Properties

Label 4009.2.a.c.1.4
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

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Newspace parameters

Level: \( N \) = \( 4009 = 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4009.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0120261703\)
Analytic rank: \(1\)
Dimension: \(71\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.67657 q^{2}\) \(+0.00971531 q^{3}\) \(+5.16401 q^{4}\) \(+0.0508514 q^{5}\) \(-0.0260037 q^{6}\) \(+0.312050 q^{7}\) \(-8.46867 q^{8}\) \(-2.99991 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.67657 q^{2}\) \(+0.00971531 q^{3}\) \(+5.16401 q^{4}\) \(+0.0508514 q^{5}\) \(-0.0260037 q^{6}\) \(+0.312050 q^{7}\) \(-8.46867 q^{8}\) \(-2.99991 q^{9}\) \(-0.136107 q^{10}\) \(+3.31590 q^{11}\) \(+0.0501699 q^{12}\) \(+5.10887 q^{13}\) \(-0.835221 q^{14}\) \(+0.000494037 q^{15}\) \(+12.3389 q^{16}\) \(+2.09802 q^{17}\) \(+8.02945 q^{18}\) \(+1.00000 q^{19}\) \(+0.262597 q^{20}\) \(+0.00303166 q^{21}\) \(-8.87522 q^{22}\) \(-7.00610 q^{23}\) \(-0.0822757 q^{24}\) \(-4.99741 q^{25}\) \(-13.6742 q^{26}\) \(-0.0582909 q^{27}\) \(+1.61143 q^{28}\) \(-8.90887 q^{29}\) \(-0.00132232 q^{30}\) \(+10.8021 q^{31}\) \(-16.0887 q^{32}\) \(+0.0322150 q^{33}\) \(-5.61550 q^{34}\) \(+0.0158681 q^{35}\) \(-15.4915 q^{36}\) \(-7.70478 q^{37}\) \(-2.67657 q^{38}\) \(+0.0496343 q^{39}\) \(-0.430643 q^{40}\) \(-7.39004 q^{41}\) \(-0.00811443 q^{42}\) \(+3.43168 q^{43}\) \(+17.1233 q^{44}\) \(-0.152549 q^{45}\) \(+18.7523 q^{46}\) \(+8.02245 q^{47}\) \(+0.119877 q^{48}\) \(-6.90263 q^{49}\) \(+13.3759 q^{50}\) \(+0.0203829 q^{51}\) \(+26.3822 q^{52}\) \(-11.8021 q^{53}\) \(+0.156020 q^{54}\) \(+0.168618 q^{55}\) \(-2.64264 q^{56}\) \(+0.00971531 q^{57}\) \(+23.8452 q^{58}\) \(+1.08863 q^{59}\) \(+0.00255121 q^{60}\) \(-7.03229 q^{61}\) \(-28.9125 q^{62}\) \(-0.936119 q^{63}\) \(+18.3845 q^{64}\) \(+0.259793 q^{65}\) \(-0.0862255 q^{66}\) \(+12.1337 q^{67}\) \(+10.8342 q^{68}\) \(-0.0680664 q^{69}\) \(-0.0424721 q^{70}\) \(-0.696458 q^{71}\) \(+25.4052 q^{72}\) \(+7.75935 q^{73}\) \(+20.6224 q^{74}\) \(-0.0485514 q^{75}\) \(+5.16401 q^{76}\) \(+1.03472 q^{77}\) \(-0.132849 q^{78}\) \(-16.1473 q^{79}\) \(+0.627452 q^{80}\) \(+8.99915 q^{81}\) \(+19.7799 q^{82}\) \(+4.89708 q^{83}\) \(+0.0156555 q^{84}\) \(+0.106687 q^{85}\) \(-9.18511 q^{86}\) \(-0.0865524 q^{87}\) \(-28.0812 q^{88}\) \(-5.11530 q^{89}\) \(+0.408308 q^{90}\) \(+1.59422 q^{91}\) \(-36.1795 q^{92}\) \(+0.104946 q^{93}\) \(-21.4726 q^{94}\) \(+0.0508514 q^{95}\) \(-0.156306 q^{96}\) \(-10.3139 q^{97}\) \(+18.4753 q^{98}\) \(-9.94738 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.67657 −1.89262 −0.946309 0.323263i \(-0.895220\pi\)
−0.946309 + 0.323263i \(0.895220\pi\)
\(3\) 0.00971531 0.00560914 0.00280457 0.999996i \(-0.499107\pi\)
0.00280457 + 0.999996i \(0.499107\pi\)
\(4\) 5.16401 2.58200
\(5\) 0.0508514 0.0227414 0.0113707 0.999935i \(-0.496381\pi\)
0.0113707 + 0.999935i \(0.496381\pi\)
\(6\) −0.0260037 −0.0106160
\(7\) 0.312050 0.117944 0.0589718 0.998260i \(-0.481218\pi\)
0.0589718 + 0.998260i \(0.481218\pi\)
\(8\) −8.46867 −2.99413
\(9\) −2.99991 −0.999969
\(10\) −0.136107 −0.0430408
\(11\) 3.31590 0.999780 0.499890 0.866089i \(-0.333374\pi\)
0.499890 + 0.866089i \(0.333374\pi\)
\(12\) 0.0501699 0.0144828
\(13\) 5.10887 1.41695 0.708473 0.705738i \(-0.249384\pi\)
0.708473 + 0.705738i \(0.249384\pi\)
\(14\) −0.835221 −0.223222
\(15\) 0.000494037 0 0.000127560 0
\(16\) 12.3389 3.08474
\(17\) 2.09802 0.508845 0.254423 0.967093i \(-0.418115\pi\)
0.254423 + 0.967093i \(0.418115\pi\)
\(18\) 8.02945 1.89256
\(19\) 1.00000 0.229416
\(20\) 0.262597 0.0587184
\(21\) 0.00303166 0.000661562 0
\(22\) −8.87522 −1.89220
\(23\) −7.00610 −1.46087 −0.730436 0.682981i \(-0.760683\pi\)
−0.730436 + 0.682981i \(0.760683\pi\)
\(24\) −0.0822757 −0.0167945
\(25\) −4.99741 −0.999483
\(26\) −13.6742 −2.68174
\(27\) −0.0582909 −0.0112181
\(28\) 1.61143 0.304531
\(29\) −8.90887 −1.65434 −0.827168 0.561955i \(-0.810050\pi\)
−0.827168 + 0.561955i \(0.810050\pi\)
\(30\) −0.00132232 −0.000241422 0
\(31\) 10.8021 1.94012 0.970058 0.242875i \(-0.0780905\pi\)
0.970058 + 0.242875i \(0.0780905\pi\)
\(32\) −16.0887 −2.84410
\(33\) 0.0322150 0.00560790
\(34\) −5.61550 −0.963049
\(35\) 0.0158681 0.00268221
\(36\) −15.4915 −2.58192
\(37\) −7.70478 −1.26666 −0.633329 0.773883i \(-0.718312\pi\)
−0.633329 + 0.773883i \(0.718312\pi\)
\(38\) −2.67657 −0.434196
\(39\) 0.0496343 0.00794784
\(40\) −0.430643 −0.0680907
\(41\) −7.39004 −1.15413 −0.577065 0.816698i \(-0.695802\pi\)
−0.577065 + 0.816698i \(0.695802\pi\)
\(42\) −0.00811443 −0.00125208
\(43\) 3.43168 0.523326 0.261663 0.965159i \(-0.415729\pi\)
0.261663 + 0.965159i \(0.415729\pi\)
\(44\) 17.1233 2.58144
\(45\) −0.152549 −0.0227407
\(46\) 18.7523 2.76487
\(47\) 8.02245 1.17019 0.585097 0.810963i \(-0.301056\pi\)
0.585097 + 0.810963i \(0.301056\pi\)
\(48\) 0.119877 0.0173027
\(49\) −6.90263 −0.986089
\(50\) 13.3759 1.89164
\(51\) 0.0203829 0.00285418
\(52\) 26.3822 3.65856
\(53\) −11.8021 −1.62114 −0.810572 0.585639i \(-0.800843\pi\)
−0.810572 + 0.585639i \(0.800843\pi\)
\(54\) 0.156020 0.0212316
\(55\) 0.168618 0.0227364
\(56\) −2.64264 −0.353138
\(57\) 0.00971531 0.00128682
\(58\) 23.8452 3.13103
\(59\) 1.08863 0.141727 0.0708636 0.997486i \(-0.477424\pi\)
0.0708636 + 0.997486i \(0.477424\pi\)
\(60\) 0.00255121 0.000329359 0
\(61\) −7.03229 −0.900392 −0.450196 0.892930i \(-0.648646\pi\)
−0.450196 + 0.892930i \(0.648646\pi\)
\(62\) −28.9125 −3.67190
\(63\) −0.936119 −0.117940
\(64\) 18.3845 2.29806
\(65\) 0.259793 0.0322234
\(66\) −0.0862255 −0.0106136
\(67\) 12.1337 1.48236 0.741182 0.671304i \(-0.234266\pi\)
0.741182 + 0.671304i \(0.234266\pi\)
\(68\) 10.8342 1.31384
\(69\) −0.0680664 −0.00819423
\(70\) −0.0424721 −0.00507639
\(71\) −0.696458 −0.0826543 −0.0413272 0.999146i \(-0.513159\pi\)
−0.0413272 + 0.999146i \(0.513159\pi\)
\(72\) 25.4052 2.99403
\(73\) 7.75935 0.908163 0.454082 0.890960i \(-0.349967\pi\)
0.454082 + 0.890960i \(0.349967\pi\)
\(74\) 20.6224 2.39730
\(75\) −0.0485514 −0.00560623
\(76\) 5.16401 0.592352
\(77\) 1.03472 0.117918
\(78\) −0.132849 −0.0150422
\(79\) −16.1473 −1.81671 −0.908354 0.418202i \(-0.862661\pi\)
−0.908354 + 0.418202i \(0.862661\pi\)
\(80\) 0.627452 0.0701513
\(81\) 8.99915 0.999906
\(82\) 19.7799 2.18433
\(83\) 4.89708 0.537524 0.268762 0.963207i \(-0.413385\pi\)
0.268762 + 0.963207i \(0.413385\pi\)
\(84\) 0.0156555 0.00170815
\(85\) 0.106687 0.0115719
\(86\) −9.18511 −0.990456
\(87\) −0.0865524 −0.00927940
\(88\) −28.0812 −2.99347
\(89\) −5.11530 −0.542221 −0.271110 0.962548i \(-0.587391\pi\)
−0.271110 + 0.962548i \(0.587391\pi\)
\(90\) 0.408308 0.0430395
\(91\) 1.59422 0.167120
\(92\) −36.1795 −3.77198
\(93\) 0.104946 0.0108824
\(94\) −21.4726 −2.21473
\(95\) 0.0508514 0.00521724
\(96\) −0.156306 −0.0159529
\(97\) −10.3139 −1.04722 −0.523611 0.851958i \(-0.675415\pi\)
−0.523611 + 0.851958i \(0.675415\pi\)
\(98\) 18.4753 1.86629
\(99\) −9.94738 −0.999749
\(100\) −25.8067 −2.58067
\(101\) −8.40702 −0.836530 −0.418265 0.908325i \(-0.637362\pi\)
−0.418265 + 0.908325i \(0.637362\pi\)
\(102\) −0.0545563 −0.00540187
\(103\) −12.7961 −1.26083 −0.630416 0.776257i \(-0.717116\pi\)
−0.630416 + 0.776257i \(0.717116\pi\)
\(104\) −43.2653 −4.24252
\(105\) 0.000154164 0 1.50449e−5 0
\(106\) 31.5891 3.06821
\(107\) 5.37377 0.519502 0.259751 0.965676i \(-0.416360\pi\)
0.259751 + 0.965676i \(0.416360\pi\)
\(108\) −0.301015 −0.0289652
\(109\) 5.55900 0.532455 0.266228 0.963910i \(-0.414223\pi\)
0.266228 + 0.963910i \(0.414223\pi\)
\(110\) −0.451317 −0.0430314
\(111\) −0.0748543 −0.00710486
\(112\) 3.85036 0.363825
\(113\) −6.14935 −0.578482 −0.289241 0.957256i \(-0.593403\pi\)
−0.289241 + 0.957256i \(0.593403\pi\)
\(114\) −0.0260037 −0.00243547
\(115\) −0.356270 −0.0332223
\(116\) −46.0055 −4.27150
\(117\) −15.3261 −1.41690
\(118\) −2.91378 −0.268235
\(119\) 0.654687 0.0600151
\(120\) −0.00418383 −0.000381930 0
\(121\) −0.00482924 −0.000439022 0
\(122\) 18.8224 1.70410
\(123\) −0.0717965 −0.00647367
\(124\) 55.7821 5.00938
\(125\) −0.508382 −0.0454711
\(126\) 2.50558 0.223215
\(127\) 10.8458 0.962410 0.481205 0.876608i \(-0.340199\pi\)
0.481205 + 0.876608i \(0.340199\pi\)
\(128\) −17.0299 −1.50525
\(129\) 0.0333398 0.00293541
\(130\) −0.695353 −0.0609865
\(131\) 21.5259 1.88072 0.940362 0.340176i \(-0.110487\pi\)
0.940362 + 0.340176i \(0.110487\pi\)
\(132\) 0.166358 0.0144796
\(133\) 0.312050 0.0270581
\(134\) −32.4766 −2.80555
\(135\) −0.00296417 −0.000255115 0
\(136\) −17.7675 −1.52355
\(137\) 0.702792 0.0600435 0.0300218 0.999549i \(-0.490442\pi\)
0.0300218 + 0.999549i \(0.490442\pi\)
\(138\) 0.182184 0.0155085
\(139\) −23.4860 −1.99205 −0.996027 0.0890479i \(-0.971618\pi\)
−0.996027 + 0.0890479i \(0.971618\pi\)
\(140\) 0.0819432 0.00692546
\(141\) 0.0779406 0.00656378
\(142\) 1.86412 0.156433
\(143\) 16.9405 1.41663
\(144\) −37.0157 −3.08464
\(145\) −0.453028 −0.0376219
\(146\) −20.7684 −1.71881
\(147\) −0.0670611 −0.00553111
\(148\) −39.7875 −3.27052
\(149\) 14.2523 1.16759 0.583797 0.811899i \(-0.301566\pi\)
0.583797 + 0.811899i \(0.301566\pi\)
\(150\) 0.129951 0.0106105
\(151\) −11.2419 −0.914851 −0.457425 0.889248i \(-0.651228\pi\)
−0.457425 + 0.889248i \(0.651228\pi\)
\(152\) −8.46867 −0.686900
\(153\) −6.29387 −0.508829
\(154\) −2.76951 −0.223173
\(155\) 0.549302 0.0441210
\(156\) 0.256312 0.0205213
\(157\) −4.16506 −0.332408 −0.166204 0.986091i \(-0.553151\pi\)
−0.166204 + 0.986091i \(0.553151\pi\)
\(158\) 43.2192 3.43834
\(159\) −0.114661 −0.00909321
\(160\) −0.818130 −0.0646789
\(161\) −2.18625 −0.172301
\(162\) −24.0868 −1.89244
\(163\) 3.76722 0.295072 0.147536 0.989057i \(-0.452866\pi\)
0.147536 + 0.989057i \(0.452866\pi\)
\(164\) −38.1622 −2.97997
\(165\) 0.00163817 0.000127532 0
\(166\) −13.1074 −1.01733
\(167\) −3.83584 −0.296826 −0.148413 0.988925i \(-0.547417\pi\)
−0.148413 + 0.988925i \(0.547417\pi\)
\(168\) −0.0256741 −0.00198080
\(169\) 13.1006 1.00774
\(170\) −0.285556 −0.0219011
\(171\) −2.99991 −0.229409
\(172\) 17.7212 1.35123
\(173\) −5.23785 −0.398226 −0.199113 0.979977i \(-0.563806\pi\)
−0.199113 + 0.979977i \(0.563806\pi\)
\(174\) 0.231663 0.0175624
\(175\) −1.55944 −0.117883
\(176\) 40.9147 3.08406
\(177\) 0.0105763 0.000794967 0
\(178\) 13.6914 1.02622
\(179\) −6.00735 −0.449010 −0.224505 0.974473i \(-0.572077\pi\)
−0.224505 + 0.974473i \(0.572077\pi\)
\(180\) −0.787765 −0.0587166
\(181\) 2.94504 0.218903 0.109452 0.993992i \(-0.465091\pi\)
0.109452 + 0.993992i \(0.465091\pi\)
\(182\) −4.26704 −0.316294
\(183\) −0.0683208 −0.00505042
\(184\) 59.3323 4.37404
\(185\) −0.391798 −0.0288056
\(186\) −0.280894 −0.0205962
\(187\) 6.95682 0.508733
\(188\) 41.4280 3.02145
\(189\) −0.0181897 −0.00132310
\(190\) −0.136107 −0.00987424
\(191\) −23.7800 −1.72066 −0.860332 0.509735i \(-0.829743\pi\)
−0.860332 + 0.509735i \(0.829743\pi\)
\(192\) 0.178611 0.0128901
\(193\) 17.8338 1.28371 0.641853 0.766828i \(-0.278166\pi\)
0.641853 + 0.766828i \(0.278166\pi\)
\(194\) 27.6059 1.98199
\(195\) 0.00252397 0.000180745 0
\(196\) −35.6452 −2.54609
\(197\) 10.1250 0.721376 0.360688 0.932687i \(-0.382542\pi\)
0.360688 + 0.932687i \(0.382542\pi\)
\(198\) 26.6248 1.89214
\(199\) 19.3464 1.37143 0.685715 0.727871i \(-0.259490\pi\)
0.685715 + 0.727871i \(0.259490\pi\)
\(200\) 42.3215 2.99258
\(201\) 0.117882 0.00831478
\(202\) 22.5019 1.58323
\(203\) −2.78001 −0.195118
\(204\) 0.105258 0.00736950
\(205\) −0.375794 −0.0262466
\(206\) 34.2495 2.38627
\(207\) 21.0176 1.46083
\(208\) 63.0381 4.37090
\(209\) 3.31590 0.229365
\(210\) −0.000412630 0 −2.84742e−5 0
\(211\) 1.00000 0.0688428
\(212\) −60.9461 −4.18580
\(213\) −0.00676630 −0.000463619 0
\(214\) −14.3832 −0.983218
\(215\) 0.174505 0.0119012
\(216\) 0.493647 0.0335884
\(217\) 3.37079 0.228824
\(218\) −14.8790 −1.00773
\(219\) 0.0753845 0.00509401
\(220\) 0.870743 0.0587055
\(221\) 10.7185 0.721006
\(222\) 0.200353 0.0134468
\(223\) 16.6180 1.11282 0.556412 0.830906i \(-0.312178\pi\)
0.556412 + 0.830906i \(0.312178\pi\)
\(224\) −5.02046 −0.335444
\(225\) 14.9918 0.999451
\(226\) 16.4592 1.09485
\(227\) −22.6242 −1.50162 −0.750812 0.660516i \(-0.770337\pi\)
−0.750812 + 0.660516i \(0.770337\pi\)
\(228\) 0.0501699 0.00332258
\(229\) −8.40073 −0.555136 −0.277568 0.960706i \(-0.589528\pi\)
−0.277568 + 0.960706i \(0.589528\pi\)
\(230\) 0.953579 0.0628771
\(231\) 0.0100527 0.000661417 0
\(232\) 75.4463 4.95329
\(233\) 9.75135 0.638832 0.319416 0.947615i \(-0.396513\pi\)
0.319416 + 0.947615i \(0.396513\pi\)
\(234\) 41.0214 2.68165
\(235\) 0.407952 0.0266119
\(236\) 5.62168 0.365940
\(237\) −0.156876 −0.0101902
\(238\) −1.75231 −0.113586
\(239\) −19.5717 −1.26599 −0.632994 0.774157i \(-0.718174\pi\)
−0.632994 + 0.774157i \(0.718174\pi\)
\(240\) 0.00609589 0.000393488 0
\(241\) 3.44503 0.221914 0.110957 0.993825i \(-0.464608\pi\)
0.110957 + 0.993825i \(0.464608\pi\)
\(242\) 0.0129258 0.000830901 0
\(243\) 0.262302 0.0168267
\(244\) −36.3148 −2.32482
\(245\) −0.351008 −0.0224251
\(246\) 0.192168 0.0122522
\(247\) 5.10887 0.325070
\(248\) −91.4795 −5.80895
\(249\) 0.0475766 0.00301505
\(250\) 1.36072 0.0860594
\(251\) 3.60550 0.227577 0.113789 0.993505i \(-0.463701\pi\)
0.113789 + 0.993505i \(0.463701\pi\)
\(252\) −4.83413 −0.304521
\(253\) −23.2315 −1.46055
\(254\) −29.0295 −1.82148
\(255\) 0.00103650 6.49081e−5 0
\(256\) 8.81280 0.550800
\(257\) −18.1123 −1.12982 −0.564908 0.825154i \(-0.691089\pi\)
−0.564908 + 0.825154i \(0.691089\pi\)
\(258\) −0.0892362 −0.00555560
\(259\) −2.40427 −0.149394
\(260\) 1.34157 0.0832008
\(261\) 26.7258 1.65428
\(262\) −57.6154 −3.55949
\(263\) −7.90176 −0.487243 −0.243622 0.969870i \(-0.578336\pi\)
−0.243622 + 0.969870i \(0.578336\pi\)
\(264\) −0.272818 −0.0167908
\(265\) −0.600153 −0.0368671
\(266\) −0.835221 −0.0512107
\(267\) −0.0496967 −0.00304139
\(268\) 62.6583 3.82747
\(269\) −11.1503 −0.679846 −0.339923 0.940453i \(-0.610401\pi\)
−0.339923 + 0.940453i \(0.610401\pi\)
\(270\) 0.00793380 0.000482836 0
\(271\) 24.3653 1.48009 0.740044 0.672559i \(-0.234805\pi\)
0.740044 + 0.672559i \(0.234805\pi\)
\(272\) 25.8874 1.56965
\(273\) 0.0154883 0.000937397 0
\(274\) −1.88107 −0.113639
\(275\) −16.5709 −0.999263
\(276\) −0.351495 −0.0211575
\(277\) 22.0031 1.32204 0.661019 0.750369i \(-0.270124\pi\)
0.661019 + 0.750369i \(0.270124\pi\)
\(278\) 62.8618 3.77020
\(279\) −32.4053 −1.94005
\(280\) −0.134382 −0.00803086
\(281\) 9.30136 0.554873 0.277436 0.960744i \(-0.410515\pi\)
0.277436 + 0.960744i \(0.410515\pi\)
\(282\) −0.208613 −0.0124227
\(283\) 11.4299 0.679435 0.339718 0.940527i \(-0.389668\pi\)
0.339718 + 0.940527i \(0.389668\pi\)
\(284\) −3.59651 −0.213414
\(285\) 0.000494037 0 2.92642e−5 0
\(286\) −45.3423 −2.68115
\(287\) −2.30606 −0.136122
\(288\) 48.2645 2.84401
\(289\) −12.5983 −0.741077
\(290\) 1.21256 0.0712040
\(291\) −0.100203 −0.00587401
\(292\) 40.0693 2.34488
\(293\) −30.7965 −1.79915 −0.899575 0.436767i \(-0.856123\pi\)
−0.899575 + 0.436767i \(0.856123\pi\)
\(294\) 0.179494 0.0104683
\(295\) 0.0553582 0.00322308
\(296\) 65.2493 3.79254
\(297\) −0.193287 −0.0112156
\(298\) −38.1472 −2.20981
\(299\) −35.7932 −2.06998
\(300\) −0.250720 −0.0144753
\(301\) 1.07085 0.0617230
\(302\) 30.0896 1.73146
\(303\) −0.0816768 −0.00469221
\(304\) 12.3389 0.707687
\(305\) −0.357601 −0.0204762
\(306\) 16.8460 0.963019
\(307\) −0.145552 −0.00830708 −0.00415354 0.999991i \(-0.501322\pi\)
−0.00415354 + 0.999991i \(0.501322\pi\)
\(308\) 5.34332 0.304464
\(309\) −0.124318 −0.00707218
\(310\) −1.47024 −0.0835041
\(311\) −12.3563 −0.700663 −0.350332 0.936626i \(-0.613931\pi\)
−0.350332 + 0.936626i \(0.613931\pi\)
\(312\) −0.420336 −0.0237968
\(313\) 19.3586 1.09421 0.547105 0.837064i \(-0.315730\pi\)
0.547105 + 0.837064i \(0.315730\pi\)
\(314\) 11.1480 0.629121
\(315\) −0.0476029 −0.00268212
\(316\) −83.3845 −4.69075
\(317\) −28.8292 −1.61921 −0.809606 0.586974i \(-0.800319\pi\)
−0.809606 + 0.586974i \(0.800319\pi\)
\(318\) 0.306898 0.0172100
\(319\) −29.5409 −1.65397
\(320\) 0.934875 0.0522611
\(321\) 0.0522078 0.00291396
\(322\) 5.85164 0.326099
\(323\) 2.09802 0.116737
\(324\) 46.4717 2.58176
\(325\) −25.5311 −1.41621
\(326\) −10.0832 −0.558458
\(327\) 0.0540074 0.00298661
\(328\) 62.5838 3.45561
\(329\) 2.50340 0.138017
\(330\) −0.00438468 −0.000241369 0
\(331\) −15.3315 −0.842698 −0.421349 0.906899i \(-0.638443\pi\)
−0.421349 + 0.906899i \(0.638443\pi\)
\(332\) 25.2886 1.38789
\(333\) 23.1136 1.26662
\(334\) 10.2669 0.561778
\(335\) 0.617014 0.0337111
\(336\) 0.0374075 0.00204074
\(337\) −8.22610 −0.448104 −0.224052 0.974577i \(-0.571929\pi\)
−0.224052 + 0.974577i \(0.571929\pi\)
\(338\) −35.0645 −1.90726
\(339\) −0.0597429 −0.00324479
\(340\) 0.550934 0.0298786
\(341\) 35.8187 1.93969
\(342\) 8.02945 0.434183
\(343\) −4.33831 −0.234247
\(344\) −29.0618 −1.56690
\(345\) −0.00346127 −0.000186348 0
\(346\) 14.0194 0.753690
\(347\) −14.9891 −0.804656 −0.402328 0.915496i \(-0.631799\pi\)
−0.402328 + 0.915496i \(0.631799\pi\)
\(348\) −0.446957 −0.0239594
\(349\) −8.38995 −0.449104 −0.224552 0.974462i \(-0.572092\pi\)
−0.224552 + 0.974462i \(0.572092\pi\)
\(350\) 4.17395 0.223107
\(351\) −0.297801 −0.0158954
\(352\) −53.3483 −2.84348
\(353\) 22.0563 1.17394 0.586969 0.809609i \(-0.300321\pi\)
0.586969 + 0.809609i \(0.300321\pi\)
\(354\) −0.0283083 −0.00150457
\(355\) −0.0354158 −0.00187968
\(356\) −26.4154 −1.40002
\(357\) 0.00636048 0.000336633 0
\(358\) 16.0791 0.849805
\(359\) −33.7608 −1.78183 −0.890913 0.454174i \(-0.849934\pi\)
−0.890913 + 0.454174i \(0.849934\pi\)
\(360\) 1.29189 0.0680885
\(361\) 1.00000 0.0526316
\(362\) −7.88259 −0.414300
\(363\) −4.69176e−5 0 −2.46253e−6 0
\(364\) 8.23257 0.431504
\(365\) 0.394573 0.0206529
\(366\) 0.182865 0.00955852
\(367\) 2.53376 0.132261 0.0661307 0.997811i \(-0.478935\pi\)
0.0661307 + 0.997811i \(0.478935\pi\)
\(368\) −86.4479 −4.50641
\(369\) 22.1694 1.15409
\(370\) 1.04867 0.0545180
\(371\) −3.68284 −0.191204
\(372\) 0.541941 0.0280983
\(373\) −20.1830 −1.04504 −0.522518 0.852628i \(-0.675007\pi\)
−0.522518 + 0.852628i \(0.675007\pi\)
\(374\) −18.6204 −0.962838
\(375\) −0.00493909 −0.000255053 0
\(376\) −67.9395 −3.50371
\(377\) −45.5143 −2.34410
\(378\) 0.0486858 0.00250413
\(379\) −5.23122 −0.268710 −0.134355 0.990933i \(-0.542896\pi\)
−0.134355 + 0.990933i \(0.542896\pi\)
\(380\) 0.262597 0.0134709
\(381\) 0.105370 0.00539829
\(382\) 63.6488 3.25656
\(383\) −22.3359 −1.14131 −0.570656 0.821189i \(-0.693311\pi\)
−0.570656 + 0.821189i \(0.693311\pi\)
\(384\) −0.165451 −0.00844314
\(385\) 0.0526171 0.00268162
\(386\) −47.7334 −2.42956
\(387\) −10.2947 −0.523310
\(388\) −53.2612 −2.70393
\(389\) 3.17900 0.161182 0.0805910 0.996747i \(-0.474319\pi\)
0.0805910 + 0.996747i \(0.474319\pi\)
\(390\) −0.00675557 −0.000342082 0
\(391\) −14.6989 −0.743358
\(392\) 58.4561 2.95248
\(393\) 0.209130 0.0105492
\(394\) −27.1002 −1.36529
\(395\) −0.821110 −0.0413145
\(396\) −51.3683 −2.58135
\(397\) 17.0059 0.853501 0.426751 0.904369i \(-0.359658\pi\)
0.426751 + 0.904369i \(0.359658\pi\)
\(398\) −51.7819 −2.59559
\(399\) 0.00303166 0.000151773 0
\(400\) −61.6628 −3.08314
\(401\) 15.9396 0.795984 0.397992 0.917389i \(-0.369707\pi\)
0.397992 + 0.917389i \(0.369707\pi\)
\(402\) −0.315520 −0.0157367
\(403\) 55.1866 2.74904
\(404\) −43.4139 −2.15992
\(405\) 0.457619 0.0227393
\(406\) 7.44088 0.369285
\(407\) −25.5483 −1.26638
\(408\) −0.172616 −0.00854578
\(409\) −26.5975 −1.31516 −0.657580 0.753385i \(-0.728420\pi\)
−0.657580 + 0.753385i \(0.728420\pi\)
\(410\) 1.00584 0.0496747
\(411\) 0.00682784 0.000336792 0
\(412\) −66.0789 −3.25547
\(413\) 0.339706 0.0167158
\(414\) −56.2551 −2.76479
\(415\) 0.249023 0.0122241
\(416\) −82.1949 −4.02994
\(417\) −0.228174 −0.0111737
\(418\) −8.87522 −0.434101
\(419\) 9.21385 0.450126 0.225063 0.974344i \(-0.427741\pi\)
0.225063 + 0.974344i \(0.427741\pi\)
\(420\) 0.000796103 0 3.88459e−5 0
\(421\) −27.3477 −1.33285 −0.666424 0.745573i \(-0.732176\pi\)
−0.666424 + 0.745573i \(0.732176\pi\)
\(422\) −2.67657 −0.130293
\(423\) −24.0666 −1.17016
\(424\) 99.9481 4.85391
\(425\) −10.4847 −0.508582
\(426\) 0.0181105 0.000877454 0
\(427\) −2.19442 −0.106196
\(428\) 27.7502 1.34135
\(429\) 0.164582 0.00794610
\(430\) −0.467075 −0.0225244
\(431\) −3.28029 −0.158006 −0.0790030 0.996874i \(-0.525174\pi\)
−0.0790030 + 0.996874i \(0.525174\pi\)
\(432\) −0.719249 −0.0346049
\(433\) −9.08006 −0.436360 −0.218180 0.975909i \(-0.570012\pi\)
−0.218180 + 0.975909i \(0.570012\pi\)
\(434\) −9.02215 −0.433077
\(435\) −0.00440131 −0.000211027 0
\(436\) 28.7067 1.37480
\(437\) −7.00610 −0.335147
\(438\) −0.201771 −0.00964101
\(439\) 28.8489 1.37688 0.688442 0.725292i \(-0.258295\pi\)
0.688442 + 0.725292i \(0.258295\pi\)
\(440\) −1.42797 −0.0680757
\(441\) 20.7072 0.986058
\(442\) −28.6888 −1.36459
\(443\) −4.54219 −0.215806 −0.107903 0.994161i \(-0.534414\pi\)
−0.107903 + 0.994161i \(0.534414\pi\)
\(444\) −0.386548 −0.0183448
\(445\) −0.260120 −0.0123309
\(446\) −44.4792 −2.10615
\(447\) 0.138466 0.00654920
\(448\) 5.73687 0.271041
\(449\) 27.7116 1.30779 0.653895 0.756586i \(-0.273134\pi\)
0.653895 + 0.756586i \(0.273134\pi\)
\(450\) −40.1265 −1.89158
\(451\) −24.5046 −1.15388
\(452\) −31.7553 −1.49364
\(453\) −0.109218 −0.00513152
\(454\) 60.5553 2.84200
\(455\) 0.0810683 0.00380054
\(456\) −0.0822757 −0.00385291
\(457\) 22.4814 1.05164 0.525818 0.850597i \(-0.323759\pi\)
0.525818 + 0.850597i \(0.323759\pi\)
\(458\) 22.4851 1.05066
\(459\) −0.122296 −0.00570827
\(460\) −1.83978 −0.0857801
\(461\) 11.3605 0.529109 0.264555 0.964371i \(-0.414775\pi\)
0.264555 + 0.964371i \(0.414775\pi\)
\(462\) −0.0269066 −0.00125181
\(463\) −4.51372 −0.209770 −0.104885 0.994484i \(-0.533447\pi\)
−0.104885 + 0.994484i \(0.533447\pi\)
\(464\) −109.926 −5.10319
\(465\) 0.00533663 0.000247480 0
\(466\) −26.1001 −1.20907
\(467\) −19.3427 −0.895074 −0.447537 0.894265i \(-0.647699\pi\)
−0.447537 + 0.894265i \(0.647699\pi\)
\(468\) −79.1442 −3.65844
\(469\) 3.78631 0.174835
\(470\) −1.09191 −0.0503661
\(471\) −0.0404648 −0.00186452
\(472\) −9.21922 −0.424349
\(473\) 11.3791 0.523211
\(474\) 0.419888 0.0192861
\(475\) −4.99741 −0.229297
\(476\) 3.38081 0.154959
\(477\) 35.4052 1.62109
\(478\) 52.3850 2.39603
\(479\) −4.07725 −0.186294 −0.0931471 0.995652i \(-0.529693\pi\)
−0.0931471 + 0.995652i \(0.529693\pi\)
\(480\) −0.00794839 −0.000362792 0
\(481\) −39.3627 −1.79479
\(482\) −9.22084 −0.419998
\(483\) −0.0212401 −0.000966457 0
\(484\) −0.0249382 −0.00113356
\(485\) −0.524478 −0.0238153
\(486\) −0.702069 −0.0318465
\(487\) 9.31487 0.422097 0.211049 0.977476i \(-0.432312\pi\)
0.211049 + 0.977476i \(0.432312\pi\)
\(488\) 59.5541 2.69589
\(489\) 0.0365997 0.00165510
\(490\) 0.939496 0.0424421
\(491\) −6.82836 −0.308160 −0.154080 0.988058i \(-0.549241\pi\)
−0.154080 + 0.988058i \(0.549241\pi\)
\(492\) −0.370758 −0.0167150
\(493\) −18.6910 −0.841801
\(494\) −13.6742 −0.615233
\(495\) −0.505838 −0.0227357
\(496\) 133.287 5.98474
\(497\) −0.217329 −0.00974855
\(498\) −0.127342 −0.00570633
\(499\) −7.56558 −0.338682 −0.169341 0.985558i \(-0.554164\pi\)
−0.169341 + 0.985558i \(0.554164\pi\)
\(500\) −2.62529 −0.117406
\(501\) −0.0372664 −0.00166494
\(502\) −9.65036 −0.430717
\(503\) 10.7541 0.479503 0.239752 0.970834i \(-0.422934\pi\)
0.239752 + 0.970834i \(0.422934\pi\)
\(504\) 7.92769 0.353127
\(505\) −0.427508 −0.0190239
\(506\) 62.1806 2.76427
\(507\) 0.127276 0.00565253
\(508\) 56.0078 2.48495
\(509\) −20.6182 −0.913888 −0.456944 0.889496i \(-0.651056\pi\)
−0.456944 + 0.889496i \(0.651056\pi\)
\(510\) −0.00277426 −0.000122846 0
\(511\) 2.42130 0.107112
\(512\) 10.4718 0.462794
\(513\) −0.0582909 −0.00257361
\(514\) 48.4789 2.13831
\(515\) −0.650696 −0.0286731
\(516\) 0.172167 0.00757923
\(517\) 26.6016 1.16994
\(518\) 6.43520 0.282746
\(519\) −0.0508873 −0.00223370
\(520\) −2.20010 −0.0964808
\(521\) 0.868898 0.0380671 0.0190335 0.999819i \(-0.493941\pi\)
0.0190335 + 0.999819i \(0.493941\pi\)
\(522\) −71.5333 −3.13093
\(523\) −6.06984 −0.265415 −0.132708 0.991155i \(-0.542367\pi\)
−0.132708 + 0.991155i \(0.542367\pi\)
\(524\) 111.160 4.85603
\(525\) −0.0151504 −0.000661220 0
\(526\) 21.1496 0.922166
\(527\) 22.6631 0.987218
\(528\) 0.397499 0.0172989
\(529\) 26.0854 1.13415
\(530\) 1.60635 0.0697753
\(531\) −3.26578 −0.141723
\(532\) 1.61143 0.0698642
\(533\) −37.7548 −1.63534
\(534\) 0.133017 0.00575619
\(535\) 0.273263 0.0118142
\(536\) −102.756 −4.43839
\(537\) −0.0583632 −0.00251856
\(538\) 29.8445 1.28669
\(539\) −22.8884 −0.985873
\(540\) −0.0153070 −0.000658709 0
\(541\) −36.9957 −1.59057 −0.795284 0.606237i \(-0.792678\pi\)
−0.795284 + 0.606237i \(0.792678\pi\)
\(542\) −65.2154 −2.80124
\(543\) 0.0286120 0.00122786
\(544\) −33.7544 −1.44721
\(545\) 0.282682 0.0121088
\(546\) −0.0414556 −0.00177414
\(547\) −15.0555 −0.643728 −0.321864 0.946786i \(-0.604309\pi\)
−0.321864 + 0.946786i \(0.604309\pi\)
\(548\) 3.62922 0.155033
\(549\) 21.0962 0.900364
\(550\) 44.3531 1.89122
\(551\) −8.90887 −0.379531
\(552\) 0.576432 0.0245346
\(553\) −5.03874 −0.214269
\(554\) −58.8927 −2.50211
\(555\) −0.00380644 −0.000161575 0
\(556\) −121.282 −5.14349
\(557\) 37.2893 1.58000 0.789999 0.613108i \(-0.210081\pi\)
0.789999 + 0.613108i \(0.210081\pi\)
\(558\) 86.7349 3.67178
\(559\) 17.5320 0.741525
\(560\) 0.195796 0.00827390
\(561\) 0.0675877 0.00285355
\(562\) −24.8957 −1.05016
\(563\) −27.5253 −1.16005 −0.580027 0.814597i \(-0.696958\pi\)
−0.580027 + 0.814597i \(0.696958\pi\)
\(564\) 0.402486 0.0169477
\(565\) −0.312703 −0.0131555
\(566\) −30.5928 −1.28591
\(567\) 2.80818 0.117933
\(568\) 5.89807 0.247478
\(569\) −22.2411 −0.932394 −0.466197 0.884681i \(-0.654376\pi\)
−0.466197 + 0.884681i \(0.654376\pi\)
\(570\) −0.00132232 −5.53859e−5 0
\(571\) −18.3074 −0.766139 −0.383070 0.923719i \(-0.625133\pi\)
−0.383070 + 0.923719i \(0.625133\pi\)
\(572\) 87.4808 3.65776
\(573\) −0.231030 −0.00965143
\(574\) 6.17232 0.257628
\(575\) 35.0124 1.46012
\(576\) −55.1517 −2.29799
\(577\) −27.2921 −1.13618 −0.568092 0.822965i \(-0.692318\pi\)
−0.568092 + 0.822965i \(0.692318\pi\)
\(578\) 33.7202 1.40257
\(579\) 0.173261 0.00720048
\(580\) −2.33944 −0.0971400
\(581\) 1.52813 0.0633976
\(582\) 0.268200 0.0111173
\(583\) −39.1346 −1.62079
\(584\) −65.7114 −2.71916
\(585\) −0.779354 −0.0322223
\(586\) 82.4288 3.40510
\(587\) 8.24350 0.340246 0.170123 0.985423i \(-0.445584\pi\)
0.170123 + 0.985423i \(0.445584\pi\)
\(588\) −0.346304 −0.0142813
\(589\) 10.8021 0.445093
\(590\) −0.148170 −0.00610005
\(591\) 0.0983674 0.00404629
\(592\) −95.0689 −3.90731
\(593\) 9.89696 0.406420 0.203210 0.979135i \(-0.434863\pi\)
0.203210 + 0.979135i \(0.434863\pi\)
\(594\) 0.517345 0.0212269
\(595\) 0.0332917 0.00136483
\(596\) 73.5990 3.01473
\(597\) 0.187956 0.00769253
\(598\) 95.8030 3.91768
\(599\) 36.1267 1.47610 0.738048 0.674749i \(-0.235748\pi\)
0.738048 + 0.674749i \(0.235748\pi\)
\(600\) 0.411166 0.0167858
\(601\) −43.3036 −1.76639 −0.883196 0.469004i \(-0.844613\pi\)
−0.883196 + 0.469004i \(0.844613\pi\)
\(602\) −2.86621 −0.116818
\(603\) −36.3999 −1.48232
\(604\) −58.0531 −2.36215
\(605\) −0.000245573 0 −9.98398e−6 0
\(606\) 0.218613 0.00888056
\(607\) −26.3375 −1.06901 −0.534503 0.845167i \(-0.679501\pi\)
−0.534503 + 0.845167i \(0.679501\pi\)
\(608\) −16.0887 −0.652481
\(609\) −0.0270086 −0.00109445
\(610\) 0.957144 0.0387536
\(611\) 40.9857 1.65810
\(612\) −32.5016 −1.31380
\(613\) 32.5703 1.31550 0.657751 0.753236i \(-0.271508\pi\)
0.657751 + 0.753236i \(0.271508\pi\)
\(614\) 0.389579 0.0157221
\(615\) −0.00365095 −0.000147221 0
\(616\) −8.76274 −0.353061
\(617\) 14.9660 0.602509 0.301255 0.953544i \(-0.402595\pi\)
0.301255 + 0.953544i \(0.402595\pi\)
\(618\) 0.332744 0.0133849
\(619\) −45.5620 −1.83129 −0.915646 0.401986i \(-0.868320\pi\)
−0.915646 + 0.401986i \(0.868320\pi\)
\(620\) 2.83660 0.113920
\(621\) 0.408392 0.0163882
\(622\) 33.0725 1.32609
\(623\) −1.59623 −0.0639515
\(624\) 0.612434 0.0245170
\(625\) 24.9612 0.998449
\(626\) −51.8145 −2.07092
\(627\) 0.0322150 0.00128654
\(628\) −21.5084 −0.858277
\(629\) −16.1648 −0.644533
\(630\) 0.127412 0.00507623
\(631\) −18.4685 −0.735220 −0.367610 0.929980i \(-0.619824\pi\)
−0.367610 + 0.929980i \(0.619824\pi\)
\(632\) 136.746 5.43946
\(633\) 0.00971531 0.000386149 0
\(634\) 77.1634 3.06455
\(635\) 0.551524 0.0218866
\(636\) −0.592110 −0.0234787
\(637\) −35.2646 −1.39724
\(638\) 79.0682 3.13034
\(639\) 2.08931 0.0826517
\(640\) −0.865995 −0.0342315
\(641\) −29.2063 −1.15358 −0.576789 0.816893i \(-0.695695\pi\)
−0.576789 + 0.816893i \(0.695695\pi\)
\(642\) −0.139738 −0.00551500
\(643\) −12.1699 −0.479935 −0.239968 0.970781i \(-0.577137\pi\)
−0.239968 + 0.970781i \(0.577137\pi\)
\(644\) −11.2898 −0.444881
\(645\) 0.00169537 6.67553e−5 0
\(646\) −5.61550 −0.220939
\(647\) 26.6135 1.04629 0.523143 0.852245i \(-0.324759\pi\)
0.523143 + 0.852245i \(0.324759\pi\)
\(648\) −76.2108 −2.99384
\(649\) 3.60978 0.141696
\(650\) 68.3358 2.68035
\(651\) 0.0327483 0.00128351
\(652\) 19.4540 0.761876
\(653\) −28.8949 −1.13075 −0.565373 0.824836i \(-0.691268\pi\)
−0.565373 + 0.824836i \(0.691268\pi\)
\(654\) −0.144554 −0.00565252
\(655\) 1.09462 0.0427703
\(656\) −91.1853 −3.56019
\(657\) −23.2773 −0.908135
\(658\) −6.70052 −0.261213
\(659\) −20.4653 −0.797215 −0.398607 0.917122i \(-0.630506\pi\)
−0.398607 + 0.917122i \(0.630506\pi\)
\(660\) 0.00845954 0.000329287 0
\(661\) −35.3546 −1.37513 −0.687567 0.726121i \(-0.741321\pi\)
−0.687567 + 0.726121i \(0.741321\pi\)
\(662\) 41.0359 1.59491
\(663\) 0.104134 0.00404422
\(664\) −41.4718 −1.60942
\(665\) 0.0158681 0.000615340 0
\(666\) −61.8651 −2.39722
\(667\) 62.4164 2.41677
\(668\) −19.8083 −0.766406
\(669\) 0.161449 0.00624198
\(670\) −1.65148 −0.0638021
\(671\) −23.3183 −0.900195
\(672\) −0.0487753 −0.00188155
\(673\) −16.1001 −0.620614 −0.310307 0.950636i \(-0.600432\pi\)
−0.310307 + 0.950636i \(0.600432\pi\)
\(674\) 22.0177 0.848090
\(675\) 0.291304 0.0112123
\(676\) 67.6514 2.60198
\(677\) 7.97048 0.306331 0.153165 0.988201i \(-0.451053\pi\)
0.153165 + 0.988201i \(0.451053\pi\)
\(678\) 0.159906 0.00614114
\(679\) −3.21846 −0.123513
\(680\) −0.903499 −0.0346476
\(681\) −0.219801 −0.00842281
\(682\) −95.8710 −3.67109
\(683\) 5.94746 0.227573 0.113787 0.993505i \(-0.463702\pi\)
0.113787 + 0.993505i \(0.463702\pi\)
\(684\) −15.4915 −0.592333
\(685\) 0.0357379 0.00136548
\(686\) 11.6118 0.443339
\(687\) −0.0816157 −0.00311383
\(688\) 42.3433 1.61432
\(689\) −60.2954 −2.29707
\(690\) 0.00926431 0.000352686 0
\(691\) 39.4169 1.49949 0.749745 0.661727i \(-0.230176\pi\)
0.749745 + 0.661727i \(0.230176\pi\)
\(692\) −27.0483 −1.02822
\(693\) −3.10407 −0.117914
\(694\) 40.1192 1.52291
\(695\) −1.19429 −0.0453021
\(696\) 0.732984 0.0277837
\(697\) −15.5045 −0.587274
\(698\) 22.4563 0.849982
\(699\) 0.0947373 0.00358330
\(700\) −8.05296 −0.304373
\(701\) −5.14126 −0.194183 −0.0970913 0.995275i \(-0.530954\pi\)
−0.0970913 + 0.995275i \(0.530954\pi\)
\(702\) 0.797084 0.0300840
\(703\) −7.70478 −0.290591
\(704\) 60.9610 2.29755
\(705\) 0.00396338 0.000149270 0
\(706\) −59.0352 −2.22182
\(707\) −2.62341 −0.0986634
\(708\) 0.0546163 0.00205261
\(709\) 28.7691 1.08045 0.540223 0.841522i \(-0.318340\pi\)
0.540223 + 0.841522i \(0.318340\pi\)
\(710\) 0.0947928 0.00355751
\(711\) 48.4403 1.81665
\(712\) 43.3198 1.62348
\(713\) −75.6806 −2.83426
\(714\) −0.0170243 −0.000637117 0
\(715\) 0.861447 0.0322163
\(716\) −31.0220 −1.15935
\(717\) −0.190145 −0.00710110
\(718\) 90.3630 3.37232
\(719\) 2.65464 0.0990012 0.0495006 0.998774i \(-0.484237\pi\)
0.0495006 + 0.998774i \(0.484237\pi\)
\(720\) −1.88230 −0.0701491
\(721\) −3.99300 −0.148707
\(722\) −2.67657 −0.0996115
\(723\) 0.0334695 0.00124474
\(724\) 15.2082 0.565208
\(725\) 44.5213 1.65348
\(726\) 0.000125578 0 4.66063e−6 0
\(727\) 5.37778 0.199451 0.0997254 0.995015i \(-0.468204\pi\)
0.0997254 + 0.995015i \(0.468204\pi\)
\(728\) −13.5009 −0.500378
\(729\) −26.9949 −0.999811
\(730\) −1.05610 −0.0390881
\(731\) 7.19974 0.266292
\(732\) −0.352809 −0.0130402
\(733\) −23.4025 −0.864392 −0.432196 0.901780i \(-0.642261\pi\)
−0.432196 + 0.901780i \(0.642261\pi\)
\(734\) −6.78178 −0.250320
\(735\) −0.00341015 −0.000125785 0
\(736\) 112.719 4.15487
\(737\) 40.2340 1.48204
\(738\) −59.3379 −2.18426
\(739\) −24.8539 −0.914264 −0.457132 0.889399i \(-0.651123\pi\)
−0.457132 + 0.889399i \(0.651123\pi\)
\(740\) −2.02325 −0.0743761
\(741\) 0.0496343 0.00182336
\(742\) 9.85737 0.361875
\(743\) 8.19222 0.300543 0.150272 0.988645i \(-0.451985\pi\)
0.150272 + 0.988645i \(0.451985\pi\)
\(744\) −0.888751 −0.0325832
\(745\) 0.724749 0.0265528
\(746\) 54.0212 1.97786
\(747\) −14.6908 −0.537508
\(748\) 35.9251 1.31355
\(749\) 1.67688 0.0612719
\(750\) 0.0132198 0.000482719 0
\(751\) 21.7064 0.792077 0.396039 0.918234i \(-0.370385\pi\)
0.396039 + 0.918234i \(0.370385\pi\)
\(752\) 98.9886 3.60974
\(753\) 0.0350285 0.00127651
\(754\) 121.822 4.43649
\(755\) −0.571665 −0.0208050
\(756\) −0.0939315 −0.00341626
\(757\) 1.64353 0.0597351 0.0298675 0.999554i \(-0.490491\pi\)
0.0298675 + 0.999554i \(0.490491\pi\)
\(758\) 14.0017 0.508565
\(759\) −0.225701 −0.00819243
\(760\) −0.430643 −0.0156211
\(761\) −50.0556 −1.81452 −0.907258 0.420576i \(-0.861828\pi\)
−0.907258 + 0.420576i \(0.861828\pi\)
\(762\) −0.282031 −0.0102169
\(763\) 1.73468 0.0627997
\(764\) −122.800 −4.44276
\(765\) −0.320052 −0.0115715
\(766\) 59.7836 2.16007
\(767\) 5.56166 0.200820
\(768\) 0.0856190 0.00308951
\(769\) −10.9413 −0.394554 −0.197277 0.980348i \(-0.563210\pi\)
−0.197277 + 0.980348i \(0.563210\pi\)
\(770\) −0.140833 −0.00507528
\(771\) −0.175967 −0.00633730
\(772\) 92.0939 3.31453
\(773\) −34.4014 −1.23733 −0.618665 0.785655i \(-0.712326\pi\)
−0.618665 + 0.785655i \(0.712326\pi\)
\(774\) 27.5545 0.990425
\(775\) −53.9826 −1.93911
\(776\) 87.3453 3.13551
\(777\) −0.0233583 −0.000837973 0
\(778\) −8.50882 −0.305056
\(779\) −7.39004 −0.264776
\(780\) 0.0130338 0.000466685 0
\(781\) −2.30938 −0.0826362
\(782\) 39.3427 1.40689
\(783\) 0.519306 0.0185585
\(784\) −85.1711 −3.04183
\(785\) −0.211799 −0.00755942
\(786\) −0.559751 −0.0199657
\(787\) 30.3404 1.08152 0.540758 0.841178i \(-0.318137\pi\)
0.540758 + 0.841178i \(0.318137\pi\)
\(788\) 52.2855 1.86259
\(789\) −0.0767680 −0.00273301
\(790\) 2.19775 0.0781926
\(791\) −1.91890 −0.0682283
\(792\) 84.2411 2.99338
\(793\) −35.9271 −1.27581
\(794\) −45.5174 −1.61535
\(795\) −0.00583067 −0.000206793 0
\(796\) 99.9049 3.54103
\(797\) 22.9082 0.811450 0.405725 0.913995i \(-0.367019\pi\)
0.405725 + 0.913995i \(0.367019\pi\)
\(798\) −0.00811443 −0.000287248 0
\(799\) 16.8313 0.595448
\(800\) 80.4017 2.84263
\(801\) 15.3454 0.542204
\(802\) −42.6633 −1.50649
\(803\) 25.7292 0.907964
\(804\) 0.608745 0.0214688
\(805\) −0.111174 −0.00391836
\(806\) −147.710 −5.20288
\(807\) −0.108329 −0.00381335
\(808\) 71.1963 2.50468
\(809\) −20.7490 −0.729494 −0.364747 0.931107i \(-0.618845\pi\)
−0.364747 + 0.931107i \(0.618845\pi\)
\(810\) −1.22485 −0.0430368
\(811\) −25.3708 −0.890891 −0.445445 0.895309i \(-0.646955\pi\)
−0.445445 + 0.895309i \(0.646955\pi\)
\(812\) −14.3560 −0.503796
\(813\) 0.236717 0.00830201
\(814\) 68.3816 2.39677
\(815\) 0.191568 0.00671035
\(816\) 0.251504 0.00880440
\(817\) 3.43168 0.120059
\(818\) 71.1898 2.48909
\(819\) −4.78251 −0.167115
\(820\) −1.94060 −0.0677687
\(821\) −13.2015 −0.460737 −0.230368 0.973104i \(-0.573993\pi\)
−0.230368 + 0.973104i \(0.573993\pi\)
\(822\) −0.0182752 −0.000637419 0
\(823\) −28.7493 −1.00214 −0.501069 0.865407i \(-0.667060\pi\)
−0.501069 + 0.865407i \(0.667060\pi\)
\(824\) 108.366 3.77509
\(825\) −0.160991 −0.00560500
\(826\) −0.909244 −0.0316367
\(827\) 51.4838 1.79027 0.895134 0.445797i \(-0.147080\pi\)
0.895134 + 0.445797i \(0.147080\pi\)
\(828\) 108.535 3.77186
\(829\) 43.9806 1.52751 0.763754 0.645507i \(-0.223354\pi\)
0.763754 + 0.645507i \(0.223354\pi\)
\(830\) −0.666527 −0.0231355
\(831\) 0.213767 0.00741549
\(832\) 93.9239 3.25623
\(833\) −14.4819 −0.501767
\(834\) 0.610721 0.0211476
\(835\) −0.195058 −0.00675025
\(836\) 17.1233 0.592222
\(837\) −0.629665 −0.0217644
\(838\) −24.6615 −0.851916
\(839\) 31.8863 1.10084 0.550419 0.834888i \(-0.314468\pi\)
0.550419 + 0.834888i \(0.314468\pi\)
\(840\) −0.00130556 −4.50462e−5 0
\(841\) 50.3680 1.73683
\(842\) 73.1980 2.52257
\(843\) 0.0903656 0.00311236
\(844\) 5.16401 0.177752
\(845\) 0.666181 0.0229173
\(846\) 64.4158 2.21466
\(847\) −0.00150696 −5.17798e−5 0
\(848\) −145.625 −5.00080
\(849\) 0.111045 0.00381104
\(850\) 28.0630 0.962551
\(851\) 53.9804 1.85043
\(852\) −0.0349412 −0.00119707
\(853\) −26.7839 −0.917062 −0.458531 0.888678i \(-0.651624\pi\)
−0.458531 + 0.888678i \(0.651624\pi\)
\(854\) 5.87352 0.200988
\(855\) −0.152549 −0.00521707
\(856\) −45.5087 −1.55545
\(857\) −51.1904 −1.74863 −0.874315 0.485359i \(-0.838689\pi\)
−0.874315 + 0.485359i \(0.838689\pi\)
\(858\) −0.440515 −0.0150389
\(859\) −50.5007 −1.72306 −0.861530 0.507706i \(-0.830494\pi\)
−0.861530 + 0.507706i \(0.830494\pi\)
\(860\) 0.901147 0.0307289
\(861\) −0.0224041 −0.000763529 0
\(862\) 8.77992 0.299045
\(863\) −32.8867 −1.11948 −0.559739 0.828669i \(-0.689098\pi\)
−0.559739 + 0.828669i \(0.689098\pi\)
\(864\) 0.937823 0.0319054
\(865\) −0.266352 −0.00905623
\(866\) 24.3034 0.825862
\(867\) −0.122396 −0.00415680
\(868\) 17.4068 0.590825
\(869\) −53.5426 −1.81631
\(870\) 0.0117804 0.000399393 0
\(871\) 61.9894 2.10043
\(872\) −47.0773 −1.59424
\(873\) 30.9408 1.04719
\(874\) 18.7523 0.634305
\(875\) −0.158640 −0.00536302
\(876\) 0.389286 0.0131527
\(877\) −24.8244 −0.838261 −0.419131 0.907926i \(-0.637665\pi\)
−0.419131 + 0.907926i \(0.637665\pi\)
\(878\) −77.2160 −2.60591
\(879\) −0.299197 −0.0100917
\(880\) 2.08057 0.0701359
\(881\) 18.5611 0.625338 0.312669 0.949862i \(-0.398777\pi\)
0.312669 + 0.949862i \(0.398777\pi\)
\(882\) −55.4243 −1.86623
\(883\) −0.804561 −0.0270756 −0.0135378 0.999908i \(-0.504309\pi\)
−0.0135378 + 0.999908i \(0.504309\pi\)
\(884\) 55.3505 1.86164
\(885\) 0.000537822 0 1.80787e−5 0
\(886\) 12.1575 0.408439
\(887\) −1.59841 −0.0536694 −0.0268347 0.999640i \(-0.508543\pi\)
−0.0268347 + 0.999640i \(0.508543\pi\)
\(888\) 0.633917 0.0212728
\(889\) 3.38443 0.113510
\(890\) 0.696228 0.0233376
\(891\) 29.8403 0.999686
\(892\) 85.8155 2.87332
\(893\) 8.02245 0.268461
\(894\) −0.370612 −0.0123951
\(895\) −0.305482 −0.0102111
\(896\) −5.31418 −0.177534
\(897\) −0.347742 −0.0116108
\(898\) −74.1718 −2.47515
\(899\) −96.2346 −3.20960
\(900\) 77.4176 2.58059
\(901\) −24.7611 −0.824911
\(902\) 65.5882 2.18385
\(903\) 0.0104037 0.000346213 0
\(904\) 52.0768 1.73205
\(905\) 0.149759 0.00497817
\(906\) 0.292330 0.00971201
\(907\) 26.2220 0.870687 0.435344 0.900264i \(-0.356627\pi\)
0.435344 + 0.900264i \(0.356627\pi\)
\(908\) −116.832 −3.87720
\(909\) 25.2203 0.836504
\(910\) −0.216985 −0.00719297
\(911\) 17.9443 0.594522 0.297261 0.954796i \(-0.403927\pi\)
0.297261 + 0.954796i \(0.403927\pi\)
\(912\) 0.119877 0.00396951
\(913\) 16.2382 0.537406
\(914\) −60.1729 −1.99034
\(915\) −0.00347421 −0.000114854 0
\(916\) −43.3814 −1.43336
\(917\) 6.71714 0.221819
\(918\) 0.327332 0.0108036
\(919\) −16.6254 −0.548422 −0.274211 0.961669i \(-0.588417\pi\)
−0.274211 + 0.961669i \(0.588417\pi\)
\(920\) 3.01713 0.0994718
\(921\) −0.00141408 −4.65956e−5 0
\(922\) −30.4070 −1.00140
\(923\) −3.55811 −0.117117
\(924\) 0.0519120 0.00170778
\(925\) 38.5040 1.26600
\(926\) 12.0813 0.397015
\(927\) 38.3869 1.26079
\(928\) 143.332 4.70510
\(929\) 26.8795 0.881886 0.440943 0.897535i \(-0.354644\pi\)
0.440943 + 0.897535i \(0.354644\pi\)
\(930\) −0.0142839 −0.000468386 0
\(931\) −6.90263 −0.226224
\(932\) 50.3560 1.64947
\(933\) −0.120046 −0.00393012
\(934\) 51.7721 1.69403
\(935\) 0.353764 0.0115693
\(936\) 129.792 4.24238
\(937\) −3.83686 −0.125345 −0.0626724 0.998034i \(-0.519962\pi\)
−0.0626724 + 0.998034i \(0.519962\pi\)
\(938\) −10.1343 −0.330897
\(939\) 0.188074 0.00613758
\(940\) 2.10667 0.0687120
\(941\) −43.9596 −1.43304 −0.716521 0.697566i \(-0.754267\pi\)
−0.716521 + 0.697566i \(0.754267\pi\)
\(942\) 0.108307 0.00352882
\(943\) 51.7753 1.68604
\(944\) 13.4325 0.437191
\(945\) −0.000924969 0 −3.00892e−5 0
\(946\) −30.4569 −0.990239
\(947\) 25.2030 0.818986 0.409493 0.912313i \(-0.365706\pi\)
0.409493 + 0.912313i \(0.365706\pi\)
\(948\) −0.810106 −0.0263110
\(949\) 39.6415 1.28682
\(950\) 13.3759 0.433972
\(951\) −0.280085 −0.00908238
\(952\) −5.54433 −0.179693
\(953\) 37.9983 1.23089 0.615443 0.788181i \(-0.288977\pi\)
0.615443 + 0.788181i \(0.288977\pi\)
\(954\) −94.7643 −3.06811
\(955\) −1.20925 −0.0391303
\(956\) −101.068 −3.26879
\(957\) −0.286999 −0.00927736
\(958\) 10.9130 0.352584
\(959\) 0.219306 0.00708175
\(960\) 0.00908260 0.000293140 0
\(961\) 85.6854 2.76405
\(962\) 105.357 3.39684
\(963\) −16.1208 −0.519485
\(964\) 17.7901 0.572982
\(965\) 0.906873 0.0291933
\(966\) 0.0568505 0.00182913
\(967\) 4.15818 0.133718 0.0668590 0.997762i \(-0.478702\pi\)
0.0668590 + 0.997762i \(0.478702\pi\)
\(968\) 0.0408972 0.00131449
\(969\) 0.0203829 0.000654794 0
\(970\) 1.40380 0.0450733
\(971\) 48.6253 1.56046 0.780230 0.625493i \(-0.215102\pi\)
0.780230 + 0.625493i \(0.215102\pi\)
\(972\) 1.35453 0.0434466
\(973\) −7.32879 −0.234950
\(974\) −24.9319 −0.798869
\(975\) −0.248043 −0.00794373
\(976\) −86.7710 −2.77747
\(977\) 19.8285 0.634369 0.317184 0.948364i \(-0.397263\pi\)
0.317184 + 0.948364i \(0.397263\pi\)
\(978\) −0.0979616 −0.00313247
\(979\) −16.9618 −0.542102
\(980\) −1.81261 −0.0579016
\(981\) −16.6765 −0.532439
\(982\) 18.2766 0.583229
\(983\) 45.9633 1.46600 0.733001 0.680228i \(-0.238119\pi\)
0.733001 + 0.680228i \(0.238119\pi\)
\(984\) 0.608021 0.0193830
\(985\) 0.514869 0.0164051
\(986\) 50.0277 1.59321
\(987\) 0.0243213 0.000774156 0
\(988\) 26.3822 0.839331
\(989\) −24.0427 −0.764512
\(990\) 1.35391 0.0430300
\(991\) −6.31435 −0.200582 −0.100291 0.994958i \(-0.531977\pi\)
−0.100291 + 0.994958i \(0.531977\pi\)
\(992\) −173.791 −5.51788
\(993\) −0.148951 −0.00472681
\(994\) 0.581696 0.0184503
\(995\) 0.983790 0.0311882
\(996\) 0.245686 0.00778486
\(997\) −12.4894 −0.395543 −0.197771 0.980248i \(-0.563370\pi\)
−0.197771 + 0.980248i \(0.563370\pi\)
\(998\) 20.2498 0.640996
\(999\) 0.449119 0.0142095
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 \(a_p\))