LMFDB - Embedded newform 10.34.a.a.1.1

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			1.1
Root			$62747.5$ 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)

$f(q)$	$=$	\(q+65536.0 q^{2} -7.12076e7 q^{3} +4.29497e9 q^{4} +1.52588e11 q^{5} -4.66666e12 q^{6} -7.62676e13 q^{7} +2.81475e14 q^{8} -4.88541e14 q^{9} +1.00000e16 q^{10} +1.14348e17 q^{11} -3.05834e17 q^{12} +3.91852e18 q^{13} -4.99828e18 q^{14} -1.08654e19 q^{15} +1.84467e19 q^{16} -1.94707e20 q^{17} -3.20170e19 q^{18} -1.21873e21 q^{19} +6.55360e20 q^{20} +5.43083e21 q^{21} +7.49389e21 q^{22} -4.03724e21 q^{23} -2.00432e22 q^{24} +2.32831e22 q^{25} +2.56804e23 q^{26} +4.30635e23 q^{27} -3.27567e23 q^{28} +1.32420e23 q^{29} -7.12076e23 q^{30} +4.55893e24 q^{31} +1.20893e24 q^{32} -8.14242e24 q^{33} -1.27603e25 q^{34} -1.16375e25 q^{35} -2.09827e24 q^{36} -4.62500e25 q^{37} -7.98704e25 q^{38} -2.79028e26 q^{39} +4.29497e25 q^{40} -4.25054e26 q^{41} +3.55915e26 q^{42} +5.95880e26 q^{43} +4.91120e26 q^{44} -7.45455e25 q^{45} -2.64585e26 q^{46} -3.08054e27 q^{47} -1.31355e27 q^{48} -1.91424e27 q^{49} +1.52588e27 q^{50} +1.38646e28 q^{51} +1.68299e28 q^{52} -5.55613e28 q^{53} +2.82221e28 q^{54} +1.74481e28 q^{55} -2.14674e28 q^{56} +8.67825e28 q^{57} +8.67826e27 q^{58} -1.85966e29 q^{59} -4.66666e28 q^{60} -1.55295e29 q^{61} +2.98774e29 q^{62} +3.72599e28 q^{63} +7.92282e28 q^{64} +5.97918e29 q^{65} -5.33622e29 q^{66} -2.16431e30 q^{67} -8.36261e29 q^{68} +2.87482e29 q^{69} -7.62676e29 q^{70} -3.10911e30 q^{71} -1.37512e29 q^{72} -7.37969e30 q^{73} -3.03104e30 q^{74} -1.65793e30 q^{75} -5.23439e30 q^{76} -8.72103e30 q^{77} -1.82864e31 q^{78} +6.89383e30 q^{79} +2.81475e30 q^{80} -2.79487e31 q^{81} -2.78563e31 q^{82} +5.09132e31 q^{83} +2.33253e31 q^{84} -2.97099e31 q^{85} +3.90516e31 q^{86} -9.42929e30 q^{87} +3.21860e31 q^{88} -2.16513e32 q^{89} -4.88541e30 q^{90} -2.98856e32 q^{91} -1.73398e31 q^{92} -3.24631e32 q^{93} -2.01886e32 q^{94} -1.85963e32 q^{95} -8.60847e31 q^{96} +1.46729e32 q^{97} -1.25452e32 q^{98} -5.58636e31 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−7.12076e7	−0.955049	−0.477524	−	0.878619i	$-0.658466\pi$
$3$	−7.12076e7	−0.955049	−0.477524	+	0.878619i	$0.658466\pi$
$4$	4.29497e9	0.500000
$5$	1.52588e11	0.447214
$5$	1.52588e11	0.447214
$6$	−4.66666e12	−0.675321
$7$	−7.62676e13	−0.867406	−0.433703	−	0.901056i	$-0.642793\pi$
$7$	−7.62676e13	−0.867406	−0.433703	+	0.901056i	$0.642793\pi$
$8$	2.81475e14	0.353553
$9$	−4.88541e14	−0.0878820
$10$	1.00000e16	0.316228
$11$	1.14348e17	0.750323	0.375161	−	0.926959i	$-0.377587\pi$
$11$	1.14348e17	0.750323	0.375161	+	0.926959i	$0.377587\pi$
$12$	−3.05834e17	−0.477524
$13$	3.91852e18	1.63326	0.816632	−	0.577159i	$-0.195839\pi$
$13$	3.91852e18	1.63326	0.816632	+	0.577159i	$0.195839\pi$
$14$	−4.99828e18	−0.613349
$15$	−1.08654e19	−0.427111
$16$	1.84467e19	0.250000
$17$	−1.94707e20	−0.970453	−0.485227	−	0.874388i	$-0.661263\pi$
$17$	−1.94707e20	−0.970453	−0.485227	+	0.874388i	$0.661263\pi$
$18$	−3.20170e19	−0.0621420
$19$	−1.21873e21	−0.969330	−0.484665	−	0.874700i	$-0.661058\pi$
$19$	−1.21873e21	−0.969330	−0.484665	+	0.874700i	$0.661058\pi$
$20$	6.55360e20	0.223607
$21$	5.43083e21	0.828415
$22$	7.49389e21	0.530558
$23$	−4.03724e21	−0.137270	−0.0686350	−	0.997642i	$-0.521864\pi$
$23$	−4.03724e21	−0.137270	−0.0686350	+	0.997642i	$0.521864\pi$
$24$	−2.00432e22	−0.337661
$25$	2.32831e22	0.200000
$26$	2.56804e23	1.15489
$27$	4.30635e23	1.03898
$28$	−3.27567e23	−0.433703
$29$	1.32420e23	0.0982621	0.0491310	−	0.998792i	$-0.484355\pi$
$29$	1.32420e23	0.0982621	0.0491310	+	0.998792i	$0.484355\pi$
$30$	−7.12076e23	−0.302013
$31$	4.55893e24	1.12563	0.562814	−	0.826583i	$-0.309719\pi$
$31$	4.55893e24	1.12563	0.562814	+	0.826583i	$0.309719\pi$
$32$	1.20893e24	0.176777
$33$	−8.14242e24	−0.716595
$34$	−1.27603e25	−0.686214
$35$	−1.16375e25	−0.387916
$36$	−2.09827e24	−0.0439410
$37$	−4.62500e25	−0.616288	−0.308144	−	0.951340i	$-0.599708\pi$
$37$	−4.62500e25	−0.616288	−0.308144	+	0.951340i	$0.599708\pi$
$38$	−7.98704e25	−0.685420
$39$	−2.79028e26	−1.55985
$40$	4.29497e25	0.158114
$41$	−4.25054e26	−1.04114	−0.520571	−	0.853818i	$-0.674281\pi$
$41$	−4.25054e26	−1.04114	−0.520571	+	0.853818i	$0.674281\pi$
$42$	3.55915e26	0.585778
$43$	5.95880e26	0.665165	0.332582	−	0.943074i	$-0.392080\pi$
$43$	5.95880e26	0.665165	0.332582	+	0.943074i	$0.392080\pi$
$44$	4.91120e26	0.375161
$45$	−7.45455e25	−0.0393020
$46$	−2.64585e26	−0.0970645
$47$	−3.08054e27	−0.792524	−0.396262	−	0.918138i	$-0.629693\pi$
$47$	−3.08054e27	−0.792524	−0.396262	+	0.918138i	$0.629693\pi$
$48$	−1.31355e27	−0.238762
$49$	−1.91424e27	−0.247606
$50$	1.52588e27	0.141421
$51$	1.38646e28	0.926830
$52$	1.68299e28	0.816632
$53$	−5.55613e28	−1.96889	−0.984443	−	0.175706i	$-0.943779\pi$
$53$	−5.55613e28	−1.96889	−0.984443	+	0.175706i	$0.943779\pi$
$54$	2.82221e28	0.734670
$55$	1.74481e28	0.335555
$56$	−2.14674e28	−0.306674
$57$	8.67825e28	0.925757
$58$	8.67826e27	0.0694818
$59$	−1.85966e29	−1.12299	−0.561494	−	0.827481i	$-0.689773\pi$
$59$	−1.85966e29	−1.12299	−0.561494	+	0.827481i	$0.689773\pi$
$60$	−4.66666e28	−0.213555
$61$	−1.55295e29	−0.541023	−0.270511	−	0.962717i	$-0.587193\pi$
$61$	−1.55295e29	−0.541023	−0.270511	+	0.962717i	$0.587193\pi$
$62$	2.98774e29	0.795940
$63$	3.72599e28	0.0762294
$64$	7.92282e28	0.125000
$65$	5.97918e29	0.730418
$66$	−5.33622e29	−0.506709
$67$	−2.16431e30	−1.60356	−0.801778	−	0.597622i	$-0.796112\pi$
$67$	−2.16431e30	−1.60356	−0.801778	+	0.597622i	$0.796112\pi$
$68$	−8.36261e29	−0.485227
$69$	2.87482e29	0.131099
$70$	−7.62676e29	−0.274298
$71$	−3.10911e30	−0.884856	−0.442428	−	0.896804i	$-0.645883\pi$
$71$	−3.10911e30	−0.884856	−0.442428	+	0.896804i	$0.645883\pi$
$72$	−1.37512e29	−0.0310710
$73$	−7.37969e30	−1.32804	−0.664020	−	0.747715i	$-0.731151\pi$
$73$	−7.37969e30	−1.32804	−0.664020	+	0.747715i	$0.731151\pi$
$74$	−3.03104e30	−0.435781
$75$	−1.65793e30	−0.191010
$76$	−5.23439e30	−0.484665
$77$	−8.72103e30	−0.650835
$78$	−1.82864e31	−1.10298
$79$	6.89383e30	0.336988	0.168494	−	0.985703i	$-0.446110\pi$
$79$	6.89383e30	0.336988	0.168494	+	0.985703i	$0.446110\pi$
$80$	2.81475e30	0.111803
$81$	−2.79487e31	−0.904395
$82$	−2.78563e31	−0.736199
$83$	5.09132e31	1.10165	0.550823	−	0.834622i	$-0.314314\pi$
$83$	5.09132e31	1.10165	0.550823	+	0.834622i	$0.314314\pi$
$84$	2.33253e31	0.414208
$85$	−2.97099e31	−0.434000
$86$	3.90516e31	0.470342
$87$	−9.42929e30	−0.0938450
$88$	3.21860e31	0.265279
$89$	−2.16513e32	−1.48098	−0.740489	−	0.672069i	$-0.765406\pi$
$89$	−2.16513e32	−1.48098	−0.740489	+	0.672069i	$0.765406\pi$
$90$	−4.88541e30	−0.0277907
$91$	−2.98856e32	−1.41670
$92$	−1.73398e31	−0.0686350
$93$	−3.24631e32	−1.07503
$94$	−2.01886e32	−0.560399
$95$	−1.85963e32	−0.433498
$96$	−8.60847e31	−0.168830
$97$	1.46729e32	0.242539	0.121270	−	0.992620i	$-0.461303\pi$
$97$	1.46729e32	0.242539	0.121270	+	0.992620i	$0.461303\pi$
$98$	−1.25452e32	−0.175084
$99$	−5.58636e31	−0.0659399
$100$	1.00000e32	0.100000
$101$	1.73454e32	0.147191	0.0735957	−	0.997288i	$-0.476553\pi$
$101$	1.73454e32	0.147191	0.0735957	+	0.997288i	$0.476553\pi$
$102$	9.08632e32	0.655368
$103$	2.04881e33	1.25802	0.629010	−	0.777397i	$-0.283460\pi$
$103$	2.04881e33	1.25802	0.629010	+	0.777397i	$0.283460\pi$
$104$	1.10296e33	0.577446
$105$	8.28679e32	0.370479
$106$	−3.64126e33	−1.39221
$107$	2.99134e33	0.979564	0.489782	−	0.871845i	$-0.337076\pi$
$107$	2.99134e33	0.979564	0.489782	+	0.871845i	$0.337076\pi$
$108$	1.84956e33	0.519490
$109$	1.01197e33	0.244136	0.122068	−	0.992522i	$-0.461047\pi$
$109$	1.01197e33	0.244136	0.122068	+	0.992522i	$0.461047\pi$
$110$	1.14348e33	0.237273
$111$	3.29335e33	0.588585
$112$	−1.40689e33	−0.216852
$113$	1.11805e34	1.48822	0.744112	−	0.668055i	$-0.232873\pi$
$113$	1.11805e34	1.48822	0.744112	+	0.668055i	$0.232873\pi$
$114$	5.68738e33	0.654609
$115$	−6.16034e32	−0.0613890
$116$	5.68739e32	0.0491310
$117$	−1.91436e33	−0.143535
$118$	−1.21875e34	−0.794073
$119$	1.48498e34	0.841777
$120$	−3.05834e33	−0.151006
$121$	−1.01498e34	−0.437015
$122$	−1.01774e34	−0.382561
$123$	3.02670e34	0.994342
$124$	1.95805e34	0.562814
$125$	3.55271e33	0.0894427
$126$	2.44186e33	0.0539023
$127$	−3.93900e33	−0.0763176	−0.0381588	−	0.999272i	$-0.512149\pi$
$127$	−3.93900e33	−0.0763176	−0.0381588	+	0.999272i	$0.512149\pi$
$128$	5.19230e33	0.0883883
$129$	−4.24312e34	−0.635265
$130$	3.91852e34	0.516484
$131$	−1.47962e35	−1.71860	−0.859298	−	0.511475i	$-0.829099\pi$
$131$	−1.47962e35	−1.71860	−0.859298	+	0.511475i	$0.829099\pi$
$132$	−3.49714e34	−0.358297
$133$	9.29493e34	0.840803
$134$	−1.41840e35	−1.13389
$135$	6.57097e34	0.464646
$136$	−5.48052e34	−0.343107
$137$	−1.94112e35	−1.07687	−0.538433	−	0.842668i	$-0.680984\pi$
$137$	−1.94112e35	−1.07687	−0.538433	+	0.842668i	$0.680984\pi$
$138$	1.88404e34	0.0927013
$139$	−2.46485e35	−1.07658	−0.538290	−	0.842760i	$-0.680929\pi$
$139$	−2.46485e35	−1.07658	−0.538290	+	0.842760i	$0.680929\pi$
$140$	−4.99828e34	−0.193958
$141$	2.19358e35	0.756899
$142$	−2.03758e35	−0.625688
$143$	4.48074e35	1.22548
$144$	−9.01200e33	−0.0219705
$145$	2.02057e34	0.0439441
$146$	−4.83636e35	−0.939066
$147$	1.36309e35	0.236476
$148$	−1.98642e35	−0.308144
$149$	3.11387e35	0.432243	0.216121	−	0.976367i	$-0.430659\pi$
$149$	3.11387e35	0.432243	0.216121	+	0.976367i	$0.430659\pi$
$150$	−1.08654e35	−0.135064
$151$	9.07358e34	0.101079	0.0505393	−	0.998722i	$-0.483906\pi$
$151$	9.07358e34	0.101079	0.0505393	+	0.998722i	$0.483906\pi$
$152$	−3.43041e35	−0.342710
$153$	9.51225e34	0.0852854
$154$	−5.71541e35	−0.460210
$155$	6.95638e35	0.503397
$156$	−1.19842e36	−0.779923
$157$	−1.67723e36	−0.982311	−0.491156	−	0.871072i	$-0.663425\pi$
$157$	−1.67723e36	−0.982311	−0.491156	+	0.871072i	$0.663425\pi$
$158$	4.51794e35	0.238286
$159$	3.95638e36	1.88038
$160$	1.84467e35	0.0790569
$161$	3.07911e35	0.119069
$162$	−1.83164e36	−0.639504
$163$	1.61172e36	0.508386	0.254193	−	0.967154i	$-0.418190\pi$
$163$	1.61172e36	0.508386	0.254193	+	0.967154i	$0.418190\pi$
$164$	−1.82559e36	−0.520571
$165$	−1.24244e36	−0.320471
$166$	3.33665e36	0.778981
$167$	4.78201e36	1.01109	0.505544	−	0.862801i	$-0.331292\pi$
$167$	4.78201e36	1.01109	0.505544	+	0.862801i	$0.331292\pi$
$168$	1.52864e36	0.292889
$169$	9.59865e36	1.66755
$170$	−1.94707e36	−0.306884
$171$	5.95398e35	0.0851867
$172$	2.55928e36	0.332582
$173$	3.21818e36	0.380057	0.190029	−	0.981779i	$-0.439142\pi$
$173$	3.21818e36	0.380057	0.190029	+	0.981779i	$0.439142\pi$
$174$	−6.17958e35	−0.0663585
$175$	−1.77574e36	−0.173481
$176$	2.10934e36	0.187581
$177$	1.32422e37	1.07251
$178$	−1.41894e37	−1.04721
$179$	7.43648e35	0.0500372	0.0250186	−	0.999687i	$-0.492036\pi$
$179$	7.43648e35	0.0500372	0.0250186	+	0.999687i	$0.492036\pi$
$180$	−3.20170e35	−0.0196510
$181$	1.48729e37	0.833103	0.416551	−	0.909112i	$-0.363239\pi$
$181$	1.48729e37	0.833103	0.416551	+	0.909112i	$0.363239\pi$
$182$	−1.95858e37	−1.00176
$183$	1.10582e37	0.516703
$184$	−1.13638e36	−0.0485323
$185$	−7.05719e36	−0.275612
$186$	−2.12750e37	−0.760161
$187$	−2.22643e37	−0.728153
$188$	−1.32308e37	−0.396262
$189$	−3.28435e37	−0.901218
$190$	−1.21873e37	−0.306529
$191$	−4.87779e36	−0.112505	−0.0562526	−	0.998417i	$-0.517915\pi$
$191$	−4.87779e36	−0.112505	−0.0562526	+	0.998417i	$0.517915\pi$
$192$	−5.64165e36	−0.119381
$193$	−7.11316e37	−1.38155	−0.690776	−	0.723069i	$-0.742731\pi$
$193$	−7.11316e37	−1.38155	−0.690776	+	0.723069i	$0.742731\pi$
$194$	9.61602e36	0.171501
$195$	−4.25763e37	−0.697585
$196$	−8.22161e36	−0.123803
$197$	−1.21522e38	−1.68252	−0.841261	−	0.540630i	$-0.818186\pi$
$197$	−1.21522e38	−1.68252	−0.841261	+	0.540630i	$0.818186\pi$
$198$	−3.66108e36	−0.0466265
$199$	1.59347e38	1.86754	0.933768	−	0.357878i	$-0.116500\pi$
$199$	1.59347e38	1.86754	0.933768	+	0.357878i	$0.116500\pi$
$200$	6.55360e36	0.0707107
$201$	1.54115e38	1.53147
$202$	1.13675e37	0.104080
$203$	−1.00993e37	−0.0852331
$204$	5.95481e37	0.463415
$205$	−6.48580e37	−0.465613
$206$	1.34271e38	0.889555
$207$	1.97236e36	0.0120636
$208$	7.22839e37	0.408316
$209$	−1.39359e38	−0.727311
$210$	5.43083e37	0.261968
$211$	−1.86059e38	−0.829832	−0.414916	−	0.909860i	$-0.636189\pi$
$211$	−1.86059e38	−0.829832	−0.414916	+	0.909860i	$0.636189\pi$
$212$	−2.38634e38	−0.984443
$213$	2.21392e38	0.845081
$214$	1.96040e38	0.692656
$215$	9.09241e37	0.297471
$216$	1.21213e38	0.367335
$217$	−3.47699e38	−0.976378
$218$	6.63207e37	0.172630
$219$	5.25490e38	1.26834
$220$	7.49389e37	0.167777
$221$	−7.62963e38	−1.58501
$222$	2.15833e38	0.416192
$223$	2.35939e38	0.422444	0.211222	−	0.977438i	$-0.432256\pi$
$223$	2.35939e38	0.422444	0.211222	+	0.977438i	$0.432256\pi$
$224$	−9.22019e37	−0.153337
$225$	−1.13747e37	−0.0175764
$226$	7.32727e38	1.05233
$227$	3.89426e38	0.519994	0.259997	−	0.965609i	$-0.416278\pi$
$227$	3.89426e38	0.519994	0.259997	+	0.965609i	$0.416278\pi$
$228$	3.72728e38	0.462879
$229$	−6.42546e38	−0.742368	−0.371184	−	0.928559i	$-0.621048\pi$
$229$	−6.42546e38	−0.742368	−0.371184	+	0.928559i	$0.621048\pi$
$230$	−4.03724e37	−0.0434086
$231$	6.21003e38	0.621579
$232$	3.72728e37	0.0347409
$233$	9.96582e38	0.865248	0.432624	−	0.901574i	$-0.357588\pi$
$233$	9.96582e38	0.865248	0.432624	+	0.901574i	$0.357588\pi$
$234$	−1.25459e38	−0.101494
$235$	−4.70053e38	−0.354427
$236$	−7.98718e38	−0.561494
$237$	−4.90893e38	−0.321839
$238$	9.73200e38	0.595226
$239$	2.06735e39	1.17991	0.589956	−	0.807435i	$-0.299145\pi$
$239$	2.06735e39	1.17991	0.589956	+	0.807435i	$0.299145\pi$
$240$	−2.00432e38	−0.106778
$241$	−2.94996e39	−1.46735	−0.733677	−	0.679498i	$-0.762197\pi$
$241$	−2.94996e39	−1.46735	−0.733677	+	0.679498i	$0.762197\pi$
$242$	−6.65174e38	−0.309017
$243$	−4.03771e38	−0.175239
$244$	−6.66987e38	−0.270511
$245$	−2.92090e38	−0.110733
$246$	1.98358e39	0.703106
$247$	−4.77560e39	−1.58317
$248$	1.28323e39	0.397970
$249$	−3.62541e39	−1.05213
$250$	2.32831e38	0.0632456
$251$	−5.46260e39	−1.38926	−0.694630	−	0.719368i	$-0.744432\pi$
$251$	−5.46260e39	−1.38926	−0.694630	+	0.719368i	$0.744432\pi$
$252$	1.60030e38	0.0381147
$253$	−4.61649e38	−0.102997
$254$	−2.58146e38	−0.0539647
$255$	2.11557e39	0.414491
$256$	3.40282e38	0.0625000
$257$	1.10808e40	1.90843	0.954213	−	0.299129i	$-0.0966960\pi$
$257$	1.10808e40	1.90843	0.954213	+	0.299129i	$0.0966960\pi$
$258$	−2.78077e39	−0.449200
$259$	3.52738e39	0.534572
$260$	2.56804e39	0.365209
$261$	−6.46925e37	−0.00863547
$262$	−9.69684e39	−1.21523
$263$	−1.40170e40	−1.64963	−0.824815	−	0.565403i	$-0.808721\pi$
$263$	−1.40170e40	−1.64963	−0.824815	+	0.565403i	$0.808721\pi$
$264$	−2.29189e39	−0.253355
$265$	−8.47798e39	−0.880512
$266$	6.09153e39	0.594538
$267$	1.54174e40	1.41441
$268$	−9.29562e39	−0.801778
$269$	−6.31508e39	−0.512232	−0.256116	−	0.966646i	$-0.582443\pi$
$269$	−6.31508e39	−0.512232	−0.256116	+	0.966646i	$0.582443\pi$
$270$	4.30635e39	0.328554
$271$	1.08648e40	0.779879	0.389939	−	0.920841i	$-0.372496\pi$
$271$	1.08648e40	0.779879	0.389939	+	0.920841i	$0.372496\pi$
$272$	−3.59171e39	−0.242613
$273$	2.12808e40	1.35302
$274$	−1.27213e40	−0.761460
$275$	2.66237e39	0.150065
$276$	1.23473e39	0.0655497
$277$	2.33494e40	1.16778	0.583889	−	0.811834i	$-0.301530\pi$
$277$	2.33494e40	1.16778	0.583889	+	0.811834i	$0.301530\pi$
$278$	−1.61536e40	−0.761257
$279$	−2.22723e39	−0.0989225
$280$	−3.27567e39	−0.137149
$281$	3.50713e40	1.38451	0.692257	−	0.721652i	$-0.256617\pi$
$281$	3.50713e40	1.38451	0.692257	+	0.721652i	$0.256617\pi$
$282$	1.43758e40	0.535208
$283$	2.34001e40	0.821753	0.410876	−	0.911691i	$-0.365223\pi$
$283$	2.34001e40	0.821753	0.410876	+	0.911691i	$0.365223\pi$
$284$	−1.33535e40	−0.442428
$285$	1.32420e40	0.414011
$286$	2.93649e40	0.866542
$287$	3.24178e40	0.903093
$288$	−5.90610e38	−0.0155355
$289$	−2.34364e39	−0.0582205
$290$	1.32420e39	0.0310732
$291$	−1.04482e40	−0.231637
$292$	−3.16955e40	−0.664020
$293$	−3.11041e40	−0.615889	−0.307944	−	0.951404i	$-0.599641\pi$
$293$	−3.11041e40	−0.615889	−0.307944	+	0.951404i	$0.599641\pi$
$294$	8.93312e39	0.167214
$295$	−2.83762e40	−0.502216
$296$	−1.30182e40	−0.217891
$297$	4.92421e40	0.779571
$298$	2.04071e40	0.305642
$299$	−1.58200e40	−0.224198
$300$	−7.12076e39	−0.0955049
$301$	−4.54463e40	−0.576968
$302$	5.94646e39	0.0714733
$303$	−1.23513e40	−0.140575
$304$	−2.24815e40	−0.242333
$305$	−2.36962e40	−0.241953
$306$	6.23395e39	0.0603059
$307$	−1.56830e41	−1.43762	−0.718811	−	0.695206i	$-0.755313\pi$
$307$	−1.56830e41	−1.43762	−0.718811	+	0.695206i	$0.755313\pi$
$308$	−3.74565e40	−0.325417
$309$	−1.45891e41	−1.20147
$310$	4.55893e40	0.355955
$311$	−1.90389e41	−1.40960	−0.704798	−	0.709408i	$-0.748963\pi$
$311$	−1.90389e41	−1.40960	−0.704798	+	0.709408i	$0.748963\pi$
$312$	−7.85394e40	−0.551489
$313$	3.43316e40	0.228671	0.114336	−	0.993442i	$-0.463526\pi$
$313$	3.43316e40	0.228671	0.114336	+	0.993442i	$0.463526\pi$
$314$	−1.09919e41	−0.694599
$315$	5.68541e39	0.0340908
$316$	2.96088e40	0.168494
$317$	2.69572e41	1.45612	0.728060	−	0.685514i	$-0.240422\pi$
$317$	2.69572e41	1.45612	0.728060	+	0.685514i	$0.240422\pi$
$318$	2.59286e41	1.32963
$319$	1.51419e40	0.0737283
$320$	1.20893e40	0.0559017
$321$	−2.13006e41	−0.935531
$322$	2.01792e40	0.0841944
$323$	2.37295e41	0.940689
$324$	−1.20039e41	−0.452197
$325$	9.12351e40	0.326653
$326$	1.05626e41	0.359483
$327$	−7.20602e40	−0.233162
$328$	−1.19642e41	−0.368099
$329$	2.34946e41	0.687440
$330$	−8.14242e40	−0.226607
$331$	1.12474e41	0.297777	0.148888	−	0.988854i	$-0.452430\pi$
$331$	1.12474e41	0.297777	0.148888	+	0.988854i	$0.452430\pi$
$332$	2.18671e41	0.550823
$333$	2.25950e40	0.0541606
$334$	3.13394e41	0.714947
$335$	−3.30247e41	−0.717132
$336$	1.00181e41	0.207104
$337$	−8.06548e41	−1.58759	−0.793793	−	0.608188i	$-0.791897\pi$
$337$	−8.06548e41	−1.58759	−0.793793	+	0.608188i	$0.791897\pi$
$338$	6.29057e41	1.17914
$339$	−7.96139e41	−1.42133
$340$	−1.27603e41	−0.217000
$341$	5.21304e41	0.844585
$342$	3.90200e40	0.0602361
$343$	7.35619e41	1.08218
$344$	1.67725e41	0.235171
$345$	4.38663e40	0.0586295
$346$	2.10906e41	0.268741
$347$	−6.20227e41	−0.753553	−0.376777	−	0.926304i	$-0.622968\pi$
$347$	−6.20227e41	−0.753553	−0.376777	+	0.926304i	$0.622968\pi$
$348$	−4.04985e40	−0.0469225
$349$	−8.80550e41	−0.973048	−0.486524	−	0.873667i	$-0.661735\pi$
$349$	−8.80550e41	−0.973048	−0.486524	+	0.873667i	$0.661735\pi$
$350$	−1.16375e41	−0.122670
$351$	1.68745e42	1.69693
$352$	1.38238e41	0.132640
$353$	1.63312e42	1.49533	0.747663	−	0.664078i	$-0.231176\pi$
$353$	1.63312e42	1.49533	0.747663	+	0.664078i	$0.231176\pi$
$354$	8.67840e41	0.758378
$355$	−4.74412e41	−0.395720
$356$	−9.29915e41	−0.740489
$357$	−1.05742e42	−0.803938
$358$	4.87357e40	0.0353816
$359$	−4.69226e41	−0.325330	−0.162665	−	0.986681i	$-0.552009\pi$
$359$	−4.69226e41	−0.325330	−0.162665	+	0.986681i	$0.552009\pi$
$360$	−2.09827e40	−0.0138954
$361$	−9.54774e40	−0.0603993
$362$	9.74709e41	0.589092
$363$	7.22739e41	0.417371
$364$	−1.28358e42	−0.708352
$365$	−1.12605e42	−0.593918
$366$	7.24709e41	0.365364
$367$	2.12758e42	1.02541	0.512704	−	0.858565i	$-0.328644\pi$
$367$	2.12758e42	1.02541	0.512704	+	0.858565i	$0.328644\pi$
$368$	−7.44740e40	−0.0343175
$369$	2.07656e41	0.0914977
$370$	−4.62500e41	−0.194887
$371$	4.23753e42	1.70782
$372$	−1.39428e42	−0.537515
$373$	−3.78223e42	−1.39493	−0.697465	−	0.716619i	$-0.745689\pi$
$373$	−3.78223e42	−1.39493	−0.697465	+	0.716619i	$0.745689\pi$
$374$	−1.45911e42	−0.514882
$375$	−2.52980e41	−0.0854222
$376$	−8.67095e41	−0.280199
$377$	5.18889e41	0.160488
$378$	−2.15243e42	−0.637257
$379$	−6.08338e42	−1.72424	−0.862121	−	0.506702i	$-0.830864\pi$
$379$	−6.08338e42	−1.72424	−0.862121	+	0.506702i	$0.830864\pi$
$380$	−7.98704e41	−0.216749
$381$	2.80487e41	0.0728870
$382$	−3.19671e41	−0.0795532
$383$	8.15229e41	0.194312	0.0971560	−	0.995269i	$-0.469025\pi$
$383$	8.15229e41	0.194312	0.0971560	+	0.995269i	$0.469025\pi$
$384$	−3.69731e41	−0.0844152
$385$	−1.33072e42	−0.291062
$386$	−4.66168e42	−0.976905
$387$	−2.91112e41	−0.0584560
$388$	6.30195e41	0.121270
$389$	−2.71183e42	−0.500143	−0.250071	−	0.968227i	$-0.580454\pi$
$389$	−2.71183e42	−0.500143	−0.250071	+	0.968227i	$0.580454\pi$
$390$	−2.79028e42	−0.493267
$391$	7.86080e41	0.133214
$392$	−5.38811e41	−0.0875420
$393$	1.05360e43	1.64134
$394$	−7.96404e42	−1.18972
$395$	1.05192e42	0.150705
$396$	−2.39932e41	−0.0329699
$397$	3.40205e42	0.448432	0.224216	−	0.974539i	$-0.428018\pi$
$397$	3.40205e42	0.448432	0.224216	+	0.974539i	$0.428018\pi$
$398$	1.04430e43	1.32055
$399$	−6.61870e42	−0.803008
$400$	4.29497e41	0.0500000
$401$	5.96117e42	0.665961	0.332981	−	0.942934i	$-0.391946\pi$
$401$	5.96117e42	0.665961	0.332981	+	0.942934i	$0.391946\pi$
$402$	1.01001e43	1.08292
$403$	1.78643e43	1.83845
$404$	7.44981e41	0.0735957
$405$	−4.26463e42	−0.404458
$406$	−6.61870e41	−0.0602689
$407$	−5.28858e42	−0.462415
$408$	3.90254e42	0.327684
$409$	−2.07282e43	−1.67158	−0.835788	−	0.549052i	$-0.814989\pi$
$409$	−2.07282e43	−1.67158	−0.835788	+	0.549052i	$0.814989\pi$
$410$	−4.25054e42	−0.329238
$411$	1.38222e43	1.02846
$412$	8.79958e42	0.629010
$413$	1.41832e43	0.974087
$414$	1.29261e41	0.00853022
$415$	7.76874e42	0.492671
$416$	4.73720e42	0.288723
$417$	1.75516e43	1.02819
$418$	−9.13300e42	−0.514286
$419$	−7.96843e42	−0.431362	−0.215681	−	0.976464i	$-0.569197\pi$
$419$	−7.96843e42	−0.431362	−0.215681	+	0.976464i	$0.569197\pi$
$420$	3.55915e42	0.185239
$421$	−1.40035e43	−0.700779	−0.350390	−	0.936604i	$-0.613951\pi$
$421$	−1.40035e43	−0.700779	−0.350390	+	0.936604i	$0.613951\pi$
$422$	−1.21936e43	−0.586780
$423$	1.50497e42	0.0696486
$424$	−1.56391e43	−0.696106
$425$	−4.53338e42	−0.194091
$426$	1.45091e43	0.597562
$427$	1.18440e43	0.469287
$428$	1.28477e43	0.489782
$429$	−3.19062e43	−1.17039
$430$	5.95880e42	0.210344
$431$	−2.19278e42	−0.0744937	−0.0372468	−	0.999306i	$-0.511859\pi$
$431$	−2.19278e42	−0.0744937	−0.0372468	+	0.999306i	$0.511859\pi$
$432$	7.94382e42	0.259745
$433$	4.94849e43	1.55748	0.778739	−	0.627348i	$-0.215859\pi$
$433$	4.94849e43	1.55748	0.778739	+	0.627348i	$0.215859\pi$
$434$	−2.27868e43	−0.690403
$435$	−1.43880e42	−0.0419688
$436$	4.34639e42	0.122068
$437$	4.92029e42	0.133060
$438$	3.44385e43	0.896854
$439$	−5.29628e43	−1.32833	−0.664165	−	0.747586i	$-0.731213\pi$
$439$	−5.29628e43	−1.32833	−0.664165	+	0.747586i	$0.731213\pi$
$440$	4.91120e42	0.118636
$441$	9.35187e41	0.0217601
$442$	−5.00016e43	−1.12077
$443$	−6.57483e43	−1.41979	−0.709893	−	0.704309i	$-0.751257\pi$
$443$	−6.57483e43	−1.41979	−0.709893	+	0.704309i	$0.751257\pi$
$444$	1.41448e43	0.294292
$445$	−3.30372e43	−0.662313
$446$	1.54625e43	0.298713
$447$	−2.21731e43	−0.412813
$448$	−6.04254e42	−0.108426
$449$	−7.00108e43	−1.21088	−0.605439	−	0.795892i	$-0.707002\pi$
$449$	−7.00108e43	−1.21088	−0.605439	+	0.795892i	$0.707002\pi$
$450$	−7.45455e41	−0.0124284
$451$	−4.86039e43	−0.781193
$452$	4.80200e43	0.744112
$453$	−6.46108e42	−0.0965349
$454$	2.55214e43	0.367692
$455$	−4.56018e43	−0.633569
$456$	2.44271e43	0.327305
$457$	−4.08696e42	−0.0528181	−0.0264091	−	0.999651i	$-0.508407\pi$
$457$	−4.08696e42	−0.0528181	−0.0264091	+	0.999651i	$0.508407\pi$
$458$	−4.21099e43	−0.524933
$459$	−8.38477e43	−1.00828
$460$	−2.64585e42	−0.0306945
$461$	5.94001e43	0.664848	0.332424	−	0.943130i	$-0.392134\pi$
$461$	5.94001e43	0.664848	0.332424	+	0.943130i	$0.392134\pi$
$462$	4.06981e43	0.439523
$463$	1.30594e44	1.36093	0.680466	−	0.732780i	$-0.261777\pi$
$463$	1.30594e44	1.36093	0.680466	+	0.732780i	$0.261777\pi$
$464$	2.44271e42	0.0245655
$465$	−4.95347e43	−0.480768
$466$	6.53120e43	0.611823
$467$	−3.66775e43	−0.331643	−0.165822	−	0.986156i	$-0.553028\pi$
$467$	−3.66775e43	−0.331643	−0.165822	+	0.986156i	$0.553028\pi$
$468$	−8.22210e42	−0.0717673
$469$	1.65066e44	1.39093
$470$	−3.08054e43	−0.250618
$471$	1.19432e44	0.938155
$472$	−5.23448e43	−0.397036
$473$	6.81375e43	0.499088
$474$	−3.21712e43	−0.227575
$475$	−2.83757e43	−0.193866
$476$	6.37796e43	0.420889
$477$	2.71440e43	0.173030
$478$	1.35486e44	0.834324
$479$	1.79143e44	1.06577	0.532885	−	0.846188i	$-0.321108\pi$
$479$	1.79143e44	1.06577	0.532885	+	0.846188i	$0.321108\pi$
$480$	−1.31355e43	−0.0755032
$481$	−1.81231e44	−1.00656
$482$	−1.93329e44	−1.03758
$483$	−2.19256e43	−0.113717
$484$	−4.35928e43	−0.218508
$485$	2.23890e43	0.108467
$486$	−2.64615e43	−0.123913
$487$	2.85315e44	1.29151	0.645753	−	0.763546i	$-0.276543\pi$
$487$	2.85315e44	1.29151	0.645753	+	0.763546i	$0.276543\pi$
$488$	−4.37117e43	−0.191280
$489$	−1.14767e44	−0.485533
$490$	−1.91424e43	−0.0783000
$491$	1.91812e44	0.758631	0.379316	−	0.925267i	$-0.376159\pi$
$491$	1.91812e44	0.758631	0.379316	+	0.925267i	$0.376159\pi$
$492$	1.29996e44	0.497171
$493$	−2.57831e43	−0.0953587
$494$	−3.12974e44	−1.11947
$495$	−8.52411e42	−0.0294892
$496$	8.40975e43	0.281407
$497$	2.37124e44	0.767530
$498$	−2.37595e44	−0.743965
$499$	2.99230e44	0.906456	0.453228	−	0.891395i	$-0.350272\pi$
$499$	2.99230e44	0.906456	0.453228	+	0.891395i	$0.350272\pi$
$500$	1.52588e43	0.0447214
$501$	−3.40515e44	−0.965638
$502$	−3.57997e44	−0.982355
$503$	2.22024e44	0.589559	0.294780	−	0.955565i	$-0.404754\pi$
$503$	2.22024e44	0.589559	0.294780	+	0.955565i	$0.404754\pi$
$504$	1.04877e43	0.0269512
$505$	2.64670e43	0.0658260
$506$	−3.02547e43	−0.0728297
$507$	−6.83496e44	−1.59259
$508$	−1.69179e43	−0.0381588
$509$	7.25178e44	1.58344	0.791720	−	0.610885i	$-0.209186\pi$
$509$	7.25178e44	1.58344	0.791720	+	0.610885i	$0.209186\pi$
$510$	1.38646e44	0.293089
$511$	5.62832e44	1.15195
$512$	2.23007e43	0.0441942
$513$	−5.24826e44	−1.00711
$514$	7.26192e44	1.34946
$515$	3.12624e44	0.562604
$516$	−1.82240e44	−0.317632
$517$	−3.52253e44	−0.594649
$518$	2.31170e44	0.377999
$519$	−2.29158e44	−0.362973
$520$	1.68299e44	0.258242
$521$	−1.11989e45	−1.66476	−0.832382	−	0.554202i	$-0.813023\pi$
$521$	−1.11989e45	−1.66476	−0.832382	+	0.554202i	$0.813023\pi$
$522$	−4.23969e42	−0.00610620
$523$	1.32139e45	1.84396	0.921981	−	0.387234i	$-0.126569\pi$
$523$	1.32139e45	1.84396	0.921981	+	0.387234i	$0.126569\pi$
$524$	−6.35492e44	−0.859298
$525$	1.26446e44	0.165683
$526$	−9.18621e44	−1.16646
$527$	−8.87657e44	−1.09237
$528$	−1.50201e44	−0.179149
$529$	−8.48706e44	−0.981157
$530$	−5.55613e44	−0.622616
$531$	9.08521e43	0.0986905
$532$	3.99214e44	0.420401
$533$	−1.66558e45	−1.70046
$534$	1.01039e45	1.00014
$535$	4.56442e44	0.438074
$536$	−6.09198e44	−0.566943
$537$	−5.29534e43	−0.0477879
$538$	−4.13865e44	−0.362203
$539$	−2.18889e44	−0.185785
$540$	2.82221e44	0.232323
$541$	7.54315e42	0.00602279	0.00301140	−	0.999995i	$-0.499041\pi$
$541$	7.54315e42	0.00602279	0.00301140	+	0.999995i	$0.499041\pi$
$542$	7.12033e44	0.551458
$543$	−1.05906e45	−0.795654
$544$	−2.35386e44	−0.171554
$545$	1.54415e44	0.109181
$546$	1.39466e45	0.956730
$547$	1.65387e45	1.10080	0.550402	−	0.834900i	$-0.314475\pi$
$547$	1.65387e45	1.10080	0.550402	+	0.834900i	$0.314475\pi$
$548$	−8.33703e44	−0.538433
$549$	7.58681e43	0.0475462
$550$	1.74481e44	0.106112
$551$	−1.61383e44	−0.0952484
$552$	8.09191e43	0.0463507
$553$	−5.25776e44	−0.292305
$554$	1.53023e45	0.825744
$555$	5.02526e44	0.263223
$556$	−1.05864e45	−0.538290
$557$	8.23792e44	0.406637	0.203318	−	0.979113i	$-0.434827\pi$
$557$	8.23792e44	0.406637	0.203318	+	0.979113i	$0.434827\pi$
$558$	−1.45964e44	−0.0699488
$559$	2.33497e45	1.08639
$560$	−2.14674e44	−0.0969790
$561$	1.58539e45	0.695422
$562$	2.29843e45	0.978999
$563$	−2.90289e45	−1.20072	−0.600360	−	0.799730i	$-0.704976\pi$
$563$	−2.90289e45	−1.20072	−0.600360	+	0.799730i	$0.704976\pi$
$564$	9.42135e44	0.378449
$565$	1.70601e45	0.665554
$566$	1.53355e45	0.581067
$567$	2.13158e45	0.784478
$568$	−8.75135e44	−0.312844
$569$	3.12951e45	1.08674	0.543369	−	0.839494i	$-0.317149\pi$
$569$	3.12951e45	1.08674	0.543369	+	0.839494i	$0.317149\pi$
$570$	8.67825e44	0.292750
$571$	−3.84526e45	−1.26017	−0.630086	−	0.776525i	$-0.716980\pi$
$571$	−3.84526e45	−1.26017	−0.630086	+	0.776525i	$0.716980\pi$
$572$	1.92446e45	0.612738
$573$	3.47336e44	0.107448
$574$	2.12454e45	0.638583
$575$	−9.39994e43	−0.0274540
$576$	−3.87062e43	−0.0109853
$577$	−2.53135e45	−0.698154	−0.349077	−	0.937094i	$-0.613505\pi$
$577$	−2.53135e45	−0.698154	−0.349077	+	0.937094i	$0.613505\pi$
$578$	−1.53593e44	−0.0411681
$579$	5.06511e45	1.31945
$580$	8.67826e43	0.0219721
$581$	−3.88303e45	−0.955575
$582$	−6.84733e44	−0.163792
$583$	−6.35331e45	−1.47730
$584$	−2.07720e45	−0.469533
$585$	−2.92108e44	−0.0641906
$586$	−2.03844e45	−0.435499
$587$	−1.89473e45	−0.393568	−0.196784	−	0.980447i	$-0.563050\pi$
$587$	−1.89473e45	−0.393568	−0.196784	+	0.980447i	$0.563050\pi$
$588$	5.85441e44	0.118238
$589$	−5.55609e45	−1.09111
$590$	−1.85966e45	−0.355120
$591$	8.65326e45	1.60689
$592$	−8.53162e44	−0.154072
$593$	−9.96728e45	−1.75055	−0.875275	−	0.483626i	$-0.839320\pi$
$593$	−9.96728e45	−1.75055	−0.875275	+	0.483626i	$0.839320\pi$
$594$	3.22713e45	0.551240
$595$	2.26591e45	0.376454
$596$	1.33740e45	0.216121
$597$	−1.13467e46	−1.78359
$598$	−1.03678e45	−0.158532
$599$	5.94982e45	0.885037	0.442518	−	0.896759i	$-0.354085\pi$
$599$	5.94982e45	0.885037	0.442518	+	0.896759i	$0.354085\pi$
$600$	−4.66666e44	−0.0675321
$601$	1.42873e45	0.201150	0.100575	−	0.994929i	$-0.467932\pi$
$601$	1.42873e45	0.201150	0.100575	+	0.994929i	$0.467932\pi$
$602$	−2.97837e45	−0.407978
$603$	1.05735e45	0.140924
$604$	3.89707e44	0.0505393
$605$	−1.54873e45	−0.195439
$606$	−8.09452e44	−0.0994015
$607$	5.41904e45	0.647603	0.323801	−	0.946125i	$-0.395039\pi$
$607$	5.41904e45	0.647603	0.323801	+	0.946125i	$0.395039\pi$
$608$	−1.47335e45	−0.171355
$609$	7.19150e44	0.0814018
$610$	−1.55295e45	−0.171086
$611$	−1.20712e46	−1.29440
$612$	4.08548e44	0.0426427
$613$	1.66868e46	1.69541	0.847705	−	0.530467i	$-0.177984\pi$
$613$	1.66868e46	1.69541	0.847705	+	0.530467i	$0.177984\pi$
$614$	−1.02780e46	−1.01655
$615$	4.61838e45	0.444683
$616$	−2.45475e45	−0.230105
$617$	−5.91960e45	−0.540240	−0.270120	−	0.962827i	$-0.587063\pi$
$617$	−5.91960e45	−0.540240	−0.270120	+	0.962827i	$0.587063\pi$
$618$	−9.56111e45	−0.849568
$619$	8.04200e45	0.695774	0.347887	−	0.937536i	$-0.386899\pi$
$619$	8.04200e45	0.695774	0.347887	+	0.937536i	$0.386899\pi$
$620$	2.98774e45	0.251698
$621$	−1.73858e45	−0.142621
$622$	−1.24773e46	−0.996736
$623$	1.65129e46	1.28461
$624$	−5.14716e45	−0.389962
$625$	5.42101e44	0.0400000
$626$	2.24995e45	0.161695
$627$	9.92339e45	0.694617
$628$	−7.20366e45	−0.491156
$629$	9.00521e45	0.598078
$630$	3.72599e44	0.0241059
$631$	−1.17738e46	−0.742050	−0.371025	−	0.928623i	$-0.620994\pi$
$631$	−1.17738e46	−0.742050	−0.371025	+	0.928623i	$0.620994\pi$
$632$	1.94044e45	0.119143
$633$	1.32488e46	0.792530
$634$	1.76667e46	1.02963
$635$	−6.01044e44	−0.0341303
$636$	1.69925e46	0.940191
$637$	−7.50099e45	−0.404406
$638$	9.92339e44	0.0521338
$639$	1.51893e45	0.0777629
$640$	7.92282e44	0.0395285
$641$	−1.99312e46	−0.969116	−0.484558	−	0.874759i	$-0.661019\pi$
$641$	−1.99312e46	−0.969116	−0.484558	+	0.874759i	$0.661019\pi$
$642$	−1.39595e46	−0.661520
$643$	3.26909e46	1.50989	0.754946	−	0.655787i	$-0.227663\pi$
$643$	3.26909e46	1.50989	0.754946	+	0.655787i	$0.227663\pi$
$644$	1.32247e45	0.0595344
$645$	−6.47448e45	−0.284099
$646$	1.55513e46	0.665168
$647$	1.84958e46	0.771174	0.385587	−	0.922672i	$-0.373999\pi$
$647$	1.84958e46	0.771174	0.385587	+	0.922672i	$0.373999\pi$
$648$	−7.86685e45	−0.319752
$649$	−2.12648e46	−0.842604
$650$	5.97918e45	0.230978
$651$	2.47588e46	0.932488
$652$	6.92228e45	0.254193
$653$	−2.33266e46	−0.835189	−0.417594	−	0.908634i	$-0.637127\pi$
$653$	−2.33266e46	−0.835189	−0.417594	+	0.908634i	$0.637127\pi$
$654$	−4.72254e45	−0.164870
$655$	−2.25772e46	−0.768580
$656$	−7.84086e45	−0.260286
$657$	3.60529e45	0.116711
$658$	1.53974e46	0.486094
$659$	1.31702e46	0.405493	0.202747	−	0.979231i	$-0.435013\pi$
$659$	1.31702e46	0.405493	0.202747	+	0.979231i	$0.435013\pi$
$660$	−5.33622e45	−0.160236
$661$	−8.17736e45	−0.239491	−0.119746	−	0.992805i	$-0.538208\pi$
$661$	−8.17736e45	−0.239491	−0.119746	+	0.992805i	$0.538208\pi$
$662$	7.37111e45	0.210560
$663$	5.43288e46	1.51376
$664$	1.43308e46	0.389491
$665$	1.41829e46	0.376019
$666$	1.48079e45	0.0382973
$667$	−5.34611e44	−0.0134884
$668$	2.05386e46	0.505544
$669$	−1.68006e46	−0.403455
$670$	−2.16431e46	−0.507089
$671$	−1.77576e46	−0.405942
$672$	6.56547e45	0.146445
$673$	−4.48159e46	−0.975401	−0.487701	−	0.873011i	$-0.662164\pi$
$673$	−4.48159e46	−0.975401	−0.487701	+	0.873011i	$0.662164\pi$
$674$	−5.28580e46	−1.12259
$675$	1.00265e46	0.207796
$676$	4.12259e46	0.833776
$677$	−5.83822e46	−1.15231	−0.576153	−	0.817342i	$-0.695447\pi$
$677$	−5.83822e46	−1.15231	−0.576153	+	0.817342i	$0.695447\pi$
$678$	−5.21757e46	−1.00503
$679$	−1.11907e46	−0.210380
$680$	−8.36261e45	−0.153442
$681$	−2.77301e46	−0.496620
$682$	3.41642e46	0.597212
$683$	2.10568e46	0.359295	0.179647	−	0.983731i	$-0.442504\pi$
$683$	2.10568e46	0.359295	0.179647	+	0.983731i	$0.442504\pi$
$684$	2.55722e45	0.0425933
$685$	−2.96191e46	−0.481589
$686$	4.82095e46	0.765218
$687$	4.57542e46	0.708997
$688$	1.09920e46	0.166291
$689$	−2.17718e47	−3.21571
$690$	2.87482e45	0.0414573
$691$	8.94914e46	1.26007	0.630033	−	0.776568i	$-0.283041\pi$
$691$	8.94914e46	1.26007	0.630033	+	0.776568i	$0.283041\pi$
$692$	1.38220e46	0.190029
$693$	4.26058e45	0.0571967
$694$	−4.06472e46	−0.532843
$695$	−3.76106e46	−0.481461
$696$	−2.65411e45	−0.0331792
$697$	8.27610e46	1.01038
$698$	−5.77077e46	−0.688049
$699$	−7.09642e46	−0.826354
$700$	−7.62676e45	−0.0867406
$701$	−6.16333e45	−0.0684650	−0.0342325	−	0.999414i	$-0.510899\pi$
$701$	−6.16333e45	−0.0684650	−0.0342325	+	0.999414i	$0.510899\pi$
$702$	1.10589e47	1.19991
$703$	5.63661e46	0.597386
$704$	9.05956e45	0.0937904
$705$	3.34714e46	0.338495
$706$	1.07028e47	1.05736
$707$	−1.32290e46	−0.127675
$708$	5.68748e46	0.536254
$709$	−4.95391e46	−0.456336	−0.228168	−	0.973622i	$-0.573274\pi$
$709$	−4.95391e46	−0.456336	−0.228168	+	0.973622i	$0.573274\pi$
$710$	−3.10911e46	−0.279816
$711$	−3.36792e45	−0.0296151
$712$	−6.09429e46	−0.523605
$713$	−1.84055e46	−0.154515
$714$	−6.92992e46	−0.568470
$715$	6.83706e46	0.548049
$716$	3.19395e45	0.0250186
$717$	−1.47211e47	−1.12687
$718$	−3.07512e46	−0.230043
$719$	−2.13187e47	−1.55860	−0.779300	−	0.626651i	$-0.784425\pi$
$719$	−2.13187e47	−1.55860	−0.779300	+	0.626651i	$0.784425\pi$
$720$	−1.37512e45	−0.00982551
$721$	−1.56258e47	−1.09122
$722$	−6.25721e45	−0.0427088
$723$	2.10060e47	1.40139
$724$	6.38785e46	0.416551
$725$	3.08314e45	0.0196524
$726$	4.73654e46	0.295126
$727$	1.31060e47	0.798273	0.399137	−	0.916891i	$-0.369310\pi$
$727$	1.31060e47	0.798273	0.399137	+	0.916891i	$0.369310\pi$
$728$	−8.41205e46	−0.500880
$729$	1.84120e47	1.07176
$730$	−7.37969e46	−0.419963
$731$	−1.16022e47	−0.645511
$732$	4.74946e46	0.258352
$733$	3.54336e47	1.88451	0.942257	−	0.334892i	$-0.108700\pi$
$733$	3.54336e47	1.88451	0.942257	+	0.334892i	$0.108700\pi$
$734$	1.39433e47	0.725073
$735$	2.07990e46	0.105755
$736$	−4.88073e45	−0.0242661
$737$	−2.47483e47	−1.20319
$738$	1.36090e46	0.0646986
$739$	2.64104e47	1.22784	0.613919	−	0.789369i	$-0.289592\pi$
$739$	2.64104e47	1.22784	0.613919	+	0.789369i	$0.289592\pi$
$740$	−3.03104e46	−0.137806
$741$	3.40059e47	1.51201
$742$	2.77711e47	1.20761
$743$	1.68076e47	0.714809	0.357404	−	0.933950i	$-0.383662\pi$
$743$	1.68076e47	0.714809	0.357404	+	0.933950i	$0.383662\pi$
$744$	−9.13754e46	−0.380081
$745$	4.75139e46	0.193305
$746$	−2.47872e47	−0.986364
$747$	−2.48732e46	−0.0968149
$748$	−9.56245e46	−0.364077
$749$	−2.28142e47	−0.849680
$750$	−1.65793e46	−0.0604026
$751$	4.23831e47	1.51055	0.755273	−	0.655410i	$-0.227504\pi$
$751$	4.23831e47	1.51055	0.755273	+	0.655410i	$0.227504\pi$
$752$	−5.68259e46	−0.198131
$753$	3.88979e47	1.32681
$754$	3.40059e46	0.113482
$755$	1.38452e46	0.0452037
$756$	−1.41062e47	−0.450609
$757$	4.49973e47	1.40639	0.703193	−	0.710999i	$-0.251757\pi$
$757$	4.49973e47	1.40639	0.703193	+	0.710999i	$0.251757\pi$
$758$	−3.98681e47	−1.21922
$759$	3.28729e46	0.0983670
$760$	−5.23439e46	−0.153265
$761$	−3.43548e47	−0.984329	−0.492164	−	0.870502i	$-0.663794\pi$
$761$	−3.43548e47	−0.984329	−0.492164	+	0.870502i	$0.663794\pi$
$762$	1.83820e46	0.0515389
$763$	−7.71808e46	−0.211765
$764$	−2.09499e46	−0.0562526
$765$	1.45145e46	0.0381408
$766$	5.34268e46	0.137399
$767$	−7.28711e47	−1.83414
$768$	−2.42307e46	−0.0596905
$769$	−7.98461e47	−1.92517	−0.962585	−	0.270981i	$-0.912652\pi$
$769$	−7.98461e47	−1.92517	−0.962585	+	0.270981i	$0.912652\pi$
$770$	−8.72103e46	−0.205812
$771$	−7.89038e47	−1.82264
$772$	−3.05508e47	−0.690776
$773$	4.85460e47	1.07446	0.537232	−	0.843435i	$-0.319470\pi$
$773$	4.85460e47	1.07446	0.537232	+	0.843435i	$0.319470\pi$
$774$	−1.90783e46	−0.0413346
$775$	1.06146e47	0.225126
$776$	4.13005e46	0.0857505
$777$	−2.51176e47	−0.510542
$778$	−1.77723e47	−0.353654
$779$	5.18024e47	1.00921
$780$	−1.82864e47	−0.348792
$781$	−3.55519e47	−0.663928
$782$	5.15165e46	0.0941966
$783$	5.70246e46	0.102092
$784$	−3.53115e46	−0.0619016
$785$	−2.55925e47	−0.439303
$786$	6.90489e47	1.16061
$787$	−4.81834e47	−0.793075	−0.396538	−	0.918018i	$-0.629788\pi$
$787$	−4.81834e47	−0.793075	−0.396538	+	0.918018i	$0.629788\pi$
$788$	−5.21931e47	−0.841261
$789$	9.98120e47	1.57548
$790$	6.89383e46	0.106565
$791$	−8.52713e47	−1.29089
$792$	−1.57242e46	−0.0233133
$793$	−6.08527e47	−0.883633
$794$	2.22956e47	0.317089
$795$	6.03696e47	0.840932
$796$	6.84392e47	0.933768
$797$	−2.06006e47	−0.275307	−0.137654	−	0.990480i	$-0.543956\pi$
$797$	−2.06006e47	−0.275307	−0.137654	+	0.990480i	$0.543956\pi$
$798$	−4.33763e47	−0.567812
$799$	5.99803e47	0.769107
$800$	2.81475e46	0.0353553
$801$	1.05775e47	0.130151
$802$	3.90671e47	0.470906
$803$	−8.43851e47	−0.996459
$804$	6.61919e47	0.765737
$805$	4.69835e46	0.0532492
$806$	1.17075e48	1.29998
$807$	4.49682e47	0.489206
$808$	4.88231e46	0.0520400
$809$	9.08440e47	0.948737	0.474368	−	0.880326i	$-0.342676\pi$
$809$	9.08440e47	0.948737	0.474368	+	0.880326i	$0.342676\pi$
$810$	−2.79487e47	−0.285995
$811$	1.62541e48	1.62974	0.814869	−	0.579646i	$-0.196809\pi$
$811$	1.62541e48	1.62974	0.814869	+	0.579646i	$0.196809\pi$
$812$	−4.33763e46	−0.0426166
$813$	−7.73654e47	−0.744822
$814$	−3.46593e47	−0.326977
$815$	2.45929e47	0.227357
$816$	2.55757e47	0.231708
$817$	−7.26214e47	−0.644764
$818$	−1.35844e48	−1.18198
$819$	1.46004e47	0.124503
$820$	−2.78563e47	−0.232807
$821$	−1.89976e48	−1.55610	−0.778048	−	0.628205i	$-0.783790\pi$
$821$	−1.89976e48	−1.55610	−0.778048	+	0.628205i	$0.783790\pi$
$822$	9.05852e47	0.727231
$823$	1.15896e48	0.911950	0.455975	−	0.889992i	$-0.349291\pi$
$823$	1.15896e48	0.911950	0.455975	+	0.889992i	$0.349291\pi$
$824$	5.76689e47	0.444778
$825$	−1.89581e47	−0.143319
$826$	9.29509e47	0.688784
$827$	−7.78559e47	−0.565524	−0.282762	−	0.959190i	$-0.591251\pi$
$827$	−7.78559e47	−0.565524	−0.282762	+	0.959190i	$0.591251\pi$
$828$	8.47122e45	0.00603178
$829$	2.22673e48	1.55424	0.777120	−	0.629353i	$-0.216680\pi$
$829$	2.22673e48	1.55424	0.777120	+	0.629353i	$0.216680\pi$
$830$	5.09132e47	0.348371
$831$	−1.66266e48	−1.11528
$832$	3.10457e47	0.204158
$833$	3.72717e47	0.240290
$834$	1.15026e48	0.727037
$835$	7.29677e47	0.452172
$836$	−5.98540e47	−0.363655
$837$	1.96324e48	1.16951
$838$	−5.22219e47	−0.305019
$839$	−1.12708e48	−0.645478	−0.322739	−	0.946488i	$-0.604604\pi$
$839$	−1.12708e48	−0.645478	−0.322739	+	0.946488i	$0.604604\pi$
$840$	2.33253e47	0.130984
$841$	−1.79854e48	−0.990345
$842$	−9.17732e47	−0.495526
$843$	−2.49734e48	−1.32228
$844$	−7.99118e47	−0.414916
$845$	1.46464e48	0.745752
$846$	9.86298e46	0.0492490
$847$	7.74097e47	0.379070
$848$	−1.02492e48	−0.492221
$849$	−1.66626e48	−0.784814
$850$	−2.97099e47	−0.137243
$851$	1.86722e47	0.0845978
$852$	9.50871e47	0.422540
$853$	3.65470e48	1.59292	0.796459	−	0.604693i	$-0.206704\pi$
$853$	3.65470e48	1.59292	0.796459	+	0.604693i	$0.206704\pi$
$854$	7.76208e47	0.331836
$855$	9.08505e46	0.0380966
$856$	8.41986e47	0.346328
$857$	1.20507e48	0.486214	0.243107	−	0.969999i	$-0.421833\pi$
$857$	1.20507e48	0.486214	0.243107	+	0.969999i	$0.421833\pi$
$858$	−2.09101e48	−0.827590
$859$	−1.13686e48	−0.441389	−0.220694	−	0.975343i	$-0.570832\pi$
$859$	−1.13686e48	−0.441389	−0.220694	+	0.975343i	$0.570832\pi$
$860$	3.90516e47	0.148735
$861$	−2.30840e48	−0.862498
$862$	−1.43706e47	−0.0526750
$863$	3.08439e46	0.0110915	0.00554576	−	0.999985i	$-0.498235\pi$
$863$	3.08439e46	0.0110915	0.00554576	+	0.999985i	$0.498235\pi$
$864$	5.20606e47	0.183668
$865$	4.91055e47	0.169967
$866$	3.24304e48	1.10130
$867$	1.66885e47	0.0556034
$868$	−1.49336e48	−0.488189
$869$	7.88294e47	0.252849
$870$	−9.42929e46	−0.0296764
$871$	−8.48087e48	−2.61903
$872$	2.84845e47	0.0863151
$873$	−7.16831e46	−0.0213148
$874$	3.22456e47	0.0940875
$875$	−2.70957e47	−0.0775832
$876$	2.25696e48	0.634171
$877$	−3.96964e48	−1.09461	−0.547303	−	0.836935i	$-0.684345\pi$
$877$	−3.96964e48	−1.09461	−0.547303	+	0.836935i	$0.684345\pi$
$878$	−3.47097e48	−0.939272
$879$	2.21485e48	0.588204
$880$	3.21860e47	0.0838887
$881$	−1.10851e48	−0.283556	−0.141778	−	0.989898i	$-0.545282\pi$
$881$	−1.10851e48	−0.283556	−0.141778	+	0.989898i	$0.545282\pi$
$882$	6.12884e46	0.0153867
$883$	3.17298e48	0.781836	0.390918	−	0.920426i	$-0.372158\pi$
$883$	3.17298e48	0.781836	0.390918	+	0.920426i	$0.372158\pi$
$884$	−3.27690e48	−0.792503
$885$	2.02060e48	0.479641
$886$	−4.30888e48	−1.00394
$887$	5.58665e47	0.127765	0.0638824	−	0.997957i	$-0.479652\pi$
$887$	5.58665e47	0.127765	0.0638824	+	0.997957i	$0.479652\pi$
$888$	9.26996e47	0.208096
$889$	3.00418e47	0.0661984
$890$	−2.16513e48	−0.468326
$891$	−3.19586e48	−0.678588
$892$	1.01335e48	0.211222
$893$	3.75434e48	0.768217
$894$	−1.45314e48	−0.291903
$895$	1.13472e47	0.0223773
$896$	−3.96004e47	−0.0766686
$897$	1.12650e48	0.214120
$898$	−4.58823e48	−0.856220
$899$	6.03693e47	0.110607
$900$	−4.88541e46	−0.00878820
$901$	1.08182e49	1.91071
$902$	−3.18531e48	−0.552387
$903$	3.23612e48	0.551033
$904$	3.14704e48	0.526166
$905$	2.26942e48	0.372575
$906$	−4.23433e47	−0.0682605
$907$	−1.20858e49	−1.91318	−0.956589	−	0.291441i	$-0.905865\pi$
$907$	−1.20858e49	−1.91318	−0.956589	+	0.291441i	$0.905865\pi$
$908$	1.67257e48	0.259997
$909$	−8.47396e46	−0.0129355
$910$	−2.98856e48	−0.448001
$911$	2.56704e48	0.377902	0.188951	−	0.981986i	$-0.439491\pi$
$911$	2.56704e48	0.377902	0.188951	+	0.981986i	$0.439491\pi$
$912$	1.60086e48	0.231439
$913$	5.82181e48	0.826590
$914$	−2.67843e47	−0.0373480
$915$	1.68735e48	0.231077
$916$	−2.75972e48	−0.371184
$917$	1.12847e49	1.49072
$918$	−5.49504e48	−0.712963
$919$	−5.63209e47	−0.0717734	−0.0358867	−	0.999356i	$-0.511426\pi$
$919$	−5.63209e47	−0.0717734	−0.0358867	+	0.999356i	$0.511426\pi$
$920$	−1.73398e47	−0.0217043
$921$	1.11675e49	1.37300
$922$	3.89285e48	0.470118
$923$	−1.21831e49	−1.44520
$924$	2.66719e48	0.310790
$925$	−1.07684e48	−0.123258
$926$	8.55860e48	0.962324
$927$	−1.00093e48	−0.110557
$928$	1.60086e47	0.0173704
$929$	3.29801e47	0.0351555	0.0175777	−	0.999845i	$-0.494405\pi$
$929$	3.29801e47	0.0351555	0.0175777	+	0.999845i	$0.494405\pi$
$930$	−3.24631e48	−0.339954
$931$	2.33294e48	0.240012
$932$	4.28029e48	0.432624
$933$	1.35571e49	1.34623
$934$	−2.40370e48	−0.234507
$935$	−3.39727e48	−0.325640
$936$	−5.38844e47	−0.0507471
$937$	−3.91522e48	−0.362287	−0.181144	−	0.983457i	$-0.557980\pi$
$937$	−3.91522e48	−0.362287	−0.181144	+	0.983457i	$0.557980\pi$
$938$	1.08178e49	0.983540
$939$	−2.44467e48	−0.218392
$940$	−2.01886e48	−0.177214
$941$	1.08951e49	0.939731	0.469866	−	0.882738i	$-0.344302\pi$
$941$	1.08951e49	0.939731	0.469866	+	0.882738i	$0.344302\pi$
$942$	7.82708e48	0.663376
$943$	1.71604e48	0.142918
$944$	−3.43047e48	−0.280747
$945$	−5.01152e48	−0.403037
$946$	4.46546e48	0.352909
$947$	−1.05116e49	−0.816382	−0.408191	−	0.912897i	$-0.633840\pi$
$947$	−1.05116e49	−0.816382	−0.408191	+	0.912897i	$0.633840\pi$
$948$	−2.10837e48	−0.160920
$949$	−2.89175e49	−2.16904
$950$	−1.85963e48	−0.137084
$951$	−1.91956e49	−1.39067
$952$	4.17986e48	0.297613
$953$	1.01486e49	0.710190	0.355095	−	0.934830i	$-0.384449\pi$
$953$	1.01486e49	0.710190	0.355095	+	0.934830i	$0.384449\pi$
$954$	1.77891e48	0.122350
$955$	−7.44292e47	−0.0503138
$956$	8.87922e48	0.589956
$957$	−1.07822e48	−0.0704141
$958$	1.17403e49	0.753613
$959$	1.48044e49	0.934081
$960$	−8.60847e47	−0.0533888
$961$	4.38039e48	0.267040
$962$	−1.18772e49	−0.711746
$963$	−1.46139e48	−0.0860860
$964$	−1.26700e49	−0.733677
$965$	−1.08538e49	−0.617849
$966$	−1.43692e48	−0.0804097
$967$	7.23400e47	0.0397962	0.0198981	−	0.999802i	$-0.493666\pi$
$967$	7.23400e47	0.0397962	0.0198981	+	0.999802i	$0.493666\pi$
$968$	−2.85690e48	−0.154508
$969$	−1.68972e49	−0.898404
$970$	1.46729e48	0.0766976
$971$	7.86578e47	0.0404226	0.0202113	−	0.999796i	$-0.493566\pi$
$971$	7.86578e47	0.0404226	0.0202113	+	0.999796i	$0.493566\pi$
$972$	−1.73418e48	−0.0876196
$973$	1.87988e49	0.933832
$974$	1.86984e49	0.913233
$975$	−6.49663e48	−0.311969
$976$	−2.86469e48	−0.135256
$977$	−2.61058e49	−1.21193	−0.605964	−	0.795492i	$-0.707213\pi$
$977$	−2.61058e49	−1.21193	−0.605964	+	0.795492i	$0.707213\pi$
$978$	−7.52134e48	−0.343324
$979$	−2.47577e49	−1.11121
$980$	−1.25452e48	−0.0553664
$981$	−4.94391e47	−0.0214552
$982$	1.25706e49	0.536433
$983$	−7.33769e48	−0.307912	−0.153956	−	0.988078i	$-0.549201\pi$
$983$	−7.33769e48	−0.307912	−0.153956	+	0.988078i	$0.549201\pi$
$984$	8.51941e48	0.351553
$985$	−1.85427e49	−0.752446
$986$	−1.68972e48	−0.0674288
$987$	−1.67299e49	−0.656539
$988$	−2.05110e49	−0.791586
$989$	−2.40571e48	−0.0913071
$990$	−5.58636e47	−0.0208520
$991$	−2.29393e49	−0.842102	−0.421051	−	0.907037i	$-0.638339\pi$
$991$	−2.29393e49	−0.842102	−0.421051	+	0.907037i	$0.638339\pi$
$992$	5.51141e48	0.198985
$993$	−8.00902e48	−0.284391
$994$	1.55402e49	0.542726
$995$	2.43145e49	0.835188
$996$	−1.55710e49	−0.526063
$997$	1.96710e49	0.653665	0.326833	−	0.945082i	$-0.394019\pi$
$997$	1.96710e49	0.653665	0.326833	+	0.945082i	$0.394019\pi$
$998$	1.96104e49	0.640961
$999$	−1.99169e49	−0.640311

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.34.a.a.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+65536.0 q^{2} -7.12076e7 q^{3} +4.29497e9 q^{4} +1.52588e11 q^{5} -4.66666e12 q^{6} -7.62676e13 q^{7} +2.81475e14 q^{8} -4.88541e14 q^{9} +1.00000e16 q^{10} +1.14348e17 q^{11} -3.05834e17 q^{12} +3.91852e18 q^{13} -4.99828e18 q^{14} -1.08654e19 q^{15} +1.84467e19 q^{16} -1.94707e20 q^{17} -3.20170e19 q^{18} -1.21873e21 q^{19} +6.55360e20 q^{20} +5.43083e21 q^{21} +7.49389e21 q^{22} -4.03724e21 q^{23} -2.00432e22 q^{24} +2.32831e22 q^{25} +2.56804e23 q^{26} +4.30635e23 q^{27} -3.27567e23 q^{28} +1.32420e23 q^{29} -7.12076e23 q^{30} +4.55893e24 q^{31} +1.20893e24 q^{32} -8.14242e24 q^{33} -1.27603e25 q^{34} -1.16375e25 q^{35} -2.09827e24 q^{36} -4.62500e25 q^{37} -7.98704e25 q^{38} -2.79028e26 q^{39} +4.29497e25 q^{40} -4.25054e26 q^{41} +3.55915e26 q^{42} +5.95880e26 q^{43} +4.91120e26 q^{44} -7.45455e25 q^{45} -2.64585e26 q^{46} -3.08054e27 q^{47} -1.31355e27 q^{48} -1.91424e27 q^{49} +1.52588e27 q^{50} +1.38646e28 q^{51} +1.68299e28 q^{52} -5.55613e28 q^{53} +2.82221e28 q^{54} +1.74481e28 q^{55} -2.14674e28 q^{56} +8.67825e28 q^{57} +8.67826e27 q^{58} -1.85966e29 q^{59} -4.66666e28 q^{60} -1.55295e29 q^{61} +2.98774e29 q^{62} +3.72599e28 q^{63} +7.92282e28 q^{64} +5.97918e29 q^{65} -5.33622e29 q^{66} -2.16431e30 q^{67} -8.36261e29 q^{68} +2.87482e29 q^{69} -7.62676e29 q^{70} -3.10911e30 q^{71} -1.37512e29 q^{72} -7.37969e30 q^{73} -3.03104e30 q^{74} -1.65793e30 q^{75} -5.23439e30 q^{76} -8.72103e30 q^{77} -1.82864e31 q^{78} +6.89383e30 q^{79} +2.81475e30 q^{80} -2.79487e31 q^{81} -2.78563e31 q^{82} +5.09132e31 q^{83} +2.33253e31 q^{84} -2.97099e31 q^{85} +3.90516e31 q^{86} -9.42929e30 q^{87} +3.21860e31 q^{88} -2.16513e32 q^{89} -4.88541e30 q^{90} -2.98856e32 q^{91} -1.73398e31 q^{92} -3.24631e32 q^{93} -2.01886e32 q^{94} -1.85963e32 q^{95} -8.60847e31 q^{96} +1.46729e32 q^{97} -1.25452e32 q^{98} -5.58636e31 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 131072 q^{2} - 74648412 q^{3} + 8589934592 q^{4} + 305175781250 q^{5} - 4892158328832 q^{6} + 20327789415556 q^{7} + 562949953421312 q^{8} - 60\!\cdots\!74 q^{9} + 20\!\cdots\!00 q^{10} - 11\!\cdots\!76 q^{11}+ \cdots + 64\!\cdots\!12 q^{99}+O(q^{100}) \) 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

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Groups

Database

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