Properties

Label 8007.2.a.f.1.42
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 1.42
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.18706 q^{2} -1.00000 q^{3} +2.78321 q^{4} +0.653611 q^{5} -2.18706 q^{6} +0.500468 q^{7} +1.71293 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.18706 q^{2} -1.00000 q^{3} +2.78321 q^{4} +0.653611 q^{5} -2.18706 q^{6} +0.500468 q^{7} +1.71293 q^{8} +1.00000 q^{9} +1.42948 q^{10} -2.54739 q^{11} -2.78321 q^{12} +4.91435 q^{13} +1.09455 q^{14} -0.653611 q^{15} -1.82016 q^{16} -1.00000 q^{17} +2.18706 q^{18} -5.72996 q^{19} +1.81914 q^{20} -0.500468 q^{21} -5.57128 q^{22} +1.05121 q^{23} -1.71293 q^{24} -4.57279 q^{25} +10.7480 q^{26} -1.00000 q^{27} +1.39291 q^{28} -6.02019 q^{29} -1.42948 q^{30} +5.10176 q^{31} -7.40664 q^{32} +2.54739 q^{33} -2.18706 q^{34} +0.327111 q^{35} +2.78321 q^{36} -4.78322 q^{37} -12.5317 q^{38} -4.91435 q^{39} +1.11959 q^{40} -5.46543 q^{41} -1.09455 q^{42} -4.78285 q^{43} -7.08993 q^{44} +0.653611 q^{45} +2.29907 q^{46} -11.0936 q^{47} +1.82016 q^{48} -6.74953 q^{49} -10.0010 q^{50} +1.00000 q^{51} +13.6777 q^{52} +6.18793 q^{53} -2.18706 q^{54} -1.66500 q^{55} +0.857265 q^{56} +5.72996 q^{57} -13.1665 q^{58} +3.15201 q^{59} -1.81914 q^{60} -1.40256 q^{61} +11.1578 q^{62} +0.500468 q^{63} -12.5584 q^{64} +3.21207 q^{65} +5.57128 q^{66} +12.7398 q^{67} -2.78321 q^{68} -1.05121 q^{69} +0.715410 q^{70} +12.0679 q^{71} +1.71293 q^{72} -12.6838 q^{73} -10.4612 q^{74} +4.57279 q^{75} -15.9477 q^{76} -1.27489 q^{77} -10.7480 q^{78} +5.61999 q^{79} -1.18967 q^{80} +1.00000 q^{81} -11.9532 q^{82} -7.83774 q^{83} -1.39291 q^{84} -0.653611 q^{85} -10.4604 q^{86} +6.02019 q^{87} -4.36349 q^{88} +14.2306 q^{89} +1.42948 q^{90} +2.45947 q^{91} +2.92575 q^{92} -5.10176 q^{93} -24.2623 q^{94} -3.74516 q^{95} +7.40664 q^{96} -9.67368 q^{97} -14.7616 q^{98} -2.54739 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.18706 1.54648 0.773241 0.634112i \(-0.218634\pi\)
0.773241 + 0.634112i \(0.218634\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.78321 1.39161
\(5\) 0.653611 0.292304 0.146152 0.989262i \(-0.453311\pi\)
0.146152 + 0.989262i \(0.453311\pi\)
\(6\) −2.18706 −0.892862
\(7\) 0.500468 0.189159 0.0945795 0.995517i \(-0.469849\pi\)
0.0945795 + 0.995517i \(0.469849\pi\)
\(8\) 1.71293 0.605611
\(9\) 1.00000 0.333333
\(10\) 1.42948 0.452042
\(11\) −2.54739 −0.768067 −0.384034 0.923319i \(-0.625465\pi\)
−0.384034 + 0.923319i \(0.625465\pi\)
\(12\) −2.78321 −0.803444
\(13\) 4.91435 1.36300 0.681498 0.731820i \(-0.261329\pi\)
0.681498 + 0.731820i \(0.261329\pi\)
\(14\) 1.09455 0.292531
\(15\) −0.653611 −0.168762
\(16\) −1.82016 −0.455039
\(17\) −1.00000 −0.242536
\(18\) 2.18706 0.515494
\(19\) −5.72996 −1.31454 −0.657271 0.753654i \(-0.728289\pi\)
−0.657271 + 0.753654i \(0.728289\pi\)
\(20\) 1.81914 0.406771
\(21\) −0.500468 −0.109211
\(22\) −5.57128 −1.18780
\(23\) 1.05121 0.219193 0.109597 0.993976i \(-0.465044\pi\)
0.109597 + 0.993976i \(0.465044\pi\)
\(24\) −1.71293 −0.349650
\(25\) −4.57279 −0.914559
\(26\) 10.7480 2.10785
\(27\) −1.00000 −0.192450
\(28\) 1.39291 0.263235
\(29\) −6.02019 −1.11792 −0.558961 0.829194i \(-0.688800\pi\)
−0.558961 + 0.829194i \(0.688800\pi\)
\(30\) −1.42948 −0.260987
\(31\) 5.10176 0.916302 0.458151 0.888874i \(-0.348512\pi\)
0.458151 + 0.888874i \(0.348512\pi\)
\(32\) −7.40664 −1.30932
\(33\) 2.54739 0.443444
\(34\) −2.18706 −0.375077
\(35\) 0.327111 0.0552919
\(36\) 2.78321 0.463869
\(37\) −4.78322 −0.786357 −0.393179 0.919462i \(-0.628625\pi\)
−0.393179 + 0.919462i \(0.628625\pi\)
\(38\) −12.5317 −2.03292
\(39\) −4.91435 −0.786926
\(40\) 1.11959 0.177022
\(41\) −5.46543 −0.853557 −0.426779 0.904356i \(-0.640352\pi\)
−0.426779 + 0.904356i \(0.640352\pi\)
\(42\) −1.09455 −0.168893
\(43\) −4.78285 −0.729377 −0.364689 0.931130i \(-0.618825\pi\)
−0.364689 + 0.931130i \(0.618825\pi\)
\(44\) −7.08993 −1.06885
\(45\) 0.653611 0.0974345
\(46\) 2.29907 0.338979
\(47\) −11.0936 −1.61817 −0.809084 0.587692i \(-0.800037\pi\)
−0.809084 + 0.587692i \(0.800037\pi\)
\(48\) 1.82016 0.262717
\(49\) −6.74953 −0.964219
\(50\) −10.0010 −1.41435
\(51\) 1.00000 0.140028
\(52\) 13.6777 1.89675
\(53\) 6.18793 0.849978 0.424989 0.905199i \(-0.360278\pi\)
0.424989 + 0.905199i \(0.360278\pi\)
\(54\) −2.18706 −0.297621
\(55\) −1.66500 −0.224509
\(56\) 0.857265 0.114557
\(57\) 5.72996 0.758951
\(58\) −13.1665 −1.72884
\(59\) 3.15201 0.410357 0.205178 0.978725i \(-0.434223\pi\)
0.205178 + 0.978725i \(0.434223\pi\)
\(60\) −1.81914 −0.234850
\(61\) −1.40256 −0.179580 −0.0897899 0.995961i \(-0.528620\pi\)
−0.0897899 + 0.995961i \(0.528620\pi\)
\(62\) 11.1578 1.41705
\(63\) 0.500468 0.0630530
\(64\) −12.5584 −1.56980
\(65\) 3.21207 0.398409
\(66\) 5.57128 0.685778
\(67\) 12.7398 1.55641 0.778207 0.628007i \(-0.216129\pi\)
0.778207 + 0.628007i \(0.216129\pi\)
\(68\) −2.78321 −0.337514
\(69\) −1.05121 −0.126551
\(70\) 0.715410 0.0855078
\(71\) 12.0679 1.43220 0.716100 0.697998i \(-0.245925\pi\)
0.716100 + 0.697998i \(0.245925\pi\)
\(72\) 1.71293 0.201870
\(73\) −12.6838 −1.48453 −0.742264 0.670107i \(-0.766248\pi\)
−0.742264 + 0.670107i \(0.766248\pi\)
\(74\) −10.4612 −1.21609
\(75\) 4.57279 0.528021
\(76\) −15.9477 −1.82932
\(77\) −1.27489 −0.145287
\(78\) −10.7480 −1.21697
\(79\) 5.61999 0.632298 0.316149 0.948710i \(-0.397610\pi\)
0.316149 + 0.948710i \(0.397610\pi\)
\(80\) −1.18967 −0.133010
\(81\) 1.00000 0.111111
\(82\) −11.9532 −1.32001
\(83\) −7.83774 −0.860304 −0.430152 0.902757i \(-0.641540\pi\)
−0.430152 + 0.902757i \(0.641540\pi\)
\(84\) −1.39291 −0.151979
\(85\) −0.653611 −0.0708940
\(86\) −10.4604 −1.12797
\(87\) 6.02019 0.645432
\(88\) −4.36349 −0.465150
\(89\) 14.2306 1.50844 0.754220 0.656622i \(-0.228015\pi\)
0.754220 + 0.656622i \(0.228015\pi\)
\(90\) 1.42948 0.150681
\(91\) 2.45947 0.257823
\(92\) 2.92575 0.305031
\(93\) −5.10176 −0.529027
\(94\) −24.2623 −2.50247
\(95\) −3.74516 −0.384245
\(96\) 7.40664 0.755937
\(97\) −9.67368 −0.982214 −0.491107 0.871099i \(-0.663408\pi\)
−0.491107 + 0.871099i \(0.663408\pi\)
\(98\) −14.7616 −1.49115
\(99\) −2.54739 −0.256022
\(100\) −12.7271 −1.27271
\(101\) 8.58394 0.854134 0.427067 0.904220i \(-0.359547\pi\)
0.427067 + 0.904220i \(0.359547\pi\)
\(102\) 2.18706 0.216551
\(103\) 2.72907 0.268903 0.134451 0.990920i \(-0.457073\pi\)
0.134451 + 0.990920i \(0.457073\pi\)
\(104\) 8.41793 0.825446
\(105\) −0.327111 −0.0319228
\(106\) 13.5334 1.31448
\(107\) 7.52449 0.727420 0.363710 0.931512i \(-0.381510\pi\)
0.363710 + 0.931512i \(0.381510\pi\)
\(108\) −2.78321 −0.267815
\(109\) 10.9829 1.05197 0.525984 0.850495i \(-0.323697\pi\)
0.525984 + 0.850495i \(0.323697\pi\)
\(110\) −3.64145 −0.347199
\(111\) 4.78322 0.454004
\(112\) −0.910929 −0.0860747
\(113\) −16.2874 −1.53219 −0.766096 0.642726i \(-0.777803\pi\)
−0.766096 + 0.642726i \(0.777803\pi\)
\(114\) 12.5317 1.17370
\(115\) 0.687085 0.0640710
\(116\) −16.7555 −1.55571
\(117\) 4.91435 0.454332
\(118\) 6.89362 0.634609
\(119\) −0.500468 −0.0458778
\(120\) −1.11959 −0.102204
\(121\) −4.51080 −0.410073
\(122\) −3.06748 −0.277717
\(123\) 5.46543 0.492802
\(124\) 14.1993 1.27513
\(125\) −6.25688 −0.559632
\(126\) 1.09455 0.0975103
\(127\) −4.90528 −0.435274 −0.217637 0.976030i \(-0.569835\pi\)
−0.217637 + 0.976030i \(0.569835\pi\)
\(128\) −12.6527 −1.11835
\(129\) 4.78285 0.421106
\(130\) 7.02499 0.616132
\(131\) −20.1165 −1.75759 −0.878794 0.477202i \(-0.841651\pi\)
−0.878794 + 0.477202i \(0.841651\pi\)
\(132\) 7.08993 0.617099
\(133\) −2.86766 −0.248657
\(134\) 27.8627 2.40697
\(135\) −0.653611 −0.0562539
\(136\) −1.71293 −0.146882
\(137\) 19.7766 1.68963 0.844813 0.535062i \(-0.179712\pi\)
0.844813 + 0.535062i \(0.179712\pi\)
\(138\) −2.29907 −0.195709
\(139\) 1.33900 0.113573 0.0567863 0.998386i \(-0.481915\pi\)
0.0567863 + 0.998386i \(0.481915\pi\)
\(140\) 0.910419 0.0769445
\(141\) 11.0936 0.934250
\(142\) 26.3932 2.21487
\(143\) −12.5188 −1.04687
\(144\) −1.82016 −0.151680
\(145\) −3.93486 −0.326772
\(146\) −27.7402 −2.29580
\(147\) 6.74953 0.556692
\(148\) −13.3127 −1.09430
\(149\) −14.0402 −1.15022 −0.575108 0.818078i \(-0.695040\pi\)
−0.575108 + 0.818078i \(0.695040\pi\)
\(150\) 10.0010 0.816574
\(151\) −4.90072 −0.398815 −0.199407 0.979917i \(-0.563902\pi\)
−0.199407 + 0.979917i \(0.563902\pi\)
\(152\) −9.81500 −0.796102
\(153\) −1.00000 −0.0808452
\(154\) −2.78825 −0.224683
\(155\) 3.33456 0.267839
\(156\) −13.6777 −1.09509
\(157\) −1.00000 −0.0798087
\(158\) 12.2912 0.977837
\(159\) −6.18793 −0.490735
\(160\) −4.84106 −0.382719
\(161\) 0.526099 0.0414624
\(162\) 2.18706 0.171831
\(163\) −13.2937 −1.04125 −0.520623 0.853787i \(-0.674300\pi\)
−0.520623 + 0.853787i \(0.674300\pi\)
\(164\) −15.2115 −1.18782
\(165\) 1.66500 0.129620
\(166\) −17.1416 −1.33044
\(167\) 2.38099 0.184246 0.0921231 0.995748i \(-0.470635\pi\)
0.0921231 + 0.995748i \(0.470635\pi\)
\(168\) −0.857265 −0.0661394
\(169\) 11.1509 0.857759
\(170\) −1.42948 −0.109636
\(171\) −5.72996 −0.438181
\(172\) −13.3117 −1.01501
\(173\) 13.3967 1.01853 0.509264 0.860610i \(-0.329918\pi\)
0.509264 + 0.860610i \(0.329918\pi\)
\(174\) 13.1665 0.998149
\(175\) −2.28853 −0.172997
\(176\) 4.63665 0.349500
\(177\) −3.15201 −0.236920
\(178\) 31.1231 2.33277
\(179\) −25.4522 −1.90239 −0.951193 0.308596i \(-0.900141\pi\)
−0.951193 + 0.308596i \(0.900141\pi\)
\(180\) 1.81914 0.135590
\(181\) −16.9026 −1.25636 −0.628179 0.778069i \(-0.716199\pi\)
−0.628179 + 0.778069i \(0.716199\pi\)
\(182\) 5.37901 0.398719
\(183\) 1.40256 0.103680
\(184\) 1.80065 0.132746
\(185\) −3.12637 −0.229855
\(186\) −11.1578 −0.818131
\(187\) 2.54739 0.186284
\(188\) −30.8759 −2.25185
\(189\) −0.500468 −0.0364037
\(190\) −8.19088 −0.594229
\(191\) −10.0403 −0.726493 −0.363246 0.931693i \(-0.618332\pi\)
−0.363246 + 0.931693i \(0.618332\pi\)
\(192\) 12.5584 0.906325
\(193\) −25.7474 −1.85334 −0.926670 0.375876i \(-0.877342\pi\)
−0.926670 + 0.375876i \(0.877342\pi\)
\(194\) −21.1569 −1.51898
\(195\) −3.21207 −0.230021
\(196\) −18.7854 −1.34181
\(197\) −12.4216 −0.885004 −0.442502 0.896768i \(-0.645909\pi\)
−0.442502 + 0.896768i \(0.645909\pi\)
\(198\) −5.57128 −0.395934
\(199\) −5.06040 −0.358722 −0.179361 0.983783i \(-0.557403\pi\)
−0.179361 + 0.983783i \(0.557403\pi\)
\(200\) −7.83286 −0.553867
\(201\) −12.7398 −0.898596
\(202\) 18.7735 1.32090
\(203\) −3.01291 −0.211465
\(204\) 2.78321 0.194864
\(205\) −3.57227 −0.249498
\(206\) 5.96862 0.415853
\(207\) 1.05121 0.0730645
\(208\) −8.94489 −0.620217
\(209\) 14.5964 1.00966
\(210\) −0.715410 −0.0493680
\(211\) 0.403603 0.0277852 0.0138926 0.999903i \(-0.495578\pi\)
0.0138926 + 0.999903i \(0.495578\pi\)
\(212\) 17.2223 1.18283
\(213\) −12.0679 −0.826881
\(214\) 16.4565 1.12494
\(215\) −3.12612 −0.213200
\(216\) −1.71293 −0.116550
\(217\) 2.55326 0.173327
\(218\) 24.0201 1.62685
\(219\) 12.6838 0.857093
\(220\) −4.63405 −0.312428
\(221\) −4.91435 −0.330575
\(222\) 10.4612 0.702108
\(223\) 3.09427 0.207208 0.103604 0.994619i \(-0.466963\pi\)
0.103604 + 0.994619i \(0.466963\pi\)
\(224\) −3.70678 −0.247670
\(225\) −4.57279 −0.304853
\(226\) −35.6215 −2.36951
\(227\) −13.5590 −0.899942 −0.449971 0.893043i \(-0.648566\pi\)
−0.449971 + 0.893043i \(0.648566\pi\)
\(228\) 15.9477 1.05616
\(229\) −0.0238185 −0.00157397 −0.000786985 1.00000i \(-0.500251\pi\)
−0.000786985 1.00000i \(0.500251\pi\)
\(230\) 1.50269 0.0990847
\(231\) 1.27489 0.0838814
\(232\) −10.3121 −0.677026
\(233\) 8.96522 0.587331 0.293666 0.955908i \(-0.405125\pi\)
0.293666 + 0.955908i \(0.405125\pi\)
\(234\) 10.7480 0.702616
\(235\) −7.25090 −0.472997
\(236\) 8.77271 0.571055
\(237\) −5.61999 −0.365057
\(238\) −1.09455 −0.0709492
\(239\) 19.3263 1.25011 0.625057 0.780579i \(-0.285076\pi\)
0.625057 + 0.780579i \(0.285076\pi\)
\(240\) 1.18967 0.0767931
\(241\) −8.63121 −0.555985 −0.277992 0.960583i \(-0.589669\pi\)
−0.277992 + 0.960583i \(0.589669\pi\)
\(242\) −9.86538 −0.634170
\(243\) −1.00000 −0.0641500
\(244\) −3.90363 −0.249904
\(245\) −4.41157 −0.281845
\(246\) 11.9532 0.762109
\(247\) −28.1590 −1.79172
\(248\) 8.73894 0.554923
\(249\) 7.83774 0.496697
\(250\) −13.6841 −0.865461
\(251\) 17.1195 1.08057 0.540286 0.841482i \(-0.318316\pi\)
0.540286 + 0.841482i \(0.318316\pi\)
\(252\) 1.39291 0.0877449
\(253\) −2.67785 −0.168355
\(254\) −10.7281 −0.673143
\(255\) 0.653611 0.0409307
\(256\) −2.55527 −0.159705
\(257\) 9.60054 0.598865 0.299433 0.954117i \(-0.403203\pi\)
0.299433 + 0.954117i \(0.403203\pi\)
\(258\) 10.4604 0.651233
\(259\) −2.39385 −0.148747
\(260\) 8.93988 0.554428
\(261\) −6.02019 −0.372640
\(262\) −43.9959 −2.71808
\(263\) 10.1839 0.627968 0.313984 0.949428i \(-0.398336\pi\)
0.313984 + 0.949428i \(0.398336\pi\)
\(264\) 4.36349 0.268555
\(265\) 4.04450 0.248452
\(266\) −6.27173 −0.384544
\(267\) −14.2306 −0.870898
\(268\) 35.4576 2.16592
\(269\) 9.29959 0.567006 0.283503 0.958971i \(-0.408503\pi\)
0.283503 + 0.958971i \(0.408503\pi\)
\(270\) −1.42948 −0.0869956
\(271\) −14.8849 −0.904191 −0.452096 0.891969i \(-0.649323\pi\)
−0.452096 + 0.891969i \(0.649323\pi\)
\(272\) 1.82016 0.110363
\(273\) −2.45947 −0.148854
\(274\) 43.2524 2.61298
\(275\) 11.6487 0.702442
\(276\) −2.92575 −0.176110
\(277\) 1.34206 0.0806365 0.0403183 0.999187i \(-0.487163\pi\)
0.0403183 + 0.999187i \(0.487163\pi\)
\(278\) 2.92847 0.175638
\(279\) 5.10176 0.305434
\(280\) 0.560317 0.0334854
\(281\) 21.8140 1.30132 0.650658 0.759371i \(-0.274493\pi\)
0.650658 + 0.759371i \(0.274493\pi\)
\(282\) 24.2623 1.44480
\(283\) 31.5233 1.87387 0.936933 0.349508i \(-0.113651\pi\)
0.936933 + 0.349508i \(0.113651\pi\)
\(284\) 33.5876 1.99306
\(285\) 3.74516 0.221844
\(286\) −27.3793 −1.61897
\(287\) −2.73527 −0.161458
\(288\) −7.40664 −0.436440
\(289\) 1.00000 0.0588235
\(290\) −8.60576 −0.505348
\(291\) 9.67368 0.567081
\(292\) −35.3018 −2.06588
\(293\) −4.29913 −0.251158 −0.125579 0.992084i \(-0.540079\pi\)
−0.125579 + 0.992084i \(0.540079\pi\)
\(294\) 14.7616 0.860914
\(295\) 2.06019 0.119949
\(296\) −8.19332 −0.476227
\(297\) 2.54739 0.147815
\(298\) −30.7066 −1.77879
\(299\) 5.16604 0.298760
\(300\) 12.7271 0.734797
\(301\) −2.39366 −0.137968
\(302\) −10.7181 −0.616760
\(303\) −8.58394 −0.493134
\(304\) 10.4294 0.598168
\(305\) −0.916730 −0.0524918
\(306\) −2.18706 −0.125026
\(307\) −1.20554 −0.0688039 −0.0344020 0.999408i \(-0.510953\pi\)
−0.0344020 + 0.999408i \(0.510953\pi\)
\(308\) −3.54828 −0.202182
\(309\) −2.72907 −0.155251
\(310\) 7.29287 0.414207
\(311\) 4.70857 0.266998 0.133499 0.991049i \(-0.457379\pi\)
0.133499 + 0.991049i \(0.457379\pi\)
\(312\) −8.41793 −0.476572
\(313\) −13.8515 −0.782935 −0.391468 0.920192i \(-0.628033\pi\)
−0.391468 + 0.920192i \(0.628033\pi\)
\(314\) −2.18706 −0.123423
\(315\) 0.327111 0.0184306
\(316\) 15.6416 0.879910
\(317\) 4.06176 0.228131 0.114066 0.993473i \(-0.463613\pi\)
0.114066 + 0.993473i \(0.463613\pi\)
\(318\) −13.5334 −0.758913
\(319\) 15.3358 0.858639
\(320\) −8.20832 −0.458859
\(321\) −7.52449 −0.419976
\(322\) 1.15061 0.0641209
\(323\) 5.72996 0.318823
\(324\) 2.78321 0.154623
\(325\) −22.4723 −1.24654
\(326\) −29.0741 −1.61027
\(327\) −10.9829 −0.607354
\(328\) −9.36189 −0.516924
\(329\) −5.55199 −0.306091
\(330\) 3.64145 0.200455
\(331\) 19.0799 1.04872 0.524362 0.851495i \(-0.324304\pi\)
0.524362 + 0.851495i \(0.324304\pi\)
\(332\) −21.8141 −1.19720
\(333\) −4.78322 −0.262119
\(334\) 5.20735 0.284934
\(335\) 8.32687 0.454946
\(336\) 0.910929 0.0496953
\(337\) −21.4920 −1.17074 −0.585372 0.810765i \(-0.699051\pi\)
−0.585372 + 0.810765i \(0.699051\pi\)
\(338\) 24.3876 1.32651
\(339\) 16.2874 0.884611
\(340\) −1.81914 −0.0986566
\(341\) −12.9962 −0.703782
\(342\) −12.5317 −0.677638
\(343\) −6.88120 −0.371550
\(344\) −8.19267 −0.441719
\(345\) −0.687085 −0.0369914
\(346\) 29.2992 1.57514
\(347\) 30.1618 1.61917 0.809584 0.587004i \(-0.199693\pi\)
0.809584 + 0.587004i \(0.199693\pi\)
\(348\) 16.7555 0.898187
\(349\) −29.9483 −1.60310 −0.801549 0.597929i \(-0.795990\pi\)
−0.801549 + 0.597929i \(0.795990\pi\)
\(350\) −5.00515 −0.267537
\(351\) −4.91435 −0.262309
\(352\) 18.8676 1.00565
\(353\) 17.6190 0.937767 0.468883 0.883260i \(-0.344656\pi\)
0.468883 + 0.883260i \(0.344656\pi\)
\(354\) −6.89362 −0.366392
\(355\) 7.88773 0.418637
\(356\) 39.6067 2.09915
\(357\) 0.500468 0.0264876
\(358\) −55.6654 −2.94201
\(359\) 31.4114 1.65783 0.828915 0.559375i \(-0.188959\pi\)
0.828915 + 0.559375i \(0.188959\pi\)
\(360\) 1.11959 0.0590075
\(361\) 13.8324 0.728021
\(362\) −36.9668 −1.94293
\(363\) 4.51080 0.236756
\(364\) 6.84524 0.358788
\(365\) −8.29028 −0.433933
\(366\) 3.06748 0.160340
\(367\) −11.0200 −0.575238 −0.287619 0.957745i \(-0.592864\pi\)
−0.287619 + 0.957745i \(0.592864\pi\)
\(368\) −1.91338 −0.0997416
\(369\) −5.46543 −0.284519
\(370\) −6.83754 −0.355467
\(371\) 3.09686 0.160781
\(372\) −14.1993 −0.736198
\(373\) −30.1282 −1.55998 −0.779989 0.625793i \(-0.784775\pi\)
−0.779989 + 0.625793i \(0.784775\pi\)
\(374\) 5.57128 0.288084
\(375\) 6.25688 0.323104
\(376\) −19.0025 −0.979981
\(377\) −29.5853 −1.52372
\(378\) −1.09455 −0.0562976
\(379\) 14.2591 0.732440 0.366220 0.930528i \(-0.380652\pi\)
0.366220 + 0.930528i \(0.380652\pi\)
\(380\) −10.4236 −0.534718
\(381\) 4.90528 0.251305
\(382\) −21.9588 −1.12351
\(383\) 36.1063 1.84494 0.922472 0.386063i \(-0.126165\pi\)
0.922472 + 0.386063i \(0.126165\pi\)
\(384\) 12.6527 0.645679
\(385\) −0.833279 −0.0424679
\(386\) −56.3111 −2.86616
\(387\) −4.78285 −0.243126
\(388\) −26.9239 −1.36685
\(389\) −32.6465 −1.65524 −0.827621 0.561288i \(-0.810306\pi\)
−0.827621 + 0.561288i \(0.810306\pi\)
\(390\) −7.02499 −0.355724
\(391\) −1.05121 −0.0531622
\(392\) −11.5615 −0.583942
\(393\) 20.1165 1.01474
\(394\) −27.1668 −1.36864
\(395\) 3.67328 0.184823
\(396\) −7.08993 −0.356282
\(397\) −3.41525 −0.171407 −0.0857033 0.996321i \(-0.527314\pi\)
−0.0857033 + 0.996321i \(0.527314\pi\)
\(398\) −11.0674 −0.554757
\(399\) 2.86766 0.143562
\(400\) 8.32320 0.416160
\(401\) −11.0896 −0.553789 −0.276894 0.960900i \(-0.589305\pi\)
−0.276894 + 0.960900i \(0.589305\pi\)
\(402\) −27.8627 −1.38966
\(403\) 25.0718 1.24892
\(404\) 23.8909 1.18862
\(405\) 0.653611 0.0324782
\(406\) −6.58940 −0.327027
\(407\) 12.1847 0.603975
\(408\) 1.71293 0.0848025
\(409\) −7.63041 −0.377300 −0.188650 0.982044i \(-0.560411\pi\)
−0.188650 + 0.982044i \(0.560411\pi\)
\(410\) −7.81275 −0.385844
\(411\) −19.7766 −0.975506
\(412\) 7.59557 0.374207
\(413\) 1.57748 0.0776226
\(414\) 2.29907 0.112993
\(415\) −5.12283 −0.251470
\(416\) −36.3988 −1.78460
\(417\) −1.33900 −0.0655712
\(418\) 31.9232 1.56142
\(419\) −27.3956 −1.33836 −0.669180 0.743100i \(-0.733355\pi\)
−0.669180 + 0.743100i \(0.733355\pi\)
\(420\) −0.910419 −0.0444239
\(421\) 9.41363 0.458792 0.229396 0.973333i \(-0.426325\pi\)
0.229396 + 0.973333i \(0.426325\pi\)
\(422\) 0.882702 0.0429693
\(423\) −11.0936 −0.539390
\(424\) 10.5995 0.514756
\(425\) 4.57279 0.221813
\(426\) −26.3932 −1.27876
\(427\) −0.701937 −0.0339691
\(428\) 20.9422 1.01228
\(429\) 12.5188 0.604412
\(430\) −6.83700 −0.329709
\(431\) −35.4419 −1.70718 −0.853589 0.520947i \(-0.825579\pi\)
−0.853589 + 0.520947i \(0.825579\pi\)
\(432\) 1.82016 0.0875723
\(433\) 18.0352 0.866716 0.433358 0.901222i \(-0.357329\pi\)
0.433358 + 0.901222i \(0.357329\pi\)
\(434\) 5.58413 0.268047
\(435\) 3.93486 0.188662
\(436\) 30.5676 1.46392
\(437\) −6.02342 −0.288139
\(438\) 27.7402 1.32548
\(439\) 19.7182 0.941096 0.470548 0.882374i \(-0.344056\pi\)
0.470548 + 0.882374i \(0.344056\pi\)
\(440\) −2.85203 −0.135965
\(441\) −6.74953 −0.321406
\(442\) −10.7480 −0.511229
\(443\) 24.9002 1.18304 0.591522 0.806289i \(-0.298527\pi\)
0.591522 + 0.806289i \(0.298527\pi\)
\(444\) 13.3127 0.631794
\(445\) 9.30127 0.440922
\(446\) 6.76734 0.320443
\(447\) 14.0402 0.664077
\(448\) −6.28508 −0.296942
\(449\) −20.9682 −0.989549 −0.494775 0.869021i \(-0.664749\pi\)
−0.494775 + 0.869021i \(0.664749\pi\)
\(450\) −10.0010 −0.471449
\(451\) 13.9226 0.655589
\(452\) −45.3313 −2.13221
\(453\) 4.90072 0.230256
\(454\) −29.6543 −1.39174
\(455\) 1.60754 0.0753626
\(456\) 9.81500 0.459629
\(457\) 33.6239 1.57286 0.786430 0.617679i \(-0.211927\pi\)
0.786430 + 0.617679i \(0.211927\pi\)
\(458\) −0.0520923 −0.00243412
\(459\) 1.00000 0.0466760
\(460\) 1.91230 0.0891616
\(461\) −6.85536 −0.319286 −0.159643 0.987175i \(-0.551034\pi\)
−0.159643 + 0.987175i \(0.551034\pi\)
\(462\) 2.78825 0.129721
\(463\) −3.21493 −0.149410 −0.0747052 0.997206i \(-0.523802\pi\)
−0.0747052 + 0.997206i \(0.523802\pi\)
\(464\) 10.9577 0.508698
\(465\) −3.33456 −0.154637
\(466\) 19.6074 0.908297
\(467\) −23.2115 −1.07410 −0.537051 0.843550i \(-0.680462\pi\)
−0.537051 + 0.843550i \(0.680462\pi\)
\(468\) 13.6777 0.632251
\(469\) 6.37586 0.294410
\(470\) −15.8581 −0.731481
\(471\) 1.00000 0.0460776
\(472\) 5.39916 0.248517
\(473\) 12.1838 0.560211
\(474\) −12.2912 −0.564555
\(475\) 26.2019 1.20223
\(476\) −1.39291 −0.0638438
\(477\) 6.18793 0.283326
\(478\) 42.2677 1.93328
\(479\) 5.27796 0.241156 0.120578 0.992704i \(-0.461525\pi\)
0.120578 + 0.992704i \(0.461525\pi\)
\(480\) 4.84106 0.220963
\(481\) −23.5065 −1.07180
\(482\) −18.8769 −0.859820
\(483\) −0.526099 −0.0239383
\(484\) −12.5545 −0.570660
\(485\) −6.32282 −0.287105
\(486\) −2.18706 −0.0992069
\(487\) −19.4554 −0.881607 −0.440804 0.897604i \(-0.645307\pi\)
−0.440804 + 0.897604i \(0.645307\pi\)
\(488\) −2.40249 −0.108756
\(489\) 13.2937 0.601164
\(490\) −9.64834 −0.435868
\(491\) 23.3226 1.05254 0.526268 0.850319i \(-0.323591\pi\)
0.526268 + 0.850319i \(0.323591\pi\)
\(492\) 15.2115 0.685786
\(493\) 6.02019 0.271136
\(494\) −61.5854 −2.77086
\(495\) −1.66500 −0.0748363
\(496\) −9.28599 −0.416953
\(497\) 6.03961 0.270913
\(498\) 17.1416 0.768132
\(499\) −6.07229 −0.271833 −0.135917 0.990720i \(-0.543398\pi\)
−0.135917 + 0.990720i \(0.543398\pi\)
\(500\) −17.4142 −0.778788
\(501\) −2.38099 −0.106375
\(502\) 37.4412 1.67108
\(503\) −12.6015 −0.561875 −0.280937 0.959726i \(-0.590645\pi\)
−0.280937 + 0.959726i \(0.590645\pi\)
\(504\) 0.857265 0.0381856
\(505\) 5.61055 0.249666
\(506\) −5.85662 −0.260358
\(507\) −11.1509 −0.495228
\(508\) −13.6524 −0.605729
\(509\) −26.1701 −1.15997 −0.579985 0.814627i \(-0.696942\pi\)
−0.579985 + 0.814627i \(0.696942\pi\)
\(510\) 1.42948 0.0632986
\(511\) −6.34784 −0.280812
\(512\) 19.7168 0.871369
\(513\) 5.72996 0.252984
\(514\) 20.9969 0.926134
\(515\) 1.78375 0.0786013
\(516\) 13.3117 0.586014
\(517\) 28.2597 1.24286
\(518\) −5.23548 −0.230034
\(519\) −13.3967 −0.588048
\(520\) 5.50205 0.241281
\(521\) −8.79900 −0.385491 −0.192746 0.981249i \(-0.561739\pi\)
−0.192746 + 0.981249i \(0.561739\pi\)
\(522\) −13.1665 −0.576282
\(523\) 14.0243 0.613240 0.306620 0.951832i \(-0.400802\pi\)
0.306620 + 0.951832i \(0.400802\pi\)
\(524\) −55.9885 −2.44587
\(525\) 2.28853 0.0998798
\(526\) 22.2728 0.971141
\(527\) −5.10176 −0.222236
\(528\) −4.63665 −0.201784
\(529\) −21.8949 −0.951954
\(530\) 8.84555 0.384226
\(531\) 3.15201 0.136786
\(532\) −7.98130 −0.346033
\(533\) −26.8591 −1.16340
\(534\) −31.1231 −1.34683
\(535\) 4.91809 0.212627
\(536\) 21.8224 0.942582
\(537\) 25.4522 1.09834
\(538\) 20.3387 0.876864
\(539\) 17.1937 0.740585
\(540\) −1.81914 −0.0782832
\(541\) −7.01524 −0.301609 −0.150804 0.988564i \(-0.548186\pi\)
−0.150804 + 0.988564i \(0.548186\pi\)
\(542\) −32.5540 −1.39832
\(543\) 16.9026 0.725358
\(544\) 7.40664 0.317557
\(545\) 7.17852 0.307494
\(546\) −5.37901 −0.230200
\(547\) 11.8495 0.506647 0.253323 0.967382i \(-0.418476\pi\)
0.253323 + 0.967382i \(0.418476\pi\)
\(548\) 55.0424 2.35129
\(549\) −1.40256 −0.0598599
\(550\) 25.4763 1.08631
\(551\) 34.4954 1.46955
\(552\) −1.80065 −0.0766410
\(553\) 2.81262 0.119605
\(554\) 2.93516 0.124703
\(555\) 3.12637 0.132707
\(556\) 3.72673 0.158048
\(557\) 6.81213 0.288639 0.144320 0.989531i \(-0.453901\pi\)
0.144320 + 0.989531i \(0.453901\pi\)
\(558\) 11.1578 0.472348
\(559\) −23.5046 −0.994139
\(560\) −0.595393 −0.0251600
\(561\) −2.54739 −0.107551
\(562\) 47.7085 2.01246
\(563\) −1.00815 −0.0424883 −0.0212442 0.999774i \(-0.506763\pi\)
−0.0212442 + 0.999774i \(0.506763\pi\)
\(564\) 30.8759 1.30011
\(565\) −10.6456 −0.447865
\(566\) 68.9432 2.89790
\(567\) 0.500468 0.0210177
\(568\) 20.6715 0.867356
\(569\) 25.1668 1.05505 0.527523 0.849541i \(-0.323121\pi\)
0.527523 + 0.849541i \(0.323121\pi\)
\(570\) 8.19088 0.343078
\(571\) −34.1475 −1.42903 −0.714513 0.699622i \(-0.753352\pi\)
−0.714513 + 0.699622i \(0.753352\pi\)
\(572\) −34.8424 −1.45683
\(573\) 10.0403 0.419441
\(574\) −5.98219 −0.249692
\(575\) −4.80699 −0.200465
\(576\) −12.5584 −0.523267
\(577\) 9.56030 0.398001 0.199000 0.979999i \(-0.436231\pi\)
0.199000 + 0.979999i \(0.436231\pi\)
\(578\) 2.18706 0.0909695
\(579\) 25.7474 1.07003
\(580\) −10.9516 −0.454738
\(581\) −3.92254 −0.162734
\(582\) 21.1569 0.876981
\(583\) −15.7631 −0.652840
\(584\) −21.7265 −0.899047
\(585\) 3.21207 0.132803
\(586\) −9.40243 −0.388411
\(587\) 39.6225 1.63540 0.817698 0.575647i \(-0.195250\pi\)
0.817698 + 0.575647i \(0.195250\pi\)
\(588\) 18.7854 0.774696
\(589\) −29.2328 −1.20452
\(590\) 4.50574 0.185499
\(591\) 12.4216 0.510957
\(592\) 8.70621 0.357823
\(593\) −43.8980 −1.80268 −0.901338 0.433117i \(-0.857414\pi\)
−0.901338 + 0.433117i \(0.857414\pi\)
\(594\) 5.57128 0.228593
\(595\) −0.327111 −0.0134102
\(596\) −39.0768 −1.60065
\(597\) 5.06040 0.207108
\(598\) 11.2984 0.462027
\(599\) 26.4191 1.07946 0.539729 0.841839i \(-0.318527\pi\)
0.539729 + 0.841839i \(0.318527\pi\)
\(600\) 7.83286 0.319775
\(601\) −2.62631 −0.107129 −0.0535647 0.998564i \(-0.517058\pi\)
−0.0535647 + 0.998564i \(0.517058\pi\)
\(602\) −5.23507 −0.213365
\(603\) 12.7398 0.518805
\(604\) −13.6397 −0.554993
\(605\) −2.94831 −0.119866
\(606\) −18.7735 −0.762623
\(607\) 7.86184 0.319102 0.159551 0.987190i \(-0.448995\pi\)
0.159551 + 0.987190i \(0.448995\pi\)
\(608\) 42.4397 1.72116
\(609\) 3.01291 0.122089
\(610\) −2.00494 −0.0811777
\(611\) −54.5179 −2.20556
\(612\) −2.78321 −0.112505
\(613\) 27.7663 1.12147 0.560735 0.827995i \(-0.310519\pi\)
0.560735 + 0.827995i \(0.310519\pi\)
\(614\) −2.63659 −0.106404
\(615\) 3.57227 0.144048
\(616\) −2.18379 −0.0879873
\(617\) −30.1083 −1.21212 −0.606058 0.795420i \(-0.707250\pi\)
−0.606058 + 0.795420i \(0.707250\pi\)
\(618\) −5.96862 −0.240093
\(619\) −18.4697 −0.742358 −0.371179 0.928561i \(-0.621046\pi\)
−0.371179 + 0.928561i \(0.621046\pi\)
\(620\) 9.28079 0.372726
\(621\) −1.05121 −0.0421838
\(622\) 10.2979 0.412908
\(623\) 7.12195 0.285335
\(624\) 8.94489 0.358082
\(625\) 18.7744 0.750976
\(626\) −30.2941 −1.21080
\(627\) −14.5964 −0.582925
\(628\) −2.78321 −0.111062
\(629\) 4.78322 0.190720
\(630\) 0.715410 0.0285026
\(631\) −9.33882 −0.371772 −0.185886 0.982571i \(-0.559516\pi\)
−0.185886 + 0.982571i \(0.559516\pi\)
\(632\) 9.62663 0.382927
\(633\) −0.403603 −0.0160418
\(634\) 8.88329 0.352800
\(635\) −3.20615 −0.127232
\(636\) −17.2223 −0.682910
\(637\) −33.1696 −1.31423
\(638\) 33.5402 1.32787
\(639\) 12.0679 0.477400
\(640\) −8.26992 −0.326897
\(641\) −22.0757 −0.871938 −0.435969 0.899962i \(-0.643594\pi\)
−0.435969 + 0.899962i \(0.643594\pi\)
\(642\) −16.4565 −0.649485
\(643\) 31.1748 1.22942 0.614708 0.788755i \(-0.289274\pi\)
0.614708 + 0.788755i \(0.289274\pi\)
\(644\) 1.46424 0.0576993
\(645\) 3.12612 0.123091
\(646\) 12.5317 0.493054
\(647\) 4.10824 0.161512 0.0807558 0.996734i \(-0.474267\pi\)
0.0807558 + 0.996734i \(0.474267\pi\)
\(648\) 1.71293 0.0672901
\(649\) −8.02940 −0.315181
\(650\) −49.1482 −1.92775
\(651\) −2.55326 −0.100070
\(652\) −36.9993 −1.44900
\(653\) 8.91722 0.348958 0.174479 0.984661i \(-0.444176\pi\)
0.174479 + 0.984661i \(0.444176\pi\)
\(654\) −24.0201 −0.939261
\(655\) −13.1484 −0.513749
\(656\) 9.94794 0.388402
\(657\) −12.6838 −0.494843
\(658\) −12.1425 −0.473364
\(659\) −30.0441 −1.17035 −0.585177 0.810906i \(-0.698975\pi\)
−0.585177 + 0.810906i \(0.698975\pi\)
\(660\) 4.63405 0.180380
\(661\) 26.2419 1.02069 0.510346 0.859969i \(-0.329517\pi\)
0.510346 + 0.859969i \(0.329517\pi\)
\(662\) 41.7287 1.62183
\(663\) 4.91435 0.190858
\(664\) −13.4255 −0.521010
\(665\) −1.87433 −0.0726835
\(666\) −10.4612 −0.405362
\(667\) −6.32851 −0.245041
\(668\) 6.62679 0.256398
\(669\) −3.09427 −0.119631
\(670\) 18.2113 0.703565
\(671\) 3.57288 0.137929
\(672\) 3.70678 0.142992
\(673\) −26.1504 −1.00803 −0.504013 0.863696i \(-0.668144\pi\)
−0.504013 + 0.863696i \(0.668144\pi\)
\(674\) −47.0042 −1.81053
\(675\) 4.57279 0.176007
\(676\) 31.0352 1.19366
\(677\) 28.8649 1.10937 0.554684 0.832061i \(-0.312839\pi\)
0.554684 + 0.832061i \(0.312839\pi\)
\(678\) 35.6215 1.36804
\(679\) −4.84136 −0.185795
\(680\) −1.11959 −0.0429342
\(681\) 13.5590 0.519582
\(682\) −28.4233 −1.08839
\(683\) −24.4882 −0.937013 −0.468507 0.883460i \(-0.655208\pi\)
−0.468507 + 0.883460i \(0.655208\pi\)
\(684\) −15.9477 −0.609775
\(685\) 12.9262 0.493884
\(686\) −15.0496 −0.574595
\(687\) 0.0238185 0.000908732 0
\(688\) 8.70553 0.331895
\(689\) 30.4097 1.15852
\(690\) −1.50269 −0.0572066
\(691\) 18.8134 0.715694 0.357847 0.933780i \(-0.383511\pi\)
0.357847 + 0.933780i \(0.383511\pi\)
\(692\) 37.2857 1.41739
\(693\) −1.27489 −0.0484289
\(694\) 65.9654 2.50401
\(695\) 0.875186 0.0331977
\(696\) 10.3121 0.390881
\(697\) 5.46543 0.207018
\(698\) −65.4987 −2.47916
\(699\) −8.96522 −0.339096
\(700\) −6.36948 −0.240744
\(701\) 46.1116 1.74161 0.870805 0.491629i \(-0.163598\pi\)
0.870805 + 0.491629i \(0.163598\pi\)
\(702\) −10.7480 −0.405656
\(703\) 27.4077 1.03370
\(704\) 31.9912 1.20571
\(705\) 7.25090 0.273085
\(706\) 38.5338 1.45024
\(707\) 4.29598 0.161567
\(708\) −8.77271 −0.329699
\(709\) 7.03007 0.264020 0.132010 0.991248i \(-0.457857\pi\)
0.132010 + 0.991248i \(0.457857\pi\)
\(710\) 17.2509 0.647415
\(711\) 5.61999 0.210766
\(712\) 24.3760 0.913528
\(713\) 5.36304 0.200848
\(714\) 1.09455 0.0409625
\(715\) −8.18241 −0.306005
\(716\) −70.8388 −2.64737
\(717\) −19.3263 −0.721754
\(718\) 68.6984 2.56380
\(719\) 28.9808 1.08080 0.540401 0.841408i \(-0.318273\pi\)
0.540401 + 0.841408i \(0.318273\pi\)
\(720\) −1.18967 −0.0443365
\(721\) 1.36581 0.0508654
\(722\) 30.2522 1.12587
\(723\) 8.63121 0.320998
\(724\) −47.0434 −1.74835
\(725\) 27.5291 1.02240
\(726\) 9.86538 0.366138
\(727\) 27.5855 1.02309 0.511544 0.859257i \(-0.329074\pi\)
0.511544 + 0.859257i \(0.329074\pi\)
\(728\) 4.21290 0.156141
\(729\) 1.00000 0.0370370
\(730\) −18.1313 −0.671070
\(731\) 4.78285 0.176900
\(732\) 3.90363 0.144282
\(733\) −20.9034 −0.772084 −0.386042 0.922481i \(-0.626158\pi\)
−0.386042 + 0.922481i \(0.626158\pi\)
\(734\) −24.1013 −0.889595
\(735\) 4.41157 0.162723
\(736\) −7.78597 −0.286995
\(737\) −32.4533 −1.19543
\(738\) −11.9532 −0.440004
\(739\) 24.2896 0.893507 0.446753 0.894657i \(-0.352580\pi\)
0.446753 + 0.894657i \(0.352580\pi\)
\(740\) −8.70134 −0.319868
\(741\) 28.1590 1.03445
\(742\) 6.77300 0.248645
\(743\) 0.789729 0.0289724 0.0144862 0.999895i \(-0.495389\pi\)
0.0144862 + 0.999895i \(0.495389\pi\)
\(744\) −8.73894 −0.320385
\(745\) −9.17681 −0.336212
\(746\) −65.8920 −2.41248
\(747\) −7.83774 −0.286768
\(748\) 7.08993 0.259233
\(749\) 3.76576 0.137598
\(750\) 13.6841 0.499674
\(751\) 19.8560 0.724557 0.362279 0.932070i \(-0.381999\pi\)
0.362279 + 0.932070i \(0.381999\pi\)
\(752\) 20.1921 0.736330
\(753\) −17.1195 −0.623868
\(754\) −64.7048 −2.35641
\(755\) −3.20316 −0.116575
\(756\) −1.39291 −0.0506595
\(757\) −5.47545 −0.199009 −0.0995043 0.995037i \(-0.531726\pi\)
−0.0995043 + 0.995037i \(0.531726\pi\)
\(758\) 31.1854 1.13271
\(759\) 2.67785 0.0972000
\(760\) −6.41519 −0.232703
\(761\) 26.6792 0.967120 0.483560 0.875311i \(-0.339343\pi\)
0.483560 + 0.875311i \(0.339343\pi\)
\(762\) 10.7281 0.388639
\(763\) 5.49657 0.198989
\(764\) −27.9444 −1.01099
\(765\) −0.653611 −0.0236313
\(766\) 78.9664 2.85317
\(767\) 15.4901 0.559315
\(768\) 2.55527 0.0922055
\(769\) 43.3183 1.56210 0.781049 0.624469i \(-0.214685\pi\)
0.781049 + 0.624469i \(0.214685\pi\)
\(770\) −1.82243 −0.0656758
\(771\) −9.60054 −0.345755
\(772\) −71.6605 −2.57912
\(773\) −6.44371 −0.231764 −0.115882 0.993263i \(-0.536969\pi\)
−0.115882 + 0.993263i \(0.536969\pi\)
\(774\) −10.4604 −0.375990
\(775\) −23.3293 −0.838012
\(776\) −16.5703 −0.594840
\(777\) 2.39385 0.0858788
\(778\) −71.3996 −2.55980
\(779\) 31.3167 1.12204
\(780\) −8.93988 −0.320099
\(781\) −30.7417 −1.10003
\(782\) −2.29907 −0.0822144
\(783\) 6.02019 0.215144
\(784\) 12.2852 0.438757
\(785\) −0.653611 −0.0233284
\(786\) 43.9959 1.56928
\(787\) −5.95214 −0.212171 −0.106086 0.994357i \(-0.533832\pi\)
−0.106086 + 0.994357i \(0.533832\pi\)
\(788\) −34.5720 −1.23158
\(789\) −10.1839 −0.362557
\(790\) 8.03368 0.285825
\(791\) −8.15133 −0.289828
\(792\) −4.36349 −0.155050
\(793\) −6.89269 −0.244767
\(794\) −7.46935 −0.265077
\(795\) −4.04450 −0.143444
\(796\) −14.0842 −0.499200
\(797\) −45.2399 −1.60248 −0.801240 0.598344i \(-0.795826\pi\)
−0.801240 + 0.598344i \(0.795826\pi\)
\(798\) 6.27173 0.222017
\(799\) 11.0936 0.392464
\(800\) 33.8690 1.19745
\(801\) 14.2306 0.502813
\(802\) −24.2536 −0.856424
\(803\) 32.3106 1.14022
\(804\) −35.4576 −1.25049
\(805\) 0.343864 0.0121196
\(806\) 54.8335 1.93143
\(807\) −9.29959 −0.327361
\(808\) 14.7037 0.517273
\(809\) −39.1783 −1.37744 −0.688718 0.725029i \(-0.741826\pi\)
−0.688718 + 0.725029i \(0.741826\pi\)
\(810\) 1.42948 0.0502269
\(811\) −29.2032 −1.02546 −0.512731 0.858549i \(-0.671366\pi\)
−0.512731 + 0.858549i \(0.671366\pi\)
\(812\) −8.38557 −0.294276
\(813\) 14.8849 0.522035
\(814\) 26.6487 0.934036
\(815\) −8.68893 −0.304360
\(816\) −1.82016 −0.0637182
\(817\) 27.4055 0.958797
\(818\) −16.6881 −0.583487
\(819\) 2.45947 0.0859410
\(820\) −9.94237 −0.347203
\(821\) 8.97149 0.313107 0.156553 0.987669i \(-0.449962\pi\)
0.156553 + 0.987669i \(0.449962\pi\)
\(822\) −43.2524 −1.50860
\(823\) 16.7956 0.585459 0.292729 0.956195i \(-0.405436\pi\)
0.292729 + 0.956195i \(0.405436\pi\)
\(824\) 4.67469 0.162851
\(825\) −11.6487 −0.405555
\(826\) 3.45003 0.120042
\(827\) 41.3024 1.43623 0.718113 0.695927i \(-0.245006\pi\)
0.718113 + 0.695927i \(0.245006\pi\)
\(828\) 2.92575 0.101677
\(829\) 7.29659 0.253421 0.126710 0.991940i \(-0.459558\pi\)
0.126710 + 0.991940i \(0.459558\pi\)
\(830\) −11.2039 −0.388894
\(831\) −1.34206 −0.0465555
\(832\) −61.7165 −2.13963
\(833\) 6.74953 0.233857
\(834\) −2.92847 −0.101405
\(835\) 1.55624 0.0538559
\(836\) 40.6250 1.40504
\(837\) −5.10176 −0.176342
\(838\) −59.9156 −2.06975
\(839\) 42.9510 1.48283 0.741417 0.671045i \(-0.234154\pi\)
0.741417 + 0.671045i \(0.234154\pi\)
\(840\) −0.560317 −0.0193328
\(841\) 7.24270 0.249748
\(842\) 20.5881 0.709514
\(843\) −21.8140 −0.751315
\(844\) 1.12331 0.0386660
\(845\) 7.28833 0.250726
\(846\) −24.2623 −0.834156
\(847\) −2.25751 −0.0775690
\(848\) −11.2630 −0.386773
\(849\) −31.5233 −1.08188
\(850\) 10.0010 0.343030
\(851\) −5.02820 −0.172364
\(852\) −33.5876 −1.15069
\(853\) −8.25293 −0.282575 −0.141288 0.989969i \(-0.545124\pi\)
−0.141288 + 0.989969i \(0.545124\pi\)
\(854\) −1.53518 −0.0525326
\(855\) −3.74516 −0.128082
\(856\) 12.8889 0.440534
\(857\) −16.0591 −0.548570 −0.274285 0.961648i \(-0.588441\pi\)
−0.274285 + 0.961648i \(0.588441\pi\)
\(858\) 27.3793 0.934712
\(859\) −29.7192 −1.01401 −0.507003 0.861944i \(-0.669247\pi\)
−0.507003 + 0.861944i \(0.669247\pi\)
\(860\) −8.70065 −0.296690
\(861\) 2.73527 0.0932178
\(862\) −77.5135 −2.64012
\(863\) −1.93361 −0.0658207 −0.0329104 0.999458i \(-0.510478\pi\)
−0.0329104 + 0.999458i \(0.510478\pi\)
\(864\) 7.40664 0.251979
\(865\) 8.75620 0.297720
\(866\) 39.4440 1.34036
\(867\) −1.00000 −0.0339618
\(868\) 7.10627 0.241203
\(869\) −14.3163 −0.485647
\(870\) 8.60576 0.291763
\(871\) 62.6079 2.12139
\(872\) 18.8128 0.637083
\(873\) −9.67368 −0.327405
\(874\) −13.1735 −0.445602
\(875\) −3.13137 −0.105859
\(876\) 35.3018 1.19274
\(877\) −6.34577 −0.214281 −0.107141 0.994244i \(-0.534170\pi\)
−0.107141 + 0.994244i \(0.534170\pi\)
\(878\) 43.1247 1.45539
\(879\) 4.29913 0.145006
\(880\) 3.03056 0.102160
\(881\) −5.77600 −0.194598 −0.0972992 0.995255i \(-0.531020\pi\)
−0.0972992 + 0.995255i \(0.531020\pi\)
\(882\) −14.7616 −0.497049
\(883\) −5.47783 −0.184344 −0.0921718 0.995743i \(-0.529381\pi\)
−0.0921718 + 0.995743i \(0.529381\pi\)
\(884\) −13.6777 −0.460030
\(885\) −2.06019 −0.0692524
\(886\) 54.4581 1.82956
\(887\) −23.5316 −0.790114 −0.395057 0.918657i \(-0.629275\pi\)
−0.395057 + 0.918657i \(0.629275\pi\)
\(888\) 8.19332 0.274950
\(889\) −2.45494 −0.0823359
\(890\) 20.3424 0.681878
\(891\) −2.54739 −0.0853408
\(892\) 8.61200 0.288351
\(893\) 63.5659 2.12715
\(894\) 30.7066 1.02698
\(895\) −16.6358 −0.556074
\(896\) −6.33225 −0.211546
\(897\) −5.16604 −0.172489
\(898\) −45.8586 −1.53032
\(899\) −30.7135 −1.02435
\(900\) −12.7271 −0.424235
\(901\) −6.18793 −0.206150
\(902\) 30.4495 1.01386
\(903\) 2.39366 0.0796560
\(904\) −27.8992 −0.927913
\(905\) −11.0477 −0.367238
\(906\) 10.7181 0.356086
\(907\) 48.3117 1.60416 0.802082 0.597213i \(-0.203725\pi\)
0.802082 + 0.597213i \(0.203725\pi\)
\(908\) −37.7376 −1.25236
\(909\) 8.58394 0.284711
\(910\) 3.51578 0.116547
\(911\) 13.8089 0.457510 0.228755 0.973484i \(-0.426535\pi\)
0.228755 + 0.973484i \(0.426535\pi\)
\(912\) −10.4294 −0.345352
\(913\) 19.9658 0.660771
\(914\) 73.5374 2.43240
\(915\) 0.916730 0.0303062
\(916\) −0.0662919 −0.00219035
\(917\) −10.0677 −0.332463
\(918\) 2.18706 0.0721836
\(919\) −42.7045 −1.40869 −0.704345 0.709858i \(-0.748759\pi\)
−0.704345 + 0.709858i \(0.748759\pi\)
\(920\) 1.17693 0.0388022
\(921\) 1.20554 0.0397240
\(922\) −14.9930 −0.493770
\(923\) 59.3061 1.95208
\(924\) 3.54828 0.116730
\(925\) 21.8727 0.719170
\(926\) −7.03122 −0.231060
\(927\) 2.72907 0.0896343
\(928\) 44.5894 1.46372
\(929\) −1.57874 −0.0517968 −0.0258984 0.999665i \(-0.508245\pi\)
−0.0258984 + 0.999665i \(0.508245\pi\)
\(930\) −7.29287 −0.239143
\(931\) 38.6745 1.26751
\(932\) 24.9521 0.817333
\(933\) −4.70857 −0.154152
\(934\) −50.7649 −1.66108
\(935\) 1.66500 0.0544514
\(936\) 8.41793 0.275149
\(937\) 39.0306 1.27507 0.637536 0.770420i \(-0.279954\pi\)
0.637536 + 0.770420i \(0.279954\pi\)
\(938\) 13.9444 0.455299
\(939\) 13.8515 0.452028
\(940\) −20.1808 −0.658225
\(941\) 38.6143 1.25879 0.629394 0.777086i \(-0.283303\pi\)
0.629394 + 0.777086i \(0.283303\pi\)
\(942\) 2.18706 0.0712581
\(943\) −5.74535 −0.187094
\(944\) −5.73715 −0.186728
\(945\) −0.327111 −0.0106409
\(946\) 26.6466 0.866356
\(947\) 36.5778 1.18862 0.594310 0.804236i \(-0.297425\pi\)
0.594310 + 0.804236i \(0.297425\pi\)
\(948\) −15.6416 −0.508016
\(949\) −62.3328 −2.02341
\(950\) 57.3050 1.85922
\(951\) −4.06176 −0.131712
\(952\) −0.857265 −0.0277841
\(953\) 13.4318 0.435100 0.217550 0.976049i \(-0.430194\pi\)
0.217550 + 0.976049i \(0.430194\pi\)
\(954\) 13.5334 0.438158
\(955\) −6.56247 −0.212356
\(956\) 53.7892 1.73967
\(957\) −15.3358 −0.495735
\(958\) 11.5432 0.372944
\(959\) 9.89753 0.319608
\(960\) 8.20832 0.264922
\(961\) −4.97208 −0.160390
\(962\) −51.4099 −1.65752
\(963\) 7.52449 0.242473
\(964\) −24.0225 −0.773712
\(965\) −16.8288 −0.541738
\(966\) −1.15061 −0.0370202
\(967\) −26.1474 −0.840844 −0.420422 0.907329i \(-0.638118\pi\)
−0.420422 + 0.907329i \(0.638118\pi\)
\(968\) −7.72668 −0.248345
\(969\) −5.72996 −0.184073
\(970\) −13.8284 −0.444002
\(971\) 30.1983 0.969111 0.484555 0.874761i \(-0.338981\pi\)
0.484555 + 0.874761i \(0.338981\pi\)
\(972\) −2.78321 −0.0892716
\(973\) 0.670127 0.0214833
\(974\) −42.5500 −1.36339
\(975\) 22.4723 0.719690
\(976\) 2.55288 0.0817158
\(977\) −14.2672 −0.456449 −0.228225 0.973608i \(-0.573292\pi\)
−0.228225 + 0.973608i \(0.573292\pi\)
\(978\) 29.0741 0.929689
\(979\) −36.2509 −1.15858
\(980\) −12.2783 −0.392217
\(981\) 10.9829 0.350656
\(982\) 51.0079 1.62773
\(983\) −54.8646 −1.74991 −0.874955 0.484205i \(-0.839109\pi\)
−0.874955 + 0.484205i \(0.839109\pi\)
\(984\) 9.36189 0.298446
\(985\) −8.11891 −0.258690
\(986\) 13.1665 0.419307
\(987\) 5.55199 0.176722
\(988\) −78.3725 −2.49336
\(989\) −5.02780 −0.159875
\(990\) −3.64145 −0.115733
\(991\) −38.0931 −1.21007 −0.605034 0.796199i \(-0.706841\pi\)
−0.605034 + 0.796199i \(0.706841\pi\)
\(992\) −37.7869 −1.19973
\(993\) −19.0799 −0.605482
\(994\) 13.2090 0.418963
\(995\) −3.30753 −0.104856
\(996\) 21.8141 0.691206
\(997\) 36.0885 1.14293 0.571467 0.820625i \(-0.306374\pi\)
0.571467 + 0.820625i \(0.306374\pi\)
\(998\) −13.2804 −0.420385
\(999\) 4.78322 0.151335
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.1.42 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.42 48 1.1 even 1 trivial