Properties

Label 6036.2.a.i.1.5
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 0
Dimension 26
CM No

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(0\)
Dimension: \(26\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-2.60444 q^{5}\) \(-1.53102 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-2.60444 q^{5}\) \(-1.53102 q^{7}\) \(+1.00000 q^{9}\) \(+4.96919 q^{11}\) \(+3.57535 q^{13}\) \(+2.60444 q^{15}\) \(-5.67149 q^{17}\) \(+7.50947 q^{19}\) \(+1.53102 q^{21}\) \(-5.35597 q^{23}\) \(+1.78310 q^{25}\) \(-1.00000 q^{27}\) \(+3.66790 q^{29}\) \(+4.23096 q^{31}\) \(-4.96919 q^{33}\) \(+3.98745 q^{35}\) \(-6.07248 q^{37}\) \(-3.57535 q^{39}\) \(-1.00478 q^{41}\) \(+1.75353 q^{43}\) \(-2.60444 q^{45}\) \(-2.20924 q^{47}\) \(-4.65597 q^{49}\) \(+5.67149 q^{51}\) \(+5.12050 q^{53}\) \(-12.9419 q^{55}\) \(-7.50947 q^{57}\) \(+1.75140 q^{59}\) \(+2.51859 q^{61}\) \(-1.53102 q^{63}\) \(-9.31177 q^{65}\) \(+12.8570 q^{67}\) \(+5.35597 q^{69}\) \(-7.52624 q^{71}\) \(-0.588232 q^{73}\) \(-1.78310 q^{75}\) \(-7.60793 q^{77}\) \(+3.18145 q^{79}\) \(+1.00000 q^{81}\) \(-1.21414 q^{83}\) \(+14.7710 q^{85}\) \(-3.66790 q^{87}\) \(-13.4526 q^{89}\) \(-5.47394 q^{91}\) \(-4.23096 q^{93}\) \(-19.5580 q^{95}\) \(-16.6053 q^{97}\) \(+4.96919 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −2.60444 −1.16474 −0.582370 0.812924i \(-0.697875\pi\)
−0.582370 + 0.812924i \(0.697875\pi\)
\(6\) 0 0
\(7\) −1.53102 −0.578672 −0.289336 0.957228i \(-0.593434\pi\)
−0.289336 + 0.957228i \(0.593434\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.96919 1.49827 0.749133 0.662420i \(-0.230470\pi\)
0.749133 + 0.662420i \(0.230470\pi\)
\(12\) 0 0
\(13\) 3.57535 0.991623 0.495811 0.868430i \(-0.334871\pi\)
0.495811 + 0.868430i \(0.334871\pi\)
\(14\) 0 0
\(15\) 2.60444 0.672463
\(16\) 0 0
\(17\) −5.67149 −1.37554 −0.687769 0.725930i \(-0.741410\pi\)
−0.687769 + 0.725930i \(0.741410\pi\)
\(18\) 0 0
\(19\) 7.50947 1.72279 0.861396 0.507935i \(-0.169591\pi\)
0.861396 + 0.507935i \(0.169591\pi\)
\(20\) 0 0
\(21\) 1.53102 0.334096
\(22\) 0 0
\(23\) −5.35597 −1.11680 −0.558399 0.829573i \(-0.688584\pi\)
−0.558399 + 0.829573i \(0.688584\pi\)
\(24\) 0 0
\(25\) 1.78310 0.356620
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 3.66790 0.681112 0.340556 0.940224i \(-0.389385\pi\)
0.340556 + 0.940224i \(0.389385\pi\)
\(30\) 0 0
\(31\) 4.23096 0.759903 0.379951 0.925006i \(-0.375941\pi\)
0.379951 + 0.925006i \(0.375941\pi\)
\(32\) 0 0
\(33\) −4.96919 −0.865024
\(34\) 0 0
\(35\) 3.98745 0.674003
\(36\) 0 0
\(37\) −6.07248 −0.998310 −0.499155 0.866513i \(-0.666356\pi\)
−0.499155 + 0.866513i \(0.666356\pi\)
\(38\) 0 0
\(39\) −3.57535 −0.572514
\(40\) 0 0
\(41\) −1.00478 −0.156921 −0.0784604 0.996917i \(-0.525000\pi\)
−0.0784604 + 0.996917i \(0.525000\pi\)
\(42\) 0 0
\(43\) 1.75353 0.267411 0.133706 0.991021i \(-0.457312\pi\)
0.133706 + 0.991021i \(0.457312\pi\)
\(44\) 0 0
\(45\) −2.60444 −0.388247
\(46\) 0 0
\(47\) −2.20924 −0.322251 −0.161126 0.986934i \(-0.551512\pi\)
−0.161126 + 0.986934i \(0.551512\pi\)
\(48\) 0 0
\(49\) −4.65597 −0.665139
\(50\) 0 0
\(51\) 5.67149 0.794167
\(52\) 0 0
\(53\) 5.12050 0.703355 0.351678 0.936121i \(-0.385611\pi\)
0.351678 + 0.936121i \(0.385611\pi\)
\(54\) 0 0
\(55\) −12.9419 −1.74509
\(56\) 0 0
\(57\) −7.50947 −0.994654
\(58\) 0 0
\(59\) 1.75140 0.228013 0.114006 0.993480i \(-0.463632\pi\)
0.114006 + 0.993480i \(0.463632\pi\)
\(60\) 0 0
\(61\) 2.51859 0.322472 0.161236 0.986916i \(-0.448452\pi\)
0.161236 + 0.986916i \(0.448452\pi\)
\(62\) 0 0
\(63\) −1.53102 −0.192891
\(64\) 0 0
\(65\) −9.31177 −1.15498
\(66\) 0 0
\(67\) 12.8570 1.57074 0.785368 0.619030i \(-0.212474\pi\)
0.785368 + 0.619030i \(0.212474\pi\)
\(68\) 0 0
\(69\) 5.35597 0.644783
\(70\) 0 0
\(71\) −7.52624 −0.893200 −0.446600 0.894734i \(-0.647365\pi\)
−0.446600 + 0.894734i \(0.647365\pi\)
\(72\) 0 0
\(73\) −0.588232 −0.0688474 −0.0344237 0.999407i \(-0.510960\pi\)
−0.0344237 + 0.999407i \(0.510960\pi\)
\(74\) 0 0
\(75\) −1.78310 −0.205894
\(76\) 0 0
\(77\) −7.60793 −0.867005
\(78\) 0 0
\(79\) 3.18145 0.357941 0.178970 0.983854i \(-0.442723\pi\)
0.178970 + 0.983854i \(0.442723\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −1.21414 −0.133269 −0.0666346 0.997777i \(-0.521226\pi\)
−0.0666346 + 0.997777i \(0.521226\pi\)
\(84\) 0 0
\(85\) 14.7710 1.60214
\(86\) 0 0
\(87\) −3.66790 −0.393240
\(88\) 0 0
\(89\) −13.4526 −1.42597 −0.712984 0.701180i \(-0.752657\pi\)
−0.712984 + 0.701180i \(0.752657\pi\)
\(90\) 0 0
\(91\) −5.47394 −0.573824
\(92\) 0 0
\(93\) −4.23096 −0.438730
\(94\) 0 0
\(95\) −19.5580 −2.00660
\(96\) 0 0
\(97\) −16.6053 −1.68601 −0.843007 0.537902i \(-0.819217\pi\)
−0.843007 + 0.537902i \(0.819217\pi\)
\(98\) 0 0
\(99\) 4.96919 0.499422
\(100\) 0 0
\(101\) 14.3577 1.42865 0.714323 0.699816i \(-0.246735\pi\)
0.714323 + 0.699816i \(0.246735\pi\)
\(102\) 0 0
\(103\) −0.930739 −0.0917084 −0.0458542 0.998948i \(-0.514601\pi\)
−0.0458542 + 0.998948i \(0.514601\pi\)
\(104\) 0 0
\(105\) −3.98745 −0.389136
\(106\) 0 0
\(107\) −18.4954 −1.78802 −0.894008 0.448051i \(-0.852118\pi\)
−0.894008 + 0.448051i \(0.852118\pi\)
\(108\) 0 0
\(109\) 5.59426 0.535833 0.267917 0.963442i \(-0.413665\pi\)
0.267917 + 0.963442i \(0.413665\pi\)
\(110\) 0 0
\(111\) 6.07248 0.576375
\(112\) 0 0
\(113\) −0.687519 −0.0646764 −0.0323382 0.999477i \(-0.510295\pi\)
−0.0323382 + 0.999477i \(0.510295\pi\)
\(114\) 0 0
\(115\) 13.9493 1.30078
\(116\) 0 0
\(117\) 3.57535 0.330541
\(118\) 0 0
\(119\) 8.68318 0.795985
\(120\) 0 0
\(121\) 13.6928 1.24480
\(122\) 0 0
\(123\) 1.00478 0.0905982
\(124\) 0 0
\(125\) 8.37822 0.749371
\(126\) 0 0
\(127\) −2.53928 −0.225324 −0.112662 0.993633i \(-0.535938\pi\)
−0.112662 + 0.993633i \(0.535938\pi\)
\(128\) 0 0
\(129\) −1.75353 −0.154390
\(130\) 0 0
\(131\) 3.99950 0.349438 0.174719 0.984618i \(-0.444098\pi\)
0.174719 + 0.984618i \(0.444098\pi\)
\(132\) 0 0
\(133\) −11.4972 −0.996931
\(134\) 0 0
\(135\) 2.60444 0.224154
\(136\) 0 0
\(137\) −3.88366 −0.331803 −0.165902 0.986142i \(-0.553053\pi\)
−0.165902 + 0.986142i \(0.553053\pi\)
\(138\) 0 0
\(139\) −11.2261 −0.952182 −0.476091 0.879396i \(-0.657947\pi\)
−0.476091 + 0.879396i \(0.657947\pi\)
\(140\) 0 0
\(141\) 2.20924 0.186052
\(142\) 0 0
\(143\) 17.7666 1.48571
\(144\) 0 0
\(145\) −9.55281 −0.793318
\(146\) 0 0
\(147\) 4.65597 0.384018
\(148\) 0 0
\(149\) −2.56685 −0.210284 −0.105142 0.994457i \(-0.533530\pi\)
−0.105142 + 0.994457i \(0.533530\pi\)
\(150\) 0 0
\(151\) 14.5577 1.18469 0.592346 0.805684i \(-0.298202\pi\)
0.592346 + 0.805684i \(0.298202\pi\)
\(152\) 0 0
\(153\) −5.67149 −0.458513
\(154\) 0 0
\(155\) −11.0193 −0.885089
\(156\) 0 0
\(157\) 17.7585 1.41728 0.708641 0.705569i \(-0.249309\pi\)
0.708641 + 0.705569i \(0.249309\pi\)
\(158\) 0 0
\(159\) −5.12050 −0.406082
\(160\) 0 0
\(161\) 8.20011 0.646260
\(162\) 0 0
\(163\) 2.77417 0.217289 0.108645 0.994081i \(-0.465349\pi\)
0.108645 + 0.994081i \(0.465349\pi\)
\(164\) 0 0
\(165\) 12.9419 1.00753
\(166\) 0 0
\(167\) −1.49278 −0.115515 −0.0577574 0.998331i \(-0.518395\pi\)
−0.0577574 + 0.998331i \(0.518395\pi\)
\(168\) 0 0
\(169\) −0.216891 −0.0166839
\(170\) 0 0
\(171\) 7.50947 0.574264
\(172\) 0 0
\(173\) 12.3514 0.939059 0.469529 0.882917i \(-0.344424\pi\)
0.469529 + 0.882917i \(0.344424\pi\)
\(174\) 0 0
\(175\) −2.72996 −0.206366
\(176\) 0 0
\(177\) −1.75140 −0.131643
\(178\) 0 0
\(179\) 1.98419 0.148305 0.0741527 0.997247i \(-0.476375\pi\)
0.0741527 + 0.997247i \(0.476375\pi\)
\(180\) 0 0
\(181\) 4.44069 0.330074 0.165037 0.986287i \(-0.447226\pi\)
0.165037 + 0.986287i \(0.447226\pi\)
\(182\) 0 0
\(183\) −2.51859 −0.186180
\(184\) 0 0
\(185\) 15.8154 1.16277
\(186\) 0 0
\(187\) −28.1827 −2.06092
\(188\) 0 0
\(189\) 1.53102 0.111365
\(190\) 0 0
\(191\) 6.71869 0.486147 0.243074 0.970008i \(-0.421844\pi\)
0.243074 + 0.970008i \(0.421844\pi\)
\(192\) 0 0
\(193\) −13.0665 −0.940547 −0.470273 0.882521i \(-0.655845\pi\)
−0.470273 + 0.882521i \(0.655845\pi\)
\(194\) 0 0
\(195\) 9.31177 0.666830
\(196\) 0 0
\(197\) 13.7962 0.982941 0.491470 0.870894i \(-0.336460\pi\)
0.491470 + 0.870894i \(0.336460\pi\)
\(198\) 0 0
\(199\) 1.87652 0.133023 0.0665113 0.997786i \(-0.478813\pi\)
0.0665113 + 0.997786i \(0.478813\pi\)
\(200\) 0 0
\(201\) −12.8570 −0.906864
\(202\) 0 0
\(203\) −5.61563 −0.394140
\(204\) 0 0
\(205\) 2.61690 0.182772
\(206\) 0 0
\(207\) −5.35597 −0.372266
\(208\) 0 0
\(209\) 37.3160 2.58120
\(210\) 0 0
\(211\) −7.48033 −0.514967 −0.257483 0.966283i \(-0.582893\pi\)
−0.257483 + 0.966283i \(0.582893\pi\)
\(212\) 0 0
\(213\) 7.52624 0.515689
\(214\) 0 0
\(215\) −4.56697 −0.311465
\(216\) 0 0
\(217\) −6.47769 −0.439734
\(218\) 0 0
\(219\) 0.588232 0.0397490
\(220\) 0 0
\(221\) −20.2775 −1.36401
\(222\) 0 0
\(223\) 24.3790 1.63254 0.816269 0.577672i \(-0.196039\pi\)
0.816269 + 0.577672i \(0.196039\pi\)
\(224\) 0 0
\(225\) 1.78310 0.118873
\(226\) 0 0
\(227\) −6.35944 −0.422091 −0.211045 0.977476i \(-0.567687\pi\)
−0.211045 + 0.977476i \(0.567687\pi\)
\(228\) 0 0
\(229\) 19.0492 1.25880 0.629402 0.777080i \(-0.283300\pi\)
0.629402 + 0.777080i \(0.283300\pi\)
\(230\) 0 0
\(231\) 7.60793 0.500565
\(232\) 0 0
\(233\) 15.3385 1.00486 0.502430 0.864618i \(-0.332440\pi\)
0.502430 + 0.864618i \(0.332440\pi\)
\(234\) 0 0
\(235\) 5.75384 0.375339
\(236\) 0 0
\(237\) −3.18145 −0.206657
\(238\) 0 0
\(239\) 20.1708 1.30474 0.652369 0.757901i \(-0.273775\pi\)
0.652369 + 0.757901i \(0.273775\pi\)
\(240\) 0 0
\(241\) 22.8061 1.46907 0.734535 0.678571i \(-0.237400\pi\)
0.734535 + 0.678571i \(0.237400\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 12.1262 0.774714
\(246\) 0 0
\(247\) 26.8490 1.70836
\(248\) 0 0
\(249\) 1.21414 0.0769430
\(250\) 0 0
\(251\) 27.2851 1.72222 0.861111 0.508417i \(-0.169769\pi\)
0.861111 + 0.508417i \(0.169769\pi\)
\(252\) 0 0
\(253\) −26.6148 −1.67326
\(254\) 0 0
\(255\) −14.7710 −0.924998
\(256\) 0 0
\(257\) 29.0322 1.81098 0.905488 0.424372i \(-0.139505\pi\)
0.905488 + 0.424372i \(0.139505\pi\)
\(258\) 0 0
\(259\) 9.29711 0.577694
\(260\) 0 0
\(261\) 3.66790 0.227037
\(262\) 0 0
\(263\) −3.16211 −0.194984 −0.0974919 0.995236i \(-0.531082\pi\)
−0.0974919 + 0.995236i \(0.531082\pi\)
\(264\) 0 0
\(265\) −13.3360 −0.819226
\(266\) 0 0
\(267\) 13.4526 0.823284
\(268\) 0 0
\(269\) −4.24758 −0.258979 −0.129490 0.991581i \(-0.541334\pi\)
−0.129490 + 0.991581i \(0.541334\pi\)
\(270\) 0 0
\(271\) 12.7020 0.771594 0.385797 0.922584i \(-0.373926\pi\)
0.385797 + 0.922584i \(0.373926\pi\)
\(272\) 0 0
\(273\) 5.47394 0.331298
\(274\) 0 0
\(275\) 8.86054 0.534311
\(276\) 0 0
\(277\) 11.3458 0.681702 0.340851 0.940117i \(-0.389285\pi\)
0.340851 + 0.940117i \(0.389285\pi\)
\(278\) 0 0
\(279\) 4.23096 0.253301
\(280\) 0 0
\(281\) −8.24035 −0.491578 −0.245789 0.969323i \(-0.579047\pi\)
−0.245789 + 0.969323i \(0.579047\pi\)
\(282\) 0 0
\(283\) 16.5964 0.986555 0.493277 0.869872i \(-0.335799\pi\)
0.493277 + 0.869872i \(0.335799\pi\)
\(284\) 0 0
\(285\) 19.5580 1.15851
\(286\) 0 0
\(287\) 1.53835 0.0908056
\(288\) 0 0
\(289\) 15.1658 0.892105
\(290\) 0 0
\(291\) 16.6053 0.973421
\(292\) 0 0
\(293\) −3.57802 −0.209030 −0.104515 0.994523i \(-0.533329\pi\)
−0.104515 + 0.994523i \(0.533329\pi\)
\(294\) 0 0
\(295\) −4.56141 −0.265575
\(296\) 0 0
\(297\) −4.96919 −0.288341
\(298\) 0 0
\(299\) −19.1495 −1.10744
\(300\) 0 0
\(301\) −2.68470 −0.154744
\(302\) 0 0
\(303\) −14.3577 −0.824829
\(304\) 0 0
\(305\) −6.55951 −0.375597
\(306\) 0 0
\(307\) 19.1089 1.09060 0.545301 0.838240i \(-0.316415\pi\)
0.545301 + 0.838240i \(0.316415\pi\)
\(308\) 0 0
\(309\) 0.930739 0.0529479
\(310\) 0 0
\(311\) 0.227763 0.0129153 0.00645764 0.999979i \(-0.497944\pi\)
0.00645764 + 0.999979i \(0.497944\pi\)
\(312\) 0 0
\(313\) −11.6885 −0.660671 −0.330335 0.943864i \(-0.607162\pi\)
−0.330335 + 0.943864i \(0.607162\pi\)
\(314\) 0 0
\(315\) 3.98745 0.224668
\(316\) 0 0
\(317\) 0.785578 0.0441225 0.0220612 0.999757i \(-0.492977\pi\)
0.0220612 + 0.999757i \(0.492977\pi\)
\(318\) 0 0
\(319\) 18.2265 1.02049
\(320\) 0 0
\(321\) 18.4954 1.03231
\(322\) 0 0
\(323\) −42.5899 −2.36976
\(324\) 0 0
\(325\) 6.37519 0.353632
\(326\) 0 0
\(327\) −5.59426 −0.309363
\(328\) 0 0
\(329\) 3.38240 0.186478
\(330\) 0 0
\(331\) −14.5158 −0.797861 −0.398931 0.916981i \(-0.630619\pi\)
−0.398931 + 0.916981i \(0.630619\pi\)
\(332\) 0 0
\(333\) −6.07248 −0.332770
\(334\) 0 0
\(335\) −33.4853 −1.82950
\(336\) 0 0
\(337\) 2.87622 0.156678 0.0783389 0.996927i \(-0.475038\pi\)
0.0783389 + 0.996927i \(0.475038\pi\)
\(338\) 0 0
\(339\) 0.687519 0.0373409
\(340\) 0 0
\(341\) 21.0244 1.13854
\(342\) 0 0
\(343\) 17.8456 0.963569
\(344\) 0 0
\(345\) −13.9493 −0.751005
\(346\) 0 0
\(347\) −19.4818 −1.04584 −0.522918 0.852383i \(-0.675157\pi\)
−0.522918 + 0.852383i \(0.675157\pi\)
\(348\) 0 0
\(349\) 35.7705 1.91475 0.957376 0.288845i \(-0.0932713\pi\)
0.957376 + 0.288845i \(0.0932713\pi\)
\(350\) 0 0
\(351\) −3.57535 −0.190838
\(352\) 0 0
\(353\) 28.4320 1.51328 0.756640 0.653831i \(-0.226839\pi\)
0.756640 + 0.653831i \(0.226839\pi\)
\(354\) 0 0
\(355\) 19.6016 1.04035
\(356\) 0 0
\(357\) −8.68318 −0.459562
\(358\) 0 0
\(359\) 23.2239 1.22571 0.612855 0.790195i \(-0.290021\pi\)
0.612855 + 0.790195i \(0.290021\pi\)
\(360\) 0 0
\(361\) 37.3922 1.96801
\(362\) 0 0
\(363\) −13.6928 −0.718686
\(364\) 0 0
\(365\) 1.53201 0.0801893
\(366\) 0 0
\(367\) 3.39674 0.177308 0.0886542 0.996062i \(-0.471743\pi\)
0.0886542 + 0.996062i \(0.471743\pi\)
\(368\) 0 0
\(369\) −1.00478 −0.0523069
\(370\) 0 0
\(371\) −7.83960 −0.407012
\(372\) 0 0
\(373\) 24.1298 1.24939 0.624697 0.780867i \(-0.285223\pi\)
0.624697 + 0.780867i \(0.285223\pi\)
\(374\) 0 0
\(375\) −8.37822 −0.432650
\(376\) 0 0
\(377\) 13.1140 0.675406
\(378\) 0 0
\(379\) −24.5331 −1.26018 −0.630090 0.776522i \(-0.716982\pi\)
−0.630090 + 0.776522i \(0.716982\pi\)
\(380\) 0 0
\(381\) 2.53928 0.130091
\(382\) 0 0
\(383\) −2.14678 −0.109695 −0.0548477 0.998495i \(-0.517467\pi\)
−0.0548477 + 0.998495i \(0.517467\pi\)
\(384\) 0 0
\(385\) 19.8144 1.00983
\(386\) 0 0
\(387\) 1.75353 0.0891371
\(388\) 0 0
\(389\) −17.1885 −0.871493 −0.435746 0.900069i \(-0.643516\pi\)
−0.435746 + 0.900069i \(0.643516\pi\)
\(390\) 0 0
\(391\) 30.3763 1.53620
\(392\) 0 0
\(393\) −3.99950 −0.201748
\(394\) 0 0
\(395\) −8.28588 −0.416908
\(396\) 0 0
\(397\) −19.8842 −0.997961 −0.498981 0.866613i \(-0.666292\pi\)
−0.498981 + 0.866613i \(0.666292\pi\)
\(398\) 0 0
\(399\) 11.4972 0.575578
\(400\) 0 0
\(401\) 13.6547 0.681883 0.340941 0.940085i \(-0.389254\pi\)
0.340941 + 0.940085i \(0.389254\pi\)
\(402\) 0 0
\(403\) 15.1271 0.753537
\(404\) 0 0
\(405\) −2.60444 −0.129416
\(406\) 0 0
\(407\) −30.1753 −1.49573
\(408\) 0 0
\(409\) 10.3286 0.510715 0.255358 0.966847i \(-0.417807\pi\)
0.255358 + 0.966847i \(0.417807\pi\)
\(410\) 0 0
\(411\) 3.88366 0.191567
\(412\) 0 0
\(413\) −2.68143 −0.131945
\(414\) 0 0
\(415\) 3.16215 0.155224
\(416\) 0 0
\(417\) 11.2261 0.549742
\(418\) 0 0
\(419\) 2.17066 0.106044 0.0530219 0.998593i \(-0.483115\pi\)
0.0530219 + 0.998593i \(0.483115\pi\)
\(420\) 0 0
\(421\) −3.17225 −0.154606 −0.0773031 0.997008i \(-0.524631\pi\)
−0.0773031 + 0.997008i \(0.524631\pi\)
\(422\) 0 0
\(423\) −2.20924 −0.107417
\(424\) 0 0
\(425\) −10.1128 −0.490544
\(426\) 0 0
\(427\) −3.85602 −0.186606
\(428\) 0 0
\(429\) −17.7666 −0.857778
\(430\) 0 0
\(431\) −9.12452 −0.439512 −0.219756 0.975555i \(-0.570526\pi\)
−0.219756 + 0.975555i \(0.570526\pi\)
\(432\) 0 0
\(433\) 7.17758 0.344933 0.172466 0.985015i \(-0.444826\pi\)
0.172466 + 0.985015i \(0.444826\pi\)
\(434\) 0 0
\(435\) 9.55281 0.458022
\(436\) 0 0
\(437\) −40.2205 −1.92401
\(438\) 0 0
\(439\) −31.6570 −1.51091 −0.755453 0.655202i \(-0.772583\pi\)
−0.755453 + 0.655202i \(0.772583\pi\)
\(440\) 0 0
\(441\) −4.65597 −0.221713
\(442\) 0 0
\(443\) −36.1949 −1.71967 −0.859837 0.510569i \(-0.829435\pi\)
−0.859837 + 0.510569i \(0.829435\pi\)
\(444\) 0 0
\(445\) 35.0364 1.66088
\(446\) 0 0
\(447\) 2.56685 0.121408
\(448\) 0 0
\(449\) −20.4497 −0.965082 −0.482541 0.875873i \(-0.660286\pi\)
−0.482541 + 0.875873i \(0.660286\pi\)
\(450\) 0 0
\(451\) −4.99295 −0.235109
\(452\) 0 0
\(453\) −14.5577 −0.683982
\(454\) 0 0
\(455\) 14.2565 0.668356
\(456\) 0 0
\(457\) −4.52653 −0.211742 −0.105871 0.994380i \(-0.533763\pi\)
−0.105871 + 0.994380i \(0.533763\pi\)
\(458\) 0 0
\(459\) 5.67149 0.264722
\(460\) 0 0
\(461\) −5.65304 −0.263288 −0.131644 0.991297i \(-0.542026\pi\)
−0.131644 + 0.991297i \(0.542026\pi\)
\(462\) 0 0
\(463\) 12.5351 0.582555 0.291277 0.956639i \(-0.405920\pi\)
0.291277 + 0.956639i \(0.405920\pi\)
\(464\) 0 0
\(465\) 11.0193 0.511006
\(466\) 0 0
\(467\) 0.431350 0.0199605 0.00998024 0.999950i \(-0.496823\pi\)
0.00998024 + 0.999950i \(0.496823\pi\)
\(468\) 0 0
\(469\) −19.6844 −0.908941
\(470\) 0 0
\(471\) −17.7585 −0.818268
\(472\) 0 0
\(473\) 8.71363 0.400653
\(474\) 0 0
\(475\) 13.3901 0.614381
\(476\) 0 0
\(477\) 5.12050 0.234452
\(478\) 0 0
\(479\) −23.5609 −1.07652 −0.538262 0.842778i \(-0.680919\pi\)
−0.538262 + 0.842778i \(0.680919\pi\)
\(480\) 0 0
\(481\) −21.7112 −0.989947
\(482\) 0 0
\(483\) −8.20011 −0.373118
\(484\) 0 0
\(485\) 43.2475 1.96377
\(486\) 0 0
\(487\) −19.9979 −0.906191 −0.453096 0.891462i \(-0.649680\pi\)
−0.453096 + 0.891462i \(0.649680\pi\)
\(488\) 0 0
\(489\) −2.77417 −0.125452
\(490\) 0 0
\(491\) −24.9543 −1.12617 −0.563086 0.826398i \(-0.690386\pi\)
−0.563086 + 0.826398i \(0.690386\pi\)
\(492\) 0 0
\(493\) −20.8024 −0.936895
\(494\) 0 0
\(495\) −12.9419 −0.581697
\(496\) 0 0
\(497\) 11.5228 0.516870
\(498\) 0 0
\(499\) 28.7102 1.28525 0.642623 0.766182i \(-0.277846\pi\)
0.642623 + 0.766182i \(0.277846\pi\)
\(500\) 0 0
\(501\) 1.49278 0.0666925
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −37.3938 −1.66400
\(506\) 0 0
\(507\) 0.216891 0.00963247
\(508\) 0 0
\(509\) 40.9096 1.81329 0.906643 0.421899i \(-0.138636\pi\)
0.906643 + 0.421899i \(0.138636\pi\)
\(510\) 0 0
\(511\) 0.900596 0.0398400
\(512\) 0 0
\(513\) −7.50947 −0.331551
\(514\) 0 0
\(515\) 2.42405 0.106816
\(516\) 0 0
\(517\) −10.9781 −0.482818
\(518\) 0 0
\(519\) −12.3514 −0.542166
\(520\) 0 0
\(521\) −36.0090 −1.57758 −0.788792 0.614660i \(-0.789293\pi\)
−0.788792 + 0.614660i \(0.789293\pi\)
\(522\) 0 0
\(523\) 19.0800 0.834310 0.417155 0.908835i \(-0.363027\pi\)
0.417155 + 0.908835i \(0.363027\pi\)
\(524\) 0 0
\(525\) 2.72996 0.119145
\(526\) 0 0
\(527\) −23.9958 −1.04527
\(528\) 0 0
\(529\) 5.68644 0.247237
\(530\) 0 0
\(531\) 1.75140 0.0760042
\(532\) 0 0
\(533\) −3.59245 −0.155606
\(534\) 0 0
\(535\) 48.1701 2.08257
\(536\) 0 0
\(537\) −1.98419 −0.0856242
\(538\) 0 0
\(539\) −23.1364 −0.996554
\(540\) 0 0
\(541\) 16.2772 0.699810 0.349905 0.936785i \(-0.386214\pi\)
0.349905 + 0.936785i \(0.386214\pi\)
\(542\) 0 0
\(543\) −4.44069 −0.190568
\(544\) 0 0
\(545\) −14.5699 −0.624106
\(546\) 0 0
\(547\) 5.83056 0.249297 0.124648 0.992201i \(-0.460220\pi\)
0.124648 + 0.992201i \(0.460220\pi\)
\(548\) 0 0
\(549\) 2.51859 0.107491
\(550\) 0 0
\(551\) 27.5440 1.17341
\(552\) 0 0
\(553\) −4.87087 −0.207130
\(554\) 0 0
\(555\) −15.8154 −0.671327
\(556\) 0 0
\(557\) 30.8077 1.30536 0.652681 0.757633i \(-0.273644\pi\)
0.652681 + 0.757633i \(0.273644\pi\)
\(558\) 0 0
\(559\) 6.26949 0.265171
\(560\) 0 0
\(561\) 28.1827 1.18987
\(562\) 0 0
\(563\) −18.7838 −0.791641 −0.395820 0.918328i \(-0.629540\pi\)
−0.395820 + 0.918328i \(0.629540\pi\)
\(564\) 0 0
\(565\) 1.79060 0.0753312
\(566\) 0 0
\(567\) −1.53102 −0.0642969
\(568\) 0 0
\(569\) 16.9298 0.709732 0.354866 0.934917i \(-0.384526\pi\)
0.354866 + 0.934917i \(0.384526\pi\)
\(570\) 0 0
\(571\) 10.7282 0.448962 0.224481 0.974478i \(-0.427931\pi\)
0.224481 + 0.974478i \(0.427931\pi\)
\(572\) 0 0
\(573\) −6.71869 −0.280677
\(574\) 0 0
\(575\) −9.55022 −0.398272
\(576\) 0 0
\(577\) −13.8899 −0.578244 −0.289122 0.957292i \(-0.593363\pi\)
−0.289122 + 0.957292i \(0.593363\pi\)
\(578\) 0 0
\(579\) 13.0665 0.543025
\(580\) 0 0
\(581\) 1.85888 0.0771191
\(582\) 0 0
\(583\) 25.4447 1.05381
\(584\) 0 0
\(585\) −9.31177 −0.384994
\(586\) 0 0
\(587\) −42.5350 −1.75561 −0.877804 0.479019i \(-0.840992\pi\)
−0.877804 + 0.479019i \(0.840992\pi\)
\(588\) 0 0
\(589\) 31.7723 1.30915
\(590\) 0 0
\(591\) −13.7962 −0.567501
\(592\) 0 0
\(593\) 16.5124 0.678082 0.339041 0.940772i \(-0.389897\pi\)
0.339041 + 0.940772i \(0.389897\pi\)
\(594\) 0 0
\(595\) −22.6148 −0.927116
\(596\) 0 0
\(597\) −1.87652 −0.0768007
\(598\) 0 0
\(599\) −33.9060 −1.38536 −0.692682 0.721243i \(-0.743571\pi\)
−0.692682 + 0.721243i \(0.743571\pi\)
\(600\) 0 0
\(601\) 27.0745 1.10439 0.552196 0.833714i \(-0.313790\pi\)
0.552196 + 0.833714i \(0.313790\pi\)
\(602\) 0 0
\(603\) 12.8570 0.523578
\(604\) 0 0
\(605\) −35.6621 −1.44987
\(606\) 0 0
\(607\) −36.1212 −1.46611 −0.733057 0.680168i \(-0.761907\pi\)
−0.733057 + 0.680168i \(0.761907\pi\)
\(608\) 0 0
\(609\) 5.61563 0.227557
\(610\) 0 0
\(611\) −7.89881 −0.319552
\(612\) 0 0
\(613\) −12.4341 −0.502209 −0.251105 0.967960i \(-0.580794\pi\)
−0.251105 + 0.967960i \(0.580794\pi\)
\(614\) 0 0
\(615\) −2.61690 −0.105523
\(616\) 0 0
\(617\) −24.9748 −1.00545 −0.502723 0.864447i \(-0.667669\pi\)
−0.502723 + 0.864447i \(0.667669\pi\)
\(618\) 0 0
\(619\) 2.49189 0.100157 0.0500787 0.998745i \(-0.484053\pi\)
0.0500787 + 0.998745i \(0.484053\pi\)
\(620\) 0 0
\(621\) 5.35597 0.214928
\(622\) 0 0
\(623\) 20.5962 0.825168
\(624\) 0 0
\(625\) −30.7361 −1.22944
\(626\) 0 0
\(627\) −37.3160 −1.49026
\(628\) 0 0
\(629\) 34.4400 1.37321
\(630\) 0 0
\(631\) 34.8386 1.38690 0.693451 0.720504i \(-0.256089\pi\)
0.693451 + 0.720504i \(0.256089\pi\)
\(632\) 0 0
\(633\) 7.48033 0.297316
\(634\) 0 0
\(635\) 6.61339 0.262444
\(636\) 0 0
\(637\) −16.6467 −0.659567
\(638\) 0 0
\(639\) −7.52624 −0.297733
\(640\) 0 0
\(641\) −27.1526 −1.07247 −0.536233 0.844070i \(-0.680153\pi\)
−0.536233 + 0.844070i \(0.680153\pi\)
\(642\) 0 0
\(643\) 12.7032 0.500965 0.250483 0.968121i \(-0.419411\pi\)
0.250483 + 0.968121i \(0.419411\pi\)
\(644\) 0 0
\(645\) 4.56697 0.179824
\(646\) 0 0
\(647\) 20.4500 0.803974 0.401987 0.915645i \(-0.368320\pi\)
0.401987 + 0.915645i \(0.368320\pi\)
\(648\) 0 0
\(649\) 8.70302 0.341624
\(650\) 0 0
\(651\) 6.47769 0.253881
\(652\) 0 0
\(653\) −10.0442 −0.393061 −0.196530 0.980498i \(-0.562967\pi\)
−0.196530 + 0.980498i \(0.562967\pi\)
\(654\) 0 0
\(655\) −10.4165 −0.407005
\(656\) 0 0
\(657\) −0.588232 −0.0229491
\(658\) 0 0
\(659\) −41.2908 −1.60846 −0.804231 0.594317i \(-0.797422\pi\)
−0.804231 + 0.594317i \(0.797422\pi\)
\(660\) 0 0
\(661\) 2.52344 0.0981504 0.0490752 0.998795i \(-0.484373\pi\)
0.0490752 + 0.998795i \(0.484373\pi\)
\(662\) 0 0
\(663\) 20.2775 0.787514
\(664\) 0 0
\(665\) 29.9437 1.16117
\(666\) 0 0
\(667\) −19.6452 −0.760664
\(668\) 0 0
\(669\) −24.3790 −0.942547
\(670\) 0 0
\(671\) 12.5153 0.483149
\(672\) 0 0
\(673\) −16.8799 −0.650670 −0.325335 0.945599i \(-0.605477\pi\)
−0.325335 + 0.945599i \(0.605477\pi\)
\(674\) 0 0
\(675\) −1.78310 −0.0686315
\(676\) 0 0
\(677\) 18.7503 0.720632 0.360316 0.932830i \(-0.382669\pi\)
0.360316 + 0.932830i \(0.382669\pi\)
\(678\) 0 0
\(679\) 25.4231 0.975649
\(680\) 0 0
\(681\) 6.35944 0.243694
\(682\) 0 0
\(683\) 47.8176 1.82969 0.914844 0.403807i \(-0.132313\pi\)
0.914844 + 0.403807i \(0.132313\pi\)
\(684\) 0 0
\(685\) 10.1147 0.386465
\(686\) 0 0
\(687\) −19.0492 −0.726771
\(688\) 0 0
\(689\) 18.3076 0.697463
\(690\) 0 0
\(691\) 20.8495 0.793151 0.396575 0.918002i \(-0.370199\pi\)
0.396575 + 0.918002i \(0.370199\pi\)
\(692\) 0 0
\(693\) −7.60793 −0.289002
\(694\) 0 0
\(695\) 29.2376 1.10904
\(696\) 0 0
\(697\) 5.69861 0.215850
\(698\) 0 0
\(699\) −15.3385 −0.580156
\(700\) 0 0
\(701\) 29.7457 1.12348 0.561741 0.827313i \(-0.310132\pi\)
0.561741 + 0.827313i \(0.310132\pi\)
\(702\) 0 0
\(703\) −45.6012 −1.71988
\(704\) 0 0
\(705\) −5.75384 −0.216702
\(706\) 0 0
\(707\) −21.9820 −0.826717
\(708\) 0 0
\(709\) 33.9443 1.27480 0.637402 0.770532i \(-0.280009\pi\)
0.637402 + 0.770532i \(0.280009\pi\)
\(710\) 0 0
\(711\) 3.18145 0.119314
\(712\) 0 0
\(713\) −22.6609 −0.848657
\(714\) 0 0
\(715\) −46.2719 −1.73047
\(716\) 0 0
\(717\) −20.1708 −0.753291
\(718\) 0 0
\(719\) −7.94929 −0.296459 −0.148229 0.988953i \(-0.547357\pi\)
−0.148229 + 0.988953i \(0.547357\pi\)
\(720\) 0 0
\(721\) 1.42498 0.0530691
\(722\) 0 0
\(723\) −22.8061 −0.848168
\(724\) 0 0
\(725\) 6.54022 0.242898
\(726\) 0 0
\(727\) −39.6257 −1.46964 −0.734818 0.678264i \(-0.762733\pi\)
−0.734818 + 0.678264i \(0.762733\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −9.94515 −0.367835
\(732\) 0 0
\(733\) 35.3545 1.30585 0.652923 0.757424i \(-0.273542\pi\)
0.652923 + 0.757424i \(0.273542\pi\)
\(734\) 0 0
\(735\) −12.1262 −0.447281
\(736\) 0 0
\(737\) 63.8889 2.35338
\(738\) 0 0
\(739\) 31.1775 1.14688 0.573441 0.819247i \(-0.305608\pi\)
0.573441 + 0.819247i \(0.305608\pi\)
\(740\) 0 0
\(741\) −26.8490 −0.986322
\(742\) 0 0
\(743\) −6.53170 −0.239625 −0.119812 0.992797i \(-0.538229\pi\)
−0.119812 + 0.992797i \(0.538229\pi\)
\(744\) 0 0
\(745\) 6.68520 0.244927
\(746\) 0 0
\(747\) −1.21414 −0.0444230
\(748\) 0 0
\(749\) 28.3168 1.03468
\(750\) 0 0
\(751\) 47.7077 1.74088 0.870439 0.492277i \(-0.163835\pi\)
0.870439 + 0.492277i \(0.163835\pi\)
\(752\) 0 0
\(753\) −27.2851 −0.994325
\(754\) 0 0
\(755\) −37.9147 −1.37986
\(756\) 0 0
\(757\) −47.8335 −1.73854 −0.869269 0.494339i \(-0.835410\pi\)
−0.869269 + 0.494339i \(0.835410\pi\)
\(758\) 0 0
\(759\) 26.6148 0.966057
\(760\) 0 0
\(761\) −0.784035 −0.0284212 −0.0142106 0.999899i \(-0.504524\pi\)
−0.0142106 + 0.999899i \(0.504524\pi\)
\(762\) 0 0
\(763\) −8.56494 −0.310072
\(764\) 0 0
\(765\) 14.7710 0.534048
\(766\) 0 0
\(767\) 6.26186 0.226103
\(768\) 0 0
\(769\) 42.1434 1.51973 0.759864 0.650082i \(-0.225265\pi\)
0.759864 + 0.650082i \(0.225265\pi\)
\(770\) 0 0
\(771\) −29.0322 −1.04557
\(772\) 0 0
\(773\) −13.2457 −0.476413 −0.238207 0.971214i \(-0.576560\pi\)
−0.238207 + 0.971214i \(0.576560\pi\)
\(774\) 0 0
\(775\) 7.54421 0.270996
\(776\) 0 0
\(777\) −9.29711 −0.333532
\(778\) 0 0
\(779\) −7.54539 −0.270342
\(780\) 0 0
\(781\) −37.3993 −1.33825
\(782\) 0 0
\(783\) −3.66790 −0.131080
\(784\) 0 0
\(785\) −46.2509 −1.65077
\(786\) 0 0
\(787\) 31.5151 1.12339 0.561696 0.827343i \(-0.310149\pi\)
0.561696 + 0.827343i \(0.310149\pi\)
\(788\) 0 0
\(789\) 3.16211 0.112574
\(790\) 0 0
\(791\) 1.05261 0.0374264
\(792\) 0 0
\(793\) 9.00483 0.319771
\(794\) 0 0
\(795\) 13.3360 0.472980
\(796\) 0 0
\(797\) 6.25486 0.221559 0.110779 0.993845i \(-0.464665\pi\)
0.110779 + 0.993845i \(0.464665\pi\)
\(798\) 0 0
\(799\) 12.5297 0.443269
\(800\) 0 0
\(801\) −13.4526 −0.475323
\(802\) 0 0
\(803\) −2.92303 −0.103152
\(804\) 0 0
\(805\) −21.3567 −0.752724
\(806\) 0 0
\(807\) 4.24758 0.149522
\(808\) 0 0
\(809\) 2.05770 0.0723448 0.0361724 0.999346i \(-0.488483\pi\)
0.0361724 + 0.999346i \(0.488483\pi\)
\(810\) 0 0
\(811\) 4.69233 0.164770 0.0823851 0.996601i \(-0.473746\pi\)
0.0823851 + 0.996601i \(0.473746\pi\)
\(812\) 0 0
\(813\) −12.7020 −0.445480
\(814\) 0 0
\(815\) −7.22514 −0.253086
\(816\) 0 0
\(817\) 13.1681 0.460694
\(818\) 0 0
\(819\) −5.47394 −0.191275
\(820\) 0 0
\(821\) −11.4084 −0.398157 −0.199078 0.979984i \(-0.563795\pi\)
−0.199078 + 0.979984i \(0.563795\pi\)
\(822\) 0 0
\(823\) 37.7270 1.31508 0.657540 0.753420i \(-0.271597\pi\)
0.657540 + 0.753420i \(0.271597\pi\)
\(824\) 0 0
\(825\) −8.86054 −0.308485
\(826\) 0 0
\(827\) 32.1800 1.11901 0.559504 0.828827i \(-0.310991\pi\)
0.559504 + 0.828827i \(0.310991\pi\)
\(828\) 0 0
\(829\) −52.4790 −1.82267 −0.911336 0.411664i \(-0.864948\pi\)
−0.911336 + 0.411664i \(0.864948\pi\)
\(830\) 0 0
\(831\) −11.3458 −0.393581
\(832\) 0 0
\(833\) 26.4063 0.914923
\(834\) 0 0
\(835\) 3.88785 0.134545
\(836\) 0 0
\(837\) −4.23096 −0.146243
\(838\) 0 0
\(839\) −11.8577 −0.409372 −0.204686 0.978828i \(-0.565617\pi\)
−0.204686 + 0.978828i \(0.565617\pi\)
\(840\) 0 0
\(841\) −15.5465 −0.536087
\(842\) 0 0
\(843\) 8.24035 0.283813
\(844\) 0 0
\(845\) 0.564880 0.0194324
\(846\) 0 0
\(847\) −20.9640 −0.720331
\(848\) 0 0
\(849\) −16.5964 −0.569588
\(850\) 0 0
\(851\) 32.5241 1.11491
\(852\) 0 0
\(853\) 24.6461 0.843868 0.421934 0.906627i \(-0.361351\pi\)
0.421934 + 0.906627i \(0.361351\pi\)
\(854\) 0 0
\(855\) −19.5580 −0.668868
\(856\) 0 0
\(857\) 24.2410 0.828057 0.414028 0.910264i \(-0.364121\pi\)
0.414028 + 0.910264i \(0.364121\pi\)
\(858\) 0 0
\(859\) −17.8246 −0.608166 −0.304083 0.952646i \(-0.598350\pi\)
−0.304083 + 0.952646i \(0.598350\pi\)
\(860\) 0 0
\(861\) −1.53835 −0.0524267
\(862\) 0 0
\(863\) −29.9302 −1.01883 −0.509417 0.860520i \(-0.670139\pi\)
−0.509417 + 0.860520i \(0.670139\pi\)
\(864\) 0 0
\(865\) −32.1684 −1.09376
\(866\) 0 0
\(867\) −15.1658 −0.515057
\(868\) 0 0
\(869\) 15.8092 0.536290
\(870\) 0 0
\(871\) 45.9683 1.55758
\(872\) 0 0
\(873\) −16.6053 −0.562005
\(874\) 0 0
\(875\) −12.8272 −0.433640
\(876\) 0 0
\(877\) 38.9181 1.31417 0.657085 0.753816i \(-0.271789\pi\)
0.657085 + 0.753816i \(0.271789\pi\)
\(878\) 0 0
\(879\) 3.57802 0.120684
\(880\) 0 0
\(881\) 10.2233 0.344431 0.172216 0.985059i \(-0.444907\pi\)
0.172216 + 0.985059i \(0.444907\pi\)
\(882\) 0 0
\(883\) −0.0661155 −0.00222497 −0.00111248 0.999999i \(-0.500354\pi\)
−0.00111248 + 0.999999i \(0.500354\pi\)
\(884\) 0 0
\(885\) 4.56141 0.153330
\(886\) 0 0
\(887\) −13.5336 −0.454412 −0.227206 0.973847i \(-0.572959\pi\)
−0.227206 + 0.973847i \(0.572959\pi\)
\(888\) 0 0
\(889\) 3.88769 0.130389
\(890\) 0 0
\(891\) 4.96919 0.166474
\(892\) 0 0
\(893\) −16.5902 −0.555171
\(894\) 0 0
\(895\) −5.16770 −0.172737
\(896\) 0 0
\(897\) 19.1495 0.639382
\(898\) 0 0
\(899\) 15.5187 0.517578
\(900\) 0 0
\(901\) −29.0409 −0.967492
\(902\) 0 0
\(903\) 2.68470 0.0893412
\(904\) 0 0
\(905\) −11.5655 −0.384450
\(906\) 0 0
\(907\) 23.1097 0.767345 0.383672 0.923469i \(-0.374659\pi\)
0.383672 + 0.923469i \(0.374659\pi\)
\(908\) 0 0
\(909\) 14.3577 0.476215
\(910\) 0 0
\(911\) 33.0818 1.09605 0.548024 0.836463i \(-0.315380\pi\)
0.548024 + 0.836463i \(0.315380\pi\)
\(912\) 0 0
\(913\) −6.03329 −0.199673
\(914\) 0 0
\(915\) 6.55951 0.216851
\(916\) 0 0
\(917\) −6.12333 −0.202210
\(918\) 0 0
\(919\) −40.3561 −1.33122 −0.665612 0.746298i \(-0.731830\pi\)
−0.665612 + 0.746298i \(0.731830\pi\)
\(920\) 0 0
\(921\) −19.1089 −0.629660
\(922\) 0 0
\(923\) −26.9089 −0.885718
\(924\) 0 0
\(925\) −10.8278 −0.356017
\(926\) 0 0
\(927\) −0.930739 −0.0305695
\(928\) 0 0
\(929\) 12.2446 0.401732 0.200866 0.979619i \(-0.435624\pi\)
0.200866 + 0.979619i \(0.435624\pi\)
\(930\) 0 0
\(931\) −34.9639 −1.14590
\(932\) 0 0
\(933\) −0.227763 −0.00745664
\(934\) 0 0
\(935\) 73.4000 2.40044
\(936\) 0 0
\(937\) 22.6841 0.741058 0.370529 0.928821i \(-0.379176\pi\)
0.370529 + 0.928821i \(0.379176\pi\)
\(938\) 0 0
\(939\) 11.6885 0.381438
\(940\) 0 0
\(941\) 29.4377 0.959640 0.479820 0.877367i \(-0.340702\pi\)
0.479820 + 0.877367i \(0.340702\pi\)
\(942\) 0 0
\(943\) 5.38159 0.175249
\(944\) 0 0
\(945\) −3.98745 −0.129712
\(946\) 0 0
\(947\) 15.6199 0.507580 0.253790 0.967259i \(-0.418323\pi\)
0.253790 + 0.967259i \(0.418323\pi\)
\(948\) 0 0
\(949\) −2.10313 −0.0682706
\(950\) 0 0
\(951\) −0.785578 −0.0254741
\(952\) 0 0
\(953\) −23.0916 −0.748011 −0.374005 0.927427i \(-0.622016\pi\)
−0.374005 + 0.927427i \(0.622016\pi\)
\(954\) 0 0
\(955\) −17.4984 −0.566235
\(956\) 0 0
\(957\) −18.2265 −0.589178
\(958\) 0 0
\(959\) 5.94597 0.192005
\(960\) 0 0
\(961\) −13.0990 −0.422548
\(962\) 0 0
\(963\) −18.4954 −0.596005
\(964\) 0 0
\(965\) 34.0309 1.09549
\(966\) 0 0
\(967\) −34.2961 −1.10289 −0.551444 0.834212i \(-0.685923\pi\)
−0.551444 + 0.834212i \(0.685923\pi\)
\(968\) 0 0
\(969\) 42.5899 1.36818
\(970\) 0 0
\(971\) 34.7796 1.11613 0.558065 0.829797i \(-0.311544\pi\)
0.558065 + 0.829797i \(0.311544\pi\)
\(972\) 0 0
\(973\) 17.1873 0.551001
\(974\) 0 0
\(975\) −6.37519 −0.204170
\(976\) 0 0
\(977\) 40.6246 1.29970 0.649848 0.760065i \(-0.274833\pi\)
0.649848 + 0.760065i \(0.274833\pi\)
\(978\) 0 0
\(979\) −66.8483 −2.13648
\(980\) 0 0
\(981\) 5.59426 0.178611
\(982\) 0 0
\(983\) 60.5150 1.93013 0.965064 0.262013i \(-0.0843864\pi\)
0.965064 + 0.262013i \(0.0843864\pi\)
\(984\) 0 0
\(985\) −35.9314 −1.14487
\(986\) 0 0
\(987\) −3.38240 −0.107663
\(988\) 0 0
\(989\) −9.39188 −0.298644
\(990\) 0 0
\(991\) −27.6457 −0.878193 −0.439097 0.898440i \(-0.644701\pi\)
−0.439097 + 0.898440i \(0.644701\pi\)
\(992\) 0 0
\(993\) 14.5158 0.460645
\(994\) 0 0
\(995\) −4.88727 −0.154937
\(996\) 0 0
\(997\) 52.5392 1.66393 0.831966 0.554826i \(-0.187215\pi\)
0.831966 + 0.554826i \(0.187215\pi\)
\(998\) 0 0
\(999\) 6.07248 0.192125
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 \(a_p\))