Properties

Label 5290.2.a.p.1.1
Level $5290$
Weight $2$
Character 5290.1
Self dual yes
Analytic conductor $42.241$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5290.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(42.2408626693\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.1509.1
Defining polynomial: \(x^{3} - x^{2} - 7 x + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.92542\) of defining polynomial
Character \(\chi\) \(=\) 5290.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.92542 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.92542 q^{6} -4.55810 q^{7} +1.00000 q^{8} +5.55810 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.92542 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.92542 q^{6} -4.55810 q^{7} +1.00000 q^{8} +5.55810 q^{9} -1.00000 q^{10} +0.925423 q^{11} -2.92542 q^{12} +2.55810 q^{13} -4.55810 q^{14} +2.92542 q^{15} +1.00000 q^{16} -6.92542 q^{17} +5.55810 q^{18} +3.29275 q^{19} -1.00000 q^{20} +13.3344 q^{21} +0.925423 q^{22} -2.92542 q^{24} +1.00000 q^{25} +2.55810 q^{26} -7.48352 q^{27} -4.55810 q^{28} -1.26535 q^{29} +2.92542 q^{30} +10.4089 q^{31} +1.00000 q^{32} -2.70725 q^{33} -6.92542 q^{34} +4.55810 q^{35} +5.55810 q^{36} -9.70169 q^{37} +3.29275 q^{38} -7.48352 q^{39} -1.00000 q^{40} -0.925423 q^{41} +13.3344 q^{42} +1.26535 q^{43} +0.925423 q^{44} -5.55810 q^{45} +10.9670 q^{47} -2.92542 q^{48} +13.7763 q^{49} +1.00000 q^{50} +20.2598 q^{51} +2.55810 q^{52} +3.11620 q^{53} -7.48352 q^{54} -0.925423 q^{55} -4.55810 q^{56} -9.63268 q^{57} -1.26535 q^{58} -7.26535 q^{59} +2.92542 q^{60} +11.8925 q^{61} +10.4089 q^{62} -25.3344 q^{63} +1.00000 q^{64} -2.55810 q^{65} -2.70725 q^{66} +7.85085 q^{67} -6.92542 q^{68} +4.55810 q^{70} -6.92542 q^{71} +5.55810 q^{72} -9.26535 q^{73} -9.70169 q^{74} -2.92542 q^{75} +3.29275 q^{76} -4.21817 q^{77} -7.48352 q^{78} +10.9670 q^{79} -1.00000 q^{80} +5.21817 q^{81} -0.925423 q^{82} -0.585493 q^{83} +13.3344 q^{84} +6.92542 q^{85} +1.26535 q^{86} +3.70169 q^{87} +0.925423 q^{88} -9.11620 q^{89} -5.55810 q^{90} -11.6601 q^{91} -30.4506 q^{93} +10.9670 q^{94} -3.29275 q^{95} -2.92542 q^{96} +3.22373 q^{97} +13.7763 q^{98} +5.14359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} - q^{3} + 3q^{4} - 3q^{5} - q^{6} - 3q^{7} + 3q^{8} + 6q^{9} + O(q^{10}) \) \( 3q + 3q^{2} - q^{3} + 3q^{4} - 3q^{5} - q^{6} - 3q^{7} + 3q^{8} + 6q^{9} - 3q^{10} - 5q^{11} - q^{12} - 3q^{13} - 3q^{14} + q^{15} + 3q^{16} - 13q^{17} + 6q^{18} + 5q^{19} - 3q^{20} + 6q^{21} - 5q^{22} - q^{24} + 3q^{25} - 3q^{26} - 4q^{27} - 3q^{28} + 2q^{29} + q^{30} + 5q^{31} + 3q^{32} - 13q^{33} - 13q^{34} + 3q^{35} + 6q^{36} + 2q^{37} + 5q^{38} - 4q^{39} - 3q^{40} + 5q^{41} + 6q^{42} - 2q^{43} - 5q^{44} - 6q^{45} - 4q^{47} - q^{48} + 18q^{49} + 3q^{50} + 19q^{51} - 3q^{52} - 12q^{53} - 4q^{54} + 5q^{55} - 3q^{56} - 26q^{57} + 2q^{58} - 16q^{59} + q^{60} - 9q^{61} + 5q^{62} - 42q^{63} + 3q^{64} + 3q^{65} - 13q^{66} + 8q^{67} - 13q^{68} + 3q^{70} - 13q^{71} + 6q^{72} - 22q^{73} + 2q^{74} - q^{75} + 5q^{76} - 4q^{78} - 4q^{79} - 3q^{80} + 3q^{81} + 5q^{82} + 8q^{83} + 6q^{84} + 13q^{85} - 2q^{86} - 20q^{87} - 5q^{88} - 6q^{89} - 6q^{90} - 33q^{91} - 36q^{93} - 4q^{94} - 5q^{95} - q^{96} + 33q^{97} + 18q^{98} - 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.92542 −1.68899 −0.844497 0.535561i \(-0.820100\pi\)
−0.844497 + 0.535561i \(0.820100\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −2.92542 −1.19430
\(7\) −4.55810 −1.72280 −0.861400 0.507928i \(-0.830412\pi\)
−0.861400 + 0.507928i \(0.830412\pi\)
\(8\) 1.00000 0.353553
\(9\) 5.55810 1.85270
\(10\) −1.00000 −0.316228
\(11\) 0.925423 0.279026 0.139513 0.990220i \(-0.455446\pi\)
0.139513 + 0.990220i \(0.455446\pi\)
\(12\) −2.92542 −0.844497
\(13\) 2.55810 0.709489 0.354745 0.934963i \(-0.384568\pi\)
0.354745 + 0.934963i \(0.384568\pi\)
\(14\) −4.55810 −1.21820
\(15\) 2.92542 0.755341
\(16\) 1.00000 0.250000
\(17\) −6.92542 −1.67966 −0.839831 0.542848i \(-0.817346\pi\)
−0.839831 + 0.542848i \(0.817346\pi\)
\(18\) 5.55810 1.31006
\(19\) 3.29275 0.755408 0.377704 0.925926i \(-0.376714\pi\)
0.377704 + 0.925926i \(0.376714\pi\)
\(20\) −1.00000 −0.223607
\(21\) 13.3344 2.90980
\(22\) 0.925423 0.197301
\(23\) 0 0
\(24\) −2.92542 −0.597149
\(25\) 1.00000 0.200000
\(26\) 2.55810 0.501685
\(27\) −7.48352 −1.44020
\(28\) −4.55810 −0.861400
\(29\) −1.26535 −0.234970 −0.117485 0.993075i \(-0.537483\pi\)
−0.117485 + 0.993075i \(0.537483\pi\)
\(30\) 2.92542 0.534107
\(31\) 10.4089 1.86950 0.934751 0.355304i \(-0.115623\pi\)
0.934751 + 0.355304i \(0.115623\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.70725 −0.471272
\(34\) −6.92542 −1.18770
\(35\) 4.55810 0.770459
\(36\) 5.55810 0.926350
\(37\) −9.70169 −1.59495 −0.797474 0.603353i \(-0.793831\pi\)
−0.797474 + 0.603353i \(0.793831\pi\)
\(38\) 3.29275 0.534154
\(39\) −7.48352 −1.19832
\(40\) −1.00000 −0.158114
\(41\) −0.925423 −0.144527 −0.0722634 0.997386i \(-0.523022\pi\)
−0.0722634 + 0.997386i \(0.523022\pi\)
\(42\) 13.3344 2.05754
\(43\) 1.26535 0.192964 0.0964822 0.995335i \(-0.469241\pi\)
0.0964822 + 0.995335i \(0.469241\pi\)
\(44\) 0.925423 0.139513
\(45\) −5.55810 −0.828553
\(46\) 0 0
\(47\) 10.9670 1.59971 0.799854 0.600195i \(-0.204910\pi\)
0.799854 + 0.600195i \(0.204910\pi\)
\(48\) −2.92542 −0.422248
\(49\) 13.7763 1.96804
\(50\) 1.00000 0.141421
\(51\) 20.2598 2.83694
\(52\) 2.55810 0.354745
\(53\) 3.11620 0.428043 0.214021 0.976829i \(-0.431344\pi\)
0.214021 + 0.976829i \(0.431344\pi\)
\(54\) −7.48352 −1.01838
\(55\) −0.925423 −0.124784
\(56\) −4.55810 −0.609102
\(57\) −9.63268 −1.27588
\(58\) −1.26535 −0.166149
\(59\) −7.26535 −0.945868 −0.472934 0.881098i \(-0.656805\pi\)
−0.472934 + 0.881098i \(0.656805\pi\)
\(60\) 2.92542 0.377670
\(61\) 11.8925 1.52267 0.761337 0.648356i \(-0.224543\pi\)
0.761337 + 0.648356i \(0.224543\pi\)
\(62\) 10.4089 1.32194
\(63\) −25.3344 −3.19183
\(64\) 1.00000 0.125000
\(65\) −2.55810 −0.317293
\(66\) −2.70725 −0.333240
\(67\) 7.85085 0.959133 0.479567 0.877505i \(-0.340794\pi\)
0.479567 + 0.877505i \(0.340794\pi\)
\(68\) −6.92542 −0.839831
\(69\) 0 0
\(70\) 4.55810 0.544797
\(71\) −6.92542 −0.821896 −0.410948 0.911659i \(-0.634802\pi\)
−0.410948 + 0.911659i \(0.634802\pi\)
\(72\) 5.55810 0.655028
\(73\) −9.26535 −1.08443 −0.542214 0.840241i \(-0.682414\pi\)
−0.542214 + 0.840241i \(0.682414\pi\)
\(74\) −9.70169 −1.12780
\(75\) −2.92542 −0.337799
\(76\) 3.29275 0.377704
\(77\) −4.21817 −0.480705
\(78\) −7.48352 −0.847342
\(79\) 10.9670 1.23389 0.616944 0.787007i \(-0.288370\pi\)
0.616944 + 0.787007i \(0.288370\pi\)
\(80\) −1.00000 −0.111803
\(81\) 5.21817 0.579797
\(82\) −0.925423 −0.102196
\(83\) −0.585493 −0.0642662 −0.0321331 0.999484i \(-0.510230\pi\)
−0.0321331 + 0.999484i \(0.510230\pi\)
\(84\) 13.3344 1.45490
\(85\) 6.92542 0.751168
\(86\) 1.26535 0.136446
\(87\) 3.70169 0.396863
\(88\) 0.925423 0.0986504
\(89\) −9.11620 −0.966315 −0.483158 0.875533i \(-0.660510\pi\)
−0.483158 + 0.875533i \(0.660510\pi\)
\(90\) −5.55810 −0.585875
\(91\) −11.6601 −1.22231
\(92\) 0 0
\(93\) −30.4506 −3.15758
\(94\) 10.9670 1.13116
\(95\) −3.29275 −0.337829
\(96\) −2.92542 −0.298575
\(97\) 3.22373 0.327320 0.163660 0.986517i \(-0.447670\pi\)
0.163660 + 0.986517i \(0.447670\pi\)
\(98\) 13.7763 1.39161
\(99\) 5.14359 0.516950
\(100\) 1.00000 0.100000
\(101\) 9.70169 0.965354 0.482677 0.875798i \(-0.339664\pi\)
0.482677 + 0.875798i \(0.339664\pi\)
\(102\) 20.2598 2.00602
\(103\) 19.7433 1.94537 0.972683 0.232136i \(-0.0745716\pi\)
0.972683 + 0.232136i \(0.0745716\pi\)
\(104\) 2.55810 0.250842
\(105\) −13.3344 −1.30130
\(106\) 3.11620 0.302672
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) −7.48352 −0.720102
\(109\) −15.2927 −1.46478 −0.732390 0.680886i \(-0.761595\pi\)
−0.732390 + 0.680886i \(0.761595\pi\)
\(110\) −0.925423 −0.0882356
\(111\) 28.3816 2.69386
\(112\) −4.55810 −0.430700
\(113\) −7.26535 −0.683467 −0.341733 0.939797i \(-0.611014\pi\)
−0.341733 + 0.939797i \(0.611014\pi\)
\(114\) −9.63268 −0.902183
\(115\) 0 0
\(116\) −1.26535 −0.117485
\(117\) 14.2182 1.31447
\(118\) −7.26535 −0.668830
\(119\) 31.5668 2.89372
\(120\) 2.92542 0.267053
\(121\) −10.1436 −0.922145
\(122\) 11.8925 1.07669
\(123\) 2.70725 0.244105
\(124\) 10.4089 0.934751
\(125\) −1.00000 −0.0894427
\(126\) −25.3344 −2.25696
\(127\) −18.2872 −1.62273 −0.811363 0.584543i \(-0.801274\pi\)
−0.811363 + 0.584543i \(0.801274\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.70169 −0.325916
\(130\) −2.55810 −0.224360
\(131\) −15.7017 −1.37186 −0.685932 0.727666i \(-0.740605\pi\)
−0.685932 + 0.727666i \(0.740605\pi\)
\(132\) −2.70725 −0.235636
\(133\) −15.0087 −1.30142
\(134\) 7.85085 0.678210
\(135\) 7.48352 0.644079
\(136\) −6.92542 −0.593850
\(137\) −2.02739 −0.173212 −0.0866060 0.996243i \(-0.527602\pi\)
−0.0866060 + 0.996243i \(0.527602\pi\)
\(138\) 0 0
\(139\) 6.14915 0.521564 0.260782 0.965398i \(-0.416020\pi\)
0.260782 + 0.965398i \(0.416020\pi\)
\(140\) 4.55810 0.385230
\(141\) −32.0832 −2.70190
\(142\) −6.92542 −0.581169
\(143\) 2.36732 0.197966
\(144\) 5.55810 0.463175
\(145\) 1.26535 0.105082
\(146\) −9.26535 −0.766806
\(147\) −40.3014 −3.32400
\(148\) −9.70169 −0.797474
\(149\) −8.70725 −0.713326 −0.356663 0.934233i \(-0.616086\pi\)
−0.356663 + 0.934233i \(0.616086\pi\)
\(150\) −2.92542 −0.238860
\(151\) 13.0746 1.06399 0.531997 0.846746i \(-0.321442\pi\)
0.531997 + 0.846746i \(0.321442\pi\)
\(152\) 3.29275 0.267077
\(153\) −38.4922 −3.11191
\(154\) −4.21817 −0.339910
\(155\) −10.4089 −0.836067
\(156\) −7.48352 −0.599161
\(157\) 4.14915 0.331139 0.165569 0.986198i \(-0.447054\pi\)
0.165569 + 0.986198i \(0.447054\pi\)
\(158\) 10.9670 0.872491
\(159\) −9.11620 −0.722962
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) 5.21817 0.409978
\(163\) −7.82345 −0.612780 −0.306390 0.951906i \(-0.599121\pi\)
−0.306390 + 0.951906i \(0.599121\pi\)
\(164\) −0.925423 −0.0722634
\(165\) 2.70725 0.210759
\(166\) −0.585493 −0.0454431
\(167\) −6.58549 −0.509601 −0.254800 0.966994i \(-0.582010\pi\)
−0.254800 + 0.966994i \(0.582010\pi\)
\(168\) 13.3344 1.02877
\(169\) −6.45613 −0.496625
\(170\) 6.92542 0.531156
\(171\) 18.3014 1.39954
\(172\) 1.26535 0.0964822
\(173\) −0.925423 −0.0703586 −0.0351793 0.999381i \(-0.511200\pi\)
−0.0351793 + 0.999381i \(0.511200\pi\)
\(174\) 3.70169 0.280625
\(175\) −4.55810 −0.344560
\(176\) 0.925423 0.0697564
\(177\) 21.2542 1.59757
\(178\) −9.11620 −0.683288
\(179\) −2.88380 −0.215545 −0.107773 0.994176i \(-0.534372\pi\)
−0.107773 + 0.994176i \(0.534372\pi\)
\(180\) −5.55810 −0.414276
\(181\) −5.82345 −0.432854 −0.216427 0.976299i \(-0.569440\pi\)
−0.216427 + 0.976299i \(0.569440\pi\)
\(182\) −11.6601 −0.864302
\(183\) −34.7905 −2.57179
\(184\) 0 0
\(185\) 9.70169 0.713283
\(186\) −30.4506 −2.23274
\(187\) −6.40895 −0.468668
\(188\) 10.9670 0.799854
\(189\) 34.1106 2.48118
\(190\) −3.29275 −0.238881
\(191\) −21.1162 −1.52791 −0.763957 0.645267i \(-0.776746\pi\)
−0.763957 + 0.645267i \(0.776746\pi\)
\(192\) −2.92542 −0.211124
\(193\) 3.85085 0.277190 0.138595 0.990349i \(-0.455741\pi\)
0.138595 + 0.990349i \(0.455741\pi\)
\(194\) 3.22373 0.231450
\(195\) 7.48352 0.535906
\(196\) 13.7763 0.984019
\(197\) −14.7763 −1.05277 −0.526383 0.850248i \(-0.676452\pi\)
−0.526383 + 0.850248i \(0.676452\pi\)
\(198\) 5.14359 0.365539
\(199\) −15.7017 −1.11306 −0.556532 0.830826i \(-0.687868\pi\)
−0.556532 + 0.830826i \(0.687868\pi\)
\(200\) 1.00000 0.0707107
\(201\) −22.9670 −1.61997
\(202\) 9.70169 0.682609
\(203\) 5.76760 0.404806
\(204\) 20.2598 1.41847
\(205\) 0.925423 0.0646343
\(206\) 19.7433 1.37558
\(207\) 0 0
\(208\) 2.55810 0.177372
\(209\) 3.04718 0.210778
\(210\) −13.3344 −0.920159
\(211\) −8.81789 −0.607049 −0.303524 0.952824i \(-0.598163\pi\)
−0.303524 + 0.952824i \(0.598163\pi\)
\(212\) 3.11620 0.214021
\(213\) 20.2598 1.38818
\(214\) −6.00000 −0.410152
\(215\) −1.26535 −0.0862963
\(216\) −7.48352 −0.509189
\(217\) −47.4450 −3.22078
\(218\) −15.2927 −1.03576
\(219\) 27.1051 1.83159
\(220\) −0.925423 −0.0623920
\(221\) −17.7159 −1.19170
\(222\) 28.3816 1.90484
\(223\) 12.3816 0.829130 0.414565 0.910020i \(-0.363934\pi\)
0.414565 + 0.910020i \(0.363934\pi\)
\(224\) −4.55810 −0.304551
\(225\) 5.55810 0.370540
\(226\) −7.26535 −0.483284
\(227\) −6.81789 −0.452519 −0.226260 0.974067i \(-0.572650\pi\)
−0.226260 + 0.974067i \(0.572650\pi\)
\(228\) −9.63268 −0.637940
\(229\) −21.7017 −1.43409 −0.717044 0.697028i \(-0.754505\pi\)
−0.717044 + 0.697028i \(0.754505\pi\)
\(230\) 0 0
\(231\) 12.3399 0.811908
\(232\) −1.26535 −0.0830745
\(233\) 7.85085 0.514326 0.257163 0.966368i \(-0.417212\pi\)
0.257163 + 0.966368i \(0.417212\pi\)
\(234\) 14.2182 0.929471
\(235\) −10.9670 −0.715411
\(236\) −7.26535 −0.472934
\(237\) −32.0832 −2.08403
\(238\) 31.5668 2.04617
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 2.92542 0.188835
\(241\) 15.7017 1.01143 0.505717 0.862699i \(-0.331228\pi\)
0.505717 + 0.862699i \(0.331228\pi\)
\(242\) −10.1436 −0.652055
\(243\) 7.18521 0.460932
\(244\) 11.8925 0.761337
\(245\) −13.7763 −0.880134
\(246\) 2.70725 0.172608
\(247\) 8.42317 0.535954
\(248\) 10.4089 0.660969
\(249\) 1.71282 0.108545
\(250\) −1.00000 −0.0632456
\(251\) −0.762041 −0.0480996 −0.0240498 0.999711i \(-0.507656\pi\)
−0.0240498 + 0.999711i \(0.507656\pi\)
\(252\) −25.3344 −1.59592
\(253\) 0 0
\(254\) −18.2872 −1.14744
\(255\) −20.2598 −1.26872
\(256\) 1.00000 0.0625000
\(257\) 6.67986 0.416678 0.208339 0.978057i \(-0.433194\pi\)
0.208339 + 0.978057i \(0.433194\pi\)
\(258\) −3.70169 −0.230457
\(259\) 44.2213 2.74778
\(260\) −2.55810 −0.158647
\(261\) −7.03296 −0.435329
\(262\) −15.7017 −0.970054
\(263\) −16.0416 −0.989169 −0.494584 0.869130i \(-0.664680\pi\)
−0.494584 + 0.869130i \(0.664680\pi\)
\(264\) −2.70725 −0.166620
\(265\) −3.11620 −0.191427
\(266\) −15.0087 −0.920240
\(267\) 26.6687 1.63210
\(268\) 7.85085 0.479567
\(269\) −23.5525 −1.43602 −0.718012 0.696031i \(-0.754948\pi\)
−0.718012 + 0.696031i \(0.754948\pi\)
\(270\) 7.48352 0.455433
\(271\) −8.99444 −0.546373 −0.273187 0.961961i \(-0.588078\pi\)
−0.273187 + 0.961961i \(0.588078\pi\)
\(272\) −6.92542 −0.419915
\(273\) 34.1106 2.06447
\(274\) −2.02739 −0.122479
\(275\) 0.925423 0.0558051
\(276\) 0 0
\(277\) 11.1710 0.671200 0.335600 0.942005i \(-0.391061\pi\)
0.335600 + 0.942005i \(0.391061\pi\)
\(278\) 6.14915 0.368802
\(279\) 57.8539 3.46363
\(280\) 4.55810 0.272399
\(281\) −26.6687 −1.59092 −0.795462 0.606004i \(-0.792772\pi\)
−0.795462 + 0.606004i \(0.792772\pi\)
\(282\) −32.0832 −1.91053
\(283\) 1.26535 0.0752174 0.0376087 0.999293i \(-0.488026\pi\)
0.0376087 + 0.999293i \(0.488026\pi\)
\(284\) −6.92542 −0.410948
\(285\) 9.63268 0.570591
\(286\) 2.36732 0.139983
\(287\) 4.21817 0.248991
\(288\) 5.55810 0.327514
\(289\) 30.9615 1.82126
\(290\) 1.26535 0.0743041
\(291\) −9.43078 −0.552842
\(292\) −9.26535 −0.542214
\(293\) 25.4034 1.48408 0.742041 0.670355i \(-0.233858\pi\)
0.742041 + 0.670355i \(0.233858\pi\)
\(294\) −40.3014 −2.35043
\(295\) 7.26535 0.423005
\(296\) −9.70169 −0.563899
\(297\) −6.92542 −0.401854
\(298\) −8.70725 −0.504398
\(299\) 0 0
\(300\) −2.92542 −0.168899
\(301\) −5.76760 −0.332439
\(302\) 13.0746 0.752357
\(303\) −28.3816 −1.63048
\(304\) 3.29275 0.188852
\(305\) −11.8925 −0.680961
\(306\) −38.4922 −2.20045
\(307\) −20.4780 −1.16874 −0.584369 0.811488i \(-0.698658\pi\)
−0.584369 + 0.811488i \(0.698658\pi\)
\(308\) −4.21817 −0.240353
\(309\) −57.7575 −3.28571
\(310\) −10.4089 −0.591188
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) −7.48352 −0.423671
\(313\) 2.02739 0.114595 0.0572975 0.998357i \(-0.481752\pi\)
0.0572975 + 0.998357i \(0.481752\pi\)
\(314\) 4.14915 0.234150
\(315\) 25.3344 1.42743
\(316\) 10.9670 0.616944
\(317\) 2.25979 0.126923 0.0634613 0.997984i \(-0.479786\pi\)
0.0634613 + 0.997984i \(0.479786\pi\)
\(318\) −9.11620 −0.511211
\(319\) −1.17099 −0.0655626
\(320\) −1.00000 −0.0559017
\(321\) 17.5525 0.979687
\(322\) 0 0
\(323\) −22.8037 −1.26883
\(324\) 5.21817 0.289898
\(325\) 2.55810 0.141898
\(326\) −7.82345 −0.433301
\(327\) 44.7378 2.47400
\(328\) −0.925423 −0.0510979
\(329\) −49.9889 −2.75598
\(330\) 2.70725 0.149029
\(331\) −5.11620 −0.281212 −0.140606 0.990066i \(-0.544905\pi\)
−0.140606 + 0.990066i \(0.544905\pi\)
\(332\) −0.585493 −0.0321331
\(333\) −53.9230 −2.95496
\(334\) −6.58549 −0.360342
\(335\) −7.85085 −0.428938
\(336\) 13.3344 0.727449
\(337\) −0.856408 −0.0466515 −0.0233257 0.999728i \(-0.507425\pi\)
−0.0233257 + 0.999728i \(0.507425\pi\)
\(338\) −6.45613 −0.351167
\(339\) 21.2542 1.15437
\(340\) 6.92542 0.375584
\(341\) 9.63268 0.521639
\(342\) 18.3014 0.989627
\(343\) −30.8869 −1.66774
\(344\) 1.26535 0.0682232
\(345\) 0 0
\(346\) −0.925423 −0.0497510
\(347\) 27.0087 1.44990 0.724951 0.688801i \(-0.241863\pi\)
0.724951 + 0.688801i \(0.241863\pi\)
\(348\) 3.70169 0.198432
\(349\) −21.6469 −1.15873 −0.579366 0.815067i \(-0.696700\pi\)
−0.579366 + 0.815067i \(0.696700\pi\)
\(350\) −4.55810 −0.243641
\(351\) −19.1436 −1.02181
\(352\) 0.925423 0.0493252
\(353\) −21.3486 −1.13627 −0.568136 0.822935i \(-0.692335\pi\)
−0.568136 + 0.822935i \(0.692335\pi\)
\(354\) 21.2542 1.12965
\(355\) 6.92542 0.367563
\(356\) −9.11620 −0.483158
\(357\) −92.3461 −4.88748
\(358\) −2.88380 −0.152414
\(359\) 14.6687 0.774186 0.387093 0.922041i \(-0.373479\pi\)
0.387093 + 0.922041i \(0.373479\pi\)
\(360\) −5.55810 −0.292938
\(361\) −8.15782 −0.429359
\(362\) −5.82345 −0.306074
\(363\) 29.6743 1.55750
\(364\) −11.6601 −0.611154
\(365\) 9.26535 0.484971
\(366\) −34.7905 −1.81853
\(367\) 1.17099 0.0611250 0.0305625 0.999533i \(-0.490270\pi\)
0.0305625 + 0.999533i \(0.490270\pi\)
\(368\) 0 0
\(369\) −5.14359 −0.267765
\(370\) 9.70169 0.504367
\(371\) −14.2039 −0.737432
\(372\) −30.4506 −1.57879
\(373\) 8.88380 0.459986 0.229993 0.973192i \(-0.426130\pi\)
0.229993 + 0.973192i \(0.426130\pi\)
\(374\) −6.40895 −0.331399
\(375\) 2.92542 0.151068
\(376\) 10.9670 0.565582
\(377\) −3.23690 −0.166709
\(378\) 34.1106 1.75446
\(379\) 23.0746 1.18526 0.592631 0.805474i \(-0.298089\pi\)
0.592631 + 0.805474i \(0.298089\pi\)
\(380\) −3.29275 −0.168914
\(381\) 53.4977 2.74077
\(382\) −21.1162 −1.08040
\(383\) 21.9341 1.12078 0.560390 0.828229i \(-0.310651\pi\)
0.560390 + 0.828229i \(0.310651\pi\)
\(384\) −2.92542 −0.149287
\(385\) 4.21817 0.214978
\(386\) 3.85085 0.196003
\(387\) 7.03296 0.357505
\(388\) 3.22373 0.163660
\(389\) 1.74331 0.0883895 0.0441947 0.999023i \(-0.485928\pi\)
0.0441947 + 0.999023i \(0.485928\pi\)
\(390\) 7.48352 0.378943
\(391\) 0 0
\(392\) 13.7763 0.695807
\(393\) 45.9341 2.31707
\(394\) −14.7763 −0.744418
\(395\) −10.9670 −0.551812
\(396\) 5.14359 0.258475
\(397\) −13.0087 −0.652886 −0.326443 0.945217i \(-0.605850\pi\)
−0.326443 + 0.945217i \(0.605850\pi\)
\(398\) −15.7017 −0.787055
\(399\) 43.9067 2.19808
\(400\) 1.00000 0.0500000
\(401\) −37.9889 −1.89707 −0.948537 0.316666i \(-0.897436\pi\)
−0.948537 + 0.316666i \(0.897436\pi\)
\(402\) −22.9670 −1.14549
\(403\) 26.6271 1.32639
\(404\) 9.70169 0.482677
\(405\) −5.21817 −0.259293
\(406\) 5.76760 0.286241
\(407\) −8.97817 −0.445031
\(408\) 20.2598 1.00301
\(409\) 10.2598 0.507314 0.253657 0.967294i \(-0.418367\pi\)
0.253657 + 0.967294i \(0.418367\pi\)
\(410\) 0.925423 0.0457034
\(411\) 5.93098 0.292554
\(412\) 19.7433 0.972683
\(413\) 33.1162 1.62954
\(414\) 0 0
\(415\) 0.585493 0.0287407
\(416\) 2.55810 0.125421
\(417\) −17.9889 −0.880919
\(418\) 3.04718 0.149043
\(419\) −16.9670 −0.828894 −0.414447 0.910073i \(-0.636025\pi\)
−0.414447 + 0.910073i \(0.636025\pi\)
\(420\) −13.3344 −0.650651
\(421\) −16.4637 −0.802393 −0.401197 0.915992i \(-0.631406\pi\)
−0.401197 + 0.915992i \(0.631406\pi\)
\(422\) −8.81789 −0.429248
\(423\) 60.9559 2.96378
\(424\) 3.11620 0.151336
\(425\) −6.92542 −0.335932
\(426\) 20.2598 0.981590
\(427\) −54.2070 −2.62326
\(428\) −6.00000 −0.290021
\(429\) −6.92542 −0.334363
\(430\) −1.26535 −0.0610207
\(431\) −8.29831 −0.399715 −0.199858 0.979825i \(-0.564048\pi\)
−0.199858 + 0.979825i \(0.564048\pi\)
\(432\) −7.48352 −0.360051
\(433\) −20.2598 −0.973623 −0.486812 0.873507i \(-0.661840\pi\)
−0.486812 + 0.873507i \(0.661840\pi\)
\(434\) −47.4450 −2.27743
\(435\) −3.70169 −0.177483
\(436\) −15.2927 −0.732390
\(437\) 0 0
\(438\) 27.1051 1.29513
\(439\) −25.7575 −1.22934 −0.614670 0.788784i \(-0.710711\pi\)
−0.614670 + 0.788784i \(0.710711\pi\)
\(440\) −0.925423 −0.0441178
\(441\) 76.5699 3.64618
\(442\) −17.7159 −0.842660
\(443\) −22.1106 −1.05051 −0.525254 0.850945i \(-0.676030\pi\)
−0.525254 + 0.850945i \(0.676030\pi\)
\(444\) 28.3816 1.34693
\(445\) 9.11620 0.432149
\(446\) 12.3816 0.586283
\(447\) 25.4724 1.20480
\(448\) −4.55810 −0.215350
\(449\) 15.0777 0.711560 0.355780 0.934570i \(-0.384215\pi\)
0.355780 + 0.934570i \(0.384215\pi\)
\(450\) 5.55810 0.262011
\(451\) −0.856408 −0.0403267
\(452\) −7.26535 −0.341733
\(453\) −38.2487 −1.79708
\(454\) −6.81789 −0.319979
\(455\) 11.6601 0.546633
\(456\) −9.63268 −0.451091
\(457\) −22.9670 −1.07435 −0.537177 0.843470i \(-0.680509\pi\)
−0.537177 + 0.843470i \(0.680509\pi\)
\(458\) −21.7017 −1.01405
\(459\) 51.8266 2.41906
\(460\) 0 0
\(461\) 27.1162 1.26293 0.631464 0.775405i \(-0.282455\pi\)
0.631464 + 0.775405i \(0.282455\pi\)
\(462\) 12.3399 0.574105
\(463\) 23.3486 1.08510 0.542551 0.840023i \(-0.317459\pi\)
0.542551 + 0.840023i \(0.317459\pi\)
\(464\) −1.26535 −0.0587425
\(465\) 30.4506 1.41211
\(466\) 7.85085 0.363683
\(467\) −0.585493 −0.0270934 −0.0135467 0.999908i \(-0.504312\pi\)
−0.0135467 + 0.999908i \(0.504312\pi\)
\(468\) 14.2182 0.657235
\(469\) −35.7849 −1.65239
\(470\) −10.9670 −0.505872
\(471\) −12.1380 −0.559291
\(472\) −7.26535 −0.334415
\(473\) 1.17099 0.0538420
\(474\) −32.0832 −1.47363
\(475\) 3.29275 0.151082
\(476\) 31.5668 1.44686
\(477\) 17.3201 0.793035
\(478\) 12.0000 0.548867
\(479\) 36.8179 1.68225 0.841126 0.540839i \(-0.181893\pi\)
0.841126 + 0.540839i \(0.181893\pi\)
\(480\) 2.92542 0.133527
\(481\) −24.8179 −1.13160
\(482\) 15.7017 0.715192
\(483\) 0 0
\(484\) −10.1436 −0.461072
\(485\) −3.22373 −0.146382
\(486\) 7.18521 0.325928
\(487\) −13.1162 −0.594352 −0.297176 0.954823i \(-0.596045\pi\)
−0.297176 + 0.954823i \(0.596045\pi\)
\(488\) 11.8925 0.538347
\(489\) 22.8869 1.03498
\(490\) −13.7763 −0.622348
\(491\) −21.1162 −0.952961 −0.476480 0.879185i \(-0.658088\pi\)
−0.476480 + 0.879185i \(0.658088\pi\)
\(492\) 2.70725 0.122052
\(493\) 8.76310 0.394670
\(494\) 8.42317 0.378976
\(495\) −5.14359 −0.231187
\(496\) 10.4089 0.467375
\(497\) 31.5668 1.41596
\(498\) 1.71282 0.0767531
\(499\) −4.43634 −0.198598 −0.0992989 0.995058i \(-0.531660\pi\)
−0.0992989 + 0.995058i \(0.531660\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 19.2654 0.860712
\(502\) −0.762041 −0.0340116
\(503\) −30.1939 −1.34628 −0.673139 0.739516i \(-0.735055\pi\)
−0.673139 + 0.739516i \(0.735055\pi\)
\(504\) −25.3344 −1.12848
\(505\) −9.70169 −0.431720
\(506\) 0 0
\(507\) 18.8869 0.838797
\(508\) −18.2872 −0.811363
\(509\) 21.0218 0.931776 0.465888 0.884844i \(-0.345735\pi\)
0.465888 + 0.884844i \(0.345735\pi\)
\(510\) −20.2598 −0.897119
\(511\) 42.2324 1.86825
\(512\) 1.00000 0.0441942
\(513\) −24.6413 −1.08794
\(514\) 6.67986 0.294636
\(515\) −19.7433 −0.869994
\(516\) −3.70169 −0.162958
\(517\) 10.1492 0.446359
\(518\) 44.2213 1.94297
\(519\) 2.70725 0.118835
\(520\) −2.55810 −0.112180
\(521\) 18.3704 0.804823 0.402412 0.915459i \(-0.368172\pi\)
0.402412 + 0.915459i \(0.368172\pi\)
\(522\) −7.03296 −0.307824
\(523\) 3.11620 0.136262 0.0681309 0.997676i \(-0.478296\pi\)
0.0681309 + 0.997676i \(0.478296\pi\)
\(524\) −15.7017 −0.685932
\(525\) 13.3344 0.581960
\(526\) −16.0416 −0.699448
\(527\) −72.0863 −3.14013
\(528\) −2.70725 −0.117818
\(529\) 0 0
\(530\) −3.11620 −0.135359
\(531\) −40.3816 −1.75241
\(532\) −15.0087 −0.650708
\(533\) −2.36732 −0.102540
\(534\) 26.6687 1.15407
\(535\) 6.00000 0.259403
\(536\) 7.85085 0.339105
\(537\) 8.43634 0.364055
\(538\) −23.5525 −1.01542
\(539\) 12.7489 0.549133
\(540\) 7.48352 0.322040
\(541\) 24.9670 1.07342 0.536709 0.843768i \(-0.319667\pi\)
0.536709 + 0.843768i \(0.319667\pi\)
\(542\) −8.99444 −0.386344
\(543\) 17.0361 0.731087
\(544\) −6.92542 −0.296925
\(545\) 15.2927 0.655069
\(546\) 34.1106 1.45980
\(547\) −4.47486 −0.191331 −0.0956655 0.995414i \(-0.530498\pi\)
−0.0956655 + 0.995414i \(0.530498\pi\)
\(548\) −2.02739 −0.0866060
\(549\) 66.0995 2.82106
\(550\) 0.925423 0.0394602
\(551\) −4.16649 −0.177498
\(552\) 0 0
\(553\) −49.9889 −2.12574
\(554\) 11.1710 0.474610
\(555\) −28.3816 −1.20473
\(556\) 6.14915 0.260782
\(557\) −34.8727 −1.47760 −0.738801 0.673923i \(-0.764608\pi\)
−0.738801 + 0.673923i \(0.764608\pi\)
\(558\) 57.8539 2.44915
\(559\) 3.23690 0.136906
\(560\) 4.55810 0.192615
\(561\) 18.7489 0.791578
\(562\) −26.6687 −1.12495
\(563\) 41.1051 1.73237 0.866186 0.499721i \(-0.166564\pi\)
0.866186 + 0.499721i \(0.166564\pi\)
\(564\) −32.0832 −1.35095
\(565\) 7.26535 0.305656
\(566\) 1.26535 0.0531867
\(567\) −23.7849 −0.998873
\(568\) −6.92542 −0.290584
\(569\) 12.6799 0.531567 0.265784 0.964033i \(-0.414369\pi\)
0.265784 + 0.964033i \(0.414369\pi\)
\(570\) 9.63268 0.403468
\(571\) 2.09641 0.0877320 0.0438660 0.999037i \(-0.486033\pi\)
0.0438660 + 0.999037i \(0.486033\pi\)
\(572\) 2.36732 0.0989828
\(573\) 61.7738 2.58064
\(574\) 4.21817 0.176063
\(575\) 0 0
\(576\) 5.55810 0.231587
\(577\) −10.8179 −0.450355 −0.225177 0.974318i \(-0.572296\pi\)
−0.225177 + 0.974318i \(0.572296\pi\)
\(578\) 30.9615 1.28783
\(579\) −11.2654 −0.468172
\(580\) 1.26535 0.0525409
\(581\) 2.66874 0.110718
\(582\) −9.43078 −0.390918
\(583\) 2.88380 0.119435
\(584\) −9.26535 −0.383403
\(585\) −14.2182 −0.587849
\(586\) 25.4034 1.04940
\(587\) 23.3070 0.961982 0.480991 0.876726i \(-0.340277\pi\)
0.480991 + 0.876726i \(0.340277\pi\)
\(588\) −40.3014 −1.66200
\(589\) 34.2740 1.41224
\(590\) 7.26535 0.299110
\(591\) 43.2268 1.77811
\(592\) −9.70169 −0.398737
\(593\) 20.5307 0.843095 0.421548 0.906806i \(-0.361487\pi\)
0.421548 + 0.906806i \(0.361487\pi\)
\(594\) −6.92542 −0.284154
\(595\) −31.5668 −1.29411
\(596\) −8.70725 −0.356663
\(597\) 45.9341 1.87996
\(598\) 0 0
\(599\) −1.37289 −0.0560946 −0.0280473 0.999607i \(-0.508929\pi\)
−0.0280473 + 0.999607i \(0.508929\pi\)
\(600\) −2.92542 −0.119430
\(601\) −23.6743 −0.965695 −0.482847 0.875705i \(-0.660397\pi\)
−0.482847 + 0.875705i \(0.660397\pi\)
\(602\) −5.76760 −0.235070
\(603\) 43.6358 1.77699
\(604\) 13.0746 0.531997
\(605\) 10.1436 0.412396
\(606\) −28.3816 −1.15292
\(607\) −21.4145 −0.869188 −0.434594 0.900626i \(-0.643108\pi\)
−0.434594 + 0.900626i \(0.643108\pi\)
\(608\) 3.29275 0.133539
\(609\) −16.8727 −0.683715
\(610\) −11.8925 −0.481512
\(611\) 28.0548 1.13498
\(612\) −38.4922 −1.55595
\(613\) 1.26535 0.0511071 0.0255536 0.999673i \(-0.491865\pi\)
0.0255536 + 0.999673i \(0.491865\pi\)
\(614\) −20.4780 −0.826423
\(615\) −2.70725 −0.109167
\(616\) −4.21817 −0.169955
\(617\) −9.45613 −0.380689 −0.190345 0.981717i \(-0.560961\pi\)
−0.190345 + 0.981717i \(0.560961\pi\)
\(618\) −57.7575 −2.32335
\(619\) 17.0056 0.683511 0.341756 0.939789i \(-0.388978\pi\)
0.341756 + 0.939789i \(0.388978\pi\)
\(620\) −10.4089 −0.418033
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) 41.5525 1.66477
\(624\) −7.48352 −0.299581
\(625\) 1.00000 0.0400000
\(626\) 2.02739 0.0810310
\(627\) −8.91430 −0.356003
\(628\) 4.14915 0.165569
\(629\) 67.1883 2.67897
\(630\) 25.3344 1.00935
\(631\) −4.38155 −0.174427 −0.0872134 0.996190i \(-0.527796\pi\)
−0.0872134 + 0.996190i \(0.527796\pi\)
\(632\) 10.9670 0.436246
\(633\) 25.7961 1.02530
\(634\) 2.25979 0.0897478
\(635\) 18.2872 0.725705
\(636\) −9.11620 −0.361481
\(637\) 35.2411 1.39630
\(638\) −1.17099 −0.0463598
\(639\) −38.4922 −1.52273
\(640\) −1.00000 −0.0395285
\(641\) 34.6139 1.36717 0.683584 0.729871i \(-0.260420\pi\)
0.683584 + 0.729871i \(0.260420\pi\)
\(642\) 17.5525 0.692743
\(643\) 32.3156 1.27440 0.637202 0.770697i \(-0.280092\pi\)
0.637202 + 0.770697i \(0.280092\pi\)
\(644\) 0 0
\(645\) 3.70169 0.145754
\(646\) −22.8037 −0.897198
\(647\) −26.3156 −1.03457 −0.517287 0.855812i \(-0.673058\pi\)
−0.517287 + 0.855812i \(0.673058\pi\)
\(648\) 5.21817 0.204989
\(649\) −6.72352 −0.263921
\(650\) 2.55810 0.100337
\(651\) 138.797 5.43987
\(652\) −7.82345 −0.306390
\(653\) 20.0274 0.783732 0.391866 0.920022i \(-0.371830\pi\)
0.391866 + 0.920022i \(0.371830\pi\)
\(654\) 44.7378 1.74938
\(655\) 15.7017 0.613516
\(656\) −0.925423 −0.0361317
\(657\) −51.4977 −2.00912
\(658\) −49.9889 −1.94877
\(659\) −22.0285 −0.858107 −0.429053 0.903279i \(-0.641153\pi\)
−0.429053 + 0.903279i \(0.641153\pi\)
\(660\) 2.70725 0.105380
\(661\) 3.12936 0.121718 0.0608591 0.998146i \(-0.480616\pi\)
0.0608591 + 0.998146i \(0.480616\pi\)
\(662\) −5.11620 −0.198847
\(663\) 51.8266 2.01278
\(664\) −0.585493 −0.0227215
\(665\) 15.0087 0.582011
\(666\) −53.9230 −2.08947
\(667\) 0 0
\(668\) −6.58549 −0.254800
\(669\) −36.2213 −1.40040
\(670\) −7.85085 −0.303305
\(671\) 11.0056 0.424865
\(672\) 13.3344 0.514384
\(673\) −41.4866 −1.59919 −0.799596 0.600538i \(-0.794953\pi\)
−0.799596 + 0.600538i \(0.794953\pi\)
\(674\) −0.856408 −0.0329876
\(675\) −7.48352 −0.288041
\(676\) −6.45613 −0.248313
\(677\) 38.9011 1.49509 0.747546 0.664210i \(-0.231232\pi\)
0.747546 + 0.664210i \(0.231232\pi\)
\(678\) 21.2542 0.816264
\(679\) −14.6941 −0.563907
\(680\) 6.92542 0.265578
\(681\) 19.9452 0.764302
\(682\) 9.63268 0.368854
\(683\) 27.8782 1.06673 0.533366 0.845885i \(-0.320927\pi\)
0.533366 + 0.845885i \(0.320927\pi\)
\(684\) 18.3014 0.699772
\(685\) 2.02739 0.0774627
\(686\) −30.8869 −1.17927
\(687\) 63.4866 2.42217
\(688\) 1.26535 0.0482411
\(689\) 7.97155 0.303692
\(690\) 0 0
\(691\) −30.7520 −1.16986 −0.584930 0.811084i \(-0.698878\pi\)
−0.584930 + 0.811084i \(0.698878\pi\)
\(692\) −0.925423 −0.0351793
\(693\) −23.4450 −0.890602
\(694\) 27.0087 1.02523
\(695\) −6.14915 −0.233251
\(696\) 3.70169 0.140312
\(697\) 6.40895 0.242756
\(698\) −21.6469 −0.819347
\(699\) −22.9670 −0.868693
\(700\) −4.55810 −0.172280
\(701\) −6.17655 −0.233285 −0.116643 0.993174i \(-0.537213\pi\)
−0.116643 + 0.993174i \(0.537213\pi\)
\(702\) −19.1436 −0.722528
\(703\) −31.9452 −1.20484
\(704\) 0.925423 0.0348782
\(705\) 32.0832 1.20832
\(706\) −21.3486 −0.803465
\(707\) −44.2213 −1.66311
\(708\) 21.2542 0.798783
\(709\) −40.9539 −1.53806 −0.769028 0.639216i \(-0.779259\pi\)
−0.769028 + 0.639216i \(0.779259\pi\)
\(710\) 6.92542 0.259906
\(711\) 60.9559 2.28603
\(712\) −9.11620 −0.341644
\(713\) 0 0
\(714\) −92.3461 −3.45597
\(715\) −2.36732 −0.0885329
\(716\) −2.88380 −0.107773
\(717\) −35.1051 −1.31102
\(718\) 14.6687 0.547432
\(719\) 7.22684 0.269515 0.134758 0.990879i \(-0.456974\pi\)
0.134758 + 0.990879i \(0.456974\pi\)
\(720\) −5.55810 −0.207138
\(721\) −89.9920 −3.35148
\(722\) −8.15782 −0.303603
\(723\) −45.9341 −1.70831
\(724\) −5.82345 −0.216427
\(725\) −1.26535 −0.0469940
\(726\) 29.6743 1.10132
\(727\) −28.7215 −1.06522 −0.532610 0.846361i \(-0.678789\pi\)
−0.532610 + 0.846361i \(0.678789\pi\)
\(728\) −11.6601 −0.432151
\(729\) −36.6743 −1.35831
\(730\) 9.26535 0.342926
\(731\) −8.76310 −0.324115
\(732\) −34.7905 −1.28589
\(733\) 10.5196 0.388550 0.194275 0.980947i \(-0.437765\pi\)
0.194275 + 0.980947i \(0.437765\pi\)
\(734\) 1.17099 0.0432219
\(735\) 40.3014 1.48654
\(736\) 0 0
\(737\) 7.26535 0.267623
\(738\) −5.14359 −0.189338
\(739\) 15.6184 0.574534 0.287267 0.957851i \(-0.407253\pi\)
0.287267 + 0.957851i \(0.407253\pi\)
\(740\) 9.70169 0.356641
\(741\) −24.6413 −0.905222
\(742\) −14.2039 −0.521443
\(743\) −3.38711 −0.124261 −0.0621306 0.998068i \(-0.519790\pi\)
−0.0621306 + 0.998068i \(0.519790\pi\)
\(744\) −30.4506 −1.11637
\(745\) 8.70725 0.319009
\(746\) 8.88380 0.325259
\(747\) −3.25423 −0.119066
\(748\) −6.40895 −0.234334
\(749\) 27.3486 0.999296
\(750\) 2.92542 0.106821
\(751\) −5.41451 −0.197578 −0.0987891 0.995108i \(-0.531497\pi\)
−0.0987891 + 0.995108i \(0.531497\pi\)
\(752\) 10.9670 0.399927
\(753\) 2.22929 0.0812400
\(754\) −3.23690 −0.117881
\(755\) −13.0746 −0.475833
\(756\) 34.1106 1.24059
\(757\) −3.11620 −0.113260 −0.0566301 0.998395i \(-0.518036\pi\)
−0.0566301 + 0.998395i \(0.518036\pi\)
\(758\) 23.0746 0.838106
\(759\) 0 0
\(760\) −3.29275 −0.119440
\(761\) 5.96148 0.216104 0.108052 0.994145i \(-0.465539\pi\)
0.108052 + 0.994145i \(0.465539\pi\)
\(762\) 53.4977 1.93802
\(763\) 69.7059 2.52352
\(764\) −21.1162 −0.763957
\(765\) 38.4922 1.39169
\(766\) 21.9341 0.792511
\(767\) −18.5855 −0.671083
\(768\) −2.92542 −0.105562
\(769\) −15.7017 −0.566217 −0.283109 0.959088i \(-0.591366\pi\)
−0.283109 + 0.959088i \(0.591366\pi\)
\(770\) 4.21817 0.152012
\(771\) −19.5414 −0.703767
\(772\) 3.85085 0.138595
\(773\) −29.7849 −1.07129 −0.535645 0.844443i \(-0.679931\pi\)
−0.535645 + 0.844443i \(0.679931\pi\)
\(774\) 7.03296 0.252794
\(775\) 10.4089 0.373900
\(776\) 3.22373 0.115725
\(777\) −129.366 −4.64098
\(778\) 1.74331 0.0625008
\(779\) −3.04718 −0.109177
\(780\) 7.48352 0.267953
\(781\) −6.40895 −0.229330
\(782\) 0 0
\(783\) 9.46929 0.338405
\(784\) 13.7763 0.492010
\(785\) −4.14915 −0.148090
\(786\) 45.9341 1.63841
\(787\) −20.3156 −0.724174 −0.362087 0.932144i \(-0.617936\pi\)
−0.362087 + 0.932144i \(0.617936\pi\)
\(788\) −14.7763 −0.526383
\(789\) 46.9285 1.67070
\(790\) −10.9670 −0.390190
\(791\) 33.1162 1.17748
\(792\) 5.14359 0.182770
\(793\) 30.4221 1.08032
\(794\) −13.0087 −0.461660
\(795\) 9.11620 0.323318
\(796\) −15.7017 −0.556532
\(797\) −36.5855 −1.29592 −0.647962 0.761672i \(-0.724379\pi\)
−0.647962 + 0.761672i \(0.724379\pi\)
\(798\) 43.9067 1.55428
\(799\) −75.9514 −2.68697
\(800\) 1.00000 0.0353553
\(801\) −50.6687 −1.79029
\(802\) −37.9889 −1.34143
\(803\) −8.57437 −0.302583
\(804\) −22.9670 −0.809985
\(805\) 0 0
\(806\) 26.6271 0.937900
\(807\) 68.9011 2.42543
\(808\) 9.70169 0.341304
\(809\) −33.0087 −1.16052 −0.580261 0.814430i \(-0.697050\pi\)
−0.580261 + 0.814430i \(0.697050\pi\)
\(810\) −5.21817 −0.183348
\(811\) 25.6073 0.899195 0.449597 0.893231i \(-0.351567\pi\)
0.449597 + 0.893231i \(0.351567\pi\)
\(812\) 5.76760 0.202403
\(813\) 26.3125 0.922821
\(814\) −8.97817 −0.314685
\(815\) 7.82345 0.274044
\(816\) 20.2598 0.709235
\(817\) 4.16649 0.145767
\(818\) 10.2598 0.358725
\(819\) −64.8078 −2.26457
\(820\) 0.925423 0.0323172
\(821\) −5.78493 −0.201896 −0.100948 0.994892i \(-0.532188\pi\)
−0.100948 + 0.994892i \(0.532188\pi\)
\(822\) 5.93098 0.206867
\(823\) −28.9011 −1.00743 −0.503715 0.863870i \(-0.668034\pi\)
−0.503715 + 0.863870i \(0.668034\pi\)
\(824\) 19.7433 0.687791
\(825\) −2.70725 −0.0942545
\(826\) 33.1162 1.15226
\(827\) −7.98888 −0.277800 −0.138900 0.990306i \(-0.544357\pi\)
−0.138900 + 0.990306i \(0.544357\pi\)
\(828\) 0 0
\(829\) −6.76310 −0.234892 −0.117446 0.993079i \(-0.537471\pi\)
−0.117446 + 0.993079i \(0.537471\pi\)
\(830\) 0.585493 0.0203228
\(831\) −32.6799 −1.13365
\(832\) 2.55810 0.0886861
\(833\) −95.4065 −3.30564
\(834\) −17.9889 −0.622904
\(835\) 6.58549 0.227900
\(836\) 3.04718 0.105389
\(837\) −77.8956 −2.69246
\(838\) −16.9670 −0.586117
\(839\) −15.2106 −0.525127 −0.262564 0.964915i \(-0.584568\pi\)
−0.262564 + 0.964915i \(0.584568\pi\)
\(840\) −13.3344 −0.460079
\(841\) −27.3989 −0.944789
\(842\) −16.4637 −0.567378
\(843\) 78.0173 2.68706
\(844\) −8.81789 −0.303524
\(845\) 6.45613 0.222098
\(846\) 60.9559 2.09571
\(847\) 46.2355 1.58867
\(848\) 3.11620 0.107011
\(849\) −3.70169 −0.127042
\(850\) −6.92542 −0.237540
\(851\) 0 0
\(852\) 20.2598 0.694089
\(853\) −5.08880 −0.174237 −0.0871187 0.996198i \(-0.527766\pi\)
−0.0871187 + 0.996198i \(0.527766\pi\)
\(854\) −54.2070 −1.85493
\(855\) −18.3014 −0.625895
\(856\) −6.00000 −0.205076
\(857\) 9.56366 0.326688 0.163344 0.986569i \(-0.447772\pi\)
0.163344 + 0.986569i \(0.447772\pi\)
\(858\) −6.92542 −0.236430
\(859\) 45.9889 1.56912 0.784560 0.620053i \(-0.212889\pi\)
0.784560 + 0.620053i \(0.212889\pi\)
\(860\) −1.26535 −0.0431482
\(861\) −12.3399 −0.420544
\(862\) −8.29831 −0.282642
\(863\) −55.4034 −1.88595 −0.942977 0.332859i \(-0.891987\pi\)
−0.942977 + 0.332859i \(0.891987\pi\)
\(864\) −7.48352 −0.254595
\(865\) 0.925423 0.0314653
\(866\) −20.2598 −0.688456
\(867\) −90.5754 −3.07610
\(868\) −47.4450 −1.61039
\(869\) 10.1492 0.344286
\(870\) −3.70169 −0.125499
\(871\) 20.0832 0.680495
\(872\) −15.2927 −0.517878
\(873\) 17.9178 0.606426
\(874\) 0 0
\(875\) 4.55810 0.154092
\(876\) 27.1051 0.915796
\(877\) 9.98683 0.337231 0.168616 0.985682i \(-0.446070\pi\)
0.168616 + 0.985682i \(0.446070\pi\)
\(878\) −25.7575 −0.869275
\(879\) −74.3156 −2.50660
\(880\) −0.925423 −0.0311960
\(881\) −32.7631 −1.10382 −0.551908 0.833905i \(-0.686100\pi\)
−0.551908 + 0.833905i \(0.686100\pi\)
\(882\) 76.5699 2.57824
\(883\) 28.2882 0.951975 0.475988 0.879452i \(-0.342091\pi\)
0.475988 + 0.879452i \(0.342091\pi\)
\(884\) −17.7159 −0.595851
\(885\) −21.2542 −0.714453
\(886\) −22.1106 −0.742821
\(887\) −48.1380 −1.61632 −0.808158 0.588965i \(-0.799536\pi\)
−0.808158 + 0.588965i \(0.799536\pi\)
\(888\) 28.3816 0.952422
\(889\) 83.3548 2.79563
\(890\) 9.11620 0.305576
\(891\) 4.82901 0.161778
\(892\) 12.3816 0.414565
\(893\) 36.1117 1.20843
\(894\) 25.4724 0.851924
\(895\) 2.88380 0.0963949
\(896\) −4.55810 −0.152275
\(897\) 0 0
\(898\) 15.0777 0.503149
\(899\) −13.1710 −0.439277
\(900\) 5.55810 0.185270
\(901\) −21.5810 −0.718967
\(902\) −0.856408 −0.0285153
\(903\) 16.8727 0.561488
\(904\) −7.26535 −0.241642
\(905\) 5.82345 0.193578
\(906\) −38.2487 −1.27073
\(907\) 0.938589 0.0311653 0.0155827 0.999879i \(-0.495040\pi\)
0.0155827 + 0.999879i \(0.495040\pi\)
\(908\) −6.81789 −0.226260
\(909\) 53.9230 1.78851
\(910\) 11.6601 0.386528
\(911\) −36.0000 −1.19273 −0.596367 0.802712i \(-0.703390\pi\)
−0.596367 + 0.802712i \(0.703390\pi\)
\(912\) −9.63268 −0.318970
\(913\) −0.541829 −0.0179319
\(914\) −22.9670 −0.759682
\(915\) 34.7905 1.15014
\(916\) −21.7017 −0.717044
\(917\) 71.5699 2.36345
\(918\) 51.8266 1.71053
\(919\) −18.7235 −0.617632 −0.308816 0.951122i \(-0.599933\pi\)
−0.308816 + 0.951122i \(0.599933\pi\)
\(920\) 0 0
\(921\) 59.9067 1.97399
\(922\) 27.1162 0.893024
\(923\) −17.7159 −0.583127
\(924\) 12.3399 0.405954
\(925\) −9.70169 −0.318990
\(926\) 23.3486 0.767282
\(927\) 109.735 3.60418
\(928\) −1.26535 −0.0415372
\(929\) −18.0000 −0.590561 −0.295280 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) 30.4506 0.998513
\(931\) 45.3618 1.48667
\(932\) 7.85085 0.257163
\(933\) −35.1051 −1.14929
\(934\) −0.585493 −0.0191579
\(935\) 6.40895 0.209595
\(936\) 14.2182 0.464735
\(937\) 55.9067 1.82639 0.913196 0.407521i \(-0.133607\pi\)
0.913196 + 0.407521i \(0.133607\pi\)
\(938\) −35.7849 −1.16842
\(939\) −5.93098 −0.193550
\(940\) −10.9670 −0.357706
\(941\) −16.2740 −0.530518 −0.265259 0.964177i \(-0.585457\pi\)
−0.265259 + 0.964177i \(0.585457\pi\)
\(942\) −12.1380 −0.395478
\(943\) 0 0
\(944\) −7.26535 −0.236467
\(945\) −34.1106 −1.10962
\(946\) 1.17099 0.0380721
\(947\) −1.53627 −0.0499220 −0.0249610 0.999688i \(-0.507946\pi\)
−0.0249610 + 0.999688i \(0.507946\pi\)
\(948\) −32.0832 −1.04202
\(949\) −23.7017 −0.769389
\(950\) 3.29275 0.106831
\(951\) −6.61084 −0.214371
\(952\) 31.5668 1.02308
\(953\) 38.3288 1.24159 0.620796 0.783972i \(-0.286810\pi\)
0.620796 + 0.783972i \(0.286810\pi\)
\(954\) 17.3201 0.560760
\(955\) 21.1162 0.683304
\(956\) 12.0000 0.388108
\(957\) 3.42563 0.110735
\(958\) 36.8179 1.18953
\(959\) 9.24106 0.298409
\(960\) 2.92542 0.0944176
\(961\) 77.3461 2.49504
\(962\) −24.8179 −0.800161
\(963\) −33.3486 −1.07464
\(964\) 15.7017 0.505717
\(965\) −3.85085 −0.123963
\(966\) 0 0
\(967\) −9.03296 −0.290480 −0.145240 0.989396i \(-0.546395\pi\)
−0.145240 + 0.989396i \(0.546395\pi\)
\(968\) −10.1436 −0.326027
\(969\) 66.7104 2.14305
\(970\) −3.22373 −0.103508
\(971\) −51.4561 −1.65131 −0.825653 0.564178i \(-0.809193\pi\)
−0.825653 + 0.564178i \(0.809193\pi\)
\(972\) 7.18521 0.230466
\(973\) −28.0285 −0.898551
\(974\) −13.1162 −0.420270
\(975\) −7.48352 −0.239665
\(976\) 11.8925 0.380669
\(977\) 42.1939 1.34990 0.674951 0.737863i \(-0.264165\pi\)
0.674951 + 0.737863i \(0.264165\pi\)
\(978\) 22.8869 0.731843
\(979\) −8.43634 −0.269627
\(980\) −13.7763 −0.440067
\(981\) −84.9986 −2.71380
\(982\) −21.1162 −0.673845
\(983\) −19.9584 −0.636573 −0.318287 0.947994i \(-0.603107\pi\)
−0.318287 + 0.947994i \(0.603107\pi\)
\(984\) 2.70725 0.0863041
\(985\) 14.7763 0.470811
\(986\) 8.76310 0.279074
\(987\) 146.239 4.65483
\(988\) 8.42317 0.267977
\(989\) 0 0
\(990\) −5.14359 −0.163474
\(991\) −40.7763 −1.29530 −0.647650 0.761938i \(-0.724248\pi\)
−0.647650 + 0.761938i \(0.724248\pi\)
\(992\) 10.4089 0.330484
\(993\) 14.9670 0.474965
\(994\) 31.5668 1.00124
\(995\) 15.7017 0.497777
\(996\) 1.71282 0.0542726
\(997\) 21.4034 0.677852 0.338926 0.940813i \(-0.389936\pi\)
0.338926 + 0.940813i \(0.389936\pi\)
\(998\) −4.43634 −0.140430
\(999\) 72.6028 2.29705
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 5290.2.a.p.1.1 3
23.22 odd 2 5290.2.a.q.1.1 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5290.2.a.p.1.1 3 1.1 even 1 trivial
5290.2.a.q.1.1 yes 3 23.22 odd 2