Properties

Label 667.2.a.c.1.2
Level $667$
Weight $2$
Character 667.1
Self dual yes
Analytic conductor $5.326$
Analytic rank $0$
Dimension $13$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 667 = 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 667.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.32602181482\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Defining polynomial: \(x^{13} - 4 x^{12} - 11 x^{11} + 58 x^{10} + 24 x^{9} - 298 x^{8} + 97 x^{7} + 641 x^{6} - 402 x^{5} - 547 x^{4} + 352 x^{3} + 219 x^{2} - 88 x - 40\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.22202\) of defining polynomial
Character \(\chi\) \(=\) 667.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.22202 q^{2} +0.328413 q^{3} +2.93739 q^{4} +2.84468 q^{5} -0.729742 q^{6} -1.80107 q^{7} -2.08291 q^{8} -2.89214 q^{9} +O(q^{10})\) \(q-2.22202 q^{2} +0.328413 q^{3} +2.93739 q^{4} +2.84468 q^{5} -0.729742 q^{6} -1.80107 q^{7} -2.08291 q^{8} -2.89214 q^{9} -6.32095 q^{10} +1.40952 q^{11} +0.964678 q^{12} +5.09892 q^{13} +4.00202 q^{14} +0.934230 q^{15} -1.24652 q^{16} -0.501226 q^{17} +6.42642 q^{18} +7.81418 q^{19} +8.35594 q^{20} -0.591495 q^{21} -3.13198 q^{22} -1.00000 q^{23} -0.684054 q^{24} +3.09220 q^{25} -11.3299 q^{26} -1.93506 q^{27} -5.29044 q^{28} +1.00000 q^{29} -2.07588 q^{30} -7.79469 q^{31} +6.93560 q^{32} +0.462904 q^{33} +1.11374 q^{34} -5.12346 q^{35} -8.49536 q^{36} +6.33384 q^{37} -17.3633 q^{38} +1.67455 q^{39} -5.92520 q^{40} +4.39300 q^{41} +1.31432 q^{42} -8.99740 q^{43} +4.14030 q^{44} -8.22723 q^{45} +2.22202 q^{46} +11.9950 q^{47} -0.409372 q^{48} -3.75615 q^{49} -6.87095 q^{50} -0.164609 q^{51} +14.9775 q^{52} +8.71106 q^{53} +4.29975 q^{54} +4.00962 q^{55} +3.75146 q^{56} +2.56628 q^{57} -2.22202 q^{58} +11.5319 q^{59} +2.74420 q^{60} -7.18620 q^{61} +17.3200 q^{62} +5.20895 q^{63} -12.9180 q^{64} +14.5048 q^{65} -1.02858 q^{66} +9.87757 q^{67} -1.47230 q^{68} -0.328413 q^{69} +11.3845 q^{70} -0.384807 q^{71} +6.02407 q^{72} +9.35756 q^{73} -14.0740 q^{74} +1.01552 q^{75} +22.9533 q^{76} -2.53864 q^{77} -3.72090 q^{78} -4.12358 q^{79} -3.54594 q^{80} +8.04094 q^{81} -9.76134 q^{82} -10.6700 q^{83} -1.73745 q^{84} -1.42583 q^{85} +19.9924 q^{86} +0.328413 q^{87} -2.93589 q^{88} +5.51277 q^{89} +18.2811 q^{90} -9.18351 q^{91} -2.93739 q^{92} -2.55988 q^{93} -26.6532 q^{94} +22.2288 q^{95} +2.27774 q^{96} +9.04550 q^{97} +8.34626 q^{98} -4.07653 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 13q + 4q^{2} + 3q^{3} + 12q^{4} + 16q^{5} + q^{7} + 6q^{8} + 14q^{9} + O(q^{10}) \) \( 13q + 4q^{2} + 3q^{3} + 12q^{4} + 16q^{5} + q^{7} + 6q^{8} + 14q^{9} + 10q^{10} + 10q^{11} + 3q^{12} + 7q^{13} - 12q^{14} + 8q^{15} + 2q^{16} + 26q^{17} + 7q^{18} + 25q^{20} + 11q^{21} - 15q^{22} - 13q^{23} + 10q^{24} + 19q^{25} - 15q^{26} + 12q^{27} + 5q^{28} + 13q^{29} + 7q^{30} - 6q^{31} + 16q^{32} + 3q^{33} + 11q^{34} + q^{35} - 22q^{36} + 15q^{37} + 8q^{38} - 4q^{39} + 14q^{40} + 9q^{41} - 34q^{42} + q^{43} + 29q^{44} + 16q^{45} - 4q^{46} + 15q^{47} - 15q^{48} + 4q^{49} + 31q^{50} - 14q^{51} - 8q^{52} + 43q^{53} - 35q^{54} - 3q^{55} - 5q^{56} + 6q^{57} + 4q^{58} - 9q^{59} + 3q^{60} + 20q^{61} + 11q^{62} + 21q^{63} - 16q^{64} - 25q^{65} - q^{66} + q^{67} + 21q^{68} - 3q^{69} - 2q^{70} + 17q^{71} - 59q^{72} + 26q^{73} + 11q^{74} - 43q^{75} + 8q^{76} + 17q^{77} - 10q^{78} + 5q^{79} + 10q^{80} - 3q^{81} - 25q^{82} + 4q^{83} - 78q^{84} + 20q^{85} - 13q^{86} + 3q^{87} - 32q^{88} + 48q^{89} + 17q^{90} - 9q^{91} - 12q^{92} - 8q^{93} - 65q^{94} + 8q^{95} + 8q^{96} + 30q^{97} + 2q^{98} + 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.22202 −1.57121 −0.785604 0.618729i \(-0.787648\pi\)
−0.785604 + 0.618729i \(0.787648\pi\)
\(3\) 0.328413 0.189609 0.0948047 0.995496i \(-0.469777\pi\)
0.0948047 + 0.995496i \(0.469777\pi\)
\(4\) 2.93739 1.46870
\(5\) 2.84468 1.27218 0.636090 0.771615i \(-0.280551\pi\)
0.636090 + 0.771615i \(0.280551\pi\)
\(6\) −0.729742 −0.297916
\(7\) −1.80107 −0.680740 −0.340370 0.940292i \(-0.610552\pi\)
−0.340370 + 0.940292i \(0.610552\pi\)
\(8\) −2.08291 −0.736418
\(9\) −2.89214 −0.964048
\(10\) −6.32095 −1.99886
\(11\) 1.40952 0.424985 0.212493 0.977163i \(-0.431842\pi\)
0.212493 + 0.977163i \(0.431842\pi\)
\(12\) 0.964678 0.278479
\(13\) 5.09892 1.41419 0.707093 0.707120i \(-0.250006\pi\)
0.707093 + 0.707120i \(0.250006\pi\)
\(14\) 4.00202 1.06958
\(15\) 0.934230 0.241217
\(16\) −1.24652 −0.311629
\(17\) −0.501226 −0.121565 −0.0607825 0.998151i \(-0.519360\pi\)
−0.0607825 + 0.998151i \(0.519360\pi\)
\(18\) 6.42642 1.51472
\(19\) 7.81418 1.79270 0.896348 0.443351i \(-0.146210\pi\)
0.896348 + 0.443351i \(0.146210\pi\)
\(20\) 8.35594 1.86844
\(21\) −0.591495 −0.129075
\(22\) −3.13198 −0.667741
\(23\) −1.00000 −0.208514
\(24\) −0.684054 −0.139632
\(25\) 3.09220 0.618441
\(26\) −11.3299 −2.22198
\(27\) −1.93506 −0.372402
\(28\) −5.29044 −0.999800
\(29\) 1.00000 0.185695
\(30\) −2.07588 −0.379003
\(31\) −7.79469 −1.39997 −0.699984 0.714159i \(-0.746809\pi\)
−0.699984 + 0.714159i \(0.746809\pi\)
\(32\) 6.93560 1.22605
\(33\) 0.462904 0.0805813
\(34\) 1.11374 0.191004
\(35\) −5.12346 −0.866024
\(36\) −8.49536 −1.41589
\(37\) 6.33384 1.04128 0.520639 0.853777i \(-0.325694\pi\)
0.520639 + 0.853777i \(0.325694\pi\)
\(38\) −17.3633 −2.81670
\(39\) 1.67455 0.268143
\(40\) −5.92520 −0.936856
\(41\) 4.39300 0.686071 0.343035 0.939322i \(-0.388545\pi\)
0.343035 + 0.939322i \(0.388545\pi\)
\(42\) 1.31432 0.202803
\(43\) −8.99740 −1.37209 −0.686046 0.727559i \(-0.740655\pi\)
−0.686046 + 0.727559i \(0.740655\pi\)
\(44\) 4.14030 0.624174
\(45\) −8.22723 −1.22644
\(46\) 2.22202 0.327620
\(47\) 11.9950 1.74965 0.874826 0.484437i \(-0.160975\pi\)
0.874826 + 0.484437i \(0.160975\pi\)
\(48\) −0.409372 −0.0590878
\(49\) −3.75615 −0.536593
\(50\) −6.87095 −0.971699
\(51\) −0.164609 −0.0230499
\(52\) 14.9775 2.07701
\(53\) 8.71106 1.19656 0.598278 0.801289i \(-0.295852\pi\)
0.598278 + 0.801289i \(0.295852\pi\)
\(54\) 4.29975 0.585121
\(55\) 4.00962 0.540658
\(56\) 3.75146 0.501310
\(57\) 2.56628 0.339912
\(58\) −2.22202 −0.291766
\(59\) 11.5319 1.50133 0.750664 0.660685i \(-0.229734\pi\)
0.750664 + 0.660685i \(0.229734\pi\)
\(60\) 2.74420 0.354275
\(61\) −7.18620 −0.920099 −0.460049 0.887893i \(-0.652168\pi\)
−0.460049 + 0.887893i \(0.652168\pi\)
\(62\) 17.3200 2.19964
\(63\) 5.20895 0.656266
\(64\) −12.9180 −1.61475
\(65\) 14.5048 1.79910
\(66\) −1.02858 −0.126610
\(67\) 9.87757 1.20674 0.603369 0.797462i \(-0.293825\pi\)
0.603369 + 0.797462i \(0.293825\pi\)
\(68\) −1.47230 −0.178542
\(69\) −0.328413 −0.0395363
\(70\) 11.3845 1.36070
\(71\) −0.384807 −0.0456682 −0.0228341 0.999739i \(-0.507269\pi\)
−0.0228341 + 0.999739i \(0.507269\pi\)
\(72\) 6.02407 0.709943
\(73\) 9.35756 1.09522 0.547610 0.836734i \(-0.315538\pi\)
0.547610 + 0.836734i \(0.315538\pi\)
\(74\) −14.0740 −1.63606
\(75\) 1.01552 0.117262
\(76\) 22.9533 2.63293
\(77\) −2.53864 −0.289305
\(78\) −3.72090 −0.421309
\(79\) −4.12358 −0.463939 −0.231969 0.972723i \(-0.574517\pi\)
−0.231969 + 0.972723i \(0.574517\pi\)
\(80\) −3.54594 −0.396448
\(81\) 8.04094 0.893437
\(82\) −9.76134 −1.07796
\(83\) −10.6700 −1.17118 −0.585591 0.810607i \(-0.699137\pi\)
−0.585591 + 0.810607i \(0.699137\pi\)
\(84\) −1.73745 −0.189572
\(85\) −1.42583 −0.154653
\(86\) 19.9924 2.15584
\(87\) 0.328413 0.0352096
\(88\) −2.93589 −0.312967
\(89\) 5.51277 0.584352 0.292176 0.956365i \(-0.405621\pi\)
0.292176 + 0.956365i \(0.405621\pi\)
\(90\) 18.2811 1.92700
\(91\) −9.18351 −0.962694
\(92\) −2.93739 −0.306244
\(93\) −2.55988 −0.265447
\(94\) −26.6532 −2.74907
\(95\) 22.2288 2.28063
\(96\) 2.27774 0.232471
\(97\) 9.04550 0.918431 0.459216 0.888325i \(-0.348131\pi\)
0.459216 + 0.888325i \(0.348131\pi\)
\(98\) 8.34626 0.843099
\(99\) −4.07653 −0.409706
\(100\) 9.08301 0.908301
\(101\) 18.4647 1.83731 0.918654 0.395063i \(-0.129277\pi\)
0.918654 + 0.395063i \(0.129277\pi\)
\(102\) 0.365765 0.0362162
\(103\) 0.820569 0.0808530 0.0404265 0.999183i \(-0.487128\pi\)
0.0404265 + 0.999183i \(0.487128\pi\)
\(104\) −10.6206 −1.04143
\(105\) −1.68261 −0.164206
\(106\) −19.3562 −1.88004
\(107\) −11.0507 −1.06831 −0.534157 0.845385i \(-0.679371\pi\)
−0.534157 + 0.845385i \(0.679371\pi\)
\(108\) −5.68402 −0.546945
\(109\) −12.5958 −1.20646 −0.603230 0.797567i \(-0.706120\pi\)
−0.603230 + 0.797567i \(0.706120\pi\)
\(110\) −8.90948 −0.849486
\(111\) 2.08012 0.197436
\(112\) 2.24506 0.212138
\(113\) 9.91984 0.933180 0.466590 0.884474i \(-0.345482\pi\)
0.466590 + 0.884474i \(0.345482\pi\)
\(114\) −5.70234 −0.534073
\(115\) −2.84468 −0.265268
\(116\) 2.93739 0.272730
\(117\) −14.7468 −1.36334
\(118\) −25.6242 −2.35890
\(119\) 0.902742 0.0827542
\(120\) −1.94591 −0.177637
\(121\) −9.01326 −0.819387
\(122\) 15.9679 1.44567
\(123\) 1.44272 0.130085
\(124\) −22.8960 −2.05613
\(125\) −5.42707 −0.485412
\(126\) −11.5744 −1.03113
\(127\) 8.01333 0.711068 0.355534 0.934663i \(-0.384299\pi\)
0.355534 + 0.934663i \(0.384299\pi\)
\(128\) 14.8330 1.31106
\(129\) −2.95487 −0.260161
\(130\) −32.2300 −2.82676
\(131\) 0.372674 0.0325607 0.0162804 0.999867i \(-0.494818\pi\)
0.0162804 + 0.999867i \(0.494818\pi\)
\(132\) 1.35973 0.118349
\(133\) −14.0739 −1.22036
\(134\) −21.9482 −1.89604
\(135\) −5.50462 −0.473762
\(136\) 1.04401 0.0895227
\(137\) 11.6518 0.995481 0.497740 0.867326i \(-0.334163\pi\)
0.497740 + 0.867326i \(0.334163\pi\)
\(138\) 0.729742 0.0621198
\(139\) −11.6120 −0.984914 −0.492457 0.870337i \(-0.663901\pi\)
−0.492457 + 0.870337i \(0.663901\pi\)
\(140\) −15.0496 −1.27192
\(141\) 3.93932 0.331751
\(142\) 0.855051 0.0717543
\(143\) 7.18702 0.601009
\(144\) 3.60510 0.300425
\(145\) 2.84468 0.236238
\(146\) −20.7927 −1.72082
\(147\) −1.23357 −0.101743
\(148\) 18.6050 1.52932
\(149\) 17.5192 1.43523 0.717613 0.696442i \(-0.245235\pi\)
0.717613 + 0.696442i \(0.245235\pi\)
\(150\) −2.25651 −0.184243
\(151\) −19.4111 −1.57965 −0.789827 0.613330i \(-0.789829\pi\)
−0.789827 + 0.613330i \(0.789829\pi\)
\(152\) −16.2762 −1.32017
\(153\) 1.44962 0.117195
\(154\) 5.64091 0.454558
\(155\) −22.1734 −1.78101
\(156\) 4.91882 0.393821
\(157\) 14.5093 1.15797 0.578984 0.815339i \(-0.303449\pi\)
0.578984 + 0.815339i \(0.303449\pi\)
\(158\) 9.16269 0.728945
\(159\) 2.86083 0.226878
\(160\) 19.7296 1.55976
\(161\) 1.80107 0.141944
\(162\) −17.8672 −1.40378
\(163\) 0.723953 0.0567044 0.0283522 0.999598i \(-0.490974\pi\)
0.0283522 + 0.999598i \(0.490974\pi\)
\(164\) 12.9039 1.00763
\(165\) 1.31681 0.102514
\(166\) 23.7089 1.84017
\(167\) −1.18921 −0.0920239 −0.0460120 0.998941i \(-0.514651\pi\)
−0.0460120 + 0.998941i \(0.514651\pi\)
\(168\) 1.23203 0.0950530
\(169\) 12.9990 0.999924
\(170\) 3.16822 0.242991
\(171\) −22.5997 −1.72825
\(172\) −26.4289 −2.01518
\(173\) −22.6406 −1.72133 −0.860666 0.509171i \(-0.829952\pi\)
−0.860666 + 0.509171i \(0.829952\pi\)
\(174\) −0.729742 −0.0553216
\(175\) −5.56927 −0.420997
\(176\) −1.75698 −0.132438
\(177\) 3.78723 0.284666
\(178\) −12.2495 −0.918139
\(179\) 3.57152 0.266948 0.133474 0.991052i \(-0.457387\pi\)
0.133474 + 0.991052i \(0.457387\pi\)
\(180\) −24.1666 −1.80127
\(181\) 3.21511 0.238978 0.119489 0.992836i \(-0.461874\pi\)
0.119489 + 0.992836i \(0.461874\pi\)
\(182\) 20.4060 1.51259
\(183\) −2.36004 −0.174459
\(184\) 2.08291 0.153554
\(185\) 18.0178 1.32469
\(186\) 5.68811 0.417073
\(187\) −0.706486 −0.0516634
\(188\) 35.2341 2.56971
\(189\) 3.48517 0.253509
\(190\) −49.3930 −3.58335
\(191\) −20.7504 −1.50145 −0.750724 0.660617i \(-0.770295\pi\)
−0.750724 + 0.660617i \(0.770295\pi\)
\(192\) −4.24245 −0.306173
\(193\) −2.47792 −0.178364 −0.0891822 0.996015i \(-0.528425\pi\)
−0.0891822 + 0.996015i \(0.528425\pi\)
\(194\) −20.0993 −1.44305
\(195\) 4.76357 0.341126
\(196\) −11.0333 −0.788092
\(197\) −4.27137 −0.304323 −0.152161 0.988356i \(-0.548623\pi\)
−0.152161 + 0.988356i \(0.548623\pi\)
\(198\) 9.05814 0.643734
\(199\) −20.3914 −1.44551 −0.722754 0.691105i \(-0.757124\pi\)
−0.722754 + 0.691105i \(0.757124\pi\)
\(200\) −6.44077 −0.455431
\(201\) 3.24392 0.228809
\(202\) −41.0290 −2.88679
\(203\) −1.80107 −0.126410
\(204\) −0.483521 −0.0338533
\(205\) 12.4967 0.872805
\(206\) −1.82332 −0.127037
\(207\) 2.89214 0.201018
\(208\) −6.35588 −0.440701
\(209\) 11.0142 0.761870
\(210\) 3.73881 0.258002
\(211\) 2.74660 0.189084 0.0945420 0.995521i \(-0.469861\pi\)
0.0945420 + 0.995521i \(0.469861\pi\)
\(212\) 25.5878 1.75738
\(213\) −0.126376 −0.00865912
\(214\) 24.5550 1.67854
\(215\) −25.5947 −1.74555
\(216\) 4.03054 0.274244
\(217\) 14.0388 0.953014
\(218\) 27.9882 1.89560
\(219\) 3.07315 0.207664
\(220\) 11.7778 0.794062
\(221\) −2.55571 −0.171916
\(222\) −4.62207 −0.310213
\(223\) 3.05964 0.204889 0.102444 0.994739i \(-0.467334\pi\)
0.102444 + 0.994739i \(0.467334\pi\)
\(224\) −12.4915 −0.834623
\(225\) −8.94310 −0.596207
\(226\) −22.0421 −1.46622
\(227\) −27.5136 −1.82614 −0.913071 0.407801i \(-0.866296\pi\)
−0.913071 + 0.407801i \(0.866296\pi\)
\(228\) 7.53817 0.499227
\(229\) −28.8643 −1.90740 −0.953702 0.300753i \(-0.902762\pi\)
−0.953702 + 0.300753i \(0.902762\pi\)
\(230\) 6.32095 0.416791
\(231\) −0.833722 −0.0548549
\(232\) −2.08291 −0.136749
\(233\) −21.1884 −1.38810 −0.694049 0.719928i \(-0.744175\pi\)
−0.694049 + 0.719928i \(0.744175\pi\)
\(234\) 32.7678 2.14210
\(235\) 34.1220 2.22587
\(236\) 33.8737 2.20499
\(237\) −1.35424 −0.0879672
\(238\) −2.00591 −0.130024
\(239\) 19.4543 1.25839 0.629197 0.777246i \(-0.283384\pi\)
0.629197 + 0.777246i \(0.283384\pi\)
\(240\) −1.16453 −0.0751702
\(241\) −6.87026 −0.442552 −0.221276 0.975211i \(-0.571022\pi\)
−0.221276 + 0.975211i \(0.571022\pi\)
\(242\) 20.0277 1.28743
\(243\) 8.44592 0.541806
\(244\) −21.1087 −1.35134
\(245\) −10.6850 −0.682643
\(246\) −3.20575 −0.204391
\(247\) 39.8439 2.53521
\(248\) 16.2356 1.03096
\(249\) −3.50416 −0.222067
\(250\) 12.0591 0.762683
\(251\) −18.4447 −1.16422 −0.582109 0.813111i \(-0.697772\pi\)
−0.582109 + 0.813111i \(0.697772\pi\)
\(252\) 15.3007 0.963855
\(253\) −1.40952 −0.0886156
\(254\) −17.8058 −1.11724
\(255\) −0.468260 −0.0293236
\(256\) −7.12319 −0.445200
\(257\) 5.21225 0.325131 0.162566 0.986698i \(-0.448023\pi\)
0.162566 + 0.986698i \(0.448023\pi\)
\(258\) 6.56578 0.408768
\(259\) −11.4077 −0.708839
\(260\) 42.6063 2.64233
\(261\) −2.89214 −0.179019
\(262\) −0.828092 −0.0511597
\(263\) 13.9972 0.863103 0.431552 0.902088i \(-0.357966\pi\)
0.431552 + 0.902088i \(0.357966\pi\)
\(264\) −0.964186 −0.0593415
\(265\) 24.7802 1.52223
\(266\) 31.2725 1.91744
\(267\) 1.81047 0.110799
\(268\) 29.0143 1.77233
\(269\) −7.68969 −0.468848 −0.234424 0.972134i \(-0.575320\pi\)
−0.234424 + 0.972134i \(0.575320\pi\)
\(270\) 12.2314 0.744379
\(271\) −25.3993 −1.54290 −0.771448 0.636292i \(-0.780467\pi\)
−0.771448 + 0.636292i \(0.780467\pi\)
\(272\) 0.624785 0.0378832
\(273\) −3.01599 −0.182536
\(274\) −25.8906 −1.56411
\(275\) 4.35851 0.262828
\(276\) −0.964678 −0.0580668
\(277\) 13.8691 0.833312 0.416656 0.909064i \(-0.363202\pi\)
0.416656 + 0.909064i \(0.363202\pi\)
\(278\) 25.8021 1.54751
\(279\) 22.5434 1.34964
\(280\) 10.6717 0.637756
\(281\) −6.93041 −0.413433 −0.206717 0.978401i \(-0.566278\pi\)
−0.206717 + 0.978401i \(0.566278\pi\)
\(282\) −8.75327 −0.521250
\(283\) 20.0345 1.19092 0.595462 0.803383i \(-0.296969\pi\)
0.595462 + 0.803383i \(0.296969\pi\)
\(284\) −1.13033 −0.0670727
\(285\) 7.30025 0.432429
\(286\) −15.9697 −0.944310
\(287\) −7.91209 −0.467036
\(288\) −20.0588 −1.18197
\(289\) −16.7488 −0.985222
\(290\) −6.32095 −0.371179
\(291\) 2.97066 0.174143
\(292\) 27.4868 1.60854
\(293\) −5.85153 −0.341850 −0.170925 0.985284i \(-0.554676\pi\)
−0.170925 + 0.985284i \(0.554676\pi\)
\(294\) 2.74102 0.159860
\(295\) 32.8046 1.90996
\(296\) −13.1928 −0.766816
\(297\) −2.72750 −0.158265
\(298\) −38.9280 −2.25504
\(299\) −5.09892 −0.294878
\(300\) 2.98298 0.172222
\(301\) 16.2049 0.934037
\(302\) 43.1319 2.48196
\(303\) 6.06406 0.348371
\(304\) −9.74050 −0.558656
\(305\) −20.4424 −1.17053
\(306\) −3.22108 −0.184137
\(307\) −7.86578 −0.448924 −0.224462 0.974483i \(-0.572062\pi\)
−0.224462 + 0.974483i \(0.572062\pi\)
\(308\) −7.45697 −0.424900
\(309\) 0.269486 0.0153305
\(310\) 49.2698 2.79834
\(311\) −20.2996 −1.15109 −0.575543 0.817772i \(-0.695209\pi\)
−0.575543 + 0.817772i \(0.695209\pi\)
\(312\) −3.48794 −0.197466
\(313\) −24.4505 −1.38203 −0.691013 0.722843i \(-0.742835\pi\)
−0.691013 + 0.722843i \(0.742835\pi\)
\(314\) −32.2400 −1.81941
\(315\) 14.8178 0.834888
\(316\) −12.1126 −0.681385
\(317\) 7.43875 0.417802 0.208901 0.977937i \(-0.433011\pi\)
0.208901 + 0.977937i \(0.433011\pi\)
\(318\) −6.35682 −0.356473
\(319\) 1.40952 0.0789178
\(320\) −36.7477 −2.05426
\(321\) −3.62921 −0.202563
\(322\) −4.00202 −0.223024
\(323\) −3.91667 −0.217929
\(324\) 23.6194 1.31219
\(325\) 15.7669 0.874591
\(326\) −1.60864 −0.0890944
\(327\) −4.13663 −0.228756
\(328\) −9.15020 −0.505235
\(329\) −21.6038 −1.19106
\(330\) −2.92599 −0.161071
\(331\) −6.99061 −0.384239 −0.192119 0.981372i \(-0.561536\pi\)
−0.192119 + 0.981372i \(0.561536\pi\)
\(332\) −31.3419 −1.72011
\(333\) −18.3184 −1.00384
\(334\) 2.64246 0.144589
\(335\) 28.0985 1.53519
\(336\) 0.737307 0.0402234
\(337\) 17.4221 0.949041 0.474520 0.880245i \(-0.342622\pi\)
0.474520 + 0.880245i \(0.342622\pi\)
\(338\) −28.8841 −1.57109
\(339\) 3.25781 0.176940
\(340\) −4.18821 −0.227138
\(341\) −10.9867 −0.594966
\(342\) 50.2172 2.71543
\(343\) 19.3726 1.04602
\(344\) 18.7407 1.01043
\(345\) −0.934230 −0.0502973
\(346\) 50.3079 2.70457
\(347\) −10.8202 −0.580858 −0.290429 0.956897i \(-0.593798\pi\)
−0.290429 + 0.956897i \(0.593798\pi\)
\(348\) 0.964678 0.0517122
\(349\) 24.1066 1.29039 0.645197 0.764016i \(-0.276775\pi\)
0.645197 + 0.764016i \(0.276775\pi\)
\(350\) 12.3751 0.661474
\(351\) −9.86671 −0.526646
\(352\) 9.77584 0.521054
\(353\) 36.3842 1.93653 0.968267 0.249916i \(-0.0804032\pi\)
0.968267 + 0.249916i \(0.0804032\pi\)
\(354\) −8.41532 −0.447269
\(355\) −1.09465 −0.0580982
\(356\) 16.1931 0.858235
\(357\) 0.296472 0.0156910
\(358\) −7.93601 −0.419431
\(359\) −3.15217 −0.166365 −0.0831826 0.996534i \(-0.526508\pi\)
−0.0831826 + 0.996534i \(0.526508\pi\)
\(360\) 17.1365 0.903175
\(361\) 42.0614 2.21376
\(362\) −7.14406 −0.375484
\(363\) −2.96007 −0.155364
\(364\) −26.9756 −1.41390
\(365\) 26.6193 1.39332
\(366\) 5.24407 0.274112
\(367\) −0.0743026 −0.00387856 −0.00193928 0.999998i \(-0.500617\pi\)
−0.00193928 + 0.999998i \(0.500617\pi\)
\(368\) 1.24652 0.0649791
\(369\) −12.7052 −0.661405
\(370\) −40.0359 −2.08137
\(371\) −15.6892 −0.814543
\(372\) −7.51936 −0.389861
\(373\) −23.7526 −1.22986 −0.614931 0.788581i \(-0.710816\pi\)
−0.614931 + 0.788581i \(0.710816\pi\)
\(374\) 1.56983 0.0811739
\(375\) −1.78232 −0.0920387
\(376\) −24.9845 −1.28848
\(377\) 5.09892 0.262608
\(378\) −7.74414 −0.398316
\(379\) 9.28844 0.477115 0.238558 0.971128i \(-0.423325\pi\)
0.238558 + 0.971128i \(0.423325\pi\)
\(380\) 65.2948 3.34955
\(381\) 2.63168 0.134825
\(382\) 46.1079 2.35909
\(383\) 2.87551 0.146932 0.0734659 0.997298i \(-0.476594\pi\)
0.0734659 + 0.997298i \(0.476594\pi\)
\(384\) 4.87135 0.248590
\(385\) −7.22161 −0.368047
\(386\) 5.50599 0.280248
\(387\) 26.0218 1.32276
\(388\) 26.5702 1.34890
\(389\) −10.5562 −0.535219 −0.267610 0.963527i \(-0.586234\pi\)
−0.267610 + 0.963527i \(0.586234\pi\)
\(390\) −10.5848 −0.535980
\(391\) 0.501226 0.0253481
\(392\) 7.82371 0.395157
\(393\) 0.122391 0.00617382
\(394\) 9.49109 0.478154
\(395\) −11.7303 −0.590214
\(396\) −11.9744 −0.601734
\(397\) −39.5081 −1.98286 −0.991428 0.130657i \(-0.958291\pi\)
−0.991428 + 0.130657i \(0.958291\pi\)
\(398\) 45.3102 2.27119
\(399\) −4.62205 −0.231392
\(400\) −3.85448 −0.192724
\(401\) 1.17595 0.0587240 0.0293620 0.999569i \(-0.490652\pi\)
0.0293620 + 0.999569i \(0.490652\pi\)
\(402\) −7.20808 −0.359506
\(403\) −39.7445 −1.97981
\(404\) 54.2381 2.69845
\(405\) 22.8739 1.13661
\(406\) 4.00202 0.198617
\(407\) 8.92766 0.442528
\(408\) 0.342865 0.0169744
\(409\) 15.8860 0.785514 0.392757 0.919642i \(-0.371521\pi\)
0.392757 + 0.919642i \(0.371521\pi\)
\(410\) −27.7679 −1.37136
\(411\) 3.82661 0.188753
\(412\) 2.41033 0.118748
\(413\) −20.7698 −1.02201
\(414\) −6.42642 −0.315841
\(415\) −30.3527 −1.48995
\(416\) 35.3641 1.73387
\(417\) −3.81352 −0.186749
\(418\) −24.4739 −1.19706
\(419\) −4.67871 −0.228570 −0.114285 0.993448i \(-0.536458\pi\)
−0.114285 + 0.993448i \(0.536458\pi\)
\(420\) −4.94249 −0.241169
\(421\) 1.42283 0.0693447 0.0346724 0.999399i \(-0.488961\pi\)
0.0346724 + 0.999399i \(0.488961\pi\)
\(422\) −6.10302 −0.297090
\(423\) −34.6913 −1.68675
\(424\) −18.1443 −0.881166
\(425\) −1.54989 −0.0751808
\(426\) 0.280810 0.0136053
\(427\) 12.9428 0.626348
\(428\) −32.4603 −1.56903
\(429\) 2.36031 0.113957
\(430\) 56.8721 2.74262
\(431\) −21.0267 −1.01282 −0.506409 0.862293i \(-0.669027\pi\)
−0.506409 + 0.862293i \(0.669027\pi\)
\(432\) 2.41208 0.116051
\(433\) −11.1203 −0.534406 −0.267203 0.963640i \(-0.586099\pi\)
−0.267203 + 0.963640i \(0.586099\pi\)
\(434\) −31.1945 −1.49738
\(435\) 0.934230 0.0447929
\(436\) −36.9988 −1.77192
\(437\) −7.81418 −0.373803
\(438\) −6.82860 −0.326283
\(439\) −17.7462 −0.846978 −0.423489 0.905901i \(-0.639195\pi\)
−0.423489 + 0.905901i \(0.639195\pi\)
\(440\) −8.35167 −0.398150
\(441\) 10.8633 0.517302
\(442\) 5.67885 0.270115
\(443\) −21.6709 −1.02962 −0.514808 0.857305i \(-0.672137\pi\)
−0.514808 + 0.857305i \(0.672137\pi\)
\(444\) 6.11012 0.289973
\(445\) 15.6821 0.743401
\(446\) −6.79860 −0.321923
\(447\) 5.75353 0.272132
\(448\) 23.2663 1.09923
\(449\) −18.1103 −0.854679 −0.427339 0.904091i \(-0.640549\pi\)
−0.427339 + 0.904091i \(0.640549\pi\)
\(450\) 19.8718 0.936765
\(451\) 6.19200 0.291570
\(452\) 29.1384 1.37056
\(453\) −6.37486 −0.299517
\(454\) 61.1359 2.86925
\(455\) −26.1241 −1.22472
\(456\) −5.34532 −0.250318
\(457\) −23.0751 −1.07941 −0.539704 0.841855i \(-0.681464\pi\)
−0.539704 + 0.841855i \(0.681464\pi\)
\(458\) 64.1371 2.99693
\(459\) 0.969901 0.0452711
\(460\) −8.35594 −0.389598
\(461\) −4.00828 −0.186684 −0.0933421 0.995634i \(-0.529755\pi\)
−0.0933421 + 0.995634i \(0.529755\pi\)
\(462\) 1.85255 0.0861885
\(463\) 12.0196 0.558597 0.279298 0.960204i \(-0.409898\pi\)
0.279298 + 0.960204i \(0.409898\pi\)
\(464\) −1.24652 −0.0578680
\(465\) −7.28203 −0.337696
\(466\) 47.0811 2.18099
\(467\) 28.1869 1.30433 0.652167 0.758075i \(-0.273860\pi\)
0.652167 + 0.758075i \(0.273860\pi\)
\(468\) −43.3172 −2.00234
\(469\) −17.7902 −0.821474
\(470\) −75.8199 −3.49731
\(471\) 4.76504 0.219562
\(472\) −24.0199 −1.10560
\(473\) −12.6820 −0.583119
\(474\) 3.00915 0.138215
\(475\) 24.1630 1.10868
\(476\) 2.65171 0.121541
\(477\) −25.1936 −1.15354
\(478\) −43.2279 −1.97720
\(479\) −17.7258 −0.809912 −0.404956 0.914336i \(-0.632713\pi\)
−0.404956 + 0.914336i \(0.632713\pi\)
\(480\) 6.47945 0.295745
\(481\) 32.2958 1.47256
\(482\) 15.2659 0.695342
\(483\) 0.591495 0.0269139
\(484\) −26.4755 −1.20343
\(485\) 25.7315 1.16841
\(486\) −18.7670 −0.851291
\(487\) 19.0479 0.863143 0.431571 0.902079i \(-0.357959\pi\)
0.431571 + 0.902079i \(0.357959\pi\)
\(488\) 14.9682 0.677578
\(489\) 0.237756 0.0107517
\(490\) 23.7424 1.07257
\(491\) −12.8644 −0.580563 −0.290281 0.956941i \(-0.593749\pi\)
−0.290281 + 0.956941i \(0.593749\pi\)
\(492\) 4.23783 0.191056
\(493\) −0.501226 −0.0225741
\(494\) −88.5341 −3.98334
\(495\) −11.5964 −0.521220
\(496\) 9.71620 0.436270
\(497\) 0.693064 0.0310882
\(498\) 7.78633 0.348914
\(499\) 5.35211 0.239593 0.119797 0.992798i \(-0.461776\pi\)
0.119797 + 0.992798i \(0.461776\pi\)
\(500\) −15.9414 −0.712922
\(501\) −0.390553 −0.0174486
\(502\) 40.9845 1.82923
\(503\) −6.72802 −0.299987 −0.149994 0.988687i \(-0.547925\pi\)
−0.149994 + 0.988687i \(0.547925\pi\)
\(504\) −10.8498 −0.483287
\(505\) 52.5262 2.33739
\(506\) 3.13198 0.139234
\(507\) 4.26905 0.189595
\(508\) 23.5383 1.04434
\(509\) −3.24589 −0.143871 −0.0719357 0.997409i \(-0.522918\pi\)
−0.0719357 + 0.997409i \(0.522918\pi\)
\(510\) 1.04049 0.0460735
\(511\) −16.8536 −0.745560
\(512\) −13.8381 −0.611562
\(513\) −15.1209 −0.667604
\(514\) −11.5818 −0.510849
\(515\) 2.33426 0.102860
\(516\) −8.67960 −0.382098
\(517\) 16.9072 0.743577
\(518\) 25.3482 1.11373
\(519\) −7.43547 −0.326381
\(520\) −30.2121 −1.32489
\(521\) −1.97409 −0.0864863 −0.0432432 0.999065i \(-0.513769\pi\)
−0.0432432 + 0.999065i \(0.513769\pi\)
\(522\) 6.42642 0.281277
\(523\) −23.5368 −1.02919 −0.514597 0.857432i \(-0.672058\pi\)
−0.514597 + 0.857432i \(0.672058\pi\)
\(524\) 1.09469 0.0478218
\(525\) −1.82902 −0.0798251
\(526\) −31.1021 −1.35611
\(527\) 3.90690 0.170187
\(528\) −0.577017 −0.0251114
\(529\) 1.00000 0.0434783
\(530\) −55.0621 −2.39175
\(531\) −33.3520 −1.44735
\(532\) −41.3405 −1.79234
\(533\) 22.3995 0.970232
\(534\) −4.02290 −0.174088
\(535\) −31.4358 −1.35909
\(536\) −20.5740 −0.888664
\(537\) 1.17294 0.0506159
\(538\) 17.0867 0.736659
\(539\) −5.29436 −0.228044
\(540\) −16.1692 −0.695813
\(541\) 8.64825 0.371817 0.185909 0.982567i \(-0.440477\pi\)
0.185909 + 0.982567i \(0.440477\pi\)
\(542\) 56.4378 2.42421
\(543\) 1.05589 0.0453124
\(544\) −3.47630 −0.149045
\(545\) −35.8310 −1.53483
\(546\) 6.70159 0.286802
\(547\) −9.69255 −0.414423 −0.207212 0.978296i \(-0.566439\pi\)
−0.207212 + 0.978296i \(0.566439\pi\)
\(548\) 34.2259 1.46206
\(549\) 20.7835 0.887020
\(550\) −9.68472 −0.412958
\(551\) 7.81418 0.332895
\(552\) 0.684054 0.0291153
\(553\) 7.42685 0.315822
\(554\) −30.8174 −1.30931
\(555\) 5.91727 0.251174
\(556\) −34.1089 −1.44654
\(557\) 13.3947 0.567551 0.283775 0.958891i \(-0.408413\pi\)
0.283775 + 0.958891i \(0.408413\pi\)
\(558\) −50.0919 −2.12056
\(559\) −45.8771 −1.94039
\(560\) 6.38648 0.269878
\(561\) −0.232019 −0.00979586
\(562\) 15.3995 0.649590
\(563\) −13.4723 −0.567789 −0.283894 0.958856i \(-0.591627\pi\)
−0.283894 + 0.958856i \(0.591627\pi\)
\(564\) 11.5713 0.487241
\(565\) 28.2188 1.18717
\(566\) −44.5170 −1.87119
\(567\) −14.4823 −0.608199
\(568\) 0.801517 0.0336309
\(569\) 24.5456 1.02901 0.514503 0.857489i \(-0.327977\pi\)
0.514503 + 0.857489i \(0.327977\pi\)
\(570\) −16.2213 −0.679436
\(571\) 25.9329 1.08526 0.542630 0.839972i \(-0.317429\pi\)
0.542630 + 0.839972i \(0.317429\pi\)
\(572\) 21.1111 0.882699
\(573\) −6.81471 −0.284689
\(574\) 17.5809 0.733811
\(575\) −3.09220 −0.128954
\(576\) 37.3608 1.55670
\(577\) −19.2044 −0.799491 −0.399745 0.916626i \(-0.630901\pi\)
−0.399745 + 0.916626i \(0.630901\pi\)
\(578\) 37.2162 1.54799
\(579\) −0.813781 −0.0338196
\(580\) 8.35594 0.346961
\(581\) 19.2174 0.797270
\(582\) −6.60088 −0.273615
\(583\) 12.2784 0.508519
\(584\) −19.4909 −0.806540
\(585\) −41.9500 −1.73442
\(586\) 13.0022 0.537118
\(587\) 25.5057 1.05273 0.526367 0.850258i \(-0.323554\pi\)
0.526367 + 0.850258i \(0.323554\pi\)
\(588\) −3.62348 −0.149430
\(589\) −60.9091 −2.50972
\(590\) −72.8926 −3.00094
\(591\) −1.40277 −0.0577024
\(592\) −7.89523 −0.324492
\(593\) 17.1281 0.703368 0.351684 0.936119i \(-0.385609\pi\)
0.351684 + 0.936119i \(0.385609\pi\)
\(594\) 6.06057 0.248668
\(595\) 2.56801 0.105278
\(596\) 51.4607 2.10791
\(597\) −6.69681 −0.274082
\(598\) 11.3299 0.463315
\(599\) 5.44669 0.222546 0.111273 0.993790i \(-0.464507\pi\)
0.111273 + 0.993790i \(0.464507\pi\)
\(600\) −2.11523 −0.0863540
\(601\) −35.1853 −1.43524 −0.717619 0.696436i \(-0.754768\pi\)
−0.717619 + 0.696436i \(0.754768\pi\)
\(602\) −36.0078 −1.46757
\(603\) −28.5674 −1.16335
\(604\) −57.0180 −2.32003
\(605\) −25.6398 −1.04241
\(606\) −13.4745 −0.547363
\(607\) −30.3496 −1.23185 −0.615926 0.787804i \(-0.711218\pi\)
−0.615926 + 0.787804i \(0.711218\pi\)
\(608\) 54.1960 2.19794
\(609\) −0.591495 −0.0239686
\(610\) 45.4236 1.83915
\(611\) 61.1617 2.47434
\(612\) 4.25809 0.172123
\(613\) 18.2357 0.736534 0.368267 0.929720i \(-0.379951\pi\)
0.368267 + 0.929720i \(0.379951\pi\)
\(614\) 17.4780 0.705353
\(615\) 4.10407 0.165492
\(616\) 5.28774 0.213049
\(617\) −11.1167 −0.447542 −0.223771 0.974642i \(-0.571837\pi\)
−0.223771 + 0.974642i \(0.571837\pi\)
\(618\) −0.598803 −0.0240874
\(619\) 23.8373 0.958101 0.479051 0.877787i \(-0.340981\pi\)
0.479051 + 0.877787i \(0.340981\pi\)
\(620\) −65.1319 −2.61576
\(621\) 1.93506 0.0776512
\(622\) 45.1062 1.80859
\(623\) −9.92887 −0.397792
\(624\) −2.08736 −0.0835611
\(625\) −30.8993 −1.23597
\(626\) 54.3297 2.17145
\(627\) 3.61722 0.144458
\(628\) 42.6195 1.70070
\(629\) −3.17468 −0.126583
\(630\) −32.9255 −1.31178
\(631\) 20.4200 0.812907 0.406454 0.913671i \(-0.366765\pi\)
0.406454 + 0.913671i \(0.366765\pi\)
\(632\) 8.58903 0.341653
\(633\) 0.902021 0.0358521
\(634\) −16.5291 −0.656454
\(635\) 22.7953 0.904606
\(636\) 8.40336 0.333215
\(637\) −19.1523 −0.758843
\(638\) −3.13198 −0.123996
\(639\) 1.11292 0.0440264
\(640\) 42.1951 1.66791
\(641\) 29.0930 1.14911 0.574553 0.818468i \(-0.305176\pi\)
0.574553 + 0.818468i \(0.305176\pi\)
\(642\) 8.06418 0.318268
\(643\) −0.376790 −0.0148592 −0.00742958 0.999972i \(-0.502365\pi\)
−0.00742958 + 0.999972i \(0.502365\pi\)
\(644\) 5.29044 0.208473
\(645\) −8.40565 −0.330972
\(646\) 8.70293 0.342412
\(647\) 29.5176 1.16046 0.580228 0.814454i \(-0.302963\pi\)
0.580228 + 0.814454i \(0.302963\pi\)
\(648\) −16.7485 −0.657944
\(649\) 16.2544 0.638042
\(650\) −35.0344 −1.37416
\(651\) 4.61052 0.180700
\(652\) 2.12653 0.0832815
\(653\) −14.7520 −0.577289 −0.288645 0.957436i \(-0.593205\pi\)
−0.288645 + 0.957436i \(0.593205\pi\)
\(654\) 9.19169 0.359424
\(655\) 1.06014 0.0414231
\(656\) −5.47594 −0.213799
\(657\) −27.0634 −1.05584
\(658\) 48.0043 1.87140
\(659\) −20.0983 −0.782920 −0.391460 0.920195i \(-0.628030\pi\)
−0.391460 + 0.920195i \(0.628030\pi\)
\(660\) 3.86800 0.150562
\(661\) 20.8457 0.810803 0.405401 0.914139i \(-0.367132\pi\)
0.405401 + 0.914139i \(0.367132\pi\)
\(662\) 15.5333 0.603719
\(663\) −0.839329 −0.0325968
\(664\) 22.2245 0.862480
\(665\) −40.0357 −1.55252
\(666\) 40.7039 1.57724
\(667\) −1.00000 −0.0387202
\(668\) −3.49318 −0.135155
\(669\) 1.00483 0.0388489
\(670\) −62.4356 −2.41210
\(671\) −10.1291 −0.391029
\(672\) −4.10237 −0.158252
\(673\) 31.2830 1.20587 0.602935 0.797790i \(-0.293998\pi\)
0.602935 + 0.797790i \(0.293998\pi\)
\(674\) −38.7123 −1.49114
\(675\) −5.98359 −0.230309
\(676\) 38.1832 1.46858
\(677\) −6.86906 −0.263999 −0.132000 0.991250i \(-0.542140\pi\)
−0.132000 + 0.991250i \(0.542140\pi\)
\(678\) −7.23892 −0.278009
\(679\) −16.2916 −0.625213
\(680\) 2.96986 0.113889
\(681\) −9.03583 −0.346254
\(682\) 24.4128 0.934815
\(683\) 21.0191 0.804275 0.402137 0.915579i \(-0.368267\pi\)
0.402137 + 0.915579i \(0.368267\pi\)
\(684\) −66.3843 −2.53827
\(685\) 33.1456 1.26643
\(686\) −43.0463 −1.64352
\(687\) −9.47941 −0.361662
\(688\) 11.2154 0.427583
\(689\) 44.4170 1.69215
\(690\) 2.07588 0.0790275
\(691\) −42.9608 −1.63431 −0.817153 0.576421i \(-0.804449\pi\)
−0.817153 + 0.576421i \(0.804449\pi\)
\(692\) −66.5042 −2.52811
\(693\) 7.34211 0.278904
\(694\) 24.0427 0.912649
\(695\) −33.0323 −1.25299
\(696\) −0.684054 −0.0259290
\(697\) −2.20188 −0.0834022
\(698\) −53.5654 −2.02748
\(699\) −6.95855 −0.263197
\(700\) −16.3591 −0.618317
\(701\) 16.1787 0.611062 0.305531 0.952182i \(-0.401166\pi\)
0.305531 + 0.952182i \(0.401166\pi\)
\(702\) 21.9241 0.827471
\(703\) 49.4938 1.86669
\(704\) −18.2082 −0.686247
\(705\) 11.2061 0.422046
\(706\) −80.8465 −3.04270
\(707\) −33.2562 −1.25073
\(708\) 11.1246 0.418087
\(709\) 46.3214 1.73964 0.869818 0.493373i \(-0.164236\pi\)
0.869818 + 0.493373i \(0.164236\pi\)
\(710\) 2.43235 0.0912843
\(711\) 11.9260 0.447260
\(712\) −11.4826 −0.430328
\(713\) 7.79469 0.291913
\(714\) −0.658769 −0.0246538
\(715\) 20.4448 0.764591
\(716\) 10.4910 0.392066
\(717\) 6.38905 0.238603
\(718\) 7.00420 0.261394
\(719\) 41.8530 1.56085 0.780426 0.625248i \(-0.215002\pi\)
0.780426 + 0.625248i \(0.215002\pi\)
\(720\) 10.2554 0.382195
\(721\) −1.47790 −0.0550399
\(722\) −93.4615 −3.47828
\(723\) −2.25628 −0.0839121
\(724\) 9.44405 0.350985
\(725\) 3.09220 0.114842
\(726\) 6.57736 0.244109
\(727\) −8.41082 −0.311940 −0.155970 0.987762i \(-0.549850\pi\)
−0.155970 + 0.987762i \(0.549850\pi\)
\(728\) 19.1284 0.708945
\(729\) −21.3491 −0.790706
\(730\) −59.1486 −2.18919
\(731\) 4.50973 0.166798
\(732\) −6.93237 −0.256228
\(733\) −10.4264 −0.385106 −0.192553 0.981287i \(-0.561677\pi\)
−0.192553 + 0.981287i \(0.561677\pi\)
\(734\) 0.165102 0.00609403
\(735\) −3.50911 −0.129435
\(736\) −6.93560 −0.255650
\(737\) 13.9226 0.512846
\(738\) 28.2312 1.03921
\(739\) 29.2951 1.07764 0.538819 0.842421i \(-0.318871\pi\)
0.538819 + 0.842421i \(0.318871\pi\)
\(740\) 52.9252 1.94557
\(741\) 13.0853 0.480699
\(742\) 34.8618 1.27982
\(743\) 19.0857 0.700186 0.350093 0.936715i \(-0.386150\pi\)
0.350093 + 0.936715i \(0.386150\pi\)
\(744\) 5.33199 0.195480
\(745\) 49.8364 1.82587
\(746\) 52.7788 1.93237
\(747\) 30.8591 1.12908
\(748\) −2.07523 −0.0758778
\(749\) 19.9031 0.727244
\(750\) 3.96036 0.144612
\(751\) 47.7446 1.74222 0.871112 0.491084i \(-0.163399\pi\)
0.871112 + 0.491084i \(0.163399\pi\)
\(752\) −14.9520 −0.545242
\(753\) −6.05747 −0.220747
\(754\) −11.3299 −0.412612
\(755\) −55.2184 −2.00960
\(756\) 10.2373 0.372328
\(757\) 35.8215 1.30196 0.650978 0.759097i \(-0.274359\pi\)
0.650978 + 0.759097i \(0.274359\pi\)
\(758\) −20.6391 −0.749647
\(759\) −0.462904 −0.0168024
\(760\) −46.3006 −1.67950
\(761\) 18.4287 0.668039 0.334019 0.942566i \(-0.391595\pi\)
0.334019 + 0.942566i \(0.391595\pi\)
\(762\) −5.84766 −0.211838
\(763\) 22.6859 0.821285
\(764\) −60.9521 −2.20517
\(765\) 4.12370 0.149093
\(766\) −6.38945 −0.230860
\(767\) 58.8003 2.12316
\(768\) −2.33935 −0.0844141
\(769\) −12.7262 −0.458920 −0.229460 0.973318i \(-0.573696\pi\)
−0.229460 + 0.973318i \(0.573696\pi\)
\(770\) 16.0466 0.578279
\(771\) 1.71177 0.0616480
\(772\) −7.27861 −0.261963
\(773\) −6.64414 −0.238973 −0.119487 0.992836i \(-0.538125\pi\)
−0.119487 + 0.992836i \(0.538125\pi\)
\(774\) −57.8211 −2.07833
\(775\) −24.1028 −0.865796
\(776\) −18.8409 −0.676350
\(777\) −3.74644 −0.134403
\(778\) 23.4561 0.840941
\(779\) 34.3277 1.22992
\(780\) 13.9925 0.501011
\(781\) −0.542392 −0.0194083
\(782\) −1.11374 −0.0398271
\(783\) −1.93506 −0.0691533
\(784\) 4.68210 0.167218
\(785\) 41.2743 1.47314
\(786\) −0.271956 −0.00970036
\(787\) 1.15831 0.0412893 0.0206446 0.999787i \(-0.493428\pi\)
0.0206446 + 0.999787i \(0.493428\pi\)
\(788\) −12.5467 −0.446957
\(789\) 4.59686 0.163653
\(790\) 26.0649 0.927349
\(791\) −17.8663 −0.635253
\(792\) 8.49102 0.301715
\(793\) −36.6419 −1.30119
\(794\) 87.7880 3.11548
\(795\) 8.13813 0.288630
\(796\) −59.8975 −2.12301
\(797\) 26.5128 0.939131 0.469566 0.882898i \(-0.344411\pi\)
0.469566 + 0.882898i \(0.344411\pi\)
\(798\) 10.2703 0.363565
\(799\) −6.01221 −0.212697
\(800\) 21.4463 0.758240
\(801\) −15.9437 −0.563344
\(802\) −2.61298 −0.0922676
\(803\) 13.1896 0.465452
\(804\) 9.52868 0.336050
\(805\) 5.12346 0.180578
\(806\) 88.3133 3.11070
\(807\) −2.52539 −0.0888981
\(808\) −38.4603 −1.35303
\(809\) −2.83108 −0.0995355 −0.0497678 0.998761i \(-0.515848\pi\)
−0.0497678 + 0.998761i \(0.515848\pi\)
\(810\) −50.8263 −1.78586
\(811\) −16.8762 −0.592605 −0.296303 0.955094i \(-0.595754\pi\)
−0.296303 + 0.955094i \(0.595754\pi\)
\(812\) −5.29044 −0.185658
\(813\) −8.34146 −0.292548
\(814\) −19.8375 −0.695303
\(815\) 2.05942 0.0721382
\(816\) 0.205188 0.00718301
\(817\) −70.3073 −2.45974
\(818\) −35.2991 −1.23421
\(819\) 26.5600 0.928083
\(820\) 36.7076 1.28189
\(821\) −43.9573 −1.53412 −0.767060 0.641575i \(-0.778281\pi\)
−0.767060 + 0.641575i \(0.778281\pi\)
\(822\) −8.50281 −0.296570
\(823\) −37.7144 −1.31464 −0.657321 0.753610i \(-0.728311\pi\)
−0.657321 + 0.753610i \(0.728311\pi\)
\(824\) −1.70917 −0.0595417
\(825\) 1.43139 0.0498347
\(826\) 46.1509 1.60580
\(827\) −12.6140 −0.438633 −0.219317 0.975654i \(-0.570383\pi\)
−0.219317 + 0.975654i \(0.570383\pi\)
\(828\) 8.49536 0.295234
\(829\) 37.1288 1.28954 0.644768 0.764378i \(-0.276954\pi\)
0.644768 + 0.764378i \(0.276954\pi\)
\(830\) 67.4443 2.34103
\(831\) 4.55479 0.158004
\(832\) −65.8681 −2.28356
\(833\) 1.88268 0.0652310
\(834\) 8.47374 0.293422
\(835\) −3.38293 −0.117071
\(836\) 32.3531 1.11895
\(837\) 15.0832 0.521351
\(838\) 10.3962 0.359131
\(839\) 8.77668 0.303005 0.151502 0.988457i \(-0.451589\pi\)
0.151502 + 0.988457i \(0.451589\pi\)
\(840\) 3.50473 0.120925
\(841\) 1.00000 0.0344828
\(842\) −3.16157 −0.108955
\(843\) −2.27604 −0.0783909
\(844\) 8.06785 0.277707
\(845\) 36.9780 1.27208
\(846\) 77.0850 2.65024
\(847\) 16.2335 0.557790
\(848\) −10.8585 −0.372881
\(849\) 6.57958 0.225811
\(850\) 3.44390 0.118125
\(851\) −6.33384 −0.217121
\(852\) −0.371215 −0.0127176
\(853\) −10.9924 −0.376374 −0.188187 0.982133i \(-0.560261\pi\)
−0.188187 + 0.982133i \(0.560261\pi\)
\(854\) −28.7593 −0.984123
\(855\) −64.2890 −2.19864
\(856\) 23.0176 0.786726
\(857\) −21.7731 −0.743754 −0.371877 0.928282i \(-0.621286\pi\)
−0.371877 + 0.928282i \(0.621286\pi\)
\(858\) −5.24467 −0.179050
\(859\) 23.3166 0.795552 0.397776 0.917483i \(-0.369782\pi\)
0.397776 + 0.917483i \(0.369782\pi\)
\(860\) −75.1817 −2.56368
\(861\) −2.59843 −0.0885544
\(862\) 46.7217 1.59135
\(863\) −33.2592 −1.13216 −0.566078 0.824351i \(-0.691540\pi\)
−0.566078 + 0.824351i \(0.691540\pi\)
\(864\) −13.4208 −0.456584
\(865\) −64.4052 −2.18984
\(866\) 24.7095 0.839663
\(867\) −5.50052 −0.186807
\(868\) 41.2374 1.39969
\(869\) −5.81226 −0.197167
\(870\) −2.07588 −0.0703790
\(871\) 50.3650 1.70655
\(872\) 26.2359 0.888459
\(873\) −26.1609 −0.885412
\(874\) 17.3633 0.587322
\(875\) 9.77453 0.330439
\(876\) 9.02703 0.304995
\(877\) 11.2534 0.380001 0.190000 0.981784i \(-0.439151\pi\)
0.190000 + 0.981784i \(0.439151\pi\)
\(878\) 39.4324 1.33078
\(879\) −1.92172 −0.0648180
\(880\) −4.99806 −0.168485
\(881\) −14.9883 −0.504969 −0.252484 0.967601i \(-0.581248\pi\)
−0.252484 + 0.967601i \(0.581248\pi\)
\(882\) −24.1386 −0.812788
\(883\) −35.7353 −1.20259 −0.601294 0.799028i \(-0.705348\pi\)
−0.601294 + 0.799028i \(0.705348\pi\)
\(884\) −7.50712 −0.252492
\(885\) 10.7735 0.362146
\(886\) 48.1533 1.61774
\(887\) −13.8883 −0.466322 −0.233161 0.972438i \(-0.574907\pi\)
−0.233161 + 0.972438i \(0.574907\pi\)
\(888\) −4.33269 −0.145396
\(889\) −14.4326 −0.484052
\(890\) −34.8459 −1.16804
\(891\) 11.3338 0.379698
\(892\) 8.98737 0.300919
\(893\) 93.7312 3.13660
\(894\) −12.7845 −0.427577
\(895\) 10.1598 0.339606
\(896\) −26.7152 −0.892494
\(897\) −1.67455 −0.0559117
\(898\) 40.2416 1.34288
\(899\) −7.79469 −0.259967
\(900\) −26.2694 −0.875646
\(901\) −4.36620 −0.145459
\(902\) −13.7588 −0.458117
\(903\) 5.32192 0.177102
\(904\) −20.6621 −0.687211
\(905\) 9.14597 0.304022
\(906\) 14.1651 0.470604
\(907\) −46.1230 −1.53149 −0.765745 0.643145i \(-0.777629\pi\)
−0.765745 + 0.643145i \(0.777629\pi\)
\(908\) −80.8182 −2.68205
\(909\) −53.4026 −1.77125
\(910\) 58.0485 1.92429
\(911\) 44.3915 1.47076 0.735378 0.677657i \(-0.237004\pi\)
0.735378 + 0.677657i \(0.237004\pi\)
\(912\) −3.19891 −0.105926
\(913\) −15.0395 −0.497735
\(914\) 51.2735 1.69598
\(915\) −6.71357 −0.221944
\(916\) −84.7856 −2.80140
\(917\) −0.671212 −0.0221654
\(918\) −2.15514 −0.0711303
\(919\) 34.6558 1.14319 0.571595 0.820536i \(-0.306325\pi\)
0.571595 + 0.820536i \(0.306325\pi\)
\(920\) 5.92520 0.195348
\(921\) −2.58323 −0.0851202
\(922\) 8.90649 0.293320
\(923\) −1.96210 −0.0645834
\(924\) −2.44897 −0.0805651
\(925\) 19.5855 0.643968
\(926\) −26.7078 −0.877671
\(927\) −2.37320 −0.0779462
\(928\) 6.93560 0.227672
\(929\) 15.0404 0.493459 0.246729 0.969084i \(-0.420644\pi\)
0.246729 + 0.969084i \(0.420644\pi\)
\(930\) 16.1809 0.530591
\(931\) −29.3512 −0.961948
\(932\) −62.2386 −2.03869
\(933\) −6.66666 −0.218257
\(934\) −62.6320 −2.04938
\(935\) −2.00973 −0.0657251
\(936\) 30.7162 1.00399
\(937\) 47.2748 1.54440 0.772201 0.635378i \(-0.219156\pi\)
0.772201 + 0.635378i \(0.219156\pi\)
\(938\) 39.5302 1.29071
\(939\) −8.02988 −0.262045
\(940\) 100.230 3.26913
\(941\) 4.38264 0.142870 0.0714351 0.997445i \(-0.477242\pi\)
0.0714351 + 0.997445i \(0.477242\pi\)
\(942\) −10.5880 −0.344977
\(943\) −4.39300 −0.143056
\(944\) −14.3747 −0.467857
\(945\) 9.91420 0.322509
\(946\) 28.1797 0.916201
\(947\) −53.8299 −1.74924 −0.874619 0.484811i \(-0.838888\pi\)
−0.874619 + 0.484811i \(0.838888\pi\)
\(948\) −3.97793 −0.129197
\(949\) 47.7135 1.54884
\(950\) −53.6908 −1.74196
\(951\) 2.44298 0.0792192
\(952\) −1.88033 −0.0609417
\(953\) −31.2581 −1.01255 −0.506275 0.862372i \(-0.668978\pi\)
−0.506275 + 0.862372i \(0.668978\pi\)
\(954\) 55.9809 1.81245
\(955\) −59.0283 −1.91011
\(956\) 57.1449 1.84820
\(957\) 0.462904 0.0149636
\(958\) 39.3871 1.27254
\(959\) −20.9857 −0.677664
\(960\) −12.0684 −0.389507
\(961\) 29.7571 0.959908
\(962\) −71.7620 −2.31370
\(963\) 31.9603 1.02991
\(964\) −20.1806 −0.649974
\(965\) −7.04888 −0.226912
\(966\) −1.31432 −0.0422874
\(967\) 10.1582 0.326665 0.163332 0.986571i \(-0.447776\pi\)
0.163332 + 0.986571i \(0.447776\pi\)
\(968\) 18.7738 0.603412
\(969\) −1.28629 −0.0413214
\(970\) −57.1761 −1.83581
\(971\) −52.2495 −1.67677 −0.838383 0.545082i \(-0.816499\pi\)
−0.838383 + 0.545082i \(0.816499\pi\)
\(972\) 24.8090 0.795749
\(973\) 20.9139 0.670470
\(974\) −42.3249 −1.35618
\(975\) 5.17806 0.165831
\(976\) 8.95771 0.286729
\(977\) 5.14710 0.164670 0.0823352 0.996605i \(-0.473762\pi\)
0.0823352 + 0.996605i \(0.473762\pi\)
\(978\) −0.528299 −0.0168931
\(979\) 7.77034 0.248341
\(980\) −31.3862 −1.00259
\(981\) 36.4289 1.16309
\(982\) 28.5850 0.912185
\(983\) 34.7181 1.10734 0.553668 0.832737i \(-0.313228\pi\)
0.553668 + 0.832737i \(0.313228\pi\)
\(984\) −3.00505 −0.0957974
\(985\) −12.1507 −0.387153
\(986\) 1.11374 0.0354686
\(987\) −7.09499 −0.225836
\(988\) 117.037 3.72345
\(989\) 8.99740 0.286101
\(990\) 25.7675 0.818945
\(991\) −38.1511 −1.21191 −0.605954 0.795499i \(-0.707209\pi\)
−0.605954 + 0.795499i \(0.707209\pi\)
\(992\) −54.0608 −1.71643
\(993\) −2.29581 −0.0728553
\(994\) −1.54001 −0.0488460
\(995\) −58.0070 −1.83895
\(996\) −10.2931 −0.326149
\(997\) −53.7247 −1.70148 −0.850740 0.525588i \(-0.823846\pi\)
−0.850740 + 0.525588i \(0.823846\pi\)
\(998\) −11.8925 −0.376451
\(999\) −12.2564 −0.387774
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 667.2.a.c.1.2 13
3.2 odd 2 6003.2.a.o.1.12 13
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
667.2.a.c.1.2 13 1.1 even 1 trivial
6003.2.a.o.1.12 13 3.2 odd 2