Properties

Label 17.10.a.a.1.4
Level $17$
Weight $10$
Character 17.1
Self dual yes
Analytic conductor $8.756$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 17.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(8.75560921479\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - 2 x^{4} - 1596 x^{3} + 5754 x^{2} + 488987 x - 2711704\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(18.8209\) of defining polynomial
Character \(\chi\) \(=\) 17.1

$q$-expansion

\(f(q)\) \(=\) \(q+11.8209 q^{2} -67.6654 q^{3} -372.266 q^{4} +2390.67 q^{5} -799.867 q^{6} -11355.8 q^{7} -10452.8 q^{8} -15104.4 q^{9} +O(q^{10})\) \(q+11.8209 q^{2} -67.6654 q^{3} -372.266 q^{4} +2390.67 q^{5} -799.867 q^{6} -11355.8 q^{7} -10452.8 q^{8} -15104.4 q^{9} +28259.9 q^{10} -17740.6 q^{11} +25189.5 q^{12} -76108.0 q^{13} -134236. q^{14} -161765. q^{15} +67038.0 q^{16} -83521.0 q^{17} -178548. q^{18} +661811. q^{19} -889964. q^{20} +768396. q^{21} -209710. q^{22} -1.64772e6 q^{23} +707295. q^{24} +3.76216e6 q^{25} -899667. q^{26} +2.35390e6 q^{27} +4.22738e6 q^{28} +1.49876e6 q^{29} -1.91222e6 q^{30} -4.40242e6 q^{31} +6.14430e6 q^{32} +1.20042e6 q^{33} -987295. q^{34} -2.71480e7 q^{35} +5.62285e6 q^{36} -5.62188e6 q^{37} +7.82322e6 q^{38} +5.14988e6 q^{39} -2.49892e7 q^{40} +2.29725e7 q^{41} +9.08315e6 q^{42} -7.92989e6 q^{43} +6.60422e6 q^{44} -3.61096e7 q^{45} -1.94776e7 q^{46} -5.69337e7 q^{47} -4.53615e6 q^{48} +8.86009e7 q^{49} +4.44722e7 q^{50} +5.65148e6 q^{51} +2.83324e7 q^{52} +2.56355e6 q^{53} +2.78253e7 q^{54} -4.24119e7 q^{55} +1.18700e8 q^{56} -4.47817e7 q^{57} +1.77167e7 q^{58} -6.87685e7 q^{59} +6.02197e7 q^{60} -1.09661e8 q^{61} -5.20406e7 q^{62} +1.71523e8 q^{63} +3.83079e7 q^{64} -1.81949e8 q^{65} +1.41901e7 q^{66} +1.44824e8 q^{67} +3.10920e7 q^{68} +1.11494e8 q^{69} -3.20914e8 q^{70} -6.07354e7 q^{71} +1.57884e8 q^{72} -1.68554e8 q^{73} -6.64557e7 q^{74} -2.54568e8 q^{75} -2.46370e8 q^{76} +2.01459e8 q^{77} +6.08763e7 q^{78} +1.00310e8 q^{79} +1.60265e8 q^{80} +1.38022e8 q^{81} +2.71557e8 q^{82} -5.82713e8 q^{83} -2.86048e8 q^{84} -1.99671e8 q^{85} -9.37386e7 q^{86} -1.01414e8 q^{87} +1.85440e8 q^{88} -1.56066e7 q^{89} -4.26848e8 q^{90} +8.64268e8 q^{91} +6.13390e8 q^{92} +2.97891e8 q^{93} -6.73009e8 q^{94} +1.58217e9 q^{95} -4.15757e8 q^{96} +1.64798e9 q^{97} +1.04734e9 q^{98} +2.67961e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 33q^{2} - 236q^{3} + 853q^{4} + 1480q^{5} + 7578q^{6} - 13202q^{7} - 42423q^{8} + 10981q^{9} + O(q^{10}) \) \( 5q - 33q^{2} - 236q^{3} + 853q^{4} + 1480q^{5} + 7578q^{6} - 13202q^{7} - 42423q^{8} + 10981q^{9} - 89328q^{10} - 68036q^{11} - 406010q^{12} - 158862q^{13} - 84700q^{14} - 687324q^{15} + 350225q^{16} - 417605q^{17} - 1911585q^{18} - 370992q^{19} + 1632640q^{20} + 1783880q^{21} + 122290q^{22} + 1645870q^{23} + 9678702q^{24} + 3270239q^{25} + 734846q^{26} - 2998268q^{27} + 183372q^{28} + 3668616q^{29} + 17048544q^{30} - 7262362q^{31} - 5605919q^{32} - 11334900q^{33} + 2756193q^{34} - 26503988q^{35} + 49782133q^{36} - 31420708q^{37} + 18513700q^{38} - 42449884q^{39} - 53930464q^{40} - 7996938q^{41} - 44519496q^{42} - 56908268q^{43} + 43323054q^{44} + 12799536q^{45} - 32063472q^{46} - 16903336q^{47} - 102794498q^{48} - 11784059q^{49} + 85921093q^{50} + 19710956q^{51} + 173619082q^{52} - 83362982q^{53} + 386329164q^{54} + 6363364q^{55} + 317409372q^{56} + 136615904q^{57} + 64577488q^{58} - 37946604q^{59} - 223158912q^{60} - 77685452q^{61} + 324855300q^{62} - 191945278q^{63} + 131623105q^{64} - 40321288q^{65} + 298037676q^{66} - 304503600q^{67} - 71243413q^{68} - 333409272q^{69} - 122787392q^{70} - 476602922q^{71} - 1301701911q^{72} - 289980486q^{73} + 262289012q^{74} - 153685772q^{75} - 1031276084q^{76} - 143385648q^{77} + 691646196q^{78} - 828240610q^{79} + 912750944q^{80} + 891328609q^{81} - 1109615654q^{82} + 194681148q^{83} + 1541719592q^{84} - 123611080q^{85} + 1164707144q^{86} + 158149884q^{87} - 1017979978q^{88} + 376848106q^{89} - 2240087472q^{90} + 194543664q^{91} + 2506713088q^{92} + 3494835920q^{93} - 2244811104q^{94} + 1498679864q^{95} + 2935047582q^{96} + 692035246q^{97} + 871744055q^{98} + 2027106408q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.8209 0.522416 0.261208 0.965283i \(-0.415879\pi\)
0.261208 + 0.965283i \(0.415879\pi\)
\(3\) −67.6654 −0.482304 −0.241152 0.970487i \(-0.577525\pi\)
−0.241152 + 0.970487i \(0.577525\pi\)
\(4\) −372.266 −0.727082
\(5\) 2390.67 1.71062 0.855311 0.518115i \(-0.173366\pi\)
0.855311 + 0.518115i \(0.173366\pi\)
\(6\) −799.867 −0.251963
\(7\) −11355.8 −1.78763 −0.893814 0.448438i \(-0.851980\pi\)
−0.893814 + 0.448438i \(0.851980\pi\)
\(8\) −10452.8 −0.902255
\(9\) −15104.4 −0.767383
\(10\) 28259.9 0.893656
\(11\) −17740.6 −0.365343 −0.182672 0.983174i \(-0.558475\pi\)
−0.182672 + 0.983174i \(0.558475\pi\)
\(12\) 25189.5 0.350675
\(13\) −76108.0 −0.739069 −0.369535 0.929217i \(-0.620483\pi\)
−0.369535 + 0.929217i \(0.620483\pi\)
\(14\) −134236. −0.933885
\(15\) −161765. −0.825040
\(16\) 67038.0 0.255730
\(17\) −83521.0 −0.242536
\(18\) −178548. −0.400893
\(19\) 661811. 1.16505 0.582523 0.812814i \(-0.302066\pi\)
0.582523 + 0.812814i \(0.302066\pi\)
\(20\) −889964. −1.24376
\(21\) 768396. 0.862180
\(22\) −209710. −0.190861
\(23\) −1.64772e6 −1.22774 −0.613872 0.789405i \(-0.710389\pi\)
−0.613872 + 0.789405i \(0.710389\pi\)
\(24\) 707295. 0.435161
\(25\) 3.76216e6 1.92623
\(26\) −899667. −0.386102
\(27\) 2.35390e6 0.852416
\(28\) 4.22738e6 1.29975
\(29\) 1.49876e6 0.393496 0.196748 0.980454i \(-0.436962\pi\)
0.196748 + 0.980454i \(0.436962\pi\)
\(30\) −1.91222e6 −0.431014
\(31\) −4.40242e6 −0.856177 −0.428089 0.903737i \(-0.640813\pi\)
−0.428089 + 0.903737i \(0.640813\pi\)
\(32\) 6.14430e6 1.03585
\(33\) 1.20042e6 0.176207
\(34\) −987295. −0.126704
\(35\) −2.71480e7 −3.05796
\(36\) 5.62285e6 0.557950
\(37\) −5.62188e6 −0.493144 −0.246572 0.969125i \(-0.579304\pi\)
−0.246572 + 0.969125i \(0.579304\pi\)
\(38\) 7.82322e6 0.608638
\(39\) 5.14988e6 0.356456
\(40\) −2.49892e7 −1.54342
\(41\) 2.29725e7 1.26964 0.634821 0.772659i \(-0.281074\pi\)
0.634821 + 0.772659i \(0.281074\pi\)
\(42\) 9.08315e6 0.450417
\(43\) −7.92989e6 −0.353720 −0.176860 0.984236i \(-0.556594\pi\)
−0.176860 + 0.984236i \(0.556594\pi\)
\(44\) 6.60422e6 0.265634
\(45\) −3.61096e7 −1.31270
\(46\) −1.94776e7 −0.641393
\(47\) −5.69337e7 −1.70188 −0.850940 0.525262i \(-0.823967\pi\)
−0.850940 + 0.525262i \(0.823967\pi\)
\(48\) −4.53615e6 −0.123339
\(49\) 8.86009e7 2.19561
\(50\) 4.44722e7 1.00629
\(51\) 5.65148e6 0.116976
\(52\) 2.83324e7 0.537364
\(53\) 2.56355e6 0.0446272 0.0223136 0.999751i \(-0.492897\pi\)
0.0223136 + 0.999751i \(0.492897\pi\)
\(54\) 2.78253e7 0.445316
\(55\) −4.24119e7 −0.624964
\(56\) 1.18700e8 1.61290
\(57\) −4.47817e7 −0.561906
\(58\) 1.77167e7 0.205569
\(59\) −6.87685e7 −0.738849 −0.369424 0.929261i \(-0.620445\pi\)
−0.369424 + 0.929261i \(0.620445\pi\)
\(60\) 6.02197e7 0.599872
\(61\) −1.09661e8 −1.01407 −0.507036 0.861925i \(-0.669259\pi\)
−0.507036 + 0.861925i \(0.669259\pi\)
\(62\) −5.20406e7 −0.447280
\(63\) 1.71523e8 1.37179
\(64\) 3.83079e7 0.285416
\(65\) −1.81949e8 −1.26427
\(66\) 1.41901e7 0.0920531
\(67\) 1.44824e8 0.878017 0.439008 0.898483i \(-0.355330\pi\)
0.439008 + 0.898483i \(0.355330\pi\)
\(68\) 3.10920e7 0.176343
\(69\) 1.11494e8 0.592147
\(70\) −3.20914e8 −1.59752
\(71\) −6.07354e7 −0.283648 −0.141824 0.989892i \(-0.545297\pi\)
−0.141824 + 0.989892i \(0.545297\pi\)
\(72\) 1.57884e8 0.692375
\(73\) −1.68554e8 −0.694684 −0.347342 0.937739i \(-0.612916\pi\)
−0.347342 + 0.937739i \(0.612916\pi\)
\(74\) −6.64557e7 −0.257626
\(75\) −2.54568e8 −0.929027
\(76\) −2.46370e8 −0.847083
\(77\) 2.01459e8 0.653098
\(78\) 6.08763e7 0.186218
\(79\) 1.00310e8 0.289749 0.144875 0.989450i \(-0.453722\pi\)
0.144875 + 0.989450i \(0.453722\pi\)
\(80\) 1.60265e8 0.437456
\(81\) 1.38022e8 0.356259
\(82\) 2.71557e8 0.663282
\(83\) −5.82713e8 −1.34773 −0.673865 0.738854i \(-0.735367\pi\)
−0.673865 + 0.738854i \(0.735367\pi\)
\(84\) −2.86048e8 −0.626876
\(85\) −1.99671e8 −0.414887
\(86\) −9.37386e7 −0.184789
\(87\) −1.01414e8 −0.189785
\(88\) 1.85440e8 0.329633
\(89\) −1.56066e7 −0.0263665 −0.0131832 0.999913i \(-0.504196\pi\)
−0.0131832 + 0.999913i \(0.504196\pi\)
\(90\) −4.26848e8 −0.685776
\(91\) 8.64268e8 1.32118
\(92\) 6.13390e8 0.892671
\(93\) 2.97891e8 0.412938
\(94\) −6.73009e8 −0.889089
\(95\) 1.58217e9 1.99295
\(96\) −4.15757e8 −0.499596
\(97\) 1.64798e9 1.89008 0.945040 0.326956i \(-0.106023\pi\)
0.945040 + 0.326956i \(0.106023\pi\)
\(98\) 1.04734e9 1.14702
\(99\) 2.67961e8 0.280358
\(100\) −1.40052e9 −1.40052
\(101\) −9.32619e8 −0.891780 −0.445890 0.895088i \(-0.647113\pi\)
−0.445890 + 0.895088i \(0.647113\pi\)
\(102\) 6.68057e7 0.0611101
\(103\) −1.88493e9 −1.65017 −0.825085 0.565009i \(-0.808873\pi\)
−0.825085 + 0.565009i \(0.808873\pi\)
\(104\) 7.95544e8 0.666829
\(105\) 1.83698e9 1.47486
\(106\) 3.03035e7 0.0233140
\(107\) −9.44012e7 −0.0696226 −0.0348113 0.999394i \(-0.511083\pi\)
−0.0348113 + 0.999394i \(0.511083\pi\)
\(108\) −8.76278e8 −0.619776
\(109\) −1.72481e9 −1.17037 −0.585183 0.810901i \(-0.698977\pi\)
−0.585183 + 0.810901i \(0.698977\pi\)
\(110\) −5.01347e8 −0.326491
\(111\) 3.80406e8 0.237845
\(112\) −7.61271e8 −0.457149
\(113\) 1.02688e9 0.592471 0.296235 0.955115i \(-0.404269\pi\)
0.296235 + 0.955115i \(0.404269\pi\)
\(114\) −5.29361e8 −0.293549
\(115\) −3.93915e9 −2.10021
\(116\) −5.57936e8 −0.286104
\(117\) 1.14957e9 0.567149
\(118\) −8.12907e8 −0.385986
\(119\) 9.48449e8 0.433563
\(120\) 1.69091e9 0.744396
\(121\) −2.04322e9 −0.866524
\(122\) −1.29630e9 −0.529767
\(123\) −1.55445e9 −0.612354
\(124\) 1.63887e9 0.622511
\(125\) 4.32481e9 1.58442
\(126\) 2.02756e9 0.716647
\(127\) 2.57593e9 0.878653 0.439327 0.898327i \(-0.355217\pi\)
0.439327 + 0.898327i \(0.355217\pi\)
\(128\) −2.69305e9 −0.886746
\(129\) 5.36579e8 0.170600
\(130\) −2.15080e9 −0.660474
\(131\) −1.67438e9 −0.496746 −0.248373 0.968664i \(-0.579896\pi\)
−0.248373 + 0.968664i \(0.579896\pi\)
\(132\) −4.46877e8 −0.128117
\(133\) −7.51540e9 −2.08267
\(134\) 1.71195e9 0.458690
\(135\) 5.62740e9 1.45816
\(136\) 8.73031e8 0.218829
\(137\) 9.77626e8 0.237099 0.118550 0.992948i \(-0.462176\pi\)
0.118550 + 0.992948i \(0.462176\pi\)
\(138\) 1.31796e9 0.309347
\(139\) −5.07318e8 −0.115269 −0.0576346 0.998338i \(-0.518356\pi\)
−0.0576346 + 0.998338i \(0.518356\pi\)
\(140\) 1.01063e10 2.22338
\(141\) 3.85244e9 0.820824
\(142\) −7.17948e8 −0.148182
\(143\) 1.35020e9 0.270014
\(144\) −1.01257e9 −0.196242
\(145\) 3.58303e9 0.673123
\(146\) −1.99247e9 −0.362914
\(147\) −5.99522e9 −1.05895
\(148\) 2.09283e9 0.358556
\(149\) −3.39357e9 −0.564052 −0.282026 0.959407i \(-0.591006\pi\)
−0.282026 + 0.959407i \(0.591006\pi\)
\(150\) −3.00923e9 −0.485339
\(151\) 2.54210e9 0.397921 0.198961 0.980007i \(-0.436243\pi\)
0.198961 + 0.980007i \(0.436243\pi\)
\(152\) −6.91780e9 −1.05117
\(153\) 1.26153e9 0.186118
\(154\) 2.38143e9 0.341189
\(155\) −1.05247e10 −1.46460
\(156\) −1.91712e9 −0.259173
\(157\) −8.59628e9 −1.12918 −0.564588 0.825373i \(-0.690965\pi\)
−0.564588 + 0.825373i \(0.690965\pi\)
\(158\) 1.18576e9 0.151370
\(159\) −1.73464e8 −0.0215239
\(160\) 1.46890e10 1.77195
\(161\) 1.87112e10 2.19475
\(162\) 1.63155e9 0.186115
\(163\) 7.22903e8 0.0802113 0.0401057 0.999195i \(-0.487231\pi\)
0.0401057 + 0.999195i \(0.487231\pi\)
\(164\) −8.55189e9 −0.923134
\(165\) 2.86982e9 0.301423
\(166\) −6.88820e9 −0.704076
\(167\) 5.77488e9 0.574538 0.287269 0.957850i \(-0.407253\pi\)
0.287269 + 0.957850i \(0.407253\pi\)
\(168\) −8.03192e9 −0.777906
\(169\) −4.81207e9 −0.453776
\(170\) −2.36029e9 −0.216743
\(171\) −9.99625e9 −0.894036
\(172\) 2.95203e9 0.257183
\(173\) −2.26224e9 −0.192014 −0.0960068 0.995381i \(-0.530607\pi\)
−0.0960068 + 0.995381i \(0.530607\pi\)
\(174\) −1.19881e9 −0.0991466
\(175\) −4.27224e10 −3.44338
\(176\) −1.18929e9 −0.0934291
\(177\) 4.65325e9 0.356350
\(178\) −1.84484e8 −0.0137743
\(179\) −3.69322e9 −0.268885 −0.134443 0.990921i \(-0.542924\pi\)
−0.134443 + 0.990921i \(0.542924\pi\)
\(180\) 1.34424e10 0.954441
\(181\) 1.91251e10 1.32449 0.662247 0.749285i \(-0.269603\pi\)
0.662247 + 0.749285i \(0.269603\pi\)
\(182\) 1.02164e10 0.690206
\(183\) 7.42027e9 0.489091
\(184\) 1.72233e10 1.10774
\(185\) −1.34400e10 −0.843582
\(186\) 3.52135e9 0.215725
\(187\) 1.48171e9 0.0886088
\(188\) 2.11945e10 1.23741
\(189\) −2.67305e10 −1.52380
\(190\) 1.87027e10 1.04115
\(191\) −4.41416e9 −0.239993 −0.119996 0.992774i \(-0.538288\pi\)
−0.119996 + 0.992774i \(0.538288\pi\)
\(192\) −2.59212e9 −0.137657
\(193\) −5.98467e9 −0.310479 −0.155239 0.987877i \(-0.549615\pi\)
−0.155239 + 0.987877i \(0.549615\pi\)
\(194\) 1.94807e10 0.987407
\(195\) 1.23116e10 0.609762
\(196\) −3.29831e10 −1.59639
\(197\) 2.74494e10 1.29848 0.649240 0.760584i \(-0.275087\pi\)
0.649240 + 0.760584i \(0.275087\pi\)
\(198\) 3.16754e9 0.146463
\(199\) 3.34164e10 1.51050 0.755250 0.655436i \(-0.227515\pi\)
0.755250 + 0.655436i \(0.227515\pi\)
\(200\) −3.93253e10 −1.73795
\(201\) −9.79955e9 −0.423471
\(202\) −1.10244e10 −0.465880
\(203\) −1.70196e10 −0.703425
\(204\) −2.10385e9 −0.0850511
\(205\) 5.49197e10 2.17188
\(206\) −2.22817e10 −0.862075
\(207\) 2.48878e10 0.942150
\(208\) −5.10212e9 −0.189002
\(209\) −1.17409e10 −0.425641
\(210\) 2.17148e10 0.770493
\(211\) 4.50084e9 0.156323 0.0781615 0.996941i \(-0.475095\pi\)
0.0781615 + 0.996941i \(0.475095\pi\)
\(212\) −9.54321e8 −0.0324477
\(213\) 4.10969e9 0.136805
\(214\) −1.11591e9 −0.0363720
\(215\) −1.89577e10 −0.605081
\(216\) −2.46050e10 −0.769097
\(217\) 4.99930e10 1.53053
\(218\) −2.03888e10 −0.611418
\(219\) 1.14053e10 0.335049
\(220\) 1.57885e10 0.454400
\(221\) 6.35662e9 0.179251
\(222\) 4.49675e9 0.124254
\(223\) −4.59996e10 −1.24561 −0.622805 0.782377i \(-0.714007\pi\)
−0.622805 + 0.782377i \(0.714007\pi\)
\(224\) −6.97736e10 −1.85172
\(225\) −5.68252e10 −1.47815
\(226\) 1.21387e10 0.309516
\(227\) 1.68405e10 0.420958 0.210479 0.977598i \(-0.432498\pi\)
0.210479 + 0.977598i \(0.432498\pi\)
\(228\) 1.66707e10 0.408552
\(229\) 4.54814e10 1.09288 0.546442 0.837497i \(-0.315982\pi\)
0.546442 + 0.837497i \(0.315982\pi\)
\(230\) −4.65644e10 −1.09718
\(231\) −1.36318e10 −0.314992
\(232\) −1.56663e10 −0.355034
\(233\) −5.00961e10 −1.11353 −0.556766 0.830669i \(-0.687958\pi\)
−0.556766 + 0.830669i \(0.687958\pi\)
\(234\) 1.35889e10 0.296288
\(235\) −1.36110e11 −2.91127
\(236\) 2.56002e10 0.537204
\(237\) −6.78751e9 −0.139747
\(238\) 1.12115e10 0.226500
\(239\) 4.75443e10 0.942558 0.471279 0.881984i \(-0.343792\pi\)
0.471279 + 0.881984i \(0.343792\pi\)
\(240\) −1.08444e10 −0.210987
\(241\) 8.24645e10 1.57467 0.787337 0.616523i \(-0.211459\pi\)
0.787337 + 0.616523i \(0.211459\pi\)
\(242\) −2.41527e10 −0.452686
\(243\) −5.56712e10 −1.02424
\(244\) 4.08231e10 0.737313
\(245\) 2.11815e11 3.75586
\(246\) −1.83750e10 −0.319903
\(247\) −5.03691e10 −0.861049
\(248\) 4.60177e10 0.772490
\(249\) 3.94295e10 0.650016
\(250\) 5.11232e10 0.827728
\(251\) −5.90523e10 −0.939085 −0.469543 0.882910i \(-0.655581\pi\)
−0.469543 + 0.882910i \(0.655581\pi\)
\(252\) −6.38520e10 −0.997407
\(253\) 2.92315e10 0.448548
\(254\) 3.04499e10 0.459022
\(255\) 1.35108e10 0.200102
\(256\) −5.14479e10 −0.748666
\(257\) 3.35982e10 0.480415 0.240207 0.970722i \(-0.422785\pi\)
0.240207 + 0.970722i \(0.422785\pi\)
\(258\) 6.34286e9 0.0891244
\(259\) 6.38410e10 0.881557
\(260\) 6.77333e10 0.919226
\(261\) −2.26378e10 −0.301962
\(262\) −1.97928e10 −0.259508
\(263\) 3.91693e9 0.0504830 0.0252415 0.999681i \(-0.491965\pi\)
0.0252415 + 0.999681i \(0.491965\pi\)
\(264\) −1.25478e10 −0.158983
\(265\) 6.12859e9 0.0763403
\(266\) −8.88390e10 −1.08802
\(267\) 1.05602e9 0.0127167
\(268\) −5.39129e10 −0.638390
\(269\) 6.33897e10 0.738131 0.369065 0.929403i \(-0.379678\pi\)
0.369065 + 0.929403i \(0.379678\pi\)
\(270\) 6.65210e10 0.761767
\(271\) 4.27576e10 0.481561 0.240781 0.970580i \(-0.422597\pi\)
0.240781 + 0.970580i \(0.422597\pi\)
\(272\) −5.59908e9 −0.0620235
\(273\) −5.84811e10 −0.637211
\(274\) 1.15564e10 0.123864
\(275\) −6.67430e10 −0.703734
\(276\) −4.15053e10 −0.430539
\(277\) −1.32848e11 −1.35580 −0.677899 0.735155i \(-0.737109\pi\)
−0.677899 + 0.735155i \(0.737109\pi\)
\(278\) −5.99696e9 −0.0602185
\(279\) 6.64958e10 0.657015
\(280\) 2.83773e11 2.75905
\(281\) −1.43951e11 −1.37733 −0.688663 0.725082i \(-0.741802\pi\)
−0.688663 + 0.725082i \(0.741802\pi\)
\(282\) 4.55394e10 0.428812
\(283\) 6.72871e10 0.623581 0.311790 0.950151i \(-0.399071\pi\)
0.311790 + 0.950151i \(0.399071\pi\)
\(284\) 2.26097e10 0.206235
\(285\) −1.07058e11 −0.961209
\(286\) 1.59606e10 0.141060
\(287\) −2.60872e11 −2.26965
\(288\) −9.28060e10 −0.794895
\(289\) 6.97576e9 0.0588235
\(290\) 4.23547e10 0.351650
\(291\) −1.11511e11 −0.911593
\(292\) 6.27470e10 0.505092
\(293\) 8.76124e10 0.694482 0.347241 0.937776i \(-0.387119\pi\)
0.347241 + 0.937776i \(0.387119\pi\)
\(294\) −7.08690e10 −0.553214
\(295\) −1.64403e11 −1.26389
\(296\) 5.87645e10 0.444941
\(297\) −4.17596e10 −0.311424
\(298\) −4.01152e10 −0.294670
\(299\) 1.25405e11 0.907389
\(300\) 9.47671e10 0.675479
\(301\) 9.00504e10 0.632319
\(302\) 3.00500e10 0.207880
\(303\) 6.31060e10 0.430109
\(304\) 4.43665e10 0.297936
\(305\) −2.62163e11 −1.73469
\(306\) 1.49125e10 0.0972308
\(307\) 2.30476e11 1.48083 0.740413 0.672153i \(-0.234630\pi\)
0.740413 + 0.672153i \(0.234630\pi\)
\(308\) −7.49963e10 −0.474855
\(309\) 1.27545e11 0.795884
\(310\) −1.24412e11 −0.765128
\(311\) 2.89033e10 0.175197 0.0875984 0.996156i \(-0.472081\pi\)
0.0875984 + 0.996156i \(0.472081\pi\)
\(312\) −5.38308e10 −0.321614
\(313\) −2.95929e11 −1.74276 −0.871382 0.490605i \(-0.836776\pi\)
−0.871382 + 0.490605i \(0.836776\pi\)
\(314\) −1.01616e11 −0.589900
\(315\) 4.10054e11 2.34662
\(316\) −3.73420e10 −0.210671
\(317\) −3.12812e11 −1.73987 −0.869934 0.493168i \(-0.835839\pi\)
−0.869934 + 0.493168i \(0.835839\pi\)
\(318\) −2.05050e9 −0.0112444
\(319\) −2.65888e10 −0.143761
\(320\) 9.15814e10 0.488239
\(321\) 6.38769e9 0.0335793
\(322\) 2.21184e11 1.14657
\(323\) −5.52751e10 −0.282565
\(324\) −5.13809e10 −0.259029
\(325\) −2.86331e11 −1.42362
\(326\) 8.54537e9 0.0419037
\(327\) 1.16710e11 0.564473
\(328\) −2.40128e11 −1.14554
\(329\) 6.46529e11 3.04233
\(330\) 3.39239e10 0.157468
\(331\) 8.91016e9 0.0408000 0.0204000 0.999792i \(-0.493506\pi\)
0.0204000 + 0.999792i \(0.493506\pi\)
\(332\) 2.16924e11 0.979910
\(333\) 8.49150e10 0.378430
\(334\) 6.82644e10 0.300148
\(335\) 3.46225e11 1.50195
\(336\) 5.15117e10 0.220485
\(337\) 2.90899e10 0.122859 0.0614296 0.998111i \(-0.480434\pi\)
0.0614296 + 0.998111i \(0.480434\pi\)
\(338\) −5.68831e10 −0.237060
\(339\) −6.94843e10 −0.285751
\(340\) 7.43306e10 0.301657
\(341\) 7.81015e10 0.312799
\(342\) −1.18165e11 −0.467058
\(343\) −5.47888e11 −2.13731
\(344\) 8.28899e10 0.319145
\(345\) 2.66544e11 1.01294
\(346\) −2.67418e10 −0.100311
\(347\) 1.09628e11 0.405918 0.202959 0.979187i \(-0.434944\pi\)
0.202959 + 0.979187i \(0.434944\pi\)
\(348\) 3.77530e10 0.137989
\(349\) −6.35598e10 −0.229334 −0.114667 0.993404i \(-0.536580\pi\)
−0.114667 + 0.993404i \(0.536580\pi\)
\(350\) −5.05018e11 −1.79887
\(351\) −1.79151e11 −0.629995
\(352\) −1.09004e11 −0.378442
\(353\) 7.79401e10 0.267162 0.133581 0.991038i \(-0.457352\pi\)
0.133581 + 0.991038i \(0.457352\pi\)
\(354\) 5.50057e10 0.186163
\(355\) −1.45198e11 −0.485214
\(356\) 5.80979e9 0.0191706
\(357\) −6.41772e10 −0.209109
\(358\) −4.36573e10 −0.140470
\(359\) 3.06852e11 0.974998 0.487499 0.873124i \(-0.337909\pi\)
0.487499 + 0.873124i \(0.337909\pi\)
\(360\) 3.77447e11 1.18439
\(361\) 1.15306e11 0.357331
\(362\) 2.26076e11 0.691937
\(363\) 1.38255e11 0.417928
\(364\) −3.21738e11 −0.960607
\(365\) −4.02957e11 −1.18834
\(366\) 8.77144e10 0.255509
\(367\) −2.13117e11 −0.613225 −0.306613 0.951834i \(-0.599196\pi\)
−0.306613 + 0.951834i \(0.599196\pi\)
\(368\) −1.10460e11 −0.313971
\(369\) −3.46986e11 −0.974302
\(370\) −1.58874e11 −0.440701
\(371\) −2.91112e10 −0.0797769
\(372\) −1.10895e11 −0.300240
\(373\) 2.27081e11 0.607423 0.303712 0.952764i \(-0.401774\pi\)
0.303712 + 0.952764i \(0.401774\pi\)
\(374\) 1.75152e10 0.0462906
\(375\) −2.92640e11 −0.764175
\(376\) 5.95119e11 1.53553
\(377\) −1.14067e11 −0.290821
\(378\) −3.15979e11 −0.796059
\(379\) 3.53633e11 0.880391 0.440196 0.897902i \(-0.354909\pi\)
0.440196 + 0.897902i \(0.354909\pi\)
\(380\) −5.88988e11 −1.44904
\(381\) −1.74301e11 −0.423778
\(382\) −5.21794e10 −0.125376
\(383\) −6.69512e11 −1.58988 −0.794939 0.606689i \(-0.792497\pi\)
−0.794939 + 0.606689i \(0.792497\pi\)
\(384\) 1.82226e11 0.427681
\(385\) 4.81621e11 1.11720
\(386\) −7.07443e10 −0.162199
\(387\) 1.19776e11 0.271438
\(388\) −6.13488e11 −1.37424
\(389\) 6.62054e11 1.46595 0.732976 0.680254i \(-0.238131\pi\)
0.732976 + 0.680254i \(0.238131\pi\)
\(390\) 1.45535e11 0.318549
\(391\) 1.37619e11 0.297772
\(392\) −9.26131e11 −1.98100
\(393\) 1.13298e11 0.239583
\(394\) 3.24477e11 0.678346
\(395\) 2.39808e11 0.495651
\(396\) −9.97527e10 −0.203843
\(397\) −6.61102e11 −1.33571 −0.667854 0.744293i \(-0.732787\pi\)
−0.667854 + 0.744293i \(0.732787\pi\)
\(398\) 3.95013e11 0.789110
\(399\) 5.08533e11 1.00448
\(400\) 2.52208e11 0.492593
\(401\) 6.56727e11 1.26834 0.634169 0.773195i \(-0.281342\pi\)
0.634169 + 0.773195i \(0.281342\pi\)
\(402\) −1.15840e11 −0.221228
\(403\) 3.35059e11 0.632774
\(404\) 3.47182e11 0.648397
\(405\) 3.29964e11 0.609424
\(406\) −2.01187e11 −0.367480
\(407\) 9.97354e10 0.180167
\(408\) −5.90740e10 −0.105542
\(409\) −4.36145e11 −0.770684 −0.385342 0.922774i \(-0.625917\pi\)
−0.385342 + 0.922774i \(0.625917\pi\)
\(410\) 6.49201e11 1.13462
\(411\) −6.61515e10 −0.114354
\(412\) 7.01697e11 1.19981
\(413\) 7.80923e11 1.32079
\(414\) 2.94197e11 0.492194
\(415\) −1.39307e12 −2.30546
\(416\) −4.67631e11 −0.765566
\(417\) 3.43279e10 0.0555948
\(418\) −1.38789e11 −0.222362
\(419\) 6.66344e11 1.05617 0.528087 0.849190i \(-0.322909\pi\)
0.528087 + 0.849190i \(0.322909\pi\)
\(420\) −6.83844e11 −1.07235
\(421\) −4.68417e11 −0.726713 −0.363357 0.931650i \(-0.618369\pi\)
−0.363357 + 0.931650i \(0.618369\pi\)
\(422\) 5.32041e10 0.0816656
\(423\) 8.59949e11 1.30599
\(424\) −2.67964e10 −0.0402651
\(425\) −3.14220e11 −0.467179
\(426\) 4.85803e10 0.0714688
\(427\) 1.24529e12 1.81278
\(428\) 3.51423e10 0.0506213
\(429\) −9.13619e10 −0.130229
\(430\) −2.24098e11 −0.316104
\(431\) −3.43298e11 −0.479207 −0.239604 0.970871i \(-0.577018\pi\)
−0.239604 + 0.970871i \(0.577018\pi\)
\(432\) 1.57801e11 0.217988
\(433\) −1.30884e12 −1.78933 −0.894666 0.446735i \(-0.852587\pi\)
−0.894666 + 0.446735i \(0.852587\pi\)
\(434\) 5.90964e11 0.799571
\(435\) −2.42447e11 −0.324650
\(436\) 6.42088e11 0.850952
\(437\) −1.09048e12 −1.43038
\(438\) 1.34821e11 0.175035
\(439\) 5.48226e11 0.704481 0.352241 0.935909i \(-0.385420\pi\)
0.352241 + 0.935909i \(0.385420\pi\)
\(440\) 4.43324e11 0.563877
\(441\) −1.33826e12 −1.68488
\(442\) 7.51411e10 0.0936434
\(443\) −1.00051e10 −0.0123426 −0.00617130 0.999981i \(-0.501964\pi\)
−0.00617130 + 0.999981i \(0.501964\pi\)
\(444\) −1.41612e11 −0.172933
\(445\) −3.73101e10 −0.0451031
\(446\) −5.43758e11 −0.650727
\(447\) 2.29628e11 0.272045
\(448\) −4.35017e11 −0.510218
\(449\) −8.97323e10 −0.104193 −0.0520967 0.998642i \(-0.516590\pi\)
−0.0520967 + 0.998642i \(0.516590\pi\)
\(450\) −6.71726e11 −0.772211
\(451\) −4.07546e11 −0.463855
\(452\) −3.82272e11 −0.430775
\(453\) −1.72012e11 −0.191919
\(454\) 1.99071e11 0.219915
\(455\) 2.06618e12 2.26004
\(456\) 4.68096e11 0.506983
\(457\) −1.13166e12 −1.21365 −0.606823 0.794837i \(-0.707556\pi\)
−0.606823 + 0.794837i \(0.707556\pi\)
\(458\) 5.37632e11 0.570940
\(459\) −1.96600e11 −0.206741
\(460\) 1.46641e12 1.52702
\(461\) −1.76123e12 −1.81620 −0.908098 0.418757i \(-0.862466\pi\)
−0.908098 + 0.418757i \(0.862466\pi\)
\(462\) −1.61140e11 −0.164557
\(463\) −6.00361e11 −0.607152 −0.303576 0.952807i \(-0.598181\pi\)
−0.303576 + 0.952807i \(0.598181\pi\)
\(464\) 1.00474e11 0.100629
\(465\) 7.12159e11 0.706380
\(466\) −5.92182e11 −0.581727
\(467\) −7.30949e11 −0.711150 −0.355575 0.934648i \(-0.615715\pi\)
−0.355575 + 0.934648i \(0.615715\pi\)
\(468\) −4.27944e11 −0.412364
\(469\) −1.64459e12 −1.56957
\(470\) −1.60894e12 −1.52090
\(471\) 5.81671e11 0.544607
\(472\) 7.18826e11 0.666630
\(473\) 1.40681e11 0.129229
\(474\) −8.02347e10 −0.0730062
\(475\) 2.48984e12 2.24414
\(476\) −3.53075e11 −0.315236
\(477\) −3.87208e10 −0.0342462
\(478\) 5.62018e11 0.492407
\(479\) −1.76035e12 −1.52788 −0.763938 0.645289i \(-0.776737\pi\)
−0.763938 + 0.645289i \(0.776737\pi\)
\(480\) −9.93936e11 −0.854619
\(481\) 4.27870e11 0.364467
\(482\) 9.74807e11 0.822634
\(483\) −1.26610e12 −1.05854
\(484\) 7.60621e11 0.630034
\(485\) 3.93978e12 3.23321
\(486\) −6.58085e11 −0.535080
\(487\) 2.40112e12 1.93434 0.967171 0.254126i \(-0.0817878\pi\)
0.967171 + 0.254126i \(0.0817878\pi\)
\(488\) 1.14627e12 0.914951
\(489\) −4.89155e10 −0.0386862
\(490\) 2.50385e12 1.96212
\(491\) −3.93654e11 −0.305666 −0.152833 0.988252i \(-0.548840\pi\)
−0.152833 + 0.988252i \(0.548840\pi\)
\(492\) 5.78667e11 0.445231
\(493\) −1.25178e11 −0.0954368
\(494\) −5.95409e11 −0.449826
\(495\) 6.40605e11 0.479587
\(496\) −2.95129e11 −0.218950
\(497\) 6.89700e11 0.507057
\(498\) 4.66093e11 0.339579
\(499\) −1.16585e12 −0.841763 −0.420881 0.907116i \(-0.638279\pi\)
−0.420881 + 0.907116i \(0.638279\pi\)
\(500\) −1.60998e12 −1.15201
\(501\) −3.90760e11 −0.277102
\(502\) −6.98053e11 −0.490593
\(503\) −1.06497e12 −0.741794 −0.370897 0.928674i \(-0.620950\pi\)
−0.370897 + 0.928674i \(0.620950\pi\)
\(504\) −1.79290e12 −1.23771
\(505\) −2.22958e12 −1.52550
\(506\) 3.45544e11 0.234329
\(507\) 3.25611e11 0.218858
\(508\) −9.58931e11 −0.638853
\(509\) −1.27920e12 −0.844711 −0.422355 0.906430i \(-0.638797\pi\)
−0.422355 + 0.906430i \(0.638797\pi\)
\(510\) 1.59710e11 0.104536
\(511\) 1.91407e12 1.24184
\(512\) 7.70679e11 0.495631
\(513\) 1.55784e12 0.993103
\(514\) 3.97161e11 0.250976
\(515\) −4.50625e12 −2.82282
\(516\) −1.99750e11 −0.124041
\(517\) 1.01004e12 0.621771
\(518\) 7.54659e11 0.460540
\(519\) 1.53076e11 0.0926089
\(520\) 1.90188e12 1.14069
\(521\) 1.01572e12 0.603955 0.301977 0.953315i \(-0.402353\pi\)
0.301977 + 0.953315i \(0.402353\pi\)
\(522\) −2.67600e11 −0.157750
\(523\) −7.26782e10 −0.0424763 −0.0212381 0.999774i \(-0.506761\pi\)
−0.0212381 + 0.999774i \(0.506761\pi\)
\(524\) 6.23316e11 0.361175
\(525\) 2.89083e12 1.66076
\(526\) 4.63017e10 0.0263731
\(527\) 3.67694e11 0.207653
\(528\) 8.04740e10 0.0450612
\(529\) 9.13829e11 0.507358
\(530\) 7.24456e10 0.0398814
\(531\) 1.03871e12 0.566980
\(532\) 2.79773e12 1.51427
\(533\) −1.74839e12 −0.938354
\(534\) 1.24832e10 0.00664339
\(535\) −2.25682e11 −0.119098
\(536\) −1.51382e12 −0.792195
\(537\) 2.49903e11 0.129684
\(538\) 7.49324e11 0.385611
\(539\) −1.57183e12 −0.802153
\(540\) −2.09489e12 −1.06020
\(541\) −4.64227e11 −0.232993 −0.116496 0.993191i \(-0.537166\pi\)
−0.116496 + 0.993191i \(0.537166\pi\)
\(542\) 5.05434e11 0.251575
\(543\) −1.29411e12 −0.638809
\(544\) −5.13178e11 −0.251231
\(545\) −4.12345e12 −2.00205
\(546\) −6.91300e11 −0.332889
\(547\) −2.64589e12 −1.26366 −0.631828 0.775109i \(-0.717695\pi\)
−0.631828 + 0.775109i \(0.717695\pi\)
\(548\) −3.63937e11 −0.172391
\(549\) 1.65637e12 0.778181
\(550\) −7.88964e11 −0.367642
\(551\) 9.91894e11 0.458441
\(552\) −1.16542e12 −0.534267
\(553\) −1.13910e12 −0.517964
\(554\) −1.57038e12 −0.708291
\(555\) 9.09425e11 0.406863
\(556\) 1.88857e11 0.0838101
\(557\) −1.89427e11 −0.0833862 −0.0416931 0.999130i \(-0.513275\pi\)
−0.0416931 + 0.999130i \(0.513275\pi\)
\(558\) 7.86042e11 0.343235
\(559\) 6.03528e11 0.261423
\(560\) −1.81994e12 −0.782009
\(561\) −1.00261e11 −0.0427364
\(562\) −1.70163e12 −0.719537
\(563\) 3.50385e12 1.46980 0.734900 0.678175i \(-0.237229\pi\)
0.734900 + 0.678175i \(0.237229\pi\)
\(564\) −1.43413e12 −0.596806
\(565\) 2.45493e12 1.01349
\(566\) 7.95395e11 0.325769
\(567\) −1.56735e12 −0.636858
\(568\) 6.34857e11 0.255923
\(569\) 4.15736e12 1.66270 0.831348 0.555752i \(-0.187570\pi\)
0.831348 + 0.555752i \(0.187570\pi\)
\(570\) −1.26553e12 −0.502151
\(571\) 3.38832e12 1.33390 0.666948 0.745104i \(-0.267600\pi\)
0.666948 + 0.745104i \(0.267600\pi\)
\(572\) −5.02634e11 −0.196322
\(573\) 2.98686e11 0.115749
\(574\) −3.08375e12 −1.18570
\(575\) −6.19899e12 −2.36492
\(576\) −5.78617e11 −0.219023
\(577\) −7.93761e11 −0.298125 −0.149062 0.988828i \(-0.547626\pi\)
−0.149062 + 0.988828i \(0.547626\pi\)
\(578\) 8.24599e10 0.0307303
\(579\) 4.04955e11 0.149745
\(580\) −1.33384e12 −0.489415
\(581\) 6.61718e12 2.40924
\(582\) −1.31817e12 −0.476231
\(583\) −4.54789e10 −0.0163043
\(584\) 1.76187e12 0.626782
\(585\) 2.74823e12 0.970178
\(586\) 1.03566e12 0.362809
\(587\) 3.50948e12 1.22003 0.610016 0.792389i \(-0.291163\pi\)
0.610016 + 0.792389i \(0.291163\pi\)
\(588\) 2.23181e12 0.769946
\(589\) −2.91357e12 −0.997485
\(590\) −1.94339e12 −0.660277
\(591\) −1.85738e12 −0.626262
\(592\) −3.76879e11 −0.126111
\(593\) 1.01035e12 0.335527 0.167763 0.985827i \(-0.446346\pi\)
0.167763 + 0.985827i \(0.446346\pi\)
\(594\) −4.93637e11 −0.162693
\(595\) 2.26743e12 0.741663
\(596\) 1.26331e12 0.410112
\(597\) −2.26114e12 −0.728521
\(598\) 1.48240e12 0.474034
\(599\) 1.26453e12 0.401337 0.200669 0.979659i \(-0.435689\pi\)
0.200669 + 0.979659i \(0.435689\pi\)
\(600\) 2.66096e12 0.838220
\(601\) 4.11286e12 1.28591 0.642953 0.765906i \(-0.277709\pi\)
0.642953 + 0.765906i \(0.277709\pi\)
\(602\) 1.06448e12 0.330334
\(603\) −2.18747e12 −0.673775
\(604\) −9.46338e11 −0.289321
\(605\) −4.88466e12 −1.48230
\(606\) 7.45971e11 0.224696
\(607\) 2.94970e12 0.881919 0.440959 0.897527i \(-0.354638\pi\)
0.440959 + 0.897527i \(0.354638\pi\)
\(608\) 4.06637e12 1.20681
\(609\) 1.15164e12 0.339265
\(610\) −3.09901e12 −0.906232
\(611\) 4.33311e12 1.25781
\(612\) −4.69626e11 −0.135323
\(613\) −1.04819e12 −0.299825 −0.149912 0.988699i \(-0.547899\pi\)
−0.149912 + 0.988699i \(0.547899\pi\)
\(614\) 2.72444e12 0.773606
\(615\) −3.71616e12 −1.04751
\(616\) −2.10582e12 −0.589261
\(617\) −2.24197e12 −0.622797 −0.311398 0.950279i \(-0.600797\pi\)
−0.311398 + 0.950279i \(0.600797\pi\)
\(618\) 1.50770e12 0.415782
\(619\) −4.31403e12 −1.18107 −0.590534 0.807013i \(-0.701083\pi\)
−0.590534 + 0.807013i \(0.701083\pi\)
\(620\) 3.91799e12 1.06488
\(621\) −3.87857e12 −1.04655
\(622\) 3.41664e11 0.0915256
\(623\) 1.77225e11 0.0471335
\(624\) 3.45237e11 0.0911564
\(625\) 2.99120e12 0.784124
\(626\) −3.49816e12 −0.910448
\(627\) 7.94454e11 0.205289
\(628\) 3.20010e12 0.821004
\(629\) 4.69545e11 0.119605
\(630\) 4.84721e12 1.22591
\(631\) −5.04376e12 −1.26655 −0.633275 0.773927i \(-0.718290\pi\)
−0.633275 + 0.773927i \(0.718290\pi\)
\(632\) −1.04852e12 −0.261428
\(633\) −3.04552e11 −0.0753953
\(634\) −3.69772e12 −0.908934
\(635\) 6.15819e12 1.50304
\(636\) 6.45745e10 0.0156496
\(637\) −6.74324e12 −1.62271
\(638\) −3.14305e11 −0.0751031
\(639\) 9.17371e11 0.217666
\(640\) −6.43818e12 −1.51689
\(641\) 4.31567e12 1.00969 0.504844 0.863210i \(-0.331550\pi\)
0.504844 + 0.863210i \(0.331550\pi\)
\(642\) 7.55084e10 0.0175423
\(643\) −4.67632e12 −1.07883 −0.539417 0.842039i \(-0.681355\pi\)
−0.539417 + 0.842039i \(0.681355\pi\)
\(644\) −6.96554e12 −1.59576
\(645\) 1.28278e12 0.291833
\(646\) −6.53403e11 −0.147616
\(647\) −2.41143e11 −0.0541010 −0.0270505 0.999634i \(-0.508611\pi\)
−0.0270505 + 0.999634i \(0.508611\pi\)
\(648\) −1.44272e12 −0.321436
\(649\) 1.21999e12 0.269933
\(650\) −3.38469e12 −0.743719
\(651\) −3.38280e12 −0.738179
\(652\) −2.69112e11 −0.0583202
\(653\) 5.60932e12 1.20726 0.603631 0.797264i \(-0.293720\pi\)
0.603631 + 0.797264i \(0.293720\pi\)
\(654\) 1.37962e12 0.294890
\(655\) −4.00289e12 −0.849744
\(656\) 1.54003e12 0.324685
\(657\) 2.54591e12 0.533088
\(658\) 7.64256e12 1.58936
\(659\) −5.89433e12 −1.21745 −0.608724 0.793382i \(-0.708318\pi\)
−0.608724 + 0.793382i \(0.708318\pi\)
\(660\) −1.06833e12 −0.219159
\(661\) −6.88972e11 −0.140377 −0.0701883 0.997534i \(-0.522360\pi\)
−0.0701883 + 0.997534i \(0.522360\pi\)
\(662\) 1.05326e11 0.0213145
\(663\) −4.30123e11 −0.0864533
\(664\) 6.09100e12 1.21600
\(665\) −1.79668e13 −3.56266
\(666\) 1.00377e12 0.197698
\(667\) −2.46953e12 −0.483113
\(668\) −2.14979e12 −0.417736
\(669\) 3.11258e12 0.600763
\(670\) 4.09270e12 0.784645
\(671\) 1.94546e12 0.370484
\(672\) 4.72126e12 0.893091
\(673\) 5.91814e12 1.11203 0.556016 0.831171i \(-0.312329\pi\)
0.556016 + 0.831171i \(0.312329\pi\)
\(674\) 3.43869e11 0.0641836
\(675\) 8.85577e12 1.64195
\(676\) 1.79137e12 0.329933
\(677\) 9.75918e12 1.78552 0.892759 0.450534i \(-0.148766\pi\)
0.892759 + 0.450534i \(0.148766\pi\)
\(678\) −8.21368e11 −0.149281
\(679\) −1.87142e13 −3.37876
\(680\) 2.08713e12 0.374334
\(681\) −1.13952e12 −0.203030
\(682\) 9.23232e11 0.163411
\(683\) −1.05702e12 −0.185862 −0.0929310 0.995673i \(-0.529624\pi\)
−0.0929310 + 0.995673i \(0.529624\pi\)
\(684\) 3.72126e12 0.650037
\(685\) 2.33718e12 0.405587
\(686\) −6.47654e12 −1.11657
\(687\) −3.07752e12 −0.527103
\(688\) −5.31604e11 −0.0904566
\(689\) −1.95107e11 −0.0329826
\(690\) 3.15080e12 0.529175
\(691\) −1.03154e12 −0.172122 −0.0860608 0.996290i \(-0.527428\pi\)
−0.0860608 + 0.996290i \(0.527428\pi\)
\(692\) 8.42156e11 0.139610
\(693\) −3.04291e12 −0.501176
\(694\) 1.29590e12 0.212058
\(695\) −1.21283e12 −0.197182
\(696\) 1.06006e12 0.171234
\(697\) −1.91869e12 −0.307934
\(698\) −7.51336e11 −0.119808
\(699\) 3.38978e12 0.537061
\(700\) 1.59041e13 2.50362
\(701\) 5.14597e12 0.804889 0.402444 0.915444i \(-0.368161\pi\)
0.402444 + 0.915444i \(0.368161\pi\)
\(702\) −2.11773e12 −0.329119
\(703\) −3.72062e12 −0.574535
\(704\) −6.79605e11 −0.104275
\(705\) 9.20991e12 1.40412
\(706\) 9.21324e11 0.139570
\(707\) 1.05906e13 1.59417
\(708\) −1.73225e12 −0.259096
\(709\) −1.28349e13 −1.90759 −0.953795 0.300458i \(-0.902861\pi\)
−0.953795 + 0.300458i \(0.902861\pi\)
\(710\) −1.71638e12 −0.253483
\(711\) −1.51512e12 −0.222348
\(712\) 1.63133e11 0.0237893
\(713\) 7.25395e12 1.05117
\(714\) −7.58633e11 −0.109242
\(715\) 3.22788e12 0.461892
\(716\) 1.37486e12 0.195501
\(717\) −3.21711e12 −0.454600
\(718\) 3.62727e12 0.509354
\(719\) −6.51717e12 −0.909451 −0.454725 0.890632i \(-0.650263\pi\)
−0.454725 + 0.890632i \(0.650263\pi\)
\(720\) −2.42071e12 −0.335697
\(721\) 2.14050e13 2.94989
\(722\) 1.36303e12 0.186675
\(723\) −5.58000e12 −0.759472
\(724\) −7.11962e12 −0.963016
\(725\) 5.63857e12 0.757963
\(726\) 1.63430e12 0.218332
\(727\) −4.75481e12 −0.631290 −0.315645 0.948877i \(-0.602221\pi\)
−0.315645 + 0.948877i \(0.602221\pi\)
\(728\) −9.03406e12 −1.19204
\(729\) 1.05033e12 0.137737
\(730\) −4.76333e12 −0.620808
\(731\) 6.62313e11 0.0857896
\(732\) −2.76231e12 −0.355609
\(733\) −4.70068e12 −0.601441 −0.300721 0.953712i \(-0.597227\pi\)
−0.300721 + 0.953712i \(0.597227\pi\)
\(734\) −2.51923e12 −0.320358
\(735\) −1.43326e13 −1.81147
\(736\) −1.01241e13 −1.27176
\(737\) −2.56926e12 −0.320778
\(738\) −4.10170e12 −0.508991
\(739\) 7.68600e12 0.947983 0.473992 0.880529i \(-0.342813\pi\)
0.473992 + 0.880529i \(0.342813\pi\)
\(740\) 5.00326e12 0.613353
\(741\) 3.40825e12 0.415288
\(742\) −3.44121e11 −0.0416767
\(743\) 1.54208e13 1.85634 0.928170 0.372156i \(-0.121382\pi\)
0.928170 + 0.372156i \(0.121382\pi\)
\(744\) −3.11381e12 −0.372575
\(745\) −8.11290e12 −0.964879
\(746\) 2.68431e12 0.317328
\(747\) 8.80152e12 1.03423
\(748\) −5.51591e11 −0.0644258
\(749\) 1.07200e12 0.124459
\(750\) −3.45927e12 −0.399217
\(751\) −6.56715e12 −0.753351 −0.376676 0.926345i \(-0.622933\pi\)
−0.376676 + 0.926345i \(0.622933\pi\)
\(752\) −3.81672e12 −0.435221
\(753\) 3.99580e12 0.452925
\(754\) −1.34838e12 −0.151929
\(755\) 6.07732e12 0.680693
\(756\) 9.95085e12 1.10793
\(757\) −1.40433e13 −1.55431 −0.777156 0.629308i \(-0.783338\pi\)
−0.777156 + 0.629308i \(0.783338\pi\)
\(758\) 4.18026e12 0.459930
\(759\) −1.97796e12 −0.216337
\(760\) −1.65382e13 −1.79815
\(761\) −9.41842e12 −1.01800 −0.508999 0.860767i \(-0.669984\pi\)
−0.508999 + 0.860767i \(0.669984\pi\)
\(762\) −2.06040e12 −0.221388
\(763\) 1.95866e13 2.09218
\(764\) 1.64324e12 0.174494
\(765\) 3.01591e12 0.318377
\(766\) −7.91425e12 −0.830578
\(767\) 5.23384e12 0.546061
\(768\) 3.48125e12 0.361085
\(769\) 1.32235e13 1.36358 0.681788 0.731550i \(-0.261203\pi\)
0.681788 + 0.731550i \(0.261203\pi\)
\(770\) 5.69321e12 0.583645
\(771\) −2.27343e12 −0.231706
\(772\) 2.22789e12 0.225744
\(773\) −1.14561e13 −1.15406 −0.577031 0.816722i \(-0.695789\pi\)
−0.577031 + 0.816722i \(0.695789\pi\)
\(774\) 1.41587e12 0.141804
\(775\) −1.65626e13 −1.64919
\(776\) −1.72261e13 −1.70533
\(777\) −4.31983e12 −0.425179
\(778\) 7.82608e12 0.765837
\(779\) 1.52035e13 1.47919
\(780\) −4.58320e12 −0.443347
\(781\) 1.07748e12 0.103629
\(782\) 1.62679e12 0.155561
\(783\) 3.52793e12 0.335422
\(784\) 5.93962e12 0.561483
\(785\) −2.05508e13 −1.93159
\(786\) 1.33929e12 0.125162
\(787\) 4.46778e12 0.415151 0.207575 0.978219i \(-0.433443\pi\)
0.207575 + 0.978219i \(0.433443\pi\)
\(788\) −1.02185e13 −0.944101
\(789\) −2.65041e11 −0.0243482
\(790\) 2.83475e12 0.258936
\(791\) −1.16611e13 −1.05912
\(792\) −2.80095e12 −0.252954
\(793\) 8.34610e12 0.749470
\(794\) −7.81484e12 −0.697795
\(795\) −4.14694e11 −0.0368193
\(796\) −1.24398e13 −1.09826
\(797\) −1.13816e13 −0.999177 −0.499589 0.866263i \(-0.666515\pi\)
−0.499589 + 0.866263i \(0.666515\pi\)
\(798\) 6.01133e12 0.524756
\(799\) 4.75516e12 0.412767
\(800\) 2.31159e13 1.99529
\(801\) 2.35728e11 0.0202332
\(802\) 7.76311e12 0.662600
\(803\) 2.99026e12 0.253798
\(804\) 3.64804e12 0.307898
\(805\) 4.47323e13 3.75439
\(806\) 3.96071e12 0.330571
\(807\) −4.28929e12 −0.356003
\(808\) 9.74851e12 0.804613
\(809\) −1.94386e13 −1.59550 −0.797748 0.602991i \(-0.793976\pi\)
−0.797748 + 0.602991i \(0.793976\pi\)
\(810\) 3.90048e12 0.318373
\(811\) 1.02059e12 0.0828431 0.0414216 0.999142i \(-0.486811\pi\)
0.0414216 + 0.999142i \(0.486811\pi\)
\(812\) 6.33582e12 0.511447
\(813\) −2.89321e12 −0.232259
\(814\) 1.17896e12 0.0941219
\(815\) 1.72822e12 0.137211
\(816\) 3.78864e11 0.0299142
\(817\) −5.24809e12 −0.412099
\(818\) −5.15564e12 −0.402618
\(819\) −1.30542e13 −1.01385
\(820\) −2.04447e13 −1.57913
\(821\) 2.88205e12 0.221390 0.110695 0.993854i \(-0.464692\pi\)
0.110695 + 0.993854i \(0.464692\pi\)
\(822\) −7.81971e11 −0.0597403
\(823\) 1.16904e13 0.888237 0.444118 0.895968i \(-0.353517\pi\)
0.444118 + 0.895968i \(0.353517\pi\)
\(824\) 1.97029e13 1.48887
\(825\) 4.51619e12 0.339414
\(826\) 9.23122e12 0.690000
\(827\) 5.81279e12 0.432126 0.216063 0.976379i \(-0.430678\pi\)
0.216063 + 0.976379i \(0.430678\pi\)
\(828\) −9.26488e12 −0.685020
\(829\) 6.40775e12 0.471205 0.235603 0.971849i \(-0.424294\pi\)
0.235603 + 0.971849i \(0.424294\pi\)
\(830\) −1.64674e13 −1.20441
\(831\) 8.98920e12 0.653907
\(832\) −2.91554e12 −0.210942
\(833\) −7.40004e12 −0.532514
\(834\) 4.05787e11 0.0290436
\(835\) 1.38058e13 0.982817
\(836\) 4.37074e12 0.309476
\(837\) −1.03629e13 −0.729819
\(838\) 7.87680e12 0.551762
\(839\) −3.65270e12 −0.254498 −0.127249 0.991871i \(-0.540615\pi\)
−0.127249 + 0.991871i \(0.540615\pi\)
\(840\) −1.92016e13 −1.33070
\(841\) −1.22609e13 −0.845161
\(842\) −5.53712e12 −0.379647
\(843\) 9.74051e12 0.664290
\(844\) −1.67551e12 −0.113660
\(845\) −1.15041e13 −0.776240
\(846\) 1.01654e13 0.682272
\(847\) 2.32024e13 1.54902
\(848\) 1.71855e11 0.0114125
\(849\) −4.55301e12 −0.300756
\(850\) −3.71436e12 −0.244062
\(851\) 9.26328e12 0.605455
\(852\) −1.52990e12 −0.0994681
\(853\) 2.63808e13 1.70615 0.853076 0.521787i \(-0.174734\pi\)
0.853076 + 0.521787i \(0.174734\pi\)
\(854\) 1.47205e13 0.947027
\(855\) −2.38977e13 −1.52936
\(856\) 9.86760e11 0.0628173
\(857\) −2.49098e13 −1.57745 −0.788726 0.614745i \(-0.789259\pi\)
−0.788726 + 0.614745i \(0.789259\pi\)
\(858\) −1.07998e12 −0.0680336
\(859\) 2.76464e13 1.73248 0.866242 0.499625i \(-0.166529\pi\)
0.866242 + 0.499625i \(0.166529\pi\)
\(860\) 7.05731e12 0.439943
\(861\) 1.76520e13 1.09466
\(862\) −4.05810e12 −0.250346
\(863\) 6.15764e12 0.377890 0.188945 0.981988i \(-0.439493\pi\)
0.188945 + 0.981988i \(0.439493\pi\)
\(864\) 1.44631e13 0.882977
\(865\) −5.40827e12 −0.328463
\(866\) −1.54717e13 −0.934776
\(867\) −4.72017e11 −0.0283708
\(868\) −1.86107e13 −1.11282
\(869\) −1.77956e12 −0.105858
\(870\) −2.86595e12 −0.169602
\(871\) −1.10222e13 −0.648915
\(872\) 1.80292e13 1.05597
\(873\) −2.48918e13 −1.45041
\(874\) −1.28905e13 −0.747252
\(875\) −4.91117e13 −2.83236
\(876\) −4.24580e12 −0.243608
\(877\) 1.26417e11 0.00721619 0.00360809 0.999993i \(-0.498852\pi\)
0.00360809 + 0.999993i \(0.498852\pi\)
\(878\) 6.48054e12 0.368032
\(879\) −5.92833e12 −0.334952
\(880\) −2.84320e12 −0.159822
\(881\) 1.81563e13 1.01540 0.507699 0.861535i \(-0.330496\pi\)
0.507699 + 0.861535i \(0.330496\pi\)
\(882\) −1.58195e13 −0.880206
\(883\) −3.40979e13 −1.88758 −0.943788 0.330553i \(-0.892765\pi\)
−0.943788 + 0.330553i \(0.892765\pi\)
\(884\) −2.36635e12 −0.130330
\(885\) 1.11244e13 0.609580
\(886\) −1.18270e11 −0.00644797
\(887\) 1.64233e13 0.890851 0.445426 0.895319i \(-0.353052\pi\)
0.445426 + 0.895319i \(0.353052\pi\)
\(888\) −3.97633e12 −0.214597
\(889\) −2.92518e13 −1.57071
\(890\) −4.41039e11 −0.0235626
\(891\) −2.44859e12 −0.130157
\(892\) 1.71241e13 0.905661
\(893\) −3.76794e13 −1.98277
\(894\) 2.71441e12 0.142120
\(895\) −8.82926e12 −0.459961
\(896\) 3.05818e13 1.58517
\(897\) −8.48556e12 −0.437637
\(898\) −1.06072e12 −0.0544323
\(899\) −6.59816e12 −0.336902
\(900\) 2.11541e13 1.07474
\(901\) −2.14110e11 −0.0108237
\(902\) −4.81757e12 −0.242325
\(903\) −6.09330e12 −0.304970
\(904\) −1.07338e13 −0.534560
\(905\) 4.57217e13 2.26571
\(906\) −2.03335e12 −0.100262
\(907\) −3.95675e12 −0.194136 −0.0970679 0.995278i \(-0.530946\pi\)
−0.0970679 + 0.995278i \(0.530946\pi\)
\(908\) −6.26915e12 −0.306071
\(909\) 1.40866e13 0.684337
\(910\) 2.44241e13 1.18068
\(911\) 9.23006e12 0.443989 0.221994 0.975048i \(-0.428743\pi\)
0.221994 + 0.975048i \(0.428743\pi\)
\(912\) −3.00207e12 −0.143696
\(913\) 1.03377e13 0.492384
\(914\) −1.33772e13 −0.634028
\(915\) 1.77394e13 0.836650
\(916\) −1.69312e13 −0.794616
\(917\) 1.90140e13 0.887997
\(918\) −2.32400e12 −0.108005
\(919\) −3.01409e13 −1.39391 −0.696957 0.717113i \(-0.745463\pi\)
−0.696957 + 0.717113i \(0.745463\pi\)
\(920\) 4.11753e13 1.89492
\(921\) −1.55953e13 −0.714208
\(922\) −2.08194e13 −0.948810
\(923\) 4.62245e12 0.209635
\(924\) 5.07465e12 0.229025
\(925\) −2.11504e13 −0.949907
\(926\) −7.09682e12 −0.317186
\(927\) 2.84708e13 1.26631
\(928\) 9.20882e12 0.407604
\(929\) 3.04484e13 1.34120 0.670601 0.741818i \(-0.266036\pi\)
0.670601 + 0.741818i \(0.266036\pi\)
\(930\) 8.41837e12 0.369024
\(931\) 5.86371e13 2.55799
\(932\) 1.86491e13 0.809629
\(933\) −1.95576e12 −0.0844981
\(934\) −8.64049e12 −0.371516
\(935\) 3.54228e12 0.151576
\(936\) −1.20162e13 −0.511713
\(937\) 2.04000e13 0.864572 0.432286 0.901736i \(-0.357707\pi\)
0.432286 + 0.901736i \(0.357707\pi\)
\(938\) −1.94406e13 −0.819967
\(939\) 2.00242e13 0.840543
\(940\) 5.06689e13 2.11673
\(941\) −2.55881e13 −1.06386 −0.531930 0.846789i \(-0.678533\pi\)
−0.531930 + 0.846789i \(0.678533\pi\)
\(942\) 6.87588e12 0.284511
\(943\) −3.78523e13 −1.55880
\(944\) −4.61010e12 −0.188945
\(945\) −6.39037e13 −2.60665
\(946\) 1.66298e12 0.0675113
\(947\) 8.56722e12 0.346151 0.173075 0.984909i \(-0.444630\pi\)
0.173075 + 0.984909i \(0.444630\pi\)
\(948\) 2.52676e12 0.101608
\(949\) 1.28283e13 0.513420
\(950\) 2.94322e13 1.17238
\(951\) 2.11665e13 0.839146
\(952\) −9.91398e12 −0.391185
\(953\) −3.84991e13 −1.51193 −0.755966 0.654611i \(-0.772832\pi\)
−0.755966 + 0.654611i \(0.772832\pi\)
\(954\) −4.57716e11 −0.0178907
\(955\) −1.05528e13 −0.410537
\(956\) −1.76991e13 −0.685317
\(957\) 1.79915e12 0.0693366
\(958\) −2.08089e13 −0.798187
\(959\) −1.11017e13 −0.423845
\(960\) −6.19689e12 −0.235480
\(961\) −7.05834e12 −0.266961
\(962\) 5.05781e12 0.190404
\(963\) 1.42587e12 0.0534272
\(964\) −3.06987e13 −1.14492
\(965\) −1.43073e13 −0.531112
\(966\) −1.49665e13 −0.552997
\(967\) 4.31991e13 1.58875 0.794375 0.607428i \(-0.207799\pi\)
0.794375 + 0.607428i \(0.207799\pi\)
\(968\) 2.13574e13 0.781826
\(969\) 3.74021e12 0.136282
\(970\) 4.65718e13 1.68908
\(971\) −1.97835e13 −0.714196 −0.357098 0.934067i \(-0.616234\pi\)
−0.357098 + 0.934067i \(0.616234\pi\)
\(972\) 2.07245e13 0.744707
\(973\) 5.76100e12 0.206058
\(974\) 2.83834e13 1.01053
\(975\) 1.93747e13 0.686616
\(976\) −7.35146e12 −0.259328
\(977\) −2.56325e13 −0.900047 −0.450024 0.893017i \(-0.648584\pi\)
−0.450024 + 0.893017i \(0.648584\pi\)
\(978\) −5.78226e11 −0.0202103
\(979\) 2.76870e11 0.00963281
\(980\) −7.88516e13 −2.73082
\(981\) 2.60522e13 0.898119
\(982\) −4.65335e12 −0.159685
\(983\) −3.03713e13 −1.03746 −0.518732 0.854937i \(-0.673596\pi\)
−0.518732 + 0.854937i \(0.673596\pi\)
\(984\) 1.62484e13 0.552499
\(985\) 6.56224e13 2.22121
\(986\) −1.47972e12 −0.0498577
\(987\) −4.37476e13 −1.46733
\(988\) 1.87507e13 0.626053
\(989\) 1.30662e13 0.434278
\(990\) 7.57254e12 0.250544
\(991\) −1.54521e13 −0.508929 −0.254465 0.967082i \(-0.581899\pi\)
−0.254465 + 0.967082i \(0.581899\pi\)
\(992\) −2.70498e13 −0.886873
\(993\) −6.02910e11 −0.0196780
\(994\) 8.15289e12 0.264894
\(995\) 7.98875e13 2.58390
\(996\) −1.46783e13 −0.472615
\(997\) −7.77458e12 −0.249201 −0.124600 0.992207i \(-0.539765\pi\)
−0.124600 + 0.992207i \(0.539765\pi\)
\(998\) −1.37814e13 −0.439750
\(999\) −1.32333e13 −0.420364
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 17.10.a.a.1.4 5
3.2 odd 2 153.10.a.c.1.2 5
4.3 odd 2 272.10.a.f.1.3 5
17.16 even 2 289.10.a.a.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.a.a.1.4 5 1.1 even 1 trivial
153.10.a.c.1.2 5 3.2 odd 2
272.10.a.f.1.3 5 4.3 odd 2
289.10.a.a.1.4 5 17.16 even 2