LMFDB - Embedded newform 10.32.a.b.1.1

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			1.1
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)

$f(q)$	$=$	\(q-32768.0 q^{2} +1.07495e7 q^{3} +1.07374e9 q^{4} -3.05176e10 q^{5} -3.52239e11 q^{6} +2.26000e13 q^{7} -3.51844e13 q^{8} -5.02122e14 q^{9} +1.00000e15 q^{10} +2.45408e16 q^{11} +1.15422e16 q^{12} -1.48420e17 q^{13} -7.40557e17 q^{14} -3.28048e17 q^{15} +1.15292e18 q^{16} +1.16191e19 q^{17} +1.64535e19 q^{18} +3.78068e19 q^{19} -3.27680e19 q^{20} +2.42938e20 q^{21} -8.04154e20 q^{22} +8.75576e20 q^{23} -3.78214e20 q^{24} +9.31323e20 q^{25} +4.86342e21 q^{26} -1.20372e22 q^{27} +2.42666e22 q^{28} -8.57580e22 q^{29} +1.07495e22 q^{30} +2.14345e22 q^{31} -3.77789e22 q^{32} +2.63801e23 q^{33} -3.80734e23 q^{34} -6.89698e23 q^{35} -5.39149e23 q^{36} -2.44667e24 q^{37} -1.23885e24 q^{38} -1.59544e24 q^{39} +1.07374e24 q^{40} +1.07003e25 q^{41} -7.96061e24 q^{42} +6.78689e24 q^{43} +2.63505e25 q^{44} +1.53235e25 q^{45} -2.86909e25 q^{46} -1.41828e26 q^{47} +1.23933e25 q^{48} +3.52985e26 q^{49} -3.05176e25 q^{50} +1.24899e26 q^{51} -1.59365e26 q^{52} +5.25772e26 q^{53} +3.94436e26 q^{54} -7.48926e26 q^{55} -7.95167e26 q^{56} +4.06404e26 q^{57} +2.81012e27 q^{58} +2.03548e27 q^{59} -3.52239e26 q^{60} +6.56027e27 q^{61} -7.02366e26 q^{62} -1.13480e28 q^{63} +1.23794e27 q^{64} +4.52941e27 q^{65} -8.64424e27 q^{66} +2.16532e28 q^{67} +1.24759e28 q^{68} +9.41199e27 q^{69} +2.26000e28 q^{70} +2.83140e28 q^{71} +1.76668e28 q^{72} +2.94533e28 q^{73} +8.01724e28 q^{74} +1.00112e28 q^{75} +4.05948e28 q^{76} +5.54623e29 q^{77} +5.22793e28 q^{78} -2.36152e29 q^{79} -3.51844e28 q^{80} +1.80753e29 q^{81} -3.50626e29 q^{82} +7.97795e29 q^{83} +2.60853e29 q^{84} -3.54586e29 q^{85} -2.22393e29 q^{86} -9.21854e29 q^{87} -8.63453e29 q^{88} +1.17539e30 q^{89} -5.02122e29 q^{90} -3.35429e30 q^{91} +9.40142e29 q^{92} +2.30410e29 q^{93} +4.64740e30 q^{94} -1.15377e30 q^{95} -4.06104e29 q^{96} -3.02840e30 q^{97} -1.15666e31 q^{98} -1.23225e31 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.07495e7	0.432522	0.216261	−	0.976336i	$-0.430614\pi$
$3$	1.07495e7	0.432522	0.216261	+	0.976336i	$0.430614\pi$
$4$	1.07374e9	0.500000
$5$	−3.05176e10	−0.447214
$5$	−3.05176e10	−0.447214
$6$	−3.52239e11	−0.305839
$7$	2.26000e13	1.79924	0.899620	−	0.436674i	$-0.143844\pi$
$7$	2.26000e13	1.79924	0.899620	+	0.436674i	$0.143844\pi$
$8$	−3.51844e13	−0.353553
$9$	−5.02122e14	−0.812925
$10$	1.00000e15	0.316228
$11$	2.45408e16	1.77134	0.885671	−	0.464313i	$-0.153699\pi$
$11$	2.45408e16	1.77134	0.885671	+	0.464313i	$0.153699\pi$
$12$	1.15422e16	0.216261
$13$	−1.48420e17	−0.804211	−0.402105	−	0.915593i	$-0.631721\pi$
$13$	−1.48420e17	−0.804211	−0.402105	+	0.915593i	$0.631721\pi$
$14$	−7.40557e17	−1.27225
$15$	−3.28048e17	−0.193430
$16$	1.15292e18	0.250000
$17$	1.16191e19	0.984496	0.492248	−	0.870455i	$-0.336175\pi$
$17$	1.16191e19	0.984496	0.492248	+	0.870455i	$0.336175\pi$
$18$	1.64535e19	0.574825
$19$	3.78068e19	0.571333	0.285667	−	0.958329i	$-0.407785\pi$
$19$	3.78068e19	0.571333	0.285667	+	0.958329i	$0.407785\pi$
$20$	−3.27680e19	−0.223607
$21$	2.42938e20	0.778211
$22$	−8.04154e20	−1.25253
$23$	8.75576e20	0.684719	0.342359	−	0.939569i	$-0.388774\pi$
$23$	8.75576e20	0.684719	0.342359	+	0.939569i	$0.388774\pi$
$24$	−3.78214e20	−0.152920
$25$	9.31323e20	0.200000
$26$	4.86342e21	0.568663
$27$	−1.20372e22	−0.784130
$28$	2.42666e22	0.899620
$29$	−8.57580e22	−1.84546	−0.922732	−	0.385443i	$-0.874049\pi$
$29$	−8.57580e22	−1.84546	−0.922732	+	0.385443i	$0.874049\pi$
$30$	1.07495e22	0.136775
$31$	2.14345e22	0.164062	0.0820308	−	0.996630i	$-0.473859\pi$
$31$	2.14345e22	0.164062	0.0820308	+	0.996630i	$0.473859\pi$
$32$	−3.77789e22	−0.176777
$33$	2.63801e23	0.766144
$34$	−3.80734e23	−0.696143
$35$	−6.89698e23	−0.804645
$36$	−5.39149e23	−0.406462
$37$	−2.44667e24	−1.20628	−0.603140	−	0.797635i	$-0.706084\pi$
$37$	−2.44667e24	−1.20628	−0.603140	+	0.797635i	$0.706084\pi$
$38$	−1.23885e24	−0.403994
$39$	−1.59544e24	−0.347839
$40$	1.07374e24	0.158114
$41$	1.07003e25	1.07459	0.537297	−	0.843393i	$-0.319445\pi$
$41$	1.07003e25	1.07459	0.537297	+	0.843393i	$0.319445\pi$
$42$	−7.96061e24	−0.550278
$43$	6.78689e24	0.325769	0.162884	−	0.986645i	$-0.447920\pi$
$43$	6.78689e24	0.325769	0.162884	+	0.986645i	$0.447920\pi$
$44$	2.63505e25	0.885671
$45$	1.53235e25	0.363551
$46$	−2.86909e25	−0.484169
$47$	−1.41828e26	−1.71492	−0.857460	−	0.514551i	$-0.827959\pi$
$47$	−1.41828e26	−1.71492	−0.857460	+	0.514551i	$0.827959\pi$
$48$	1.23933e25	0.108130
$49$	3.52985e26	2.23726
$50$	−3.05176e25	−0.141421
$51$	1.24899e26	0.425816
$52$	−1.59365e26	−0.402105
$53$	5.25772e26	0.987464	0.493732	−	0.869614i	$-0.335632\pi$
$53$	5.25772e26	0.987464	0.493732	+	0.869614i	$0.335632\pi$
$54$	3.94436e26	0.554464
$55$	−7.48926e26	−0.792168
$56$	−7.95167e26	−0.636127
$57$	4.06404e26	0.247114
$58$	2.81012e27	1.30494
$59$	2.03548e27	0.725203	0.362602	−	0.931944i	$-0.381889\pi$
$59$	2.03548e27	0.725203	0.362602	+	0.931944i	$0.381889\pi$
$60$	−3.52239e26	−0.0967149
$61$	6.56027e27	1.39415	0.697074	−	0.716999i	$-0.254485\pi$
$61$	6.56027e27	1.39415	0.697074	+	0.716999i	$0.254485\pi$
$62$	−7.02366e26	−0.116009
$63$	−1.13480e28	−1.46265
$64$	1.23794e27	0.125000
$65$	4.52941e27	0.359654
$66$	−8.64424e27	−0.541746
$67$	2.16532e28	1.07489	0.537444	−	0.843299i	$-0.319390\pi$
$67$	2.16532e28	1.07489	0.537444	+	0.843299i	$0.319390\pi$
$68$	1.24759e28	0.492248
$69$	9.41199e27	0.296156
$70$	2.26000e28	0.568970
$71$	2.83140e28	0.572133	0.286066	−	0.958210i	$-0.407652\pi$
$71$	2.83140e28	0.572133	0.286066	+	0.958210i	$0.407652\pi$
$72$	1.76668e28	0.287412
$73$	2.94533e28	0.386928	0.193464	−	0.981107i	$-0.438028\pi$
$73$	2.94533e28	0.386928	0.193464	+	0.981107i	$0.438028\pi$
$74$	8.01724e28	0.852969
$75$	1.00112e28	0.0865044
$76$	4.05948e28	0.285667
$77$	5.54623e29	3.18707
$78$	5.22793e28	0.245959
$79$	−2.36152e29	−0.911951	−0.455976	−	0.889992i	$-0.650710\pi$
$79$	−2.36152e29	−0.911951	−0.455976	+	0.889992i	$0.650710\pi$
$80$	−3.51844e28	−0.111803
$81$	1.80753e29	0.473771
$82$	−3.50626e29	−0.759853
$83$	7.97795e29	1.43279	0.716393	−	0.697697i	$-0.245792\pi$
$83$	7.97795e29	1.43279	0.716393	+	0.697697i	$0.245792\pi$
$84$	2.60853e29	0.389105
$85$	−3.54586e29	−0.440280
$86$	−2.22393e29	−0.230353
$87$	−9.21854e29	−0.798204
$88$	−8.63453e29	−0.626264
$89$	1.17539e30	0.715542	0.357771	−	0.933809i	$-0.383537\pi$
$89$	1.17539e30	0.715542	0.357771	+	0.933809i	$0.383537\pi$
$90$	−5.02122e29	−0.257069
$91$	−3.35429e30	−1.44697
$92$	9.40142e29	0.342359
$93$	2.30410e29	0.0709603
$94$	4.64740e30	1.21263
$95$	−1.15377e30	−0.255508
$96$	−4.06104e29	−0.0764598
$97$	−3.02840e30	−0.485570	−0.242785	−	0.970080i	$-0.578061\pi$
$97$	−3.02840e30	−0.485570	−0.242785	+	0.970080i	$0.578061\pi$
$98$	−1.15666e31	−1.58198
$99$	−1.23225e31	−1.43997
$100$	1.00000e30	0.100000
$101$	1.24493e31	1.06699	0.533497	−	0.845802i	$-0.320877\pi$
$101$	1.24493e31	1.06699	0.533497	+	0.845802i	$0.320877\pi$
$102$	−4.09270e30	−0.301097
$103$	5.50424e30	0.348113	0.174056	−	0.984736i	$-0.444312\pi$
$103$	5.50424e30	0.348113	0.174056	+	0.984736i	$0.444312\pi$
$104$	5.22206e30	0.284331
$105$	−7.41389e30	−0.348026
$106$	−1.72285e31	−0.698242
$107$	2.87060e31	1.00583	0.502914	−	0.864336i	$-0.332261\pi$
$107$	2.87060e31	1.00583	0.502914	+	0.864336i	$0.332261\pi$
$108$	−1.29249e31	−0.392065
$109$	−6.39739e31	−1.68226	−0.841128	−	0.540837i	$-0.818108\pi$
$109$	−6.39739e31	−1.68226	−0.841128	+	0.540837i	$0.818108\pi$
$110$	2.45408e31	0.560148
$111$	−2.63004e31	−0.521743
$112$	2.60560e31	0.449810
$113$	−5.00616e31	−0.752990	−0.376495	−	0.926419i	$-0.622871\pi$
$113$	−5.00616e31	−0.752990	−0.376495	+	0.926419i	$0.622871\pi$
$114$	−1.33170e31	−0.174736
$115$	−2.67204e31	−0.306216
$116$	−9.20819e31	−0.922732
$117$	7.45249e31	0.653763
$118$	−6.66985e31	−0.512796
$119$	2.62592e32	1.77134
$120$	1.15422e31	0.0683877
$121$	4.10309e32	2.13765
$122$	−2.14967e32	−0.985812
$123$	1.15022e32	0.464786
$124$	2.30151e31	0.0820308
$125$	−2.84217e31	−0.0894427
$126$	3.71850e32	1.03425
$127$	−1.96018e32	−0.482324	−0.241162	−	0.970485i	$-0.577528\pi$
$127$	−1.96018e32	−0.482324	−0.241162	+	0.970485i	$0.577528\pi$
$128$	−4.05648e31	−0.0883883
$129$	7.29555e31	0.140902
$130$	−1.48420e32	−0.254314
$131$	8.78188e32	1.33623	0.668117	−	0.744056i	$-0.267101\pi$
$131$	8.78188e32	1.33623	0.668117	+	0.744056i	$0.267101\pi$
$132$	2.83254e32	0.383072
$133$	8.54435e32	1.02797
$134$	−7.09533e32	−0.760061
$135$	3.67347e32	0.350674
$136$	−4.08810e32	−0.348072
$137$	1.58360e33	1.20359	0.601794	−	0.798651i	$-0.294453\pi$
$137$	1.58360e33	1.20359	0.601794	+	0.798651i	$0.294453\pi$
$138$	−3.08412e32	−0.209414
$139$	1.84495e31	0.0112009	0.00560047	−	0.999984i	$-0.498217\pi$
$139$	1.84495e31	0.0112009	0.00560047	+	0.999984i	$0.498217\pi$
$140$	−7.40557e32	−0.402322
$141$	−1.52457e33	−0.741740
$142$	−9.27793e32	−0.404559
$143$	−3.64234e33	−1.42453
$144$	−5.78907e32	−0.203231
$145$	2.61713e33	0.825316
$146$	−9.65126e32	−0.273599
$147$	3.79441e33	0.967666
$148$	−2.62709e33	−0.603140
$149$	5.96260e32	0.123324	0.0616621	−	0.998097i	$-0.480360\pi$
$149$	5.96260e32	0.123324	0.0616621	+	0.998097i	$0.480360\pi$
$150$	−3.28048e32	−0.0611678
$151$	−8.01584e33	−1.34836	−0.674180	−	0.738567i	$-0.735503\pi$
$151$	−8.01584e33	−1.34836	−0.674180	+	0.738567i	$0.735503\pi$
$152$	−1.33021e33	−0.201997
$153$	−5.83420e33	−0.800321
$154$	−1.81739e34	−2.25360
$155$	−6.54129e32	−0.0733706
$156$	−1.71309e33	−0.173919
$157$	5.03735e33	0.463189	0.231594	−	0.972812i	$-0.425606\pi$
$157$	5.03735e33	0.463189	0.231594	+	0.972812i	$0.425606\pi$
$158$	7.73823e33	0.644847
$159$	5.65177e33	0.427100
$160$	1.15292e33	0.0790569
$161$	1.97880e34	1.23197
$162$	−5.92293e33	−0.335007
$163$	2.60494e34	1.33933	0.669667	−	0.742661i	$-0.266437\pi$
$163$	2.60494e34	1.33933	0.669667	+	0.742661i	$0.266437\pi$
$164$	1.14893e34	0.537297
$165$	−8.05057e33	−0.342630
$166$	−2.61422e34	−1.01313
$167$	1.50501e34	0.531415	0.265708	−	0.964054i	$-0.414394\pi$
$167$	1.50501e34	0.531415	0.265708	+	0.964054i	$0.414394\pi$
$168$	−8.54764e33	−0.275139
$169$	−1.20315e34	−0.353245
$170$	1.16191e34	0.311325
$171$	−1.89836e34	−0.464451
$172$	7.28737e33	0.162884
$173$	2.58953e33	0.0529062	0.0264531	−	0.999650i	$-0.491579\pi$
$173$	2.58953e33	0.0529062	0.0264531	+	0.999650i	$0.491579\pi$
$174$	3.02073e34	0.564415
$175$	2.10479e34	0.359848
$176$	2.82936e34	0.442836
$177$	2.18803e34	0.313666
$178$	−3.85150e34	−0.505965
$179$	−8.17306e34	−0.984380	−0.492190	−	0.870488i	$-0.663803\pi$
$179$	−8.17306e34	−0.984380	−0.492190	+	0.870488i	$0.663803\pi$
$180$	1.64535e34	0.181775
$181$	2.40793e34	0.244133	0.122066	−	0.992522i	$-0.461048\pi$
$181$	2.40793e34	0.244133	0.122066	+	0.992522i	$0.461048\pi$
$182$	1.09913e35	1.02316
$183$	7.05195e34	0.603000
$184$	−3.08066e34	−0.242085
$185$	7.46664e34	0.539465
$186$	−7.55007e33	−0.0501765
$187$	2.85142e35	1.74388
$188$	−1.52286e35	−0.857460
$189$	−2.72041e35	−1.41084
$190$	3.78068e34	0.180671
$191$	−1.66142e35	−0.731916	−0.365958	−	0.930631i	$-0.619259\pi$
$191$	−1.66142e35	−0.731916	−0.365958	+	0.930631i	$0.619259\pi$
$192$	1.33072e34	0.0540652
$193$	1.35705e35	0.508694	0.254347	−	0.967113i	$-0.418140\pi$
$193$	1.35705e35	0.508694	0.254347	+	0.967113i	$0.418140\pi$
$194$	9.92347e34	0.343350
$195$	4.86889e34	0.155558
$196$	3.79015e35	1.11863
$197$	−1.30234e35	−0.355220	−0.177610	−	0.984101i	$-0.556837\pi$
$197$	−1.30234e35	−0.355220	−0.177610	+	0.984101i	$0.556837\pi$
$198$	4.03783e35	1.01821
$199$	−5.17445e35	−1.20682	−0.603409	−	0.797432i	$-0.706191\pi$
$199$	−5.17445e35	−1.20682	−0.603409	+	0.797432i	$0.706191\pi$
$200$	−3.27680e34	−0.0707107
$201$	2.32761e35	0.464913
$202$	−4.07937e35	−0.754479
$203$	−1.93813e36	−3.32043
$204$	1.34110e35	0.212908
$205$	−3.26546e35	−0.480573
$206$	−1.80363e35	−0.246153
$207$	−4.39646e35	−0.556625
$208$	−1.71116e35	−0.201053
$209$	9.27811e35	1.01203
$210$	2.42938e35	0.246092
$211$	−1.18735e36	−1.11738	−0.558689	−	0.829377i	$-0.688695\pi$
$211$	−1.18735e36	−1.11738	−0.558689	+	0.829377i	$0.688695\pi$
$212$	5.64543e35	0.493732
$213$	3.04361e35	0.247460
$214$	−9.40638e35	−0.711228
$215$	−2.07119e35	−0.145688
$216$	4.23522e35	0.277232
$217$	4.84420e35	0.295186
$218$	2.09630e36	1.18953
$219$	3.16608e35	0.167355
$220$	−8.04154e35	−0.396084
$221$	−1.72450e36	−0.791742
$222$	8.61812e35	0.368928
$223$	2.87825e35	0.114922	0.0574611	−	0.998348i	$-0.481699\pi$
$223$	2.87825e35	0.114922	0.0574611	+	0.998348i	$0.481699\pi$
$224$	−8.53804e35	−0.318064
$225$	−4.67638e35	−0.162585
$226$	1.64042e36	0.532444
$227$	3.90915e36	1.18490	0.592450	−	0.805607i	$-0.298161\pi$
$227$	3.90915e36	1.18490	0.592450	+	0.805607i	$0.298161\pi$
$228$	4.36373e35	0.123557
$229$	−9.35252e35	−0.247445	−0.123723	−	0.992317i	$-0.539483\pi$
$229$	−9.35252e35	−0.247445	−0.123723	+	0.992317i	$0.539483\pi$
$230$	8.75576e35	0.216527
$231$	5.96191e36	1.37848
$232$	3.01734e36	0.652470
$233$	2.81203e36	0.568856	0.284428	−	0.958697i	$-0.408196\pi$
$233$	2.81203e36	0.568856	0.284428	+	0.958697i	$0.408196\pi$
$234$	−2.44203e36	−0.462280
$235$	4.32823e36	0.766935
$236$	2.18558e36	0.362602
$237$	−2.53851e36	−0.394439
$238$	−8.60460e36	−1.25253
$239$	9.22821e36	1.25878	0.629391	−	0.777089i	$-0.283305\pi$
$239$	9.22821e36	1.25878	0.629391	+	0.777089i	$0.283305\pi$
$240$	−3.78214e35	−0.0483574
$241$	−2.25483e36	−0.270303	−0.135151	−	0.990825i	$-0.543152\pi$
$241$	−2.25483e36	−0.270303	−0.135151	+	0.990825i	$0.543152\pi$
$242$	−1.34450e37	−1.51155
$243$	9.37808e36	0.989046
$244$	7.04403e36	0.697074
$245$	−1.07723e37	−1.00053
$246$	−3.76905e36	−0.328653
$247$	−5.61128e36	−0.459472
$248$	−7.54159e35	−0.0580046
$249$	8.57589e36	0.619711
$250$	9.31323e35	0.0632456
$251$	−1.87833e37	−1.19903	−0.599515	−	0.800364i	$-0.704640\pi$
$251$	−1.87833e37	−1.19903	−0.599515	+	0.800364i	$0.704640\pi$
$252$	−1.21848e37	−0.731323
$253$	2.14873e37	1.21287
$254$	6.42312e36	0.341054
$255$	−3.81162e36	−0.190431
$256$	1.32923e36	0.0625000
$257$	−1.96277e37	−0.868773	−0.434386	−	0.900727i	$-0.643035\pi$
$257$	−1.96277e37	−0.868773	−0.434386	+	0.900727i	$0.643035\pi$
$258$	−2.39061e36	−0.0996329
$259$	−5.52947e37	−2.17039
$260$	4.86342e36	0.179827
$261$	4.30610e37	1.50022
$262$	−2.87765e37	−0.944860
$263$	1.77659e37	0.549886	0.274943	−	0.961461i	$-0.411341\pi$
$263$	1.77659e37	0.549886	0.274943	+	0.961461i	$0.411341\pi$
$264$	−9.28168e36	−0.270873
$265$	−1.60453e37	−0.441607
$266$	−2.79981e37	−0.726881
$267$	1.26348e37	0.309488
$268$	2.32500e37	0.537444
$269$	4.11974e37	0.898897	0.449449	−	0.893306i	$-0.351621\pi$
$269$	4.11974e37	0.898897	0.449449	+	0.893306i	$0.351621\pi$
$270$	−1.20372e37	−0.247964
$271$	2.67128e37	0.519631	0.259816	−	0.965658i	$-0.416338\pi$
$271$	2.67128e37	0.519631	0.259816	+	0.965658i	$0.416338\pi$
$272$	1.33959e37	0.246124
$273$	−3.60569e37	−0.625846
$274$	−5.18915e37	−0.851065
$275$	2.28554e37	0.354268
$276$	1.01060e37	0.148078
$277$	−1.71079e37	−0.237007	−0.118503	−	0.992954i	$-0.537810\pi$
$277$	−1.71079e37	−0.237007	−0.118503	+	0.992954i	$0.537810\pi$
$278$	−6.04552e35	−0.00792025
$279$	−1.07627e37	−0.133370
$280$	2.42666e37	0.284485
$281$	−8.17662e37	−0.907038	−0.453519	−	0.891247i	$-0.649832\pi$
$281$	−8.17662e37	−0.907038	−0.453519	+	0.891247i	$0.649832\pi$
$282$	4.99572e37	0.524490
$283$	3.56430e36	0.0354229	0.0177115	−	0.999843i	$-0.494362\pi$
$283$	3.56430e36	0.0354229	0.0177115	+	0.999843i	$0.494362\pi$
$284$	3.04019e37	0.286066
$285$	−1.24025e37	−0.110513
$286$	1.19352e38	1.00730
$287$	2.41826e38	1.93345
$288$	1.89696e37	0.143706
$289$	−4.28571e36	−0.0307685
$290$	−8.57580e37	−0.583587
$291$	−3.25538e37	−0.210020
$292$	3.16253e37	0.193464
$293$	1.72791e38	1.00248	0.501238	−	0.865310i	$-0.332878\pi$
$293$	1.72791e38	1.00248	0.501238	+	0.865310i	$0.332878\pi$
$294$	−1.24335e38	−0.684243
$295$	−6.21178e37	−0.324321
$296$	8.60844e37	0.426484
$297$	−2.95403e38	−1.38896
$298$	−1.95383e37	−0.0872034
$299$	−1.29953e38	−0.550658
$300$	1.07495e37	0.0432522
$301$	1.53384e38	0.586136
$302$	2.62663e38	0.953435
$303$	1.33823e38	0.461499
$304$	4.35883e37	0.142833
$305$	−2.00203e38	−0.623482
$306$	1.91175e38	0.565912
$307$	−1.39185e38	−0.391694	−0.195847	−	0.980634i	$-0.562746\pi$
$307$	−1.39185e38	−0.391694	−0.195847	+	0.980634i	$0.562746\pi$
$308$	5.95522e38	1.59353
$309$	5.91677e37	0.150567
$310$	2.14345e37	0.0518809
$311$	−7.23579e37	−0.166610	−0.0833048	−	0.996524i	$-0.526548\pi$
$311$	−7.23579e37	−0.166610	−0.0833048	+	0.996524i	$0.526548\pi$
$312$	5.61344e37	0.122980
$313$	−7.16835e38	−1.49445	−0.747226	−	0.664570i	$-0.768615\pi$
$313$	−7.16835e38	−1.49445	−0.747226	+	0.664570i	$0.768615\pi$
$314$	−1.65064e38	−0.327524
$315$	3.46312e38	0.654115
$316$	−2.53566e38	−0.455976
$317$	1.01778e39	1.74275	0.871373	−	0.490620i	$-0.163230\pi$
$317$	1.01778e39	1.74275	0.871373	+	0.490620i	$0.163230\pi$
$318$	−1.85197e38	−0.302005
$319$	−2.10457e39	−3.26895
$320$	−3.77789e37	−0.0559017
$321$	3.08575e38	0.435043
$322$	−6.48414e38	−0.871137
$323$	4.39281e38	0.562475
$324$	1.94083e38	0.236886
$325$	−1.38227e38	−0.160842
$326$	−8.53585e38	−0.947053
$327$	−6.87686e38	−0.727612
$328$	−3.76482e38	−0.379926
$329$	−3.20530e39	−3.08555
$330$	2.63801e38	0.242276
$331$	1.30666e39	1.14506	0.572529	−	0.819885i	$-0.305963\pi$
$331$	1.30666e39	1.14506	0.572529	+	0.819885i	$0.305963\pi$
$332$	8.56626e38	0.716393
$333$	1.22853e39	0.980615
$334$	−4.93161e38	−0.375767
$335$	−6.60805e38	−0.480705
$336$	2.80089e38	0.194553
$337$	1.56627e39	1.03897	0.519486	−	0.854479i	$-0.326123\pi$
$337$	1.56627e39	1.03897	0.519486	+	0.854479i	$0.326123\pi$
$338$	3.94248e38	0.249782
$339$	−5.38137e38	−0.325685
$340$	−3.80734e38	−0.220140
$341$	5.26020e38	0.290609
$342$	6.22056e38	0.328416
$343$	4.41174e39	2.22614
$344$	−2.38792e38	−0.115177
$345$	−2.87231e38	−0.132445
$346$	−8.48537e37	−0.0374103
$347$	−1.53164e39	−0.645726	−0.322863	−	0.946446i	$-0.604645\pi$
$347$	−1.53164e39	−0.645726	−0.322863	+	0.946446i	$0.604645\pi$
$348$	−9.89833e38	−0.399102
$349$	2.63344e39	1.01562	0.507808	−	0.861470i	$-0.330456\pi$
$349$	2.63344e39	1.01562	0.507808	+	0.861470i	$0.330456\pi$
$350$	−6.89698e38	−0.254451
$351$	1.78656e39	0.630606
$352$	−9.27126e38	−0.313132
$353$	4.56209e39	1.47454	0.737269	−	0.675600i	$-0.236115\pi$
$353$	4.56209e39	1.47454	0.737269	+	0.675600i	$0.236115\pi$
$354$	−7.16974e38	−0.221796
$355$	−8.64075e38	−0.255866
$356$	1.26206e39	0.357771
$357$	2.82272e39	0.766145
$358$	2.67815e39	0.696062
$359$	2.02315e39	0.503575	0.251787	−	0.967783i	$-0.418982\pi$
$359$	2.02315e39	0.503575	0.251787	+	0.967783i	$0.418982\pi$
$360$	−5.39149e38	−0.128535
$361$	−2.94951e39	−0.673578
$362$	−7.89031e38	−0.172628
$363$	4.41061e39	0.924582
$364$	−3.60164e39	−0.723484
$365$	−8.98844e38	−0.173039
$366$	−2.31078e39	−0.426385
$367$	−1.03029e40	−1.82237	−0.911185	−	0.411998i	$-0.864831\pi$
$367$	−1.03029e40	−1.82237	−0.911185	+	0.411998i	$0.864831\pi$
$368$	1.00947e39	0.171180
$369$	−5.37284e39	−0.873564
$370$	−2.44667e39	−0.381459
$371$	1.18824e40	1.77668
$372$	2.47401e38	0.0354801
$373$	−4.89843e39	−0.673860	−0.336930	−	0.941530i	$-0.609389\pi$
$373$	−4.89843e39	−0.673860	−0.336930	+	0.941530i	$0.609389\pi$
$374$	−9.34353e39	−1.23311
$375$	−3.05519e38	−0.0386859
$376$	4.99011e39	0.606316
$377$	1.27282e40	1.48414
$378$	8.91425e39	0.997613
$379$	−1.32326e40	−1.42147	−0.710737	−	0.703458i	$-0.751638\pi$
$379$	−1.32326e40	−1.42147	−0.710737	+	0.703458i	$0.751638\pi$
$380$	−1.23885e39	−0.127754
$381$	−2.10709e39	−0.208616
$382$	5.44413e39	0.517543
$383$	2.21210e39	0.201940	0.100970	−	0.994889i	$-0.467805\pi$
$383$	2.21210e39	0.201940	0.100970	+	0.994889i	$0.467805\pi$
$384$	−4.36051e38	−0.0382299
$385$	−1.69257e40	−1.42530
$386$	−4.44677e39	−0.359701
$387$	−3.40785e39	−0.264826
$388$	−3.25172e39	−0.242785
$389$	−1.98512e40	−1.42419	−0.712096	−	0.702082i	$-0.752254\pi$
$389$	−1.98512e40	−1.42419	−0.712096	+	0.702082i	$0.752254\pi$
$390$	−1.59544e39	−0.109996
$391$	1.01734e40	0.674103
$392$	−1.24196e40	−0.790992
$393$	9.44007e39	0.577950
$394$	4.26750e39	0.251178
$395$	7.20679e39	0.407837
$396$	−1.32312e40	−0.719984
$397$	4.66363e39	0.244046	0.122023	−	0.992527i	$-0.461062\pi$
$397$	4.66363e39	0.244046	0.122023	+	0.992527i	$0.461062\pi$
$398$	1.69556e40	0.853349
$399$	9.18474e39	0.444618
$400$	1.07374e39	0.0500000
$401$	−1.07728e40	−0.482605	−0.241303	−	0.970450i	$-0.577575\pi$
$401$	−1.07728e40	−0.482605	−0.241303	+	0.970450i	$0.577575\pi$
$402$	−7.62712e39	−0.328743
$403$	−3.18130e39	−0.131940
$404$	1.33673e40	0.533497
$405$	−5.51616e39	−0.211877
$406$	6.35087e40	2.34790
$407$	−6.00432e40	−2.13674
$408$	−4.39450e39	−0.150549
$409$	−1.59543e40	−0.526219	−0.263110	−	0.964766i	$-0.584748\pi$
$409$	−1.59543e40	−0.526219	−0.263110	+	0.964766i	$0.584748\pi$
$410$	1.07003e40	0.339817
$411$	1.70229e40	0.520578
$412$	5.91013e39	0.174056
$413$	4.60018e40	1.30481
$414$	1.44063e40	0.393593
$415$	−2.43468e40	−0.640761
$416$	5.60714e39	0.142166
$417$	1.98322e38	0.00484465
$418$	−3.04025e40	−0.715611
$419$	−5.46661e40	−1.23994	−0.619971	−	0.784625i	$-0.712855\pi$
$419$	−5.46661e40	−1.23994	−0.619971	+	0.784625i	$0.712855\pi$
$420$	−7.96061e39	−0.174013
$421$	−2.46945e40	−0.520270	−0.260135	−	0.965572i	$-0.583767\pi$
$421$	−2.46945e40	−0.520270	−0.260135	+	0.965572i	$0.583767\pi$
$422$	3.89070e40	0.790105
$423$	7.12147e40	1.39410
$424$	−1.84989e40	−0.349121
$425$	1.08211e40	0.196899
$426$	−9.97330e39	−0.174981
$427$	1.48262e41	2.50841
$428$	3.08228e40	0.502914
$429$	−3.91533e40	−0.616142
$430$	6.78689e39	0.103017
$431$	4.73716e40	0.693618	0.346809	−	0.937936i	$-0.387265\pi$
$431$	4.73716e40	0.693618	0.346809	+	0.937936i	$0.387265\pi$
$432$	−1.38780e40	−0.196032
$433$	−3.30096e38	−0.00449860	−0.00224930	−	0.999997i	$-0.500716\pi$
$433$	−3.30096e38	−0.00449860	−0.00224930	+	0.999997i	$0.500716\pi$
$434$	−1.58735e40	−0.208728
$435$	2.81327e40	0.356967
$436$	−6.86914e40	−0.841128
$437$	3.31027e40	0.391203
$438$	−1.03746e40	−0.118338
$439$	−1.10291e39	−0.0121434	−0.00607170	−	0.999982i	$-0.501933\pi$
$439$	−1.10291e39	−0.0121434	−0.00607170	+	0.999982i	$0.501933\pi$
$440$	2.63505e40	0.280074
$441$	−1.77242e41	−1.81873
$442$	5.65085e40	0.559846
$443$	−1.21843e41	−1.16558	−0.582791	−	0.812622i	$-0.698039\pi$
$443$	−1.21843e41	−1.16558	−0.582791	+	0.812622i	$0.698039\pi$
$444$	−2.82399e40	−0.260871
$445$	−3.58699e40	−0.320000
$446$	−9.43146e39	−0.0812622
$447$	6.40949e39	0.0533405
$448$	2.79775e40	0.224905
$449$	1.34618e41	1.04540	0.522702	−	0.852515i	$-0.324924\pi$
$449$	1.34618e41	1.04540	0.522702	+	0.852515i	$0.324924\pi$
$450$	1.53235e40	0.114965
$451$	2.62593e41	1.90347
$452$	−5.37533e40	−0.376495
$453$	−8.61661e40	−0.583196
$454$	−1.28095e41	−0.837851
$455$	1.02365e41	0.647104
$456$	−1.42991e40	−0.0873681
$457$	6.73134e40	0.397558	0.198779	−	0.980044i	$-0.436302\pi$
$457$	6.73134e40	0.397558	0.198779	+	0.980044i	$0.436302\pi$
$458$	3.06463e40	0.174970
$459$	−1.39862e41	−0.771972
$460$	−2.86909e40	−0.153108
$461$	−3.76769e41	−1.94407	−0.972033	−	0.234842i	$-0.924543\pi$
$461$	−3.76769e41	−1.94407	−0.972033	+	0.234842i	$0.924543\pi$
$462$	−1.95360e41	−0.974731
$463$	−3.37703e41	−1.62941	−0.814704	−	0.579877i	$-0.803100\pi$
$463$	−3.37703e41	−1.62941	−0.814704	+	0.579877i	$0.803100\pi$
$464$	−9.88722e40	−0.461366
$465$	−7.03155e39	−0.0317344
$466$	−9.21445e40	−0.402242
$467$	−1.12227e41	−0.473900	−0.236950	−	0.971522i	$-0.576148\pi$
$467$	−1.12227e41	−0.473900	−0.236950	+	0.971522i	$0.576148\pi$
$468$	8.00205e40	0.326881
$469$	4.89364e41	1.93398
$470$	−1.41828e41	−0.542305
$471$	5.41490e40	0.200339
$472$	−7.16169e40	−0.256398
$473$	1.66556e41	0.577048
$474$	8.31820e40	0.278911
$475$	3.52104e40	0.114267
$476$	2.81956e41	0.885672
$477$	−2.64001e41	−0.802734
$478$	−3.02390e41	−0.890093
$479$	9.96622e40	0.284008	0.142004	−	0.989866i	$-0.454645\pi$
$479$	9.96622e40	0.284008	0.142004	+	0.989866i	$0.454645\pi$
$480$	1.23933e40	0.0341939
$481$	3.63134e41	0.970104
$482$	7.38864e40	0.191133
$483$	2.12711e41	0.532856
$484$	4.40565e41	1.06883
$485$	9.24195e40	0.217153
$486$	−3.07301e41	−0.699361
$487$	1.24135e41	0.273650	0.136825	−	0.990595i	$-0.456310\pi$
$487$	1.24135e41	0.273650	0.136825	+	0.990595i	$0.456310\pi$
$488$	−2.30819e41	−0.492906
$489$	2.80017e41	0.579292
$490$	3.52985e41	0.707485
$491$	2.86826e40	0.0557000	0.0278500	−	0.999612i	$-0.491134\pi$
$491$	2.86826e40	0.0557000	0.0278500	+	0.999612i	$0.491134\pi$
$492$	1.23504e41	0.232393
$493$	−9.96429e41	−1.81685
$494$	1.83871e41	0.324896
$495$	3.76052e41	0.643973
$496$	2.47123e40	0.0410154
$497$	6.39897e41	1.02940
$498$	−2.81015e41	−0.438202
$499$	9.27513e41	1.40204	0.701022	−	0.713140i	$-0.252728\pi$
$499$	9.27513e41	1.40204	0.701022	+	0.713140i	$0.252728\pi$
$500$	−3.05176e40	−0.0447214
$501$	1.61781e41	0.229849
$502$	6.15492e41	0.847842
$503$	2.27661e41	0.304078	0.152039	−	0.988375i	$-0.451416\pi$
$503$	2.27661e41	0.304078	0.152039	+	0.988375i	$0.451416\pi$
$504$	3.99271e41	0.517124
$505$	−3.79921e41	−0.477175
$506$	−7.04097e41	−0.857630
$507$	−1.29332e41	−0.152786
$508$	−2.10473e41	−0.241162
$509$	−4.37667e40	−0.0486427	−0.0243214	−	0.999704i	$-0.507742\pi$
$509$	−4.37667e40	−0.0486427	−0.0243214	+	0.999704i	$0.507742\pi$
$510$	1.24899e41	0.134655
$511$	6.65645e41	0.696176
$512$	−4.35561e40	−0.0441942
$513$	−4.55089e41	−0.447999
$514$	6.43161e41	0.614315
$515$	−1.67976e41	−0.155681
$516$	7.83354e40	0.0704511
$517$	−3.48056e42	−3.03771
$518$	1.81190e42	1.53470
$519$	2.78361e40	0.0228831
$520$	−1.59365e41	−0.127157
$521$	−1.96331e42	−1.52057	−0.760283	−	0.649592i	$-0.774940\pi$
$521$	−1.96331e42	−1.52057	−0.760283	+	0.649592i	$0.774940\pi$
$522$	−1.41102e42	−1.06082
$523$	−1.34397e42	−0.980874	−0.490437	−	0.871477i	$-0.663163\pi$
$523$	−1.34397e42	−0.980874	−0.490437	+	0.871477i	$0.663163\pi$
$524$	9.42947e41	0.668117
$525$	2.26254e41	0.155642
$526$	−5.82152e41	−0.388828
$527$	2.49049e41	0.161518
$528$	3.04142e41	0.191536
$529$	−8.68537e41	−0.531160
$530$	5.25772e41	0.312263
$531$	−1.02206e42	−0.589536
$532$	9.17443e41	0.513983
$533$	−1.58813e42	−0.864200
$534$	−4.14017e41	−0.218841
$535$	−8.76038e41	−0.449820
$536$	−7.61856e41	−0.380031
$537$	−8.78562e41	−0.425766
$538$	−1.34996e42	−0.635616
$539$	8.66255e42	3.96296
$540$	3.94436e41	0.175337
$541$	−5.23970e40	−0.0226333	−0.0113167	−	0.999936i	$-0.503602\pi$
$541$	−5.23970e40	−0.0226333	−0.0113167	+	0.999936i	$0.503602\pi$
$542$	−8.75325e41	−0.367435
$543$	2.58840e41	0.105593
$544$	−4.38957e41	−0.174036
$545$	1.95233e42	0.752327
$546$	1.18151e42	0.442540
$547$	6.69118e41	0.243612	0.121806	−	0.992554i	$-0.461131\pi$
$547$	6.69118e41	0.243612	0.121806	+	0.992554i	$0.461131\pi$
$548$	1.70038e42	0.601794
$549$	−3.29405e42	−1.13334
$550$	−7.48926e41	−0.250506
$551$	−3.24224e42	−1.05437
$552$	−3.31155e41	−0.104707
$553$	−5.33704e42	−1.64082
$554$	5.60593e41	0.167589
$555$	8.02625e41	0.233330
$556$	1.98099e40	0.00560047
$557$	6.32573e42	1.73922	0.869612	−	0.493736i	$-0.164369\pi$
$557$	6.32573e42	1.73922	0.869612	+	0.493736i	$0.164369\pi$
$558$	3.52673e41	0.0943067
$559$	−1.00731e42	−0.261987
$560$	−7.95167e41	−0.201161
$561$	3.06513e42	0.754266
$562$	2.67931e42	0.641373
$563$	2.31235e42	0.538485	0.269242	−	0.963072i	$-0.413227\pi$
$563$	2.31235e42	0.538485	0.269242	+	0.963072i	$0.413227\pi$
$564$	−1.63700e42	−0.370870
$565$	1.52776e42	0.336747
$566$	−1.16795e41	−0.0250478
$567$	4.08503e42	0.852428
$568$	−9.96210e41	−0.202279
$569$	−4.99520e42	−0.986990	−0.493495	−	0.869749i	$-0.664281\pi$
$569$	−4.99520e42	−0.986990	−0.493495	+	0.869749i	$0.664281\pi$
$570$	4.06404e41	0.0781444
$571$	2.08977e42	0.391056	0.195528	−	0.980698i	$-0.437358\pi$
$571$	2.08977e42	0.391056	0.195528	+	0.980698i	$0.437358\pi$
$572$	−3.91094e42	−0.712266
$573$	−1.78594e42	−0.316570
$574$	−7.92416e42	−1.36716
$575$	8.15443e41	0.136944
$576$	−6.21597e41	−0.101616
$577$	−3.85855e42	−0.614044	−0.307022	−	0.951702i	$-0.599333\pi$
$577$	−3.85855e42	−0.614044	−0.307022	+	0.951702i	$0.599333\pi$
$578$	1.40434e41	0.0217566
$579$	1.45875e42	0.220021
$580$	2.81012e42	0.412658
$581$	1.80302e43	2.57792
$582$	1.06672e42	0.148506
$583$	1.29029e43	1.74914
$584$	−1.03630e42	−0.136800
$585$	−2.27432e42	−0.292372
$586$	−5.66203e42	−0.708857
$587$	9.46507e42	1.15407	0.577037	−	0.816718i	$-0.304209\pi$
$587$	9.46507e42	1.15407	0.577037	+	0.816718i	$0.304209\pi$
$588$	4.07422e42	0.483833
$589$	8.10371e41	0.0937339
$590$	2.03548e42	0.229329
$591$	−1.39995e42	−0.153640
$592$	−2.82082e42	−0.301570
$593$	−1.21956e43	−1.27015	−0.635075	−	0.772450i	$-0.719031\pi$
$593$	−1.21956e43	−1.27015	−0.635075	+	0.772450i	$0.719031\pi$
$594$	9.67978e42	0.982145
$595$	−8.01366e42	−0.792169
$596$	6.40229e41	0.0616621
$597$	−5.56227e42	−0.521975
$598$	4.25829e42	0.389374
$599$	4.86657e42	0.433618	0.216809	−	0.976214i	$-0.430435\pi$
$599$	4.86657e42	0.433618	0.216809	+	0.976214i	$0.430435\pi$
$600$	−3.52239e41	−0.0305839
$601$	−1.25867e43	−1.06502	−0.532508	−	0.846425i	$-0.678750\pi$
$601$	−1.25867e43	−1.06502	−0.532508	+	0.846425i	$0.678750\pi$
$602$	−5.02608e42	−0.414461
$603$	−1.08726e43	−0.873804
$604$	−8.60694e42	−0.674180
$605$	−1.25216e43	−0.955988
$606$	−4.38512e42	−0.326329
$607$	1.81008e43	1.31303	0.656513	−	0.754315i	$-0.272031\pi$
$607$	1.81008e43	1.31303	0.656513	+	0.754315i	$0.272031\pi$
$608$	−1.42830e42	−0.100998
$609$	−2.08339e43	−1.43616
$610$	6.56027e42	0.440868
$611$	2.10500e43	1.37916
$612$	−6.26442e42	−0.400160
$613$	1.34234e43	0.836037	0.418018	−	0.908439i	$-0.362725\pi$
$613$	1.34234e43	0.836037	0.418018	+	0.908439i	$0.362725\pi$
$614$	4.56081e42	0.276970
$615$	−3.51020e42	−0.207858
$616$	−1.95141e43	−1.12680
$617$	−3.23957e42	−0.182418	−0.0912089	−	0.995832i	$-0.529073\pi$
$617$	−3.23957e42	−0.182418	−0.0912089	+	0.995832i	$0.529073\pi$
$618$	−1.93881e42	−0.106467
$619$	−2.85690e43	−1.52999	−0.764997	−	0.644034i	$-0.777260\pi$
$619$	−2.85690e43	−1.52999	−0.764997	+	0.644034i	$0.777260\pi$
$620$	−7.02366e41	−0.0366853
$621$	−1.05395e43	−0.536908
$622$	2.37102e42	0.117811
$623$	2.65637e43	1.28743
$624$	−1.83941e42	−0.0869597
$625$	8.67362e41	0.0400000
$626$	2.34893e43	1.05674
$627$	9.97349e42	0.437724
$628$	5.40882e42	0.231594
$629$	−2.84280e43	−1.18758
$630$	−1.13480e43	−0.462529
$631$	−8.68109e42	−0.345239	−0.172619	−	0.984989i	$-0.555223\pi$
$631$	−8.68109e42	−0.345239	−0.172619	+	0.984989i	$0.555223\pi$
$632$	8.30886e42	0.322424
$633$	−1.27634e43	−0.483290
$634$	−3.33505e43	−1.23231
$635$	5.98200e42	0.215702
$636$	6.06855e42	0.213550
$637$	−5.23900e43	−1.79923
$638$	6.89626e43	2.31150
$639$	−1.42171e43	−0.465101
$640$	1.23794e42	0.0395285
$641$	4.01231e43	1.25053	0.625267	−	0.780411i	$-0.284990\pi$
$641$	4.01231e43	1.25053	0.625267	+	0.780411i	$0.284990\pi$
$642$	−1.01114e43	−0.307622
$643$	−1.38043e43	−0.409964	−0.204982	−	0.978766i	$-0.565714\pi$
$643$	−1.38043e43	−0.409964	−0.204982	+	0.978766i	$0.565714\pi$
$644$	2.12472e43	0.615987
$645$	−2.22643e42	−0.0630134
$646$	−1.43944e43	−0.397730
$647$	4.95630e43	1.33703	0.668515	−	0.743699i	$-0.266930\pi$
$647$	4.95630e43	1.33703	0.668515	+	0.743699i	$0.266930\pi$
$648$	−6.35970e42	−0.167503
$649$	4.99522e43	1.28458
$650$	4.52941e42	0.113733
$651$	5.20727e42	0.127675
$652$	2.79703e43	0.669667
$653$	8.53813e42	0.199622	0.0998110	−	0.995006i	$-0.468176\pi$
$653$	8.53813e42	0.199622	0.0998110	+	0.995006i	$0.468176\pi$
$654$	2.25341e43	0.514500
$655$	−2.68002e43	−0.597582
$656$	1.23366e43	0.268649
$657$	−1.47892e43	−0.314543
$658$	1.05031e44	2.18181
$659$	3.89436e43	0.790154	0.395077	−	0.918648i	$-0.370718\pi$
$659$	3.89436e43	0.790154	0.395077	+	0.918648i	$0.370718\pi$
$660$	−8.64424e42	−0.171315
$661$	−8.37311e42	−0.162093	−0.0810465	−	0.996710i	$-0.525826\pi$
$661$	−8.37311e42	−0.162093	−0.0810465	+	0.996710i	$0.525826\pi$
$662$	−4.28165e43	−0.809678
$663$	−1.85375e43	−0.342446
$664$	−2.80699e43	−0.506566
$665$	−2.60753e43	−0.459720
$666$	−4.02563e43	−0.693399
$667$	−7.50876e43	−1.26362
$668$	1.61599e43	0.265708
$669$	3.09398e42	0.0497064
$670$	2.16532e43	0.339910
$671$	1.60994e44	2.46951
$672$	−9.17796e42	−0.137570
$673$	9.42152e43	1.38003	0.690013	−	0.723797i	$-0.257605\pi$
$673$	9.42152e43	1.38003	0.690013	+	0.723797i	$0.257605\pi$
$674$	−5.13236e43	−0.734664
$675$	−1.12105e43	−0.156826
$676$	−1.29187e43	−0.176622
$677$	−1.26241e42	−0.0168685	−0.00843423	−	0.999964i	$-0.502685\pi$
$677$	−1.26241e42	−0.0168685	−0.00843423	+	0.999964i	$0.502685\pi$
$678$	1.76337e43	0.230294
$679$	−6.84419e43	−0.873657
$680$	1.24759e43	0.155662
$681$	4.20213e43	0.512495
$682$	−1.72366e43	−0.205492
$683$	−5.02289e43	−0.585373	−0.292686	−	0.956209i	$-0.594549\pi$
$683$	−5.02289e43	−0.585373	−0.292686	+	0.956209i	$0.594549\pi$
$684$	−2.03835e43	−0.232225
$685$	−4.83278e43	−0.538261
$686$	−1.44564e44	−1.57412
$687$	−1.00535e43	−0.107025
$688$	7.82475e42	0.0814422
$689$	−7.80349e43	−0.794129
$690$	9.41199e42	0.0936527
$691$	5.98132e43	0.581952	0.290976	−	0.956730i	$-0.406020\pi$
$691$	5.98132e43	0.581952	0.290976	+	0.956730i	$0.406020\pi$
$692$	2.78049e42	0.0264531
$693$	−2.78488e44	−2.59085
$694$	5.01886e43	0.456597
$695$	−5.63033e41	−0.00500921
$696$	3.24348e43	0.282208
$697$	1.24327e44	1.05793
$698$	−8.62926e43	−0.718149
$699$	3.02278e43	0.246043
$700$	2.26000e43	0.179924
$701$	−1.56022e44	−1.21495	−0.607473	−	0.794340i	$-0.707817\pi$
$701$	−1.56022e44	−1.21495	−0.607473	+	0.794340i	$0.707817\pi$
$702$	−5.85421e43	−0.445906
$703$	−9.25007e43	−0.689188
$704$	3.03801e43	0.221418
$705$	4.65263e43	0.331716
$706$	−1.49490e44	−1.04266
$707$	2.81353e44	1.91978
$708$	2.34938e43	0.156833
$709$	−8.54271e43	−0.557929	−0.278964	−	0.960301i	$-0.589991\pi$
$709$	−8.54271e43	−0.557929	−0.278964	+	0.960301i	$0.589991\pi$
$710$	2.83140e43	0.180924
$711$	1.18577e44	0.741348
$712$	−4.13552e43	−0.252982
$713$	1.87675e43	0.112336
$714$	−9.24950e43	−0.541746
$715$	1.11156e44	0.637070
$716$	−8.77575e43	−0.492190
$717$	9.91985e43	0.544450
$718$	−6.62945e43	−0.356081
$719$	2.30590e44	1.21211	0.606057	−	0.795421i	$-0.292750\pi$
$719$	2.30590e44	1.21211	0.606057	+	0.795421i	$0.292750\pi$
$720$	1.76668e43	0.0908877
$721$	1.24396e44	0.626339
$722$	9.66495e43	0.476292
$723$	−2.42383e43	−0.116912
$724$	2.58550e43	0.122066
$725$	−7.98683e43	−0.369093
$726$	−1.44527e44	−0.653778
$727$	−3.33530e44	−1.47690	−0.738450	−	0.674308i	$-0.764442\pi$
$727$	−3.33530e44	−1.47690	−0.738450	+	0.674308i	$0.764442\pi$
$728$	1.18019e44	0.511581
$729$	−1.08371e43	−0.0459871
$730$	2.94533e43	0.122357
$731$	7.88574e43	0.320718
$732$	7.57197e43	0.301500
$733$	6.64546e43	0.259068	0.129534	−	0.991575i	$-0.458652\pi$
$733$	6.64546e43	0.259068	0.129534	+	0.991575i	$0.458652\pi$
$734$	3.37606e44	1.28861
$735$	−1.15796e44	−0.432753
$736$	−3.30783e43	−0.121042
$737$	5.31388e44	1.90400
$738$	1.76057e44	0.617703
$739$	5.13394e43	0.176385	0.0881926	−	0.996103i	$-0.471891\pi$
$739$	5.13394e43	0.176385	0.0881926	+	0.996103i	$0.471891\pi$
$740$	8.01724e43	0.269732
$741$	−6.03184e43	−0.198732
$742$	−3.89364e44	−1.25631
$743$	−5.18614e44	−1.63877	−0.819385	−	0.573244i	$-0.805685\pi$
$743$	−5.18614e44	−1.63877	−0.819385	+	0.573244i	$0.805685\pi$
$744$	−8.10682e42	−0.0250882
$745$	−1.81964e43	−0.0551523
$746$	1.60512e44	0.476491
$747$	−4.00591e44	−1.16475
$748$	3.06169e44	0.871939
$749$	6.48756e44	1.80973
$750$	1.00112e43	0.0273551
$751$	1.16699e44	0.312356	0.156178	−	0.987729i	$-0.450083\pi$
$751$	1.16699e44	0.312356	0.156178	+	0.987729i	$0.450083\pi$
$752$	−1.63516e44	−0.428730
$753$	−2.01911e44	−0.518607
$754$	−4.17077e44	−1.04945
$755$	2.44624e44	0.603005
$756$	−2.92102e44	−0.705419
$757$	7.15124e44	1.69198	0.845990	−	0.533199i	$-0.179010\pi$
$757$	7.15124e44	1.69198	0.845990	+	0.533199i	$0.179010\pi$
$758$	4.33607e44	1.00513
$759$	2.30978e44	0.524593
$760$	4.05948e43	0.0903357
$761$	−2.08933e44	−0.455559	−0.227779	−	0.973713i	$-0.573146\pi$
$761$	−2.08933e44	−0.455559	−0.227779	+	0.973713i	$0.573146\pi$
$762$	6.90453e43	0.147514
$763$	−1.44581e45	−3.02678
$764$	−1.78393e44	−0.365958
$765$	1.78046e44	0.357914
$766$	−7.24860e43	−0.142793
$767$	−3.02105e44	−0.583216
$768$	1.42885e43	0.0270326
$769$	4.48666e44	0.831889	0.415944	−	0.909390i	$-0.363451\pi$
$769$	4.48666e44	0.831889	0.415944	+	0.909390i	$0.363451\pi$
$770$	5.54623e44	1.00784
$771$	−2.10988e44	−0.375763
$772$	1.45712e44	0.254347
$773$	−9.87774e44	−1.68996	−0.844978	−	0.534800i	$-0.820387\pi$
$773$	−9.87774e44	−1.68996	−0.844978	+	0.534800i	$0.820387\pi$
$774$	1.11668e44	0.187260
$775$	1.99624e43	0.0328123
$776$	1.06552e44	0.171675
$777$	−5.94390e44	−0.938740
$778$	6.50485e44	1.00706
$779$	4.04543e44	0.613952
$780$	5.22793e43	0.0777791
$781$	6.94849e44	1.01344
$782$	−3.33362e44	−0.476662
$783$	1.03229e45	1.44708
$784$	4.06964e44	0.559316
$785$	−1.53728e44	−0.207144
$786$	−3.09332e44	−0.408673
$787$	−8.12711e44	−1.05276	−0.526378	−	0.850251i	$-0.676450\pi$
$787$	−8.12711e44	−1.05276	−0.526378	+	0.850251i	$0.676450\pi$
$788$	−1.39838e44	−0.177610
$789$	1.90974e44	0.237838
$790$	−2.36152e44	−0.288384
$791$	−1.13139e45	−1.35481
$792$	4.33559e44	0.509106
$793$	−9.73673e44	−1.12119
$794$	−1.52818e44	−0.172566
$795$	−1.72478e44	−0.191005
$796$	−5.55603e44	−0.603409
$797$	2.32602e44	0.247748	0.123874	−	0.992298i	$-0.460468\pi$
$797$	2.32602e44	0.247748	0.123874	+	0.992298i	$0.460468\pi$
$798$	−3.00965e44	−0.314392
$799$	−1.64791e45	−1.68833
$800$	−3.51844e43	−0.0353553
$801$	−5.90187e44	−0.581682
$802$	3.53004e44	0.341253
$803$	7.22808e44	0.685381
$804$	2.49925e44	0.232456
$805$	−6.03882e44	−0.550955
$806$	1.04245e44	0.0932958
$807$	4.42851e44	0.388793
$808$	−4.38019e44	−0.377240
$809$	1.01189e45	0.854931	0.427466	−	0.904032i	$-0.359407\pi$
$809$	1.01189e45	0.854931	0.427466	+	0.904032i	$0.359407\pi$
$810$	1.80753e44	0.149820
$811$	7.77255e44	0.632034	0.316017	−	0.948754i	$-0.397654\pi$
$811$	7.77255e44	0.632034	0.316017	+	0.948754i	$0.397654\pi$
$812$	−2.08105e45	−1.66022
$813$	2.87149e44	0.224752
$814$	1.96750e45	1.51090
$815$	−7.94963e44	−0.598969
$816$	1.43999e44	0.106454
$817$	2.56591e44	0.186123
$818$	5.22791e44	0.372093
$819$	1.68426e45	1.17628
$820$	−3.50626e44	−0.240287
$821$	2.49289e45	1.67642	0.838212	−	0.545344i	$-0.183601\pi$
$821$	2.49289e45	1.67642	0.838212	+	0.545344i	$0.183601\pi$
$822$	−5.57807e44	−0.368104
$823$	−2.55800e45	−1.65654	−0.828272	−	0.560326i	$-0.810676\pi$
$823$	−2.55800e45	−1.65654	−0.828272	+	0.560326i	$0.810676\pi$
$824$	−1.93663e44	−0.123077
$825$	2.45684e44	0.153229
$826$	−1.50739e45	−0.922643
$827$	−1.08245e45	−0.650240	−0.325120	−	0.945673i	$-0.605405\pi$
$827$	−1.08245e45	−0.650240	−0.325120	+	0.945673i	$0.605405\pi$
$828$	−4.72066e44	−0.278312
$829$	8.46679e43	0.0489918	0.0244959	−	0.999700i	$-0.492202\pi$
$829$	8.46679e43	0.0489918	0.0244959	+	0.999700i	$0.492202\pi$
$830$	7.97795e44	0.453086
$831$	−1.83901e44	−0.102511
$832$	−1.83735e44	−0.100526
$833$	4.10137e45	2.20258
$834$	−6.49862e42	−0.00342568
$835$	−4.59292e44	−0.237656
$836$	9.96229e44	0.506013
$837$	−2.58012e44	−0.128646
$838$	1.79130e45	0.876771
$839$	−6.17907e43	−0.0296902	−0.0148451	−	0.999890i	$-0.504726\pi$
$839$	−6.17907e43	−0.0296902	−0.0148451	+	0.999890i	$0.504726\pi$
$840$	2.60853e44	0.123046
$841$	5.19500e45	2.40574
$842$	8.09191e44	0.367886
$843$	−8.78944e44	−0.392314
$844$	−1.27490e45	−0.558689
$845$	3.67172e44	0.157976
$846$	−2.33356e45	−0.985778
$847$	9.27298e45	3.84615
$848$	6.06173e44	0.246866
$849$	3.83144e43	0.0153212
$850$	−3.54586e44	−0.139229
$851$	−2.14224e45	−0.825963
$852$	3.26805e44	0.123730
$853$	1.05224e45	0.391205	0.195602	−	0.980683i	$-0.437334\pi$
$853$	1.05224e45	0.391205	0.195602	+	0.980683i	$0.437334\pi$
$854$	−4.85825e45	−1.77371
$855$	5.79335e44	0.207709
$856$	−1.01000e45	−0.355614
$857$	−2.23665e45	−0.773383	−0.386692	−	0.922209i	$-0.626382\pi$
$857$	−2.23665e45	−0.773383	−0.386692	+	0.922209i	$0.626382\pi$
$858$	1.28298e45	0.435678
$859$	−4.60157e45	−1.53466	−0.767329	−	0.641254i	$-0.778415\pi$
$859$	−4.60157e45	−1.53466	−0.767329	+	0.641254i	$0.778415\pi$
$860$	−2.22393e44	−0.0728441
$861$	2.59951e45	0.836261
$862$	−1.55227e45	−0.490462
$863$	−4.42805e45	−1.37419	−0.687093	−	0.726569i	$-0.741114\pi$
$863$	−4.42805e45	−1.37419	−0.687093	+	0.726569i	$0.741114\pi$
$864$	4.54753e44	0.138616
$865$	−7.90262e43	−0.0236604
$866$	1.08166e43	0.00318099
$867$	−4.60692e43	−0.0133080
$868$	5.20142e44	0.147593
$869$	−5.79536e45	−1.61538
$870$	−9.21854e44	−0.252414
$871$	−3.21377e45	−0.864437
$872$	2.25088e45	0.594767
$873$	1.52063e45	0.394732
$874$	−1.08471e45	−0.276622
$875$	−6.42331e44	−0.160929
$876$	3.39955e44	0.0836774
$877$	−5.41361e45	−1.30916	−0.654581	−	0.755992i	$-0.727155\pi$
$877$	−5.41361e45	−1.30916	−0.654581	+	0.755992i	$0.727155\pi$
$878$	3.61402e43	0.00858668
$879$	1.85742e45	0.433593
$880$	−8.63453e44	−0.198042
$881$	−4.09130e45	−0.922008	−0.461004	−	0.887398i	$-0.652511\pi$
$881$	−4.09130e45	−0.922008	−0.461004	+	0.887398i	$0.652511\pi$
$882$	5.80785e45	1.28603
$883$	7.61955e45	1.65782	0.828912	−	0.559379i	$-0.188960\pi$
$883$	7.61955e45	1.65782	0.828912	+	0.559379i	$0.188960\pi$
$884$	−1.85167e45	−0.395871
$885$	−6.67734e44	−0.140276
$886$	3.99255e45	0.824190
$887$	−4.92537e45	−0.999131	−0.499566	−	0.866276i	$-0.666507\pi$
$887$	−4.92537e45	−0.999131	−0.499566	+	0.866276i	$0.666507\pi$
$888$	9.25363e44	0.184464
$889$	−4.43001e45	−0.867816
$890$	1.17539e45	0.226274
$891$	4.43584e45	0.839211
$892$	3.09050e44	0.0574611
$893$	−5.36205e45	−0.979791
$894$	−2.10026e44	−0.0377174
$895$	2.49422e45	0.440228
$896$	−9.16765e44	−0.159032
$897$	−1.39693e45	−0.238172
$898$	−4.41116e45	−0.739213
$899$	−1.83818e45	−0.302770
$900$	−5.02122e44	−0.0812925
$901$	6.10899e45	0.972154
$902$	−8.60465e45	−1.34596
$903$	1.64880e45	0.253517
$904$	1.76139e45	0.266222
$905$	−7.34842e44	−0.109180
$906$	2.82349e45	0.412382
$907$	−2.39988e45	−0.344570	−0.172285	−	0.985047i	$-0.555115\pi$
$907$	−2.39988e45	−0.344570	−0.172285	+	0.985047i	$0.555115\pi$
$908$	4.19742e45	0.592450
$909$	−6.25105e45	−0.867386
$910$	−3.35429e45	−0.457572
$911$	−1.27477e46	−1.70961	−0.854805	−	0.518949i	$-0.826324\pi$
$911$	−1.27477e46	−1.70961	−0.854805	+	0.518949i	$0.826324\pi$
$912$	4.68552e44	0.0617786
$913$	1.95786e46	2.53795
$914$	−2.20573e45	−0.281116
$915$	−2.15208e45	−0.269670
$916$	−1.00422e45	−0.123723
$917$	1.98471e46	2.40420
$918$	4.58298e45	0.545867
$919$	−8.11185e44	−0.0950013	−0.0475007	−	0.998871i	$-0.515126\pi$
$919$	−8.11185e44	−0.0950013	−0.0475007	+	0.998871i	$0.515126\pi$
$920$	9.40142e44	0.108264
$921$	−1.49617e45	−0.169416
$922$	1.23460e46	1.37466
$923$	−4.20236e45	−0.460115
$924$	6.40155e45	0.689239
$925$	−2.27864e45	−0.241256
$926$	1.10659e46	1.15217
$927$	−2.76380e45	−0.282990
$928$	3.23984e45	0.326235
$929$	−8.34797e45	−0.826680	−0.413340	−	0.910577i	$-0.635638\pi$
$929$	−8.34797e45	−0.826680	−0.413340	+	0.910577i	$0.635638\pi$
$930$	2.30410e44	0.0224396
$931$	1.33453e46	1.27822
$932$	3.01939e45	0.284428
$933$	−7.77810e44	−0.0720623
$934$	3.67746e45	0.335098
$935$	−8.70184e45	−0.779886
$936$	−2.62211e45	−0.231140
$937$	7.08971e45	0.614703	0.307351	−	0.951596i	$-0.400557\pi$
$937$	7.08971e45	0.614703	0.307351	+	0.951596i	$0.400557\pi$
$938$	−1.60355e46	−1.36753
$939$	−7.70561e45	−0.646384
$940$	4.64740e45	0.383468
$941$	−1.27325e46	−1.03341	−0.516706	−	0.856163i	$-0.672842\pi$
$941$	−1.27325e46	−1.03341	−0.516706	+	0.856163i	$0.672842\pi$
$942$	−1.77435e45	−0.141661
$943$	9.36889e45	0.735795
$944$	2.34674e45	0.181301
$945$	8.30204e45	0.630946
$946$	−5.45770e45	−0.408035
$947$	8.84487e45	0.650529	0.325265	−	0.945623i	$-0.394547\pi$
$947$	8.84487e45	0.650529	0.325265	+	0.945623i	$0.394547\pi$
$948$	−2.72571e45	−0.197220
$949$	−4.37145e45	−0.311171
$950$	−1.15377e45	−0.0807987
$951$	1.09406e46	0.753776
$952$	−9.23912e45	−0.626265
$953$	9.38297e44	0.0625749	0.0312875	−	0.999510i	$-0.490039\pi$
$953$	9.38297e44	0.0625749	0.0312875	+	0.999510i	$0.490039\pi$
$954$	8.65080e45	0.567618
$955$	5.07024e45	0.327323
$956$	9.90872e45	0.629391
$957$	−2.26231e46	−1.41389
$958$	−3.26573e45	−0.200824
$959$	3.57895e46	2.16554
$960$	−4.06104e44	−0.0241787
$961$	−1.66097e46	−0.973084
$962$	−1.18992e46	−0.685967
$963$	−1.44139e46	−0.817663
$964$	−2.42111e45	−0.135151
$965$	−4.14138e45	−0.227495
$966$	−6.97011e45	−0.376786
$967$	−1.81981e46	−0.968092	−0.484046	−	0.875043i	$-0.660833\pi$
$967$	−1.81981e46	−0.968092	−0.484046	+	0.875043i	$0.660833\pi$
$968$	−1.44364e46	−0.755775
$969$	4.72204e45	0.243283
$970$	−3.02840e45	−0.153551
$971$	−1.52145e46	−0.759205	−0.379602	−	0.925150i	$-0.623939\pi$
$971$	−1.52145e46	−0.759205	−0.379602	+	0.925150i	$0.623939\pi$
$972$	1.00696e46	0.494523
$973$	4.16958e44	0.0201532
$974$	−4.06766e45	−0.193500
$975$	−1.48587e45	−0.0695678
$976$	7.56347e45	0.348537
$977$	−1.63297e46	−0.740650	−0.370325	−	0.928902i	$-0.620754\pi$
$977$	−1.63297e46	−0.740650	−0.370325	+	0.928902i	$0.620754\pi$
$978$	−9.17560e45	−0.409621
$979$	2.88449e46	1.26747
$980$	−1.15666e46	−0.500267
$981$	3.21227e46	1.36755
$982$	−9.39872e44	−0.0393859
$983$	2.28872e46	0.944089	0.472044	−	0.881575i	$-0.343516\pi$
$983$	2.28872e46	0.944089	0.472044	+	0.881575i	$0.343516\pi$
$984$	−4.04699e45	−0.164327
$985$	3.97442e45	0.158859
$986$	3.26510e46	1.28471
$987$	−3.44554e46	−1.33457
$988$	−6.02507e45	−0.229736
$989$	5.94243e45	0.223060
$990$	−1.23225e46	−0.455358
$991$	−1.29262e46	−0.470250	−0.235125	−	0.971965i	$-0.575550\pi$
$991$	−1.29262e46	−0.470250	−0.235125	+	0.971965i	$0.575550\pi$
$992$	−8.09773e44	−0.0290023
$993$	1.40459e46	0.495262
$994$	−2.09681e46	−0.727898
$995$	1.57912e46	0.539705
$996$	9.20829e45	0.309856
$997$	−7.75877e45	−0.257050	−0.128525	−	0.991706i	$-0.541024\pi$
$997$	−7.75877e45	−0.257050	−0.128525	+	0.991706i	$0.541024\pi$
$998$	−3.03927e46	−0.991394
$999$	2.94511e46	0.945880

Twists

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

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

\(f(q)\)	\(=\)	\(q-32768.0 q^{2} +1.07495e7 q^{3} +1.07374e9 q^{4} -3.05176e10 q^{5} -3.52239e11 q^{6} +2.26000e13 q^{7} -3.51844e13 q^{8} -5.02122e14 q^{9} +1.00000e15 q^{10} +2.45408e16 q^{11} +1.15422e16 q^{12} -1.48420e17 q^{13} -7.40557e17 q^{14} -3.28048e17 q^{15} +1.15292e18 q^{16} +1.16191e19 q^{17} +1.64535e19 q^{18} +3.78068e19 q^{19} -3.27680e19 q^{20} +2.42938e20 q^{21} -8.04154e20 q^{22} +8.75576e20 q^{23} -3.78214e20 q^{24} +9.31323e20 q^{25} +4.86342e21 q^{26} -1.20372e22 q^{27} +2.42666e22 q^{28} -8.57580e22 q^{29} +1.07495e22 q^{30} +2.14345e22 q^{31} -3.77789e22 q^{32} +2.63801e23 q^{33} -3.80734e23 q^{34} -6.89698e23 q^{35} -5.39149e23 q^{36} -2.44667e24 q^{37} -1.23885e24 q^{38} -1.59544e24 q^{39} +1.07374e24 q^{40} +1.07003e25 q^{41} -7.96061e24 q^{42} +6.78689e24 q^{43} +2.63505e25 q^{44} +1.53235e25 q^{45} -2.86909e25 q^{46} -1.41828e26 q^{47} +1.23933e25 q^{48} +3.52985e26 q^{49} -3.05176e25 q^{50} +1.24899e26 q^{51} -1.59365e26 q^{52} +5.25772e26 q^{53} +3.94436e26 q^{54} -7.48926e26 q^{55} -7.95167e26 q^{56} +4.06404e26 q^{57} +2.81012e27 q^{58} +2.03548e27 q^{59} -3.52239e26 q^{60} +6.56027e27 q^{61} -7.02366e26 q^{62} -1.13480e28 q^{63} +1.23794e27 q^{64} +4.52941e27 q^{65} -8.64424e27 q^{66} +2.16532e28 q^{67} +1.24759e28 q^{68} +9.41199e27 q^{69} +2.26000e28 q^{70} +2.83140e28 q^{71} +1.76668e28 q^{72} +2.94533e28 q^{73} +8.01724e28 q^{74} +1.00112e28 q^{75} +4.05948e28 q^{76} +5.54623e29 q^{77} +5.22793e28 q^{78} -2.36152e29 q^{79} -3.51844e28 q^{80} +1.80753e29 q^{81} -3.50626e29 q^{82} +7.97795e29 q^{83} +2.60853e29 q^{84} -3.54586e29 q^{85} -2.22393e29 q^{86} -9.21854e29 q^{87} -8.63453e29 q^{88} +1.17539e30 q^{89} -5.02122e29 q^{90} -3.35429e30 q^{91} +9.40142e29 q^{92} +2.30410e29 q^{93} +4.64740e30 q^{94} -1.15377e30 q^{95} -4.06104e29 q^{96} -3.02840e30 q^{97} -1.15666e31 q^{98} -1.23225e31 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 65536 q^{2} + 29024244 q^{3} + 2147483648 q^{4} - 61035156250 q^{5} - 951066427392 q^{6} + 12795158105212 q^{7} - 70368744177664 q^{8} - 785828540134926 q^{9} + 20\!\cdots\!00 q^{10} - 500906012122176 q^{11}+ \cdots - 52\!\cdots\!12 q^{99}+O(q^{100}) \) 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

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Groups

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