Properties

Label 8001.2.a.u.1.2
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 18
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.24824\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.24824 q^{2}\) \(+3.05458 q^{4}\) \(+3.31434 q^{5}\) \(+1.00000 q^{7}\) \(-2.37095 q^{8}\) \(+O(q^{10})\) \(q\)\(-2.24824 q^{2}\) \(+3.05458 q^{4}\) \(+3.31434 q^{5}\) \(+1.00000 q^{7}\) \(-2.37095 q^{8}\) \(-7.45143 q^{10}\) \(-5.47711 q^{11}\) \(-4.39594 q^{13}\) \(-2.24824 q^{14}\) \(-0.778706 q^{16}\) \(+2.99559 q^{17}\) \(-0.499179 q^{19}\) \(+10.1239 q^{20}\) \(+12.3138 q^{22}\) \(+6.47149 q^{23}\) \(+5.98485 q^{25}\) \(+9.88313 q^{26}\) \(+3.05458 q^{28}\) \(-2.28220 q^{29}\) \(+4.20474 q^{31}\) \(+6.49261 q^{32}\) \(-6.73481 q^{34}\) \(+3.31434 q^{35}\) \(-7.84180 q^{37}\) \(+1.12227 q^{38}\) \(-7.85812 q^{40}\) \(+7.43947 q^{41}\) \(+6.74366 q^{43}\) \(-16.7303 q^{44}\) \(-14.5494 q^{46}\) \(+8.99909 q^{47}\) \(+1.00000 q^{49}\) \(-13.4554 q^{50}\) \(-13.4278 q^{52}\) \(+1.35946 q^{53}\) \(-18.1530 q^{55}\) \(-2.37095 q^{56}\) \(+5.13092 q^{58}\) \(+5.28556 q^{59}\) \(+0.533481 q^{61}\) \(-9.45326 q^{62}\) \(-13.0395 q^{64}\) \(-14.5696 q^{65}\) \(-14.0967 q^{67}\) \(+9.15028 q^{68}\) \(-7.45143 q^{70}\) \(+6.62684 q^{71}\) \(+6.36264 q^{73}\) \(+17.6302 q^{74}\) \(-1.52478 q^{76}\) \(-5.47711 q^{77}\) \(-15.8144 q^{79}\) \(-2.58089 q^{80}\) \(-16.7257 q^{82}\) \(-5.96805 q^{83}\) \(+9.92842 q^{85}\) \(-15.1614 q^{86}\) \(+12.9859 q^{88}\) \(-6.57010 q^{89}\) \(-4.39594 q^{91}\) \(+19.7677 q^{92}\) \(-20.2321 q^{94}\) \(-1.65445 q^{95}\) \(+12.5689 q^{97}\) \(-2.24824 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 25q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 21q^{20} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut +\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut +\mathstrut 22q^{38} \) \(\mathstrut -\mathstrut q^{40} \) \(\mathstrut +\mathstrut 17q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut +\mathstrut 33q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut +\mathstrut 31q^{47} \) \(\mathstrut +\mathstrut 18q^{49} \) \(\mathstrut +\mathstrut 35q^{50} \) \(\mathstrut -\mathstrut 70q^{52} \) \(\mathstrut +\mathstrut 35q^{53} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 46q^{59} \) \(\mathstrut -\mathstrut 5q^{61} \) \(\mathstrut +\mathstrut 10q^{62} \) \(\mathstrut +\mathstrut 63q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 56q^{68} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 18q^{74} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 46q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 46q^{83} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 18q^{86} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 48q^{92} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 35q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.24824 −1.58975 −0.794873 0.606776i \(-0.792462\pi\)
−0.794873 + 0.606776i \(0.792462\pi\)
\(3\) 0 0
\(4\) 3.05458 1.52729
\(5\) 3.31434 1.48222 0.741109 0.671385i \(-0.234300\pi\)
0.741109 + 0.671385i \(0.234300\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −2.37095 −0.838256
\(9\) 0 0
\(10\) −7.45143 −2.35635
\(11\) −5.47711 −1.65141 −0.825705 0.564102i \(-0.809222\pi\)
−0.825705 + 0.564102i \(0.809222\pi\)
\(12\) 0 0
\(13\) −4.39594 −1.21921 −0.609607 0.792703i \(-0.708673\pi\)
−0.609607 + 0.792703i \(0.708673\pi\)
\(14\) −2.24824 −0.600867
\(15\) 0 0
\(16\) −0.778706 −0.194676
\(17\) 2.99559 0.726538 0.363269 0.931684i \(-0.381661\pi\)
0.363269 + 0.931684i \(0.381661\pi\)
\(18\) 0 0
\(19\) −0.499179 −0.114519 −0.0572597 0.998359i \(-0.518236\pi\)
−0.0572597 + 0.998359i \(0.518236\pi\)
\(20\) 10.1239 2.26378
\(21\) 0 0
\(22\) 12.3138 2.62532
\(23\) 6.47149 1.34940 0.674699 0.738093i \(-0.264273\pi\)
0.674699 + 0.738093i \(0.264273\pi\)
\(24\) 0 0
\(25\) 5.98485 1.19697
\(26\) 9.88313 1.93824
\(27\) 0 0
\(28\) 3.05458 0.577261
\(29\) −2.28220 −0.423793 −0.211897 0.977292i \(-0.567964\pi\)
−0.211897 + 0.977292i \(0.567964\pi\)
\(30\) 0 0
\(31\) 4.20474 0.755193 0.377597 0.925970i \(-0.376751\pi\)
0.377597 + 0.925970i \(0.376751\pi\)
\(32\) 6.49261 1.14774
\(33\) 0 0
\(34\) −6.73481 −1.15501
\(35\) 3.31434 0.560226
\(36\) 0 0
\(37\) −7.84180 −1.28918 −0.644592 0.764526i \(-0.722973\pi\)
−0.644592 + 0.764526i \(0.722973\pi\)
\(38\) 1.12227 0.182057
\(39\) 0 0
\(40\) −7.85812 −1.24248
\(41\) 7.43947 1.16185 0.580925 0.813957i \(-0.302691\pi\)
0.580925 + 0.813957i \(0.302691\pi\)
\(42\) 0 0
\(43\) 6.74366 1.02840 0.514200 0.857671i \(-0.328089\pi\)
0.514200 + 0.857671i \(0.328089\pi\)
\(44\) −16.7303 −2.52218
\(45\) 0 0
\(46\) −14.5494 −2.14520
\(47\) 8.99909 1.31265 0.656326 0.754477i \(-0.272110\pi\)
0.656326 + 0.754477i \(0.272110\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −13.4554 −1.90288
\(51\) 0 0
\(52\) −13.4278 −1.86209
\(53\) 1.35946 0.186736 0.0933679 0.995632i \(-0.470237\pi\)
0.0933679 + 0.995632i \(0.470237\pi\)
\(54\) 0 0
\(55\) −18.1530 −2.44775
\(56\) −2.37095 −0.316831
\(57\) 0 0
\(58\) 5.13092 0.673723
\(59\) 5.28556 0.688121 0.344061 0.938947i \(-0.388197\pi\)
0.344061 + 0.938947i \(0.388197\pi\)
\(60\) 0 0
\(61\) 0.533481 0.0683053 0.0341526 0.999417i \(-0.489127\pi\)
0.0341526 + 0.999417i \(0.489127\pi\)
\(62\) −9.45326 −1.20057
\(63\) 0 0
\(64\) −13.0395 −1.62994
\(65\) −14.5696 −1.80714
\(66\) 0 0
\(67\) −14.0967 −1.72218 −0.861092 0.508449i \(-0.830219\pi\)
−0.861092 + 0.508449i \(0.830219\pi\)
\(68\) 9.15028 1.10963
\(69\) 0 0
\(70\) −7.45143 −0.890616
\(71\) 6.62684 0.786461 0.393231 0.919440i \(-0.371357\pi\)
0.393231 + 0.919440i \(0.371357\pi\)
\(72\) 0 0
\(73\) 6.36264 0.744691 0.372345 0.928094i \(-0.378554\pi\)
0.372345 + 0.928094i \(0.378554\pi\)
\(74\) 17.6302 2.04947
\(75\) 0 0
\(76\) −1.52478 −0.174904
\(77\) −5.47711 −0.624174
\(78\) 0 0
\(79\) −15.8144 −1.77926 −0.889628 0.456686i \(-0.849036\pi\)
−0.889628 + 0.456686i \(0.849036\pi\)
\(80\) −2.58089 −0.288553
\(81\) 0 0
\(82\) −16.7257 −1.84705
\(83\) −5.96805 −0.655079 −0.327539 0.944838i \(-0.606219\pi\)
−0.327539 + 0.944838i \(0.606219\pi\)
\(84\) 0 0
\(85\) 9.92842 1.07689
\(86\) −15.1614 −1.63489
\(87\) 0 0
\(88\) 12.9859 1.38430
\(89\) −6.57010 −0.696429 −0.348215 0.937415i \(-0.613212\pi\)
−0.348215 + 0.937415i \(0.613212\pi\)
\(90\) 0 0
\(91\) −4.39594 −0.460820
\(92\) 19.7677 2.06092
\(93\) 0 0
\(94\) −20.2321 −2.08678
\(95\) −1.65445 −0.169743
\(96\) 0 0
\(97\) 12.5689 1.27618 0.638092 0.769960i \(-0.279724\pi\)
0.638092 + 0.769960i \(0.279724\pi\)
\(98\) −2.24824 −0.227106
\(99\) 0 0
\(100\) 18.2812 1.82812
\(101\) 4.31831 0.429688 0.214844 0.976648i \(-0.431076\pi\)
0.214844 + 0.976648i \(0.431076\pi\)
\(102\) 0 0
\(103\) −7.67776 −0.756512 −0.378256 0.925701i \(-0.623476\pi\)
−0.378256 + 0.925701i \(0.623476\pi\)
\(104\) 10.4225 1.02201
\(105\) 0 0
\(106\) −3.05638 −0.296862
\(107\) 6.15637 0.595159 0.297579 0.954697i \(-0.403821\pi\)
0.297579 + 0.954697i \(0.403821\pi\)
\(108\) 0 0
\(109\) −15.1231 −1.44853 −0.724263 0.689524i \(-0.757820\pi\)
−0.724263 + 0.689524i \(0.757820\pi\)
\(110\) 40.8123 3.89130
\(111\) 0 0
\(112\) −0.778706 −0.0735808
\(113\) −1.57617 −0.148273 −0.0741366 0.997248i \(-0.523620\pi\)
−0.0741366 + 0.997248i \(0.523620\pi\)
\(114\) 0 0
\(115\) 21.4487 2.00010
\(116\) −6.97115 −0.647255
\(117\) 0 0
\(118\) −11.8832 −1.09394
\(119\) 2.99559 0.274606
\(120\) 0 0
\(121\) 18.9987 1.72715
\(122\) −1.19939 −0.108588
\(123\) 0 0
\(124\) 12.8437 1.15340
\(125\) 3.26412 0.291951
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 16.3307 1.44345
\(129\) 0 0
\(130\) 32.7560 2.87289
\(131\) −0.0249085 −0.00217626 −0.00108813 0.999999i \(-0.500346\pi\)
−0.00108813 + 0.999999i \(0.500346\pi\)
\(132\) 0 0
\(133\) −0.499179 −0.0432843
\(134\) 31.6927 2.73783
\(135\) 0 0
\(136\) −7.10239 −0.609025
\(137\) −19.2352 −1.64337 −0.821685 0.569942i \(-0.806966\pi\)
−0.821685 + 0.569942i \(0.806966\pi\)
\(138\) 0 0
\(139\) 6.80780 0.577430 0.288715 0.957415i \(-0.406772\pi\)
0.288715 + 0.957415i \(0.406772\pi\)
\(140\) 10.1239 0.855627
\(141\) 0 0
\(142\) −14.8987 −1.25027
\(143\) 24.0770 2.01342
\(144\) 0 0
\(145\) −7.56397 −0.628154
\(146\) −14.3047 −1.18387
\(147\) 0 0
\(148\) −23.9534 −1.96896
\(149\) 11.2791 0.924021 0.462010 0.886874i \(-0.347128\pi\)
0.462010 + 0.886874i \(0.347128\pi\)
\(150\) 0 0
\(151\) 2.10031 0.170920 0.0854602 0.996342i \(-0.472764\pi\)
0.0854602 + 0.996342i \(0.472764\pi\)
\(152\) 1.18353 0.0959966
\(153\) 0 0
\(154\) 12.3138 0.992278
\(155\) 13.9359 1.11936
\(156\) 0 0
\(157\) 14.5687 1.16271 0.581353 0.813651i \(-0.302523\pi\)
0.581353 + 0.813651i \(0.302523\pi\)
\(158\) 35.5545 2.82856
\(159\) 0 0
\(160\) 21.5187 1.70120
\(161\) 6.47149 0.510025
\(162\) 0 0
\(163\) −2.35015 −0.184078 −0.0920390 0.995755i \(-0.529338\pi\)
−0.0920390 + 0.995755i \(0.529338\pi\)
\(164\) 22.7245 1.77448
\(165\) 0 0
\(166\) 13.4176 1.04141
\(167\) 23.4699 1.81616 0.908079 0.418800i \(-0.137549\pi\)
0.908079 + 0.418800i \(0.137549\pi\)
\(168\) 0 0
\(169\) 6.32430 0.486485
\(170\) −22.3215 −1.71198
\(171\) 0 0
\(172\) 20.5991 1.57066
\(173\) −2.47947 −0.188511 −0.0942555 0.995548i \(-0.530047\pi\)
−0.0942555 + 0.995548i \(0.530047\pi\)
\(174\) 0 0
\(175\) 5.98485 0.452412
\(176\) 4.26505 0.321490
\(177\) 0 0
\(178\) 14.7712 1.10715
\(179\) −9.59334 −0.717040 −0.358520 0.933522i \(-0.616718\pi\)
−0.358520 + 0.933522i \(0.616718\pi\)
\(180\) 0 0
\(181\) 1.01943 0.0757737 0.0378868 0.999282i \(-0.487937\pi\)
0.0378868 + 0.999282i \(0.487937\pi\)
\(182\) 9.88313 0.732586
\(183\) 0 0
\(184\) −15.3435 −1.13114
\(185\) −25.9904 −1.91085
\(186\) 0 0
\(187\) −16.4072 −1.19981
\(188\) 27.4884 2.00480
\(189\) 0 0
\(190\) 3.71959 0.269848
\(191\) −9.93407 −0.718804 −0.359402 0.933183i \(-0.617019\pi\)
−0.359402 + 0.933183i \(0.617019\pi\)
\(192\) 0 0
\(193\) 15.2597 1.09842 0.549209 0.835685i \(-0.314929\pi\)
0.549209 + 0.835685i \(0.314929\pi\)
\(194\) −28.2580 −2.02881
\(195\) 0 0
\(196\) 3.05458 0.218184
\(197\) 12.0045 0.855287 0.427644 0.903947i \(-0.359344\pi\)
0.427644 + 0.903947i \(0.359344\pi\)
\(198\) 0 0
\(199\) 22.0679 1.56435 0.782174 0.623060i \(-0.214111\pi\)
0.782174 + 0.623060i \(0.214111\pi\)
\(200\) −14.1897 −1.00337
\(201\) 0 0
\(202\) −9.70860 −0.683095
\(203\) −2.28220 −0.160179
\(204\) 0 0
\(205\) 24.6569 1.72211
\(206\) 17.2614 1.20266
\(207\) 0 0
\(208\) 3.42314 0.237352
\(209\) 2.73405 0.189119
\(210\) 0 0
\(211\) 23.3444 1.60710 0.803548 0.595239i \(-0.202943\pi\)
0.803548 + 0.595239i \(0.202943\pi\)
\(212\) 4.15257 0.285200
\(213\) 0 0
\(214\) −13.8410 −0.946151
\(215\) 22.3508 1.52431
\(216\) 0 0
\(217\) 4.20474 0.285436
\(218\) 34.0002 2.30279
\(219\) 0 0
\(220\) −55.4497 −3.73842
\(221\) −13.1685 −0.885807
\(222\) 0 0
\(223\) 7.33378 0.491106 0.245553 0.969383i \(-0.421030\pi\)
0.245553 + 0.969383i \(0.421030\pi\)
\(224\) 6.49261 0.433806
\(225\) 0 0
\(226\) 3.54360 0.235717
\(227\) 27.0309 1.79411 0.897053 0.441924i \(-0.145704\pi\)
0.897053 + 0.441924i \(0.145704\pi\)
\(228\) 0 0
\(229\) −13.0556 −0.862737 −0.431368 0.902176i \(-0.641969\pi\)
−0.431368 + 0.902176i \(0.641969\pi\)
\(230\) −48.2218 −3.17965
\(231\) 0 0
\(232\) 5.41096 0.355247
\(233\) 23.6719 1.55080 0.775398 0.631473i \(-0.217549\pi\)
0.775398 + 0.631473i \(0.217549\pi\)
\(234\) 0 0
\(235\) 29.8260 1.94564
\(236\) 16.1452 1.05096
\(237\) 0 0
\(238\) −6.73481 −0.436553
\(239\) −28.3744 −1.83539 −0.917693 0.397289i \(-0.869951\pi\)
−0.917693 + 0.397289i \(0.869951\pi\)
\(240\) 0 0
\(241\) −6.89559 −0.444184 −0.222092 0.975026i \(-0.571288\pi\)
−0.222092 + 0.975026i \(0.571288\pi\)
\(242\) −42.7136 −2.74573
\(243\) 0 0
\(244\) 1.62956 0.104322
\(245\) 3.31434 0.211745
\(246\) 0 0
\(247\) 2.19436 0.139624
\(248\) −9.96921 −0.633045
\(249\) 0 0
\(250\) −7.33851 −0.464128
\(251\) −18.5391 −1.17018 −0.585090 0.810968i \(-0.698941\pi\)
−0.585090 + 0.810968i \(0.698941\pi\)
\(252\) 0 0
\(253\) −35.4450 −2.22841
\(254\) −2.24824 −0.141067
\(255\) 0 0
\(256\) −10.6364 −0.664774
\(257\) −14.7593 −0.920662 −0.460331 0.887747i \(-0.652269\pi\)
−0.460331 + 0.887747i \(0.652269\pi\)
\(258\) 0 0
\(259\) −7.84180 −0.487266
\(260\) −44.5041 −2.76003
\(261\) 0 0
\(262\) 0.0560002 0.00345971
\(263\) −10.8798 −0.670877 −0.335439 0.942062i \(-0.608884\pi\)
−0.335439 + 0.942062i \(0.608884\pi\)
\(264\) 0 0
\(265\) 4.50570 0.276783
\(266\) 1.12227 0.0688110
\(267\) 0 0
\(268\) −43.0594 −2.63027
\(269\) −10.9718 −0.668960 −0.334480 0.942403i \(-0.608561\pi\)
−0.334480 + 0.942403i \(0.608561\pi\)
\(270\) 0 0
\(271\) 12.1714 0.739362 0.369681 0.929159i \(-0.379467\pi\)
0.369681 + 0.929159i \(0.379467\pi\)
\(272\) −2.33269 −0.141440
\(273\) 0 0
\(274\) 43.2452 2.61254
\(275\) −32.7796 −1.97669
\(276\) 0 0
\(277\) 18.1659 1.09149 0.545743 0.837953i \(-0.316247\pi\)
0.545743 + 0.837953i \(0.316247\pi\)
\(278\) −15.3056 −0.917966
\(279\) 0 0
\(280\) −7.85812 −0.469612
\(281\) 11.9874 0.715107 0.357554 0.933893i \(-0.383611\pi\)
0.357554 + 0.933893i \(0.383611\pi\)
\(282\) 0 0
\(283\) −3.09385 −0.183910 −0.0919552 0.995763i \(-0.529312\pi\)
−0.0919552 + 0.995763i \(0.529312\pi\)
\(284\) 20.2422 1.20115
\(285\) 0 0
\(286\) −54.1309 −3.20083
\(287\) 7.43947 0.439138
\(288\) 0 0
\(289\) −8.02641 −0.472142
\(290\) 17.0056 0.998604
\(291\) 0 0
\(292\) 19.4352 1.13736
\(293\) 22.8848 1.33694 0.668471 0.743738i \(-0.266949\pi\)
0.668471 + 0.743738i \(0.266949\pi\)
\(294\) 0 0
\(295\) 17.5181 1.01995
\(296\) 18.5925 1.08067
\(297\) 0 0
\(298\) −25.3581 −1.46896
\(299\) −28.4483 −1.64521
\(300\) 0 0
\(301\) 6.74366 0.388698
\(302\) −4.72199 −0.271720
\(303\) 0 0
\(304\) 0.388713 0.0222942
\(305\) 1.76814 0.101243
\(306\) 0 0
\(307\) −27.6006 −1.57525 −0.787625 0.616155i \(-0.788689\pi\)
−0.787625 + 0.616155i \(0.788689\pi\)
\(308\) −16.7303 −0.953295
\(309\) 0 0
\(310\) −31.3313 −1.77950
\(311\) −11.1839 −0.634182 −0.317091 0.948395i \(-0.602706\pi\)
−0.317091 + 0.948395i \(0.602706\pi\)
\(312\) 0 0
\(313\) 30.9402 1.74884 0.874422 0.485166i \(-0.161241\pi\)
0.874422 + 0.485166i \(0.161241\pi\)
\(314\) −32.7539 −1.84841
\(315\) 0 0
\(316\) −48.3062 −2.71744
\(317\) −5.00488 −0.281102 −0.140551 0.990073i \(-0.544887\pi\)
−0.140551 + 0.990073i \(0.544887\pi\)
\(318\) 0 0
\(319\) 12.4998 0.699856
\(320\) −43.2174 −2.41593
\(321\) 0 0
\(322\) −14.5494 −0.810809
\(323\) −1.49534 −0.0832028
\(324\) 0 0
\(325\) −26.3090 −1.45936
\(326\) 5.28370 0.292637
\(327\) 0 0
\(328\) −17.6386 −0.973928
\(329\) 8.99909 0.496136
\(330\) 0 0
\(331\) 10.7088 0.588609 0.294305 0.955712i \(-0.404912\pi\)
0.294305 + 0.955712i \(0.404912\pi\)
\(332\) −18.2299 −1.00049
\(333\) 0 0
\(334\) −52.7660 −2.88723
\(335\) −46.7212 −2.55265
\(336\) 0 0
\(337\) −8.32836 −0.453675 −0.226837 0.973933i \(-0.572839\pi\)
−0.226837 + 0.973933i \(0.572839\pi\)
\(338\) −14.2185 −0.773387
\(339\) 0 0
\(340\) 30.3271 1.64472
\(341\) −23.0298 −1.24713
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −15.9889 −0.862062
\(345\) 0 0
\(346\) 5.57445 0.299684
\(347\) −4.09711 −0.219945 −0.109972 0.993935i \(-0.535076\pi\)
−0.109972 + 0.993935i \(0.535076\pi\)
\(348\) 0 0
\(349\) 24.8638 1.33093 0.665465 0.746429i \(-0.268233\pi\)
0.665465 + 0.746429i \(0.268233\pi\)
\(350\) −13.4554 −0.719220
\(351\) 0 0
\(352\) −35.5607 −1.89539
\(353\) 2.37283 0.126293 0.0631465 0.998004i \(-0.479886\pi\)
0.0631465 + 0.998004i \(0.479886\pi\)
\(354\) 0 0
\(355\) 21.9636 1.16571
\(356\) −20.0689 −1.06365
\(357\) 0 0
\(358\) 21.5681 1.13991
\(359\) 8.59806 0.453788 0.226894 0.973919i \(-0.427143\pi\)
0.226894 + 0.973919i \(0.427143\pi\)
\(360\) 0 0
\(361\) −18.7508 −0.986885
\(362\) −2.29192 −0.120461
\(363\) 0 0
\(364\) −13.4278 −0.703805
\(365\) 21.0880 1.10379
\(366\) 0 0
\(367\) 8.33703 0.435189 0.217595 0.976039i \(-0.430179\pi\)
0.217595 + 0.976039i \(0.430179\pi\)
\(368\) −5.03938 −0.262696
\(369\) 0 0
\(370\) 58.4326 3.03777
\(371\) 1.35946 0.0705795
\(372\) 0 0
\(373\) 14.4028 0.745747 0.372873 0.927882i \(-0.378373\pi\)
0.372873 + 0.927882i \(0.378373\pi\)
\(374\) 36.8873 1.90740
\(375\) 0 0
\(376\) −21.3364 −1.10034
\(377\) 10.0324 0.516695
\(378\) 0 0
\(379\) 13.5035 0.693626 0.346813 0.937934i \(-0.387264\pi\)
0.346813 + 0.937934i \(0.387264\pi\)
\(380\) −5.05364 −0.259246
\(381\) 0 0
\(382\) 22.3342 1.14272
\(383\) 11.1740 0.570962 0.285481 0.958384i \(-0.407847\pi\)
0.285481 + 0.958384i \(0.407847\pi\)
\(384\) 0 0
\(385\) −18.1530 −0.925162
\(386\) −34.3075 −1.74620
\(387\) 0 0
\(388\) 38.3928 1.94910
\(389\) 29.1166 1.47627 0.738134 0.674654i \(-0.235707\pi\)
0.738134 + 0.674654i \(0.235707\pi\)
\(390\) 0 0
\(391\) 19.3860 0.980390
\(392\) −2.37095 −0.119751
\(393\) 0 0
\(394\) −26.9891 −1.35969
\(395\) −52.4142 −2.63724
\(396\) 0 0
\(397\) 15.2799 0.766878 0.383439 0.923566i \(-0.374740\pi\)
0.383439 + 0.923566i \(0.374740\pi\)
\(398\) −49.6138 −2.48692
\(399\) 0 0
\(400\) −4.66043 −0.233022
\(401\) −27.6205 −1.37930 −0.689652 0.724141i \(-0.742236\pi\)
−0.689652 + 0.724141i \(0.742236\pi\)
\(402\) 0 0
\(403\) −18.4838 −0.920743
\(404\) 13.1906 0.656258
\(405\) 0 0
\(406\) 5.13092 0.254643
\(407\) 42.9504 2.12897
\(408\) 0 0
\(409\) 5.51095 0.272499 0.136249 0.990675i \(-0.456495\pi\)
0.136249 + 0.990675i \(0.456495\pi\)
\(410\) −55.4347 −2.73772
\(411\) 0 0
\(412\) −23.4523 −1.15541
\(413\) 5.28556 0.260085
\(414\) 0 0
\(415\) −19.7801 −0.970969
\(416\) −28.5411 −1.39934
\(417\) 0 0
\(418\) −6.14681 −0.300650
\(419\) 26.9938 1.31873 0.659366 0.751822i \(-0.270825\pi\)
0.659366 + 0.751822i \(0.270825\pi\)
\(420\) 0 0
\(421\) −22.9232 −1.11721 −0.558605 0.829434i \(-0.688663\pi\)
−0.558605 + 0.829434i \(0.688663\pi\)
\(422\) −52.4839 −2.55487
\(423\) 0 0
\(424\) −3.22320 −0.156532
\(425\) 17.9282 0.869644
\(426\) 0 0
\(427\) 0.533481 0.0258170
\(428\) 18.8051 0.908980
\(429\) 0 0
\(430\) −50.2499 −2.42327
\(431\) 6.16714 0.297061 0.148530 0.988908i \(-0.452546\pi\)
0.148530 + 0.988908i \(0.452546\pi\)
\(432\) 0 0
\(433\) −20.1082 −0.966340 −0.483170 0.875526i \(-0.660515\pi\)
−0.483170 + 0.875526i \(0.660515\pi\)
\(434\) −9.45326 −0.453771
\(435\) 0 0
\(436\) −46.1946 −2.21232
\(437\) −3.23043 −0.154532
\(438\) 0 0
\(439\) 13.8552 0.661273 0.330636 0.943758i \(-0.392737\pi\)
0.330636 + 0.943758i \(0.392737\pi\)
\(440\) 43.0397 2.05184
\(441\) 0 0
\(442\) 29.6058 1.40821
\(443\) 14.4784 0.687890 0.343945 0.938990i \(-0.388237\pi\)
0.343945 + 0.938990i \(0.388237\pi\)
\(444\) 0 0
\(445\) −21.7755 −1.03226
\(446\) −16.4881 −0.780734
\(447\) 0 0
\(448\) −13.0395 −0.616060
\(449\) 27.1832 1.28286 0.641428 0.767183i \(-0.278342\pi\)
0.641428 + 0.767183i \(0.278342\pi\)
\(450\) 0 0
\(451\) −40.7468 −1.91869
\(452\) −4.81452 −0.226456
\(453\) 0 0
\(454\) −60.7720 −2.85217
\(455\) −14.5696 −0.683035
\(456\) 0 0
\(457\) 5.56791 0.260456 0.130228 0.991484i \(-0.458429\pi\)
0.130228 + 0.991484i \(0.458429\pi\)
\(458\) 29.3521 1.37153
\(459\) 0 0
\(460\) 65.5168 3.05473
\(461\) 9.34013 0.435013 0.217507 0.976059i \(-0.430208\pi\)
0.217507 + 0.976059i \(0.430208\pi\)
\(462\) 0 0
\(463\) −2.05307 −0.0954144 −0.0477072 0.998861i \(-0.515191\pi\)
−0.0477072 + 0.998861i \(0.515191\pi\)
\(464\) 1.77716 0.0825025
\(465\) 0 0
\(466\) −53.2200 −2.46537
\(467\) 32.0662 1.48384 0.741922 0.670486i \(-0.233914\pi\)
0.741922 + 0.670486i \(0.233914\pi\)
\(468\) 0 0
\(469\) −14.0967 −0.650925
\(470\) −67.0561 −3.09307
\(471\) 0 0
\(472\) −12.5318 −0.576822
\(473\) −36.9358 −1.69831
\(474\) 0 0
\(475\) −2.98751 −0.137076
\(476\) 9.15028 0.419402
\(477\) 0 0
\(478\) 63.7924 2.91780
\(479\) 25.0510 1.14461 0.572305 0.820041i \(-0.306049\pi\)
0.572305 + 0.820041i \(0.306049\pi\)
\(480\) 0 0
\(481\) 34.4721 1.57179
\(482\) 15.5029 0.706139
\(483\) 0 0
\(484\) 58.0330 2.63786
\(485\) 41.6578 1.89158
\(486\) 0 0
\(487\) −24.1154 −1.09277 −0.546386 0.837534i \(-0.683997\pi\)
−0.546386 + 0.837534i \(0.683997\pi\)
\(488\) −1.26486 −0.0572573
\(489\) 0 0
\(490\) −7.45143 −0.336621
\(491\) 41.4602 1.87107 0.935535 0.353233i \(-0.114918\pi\)
0.935535 + 0.353233i \(0.114918\pi\)
\(492\) 0 0
\(493\) −6.83653 −0.307902
\(494\) −4.93345 −0.221966
\(495\) 0 0
\(496\) −3.27425 −0.147018
\(497\) 6.62684 0.297254
\(498\) 0 0
\(499\) 6.32228 0.283024 0.141512 0.989937i \(-0.454804\pi\)
0.141512 + 0.989937i \(0.454804\pi\)
\(500\) 9.97050 0.445894
\(501\) 0 0
\(502\) 41.6804 1.86029
\(503\) 30.3857 1.35483 0.677416 0.735600i \(-0.263100\pi\)
0.677416 + 0.735600i \(0.263100\pi\)
\(504\) 0 0
\(505\) 14.3124 0.636891
\(506\) 79.6889 3.54260
\(507\) 0 0
\(508\) 3.05458 0.135525
\(509\) 43.5835 1.93181 0.965903 0.258906i \(-0.0833618\pi\)
0.965903 + 0.258906i \(0.0833618\pi\)
\(510\) 0 0
\(511\) 6.36264 0.281467
\(512\) −8.74837 −0.386627
\(513\) 0 0
\(514\) 33.1825 1.46362
\(515\) −25.4467 −1.12132
\(516\) 0 0
\(517\) −49.2890 −2.16773
\(518\) 17.6302 0.774629
\(519\) 0 0
\(520\) 34.5438 1.51485
\(521\) −3.41203 −0.149484 −0.0747419 0.997203i \(-0.523813\pi\)
−0.0747419 + 0.997203i \(0.523813\pi\)
\(522\) 0 0
\(523\) −4.13861 −0.180969 −0.0904844 0.995898i \(-0.528842\pi\)
−0.0904844 + 0.995898i \(0.528842\pi\)
\(524\) −0.0760849 −0.00332379
\(525\) 0 0
\(526\) 24.4604 1.06652
\(527\) 12.5957 0.548677
\(528\) 0 0
\(529\) 18.8801 0.820876
\(530\) −10.1299 −0.440015
\(531\) 0 0
\(532\) −1.52478 −0.0661076
\(533\) −32.7035 −1.41655
\(534\) 0 0
\(535\) 20.4043 0.882155
\(536\) 33.4225 1.44363
\(537\) 0 0
\(538\) 24.6671 1.06348
\(539\) −5.47711 −0.235916
\(540\) 0 0
\(541\) 30.5714 1.31437 0.657184 0.753730i \(-0.271747\pi\)
0.657184 + 0.753730i \(0.271747\pi\)
\(542\) −27.3643 −1.17540
\(543\) 0 0
\(544\) 19.4492 0.833878
\(545\) −50.1229 −2.14703
\(546\) 0 0
\(547\) −34.9946 −1.49626 −0.748131 0.663551i \(-0.769049\pi\)
−0.748131 + 0.663551i \(0.769049\pi\)
\(548\) −58.7553 −2.50990
\(549\) 0 0
\(550\) 73.6965 3.14243
\(551\) 1.13922 0.0485325
\(552\) 0 0
\(553\) −15.8144 −0.672495
\(554\) −40.8414 −1.73518
\(555\) 0 0
\(556\) 20.7950 0.881903
\(557\) −2.88453 −0.122222 −0.0611108 0.998131i \(-0.519464\pi\)
−0.0611108 + 0.998131i \(0.519464\pi\)
\(558\) 0 0
\(559\) −29.6448 −1.25384
\(560\) −2.58089 −0.109063
\(561\) 0 0
\(562\) −26.9505 −1.13684
\(563\) 12.0756 0.508924 0.254462 0.967083i \(-0.418102\pi\)
0.254462 + 0.967083i \(0.418102\pi\)
\(564\) 0 0
\(565\) −5.22395 −0.219773
\(566\) 6.95572 0.292371
\(567\) 0 0
\(568\) −15.7119 −0.659256
\(569\) −4.27015 −0.179014 −0.0895070 0.995986i \(-0.528529\pi\)
−0.0895070 + 0.995986i \(0.528529\pi\)
\(570\) 0 0
\(571\) 30.6795 1.28390 0.641949 0.766747i \(-0.278126\pi\)
0.641949 + 0.766747i \(0.278126\pi\)
\(572\) 73.5452 3.07508
\(573\) 0 0
\(574\) −16.7257 −0.698118
\(575\) 38.7309 1.61519
\(576\) 0 0
\(577\) −1.83635 −0.0764482 −0.0382241 0.999269i \(-0.512170\pi\)
−0.0382241 + 0.999269i \(0.512170\pi\)
\(578\) 18.0453 0.750585
\(579\) 0 0
\(580\) −23.1047 −0.959372
\(581\) −5.96805 −0.247596
\(582\) 0 0
\(583\) −7.44589 −0.308377
\(584\) −15.0855 −0.624241
\(585\) 0 0
\(586\) −51.4504 −2.12540
\(587\) 38.6222 1.59411 0.797054 0.603908i \(-0.206390\pi\)
0.797054 + 0.603908i \(0.206390\pi\)
\(588\) 0 0
\(589\) −2.09892 −0.0864843
\(590\) −39.3850 −1.62145
\(591\) 0 0
\(592\) 6.10646 0.250974
\(593\) 19.1132 0.784886 0.392443 0.919776i \(-0.371630\pi\)
0.392443 + 0.919776i \(0.371630\pi\)
\(594\) 0 0
\(595\) 9.92842 0.407025
\(596\) 34.4529 1.41125
\(597\) 0 0
\(598\) 63.9585 2.61546
\(599\) 9.55259 0.390308 0.195154 0.980773i \(-0.437479\pi\)
0.195154 + 0.980773i \(0.437479\pi\)
\(600\) 0 0
\(601\) 39.7388 1.62098 0.810490 0.585752i \(-0.199201\pi\)
0.810490 + 0.585752i \(0.199201\pi\)
\(602\) −15.1614 −0.617931
\(603\) 0 0
\(604\) 6.41555 0.261045
\(605\) 62.9681 2.56002
\(606\) 0 0
\(607\) 31.6818 1.28592 0.642962 0.765898i \(-0.277705\pi\)
0.642962 + 0.765898i \(0.277705\pi\)
\(608\) −3.24097 −0.131439
\(609\) 0 0
\(610\) −3.97520 −0.160951
\(611\) −39.5595 −1.60041
\(612\) 0 0
\(613\) −17.6030 −0.710980 −0.355490 0.934680i \(-0.615686\pi\)
−0.355490 + 0.934680i \(0.615686\pi\)
\(614\) 62.0528 2.50425
\(615\) 0 0
\(616\) 12.9859 0.523218
\(617\) 20.1237 0.810149 0.405075 0.914284i \(-0.367246\pi\)
0.405075 + 0.914284i \(0.367246\pi\)
\(618\) 0 0
\(619\) −4.89268 −0.196653 −0.0983267 0.995154i \(-0.531349\pi\)
−0.0983267 + 0.995154i \(0.531349\pi\)
\(620\) 42.5684 1.70959
\(621\) 0 0
\(622\) 25.1441 1.00819
\(623\) −6.57010 −0.263226
\(624\) 0 0
\(625\) −19.1058 −0.764234
\(626\) −69.5610 −2.78022
\(627\) 0 0
\(628\) 44.5012 1.77579
\(629\) −23.4909 −0.936642
\(630\) 0 0
\(631\) 14.6120 0.581695 0.290848 0.956769i \(-0.406063\pi\)
0.290848 + 0.956769i \(0.406063\pi\)
\(632\) 37.4950 1.49147
\(633\) 0 0
\(634\) 11.2522 0.446880
\(635\) 3.31434 0.131526
\(636\) 0 0
\(637\) −4.39594 −0.174174
\(638\) −28.1026 −1.11259
\(639\) 0 0
\(640\) 54.1256 2.13950
\(641\) −30.1442 −1.19062 −0.595312 0.803495i \(-0.702972\pi\)
−0.595312 + 0.803495i \(0.702972\pi\)
\(642\) 0 0
\(643\) 2.02706 0.0799396 0.0399698 0.999201i \(-0.487274\pi\)
0.0399698 + 0.999201i \(0.487274\pi\)
\(644\) 19.7677 0.778955
\(645\) 0 0
\(646\) 3.36188 0.132271
\(647\) −31.2618 −1.22903 −0.614514 0.788906i \(-0.710648\pi\)
−0.614514 + 0.788906i \(0.710648\pi\)
\(648\) 0 0
\(649\) −28.9496 −1.13637
\(650\) 59.1490 2.32001
\(651\) 0 0
\(652\) −7.17872 −0.281140
\(653\) −40.2091 −1.57350 −0.786752 0.617270i \(-0.788239\pi\)
−0.786752 + 0.617270i \(0.788239\pi\)
\(654\) 0 0
\(655\) −0.0825552 −0.00322570
\(656\) −5.79316 −0.226185
\(657\) 0 0
\(658\) −20.2321 −0.788730
\(659\) 39.3476 1.53276 0.766382 0.642385i \(-0.222055\pi\)
0.766382 + 0.642385i \(0.222055\pi\)
\(660\) 0 0
\(661\) 2.03809 0.0792724 0.0396362 0.999214i \(-0.487380\pi\)
0.0396362 + 0.999214i \(0.487380\pi\)
\(662\) −24.0760 −0.935739
\(663\) 0 0
\(664\) 14.1499 0.549123
\(665\) −1.65445 −0.0641567
\(666\) 0 0
\(667\) −14.7692 −0.571866
\(668\) 71.6907 2.77380
\(669\) 0 0
\(670\) 105.040 4.05807
\(671\) −2.92193 −0.112800
\(672\) 0 0
\(673\) −36.3745 −1.40213 −0.701067 0.713095i \(-0.747293\pi\)
−0.701067 + 0.713095i \(0.747293\pi\)
\(674\) 18.7241 0.721227
\(675\) 0 0
\(676\) 19.3181 0.743003
\(677\) 8.76754 0.336964 0.168482 0.985705i \(-0.446113\pi\)
0.168482 + 0.985705i \(0.446113\pi\)
\(678\) 0 0
\(679\) 12.5689 0.482352
\(680\) −23.5397 −0.902708
\(681\) 0 0
\(682\) 51.7765 1.98262
\(683\) −28.0592 −1.07366 −0.536828 0.843692i \(-0.680377\pi\)
−0.536828 + 0.843692i \(0.680377\pi\)
\(684\) 0 0
\(685\) −63.7518 −2.43583
\(686\) −2.24824 −0.0858382
\(687\) 0 0
\(688\) −5.25133 −0.200205
\(689\) −5.97609 −0.227671
\(690\) 0 0
\(691\) 49.3493 1.87734 0.938668 0.344821i \(-0.112060\pi\)
0.938668 + 0.344821i \(0.112060\pi\)
\(692\) −7.57375 −0.287911
\(693\) 0 0
\(694\) 9.21129 0.349656
\(695\) 22.5634 0.855877
\(696\) 0 0
\(697\) 22.2856 0.844129
\(698\) −55.8998 −2.11584
\(699\) 0 0
\(700\) 18.2812 0.690964
\(701\) −43.6097 −1.64712 −0.823558 0.567232i \(-0.808014\pi\)
−0.823558 + 0.567232i \(0.808014\pi\)
\(702\) 0 0
\(703\) 3.91446 0.147637
\(704\) 71.4188 2.69170
\(705\) 0 0
\(706\) −5.33469 −0.200774
\(707\) 4.31831 0.162407
\(708\) 0 0
\(709\) −37.8878 −1.42291 −0.711454 0.702733i \(-0.751963\pi\)
−0.711454 + 0.702733i \(0.751963\pi\)
\(710\) −49.3794 −1.85318
\(711\) 0 0
\(712\) 15.5774 0.583786
\(713\) 27.2109 1.01906
\(714\) 0 0
\(715\) 79.7995 2.98433
\(716\) −29.3036 −1.09513
\(717\) 0 0
\(718\) −19.3305 −0.721407
\(719\) 50.6110 1.88747 0.943736 0.330699i \(-0.107285\pi\)
0.943736 + 0.330699i \(0.107285\pi\)
\(720\) 0 0
\(721\) −7.67776 −0.285935
\(722\) 42.1563 1.56890
\(723\) 0 0
\(724\) 3.11393 0.115728
\(725\) −13.6586 −0.507267
\(726\) 0 0
\(727\) 19.5430 0.724809 0.362404 0.932021i \(-0.381956\pi\)
0.362404 + 0.932021i \(0.381956\pi\)
\(728\) 10.4225 0.386285
\(729\) 0 0
\(730\) −47.4108 −1.75475
\(731\) 20.2013 0.747172
\(732\) 0 0
\(733\) −17.8762 −0.660274 −0.330137 0.943933i \(-0.607095\pi\)
−0.330137 + 0.943933i \(0.607095\pi\)
\(734\) −18.7436 −0.691840
\(735\) 0 0
\(736\) 42.0168 1.54876
\(737\) 77.2091 2.84403
\(738\) 0 0
\(739\) 23.3724 0.859768 0.429884 0.902884i \(-0.358554\pi\)
0.429884 + 0.902884i \(0.358554\pi\)
\(740\) −79.3897 −2.91842
\(741\) 0 0
\(742\) −3.05638 −0.112203
\(743\) −21.1697 −0.776640 −0.388320 0.921525i \(-0.626944\pi\)
−0.388320 + 0.921525i \(0.626944\pi\)
\(744\) 0 0
\(745\) 37.3828 1.36960
\(746\) −32.3809 −1.18555
\(747\) 0 0
\(748\) −50.1171 −1.83246
\(749\) 6.15637 0.224949
\(750\) 0 0
\(751\) 49.7278 1.81459 0.907296 0.420492i \(-0.138142\pi\)
0.907296 + 0.420492i \(0.138142\pi\)
\(752\) −7.00764 −0.255542
\(753\) 0 0
\(754\) −22.5552 −0.821413
\(755\) 6.96113 0.253341
\(756\) 0 0
\(757\) 0.699544 0.0254254 0.0127127 0.999919i \(-0.495953\pi\)
0.0127127 + 0.999919i \(0.495953\pi\)
\(758\) −30.3590 −1.10269
\(759\) 0 0
\(760\) 3.92261 0.142288
\(761\) −14.4262 −0.522949 −0.261474 0.965210i \(-0.584209\pi\)
−0.261474 + 0.965210i \(0.584209\pi\)
\(762\) 0 0
\(763\) −15.1231 −0.547491
\(764\) −30.3444 −1.09782
\(765\) 0 0
\(766\) −25.1217 −0.907685
\(767\) −23.2350 −0.838968
\(768\) 0 0
\(769\) −23.0451 −0.831026 −0.415513 0.909587i \(-0.636398\pi\)
−0.415513 + 0.909587i \(0.636398\pi\)
\(770\) 40.8123 1.47077
\(771\) 0 0
\(772\) 46.6120 1.67760
\(773\) 1.43085 0.0514640 0.0257320 0.999669i \(-0.491808\pi\)
0.0257320 + 0.999669i \(0.491808\pi\)
\(774\) 0 0
\(775\) 25.1647 0.903943
\(776\) −29.8003 −1.06977
\(777\) 0 0
\(778\) −65.4610 −2.34689
\(779\) −3.71363 −0.133054
\(780\) 0 0
\(781\) −36.2959 −1.29877
\(782\) −43.5843 −1.55857
\(783\) 0 0
\(784\) −0.778706 −0.0278109
\(785\) 48.2855 1.72338
\(786\) 0 0
\(787\) −50.3549 −1.79496 −0.897479 0.441057i \(-0.854604\pi\)
−0.897479 + 0.441057i \(0.854604\pi\)
\(788\) 36.6688 1.30627
\(789\) 0 0
\(790\) 117.840 4.19255
\(791\) −1.57617 −0.0560420
\(792\) 0 0
\(793\) −2.34515 −0.0832788
\(794\) −34.3530 −1.21914
\(795\) 0 0
\(796\) 67.4080 2.38921
\(797\) −17.2393 −0.610647 −0.305323 0.952249i \(-0.598765\pi\)
−0.305323 + 0.952249i \(0.598765\pi\)
\(798\) 0 0
\(799\) 26.9576 0.953692
\(800\) 38.8573 1.37381
\(801\) 0 0
\(802\) 62.0975 2.19274
\(803\) −34.8489 −1.22979
\(804\) 0 0
\(805\) 21.4487 0.755967
\(806\) 41.5560 1.46375
\(807\) 0 0
\(808\) −10.2385 −0.360189
\(809\) −40.4761 −1.42306 −0.711532 0.702654i \(-0.751998\pi\)
−0.711532 + 0.702654i \(0.751998\pi\)
\(810\) 0 0
\(811\) −9.44221 −0.331561 −0.165780 0.986163i \(-0.553014\pi\)
−0.165780 + 0.986163i \(0.553014\pi\)
\(812\) −6.97115 −0.244639
\(813\) 0 0
\(814\) −96.5628 −3.38452
\(815\) −7.78920 −0.272844
\(816\) 0 0
\(817\) −3.36629 −0.117772
\(818\) −12.3899 −0.433204
\(819\) 0 0
\(820\) 75.3165 2.63017
\(821\) 26.8033 0.935440 0.467720 0.883877i \(-0.345076\pi\)
0.467720 + 0.883877i \(0.345076\pi\)
\(822\) 0 0
\(823\) −11.0877 −0.386492 −0.193246 0.981150i \(-0.561901\pi\)
−0.193246 + 0.981150i \(0.561901\pi\)
\(824\) 18.2035 0.634150
\(825\) 0 0
\(826\) −11.8832 −0.413469
\(827\) −20.6815 −0.719167 −0.359584 0.933113i \(-0.617081\pi\)
−0.359584 + 0.933113i \(0.617081\pi\)
\(828\) 0 0
\(829\) −5.98033 −0.207705 −0.103853 0.994593i \(-0.533117\pi\)
−0.103853 + 0.994593i \(0.533117\pi\)
\(830\) 44.4705 1.54359
\(831\) 0 0
\(832\) 57.3210 1.98725
\(833\) 2.99559 0.103791
\(834\) 0 0
\(835\) 77.7873 2.69194
\(836\) 8.35139 0.288839
\(837\) 0 0
\(838\) −60.6885 −2.09645
\(839\) 28.0769 0.969321 0.484661 0.874702i \(-0.338943\pi\)
0.484661 + 0.874702i \(0.338943\pi\)
\(840\) 0 0
\(841\) −23.7916 −0.820399
\(842\) 51.5369 1.77608
\(843\) 0 0
\(844\) 71.3074 2.45450
\(845\) 20.9609 0.721076
\(846\) 0 0
\(847\) 18.9987 0.652803
\(848\) −1.05862 −0.0363530
\(849\) 0 0
\(850\) −40.3068 −1.38251
\(851\) −50.7481 −1.73962
\(852\) 0 0
\(853\) −25.3187 −0.866894 −0.433447 0.901179i \(-0.642703\pi\)
−0.433447 + 0.901179i \(0.642703\pi\)
\(854\) −1.19939 −0.0410424
\(855\) 0 0
\(856\) −14.5964 −0.498895
\(857\) 4.04901 0.138312 0.0691558 0.997606i \(-0.477969\pi\)
0.0691558 + 0.997606i \(0.477969\pi\)
\(858\) 0 0
\(859\) −0.0822329 −0.00280575 −0.00140287 0.999999i \(-0.500447\pi\)
−0.00140287 + 0.999999i \(0.500447\pi\)
\(860\) 68.2723 2.32806
\(861\) 0 0
\(862\) −13.8652 −0.472251
\(863\) 27.8324 0.947425 0.473712 0.880680i \(-0.342914\pi\)
0.473712 + 0.880680i \(0.342914\pi\)
\(864\) 0 0
\(865\) −8.21782 −0.279414
\(866\) 45.2081 1.53623
\(867\) 0 0
\(868\) 12.8437 0.435944
\(869\) 86.6170 2.93828
\(870\) 0 0
\(871\) 61.9682 2.09971
\(872\) 35.8559 1.21424
\(873\) 0 0
\(874\) 7.26278 0.245667
\(875\) 3.26412 0.110347
\(876\) 0 0
\(877\) −45.7277 −1.54412 −0.772058 0.635553i \(-0.780772\pi\)
−0.772058 + 0.635553i \(0.780772\pi\)
\(878\) −31.1498 −1.05126
\(879\) 0 0
\(880\) 14.1358 0.476519
\(881\) −47.0656 −1.58568 −0.792840 0.609430i \(-0.791398\pi\)
−0.792840 + 0.609430i \(0.791398\pi\)
\(882\) 0 0
\(883\) −31.6005 −1.06344 −0.531721 0.846920i \(-0.678454\pi\)
−0.531721 + 0.846920i \(0.678454\pi\)
\(884\) −40.2241 −1.35288
\(885\) 0 0
\(886\) −32.5509 −1.09357
\(887\) 30.9114 1.03790 0.518951 0.854804i \(-0.326323\pi\)
0.518951 + 0.854804i \(0.326323\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 48.9566 1.64103
\(891\) 0 0
\(892\) 22.4016 0.750062
\(893\) −4.49215 −0.150324
\(894\) 0 0
\(895\) −31.7956 −1.06281
\(896\) 16.3307 0.545572
\(897\) 0 0
\(898\) −61.1144 −2.03942
\(899\) −9.59604 −0.320046
\(900\) 0 0
\(901\) 4.07238 0.135671
\(902\) 91.6085 3.05023
\(903\) 0 0
\(904\) 3.73700 0.124291
\(905\) 3.37874 0.112313
\(906\) 0 0
\(907\) −16.1542 −0.536390 −0.268195 0.963365i \(-0.586427\pi\)
−0.268195 + 0.963365i \(0.586427\pi\)
\(908\) 82.5681 2.74012
\(909\) 0 0
\(910\) 32.7560 1.08585
\(911\) 30.7252 1.01797 0.508985 0.860775i \(-0.330021\pi\)
0.508985 + 0.860775i \(0.330021\pi\)
\(912\) 0 0
\(913\) 32.6876 1.08180
\(914\) −12.5180 −0.414058
\(915\) 0 0
\(916\) −39.8793 −1.31765
\(917\) −0.0249085 −0.000822551 0
\(918\) 0 0
\(919\) 36.6178 1.20791 0.603955 0.797018i \(-0.293590\pi\)
0.603955 + 0.797018i \(0.293590\pi\)
\(920\) −50.8537 −1.67660
\(921\) 0 0
\(922\) −20.9988 −0.691560
\(923\) −29.1312 −0.958865
\(924\) 0 0
\(925\) −46.9320 −1.54311
\(926\) 4.61580 0.151685
\(927\) 0 0
\(928\) −14.8174 −0.486405
\(929\) 3.45942 0.113500 0.0567500 0.998388i \(-0.481926\pi\)
0.0567500 + 0.998388i \(0.481926\pi\)
\(930\) 0 0
\(931\) −0.499179 −0.0163599
\(932\) 72.3076 2.36851
\(933\) 0 0
\(934\) −72.0924 −2.35893
\(935\) −54.3790 −1.77838
\(936\) 0 0
\(937\) 27.2761 0.891073 0.445536 0.895264i \(-0.353013\pi\)
0.445536 + 0.895264i \(0.353013\pi\)
\(938\) 31.6927 1.03480
\(939\) 0 0
\(940\) 91.1060 2.97155
\(941\) 50.5133 1.64669 0.823343 0.567544i \(-0.192106\pi\)
0.823343 + 0.567544i \(0.192106\pi\)
\(942\) 0 0
\(943\) 48.1444 1.56780
\(944\) −4.11589 −0.133961
\(945\) 0 0
\(946\) 83.0404 2.69988
\(947\) −31.7991 −1.03333 −0.516666 0.856187i \(-0.672827\pi\)
−0.516666 + 0.856187i \(0.672827\pi\)
\(948\) 0 0
\(949\) −27.9698 −0.907938
\(950\) 6.71663 0.217916
\(951\) 0 0
\(952\) −7.10239 −0.230190
\(953\) −32.8952 −1.06558 −0.532790 0.846247i \(-0.678856\pi\)
−0.532790 + 0.846247i \(0.678856\pi\)
\(954\) 0 0
\(955\) −32.9249 −1.06542
\(956\) −86.6718 −2.80317
\(957\) 0 0
\(958\) −56.3206 −1.81964
\(959\) −19.2352 −0.621136
\(960\) 0 0
\(961\) −13.3202 −0.429683
\(962\) −77.5016 −2.49875
\(963\) 0 0
\(964\) −21.0631 −0.678397
\(965\) 50.5759 1.62809
\(966\) 0 0
\(967\) 60.1512 1.93433 0.967166 0.254147i \(-0.0817947\pi\)
0.967166 + 0.254147i \(0.0817947\pi\)
\(968\) −45.0449 −1.44780
\(969\) 0 0
\(970\) −93.6566 −3.00713
\(971\) 49.3664 1.58424 0.792122 0.610363i \(-0.208976\pi\)
0.792122 + 0.610363i \(0.208976\pi\)
\(972\) 0 0
\(973\) 6.80780 0.218248
\(974\) 54.2171 1.73723
\(975\) 0 0
\(976\) −0.415425 −0.0132974
\(977\) 1.19493 0.0382293 0.0191147 0.999817i \(-0.493915\pi\)
0.0191147 + 0.999817i \(0.493915\pi\)
\(978\) 0 0
\(979\) 35.9851 1.15009
\(980\) 10.1239 0.323396
\(981\) 0 0
\(982\) −93.2124 −2.97453
\(983\) −45.1609 −1.44041 −0.720204 0.693762i \(-0.755952\pi\)
−0.720204 + 0.693762i \(0.755952\pi\)
\(984\) 0 0
\(985\) 39.7871 1.26772
\(986\) 15.3702 0.489486
\(987\) 0 0
\(988\) 6.70285 0.213246
\(989\) 43.6415 1.38772
\(990\) 0 0
\(991\) 10.1543 0.322562 0.161281 0.986908i \(-0.448437\pi\)
0.161281 + 0.986908i \(0.448437\pi\)
\(992\) 27.2997 0.866767
\(993\) 0 0
\(994\) −14.8987 −0.472559
\(995\) 73.1404 2.31871
\(996\) 0 0
\(997\) −59.1360 −1.87286 −0.936428 0.350860i \(-0.885889\pi\)
−0.936428 + 0.350860i \(0.885889\pi\)
\(998\) −14.2140 −0.449936
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))