Properties

Label 8048.2.a.v.1.6
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.95835 q^{3}\) \(+0.337153 q^{5}\) \(-0.830729 q^{7}\) \(+0.835124 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.95835 q^{3}\) \(+0.337153 q^{5}\) \(-0.830729 q^{7}\) \(+0.835124 q^{9}\) \(+5.82988 q^{11}\) \(+4.14912 q^{13}\) \(-0.660263 q^{15}\) \(-4.44743 q^{17}\) \(-1.68929 q^{19}\) \(+1.62686 q^{21}\) \(+6.61850 q^{23}\) \(-4.88633 q^{25}\) \(+4.23958 q^{27}\) \(-6.73612 q^{29}\) \(-0.271306 q^{31}\) \(-11.4169 q^{33}\) \(-0.280083 q^{35}\) \(-4.23650 q^{37}\) \(-8.12541 q^{39}\) \(-8.53349 q^{41}\) \(+0.824655 q^{43}\) \(+0.281565 q^{45}\) \(-8.45594 q^{47}\) \(-6.30989 q^{49}\) \(+8.70961 q^{51}\) \(-2.66412 q^{53}\) \(+1.96556 q^{55}\) \(+3.30822 q^{57}\) \(+5.99137 q^{59}\) \(+15.2825 q^{61}\) \(-0.693761 q^{63}\) \(+1.39889 q^{65}\) \(-8.68864 q^{67}\) \(-12.9613 q^{69}\) \(+11.4284 q^{71}\) \(+13.3274 q^{73}\) \(+9.56913 q^{75}\) \(-4.84305 q^{77}\) \(-10.2656 q^{79}\) \(-10.8079 q^{81}\) \(-15.4136 q^{83}\) \(-1.49947 q^{85}\) \(+13.1917 q^{87}\) \(-4.23120 q^{89}\) \(-3.44679 q^{91}\) \(+0.531311 q^{93}\) \(-0.569550 q^{95}\) \(-11.3532 q^{97}\) \(+4.86867 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.95835 −1.13065 −0.565326 0.824867i \(-0.691250\pi\)
−0.565326 + 0.824867i \(0.691250\pi\)
\(4\) 0 0
\(5\) 0.337153 0.150780 0.0753898 0.997154i \(-0.475980\pi\)
0.0753898 + 0.997154i \(0.475980\pi\)
\(6\) 0 0
\(7\) −0.830729 −0.313986 −0.156993 0.987600i \(-0.550180\pi\)
−0.156993 + 0.987600i \(0.550180\pi\)
\(8\) 0 0
\(9\) 0.835124 0.278375
\(10\) 0 0
\(11\) 5.82988 1.75777 0.878887 0.477029i \(-0.158286\pi\)
0.878887 + 0.477029i \(0.158286\pi\)
\(12\) 0 0
\(13\) 4.14912 1.15076 0.575379 0.817887i \(-0.304855\pi\)
0.575379 + 0.817887i \(0.304855\pi\)
\(14\) 0 0
\(15\) −0.660263 −0.170479
\(16\) 0 0
\(17\) −4.44743 −1.07866 −0.539330 0.842095i \(-0.681322\pi\)
−0.539330 + 0.842095i \(0.681322\pi\)
\(18\) 0 0
\(19\) −1.68929 −0.387550 −0.193775 0.981046i \(-0.562073\pi\)
−0.193775 + 0.981046i \(0.562073\pi\)
\(20\) 0 0
\(21\) 1.62686 0.355009
\(22\) 0 0
\(23\) 6.61850 1.38005 0.690026 0.723784i \(-0.257599\pi\)
0.690026 + 0.723784i \(0.257599\pi\)
\(24\) 0 0
\(25\) −4.88633 −0.977266
\(26\) 0 0
\(27\) 4.23958 0.815907
\(28\) 0 0
\(29\) −6.73612 −1.25087 −0.625433 0.780278i \(-0.715078\pi\)
−0.625433 + 0.780278i \(0.715078\pi\)
\(30\) 0 0
\(31\) −0.271306 −0.0487279 −0.0243640 0.999703i \(-0.507756\pi\)
−0.0243640 + 0.999703i \(0.507756\pi\)
\(32\) 0 0
\(33\) −11.4169 −1.98743
\(34\) 0 0
\(35\) −0.280083 −0.0473427
\(36\) 0 0
\(37\) −4.23650 −0.696476 −0.348238 0.937406i \(-0.613220\pi\)
−0.348238 + 0.937406i \(0.613220\pi\)
\(38\) 0 0
\(39\) −8.12541 −1.30111
\(40\) 0 0
\(41\) −8.53349 −1.33271 −0.666354 0.745636i \(-0.732146\pi\)
−0.666354 + 0.745636i \(0.732146\pi\)
\(42\) 0 0
\(43\) 0.824655 0.125759 0.0628794 0.998021i \(-0.479972\pi\)
0.0628794 + 0.998021i \(0.479972\pi\)
\(44\) 0 0
\(45\) 0.281565 0.0419732
\(46\) 0 0
\(47\) −8.45594 −1.23343 −0.616713 0.787188i \(-0.711536\pi\)
−0.616713 + 0.787188i \(0.711536\pi\)
\(48\) 0 0
\(49\) −6.30989 −0.901413
\(50\) 0 0
\(51\) 8.70961 1.21959
\(52\) 0 0
\(53\) −2.66412 −0.365945 −0.182973 0.983118i \(-0.558572\pi\)
−0.182973 + 0.983118i \(0.558572\pi\)
\(54\) 0 0
\(55\) 1.96556 0.265037
\(56\) 0 0
\(57\) 3.30822 0.438184
\(58\) 0 0
\(59\) 5.99137 0.780010 0.390005 0.920813i \(-0.372473\pi\)
0.390005 + 0.920813i \(0.372473\pi\)
\(60\) 0 0
\(61\) 15.2825 1.95672 0.978359 0.206914i \(-0.0663421\pi\)
0.978359 + 0.206914i \(0.0663421\pi\)
\(62\) 0 0
\(63\) −0.693761 −0.0874057
\(64\) 0 0
\(65\) 1.39889 0.173511
\(66\) 0 0
\(67\) −8.68864 −1.06149 −0.530743 0.847533i \(-0.678087\pi\)
−0.530743 + 0.847533i \(0.678087\pi\)
\(68\) 0 0
\(69\) −12.9613 −1.56036
\(70\) 0 0
\(71\) 11.4284 1.35630 0.678150 0.734924i \(-0.262782\pi\)
0.678150 + 0.734924i \(0.262782\pi\)
\(72\) 0 0
\(73\) 13.3274 1.55986 0.779930 0.625867i \(-0.215255\pi\)
0.779930 + 0.625867i \(0.215255\pi\)
\(74\) 0 0
\(75\) 9.56913 1.10495
\(76\) 0 0
\(77\) −4.84305 −0.551916
\(78\) 0 0
\(79\) −10.2656 −1.15497 −0.577487 0.816400i \(-0.695966\pi\)
−0.577487 + 0.816400i \(0.695966\pi\)
\(80\) 0 0
\(81\) −10.8079 −1.20088
\(82\) 0 0
\(83\) −15.4136 −1.69186 −0.845931 0.533293i \(-0.820954\pi\)
−0.845931 + 0.533293i \(0.820954\pi\)
\(84\) 0 0
\(85\) −1.49947 −0.162640
\(86\) 0 0
\(87\) 13.1917 1.41430
\(88\) 0 0
\(89\) −4.23120 −0.448506 −0.224253 0.974531i \(-0.571994\pi\)
−0.224253 + 0.974531i \(0.571994\pi\)
\(90\) 0 0
\(91\) −3.44679 −0.361322
\(92\) 0 0
\(93\) 0.531311 0.0550944
\(94\) 0 0
\(95\) −0.569550 −0.0584346
\(96\) 0 0
\(97\) −11.3532 −1.15274 −0.576371 0.817188i \(-0.695532\pi\)
−0.576371 + 0.817188i \(0.695532\pi\)
\(98\) 0 0
\(99\) 4.86867 0.489320
\(100\) 0 0
\(101\) 17.2476 1.71620 0.858099 0.513484i \(-0.171645\pi\)
0.858099 + 0.513484i \(0.171645\pi\)
\(102\) 0 0
\(103\) 8.88423 0.875389 0.437695 0.899124i \(-0.355795\pi\)
0.437695 + 0.899124i \(0.355795\pi\)
\(104\) 0 0
\(105\) 0.548500 0.0535281
\(106\) 0 0
\(107\) 13.9665 1.35019 0.675096 0.737730i \(-0.264102\pi\)
0.675096 + 0.737730i \(0.264102\pi\)
\(108\) 0 0
\(109\) −3.83880 −0.367691 −0.183845 0.982955i \(-0.558855\pi\)
−0.183845 + 0.982955i \(0.558855\pi\)
\(110\) 0 0
\(111\) 8.29653 0.787472
\(112\) 0 0
\(113\) −9.39443 −0.883754 −0.441877 0.897076i \(-0.645687\pi\)
−0.441877 + 0.897076i \(0.645687\pi\)
\(114\) 0 0
\(115\) 2.23145 0.208084
\(116\) 0 0
\(117\) 3.46503 0.320342
\(118\) 0 0
\(119\) 3.69461 0.338684
\(120\) 0 0
\(121\) 22.9875 2.08977
\(122\) 0 0
\(123\) 16.7115 1.50683
\(124\) 0 0
\(125\) −3.33321 −0.298131
\(126\) 0 0
\(127\) −2.13992 −0.189887 −0.0949436 0.995483i \(-0.530267\pi\)
−0.0949436 + 0.995483i \(0.530267\pi\)
\(128\) 0 0
\(129\) −1.61496 −0.142189
\(130\) 0 0
\(131\) 8.91725 0.779104 0.389552 0.921005i \(-0.372630\pi\)
0.389552 + 0.921005i \(0.372630\pi\)
\(132\) 0 0
\(133\) 1.40334 0.121685
\(134\) 0 0
\(135\) 1.42939 0.123022
\(136\) 0 0
\(137\) 12.0499 1.02949 0.514746 0.857343i \(-0.327886\pi\)
0.514746 + 0.857343i \(0.327886\pi\)
\(138\) 0 0
\(139\) −7.30684 −0.619758 −0.309879 0.950776i \(-0.600289\pi\)
−0.309879 + 0.950776i \(0.600289\pi\)
\(140\) 0 0
\(141\) 16.5597 1.39458
\(142\) 0 0
\(143\) 24.1888 2.02277
\(144\) 0 0
\(145\) −2.27111 −0.188605
\(146\) 0 0
\(147\) 12.3570 1.01918
\(148\) 0 0
\(149\) −2.54557 −0.208542 −0.104271 0.994549i \(-0.533251\pi\)
−0.104271 + 0.994549i \(0.533251\pi\)
\(150\) 0 0
\(151\) −1.49133 −0.121363 −0.0606815 0.998157i \(-0.519327\pi\)
−0.0606815 + 0.998157i \(0.519327\pi\)
\(152\) 0 0
\(153\) −3.71415 −0.300272
\(154\) 0 0
\(155\) −0.0914716 −0.00734718
\(156\) 0 0
\(157\) −19.7688 −1.57772 −0.788862 0.614571i \(-0.789329\pi\)
−0.788862 + 0.614571i \(0.789329\pi\)
\(158\) 0 0
\(159\) 5.21727 0.413757
\(160\) 0 0
\(161\) −5.49818 −0.433317
\(162\) 0 0
\(163\) 5.08030 0.397920 0.198960 0.980008i \(-0.436244\pi\)
0.198960 + 0.980008i \(0.436244\pi\)
\(164\) 0 0
\(165\) −3.84926 −0.299664
\(166\) 0 0
\(167\) −17.2333 −1.33355 −0.666775 0.745259i \(-0.732326\pi\)
−0.666775 + 0.745259i \(0.732326\pi\)
\(168\) 0 0
\(169\) 4.21516 0.324243
\(170\) 0 0
\(171\) −1.41077 −0.107884
\(172\) 0 0
\(173\) −11.6750 −0.887630 −0.443815 0.896118i \(-0.646375\pi\)
−0.443815 + 0.896118i \(0.646375\pi\)
\(174\) 0 0
\(175\) 4.05921 0.306848
\(176\) 0 0
\(177\) −11.7332 −0.881920
\(178\) 0 0
\(179\) −6.74740 −0.504324 −0.252162 0.967685i \(-0.581142\pi\)
−0.252162 + 0.967685i \(0.581142\pi\)
\(180\) 0 0
\(181\) 7.68546 0.571256 0.285628 0.958341i \(-0.407798\pi\)
0.285628 + 0.958341i \(0.407798\pi\)
\(182\) 0 0
\(183\) −29.9284 −2.21237
\(184\) 0 0
\(185\) −1.42835 −0.105014
\(186\) 0 0
\(187\) −25.9280 −1.89604
\(188\) 0 0
\(189\) −3.52194 −0.256183
\(190\) 0 0
\(191\) 8.61634 0.623456 0.311728 0.950171i \(-0.399092\pi\)
0.311728 + 0.950171i \(0.399092\pi\)
\(192\) 0 0
\(193\) 8.20122 0.590337 0.295168 0.955445i \(-0.404624\pi\)
0.295168 + 0.955445i \(0.404624\pi\)
\(194\) 0 0
\(195\) −2.73951 −0.196180
\(196\) 0 0
\(197\) 11.7837 0.839557 0.419778 0.907627i \(-0.362108\pi\)
0.419778 + 0.907627i \(0.362108\pi\)
\(198\) 0 0
\(199\) 4.19649 0.297481 0.148741 0.988876i \(-0.452478\pi\)
0.148741 + 0.988876i \(0.452478\pi\)
\(200\) 0 0
\(201\) 17.0154 1.20017
\(202\) 0 0
\(203\) 5.59589 0.392755
\(204\) 0 0
\(205\) −2.87710 −0.200945
\(206\) 0 0
\(207\) 5.52727 0.384172
\(208\) 0 0
\(209\) −9.84836 −0.681225
\(210\) 0 0
\(211\) −19.0815 −1.31362 −0.656811 0.754055i \(-0.728095\pi\)
−0.656811 + 0.754055i \(0.728095\pi\)
\(212\) 0 0
\(213\) −22.3808 −1.53350
\(214\) 0 0
\(215\) 0.278035 0.0189619
\(216\) 0 0
\(217\) 0.225381 0.0152999
\(218\) 0 0
\(219\) −26.0998 −1.76366
\(220\) 0 0
\(221\) −18.4529 −1.24128
\(222\) 0 0
\(223\) 11.5825 0.775621 0.387810 0.921739i \(-0.373231\pi\)
0.387810 + 0.921739i \(0.373231\pi\)
\(224\) 0 0
\(225\) −4.08069 −0.272046
\(226\) 0 0
\(227\) −29.0726 −1.92962 −0.964808 0.262955i \(-0.915303\pi\)
−0.964808 + 0.262955i \(0.915303\pi\)
\(228\) 0 0
\(229\) −19.1259 −1.26387 −0.631937 0.775020i \(-0.717740\pi\)
−0.631937 + 0.775020i \(0.717740\pi\)
\(230\) 0 0
\(231\) 9.48437 0.624026
\(232\) 0 0
\(233\) −25.6549 −1.68071 −0.840353 0.542040i \(-0.817652\pi\)
−0.840353 + 0.542040i \(0.817652\pi\)
\(234\) 0 0
\(235\) −2.85095 −0.185975
\(236\) 0 0
\(237\) 20.1037 1.30587
\(238\) 0 0
\(239\) 2.56292 0.165781 0.0828906 0.996559i \(-0.473585\pi\)
0.0828906 + 0.996559i \(0.473585\pi\)
\(240\) 0 0
\(241\) 6.98525 0.449959 0.224980 0.974363i \(-0.427768\pi\)
0.224980 + 0.974363i \(0.427768\pi\)
\(242\) 0 0
\(243\) 8.44696 0.541873
\(244\) 0 0
\(245\) −2.12740 −0.135915
\(246\) 0 0
\(247\) −7.00906 −0.445976
\(248\) 0 0
\(249\) 30.1852 1.91291
\(250\) 0 0
\(251\) 3.29264 0.207829 0.103915 0.994586i \(-0.466863\pi\)
0.103915 + 0.994586i \(0.466863\pi\)
\(252\) 0 0
\(253\) 38.5850 2.42582
\(254\) 0 0
\(255\) 2.93647 0.183889
\(256\) 0 0
\(257\) 14.8611 0.927013 0.463506 0.886094i \(-0.346591\pi\)
0.463506 + 0.886094i \(0.346591\pi\)
\(258\) 0 0
\(259\) 3.51938 0.218684
\(260\) 0 0
\(261\) −5.62550 −0.348210
\(262\) 0 0
\(263\) −8.92149 −0.550122 −0.275061 0.961427i \(-0.588698\pi\)
−0.275061 + 0.961427i \(0.588698\pi\)
\(264\) 0 0
\(265\) −0.898217 −0.0551770
\(266\) 0 0
\(267\) 8.28615 0.507104
\(268\) 0 0
\(269\) −12.3663 −0.753984 −0.376992 0.926217i \(-0.623042\pi\)
−0.376992 + 0.926217i \(0.623042\pi\)
\(270\) 0 0
\(271\) 3.33563 0.202625 0.101313 0.994855i \(-0.467696\pi\)
0.101313 + 0.994855i \(0.467696\pi\)
\(272\) 0 0
\(273\) 6.75001 0.408529
\(274\) 0 0
\(275\) −28.4867 −1.71781
\(276\) 0 0
\(277\) −10.8733 −0.653312 −0.326656 0.945143i \(-0.605922\pi\)
−0.326656 + 0.945143i \(0.605922\pi\)
\(278\) 0 0
\(279\) −0.226574 −0.0135646
\(280\) 0 0
\(281\) −12.7151 −0.758517 −0.379258 0.925291i \(-0.623821\pi\)
−0.379258 + 0.925291i \(0.623821\pi\)
\(282\) 0 0
\(283\) 28.8004 1.71201 0.856003 0.516970i \(-0.172940\pi\)
0.856003 + 0.516970i \(0.172940\pi\)
\(284\) 0 0
\(285\) 1.11538 0.0660692
\(286\) 0 0
\(287\) 7.08902 0.418451
\(288\) 0 0
\(289\) 2.77961 0.163507
\(290\) 0 0
\(291\) 22.2335 1.30335
\(292\) 0 0
\(293\) −26.2273 −1.53221 −0.766107 0.642713i \(-0.777809\pi\)
−0.766107 + 0.642713i \(0.777809\pi\)
\(294\) 0 0
\(295\) 2.02001 0.117610
\(296\) 0 0
\(297\) 24.7162 1.43418
\(298\) 0 0
\(299\) 27.4609 1.58811
\(300\) 0 0
\(301\) −0.685065 −0.0394865
\(302\) 0 0
\(303\) −33.7767 −1.94042
\(304\) 0 0
\(305\) 5.15253 0.295033
\(306\) 0 0
\(307\) 18.5057 1.05618 0.528089 0.849189i \(-0.322909\pi\)
0.528089 + 0.849189i \(0.322909\pi\)
\(308\) 0 0
\(309\) −17.3984 −0.989761
\(310\) 0 0
\(311\) −8.98655 −0.509581 −0.254790 0.966996i \(-0.582006\pi\)
−0.254790 + 0.966996i \(0.582006\pi\)
\(312\) 0 0
\(313\) −1.26787 −0.0716641 −0.0358320 0.999358i \(-0.511408\pi\)
−0.0358320 + 0.999358i \(0.511408\pi\)
\(314\) 0 0
\(315\) −0.233904 −0.0131790
\(316\) 0 0
\(317\) −18.1367 −1.01866 −0.509330 0.860572i \(-0.670107\pi\)
−0.509330 + 0.860572i \(0.670107\pi\)
\(318\) 0 0
\(319\) −39.2708 −2.19874
\(320\) 0 0
\(321\) −27.3513 −1.52660
\(322\) 0 0
\(323\) 7.51299 0.418034
\(324\) 0 0
\(325\) −20.2739 −1.12460
\(326\) 0 0
\(327\) 7.51771 0.415730
\(328\) 0 0
\(329\) 7.02459 0.387278
\(330\) 0 0
\(331\) −19.8368 −1.09033 −0.545166 0.838328i \(-0.683533\pi\)
−0.545166 + 0.838328i \(0.683533\pi\)
\(332\) 0 0
\(333\) −3.53800 −0.193881
\(334\) 0 0
\(335\) −2.92940 −0.160050
\(336\) 0 0
\(337\) −0.953395 −0.0519347 −0.0259674 0.999663i \(-0.508267\pi\)
−0.0259674 + 0.999663i \(0.508267\pi\)
\(338\) 0 0
\(339\) 18.3976 0.999218
\(340\) 0 0
\(341\) −1.58168 −0.0856527
\(342\) 0 0
\(343\) 11.0569 0.597017
\(344\) 0 0
\(345\) −4.36995 −0.235270
\(346\) 0 0
\(347\) −0.867113 −0.0465491 −0.0232745 0.999729i \(-0.507409\pi\)
−0.0232745 + 0.999729i \(0.507409\pi\)
\(348\) 0 0
\(349\) 8.67195 0.464199 0.232100 0.972692i \(-0.425440\pi\)
0.232100 + 0.972692i \(0.425440\pi\)
\(350\) 0 0
\(351\) 17.5905 0.938912
\(352\) 0 0
\(353\) 34.8386 1.85427 0.927136 0.374725i \(-0.122263\pi\)
0.927136 + 0.374725i \(0.122263\pi\)
\(354\) 0 0
\(355\) 3.85312 0.204502
\(356\) 0 0
\(357\) −7.23532 −0.382934
\(358\) 0 0
\(359\) −4.92500 −0.259931 −0.129966 0.991518i \(-0.541487\pi\)
−0.129966 + 0.991518i \(0.541487\pi\)
\(360\) 0 0
\(361\) −16.1463 −0.849805
\(362\) 0 0
\(363\) −45.0175 −2.36281
\(364\) 0 0
\(365\) 4.49339 0.235195
\(366\) 0 0
\(367\) 11.8092 0.616435 0.308218 0.951316i \(-0.400267\pi\)
0.308218 + 0.951316i \(0.400267\pi\)
\(368\) 0 0
\(369\) −7.12652 −0.370992
\(370\) 0 0
\(371\) 2.21316 0.114902
\(372\) 0 0
\(373\) 18.6256 0.964399 0.482199 0.876062i \(-0.339838\pi\)
0.482199 + 0.876062i \(0.339838\pi\)
\(374\) 0 0
\(375\) 6.52758 0.337083
\(376\) 0 0
\(377\) −27.9490 −1.43944
\(378\) 0 0
\(379\) −8.00820 −0.411354 −0.205677 0.978620i \(-0.565940\pi\)
−0.205677 + 0.978620i \(0.565940\pi\)
\(380\) 0 0
\(381\) 4.19071 0.214696
\(382\) 0 0
\(383\) −34.3412 −1.75476 −0.877378 0.479800i \(-0.840709\pi\)
−0.877378 + 0.479800i \(0.840709\pi\)
\(384\) 0 0
\(385\) −1.63285 −0.0832177
\(386\) 0 0
\(387\) 0.688689 0.0350081
\(388\) 0 0
\(389\) −35.0751 −1.77838 −0.889190 0.457539i \(-0.848731\pi\)
−0.889190 + 0.457539i \(0.848731\pi\)
\(390\) 0 0
\(391\) −29.4353 −1.48861
\(392\) 0 0
\(393\) −17.4631 −0.880896
\(394\) 0 0
\(395\) −3.46109 −0.174146
\(396\) 0 0
\(397\) 12.9832 0.651608 0.325804 0.945437i \(-0.394365\pi\)
0.325804 + 0.945437i \(0.394365\pi\)
\(398\) 0 0
\(399\) −2.74823 −0.137584
\(400\) 0 0
\(401\) 18.6205 0.929862 0.464931 0.885347i \(-0.346079\pi\)
0.464931 + 0.885347i \(0.346079\pi\)
\(402\) 0 0
\(403\) −1.12568 −0.0560741
\(404\) 0 0
\(405\) −3.64393 −0.181069
\(406\) 0 0
\(407\) −24.6983 −1.22425
\(408\) 0 0
\(409\) −27.0572 −1.33789 −0.668946 0.743311i \(-0.733254\pi\)
−0.668946 + 0.743311i \(0.733254\pi\)
\(410\) 0 0
\(411\) −23.5979 −1.16400
\(412\) 0 0
\(413\) −4.97720 −0.244912
\(414\) 0 0
\(415\) −5.19675 −0.255098
\(416\) 0 0
\(417\) 14.3093 0.700731
\(418\) 0 0
\(419\) −7.16488 −0.350027 −0.175014 0.984566i \(-0.555997\pi\)
−0.175014 + 0.984566i \(0.555997\pi\)
\(420\) 0 0
\(421\) −19.5823 −0.954381 −0.477190 0.878800i \(-0.658345\pi\)
−0.477190 + 0.878800i \(0.658345\pi\)
\(422\) 0 0
\(423\) −7.06176 −0.343354
\(424\) 0 0
\(425\) 21.7316 1.05414
\(426\) 0 0
\(427\) −12.6956 −0.614382
\(428\) 0 0
\(429\) −47.3702 −2.28705
\(430\) 0 0
\(431\) −19.1575 −0.922785 −0.461392 0.887196i \(-0.652650\pi\)
−0.461392 + 0.887196i \(0.652650\pi\)
\(432\) 0 0
\(433\) −29.6346 −1.42415 −0.712074 0.702104i \(-0.752244\pi\)
−0.712074 + 0.702104i \(0.752244\pi\)
\(434\) 0 0
\(435\) 4.44762 0.213247
\(436\) 0 0
\(437\) −11.1806 −0.534839
\(438\) 0 0
\(439\) 35.4331 1.69113 0.845564 0.533874i \(-0.179264\pi\)
0.845564 + 0.533874i \(0.179264\pi\)
\(440\) 0 0
\(441\) −5.26954 −0.250931
\(442\) 0 0
\(443\) 3.25789 0.154787 0.0773936 0.997001i \(-0.475340\pi\)
0.0773936 + 0.997001i \(0.475340\pi\)
\(444\) 0 0
\(445\) −1.42656 −0.0676255
\(446\) 0 0
\(447\) 4.98512 0.235788
\(448\) 0 0
\(449\) 10.6219 0.501280 0.250640 0.968080i \(-0.419359\pi\)
0.250640 + 0.968080i \(0.419359\pi\)
\(450\) 0 0
\(451\) −49.7492 −2.34260
\(452\) 0 0
\(453\) 2.92055 0.137219
\(454\) 0 0
\(455\) −1.16210 −0.0544799
\(456\) 0 0
\(457\) −28.1742 −1.31794 −0.658968 0.752171i \(-0.729007\pi\)
−0.658968 + 0.752171i \(0.729007\pi\)
\(458\) 0 0
\(459\) −18.8552 −0.880086
\(460\) 0 0
\(461\) 30.6957 1.42964 0.714820 0.699308i \(-0.246508\pi\)
0.714820 + 0.699308i \(0.246508\pi\)
\(462\) 0 0
\(463\) 3.89086 0.180824 0.0904118 0.995904i \(-0.471182\pi\)
0.0904118 + 0.995904i \(0.471182\pi\)
\(464\) 0 0
\(465\) 0.179133 0.00830710
\(466\) 0 0
\(467\) −32.3849 −1.49859 −0.749297 0.662234i \(-0.769608\pi\)
−0.749297 + 0.662234i \(0.769608\pi\)
\(468\) 0 0
\(469\) 7.21790 0.333292
\(470\) 0 0
\(471\) 38.7142 1.78386
\(472\) 0 0
\(473\) 4.80764 0.221056
\(474\) 0 0
\(475\) 8.25442 0.378739
\(476\) 0 0
\(477\) −2.22487 −0.101870
\(478\) 0 0
\(479\) 16.8962 0.772008 0.386004 0.922497i \(-0.373855\pi\)
0.386004 + 0.922497i \(0.373855\pi\)
\(480\) 0 0
\(481\) −17.5777 −0.801475
\(482\) 0 0
\(483\) 10.7673 0.489931
\(484\) 0 0
\(485\) −3.82777 −0.173810
\(486\) 0 0
\(487\) −22.4159 −1.01576 −0.507880 0.861428i \(-0.669571\pi\)
−0.507880 + 0.861428i \(0.669571\pi\)
\(488\) 0 0
\(489\) −9.94899 −0.449909
\(490\) 0 0
\(491\) 3.05607 0.137919 0.0689593 0.997619i \(-0.478032\pi\)
0.0689593 + 0.997619i \(0.478032\pi\)
\(492\) 0 0
\(493\) 29.9584 1.34926
\(494\) 0 0
\(495\) 1.64149 0.0737795
\(496\) 0 0
\(497\) −9.49389 −0.425859
\(498\) 0 0
\(499\) 33.0137 1.47790 0.738948 0.673763i \(-0.235323\pi\)
0.738948 + 0.673763i \(0.235323\pi\)
\(500\) 0 0
\(501\) 33.7487 1.50778
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 5.81508 0.258768
\(506\) 0 0
\(507\) −8.25475 −0.366606
\(508\) 0 0
\(509\) −23.8182 −1.05572 −0.527862 0.849330i \(-0.677006\pi\)
−0.527862 + 0.849330i \(0.677006\pi\)
\(510\) 0 0
\(511\) −11.0715 −0.489774
\(512\) 0 0
\(513\) −7.16188 −0.316205
\(514\) 0 0
\(515\) 2.99535 0.131991
\(516\) 0 0
\(517\) −49.2971 −2.16808
\(518\) 0 0
\(519\) 22.8636 1.00360
\(520\) 0 0
\(521\) 40.5560 1.77679 0.888396 0.459077i \(-0.151820\pi\)
0.888396 + 0.459077i \(0.151820\pi\)
\(522\) 0 0
\(523\) −23.2705 −1.01755 −0.508774 0.860900i \(-0.669901\pi\)
−0.508774 + 0.860900i \(0.669901\pi\)
\(524\) 0 0
\(525\) −7.94935 −0.346938
\(526\) 0 0
\(527\) 1.20661 0.0525609
\(528\) 0 0
\(529\) 20.8045 0.904545
\(530\) 0 0
\(531\) 5.00354 0.217135
\(532\) 0 0
\(533\) −35.4064 −1.53362
\(534\) 0 0
\(535\) 4.70885 0.203581
\(536\) 0 0
\(537\) 13.2138 0.570216
\(538\) 0 0
\(539\) −36.7859 −1.58448
\(540\) 0 0
\(541\) −24.2040 −1.04061 −0.520305 0.853980i \(-0.674182\pi\)
−0.520305 + 0.853980i \(0.674182\pi\)
\(542\) 0 0
\(543\) −15.0508 −0.645891
\(544\) 0 0
\(545\) −1.29427 −0.0554402
\(546\) 0 0
\(547\) 2.59891 0.111121 0.0555607 0.998455i \(-0.482305\pi\)
0.0555607 + 0.998455i \(0.482305\pi\)
\(548\) 0 0
\(549\) 12.7627 0.544701
\(550\) 0 0
\(551\) 11.3793 0.484773
\(552\) 0 0
\(553\) 8.52795 0.362645
\(554\) 0 0
\(555\) 2.79720 0.118735
\(556\) 0 0
\(557\) 29.0709 1.23178 0.615888 0.787834i \(-0.288798\pi\)
0.615888 + 0.787834i \(0.288798\pi\)
\(558\) 0 0
\(559\) 3.42159 0.144718
\(560\) 0 0
\(561\) 50.7760 2.14376
\(562\) 0 0
\(563\) −31.1925 −1.31461 −0.657304 0.753625i \(-0.728303\pi\)
−0.657304 + 0.753625i \(0.728303\pi\)
\(564\) 0 0
\(565\) −3.16736 −0.133252
\(566\) 0 0
\(567\) 8.97846 0.377060
\(568\) 0 0
\(569\) −6.64159 −0.278430 −0.139215 0.990262i \(-0.544458\pi\)
−0.139215 + 0.990262i \(0.544458\pi\)
\(570\) 0 0
\(571\) −15.7632 −0.659670 −0.329835 0.944039i \(-0.606993\pi\)
−0.329835 + 0.944039i \(0.606993\pi\)
\(572\) 0 0
\(573\) −16.8738 −0.704912
\(574\) 0 0
\(575\) −32.3402 −1.34868
\(576\) 0 0
\(577\) −35.3843 −1.47307 −0.736534 0.676400i \(-0.763539\pi\)
−0.736534 + 0.676400i \(0.763539\pi\)
\(578\) 0 0
\(579\) −16.0608 −0.667466
\(580\) 0 0
\(581\) 12.8045 0.531221
\(582\) 0 0
\(583\) −15.5315 −0.643249
\(584\) 0 0
\(585\) 1.16825 0.0483010
\(586\) 0 0
\(587\) 21.3362 0.880640 0.440320 0.897841i \(-0.354865\pi\)
0.440320 + 0.897841i \(0.354865\pi\)
\(588\) 0 0
\(589\) 0.458314 0.0188845
\(590\) 0 0
\(591\) −23.0767 −0.949247
\(592\) 0 0
\(593\) −44.1255 −1.81202 −0.906009 0.423258i \(-0.860887\pi\)
−0.906009 + 0.423258i \(0.860887\pi\)
\(594\) 0 0
\(595\) 1.24565 0.0510666
\(596\) 0 0
\(597\) −8.21819 −0.336348
\(598\) 0 0
\(599\) −4.83858 −0.197699 −0.0988495 0.995102i \(-0.531516\pi\)
−0.0988495 + 0.995102i \(0.531516\pi\)
\(600\) 0 0
\(601\) −9.72151 −0.396549 −0.198274 0.980147i \(-0.563534\pi\)
−0.198274 + 0.980147i \(0.563534\pi\)
\(602\) 0 0
\(603\) −7.25609 −0.295491
\(604\) 0 0
\(605\) 7.75031 0.315095
\(606\) 0 0
\(607\) 42.5935 1.72882 0.864408 0.502791i \(-0.167693\pi\)
0.864408 + 0.502791i \(0.167693\pi\)
\(608\) 0 0
\(609\) −10.9587 −0.444069
\(610\) 0 0
\(611\) −35.0847 −1.41937
\(612\) 0 0
\(613\) −11.5162 −0.465134 −0.232567 0.972580i \(-0.574712\pi\)
−0.232567 + 0.972580i \(0.574712\pi\)
\(614\) 0 0
\(615\) 5.63435 0.227199
\(616\) 0 0
\(617\) 34.1232 1.37375 0.686875 0.726776i \(-0.258982\pi\)
0.686875 + 0.726776i \(0.258982\pi\)
\(618\) 0 0
\(619\) −9.13729 −0.367259 −0.183629 0.982996i \(-0.558785\pi\)
−0.183629 + 0.982996i \(0.558785\pi\)
\(620\) 0 0
\(621\) 28.0596 1.12599
\(622\) 0 0
\(623\) 3.51498 0.140825
\(624\) 0 0
\(625\) 23.3078 0.932313
\(626\) 0 0
\(627\) 19.2865 0.770229
\(628\) 0 0
\(629\) 18.8415 0.751260
\(630\) 0 0
\(631\) 17.3463 0.690543 0.345272 0.938503i \(-0.387787\pi\)
0.345272 + 0.938503i \(0.387787\pi\)
\(632\) 0 0
\(633\) 37.3682 1.48525
\(634\) 0 0
\(635\) −0.721481 −0.0286311
\(636\) 0 0
\(637\) −26.1805 −1.03731
\(638\) 0 0
\(639\) 9.54412 0.377560
\(640\) 0 0
\(641\) 4.45039 0.175780 0.0878899 0.996130i \(-0.471988\pi\)
0.0878899 + 0.996130i \(0.471988\pi\)
\(642\) 0 0
\(643\) 8.21021 0.323779 0.161889 0.986809i \(-0.448241\pi\)
0.161889 + 0.986809i \(0.448241\pi\)
\(644\) 0 0
\(645\) −0.544490 −0.0214393
\(646\) 0 0
\(647\) 23.1289 0.909292 0.454646 0.890672i \(-0.349766\pi\)
0.454646 + 0.890672i \(0.349766\pi\)
\(648\) 0 0
\(649\) 34.9290 1.37108
\(650\) 0 0
\(651\) −0.441375 −0.0172989
\(652\) 0 0
\(653\) 5.34044 0.208988 0.104494 0.994526i \(-0.466678\pi\)
0.104494 + 0.994526i \(0.466678\pi\)
\(654\) 0 0
\(655\) 3.00648 0.117473
\(656\) 0 0
\(657\) 11.1301 0.434225
\(658\) 0 0
\(659\) −25.7109 −1.00156 −0.500778 0.865576i \(-0.666953\pi\)
−0.500778 + 0.865576i \(0.666953\pi\)
\(660\) 0 0
\(661\) −7.28360 −0.283299 −0.141650 0.989917i \(-0.545241\pi\)
−0.141650 + 0.989917i \(0.545241\pi\)
\(662\) 0 0
\(663\) 36.1372 1.40345
\(664\) 0 0
\(665\) 0.473141 0.0183476
\(666\) 0 0
\(667\) −44.5830 −1.72626
\(668\) 0 0
\(669\) −22.6825 −0.876958
\(670\) 0 0
\(671\) 89.0949 3.43947
\(672\) 0 0
\(673\) −36.3831 −1.40247 −0.701233 0.712932i \(-0.747367\pi\)
−0.701233 + 0.712932i \(0.747367\pi\)
\(674\) 0 0
\(675\) −20.7160 −0.797358
\(676\) 0 0
\(677\) −29.9056 −1.14937 −0.574684 0.818376i \(-0.694875\pi\)
−0.574684 + 0.818376i \(0.694875\pi\)
\(678\) 0 0
\(679\) 9.43142 0.361945
\(680\) 0 0
\(681\) 56.9342 2.18172
\(682\) 0 0
\(683\) −5.12594 −0.196139 −0.0980694 0.995180i \(-0.531267\pi\)
−0.0980694 + 0.995180i \(0.531267\pi\)
\(684\) 0 0
\(685\) 4.06266 0.155226
\(686\) 0 0
\(687\) 37.4551 1.42900
\(688\) 0 0
\(689\) −11.0537 −0.421114
\(690\) 0 0
\(691\) −28.5616 −1.08653 −0.543267 0.839560i \(-0.682813\pi\)
−0.543267 + 0.839560i \(0.682813\pi\)
\(692\) 0 0
\(693\) −4.04455 −0.153640
\(694\) 0 0
\(695\) −2.46353 −0.0934469
\(696\) 0 0
\(697\) 37.9521 1.43754
\(698\) 0 0
\(699\) 50.2411 1.90029
\(700\) 0 0
\(701\) 9.07775 0.342862 0.171431 0.985196i \(-0.445161\pi\)
0.171431 + 0.985196i \(0.445161\pi\)
\(702\) 0 0
\(703\) 7.15667 0.269919
\(704\) 0 0
\(705\) 5.58315 0.210274
\(706\) 0 0
\(707\) −14.3281 −0.538862
\(708\) 0 0
\(709\) 2.17002 0.0814968 0.0407484 0.999169i \(-0.487026\pi\)
0.0407484 + 0.999169i \(0.487026\pi\)
\(710\) 0 0
\(711\) −8.57307 −0.321515
\(712\) 0 0
\(713\) −1.79564 −0.0672471
\(714\) 0 0
\(715\) 8.15535 0.304993
\(716\) 0 0
\(717\) −5.01908 −0.187441
\(718\) 0 0
\(719\) −11.4247 −0.426069 −0.213034 0.977045i \(-0.568335\pi\)
−0.213034 + 0.977045i \(0.568335\pi\)
\(720\) 0 0
\(721\) −7.38039 −0.274860
\(722\) 0 0
\(723\) −13.6795 −0.508748
\(724\) 0 0
\(725\) 32.9149 1.22243
\(726\) 0 0
\(727\) 37.4513 1.38899 0.694496 0.719497i \(-0.255628\pi\)
0.694496 + 0.719497i \(0.255628\pi\)
\(728\) 0 0
\(729\) 15.8817 0.588212
\(730\) 0 0
\(731\) −3.66759 −0.135651
\(732\) 0 0
\(733\) −33.3356 −1.23128 −0.615639 0.788028i \(-0.711102\pi\)
−0.615639 + 0.788028i \(0.711102\pi\)
\(734\) 0 0
\(735\) 4.16619 0.153672
\(736\) 0 0
\(737\) −50.6537 −1.86585
\(738\) 0 0
\(739\) −29.1025 −1.07055 −0.535277 0.844677i \(-0.679793\pi\)
−0.535277 + 0.844677i \(0.679793\pi\)
\(740\) 0 0
\(741\) 13.7262 0.504244
\(742\) 0 0
\(743\) 20.7059 0.759627 0.379814 0.925063i \(-0.375988\pi\)
0.379814 + 0.925063i \(0.375988\pi\)
\(744\) 0 0
\(745\) −0.858249 −0.0314438
\(746\) 0 0
\(747\) −12.8723 −0.470971
\(748\) 0 0
\(749\) −11.6024 −0.423941
\(750\) 0 0
\(751\) −25.8005 −0.941472 −0.470736 0.882274i \(-0.656012\pi\)
−0.470736 + 0.882274i \(0.656012\pi\)
\(752\) 0 0
\(753\) −6.44813 −0.234983
\(754\) 0 0
\(755\) −0.502808 −0.0182991
\(756\) 0 0
\(757\) −45.7420 −1.66252 −0.831261 0.555882i \(-0.812381\pi\)
−0.831261 + 0.555882i \(0.812381\pi\)
\(758\) 0 0
\(759\) −75.5629 −2.74276
\(760\) 0 0
\(761\) −15.2372 −0.552348 −0.276174 0.961108i \(-0.589067\pi\)
−0.276174 + 0.961108i \(0.589067\pi\)
\(762\) 0 0
\(763\) 3.18900 0.115450
\(764\) 0 0
\(765\) −1.25224 −0.0452748
\(766\) 0 0
\(767\) 24.8589 0.897603
\(768\) 0 0
\(769\) 42.5754 1.53531 0.767654 0.640865i \(-0.221424\pi\)
0.767654 + 0.640865i \(0.221424\pi\)
\(770\) 0 0
\(771\) −29.1033 −1.04813
\(772\) 0 0
\(773\) −39.1472 −1.40803 −0.704013 0.710187i \(-0.748610\pi\)
−0.704013 + 0.710187i \(0.748610\pi\)
\(774\) 0 0
\(775\) 1.32569 0.0476201
\(776\) 0 0
\(777\) −6.89216 −0.247255
\(778\) 0 0
\(779\) 14.4155 0.516490
\(780\) 0 0
\(781\) 66.6261 2.38407
\(782\) 0 0
\(783\) −28.5583 −1.02059
\(784\) 0 0
\(785\) −6.66512 −0.237888
\(786\) 0 0
\(787\) −3.22182 −0.114845 −0.0574227 0.998350i \(-0.518288\pi\)
−0.0574227 + 0.998350i \(0.518288\pi\)
\(788\) 0 0
\(789\) 17.4714 0.621997
\(790\) 0 0
\(791\) 7.80422 0.277486
\(792\) 0 0
\(793\) 63.4087 2.25171
\(794\) 0 0
\(795\) 1.75902 0.0623860
\(796\) 0 0
\(797\) 43.1582 1.52874 0.764371 0.644777i \(-0.223050\pi\)
0.764371 + 0.644777i \(0.223050\pi\)
\(798\) 0 0
\(799\) 37.6072 1.33045
\(800\) 0 0
\(801\) −3.53357 −0.124853
\(802\) 0 0
\(803\) 77.6974 2.74188
\(804\) 0 0
\(805\) −1.85373 −0.0653354
\(806\) 0 0
\(807\) 24.2174 0.852494
\(808\) 0 0
\(809\) 39.5555 1.39070 0.695348 0.718673i \(-0.255250\pi\)
0.695348 + 0.718673i \(0.255250\pi\)
\(810\) 0 0
\(811\) −19.7483 −0.693455 −0.346728 0.937966i \(-0.612707\pi\)
−0.346728 + 0.937966i \(0.612707\pi\)
\(812\) 0 0
\(813\) −6.53232 −0.229099
\(814\) 0 0
\(815\) 1.71284 0.0599982
\(816\) 0 0
\(817\) −1.39308 −0.0487378
\(818\) 0 0
\(819\) −2.87850 −0.100583
\(820\) 0 0
\(821\) −26.9925 −0.942046 −0.471023 0.882121i \(-0.656115\pi\)
−0.471023 + 0.882121i \(0.656115\pi\)
\(822\) 0 0
\(823\) −47.4789 −1.65501 −0.827505 0.561458i \(-0.810241\pi\)
−0.827505 + 0.561458i \(0.810241\pi\)
\(824\) 0 0
\(825\) 55.7868 1.94225
\(826\) 0 0
\(827\) 50.5127 1.75650 0.878249 0.478204i \(-0.158712\pi\)
0.878249 + 0.478204i \(0.158712\pi\)
\(828\) 0 0
\(829\) −32.6321 −1.13336 −0.566679 0.823939i \(-0.691772\pi\)
−0.566679 + 0.823939i \(0.691772\pi\)
\(830\) 0 0
\(831\) 21.2937 0.738669
\(832\) 0 0
\(833\) 28.0628 0.972318
\(834\) 0 0
\(835\) −5.81025 −0.201072
\(836\) 0 0
\(837\) −1.15022 −0.0397575
\(838\) 0 0
\(839\) 18.2513 0.630103 0.315052 0.949075i \(-0.397978\pi\)
0.315052 + 0.949075i \(0.397978\pi\)
\(840\) 0 0
\(841\) 16.3754 0.564668
\(842\) 0 0
\(843\) 24.9005 0.857619
\(844\) 0 0
\(845\) 1.42116 0.0488893
\(846\) 0 0
\(847\) −19.0964 −0.656159
\(848\) 0 0
\(849\) −56.4012 −1.93568
\(850\) 0 0
\(851\) −28.0392 −0.961173
\(852\) 0 0
\(853\) −8.54962 −0.292734 −0.146367 0.989230i \(-0.546758\pi\)
−0.146367 + 0.989230i \(0.546758\pi\)
\(854\) 0 0
\(855\) −0.475645 −0.0162667
\(856\) 0 0
\(857\) −48.2767 −1.64910 −0.824551 0.565788i \(-0.808572\pi\)
−0.824551 + 0.565788i \(0.808572\pi\)
\(858\) 0 0
\(859\) −52.1046 −1.77779 −0.888893 0.458114i \(-0.848525\pi\)
−0.888893 + 0.458114i \(0.848525\pi\)
\(860\) 0 0
\(861\) −13.8828 −0.473123
\(862\) 0 0
\(863\) −31.5867 −1.07522 −0.537612 0.843192i \(-0.680673\pi\)
−0.537612 + 0.843192i \(0.680673\pi\)
\(864\) 0 0
\(865\) −3.93625 −0.133837
\(866\) 0 0
\(867\) −5.44344 −0.184869
\(868\) 0 0
\(869\) −59.8474 −2.03018
\(870\) 0 0
\(871\) −36.0502 −1.22151
\(872\) 0 0
\(873\) −9.48132 −0.320894
\(874\) 0 0
\(875\) 2.76899 0.0936090
\(876\) 0 0
\(877\) 2.58569 0.0873126 0.0436563 0.999047i \(-0.486099\pi\)
0.0436563 + 0.999047i \(0.486099\pi\)
\(878\) 0 0
\(879\) 51.3621 1.73240
\(880\) 0 0
\(881\) 42.1813 1.42113 0.710563 0.703634i \(-0.248441\pi\)
0.710563 + 0.703634i \(0.248441\pi\)
\(882\) 0 0
\(883\) 31.0086 1.04352 0.521761 0.853091i \(-0.325275\pi\)
0.521761 + 0.853091i \(0.325275\pi\)
\(884\) 0 0
\(885\) −3.95588 −0.132976
\(886\) 0 0
\(887\) −54.8971 −1.84326 −0.921631 0.388067i \(-0.873143\pi\)
−0.921631 + 0.388067i \(0.873143\pi\)
\(888\) 0 0
\(889\) 1.77769 0.0596219
\(890\) 0 0
\(891\) −63.0090 −2.11088
\(892\) 0 0
\(893\) 14.2845 0.478014
\(894\) 0 0
\(895\) −2.27491 −0.0760418
\(896\) 0 0
\(897\) −53.7780 −1.79560
\(898\) 0 0
\(899\) 1.82755 0.0609522
\(900\) 0 0
\(901\) 11.8485 0.394730
\(902\) 0 0
\(903\) 1.34159 0.0446455
\(904\) 0 0
\(905\) 2.59118 0.0861337
\(906\) 0 0
\(907\) 14.0123 0.465272 0.232636 0.972564i \(-0.425265\pi\)
0.232636 + 0.972564i \(0.425265\pi\)
\(908\) 0 0
\(909\) 14.4039 0.477746
\(910\) 0 0
\(911\) 27.9212 0.925070 0.462535 0.886601i \(-0.346940\pi\)
0.462535 + 0.886601i \(0.346940\pi\)
\(912\) 0 0
\(913\) −89.8594 −2.97391
\(914\) 0 0
\(915\) −10.0904 −0.333580
\(916\) 0 0
\(917\) −7.40782 −0.244628
\(918\) 0 0
\(919\) 17.4349 0.575126 0.287563 0.957762i \(-0.407155\pi\)
0.287563 + 0.957762i \(0.407155\pi\)
\(920\) 0 0
\(921\) −36.2407 −1.19417
\(922\) 0 0
\(923\) 47.4177 1.56077
\(924\) 0 0
\(925\) 20.7009 0.680642
\(926\) 0 0
\(927\) 7.41944 0.243686
\(928\) 0 0
\(929\) −0.571374 −0.0187462 −0.00937309 0.999956i \(-0.502984\pi\)
−0.00937309 + 0.999956i \(0.502984\pi\)
\(930\) 0 0
\(931\) 10.6592 0.349342
\(932\) 0 0
\(933\) 17.5988 0.576159
\(934\) 0 0
\(935\) −8.74170 −0.285884
\(936\) 0 0
\(937\) −20.3397 −0.664469 −0.332234 0.943197i \(-0.607802\pi\)
−0.332234 + 0.943197i \(0.607802\pi\)
\(938\) 0 0
\(939\) 2.48292 0.0810271
\(940\) 0 0
\(941\) −0.0177050 −0.000577166 0 −0.000288583 1.00000i \(-0.500092\pi\)
−0.000288583 1.00000i \(0.500092\pi\)
\(942\) 0 0
\(943\) −56.4789 −1.83921
\(944\) 0 0
\(945\) −1.18743 −0.0386272
\(946\) 0 0
\(947\) 15.6708 0.509233 0.254616 0.967042i \(-0.418051\pi\)
0.254616 + 0.967042i \(0.418051\pi\)
\(948\) 0 0
\(949\) 55.2971 1.79502
\(950\) 0 0
\(951\) 35.5180 1.15175
\(952\) 0 0
\(953\) −23.4298 −0.758964 −0.379482 0.925199i \(-0.623898\pi\)
−0.379482 + 0.925199i \(0.623898\pi\)
\(954\) 0 0
\(955\) 2.90503 0.0940045
\(956\) 0 0
\(957\) 76.9058 2.48601
\(958\) 0 0
\(959\) −10.0102 −0.323246
\(960\) 0 0
\(961\) −30.9264 −0.997626
\(962\) 0 0
\(963\) 11.6638 0.375859
\(964\) 0 0
\(965\) 2.76507 0.0890108
\(966\) 0 0
\(967\) −25.3559 −0.815390 −0.407695 0.913118i \(-0.633667\pi\)
−0.407695 + 0.913118i \(0.633667\pi\)
\(968\) 0 0
\(969\) −14.7131 −0.472651
\(970\) 0 0
\(971\) −10.0972 −0.324034 −0.162017 0.986788i \(-0.551800\pi\)
−0.162017 + 0.986788i \(0.551800\pi\)
\(972\) 0 0
\(973\) 6.07000 0.194595
\(974\) 0 0
\(975\) 39.7034 1.27153
\(976\) 0 0
\(977\) −3.26710 −0.104524 −0.0522619 0.998633i \(-0.516643\pi\)
−0.0522619 + 0.998633i \(0.516643\pi\)
\(978\) 0 0
\(979\) −24.6674 −0.788372
\(980\) 0 0
\(981\) −3.20588 −0.102356
\(982\) 0 0
\(983\) 25.2017 0.803809 0.401905 0.915682i \(-0.368348\pi\)
0.401905 + 0.915682i \(0.368348\pi\)
\(984\) 0 0
\(985\) 3.97293 0.126588
\(986\) 0 0
\(987\) −13.7566 −0.437877
\(988\) 0 0
\(989\) 5.45798 0.173554
\(990\) 0 0
\(991\) −9.06526 −0.287967 −0.143984 0.989580i \(-0.545991\pi\)
−0.143984 + 0.989580i \(0.545991\pi\)
\(992\) 0 0
\(993\) 38.8474 1.23279
\(994\) 0 0
\(995\) 1.41486 0.0448541
\(996\) 0 0
\(997\) −17.8356 −0.564860 −0.282430 0.959288i \(-0.591140\pi\)
−0.282430 + 0.959288i \(0.591140\pi\)
\(998\) 0 0
\(999\) −17.9610 −0.568260
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 \(a_p\))