Properties

Label 6039.2.a.j.1.13
Level 6039
Weight 2
Character 6039.1
Self dual Yes
Analytic conductor 48.222
Analytic rank 0
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6039 = 3^{2} \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6039.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2216577807\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Root \(2.45909\)
Character \(\chi\) = 6039.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.45909 q^{2}\) \(+4.04715 q^{4}\) \(+1.85442 q^{5}\) \(+2.32343 q^{7}\) \(+5.03413 q^{8}\) \(+O(q^{10})\) \(q\)\(+2.45909 q^{2}\) \(+4.04715 q^{4}\) \(+1.85442 q^{5}\) \(+2.32343 q^{7}\) \(+5.03413 q^{8}\) \(+4.56020 q^{10}\) \(+1.00000 q^{11}\) \(+6.54120 q^{13}\) \(+5.71353 q^{14}\) \(+4.28511 q^{16}\) \(-2.94936 q^{17}\) \(+6.42989 q^{19}\) \(+7.50511 q^{20}\) \(+2.45909 q^{22}\) \(+1.80034 q^{23}\) \(-1.56112 q^{25}\) \(+16.0854 q^{26}\) \(+9.40326 q^{28}\) \(-8.87924 q^{29}\) \(+2.72079 q^{31}\) \(+0.469234 q^{32}\) \(-7.25276 q^{34}\) \(+4.30862 q^{35}\) \(-3.53485 q^{37}\) \(+15.8117 q^{38}\) \(+9.33540 q^{40}\) \(+2.27369 q^{41}\) \(-3.10603 q^{43}\) \(+4.04715 q^{44}\) \(+4.42721 q^{46}\) \(-11.7194 q^{47}\) \(-1.60167 q^{49}\) \(-3.83895 q^{50}\) \(+26.4732 q^{52}\) \(-7.91063 q^{53}\) \(+1.85442 q^{55}\) \(+11.6965 q^{56}\) \(-21.8349 q^{58}\) \(+5.84081 q^{59}\) \(+1.00000 q^{61}\) \(+6.69069 q^{62}\) \(-7.41633 q^{64}\) \(+12.1301 q^{65}\) \(-10.0882 q^{67}\) \(-11.9365 q^{68}\) \(+10.5953 q^{70}\) \(-13.7123 q^{71}\) \(-14.7140 q^{73}\) \(-8.69254 q^{74}\) \(+26.0227 q^{76}\) \(+2.32343 q^{77}\) \(+3.60431 q^{79}\) \(+7.94640 q^{80}\) \(+5.59122 q^{82}\) \(+5.22564 q^{83}\) \(-5.46935 q^{85}\) \(-7.63802 q^{86}\) \(+5.03413 q^{88}\) \(+14.1984 q^{89}\) \(+15.1980 q^{91}\) \(+7.28625 q^{92}\) \(-28.8191 q^{94}\) \(+11.9237 q^{95}\) \(+17.9948 q^{97}\) \(-3.93867 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 17q^{16} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 23q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 37q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 25q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 36q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 13q^{52} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 40q^{56} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 6q^{64} \) \(\mathstrut +\mathstrut 61q^{65} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 66q^{68} \) \(\mathstrut +\mathstrut 44q^{70} \) \(\mathstrut +\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 49q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 21q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 14q^{92} \) \(\mathstrut -\mathstrut 31q^{94} \) \(\mathstrut -\mathstrut 23q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut +\mathstrut 38q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.45909 1.73884 0.869421 0.494071i \(-0.164492\pi\)
0.869421 + 0.494071i \(0.164492\pi\)
\(3\) 0 0
\(4\) 4.04715 2.02357
\(5\) 1.85442 0.829322 0.414661 0.909976i \(-0.363900\pi\)
0.414661 + 0.909976i \(0.363900\pi\)
\(6\) 0 0
\(7\) 2.32343 0.878174 0.439087 0.898445i \(-0.355302\pi\)
0.439087 + 0.898445i \(0.355302\pi\)
\(8\) 5.03413 1.77983
\(9\) 0 0
\(10\) 4.56020 1.44206
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 6.54120 1.81420 0.907101 0.420913i \(-0.138290\pi\)
0.907101 + 0.420913i \(0.138290\pi\)
\(14\) 5.71353 1.52701
\(15\) 0 0
\(16\) 4.28511 1.07128
\(17\) −2.94936 −0.715325 −0.357663 0.933851i \(-0.616426\pi\)
−0.357663 + 0.933851i \(0.616426\pi\)
\(18\) 0 0
\(19\) 6.42989 1.47512 0.737558 0.675283i \(-0.235979\pi\)
0.737558 + 0.675283i \(0.235979\pi\)
\(20\) 7.50511 1.67819
\(21\) 0 0
\(22\) 2.45909 0.524281
\(23\) 1.80034 0.375397 0.187699 0.982227i \(-0.439897\pi\)
0.187699 + 0.982227i \(0.439897\pi\)
\(24\) 0 0
\(25\) −1.56112 −0.312225
\(26\) 16.0854 3.15461
\(27\) 0 0
\(28\) 9.40326 1.77705
\(29\) −8.87924 −1.64883 −0.824417 0.565983i \(-0.808497\pi\)
−0.824417 + 0.565983i \(0.808497\pi\)
\(30\) 0 0
\(31\) 2.72079 0.488669 0.244335 0.969691i \(-0.421431\pi\)
0.244335 + 0.969691i \(0.421431\pi\)
\(32\) 0.469234 0.0829497
\(33\) 0 0
\(34\) −7.25276 −1.24384
\(35\) 4.30862 0.728289
\(36\) 0 0
\(37\) −3.53485 −0.581126 −0.290563 0.956856i \(-0.593843\pi\)
−0.290563 + 0.956856i \(0.593843\pi\)
\(38\) 15.8117 2.56500
\(39\) 0 0
\(40\) 9.33540 1.47606
\(41\) 2.27369 0.355091 0.177545 0.984113i \(-0.443184\pi\)
0.177545 + 0.984113i \(0.443184\pi\)
\(42\) 0 0
\(43\) −3.10603 −0.473665 −0.236832 0.971550i \(-0.576109\pi\)
−0.236832 + 0.971550i \(0.576109\pi\)
\(44\) 4.04715 0.610131
\(45\) 0 0
\(46\) 4.42721 0.652757
\(47\) −11.7194 −1.70945 −0.854724 0.519082i \(-0.826274\pi\)
−0.854724 + 0.519082i \(0.826274\pi\)
\(48\) 0 0
\(49\) −1.60167 −0.228811
\(50\) −3.83895 −0.542910
\(51\) 0 0
\(52\) 26.4732 3.67117
\(53\) −7.91063 −1.08661 −0.543304 0.839536i \(-0.682827\pi\)
−0.543304 + 0.839536i \(0.682827\pi\)
\(54\) 0 0
\(55\) 1.85442 0.250050
\(56\) 11.6965 1.56300
\(57\) 0 0
\(58\) −21.8349 −2.86706
\(59\) 5.84081 0.760409 0.380204 0.924903i \(-0.375854\pi\)
0.380204 + 0.924903i \(0.375854\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037
\(62\) 6.69069 0.849719
\(63\) 0 0
\(64\) −7.41633 −0.927042
\(65\) 12.1301 1.50456
\(66\) 0 0
\(67\) −10.0882 −1.23246 −0.616232 0.787564i \(-0.711342\pi\)
−0.616232 + 0.787564i \(0.711342\pi\)
\(68\) −11.9365 −1.44751
\(69\) 0 0
\(70\) 10.5953 1.26638
\(71\) −13.7123 −1.62735 −0.813676 0.581319i \(-0.802537\pi\)
−0.813676 + 0.581319i \(0.802537\pi\)
\(72\) 0 0
\(73\) −14.7140 −1.72214 −0.861070 0.508486i \(-0.830205\pi\)
−0.861070 + 0.508486i \(0.830205\pi\)
\(74\) −8.69254 −1.01049
\(75\) 0 0
\(76\) 26.0227 2.98501
\(77\) 2.32343 0.264779
\(78\) 0 0
\(79\) 3.60431 0.405517 0.202758 0.979229i \(-0.435009\pi\)
0.202758 + 0.979229i \(0.435009\pi\)
\(80\) 7.94640 0.888435
\(81\) 0 0
\(82\) 5.59122 0.617447
\(83\) 5.22564 0.573589 0.286794 0.957992i \(-0.407410\pi\)
0.286794 + 0.957992i \(0.407410\pi\)
\(84\) 0 0
\(85\) −5.46935 −0.593235
\(86\) −7.63802 −0.823629
\(87\) 0 0
\(88\) 5.03413 0.536640
\(89\) 14.1984 1.50502 0.752511 0.658579i \(-0.228842\pi\)
0.752511 + 0.658579i \(0.228842\pi\)
\(90\) 0 0
\(91\) 15.1980 1.59318
\(92\) 7.28625 0.759644
\(93\) 0 0
\(94\) −28.8191 −2.97246
\(95\) 11.9237 1.22335
\(96\) 0 0
\(97\) 17.9948 1.82709 0.913547 0.406734i \(-0.133332\pi\)
0.913547 + 0.406734i \(0.133332\pi\)
\(98\) −3.93867 −0.397866
\(99\) 0 0
\(100\) −6.31810 −0.631810
\(101\) 16.6067 1.65243 0.826216 0.563354i \(-0.190489\pi\)
0.826216 + 0.563354i \(0.190489\pi\)
\(102\) 0 0
\(103\) 7.44597 0.733673 0.366836 0.930285i \(-0.380441\pi\)
0.366836 + 0.930285i \(0.380441\pi\)
\(104\) 32.9292 3.22898
\(105\) 0 0
\(106\) −19.4530 −1.88944
\(107\) −12.3092 −1.18997 −0.594986 0.803736i \(-0.702842\pi\)
−0.594986 + 0.803736i \(0.702842\pi\)
\(108\) 0 0
\(109\) −14.4228 −1.38146 −0.690728 0.723115i \(-0.742710\pi\)
−0.690728 + 0.723115i \(0.742710\pi\)
\(110\) 4.56020 0.434798
\(111\) 0 0
\(112\) 9.95616 0.940768
\(113\) 7.36553 0.692891 0.346446 0.938070i \(-0.387389\pi\)
0.346446 + 0.938070i \(0.387389\pi\)
\(114\) 0 0
\(115\) 3.33859 0.311325
\(116\) −35.9356 −3.33654
\(117\) 0 0
\(118\) 14.3631 1.32223
\(119\) −6.85263 −0.628180
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 2.45909 0.222636
\(123\) 0 0
\(124\) 11.0115 0.988858
\(125\) −12.1671 −1.08826
\(126\) 0 0
\(127\) 10.7526 0.954136 0.477068 0.878867i \(-0.341700\pi\)
0.477068 + 0.878867i \(0.341700\pi\)
\(128\) −19.1759 −1.69493
\(129\) 0 0
\(130\) 29.8291 2.61619
\(131\) 14.8878 1.30076 0.650378 0.759611i \(-0.274611\pi\)
0.650378 + 0.759611i \(0.274611\pi\)
\(132\) 0 0
\(133\) 14.9394 1.29541
\(134\) −24.8077 −2.14306
\(135\) 0 0
\(136\) −14.8475 −1.27316
\(137\) 12.2986 1.05074 0.525371 0.850873i \(-0.323926\pi\)
0.525371 + 0.850873i \(0.323926\pi\)
\(138\) 0 0
\(139\) −15.3998 −1.30620 −0.653099 0.757273i \(-0.726531\pi\)
−0.653099 + 0.757273i \(0.726531\pi\)
\(140\) 17.4376 1.47375
\(141\) 0 0
\(142\) −33.7199 −2.82971
\(143\) 6.54120 0.547002
\(144\) 0 0
\(145\) −16.4658 −1.36741
\(146\) −36.1831 −2.99453
\(147\) 0 0
\(148\) −14.3061 −1.17595
\(149\) −20.3781 −1.66944 −0.834721 0.550673i \(-0.814371\pi\)
−0.834721 + 0.550673i \(0.814371\pi\)
\(150\) 0 0
\(151\) 5.79859 0.471883 0.235941 0.971767i \(-0.424183\pi\)
0.235941 + 0.971767i \(0.424183\pi\)
\(152\) 32.3689 2.62546
\(153\) 0 0
\(154\) 5.71353 0.460410
\(155\) 5.04550 0.405264
\(156\) 0 0
\(157\) 12.4274 0.991817 0.495909 0.868375i \(-0.334835\pi\)
0.495909 + 0.868375i \(0.334835\pi\)
\(158\) 8.86334 0.705129
\(159\) 0 0
\(160\) 0.870157 0.0687920
\(161\) 4.18297 0.329664
\(162\) 0 0
\(163\) 15.7740 1.23551 0.617757 0.786369i \(-0.288042\pi\)
0.617757 + 0.786369i \(0.288042\pi\)
\(164\) 9.20195 0.718552
\(165\) 0 0
\(166\) 12.8503 0.997380
\(167\) 11.8094 0.913840 0.456920 0.889508i \(-0.348953\pi\)
0.456920 + 0.889508i \(0.348953\pi\)
\(168\) 0 0
\(169\) 29.7873 2.29133
\(170\) −13.4497 −1.03154
\(171\) 0 0
\(172\) −12.5706 −0.958496
\(173\) −24.1903 −1.83916 −0.919578 0.392907i \(-0.871469\pi\)
−0.919578 + 0.392907i \(0.871469\pi\)
\(174\) 0 0
\(175\) −3.62716 −0.274188
\(176\) 4.28511 0.323002
\(177\) 0 0
\(178\) 34.9151 2.61700
\(179\) 13.3687 0.999224 0.499612 0.866249i \(-0.333476\pi\)
0.499612 + 0.866249i \(0.333476\pi\)
\(180\) 0 0
\(181\) −18.9666 −1.40977 −0.704887 0.709320i \(-0.749002\pi\)
−0.704887 + 0.709320i \(0.749002\pi\)
\(182\) 37.3734 2.77030
\(183\) 0 0
\(184\) 9.06316 0.668145
\(185\) −6.55510 −0.481941
\(186\) 0 0
\(187\) −2.94936 −0.215679
\(188\) −47.4301 −3.45920
\(189\) 0 0
\(190\) 29.3215 2.12721
\(191\) −11.3313 −0.819908 −0.409954 0.912106i \(-0.634455\pi\)
−0.409954 + 0.912106i \(0.634455\pi\)
\(192\) 0 0
\(193\) 0.588060 0.0423295 0.0211647 0.999776i \(-0.493263\pi\)
0.0211647 + 0.999776i \(0.493263\pi\)
\(194\) 44.2509 3.17703
\(195\) 0 0
\(196\) −6.48221 −0.463015
\(197\) −26.5822 −1.89390 −0.946952 0.321376i \(-0.895855\pi\)
−0.946952 + 0.321376i \(0.895855\pi\)
\(198\) 0 0
\(199\) −4.56330 −0.323484 −0.161742 0.986833i \(-0.551711\pi\)
−0.161742 + 0.986833i \(0.551711\pi\)
\(200\) −7.85891 −0.555709
\(201\) 0 0
\(202\) 40.8375 2.87332
\(203\) −20.6303 −1.44796
\(204\) 0 0
\(205\) 4.21637 0.294484
\(206\) 18.3103 1.27574
\(207\) 0 0
\(208\) 28.0298 1.94351
\(209\) 6.42989 0.444764
\(210\) 0 0
\(211\) 18.2987 1.25973 0.629867 0.776703i \(-0.283109\pi\)
0.629867 + 0.776703i \(0.283109\pi\)
\(212\) −32.0155 −2.19883
\(213\) 0 0
\(214\) −30.2694 −2.06917
\(215\) −5.75988 −0.392821
\(216\) 0 0
\(217\) 6.32157 0.429136
\(218\) −35.4671 −2.40213
\(219\) 0 0
\(220\) 7.50511 0.505995
\(221\) −19.2923 −1.29774
\(222\) 0 0
\(223\) −4.67679 −0.313181 −0.156590 0.987664i \(-0.550050\pi\)
−0.156590 + 0.987664i \(0.550050\pi\)
\(224\) 1.09023 0.0728442
\(225\) 0 0
\(226\) 18.1125 1.20483
\(227\) −9.63473 −0.639480 −0.319740 0.947505i \(-0.603596\pi\)
−0.319740 + 0.947505i \(0.603596\pi\)
\(228\) 0 0
\(229\) 19.6987 1.30173 0.650863 0.759195i \(-0.274407\pi\)
0.650863 + 0.759195i \(0.274407\pi\)
\(230\) 8.20991 0.541345
\(231\) 0 0
\(232\) −44.6993 −2.93465
\(233\) −9.18049 −0.601434 −0.300717 0.953713i \(-0.597226\pi\)
−0.300717 + 0.953713i \(0.597226\pi\)
\(234\) 0 0
\(235\) −21.7327 −1.41768
\(236\) 23.6386 1.53874
\(237\) 0 0
\(238\) −16.8513 −1.09231
\(239\) 7.54022 0.487736 0.243868 0.969808i \(-0.421584\pi\)
0.243868 + 0.969808i \(0.421584\pi\)
\(240\) 0 0
\(241\) 18.7468 1.20759 0.603794 0.797141i \(-0.293655\pi\)
0.603794 + 0.797141i \(0.293655\pi\)
\(242\) 2.45909 0.158077
\(243\) 0 0
\(244\) 4.04715 0.259092
\(245\) −2.97018 −0.189758
\(246\) 0 0
\(247\) 42.0592 2.67616
\(248\) 13.6968 0.869750
\(249\) 0 0
\(250\) −29.9200 −1.89231
\(251\) 11.1054 0.700965 0.350482 0.936569i \(-0.386018\pi\)
0.350482 + 0.936569i \(0.386018\pi\)
\(252\) 0 0
\(253\) 1.80034 0.113187
\(254\) 26.4416 1.65909
\(255\) 0 0
\(256\) −32.3228 −2.02017
\(257\) −14.2372 −0.888092 −0.444046 0.896004i \(-0.646457\pi\)
−0.444046 + 0.896004i \(0.646457\pi\)
\(258\) 0 0
\(259\) −8.21298 −0.510330
\(260\) 49.0924 3.04458
\(261\) 0 0
\(262\) 36.6106 2.26181
\(263\) −23.3083 −1.43725 −0.718627 0.695396i \(-0.755229\pi\)
−0.718627 + 0.695396i \(0.755229\pi\)
\(264\) 0 0
\(265\) −14.6696 −0.901148
\(266\) 36.7374 2.25251
\(267\) 0 0
\(268\) −40.8283 −2.49398
\(269\) 0.631304 0.0384913 0.0192456 0.999815i \(-0.493874\pi\)
0.0192456 + 0.999815i \(0.493874\pi\)
\(270\) 0 0
\(271\) −12.0422 −0.731510 −0.365755 0.930711i \(-0.619189\pi\)
−0.365755 + 0.930711i \(0.619189\pi\)
\(272\) −12.6383 −0.766312
\(273\) 0 0
\(274\) 30.2435 1.82708
\(275\) −1.56112 −0.0941393
\(276\) 0 0
\(277\) 4.99666 0.300220 0.150110 0.988669i \(-0.452037\pi\)
0.150110 + 0.988669i \(0.452037\pi\)
\(278\) −37.8697 −2.27127
\(279\) 0 0
\(280\) 21.6901 1.29623
\(281\) 21.8369 1.30268 0.651340 0.758786i \(-0.274207\pi\)
0.651340 + 0.758786i \(0.274207\pi\)
\(282\) 0 0
\(283\) 9.38159 0.557678 0.278839 0.960338i \(-0.410050\pi\)
0.278839 + 0.960338i \(0.410050\pi\)
\(284\) −55.4957 −3.29307
\(285\) 0 0
\(286\) 16.0854 0.951151
\(287\) 5.28276 0.311831
\(288\) 0 0
\(289\) −8.30127 −0.488310
\(290\) −40.4911 −2.37772
\(291\) 0 0
\(292\) −59.5496 −3.48488
\(293\) −2.56663 −0.149944 −0.0749720 0.997186i \(-0.523887\pi\)
−0.0749720 + 0.997186i \(0.523887\pi\)
\(294\) 0 0
\(295\) 10.8313 0.630624
\(296\) −17.7949 −1.03431
\(297\) 0 0
\(298\) −50.1118 −2.90290
\(299\) 11.7764 0.681046
\(300\) 0 0
\(301\) −7.21664 −0.415960
\(302\) 14.2593 0.820530
\(303\) 0 0
\(304\) 27.5528 1.58026
\(305\) 1.85442 0.106184
\(306\) 0 0
\(307\) 11.7513 0.670681 0.335341 0.942097i \(-0.391149\pi\)
0.335341 + 0.942097i \(0.391149\pi\)
\(308\) 9.40326 0.535801
\(309\) 0 0
\(310\) 12.4074 0.704690
\(311\) −0.0431092 −0.00244450 −0.00122225 0.999999i \(-0.500389\pi\)
−0.00122225 + 0.999999i \(0.500389\pi\)
\(312\) 0 0
\(313\) −9.75221 −0.551227 −0.275614 0.961268i \(-0.588881\pi\)
−0.275614 + 0.961268i \(0.588881\pi\)
\(314\) 30.5602 1.72461
\(315\) 0 0
\(316\) 14.5872 0.820593
\(317\) 12.6416 0.710023 0.355011 0.934862i \(-0.384477\pi\)
0.355011 + 0.934862i \(0.384477\pi\)
\(318\) 0 0
\(319\) −8.87924 −0.497142
\(320\) −13.7530 −0.768816
\(321\) 0 0
\(322\) 10.2863 0.573234
\(323\) −18.9641 −1.05519
\(324\) 0 0
\(325\) −10.2116 −0.566439
\(326\) 38.7897 2.14836
\(327\) 0 0
\(328\) 11.4460 0.632002
\(329\) −27.2292 −1.50119
\(330\) 0 0
\(331\) 24.4514 1.34397 0.671986 0.740564i \(-0.265441\pi\)
0.671986 + 0.740564i \(0.265441\pi\)
\(332\) 21.1489 1.16070
\(333\) 0 0
\(334\) 29.0405 1.58902
\(335\) −18.7077 −1.02211
\(336\) 0 0
\(337\) 2.71105 0.147680 0.0738402 0.997270i \(-0.476475\pi\)
0.0738402 + 0.997270i \(0.476475\pi\)
\(338\) 73.2497 3.98426
\(339\) 0 0
\(340\) −22.1353 −1.20045
\(341\) 2.72079 0.147339
\(342\) 0 0
\(343\) −19.9854 −1.07911
\(344\) −15.6362 −0.843045
\(345\) 0 0
\(346\) −59.4863 −3.19800
\(347\) 16.5889 0.890541 0.445271 0.895396i \(-0.353108\pi\)
0.445271 + 0.895396i \(0.353108\pi\)
\(348\) 0 0
\(349\) 24.3034 1.30093 0.650465 0.759536i \(-0.274574\pi\)
0.650465 + 0.759536i \(0.274574\pi\)
\(350\) −8.91954 −0.476769
\(351\) 0 0
\(352\) 0.469234 0.0250103
\(353\) 1.04268 0.0554963 0.0277482 0.999615i \(-0.491166\pi\)
0.0277482 + 0.999615i \(0.491166\pi\)
\(354\) 0 0
\(355\) −25.4284 −1.34960
\(356\) 57.4628 3.04552
\(357\) 0 0
\(358\) 32.8749 1.73749
\(359\) −9.78110 −0.516226 −0.258113 0.966115i \(-0.583101\pi\)
−0.258113 + 0.966115i \(0.583101\pi\)
\(360\) 0 0
\(361\) 22.3434 1.17597
\(362\) −46.6406 −2.45138
\(363\) 0 0
\(364\) 61.5086 3.22393
\(365\) −27.2859 −1.42821
\(366\) 0 0
\(367\) 5.48502 0.286316 0.143158 0.989700i \(-0.454274\pi\)
0.143158 + 0.989700i \(0.454274\pi\)
\(368\) 7.71467 0.402155
\(369\) 0 0
\(370\) −16.1196 −0.838019
\(371\) −18.3798 −0.954231
\(372\) 0 0
\(373\) −21.6216 −1.11952 −0.559761 0.828654i \(-0.689107\pi\)
−0.559761 + 0.828654i \(0.689107\pi\)
\(374\) −7.25276 −0.375031
\(375\) 0 0
\(376\) −58.9969 −3.04254
\(377\) −58.0809 −2.99132
\(378\) 0 0
\(379\) 29.0189 1.49060 0.745301 0.666729i \(-0.232306\pi\)
0.745301 + 0.666729i \(0.232306\pi\)
\(380\) 48.2570 2.47553
\(381\) 0 0
\(382\) −27.8649 −1.42569
\(383\) 3.92201 0.200406 0.100203 0.994967i \(-0.468051\pi\)
0.100203 + 0.994967i \(0.468051\pi\)
\(384\) 0 0
\(385\) 4.30862 0.219587
\(386\) 1.44610 0.0736043
\(387\) 0 0
\(388\) 72.8276 3.69726
\(389\) 25.9769 1.31708 0.658541 0.752545i \(-0.271174\pi\)
0.658541 + 0.752545i \(0.271174\pi\)
\(390\) 0 0
\(391\) −5.30986 −0.268531
\(392\) −8.06304 −0.407245
\(393\) 0 0
\(394\) −65.3681 −3.29320
\(395\) 6.68391 0.336304
\(396\) 0 0
\(397\) 19.1899 0.963114 0.481557 0.876415i \(-0.340071\pi\)
0.481557 + 0.876415i \(0.340071\pi\)
\(398\) −11.2216 −0.562488
\(399\) 0 0
\(400\) −6.68959 −0.334480
\(401\) −9.45087 −0.471954 −0.235977 0.971759i \(-0.575829\pi\)
−0.235977 + 0.971759i \(0.575829\pi\)
\(402\) 0 0
\(403\) 17.7972 0.886544
\(404\) 67.2099 3.34382
\(405\) 0 0
\(406\) −50.7319 −2.51778
\(407\) −3.53485 −0.175216
\(408\) 0 0
\(409\) −25.7554 −1.27352 −0.636762 0.771061i \(-0.719727\pi\)
−0.636762 + 0.771061i \(0.719727\pi\)
\(410\) 10.3685 0.512062
\(411\) 0 0
\(412\) 30.1349 1.48464
\(413\) 13.5707 0.667771
\(414\) 0 0
\(415\) 9.69054 0.475690
\(416\) 3.06935 0.150487
\(417\) 0 0
\(418\) 15.8117 0.773376
\(419\) 7.79219 0.380674 0.190337 0.981719i \(-0.439042\pi\)
0.190337 + 0.981719i \(0.439042\pi\)
\(420\) 0 0
\(421\) −28.5371 −1.39081 −0.695407 0.718616i \(-0.744776\pi\)
−0.695407 + 0.718616i \(0.744776\pi\)
\(422\) 44.9983 2.19048
\(423\) 0 0
\(424\) −39.8231 −1.93398
\(425\) 4.60432 0.223342
\(426\) 0 0
\(427\) 2.32343 0.112439
\(428\) −49.8170 −2.40800
\(429\) 0 0
\(430\) −14.1641 −0.683054
\(431\) 0.647148 0.0311720 0.0155860 0.999879i \(-0.495039\pi\)
0.0155860 + 0.999879i \(0.495039\pi\)
\(432\) 0 0
\(433\) −18.4583 −0.887052 −0.443526 0.896262i \(-0.646273\pi\)
−0.443526 + 0.896262i \(0.646273\pi\)
\(434\) 15.5453 0.746201
\(435\) 0 0
\(436\) −58.3713 −2.79548
\(437\) 11.5760 0.553755
\(438\) 0 0
\(439\) 8.86799 0.423246 0.211623 0.977351i \(-0.432125\pi\)
0.211623 + 0.977351i \(0.432125\pi\)
\(440\) 9.33540 0.445048
\(441\) 0 0
\(442\) −47.4417 −2.25657
\(443\) −11.3375 −0.538661 −0.269330 0.963048i \(-0.586802\pi\)
−0.269330 + 0.963048i \(0.586802\pi\)
\(444\) 0 0
\(445\) 26.3297 1.24815
\(446\) −11.5007 −0.544572
\(447\) 0 0
\(448\) −17.2313 −0.814104
\(449\) 17.3627 0.819397 0.409698 0.912221i \(-0.365634\pi\)
0.409698 + 0.912221i \(0.365634\pi\)
\(450\) 0 0
\(451\) 2.27369 0.107064
\(452\) 29.8094 1.40212
\(453\) 0 0
\(454\) −23.6927 −1.11195
\(455\) 28.1835 1.32126
\(456\) 0 0
\(457\) −16.9050 −0.790783 −0.395391 0.918513i \(-0.629391\pi\)
−0.395391 + 0.918513i \(0.629391\pi\)
\(458\) 48.4409 2.26350
\(459\) 0 0
\(460\) 13.5118 0.629990
\(461\) 31.3017 1.45786 0.728932 0.684586i \(-0.240017\pi\)
0.728932 + 0.684586i \(0.240017\pi\)
\(462\) 0 0
\(463\) −21.3893 −0.994044 −0.497022 0.867738i \(-0.665573\pi\)
−0.497022 + 0.867738i \(0.665573\pi\)
\(464\) −38.0485 −1.76636
\(465\) 0 0
\(466\) −22.5757 −1.04580
\(467\) −38.0400 −1.76028 −0.880142 0.474711i \(-0.842552\pi\)
−0.880142 + 0.474711i \(0.842552\pi\)
\(468\) 0 0
\(469\) −23.4391 −1.08232
\(470\) −53.4427 −2.46513
\(471\) 0 0
\(472\) 29.4034 1.35340
\(473\) −3.10603 −0.142815
\(474\) 0 0
\(475\) −10.0379 −0.460568
\(476\) −27.7336 −1.27117
\(477\) 0 0
\(478\) 18.5421 0.848096
\(479\) −36.1392 −1.65124 −0.825621 0.564226i \(-0.809175\pi\)
−0.825621 + 0.564226i \(0.809175\pi\)
\(480\) 0 0
\(481\) −23.1222 −1.05428
\(482\) 46.1001 2.09980
\(483\) 0 0
\(484\) 4.04715 0.183961
\(485\) 33.3699 1.51525
\(486\) 0 0
\(487\) −19.8680 −0.900306 −0.450153 0.892951i \(-0.648631\pi\)
−0.450153 + 0.892951i \(0.648631\pi\)
\(488\) 5.03413 0.227884
\(489\) 0 0
\(490\) −7.30395 −0.329959
\(491\) 23.2929 1.05119 0.525597 0.850733i \(-0.323842\pi\)
0.525597 + 0.850733i \(0.323842\pi\)
\(492\) 0 0
\(493\) 26.1881 1.17945
\(494\) 103.427 4.65342
\(495\) 0 0
\(496\) 11.6589 0.523500
\(497\) −31.8596 −1.42910
\(498\) 0 0
\(499\) −18.7308 −0.838504 −0.419252 0.907870i \(-0.637708\pi\)
−0.419252 + 0.907870i \(0.637708\pi\)
\(500\) −49.2420 −2.20217
\(501\) 0 0
\(502\) 27.3092 1.21887
\(503\) 22.9645 1.02393 0.511967 0.859005i \(-0.328917\pi\)
0.511967 + 0.859005i \(0.328917\pi\)
\(504\) 0 0
\(505\) 30.7959 1.37040
\(506\) 4.42721 0.196814
\(507\) 0 0
\(508\) 43.5172 1.93076
\(509\) 16.0499 0.711398 0.355699 0.934601i \(-0.384243\pi\)
0.355699 + 0.934601i \(0.384243\pi\)
\(510\) 0 0
\(511\) −34.1869 −1.51234
\(512\) −41.1329 −1.81784
\(513\) 0 0
\(514\) −35.0106 −1.54425
\(515\) 13.8080 0.608451
\(516\) 0 0
\(517\) −11.7194 −0.515418
\(518\) −20.1965 −0.887383
\(519\) 0 0
\(520\) 61.0647 2.67786
\(521\) 31.7652 1.39166 0.695829 0.718208i \(-0.255037\pi\)
0.695829 + 0.718208i \(0.255037\pi\)
\(522\) 0 0
\(523\) 21.3136 0.931979 0.465990 0.884790i \(-0.345698\pi\)
0.465990 + 0.884790i \(0.345698\pi\)
\(524\) 60.2532 2.63217
\(525\) 0 0
\(526\) −57.3174 −2.49916
\(527\) −8.02460 −0.349557
\(528\) 0 0
\(529\) −19.7588 −0.859077
\(530\) −36.0740 −1.56695
\(531\) 0 0
\(532\) 60.4619 2.62136
\(533\) 14.8726 0.644206
\(534\) 0 0
\(535\) −22.8264 −0.986870
\(536\) −50.7851 −2.19358
\(537\) 0 0
\(538\) 1.55244 0.0669302
\(539\) −1.60167 −0.0689890
\(540\) 0 0
\(541\) 26.7223 1.14888 0.574440 0.818547i \(-0.305220\pi\)
0.574440 + 0.818547i \(0.305220\pi\)
\(542\) −29.6128 −1.27198
\(543\) 0 0
\(544\) −1.38394 −0.0593360
\(545\) −26.7460 −1.14567
\(546\) 0 0
\(547\) −1.28637 −0.0550010 −0.0275005 0.999622i \(-0.508755\pi\)
−0.0275005 + 0.999622i \(0.508755\pi\)
\(548\) 49.7744 2.12626
\(549\) 0 0
\(550\) −3.83895 −0.163694
\(551\) −57.0925 −2.43222
\(552\) 0 0
\(553\) 8.37436 0.356114
\(554\) 12.2873 0.522036
\(555\) 0 0
\(556\) −62.3254 −2.64319
\(557\) −5.02337 −0.212847 −0.106424 0.994321i \(-0.533940\pi\)
−0.106424 + 0.994321i \(0.533940\pi\)
\(558\) 0 0
\(559\) −20.3171 −0.859324
\(560\) 18.4629 0.780200
\(561\) 0 0
\(562\) 53.6990 2.26516
\(563\) −27.1450 −1.14402 −0.572012 0.820245i \(-0.693837\pi\)
−0.572012 + 0.820245i \(0.693837\pi\)
\(564\) 0 0
\(565\) 13.6588 0.574630
\(566\) 23.0702 0.969714
\(567\) 0 0
\(568\) −69.0296 −2.89642
\(569\) 16.5905 0.695511 0.347756 0.937585i \(-0.386944\pi\)
0.347756 + 0.937585i \(0.386944\pi\)
\(570\) 0 0
\(571\) −6.50125 −0.272069 −0.136035 0.990704i \(-0.543436\pi\)
−0.136035 + 0.990704i \(0.543436\pi\)
\(572\) 26.4732 1.10690
\(573\) 0 0
\(574\) 12.9908 0.542225
\(575\) −2.81056 −0.117208
\(576\) 0 0
\(577\) 0.0196890 0.000819665 0 0.000409832 1.00000i \(-0.499870\pi\)
0.000409832 1.00000i \(0.499870\pi\)
\(578\) −20.4136 −0.849094
\(579\) 0 0
\(580\) −66.6397 −2.76706
\(581\) 12.1414 0.503711
\(582\) 0 0
\(583\) −7.91063 −0.327625
\(584\) −74.0721 −3.06513
\(585\) 0 0
\(586\) −6.31159 −0.260729
\(587\) −4.04780 −0.167070 −0.0835352 0.996505i \(-0.526621\pi\)
−0.0835352 + 0.996505i \(0.526621\pi\)
\(588\) 0 0
\(589\) 17.4944 0.720844
\(590\) 26.6352 1.09656
\(591\) 0 0
\(592\) −15.1472 −0.622548
\(593\) 3.29700 0.135391 0.0676957 0.997706i \(-0.478435\pi\)
0.0676957 + 0.997706i \(0.478435\pi\)
\(594\) 0 0
\(595\) −12.7077 −0.520963
\(596\) −82.4734 −3.37824
\(597\) 0 0
\(598\) 28.9593 1.18423
\(599\) −21.4453 −0.876232 −0.438116 0.898918i \(-0.644354\pi\)
−0.438116 + 0.898918i \(0.644354\pi\)
\(600\) 0 0
\(601\) −13.2402 −0.540080 −0.270040 0.962849i \(-0.587037\pi\)
−0.270040 + 0.962849i \(0.587037\pi\)
\(602\) −17.7464 −0.723289
\(603\) 0 0
\(604\) 23.4678 0.954890
\(605\) 1.85442 0.0753929
\(606\) 0 0
\(607\) −34.8370 −1.41399 −0.706995 0.707218i \(-0.749950\pi\)
−0.706995 + 0.707218i \(0.749950\pi\)
\(608\) 3.01712 0.122360
\(609\) 0 0
\(610\) 4.56020 0.184637
\(611\) −76.6588 −3.10128
\(612\) 0 0
\(613\) −12.0906 −0.488335 −0.244167 0.969733i \(-0.578515\pi\)
−0.244167 + 0.969733i \(0.578515\pi\)
\(614\) 28.8975 1.16621
\(615\) 0 0
\(616\) 11.6965 0.471263
\(617\) 25.9928 1.04643 0.523215 0.852201i \(-0.324733\pi\)
0.523215 + 0.852201i \(0.324733\pi\)
\(618\) 0 0
\(619\) 22.1655 0.890908 0.445454 0.895305i \(-0.353042\pi\)
0.445454 + 0.895305i \(0.353042\pi\)
\(620\) 20.4199 0.820082
\(621\) 0 0
\(622\) −0.106010 −0.00425060
\(623\) 32.9889 1.32167
\(624\) 0 0
\(625\) −14.7573 −0.590291
\(626\) −23.9816 −0.958498
\(627\) 0 0
\(628\) 50.2957 2.00702
\(629\) 10.4256 0.415694
\(630\) 0 0
\(631\) 16.8967 0.672649 0.336324 0.941746i \(-0.390816\pi\)
0.336324 + 0.941746i \(0.390816\pi\)
\(632\) 18.1446 0.721752
\(633\) 0 0
\(634\) 31.0869 1.23462
\(635\) 19.9398 0.791286
\(636\) 0 0
\(637\) −10.4769 −0.415109
\(638\) −21.8349 −0.864452
\(639\) 0 0
\(640\) −35.5602 −1.40564
\(641\) −15.5118 −0.612680 −0.306340 0.951922i \(-0.599104\pi\)
−0.306340 + 0.951922i \(0.599104\pi\)
\(642\) 0 0
\(643\) 28.4440 1.12172 0.560861 0.827910i \(-0.310470\pi\)
0.560861 + 0.827910i \(0.310470\pi\)
\(644\) 16.9291 0.667099
\(645\) 0 0
\(646\) −46.6344 −1.83481
\(647\) −10.2252 −0.401993 −0.200996 0.979592i \(-0.564418\pi\)
−0.200996 + 0.979592i \(0.564418\pi\)
\(648\) 0 0
\(649\) 5.84081 0.229272
\(650\) −25.1114 −0.984948
\(651\) 0 0
\(652\) 63.8396 2.50015
\(653\) 17.9727 0.703325 0.351663 0.936127i \(-0.385616\pi\)
0.351663 + 0.936127i \(0.385616\pi\)
\(654\) 0 0
\(655\) 27.6083 1.07874
\(656\) 9.74301 0.380401
\(657\) 0 0
\(658\) −66.9591 −2.61034
\(659\) −29.6229 −1.15394 −0.576972 0.816764i \(-0.695766\pi\)
−0.576972 + 0.816764i \(0.695766\pi\)
\(660\) 0 0
\(661\) −27.7945 −1.08108 −0.540540 0.841319i \(-0.681780\pi\)
−0.540540 + 0.841319i \(0.681780\pi\)
\(662\) 60.1284 2.33696
\(663\) 0 0
\(664\) 26.3066 1.02089
\(665\) 27.7039 1.07431
\(666\) 0 0
\(667\) −15.9857 −0.618968
\(668\) 47.7945 1.84922
\(669\) 0 0
\(670\) −46.0040 −1.77729
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) 12.3964 0.477846 0.238923 0.971039i \(-0.423206\pi\)
0.238923 + 0.971039i \(0.423206\pi\)
\(674\) 6.66674 0.256793
\(675\) 0 0
\(676\) 120.553 4.63667
\(677\) −34.3788 −1.32128 −0.660642 0.750701i \(-0.729716\pi\)
−0.660642 + 0.750701i \(0.729716\pi\)
\(678\) 0 0
\(679\) 41.8096 1.60451
\(680\) −27.5335 −1.05586
\(681\) 0 0
\(682\) 6.69069 0.256200
\(683\) −38.8947 −1.48826 −0.744132 0.668033i \(-0.767137\pi\)
−0.744132 + 0.668033i \(0.767137\pi\)
\(684\) 0 0
\(685\) 22.8068 0.871404
\(686\) −49.1460 −1.87640
\(687\) 0 0
\(688\) −13.3097 −0.507427
\(689\) −51.7450 −1.97133
\(690\) 0 0
\(691\) 16.0503 0.610583 0.305291 0.952259i \(-0.401246\pi\)
0.305291 + 0.952259i \(0.401246\pi\)
\(692\) −97.9018 −3.72167
\(693\) 0 0
\(694\) 40.7938 1.54851
\(695\) −28.5578 −1.08326
\(696\) 0 0
\(697\) −6.70593 −0.254005
\(698\) 59.7643 2.26211
\(699\) 0 0
\(700\) −14.6797 −0.554839
\(701\) −13.3561 −0.504454 −0.252227 0.967668i \(-0.581163\pi\)
−0.252227 + 0.967668i \(0.581163\pi\)
\(702\) 0 0
\(703\) −22.7287 −0.857229
\(704\) −7.41633 −0.279514
\(705\) 0 0
\(706\) 2.56405 0.0964994
\(707\) 38.5846 1.45112
\(708\) 0 0
\(709\) 3.35828 0.126123 0.0630615 0.998010i \(-0.479914\pi\)
0.0630615 + 0.998010i \(0.479914\pi\)
\(710\) −62.5308 −2.34674
\(711\) 0 0
\(712\) 71.4764 2.67869
\(713\) 4.89836 0.183445
\(714\) 0 0
\(715\) 12.1301 0.453641
\(716\) 54.1051 2.02200
\(717\) 0 0
\(718\) −24.0526 −0.897637
\(719\) −27.5080 −1.02588 −0.512938 0.858426i \(-0.671443\pi\)
−0.512938 + 0.858426i \(0.671443\pi\)
\(720\) 0 0
\(721\) 17.3002 0.644292
\(722\) 54.9446 2.04483
\(723\) 0 0
\(724\) −76.7605 −2.85278
\(725\) 13.8616 0.514807
\(726\) 0 0
\(727\) 0.693006 0.0257022 0.0128511 0.999917i \(-0.495909\pi\)
0.0128511 + 0.999917i \(0.495909\pi\)
\(728\) 76.5088 2.83560
\(729\) 0 0
\(730\) −67.0986 −2.48343
\(731\) 9.16080 0.338824
\(732\) 0 0
\(733\) 32.4941 1.20020 0.600098 0.799927i \(-0.295128\pi\)
0.600098 + 0.799927i \(0.295128\pi\)
\(734\) 13.4882 0.497858
\(735\) 0 0
\(736\) 0.844782 0.0311391
\(737\) −10.0882 −0.371602
\(738\) 0 0
\(739\) 14.7986 0.544374 0.272187 0.962244i \(-0.412253\pi\)
0.272187 + 0.962244i \(0.412253\pi\)
\(740\) −26.5295 −0.975243
\(741\) 0 0
\(742\) −45.1976 −1.65926
\(743\) 24.8498 0.911649 0.455825 0.890070i \(-0.349344\pi\)
0.455825 + 0.890070i \(0.349344\pi\)
\(744\) 0 0
\(745\) −37.7896 −1.38451
\(746\) −53.1695 −1.94667
\(747\) 0 0
\(748\) −11.9365 −0.436442
\(749\) −28.5995 −1.04500
\(750\) 0 0
\(751\) −8.05201 −0.293822 −0.146911 0.989150i \(-0.546933\pi\)
−0.146911 + 0.989150i \(0.546933\pi\)
\(752\) −50.2189 −1.83129
\(753\) 0 0
\(754\) −142.826 −5.20143
\(755\) 10.7530 0.391343
\(756\) 0 0
\(757\) 41.7999 1.51924 0.759622 0.650365i \(-0.225384\pi\)
0.759622 + 0.650365i \(0.225384\pi\)
\(758\) 71.3602 2.59192
\(759\) 0 0
\(760\) 60.0255 2.17736
\(761\) 50.6166 1.83485 0.917425 0.397909i \(-0.130264\pi\)
0.917425 + 0.397909i \(0.130264\pi\)
\(762\) 0 0
\(763\) −33.5104 −1.21316
\(764\) −45.8596 −1.65914
\(765\) 0 0
\(766\) 9.64460 0.348474
\(767\) 38.2059 1.37953
\(768\) 0 0
\(769\) 40.3462 1.45492 0.727461 0.686149i \(-0.240700\pi\)
0.727461 + 0.686149i \(0.240700\pi\)
\(770\) 10.5953 0.381828
\(771\) 0 0
\(772\) 2.37997 0.0856568
\(773\) −11.9238 −0.428869 −0.214434 0.976738i \(-0.568791\pi\)
−0.214434 + 0.976738i \(0.568791\pi\)
\(774\) 0 0
\(775\) −4.24750 −0.152575
\(776\) 90.5881 3.25192
\(777\) 0 0
\(778\) 63.8797 2.29020
\(779\) 14.6196 0.523800
\(780\) 0 0
\(781\) −13.7123 −0.490665
\(782\) −13.0574 −0.466933
\(783\) 0 0
\(784\) −6.86336 −0.245120
\(785\) 23.0457 0.822536
\(786\) 0 0
\(787\) −48.7632 −1.73822 −0.869111 0.494618i \(-0.835308\pi\)
−0.869111 + 0.494618i \(0.835308\pi\)
\(788\) −107.582 −3.83245
\(789\) 0 0
\(790\) 16.4364 0.584779
\(791\) 17.1133 0.608479
\(792\) 0 0
\(793\) 6.54120 0.232285
\(794\) 47.1898 1.67470
\(795\) 0 0
\(796\) −18.4684 −0.654594
\(797\) 19.5299 0.691785 0.345893 0.938274i \(-0.387576\pi\)
0.345893 + 0.938274i \(0.387576\pi\)
\(798\) 0 0
\(799\) 34.5647 1.22281
\(800\) −0.732533 −0.0258989
\(801\) 0 0
\(802\) −23.2406 −0.820654
\(803\) −14.7140 −0.519245
\(804\) 0 0
\(805\) 7.75698 0.273398
\(806\) 43.7651 1.54156
\(807\) 0 0
\(808\) 83.6005 2.94106
\(809\) 26.1404 0.919049 0.459524 0.888165i \(-0.348020\pi\)
0.459524 + 0.888165i \(0.348020\pi\)
\(810\) 0 0
\(811\) 39.3822 1.38289 0.691447 0.722427i \(-0.256973\pi\)
0.691447 + 0.722427i \(0.256973\pi\)
\(812\) −83.4939 −2.93006
\(813\) 0 0
\(814\) −8.69254 −0.304673
\(815\) 29.2516 1.02464
\(816\) 0 0
\(817\) −19.9714 −0.698711
\(818\) −63.3350 −2.21446
\(819\) 0 0
\(820\) 17.0643 0.595911
\(821\) −18.4817 −0.645016 −0.322508 0.946567i \(-0.604526\pi\)
−0.322508 + 0.946567i \(0.604526\pi\)
\(822\) 0 0
\(823\) −3.67700 −0.128172 −0.0640861 0.997944i \(-0.520413\pi\)
−0.0640861 + 0.997944i \(0.520413\pi\)
\(824\) 37.4840 1.30582
\(825\) 0 0
\(826\) 33.3717 1.16115
\(827\) 3.52277 0.122499 0.0612493 0.998123i \(-0.480492\pi\)
0.0612493 + 0.998123i \(0.480492\pi\)
\(828\) 0 0
\(829\) 36.1379 1.25512 0.627560 0.778568i \(-0.284054\pi\)
0.627560 + 0.778568i \(0.284054\pi\)
\(830\) 23.8299 0.827150
\(831\) 0 0
\(832\) −48.5117 −1.68184
\(833\) 4.72392 0.163674
\(834\) 0 0
\(835\) 21.8996 0.757868
\(836\) 26.0227 0.900014
\(837\) 0 0
\(838\) 19.1617 0.661931
\(839\) −40.7462 −1.40672 −0.703358 0.710836i \(-0.748317\pi\)
−0.703358 + 0.710836i \(0.748317\pi\)
\(840\) 0 0
\(841\) 49.8409 1.71865
\(842\) −70.1755 −2.41841
\(843\) 0 0
\(844\) 74.0576 2.54917
\(845\) 55.2381 1.90025
\(846\) 0 0
\(847\) 2.32343 0.0798340
\(848\) −33.8979 −1.16406
\(849\) 0 0
\(850\) 11.3225 0.388357
\(851\) −6.36394 −0.218153
\(852\) 0 0
\(853\) 42.9702 1.47127 0.735636 0.677377i \(-0.236883\pi\)
0.735636 + 0.677377i \(0.236883\pi\)
\(854\) 5.71353 0.195513
\(855\) 0 0
\(856\) −61.9660 −2.11795
\(857\) 51.7558 1.76794 0.883972 0.467540i \(-0.154859\pi\)
0.883972 + 0.467540i \(0.154859\pi\)
\(858\) 0 0
\(859\) −6.73686 −0.229859 −0.114929 0.993374i \(-0.536664\pi\)
−0.114929 + 0.993374i \(0.536664\pi\)
\(860\) −23.3111 −0.794902
\(861\) 0 0
\(862\) 1.59140 0.0542033
\(863\) −24.2044 −0.823929 −0.411964 0.911200i \(-0.635157\pi\)
−0.411964 + 0.911200i \(0.635157\pi\)
\(864\) 0 0
\(865\) −44.8590 −1.52525
\(866\) −45.3908 −1.54244
\(867\) 0 0
\(868\) 25.5843 0.868389
\(869\) 3.60431 0.122268
\(870\) 0 0
\(871\) −65.9886 −2.23594
\(872\) −72.6064 −2.45876
\(873\) 0 0
\(874\) 28.4665 0.962892
\(875\) −28.2694 −0.955679
\(876\) 0 0
\(877\) −6.49029 −0.219162 −0.109581 0.993978i \(-0.534951\pi\)
−0.109581 + 0.993978i \(0.534951\pi\)
\(878\) 21.8072 0.735958
\(879\) 0 0
\(880\) 7.94640 0.267873
\(881\) −27.3311 −0.920807 −0.460403 0.887710i \(-0.652295\pi\)
−0.460403 + 0.887710i \(0.652295\pi\)
\(882\) 0 0
\(883\) 26.5968 0.895055 0.447528 0.894270i \(-0.352305\pi\)
0.447528 + 0.894270i \(0.352305\pi\)
\(884\) −78.0790 −2.62608
\(885\) 0 0
\(886\) −27.8800 −0.936647
\(887\) −0.875150 −0.0293846 −0.0146923 0.999892i \(-0.504677\pi\)
−0.0146923 + 0.999892i \(0.504677\pi\)
\(888\) 0 0
\(889\) 24.9828 0.837897
\(890\) 64.7473 2.17033
\(891\) 0 0
\(892\) −18.9277 −0.633745
\(893\) −75.3543 −2.52164
\(894\) 0 0
\(895\) 24.7912 0.828678
\(896\) −44.5539 −1.48844
\(897\) 0 0
\(898\) 42.6966 1.42480
\(899\) −24.1586 −0.805734
\(900\) 0 0
\(901\) 23.3313 0.777278
\(902\) 5.59122 0.186167
\(903\) 0 0
\(904\) 37.0791 1.23323
\(905\) −35.1720 −1.16916
\(906\) 0 0
\(907\) −41.9567 −1.39315 −0.696575 0.717484i \(-0.745294\pi\)
−0.696575 + 0.717484i \(0.745294\pi\)
\(908\) −38.9932 −1.29403
\(909\) 0 0
\(910\) 69.3059 2.29747
\(911\) −28.2659 −0.936493 −0.468246 0.883598i \(-0.655114\pi\)
−0.468246 + 0.883598i \(0.655114\pi\)
\(912\) 0 0
\(913\) 5.22564 0.172943
\(914\) −41.5710 −1.37505
\(915\) 0 0
\(916\) 79.7235 2.63414
\(917\) 34.5908 1.14229
\(918\) 0 0
\(919\) −19.4057 −0.640136 −0.320068 0.947395i \(-0.603706\pi\)
−0.320068 + 0.947395i \(0.603706\pi\)
\(920\) 16.8069 0.554107
\(921\) 0 0
\(922\) 76.9738 2.53500
\(923\) −89.6949 −2.95234
\(924\) 0 0
\(925\) 5.51834 0.181442
\(926\) −52.5982 −1.72849
\(927\) 0 0
\(928\) −4.16644 −0.136770
\(929\) −32.2579 −1.05835 −0.529174 0.848513i \(-0.677498\pi\)
−0.529174 + 0.848513i \(0.677498\pi\)
\(930\) 0 0
\(931\) −10.2986 −0.337522
\(932\) −37.1548 −1.21705
\(933\) 0 0
\(934\) −93.5441 −3.06086
\(935\) −5.46935 −0.178867
\(936\) 0 0
\(937\) −24.4476 −0.798669 −0.399334 0.916805i \(-0.630759\pi\)
−0.399334 + 0.916805i \(0.630759\pi\)
\(938\) −57.6390 −1.88198
\(939\) 0 0
\(940\) −87.9554 −2.86879
\(941\) 6.11565 0.199365 0.0996823 0.995019i \(-0.468217\pi\)
0.0996823 + 0.995019i \(0.468217\pi\)
\(942\) 0 0
\(943\) 4.09342 0.133300
\(944\) 25.0285 0.814609
\(945\) 0 0
\(946\) −7.63802 −0.248333
\(947\) −26.7450 −0.869094 −0.434547 0.900649i \(-0.643092\pi\)
−0.434547 + 0.900649i \(0.643092\pi\)
\(948\) 0 0
\(949\) −96.2470 −3.12431
\(950\) −24.6840 −0.800856
\(951\) 0 0
\(952\) −34.4971 −1.11806
\(953\) −12.5656 −0.407041 −0.203520 0.979071i \(-0.565238\pi\)
−0.203520 + 0.979071i \(0.565238\pi\)
\(954\) 0 0
\(955\) −21.0131 −0.679967
\(956\) 30.5164 0.986970
\(957\) 0 0
\(958\) −88.8697 −2.87125
\(959\) 28.5750 0.922735
\(960\) 0 0
\(961\) −23.5973 −0.761203
\(962\) −56.8596 −1.83323
\(963\) 0 0
\(964\) 75.8711 2.44364
\(965\) 1.09051 0.0351048
\(966\) 0 0
\(967\) −3.19458 −0.102731 −0.0513655 0.998680i \(-0.516357\pi\)
−0.0513655 + 0.998680i \(0.516357\pi\)
\(968\) 5.03413 0.161803
\(969\) 0 0
\(970\) 82.0598 2.63478
\(971\) 29.2651 0.939161 0.469581 0.882890i \(-0.344405\pi\)
0.469581 + 0.882890i \(0.344405\pi\)
\(972\) 0 0
\(973\) −35.7805 −1.14707
\(974\) −48.8574 −1.56549
\(975\) 0 0
\(976\) 4.28511 0.137163
\(977\) 15.0225 0.480614 0.240307 0.970697i \(-0.422752\pi\)
0.240307 + 0.970697i \(0.422752\pi\)
\(978\) 0 0
\(979\) 14.1984 0.453781
\(980\) −12.0208 −0.383989
\(981\) 0 0
\(982\) 57.2795 1.82786
\(983\) 0.886011 0.0282594 0.0141297 0.999900i \(-0.495502\pi\)
0.0141297 + 0.999900i \(0.495502\pi\)
\(984\) 0 0
\(985\) −49.2946 −1.57066
\(986\) 64.3990 2.05088
\(987\) 0 0
\(988\) 170.220 5.41541
\(989\) −5.59191 −0.177812
\(990\) 0 0
\(991\) 19.8350 0.630079 0.315040 0.949079i \(-0.397982\pi\)
0.315040 + 0.949079i \(0.397982\pi\)
\(992\) 1.27669 0.0405349
\(993\) 0 0
\(994\) −78.3457 −2.48498
\(995\) −8.46228 −0.268272
\(996\) 0 0
\(997\) −17.9119 −0.567275 −0.283638 0.958932i \(-0.591541\pi\)
−0.283638 + 0.958932i \(0.591541\pi\)
\(998\) −46.0607 −1.45803
\(999\) 0 0
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 \(a_p\))