LMFDB - Embedded newform 10.32.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,32,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, 32, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 32);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 32 $
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:	$60.8771328190$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{337159}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 337159 $ x^2 - 337159
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$580.654$ 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)

$f(q)$	$=$	\(q-32768.0 q^{2} +1.82748e7 q^{3} +1.07374e9 q^{4} -3.05176e10 q^{5} -5.98827e11 q^{6} -9.80486e12 q^{7} -3.51844e13 q^{8} -2.83707e14 q^{9} +1.00000e15 q^{10} -2.50417e16 q^{11} +1.96224e16 q^{12} -5.10202e16 q^{13} +3.21285e17 q^{14} -5.57701e17 q^{15} +1.15292e18 q^{16} +5.39972e17 q^{17} +9.29650e18 q^{18} +8.95940e19 q^{19} -3.27680e19 q^{20} -1.79181e20 q^{21} +8.20567e20 q^{22} +3.91328e20 q^{23} -6.42986e20 q^{24} +9.31323e20 q^{25} +1.67183e21 q^{26} -1.64725e22 q^{27} -1.05279e22 q^{28} +7.65729e22 q^{29} +1.82748e22 q^{30} -1.67730e23 q^{31} -3.77789e22 q^{32} -4.57632e23 q^{33} -1.76938e22 q^{34} +2.99220e23 q^{35} -3.04628e23 q^{36} -2.35029e24 q^{37} -2.93582e24 q^{38} -9.32383e23 q^{39} +1.07374e24 q^{40} +4.23536e24 q^{41} +5.87142e24 q^{42} +2.21121e25 q^{43} -2.68884e25 q^{44} +8.65804e24 q^{45} -1.28230e25 q^{46} +9.02140e25 q^{47} +2.10694e25 q^{48} -6.16402e25 q^{49} -3.05176e25 q^{50} +9.86786e24 q^{51} -5.47826e25 q^{52} +8.66817e25 q^{53} +5.39771e26 q^{54} +7.64213e26 q^{55} +3.44978e26 q^{56} +1.63731e27 q^{57} -2.50914e27 q^{58} +3.37162e27 q^{59} -5.98827e26 q^{60} -3.72439e27 q^{61} +5.49619e27 q^{62} +2.78170e27 q^{63} +1.23794e27 q^{64} +1.55701e27 q^{65} +1.49957e28 q^{66} -1.08156e28 q^{67} +5.79791e26 q^{68} +7.15142e27 q^{69} -9.80486e27 q^{70} +3.01084e28 q^{71} +9.98204e27 q^{72} +1.41961e29 q^{73} +7.70144e28 q^{74} +1.70197e28 q^{75} +9.62009e28 q^{76} +2.45531e29 q^{77} +3.05523e28 q^{78} +4.24928e29 q^{79} -3.51844e28 q^{80} -1.25793e29 q^{81} -1.38784e29 q^{82} -2.61223e29 q^{83} -1.92395e29 q^{84} -1.64786e28 q^{85} -7.24570e29 q^{86} +1.39935e30 q^{87} +8.81077e29 q^{88} -1.92566e30 q^{89} -2.83707e29 q^{90} +5.00246e29 q^{91} +4.20185e29 q^{92} -3.06523e30 q^{93} -2.95613e30 q^{94} -2.73419e30 q^{95} -6.90401e29 q^{96} -1.19769e30 q^{97} +2.01983e30 q^{98} +7.10450e30 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 65536 q^{2} + 29024244 q^{3} + 2147483648 q^{4} - 61035156250 q^{5} - 951066427392 q^{6} + 12795158105212 q^{7} - 70368744177664 q^{8} - 785828540134926 q^{9} + 20\!\cdots\!00 q^{10} - 500906012122176 q^{11}+ \cdots - 52\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 65536 * q^2 + 29024244 * q^3 + 2147483648 * q^4 - 61035156250 * q^5 - 951066427392 * q^6 + 12795158105212 * q^7 - 70368744177664 * q^8 - 785828540134926 * q^9 + 2000000000000000 * q^10 - 500906012122176 * q^11 + 31164544692781056 * q^12 - 199440062300108396 * q^13 - 419271740791586816 * q^14 - 885749633789062500 * q^15 + 2305843009213693952 * q^16 + 12159060327494700852 * q^17 + 25750029603141255168 * q^18 + 127400875596685413160 * q^19 - 65536000000000000000 * q^20 + 63757121557979677464 * q^21 + 16413688205219463168 * q^22 + 1266903156187203120564 * q^23 - 1021199800493049643008 * q^24 + 1862645149230957031250 * q^25 + 6535251961449951920128 * q^26 - 28509724951692639267240 * q^27 + 13738696402258716786688 * q^28 - 9185091177630833257860 * q^29 + 29024244000000000000000 * q^30 - 146295843292215232250936 * q^31 - 75557863725914323419136 * q^32 - 193830377630097097798272 * q^33 - 398428088811346357518336 * q^34 - 390477237097534179687500 * q^35 - 843776970035732649345024 * q^36 - 4796960187038756074101068 * q^37 - 4174671891552187618426880 * q^38 - 2527819231419957051969912 * q^39 + 2147483648000000000000000 * q^40 + 14935619514300516260083884 * q^41 - 2089193359211878071140352 * q^42 + 28899014613348735583843684 * q^43 - 537843735108631369089024 * q^44 + 23981583866422302246093750 * q^45 - 41513882621942271854641152 * q^46 - 51613521705752647137207828 * q^47 + 33462675062556250702086144 * q^48 + 291345014964521476498437786 * q^49 - 61035156250000000000000000 * q^50 + 134767069271392484976262344 * q^51 - 214147136272792024518754304 * q^52 + 612453197337950081085508644 * q^53 + 934206667217064403508920320 * q^54 + 15286438358220703125000000 * q^55 - 450189603709213631666192384 * q^56 + 2043713526810613838894722320 * q^57 + 300977067708607144193556480 * q^58 + 5407094693613569560863134280 * q^59 - 951066427392000000000000000 * q^60 + 2835877556240957667189879124 * q^61 + 4793822192999308730398670848 * q^62 - 8566261666607186084500902756 * q^63 + 2475880078570760549798248448 * q^64 + 6086427682498425170898437500 * q^65 + 6351433814183021700653776896 * q^66 + 10837595864228774593398202252 * q^67 + 13055691614170197443160834048 * q^68 + 16563402888409735784762968008 * q^69 + 12795158105212000000000000000 * q^70 + 58422436263671389450567835544 * q^71 + 27648883754130887453737746432 * q^72 + 171414457291735665495284849764 * q^73 + 157186791408885959036143796224 * q^74 + 27030933648347854614257812500 * q^75 + 136795648542382083880612003840 * q^76 + 800153433605242701833643682944 * q^77 + 82831580575169152678950076416 * q^78 + 188775939965441260340578960240 * q^79 - 70368744177664000000000000000 * q^80 + 54960429466999252255967047242 * q^81 - 489410380244599316810428710912 * q^82 + 536572539310341029223184308324 * q^83 + 68458687994654820635127054336 * q^84 - 371065073470907618774414062500 * q^85 - 946962910850211367611389837312 * q^86 + 477496900561204346619073126680 * q^87 + 17624063512039632702309138432 * q^88 - 750272557446280683624160755180 * q^89 - 785828540134926000000000000000 * q^90 - 2854043706700147924065243188776 * q^91 + 1360326905755804364132881268736 * q^92 - 2834821865488342767082586415792 * q^93 + 1691271879254102741392026107904 * q^94 - 3887966174215253087158203125000 * q^95 - 1096504936449843223005958766592 * q^96 - 4226089759761369848050283653628 * q^97 - 9546793450357439741900809371648 * q^98 - 5217983754520789466685211355712 * 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 $

$2$	−32768.0	−0.707107
$2$	−32768.0	−0.707107
$3$	1.82748e7	0.735313	0.367656	−	0.929962i	$-0.380160\pi$
$3$	1.82748e7	0.735313	0.367656	+	0.929962i	$0.380160\pi$
$4$	1.07374e9	0.500000
$5$	−3.05176e10	−0.447214
$5$	−3.05176e10	−0.447214
$6$	−5.98827e11	−0.519945
$7$	−9.80486e12	−0.780587	−0.390294	−	0.920690i	$-0.627627\pi$
$7$	−9.80486e12	−0.780587	−0.390294	+	0.920690i	$0.627627\pi$
$8$	−3.51844e13	−0.353553
$9$	−2.83707e14	−0.459315
$10$	1.00000e15	0.316228
$11$	−2.50417e16	−1.80750	−0.903749	−	0.428063i	$-0.859196\pi$
$11$	−2.50417e16	−1.80750	−0.903749	+	0.428063i	$0.859196\pi$
$12$	1.96224e16	0.367656
$13$	−5.10202e16	−0.276453	−0.138226	−	0.990401i	$-0.544140\pi$
$13$	−5.10202e16	−0.276453	−0.138226	+	0.990401i	$0.544140\pi$
$14$	3.21285e17	0.551959
$15$	−5.57701e17	−0.328842
$16$	1.15292e18	0.250000
$17$	5.39972e17	0.0457523	0.0228762	−	0.999738i	$-0.492718\pi$
$17$	5.39972e17	0.0457523	0.0228762	+	0.999738i	$0.492718\pi$
$18$	9.29650e18	0.324785
$19$	8.95940e19	1.35394	0.676968	−	0.736012i	$-0.263293\pi$
$19$	8.95940e19	1.35394	0.676968	+	0.736012i	$0.263293\pi$
$20$	−3.27680e19	−0.223607
$21$	−1.79181e20	−0.573976
$22$	8.20567e20	1.27809
$23$	3.91328e20	0.306026	0.153013	−	0.988224i	$-0.451102\pi$
$23$	3.91328e20	0.306026	0.153013	+	0.988224i	$0.451102\pi$
$24$	−6.42986e20	−0.259972
$25$	9.31323e20	0.200000
$26$	1.67183e21	0.195481
$27$	−1.64725e22	−1.07305
$28$	−1.05279e22	−0.390294
$29$	7.65729e22	1.64781	0.823903	−	0.566731i	$-0.191792\pi$
$29$	7.65729e22	1.64781	0.823903	+	0.566731i	$0.191792\pi$
$30$	1.82748e22	0.232526
$31$	−1.67730e23	−1.28382	−0.641912	−	0.766778i	$-0.721858\pi$
$31$	−1.67730e23	−1.28382	−0.641912	+	0.766778i	$0.721858\pi$
$32$	−3.77789e22	−0.176777
$33$	−4.57632e23	−1.32908
$34$	−1.76938e22	−0.0323518
$35$	2.99220e23	0.349089
$36$	−3.04628e23	−0.229657
$37$	−2.35029e24	−1.15876	−0.579382	−	0.815056i	$-0.696706\pi$
$37$	−2.35029e24	−1.15876	−0.579382	+	0.815056i	$0.696706\pi$
$38$	−2.93582e24	−0.957378
$39$	−9.32383e23	−0.203279
$40$	1.07374e24	0.158114
$41$	4.23536e24	0.425344	0.212672	−	0.977124i	$-0.431783\pi$
$41$	4.23536e24	0.425344	0.212672	+	0.977124i	$0.431783\pi$
$42$	5.87142e24	0.405862
$43$	2.21121e25	1.06138	0.530688	−	0.847567i	$-0.321934\pi$
$43$	2.21121e25	1.06138	0.530688	+	0.847567i	$0.321934\pi$
$44$	−2.68884e25	−0.903749
$45$	8.65804e24	0.205412
$46$	−1.28230e25	−0.216393
$47$	9.02140e25	1.09083	0.545415	−	0.838166i	$-0.316372\pi$
$47$	9.02140e25	1.09083	0.545415	+	0.838166i	$0.316372\pi$
$48$	2.10694e25	0.183828
$49$	−6.16402e25	−0.390683
$50$	−3.05176e25	−0.141421
$51$	9.86786e24	0.0336423
$52$	−5.47826e25	−0.138226
$53$	8.66817e25	0.162799	0.0813994	−	0.996682i	$-0.474061\pi$
$53$	8.66817e25	0.162799	0.0813994	+	0.996682i	$0.474061\pi$
$54$	5.39771e26	0.758763
$55$	7.64213e26	0.808337
$56$	3.44978e26	0.275979
$57$	1.63731e27	0.995567
$58$	−2.50914e27	−1.16517
$59$	3.37162e27	1.20125	0.600624	−	0.799532i	$-0.294919\pi$
$59$	3.37162e27	1.20125	0.600624	+	0.799532i	$0.294919\pi$
$60$	−5.98827e26	−0.164421
$61$	−3.72439e27	−0.791485	−0.395742	−	0.918362i	$-0.629513\pi$
$61$	−3.72439e27	−0.791485	−0.395742	+	0.918362i	$0.629513\pi$
$62$	5.49619e27	0.907800
$63$	2.78170e27	0.358535
$64$	1.23794e27	0.125000
$65$	1.55701e27	0.123633
$66$	1.49957e28	0.939799
$67$	−1.08156e28	−0.536900	−0.268450	−	0.963294i	$-0.586511\pi$
$67$	−1.08156e28	−0.536900	−0.268450	+	0.963294i	$0.586511\pi$
$68$	5.79791e26	0.0228762
$69$	7.15142e27	0.225025
$70$	−9.80486e27	−0.246843
$71$	3.01084e28	0.608393	0.304196	−	0.952609i	$-0.401612\pi$
$71$	3.01084e28	0.608393	0.304196	+	0.952609i	$0.401612\pi$
$72$	9.98204e27	0.162392
$73$	1.41961e29	1.86494	0.932471	−	0.361246i	$-0.117648\pi$
$73$	1.41961e29	1.86494	0.932471	+	0.361246i	$0.117648\pi$
$74$	7.70144e28	0.819370
$75$	1.70197e28	0.147063
$76$	9.62009e28	0.676968
$77$	2.45531e29	1.41091
$78$	3.05523e28	0.143740
$79$	4.24928e29	1.64095	0.820475	−	0.571682i	$-0.193709\pi$
$79$	4.24928e29	1.64095	0.820475	+	0.571682i	$0.193709\pi$
$80$	−3.51844e28	−0.111803
$81$	−1.25793e29	−0.329715
$82$	−1.38784e29	−0.300764
$83$	−2.61223e29	−0.469138	−0.234569	−	0.972099i	$-0.575368\pi$
$83$	−2.61223e29	−0.469138	−0.234569	+	0.972099i	$0.575368\pi$
$84$	−1.92395e29	−0.286988
$85$	−1.64786e28	−0.0204611
$86$	−7.24570e29	−0.750506
$87$	1.39935e30	1.21165
$88$	8.81077e29	0.639047
$89$	−1.92566e30	−1.17229	−0.586144	−	0.810207i	$-0.699355\pi$
$89$	−1.92566e30	−1.17229	−0.586144	+	0.810207i	$0.699355\pi$
$90$	−2.83707e29	−0.145248
$91$	5.00246e29	0.215795
$92$	4.20185e29	0.153013
$93$	−3.06523e30	−0.944012
$94$	−2.95613e30	−0.771333
$95$	−2.73419e30	−0.605499
$96$	−6.90401e29	−0.129986
$97$	−1.19769e30	−0.192035	−0.0960177	−	0.995380i	$-0.530611\pi$
$97$	−1.19769e30	−0.192035	−0.0960177	+	0.995380i	$0.530611\pi$
$98$	2.01983e30	0.276255
$99$	7.10450e30	0.830210
$100$	1.00000e30	0.100000
$101$	−1.82554e30	−0.156462	−0.0782311	−	0.996935i	$-0.524927\pi$
$101$	−1.82554e30	−0.156462	−0.0782311	+	0.996935i	$0.524927\pi$
$102$	−3.23350e29	−0.0237887
$103$	−3.09796e31	−1.95929	−0.979644	−	0.200744i	$-0.935664\pi$
$103$	−3.09796e31	−1.95929	−0.979644	+	0.200744i	$0.935664\pi$
$104$	1.79512e30	0.0977407
$105$	5.46818e30	0.256690
$106$	−2.84038e30	−0.115116
$107$	−7.75249e30	−0.271639	−0.135820	−	0.990734i	$-0.543367\pi$
$107$	−7.75249e30	−0.271639	−0.135820	+	0.990734i	$0.543367\pi$
$108$	−1.76872e31	−0.536527
$109$	2.74905e31	0.722890	0.361445	−	0.932393i	$-0.382284\pi$
$109$	2.74905e31	0.722890	0.361445	+	0.932393i	$0.382284\pi$
$110$	−2.50417e31	−0.571581
$111$	−4.29510e31	−0.852055
$112$	−1.13042e31	−0.195147
$113$	3.04360e31	0.457796	0.228898	−	0.973450i	$-0.426488\pi$
$113$	3.04360e31	0.457796	0.228898	+	0.973450i	$0.426488\pi$
$114$	−5.36514e31	−0.703972
$115$	−1.19424e31	−0.136859
$116$	8.22195e31	0.823903
$117$	1.44748e31	0.126979
$118$	−1.10481e32	−0.849410
$119$	−5.29435e30	−0.0357137
$120$	1.96224e31	0.116263
$121$	4.35145e32	2.26705
$122$	1.22041e32	0.559664
$123$	7.74002e31	0.312761
$124$	−1.80099e32	−0.641912
$125$	−2.84217e31	−0.0894427
$126$	−9.11508e31	−0.253523
$127$	5.99688e32	1.47560	0.737798	−	0.675021i	$-0.235865\pi$
$127$	5.99688e32	1.47560	0.737798	+	0.675021i	$0.235865\pi$
$128$	−4.05648e31	−0.0883883
$129$	4.04094e32	0.780444
$130$	−5.10202e31	−0.0874220
$131$	8.06361e32	1.22694	0.613471	−	0.789717i	$-0.289773\pi$
$131$	8.06361e32	1.22694	0.613471	+	0.789717i	$0.289773\pi$
$132$	−4.91378e32	−0.664538
$133$	−8.78457e32	−1.05687
$134$	3.54407e32	0.379645
$135$	5.02701e32	0.479884
$136$	−1.89986e31	−0.0161759
$137$	1.25859e33	0.956566	0.478283	−	0.878206i	$-0.341259\pi$
$137$	1.25859e33	0.956566	0.478283	+	0.878206i	$0.341259\pi$
$138$	−2.34338e32	−0.159117
$139$	−1.28760e33	−0.781721	−0.390861	−	0.920450i	$-0.627823\pi$
$139$	−1.28760e33	−0.781721	−0.390861	+	0.920450i	$0.627823\pi$
$140$	3.21285e32	0.174545
$141$	1.64864e33	0.802102
$142$	−9.86593e32	−0.430198
$143$	1.27764e33	0.499687
$144$	−3.27091e32	−0.114829
$145$	−2.33682e33	−0.736921
$146$	−4.65178e33	−1.31871
$147$	−1.12646e33	−0.287274
$148$	−2.52361e33	−0.579382
$149$	−4.23721e31	−0.00876380	−0.00438190	−	0.999990i	$-0.501395\pi$
$149$	−4.23721e31	−0.00876380	−0.00438190	+	0.999990i	$0.501395\pi$
$150$	−5.57701e32	−0.103989
$151$	−7.07794e33	−1.19060	−0.595298	−	0.803505i	$-0.702966\pi$
$151$	−7.07794e33	−1.19060	−0.595298	+	0.803505i	$0.702966\pi$
$152$	−3.15231e33	−0.478689
$153$	−1.53194e32	−0.0210147
$154$	−8.04554e33	−0.997664
$155$	5.11872e33	0.574143
$156$	−1.00114e33	−0.101640
$157$	1.32372e34	1.21717	0.608583	−	0.793490i	$-0.291738\pi$
$157$	1.32372e34	1.21717	0.608583	+	0.793490i	$0.291738\pi$
$158$	−1.39240e34	−1.16033
$159$	1.58409e33	0.119708
$160$	1.15292e33	0.0790569
$161$	−3.83691e33	−0.238880
$162$	4.12199e33	0.233144
$163$	1.78685e34	0.918715	0.459358	−	0.888251i	$-0.348080\pi$
$163$	1.78685e34	0.918715	0.459358	+	0.888251i	$0.348080\pi$
$164$	4.54768e33	0.212672
$165$	1.39658e34	0.594381
$166$	8.55975e33	0.331731
$167$	1.88144e34	0.664331	0.332165	−	0.943221i	$-0.392221\pi$
$167$	1.88144e34	0.664331	0.332165	+	0.943221i	$0.392221\pi$
$168$	6.30438e33	0.202931
$169$	−3.14569e34	−0.923574
$170$	5.39972e32	0.0144682
$171$	−2.54184e34	−0.621883
$172$	2.37427e34	0.530688
$173$	3.38111e34	0.690789	0.345394	−	0.938458i	$-0.387745\pi$
$173$	3.38111e34	0.690789	0.345394	+	0.938458i	$0.387745\pi$
$174$	−4.58539e34	−0.856768
$175$	−9.13148e33	−0.156117
$176$	−2.88711e34	−0.451874
$177$	6.16155e34	0.883293
$178$	6.31000e34	0.828932
$179$	−2.41562e34	−0.290942	−0.145471	−	0.989362i	$-0.546470\pi$
$179$	−2.41562e34	−0.290942	−0.145471	+	0.989362i	$0.546470\pi$
$180$	9.29650e33	0.102706
$181$	3.12629e34	0.316965	0.158482	−	0.987362i	$-0.449340\pi$
$181$	3.12629e34	0.316965	0.158482	+	0.987362i	$0.449340\pi$
$182$	−1.63921e34	−0.152590
$183$	−6.80623e34	−0.581989
$184$	−1.37686e34	−0.108197
$185$	7.17253e34	0.518215
$186$	1.00442e35	0.667517
$187$	−1.35218e34	−0.0826972
$188$	9.68666e34	0.545415
$189$	1.61510e35	0.837612
$190$	8.95940e34	0.428152
$191$	−5.87939e33	−0.0259009	−0.0129504	−	0.999916i	$-0.504122\pi$
$191$	−5.87939e33	−0.0259009	−0.0129504	+	0.999916i	$0.504122\pi$
$192$	2.26231e34	0.0919141
$193$	−2.74156e35	−1.02768	−0.513841	−	0.857885i	$-0.671778\pi$
$193$	−2.74156e35	−1.02768	−0.513841	+	0.857885i	$0.671778\pi$
$194$	3.92458e34	0.135790
$195$	2.84541e34	0.0909092
$196$	−6.61857e34	−0.195342
$197$	2.83335e35	0.772812	0.386406	−	0.922329i	$-0.373716\pi$
$197$	2.83335e35	0.772812	0.386406	+	0.922329i	$0.373716\pi$
$198$	−2.32800e35	−0.587047
$199$	−5.63487e35	−1.31420	−0.657100	−	0.753803i	$-0.728217\pi$
$199$	−5.63487e35	−1.31420	−0.657100	+	0.753803i	$0.728217\pi$
$200$	−3.27680e34	−0.0707107
$201$	−1.97653e35	−0.394789
$202$	5.98192e34	0.110636
$203$	−7.50786e35	−1.28626
$204$	1.05955e34	0.0168211
$205$	−1.29253e35	−0.190220
$206$	1.01514e36	1.38543
$207$	−1.11022e35	−0.140562
$208$	−5.88223e34	−0.0691131
$209$	−2.24359e36	−2.44724
$210$	−1.79181e35	−0.181507
$211$	−1.37274e36	−1.29184	−0.645920	−	0.763405i	$-0.723526\pi$
$211$	−1.37274e36	−1.29184	−0.645920	+	0.763405i	$0.723526\pi$
$212$	9.30737e34	0.0813994
$213$	5.50225e35	0.447359
$214$	2.54034e35	0.192078
$215$	−6.74809e35	−0.474662
$216$	5.79575e35	0.379382
$217$	1.64457e36	1.00214
$218$	−9.00809e35	−0.511160
$219$	2.59431e36	1.37132
$220$	8.20567e35	0.404169
$221$	−2.75495e34	−0.0126483
$222$	1.40742e36	0.602494
$223$	5.24242e34	0.0209318	0.0104659	−	0.999945i	$-0.496669\pi$
$223$	5.24242e34	0.0209318	0.0104659	+	0.999945i	$0.496669\pi$
$224$	3.70417e35	0.137990
$225$	−2.64222e35	−0.0918630
$226$	−9.97327e35	−0.323710
$227$	−2.30435e36	−0.698471	−0.349235	−	0.937035i	$-0.613559\pi$
$227$	−2.30435e36	−0.698471	−0.349235	+	0.937035i	$0.613559\pi$
$228$	1.75805e36	0.497784
$229$	3.22039e36	0.852037	0.426019	−	0.904714i	$-0.359916\pi$
$229$	3.22039e36	0.852037	0.426019	+	0.904714i	$0.359916\pi$
$230$	3.91328e35	0.0967740
$231$	4.48701e36	1.03746
$232$	−2.69417e36	−0.582587
$233$	3.35115e36	0.677917	0.338959	−	0.940801i	$-0.389925\pi$
$233$	3.35115e36	0.677917	0.338959	+	0.940801i	$0.389925\pi$
$234$	−4.74310e35	−0.0897875
$235$	−2.75311e36	−0.487834
$236$	3.62025e36	0.600624
$237$	7.76546e36	1.20661
$238$	1.73485e35	0.0252534
$239$	5.41220e36	0.738255	0.369127	−	0.929379i	$-0.379657\pi$
$239$	5.41220e36	0.738255	0.369127	+	0.929379i	$0.379657\pi$
$240$	−6.42986e35	−0.0822105
$241$	−3.64065e36	−0.436430	−0.218215	−	0.975901i	$-0.570023\pi$
$241$	−3.64065e36	−0.436430	−0.218215	+	0.975901i	$0.570023\pi$
$242$	−1.42588e37	−1.60304
$243$	7.87579e36	0.830609
$244$	−3.99903e36	−0.395742
$245$	1.88111e36	0.174719
$246$	−2.53625e36	−0.221155
$247$	−4.57111e36	−0.374299
$248$	5.90149e36	0.453900
$249$	−4.77379e36	−0.344963
$250$	9.31323e35	0.0632456
$251$	−6.60375e36	−0.421549	−0.210774	−	0.977535i	$-0.567599\pi$
$251$	−6.60375e36	−0.421549	−0.210774	+	0.977535i	$0.567599\pi$
$252$	2.98683e36	0.179268
$253$	−9.79952e36	−0.553142
$254$	−1.96506e37	−1.04340
$255$	−3.01143e35	−0.0150453
$256$	1.32923e36	0.0625000
$257$	−1.70943e37	−0.756638	−0.378319	−	0.925675i	$-0.623498\pi$
$257$	−1.70943e37	−0.756638	−0.378319	+	0.925675i	$0.623498\pi$
$258$	−1.32413e37	−0.551857
$259$	2.30443e37	0.904517
$260$	1.67183e36	0.0618167
$261$	−2.17242e37	−0.756862
$262$	−2.64228e37	−0.867580
$263$	6.06914e37	1.87851	0.939254	−	0.343224i	$-0.111519\pi$
$263$	6.06914e37	1.87851	0.939254	+	0.343224i	$0.111519\pi$
$264$	1.61015e37	0.469899
$265$	−2.64531e36	−0.0728058
$266$	2.87853e37	0.747317
$267$	−3.51909e37	−0.861998
$268$	−1.16132e37	−0.268450
$269$	−4.69833e37	−1.02514	−0.512570	−	0.858646i	$-0.671306\pi$
$269$	−4.69833e37	−1.02514	−0.512570	+	0.858646i	$0.671306\pi$
$270$	−1.64725e37	−0.339329
$271$	−2.99460e37	−0.582526	−0.291263	−	0.956643i	$-0.594075\pi$
$271$	−2.99460e37	−0.582526	−0.291263	+	0.956643i	$0.594075\pi$
$272$	6.22546e35	0.0114381
$273$	9.14188e36	0.158677
$274$	−4.12414e37	−0.676394
$275$	−2.33219e37	−0.361499
$276$	7.67877e36	0.112513
$277$	7.82408e37	1.08392	0.541960	−	0.840404i	$-0.317682\pi$
$277$	7.82408e37	1.08392	0.541960	+	0.840404i	$0.317682\pi$
$278$	4.21921e37	0.552760
$279$	4.75862e37	0.589679
$280$	−1.05279e37	−0.123422
$281$	1.79861e38	1.99522	0.997608	−	0.0691186i	$-0.0220187\pi$
$281$	1.79861e38	1.99522	0.997608	+	0.0691186i	$0.0220187\pi$
$282$	−5.40226e37	−0.567172
$283$	1.02428e38	1.01796	0.508979	−	0.860779i	$-0.330023\pi$
$283$	1.02428e38	1.01796	0.508979	+	0.860779i	$0.330023\pi$
$284$	3.23287e37	0.304196
$285$	−4.99667e37	−0.445231
$286$	−4.18655e37	−0.353332
$287$	−4.15271e37	−0.332018
$288$	1.07181e37	0.0811962
$289$	−1.38997e38	−0.997907
$290$	7.65729e37	0.521082
$291$	−2.18874e37	−0.141206
$292$	1.52430e38	0.932471
$293$	−2.65665e38	−1.54129	−0.770647	−	0.637262i	$-0.780067\pi$
$293$	−2.65665e38	−1.54129	−0.770647	+	0.637262i	$0.780067\pi$
$294$	3.69118e37	0.203134
$295$	−1.02894e38	−0.537214
$296$	8.26936e37	0.409685
$297$	4.12500e38	1.93954
$298$	1.38845e36	0.00619694
$299$	−1.99656e37	−0.0846018
$300$	1.82748e37	0.0735313
$301$	−2.16806e38	−0.828497
$302$	2.31930e38	0.841879
$303$	−3.33613e37	−0.115049
$304$	1.03295e38	0.338484
$305$	1.13659e38	0.353963
$306$	5.01985e36	0.0148597
$307$	−1.23731e38	−0.348204	−0.174102	−	0.984728i	$-0.555702\pi$
$307$	−1.23731e38	−0.348204	−0.174102	+	0.984728i	$0.555702\pi$
$308$	2.63636e38	0.705455
$309$	−5.66144e38	−1.44069
$310$	−1.67730e38	−0.405981
$311$	7.02325e38	1.61716	0.808579	−	0.588388i	$-0.200237\pi$
$311$	7.02325e38	1.61716	0.808579	+	0.588388i	$0.200237\pi$
$312$	3.28053e37	0.0718700
$313$	6.10426e38	1.27261	0.636306	−	0.771437i	$-0.280462\pi$
$313$	6.10426e38	1.27261	0.636306	+	0.771437i	$0.280462\pi$
$314$	−4.33755e38	−0.860667
$315$	−8.48908e37	−0.160342
$316$	4.56263e38	0.820475
$317$	−5.90092e38	−1.01042	−0.505209	−	0.862997i	$-0.668585\pi$
$317$	−5.90092e38	−1.01042	−0.505209	+	0.862997i	$0.668585\pi$
$318$	−5.19073e37	−0.0846464
$319$	−1.91752e39	−2.97840
$320$	−3.77789e37	−0.0559017
$321$	−1.41675e38	−0.199740
$322$	1.25728e38	0.168914
$323$	4.83783e37	0.0619457
$324$	−1.35069e38	−0.164858
$325$	−4.75163e37	−0.0552905
$326$	−5.85516e38	−0.649630
$327$	5.02383e38	0.531550
$328$	−1.49018e38	−0.150382
$329$	−8.84535e38	−0.851488
$330$	−4.57632e38	−0.420291
$331$	−1.26563e39	−1.10910	−0.554552	−	0.832149i	$-0.687110\pi$
$331$	−1.26563e39	−1.10910	−0.554552	+	0.832149i	$0.687110\pi$
$332$	−2.80486e38	−0.234569
$333$	6.66794e38	0.532238
$334$	−6.16509e38	−0.469753
$335$	3.30067e38	0.240109
$336$	−2.06582e38	−0.143494
$337$	−1.15260e39	−0.764565	−0.382283	−	0.924045i	$-0.624862\pi$
$337$	−1.15260e39	−0.764565	−0.382283	+	0.924045i	$0.624862\pi$
$338$	1.03078e39	0.653065
$339$	5.56211e38	0.336623
$340$	−1.76938e37	−0.0102305
$341$	4.20026e39	2.32051
$342$	8.32911e38	0.439738
$343$	2.15134e39	1.08555
$344$	−7.78001e38	−0.375253
$345$	−2.18244e38	−0.100634
$346$	−1.10792e39	−0.488461
$347$	3.25921e39	1.37406	0.687029	−	0.726630i	$-0.258914\pi$
$347$	3.25921e39	1.37406	0.687029	+	0.726630i	$0.258914\pi$
$348$	1.50254e39	0.605826
$349$	6.30486e37	0.0243154	0.0121577	−	0.999926i	$-0.496130\pi$
$349$	6.30486e37	0.0243154	0.0121577	+	0.999926i	$0.496130\pi$
$350$	2.99220e38	0.110392
$351$	8.40431e38	0.296648
$352$	9.46050e38	0.319523
$353$	4.15083e39	1.34161	0.670807	−	0.741632i	$-0.265948\pi$
$353$	4.15083e39	1.34161	0.670807	+	0.741632i	$0.265948\pi$
$354$	−2.01902e39	−0.624582
$355$	−9.18837e38	−0.272081
$356$	−2.06766e39	−0.586144
$357$	−9.67530e37	−0.0262607
$358$	7.91551e38	0.205727
$359$	−7.62845e39	−1.89877	−0.949385	−	0.314114i	$-0.898293\pi$
$359$	−7.62845e39	−1.89877	−0.949385	+	0.314114i	$0.898293\pi$
$360$	−3.04628e38	−0.0726241
$361$	3.64823e39	0.833144
$362$	−1.02442e39	−0.224128
$363$	7.95217e39	1.66699
$364$	5.37135e38	0.107898
$365$	−4.33231e39	−0.834027
$366$	2.23027e39	0.411528
$367$	−4.70956e38	−0.0833021	−0.0416510	−	0.999132i	$-0.513262\pi$
$367$	−4.70956e38	−0.0833021	−0.0416510	+	0.999132i	$0.513262\pi$
$368$	4.51170e38	0.0765066
$369$	−1.20160e39	−0.195367
$370$	−2.35029e39	−0.366434
$371$	−8.49901e38	−0.127079
$372$	−3.29127e39	−0.472006
$373$	5.24767e38	0.0721904	0.0360952	−	0.999348i	$-0.488508\pi$
$373$	5.24767e38	0.0721904	0.0360952	+	0.999348i	$0.488508\pi$
$374$	4.43084e38	0.0584757
$375$	−5.19400e38	−0.0657684
$376$	−3.17412e39	−0.385667
$377$	−3.90677e39	−0.455540
$378$	−5.29238e39	−0.592281
$379$	−4.30594e39	−0.462551	−0.231276	−	0.972888i	$-0.574290\pi$
$379$	−4.30594e39	−0.462551	−0.231276	+	0.972888i	$0.574290\pi$
$380$	−2.93582e39	−0.302749
$381$	1.09592e40	1.08503
$382$	1.92656e38	0.0183147
$383$	2.43638e39	0.222415	0.111208	−	0.993797i	$-0.464528\pi$
$383$	2.43638e39	0.222415	0.111208	+	0.993797i	$0.464528\pi$
$384$	−7.41312e38	−0.0649931
$385$	−7.49300e39	−0.630978
$386$	8.98354e39	0.726682
$387$	−6.27336e39	−0.487506
$388$	−1.28601e39	−0.0960177
$389$	−1.05964e40	−0.760219	−0.380110	−	0.924941i	$-0.624114\pi$
$389$	−1.05964e40	−0.760219	−0.380110	+	0.924941i	$0.624114\pi$
$390$	−9.32383e38	−0.0642825
$391$	2.11306e38	0.0140014
$392$	2.16877e39	0.138127
$393$	1.47361e40	0.902187
$394$	−9.28432e39	−0.546461
$395$	−1.29678e40	−0.733855
$396$	7.62840e39	0.415105
$397$	−2.43442e40	−1.27392	−0.636962	−	0.770896i	$-0.719809\pi$
$397$	−2.43442e40	−1.27392	−0.636962	+	0.770896i	$0.719809\pi$
$398$	1.84644e40	0.929280
$399$	−1.60536e40	−0.777127
$400$	1.07374e39	0.0500000
$401$	−1.19933e40	−0.537279	−0.268639	−	0.963241i	$-0.586574\pi$
$401$	−1.19933e40	−0.537279	−0.268639	+	0.963241i	$0.586574\pi$
$402$	6.47670e39	0.279158
$403$	8.55764e39	0.354916
$404$	−1.96016e39	−0.0782311
$405$	3.83890e39	0.147453
$406$	2.46018e40	0.909521
$407$	5.88554e40	2.09446
$408$	−3.47195e38	−0.0118943
$409$	−5.19301e40	−1.71281	−0.856403	−	0.516308i	$-0.827306\pi$
$409$	−5.19301e40	−1.71281	−0.856403	+	0.516308i	$0.827306\pi$
$410$	4.23536e39	0.134506
$411$	2.30004e40	0.703376
$412$	−3.32640e40	−0.979644
$413$	−3.30582e40	−0.937678
$414$	3.63797e39	0.0993927
$415$	7.97189e39	0.209805
$416$	1.92749e39	0.0488704
$417$	−2.35306e40	−0.574810
$418$	7.35179e40	1.73046
$419$	5.00033e40	1.13418	0.567089	−	0.823656i	$-0.308069\pi$
$419$	5.00033e40	1.13418	0.567089	+	0.823656i	$0.308069\pi$
$420$	5.87142e39	0.128345
$421$	−9.66156e39	−0.203552	−0.101776	−	0.994807i	$-0.532452\pi$
$421$	−9.66156e39	−0.203552	−0.101776	+	0.994807i	$0.532452\pi$
$422$	4.49818e40	0.913469
$423$	−2.55943e40	−0.501035
$424$	−3.04984e39	−0.0575581
$425$	5.02888e38	0.00915046
$426$	−1.80298e40	−0.316331
$427$	3.65171e40	0.617823
$428$	−8.32417e39	−0.135820
$429$	2.33485e40	0.367427
$430$	2.21121e40	0.335637
$431$	−6.30614e40	−0.923350	−0.461675	−	0.887049i	$-0.652751\pi$
$431$	−6.30614e40	−0.923350	−0.461675	+	0.887049i	$0.652751\pi$
$432$	−1.89915e40	−0.268263
$433$	1.25919e41	1.71605	0.858026	−	0.513606i	$-0.171691\pi$
$433$	1.25919e41	1.71605	0.858026	+	0.513606i	$0.171691\pi$
$434$	−5.38893e40	−0.708618
$435$	−4.27048e40	−0.541868
$436$	2.95177e40	0.361445
$437$	3.50606e40	0.414340
$438$	−8.50102e40	−0.969667
$439$	−8.26623e39	−0.0910138	−0.0455069	−	0.998964i	$-0.514490\pi$
$439$	−8.26623e39	−0.0910138	−0.0455069	+	0.998964i	$0.514490\pi$
$440$	−2.68884e40	−0.285790
$441$	1.74877e40	0.179447
$442$	9.02742e38	0.00894373
$443$	1.43030e41	1.36826	0.684132	−	0.729358i	$-0.260181\pi$
$443$	1.43030e41	1.36826	0.684132	+	0.729358i	$0.260181\pi$
$444$	−4.61183e40	−0.426027
$445$	5.87664e40	0.524263
$446$	−1.71784e39	−0.0148010
$447$	−7.74339e38	−0.00644414
$448$	−1.21378e40	−0.0975734
$449$	−1.81047e41	−1.40596	−0.702980	−	0.711210i	$-0.748148\pi$
$449$	−1.81047e41	−1.40596	−0.702980	+	0.711210i	$0.748148\pi$
$450$	8.65804e39	0.0649569
$451$	−1.06061e41	−0.768808
$452$	3.26804e40	0.228898
$453$	−1.29348e41	−0.875461
$454$	7.55091e40	0.493893
$455$	−1.52663e40	−0.0965066
$456$	−5.76077e40	−0.351986
$457$	1.94398e41	1.14813	0.574064	−	0.818810i	$-0.305366\pi$
$457$	1.94398e41	1.14813	0.574064	+	0.818810i	$0.305366\pi$
$458$	−1.05526e41	−0.602481
$459$	−8.89469e39	−0.0490947
$460$	−1.28230e40	−0.0684296
$461$	−1.15427e41	−0.595582	−0.297791	−	0.954631i	$-0.596250\pi$
$461$	−1.15427e41	−0.595582	−0.297791	+	0.954631i	$0.596250\pi$
$462$	−1.47030e41	−0.733595
$463$	−1.83772e41	−0.886694	−0.443347	−	0.896350i	$-0.646209\pi$
$463$	−1.83772e41	−0.886694	−0.443347	+	0.896350i	$0.646209\pi$
$464$	8.82825e40	0.411951
$465$	9.35434e40	0.422175
$466$	−1.09810e41	−0.479360
$467$	−1.32162e41	−0.558078	−0.279039	−	0.960280i	$-0.590016\pi$
$467$	−1.32162e41	−0.558078	−0.279039	+	0.960280i	$0.590016\pi$
$468$	1.55422e40	0.0634894
$469$	1.06046e41	0.419097
$470$	9.02140e40	0.344951
$471$	2.41906e41	0.894998
$472$	−1.18628e41	−0.424705
$473$	−5.53726e41	−1.91844
$474$	−2.54458e41	−0.853203
$475$	8.34410e40	0.270787
$476$	−5.68476e39	−0.0178568
$477$	−2.45922e40	−0.0747759
$478$	−1.77347e41	−0.522025
$479$	6.48535e41	1.84813	0.924066	−	0.382233i	$-0.124845\pi$
$479$	6.48535e41	1.84813	0.924066	+	0.382233i	$0.124845\pi$
$480$	2.10694e40	0.0581316
$481$	1.19913e41	0.320343
$482$	1.19297e41	0.308603
$483$	−7.01186e40	−0.175652
$484$	4.67233e41	1.13352
$485$	3.65505e40	0.0858809
$486$	−2.58074e41	−0.587330
$487$	1.77648e41	0.391617	0.195808	−	0.980642i	$-0.437267\pi$
$487$	1.77648e41	0.391617	0.195808	+	0.980642i	$0.437267\pi$
$488$	1.31040e41	0.279832
$489$	3.26543e41	0.675543
$490$	−6.16402e40	−0.123545
$491$	7.79527e41	1.51380	0.756900	−	0.653531i	$-0.226713\pi$
$491$	7.79527e41	1.51380	0.756900	+	0.653531i	$0.226713\pi$
$492$	8.31078e40	0.156381
$493$	4.13472e40	0.0753909
$494$	1.49786e41	0.264669
$495$	−2.16812e41	−0.371281
$496$	−1.93380e41	−0.320956
$497$	−2.95209e41	−0.474904
$498$	1.56427e41	0.243926
$499$	8.45266e41	1.27772	0.638859	−	0.769324i	$-0.279407\pi$
$499$	8.45266e41	1.27772	0.638859	+	0.769324i	$0.279407\pi$
$500$	−3.05176e40	−0.0447214
$501$	3.43828e41	0.488491
$502$	2.16392e41	0.298080
$503$	−2.43928e41	−0.325805	−0.162903	−	0.986642i	$-0.552086\pi$
$503$	−2.43928e41	−0.325805	−0.162903	+	0.986642i	$0.552086\pi$
$504$	−9.78724e40	−0.126761
$505$	5.57110e40	0.0699720
$506$	3.21111e41	0.391130
$507$	−5.74867e41	−0.679116
$508$	6.43910e41	0.737798
$509$	9.04219e41	1.00496	0.502479	−	0.864589i	$-0.332421\pi$
$509$	9.04219e41	1.00496	0.502479	+	0.864589i	$0.332421\pi$
$510$	9.86786e39	0.0106386
$511$	−1.39191e42	−1.45575
$512$	−4.35561e40	−0.0441942
$513$	−1.47584e42	−1.45285
$514$	5.60146e41	0.535024
$515$	9.45421e41	0.876220
$516$	4.33892e41	0.390222
$517$	−2.25911e42	−1.97167
$518$	−7.55115e41	−0.639590
$519$	6.17890e41	0.507946
$520$	−5.47826e40	−0.0437110
$521$	−1.32797e42	−1.02850	−0.514249	−	0.857641i	$-0.671929\pi$
$521$	−1.32797e42	−1.02850	−0.514249	+	0.857641i	$0.671929\pi$
$522$	7.11859e41	0.535182
$523$	−6.64786e41	−0.485183	−0.242591	−	0.970129i	$-0.577997\pi$
$523$	−6.64786e41	−0.485183	−0.242591	+	0.970129i	$0.577997\pi$
$524$	8.65823e41	0.613471
$525$	−1.66876e41	−0.114795
$526$	−1.98874e42	−1.32831
$527$	−9.05697e40	−0.0587379
$528$	−5.27613e41	−0.332269
$529$	−1.48203e42	−0.906348
$530$	8.66817e40	0.0514815
$531$	−9.56551e41	−0.551751
$532$	−9.43236e41	−0.528433
$533$	−2.16089e41	−0.117587
$534$	1.15314e42	0.609525
$535$	2.36587e41	0.121481
$536$	3.80542e41	0.189823
$537$	−4.41449e41	−0.213934
$538$	1.53955e42	0.724883
$539$	1.54358e42	0.706159
$540$	5.39771e41	0.239942
$541$	−3.24428e42	−1.40140	−0.700699	−	0.713457i	$-0.747128\pi$
$541$	−3.24428e42	−1.40140	−0.700699	+	0.713457i	$0.747128\pi$
$542$	9.81271e41	0.411908
$543$	5.71322e41	0.233068
$544$	−2.03996e40	−0.00808794
$545$	−8.38944e41	−0.323286
$546$	−2.99561e41	−0.112202
$547$	4.67015e42	1.70031	0.850153	−	0.526536i	$-0.176510\pi$
$547$	4.67015e42	1.70031	0.850153	+	0.526536i	$0.176510\pi$
$548$	1.35140e42	0.478283
$549$	1.05663e42	0.363541
$550$	7.64213e41	0.255619
$551$	6.86047e42	2.23102
$552$	−2.51618e41	−0.0795584
$553$	−4.16636e42	−1.28091
$554$	−2.56380e42	−0.766447
$555$	1.31076e42	0.381050
$556$	−1.38255e42	−0.390861
$557$	−3.04905e42	−0.838320	−0.419160	−	0.907912i	$-0.637675\pi$
$557$	−3.04905e42	−0.838320	−0.419160	+	0.907912i	$0.637675\pi$
$558$	−1.55930e42	−0.416966
$559$	−1.12817e42	−0.293420
$560$	3.44978e41	0.0872723
$561$	−2.47108e41	−0.0608083
$562$	−5.89370e42	−1.41083
$563$	6.25531e41	0.145669	0.0728347	−	0.997344i	$-0.476795\pi$
$563$	6.25531e41	0.145669	0.0728347	+	0.997344i	$0.476795\pi$
$564$	1.77021e42	0.401051
$565$	−9.28833e41	−0.204732
$566$	−3.35637e42	−0.719805
$567$	1.23338e42	0.257371
$568$	−1.05935e42	−0.215099
$569$	6.38935e42	1.26246	0.631228	−	0.775597i	$-0.282551\pi$
$569$	6.38935e42	1.26246	0.631228	+	0.775597i	$0.282551\pi$
$570$	1.63731e42	0.314826
$571$	4.53027e42	0.847744	0.423872	−	0.905722i	$-0.360671\pi$
$571$	4.53027e42	0.847744	0.423872	+	0.905722i	$0.360671\pi$
$572$	1.37185e42	0.249844
$573$	−1.07444e41	−0.0190453
$574$	1.36076e42	0.234772
$575$	3.64452e41	0.0612053
$576$	−3.51212e41	−0.0574144
$577$	9.48731e42	1.50980	0.754898	−	0.655843i	$-0.227687\pi$
$577$	9.48731e42	1.50980	0.754898	+	0.655843i	$0.227687\pi$
$578$	4.55467e42	0.705627
$579$	−5.01013e42	−0.755669
$580$	−2.50914e42	−0.368461
$581$	2.56125e42	0.366203
$582$	7.17208e41	0.0998478
$583$	−2.17066e42	−0.294258
$584$	−4.99481e42	−0.659356
$585$	−4.41735e41	−0.0567866
$586$	8.70530e42	1.08986
$587$	1.48304e43	1.80827	0.904134	−	0.427250i	$-0.140518\pi$
$587$	1.48304e43	1.80827	0.904134	+	0.427250i	$0.140518\pi$
$588$	−1.20953e42	−0.143637
$589$	−1.50276e43	−1.73822
$590$	3.37162e42	0.379868
$591$	5.17788e42	0.568259
$592$	−2.70970e42	−0.289691
$593$	6.85391e42	0.713823	0.356912	−	0.934138i	$-0.383830\pi$
$593$	6.85391e42	0.713823	0.356912	+	0.934138i	$0.383830\pi$
$594$	−1.35168e43	−1.37146
$595$	1.61571e41	0.0159716
$596$	−4.54967e40	−0.00438190
$597$	−1.02976e43	−0.966349
$598$	6.54234e41	0.0598225
$599$	1.05394e43	0.939078	0.469539	−	0.882912i	$-0.344420\pi$
$599$	1.05394e43	0.939078	0.469539	+	0.882912i	$0.344420\pi$
$600$	−5.98827e41	−0.0519945
$601$	−4.18011e42	−0.353698	−0.176849	−	0.984238i	$-0.556591\pi$
$601$	−4.18011e42	−0.353698	−0.176849	+	0.984238i	$0.556591\pi$
$602$	7.10431e42	0.585836
$603$	3.06847e42	0.246606
$604$	−7.59988e42	−0.595298
$605$	−1.32796e43	−1.01385
$606$	1.09318e42	0.0813517
$607$	4.39468e40	0.00318788	0.00159394	−	0.999999i	$-0.499493\pi$
$607$	4.39468e40	0.00318788	0.00159394	+	0.999999i	$0.499493\pi$
$608$	−3.38477e42	−0.239344
$609$	−1.37204e43	−0.945801
$610$	−3.72439e42	−0.250289
$611$	−4.60274e42	−0.301563
$612$	−1.64490e41	−0.0105074
$613$	−2.74553e43	−1.70997	−0.854985	−	0.518653i	$-0.826434\pi$
$613$	−2.74553e43	−1.70997	−0.854985	+	0.518653i	$0.826434\pi$
$614$	4.05442e42	0.246217
$615$	−2.36207e42	−0.139871
$616$	−8.63884e42	−0.498832
$617$	2.93144e43	1.65067	0.825336	−	0.564641i	$-0.190986\pi$
$617$	2.93144e43	1.65067	0.825336	+	0.564641i	$0.190986\pi$
$618$	1.85514e43	1.01872
$619$	−5.48823e42	−0.293919	−0.146959	−	0.989143i	$-0.546949\pi$
$619$	−5.48823e42	−0.293919	−0.146959	+	0.989143i	$0.546949\pi$
$620$	5.49619e42	0.287072
$621$	−6.44614e42	−0.328383
$622$	−2.30138e43	−1.14350
$623$	1.88808e43	0.915073
$624$	−1.07496e42	−0.0508198
$625$	8.67362e41	0.0400000
$626$	−2.00024e43	−0.899873
$627$	−4.10011e43	−1.79948
$628$	1.42133e43	0.608583
$629$	−1.26909e42	−0.0530162
$630$	2.78170e42	0.113379
$631$	2.48327e43	0.987572	0.493786	−	0.869583i	$-0.335613\pi$
$631$	2.48327e43	0.987572	0.493786	+	0.869583i	$0.335613\pi$
$632$	−1.49508e43	−0.580163
$633$	−2.50864e43	−0.949907
$634$	1.93361e43	0.714474
$635$	−1.83010e43	−0.659907
$636$	1.70090e42	0.0598540
$637$	3.14490e42	0.108005
$638$	6.28332e43	2.10605
$639$	−8.54196e42	−0.279444
$640$	1.23794e42	0.0395285
$641$	2.55989e43	0.797850	0.398925	−	0.916984i	$-0.369383\pi$
$641$	2.55989e43	0.797850	0.398925	+	0.916984i	$0.369383\pi$
$642$	4.64240e42	0.141237
$643$	4.50652e43	1.33836	0.669178	−	0.743103i	$-0.266647\pi$
$643$	4.50652e43	1.33836	0.669178	+	0.743103i	$0.266647\pi$
$644$	−4.11985e42	−0.119440
$645$	−1.23320e43	−0.349025
$646$	−1.58526e42	−0.0438022
$647$	7.99244e42	0.215607	0.107804	−	0.994172i	$-0.465618\pi$
$647$	7.99244e42	0.215607	0.107804	+	0.994172i	$0.465618\pi$
$648$	4.42595e42	0.116572
$649$	−8.44312e43	−2.17125
$650$	1.55701e42	0.0390963
$651$	3.00542e43	0.736884
$652$	1.91862e43	0.459358
$653$	6.70562e43	1.56778	0.783890	−	0.620900i	$-0.213233\pi$
$653$	6.70562e43	1.56778	0.783890	+	0.620900i	$0.213233\pi$
$654$	−1.64621e43	−0.375863
$655$	−2.46082e43	−0.548706
$656$	4.88304e42	0.106336
$657$	−4.02753e43	−0.856595
$658$	2.89845e43	0.602093
$659$	2.04703e43	0.415337	0.207668	−	0.978199i	$-0.433412\pi$
$659$	2.04703e43	0.415337	0.207668	+	0.978199i	$0.433412\pi$
$660$	1.49957e43	0.297190
$661$	1.02079e43	0.197611	0.0988057	−	0.995107i	$-0.468498\pi$
$661$	1.02079e43	0.197611	0.0988057	+	0.995107i	$0.468498\pi$
$662$	4.14721e43	0.784254
$663$	−5.03461e41	−0.00930049
$664$	9.19096e42	0.165865
$665$	2.68084e43	0.472645
$666$	−2.18495e43	−0.376349
$667$	2.99651e43	0.504272
$668$	2.02018e43	0.332165
$669$	9.58040e41	0.0153914
$670$	−1.08156e43	−0.169783
$671$	9.32651e43	1.43061
$672$	6.76928e42	0.101466
$673$	−1.16828e43	−0.171125	−0.0855623	−	0.996333i	$-0.527269\pi$
$673$	−1.16828e43	−0.171125	−0.0855623	+	0.996333i	$0.527269\pi$
$674$	3.77683e43	0.540629
$675$	−1.53412e43	−0.214611
$676$	−3.37766e43	−0.461787
$677$	−5.20282e43	−0.695208	−0.347604	−	0.937641i	$-0.613005\pi$
$677$	−5.20282e43	−0.695208	−0.347604	+	0.937641i	$0.613005\pi$
$678$	−1.82259e43	−0.238029
$679$	1.17431e43	0.149900
$680$	5.79791e41	0.00723408
$681$	−4.21115e43	−0.513595
$682$	−1.37634e44	−1.64085
$683$	−1.36522e44	−1.59104	−0.795521	−	0.605926i	$-0.792803\pi$
$683$	−1.36522e44	−1.59104	−0.795521	+	0.605926i	$0.792803\pi$
$684$	−2.72928e43	−0.310942
$685$	−3.84091e43	−0.427789
$686$	−7.04950e43	−0.767600
$687$	5.88519e43	0.626514
$688$	2.54935e43	0.265344
$689$	−4.42252e42	−0.0450061
$690$	7.15142e42	0.0711592
$691$	1.03195e44	1.00404	0.502020	−	0.864856i	$-0.332590\pi$
$691$	1.03195e44	1.00404	0.502020	+	0.864856i	$0.332590\pi$
$692$	3.63044e43	0.345394
$693$	−6.96586e43	−0.648052
$694$	−1.06798e44	−0.971606
$695$	3.92945e43	0.349596
$696$	−4.92353e43	−0.428384
$697$	2.28698e42	0.0194605
$698$	−2.06598e42	−0.0171936
$699$	6.12414e43	0.498482
$700$	−9.80486e42	−0.0780587
$701$	1.21223e44	0.943967	0.471983	−	0.881607i	$-0.343538\pi$
$701$	1.21223e44	0.943967	0.471983	+	0.881607i	$0.343538\pi$
$702$	−2.75392e43	−0.209762
$703$	−2.10572e44	−1.56889
$704$	−3.10002e43	−0.225937
$705$	−5.03125e43	−0.358711
$706$	−1.36015e44	−0.948664
$707$	1.78991e43	0.122132
$708$	6.61592e43	0.441646
$709$	−2.19198e43	−0.143159	−0.0715797	−	0.997435i	$-0.522804\pi$
$709$	−2.19198e43	−0.143159	−0.0715797	+	0.997435i	$0.522804\pi$
$710$	3.01084e43	0.192391
$711$	−1.20555e44	−0.753713
$712$	6.77531e43	0.414466
$713$	−6.56375e43	−0.392884
$714$	3.17040e42	0.0185691
$715$	−3.89903e43	−0.223467
$716$	−2.59375e43	−0.145471
$717$	9.89066e43	0.542848
$718$	2.49969e44	1.34263
$719$	9.40579e43	0.494422	0.247211	−	0.968962i	$-0.420486\pi$
$719$	9.40579e43	0.494422	0.247211	+	0.968962i	$0.420486\pi$
$720$	9.98204e42	0.0513530
$721$	3.03750e44	1.52940
$722$	−1.19545e44	−0.589122
$723$	−6.65320e43	−0.320913
$724$	3.35683e43	0.158482
$725$	7.13140e43	0.329561
$726$	−2.60577e44	−1.17874
$727$	4.09641e44	1.81393	0.906965	−	0.421207i	$-0.138393\pi$
$727$	4.09641e44	1.81393	0.906965	+	0.421207i	$0.138393\pi$
$728$	−1.76008e43	−0.0762952
$729$	2.21627e44	0.940473
$730$	1.41961e44	0.589746
$731$	1.19399e43	0.0485604
$732$	−7.30813e43	−0.290994
$733$	−4.57092e44	−1.78194	−0.890968	−	0.454067i	$-0.849973\pi$
$733$	−4.57092e44	−1.78194	−0.890968	+	0.454067i	$0.849973\pi$
$734$	1.54323e43	0.0589035
$735$	3.43768e43	0.128473
$736$	−1.47839e43	−0.0540983
$737$	2.70842e44	0.970445
$738$	3.93740e43	0.138145
$739$	1.00404e44	0.344957	0.172478	−	0.985013i	$-0.444823\pi$
$739$	1.00404e44	0.344957	0.172478	+	0.985013i	$0.444823\pi$
$740$	7.70144e43	0.259108
$741$	−8.35359e43	−0.275227
$742$	2.78496e43	0.0898582
$743$	−7.43485e43	−0.234934	−0.117467	−	0.993077i	$-0.537477\pi$
$743$	−7.43485e43	−0.234934	−0.117467	+	0.993077i	$0.537477\pi$
$744$	1.07848e44	0.333759
$745$	1.29309e42	0.00391929
$746$	−1.71956e43	−0.0510463
$747$	7.41106e43	0.215482
$748$	−1.45190e43	−0.0413486
$749$	7.60121e43	0.212038
$750$	1.70197e43	0.0465053
$751$	−5.97546e44	−1.59938	−0.799691	−	0.600411i	$-0.795003\pi$
$751$	−5.97546e44	−1.59938	−0.799691	+	0.600411i	$0.795003\pi$
$752$	1.04010e44	0.272708
$753$	−1.20682e44	−0.309970
$754$	1.28017e44	0.322115
$755$	2.16002e44	0.532451
$756$	1.73421e44	0.418806
$757$	−6.25091e44	−1.47896	−0.739481	−	0.673177i	$-0.764929\pi$
$757$	−6.25091e44	−1.47896	−0.739481	+	0.673177i	$0.764929\pi$
$758$	1.41097e44	0.327073
$759$	−1.79084e44	−0.406732
$760$	9.62009e43	0.214076
$761$	8.11145e44	1.76863	0.884314	−	0.466892i	$-0.154626\pi$
$761$	8.11145e44	1.76863	0.884314	+	0.466892i	$0.154626\pi$
$762$	−3.59110e44	−0.767229
$763$	−2.69541e44	−0.564279
$764$	−6.31294e42	−0.0129504
$765$	4.67510e42	0.00939807
$766$	−7.98354e43	−0.157271
$767$	−1.72021e44	−0.332088
$768$	2.42913e43	0.0459571
$769$	4.74855e44	0.880446	0.440223	−	0.897888i	$-0.354899\pi$
$769$	4.74855e44	0.880446	0.440223	+	0.897888i	$0.354899\pi$
$770$	2.45531e44	0.446169
$771$	−3.12394e44	−0.556366
$772$	−2.94373e44	−0.513841
$773$	3.40400e44	0.582380	0.291190	−	0.956665i	$-0.405949\pi$
$773$	3.40400e44	0.582380	0.291190	+	0.956665i	$0.405949\pi$
$774$	2.05565e44	0.344719
$775$	−1.56211e44	−0.256765
$776$	4.21399e43	0.0678948
$777$	4.21129e44	0.665103
$778$	3.47222e44	0.537556
$779$	3.79463e44	0.575889
$780$	3.05523e43	0.0454546
$781$	−7.53967e44	−1.09967
$782$	−6.92407e42	−0.00990050
$783$	−1.26135e45	−1.76818
$784$	−7.10663e43	−0.0976708
$785$	−4.03966e44	−0.544334
$786$	−4.82871e44	−0.637943
$787$	−1.06793e45	−1.38336	−0.691678	−	0.722206i	$-0.743128\pi$
$787$	−1.06793e45	−1.38336	−0.691678	+	0.722206i	$0.743128\pi$
$788$	3.04229e44	0.386406
$789$	1.10912e45	1.38129
$790$	4.24928e44	0.518914
$791$	−2.98421e44	−0.357350
$792$	−2.49967e44	−0.293524
$793$	1.90019e44	0.218808
$794$	7.97712e44	0.900800
$795$	−4.83425e43	−0.0535351
$796$	−6.05040e44	−0.657100
$797$	−9.48957e43	−0.101075	−0.0505374	−	0.998722i	$-0.516093\pi$
$797$	−9.48957e43	−0.101075	−0.0505374	+	0.998722i	$0.516093\pi$
$798$	5.26044e44	0.549512
$799$	4.87131e43	0.0499080
$800$	−3.51844e43	−0.0353553
$801$	5.46322e44	0.538449
$802$	3.92995e44	0.379913
$803$	−3.55495e45	−3.37088
$804$	−2.12229e44	−0.197395
$805$	1.17093e44	0.106831
$806$	−2.80417e44	−0.250964
$807$	−8.58608e44	−0.753798
$808$	6.42304e43	0.0553178
$809$	5.97219e44	0.504582	0.252291	−	0.967651i	$-0.418816\pi$
$809$	5.97219e44	0.504582	0.252291	+	0.967651i	$0.418816\pi$
$810$	−1.25793e44	−0.104265
$811$	9.30989e44	0.757045	0.378522	−	0.925592i	$-0.376432\pi$
$811$	9.30989e44	0.757045	0.378522	+	0.925592i	$0.376432\pi$
$812$	−8.06150e44	−0.643128
$813$	−5.47256e44	−0.428339
$814$	−1.92857e45	−1.48101
$815$	−5.45304e44	−0.410862
$816$	1.13769e43	0.00841057
$817$	1.98111e45	1.43704
$818$	1.70165e45	1.21114
$819$	−1.41923e44	−0.0991180
$820$	−1.38784e44	−0.0951098
$821$	4.88604e44	0.328578	0.164289	−	0.986412i	$-0.447467\pi$
$821$	4.88604e44	0.328578	0.164289	+	0.986412i	$0.447467\pi$
$822$	−7.53677e44	−0.497362
$823$	2.61589e45	1.69403	0.847017	−	0.531566i	$-0.178396\pi$
$823$	2.61589e45	1.69403	0.847017	+	0.531566i	$0.178396\pi$
$824$	1.09000e45	0.692713
$825$	−4.26203e44	−0.265815
$826$	1.08325e45	0.663039
$827$	2.59698e45	1.56003	0.780015	−	0.625761i	$-0.215211\pi$
$827$	2.59698e45	1.56003	0.780015	+	0.625761i	$0.215211\pi$
$828$	−1.19209e44	−0.0702812
$829$	−2.36709e45	−1.36968	−0.684842	−	0.728692i	$-0.740129\pi$
$829$	−2.36709e45	−1.36968	−0.684842	+	0.728692i	$0.740129\pi$
$830$	−2.61223e44	−0.148355
$831$	1.42983e45	0.797020
$832$	−6.31600e43	−0.0345566
$833$	−3.32840e43	−0.0178747
$834$	7.71051e44	0.406452
$835$	−5.74169e44	−0.297098
$836$	−2.40904e45	−1.22362
$837$	2.76294e45	1.37761
$838$	−1.63851e45	−0.801985
$839$	2.59287e45	1.24586	0.622930	−	0.782277i	$-0.285942\pi$
$839$	2.59287e45	1.24586	0.622930	+	0.782277i	$0.285942\pi$
$840$	−1.92395e44	−0.0907536
$841$	3.70398e45	1.71526
$842$	3.16590e44	0.143933
$843$	3.28692e45	1.46711
$844$	−1.47396e45	−0.645920
$845$	9.59988e44	0.413035
$846$	8.38674e44	0.354285
$847$	−4.26653e45	−1.76963
$848$	9.99371e43	0.0406997
$849$	1.87185e45	0.748518
$850$	−1.64786e43	−0.00647035
$851$	−9.19734e44	−0.354613
$852$	5.90799e44	0.223679
$853$	1.97911e45	0.735799	0.367900	−	0.929866i	$-0.380077\pi$
$853$	1.97911e45	0.735799	0.367900	+	0.929866i	$0.380077\pi$
$854$	−1.19659e45	−0.436867
$855$	7.75709e44	0.278115
$856$	2.72767e44	0.0960390
$857$	−2.57732e45	−0.891181	−0.445591	−	0.895237i	$-0.647006\pi$
$857$	−2.57732e45	−0.891181	−0.445591	+	0.895237i	$0.647006\pi$
$858$	−7.65083e44	−0.259810
$859$	5.92532e44	0.197614	0.0988069	−	0.995107i	$-0.468497\pi$
$859$	5.92532e44	0.197614	0.0988069	+	0.995107i	$0.468497\pi$
$860$	−7.24570e44	−0.237331
$861$	−7.58897e44	−0.244137
$862$	2.06640e45	0.652907
$863$	−3.98009e45	−1.23517	−0.617583	−	0.786506i	$-0.711888\pi$
$863$	−3.98009e45	−1.23517	−0.617583	+	0.786506i	$0.711888\pi$
$864$	6.22314e44	0.189691
$865$	−1.03183e45	−0.308930
$866$	−4.12613e45	−1.21343
$867$	−2.54014e45	−0.733774
$868$	1.76585e45	0.501068
$869$	−1.06409e46	−2.96601
$870$	1.39935e45	0.383158
$871$	5.51817e44	0.148427
$872$	−9.67237e44	−0.255580
$873$	3.39792e44	0.0882047
$874$	−1.14887e45	−0.292983
$875$	2.78671e44	0.0698179
$876$	2.78561e45	0.685658
$877$	6.85482e45	1.65769	0.828844	−	0.559480i	$-0.188999\pi$
$877$	6.85482e45	1.65769	0.828844	+	0.559480i	$0.188999\pi$
$878$	2.70868e44	0.0643565
$879$	−4.85496e45	−1.13333
$880$	8.81077e44	0.202084
$881$	−1.78938e44	−0.0403251	−0.0201625	−	0.999797i	$-0.506418\pi$
$881$	−1.78938e44	−0.0403251	−0.0201625	+	0.999797i	$0.506418\pi$
$882$	−5.73038e44	−0.126888
$883$	1.67939e45	0.365393	0.182696	−	0.983169i	$-0.441518\pi$
$883$	1.67939e45	0.365393	0.182696	+	0.983169i	$0.441518\pi$
$884$	−2.95811e43	−0.00632417
$885$	−1.88036e45	−0.395020
$886$	−4.68681e45	−0.967509
$887$	9.72650e43	0.0197306	0.00986530	−	0.999951i	$-0.496860\pi$
$887$	9.72650e43	0.0197306	0.00986530	+	0.999951i	$0.496860\pi$
$888$	1.51121e45	0.301247
$889$	−5.87986e45	−1.15183
$890$	−1.92566e45	−0.370710
$891$	3.15007e45	0.595959
$892$	5.62901e43	0.0104659
$893$	8.08264e45	1.47691
$894$	2.53736e43	0.00455669
$895$	7.37189e44	0.130113
$896$	3.97732e44	0.0689948
$897$	−3.64867e44	−0.0622088
$898$	5.93255e45	0.994164
$899$	−1.28436e46	−2.11549
$900$	−2.83707e44	−0.0459315
$901$	4.68057e43	0.00744842
$902$	3.47540e45	0.543630
$903$	−3.96208e45	−0.609205
$904$	−1.07087e45	−0.161855
$905$	−9.54068e44	−0.141751
$906$	4.23847e45	0.619044
$907$	5.07003e44	0.0727943	0.0363972	−	0.999337i	$-0.488412\pi$
$907$	5.07003e44	0.0727943	0.0363972	+	0.999337i	$0.488412\pi$
$908$	−2.47428e45	−0.349235
$909$	5.17917e44	0.0718654
$910$	5.00246e44	0.0682405
$911$	−8.33096e44	−0.111728	−0.0558638	−	0.998438i	$-0.517791\pi$
$911$	−8.33096e44	−0.111728	−0.0558638	+	0.998438i	$0.517791\pi$
$912$	1.88769e45	0.248892
$913$	6.54147e45	0.847966
$914$	−6.37003e45	−0.811850
$915$	2.07710e45	0.260273
$916$	3.45787e45	0.426019
$917$	−7.90625e45	−0.957736
$918$	2.91461e44	0.0347152
$919$	7.80049e45	0.913549	0.456774	−	0.889583i	$-0.349005\pi$
$919$	7.80049e45	0.913549	0.456774	+	0.889583i	$0.349005\pi$
$920$	4.20185e44	0.0483870
$921$	−2.26115e45	−0.256039
$922$	3.78230e45	0.421140
$923$	−1.53614e45	−0.168192
$924$	4.81789e45	0.518730
$925$	−2.18888e45	−0.231753
$926$	6.02184e45	0.626987
$927$	8.78910e45	0.899930
$928$	−2.89284e45	−0.291294
$929$	9.20353e45	0.911404	0.455702	−	0.890133i	$-0.349388\pi$
$929$	9.20353e45	0.911404	0.455702	+	0.890133i	$0.349388\pi$
$930$	−3.06523e45	−0.298523
$931$	−5.52259e45	−0.528960
$932$	3.59827e45	0.338959
$933$	1.28348e46	1.18912
$934$	4.33068e45	0.394621
$935$	4.12654e44	0.0369833
$936$	−5.09286e44	−0.0448938
$937$	1.17829e46	1.02162	0.510808	−	0.859695i	$-0.329346\pi$
$937$	1.17829e46	1.02162	0.510808	+	0.859695i	$0.329346\pi$
$938$	−3.47491e45	−0.296346
$939$	1.11554e46	0.935768
$940$	−2.95613e45	−0.243917
$941$	−6.87236e45	−0.557785	−0.278892	−	0.960322i	$-0.589967\pi$
$941$	−6.87236e45	−0.557785	−0.278892	+	0.960322i	$0.589967\pi$
$942$	−7.92677e45	−0.632859
$943$	1.65741e45	0.130167
$944$	3.88721e45	0.300312
$945$	−4.92891e45	−0.374591
$946$	1.81445e46	1.35654
$947$	−8.94323e45	−0.657763	−0.328882	−	0.944371i	$-0.606672\pi$
$947$	−8.94323e45	−0.657763	−0.328882	+	0.944371i	$0.606672\pi$
$948$	8.33810e45	0.603306
$949$	−7.24289e45	−0.515568
$950$	−2.73419e45	−0.191476
$951$	−1.07838e46	−0.742974
$952$	1.86278e44	0.0126267
$953$	−7.57551e45	−0.505210	−0.252605	−	0.967569i	$-0.581287\pi$
$953$	−7.57551e45	−0.505210	−0.252605	+	0.967569i	$0.581287\pi$
$954$	8.05836e44	0.0528746
$955$	1.79425e44	0.0115832
$956$	5.81130e45	0.369127
$957$	−3.50422e46	−2.19006
$958$	−2.12512e46	−1.30683
$959$	−1.23403e46	−0.746684
$960$	−6.90401e44	−0.0411052
$961$	1.10643e46	0.648203
$962$	−3.92929e45	−0.226517
$963$	2.19943e45	0.124768
$964$	−3.90912e45	−0.218215
$965$	8.36657e45	0.459594
$966$	2.29765e45	0.124205
$967$	3.23805e46	1.72255	0.861277	−	0.508136i	$-0.169665\pi$
$967$	3.23805e46	1.72255	0.861277	+	0.508136i	$0.169665\pi$
$968$	−1.53103e46	−0.801522
$969$	8.84102e44	0.0455495
$970$	−1.19769e45	−0.0607270
$971$	−9.38917e44	−0.0468521	−0.0234260	−	0.999726i	$-0.507457\pi$
$971$	−9.38917e44	−0.0468521	−0.0234260	+	0.999726i	$0.507457\pi$
$972$	8.45656e45	0.415305
$973$	1.26247e46	0.610202
$974$	−5.82117e45	−0.276915
$975$	−8.68349e44	−0.0406558
$976$	−4.29393e45	−0.197871
$977$	−2.21995e46	−1.00688	−0.503441	−	0.864030i	$-0.667933\pi$
$977$	−2.21995e46	−1.00688	−0.503441	+	0.864030i	$0.667933\pi$
$978$	−1.07002e46	−0.477681
$979$	4.82218e46	2.11891
$980$	2.01983e45	0.0873594
$981$	−7.79924e45	−0.332034
$982$	−2.55436e46	−1.07042
$983$	−9.42127e45	−0.388624	−0.194312	−	0.980940i	$-0.562247\pi$
$983$	−9.42127e45	−0.388624	−0.194312	+	0.980940i	$0.562247\pi$
$984$	−2.72328e45	−0.110578
$985$	−8.64670e45	−0.345612
$986$	−1.35487e45	−0.0533094
$987$	−1.61647e46	−0.626110
$988$	−4.90819e45	−0.187150
$989$	8.65308e45	0.324809
$990$	7.10450e45	0.262536
$991$	−5.11507e44	−0.0186084	−0.00930422	−	0.999957i	$-0.502962\pi$
$991$	−5.11507e44	−0.0186084	−0.00930422	+	0.999957i	$0.502962\pi$
$992$	6.33667e45	0.226950
$993$	−2.31290e46	−0.815538
$994$	9.67341e45	0.335808
$995$	1.71963e46	0.587728
$996$	−5.12581e45	−0.172482
$997$	9.34514e45	0.309607	0.154804	−	0.987945i	$-0.450526\pi$
$997$	9.34514e45	0.309607	0.154804	+	0.987945i	$0.450526\pi$
$998$	−2.76977e46	−0.903483
$999$	3.87152e46	1.24342

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.32.a.b.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.32.a.b.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:	\( k \)	\(=\)	\( 32 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q-32768.0 q^{2} +1.82748e7 q^{3} +1.07374e9 q^{4} -3.05176e10 q^{5} -5.98827e11 q^{6} -9.80486e12 q^{7} -3.51844e13 q^{8} -2.83707e14 q^{9} +1.00000e15 q^{10} -2.50417e16 q^{11} +1.96224e16 q^{12} -5.10202e16 q^{13} +3.21285e17 q^{14} -5.57701e17 q^{15} +1.15292e18 q^{16} +5.39972e17 q^{17} +9.29650e18 q^{18} +8.95940e19 q^{19} -3.27680e19 q^{20} -1.79181e20 q^{21} +8.20567e20 q^{22} +3.91328e20 q^{23} -6.42986e20 q^{24} +9.31323e20 q^{25} +1.67183e21 q^{26} -1.64725e22 q^{27} -1.05279e22 q^{28} +7.65729e22 q^{29} +1.82748e22 q^{30} -1.67730e23 q^{31} -3.77789e22 q^{32} -4.57632e23 q^{33} -1.76938e22 q^{34} +2.99220e23 q^{35} -3.04628e23 q^{36} -2.35029e24 q^{37} -2.93582e24 q^{38} -9.32383e23 q^{39} +1.07374e24 q^{40} +4.23536e24 q^{41} +5.87142e24 q^{42} +2.21121e25 q^{43} -2.68884e25 q^{44} +8.65804e24 q^{45} -1.28230e25 q^{46} +9.02140e25 q^{47} +2.10694e25 q^{48} -6.16402e25 q^{49} -3.05176e25 q^{50} +9.86786e24 q^{51} -5.47826e25 q^{52} +8.66817e25 q^{53} +5.39771e26 q^{54} +7.64213e26 q^{55} +3.44978e26 q^{56} +1.63731e27 q^{57} -2.50914e27 q^{58} +3.37162e27 q^{59} -5.98827e26 q^{60} -3.72439e27 q^{61} +5.49619e27 q^{62} +2.78170e27 q^{63} +1.23794e27 q^{64} +1.55701e27 q^{65} +1.49957e28 q^{66} -1.08156e28 q^{67} +5.79791e26 q^{68} +7.15142e27 q^{69} -9.80486e27 q^{70} +3.01084e28 q^{71} +9.98204e27 q^{72} +1.41961e29 q^{73} +7.70144e28 q^{74} +1.70197e28 q^{75} +9.62009e28 q^{76} +2.45531e29 q^{77} +3.05523e28 q^{78} +4.24928e29 q^{79} -3.51844e28 q^{80} -1.25793e29 q^{81} -1.38784e29 q^{82} -2.61223e29 q^{83} -1.92395e29 q^{84} -1.64786e28 q^{85} -7.24570e29 q^{86} +1.39935e30 q^{87} +8.81077e29 q^{88} -1.92566e30 q^{89} -2.83707e29 q^{90} +5.00246e29 q^{91} +4.20185e29 q^{92} -3.06523e30 q^{93} -2.95613e30 q^{94} -2.73419e30 q^{95} -6.90401e29 q^{96} -1.19769e30 q^{97} +2.01983e30 q^{98} +7.10450e30 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 65536 q^{2} + 29024244 q^{3} + 2147483648 q^{4} - 61035156250 q^{5} - 951066427392 q^{6} + 12795158105212 q^{7} - 70368744177664 q^{8} - 785828540134926 q^{9} + 20\!\cdots\!00 q^{10} - 500906012122176 q^{11}+ \cdots - 52\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 65536 * q^2 + 29024244 * q^3 + 2147483648 * q^4 - 61035156250 * q^5 - 951066427392 * q^6 + 12795158105212 * q^7 - 70368744177664 * q^8 - 785828540134926 * q^9 + 2000000000000000 * q^10 - 500906012122176 * q^11 + 31164544692781056 * q^12 - 199440062300108396 * q^13 - 419271740791586816 * q^14 - 885749633789062500 * q^15 + 2305843009213693952 * q^16 + 12159060327494700852 * q^17 + 25750029603141255168 * q^18 + 127400875596685413160 * q^19 - 65536000000000000000 * q^20 + 63757121557979677464 * q^21 + 16413688205219463168 * q^22 + 1266903156187203120564 * q^23 - 1021199800493049643008 * q^24 + 1862645149230957031250 * q^25 + 6535251961449951920128 * q^26 - 28509724951692639267240 * q^27 + 13738696402258716786688 * q^28 - 9185091177630833257860 * q^29 + 29024244000000000000000 * q^30 - 146295843292215232250936 * q^31 - 75557863725914323419136 * q^32 - 193830377630097097798272 * q^33 - 398428088811346357518336 * q^34 - 390477237097534179687500 * q^35 - 843776970035732649345024 * q^36 - 4796960187038756074101068 * q^37 - 4174671891552187618426880 * q^38 - 2527819231419957051969912 * q^39 + 2147483648000000000000000 * q^40 + 14935619514300516260083884 * q^41 - 2089193359211878071140352 * q^42 + 28899014613348735583843684 * q^43 - 537843735108631369089024 * q^44 + 23981583866422302246093750 * q^45 - 41513882621942271854641152 * q^46 - 51613521705752647137207828 * q^47 + 33462675062556250702086144 * q^48 + 291345014964521476498437786 * q^49 - 61035156250000000000000000 * q^50 + 134767069271392484976262344 * q^51 - 214147136272792024518754304 * q^52 + 612453197337950081085508644 * q^53 + 934206667217064403508920320 * q^54 + 15286438358220703125000000 * q^55 - 450189603709213631666192384 * q^56 + 2043713526810613838894722320 * q^57 + 300977067708607144193556480 * q^58 + 5407094693613569560863134280 * q^59 - 951066427392000000000000000 * q^60 + 2835877556240957667189879124 * q^61 + 4793822192999308730398670848 * q^62 - 8566261666607186084500902756 * q^63 + 2475880078570760549798248448 * q^64 + 6086427682498425170898437500 * q^65 + 6351433814183021700653776896 * q^66 + 10837595864228774593398202252 * q^67 + 13055691614170197443160834048 * q^68 + 16563402888409735784762968008 * q^69 + 12795158105212000000000000000 * q^70 + 58422436263671389450567835544 * q^71 + 27648883754130887453737746432 * q^72 + 171414457291735665495284849764 * q^73 + 157186791408885959036143796224 * q^74 + 27030933648347854614257812500 * q^75 + 136795648542382083880612003840 * q^76 + 800153433605242701833643682944 * q^77 + 82831580575169152678950076416 * q^78 + 188775939965441260340578960240 * q^79 - 70368744177664000000000000000 * q^80 + 54960429466999252255967047242 * q^81 - 489410380244599316810428710912 * q^82 + 536572539310341029223184308324 * q^83 + 68458687994654820635127054336 * q^84 - 371065073470907618774414062500 * q^85 - 946962910850211367611389837312 * q^86 + 477496900561204346619073126680 * q^87 + 17624063512039632702309138432 * q^88 - 750272557446280683624160755180 * q^89 - 785828540134926000000000000000 * q^90 - 2854043706700147924065243188776 * q^91 + 1360326905755804364132881268736 * q^92 - 2834821865488342767082586415792 * q^93 + 1691271879254102741392026107904 * q^94 - 3887966174215253087158203125000 * q^95 - 1096504936449843223005958766592 * q^96 - 4226089759761369848050283653628 * q^97 - 9546793450357439741900809371648 * q^98 - 5217983754520789466685211355712 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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