Properties

Label 5290.2.a.q.1.1
Level $5290$
Weight $2$
Character 5290.1
Self dual yes
Analytic conductor $42.241$
Analytic rank $0$
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: \(0\)
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

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

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 \(-0.169588\pi\)
0.861400 + 0.507928i \(0.169588\pi\)
\(8\) 1.00000 0.353553
\(9\) 5.55810 1.85270
\(10\) 1.00000 0.316228
\(11\) −0.925423 −0.279026 −0.139513 0.990220i \(-0.544554\pi\)
−0.139513 + 0.990220i \(0.544554\pi\)
\(12\) −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 \(-0.182654\pi\)
0.839831 + 0.542848i \(0.182654\pi\)
\(18\) 5.55810 1.31006
\(19\) −3.29275 −0.755408 −0.377704 0.925926i \(-0.623286\pi\)
−0.377704 + 0.925926i \(0.623286\pi\)
\(20\) 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 \(-0.206169\pi\)
0.797474 + 0.603353i \(0.206169\pi\)
\(38\) −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 \(-0.530759\pi\)
−0.0964822 + 0.995335i \(0.530759\pi\)
\(44\) −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 \(-0.568656\pi\)
−0.214021 + 0.976829i \(0.568656\pi\)
\(54\) −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 \(-0.775457\pi\)
−0.761337 + 0.648356i \(0.775457\pi\)
\(62\) 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 \(-0.659206\pi\)
−0.479567 + 0.877505i \(0.659206\pi\)
\(68\) 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 \(-0.711630\pi\)
−0.616944 + 0.787007i \(0.711630\pi\)
\(80\) 1.00000 0.111803
\(81\) 5.21817 0.579797
\(82\) −0.925423 −0.102196
\(83\) 0.585493 0.0642662 0.0321331 0.999484i \(-0.489770\pi\)
0.0321331 + 0.999484i \(0.489770\pi\)
\(84\) −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 \(-0.339490\pi\)
0.483158 + 0.875533i \(0.339490\pi\)
\(90\) 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 \(-0.552330\pi\)
−0.163660 + 0.986517i \(0.552330\pi\)
\(98\) 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 \(-0.925428\pi\)
−0.972683 + 0.232136i \(0.925428\pi\)
\(104\) 2.55810 0.250842
\(105\) −13.3344 −1.30130
\(106\) −3.11620 −0.302672
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) −7.48352 −0.720102
\(109\) 15.2927 1.46478 0.732390 0.680886i \(-0.238405\pi\)
0.732390 + 0.680886i \(0.238405\pi\)
\(110\) −0.925423 −0.0882356
\(111\) −28.3816 −2.69386
\(112\) 4.55810 0.430700
\(113\) 7.26535 0.683467 0.341733 0.939797i \(-0.388986\pi\)
0.341733 + 0.939797i \(0.388986\pi\)
\(114\) 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 \(-0.472398\pi\)
0.0866060 + 0.996243i \(0.472398\pi\)
\(138\) 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 \(-0.383914\pi\)
0.356663 + 0.934233i \(0.383914\pi\)
\(150\) −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 \(-0.552946\pi\)
−0.165569 + 0.986198i \(0.552946\pi\)
\(158\) −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 \(-0.430560\pi\)
0.216427 + 0.976299i \(0.430560\pi\)
\(182\) 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 \(-0.223254\pi\)
0.763957 + 0.645267i \(0.223254\pi\)
\(192\) −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 \(-0.312132\pi\)
0.556532 + 0.830826i \(0.312132\pi\)
\(200\) 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 \(-0.427350\pi\)
0.226260 + 0.974067i \(0.427350\pi\)
\(228\) 9.63268 0.637940
\(229\) 21.7017 1.43409 0.717044 0.697028i \(-0.245495\pi\)
0.717044 + 0.697028i \(0.245495\pi\)
\(230\) 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 \(-0.668772\pi\)
−0.505717 + 0.862699i \(0.668772\pi\)
\(242\) −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 \(-0.492344\pi\)
0.0240498 + 0.999711i \(0.492344\pi\)
\(252\) 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 \(-0.335320\pi\)
0.494584 + 0.869130i \(0.335320\pi\)
\(264\) 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 \(-0.207228\pi\)
0.795462 + 0.606004i \(0.207228\pi\)
\(282\) −32.0832 −1.91053
\(283\) −1.26535 −0.0752174 −0.0376087 0.999293i \(-0.511974\pi\)
−0.0376087 + 0.999293i \(0.511974\pi\)
\(284\) −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 \(-0.766142\pi\)
−0.742041 + 0.670355i \(0.766142\pi\)
\(294\) −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 \(-0.518248\pi\)
−0.0572975 + 0.998357i \(0.518248\pi\)
\(314\) −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 \(-0.492575\pi\)
0.0233257 + 0.999728i \(0.492575\pi\)
\(338\) −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 \(-0.626521\pi\)
−0.387093 + 0.922041i \(0.626521\pi\)
\(360\) 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 \(-0.509730\pi\)
−0.0305625 + 0.999533i \(0.509730\pi\)
\(368\) 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 \(-0.573870\pi\)
−0.229993 + 0.973192i \(0.573870\pi\)
\(374\) −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 \(-0.701911\pi\)
−0.592631 + 0.805474i \(0.701911\pi\)
\(380\) −3.29275 −0.168914
\(381\) 53.4977 2.74077
\(382\) 21.1162 1.08040
\(383\) −21.9341 −1.12078 −0.560390 0.828229i \(-0.689349\pi\)
−0.560390 + 0.828229i \(0.689349\pi\)
\(384\) −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 \(-0.514072\pi\)
−0.0441947 + 0.999023i \(0.514072\pi\)
\(390\) −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 \(-0.102564\pi\)
0.948537 + 0.316666i \(0.102564\pi\)
\(402\) 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 \(-0.363975\pi\)
0.414447 + 0.910073i \(0.363975\pi\)
\(420\) −13.3344 −0.650651
\(421\) 16.4637 0.802393 0.401197 0.915992i \(-0.368594\pi\)
0.401197 + 0.915992i \(0.368594\pi\)
\(422\) −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 \(-0.435952\pi\)
0.199858 + 0.979825i \(0.435952\pi\)
\(432\) −7.48352 −0.360051
\(433\) 20.2598 0.973623 0.486812 0.873507i \(-0.338160\pi\)
0.486812 + 0.873507i \(0.338160\pi\)
\(434\) 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 \(-0.319491\pi\)
0.537177 + 0.843470i \(0.319491\pi\)
\(458\) 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 \(-0.495688\pi\)
0.0135467 + 0.999908i \(0.495688\pi\)
\(468\) 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 \(-0.818107\pi\)
−0.841126 + 0.540839i \(0.818107\pi\)
\(480\) −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 \(-0.264945\pi\)
0.673139 + 0.739516i \(0.264945\pi\)
\(504\) 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 \(-0.631828\pi\)
−0.402412 + 0.915459i \(0.631828\pi\)
\(522\) −7.03296 −0.307824
\(523\) −3.11620 −0.136262 −0.0681309 0.997676i \(-0.521704\pi\)
−0.0681309 + 0.997676i \(0.521704\pi\)
\(524\) −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 \(-0.235392\pi\)
0.738801 + 0.673923i \(0.235392\pi\)
\(558\) 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 \(-0.833436\pi\)
−0.866186 + 0.499721i \(0.833436\pi\)
\(564\) −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 \(-0.585631\pi\)
−0.265784 + 0.964033i \(0.585631\pi\)
\(570\) 9.63268 0.403468
\(571\) −2.09641 −0.0877320 −0.0438660 0.999037i \(-0.513967\pi\)
−0.0438660 + 0.999037i \(0.513967\pi\)
\(572\) −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 \(-0.508135\pi\)
−0.0255536 + 0.999673i \(0.508135\pi\)
\(614\) −20.4780 −0.826423
\(615\) 2.70725 0.109167
\(616\) −4.21817 −0.169955
\(617\) 9.45613 0.380689 0.190345 0.981717i \(-0.439039\pi\)
0.190345 + 0.981717i \(0.439039\pi\)
\(618\) 57.7575 2.32335
\(619\) −17.0056 −0.683511 −0.341756 0.939789i \(-0.611022\pi\)
−0.341756 + 0.939789i \(0.611022\pi\)
\(620\) 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 \(-0.472204\pi\)
0.0872134 + 0.996190i \(0.472204\pi\)
\(632\) −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 \(-0.739580\pi\)
−0.683584 + 0.729871i \(0.739580\pi\)
\(642\) −17.5525 −0.692743
\(643\) −32.3156 −1.27440 −0.637202 0.770697i \(-0.719908\pi\)
−0.637202 + 0.770697i \(0.719908\pi\)
\(644\) 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 \(-0.358847\pi\)
0.429053 + 0.903279i \(0.358847\pi\)
\(660\) 2.70725 0.105380
\(661\) −3.12936 −0.121718 −0.0608591 0.998146i \(-0.519384\pi\)
−0.0608591 + 0.998146i \(0.519384\pi\)
\(662\) −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 \(-0.768768\pi\)
−0.747546 + 0.664210i \(0.768768\pi\)
\(678\) −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 \(-0.462787\pi\)
0.116643 + 0.993174i \(0.462787\pi\)
\(702\) −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 \(-0.220741\pi\)
0.769028 + 0.639216i \(0.220741\pi\)
\(710\) −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 \(-0.321211\pi\)
0.532610 + 0.846361i \(0.321211\pi\)
\(728\) 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 \(-0.562235\pi\)
−0.194275 + 0.980947i \(0.562235\pi\)
\(734\) −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 \(-0.480210\pi\)
0.0621306 + 0.998068i \(0.480210\pi\)
\(744\) −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 \(-0.468503\pi\)
0.0987891 + 0.995108i \(0.468503\pi\)
\(752\) 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 \(-0.481964\pi\)
0.0566301 + 0.998395i \(0.481964\pi\)
\(758\) −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 \(-0.408634\pi\)
0.283109 + 0.959088i \(0.408634\pi\)
\(770\) −4.21817 −0.152012
\(771\) −19.5414 −0.703767
\(772\) 3.85085 0.138595
\(773\) 29.7849 1.07129 0.535645 0.844443i \(-0.320069\pi\)
0.535645 + 0.844443i \(0.320069\pi\)
\(774\) −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 \(-0.382064\pi\)
0.362087 + 0.932144i \(0.382064\pi\)
\(788\) −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 \(-0.275621\pi\)
0.647962 + 0.761672i \(0.275621\pi\)
\(798\) 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 \(-0.455643\pi\)
0.138900 + 0.990306i \(0.455643\pi\)
\(828\) 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 \(-0.415432\pi\)
0.262564 + 0.964915i \(0.415432\pi\)
\(840\) −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 \(-0.313900\pi\)
0.551908 + 0.833905i \(0.313900\pi\)
\(882\) 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 \(-0.504960\pi\)
−0.0155827 + 0.999879i \(0.504960\pi\)
\(908\) 6.81789 0.226260
\(909\) 53.9230 1.78851
\(910\) 11.6601 0.386528
\(911\) 36.0000 1.19273 0.596367 0.802712i \(-0.296610\pi\)
0.596367 + 0.802712i \(0.296610\pi\)
\(912\) 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 \(-0.400067\pi\)
0.308816 + 0.951122i \(0.400067\pi\)
\(920\) 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 \(-0.866393\pi\)
−0.913196 + 0.407521i \(0.866393\pi\)
\(938\) −35.7849 −1.16842
\(939\) 5.93098 0.193550
\(940\) 10.9670 0.357706
\(941\) 16.2740 0.530518 0.265259 0.964177i \(-0.414543\pi\)
0.265259 + 0.964177i \(0.414543\pi\)
\(942\) 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 \(-0.713190\pi\)
−0.620796 + 0.783972i \(0.713190\pi\)
\(954\) −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 \(-0.190807\pi\)
0.825653 + 0.564178i \(0.190807\pi\)
\(972\) 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 \(-0.735835\pi\)
−0.674951 + 0.737863i \(0.735835\pi\)
\(978\) 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 \(-0.396893\pi\)
0.318287 + 0.947994i \(0.396893\pi\)
\(984\) 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.q.1.1 yes 3
23.22 odd 2 5290.2.a.p.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5290.2.a.p.1.1 3 23.22 odd 2
5290.2.a.q.1.1 yes 3 1.1 even 1 trivial