Properties

Label 4003.2.a.c.1.14
Level 4003
Weight 2
Character 4003.1
Self dual yes
Analytic conductor 31.964
Analytic rank 0
Dimension 179
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(0\)
Dimension: \(179\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.40245 q^{2} +0.531316 q^{3} +3.77174 q^{4} +3.68505 q^{5} -1.27646 q^{6} -3.72446 q^{7} -4.25652 q^{8} -2.71770 q^{9} +O(q^{10})\) \(q-2.40245 q^{2} +0.531316 q^{3} +3.77174 q^{4} +3.68505 q^{5} -1.27646 q^{6} -3.72446 q^{7} -4.25652 q^{8} -2.71770 q^{9} -8.85314 q^{10} -4.55164 q^{11} +2.00399 q^{12} -0.961640 q^{13} +8.94782 q^{14} +1.95793 q^{15} +2.68256 q^{16} -4.53477 q^{17} +6.52913 q^{18} -1.62642 q^{19} +13.8991 q^{20} -1.97887 q^{21} +10.9351 q^{22} +0.930366 q^{23} -2.26156 q^{24} +8.57962 q^{25} +2.31029 q^{26} -3.03791 q^{27} -14.0477 q^{28} +6.79752 q^{29} -4.70381 q^{30} -5.57489 q^{31} +2.06833 q^{32} -2.41836 q^{33} +10.8945 q^{34} -13.7248 q^{35} -10.2505 q^{36} +2.73533 q^{37} +3.90738 q^{38} -0.510935 q^{39} -15.6855 q^{40} -9.14250 q^{41} +4.75412 q^{42} +1.82354 q^{43} -17.1676 q^{44} -10.0149 q^{45} -2.23515 q^{46} +0.00696210 q^{47} +1.42529 q^{48} +6.87162 q^{49} -20.6121 q^{50} -2.40940 q^{51} -3.62706 q^{52} -8.51154 q^{53} +7.29841 q^{54} -16.7730 q^{55} +15.8532 q^{56} -0.864141 q^{57} -16.3307 q^{58} +5.88485 q^{59} +7.38480 q^{60} +13.4394 q^{61} +13.3934 q^{62} +10.1220 q^{63} -10.3342 q^{64} -3.54369 q^{65} +5.80998 q^{66} +12.6636 q^{67} -17.1040 q^{68} +0.494318 q^{69} +32.9732 q^{70} +13.4749 q^{71} +11.5679 q^{72} +5.62058 q^{73} -6.57149 q^{74} +4.55849 q^{75} -6.13442 q^{76} +16.9524 q^{77} +1.22749 q^{78} -8.28466 q^{79} +9.88538 q^{80} +6.53902 q^{81} +21.9644 q^{82} -7.24734 q^{83} -7.46378 q^{84} -16.7109 q^{85} -4.38096 q^{86} +3.61163 q^{87} +19.3741 q^{88} -4.63487 q^{89} +24.0602 q^{90} +3.58159 q^{91} +3.50910 q^{92} -2.96203 q^{93} -0.0167261 q^{94} -5.99343 q^{95} +1.09893 q^{96} +16.1394 q^{97} -16.5087 q^{98} +12.3700 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.40245 −1.69879 −0.849393 0.527761i \(-0.823032\pi\)
−0.849393 + 0.527761i \(0.823032\pi\)
\(3\) 0.531316 0.306755 0.153378 0.988168i \(-0.450985\pi\)
0.153378 + 0.988168i \(0.450985\pi\)
\(4\) 3.77174 1.88587
\(5\) 3.68505 1.64801 0.824003 0.566586i \(-0.191736\pi\)
0.824003 + 0.566586i \(0.191736\pi\)
\(6\) −1.27646 −0.521112
\(7\) −3.72446 −1.40771 −0.703857 0.710341i \(-0.748541\pi\)
−0.703857 + 0.710341i \(0.748541\pi\)
\(8\) −4.25652 −1.50491
\(9\) −2.71770 −0.905901
\(10\) −8.85314 −2.79961
\(11\) −4.55164 −1.37237 −0.686186 0.727426i \(-0.740716\pi\)
−0.686186 + 0.727426i \(0.740716\pi\)
\(12\) 2.00399 0.578501
\(13\) −0.961640 −0.266711 −0.133355 0.991068i \(-0.542575\pi\)
−0.133355 + 0.991068i \(0.542575\pi\)
\(14\) 8.94782 2.39140
\(15\) 1.95793 0.505535
\(16\) 2.68256 0.670640
\(17\) −4.53477 −1.09984 −0.549922 0.835216i \(-0.685342\pi\)
−0.549922 + 0.835216i \(0.685342\pi\)
\(18\) 6.52913 1.53893
\(19\) −1.62642 −0.373125 −0.186563 0.982443i \(-0.559735\pi\)
−0.186563 + 0.982443i \(0.559735\pi\)
\(20\) 13.8991 3.10793
\(21\) −1.97887 −0.431824
\(22\) 10.9351 2.33137
\(23\) 0.930366 0.193995 0.0969974 0.995285i \(-0.469076\pi\)
0.0969974 + 0.995285i \(0.469076\pi\)
\(24\) −2.26156 −0.461638
\(25\) 8.57962 1.71592
\(26\) 2.31029 0.453085
\(27\) −3.03791 −0.584645
\(28\) −14.0477 −2.65477
\(29\) 6.79752 1.26227 0.631134 0.775674i \(-0.282590\pi\)
0.631134 + 0.775674i \(0.282590\pi\)
\(30\) −4.70381 −0.858795
\(31\) −5.57489 −1.00128 −0.500640 0.865656i \(-0.666902\pi\)
−0.500640 + 0.865656i \(0.666902\pi\)
\(32\) 2.06833 0.365632
\(33\) −2.41836 −0.420982
\(34\) 10.8945 1.86840
\(35\) −13.7248 −2.31992
\(36\) −10.2505 −1.70841
\(37\) 2.73533 0.449686 0.224843 0.974395i \(-0.427813\pi\)
0.224843 + 0.974395i \(0.427813\pi\)
\(38\) 3.90738 0.633860
\(39\) −0.510935 −0.0818150
\(40\) −15.6855 −2.48009
\(41\) −9.14250 −1.42782 −0.713909 0.700238i \(-0.753077\pi\)
−0.713909 + 0.700238i \(0.753077\pi\)
\(42\) 4.75412 0.733576
\(43\) 1.82354 0.278087 0.139044 0.990286i \(-0.455597\pi\)
0.139044 + 0.990286i \(0.455597\pi\)
\(44\) −17.1676 −2.58812
\(45\) −10.0149 −1.49293
\(46\) −2.23515 −0.329556
\(47\) 0.00696210 0.00101553 0.000507764 1.00000i \(-0.499838\pi\)
0.000507764 1.00000i \(0.499838\pi\)
\(48\) 1.42529 0.205723
\(49\) 6.87162 0.981660
\(50\) −20.6121 −2.91499
\(51\) −2.40940 −0.337383
\(52\) −3.62706 −0.502983
\(53\) −8.51154 −1.16915 −0.584575 0.811340i \(-0.698739\pi\)
−0.584575 + 0.811340i \(0.698739\pi\)
\(54\) 7.29841 0.993187
\(55\) −16.7730 −2.26168
\(56\) 15.8532 2.11848
\(57\) −0.864141 −0.114458
\(58\) −16.3307 −2.14432
\(59\) 5.88485 0.766142 0.383071 0.923719i \(-0.374866\pi\)
0.383071 + 0.923719i \(0.374866\pi\)
\(60\) 7.38480 0.953374
\(61\) 13.4394 1.72074 0.860372 0.509666i \(-0.170231\pi\)
0.860372 + 0.509666i \(0.170231\pi\)
\(62\) 13.3934 1.70096
\(63\) 10.1220 1.27525
\(64\) −10.3342 −1.29177
\(65\) −3.54369 −0.439541
\(66\) 5.80998 0.715159
\(67\) 12.6636 1.54710 0.773550 0.633735i \(-0.218479\pi\)
0.773550 + 0.633735i \(0.218479\pi\)
\(68\) −17.1040 −2.07416
\(69\) 0.494318 0.0595090
\(70\) 32.9732 3.94105
\(71\) 13.4749 1.59917 0.799586 0.600552i \(-0.205052\pi\)
0.799586 + 0.600552i \(0.205052\pi\)
\(72\) 11.5679 1.36330
\(73\) 5.62058 0.657839 0.328919 0.944358i \(-0.393316\pi\)
0.328919 + 0.944358i \(0.393316\pi\)
\(74\) −6.57149 −0.763920
\(75\) 4.55849 0.526369
\(76\) −6.13442 −0.703667
\(77\) 16.9524 1.93191
\(78\) 1.22749 0.138986
\(79\) −8.28466 −0.932097 −0.466048 0.884759i \(-0.654323\pi\)
−0.466048 + 0.884759i \(0.654323\pi\)
\(80\) 9.88538 1.10522
\(81\) 6.53902 0.726558
\(82\) 21.9644 2.42556
\(83\) −7.24734 −0.795499 −0.397750 0.917494i \(-0.630209\pi\)
−0.397750 + 0.917494i \(0.630209\pi\)
\(84\) −7.46378 −0.814365
\(85\) −16.7109 −1.81255
\(86\) −4.38096 −0.472411
\(87\) 3.61163 0.387208
\(88\) 19.3741 2.06529
\(89\) −4.63487 −0.491295 −0.245648 0.969359i \(-0.579001\pi\)
−0.245648 + 0.969359i \(0.579001\pi\)
\(90\) 24.0602 2.53617
\(91\) 3.58159 0.375453
\(92\) 3.50910 0.365849
\(93\) −2.96203 −0.307148
\(94\) −0.0167261 −0.00172516
\(95\) −5.99343 −0.614913
\(96\) 1.09893 0.112160
\(97\) 16.1394 1.63871 0.819354 0.573288i \(-0.194332\pi\)
0.819354 + 0.573288i \(0.194332\pi\)
\(98\) −16.5087 −1.66763
\(99\) 12.3700 1.24323
\(100\) 32.3601 3.23601
\(101\) 14.9590 1.48848 0.744240 0.667913i \(-0.232812\pi\)
0.744240 + 0.667913i \(0.232812\pi\)
\(102\) 5.78844 0.573141
\(103\) 4.30526 0.424210 0.212105 0.977247i \(-0.431968\pi\)
0.212105 + 0.977247i \(0.431968\pi\)
\(104\) 4.09324 0.401375
\(105\) −7.29223 −0.711649
\(106\) 20.4485 1.98614
\(107\) 4.05218 0.391739 0.195869 0.980630i \(-0.437247\pi\)
0.195869 + 0.980630i \(0.437247\pi\)
\(108\) −11.4582 −1.10257
\(109\) −5.95759 −0.570633 −0.285317 0.958433i \(-0.592099\pi\)
−0.285317 + 0.958433i \(0.592099\pi\)
\(110\) 40.2963 3.84210
\(111\) 1.45333 0.137944
\(112\) −9.99110 −0.944070
\(113\) 8.51615 0.801132 0.400566 0.916268i \(-0.368814\pi\)
0.400566 + 0.916268i \(0.368814\pi\)
\(114\) 2.07605 0.194440
\(115\) 3.42845 0.319705
\(116\) 25.6385 2.38048
\(117\) 2.61345 0.241614
\(118\) −14.1380 −1.30151
\(119\) 16.8896 1.54827
\(120\) −8.33395 −0.760782
\(121\) 9.71745 0.883404
\(122\) −32.2875 −2.92318
\(123\) −4.85756 −0.437991
\(124\) −21.0270 −1.88828
\(125\) 13.1911 1.17985
\(126\) −24.3175 −2.16638
\(127\) 1.59636 0.141654 0.0708271 0.997489i \(-0.477436\pi\)
0.0708271 + 0.997489i \(0.477436\pi\)
\(128\) 20.6906 1.82881
\(129\) 0.968876 0.0853048
\(130\) 8.51353 0.746686
\(131\) 9.27761 0.810588 0.405294 0.914186i \(-0.367169\pi\)
0.405294 + 0.914186i \(0.367169\pi\)
\(132\) −9.12143 −0.793919
\(133\) 6.05752 0.525254
\(134\) −30.4235 −2.62819
\(135\) −11.1948 −0.963499
\(136\) 19.3023 1.65516
\(137\) −0.567671 −0.0484994 −0.0242497 0.999706i \(-0.507720\pi\)
−0.0242497 + 0.999706i \(0.507720\pi\)
\(138\) −1.18757 −0.101093
\(139\) −14.5660 −1.23547 −0.617735 0.786386i \(-0.711950\pi\)
−0.617735 + 0.786386i \(0.711950\pi\)
\(140\) −51.7666 −4.37507
\(141\) 0.00369908 0.000311518 0
\(142\) −32.3726 −2.71665
\(143\) 4.37704 0.366027
\(144\) −7.29041 −0.607534
\(145\) 25.0492 2.08023
\(146\) −13.5031 −1.11753
\(147\) 3.65100 0.301130
\(148\) 10.3170 0.848050
\(149\) 15.0172 1.23026 0.615130 0.788426i \(-0.289104\pi\)
0.615130 + 0.788426i \(0.289104\pi\)
\(150\) −10.9515 −0.894188
\(151\) −5.15372 −0.419404 −0.209702 0.977765i \(-0.567249\pi\)
−0.209702 + 0.977765i \(0.567249\pi\)
\(152\) 6.92287 0.561519
\(153\) 12.3242 0.996349
\(154\) −40.7273 −3.28190
\(155\) −20.5438 −1.65011
\(156\) −1.92711 −0.154293
\(157\) 0.592735 0.0473054 0.0236527 0.999720i \(-0.492470\pi\)
0.0236527 + 0.999720i \(0.492470\pi\)
\(158\) 19.9034 1.58343
\(159\) −4.52232 −0.358643
\(160\) 7.62189 0.602563
\(161\) −3.46511 −0.273089
\(162\) −15.7096 −1.23427
\(163\) 8.45251 0.662052 0.331026 0.943622i \(-0.392605\pi\)
0.331026 + 0.943622i \(0.392605\pi\)
\(164\) −34.4832 −2.69268
\(165\) −8.91179 −0.693782
\(166\) 17.4113 1.35138
\(167\) 4.67789 0.361986 0.180993 0.983484i \(-0.442069\pi\)
0.180993 + 0.983484i \(0.442069\pi\)
\(168\) 8.42308 0.649855
\(169\) −12.0752 −0.928865
\(170\) 40.1469 3.07913
\(171\) 4.42012 0.338015
\(172\) 6.87793 0.524437
\(173\) 14.3882 1.09391 0.546957 0.837161i \(-0.315786\pi\)
0.546957 + 0.837161i \(0.315786\pi\)
\(174\) −8.67675 −0.657783
\(175\) −31.9545 −2.41553
\(176\) −12.2101 −0.920368
\(177\) 3.12671 0.235018
\(178\) 11.1350 0.834605
\(179\) −5.02893 −0.375880 −0.187940 0.982181i \(-0.560181\pi\)
−0.187940 + 0.982181i \(0.560181\pi\)
\(180\) −37.7736 −2.81548
\(181\) 13.9492 1.03684 0.518419 0.855127i \(-0.326521\pi\)
0.518419 + 0.855127i \(0.326521\pi\)
\(182\) −8.60458 −0.637814
\(183\) 7.14059 0.527848
\(184\) −3.96012 −0.291944
\(185\) 10.0799 0.741085
\(186\) 7.11611 0.521778
\(187\) 20.6406 1.50939
\(188\) 0.0262593 0.00191515
\(189\) 11.3146 0.823014
\(190\) 14.3989 1.04460
\(191\) 2.30215 0.166578 0.0832888 0.996525i \(-0.473458\pi\)
0.0832888 + 0.996525i \(0.473458\pi\)
\(192\) −5.49071 −0.396258
\(193\) 5.40944 0.389380 0.194690 0.980865i \(-0.437630\pi\)
0.194690 + 0.980865i \(0.437630\pi\)
\(194\) −38.7740 −2.78381
\(195\) −1.88282 −0.134832
\(196\) 25.9180 1.85128
\(197\) −5.41283 −0.385648 −0.192824 0.981233i \(-0.561765\pi\)
−0.192824 + 0.981233i \(0.561765\pi\)
\(198\) −29.7183 −2.11199
\(199\) −0.666988 −0.0472816 −0.0236408 0.999721i \(-0.507526\pi\)
−0.0236408 + 0.999721i \(0.507526\pi\)
\(200\) −36.5193 −2.58230
\(201\) 6.72835 0.474582
\(202\) −35.9383 −2.52861
\(203\) −25.3171 −1.77691
\(204\) −9.08762 −0.636261
\(205\) −33.6906 −2.35305
\(206\) −10.3431 −0.720641
\(207\) −2.52846 −0.175740
\(208\) −2.57966 −0.178867
\(209\) 7.40286 0.512067
\(210\) 17.5192 1.20894
\(211\) 6.99575 0.481607 0.240804 0.970574i \(-0.422589\pi\)
0.240804 + 0.970574i \(0.422589\pi\)
\(212\) −32.1033 −2.20487
\(213\) 7.15941 0.490555
\(214\) −9.73514 −0.665480
\(215\) 6.71984 0.458289
\(216\) 12.9309 0.879836
\(217\) 20.7635 1.40952
\(218\) 14.3128 0.969384
\(219\) 2.98630 0.201796
\(220\) −63.2636 −4.26523
\(221\) 4.36082 0.293340
\(222\) −3.49154 −0.234337
\(223\) −2.58693 −0.173234 −0.0866168 0.996242i \(-0.527606\pi\)
−0.0866168 + 0.996242i \(0.527606\pi\)
\(224\) −7.70340 −0.514705
\(225\) −23.3169 −1.55446
\(226\) −20.4596 −1.36095
\(227\) −20.2380 −1.34324 −0.671620 0.740896i \(-0.734401\pi\)
−0.671620 + 0.740896i \(0.734401\pi\)
\(228\) −3.25932 −0.215854
\(229\) −11.7467 −0.776241 −0.388120 0.921609i \(-0.626876\pi\)
−0.388120 + 0.921609i \(0.626876\pi\)
\(230\) −8.23666 −0.543109
\(231\) 9.00709 0.592623
\(232\) −28.9338 −1.89959
\(233\) 10.7120 0.701764 0.350882 0.936420i \(-0.385882\pi\)
0.350882 + 0.936420i \(0.385882\pi\)
\(234\) −6.27868 −0.410450
\(235\) 0.0256557 0.00167359
\(236\) 22.1961 1.44485
\(237\) −4.40177 −0.285926
\(238\) −40.5763 −2.63017
\(239\) −6.62790 −0.428723 −0.214362 0.976754i \(-0.568767\pi\)
−0.214362 + 0.976754i \(0.568767\pi\)
\(240\) 5.25226 0.339032
\(241\) −12.4011 −0.798827 −0.399414 0.916771i \(-0.630786\pi\)
−0.399414 + 0.916771i \(0.630786\pi\)
\(242\) −23.3456 −1.50071
\(243\) 12.5880 0.807521
\(244\) 50.6901 3.24510
\(245\) 25.3223 1.61778
\(246\) 11.6700 0.744053
\(247\) 1.56403 0.0995166
\(248\) 23.7296 1.50683
\(249\) −3.85063 −0.244024
\(250\) −31.6908 −2.00430
\(251\) −3.81667 −0.240906 −0.120453 0.992719i \(-0.538435\pi\)
−0.120453 + 0.992719i \(0.538435\pi\)
\(252\) 38.1775 2.40496
\(253\) −4.23469 −0.266233
\(254\) −3.83517 −0.240640
\(255\) −8.87875 −0.556009
\(256\) −29.0397 −1.81498
\(257\) −13.1308 −0.819078 −0.409539 0.912293i \(-0.634310\pi\)
−0.409539 + 0.912293i \(0.634310\pi\)
\(258\) −2.32767 −0.144914
\(259\) −10.1876 −0.633030
\(260\) −13.3659 −0.828918
\(261\) −18.4736 −1.14349
\(262\) −22.2889 −1.37702
\(263\) 0.683836 0.0421671 0.0210836 0.999778i \(-0.493288\pi\)
0.0210836 + 0.999778i \(0.493288\pi\)
\(264\) 10.2938 0.633539
\(265\) −31.3655 −1.92677
\(266\) −14.5529 −0.892294
\(267\) −2.46258 −0.150707
\(268\) 47.7637 2.91763
\(269\) 8.79990 0.536539 0.268270 0.963344i \(-0.413548\pi\)
0.268270 + 0.963344i \(0.413548\pi\)
\(270\) 26.8950 1.63678
\(271\) −18.8359 −1.14420 −0.572098 0.820185i \(-0.693870\pi\)
−0.572098 + 0.820185i \(0.693870\pi\)
\(272\) −12.1648 −0.737599
\(273\) 1.90296 0.115172
\(274\) 1.36380 0.0823901
\(275\) −39.0513 −2.35488
\(276\) 1.86444 0.112226
\(277\) 14.6318 0.879138 0.439569 0.898209i \(-0.355131\pi\)
0.439569 + 0.898209i \(0.355131\pi\)
\(278\) 34.9940 2.09880
\(279\) 15.1509 0.907060
\(280\) 58.4200 3.49126
\(281\) 31.4621 1.87687 0.938435 0.345456i \(-0.112276\pi\)
0.938435 + 0.345456i \(0.112276\pi\)
\(282\) −0.00888683 −0.000529203 0
\(283\) −28.2365 −1.67849 −0.839244 0.543755i \(-0.817002\pi\)
−0.839244 + 0.543755i \(0.817002\pi\)
\(284\) 50.8237 3.01583
\(285\) −3.18440 −0.188628
\(286\) −10.5156 −0.621801
\(287\) 34.0509 2.00996
\(288\) −5.62110 −0.331226
\(289\) 3.56413 0.209655
\(290\) −60.1794 −3.53386
\(291\) 8.57512 0.502683
\(292\) 21.1994 1.24060
\(293\) −16.1451 −0.943206 −0.471603 0.881811i \(-0.656324\pi\)
−0.471603 + 0.881811i \(0.656324\pi\)
\(294\) −8.77133 −0.511554
\(295\) 21.6860 1.26261
\(296\) −11.6430 −0.676735
\(297\) 13.8275 0.802351
\(298\) −36.0781 −2.08995
\(299\) −0.894678 −0.0517405
\(300\) 17.1934 0.992664
\(301\) −6.79171 −0.391467
\(302\) 12.3815 0.712477
\(303\) 7.94797 0.456599
\(304\) −4.36296 −0.250233
\(305\) 49.5251 2.83580
\(306\) −29.6081 −1.69258
\(307\) −21.6345 −1.23475 −0.617373 0.786671i \(-0.711803\pi\)
−0.617373 + 0.786671i \(0.711803\pi\)
\(308\) 63.9402 3.64333
\(309\) 2.28745 0.130129
\(310\) 49.3553 2.80319
\(311\) −33.0908 −1.87641 −0.938205 0.346081i \(-0.887512\pi\)
−0.938205 + 0.346081i \(0.887512\pi\)
\(312\) 2.17480 0.123124
\(313\) 17.5740 0.993339 0.496670 0.867940i \(-0.334556\pi\)
0.496670 + 0.867940i \(0.334556\pi\)
\(314\) −1.42401 −0.0803617
\(315\) 37.3000 2.10162
\(316\) −31.2476 −1.75782
\(317\) 26.9746 1.51504 0.757521 0.652811i \(-0.226410\pi\)
0.757521 + 0.652811i \(0.226410\pi\)
\(318\) 10.8646 0.609258
\(319\) −30.9399 −1.73230
\(320\) −38.0819 −2.12885
\(321\) 2.15299 0.120168
\(322\) 8.32475 0.463920
\(323\) 7.37542 0.410379
\(324\) 24.6635 1.37020
\(325\) −8.25050 −0.457656
\(326\) −20.3067 −1.12468
\(327\) −3.16536 −0.175045
\(328\) 38.9152 2.14873
\(329\) −0.0259301 −0.00142957
\(330\) 21.4101 1.17859
\(331\) 15.0177 0.825450 0.412725 0.910856i \(-0.364577\pi\)
0.412725 + 0.910856i \(0.364577\pi\)
\(332\) −27.3351 −1.50021
\(333\) −7.43383 −0.407371
\(334\) −11.2384 −0.614936
\(335\) 46.6659 2.54963
\(336\) −5.30843 −0.289599
\(337\) −17.8446 −0.972057 −0.486028 0.873943i \(-0.661555\pi\)
−0.486028 + 0.873943i \(0.661555\pi\)
\(338\) 29.0101 1.57794
\(339\) 4.52477 0.245752
\(340\) −63.0291 −3.41823
\(341\) 25.3749 1.37413
\(342\) −10.6191 −0.574214
\(343\) 0.478148 0.0258176
\(344\) −7.76193 −0.418495
\(345\) 1.82159 0.0980711
\(346\) −34.5669 −1.85833
\(347\) 21.1764 1.13681 0.568404 0.822750i \(-0.307561\pi\)
0.568404 + 0.822750i \(0.307561\pi\)
\(348\) 13.6221 0.730224
\(349\) −28.2073 −1.50990 −0.754951 0.655781i \(-0.772339\pi\)
−0.754951 + 0.655781i \(0.772339\pi\)
\(350\) 76.7688 4.10347
\(351\) 2.92137 0.155931
\(352\) −9.41428 −0.501783
\(353\) 14.4580 0.769524 0.384762 0.923016i \(-0.374284\pi\)
0.384762 + 0.923016i \(0.374284\pi\)
\(354\) −7.51176 −0.399246
\(355\) 49.6556 2.63545
\(356\) −17.4815 −0.926520
\(357\) 8.97370 0.474939
\(358\) 12.0817 0.638539
\(359\) −30.3420 −1.60139 −0.800694 0.599073i \(-0.795536\pi\)
−0.800694 + 0.599073i \(0.795536\pi\)
\(360\) 42.6285 2.24672
\(361\) −16.3548 −0.860777
\(362\) −33.5123 −1.76137
\(363\) 5.16304 0.270989
\(364\) 13.5088 0.708056
\(365\) 20.7121 1.08412
\(366\) −17.1549 −0.896700
\(367\) 26.8768 1.40296 0.701480 0.712689i \(-0.252523\pi\)
0.701480 + 0.712689i \(0.252523\pi\)
\(368\) 2.49576 0.130101
\(369\) 24.8466 1.29346
\(370\) −24.2163 −1.25895
\(371\) 31.7009 1.64583
\(372\) −11.1720 −0.579242
\(373\) −10.9308 −0.565975 −0.282988 0.959124i \(-0.591326\pi\)
−0.282988 + 0.959124i \(0.591326\pi\)
\(374\) −49.5880 −2.56414
\(375\) 7.00863 0.361924
\(376\) −0.0296343 −0.00152827
\(377\) −6.53677 −0.336661
\(378\) −27.1826 −1.39812
\(379\) 23.9213 1.22875 0.614377 0.789013i \(-0.289408\pi\)
0.614377 + 0.789013i \(0.289408\pi\)
\(380\) −22.6057 −1.15965
\(381\) 0.848172 0.0434532
\(382\) −5.53078 −0.282980
\(383\) 34.5908 1.76751 0.883754 0.467952i \(-0.155008\pi\)
0.883754 + 0.467952i \(0.155008\pi\)
\(384\) 10.9933 0.560997
\(385\) 62.4706 3.18380
\(386\) −12.9959 −0.661473
\(387\) −4.95584 −0.251920
\(388\) 60.8737 3.09039
\(389\) 14.7327 0.746980 0.373490 0.927634i \(-0.378161\pi\)
0.373490 + 0.927634i \(0.378161\pi\)
\(390\) 4.52338 0.229050
\(391\) −4.21900 −0.213364
\(392\) −29.2492 −1.47731
\(393\) 4.92934 0.248652
\(394\) 13.0040 0.655134
\(395\) −30.5294 −1.53610
\(396\) 46.6565 2.34458
\(397\) 9.26071 0.464782 0.232391 0.972622i \(-0.425345\pi\)
0.232391 + 0.972622i \(0.425345\pi\)
\(398\) 1.60240 0.0803212
\(399\) 3.21846 0.161125
\(400\) 23.0153 1.15077
\(401\) −8.29084 −0.414025 −0.207012 0.978338i \(-0.566374\pi\)
−0.207012 + 0.978338i \(0.566374\pi\)
\(402\) −16.1645 −0.806212
\(403\) 5.36104 0.267052
\(404\) 56.4216 2.80708
\(405\) 24.0966 1.19737
\(406\) 60.8230 3.01859
\(407\) −12.4503 −0.617137
\(408\) 10.2556 0.507729
\(409\) −31.7640 −1.57063 −0.785314 0.619098i \(-0.787498\pi\)
−0.785314 + 0.619098i \(0.787498\pi\)
\(410\) 80.9398 3.99733
\(411\) −0.301613 −0.0148775
\(412\) 16.2383 0.800005
\(413\) −21.9179 −1.07851
\(414\) 6.07449 0.298545
\(415\) −26.7068 −1.31099
\(416\) −1.98899 −0.0975180
\(417\) −7.73914 −0.378987
\(418\) −17.7850 −0.869892
\(419\) 25.6892 1.25500 0.627499 0.778617i \(-0.284079\pi\)
0.627499 + 0.778617i \(0.284079\pi\)
\(420\) −27.5044 −1.34208
\(421\) −2.80135 −0.136529 −0.0682647 0.997667i \(-0.521746\pi\)
−0.0682647 + 0.997667i \(0.521746\pi\)
\(422\) −16.8069 −0.818147
\(423\) −0.0189209 −0.000919967 0
\(424\) 36.2295 1.75946
\(425\) −38.9066 −1.88725
\(426\) −17.2001 −0.833347
\(427\) −50.0547 −2.42232
\(428\) 15.2838 0.738769
\(429\) 2.32559 0.112281
\(430\) −16.1441 −0.778535
\(431\) 9.53568 0.459317 0.229659 0.973271i \(-0.426239\pi\)
0.229659 + 0.973271i \(0.426239\pi\)
\(432\) −8.14937 −0.392087
\(433\) 35.6273 1.71214 0.856068 0.516862i \(-0.172900\pi\)
0.856068 + 0.516862i \(0.172900\pi\)
\(434\) −49.8831 −2.39446
\(435\) 13.3091 0.638120
\(436\) −22.4705 −1.07614
\(437\) −1.51316 −0.0723844
\(438\) −7.17443 −0.342807
\(439\) −14.0985 −0.672885 −0.336443 0.941704i \(-0.609224\pi\)
−0.336443 + 0.941704i \(0.609224\pi\)
\(440\) 71.3947 3.40361
\(441\) −18.6750 −0.889287
\(442\) −10.4766 −0.498322
\(443\) 20.7098 0.983953 0.491977 0.870608i \(-0.336275\pi\)
0.491977 + 0.870608i \(0.336275\pi\)
\(444\) 5.48158 0.260144
\(445\) −17.0797 −0.809657
\(446\) 6.21495 0.294287
\(447\) 7.97890 0.377389
\(448\) 38.4892 1.81844
\(449\) 31.4922 1.48621 0.743105 0.669175i \(-0.233352\pi\)
0.743105 + 0.669175i \(0.233352\pi\)
\(450\) 56.0175 2.64069
\(451\) 41.6134 1.95950
\(452\) 32.1207 1.51083
\(453\) −2.73826 −0.128654
\(454\) 48.6206 2.28188
\(455\) 13.1984 0.618749
\(456\) 3.67823 0.172249
\(457\) −5.33720 −0.249664 −0.124832 0.992178i \(-0.539839\pi\)
−0.124832 + 0.992178i \(0.539839\pi\)
\(458\) 28.2207 1.31867
\(459\) 13.7762 0.643018
\(460\) 12.9312 0.602922
\(461\) 4.49903 0.209541 0.104770 0.994496i \(-0.466589\pi\)
0.104770 + 0.994496i \(0.466589\pi\)
\(462\) −21.6390 −1.00674
\(463\) −26.9593 −1.25291 −0.626453 0.779460i \(-0.715494\pi\)
−0.626453 + 0.779460i \(0.715494\pi\)
\(464\) 18.2348 0.846528
\(465\) −10.9152 −0.506182
\(466\) −25.7349 −1.19215
\(467\) 14.1420 0.654413 0.327207 0.944953i \(-0.393893\pi\)
0.327207 + 0.944953i \(0.393893\pi\)
\(468\) 9.85727 0.455653
\(469\) −47.1650 −2.17788
\(470\) −0.0616365 −0.00284308
\(471\) 0.314930 0.0145112
\(472\) −25.0490 −1.15297
\(473\) −8.30010 −0.381639
\(474\) 10.5750 0.485727
\(475\) −13.9540 −0.640255
\(476\) 63.7032 2.91983
\(477\) 23.1318 1.05913
\(478\) 15.9232 0.728309
\(479\) −40.2979 −1.84126 −0.920630 0.390436i \(-0.872324\pi\)
−0.920630 + 0.390436i \(0.872324\pi\)
\(480\) 4.04963 0.184840
\(481\) −2.63041 −0.119936
\(482\) 29.7930 1.35704
\(483\) −1.84107 −0.0837716
\(484\) 36.6517 1.66599
\(485\) 59.4746 2.70060
\(486\) −30.2420 −1.37180
\(487\) 23.9537 1.08544 0.542722 0.839912i \(-0.317394\pi\)
0.542722 + 0.839912i \(0.317394\pi\)
\(488\) −57.2052 −2.58956
\(489\) 4.49095 0.203088
\(490\) −60.8354 −2.74826
\(491\) 10.1271 0.457029 0.228515 0.973541i \(-0.426613\pi\)
0.228515 + 0.973541i \(0.426613\pi\)
\(492\) −18.3215 −0.825995
\(493\) −30.8252 −1.38830
\(494\) −3.75749 −0.169057
\(495\) 45.5842 2.04886
\(496\) −14.9550 −0.671498
\(497\) −50.1866 −2.25118
\(498\) 9.25093 0.414544
\(499\) −16.4721 −0.737391 −0.368695 0.929550i \(-0.620195\pi\)
−0.368695 + 0.929550i \(0.620195\pi\)
\(500\) 49.7534 2.22504
\(501\) 2.48544 0.111041
\(502\) 9.16933 0.409247
\(503\) −42.7945 −1.90811 −0.954057 0.299625i \(-0.903138\pi\)
−0.954057 + 0.299625i \(0.903138\pi\)
\(504\) −43.0844 −1.91913
\(505\) 55.1248 2.45302
\(506\) 10.1736 0.452273
\(507\) −6.41577 −0.284934
\(508\) 6.02106 0.267142
\(509\) −10.4592 −0.463594 −0.231797 0.972764i \(-0.574461\pi\)
−0.231797 + 0.972764i \(0.574461\pi\)
\(510\) 21.3307 0.944540
\(511\) −20.9336 −0.926049
\(512\) 28.3851 1.25446
\(513\) 4.94090 0.218146
\(514\) 31.5461 1.39144
\(515\) 15.8651 0.699100
\(516\) 3.65435 0.160874
\(517\) −0.0316890 −0.00139368
\(518\) 24.4753 1.07538
\(519\) 7.64468 0.335564
\(520\) 15.0838 0.661468
\(521\) 22.9617 1.00597 0.502985 0.864295i \(-0.332235\pi\)
0.502985 + 0.864295i \(0.332235\pi\)
\(522\) 44.3819 1.94254
\(523\) −13.0327 −0.569880 −0.284940 0.958545i \(-0.591974\pi\)
−0.284940 + 0.958545i \(0.591974\pi\)
\(524\) 34.9928 1.52867
\(525\) −16.9779 −0.740977
\(526\) −1.64288 −0.0716329
\(527\) 25.2808 1.10125
\(528\) −6.48740 −0.282328
\(529\) −22.1344 −0.962366
\(530\) 75.3539 3.27316
\(531\) −15.9933 −0.694049
\(532\) 22.8474 0.990562
\(533\) 8.79179 0.380815
\(534\) 5.91621 0.256020
\(535\) 14.9325 0.645588
\(536\) −53.9027 −2.32824
\(537\) −2.67195 −0.115303
\(538\) −21.1413 −0.911465
\(539\) −31.2772 −1.34720
\(540\) −42.2241 −1.81704
\(541\) 0.553213 0.0237845 0.0118922 0.999929i \(-0.496214\pi\)
0.0118922 + 0.999929i \(0.496214\pi\)
\(542\) 45.2521 1.94374
\(543\) 7.41145 0.318056
\(544\) −9.37938 −0.402138
\(545\) −21.9540 −0.940407
\(546\) −4.57175 −0.195653
\(547\) 29.4848 1.26068 0.630339 0.776320i \(-0.282916\pi\)
0.630339 + 0.776320i \(0.282916\pi\)
\(548\) −2.14111 −0.0914637
\(549\) −36.5244 −1.55882
\(550\) 93.8187 4.00044
\(551\) −11.0556 −0.470984
\(552\) −2.10407 −0.0895554
\(553\) 30.8559 1.31213
\(554\) −35.1520 −1.49347
\(555\) 5.35559 0.227332
\(556\) −54.9392 −2.32994
\(557\) 28.1256 1.19172 0.595859 0.803089i \(-0.296812\pi\)
0.595859 + 0.803089i \(0.296812\pi\)
\(558\) −36.3992 −1.54090
\(559\) −1.75359 −0.0741689
\(560\) −36.8177 −1.55583
\(561\) 10.9667 0.463015
\(562\) −75.5859 −3.18840
\(563\) −24.1593 −1.01819 −0.509097 0.860709i \(-0.670021\pi\)
−0.509097 + 0.860709i \(0.670021\pi\)
\(564\) 0.0139520 0.000587484 0
\(565\) 31.3825 1.32027
\(566\) 67.8367 2.85139
\(567\) −24.3543 −1.02279
\(568\) −57.3560 −2.40660
\(569\) −0.973316 −0.0408035 −0.0204018 0.999792i \(-0.506495\pi\)
−0.0204018 + 0.999792i \(0.506495\pi\)
\(570\) 7.65036 0.320438
\(571\) 4.56550 0.191060 0.0955302 0.995427i \(-0.469545\pi\)
0.0955302 + 0.995427i \(0.469545\pi\)
\(572\) 16.5091 0.690279
\(573\) 1.22317 0.0510986
\(574\) −81.8054 −3.41449
\(575\) 7.98219 0.332880
\(576\) 28.0852 1.17022
\(577\) 6.52578 0.271672 0.135836 0.990731i \(-0.456628\pi\)
0.135836 + 0.990731i \(0.456628\pi\)
\(578\) −8.56264 −0.356159
\(579\) 2.87412 0.119444
\(580\) 94.4793 3.92304
\(581\) 26.9925 1.11984
\(582\) −20.6013 −0.853950
\(583\) 38.7415 1.60451
\(584\) −23.9241 −0.989985
\(585\) 9.63071 0.398181
\(586\) 38.7877 1.60230
\(587\) −9.16410 −0.378243 −0.189122 0.981954i \(-0.560564\pi\)
−0.189122 + 0.981954i \(0.560564\pi\)
\(588\) 13.7706 0.567892
\(589\) 9.06709 0.373603
\(590\) −52.0994 −2.14490
\(591\) −2.87592 −0.118300
\(592\) 7.33770 0.301578
\(593\) 39.4750 1.62104 0.810522 0.585709i \(-0.199184\pi\)
0.810522 + 0.585709i \(0.199184\pi\)
\(594\) −33.2197 −1.36302
\(595\) 62.2390 2.55155
\(596\) 56.6412 2.32011
\(597\) −0.354382 −0.0145039
\(598\) 2.14941 0.0878961
\(599\) 1.12553 0.0459878 0.0229939 0.999736i \(-0.492680\pi\)
0.0229939 + 0.999736i \(0.492680\pi\)
\(600\) −19.4033 −0.792135
\(601\) −27.8163 −1.13465 −0.567324 0.823494i \(-0.692021\pi\)
−0.567324 + 0.823494i \(0.692021\pi\)
\(602\) 16.3167 0.665019
\(603\) −34.4158 −1.40152
\(604\) −19.4385 −0.790942
\(605\) 35.8093 1.45586
\(606\) −19.0946 −0.775664
\(607\) −39.2607 −1.59354 −0.796772 0.604280i \(-0.793461\pi\)
−0.796772 + 0.604280i \(0.793461\pi\)
\(608\) −3.36396 −0.136427
\(609\) −13.4514 −0.545078
\(610\) −118.981 −4.81741
\(611\) −0.00669504 −0.000270852 0
\(612\) 46.4836 1.87899
\(613\) −33.3735 −1.34794 −0.673972 0.738757i \(-0.735413\pi\)
−0.673972 + 0.738757i \(0.735413\pi\)
\(614\) 51.9757 2.09757
\(615\) −17.9003 −0.721812
\(616\) −72.1583 −2.90734
\(617\) 32.9871 1.32801 0.664006 0.747728i \(-0.268855\pi\)
0.664006 + 0.747728i \(0.268855\pi\)
\(618\) −5.49548 −0.221061
\(619\) −25.1461 −1.01071 −0.505354 0.862912i \(-0.668638\pi\)
−0.505354 + 0.862912i \(0.668638\pi\)
\(620\) −77.4858 −3.11190
\(621\) −2.82637 −0.113418
\(622\) 79.4989 3.18762
\(623\) 17.2624 0.691603
\(624\) −1.37061 −0.0548685
\(625\) 5.71173 0.228469
\(626\) −42.2205 −1.68747
\(627\) 3.93326 0.157079
\(628\) 2.23564 0.0892119
\(629\) −12.4041 −0.494584
\(630\) −89.6113 −3.57020
\(631\) −12.5900 −0.501199 −0.250600 0.968091i \(-0.580628\pi\)
−0.250600 + 0.968091i \(0.580628\pi\)
\(632\) 35.2638 1.40272
\(633\) 3.71695 0.147736
\(634\) −64.8049 −2.57373
\(635\) 5.88268 0.233447
\(636\) −17.0570 −0.676355
\(637\) −6.60803 −0.261819
\(638\) 74.3314 2.94281
\(639\) −36.6207 −1.44869
\(640\) 76.2460 3.01389
\(641\) 9.64446 0.380933 0.190467 0.981694i \(-0.439000\pi\)
0.190467 + 0.981694i \(0.439000\pi\)
\(642\) −5.17243 −0.204140
\(643\) −30.6630 −1.20923 −0.604615 0.796518i \(-0.706673\pi\)
−0.604615 + 0.796518i \(0.706673\pi\)
\(644\) −13.0695 −0.515011
\(645\) 3.57036 0.140583
\(646\) −17.7190 −0.697147
\(647\) 4.70041 0.184792 0.0923961 0.995722i \(-0.470547\pi\)
0.0923961 + 0.995722i \(0.470547\pi\)
\(648\) −27.8335 −1.09340
\(649\) −26.7857 −1.05143
\(650\) 19.8214 0.777459
\(651\) 11.0320 0.432377
\(652\) 31.8807 1.24854
\(653\) 1.28980 0.0504737 0.0252368 0.999682i \(-0.491966\pi\)
0.0252368 + 0.999682i \(0.491966\pi\)
\(654\) 7.60461 0.297364
\(655\) 34.1885 1.33585
\(656\) −24.5253 −0.957553
\(657\) −15.2751 −0.595937
\(658\) 0.0622956 0.00242854
\(659\) 2.27456 0.0886044 0.0443022 0.999018i \(-0.485894\pi\)
0.0443022 + 0.999018i \(0.485894\pi\)
\(660\) −33.6130 −1.30838
\(661\) −34.9853 −1.36077 −0.680384 0.732855i \(-0.738187\pi\)
−0.680384 + 0.732855i \(0.738187\pi\)
\(662\) −36.0793 −1.40226
\(663\) 2.31697 0.0899837
\(664\) 30.8484 1.19715
\(665\) 22.3223 0.865622
\(666\) 17.8594 0.692036
\(667\) 6.32419 0.244873
\(668\) 17.6438 0.682659
\(669\) −1.37448 −0.0531403
\(670\) −112.112 −4.33128
\(671\) −61.1715 −2.36150
\(672\) −4.09294 −0.157889
\(673\) 19.3350 0.745310 0.372655 0.927970i \(-0.378447\pi\)
0.372655 + 0.927970i \(0.378447\pi\)
\(674\) 42.8706 1.65132
\(675\) −26.0641 −1.00321
\(676\) −45.5447 −1.75172
\(677\) 2.44623 0.0940161 0.0470081 0.998895i \(-0.485031\pi\)
0.0470081 + 0.998895i \(0.485031\pi\)
\(678\) −10.8705 −0.417479
\(679\) −60.1106 −2.30683
\(680\) 71.1301 2.72771
\(681\) −10.7528 −0.412046
\(682\) −60.9618 −2.33435
\(683\) 43.6124 1.66878 0.834391 0.551173i \(-0.185820\pi\)
0.834391 + 0.551173i \(0.185820\pi\)
\(684\) 16.6715 0.637452
\(685\) −2.09190 −0.0799273
\(686\) −1.14872 −0.0438585
\(687\) −6.24118 −0.238116
\(688\) 4.89176 0.186497
\(689\) 8.18504 0.311825
\(690\) −4.37627 −0.166602
\(691\) 7.34138 0.279279 0.139640 0.990202i \(-0.455406\pi\)
0.139640 + 0.990202i \(0.455406\pi\)
\(692\) 54.2686 2.06298
\(693\) −46.0717 −1.75012
\(694\) −50.8751 −1.93119
\(695\) −53.6764 −2.03606
\(696\) −15.3730 −0.582711
\(697\) 41.4591 1.57038
\(698\) 67.7665 2.56500
\(699\) 5.69144 0.215270
\(700\) −120.524 −4.55538
\(701\) −23.0622 −0.871047 −0.435523 0.900177i \(-0.643437\pi\)
−0.435523 + 0.900177i \(0.643437\pi\)
\(702\) −7.01844 −0.264894
\(703\) −4.44879 −0.167789
\(704\) 47.0374 1.77279
\(705\) 0.0136313 0.000513384 0
\(706\) −34.7346 −1.30726
\(707\) −55.7144 −2.09535
\(708\) 11.7932 0.443214
\(709\) 24.0778 0.904262 0.452131 0.891952i \(-0.350664\pi\)
0.452131 + 0.891952i \(0.350664\pi\)
\(710\) −119.295 −4.47706
\(711\) 22.5152 0.844388
\(712\) 19.7284 0.739353
\(713\) −5.18669 −0.194243
\(714\) −21.5588 −0.806819
\(715\) 16.1296 0.603214
\(716\) −18.9678 −0.708861
\(717\) −3.52151 −0.131513
\(718\) 72.8950 2.72042
\(719\) −12.9172 −0.481732 −0.240866 0.970558i \(-0.577431\pi\)
−0.240866 + 0.970558i \(0.577431\pi\)
\(720\) −26.8655 −1.00122
\(721\) −16.0348 −0.597166
\(722\) 39.2914 1.46228
\(723\) −6.58892 −0.245045
\(724\) 52.6129 1.95534
\(725\) 58.3201 2.16596
\(726\) −12.4039 −0.460352
\(727\) −23.3028 −0.864254 −0.432127 0.901813i \(-0.642237\pi\)
−0.432127 + 0.901813i \(0.642237\pi\)
\(728\) −15.2451 −0.565021
\(729\) −12.9289 −0.478846
\(730\) −49.7597 −1.84169
\(731\) −8.26933 −0.305852
\(732\) 26.9325 0.995453
\(733\) −5.86554 −0.216649 −0.108324 0.994116i \(-0.534549\pi\)
−0.108324 + 0.994116i \(0.534549\pi\)
\(734\) −64.5701 −2.38333
\(735\) 13.4541 0.496263
\(736\) 1.92430 0.0709307
\(737\) −57.6400 −2.12320
\(738\) −59.6926 −2.19731
\(739\) −14.6011 −0.537110 −0.268555 0.963264i \(-0.586546\pi\)
−0.268555 + 0.963264i \(0.586546\pi\)
\(740\) 38.0186 1.39759
\(741\) 0.830992 0.0305273
\(742\) −76.1597 −2.79591
\(743\) −0.784316 −0.0287738 −0.0143869 0.999897i \(-0.504580\pi\)
−0.0143869 + 0.999897i \(0.504580\pi\)
\(744\) 12.6079 0.462229
\(745\) 55.3393 2.02748
\(746\) 26.2606 0.961471
\(747\) 19.6961 0.720644
\(748\) 77.8512 2.84652
\(749\) −15.0922 −0.551456
\(750\) −16.8378 −0.614831
\(751\) 47.0600 1.71724 0.858622 0.512610i \(-0.171321\pi\)
0.858622 + 0.512610i \(0.171321\pi\)
\(752\) 0.0186763 0.000681054 0
\(753\) −2.02786 −0.0738992
\(754\) 15.7042 0.571914
\(755\) −18.9917 −0.691180
\(756\) 42.6757 1.55210
\(757\) 31.3356 1.13891 0.569457 0.822021i \(-0.307154\pi\)
0.569457 + 0.822021i \(0.307154\pi\)
\(758\) −57.4695 −2.08739
\(759\) −2.24996 −0.0816684
\(760\) 25.5111 0.925386
\(761\) 30.2889 1.09797 0.548986 0.835832i \(-0.315014\pi\)
0.548986 + 0.835832i \(0.315014\pi\)
\(762\) −2.03769 −0.0738176
\(763\) 22.1888 0.803289
\(764\) 8.68311 0.314144
\(765\) 45.4152 1.64199
\(766\) −83.1025 −3.00262
\(767\) −5.65911 −0.204339
\(768\) −15.4293 −0.556756
\(769\) 32.8298 1.18387 0.591936 0.805985i \(-0.298364\pi\)
0.591936 + 0.805985i \(0.298364\pi\)
\(770\) −150.082 −5.40858
\(771\) −6.97662 −0.251257
\(772\) 20.4030 0.734321
\(773\) −19.8103 −0.712529 −0.356264 0.934385i \(-0.615950\pi\)
−0.356264 + 0.934385i \(0.615950\pi\)
\(774\) 11.9061 0.427957
\(775\) −47.8304 −1.71812
\(776\) −68.6976 −2.46610
\(777\) −5.41286 −0.194185
\(778\) −35.3946 −1.26896
\(779\) 14.8695 0.532755
\(780\) −7.10152 −0.254275
\(781\) −61.3328 −2.19466
\(782\) 10.1359 0.362459
\(783\) −20.6502 −0.737979
\(784\) 18.4335 0.658341
\(785\) 2.18426 0.0779596
\(786\) −11.8425 −0.422407
\(787\) 27.1225 0.966814 0.483407 0.875396i \(-0.339399\pi\)
0.483407 + 0.875396i \(0.339399\pi\)
\(788\) −20.4158 −0.727283
\(789\) 0.363333 0.0129350
\(790\) 73.3452 2.60951
\(791\) −31.7181 −1.12777
\(792\) −52.6532 −1.87095
\(793\) −12.9239 −0.458941
\(794\) −22.2484 −0.789565
\(795\) −16.6650 −0.591046
\(796\) −2.51571 −0.0891669
\(797\) 33.4659 1.18542 0.592711 0.805415i \(-0.298058\pi\)
0.592711 + 0.805415i \(0.298058\pi\)
\(798\) −7.73217 −0.273716
\(799\) −0.0315715 −0.00111692
\(800\) 17.7454 0.627396
\(801\) 12.5962 0.445065
\(802\) 19.9183 0.703339
\(803\) −25.5829 −0.902799
\(804\) 25.3776 0.895000
\(805\) −12.7691 −0.450053
\(806\) −12.8796 −0.453664
\(807\) 4.67553 0.164586
\(808\) −63.6734 −2.24002
\(809\) 50.1002 1.76143 0.880715 0.473647i \(-0.157063\pi\)
0.880715 + 0.473647i \(0.157063\pi\)
\(810\) −57.8909 −2.03408
\(811\) 45.4847 1.59718 0.798591 0.601874i \(-0.205579\pi\)
0.798591 + 0.601874i \(0.205579\pi\)
\(812\) −95.4897 −3.35103
\(813\) −10.0078 −0.350989
\(814\) 29.9111 1.04838
\(815\) 31.1480 1.09107
\(816\) −6.46335 −0.226263
\(817\) −2.96583 −0.103761
\(818\) 76.3112 2.66816
\(819\) −9.73371 −0.340123
\(820\) −127.072 −4.43756
\(821\) −8.80201 −0.307192 −0.153596 0.988134i \(-0.549085\pi\)
−0.153596 + 0.988134i \(0.549085\pi\)
\(822\) 0.724608 0.0252736
\(823\) 39.6846 1.38332 0.691660 0.722224i \(-0.256880\pi\)
0.691660 + 0.722224i \(0.256880\pi\)
\(824\) −18.3254 −0.638396
\(825\) −20.7486 −0.722374
\(826\) 52.6566 1.83216
\(827\) −5.61691 −0.195319 −0.0976595 0.995220i \(-0.531136\pi\)
−0.0976595 + 0.995220i \(0.531136\pi\)
\(828\) −9.53670 −0.331423
\(829\) −49.5241 −1.72004 −0.860022 0.510257i \(-0.829550\pi\)
−0.860022 + 0.510257i \(0.829550\pi\)
\(830\) 64.1617 2.22709
\(831\) 7.77409 0.269680
\(832\) 9.93775 0.344529
\(833\) −31.1612 −1.07967
\(834\) 18.5929 0.643818
\(835\) 17.2383 0.596555
\(836\) 27.9217 0.965692
\(837\) 16.9360 0.585394
\(838\) −61.7168 −2.13197
\(839\) 17.9937 0.621210 0.310605 0.950539i \(-0.399468\pi\)
0.310605 + 0.950539i \(0.399468\pi\)
\(840\) 31.0395 1.07096
\(841\) 17.2063 0.593321
\(842\) 6.73009 0.231934
\(843\) 16.7163 0.575740
\(844\) 26.3862 0.908249
\(845\) −44.4979 −1.53078
\(846\) 0.0454565 0.00156283
\(847\) −36.1923 −1.24358
\(848\) −22.8327 −0.784079
\(849\) −15.0025 −0.514885
\(850\) 93.4709 3.20603
\(851\) 2.54486 0.0872368
\(852\) 27.0035 0.925123
\(853\) 1.68063 0.0575437 0.0287718 0.999586i \(-0.490840\pi\)
0.0287718 + 0.999586i \(0.490840\pi\)
\(854\) 120.254 4.11500
\(855\) 16.2884 0.557050
\(856\) −17.2482 −0.589530
\(857\) 54.6431 1.86657 0.933287 0.359132i \(-0.116927\pi\)
0.933287 + 0.359132i \(0.116927\pi\)
\(858\) −5.58711 −0.190741
\(859\) 49.5204 1.68961 0.844807 0.535070i \(-0.179715\pi\)
0.844807 + 0.535070i \(0.179715\pi\)
\(860\) 25.3455 0.864275
\(861\) 18.0918 0.616566
\(862\) −22.9089 −0.780282
\(863\) 11.8646 0.403876 0.201938 0.979398i \(-0.435276\pi\)
0.201938 + 0.979398i \(0.435276\pi\)
\(864\) −6.28338 −0.213765
\(865\) 53.0213 1.80278
\(866\) −85.5926 −2.90855
\(867\) 1.89368 0.0643128
\(868\) 78.3144 2.65817
\(869\) 37.7088 1.27918
\(870\) −31.9743 −1.08403
\(871\) −12.1778 −0.412629
\(872\) 25.3586 0.858750
\(873\) −43.8621 −1.48451
\(874\) 3.63529 0.122966
\(875\) −49.1297 −1.66089
\(876\) 11.2636 0.380561
\(877\) −0.524102 −0.0176977 −0.00884884 0.999961i \(-0.502817\pi\)
−0.00884884 + 0.999961i \(0.502817\pi\)
\(878\) 33.8709 1.14309
\(879\) −8.57814 −0.289333
\(880\) −44.9947 −1.51677
\(881\) −29.9250 −1.00820 −0.504100 0.863646i \(-0.668176\pi\)
−0.504100 + 0.863646i \(0.668176\pi\)
\(882\) 44.8657 1.51071
\(883\) 13.9165 0.468327 0.234164 0.972197i \(-0.424765\pi\)
0.234164 + 0.972197i \(0.424765\pi\)
\(884\) 16.4479 0.553202
\(885\) 11.5221 0.387311
\(886\) −49.7542 −1.67153
\(887\) 6.80436 0.228468 0.114234 0.993454i \(-0.463559\pi\)
0.114234 + 0.993454i \(0.463559\pi\)
\(888\) −6.18611 −0.207592
\(889\) −5.94559 −0.199409
\(890\) 41.0331 1.37543
\(891\) −29.7633 −0.997108
\(892\) −9.75723 −0.326696
\(893\) −0.0113233 −0.000378919 0
\(894\) −19.1689 −0.641103
\(895\) −18.5319 −0.619452
\(896\) −77.0614 −2.57444
\(897\) −0.475356 −0.0158717
\(898\) −75.6583 −2.52475
\(899\) −37.8954 −1.26388
\(900\) −87.9452 −2.93151
\(901\) 38.5979 1.28588
\(902\) −99.9739 −3.32877
\(903\) −3.60854 −0.120085
\(904\) −36.2491 −1.20563
\(905\) 51.4037 1.70872
\(906\) 6.57851 0.218556
\(907\) −31.3774 −1.04187 −0.520935 0.853596i \(-0.674417\pi\)
−0.520935 + 0.853596i \(0.674417\pi\)
\(908\) −76.3324 −2.53318
\(909\) −40.6542 −1.34842
\(910\) −31.7083 −1.05112
\(911\) 38.0252 1.25983 0.629916 0.776664i \(-0.283089\pi\)
0.629916 + 0.776664i \(0.283089\pi\)
\(912\) −2.31811 −0.0767603
\(913\) 32.9873 1.09172
\(914\) 12.8223 0.424125
\(915\) 26.3135 0.869896
\(916\) −44.3054 −1.46389
\(917\) −34.5541 −1.14108
\(918\) −33.0966 −1.09235
\(919\) 25.1917 0.830996 0.415498 0.909594i \(-0.363607\pi\)
0.415498 + 0.909594i \(0.363607\pi\)
\(920\) −14.5933 −0.481125
\(921\) −11.4948 −0.378765
\(922\) −10.8087 −0.355965
\(923\) −12.9580 −0.426517
\(924\) 33.9724 1.11761
\(925\) 23.4681 0.771627
\(926\) 64.7683 2.12842
\(927\) −11.7004 −0.384292
\(928\) 14.0595 0.461525
\(929\) −10.1468 −0.332905 −0.166452 0.986049i \(-0.553231\pi\)
−0.166452 + 0.986049i \(0.553231\pi\)
\(930\) 26.2232 0.859894
\(931\) −11.1761 −0.366282
\(932\) 40.4028 1.32344
\(933\) −17.5817 −0.575599
\(934\) −33.9754 −1.11171
\(935\) 76.0619 2.48749
\(936\) −11.1242 −0.363606
\(937\) 9.16785 0.299501 0.149750 0.988724i \(-0.452153\pi\)
0.149750 + 0.988724i \(0.452153\pi\)
\(938\) 113.311 3.69974
\(939\) 9.33733 0.304712
\(940\) 0.0967668 0.00315619
\(941\) 42.8846 1.39800 0.698998 0.715123i \(-0.253629\pi\)
0.698998 + 0.715123i \(0.253629\pi\)
\(942\) −0.756601 −0.0246514
\(943\) −8.50587 −0.276989
\(944\) 15.7865 0.513806
\(945\) 41.6948 1.35633
\(946\) 19.9405 0.648323
\(947\) −27.5142 −0.894093 −0.447046 0.894511i \(-0.647524\pi\)
−0.447046 + 0.894511i \(0.647524\pi\)
\(948\) −16.6024 −0.539219
\(949\) −5.40497 −0.175453
\(950\) 33.5238 1.08766
\(951\) 14.3320 0.464747
\(952\) −71.8908 −2.32999
\(953\) 56.2198 1.82114 0.910568 0.413358i \(-0.135644\pi\)
0.910568 + 0.413358i \(0.135644\pi\)
\(954\) −55.5730 −1.79924
\(955\) 8.48354 0.274521
\(956\) −24.9987 −0.808517
\(957\) −16.4389 −0.531393
\(958\) 96.8136 3.12791
\(959\) 2.11427 0.0682733
\(960\) −20.2335 −0.653035
\(961\) 0.0793760 0.00256052
\(962\) 6.31941 0.203746
\(963\) −11.0126 −0.354877
\(964\) −46.7739 −1.50649
\(965\) 19.9341 0.641700
\(966\) 4.42307 0.142310
\(967\) 34.3461 1.10450 0.552249 0.833679i \(-0.313770\pi\)
0.552249 + 0.833679i \(0.313770\pi\)
\(968\) −41.3625 −1.32944
\(969\) 3.91868 0.125886
\(970\) −142.884 −4.58774
\(971\) −40.9303 −1.31352 −0.656758 0.754101i \(-0.728073\pi\)
−0.656758 + 0.754101i \(0.728073\pi\)
\(972\) 47.4787 1.52288
\(973\) 54.2505 1.73919
\(974\) −57.5474 −1.84394
\(975\) −4.38362 −0.140388
\(976\) 36.0521 1.15400
\(977\) −12.6748 −0.405502 −0.202751 0.979230i \(-0.564988\pi\)
−0.202751 + 0.979230i \(0.564988\pi\)
\(978\) −10.7893 −0.345003
\(979\) 21.0963 0.674240
\(980\) 95.5092 3.05093
\(981\) 16.1910 0.516937
\(982\) −24.3298 −0.776394
\(983\) −32.7916 −1.04589 −0.522945 0.852366i \(-0.675167\pi\)
−0.522945 + 0.852366i \(0.675167\pi\)
\(984\) 20.6763 0.659135
\(985\) −19.9466 −0.635551
\(986\) 74.0558 2.35842
\(987\) −0.0137771 −0.000438529 0
\(988\) 5.89911 0.187676
\(989\) 1.69656 0.0539475
\(990\) −109.513 −3.48057
\(991\) 4.19767 0.133343 0.0666717 0.997775i \(-0.478762\pi\)
0.0666717 + 0.997775i \(0.478762\pi\)
\(992\) −11.5307 −0.366100
\(993\) 7.97917 0.253211
\(994\) 120.571 3.82427
\(995\) −2.45789 −0.0779203
\(996\) −14.5236 −0.460197
\(997\) 6.60567 0.209204 0.104602 0.994514i \(-0.466643\pi\)
0.104602 + 0.994514i \(0.466643\pi\)
\(998\) 39.5732 1.25267
\(999\) −8.30969 −0.262907
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 4003.2.a.c.1.14 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.14 179 1.1 even 1 trivial