Properties

Label 177.12.a.a.1.6
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $1$
Dimension $26$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(1\)
Dimension: \(26\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-60.8905 q^{2} -243.000 q^{3} +1659.66 q^{4} -4960.99 q^{5} +14796.4 q^{6} -87058.0 q^{7} +23646.5 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-60.8905 q^{2} -243.000 q^{3} +1659.66 q^{4} -4960.99 q^{5} +14796.4 q^{6} -87058.0 q^{7} +23646.5 q^{8} +59049.0 q^{9} +302077. q^{10} -683008. q^{11} -403296. q^{12} -974154. q^{13} +5.30101e6 q^{14} +1.20552e6 q^{15} -4.83882e6 q^{16} -6.81665e6 q^{17} -3.59552e6 q^{18} +1.81310e7 q^{19} -8.23354e6 q^{20} +2.11551e7 q^{21} +4.15887e7 q^{22} -3.49174e7 q^{23} -5.74610e6 q^{24} -2.42167e7 q^{25} +5.93168e7 q^{26} -1.43489e7 q^{27} -1.44486e8 q^{28} +9.30111e7 q^{29} -7.34048e7 q^{30} -1.05378e8 q^{31} +2.46210e8 q^{32} +1.65971e8 q^{33} +4.15070e8 q^{34} +4.31894e8 q^{35} +9.80010e7 q^{36} -2.32051e8 q^{37} -1.10401e9 q^{38} +2.36720e8 q^{39} -1.17310e8 q^{40} +1.02676e9 q^{41} -1.28815e9 q^{42} -1.24232e9 q^{43} -1.13356e9 q^{44} -2.92942e8 q^{45} +2.12614e9 q^{46} -2.18627e9 q^{47} +1.17583e9 q^{48} +5.60177e9 q^{49} +1.47457e9 q^{50} +1.65645e9 q^{51} -1.61676e9 q^{52} -4.40486e9 q^{53} +8.73712e8 q^{54} +3.38840e9 q^{55} -2.05862e9 q^{56} -4.40584e9 q^{57} -5.66350e9 q^{58} +7.14924e8 q^{59} +2.00075e9 q^{60} +8.44479e9 q^{61} +6.41652e9 q^{62} -5.14069e9 q^{63} -5.08197e9 q^{64} +4.83277e9 q^{65} -1.01061e10 q^{66} +2.45494e9 q^{67} -1.13133e10 q^{68} +8.48493e9 q^{69} -2.62983e10 q^{70} +1.56746e10 q^{71} +1.39630e9 q^{72} +1.89412e10 q^{73} +1.41297e10 q^{74} +5.88465e9 q^{75} +3.00913e10 q^{76} +5.94613e10 q^{77} -1.44140e10 q^{78} +1.99876e10 q^{79} +2.40054e10 q^{80} +3.48678e9 q^{81} -6.25200e10 q^{82} +6.31770e10 q^{83} +3.51102e10 q^{84} +3.38174e10 q^{85} +7.56453e10 q^{86} -2.26017e10 q^{87} -1.61508e10 q^{88} +1.84273e10 q^{89} +1.78374e10 q^{90} +8.48080e10 q^{91} -5.79509e10 q^{92} +2.56068e10 q^{93} +1.33123e11 q^{94} -8.99479e10 q^{95} -5.98291e10 q^{96} +4.38615e10 q^{97} -3.41095e11 q^{98} -4.03310e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) \) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −60.8905 −1.34550 −0.672752 0.739868i \(-0.734888\pi\)
−0.672752 + 0.739868i \(0.734888\pi\)
\(3\) −243.000 −0.577350
\(4\) 1659.66 0.810379
\(5\) −4960.99 −0.709959 −0.354980 0.934874i \(-0.615512\pi\)
−0.354980 + 0.934874i \(0.615512\pi\)
\(6\) 14796.4 0.776827
\(7\) −87058.0 −1.95781 −0.978903 0.204326i \(-0.934500\pi\)
−0.978903 + 0.204326i \(0.934500\pi\)
\(8\) 23646.5 0.255136
\(9\) 59049.0 0.333333
\(10\) 302077. 0.955253
\(11\) −683008. −1.27869 −0.639346 0.768919i \(-0.720795\pi\)
−0.639346 + 0.768919i \(0.720795\pi\)
\(12\) −403296. −0.467872
\(13\) −974154. −0.727678 −0.363839 0.931462i \(-0.618534\pi\)
−0.363839 + 0.931462i \(0.618534\pi\)
\(14\) 5.30101e6 2.63423
\(15\) 1.20552e6 0.409895
\(16\) −4.83882e6 −1.15367
\(17\) −6.81665e6 −1.16440 −0.582200 0.813046i \(-0.697808\pi\)
−0.582200 + 0.813046i \(0.697808\pi\)
\(18\) −3.59552e6 −0.448501
\(19\) 1.81310e7 1.67988 0.839939 0.542681i \(-0.182591\pi\)
0.839939 + 0.542681i \(0.182591\pi\)
\(20\) −8.23354e6 −0.575336
\(21\) 2.11551e7 1.13034
\(22\) 4.15887e7 1.72048
\(23\) −3.49174e7 −1.13120 −0.565599 0.824680i \(-0.691355\pi\)
−0.565599 + 0.824680i \(0.691355\pi\)
\(24\) −5.74610e6 −0.147303
\(25\) −2.42167e7 −0.495958
\(26\) 5.93168e7 0.979093
\(27\) −1.43489e7 −0.192450
\(28\) −1.44486e8 −1.58656
\(29\) 9.30111e7 0.842066 0.421033 0.907045i \(-0.361668\pi\)
0.421033 + 0.907045i \(0.361668\pi\)
\(30\) −7.34048e7 −0.551515
\(31\) −1.05378e8 −0.661090 −0.330545 0.943790i \(-0.607233\pi\)
−0.330545 + 0.943790i \(0.607233\pi\)
\(32\) 2.46210e8 1.29712
\(33\) 1.65971e8 0.738253
\(34\) 4.15070e8 1.56670
\(35\) 4.31894e8 1.38996
\(36\) 9.80010e7 0.270126
\(37\) −2.32051e8 −0.550141 −0.275071 0.961424i \(-0.588701\pi\)
−0.275071 + 0.961424i \(0.588701\pi\)
\(38\) −1.10401e9 −2.26028
\(39\) 2.36720e8 0.420125
\(40\) −1.17310e8 −0.181136
\(41\) 1.02676e9 1.38407 0.692035 0.721864i \(-0.256714\pi\)
0.692035 + 0.721864i \(0.256714\pi\)
\(42\) −1.28815e9 −1.52088
\(43\) −1.24232e9 −1.28871 −0.644355 0.764726i \(-0.722874\pi\)
−0.644355 + 0.764726i \(0.722874\pi\)
\(44\) −1.13356e9 −1.03623
\(45\) −2.92942e8 −0.236653
\(46\) 2.12614e9 1.52203
\(47\) −2.18627e9 −1.39048 −0.695242 0.718776i \(-0.744703\pi\)
−0.695242 + 0.718776i \(0.744703\pi\)
\(48\) 1.17583e9 0.666069
\(49\) 5.60177e9 2.83300
\(50\) 1.47457e9 0.667313
\(51\) 1.65645e9 0.672267
\(52\) −1.61676e9 −0.589695
\(53\) −4.40486e9 −1.44682 −0.723411 0.690418i \(-0.757427\pi\)
−0.723411 + 0.690418i \(0.757427\pi\)
\(54\) 8.73712e8 0.258942
\(55\) 3.38840e9 0.907820
\(56\) −2.05862e9 −0.499507
\(57\) −4.40584e9 −0.969878
\(58\) −5.66350e9 −1.13300
\(59\) 7.14924e8 0.130189
\(60\) 2.00075e9 0.332170
\(61\) 8.44479e9 1.28019 0.640096 0.768295i \(-0.278895\pi\)
0.640096 + 0.768295i \(0.278895\pi\)
\(62\) 6.41652e9 0.889498
\(63\) −5.14069e9 −0.652602
\(64\) −5.08197e9 −0.591619
\(65\) 4.83277e9 0.516622
\(66\) −1.01061e10 −0.993322
\(67\) 2.45494e9 0.222141 0.111071 0.993813i \(-0.464572\pi\)
0.111071 + 0.993813i \(0.464572\pi\)
\(68\) −1.13133e10 −0.943605
\(69\) 8.48493e9 0.653098
\(70\) −2.62983e10 −1.87020
\(71\) 1.56746e10 1.03104 0.515521 0.856877i \(-0.327598\pi\)
0.515521 + 0.856877i \(0.327598\pi\)
\(72\) 1.39630e9 0.0850454
\(73\) 1.89412e10 1.06938 0.534689 0.845049i \(-0.320429\pi\)
0.534689 + 0.845049i \(0.320429\pi\)
\(74\) 1.41297e10 0.740217
\(75\) 5.88465e9 0.286341
\(76\) 3.00913e10 1.36134
\(77\) 5.94613e10 2.50343
\(78\) −1.44140e10 −0.565280
\(79\) 1.99876e10 0.730821 0.365410 0.930846i \(-0.380929\pi\)
0.365410 + 0.930846i \(0.380929\pi\)
\(80\) 2.40054e10 0.819055
\(81\) 3.48678e9 0.111111
\(82\) −6.25200e10 −1.86227
\(83\) 6.31770e10 1.76047 0.880237 0.474535i \(-0.157384\pi\)
0.880237 + 0.474535i \(0.157384\pi\)
\(84\) 3.51102e10 0.916003
\(85\) 3.38174e10 0.826677
\(86\) 7.56453e10 1.73396
\(87\) −2.26017e10 −0.486167
\(88\) −1.61508e10 −0.326241
\(89\) 1.84273e10 0.349798 0.174899 0.984586i \(-0.444040\pi\)
0.174899 + 0.984586i \(0.444040\pi\)
\(90\) 1.78374e10 0.318418
\(91\) 8.48080e10 1.42465
\(92\) −5.79509e10 −0.916699
\(93\) 2.56068e10 0.381680
\(94\) 1.33123e11 1.87090
\(95\) −8.99479e10 −1.19265
\(96\) −5.98291e10 −0.748895
\(97\) 4.38615e10 0.518607 0.259304 0.965796i \(-0.416507\pi\)
0.259304 + 0.965796i \(0.416507\pi\)
\(98\) −3.41095e11 −3.81181
\(99\) −4.03310e10 −0.426231
\(100\) −4.01913e10 −0.401913
\(101\) 4.59353e9 0.0434889 0.0217445 0.999764i \(-0.493078\pi\)
0.0217445 + 0.999764i \(0.493078\pi\)
\(102\) −1.00862e11 −0.904537
\(103\) −8.20219e10 −0.697148 −0.348574 0.937281i \(-0.613334\pi\)
−0.348574 + 0.937281i \(0.613334\pi\)
\(104\) −2.30353e10 −0.185657
\(105\) −1.04950e11 −0.802495
\(106\) 2.68214e11 1.94670
\(107\) −4.02988e9 −0.0277767 −0.0138884 0.999904i \(-0.504421\pi\)
−0.0138884 + 0.999904i \(0.504421\pi\)
\(108\) −2.38142e10 −0.155957
\(109\) −1.10801e11 −0.689761 −0.344881 0.938647i \(-0.612081\pi\)
−0.344881 + 0.938647i \(0.612081\pi\)
\(110\) −2.06321e11 −1.22147
\(111\) 5.63884e10 0.317624
\(112\) 4.21258e11 2.25865
\(113\) 3.21195e11 1.63998 0.819988 0.572380i \(-0.193980\pi\)
0.819988 + 0.572380i \(0.193980\pi\)
\(114\) 2.68274e11 1.30497
\(115\) 1.73225e11 0.803105
\(116\) 1.54366e11 0.682392
\(117\) −5.75228e10 −0.242559
\(118\) −4.35321e10 −0.175170
\(119\) 5.93444e11 2.27967
\(120\) 2.85064e10 0.104579
\(121\) 1.81189e11 0.635055
\(122\) −5.14208e11 −1.72250
\(123\) −2.49503e11 −0.799094
\(124\) −1.74891e11 −0.535733
\(125\) 3.62375e11 1.06207
\(126\) 3.13019e11 0.878078
\(127\) −5.54356e11 −1.48891 −0.744454 0.667674i \(-0.767290\pi\)
−0.744454 + 0.667674i \(0.767290\pi\)
\(128\) −1.94795e11 −0.501099
\(129\) 3.01883e11 0.744038
\(130\) −2.94270e11 −0.695116
\(131\) 5.36802e11 1.21569 0.607843 0.794057i \(-0.292035\pi\)
0.607843 + 0.794057i \(0.292035\pi\)
\(132\) 2.75455e11 0.598265
\(133\) −1.57845e12 −3.28887
\(134\) −1.49482e11 −0.298892
\(135\) 7.11848e10 0.136632
\(136\) −1.61190e11 −0.297081
\(137\) 6.22947e9 0.0110278 0.00551389 0.999985i \(-0.498245\pi\)
0.00551389 + 0.999985i \(0.498245\pi\)
\(138\) −5.16652e11 −0.878745
\(139\) 1.94678e11 0.318226 0.159113 0.987260i \(-0.449137\pi\)
0.159113 + 0.987260i \(0.449137\pi\)
\(140\) 7.16796e11 1.12640
\(141\) 5.31264e11 0.802796
\(142\) −9.54436e11 −1.38727
\(143\) 6.65355e11 0.930477
\(144\) −2.85728e11 −0.384555
\(145\) −4.61427e11 −0.597832
\(146\) −1.15334e12 −1.43885
\(147\) −1.36123e12 −1.63564
\(148\) −3.85125e11 −0.445823
\(149\) −7.82207e11 −0.872564 −0.436282 0.899810i \(-0.643705\pi\)
−0.436282 + 0.899810i \(0.643705\pi\)
\(150\) −3.58320e11 −0.385273
\(151\) −7.19235e11 −0.745586 −0.372793 0.927915i \(-0.621600\pi\)
−0.372793 + 0.927915i \(0.621600\pi\)
\(152\) 4.28736e11 0.428598
\(153\) −4.02517e11 −0.388133
\(154\) −3.62063e12 −3.36837
\(155\) 5.22779e11 0.469347
\(156\) 3.92873e11 0.340460
\(157\) 7.68037e11 0.642590 0.321295 0.946979i \(-0.395882\pi\)
0.321295 + 0.946979i \(0.395882\pi\)
\(158\) −1.21705e12 −0.983322
\(159\) 1.07038e12 0.835323
\(160\) −1.22145e12 −0.920905
\(161\) 3.03984e12 2.21467
\(162\) −2.12312e11 −0.149500
\(163\) 2.10422e11 0.143238 0.0716192 0.997432i \(-0.477183\pi\)
0.0716192 + 0.997432i \(0.477183\pi\)
\(164\) 1.70407e12 1.12162
\(165\) −8.23381e11 −0.524130
\(166\) −3.84688e12 −2.36872
\(167\) 1.90238e12 1.13333 0.566664 0.823949i \(-0.308234\pi\)
0.566664 + 0.823949i \(0.308234\pi\)
\(168\) 5.00244e11 0.288391
\(169\) −8.43184e11 −0.470484
\(170\) −2.05916e12 −1.11230
\(171\) 1.07062e12 0.559959
\(172\) −2.06182e12 −1.04434
\(173\) −7.99218e11 −0.392113 −0.196057 0.980593i \(-0.562814\pi\)
−0.196057 + 0.980593i \(0.562814\pi\)
\(174\) 1.37623e12 0.654139
\(175\) 2.10826e12 0.970989
\(176\) 3.30496e12 1.47518
\(177\) −1.73727e11 −0.0751646
\(178\) −1.12205e12 −0.470655
\(179\) −4.49912e12 −1.82994 −0.914968 0.403526i \(-0.867784\pi\)
−0.914968 + 0.403526i \(0.867784\pi\)
\(180\) −4.86182e11 −0.191779
\(181\) −3.39167e12 −1.29772 −0.648860 0.760908i \(-0.724754\pi\)
−0.648860 + 0.760908i \(0.724754\pi\)
\(182\) −5.16400e12 −1.91687
\(183\) −2.05209e12 −0.739119
\(184\) −8.25675e11 −0.288610
\(185\) 1.15120e12 0.390578
\(186\) −1.55921e12 −0.513552
\(187\) 4.65583e12 1.48891
\(188\) −3.62846e12 −1.12682
\(189\) 1.24919e12 0.376780
\(190\) 5.47698e12 1.60471
\(191\) −5.32518e11 −0.151583 −0.0757916 0.997124i \(-0.524148\pi\)
−0.0757916 + 0.997124i \(0.524148\pi\)
\(192\) 1.23492e12 0.341571
\(193\) −5.16210e12 −1.38759 −0.693795 0.720172i \(-0.744063\pi\)
−0.693795 + 0.720172i \(0.744063\pi\)
\(194\) −2.67075e12 −0.697787
\(195\) −1.17436e12 −0.298272
\(196\) 9.29701e12 2.29581
\(197\) 4.31197e12 1.03541 0.517704 0.855560i \(-0.326787\pi\)
0.517704 + 0.855560i \(0.326787\pi\)
\(198\) 2.45577e12 0.573495
\(199\) −8.47690e12 −1.92551 −0.962754 0.270380i \(-0.912851\pi\)
−0.962754 + 0.270380i \(0.912851\pi\)
\(200\) −5.72640e11 −0.126537
\(201\) −5.96550e11 −0.128253
\(202\) −2.79702e11 −0.0585145
\(203\) −8.09736e12 −1.64860
\(204\) 2.74913e12 0.544790
\(205\) −5.09375e12 −0.982634
\(206\) 4.99436e12 0.938015
\(207\) −2.06184e12 −0.377066
\(208\) 4.71376e12 0.839497
\(209\) −1.23836e13 −2.14805
\(210\) 6.39048e12 1.07976
\(211\) 2.82447e12 0.464925 0.232463 0.972605i \(-0.425322\pi\)
0.232463 + 0.972605i \(0.425322\pi\)
\(212\) −7.31055e12 −1.17247
\(213\) −3.80893e12 −0.595272
\(214\) 2.45381e11 0.0373737
\(215\) 6.16312e12 0.914932
\(216\) −3.39301e11 −0.0491010
\(217\) 9.17400e12 1.29429
\(218\) 6.74674e12 0.928076
\(219\) −4.60271e12 −0.617406
\(220\) 5.62357e12 0.735678
\(221\) 6.64047e12 0.847308
\(222\) −3.43352e12 −0.427364
\(223\) 8.45247e11 0.102638 0.0513188 0.998682i \(-0.483658\pi\)
0.0513188 + 0.998682i \(0.483658\pi\)
\(224\) −2.14346e13 −2.53952
\(225\) −1.42997e12 −0.165319
\(226\) −1.95577e13 −2.20659
\(227\) 7.13636e12 0.785841 0.392921 0.919572i \(-0.371465\pi\)
0.392921 + 0.919572i \(0.371465\pi\)
\(228\) −7.31218e12 −0.785968
\(229\) −8.15017e12 −0.855208 −0.427604 0.903966i \(-0.640642\pi\)
−0.427604 + 0.903966i \(0.640642\pi\)
\(230\) −1.05478e13 −1.08058
\(231\) −1.44491e13 −1.44536
\(232\) 2.19939e12 0.214841
\(233\) −1.14160e12 −0.108907 −0.0544536 0.998516i \(-0.517342\pi\)
−0.0544536 + 0.998516i \(0.517342\pi\)
\(234\) 3.50260e12 0.326364
\(235\) 1.08461e13 0.987187
\(236\) 1.18653e12 0.105502
\(237\) −4.85698e12 −0.421940
\(238\) −3.61351e13 −3.06730
\(239\) 1.86809e12 0.154956 0.0774782 0.996994i \(-0.475313\pi\)
0.0774782 + 0.996994i \(0.475313\pi\)
\(240\) −5.83330e12 −0.472882
\(241\) −4.14653e12 −0.328542 −0.164271 0.986415i \(-0.552527\pi\)
−0.164271 + 0.986415i \(0.552527\pi\)
\(242\) −1.10327e13 −0.854468
\(243\) −8.47289e11 −0.0641500
\(244\) 1.40154e13 1.03744
\(245\) −2.77904e13 −2.01132
\(246\) 1.51924e13 1.07518
\(247\) −1.76624e13 −1.22241
\(248\) −2.49182e12 −0.168668
\(249\) −1.53520e13 −1.01641
\(250\) −2.20652e13 −1.42902
\(251\) 2.14857e13 1.36127 0.680636 0.732622i \(-0.261704\pi\)
0.680636 + 0.732622i \(0.261704\pi\)
\(252\) −8.53177e12 −0.528855
\(253\) 2.38489e13 1.44646
\(254\) 3.37550e13 2.00333
\(255\) −8.21762e12 −0.477282
\(256\) 2.22690e13 1.26585
\(257\) 1.30208e12 0.0724445 0.0362222 0.999344i \(-0.488468\pi\)
0.0362222 + 0.999344i \(0.488468\pi\)
\(258\) −1.83818e13 −1.00110
\(259\) 2.02019e13 1.07707
\(260\) 8.02074e12 0.418659
\(261\) 5.49221e12 0.280689
\(262\) −3.26861e13 −1.63571
\(263\) 1.67130e13 0.819026 0.409513 0.912304i \(-0.365699\pi\)
0.409513 + 0.912304i \(0.365699\pi\)
\(264\) 3.92463e12 0.188355
\(265\) 2.18525e13 1.02718
\(266\) 9.61128e13 4.42519
\(267\) −4.47784e12 −0.201956
\(268\) 4.07435e12 0.180018
\(269\) 4.83228e12 0.209177 0.104589 0.994516i \(-0.466647\pi\)
0.104589 + 0.994516i \(0.466647\pi\)
\(270\) −4.33448e12 −0.183838
\(271\) −1.47869e13 −0.614535 −0.307268 0.951623i \(-0.599415\pi\)
−0.307268 + 0.951623i \(0.599415\pi\)
\(272\) 3.29846e13 1.34333
\(273\) −2.06083e13 −0.822523
\(274\) −3.79316e11 −0.0148379
\(275\) 1.65402e13 0.634177
\(276\) 1.40821e13 0.529256
\(277\) −4.09753e13 −1.50968 −0.754838 0.655911i \(-0.772284\pi\)
−0.754838 + 0.655911i \(0.772284\pi\)
\(278\) −1.18540e13 −0.428174
\(279\) −6.22246e12 −0.220363
\(280\) 1.02128e13 0.354630
\(281\) 3.23692e13 1.10217 0.551083 0.834450i \(-0.314215\pi\)
0.551083 + 0.834450i \(0.314215\pi\)
\(282\) −3.23489e13 −1.08016
\(283\) 4.42602e13 1.44940 0.724700 0.689064i \(-0.241978\pi\)
0.724700 + 0.689064i \(0.241978\pi\)
\(284\) 2.60145e13 0.835534
\(285\) 2.18573e13 0.688574
\(286\) −4.05138e13 −1.25196
\(287\) −8.93878e13 −2.70974
\(288\) 1.45385e13 0.432375
\(289\) 1.21949e13 0.355827
\(290\) 2.80966e13 0.804385
\(291\) −1.06583e13 −0.299418
\(292\) 3.14358e13 0.866601
\(293\) 3.46245e13 0.936724 0.468362 0.883537i \(-0.344844\pi\)
0.468362 + 0.883537i \(0.344844\pi\)
\(294\) 8.28861e13 2.20075
\(295\) −3.54673e12 −0.0924288
\(296\) −5.48720e12 −0.140361
\(297\) 9.80042e12 0.246084
\(298\) 4.76290e13 1.17404
\(299\) 3.40149e13 0.823148
\(300\) 9.76650e12 0.232045
\(301\) 1.08154e14 2.52305
\(302\) 4.37946e13 1.00319
\(303\) −1.11623e12 −0.0251083
\(304\) −8.77328e13 −1.93802
\(305\) −4.18946e13 −0.908884
\(306\) 2.45094e13 0.522235
\(307\) −1.40721e13 −0.294509 −0.147255 0.989099i \(-0.547044\pi\)
−0.147255 + 0.989099i \(0.547044\pi\)
\(308\) 9.86853e13 2.02873
\(309\) 1.99313e13 0.402499
\(310\) −3.18323e13 −0.631508
\(311\) −2.59276e12 −0.0505336 −0.0252668 0.999681i \(-0.508044\pi\)
−0.0252668 + 0.999681i \(0.508044\pi\)
\(312\) 5.59759e12 0.107189
\(313\) 6.91494e13 1.30105 0.650526 0.759484i \(-0.274549\pi\)
0.650526 + 0.759484i \(0.274549\pi\)
\(314\) −4.67662e13 −0.864607
\(315\) 2.55029e13 0.463321
\(316\) 3.31725e13 0.592242
\(317\) −5.31356e13 −0.932308 −0.466154 0.884704i \(-0.654361\pi\)
−0.466154 + 0.884704i \(0.654361\pi\)
\(318\) −6.51761e13 −1.12393
\(319\) −6.35274e13 −1.07674
\(320\) 2.52116e13 0.420026
\(321\) 9.79260e11 0.0160369
\(322\) −1.85097e14 −2.97984
\(323\) −1.23593e14 −1.95605
\(324\) 5.78686e12 0.0900421
\(325\) 2.35908e13 0.360898
\(326\) −1.28127e13 −0.192728
\(327\) 2.69247e13 0.398234
\(328\) 2.42793e13 0.353126
\(329\) 1.90333e14 2.72230
\(330\) 5.01361e13 0.705219
\(331\) −1.19507e14 −1.65325 −0.826626 0.562751i \(-0.809743\pi\)
−0.826626 + 0.562751i \(0.809743\pi\)
\(332\) 1.04852e14 1.42665
\(333\) −1.37024e13 −0.183380
\(334\) −1.15837e14 −1.52490
\(335\) −1.21789e13 −0.157711
\(336\) −1.02366e14 −1.30403
\(337\) 1.13746e14 1.42551 0.712755 0.701413i \(-0.247447\pi\)
0.712755 + 0.701413i \(0.247447\pi\)
\(338\) 5.13419e13 0.633038
\(339\) −7.80505e13 −0.946841
\(340\) 5.61252e13 0.669921
\(341\) 7.19740e13 0.845331
\(342\) −6.51906e13 −0.753427
\(343\) −3.15537e14 −3.58866
\(344\) −2.93764e13 −0.328797
\(345\) −4.20937e13 −0.463673
\(346\) 4.86648e13 0.527589
\(347\) −5.34150e12 −0.0569969 −0.0284985 0.999594i \(-0.509073\pi\)
−0.0284985 + 0.999594i \(0.509073\pi\)
\(348\) −3.75110e13 −0.393979
\(349\) −1.19303e14 −1.23342 −0.616712 0.787189i \(-0.711536\pi\)
−0.616712 + 0.787189i \(0.711536\pi\)
\(350\) −1.28373e14 −1.30647
\(351\) 1.39781e13 0.140042
\(352\) −1.68164e14 −1.65862
\(353\) 1.07357e14 1.04248 0.521240 0.853410i \(-0.325470\pi\)
0.521240 + 0.853410i \(0.325470\pi\)
\(354\) 1.05783e13 0.101134
\(355\) −7.77617e13 −0.731998
\(356\) 3.05830e13 0.283469
\(357\) −1.44207e14 −1.31617
\(358\) 2.73954e14 2.46218
\(359\) −1.16906e14 −1.03471 −0.517355 0.855771i \(-0.673083\pi\)
−0.517355 + 0.855771i \(0.673083\pi\)
\(360\) −6.92705e12 −0.0603788
\(361\) 2.12244e14 1.82199
\(362\) 2.06520e14 1.74609
\(363\) −4.40288e13 −0.366649
\(364\) 1.40752e14 1.15451
\(365\) −9.39670e13 −0.759215
\(366\) 1.24953e14 0.994487
\(367\) −7.67484e13 −0.601736 −0.300868 0.953666i \(-0.597276\pi\)
−0.300868 + 0.953666i \(0.597276\pi\)
\(368\) 1.68959e14 1.30502
\(369\) 6.06292e13 0.461357
\(370\) −7.00974e13 −0.525524
\(371\) 3.83478e14 2.83260
\(372\) 4.24985e13 0.309306
\(373\) 1.46951e14 1.05384 0.526920 0.849915i \(-0.323347\pi\)
0.526920 + 0.849915i \(0.323347\pi\)
\(374\) −2.83496e14 −2.00333
\(375\) −8.80571e13 −0.613186
\(376\) −5.16977e13 −0.354763
\(377\) −9.06072e13 −0.612753
\(378\) −7.60637e13 −0.506959
\(379\) −1.11895e14 −0.735010 −0.367505 0.930021i \(-0.619788\pi\)
−0.367505 + 0.930021i \(0.619788\pi\)
\(380\) −1.49283e14 −0.966494
\(381\) 1.34708e14 0.859622
\(382\) 3.24253e13 0.203956
\(383\) −1.07972e14 −0.669448 −0.334724 0.942316i \(-0.608643\pi\)
−0.334724 + 0.942316i \(0.608643\pi\)
\(384\) 4.73352e13 0.289309
\(385\) −2.94987e14 −1.77733
\(386\) 3.14323e14 1.86701
\(387\) −7.33575e13 −0.429570
\(388\) 7.27949e13 0.420268
\(389\) 1.40085e14 0.797389 0.398694 0.917084i \(-0.369463\pi\)
0.398694 + 0.917084i \(0.369463\pi\)
\(390\) 7.15076e13 0.401326
\(391\) 2.38020e14 1.31717
\(392\) 1.32462e14 0.722802
\(393\) −1.30443e14 −0.701877
\(394\) −2.62558e14 −1.39315
\(395\) −9.91582e13 −0.518853
\(396\) −6.69355e13 −0.345408
\(397\) −2.93432e14 −1.49334 −0.746671 0.665194i \(-0.768349\pi\)
−0.746671 + 0.665194i \(0.768349\pi\)
\(398\) 5.16163e14 2.59078
\(399\) 3.83564e14 1.89883
\(400\) 1.17180e14 0.572169
\(401\) −1.66166e14 −0.800293 −0.400146 0.916451i \(-0.631041\pi\)
−0.400146 + 0.916451i \(0.631041\pi\)
\(402\) 3.63242e13 0.172565
\(403\) 1.02654e14 0.481061
\(404\) 7.62367e12 0.0352425
\(405\) −1.72979e13 −0.0788844
\(406\) 4.93053e14 2.21820
\(407\) 1.58493e14 0.703462
\(408\) 3.91692e13 0.171520
\(409\) 4.04981e14 1.74967 0.874836 0.484420i \(-0.160969\pi\)
0.874836 + 0.484420i \(0.160969\pi\)
\(410\) 3.10161e14 1.32214
\(411\) −1.51376e12 −0.00636689
\(412\) −1.36128e14 −0.564954
\(413\) −6.22399e13 −0.254885
\(414\) 1.25546e14 0.507344
\(415\) −3.13421e14 −1.24986
\(416\) −2.39847e14 −0.943889
\(417\) −4.73067e13 −0.183728
\(418\) 7.54047e14 2.89020
\(419\) −4.37489e14 −1.65497 −0.827485 0.561488i \(-0.810229\pi\)
−0.827485 + 0.561488i \(0.810229\pi\)
\(420\) −1.74181e14 −0.650325
\(421\) −2.90114e14 −1.06910 −0.534548 0.845138i \(-0.679518\pi\)
−0.534548 + 0.845138i \(0.679518\pi\)
\(422\) −1.71983e14 −0.625558
\(423\) −1.29097e14 −0.463495
\(424\) −1.04160e14 −0.369136
\(425\) 1.65077e14 0.577493
\(426\) 2.31928e14 0.800941
\(427\) −7.35187e14 −2.50637
\(428\) −6.68821e12 −0.0225097
\(429\) −1.61681e14 −0.537211
\(430\) −3.75276e14 −1.23104
\(431\) 3.55443e14 1.15119 0.575593 0.817736i \(-0.304771\pi\)
0.575593 + 0.817736i \(0.304771\pi\)
\(432\) 6.94318e13 0.222023
\(433\) 1.26989e14 0.400942 0.200471 0.979700i \(-0.435753\pi\)
0.200471 + 0.979700i \(0.435753\pi\)
\(434\) −5.58610e14 −1.74147
\(435\) 1.12127e14 0.345159
\(436\) −1.83892e14 −0.558968
\(437\) −6.33089e14 −1.90028
\(438\) 2.80261e14 0.830721
\(439\) 4.00751e14 1.17306 0.586530 0.809928i \(-0.300494\pi\)
0.586530 + 0.809928i \(0.300494\pi\)
\(440\) 8.01238e13 0.231618
\(441\) 3.30779e14 0.944334
\(442\) −4.04342e14 −1.14006
\(443\) −3.89507e14 −1.08466 −0.542331 0.840165i \(-0.682458\pi\)
−0.542331 + 0.840165i \(0.682458\pi\)
\(444\) 9.35854e13 0.257396
\(445\) −9.14179e13 −0.248343
\(446\) −5.14675e13 −0.138099
\(447\) 1.90076e14 0.503775
\(448\) 4.42426e14 1.15828
\(449\) −4.11391e14 −1.06390 −0.531949 0.846776i \(-0.678540\pi\)
−0.531949 + 0.846776i \(0.678540\pi\)
\(450\) 8.70717e13 0.222438
\(451\) −7.01286e14 −1.76980
\(452\) 5.33073e14 1.32900
\(453\) 1.74774e14 0.430464
\(454\) −4.34537e14 −1.05735
\(455\) −4.20732e14 −1.01145
\(456\) −1.04183e14 −0.247451
\(457\) 3.04151e14 0.713758 0.356879 0.934151i \(-0.383841\pi\)
0.356879 + 0.934151i \(0.383841\pi\)
\(458\) 4.96268e14 1.15068
\(459\) 9.78115e13 0.224089
\(460\) 2.87494e14 0.650819
\(461\) 8.14598e14 1.82217 0.911084 0.412221i \(-0.135247\pi\)
0.911084 + 0.412221i \(0.135247\pi\)
\(462\) 8.79814e14 1.94473
\(463\) 5.28967e14 1.15540 0.577701 0.816248i \(-0.303950\pi\)
0.577701 + 0.816248i \(0.303950\pi\)
\(464\) −4.50064e14 −0.971462
\(465\) −1.27035e14 −0.270978
\(466\) 6.95126e13 0.146535
\(467\) 4.17896e14 0.870613 0.435307 0.900282i \(-0.356640\pi\)
0.435307 + 0.900282i \(0.356640\pi\)
\(468\) −9.54681e13 −0.196565
\(469\) −2.13722e14 −0.434909
\(470\) −6.60423e14 −1.32826
\(471\) −1.86633e14 −0.371000
\(472\) 1.69055e13 0.0332159
\(473\) 8.48512e14 1.64787
\(474\) 2.95744e14 0.567721
\(475\) −4.39073e14 −0.833148
\(476\) 9.84913e14 1.84739
\(477\) −2.60103e14 −0.482274
\(478\) −1.13749e14 −0.208494
\(479\) 7.53061e14 1.36453 0.682267 0.731103i \(-0.260994\pi\)
0.682267 + 0.731103i \(0.260994\pi\)
\(480\) 2.96812e14 0.531685
\(481\) 2.26054e14 0.400326
\(482\) 2.52484e14 0.442054
\(483\) −7.38681e14 −1.27864
\(484\) 3.00710e14 0.514635
\(485\) −2.17596e14 −0.368190
\(486\) 5.15918e13 0.0863141
\(487\) 3.30902e14 0.547382 0.273691 0.961818i \(-0.411755\pi\)
0.273691 + 0.961818i \(0.411755\pi\)
\(488\) 1.99690e14 0.326623
\(489\) −5.11326e13 −0.0826987
\(490\) 1.69217e15 2.70623
\(491\) −1.25595e14 −0.198620 −0.0993101 0.995057i \(-0.531664\pi\)
−0.0993101 + 0.995057i \(0.531664\pi\)
\(492\) −4.14089e14 −0.647568
\(493\) −6.34025e14 −0.980501
\(494\) 1.07547e15 1.64476
\(495\) 2.00082e14 0.302607
\(496\) 5.09905e14 0.762676
\(497\) −1.36460e15 −2.01858
\(498\) 9.34792e14 1.36758
\(499\) 7.30727e13 0.105731 0.0528655 0.998602i \(-0.483165\pi\)
0.0528655 + 0.998602i \(0.483165\pi\)
\(500\) 6.01417e14 0.860678
\(501\) −4.62277e14 −0.654327
\(502\) −1.30828e15 −1.83160
\(503\) −1.16655e15 −1.61540 −0.807701 0.589592i \(-0.799289\pi\)
−0.807701 + 0.589592i \(0.799289\pi\)
\(504\) −1.21559e14 −0.166502
\(505\) −2.27885e13 −0.0308754
\(506\) −1.45217e15 −1.94621
\(507\) 2.04894e14 0.271634
\(508\) −9.20039e14 −1.20658
\(509\) 5.44791e14 0.706776 0.353388 0.935477i \(-0.385030\pi\)
0.353388 + 0.935477i \(0.385030\pi\)
\(510\) 5.00375e14 0.642184
\(511\) −1.64898e15 −2.09363
\(512\) −9.57033e14 −1.20210
\(513\) −2.60161e14 −0.323293
\(514\) −7.92843e13 −0.0974743
\(515\) 4.06910e14 0.494947
\(516\) 5.01021e14 0.602952
\(517\) 1.49324e15 1.77800
\(518\) −1.23011e15 −1.44920
\(519\) 1.94210e14 0.226387
\(520\) 1.14278e14 0.131809
\(521\) −5.49458e14 −0.627085 −0.313543 0.949574i \(-0.601516\pi\)
−0.313543 + 0.949574i \(0.601516\pi\)
\(522\) −3.34424e14 −0.377667
\(523\) −6.96940e14 −0.778818 −0.389409 0.921065i \(-0.627321\pi\)
−0.389409 + 0.921065i \(0.627321\pi\)
\(524\) 8.90906e14 0.985167
\(525\) −5.12306e14 −0.560601
\(526\) −1.01766e15 −1.10200
\(527\) 7.18325e14 0.769773
\(528\) −8.03104e14 −0.851697
\(529\) 2.66415e14 0.279610
\(530\) −1.33061e15 −1.38208
\(531\) 4.22156e13 0.0433963
\(532\) −2.61969e15 −2.66523
\(533\) −1.00022e15 −1.00716
\(534\) 2.72658e14 0.271733
\(535\) 1.99922e13 0.0197204
\(536\) 5.80507e13 0.0566762
\(537\) 1.09329e15 1.05651
\(538\) −2.94240e14 −0.281448
\(539\) −3.82606e15 −3.62254
\(540\) 1.18142e14 0.110723
\(541\) 8.39054e14 0.778404 0.389202 0.921153i \(-0.372751\pi\)
0.389202 + 0.921153i \(0.372751\pi\)
\(542\) 9.00383e14 0.826859
\(543\) 8.24175e14 0.749239
\(544\) −1.67833e15 −1.51037
\(545\) 5.49684e14 0.489702
\(546\) 1.25485e15 1.10671
\(547\) 7.76092e13 0.0677615 0.0338807 0.999426i \(-0.489213\pi\)
0.0338807 + 0.999426i \(0.489213\pi\)
\(548\) 1.03388e13 0.00893667
\(549\) 4.98657e14 0.426731
\(550\) −1.00714e15 −0.853288
\(551\) 1.68639e15 1.41457
\(552\) 2.00639e14 0.166629
\(553\) −1.74008e15 −1.43081
\(554\) 2.49501e15 2.03127
\(555\) −2.79743e14 −0.225500
\(556\) 3.23098e14 0.257883
\(557\) 3.82777e14 0.302511 0.151256 0.988495i \(-0.451668\pi\)
0.151256 + 0.988495i \(0.451668\pi\)
\(558\) 3.78889e14 0.296499
\(559\) 1.21021e15 0.937767
\(560\) −2.08986e15 −1.60355
\(561\) −1.13137e15 −0.859622
\(562\) −1.97098e15 −1.48297
\(563\) 1.66881e15 1.24340 0.621699 0.783256i \(-0.286443\pi\)
0.621699 + 0.783256i \(0.286443\pi\)
\(564\) 8.81715e14 0.650569
\(565\) −1.59345e15 −1.16432
\(566\) −2.69503e15 −1.95017
\(567\) −3.03553e14 −0.217534
\(568\) 3.70650e14 0.263056
\(569\) 2.65262e14 0.186448 0.0932239 0.995645i \(-0.470283\pi\)
0.0932239 + 0.995645i \(0.470283\pi\)
\(570\) −1.33090e15 −0.926478
\(571\) −1.76526e15 −1.21706 −0.608528 0.793532i \(-0.708240\pi\)
−0.608528 + 0.793532i \(0.708240\pi\)
\(572\) 1.10426e15 0.754038
\(573\) 1.29402e14 0.0875166
\(574\) 5.44287e15 3.64597
\(575\) 8.45584e14 0.561027
\(576\) −3.00085e14 −0.197206
\(577\) 1.87176e14 0.121838 0.0609191 0.998143i \(-0.480597\pi\)
0.0609191 + 0.998143i \(0.480597\pi\)
\(578\) −7.42552e14 −0.478767
\(579\) 1.25439e15 0.801126
\(580\) −7.65811e14 −0.484471
\(581\) −5.50007e15 −3.44667
\(582\) 6.48991e14 0.402868
\(583\) 3.00856e15 1.85004
\(584\) 4.47893e14 0.272837
\(585\) 2.85370e14 0.172207
\(586\) −2.10830e15 −1.26036
\(587\) −5.72887e13 −0.0339281 −0.0169641 0.999856i \(-0.505400\pi\)
−0.0169641 + 0.999856i \(0.505400\pi\)
\(588\) −2.25917e15 −1.32548
\(589\) −1.91061e15 −1.11055
\(590\) 2.15962e14 0.124363
\(591\) −1.04781e15 −0.597793
\(592\) 1.12285e15 0.634679
\(593\) −1.39022e15 −0.778544 −0.389272 0.921123i \(-0.627273\pi\)
−0.389272 + 0.921123i \(0.627273\pi\)
\(594\) −5.96753e14 −0.331107
\(595\) −2.94407e15 −1.61847
\(596\) −1.29819e15 −0.707107
\(597\) 2.05989e15 1.11169
\(598\) −2.07119e15 −1.10755
\(599\) −1.83862e15 −0.974192 −0.487096 0.873348i \(-0.661944\pi\)
−0.487096 + 0.873348i \(0.661944\pi\)
\(600\) 1.39151e14 0.0730560
\(601\) −4.19499e14 −0.218233 −0.109117 0.994029i \(-0.534802\pi\)
−0.109117 + 0.994029i \(0.534802\pi\)
\(602\) −6.58553e15 −3.39477
\(603\) 1.44962e14 0.0740471
\(604\) −1.19368e15 −0.604207
\(605\) −8.98875e14 −0.450863
\(606\) 6.79676e13 0.0337834
\(607\) 1.29935e15 0.640011 0.320005 0.947416i \(-0.396315\pi\)
0.320005 + 0.947416i \(0.396315\pi\)
\(608\) 4.46405e15 2.17901
\(609\) 1.96766e15 0.951820
\(610\) 2.55098e15 1.22291
\(611\) 2.12977e15 1.01182
\(612\) −6.68039e14 −0.314535
\(613\) −7.25013e14 −0.338309 −0.169154 0.985590i \(-0.554104\pi\)
−0.169154 + 0.985590i \(0.554104\pi\)
\(614\) 8.56860e14 0.396263
\(615\) 1.23778e15 0.567324
\(616\) 1.40605e15 0.638716
\(617\) 6.49787e14 0.292552 0.146276 0.989244i \(-0.453271\pi\)
0.146276 + 0.989244i \(0.453271\pi\)
\(618\) −1.21363e15 −0.541563
\(619\) 1.59102e14 0.0703684 0.0351842 0.999381i \(-0.488798\pi\)
0.0351842 + 0.999381i \(0.488798\pi\)
\(620\) 8.67633e14 0.380349
\(621\) 5.01027e14 0.217699
\(622\) 1.57875e14 0.0679931
\(623\) −1.60425e15 −0.684837
\(624\) −1.14544e15 −0.484684
\(625\) −6.15283e14 −0.258068
\(626\) −4.21054e15 −1.75057
\(627\) 3.00923e15 1.24018
\(628\) 1.27468e15 0.520741
\(629\) 1.58181e15 0.640585
\(630\) −1.55289e15 −0.623400
\(631\) 4.44997e15 1.77091 0.885453 0.464728i \(-0.153848\pi\)
0.885453 + 0.464728i \(0.153848\pi\)
\(632\) 4.72636e14 0.186459
\(633\) −6.86346e14 −0.268425
\(634\) 3.23545e15 1.25442
\(635\) 2.75015e15 1.05706
\(636\) 1.77646e15 0.676928
\(637\) −5.45699e15 −2.06151
\(638\) 3.86821e15 1.44876
\(639\) 9.25571e14 0.343681
\(640\) 9.66377e14 0.355760
\(641\) −5.79024e14 −0.211338 −0.105669 0.994401i \(-0.533698\pi\)
−0.105669 + 0.994401i \(0.533698\pi\)
\(642\) −5.96277e13 −0.0215777
\(643\) −4.91174e15 −1.76228 −0.881141 0.472854i \(-0.843224\pi\)
−0.881141 + 0.472854i \(0.843224\pi\)
\(644\) 5.04509e15 1.79472
\(645\) −1.49764e15 −0.528237
\(646\) 7.52564e15 2.63187
\(647\) 2.42235e15 0.839970 0.419985 0.907531i \(-0.362035\pi\)
0.419985 + 0.907531i \(0.362035\pi\)
\(648\) 8.24503e13 0.0283485
\(649\) −4.88299e14 −0.166472
\(650\) −1.43646e15 −0.485589
\(651\) −2.22928e15 −0.747256
\(652\) 3.49228e14 0.116077
\(653\) −1.71942e15 −0.566707 −0.283353 0.959016i \(-0.591447\pi\)
−0.283353 + 0.959016i \(0.591447\pi\)
\(654\) −1.63946e15 −0.535825
\(655\) −2.66307e15 −0.863088
\(656\) −4.96832e15 −1.59675
\(657\) 1.11846e15 0.356459
\(658\) −1.15894e16 −3.66286
\(659\) −1.26828e14 −0.0397509 −0.0198754 0.999802i \(-0.506327\pi\)
−0.0198754 + 0.999802i \(0.506327\pi\)
\(660\) −1.36653e15 −0.424744
\(661\) 4.61309e15 1.42195 0.710974 0.703218i \(-0.248254\pi\)
0.710974 + 0.703218i \(0.248254\pi\)
\(662\) 7.27684e15 2.22446
\(663\) −1.61363e15 −0.489194
\(664\) 1.49392e15 0.449161
\(665\) 7.83069e15 2.33497
\(666\) 8.34346e14 0.246739
\(667\) −3.24771e15 −0.952543
\(668\) 3.15729e15 0.918425
\(669\) −2.05395e14 −0.0592579
\(670\) 7.41581e14 0.212201
\(671\) −5.76786e15 −1.63697
\(672\) 5.20860e15 1.46619
\(673\) 5.73851e15 1.60220 0.801099 0.598531i \(-0.204249\pi\)
0.801099 + 0.598531i \(0.204249\pi\)
\(674\) −6.92603e15 −1.91803
\(675\) 3.47483e14 0.0954471
\(676\) −1.39939e15 −0.381271
\(677\) −1.95747e15 −0.529003 −0.264501 0.964385i \(-0.585207\pi\)
−0.264501 + 0.964385i \(0.585207\pi\)
\(678\) 4.75253e15 1.27398
\(679\) −3.81849e15 −1.01533
\(680\) 7.99663e14 0.210915
\(681\) −1.73414e15 −0.453706
\(682\) −4.38254e15 −1.13740
\(683\) −3.45210e15 −0.888730 −0.444365 0.895846i \(-0.646571\pi\)
−0.444365 + 0.895846i \(0.646571\pi\)
\(684\) 1.77686e15 0.453779
\(685\) −3.09043e13 −0.00782927
\(686\) 1.92132e16 4.82856
\(687\) 1.98049e15 0.493754
\(688\) 6.01135e15 1.48674
\(689\) 4.29101e15 1.05282
\(690\) 2.56311e15 0.623873
\(691\) −1.20060e15 −0.289914 −0.144957 0.989438i \(-0.546304\pi\)
−0.144957 + 0.989438i \(0.546304\pi\)
\(692\) −1.32643e15 −0.317760
\(693\) 3.51113e15 0.834477
\(694\) 3.25247e14 0.0766895
\(695\) −9.65796e14 −0.225927
\(696\) −5.34451e14 −0.124039
\(697\) −6.99908e15 −1.61161
\(698\) 7.26444e15 1.65958
\(699\) 2.77409e14 0.0628776
\(700\) 3.49898e15 0.786868
\(701\) −6.69273e14 −0.149333 −0.0746663 0.997209i \(-0.523789\pi\)
−0.0746663 + 0.997209i \(0.523789\pi\)
\(702\) −8.51131e14 −0.188427
\(703\) −4.20733e15 −0.924170
\(704\) 3.47103e15 0.756499
\(705\) −2.63560e15 −0.569953
\(706\) −6.53699e15 −1.40266
\(707\) −3.99903e14 −0.0851429
\(708\) −2.88326e14 −0.0609118
\(709\) −2.58351e15 −0.541572 −0.270786 0.962640i \(-0.587284\pi\)
−0.270786 + 0.962640i \(0.587284\pi\)
\(710\) 4.73495e15 0.984905
\(711\) 1.18025e15 0.243607
\(712\) 4.35742e14 0.0892462
\(713\) 3.67952e15 0.747824
\(714\) 8.78084e15 1.77091
\(715\) −3.30082e15 −0.660601
\(716\) −7.46699e15 −1.48294
\(717\) −4.53946e14 −0.0894641
\(718\) 7.11849e15 1.39221
\(719\) 2.22712e15 0.432249 0.216125 0.976366i \(-0.430658\pi\)
0.216125 + 0.976366i \(0.430658\pi\)
\(720\) 1.41749e15 0.273018
\(721\) 7.14066e15 1.36488
\(722\) −1.29237e16 −2.45149
\(723\) 1.00761e15 0.189684
\(724\) −5.62900e15 −1.05164
\(725\) −2.25242e15 −0.417629
\(726\) 2.68094e15 0.493327
\(727\) 8.31113e13 0.0151782 0.00758911 0.999971i \(-0.497584\pi\)
0.00758911 + 0.999971i \(0.497584\pi\)
\(728\) 2.00541e15 0.363480
\(729\) 2.05891e14 0.0370370
\(730\) 5.72170e15 1.02153
\(731\) 8.46844e15 1.50058
\(732\) −3.40575e15 −0.598966
\(733\) 8.81391e15 1.53850 0.769249 0.638950i \(-0.220631\pi\)
0.769249 + 0.638950i \(0.220631\pi\)
\(734\) 4.67325e15 0.809638
\(735\) 6.75306e15 1.16123
\(736\) −8.59703e15 −1.46730
\(737\) −1.67674e15 −0.284050
\(738\) −3.69175e15 −0.620757
\(739\) 2.56306e15 0.427774 0.213887 0.976858i \(-0.431388\pi\)
0.213887 + 0.976858i \(0.431388\pi\)
\(740\) 1.91060e15 0.316516
\(741\) 4.29197e15 0.705759
\(742\) −2.33502e16 −3.81127
\(743\) 9.06237e15 1.46826 0.734130 0.679009i \(-0.237590\pi\)
0.734130 + 0.679009i \(0.237590\pi\)
\(744\) 6.05512e14 0.0973805
\(745\) 3.88052e15 0.619485
\(746\) −8.94794e15 −1.41794
\(747\) 3.73054e15 0.586825
\(748\) 7.72707e15 1.20658
\(749\) 3.50833e14 0.0543814
\(750\) 5.36184e15 0.825044
\(751\) 2.67908e15 0.409229 0.204614 0.978843i \(-0.434406\pi\)
0.204614 + 0.978843i \(0.434406\pi\)
\(752\) 1.05790e16 1.60415
\(753\) −5.22104e15 −0.785931
\(754\) 5.51712e15 0.824461
\(755\) 3.56812e15 0.529336
\(756\) 2.07322e15 0.305334
\(757\) 1.54640e15 0.226097 0.113049 0.993589i \(-0.463938\pi\)
0.113049 + 0.993589i \(0.463938\pi\)
\(758\) 6.81332e15 0.988959
\(759\) −5.79528e15 −0.835111
\(760\) −2.12695e15 −0.304287
\(761\) 6.80674e15 0.966771 0.483385 0.875408i \(-0.339407\pi\)
0.483385 + 0.875408i \(0.339407\pi\)
\(762\) −8.20247e15 −1.15662
\(763\) 9.64613e15 1.35042
\(764\) −8.83797e14 −0.122840
\(765\) 1.99688e15 0.275559
\(766\) 6.57445e15 0.900744
\(767\) −6.96447e14 −0.0947356
\(768\) −5.41138e15 −0.730838
\(769\) 7.08886e15 0.950564 0.475282 0.879834i \(-0.342346\pi\)
0.475282 + 0.879834i \(0.342346\pi\)
\(770\) 1.79619e16 2.39141
\(771\) −3.16405e14 −0.0418258
\(772\) −8.56731e15 −1.12447
\(773\) 1.17195e16 1.52729 0.763643 0.645639i \(-0.223409\pi\)
0.763643 + 0.645639i \(0.223409\pi\)
\(774\) 4.46678e15 0.577988
\(775\) 2.55190e15 0.327873
\(776\) 1.03717e15 0.132315
\(777\) −4.90907e15 −0.621847
\(778\) −8.52988e15 −1.07289
\(779\) 1.86162e16 2.32507
\(780\) −1.94904e15 −0.241713
\(781\) −1.07059e16 −1.31839
\(782\) −1.44932e16 −1.77225
\(783\) −1.33461e15 −0.162056
\(784\) −2.71060e16 −3.26834
\(785\) −3.81022e15 −0.456213
\(786\) 7.94273e15 0.944378
\(787\) 1.65457e16 1.95354 0.976772 0.214279i \(-0.0687402\pi\)
0.976772 + 0.214279i \(0.0687402\pi\)
\(788\) 7.15639e15 0.839073
\(789\) −4.06126e15 −0.472865
\(790\) 6.03779e15 0.698119
\(791\) −2.79626e16 −3.21076
\(792\) −9.53686e14 −0.108747
\(793\) −8.22653e15 −0.931568
\(794\) 1.78672e16 2.00930
\(795\) −5.31015e15 −0.593045
\(796\) −1.40687e16 −1.56039
\(797\) 1.06176e16 1.16952 0.584758 0.811208i \(-0.301189\pi\)
0.584758 + 0.811208i \(0.301189\pi\)
\(798\) −2.33554e16 −2.55489
\(799\) 1.49031e16 1.61908
\(800\) −5.96240e15 −0.643318
\(801\) 1.08812e15 0.116599
\(802\) 1.01180e16 1.07680
\(803\) −1.29370e16 −1.36741
\(804\) −9.90067e14 −0.103934
\(805\) −1.50806e16 −1.57232
\(806\) −6.25068e15 −0.647269
\(807\) −1.17424e15 −0.120768
\(808\) 1.08621e14 0.0110956
\(809\) 1.07657e15 0.109226 0.0546130 0.998508i \(-0.482607\pi\)
0.0546130 + 0.998508i \(0.482607\pi\)
\(810\) 1.05328e15 0.106139
\(811\) 3.90930e15 0.391277 0.195639 0.980676i \(-0.437322\pi\)
0.195639 + 0.980676i \(0.437322\pi\)
\(812\) −1.34388e16 −1.33599
\(813\) 3.59322e15 0.354802
\(814\) −9.65071e15 −0.946510
\(815\) −1.04390e15 −0.101693
\(816\) −8.01525e15 −0.775571
\(817\) −2.25245e16 −2.16488
\(818\) −2.46595e16 −2.35419
\(819\) 5.00782e15 0.474884
\(820\) −8.45388e15 −0.796306
\(821\) 1.05915e16 0.990989 0.495495 0.868611i \(-0.334987\pi\)
0.495495 + 0.868611i \(0.334987\pi\)
\(822\) 9.21737e13 0.00856667
\(823\) 1.08752e16 1.00401 0.502006 0.864864i \(-0.332596\pi\)
0.502006 + 0.864864i \(0.332596\pi\)
\(824\) −1.93953e15 −0.177868
\(825\) −4.01927e15 −0.366142
\(826\) 3.78982e15 0.342948
\(827\) 2.27647e15 0.204636 0.102318 0.994752i \(-0.467374\pi\)
0.102318 + 0.994752i \(0.467374\pi\)
\(828\) −3.42194e15 −0.305566
\(829\) 8.11215e15 0.719592 0.359796 0.933031i \(-0.382846\pi\)
0.359796 + 0.933031i \(0.382846\pi\)
\(830\) 1.90843e16 1.68170
\(831\) 9.95700e15 0.871612
\(832\) 4.95062e15 0.430508
\(833\) −3.81853e16 −3.29875
\(834\) 2.88053e15 0.247206
\(835\) −9.43767e15 −0.804617
\(836\) −2.05526e16 −1.74073
\(837\) 1.51206e15 0.127227
\(838\) 2.66389e16 2.22677
\(839\) −4.64454e15 −0.385702 −0.192851 0.981228i \(-0.561773\pi\)
−0.192851 + 0.981228i \(0.561773\pi\)
\(840\) −2.48171e15 −0.204746
\(841\) −3.54944e15 −0.290926
\(842\) 1.76652e16 1.43847
\(843\) −7.86572e15 −0.636336
\(844\) 4.68764e15 0.376766
\(845\) 4.18303e15 0.334025
\(846\) 7.86079e15 0.623633
\(847\) −1.57739e16 −1.24331
\(848\) 2.13143e16 1.66915
\(849\) −1.07552e16 −0.836812
\(850\) −1.00516e16 −0.777019
\(851\) 8.10262e15 0.622319
\(852\) −6.32152e15 −0.482396
\(853\) −2.47562e16 −1.87700 −0.938500 0.345279i \(-0.887784\pi\)
−0.938500 + 0.345279i \(0.887784\pi\)
\(854\) 4.47659e16 3.37232
\(855\) −5.31133e15 −0.397548
\(856\) −9.52925e13 −0.00708685
\(857\) −2.43666e16 −1.80053 −0.900264 0.435344i \(-0.856627\pi\)
−0.900264 + 0.435344i \(0.856627\pi\)
\(858\) 9.84486e15 0.722819
\(859\) −1.82706e16 −1.33288 −0.666440 0.745559i \(-0.732183\pi\)
−0.666440 + 0.745559i \(0.732183\pi\)
\(860\) 1.02287e16 0.741442
\(861\) 2.17212e16 1.56447
\(862\) −2.16431e16 −1.54892
\(863\) 2.15127e16 1.52980 0.764901 0.644148i \(-0.222788\pi\)
0.764901 + 0.644148i \(0.222788\pi\)
\(864\) −3.53285e15 −0.249632
\(865\) 3.96491e15 0.278384
\(866\) −7.73241e15 −0.539469
\(867\) −2.96335e15 −0.205437
\(868\) 1.52257e16 1.04886
\(869\) −1.36517e16 −0.934495
\(870\) −6.82746e15 −0.464412
\(871\) −2.39149e15 −0.161647
\(872\) −2.62006e15 −0.175983
\(873\) 2.58997e15 0.172869
\(874\) 3.85491e16 2.55683
\(875\) −3.15476e16 −2.07933
\(876\) −7.63891e15 −0.500332
\(877\) −1.62970e16 −1.06074 −0.530372 0.847765i \(-0.677948\pi\)
−0.530372 + 0.847765i \(0.677948\pi\)
\(878\) −2.44019e16 −1.57835
\(879\) −8.41375e15 −0.540818
\(880\) −1.63959e16 −1.04732
\(881\) −2.42995e15 −0.154252 −0.0771259 0.997021i \(-0.524574\pi\)
−0.0771259 + 0.997021i \(0.524574\pi\)
\(882\) −2.01413e16 −1.27060
\(883\) −1.73372e16 −1.08691 −0.543456 0.839438i \(-0.682884\pi\)
−0.543456 + 0.839438i \(0.682884\pi\)
\(884\) 1.10209e16 0.686641
\(885\) 8.61856e14 0.0533638
\(886\) 2.37173e16 1.45942
\(887\) 1.04560e16 0.639418 0.319709 0.947516i \(-0.396415\pi\)
0.319709 + 0.947516i \(0.396415\pi\)
\(888\) 1.33339e15 0.0810374
\(889\) 4.82611e16 2.91499
\(890\) 5.56648e15 0.334146
\(891\) −2.38150e15 −0.142077
\(892\) 1.40282e15 0.0831754
\(893\) −3.96394e16 −2.33584
\(894\) −1.15738e16 −0.677831
\(895\) 2.23201e16 1.29918
\(896\) 1.69585e16 0.981054
\(897\) −8.26563e15 −0.475245
\(898\) 2.50498e16 1.43148
\(899\) −9.80132e15 −0.556681
\(900\) −2.37326e15 −0.133971
\(901\) 3.00264e16 1.68468
\(902\) 4.27017e16 2.38127
\(903\) −2.62813e16 −1.45668
\(904\) 7.59515e15 0.418417
\(905\) 1.68260e16 0.921329
\(906\) −1.06421e16 −0.579191
\(907\) −1.16136e16 −0.628243 −0.314121 0.949383i \(-0.601710\pi\)
−0.314121 + 0.949383i \(0.601710\pi\)
\(908\) 1.18439e16 0.636829
\(909\) 2.71243e14 0.0144963
\(910\) 2.56186e16 1.36090
\(911\) −2.10621e16 −1.11212 −0.556058 0.831144i \(-0.687687\pi\)
−0.556058 + 0.831144i \(0.687687\pi\)
\(912\) 2.13191e16 1.11891
\(913\) −4.31504e16 −2.25110
\(914\) −1.85199e16 −0.960363
\(915\) 1.01804e16 0.524745
\(916\) −1.35265e16 −0.693042
\(917\) −4.67329e16 −2.38008
\(918\) −5.95580e15 −0.301512
\(919\) −1.96640e15 −0.0989545 −0.0494772 0.998775i \(-0.515756\pi\)
−0.0494772 + 0.998775i \(0.515756\pi\)
\(920\) 4.09616e15 0.204901
\(921\) 3.41953e15 0.170035
\(922\) −4.96013e16 −2.45173
\(923\) −1.52695e16 −0.750266
\(924\) −2.39805e16 −1.17129
\(925\) 5.61951e15 0.272847
\(926\) −3.22091e16 −1.55460
\(927\) −4.84331e15 −0.232383
\(928\) 2.29003e16 1.09226
\(929\) −1.42554e16 −0.675917 −0.337958 0.941161i \(-0.609736\pi\)
−0.337958 + 0.941161i \(0.609736\pi\)
\(930\) 7.73525e15 0.364601
\(931\) 1.01566e17 4.75910
\(932\) −1.89466e15 −0.0882561
\(933\) 6.30041e14 0.0291756
\(934\) −2.54459e16 −1.17141
\(935\) −2.30975e16 −1.05707
\(936\) −1.36021e15 −0.0618857
\(937\) 2.82587e16 1.27816 0.639079 0.769141i \(-0.279316\pi\)
0.639079 + 0.769141i \(0.279316\pi\)
\(938\) 1.30136e16 0.585172
\(939\) −1.68033e16 −0.751162
\(940\) 1.80008e16 0.799995
\(941\) 3.12522e15 0.138082 0.0690412 0.997614i \(-0.478006\pi\)
0.0690412 + 0.997614i \(0.478006\pi\)
\(942\) 1.13642e16 0.499181
\(943\) −3.58518e16 −1.56566
\(944\) −3.45939e15 −0.150194
\(945\) −6.19721e15 −0.267498
\(946\) −5.16663e16 −2.21721
\(947\) −8.86812e14 −0.0378361 −0.0189181 0.999821i \(-0.506022\pi\)
−0.0189181 + 0.999821i \(0.506022\pi\)
\(948\) −8.06091e15 −0.341931
\(949\) −1.84516e16 −0.778163
\(950\) 2.67354e16 1.12100
\(951\) 1.29119e16 0.538268
\(952\) 1.40329e16 0.581626
\(953\) 3.73597e16 1.53954 0.769772 0.638319i \(-0.220370\pi\)
0.769772 + 0.638319i \(0.220370\pi\)
\(954\) 1.58378e16 0.648901
\(955\) 2.64182e15 0.107618
\(956\) 3.10039e15 0.125573
\(957\) 1.54371e16 0.621658
\(958\) −4.58542e16 −1.83599
\(959\) −5.42325e14 −0.0215902
\(960\) −6.12642e15 −0.242502
\(961\) −1.43040e16 −0.562960
\(962\) −1.37645e16 −0.538640
\(963\) −2.37960e14 −0.00925891
\(964\) −6.88180e15 −0.266243
\(965\) 2.56091e16 0.985133
\(966\) 4.49787e16 1.72041
\(967\) 6.73354e15 0.256093 0.128047 0.991768i \(-0.459129\pi\)
0.128047 + 0.991768i \(0.459129\pi\)
\(968\) 4.28447e15 0.162025
\(969\) 3.00331e16 1.12933
\(970\) 1.32496e16 0.495401
\(971\) 4.27408e16 1.58905 0.794524 0.607233i \(-0.207720\pi\)
0.794524 + 0.607233i \(0.207720\pi\)
\(972\) −1.40621e15 −0.0519858
\(973\) −1.69483e16 −0.623024
\(974\) −2.01488e16 −0.736504
\(975\) −5.73256e15 −0.208364
\(976\) −4.08629e16 −1.47691
\(977\) −4.16013e16 −1.49516 −0.747579 0.664173i \(-0.768784\pi\)
−0.747579 + 0.664173i \(0.768784\pi\)
\(978\) 3.11349e15 0.111271
\(979\) −1.25860e16 −0.447284
\(980\) −4.61224e16 −1.62993
\(981\) −6.54270e15 −0.229920
\(982\) 7.64753e15 0.267244
\(983\) 2.02106e16 0.702320 0.351160 0.936315i \(-0.385787\pi\)
0.351160 + 0.936315i \(0.385787\pi\)
\(984\) −5.89987e15 −0.203878
\(985\) −2.13917e16 −0.735098
\(986\) 3.86061e16 1.31927
\(987\) −4.62508e16 −1.57172
\(988\) −2.93135e16 −0.990615
\(989\) 4.33784e16 1.45779
\(990\) −1.21831e16 −0.407158
\(991\) 2.16397e15 0.0719194 0.0359597 0.999353i \(-0.488551\pi\)
0.0359597 + 0.999353i \(0.488551\pi\)
\(992\) −2.59451e16 −0.857515
\(993\) 2.90402e16 0.954506
\(994\) 8.30913e16 2.71600
\(995\) 4.20538e16 1.36703
\(996\) −2.54791e16 −0.823677
\(997\) 3.16920e15 0.101889 0.0509444 0.998701i \(-0.483777\pi\)
0.0509444 + 0.998701i \(0.483777\pi\)
\(998\) −4.44944e15 −0.142261
\(999\) 3.32968e15 0.105875
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.12.a.a.1.6 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.a.1.6 26 1.1 even 1 trivial