Properties

Label 6001.2.a.d.1.7
Level 6001
Weight 2
Character 6001.1
Self dual yes
Analytic conductor 47.918
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9182262530\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.53489 q^{2} +1.89170 q^{3} +4.42568 q^{4} -3.70427 q^{5} -4.79525 q^{6} +1.26299 q^{7} -6.14885 q^{8} +0.578524 q^{9} +O(q^{10})\) \(q-2.53489 q^{2} +1.89170 q^{3} +4.42568 q^{4} -3.70427 q^{5} -4.79525 q^{6} +1.26299 q^{7} -6.14885 q^{8} +0.578524 q^{9} +9.38992 q^{10} +2.05827 q^{11} +8.37206 q^{12} -4.01998 q^{13} -3.20155 q^{14} -7.00736 q^{15} +6.73530 q^{16} +1.00000 q^{17} -1.46650 q^{18} -7.14159 q^{19} -16.3939 q^{20} +2.38920 q^{21} -5.21750 q^{22} +5.87831 q^{23} -11.6318 q^{24} +8.72160 q^{25} +10.1902 q^{26} -4.58070 q^{27} +5.58960 q^{28} -7.52141 q^{29} +17.7629 q^{30} -9.88256 q^{31} -4.77558 q^{32} +3.89363 q^{33} -2.53489 q^{34} -4.67846 q^{35} +2.56036 q^{36} +5.71734 q^{37} +18.1032 q^{38} -7.60459 q^{39} +22.7770 q^{40} +2.81357 q^{41} -6.05637 q^{42} -11.9844 q^{43} +9.10926 q^{44} -2.14301 q^{45} -14.9009 q^{46} +12.0896 q^{47} +12.7412 q^{48} -5.40485 q^{49} -22.1083 q^{50} +1.89170 q^{51} -17.7912 q^{52} -5.95956 q^{53} +11.6116 q^{54} -7.62439 q^{55} -7.76594 q^{56} -13.5097 q^{57} +19.0660 q^{58} +4.96138 q^{59} -31.0123 q^{60} -1.33305 q^{61} +25.0512 q^{62} +0.730671 q^{63} -1.36503 q^{64} +14.8911 q^{65} -9.86994 q^{66} +9.10999 q^{67} +4.42568 q^{68} +11.1200 q^{69} +11.8594 q^{70} +11.8612 q^{71} -3.55726 q^{72} +12.7868 q^{73} -14.4928 q^{74} +16.4986 q^{75} -31.6064 q^{76} +2.59958 q^{77} +19.2768 q^{78} +3.67665 q^{79} -24.9494 q^{80} -10.4009 q^{81} -7.13211 q^{82} -11.3091 q^{83} +10.5738 q^{84} -3.70427 q^{85} +30.3792 q^{86} -14.2282 q^{87} -12.6560 q^{88} +2.88543 q^{89} +5.43230 q^{90} -5.07720 q^{91} +26.0156 q^{92} -18.6948 q^{93} -30.6460 q^{94} +26.4543 q^{95} -9.03395 q^{96} -10.6742 q^{97} +13.7007 q^{98} +1.19076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + O(q^{10}) \) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + 19q^{10} + 48q^{11} + 43q^{12} + 6q^{13} + 40q^{14} + 49q^{15} + 135q^{16} + 121q^{17} + 30q^{19} + 50q^{20} + 18q^{21} + 24q^{22} + 75q^{23} + 24q^{24} + 128q^{25} + 59q^{26} + 75q^{27} + 52q^{28} + 49q^{29} - 34q^{30} + 101q^{31} + 47q^{32} + 20q^{33} + 9q^{34} + 47q^{35} + 138q^{36} + 32q^{37} + 30q^{38} + 101q^{39} + 36q^{40} + 83q^{41} - 11q^{42} + 8q^{43} + 98q^{44} + 49q^{45} + 45q^{46} + 135q^{47} + 54q^{48} + 116q^{49} + 3q^{50} + 21q^{51} - 5q^{52} + 28q^{53} + 10q^{54} + 37q^{55} + 75q^{56} + 31q^{58} + 150q^{59} + 50q^{60} + 36q^{61} + 34q^{62} + 118q^{63} + 110q^{64} + 18q^{65} - 28q^{66} - 6q^{67} + 127q^{68} + 25q^{69} - 22q^{70} + 223q^{71} + q^{72} + 38q^{73} - 10q^{74} + 88q^{75} - 4q^{76} + 38q^{77} + 42q^{78} + 74q^{79} + 106q^{80} + 133q^{81} + 28q^{82} + 55q^{83} + 10q^{84} + 27q^{85} + 64q^{86} + 14q^{87} + 56q^{88} + 118q^{89} + 51q^{90} + 73q^{91} + 82q^{92} + 31q^{93} + 33q^{94} + 106q^{95} + 38q^{96} + 37q^{97} + 88q^{98} + 81q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53489 −1.79244 −0.896220 0.443610i \(-0.853698\pi\)
−0.896220 + 0.443610i \(0.853698\pi\)
\(3\) 1.89170 1.09217 0.546086 0.837729i \(-0.316117\pi\)
0.546086 + 0.837729i \(0.316117\pi\)
\(4\) 4.42568 2.21284
\(5\) −3.70427 −1.65660 −0.828300 0.560286i \(-0.810691\pi\)
−0.828300 + 0.560286i \(0.810691\pi\)
\(6\) −4.79525 −1.95765
\(7\) 1.26299 0.477366 0.238683 0.971098i \(-0.423284\pi\)
0.238683 + 0.971098i \(0.423284\pi\)
\(8\) −6.14885 −2.17395
\(9\) 0.578524 0.192841
\(10\) 9.38992 2.96935
\(11\) 2.05827 0.620592 0.310296 0.950640i \(-0.399572\pi\)
0.310296 + 0.950640i \(0.399572\pi\)
\(12\) 8.37206 2.41681
\(13\) −4.01998 −1.11494 −0.557471 0.830196i \(-0.688228\pi\)
−0.557471 + 0.830196i \(0.688228\pi\)
\(14\) −3.20155 −0.855650
\(15\) −7.00736 −1.80929
\(16\) 6.73530 1.68383
\(17\) 1.00000 0.242536
\(18\) −1.46650 −0.345657
\(19\) −7.14159 −1.63839 −0.819196 0.573514i \(-0.805580\pi\)
−0.819196 + 0.573514i \(0.805580\pi\)
\(20\) −16.3939 −3.66579
\(21\) 2.38920 0.521366
\(22\) −5.21750 −1.11237
\(23\) 5.87831 1.22571 0.612857 0.790194i \(-0.290020\pi\)
0.612857 + 0.790194i \(0.290020\pi\)
\(24\) −11.6318 −2.37432
\(25\) 8.72160 1.74432
\(26\) 10.1902 1.99847
\(27\) −4.58070 −0.881557
\(28\) 5.58960 1.05634
\(29\) −7.52141 −1.39669 −0.698345 0.715761i \(-0.746080\pi\)
−0.698345 + 0.715761i \(0.746080\pi\)
\(30\) 17.7629 3.24305
\(31\) −9.88256 −1.77496 −0.887480 0.460845i \(-0.847546\pi\)
−0.887480 + 0.460845i \(0.847546\pi\)
\(32\) −4.77558 −0.844211
\(33\) 3.89363 0.677794
\(34\) −2.53489 −0.434731
\(35\) −4.67846 −0.790804
\(36\) 2.56036 0.426727
\(37\) 5.71734 0.939925 0.469962 0.882686i \(-0.344267\pi\)
0.469962 + 0.882686i \(0.344267\pi\)
\(38\) 18.1032 2.93672
\(39\) −7.60459 −1.21771
\(40\) 22.7770 3.60136
\(41\) 2.81357 0.439406 0.219703 0.975567i \(-0.429491\pi\)
0.219703 + 0.975567i \(0.429491\pi\)
\(42\) −6.05637 −0.934518
\(43\) −11.9844 −1.82760 −0.913801 0.406161i \(-0.866867\pi\)
−0.913801 + 0.406161i \(0.866867\pi\)
\(44\) 9.10926 1.37327
\(45\) −2.14301 −0.319461
\(46\) −14.9009 −2.19702
\(47\) 12.0896 1.76346 0.881728 0.471758i \(-0.156380\pi\)
0.881728 + 0.471758i \(0.156380\pi\)
\(48\) 12.7412 1.83903
\(49\) −5.40485 −0.772122
\(50\) −22.1083 −3.12659
\(51\) 1.89170 0.264891
\(52\) −17.7912 −2.46719
\(53\) −5.95956 −0.818609 −0.409304 0.912398i \(-0.634229\pi\)
−0.409304 + 0.912398i \(0.634229\pi\)
\(54\) 11.6116 1.58014
\(55\) −7.62439 −1.02807
\(56\) −7.76594 −1.03777
\(57\) −13.5097 −1.78941
\(58\) 19.0660 2.50348
\(59\) 4.96138 0.645916 0.322958 0.946413i \(-0.395323\pi\)
0.322958 + 0.946413i \(0.395323\pi\)
\(60\) −31.0123 −4.00368
\(61\) −1.33305 −0.170680 −0.0853398 0.996352i \(-0.527198\pi\)
−0.0853398 + 0.996352i \(0.527198\pi\)
\(62\) 25.0512 3.18151
\(63\) 0.730671 0.0920559
\(64\) −1.36503 −0.170628
\(65\) 14.8911 1.84701
\(66\) −9.86994 −1.21491
\(67\) 9.10999 1.11296 0.556481 0.830860i \(-0.312151\pi\)
0.556481 + 0.830860i \(0.312151\pi\)
\(68\) 4.42568 0.536693
\(69\) 11.1200 1.33869
\(70\) 11.8594 1.41747
\(71\) 11.8612 1.40767 0.703835 0.710363i \(-0.251469\pi\)
0.703835 + 0.710363i \(0.251469\pi\)
\(72\) −3.55726 −0.419227
\(73\) 12.7868 1.49659 0.748293 0.663369i \(-0.230874\pi\)
0.748293 + 0.663369i \(0.230874\pi\)
\(74\) −14.4928 −1.68476
\(75\) 16.4986 1.90510
\(76\) −31.6064 −3.62550
\(77\) 2.59958 0.296250
\(78\) 19.2768 2.18267
\(79\) 3.67665 0.413655 0.206828 0.978377i \(-0.433686\pi\)
0.206828 + 0.978377i \(0.433686\pi\)
\(80\) −24.9494 −2.78942
\(81\) −10.4009 −1.15565
\(82\) −7.13211 −0.787609
\(83\) −11.3091 −1.24133 −0.620667 0.784074i \(-0.713138\pi\)
−0.620667 + 0.784074i \(0.713138\pi\)
\(84\) 10.5738 1.15370
\(85\) −3.70427 −0.401784
\(86\) 30.3792 3.27587
\(87\) −14.2282 −1.52543
\(88\) −12.6560 −1.34913
\(89\) 2.88543 0.305855 0.152928 0.988237i \(-0.451130\pi\)
0.152928 + 0.988237i \(0.451130\pi\)
\(90\) 5.43230 0.572614
\(91\) −5.07720 −0.532235
\(92\) 26.0156 2.71231
\(93\) −18.6948 −1.93856
\(94\) −30.6460 −3.16089
\(95\) 26.4543 2.71416
\(96\) −9.03395 −0.922024
\(97\) −10.6742 −1.08380 −0.541899 0.840444i \(-0.682294\pi\)
−0.541899 + 0.840444i \(0.682294\pi\)
\(98\) 13.7007 1.38398
\(99\) 1.19076 0.119676
\(100\) 38.5990 3.85990
\(101\) 12.6502 1.25874 0.629369 0.777107i \(-0.283314\pi\)
0.629369 + 0.777107i \(0.283314\pi\)
\(102\) −4.79525 −0.474801
\(103\) 10.0135 0.986664 0.493332 0.869841i \(-0.335779\pi\)
0.493332 + 0.869841i \(0.335779\pi\)
\(104\) 24.7182 2.42382
\(105\) −8.85024 −0.863695
\(106\) 15.1069 1.46731
\(107\) 8.88696 0.859135 0.429568 0.903035i \(-0.358666\pi\)
0.429568 + 0.903035i \(0.358666\pi\)
\(108\) −20.2727 −1.95074
\(109\) −8.67676 −0.831083 −0.415541 0.909574i \(-0.636408\pi\)
−0.415541 + 0.909574i \(0.636408\pi\)
\(110\) 19.3270 1.84276
\(111\) 10.8155 1.02656
\(112\) 8.50663 0.803801
\(113\) 1.02680 0.0965934 0.0482967 0.998833i \(-0.484621\pi\)
0.0482967 + 0.998833i \(0.484621\pi\)
\(114\) 34.2457 3.20741
\(115\) −21.7748 −2.03052
\(116\) −33.2874 −3.09066
\(117\) −2.32566 −0.215007
\(118\) −12.5766 −1.15777
\(119\) 1.26299 0.115778
\(120\) 43.0872 3.93330
\(121\) −6.76352 −0.614865
\(122\) 3.37914 0.305933
\(123\) 5.32243 0.479908
\(124\) −43.7371 −3.92771
\(125\) −13.7858 −1.23304
\(126\) −1.85217 −0.165005
\(127\) −7.10141 −0.630148 −0.315074 0.949067i \(-0.602029\pi\)
−0.315074 + 0.949067i \(0.602029\pi\)
\(128\) 13.0114 1.15005
\(129\) −22.6709 −1.99606
\(130\) −37.7473 −3.31066
\(131\) −1.90149 −0.166134 −0.0830669 0.996544i \(-0.526472\pi\)
−0.0830669 + 0.996544i \(0.526472\pi\)
\(132\) 17.2320 1.49985
\(133\) −9.01976 −0.782113
\(134\) −23.0929 −1.99492
\(135\) 16.9682 1.46039
\(136\) −6.14885 −0.527259
\(137\) 0.346599 0.0296120 0.0148060 0.999890i \(-0.495287\pi\)
0.0148060 + 0.999890i \(0.495287\pi\)
\(138\) −28.1880 −2.39952
\(139\) −10.8123 −0.917083 −0.458542 0.888673i \(-0.651628\pi\)
−0.458542 + 0.888673i \(0.651628\pi\)
\(140\) −20.7054 −1.74992
\(141\) 22.8700 1.92600
\(142\) −30.0670 −2.52316
\(143\) −8.27421 −0.691924
\(144\) 3.89653 0.324711
\(145\) 27.8613 2.31376
\(146\) −32.4132 −2.68254
\(147\) −10.2244 −0.843290
\(148\) 25.3031 2.07990
\(149\) −20.9508 −1.71636 −0.858178 0.513353i \(-0.828403\pi\)
−0.858178 + 0.513353i \(0.828403\pi\)
\(150\) −41.8223 −3.41478
\(151\) 8.98956 0.731560 0.365780 0.930701i \(-0.380802\pi\)
0.365780 + 0.930701i \(0.380802\pi\)
\(152\) 43.9125 3.56177
\(153\) 0.578524 0.0467709
\(154\) −6.58966 −0.531010
\(155\) 36.6077 2.94040
\(156\) −33.6555 −2.69460
\(157\) 14.2418 1.13662 0.568308 0.822816i \(-0.307598\pi\)
0.568308 + 0.822816i \(0.307598\pi\)
\(158\) −9.31991 −0.741452
\(159\) −11.2737 −0.894062
\(160\) 17.6900 1.39852
\(161\) 7.42426 0.585114
\(162\) 26.3651 2.07144
\(163\) 7.43863 0.582639 0.291319 0.956626i \(-0.405906\pi\)
0.291319 + 0.956626i \(0.405906\pi\)
\(164\) 12.4520 0.972336
\(165\) −14.4230 −1.12283
\(166\) 28.6674 2.22502
\(167\) −5.88825 −0.455646 −0.227823 0.973703i \(-0.573161\pi\)
−0.227823 + 0.973703i \(0.573161\pi\)
\(168\) −14.6908 −1.13342
\(169\) 3.16025 0.243096
\(170\) 9.38992 0.720174
\(171\) −4.13158 −0.315950
\(172\) −53.0391 −4.04419
\(173\) 7.33461 0.557640 0.278820 0.960343i \(-0.410057\pi\)
0.278820 + 0.960343i \(0.410057\pi\)
\(174\) 36.0671 2.73424
\(175\) 11.0153 0.832679
\(176\) 13.8631 1.04497
\(177\) 9.38543 0.705452
\(178\) −7.31426 −0.548227
\(179\) 16.6045 1.24108 0.620539 0.784175i \(-0.286914\pi\)
0.620539 + 0.784175i \(0.286914\pi\)
\(180\) −9.48428 −0.706916
\(181\) −17.8160 −1.32425 −0.662126 0.749392i \(-0.730346\pi\)
−0.662126 + 0.749392i \(0.730346\pi\)
\(182\) 12.8702 0.954000
\(183\) −2.52173 −0.186412
\(184\) −36.1448 −2.66463
\(185\) −21.1786 −1.55708
\(186\) 47.3894 3.47476
\(187\) 2.05827 0.150516
\(188\) 53.5049 3.90225
\(189\) −5.78539 −0.420825
\(190\) −67.0589 −4.86497
\(191\) −13.1314 −0.950154 −0.475077 0.879944i \(-0.657580\pi\)
−0.475077 + 0.879944i \(0.657580\pi\)
\(192\) −2.58222 −0.186356
\(193\) 12.6791 0.912664 0.456332 0.889810i \(-0.349163\pi\)
0.456332 + 0.889810i \(0.349163\pi\)
\(194\) 27.0579 1.94264
\(195\) 28.1694 2.01726
\(196\) −23.9202 −1.70858
\(197\) −3.74763 −0.267007 −0.133504 0.991048i \(-0.542623\pi\)
−0.133504 + 0.991048i \(0.542623\pi\)
\(198\) −3.01845 −0.214512
\(199\) 16.0413 1.13714 0.568568 0.822636i \(-0.307498\pi\)
0.568568 + 0.822636i \(0.307498\pi\)
\(200\) −53.6278 −3.79206
\(201\) 17.2334 1.21555
\(202\) −32.0668 −2.25621
\(203\) −9.49948 −0.666733
\(204\) 8.37206 0.586161
\(205\) −10.4222 −0.727920
\(206\) −25.3833 −1.76854
\(207\) 3.40075 0.236368
\(208\) −27.0758 −1.87737
\(209\) −14.6993 −1.01677
\(210\) 22.4344 1.54812
\(211\) 9.74457 0.670844 0.335422 0.942068i \(-0.391121\pi\)
0.335422 + 0.942068i \(0.391121\pi\)
\(212\) −26.3751 −1.81145
\(213\) 22.4379 1.53742
\(214\) −22.5275 −1.53995
\(215\) 44.3934 3.02760
\(216\) 28.1660 1.91646
\(217\) −12.4816 −0.847306
\(218\) 21.9947 1.48967
\(219\) 24.1888 1.63453
\(220\) −33.7431 −2.27496
\(221\) −4.01998 −0.270413
\(222\) −27.4161 −1.84005
\(223\) 25.5681 1.71217 0.856084 0.516837i \(-0.172891\pi\)
0.856084 + 0.516837i \(0.172891\pi\)
\(224\) −6.03151 −0.402997
\(225\) 5.04566 0.336377
\(226\) −2.60283 −0.173138
\(227\) −11.3696 −0.754628 −0.377314 0.926085i \(-0.623152\pi\)
−0.377314 + 0.926085i \(0.623152\pi\)
\(228\) −59.7898 −3.95967
\(229\) 22.9864 1.51899 0.759493 0.650515i \(-0.225447\pi\)
0.759493 + 0.650515i \(0.225447\pi\)
\(230\) 55.1969 3.63958
\(231\) 4.91762 0.323556
\(232\) 46.2480 3.03633
\(233\) −17.8690 −1.17064 −0.585319 0.810803i \(-0.699031\pi\)
−0.585319 + 0.810803i \(0.699031\pi\)
\(234\) 5.89529 0.385387
\(235\) −44.7833 −2.92134
\(236\) 21.9575 1.42931
\(237\) 6.95511 0.451783
\(238\) −3.20155 −0.207526
\(239\) 11.8831 0.768655 0.384328 0.923197i \(-0.374433\pi\)
0.384328 + 0.923197i \(0.374433\pi\)
\(240\) −47.1967 −3.04653
\(241\) 10.9992 0.708519 0.354260 0.935147i \(-0.384733\pi\)
0.354260 + 0.935147i \(0.384733\pi\)
\(242\) 17.1448 1.10211
\(243\) −5.93323 −0.380617
\(244\) −5.89965 −0.377687
\(245\) 20.0210 1.27910
\(246\) −13.4918 −0.860205
\(247\) 28.7090 1.82671
\(248\) 60.7664 3.85867
\(249\) −21.3934 −1.35575
\(250\) 34.9456 2.21015
\(251\) 10.5157 0.663746 0.331873 0.943324i \(-0.392320\pi\)
0.331873 + 0.943324i \(0.392320\pi\)
\(252\) 3.23372 0.203705
\(253\) 12.0992 0.760668
\(254\) 18.0013 1.12950
\(255\) −7.00736 −0.438818
\(256\) −30.2523 −1.89077
\(257\) 10.7008 0.667498 0.333749 0.942662i \(-0.391686\pi\)
0.333749 + 0.942662i \(0.391686\pi\)
\(258\) 57.4682 3.57781
\(259\) 7.22095 0.448688
\(260\) 65.9032 4.08714
\(261\) −4.35132 −0.269340
\(262\) 4.82007 0.297785
\(263\) −15.5644 −0.959740 −0.479870 0.877340i \(-0.659316\pi\)
−0.479870 + 0.877340i \(0.659316\pi\)
\(264\) −23.9413 −1.47349
\(265\) 22.0758 1.35611
\(266\) 22.8641 1.40189
\(267\) 5.45837 0.334047
\(268\) 40.3179 2.46281
\(269\) 11.2145 0.683762 0.341881 0.939743i \(-0.388936\pi\)
0.341881 + 0.939743i \(0.388936\pi\)
\(270\) −43.0124 −2.61765
\(271\) 7.13795 0.433600 0.216800 0.976216i \(-0.430438\pi\)
0.216800 + 0.976216i \(0.430438\pi\)
\(272\) 6.73530 0.408388
\(273\) −9.60454 −0.581293
\(274\) −0.878592 −0.0530777
\(275\) 17.9514 1.08251
\(276\) 49.2136 2.96231
\(277\) −18.9183 −1.13669 −0.568345 0.822791i \(-0.692416\pi\)
−0.568345 + 0.822791i \(0.692416\pi\)
\(278\) 27.4079 1.64382
\(279\) −5.71730 −0.342286
\(280\) 28.7671 1.71916
\(281\) 30.2096 1.80216 0.901078 0.433658i \(-0.142777\pi\)
0.901078 + 0.433658i \(0.142777\pi\)
\(282\) −57.9729 −3.45224
\(283\) 15.3575 0.912907 0.456454 0.889747i \(-0.349119\pi\)
0.456454 + 0.889747i \(0.349119\pi\)
\(284\) 52.4941 3.11495
\(285\) 50.0437 2.96433
\(286\) 20.9742 1.24023
\(287\) 3.55352 0.209758
\(288\) −2.76279 −0.162799
\(289\) 1.00000 0.0588235
\(290\) −70.6255 −4.14727
\(291\) −20.1923 −1.18369
\(292\) 56.5905 3.31171
\(293\) −5.51362 −0.322109 −0.161054 0.986946i \(-0.551489\pi\)
−0.161054 + 0.986946i \(0.551489\pi\)
\(294\) 25.9176 1.51155
\(295\) −18.3783 −1.07002
\(296\) −35.1550 −2.04334
\(297\) −9.42833 −0.547087
\(298\) 53.1080 3.07646
\(299\) −23.6307 −1.36660
\(300\) 73.0178 4.21568
\(301\) −15.1362 −0.872435
\(302\) −22.7876 −1.31128
\(303\) 23.9303 1.37476
\(304\) −48.1007 −2.75877
\(305\) 4.93797 0.282748
\(306\) −1.46650 −0.0838341
\(307\) −26.8568 −1.53280 −0.766398 0.642366i \(-0.777953\pi\)
−0.766398 + 0.642366i \(0.777953\pi\)
\(308\) 11.5049 0.655553
\(309\) 18.9426 1.07761
\(310\) −92.7965 −5.27049
\(311\) 16.8862 0.957530 0.478765 0.877943i \(-0.341085\pi\)
0.478765 + 0.877943i \(0.341085\pi\)
\(312\) 46.7595 2.64723
\(313\) 13.0636 0.738400 0.369200 0.929350i \(-0.379632\pi\)
0.369200 + 0.929350i \(0.379632\pi\)
\(314\) −36.1013 −2.03732
\(315\) −2.70660 −0.152500
\(316\) 16.2717 0.915354
\(317\) −11.0945 −0.623131 −0.311565 0.950225i \(-0.600853\pi\)
−0.311565 + 0.950225i \(0.600853\pi\)
\(318\) 28.5776 1.60255
\(319\) −15.4811 −0.866776
\(320\) 5.05643 0.282663
\(321\) 16.8115 0.938324
\(322\) −18.8197 −1.04878
\(323\) −7.14159 −0.397368
\(324\) −46.0310 −2.55728
\(325\) −35.0607 −1.94482
\(326\) −18.8561 −1.04434
\(327\) −16.4138 −0.907686
\(328\) −17.3002 −0.955245
\(329\) 15.2691 0.841814
\(330\) 36.5609 2.01261
\(331\) −7.61598 −0.418612 −0.209306 0.977850i \(-0.567120\pi\)
−0.209306 + 0.977850i \(0.567120\pi\)
\(332\) −50.0505 −2.74688
\(333\) 3.30762 0.181256
\(334\) 14.9261 0.816718
\(335\) −33.7459 −1.84373
\(336\) 16.0920 0.877889
\(337\) −22.5953 −1.23084 −0.615422 0.788198i \(-0.711014\pi\)
−0.615422 + 0.788198i \(0.711014\pi\)
\(338\) −8.01088 −0.435735
\(339\) 1.94240 0.105497
\(340\) −16.3939 −0.889085
\(341\) −20.3410 −1.10153
\(342\) 10.4731 0.566321
\(343\) −15.6672 −0.845951
\(344\) 73.6902 3.97311
\(345\) −41.1915 −2.21767
\(346\) −18.5924 −0.999536
\(347\) 29.7595 1.59758 0.798788 0.601612i \(-0.205475\pi\)
0.798788 + 0.601612i \(0.205475\pi\)
\(348\) −62.9697 −3.37553
\(349\) 33.1584 1.77493 0.887464 0.460877i \(-0.152465\pi\)
0.887464 + 0.460877i \(0.152465\pi\)
\(350\) −27.9226 −1.49253
\(351\) 18.4143 0.982885
\(352\) −9.82943 −0.523911
\(353\) −1.00000 −0.0532246
\(354\) −23.7911 −1.26448
\(355\) −43.9372 −2.33195
\(356\) 12.7700 0.676809
\(357\) 2.38920 0.126450
\(358\) −42.0906 −2.22456
\(359\) −16.5427 −0.873090 −0.436545 0.899682i \(-0.643798\pi\)
−0.436545 + 0.899682i \(0.643798\pi\)
\(360\) 13.1770 0.694490
\(361\) 32.0022 1.68433
\(362\) 45.1617 2.37364
\(363\) −12.7945 −0.671539
\(364\) −22.4701 −1.17775
\(365\) −47.3658 −2.47924
\(366\) 6.39231 0.334131
\(367\) 7.99489 0.417330 0.208665 0.977987i \(-0.433088\pi\)
0.208665 + 0.977987i \(0.433088\pi\)
\(368\) 39.5922 2.06389
\(369\) 1.62772 0.0847357
\(370\) 53.6854 2.79097
\(371\) −7.52688 −0.390776
\(372\) −82.7374 −4.28973
\(373\) 12.6648 0.655759 0.327880 0.944720i \(-0.393666\pi\)
0.327880 + 0.944720i \(0.393666\pi\)
\(374\) −5.21750 −0.269790
\(375\) −26.0786 −1.34669
\(376\) −74.3374 −3.83366
\(377\) 30.2359 1.55723
\(378\) 14.6653 0.754304
\(379\) −19.2240 −0.987471 −0.493735 0.869612i \(-0.664369\pi\)
−0.493735 + 0.869612i \(0.664369\pi\)
\(380\) 117.079 6.00600
\(381\) −13.4337 −0.688230
\(382\) 33.2867 1.70309
\(383\) −13.0961 −0.669179 −0.334590 0.942364i \(-0.608598\pi\)
−0.334590 + 0.942364i \(0.608598\pi\)
\(384\) 24.6136 1.25606
\(385\) −9.62954 −0.490767
\(386\) −32.1403 −1.63590
\(387\) −6.93326 −0.352437
\(388\) −47.2405 −2.39827
\(389\) −30.7458 −1.55887 −0.779436 0.626481i \(-0.784494\pi\)
−0.779436 + 0.626481i \(0.784494\pi\)
\(390\) −71.4065 −3.61581
\(391\) 5.87831 0.297279
\(392\) 33.2336 1.67855
\(393\) −3.59704 −0.181447
\(394\) 9.49984 0.478595
\(395\) −13.6193 −0.685261
\(396\) 5.26993 0.264824
\(397\) 4.66852 0.234306 0.117153 0.993114i \(-0.462623\pi\)
0.117153 + 0.993114i \(0.462623\pi\)
\(398\) −40.6629 −2.03825
\(399\) −17.0627 −0.854202
\(400\) 58.7426 2.93713
\(401\) −9.86032 −0.492401 −0.246200 0.969219i \(-0.579182\pi\)
−0.246200 + 0.969219i \(0.579182\pi\)
\(402\) −43.6847 −2.17880
\(403\) 39.7277 1.97898
\(404\) 55.9856 2.78539
\(405\) 38.5277 1.91445
\(406\) 24.0802 1.19508
\(407\) 11.7678 0.583310
\(408\) −11.6318 −0.575858
\(409\) 37.4412 1.85135 0.925674 0.378321i \(-0.123498\pi\)
0.925674 + 0.378321i \(0.123498\pi\)
\(410\) 26.4192 1.30475
\(411\) 0.655662 0.0323414
\(412\) 44.3168 2.18333
\(413\) 6.26618 0.308338
\(414\) −8.62053 −0.423676
\(415\) 41.8919 2.05639
\(416\) 19.1977 0.941246
\(417\) −20.4535 −1.00161
\(418\) 37.2612 1.82251
\(419\) 8.28899 0.404944 0.202472 0.979288i \(-0.435103\pi\)
0.202472 + 0.979288i \(0.435103\pi\)
\(420\) −39.1683 −1.91122
\(421\) −1.96341 −0.0956906 −0.0478453 0.998855i \(-0.515235\pi\)
−0.0478453 + 0.998855i \(0.515235\pi\)
\(422\) −24.7014 −1.20245
\(423\) 6.99415 0.340067
\(424\) 36.6444 1.77961
\(425\) 8.72160 0.423060
\(426\) −56.8777 −2.75573
\(427\) −1.68363 −0.0814766
\(428\) 39.3309 1.90113
\(429\) −15.6523 −0.755701
\(430\) −112.533 −5.42680
\(431\) −7.65239 −0.368603 −0.184301 0.982870i \(-0.559002\pi\)
−0.184301 + 0.982870i \(0.559002\pi\)
\(432\) −30.8524 −1.48439
\(433\) 1.88101 0.0903953 0.0451977 0.998978i \(-0.485608\pi\)
0.0451977 + 0.998978i \(0.485608\pi\)
\(434\) 31.6395 1.51875
\(435\) 52.7052 2.52702
\(436\) −38.4006 −1.83905
\(437\) −41.9805 −2.00820
\(438\) −61.3161 −2.92980
\(439\) 3.93308 0.187715 0.0938577 0.995586i \(-0.470080\pi\)
0.0938577 + 0.995586i \(0.470080\pi\)
\(440\) 46.8812 2.23497
\(441\) −3.12684 −0.148897
\(442\) 10.1902 0.484699
\(443\) −0.541180 −0.0257123 −0.0128561 0.999917i \(-0.504092\pi\)
−0.0128561 + 0.999917i \(0.504092\pi\)
\(444\) 47.8659 2.27161
\(445\) −10.6884 −0.506680
\(446\) −64.8124 −3.06896
\(447\) −39.6326 −1.87456
\(448\) −1.72402 −0.0814522
\(449\) −13.4213 −0.633391 −0.316696 0.948527i \(-0.602573\pi\)
−0.316696 + 0.948527i \(0.602573\pi\)
\(450\) −12.7902 −0.602936
\(451\) 5.79110 0.272692
\(452\) 4.54430 0.213746
\(453\) 17.0055 0.798990
\(454\) 28.8208 1.35263
\(455\) 18.8073 0.881701
\(456\) 83.0692 3.89007
\(457\) −20.2253 −0.946100 −0.473050 0.881035i \(-0.656847\pi\)
−0.473050 + 0.881035i \(0.656847\pi\)
\(458\) −58.2682 −2.72269
\(459\) −4.58070 −0.213809
\(460\) −96.3686 −4.49321
\(461\) 34.6466 1.61365 0.806827 0.590787i \(-0.201183\pi\)
0.806827 + 0.590787i \(0.201183\pi\)
\(462\) −12.4656 −0.579954
\(463\) −9.18308 −0.426774 −0.213387 0.976968i \(-0.568449\pi\)
−0.213387 + 0.976968i \(0.568449\pi\)
\(464\) −50.6590 −2.35178
\(465\) 69.2507 3.21142
\(466\) 45.2960 2.09830
\(467\) 0.159268 0.00737004 0.00368502 0.999993i \(-0.498827\pi\)
0.00368502 + 0.999993i \(0.498827\pi\)
\(468\) −10.2926 −0.475776
\(469\) 11.5058 0.531291
\(470\) 113.521 5.23633
\(471\) 26.9411 1.24138
\(472\) −30.5067 −1.40419
\(473\) −24.6671 −1.13420
\(474\) −17.6305 −0.809794
\(475\) −62.2861 −2.85788
\(476\) 5.58960 0.256199
\(477\) −3.44775 −0.157862
\(478\) −30.1224 −1.37777
\(479\) 14.3314 0.654818 0.327409 0.944883i \(-0.393825\pi\)
0.327409 + 0.944883i \(0.393825\pi\)
\(480\) 33.4642 1.52742
\(481\) −22.9836 −1.04796
\(482\) −27.8817 −1.26998
\(483\) 14.0445 0.639045
\(484\) −29.9332 −1.36060
\(485\) 39.5400 1.79542
\(486\) 15.0401 0.682233
\(487\) 0.835205 0.0378468 0.0189234 0.999821i \(-0.493976\pi\)
0.0189234 + 0.999821i \(0.493976\pi\)
\(488\) 8.19672 0.371048
\(489\) 14.0717 0.636342
\(490\) −50.7511 −2.29270
\(491\) −8.07830 −0.364568 −0.182284 0.983246i \(-0.558349\pi\)
−0.182284 + 0.983246i \(0.558349\pi\)
\(492\) 23.5554 1.06196
\(493\) −7.52141 −0.338747
\(494\) −72.7743 −3.27427
\(495\) −4.41089 −0.198255
\(496\) −66.5620 −2.98872
\(497\) 14.9806 0.671974
\(498\) 54.2300 2.43010
\(499\) 8.76958 0.392580 0.196290 0.980546i \(-0.437111\pi\)
0.196290 + 0.980546i \(0.437111\pi\)
\(500\) −61.0116 −2.72852
\(501\) −11.1388 −0.497644
\(502\) −26.6562 −1.18972
\(503\) 27.6402 1.23242 0.616208 0.787583i \(-0.288668\pi\)
0.616208 + 0.787583i \(0.288668\pi\)
\(504\) −4.49278 −0.200125
\(505\) −46.8596 −2.08522
\(506\) −30.6701 −1.36345
\(507\) 5.97823 0.265503
\(508\) −31.4286 −1.39442
\(509\) 10.2374 0.453763 0.226881 0.973922i \(-0.427147\pi\)
0.226881 + 0.973922i \(0.427147\pi\)
\(510\) 17.7629 0.786555
\(511\) 16.1497 0.714419
\(512\) 50.6637 2.23904
\(513\) 32.7135 1.44434
\(514\) −27.1254 −1.19645
\(515\) −37.0928 −1.63451
\(516\) −100.334 −4.41696
\(517\) 24.8838 1.09439
\(518\) −18.3043 −0.804247
\(519\) 13.8749 0.609039
\(520\) −91.5630 −4.01530
\(521\) 30.7483 1.34711 0.673554 0.739138i \(-0.264767\pi\)
0.673554 + 0.739138i \(0.264767\pi\)
\(522\) 11.0301 0.482775
\(523\) −35.6191 −1.55751 −0.778756 0.627327i \(-0.784149\pi\)
−0.778756 + 0.627327i \(0.784149\pi\)
\(524\) −8.41538 −0.367628
\(525\) 20.8376 0.909430
\(526\) 39.4540 1.72028
\(527\) −9.88256 −0.430491
\(528\) 26.2248 1.14129
\(529\) 11.5546 0.502373
\(530\) −55.9598 −2.43074
\(531\) 2.87028 0.124559
\(532\) −39.9186 −1.73069
\(533\) −11.3105 −0.489912
\(534\) −13.8364 −0.598759
\(535\) −32.9197 −1.42324
\(536\) −56.0159 −2.41952
\(537\) 31.4107 1.35547
\(538\) −28.4276 −1.22560
\(539\) −11.1247 −0.479173
\(540\) 75.0956 3.23160
\(541\) 25.4079 1.09237 0.546186 0.837664i \(-0.316079\pi\)
0.546186 + 0.837664i \(0.316079\pi\)
\(542\) −18.0940 −0.777202
\(543\) −33.7025 −1.44631
\(544\) −4.77558 −0.204751
\(545\) 32.1410 1.37677
\(546\) 24.3465 1.04193
\(547\) −7.19318 −0.307558 −0.153779 0.988105i \(-0.549144\pi\)
−0.153779 + 0.988105i \(0.549144\pi\)
\(548\) 1.53394 0.0655266
\(549\) −0.771201 −0.0329141
\(550\) −45.5049 −1.94034
\(551\) 53.7148 2.28833
\(552\) −68.3752 −2.91024
\(553\) 4.64358 0.197465
\(554\) 47.9558 2.03745
\(555\) −40.0634 −1.70060
\(556\) −47.8516 −2.02936
\(557\) 12.9529 0.548832 0.274416 0.961611i \(-0.411516\pi\)
0.274416 + 0.961611i \(0.411516\pi\)
\(558\) 14.4928 0.613527
\(559\) 48.1770 2.03767
\(560\) −31.5108 −1.33158
\(561\) 3.89363 0.164389
\(562\) −76.5782 −3.23026
\(563\) 24.0665 1.01428 0.507140 0.861864i \(-0.330703\pi\)
0.507140 + 0.861864i \(0.330703\pi\)
\(564\) 101.215 4.26193
\(565\) −3.80355 −0.160016
\(566\) −38.9296 −1.63633
\(567\) −13.1362 −0.551670
\(568\) −72.9329 −3.06020
\(569\) 18.9215 0.793231 0.396615 0.917985i \(-0.370185\pi\)
0.396615 + 0.917985i \(0.370185\pi\)
\(570\) −126.855 −5.31338
\(571\) 17.0666 0.714214 0.357107 0.934063i \(-0.383763\pi\)
0.357107 + 0.934063i \(0.383763\pi\)
\(572\) −36.6190 −1.53112
\(573\) −24.8406 −1.03773
\(574\) −9.00779 −0.375978
\(575\) 51.2683 2.13804
\(576\) −0.789702 −0.0329042
\(577\) 20.5748 0.856541 0.428271 0.903650i \(-0.359123\pi\)
0.428271 + 0.903650i \(0.359123\pi\)
\(578\) −2.53489 −0.105438
\(579\) 23.9851 0.996787
\(580\) 123.305 5.11998
\(581\) −14.2833 −0.592571
\(582\) 51.1853 2.12170
\(583\) −12.2664 −0.508022
\(584\) −78.6243 −3.25349
\(585\) 8.61485 0.356180
\(586\) 13.9764 0.577361
\(587\) 45.1252 1.86252 0.931258 0.364360i \(-0.118712\pi\)
0.931258 + 0.364360i \(0.118712\pi\)
\(588\) −45.2497 −1.86607
\(589\) 70.5772 2.90808
\(590\) 46.5869 1.91795
\(591\) −7.08938 −0.291618
\(592\) 38.5080 1.58267
\(593\) −36.2490 −1.48857 −0.744283 0.667864i \(-0.767209\pi\)
−0.744283 + 0.667864i \(0.767209\pi\)
\(594\) 23.8998 0.980621
\(595\) −4.67846 −0.191798
\(596\) −92.7215 −3.79802
\(597\) 30.3452 1.24195
\(598\) 59.9013 2.44955
\(599\) 36.6703 1.49831 0.749155 0.662395i \(-0.230460\pi\)
0.749155 + 0.662395i \(0.230460\pi\)
\(600\) −101.448 −4.14158
\(601\) −41.3365 −1.68615 −0.843075 0.537795i \(-0.819257\pi\)
−0.843075 + 0.537795i \(0.819257\pi\)
\(602\) 38.3686 1.56379
\(603\) 5.27035 0.214625
\(604\) 39.7849 1.61883
\(605\) 25.0539 1.01859
\(606\) −60.6607 −2.46417
\(607\) −46.8989 −1.90357 −0.951783 0.306771i \(-0.900751\pi\)
−0.951783 + 0.306771i \(0.900751\pi\)
\(608\) 34.1052 1.38315
\(609\) −17.9702 −0.728187
\(610\) −12.5172 −0.506808
\(611\) −48.6001 −1.96615
\(612\) 2.56036 0.103497
\(613\) 40.5133 1.63632 0.818159 0.574992i \(-0.194995\pi\)
0.818159 + 0.574992i \(0.194995\pi\)
\(614\) 68.0790 2.74745
\(615\) −19.7157 −0.795014
\(616\) −15.9844 −0.644030
\(617\) 37.2429 1.49934 0.749672 0.661810i \(-0.230211\pi\)
0.749672 + 0.661810i \(0.230211\pi\)
\(618\) −48.0175 −1.93155
\(619\) −44.6149 −1.79322 −0.896611 0.442818i \(-0.853979\pi\)
−0.896611 + 0.442818i \(0.853979\pi\)
\(620\) 162.014 6.50664
\(621\) −26.9268 −1.08054
\(622\) −42.8048 −1.71632
\(623\) 3.64428 0.146005
\(624\) −51.2192 −2.05041
\(625\) 7.45832 0.298333
\(626\) −33.1149 −1.32354
\(627\) −27.8067 −1.11049
\(628\) 63.0295 2.51515
\(629\) 5.71734 0.227965
\(630\) 6.86095 0.273347
\(631\) 35.5835 1.41656 0.708279 0.705933i \(-0.249472\pi\)
0.708279 + 0.705933i \(0.249472\pi\)
\(632\) −22.6071 −0.899264
\(633\) 18.4338 0.732677
\(634\) 28.1234 1.11692
\(635\) 26.3055 1.04390
\(636\) −49.8938 −1.97842
\(637\) 21.7274 0.860871
\(638\) 39.2429 1.55364
\(639\) 6.86202 0.271457
\(640\) −48.1975 −1.90517
\(641\) −18.1886 −0.718405 −0.359203 0.933260i \(-0.616951\pi\)
−0.359203 + 0.933260i \(0.616951\pi\)
\(642\) −42.6152 −1.68189
\(643\) −37.5065 −1.47911 −0.739557 0.673094i \(-0.764965\pi\)
−0.739557 + 0.673094i \(0.764965\pi\)
\(644\) 32.8574 1.29476
\(645\) 83.9789 3.30667
\(646\) 18.1032 0.712259
\(647\) −11.2084 −0.440649 −0.220325 0.975427i \(-0.570712\pi\)
−0.220325 + 0.975427i \(0.570712\pi\)
\(648\) 63.9534 2.51233
\(649\) 10.2119 0.400851
\(650\) 88.8750 3.48597
\(651\) −23.6114 −0.925405
\(652\) 32.9210 1.28929
\(653\) −13.1738 −0.515532 −0.257766 0.966207i \(-0.582986\pi\)
−0.257766 + 0.966207i \(0.582986\pi\)
\(654\) 41.6073 1.62697
\(655\) 7.04362 0.275217
\(656\) 18.9503 0.739883
\(657\) 7.39749 0.288604
\(658\) −38.7056 −1.50890
\(659\) −1.27800 −0.0497840 −0.0248920 0.999690i \(-0.507924\pi\)
−0.0248920 + 0.999690i \(0.507924\pi\)
\(660\) −63.8318 −2.48465
\(661\) 29.0887 1.13142 0.565709 0.824605i \(-0.308602\pi\)
0.565709 + 0.824605i \(0.308602\pi\)
\(662\) 19.3057 0.750337
\(663\) −7.60459 −0.295338
\(664\) 69.5379 2.69859
\(665\) 33.4116 1.29565
\(666\) −8.38446 −0.324891
\(667\) −44.2132 −1.71194
\(668\) −26.0595 −1.00827
\(669\) 48.3672 1.86998
\(670\) 85.5421 3.30478
\(671\) −2.74378 −0.105922
\(672\) −11.4098 −0.440143
\(673\) 29.8126 1.14919 0.574595 0.818438i \(-0.305159\pi\)
0.574595 + 0.818438i \(0.305159\pi\)
\(674\) 57.2766 2.20621
\(675\) −39.9511 −1.53772
\(676\) 13.9862 0.537932
\(677\) 31.6439 1.21617 0.608087 0.793870i \(-0.291937\pi\)
0.608087 + 0.793870i \(0.291937\pi\)
\(678\) −4.92377 −0.189096
\(679\) −13.4814 −0.517368
\(680\) 22.7770 0.873457
\(681\) −21.5079 −0.824184
\(682\) 51.5623 1.97442
\(683\) −24.8039 −0.949096 −0.474548 0.880230i \(-0.657389\pi\)
−0.474548 + 0.880230i \(0.657389\pi\)
\(684\) −18.2851 −0.699147
\(685\) −1.28390 −0.0490552
\(686\) 39.7147 1.51632
\(687\) 43.4834 1.65900
\(688\) −80.7185 −3.07736
\(689\) 23.9573 0.912702
\(690\) 104.416 3.97505
\(691\) −1.91205 −0.0727380 −0.0363690 0.999338i \(-0.511579\pi\)
−0.0363690 + 0.999338i \(0.511579\pi\)
\(692\) 32.4606 1.23397
\(693\) 1.50392 0.0571292
\(694\) −75.4373 −2.86356
\(695\) 40.0515 1.51924
\(696\) 87.4873 3.31620
\(697\) 2.81357 0.106572
\(698\) −84.0530 −3.18145
\(699\) −33.8028 −1.27854
\(700\) 48.7503 1.84259
\(701\) −14.7393 −0.556695 −0.278347 0.960480i \(-0.589787\pi\)
−0.278347 + 0.960480i \(0.589787\pi\)
\(702\) −46.6784 −1.76176
\(703\) −40.8309 −1.53997
\(704\) −2.80960 −0.105891
\(705\) −84.7165 −3.19061
\(706\) 2.53489 0.0954020
\(707\) 15.9770 0.600878
\(708\) 41.5369 1.56105
\(709\) 29.6627 1.11401 0.557003 0.830510i \(-0.311951\pi\)
0.557003 + 0.830510i \(0.311951\pi\)
\(710\) 111.376 4.17987
\(711\) 2.12703 0.0797699
\(712\) −17.7421 −0.664913
\(713\) −58.0928 −2.17559
\(714\) −6.05637 −0.226654
\(715\) 30.6499 1.14624
\(716\) 73.4862 2.74631
\(717\) 22.4793 0.839504
\(718\) 41.9340 1.56496
\(719\) −39.0871 −1.45770 −0.728851 0.684672i \(-0.759946\pi\)
−0.728851 + 0.684672i \(0.759946\pi\)
\(720\) −14.4338 −0.537916
\(721\) 12.6470 0.471000
\(722\) −81.1223 −3.01906
\(723\) 20.8071 0.773825
\(724\) −78.8480 −2.93036
\(725\) −65.5987 −2.43628
\(726\) 32.4328 1.20369
\(727\) 1.92745 0.0714850 0.0357425 0.999361i \(-0.488620\pi\)
0.0357425 + 0.999361i \(0.488620\pi\)
\(728\) 31.2189 1.15705
\(729\) 19.9788 0.739954
\(730\) 120.067 4.44389
\(731\) −11.9844 −0.443259
\(732\) −11.1604 −0.412499
\(733\) 25.9978 0.960250 0.480125 0.877200i \(-0.340591\pi\)
0.480125 + 0.877200i \(0.340591\pi\)
\(734\) −20.2662 −0.748039
\(735\) 37.8737 1.39699
\(736\) −28.0723 −1.03476
\(737\) 18.7508 0.690696
\(738\) −4.12610 −0.151884
\(739\) 4.19370 0.154268 0.0771338 0.997021i \(-0.475423\pi\)
0.0771338 + 0.997021i \(0.475423\pi\)
\(740\) −93.7296 −3.44557
\(741\) 54.3089 1.99509
\(742\) 19.0798 0.700443
\(743\) 42.1031 1.54461 0.772307 0.635250i \(-0.219103\pi\)
0.772307 + 0.635250i \(0.219103\pi\)
\(744\) 114.952 4.21433
\(745\) 77.6073 2.84331
\(746\) −32.1039 −1.17541
\(747\) −6.54259 −0.239381
\(748\) 9.10926 0.333067
\(749\) 11.2242 0.410122
\(750\) 66.1065 2.41387
\(751\) 23.8813 0.871441 0.435720 0.900082i \(-0.356494\pi\)
0.435720 + 0.900082i \(0.356494\pi\)
\(752\) 81.4274 2.96935
\(753\) 19.8926 0.724925
\(754\) −76.6448 −2.79124
\(755\) −33.2997 −1.21190
\(756\) −25.6043 −0.931219
\(757\) −38.9490 −1.41562 −0.707812 0.706401i \(-0.750318\pi\)
−0.707812 + 0.706401i \(0.750318\pi\)
\(758\) 48.7308 1.76998
\(759\) 22.8880 0.830781
\(760\) −162.664 −5.90043
\(761\) 10.5514 0.382486 0.191243 0.981543i \(-0.438748\pi\)
0.191243 + 0.981543i \(0.438748\pi\)
\(762\) 34.0530 1.23361
\(763\) −10.9587 −0.396731
\(764\) −58.1154 −2.10254
\(765\) −2.14301 −0.0774806
\(766\) 33.1972 1.19946
\(767\) −19.9446 −0.720159
\(768\) −57.2283 −2.06505
\(769\) 32.8447 1.18441 0.592205 0.805787i \(-0.298257\pi\)
0.592205 + 0.805787i \(0.298257\pi\)
\(770\) 24.4099 0.879670
\(771\) 20.2427 0.729024
\(772\) 56.1138 2.01958
\(773\) 9.91906 0.356764 0.178382 0.983961i \(-0.442914\pi\)
0.178382 + 0.983961i \(0.442914\pi\)
\(774\) 17.5751 0.631723
\(775\) −86.1918 −3.09610
\(776\) 65.6338 2.35612
\(777\) 13.6599 0.490045
\(778\) 77.9373 2.79419
\(779\) −20.0934 −0.719920
\(780\) 124.669 4.46387
\(781\) 24.4137 0.873589
\(782\) −14.9009 −0.532855
\(783\) 34.4533 1.23126
\(784\) −36.4033 −1.30012
\(785\) −52.7553 −1.88292
\(786\) 9.11811 0.325232
\(787\) 33.7039 1.20142 0.600708 0.799469i \(-0.294886\pi\)
0.600708 + 0.799469i \(0.294886\pi\)
\(788\) −16.5858 −0.590845
\(789\) −29.4431 −1.04820
\(790\) 34.5234 1.22829
\(791\) 1.29684 0.0461104
\(792\) −7.32180 −0.260169
\(793\) 5.35883 0.190298
\(794\) −11.8342 −0.419980
\(795\) 41.7608 1.48110
\(796\) 70.9936 2.51630
\(797\) −3.67313 −0.130109 −0.0650544 0.997882i \(-0.520722\pi\)
−0.0650544 + 0.997882i \(0.520722\pi\)
\(798\) 43.2521 1.53111
\(799\) 12.0896 0.427701
\(800\) −41.6507 −1.47257
\(801\) 1.66929 0.0589816
\(802\) 24.9948 0.882599
\(803\) 26.3188 0.928769
\(804\) 76.2694 2.68981
\(805\) −27.5015 −0.969299
\(806\) −100.706 −3.54720
\(807\) 21.2145 0.746786
\(808\) −77.7838 −2.73643
\(809\) 3.30616 0.116239 0.0581193 0.998310i \(-0.481490\pi\)
0.0581193 + 0.998310i \(0.481490\pi\)
\(810\) −97.6635 −3.43155
\(811\) 16.5693 0.581828 0.290914 0.956749i \(-0.406041\pi\)
0.290914 + 0.956749i \(0.406041\pi\)
\(812\) −42.0417 −1.47537
\(813\) 13.5029 0.473566
\(814\) −29.8302 −1.04555
\(815\) −27.5547 −0.965199
\(816\) 12.7412 0.446030
\(817\) 85.5876 2.99433
\(818\) −94.9095 −3.31843
\(819\) −2.93728 −0.102637
\(820\) −46.1255 −1.61077
\(821\) 43.1270 1.50514 0.752571 0.658511i \(-0.228813\pi\)
0.752571 + 0.658511i \(0.228813\pi\)
\(822\) −1.66203 −0.0579700
\(823\) 2.77092 0.0965881 0.0482940 0.998833i \(-0.484622\pi\)
0.0482940 + 0.998833i \(0.484622\pi\)
\(824\) −61.5717 −2.14495
\(825\) 33.9587 1.18229
\(826\) −15.8841 −0.552678
\(827\) −46.0538 −1.60145 −0.800723 0.599034i \(-0.795551\pi\)
−0.800723 + 0.599034i \(0.795551\pi\)
\(828\) 15.0506 0.523045
\(829\) 7.48886 0.260099 0.130049 0.991508i \(-0.458486\pi\)
0.130049 + 0.991508i \(0.458486\pi\)
\(830\) −106.192 −3.68596
\(831\) −35.7877 −1.24146
\(832\) 5.48739 0.190241
\(833\) −5.40485 −0.187267
\(834\) 51.8475 1.79533
\(835\) 21.8116 0.754823
\(836\) −65.0545 −2.24996
\(837\) 45.2691 1.56473
\(838\) −21.0117 −0.725837
\(839\) 4.79257 0.165458 0.0827290 0.996572i \(-0.473636\pi\)
0.0827290 + 0.996572i \(0.473636\pi\)
\(840\) 54.4187 1.87762
\(841\) 27.5716 0.950745
\(842\) 4.97703 0.171520
\(843\) 57.1475 1.96826
\(844\) 43.1264 1.48447
\(845\) −11.7064 −0.402712
\(846\) −17.7294 −0.609550
\(847\) −8.54227 −0.293516
\(848\) −40.1395 −1.37839
\(849\) 29.0517 0.997052
\(850\) −22.1083 −0.758309
\(851\) 33.6083 1.15208
\(852\) 99.3030 3.40206
\(853\) −1.55519 −0.0532489 −0.0266244 0.999646i \(-0.508476\pi\)
−0.0266244 + 0.999646i \(0.508476\pi\)
\(854\) 4.26782 0.146042
\(855\) 15.3045 0.523402
\(856\) −54.6446 −1.86771
\(857\) 2.16560 0.0739754 0.0369877 0.999316i \(-0.488224\pi\)
0.0369877 + 0.999316i \(0.488224\pi\)
\(858\) 39.6770 1.35455
\(859\) 3.08914 0.105400 0.0527000 0.998610i \(-0.483217\pi\)
0.0527000 + 0.998610i \(0.483217\pi\)
\(860\) 196.471 6.69961
\(861\) 6.72219 0.229092
\(862\) 19.3980 0.660698
\(863\) 28.3208 0.964052 0.482026 0.876157i \(-0.339901\pi\)
0.482026 + 0.876157i \(0.339901\pi\)
\(864\) 21.8755 0.744219
\(865\) −27.1693 −0.923786
\(866\) −4.76815 −0.162028
\(867\) 1.89170 0.0642455
\(868\) −55.2396 −1.87495
\(869\) 7.56754 0.256711
\(870\) −133.602 −4.52954
\(871\) −36.6220 −1.24089
\(872\) 53.3520 1.80673
\(873\) −6.17526 −0.209001
\(874\) 106.416 3.59958
\(875\) −17.4114 −0.588611
\(876\) 107.052 3.61696
\(877\) 13.1320 0.443436 0.221718 0.975111i \(-0.428834\pi\)
0.221718 + 0.975111i \(0.428834\pi\)
\(878\) −9.96993 −0.336469
\(879\) −10.4301 −0.351799
\(880\) −51.3526 −1.73109
\(881\) −11.8407 −0.398923 −0.199461 0.979906i \(-0.563919\pi\)
−0.199461 + 0.979906i \(0.563919\pi\)
\(882\) 7.92620 0.266889
\(883\) −32.7068 −1.10067 −0.550336 0.834943i \(-0.685501\pi\)
−0.550336 + 0.834943i \(0.685501\pi\)
\(884\) −17.7912 −0.598381
\(885\) −34.7661 −1.16865
\(886\) 1.37183 0.0460877
\(887\) 56.3390 1.89168 0.945839 0.324636i \(-0.105242\pi\)
0.945839 + 0.324636i \(0.105242\pi\)
\(888\) −66.5027 −2.23169
\(889\) −8.96902 −0.300811
\(890\) 27.0940 0.908193
\(891\) −21.4078 −0.717190
\(892\) 113.156 3.78875
\(893\) −86.3392 −2.88923
\(894\) 100.464 3.36003
\(895\) −61.5075 −2.05597
\(896\) 16.4332 0.548996
\(897\) −44.7022 −1.49256
\(898\) 34.0216 1.13532
\(899\) 74.3308 2.47907
\(900\) 22.3305 0.744349
\(901\) −5.95956 −0.198542
\(902\) −14.6798 −0.488784
\(903\) −28.6331 −0.952850
\(904\) −6.31364 −0.209989
\(905\) 65.9952 2.19376
\(906\) −43.1072 −1.43214
\(907\) 12.0674 0.400691 0.200346 0.979725i \(-0.435793\pi\)
0.200346 + 0.979725i \(0.435793\pi\)
\(908\) −50.3183 −1.66987
\(909\) 7.31842 0.242737
\(910\) −47.6745 −1.58040
\(911\) −34.9689 −1.15857 −0.579286 0.815124i \(-0.696669\pi\)
−0.579286 + 0.815124i \(0.696669\pi\)
\(912\) −90.9921 −3.01305
\(913\) −23.2772 −0.770363
\(914\) 51.2690 1.69583
\(915\) 9.34116 0.308809
\(916\) 101.731 3.36128
\(917\) −2.40156 −0.0793066
\(918\) 11.6116 0.383240
\(919\) −12.2329 −0.403527 −0.201764 0.979434i \(-0.564667\pi\)
−0.201764 + 0.979434i \(0.564667\pi\)
\(920\) 133.890 4.41423
\(921\) −50.8049 −1.67408
\(922\) −87.8255 −2.89238
\(923\) −47.6820 −1.56947
\(924\) 21.7638 0.715978
\(925\) 49.8644 1.63953
\(926\) 23.2781 0.764966
\(927\) 5.79308 0.190270
\(928\) 35.9191 1.17910
\(929\) 33.2595 1.09121 0.545605 0.838043i \(-0.316300\pi\)
0.545605 + 0.838043i \(0.316300\pi\)
\(930\) −175.543 −5.75628
\(931\) 38.5992 1.26504
\(932\) −79.0826 −2.59044
\(933\) 31.9437 1.04579
\(934\) −0.403727 −0.0132104
\(935\) −7.62439 −0.249344
\(936\) 14.3001 0.467413
\(937\) −46.9777 −1.53470 −0.767348 0.641231i \(-0.778424\pi\)
−0.767348 + 0.641231i \(0.778424\pi\)
\(938\) −29.1661 −0.952306
\(939\) 24.7124 0.806460
\(940\) −198.197 −6.46446
\(941\) 51.3962 1.67547 0.837734 0.546078i \(-0.183880\pi\)
0.837734 + 0.546078i \(0.183880\pi\)
\(942\) −68.2928 −2.22510
\(943\) 16.5391 0.538586
\(944\) 33.4164 1.08761
\(945\) 21.4306 0.697139
\(946\) 62.5285 2.03298
\(947\) −22.9063 −0.744354 −0.372177 0.928162i \(-0.621389\pi\)
−0.372177 + 0.928162i \(0.621389\pi\)
\(948\) 30.7811 0.999724
\(949\) −51.4028 −1.66861
\(950\) 157.889 5.12258
\(951\) −20.9875 −0.680567
\(952\) −7.76594 −0.251696
\(953\) 1.22177 0.0395771 0.0197885 0.999804i \(-0.493701\pi\)
0.0197885 + 0.999804i \(0.493701\pi\)
\(954\) 8.73968 0.282958
\(955\) 48.6422 1.57402
\(956\) 52.5909 1.70091
\(957\) −29.2856 −0.946669
\(958\) −36.3285 −1.17372
\(959\) 0.437752 0.0141358
\(960\) 9.56524 0.308717
\(961\) 66.6651 2.15049
\(962\) 58.2609 1.87841
\(963\) 5.14132 0.165677
\(964\) 48.6789 1.56784
\(965\) −46.9669 −1.51192
\(966\) −35.6012 −1.14545
\(967\) 9.85707 0.316982 0.158491 0.987360i \(-0.449337\pi\)
0.158491 + 0.987360i \(0.449337\pi\)
\(968\) 41.5878 1.33668
\(969\) −13.5097 −0.433995
\(970\) −100.230 −3.21818
\(971\) −10.2777 −0.329828 −0.164914 0.986308i \(-0.552735\pi\)
−0.164914 + 0.986308i \(0.552735\pi\)
\(972\) −26.2586 −0.842244
\(973\) −13.6558 −0.437784
\(974\) −2.11716 −0.0678381
\(975\) −66.3242 −2.12408
\(976\) −8.97849 −0.287394
\(977\) 55.0147 1.76008 0.880039 0.474902i \(-0.157516\pi\)
0.880039 + 0.474902i \(0.157516\pi\)
\(978\) −35.6701 −1.14061
\(979\) 5.93901 0.189811
\(980\) 88.6067 2.83044
\(981\) −5.01971 −0.160267
\(982\) 20.4776 0.653467
\(983\) 52.4702 1.67354 0.836769 0.547556i \(-0.184442\pi\)
0.836769 + 0.547556i \(0.184442\pi\)
\(984\) −32.7268 −1.04329
\(985\) 13.8822 0.442324
\(986\) 19.0660 0.607184
\(987\) 28.8846 0.919406
\(988\) 127.057 4.04222
\(989\) −70.4480 −2.24012
\(990\) 11.1811 0.355360
\(991\) 44.9375 1.42749 0.713743 0.700407i \(-0.246998\pi\)
0.713743 + 0.700407i \(0.246998\pi\)
\(992\) 47.1949 1.49844
\(993\) −14.4071 −0.457197
\(994\) −37.9743 −1.20447
\(995\) −59.4212 −1.88378
\(996\) −94.6804 −3.00006
\(997\) −14.0423 −0.444725 −0.222363 0.974964i \(-0.571377\pi\)
−0.222363 + 0.974964i \(0.571377\pi\)
\(998\) −22.2300 −0.703677
\(999\) −26.1894 −0.828597
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 6001.2.a.d.1.7 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.d.1.7 121 1.1 even 1 trivial