Properties

Label 4015.2.a.h.1.11
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(37\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.16251 q^{2}\) \(-1.28072 q^{3}\) \(-0.648575 q^{4}\) \(+1.00000 q^{5}\) \(+1.48884 q^{6}\) \(-0.641997 q^{7}\) \(+3.07899 q^{8}\) \(-1.35976 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.16251 q^{2}\) \(-1.28072 q^{3}\) \(-0.648575 q^{4}\) \(+1.00000 q^{5}\) \(+1.48884 q^{6}\) \(-0.641997 q^{7}\) \(+3.07899 q^{8}\) \(-1.35976 q^{9}\) \(-1.16251 q^{10}\) \(+1.00000 q^{11}\) \(+0.830642 q^{12}\) \(-2.10809 q^{13}\) \(+0.746327 q^{14}\) \(-1.28072 q^{15}\) \(-2.28220 q^{16}\) \(+0.343722 q^{17}\) \(+1.58073 q^{18}\) \(-5.83884 q^{19}\) \(-0.648575 q^{20}\) \(+0.822217 q^{21}\) \(-1.16251 q^{22}\) \(-6.18504 q^{23}\) \(-3.94332 q^{24}\) \(+1.00000 q^{25}\) \(+2.45067 q^{26}\) \(+5.58362 q^{27}\) \(+0.416383 q^{28}\) \(+7.74570 q^{29}\) \(+1.48884 q^{30}\) \(+2.91101 q^{31}\) \(-3.50490 q^{32}\) \(-1.28072 q^{33}\) \(-0.399579 q^{34}\) \(-0.641997 q^{35}\) \(+0.881908 q^{36}\) \(+0.493087 q^{37}\) \(+6.78770 q^{38}\) \(+2.69986 q^{39}\) \(+3.07899 q^{40}\) \(-8.13803 q^{41}\) \(-0.955834 q^{42}\) \(+3.22980 q^{43}\) \(-0.648575 q^{44}\) \(-1.35976 q^{45}\) \(+7.19015 q^{46}\) \(-8.99741 q^{47}\) \(+2.92285 q^{48}\) \(-6.58784 q^{49}\) \(-1.16251 q^{50}\) \(-0.440211 q^{51}\) \(+1.36725 q^{52}\) \(+11.9039 q^{53}\) \(-6.49101 q^{54}\) \(+1.00000 q^{55}\) \(-1.97670 q^{56}\) \(+7.47791 q^{57}\) \(-9.00444 q^{58}\) \(-10.3591 q^{59}\) \(+0.830642 q^{60}\) \(+7.45034 q^{61}\) \(-3.38407 q^{62}\) \(+0.872963 q^{63}\) \(+8.63888 q^{64}\) \(-2.10809 q^{65}\) \(+1.48884 q^{66}\) \(-2.50494 q^{67}\) \(-0.222929 q^{68}\) \(+7.92129 q^{69}\) \(+0.746327 q^{70}\) \(+12.8491 q^{71}\) \(-4.18669 q^{72}\) \(+1.00000 q^{73}\) \(-0.573217 q^{74}\) \(-1.28072 q^{75}\) \(+3.78693 q^{76}\) \(-0.641997 q^{77}\) \(-3.13861 q^{78}\) \(+0.783251 q^{79}\) \(-2.28220 q^{80}\) \(-3.07176 q^{81}\) \(+9.46053 q^{82}\) \(-10.4618 q^{83}\) \(-0.533270 q^{84}\) \(+0.343722 q^{85}\) \(-3.75467 q^{86}\) \(-9.92006 q^{87}\) \(+3.07899 q^{88}\) \(-2.69997 q^{89}\) \(+1.58073 q^{90}\) \(+1.35339 q^{91}\) \(+4.01146 q^{92}\) \(-3.72818 q^{93}\) \(+10.4596 q^{94}\) \(-5.83884 q^{95}\) \(+4.48879 q^{96}\) \(+9.65525 q^{97}\) \(+7.65842 q^{98}\) \(-1.35976 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.16251 −0.822017 −0.411009 0.911631i \(-0.634823\pi\)
−0.411009 + 0.911631i \(0.634823\pi\)
\(3\) −1.28072 −0.739423 −0.369711 0.929147i \(-0.620543\pi\)
−0.369711 + 0.929147i \(0.620543\pi\)
\(4\) −0.648575 −0.324288
\(5\) 1.00000 0.447214
\(6\) 1.48884 0.607818
\(7\) −0.641997 −0.242652 −0.121326 0.992613i \(-0.538715\pi\)
−0.121326 + 0.992613i \(0.538715\pi\)
\(8\) 3.07899 1.08859
\(9\) −1.35976 −0.453254
\(10\) −1.16251 −0.367617
\(11\) 1.00000 0.301511
\(12\) 0.830642 0.239786
\(13\) −2.10809 −0.584678 −0.292339 0.956315i \(-0.594434\pi\)
−0.292339 + 0.956315i \(0.594434\pi\)
\(14\) 0.746327 0.199464
\(15\) −1.28072 −0.330680
\(16\) −2.28220 −0.570550
\(17\) 0.343722 0.0833648 0.0416824 0.999131i \(-0.486728\pi\)
0.0416824 + 0.999131i \(0.486728\pi\)
\(18\) 1.58073 0.372583
\(19\) −5.83884 −1.33952 −0.669761 0.742576i \(-0.733604\pi\)
−0.669761 + 0.742576i \(0.733604\pi\)
\(20\) −0.648575 −0.145026
\(21\) 0.822217 0.179422
\(22\) −1.16251 −0.247848
\(23\) −6.18504 −1.28967 −0.644835 0.764322i \(-0.723074\pi\)
−0.644835 + 0.764322i \(0.723074\pi\)
\(24\) −3.94332 −0.804926
\(25\) 1.00000 0.200000
\(26\) 2.45067 0.480616
\(27\) 5.58362 1.07457
\(28\) 0.416383 0.0786891
\(29\) 7.74570 1.43834 0.719170 0.694834i \(-0.244522\pi\)
0.719170 + 0.694834i \(0.244522\pi\)
\(30\) 1.48884 0.271825
\(31\) 2.91101 0.522832 0.261416 0.965226i \(-0.415811\pi\)
0.261416 + 0.965226i \(0.415811\pi\)
\(32\) −3.50490 −0.619585
\(33\) −1.28072 −0.222944
\(34\) −0.399579 −0.0685273
\(35\) −0.641997 −0.108517
\(36\) 0.881908 0.146985
\(37\) 0.493087 0.0810630 0.0405315 0.999178i \(-0.487095\pi\)
0.0405315 + 0.999178i \(0.487095\pi\)
\(38\) 6.78770 1.10111
\(39\) 2.69986 0.432324
\(40\) 3.07899 0.486831
\(41\) −8.13803 −1.27095 −0.635474 0.772122i \(-0.719195\pi\)
−0.635474 + 0.772122i \(0.719195\pi\)
\(42\) −0.955834 −0.147488
\(43\) 3.22980 0.492540 0.246270 0.969201i \(-0.420795\pi\)
0.246270 + 0.969201i \(0.420795\pi\)
\(44\) −0.648575 −0.0977764
\(45\) −1.35976 −0.202701
\(46\) 7.19015 1.06013
\(47\) −8.99741 −1.31241 −0.656204 0.754584i \(-0.727839\pi\)
−0.656204 + 0.754584i \(0.727839\pi\)
\(48\) 2.92285 0.421878
\(49\) −6.58784 −0.941120
\(50\) −1.16251 −0.164403
\(51\) −0.440211 −0.0616418
\(52\) 1.36725 0.189604
\(53\) 11.9039 1.63513 0.817563 0.575840i \(-0.195325\pi\)
0.817563 + 0.575840i \(0.195325\pi\)
\(54\) −6.49101 −0.883314
\(55\) 1.00000 0.134840
\(56\) −1.97670 −0.264148
\(57\) 7.47791 0.990474
\(58\) −9.00444 −1.18234
\(59\) −10.3591 −1.34863 −0.674317 0.738442i \(-0.735562\pi\)
−0.674317 + 0.738442i \(0.735562\pi\)
\(60\) 0.830642 0.107235
\(61\) 7.45034 0.953918 0.476959 0.878926i \(-0.341739\pi\)
0.476959 + 0.878926i \(0.341739\pi\)
\(62\) −3.38407 −0.429777
\(63\) 0.872963 0.109983
\(64\) 8.63888 1.07986
\(65\) −2.10809 −0.261476
\(66\) 1.48884 0.183264
\(67\) −2.50494 −0.306027 −0.153014 0.988224i \(-0.548898\pi\)
−0.153014 + 0.988224i \(0.548898\pi\)
\(68\) −0.222929 −0.0270342
\(69\) 7.92129 0.953611
\(70\) 0.746327 0.0892031
\(71\) 12.8491 1.52491 0.762456 0.647040i \(-0.223993\pi\)
0.762456 + 0.647040i \(0.223993\pi\)
\(72\) −4.18669 −0.493407
\(73\) 1.00000 0.117041
\(74\) −0.573217 −0.0666352
\(75\) −1.28072 −0.147885
\(76\) 3.78693 0.434391
\(77\) −0.641997 −0.0731623
\(78\) −3.13861 −0.355378
\(79\) 0.783251 0.0881227 0.0440613 0.999029i \(-0.485970\pi\)
0.0440613 + 0.999029i \(0.485970\pi\)
\(80\) −2.28220 −0.255158
\(81\) −3.07176 −0.341307
\(82\) 9.46053 1.04474
\(83\) −10.4618 −1.14834 −0.574168 0.818738i \(-0.694674\pi\)
−0.574168 + 0.818738i \(0.694674\pi\)
\(84\) −0.533270 −0.0581845
\(85\) 0.343722 0.0372819
\(86\) −3.75467 −0.404876
\(87\) −9.92006 −1.06354
\(88\) 3.07899 0.328221
\(89\) −2.69997 −0.286197 −0.143098 0.989708i \(-0.545707\pi\)
−0.143098 + 0.989708i \(0.545707\pi\)
\(90\) 1.58073 0.166624
\(91\) 1.35339 0.141873
\(92\) 4.01146 0.418224
\(93\) −3.72818 −0.386594
\(94\) 10.4596 1.07882
\(95\) −5.83884 −0.599053
\(96\) 4.48879 0.458136
\(97\) 9.65525 0.980342 0.490171 0.871626i \(-0.336934\pi\)
0.490171 + 0.871626i \(0.336934\pi\)
\(98\) 7.65842 0.773617
\(99\) −1.35976 −0.136661
\(100\) −0.648575 −0.0648575
\(101\) −10.1399 −1.00896 −0.504480 0.863423i \(-0.668316\pi\)
−0.504480 + 0.863423i \(0.668316\pi\)
\(102\) 0.511748 0.0506706
\(103\) −10.8550 −1.06957 −0.534787 0.844987i \(-0.679608\pi\)
−0.534787 + 0.844987i \(0.679608\pi\)
\(104\) −6.49078 −0.636473
\(105\) 0.822217 0.0802402
\(106\) −13.8384 −1.34410
\(107\) −14.2220 −1.37489 −0.687444 0.726237i \(-0.741267\pi\)
−0.687444 + 0.726237i \(0.741267\pi\)
\(108\) −3.62140 −0.348469
\(109\) −1.17084 −0.112146 −0.0560729 0.998427i \(-0.517858\pi\)
−0.0560729 + 0.998427i \(0.517858\pi\)
\(110\) −1.16251 −0.110841
\(111\) −0.631505 −0.0599398
\(112\) 1.46517 0.138445
\(113\) −7.96633 −0.749409 −0.374704 0.927144i \(-0.622256\pi\)
−0.374704 + 0.927144i \(0.622256\pi\)
\(114\) −8.69313 −0.814186
\(115\) −6.18504 −0.576758
\(116\) −5.02367 −0.466436
\(117\) 2.86650 0.265008
\(118\) 12.0425 1.10860
\(119\) −0.220668 −0.0202286
\(120\) −3.94332 −0.359974
\(121\) 1.00000 0.0909091
\(122\) −8.66107 −0.784137
\(123\) 10.4225 0.939767
\(124\) −1.88801 −0.169548
\(125\) 1.00000 0.0894427
\(126\) −1.01483 −0.0904079
\(127\) −14.7034 −1.30471 −0.652357 0.757912i \(-0.726220\pi\)
−0.652357 + 0.757912i \(0.726220\pi\)
\(128\) −3.03296 −0.268078
\(129\) −4.13646 −0.364195
\(130\) 2.45067 0.214938
\(131\) 9.68402 0.846097 0.423048 0.906107i \(-0.360960\pi\)
0.423048 + 0.906107i \(0.360960\pi\)
\(132\) 0.830642 0.0722981
\(133\) 3.74852 0.325038
\(134\) 2.91202 0.251560
\(135\) 5.58362 0.480562
\(136\) 1.05832 0.0907498
\(137\) −9.21897 −0.787630 −0.393815 0.919190i \(-0.628845\pi\)
−0.393815 + 0.919190i \(0.628845\pi\)
\(138\) −9.20856 −0.783884
\(139\) 20.7333 1.75857 0.879287 0.476291i \(-0.158019\pi\)
0.879287 + 0.476291i \(0.158019\pi\)
\(140\) 0.416383 0.0351908
\(141\) 11.5231 0.970424
\(142\) −14.9372 −1.25350
\(143\) −2.10809 −0.176287
\(144\) 3.10325 0.258604
\(145\) 7.74570 0.643246
\(146\) −1.16251 −0.0962098
\(147\) 8.43716 0.695885
\(148\) −0.319804 −0.0262877
\(149\) −16.8512 −1.38051 −0.690254 0.723567i \(-0.742501\pi\)
−0.690254 + 0.723567i \(0.742501\pi\)
\(150\) 1.48884 0.121564
\(151\) 14.4040 1.17218 0.586091 0.810245i \(-0.300666\pi\)
0.586091 + 0.810245i \(0.300666\pi\)
\(152\) −17.9777 −1.45819
\(153\) −0.467380 −0.0377854
\(154\) 0.746327 0.0601407
\(155\) 2.91101 0.233818
\(156\) −1.75107 −0.140197
\(157\) 10.5072 0.838566 0.419283 0.907856i \(-0.362282\pi\)
0.419283 + 0.907856i \(0.362282\pi\)
\(158\) −0.910536 −0.0724384
\(159\) −15.2455 −1.20905
\(160\) −3.50490 −0.277087
\(161\) 3.97077 0.312941
\(162\) 3.57095 0.280560
\(163\) −8.50054 −0.665814 −0.332907 0.942960i \(-0.608030\pi\)
−0.332907 + 0.942960i \(0.608030\pi\)
\(164\) 5.27813 0.412153
\(165\) −1.28072 −0.0997037
\(166\) 12.1620 0.943952
\(167\) 16.5246 1.27871 0.639357 0.768910i \(-0.279200\pi\)
0.639357 + 0.768910i \(0.279200\pi\)
\(168\) 2.53160 0.195317
\(169\) −8.55597 −0.658151
\(170\) −0.399579 −0.0306463
\(171\) 7.93944 0.607144
\(172\) −2.09477 −0.159725
\(173\) 24.6751 1.87601 0.938005 0.346622i \(-0.112671\pi\)
0.938005 + 0.346622i \(0.112671\pi\)
\(174\) 11.5321 0.874250
\(175\) −0.641997 −0.0485304
\(176\) −2.28220 −0.172027
\(177\) 13.2670 0.997211
\(178\) 3.13874 0.235259
\(179\) 8.44486 0.631199 0.315599 0.948893i \(-0.397794\pi\)
0.315599 + 0.948893i \(0.397794\pi\)
\(180\) 0.881908 0.0657336
\(181\) 3.37821 0.251100 0.125550 0.992087i \(-0.459930\pi\)
0.125550 + 0.992087i \(0.459930\pi\)
\(182\) −1.57332 −0.116622
\(183\) −9.54178 −0.705348
\(184\) −19.0437 −1.40392
\(185\) 0.493087 0.0362525
\(186\) 4.33403 0.317787
\(187\) 0.343722 0.0251354
\(188\) 5.83550 0.425598
\(189\) −3.58467 −0.260746
\(190\) 6.78770 0.492432
\(191\) 21.2462 1.53732 0.768660 0.639657i \(-0.220924\pi\)
0.768660 + 0.639657i \(0.220924\pi\)
\(192\) −11.0640 −0.798473
\(193\) −20.8242 −1.49896 −0.749481 0.662026i \(-0.769697\pi\)
−0.749481 + 0.662026i \(0.769697\pi\)
\(194\) −11.2243 −0.805858
\(195\) 2.69986 0.193341
\(196\) 4.27271 0.305194
\(197\) 19.9368 1.42044 0.710220 0.703980i \(-0.248596\pi\)
0.710220 + 0.703980i \(0.248596\pi\)
\(198\) 1.58073 0.112338
\(199\) 4.40291 0.312114 0.156057 0.987748i \(-0.450122\pi\)
0.156057 + 0.987748i \(0.450122\pi\)
\(200\) 3.07899 0.217717
\(201\) 3.20812 0.226284
\(202\) 11.7877 0.829383
\(203\) −4.97272 −0.349016
\(204\) 0.285510 0.0199897
\(205\) −8.13803 −0.568385
\(206\) 12.6190 0.879209
\(207\) 8.41018 0.584548
\(208\) 4.81108 0.333588
\(209\) −5.83884 −0.403881
\(210\) −0.955834 −0.0659588
\(211\) 3.29263 0.226674 0.113337 0.993557i \(-0.463846\pi\)
0.113337 + 0.993557i \(0.463846\pi\)
\(212\) −7.72057 −0.530251
\(213\) −16.4561 −1.12755
\(214\) 16.5331 1.13018
\(215\) 3.22980 0.220271
\(216\) 17.1919 1.16976
\(217\) −1.86886 −0.126866
\(218\) 1.36111 0.0921858
\(219\) −1.28072 −0.0865429
\(220\) −0.648575 −0.0437269
\(221\) −0.724596 −0.0487416
\(222\) 0.734130 0.0492716
\(223\) 8.17772 0.547620 0.273810 0.961784i \(-0.411716\pi\)
0.273810 + 0.961784i \(0.411716\pi\)
\(224\) 2.25014 0.150344
\(225\) −1.35976 −0.0906508
\(226\) 9.26092 0.616027
\(227\) 0.158982 0.0105520 0.00527600 0.999986i \(-0.498321\pi\)
0.00527600 + 0.999986i \(0.498321\pi\)
\(228\) −4.84999 −0.321198
\(229\) 18.7188 1.23698 0.618488 0.785794i \(-0.287746\pi\)
0.618488 + 0.785794i \(0.287746\pi\)
\(230\) 7.19015 0.474105
\(231\) 0.822217 0.0540979
\(232\) 23.8489 1.56576
\(233\) 9.43469 0.618087 0.309044 0.951048i \(-0.399991\pi\)
0.309044 + 0.951048i \(0.399991\pi\)
\(234\) −3.33233 −0.217841
\(235\) −8.99741 −0.586927
\(236\) 6.71863 0.437345
\(237\) −1.00312 −0.0651599
\(238\) 0.256529 0.0166283
\(239\) −20.0848 −1.29918 −0.649589 0.760286i \(-0.725059\pi\)
−0.649589 + 0.760286i \(0.725059\pi\)
\(240\) 2.92285 0.188669
\(241\) −7.05229 −0.454278 −0.227139 0.973862i \(-0.572937\pi\)
−0.227139 + 0.973862i \(0.572937\pi\)
\(242\) −1.16251 −0.0747288
\(243\) −12.8168 −0.822199
\(244\) −4.83210 −0.309344
\(245\) −6.58784 −0.420882
\(246\) −12.1163 −0.772505
\(247\) 12.3088 0.783190
\(248\) 8.96296 0.569148
\(249\) 13.3987 0.849105
\(250\) −1.16251 −0.0735235
\(251\) 20.0992 1.26865 0.634326 0.773065i \(-0.281278\pi\)
0.634326 + 0.773065i \(0.281278\pi\)
\(252\) −0.566182 −0.0356661
\(253\) −6.18504 −0.388850
\(254\) 17.0928 1.07250
\(255\) −0.440211 −0.0275671
\(256\) −13.7519 −0.859495
\(257\) −5.22396 −0.325862 −0.162931 0.986637i \(-0.552095\pi\)
−0.162931 + 0.986637i \(0.552095\pi\)
\(258\) 4.80867 0.299375
\(259\) −0.316560 −0.0196701
\(260\) 1.36725 0.0847935
\(261\) −10.5323 −0.651934
\(262\) −11.2577 −0.695506
\(263\) −17.9094 −1.10434 −0.552170 0.833732i \(-0.686200\pi\)
−0.552170 + 0.833732i \(0.686200\pi\)
\(264\) −3.94332 −0.242694
\(265\) 11.9039 0.731250
\(266\) −4.35768 −0.267187
\(267\) 3.45790 0.211620
\(268\) 1.62464 0.0992409
\(269\) 23.2089 1.41507 0.707537 0.706677i \(-0.249806\pi\)
0.707537 + 0.706677i \(0.249806\pi\)
\(270\) −6.49101 −0.395030
\(271\) 17.8723 1.08566 0.542832 0.839841i \(-0.317352\pi\)
0.542832 + 0.839841i \(0.317352\pi\)
\(272\) −0.784442 −0.0475638
\(273\) −1.73331 −0.104904
\(274\) 10.7171 0.647445
\(275\) 1.00000 0.0603023
\(276\) −5.13755 −0.309244
\(277\) 31.9780 1.92137 0.960687 0.277633i \(-0.0895500\pi\)
0.960687 + 0.277633i \(0.0895500\pi\)
\(278\) −24.1026 −1.44558
\(279\) −3.95828 −0.236976
\(280\) −1.97670 −0.118131
\(281\) 16.4603 0.981941 0.490970 0.871176i \(-0.336642\pi\)
0.490970 + 0.871176i \(0.336642\pi\)
\(282\) −13.3957 −0.797705
\(283\) −17.7881 −1.05740 −0.528698 0.848810i \(-0.677320\pi\)
−0.528698 + 0.848810i \(0.677320\pi\)
\(284\) −8.33363 −0.494510
\(285\) 7.47791 0.442953
\(286\) 2.45067 0.144911
\(287\) 5.22459 0.308398
\(288\) 4.76584 0.280830
\(289\) −16.8819 −0.993050
\(290\) −9.00444 −0.528759
\(291\) −12.3657 −0.724887
\(292\) −0.648575 −0.0379550
\(293\) −0.740470 −0.0432587 −0.0216294 0.999766i \(-0.506885\pi\)
−0.0216294 + 0.999766i \(0.506885\pi\)
\(294\) −9.80827 −0.572030
\(295\) −10.3591 −0.603127
\(296\) 1.51821 0.0882441
\(297\) 5.58362 0.323995
\(298\) 19.5897 1.13480
\(299\) 13.0386 0.754042
\(300\) 0.830642 0.0479571
\(301\) −2.07352 −0.119516
\(302\) −16.7448 −0.963553
\(303\) 12.9864 0.746048
\(304\) 13.3254 0.764265
\(305\) 7.45034 0.426605
\(306\) 0.543333 0.0310603
\(307\) 22.9235 1.30831 0.654155 0.756360i \(-0.273024\pi\)
0.654155 + 0.756360i \(0.273024\pi\)
\(308\) 0.416383 0.0237256
\(309\) 13.9022 0.790868
\(310\) −3.38407 −0.192202
\(311\) 15.5490 0.881704 0.440852 0.897580i \(-0.354676\pi\)
0.440852 + 0.897580i \(0.354676\pi\)
\(312\) 8.31286 0.470623
\(313\) 29.1446 1.64735 0.823676 0.567061i \(-0.191920\pi\)
0.823676 + 0.567061i \(0.191920\pi\)
\(314\) −12.2147 −0.689316
\(315\) 0.872963 0.0491859
\(316\) −0.507997 −0.0285771
\(317\) −20.5857 −1.15621 −0.578103 0.815964i \(-0.696207\pi\)
−0.578103 + 0.815964i \(0.696207\pi\)
\(318\) 17.7230 0.993859
\(319\) 7.74570 0.433676
\(320\) 8.63888 0.482928
\(321\) 18.2143 1.01662
\(322\) −4.61606 −0.257243
\(323\) −2.00694 −0.111669
\(324\) 1.99227 0.110682
\(325\) −2.10809 −0.116936
\(326\) 9.88195 0.547311
\(327\) 1.49951 0.0829231
\(328\) −25.0569 −1.38354
\(329\) 5.77631 0.318458
\(330\) 1.48884 0.0819582
\(331\) 12.4856 0.686270 0.343135 0.939286i \(-0.388511\pi\)
0.343135 + 0.939286i \(0.388511\pi\)
\(332\) 6.78529 0.372391
\(333\) −0.670481 −0.0367421
\(334\) −19.2100 −1.05113
\(335\) −2.50494 −0.136860
\(336\) −1.87646 −0.102369
\(337\) −21.3598 −1.16354 −0.581771 0.813353i \(-0.697640\pi\)
−0.581771 + 0.813353i \(0.697640\pi\)
\(338\) 9.94638 0.541012
\(339\) 10.2026 0.554130
\(340\) −0.222929 −0.0120900
\(341\) 2.91101 0.157640
\(342\) −9.22966 −0.499083
\(343\) 8.72335 0.471017
\(344\) 9.94452 0.536173
\(345\) 7.92129 0.426468
\(346\) −28.6850 −1.54211
\(347\) −15.9975 −0.858789 −0.429395 0.903117i \(-0.641273\pi\)
−0.429395 + 0.903117i \(0.641273\pi\)
\(348\) 6.43390 0.344893
\(349\) 34.9206 1.86926 0.934630 0.355623i \(-0.115731\pi\)
0.934630 + 0.355623i \(0.115731\pi\)
\(350\) 0.746327 0.0398928
\(351\) −11.7708 −0.628277
\(352\) −3.50490 −0.186812
\(353\) −0.409740 −0.0218083 −0.0109041 0.999941i \(-0.503471\pi\)
−0.0109041 + 0.999941i \(0.503471\pi\)
\(354\) −15.4230 −0.819724
\(355\) 12.8491 0.681961
\(356\) 1.75114 0.0928100
\(357\) 0.282614 0.0149575
\(358\) −9.81722 −0.518856
\(359\) 23.9073 1.26178 0.630888 0.775874i \(-0.282691\pi\)
0.630888 + 0.775874i \(0.282691\pi\)
\(360\) −4.18669 −0.220658
\(361\) 15.0921 0.794321
\(362\) −3.92719 −0.206409
\(363\) −1.28072 −0.0672202
\(364\) −0.877773 −0.0460078
\(365\) 1.00000 0.0523424
\(366\) 11.0924 0.579809
\(367\) −20.4451 −1.06722 −0.533612 0.845729i \(-0.679166\pi\)
−0.533612 + 0.845729i \(0.679166\pi\)
\(368\) 14.1155 0.735821
\(369\) 11.0658 0.576062
\(370\) −0.573217 −0.0298002
\(371\) −7.64226 −0.396766
\(372\) 2.41800 0.125368
\(373\) −12.2237 −0.632919 −0.316459 0.948606i \(-0.602494\pi\)
−0.316459 + 0.948606i \(0.602494\pi\)
\(374\) −0.399579 −0.0206618
\(375\) −1.28072 −0.0661360
\(376\) −27.7029 −1.42867
\(377\) −16.3286 −0.840967
\(378\) 4.16721 0.214338
\(379\) −12.2749 −0.630518 −0.315259 0.949006i \(-0.602091\pi\)
−0.315259 + 0.949006i \(0.602091\pi\)
\(380\) 3.78693 0.194265
\(381\) 18.8309 0.964736
\(382\) −24.6989 −1.26370
\(383\) 6.57504 0.335969 0.167985 0.985790i \(-0.446274\pi\)
0.167985 + 0.985790i \(0.446274\pi\)
\(384\) 3.88436 0.198223
\(385\) −0.641997 −0.0327192
\(386\) 24.2083 1.23217
\(387\) −4.39176 −0.223246
\(388\) −6.26216 −0.317913
\(389\) 34.0102 1.72439 0.862193 0.506580i \(-0.169091\pi\)
0.862193 + 0.506580i \(0.169091\pi\)
\(390\) −3.13861 −0.158930
\(391\) −2.12593 −0.107513
\(392\) −20.2839 −1.02449
\(393\) −12.4025 −0.625623
\(394\) −23.1767 −1.16763
\(395\) 0.783251 0.0394097
\(396\) 0.881908 0.0443176
\(397\) 37.8535 1.89981 0.949907 0.312532i \(-0.101177\pi\)
0.949907 + 0.312532i \(0.101177\pi\)
\(398\) −5.11842 −0.256563
\(399\) −4.80080 −0.240340
\(400\) −2.28220 −0.114110
\(401\) 19.2150 0.959550 0.479775 0.877391i \(-0.340718\pi\)
0.479775 + 0.877391i \(0.340718\pi\)
\(402\) −3.72947 −0.186009
\(403\) −6.13665 −0.305689
\(404\) 6.57651 0.327193
\(405\) −3.07176 −0.152637
\(406\) 5.78082 0.286897
\(407\) 0.493087 0.0244414
\(408\) −1.35540 −0.0671025
\(409\) 38.3034 1.89398 0.946992 0.321258i \(-0.104106\pi\)
0.946992 + 0.321258i \(0.104106\pi\)
\(410\) 9.46053 0.467222
\(411\) 11.8069 0.582392
\(412\) 7.04028 0.346850
\(413\) 6.65048 0.327249
\(414\) −9.77690 −0.480508
\(415\) −10.4618 −0.513551
\(416\) 7.38864 0.362258
\(417\) −26.5535 −1.30033
\(418\) 6.78770 0.331997
\(419\) 31.2650 1.52739 0.763697 0.645575i \(-0.223382\pi\)
0.763697 + 0.645575i \(0.223382\pi\)
\(420\) −0.533270 −0.0260209
\(421\) 36.3796 1.77303 0.886516 0.462698i \(-0.153119\pi\)
0.886516 + 0.462698i \(0.153119\pi\)
\(422\) −3.82770 −0.186330
\(423\) 12.2343 0.594854
\(424\) 36.6520 1.77998
\(425\) 0.343722 0.0166730
\(426\) 19.1304 0.926869
\(427\) −4.78309 −0.231470
\(428\) 9.22401 0.445859
\(429\) 2.69986 0.130351
\(430\) −3.75467 −0.181066
\(431\) 25.4862 1.22763 0.613814 0.789451i \(-0.289635\pi\)
0.613814 + 0.789451i \(0.289635\pi\)
\(432\) −12.7429 −0.613095
\(433\) −22.0419 −1.05927 −0.529633 0.848227i \(-0.677670\pi\)
−0.529633 + 0.848227i \(0.677670\pi\)
\(434\) 2.17256 0.104286
\(435\) −9.92006 −0.475630
\(436\) 0.759376 0.0363675
\(437\) 36.1135 1.72754
\(438\) 1.48884 0.0711397
\(439\) −19.8566 −0.947703 −0.473851 0.880605i \(-0.657137\pi\)
−0.473851 + 0.880605i \(0.657137\pi\)
\(440\) 3.07899 0.146785
\(441\) 8.95790 0.426566
\(442\) 0.842348 0.0400664
\(443\) 10.3372 0.491137 0.245569 0.969379i \(-0.421025\pi\)
0.245569 + 0.969379i \(0.421025\pi\)
\(444\) 0.409579 0.0194377
\(445\) −2.69997 −0.127991
\(446\) −9.50666 −0.450153
\(447\) 21.5817 1.02078
\(448\) −5.54613 −0.262030
\(449\) −26.5637 −1.25362 −0.626809 0.779173i \(-0.715639\pi\)
−0.626809 + 0.779173i \(0.715639\pi\)
\(450\) 1.58073 0.0745165
\(451\) −8.13803 −0.383205
\(452\) 5.16676 0.243024
\(453\) −18.4475 −0.866738
\(454\) −0.184818 −0.00867392
\(455\) 1.35339 0.0634477
\(456\) 23.0244 1.07822
\(457\) −15.1963 −0.710855 −0.355427 0.934704i \(-0.615665\pi\)
−0.355427 + 0.934704i \(0.615665\pi\)
\(458\) −21.7608 −1.01682
\(459\) 1.91921 0.0895812
\(460\) 4.01146 0.187035
\(461\) 1.16768 0.0543844 0.0271922 0.999630i \(-0.491343\pi\)
0.0271922 + 0.999630i \(0.491343\pi\)
\(462\) −0.955834 −0.0444694
\(463\) 16.7162 0.776867 0.388434 0.921477i \(-0.373016\pi\)
0.388434 + 0.921477i \(0.373016\pi\)
\(464\) −17.6772 −0.820645
\(465\) −3.72818 −0.172890
\(466\) −10.9679 −0.508078
\(467\) −29.8868 −1.38300 −0.691498 0.722378i \(-0.743049\pi\)
−0.691498 + 0.722378i \(0.743049\pi\)
\(468\) −1.85914 −0.0859388
\(469\) 1.60817 0.0742582
\(470\) 10.4596 0.482464
\(471\) −13.4568 −0.620055
\(472\) −31.8954 −1.46811
\(473\) 3.22980 0.148506
\(474\) 1.16614 0.0535626
\(475\) −5.83884 −0.267905
\(476\) 0.143120 0.00655990
\(477\) −16.1865 −0.741127
\(478\) 23.3487 1.06795
\(479\) 11.4894 0.524963 0.262482 0.964937i \(-0.415459\pi\)
0.262482 + 0.964937i \(0.415459\pi\)
\(480\) 4.48879 0.204884
\(481\) −1.03947 −0.0473958
\(482\) 8.19834 0.373424
\(483\) −5.08544 −0.231396
\(484\) −0.648575 −0.0294807
\(485\) 9.65525 0.438422
\(486\) 14.8997 0.675862
\(487\) −12.7468 −0.577611 −0.288805 0.957388i \(-0.593258\pi\)
−0.288805 + 0.957388i \(0.593258\pi\)
\(488\) 22.9395 1.03842
\(489\) 10.8868 0.492318
\(490\) 7.65842 0.345972
\(491\) 15.7570 0.711104 0.355552 0.934657i \(-0.384293\pi\)
0.355552 + 0.934657i \(0.384293\pi\)
\(492\) −6.75979 −0.304755
\(493\) 2.66237 0.119907
\(494\) −14.3091 −0.643796
\(495\) −1.35976 −0.0611168
\(496\) −6.64350 −0.298302
\(497\) −8.24911 −0.370023
\(498\) −15.5760 −0.697979
\(499\) −32.0281 −1.43377 −0.716887 0.697189i \(-0.754434\pi\)
−0.716887 + 0.697189i \(0.754434\pi\)
\(500\) −0.648575 −0.0290052
\(501\) −21.1634 −0.945511
\(502\) −23.3655 −1.04285
\(503\) 6.01405 0.268153 0.134077 0.990971i \(-0.457193\pi\)
0.134077 + 0.990971i \(0.457193\pi\)
\(504\) 2.68784 0.119726
\(505\) −10.1399 −0.451221
\(506\) 7.19015 0.319641
\(507\) 10.9578 0.486652
\(508\) 9.53625 0.423103
\(509\) −21.9128 −0.971269 −0.485635 0.874162i \(-0.661411\pi\)
−0.485635 + 0.874162i \(0.661411\pi\)
\(510\) 0.511748 0.0226606
\(511\) −0.641997 −0.0284003
\(512\) 22.0526 0.974598
\(513\) −32.6019 −1.43941
\(514\) 6.07290 0.267864
\(515\) −10.8550 −0.478328
\(516\) 2.68281 0.118104
\(517\) −8.99741 −0.395706
\(518\) 0.368004 0.0161692
\(519\) −31.6018 −1.38716
\(520\) −6.49078 −0.284640
\(521\) 0.338487 0.0148294 0.00741468 0.999973i \(-0.497640\pi\)
0.00741468 + 0.999973i \(0.497640\pi\)
\(522\) 12.2439 0.535901
\(523\) 10.0100 0.437707 0.218853 0.975758i \(-0.429768\pi\)
0.218853 + 0.975758i \(0.429768\pi\)
\(524\) −6.28081 −0.274379
\(525\) 0.822217 0.0358845
\(526\) 20.8198 0.907786
\(527\) 1.00058 0.0435858
\(528\) 2.92285 0.127201
\(529\) 15.2547 0.663247
\(530\) −13.8384 −0.601100
\(531\) 14.0859 0.611274
\(532\) −2.43120 −0.105406
\(533\) 17.1557 0.743095
\(534\) −4.01984 −0.173956
\(535\) −14.2220 −0.614869
\(536\) −7.71269 −0.333138
\(537\) −10.8155 −0.466723
\(538\) −26.9806 −1.16321
\(539\) −6.58784 −0.283758
\(540\) −3.62140 −0.155840
\(541\) 2.06743 0.0888858 0.0444429 0.999012i \(-0.485849\pi\)
0.0444429 + 0.999012i \(0.485849\pi\)
\(542\) −20.7767 −0.892435
\(543\) −4.32653 −0.185669
\(544\) −1.20471 −0.0516516
\(545\) −1.17084 −0.0501531
\(546\) 2.01498 0.0862332
\(547\) −42.6737 −1.82460 −0.912298 0.409526i \(-0.865694\pi\)
−0.912298 + 0.409526i \(0.865694\pi\)
\(548\) 5.97920 0.255419
\(549\) −10.1307 −0.432367
\(550\) −1.16251 −0.0495695
\(551\) −45.2259 −1.92669
\(552\) 24.3896 1.03809
\(553\) −0.502845 −0.0213831
\(554\) −37.1747 −1.57940
\(555\) −0.631505 −0.0268059
\(556\) −13.4471 −0.570284
\(557\) 2.53121 0.107251 0.0536255 0.998561i \(-0.482922\pi\)
0.0536255 + 0.998561i \(0.482922\pi\)
\(558\) 4.60153 0.194798
\(559\) −6.80870 −0.287977
\(560\) 1.46517 0.0619145
\(561\) −0.440211 −0.0185857
\(562\) −19.1353 −0.807172
\(563\) 0.616117 0.0259662 0.0129831 0.999916i \(-0.495867\pi\)
0.0129831 + 0.999916i \(0.495867\pi\)
\(564\) −7.47363 −0.314696
\(565\) −7.96633 −0.335146
\(566\) 20.6789 0.869198
\(567\) 1.97206 0.0828188
\(568\) 39.5624 1.66000
\(569\) 43.1724 1.80988 0.904941 0.425537i \(-0.139915\pi\)
0.904941 + 0.425537i \(0.139915\pi\)
\(570\) −8.69313 −0.364115
\(571\) −2.74532 −0.114888 −0.0574440 0.998349i \(-0.518295\pi\)
−0.0574440 + 0.998349i \(0.518295\pi\)
\(572\) 1.36725 0.0571677
\(573\) −27.2104 −1.13673
\(574\) −6.07363 −0.253508
\(575\) −6.18504 −0.257934
\(576\) −11.7468 −0.489451
\(577\) 44.2576 1.84247 0.921235 0.389007i \(-0.127182\pi\)
0.921235 + 0.389007i \(0.127182\pi\)
\(578\) 19.6253 0.816304
\(579\) 26.6700 1.10837
\(580\) −5.02367 −0.208597
\(581\) 6.71647 0.278646
\(582\) 14.3752 0.595870
\(583\) 11.9039 0.493009
\(584\) 3.07899 0.127410
\(585\) 2.86650 0.118515
\(586\) 0.860803 0.0355594
\(587\) −15.7514 −0.650128 −0.325064 0.945692i \(-0.605386\pi\)
−0.325064 + 0.945692i \(0.605386\pi\)
\(588\) −5.47214 −0.225667
\(589\) −16.9969 −0.700345
\(590\) 12.0425 0.495781
\(591\) −25.5334 −1.05031
\(592\) −1.12532 −0.0462505
\(593\) 39.7770 1.63345 0.816724 0.577029i \(-0.195788\pi\)
0.816724 + 0.577029i \(0.195788\pi\)
\(594\) −6.49101 −0.266329
\(595\) −0.220668 −0.00904652
\(596\) 10.9293 0.447681
\(597\) −5.63889 −0.230784
\(598\) −15.1575 −0.619835
\(599\) −21.0557 −0.860314 −0.430157 0.902754i \(-0.641542\pi\)
−0.430157 + 0.902754i \(0.641542\pi\)
\(600\) −3.94332 −0.160985
\(601\) −48.0495 −1.95998 −0.979991 0.199042i \(-0.936217\pi\)
−0.979991 + 0.199042i \(0.936217\pi\)
\(602\) 2.41049 0.0982441
\(603\) 3.40613 0.138708
\(604\) −9.34208 −0.380124
\(605\) 1.00000 0.0406558
\(606\) −15.0968 −0.613265
\(607\) 27.7153 1.12493 0.562464 0.826822i \(-0.309853\pi\)
0.562464 + 0.826822i \(0.309853\pi\)
\(608\) 20.4646 0.829949
\(609\) 6.36865 0.258071
\(610\) −8.66107 −0.350677
\(611\) 18.9673 0.767336
\(612\) 0.303131 0.0122533
\(613\) −33.4178 −1.34973 −0.674866 0.737941i \(-0.735798\pi\)
−0.674866 + 0.737941i \(0.735798\pi\)
\(614\) −26.6487 −1.07545
\(615\) 10.4225 0.420277
\(616\) −1.97670 −0.0796436
\(617\) 23.1616 0.932452 0.466226 0.884666i \(-0.345613\pi\)
0.466226 + 0.884666i \(0.345613\pi\)
\(618\) −16.1614 −0.650107
\(619\) −5.26923 −0.211788 −0.105894 0.994377i \(-0.533770\pi\)
−0.105894 + 0.994377i \(0.533770\pi\)
\(620\) −1.88801 −0.0758242
\(621\) −34.5349 −1.38584
\(622\) −18.0759 −0.724776
\(623\) 1.73337 0.0694462
\(624\) −6.16163 −0.246663
\(625\) 1.00000 0.0400000
\(626\) −33.8809 −1.35415
\(627\) 7.47791 0.298639
\(628\) −6.81471 −0.271937
\(629\) 0.169485 0.00675780
\(630\) −1.01483 −0.0404317
\(631\) 17.2592 0.687080 0.343540 0.939138i \(-0.388374\pi\)
0.343540 + 0.939138i \(0.388374\pi\)
\(632\) 2.41162 0.0959292
\(633\) −4.21692 −0.167608
\(634\) 23.9310 0.950421
\(635\) −14.7034 −0.583486
\(636\) 9.88787 0.392080
\(637\) 13.8877 0.550252
\(638\) −9.00444 −0.356489
\(639\) −17.4718 −0.691173
\(640\) −3.03296 −0.119888
\(641\) 21.7023 0.857191 0.428595 0.903497i \(-0.359009\pi\)
0.428595 + 0.903497i \(0.359009\pi\)
\(642\) −21.1743 −0.835682
\(643\) 18.3770 0.724717 0.362359 0.932039i \(-0.381972\pi\)
0.362359 + 0.932039i \(0.381972\pi\)
\(644\) −2.57535 −0.101483
\(645\) −4.13646 −0.162873
\(646\) 2.33308 0.0917939
\(647\) 25.1345 0.988139 0.494070 0.869422i \(-0.335509\pi\)
0.494070 + 0.869422i \(0.335509\pi\)
\(648\) −9.45792 −0.371542
\(649\) −10.3591 −0.406628
\(650\) 2.45067 0.0961231
\(651\) 2.39348 0.0938078
\(652\) 5.51324 0.215915
\(653\) −37.8993 −1.48311 −0.741557 0.670889i \(-0.765913\pi\)
−0.741557 + 0.670889i \(0.765913\pi\)
\(654\) −1.74319 −0.0681643
\(655\) 9.68402 0.378386
\(656\) 18.5726 0.725139
\(657\) −1.35976 −0.0530494
\(658\) −6.71501 −0.261778
\(659\) 24.0360 0.936311 0.468155 0.883646i \(-0.344919\pi\)
0.468155 + 0.883646i \(0.344919\pi\)
\(660\) 0.830642 0.0323327
\(661\) 18.3613 0.714173 0.357087 0.934071i \(-0.383770\pi\)
0.357087 + 0.934071i \(0.383770\pi\)
\(662\) −14.5146 −0.564126
\(663\) 0.928002 0.0360406
\(664\) −32.2119 −1.25006
\(665\) 3.74852 0.145361
\(666\) 0.779439 0.0302027
\(667\) −47.9074 −1.85498
\(668\) −10.7175 −0.414671
\(669\) −10.4733 −0.404923
\(670\) 2.91202 0.112501
\(671\) 7.45034 0.287617
\(672\) −2.88179 −0.111168
\(673\) 23.3996 0.901990 0.450995 0.892527i \(-0.351069\pi\)
0.450995 + 0.892527i \(0.351069\pi\)
\(674\) 24.8309 0.956451
\(675\) 5.58362 0.214914
\(676\) 5.54919 0.213430
\(677\) −19.3597 −0.744054 −0.372027 0.928222i \(-0.621337\pi\)
−0.372027 + 0.928222i \(0.621337\pi\)
\(678\) −11.8606 −0.455504
\(679\) −6.19864 −0.237882
\(680\) 1.05832 0.0405846
\(681\) −0.203611 −0.00780238
\(682\) −3.38407 −0.129583
\(683\) 24.8583 0.951176 0.475588 0.879668i \(-0.342235\pi\)
0.475588 + 0.879668i \(0.342235\pi\)
\(684\) −5.14932 −0.196889
\(685\) −9.21897 −0.352239
\(686\) −10.1410 −0.387184
\(687\) −23.9735 −0.914648
\(688\) −7.37105 −0.281019
\(689\) −25.0944 −0.956022
\(690\) −9.20856 −0.350564
\(691\) −13.0023 −0.494629 −0.247315 0.968935i \(-0.579548\pi\)
−0.247315 + 0.968935i \(0.579548\pi\)
\(692\) −16.0036 −0.608367
\(693\) 0.872963 0.0331611
\(694\) 18.5972 0.705940
\(695\) 20.7333 0.786459
\(696\) −30.5438 −1.15776
\(697\) −2.79722 −0.105952
\(698\) −40.5955 −1.53656
\(699\) −12.0832 −0.457028
\(700\) 0.416383 0.0157378
\(701\) 43.9312 1.65926 0.829630 0.558314i \(-0.188551\pi\)
0.829630 + 0.558314i \(0.188551\pi\)
\(702\) 13.6836 0.516455
\(703\) −2.87906 −0.108586
\(704\) 8.63888 0.325590
\(705\) 11.5231 0.433987
\(706\) 0.476327 0.0179268
\(707\) 6.50980 0.244826
\(708\) −8.60466 −0.323383
\(709\) −37.5591 −1.41056 −0.705282 0.708927i \(-0.749179\pi\)
−0.705282 + 0.708927i \(0.749179\pi\)
\(710\) −14.9372 −0.560584
\(711\) −1.06504 −0.0399420
\(712\) −8.31319 −0.311550
\(713\) −18.0047 −0.674280
\(714\) −0.328541 −0.0122953
\(715\) −2.10809 −0.0788380
\(716\) −5.47713 −0.204690
\(717\) 25.7230 0.960642
\(718\) −27.7924 −1.03720
\(719\) 18.2787 0.681682 0.340841 0.940121i \(-0.389288\pi\)
0.340841 + 0.940121i \(0.389288\pi\)
\(720\) 3.10325 0.115651
\(721\) 6.96887 0.259534
\(722\) −17.5447 −0.652946
\(723\) 9.03199 0.335903
\(724\) −2.19102 −0.0814287
\(725\) 7.74570 0.287668
\(726\) 1.48884 0.0552562
\(727\) −22.7314 −0.843062 −0.421531 0.906814i \(-0.638507\pi\)
−0.421531 + 0.906814i \(0.638507\pi\)
\(728\) 4.16706 0.154442
\(729\) 25.6300 0.949259
\(730\) −1.16251 −0.0430263
\(731\) 1.11015 0.0410605
\(732\) 6.18856 0.228736
\(733\) 22.9236 0.846702 0.423351 0.905966i \(-0.360854\pi\)
0.423351 + 0.905966i \(0.360854\pi\)
\(734\) 23.7676 0.877277
\(735\) 8.43716 0.311209
\(736\) 21.6780 0.799060
\(737\) −2.50494 −0.0922707
\(738\) −12.8641 −0.473533
\(739\) 11.4772 0.422196 0.211098 0.977465i \(-0.432296\pi\)
0.211098 + 0.977465i \(0.432296\pi\)
\(740\) −0.319804 −0.0117562
\(741\) −15.7641 −0.579108
\(742\) 8.88419 0.326149
\(743\) −36.9618 −1.35600 −0.677998 0.735064i \(-0.737152\pi\)
−0.677998 + 0.735064i \(0.737152\pi\)
\(744\) −11.4790 −0.420841
\(745\) −16.8512 −0.617382
\(746\) 14.2101 0.520270
\(747\) 14.2256 0.520488
\(748\) −0.222929 −0.00815111
\(749\) 9.13045 0.333620
\(750\) 1.48884 0.0543649
\(751\) −40.1220 −1.46407 −0.732036 0.681266i \(-0.761430\pi\)
−0.732036 + 0.681266i \(0.761430\pi\)
\(752\) 20.5339 0.748794
\(753\) −25.7415 −0.938071
\(754\) 18.9821 0.691289
\(755\) 14.4040 0.524215
\(756\) 2.32493 0.0845568
\(757\) 22.2082 0.807172 0.403586 0.914942i \(-0.367764\pi\)
0.403586 + 0.914942i \(0.367764\pi\)
\(758\) 14.2696 0.518297
\(759\) 7.92129 0.287524
\(760\) −17.9777 −0.652121
\(761\) 7.05678 0.255808 0.127904 0.991787i \(-0.459175\pi\)
0.127904 + 0.991787i \(0.459175\pi\)
\(762\) −21.8911 −0.793029
\(763\) 0.751673 0.0272124
\(764\) −13.7798 −0.498534
\(765\) −0.467380 −0.0168982
\(766\) −7.64354 −0.276172
\(767\) 21.8378 0.788517
\(768\) 17.6123 0.635530
\(769\) −6.98753 −0.251977 −0.125988 0.992032i \(-0.540210\pi\)
−0.125988 + 0.992032i \(0.540210\pi\)
\(770\) 0.746327 0.0268957
\(771\) 6.69042 0.240950
\(772\) 13.5061 0.486095
\(773\) 12.1432 0.436760 0.218380 0.975864i \(-0.429923\pi\)
0.218380 + 0.975864i \(0.429923\pi\)
\(774\) 5.10546 0.183512
\(775\) 2.91101 0.104566
\(776\) 29.7284 1.06719
\(777\) 0.405424 0.0145445
\(778\) −39.5371 −1.41747
\(779\) 47.5167 1.70246
\(780\) −1.75107 −0.0626982
\(781\) 12.8491 0.459778
\(782\) 2.47141 0.0883775
\(783\) 43.2491 1.54560
\(784\) 15.0348 0.536956
\(785\) 10.5072 0.375018
\(786\) 14.4180 0.514273
\(787\) 23.6451 0.842857 0.421428 0.906862i \(-0.361529\pi\)
0.421428 + 0.906862i \(0.361529\pi\)
\(788\) −12.9305 −0.460631
\(789\) 22.9369 0.816574
\(790\) −0.910536 −0.0323954
\(791\) 5.11436 0.181846
\(792\) −4.18669 −0.148768
\(793\) −15.7060 −0.557735
\(794\) −44.0050 −1.56168
\(795\) −15.2455 −0.540703
\(796\) −2.85562 −0.101215
\(797\) 10.2348 0.362536 0.181268 0.983434i \(-0.441980\pi\)
0.181268 + 0.983434i \(0.441980\pi\)
\(798\) 5.58096 0.197564
\(799\) −3.09261 −0.109409
\(800\) −3.50490 −0.123917
\(801\) 3.67132 0.129720
\(802\) −22.3376 −0.788767
\(803\) 1.00000 0.0352892
\(804\) −2.08071 −0.0733810
\(805\) 3.97077 0.139951
\(806\) 7.13391 0.251281
\(807\) −29.7241 −1.04634
\(808\) −31.2207 −1.09834
\(809\) 38.6785 1.35986 0.679931 0.733276i \(-0.262010\pi\)
0.679931 + 0.733276i \(0.262010\pi\)
\(810\) 3.57095 0.125470
\(811\) −19.1862 −0.673720 −0.336860 0.941555i \(-0.609365\pi\)
−0.336860 + 0.941555i \(0.609365\pi\)
\(812\) 3.22518 0.113182
\(813\) −22.8894 −0.802765
\(814\) −0.573217 −0.0200913
\(815\) −8.50054 −0.297761
\(816\) 1.00465 0.0351697
\(817\) −18.8583 −0.659768
\(818\) −44.5281 −1.55689
\(819\) −1.84028 −0.0643047
\(820\) 5.27813 0.184320
\(821\) −9.70172 −0.338592 −0.169296 0.985565i \(-0.554149\pi\)
−0.169296 + 0.985565i \(0.554149\pi\)
\(822\) −13.7256 −0.478736
\(823\) −14.3591 −0.500526 −0.250263 0.968178i \(-0.580517\pi\)
−0.250263 + 0.968178i \(0.580517\pi\)
\(824\) −33.4224 −1.16433
\(825\) −1.28072 −0.0445889
\(826\) −7.73124 −0.269004
\(827\) −13.1106 −0.455901 −0.227951 0.973673i \(-0.573202\pi\)
−0.227951 + 0.973673i \(0.573202\pi\)
\(828\) −5.45463 −0.189562
\(829\) −38.9606 −1.35316 −0.676578 0.736371i \(-0.736538\pi\)
−0.676578 + 0.736371i \(0.736538\pi\)
\(830\) 12.1620 0.422148
\(831\) −40.9548 −1.42071
\(832\) −18.2115 −0.631371
\(833\) −2.26438 −0.0784563
\(834\) 30.8686 1.06889
\(835\) 16.5246 0.571859
\(836\) 3.78693 0.130974
\(837\) 16.2540 0.561819
\(838\) −36.3458 −1.25554
\(839\) −21.7647 −0.751400 −0.375700 0.926741i \(-0.622598\pi\)
−0.375700 + 0.926741i \(0.622598\pi\)
\(840\) 2.53160 0.0873484
\(841\) 30.9959 1.06882
\(842\) −42.2915 −1.45746
\(843\) −21.0810 −0.726069
\(844\) −2.13552 −0.0735075
\(845\) −8.55597 −0.294334
\(846\) −14.2225 −0.488980
\(847\) −0.641997 −0.0220593
\(848\) −27.1671 −0.932921
\(849\) 22.7816 0.781862
\(850\) −0.399579 −0.0137055
\(851\) −3.04976 −0.104544
\(852\) 10.6730 0.365652
\(853\) 38.6878 1.32465 0.662323 0.749219i \(-0.269571\pi\)
0.662323 + 0.749219i \(0.269571\pi\)
\(854\) 5.56038 0.190272
\(855\) 7.93944 0.271523
\(856\) −43.7893 −1.49669
\(857\) −38.2257 −1.30577 −0.652883 0.757459i \(-0.726440\pi\)
−0.652883 + 0.757459i \(0.726440\pi\)
\(858\) −3.13861 −0.107151
\(859\) −41.9322 −1.43071 −0.715355 0.698762i \(-0.753735\pi\)
−0.715355 + 0.698762i \(0.753735\pi\)
\(860\) −2.09477 −0.0714310
\(861\) −6.69123 −0.228036
\(862\) −29.6279 −1.00913
\(863\) −35.3178 −1.20223 −0.601116 0.799162i \(-0.705277\pi\)
−0.601116 + 0.799162i \(0.705277\pi\)
\(864\) −19.5701 −0.665787
\(865\) 24.6751 0.838977
\(866\) 25.6239 0.870735
\(867\) 21.6209 0.734284
\(868\) 1.21209 0.0411412
\(869\) 0.783251 0.0265700
\(870\) 11.5321 0.390976
\(871\) 5.28064 0.178928
\(872\) −3.60499 −0.122080
\(873\) −13.1288 −0.444344
\(874\) −41.9822 −1.42007
\(875\) −0.641997 −0.0217035
\(876\) 0.830642 0.0280648
\(877\) 41.4778 1.40061 0.700303 0.713846i \(-0.253048\pi\)
0.700303 + 0.713846i \(0.253048\pi\)
\(878\) 23.0834 0.779028
\(879\) 0.948334 0.0319865
\(880\) −2.28220 −0.0769329
\(881\) −59.2808 −1.99722 −0.998611 0.0526882i \(-0.983221\pi\)
−0.998611 + 0.0526882i \(0.983221\pi\)
\(882\) −10.4136 −0.350645
\(883\) −27.8672 −0.937807 −0.468904 0.883249i \(-0.655351\pi\)
−0.468904 + 0.883249i \(0.655351\pi\)
\(884\) 0.469955 0.0158063
\(885\) 13.2670 0.445966
\(886\) −12.0171 −0.403723
\(887\) 48.6053 1.63201 0.816003 0.578047i \(-0.196185\pi\)
0.816003 + 0.578047i \(0.196185\pi\)
\(888\) −1.94440 −0.0652497
\(889\) 9.43953 0.316592
\(890\) 3.13874 0.105211
\(891\) −3.07176 −0.102908
\(892\) −5.30386 −0.177586
\(893\) 52.5345 1.75800
\(894\) −25.0889 −0.839098
\(895\) 8.44486 0.282281
\(896\) 1.94715 0.0650497
\(897\) −16.6988 −0.557555
\(898\) 30.8805 1.03050
\(899\) 22.5478 0.752011
\(900\) 0.881908 0.0293969
\(901\) 4.09163 0.136312
\(902\) 9.46053 0.315001
\(903\) 2.65560 0.0883727
\(904\) −24.5282 −0.815797
\(905\) 3.37821 0.112295
\(906\) 21.4453 0.712473
\(907\) −30.0342 −0.997270 −0.498635 0.866812i \(-0.666165\pi\)
−0.498635 + 0.866812i \(0.666165\pi\)
\(908\) −0.103112 −0.00342188
\(909\) 13.7879 0.457316
\(910\) −1.57332 −0.0521551
\(911\) −12.7657 −0.422947 −0.211474 0.977384i \(-0.567826\pi\)
−0.211474 + 0.977384i \(0.567826\pi\)
\(912\) −17.0661 −0.565115
\(913\) −10.4618 −0.346236
\(914\) 17.6659 0.584335
\(915\) −9.54178 −0.315441
\(916\) −12.1406 −0.401136
\(917\) −6.21711 −0.205307
\(918\) −2.23110 −0.0736373
\(919\) −25.0385 −0.825943 −0.412971 0.910744i \(-0.635509\pi\)
−0.412971 + 0.910744i \(0.635509\pi\)
\(920\) −19.0437 −0.627851
\(921\) −29.3585 −0.967395
\(922\) −1.35744 −0.0447049
\(923\) −27.0871 −0.891583
\(924\) −0.533270 −0.0175433
\(925\) 0.493087 0.0162126
\(926\) −19.4327 −0.638598
\(927\) 14.7602 0.484789
\(928\) −27.1479 −0.891175
\(929\) −23.7027 −0.777662 −0.388831 0.921309i \(-0.627121\pi\)
−0.388831 + 0.921309i \(0.627121\pi\)
\(930\) 4.33403 0.142119
\(931\) 38.4654 1.26065
\(932\) −6.11911 −0.200438
\(933\) −19.9139 −0.651952
\(934\) 34.7437 1.13685
\(935\) 0.343722 0.0112409
\(936\) 8.82592 0.288484
\(937\) −25.9282 −0.847037 −0.423518 0.905887i \(-0.639205\pi\)
−0.423518 + 0.905887i \(0.639205\pi\)
\(938\) −1.86951 −0.0610415
\(939\) −37.3260 −1.21809
\(940\) 5.83550 0.190333
\(941\) 5.08695 0.165830 0.0829149 0.996557i \(-0.473577\pi\)
0.0829149 + 0.996557i \(0.473577\pi\)
\(942\) 15.6436 0.509696
\(943\) 50.3340 1.63910
\(944\) 23.6414 0.769463
\(945\) −3.58467 −0.116609
\(946\) −3.75467 −0.122075
\(947\) −14.8039 −0.481063 −0.240532 0.970641i \(-0.577322\pi\)
−0.240532 + 0.970641i \(0.577322\pi\)
\(948\) 0.650601 0.0211305
\(949\) −2.10809 −0.0684314
\(950\) 6.78770 0.220222
\(951\) 26.3644 0.854925
\(952\) −0.679436 −0.0220206
\(953\) −0.375995 −0.0121797 −0.00608983 0.999981i \(-0.501938\pi\)
−0.00608983 + 0.999981i \(0.501938\pi\)
\(954\) 18.8169 0.609219
\(955\) 21.2462 0.687511
\(956\) 13.0265 0.421307
\(957\) −9.92006 −0.320670
\(958\) −13.3565 −0.431529
\(959\) 5.91855 0.191120
\(960\) −11.0640 −0.357088
\(961\) −22.5260 −0.726647
\(962\) 1.20839 0.0389601
\(963\) 19.3385 0.623174
\(964\) 4.57394 0.147317
\(965\) −20.8242 −0.670356
\(966\) 5.91187 0.190211
\(967\) 23.3201 0.749923 0.374961 0.927040i \(-0.377656\pi\)
0.374961 + 0.927040i \(0.377656\pi\)
\(968\) 3.07899 0.0989625
\(969\) 2.57032 0.0825706
\(970\) −11.2243 −0.360391
\(971\) 42.7422 1.37166 0.685832 0.727760i \(-0.259439\pi\)
0.685832 + 0.727760i \(0.259439\pi\)
\(972\) 8.31267 0.266629
\(973\) −13.3107 −0.426722
\(974\) 14.8182 0.474806
\(975\) 2.69986 0.0864649
\(976\) −17.0032 −0.544258
\(977\) 3.09301 0.0989543 0.0494771 0.998775i \(-0.484245\pi\)
0.0494771 + 0.998775i \(0.484245\pi\)
\(978\) −12.6560 −0.404694
\(979\) −2.69997 −0.0862915
\(980\) 4.27271 0.136487
\(981\) 1.59206 0.0508305
\(982\) −18.3176 −0.584540
\(983\) −25.8146 −0.823359 −0.411680 0.911329i \(-0.635058\pi\)
−0.411680 + 0.911329i \(0.635058\pi\)
\(984\) 32.0908 1.02302
\(985\) 19.9368 0.635240
\(986\) −3.09502 −0.0985656
\(987\) −7.39783 −0.235475
\(988\) −7.98318 −0.253979
\(989\) −19.9764 −0.635214
\(990\) 1.58073 0.0502390
\(991\) −32.2806 −1.02543 −0.512714 0.858559i \(-0.671360\pi\)
−0.512714 + 0.858559i \(0.671360\pi\)
\(992\) −10.2028 −0.323939
\(993\) −15.9905 −0.507444
\(994\) 9.58965 0.304165
\(995\) 4.40291 0.139582
\(996\) −8.69004 −0.275354
\(997\) −38.9896 −1.23481 −0.617406 0.786644i \(-0.711817\pi\)
−0.617406 + 0.786644i \(0.711817\pi\)
\(998\) 37.2329 1.17859
\(999\) 2.75321 0.0871078
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 \(a_p\))