$621$	1.26362e45	0.103658
$622$	1.10442e45	0.0882249
$623$	6.28878e45	0.489231
$624$	2.43591e44	0.0184550
$625$	5.42101e44	0.0400000
$626$	−3.61331e44	−0.0259674
$627$	−5.25834e44	−0.0368073
$628$	8.52993e45	0.581582
$629$	1.55210e45	0.103082
$630$	−5.35836e45	−0.346667
$631$	1.71214e46	1.07908	0.539540	−	0.841960i	$-0.318598\pi$
$631$	1.71214e46	1.07908	0.539540	+	0.841960i	$0.318598\pi$
$632$	−7.36153e45	−0.451998
$633$	−7.24345e44	−0.0433296
$634$	−1.37265e46	−0.799995
$635$	−3.26643e44	−0.0185484
$636$	−4.73044e44	−0.0261733
$637$	−6.13919e45	−0.330986
$638$	−4.42533e45	−0.232490
$639$	3.13334e46	1.60414
$640$	7.92282e44	0.0395285
$641$	−3.25948e46	−1.58486	−0.792429	−	0.609964i	$-0.791184\pi$
$641$	−3.25948e46	−1.58486	−0.792429	+	0.609964i	$0.791184\pi$
$642$	−6.41456e44	−0.0303976
$643$	3.81037e46	1.75989	0.879947	−	0.475073i	$-0.157578\pi$
$643$	3.81037e46	1.75989	0.879947	+	0.475073i	$0.157578\pi$
$644$	1.37183e46	0.617565
$645$	6.32432e44	0.0277510
$646$	8.97344e44	0.0383815
$647$	1.23656e46	0.515580	0.257790	−	0.966201i	$-0.417006\pi$
$647$	1.23656e46	0.515580	0.257790	+	0.966201i	$0.417006\pi$
$648$	8.64293e45	0.351296
$649$	−2.62027e46	−1.03827
$650$	−5.85595e45	−0.226218
$651$	1.40315e45	0.0528467
$652$	1.93038e46	0.708854
$653$	4.34456e45	0.155553	0.0777764	−	0.996971i	$-0.475218\pi$
$653$	4.34456e45	0.155553	0.0777764	+	0.996971i	$0.475218\pi$
$654$	−1.58695e45	−0.0554027
$655$	1.17668e46	0.400569
$656$	8.10462e45	0.269042
$657$	3.62143e45	0.117233
$658$	−2.25763e46	−0.712732
$659$	−3.61863e46	−1.11413	−0.557063	−	0.830470i	$-0.688072\pi$
$659$	−3.61863e46	−1.11413	−0.557063	+	0.830470i	$0.688072\pi$
$660$	2.83294e44	0.00850673
$661$	−1.31841e46	−0.386124	−0.193062	−	0.981187i	$-0.561842\pi$
$661$	−1.31841e46	−0.386124	−0.193062	+	0.981187i	$0.561842\pi$
$662$	9.12140e45	0.260558
$663$	−1.48638e44	−0.00414149
$664$	−2.21990e46	−0.603338
$665$	−1.79295e46	−0.475347
$666$	5.01286e46	1.29647
$667$	1.77728e46	0.448413
$668$	−6.82575e45	−0.168012
$669$	−8.59040e44	−0.0206292
$670$	−3.61772e45	−0.0847618
$671$	2.31672e46	0.529606
$672$	−4.01809e44	−0.00896245
$673$	4.84617e46	1.05475	0.527375	−	0.849633i	$-0.323176\pi$
$673$	4.84617e46	1.05475	0.527375	+	0.849633i	$0.323176\pi$
$674$	−3.04506e46	−0.646707
$675$	8.89759e44	0.0184400
$676$	3.85355e46	0.779364
$677$	−4.32560e46	−0.853755	−0.426877	−	0.904310i	$-0.640386\pi$
$677$	−4.32560e46	−0.853755	−0.426877	+	0.904310i	$0.640386\pi$
$678$	7.26594e44	0.0139959
$679$	−7.36762e46	−1.38508
$680$	−4.83446e44	−0.00887056
$681$	1.20119e45	0.0215122
$682$	3.47583e46	0.607597
$683$	−6.34451e45	−0.108257	−0.0541286	−	0.998534i	$-0.517238\pi$
$683$	−6.34451e45	−0.108257	−0.0541286	+	0.998534i	$0.517238\pi$
$684$	2.89819e46	0.482726
$685$	−4.37135e46	−0.710756
$686$	−3.88141e46	−0.616087
$687$	−3.02228e45	−0.0468327
$688$	−2.22203e46	−0.336156
$689$	−1.22844e47	−1.81442
$690$	−1.13775e45	−0.0164073
$691$	−5.27291e46	−0.742442	−0.371221	−	0.928545i	$-0.621061\pi$
$691$	−5.27291e46	−0.742442	−0.371221	+	0.928545i	$0.621061\pi$
$692$	2.92749e46	0.402480
$693$	6.73172e46	0.903707
$694$	2.45367e46	0.321652
$695$	6.36373e45	0.0814633
$696$	−5.20566e44	−0.00650763
$697$	−4.94540e45	−0.0603755
$698$	−2.07836e46	−0.247803
$699$	−6.50937e44	−0.00757994
$700$	9.65954e45	0.109860
$701$	−1.32738e47	−1.47451	−0.737255	−	0.675614i	$-0.763879\pi$
$701$	−1.32738e47	−1.47451	−0.737255	+	0.675614i	$0.763879\pi$
$702$	−9.61147e45	−0.104286
$703$	1.67734e47	1.77770
$704$	−9.95345e45	−0.103044
$705$	1.87241e45	0.0189357
$706$	8.48996e46	0.838741
$707$	−3.75786e46	−0.362677
$708$	−3.08231e45	−0.0290621
$709$	−1.89943e47	−1.74968	−0.874841	−	0.484409i	$-0.839035\pi$
$709$	−1.89943e47	−1.74968	−0.874841	+	0.484409i	$0.839035\pi$
$710$	−5.64849e46	−0.508358
$711$	1.45079e47	1.27572
$712$	1.83252e46	0.157445
$713$	−1.39594e47	−1.17190
$714$	2.45182e44	0.00201126
$715$	7.35684e46	0.589714
$716$	3.02374e46	0.236853
$717$	8.49004e45	0.0649895
$718$	7.83917e46	0.586430
$719$	−1.12722e47	−0.824104	−0.412052	−	0.911160i	$-0.635188\pi$
$719$	−1.12722e47	−0.824104	−0.412052	+	0.911160i	$0.635188\pi$
$720$	−1.56140e46	−0.111565
$721$	1.69576e47	1.18422
$722$	−6.62196e45	−0.0451984
$723$	1.13646e46	0.0758181
$724$	7.79417e45	0.0508257
$725$	1.25145e46	0.0797692
$726$	1.67821e45	0.0104566
$727$	1.60341e47	0.976626	0.488313	−	0.872669i	$-0.337613\pi$
$727$	1.60341e47	0.976626	0.488313	+	0.872669i	$0.337613\pi$
$728$	−1.04346e47	−0.621307
$729$	−1.69601e47	−0.987244
$730$	−6.52836e45	−0.0371516
$731$	1.35587e46	0.0754365
$732$	2.72523e45	0.0148242
$733$	3.44847e47	1.83405	0.917024	−	0.398832i	$-0.130584\pi$
$733$	3.44847e47	1.83405	0.917024	+	0.398832i	$0.130584\pi$
$734$	−1.47371e47	−0.766351
$735$	−8.39880e44	−0.00427047
$736$	3.99744e46	0.198746
$737$	4.54494e46	0.220961
$738$	−1.59723e47	−0.759344
$739$	2.87632e47	1.33722	0.668611	−	0.743612i	$-0.266889\pi$
$739$	2.87632e47	1.33722	0.668611	+	0.743612i	$0.266889\pi$
$740$	−9.03671e46	−0.410853
$741$	−1.60632e46	−0.0714219
$742$	2.02635e47	0.881149
$743$	3.46436e47	1.47335	0.736677	−	0.676244i	$-0.236394\pi$
$743$	3.46436e47	1.47335	0.736677	+	0.676244i	$0.236394\pi$
$744$	4.08872e45	0.0170073
$745$	3.32193e46	0.135149
$746$	3.16441e47	1.25922
$747$	4.37491e47	1.70286
$748$	6.07354e45	0.0231241
$749$	2.74777e47	1.02336
$750$	−8.01132e44	−0.00291872
$751$	−4.94603e47	−1.76278	−0.881389	−	0.472391i	$-0.843391\pi$
$751$	−4.94603e47	−1.76278	−0.881389	+	0.472391i	$0.843391\pi$
$752$	−6.57865e46	−0.229373
$753$	−9.65759e45	−0.0329421
$754$	−1.35185e47	−0.451131
$755$	−5.80783e46	−0.189622
$756$	1.58544e46	0.0506453
$757$	−5.29375e47	−1.65456	−0.827278	−	0.561793i	$-0.810112\pi$
$757$	−5.29375e47	−1.65456	−0.827278	+	0.561793i	$0.810112\pi$
$758$	−2.79233e47	−0.853935
$759$	1.42936e46	0.0427712
$760$	−5.22457e46	−0.152977
$761$	−5.45469e47	−1.56287	−0.781436	−	0.623985i	$-0.785513\pi$
$761$	−5.45469e47	−1.56287	−0.781436	+	0.623985i	$0.785513\pi$
$762$	4.82722e44	0.00135344
$763$	6.79793e47	1.86519
$764$	−2.35019e47	−0.631047
$765$	9.52761e45	0.0250363
$766$	5.63717e46	0.144973
$767$	−8.00442e47	−2.01468
$768$	−1.17086e45	−0.00288432
$769$	6.99140e47	1.68570	0.842848	−	0.538151i	$-0.180877\pi$
$769$	6.99140e47	1.68570	0.842848	+	0.538151i	$0.180877\pi$
$770$	−1.21353e47	−0.286387
$771$	2.50927e46	0.0579628
$772$	−1.96621e47	−0.444574
$773$	−7.98533e47	−1.76738	−0.883692	−	0.468069i	$-0.844950\pi$
$773$	−7.98533e47	−1.76738	−0.883692	+	0.468069i	$0.844950\pi$
$774$	4.37911e47	0.948767
$775$	−9.82934e46	−0.208471
$776$	−2.14689e47	−0.445751
$777$	4.58301e46	0.0931545
$778$	−6.61464e47	−1.31626
$779$	−5.34446e47	−1.04120
$780$	8.65408e45	0.0165067
$781$	7.09620e47	1.32521
$782$	−2.43922e46	−0.0446005
$783$	2.05402e46	0.0367735
$784$	2.95089e46	0.0517295
$785$	3.03044e47	0.520183
$786$	−1.73893e46	−0.0292287
$787$	−3.34859e47	−0.551161	−0.275580	−	0.961278i	$-0.588870\pi$
$787$	−3.34859e47	−0.551161	−0.275580	+	0.961278i	$0.588870\pi$
$788$	−3.21551e47	−0.518284
$789$	−3.01645e46	−0.0476130
$790$	−2.61534e47	−0.404279
$791$	−3.11246e47	−0.471186
$792$	1.96159e47	0.290833
$793$	7.07714e47	1.02766
$794$	5.57736e47	0.793214
$795$	−1.68059e46	−0.0234101
$796$	1.69403e47	0.231129
$797$	−9.43634e47	−1.26108	−0.630538	−	0.776159i	$-0.717166\pi$
$797$	−9.43634e47	−1.26108	−0.630538	+	0.776159i	$0.717166\pi$
$798$	2.64967e46	0.0346851
$799$	4.01426e46	0.0514735
$800$	2.81475e46	0.0353553
$801$	−3.61148e47	−0.444374
$802$	3.73397e47	0.450084
$803$	8.20159e46	0.0968482
$804$	5.34636e45	0.00618491
$805$	4.87371e47	0.552367
$806$	1.06180e48	1.17900
$807$	−7.19536e46	−0.0782779
$808$	−1.09502e47	−0.116717
$809$	−2.25513e47	−0.235516	−0.117758	−	0.993042i	$-0.537571\pi$
$809$	−2.25513e47	−0.235516	−0.117758	+	0.993042i	$0.537571\pi$
$810$	3.07058e47	0.314209
$811$	−1.37037e48	−1.37402	−0.687009	−	0.726649i	$-0.741077\pi$
$811$	−1.37037e48	−1.37402	−0.687009	+	0.726649i	$0.741077\pi$
$812$	2.22992e47	0.219086
$813$	−3.95927e45	−0.00381172
$814$	1.13528e48	1.07103
$815$	6.85808e47	0.634019
$816$	7.14450e44	0.000647268 0
$817$	1.46528e48	1.30094
$818$	−1.00066e48	−0.870675
$819$	2.05641e48	1.75358
$820$	2.87934e47	0.240638
$821$	−4.56387e47	−0.373827	−0.186914	−	0.982376i	$-0.559848\pi$
$821$	−4.56387e47	−0.373827	−0.186914	+	0.982376i	$0.559848\pi$
$822$	6.46009e46	0.0518625
$823$	−8.98179e47	−0.706750	−0.353375	−	0.935482i	$-0.614966\pi$
$823$	−8.98179e47	−0.706750	−0.353375	+	0.935482i	$0.614966\pi$
$824$	4.94139e47	0.381109
$825$	1.00646e46	0.00760865
$826$	1.32035e48	0.978403
$827$	4.00288e47	0.290758	0.145379	−	0.989376i	$-0.453560\pi$
$827$	4.00288e47	0.290758	0.145379	+	0.989376i	$0.453560\pi$
$828$	−7.87804e47	−0.560942
$829$	−7.44189e47	−0.519437	−0.259719	−	0.965684i	$-0.583630\pi$
$829$	−7.44189e47	−0.519437	−0.259719	+	0.965684i	$0.583630\pi$
$830$	−7.88667e47	−0.539642
$831$	−9.58829e46	−0.0643168
$832$	−3.04058e47	−0.199950
$833$	−1.80062e46	−0.0116086
$834$	−9.40449e45	−0.00594422
$835$	−2.42500e47	−0.150274
$836$	6.56364e47	0.398787
$837$	−1.61331e47	−0.0961051
$838$	−1.93743e48	−1.13162
$839$	2.38585e48	1.36638	0.683188	−	0.730243i	$-0.260593\pi$
$839$	2.38585e48	1.36638	0.683188	+	0.730243i	$0.260593\pi$
$840$	−1.42751e46	−0.00801626
$841$	−1.52718e48	−0.840922
$842$	1.61111e48	0.869910
$843$	−1.69815e47	−0.0899126
$844$	9.04153e47	0.469452
$845$	1.36906e48	0.697085
$846$	1.29650e48	0.647384
$847$	−7.18884e47	−0.352032
$848$	5.90469e47	0.283574
$849$	5.42622e46	0.0255576
$850$	−1.71755e46	−0.00793407
$851$	−4.55946e48	−2.06574
$852$	8.34749e46	0.0370939
$853$	1.91914e48	0.836466	0.418233	−	0.908340i	$-0.362650\pi$
$853$	1.91914e48	0.836466	0.418233	+	0.908340i	$0.362650\pi$
$854$	−1.16739e48	−0.499070
$855$	1.02964e48	0.431763
$856$	8.00687e47	0.329341
$857$	−4.27431e48	−1.72458	−0.862289	−	0.506417i	$-0.830970\pi$
$857$	−4.27431e48	−1.72458	−0.862289	+	0.506417i	$0.830970\pi$
$858$	−1.08721e47	−0.0430303
$859$	−2.08295e48	−0.808707	−0.404353	−	0.914603i	$-0.632503\pi$
$859$	−2.08295e48	−0.808707	−0.404353	+	0.914603i	$0.632503\pi$
$860$	−7.89424e47	−0.300667
$861$	−1.46027e47	−0.0545609
$862$	1.01411e48	0.371721
$863$	−2.59078e48	−0.931650	−0.465825	−	0.884877i	$-0.654242\pi$
$863$	−2.59078e48	−0.931650	−0.465825	+	0.884877i	$0.654242\pi$
$864$	4.61989e46	0.0162988
$865$	1.04005e48	0.359989
$866$	−2.85989e48	−0.971191
$867$	1.38073e47	0.0460038
$868$	−1.75146e48	−0.572565
$869$	3.28566e48	1.05389
$870$	−1.84942e46	−0.00582060
$871$	1.38839e48	0.428758
$872$	1.98089e48	0.600258
$873$	4.23103e48	1.25809
$874$	−2.63605e48	−0.769157
$875$	3.43176e47	0.0982616
$876$	9.64779e45	0.00271088
$877$	5.50587e48	1.51821	0.759107	−	0.650966i	$-0.225636\pi$
$877$	5.50587e48	1.51821	0.759107	+	0.650966i	$0.225636\pi$
$878$	−4.22661e48	−1.14375
$879$	−1.32796e47	−0.0352671
$880$	−3.53617e47	−0.0921658
$881$	−1.00108e48	−0.256076	−0.128038	−	0.991769i	$-0.540868\pi$
$881$	−1.00108e48	−0.256076	−0.128038	+	0.991769i	$0.540868\pi$
$882$	−5.81552e47	−0.146001
$883$	−7.50570e48	−1.84944	−0.924719	−	0.380652i	$-0.875700\pi$
$883$	−7.50570e48	−1.84944	−0.924719	+	0.380652i	$0.875700\pi$
$884$	1.85535e47	0.0448707
$885$	−1.09506e47	−0.0259939
$886$	1.99311e48	0.464382
$887$	−1.00895e48	−0.230744	−0.115372	−	0.993322i	$-0.536806\pi$
$887$	−1.00895e48	−0.230744	−0.115372	+	0.993322i	$0.536806\pi$
$888$	1.33547e47	0.0299792
$889$	−2.06781e47	−0.0455650
$890$	6.51043e47	0.140823
$891$	−3.85758e48	−0.819092
$892$	1.07228e48	0.223506
$893$	4.33819e48	0.887685
$894$	−4.90923e46	−0.00986154
$895$	1.07425e48	0.211848
$896$	5.01552e47	0.0971033
$897$	4.36640e47	0.0829944
$898$	−4.39311e48	−0.819809
$899$	−2.26911e48	−0.415739
$900$	−5.54722e47	−0.0997870
$901$	−3.60301e47	−0.0636366
$902$	−3.61732e48	−0.627305
$903$	4.00360e47	0.0681715
$904$	−9.06959e47	−0.151638
$905$	2.76904e47	0.0454599
$906$	8.58296e46	0.0138364
$907$	−4.59452e47	−0.0727310	−0.0363655	−	0.999339i	$-0.511578\pi$
$907$	−4.59452e47	−0.0727310	−0.0363655	+	0.999339i	$0.511578\pi$
$908$	−1.49937e48	−0.233073
$909$	2.15804e48	0.329424
$910$	−3.70710e48	−0.555714
$911$	6.61697e48	0.974105	0.487053	−	0.873373i	$-0.338072\pi$
$911$	6.61697e48	0.974105	0.487053	+	0.873373i	$0.338072\pi$
$912$	7.72101e46	0.0111624
$913$	9.90804e48	1.40676
$914$	3.34214e48	0.466028
$915$	9.68198e46	0.0132592
$916$	3.77252e48	0.507406
$917$	7.44895e48	0.984013
$918$	−2.81904e46	−0.00365760
$919$	−1.20821e49	−1.53971	−0.769854	−	0.638220i	$-0.779671\pi$
$919$	−1.20821e49	−1.53971	−0.769854	+	0.638220i	$0.779671\pi$
$920$	1.42018e48	0.177764
$921$	−2.85260e47	−0.0350717
$922$	−5.05066e48	−0.609942
$923$	2.16775e49	2.57147
$924$	1.79339e47	0.0208971
$925$	−3.21048e48	−0.367478
$926$	2.74677e48	0.308846
$927$	−9.73833e48	−1.07564
$928$	6.49788e47	0.0705067
$929$	5.93684e48	0.632843	0.316422	−	0.948619i	$-0.397519\pi$
$929$	5.93684e48	0.632843	0.316422	+	0.948619i	$0.397519\pi$
$930$	1.45261e47	0.0152118
$931$	−1.94592e48	−0.200196
$932$	8.12522e47	0.0821245
$933$	−5.79851e46	−0.00575797
$934$	7.64268e48	0.745628
$935$	2.15776e47	0.0206829
$936$	5.99229e48	0.564340
$937$	−1.17439e49	−1.08670	−0.543349	−	0.839507i	$-0.682844\pi$
$937$	−1.17439e49	−1.08670	−0.543349	+	0.839507i	$0.682844\pi$
$938$	−2.29019e48	−0.208221
$939$	1.89709e46	0.00169475
$940$	−2.33721e48	−0.205158
$941$	1.07666e49	0.928646	0.464323	−	0.885666i	$-0.346298\pi$
$941$	1.07666e49	0.928646	0.464323	+	0.885666i	$0.346298\pi$
$942$	−4.47846e47	−0.0379568
$943$	1.45277e49	1.20991
$944$	3.84744e48	0.314872
$945$	5.63260e47	0.0452985
$946$	9.91754e48	0.783791
$947$	−2.67196e48	−0.207518	−0.103759	−	0.994602i	$-0.533087\pi$
$947$	−2.67196e48	−0.207518	−0.103759	+	0.994602i	$0.533087\pi$
$948$	3.86502e47	0.0294995
$949$	2.50543e48	0.187927
$950$	−1.85614e48	−0.136827
$951$	7.20682e47	0.0522114
$952$	−3.06044e47	−0.0217909
$953$	−5.75060e48	−0.402421	−0.201210	−	0.979548i	$-0.564487\pi$
$953$	−5.75060e48	−0.402421	−0.201210	+	0.979548i	$0.564487\pi$
$954$	−1.16368e49	−0.800359
$955$	−8.34954e48	−0.564426
$956$	−1.05976e49	−0.704126
$957$	2.32343e47	0.0151734
$958$	9.66390e48	0.620328
$959$	−2.76727e49	−1.74600
$960$	−4.15971e46	−0.00257981
$961$	1.41901e48	0.0865066
$962$	3.46807e49	2.07826
$963$	−1.57797e49	−0.929533
$964$	−1.41857e49	−0.821447
$965$	−6.98537e48	−0.397639
$966$	−7.20250e47	−0.0403051
$967$	−1.91342e49	−1.05262	−0.526311	−	0.850292i	$-0.676425\pi$
$967$	−1.91342e49	−1.05262	−0.526311	+	0.850292i	$0.676425\pi$
$968$	−2.09480e48	−0.113292
$969$	−4.71132e46	−0.00250496
$970$	−7.62730e48	−0.398692
$971$	−1.56571e49	−0.804625	−0.402313	−	0.915502i	$-0.631794\pi$
$971$	−1.56571e49	−0.804625	−0.402313	+	0.915502i	$0.631794\pi$
$972$	−1.36620e48	−0.0690271
$973$	4.02854e48	0.200118
$974$	9.58412e48	0.468090
$975$	3.07455e47	0.0147640
$976$	−3.40173e48	−0.160612
$977$	1.35623e49	0.629614	0.314807	−	0.949156i	$-0.398060\pi$
$977$	1.35623e49	0.629614	0.314807	+	0.949156i	$0.398060\pi$
$978$	−1.01351e48	−0.0462631
$979$	−8.17907e48	−0.367104
$980$	1.04837e48	0.0462683
$981$	−3.90388e49	−1.69417
$982$	−1.28811e49	−0.549686
$983$	1.58986e49	0.667155	0.333578	−	0.942723i	$-0.391744\pi$
$983$	1.58986e49	0.667155	0.333578	+	0.942723i	$0.391744\pi$
$984$	−4.25517e47	−0.0175589
$985$	−1.14238e49	−0.463567
$986$	−3.96497e47	−0.0158224
$987$	1.18533e48	0.0465162
$988$	2.00506e49	0.773818
$989$	−3.98302e49	−1.51173
$990$	6.96898e48	0.260129
$991$	1.36513e49	0.501141	0.250570	−	0.968098i	$-0.419382\pi$
$991$	1.36513e49	0.501141	0.250570	+	0.968098i	$0.419382\pi$
$992$	−5.10368e48	−0.184264
$993$	−4.78900e47	−0.0170052
$994$	−3.57576e49	−1.24880
$995$	6.01839e48	0.206728
$996$	1.16551e48	0.0393766
$997$	3.08204e49	1.02416	0.512081	−	0.858937i	$-0.328875\pi$
$997$	3.08204e49	1.02416	0.512081	+	0.858937i	$0.328875\pi$
$998$	3.32011e49	1.08517
$999$	−5.26942e48	−0.169407

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.34.a.a.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.34.a.a.1.2	✓	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+65536.0 q^{2} -3.44083e6 q^{3} +4.29497e9 q^{4} +1.52588e11 q^{5} -2.25498e11 q^{6} +9.65954e13 q^{7} +2.81475e14 q^{8} -5.54722e15 q^{9} +1.00000e16 q^{10} -1.25630e17 q^{11} -1.47783e16 q^{12} -3.83776e18 q^{13} +6.33048e18 q^{14} -5.25030e17 q^{15} +1.84467e19 q^{16} -1.12561e19 q^{17} -3.63543e20 q^{18} -1.21644e21 q^{19} +6.55360e20 q^{20} -3.32369e20 q^{21} -8.23330e21 q^{22} +3.30661e22 q^{23} -9.68509e20 q^{24} +2.32831e22 q^{25} -2.51511e23 q^{26} +3.82149e22 q^{27} +4.14874e23 q^{28} +5.37492e23 q^{29} -3.44083e22 q^{30} -4.22167e24 q^{31} +1.20893e24 q^{32} +4.32273e23 q^{33} -7.37680e23 q^{34} +1.47393e25 q^{35} -2.38251e25 q^{36} -1.37889e26 q^{37} -7.97206e25 q^{38} +1.32051e25 q^{39} +4.29497e25 q^{40} +4.39352e26 q^{41} -2.17821e25 q^{42} -1.20456e27 q^{43} -5.39577e26 q^{44} -8.46439e26 q^{45} +2.16702e27 q^{46} -3.56629e27 q^{47} -6.34722e25 q^{48} +1.59968e27 q^{49} +1.52588e27 q^{50} +3.87304e25 q^{51} -1.64830e28 q^{52} +3.20094e28 q^{53} +2.50445e27 q^{54} -1.91696e28 q^{55} +2.71892e28 q^{56} +4.18557e27 q^{57} +3.52251e28 q^{58} +2.08570e29 q^{59} -2.25498e27 q^{60} -1.84408e29 q^{61} -2.76671e29 q^{62} -5.35836e29 q^{63} +7.92282e28 q^{64} -5.85595e29 q^{65} +2.83294e28 q^{66} -3.61772e29 q^{67} -4.83446e28 q^{68} -1.13775e29 q^{69} +9.65954e29 q^{70} -5.64849e30 q^{71} -1.56140e30 q^{72} -6.52836e29 q^{73} -9.03671e30 q^{74} -8.01132e28 q^{75} -5.22457e30 q^{76} -1.21353e31 q^{77} +8.65408e29 q^{78} -2.61534e31 q^{79} +2.81475e30 q^{80} +3.07058e31 q^{81} +2.87934e31 q^{82} -7.88667e31 q^{83} -1.42751e30 q^{84} -1.71755e30 q^{85} -7.89424e31 q^{86} -1.84942e30 q^{87} -3.53617e31 q^{88} +6.51043e31 q^{89} -5.54722e31 q^{90} -3.70710e32 q^{91} +1.42018e32 q^{92} +1.45261e31 q^{93} -2.33721e32 q^{94} -1.85614e32 q^{95} -4.15971e30 q^{96} -7.62730e32 q^{97} +1.04837e32 q^{98} +6.96898e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 131072 q^{2} - 74648412 q^{3} + 8589934592 q^{4} + 305175781250 q^{5} - 4892158328832 q^{6} + 20327789415556 q^{7} + 562949953421312 q^{8} - 60\!\cdots\!74 q^{9} + 20\!\cdots\!00 q^{10} - 11\!\cdots\!76 q^{11}+ \cdots + 64\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q + 131072 * q^2 - 74648412 * q^3 + 8589934592 * q^4 + 305175781250 * q^5 - 4892158328832 * q^6 + 20327789415556 * q^7 + 562949953421312 * q^8 - 6035762623792374 * q^9 + 20000000000000000 * q^10 - 11282427183095376 * q^11 - 320612488238333952 * q^12 + 80760781784046988 * q^13 + 1332202007137878016 * q^14 - 11390443725585937500 * q^15 + 36893488147419103232 * q^16 - 205963221786194409324 * q^17 - 395559739312857022464 * q^18 - 2435166480698605800200 * q^19 + 1310720000000000000000 * q^20 + 5098464356293085660064 * q^21 - 739405147871338561536 * q^22 + 29028845471264700782748 * q^23 - 21011660029187453878272 * q^24 + 46566128730773925781250 * q^25 + 5292738594999303405568 * q^26 + 468849960215466385570920 * q^27 + 87307190739787973656576 * q^28 + 669911834369977099655580 * q^29 - 746484120000000000000000 * q^30 + 337264281536360263914904 * q^31 + 2417851639229258349412352 * q^32 - 7710152394128777821944144 * q^33 - 13498005702980036809457664 * q^34 + 3101774507988891601562500 * q^35 - 25923403075607397824200704 * q^36 - 184139192244080353693197524 * q^37 - 159591070479063829721907200 * q^38 - 265823042069990418214193928 * q^39 + 85899345920000000000000000 * q^40 + 14298843461054952714348324 * q^41 + 334132960054023661817954304 * q^42 - 608685062932886434615318652 * q^43 - 48457655770896043968823296 * q^44 - 920984287077693786621093750 * q^45 + 1902434416804803430498172928 * q^46 - 6646835622774856917274050444 * q^47 - 1377020151672828977366433792 * q^48 - 314561308595229853488986046 * q^49 + 3051757812500000000000000000 * q^50 + 13903352393449636924474059144 * q^51 + 346864916561874347987304448 * q^52 - 23551888524780401802822701892 * q^53 + 30726550992680805044775813120 * q^54 - 1721561764998684082031250000 * q^55 + 5721764052322744641557364736 * q^56 + 90968097453666874117923963600 * q^57 + 43903341977270819203028090880 * q^58 + 22604203336846958159402367960 * q^59 - 48921583288320000000000000000 * q^60 - 339703294897757897934093836996 * q^61 + 22102951954766906255927148544 * q^62 - 498576262245539929538020028172 * q^63 + 158456325028528675187087900672 * q^64 + 12323117337653654174804687500 * q^65 - 505292547301623583338931421184 * q^66 - 2526076586974742197515421878164 * q^67 - 884605301750499692344617467904 * q^68 + 173707302971204205114453695712 * q^69 + 203277894155560000000000000000 * q^70 - 8757591773294778824971571836536 * q^71 - 1698916143963006423806817337344 * q^72 - 8032530857221267753332158819132 * q^73 - 12067746102908050059637392932864 * q^74 - 1738043781369924545288085937500 * q^75 - 10458960394915927144654910259200 * q^76 - 20856327865334287425485502151728 * q^77 - 17420978885098892048085413265408 * q^78 - 19259566961569543032032618239280 * q^79 + 5629499534213120000000000000000 * q^80 + 2757197276039678745749615255682 * q^81 + 937089005063697381087531761664 * q^82 - 27953508025018595447820979950492 * q^83 + 21897737670100494700901453266944 * q^84 - 31427493558684449664916992187500 * q^85 - 39890784284369645378949523177472 * q^86 - 11278711205229412420659895252680 * q^87 - 3175720928601443137540803526656 * q^88 - 151408466968396001182516810504620 * q^89 - 60357626237923740000000000000000 * q^90 - 669565717488479778480411355776136 * q^91 + 124677941939719597621128261009408 * q^92 - 310104499419190165213555069751424 * q^93 - 435607019374173022930472169897984 * q^94 - 371576916610505035430908203125000 * q^95 - 90244392660030519860686604992512 * q^96 - 616001214102537194391941400541484 * q^97 - 20615089920096983678254189510656 * q^98 + 641034674983890137043915947758512 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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