Properties

Label 6037.2.a.b.1.16
Level 6037
Weight 2
Character 6037.1
Self dual yes
Analytic conductor 48.206
Analytic rank 0
Dimension 259
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 6037 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6037.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.2056877002\)
Analytic rank: \(0\)
Dimension: \(259\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.44806 q^{2} +0.638947 q^{3} +3.99301 q^{4} +2.71697 q^{5} -1.56418 q^{6} -2.58742 q^{7} -4.87901 q^{8} -2.59175 q^{9} +O(q^{10})\) \(q-2.44806 q^{2} +0.638947 q^{3} +3.99301 q^{4} +2.71697 q^{5} -1.56418 q^{6} -2.58742 q^{7} -4.87901 q^{8} -2.59175 q^{9} -6.65132 q^{10} -1.21810 q^{11} +2.55132 q^{12} +3.03775 q^{13} +6.33417 q^{14} +1.73600 q^{15} +3.95809 q^{16} -7.02111 q^{17} +6.34476 q^{18} -2.68795 q^{19} +10.8489 q^{20} -1.65323 q^{21} +2.98198 q^{22} +3.79072 q^{23} -3.11742 q^{24} +2.38195 q^{25} -7.43660 q^{26} -3.57283 q^{27} -10.3316 q^{28} +2.04796 q^{29} -4.24984 q^{30} +1.27817 q^{31} +0.0683552 q^{32} -0.778299 q^{33} +17.1881 q^{34} -7.02997 q^{35} -10.3489 q^{36} -1.90866 q^{37} +6.58026 q^{38} +1.94096 q^{39} -13.2561 q^{40} +5.31602 q^{41} +4.04720 q^{42} +10.0162 q^{43} -4.86387 q^{44} -7.04171 q^{45} -9.27992 q^{46} -0.542905 q^{47} +2.52901 q^{48} -0.305236 q^{49} -5.83116 q^{50} -4.48611 q^{51} +12.1298 q^{52} -0.780766 q^{53} +8.74650 q^{54} -3.30954 q^{55} +12.6241 q^{56} -1.71745 q^{57} -5.01354 q^{58} +1.67584 q^{59} +6.93187 q^{60} +3.68160 q^{61} -3.12905 q^{62} +6.70595 q^{63} -8.08352 q^{64} +8.25349 q^{65} +1.90532 q^{66} -3.02607 q^{67} -28.0353 q^{68} +2.42207 q^{69} +17.2098 q^{70} -6.94609 q^{71} +12.6451 q^{72} -9.17151 q^{73} +4.67251 q^{74} +1.52194 q^{75} -10.7330 q^{76} +3.15173 q^{77} -4.75159 q^{78} -10.3060 q^{79} +10.7540 q^{80} +5.49240 q^{81} -13.0140 q^{82} +2.04260 q^{83} -6.60134 q^{84} -19.0762 q^{85} -24.5203 q^{86} +1.30854 q^{87} +5.94310 q^{88} +7.64182 q^{89} +17.2385 q^{90} -7.85995 q^{91} +15.1364 q^{92} +0.816685 q^{93} +1.32907 q^{94} -7.30308 q^{95} +0.0436753 q^{96} +10.5494 q^{97} +0.747237 q^{98} +3.15700 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.44806 −1.73104 −0.865521 0.500873i \(-0.833012\pi\)
−0.865521 + 0.500873i \(0.833012\pi\)
\(3\) 0.638947 0.368896 0.184448 0.982842i \(-0.440950\pi\)
0.184448 + 0.982842i \(0.440950\pi\)
\(4\) 3.99301 1.99650
\(5\) 2.71697 1.21507 0.607534 0.794294i \(-0.292159\pi\)
0.607534 + 0.794294i \(0.292159\pi\)
\(6\) −1.56418 −0.638574
\(7\) −2.58742 −0.977954 −0.488977 0.872297i \(-0.662630\pi\)
−0.488977 + 0.872297i \(0.662630\pi\)
\(8\) −4.87901 −1.72499
\(9\) −2.59175 −0.863916
\(10\) −6.65132 −2.10333
\(11\) −1.21810 −0.367270 −0.183635 0.982994i \(-0.558786\pi\)
−0.183635 + 0.982994i \(0.558786\pi\)
\(12\) 2.55132 0.736502
\(13\) 3.03775 0.842520 0.421260 0.906940i \(-0.361588\pi\)
0.421260 + 0.906940i \(0.361588\pi\)
\(14\) 6.33417 1.69288
\(15\) 1.73600 0.448234
\(16\) 3.95809 0.989523
\(17\) −7.02111 −1.70287 −0.851434 0.524461i \(-0.824267\pi\)
−0.851434 + 0.524461i \(0.824267\pi\)
\(18\) 6.34476 1.49547
\(19\) −2.68795 −0.616657 −0.308329 0.951280i \(-0.599770\pi\)
−0.308329 + 0.951280i \(0.599770\pi\)
\(20\) 10.8489 2.42589
\(21\) −1.65323 −0.360763
\(22\) 2.98198 0.635760
\(23\) 3.79072 0.790420 0.395210 0.918591i \(-0.370672\pi\)
0.395210 + 0.918591i \(0.370672\pi\)
\(24\) −3.11742 −0.636342
\(25\) 2.38195 0.476390
\(26\) −7.43660 −1.45844
\(27\) −3.57283 −0.687591
\(28\) −10.3316 −1.95249
\(29\) 2.04796 0.380297 0.190149 0.981755i \(-0.439103\pi\)
0.190149 + 0.981755i \(0.439103\pi\)
\(30\) −4.24984 −0.775911
\(31\) 1.27817 0.229567 0.114783 0.993391i \(-0.463383\pi\)
0.114783 + 0.993391i \(0.463383\pi\)
\(32\) 0.0683552 0.0120836
\(33\) −0.778299 −0.135484
\(34\) 17.1881 2.94774
\(35\) −7.02997 −1.18828
\(36\) −10.3489 −1.72481
\(37\) −1.90866 −0.313781 −0.156891 0.987616i \(-0.550147\pi\)
−0.156891 + 0.987616i \(0.550147\pi\)
\(38\) 6.58026 1.06746
\(39\) 1.94096 0.310802
\(40\) −13.2561 −2.09598
\(41\) 5.31602 0.830223 0.415112 0.909770i \(-0.363742\pi\)
0.415112 + 0.909770i \(0.363742\pi\)
\(42\) 4.04720 0.624496
\(43\) 10.0162 1.52745 0.763727 0.645539i \(-0.223367\pi\)
0.763727 + 0.645539i \(0.223367\pi\)
\(44\) −4.86387 −0.733256
\(45\) −7.04171 −1.04972
\(46\) −9.27992 −1.36825
\(47\) −0.542905 −0.0791909 −0.0395954 0.999216i \(-0.512607\pi\)
−0.0395954 + 0.999216i \(0.512607\pi\)
\(48\) 2.52901 0.365031
\(49\) −0.305236 −0.0436052
\(50\) −5.83116 −0.824651
\(51\) −4.48611 −0.628182
\(52\) 12.1298 1.68209
\(53\) −0.780766 −0.107246 −0.0536232 0.998561i \(-0.517077\pi\)
−0.0536232 + 0.998561i \(0.517077\pi\)
\(54\) 8.74650 1.19025
\(55\) −3.30954 −0.446258
\(56\) 12.6241 1.68696
\(57\) −1.71745 −0.227482
\(58\) −5.01354 −0.658310
\(59\) 1.67584 0.218176 0.109088 0.994032i \(-0.465207\pi\)
0.109088 + 0.994032i \(0.465207\pi\)
\(60\) 6.93187 0.894900
\(61\) 3.68160 0.471380 0.235690 0.971828i \(-0.424265\pi\)
0.235690 + 0.971828i \(0.424265\pi\)
\(62\) −3.12905 −0.397390
\(63\) 6.70595 0.844870
\(64\) −8.08352 −1.01044
\(65\) 8.25349 1.02372
\(66\) 1.90532 0.234529
\(67\) −3.02607 −0.369694 −0.184847 0.982767i \(-0.559179\pi\)
−0.184847 + 0.982767i \(0.559179\pi\)
\(68\) −28.0353 −3.39978
\(69\) 2.42207 0.291583
\(70\) 17.2098 2.05696
\(71\) −6.94609 −0.824350 −0.412175 0.911105i \(-0.635231\pi\)
−0.412175 + 0.911105i \(0.635231\pi\)
\(72\) 12.6451 1.49024
\(73\) −9.17151 −1.07344 −0.536722 0.843759i \(-0.680338\pi\)
−0.536722 + 0.843759i \(0.680338\pi\)
\(74\) 4.67251 0.543168
\(75\) 1.52194 0.175738
\(76\) −10.7330 −1.23116
\(77\) 3.15173 0.359173
\(78\) −4.75159 −0.538012
\(79\) −10.3060 −1.15952 −0.579760 0.814787i \(-0.696854\pi\)
−0.579760 + 0.814787i \(0.696854\pi\)
\(80\) 10.7540 1.20234
\(81\) 5.49240 0.610266
\(82\) −13.0140 −1.43715
\(83\) 2.04260 0.224204 0.112102 0.993697i \(-0.464242\pi\)
0.112102 + 0.993697i \(0.464242\pi\)
\(84\) −6.60134 −0.720266
\(85\) −19.0762 −2.06910
\(86\) −24.5203 −2.64409
\(87\) 1.30854 0.140290
\(88\) 5.94310 0.633537
\(89\) 7.64182 0.810031 0.405016 0.914310i \(-0.367266\pi\)
0.405016 + 0.914310i \(0.367266\pi\)
\(90\) 17.2385 1.81710
\(91\) −7.85995 −0.823946
\(92\) 15.1364 1.57808
\(93\) 0.816685 0.0846863
\(94\) 1.32907 0.137083
\(95\) −7.30308 −0.749280
\(96\) 0.0436753 0.00445759
\(97\) 10.5494 1.07113 0.535564 0.844495i \(-0.320099\pi\)
0.535564 + 0.844495i \(0.320099\pi\)
\(98\) 0.747237 0.0754823
\(99\) 3.15700 0.317290
\(100\) 9.51114 0.951114
\(101\) −14.3572 −1.42860 −0.714298 0.699842i \(-0.753254\pi\)
−0.714298 + 0.699842i \(0.753254\pi\)
\(102\) 10.9823 1.08741
\(103\) 2.84322 0.280150 0.140075 0.990141i \(-0.455266\pi\)
0.140075 + 0.990141i \(0.455266\pi\)
\(104\) −14.8212 −1.45334
\(105\) −4.49177 −0.438352
\(106\) 1.91136 0.185648
\(107\) −5.30612 −0.512962 −0.256481 0.966549i \(-0.582563\pi\)
−0.256481 + 0.966549i \(0.582563\pi\)
\(108\) −14.2663 −1.37278
\(109\) 14.6961 1.40763 0.703816 0.710382i \(-0.251478\pi\)
0.703816 + 0.710382i \(0.251478\pi\)
\(110\) 8.10196 0.772491
\(111\) −1.21953 −0.115753
\(112\) −10.2413 −0.967708
\(113\) 6.47672 0.609279 0.304639 0.952468i \(-0.401464\pi\)
0.304639 + 0.952468i \(0.401464\pi\)
\(114\) 4.20443 0.393781
\(115\) 10.2993 0.960414
\(116\) 8.17754 0.759265
\(117\) −7.87308 −0.727866
\(118\) −4.10256 −0.377671
\(119\) 18.1666 1.66533
\(120\) −8.46996 −0.773198
\(121\) −9.51624 −0.865113
\(122\) −9.01278 −0.815979
\(123\) 3.39666 0.306266
\(124\) 5.10376 0.458331
\(125\) −7.11317 −0.636222
\(126\) −16.4166 −1.46251
\(127\) 21.4938 1.90726 0.953632 0.300975i \(-0.0973122\pi\)
0.953632 + 0.300975i \(0.0973122\pi\)
\(128\) 19.6523 1.73703
\(129\) 6.39981 0.563472
\(130\) −20.2050 −1.77210
\(131\) 17.9998 1.57265 0.786323 0.617816i \(-0.211982\pi\)
0.786323 + 0.617816i \(0.211982\pi\)
\(132\) −3.10775 −0.270495
\(133\) 6.95486 0.603063
\(134\) 7.40801 0.639955
\(135\) −9.70728 −0.835470
\(136\) 34.2560 2.93743
\(137\) −20.2559 −1.73058 −0.865291 0.501270i \(-0.832866\pi\)
−0.865291 + 0.501270i \(0.832866\pi\)
\(138\) −5.92937 −0.504742
\(139\) 19.5490 1.65813 0.829063 0.559155i \(-0.188874\pi\)
0.829063 + 0.559155i \(0.188874\pi\)
\(140\) −28.0707 −2.37241
\(141\) −0.346887 −0.0292132
\(142\) 17.0045 1.42698
\(143\) −3.70027 −0.309432
\(144\) −10.2584 −0.854865
\(145\) 5.56427 0.462087
\(146\) 22.4524 1.85818
\(147\) −0.195030 −0.0160858
\(148\) −7.62128 −0.626465
\(149\) 23.8697 1.95548 0.977739 0.209825i \(-0.0672893\pi\)
0.977739 + 0.209825i \(0.0672893\pi\)
\(150\) −3.72580 −0.304210
\(151\) 3.46765 0.282193 0.141096 0.989996i \(-0.454937\pi\)
0.141096 + 0.989996i \(0.454937\pi\)
\(152\) 13.1145 1.06373
\(153\) 18.1969 1.47114
\(154\) −7.71564 −0.621744
\(155\) 3.47277 0.278939
\(156\) 7.75027 0.620518
\(157\) −14.7265 −1.17531 −0.587653 0.809113i \(-0.699948\pi\)
−0.587653 + 0.809113i \(0.699948\pi\)
\(158\) 25.2298 2.00718
\(159\) −0.498868 −0.0395628
\(160\) 0.185719 0.0146824
\(161\) −9.80820 −0.772995
\(162\) −13.4457 −1.05640
\(163\) −15.3276 −1.20055 −0.600274 0.799795i \(-0.704942\pi\)
−0.600274 + 0.799795i \(0.704942\pi\)
\(164\) 21.2269 1.65754
\(165\) −2.11462 −0.164623
\(166\) −5.00040 −0.388107
\(167\) 16.4302 1.27141 0.635705 0.771932i \(-0.280709\pi\)
0.635705 + 0.771932i \(0.280709\pi\)
\(168\) 8.06610 0.622313
\(169\) −3.77208 −0.290160
\(170\) 46.6996 3.58170
\(171\) 6.96648 0.532740
\(172\) 39.9947 3.04957
\(173\) 18.0974 1.37592 0.687959 0.725749i \(-0.258507\pi\)
0.687959 + 0.725749i \(0.258507\pi\)
\(174\) −3.20339 −0.242848
\(175\) −6.16312 −0.465888
\(176\) −4.82134 −0.363422
\(177\) 1.07077 0.0804842
\(178\) −18.7077 −1.40220
\(179\) −13.6150 −1.01763 −0.508815 0.860876i \(-0.669916\pi\)
−0.508815 + 0.860876i \(0.669916\pi\)
\(180\) −28.1176 −2.09576
\(181\) 18.8659 1.40229 0.701144 0.713019i \(-0.252673\pi\)
0.701144 + 0.713019i \(0.252673\pi\)
\(182\) 19.2416 1.42628
\(183\) 2.35234 0.173890
\(184\) −18.4949 −1.36347
\(185\) −5.18577 −0.381265
\(186\) −1.99930 −0.146596
\(187\) 8.55239 0.625413
\(188\) −2.16782 −0.158105
\(189\) 9.24442 0.672433
\(190\) 17.8784 1.29704
\(191\) 24.6849 1.78614 0.893070 0.449918i \(-0.148547\pi\)
0.893070 + 0.449918i \(0.148547\pi\)
\(192\) −5.16494 −0.372747
\(193\) 4.00533 0.288310 0.144155 0.989555i \(-0.453954\pi\)
0.144155 + 0.989555i \(0.453954\pi\)
\(194\) −25.8255 −1.85417
\(195\) 5.27354 0.377646
\(196\) −1.21881 −0.0870579
\(197\) 12.4603 0.887762 0.443881 0.896086i \(-0.353601\pi\)
0.443881 + 0.896086i \(0.353601\pi\)
\(198\) −7.72853 −0.549243
\(199\) −8.10231 −0.574358 −0.287179 0.957877i \(-0.592717\pi\)
−0.287179 + 0.957877i \(0.592717\pi\)
\(200\) −11.6215 −0.821768
\(201\) −1.93350 −0.136378
\(202\) 35.1473 2.47296
\(203\) −5.29895 −0.371913
\(204\) −17.9131 −1.25417
\(205\) 14.4435 1.00878
\(206\) −6.96037 −0.484952
\(207\) −9.82459 −0.682856
\(208\) 12.0237 0.833693
\(209\) 3.27418 0.226480
\(210\) 10.9961 0.758806
\(211\) −1.81191 −0.124737 −0.0623685 0.998053i \(-0.519865\pi\)
−0.0623685 + 0.998053i \(0.519865\pi\)
\(212\) −3.11760 −0.214118
\(213\) −4.43818 −0.304099
\(214\) 12.9897 0.887959
\(215\) 27.2137 1.85596
\(216\) 17.4318 1.18609
\(217\) −3.30718 −0.224506
\(218\) −35.9770 −2.43667
\(219\) −5.86010 −0.395989
\(220\) −13.2150 −0.890956
\(221\) −21.3284 −1.43470
\(222\) 2.98548 0.200373
\(223\) 15.7492 1.05464 0.527321 0.849666i \(-0.323196\pi\)
0.527321 + 0.849666i \(0.323196\pi\)
\(224\) −0.176864 −0.0118172
\(225\) −6.17341 −0.411561
\(226\) −15.8554 −1.05469
\(227\) 28.2574 1.87551 0.937755 0.347298i \(-0.112901\pi\)
0.937755 + 0.347298i \(0.112901\pi\)
\(228\) −6.85781 −0.454169
\(229\) 4.06379 0.268543 0.134271 0.990945i \(-0.457131\pi\)
0.134271 + 0.990945i \(0.457131\pi\)
\(230\) −25.2133 −1.66252
\(231\) 2.01379 0.132498
\(232\) −9.99203 −0.656009
\(233\) −12.5962 −0.825205 −0.412603 0.910911i \(-0.635380\pi\)
−0.412603 + 0.910911i \(0.635380\pi\)
\(234\) 19.2738 1.25997
\(235\) −1.47506 −0.0962223
\(236\) 6.69164 0.435589
\(237\) −6.58501 −0.427742
\(238\) −44.4729 −2.88275
\(239\) −9.72816 −0.629263 −0.314631 0.949214i \(-0.601881\pi\)
−0.314631 + 0.949214i \(0.601881\pi\)
\(240\) 6.87126 0.443538
\(241\) −3.20338 −0.206348 −0.103174 0.994663i \(-0.532900\pi\)
−0.103174 + 0.994663i \(0.532900\pi\)
\(242\) 23.2963 1.49755
\(243\) 14.2278 0.912716
\(244\) 14.7006 0.941112
\(245\) −0.829319 −0.0529832
\(246\) −8.31522 −0.530159
\(247\) −8.16531 −0.519546
\(248\) −6.23622 −0.396000
\(249\) 1.30511 0.0827080
\(250\) 17.4135 1.10133
\(251\) −6.66846 −0.420909 −0.210455 0.977604i \(-0.567494\pi\)
−0.210455 + 0.977604i \(0.567494\pi\)
\(252\) 26.7769 1.68679
\(253\) −4.61747 −0.290298
\(254\) −52.6181 −3.30155
\(255\) −12.1887 −0.763283
\(256\) −31.9429 −1.99643
\(257\) 13.3549 0.833057 0.416529 0.909123i \(-0.363247\pi\)
0.416529 + 0.909123i \(0.363247\pi\)
\(258\) −15.6671 −0.975393
\(259\) 4.93850 0.306864
\(260\) 32.9562 2.04386
\(261\) −5.30780 −0.328545
\(262\) −44.0645 −2.72231
\(263\) 4.48350 0.276464 0.138232 0.990400i \(-0.455858\pi\)
0.138232 + 0.990400i \(0.455858\pi\)
\(264\) 3.79733 0.233709
\(265\) −2.12132 −0.130312
\(266\) −17.0259 −1.04393
\(267\) 4.88272 0.298817
\(268\) −12.0831 −0.738095
\(269\) 7.97761 0.486404 0.243202 0.969976i \(-0.421802\pi\)
0.243202 + 0.969976i \(0.421802\pi\)
\(270\) 23.7640 1.44623
\(271\) −29.8671 −1.81430 −0.907148 0.420812i \(-0.861745\pi\)
−0.907148 + 0.420812i \(0.861745\pi\)
\(272\) −27.7902 −1.68503
\(273\) −5.02209 −0.303950
\(274\) 49.5878 2.99571
\(275\) −2.90145 −0.174964
\(276\) 9.67133 0.582146
\(277\) 29.3875 1.76573 0.882863 0.469631i \(-0.155613\pi\)
0.882863 + 0.469631i \(0.155613\pi\)
\(278\) −47.8572 −2.87029
\(279\) −3.31271 −0.198326
\(280\) 34.2992 2.04977
\(281\) 19.0313 1.13531 0.567655 0.823266i \(-0.307851\pi\)
0.567655 + 0.823266i \(0.307851\pi\)
\(282\) 0.849202 0.0505692
\(283\) 10.1295 0.602137 0.301068 0.953603i \(-0.402657\pi\)
0.301068 + 0.953603i \(0.402657\pi\)
\(284\) −27.7358 −1.64582
\(285\) −4.66628 −0.276407
\(286\) 9.05850 0.535640
\(287\) −13.7548 −0.811921
\(288\) −0.177159 −0.0104392
\(289\) 32.2960 1.89976
\(290\) −13.6217 −0.799892
\(291\) 6.74049 0.395135
\(292\) −36.6219 −2.14313
\(293\) 5.97991 0.349350 0.174675 0.984626i \(-0.444113\pi\)
0.174675 + 0.984626i \(0.444113\pi\)
\(294\) 0.477445 0.0278451
\(295\) 4.55322 0.265099
\(296\) 9.31234 0.541269
\(297\) 4.35205 0.252532
\(298\) −58.4344 −3.38501
\(299\) 11.5153 0.665945
\(300\) 6.07711 0.350862
\(301\) −25.9161 −1.49378
\(302\) −8.48901 −0.488488
\(303\) −9.17349 −0.527003
\(304\) −10.6391 −0.610197
\(305\) 10.0028 0.572759
\(306\) −44.5472 −2.54660
\(307\) −6.15134 −0.351076 −0.175538 0.984473i \(-0.556166\pi\)
−0.175538 + 0.984473i \(0.556166\pi\)
\(308\) 12.5849 0.717091
\(309\) 1.81666 0.103346
\(310\) −8.50155 −0.482856
\(311\) −18.2099 −1.03259 −0.516294 0.856411i \(-0.672689\pi\)
−0.516294 + 0.856411i \(0.672689\pi\)
\(312\) −9.46995 −0.536131
\(313\) −4.30348 −0.243247 −0.121624 0.992576i \(-0.538810\pi\)
−0.121624 + 0.992576i \(0.538810\pi\)
\(314\) 36.0515 2.03450
\(315\) 18.2199 1.02657
\(316\) −41.1521 −2.31498
\(317\) 4.32905 0.243144 0.121572 0.992583i \(-0.461207\pi\)
0.121572 + 0.992583i \(0.461207\pi\)
\(318\) 1.22126 0.0684848
\(319\) −2.49462 −0.139672
\(320\) −21.9627 −1.22775
\(321\) −3.39033 −0.189230
\(322\) 24.0111 1.33809
\(323\) 18.8724 1.05009
\(324\) 21.9312 1.21840
\(325\) 7.23577 0.401368
\(326\) 37.5228 2.07820
\(327\) 9.39003 0.519270
\(328\) −25.9369 −1.43213
\(329\) 1.40473 0.0774450
\(330\) 5.17672 0.284969
\(331\) −22.7375 −1.24977 −0.624883 0.780718i \(-0.714853\pi\)
−0.624883 + 0.780718i \(0.714853\pi\)
\(332\) 8.15610 0.447624
\(333\) 4.94675 0.271080
\(334\) −40.2222 −2.20086
\(335\) −8.22176 −0.449203
\(336\) −6.54362 −0.356984
\(337\) −26.8457 −1.46238 −0.731190 0.682174i \(-0.761035\pi\)
−0.731190 + 0.682174i \(0.761035\pi\)
\(338\) 9.23428 0.502279
\(339\) 4.13828 0.224761
\(340\) −76.1713 −4.13097
\(341\) −1.55694 −0.0843131
\(342\) −17.0544 −0.922195
\(343\) 18.9017 1.02060
\(344\) −48.8690 −2.63484
\(345\) 6.58070 0.354293
\(346\) −44.3035 −2.38177
\(347\) 0.623186 0.0334544 0.0167272 0.999860i \(-0.494675\pi\)
0.0167272 + 0.999860i \(0.494675\pi\)
\(348\) 5.22501 0.280090
\(349\) −21.0827 −1.12853 −0.564266 0.825593i \(-0.690841\pi\)
−0.564266 + 0.825593i \(0.690841\pi\)
\(350\) 15.0877 0.806471
\(351\) −10.8534 −0.579309
\(352\) −0.0832632 −0.00443795
\(353\) −13.9529 −0.742637 −0.371319 0.928506i \(-0.621094\pi\)
−0.371319 + 0.928506i \(0.621094\pi\)
\(354\) −2.62132 −0.139321
\(355\) −18.8724 −1.00164
\(356\) 30.5138 1.61723
\(357\) 11.6075 0.614333
\(358\) 33.3303 1.76156
\(359\) 9.05258 0.477777 0.238888 0.971047i \(-0.423217\pi\)
0.238888 + 0.971047i \(0.423217\pi\)
\(360\) 34.3565 1.81075
\(361\) −11.7749 −0.619734
\(362\) −46.1848 −2.42742
\(363\) −6.08037 −0.319137
\(364\) −31.3848 −1.64501
\(365\) −24.9188 −1.30431
\(366\) −5.75868 −0.301011
\(367\) 19.7610 1.03152 0.515758 0.856734i \(-0.327510\pi\)
0.515758 + 0.856734i \(0.327510\pi\)
\(368\) 15.0040 0.782139
\(369\) −13.7778 −0.717243
\(370\) 12.6951 0.659986
\(371\) 2.02017 0.104882
\(372\) 3.26103 0.169077
\(373\) 5.28206 0.273495 0.136747 0.990606i \(-0.456335\pi\)
0.136747 + 0.990606i \(0.456335\pi\)
\(374\) −20.9368 −1.08262
\(375\) −4.54494 −0.234700
\(376\) 2.64884 0.136603
\(377\) 6.22120 0.320408
\(378\) −22.6309 −1.16401
\(379\) 4.91493 0.252463 0.126232 0.992001i \(-0.459712\pi\)
0.126232 + 0.992001i \(0.459712\pi\)
\(380\) −29.1613 −1.49594
\(381\) 13.7334 0.703582
\(382\) −60.4303 −3.09188
\(383\) 12.4502 0.636175 0.318087 0.948061i \(-0.396959\pi\)
0.318087 + 0.948061i \(0.396959\pi\)
\(384\) 12.5567 0.640784
\(385\) 8.56318 0.436420
\(386\) −9.80529 −0.499076
\(387\) −25.9594 −1.31959
\(388\) 42.1238 2.13851
\(389\) 5.73019 0.290532 0.145266 0.989393i \(-0.453596\pi\)
0.145266 + 0.989393i \(0.453596\pi\)
\(390\) −12.9099 −0.653721
\(391\) −26.6151 −1.34598
\(392\) 1.48925 0.0752184
\(393\) 11.5009 0.580143
\(394\) −30.5037 −1.53675
\(395\) −28.0012 −1.40889
\(396\) 12.6059 0.633472
\(397\) 24.0411 1.20659 0.603295 0.797518i \(-0.293854\pi\)
0.603295 + 0.797518i \(0.293854\pi\)
\(398\) 19.8350 0.994237
\(399\) 4.44378 0.222467
\(400\) 9.42798 0.471399
\(401\) −19.7439 −0.985963 −0.492981 0.870040i \(-0.664093\pi\)
−0.492981 + 0.870040i \(0.664093\pi\)
\(402\) 4.73332 0.236077
\(403\) 3.88277 0.193415
\(404\) −57.3285 −2.85220
\(405\) 14.9227 0.741515
\(406\) 12.9722 0.643798
\(407\) 2.32493 0.115242
\(408\) 21.8878 1.08361
\(409\) −24.3986 −1.20643 −0.603216 0.797578i \(-0.706114\pi\)
−0.603216 + 0.797578i \(0.706114\pi\)
\(410\) −35.3586 −1.74624
\(411\) −12.9425 −0.638405
\(412\) 11.3530 0.559321
\(413\) −4.33611 −0.213366
\(414\) 24.0512 1.18205
\(415\) 5.54968 0.272423
\(416\) 0.207646 0.0101807
\(417\) 12.4908 0.611676
\(418\) −8.01540 −0.392046
\(419\) 27.3441 1.33585 0.667923 0.744231i \(-0.267184\pi\)
0.667923 + 0.744231i \(0.267184\pi\)
\(420\) −17.9357 −0.875172
\(421\) −19.0243 −0.927190 −0.463595 0.886047i \(-0.653441\pi\)
−0.463595 + 0.886047i \(0.653441\pi\)
\(422\) 4.43567 0.215925
\(423\) 1.40707 0.0684142
\(424\) 3.80936 0.184999
\(425\) −16.7239 −0.811230
\(426\) 10.8649 0.526408
\(427\) −9.52585 −0.460988
\(428\) −21.1874 −1.02413
\(429\) −2.36428 −0.114148
\(430\) −66.6209 −3.21275
\(431\) 26.9087 1.29615 0.648074 0.761577i \(-0.275575\pi\)
0.648074 + 0.761577i \(0.275575\pi\)
\(432\) −14.1416 −0.680387
\(433\) 1.64122 0.0788718 0.0394359 0.999222i \(-0.487444\pi\)
0.0394359 + 0.999222i \(0.487444\pi\)
\(434\) 8.09618 0.388629
\(435\) 3.55527 0.170462
\(436\) 58.6817 2.81034
\(437\) −10.1893 −0.487418
\(438\) 14.3459 0.685474
\(439\) 2.23271 0.106562 0.0532808 0.998580i \(-0.483032\pi\)
0.0532808 + 0.998580i \(0.483032\pi\)
\(440\) 16.1473 0.769790
\(441\) 0.791095 0.0376712
\(442\) 52.2132 2.48353
\(443\) −16.8275 −0.799497 −0.399749 0.916625i \(-0.630903\pi\)
−0.399749 + 0.916625i \(0.630903\pi\)
\(444\) −4.86959 −0.231101
\(445\) 20.7626 0.984243
\(446\) −38.5550 −1.82563
\(447\) 15.2514 0.721368
\(448\) 20.9155 0.988165
\(449\) −25.1524 −1.18702 −0.593508 0.804828i \(-0.702258\pi\)
−0.593508 + 0.804828i \(0.702258\pi\)
\(450\) 15.1129 0.712429
\(451\) −6.47543 −0.304916
\(452\) 25.8616 1.21643
\(453\) 2.21564 0.104100
\(454\) −69.1759 −3.24658
\(455\) −21.3553 −1.00115
\(456\) 8.37947 0.392405
\(457\) 6.34089 0.296614 0.148307 0.988941i \(-0.452618\pi\)
0.148307 + 0.988941i \(0.452618\pi\)
\(458\) −9.94841 −0.464859
\(459\) 25.0852 1.17088
\(460\) 41.1251 1.91747
\(461\) 36.9823 1.72244 0.861220 0.508233i \(-0.169701\pi\)
0.861220 + 0.508233i \(0.169701\pi\)
\(462\) −4.92988 −0.229359
\(463\) 2.01797 0.0937829 0.0468915 0.998900i \(-0.485069\pi\)
0.0468915 + 0.998900i \(0.485069\pi\)
\(464\) 8.10603 0.376313
\(465\) 2.21891 0.102900
\(466\) 30.8363 1.42846
\(467\) 10.4813 0.485017 0.242508 0.970149i \(-0.422030\pi\)
0.242508 + 0.970149i \(0.422030\pi\)
\(468\) −31.4373 −1.45319
\(469\) 7.82973 0.361543
\(470\) 3.61104 0.166565
\(471\) −9.40947 −0.433566
\(472\) −8.17644 −0.376351
\(473\) −12.2007 −0.560988
\(474\) 16.1205 0.740439
\(475\) −6.40255 −0.293769
\(476\) 72.5393 3.32483
\(477\) 2.02355 0.0926519
\(478\) 23.8151 1.08928
\(479\) 3.18121 0.145353 0.0726766 0.997356i \(-0.476846\pi\)
0.0726766 + 0.997356i \(0.476846\pi\)
\(480\) 0.118665 0.00541628
\(481\) −5.79802 −0.264367
\(482\) 7.84207 0.357197
\(483\) −6.26692 −0.285155
\(484\) −37.9984 −1.72720
\(485\) 28.6624 1.30149
\(486\) −34.8306 −1.57995
\(487\) 19.3044 0.874765 0.437383 0.899276i \(-0.355906\pi\)
0.437383 + 0.899276i \(0.355906\pi\)
\(488\) −17.9625 −0.813126
\(489\) −9.79350 −0.442877
\(490\) 2.03022 0.0917162
\(491\) 11.5390 0.520747 0.260373 0.965508i \(-0.416154\pi\)
0.260373 + 0.965508i \(0.416154\pi\)
\(492\) 13.5629 0.611461
\(493\) −14.3790 −0.647597
\(494\) 19.9892 0.899356
\(495\) 8.57749 0.385529
\(496\) 5.05913 0.227162
\(497\) 17.9725 0.806176
\(498\) −3.19499 −0.143171
\(499\) 14.8497 0.664764 0.332382 0.943145i \(-0.392148\pi\)
0.332382 + 0.943145i \(0.392148\pi\)
\(500\) −28.4030 −1.27022
\(501\) 10.4980 0.469018
\(502\) 16.3248 0.728612
\(503\) 26.7758 1.19387 0.596937 0.802288i \(-0.296384\pi\)
0.596937 + 0.802288i \(0.296384\pi\)
\(504\) −32.7184 −1.45739
\(505\) −39.0082 −1.73584
\(506\) 11.3038 0.502517
\(507\) −2.41016 −0.107039
\(508\) 85.8248 3.80786
\(509\) 3.91792 0.173659 0.0868294 0.996223i \(-0.472326\pi\)
0.0868294 + 0.996223i \(0.472326\pi\)
\(510\) 29.8386 1.32127
\(511\) 23.7306 1.04978
\(512\) 38.8937 1.71887
\(513\) 9.60357 0.424008
\(514\) −32.6937 −1.44206
\(515\) 7.72495 0.340402
\(516\) 25.5545 1.12497
\(517\) 0.661311 0.0290844
\(518\) −12.0898 −0.531194
\(519\) 11.5633 0.507571
\(520\) −40.2688 −1.76590
\(521\) 22.1673 0.971168 0.485584 0.874190i \(-0.338607\pi\)
0.485584 + 0.874190i \(0.338607\pi\)
\(522\) 12.9938 0.568725
\(523\) 16.9234 0.740010 0.370005 0.929030i \(-0.379356\pi\)
0.370005 + 0.929030i \(0.379356\pi\)
\(524\) 71.8731 3.13979
\(525\) −3.93790 −0.171864
\(526\) −10.9759 −0.478571
\(527\) −8.97420 −0.390922
\(528\) −3.08058 −0.134065
\(529\) −8.63044 −0.375237
\(530\) 5.19313 0.225575
\(531\) −4.34336 −0.188486
\(532\) 27.7708 1.20402
\(533\) 16.1487 0.699480
\(534\) −11.9532 −0.517265
\(535\) −14.4166 −0.623284
\(536\) 14.7642 0.637717
\(537\) −8.69924 −0.375400
\(538\) −19.5297 −0.841985
\(539\) 0.371807 0.0160149
\(540\) −38.7613 −1.66802
\(541\) 4.86672 0.209236 0.104618 0.994512i \(-0.466638\pi\)
0.104618 + 0.994512i \(0.466638\pi\)
\(542\) 73.1165 3.14062
\(543\) 12.0543 0.517299
\(544\) −0.479929 −0.0205768
\(545\) 39.9290 1.71037
\(546\) 12.2944 0.526151
\(547\) 39.9013 1.70606 0.853028 0.521866i \(-0.174764\pi\)
0.853028 + 0.521866i \(0.174764\pi\)
\(548\) −80.8821 −3.45511
\(549\) −9.54177 −0.407233
\(550\) 7.10292 0.302870
\(551\) −5.50482 −0.234513
\(552\) −11.8173 −0.502977
\(553\) 26.6661 1.13396
\(554\) −71.9425 −3.05654
\(555\) −3.31343 −0.140647
\(556\) 78.0594 3.31046
\(557\) −15.0197 −0.636407 −0.318204 0.948022i \(-0.603080\pi\)
−0.318204 + 0.948022i \(0.603080\pi\)
\(558\) 8.10971 0.343311
\(559\) 30.4267 1.28691
\(560\) −27.8253 −1.17583
\(561\) 5.46452 0.230712
\(562\) −46.5897 −1.96527
\(563\) −4.39769 −0.185340 −0.0926702 0.995697i \(-0.529540\pi\)
−0.0926702 + 0.995697i \(0.529540\pi\)
\(564\) −1.38512 −0.0583242
\(565\) 17.5971 0.740315
\(566\) −24.7977 −1.04232
\(567\) −14.2112 −0.596812
\(568\) 33.8900 1.42199
\(569\) −0.103258 −0.00432879 −0.00216439 0.999998i \(-0.500689\pi\)
−0.00216439 + 0.999998i \(0.500689\pi\)
\(570\) 11.4233 0.478471
\(571\) −20.3614 −0.852099 −0.426050 0.904700i \(-0.640095\pi\)
−0.426050 + 0.904700i \(0.640095\pi\)
\(572\) −14.7752 −0.617783
\(573\) 15.7724 0.658900
\(574\) 33.6726 1.40547
\(575\) 9.02931 0.376548
\(576\) 20.9504 0.872935
\(577\) 0.522539 0.0217536 0.0108768 0.999941i \(-0.496538\pi\)
0.0108768 + 0.999941i \(0.496538\pi\)
\(578\) −79.0625 −3.28857
\(579\) 2.55919 0.106356
\(580\) 22.2182 0.922559
\(581\) −5.28506 −0.219261
\(582\) −16.5011 −0.683994
\(583\) 0.951049 0.0393884
\(584\) 44.7478 1.85168
\(585\) −21.3910 −0.884407
\(586\) −14.6392 −0.604739
\(587\) −8.92951 −0.368560 −0.184280 0.982874i \(-0.558995\pi\)
−0.184280 + 0.982874i \(0.558995\pi\)
\(588\) −0.778755 −0.0321153
\(589\) −3.43566 −0.141564
\(590\) −11.1466 −0.458896
\(591\) 7.96149 0.327492
\(592\) −7.55464 −0.310494
\(593\) 34.6067 1.42113 0.710563 0.703634i \(-0.248440\pi\)
0.710563 + 0.703634i \(0.248440\pi\)
\(594\) −10.6541 −0.437143
\(595\) 49.3581 2.02349
\(596\) 95.3117 3.90412
\(597\) −5.17695 −0.211878
\(598\) −28.1901 −1.15278
\(599\) 3.81199 0.155754 0.0778768 0.996963i \(-0.475186\pi\)
0.0778768 + 0.996963i \(0.475186\pi\)
\(600\) −7.42555 −0.303147
\(601\) 25.1906 1.02755 0.513773 0.857926i \(-0.328247\pi\)
0.513773 + 0.857926i \(0.328247\pi\)
\(602\) 63.4443 2.58580
\(603\) 7.84281 0.319384
\(604\) 13.8463 0.563399
\(605\) −25.8554 −1.05117
\(606\) 22.4573 0.912265
\(607\) 17.8056 0.722707 0.361353 0.932429i \(-0.382315\pi\)
0.361353 + 0.932429i \(0.382315\pi\)
\(608\) −0.183735 −0.00745144
\(609\) −3.38575 −0.137197
\(610\) −24.4875 −0.991469
\(611\) −1.64921 −0.0667199
\(612\) 72.6605 2.93713
\(613\) −35.7770 −1.44502 −0.722510 0.691361i \(-0.757012\pi\)
−0.722510 + 0.691361i \(0.757012\pi\)
\(614\) 15.0589 0.607726
\(615\) 9.22863 0.372134
\(616\) −15.3773 −0.619570
\(617\) 33.8685 1.36349 0.681747 0.731588i \(-0.261220\pi\)
0.681747 + 0.731588i \(0.261220\pi\)
\(618\) −4.44731 −0.178897
\(619\) 11.4125 0.458708 0.229354 0.973343i \(-0.426339\pi\)
0.229354 + 0.973343i \(0.426339\pi\)
\(620\) 13.8668 0.556904
\(621\) −13.5436 −0.543486
\(622\) 44.5790 1.78745
\(623\) −19.7726 −0.792174
\(624\) 7.68250 0.307546
\(625\) −31.2361 −1.24944
\(626\) 10.5352 0.421071
\(627\) 2.09203 0.0835475
\(628\) −58.8032 −2.34650
\(629\) 13.4009 0.534328
\(630\) −44.6034 −1.77704
\(631\) −14.0788 −0.560470 −0.280235 0.959931i \(-0.590412\pi\)
−0.280235 + 0.959931i \(0.590412\pi\)
\(632\) 50.2832 2.00016
\(633\) −1.15771 −0.0460150
\(634\) −10.5978 −0.420892
\(635\) 58.3980 2.31746
\(636\) −1.99198 −0.0789873
\(637\) −0.927231 −0.0367382
\(638\) 6.10698 0.241778
\(639\) 18.0025 0.712169
\(640\) 53.3947 2.11061
\(641\) 4.23496 0.167271 0.0836355 0.996496i \(-0.473347\pi\)
0.0836355 + 0.996496i \(0.473347\pi\)
\(642\) 8.29974 0.327565
\(643\) −28.9268 −1.14076 −0.570382 0.821380i \(-0.693205\pi\)
−0.570382 + 0.821380i \(0.693205\pi\)
\(644\) −39.1642 −1.54329
\(645\) 17.3881 0.684657
\(646\) −46.2007 −1.81774
\(647\) 37.9455 1.49179 0.745897 0.666062i \(-0.232021\pi\)
0.745897 + 0.666062i \(0.232021\pi\)
\(648\) −26.7974 −1.05270
\(649\) −2.04134 −0.0801295
\(650\) −17.7136 −0.694785
\(651\) −2.11311 −0.0828194
\(652\) −61.2031 −2.39690
\(653\) 7.20271 0.281864 0.140932 0.990019i \(-0.454990\pi\)
0.140932 + 0.990019i \(0.454990\pi\)
\(654\) −22.9874 −0.898877
\(655\) 48.9049 1.91087
\(656\) 21.0413 0.821525
\(657\) 23.7702 0.927365
\(658\) −3.43886 −0.134061
\(659\) 15.8633 0.617945 0.308972 0.951071i \(-0.400015\pi\)
0.308972 + 0.951071i \(0.400015\pi\)
\(660\) −8.44369 −0.328670
\(661\) −11.9083 −0.463179 −0.231589 0.972814i \(-0.574393\pi\)
−0.231589 + 0.972814i \(0.574393\pi\)
\(662\) 55.6628 2.16340
\(663\) −13.6277 −0.529256
\(664\) −9.96584 −0.386750
\(665\) 18.8962 0.732762
\(666\) −12.1100 −0.469251
\(667\) 7.76326 0.300595
\(668\) 65.6061 2.53838
\(669\) 10.0629 0.389054
\(670\) 20.1274 0.777589
\(671\) −4.48454 −0.173124
\(672\) −0.113007 −0.00435932
\(673\) −34.1140 −1.31500 −0.657499 0.753455i \(-0.728386\pi\)
−0.657499 + 0.753455i \(0.728386\pi\)
\(674\) 65.7200 2.53144
\(675\) −8.51030 −0.327562
\(676\) −15.0619 −0.579305
\(677\) −8.36864 −0.321633 −0.160816 0.986984i \(-0.551413\pi\)
−0.160816 + 0.986984i \(0.551413\pi\)
\(678\) −10.1308 −0.389070
\(679\) −27.2957 −1.04751
\(680\) 93.0727 3.56918
\(681\) 18.0550 0.691868
\(682\) 3.81149 0.145949
\(683\) −5.73012 −0.219257 −0.109628 0.993973i \(-0.534966\pi\)
−0.109628 + 0.993973i \(0.534966\pi\)
\(684\) 27.8172 1.06362
\(685\) −55.0349 −2.10277
\(686\) −46.2726 −1.76670
\(687\) 2.59655 0.0990644
\(688\) 39.6450 1.51145
\(689\) −2.37177 −0.0903573
\(690\) −16.1100 −0.613295
\(691\) −39.9477 −1.51968 −0.759840 0.650110i \(-0.774723\pi\)
−0.759840 + 0.650110i \(0.774723\pi\)
\(692\) 72.2630 2.74703
\(693\) −8.16850 −0.310296
\(694\) −1.52560 −0.0579109
\(695\) 53.1142 2.01474
\(696\) −6.38437 −0.241999
\(697\) −37.3244 −1.41376
\(698\) 51.6118 1.95354
\(699\) −8.04831 −0.304415
\(700\) −24.6094 −0.930147
\(701\) −46.1558 −1.74328 −0.871639 0.490148i \(-0.836943\pi\)
−0.871639 + 0.490148i \(0.836943\pi\)
\(702\) 26.5697 1.00281
\(703\) 5.13037 0.193495
\(704\) 9.84652 0.371105
\(705\) −0.942484 −0.0354960
\(706\) 34.1575 1.28554
\(707\) 37.1482 1.39710
\(708\) 4.27560 0.160687
\(709\) 29.9827 1.12602 0.563011 0.826449i \(-0.309643\pi\)
0.563011 + 0.826449i \(0.309643\pi\)
\(710\) 46.2007 1.73388
\(711\) 26.7106 1.00173
\(712\) −37.2845 −1.39730
\(713\) 4.84520 0.181454
\(714\) −28.4158 −1.06344
\(715\) −10.0536 −0.375981
\(716\) −54.3647 −2.03170
\(717\) −6.21578 −0.232132
\(718\) −22.1613 −0.827052
\(719\) −14.2178 −0.530234 −0.265117 0.964216i \(-0.585411\pi\)
−0.265117 + 0.964216i \(0.585411\pi\)
\(720\) −27.8717 −1.03872
\(721\) −7.35661 −0.273974
\(722\) 28.8258 1.07278
\(723\) −2.04679 −0.0761209
\(724\) 75.3315 2.79967
\(725\) 4.87815 0.181170
\(726\) 14.8851 0.552439
\(727\) −12.0364 −0.446406 −0.223203 0.974772i \(-0.571651\pi\)
−0.223203 + 0.974772i \(0.571651\pi\)
\(728\) 38.3487 1.42130
\(729\) −7.38636 −0.273569
\(730\) 61.0027 2.25781
\(731\) −70.3247 −2.60105
\(732\) 9.39293 0.347173
\(733\) −24.0115 −0.886886 −0.443443 0.896303i \(-0.646243\pi\)
−0.443443 + 0.896303i \(0.646243\pi\)
\(734\) −48.3762 −1.78560
\(735\) −0.529890 −0.0195453
\(736\) 0.259115 0.00955112
\(737\) 3.68605 0.135777
\(738\) 33.7289 1.24158
\(739\) −17.3153 −0.636952 −0.318476 0.947931i \(-0.603171\pi\)
−0.318476 + 0.947931i \(0.603171\pi\)
\(740\) −20.7068 −0.761198
\(741\) −5.21720 −0.191658
\(742\) −4.94551 −0.181555
\(743\) 42.7128 1.56698 0.783490 0.621404i \(-0.213437\pi\)
0.783490 + 0.621404i \(0.213437\pi\)
\(744\) −3.98461 −0.146083
\(745\) 64.8532 2.37604
\(746\) −12.9308 −0.473431
\(747\) −5.29389 −0.193693
\(748\) 34.1498 1.24864
\(749\) 13.7292 0.501654
\(750\) 11.1263 0.406275
\(751\) −0.177872 −0.00649063 −0.00324532 0.999995i \(-0.501033\pi\)
−0.00324532 + 0.999995i \(0.501033\pi\)
\(752\) −2.14887 −0.0783612
\(753\) −4.26079 −0.155272
\(754\) −15.2299 −0.554640
\(755\) 9.42150 0.342884
\(756\) 36.9130 1.34251
\(757\) −34.5227 −1.25475 −0.627374 0.778718i \(-0.715870\pi\)
−0.627374 + 0.778718i \(0.715870\pi\)
\(758\) −12.0321 −0.437024
\(759\) −2.95031 −0.107090
\(760\) 35.6318 1.29250
\(761\) −7.64193 −0.277020 −0.138510 0.990361i \(-0.544231\pi\)
−0.138510 + 0.990361i \(0.544231\pi\)
\(762\) −33.6201 −1.21793
\(763\) −38.0251 −1.37660
\(764\) 98.5672 3.56603
\(765\) 49.4406 1.78753
\(766\) −30.4788 −1.10124
\(767\) 5.09078 0.183818
\(768\) −20.4098 −0.736475
\(769\) −46.0228 −1.65962 −0.829812 0.558044i \(-0.811552\pi\)
−0.829812 + 0.558044i \(0.811552\pi\)
\(770\) −20.9632 −0.755461
\(771\) 8.53308 0.307311
\(772\) 15.9933 0.575612
\(773\) 34.0479 1.22462 0.612309 0.790619i \(-0.290241\pi\)
0.612309 + 0.790619i \(0.290241\pi\)
\(774\) 63.5503 2.28427
\(775\) 3.04455 0.109363
\(776\) −51.4705 −1.84768
\(777\) 3.15544 0.113201
\(778\) −14.0279 −0.502923
\(779\) −14.2892 −0.511963
\(780\) 21.0573 0.753971
\(781\) 8.46102 0.302759
\(782\) 65.1553 2.32995
\(783\) −7.31702 −0.261489
\(784\) −1.20815 −0.0431483
\(785\) −40.0116 −1.42808
\(786\) −28.1549 −1.00425
\(787\) 16.6027 0.591821 0.295910 0.955216i \(-0.404377\pi\)
0.295910 + 0.955216i \(0.404377\pi\)
\(788\) 49.7542 1.77242
\(789\) 2.86472 0.101987
\(790\) 68.5488 2.43886
\(791\) −16.7580 −0.595847
\(792\) −15.4030 −0.547322
\(793\) 11.1838 0.397147
\(794\) −58.8542 −2.08866
\(795\) −1.35541 −0.0480715
\(796\) −32.3526 −1.14671
\(797\) 40.0029 1.41698 0.708488 0.705723i \(-0.249378\pi\)
0.708488 + 0.705723i \(0.249378\pi\)
\(798\) −10.8787 −0.385100
\(799\) 3.81180 0.134852
\(800\) 0.162819 0.00575651
\(801\) −19.8057 −0.699799
\(802\) 48.3343 1.70674
\(803\) 11.1718 0.394244
\(804\) −7.72047 −0.272280
\(805\) −26.6486 −0.939241
\(806\) −9.50527 −0.334809
\(807\) 5.09727 0.179432
\(808\) 70.0489 2.46431
\(809\) −18.6479 −0.655626 −0.327813 0.944743i \(-0.606312\pi\)
−0.327813 + 0.944743i \(0.606312\pi\)
\(810\) −36.5317 −1.28359
\(811\) 4.36721 0.153354 0.0766768 0.997056i \(-0.475569\pi\)
0.0766768 + 0.997056i \(0.475569\pi\)
\(812\) −21.1588 −0.742527
\(813\) −19.0835 −0.669287
\(814\) −5.69157 −0.199489
\(815\) −41.6446 −1.45875
\(816\) −17.7565 −0.621600
\(817\) −26.9230 −0.941916
\(818\) 59.7292 2.08838
\(819\) 20.3710 0.711820
\(820\) 57.6730 2.01403
\(821\) 55.9785 1.95366 0.976831 0.214011i \(-0.0686530\pi\)
0.976831 + 0.214011i \(0.0686530\pi\)
\(822\) 31.6839 1.10510
\(823\) 49.9579 1.74142 0.870711 0.491795i \(-0.163659\pi\)
0.870711 + 0.491795i \(0.163659\pi\)
\(824\) −13.8721 −0.483256
\(825\) −1.85387 −0.0645435
\(826\) 10.6151 0.369345
\(827\) 35.3047 1.22767 0.613833 0.789436i \(-0.289627\pi\)
0.613833 + 0.789436i \(0.289627\pi\)
\(828\) −39.2297 −1.36332
\(829\) 38.9067 1.35129 0.675643 0.737229i \(-0.263866\pi\)
0.675643 + 0.737229i \(0.263866\pi\)
\(830\) −13.5860 −0.471576
\(831\) 18.7771 0.651369
\(832\) −24.5557 −0.851316
\(833\) 2.14310 0.0742539
\(834\) −30.5782 −1.05884
\(835\) 44.6405 1.54485
\(836\) 13.0738 0.452168
\(837\) −4.56670 −0.157848
\(838\) −66.9400 −2.31240
\(839\) 28.2054 0.973759 0.486880 0.873469i \(-0.338135\pi\)
0.486880 + 0.873469i \(0.338135\pi\)
\(840\) 21.9154 0.756153
\(841\) −24.8058 −0.855374
\(842\) 46.5728 1.60500
\(843\) 12.1600 0.418811
\(844\) −7.23497 −0.249038
\(845\) −10.2486 −0.352564
\(846\) −3.44460 −0.118428
\(847\) 24.6225 0.846041
\(848\) −3.09034 −0.106123
\(849\) 6.47222 0.222126
\(850\) 40.9412 1.40427
\(851\) −7.23518 −0.248019
\(852\) −17.7217 −0.607135
\(853\) 37.3608 1.27921 0.639604 0.768705i \(-0.279098\pi\)
0.639604 + 0.768705i \(0.279098\pi\)
\(854\) 23.3199 0.797990
\(855\) 18.9277 0.647315
\(856\) 25.8886 0.884854
\(857\) −30.0266 −1.02569 −0.512844 0.858482i \(-0.671408\pi\)
−0.512844 + 0.858482i \(0.671408\pi\)
\(858\) 5.78790 0.197596
\(859\) −12.2446 −0.417780 −0.208890 0.977939i \(-0.566985\pi\)
−0.208890 + 0.977939i \(0.566985\pi\)
\(860\) 108.665 3.70543
\(861\) −8.78859 −0.299514
\(862\) −65.8743 −2.24369
\(863\) 42.7517 1.45529 0.727643 0.685956i \(-0.240616\pi\)
0.727643 + 0.685956i \(0.240616\pi\)
\(864\) −0.244221 −0.00830858
\(865\) 49.1701 1.67183
\(866\) −4.01780 −0.136530
\(867\) 20.6354 0.700815
\(868\) −13.2056 −0.448227
\(869\) 12.5538 0.425857
\(870\) −8.70352 −0.295077
\(871\) −9.19245 −0.311474
\(872\) −71.7024 −2.42815
\(873\) −27.3413 −0.925364
\(874\) 24.9439 0.843741
\(875\) 18.4048 0.622196
\(876\) −23.3994 −0.790594
\(877\) −11.1387 −0.376128 −0.188064 0.982157i \(-0.560221\pi\)
−0.188064 + 0.982157i \(0.560221\pi\)
\(878\) −5.46582 −0.184462
\(879\) 3.82084 0.128874
\(880\) −13.0995 −0.441583
\(881\) −20.6608 −0.696080 −0.348040 0.937480i \(-0.613153\pi\)
−0.348040 + 0.937480i \(0.613153\pi\)
\(882\) −1.93665 −0.0652104
\(883\) −31.2664 −1.05220 −0.526099 0.850423i \(-0.676346\pi\)
−0.526099 + 0.850423i \(0.676346\pi\)
\(884\) −85.1643 −2.86439
\(885\) 2.90926 0.0977938
\(886\) 41.1947 1.38396
\(887\) 18.9698 0.636942 0.318471 0.947933i \(-0.396831\pi\)
0.318471 + 0.947933i \(0.396831\pi\)
\(888\) 5.95009 0.199672
\(889\) −55.6135 −1.86522
\(890\) −50.8282 −1.70377
\(891\) −6.69027 −0.224133
\(892\) 62.8866 2.10560
\(893\) 1.45930 0.0488336
\(894\) −37.3365 −1.24872
\(895\) −36.9915 −1.23649
\(896\) −50.8487 −1.69874
\(897\) 7.35764 0.245664
\(898\) 61.5747 2.05477
\(899\) 2.61766 0.0873037
\(900\) −24.6505 −0.821683
\(901\) 5.48184 0.182627
\(902\) 15.8523 0.527823
\(903\) −16.5590 −0.551050
\(904\) −31.6000 −1.05100
\(905\) 51.2581 1.70388
\(906\) −5.42403 −0.180201
\(907\) 3.60840 0.119815 0.0599075 0.998204i \(-0.480919\pi\)
0.0599075 + 0.998204i \(0.480919\pi\)
\(908\) 112.832 3.74446
\(909\) 37.2103 1.23419
\(910\) 52.2790 1.73303
\(911\) −20.8948 −0.692276 −0.346138 0.938184i \(-0.612507\pi\)
−0.346138 + 0.938184i \(0.612507\pi\)
\(912\) −6.79784 −0.225099
\(913\) −2.48808 −0.0823435
\(914\) −15.5229 −0.513451
\(915\) 6.39126 0.211288
\(916\) 16.2267 0.536147
\(917\) −46.5730 −1.53798
\(918\) −61.4102 −2.02684
\(919\) 3.58842 0.118371 0.0591855 0.998247i \(-0.481150\pi\)
0.0591855 + 0.998247i \(0.481150\pi\)
\(920\) −50.2503 −1.65670
\(921\) −3.93038 −0.129510
\(922\) −90.5351 −2.98161
\(923\) −21.1005 −0.694531
\(924\) 8.04108 0.264532
\(925\) −4.54632 −0.149482
\(926\) −4.94011 −0.162342
\(927\) −7.36890 −0.242026
\(928\) 0.139989 0.00459536
\(929\) 23.8636 0.782938 0.391469 0.920191i \(-0.371967\pi\)
0.391469 + 0.920191i \(0.371967\pi\)
\(930\) −5.43204 −0.178124
\(931\) 0.820458 0.0268894
\(932\) −50.2968 −1.64752
\(933\) −11.6352 −0.380918
\(934\) −25.6589 −0.839584
\(935\) 23.2366 0.759919
\(936\) 38.4128 1.25556
\(937\) −9.58015 −0.312970 −0.156485 0.987680i \(-0.550016\pi\)
−0.156485 + 0.987680i \(0.550016\pi\)
\(938\) −19.1677 −0.625847
\(939\) −2.74970 −0.0897330
\(940\) −5.88992 −0.192108
\(941\) −20.9329 −0.682393 −0.341197 0.939992i \(-0.610832\pi\)
−0.341197 + 0.939992i \(0.610832\pi\)
\(942\) 23.0350 0.750520
\(943\) 20.1516 0.656225
\(944\) 6.63313 0.215890
\(945\) 25.1169 0.817051
\(946\) 29.8681 0.971094
\(947\) −5.83448 −0.189595 −0.0947976 0.995497i \(-0.530220\pi\)
−0.0947976 + 0.995497i \(0.530220\pi\)
\(948\) −26.2940 −0.853989
\(949\) −27.8607 −0.904398
\(950\) 15.6739 0.508527
\(951\) 2.76603 0.0896947
\(952\) −88.6349 −2.87267
\(953\) −25.6994 −0.832484 −0.416242 0.909254i \(-0.636653\pi\)
−0.416242 + 0.909254i \(0.636653\pi\)
\(954\) −4.95377 −0.160384
\(955\) 67.0684 2.17028
\(956\) −38.8446 −1.25633
\(957\) −1.59393 −0.0515244
\(958\) −7.78779 −0.251612
\(959\) 52.4107 1.69243
\(960\) −14.0330 −0.452913
\(961\) −29.3663 −0.947299
\(962\) 14.1939 0.457630
\(963\) 13.7521 0.443156
\(964\) −12.7911 −0.411974
\(965\) 10.8824 0.350316
\(966\) 15.3418 0.493614
\(967\) −45.6525 −1.46808 −0.734042 0.679104i \(-0.762369\pi\)
−0.734042 + 0.679104i \(0.762369\pi\)
\(968\) 46.4298 1.49231
\(969\) 12.0584 0.387373
\(970\) −70.1673 −2.25294
\(971\) 17.4439 0.559802 0.279901 0.960029i \(-0.409698\pi\)
0.279901 + 0.960029i \(0.409698\pi\)
\(972\) 56.8118 1.82224
\(973\) −50.5816 −1.62157
\(974\) −47.2583 −1.51425
\(975\) 4.62327 0.148063
\(976\) 14.5721 0.466442
\(977\) 23.6939 0.758035 0.379018 0.925389i \(-0.376262\pi\)
0.379018 + 0.925389i \(0.376262\pi\)
\(978\) 23.9751 0.766639
\(979\) −9.30848 −0.297500
\(980\) −3.31148 −0.105781
\(981\) −38.0886 −1.21608
\(982\) −28.2481 −0.901434
\(983\) −8.88218 −0.283298 −0.141649 0.989917i \(-0.545240\pi\)
−0.141649 + 0.989917i \(0.545240\pi\)
\(984\) −16.5723 −0.528306
\(985\) 33.8544 1.07869
\(986\) 35.2006 1.12102
\(987\) 0.897545 0.0285692
\(988\) −32.6041 −1.03728
\(989\) 37.9686 1.20733
\(990\) −20.9982 −0.667367
\(991\) 36.1718 1.14904 0.574518 0.818492i \(-0.305190\pi\)
0.574518 + 0.818492i \(0.305190\pi\)
\(992\) 0.0873698 0.00277399
\(993\) −14.5281 −0.461034
\(994\) −43.9978 −1.39552
\(995\) −22.0138 −0.697884
\(996\) 5.21131 0.165127
\(997\) 37.4471 1.18596 0.592980 0.805217i \(-0.297951\pi\)
0.592980 + 0.805217i \(0.297951\pi\)
\(998\) −36.3530 −1.15073
\(999\) 6.81930 0.215753
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 6037.2.a.b.1.16 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.16 259 1.1 even 1 trivial