Properties

Label 945.2.a.j.1.2
Level 945
Weight 2
Character 945.1
Self dual Yes
Analytic conductor 7.546
Analytic rank 0
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 945.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(7.54586299101\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.30278\)
Character \(\chi\) = 945.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.30278 q^{2} +3.30278 q^{4} +1.00000 q^{5} +1.00000 q^{7} +3.00000 q^{8} +O(q^{10})\) \(q+2.30278 q^{2} +3.30278 q^{4} +1.00000 q^{5} +1.00000 q^{7} +3.00000 q^{8} +2.30278 q^{10} +3.00000 q^{11} +1.30278 q^{13} +2.30278 q^{14} +0.302776 q^{16} -2.30278 q^{17} -3.30278 q^{19} +3.30278 q^{20} +6.90833 q^{22} +0.697224 q^{23} +1.00000 q^{25} +3.00000 q^{26} +3.30278 q^{28} +5.30278 q^{29} -2.39445 q^{31} -5.30278 q^{32} -5.30278 q^{34} +1.00000 q^{35} +3.60555 q^{37} -7.60555 q^{38} +3.00000 q^{40} -6.90833 q^{41} -4.21110 q^{43} +9.90833 q^{44} +1.60555 q^{46} +7.60555 q^{47} +1.00000 q^{49} +2.30278 q^{50} +4.30278 q^{52} -5.51388 q^{53} +3.00000 q^{55} +3.00000 q^{56} +12.2111 q^{58} +6.21110 q^{59} -11.1194 q^{61} -5.51388 q^{62} -12.8167 q^{64} +1.30278 q^{65} +13.5139 q^{67} -7.60555 q^{68} +2.30278 q^{70} +2.09167 q^{71} -10.2111 q^{73} +8.30278 q^{74} -10.9083 q^{76} +3.00000 q^{77} -16.9083 q^{79} +0.302776 q^{80} -15.9083 q^{82} -12.2111 q^{83} -2.30278 q^{85} -9.69722 q^{86} +9.00000 q^{88} +10.8167 q^{89} +1.30278 q^{91} +2.30278 q^{92} +17.5139 q^{94} -3.30278 q^{95} -9.51388 q^{97} +2.30278 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + 3q^{4} + 2q^{5} + 2q^{7} + 6q^{8} + O(q^{10}) \) \( 2q + q^{2} + 3q^{4} + 2q^{5} + 2q^{7} + 6q^{8} + q^{10} + 6q^{11} - q^{13} + q^{14} - 3q^{16} - q^{17} - 3q^{19} + 3q^{20} + 3q^{22} + 5q^{23} + 2q^{25} + 6q^{26} + 3q^{28} + 7q^{29} - 12q^{31} - 7q^{32} - 7q^{34} + 2q^{35} - 8q^{38} + 6q^{40} - 3q^{41} + 6q^{43} + 9q^{44} - 4q^{46} + 8q^{47} + 2q^{49} + q^{50} + 5q^{52} + 7q^{53} + 6q^{55} + 6q^{56} + 10q^{58} - 2q^{59} + 3q^{61} + 7q^{62} - 4q^{64} - q^{65} + 9q^{67} - 8q^{68} + q^{70} + 15q^{71} - 6q^{73} + 13q^{74} - 11q^{76} + 6q^{77} - 23q^{79} - 3q^{80} - 21q^{82} - 10q^{83} - q^{85} - 23q^{86} + 18q^{88} - q^{91} + q^{92} + 17q^{94} - 3q^{95} - q^{97} + q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.30278 1.62831 0.814154 0.580649i \(-0.197201\pi\)
0.814154 + 0.580649i \(0.197201\pi\)
\(3\) 0 0
\(4\) 3.30278 1.65139
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) 2.30278 0.728202
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) 1.30278 0.361325 0.180662 0.983545i \(-0.442176\pi\)
0.180662 + 0.983545i \(0.442176\pi\)
\(14\) 2.30278 0.615443
\(15\) 0 0
\(16\) 0.302776 0.0756939
\(17\) −2.30278 −0.558505 −0.279253 0.960218i \(-0.590087\pi\)
−0.279253 + 0.960218i \(0.590087\pi\)
\(18\) 0 0
\(19\) −3.30278 −0.757709 −0.378854 0.925456i \(-0.623682\pi\)
−0.378854 + 0.925456i \(0.623682\pi\)
\(20\) 3.30278 0.738523
\(21\) 0 0
\(22\) 6.90833 1.47286
\(23\) 0.697224 0.145381 0.0726907 0.997355i \(-0.476841\pi\)
0.0726907 + 0.997355i \(0.476841\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 3.00000 0.588348
\(27\) 0 0
\(28\) 3.30278 0.624166
\(29\) 5.30278 0.984701 0.492350 0.870397i \(-0.336138\pi\)
0.492350 + 0.870397i \(0.336138\pi\)
\(30\) 0 0
\(31\) −2.39445 −0.430056 −0.215028 0.976608i \(-0.568984\pi\)
−0.215028 + 0.976608i \(0.568984\pi\)
\(32\) −5.30278 −0.937407
\(33\) 0 0
\(34\) −5.30278 −0.909419
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) 3.60555 0.592749 0.296374 0.955072i \(-0.404222\pi\)
0.296374 + 0.955072i \(0.404222\pi\)
\(38\) −7.60555 −1.23378
\(39\) 0 0
\(40\) 3.00000 0.474342
\(41\) −6.90833 −1.07890 −0.539450 0.842018i \(-0.681368\pi\)
−0.539450 + 0.842018i \(0.681368\pi\)
\(42\) 0 0
\(43\) −4.21110 −0.642187 −0.321094 0.947047i \(-0.604050\pi\)
−0.321094 + 0.947047i \(0.604050\pi\)
\(44\) 9.90833 1.49374
\(45\) 0 0
\(46\) 1.60555 0.236726
\(47\) 7.60555 1.10938 0.554692 0.832056i \(-0.312836\pi\)
0.554692 + 0.832056i \(0.312836\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 2.30278 0.325662
\(51\) 0 0
\(52\) 4.30278 0.596688
\(53\) −5.51388 −0.757389 −0.378695 0.925522i \(-0.623627\pi\)
−0.378695 + 0.925522i \(0.623627\pi\)
\(54\) 0 0
\(55\) 3.00000 0.404520
\(56\) 3.00000 0.400892
\(57\) 0 0
\(58\) 12.2111 1.60340
\(59\) 6.21110 0.808617 0.404308 0.914623i \(-0.367512\pi\)
0.404308 + 0.914623i \(0.367512\pi\)
\(60\) 0 0
\(61\) −11.1194 −1.42370 −0.711849 0.702333i \(-0.752142\pi\)
−0.711849 + 0.702333i \(0.752142\pi\)
\(62\) −5.51388 −0.700263
\(63\) 0 0
\(64\) −12.8167 −1.60208
\(65\) 1.30278 0.161589
\(66\) 0 0
\(67\) 13.5139 1.65098 0.825491 0.564415i \(-0.190898\pi\)
0.825491 + 0.564415i \(0.190898\pi\)
\(68\) −7.60555 −0.922309
\(69\) 0 0
\(70\) 2.30278 0.275234
\(71\) 2.09167 0.248236 0.124118 0.992267i \(-0.460390\pi\)
0.124118 + 0.992267i \(0.460390\pi\)
\(72\) 0 0
\(73\) −10.2111 −1.19512 −0.597560 0.801825i \(-0.703863\pi\)
−0.597560 + 0.801825i \(0.703863\pi\)
\(74\) 8.30278 0.965178
\(75\) 0 0
\(76\) −10.9083 −1.25127
\(77\) 3.00000 0.341882
\(78\) 0 0
\(79\) −16.9083 −1.90234 −0.951168 0.308675i \(-0.900115\pi\)
−0.951168 + 0.308675i \(0.900115\pi\)
\(80\) 0.302776 0.0338513
\(81\) 0 0
\(82\) −15.9083 −1.75678
\(83\) −12.2111 −1.34034 −0.670171 0.742206i \(-0.733779\pi\)
−0.670171 + 0.742206i \(0.733779\pi\)
\(84\) 0 0
\(85\) −2.30278 −0.249771
\(86\) −9.69722 −1.04568
\(87\) 0 0
\(88\) 9.00000 0.959403
\(89\) 10.8167 1.14656 0.573282 0.819358i \(-0.305670\pi\)
0.573282 + 0.819358i \(0.305670\pi\)
\(90\) 0 0
\(91\) 1.30278 0.136568
\(92\) 2.30278 0.240081
\(93\) 0 0
\(94\) 17.5139 1.80642
\(95\) −3.30278 −0.338858
\(96\) 0 0
\(97\) −9.51388 −0.965988 −0.482994 0.875624i \(-0.660451\pi\)
−0.482994 + 0.875624i \(0.660451\pi\)
\(98\) 2.30278 0.232615
\(99\) 0 0
\(100\) 3.30278 0.330278
\(101\) −9.21110 −0.916539 −0.458269 0.888813i \(-0.651531\pi\)
−0.458269 + 0.888813i \(0.651531\pi\)
\(102\) 0 0
\(103\) −15.7250 −1.54943 −0.774714 0.632312i \(-0.782106\pi\)
−0.774714 + 0.632312i \(0.782106\pi\)
\(104\) 3.90833 0.383243
\(105\) 0 0
\(106\) −12.6972 −1.23326
\(107\) 15.0000 1.45010 0.725052 0.688694i \(-0.241816\pi\)
0.725052 + 0.688694i \(0.241816\pi\)
\(108\) 0 0
\(109\) −1.69722 −0.162565 −0.0812823 0.996691i \(-0.525902\pi\)
−0.0812823 + 0.996691i \(0.525902\pi\)
\(110\) 6.90833 0.658683
\(111\) 0 0
\(112\) 0.302776 0.0286096
\(113\) 15.9083 1.49653 0.748265 0.663400i \(-0.230887\pi\)
0.748265 + 0.663400i \(0.230887\pi\)
\(114\) 0 0
\(115\) 0.697224 0.0650165
\(116\) 17.5139 1.62612
\(117\) 0 0
\(118\) 14.3028 1.31668
\(119\) −2.30278 −0.211095
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) −25.6056 −2.31822
\(123\) 0 0
\(124\) −7.90833 −0.710189
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −18.7250 −1.66157 −0.830787 0.556591i \(-0.812109\pi\)
−0.830787 + 0.556591i \(0.812109\pi\)
\(128\) −18.9083 −1.67128
\(129\) 0 0
\(130\) 3.00000 0.263117
\(131\) −8.30278 −0.725417 −0.362708 0.931903i \(-0.618148\pi\)
−0.362708 + 0.931903i \(0.618148\pi\)
\(132\) 0 0
\(133\) −3.30278 −0.286387
\(134\) 31.1194 2.68831
\(135\) 0 0
\(136\) −6.90833 −0.592384
\(137\) 18.4222 1.57392 0.786958 0.617007i \(-0.211655\pi\)
0.786958 + 0.617007i \(0.211655\pi\)
\(138\) 0 0
\(139\) −5.60555 −0.475457 −0.237728 0.971332i \(-0.576403\pi\)
−0.237728 + 0.971332i \(0.576403\pi\)
\(140\) 3.30278 0.279135
\(141\) 0 0
\(142\) 4.81665 0.404205
\(143\) 3.90833 0.326831
\(144\) 0 0
\(145\) 5.30278 0.440372
\(146\) −23.5139 −1.94602
\(147\) 0 0
\(148\) 11.9083 0.978858
\(149\) 5.51388 0.451715 0.225857 0.974160i \(-0.427482\pi\)
0.225857 + 0.974160i \(0.427482\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788 −0.0406894 0.999172i \(-0.512955\pi\)
−0.0406894 + 0.999172i \(0.512955\pi\)
\(152\) −9.90833 −0.803671
\(153\) 0 0
\(154\) 6.90833 0.556689
\(155\) −2.39445 −0.192327
\(156\) 0 0
\(157\) 6.60555 0.527180 0.263590 0.964635i \(-0.415093\pi\)
0.263590 + 0.964635i \(0.415093\pi\)
\(158\) −38.9361 −3.09759
\(159\) 0 0
\(160\) −5.30278 −0.419221
\(161\) 0.697224 0.0549490
\(162\) 0 0
\(163\) 23.2111 1.81803 0.909017 0.416759i \(-0.136834\pi\)
0.909017 + 0.416759i \(0.136834\pi\)
\(164\) −22.8167 −1.78168
\(165\) 0 0
\(166\) −28.1194 −2.18249
\(167\) 19.6056 1.51712 0.758562 0.651601i \(-0.225902\pi\)
0.758562 + 0.651601i \(0.225902\pi\)
\(168\) 0 0
\(169\) −11.3028 −0.869444
\(170\) −5.30278 −0.406704
\(171\) 0 0
\(172\) −13.9083 −1.06050
\(173\) −16.8167 −1.27855 −0.639273 0.768980i \(-0.720765\pi\)
−0.639273 + 0.768980i \(0.720765\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 0.908327 0.0684677
\(177\) 0 0
\(178\) 24.9083 1.86696
\(179\) 16.8167 1.25694 0.628468 0.777836i \(-0.283682\pi\)
0.628468 + 0.777836i \(0.283682\pi\)
\(180\) 0 0
\(181\) 17.4222 1.29498 0.647491 0.762073i \(-0.275818\pi\)
0.647491 + 0.762073i \(0.275818\pi\)
\(182\) 3.00000 0.222375
\(183\) 0 0
\(184\) 2.09167 0.154200
\(185\) 3.60555 0.265085
\(186\) 0 0
\(187\) −6.90833 −0.505187
\(188\) 25.1194 1.83202
\(189\) 0 0
\(190\) −7.60555 −0.551765
\(191\) −6.69722 −0.484594 −0.242297 0.970202i \(-0.577901\pi\)
−0.242297 + 0.970202i \(0.577901\pi\)
\(192\) 0 0
\(193\) 6.11943 0.440486 0.220243 0.975445i \(-0.429315\pi\)
0.220243 + 0.975445i \(0.429315\pi\)
\(194\) −21.9083 −1.57293
\(195\) 0 0
\(196\) 3.30278 0.235913
\(197\) −22.8167 −1.62562 −0.812810 0.582529i \(-0.802063\pi\)
−0.812810 + 0.582529i \(0.802063\pi\)
\(198\) 0 0
\(199\) 22.7250 1.61093 0.805466 0.592643i \(-0.201915\pi\)
0.805466 + 0.592643i \(0.201915\pi\)
\(200\) 3.00000 0.212132
\(201\) 0 0
\(202\) −21.2111 −1.49241
\(203\) 5.30278 0.372182
\(204\) 0 0
\(205\) −6.90833 −0.482498
\(206\) −36.2111 −2.52295
\(207\) 0 0
\(208\) 0.394449 0.0273501
\(209\) −9.90833 −0.685373
\(210\) 0 0
\(211\) −11.3944 −0.784426 −0.392213 0.919874i \(-0.628290\pi\)
−0.392213 + 0.919874i \(0.628290\pi\)
\(212\) −18.2111 −1.25074
\(213\) 0 0
\(214\) 34.5416 2.36122
\(215\) −4.21110 −0.287195
\(216\) 0 0
\(217\) −2.39445 −0.162546
\(218\) −3.90833 −0.264705
\(219\) 0 0
\(220\) 9.90833 0.668019
\(221\) −3.00000 −0.201802
\(222\) 0 0
\(223\) 20.2111 1.35344 0.676718 0.736243i \(-0.263402\pi\)
0.676718 + 0.736243i \(0.263402\pi\)
\(224\) −5.30278 −0.354307
\(225\) 0 0
\(226\) 36.6333 2.43681
\(227\) −6.48612 −0.430499 −0.215250 0.976559i \(-0.569056\pi\)
−0.215250 + 0.976559i \(0.569056\pi\)
\(228\) 0 0
\(229\) 1.78890 0.118214 0.0591068 0.998252i \(-0.481175\pi\)
0.0591068 + 0.998252i \(0.481175\pi\)
\(230\) 1.60555 0.105867
\(231\) 0 0
\(232\) 15.9083 1.04443
\(233\) −9.90833 −0.649116 −0.324558 0.945866i \(-0.605216\pi\)
−0.324558 + 0.945866i \(0.605216\pi\)
\(234\) 0 0
\(235\) 7.60555 0.496131
\(236\) 20.5139 1.33534
\(237\) 0 0
\(238\) −5.30278 −0.343728
\(239\) 5.78890 0.374453 0.187226 0.982317i \(-0.440050\pi\)
0.187226 + 0.982317i \(0.440050\pi\)
\(240\) 0 0
\(241\) 0.119429 0.00769313 0.00384656 0.999993i \(-0.498776\pi\)
0.00384656 + 0.999993i \(0.498776\pi\)
\(242\) −4.60555 −0.296056
\(243\) 0 0
\(244\) −36.7250 −2.35108
\(245\) 1.00000 0.0638877
\(246\) 0 0
\(247\) −4.30278 −0.273779
\(248\) −7.18335 −0.456143
\(249\) 0 0
\(250\) 2.30278 0.145640
\(251\) 4.18335 0.264050 0.132025 0.991246i \(-0.457852\pi\)
0.132025 + 0.991246i \(0.457852\pi\)
\(252\) 0 0
\(253\) 2.09167 0.131502
\(254\) −43.1194 −2.70555
\(255\) 0 0
\(256\) −17.9083 −1.11927
\(257\) −12.0000 −0.748539 −0.374270 0.927320i \(-0.622107\pi\)
−0.374270 + 0.927320i \(0.622107\pi\)
\(258\) 0 0
\(259\) 3.60555 0.224038
\(260\) 4.30278 0.266847
\(261\) 0 0
\(262\) −19.1194 −1.18120
\(263\) 12.4861 0.769927 0.384964 0.922932i \(-0.374214\pi\)
0.384964 + 0.922932i \(0.374214\pi\)
\(264\) 0 0
\(265\) −5.51388 −0.338715
\(266\) −7.60555 −0.466326
\(267\) 0 0
\(268\) 44.6333 2.72641
\(269\) 9.42221 0.574482 0.287241 0.957858i \(-0.407262\pi\)
0.287241 + 0.957858i \(0.407262\pi\)
\(270\) 0 0
\(271\) 12.1194 0.736203 0.368101 0.929786i \(-0.380008\pi\)
0.368101 + 0.929786i \(0.380008\pi\)
\(272\) −0.697224 −0.0422754
\(273\) 0 0
\(274\) 42.4222 2.56282
\(275\) 3.00000 0.180907
\(276\) 0 0
\(277\) −3.09167 −0.185761 −0.0928803 0.995677i \(-0.529607\pi\)
−0.0928803 + 0.995677i \(0.529607\pi\)
\(278\) −12.9083 −0.774190
\(279\) 0 0
\(280\) 3.00000 0.179284
\(281\) −20.7250 −1.23635 −0.618174 0.786041i \(-0.712127\pi\)
−0.618174 + 0.786041i \(0.712127\pi\)
\(282\) 0 0
\(283\) 2.90833 0.172882 0.0864410 0.996257i \(-0.472451\pi\)
0.0864410 + 0.996257i \(0.472451\pi\)
\(284\) 6.90833 0.409934
\(285\) 0 0
\(286\) 9.00000 0.532181
\(287\) −6.90833 −0.407786
\(288\) 0 0
\(289\) −11.6972 −0.688072
\(290\) 12.2111 0.717061
\(291\) 0 0
\(292\) −33.7250 −1.97361
\(293\) 20.2389 1.18237 0.591183 0.806537i \(-0.298661\pi\)
0.591183 + 0.806537i \(0.298661\pi\)
\(294\) 0 0
\(295\) 6.21110 0.361624
\(296\) 10.8167 0.628705
\(297\) 0 0
\(298\) 12.6972 0.735530
\(299\) 0.908327 0.0525299
\(300\) 0 0
\(301\) −4.21110 −0.242724
\(302\) −2.30278 −0.132510
\(303\) 0 0
\(304\) −1.00000 −0.0573539
\(305\) −11.1194 −0.636697
\(306\) 0 0
\(307\) 32.8444 1.87453 0.937265 0.348618i \(-0.113349\pi\)
0.937265 + 0.348618i \(0.113349\pi\)
\(308\) 9.90833 0.564579
\(309\) 0 0
\(310\) −5.51388 −0.313167
\(311\) 14.0917 0.799065 0.399533 0.916719i \(-0.369172\pi\)
0.399533 + 0.916719i \(0.369172\pi\)
\(312\) 0 0
\(313\) −14.8167 −0.837487 −0.418743 0.908105i \(-0.637529\pi\)
−0.418743 + 0.908105i \(0.637529\pi\)
\(314\) 15.2111 0.858412
\(315\) 0 0
\(316\) −55.8444 −3.14149
\(317\) 17.2389 0.968231 0.484115 0.875004i \(-0.339141\pi\)
0.484115 + 0.875004i \(0.339141\pi\)
\(318\) 0 0
\(319\) 15.9083 0.890695
\(320\) −12.8167 −0.716473
\(321\) 0 0
\(322\) 1.60555 0.0894739
\(323\) 7.60555 0.423184
\(324\) 0 0
\(325\) 1.30278 0.0722650
\(326\) 53.4500 2.96032
\(327\) 0 0
\(328\) −20.7250 −1.14435
\(329\) 7.60555 0.419308
\(330\) 0 0
\(331\) 13.3028 0.731187 0.365593 0.930775i \(-0.380866\pi\)
0.365593 + 0.930775i \(0.380866\pi\)
\(332\) −40.3305 −2.21343
\(333\) 0 0
\(334\) 45.1472 2.47034
\(335\) 13.5139 0.738342
\(336\) 0 0
\(337\) 8.69722 0.473768 0.236884 0.971538i \(-0.423874\pi\)
0.236884 + 0.971538i \(0.423874\pi\)
\(338\) −26.0278 −1.41572
\(339\) 0 0
\(340\) −7.60555 −0.412469
\(341\) −7.18335 −0.389000
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −12.6333 −0.681142
\(345\) 0 0
\(346\) −38.7250 −2.08187
\(347\) 19.3944 1.04115 0.520574 0.853816i \(-0.325718\pi\)
0.520574 + 0.853816i \(0.325718\pi\)
\(348\) 0 0
\(349\) 26.6333 1.42565 0.712824 0.701343i \(-0.247416\pi\)
0.712824 + 0.701343i \(0.247416\pi\)
\(350\) 2.30278 0.123089
\(351\) 0 0
\(352\) −15.9083 −0.847917
\(353\) 23.7250 1.26275 0.631377 0.775476i \(-0.282490\pi\)
0.631377 + 0.775476i \(0.282490\pi\)
\(354\) 0 0
\(355\) 2.09167 0.111014
\(356\) 35.7250 1.89342
\(357\) 0 0
\(358\) 38.7250 2.04668
\(359\) 1.18335 0.0624546 0.0312273 0.999512i \(-0.490058\pi\)
0.0312273 + 0.999512i \(0.490058\pi\)
\(360\) 0 0
\(361\) −8.09167 −0.425878
\(362\) 40.1194 2.10863
\(363\) 0 0
\(364\) 4.30278 0.225527
\(365\) −10.2111 −0.534474
\(366\) 0 0
\(367\) −6.30278 −0.329002 −0.164501 0.986377i \(-0.552601\pi\)
−0.164501 + 0.986377i \(0.552601\pi\)
\(368\) 0.211103 0.0110045
\(369\) 0 0
\(370\) 8.30278 0.431641
\(371\) −5.51388 −0.286266
\(372\) 0 0
\(373\) −1.90833 −0.0988094 −0.0494047 0.998779i \(-0.515732\pi\)
−0.0494047 + 0.998779i \(0.515732\pi\)
\(374\) −15.9083 −0.822600
\(375\) 0 0
\(376\) 22.8167 1.17668
\(377\) 6.90833 0.355797
\(378\) 0 0
\(379\) −25.6333 −1.31669 −0.658347 0.752714i \(-0.728744\pi\)
−0.658347 + 0.752714i \(0.728744\pi\)
\(380\) −10.9083 −0.559585
\(381\) 0 0
\(382\) −15.4222 −0.789069
\(383\) 0.211103 0.0107868 0.00539342 0.999985i \(-0.498283\pi\)
0.00539342 + 0.999985i \(0.498283\pi\)
\(384\) 0 0
\(385\) 3.00000 0.152894
\(386\) 14.0917 0.717247
\(387\) 0 0
\(388\) −31.4222 −1.59522
\(389\) −8.72498 −0.442374 −0.221187 0.975231i \(-0.570993\pi\)
−0.221187 + 0.975231i \(0.570993\pi\)
\(390\) 0 0
\(391\) −1.60555 −0.0811962
\(392\) 3.00000 0.151523
\(393\) 0 0
\(394\) −52.5416 −2.64701
\(395\) −16.9083 −0.850750
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) 52.3305 2.62309
\(399\) 0 0
\(400\) 0.302776 0.0151388
\(401\) −5.72498 −0.285892 −0.142946 0.989730i \(-0.545658\pi\)
−0.142946 + 0.989730i \(0.545658\pi\)
\(402\) 0 0
\(403\) −3.11943 −0.155390
\(404\) −30.4222 −1.51356
\(405\) 0 0
\(406\) 12.2111 0.606027
\(407\) 10.8167 0.536162
\(408\) 0 0
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) −15.9083 −0.785656
\(411\) 0 0
\(412\) −51.9361 −2.55871
\(413\) 6.21110 0.305628
\(414\) 0 0
\(415\) −12.2111 −0.599419
\(416\) −6.90833 −0.338709
\(417\) 0 0
\(418\) −22.8167 −1.11600
\(419\) 13.1833 0.644049 0.322024 0.946731i \(-0.395637\pi\)
0.322024 + 0.946731i \(0.395637\pi\)
\(420\) 0 0
\(421\) 2.69722 0.131455 0.0657273 0.997838i \(-0.479063\pi\)
0.0657273 + 0.997838i \(0.479063\pi\)
\(422\) −26.2389 −1.27729
\(423\) 0 0
\(424\) −16.5416 −0.803333
\(425\) −2.30278 −0.111701
\(426\) 0 0
\(427\) −11.1194 −0.538107
\(428\) 49.5416 2.39469
\(429\) 0 0
\(430\) −9.69722 −0.467642
\(431\) 35.9361 1.73098 0.865490 0.500926i \(-0.167007\pi\)
0.865490 + 0.500926i \(0.167007\pi\)
\(432\) 0 0
\(433\) 15.3305 0.736738 0.368369 0.929680i \(-0.379916\pi\)
0.368369 + 0.929680i \(0.379916\pi\)
\(434\) −5.51388 −0.264675
\(435\) 0 0
\(436\) −5.60555 −0.268457
\(437\) −2.30278 −0.110157
\(438\) 0 0
\(439\) −26.3944 −1.25974 −0.629869 0.776701i \(-0.716891\pi\)
−0.629869 + 0.776701i \(0.716891\pi\)
\(440\) 9.00000 0.429058
\(441\) 0 0
\(442\) −6.90833 −0.328596
\(443\) −0.275019 −0.0130666 −0.00653328 0.999979i \(-0.502080\pi\)
−0.00653328 + 0.999979i \(0.502080\pi\)
\(444\) 0 0
\(445\) 10.8167 0.512759
\(446\) 46.5416 2.20381
\(447\) 0 0
\(448\) −12.8167 −0.605530
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) −20.7250 −0.975901
\(452\) 52.5416 2.47135
\(453\) 0 0
\(454\) −14.9361 −0.700985
\(455\) 1.30278 0.0610751
\(456\) 0 0
\(457\) 22.3028 1.04328 0.521640 0.853166i \(-0.325320\pi\)
0.521640 + 0.853166i \(0.325320\pi\)
\(458\) 4.11943 0.192488
\(459\) 0 0
\(460\) 2.30278 0.107367
\(461\) −26.5139 −1.23487 −0.617437 0.786620i \(-0.711829\pi\)
−0.617437 + 0.786620i \(0.711829\pi\)
\(462\) 0 0
\(463\) 10.9361 0.508243 0.254121 0.967172i \(-0.418214\pi\)
0.254121 + 0.967172i \(0.418214\pi\)
\(464\) 1.60555 0.0745358
\(465\) 0 0
\(466\) −22.8167 −1.05696
\(467\) 9.21110 0.426239 0.213119 0.977026i \(-0.431638\pi\)
0.213119 + 0.977026i \(0.431638\pi\)
\(468\) 0 0
\(469\) 13.5139 0.624013
\(470\) 17.5139 0.807855
\(471\) 0 0
\(472\) 18.6333 0.857668
\(473\) −12.6333 −0.580880
\(474\) 0 0
\(475\) −3.30278 −0.151542
\(476\) −7.60555 −0.348600
\(477\) 0 0
\(478\) 13.3305 0.609724
\(479\) −11.9361 −0.545374 −0.272687 0.962103i \(-0.587912\pi\)
−0.272687 + 0.962103i \(0.587912\pi\)
\(480\) 0 0
\(481\) 4.69722 0.214175
\(482\) 0.275019 0.0125268
\(483\) 0 0
\(484\) −6.60555 −0.300252
\(485\) −9.51388 −0.432003
\(486\) 0 0
\(487\) 38.0000 1.72194 0.860972 0.508652i \(-0.169856\pi\)
0.860972 + 0.508652i \(0.169856\pi\)
\(488\) −33.3583 −1.51006
\(489\) 0 0
\(490\) 2.30278 0.104029
\(491\) −20.7250 −0.935305 −0.467653 0.883912i \(-0.654900\pi\)
−0.467653 + 0.883912i \(0.654900\pi\)
\(492\) 0 0
\(493\) −12.2111 −0.549960
\(494\) −9.90833 −0.445797
\(495\) 0 0
\(496\) −0.724981 −0.0325526
\(497\) 2.09167 0.0938244
\(498\) 0 0
\(499\) −40.6333 −1.81900 −0.909498 0.415708i \(-0.863534\pi\)
−0.909498 + 0.415708i \(0.863534\pi\)
\(500\) 3.30278 0.147705
\(501\) 0 0
\(502\) 9.63331 0.429956
\(503\) 19.1194 0.852493 0.426247 0.904607i \(-0.359836\pi\)
0.426247 + 0.904607i \(0.359836\pi\)
\(504\) 0 0
\(505\) −9.21110 −0.409889
\(506\) 4.81665 0.214126
\(507\) 0 0
\(508\) −61.8444 −2.74390
\(509\) −23.2389 −1.03004 −0.515022 0.857177i \(-0.672216\pi\)
−0.515022 + 0.857177i \(0.672216\pi\)
\(510\) 0 0
\(511\) −10.2111 −0.451713
\(512\) −3.42221 −0.151242
\(513\) 0 0
\(514\) −27.6333 −1.21885
\(515\) −15.7250 −0.692925
\(516\) 0 0
\(517\) 22.8167 1.00348
\(518\) 8.30278 0.364803
\(519\) 0 0
\(520\) 3.90833 0.171391
\(521\) −43.6056 −1.91039 −0.955197 0.295971i \(-0.904357\pi\)
−0.955197 + 0.295971i \(0.904357\pi\)
\(522\) 0 0
\(523\) 13.7250 0.600152 0.300076 0.953915i \(-0.402988\pi\)
0.300076 + 0.953915i \(0.402988\pi\)
\(524\) −27.4222 −1.19794
\(525\) 0 0
\(526\) 28.7527 1.25368
\(527\) 5.51388 0.240188
\(528\) 0 0
\(529\) −22.5139 −0.978864
\(530\) −12.6972 −0.551532
\(531\) 0 0
\(532\) −10.9083 −0.472936
\(533\) −9.00000 −0.389833
\(534\) 0 0
\(535\) 15.0000 0.648507
\(536\) 40.5416 1.75113
\(537\) 0 0
\(538\) 21.6972 0.935434
\(539\) 3.00000 0.129219
\(540\) 0 0
\(541\) −15.5139 −0.666994 −0.333497 0.942751i \(-0.608229\pi\)
−0.333497 + 0.942751i \(0.608229\pi\)
\(542\) 27.9083 1.19877
\(543\) 0 0
\(544\) 12.2111 0.523547
\(545\) −1.69722 −0.0727011
\(546\) 0 0
\(547\) 38.2111 1.63379 0.816894 0.576787i \(-0.195694\pi\)
0.816894 + 0.576787i \(0.195694\pi\)
\(548\) 60.8444 2.59914
\(549\) 0 0
\(550\) 6.90833 0.294572
\(551\) −17.5139 −0.746116
\(552\) 0 0
\(553\) −16.9083 −0.719015
\(554\) −7.11943 −0.302476
\(555\) 0 0
\(556\) −18.5139 −0.785163
\(557\) −15.4861 −0.656168 −0.328084 0.944649i \(-0.606403\pi\)
−0.328084 + 0.944649i \(0.606403\pi\)
\(558\) 0 0
\(559\) −5.48612 −0.232038
\(560\) 0.302776 0.0127946
\(561\) 0 0
\(562\) −47.7250 −2.01316
\(563\) 35.9361 1.51453 0.757263 0.653110i \(-0.226536\pi\)
0.757263 + 0.653110i \(0.226536\pi\)
\(564\) 0 0
\(565\) 15.9083 0.669268
\(566\) 6.69722 0.281505
\(567\) 0 0
\(568\) 6.27502 0.263294
\(569\) −30.6333 −1.28422 −0.642108 0.766615i \(-0.721940\pi\)
−0.642108 + 0.766615i \(0.721940\pi\)
\(570\) 0 0
\(571\) 19.9361 0.834299 0.417150 0.908838i \(-0.363029\pi\)
0.417150 + 0.908838i \(0.363029\pi\)
\(572\) 12.9083 0.539724
\(573\) 0 0
\(574\) −15.9083 −0.664001
\(575\) 0.697224 0.0290763
\(576\) 0 0
\(577\) 39.6056 1.64880 0.824400 0.566007i \(-0.191513\pi\)
0.824400 + 0.566007i \(0.191513\pi\)
\(578\) −26.9361 −1.12039
\(579\) 0 0
\(580\) 17.5139 0.727224
\(581\) −12.2111 −0.506602
\(582\) 0 0
\(583\) −16.5416 −0.685085
\(584\) −30.6333 −1.26762
\(585\) 0 0
\(586\) 46.6056 1.92526
\(587\) −2.09167 −0.0863326 −0.0431663 0.999068i \(-0.513745\pi\)
−0.0431663 + 0.999068i \(0.513745\pi\)
\(588\) 0 0
\(589\) 7.90833 0.325857
\(590\) 14.3028 0.588836
\(591\) 0 0
\(592\) 1.09167 0.0448675
\(593\) −34.8167 −1.42975 −0.714874 0.699253i \(-0.753516\pi\)
−0.714874 + 0.699253i \(0.753516\pi\)
\(594\) 0 0
\(595\) −2.30278 −0.0944046
\(596\) 18.2111 0.745956
\(597\) 0 0
\(598\) 2.09167 0.0855349
\(599\) 36.4222 1.48817 0.744085 0.668084i \(-0.232886\pi\)
0.744085 + 0.668084i \(0.232886\pi\)
\(600\) 0 0
\(601\) 45.1194 1.84046 0.920230 0.391378i \(-0.128002\pi\)
0.920230 + 0.391378i \(0.128002\pi\)
\(602\) −9.69722 −0.395229
\(603\) 0 0
\(604\) −3.30278 −0.134388
\(605\) −2.00000 −0.0813116
\(606\) 0 0
\(607\) 14.6333 0.593948 0.296974 0.954886i \(-0.404023\pi\)
0.296974 + 0.954886i \(0.404023\pi\)
\(608\) 17.5139 0.710282
\(609\) 0 0
\(610\) −25.6056 −1.03674
\(611\) 9.90833 0.400848
\(612\) 0 0
\(613\) −27.2389 −1.10017 −0.550084 0.835110i \(-0.685404\pi\)
−0.550084 + 0.835110i \(0.685404\pi\)
\(614\) 75.6333 3.05231
\(615\) 0 0
\(616\) 9.00000 0.362620
\(617\) 42.9083 1.72742 0.863712 0.503986i \(-0.168134\pi\)
0.863712 + 0.503986i \(0.168134\pi\)
\(618\) 0 0
\(619\) 16.0278 0.644210 0.322105 0.946704i \(-0.395610\pi\)
0.322105 + 0.946704i \(0.395610\pi\)
\(620\) −7.90833 −0.317606
\(621\) 0 0
\(622\) 32.4500 1.30112
\(623\) 10.8167 0.433360
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −34.1194 −1.36369
\(627\) 0 0
\(628\) 21.8167 0.870579
\(629\) −8.30278 −0.331053
\(630\) 0 0
\(631\) −30.7889 −1.22569 −0.612843 0.790204i \(-0.709974\pi\)
−0.612843 + 0.790204i \(0.709974\pi\)
\(632\) −50.7250 −2.01773
\(633\) 0 0
\(634\) 39.6972 1.57658
\(635\) −18.7250 −0.743078
\(636\) 0 0
\(637\) 1.30278 0.0516179
\(638\) 36.6333 1.45033
\(639\) 0 0
\(640\) −18.9083 −0.747417
\(641\) 5.72498 0.226123 0.113062 0.993588i \(-0.463934\pi\)
0.113062 + 0.993588i \(0.463934\pi\)
\(642\) 0 0
\(643\) −13.4861 −0.531841 −0.265920 0.963995i \(-0.585676\pi\)
−0.265920 + 0.963995i \(0.585676\pi\)
\(644\) 2.30278 0.0907421
\(645\) 0 0
\(646\) 17.5139 0.689074
\(647\) 30.0000 1.17942 0.589711 0.807614i \(-0.299242\pi\)
0.589711 + 0.807614i \(0.299242\pi\)
\(648\) 0 0
\(649\) 18.6333 0.731421
\(650\) 3.00000 0.117670
\(651\) 0 0
\(652\) 76.6611 3.00228
\(653\) 4.88057 0.190991 0.0954957 0.995430i \(-0.469556\pi\)
0.0954957 + 0.995430i \(0.469556\pi\)
\(654\) 0 0
\(655\) −8.30278 −0.324416
\(656\) −2.09167 −0.0816661
\(657\) 0 0
\(658\) 17.5139 0.682762
\(659\) −22.1833 −0.864140 −0.432070 0.901840i \(-0.642217\pi\)
−0.432070 + 0.901840i \(0.642217\pi\)
\(660\) 0 0
\(661\) 7.72498 0.300467 0.150233 0.988651i \(-0.451997\pi\)
0.150233 + 0.988651i \(0.451997\pi\)
\(662\) 30.6333 1.19060
\(663\) 0 0
\(664\) −36.6333 −1.42165
\(665\) −3.30278 −0.128076
\(666\) 0 0
\(667\) 3.69722 0.143157
\(668\) 64.7527 2.50536
\(669\) 0 0
\(670\) 31.1194 1.20225
\(671\) −33.3583 −1.28778
\(672\) 0 0
\(673\) −28.0000 −1.07932 −0.539660 0.841883i \(-0.681447\pi\)
−0.539660 + 0.841883i \(0.681447\pi\)
\(674\) 20.0278 0.771440
\(675\) 0 0
\(676\) −37.3305 −1.43579
\(677\) −17.7889 −0.683683 −0.341841 0.939758i \(-0.611051\pi\)
−0.341841 + 0.939758i \(0.611051\pi\)
\(678\) 0 0
\(679\) −9.51388 −0.365109
\(680\) −6.90833 −0.264922
\(681\) 0 0
\(682\) −16.5416 −0.633412
\(683\) −45.3583 −1.73559 −0.867793 0.496925i \(-0.834462\pi\)
−0.867793 + 0.496925i \(0.834462\pi\)
\(684\) 0 0
\(685\) 18.4222 0.703876
\(686\) 2.30278 0.0879204
\(687\) 0 0
\(688\) −1.27502 −0.0486097
\(689\) −7.18335 −0.273664
\(690\) 0 0
\(691\) −7.42221 −0.282354 −0.141177 0.989984i \(-0.545089\pi\)
−0.141177 + 0.989984i \(0.545089\pi\)
\(692\) −55.5416 −2.11138
\(693\) 0 0
\(694\) 44.6611 1.69531
\(695\) −5.60555 −0.212631
\(696\) 0 0
\(697\) 15.9083 0.602571
\(698\) 61.3305 2.32139
\(699\) 0 0
\(700\) 3.30278 0.124833
\(701\) 26.0278 0.983055 0.491527 0.870862i \(-0.336439\pi\)
0.491527 + 0.870862i \(0.336439\pi\)
\(702\) 0 0
\(703\) −11.9083 −0.449131
\(704\) −38.4500 −1.44914
\(705\) 0 0
\(706\) 54.6333 2.05615
\(707\) −9.21110 −0.346419
\(708\) 0 0
\(709\) −45.0278 −1.69105 −0.845526 0.533934i \(-0.820713\pi\)
−0.845526 + 0.533934i \(0.820713\pi\)
\(710\) 4.81665 0.180766
\(711\) 0 0
\(712\) 32.4500 1.21611
\(713\) −1.66947 −0.0625221
\(714\) 0 0
\(715\) 3.90833 0.146163
\(716\) 55.5416 2.07569
\(717\) 0 0
\(718\) 2.72498 0.101695
\(719\) 19.3305 0.720907 0.360454 0.932777i \(-0.382622\pi\)
0.360454 + 0.932777i \(0.382622\pi\)
\(720\) 0 0
\(721\) −15.7250 −0.585629
\(722\) −18.6333 −0.693460
\(723\) 0 0
\(724\) 57.5416 2.13852
\(725\) 5.30278 0.196940
\(726\) 0 0
\(727\) −19.4861 −0.722700 −0.361350 0.932430i \(-0.617684\pi\)
−0.361350 + 0.932430i \(0.617684\pi\)
\(728\) 3.90833 0.144852
\(729\) 0 0
\(730\) −23.5139 −0.870288
\(731\) 9.69722 0.358665
\(732\) 0 0
\(733\) 12.5416 0.463236 0.231618 0.972807i \(-0.425598\pi\)
0.231618 + 0.972807i \(0.425598\pi\)
\(734\) −14.5139 −0.535717
\(735\) 0 0
\(736\) −3.69722 −0.136281
\(737\) 40.5416 1.49337
\(738\) 0 0
\(739\) −20.1833 −0.742456 −0.371228 0.928542i \(-0.621063\pi\)
−0.371228 + 0.928542i \(0.621063\pi\)
\(740\) 11.9083 0.437759
\(741\) 0 0
\(742\) −12.6972 −0.466130
\(743\) 34.5416 1.26721 0.633605 0.773657i \(-0.281575\pi\)
0.633605 + 0.773657i \(0.281575\pi\)
\(744\) 0 0
\(745\) 5.51388 0.202013
\(746\) −4.39445 −0.160892
\(747\) 0 0
\(748\) −22.8167 −0.834259
\(749\) 15.0000 0.548088
\(750\) 0 0
\(751\) 14.0000 0.510867 0.255434 0.966827i \(-0.417782\pi\)
0.255434 + 0.966827i \(0.417782\pi\)
\(752\) 2.30278 0.0839736
\(753\) 0 0
\(754\) 15.9083 0.579347
\(755\) −1.00000 −0.0363937
\(756\) 0 0
\(757\) −14.5416 −0.528525 −0.264262 0.964451i \(-0.585128\pi\)
−0.264262 + 0.964451i \(0.585128\pi\)
\(758\) −59.0278 −2.14398
\(759\) 0 0
\(760\) −9.90833 −0.359413
\(761\) 13.5416 0.490884 0.245442 0.969411i \(-0.421067\pi\)
0.245442 + 0.969411i \(0.421067\pi\)
\(762\) 0 0
\(763\) −1.69722 −0.0614436
\(764\) −22.1194 −0.800253
\(765\) 0 0
\(766\) 0.486122 0.0175643
\(767\) 8.09167 0.292173
\(768\) 0 0
\(769\) −26.8167 −0.967033 −0.483517 0.875335i \(-0.660641\pi\)
−0.483517 + 0.875335i \(0.660641\pi\)
\(770\) 6.90833 0.248959
\(771\) 0 0
\(772\) 20.2111 0.727413
\(773\) 1.54163 0.0554487 0.0277244 0.999616i \(-0.491174\pi\)
0.0277244 + 0.999616i \(0.491174\pi\)
\(774\) 0 0
\(775\) −2.39445 −0.0860111
\(776\) −28.5416 −1.02458
\(777\) 0 0
\(778\) −20.0917 −0.720321
\(779\) 22.8167 0.817491
\(780\) 0 0
\(781\) 6.27502 0.224538
\(782\) −3.69722 −0.132212
\(783\) 0 0
\(784\) 0.302776 0.0108134
\(785\) 6.60555 0.235762
\(786\) 0 0
\(787\) −3.02776 −0.107928 −0.0539639 0.998543i \(-0.517186\pi\)
−0.0539639 + 0.998543i \(0.517186\pi\)
\(788\) −75.3583 −2.68453
\(789\) 0 0
\(790\) −38.9361 −1.38528
\(791\) 15.9083 0.565635
\(792\) 0 0
\(793\) −14.4861 −0.514417
\(794\) 4.60555 0.163445
\(795\) 0 0
\(796\) 75.0555 2.66027
\(797\) −42.9083 −1.51989 −0.759945 0.649987i \(-0.774774\pi\)
−0.759945 + 0.649987i \(0.774774\pi\)
\(798\) 0 0
\(799\) −17.5139 −0.619596
\(800\) −5.30278 −0.187481
\(801\) 0 0
\(802\) −13.1833 −0.465520
\(803\) −30.6333 −1.08103
\(804\) 0 0
\(805\) 0.697224 0.0245739
\(806\) −7.18335 −0.253023
\(807\) 0 0
\(808\) −27.6333 −0.972136
\(809\) −19.1833 −0.674451 −0.337225 0.941424i \(-0.609488\pi\)
−0.337225 + 0.941424i \(0.609488\pi\)
\(810\) 0 0
\(811\) −24.5139 −0.860799 −0.430399 0.902639i \(-0.641627\pi\)
−0.430399 + 0.902639i \(0.641627\pi\)
\(812\) 17.5139 0.614617
\(813\) 0 0
\(814\) 24.9083 0.873036
\(815\) 23.2111 0.813049
\(816\) 0 0
\(817\) 13.9083 0.486591
\(818\) 32.2389 1.12721
\(819\) 0 0
\(820\) −22.8167 −0.796792
\(821\) 10.8167 0.377504 0.188752 0.982025i \(-0.439556\pi\)
0.188752 + 0.982025i \(0.439556\pi\)
\(822\) 0 0
\(823\) 32.6333 1.13753 0.568763 0.822502i \(-0.307422\pi\)
0.568763 + 0.822502i \(0.307422\pi\)
\(824\) −47.1749 −1.64342
\(825\) 0 0
\(826\) 14.3028 0.497657
\(827\) 0.633308 0.0220223 0.0110111 0.999939i \(-0.496495\pi\)
0.0110111 + 0.999939i \(0.496495\pi\)
\(828\) 0 0
\(829\) −23.0555 −0.800751 −0.400376 0.916351i \(-0.631120\pi\)
−0.400376 + 0.916351i \(0.631120\pi\)
\(830\) −28.1194 −0.976040
\(831\) 0 0
\(832\) −16.6972 −0.578872
\(833\) −2.30278 −0.0797864
\(834\) 0 0
\(835\) 19.6056 0.678478
\(836\) −32.7250 −1.13182
\(837\) 0 0
\(838\) 30.3583 1.04871
\(839\) −11.0917 −0.382927 −0.191464 0.981500i \(-0.561323\pi\)
−0.191464 + 0.981500i \(0.561323\pi\)
\(840\) 0 0
\(841\) −0.880571 −0.0303645
\(842\) 6.21110 0.214049
\(843\) 0 0
\(844\) −37.6333 −1.29539
\(845\) −11.3028 −0.388827
\(846\) 0 0
\(847\) −2.00000 −0.0687208
\(848\) −1.66947 −0.0573298
\(849\) 0 0
\(850\) −5.30278 −0.181884
\(851\) 2.51388 0.0861746
\(852\) 0 0
\(853\) 29.8444 1.02185 0.510927 0.859624i \(-0.329302\pi\)
0.510927 + 0.859624i \(0.329302\pi\)
\(854\) −25.6056 −0.876204
\(855\) 0 0
\(856\) 45.0000 1.53807
\(857\) −34.2666 −1.17053 −0.585263 0.810844i \(-0.699009\pi\)
−0.585263 + 0.810844i \(0.699009\pi\)
\(858\) 0 0
\(859\) 27.8167 0.949092 0.474546 0.880231i \(-0.342612\pi\)
0.474546 + 0.880231i \(0.342612\pi\)
\(860\) −13.9083 −0.474270
\(861\) 0 0
\(862\) 82.7527 2.81857
\(863\) −31.2666 −1.06433 −0.532164 0.846641i \(-0.678621\pi\)
−0.532164 + 0.846641i \(0.678621\pi\)
\(864\) 0 0
\(865\) −16.8167 −0.571783
\(866\) 35.3028 1.19964
\(867\) 0 0
\(868\) −7.90833 −0.268426
\(869\) −50.7250 −1.72073
\(870\) 0 0
\(871\) 17.6056 0.596541
\(872\) −5.09167 −0.172426
\(873\) 0 0
\(874\) −5.30278 −0.179369
\(875\) 1.00000 0.0338062
\(876\) 0 0
\(877\) −22.6333 −0.764272 −0.382136 0.924106i \(-0.624811\pi\)
−0.382136 + 0.924106i \(0.624811\pi\)
\(878\) −60.7805 −2.05124
\(879\) 0 0
\(880\) 0.908327 0.0306197
\(881\) −45.6333 −1.53743 −0.768713 0.639594i \(-0.779102\pi\)
−0.768713 + 0.639594i \(0.779102\pi\)
\(882\) 0 0
\(883\) −6.02776 −0.202850 −0.101425 0.994843i \(-0.532340\pi\)
−0.101425 + 0.994843i \(0.532340\pi\)
\(884\) −9.90833 −0.333253
\(885\) 0 0
\(886\) −0.633308 −0.0212764
\(887\) −22.6056 −0.759020 −0.379510 0.925188i \(-0.623907\pi\)
−0.379510 + 0.925188i \(0.623907\pi\)
\(888\) 0 0
\(889\) −18.7250 −0.628016
\(890\) 24.9083 0.834929
\(891\) 0 0
\(892\) 66.7527 2.23505
\(893\) −25.1194 −0.840590
\(894\) 0 0
\(895\) 16.8167 0.562119
\(896\) −18.9083 −0.631683
\(897\) 0 0
\(898\) −41.4500 −1.38320
\(899\) −12.6972 −0.423476
\(900\) 0 0
\(901\) 12.6972 0.423006
\(902\) −47.7250 −1.58907
\(903\) 0 0
\(904\) 47.7250 1.58731
\(905\) 17.4222 0.579134
\(906\) 0 0
\(907\) −52.5694 −1.74554 −0.872769 0.488133i \(-0.837678\pi\)
−0.872769 + 0.488133i \(0.837678\pi\)
\(908\) −21.4222 −0.710921
\(909\) 0 0
\(910\) 3.00000 0.0994490
\(911\) −27.6333 −0.915532 −0.457766 0.889073i \(-0.651350\pi\)
−0.457766 + 0.889073i \(0.651350\pi\)
\(912\) 0 0
\(913\) −36.6333 −1.21239
\(914\) 51.3583 1.69878
\(915\) 0 0
\(916\) 5.90833 0.195217
\(917\) −8.30278 −0.274182
\(918\) 0 0
\(919\) 2.48612 0.0820096 0.0410048 0.999159i \(-0.486944\pi\)
0.0410048 + 0.999159i \(0.486944\pi\)
\(920\) 2.09167 0.0689604
\(921\) 0 0
\(922\) −61.0555 −2.01076
\(923\) 2.72498 0.0896938
\(924\) 0 0
\(925\) 3.60555 0.118550
\(926\) 25.1833 0.827576
\(927\) 0 0
\(928\) −28.1194 −0.923065
\(929\) 39.5694 1.29823 0.649115 0.760690i \(-0.275139\pi\)
0.649115 + 0.760690i \(0.275139\pi\)
\(930\) 0 0
\(931\) −3.30278 −0.108244
\(932\) −32.7250 −1.07194
\(933\) 0 0
\(934\) 21.2111 0.694048
\(935\) −6.90833 −0.225926
\(936\) 0 0
\(937\) 44.4222 1.45121 0.725605 0.688111i \(-0.241560\pi\)
0.725605 + 0.688111i \(0.241560\pi\)
\(938\) 31.1194 1.01609
\(939\) 0 0
\(940\) 25.1194 0.819305
\(941\) −34.2666 −1.11706 −0.558530 0.829484i \(-0.688634\pi\)
−0.558530 + 0.829484i \(0.688634\pi\)
\(942\) 0 0
\(943\) −4.81665 −0.156852
\(944\) 1.88057 0.0612074
\(945\) 0 0
\(946\) −29.0917 −0.945852
\(947\) 1.33053 0.0432365 0.0216182 0.999766i \(-0.493118\pi\)
0.0216182 + 0.999766i \(0.493118\pi\)
\(948\) 0 0
\(949\) −13.3028 −0.431826
\(950\) −7.60555 −0.246757
\(951\) 0 0
\(952\) −6.90833 −0.223900
\(953\) −51.4222 −1.66573 −0.832864 0.553477i \(-0.813301\pi\)
−0.832864 + 0.553477i \(0.813301\pi\)
\(954\) 0 0
\(955\) −6.69722 −0.216717
\(956\) 19.1194 0.618367
\(957\) 0 0
\(958\) −27.4861 −0.888036
\(959\) 18.4222 0.594884
\(960\) 0 0
\(961\) −25.2666 −0.815052
\(962\) 10.8167 0.348743
\(963\) 0 0
\(964\) 0.394449 0.0127043
\(965\) 6.11943 0.196991
\(966\) 0 0
\(967\) −25.8444 −0.831100 −0.415550 0.909570i \(-0.636411\pi\)
−0.415550 + 0.909570i \(0.636411\pi\)
\(968\) −6.00000 −0.192847
\(969\) 0 0
\(970\) −21.9083 −0.703434
\(971\) −5.57779 −0.179000 −0.0895000 0.995987i \(-0.528527\pi\)
−0.0895000 + 0.995987i \(0.528527\pi\)
\(972\) 0 0
\(973\) −5.60555 −0.179706
\(974\) 87.5055 2.80386
\(975\) 0 0
\(976\) −3.36669 −0.107765
\(977\) 0.422205 0.0135075 0.00675377 0.999977i \(-0.497850\pi\)
0.00675377 + 0.999977i \(0.497850\pi\)
\(978\) 0 0
\(979\) 32.4500 1.03711
\(980\) 3.30278 0.105503
\(981\) 0 0
\(982\) −47.7250 −1.52297
\(983\) 20.5139 0.654291 0.327146 0.944974i \(-0.393913\pi\)
0.327146 + 0.944974i \(0.393913\pi\)
\(984\) 0 0
\(985\) −22.8167 −0.726999
\(986\) −28.1194 −0.895505
\(987\) 0 0
\(988\) −14.2111 −0.452115
\(989\) −2.93608 −0.0933620
\(990\) 0 0
\(991\) −59.0555 −1.87596 −0.937980 0.346689i \(-0.887306\pi\)
−0.937980 + 0.346689i \(0.887306\pi\)
\(992\) 12.6972 0.403137
\(993\) 0 0
\(994\) 4.81665 0.152775
\(995\) 22.7250 0.720430
\(996\) 0 0
\(997\) −14.8167 −0.469248 −0.234624 0.972086i \(-0.575386\pi\)
−0.234624 + 0.972086i \(0.575386\pi\)
\(998\) −93.5694 −2.96189
\(999\) 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 \(a_p\))