Properties

Label 8007.2.a.f.1.24
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 1.24
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.0648705 q^{2} -1.00000 q^{3} -1.99579 q^{4} +0.118616 q^{5} +0.0648705 q^{6} -4.97378 q^{7} +0.259209 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.0648705 q^{2} -1.00000 q^{3} -1.99579 q^{4} +0.118616 q^{5} +0.0648705 q^{6} -4.97378 q^{7} +0.259209 q^{8} +1.00000 q^{9} -0.00769468 q^{10} -4.34142 q^{11} +1.99579 q^{12} +3.46263 q^{13} +0.322652 q^{14} -0.118616 q^{15} +3.97477 q^{16} -1.00000 q^{17} -0.0648705 q^{18} -0.806909 q^{19} -0.236733 q^{20} +4.97378 q^{21} +0.281631 q^{22} +5.73717 q^{23} -0.259209 q^{24} -4.98593 q^{25} -0.224623 q^{26} -1.00000 q^{27} +9.92662 q^{28} -6.51973 q^{29} +0.00769468 q^{30} -2.26114 q^{31} -0.776264 q^{32} +4.34142 q^{33} +0.0648705 q^{34} -0.589969 q^{35} -1.99579 q^{36} -2.01285 q^{37} +0.0523446 q^{38} -3.46263 q^{39} +0.0307463 q^{40} +6.33093 q^{41} -0.322652 q^{42} +3.21798 q^{43} +8.66458 q^{44} +0.118616 q^{45} -0.372173 q^{46} +9.60026 q^{47} -3.97477 q^{48} +17.7385 q^{49} +0.323440 q^{50} +1.00000 q^{51} -6.91069 q^{52} -10.1285 q^{53} +0.0648705 q^{54} -0.514962 q^{55} -1.28925 q^{56} +0.806909 q^{57} +0.422939 q^{58} +2.31048 q^{59} +0.236733 q^{60} -7.66422 q^{61} +0.146681 q^{62} -4.97378 q^{63} -7.89918 q^{64} +0.410723 q^{65} -0.281631 q^{66} +8.05732 q^{67} +1.99579 q^{68} -5.73717 q^{69} +0.0382716 q^{70} +11.9634 q^{71} +0.259209 q^{72} +5.38589 q^{73} +0.130575 q^{74} +4.98593 q^{75} +1.61042 q^{76} +21.5933 q^{77} +0.224623 q^{78} +9.95475 q^{79} +0.471471 q^{80} +1.00000 q^{81} -0.410691 q^{82} +11.4537 q^{83} -9.92662 q^{84} -0.118616 q^{85} -0.208752 q^{86} +6.51973 q^{87} -1.12534 q^{88} -10.1718 q^{89} -0.00769468 q^{90} -17.2223 q^{91} -11.4502 q^{92} +2.26114 q^{93} -0.622774 q^{94} -0.0957122 q^{95} +0.776264 q^{96} -8.31464 q^{97} -1.15070 q^{98} -4.34142 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0648705 −0.0458704 −0.0229352 0.999737i \(-0.507301\pi\)
−0.0229352 + 0.999737i \(0.507301\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.99579 −0.997896
\(5\) 0.118616 0.0530467 0.0265233 0.999648i \(-0.491556\pi\)
0.0265233 + 0.999648i \(0.491556\pi\)
\(6\) 0.0648705 0.0264833
\(7\) −4.97378 −1.87991 −0.939956 0.341297i \(-0.889134\pi\)
−0.939956 + 0.341297i \(0.889134\pi\)
\(8\) 0.259209 0.0916443
\(9\) 1.00000 0.333333
\(10\) −0.00769468 −0.00243327
\(11\) −4.34142 −1.30899 −0.654494 0.756067i \(-0.727118\pi\)
−0.654494 + 0.756067i \(0.727118\pi\)
\(12\) 1.99579 0.576135
\(13\) 3.46263 0.960360 0.480180 0.877170i \(-0.340571\pi\)
0.480180 + 0.877170i \(0.340571\pi\)
\(14\) 0.322652 0.0862323
\(15\) −0.118616 −0.0306265
\(16\) 3.97477 0.993692
\(17\) −1.00000 −0.242536
\(18\) −0.0648705 −0.0152901
\(19\) −0.806909 −0.185118 −0.0925588 0.995707i \(-0.529505\pi\)
−0.0925588 + 0.995707i \(0.529505\pi\)
\(20\) −0.236733 −0.0529350
\(21\) 4.97378 1.08537
\(22\) 0.281631 0.0600438
\(23\) 5.73717 1.19628 0.598141 0.801391i \(-0.295906\pi\)
0.598141 + 0.801391i \(0.295906\pi\)
\(24\) −0.259209 −0.0529109
\(25\) −4.98593 −0.997186
\(26\) −0.224623 −0.0440521
\(27\) −1.00000 −0.192450
\(28\) 9.92662 1.87596
\(29\) −6.51973 −1.21068 −0.605342 0.795965i \(-0.706964\pi\)
−0.605342 + 0.795965i \(0.706964\pi\)
\(30\) 0.00769468 0.00140485
\(31\) −2.26114 −0.406113 −0.203056 0.979167i \(-0.565087\pi\)
−0.203056 + 0.979167i \(0.565087\pi\)
\(32\) −0.776264 −0.137225
\(33\) 4.34142 0.755745
\(34\) 0.0648705 0.0111252
\(35\) −0.589969 −0.0997230
\(36\) −1.99579 −0.332632
\(37\) −2.01285 −0.330910 −0.165455 0.986217i \(-0.552909\pi\)
−0.165455 + 0.986217i \(0.552909\pi\)
\(38\) 0.0523446 0.00849142
\(39\) −3.46263 −0.554464
\(40\) 0.0307463 0.00486142
\(41\) 6.33093 0.988725 0.494363 0.869256i \(-0.335401\pi\)
0.494363 + 0.869256i \(0.335401\pi\)
\(42\) −0.322652 −0.0497862
\(43\) 3.21798 0.490738 0.245369 0.969430i \(-0.421091\pi\)
0.245369 + 0.969430i \(0.421091\pi\)
\(44\) 8.66458 1.30623
\(45\) 0.118616 0.0176822
\(46\) −0.372173 −0.0548740
\(47\) 9.60026 1.40034 0.700171 0.713975i \(-0.253107\pi\)
0.700171 + 0.713975i \(0.253107\pi\)
\(48\) −3.97477 −0.573708
\(49\) 17.7385 2.53407
\(50\) 0.323440 0.0457413
\(51\) 1.00000 0.140028
\(52\) −6.91069 −0.958340
\(53\) −10.1285 −1.39125 −0.695627 0.718403i \(-0.744873\pi\)
−0.695627 + 0.718403i \(0.744873\pi\)
\(54\) 0.0648705 0.00882776
\(55\) −0.514962 −0.0694375
\(56\) −1.28925 −0.172283
\(57\) 0.806909 0.106878
\(58\) 0.422939 0.0555346
\(59\) 2.31048 0.300799 0.150399 0.988625i \(-0.451944\pi\)
0.150399 + 0.988625i \(0.451944\pi\)
\(60\) 0.236733 0.0305621
\(61\) −7.66422 −0.981303 −0.490652 0.871356i \(-0.663241\pi\)
−0.490652 + 0.871356i \(0.663241\pi\)
\(62\) 0.146681 0.0186286
\(63\) −4.97378 −0.626637
\(64\) −7.89918 −0.987398
\(65\) 0.410723 0.0509439
\(66\) −0.281631 −0.0346663
\(67\) 8.05732 0.984358 0.492179 0.870494i \(-0.336200\pi\)
0.492179 + 0.870494i \(0.336200\pi\)
\(68\) 1.99579 0.242025
\(69\) −5.73717 −0.690674
\(70\) 0.0382716 0.00457433
\(71\) 11.9634 1.41979 0.709897 0.704305i \(-0.248741\pi\)
0.709897 + 0.704305i \(0.248741\pi\)
\(72\) 0.259209 0.0305481
\(73\) 5.38589 0.630371 0.315185 0.949030i \(-0.397933\pi\)
0.315185 + 0.949030i \(0.397933\pi\)
\(74\) 0.130575 0.0151790
\(75\) 4.98593 0.575726
\(76\) 1.61042 0.184728
\(77\) 21.5933 2.46078
\(78\) 0.224623 0.0254335
\(79\) 9.95475 1.12000 0.559998 0.828494i \(-0.310802\pi\)
0.559998 + 0.828494i \(0.310802\pi\)
\(80\) 0.471471 0.0527120
\(81\) 1.00000 0.111111
\(82\) −0.410691 −0.0453532
\(83\) 11.4537 1.25721 0.628603 0.777726i \(-0.283627\pi\)
0.628603 + 0.777726i \(0.283627\pi\)
\(84\) −9.92662 −1.08308
\(85\) −0.118616 −0.0128657
\(86\) −0.208752 −0.0225103
\(87\) 6.51973 0.698989
\(88\) −1.12534 −0.119961
\(89\) −10.1718 −1.07821 −0.539103 0.842240i \(-0.681237\pi\)
−0.539103 + 0.842240i \(0.681237\pi\)
\(90\) −0.00769468 −0.000811090 0
\(91\) −17.2223 −1.80539
\(92\) −11.4502 −1.19377
\(93\) 2.26114 0.234469
\(94\) −0.622774 −0.0642342
\(95\) −0.0957122 −0.00981987
\(96\) 0.776264 0.0792271
\(97\) −8.31464 −0.844224 −0.422112 0.906544i \(-0.638711\pi\)
−0.422112 + 0.906544i \(0.638711\pi\)
\(98\) −1.15070 −0.116239
\(99\) −4.34142 −0.436330
\(100\) 9.95088 0.995088
\(101\) 7.93840 0.789900 0.394950 0.918703i \(-0.370762\pi\)
0.394950 + 0.918703i \(0.370762\pi\)
\(102\) −0.0648705 −0.00642314
\(103\) 12.0039 1.18277 0.591387 0.806388i \(-0.298580\pi\)
0.591387 + 0.806388i \(0.298580\pi\)
\(104\) 0.897545 0.0880115
\(105\) 0.589969 0.0575751
\(106\) 0.657040 0.0638174
\(107\) −4.01437 −0.388084 −0.194042 0.980993i \(-0.562160\pi\)
−0.194042 + 0.980993i \(0.562160\pi\)
\(108\) 1.99579 0.192045
\(109\) 6.05499 0.579963 0.289982 0.957032i \(-0.406351\pi\)
0.289982 + 0.957032i \(0.406351\pi\)
\(110\) 0.0334059 0.00318512
\(111\) 2.01285 0.191051
\(112\) −19.7696 −1.86805
\(113\) −2.48475 −0.233745 −0.116873 0.993147i \(-0.537287\pi\)
−0.116873 + 0.993147i \(0.537287\pi\)
\(114\) −0.0523446 −0.00490252
\(115\) 0.680520 0.0634588
\(116\) 13.0120 1.20814
\(117\) 3.46263 0.320120
\(118\) −0.149882 −0.0137977
\(119\) 4.97378 0.455945
\(120\) −0.0307463 −0.00280674
\(121\) 7.84797 0.713451
\(122\) 0.497182 0.0450128
\(123\) −6.33093 −0.570841
\(124\) 4.51277 0.405258
\(125\) −1.18449 −0.105944
\(126\) 0.322652 0.0287441
\(127\) 4.37521 0.388237 0.194119 0.980978i \(-0.437815\pi\)
0.194119 + 0.980978i \(0.437815\pi\)
\(128\) 2.06495 0.182518
\(129\) −3.21798 −0.283328
\(130\) −0.0266438 −0.00233682
\(131\) 1.76672 0.154359 0.0771796 0.997017i \(-0.475409\pi\)
0.0771796 + 0.997017i \(0.475409\pi\)
\(132\) −8.66458 −0.754155
\(133\) 4.01338 0.348005
\(134\) −0.522683 −0.0451529
\(135\) −0.118616 −0.0102088
\(136\) −0.259209 −0.0222270
\(137\) −1.71579 −0.146590 −0.0732950 0.997310i \(-0.523351\pi\)
−0.0732950 + 0.997310i \(0.523351\pi\)
\(138\) 0.372173 0.0316815
\(139\) 15.5724 1.32083 0.660417 0.750899i \(-0.270380\pi\)
0.660417 + 0.750899i \(0.270380\pi\)
\(140\) 1.17746 0.0995132
\(141\) −9.60026 −0.808488
\(142\) −0.776072 −0.0651265
\(143\) −15.0327 −1.25710
\(144\) 3.97477 0.331231
\(145\) −0.773344 −0.0642228
\(146\) −0.349385 −0.0289153
\(147\) −17.7385 −1.46304
\(148\) 4.01723 0.330214
\(149\) 5.85511 0.479669 0.239834 0.970814i \(-0.422907\pi\)
0.239834 + 0.970814i \(0.422907\pi\)
\(150\) −0.323440 −0.0264088
\(151\) 9.72038 0.791033 0.395517 0.918459i \(-0.370566\pi\)
0.395517 + 0.918459i \(0.370566\pi\)
\(152\) −0.209158 −0.0169650
\(153\) −1.00000 −0.0808452
\(154\) −1.40077 −0.112877
\(155\) −0.268207 −0.0215429
\(156\) 6.91069 0.553298
\(157\) −1.00000 −0.0798087
\(158\) −0.645770 −0.0513747
\(159\) 10.1285 0.803241
\(160\) −0.0920772 −0.00727935
\(161\) −28.5354 −2.24891
\(162\) −0.0648705 −0.00509671
\(163\) 8.84608 0.692879 0.346439 0.938072i \(-0.387391\pi\)
0.346439 + 0.938072i \(0.387391\pi\)
\(164\) −12.6352 −0.986645
\(165\) 0.514962 0.0400897
\(166\) −0.743007 −0.0576685
\(167\) −18.1414 −1.40383 −0.701913 0.712263i \(-0.747670\pi\)
−0.701913 + 0.712263i \(0.747670\pi\)
\(168\) 1.28925 0.0994677
\(169\) −1.01020 −0.0777078
\(170\) 0.00769468 0.000590155 0
\(171\) −0.806909 −0.0617059
\(172\) −6.42242 −0.489705
\(173\) 15.4822 1.17709 0.588546 0.808464i \(-0.299701\pi\)
0.588546 + 0.808464i \(0.299701\pi\)
\(174\) −0.422939 −0.0320629
\(175\) 24.7989 1.87462
\(176\) −17.2562 −1.30073
\(177\) −2.31048 −0.173666
\(178\) 0.659849 0.0494578
\(179\) −3.74689 −0.280055 −0.140028 0.990148i \(-0.544719\pi\)
−0.140028 + 0.990148i \(0.544719\pi\)
\(180\) −0.236733 −0.0176450
\(181\) −11.7797 −0.875580 −0.437790 0.899077i \(-0.644239\pi\)
−0.437790 + 0.899077i \(0.644239\pi\)
\(182\) 1.11722 0.0828141
\(183\) 7.66422 0.566556
\(184\) 1.48713 0.109632
\(185\) −0.238756 −0.0175537
\(186\) −0.146681 −0.0107552
\(187\) 4.34142 0.317476
\(188\) −19.1601 −1.39740
\(189\) 4.97378 0.361789
\(190\) 0.00620890 0.000450441 0
\(191\) −22.8104 −1.65050 −0.825251 0.564765i \(-0.808967\pi\)
−0.825251 + 0.564765i \(0.808967\pi\)
\(192\) 7.89918 0.570074
\(193\) −7.13856 −0.513845 −0.256922 0.966432i \(-0.582708\pi\)
−0.256922 + 0.966432i \(0.582708\pi\)
\(194\) 0.539375 0.0387249
\(195\) −0.410723 −0.0294125
\(196\) −35.4023 −2.52873
\(197\) 1.71391 0.122111 0.0610556 0.998134i \(-0.480553\pi\)
0.0610556 + 0.998134i \(0.480553\pi\)
\(198\) 0.281631 0.0200146
\(199\) −2.59523 −0.183971 −0.0919853 0.995760i \(-0.529321\pi\)
−0.0919853 + 0.995760i \(0.529321\pi\)
\(200\) −1.29240 −0.0913864
\(201\) −8.05732 −0.568320
\(202\) −0.514968 −0.0362330
\(203\) 32.4277 2.27598
\(204\) −1.99579 −0.139733
\(205\) 0.750949 0.0524486
\(206\) −0.778696 −0.0542543
\(207\) 5.73717 0.398761
\(208\) 13.7631 0.954303
\(209\) 3.50313 0.242317
\(210\) −0.0382716 −0.00264099
\(211\) −13.2324 −0.910958 −0.455479 0.890247i \(-0.650532\pi\)
−0.455479 + 0.890247i \(0.650532\pi\)
\(212\) 20.2143 1.38833
\(213\) −11.9634 −0.819719
\(214\) 0.260415 0.0178016
\(215\) 0.381704 0.0260320
\(216\) −0.259209 −0.0176370
\(217\) 11.2464 0.763456
\(218\) −0.392791 −0.0266031
\(219\) −5.38589 −0.363945
\(220\) 1.02776 0.0692914
\(221\) −3.46263 −0.232922
\(222\) −0.130575 −0.00876359
\(223\) −2.45175 −0.164181 −0.0820905 0.996625i \(-0.526160\pi\)
−0.0820905 + 0.996625i \(0.526160\pi\)
\(224\) 3.86096 0.257971
\(225\) −4.98593 −0.332395
\(226\) 0.161187 0.0107220
\(227\) −16.6359 −1.10416 −0.552082 0.833790i \(-0.686167\pi\)
−0.552082 + 0.833790i \(0.686167\pi\)
\(228\) −1.61042 −0.106653
\(229\) −17.1990 −1.13654 −0.568270 0.822842i \(-0.692387\pi\)
−0.568270 + 0.822842i \(0.692387\pi\)
\(230\) −0.0441457 −0.00291088
\(231\) −21.5933 −1.42073
\(232\) −1.68997 −0.110952
\(233\) −3.83870 −0.251482 −0.125741 0.992063i \(-0.540131\pi\)
−0.125741 + 0.992063i \(0.540131\pi\)
\(234\) −0.224623 −0.0146840
\(235\) 1.13874 0.0742835
\(236\) −4.61123 −0.300166
\(237\) −9.95475 −0.646630
\(238\) −0.322652 −0.0209144
\(239\) 7.17770 0.464286 0.232143 0.972682i \(-0.425426\pi\)
0.232143 + 0.972682i \(0.425426\pi\)
\(240\) −0.471471 −0.0304333
\(241\) −23.1575 −1.49171 −0.745853 0.666110i \(-0.767958\pi\)
−0.745853 + 0.666110i \(0.767958\pi\)
\(242\) −0.509102 −0.0327263
\(243\) −1.00000 −0.0641500
\(244\) 15.2962 0.979239
\(245\) 2.10406 0.134424
\(246\) 0.410691 0.0261847
\(247\) −2.79403 −0.177780
\(248\) −0.586108 −0.0372179
\(249\) −11.4537 −0.725848
\(250\) 0.0768385 0.00485970
\(251\) 21.1381 1.33422 0.667112 0.744957i \(-0.267530\pi\)
0.667112 + 0.744957i \(0.267530\pi\)
\(252\) 9.92662 0.625319
\(253\) −24.9075 −1.56592
\(254\) −0.283822 −0.0178086
\(255\) 0.118616 0.00742802
\(256\) 15.6644 0.979025
\(257\) −13.3372 −0.831950 −0.415975 0.909376i \(-0.636560\pi\)
−0.415975 + 0.909376i \(0.636560\pi\)
\(258\) 0.208752 0.0129963
\(259\) 10.0115 0.622082
\(260\) −0.819717 −0.0508367
\(261\) −6.51973 −0.403561
\(262\) −0.114608 −0.00708052
\(263\) −22.0305 −1.35846 −0.679228 0.733927i \(-0.737685\pi\)
−0.679228 + 0.733927i \(0.737685\pi\)
\(264\) 1.12534 0.0692597
\(265\) −1.20140 −0.0738014
\(266\) −0.260350 −0.0159631
\(267\) 10.1718 0.622503
\(268\) −16.0807 −0.982287
\(269\) −7.05221 −0.429981 −0.214990 0.976616i \(-0.568972\pi\)
−0.214990 + 0.976616i \(0.568972\pi\)
\(270\) 0.00769468 0.000468283 0
\(271\) −11.5716 −0.702926 −0.351463 0.936202i \(-0.614316\pi\)
−0.351463 + 0.936202i \(0.614316\pi\)
\(272\) −3.97477 −0.241006
\(273\) 17.2223 1.04234
\(274\) 0.111304 0.00672414
\(275\) 21.6460 1.30531
\(276\) 11.4502 0.689221
\(277\) 8.51107 0.511381 0.255690 0.966759i \(-0.417697\pi\)
0.255690 + 0.966759i \(0.417697\pi\)
\(278\) −1.01019 −0.0605871
\(279\) −2.26114 −0.135371
\(280\) −0.152925 −0.00913904
\(281\) −17.8087 −1.06238 −0.531189 0.847254i \(-0.678254\pi\)
−0.531189 + 0.847254i \(0.678254\pi\)
\(282\) 0.622774 0.0370857
\(283\) −21.5937 −1.28361 −0.641805 0.766868i \(-0.721814\pi\)
−0.641805 + 0.766868i \(0.721814\pi\)
\(284\) −23.8765 −1.41681
\(285\) 0.0957122 0.00566950
\(286\) 0.975182 0.0576637
\(287\) −31.4886 −1.85872
\(288\) −0.776264 −0.0457418
\(289\) 1.00000 0.0588235
\(290\) 0.0501673 0.00294592
\(291\) 8.31464 0.487413
\(292\) −10.7491 −0.629044
\(293\) −18.1737 −1.06172 −0.530860 0.847460i \(-0.678131\pi\)
−0.530860 + 0.847460i \(0.678131\pi\)
\(294\) 1.15070 0.0671104
\(295\) 0.274059 0.0159564
\(296\) −0.521749 −0.0303260
\(297\) 4.34142 0.251915
\(298\) −0.379824 −0.0220026
\(299\) 19.8657 1.14886
\(300\) −9.95088 −0.574514
\(301\) −16.0055 −0.922543
\(302\) −0.630566 −0.0362850
\(303\) −7.93840 −0.456049
\(304\) −3.20728 −0.183950
\(305\) −0.909099 −0.0520549
\(306\) 0.0648705 0.00370840
\(307\) −3.61718 −0.206443 −0.103222 0.994658i \(-0.532915\pi\)
−0.103222 + 0.994658i \(0.532915\pi\)
\(308\) −43.0957 −2.45560
\(309\) −12.0039 −0.682875
\(310\) 0.0173988 0.000988183 0
\(311\) −22.1185 −1.25423 −0.627113 0.778929i \(-0.715763\pi\)
−0.627113 + 0.778929i \(0.715763\pi\)
\(312\) −0.897545 −0.0508135
\(313\) 11.2934 0.638338 0.319169 0.947698i \(-0.396596\pi\)
0.319169 + 0.947698i \(0.396596\pi\)
\(314\) 0.0648705 0.00366086
\(315\) −0.589969 −0.0332410
\(316\) −19.8676 −1.11764
\(317\) −7.17556 −0.403019 −0.201510 0.979487i \(-0.564585\pi\)
−0.201510 + 0.979487i \(0.564585\pi\)
\(318\) −0.657040 −0.0368450
\(319\) 28.3049 1.58477
\(320\) −0.936969 −0.0523781
\(321\) 4.01437 0.224060
\(322\) 1.85111 0.103158
\(323\) 0.806909 0.0448976
\(324\) −1.99579 −0.110877
\(325\) −17.2644 −0.957658
\(326\) −0.573850 −0.0317826
\(327\) −6.05499 −0.334842
\(328\) 1.64104 0.0906110
\(329\) −47.7496 −2.63252
\(330\) −0.0334059 −0.00183893
\(331\) 19.5660 1.07544 0.537722 0.843122i \(-0.319285\pi\)
0.537722 + 0.843122i \(0.319285\pi\)
\(332\) −22.8592 −1.25456
\(333\) −2.01285 −0.110303
\(334\) 1.17684 0.0643940
\(335\) 0.955726 0.0522169
\(336\) 19.7696 1.07852
\(337\) 26.5021 1.44366 0.721831 0.692070i \(-0.243301\pi\)
0.721831 + 0.692070i \(0.243301\pi\)
\(338\) 0.0655323 0.00356449
\(339\) 2.48475 0.134953
\(340\) 0.236733 0.0128386
\(341\) 9.81657 0.531597
\(342\) 0.0523446 0.00283047
\(343\) −53.4107 −2.88391
\(344\) 0.834130 0.0449733
\(345\) −0.680520 −0.0366380
\(346\) −1.00434 −0.0539937
\(347\) 16.9944 0.912306 0.456153 0.889901i \(-0.349227\pi\)
0.456153 + 0.889901i \(0.349227\pi\)
\(348\) −13.0120 −0.697518
\(349\) 26.6567 1.42690 0.713451 0.700705i \(-0.247131\pi\)
0.713451 + 0.700705i \(0.247131\pi\)
\(350\) −1.60872 −0.0859896
\(351\) −3.46263 −0.184821
\(352\) 3.37009 0.179626
\(353\) 14.5904 0.776566 0.388283 0.921540i \(-0.373068\pi\)
0.388283 + 0.921540i \(0.373068\pi\)
\(354\) 0.149882 0.00796613
\(355\) 1.41905 0.0753153
\(356\) 20.3008 1.07594
\(357\) −4.97378 −0.263240
\(358\) 0.243062 0.0128463
\(359\) −15.3922 −0.812368 −0.406184 0.913791i \(-0.633141\pi\)
−0.406184 + 0.913791i \(0.633141\pi\)
\(360\) 0.0307463 0.00162047
\(361\) −18.3489 −0.965731
\(362\) 0.764157 0.0401632
\(363\) −7.84797 −0.411911
\(364\) 34.3722 1.80159
\(365\) 0.638852 0.0334391
\(366\) −0.497182 −0.0259881
\(367\) −12.3531 −0.644829 −0.322415 0.946599i \(-0.604494\pi\)
−0.322415 + 0.946599i \(0.604494\pi\)
\(368\) 22.8039 1.18874
\(369\) 6.33093 0.329575
\(370\) 0.0154882 0.000805195 0
\(371\) 50.3768 2.61543
\(372\) −4.51277 −0.233976
\(373\) 15.3806 0.796378 0.398189 0.917303i \(-0.369639\pi\)
0.398189 + 0.917303i \(0.369639\pi\)
\(374\) −0.281631 −0.0145628
\(375\) 1.18449 0.0611668
\(376\) 2.48848 0.128333
\(377\) −22.5754 −1.16269
\(378\) −0.322652 −0.0165954
\(379\) −25.3664 −1.30299 −0.651493 0.758655i \(-0.725857\pi\)
−0.651493 + 0.758655i \(0.725857\pi\)
\(380\) 0.191022 0.00979921
\(381\) −4.37521 −0.224149
\(382\) 1.47972 0.0757092
\(383\) 25.1142 1.28328 0.641638 0.767008i \(-0.278255\pi\)
0.641638 + 0.767008i \(0.278255\pi\)
\(384\) −2.06495 −0.105377
\(385\) 2.56131 0.130536
\(386\) 0.463082 0.0235703
\(387\) 3.21798 0.163579
\(388\) 16.5943 0.842448
\(389\) −13.9009 −0.704805 −0.352402 0.935849i \(-0.614635\pi\)
−0.352402 + 0.935849i \(0.614635\pi\)
\(390\) 0.0266438 0.00134916
\(391\) −5.73717 −0.290141
\(392\) 4.59797 0.232233
\(393\) −1.76672 −0.0891193
\(394\) −0.111182 −0.00560129
\(395\) 1.18079 0.0594121
\(396\) 8.66458 0.435411
\(397\) 33.7127 1.69199 0.845996 0.533190i \(-0.179007\pi\)
0.845996 + 0.533190i \(0.179007\pi\)
\(398\) 0.168354 0.00843881
\(399\) −4.01338 −0.200921
\(400\) −19.8179 −0.990896
\(401\) −8.36903 −0.417929 −0.208965 0.977923i \(-0.567009\pi\)
−0.208965 + 0.977923i \(0.567009\pi\)
\(402\) 0.522683 0.0260690
\(403\) −7.82949 −0.390015
\(404\) −15.8434 −0.788238
\(405\) 0.118616 0.00589407
\(406\) −2.10360 −0.104400
\(407\) 8.73863 0.433158
\(408\) 0.259209 0.0128328
\(409\) 2.67132 0.132089 0.0660443 0.997817i \(-0.478962\pi\)
0.0660443 + 0.997817i \(0.478962\pi\)
\(410\) −0.0487145 −0.00240584
\(411\) 1.71579 0.0846338
\(412\) −23.9572 −1.18029
\(413\) −11.4918 −0.565475
\(414\) −0.372173 −0.0182913
\(415\) 1.35859 0.0666906
\(416\) −2.68791 −0.131786
\(417\) −15.5724 −0.762583
\(418\) −0.227250 −0.0111152
\(419\) 31.8284 1.55492 0.777460 0.628932i \(-0.216508\pi\)
0.777460 + 0.628932i \(0.216508\pi\)
\(420\) −1.17746 −0.0574540
\(421\) −5.03737 −0.245506 −0.122753 0.992437i \(-0.539172\pi\)
−0.122753 + 0.992437i \(0.539172\pi\)
\(422\) 0.858394 0.0417860
\(423\) 9.60026 0.466781
\(424\) −2.62539 −0.127500
\(425\) 4.98593 0.241853
\(426\) 0.776072 0.0376008
\(427\) 38.1201 1.84476
\(428\) 8.01185 0.387268
\(429\) 15.0327 0.725788
\(430\) −0.0247613 −0.00119410
\(431\) 16.2108 0.780849 0.390425 0.920635i \(-0.372328\pi\)
0.390425 + 0.920635i \(0.372328\pi\)
\(432\) −3.97477 −0.191236
\(433\) 19.9519 0.958829 0.479414 0.877589i \(-0.340849\pi\)
0.479414 + 0.877589i \(0.340849\pi\)
\(434\) −0.729561 −0.0350200
\(435\) 0.773344 0.0370790
\(436\) −12.0845 −0.578743
\(437\) −4.62937 −0.221453
\(438\) 0.349385 0.0166943
\(439\) −7.04627 −0.336300 −0.168150 0.985761i \(-0.553779\pi\)
−0.168150 + 0.985761i \(0.553779\pi\)
\(440\) −0.133483 −0.00636355
\(441\) 17.7385 0.844689
\(442\) 0.224623 0.0106842
\(443\) 30.8886 1.46756 0.733782 0.679385i \(-0.237753\pi\)
0.733782 + 0.679385i \(0.237753\pi\)
\(444\) −4.01723 −0.190649
\(445\) −1.20654 −0.0571953
\(446\) 0.159046 0.00753105
\(447\) −5.85511 −0.276937
\(448\) 39.2888 1.85622
\(449\) 6.88966 0.325143 0.162572 0.986697i \(-0.448021\pi\)
0.162572 + 0.986697i \(0.448021\pi\)
\(450\) 0.323440 0.0152471
\(451\) −27.4853 −1.29423
\(452\) 4.95903 0.233253
\(453\) −9.72038 −0.456703
\(454\) 1.07918 0.0506485
\(455\) −2.04284 −0.0957700
\(456\) 0.209158 0.00979473
\(457\) −8.68547 −0.406289 −0.203145 0.979149i \(-0.565116\pi\)
−0.203145 + 0.979149i \(0.565116\pi\)
\(458\) 1.11571 0.0521336
\(459\) 1.00000 0.0466760
\(460\) −1.35818 −0.0633253
\(461\) −13.6759 −0.636952 −0.318476 0.947931i \(-0.603171\pi\)
−0.318476 + 0.947931i \(0.603171\pi\)
\(462\) 1.40077 0.0651696
\(463\) 1.94603 0.0904395 0.0452197 0.998977i \(-0.485601\pi\)
0.0452197 + 0.998977i \(0.485601\pi\)
\(464\) −25.9144 −1.20305
\(465\) 0.268207 0.0124378
\(466\) 0.249019 0.0115356
\(467\) 12.0677 0.558427 0.279214 0.960229i \(-0.409926\pi\)
0.279214 + 0.960229i \(0.409926\pi\)
\(468\) −6.91069 −0.319447
\(469\) −40.0753 −1.85051
\(470\) −0.0738709 −0.00340741
\(471\) 1.00000 0.0460776
\(472\) 0.598897 0.0275665
\(473\) −13.9706 −0.642370
\(474\) 0.645770 0.0296612
\(475\) 4.02319 0.184597
\(476\) −9.92662 −0.454986
\(477\) −10.1285 −0.463751
\(478\) −0.465621 −0.0212970
\(479\) 16.5252 0.755056 0.377528 0.925998i \(-0.376774\pi\)
0.377528 + 0.925998i \(0.376774\pi\)
\(480\) 0.0920772 0.00420273
\(481\) −6.96975 −0.317793
\(482\) 1.50224 0.0684252
\(483\) 28.5354 1.29841
\(484\) −15.6629 −0.711950
\(485\) −0.986249 −0.0447833
\(486\) 0.0648705 0.00294259
\(487\) −13.4957 −0.611549 −0.305774 0.952104i \(-0.598915\pi\)
−0.305774 + 0.952104i \(0.598915\pi\)
\(488\) −1.98664 −0.0899308
\(489\) −8.84608 −0.400034
\(490\) −0.136492 −0.00616607
\(491\) −0.838904 −0.0378592 −0.0189296 0.999821i \(-0.506026\pi\)
−0.0189296 + 0.999821i \(0.506026\pi\)
\(492\) 12.6352 0.569640
\(493\) 6.51973 0.293634
\(494\) 0.181250 0.00815482
\(495\) −0.514962 −0.0231458
\(496\) −8.98751 −0.403551
\(497\) −59.5033 −2.66909
\(498\) 0.743007 0.0332949
\(499\) 20.7838 0.930411 0.465206 0.885203i \(-0.345980\pi\)
0.465206 + 0.885203i \(0.345980\pi\)
\(500\) 2.36400 0.105721
\(501\) 18.1414 0.810499
\(502\) −1.37124 −0.0612014
\(503\) −22.3605 −0.997005 −0.498502 0.866888i \(-0.666116\pi\)
−0.498502 + 0.866888i \(0.666116\pi\)
\(504\) −1.28925 −0.0574277
\(505\) 0.941620 0.0419016
\(506\) 1.61576 0.0718294
\(507\) 1.01020 0.0448646
\(508\) −8.73201 −0.387420
\(509\) −35.2943 −1.56439 −0.782196 0.623032i \(-0.785901\pi\)
−0.782196 + 0.623032i \(0.785901\pi\)
\(510\) −0.00769468 −0.000340726 0
\(511\) −26.7882 −1.18504
\(512\) −5.14606 −0.227426
\(513\) 0.806909 0.0356259
\(514\) 0.865190 0.0381619
\(515\) 1.42385 0.0627422
\(516\) 6.42242 0.282731
\(517\) −41.6788 −1.83303
\(518\) −0.649449 −0.0285352
\(519\) −15.4822 −0.679594
\(520\) 0.106463 0.00466872
\(521\) −29.4016 −1.28811 −0.644055 0.764979i \(-0.722749\pi\)
−0.644055 + 0.764979i \(0.722749\pi\)
\(522\) 0.422939 0.0185115
\(523\) −14.3280 −0.626522 −0.313261 0.949667i \(-0.601421\pi\)
−0.313261 + 0.949667i \(0.601421\pi\)
\(524\) −3.52601 −0.154034
\(525\) −24.7989 −1.08231
\(526\) 1.42913 0.0623130
\(527\) 2.26114 0.0984968
\(528\) 17.2562 0.750978
\(529\) 9.91513 0.431093
\(530\) 0.0779354 0.00338530
\(531\) 2.31048 0.100266
\(532\) −8.00988 −0.347272
\(533\) 21.9217 0.949533
\(534\) −0.659849 −0.0285545
\(535\) −0.476169 −0.0205866
\(536\) 2.08853 0.0902108
\(537\) 3.74689 0.161690
\(538\) 0.457480 0.0197234
\(539\) −77.0102 −3.31706
\(540\) 0.236733 0.0101874
\(541\) −23.4474 −1.00808 −0.504042 0.863679i \(-0.668154\pi\)
−0.504042 + 0.863679i \(0.668154\pi\)
\(542\) 0.750657 0.0322435
\(543\) 11.7797 0.505516
\(544\) 0.776264 0.0332820
\(545\) 0.718219 0.0307651
\(546\) −1.11722 −0.0478127
\(547\) −35.2307 −1.50636 −0.753178 0.657817i \(-0.771480\pi\)
−0.753178 + 0.657817i \(0.771480\pi\)
\(548\) 3.42436 0.146282
\(549\) −7.66422 −0.327101
\(550\) −1.40419 −0.0598749
\(551\) 5.26083 0.224119
\(552\) −1.48713 −0.0632963
\(553\) −49.5127 −2.10549
\(554\) −0.552118 −0.0234572
\(555\) 0.238756 0.0101346
\(556\) −31.0793 −1.31805
\(557\) 2.37181 0.100497 0.0502484 0.998737i \(-0.483999\pi\)
0.0502484 + 0.998737i \(0.483999\pi\)
\(558\) 0.146681 0.00620952
\(559\) 11.1427 0.471285
\(560\) −2.34499 −0.0990940
\(561\) −4.34142 −0.183295
\(562\) 1.15526 0.0487317
\(563\) 16.2262 0.683854 0.341927 0.939727i \(-0.388920\pi\)
0.341927 + 0.939727i \(0.388920\pi\)
\(564\) 19.1601 0.806787
\(565\) −0.294730 −0.0123994
\(566\) 1.40079 0.0588797
\(567\) −4.97378 −0.208879
\(568\) 3.10102 0.130116
\(569\) 36.0438 1.51104 0.755518 0.655128i \(-0.227385\pi\)
0.755518 + 0.655128i \(0.227385\pi\)
\(570\) −0.00620890 −0.000260062 0
\(571\) 38.1300 1.59569 0.797845 0.602862i \(-0.205973\pi\)
0.797845 + 0.602862i \(0.205973\pi\)
\(572\) 30.0022 1.25446
\(573\) 22.8104 0.952918
\(574\) 2.04269 0.0852600
\(575\) −28.6051 −1.19292
\(576\) −7.89918 −0.329133
\(577\) −0.446766 −0.0185991 −0.00929956 0.999957i \(-0.502960\pi\)
−0.00929956 + 0.999957i \(0.502960\pi\)
\(578\) −0.0648705 −0.00269826
\(579\) 7.13856 0.296668
\(580\) 1.54343 0.0640876
\(581\) −56.9681 −2.36344
\(582\) −0.539375 −0.0223578
\(583\) 43.9720 1.82114
\(584\) 1.39607 0.0577699
\(585\) 0.410723 0.0169813
\(586\) 1.17894 0.0487015
\(587\) 24.5870 1.01481 0.507406 0.861707i \(-0.330604\pi\)
0.507406 + 0.861707i \(0.330604\pi\)
\(588\) 35.4023 1.45997
\(589\) 1.82453 0.0751786
\(590\) −0.0177784 −0.000731924 0
\(591\) −1.71391 −0.0705009
\(592\) −8.00061 −0.328823
\(593\) −11.0526 −0.453877 −0.226938 0.973909i \(-0.572872\pi\)
−0.226938 + 0.973909i \(0.572872\pi\)
\(594\) −0.281631 −0.0115554
\(595\) 0.589969 0.0241864
\(596\) −11.6856 −0.478660
\(597\) 2.59523 0.106215
\(598\) −1.28870 −0.0526988
\(599\) 35.2735 1.44124 0.720618 0.693332i \(-0.243858\pi\)
0.720618 + 0.693332i \(0.243858\pi\)
\(600\) 1.29240 0.0527620
\(601\) −42.5574 −1.73595 −0.867976 0.496606i \(-0.834579\pi\)
−0.867976 + 0.496606i \(0.834579\pi\)
\(602\) 1.03829 0.0423174
\(603\) 8.05732 0.328119
\(604\) −19.3998 −0.789369
\(605\) 0.930894 0.0378462
\(606\) 0.514968 0.0209191
\(607\) −7.52398 −0.305389 −0.152694 0.988273i \(-0.548795\pi\)
−0.152694 + 0.988273i \(0.548795\pi\)
\(608\) 0.626374 0.0254028
\(609\) −32.4277 −1.31404
\(610\) 0.0589737 0.00238778
\(611\) 33.2421 1.34483
\(612\) 1.99579 0.0806751
\(613\) 48.7096 1.96736 0.983680 0.179924i \(-0.0575853\pi\)
0.983680 + 0.179924i \(0.0575853\pi\)
\(614\) 0.234648 0.00946964
\(615\) −0.750949 −0.0302812
\(616\) 5.59718 0.225517
\(617\) −46.3020 −1.86405 −0.932024 0.362397i \(-0.881959\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(618\) 0.778696 0.0313238
\(619\) −2.14850 −0.0863555 −0.0431777 0.999067i \(-0.513748\pi\)
−0.0431777 + 0.999067i \(0.513748\pi\)
\(620\) 0.535286 0.0214976
\(621\) −5.73717 −0.230225
\(622\) 1.43484 0.0575318
\(623\) 50.5922 2.02693
\(624\) −13.7631 −0.550967
\(625\) 24.7892 0.991566
\(626\) −0.732606 −0.0292808
\(627\) −3.50313 −0.139902
\(628\) 1.99579 0.0796408
\(629\) 2.01285 0.0802576
\(630\) 0.0382716 0.00152478
\(631\) 30.3936 1.20995 0.604975 0.796244i \(-0.293183\pi\)
0.604975 + 0.796244i \(0.293183\pi\)
\(632\) 2.58036 0.102641
\(633\) 13.2324 0.525942
\(634\) 0.465482 0.0184867
\(635\) 0.518970 0.0205947
\(636\) −20.2143 −0.801551
\(637\) 61.4217 2.43362
\(638\) −1.83616 −0.0726941
\(639\) 11.9634 0.473265
\(640\) 0.244936 0.00968195
\(641\) 24.6608 0.974044 0.487022 0.873390i \(-0.338083\pi\)
0.487022 + 0.873390i \(0.338083\pi\)
\(642\) −0.260415 −0.0102777
\(643\) −43.5581 −1.71776 −0.858882 0.512173i \(-0.828841\pi\)
−0.858882 + 0.512173i \(0.828841\pi\)
\(644\) 56.9507 2.24417
\(645\) −0.381704 −0.0150296
\(646\) −0.0523446 −0.00205947
\(647\) 10.6798 0.419867 0.209934 0.977716i \(-0.432675\pi\)
0.209934 + 0.977716i \(0.432675\pi\)
\(648\) 0.259209 0.0101827
\(649\) −10.0308 −0.393742
\(650\) 1.11995 0.0439282
\(651\) −11.2464 −0.440782
\(652\) −17.6549 −0.691421
\(653\) −10.7084 −0.419052 −0.209526 0.977803i \(-0.567192\pi\)
−0.209526 + 0.977803i \(0.567192\pi\)
\(654\) 0.392791 0.0153593
\(655\) 0.209561 0.00818824
\(656\) 25.1640 0.982489
\(657\) 5.38589 0.210124
\(658\) 3.09754 0.120755
\(659\) −6.67168 −0.259892 −0.129946 0.991521i \(-0.541480\pi\)
−0.129946 + 0.991521i \(0.541480\pi\)
\(660\) −1.02776 −0.0400054
\(661\) 13.4694 0.523899 0.261949 0.965082i \(-0.415635\pi\)
0.261949 + 0.965082i \(0.415635\pi\)
\(662\) −1.26926 −0.0493311
\(663\) 3.46263 0.134477
\(664\) 2.96890 0.115216
\(665\) 0.476051 0.0184605
\(666\) 0.130575 0.00505966
\(667\) −37.4048 −1.44832
\(668\) 36.2065 1.40087
\(669\) 2.45175 0.0947900
\(670\) −0.0619985 −0.00239521
\(671\) 33.2737 1.28452
\(672\) −3.86096 −0.148940
\(673\) −24.5621 −0.946798 −0.473399 0.880848i \(-0.656973\pi\)
−0.473399 + 0.880848i \(0.656973\pi\)
\(674\) −1.71921 −0.0662213
\(675\) 4.98593 0.191909
\(676\) 2.01615 0.0775443
\(677\) 32.6567 1.25510 0.627549 0.778577i \(-0.284058\pi\)
0.627549 + 0.778577i \(0.284058\pi\)
\(678\) −0.161187 −0.00619034
\(679\) 41.3552 1.58707
\(680\) −0.0307463 −0.00117907
\(681\) 16.6359 0.637490
\(682\) −0.636806 −0.0243846
\(683\) 21.1801 0.810435 0.405218 0.914220i \(-0.367196\pi\)
0.405218 + 0.914220i \(0.367196\pi\)
\(684\) 1.61042 0.0615760
\(685\) −0.203520 −0.00777611
\(686\) 3.46478 0.132286
\(687\) 17.1990 0.656182
\(688\) 12.7907 0.487642
\(689\) −35.0712 −1.33611
\(690\) 0.0441457 0.00168060
\(691\) −40.0266 −1.52268 −0.761341 0.648351i \(-0.775459\pi\)
−0.761341 + 0.648351i \(0.775459\pi\)
\(692\) −30.8993 −1.17462
\(693\) 21.5933 0.820261
\(694\) −1.10243 −0.0418478
\(695\) 1.84713 0.0700658
\(696\) 1.68997 0.0640583
\(697\) −6.33093 −0.239801
\(698\) −1.72924 −0.0654526
\(699\) 3.83870 0.145193
\(700\) −49.4935 −1.87068
\(701\) −15.2192 −0.574819 −0.287410 0.957808i \(-0.592794\pi\)
−0.287410 + 0.957808i \(0.592794\pi\)
\(702\) 0.224623 0.00847783
\(703\) 1.62419 0.0612573
\(704\) 34.2937 1.29249
\(705\) −1.13874 −0.0428876
\(706\) −0.946484 −0.0356214
\(707\) −39.4838 −1.48494
\(708\) 4.61123 0.173301
\(709\) 42.8476 1.60917 0.804587 0.593834i \(-0.202387\pi\)
0.804587 + 0.593834i \(0.202387\pi\)
\(710\) −0.0920545 −0.00345474
\(711\) 9.95475 0.373332
\(712\) −2.63662 −0.0988115
\(713\) −12.9725 −0.485826
\(714\) 0.322652 0.0120749
\(715\) −1.78312 −0.0666850
\(716\) 7.47800 0.279466
\(717\) −7.17770 −0.268056
\(718\) 0.998499 0.0372637
\(719\) 10.8590 0.404972 0.202486 0.979285i \(-0.435098\pi\)
0.202486 + 0.979285i \(0.435098\pi\)
\(720\) 0.471471 0.0175707
\(721\) −59.7045 −2.22351
\(722\) 1.19030 0.0442985
\(723\) 23.1575 0.861237
\(724\) 23.5099 0.873738
\(725\) 32.5069 1.20728
\(726\) 0.509102 0.0188945
\(727\) −22.6353 −0.839497 −0.419748 0.907640i \(-0.637882\pi\)
−0.419748 + 0.907640i \(0.637882\pi\)
\(728\) −4.46419 −0.165454
\(729\) 1.00000 0.0370370
\(730\) −0.0414427 −0.00153386
\(731\) −3.21798 −0.119021
\(732\) −15.2962 −0.565364
\(733\) 27.3952 1.01186 0.505932 0.862573i \(-0.331149\pi\)
0.505932 + 0.862573i \(0.331149\pi\)
\(734\) 0.801355 0.0295786
\(735\) −2.10406 −0.0776096
\(736\) −4.45356 −0.164160
\(737\) −34.9802 −1.28851
\(738\) −0.410691 −0.0151177
\(739\) −40.0980 −1.47503 −0.737514 0.675332i \(-0.764000\pi\)
−0.737514 + 0.675332i \(0.764000\pi\)
\(740\) 0.476507 0.0175168
\(741\) 2.79403 0.102641
\(742\) −3.26797 −0.119971
\(743\) −5.27356 −0.193468 −0.0967341 0.995310i \(-0.530840\pi\)
−0.0967341 + 0.995310i \(0.530840\pi\)
\(744\) 0.586108 0.0214878
\(745\) 0.694509 0.0254448
\(746\) −0.997749 −0.0365302
\(747\) 11.4537 0.419069
\(748\) −8.66458 −0.316808
\(749\) 19.9666 0.729564
\(750\) −0.0768385 −0.00280575
\(751\) −21.2154 −0.774161 −0.387080 0.922046i \(-0.626516\pi\)
−0.387080 + 0.922046i \(0.626516\pi\)
\(752\) 38.1588 1.39151
\(753\) −21.1381 −0.770315
\(754\) 1.46448 0.0533332
\(755\) 1.15299 0.0419617
\(756\) −9.92662 −0.361028
\(757\) −15.5366 −0.564688 −0.282344 0.959313i \(-0.591112\pi\)
−0.282344 + 0.959313i \(0.591112\pi\)
\(758\) 1.64553 0.0597685
\(759\) 24.9075 0.904085
\(760\) −0.0248095 −0.000899935 0
\(761\) 23.2789 0.843858 0.421929 0.906629i \(-0.361353\pi\)
0.421929 + 0.906629i \(0.361353\pi\)
\(762\) 0.283822 0.0102818
\(763\) −30.1162 −1.09028
\(764\) 45.5248 1.64703
\(765\) −0.118616 −0.00428857
\(766\) −1.62917 −0.0588644
\(767\) 8.00033 0.288875
\(768\) −15.6644 −0.565241
\(769\) −39.8062 −1.43545 −0.717724 0.696328i \(-0.754816\pi\)
−0.717724 + 0.696328i \(0.754816\pi\)
\(770\) −0.166153 −0.00598775
\(771\) 13.3372 0.480327
\(772\) 14.2471 0.512763
\(773\) 0.618675 0.0222522 0.0111261 0.999938i \(-0.496458\pi\)
0.0111261 + 0.999938i \(0.496458\pi\)
\(774\) −0.208752 −0.00750344
\(775\) 11.2739 0.404970
\(776\) −2.15523 −0.0773683
\(777\) −10.0115 −0.359159
\(778\) 0.901760 0.0323297
\(779\) −5.10848 −0.183030
\(780\) 0.819717 0.0293506
\(781\) −51.9382 −1.85849
\(782\) 0.372173 0.0133089
\(783\) 6.51973 0.232996
\(784\) 70.5063 2.51808
\(785\) −0.118616 −0.00423358
\(786\) 0.114608 0.00408794
\(787\) −30.6959 −1.09419 −0.547096 0.837070i \(-0.684267\pi\)
−0.547096 + 0.837070i \(0.684267\pi\)
\(788\) −3.42061 −0.121854
\(789\) 22.0305 0.784305
\(790\) −0.0765986 −0.00272526
\(791\) 12.3586 0.439420
\(792\) −1.12534 −0.0399871
\(793\) −26.5384 −0.942405
\(794\) −2.18696 −0.0776123
\(795\) 1.20140 0.0426092
\(796\) 5.17953 0.183584
\(797\) 9.23042 0.326958 0.163479 0.986547i \(-0.447728\pi\)
0.163479 + 0.986547i \(0.447728\pi\)
\(798\) 0.260350 0.00921631
\(799\) −9.60026 −0.339633
\(800\) 3.87040 0.136839
\(801\) −10.1718 −0.359402
\(802\) 0.542903 0.0191706
\(803\) −23.3824 −0.825148
\(804\) 16.0807 0.567124
\(805\) −3.38475 −0.119297
\(806\) 0.507903 0.0178901
\(807\) 7.05221 0.248249
\(808\) 2.05771 0.0723898
\(809\) −3.92763 −0.138088 −0.0690440 0.997614i \(-0.521995\pi\)
−0.0690440 + 0.997614i \(0.521995\pi\)
\(810\) −0.00769468 −0.000270363 0
\(811\) −36.1806 −1.27047 −0.635236 0.772318i \(-0.719097\pi\)
−0.635236 + 0.772318i \(0.719097\pi\)
\(812\) −64.7189 −2.27119
\(813\) 11.5716 0.405835
\(814\) −0.566880 −0.0198691
\(815\) 1.04929 0.0367549
\(816\) 3.97477 0.139145
\(817\) −2.59662 −0.0908442
\(818\) −0.173290 −0.00605895
\(819\) −17.2223 −0.601797
\(820\) −1.49874 −0.0523382
\(821\) −21.1093 −0.736720 −0.368360 0.929683i \(-0.620081\pi\)
−0.368360 + 0.929683i \(0.620081\pi\)
\(822\) −0.111304 −0.00388218
\(823\) −31.6091 −1.10182 −0.550912 0.834563i \(-0.685720\pi\)
−0.550912 + 0.834563i \(0.685720\pi\)
\(824\) 3.11151 0.108395
\(825\) −21.6460 −0.753618
\(826\) 0.745479 0.0259385
\(827\) −20.8886 −0.726367 −0.363183 0.931718i \(-0.618310\pi\)
−0.363183 + 0.931718i \(0.618310\pi\)
\(828\) −11.4502 −0.397922
\(829\) −31.4468 −1.09219 −0.546096 0.837723i \(-0.683887\pi\)
−0.546096 + 0.837723i \(0.683887\pi\)
\(830\) −0.0881325 −0.00305912
\(831\) −8.51107 −0.295246
\(832\) −27.3519 −0.948258
\(833\) −17.7385 −0.614601
\(834\) 1.01019 0.0349800
\(835\) −2.15186 −0.0744682
\(836\) −6.99153 −0.241807
\(837\) 2.26114 0.0781564
\(838\) −2.06473 −0.0713248
\(839\) 23.1505 0.799245 0.399622 0.916680i \(-0.369141\pi\)
0.399622 + 0.916680i \(0.369141\pi\)
\(840\) 0.152925 0.00527643
\(841\) 13.5069 0.465756
\(842\) 0.326777 0.0112615
\(843\) 17.8087 0.613364
\(844\) 26.4092 0.909041
\(845\) −0.119826 −0.00412214
\(846\) −0.622774 −0.0214114
\(847\) −39.0340 −1.34123
\(848\) −40.2584 −1.38248
\(849\) 21.5937 0.741093
\(850\) −0.323440 −0.0110939
\(851\) −11.5481 −0.395862
\(852\) 23.8765 0.817994
\(853\) −54.9840 −1.88262 −0.941308 0.337548i \(-0.890403\pi\)
−0.941308 + 0.337548i \(0.890403\pi\)
\(854\) −2.47287 −0.0846200
\(855\) −0.0957122 −0.00327329
\(856\) −1.04056 −0.0355657
\(857\) 32.0628 1.09524 0.547622 0.836726i \(-0.315533\pi\)
0.547622 + 0.836726i \(0.315533\pi\)
\(858\) −0.975182 −0.0332922
\(859\) −35.0132 −1.19463 −0.597317 0.802005i \(-0.703767\pi\)
−0.597317 + 0.802005i \(0.703767\pi\)
\(860\) −0.761802 −0.0259772
\(861\) 31.4886 1.07313
\(862\) −1.05161 −0.0358179
\(863\) 23.9360 0.814793 0.407396 0.913251i \(-0.366437\pi\)
0.407396 + 0.913251i \(0.366437\pi\)
\(864\) 0.776264 0.0264090
\(865\) 1.83644 0.0624408
\(866\) −1.29429 −0.0439818
\(867\) −1.00000 −0.0339618
\(868\) −22.4455 −0.761850
\(869\) −43.2178 −1.46606
\(870\) −0.0501673 −0.00170083
\(871\) 27.8995 0.945339
\(872\) 1.56951 0.0531503
\(873\) −8.31464 −0.281408
\(874\) 0.300310 0.0101581
\(875\) 5.89139 0.199165
\(876\) 10.7491 0.363179
\(877\) 8.94810 0.302156 0.151078 0.988522i \(-0.451726\pi\)
0.151078 + 0.988522i \(0.451726\pi\)
\(878\) 0.457096 0.0154262
\(879\) 18.1737 0.612984
\(880\) −2.04686 −0.0689995
\(881\) 40.0704 1.35001 0.675004 0.737814i \(-0.264142\pi\)
0.675004 + 0.737814i \(0.264142\pi\)
\(882\) −1.15070 −0.0387462
\(883\) 41.9711 1.41244 0.706221 0.707992i \(-0.250399\pi\)
0.706221 + 0.707992i \(0.250399\pi\)
\(884\) 6.91069 0.232432
\(885\) −0.274059 −0.00921241
\(886\) −2.00376 −0.0673177
\(887\) −12.5179 −0.420309 −0.210154 0.977668i \(-0.567397\pi\)
−0.210154 + 0.977668i \(0.567397\pi\)
\(888\) 0.521749 0.0175087
\(889\) −21.7613 −0.729851
\(890\) 0.0782686 0.00262357
\(891\) −4.34142 −0.145443
\(892\) 4.89318 0.163836
\(893\) −7.74654 −0.259228
\(894\) 0.379824 0.0127032
\(895\) −0.444440 −0.0148560
\(896\) −10.2706 −0.343117
\(897\) −19.8657 −0.663296
\(898\) −0.446936 −0.0149144
\(899\) 14.7420 0.491674
\(900\) 9.95088 0.331696
\(901\) 10.1285 0.337429
\(902\) 1.78298 0.0593669
\(903\) 16.0055 0.532631
\(904\) −0.644069 −0.0214214
\(905\) −1.39726 −0.0464466
\(906\) 0.630566 0.0209492
\(907\) 25.4570 0.845287 0.422644 0.906296i \(-0.361102\pi\)
0.422644 + 0.906296i \(0.361102\pi\)
\(908\) 33.2018 1.10184
\(909\) 7.93840 0.263300
\(910\) 0.132520 0.00439301
\(911\) −28.7376 −0.952118 −0.476059 0.879413i \(-0.657935\pi\)
−0.476059 + 0.879413i \(0.657935\pi\)
\(912\) 3.20728 0.106204
\(913\) −49.7253 −1.64567
\(914\) 0.563431 0.0186366
\(915\) 0.909099 0.0300539
\(916\) 34.3256 1.13415
\(917\) −8.78728 −0.290182
\(918\) −0.0648705 −0.00214105
\(919\) 34.9113 1.15162 0.575809 0.817584i \(-0.304687\pi\)
0.575809 + 0.817584i \(0.304687\pi\)
\(920\) 0.176397 0.00581564
\(921\) 3.61718 0.119190
\(922\) 0.887165 0.0292172
\(923\) 41.4248 1.36351
\(924\) 43.0957 1.41774
\(925\) 10.0359 0.329979
\(926\) −0.126240 −0.00414850
\(927\) 12.0039 0.394258
\(928\) 5.06103 0.166137
\(929\) 41.1661 1.35062 0.675308 0.737536i \(-0.264011\pi\)
0.675308 + 0.737536i \(0.264011\pi\)
\(930\) −0.0173988 −0.000570528 0
\(931\) −14.3133 −0.469100
\(932\) 7.66125 0.250953
\(933\) 22.1185 0.724127
\(934\) −0.782839 −0.0256153
\(935\) 0.514962 0.0168411
\(936\) 0.897545 0.0293372
\(937\) −32.2313 −1.05295 −0.526475 0.850191i \(-0.676487\pi\)
−0.526475 + 0.850191i \(0.676487\pi\)
\(938\) 2.59971 0.0848834
\(939\) −11.2934 −0.368545
\(940\) −2.27270 −0.0741272
\(941\) −9.17313 −0.299035 −0.149518 0.988759i \(-0.547772\pi\)
−0.149518 + 0.988759i \(0.547772\pi\)
\(942\) −0.0648705 −0.00211360
\(943\) 36.3216 1.18280
\(944\) 9.18361 0.298901
\(945\) 0.589969 0.0191917
\(946\) 0.906282 0.0294658
\(947\) −28.3405 −0.920944 −0.460472 0.887674i \(-0.652320\pi\)
−0.460472 + 0.887674i \(0.652320\pi\)
\(948\) 19.8676 0.645270
\(949\) 18.6493 0.605383
\(950\) −0.260987 −0.00846752
\(951\) 7.17556 0.232683
\(952\) 1.28925 0.0417848
\(953\) 7.59226 0.245937 0.122969 0.992411i \(-0.460759\pi\)
0.122969 + 0.992411i \(0.460759\pi\)
\(954\) 0.657040 0.0212725
\(955\) −2.70568 −0.0875537
\(956\) −14.3252 −0.463310
\(957\) −28.3049 −0.914969
\(958\) −1.07200 −0.0346347
\(959\) 8.53397 0.275576
\(960\) 0.936969 0.0302405
\(961\) −25.8872 −0.835072
\(962\) 0.452131 0.0145773
\(963\) −4.01437 −0.129361
\(964\) 46.2176 1.48857
\(965\) −0.846747 −0.0272577
\(966\) −1.85111 −0.0595584
\(967\) −14.0558 −0.452005 −0.226002 0.974127i \(-0.572566\pi\)
−0.226002 + 0.974127i \(0.572566\pi\)
\(968\) 2.03426 0.0653837
\(969\) −0.806909 −0.0259216
\(970\) 0.0639785 0.00205423
\(971\) −19.6087 −0.629273 −0.314636 0.949212i \(-0.601883\pi\)
−0.314636 + 0.949212i \(0.601883\pi\)
\(972\) 1.99579 0.0640151
\(973\) −77.4536 −2.48305
\(974\) 0.875474 0.0280520
\(975\) 17.2644 0.552904
\(976\) −30.4635 −0.975113
\(977\) 33.3842 1.06806 0.534028 0.845467i \(-0.320678\pi\)
0.534028 + 0.845467i \(0.320678\pi\)
\(978\) 0.573850 0.0183497
\(979\) 44.1600 1.41136
\(980\) −4.19927 −0.134141
\(981\) 6.05499 0.193321
\(982\) 0.0544201 0.00173662
\(983\) −55.2412 −1.76192 −0.880960 0.473190i \(-0.843102\pi\)
−0.880960 + 0.473190i \(0.843102\pi\)
\(984\) −1.64104 −0.0523143
\(985\) 0.203297 0.00647759
\(986\) −0.422939 −0.0134691
\(987\) 47.7496 1.51989
\(988\) 5.57629 0.177406
\(989\) 18.4621 0.587061
\(990\) 0.0334059 0.00106171
\(991\) −21.6242 −0.686916 −0.343458 0.939168i \(-0.611598\pi\)
−0.343458 + 0.939168i \(0.611598\pi\)
\(992\) 1.75524 0.0557290
\(993\) −19.5660 −0.620908
\(994\) 3.86001 0.122432
\(995\) −0.307835 −0.00975903
\(996\) 22.8592 0.724321
\(997\) −34.0508 −1.07840 −0.539200 0.842178i \(-0.681273\pi\)
−0.539200 + 0.842178i \(0.681273\pi\)
\(998\) −1.34826 −0.0426783
\(999\) 2.01285 0.0636837
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.1.24 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.24 48 1.1 even 1 trivial