Properties

Label 4033.2.a.f.1.5
Level 4033
Weight 2
Character 4033.1
Self dual yes
Analytic conductor 32.204
Analytic rank 0
Dimension 85
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(0\)
Dimension: \(85\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.49324 q^{2} -1.70202 q^{3} +4.21624 q^{4} -1.58478 q^{5} +4.24353 q^{6} +2.99306 q^{7} -5.52560 q^{8} -0.103143 q^{9} +O(q^{10})\) \(q-2.49324 q^{2} -1.70202 q^{3} +4.21624 q^{4} -1.58478 q^{5} +4.24353 q^{6} +2.99306 q^{7} -5.52560 q^{8} -0.103143 q^{9} +3.95124 q^{10} +1.39137 q^{11} -7.17610 q^{12} -6.59651 q^{13} -7.46240 q^{14} +2.69733 q^{15} +5.34417 q^{16} +4.23076 q^{17} +0.257160 q^{18} -3.71775 q^{19} -6.68182 q^{20} -5.09423 q^{21} -3.46902 q^{22} -5.72353 q^{23} +9.40466 q^{24} -2.48846 q^{25} +16.4467 q^{26} +5.28160 q^{27} +12.6194 q^{28} -2.80076 q^{29} -6.72508 q^{30} -6.13831 q^{31} -2.27308 q^{32} -2.36814 q^{33} -10.5483 q^{34} -4.74335 q^{35} -0.434875 q^{36} +1.00000 q^{37} +9.26925 q^{38} +11.2274 q^{39} +8.75688 q^{40} -0.116706 q^{41} +12.7011 q^{42} -9.64444 q^{43} +5.86635 q^{44} +0.163459 q^{45} +14.2701 q^{46} +1.53133 q^{47} -9.09586 q^{48} +1.95838 q^{49} +6.20432 q^{50} -7.20082 q^{51} -27.8124 q^{52} +0.281857 q^{53} -13.1683 q^{54} -2.20502 q^{55} -16.5384 q^{56} +6.32768 q^{57} +6.98297 q^{58} +8.00795 q^{59} +11.3726 q^{60} -8.40487 q^{61} +15.3043 q^{62} -0.308713 q^{63} -5.02100 q^{64} +10.4540 q^{65} +5.90433 q^{66} +12.5217 q^{67} +17.8379 q^{68} +9.74154 q^{69} +11.8263 q^{70} +7.06143 q^{71} +0.569927 q^{72} +6.50223 q^{73} -2.49324 q^{74} +4.23540 q^{75} -15.6749 q^{76} +4.16445 q^{77} -27.9925 q^{78} +1.04239 q^{79} -8.46935 q^{80} -8.67993 q^{81} +0.290976 q^{82} +1.37143 q^{83} -21.4785 q^{84} -6.70484 q^{85} +24.0459 q^{86} +4.76694 q^{87} -7.68817 q^{88} -4.27966 q^{89} -0.407543 q^{90} -19.7437 q^{91} -24.1318 q^{92} +10.4475 q^{93} -3.81796 q^{94} +5.89184 q^{95} +3.86882 q^{96} +6.81532 q^{97} -4.88272 q^{98} -0.143510 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + O(q^{10}) \) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + 9q^{10} + 37q^{11} + 44q^{12} + 14q^{13} + 26q^{14} + 27q^{15} + 85q^{16} + 34q^{17} + 3q^{18} + 15q^{19} + 15q^{20} + 17q^{21} + q^{22} + 72q^{23} + 15q^{24} + 85q^{25} + 33q^{26} + 69q^{27} + 7q^{28} + 19q^{29} - 9q^{30} + 23q^{31} + 51q^{32} + 32q^{33} + 49q^{34} + 40q^{35} + 121q^{36} + 85q^{37} + 84q^{38} + 39q^{39} + 22q^{40} + 55q^{41} - 28q^{42} + 78q^{44} + 28q^{45} + 17q^{46} + 184q^{47} + 97q^{48} + 88q^{49} + 26q^{50} + 27q^{51} + 73q^{52} + 64q^{53} + 31q^{54} + 39q^{55} + 68q^{56} - 33q^{57} + 28q^{58} + 60q^{59} - 22q^{60} + 7q^{61} + 70q^{62} + 28q^{63} + 102q^{64} + 17q^{65} - 15q^{66} + 82q^{67} + 92q^{68} + 22q^{69} - 41q^{70} + 113q^{71} - 19q^{73} + 11q^{74} + 45q^{75} + 34q^{76} + 64q^{77} + 29q^{78} + 23q^{79} + 54q^{80} + 149q^{81} + 4q^{82} + 100q^{83} - 49q^{84} - 5q^{85} - 24q^{86} + 65q^{87} + 14q^{88} + 84q^{89} - 21q^{90} + 32q^{91} + 95q^{92} + 19q^{93} - 47q^{94} + 102q^{95} + 29q^{96} + 7q^{97} + 26q^{98} + 107q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.49324 −1.76299 −0.881493 0.472198i \(-0.843461\pi\)
−0.881493 + 0.472198i \(0.843461\pi\)
\(3\) −1.70202 −0.982659 −0.491330 0.870974i \(-0.663489\pi\)
−0.491330 + 0.870974i \(0.663489\pi\)
\(4\) 4.21624 2.10812
\(5\) −1.58478 −0.708737 −0.354368 0.935106i \(-0.615304\pi\)
−0.354368 + 0.935106i \(0.615304\pi\)
\(6\) 4.24353 1.73241
\(7\) 2.99306 1.13127 0.565634 0.824656i \(-0.308631\pi\)
0.565634 + 0.824656i \(0.308631\pi\)
\(8\) −5.52560 −1.95360
\(9\) −0.103143 −0.0343810
\(10\) 3.95124 1.24949
\(11\) 1.39137 0.419514 0.209757 0.977754i \(-0.432733\pi\)
0.209757 + 0.977754i \(0.432733\pi\)
\(12\) −7.17610 −2.07156
\(13\) −6.59651 −1.82954 −0.914772 0.403972i \(-0.867629\pi\)
−0.914772 + 0.403972i \(0.867629\pi\)
\(14\) −7.46240 −1.99441
\(15\) 2.69733 0.696447
\(16\) 5.34417 1.33604
\(17\) 4.23076 1.02611 0.513055 0.858356i \(-0.328514\pi\)
0.513055 + 0.858356i \(0.328514\pi\)
\(18\) 0.257160 0.0606132
\(19\) −3.71775 −0.852911 −0.426456 0.904508i \(-0.640238\pi\)
−0.426456 + 0.904508i \(0.640238\pi\)
\(20\) −6.68182 −1.49410
\(21\) −5.09423 −1.11165
\(22\) −3.46902 −0.739598
\(23\) −5.72353 −1.19344 −0.596719 0.802450i \(-0.703529\pi\)
−0.596719 + 0.802450i \(0.703529\pi\)
\(24\) 9.40466 1.91972
\(25\) −2.48846 −0.497692
\(26\) 16.4467 3.22546
\(27\) 5.28160 1.01644
\(28\) 12.6194 2.38485
\(29\) −2.80076 −0.520088 −0.260044 0.965597i \(-0.583737\pi\)
−0.260044 + 0.965597i \(0.583737\pi\)
\(30\) −6.72508 −1.22783
\(31\) −6.13831 −1.10247 −0.551236 0.834349i \(-0.685844\pi\)
−0.551236 + 0.834349i \(0.685844\pi\)
\(32\) −2.27308 −0.401828
\(33\) −2.36814 −0.412240
\(34\) −10.5483 −1.80902
\(35\) −4.74335 −0.801772
\(36\) −0.434875 −0.0724792
\(37\) 1.00000 0.164399
\(38\) 9.26925 1.50367
\(39\) 11.2274 1.79782
\(40\) 8.75688 1.38458
\(41\) −0.116706 −0.0182265 −0.00911323 0.999958i \(-0.502901\pi\)
−0.00911323 + 0.999958i \(0.502901\pi\)
\(42\) 12.7011 1.95983
\(43\) −9.64444 −1.47076 −0.735381 0.677654i \(-0.762997\pi\)
−0.735381 + 0.677654i \(0.762997\pi\)
\(44\) 5.86635 0.884386
\(45\) 0.163459 0.0243671
\(46\) 14.2701 2.10401
\(47\) 1.53133 0.223367 0.111683 0.993744i \(-0.464376\pi\)
0.111683 + 0.993744i \(0.464376\pi\)
\(48\) −9.09586 −1.31287
\(49\) 1.95838 0.279769
\(50\) 6.20432 0.877424
\(51\) −7.20082 −1.00832
\(52\) −27.8124 −3.85689
\(53\) 0.281857 0.0387160 0.0193580 0.999813i \(-0.493838\pi\)
0.0193580 + 0.999813i \(0.493838\pi\)
\(54\) −13.1683 −1.79198
\(55\) −2.20502 −0.297325
\(56\) −16.5384 −2.21004
\(57\) 6.32768 0.838121
\(58\) 6.98297 0.916908
\(59\) 8.00795 1.04255 0.521273 0.853390i \(-0.325457\pi\)
0.521273 + 0.853390i \(0.325457\pi\)
\(60\) 11.3726 1.46819
\(61\) −8.40487 −1.07613 −0.538067 0.842902i \(-0.680845\pi\)
−0.538067 + 0.842902i \(0.680845\pi\)
\(62\) 15.3043 1.94364
\(63\) −0.308713 −0.0388942
\(64\) −5.02100 −0.627626
\(65\) 10.4540 1.29666
\(66\) 5.90433 0.726772
\(67\) 12.5217 1.52977 0.764884 0.644168i \(-0.222796\pi\)
0.764884 + 0.644168i \(0.222796\pi\)
\(68\) 17.8379 2.16316
\(69\) 9.74154 1.17274
\(70\) 11.8263 1.41351
\(71\) 7.06143 0.838037 0.419019 0.907978i \(-0.362374\pi\)
0.419019 + 0.907978i \(0.362374\pi\)
\(72\) 0.569927 0.0671666
\(73\) 6.50223 0.761029 0.380514 0.924775i \(-0.375747\pi\)
0.380514 + 0.924775i \(0.375747\pi\)
\(74\) −2.49324 −0.289833
\(75\) 4.23540 0.489062
\(76\) −15.6749 −1.79804
\(77\) 4.16445 0.474584
\(78\) −27.9925 −3.16953
\(79\) 1.04239 0.117278 0.0586388 0.998279i \(-0.481324\pi\)
0.0586388 + 0.998279i \(0.481324\pi\)
\(80\) −8.46935 −0.946902
\(81\) −8.67993 −0.964437
\(82\) 0.290976 0.0321330
\(83\) 1.37143 0.150533 0.0752667 0.997163i \(-0.476019\pi\)
0.0752667 + 0.997163i \(0.476019\pi\)
\(84\) −21.4785 −2.34349
\(85\) −6.70484 −0.727242
\(86\) 24.0459 2.59293
\(87\) 4.76694 0.511070
\(88\) −7.68817 −0.819561
\(89\) −4.27966 −0.453643 −0.226821 0.973936i \(-0.572833\pi\)
−0.226821 + 0.973936i \(0.572833\pi\)
\(90\) −0.407543 −0.0429588
\(91\) −19.7437 −2.06971
\(92\) −24.1318 −2.51591
\(93\) 10.4475 1.08335
\(94\) −3.81796 −0.393793
\(95\) 5.89184 0.604490
\(96\) 3.86882 0.394860
\(97\) 6.81532 0.691990 0.345995 0.938236i \(-0.387541\pi\)
0.345995 + 0.938236i \(0.387541\pi\)
\(98\) −4.88272 −0.493229
\(99\) −0.143510 −0.0144233
\(100\) −10.4919 −1.04919
\(101\) −6.41017 −0.637836 −0.318918 0.947782i \(-0.603319\pi\)
−0.318918 + 0.947782i \(0.603319\pi\)
\(102\) 17.9534 1.77765
\(103\) −8.92590 −0.879495 −0.439747 0.898122i \(-0.644932\pi\)
−0.439747 + 0.898122i \(0.644932\pi\)
\(104\) 36.4497 3.57419
\(105\) 8.07325 0.787869
\(106\) −0.702736 −0.0682557
\(107\) −13.3330 −1.28895 −0.644477 0.764624i \(-0.722925\pi\)
−0.644477 + 0.764624i \(0.722925\pi\)
\(108\) 22.2685 2.14278
\(109\) −1.00000 −0.0957826
\(110\) 5.49765 0.524180
\(111\) −1.70202 −0.161548
\(112\) 15.9954 1.51142
\(113\) 6.07191 0.571197 0.285599 0.958349i \(-0.407808\pi\)
0.285599 + 0.958349i \(0.407808\pi\)
\(114\) −15.7764 −1.47760
\(115\) 9.07056 0.845834
\(116\) −11.8087 −1.09641
\(117\) 0.680384 0.0629015
\(118\) −19.9657 −1.83799
\(119\) 12.6629 1.16081
\(120\) −14.9044 −1.36058
\(121\) −9.06408 −0.824008
\(122\) 20.9553 1.89721
\(123\) 0.198636 0.0179104
\(124\) −25.8805 −2.32414
\(125\) 11.8676 1.06147
\(126\) 0.769695 0.0685699
\(127\) −15.1401 −1.34347 −0.671733 0.740793i \(-0.734450\pi\)
−0.671733 + 0.740793i \(0.734450\pi\)
\(128\) 17.0647 1.50832
\(129\) 16.4150 1.44526
\(130\) −26.0644 −2.28600
\(131\) −14.9529 −1.30644 −0.653219 0.757169i \(-0.726582\pi\)
−0.653219 + 0.757169i \(0.726582\pi\)
\(132\) −9.98462 −0.869050
\(133\) −11.1274 −0.964872
\(134\) −31.2196 −2.69696
\(135\) −8.37019 −0.720391
\(136\) −23.3775 −2.00460
\(137\) 14.7596 1.26100 0.630501 0.776189i \(-0.282850\pi\)
0.630501 + 0.776189i \(0.282850\pi\)
\(138\) −24.2880 −2.06753
\(139\) −10.3731 −0.879835 −0.439917 0.898038i \(-0.644992\pi\)
−0.439917 + 0.898038i \(0.644992\pi\)
\(140\) −19.9991 −1.69023
\(141\) −2.60634 −0.219494
\(142\) −17.6058 −1.47745
\(143\) −9.17820 −0.767520
\(144\) −0.551214 −0.0459345
\(145\) 4.43860 0.368606
\(146\) −16.2116 −1.34168
\(147\) −3.33320 −0.274918
\(148\) 4.21624 0.346572
\(149\) 4.59761 0.376651 0.188326 0.982107i \(-0.439694\pi\)
0.188326 + 0.982107i \(0.439694\pi\)
\(150\) −10.5599 −0.862209
\(151\) 0.152984 0.0124497 0.00622484 0.999981i \(-0.498019\pi\)
0.00622484 + 0.999981i \(0.498019\pi\)
\(152\) 20.5428 1.66624
\(153\) −0.436374 −0.0352787
\(154\) −10.3830 −0.836684
\(155\) 9.72789 0.781363
\(156\) 47.3372 3.79001
\(157\) −3.31183 −0.264313 −0.132156 0.991229i \(-0.542190\pi\)
−0.132156 + 0.991229i \(0.542190\pi\)
\(158\) −2.59892 −0.206759
\(159\) −0.479724 −0.0380446
\(160\) 3.60234 0.284790
\(161\) −17.1308 −1.35010
\(162\) 21.6411 1.70029
\(163\) −15.4073 −1.20679 −0.603394 0.797443i \(-0.706186\pi\)
−0.603394 + 0.797443i \(0.706186\pi\)
\(164\) −0.492061 −0.0384235
\(165\) 3.75298 0.292169
\(166\) −3.41929 −0.265388
\(167\) −1.62391 −0.125662 −0.0628312 0.998024i \(-0.520013\pi\)
−0.0628312 + 0.998024i \(0.520013\pi\)
\(168\) 28.1487 2.17172
\(169\) 30.5140 2.34723
\(170\) 16.7168 1.28212
\(171\) 0.383461 0.0293240
\(172\) −40.6632 −3.10054
\(173\) 9.00680 0.684774 0.342387 0.939559i \(-0.388765\pi\)
0.342387 + 0.939559i \(0.388765\pi\)
\(174\) −11.8851 −0.901008
\(175\) −7.44810 −0.563024
\(176\) 7.43573 0.560489
\(177\) −13.6297 −1.02447
\(178\) 10.6702 0.799766
\(179\) −21.0962 −1.57681 −0.788403 0.615159i \(-0.789092\pi\)
−0.788403 + 0.615159i \(0.789092\pi\)
\(180\) 0.689183 0.0513687
\(181\) 9.68809 0.720110 0.360055 0.932931i \(-0.382758\pi\)
0.360055 + 0.932931i \(0.382758\pi\)
\(182\) 49.2258 3.64886
\(183\) 14.3052 1.05747
\(184\) 31.6259 2.33150
\(185\) −1.58478 −0.116516
\(186\) −26.0481 −1.90994
\(187\) 5.88656 0.430468
\(188\) 6.45643 0.470884
\(189\) 15.8081 1.14987
\(190\) −14.6898 −1.06571
\(191\) −0.385765 −0.0279130 −0.0139565 0.999903i \(-0.504443\pi\)
−0.0139565 + 0.999903i \(0.504443\pi\)
\(192\) 8.54583 0.616742
\(193\) 17.5219 1.26125 0.630625 0.776088i \(-0.282799\pi\)
0.630625 + 0.776088i \(0.282799\pi\)
\(194\) −16.9922 −1.21997
\(195\) −17.7929 −1.27418
\(196\) 8.25701 0.589786
\(197\) −7.33608 −0.522674 −0.261337 0.965248i \(-0.584163\pi\)
−0.261337 + 0.965248i \(0.584163\pi\)
\(198\) 0.357805 0.0254281
\(199\) 26.9955 1.91366 0.956831 0.290646i \(-0.0938703\pi\)
0.956831 + 0.290646i \(0.0938703\pi\)
\(200\) 13.7502 0.972289
\(201\) −21.3121 −1.50324
\(202\) 15.9821 1.12450
\(203\) −8.38284 −0.588360
\(204\) −30.3604 −2.12565
\(205\) 0.184954 0.0129178
\(206\) 22.2544 1.55054
\(207\) 0.590342 0.0410316
\(208\) −35.2529 −2.44435
\(209\) −5.17278 −0.357809
\(210\) −20.1285 −1.38900
\(211\) 6.40928 0.441233 0.220617 0.975361i \(-0.429193\pi\)
0.220617 + 0.975361i \(0.429193\pi\)
\(212\) 1.18837 0.0816179
\(213\) −12.0187 −0.823505
\(214\) 33.2424 2.27241
\(215\) 15.2843 1.04238
\(216\) −29.1840 −1.98572
\(217\) −18.3723 −1.24719
\(218\) 2.49324 0.168863
\(219\) −11.0669 −0.747832
\(220\) −9.29690 −0.626797
\(221\) −27.9083 −1.87731
\(222\) 4.24353 0.284807
\(223\) −12.6122 −0.844578 −0.422289 0.906461i \(-0.638773\pi\)
−0.422289 + 0.906461i \(0.638773\pi\)
\(224\) −6.80346 −0.454575
\(225\) 0.256667 0.0171112
\(226\) −15.1387 −1.00701
\(227\) 3.48278 0.231160 0.115580 0.993298i \(-0.463127\pi\)
0.115580 + 0.993298i \(0.463127\pi\)
\(228\) 26.6790 1.76686
\(229\) −22.7805 −1.50538 −0.752688 0.658378i \(-0.771243\pi\)
−0.752688 + 0.658378i \(0.771243\pi\)
\(230\) −22.6151 −1.49119
\(231\) −7.08797 −0.466354
\(232\) 15.4759 1.01604
\(233\) −27.6590 −1.81200 −0.906002 0.423273i \(-0.860881\pi\)
−0.906002 + 0.423273i \(0.860881\pi\)
\(234\) −1.69636 −0.110895
\(235\) −2.42682 −0.158308
\(236\) 33.7634 2.19781
\(237\) −1.77416 −0.115244
\(238\) −31.5716 −2.04649
\(239\) −0.479899 −0.0310421 −0.0155210 0.999880i \(-0.504941\pi\)
−0.0155210 + 0.999880i \(0.504941\pi\)
\(240\) 14.4150 0.930482
\(241\) −19.9683 −1.28627 −0.643137 0.765751i \(-0.722367\pi\)
−0.643137 + 0.765751i \(0.722367\pi\)
\(242\) 22.5989 1.45271
\(243\) −1.07141 −0.0687312
\(244\) −35.4369 −2.26862
\(245\) −3.10362 −0.198283
\(246\) −0.495246 −0.0315758
\(247\) 24.5242 1.56044
\(248\) 33.9178 2.15378
\(249\) −2.33419 −0.147923
\(250\) −29.5887 −1.87136
\(251\) −20.2738 −1.27967 −0.639836 0.768511i \(-0.720998\pi\)
−0.639836 + 0.768511i \(0.720998\pi\)
\(252\) −1.30161 −0.0819935
\(253\) −7.96356 −0.500665
\(254\) 37.7479 2.36851
\(255\) 11.4117 0.714631
\(256\) −32.5044 −2.03153
\(257\) 19.2125 1.19844 0.599220 0.800584i \(-0.295477\pi\)
0.599220 + 0.800584i \(0.295477\pi\)
\(258\) −40.9264 −2.54797
\(259\) 2.99306 0.185979
\(260\) 44.0767 2.73352
\(261\) 0.288879 0.0178812
\(262\) 37.2811 2.30323
\(263\) 31.2820 1.92893 0.964466 0.264206i \(-0.0851097\pi\)
0.964466 + 0.264206i \(0.0851097\pi\)
\(264\) 13.0854 0.805349
\(265\) −0.446682 −0.0274394
\(266\) 27.7434 1.70106
\(267\) 7.28404 0.445776
\(268\) 52.7944 3.22493
\(269\) 2.81973 0.171922 0.0859611 0.996298i \(-0.472604\pi\)
0.0859611 + 0.996298i \(0.472604\pi\)
\(270\) 20.8689 1.27004
\(271\) −5.56203 −0.337870 −0.168935 0.985627i \(-0.554033\pi\)
−0.168935 + 0.985627i \(0.554033\pi\)
\(272\) 22.6099 1.37093
\(273\) 33.6041 2.03381
\(274\) −36.7993 −2.22313
\(275\) −3.46237 −0.208789
\(276\) 41.0726 2.47228
\(277\) 6.07053 0.364743 0.182371 0.983230i \(-0.441623\pi\)
0.182371 + 0.983230i \(0.441623\pi\)
\(278\) 25.8626 1.55114
\(279\) 0.633123 0.0379041
\(280\) 26.2098 1.56634
\(281\) −12.5779 −0.750337 −0.375168 0.926957i \(-0.622415\pi\)
−0.375168 + 0.926957i \(0.622415\pi\)
\(282\) 6.49823 0.386964
\(283\) 14.5908 0.867331 0.433665 0.901074i \(-0.357220\pi\)
0.433665 + 0.901074i \(0.357220\pi\)
\(284\) 29.7726 1.76668
\(285\) −10.0280 −0.594007
\(286\) 22.8834 1.35313
\(287\) −0.349308 −0.0206190
\(288\) 0.234453 0.0138152
\(289\) 0.899343 0.0529025
\(290\) −11.0665 −0.649847
\(291\) −11.5998 −0.679991
\(292\) 27.4149 1.60434
\(293\) 32.0991 1.87525 0.937623 0.347653i \(-0.113021\pi\)
0.937623 + 0.347653i \(0.113021\pi\)
\(294\) 8.31046 0.484676
\(295\) −12.6909 −0.738891
\(296\) −5.52560 −0.321169
\(297\) 7.34867 0.426413
\(298\) −11.4629 −0.664031
\(299\) 37.7553 2.18345
\(300\) 17.8574 1.03100
\(301\) −28.8663 −1.66383
\(302\) −0.381426 −0.0219486
\(303\) 10.9102 0.626775
\(304\) −19.8683 −1.13953
\(305\) 13.3199 0.762695
\(306\) 1.08798 0.0621959
\(307\) −12.4742 −0.711941 −0.355971 0.934497i \(-0.615850\pi\)
−0.355971 + 0.934497i \(0.615850\pi\)
\(308\) 17.5583 1.00048
\(309\) 15.1920 0.864243
\(310\) −24.2539 −1.37753
\(311\) 1.96281 0.111301 0.0556504 0.998450i \(-0.482277\pi\)
0.0556504 + 0.998450i \(0.482277\pi\)
\(312\) −62.0379 −3.51221
\(313\) 2.19086 0.123835 0.0619174 0.998081i \(-0.480278\pi\)
0.0619174 + 0.998081i \(0.480278\pi\)
\(314\) 8.25717 0.465979
\(315\) 0.489243 0.0275657
\(316\) 4.39495 0.247235
\(317\) 28.2527 1.58683 0.793414 0.608683i \(-0.208302\pi\)
0.793414 + 0.608683i \(0.208302\pi\)
\(318\) 1.19607 0.0670721
\(319\) −3.89690 −0.218185
\(320\) 7.95721 0.444821
\(321\) 22.6930 1.26660
\(322\) 42.7113 2.38021
\(323\) −15.7289 −0.875181
\(324\) −36.5966 −2.03315
\(325\) 16.4152 0.910549
\(326\) 38.4139 2.12755
\(327\) 1.70202 0.0941217
\(328\) 0.644872 0.0356071
\(329\) 4.58335 0.252688
\(330\) −9.35708 −0.515090
\(331\) 31.4677 1.72962 0.864810 0.502100i \(-0.167439\pi\)
0.864810 + 0.502100i \(0.167439\pi\)
\(332\) 5.78225 0.317342
\(333\) −0.103143 −0.00565220
\(334\) 4.04881 0.221541
\(335\) −19.8442 −1.08420
\(336\) −27.2244 −1.48521
\(337\) 8.37852 0.456407 0.228204 0.973613i \(-0.426715\pi\)
0.228204 + 0.973613i \(0.426715\pi\)
\(338\) −76.0786 −4.13813
\(339\) −10.3345 −0.561292
\(340\) −28.2692 −1.53311
\(341\) −8.54066 −0.462503
\(342\) −0.956058 −0.0516977
\(343\) −15.0898 −0.814775
\(344\) 53.2913 2.87327
\(345\) −15.4382 −0.831166
\(346\) −22.4561 −1.20725
\(347\) 24.9518 1.33948 0.669742 0.742594i \(-0.266405\pi\)
0.669742 + 0.742594i \(0.266405\pi\)
\(348\) 20.0985 1.07739
\(349\) 19.3970 1.03830 0.519148 0.854684i \(-0.326249\pi\)
0.519148 + 0.854684i \(0.326249\pi\)
\(350\) 18.5699 0.992602
\(351\) −34.8401 −1.85963
\(352\) −3.16270 −0.168573
\(353\) −2.85115 −0.151751 −0.0758757 0.997117i \(-0.524175\pi\)
−0.0758757 + 0.997117i \(0.524175\pi\)
\(354\) 33.9820 1.80612
\(355\) −11.1908 −0.593948
\(356\) −18.0440 −0.956332
\(357\) −21.5525 −1.14068
\(358\) 52.5979 2.77988
\(359\) 20.2350 1.06796 0.533982 0.845496i \(-0.320695\pi\)
0.533982 + 0.845496i \(0.320695\pi\)
\(360\) −0.903212 −0.0476034
\(361\) −5.17830 −0.272542
\(362\) −24.1547 −1.26954
\(363\) 15.4272 0.809719
\(364\) −83.2442 −4.36318
\(365\) −10.3046 −0.539369
\(366\) −35.6663 −1.86431
\(367\) 11.5117 0.600905 0.300453 0.953797i \(-0.402862\pi\)
0.300453 + 0.953797i \(0.402862\pi\)
\(368\) −30.5875 −1.59448
\(369\) 0.0120374 0.000626644 0
\(370\) 3.95124 0.205415
\(371\) 0.843613 0.0437982
\(372\) 44.0491 2.28384
\(373\) −13.9839 −0.724061 −0.362030 0.932166i \(-0.617916\pi\)
−0.362030 + 0.932166i \(0.617916\pi\)
\(374\) −14.6766 −0.758909
\(375\) −20.1988 −1.04306
\(376\) −8.46150 −0.436368
\(377\) 18.4753 0.951524
\(378\) −39.4134 −2.02721
\(379\) −34.2917 −1.76145 −0.880724 0.473630i \(-0.842943\pi\)
−0.880724 + 0.473630i \(0.842943\pi\)
\(380\) 24.8414 1.27434
\(381\) 25.7687 1.32017
\(382\) 0.961804 0.0492102
\(383\) 35.4624 1.81205 0.906023 0.423228i \(-0.139103\pi\)
0.906023 + 0.423228i \(0.139103\pi\)
\(384\) −29.0444 −1.48217
\(385\) −6.59976 −0.336355
\(386\) −43.6861 −2.22357
\(387\) 0.994756 0.0505663
\(388\) 28.7350 1.45880
\(389\) 2.63939 0.133822 0.0669112 0.997759i \(-0.478686\pi\)
0.0669112 + 0.997759i \(0.478686\pi\)
\(390\) 44.3620 2.24636
\(391\) −24.2149 −1.22460
\(392\) −10.8213 −0.546556
\(393\) 25.4500 1.28378
\(394\) 18.2906 0.921467
\(395\) −1.65196 −0.0831190
\(396\) −0.605073 −0.0304061
\(397\) 23.0194 1.15531 0.577654 0.816282i \(-0.303968\pi\)
0.577654 + 0.816282i \(0.303968\pi\)
\(398\) −67.3062 −3.37376
\(399\) 18.9391 0.948140
\(400\) −13.2988 −0.664938
\(401\) 2.88188 0.143914 0.0719571 0.997408i \(-0.477076\pi\)
0.0719571 + 0.997408i \(0.477076\pi\)
\(402\) 53.1362 2.65019
\(403\) 40.4914 2.01702
\(404\) −27.0268 −1.34463
\(405\) 13.7558 0.683532
\(406\) 20.9004 1.03727
\(407\) 1.39137 0.0689677
\(408\) 39.7889 1.96984
\(409\) 0.923529 0.0456656 0.0228328 0.999739i \(-0.492731\pi\)
0.0228328 + 0.999739i \(0.492731\pi\)
\(410\) −0.461135 −0.0227738
\(411\) −25.1211 −1.23913
\(412\) −37.6337 −1.85408
\(413\) 23.9682 1.17940
\(414\) −1.47186 −0.0723382
\(415\) −2.17341 −0.106689
\(416\) 14.9944 0.735161
\(417\) 17.6552 0.864578
\(418\) 12.8970 0.630811
\(419\) −2.34142 −0.114386 −0.0571928 0.998363i \(-0.518215\pi\)
−0.0571928 + 0.998363i \(0.518215\pi\)
\(420\) 34.0387 1.66092
\(421\) −12.7400 −0.620912 −0.310456 0.950588i \(-0.600482\pi\)
−0.310456 + 0.950588i \(0.600482\pi\)
\(422\) −15.9799 −0.777888
\(423\) −0.157946 −0.00767958
\(424\) −1.55743 −0.0756354
\(425\) −10.5281 −0.510687
\(426\) 29.9654 1.45183
\(427\) −25.1562 −1.21740
\(428\) −56.2152 −2.71727
\(429\) 15.6214 0.754210
\(430\) −38.1075 −1.83771
\(431\) 14.2316 0.685514 0.342757 0.939424i \(-0.388639\pi\)
0.342757 + 0.939424i \(0.388639\pi\)
\(432\) 28.2258 1.35801
\(433\) 15.5467 0.747129 0.373565 0.927604i \(-0.378135\pi\)
0.373565 + 0.927604i \(0.378135\pi\)
\(434\) 45.8065 2.19878
\(435\) −7.55457 −0.362214
\(436\) −4.21624 −0.201921
\(437\) 21.2787 1.01790
\(438\) 27.5924 1.31842
\(439\) 40.7184 1.94338 0.971692 0.236251i \(-0.0759187\pi\)
0.971692 + 0.236251i \(0.0759187\pi\)
\(440\) 12.1841 0.580853
\(441\) −0.201994 −0.00961875
\(442\) 69.5819 3.30968
\(443\) −17.4186 −0.827581 −0.413790 0.910372i \(-0.635795\pi\)
−0.413790 + 0.910372i \(0.635795\pi\)
\(444\) −7.17610 −0.340563
\(445\) 6.78233 0.321513
\(446\) 31.4453 1.48898
\(447\) −7.82521 −0.370120
\(448\) −15.0281 −0.710013
\(449\) 13.0979 0.618130 0.309065 0.951041i \(-0.399984\pi\)
0.309065 + 0.951041i \(0.399984\pi\)
\(450\) −0.639933 −0.0301667
\(451\) −0.162382 −0.00764626
\(452\) 25.6006 1.20415
\(453\) −0.260381 −0.0122338
\(454\) −8.68340 −0.407532
\(455\) 31.2895 1.46688
\(456\) −34.9642 −1.63735
\(457\) 15.5419 0.727017 0.363509 0.931591i \(-0.381579\pi\)
0.363509 + 0.931591i \(0.381579\pi\)
\(458\) 56.7971 2.65395
\(459\) 22.3452 1.04298
\(460\) 38.2436 1.78312
\(461\) 17.1571 0.799086 0.399543 0.916714i \(-0.369169\pi\)
0.399543 + 0.916714i \(0.369169\pi\)
\(462\) 17.6720 0.822175
\(463\) 20.5558 0.955308 0.477654 0.878548i \(-0.341487\pi\)
0.477654 + 0.878548i \(0.341487\pi\)
\(464\) −14.9677 −0.694860
\(465\) −16.5570 −0.767813
\(466\) 68.9606 3.19454
\(467\) −1.13738 −0.0526316 −0.0263158 0.999654i \(-0.508378\pi\)
−0.0263158 + 0.999654i \(0.508378\pi\)
\(468\) 2.86866 0.132604
\(469\) 37.4781 1.73058
\(470\) 6.05064 0.279095
\(471\) 5.63678 0.259729
\(472\) −44.2487 −2.03671
\(473\) −13.4190 −0.617006
\(474\) 4.42340 0.203173
\(475\) 9.25149 0.424487
\(476\) 53.3898 2.44712
\(477\) −0.0290716 −0.00133109
\(478\) 1.19650 0.0547267
\(479\) −2.01624 −0.0921242 −0.0460621 0.998939i \(-0.514667\pi\)
−0.0460621 + 0.998939i \(0.514667\pi\)
\(480\) −6.13124 −0.279852
\(481\) −6.59651 −0.300775
\(482\) 49.7858 2.26768
\(483\) 29.1570 1.32669
\(484\) −38.2163 −1.73711
\(485\) −10.8008 −0.490439
\(486\) 2.67129 0.121172
\(487\) −23.3912 −1.05996 −0.529978 0.848011i \(-0.677800\pi\)
−0.529978 + 0.848011i \(0.677800\pi\)
\(488\) 46.4420 2.10233
\(489\) 26.2234 1.18586
\(490\) 7.73805 0.349570
\(491\) −43.5025 −1.96324 −0.981620 0.190844i \(-0.938878\pi\)
−0.981620 + 0.190844i \(0.938878\pi\)
\(492\) 0.837495 0.0377572
\(493\) −11.8494 −0.533668
\(494\) −61.1447 −2.75103
\(495\) 0.227433 0.0102223
\(496\) −32.8041 −1.47295
\(497\) 21.1352 0.948045
\(498\) 5.81968 0.260786
\(499\) −10.8956 −0.487752 −0.243876 0.969806i \(-0.578419\pi\)
−0.243876 + 0.969806i \(0.578419\pi\)
\(500\) 50.0366 2.23770
\(501\) 2.76393 0.123483
\(502\) 50.5475 2.25604
\(503\) 10.7096 0.477516 0.238758 0.971079i \(-0.423260\pi\)
0.238758 + 0.971079i \(0.423260\pi\)
\(504\) 1.70582 0.0759835
\(505\) 10.1587 0.452058
\(506\) 19.8550 0.882664
\(507\) −51.9352 −2.30652
\(508\) −63.8342 −2.83219
\(509\) −21.4863 −0.952365 −0.476183 0.879346i \(-0.657980\pi\)
−0.476183 + 0.879346i \(0.657980\pi\)
\(510\) −28.4522 −1.25988
\(511\) 19.4615 0.860928
\(512\) 46.9118 2.07323
\(513\) −19.6357 −0.866937
\(514\) −47.9012 −2.11283
\(515\) 14.1456 0.623330
\(516\) 69.2094 3.04677
\(517\) 2.13064 0.0937056
\(518\) −7.46240 −0.327879
\(519\) −15.3297 −0.672899
\(520\) −57.7649 −2.53316
\(521\) −5.53992 −0.242708 −0.121354 0.992609i \(-0.538724\pi\)
−0.121354 + 0.992609i \(0.538724\pi\)
\(522\) −0.720244 −0.0315242
\(523\) 6.77666 0.296323 0.148161 0.988963i \(-0.452665\pi\)
0.148161 + 0.988963i \(0.452665\pi\)
\(524\) −63.0448 −2.75413
\(525\) 12.6768 0.553260
\(526\) −77.9936 −3.40068
\(527\) −25.9697 −1.13126
\(528\) −12.6557 −0.550770
\(529\) 9.75880 0.424296
\(530\) 1.11368 0.0483753
\(531\) −0.825964 −0.0358438
\(532\) −46.9159 −2.03406
\(533\) 0.769854 0.0333461
\(534\) −18.1609 −0.785897
\(535\) 21.1300 0.913529
\(536\) −69.1899 −2.98855
\(537\) 35.9061 1.54946
\(538\) −7.03026 −0.303096
\(539\) 2.72484 0.117367
\(540\) −35.2907 −1.51867
\(541\) −0.708751 −0.0304716 −0.0152358 0.999884i \(-0.504850\pi\)
−0.0152358 + 0.999884i \(0.504850\pi\)
\(542\) 13.8675 0.595659
\(543\) −16.4893 −0.707623
\(544\) −9.61687 −0.412320
\(545\) 1.58478 0.0678847
\(546\) −83.7831 −3.58559
\(547\) 13.2615 0.567020 0.283510 0.958969i \(-0.408501\pi\)
0.283510 + 0.958969i \(0.408501\pi\)
\(548\) 62.2301 2.65834
\(549\) 0.866904 0.0369985
\(550\) 8.63252 0.368092
\(551\) 10.4125 0.443589
\(552\) −53.8279 −2.29107
\(553\) 3.11992 0.132673
\(554\) −15.1353 −0.643037
\(555\) 2.69733 0.114495
\(556\) −43.7354 −1.85479
\(557\) −14.6434 −0.620460 −0.310230 0.950662i \(-0.600406\pi\)
−0.310230 + 0.950662i \(0.600406\pi\)
\(558\) −1.57853 −0.0668244
\(559\) 63.6196 2.69082
\(560\) −25.3492 −1.07120
\(561\) −10.0190 −0.423003
\(562\) 31.3598 1.32283
\(563\) 11.6698 0.491822 0.245911 0.969292i \(-0.420913\pi\)
0.245911 + 0.969292i \(0.420913\pi\)
\(564\) −10.9889 −0.462718
\(565\) −9.62266 −0.404828
\(566\) −36.3782 −1.52909
\(567\) −25.9795 −1.09104
\(568\) −39.0186 −1.63719
\(569\) −16.7665 −0.702888 −0.351444 0.936209i \(-0.614309\pi\)
−0.351444 + 0.936209i \(0.614309\pi\)
\(570\) 25.0022 1.04723
\(571\) 35.2518 1.47524 0.737621 0.675215i \(-0.235949\pi\)
0.737621 + 0.675215i \(0.235949\pi\)
\(572\) −38.6974 −1.61802
\(573\) 0.656578 0.0274289
\(574\) 0.870909 0.0363510
\(575\) 14.2428 0.593965
\(576\) 0.517882 0.0215784
\(577\) −18.2934 −0.761563 −0.380782 0.924665i \(-0.624345\pi\)
−0.380782 + 0.924665i \(0.624345\pi\)
\(578\) −2.24228 −0.0932664
\(579\) −29.8225 −1.23938
\(580\) 18.7142 0.777064
\(581\) 4.10475 0.170294
\(582\) 28.9210 1.19881
\(583\) 0.392167 0.0162419
\(584\) −35.9288 −1.48674
\(585\) −1.07826 −0.0445806
\(586\) −80.0306 −3.30603
\(587\) 13.0575 0.538942 0.269471 0.963008i \(-0.413151\pi\)
0.269471 + 0.963008i \(0.413151\pi\)
\(588\) −14.0536 −0.579559
\(589\) 22.8207 0.940311
\(590\) 31.6413 1.30265
\(591\) 12.4861 0.513610
\(592\) 5.34417 0.219644
\(593\) −14.7763 −0.606788 −0.303394 0.952865i \(-0.598120\pi\)
−0.303394 + 0.952865i \(0.598120\pi\)
\(594\) −18.3220 −0.751760
\(595\) −20.0680 −0.822707
\(596\) 19.3846 0.794025
\(597\) −45.9468 −1.88048
\(598\) −94.1330 −3.84939
\(599\) 29.5946 1.20920 0.604601 0.796529i \(-0.293333\pi\)
0.604601 + 0.796529i \(0.293333\pi\)
\(600\) −23.4031 −0.955429
\(601\) 16.4013 0.669023 0.334512 0.942392i \(-0.391429\pi\)
0.334512 + 0.942392i \(0.391429\pi\)
\(602\) 71.9706 2.93330
\(603\) −1.29153 −0.0525950
\(604\) 0.645017 0.0262454
\(605\) 14.3646 0.584005
\(606\) −27.2017 −1.10500
\(607\) 16.7133 0.678371 0.339186 0.940720i \(-0.389849\pi\)
0.339186 + 0.940720i \(0.389849\pi\)
\(608\) 8.45076 0.342724
\(609\) 14.2677 0.578157
\(610\) −33.2097 −1.34462
\(611\) −10.1014 −0.408659
\(612\) −1.83985 −0.0743717
\(613\) −17.7616 −0.717383 −0.358692 0.933456i \(-0.616777\pi\)
−0.358692 + 0.933456i \(0.616777\pi\)
\(614\) 31.1012 1.25514
\(615\) −0.314795 −0.0126938
\(616\) −23.0111 −0.927144
\(617\) 5.76633 0.232144 0.116072 0.993241i \(-0.462970\pi\)
0.116072 + 0.993241i \(0.462970\pi\)
\(618\) −37.8773 −1.52365
\(619\) −10.1536 −0.408108 −0.204054 0.978960i \(-0.565412\pi\)
−0.204054 + 0.978960i \(0.565412\pi\)
\(620\) 41.0151 1.64720
\(621\) −30.2294 −1.21306
\(622\) −4.89376 −0.196222
\(623\) −12.8093 −0.513192
\(624\) 60.0009 2.40196
\(625\) −6.36526 −0.254611
\(626\) −5.46234 −0.218319
\(627\) 8.80415 0.351604
\(628\) −13.9634 −0.557202
\(629\) 4.23076 0.168692
\(630\) −1.21980 −0.0485980
\(631\) 36.5881 1.45655 0.728274 0.685286i \(-0.240323\pi\)
0.728274 + 0.685286i \(0.240323\pi\)
\(632\) −5.75981 −0.229113
\(633\) −10.9087 −0.433582
\(634\) −70.4406 −2.79755
\(635\) 23.9938 0.952164
\(636\) −2.02263 −0.0802025
\(637\) −12.9185 −0.511850
\(638\) 9.71590 0.384656
\(639\) −0.728337 −0.0288126
\(640\) −27.0439 −1.06900
\(641\) −9.14572 −0.361234 −0.180617 0.983553i \(-0.557809\pi\)
−0.180617 + 0.983553i \(0.557809\pi\)
\(642\) −56.5791 −2.23300
\(643\) 13.4331 0.529750 0.264875 0.964283i \(-0.414669\pi\)
0.264875 + 0.964283i \(0.414669\pi\)
\(644\) −72.2277 −2.84617
\(645\) −26.0142 −1.02431
\(646\) 39.2160 1.54293
\(647\) 36.7502 1.44480 0.722399 0.691477i \(-0.243040\pi\)
0.722399 + 0.691477i \(0.243040\pi\)
\(648\) 47.9618 1.88412
\(649\) 11.1420 0.437363
\(650\) −40.9269 −1.60528
\(651\) 31.2699 1.22557
\(652\) −64.9606 −2.54405
\(653\) −32.4830 −1.27116 −0.635579 0.772036i \(-0.719239\pi\)
−0.635579 + 0.772036i \(0.719239\pi\)
\(654\) −4.24353 −0.165935
\(655\) 23.6971 0.925921
\(656\) −0.623698 −0.0243513
\(657\) −0.670660 −0.0261649
\(658\) −11.4274 −0.445485
\(659\) −0.877630 −0.0341876 −0.0170938 0.999854i \(-0.505441\pi\)
−0.0170938 + 0.999854i \(0.505441\pi\)
\(660\) 15.8235 0.615927
\(661\) 43.5286 1.69307 0.846534 0.532335i \(-0.178685\pi\)
0.846534 + 0.532335i \(0.178685\pi\)
\(662\) −78.4564 −3.04929
\(663\) 47.5003 1.84476
\(664\) −7.57795 −0.294081
\(665\) 17.6346 0.683840
\(666\) 0.257160 0.00996475
\(667\) 16.0302 0.620694
\(668\) −6.84681 −0.264911
\(669\) 21.4662 0.829932
\(670\) 49.4763 1.91143
\(671\) −11.6943 −0.451453
\(672\) 11.5796 0.446693
\(673\) 25.2504 0.973331 0.486665 0.873588i \(-0.338213\pi\)
0.486665 + 0.873588i \(0.338213\pi\)
\(674\) −20.8897 −0.804639
\(675\) −13.1430 −0.505876
\(676\) 128.654 4.94823
\(677\) 22.6393 0.870098 0.435049 0.900407i \(-0.356731\pi\)
0.435049 + 0.900407i \(0.356731\pi\)
\(678\) 25.7663 0.989550
\(679\) 20.3986 0.782827
\(680\) 37.0483 1.42074
\(681\) −5.92775 −0.227152
\(682\) 21.2939 0.815386
\(683\) 14.7272 0.563521 0.281761 0.959485i \(-0.409082\pi\)
0.281761 + 0.959485i \(0.409082\pi\)
\(684\) 1.61676 0.0618184
\(685\) −23.3908 −0.893718
\(686\) 37.6226 1.43644
\(687\) 38.7727 1.47927
\(688\) −51.5415 −1.96500
\(689\) −1.85927 −0.0708326
\(690\) 38.4912 1.46533
\(691\) 15.2634 0.580647 0.290324 0.956929i \(-0.406237\pi\)
0.290324 + 0.956929i \(0.406237\pi\)
\(692\) 37.9748 1.44358
\(693\) −0.429534 −0.0163167
\(694\) −62.2108 −2.36149
\(695\) 16.4391 0.623571
\(696\) −26.3402 −0.998423
\(697\) −0.493756 −0.0187024
\(698\) −48.3613 −1.83050
\(699\) 47.0761 1.78058
\(700\) −31.4029 −1.18692
\(701\) 8.54458 0.322724 0.161362 0.986895i \(-0.448411\pi\)
0.161362 + 0.986895i \(0.448411\pi\)
\(702\) 86.8647 3.27850
\(703\) −3.71775 −0.140218
\(704\) −6.98608 −0.263298
\(705\) 4.13049 0.155563
\(706\) 7.10860 0.267536
\(707\) −19.1860 −0.721564
\(708\) −57.4658 −2.15970
\(709\) 5.11377 0.192052 0.0960258 0.995379i \(-0.469387\pi\)
0.0960258 + 0.995379i \(0.469387\pi\)
\(710\) 27.9014 1.04712
\(711\) −0.107515 −0.00403212
\(712\) 23.6477 0.886234
\(713\) 35.1328 1.31573
\(714\) 53.7354 2.01100
\(715\) 14.5455 0.543969
\(716\) −88.9466 −3.32409
\(717\) 0.816795 0.0305038
\(718\) −50.4508 −1.88281
\(719\) −26.8457 −1.00117 −0.500587 0.865686i \(-0.666882\pi\)
−0.500587 + 0.865686i \(0.666882\pi\)
\(720\) 0.873555 0.0325555
\(721\) −26.7157 −0.994945
\(722\) 12.9107 0.480488
\(723\) 33.9864 1.26397
\(724\) 40.8473 1.51808
\(725\) 6.96958 0.258844
\(726\) −38.4637 −1.42752
\(727\) −50.0337 −1.85565 −0.927823 0.373021i \(-0.878322\pi\)
−0.927823 + 0.373021i \(0.878322\pi\)
\(728\) 109.096 4.04337
\(729\) 27.8634 1.03198
\(730\) 25.6919 0.950900
\(731\) −40.8033 −1.50916
\(732\) 60.3142 2.22928
\(733\) −38.2718 −1.41360 −0.706801 0.707412i \(-0.749862\pi\)
−0.706801 + 0.707412i \(0.749862\pi\)
\(734\) −28.7014 −1.05939
\(735\) 5.28240 0.194844
\(736\) 13.0101 0.479557
\(737\) 17.4223 0.641760
\(738\) −0.0300122 −0.00110476
\(739\) 17.5963 0.647290 0.323645 0.946179i \(-0.395092\pi\)
0.323645 + 0.946179i \(0.395092\pi\)
\(740\) −6.68182 −0.245629
\(741\) −41.7406 −1.53338
\(742\) −2.10333 −0.0772156
\(743\) −36.5220 −1.33986 −0.669930 0.742424i \(-0.733676\pi\)
−0.669930 + 0.742424i \(0.733676\pi\)
\(744\) −57.7287 −2.11644
\(745\) −7.28622 −0.266947
\(746\) 34.8653 1.27651
\(747\) −0.141453 −0.00517549
\(748\) 24.8191 0.907477
\(749\) −39.9065 −1.45815
\(750\) 50.3605 1.83890
\(751\) 38.0589 1.38879 0.694395 0.719594i \(-0.255672\pi\)
0.694395 + 0.719594i \(0.255672\pi\)
\(752\) 8.18367 0.298428
\(753\) 34.5064 1.25748
\(754\) −46.0632 −1.67752
\(755\) −0.242447 −0.00882354
\(756\) 66.6507 2.42406
\(757\) 31.9110 1.15982 0.579912 0.814679i \(-0.303087\pi\)
0.579912 + 0.814679i \(0.303087\pi\)
\(758\) 85.4974 3.10541
\(759\) 13.5541 0.491983
\(760\) −32.5559 −1.18093
\(761\) 1.04214 0.0377777 0.0188888 0.999822i \(-0.493987\pi\)
0.0188888 + 0.999822i \(0.493987\pi\)
\(762\) −64.2475 −2.32744
\(763\) −2.99306 −0.108356
\(764\) −1.62648 −0.0588438
\(765\) 0.691558 0.0250033
\(766\) −88.4163 −3.19461
\(767\) −52.8245 −1.90738
\(768\) 55.3230 1.99630
\(769\) −5.16536 −0.186268 −0.0931338 0.995654i \(-0.529688\pi\)
−0.0931338 + 0.995654i \(0.529688\pi\)
\(770\) 16.4548 0.592989
\(771\) −32.6999 −1.17766
\(772\) 73.8762 2.65886
\(773\) 35.1011 1.26250 0.631250 0.775579i \(-0.282542\pi\)
0.631250 + 0.775579i \(0.282542\pi\)
\(774\) −2.48016 −0.0891477
\(775\) 15.2749 0.548692
\(776\) −37.6587 −1.35187
\(777\) −5.09423 −0.182754
\(778\) −6.58062 −0.235927
\(779\) 0.433885 0.0155456
\(780\) −75.0192 −2.68612
\(781\) 9.82507 0.351569
\(782\) 60.3735 2.15895
\(783\) −14.7925 −0.528641
\(784\) 10.4659 0.373784
\(785\) 5.24853 0.187328
\(786\) −63.4529 −2.26329
\(787\) −37.3326 −1.33077 −0.665383 0.746503i \(-0.731732\pi\)
−0.665383 + 0.746503i \(0.731732\pi\)
\(788\) −30.9306 −1.10186
\(789\) −53.2425 −1.89548
\(790\) 4.11872 0.146538
\(791\) 18.1736 0.646177
\(792\) 0.792981 0.0281773
\(793\) 55.4428 1.96883
\(794\) −57.3927 −2.03679
\(795\) 0.760259 0.0269636
\(796\) 113.819 4.03422
\(797\) −25.5257 −0.904167 −0.452084 0.891976i \(-0.649319\pi\)
−0.452084 + 0.891976i \(0.649319\pi\)
\(798\) −47.2197 −1.67156
\(799\) 6.47868 0.229199
\(800\) 5.65647 0.199987
\(801\) 0.441417 0.0155967
\(802\) −7.18521 −0.253719
\(803\) 9.04702 0.319263
\(804\) −89.8569 −3.16901
\(805\) 27.1487 0.956866
\(806\) −100.955 −3.55598
\(807\) −4.79923 −0.168941
\(808\) 35.4200 1.24607
\(809\) −28.4137 −0.998974 −0.499487 0.866322i \(-0.666478\pi\)
−0.499487 + 0.866322i \(0.666478\pi\)
\(810\) −34.2965 −1.20506
\(811\) 16.7788 0.589183 0.294592 0.955623i \(-0.404816\pi\)
0.294592 + 0.955623i \(0.404816\pi\)
\(812\) −35.3440 −1.24033
\(813\) 9.46667 0.332011
\(814\) −3.46902 −0.121589
\(815\) 24.4172 0.855296
\(816\) −38.4824 −1.34715
\(817\) 35.8556 1.25443
\(818\) −2.30258 −0.0805077
\(819\) 2.03643 0.0711586
\(820\) 0.779810 0.0272322
\(821\) 32.6332 1.13891 0.569453 0.822024i \(-0.307155\pi\)
0.569453 + 0.822024i \(0.307155\pi\)
\(822\) 62.6330 2.18458
\(823\) −9.43933 −0.329034 −0.164517 0.986374i \(-0.552607\pi\)
−0.164517 + 0.986374i \(0.552607\pi\)
\(824\) 49.3209 1.71818
\(825\) 5.89301 0.205168
\(826\) −59.7585 −2.07926
\(827\) −21.6195 −0.751784 −0.375892 0.926663i \(-0.622664\pi\)
−0.375892 + 0.926663i \(0.622664\pi\)
\(828\) 2.48902 0.0864995
\(829\) −53.5917 −1.86132 −0.930659 0.365887i \(-0.880766\pi\)
−0.930659 + 0.365887i \(0.880766\pi\)
\(830\) 5.41883 0.188090
\(831\) −10.3321 −0.358418
\(832\) 33.1211 1.14827
\(833\) 8.28546 0.287074
\(834\) −44.0185 −1.52424
\(835\) 2.57355 0.0890615
\(836\) −21.8097 −0.754303
\(837\) −32.4201 −1.12060
\(838\) 5.83771 0.201660
\(839\) 27.9506 0.964961 0.482480 0.875907i \(-0.339736\pi\)
0.482480 + 0.875907i \(0.339736\pi\)
\(840\) −44.6096 −1.53918
\(841\) −21.1557 −0.729508
\(842\) 31.7640 1.09466
\(843\) 21.4078 0.737325
\(844\) 27.0230 0.930172
\(845\) −48.3580 −1.66357
\(846\) 0.393796 0.0135390
\(847\) −27.1293 −0.932174
\(848\) 1.50629 0.0517262
\(849\) −24.8337 −0.852291
\(850\) 26.2490 0.900334
\(851\) −5.72353 −0.196200
\(852\) −50.6735 −1.73605
\(853\) −1.60888 −0.0550869 −0.0275435 0.999621i \(-0.508768\pi\)
−0.0275435 + 0.999621i \(0.508768\pi\)
\(854\) 62.7205 2.14625
\(855\) −0.607702 −0.0207830
\(856\) 73.6731 2.51809
\(857\) 33.7948 1.15441 0.577204 0.816600i \(-0.304144\pi\)
0.577204 + 0.816600i \(0.304144\pi\)
\(858\) −38.9480 −1.32966
\(859\) 20.1705 0.688207 0.344104 0.938932i \(-0.388183\pi\)
0.344104 + 0.938932i \(0.388183\pi\)
\(860\) 64.4424 2.19747
\(861\) 0.594528 0.0202615
\(862\) −35.4829 −1.20855
\(863\) 13.8311 0.470817 0.235408 0.971897i \(-0.424357\pi\)
0.235408 + 0.971897i \(0.424357\pi\)
\(864\) −12.0055 −0.408436
\(865\) −14.2738 −0.485325
\(866\) −38.7617 −1.31718
\(867\) −1.53070 −0.0519852
\(868\) −77.4619 −2.62923
\(869\) 1.45035 0.0491997
\(870\) 18.8353 0.638578
\(871\) −82.5995 −2.79878
\(872\) 5.52560 0.187120
\(873\) −0.702952 −0.0237913
\(874\) −53.0528 −1.79454
\(875\) 35.5204 1.20081
\(876\) −46.6607 −1.57652
\(877\) 29.2667 0.988265 0.494133 0.869387i \(-0.335486\pi\)
0.494133 + 0.869387i \(0.335486\pi\)
\(878\) −101.521 −3.42616
\(879\) −54.6331 −1.84273
\(880\) −11.7840 −0.397239
\(881\) 10.0474 0.338506 0.169253 0.985573i \(-0.445865\pi\)
0.169253 + 0.985573i \(0.445865\pi\)
\(882\) 0.503618 0.0169577
\(883\) 19.9527 0.671461 0.335731 0.941958i \(-0.391017\pi\)
0.335731 + 0.941958i \(0.391017\pi\)
\(884\) −117.668 −3.95760
\(885\) 21.6000 0.726078
\(886\) 43.4286 1.45901
\(887\) 45.4250 1.52522 0.762612 0.646856i \(-0.223917\pi\)
0.762612 + 0.646856i \(0.223917\pi\)
\(888\) 9.40466 0.315600
\(889\) −45.3152 −1.51982
\(890\) −16.9100 −0.566823
\(891\) −12.0770 −0.404595
\(892\) −53.1762 −1.78047
\(893\) −5.69310 −0.190512
\(894\) 19.5101 0.652516
\(895\) 33.4329 1.11754
\(896\) 51.0757 1.70632
\(897\) −64.2602 −2.14558
\(898\) −32.6563 −1.08975
\(899\) 17.1919 0.573383
\(900\) 1.08217 0.0360723
\(901\) 1.19247 0.0397269
\(902\) 0.404856 0.0134802
\(903\) 49.1310 1.63498
\(904\) −33.5509 −1.11589
\(905\) −15.3535 −0.510369
\(906\) 0.649193 0.0215680
\(907\) −59.6667 −1.98120 −0.990600 0.136791i \(-0.956321\pi\)
−0.990600 + 0.136791i \(0.956321\pi\)
\(908\) 14.6842 0.487313
\(909\) 0.661164 0.0219294
\(910\) −78.0123 −2.58608
\(911\) 41.4942 1.37476 0.687382 0.726296i \(-0.258760\pi\)
0.687382 + 0.726296i \(0.258760\pi\)
\(912\) 33.8162 1.11977
\(913\) 1.90816 0.0631510
\(914\) −38.7496 −1.28172
\(915\) −22.6707 −0.749469
\(916\) −96.0478 −3.17351
\(917\) −44.7548 −1.47793
\(918\) −55.7119 −1.83877
\(919\) −5.00036 −0.164947 −0.0824733 0.996593i \(-0.526282\pi\)
−0.0824733 + 0.996593i \(0.526282\pi\)
\(920\) −50.1203 −1.65242
\(921\) 21.2313 0.699596
\(922\) −42.7767 −1.40878
\(923\) −46.5808 −1.53323
\(924\) −29.8845 −0.983129
\(925\) −2.48846 −0.0818201
\(926\) −51.2504 −1.68419
\(927\) 0.920644 0.0302379
\(928\) 6.36636 0.208986
\(929\) −33.9925 −1.11526 −0.557629 0.830090i \(-0.688289\pi\)
−0.557629 + 0.830090i \(0.688289\pi\)
\(930\) 41.2806 1.35364
\(931\) −7.28079 −0.238618
\(932\) −116.617 −3.81992
\(933\) −3.34074 −0.109371
\(934\) 2.83576 0.0927887
\(935\) −9.32893 −0.305089
\(936\) −3.75953 −0.122884
\(937\) 32.1542 1.05043 0.525216 0.850969i \(-0.323984\pi\)
0.525216 + 0.850969i \(0.323984\pi\)
\(938\) −93.4419 −3.05099
\(939\) −3.72888 −0.121687
\(940\) −10.2320 −0.333733
\(941\) 10.3603 0.337736 0.168868 0.985639i \(-0.445989\pi\)
0.168868 + 0.985639i \(0.445989\pi\)
\(942\) −14.0538 −0.457899
\(943\) 0.667972 0.0217522
\(944\) 42.7958 1.39289
\(945\) −25.0524 −0.814956
\(946\) 33.4567 1.08777
\(947\) −8.59632 −0.279343 −0.139671 0.990198i \(-0.544605\pi\)
−0.139671 + 0.990198i \(0.544605\pi\)
\(948\) −7.48027 −0.242948
\(949\) −42.8921 −1.39234
\(950\) −23.0662 −0.748365
\(951\) −48.0865 −1.55931
\(952\) −69.9702 −2.26775
\(953\) −28.2227 −0.914221 −0.457111 0.889410i \(-0.651116\pi\)
−0.457111 + 0.889410i \(0.651116\pi\)
\(954\) 0.0724823 0.00234670
\(955\) 0.611354 0.0197830
\(956\) −2.02337 −0.0654404
\(957\) 6.63259 0.214401
\(958\) 5.02696 0.162414
\(959\) 44.1764 1.42653
\(960\) −13.5433 −0.437108
\(961\) 6.67879 0.215445
\(962\) 16.4467 0.530262
\(963\) 1.37521 0.0443155
\(964\) −84.1912 −2.71162
\(965\) −27.7683 −0.893895
\(966\) −72.6953 −2.33893
\(967\) 35.4158 1.13889 0.569447 0.822028i \(-0.307157\pi\)
0.569447 + 0.822028i \(0.307157\pi\)
\(968\) 50.0845 1.60978
\(969\) 26.7709 0.860005
\(970\) 26.9290 0.864637
\(971\) −32.1471 −1.03165 −0.515825 0.856694i \(-0.672515\pi\)
−0.515825 + 0.856694i \(0.672515\pi\)
\(972\) −4.51733 −0.144893
\(973\) −31.0473 −0.995330
\(974\) 58.3198 1.86869
\(975\) −27.9389 −0.894759
\(976\) −44.9170 −1.43776
\(977\) −56.5001 −1.80760 −0.903800 0.427955i \(-0.859234\pi\)
−0.903800 + 0.427955i \(0.859234\pi\)
\(978\) −65.3811 −2.09066
\(979\) −5.95459 −0.190310
\(980\) −13.0856 −0.418003
\(981\) 0.103143 0.00329310
\(982\) 108.462 3.46117
\(983\) −28.6677 −0.914357 −0.457179 0.889375i \(-0.651140\pi\)
−0.457179 + 0.889375i \(0.651140\pi\)
\(984\) −1.09758 −0.0349897
\(985\) 11.6261 0.370438
\(986\) 29.5433 0.940849
\(987\) −7.80092 −0.248306
\(988\) 103.400 3.28959
\(989\) 55.2002 1.75526
\(990\) −0.567044 −0.0180218
\(991\) 11.2638 0.357806 0.178903 0.983867i \(-0.442745\pi\)
0.178903 + 0.983867i \(0.442745\pi\)
\(992\) 13.9529 0.443004
\(993\) −53.5585 −1.69963
\(994\) −52.6952 −1.67139
\(995\) −42.7820 −1.35628
\(996\) −9.84148 −0.311839
\(997\) −38.7561 −1.22742 −0.613710 0.789532i \(-0.710323\pi\)
−0.613710 + 0.789532i \(0.710323\pi\)
\(998\) 27.1652 0.859900
\(999\) 5.28160 0.167102
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 4033.2.a.f.1.5 85
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.f.1.5 85 1.1 even 1 trivial