Properties

Label 4027.2.a.c.1.10
Level 4027
Weight 2
Character 4027.1
Self dual yes
Analytic conductor 32.156
Analytic rank 0
Dimension 174
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4027 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4027.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1557568940\)
Analytic rank: \(0\)
Dimension: \(174\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.51686 q^{2} -1.86760 q^{3} +4.33456 q^{4} -3.04693 q^{5} +4.70049 q^{6} -0.421908 q^{7} -5.87575 q^{8} +0.487938 q^{9} +O(q^{10})\) \(q-2.51686 q^{2} -1.86760 q^{3} +4.33456 q^{4} -3.04693 q^{5} +4.70049 q^{6} -0.421908 q^{7} -5.87575 q^{8} +0.487938 q^{9} +7.66868 q^{10} -0.625941 q^{11} -8.09524 q^{12} -3.42323 q^{13} +1.06188 q^{14} +5.69045 q^{15} +6.11930 q^{16} +7.89702 q^{17} -1.22807 q^{18} +8.21388 q^{19} -13.2071 q^{20} +0.787957 q^{21} +1.57540 q^{22} +7.05488 q^{23} +10.9736 q^{24} +4.28378 q^{25} +8.61578 q^{26} +4.69153 q^{27} -1.82879 q^{28} +8.83383 q^{29} -14.3220 q^{30} -9.72357 q^{31} -3.64989 q^{32} +1.16901 q^{33} -19.8757 q^{34} +1.28552 q^{35} +2.11500 q^{36} -6.32965 q^{37} -20.6731 q^{38} +6.39324 q^{39} +17.9030 q^{40} -9.06189 q^{41} -1.98317 q^{42} -1.16729 q^{43} -2.71318 q^{44} -1.48671 q^{45} -17.7561 q^{46} +3.30942 q^{47} -11.4284 q^{48} -6.82199 q^{49} -10.7816 q^{50} -14.7485 q^{51} -14.8382 q^{52} +11.6817 q^{53} -11.8079 q^{54} +1.90720 q^{55} +2.47903 q^{56} -15.3403 q^{57} -22.2335 q^{58} -6.06589 q^{59} +24.6656 q^{60} +5.01268 q^{61} +24.4728 q^{62} -0.205865 q^{63} -3.05236 q^{64} +10.4303 q^{65} -2.94222 q^{66} +2.89581 q^{67} +34.2301 q^{68} -13.1757 q^{69} -3.23548 q^{70} +12.5189 q^{71} -2.86701 q^{72} +10.7893 q^{73} +15.9308 q^{74} -8.00039 q^{75} +35.6036 q^{76} +0.264090 q^{77} -16.0909 q^{78} -0.898442 q^{79} -18.6451 q^{80} -10.2257 q^{81} +22.8075 q^{82} +8.49727 q^{83} +3.41545 q^{84} -24.0617 q^{85} +2.93789 q^{86} -16.4981 q^{87} +3.67787 q^{88} -8.17918 q^{89} +3.74184 q^{90} +1.44429 q^{91} +30.5798 q^{92} +18.1598 q^{93} -8.32932 q^{94} -25.0271 q^{95} +6.81654 q^{96} +3.27109 q^{97} +17.1700 q^{98} -0.305420 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51686 −1.77969 −0.889843 0.456267i \(-0.849186\pi\)
−0.889843 + 0.456267i \(0.849186\pi\)
\(3\) −1.86760 −1.07826 −0.539130 0.842222i \(-0.681247\pi\)
−0.539130 + 0.842222i \(0.681247\pi\)
\(4\) 4.33456 2.16728
\(5\) −3.04693 −1.36263 −0.681314 0.731991i \(-0.738591\pi\)
−0.681314 + 0.731991i \(0.738591\pi\)
\(6\) 4.70049 1.91897
\(7\) −0.421908 −0.159466 −0.0797332 0.996816i \(-0.525407\pi\)
−0.0797332 + 0.996816i \(0.525407\pi\)
\(8\) −5.87575 −2.07739
\(9\) 0.487938 0.162646
\(10\) 7.66868 2.42505
\(11\) −0.625941 −0.188728 −0.0943641 0.995538i \(-0.530082\pi\)
−0.0943641 + 0.995538i \(0.530082\pi\)
\(12\) −8.09524 −2.33689
\(13\) −3.42323 −0.949434 −0.474717 0.880139i \(-0.657450\pi\)
−0.474717 + 0.880139i \(0.657450\pi\)
\(14\) 1.06188 0.283800
\(15\) 5.69045 1.46927
\(16\) 6.11930 1.52983
\(17\) 7.89702 1.91531 0.957655 0.287919i \(-0.0929635\pi\)
0.957655 + 0.287919i \(0.0929635\pi\)
\(18\) −1.22807 −0.289459
\(19\) 8.21388 1.88439 0.942196 0.335061i \(-0.108757\pi\)
0.942196 + 0.335061i \(0.108757\pi\)
\(20\) −13.2071 −2.95320
\(21\) 0.787957 0.171946
\(22\) 1.57540 0.335877
\(23\) 7.05488 1.47104 0.735522 0.677501i \(-0.236937\pi\)
0.735522 + 0.677501i \(0.236937\pi\)
\(24\) 10.9736 2.23997
\(25\) 4.28378 0.856755
\(26\) 8.61578 1.68969
\(27\) 4.69153 0.902886
\(28\) −1.82879 −0.345608
\(29\) 8.83383 1.64040 0.820200 0.572076i \(-0.193862\pi\)
0.820200 + 0.572076i \(0.193862\pi\)
\(30\) −14.3220 −2.61484
\(31\) −9.72357 −1.74640 −0.873202 0.487358i \(-0.837961\pi\)
−0.873202 + 0.487358i \(0.837961\pi\)
\(32\) −3.64989 −0.645216
\(33\) 1.16901 0.203498
\(34\) −19.8757 −3.40865
\(35\) 1.28552 0.217293
\(36\) 2.11500 0.352500
\(37\) −6.32965 −1.04059 −0.520294 0.853987i \(-0.674178\pi\)
−0.520294 + 0.853987i \(0.674178\pi\)
\(38\) −20.6731 −3.35363
\(39\) 6.39324 1.02374
\(40\) 17.9030 2.83071
\(41\) −9.06189 −1.41523 −0.707615 0.706598i \(-0.750229\pi\)
−0.707615 + 0.706598i \(0.750229\pi\)
\(42\) −1.98317 −0.306010
\(43\) −1.16729 −0.178010 −0.0890048 0.996031i \(-0.528369\pi\)
−0.0890048 + 0.996031i \(0.528369\pi\)
\(44\) −2.71318 −0.409027
\(45\) −1.48671 −0.221626
\(46\) −17.7561 −2.61800
\(47\) 3.30942 0.482728 0.241364 0.970435i \(-0.422405\pi\)
0.241364 + 0.970435i \(0.422405\pi\)
\(48\) −11.4284 −1.64955
\(49\) −6.82199 −0.974570
\(50\) −10.7816 −1.52475
\(51\) −14.7485 −2.06520
\(52\) −14.8382 −2.05769
\(53\) 11.6817 1.60461 0.802305 0.596914i \(-0.203607\pi\)
0.802305 + 0.596914i \(0.203607\pi\)
\(54\) −11.8079 −1.60685
\(55\) 1.90720 0.257166
\(56\) 2.47903 0.331274
\(57\) −15.3403 −2.03187
\(58\) −22.2335 −2.91940
\(59\) −6.06589 −0.789712 −0.394856 0.918743i \(-0.629205\pi\)
−0.394856 + 0.918743i \(0.629205\pi\)
\(60\) 24.6656 3.18432
\(61\) 5.01268 0.641808 0.320904 0.947112i \(-0.396013\pi\)
0.320904 + 0.947112i \(0.396013\pi\)
\(62\) 24.4728 3.10805
\(63\) −0.205865 −0.0259366
\(64\) −3.05236 −0.381545
\(65\) 10.4303 1.29373
\(66\) −2.94222 −0.362163
\(67\) 2.89581 0.353780 0.176890 0.984231i \(-0.443396\pi\)
0.176890 + 0.984231i \(0.443396\pi\)
\(68\) 34.2301 4.15101
\(69\) −13.1757 −1.58617
\(70\) −3.23548 −0.386714
\(71\) 12.5189 1.48572 0.742859 0.669448i \(-0.233469\pi\)
0.742859 + 0.669448i \(0.233469\pi\)
\(72\) −2.86701 −0.337880
\(73\) 10.7893 1.26279 0.631394 0.775462i \(-0.282483\pi\)
0.631394 + 0.775462i \(0.282483\pi\)
\(74\) 15.9308 1.85192
\(75\) −8.00039 −0.923805
\(76\) 35.6036 4.08401
\(77\) 0.264090 0.0300958
\(78\) −16.0909 −1.82193
\(79\) −0.898442 −0.101083 −0.0505413 0.998722i \(-0.516095\pi\)
−0.0505413 + 0.998722i \(0.516095\pi\)
\(80\) −18.6451 −2.08458
\(81\) −10.2257 −1.13619
\(82\) 22.8075 2.51866
\(83\) 8.49727 0.932697 0.466349 0.884601i \(-0.345569\pi\)
0.466349 + 0.884601i \(0.345569\pi\)
\(84\) 3.41545 0.372656
\(85\) −24.0617 −2.60985
\(86\) 2.93789 0.316801
\(87\) −16.4981 −1.76878
\(88\) 3.67787 0.392063
\(89\) −8.17918 −0.866991 −0.433496 0.901156i \(-0.642720\pi\)
−0.433496 + 0.901156i \(0.642720\pi\)
\(90\) 3.74184 0.394425
\(91\) 1.44429 0.151403
\(92\) 30.5798 3.18817
\(93\) 18.1598 1.88308
\(94\) −8.32932 −0.859104
\(95\) −25.0271 −2.56773
\(96\) 6.81654 0.695711
\(97\) 3.27109 0.332129 0.166064 0.986115i \(-0.446894\pi\)
0.166064 + 0.986115i \(0.446894\pi\)
\(98\) 17.1700 1.73443
\(99\) −0.305420 −0.0306959
\(100\) 18.5683 1.85683
\(101\) −11.4789 −1.14220 −0.571099 0.820881i \(-0.693483\pi\)
−0.571099 + 0.820881i \(0.693483\pi\)
\(102\) 37.1198 3.67541
\(103\) −5.68400 −0.560061 −0.280031 0.959991i \(-0.590345\pi\)
−0.280031 + 0.959991i \(0.590345\pi\)
\(104\) 20.1141 1.97235
\(105\) −2.40085 −0.234299
\(106\) −29.4013 −2.85570
\(107\) −12.0407 −1.16402 −0.582008 0.813183i \(-0.697733\pi\)
−0.582008 + 0.813183i \(0.697733\pi\)
\(108\) 20.3357 1.95681
\(109\) −15.7749 −1.51096 −0.755480 0.655171i \(-0.772596\pi\)
−0.755480 + 0.655171i \(0.772596\pi\)
\(110\) −4.80014 −0.457675
\(111\) 11.8213 1.12202
\(112\) −2.58179 −0.243956
\(113\) 3.17564 0.298740 0.149370 0.988781i \(-0.452276\pi\)
0.149370 + 0.988781i \(0.452276\pi\)
\(114\) 38.6092 3.61608
\(115\) −21.4957 −2.00449
\(116\) 38.2908 3.55521
\(117\) −1.67033 −0.154422
\(118\) 15.2670 1.40544
\(119\) −3.33182 −0.305427
\(120\) −33.4357 −3.05225
\(121\) −10.6082 −0.964382
\(122\) −12.6162 −1.14222
\(123\) 16.9240 1.52599
\(124\) −42.1474 −3.78495
\(125\) 2.18229 0.195190
\(126\) 0.518133 0.0461590
\(127\) −0.376385 −0.0333988 −0.0166994 0.999861i \(-0.505316\pi\)
−0.0166994 + 0.999861i \(0.505316\pi\)
\(128\) 14.9821 1.32425
\(129\) 2.18003 0.191941
\(130\) −26.2517 −2.30242
\(131\) −4.14153 −0.361847 −0.180924 0.983497i \(-0.557909\pi\)
−0.180924 + 0.983497i \(0.557909\pi\)
\(132\) 5.06714 0.441038
\(133\) −3.46550 −0.300497
\(134\) −7.28834 −0.629616
\(135\) −14.2948 −1.23030
\(136\) −46.4010 −3.97885
\(137\) −10.0622 −0.859673 −0.429836 0.902907i \(-0.641429\pi\)
−0.429836 + 0.902907i \(0.641429\pi\)
\(138\) 33.1614 2.82288
\(139\) 23.2770 1.97433 0.987165 0.159703i \(-0.0510536\pi\)
0.987165 + 0.159703i \(0.0510536\pi\)
\(140\) 5.57219 0.470936
\(141\) −6.18067 −0.520506
\(142\) −31.5082 −2.64411
\(143\) 2.14274 0.179185
\(144\) 2.98584 0.248820
\(145\) −26.9160 −2.23526
\(146\) −27.1550 −2.24736
\(147\) 12.7408 1.05084
\(148\) −27.4363 −2.25525
\(149\) 5.48939 0.449708 0.224854 0.974392i \(-0.427809\pi\)
0.224854 + 0.974392i \(0.427809\pi\)
\(150\) 20.1358 1.64408
\(151\) −8.01850 −0.652536 −0.326268 0.945277i \(-0.605791\pi\)
−0.326268 + 0.945277i \(0.605791\pi\)
\(152\) −48.2627 −3.91462
\(153\) 3.85326 0.311518
\(154\) −0.664675 −0.0535611
\(155\) 29.6270 2.37970
\(156\) 27.7119 2.21873
\(157\) 9.72834 0.776406 0.388203 0.921574i \(-0.373096\pi\)
0.388203 + 0.921574i \(0.373096\pi\)
\(158\) 2.26125 0.179895
\(159\) −21.8168 −1.73019
\(160\) 11.1210 0.879189
\(161\) −2.97651 −0.234582
\(162\) 25.7367 2.02207
\(163\) −8.54420 −0.669233 −0.334617 0.942354i \(-0.608607\pi\)
−0.334617 + 0.942354i \(0.608607\pi\)
\(164\) −39.2793 −3.06720
\(165\) −3.56188 −0.277292
\(166\) −21.3864 −1.65991
\(167\) 7.00039 0.541707 0.270853 0.962621i \(-0.412694\pi\)
0.270853 + 0.962621i \(0.412694\pi\)
\(168\) −4.62984 −0.357200
\(169\) −1.28148 −0.0985754
\(170\) 60.5597 4.64472
\(171\) 4.00787 0.306489
\(172\) −5.05968 −0.385797
\(173\) 5.13502 0.390408 0.195204 0.980763i \(-0.437463\pi\)
0.195204 + 0.980763i \(0.437463\pi\)
\(174\) 41.5233 3.14787
\(175\) −1.80736 −0.136624
\(176\) −3.83032 −0.288721
\(177\) 11.3287 0.851515
\(178\) 20.5858 1.54297
\(179\) 1.24979 0.0934137 0.0467069 0.998909i \(-0.485127\pi\)
0.0467069 + 0.998909i \(0.485127\pi\)
\(180\) −6.44425 −0.480326
\(181\) 10.7048 0.795684 0.397842 0.917454i \(-0.369759\pi\)
0.397842 + 0.917454i \(0.369759\pi\)
\(182\) −3.63507 −0.269449
\(183\) −9.36170 −0.692037
\(184\) −41.4528 −3.05594
\(185\) 19.2860 1.41793
\(186\) −45.7055 −3.35129
\(187\) −4.94307 −0.361473
\(188\) 14.3449 1.04621
\(189\) −1.97940 −0.143980
\(190\) 62.9896 4.56975
\(191\) 4.92943 0.356681 0.178340 0.983969i \(-0.442927\pi\)
0.178340 + 0.983969i \(0.442927\pi\)
\(192\) 5.70059 0.411405
\(193\) 7.98175 0.574539 0.287269 0.957850i \(-0.407253\pi\)
0.287269 + 0.957850i \(0.407253\pi\)
\(194\) −8.23286 −0.591085
\(195\) −19.4797 −1.39497
\(196\) −29.5704 −2.11217
\(197\) −8.52505 −0.607384 −0.303692 0.952770i \(-0.598219\pi\)
−0.303692 + 0.952770i \(0.598219\pi\)
\(198\) 0.768699 0.0546290
\(199\) 22.5631 1.59945 0.799726 0.600365i \(-0.204978\pi\)
0.799726 + 0.600365i \(0.204978\pi\)
\(200\) −25.1704 −1.77982
\(201\) −5.40822 −0.381467
\(202\) 28.8909 2.03275
\(203\) −3.72707 −0.261589
\(204\) −63.9283 −4.47587
\(205\) 27.6109 1.92843
\(206\) 14.3058 0.996733
\(207\) 3.44235 0.239260
\(208\) −20.9478 −1.45247
\(209\) −5.14140 −0.355638
\(210\) 6.04259 0.416978
\(211\) −23.8634 −1.64282 −0.821412 0.570335i \(-0.806813\pi\)
−0.821412 + 0.570335i \(0.806813\pi\)
\(212\) 50.6352 3.47764
\(213\) −23.3803 −1.60199
\(214\) 30.3046 2.07158
\(215\) 3.55664 0.242561
\(216\) −27.5663 −1.87565
\(217\) 4.10245 0.278493
\(218\) 39.7031 2.68903
\(219\) −20.1500 −1.36161
\(220\) 8.26686 0.557352
\(221\) −27.0333 −1.81846
\(222\) −29.7524 −1.99685
\(223\) 8.20803 0.549650 0.274825 0.961494i \(-0.411380\pi\)
0.274825 + 0.961494i \(0.411380\pi\)
\(224\) 1.53992 0.102890
\(225\) 2.09022 0.139348
\(226\) −7.99264 −0.531662
\(227\) −6.40227 −0.424933 −0.212467 0.977168i \(-0.568150\pi\)
−0.212467 + 0.977168i \(0.568150\pi\)
\(228\) −66.4933 −4.40363
\(229\) −4.87963 −0.322455 −0.161228 0.986917i \(-0.551545\pi\)
−0.161228 + 0.986917i \(0.551545\pi\)
\(230\) 54.1016 3.56736
\(231\) −0.493214 −0.0324511
\(232\) −51.9054 −3.40776
\(233\) −12.1245 −0.794303 −0.397151 0.917753i \(-0.630001\pi\)
−0.397151 + 0.917753i \(0.630001\pi\)
\(234\) 4.20397 0.274822
\(235\) −10.0836 −0.657778
\(236\) −26.2930 −1.71153
\(237\) 1.67793 0.108993
\(238\) 8.38571 0.543565
\(239\) −4.61414 −0.298464 −0.149232 0.988802i \(-0.547680\pi\)
−0.149232 + 0.988802i \(0.547680\pi\)
\(240\) 34.8216 2.24772
\(241\) −8.80630 −0.567263 −0.283632 0.958933i \(-0.591539\pi\)
−0.283632 + 0.958933i \(0.591539\pi\)
\(242\) 26.6993 1.71630
\(243\) 5.02300 0.322226
\(244\) 21.7278 1.39098
\(245\) 20.7861 1.32798
\(246\) −42.5953 −2.71578
\(247\) −28.1180 −1.78911
\(248\) 57.1333 3.62797
\(249\) −15.8695 −1.00569
\(250\) −5.49250 −0.347376
\(251\) 23.7635 1.49994 0.749970 0.661472i \(-0.230068\pi\)
0.749970 + 0.661472i \(0.230068\pi\)
\(252\) −0.892336 −0.0562119
\(253\) −4.41594 −0.277628
\(254\) 0.947308 0.0594394
\(255\) 44.9376 2.81410
\(256\) −31.6031 −1.97520
\(257\) −11.6179 −0.724705 −0.362353 0.932041i \(-0.618026\pi\)
−0.362353 + 0.932041i \(0.618026\pi\)
\(258\) −5.48681 −0.341594
\(259\) 2.67053 0.165939
\(260\) 45.2110 2.80387
\(261\) 4.31036 0.266805
\(262\) 10.4236 0.643974
\(263\) 9.71188 0.598860 0.299430 0.954118i \(-0.403203\pi\)
0.299430 + 0.954118i \(0.403203\pi\)
\(264\) −6.86880 −0.422746
\(265\) −35.5934 −2.18649
\(266\) 8.72217 0.534791
\(267\) 15.2755 0.934843
\(268\) 12.5521 0.766740
\(269\) 6.09983 0.371913 0.185956 0.982558i \(-0.440462\pi\)
0.185956 + 0.982558i \(0.440462\pi\)
\(270\) 35.9779 2.18954
\(271\) 9.59737 0.582999 0.291499 0.956571i \(-0.405846\pi\)
0.291499 + 0.956571i \(0.405846\pi\)
\(272\) 48.3243 2.93009
\(273\) −2.69736 −0.163252
\(274\) 25.3251 1.52995
\(275\) −2.68139 −0.161694
\(276\) −57.1109 −3.43767
\(277\) −3.05396 −0.183495 −0.0917475 0.995782i \(-0.529245\pi\)
−0.0917475 + 0.995782i \(0.529245\pi\)
\(278\) −58.5849 −3.51369
\(279\) −4.74450 −0.284046
\(280\) −7.55343 −0.451404
\(281\) −14.2595 −0.850650 −0.425325 0.905041i \(-0.639840\pi\)
−0.425325 + 0.905041i \(0.639840\pi\)
\(282\) 15.5559 0.926338
\(283\) 6.62530 0.393833 0.196917 0.980420i \(-0.436907\pi\)
0.196917 + 0.980420i \(0.436907\pi\)
\(284\) 54.2638 3.21997
\(285\) 46.7407 2.76868
\(286\) −5.39297 −0.318893
\(287\) 3.82329 0.225682
\(288\) −1.78092 −0.104942
\(289\) 45.3630 2.66841
\(290\) 67.7438 3.97805
\(291\) −6.10910 −0.358122
\(292\) 46.7667 2.73681
\(293\) 30.7371 1.79568 0.897841 0.440320i \(-0.145135\pi\)
0.897841 + 0.440320i \(0.145135\pi\)
\(294\) −32.0667 −1.87017
\(295\) 18.4823 1.07608
\(296\) 37.1915 2.16171
\(297\) −2.93662 −0.170400
\(298\) −13.8160 −0.800339
\(299\) −24.1505 −1.39666
\(300\) −34.6782 −2.00215
\(301\) 0.492488 0.0283865
\(302\) 20.1814 1.16131
\(303\) 21.4381 1.23159
\(304\) 50.2632 2.88279
\(305\) −15.2733 −0.874546
\(306\) −9.69810 −0.554403
\(307\) −30.6461 −1.74907 −0.874533 0.484966i \(-0.838832\pi\)
−0.874533 + 0.484966i \(0.838832\pi\)
\(308\) 1.14471 0.0652261
\(309\) 10.6155 0.603892
\(310\) −74.5669 −4.23512
\(311\) −19.5707 −1.10975 −0.554877 0.831932i \(-0.687235\pi\)
−0.554877 + 0.831932i \(0.687235\pi\)
\(312\) −37.5651 −2.12670
\(313\) 4.20795 0.237848 0.118924 0.992903i \(-0.462056\pi\)
0.118924 + 0.992903i \(0.462056\pi\)
\(314\) −24.4848 −1.38176
\(315\) 0.627257 0.0353419
\(316\) −3.89435 −0.219074
\(317\) −11.0157 −0.618701 −0.309350 0.950948i \(-0.600112\pi\)
−0.309350 + 0.950948i \(0.600112\pi\)
\(318\) 54.9098 3.07919
\(319\) −5.52945 −0.309590
\(320\) 9.30032 0.519904
\(321\) 22.4872 1.25511
\(322\) 7.49146 0.417483
\(323\) 64.8652 3.60920
\(324\) −44.3241 −2.46245
\(325\) −14.6644 −0.813432
\(326\) 21.5045 1.19102
\(327\) 29.4612 1.62921
\(328\) 53.2455 2.93999
\(329\) −1.39627 −0.0769789
\(330\) 8.96475 0.493493
\(331\) 27.6843 1.52167 0.760833 0.648948i \(-0.224791\pi\)
0.760833 + 0.648948i \(0.224791\pi\)
\(332\) 36.8320 2.02142
\(333\) −3.08848 −0.169248
\(334\) −17.6190 −0.964067
\(335\) −8.82333 −0.482070
\(336\) 4.82175 0.263048
\(337\) 21.6127 1.17732 0.588660 0.808381i \(-0.299656\pi\)
0.588660 + 0.808381i \(0.299656\pi\)
\(338\) 3.22530 0.175433
\(339\) −5.93084 −0.322119
\(340\) −104.297 −5.65629
\(341\) 6.08637 0.329596
\(342\) −10.0872 −0.545454
\(343\) 5.83162 0.314878
\(344\) 6.85869 0.369796
\(345\) 40.1455 2.16136
\(346\) −12.9241 −0.694804
\(347\) 29.6079 1.58943 0.794717 0.606980i \(-0.207619\pi\)
0.794717 + 0.606980i \(0.207619\pi\)
\(348\) −71.5119 −3.83344
\(349\) 9.96564 0.533449 0.266724 0.963773i \(-0.414059\pi\)
0.266724 + 0.963773i \(0.414059\pi\)
\(350\) 4.54887 0.243147
\(351\) −16.0602 −0.857230
\(352\) 2.28461 0.121770
\(353\) −13.1278 −0.698723 −0.349362 0.936988i \(-0.613602\pi\)
−0.349362 + 0.936988i \(0.613602\pi\)
\(354\) −28.5126 −1.51543
\(355\) −38.1441 −2.02448
\(356\) −35.4532 −1.87901
\(357\) 6.22252 0.329330
\(358\) −3.14554 −0.166247
\(359\) −30.8915 −1.63039 −0.815195 0.579186i \(-0.803370\pi\)
−0.815195 + 0.579186i \(0.803370\pi\)
\(360\) 8.73556 0.460405
\(361\) 48.4678 2.55094
\(362\) −26.9425 −1.41607
\(363\) 19.8119 1.03985
\(364\) 6.26037 0.328132
\(365\) −32.8741 −1.72071
\(366\) 23.5620 1.23161
\(367\) −5.79545 −0.302520 −0.151260 0.988494i \(-0.548333\pi\)
−0.151260 + 0.988494i \(0.548333\pi\)
\(368\) 43.1710 2.25044
\(369\) −4.42164 −0.230182
\(370\) −48.5400 −2.52348
\(371\) −4.92862 −0.255881
\(372\) 78.7146 4.08116
\(373\) −30.6891 −1.58902 −0.794512 0.607249i \(-0.792273\pi\)
−0.794512 + 0.607249i \(0.792273\pi\)
\(374\) 12.4410 0.643308
\(375\) −4.07564 −0.210465
\(376\) −19.4453 −1.00282
\(377\) −30.2402 −1.55745
\(378\) 4.98186 0.256239
\(379\) 0.770433 0.0395745 0.0197873 0.999804i \(-0.493701\pi\)
0.0197873 + 0.999804i \(0.493701\pi\)
\(380\) −108.482 −5.56498
\(381\) 0.702938 0.0360126
\(382\) −12.4067 −0.634779
\(383\) −23.9926 −1.22597 −0.612984 0.790096i \(-0.710031\pi\)
−0.612984 + 0.790096i \(0.710031\pi\)
\(384\) −27.9807 −1.42788
\(385\) −0.804662 −0.0410094
\(386\) −20.0889 −1.02250
\(387\) −0.569564 −0.0289526
\(388\) 14.1787 0.719817
\(389\) 17.3394 0.879141 0.439571 0.898208i \(-0.355131\pi\)
0.439571 + 0.898208i \(0.355131\pi\)
\(390\) 49.0277 2.48261
\(391\) 55.7126 2.81751
\(392\) 40.0844 2.02457
\(393\) 7.73473 0.390166
\(394\) 21.4563 1.08095
\(395\) 2.73749 0.137738
\(396\) −1.32386 −0.0665266
\(397\) 27.9041 1.40047 0.700233 0.713914i \(-0.253079\pi\)
0.700233 + 0.713914i \(0.253079\pi\)
\(398\) −56.7879 −2.84652
\(399\) 6.47218 0.324014
\(400\) 26.2137 1.31069
\(401\) 8.31671 0.415317 0.207658 0.978201i \(-0.433416\pi\)
0.207658 + 0.978201i \(0.433416\pi\)
\(402\) 13.6117 0.678891
\(403\) 33.2860 1.65810
\(404\) −49.7562 −2.47546
\(405\) 31.1571 1.54821
\(406\) 9.38049 0.465546
\(407\) 3.96198 0.196388
\(408\) 86.6586 4.29024
\(409\) 12.2841 0.607411 0.303705 0.952766i \(-0.401776\pi\)
0.303705 + 0.952766i \(0.401776\pi\)
\(410\) −69.4927 −3.43200
\(411\) 18.7922 0.926951
\(412\) −24.6377 −1.21381
\(413\) 2.55925 0.125932
\(414\) −8.66389 −0.425807
\(415\) −25.8906 −1.27092
\(416\) 12.4944 0.612589
\(417\) −43.4722 −2.12884
\(418\) 12.9402 0.632924
\(419\) −14.2080 −0.694105 −0.347053 0.937846i \(-0.612817\pi\)
−0.347053 + 0.937846i \(0.612817\pi\)
\(420\) −10.4066 −0.507792
\(421\) 3.46179 0.168717 0.0843586 0.996435i \(-0.473116\pi\)
0.0843586 + 0.996435i \(0.473116\pi\)
\(422\) 60.0607 2.92371
\(423\) 1.61479 0.0785138
\(424\) −68.6390 −3.33341
\(425\) 33.8291 1.64095
\(426\) 58.8448 2.85104
\(427\) −2.11489 −0.102347
\(428\) −52.1911 −2.52275
\(429\) −4.00179 −0.193208
\(430\) −8.95155 −0.431682
\(431\) 27.1709 1.30878 0.654388 0.756159i \(-0.272926\pi\)
0.654388 + 0.756159i \(0.272926\pi\)
\(432\) 28.7089 1.38126
\(433\) −1.63696 −0.0786672 −0.0393336 0.999226i \(-0.512524\pi\)
−0.0393336 + 0.999226i \(0.512524\pi\)
\(434\) −10.3253 −0.495630
\(435\) 50.2685 2.41019
\(436\) −68.3772 −3.27468
\(437\) 57.9479 2.77203
\(438\) 50.7148 2.42324
\(439\) −3.27286 −0.156205 −0.0781026 0.996945i \(-0.524886\pi\)
−0.0781026 + 0.996945i \(0.524886\pi\)
\(440\) −11.2062 −0.534235
\(441\) −3.32871 −0.158510
\(442\) 68.0390 3.23629
\(443\) 15.4438 0.733756 0.366878 0.930269i \(-0.380427\pi\)
0.366878 + 0.930269i \(0.380427\pi\)
\(444\) 51.2400 2.43174
\(445\) 24.9214 1.18139
\(446\) −20.6584 −0.978205
\(447\) −10.2520 −0.484903
\(448\) 1.28782 0.0608436
\(449\) 19.9001 0.939145 0.469572 0.882894i \(-0.344408\pi\)
0.469572 + 0.882894i \(0.344408\pi\)
\(450\) −5.26078 −0.247995
\(451\) 5.67221 0.267094
\(452\) 13.7650 0.647452
\(453\) 14.9754 0.703604
\(454\) 16.1136 0.756248
\(455\) −4.40065 −0.206306
\(456\) 90.1356 4.22099
\(457\) −15.1854 −0.710345 −0.355172 0.934801i \(-0.615578\pi\)
−0.355172 + 0.934801i \(0.615578\pi\)
\(458\) 12.2813 0.573869
\(459\) 37.0491 1.72931
\(460\) −93.1745 −4.34428
\(461\) −22.9396 −1.06841 −0.534203 0.845356i \(-0.679388\pi\)
−0.534203 + 0.845356i \(0.679388\pi\)
\(462\) 1.24135 0.0577528
\(463\) 1.90155 0.0883726 0.0441863 0.999023i \(-0.485930\pi\)
0.0441863 + 0.999023i \(0.485930\pi\)
\(464\) 54.0569 2.50953
\(465\) −55.3315 −2.56594
\(466\) 30.5156 1.41361
\(467\) 22.3592 1.03466 0.517330 0.855786i \(-0.326926\pi\)
0.517330 + 0.855786i \(0.326926\pi\)
\(468\) −7.24013 −0.334675
\(469\) −1.22177 −0.0564160
\(470\) 25.3788 1.17064
\(471\) −18.1687 −0.837168
\(472\) 35.6417 1.64054
\(473\) 0.730652 0.0335954
\(474\) −4.22311 −0.193974
\(475\) 35.1864 1.61446
\(476\) −14.4420 −0.661947
\(477\) 5.69997 0.260984
\(478\) 11.6131 0.531172
\(479\) −28.8129 −1.31649 −0.658247 0.752802i \(-0.728702\pi\)
−0.658247 + 0.752802i \(0.728702\pi\)
\(480\) −20.7695 −0.947995
\(481\) 21.6679 0.987969
\(482\) 22.1642 1.00955
\(483\) 5.55894 0.252941
\(484\) −45.9819 −2.09009
\(485\) −9.96678 −0.452568
\(486\) −12.6422 −0.573461
\(487\) −25.4891 −1.15502 −0.577510 0.816383i \(-0.695976\pi\)
−0.577510 + 0.816383i \(0.695976\pi\)
\(488\) −29.4533 −1.33329
\(489\) 15.9572 0.721608
\(490\) −52.3157 −2.36338
\(491\) −6.17984 −0.278892 −0.139446 0.990230i \(-0.544532\pi\)
−0.139446 + 0.990230i \(0.544532\pi\)
\(492\) 73.3582 3.30724
\(493\) 69.7609 3.14187
\(494\) 70.7690 3.18405
\(495\) 0.930594 0.0418271
\(496\) −59.5014 −2.67169
\(497\) −5.28182 −0.236922
\(498\) 39.9413 1.78981
\(499\) −18.2921 −0.818866 −0.409433 0.912340i \(-0.634273\pi\)
−0.409433 + 0.912340i \(0.634273\pi\)
\(500\) 9.45925 0.423031
\(501\) −13.0739 −0.584101
\(502\) −59.8093 −2.66942
\(503\) 17.8505 0.795915 0.397958 0.917404i \(-0.369719\pi\)
0.397958 + 0.917404i \(0.369719\pi\)
\(504\) 1.20961 0.0538805
\(505\) 34.9755 1.55639
\(506\) 11.1143 0.494090
\(507\) 2.39330 0.106290
\(508\) −1.63147 −0.0723846
\(509\) 11.4984 0.509657 0.254829 0.966986i \(-0.417981\pi\)
0.254829 + 0.966986i \(0.417981\pi\)
\(510\) −113.102 −5.00822
\(511\) −4.55208 −0.201372
\(512\) 49.5763 2.19098
\(513\) 38.5357 1.70139
\(514\) 29.2406 1.28975
\(515\) 17.3188 0.763155
\(516\) 9.44946 0.415989
\(517\) −2.07150 −0.0911043
\(518\) −6.72134 −0.295319
\(519\) −9.59017 −0.420962
\(520\) −61.2861 −2.68758
\(521\) −40.1587 −1.75939 −0.879693 0.475543i \(-0.842252\pi\)
−0.879693 + 0.475543i \(0.842252\pi\)
\(522\) −10.8486 −0.474829
\(523\) 34.1629 1.49384 0.746920 0.664914i \(-0.231532\pi\)
0.746920 + 0.664914i \(0.231532\pi\)
\(524\) −17.9517 −0.784224
\(525\) 3.37543 0.147316
\(526\) −24.4434 −1.06578
\(527\) −76.7872 −3.34490
\(528\) 7.15351 0.311317
\(529\) 26.7714 1.16397
\(530\) 89.5835 3.89126
\(531\) −2.95978 −0.128444
\(532\) −15.0214 −0.651262
\(533\) 31.0210 1.34367
\(534\) −38.4461 −1.66373
\(535\) 36.6871 1.58612
\(536\) −17.0151 −0.734939
\(537\) −2.33411 −0.100724
\(538\) −15.3524 −0.661888
\(539\) 4.27016 0.183929
\(540\) −61.9615 −2.66640
\(541\) 32.3019 1.38877 0.694383 0.719606i \(-0.255678\pi\)
0.694383 + 0.719606i \(0.255678\pi\)
\(542\) −24.1552 −1.03755
\(543\) −19.9924 −0.857955
\(544\) −28.8233 −1.23579
\(545\) 48.0650 2.05888
\(546\) 6.78887 0.290537
\(547\) −29.3555 −1.25515 −0.627575 0.778556i \(-0.715952\pi\)
−0.627575 + 0.778556i \(0.715952\pi\)
\(548\) −43.6153 −1.86315
\(549\) 2.44588 0.104388
\(550\) 6.74867 0.287764
\(551\) 72.5600 3.09116
\(552\) 77.4173 3.29510
\(553\) 0.379060 0.0161193
\(554\) 7.68639 0.326563
\(555\) −36.0186 −1.52890
\(556\) 100.896 4.27893
\(557\) −21.4737 −0.909868 −0.454934 0.890525i \(-0.650337\pi\)
−0.454934 + 0.890525i \(0.650337\pi\)
\(558\) 11.9412 0.505512
\(559\) 3.99589 0.169008
\(560\) 7.86652 0.332421
\(561\) 9.23168 0.389762
\(562\) 35.8891 1.51389
\(563\) −20.5242 −0.864992 −0.432496 0.901636i \(-0.642367\pi\)
−0.432496 + 0.901636i \(0.642367\pi\)
\(564\) −26.7905 −1.12808
\(565\) −9.67596 −0.407071
\(566\) −16.6749 −0.700900
\(567\) 4.31432 0.181185
\(568\) −73.5578 −3.08642
\(569\) 14.8410 0.622165 0.311083 0.950383i \(-0.399308\pi\)
0.311083 + 0.950383i \(0.399308\pi\)
\(570\) −117.640 −4.92738
\(571\) −24.9780 −1.04530 −0.522648 0.852549i \(-0.675056\pi\)
−0.522648 + 0.852549i \(0.675056\pi\)
\(572\) 9.28784 0.388344
\(573\) −9.20621 −0.384595
\(574\) −9.62267 −0.401642
\(575\) 30.2215 1.26032
\(576\) −1.48936 −0.0620568
\(577\) 15.6073 0.649740 0.324870 0.945759i \(-0.394680\pi\)
0.324870 + 0.945759i \(0.394680\pi\)
\(578\) −114.172 −4.74893
\(579\) −14.9067 −0.619502
\(580\) −116.669 −4.84443
\(581\) −3.58507 −0.148734
\(582\) 15.3757 0.637344
\(583\) −7.31207 −0.302835
\(584\) −63.3950 −2.62331
\(585\) 5.08936 0.210419
\(586\) −77.3609 −3.19575
\(587\) 38.5200 1.58989 0.794945 0.606681i \(-0.207499\pi\)
0.794945 + 0.606681i \(0.207499\pi\)
\(588\) 55.2257 2.27747
\(589\) −79.8682 −3.29091
\(590\) −46.5174 −1.91509
\(591\) 15.9214 0.654919
\(592\) −38.7330 −1.59192
\(593\) −21.2432 −0.872353 −0.436176 0.899861i \(-0.643668\pi\)
−0.436176 + 0.899861i \(0.643668\pi\)
\(594\) 7.39105 0.303258
\(595\) 10.1518 0.416184
\(596\) 23.7941 0.974644
\(597\) −42.1388 −1.72463
\(598\) 60.7833 2.48561
\(599\) 4.24263 0.173349 0.0866746 0.996237i \(-0.472376\pi\)
0.0866746 + 0.996237i \(0.472376\pi\)
\(600\) 47.0083 1.91911
\(601\) −20.2350 −0.825404 −0.412702 0.910866i \(-0.635415\pi\)
−0.412702 + 0.910866i \(0.635415\pi\)
\(602\) −1.23952 −0.0505191
\(603\) 1.41298 0.0575409
\(604\) −34.7567 −1.41423
\(605\) 32.3224 1.31409
\(606\) −53.9566 −2.19184
\(607\) 0.896137 0.0363731 0.0181865 0.999835i \(-0.494211\pi\)
0.0181865 + 0.999835i \(0.494211\pi\)
\(608\) −29.9798 −1.21584
\(609\) 6.96068 0.282061
\(610\) 38.4407 1.55642
\(611\) −11.3289 −0.458318
\(612\) 16.7022 0.675146
\(613\) 35.2242 1.42269 0.711346 0.702842i \(-0.248086\pi\)
0.711346 + 0.702842i \(0.248086\pi\)
\(614\) 77.1318 3.11279
\(615\) −51.5663 −2.07935
\(616\) −1.55173 −0.0625208
\(617\) 0.444864 0.0179096 0.00895478 0.999960i \(-0.497150\pi\)
0.00895478 + 0.999960i \(0.497150\pi\)
\(618\) −26.7176 −1.07474
\(619\) 0.838571 0.0337050 0.0168525 0.999858i \(-0.494635\pi\)
0.0168525 + 0.999858i \(0.494635\pi\)
\(620\) 128.420 5.15748
\(621\) 33.0982 1.32819
\(622\) 49.2567 1.97501
\(623\) 3.45086 0.138256
\(624\) 39.1221 1.56614
\(625\) −28.0681 −1.12273
\(626\) −10.5908 −0.423294
\(627\) 9.60209 0.383470
\(628\) 42.1681 1.68269
\(629\) −49.9854 −1.99305
\(630\) −1.57871 −0.0628975
\(631\) −14.0658 −0.559951 −0.279975 0.960007i \(-0.590326\pi\)
−0.279975 + 0.960007i \(0.590326\pi\)
\(632\) 5.27902 0.209988
\(633\) 44.5674 1.77139
\(634\) 27.7248 1.10109
\(635\) 1.14682 0.0455102
\(636\) −94.5665 −3.74980
\(637\) 23.3533 0.925290
\(638\) 13.9168 0.550973
\(639\) 6.10844 0.241646
\(640\) −45.6495 −1.80445
\(641\) 22.6468 0.894496 0.447248 0.894410i \(-0.352404\pi\)
0.447248 + 0.894410i \(0.352404\pi\)
\(642\) −56.5970 −2.23371
\(643\) −33.4321 −1.31843 −0.659217 0.751952i \(-0.729112\pi\)
−0.659217 + 0.751952i \(0.729112\pi\)
\(644\) −12.9019 −0.508405
\(645\) −6.64239 −0.261544
\(646\) −163.256 −6.42323
\(647\) 5.78670 0.227498 0.113749 0.993509i \(-0.463714\pi\)
0.113749 + 0.993509i \(0.463714\pi\)
\(648\) 60.0839 2.36032
\(649\) 3.79689 0.149041
\(650\) 36.9081 1.44765
\(651\) −7.66175 −0.300288
\(652\) −37.0354 −1.45042
\(653\) 1.82953 0.0715952 0.0357976 0.999359i \(-0.488603\pi\)
0.0357976 + 0.999359i \(0.488603\pi\)
\(654\) −74.1496 −2.89948
\(655\) 12.6189 0.493063
\(656\) −55.4525 −2.16505
\(657\) 5.26449 0.205387
\(658\) 3.51421 0.136998
\(659\) 16.2713 0.633840 0.316920 0.948452i \(-0.397351\pi\)
0.316920 + 0.948452i \(0.397351\pi\)
\(660\) −15.4392 −0.600970
\(661\) 50.6801 1.97123 0.985614 0.169014i \(-0.0540583\pi\)
0.985614 + 0.169014i \(0.0540583\pi\)
\(662\) −69.6773 −2.70809
\(663\) 50.4875 1.96077
\(664\) −49.9279 −1.93758
\(665\) 10.5591 0.409466
\(666\) 7.77325 0.301207
\(667\) 62.3216 2.41310
\(668\) 30.3436 1.17403
\(669\) −15.3293 −0.592666
\(670\) 22.2070 0.857933
\(671\) −3.13764 −0.121127
\(672\) −2.87596 −0.110942
\(673\) −34.2687 −1.32096 −0.660481 0.750843i \(-0.729648\pi\)
−0.660481 + 0.750843i \(0.729648\pi\)
\(674\) −54.3961 −2.09526
\(675\) 20.0975 0.773552
\(676\) −5.55466 −0.213641
\(677\) −1.02388 −0.0393509 −0.0196754 0.999806i \(-0.506263\pi\)
−0.0196754 + 0.999806i \(0.506263\pi\)
\(678\) 14.9271 0.573271
\(679\) −1.38010 −0.0529634
\(680\) 141.380 5.42169
\(681\) 11.9569 0.458189
\(682\) −15.3185 −0.586577
\(683\) 15.6370 0.598332 0.299166 0.954201i \(-0.403292\pi\)
0.299166 + 0.954201i \(0.403292\pi\)
\(684\) 17.3723 0.664248
\(685\) 30.6588 1.17141
\(686\) −14.6773 −0.560383
\(687\) 9.11321 0.347691
\(688\) −7.14298 −0.272324
\(689\) −39.9893 −1.52347
\(690\) −101.040 −3.84654
\(691\) −26.4333 −1.00557 −0.502785 0.864411i \(-0.667691\pi\)
−0.502785 + 0.864411i \(0.667691\pi\)
\(692\) 22.2580 0.846124
\(693\) 0.128859 0.00489496
\(694\) −74.5188 −2.82869
\(695\) −70.9234 −2.69028
\(696\) 96.9387 3.67445
\(697\) −71.5620 −2.71060
\(698\) −25.0821 −0.949371
\(699\) 22.6437 0.856465
\(700\) −7.83412 −0.296102
\(701\) 35.4643 1.33947 0.669735 0.742600i \(-0.266408\pi\)
0.669735 + 0.742600i \(0.266408\pi\)
\(702\) 40.4212 1.52560
\(703\) −51.9910 −1.96088
\(704\) 1.91059 0.0720082
\(705\) 18.8321 0.709257
\(706\) 33.0408 1.24351
\(707\) 4.84307 0.182142
\(708\) 49.1048 1.84547
\(709\) 13.2221 0.496566 0.248283 0.968687i \(-0.420134\pi\)
0.248283 + 0.968687i \(0.420134\pi\)
\(710\) 96.0032 3.60294
\(711\) −0.438384 −0.0164407
\(712\) 48.0589 1.80108
\(713\) −68.5986 −2.56904
\(714\) −15.6612 −0.586105
\(715\) −6.52878 −0.244162
\(716\) 5.41729 0.202454
\(717\) 8.61738 0.321822
\(718\) 77.7494 2.90158
\(719\) 36.1837 1.34943 0.674713 0.738080i \(-0.264268\pi\)
0.674713 + 0.738080i \(0.264268\pi\)
\(720\) −9.09765 −0.339049
\(721\) 2.39813 0.0893110
\(722\) −121.986 −4.53987
\(723\) 16.4467 0.611658
\(724\) 46.4007 1.72447
\(725\) 37.8421 1.40542
\(726\) −49.8637 −1.85061
\(727\) 21.9825 0.815286 0.407643 0.913141i \(-0.366351\pi\)
0.407643 + 0.913141i \(0.366351\pi\)
\(728\) −8.48630 −0.314523
\(729\) 21.2962 0.788749
\(730\) 82.7394 3.06232
\(731\) −9.21809 −0.340943
\(732\) −40.5789 −1.49984
\(733\) 19.8639 0.733689 0.366845 0.930282i \(-0.380438\pi\)
0.366845 + 0.930282i \(0.380438\pi\)
\(734\) 14.5863 0.538390
\(735\) −38.8202 −1.43191
\(736\) −25.7495 −0.949141
\(737\) −1.81261 −0.0667682
\(738\) 11.1286 0.409651
\(739\) −5.39886 −0.198600 −0.0993002 0.995058i \(-0.531660\pi\)
−0.0993002 + 0.995058i \(0.531660\pi\)
\(740\) 83.5963 3.07306
\(741\) 52.5133 1.92912
\(742\) 12.4046 0.455389
\(743\) −14.4042 −0.528439 −0.264220 0.964463i \(-0.585114\pi\)
−0.264220 + 0.964463i \(0.585114\pi\)
\(744\) −106.702 −3.91189
\(745\) −16.7258 −0.612785
\(746\) 77.2401 2.82796
\(747\) 4.14615 0.151700
\(748\) −21.4260 −0.783413
\(749\) 5.08006 0.185621
\(750\) 10.2578 0.374562
\(751\) 3.43080 0.125192 0.0625958 0.998039i \(-0.480062\pi\)
0.0625958 + 0.998039i \(0.480062\pi\)
\(752\) 20.2513 0.738489
\(753\) −44.3808 −1.61733
\(754\) 76.1103 2.77177
\(755\) 24.4318 0.889164
\(756\) −8.57982 −0.312045
\(757\) −53.0727 −1.92896 −0.964479 0.264158i \(-0.914906\pi\)
−0.964479 + 0.264158i \(0.914906\pi\)
\(758\) −1.93907 −0.0704302
\(759\) 8.24721 0.299355
\(760\) 147.053 5.33418
\(761\) 8.29150 0.300567 0.150283 0.988643i \(-0.451981\pi\)
0.150283 + 0.988643i \(0.451981\pi\)
\(762\) −1.76919 −0.0640911
\(763\) 6.65556 0.240947
\(764\) 21.3669 0.773027
\(765\) −11.7406 −0.424483
\(766\) 60.3860 2.18184
\(767\) 20.7650 0.749779
\(768\) 59.0221 2.12978
\(769\) 4.76233 0.171734 0.0858670 0.996307i \(-0.472634\pi\)
0.0858670 + 0.996307i \(0.472634\pi\)
\(770\) 2.02522 0.0729838
\(771\) 21.6976 0.781421
\(772\) 34.5974 1.24519
\(773\) 36.9428 1.32874 0.664369 0.747404i \(-0.268700\pi\)
0.664369 + 0.747404i \(0.268700\pi\)
\(774\) 1.43351 0.0515265
\(775\) −41.6536 −1.49624
\(776\) −19.2201 −0.689962
\(777\) −4.98749 −0.178925
\(778\) −43.6407 −1.56460
\(779\) −74.4333 −2.66685
\(780\) −84.4361 −3.02330
\(781\) −7.83607 −0.280397
\(782\) −140.220 −5.01427
\(783\) 41.4442 1.48109
\(784\) −41.7458 −1.49092
\(785\) −29.6416 −1.05795
\(786\) −19.4672 −0.694372
\(787\) 31.1118 1.10902 0.554508 0.832178i \(-0.312906\pi\)
0.554508 + 0.832178i \(0.312906\pi\)
\(788\) −36.9523 −1.31637
\(789\) −18.1379 −0.645728
\(790\) −6.88986 −0.245130
\(791\) −1.33983 −0.0476389
\(792\) 1.79457 0.0637674
\(793\) −17.1596 −0.609354
\(794\) −70.2306 −2.49239
\(795\) 66.4744 2.35760
\(796\) 97.8010 3.46646
\(797\) −0.208018 −0.00736837 −0.00368418 0.999993i \(-0.501173\pi\)
−0.00368418 + 0.999993i \(0.501173\pi\)
\(798\) −16.2896 −0.576644
\(799\) 26.1345 0.924573
\(800\) −15.6353 −0.552792
\(801\) −3.99093 −0.141013
\(802\) −20.9320 −0.739133
\(803\) −6.75343 −0.238324
\(804\) −23.4423 −0.826745
\(805\) 9.06923 0.319648
\(806\) −83.7761 −2.95089
\(807\) −11.3920 −0.401019
\(808\) 67.4475 2.37279
\(809\) 33.6358 1.18257 0.591286 0.806462i \(-0.298621\pi\)
0.591286 + 0.806462i \(0.298621\pi\)
\(810\) −78.4179 −2.75532
\(811\) −34.6459 −1.21658 −0.608292 0.793713i \(-0.708145\pi\)
−0.608292 + 0.793713i \(0.708145\pi\)
\(812\) −16.1552 −0.566936
\(813\) −17.9241 −0.628624
\(814\) −9.97174 −0.349509
\(815\) 26.0336 0.911916
\(816\) −90.2505 −3.15940
\(817\) −9.58795 −0.335440
\(818\) −30.9174 −1.08100
\(819\) 0.704725 0.0246251
\(820\) 119.681 4.17945
\(821\) −0.845559 −0.0295102 −0.0147551 0.999891i \(-0.504697\pi\)
−0.0147551 + 0.999891i \(0.504697\pi\)
\(822\) −47.2973 −1.64968
\(823\) 46.0151 1.60399 0.801994 0.597333i \(-0.203773\pi\)
0.801994 + 0.597333i \(0.203773\pi\)
\(824\) 33.3978 1.16347
\(825\) 5.00777 0.174348
\(826\) −6.44126 −0.224120
\(827\) −7.07276 −0.245944 −0.122972 0.992410i \(-0.539243\pi\)
−0.122972 + 0.992410i \(0.539243\pi\)
\(828\) 14.9211 0.518543
\(829\) −8.42234 −0.292520 −0.146260 0.989246i \(-0.546724\pi\)
−0.146260 + 0.989246i \(0.546724\pi\)
\(830\) 65.1629 2.26184
\(831\) 5.70359 0.197855
\(832\) 10.4489 0.362252
\(833\) −53.8734 −1.86660
\(834\) 109.413 3.78867
\(835\) −21.3297 −0.738145
\(836\) −22.2857 −0.770767
\(837\) −45.6184 −1.57680
\(838\) 35.7594 1.23529
\(839\) 49.5685 1.71129 0.855647 0.517560i \(-0.173160\pi\)
0.855647 + 0.517560i \(0.173160\pi\)
\(840\) 14.1068 0.486731
\(841\) 49.0365 1.69091
\(842\) −8.71282 −0.300264
\(843\) 26.6311 0.917223
\(844\) −103.437 −3.56046
\(845\) 3.90458 0.134322
\(846\) −4.06419 −0.139730
\(847\) 4.47569 0.153786
\(848\) 71.4841 2.45477
\(849\) −12.3734 −0.424655
\(850\) −85.1429 −2.92038
\(851\) −44.6549 −1.53075
\(852\) −101.343 −3.47196
\(853\) 0.428189 0.0146609 0.00733046 0.999973i \(-0.497667\pi\)
0.00733046 + 0.999973i \(0.497667\pi\)
\(854\) 5.32288 0.182145
\(855\) −12.2117 −0.417631
\(856\) 70.7481 2.41812
\(857\) 29.4590 1.00630 0.503150 0.864199i \(-0.332174\pi\)
0.503150 + 0.864199i \(0.332174\pi\)
\(858\) 10.0719 0.343850
\(859\) −17.1675 −0.585749 −0.292874 0.956151i \(-0.594612\pi\)
−0.292874 + 0.956151i \(0.594612\pi\)
\(860\) 15.4165 0.525697
\(861\) −7.14038 −0.243344
\(862\) −68.3852 −2.32921
\(863\) 6.55695 0.223201 0.111601 0.993753i \(-0.464402\pi\)
0.111601 + 0.993753i \(0.464402\pi\)
\(864\) −17.1236 −0.582556
\(865\) −15.6460 −0.531981
\(866\) 4.11999 0.140003
\(867\) −84.7200 −2.87724
\(868\) 17.7823 0.603572
\(869\) 0.562371 0.0190771
\(870\) −126.518 −4.28938
\(871\) −9.91303 −0.335890
\(872\) 92.6894 3.13886
\(873\) 1.59609 0.0540195
\(874\) −145.847 −4.93333
\(875\) −0.920725 −0.0311262
\(876\) −87.3416 −2.95100
\(877\) 45.4608 1.53510 0.767551 0.640988i \(-0.221475\pi\)
0.767551 + 0.640988i \(0.221475\pi\)
\(878\) 8.23732 0.277996
\(879\) −57.4047 −1.93621
\(880\) 11.6707 0.393420
\(881\) 16.4479 0.554144 0.277072 0.960849i \(-0.410636\pi\)
0.277072 + 0.960849i \(0.410636\pi\)
\(882\) 8.37789 0.282098
\(883\) −30.5636 −1.02855 −0.514274 0.857626i \(-0.671939\pi\)
−0.514274 + 0.857626i \(0.671939\pi\)
\(884\) −117.178 −3.94111
\(885\) −34.5177 −1.16030
\(886\) −38.8697 −1.30585
\(887\) −38.6474 −1.29765 −0.648826 0.760937i \(-0.724740\pi\)
−0.648826 + 0.760937i \(0.724740\pi\)
\(888\) −69.4589 −2.33089
\(889\) 0.158800 0.00532599
\(890\) −62.7235 −2.10250
\(891\) 6.40070 0.214431
\(892\) 35.5782 1.19125
\(893\) 27.1831 0.909649
\(894\) 25.8028 0.862974
\(895\) −3.80802 −0.127288
\(896\) −6.32108 −0.211173
\(897\) 45.1035 1.50596
\(898\) −50.0857 −1.67138
\(899\) −85.8963 −2.86480
\(900\) 9.06018 0.302006
\(901\) 92.2510 3.07333
\(902\) −14.2761 −0.475343
\(903\) −0.919772 −0.0306081
\(904\) −18.6593 −0.620599
\(905\) −32.6169 −1.08422
\(906\) −37.6908 −1.25219
\(907\) 45.7578 1.51936 0.759682 0.650295i \(-0.225355\pi\)
0.759682 + 0.650295i \(0.225355\pi\)
\(908\) −27.7510 −0.920950
\(909\) −5.60102 −0.185774
\(910\) 11.0758 0.367159
\(911\) −15.6700 −0.519172 −0.259586 0.965720i \(-0.583586\pi\)
−0.259586 + 0.965720i \(0.583586\pi\)
\(912\) −93.8717 −3.10840
\(913\) −5.31879 −0.176026
\(914\) 38.2196 1.26419
\(915\) 28.5244 0.942988
\(916\) −21.1511 −0.698851
\(917\) 1.74735 0.0577025
\(918\) −93.2473 −3.07762
\(919\) 6.57944 0.217036 0.108518 0.994095i \(-0.465390\pi\)
0.108518 + 0.994095i \(0.465390\pi\)
\(920\) 126.304 4.16411
\(921\) 57.2348 1.88595
\(922\) 57.7358 1.90143
\(923\) −42.8550 −1.41059
\(924\) −2.13787 −0.0703307
\(925\) −27.1148 −0.891529
\(926\) −4.78593 −0.157275
\(927\) −2.77344 −0.0910918
\(928\) −32.2425 −1.05841
\(929\) −48.1614 −1.58012 −0.790062 0.613027i \(-0.789952\pi\)
−0.790062 + 0.613027i \(0.789952\pi\)
\(930\) 139.261 4.56656
\(931\) −56.0350 −1.83647
\(932\) −52.5544 −1.72148
\(933\) 36.5503 1.19660
\(934\) −56.2748 −1.84137
\(935\) 15.0612 0.492553
\(936\) 9.81443 0.320795
\(937\) −10.5352 −0.344170 −0.172085 0.985082i \(-0.555050\pi\)
−0.172085 + 0.985082i \(0.555050\pi\)
\(938\) 3.07501 0.100403
\(939\) −7.85878 −0.256462
\(940\) −43.7078 −1.42559
\(941\) 44.5616 1.45267 0.726333 0.687343i \(-0.241223\pi\)
0.726333 + 0.687343i \(0.241223\pi\)
\(942\) 45.7279 1.48990
\(943\) −63.9306 −2.08187
\(944\) −37.1190 −1.20812
\(945\) 6.03108 0.196191
\(946\) −1.83895 −0.0597893
\(947\) −35.0070 −1.13757 −0.568787 0.822485i \(-0.692587\pi\)
−0.568787 + 0.822485i \(0.692587\pi\)
\(948\) 7.27310 0.236219
\(949\) −36.9341 −1.19893
\(950\) −88.5591 −2.87324
\(951\) 20.5729 0.667121
\(952\) 19.5770 0.634493
\(953\) 45.0703 1.45997 0.729985 0.683464i \(-0.239527\pi\)
0.729985 + 0.683464i \(0.239527\pi\)
\(954\) −14.3460 −0.464469
\(955\) −15.0196 −0.486023
\(956\) −20.0003 −0.646856
\(957\) 10.3268 0.333819
\(958\) 72.5178 2.34294
\(959\) 4.24533 0.137089
\(960\) −17.3693 −0.560592
\(961\) 63.5477 2.04993
\(962\) −54.5349 −1.75827
\(963\) −5.87511 −0.189323
\(964\) −38.1714 −1.22942
\(965\) −24.3198 −0.782882
\(966\) −13.9911 −0.450155
\(967\) 48.4112 1.55680 0.778400 0.627768i \(-0.216031\pi\)
0.778400 + 0.627768i \(0.216031\pi\)
\(968\) 62.3312 2.00340
\(969\) −121.142 −3.89165
\(970\) 25.0849 0.805429
\(971\) −32.8024 −1.05268 −0.526339 0.850275i \(-0.676436\pi\)
−0.526339 + 0.850275i \(0.676436\pi\)
\(972\) 21.7725 0.698354
\(973\) −9.82077 −0.314839
\(974\) 64.1524 2.05557
\(975\) 27.3872 0.877092
\(976\) 30.6741 0.981855
\(977\) 5.16110 0.165118 0.0825592 0.996586i \(-0.473691\pi\)
0.0825592 + 0.996586i \(0.473691\pi\)
\(978\) −40.1619 −1.28424
\(979\) 5.11968 0.163626
\(980\) 90.0988 2.87810
\(981\) −7.69717 −0.245752
\(982\) 15.5538 0.496341
\(983\) −13.9145 −0.443804 −0.221902 0.975069i \(-0.571227\pi\)
−0.221902 + 0.975069i \(0.571227\pi\)
\(984\) −99.4413 −3.17007
\(985\) 25.9752 0.827639
\(986\) −175.578 −5.59155
\(987\) 2.60768 0.0830033
\(988\) −121.879 −3.87750
\(989\) −8.23507 −0.261860
\(990\) −2.34217 −0.0744391
\(991\) −45.2288 −1.43674 −0.718370 0.695661i \(-0.755111\pi\)
−0.718370 + 0.695661i \(0.755111\pi\)
\(992\) 35.4899 1.12681
\(993\) −51.7032 −1.64075
\(994\) 13.2936 0.421647
\(995\) −68.7480 −2.17946
\(996\) −68.7875 −2.17961
\(997\) 31.0000 0.981781 0.490891 0.871221i \(-0.336671\pi\)
0.490891 + 0.871221i \(0.336671\pi\)
\(998\) 46.0385 1.45732
\(999\) −29.6957 −0.939532
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 4027.2.a.c.1.10 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.10 174 1.1 even 1 trivial