Properties

Label 8007.2.a.f.1.48
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 1.48
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.78887 q^{2} -1.00000 q^{3} +5.77777 q^{4} -2.00554 q^{5} -2.78887 q^{6} +0.938230 q^{7} +10.5357 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.78887 q^{2} -1.00000 q^{3} +5.77777 q^{4} -2.00554 q^{5} -2.78887 q^{6} +0.938230 q^{7} +10.5357 q^{8} +1.00000 q^{9} -5.59318 q^{10} -5.68987 q^{11} -5.77777 q^{12} +0.884003 q^{13} +2.61660 q^{14} +2.00554 q^{15} +17.8271 q^{16} -1.00000 q^{17} +2.78887 q^{18} -2.71161 q^{19} -11.5876 q^{20} -0.938230 q^{21} -15.8683 q^{22} -5.54959 q^{23} -10.5357 q^{24} -0.977804 q^{25} +2.46536 q^{26} -1.00000 q^{27} +5.42087 q^{28} -2.01589 q^{29} +5.59318 q^{30} -8.73145 q^{31} +28.6459 q^{32} +5.68987 q^{33} -2.78887 q^{34} -1.88166 q^{35} +5.77777 q^{36} -2.54729 q^{37} -7.56231 q^{38} -0.884003 q^{39} -21.1298 q^{40} -0.0735028 q^{41} -2.61660 q^{42} -9.11491 q^{43} -32.8747 q^{44} -2.00554 q^{45} -15.4771 q^{46} +6.75641 q^{47} -17.8271 q^{48} -6.11973 q^{49} -2.72696 q^{50} +1.00000 q^{51} +5.10756 q^{52} -6.52204 q^{53} -2.78887 q^{54} +11.4113 q^{55} +9.88489 q^{56} +2.71161 q^{57} -5.62204 q^{58} +4.86184 q^{59} +11.5876 q^{60} +5.04917 q^{61} -24.3508 q^{62} +0.938230 q^{63} +44.2355 q^{64} -1.77290 q^{65} +15.8683 q^{66} -4.00085 q^{67} -5.77777 q^{68} +5.54959 q^{69} -5.24769 q^{70} +13.2959 q^{71} +10.5357 q^{72} +11.9510 q^{73} -7.10404 q^{74} +0.977804 q^{75} -15.6670 q^{76} -5.33840 q^{77} -2.46536 q^{78} -8.53302 q^{79} -35.7529 q^{80} +1.00000 q^{81} -0.204989 q^{82} +3.13577 q^{83} -5.42087 q^{84} +2.00554 q^{85} -25.4203 q^{86} +2.01589 q^{87} -59.9467 q^{88} -9.82268 q^{89} -5.59318 q^{90} +0.829398 q^{91} -32.0642 q^{92} +8.73145 q^{93} +18.8427 q^{94} +5.43824 q^{95} -28.6459 q^{96} -8.29213 q^{97} -17.0671 q^{98} -5.68987 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.78887 1.97203 0.986013 0.166670i \(-0.0533015\pi\)
0.986013 + 0.166670i \(0.0533015\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.77777 2.88888
\(5\) −2.00554 −0.896905 −0.448453 0.893807i \(-0.648025\pi\)
−0.448453 + 0.893807i \(0.648025\pi\)
\(6\) −2.78887 −1.13855
\(7\) 0.938230 0.354617 0.177309 0.984155i \(-0.443261\pi\)
0.177309 + 0.984155i \(0.443261\pi\)
\(8\) 10.5357 3.72493
\(9\) 1.00000 0.333333
\(10\) −5.59318 −1.76872
\(11\) −5.68987 −1.71556 −0.857780 0.514018i \(-0.828157\pi\)
−0.857780 + 0.514018i \(0.828157\pi\)
\(12\) −5.77777 −1.66790
\(13\) 0.884003 0.245178 0.122589 0.992458i \(-0.460880\pi\)
0.122589 + 0.992458i \(0.460880\pi\)
\(14\) 2.61660 0.699315
\(15\) 2.00554 0.517829
\(16\) 17.8271 4.45677
\(17\) −1.00000 −0.242536
\(18\) 2.78887 0.657342
\(19\) −2.71161 −0.622086 −0.311043 0.950396i \(-0.600678\pi\)
−0.311043 + 0.950396i \(0.600678\pi\)
\(20\) −11.5876 −2.59106
\(21\) −0.938230 −0.204738
\(22\) −15.8683 −3.38313
\(23\) −5.54959 −1.15717 −0.578585 0.815622i \(-0.696395\pi\)
−0.578585 + 0.815622i \(0.696395\pi\)
\(24\) −10.5357 −2.15059
\(25\) −0.977804 −0.195561
\(26\) 2.46536 0.483498
\(27\) −1.00000 −0.192450
\(28\) 5.42087 1.02445
\(29\) −2.01589 −0.374341 −0.187170 0.982327i \(-0.559932\pi\)
−0.187170 + 0.982327i \(0.559932\pi\)
\(30\) 5.59318 1.02117
\(31\) −8.73145 −1.56821 −0.784107 0.620625i \(-0.786879\pi\)
−0.784107 + 0.620625i \(0.786879\pi\)
\(32\) 28.6459 5.06393
\(33\) 5.68987 0.990479
\(34\) −2.78887 −0.478286
\(35\) −1.88166 −0.318058
\(36\) 5.77777 0.962961
\(37\) −2.54729 −0.418771 −0.209386 0.977833i \(-0.567146\pi\)
−0.209386 + 0.977833i \(0.567146\pi\)
\(38\) −7.56231 −1.22677
\(39\) −0.884003 −0.141554
\(40\) −21.1298 −3.34091
\(41\) −0.0735028 −0.0114792 −0.00573960 0.999984i \(-0.501827\pi\)
−0.00573960 + 0.999984i \(0.501827\pi\)
\(42\) −2.61660 −0.403750
\(43\) −9.11491 −1.39001 −0.695005 0.719004i \(-0.744598\pi\)
−0.695005 + 0.719004i \(0.744598\pi\)
\(44\) −32.8747 −4.95605
\(45\) −2.00554 −0.298968
\(46\) −15.4771 −2.28197
\(47\) 6.75641 0.985523 0.492762 0.870164i \(-0.335987\pi\)
0.492762 + 0.870164i \(0.335987\pi\)
\(48\) −17.8271 −2.57312
\(49\) −6.11973 −0.874246
\(50\) −2.72696 −0.385651
\(51\) 1.00000 0.140028
\(52\) 5.10756 0.708292
\(53\) −6.52204 −0.895871 −0.447936 0.894066i \(-0.647841\pi\)
−0.447936 + 0.894066i \(0.647841\pi\)
\(54\) −2.78887 −0.379516
\(55\) 11.4113 1.53869
\(56\) 9.88489 1.32092
\(57\) 2.71161 0.359161
\(58\) −5.62204 −0.738210
\(59\) 4.86184 0.632957 0.316479 0.948600i \(-0.397499\pi\)
0.316479 + 0.948600i \(0.397499\pi\)
\(60\) 11.5876 1.49595
\(61\) 5.04917 0.646480 0.323240 0.946317i \(-0.395228\pi\)
0.323240 + 0.946317i \(0.395228\pi\)
\(62\) −24.3508 −3.09256
\(63\) 0.938230 0.118206
\(64\) 44.2355 5.52943
\(65\) −1.77290 −0.219902
\(66\) 15.8683 1.95325
\(67\) −4.00085 −0.488781 −0.244391 0.969677i \(-0.578588\pi\)
−0.244391 + 0.969677i \(0.578588\pi\)
\(68\) −5.77777 −0.700657
\(69\) 5.54959 0.668092
\(70\) −5.24769 −0.627219
\(71\) 13.2959 1.57793 0.788965 0.614438i \(-0.210617\pi\)
0.788965 + 0.614438i \(0.210617\pi\)
\(72\) 10.5357 1.24164
\(73\) 11.9510 1.39876 0.699379 0.714751i \(-0.253460\pi\)
0.699379 + 0.714751i \(0.253460\pi\)
\(74\) −7.10404 −0.825828
\(75\) 0.977804 0.112907
\(76\) −15.6670 −1.79713
\(77\) −5.33840 −0.608367
\(78\) −2.46536 −0.279148
\(79\) −8.53302 −0.960039 −0.480020 0.877258i \(-0.659370\pi\)
−0.480020 + 0.877258i \(0.659370\pi\)
\(80\) −35.7529 −3.99730
\(81\) 1.00000 0.111111
\(82\) −0.204989 −0.0226373
\(83\) 3.13577 0.344196 0.172098 0.985080i \(-0.444945\pi\)
0.172098 + 0.985080i \(0.444945\pi\)
\(84\) −5.42087 −0.591466
\(85\) 2.00554 0.217531
\(86\) −25.4203 −2.74114
\(87\) 2.01589 0.216126
\(88\) −59.9467 −6.39033
\(89\) −9.82268 −1.04120 −0.520601 0.853800i \(-0.674292\pi\)
−0.520601 + 0.853800i \(0.674292\pi\)
\(90\) −5.59318 −0.589573
\(91\) 0.829398 0.0869445
\(92\) −32.0642 −3.34293
\(93\) 8.73145 0.905409
\(94\) 18.8427 1.94348
\(95\) 5.43824 0.557952
\(96\) −28.6459 −2.92366
\(97\) −8.29213 −0.841938 −0.420969 0.907075i \(-0.638310\pi\)
−0.420969 + 0.907075i \(0.638310\pi\)
\(98\) −17.0671 −1.72404
\(99\) −5.68987 −0.571853
\(100\) −5.64953 −0.564953
\(101\) 6.21399 0.618316 0.309158 0.951011i \(-0.399953\pi\)
0.309158 + 0.951011i \(0.399953\pi\)
\(102\) 2.78887 0.276139
\(103\) −0.886060 −0.0873061 −0.0436530 0.999047i \(-0.513900\pi\)
−0.0436530 + 0.999047i \(0.513900\pi\)
\(104\) 9.31358 0.913271
\(105\) 1.88166 0.183631
\(106\) −18.1891 −1.76668
\(107\) 18.0354 1.74355 0.871775 0.489907i \(-0.162969\pi\)
0.871775 + 0.489907i \(0.162969\pi\)
\(108\) −5.77777 −0.555966
\(109\) −7.83931 −0.750869 −0.375435 0.926849i \(-0.622507\pi\)
−0.375435 + 0.926849i \(0.622507\pi\)
\(110\) 31.8245 3.03434
\(111\) 2.54729 0.241778
\(112\) 16.7259 1.58045
\(113\) −10.4815 −0.986020 −0.493010 0.870024i \(-0.664103\pi\)
−0.493010 + 0.870024i \(0.664103\pi\)
\(114\) 7.56231 0.708275
\(115\) 11.1299 1.03787
\(116\) −11.6473 −1.08143
\(117\) 0.884003 0.0817261
\(118\) 13.5590 1.24821
\(119\) −0.938230 −0.0860074
\(120\) 21.1298 1.92887
\(121\) 21.3746 1.94314
\(122\) 14.0814 1.27487
\(123\) 0.0735028 0.00662752
\(124\) −50.4483 −4.53039
\(125\) 11.9887 1.07230
\(126\) 2.61660 0.233105
\(127\) −2.15624 −0.191335 −0.0956676 0.995413i \(-0.530499\pi\)
−0.0956676 + 0.995413i \(0.530499\pi\)
\(128\) 66.0749 5.84025
\(129\) 9.11491 0.802523
\(130\) −4.94439 −0.433652
\(131\) 0.296009 0.0258624 0.0129312 0.999916i \(-0.495884\pi\)
0.0129312 + 0.999916i \(0.495884\pi\)
\(132\) 32.8747 2.86138
\(133\) −2.54411 −0.220602
\(134\) −11.1578 −0.963889
\(135\) 2.00554 0.172610
\(136\) −10.5357 −0.903428
\(137\) −16.2587 −1.38907 −0.694535 0.719459i \(-0.744390\pi\)
−0.694535 + 0.719459i \(0.744390\pi\)
\(138\) 15.4771 1.31749
\(139\) −4.25297 −0.360732 −0.180366 0.983600i \(-0.557728\pi\)
−0.180366 + 0.983600i \(0.557728\pi\)
\(140\) −10.8718 −0.918834
\(141\) −6.75641 −0.568992
\(142\) 37.0804 3.11172
\(143\) −5.02986 −0.420618
\(144\) 17.8271 1.48559
\(145\) 4.04295 0.335748
\(146\) 33.3297 2.75839
\(147\) 6.11973 0.504746
\(148\) −14.7176 −1.20978
\(149\) −0.706085 −0.0578447 −0.0289224 0.999582i \(-0.509208\pi\)
−0.0289224 + 0.999582i \(0.509208\pi\)
\(150\) 2.72696 0.222656
\(151\) −7.34120 −0.597418 −0.298709 0.954344i \(-0.596556\pi\)
−0.298709 + 0.954344i \(0.596556\pi\)
\(152\) −28.5687 −2.31722
\(153\) −1.00000 −0.0808452
\(154\) −14.8881 −1.19972
\(155\) 17.5113 1.40654
\(156\) −5.10756 −0.408932
\(157\) −1.00000 −0.0798087
\(158\) −23.7974 −1.89322
\(159\) 6.52204 0.517232
\(160\) −57.4506 −4.54187
\(161\) −5.20679 −0.410353
\(162\) 2.78887 0.219114
\(163\) −12.9110 −1.01127 −0.505634 0.862748i \(-0.668741\pi\)
−0.505634 + 0.862748i \(0.668741\pi\)
\(164\) −0.424682 −0.0331621
\(165\) −11.4113 −0.888366
\(166\) 8.74524 0.678762
\(167\) 8.55471 0.661984 0.330992 0.943634i \(-0.392617\pi\)
0.330992 + 0.943634i \(0.392617\pi\)
\(168\) −9.88489 −0.762636
\(169\) −12.2185 −0.939888
\(170\) 5.59318 0.428978
\(171\) −2.71161 −0.207362
\(172\) −52.6639 −4.01558
\(173\) 8.36711 0.636139 0.318070 0.948067i \(-0.396965\pi\)
0.318070 + 0.948067i \(0.396965\pi\)
\(174\) 5.62204 0.426206
\(175\) −0.917405 −0.0693493
\(176\) −101.434 −7.64585
\(177\) −4.86184 −0.365438
\(178\) −27.3941 −2.05328
\(179\) 17.5766 1.31374 0.656868 0.754006i \(-0.271881\pi\)
0.656868 + 0.754006i \(0.271881\pi\)
\(180\) −11.5876 −0.863685
\(181\) −12.0620 −0.896565 −0.448282 0.893892i \(-0.647964\pi\)
−0.448282 + 0.893892i \(0.647964\pi\)
\(182\) 2.31308 0.171457
\(183\) −5.04917 −0.373245
\(184\) −58.4687 −4.31037
\(185\) 5.10869 0.375598
\(186\) 24.3508 1.78549
\(187\) 5.68987 0.416084
\(188\) 39.0369 2.84706
\(189\) −0.938230 −0.0682462
\(190\) 15.1665 1.10030
\(191\) 1.26448 0.0914949 0.0457474 0.998953i \(-0.485433\pi\)
0.0457474 + 0.998953i \(0.485433\pi\)
\(192\) −44.2355 −3.19242
\(193\) 12.4851 0.898696 0.449348 0.893357i \(-0.351656\pi\)
0.449348 + 0.893357i \(0.351656\pi\)
\(194\) −23.1256 −1.66032
\(195\) 1.77290 0.126960
\(196\) −35.3584 −2.52560
\(197\) −24.2350 −1.72667 −0.863335 0.504632i \(-0.831628\pi\)
−0.863335 + 0.504632i \(0.831628\pi\)
\(198\) −15.8683 −1.12771
\(199\) −19.0665 −1.35159 −0.675794 0.737091i \(-0.736199\pi\)
−0.675794 + 0.737091i \(0.736199\pi\)
\(200\) −10.3018 −0.728450
\(201\) 4.00085 0.282198
\(202\) 17.3300 1.21933
\(203\) −1.89137 −0.132748
\(204\) 5.77777 0.404525
\(205\) 0.147413 0.0102958
\(206\) −2.47110 −0.172170
\(207\) −5.54959 −0.385723
\(208\) 15.7592 1.09270
\(209\) 15.4287 1.06722
\(210\) 5.24769 0.362125
\(211\) −19.2721 −1.32675 −0.663375 0.748287i \(-0.730876\pi\)
−0.663375 + 0.748287i \(0.730876\pi\)
\(212\) −37.6828 −2.58807
\(213\) −13.2959 −0.911018
\(214\) 50.2983 3.43832
\(215\) 18.2803 1.24671
\(216\) −10.5357 −0.716863
\(217\) −8.19211 −0.556116
\(218\) −21.8628 −1.48073
\(219\) −11.9510 −0.807574
\(220\) 65.9316 4.44511
\(221\) −0.884003 −0.0594645
\(222\) 7.10404 0.476792
\(223\) 10.6893 0.715811 0.357906 0.933758i \(-0.383491\pi\)
0.357906 + 0.933758i \(0.383491\pi\)
\(224\) 26.8765 1.79576
\(225\) −0.977804 −0.0651869
\(226\) −29.2316 −1.94446
\(227\) 22.9635 1.52414 0.762071 0.647494i \(-0.224183\pi\)
0.762071 + 0.647494i \(0.224183\pi\)
\(228\) 15.6670 1.03758
\(229\) −14.5969 −0.964587 −0.482294 0.876010i \(-0.660196\pi\)
−0.482294 + 0.876010i \(0.660196\pi\)
\(230\) 31.0399 2.04671
\(231\) 5.33840 0.351241
\(232\) −21.2388 −1.39439
\(233\) −3.28987 −0.215527 −0.107763 0.994177i \(-0.534369\pi\)
−0.107763 + 0.994177i \(0.534369\pi\)
\(234\) 2.46536 0.161166
\(235\) −13.5503 −0.883921
\(236\) 28.0906 1.82854
\(237\) 8.53302 0.554279
\(238\) −2.61660 −0.169609
\(239\) 25.3732 1.64126 0.820628 0.571463i \(-0.193624\pi\)
0.820628 + 0.571463i \(0.193624\pi\)
\(240\) 35.7529 2.30784
\(241\) −20.3604 −1.31153 −0.655765 0.754965i \(-0.727654\pi\)
−0.655765 + 0.754965i \(0.727654\pi\)
\(242\) 59.6108 3.83193
\(243\) −1.00000 −0.0641500
\(244\) 29.1729 1.86760
\(245\) 12.2734 0.784116
\(246\) 0.204989 0.0130696
\(247\) −2.39707 −0.152522
\(248\) −91.9918 −5.84149
\(249\) −3.13577 −0.198721
\(250\) 33.4350 2.11461
\(251\) 22.3281 1.40934 0.704669 0.709536i \(-0.251095\pi\)
0.704669 + 0.709536i \(0.251095\pi\)
\(252\) 5.42087 0.341483
\(253\) 31.5764 1.98519
\(254\) −6.01346 −0.377318
\(255\) −2.00554 −0.125592
\(256\) 95.8031 5.98769
\(257\) −22.6630 −1.41368 −0.706839 0.707374i \(-0.749879\pi\)
−0.706839 + 0.707374i \(0.749879\pi\)
\(258\) 25.4203 1.58260
\(259\) −2.38994 −0.148504
\(260\) −10.2434 −0.635271
\(261\) −2.01589 −0.124780
\(262\) 0.825529 0.0510013
\(263\) −29.3086 −1.80725 −0.903623 0.428328i \(-0.859103\pi\)
−0.903623 + 0.428328i \(0.859103\pi\)
\(264\) 59.9467 3.68946
\(265\) 13.0802 0.803512
\(266\) −7.09518 −0.435034
\(267\) 9.82268 0.601138
\(268\) −23.1160 −1.41203
\(269\) 6.06184 0.369597 0.184798 0.982776i \(-0.440837\pi\)
0.184798 + 0.982776i \(0.440837\pi\)
\(270\) 5.59318 0.340390
\(271\) 15.8326 0.961760 0.480880 0.876787i \(-0.340317\pi\)
0.480880 + 0.876787i \(0.340317\pi\)
\(272\) −17.8271 −1.08093
\(273\) −0.829398 −0.0501974
\(274\) −45.3432 −2.73928
\(275\) 5.56357 0.335496
\(276\) 32.0642 1.93004
\(277\) −4.68921 −0.281747 −0.140874 0.990028i \(-0.544991\pi\)
−0.140874 + 0.990028i \(0.544991\pi\)
\(278\) −11.8610 −0.711373
\(279\) −8.73145 −0.522738
\(280\) −19.8246 −1.18474
\(281\) −16.1476 −0.963288 −0.481644 0.876367i \(-0.659960\pi\)
−0.481644 + 0.876367i \(0.659960\pi\)
\(282\) −18.8427 −1.12207
\(283\) 27.1922 1.61641 0.808205 0.588901i \(-0.200439\pi\)
0.808205 + 0.588901i \(0.200439\pi\)
\(284\) 76.8205 4.55846
\(285\) −5.43824 −0.322134
\(286\) −14.0276 −0.829469
\(287\) −0.0689625 −0.00407073
\(288\) 28.6459 1.68798
\(289\) 1.00000 0.0588235
\(290\) 11.2752 0.662104
\(291\) 8.29213 0.486093
\(292\) 69.0501 4.04085
\(293\) −4.54065 −0.265268 −0.132634 0.991165i \(-0.542343\pi\)
−0.132634 + 0.991165i \(0.542343\pi\)
\(294\) 17.0671 0.995373
\(295\) −9.75061 −0.567703
\(296\) −26.8374 −1.55989
\(297\) 5.68987 0.330160
\(298\) −1.96918 −0.114071
\(299\) −4.90585 −0.283713
\(300\) 5.64953 0.326175
\(301\) −8.55188 −0.492922
\(302\) −20.4736 −1.17812
\(303\) −6.21399 −0.356985
\(304\) −48.3400 −2.77249
\(305\) −10.1263 −0.579831
\(306\) −2.78887 −0.159429
\(307\) 5.71063 0.325923 0.162961 0.986632i \(-0.447895\pi\)
0.162961 + 0.986632i \(0.447895\pi\)
\(308\) −30.8440 −1.75750
\(309\) 0.886060 0.0504062
\(310\) 48.8366 2.77373
\(311\) −21.9814 −1.24645 −0.623227 0.782041i \(-0.714179\pi\)
−0.623227 + 0.782041i \(0.714179\pi\)
\(312\) −9.31358 −0.527278
\(313\) −15.8885 −0.898073 −0.449037 0.893513i \(-0.648233\pi\)
−0.449037 + 0.893513i \(0.648233\pi\)
\(314\) −2.78887 −0.157385
\(315\) −1.88166 −0.106019
\(316\) −49.3018 −2.77344
\(317\) 29.9059 1.67968 0.839841 0.542833i \(-0.182648\pi\)
0.839841 + 0.542833i \(0.182648\pi\)
\(318\) 18.1891 1.01999
\(319\) 11.4701 0.642204
\(320\) −88.7161 −4.95938
\(321\) −18.0354 −1.00664
\(322\) −14.5210 −0.809226
\(323\) 2.71161 0.150878
\(324\) 5.77777 0.320987
\(325\) −0.864382 −0.0479473
\(326\) −36.0070 −1.99425
\(327\) 7.83931 0.433515
\(328\) −0.774403 −0.0427592
\(329\) 6.33906 0.349484
\(330\) −31.8245 −1.75188
\(331\) 10.0149 0.550469 0.275235 0.961377i \(-0.411244\pi\)
0.275235 + 0.961377i \(0.411244\pi\)
\(332\) 18.1178 0.994341
\(333\) −2.54729 −0.139590
\(334\) 23.8579 1.30545
\(335\) 8.02386 0.438390
\(336\) −16.7259 −0.912472
\(337\) 5.69196 0.310061 0.155030 0.987910i \(-0.450452\pi\)
0.155030 + 0.987910i \(0.450452\pi\)
\(338\) −34.0759 −1.85348
\(339\) 10.4815 0.569279
\(340\) 11.5876 0.628423
\(341\) 49.6808 2.69037
\(342\) −7.56231 −0.408923
\(343\) −12.3093 −0.664641
\(344\) −96.0319 −5.17769
\(345\) −11.1299 −0.599215
\(346\) 23.3347 1.25448
\(347\) 17.8930 0.960549 0.480274 0.877118i \(-0.340537\pi\)
0.480274 + 0.877118i \(0.340537\pi\)
\(348\) 11.6473 0.624363
\(349\) 6.00639 0.321515 0.160757 0.986994i \(-0.448606\pi\)
0.160757 + 0.986994i \(0.448606\pi\)
\(350\) −2.55852 −0.136759
\(351\) −0.884003 −0.0471846
\(352\) −162.991 −8.68748
\(353\) 1.82292 0.0970241 0.0485121 0.998823i \(-0.484552\pi\)
0.0485121 + 0.998823i \(0.484552\pi\)
\(354\) −13.5590 −0.720653
\(355\) −26.6654 −1.41525
\(356\) −56.7532 −3.00791
\(357\) 0.938230 0.0496564
\(358\) 49.0187 2.59072
\(359\) −4.99403 −0.263575 −0.131788 0.991278i \(-0.542072\pi\)
−0.131788 + 0.991278i \(0.542072\pi\)
\(360\) −21.1298 −1.11364
\(361\) −11.6472 −0.613010
\(362\) −33.6394 −1.76805
\(363\) −21.3746 −1.12187
\(364\) 4.79207 0.251173
\(365\) −23.9682 −1.25455
\(366\) −14.0814 −0.736049
\(367\) 1.96232 0.102432 0.0512162 0.998688i \(-0.483690\pi\)
0.0512162 + 0.998688i \(0.483690\pi\)
\(368\) −98.9330 −5.15724
\(369\) −0.0735028 −0.00382640
\(370\) 14.2474 0.740689
\(371\) −6.11917 −0.317692
\(372\) 50.4483 2.61562
\(373\) −23.2455 −1.20361 −0.601804 0.798644i \(-0.705551\pi\)
−0.601804 + 0.798644i \(0.705551\pi\)
\(374\) 15.8683 0.820529
\(375\) −11.9887 −0.619096
\(376\) 71.1834 3.67100
\(377\) −1.78205 −0.0917803
\(378\) −2.61660 −0.134583
\(379\) 18.1998 0.934860 0.467430 0.884030i \(-0.345180\pi\)
0.467430 + 0.884030i \(0.345180\pi\)
\(380\) 31.4209 1.61186
\(381\) 2.15624 0.110467
\(382\) 3.52648 0.180430
\(383\) −22.7595 −1.16296 −0.581478 0.813562i \(-0.697525\pi\)
−0.581478 + 0.813562i \(0.697525\pi\)
\(384\) −66.0749 −3.37187
\(385\) 10.7064 0.545648
\(386\) 34.8192 1.77225
\(387\) −9.11491 −0.463337
\(388\) −47.9100 −2.43226
\(389\) 24.9987 1.26748 0.633742 0.773545i \(-0.281518\pi\)
0.633742 + 0.773545i \(0.281518\pi\)
\(390\) 4.94439 0.250369
\(391\) 5.54959 0.280655
\(392\) −64.4755 −3.25650
\(393\) −0.296009 −0.0149317
\(394\) −67.5880 −3.40504
\(395\) 17.1133 0.861064
\(396\) −32.8747 −1.65202
\(397\) 22.5186 1.13018 0.565089 0.825030i \(-0.308842\pi\)
0.565089 + 0.825030i \(0.308842\pi\)
\(398\) −53.1739 −2.66537
\(399\) 2.54411 0.127365
\(400\) −17.4314 −0.871569
\(401\) −4.59371 −0.229399 −0.114699 0.993400i \(-0.536591\pi\)
−0.114699 + 0.993400i \(0.536591\pi\)
\(402\) 11.1578 0.556501
\(403\) −7.71863 −0.384492
\(404\) 35.9030 1.78624
\(405\) −2.00554 −0.0996561
\(406\) −5.27476 −0.261782
\(407\) 14.4937 0.718427
\(408\) 10.5357 0.521594
\(409\) 6.36177 0.314569 0.157285 0.987553i \(-0.449726\pi\)
0.157285 + 0.987553i \(0.449726\pi\)
\(410\) 0.411115 0.0203035
\(411\) 16.2587 0.801980
\(412\) −5.11945 −0.252217
\(413\) 4.56152 0.224458
\(414\) −15.4771 −0.760656
\(415\) −6.28892 −0.308711
\(416\) 25.3231 1.24157
\(417\) 4.25297 0.208269
\(418\) 43.0285 2.10459
\(419\) 21.9054 1.07015 0.535074 0.844805i \(-0.320284\pi\)
0.535074 + 0.844805i \(0.320284\pi\)
\(420\) 10.8718 0.530489
\(421\) −17.4055 −0.848290 −0.424145 0.905594i \(-0.639425\pi\)
−0.424145 + 0.905594i \(0.639425\pi\)
\(422\) −53.7474 −2.61638
\(423\) 6.75641 0.328508
\(424\) −68.7142 −3.33706
\(425\) 0.977804 0.0474305
\(426\) −37.0804 −1.79655
\(427\) 4.73728 0.229253
\(428\) 104.204 5.03691
\(429\) 5.02986 0.242844
\(430\) 50.9814 2.45854
\(431\) 6.62138 0.318940 0.159470 0.987203i \(-0.449021\pi\)
0.159470 + 0.987203i \(0.449021\pi\)
\(432\) −17.8271 −0.857705
\(433\) −13.8039 −0.663373 −0.331686 0.943390i \(-0.607618\pi\)
−0.331686 + 0.943390i \(0.607618\pi\)
\(434\) −22.8467 −1.09668
\(435\) −4.04295 −0.193844
\(436\) −45.2937 −2.16918
\(437\) 15.0483 0.719858
\(438\) −33.3297 −1.59256
\(439\) 37.4976 1.78967 0.894833 0.446402i \(-0.147295\pi\)
0.894833 + 0.446402i \(0.147295\pi\)
\(440\) 120.225 5.73153
\(441\) −6.11973 −0.291415
\(442\) −2.46536 −0.117265
\(443\) 33.8075 1.60624 0.803121 0.595816i \(-0.203171\pi\)
0.803121 + 0.595816i \(0.203171\pi\)
\(444\) 14.7176 0.698468
\(445\) 19.6998 0.933860
\(446\) 29.8111 1.41160
\(447\) 0.706085 0.0333967
\(448\) 41.5030 1.96083
\(449\) −27.7681 −1.31046 −0.655229 0.755430i \(-0.727428\pi\)
−0.655229 + 0.755430i \(0.727428\pi\)
\(450\) −2.72696 −0.128550
\(451\) 0.418221 0.0196933
\(452\) −60.5599 −2.84850
\(453\) 7.34120 0.344919
\(454\) 64.0421 3.00565
\(455\) −1.66339 −0.0779810
\(456\) 28.5687 1.33785
\(457\) −10.7153 −0.501241 −0.250620 0.968085i \(-0.580635\pi\)
−0.250620 + 0.968085i \(0.580635\pi\)
\(458\) −40.7087 −1.90219
\(459\) 1.00000 0.0466760
\(460\) 64.3062 2.99829
\(461\) 2.41294 0.112382 0.0561909 0.998420i \(-0.482104\pi\)
0.0561909 + 0.998420i \(0.482104\pi\)
\(462\) 14.8881 0.692656
\(463\) −9.50331 −0.441656 −0.220828 0.975313i \(-0.570876\pi\)
−0.220828 + 0.975313i \(0.570876\pi\)
\(464\) −35.9374 −1.66835
\(465\) −17.5113 −0.812066
\(466\) −9.17501 −0.425024
\(467\) 13.1964 0.610654 0.305327 0.952248i \(-0.401234\pi\)
0.305327 + 0.952248i \(0.401234\pi\)
\(468\) 5.10756 0.236097
\(469\) −3.75371 −0.173330
\(470\) −37.7898 −1.74311
\(471\) 1.00000 0.0460776
\(472\) 51.2228 2.35772
\(473\) 51.8626 2.38465
\(474\) 23.7974 1.09305
\(475\) 2.65142 0.121656
\(476\) −5.42087 −0.248465
\(477\) −6.52204 −0.298624
\(478\) 70.7625 3.23660
\(479\) −3.19467 −0.145968 −0.0729842 0.997333i \(-0.523252\pi\)
−0.0729842 + 0.997333i \(0.523252\pi\)
\(480\) 57.4506 2.62225
\(481\) −2.25181 −0.102674
\(482\) −56.7825 −2.58637
\(483\) 5.20679 0.236917
\(484\) 123.497 5.61352
\(485\) 16.6302 0.755139
\(486\) −2.78887 −0.126505
\(487\) −34.6541 −1.57033 −0.785163 0.619289i \(-0.787421\pi\)
−0.785163 + 0.619289i \(0.787421\pi\)
\(488\) 53.1964 2.40809
\(489\) 12.9110 0.583856
\(490\) 34.2288 1.54630
\(491\) 10.6240 0.479455 0.239728 0.970840i \(-0.422942\pi\)
0.239728 + 0.970840i \(0.422942\pi\)
\(492\) 0.424682 0.0191462
\(493\) 2.01589 0.0907910
\(494\) −6.68510 −0.300777
\(495\) 11.4113 0.512898
\(496\) −155.656 −6.98917
\(497\) 12.4746 0.559562
\(498\) −8.74524 −0.391884
\(499\) −16.3321 −0.731126 −0.365563 0.930787i \(-0.619124\pi\)
−0.365563 + 0.930787i \(0.619124\pi\)
\(500\) 69.2681 3.09776
\(501\) −8.55471 −0.382196
\(502\) 62.2701 2.77925
\(503\) 38.8392 1.73175 0.865876 0.500258i \(-0.166762\pi\)
0.865876 + 0.500258i \(0.166762\pi\)
\(504\) 9.88489 0.440308
\(505\) −12.4624 −0.554570
\(506\) 88.0624 3.91485
\(507\) 12.2185 0.542644
\(508\) −12.4582 −0.552745
\(509\) −6.19319 −0.274508 −0.137254 0.990536i \(-0.543828\pi\)
−0.137254 + 0.990536i \(0.543828\pi\)
\(510\) −5.59318 −0.247670
\(511\) 11.2128 0.496024
\(512\) 135.032 5.96763
\(513\) 2.71161 0.119720
\(514\) −63.2040 −2.78781
\(515\) 1.77703 0.0783053
\(516\) 52.6639 2.31840
\(517\) −38.4430 −1.69072
\(518\) −6.66522 −0.292853
\(519\) −8.36711 −0.367275
\(520\) −18.6788 −0.819118
\(521\) 42.3152 1.85386 0.926932 0.375230i \(-0.122436\pi\)
0.926932 + 0.375230i \(0.122436\pi\)
\(522\) −5.62204 −0.246070
\(523\) 44.6336 1.95169 0.975845 0.218464i \(-0.0701047\pi\)
0.975845 + 0.218464i \(0.0701047\pi\)
\(524\) 1.71027 0.0747135
\(525\) 0.917405 0.0400388
\(526\) −81.7378 −3.56394
\(527\) 8.73145 0.380348
\(528\) 101.434 4.41433
\(529\) 7.79795 0.339041
\(530\) 36.4790 1.58455
\(531\) 4.86184 0.210986
\(532\) −14.6993 −0.637295
\(533\) −0.0649767 −0.00281445
\(534\) 27.3941 1.18546
\(535\) −36.1708 −1.56380
\(536\) −42.1517 −1.82067
\(537\) −17.5766 −0.758485
\(538\) 16.9056 0.728854
\(539\) 34.8204 1.49982
\(540\) 11.5876 0.498649
\(541\) −8.83809 −0.379979 −0.189990 0.981786i \(-0.560845\pi\)
−0.189990 + 0.981786i \(0.560845\pi\)
\(542\) 44.1549 1.89661
\(543\) 12.0620 0.517632
\(544\) −28.6459 −1.22818
\(545\) 15.7221 0.673459
\(546\) −2.31308 −0.0989906
\(547\) 15.5898 0.666571 0.333285 0.942826i \(-0.391843\pi\)
0.333285 + 0.942826i \(0.391843\pi\)
\(548\) −93.9388 −4.01286
\(549\) 5.04917 0.215493
\(550\) 15.5161 0.661607
\(551\) 5.46630 0.232872
\(552\) 58.4687 2.48860
\(553\) −8.00593 −0.340447
\(554\) −13.0776 −0.555612
\(555\) −5.10869 −0.216852
\(556\) −24.5727 −1.04211
\(557\) −26.0451 −1.10357 −0.551784 0.833987i \(-0.686053\pi\)
−0.551784 + 0.833987i \(0.686053\pi\)
\(558\) −24.3508 −1.03085
\(559\) −8.05761 −0.340801
\(560\) −33.5445 −1.41751
\(561\) −5.68987 −0.240226
\(562\) −45.0336 −1.89963
\(563\) −15.0479 −0.634195 −0.317098 0.948393i \(-0.602708\pi\)
−0.317098 + 0.948393i \(0.602708\pi\)
\(564\) −39.0369 −1.64375
\(565\) 21.0212 0.884367
\(566\) 75.8354 3.18760
\(567\) 0.938230 0.0394019
\(568\) 140.081 5.87768
\(569\) −24.9562 −1.04622 −0.523109 0.852266i \(-0.675228\pi\)
−0.523109 + 0.852266i \(0.675228\pi\)
\(570\) −15.1665 −0.635256
\(571\) −12.0208 −0.503056 −0.251528 0.967850i \(-0.580933\pi\)
−0.251528 + 0.967850i \(0.580933\pi\)
\(572\) −29.0614 −1.21512
\(573\) −1.26448 −0.0528246
\(574\) −0.192327 −0.00802758
\(575\) 5.42641 0.226297
\(576\) 44.2355 1.84314
\(577\) −10.1479 −0.422464 −0.211232 0.977436i \(-0.567748\pi\)
−0.211232 + 0.977436i \(0.567748\pi\)
\(578\) 2.78887 0.116001
\(579\) −12.4851 −0.518862
\(580\) 23.3592 0.969938
\(581\) 2.94207 0.122058
\(582\) 23.1256 0.958588
\(583\) 37.1095 1.53692
\(584\) 125.912 5.21028
\(585\) −1.77290 −0.0733006
\(586\) −12.6633 −0.523115
\(587\) −4.30570 −0.177715 −0.0888577 0.996044i \(-0.528322\pi\)
−0.0888577 + 0.996044i \(0.528322\pi\)
\(588\) 35.3584 1.45815
\(589\) 23.6763 0.975564
\(590\) −27.1931 −1.11952
\(591\) 24.2350 0.996893
\(592\) −45.4107 −1.86637
\(593\) 1.35234 0.0555340 0.0277670 0.999614i \(-0.491160\pi\)
0.0277670 + 0.999614i \(0.491160\pi\)
\(594\) 15.8683 0.651083
\(595\) 1.88166 0.0771405
\(596\) −4.07959 −0.167107
\(597\) 19.0665 0.780340
\(598\) −13.6818 −0.559489
\(599\) −21.2709 −0.869107 −0.434554 0.900646i \(-0.643094\pi\)
−0.434554 + 0.900646i \(0.643094\pi\)
\(600\) 10.3018 0.420571
\(601\) −30.1489 −1.22980 −0.614899 0.788606i \(-0.710803\pi\)
−0.614899 + 0.788606i \(0.710803\pi\)
\(602\) −23.8500 −0.972055
\(603\) −4.00085 −0.162927
\(604\) −42.4157 −1.72587
\(605\) −42.8676 −1.74282
\(606\) −17.3300 −0.703983
\(607\) −40.4498 −1.64181 −0.820904 0.571066i \(-0.806530\pi\)
−0.820904 + 0.571066i \(0.806530\pi\)
\(608\) −77.6765 −3.15020
\(609\) 1.89137 0.0766420
\(610\) −28.2409 −1.14344
\(611\) 5.97268 0.241629
\(612\) −5.77777 −0.233552
\(613\) 30.4405 1.22948 0.614740 0.788730i \(-0.289261\pi\)
0.614740 + 0.788730i \(0.289261\pi\)
\(614\) 15.9262 0.642728
\(615\) −0.147413 −0.00594426
\(616\) −56.2437 −2.26612
\(617\) 16.1377 0.649679 0.324839 0.945769i \(-0.394690\pi\)
0.324839 + 0.945769i \(0.394690\pi\)
\(618\) 2.47110 0.0994023
\(619\) 8.19642 0.329442 0.164721 0.986340i \(-0.447328\pi\)
0.164721 + 0.986340i \(0.447328\pi\)
\(620\) 101.176 4.06333
\(621\) 5.54959 0.222697
\(622\) −61.3033 −2.45804
\(623\) −9.21593 −0.369228
\(624\) −15.7592 −0.630872
\(625\) −19.1549 −0.766195
\(626\) −44.3110 −1.77102
\(627\) −15.4287 −0.616162
\(628\) −5.77777 −0.230558
\(629\) 2.54729 0.101567
\(630\) −5.24769 −0.209073
\(631\) 26.5909 1.05857 0.529284 0.848445i \(-0.322461\pi\)
0.529284 + 0.848445i \(0.322461\pi\)
\(632\) −89.9012 −3.57608
\(633\) 19.2721 0.765999
\(634\) 83.4035 3.31238
\(635\) 4.32442 0.171610
\(636\) 37.6828 1.49422
\(637\) −5.40985 −0.214346
\(638\) 31.9887 1.26644
\(639\) 13.2959 0.525977
\(640\) −132.516 −5.23816
\(641\) 45.5788 1.80025 0.900127 0.435628i \(-0.143474\pi\)
0.900127 + 0.435628i \(0.143474\pi\)
\(642\) −50.2983 −1.98512
\(643\) 37.0813 1.46234 0.731171 0.682194i \(-0.238974\pi\)
0.731171 + 0.682194i \(0.238974\pi\)
\(644\) −30.0836 −1.18546
\(645\) −18.2803 −0.719787
\(646\) 7.56231 0.297535
\(647\) 4.44752 0.174850 0.0874251 0.996171i \(-0.472136\pi\)
0.0874251 + 0.996171i \(0.472136\pi\)
\(648\) 10.5357 0.413881
\(649\) −27.6632 −1.08588
\(650\) −2.41064 −0.0945532
\(651\) 8.19211 0.321074
\(652\) −74.5968 −2.92144
\(653\) 17.6054 0.688951 0.344475 0.938795i \(-0.388057\pi\)
0.344475 + 0.938795i \(0.388057\pi\)
\(654\) 21.8628 0.854902
\(655\) −0.593658 −0.0231961
\(656\) −1.31034 −0.0511602
\(657\) 11.9510 0.466253
\(658\) 17.6788 0.689191
\(659\) 2.98395 0.116238 0.0581192 0.998310i \(-0.481490\pi\)
0.0581192 + 0.998310i \(0.481490\pi\)
\(660\) −65.9316 −2.56639
\(661\) −40.4272 −1.57243 −0.786217 0.617951i \(-0.787963\pi\)
−0.786217 + 0.617951i \(0.787963\pi\)
\(662\) 27.9302 1.08554
\(663\) 0.884003 0.0343318
\(664\) 33.0375 1.28210
\(665\) 5.10232 0.197859
\(666\) −7.10404 −0.275276
\(667\) 11.1874 0.433176
\(668\) 49.4271 1.91239
\(669\) −10.6893 −0.413274
\(670\) 22.3775 0.864517
\(671\) −28.7291 −1.10907
\(672\) −26.8765 −1.03678
\(673\) 46.3881 1.78813 0.894066 0.447936i \(-0.147841\pi\)
0.894066 + 0.447936i \(0.147841\pi\)
\(674\) 15.8741 0.611448
\(675\) 0.977804 0.0376357
\(676\) −70.5959 −2.71523
\(677\) −6.82054 −0.262135 −0.131067 0.991373i \(-0.541840\pi\)
−0.131067 + 0.991373i \(0.541840\pi\)
\(678\) 29.2316 1.12263
\(679\) −7.77992 −0.298566
\(680\) 21.1298 0.810289
\(681\) −22.9635 −0.879964
\(682\) 138.553 5.30547
\(683\) −5.98157 −0.228879 −0.114439 0.993430i \(-0.536507\pi\)
−0.114439 + 0.993430i \(0.536507\pi\)
\(684\) −15.6670 −0.599044
\(685\) 32.6074 1.24587
\(686\) −34.3290 −1.31069
\(687\) 14.5969 0.556905
\(688\) −162.492 −6.19496
\(689\) −5.76550 −0.219648
\(690\) −31.0399 −1.18167
\(691\) −20.4733 −0.778842 −0.389421 0.921060i \(-0.627325\pi\)
−0.389421 + 0.921060i \(0.627325\pi\)
\(692\) 48.3432 1.83773
\(693\) −5.33840 −0.202789
\(694\) 49.9013 1.89423
\(695\) 8.52951 0.323543
\(696\) 21.2388 0.805053
\(697\) 0.0735028 0.00278412
\(698\) 16.7510 0.634035
\(699\) 3.28987 0.124434
\(700\) −5.30055 −0.200342
\(701\) 8.21987 0.310460 0.155230 0.987878i \(-0.450388\pi\)
0.155230 + 0.987878i \(0.450388\pi\)
\(702\) −2.46536 −0.0930492
\(703\) 6.90724 0.260512
\(704\) −251.694 −9.48607
\(705\) 13.5503 0.510332
\(706\) 5.08387 0.191334
\(707\) 5.83015 0.219265
\(708\) −28.0906 −1.05571
\(709\) 5.10933 0.191885 0.0959424 0.995387i \(-0.469414\pi\)
0.0959424 + 0.995387i \(0.469414\pi\)
\(710\) −74.3663 −2.79092
\(711\) −8.53302 −0.320013
\(712\) −103.489 −3.87840
\(713\) 48.4560 1.81469
\(714\) 2.61660 0.0979236
\(715\) 10.0876 0.377254
\(716\) 101.553 3.79523
\(717\) −25.3732 −0.947580
\(718\) −13.9277 −0.519777
\(719\) −52.6042 −1.96180 −0.980902 0.194503i \(-0.937691\pi\)
−0.980902 + 0.194503i \(0.937691\pi\)
\(720\) −35.7529 −1.33243
\(721\) −0.831328 −0.0309603
\(722\) −32.4824 −1.20887
\(723\) 20.3604 0.757212
\(724\) −69.6917 −2.59007
\(725\) 1.97114 0.0732064
\(726\) −59.6108 −2.21236
\(727\) −1.08047 −0.0400726 −0.0200363 0.999799i \(-0.506378\pi\)
−0.0200363 + 0.999799i \(0.506378\pi\)
\(728\) 8.73828 0.323862
\(729\) 1.00000 0.0370370
\(730\) −66.8442 −2.47401
\(731\) 9.11491 0.337127
\(732\) −29.1729 −1.07826
\(733\) 15.7632 0.582229 0.291114 0.956688i \(-0.405974\pi\)
0.291114 + 0.956688i \(0.405974\pi\)
\(734\) 5.47265 0.201999
\(735\) −12.2734 −0.452710
\(736\) −158.973 −5.85983
\(737\) 22.7643 0.838533
\(738\) −0.204989 −0.00754576
\(739\) −38.2517 −1.40711 −0.703556 0.710640i \(-0.748406\pi\)
−0.703556 + 0.710640i \(0.748406\pi\)
\(740\) 29.5168 1.08506
\(741\) 2.39707 0.0880585
\(742\) −17.0655 −0.626496
\(743\) −22.1121 −0.811215 −0.405607 0.914047i \(-0.632940\pi\)
−0.405607 + 0.914047i \(0.632940\pi\)
\(744\) 91.9918 3.37258
\(745\) 1.41608 0.0518812
\(746\) −64.8287 −2.37355
\(747\) 3.13577 0.114732
\(748\) 32.8747 1.20202
\(749\) 16.9214 0.618293
\(750\) −33.4350 −1.22087
\(751\) 48.0731 1.75421 0.877106 0.480297i \(-0.159471\pi\)
0.877106 + 0.480297i \(0.159471\pi\)
\(752\) 120.447 4.39225
\(753\) −22.3281 −0.813682
\(754\) −4.96990 −0.180993
\(755\) 14.7231 0.535827
\(756\) −5.42087 −0.197155
\(757\) −16.0190 −0.582219 −0.291109 0.956690i \(-0.594024\pi\)
−0.291109 + 0.956690i \(0.594024\pi\)
\(758\) 50.7567 1.84357
\(759\) −31.5764 −1.14615
\(760\) 57.2956 2.07833
\(761\) −18.7214 −0.678652 −0.339326 0.940669i \(-0.610199\pi\)
−0.339326 + 0.940669i \(0.610199\pi\)
\(762\) 6.01346 0.217845
\(763\) −7.35507 −0.266271
\(764\) 7.30590 0.264318
\(765\) 2.00554 0.0725105
\(766\) −63.4731 −2.29338
\(767\) 4.29788 0.155187
\(768\) −95.8031 −3.45700
\(769\) 5.48298 0.197721 0.0988607 0.995101i \(-0.468480\pi\)
0.0988607 + 0.995101i \(0.468480\pi\)
\(770\) 29.8587 1.07603
\(771\) 22.6630 0.816187
\(772\) 72.1359 2.59623
\(773\) 28.4559 1.02349 0.511744 0.859138i \(-0.329000\pi\)
0.511744 + 0.859138i \(0.329000\pi\)
\(774\) −25.4203 −0.913712
\(775\) 8.53765 0.306681
\(776\) −87.3633 −3.13616
\(777\) 2.38994 0.0857386
\(778\) 69.7180 2.49951
\(779\) 0.199311 0.00714105
\(780\) 10.2434 0.366774
\(781\) −75.6518 −2.70703
\(782\) 15.4771 0.553459
\(783\) 2.01589 0.0720420
\(784\) −109.097 −3.89631
\(785\) 2.00554 0.0715808
\(786\) −0.825529 −0.0294456
\(787\) −37.9070 −1.35124 −0.675620 0.737250i \(-0.736124\pi\)
−0.675620 + 0.737250i \(0.736124\pi\)
\(788\) −140.024 −4.98815
\(789\) 29.3086 1.04341
\(790\) 47.7267 1.69804
\(791\) −9.83409 −0.349660
\(792\) −59.9467 −2.13011
\(793\) 4.46348 0.158503
\(794\) 62.8014 2.22874
\(795\) −13.0802 −0.463908
\(796\) −110.162 −3.90458
\(797\) −45.2388 −1.60244 −0.801220 0.598370i \(-0.795815\pi\)
−0.801220 + 0.598370i \(0.795815\pi\)
\(798\) 7.09518 0.251167
\(799\) −6.75641 −0.239024
\(800\) −28.0101 −0.990307
\(801\) −9.82268 −0.347067
\(802\) −12.8112 −0.452380
\(803\) −67.9996 −2.39965
\(804\) 23.1160 0.815237
\(805\) 10.4424 0.368047
\(806\) −21.5262 −0.758228
\(807\) −6.06184 −0.213387
\(808\) 65.4687 2.30318
\(809\) −49.3446 −1.73487 −0.867433 0.497555i \(-0.834231\pi\)
−0.867433 + 0.497555i \(0.834231\pi\)
\(810\) −5.59318 −0.196524
\(811\) −24.2622 −0.851962 −0.425981 0.904732i \(-0.640071\pi\)
−0.425981 + 0.904732i \(0.640071\pi\)
\(812\) −10.9279 −0.383493
\(813\) −15.8326 −0.555272
\(814\) 40.4210 1.41676
\(815\) 25.8935 0.907011
\(816\) 17.8271 0.624072
\(817\) 24.7161 0.864706
\(818\) 17.7421 0.620339
\(819\) 0.829398 0.0289815
\(820\) 0.851718 0.0297433
\(821\) 3.36764 0.117531 0.0587657 0.998272i \(-0.481284\pi\)
0.0587657 + 0.998272i \(0.481284\pi\)
\(822\) 45.3432 1.58153
\(823\) 28.3350 0.987695 0.493848 0.869548i \(-0.335590\pi\)
0.493848 + 0.869548i \(0.335590\pi\)
\(824\) −9.33525 −0.325209
\(825\) −5.56357 −0.193699
\(826\) 12.7215 0.442636
\(827\) 33.9009 1.17885 0.589425 0.807823i \(-0.299354\pi\)
0.589425 + 0.807823i \(0.299354\pi\)
\(828\) −32.0642 −1.11431
\(829\) 30.0976 1.04533 0.522666 0.852537i \(-0.324937\pi\)
0.522666 + 0.852537i \(0.324937\pi\)
\(830\) −17.5389 −0.608786
\(831\) 4.68921 0.162667
\(832\) 39.1043 1.35570
\(833\) 6.11973 0.212036
\(834\) 11.8610 0.410711
\(835\) −17.1568 −0.593737
\(836\) 89.1434 3.08309
\(837\) 8.73145 0.301803
\(838\) 61.0912 2.11036
\(839\) −22.2183 −0.767062 −0.383531 0.923528i \(-0.625292\pi\)
−0.383531 + 0.923528i \(0.625292\pi\)
\(840\) 19.8246 0.684012
\(841\) −24.9362 −0.859869
\(842\) −48.5415 −1.67285
\(843\) 16.1476 0.556154
\(844\) −111.350 −3.83283
\(845\) 24.5048 0.842990
\(846\) 18.8427 0.647826
\(847\) 20.0543 0.689073
\(848\) −116.269 −3.99269
\(849\) −27.1922 −0.933235
\(850\) 2.72696 0.0935341
\(851\) 14.1364 0.484589
\(852\) −76.8205 −2.63183
\(853\) 21.2252 0.726737 0.363369 0.931645i \(-0.381627\pi\)
0.363369 + 0.931645i \(0.381627\pi\)
\(854\) 13.2116 0.452093
\(855\) 5.43824 0.185984
\(856\) 190.015 6.49459
\(857\) 4.71001 0.160891 0.0804455 0.996759i \(-0.474366\pi\)
0.0804455 + 0.996759i \(0.474366\pi\)
\(858\) 14.0276 0.478894
\(859\) −3.67869 −0.125515 −0.0627577 0.998029i \(-0.519990\pi\)
−0.0627577 + 0.998029i \(0.519990\pi\)
\(860\) 105.620 3.60160
\(861\) 0.0689625 0.00235024
\(862\) 18.4661 0.628959
\(863\) 9.88978 0.336652 0.168326 0.985731i \(-0.446164\pi\)
0.168326 + 0.985731i \(0.446164\pi\)
\(864\) −28.6459 −0.974554
\(865\) −16.7806 −0.570557
\(866\) −38.4972 −1.30819
\(867\) −1.00000 −0.0339618
\(868\) −47.3321 −1.60656
\(869\) 48.5517 1.64700
\(870\) −11.2752 −0.382266
\(871\) −3.53676 −0.119839
\(872\) −82.5925 −2.79693
\(873\) −8.29213 −0.280646
\(874\) 41.9677 1.41958
\(875\) 11.2482 0.380258
\(876\) −69.0501 −2.33299
\(877\) 0.562270 0.0189865 0.00949326 0.999955i \(-0.496978\pi\)
0.00949326 + 0.999955i \(0.496978\pi\)
\(878\) 104.576 3.52927
\(879\) 4.54065 0.153152
\(880\) 203.429 6.85760
\(881\) 29.9300 1.00837 0.504184 0.863596i \(-0.331793\pi\)
0.504184 + 0.863596i \(0.331793\pi\)
\(882\) −17.0671 −0.574679
\(883\) −13.6135 −0.458130 −0.229065 0.973411i \(-0.573567\pi\)
−0.229065 + 0.973411i \(0.573567\pi\)
\(884\) −5.10756 −0.171786
\(885\) 9.75061 0.327763
\(886\) 94.2845 3.16755
\(887\) 4.32667 0.145275 0.0726377 0.997358i \(-0.476858\pi\)
0.0726377 + 0.997358i \(0.476858\pi\)
\(888\) 26.8374 0.900605
\(889\) −2.02305 −0.0678508
\(890\) 54.9401 1.84160
\(891\) −5.68987 −0.190618
\(892\) 61.7605 2.06790
\(893\) −18.3207 −0.613080
\(894\) 1.96918 0.0658591
\(895\) −35.2506 −1.17830
\(896\) 61.9935 2.07106
\(897\) 4.90585 0.163802
\(898\) −77.4415 −2.58426
\(899\) 17.6016 0.587047
\(900\) −5.64953 −0.188318
\(901\) 6.52204 0.217281
\(902\) 1.16636 0.0388356
\(903\) 8.55188 0.284589
\(904\) −110.430 −3.67285
\(905\) 24.1909 0.804134
\(906\) 20.4736 0.680190
\(907\) −6.02218 −0.199963 −0.0999816 0.994989i \(-0.531878\pi\)
−0.0999816 + 0.994989i \(0.531878\pi\)
\(908\) 132.678 4.40307
\(909\) 6.21399 0.206105
\(910\) −4.63897 −0.153781
\(911\) −34.2084 −1.13337 −0.566687 0.823933i \(-0.691775\pi\)
−0.566687 + 0.823933i \(0.691775\pi\)
\(912\) 48.3400 1.60070
\(913\) −17.8421 −0.590488
\(914\) −29.8835 −0.988460
\(915\) 10.1263 0.334766
\(916\) −84.3373 −2.78658
\(917\) 0.277724 0.00917126
\(918\) 2.78887 0.0920463
\(919\) −19.8603 −0.655129 −0.327565 0.944829i \(-0.606228\pi\)
−0.327565 + 0.944829i \(0.606228\pi\)
\(920\) 117.261 3.86600
\(921\) −5.71063 −0.188172
\(922\) 6.72936 0.221620
\(923\) 11.7536 0.386874
\(924\) 30.8440 1.01469
\(925\) 2.49075 0.0818953
\(926\) −26.5034 −0.870957
\(927\) −0.886060 −0.0291020
\(928\) −57.7470 −1.89564
\(929\) −10.7504 −0.352711 −0.176355 0.984327i \(-0.556431\pi\)
−0.176355 + 0.984327i \(0.556431\pi\)
\(930\) −48.8366 −1.60142
\(931\) 16.5943 0.543856
\(932\) −19.0081 −0.622632
\(933\) 21.9814 0.719640
\(934\) 36.8028 1.20423
\(935\) −11.4113 −0.373188
\(936\) 9.31358 0.304424
\(937\) 6.57146 0.214680 0.107340 0.994222i \(-0.465767\pi\)
0.107340 + 0.994222i \(0.465767\pi\)
\(938\) −10.4686 −0.341812
\(939\) 15.8885 0.518503
\(940\) −78.2902 −2.55355
\(941\) −35.3121 −1.15114 −0.575570 0.817752i \(-0.695220\pi\)
−0.575570 + 0.817752i \(0.695220\pi\)
\(942\) 2.78887 0.0908661
\(943\) 0.407910 0.0132834
\(944\) 86.6723 2.82094
\(945\) 1.88166 0.0612103
\(946\) 144.638 4.70258
\(947\) −60.1124 −1.95339 −0.976696 0.214628i \(-0.931146\pi\)
−0.976696 + 0.214628i \(0.931146\pi\)
\(948\) 49.3018 1.60125
\(949\) 10.5647 0.342945
\(950\) 7.39446 0.239908
\(951\) −29.9059 −0.969765
\(952\) −9.88489 −0.320371
\(953\) 8.40854 0.272379 0.136190 0.990683i \(-0.456514\pi\)
0.136190 + 0.990683i \(0.456514\pi\)
\(954\) −18.1891 −0.588894
\(955\) −2.53598 −0.0820622
\(956\) 146.601 4.74140
\(957\) −11.4701 −0.370777
\(958\) −8.90951 −0.287853
\(959\) −15.2544 −0.492589
\(960\) 88.7161 2.86330
\(961\) 45.2382 1.45930
\(962\) −6.27999 −0.202475
\(963\) 18.0354 0.581183
\(964\) −117.638 −3.78886
\(965\) −25.0394 −0.806045
\(966\) 14.5210 0.467207
\(967\) 13.7991 0.443748 0.221874 0.975075i \(-0.428783\pi\)
0.221874 + 0.975075i \(0.428783\pi\)
\(968\) 225.196 7.23807
\(969\) −2.71161 −0.0871094
\(970\) 46.3794 1.48915
\(971\) 36.4302 1.16910 0.584551 0.811357i \(-0.301271\pi\)
0.584551 + 0.811357i \(0.301271\pi\)
\(972\) −5.77777 −0.185322
\(973\) −3.99026 −0.127922
\(974\) −96.6456 −3.09672
\(975\) 0.864382 0.0276824
\(976\) 90.0119 2.88121
\(977\) −49.0046 −1.56780 −0.783898 0.620889i \(-0.786772\pi\)
−0.783898 + 0.620889i \(0.786772\pi\)
\(978\) 36.0070 1.15138
\(979\) 55.8897 1.78624
\(980\) 70.9126 2.26522
\(981\) −7.83931 −0.250290
\(982\) 29.6290 0.945498
\(983\) 41.6683 1.32901 0.664505 0.747283i \(-0.268642\pi\)
0.664505 + 0.747283i \(0.268642\pi\)
\(984\) 0.774403 0.0246871
\(985\) 48.6042 1.54866
\(986\) 5.62204 0.179042
\(987\) −6.33906 −0.201775
\(988\) −13.8497 −0.440618
\(989\) 50.5840 1.60848
\(990\) 31.8245 1.01145
\(991\) 14.3526 0.455924 0.227962 0.973670i \(-0.426794\pi\)
0.227962 + 0.973670i \(0.426794\pi\)
\(992\) −250.120 −7.94133
\(993\) −10.0149 −0.317813
\(994\) 34.7899 1.10347
\(995\) 38.2386 1.21225
\(996\) −18.1178 −0.574083
\(997\) −37.0351 −1.17291 −0.586457 0.809981i \(-0.699478\pi\)
−0.586457 + 0.809981i \(0.699478\pi\)
\(998\) −45.5481 −1.44180
\(999\) 2.54729 0.0805926
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.1.48 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.48 48 1.1 even 1 trivial