Properties

Label 6001.2.a.d.1.14
Level 6001
Weight 2
Character 6001.1
Self dual yes
Analytic conductor 47.918
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.25245 q^{2} -3.40363 q^{3} +3.07353 q^{4} -2.33953 q^{5} +7.66650 q^{6} +2.81637 q^{7} -2.41808 q^{8} +8.58466 q^{9} +O(q^{10})\) \(q-2.25245 q^{2} -3.40363 q^{3} +3.07353 q^{4} -2.33953 q^{5} +7.66650 q^{6} +2.81637 q^{7} -2.41808 q^{8} +8.58466 q^{9} +5.26966 q^{10} +1.91833 q^{11} -10.4612 q^{12} -4.71647 q^{13} -6.34373 q^{14} +7.96287 q^{15} -0.700463 q^{16} +1.00000 q^{17} -19.3365 q^{18} -2.11506 q^{19} -7.19061 q^{20} -9.58586 q^{21} -4.32095 q^{22} -5.88844 q^{23} +8.23023 q^{24} +0.473377 q^{25} +10.6236 q^{26} -19.0081 q^{27} +8.65620 q^{28} +6.32875 q^{29} -17.9360 q^{30} +6.02410 q^{31} +6.41392 q^{32} -6.52928 q^{33} -2.25245 q^{34} -6.58896 q^{35} +26.3852 q^{36} -6.28639 q^{37} +4.76406 q^{38} +16.0531 q^{39} +5.65716 q^{40} +1.40476 q^{41} +21.5917 q^{42} -4.35602 q^{43} +5.89606 q^{44} -20.0840 q^{45} +13.2634 q^{46} +0.504651 q^{47} +2.38411 q^{48} +0.931923 q^{49} -1.06626 q^{50} -3.40363 q^{51} -14.4962 q^{52} -3.90983 q^{53} +42.8148 q^{54} -4.48799 q^{55} -6.81020 q^{56} +7.19886 q^{57} -14.2552 q^{58} +5.35540 q^{59} +24.4741 q^{60} +7.70600 q^{61} -13.5690 q^{62} +24.1776 q^{63} -13.0461 q^{64} +11.0343 q^{65} +14.7069 q^{66} +6.86600 q^{67} +3.07353 q^{68} +20.0420 q^{69} +14.8413 q^{70} +0.718934 q^{71} -20.7584 q^{72} -6.38377 q^{73} +14.1598 q^{74} -1.61120 q^{75} -6.50069 q^{76} +5.40273 q^{77} -36.1588 q^{78} -11.0359 q^{79} +1.63875 q^{80} +38.9425 q^{81} -3.16415 q^{82} +11.9956 q^{83} -29.4624 q^{84} -2.33953 q^{85} +9.81171 q^{86} -21.5407 q^{87} -4.63868 q^{88} +5.28593 q^{89} +45.2383 q^{90} -13.2833 q^{91} -18.0983 q^{92} -20.5038 q^{93} -1.13670 q^{94} +4.94822 q^{95} -21.8306 q^{96} +17.3091 q^{97} -2.09911 q^{98} +16.4682 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + O(q^{10}) \) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + 19q^{10} + 48q^{11} + 43q^{12} + 6q^{13} + 40q^{14} + 49q^{15} + 135q^{16} + 121q^{17} + 30q^{19} + 50q^{20} + 18q^{21} + 24q^{22} + 75q^{23} + 24q^{24} + 128q^{25} + 59q^{26} + 75q^{27} + 52q^{28} + 49q^{29} - 34q^{30} + 101q^{31} + 47q^{32} + 20q^{33} + 9q^{34} + 47q^{35} + 138q^{36} + 32q^{37} + 30q^{38} + 101q^{39} + 36q^{40} + 83q^{41} - 11q^{42} + 8q^{43} + 98q^{44} + 49q^{45} + 45q^{46} + 135q^{47} + 54q^{48} + 116q^{49} + 3q^{50} + 21q^{51} - 5q^{52} + 28q^{53} + 10q^{54} + 37q^{55} + 75q^{56} + 31q^{58} + 150q^{59} + 50q^{60} + 36q^{61} + 34q^{62} + 118q^{63} + 110q^{64} + 18q^{65} - 28q^{66} - 6q^{67} + 127q^{68} + 25q^{69} - 22q^{70} + 223q^{71} + q^{72} + 38q^{73} - 10q^{74} + 88q^{75} - 4q^{76} + 38q^{77} + 42q^{78} + 74q^{79} + 106q^{80} + 133q^{81} + 28q^{82} + 55q^{83} + 10q^{84} + 27q^{85} + 64q^{86} + 14q^{87} + 56q^{88} + 118q^{89} + 51q^{90} + 73q^{91} + 82q^{92} + 31q^{93} + 33q^{94} + 106q^{95} + 38q^{96} + 37q^{97} + 88q^{98} + 81q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.25245 −1.59272 −0.796361 0.604821i \(-0.793245\pi\)
−0.796361 + 0.604821i \(0.793245\pi\)
\(3\) −3.40363 −1.96508 −0.982542 0.186041i \(-0.940434\pi\)
−0.982542 + 0.186041i \(0.940434\pi\)
\(4\) 3.07353 1.53677
\(5\) −2.33953 −1.04627 −0.523134 0.852251i \(-0.675237\pi\)
−0.523134 + 0.852251i \(0.675237\pi\)
\(6\) 7.66650 3.12983
\(7\) 2.81637 1.06449 0.532243 0.846591i \(-0.321349\pi\)
0.532243 + 0.846591i \(0.321349\pi\)
\(8\) −2.41808 −0.854920
\(9\) 8.58466 2.86155
\(10\) 5.26966 1.66641
\(11\) 1.91833 0.578399 0.289199 0.957269i \(-0.406611\pi\)
0.289199 + 0.957269i \(0.406611\pi\)
\(12\) −10.4612 −3.01987
\(13\) −4.71647 −1.30811 −0.654057 0.756445i \(-0.726934\pi\)
−0.654057 + 0.756445i \(0.726934\pi\)
\(14\) −6.34373 −1.69543
\(15\) 7.96287 2.05600
\(16\) −0.700463 −0.175116
\(17\) 1.00000 0.242536
\(18\) −19.3365 −4.55766
\(19\) −2.11506 −0.485227 −0.242613 0.970123i \(-0.578005\pi\)
−0.242613 + 0.970123i \(0.578005\pi\)
\(20\) −7.19061 −1.60787
\(21\) −9.58586 −2.09181
\(22\) −4.32095 −0.921229
\(23\) −5.88844 −1.22782 −0.613912 0.789374i \(-0.710405\pi\)
−0.613912 + 0.789374i \(0.710405\pi\)
\(24\) 8.23023 1.67999
\(25\) 0.473377 0.0946755
\(26\) 10.6236 2.08346
\(27\) −19.0081 −3.65811
\(28\) 8.65620 1.63587
\(29\) 6.32875 1.17522 0.587610 0.809145i \(-0.300069\pi\)
0.587610 + 0.809145i \(0.300069\pi\)
\(30\) −17.9360 −3.27464
\(31\) 6.02410 1.08196 0.540980 0.841035i \(-0.318053\pi\)
0.540980 + 0.841035i \(0.318053\pi\)
\(32\) 6.41392 1.13383
\(33\) −6.52928 −1.13660
\(34\) −2.25245 −0.386292
\(35\) −6.58896 −1.11374
\(36\) 26.3852 4.39754
\(37\) −6.28639 −1.03348 −0.516738 0.856144i \(-0.672854\pi\)
−0.516738 + 0.856144i \(0.672854\pi\)
\(38\) 4.76406 0.772832
\(39\) 16.0531 2.57055
\(40\) 5.65716 0.894475
\(41\) 1.40476 0.219386 0.109693 0.993965i \(-0.465013\pi\)
0.109693 + 0.993965i \(0.465013\pi\)
\(42\) 21.5917 3.33167
\(43\) −4.35602 −0.664286 −0.332143 0.943229i \(-0.607772\pi\)
−0.332143 + 0.943229i \(0.607772\pi\)
\(44\) 5.89606 0.888864
\(45\) −20.0840 −2.99395
\(46\) 13.2634 1.95558
\(47\) 0.504651 0.0736109 0.0368054 0.999322i \(-0.488282\pi\)
0.0368054 + 0.999322i \(0.488282\pi\)
\(48\) 2.38411 0.344117
\(49\) 0.931923 0.133132
\(50\) −1.06626 −0.150792
\(51\) −3.40363 −0.476603
\(52\) −14.4962 −2.01027
\(53\) −3.90983 −0.537056 −0.268528 0.963272i \(-0.586537\pi\)
−0.268528 + 0.963272i \(0.586537\pi\)
\(54\) 42.8148 5.82636
\(55\) −4.48799 −0.605160
\(56\) −6.81020 −0.910051
\(57\) 7.19886 0.953512
\(58\) −14.2552 −1.87180
\(59\) 5.35540 0.697214 0.348607 0.937269i \(-0.386655\pi\)
0.348607 + 0.937269i \(0.386655\pi\)
\(60\) 24.4741 3.15960
\(61\) 7.70600 0.986652 0.493326 0.869845i \(-0.335781\pi\)
0.493326 + 0.869845i \(0.335781\pi\)
\(62\) −13.5690 −1.72326
\(63\) 24.1776 3.04609
\(64\) −13.0461 −1.63076
\(65\) 11.0343 1.36864
\(66\) 14.7069 1.81029
\(67\) 6.86600 0.838816 0.419408 0.907798i \(-0.362238\pi\)
0.419408 + 0.907798i \(0.362238\pi\)
\(68\) 3.07353 0.372721
\(69\) 20.0420 2.41278
\(70\) 14.8413 1.77388
\(71\) 0.718934 0.0853218 0.0426609 0.999090i \(-0.486416\pi\)
0.0426609 + 0.999090i \(0.486416\pi\)
\(72\) −20.7584 −2.44640
\(73\) −6.38377 −0.747163 −0.373582 0.927597i \(-0.621870\pi\)
−0.373582 + 0.927597i \(0.621870\pi\)
\(74\) 14.1598 1.64604
\(75\) −1.61120 −0.186045
\(76\) −6.50069 −0.745680
\(77\) 5.40273 0.615698
\(78\) −36.1588 −4.09418
\(79\) −11.0359 −1.24164 −0.620819 0.783954i \(-0.713200\pi\)
−0.620819 + 0.783954i \(0.713200\pi\)
\(80\) 1.63875 0.183218
\(81\) 38.9425 4.32694
\(82\) −3.16415 −0.349422
\(83\) 11.9956 1.31669 0.658346 0.752715i \(-0.271256\pi\)
0.658346 + 0.752715i \(0.271256\pi\)
\(84\) −29.4624 −3.21462
\(85\) −2.33953 −0.253757
\(86\) 9.81171 1.05802
\(87\) −21.5407 −2.30940
\(88\) −4.63868 −0.494485
\(89\) 5.28593 0.560308 0.280154 0.959955i \(-0.409614\pi\)
0.280154 + 0.959955i \(0.409614\pi\)
\(90\) 45.2383 4.76854
\(91\) −13.2833 −1.39247
\(92\) −18.0983 −1.88688
\(93\) −20.5038 −2.12614
\(94\) −1.13670 −0.117242
\(95\) 4.94822 0.507677
\(96\) −21.8306 −2.22807
\(97\) 17.3091 1.75748 0.878738 0.477304i \(-0.158386\pi\)
0.878738 + 0.477304i \(0.158386\pi\)
\(98\) −2.09911 −0.212042
\(99\) 16.4682 1.65512
\(100\) 1.45494 0.145494
\(101\) −2.02067 −0.201064 −0.100532 0.994934i \(-0.532054\pi\)
−0.100532 + 0.994934i \(0.532054\pi\)
\(102\) 7.66650 0.759096
\(103\) 10.6820 1.05253 0.526267 0.850320i \(-0.323591\pi\)
0.526267 + 0.850320i \(0.323591\pi\)
\(104\) 11.4048 1.11833
\(105\) 22.4264 2.18859
\(106\) 8.80669 0.855381
\(107\) −15.5427 −1.50257 −0.751285 0.659978i \(-0.770565\pi\)
−0.751285 + 0.659978i \(0.770565\pi\)
\(108\) −58.4220 −5.62166
\(109\) −2.08085 −0.199309 −0.0996545 0.995022i \(-0.531774\pi\)
−0.0996545 + 0.995022i \(0.531774\pi\)
\(110\) 10.1090 0.963852
\(111\) 21.3965 2.03087
\(112\) −1.97276 −0.186408
\(113\) −3.39374 −0.319256 −0.159628 0.987177i \(-0.551030\pi\)
−0.159628 + 0.987177i \(0.551030\pi\)
\(114\) −16.2151 −1.51868
\(115\) 13.7762 1.28463
\(116\) 19.4516 1.80604
\(117\) −40.4893 −3.74324
\(118\) −12.0628 −1.11047
\(119\) 2.81637 0.258176
\(120\) −19.2548 −1.75772
\(121\) −7.32000 −0.665455
\(122\) −17.3574 −1.57146
\(123\) −4.78127 −0.431113
\(124\) 18.5153 1.66272
\(125\) 10.5901 0.947212
\(126\) −54.4588 −4.85157
\(127\) −5.77986 −0.512880 −0.256440 0.966560i \(-0.582550\pi\)
−0.256440 + 0.966560i \(0.582550\pi\)
\(128\) 16.5579 1.46352
\(129\) 14.8262 1.30538
\(130\) −24.8542 −2.17986
\(131\) −8.16177 −0.713097 −0.356548 0.934277i \(-0.616047\pi\)
−0.356548 + 0.934277i \(0.616047\pi\)
\(132\) −20.0680 −1.74669
\(133\) −5.95677 −0.516518
\(134\) −15.4653 −1.33600
\(135\) 44.4699 3.82736
\(136\) −2.41808 −0.207349
\(137\) 11.4961 0.982179 0.491089 0.871109i \(-0.336599\pi\)
0.491089 + 0.871109i \(0.336599\pi\)
\(138\) −45.1437 −3.84289
\(139\) −14.8888 −1.26285 −0.631425 0.775437i \(-0.717530\pi\)
−0.631425 + 0.775437i \(0.717530\pi\)
\(140\) −20.2514 −1.71155
\(141\) −1.71764 −0.144652
\(142\) −1.61936 −0.135894
\(143\) −9.04776 −0.756612
\(144\) −6.01324 −0.501103
\(145\) −14.8063 −1.22959
\(146\) 14.3791 1.19002
\(147\) −3.17192 −0.261615
\(148\) −19.3214 −1.58821
\(149\) −22.0689 −1.80796 −0.903979 0.427577i \(-0.859367\pi\)
−0.903979 + 0.427577i \(0.859367\pi\)
\(150\) 3.62915 0.296319
\(151\) −12.5067 −1.01778 −0.508890 0.860831i \(-0.669944\pi\)
−0.508890 + 0.860831i \(0.669944\pi\)
\(152\) 5.11437 0.414830
\(153\) 8.58466 0.694029
\(154\) −12.1694 −0.980636
\(155\) −14.0935 −1.13202
\(156\) 49.3397 3.95034
\(157\) −12.0096 −0.958471 −0.479236 0.877686i \(-0.659086\pi\)
−0.479236 + 0.877686i \(0.659086\pi\)
\(158\) 24.8578 1.97758
\(159\) 13.3076 1.05536
\(160\) −15.0055 −1.18629
\(161\) −16.5840 −1.30700
\(162\) −87.7160 −6.89162
\(163\) −14.5070 −1.13627 −0.568137 0.822934i \(-0.692336\pi\)
−0.568137 + 0.822934i \(0.692336\pi\)
\(164\) 4.31757 0.337146
\(165\) 15.2754 1.18919
\(166\) −27.0196 −2.09713
\(167\) 17.6656 1.36701 0.683504 0.729947i \(-0.260455\pi\)
0.683504 + 0.729947i \(0.260455\pi\)
\(168\) 23.1794 1.78833
\(169\) 9.24512 0.711163
\(170\) 5.26966 0.404165
\(171\) −18.1570 −1.38850
\(172\) −13.3884 −1.02085
\(173\) 19.4602 1.47953 0.739766 0.672864i \(-0.234936\pi\)
0.739766 + 0.672864i \(0.234936\pi\)
\(174\) 48.5193 3.67824
\(175\) 1.33320 0.100781
\(176\) −1.34372 −0.101287
\(177\) −18.2278 −1.37008
\(178\) −11.9063 −0.892415
\(179\) 22.1857 1.65824 0.829119 0.559072i \(-0.188842\pi\)
0.829119 + 0.559072i \(0.188842\pi\)
\(180\) −61.7289 −4.60100
\(181\) −4.67189 −0.347259 −0.173629 0.984811i \(-0.555549\pi\)
−0.173629 + 0.984811i \(0.555549\pi\)
\(182\) 29.9200 2.21782
\(183\) −26.2283 −1.93885
\(184\) 14.2387 1.04969
\(185\) 14.7072 1.08129
\(186\) 46.1837 3.38636
\(187\) 1.91833 0.140282
\(188\) 1.55106 0.113123
\(189\) −53.5338 −3.89401
\(190\) −11.1456 −0.808589
\(191\) 1.57262 0.113791 0.0568956 0.998380i \(-0.481880\pi\)
0.0568956 + 0.998380i \(0.481880\pi\)
\(192\) 44.4040 3.20459
\(193\) −24.5542 −1.76745 −0.883725 0.468006i \(-0.844972\pi\)
−0.883725 + 0.468006i \(0.844972\pi\)
\(194\) −38.9880 −2.79917
\(195\) −37.5566 −2.68949
\(196\) 2.86429 0.204592
\(197\) −3.58665 −0.255538 −0.127769 0.991804i \(-0.540782\pi\)
−0.127769 + 0.991804i \(0.540782\pi\)
\(198\) −37.0939 −2.63615
\(199\) 15.0746 1.06861 0.534306 0.845291i \(-0.320573\pi\)
0.534306 + 0.845291i \(0.320573\pi\)
\(200\) −1.14466 −0.0809399
\(201\) −23.3693 −1.64834
\(202\) 4.55145 0.320239
\(203\) 17.8241 1.25101
\(204\) −10.4612 −0.732427
\(205\) −3.28647 −0.229537
\(206\) −24.0608 −1.67639
\(207\) −50.5503 −3.51349
\(208\) 3.30372 0.229071
\(209\) −4.05738 −0.280655
\(210\) −50.5142 −3.48581
\(211\) 14.3476 0.987730 0.493865 0.869539i \(-0.335584\pi\)
0.493865 + 0.869539i \(0.335584\pi\)
\(212\) −12.0170 −0.825329
\(213\) −2.44698 −0.167665
\(214\) 35.0092 2.39318
\(215\) 10.1910 0.695021
\(216\) 45.9631 3.12739
\(217\) 16.9661 1.15173
\(218\) 4.68700 0.317444
\(219\) 21.7280 1.46824
\(220\) −13.7940 −0.929989
\(221\) −4.71647 −0.317264
\(222\) −48.1946 −3.23461
\(223\) 11.7569 0.787302 0.393651 0.919260i \(-0.371212\pi\)
0.393651 + 0.919260i \(0.371212\pi\)
\(224\) 18.0639 1.20695
\(225\) 4.06379 0.270919
\(226\) 7.64423 0.508487
\(227\) −22.2907 −1.47949 −0.739744 0.672889i \(-0.765053\pi\)
−0.739744 + 0.672889i \(0.765053\pi\)
\(228\) 22.1259 1.46532
\(229\) −6.04812 −0.399671 −0.199836 0.979829i \(-0.564041\pi\)
−0.199836 + 0.979829i \(0.564041\pi\)
\(230\) −31.0301 −2.04606
\(231\) −18.3889 −1.20990
\(232\) −15.3034 −1.00472
\(233\) −5.98731 −0.392241 −0.196121 0.980580i \(-0.562834\pi\)
−0.196121 + 0.980580i \(0.562834\pi\)
\(234\) 91.2002 5.96195
\(235\) −1.18064 −0.0770167
\(236\) 16.4600 1.07145
\(237\) 37.5621 2.43992
\(238\) −6.34373 −0.411203
\(239\) −13.2808 −0.859065 −0.429533 0.903051i \(-0.641322\pi\)
−0.429533 + 0.903051i \(0.641322\pi\)
\(240\) −5.57769 −0.360039
\(241\) −15.1893 −0.978428 −0.489214 0.872164i \(-0.662716\pi\)
−0.489214 + 0.872164i \(0.662716\pi\)
\(242\) 16.4879 1.05988
\(243\) −75.5213 −4.84469
\(244\) 23.6846 1.51625
\(245\) −2.18026 −0.139291
\(246\) 10.7696 0.686643
\(247\) 9.97560 0.634732
\(248\) −14.5667 −0.924989
\(249\) −40.8286 −2.58741
\(250\) −23.8538 −1.50865
\(251\) −10.7655 −0.679513 −0.339756 0.940513i \(-0.610345\pi\)
−0.339756 + 0.940513i \(0.610345\pi\)
\(252\) 74.3105 4.68112
\(253\) −11.2960 −0.710172
\(254\) 13.0189 0.816875
\(255\) 7.96287 0.498654
\(256\) −11.2036 −0.700222
\(257\) 26.8539 1.67510 0.837551 0.546359i \(-0.183986\pi\)
0.837551 + 0.546359i \(0.183986\pi\)
\(258\) −33.3954 −2.07911
\(259\) −17.7048 −1.10012
\(260\) 33.9143 2.10328
\(261\) 54.3302 3.36295
\(262\) 18.3840 1.13577
\(263\) 10.9656 0.676167 0.338084 0.941116i \(-0.390221\pi\)
0.338084 + 0.941116i \(0.390221\pi\)
\(264\) 15.7883 0.971704
\(265\) 9.14713 0.561904
\(266\) 13.4173 0.822669
\(267\) −17.9913 −1.10105
\(268\) 21.1029 1.28906
\(269\) 25.7016 1.56706 0.783528 0.621357i \(-0.213418\pi\)
0.783528 + 0.621357i \(0.213418\pi\)
\(270\) −100.166 −6.09593
\(271\) 19.5897 1.18999 0.594995 0.803729i \(-0.297154\pi\)
0.594995 + 0.803729i \(0.297154\pi\)
\(272\) −0.700463 −0.0424718
\(273\) 45.2114 2.73632
\(274\) −25.8944 −1.56434
\(275\) 0.908095 0.0547602
\(276\) 61.5999 3.70788
\(277\) 10.5097 0.631466 0.315733 0.948848i \(-0.397750\pi\)
0.315733 + 0.948848i \(0.397750\pi\)
\(278\) 33.5362 2.01137
\(279\) 51.7149 3.09609
\(280\) 15.9326 0.952156
\(281\) −4.74110 −0.282830 −0.141415 0.989950i \(-0.545165\pi\)
−0.141415 + 0.989950i \(0.545165\pi\)
\(282\) 3.86890 0.230390
\(283\) 19.3457 1.14998 0.574990 0.818160i \(-0.305006\pi\)
0.574990 + 0.818160i \(0.305006\pi\)
\(284\) 2.20967 0.131120
\(285\) −16.8419 −0.997628
\(286\) 20.3796 1.20507
\(287\) 3.95631 0.233534
\(288\) 55.0613 3.24452
\(289\) 1.00000 0.0588235
\(290\) 33.3504 1.95840
\(291\) −58.9138 −3.45359
\(292\) −19.6207 −1.14822
\(293\) −15.5157 −0.906437 −0.453218 0.891400i \(-0.649724\pi\)
−0.453218 + 0.891400i \(0.649724\pi\)
\(294\) 7.14458 0.416680
\(295\) −12.5291 −0.729472
\(296\) 15.2010 0.883539
\(297\) −36.4639 −2.11585
\(298\) 49.7092 2.87958
\(299\) 27.7727 1.60613
\(300\) −4.95207 −0.285908
\(301\) −12.2681 −0.707124
\(302\) 28.1707 1.62104
\(303\) 6.87759 0.395107
\(304\) 1.48152 0.0849709
\(305\) −18.0284 −1.03230
\(306\) −19.3365 −1.10540
\(307\) −31.2132 −1.78143 −0.890715 0.454562i \(-0.849796\pi\)
−0.890715 + 0.454562i \(0.849796\pi\)
\(308\) 16.6055 0.946184
\(309\) −36.3577 −2.06832
\(310\) 31.7450 1.80299
\(311\) −2.59411 −0.147098 −0.0735492 0.997292i \(-0.523433\pi\)
−0.0735492 + 0.997292i \(0.523433\pi\)
\(312\) −38.8177 −2.19762
\(313\) −8.42346 −0.476122 −0.238061 0.971250i \(-0.576512\pi\)
−0.238061 + 0.971250i \(0.576512\pi\)
\(314\) 27.0510 1.52658
\(315\) −56.5640 −3.18702
\(316\) −33.9192 −1.90811
\(317\) 9.58978 0.538615 0.269308 0.963054i \(-0.413205\pi\)
0.269308 + 0.963054i \(0.413205\pi\)
\(318\) −29.9747 −1.68090
\(319\) 12.1406 0.679746
\(320\) 30.5217 1.70621
\(321\) 52.9015 2.95268
\(322\) 37.3547 2.08169
\(323\) −2.11506 −0.117685
\(324\) 119.691 6.64950
\(325\) −2.23267 −0.123846
\(326\) 32.6762 1.80977
\(327\) 7.08242 0.391659
\(328\) −3.39682 −0.187558
\(329\) 1.42128 0.0783578
\(330\) −34.4071 −1.89405
\(331\) −28.8689 −1.58678 −0.793390 0.608714i \(-0.791686\pi\)
−0.793390 + 0.608714i \(0.791686\pi\)
\(332\) 36.8690 2.02345
\(333\) −53.9665 −2.95735
\(334\) −39.7910 −2.17727
\(335\) −16.0632 −0.877626
\(336\) 6.71454 0.366308
\(337\) 1.63256 0.0889310 0.0444655 0.999011i \(-0.485842\pi\)
0.0444655 + 0.999011i \(0.485842\pi\)
\(338\) −20.8242 −1.13269
\(339\) 11.5510 0.627365
\(340\) −7.19061 −0.389965
\(341\) 11.5562 0.625804
\(342\) 40.8978 2.21150
\(343\) −17.0899 −0.922770
\(344\) 10.5332 0.567911
\(345\) −46.8889 −2.52441
\(346\) −43.8332 −2.35649
\(347\) 8.59351 0.461324 0.230662 0.973034i \(-0.425911\pi\)
0.230662 + 0.973034i \(0.425911\pi\)
\(348\) −66.2060 −3.54902
\(349\) 14.8116 0.792845 0.396423 0.918068i \(-0.370252\pi\)
0.396423 + 0.918068i \(0.370252\pi\)
\(350\) −3.00298 −0.160516
\(351\) 89.6512 4.78523
\(352\) 12.3040 0.655806
\(353\) −1.00000 −0.0532246
\(354\) 41.0572 2.18216
\(355\) −1.68197 −0.0892694
\(356\) 16.2465 0.861062
\(357\) −9.58586 −0.507337
\(358\) −49.9722 −2.64111
\(359\) −12.1624 −0.641905 −0.320952 0.947095i \(-0.604003\pi\)
−0.320952 + 0.947095i \(0.604003\pi\)
\(360\) 48.5648 2.55959
\(361\) −14.5265 −0.764555
\(362\) 10.5232 0.553087
\(363\) 24.9145 1.30767
\(364\) −40.8267 −2.13990
\(365\) 14.9350 0.781733
\(366\) 59.0780 3.08806
\(367\) −18.2751 −0.953952 −0.476976 0.878916i \(-0.658267\pi\)
−0.476976 + 0.878916i \(0.658267\pi\)
\(368\) 4.12463 0.215011
\(369\) 12.0594 0.627786
\(370\) −33.1271 −1.72220
\(371\) −11.0115 −0.571689
\(372\) −63.0190 −3.26738
\(373\) 1.43315 0.0742056 0.0371028 0.999311i \(-0.488187\pi\)
0.0371028 + 0.999311i \(0.488187\pi\)
\(374\) −4.32095 −0.223431
\(375\) −36.0449 −1.86135
\(376\) −1.22029 −0.0629314
\(377\) −29.8494 −1.53732
\(378\) 120.582 6.20208
\(379\) 12.0412 0.618516 0.309258 0.950978i \(-0.399919\pi\)
0.309258 + 0.950978i \(0.399919\pi\)
\(380\) 15.2085 0.780181
\(381\) 19.6725 1.00785
\(382\) −3.54226 −0.181238
\(383\) −6.19285 −0.316440 −0.158220 0.987404i \(-0.550576\pi\)
−0.158220 + 0.987404i \(0.550576\pi\)
\(384\) −56.3568 −2.87594
\(385\) −12.6398 −0.644185
\(386\) 55.3071 2.81506
\(387\) −37.3949 −1.90089
\(388\) 53.2002 2.70083
\(389\) −12.1637 −0.616723 −0.308361 0.951269i \(-0.599781\pi\)
−0.308361 + 0.951269i \(0.599781\pi\)
\(390\) 84.5945 4.28361
\(391\) −5.88844 −0.297791
\(392\) −2.25346 −0.113817
\(393\) 27.7796 1.40130
\(394\) 8.07876 0.407002
\(395\) 25.8188 1.29908
\(396\) 50.6157 2.54353
\(397\) −23.4312 −1.17598 −0.587990 0.808868i \(-0.700081\pi\)
−0.587990 + 0.808868i \(0.700081\pi\)
\(398\) −33.9548 −1.70200
\(399\) 20.2746 1.01500
\(400\) −0.331583 −0.0165792
\(401\) 29.0965 1.45301 0.726504 0.687162i \(-0.241144\pi\)
0.726504 + 0.687162i \(0.241144\pi\)
\(402\) 52.6382 2.62535
\(403\) −28.4125 −1.41533
\(404\) −6.21058 −0.308988
\(405\) −91.1069 −4.52714
\(406\) −40.1479 −1.99250
\(407\) −12.0594 −0.597761
\(408\) 8.23023 0.407457
\(409\) −5.84381 −0.288958 −0.144479 0.989508i \(-0.546151\pi\)
−0.144479 + 0.989508i \(0.546151\pi\)
\(410\) 7.40260 0.365588
\(411\) −39.1284 −1.93006
\(412\) 32.8316 1.61750
\(413\) 15.0828 0.742175
\(414\) 113.862 5.59601
\(415\) −28.0641 −1.37761
\(416\) −30.2511 −1.48318
\(417\) 50.6758 2.48161
\(418\) 9.13904 0.447005
\(419\) −20.0852 −0.981224 −0.490612 0.871378i \(-0.663227\pi\)
−0.490612 + 0.871378i \(0.663227\pi\)
\(420\) 68.9281 3.36335
\(421\) −23.8848 −1.16407 −0.582037 0.813162i \(-0.697744\pi\)
−0.582037 + 0.813162i \(0.697744\pi\)
\(422\) −32.3173 −1.57318
\(423\) 4.33226 0.210642
\(424\) 9.45427 0.459140
\(425\) 0.473377 0.0229622
\(426\) 5.51171 0.267043
\(427\) 21.7029 1.05028
\(428\) −47.7710 −2.30910
\(429\) 30.7952 1.48681
\(430\) −22.9547 −1.10698
\(431\) −15.6286 −0.752801 −0.376401 0.926457i \(-0.622838\pi\)
−0.376401 + 0.926457i \(0.622838\pi\)
\(432\) 13.3145 0.640593
\(433\) 15.3464 0.737500 0.368750 0.929529i \(-0.379786\pi\)
0.368750 + 0.929529i \(0.379786\pi\)
\(434\) −38.2152 −1.83439
\(435\) 50.3950 2.41625
\(436\) −6.39555 −0.306291
\(437\) 12.4544 0.595774
\(438\) −48.9411 −2.33850
\(439\) 19.1595 0.914434 0.457217 0.889355i \(-0.348846\pi\)
0.457217 + 0.889355i \(0.348846\pi\)
\(440\) 10.8523 0.517363
\(441\) 8.00024 0.380964
\(442\) 10.6236 0.505314
\(443\) 7.16237 0.340295 0.170147 0.985419i \(-0.445576\pi\)
0.170147 + 0.985419i \(0.445576\pi\)
\(444\) 65.7629 3.12097
\(445\) −12.3666 −0.586232
\(446\) −26.4819 −1.25395
\(447\) 75.1144 3.55279
\(448\) −36.7426 −1.73592
\(449\) 26.3422 1.24317 0.621584 0.783348i \(-0.286490\pi\)
0.621584 + 0.783348i \(0.286490\pi\)
\(450\) −9.15348 −0.431499
\(451\) 2.69479 0.126893
\(452\) −10.4308 −0.490622
\(453\) 42.5681 2.00002
\(454\) 50.2088 2.35641
\(455\) 31.0767 1.45690
\(456\) −17.4074 −0.815176
\(457\) 19.3598 0.905614 0.452807 0.891609i \(-0.350423\pi\)
0.452807 + 0.891609i \(0.350423\pi\)
\(458\) 13.6231 0.636565
\(459\) −19.0081 −0.887222
\(460\) 42.3414 1.97418
\(461\) −31.9895 −1.48990 −0.744951 0.667120i \(-0.767527\pi\)
−0.744951 + 0.667120i \(0.767527\pi\)
\(462\) 41.4200 1.92703
\(463\) 27.1119 1.26000 0.629999 0.776596i \(-0.283055\pi\)
0.629999 + 0.776596i \(0.283055\pi\)
\(464\) −4.43306 −0.205799
\(465\) 47.9691 2.22451
\(466\) 13.4861 0.624732
\(467\) −7.76730 −0.359428 −0.179714 0.983719i \(-0.557517\pi\)
−0.179714 + 0.983719i \(0.557517\pi\)
\(468\) −124.445 −5.75249
\(469\) 19.3372 0.892908
\(470\) 2.65934 0.122666
\(471\) 40.8762 1.88348
\(472\) −12.9498 −0.596062
\(473\) −8.35628 −0.384222
\(474\) −84.6068 −3.88612
\(475\) −1.00122 −0.0459391
\(476\) 8.65620 0.396756
\(477\) −33.5645 −1.53681
\(478\) 29.9144 1.36825
\(479\) 20.0416 0.915723 0.457861 0.889024i \(-0.348616\pi\)
0.457861 + 0.889024i \(0.348616\pi\)
\(480\) 51.0732 2.33116
\(481\) 29.6496 1.35190
\(482\) 34.2131 1.55836
\(483\) 56.4457 2.56837
\(484\) −22.4983 −1.02265
\(485\) −40.4952 −1.83879
\(486\) 170.108 7.71625
\(487\) −37.4645 −1.69768 −0.848840 0.528650i \(-0.822698\pi\)
−0.848840 + 0.528650i \(0.822698\pi\)
\(488\) −18.6337 −0.843508
\(489\) 49.3763 2.23287
\(490\) 4.91092 0.221853
\(491\) 6.41698 0.289594 0.144797 0.989461i \(-0.453747\pi\)
0.144797 + 0.989461i \(0.453747\pi\)
\(492\) −14.6954 −0.662519
\(493\) 6.32875 0.285033
\(494\) −22.4695 −1.01095
\(495\) −38.5279 −1.73170
\(496\) −4.21966 −0.189468
\(497\) 2.02478 0.0908239
\(498\) 91.9645 4.12103
\(499\) 23.2208 1.03950 0.519752 0.854317i \(-0.326024\pi\)
0.519752 + 0.854317i \(0.326024\pi\)
\(500\) 32.5492 1.45564
\(501\) −60.1272 −2.68629
\(502\) 24.2488 1.08228
\(503\) 37.5766 1.67546 0.837729 0.546087i \(-0.183883\pi\)
0.837729 + 0.546087i \(0.183883\pi\)
\(504\) −58.4633 −2.60416
\(505\) 4.72740 0.210366
\(506\) 25.4436 1.13111
\(507\) −31.4669 −1.39750
\(508\) −17.7646 −0.788176
\(509\) 6.85844 0.303995 0.151998 0.988381i \(-0.451429\pi\)
0.151998 + 0.988381i \(0.451429\pi\)
\(510\) −17.9360 −0.794218
\(511\) −17.9790 −0.795345
\(512\) −7.88026 −0.348262
\(513\) 40.2032 1.77501
\(514\) −60.4872 −2.66797
\(515\) −24.9909 −1.10123
\(516\) 45.5689 2.00606
\(517\) 0.968088 0.0425765
\(518\) 39.8791 1.75219
\(519\) −66.2353 −2.90741
\(520\) −26.6818 −1.17008
\(521\) 25.4863 1.11657 0.558287 0.829648i \(-0.311459\pi\)
0.558287 + 0.829648i \(0.311459\pi\)
\(522\) −122.376 −5.35626
\(523\) 10.9109 0.477102 0.238551 0.971130i \(-0.423328\pi\)
0.238551 + 0.971130i \(0.423328\pi\)
\(524\) −25.0855 −1.09586
\(525\) −4.53773 −0.198043
\(526\) −24.6994 −1.07695
\(527\) 6.02410 0.262414
\(528\) 4.57352 0.199037
\(529\) 11.6737 0.507553
\(530\) −20.6035 −0.894957
\(531\) 45.9743 1.99512
\(532\) −18.3083 −0.793767
\(533\) −6.62550 −0.286982
\(534\) 40.5246 1.75367
\(535\) 36.3625 1.57209
\(536\) −16.6025 −0.717120
\(537\) −75.5119 −3.25858
\(538\) −57.8916 −2.49588
\(539\) 1.78774 0.0770033
\(540\) 136.680 5.88176
\(541\) −2.19008 −0.0941589 −0.0470794 0.998891i \(-0.514991\pi\)
−0.0470794 + 0.998891i \(0.514991\pi\)
\(542\) −44.1248 −1.89532
\(543\) 15.9014 0.682393
\(544\) 6.41392 0.274994
\(545\) 4.86819 0.208531
\(546\) −101.837 −4.35820
\(547\) 19.9862 0.854546 0.427273 0.904123i \(-0.359474\pi\)
0.427273 + 0.904123i \(0.359474\pi\)
\(548\) 35.3337 1.50938
\(549\) 66.1534 2.82336
\(550\) −2.04544 −0.0872178
\(551\) −13.3857 −0.570248
\(552\) −48.4632 −2.06273
\(553\) −31.0812 −1.32171
\(554\) −23.6726 −1.00575
\(555\) −50.0577 −2.12483
\(556\) −45.7611 −1.94070
\(557\) −33.2761 −1.40995 −0.704976 0.709231i \(-0.749042\pi\)
−0.704976 + 0.709231i \(0.749042\pi\)
\(558\) −116.485 −4.93121
\(559\) 20.5450 0.868962
\(560\) 4.61532 0.195033
\(561\) −6.52928 −0.275667
\(562\) 10.6791 0.450470
\(563\) 9.27010 0.390688 0.195344 0.980735i \(-0.437418\pi\)
0.195344 + 0.980735i \(0.437418\pi\)
\(564\) −5.27923 −0.222296
\(565\) 7.93974 0.334027
\(566\) −43.5752 −1.83160
\(567\) 109.676 4.60597
\(568\) −1.73844 −0.0729433
\(569\) −2.11662 −0.0887334 −0.0443667 0.999015i \(-0.514127\pi\)
−0.0443667 + 0.999015i \(0.514127\pi\)
\(570\) 37.9355 1.58895
\(571\) 33.3929 1.39745 0.698724 0.715391i \(-0.253751\pi\)
0.698724 + 0.715391i \(0.253751\pi\)
\(572\) −27.8086 −1.16274
\(573\) −5.35262 −0.223609
\(574\) −8.91140 −0.371955
\(575\) −2.78745 −0.116245
\(576\) −111.996 −4.66652
\(577\) −33.8918 −1.41093 −0.705467 0.708743i \(-0.749263\pi\)
−0.705467 + 0.708743i \(0.749263\pi\)
\(578\) −2.25245 −0.0936896
\(579\) 83.5733 3.47319
\(580\) −45.5075 −1.88960
\(581\) 33.7841 1.40160
\(582\) 132.700 5.50061
\(583\) −7.50034 −0.310632
\(584\) 15.4365 0.638765
\(585\) 94.7258 3.91643
\(586\) 34.9483 1.44370
\(587\) −40.0112 −1.65144 −0.825719 0.564082i \(-0.809230\pi\)
−0.825719 + 0.564082i \(0.809230\pi\)
\(588\) −9.74899 −0.402041
\(589\) −12.7413 −0.524996
\(590\) 28.2212 1.16185
\(591\) 12.2076 0.502155
\(592\) 4.40338 0.180978
\(593\) −42.0638 −1.72735 −0.863677 0.504046i \(-0.831844\pi\)
−0.863677 + 0.504046i \(0.831844\pi\)
\(594\) 82.1330 3.36996
\(595\) −6.58896 −0.270121
\(596\) −67.8296 −2.77841
\(597\) −51.3084 −2.09991
\(598\) −62.5566 −2.55813
\(599\) 32.0738 1.31050 0.655250 0.755412i \(-0.272563\pi\)
0.655250 + 0.755412i \(0.272563\pi\)
\(600\) 3.89601 0.159054
\(601\) −41.0256 −1.67347 −0.836734 0.547609i \(-0.815538\pi\)
−0.836734 + 0.547609i \(0.815538\pi\)
\(602\) 27.6334 1.12625
\(603\) 58.9423 2.40032
\(604\) −38.4397 −1.56409
\(605\) 17.1253 0.696244
\(606\) −15.4914 −0.629296
\(607\) 45.1361 1.83202 0.916008 0.401160i \(-0.131393\pi\)
0.916008 + 0.401160i \(0.131393\pi\)
\(608\) −13.5658 −0.550165
\(609\) −60.6665 −2.45833
\(610\) 40.6080 1.64417
\(611\) −2.38017 −0.0962915
\(612\) 26.3852 1.06656
\(613\) −9.24592 −0.373439 −0.186720 0.982413i \(-0.559786\pi\)
−0.186720 + 0.982413i \(0.559786\pi\)
\(614\) 70.3061 2.83732
\(615\) 11.1859 0.451059
\(616\) −13.0642 −0.526372
\(617\) 28.9428 1.16519 0.582597 0.812761i \(-0.302037\pi\)
0.582597 + 0.812761i \(0.302037\pi\)
\(618\) 81.8939 3.29425
\(619\) −3.29173 −0.132306 −0.0661528 0.997810i \(-0.521072\pi\)
−0.0661528 + 0.997810i \(0.521072\pi\)
\(620\) −43.3169 −1.73965
\(621\) 111.928 4.49152
\(622\) 5.84310 0.234287
\(623\) 14.8871 0.596440
\(624\) −11.2446 −0.450145
\(625\) −27.1428 −1.08571
\(626\) 18.9734 0.758330
\(627\) 13.8098 0.551510
\(628\) −36.9119 −1.47295
\(629\) −6.28639 −0.250655
\(630\) 127.408 5.07604
\(631\) −45.3961 −1.80719 −0.903595 0.428388i \(-0.859081\pi\)
−0.903595 + 0.428388i \(0.859081\pi\)
\(632\) 26.6857 1.06150
\(633\) −48.8339 −1.94097
\(634\) −21.6005 −0.857865
\(635\) 13.5221 0.536609
\(636\) 40.9013 1.62184
\(637\) −4.39539 −0.174152
\(638\) −27.3462 −1.08265
\(639\) 6.17181 0.244153
\(640\) −38.7375 −1.53124
\(641\) 20.1778 0.796975 0.398487 0.917174i \(-0.369535\pi\)
0.398487 + 0.917174i \(0.369535\pi\)
\(642\) −119.158 −4.70279
\(643\) −3.98062 −0.156980 −0.0784902 0.996915i \(-0.525010\pi\)
−0.0784902 + 0.996915i \(0.525010\pi\)
\(644\) −50.9715 −2.00856
\(645\) −34.6864 −1.36577
\(646\) 4.76406 0.187439
\(647\) 5.09085 0.200142 0.100071 0.994980i \(-0.468093\pi\)
0.100071 + 0.994980i \(0.468093\pi\)
\(648\) −94.1660 −3.69919
\(649\) 10.2734 0.403268
\(650\) 5.02898 0.197253
\(651\) −57.7461 −2.26325
\(652\) −44.5876 −1.74619
\(653\) −24.4843 −0.958146 −0.479073 0.877775i \(-0.659027\pi\)
−0.479073 + 0.877775i \(0.659027\pi\)
\(654\) −15.9528 −0.623804
\(655\) 19.0947 0.746090
\(656\) −0.983981 −0.0384180
\(657\) −54.8025 −2.13805
\(658\) −3.20137 −0.124802
\(659\) 33.0011 1.28554 0.642770 0.766059i \(-0.277785\pi\)
0.642770 + 0.766059i \(0.277785\pi\)
\(660\) 46.9495 1.82751
\(661\) −25.5147 −0.992408 −0.496204 0.868206i \(-0.665273\pi\)
−0.496204 + 0.868206i \(0.665273\pi\)
\(662\) 65.0258 2.52730
\(663\) 16.0531 0.623451
\(664\) −29.0064 −1.12567
\(665\) 13.9360 0.540416
\(666\) 121.557 4.71024
\(667\) −37.2665 −1.44296
\(668\) 54.2959 2.10077
\(669\) −40.0161 −1.54711
\(670\) 36.1815 1.39781
\(671\) 14.7827 0.570678
\(672\) −61.4829 −2.37175
\(673\) −42.7605 −1.64830 −0.824149 0.566373i \(-0.808346\pi\)
−0.824149 + 0.566373i \(0.808346\pi\)
\(674\) −3.67725 −0.141642
\(675\) −8.99801 −0.346333
\(676\) 28.4152 1.09289
\(677\) 12.2154 0.469475 0.234738 0.972059i \(-0.424577\pi\)
0.234738 + 0.972059i \(0.424577\pi\)
\(678\) −26.0181 −0.999219
\(679\) 48.7489 1.87081
\(680\) 5.65716 0.216942
\(681\) 75.8693 2.90732
\(682\) −26.0298 −0.996733
\(683\) −9.86422 −0.377444 −0.188722 0.982031i \(-0.560435\pi\)
−0.188722 + 0.982031i \(0.560435\pi\)
\(684\) −55.8063 −2.13381
\(685\) −26.8954 −1.02762
\(686\) 38.4942 1.46972
\(687\) 20.5855 0.785387
\(688\) 3.05123 0.116327
\(689\) 18.4406 0.702530
\(690\) 105.615 4.02069
\(691\) 12.1041 0.460463 0.230232 0.973136i \(-0.426052\pi\)
0.230232 + 0.973136i \(0.426052\pi\)
\(692\) 59.8116 2.27370
\(693\) 46.3806 1.76185
\(694\) −19.3564 −0.734761
\(695\) 34.8327 1.32128
\(696\) 52.0871 1.97436
\(697\) 1.40476 0.0532090
\(698\) −33.3623 −1.26278
\(699\) 20.3785 0.770787
\(700\) 4.09765 0.154876
\(701\) −42.6567 −1.61112 −0.805561 0.592513i \(-0.798136\pi\)
−0.805561 + 0.592513i \(0.798136\pi\)
\(702\) −201.935 −7.62154
\(703\) 13.2961 0.501470
\(704\) −25.0268 −0.943231
\(705\) 4.01847 0.151344
\(706\) 2.25245 0.0847721
\(707\) −5.69094 −0.214030
\(708\) −56.0237 −2.10550
\(709\) −3.78495 −0.142147 −0.0710733 0.997471i \(-0.522642\pi\)
−0.0710733 + 0.997471i \(0.522642\pi\)
\(710\) 3.78854 0.142181
\(711\) −94.7396 −3.55301
\(712\) −12.7818 −0.479018
\(713\) −35.4725 −1.32846
\(714\) 21.5917 0.808048
\(715\) 21.1675 0.791618
\(716\) 68.1885 2.54832
\(717\) 45.2030 1.68814
\(718\) 27.3951 1.02238
\(719\) 24.3854 0.909421 0.454710 0.890639i \(-0.349743\pi\)
0.454710 + 0.890639i \(0.349743\pi\)
\(720\) 14.0681 0.524288
\(721\) 30.0846 1.12041
\(722\) 32.7203 1.21772
\(723\) 51.6986 1.92269
\(724\) −14.3592 −0.533656
\(725\) 2.99589 0.111264
\(726\) −56.1188 −2.08276
\(727\) 6.19986 0.229940 0.114970 0.993369i \(-0.463323\pi\)
0.114970 + 0.993369i \(0.463323\pi\)
\(728\) 32.1201 1.19045
\(729\) 140.219 5.19328
\(730\) −33.6403 −1.24508
\(731\) −4.35602 −0.161113
\(732\) −80.6136 −2.97957
\(733\) −22.3792 −0.826594 −0.413297 0.910596i \(-0.635623\pi\)
−0.413297 + 0.910596i \(0.635623\pi\)
\(734\) 41.1638 1.51938
\(735\) 7.42078 0.273719
\(736\) −37.7680 −1.39215
\(737\) 13.1713 0.485170
\(738\) −27.1631 −0.999889
\(739\) 21.0870 0.775699 0.387850 0.921723i \(-0.373218\pi\)
0.387850 + 0.921723i \(0.373218\pi\)
\(740\) 45.2029 1.66169
\(741\) −33.9532 −1.24730
\(742\) 24.8029 0.910542
\(743\) −35.9850 −1.32016 −0.660081 0.751195i \(-0.729478\pi\)
−0.660081 + 0.751195i \(0.729478\pi\)
\(744\) 49.5797 1.81768
\(745\) 51.6308 1.89161
\(746\) −3.22810 −0.118189
\(747\) 102.979 3.76779
\(748\) 5.89606 0.215581
\(749\) −43.7739 −1.59947
\(750\) 81.1893 2.96462
\(751\) 0.317378 0.0115813 0.00579064 0.999983i \(-0.498157\pi\)
0.00579064 + 0.999983i \(0.498157\pi\)
\(752\) −0.353489 −0.0128904
\(753\) 36.6417 1.33530
\(754\) 67.2343 2.44853
\(755\) 29.2597 1.06487
\(756\) −164.538 −5.98418
\(757\) 1.42769 0.0518901 0.0259451 0.999663i \(-0.491741\pi\)
0.0259451 + 0.999663i \(0.491741\pi\)
\(758\) −27.1223 −0.985125
\(759\) 38.4473 1.39555
\(760\) −11.9652 −0.434023
\(761\) 7.38254 0.267617 0.133808 0.991007i \(-0.457279\pi\)
0.133808 + 0.991007i \(0.457279\pi\)
\(762\) −44.3113 −1.60523
\(763\) −5.86043 −0.212162
\(764\) 4.83351 0.174870
\(765\) −20.0840 −0.726140
\(766\) 13.9491 0.504001
\(767\) −25.2586 −0.912035
\(768\) 38.1327 1.37600
\(769\) −23.5794 −0.850295 −0.425148 0.905124i \(-0.639778\pi\)
−0.425148 + 0.905124i \(0.639778\pi\)
\(770\) 28.4706 1.02601
\(771\) −91.4007 −3.29172
\(772\) −75.4681 −2.71616
\(773\) 47.2890 1.70087 0.850433 0.526083i \(-0.176340\pi\)
0.850433 + 0.526083i \(0.176340\pi\)
\(774\) 84.2302 3.02759
\(775\) 2.85167 0.102435
\(776\) −41.8549 −1.50250
\(777\) 60.2604 2.16183
\(778\) 27.3981 0.982268
\(779\) −2.97114 −0.106452
\(780\) −115.432 −4.13311
\(781\) 1.37916 0.0493500
\(782\) 13.2634 0.474299
\(783\) −120.298 −4.29908
\(784\) −0.652777 −0.0233135
\(785\) 28.0968 1.00282
\(786\) −62.5722 −2.23188
\(787\) 48.6628 1.73464 0.867320 0.497751i \(-0.165841\pi\)
0.867320 + 0.497751i \(0.165841\pi\)
\(788\) −11.0237 −0.392703
\(789\) −37.3228 −1.32873
\(790\) −58.1556 −2.06908
\(791\) −9.55802 −0.339844
\(792\) −39.8215 −1.41500
\(793\) −36.3451 −1.29065
\(794\) 52.7777 1.87301
\(795\) −31.1334 −1.10419
\(796\) 46.3324 1.64221
\(797\) −37.6676 −1.33425 −0.667127 0.744944i \(-0.732476\pi\)
−0.667127 + 0.744944i \(0.732476\pi\)
\(798\) −45.6676 −1.61661
\(799\) 0.504651 0.0178533
\(800\) 3.03620 0.107346
\(801\) 45.3780 1.60335
\(802\) −65.5383 −2.31424
\(803\) −12.2462 −0.432158
\(804\) −71.8263 −2.53312
\(805\) 38.7987 1.36747
\(806\) 63.9977 2.25422
\(807\) −87.4787 −3.07939
\(808\) 4.88613 0.171893
\(809\) 48.9458 1.72084 0.860421 0.509583i \(-0.170200\pi\)
0.860421 + 0.509583i \(0.170200\pi\)
\(810\) 205.214 7.21048
\(811\) 0.323004 0.0113422 0.00567110 0.999984i \(-0.498195\pi\)
0.00567110 + 0.999984i \(0.498195\pi\)
\(812\) 54.7829 1.92250
\(813\) −66.6760 −2.33843
\(814\) 27.1632 0.952068
\(815\) 33.9394 1.18885
\(816\) 2.38411 0.0834607
\(817\) 9.21321 0.322330
\(818\) 13.1629 0.460230
\(819\) −114.033 −3.98463
\(820\) −10.1011 −0.352744
\(821\) 27.4230 0.957071 0.478535 0.878068i \(-0.341168\pi\)
0.478535 + 0.878068i \(0.341168\pi\)
\(822\) 88.1349 3.07406
\(823\) 35.6827 1.24382 0.621911 0.783088i \(-0.286356\pi\)
0.621911 + 0.783088i \(0.286356\pi\)
\(824\) −25.8300 −0.899832
\(825\) −3.09081 −0.107608
\(826\) −33.9732 −1.18208
\(827\) −9.97304 −0.346797 −0.173398 0.984852i \(-0.555475\pi\)
−0.173398 + 0.984852i \(0.555475\pi\)
\(828\) −155.368 −5.39941
\(829\) 31.8550 1.10637 0.553185 0.833059i \(-0.313412\pi\)
0.553185 + 0.833059i \(0.313412\pi\)
\(830\) 63.2130 2.19415
\(831\) −35.7711 −1.24088
\(832\) 61.5316 2.13322
\(833\) 0.931923 0.0322892
\(834\) −114.145 −3.95251
\(835\) −41.3292 −1.43026
\(836\) −12.4705 −0.431301
\(837\) −114.507 −3.95793
\(838\) 45.2408 1.56282
\(839\) 42.8148 1.47813 0.739065 0.673634i \(-0.235268\pi\)
0.739065 + 0.673634i \(0.235268\pi\)
\(840\) −54.2287 −1.87107
\(841\) 11.0531 0.381141
\(842\) 53.7993 1.85405
\(843\) 16.1369 0.555785
\(844\) 44.0978 1.51791
\(845\) −21.6292 −0.744067
\(846\) −9.75820 −0.335494
\(847\) −20.6158 −0.708368
\(848\) 2.73869 0.0940469
\(849\) −65.8454 −2.25981
\(850\) −1.06626 −0.0365724
\(851\) 37.0170 1.26893
\(852\) −7.52088 −0.257661
\(853\) 43.9031 1.50321 0.751607 0.659611i \(-0.229279\pi\)
0.751607 + 0.659611i \(0.229279\pi\)
\(854\) −48.8847 −1.67280
\(855\) 42.4789 1.45275
\(856\) 37.5835 1.28458
\(857\) 3.30783 0.112993 0.0564966 0.998403i \(-0.482007\pi\)
0.0564966 + 0.998403i \(0.482007\pi\)
\(858\) −69.3646 −2.36807
\(859\) 3.95602 0.134978 0.0674889 0.997720i \(-0.478501\pi\)
0.0674889 + 0.997720i \(0.478501\pi\)
\(860\) 31.3224 1.06808
\(861\) −13.4658 −0.458914
\(862\) 35.2026 1.19900
\(863\) 6.61363 0.225131 0.112565 0.993644i \(-0.464093\pi\)
0.112565 + 0.993644i \(0.464093\pi\)
\(864\) −121.916 −4.14768
\(865\) −45.5277 −1.54799
\(866\) −34.5669 −1.17463
\(867\) −3.40363 −0.115593
\(868\) 52.1458 1.76994
\(869\) −21.1705 −0.718162
\(870\) −113.512 −3.84842
\(871\) −32.3833 −1.09727
\(872\) 5.03165 0.170393
\(873\) 148.593 5.02912
\(874\) −28.0529 −0.948902
\(875\) 29.8257 1.00829
\(876\) 66.7816 2.25634
\(877\) −42.6371 −1.43975 −0.719877 0.694102i \(-0.755802\pi\)
−0.719877 + 0.694102i \(0.755802\pi\)
\(878\) −43.1559 −1.45644
\(879\) 52.8096 1.78122
\(880\) 3.14367 0.105973
\(881\) −34.7636 −1.17121 −0.585607 0.810595i \(-0.699144\pi\)
−0.585607 + 0.810595i \(0.699144\pi\)
\(882\) −18.0202 −0.606770
\(883\) 36.0538 1.21331 0.606653 0.794967i \(-0.292512\pi\)
0.606653 + 0.794967i \(0.292512\pi\)
\(884\) −14.4962 −0.487561
\(885\) 42.6443 1.43347
\(886\) −16.1329 −0.541995
\(887\) −49.7192 −1.66941 −0.834703 0.550700i \(-0.814361\pi\)
−0.834703 + 0.550700i \(0.814361\pi\)
\(888\) −51.7384 −1.73623
\(889\) −16.2782 −0.545954
\(890\) 27.8551 0.933705
\(891\) 74.7046 2.50270
\(892\) 36.1353 1.20990
\(893\) −1.06736 −0.0357180
\(894\) −169.191 −5.65861
\(895\) −51.9040 −1.73496
\(896\) 46.6330 1.55790
\(897\) −94.5278 −3.15619
\(898\) −59.3346 −1.98002
\(899\) 38.1250 1.27154
\(900\) 12.4902 0.416339
\(901\) −3.90983 −0.130255
\(902\) −6.06989 −0.202105
\(903\) 41.7561 1.38956
\(904\) 8.20633 0.272938
\(905\) 10.9300 0.363326
\(906\) −95.8826 −3.18549
\(907\) 10.9067 0.362150 0.181075 0.983469i \(-0.442042\pi\)
0.181075 + 0.983469i \(0.442042\pi\)
\(908\) −68.5113 −2.27363
\(909\) −17.3467 −0.575355
\(910\) −69.9986 −2.32043
\(911\) 1.32015 0.0437384 0.0218692 0.999761i \(-0.493038\pi\)
0.0218692 + 0.999761i \(0.493038\pi\)
\(912\) −5.04253 −0.166975
\(913\) 23.0116 0.761573
\(914\) −43.6070 −1.44239
\(915\) 61.3618 2.02856
\(916\) −18.5891 −0.614201
\(917\) −22.9865 −0.759082
\(918\) 42.8148 1.41310
\(919\) −43.7446 −1.44300 −0.721501 0.692414i \(-0.756547\pi\)
−0.721501 + 0.692414i \(0.756547\pi\)
\(920\) −33.3118 −1.09826
\(921\) 106.238 3.50066
\(922\) 72.0548 2.37300
\(923\) −3.39084 −0.111611
\(924\) −56.5188 −1.85933
\(925\) −2.97583 −0.0978448
\(926\) −61.0683 −2.00683
\(927\) 91.7018 3.01188
\(928\) 40.5921 1.33250
\(929\) 6.81195 0.223493 0.111746 0.993737i \(-0.464356\pi\)
0.111746 + 0.993737i \(0.464356\pi\)
\(930\) −108.048 −3.54303
\(931\) −1.97107 −0.0645991
\(932\) −18.4022 −0.602783
\(933\) 8.82938 0.289061
\(934\) 17.4955 0.572469
\(935\) −4.48799 −0.146773
\(936\) 97.9064 3.20017
\(937\) 6.33273 0.206881 0.103441 0.994636i \(-0.467015\pi\)
0.103441 + 0.994636i \(0.467015\pi\)
\(938\) −43.5560 −1.42216
\(939\) 28.6703 0.935620
\(940\) −3.62875 −0.118357
\(941\) 37.0263 1.20702 0.603511 0.797355i \(-0.293768\pi\)
0.603511 + 0.797355i \(0.293768\pi\)
\(942\) −92.0716 −2.99986
\(943\) −8.27183 −0.269368
\(944\) −3.75126 −0.122093
\(945\) 125.244 4.07418
\(946\) 18.8221 0.611960
\(947\) 55.4292 1.80121 0.900603 0.434643i \(-0.143125\pi\)
0.900603 + 0.434643i \(0.143125\pi\)
\(948\) 115.448 3.74959
\(949\) 30.1089 0.977375
\(950\) 2.25520 0.0731682
\(951\) −32.6400 −1.05842
\(952\) −6.81020 −0.220720
\(953\) −16.3276 −0.528902 −0.264451 0.964399i \(-0.585191\pi\)
−0.264451 + 0.964399i \(0.585191\pi\)
\(954\) 75.6025 2.44772
\(955\) −3.67919 −0.119056
\(956\) −40.8191 −1.32018
\(957\) −41.3222 −1.33576
\(958\) −45.1426 −1.45849
\(959\) 32.3773 1.04552
\(960\) −103.884 −3.35285
\(961\) 5.28975 0.170637
\(962\) −66.7842 −2.15321
\(963\) −133.429 −4.29969
\(964\) −46.6847 −1.50361
\(965\) 57.4452 1.84923
\(966\) −127.141 −4.09070
\(967\) −20.1035 −0.646484 −0.323242 0.946316i \(-0.604773\pi\)
−0.323242 + 0.946316i \(0.604773\pi\)
\(968\) 17.7003 0.568910
\(969\) 7.19886 0.231261
\(970\) 91.2134 2.92868
\(971\) −28.3035 −0.908302 −0.454151 0.890925i \(-0.650057\pi\)
−0.454151 + 0.890925i \(0.650057\pi\)
\(972\) −232.117 −7.44516
\(973\) −41.9323 −1.34429
\(974\) 84.3870 2.70393
\(975\) 7.59918 0.243368
\(976\) −5.39777 −0.172778
\(977\) −23.3419 −0.746774 −0.373387 0.927676i \(-0.621804\pi\)
−0.373387 + 0.927676i \(0.621804\pi\)
\(978\) −111.218 −3.55635
\(979\) 10.1402 0.324081
\(980\) −6.70109 −0.214058
\(981\) −17.8634 −0.570334
\(982\) −14.4539 −0.461244
\(983\) 25.0797 0.799918 0.399959 0.916533i \(-0.369024\pi\)
0.399959 + 0.916533i \(0.369024\pi\)
\(984\) 11.5615 0.368567
\(985\) 8.39107 0.267362
\(986\) −14.2552 −0.453978
\(987\) −4.83751 −0.153980
\(988\) 30.6603 0.975435
\(989\) 25.6501 0.815627
\(990\) 86.7821 2.75812
\(991\) 49.7530 1.58045 0.790227 0.612814i \(-0.209962\pi\)
0.790227 + 0.612814i \(0.209962\pi\)
\(992\) 38.6381 1.22676
\(993\) 98.2590 3.11816
\(994\) −4.56072 −0.144657
\(995\) −35.2675 −1.11805
\(996\) −125.488 −3.97624
\(997\) −2.77539 −0.0878974 −0.0439487 0.999034i \(-0.513994\pi\)
−0.0439487 + 0.999034i \(0.513994\pi\)
\(998\) −52.3036 −1.65564
\(999\) 119.492 3.78057
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 6001.2.a.d.1.14 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.d.1.14 121 1.1 even 1 trivial