Properties

Label 8048.2.a.v.1.1
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 1.1
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-3.18633 q^{3}\) \(-1.57145 q^{5}\) \(+3.06067 q^{7}\) \(+7.15268 q^{9}\) \(+O(q^{10})\) \(q\)\(-3.18633 q^{3}\) \(-1.57145 q^{5}\) \(+3.06067 q^{7}\) \(+7.15268 q^{9}\) \(-0.545150 q^{11}\) \(-1.64668 q^{13}\) \(+5.00716 q^{15}\) \(-3.65160 q^{17}\) \(+2.61130 q^{19}\) \(-9.75229 q^{21}\) \(+3.92971 q^{23}\) \(-2.53054 q^{25}\) \(-13.2318 q^{27}\) \(+7.11113 q^{29}\) \(+7.75620 q^{31}\) \(+1.73703 q^{33}\) \(-4.80969 q^{35}\) \(-9.57716 q^{37}\) \(+5.24686 q^{39}\) \(-1.04104 q^{41}\) \(-10.0422 q^{43}\) \(-11.2401 q^{45}\) \(+2.76111 q^{47}\) \(+2.36768 q^{49}\) \(+11.6352 q^{51}\) \(-9.38236 q^{53}\) \(+0.856678 q^{55}\) \(-8.32047 q^{57}\) \(+2.80183 q^{59}\) \(+5.26624 q^{61}\) \(+21.8920 q^{63}\) \(+2.58768 q^{65}\) \(-7.28320 q^{67}\) \(-12.5214 q^{69}\) \(+3.46671 q^{71}\) \(-15.1421 q^{73}\) \(+8.06313 q^{75}\) \(-1.66852 q^{77}\) \(+9.12623 q^{79}\) \(+20.7028 q^{81}\) \(-5.33358 q^{83}\) \(+5.73832 q^{85}\) \(-22.6584 q^{87}\) \(-12.2732 q^{89}\) \(-5.03994 q^{91}\) \(-24.7138 q^{93}\) \(-4.10354 q^{95}\) \(+12.0744 q^{97}\) \(-3.89929 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −3.18633 −1.83963 −0.919814 0.392356i \(-0.871660\pi\)
−0.919814 + 0.392356i \(0.871660\pi\)
\(4\) 0 0
\(5\) −1.57145 −0.702775 −0.351387 0.936230i \(-0.614290\pi\)
−0.351387 + 0.936230i \(0.614290\pi\)
\(6\) 0 0
\(7\) 3.06067 1.15682 0.578412 0.815745i \(-0.303673\pi\)
0.578412 + 0.815745i \(0.303673\pi\)
\(8\) 0 0
\(9\) 7.15268 2.38423
\(10\) 0 0
\(11\) −0.545150 −0.164369 −0.0821845 0.996617i \(-0.526190\pi\)
−0.0821845 + 0.996617i \(0.526190\pi\)
\(12\) 0 0
\(13\) −1.64668 −0.456707 −0.228353 0.973578i \(-0.573334\pi\)
−0.228353 + 0.973578i \(0.573334\pi\)
\(14\) 0 0
\(15\) 5.00716 1.29284
\(16\) 0 0
\(17\) −3.65160 −0.885644 −0.442822 0.896610i \(-0.646023\pi\)
−0.442822 + 0.896610i \(0.646023\pi\)
\(18\) 0 0
\(19\) 2.61130 0.599074 0.299537 0.954085i \(-0.403168\pi\)
0.299537 + 0.954085i \(0.403168\pi\)
\(20\) 0 0
\(21\) −9.75229 −2.12812
\(22\) 0 0
\(23\) 3.92971 0.819402 0.409701 0.912220i \(-0.365633\pi\)
0.409701 + 0.912220i \(0.365633\pi\)
\(24\) 0 0
\(25\) −2.53054 −0.506108
\(26\) 0 0
\(27\) −13.2318 −2.54646
\(28\) 0 0
\(29\) 7.11113 1.32050 0.660252 0.751044i \(-0.270450\pi\)
0.660252 + 0.751044i \(0.270450\pi\)
\(30\) 0 0
\(31\) 7.75620 1.39305 0.696527 0.717531i \(-0.254728\pi\)
0.696527 + 0.717531i \(0.254728\pi\)
\(32\) 0 0
\(33\) 1.73703 0.302378
\(34\) 0 0
\(35\) −4.80969 −0.812986
\(36\) 0 0
\(37\) −9.57716 −1.57448 −0.787238 0.616650i \(-0.788490\pi\)
−0.787238 + 0.616650i \(0.788490\pi\)
\(38\) 0 0
\(39\) 5.24686 0.840170
\(40\) 0 0
\(41\) −1.04104 −0.162583 −0.0812917 0.996690i \(-0.525905\pi\)
−0.0812917 + 0.996690i \(0.525905\pi\)
\(42\) 0 0
\(43\) −10.0422 −1.53141 −0.765707 0.643190i \(-0.777611\pi\)
−0.765707 + 0.643190i \(0.777611\pi\)
\(44\) 0 0
\(45\) −11.2401 −1.67557
\(46\) 0 0
\(47\) 2.76111 0.402749 0.201375 0.979514i \(-0.435459\pi\)
0.201375 + 0.979514i \(0.435459\pi\)
\(48\) 0 0
\(49\) 2.36768 0.338240
\(50\) 0 0
\(51\) 11.6352 1.62925
\(52\) 0 0
\(53\) −9.38236 −1.28877 −0.644383 0.764703i \(-0.722886\pi\)
−0.644383 + 0.764703i \(0.722886\pi\)
\(54\) 0 0
\(55\) 0.856678 0.115514
\(56\) 0 0
\(57\) −8.32047 −1.10207
\(58\) 0 0
\(59\) 2.80183 0.364767 0.182383 0.983228i \(-0.441619\pi\)
0.182383 + 0.983228i \(0.441619\pi\)
\(60\) 0 0
\(61\) 5.26624 0.674273 0.337136 0.941456i \(-0.390542\pi\)
0.337136 + 0.941456i \(0.390542\pi\)
\(62\) 0 0
\(63\) 21.8920 2.75813
\(64\) 0 0
\(65\) 2.58768 0.320962
\(66\) 0 0
\(67\) −7.28320 −0.889784 −0.444892 0.895584i \(-0.646758\pi\)
−0.444892 + 0.895584i \(0.646758\pi\)
\(68\) 0 0
\(69\) −12.5214 −1.50739
\(70\) 0 0
\(71\) 3.46671 0.411422 0.205711 0.978613i \(-0.434049\pi\)
0.205711 + 0.978613i \(0.434049\pi\)
\(72\) 0 0
\(73\) −15.1421 −1.77225 −0.886123 0.463450i \(-0.846612\pi\)
−0.886123 + 0.463450i \(0.846612\pi\)
\(74\) 0 0
\(75\) 8.06313 0.931050
\(76\) 0 0
\(77\) −1.66852 −0.190146
\(78\) 0 0
\(79\) 9.12623 1.02678 0.513391 0.858155i \(-0.328389\pi\)
0.513391 + 0.858155i \(0.328389\pi\)
\(80\) 0 0
\(81\) 20.7028 2.30031
\(82\) 0 0
\(83\) −5.33358 −0.585436 −0.292718 0.956199i \(-0.594560\pi\)
−0.292718 + 0.956199i \(0.594560\pi\)
\(84\) 0 0
\(85\) 5.73832 0.622408
\(86\) 0 0
\(87\) −22.6584 −2.42923
\(88\) 0 0
\(89\) −12.2732 −1.30096 −0.650481 0.759523i \(-0.725432\pi\)
−0.650481 + 0.759523i \(0.725432\pi\)
\(90\) 0 0
\(91\) −5.03994 −0.528329
\(92\) 0 0
\(93\) −24.7138 −2.56270
\(94\) 0 0
\(95\) −4.10354 −0.421014
\(96\) 0 0
\(97\) 12.0744 1.22597 0.612983 0.790096i \(-0.289970\pi\)
0.612983 + 0.790096i \(0.289970\pi\)
\(98\) 0 0
\(99\) −3.89929 −0.391893
\(100\) 0 0
\(101\) 18.6218 1.85294 0.926468 0.376374i \(-0.122829\pi\)
0.926468 + 0.376374i \(0.122829\pi\)
\(102\) 0 0
\(103\) 1.34086 0.132119 0.0660596 0.997816i \(-0.478957\pi\)
0.0660596 + 0.997816i \(0.478957\pi\)
\(104\) 0 0
\(105\) 15.3252 1.49559
\(106\) 0 0
\(107\) −0.0262517 −0.00253785 −0.00126892 0.999999i \(-0.500404\pi\)
−0.00126892 + 0.999999i \(0.500404\pi\)
\(108\) 0 0
\(109\) 0.350614 0.0335828 0.0167914 0.999859i \(-0.494655\pi\)
0.0167914 + 0.999859i \(0.494655\pi\)
\(110\) 0 0
\(111\) 30.5160 2.89645
\(112\) 0 0
\(113\) 2.16637 0.203795 0.101897 0.994795i \(-0.467509\pi\)
0.101897 + 0.994795i \(0.467509\pi\)
\(114\) 0 0
\(115\) −6.17535 −0.575855
\(116\) 0 0
\(117\) −11.7782 −1.08889
\(118\) 0 0
\(119\) −11.1763 −1.02453
\(120\) 0 0
\(121\) −10.7028 −0.972983
\(122\) 0 0
\(123\) 3.31710 0.299093
\(124\) 0 0
\(125\) 11.8339 1.05845
\(126\) 0 0
\(127\) 3.24877 0.288282 0.144141 0.989557i \(-0.453958\pi\)
0.144141 + 0.989557i \(0.453958\pi\)
\(128\) 0 0
\(129\) 31.9976 2.81723
\(130\) 0 0
\(131\) 5.29059 0.462241 0.231120 0.972925i \(-0.425761\pi\)
0.231120 + 0.972925i \(0.425761\pi\)
\(132\) 0 0
\(133\) 7.99233 0.693023
\(134\) 0 0
\(135\) 20.7932 1.78959
\(136\) 0 0
\(137\) 16.5680 1.41550 0.707751 0.706462i \(-0.249710\pi\)
0.707751 + 0.706462i \(0.249710\pi\)
\(138\) 0 0
\(139\) 14.2940 1.21240 0.606202 0.795311i \(-0.292692\pi\)
0.606202 + 0.795311i \(0.292692\pi\)
\(140\) 0 0
\(141\) −8.79780 −0.740909
\(142\) 0 0
\(143\) 0.897688 0.0750685
\(144\) 0 0
\(145\) −11.1748 −0.928016
\(146\) 0 0
\(147\) −7.54421 −0.622236
\(148\) 0 0
\(149\) 2.98494 0.244536 0.122268 0.992497i \(-0.460983\pi\)
0.122268 + 0.992497i \(0.460983\pi\)
\(150\) 0 0
\(151\) 11.2406 0.914744 0.457372 0.889276i \(-0.348791\pi\)
0.457372 + 0.889276i \(0.348791\pi\)
\(152\) 0 0
\(153\) −26.1188 −2.11158
\(154\) 0 0
\(155\) −12.1885 −0.979003
\(156\) 0 0
\(157\) 11.9185 0.951201 0.475601 0.879661i \(-0.342231\pi\)
0.475601 + 0.879661i \(0.342231\pi\)
\(158\) 0 0
\(159\) 29.8953 2.37085
\(160\) 0 0
\(161\) 12.0275 0.947903
\(162\) 0 0
\(163\) −11.8331 −0.926840 −0.463420 0.886139i \(-0.653378\pi\)
−0.463420 + 0.886139i \(0.653378\pi\)
\(164\) 0 0
\(165\) −2.72966 −0.212503
\(166\) 0 0
\(167\) 5.94973 0.460404 0.230202 0.973143i \(-0.426061\pi\)
0.230202 + 0.973143i \(0.426061\pi\)
\(168\) 0 0
\(169\) −10.2884 −0.791419
\(170\) 0 0
\(171\) 18.6778 1.42833
\(172\) 0 0
\(173\) −8.47330 −0.644213 −0.322107 0.946703i \(-0.604391\pi\)
−0.322107 + 0.946703i \(0.604391\pi\)
\(174\) 0 0
\(175\) −7.74514 −0.585477
\(176\) 0 0
\(177\) −8.92754 −0.671035
\(178\) 0 0
\(179\) 18.8938 1.41219 0.706094 0.708118i \(-0.250455\pi\)
0.706094 + 0.708118i \(0.250455\pi\)
\(180\) 0 0
\(181\) 8.01854 0.596013 0.298007 0.954564i \(-0.403678\pi\)
0.298007 + 0.954564i \(0.403678\pi\)
\(182\) 0 0
\(183\) −16.7800 −1.24041
\(184\) 0 0
\(185\) 15.0500 1.10650
\(186\) 0 0
\(187\) 1.99067 0.145572
\(188\) 0 0
\(189\) −40.4982 −2.94581
\(190\) 0 0
\(191\) −24.1165 −1.74501 −0.872503 0.488609i \(-0.837504\pi\)
−0.872503 + 0.488609i \(0.837504\pi\)
\(192\) 0 0
\(193\) −8.50608 −0.612281 −0.306140 0.951986i \(-0.599038\pi\)
−0.306140 + 0.951986i \(0.599038\pi\)
\(194\) 0 0
\(195\) −8.24519 −0.590450
\(196\) 0 0
\(197\) −25.3232 −1.80420 −0.902101 0.431524i \(-0.857976\pi\)
−0.902101 + 0.431524i \(0.857976\pi\)
\(198\) 0 0
\(199\) −3.62162 −0.256730 −0.128365 0.991727i \(-0.540973\pi\)
−0.128365 + 0.991727i \(0.540973\pi\)
\(200\) 0 0
\(201\) 23.2066 1.63687
\(202\) 0 0
\(203\) 21.7648 1.52759
\(204\) 0 0
\(205\) 1.63595 0.114259
\(206\) 0 0
\(207\) 28.1080 1.95364
\(208\) 0 0
\(209\) −1.42355 −0.0984692
\(210\) 0 0
\(211\) −3.15954 −0.217512 −0.108756 0.994068i \(-0.534687\pi\)
−0.108756 + 0.994068i \(0.534687\pi\)
\(212\) 0 0
\(213\) −11.0461 −0.756864
\(214\) 0 0
\(215\) 15.7808 1.07624
\(216\) 0 0
\(217\) 23.7391 1.61152
\(218\) 0 0
\(219\) 48.2476 3.26027
\(220\) 0 0
\(221\) 6.01302 0.404480
\(222\) 0 0
\(223\) −1.82132 −0.121965 −0.0609824 0.998139i \(-0.519423\pi\)
−0.0609824 + 0.998139i \(0.519423\pi\)
\(224\) 0 0
\(225\) −18.1001 −1.20668
\(226\) 0 0
\(227\) 19.8468 1.31728 0.658638 0.752460i \(-0.271133\pi\)
0.658638 + 0.752460i \(0.271133\pi\)
\(228\) 0 0
\(229\) −15.0063 −0.991645 −0.495822 0.868424i \(-0.665133\pi\)
−0.495822 + 0.868424i \(0.665133\pi\)
\(230\) 0 0
\(231\) 5.31646 0.349798
\(232\) 0 0
\(233\) −7.99972 −0.524079 −0.262039 0.965057i \(-0.584395\pi\)
−0.262039 + 0.965057i \(0.584395\pi\)
\(234\) 0 0
\(235\) −4.33895 −0.283042
\(236\) 0 0
\(237\) −29.0792 −1.88889
\(238\) 0 0
\(239\) 10.0846 0.652318 0.326159 0.945315i \(-0.394246\pi\)
0.326159 + 0.945315i \(0.394246\pi\)
\(240\) 0 0
\(241\) 8.19257 0.527730 0.263865 0.964560i \(-0.415003\pi\)
0.263865 + 0.964560i \(0.415003\pi\)
\(242\) 0 0
\(243\) −26.2706 −1.68526
\(244\) 0 0
\(245\) −3.72070 −0.237707
\(246\) 0 0
\(247\) −4.29998 −0.273601
\(248\) 0 0
\(249\) 16.9945 1.07698
\(250\) 0 0
\(251\) −14.1224 −0.891396 −0.445698 0.895183i \(-0.647044\pi\)
−0.445698 + 0.895183i \(0.647044\pi\)
\(252\) 0 0
\(253\) −2.14228 −0.134684
\(254\) 0 0
\(255\) −18.2842 −1.14500
\(256\) 0 0
\(257\) 1.57153 0.0980294 0.0490147 0.998798i \(-0.484392\pi\)
0.0490147 + 0.998798i \(0.484392\pi\)
\(258\) 0 0
\(259\) −29.3125 −1.82139
\(260\) 0 0
\(261\) 50.8637 3.14838
\(262\) 0 0
\(263\) −5.79538 −0.357358 −0.178679 0.983907i \(-0.557182\pi\)
−0.178679 + 0.983907i \(0.557182\pi\)
\(264\) 0 0
\(265\) 14.7439 0.905713
\(266\) 0 0
\(267\) 39.1066 2.39328
\(268\) 0 0
\(269\) 1.77372 0.108145 0.0540727 0.998537i \(-0.482780\pi\)
0.0540727 + 0.998537i \(0.482780\pi\)
\(270\) 0 0
\(271\) −16.7882 −1.01981 −0.509905 0.860231i \(-0.670319\pi\)
−0.509905 + 0.860231i \(0.670319\pi\)
\(272\) 0 0
\(273\) 16.0589 0.971928
\(274\) 0 0
\(275\) 1.37952 0.0831885
\(276\) 0 0
\(277\) 15.1740 0.911716 0.455858 0.890053i \(-0.349333\pi\)
0.455858 + 0.890053i \(0.349333\pi\)
\(278\) 0 0
\(279\) 55.4776 3.32136
\(280\) 0 0
\(281\) −31.1977 −1.86110 −0.930548 0.366170i \(-0.880669\pi\)
−0.930548 + 0.366170i \(0.880669\pi\)
\(282\) 0 0
\(283\) 14.6509 0.870908 0.435454 0.900211i \(-0.356588\pi\)
0.435454 + 0.900211i \(0.356588\pi\)
\(284\) 0 0
\(285\) 13.0752 0.774509
\(286\) 0 0
\(287\) −3.18628 −0.188080
\(288\) 0 0
\(289\) −3.66579 −0.215635
\(290\) 0 0
\(291\) −38.4729 −2.25532
\(292\) 0 0
\(293\) 6.59868 0.385499 0.192749 0.981248i \(-0.438260\pi\)
0.192749 + 0.981248i \(0.438260\pi\)
\(294\) 0 0
\(295\) −4.40293 −0.256349
\(296\) 0 0
\(297\) 7.21333 0.418560
\(298\) 0 0
\(299\) −6.47098 −0.374226
\(300\) 0 0
\(301\) −30.7357 −1.77158
\(302\) 0 0
\(303\) −59.3351 −3.40871
\(304\) 0 0
\(305\) −8.27564 −0.473862
\(306\) 0 0
\(307\) −27.4053 −1.56410 −0.782052 0.623213i \(-0.785827\pi\)
−0.782052 + 0.623213i \(0.785827\pi\)
\(308\) 0 0
\(309\) −4.27243 −0.243050
\(310\) 0 0
\(311\) −2.28546 −0.129596 −0.0647982 0.997898i \(-0.520640\pi\)
−0.0647982 + 0.997898i \(0.520640\pi\)
\(312\) 0 0
\(313\) 21.2333 1.20018 0.600090 0.799933i \(-0.295132\pi\)
0.600090 + 0.799933i \(0.295132\pi\)
\(314\) 0 0
\(315\) −34.4022 −1.93834
\(316\) 0 0
\(317\) 27.7858 1.56060 0.780302 0.625403i \(-0.215065\pi\)
0.780302 + 0.625403i \(0.215065\pi\)
\(318\) 0 0
\(319\) −3.87664 −0.217050
\(320\) 0 0
\(321\) 0.0836465 0.00466869
\(322\) 0 0
\(323\) −9.53545 −0.530566
\(324\) 0 0
\(325\) 4.16699 0.231143
\(326\) 0 0
\(327\) −1.11717 −0.0617798
\(328\) 0 0
\(329\) 8.45084 0.465910
\(330\) 0 0
\(331\) −28.7972 −1.58284 −0.791418 0.611275i \(-0.790657\pi\)
−0.791418 + 0.611275i \(0.790657\pi\)
\(332\) 0 0
\(333\) −68.5024 −3.75391
\(334\) 0 0
\(335\) 11.4452 0.625318
\(336\) 0 0
\(337\) 14.5387 0.791974 0.395987 0.918256i \(-0.370402\pi\)
0.395987 + 0.918256i \(0.370402\pi\)
\(338\) 0 0
\(339\) −6.90275 −0.374906
\(340\) 0 0
\(341\) −4.22829 −0.228975
\(342\) 0 0
\(343\) −14.1780 −0.765539
\(344\) 0 0
\(345\) 19.6767 1.05936
\(346\) 0 0
\(347\) −4.66898 −0.250644 −0.125322 0.992116i \(-0.539996\pi\)
−0.125322 + 0.992116i \(0.539996\pi\)
\(348\) 0 0
\(349\) −7.22552 −0.386773 −0.193387 0.981123i \(-0.561947\pi\)
−0.193387 + 0.981123i \(0.561947\pi\)
\(350\) 0 0
\(351\) 21.7886 1.16299
\(352\) 0 0
\(353\) 4.51906 0.240525 0.120263 0.992742i \(-0.461626\pi\)
0.120263 + 0.992742i \(0.461626\pi\)
\(354\) 0 0
\(355\) −5.44776 −0.289137
\(356\) 0 0
\(357\) 35.6115 1.88476
\(358\) 0 0
\(359\) 12.1764 0.642644 0.321322 0.946970i \(-0.395873\pi\)
0.321322 + 0.946970i \(0.395873\pi\)
\(360\) 0 0
\(361\) −12.1811 −0.641110
\(362\) 0 0
\(363\) 34.1027 1.78993
\(364\) 0 0
\(365\) 23.7951 1.24549
\(366\) 0 0
\(367\) −30.4937 −1.59176 −0.795878 0.605457i \(-0.792990\pi\)
−0.795878 + 0.605457i \(0.792990\pi\)
\(368\) 0 0
\(369\) −7.44624 −0.387636
\(370\) 0 0
\(371\) −28.7163 −1.49088
\(372\) 0 0
\(373\) −26.7772 −1.38647 −0.693235 0.720711i \(-0.743815\pi\)
−0.693235 + 0.720711i \(0.743815\pi\)
\(374\) 0 0
\(375\) −37.7066 −1.94716
\(376\) 0 0
\(377\) −11.7098 −0.603083
\(378\) 0 0
\(379\) −18.4204 −0.946193 −0.473096 0.881011i \(-0.656864\pi\)
−0.473096 + 0.881011i \(0.656864\pi\)
\(380\) 0 0
\(381\) −10.3516 −0.530331
\(382\) 0 0
\(383\) 12.8232 0.655236 0.327618 0.944810i \(-0.393754\pi\)
0.327618 + 0.944810i \(0.393754\pi\)
\(384\) 0 0
\(385\) 2.62200 0.133630
\(386\) 0 0
\(387\) −71.8283 −3.65124
\(388\) 0 0
\(389\) 5.97406 0.302897 0.151448 0.988465i \(-0.451606\pi\)
0.151448 + 0.988465i \(0.451606\pi\)
\(390\) 0 0
\(391\) −14.3498 −0.725698
\(392\) 0 0
\(393\) −16.8575 −0.850351
\(394\) 0 0
\(395\) −14.3414 −0.721596
\(396\) 0 0
\(397\) 4.22139 0.211866 0.105933 0.994373i \(-0.466217\pi\)
0.105933 + 0.994373i \(0.466217\pi\)
\(398\) 0 0
\(399\) −25.4662 −1.27490
\(400\) 0 0
\(401\) −24.8341 −1.24015 −0.620077 0.784541i \(-0.712899\pi\)
−0.620077 + 0.784541i \(0.712899\pi\)
\(402\) 0 0
\(403\) −12.7720 −0.636217
\(404\) 0 0
\(405\) −32.5335 −1.61660
\(406\) 0 0
\(407\) 5.22099 0.258795
\(408\) 0 0
\(409\) −7.51909 −0.371795 −0.185897 0.982569i \(-0.559519\pi\)
−0.185897 + 0.982569i \(0.559519\pi\)
\(410\) 0 0
\(411\) −52.7912 −2.60400
\(412\) 0 0
\(413\) 8.57546 0.421971
\(414\) 0 0
\(415\) 8.38146 0.411430
\(416\) 0 0
\(417\) −45.5454 −2.23037
\(418\) 0 0
\(419\) −30.7864 −1.50402 −0.752008 0.659154i \(-0.770915\pi\)
−0.752008 + 0.659154i \(0.770915\pi\)
\(420\) 0 0
\(421\) −36.6540 −1.78641 −0.893203 0.449654i \(-0.851547\pi\)
−0.893203 + 0.449654i \(0.851547\pi\)
\(422\) 0 0
\(423\) 19.7493 0.960246
\(424\) 0 0
\(425\) 9.24053 0.448231
\(426\) 0 0
\(427\) 16.1182 0.780014
\(428\) 0 0
\(429\) −2.86033 −0.138098
\(430\) 0 0
\(431\) 6.47534 0.311906 0.155953 0.987764i \(-0.450155\pi\)
0.155953 + 0.987764i \(0.450155\pi\)
\(432\) 0 0
\(433\) −5.97327 −0.287057 −0.143529 0.989646i \(-0.545845\pi\)
−0.143529 + 0.989646i \(0.545845\pi\)
\(434\) 0 0
\(435\) 35.6066 1.70720
\(436\) 0 0
\(437\) 10.2617 0.490882
\(438\) 0 0
\(439\) 12.5237 0.597724 0.298862 0.954296i \(-0.403393\pi\)
0.298862 + 0.954296i \(0.403393\pi\)
\(440\) 0 0
\(441\) 16.9353 0.806442
\(442\) 0 0
\(443\) 28.1272 1.33636 0.668182 0.743997i \(-0.267073\pi\)
0.668182 + 0.743997i \(0.267073\pi\)
\(444\) 0 0
\(445\) 19.2868 0.914282
\(446\) 0 0
\(447\) −9.51099 −0.449855
\(448\) 0 0
\(449\) 3.84589 0.181499 0.0907493 0.995874i \(-0.471074\pi\)
0.0907493 + 0.995874i \(0.471074\pi\)
\(450\) 0 0
\(451\) 0.567524 0.0267237
\(452\) 0 0
\(453\) −35.8161 −1.68279
\(454\) 0 0
\(455\) 7.92002 0.371296
\(456\) 0 0
\(457\) 29.3780 1.37424 0.687122 0.726542i \(-0.258874\pi\)
0.687122 + 0.726542i \(0.258874\pi\)
\(458\) 0 0
\(459\) 48.3173 2.25526
\(460\) 0 0
\(461\) 11.2331 0.523179 0.261590 0.965179i \(-0.415753\pi\)
0.261590 + 0.965179i \(0.415753\pi\)
\(462\) 0 0
\(463\) −6.77063 −0.314658 −0.157329 0.987546i \(-0.550288\pi\)
−0.157329 + 0.987546i \(0.550288\pi\)
\(464\) 0 0
\(465\) 38.8365 1.80100
\(466\) 0 0
\(467\) −37.2784 −1.72504 −0.862518 0.506026i \(-0.831114\pi\)
−0.862518 + 0.506026i \(0.831114\pi\)
\(468\) 0 0
\(469\) −22.2914 −1.02932
\(470\) 0 0
\(471\) −37.9763 −1.74986
\(472\) 0 0
\(473\) 5.47448 0.251717
\(474\) 0 0
\(475\) −6.60801 −0.303196
\(476\) 0 0
\(477\) −67.1091 −3.07271
\(478\) 0 0
\(479\) 32.4426 1.48234 0.741171 0.671317i \(-0.234271\pi\)
0.741171 + 0.671317i \(0.234271\pi\)
\(480\) 0 0
\(481\) 15.7705 0.719074
\(482\) 0 0
\(483\) −38.3237 −1.74379
\(484\) 0 0
\(485\) −18.9743 −0.861577
\(486\) 0 0
\(487\) −19.8614 −0.900004 −0.450002 0.893028i \(-0.648577\pi\)
−0.450002 + 0.893028i \(0.648577\pi\)
\(488\) 0 0
\(489\) 37.7041 1.70504
\(490\) 0 0
\(491\) −1.44852 −0.0653710 −0.0326855 0.999466i \(-0.510406\pi\)
−0.0326855 + 0.999466i \(0.510406\pi\)
\(492\) 0 0
\(493\) −25.9670 −1.16950
\(494\) 0 0
\(495\) 6.12754 0.275413
\(496\) 0 0
\(497\) 10.6104 0.475943
\(498\) 0 0
\(499\) −7.13499 −0.319406 −0.159703 0.987165i \(-0.551054\pi\)
−0.159703 + 0.987165i \(0.551054\pi\)
\(500\) 0 0
\(501\) −18.9578 −0.846972
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −29.2632 −1.30220
\(506\) 0 0
\(507\) 32.7824 1.45592
\(508\) 0 0
\(509\) −13.4239 −0.595005 −0.297502 0.954721i \(-0.596154\pi\)
−0.297502 + 0.954721i \(0.596154\pi\)
\(510\) 0 0
\(511\) −46.3449 −2.05018
\(512\) 0 0
\(513\) −34.5523 −1.52552
\(514\) 0 0
\(515\) −2.10710 −0.0928501
\(516\) 0 0
\(517\) −1.50522 −0.0661995
\(518\) 0 0
\(519\) 26.9987 1.18511
\(520\) 0 0
\(521\) −15.8555 −0.694640 −0.347320 0.937747i \(-0.612908\pi\)
−0.347320 + 0.937747i \(0.612908\pi\)
\(522\) 0 0
\(523\) −37.0927 −1.62195 −0.810974 0.585082i \(-0.801062\pi\)
−0.810974 + 0.585082i \(0.801062\pi\)
\(524\) 0 0
\(525\) 24.6785 1.07706
\(526\) 0 0
\(527\) −28.3226 −1.23375
\(528\) 0 0
\(529\) −7.55736 −0.328581
\(530\) 0 0
\(531\) 20.0406 0.869687
\(532\) 0 0
\(533\) 1.71426 0.0742529
\(534\) 0 0
\(535\) 0.0412533 0.00178353
\(536\) 0 0
\(537\) −60.2018 −2.59790
\(538\) 0 0
\(539\) −1.29074 −0.0555962
\(540\) 0 0
\(541\) −33.4083 −1.43633 −0.718167 0.695871i \(-0.755019\pi\)
−0.718167 + 0.695871i \(0.755019\pi\)
\(542\) 0 0
\(543\) −25.5497 −1.09644
\(544\) 0 0
\(545\) −0.550973 −0.0236011
\(546\) 0 0
\(547\) −15.3912 −0.658081 −0.329041 0.944316i \(-0.606725\pi\)
−0.329041 + 0.944316i \(0.606725\pi\)
\(548\) 0 0
\(549\) 37.6677 1.60762
\(550\) 0 0
\(551\) 18.5693 0.791079
\(552\) 0 0
\(553\) 27.9323 1.18780
\(554\) 0 0
\(555\) −47.9544 −2.03555
\(556\) 0 0
\(557\) 36.8442 1.56114 0.780570 0.625068i \(-0.214929\pi\)
0.780570 + 0.625068i \(0.214929\pi\)
\(558\) 0 0
\(559\) 16.5362 0.699407
\(560\) 0 0
\(561\) −6.34294 −0.267799
\(562\) 0 0
\(563\) 22.6230 0.953445 0.476723 0.879054i \(-0.341825\pi\)
0.476723 + 0.879054i \(0.341825\pi\)
\(564\) 0 0
\(565\) −3.40434 −0.143222
\(566\) 0 0
\(567\) 63.3645 2.66106
\(568\) 0 0
\(569\) −29.5554 −1.23903 −0.619514 0.784986i \(-0.712670\pi\)
−0.619514 + 0.784986i \(0.712670\pi\)
\(570\) 0 0
\(571\) −29.1394 −1.21945 −0.609723 0.792614i \(-0.708719\pi\)
−0.609723 + 0.792614i \(0.708719\pi\)
\(572\) 0 0
\(573\) 76.8429 3.21016
\(574\) 0 0
\(575\) −9.94429 −0.414706
\(576\) 0 0
\(577\) 2.88102 0.119939 0.0599693 0.998200i \(-0.480900\pi\)
0.0599693 + 0.998200i \(0.480900\pi\)
\(578\) 0 0
\(579\) 27.1031 1.12637
\(580\) 0 0
\(581\) −16.3243 −0.677246
\(582\) 0 0
\(583\) 5.11480 0.211833
\(584\) 0 0
\(585\) 18.5088 0.765246
\(586\) 0 0
\(587\) −21.1371 −0.872422 −0.436211 0.899844i \(-0.643680\pi\)
−0.436211 + 0.899844i \(0.643680\pi\)
\(588\) 0 0
\(589\) 20.2538 0.834542
\(590\) 0 0
\(591\) 80.6880 3.31906
\(592\) 0 0
\(593\) −20.4767 −0.840879 −0.420439 0.907321i \(-0.638124\pi\)
−0.420439 + 0.907321i \(0.638124\pi\)
\(594\) 0 0
\(595\) 17.5631 0.720016
\(596\) 0 0
\(597\) 11.5397 0.472287
\(598\) 0 0
\(599\) −24.4801 −1.00023 −0.500115 0.865959i \(-0.666709\pi\)
−0.500115 + 0.865959i \(0.666709\pi\)
\(600\) 0 0
\(601\) −34.3885 −1.40274 −0.701368 0.712799i \(-0.747427\pi\)
−0.701368 + 0.712799i \(0.747427\pi\)
\(602\) 0 0
\(603\) −52.0944 −2.12145
\(604\) 0 0
\(605\) 16.8190 0.683788
\(606\) 0 0
\(607\) −20.6276 −0.837247 −0.418624 0.908160i \(-0.637487\pi\)
−0.418624 + 0.908160i \(0.637487\pi\)
\(608\) 0 0
\(609\) −69.3498 −2.81019
\(610\) 0 0
\(611\) −4.54666 −0.183938
\(612\) 0 0
\(613\) 1.90684 0.0770164 0.0385082 0.999258i \(-0.487739\pi\)
0.0385082 + 0.999258i \(0.487739\pi\)
\(614\) 0 0
\(615\) −5.21266 −0.210195
\(616\) 0 0
\(617\) 19.1072 0.769227 0.384613 0.923078i \(-0.374335\pi\)
0.384613 + 0.923078i \(0.374335\pi\)
\(618\) 0 0
\(619\) 19.2943 0.775504 0.387752 0.921764i \(-0.373252\pi\)
0.387752 + 0.921764i \(0.373252\pi\)
\(620\) 0 0
\(621\) −51.9972 −2.08658
\(622\) 0 0
\(623\) −37.5643 −1.50498
\(624\) 0 0
\(625\) −5.94368 −0.237747
\(626\) 0 0
\(627\) 4.53591 0.181147
\(628\) 0 0
\(629\) 34.9720 1.39442
\(630\) 0 0
\(631\) 44.1125 1.75609 0.878045 0.478577i \(-0.158847\pi\)
0.878045 + 0.478577i \(0.158847\pi\)
\(632\) 0 0
\(633\) 10.0673 0.400140
\(634\) 0 0
\(635\) −5.10529 −0.202597
\(636\) 0 0
\(637\) −3.89881 −0.154477
\(638\) 0 0
\(639\) 24.7962 0.980924
\(640\) 0 0
\(641\) 13.0671 0.516120 0.258060 0.966129i \(-0.416917\pi\)
0.258060 + 0.966129i \(0.416917\pi\)
\(642\) 0 0
\(643\) −23.6402 −0.932279 −0.466139 0.884711i \(-0.654356\pi\)
−0.466139 + 0.884711i \(0.654356\pi\)
\(644\) 0 0
\(645\) −50.2827 −1.97988
\(646\) 0 0
\(647\) 17.2476 0.678073 0.339036 0.940773i \(-0.389899\pi\)
0.339036 + 0.940773i \(0.389899\pi\)
\(648\) 0 0
\(649\) −1.52742 −0.0599563
\(650\) 0 0
\(651\) −75.6407 −2.96459
\(652\) 0 0
\(653\) −4.73847 −0.185431 −0.0927154 0.995693i \(-0.529555\pi\)
−0.0927154 + 0.995693i \(0.529555\pi\)
\(654\) 0 0
\(655\) −8.31390 −0.324851
\(656\) 0 0
\(657\) −108.307 −4.22544
\(658\) 0 0
\(659\) 27.0030 1.05189 0.525943 0.850520i \(-0.323712\pi\)
0.525943 + 0.850520i \(0.323712\pi\)
\(660\) 0 0
\(661\) 40.0848 1.55912 0.779560 0.626328i \(-0.215443\pi\)
0.779560 + 0.626328i \(0.215443\pi\)
\(662\) 0 0
\(663\) −19.1595 −0.744092
\(664\) 0 0
\(665\) −12.5596 −0.487039
\(666\) 0 0
\(667\) 27.9447 1.08202
\(668\) 0 0
\(669\) 5.80333 0.224370
\(670\) 0 0
\(671\) −2.87089 −0.110830
\(672\) 0 0
\(673\) −17.5878 −0.677959 −0.338980 0.940794i \(-0.610082\pi\)
−0.338980 + 0.940794i \(0.610082\pi\)
\(674\) 0 0
\(675\) 33.4836 1.28878
\(676\) 0 0
\(677\) −27.6314 −1.06196 −0.530981 0.847384i \(-0.678177\pi\)
−0.530981 + 0.847384i \(0.678177\pi\)
\(678\) 0 0
\(679\) 36.9556 1.41823
\(680\) 0 0
\(681\) −63.2383 −2.42330
\(682\) 0 0
\(683\) 15.4621 0.591639 0.295820 0.955244i \(-0.404407\pi\)
0.295820 + 0.955244i \(0.404407\pi\)
\(684\) 0 0
\(685\) −26.0359 −0.994780
\(686\) 0 0
\(687\) 47.8150 1.82426
\(688\) 0 0
\(689\) 15.4498 0.588589
\(690\) 0 0
\(691\) −9.92880 −0.377709 −0.188855 0.982005i \(-0.560478\pi\)
−0.188855 + 0.982005i \(0.560478\pi\)
\(692\) 0 0
\(693\) −11.9344 −0.453351
\(694\) 0 0
\(695\) −22.4624 −0.852046
\(696\) 0 0
\(697\) 3.80147 0.143991
\(698\) 0 0
\(699\) 25.4897 0.964110
\(700\) 0 0
\(701\) −50.4195 −1.90432 −0.952158 0.305605i \(-0.901141\pi\)
−0.952158 + 0.305605i \(0.901141\pi\)
\(702\) 0 0
\(703\) −25.0089 −0.943227
\(704\) 0 0
\(705\) 13.8253 0.520692
\(706\) 0 0
\(707\) 56.9950 2.14352
\(708\) 0 0
\(709\) −49.2180 −1.84842 −0.924210 0.381885i \(-0.875275\pi\)
−0.924210 + 0.381885i \(0.875275\pi\)
\(710\) 0 0
\(711\) 65.2770 2.44808
\(712\) 0 0
\(713\) 30.4796 1.14147
\(714\) 0 0
\(715\) −1.41067 −0.0527562
\(716\) 0 0
\(717\) −32.1328 −1.20002
\(718\) 0 0
\(719\) 10.8606 0.405033 0.202516 0.979279i \(-0.435088\pi\)
0.202516 + 0.979279i \(0.435088\pi\)
\(720\) 0 0
\(721\) 4.10394 0.152839
\(722\) 0 0
\(723\) −26.1042 −0.970826
\(724\) 0 0
\(725\) −17.9950 −0.668317
\(726\) 0 0
\(727\) −14.7206 −0.545958 −0.272979 0.962020i \(-0.588009\pi\)
−0.272979 + 0.962020i \(0.588009\pi\)
\(728\) 0 0
\(729\) 21.5981 0.799931
\(730\) 0 0
\(731\) 36.6700 1.35629
\(732\) 0 0
\(733\) 35.9113 1.32642 0.663208 0.748435i \(-0.269195\pi\)
0.663208 + 0.748435i \(0.269195\pi\)
\(734\) 0 0
\(735\) 11.8554 0.437291
\(736\) 0 0
\(737\) 3.97044 0.146253
\(738\) 0 0
\(739\) −31.0887 −1.14362 −0.571808 0.820387i \(-0.693758\pi\)
−0.571808 + 0.820387i \(0.693758\pi\)
\(740\) 0 0
\(741\) 13.7011 0.503324
\(742\) 0 0
\(743\) −22.9725 −0.842779 −0.421389 0.906880i \(-0.638457\pi\)
−0.421389 + 0.906880i \(0.638457\pi\)
\(744\) 0 0
\(745\) −4.69069 −0.171853
\(746\) 0 0
\(747\) −38.1494 −1.39581
\(748\) 0 0
\(749\) −0.0803477 −0.00293584
\(750\) 0 0
\(751\) 39.7768 1.45148 0.725739 0.687971i \(-0.241498\pi\)
0.725739 + 0.687971i \(0.241498\pi\)
\(752\) 0 0
\(753\) 44.9985 1.63984
\(754\) 0 0
\(755\) −17.6640 −0.642859
\(756\) 0 0
\(757\) −9.07248 −0.329745 −0.164872 0.986315i \(-0.552721\pi\)
−0.164872 + 0.986315i \(0.552721\pi\)
\(758\) 0 0
\(759\) 6.82602 0.247769
\(760\) 0 0
\(761\) −3.44813 −0.124995 −0.0624973 0.998045i \(-0.519906\pi\)
−0.0624973 + 0.998045i \(0.519906\pi\)
\(762\) 0 0
\(763\) 1.07311 0.0388493
\(764\) 0 0
\(765\) 41.0444 1.48396
\(766\) 0 0
\(767\) −4.61371 −0.166591
\(768\) 0 0
\(769\) −16.8510 −0.607664 −0.303832 0.952726i \(-0.598266\pi\)
−0.303832 + 0.952726i \(0.598266\pi\)
\(770\) 0 0
\(771\) −5.00741 −0.180337
\(772\) 0 0
\(773\) −2.58677 −0.0930396 −0.0465198 0.998917i \(-0.514813\pi\)
−0.0465198 + 0.998917i \(0.514813\pi\)
\(774\) 0 0
\(775\) −19.6274 −0.705036
\(776\) 0 0
\(777\) 93.3992 3.35068
\(778\) 0 0
\(779\) −2.71848 −0.0973995
\(780\) 0 0
\(781\) −1.88988 −0.0676251
\(782\) 0 0
\(783\) −94.0931 −3.36261
\(784\) 0 0
\(785\) −18.7294 −0.668480
\(786\) 0 0
\(787\) 33.6266 1.19866 0.599329 0.800503i \(-0.295434\pi\)
0.599329 + 0.800503i \(0.295434\pi\)
\(788\) 0 0
\(789\) 18.4660 0.657406
\(790\) 0 0
\(791\) 6.63053 0.235754
\(792\) 0 0
\(793\) −8.67181 −0.307945
\(794\) 0 0
\(795\) −46.9790 −1.66617
\(796\) 0 0
\(797\) 42.9826 1.52252 0.761261 0.648445i \(-0.224580\pi\)
0.761261 + 0.648445i \(0.224580\pi\)
\(798\) 0 0
\(799\) −10.0825 −0.356693
\(800\) 0 0
\(801\) −87.7866 −3.10179
\(802\) 0 0
\(803\) 8.25471 0.291302
\(804\) 0 0
\(805\) −18.9007 −0.666162
\(806\) 0 0
\(807\) −5.65164 −0.198947
\(808\) 0 0
\(809\) −12.7197 −0.447202 −0.223601 0.974681i \(-0.571781\pi\)
−0.223601 + 0.974681i \(0.571781\pi\)
\(810\) 0 0
\(811\) −23.3898 −0.821326 −0.410663 0.911787i \(-0.634703\pi\)
−0.410663 + 0.911787i \(0.634703\pi\)
\(812\) 0 0
\(813\) 53.4927 1.87607
\(814\) 0 0
\(815\) 18.5952 0.651360
\(816\) 0 0
\(817\) −26.2231 −0.917430
\(818\) 0 0
\(819\) −36.0491 −1.25966
\(820\) 0 0
\(821\) −20.6853 −0.721923 −0.360961 0.932581i \(-0.617551\pi\)
−0.360961 + 0.932581i \(0.617551\pi\)
\(822\) 0 0
\(823\) −16.0268 −0.558658 −0.279329 0.960195i \(-0.590112\pi\)
−0.279329 + 0.960195i \(0.590112\pi\)
\(824\) 0 0
\(825\) −4.39562 −0.153036
\(826\) 0 0
\(827\) −38.5677 −1.34113 −0.670565 0.741851i \(-0.733948\pi\)
−0.670565 + 0.741851i \(0.733948\pi\)
\(828\) 0 0
\(829\) 38.3558 1.33215 0.666075 0.745885i \(-0.267973\pi\)
0.666075 + 0.745885i \(0.267973\pi\)
\(830\) 0 0
\(831\) −48.3493 −1.67722
\(832\) 0 0
\(833\) −8.64583 −0.299560
\(834\) 0 0
\(835\) −9.34972 −0.323560
\(836\) 0 0
\(837\) −102.629 −3.54736
\(838\) 0 0
\(839\) −16.6698 −0.575505 −0.287752 0.957705i \(-0.592908\pi\)
−0.287752 + 0.957705i \(0.592908\pi\)
\(840\) 0 0
\(841\) 21.5682 0.743730
\(842\) 0 0
\(843\) 99.4059 3.42372
\(844\) 0 0
\(845\) 16.1678 0.556189
\(846\) 0 0
\(847\) −32.7577 −1.12557
\(848\) 0 0
\(849\) −46.6827 −1.60215
\(850\) 0 0
\(851\) −37.6355 −1.29013
\(852\) 0 0
\(853\) 15.3583 0.525859 0.262929 0.964815i \(-0.415311\pi\)
0.262929 + 0.964815i \(0.415311\pi\)
\(854\) 0 0
\(855\) −29.3513 −1.00379
\(856\) 0 0
\(857\) 6.90657 0.235924 0.117962 0.993018i \(-0.462364\pi\)
0.117962 + 0.993018i \(0.462364\pi\)
\(858\) 0 0
\(859\) 42.8992 1.46370 0.731851 0.681465i \(-0.238657\pi\)
0.731851 + 0.681465i \(0.238657\pi\)
\(860\) 0 0
\(861\) 10.1525 0.345997
\(862\) 0 0
\(863\) 42.2767 1.43912 0.719558 0.694432i \(-0.244344\pi\)
0.719558 + 0.694432i \(0.244344\pi\)
\(864\) 0 0
\(865\) 13.3154 0.452737
\(866\) 0 0
\(867\) 11.6804 0.396687
\(868\) 0 0
\(869\) −4.97517 −0.168771
\(870\) 0 0
\(871\) 11.9931 0.406370
\(872\) 0 0
\(873\) 86.3641 2.92298
\(874\) 0 0
\(875\) 36.2196 1.22444
\(876\) 0 0
\(877\) 10.5272 0.355478 0.177739 0.984078i \(-0.443122\pi\)
0.177739 + 0.984078i \(0.443122\pi\)
\(878\) 0 0
\(879\) −21.0255 −0.709174
\(880\) 0 0
\(881\) 26.8995 0.906266 0.453133 0.891443i \(-0.350306\pi\)
0.453133 + 0.891443i \(0.350306\pi\)
\(882\) 0 0
\(883\) −27.1797 −0.914669 −0.457334 0.889295i \(-0.651196\pi\)
−0.457334 + 0.889295i \(0.651196\pi\)
\(884\) 0 0
\(885\) 14.0292 0.471586
\(886\) 0 0
\(887\) 13.2469 0.444787 0.222393 0.974957i \(-0.428613\pi\)
0.222393 + 0.974957i \(0.428613\pi\)
\(888\) 0 0
\(889\) 9.94340 0.333491
\(890\) 0 0
\(891\) −11.2862 −0.378100
\(892\) 0 0
\(893\) 7.21010 0.241277
\(894\) 0 0
\(895\) −29.6907 −0.992450
\(896\) 0 0
\(897\) 20.6187 0.688437
\(898\) 0 0
\(899\) 55.1553 1.83953
\(900\) 0 0
\(901\) 34.2607 1.14139
\(902\) 0 0
\(903\) 97.9339 3.25904
\(904\) 0 0
\(905\) −12.6007 −0.418863
\(906\) 0 0
\(907\) 28.9672 0.961840 0.480920 0.876764i \(-0.340303\pi\)
0.480920 + 0.876764i \(0.340303\pi\)
\(908\) 0 0
\(909\) 133.196 4.41782
\(910\) 0 0
\(911\) 9.28341 0.307573 0.153787 0.988104i \(-0.450853\pi\)
0.153787 + 0.988104i \(0.450853\pi\)
\(912\) 0 0
\(913\) 2.90760 0.0962275
\(914\) 0 0
\(915\) 26.3689 0.871729
\(916\) 0 0
\(917\) 16.1927 0.534731
\(918\) 0 0
\(919\) −19.2457 −0.634859 −0.317429 0.948282i \(-0.602820\pi\)
−0.317429 + 0.948282i \(0.602820\pi\)
\(920\) 0 0
\(921\) 87.3223 2.87737
\(922\) 0 0
\(923\) −5.70855 −0.187899
\(924\) 0 0
\(925\) 24.2354 0.796854
\(926\) 0 0
\(927\) 9.59078 0.315002
\(928\) 0 0
\(929\) 38.1294 1.25098 0.625492 0.780230i \(-0.284898\pi\)
0.625492 + 0.780230i \(0.284898\pi\)
\(930\) 0 0
\(931\) 6.18273 0.202631
\(932\) 0 0
\(933\) 7.28222 0.238409
\(934\) 0 0
\(935\) −3.12825 −0.102305
\(936\) 0 0
\(937\) −0.539014 −0.0176088 −0.00880440 0.999961i \(-0.502803\pi\)
−0.00880440 + 0.999961i \(0.502803\pi\)
\(938\) 0 0
\(939\) −67.6564 −2.20788
\(940\) 0 0
\(941\) 11.9849 0.390695 0.195348 0.980734i \(-0.437416\pi\)
0.195348 + 0.980734i \(0.437416\pi\)
\(942\) 0 0
\(943\) −4.09099 −0.133221
\(944\) 0 0
\(945\) 63.6409 2.07024
\(946\) 0 0
\(947\) 59.1562 1.92232 0.961158 0.275997i \(-0.0890081\pi\)
0.961158 + 0.275997i \(0.0890081\pi\)
\(948\) 0 0
\(949\) 24.9342 0.809397
\(950\) 0 0
\(951\) −88.5345 −2.87093
\(952\) 0 0
\(953\) −45.7815 −1.48301 −0.741505 0.670948i \(-0.765887\pi\)
−0.741505 + 0.670948i \(0.765887\pi\)
\(954\) 0 0
\(955\) 37.8979 1.22635
\(956\) 0 0
\(957\) 12.3522 0.399291
\(958\) 0 0
\(959\) 50.7092 1.63749
\(960\) 0 0
\(961\) 29.1586 0.940599
\(962\) 0 0
\(963\) −0.187770 −0.00605080
\(964\) 0 0
\(965\) 13.3669 0.430295
\(966\) 0 0
\(967\) −44.8467 −1.44217 −0.721086 0.692846i \(-0.756357\pi\)
−0.721086 + 0.692846i \(0.756357\pi\)
\(968\) 0 0
\(969\) 30.3831 0.976044
\(970\) 0 0
\(971\) 10.2798 0.329895 0.164948 0.986302i \(-0.447254\pi\)
0.164948 + 0.986302i \(0.447254\pi\)
\(972\) 0 0
\(973\) 43.7492 1.40254
\(974\) 0 0
\(975\) −13.2774 −0.425217
\(976\) 0 0
\(977\) 9.74691 0.311831 0.155916 0.987770i \(-0.450167\pi\)
0.155916 + 0.987770i \(0.450167\pi\)
\(978\) 0 0
\(979\) 6.69076 0.213838
\(980\) 0 0
\(981\) 2.50783 0.0800689
\(982\) 0 0
\(983\) −39.1336 −1.24817 −0.624084 0.781357i \(-0.714528\pi\)
−0.624084 + 0.781357i \(0.714528\pi\)
\(984\) 0 0
\(985\) 39.7942 1.26795
\(986\) 0 0
\(987\) −26.9271 −0.857100
\(988\) 0 0
\(989\) −39.4628 −1.25484
\(990\) 0 0
\(991\) −37.3199 −1.18551 −0.592754 0.805384i \(-0.701959\pi\)
−0.592754 + 0.805384i \(0.701959\pi\)
\(992\) 0 0
\(993\) 91.7573 2.91183
\(994\) 0 0
\(995\) 5.69120 0.180423
\(996\) 0 0
\(997\) −55.6608 −1.76279 −0.881397 0.472376i \(-0.843396\pi\)
−0.881397 + 0.472376i \(0.843396\pi\)
\(998\) 0 0
\(999\) 126.723 4.00934
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 \(a_p\))