Properties

Label 8007.2.a.f.1.2
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.66751 q^{2} -1.00000 q^{3} +5.11563 q^{4} -0.759881 q^{5} +2.66751 q^{6} -3.14723 q^{7} -8.31098 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.66751 q^{2} -1.00000 q^{3} +5.11563 q^{4} -0.759881 q^{5} +2.66751 q^{6} -3.14723 q^{7} -8.31098 q^{8} +1.00000 q^{9} +2.02699 q^{10} +2.82913 q^{11} -5.11563 q^{12} -3.24759 q^{13} +8.39529 q^{14} +0.759881 q^{15} +11.9384 q^{16} -1.00000 q^{17} -2.66751 q^{18} +6.68456 q^{19} -3.88727 q^{20} +3.14723 q^{21} -7.54675 q^{22} +3.37760 q^{23} +8.31098 q^{24} -4.42258 q^{25} +8.66298 q^{26} -1.00000 q^{27} -16.1001 q^{28} +3.85637 q^{29} -2.02699 q^{30} +2.88443 q^{31} -15.2239 q^{32} -2.82913 q^{33} +2.66751 q^{34} +2.39153 q^{35} +5.11563 q^{36} -4.84157 q^{37} -17.8312 q^{38} +3.24759 q^{39} +6.31536 q^{40} -2.20878 q^{41} -8.39529 q^{42} -7.84352 q^{43} +14.4728 q^{44} -0.759881 q^{45} -9.00979 q^{46} -8.89782 q^{47} -11.9384 q^{48} +2.90509 q^{49} +11.7973 q^{50} +1.00000 q^{51} -16.6134 q^{52} +6.46681 q^{53} +2.66751 q^{54} -2.14981 q^{55} +26.1566 q^{56} -6.68456 q^{57} -10.2869 q^{58} -2.68202 q^{59} +3.88727 q^{60} +0.513119 q^{61} -7.69425 q^{62} -3.14723 q^{63} +16.7331 q^{64} +2.46778 q^{65} +7.54675 q^{66} +0.811036 q^{67} -5.11563 q^{68} -3.37760 q^{69} -6.37943 q^{70} -2.81349 q^{71} -8.31098 q^{72} +9.87519 q^{73} +12.9149 q^{74} +4.42258 q^{75} +34.1957 q^{76} -8.90395 q^{77} -8.66298 q^{78} -11.0802 q^{79} -9.07177 q^{80} +1.00000 q^{81} +5.89195 q^{82} -2.15464 q^{83} +16.1001 q^{84} +0.759881 q^{85} +20.9227 q^{86} -3.85637 q^{87} -23.5129 q^{88} +1.54344 q^{89} +2.02699 q^{90} +10.2209 q^{91} +17.2785 q^{92} -2.88443 q^{93} +23.7350 q^{94} -5.07947 q^{95} +15.2239 q^{96} -1.93782 q^{97} -7.74936 q^{98} +2.82913 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66751 −1.88622 −0.943108 0.332485i \(-0.892113\pi\)
−0.943108 + 0.332485i \(0.892113\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.11563 2.55781
\(5\) −0.759881 −0.339829 −0.169915 0.985459i \(-0.554349\pi\)
−0.169915 + 0.985459i \(0.554349\pi\)
\(6\) 2.66751 1.08901
\(7\) −3.14723 −1.18954 −0.594771 0.803895i \(-0.702757\pi\)
−0.594771 + 0.803895i \(0.702757\pi\)
\(8\) −8.31098 −2.93838
\(9\) 1.00000 0.333333
\(10\) 2.02699 0.640992
\(11\) 2.82913 0.853016 0.426508 0.904484i \(-0.359744\pi\)
0.426508 + 0.904484i \(0.359744\pi\)
\(12\) −5.11563 −1.47675
\(13\) −3.24759 −0.900718 −0.450359 0.892848i \(-0.648704\pi\)
−0.450359 + 0.892848i \(0.648704\pi\)
\(14\) 8.39529 2.24374
\(15\) 0.759881 0.196201
\(16\) 11.9384 2.98460
\(17\) −1.00000 −0.242536
\(18\) −2.66751 −0.628739
\(19\) 6.68456 1.53354 0.766772 0.641920i \(-0.221862\pi\)
0.766772 + 0.641920i \(0.221862\pi\)
\(20\) −3.88727 −0.869220
\(21\) 3.14723 0.686783
\(22\) −7.54675 −1.60897
\(23\) 3.37760 0.704278 0.352139 0.935948i \(-0.385454\pi\)
0.352139 + 0.935948i \(0.385454\pi\)
\(24\) 8.31098 1.69647
\(25\) −4.42258 −0.884516
\(26\) 8.66298 1.69895
\(27\) −1.00000 −0.192450
\(28\) −16.1001 −3.04263
\(29\) 3.85637 0.716109 0.358055 0.933701i \(-0.383440\pi\)
0.358055 + 0.933701i \(0.383440\pi\)
\(30\) −2.02699 −0.370077
\(31\) 2.88443 0.518058 0.259029 0.965870i \(-0.416597\pi\)
0.259029 + 0.965870i \(0.416597\pi\)
\(32\) −15.2239 −2.69123
\(33\) −2.82913 −0.492489
\(34\) 2.66751 0.457475
\(35\) 2.39153 0.404242
\(36\) 5.11563 0.852605
\(37\) −4.84157 −0.795949 −0.397974 0.917397i \(-0.630287\pi\)
−0.397974 + 0.917397i \(0.630287\pi\)
\(38\) −17.8312 −2.89260
\(39\) 3.24759 0.520030
\(40\) 6.31536 0.998546
\(41\) −2.20878 −0.344954 −0.172477 0.985014i \(-0.555177\pi\)
−0.172477 + 0.985014i \(0.555177\pi\)
\(42\) −8.39529 −1.29542
\(43\) −7.84352 −1.19612 −0.598062 0.801450i \(-0.704063\pi\)
−0.598062 + 0.801450i \(0.704063\pi\)
\(44\) 14.4728 2.18186
\(45\) −0.759881 −0.113276
\(46\) −9.00979 −1.32842
\(47\) −8.89782 −1.29788 −0.648940 0.760840i \(-0.724787\pi\)
−0.648940 + 0.760840i \(0.724787\pi\)
\(48\) −11.9384 −1.72316
\(49\) 2.90509 0.415013
\(50\) 11.7973 1.66839
\(51\) 1.00000 0.140028
\(52\) −16.6134 −2.30387
\(53\) 6.46681 0.888284 0.444142 0.895956i \(-0.353508\pi\)
0.444142 + 0.895956i \(0.353508\pi\)
\(54\) 2.66751 0.363003
\(55\) −2.14981 −0.289880
\(56\) 26.1566 3.49532
\(57\) −6.68456 −0.885392
\(58\) −10.2869 −1.35074
\(59\) −2.68202 −0.349169 −0.174585 0.984642i \(-0.555858\pi\)
−0.174585 + 0.984642i \(0.555858\pi\)
\(60\) 3.88727 0.501844
\(61\) 0.513119 0.0656981 0.0328491 0.999460i \(-0.489542\pi\)
0.0328491 + 0.999460i \(0.489542\pi\)
\(62\) −7.69425 −0.977170
\(63\) −3.14723 −0.396514
\(64\) 16.7331 2.09164
\(65\) 2.46778 0.306090
\(66\) 7.54675 0.928941
\(67\) 0.811036 0.0990839 0.0495419 0.998772i \(-0.484224\pi\)
0.0495419 + 0.998772i \(0.484224\pi\)
\(68\) −5.11563 −0.620361
\(69\) −3.37760 −0.406615
\(70\) −6.37943 −0.762487
\(71\) −2.81349 −0.333900 −0.166950 0.985965i \(-0.553392\pi\)
−0.166950 + 0.985965i \(0.553392\pi\)
\(72\) −8.31098 −0.979458
\(73\) 9.87519 1.15580 0.577902 0.816106i \(-0.303872\pi\)
0.577902 + 0.816106i \(0.303872\pi\)
\(74\) 12.9149 1.50133
\(75\) 4.42258 0.510676
\(76\) 34.1957 3.92252
\(77\) −8.90395 −1.01470
\(78\) −8.66298 −0.980889
\(79\) −11.0802 −1.24662 −0.623310 0.781975i \(-0.714213\pi\)
−0.623310 + 0.781975i \(0.714213\pi\)
\(80\) −9.07177 −1.01425
\(81\) 1.00000 0.111111
\(82\) 5.89195 0.650657
\(83\) −2.15464 −0.236503 −0.118251 0.992984i \(-0.537729\pi\)
−0.118251 + 0.992984i \(0.537729\pi\)
\(84\) 16.1001 1.75666
\(85\) 0.759881 0.0824207
\(86\) 20.9227 2.25615
\(87\) −3.85637 −0.413446
\(88\) −23.5129 −2.50648
\(89\) 1.54344 0.163604 0.0818019 0.996649i \(-0.473933\pi\)
0.0818019 + 0.996649i \(0.473933\pi\)
\(90\) 2.02699 0.213664
\(91\) 10.2209 1.07144
\(92\) 17.2785 1.80141
\(93\) −2.88443 −0.299101
\(94\) 23.7350 2.44808
\(95\) −5.07947 −0.521143
\(96\) 15.2239 1.55378
\(97\) −1.93782 −0.196756 −0.0983778 0.995149i \(-0.531365\pi\)
−0.0983778 + 0.995149i \(0.531365\pi\)
\(98\) −7.74936 −0.782804
\(99\) 2.82913 0.284339
\(100\) −22.6243 −2.26243
\(101\) 12.3656 1.23042 0.615212 0.788361i \(-0.289070\pi\)
0.615212 + 0.788361i \(0.289070\pi\)
\(102\) −2.66751 −0.264123
\(103\) 2.43192 0.239624 0.119812 0.992797i \(-0.461771\pi\)
0.119812 + 0.992797i \(0.461771\pi\)
\(104\) 26.9906 2.64665
\(105\) −2.39153 −0.233389
\(106\) −17.2503 −1.67550
\(107\) 15.3997 1.48874 0.744370 0.667767i \(-0.232750\pi\)
0.744370 + 0.667767i \(0.232750\pi\)
\(108\) −5.11563 −0.492252
\(109\) −6.96117 −0.666759 −0.333380 0.942793i \(-0.608189\pi\)
−0.333380 + 0.942793i \(0.608189\pi\)
\(110\) 5.73464 0.546776
\(111\) 4.84157 0.459541
\(112\) −37.5729 −3.55031
\(113\) 13.1260 1.23479 0.617393 0.786655i \(-0.288189\pi\)
0.617393 + 0.786655i \(0.288189\pi\)
\(114\) 17.8312 1.67004
\(115\) −2.56657 −0.239334
\(116\) 19.7277 1.83167
\(117\) −3.24759 −0.300239
\(118\) 7.15432 0.658609
\(119\) 3.14723 0.288507
\(120\) −6.31536 −0.576511
\(121\) −2.99600 −0.272364
\(122\) −1.36875 −0.123921
\(123\) 2.20878 0.199159
\(124\) 14.7557 1.32510
\(125\) 7.16004 0.640414
\(126\) 8.39529 0.747912
\(127\) −2.80815 −0.249183 −0.124591 0.992208i \(-0.539762\pi\)
−0.124591 + 0.992208i \(0.539762\pi\)
\(128\) −14.1880 −1.25405
\(129\) 7.84352 0.690583
\(130\) −6.58284 −0.577353
\(131\) −7.57495 −0.661826 −0.330913 0.943661i \(-0.607357\pi\)
−0.330913 + 0.943661i \(0.607357\pi\)
\(132\) −14.4728 −1.25970
\(133\) −21.0379 −1.82422
\(134\) −2.16345 −0.186894
\(135\) 0.759881 0.0654002
\(136\) 8.31098 0.712661
\(137\) 14.2870 1.22062 0.610311 0.792162i \(-0.291045\pi\)
0.610311 + 0.792162i \(0.291045\pi\)
\(138\) 9.00979 0.766964
\(139\) −9.78869 −0.830266 −0.415133 0.909761i \(-0.636265\pi\)
−0.415133 + 0.909761i \(0.636265\pi\)
\(140\) 12.2342 1.03397
\(141\) 8.89782 0.749331
\(142\) 7.50503 0.629808
\(143\) −9.18785 −0.768327
\(144\) 11.9384 0.994866
\(145\) −2.93038 −0.243355
\(146\) −26.3422 −2.18010
\(147\) −2.90509 −0.239608
\(148\) −24.7677 −2.03589
\(149\) 19.6890 1.61299 0.806495 0.591241i \(-0.201362\pi\)
0.806495 + 0.591241i \(0.201362\pi\)
\(150\) −11.7973 −0.963245
\(151\) 17.7580 1.44513 0.722564 0.691304i \(-0.242964\pi\)
0.722564 + 0.691304i \(0.242964\pi\)
\(152\) −55.5553 −4.50613
\(153\) −1.00000 −0.0808452
\(154\) 23.7514 1.91394
\(155\) −2.19182 −0.176051
\(156\) 16.6134 1.33014
\(157\) −1.00000 −0.0798087
\(158\) 29.5566 2.35140
\(159\) −6.46681 −0.512851
\(160\) 11.5683 0.914557
\(161\) −10.6301 −0.837769
\(162\) −2.66751 −0.209580
\(163\) −5.38266 −0.421602 −0.210801 0.977529i \(-0.567607\pi\)
−0.210801 + 0.977529i \(0.567607\pi\)
\(164\) −11.2993 −0.882327
\(165\) 2.14981 0.167362
\(166\) 5.74754 0.446096
\(167\) 7.00409 0.541993 0.270997 0.962580i \(-0.412647\pi\)
0.270997 + 0.962580i \(0.412647\pi\)
\(168\) −26.1566 −2.01803
\(169\) −2.45319 −0.188707
\(170\) −2.02699 −0.155463
\(171\) 6.68456 0.511181
\(172\) −40.1245 −3.05947
\(173\) 15.4732 1.17640 0.588202 0.808714i \(-0.299836\pi\)
0.588202 + 0.808714i \(0.299836\pi\)
\(174\) 10.2869 0.779848
\(175\) 13.9189 1.05217
\(176\) 33.7753 2.54591
\(177\) 2.68202 0.201593
\(178\) −4.11714 −0.308592
\(179\) −4.49026 −0.335618 −0.167809 0.985820i \(-0.553669\pi\)
−0.167809 + 0.985820i \(0.553669\pi\)
\(180\) −3.88727 −0.289740
\(181\) −12.5814 −0.935165 −0.467583 0.883949i \(-0.654875\pi\)
−0.467583 + 0.883949i \(0.654875\pi\)
\(182\) −27.2644 −2.02097
\(183\) −0.513119 −0.0379308
\(184\) −28.0711 −2.06943
\(185\) 3.67902 0.270487
\(186\) 7.69425 0.564169
\(187\) −2.82913 −0.206887
\(188\) −45.5179 −3.31974
\(189\) 3.14723 0.228928
\(190\) 13.5496 0.982989
\(191\) 10.5539 0.763653 0.381826 0.924234i \(-0.375295\pi\)
0.381826 + 0.924234i \(0.375295\pi\)
\(192\) −16.7331 −1.20761
\(193\) −6.12973 −0.441228 −0.220614 0.975361i \(-0.570806\pi\)
−0.220614 + 0.975361i \(0.570806\pi\)
\(194\) 5.16915 0.371124
\(195\) −2.46778 −0.176721
\(196\) 14.8613 1.06152
\(197\) −0.641410 −0.0456985 −0.0228493 0.999739i \(-0.507274\pi\)
−0.0228493 + 0.999739i \(0.507274\pi\)
\(198\) −7.54675 −0.536324
\(199\) 0.0117886 0.000835670 0 0.000417835 1.00000i \(-0.499867\pi\)
0.000417835 1.00000i \(0.499867\pi\)
\(200\) 36.7560 2.59904
\(201\) −0.811036 −0.0572061
\(202\) −32.9854 −2.32085
\(203\) −12.1369 −0.851843
\(204\) 5.11563 0.358166
\(205\) 1.67841 0.117225
\(206\) −6.48718 −0.451983
\(207\) 3.37760 0.234759
\(208\) −38.7710 −2.68828
\(209\) 18.9115 1.30814
\(210\) 6.37943 0.440222
\(211\) −15.8802 −1.09324 −0.546618 0.837382i \(-0.684085\pi\)
−0.546618 + 0.837382i \(0.684085\pi\)
\(212\) 33.0818 2.27207
\(213\) 2.81349 0.192777
\(214\) −41.0788 −2.80809
\(215\) 5.96014 0.406478
\(216\) 8.31098 0.565491
\(217\) −9.07797 −0.616253
\(218\) 18.5690 1.25765
\(219\) −9.87519 −0.667303
\(220\) −10.9976 −0.741459
\(221\) 3.24759 0.218456
\(222\) −12.9149 −0.866794
\(223\) 5.26595 0.352634 0.176317 0.984333i \(-0.443582\pi\)
0.176317 + 0.984333i \(0.443582\pi\)
\(224\) 47.9131 3.20133
\(225\) −4.42258 −0.294839
\(226\) −35.0137 −2.32908
\(227\) 1.83842 0.122021 0.0610103 0.998137i \(-0.480568\pi\)
0.0610103 + 0.998137i \(0.480568\pi\)
\(228\) −34.1957 −2.26467
\(229\) 6.83685 0.451792 0.225896 0.974151i \(-0.427469\pi\)
0.225896 + 0.974151i \(0.427469\pi\)
\(230\) 6.84637 0.451436
\(231\) 8.90395 0.585837
\(232\) −32.0502 −2.10420
\(233\) 8.06025 0.528044 0.264022 0.964517i \(-0.414951\pi\)
0.264022 + 0.964517i \(0.414951\pi\)
\(234\) 8.66298 0.566317
\(235\) 6.76129 0.441058
\(236\) −13.7202 −0.893110
\(237\) 11.0802 0.719737
\(238\) −8.39529 −0.544186
\(239\) −12.4804 −0.807292 −0.403646 0.914915i \(-0.632257\pi\)
−0.403646 + 0.914915i \(0.632257\pi\)
\(240\) 9.07177 0.585580
\(241\) −0.772995 −0.0497930 −0.0248965 0.999690i \(-0.507926\pi\)
−0.0248965 + 0.999690i \(0.507926\pi\)
\(242\) 7.99188 0.513738
\(243\) −1.00000 −0.0641500
\(244\) 2.62492 0.168044
\(245\) −2.20752 −0.141033
\(246\) −5.89195 −0.375657
\(247\) −21.7087 −1.38129
\(248\) −23.9724 −1.52225
\(249\) 2.15464 0.136545
\(250\) −19.0995 −1.20796
\(251\) 5.60340 0.353684 0.176842 0.984239i \(-0.443412\pi\)
0.176842 + 0.984239i \(0.443412\pi\)
\(252\) −16.1001 −1.01421
\(253\) 9.55567 0.600760
\(254\) 7.49077 0.470013
\(255\) −0.759881 −0.0475856
\(256\) 4.38052 0.273782
\(257\) −12.4898 −0.779093 −0.389546 0.921007i \(-0.627368\pi\)
−0.389546 + 0.921007i \(0.627368\pi\)
\(258\) −20.9227 −1.30259
\(259\) 15.2375 0.946815
\(260\) 12.6242 0.782922
\(261\) 3.85637 0.238703
\(262\) 20.2063 1.24835
\(263\) −24.6807 −1.52188 −0.760939 0.648824i \(-0.775261\pi\)
−0.760939 + 0.648824i \(0.775261\pi\)
\(264\) 23.5129 1.44712
\(265\) −4.91401 −0.301865
\(266\) 56.1188 3.44087
\(267\) −1.54344 −0.0944567
\(268\) 4.14896 0.253438
\(269\) −22.8330 −1.39215 −0.696077 0.717967i \(-0.745073\pi\)
−0.696077 + 0.717967i \(0.745073\pi\)
\(270\) −2.02699 −0.123359
\(271\) 32.3091 1.96264 0.981318 0.192393i \(-0.0616249\pi\)
0.981318 + 0.192393i \(0.0616249\pi\)
\(272\) −11.9384 −0.723872
\(273\) −10.2209 −0.618598
\(274\) −38.1108 −2.30236
\(275\) −12.5121 −0.754506
\(276\) −17.2785 −1.04005
\(277\) −6.19453 −0.372193 −0.186096 0.982531i \(-0.559584\pi\)
−0.186096 + 0.982531i \(0.559584\pi\)
\(278\) 26.1115 1.56606
\(279\) 2.88443 0.172686
\(280\) −19.8759 −1.18781
\(281\) −9.37561 −0.559302 −0.279651 0.960102i \(-0.590219\pi\)
−0.279651 + 0.960102i \(0.590219\pi\)
\(282\) −23.7350 −1.41340
\(283\) −4.59361 −0.273062 −0.136531 0.990636i \(-0.543595\pi\)
−0.136531 + 0.990636i \(0.543595\pi\)
\(284\) −14.3928 −0.854055
\(285\) 5.07947 0.300882
\(286\) 24.5087 1.44923
\(287\) 6.95155 0.410337
\(288\) −15.2239 −0.897075
\(289\) 1.00000 0.0588235
\(290\) 7.81683 0.459020
\(291\) 1.93782 0.113597
\(292\) 50.5178 2.95633
\(293\) 12.3861 0.723605 0.361802 0.932255i \(-0.382162\pi\)
0.361802 + 0.932255i \(0.382162\pi\)
\(294\) 7.74936 0.451952
\(295\) 2.03802 0.118658
\(296\) 40.2382 2.33880
\(297\) −2.82913 −0.164163
\(298\) −52.5208 −3.04245
\(299\) −10.9690 −0.634356
\(300\) 22.6243 1.30621
\(301\) 24.6854 1.42284
\(302\) −47.3698 −2.72582
\(303\) −12.3656 −0.710386
\(304\) 79.8029 4.57701
\(305\) −0.389909 −0.0223261
\(306\) 2.66751 0.152492
\(307\) −5.33559 −0.304518 −0.152259 0.988341i \(-0.548655\pi\)
−0.152259 + 0.988341i \(0.548655\pi\)
\(308\) −45.5493 −2.59541
\(309\) −2.43192 −0.138347
\(310\) 5.84671 0.332071
\(311\) 12.3195 0.698576 0.349288 0.937015i \(-0.386424\pi\)
0.349288 + 0.937015i \(0.386424\pi\)
\(312\) −26.9906 −1.52804
\(313\) 22.9268 1.29590 0.647948 0.761684i \(-0.275627\pi\)
0.647948 + 0.761684i \(0.275627\pi\)
\(314\) 2.66751 0.150536
\(315\) 2.39153 0.134747
\(316\) −56.6822 −3.18862
\(317\) −9.94107 −0.558346 −0.279173 0.960241i \(-0.590060\pi\)
−0.279173 + 0.960241i \(0.590060\pi\)
\(318\) 17.2503 0.967349
\(319\) 10.9102 0.610852
\(320\) −12.7152 −0.710799
\(321\) −15.3997 −0.859525
\(322\) 28.3559 1.58021
\(323\) −6.68456 −0.371939
\(324\) 5.11563 0.284202
\(325\) 14.3627 0.796700
\(326\) 14.3583 0.795233
\(327\) 6.96117 0.384954
\(328\) 18.3571 1.01360
\(329\) 28.0035 1.54388
\(330\) −5.73464 −0.315681
\(331\) −6.48028 −0.356188 −0.178094 0.984013i \(-0.556993\pi\)
−0.178094 + 0.984013i \(0.556993\pi\)
\(332\) −11.0224 −0.604930
\(333\) −4.84157 −0.265316
\(334\) −18.6835 −1.02232
\(335\) −0.616291 −0.0336716
\(336\) 37.5729 2.04977
\(337\) 28.1226 1.53194 0.765968 0.642878i \(-0.222260\pi\)
0.765968 + 0.642878i \(0.222260\pi\)
\(338\) 6.54392 0.355942
\(339\) −13.1260 −0.712904
\(340\) 3.88727 0.210817
\(341\) 8.16043 0.441912
\(342\) −17.8312 −0.964198
\(343\) 12.8877 0.695868
\(344\) 65.1873 3.51466
\(345\) 2.56657 0.138180
\(346\) −41.2749 −2.21895
\(347\) 8.85764 0.475503 0.237751 0.971326i \(-0.423590\pi\)
0.237751 + 0.971326i \(0.423590\pi\)
\(348\) −19.7277 −1.05752
\(349\) −35.0088 −1.87398 −0.936988 0.349361i \(-0.886399\pi\)
−0.936988 + 0.349361i \(0.886399\pi\)
\(350\) −37.1289 −1.98462
\(351\) 3.24759 0.173343
\(352\) −43.0704 −2.29566
\(353\) −14.7136 −0.783127 −0.391564 0.920151i \(-0.628066\pi\)
−0.391564 + 0.920151i \(0.628066\pi\)
\(354\) −7.15432 −0.380248
\(355\) 2.13792 0.113469
\(356\) 7.89564 0.418468
\(357\) −3.14723 −0.166569
\(358\) 11.9778 0.633048
\(359\) 24.9632 1.31751 0.658754 0.752358i \(-0.271084\pi\)
0.658754 + 0.752358i \(0.271084\pi\)
\(360\) 6.31536 0.332849
\(361\) 25.6833 1.35176
\(362\) 33.5610 1.76392
\(363\) 2.99600 0.157249
\(364\) 52.2864 2.74055
\(365\) −7.50397 −0.392776
\(366\) 1.36875 0.0715458
\(367\) −4.99446 −0.260709 −0.130354 0.991467i \(-0.541612\pi\)
−0.130354 + 0.991467i \(0.541612\pi\)
\(368\) 40.3231 2.10199
\(369\) −2.20878 −0.114985
\(370\) −9.81382 −0.510196
\(371\) −20.3526 −1.05665
\(372\) −14.7557 −0.765045
\(373\) 34.4089 1.78162 0.890812 0.454372i \(-0.150136\pi\)
0.890812 + 0.454372i \(0.150136\pi\)
\(374\) 7.54675 0.390233
\(375\) −7.16004 −0.369743
\(376\) 73.9496 3.81366
\(377\) −12.5239 −0.645012
\(378\) −8.39529 −0.431807
\(379\) −24.9110 −1.27959 −0.639796 0.768545i \(-0.720981\pi\)
−0.639796 + 0.768545i \(0.720981\pi\)
\(380\) −25.9847 −1.33299
\(381\) 2.80815 0.143866
\(382\) −28.1527 −1.44041
\(383\) −21.9404 −1.12110 −0.560551 0.828120i \(-0.689411\pi\)
−0.560551 + 0.828120i \(0.689411\pi\)
\(384\) 14.1880 0.724029
\(385\) 6.76594 0.344824
\(386\) 16.3511 0.832251
\(387\) −7.84352 −0.398708
\(388\) −9.91315 −0.503264
\(389\) −29.5598 −1.49874 −0.749370 0.662152i \(-0.769643\pi\)
−0.749370 + 0.662152i \(0.769643\pi\)
\(390\) 6.58284 0.333335
\(391\) −3.37760 −0.170812
\(392\) −24.1441 −1.21946
\(393\) 7.57495 0.382105
\(394\) 1.71097 0.0861974
\(395\) 8.41964 0.423638
\(396\) 14.4728 0.727285
\(397\) 13.6910 0.687132 0.343566 0.939128i \(-0.388365\pi\)
0.343566 + 0.939128i \(0.388365\pi\)
\(398\) −0.0314462 −0.00157626
\(399\) 21.0379 1.05321
\(400\) −52.7985 −2.63993
\(401\) −12.4462 −0.621535 −0.310767 0.950486i \(-0.600586\pi\)
−0.310767 + 0.950486i \(0.600586\pi\)
\(402\) 2.16345 0.107903
\(403\) −9.36742 −0.466624
\(404\) 63.2579 3.14720
\(405\) −0.759881 −0.0377588
\(406\) 32.3753 1.60676
\(407\) −13.6974 −0.678957
\(408\) −8.31098 −0.411455
\(409\) −6.29135 −0.311087 −0.155544 0.987829i \(-0.549713\pi\)
−0.155544 + 0.987829i \(0.549713\pi\)
\(410\) −4.47718 −0.221112
\(411\) −14.2870 −0.704726
\(412\) 12.4408 0.612914
\(413\) 8.44094 0.415352
\(414\) −9.00979 −0.442807
\(415\) 1.63727 0.0803706
\(416\) 49.4408 2.42404
\(417\) 9.78869 0.479354
\(418\) −50.4467 −2.46743
\(419\) 17.2067 0.840602 0.420301 0.907385i \(-0.361925\pi\)
0.420301 + 0.907385i \(0.361925\pi\)
\(420\) −12.2342 −0.596966
\(421\) −0.690778 −0.0336664 −0.0168332 0.999858i \(-0.505358\pi\)
−0.0168332 + 0.999858i \(0.505358\pi\)
\(422\) 42.3606 2.06208
\(423\) −8.89782 −0.432627
\(424\) −53.7455 −2.61011
\(425\) 4.42258 0.214527
\(426\) −7.50503 −0.363620
\(427\) −1.61491 −0.0781507
\(428\) 78.7789 3.80792
\(429\) 9.18785 0.443594
\(430\) −15.8988 −0.766706
\(431\) 38.5781 1.85824 0.929120 0.369778i \(-0.120566\pi\)
0.929120 + 0.369778i \(0.120566\pi\)
\(432\) −11.9384 −0.574386
\(433\) 13.0955 0.629328 0.314664 0.949203i \(-0.398108\pi\)
0.314664 + 0.949203i \(0.398108\pi\)
\(434\) 24.2156 1.16239
\(435\) 2.93038 0.140501
\(436\) −35.6108 −1.70545
\(437\) 22.5778 1.08004
\(438\) 26.3422 1.25868
\(439\) 13.1677 0.628459 0.314230 0.949347i \(-0.398254\pi\)
0.314230 + 0.949347i \(0.398254\pi\)
\(440\) 17.8670 0.851776
\(441\) 2.90509 0.138338
\(442\) −8.66298 −0.412056
\(443\) −4.89848 −0.232734 −0.116367 0.993206i \(-0.537125\pi\)
−0.116367 + 0.993206i \(0.537125\pi\)
\(444\) 24.7677 1.17542
\(445\) −1.17283 −0.0555974
\(446\) −14.0470 −0.665145
\(447\) −19.6890 −0.931260
\(448\) −52.6630 −2.48809
\(449\) −23.1431 −1.09219 −0.546095 0.837723i \(-0.683886\pi\)
−0.546095 + 0.837723i \(0.683886\pi\)
\(450\) 11.7973 0.556130
\(451\) −6.24893 −0.294251
\(452\) 67.1475 3.15835
\(453\) −17.7580 −0.834345
\(454\) −4.90402 −0.230157
\(455\) −7.76668 −0.364108
\(456\) 55.5553 2.60161
\(457\) −25.7840 −1.20612 −0.603062 0.797694i \(-0.706053\pi\)
−0.603062 + 0.797694i \(0.706053\pi\)
\(458\) −18.2374 −0.852177
\(459\) 1.00000 0.0466760
\(460\) −13.1296 −0.612172
\(461\) 13.4365 0.625799 0.312899 0.949786i \(-0.398700\pi\)
0.312899 + 0.949786i \(0.398700\pi\)
\(462\) −23.7514 −1.10502
\(463\) 0.619263 0.0287796 0.0143898 0.999896i \(-0.495419\pi\)
0.0143898 + 0.999896i \(0.495419\pi\)
\(464\) 46.0388 2.13730
\(465\) 2.19182 0.101643
\(466\) −21.5008 −0.996006
\(467\) 24.8542 1.15011 0.575057 0.818113i \(-0.304980\pi\)
0.575057 + 0.818113i \(0.304980\pi\)
\(468\) −16.6134 −0.767956
\(469\) −2.55252 −0.117865
\(470\) −18.0358 −0.831930
\(471\) 1.00000 0.0460776
\(472\) 22.2902 1.02599
\(473\) −22.1903 −1.02031
\(474\) −29.5566 −1.35758
\(475\) −29.5630 −1.35644
\(476\) 16.1001 0.737946
\(477\) 6.46681 0.296095
\(478\) 33.2917 1.52273
\(479\) 9.89026 0.451897 0.225949 0.974139i \(-0.427452\pi\)
0.225949 + 0.974139i \(0.427452\pi\)
\(480\) −11.5683 −0.528020
\(481\) 15.7234 0.716925
\(482\) 2.06197 0.0939203
\(483\) 10.6301 0.483686
\(484\) −15.3264 −0.696657
\(485\) 1.47251 0.0668633
\(486\) 2.66751 0.121001
\(487\) 24.4457 1.10774 0.553869 0.832604i \(-0.313151\pi\)
0.553869 + 0.832604i \(0.313151\pi\)
\(488\) −4.26452 −0.193046
\(489\) 5.38266 0.243412
\(490\) 5.88860 0.266020
\(491\) −8.26575 −0.373028 −0.186514 0.982452i \(-0.559719\pi\)
−0.186514 + 0.982452i \(0.559719\pi\)
\(492\) 11.2993 0.509412
\(493\) −3.85637 −0.173682
\(494\) 57.9082 2.60541
\(495\) −2.14981 −0.0966266
\(496\) 34.4354 1.54620
\(497\) 8.85473 0.397189
\(498\) −5.74754 −0.257553
\(499\) −7.59437 −0.339971 −0.169985 0.985447i \(-0.554372\pi\)
−0.169985 + 0.985447i \(0.554372\pi\)
\(500\) 36.6281 1.63806
\(501\) −7.00409 −0.312920
\(502\) −14.9472 −0.667124
\(503\) −1.76162 −0.0785466 −0.0392733 0.999229i \(-0.512504\pi\)
−0.0392733 + 0.999229i \(0.512504\pi\)
\(504\) 26.1566 1.16511
\(505\) −9.39640 −0.418134
\(506\) −25.4899 −1.13316
\(507\) 2.45319 0.108950
\(508\) −14.3654 −0.637363
\(509\) −8.11323 −0.359613 −0.179806 0.983702i \(-0.557547\pi\)
−0.179806 + 0.983702i \(0.557547\pi\)
\(510\) 2.02699 0.0897568
\(511\) −31.0795 −1.37488
\(512\) 16.6909 0.737642
\(513\) −6.68456 −0.295131
\(514\) 33.3167 1.46954
\(515\) −1.84797 −0.0814313
\(516\) 40.1245 1.76638
\(517\) −25.1731 −1.10711
\(518\) −40.6464 −1.78590
\(519\) −15.4732 −0.679198
\(520\) −20.5097 −0.899408
\(521\) −4.52635 −0.198303 −0.0991515 0.995072i \(-0.531613\pi\)
−0.0991515 + 0.995072i \(0.531613\pi\)
\(522\) −10.2869 −0.450246
\(523\) −10.0719 −0.440412 −0.220206 0.975453i \(-0.570673\pi\)
−0.220206 + 0.975453i \(0.570673\pi\)
\(524\) −38.7506 −1.69283
\(525\) −13.9189 −0.607471
\(526\) 65.8361 2.87059
\(527\) −2.88443 −0.125648
\(528\) −33.7753 −1.46988
\(529\) −11.5918 −0.503993
\(530\) 13.1082 0.569383
\(531\) −2.68202 −0.116390
\(532\) −107.622 −4.66600
\(533\) 7.17320 0.310706
\(534\) 4.11714 0.178166
\(535\) −11.7019 −0.505918
\(536\) −6.74051 −0.291146
\(537\) 4.49026 0.193769
\(538\) 60.9074 2.62590
\(539\) 8.21888 0.354012
\(540\) 3.88727 0.167281
\(541\) 9.80129 0.421390 0.210695 0.977552i \(-0.432427\pi\)
0.210695 + 0.977552i \(0.432427\pi\)
\(542\) −86.1849 −3.70196
\(543\) 12.5814 0.539918
\(544\) 15.2239 0.652718
\(545\) 5.28966 0.226584
\(546\) 27.2644 1.16681
\(547\) 29.0640 1.24269 0.621344 0.783538i \(-0.286587\pi\)
0.621344 + 0.783538i \(0.286587\pi\)
\(548\) 73.0870 3.12212
\(549\) 0.513119 0.0218994
\(550\) 33.3761 1.42316
\(551\) 25.7781 1.09818
\(552\) 28.0711 1.19479
\(553\) 34.8720 1.48291
\(554\) 16.5240 0.702037
\(555\) −3.67902 −0.156166
\(556\) −50.0753 −2.12367
\(557\) −9.33729 −0.395634 −0.197817 0.980239i \(-0.563385\pi\)
−0.197817 + 0.980239i \(0.563385\pi\)
\(558\) −7.69425 −0.325723
\(559\) 25.4725 1.07737
\(560\) 28.5510 1.20650
\(561\) 2.82913 0.119446
\(562\) 25.0096 1.05497
\(563\) −15.9171 −0.670826 −0.335413 0.942071i \(-0.608876\pi\)
−0.335413 + 0.942071i \(0.608876\pi\)
\(564\) 45.5179 1.91665
\(565\) −9.97417 −0.419617
\(566\) 12.2535 0.515053
\(567\) −3.14723 −0.132171
\(568\) 23.3829 0.981124
\(569\) −12.6052 −0.528437 −0.264218 0.964463i \(-0.585114\pi\)
−0.264218 + 0.964463i \(0.585114\pi\)
\(570\) −13.5496 −0.567529
\(571\) −26.5004 −1.10901 −0.554504 0.832181i \(-0.687092\pi\)
−0.554504 + 0.832181i \(0.687092\pi\)
\(572\) −47.0016 −1.96524
\(573\) −10.5539 −0.440895
\(574\) −18.5434 −0.773985
\(575\) −14.9377 −0.622945
\(576\) 16.7331 0.697212
\(577\) 13.4575 0.560244 0.280122 0.959964i \(-0.409625\pi\)
0.280122 + 0.959964i \(0.409625\pi\)
\(578\) −2.66751 −0.110954
\(579\) 6.12973 0.254743
\(580\) −14.9907 −0.622456
\(581\) 6.78117 0.281330
\(582\) −5.16915 −0.214268
\(583\) 18.2955 0.757721
\(584\) −82.0725 −3.39618
\(585\) 2.46778 0.102030
\(586\) −33.0401 −1.36488
\(587\) −1.73388 −0.0715648 −0.0357824 0.999360i \(-0.511392\pi\)
−0.0357824 + 0.999360i \(0.511392\pi\)
\(588\) −14.8613 −0.612872
\(589\) 19.2811 0.794465
\(590\) −5.43644 −0.223815
\(591\) 0.641410 0.0263841
\(592\) −57.8005 −2.37559
\(593\) −31.5011 −1.29360 −0.646798 0.762661i \(-0.723892\pi\)
−0.646798 + 0.762661i \(0.723892\pi\)
\(594\) 7.54675 0.309647
\(595\) −2.39153 −0.0980430
\(596\) 100.722 4.12573
\(597\) −0.0117886 −0.000482474 0
\(598\) 29.2601 1.19653
\(599\) 10.1964 0.416612 0.208306 0.978064i \(-0.433205\pi\)
0.208306 + 0.978064i \(0.433205\pi\)
\(600\) −36.7560 −1.50056
\(601\) −37.4615 −1.52809 −0.764043 0.645165i \(-0.776788\pi\)
−0.764043 + 0.645165i \(0.776788\pi\)
\(602\) −65.8486 −2.68379
\(603\) 0.811036 0.0330280
\(604\) 90.8435 3.69637
\(605\) 2.27661 0.0925573
\(606\) 32.9854 1.33994
\(607\) 34.0661 1.38270 0.691351 0.722519i \(-0.257016\pi\)
0.691351 + 0.722519i \(0.257016\pi\)
\(608\) −101.765 −4.12711
\(609\) 12.1369 0.491812
\(610\) 1.04009 0.0421120
\(611\) 28.8964 1.16902
\(612\) −5.11563 −0.206787
\(613\) 13.1212 0.529962 0.264981 0.964254i \(-0.414634\pi\)
0.264981 + 0.964254i \(0.414634\pi\)
\(614\) 14.2328 0.574387
\(615\) −1.67841 −0.0676801
\(616\) 74.0005 2.98157
\(617\) 24.5517 0.988415 0.494208 0.869344i \(-0.335458\pi\)
0.494208 + 0.869344i \(0.335458\pi\)
\(618\) 6.48718 0.260952
\(619\) −45.6370 −1.83431 −0.917154 0.398534i \(-0.869519\pi\)
−0.917154 + 0.398534i \(0.869519\pi\)
\(620\) −11.2125 −0.450307
\(621\) −3.37760 −0.135538
\(622\) −32.8625 −1.31767
\(623\) −4.85755 −0.194614
\(624\) 38.7710 1.55208
\(625\) 16.6721 0.666885
\(626\) −61.1574 −2.44434
\(627\) −18.9115 −0.755253
\(628\) −5.11563 −0.204136
\(629\) 4.84157 0.193046
\(630\) −6.37943 −0.254162
\(631\) −35.7625 −1.42368 −0.711841 0.702340i \(-0.752139\pi\)
−0.711841 + 0.702340i \(0.752139\pi\)
\(632\) 92.0874 3.66304
\(633\) 15.8802 0.631180
\(634\) 26.5179 1.05316
\(635\) 2.13386 0.0846796
\(636\) −33.0818 −1.31178
\(637\) −9.43452 −0.373809
\(638\) −29.1030 −1.15220
\(639\) −2.81349 −0.111300
\(640\) 10.7812 0.426165
\(641\) −44.2584 −1.74810 −0.874051 0.485834i \(-0.838516\pi\)
−0.874051 + 0.485834i \(0.838516\pi\)
\(642\) 41.0788 1.62125
\(643\) −1.36480 −0.0538225 −0.0269112 0.999638i \(-0.508567\pi\)
−0.0269112 + 0.999638i \(0.508567\pi\)
\(644\) −54.3796 −2.14286
\(645\) −5.96014 −0.234680
\(646\) 17.8312 0.701557
\(647\) −14.8379 −0.583340 −0.291670 0.956519i \(-0.594211\pi\)
−0.291670 + 0.956519i \(0.594211\pi\)
\(648\) −8.31098 −0.326486
\(649\) −7.58779 −0.297847
\(650\) −38.3127 −1.50275
\(651\) 9.07797 0.355794
\(652\) −27.5357 −1.07838
\(653\) −29.1855 −1.14212 −0.571059 0.820909i \(-0.693467\pi\)
−0.571059 + 0.820909i \(0.693467\pi\)
\(654\) −18.5690 −0.726106
\(655\) 5.75606 0.224908
\(656\) −26.3693 −1.02955
\(657\) 9.87519 0.385268
\(658\) −74.6998 −2.91210
\(659\) −33.3257 −1.29819 −0.649093 0.760709i \(-0.724851\pi\)
−0.649093 + 0.760709i \(0.724851\pi\)
\(660\) 10.9976 0.428081
\(661\) 32.2325 1.25370 0.626849 0.779141i \(-0.284344\pi\)
0.626849 + 0.779141i \(0.284344\pi\)
\(662\) 17.2862 0.671848
\(663\) −3.24759 −0.126126
\(664\) 17.9072 0.694934
\(665\) 15.9863 0.619922
\(666\) 12.9149 0.500444
\(667\) 13.0253 0.504340
\(668\) 35.8303 1.38632
\(669\) −5.26595 −0.203594
\(670\) 1.64397 0.0635119
\(671\) 1.45168 0.0560415
\(672\) −47.9131 −1.84829
\(673\) −19.6485 −0.757394 −0.378697 0.925521i \(-0.623628\pi\)
−0.378697 + 0.925521i \(0.623628\pi\)
\(674\) −75.0175 −2.88956
\(675\) 4.42258 0.170225
\(676\) −12.5496 −0.482677
\(677\) −18.9303 −0.727549 −0.363775 0.931487i \(-0.618512\pi\)
−0.363775 + 0.931487i \(0.618512\pi\)
\(678\) 35.0137 1.34469
\(679\) 6.09877 0.234049
\(680\) −6.31536 −0.242183
\(681\) −1.83842 −0.0704486
\(682\) −21.7680 −0.833542
\(683\) 14.8209 0.567107 0.283554 0.958956i \(-0.408487\pi\)
0.283554 + 0.958956i \(0.408487\pi\)
\(684\) 34.1957 1.30751
\(685\) −10.8564 −0.414803
\(686\) −34.3780 −1.31256
\(687\) −6.83685 −0.260842
\(688\) −93.6390 −3.56995
\(689\) −21.0015 −0.800094
\(690\) −6.84637 −0.260637
\(691\) −22.7929 −0.867083 −0.433542 0.901134i \(-0.642736\pi\)
−0.433542 + 0.901134i \(0.642736\pi\)
\(692\) 79.1551 3.00902
\(693\) −8.90395 −0.338233
\(694\) −23.6279 −0.896902
\(695\) 7.43825 0.282149
\(696\) 32.0502 1.21486
\(697\) 2.20878 0.0836635
\(698\) 93.3864 3.53473
\(699\) −8.06025 −0.304867
\(700\) 71.2039 2.69126
\(701\) 1.59758 0.0603396 0.0301698 0.999545i \(-0.490395\pi\)
0.0301698 + 0.999545i \(0.490395\pi\)
\(702\) −8.66298 −0.326963
\(703\) −32.3637 −1.22062
\(704\) 47.3402 1.78420
\(705\) −6.76129 −0.254645
\(706\) 39.2488 1.47715
\(707\) −38.9175 −1.46364
\(708\) 13.7202 0.515637
\(709\) −46.1682 −1.73388 −0.866941 0.498411i \(-0.833917\pi\)
−0.866941 + 0.498411i \(0.833917\pi\)
\(710\) −5.70293 −0.214027
\(711\) −11.0802 −0.415540
\(712\) −12.8275 −0.480730
\(713\) 9.74243 0.364857
\(714\) 8.39529 0.314186
\(715\) 6.98168 0.261100
\(716\) −22.9705 −0.858448
\(717\) 12.4804 0.466090
\(718\) −66.5897 −2.48511
\(719\) 10.1788 0.379605 0.189803 0.981822i \(-0.439215\pi\)
0.189803 + 0.981822i \(0.439215\pi\)
\(720\) −9.07177 −0.338085
\(721\) −7.65382 −0.285043
\(722\) −68.5107 −2.54970
\(723\) 0.772995 0.0287480
\(724\) −64.3616 −2.39198
\(725\) −17.0551 −0.633410
\(726\) −7.99188 −0.296607
\(727\) 19.1832 0.711466 0.355733 0.934588i \(-0.384231\pi\)
0.355733 + 0.934588i \(0.384231\pi\)
\(728\) −84.9458 −3.14830
\(729\) 1.00000 0.0370370
\(730\) 20.0169 0.740861
\(731\) 7.84352 0.290103
\(732\) −2.62492 −0.0970200
\(733\) 52.3403 1.93323 0.966617 0.256225i \(-0.0824789\pi\)
0.966617 + 0.256225i \(0.0824789\pi\)
\(734\) 13.3228 0.491754
\(735\) 2.20752 0.0814257
\(736\) −51.4201 −1.89537
\(737\) 2.29453 0.0845201
\(738\) 5.89195 0.216886
\(739\) −1.11122 −0.0408767 −0.0204384 0.999791i \(-0.506506\pi\)
−0.0204384 + 0.999791i \(0.506506\pi\)
\(740\) 18.8205 0.691855
\(741\) 21.7087 0.797488
\(742\) 54.2907 1.99308
\(743\) −36.5068 −1.33930 −0.669652 0.742675i \(-0.733557\pi\)
−0.669652 + 0.742675i \(0.733557\pi\)
\(744\) 23.9724 0.878871
\(745\) −14.9613 −0.548141
\(746\) −91.7861 −3.36053
\(747\) −2.15464 −0.0788343
\(748\) −14.4728 −0.529178
\(749\) −48.4663 −1.77092
\(750\) 19.0995 0.697416
\(751\) 0.573211 0.0209168 0.0104584 0.999945i \(-0.496671\pi\)
0.0104584 + 0.999945i \(0.496671\pi\)
\(752\) −106.226 −3.87365
\(753\) −5.60340 −0.204199
\(754\) 33.4076 1.21663
\(755\) −13.4940 −0.491097
\(756\) 16.1001 0.585554
\(757\) −37.0281 −1.34581 −0.672905 0.739729i \(-0.734954\pi\)
−0.672905 + 0.739729i \(0.734954\pi\)
\(758\) 66.4505 2.41359
\(759\) −9.55567 −0.346849
\(760\) 42.2154 1.53131
\(761\) −32.2101 −1.16762 −0.583808 0.811892i \(-0.698438\pi\)
−0.583808 + 0.811892i \(0.698438\pi\)
\(762\) −7.49077 −0.271362
\(763\) 21.9084 0.793139
\(764\) 53.9898 1.95328
\(765\) 0.759881 0.0274736
\(766\) 58.5263 2.11464
\(767\) 8.71008 0.314503
\(768\) −4.38052 −0.158068
\(769\) −32.9179 −1.18705 −0.593525 0.804815i \(-0.702264\pi\)
−0.593525 + 0.804815i \(0.702264\pi\)
\(770\) −18.0482 −0.650414
\(771\) 12.4898 0.449809
\(772\) −31.3574 −1.12858
\(773\) 20.2927 0.729876 0.364938 0.931032i \(-0.381090\pi\)
0.364938 + 0.931032i \(0.381090\pi\)
\(774\) 20.9227 0.752050
\(775\) −12.7566 −0.458231
\(776\) 16.1052 0.578142
\(777\) −15.2375 −0.546644
\(778\) 78.8511 2.82695
\(779\) −14.7647 −0.529001
\(780\) −12.6242 −0.452020
\(781\) −7.95975 −0.284822
\(782\) 9.00979 0.322189
\(783\) −3.85637 −0.137815
\(784\) 34.6821 1.23865
\(785\) 0.759881 0.0271213
\(786\) −20.2063 −0.720734
\(787\) −21.3572 −0.761300 −0.380650 0.924719i \(-0.624300\pi\)
−0.380650 + 0.924719i \(0.624300\pi\)
\(788\) −3.28121 −0.116888
\(789\) 24.6807 0.878656
\(790\) −22.4595 −0.799073
\(791\) −41.3105 −1.46883
\(792\) −23.5129 −0.835494
\(793\) −1.66640 −0.0591755
\(794\) −36.5210 −1.29608
\(795\) 4.91401 0.174282
\(796\) 0.0603060 0.00213749
\(797\) −30.8470 −1.09266 −0.546329 0.837571i \(-0.683975\pi\)
−0.546329 + 0.837571i \(0.683975\pi\)
\(798\) −56.1188 −1.98659
\(799\) 8.89782 0.314782
\(800\) 67.3288 2.38043
\(801\) 1.54344 0.0545346
\(802\) 33.2005 1.17235
\(803\) 27.9382 0.985919
\(804\) −4.14896 −0.146323
\(805\) 8.07761 0.284698
\(806\) 24.9877 0.880155
\(807\) 22.8330 0.803760
\(808\) −102.770 −3.61545
\(809\) −22.5476 −0.792731 −0.396365 0.918093i \(-0.629729\pi\)
−0.396365 + 0.918093i \(0.629729\pi\)
\(810\) 2.02699 0.0712213
\(811\) 10.1874 0.357728 0.178864 0.983874i \(-0.442758\pi\)
0.178864 + 0.983874i \(0.442758\pi\)
\(812\) −62.0878 −2.17886
\(813\) −32.3091 −1.13313
\(814\) 36.5381 1.28066
\(815\) 4.09018 0.143273
\(816\) 11.9384 0.417927
\(817\) −52.4304 −1.83431
\(818\) 16.7823 0.586778
\(819\) 10.2209 0.357148
\(820\) 8.58613 0.299841
\(821\) 16.8083 0.586613 0.293306 0.956018i \(-0.405244\pi\)
0.293306 + 0.956018i \(0.405244\pi\)
\(822\) 38.1108 1.32927
\(823\) −31.5932 −1.10127 −0.550634 0.834746i \(-0.685614\pi\)
−0.550634 + 0.834746i \(0.685614\pi\)
\(824\) −20.2116 −0.704105
\(825\) 12.5121 0.435614
\(826\) −22.5163 −0.783443
\(827\) 16.1401 0.561246 0.280623 0.959818i \(-0.409459\pi\)
0.280623 + 0.959818i \(0.409459\pi\)
\(828\) 17.2785 0.600471
\(829\) 9.65887 0.335467 0.167733 0.985832i \(-0.446355\pi\)
0.167733 + 0.985832i \(0.446355\pi\)
\(830\) −4.36745 −0.151596
\(831\) 6.19453 0.214886
\(832\) −54.3422 −1.88398
\(833\) −2.90509 −0.100655
\(834\) −26.1115 −0.904166
\(835\) −5.32228 −0.184185
\(836\) 96.7443 3.34597
\(837\) −2.88443 −0.0997004
\(838\) −45.8991 −1.58556
\(839\) 3.22548 0.111356 0.0556779 0.998449i \(-0.482268\pi\)
0.0556779 + 0.998449i \(0.482268\pi\)
\(840\) 19.8759 0.685784
\(841\) −14.1284 −0.487188
\(842\) 1.84266 0.0635022
\(843\) 9.37561 0.322913
\(844\) −81.2370 −2.79629
\(845\) 1.86413 0.0641281
\(846\) 23.7350 0.816028
\(847\) 9.42913 0.323989
\(848\) 77.2033 2.65117
\(849\) 4.59361 0.157652
\(850\) −11.7973 −0.404644
\(851\) −16.3529 −0.560569
\(852\) 14.3928 0.493089
\(853\) −3.62450 −0.124100 −0.0620502 0.998073i \(-0.519764\pi\)
−0.0620502 + 0.998073i \(0.519764\pi\)
\(854\) 4.30778 0.147409
\(855\) −5.07947 −0.173714
\(856\) −127.986 −4.37448
\(857\) −1.86891 −0.0638408 −0.0319204 0.999490i \(-0.510162\pi\)
−0.0319204 + 0.999490i \(0.510162\pi\)
\(858\) −24.5087 −0.836714
\(859\) −3.90668 −0.133294 −0.0666471 0.997777i \(-0.521230\pi\)
−0.0666471 + 0.997777i \(0.521230\pi\)
\(860\) 30.4899 1.03970
\(861\) −6.95155 −0.236908
\(862\) −102.908 −3.50504
\(863\) −17.9763 −0.611921 −0.305961 0.952044i \(-0.598978\pi\)
−0.305961 + 0.952044i \(0.598978\pi\)
\(864\) 15.2239 0.517927
\(865\) −11.7578 −0.399777
\(866\) −34.9323 −1.18705
\(867\) −1.00000 −0.0339618
\(868\) −46.4395 −1.57626
\(869\) −31.3474 −1.06339
\(870\) −7.81683 −0.265015
\(871\) −2.63391 −0.0892466
\(872\) 57.8542 1.95919
\(873\) −1.93782 −0.0655852
\(874\) −60.2265 −2.03719
\(875\) −22.5343 −0.761800
\(876\) −50.5178 −1.70684
\(877\) −2.79679 −0.0944408 −0.0472204 0.998884i \(-0.515036\pi\)
−0.0472204 + 0.998884i \(0.515036\pi\)
\(878\) −35.1250 −1.18541
\(879\) −12.3861 −0.417773
\(880\) −25.6652 −0.865175
\(881\) 37.1342 1.25108 0.625542 0.780190i \(-0.284878\pi\)
0.625542 + 0.780190i \(0.284878\pi\)
\(882\) −7.74936 −0.260935
\(883\) −7.30786 −0.245929 −0.122965 0.992411i \(-0.539240\pi\)
−0.122965 + 0.992411i \(0.539240\pi\)
\(884\) 16.6134 0.558770
\(885\) −2.03802 −0.0685072
\(886\) 13.0668 0.438987
\(887\) −58.8423 −1.97573 −0.987866 0.155309i \(-0.950363\pi\)
−0.987866 + 0.155309i \(0.950363\pi\)
\(888\) −40.2382 −1.35030
\(889\) 8.83790 0.296414
\(890\) 3.12853 0.104869
\(891\) 2.82913 0.0947795
\(892\) 26.9387 0.901973
\(893\) −59.4780 −1.99036
\(894\) 52.5208 1.75656
\(895\) 3.41206 0.114053
\(896\) 44.6530 1.49175
\(897\) 10.9690 0.366245
\(898\) 61.7345 2.06011
\(899\) 11.1234 0.370986
\(900\) −22.6243 −0.754143
\(901\) −6.46681 −0.215441
\(902\) 16.6691 0.555021
\(903\) −24.6854 −0.821478
\(904\) −109.090 −3.62827
\(905\) 9.56034 0.317797
\(906\) 47.3698 1.57376
\(907\) 1.07045 0.0355438 0.0177719 0.999842i \(-0.494343\pi\)
0.0177719 + 0.999842i \(0.494343\pi\)
\(908\) 9.40470 0.312106
\(909\) 12.3656 0.410142
\(910\) 20.7177 0.686786
\(911\) −14.1314 −0.468193 −0.234097 0.972213i \(-0.575213\pi\)
−0.234097 + 0.972213i \(0.575213\pi\)
\(912\) −79.8029 −2.64254
\(913\) −6.09577 −0.201741
\(914\) 68.7791 2.27501
\(915\) 0.389909 0.0128900
\(916\) 34.9748 1.15560
\(917\) 23.8401 0.787271
\(918\) −2.66751 −0.0880411
\(919\) 44.3813 1.46401 0.732003 0.681302i \(-0.238586\pi\)
0.732003 + 0.681302i \(0.238586\pi\)
\(920\) 21.3307 0.703254
\(921\) 5.33559 0.175814
\(922\) −35.8420 −1.18039
\(923\) 9.13706 0.300750
\(924\) 45.5493 1.49846
\(925\) 21.4122 0.704029
\(926\) −1.65189 −0.0542845
\(927\) 2.43192 0.0798747
\(928\) −58.7088 −1.92721
\(929\) 0.674930 0.0221437 0.0110719 0.999939i \(-0.496476\pi\)
0.0110719 + 0.999939i \(0.496476\pi\)
\(930\) −5.84671 −0.191721
\(931\) 19.4192 0.636440
\(932\) 41.2332 1.35064
\(933\) −12.3195 −0.403323
\(934\) −66.2989 −2.16936
\(935\) 2.14981 0.0703062
\(936\) 26.9906 0.882216
\(937\) −12.7371 −0.416103 −0.208052 0.978118i \(-0.566712\pi\)
−0.208052 + 0.978118i \(0.566712\pi\)
\(938\) 6.80889 0.222318
\(939\) −22.9268 −0.748186
\(940\) 34.5882 1.12814
\(941\) −48.5758 −1.58352 −0.791762 0.610829i \(-0.790836\pi\)
−0.791762 + 0.610829i \(0.790836\pi\)
\(942\) −2.66751 −0.0869123
\(943\) −7.46037 −0.242943
\(944\) −32.0190 −1.04213
\(945\) −2.39153 −0.0777963
\(946\) 59.1931 1.92453
\(947\) −3.47933 −0.113063 −0.0565315 0.998401i \(-0.518004\pi\)
−0.0565315 + 0.998401i \(0.518004\pi\)
\(948\) 56.6822 1.84095
\(949\) −32.0705 −1.04105
\(950\) 78.8597 2.55855
\(951\) 9.94107 0.322361
\(952\) −26.1566 −0.847741
\(953\) −44.1556 −1.43034 −0.715171 0.698950i \(-0.753651\pi\)
−0.715171 + 0.698950i \(0.753651\pi\)
\(954\) −17.2503 −0.558499
\(955\) −8.01971 −0.259512
\(956\) −63.8453 −2.06490
\(957\) −10.9102 −0.352676
\(958\) −26.3824 −0.852376
\(959\) −44.9646 −1.45198
\(960\) 12.7152 0.410380
\(961\) −22.6801 −0.731616
\(962\) −41.9424 −1.35228
\(963\) 15.3997 0.496247
\(964\) −3.95435 −0.127361
\(965\) 4.65787 0.149942
\(966\) −28.3559 −0.912337
\(967\) 26.8292 0.862768 0.431384 0.902169i \(-0.358026\pi\)
0.431384 + 0.902169i \(0.358026\pi\)
\(968\) 24.8997 0.800308
\(969\) 6.68456 0.214739
\(970\) −3.92794 −0.126119
\(971\) −4.26089 −0.136738 −0.0683692 0.997660i \(-0.521780\pi\)
−0.0683692 + 0.997660i \(0.521780\pi\)
\(972\) −5.11563 −0.164084
\(973\) 30.8073 0.987637
\(974\) −65.2091 −2.08943
\(975\) −14.3627 −0.459975
\(976\) 6.12582 0.196083
\(977\) −40.5153 −1.29620 −0.648100 0.761555i \(-0.724436\pi\)
−0.648100 + 0.761555i \(0.724436\pi\)
\(978\) −14.3583 −0.459128
\(979\) 4.36659 0.139557
\(980\) −11.2929 −0.360737
\(981\) −6.96117 −0.222253
\(982\) 22.0490 0.703612
\(983\) 22.5853 0.720358 0.360179 0.932883i \(-0.382716\pi\)
0.360179 + 0.932883i \(0.382716\pi\)
\(984\) −18.3571 −0.585204
\(985\) 0.487395 0.0155297
\(986\) 10.2869 0.327602
\(987\) −28.0035 −0.891362
\(988\) −111.054 −3.53308
\(989\) −26.4922 −0.842404
\(990\) 5.73464 0.182259
\(991\) −49.4913 −1.57214 −0.786072 0.618135i \(-0.787889\pi\)
−0.786072 + 0.618135i \(0.787889\pi\)
\(992\) −43.9121 −1.39421
\(993\) 6.48028 0.205645
\(994\) −23.6201 −0.749184
\(995\) −0.00895792 −0.000283985 0
\(996\) 11.0224 0.349257
\(997\) −45.5599 −1.44290 −0.721448 0.692468i \(-0.756523\pi\)
−0.721448 + 0.692468i \(0.756523\pi\)
\(998\) 20.2581 0.641259
\(999\) 4.84157 0.153180
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 8007.2.a.f.1.2 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.2 48 1.1 even 1 trivial