Properties

Label 1183.2.a.c.1.1
Level $1183$
Weight $2$
Character 1183.1
Self dual yes
Analytic conductor $9.446$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(9.44630255912\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \(x^{2} - x - 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 1183.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.61803 q^{2} -2.61803 q^{3} +4.85410 q^{4} -2.61803 q^{5} +6.85410 q^{6} -1.00000 q^{7} -7.47214 q^{8} +3.85410 q^{9} +O(q^{10})\) \(q-2.61803 q^{2} -2.61803 q^{3} +4.85410 q^{4} -2.61803 q^{5} +6.85410 q^{6} -1.00000 q^{7} -7.47214 q^{8} +3.85410 q^{9} +6.85410 q^{10} -1.85410 q^{11} -12.7082 q^{12} +2.61803 q^{14} +6.85410 q^{15} +9.85410 q^{16} -1.47214 q^{17} -10.0902 q^{18} +1.85410 q^{19} -12.7082 q^{20} +2.61803 q^{21} +4.85410 q^{22} -4.47214 q^{23} +19.5623 q^{24} +1.85410 q^{25} -2.23607 q^{27} -4.85410 q^{28} +7.09017 q^{29} -17.9443 q^{30} +4.70820 q^{31} -10.8541 q^{32} +4.85410 q^{33} +3.85410 q^{34} +2.61803 q^{35} +18.7082 q^{36} -4.00000 q^{37} -4.85410 q^{38} +19.5623 q^{40} -0.763932 q^{41} -6.85410 q^{42} +12.5623 q^{43} -9.00000 q^{44} -10.0902 q^{45} +11.7082 q^{46} +2.23607 q^{47} -25.7984 q^{48} +1.00000 q^{49} -4.85410 q^{50} +3.85410 q^{51} +3.76393 q^{53} +5.85410 q^{54} +4.85410 q^{55} +7.47214 q^{56} -4.85410 q^{57} -18.5623 q^{58} +2.23607 q^{59} +33.2705 q^{60} -6.00000 q^{61} -12.3262 q^{62} -3.85410 q^{63} +8.70820 q^{64} -12.7082 q^{66} +12.7082 q^{67} -7.14590 q^{68} +11.7082 q^{69} -6.85410 q^{70} +14.1803 q^{71} -28.7984 q^{72} +2.00000 q^{73} +10.4721 q^{74} -4.85410 q^{75} +9.00000 q^{76} +1.85410 q^{77} +4.00000 q^{79} -25.7984 q^{80} -5.70820 q^{81} +2.00000 q^{82} -6.70820 q^{83} +12.7082 q^{84} +3.85410 q^{85} -32.8885 q^{86} -18.5623 q^{87} +13.8541 q^{88} -4.90983 q^{89} +26.4164 q^{90} -21.7082 q^{92} -12.3262 q^{93} -5.85410 q^{94} -4.85410 q^{95} +28.4164 q^{96} -18.8541 q^{97} -2.61803 q^{98} -7.14590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 3q^{2} - 3q^{3} + 3q^{4} - 3q^{5} + 7q^{6} - 2q^{7} - 6q^{8} + q^{9} + O(q^{10}) \) \( 2q - 3q^{2} - 3q^{3} + 3q^{4} - 3q^{5} + 7q^{6} - 2q^{7} - 6q^{8} + q^{9} + 7q^{10} + 3q^{11} - 12q^{12} + 3q^{14} + 7q^{15} + 13q^{16} + 6q^{17} - 9q^{18} - 3q^{19} - 12q^{20} + 3q^{21} + 3q^{22} + 19q^{24} - 3q^{25} - 3q^{28} + 3q^{29} - 18q^{30} - 4q^{31} - 15q^{32} + 3q^{33} + q^{34} + 3q^{35} + 24q^{36} - 8q^{37} - 3q^{38} + 19q^{40} - 6q^{41} - 7q^{42} + 5q^{43} - 18q^{44} - 9q^{45} + 10q^{46} - 27q^{48} + 2q^{49} - 3q^{50} + q^{51} + 12q^{53} + 5q^{54} + 3q^{55} + 6q^{56} - 3q^{57} - 17q^{58} + 33q^{60} - 12q^{61} - 9q^{62} - q^{63} + 4q^{64} - 12q^{66} + 12q^{67} - 21q^{68} + 10q^{69} - 7q^{70} + 6q^{71} - 33q^{72} + 4q^{73} + 12q^{74} - 3q^{75} + 18q^{76} - 3q^{77} + 8q^{79} - 27q^{80} + 2q^{81} + 4q^{82} + 12q^{84} + q^{85} - 30q^{86} - 17q^{87} + 21q^{88} - 21q^{89} + 26q^{90} - 30q^{92} - 9q^{93} - 5q^{94} - 3q^{95} + 30q^{96} - 31q^{97} - 3q^{98} - 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61803 −1.85123 −0.925615 0.378467i \(-0.876451\pi\)
−0.925615 + 0.378467i \(0.876451\pi\)
\(3\) −2.61803 −1.51152 −0.755761 0.654847i \(-0.772733\pi\)
−0.755761 + 0.654847i \(0.772733\pi\)
\(4\) 4.85410 2.42705
\(5\) −2.61803 −1.17082 −0.585410 0.810737i \(-0.699067\pi\)
−0.585410 + 0.810737i \(0.699067\pi\)
\(6\) 6.85410 2.79818
\(7\) −1.00000 −0.377964
\(8\) −7.47214 −2.64180
\(9\) 3.85410 1.28470
\(10\) 6.85410 2.16746
\(11\) −1.85410 −0.559033 −0.279516 0.960141i \(-0.590174\pi\)
−0.279516 + 0.960141i \(0.590174\pi\)
\(12\) −12.7082 −3.66854
\(13\) 0 0
\(14\) 2.61803 0.699699
\(15\) 6.85410 1.76972
\(16\) 9.85410 2.46353
\(17\) −1.47214 −0.357045 −0.178523 0.983936i \(-0.557132\pi\)
−0.178523 + 0.983936i \(0.557132\pi\)
\(18\) −10.0902 −2.37828
\(19\) 1.85410 0.425360 0.212680 0.977122i \(-0.431781\pi\)
0.212680 + 0.977122i \(0.431781\pi\)
\(20\) −12.7082 −2.84164
\(21\) 2.61803 0.571302
\(22\) 4.85410 1.03490
\(23\) −4.47214 −0.932505 −0.466252 0.884652i \(-0.654396\pi\)
−0.466252 + 0.884652i \(0.654396\pi\)
\(24\) 19.5623 3.99314
\(25\) 1.85410 0.370820
\(26\) 0 0
\(27\) −2.23607 −0.430331
\(28\) −4.85410 −0.917339
\(29\) 7.09017 1.31661 0.658306 0.752751i \(-0.271273\pi\)
0.658306 + 0.752751i \(0.271273\pi\)
\(30\) −17.9443 −3.27616
\(31\) 4.70820 0.845618 0.422809 0.906219i \(-0.361044\pi\)
0.422809 + 0.906219i \(0.361044\pi\)
\(32\) −10.8541 −1.91875
\(33\) 4.85410 0.844991
\(34\) 3.85410 0.660973
\(35\) 2.61803 0.442529
\(36\) 18.7082 3.11803
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) −4.85410 −0.787439
\(39\) 0 0
\(40\) 19.5623 3.09307
\(41\) −0.763932 −0.119306 −0.0596531 0.998219i \(-0.518999\pi\)
−0.0596531 + 0.998219i \(0.518999\pi\)
\(42\) −6.85410 −1.05761
\(43\) 12.5623 1.91573 0.957867 0.287213i \(-0.0927286\pi\)
0.957867 + 0.287213i \(0.0927286\pi\)
\(44\) −9.00000 −1.35680
\(45\) −10.0902 −1.50415
\(46\) 11.7082 1.72628
\(47\) 2.23607 0.326164 0.163082 0.986613i \(-0.447856\pi\)
0.163082 + 0.986613i \(0.447856\pi\)
\(48\) −25.7984 −3.72367
\(49\) 1.00000 0.142857
\(50\) −4.85410 −0.686474
\(51\) 3.85410 0.539682
\(52\) 0 0
\(53\) 3.76393 0.517016 0.258508 0.966009i \(-0.416769\pi\)
0.258508 + 0.966009i \(0.416769\pi\)
\(54\) 5.85410 0.796642
\(55\) 4.85410 0.654527
\(56\) 7.47214 0.998506
\(57\) −4.85410 −0.642942
\(58\) −18.5623 −2.43735
\(59\) 2.23607 0.291111 0.145556 0.989350i \(-0.453503\pi\)
0.145556 + 0.989350i \(0.453503\pi\)
\(60\) 33.2705 4.29520
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) −12.3262 −1.56543
\(63\) −3.85410 −0.485571
\(64\) 8.70820 1.08853
\(65\) 0 0
\(66\) −12.7082 −1.56427
\(67\) 12.7082 1.55255 0.776277 0.630392i \(-0.217106\pi\)
0.776277 + 0.630392i \(0.217106\pi\)
\(68\) −7.14590 −0.866567
\(69\) 11.7082 1.40950
\(70\) −6.85410 −0.819222
\(71\) 14.1803 1.68290 0.841448 0.540338i \(-0.181703\pi\)
0.841448 + 0.540338i \(0.181703\pi\)
\(72\) −28.7984 −3.39392
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 10.4721 1.21736
\(75\) −4.85410 −0.560503
\(76\) 9.00000 1.03237
\(77\) 1.85410 0.211295
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) −25.7984 −2.88435
\(81\) −5.70820 −0.634245
\(82\) 2.00000 0.220863
\(83\) −6.70820 −0.736321 −0.368161 0.929762i \(-0.620012\pi\)
−0.368161 + 0.929762i \(0.620012\pi\)
\(84\) 12.7082 1.38658
\(85\) 3.85410 0.418036
\(86\) −32.8885 −3.54646
\(87\) −18.5623 −1.99009
\(88\) 13.8541 1.47685
\(89\) −4.90983 −0.520441 −0.260220 0.965549i \(-0.583795\pi\)
−0.260220 + 0.965549i \(0.583795\pi\)
\(90\) 26.4164 2.78453
\(91\) 0 0
\(92\) −21.7082 −2.26324
\(93\) −12.3262 −1.27817
\(94\) −5.85410 −0.603805
\(95\) −4.85410 −0.498020
\(96\) 28.4164 2.90024
\(97\) −18.8541 −1.91434 −0.957172 0.289520i \(-0.906504\pi\)
−0.957172 + 0.289520i \(0.906504\pi\)
\(98\) −2.61803 −0.264461
\(99\) −7.14590 −0.718190
\(100\) 9.00000 0.900000
\(101\) −11.5623 −1.15049 −0.575246 0.817980i \(-0.695094\pi\)
−0.575246 + 0.817980i \(0.695094\pi\)
\(102\) −10.0902 −0.999076
\(103\) −8.70820 −0.858045 −0.429022 0.903294i \(-0.641142\pi\)
−0.429022 + 0.903294i \(0.641142\pi\)
\(104\) 0 0
\(105\) −6.85410 −0.668892
\(106\) −9.85410 −0.957115
\(107\) −3.38197 −0.326947 −0.163473 0.986548i \(-0.552270\pi\)
−0.163473 + 0.986548i \(0.552270\pi\)
\(108\) −10.8541 −1.04444
\(109\) 2.70820 0.259399 0.129699 0.991553i \(-0.458599\pi\)
0.129699 + 0.991553i \(0.458599\pi\)
\(110\) −12.7082 −1.21168
\(111\) 10.4721 0.993971
\(112\) −9.85410 −0.931125
\(113\) 1.47214 0.138487 0.0692435 0.997600i \(-0.477941\pi\)
0.0692435 + 0.997600i \(0.477941\pi\)
\(114\) 12.7082 1.19023
\(115\) 11.7082 1.09180
\(116\) 34.4164 3.19548
\(117\) 0 0
\(118\) −5.85410 −0.538914
\(119\) 1.47214 0.134950
\(120\) −51.2148 −4.67525
\(121\) −7.56231 −0.687482
\(122\) 15.7082 1.42215
\(123\) 2.00000 0.180334
\(124\) 22.8541 2.05236
\(125\) 8.23607 0.736656
\(126\) 10.0902 0.898904
\(127\) −20.8541 −1.85050 −0.925251 0.379355i \(-0.876146\pi\)
−0.925251 + 0.379355i \(0.876146\pi\)
\(128\) −1.09017 −0.0963583
\(129\) −32.8885 −2.89567
\(130\) 0 0
\(131\) −15.3262 −1.33906 −0.669530 0.742785i \(-0.733504\pi\)
−0.669530 + 0.742785i \(0.733504\pi\)
\(132\) 23.5623 2.05084
\(133\) −1.85410 −0.160771
\(134\) −33.2705 −2.87413
\(135\) 5.85410 0.503841
\(136\) 11.0000 0.943242
\(137\) 2.61803 0.223674 0.111837 0.993727i \(-0.464327\pi\)
0.111837 + 0.993727i \(0.464327\pi\)
\(138\) −30.6525 −2.60931
\(139\) 4.56231 0.386970 0.193485 0.981103i \(-0.438021\pi\)
0.193485 + 0.981103i \(0.438021\pi\)
\(140\) 12.7082 1.07404
\(141\) −5.85410 −0.493004
\(142\) −37.1246 −3.11543
\(143\) 0 0
\(144\) 37.9787 3.16489
\(145\) −18.5623 −1.54152
\(146\) −5.23607 −0.433340
\(147\) −2.61803 −0.215932
\(148\) −19.4164 −1.59602
\(149\) −1.85410 −0.151894 −0.0759470 0.997112i \(-0.524198\pi\)
−0.0759470 + 0.997112i \(0.524198\pi\)
\(150\) 12.7082 1.03762
\(151\) 1.29180 0.105125 0.0525624 0.998618i \(-0.483261\pi\)
0.0525624 + 0.998618i \(0.483261\pi\)
\(152\) −13.8541 −1.12372
\(153\) −5.67376 −0.458696
\(154\) −4.85410 −0.391155
\(155\) −12.3262 −0.990067
\(156\) 0 0
\(157\) 14.8541 1.18549 0.592743 0.805392i \(-0.298045\pi\)
0.592743 + 0.805392i \(0.298045\pi\)
\(158\) −10.4721 −0.833118
\(159\) −9.85410 −0.781481
\(160\) 28.4164 2.24651
\(161\) 4.47214 0.352454
\(162\) 14.9443 1.17413
\(163\) 3.70820 0.290449 0.145224 0.989399i \(-0.453610\pi\)
0.145224 + 0.989399i \(0.453610\pi\)
\(164\) −3.70820 −0.289562
\(165\) −12.7082 −0.989332
\(166\) 17.5623 1.36310
\(167\) −14.2361 −1.10162 −0.550810 0.834631i \(-0.685681\pi\)
−0.550810 + 0.834631i \(0.685681\pi\)
\(168\) −19.5623 −1.50926
\(169\) 0 0
\(170\) −10.0902 −0.773881
\(171\) 7.14590 0.546460
\(172\) 60.9787 4.64958
\(173\) −9.00000 −0.684257 −0.342129 0.939653i \(-0.611148\pi\)
−0.342129 + 0.939653i \(0.611148\pi\)
\(174\) 48.5967 3.68411
\(175\) −1.85410 −0.140157
\(176\) −18.2705 −1.37719
\(177\) −5.85410 −0.440021
\(178\) 12.8541 0.963456
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) −48.9787 −3.65066
\(181\) 9.70820 0.721605 0.360803 0.932642i \(-0.382503\pi\)
0.360803 + 0.932642i \(0.382503\pi\)
\(182\) 0 0
\(183\) 15.7082 1.16118
\(184\) 33.4164 2.46349
\(185\) 10.4721 0.769927
\(186\) 32.2705 2.36619
\(187\) 2.72949 0.199600
\(188\) 10.8541 0.791617
\(189\) 2.23607 0.162650
\(190\) 12.7082 0.921950
\(191\) 21.3820 1.54714 0.773572 0.633708i \(-0.218468\pi\)
0.773572 + 0.633708i \(0.218468\pi\)
\(192\) −22.7984 −1.64533
\(193\) 6.00000 0.431889 0.215945 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) 49.3607 3.54389
\(195\) 0 0
\(196\) 4.85410 0.346722
\(197\) 16.7984 1.19683 0.598417 0.801185i \(-0.295797\pi\)
0.598417 + 0.801185i \(0.295797\pi\)
\(198\) 18.7082 1.32953
\(199\) −24.4164 −1.73083 −0.865417 0.501053i \(-0.832946\pi\)
−0.865417 + 0.501053i \(0.832946\pi\)
\(200\) −13.8541 −0.979633
\(201\) −33.2705 −2.34672
\(202\) 30.2705 2.12983
\(203\) −7.09017 −0.497632
\(204\) 18.7082 1.30984
\(205\) 2.00000 0.139686
\(206\) 22.7984 1.58844
\(207\) −17.2361 −1.19799
\(208\) 0 0
\(209\) −3.43769 −0.237790
\(210\) 17.9443 1.23827
\(211\) 4.70820 0.324126 0.162063 0.986780i \(-0.448185\pi\)
0.162063 + 0.986780i \(0.448185\pi\)
\(212\) 18.2705 1.25482
\(213\) −37.1246 −2.54374
\(214\) 8.85410 0.605254
\(215\) −32.8885 −2.24298
\(216\) 16.7082 1.13685
\(217\) −4.70820 −0.319614
\(218\) −7.09017 −0.480207
\(219\) −5.23607 −0.353821
\(220\) 23.5623 1.58857
\(221\) 0 0
\(222\) −27.4164 −1.84007
\(223\) −20.2705 −1.35741 −0.678707 0.734409i \(-0.737459\pi\)
−0.678707 + 0.734409i \(0.737459\pi\)
\(224\) 10.8541 0.725220
\(225\) 7.14590 0.476393
\(226\) −3.85410 −0.256371
\(227\) −1.47214 −0.0977091 −0.0488545 0.998806i \(-0.515557\pi\)
−0.0488545 + 0.998806i \(0.515557\pi\)
\(228\) −23.5623 −1.56045
\(229\) 13.1246 0.867299 0.433649 0.901082i \(-0.357226\pi\)
0.433649 + 0.901082i \(0.357226\pi\)
\(230\) −30.6525 −2.02116
\(231\) −4.85410 −0.319376
\(232\) −52.9787 −3.47822
\(233\) 2.61803 0.171513 0.0857566 0.996316i \(-0.472669\pi\)
0.0857566 + 0.996316i \(0.472669\pi\)
\(234\) 0 0
\(235\) −5.85410 −0.381880
\(236\) 10.8541 0.706542
\(237\) −10.4721 −0.680238
\(238\) −3.85410 −0.249824
\(239\) 24.7082 1.59824 0.799120 0.601171i \(-0.205299\pi\)
0.799120 + 0.601171i \(0.205299\pi\)
\(240\) 67.5410 4.35975
\(241\) −24.5623 −1.58220 −0.791099 0.611689i \(-0.790491\pi\)
−0.791099 + 0.611689i \(0.790491\pi\)
\(242\) 19.7984 1.27269
\(243\) 21.6525 1.38901
\(244\) −29.1246 −1.86451
\(245\) −2.61803 −0.167260
\(246\) −5.23607 −0.333840
\(247\) 0 0
\(248\) −35.1803 −2.23395
\(249\) 17.5623 1.11297
\(250\) −21.5623 −1.36372
\(251\) 0.763932 0.0482190 0.0241095 0.999709i \(-0.492325\pi\)
0.0241095 + 0.999709i \(0.492325\pi\)
\(252\) −18.7082 −1.17851
\(253\) 8.29180 0.521301
\(254\) 54.5967 3.42570
\(255\) −10.0902 −0.631871
\(256\) −14.5623 −0.910144
\(257\) 16.7426 1.04438 0.522189 0.852830i \(-0.325116\pi\)
0.522189 + 0.852830i \(0.325116\pi\)
\(258\) 86.1033 5.36056
\(259\) 4.00000 0.248548
\(260\) 0 0
\(261\) 27.3262 1.69145
\(262\) 40.1246 2.47891
\(263\) 9.00000 0.554964 0.277482 0.960731i \(-0.410500\pi\)
0.277482 + 0.960731i \(0.410500\pi\)
\(264\) −36.2705 −2.23230
\(265\) −9.85410 −0.605333
\(266\) 4.85410 0.297624
\(267\) 12.8541 0.786658
\(268\) 61.6869 3.76813
\(269\) −28.7426 −1.75247 −0.876235 0.481884i \(-0.839953\pi\)
−0.876235 + 0.481884i \(0.839953\pi\)
\(270\) −15.3262 −0.932725
\(271\) 8.41641 0.511260 0.255630 0.966775i \(-0.417717\pi\)
0.255630 + 0.966775i \(0.417717\pi\)
\(272\) −14.5066 −0.879590
\(273\) 0 0
\(274\) −6.85410 −0.414071
\(275\) −3.43769 −0.207301
\(276\) 56.8328 3.42093
\(277\) −5.00000 −0.300421 −0.150210 0.988654i \(-0.547995\pi\)
−0.150210 + 0.988654i \(0.547995\pi\)
\(278\) −11.9443 −0.716370
\(279\) 18.1459 1.08637
\(280\) −19.5623 −1.16907
\(281\) −20.1803 −1.20386 −0.601929 0.798550i \(-0.705601\pi\)
−0.601929 + 0.798550i \(0.705601\pi\)
\(282\) 15.3262 0.912664
\(283\) 13.4164 0.797523 0.398761 0.917055i \(-0.369440\pi\)
0.398761 + 0.917055i \(0.369440\pi\)
\(284\) 68.8328 4.08448
\(285\) 12.7082 0.752769
\(286\) 0 0
\(287\) 0.763932 0.0450935
\(288\) −41.8328 −2.46502
\(289\) −14.8328 −0.872519
\(290\) 48.5967 2.85370
\(291\) 49.3607 2.89357
\(292\) 9.70820 0.568130
\(293\) 6.76393 0.395153 0.197577 0.980287i \(-0.436693\pi\)
0.197577 + 0.980287i \(0.436693\pi\)
\(294\) 6.85410 0.399739
\(295\) −5.85410 −0.340839
\(296\) 29.8885 1.73724
\(297\) 4.14590 0.240569
\(298\) 4.85410 0.281191
\(299\) 0 0
\(300\) −23.5623 −1.36037
\(301\) −12.5623 −0.724079
\(302\) −3.38197 −0.194610
\(303\) 30.2705 1.73900
\(304\) 18.2705 1.04789
\(305\) 15.7082 0.899449
\(306\) 14.8541 0.849152
\(307\) 4.85410 0.277038 0.138519 0.990360i \(-0.455766\pi\)
0.138519 + 0.990360i \(0.455766\pi\)
\(308\) 9.00000 0.512823
\(309\) 22.7984 1.29695
\(310\) 32.2705 1.83284
\(311\) 3.32624 0.188614 0.0943068 0.995543i \(-0.469937\pi\)
0.0943068 + 0.995543i \(0.469937\pi\)
\(312\) 0 0
\(313\) 25.1246 1.42013 0.710064 0.704138i \(-0.248666\pi\)
0.710064 + 0.704138i \(0.248666\pi\)
\(314\) −38.8885 −2.19461
\(315\) 10.0902 0.568517
\(316\) 19.4164 1.09226
\(317\) −26.2361 −1.47356 −0.736782 0.676130i \(-0.763656\pi\)
−0.736782 + 0.676130i \(0.763656\pi\)
\(318\) 25.7984 1.44670
\(319\) −13.1459 −0.736029
\(320\) −22.7984 −1.27447
\(321\) 8.85410 0.494188
\(322\) −11.7082 −0.652473
\(323\) −2.72949 −0.151873
\(324\) −27.7082 −1.53934
\(325\) 0 0
\(326\) −9.70820 −0.537688
\(327\) −7.09017 −0.392087
\(328\) 5.70820 0.315183
\(329\) −2.23607 −0.123278
\(330\) 33.2705 1.83148
\(331\) 10.1459 0.557669 0.278834 0.960339i \(-0.410052\pi\)
0.278834 + 0.960339i \(0.410052\pi\)
\(332\) −32.5623 −1.78709
\(333\) −15.4164 −0.844814
\(334\) 37.2705 2.03935
\(335\) −33.2705 −1.81776
\(336\) 25.7984 1.40742
\(337\) −11.5623 −0.629839 −0.314919 0.949118i \(-0.601978\pi\)
−0.314919 + 0.949118i \(0.601978\pi\)
\(338\) 0 0
\(339\) −3.85410 −0.209326
\(340\) 18.7082 1.01459
\(341\) −8.72949 −0.472728
\(342\) −18.7082 −1.01162
\(343\) −1.00000 −0.0539949
\(344\) −93.8673 −5.06098
\(345\) −30.6525 −1.65027
\(346\) 23.5623 1.26672
\(347\) 30.7639 1.65149 0.825747 0.564040i \(-0.190754\pi\)
0.825747 + 0.564040i \(0.190754\pi\)
\(348\) −90.1033 −4.83005
\(349\) −20.7082 −1.10848 −0.554242 0.832355i \(-0.686992\pi\)
−0.554242 + 0.832355i \(0.686992\pi\)
\(350\) 4.85410 0.259463
\(351\) 0 0
\(352\) 20.1246 1.07265
\(353\) −22.1459 −1.17871 −0.589354 0.807875i \(-0.700618\pi\)
−0.589354 + 0.807875i \(0.700618\pi\)
\(354\) 15.3262 0.814580
\(355\) −37.1246 −1.97037
\(356\) −23.8328 −1.26314
\(357\) −3.85410 −0.203981
\(358\) 23.5623 1.24531
\(359\) 22.0902 1.16587 0.582937 0.812517i \(-0.301903\pi\)
0.582937 + 0.812517i \(0.301903\pi\)
\(360\) 75.3951 3.97367
\(361\) −15.5623 −0.819069
\(362\) −25.4164 −1.33586
\(363\) 19.7984 1.03915
\(364\) 0 0
\(365\) −5.23607 −0.274068
\(366\) −41.1246 −2.14962
\(367\) −1.41641 −0.0739359 −0.0369679 0.999316i \(-0.511770\pi\)
−0.0369679 + 0.999316i \(0.511770\pi\)
\(368\) −44.0689 −2.29725
\(369\) −2.94427 −0.153273
\(370\) −27.4164 −1.42531
\(371\) −3.76393 −0.195414
\(372\) −59.8328 −3.10219
\(373\) −20.5623 −1.06468 −0.532338 0.846532i \(-0.678686\pi\)
−0.532338 + 0.846532i \(0.678686\pi\)
\(374\) −7.14590 −0.369506
\(375\) −21.5623 −1.11347
\(376\) −16.7082 −0.861660
\(377\) 0 0
\(378\) −5.85410 −0.301103
\(379\) 6.14590 0.315694 0.157847 0.987464i \(-0.449545\pi\)
0.157847 + 0.987464i \(0.449545\pi\)
\(380\) −23.5623 −1.20872
\(381\) 54.5967 2.79708
\(382\) −55.9787 −2.86412
\(383\) 21.9787 1.12306 0.561530 0.827456i \(-0.310213\pi\)
0.561530 + 0.827456i \(0.310213\pi\)
\(384\) 2.85410 0.145648
\(385\) −4.85410 −0.247388
\(386\) −15.7082 −0.799527
\(387\) 48.4164 2.46114
\(388\) −91.5197 −4.64621
\(389\) −11.8885 −0.602773 −0.301387 0.953502i \(-0.597449\pi\)
−0.301387 + 0.953502i \(0.597449\pi\)
\(390\) 0 0
\(391\) 6.58359 0.332947
\(392\) −7.47214 −0.377400
\(393\) 40.1246 2.02402
\(394\) −43.9787 −2.21562
\(395\) −10.4721 −0.526910
\(396\) −34.6869 −1.74308
\(397\) −1.41641 −0.0710875 −0.0355437 0.999368i \(-0.511316\pi\)
−0.0355437 + 0.999368i \(0.511316\pi\)
\(398\) 63.9230 3.20417
\(399\) 4.85410 0.243009
\(400\) 18.2705 0.913525
\(401\) −35.4508 −1.77033 −0.885165 0.465276i \(-0.845955\pi\)
−0.885165 + 0.465276i \(0.845955\pi\)
\(402\) 87.1033 4.34432
\(403\) 0 0
\(404\) −56.1246 −2.79230
\(405\) 14.9443 0.742587
\(406\) 18.5623 0.921232
\(407\) 7.41641 0.367618
\(408\) −28.7984 −1.42573
\(409\) −14.4377 −0.713898 −0.356949 0.934124i \(-0.616183\pi\)
−0.356949 + 0.934124i \(0.616183\pi\)
\(410\) −5.23607 −0.258591
\(411\) −6.85410 −0.338088
\(412\) −42.2705 −2.08252
\(413\) −2.23607 −0.110030
\(414\) 45.1246 2.21775
\(415\) 17.5623 0.862100
\(416\) 0 0
\(417\) −11.9443 −0.584914
\(418\) 9.00000 0.440204
\(419\) −11.9443 −0.583516 −0.291758 0.956492i \(-0.594240\pi\)
−0.291758 + 0.956492i \(0.594240\pi\)
\(420\) −33.2705 −1.62343
\(421\) −1.41641 −0.0690315 −0.0345157 0.999404i \(-0.510989\pi\)
−0.0345157 + 0.999404i \(0.510989\pi\)
\(422\) −12.3262 −0.600032
\(423\) 8.61803 0.419023
\(424\) −28.1246 −1.36585
\(425\) −2.72949 −0.132400
\(426\) 97.1935 4.70904
\(427\) 6.00000 0.290360
\(428\) −16.4164 −0.793517
\(429\) 0 0
\(430\) 86.1033 4.15227
\(431\) −7.79837 −0.375634 −0.187817 0.982204i \(-0.560141\pi\)
−0.187817 + 0.982204i \(0.560141\pi\)
\(432\) −22.0344 −1.06013
\(433\) 1.00000 0.0480569 0.0240285 0.999711i \(-0.492351\pi\)
0.0240285 + 0.999711i \(0.492351\pi\)
\(434\) 12.3262 0.591678
\(435\) 48.5967 2.33004
\(436\) 13.1459 0.629574
\(437\) −8.29180 −0.396650
\(438\) 13.7082 0.655003
\(439\) 14.8541 0.708948 0.354474 0.935066i \(-0.384660\pi\)
0.354474 + 0.935066i \(0.384660\pi\)
\(440\) −36.2705 −1.72913
\(441\) 3.85410 0.183529
\(442\) 0 0
\(443\) −5.23607 −0.248773 −0.124387 0.992234i \(-0.539696\pi\)
−0.124387 + 0.992234i \(0.539696\pi\)
\(444\) 50.8328 2.41242
\(445\) 12.8541 0.609343
\(446\) 53.0689 2.51288
\(447\) 4.85410 0.229591
\(448\) −8.70820 −0.411424
\(449\) −19.5279 −0.921577 −0.460788 0.887510i \(-0.652433\pi\)
−0.460788 + 0.887510i \(0.652433\pi\)
\(450\) −18.7082 −0.881913
\(451\) 1.41641 0.0666960
\(452\) 7.14590 0.336115
\(453\) −3.38197 −0.158899
\(454\) 3.85410 0.180882
\(455\) 0 0
\(456\) 36.2705 1.69852
\(457\) −15.4164 −0.721149 −0.360575 0.932730i \(-0.617419\pi\)
−0.360575 + 0.932730i \(0.617419\pi\)
\(458\) −34.3607 −1.60557
\(459\) 3.29180 0.153648
\(460\) 56.8328 2.64984
\(461\) 12.2148 0.568899 0.284450 0.958691i \(-0.408189\pi\)
0.284450 + 0.958691i \(0.408189\pi\)
\(462\) 12.7082 0.591239
\(463\) −6.70820 −0.311757 −0.155878 0.987776i \(-0.549821\pi\)
−0.155878 + 0.987776i \(0.549821\pi\)
\(464\) 69.8673 3.24351
\(465\) 32.2705 1.49651
\(466\) −6.85410 −0.317510
\(467\) 2.34752 0.108630 0.0543152 0.998524i \(-0.482702\pi\)
0.0543152 + 0.998524i \(0.482702\pi\)
\(468\) 0 0
\(469\) −12.7082 −0.586810
\(470\) 15.3262 0.706947
\(471\) −38.8885 −1.79189
\(472\) −16.7082 −0.769057
\(473\) −23.2918 −1.07096
\(474\) 27.4164 1.25928
\(475\) 3.43769 0.157732
\(476\) 7.14590 0.327532
\(477\) 14.5066 0.664211
\(478\) −64.6869 −2.95871
\(479\) −24.9787 −1.14131 −0.570653 0.821191i \(-0.693310\pi\)
−0.570653 + 0.821191i \(0.693310\pi\)
\(480\) −74.3951 −3.39566
\(481\) 0 0
\(482\) 64.3050 2.92901
\(483\) −11.7082 −0.532742
\(484\) −36.7082 −1.66855
\(485\) 49.3607 2.24135
\(486\) −56.6869 −2.57137
\(487\) −29.9787 −1.35847 −0.679233 0.733923i \(-0.737687\pi\)
−0.679233 + 0.733923i \(0.737687\pi\)
\(488\) 44.8328 2.02949
\(489\) −9.70820 −0.439020
\(490\) 6.85410 0.309637
\(491\) 12.3820 0.558790 0.279395 0.960176i \(-0.409866\pi\)
0.279395 + 0.960176i \(0.409866\pi\)
\(492\) 9.70820 0.437680
\(493\) −10.4377 −0.470090
\(494\) 0 0
\(495\) 18.7082 0.840871
\(496\) 46.3951 2.08320
\(497\) −14.1803 −0.636075
\(498\) −45.9787 −2.06036
\(499\) −14.8541 −0.664961 −0.332480 0.943110i \(-0.607886\pi\)
−0.332480 + 0.943110i \(0.607886\pi\)
\(500\) 39.9787 1.78790
\(501\) 37.2705 1.66512
\(502\) −2.00000 −0.0892644
\(503\) 26.6180 1.18684 0.593420 0.804893i \(-0.297777\pi\)
0.593420 + 0.804893i \(0.297777\pi\)
\(504\) 28.7984 1.28278
\(505\) 30.2705 1.34702
\(506\) −21.7082 −0.965047
\(507\) 0 0
\(508\) −101.228 −4.49126
\(509\) 18.5967 0.824286 0.412143 0.911119i \(-0.364780\pi\)
0.412143 + 0.911119i \(0.364780\pi\)
\(510\) 26.4164 1.16974
\(511\) −2.00000 −0.0884748
\(512\) 40.3050 1.78124
\(513\) −4.14590 −0.183046
\(514\) −43.8328 −1.93338
\(515\) 22.7984 1.00462
\(516\) −159.644 −7.02795
\(517\) −4.14590 −0.182336
\(518\) −10.4721 −0.460119
\(519\) 23.5623 1.03427
\(520\) 0 0
\(521\) 18.6525 0.817180 0.408590 0.912718i \(-0.366021\pi\)
0.408590 + 0.912718i \(0.366021\pi\)
\(522\) −71.5410 −3.13127
\(523\) 1.12461 0.0491758 0.0245879 0.999698i \(-0.492173\pi\)
0.0245879 + 0.999698i \(0.492173\pi\)
\(524\) −74.3951 −3.24997
\(525\) 4.85410 0.211850
\(526\) −23.5623 −1.02737
\(527\) −6.93112 −0.301924
\(528\) 47.8328 2.08166
\(529\) −3.00000 −0.130435
\(530\) 25.7984 1.12061
\(531\) 8.61803 0.373991
\(532\) −9.00000 −0.390199
\(533\) 0 0
\(534\) −33.6525 −1.45629
\(535\) 8.85410 0.382796
\(536\) −94.9574 −4.10154
\(537\) 23.5623 1.01679
\(538\) 75.2492 3.24422
\(539\) −1.85410 −0.0798618
\(540\) 28.4164 1.22285
\(541\) −35.2705 −1.51640 −0.758199 0.652023i \(-0.773920\pi\)
−0.758199 + 0.652023i \(0.773920\pi\)
\(542\) −22.0344 −0.946460
\(543\) −25.4164 −1.09072
\(544\) 15.9787 0.685082
\(545\) −7.09017 −0.303710
\(546\) 0 0
\(547\) −3.00000 −0.128271 −0.0641354 0.997941i \(-0.520429\pi\)
−0.0641354 + 0.997941i \(0.520429\pi\)
\(548\) 12.7082 0.542868
\(549\) −23.1246 −0.986934
\(550\) 9.00000 0.383761
\(551\) 13.1459 0.560034
\(552\) −87.4853 −3.72362
\(553\) −4.00000 −0.170097
\(554\) 13.0902 0.556148
\(555\) −27.4164 −1.16376
\(556\) 22.1459 0.939195
\(557\) 27.9787 1.18550 0.592748 0.805388i \(-0.298043\pi\)
0.592748 + 0.805388i \(0.298043\pi\)
\(558\) −47.5066 −2.01111
\(559\) 0 0
\(560\) 25.7984 1.09018
\(561\) −7.14590 −0.301700
\(562\) 52.8328 2.22862
\(563\) −21.0557 −0.887393 −0.443697 0.896177i \(-0.646333\pi\)
−0.443697 + 0.896177i \(0.646333\pi\)
\(564\) −28.4164 −1.19655
\(565\) −3.85410 −0.162143
\(566\) −35.1246 −1.47640
\(567\) 5.70820 0.239722
\(568\) −105.957 −4.44587
\(569\) 14.9443 0.626496 0.313248 0.949671i \(-0.398583\pi\)
0.313248 + 0.949671i \(0.398583\pi\)
\(570\) −33.2705 −1.39355
\(571\) 24.6869 1.03312 0.516558 0.856252i \(-0.327213\pi\)
0.516558 + 0.856252i \(0.327213\pi\)
\(572\) 0 0
\(573\) −55.9787 −2.33854
\(574\) −2.00000 −0.0834784
\(575\) −8.29180 −0.345792
\(576\) 33.5623 1.39843
\(577\) 43.8328 1.82478 0.912392 0.409318i \(-0.134233\pi\)
0.912392 + 0.409318i \(0.134233\pi\)
\(578\) 38.8328 1.61523
\(579\) −15.7082 −0.652811
\(580\) −90.1033 −3.74134
\(581\) 6.70820 0.278303
\(582\) −129.228 −5.35667
\(583\) −6.97871 −0.289029
\(584\) −14.9443 −0.618398
\(585\) 0 0
\(586\) −17.7082 −0.731519
\(587\) 19.9098 0.821767 0.410883 0.911688i \(-0.365220\pi\)
0.410883 + 0.911688i \(0.365220\pi\)
\(588\) −12.7082 −0.524077
\(589\) 8.72949 0.359692
\(590\) 15.3262 0.630971
\(591\) −43.9787 −1.80904
\(592\) −39.4164 −1.62000
\(593\) −43.7984 −1.79858 −0.899292 0.437349i \(-0.855917\pi\)
−0.899292 + 0.437349i \(0.855917\pi\)
\(594\) −10.8541 −0.445349
\(595\) −3.85410 −0.158003
\(596\) −9.00000 −0.368654
\(597\) 63.9230 2.61619
\(598\) 0 0
\(599\) 29.5066 1.20561 0.602803 0.797890i \(-0.294050\pi\)
0.602803 + 0.797890i \(0.294050\pi\)
\(600\) 36.2705 1.48074
\(601\) 40.3951 1.64775 0.823876 0.566771i \(-0.191807\pi\)
0.823876 + 0.566771i \(0.191807\pi\)
\(602\) 32.8885 1.34044
\(603\) 48.9787 1.99457
\(604\) 6.27051 0.255143
\(605\) 19.7984 0.804918
\(606\) −79.2492 −3.21928
\(607\) −23.0000 −0.933541 −0.466771 0.884378i \(-0.654583\pi\)
−0.466771 + 0.884378i \(0.654583\pi\)
\(608\) −20.1246 −0.816161
\(609\) 18.5623 0.752183
\(610\) −41.1246 −1.66509
\(611\) 0 0
\(612\) −27.5410 −1.11328
\(613\) −34.5623 −1.39596 −0.697979 0.716118i \(-0.745917\pi\)
−0.697979 + 0.716118i \(0.745917\pi\)
\(614\) −12.7082 −0.512861
\(615\) −5.23607 −0.211139
\(616\) −13.8541 −0.558198
\(617\) −0.0557281 −0.00224353 −0.00112176 0.999999i \(-0.500357\pi\)
−0.00112176 + 0.999999i \(0.500357\pi\)
\(618\) −59.6869 −2.40096
\(619\) −9.41641 −0.378477 −0.189239 0.981931i \(-0.560602\pi\)
−0.189239 + 0.981931i \(0.560602\pi\)
\(620\) −59.8328 −2.40294
\(621\) 10.0000 0.401286
\(622\) −8.70820 −0.349167
\(623\) 4.90983 0.196708
\(624\) 0 0
\(625\) −30.8328 −1.23331
\(626\) −65.7771 −2.62898
\(627\) 9.00000 0.359425
\(628\) 72.1033 2.87724
\(629\) 5.88854 0.234792
\(630\) −26.4164 −1.05245
\(631\) −34.3951 −1.36925 −0.684624 0.728896i \(-0.740034\pi\)
−0.684624 + 0.728896i \(0.740034\pi\)
\(632\) −29.8885 −1.18890
\(633\) −12.3262 −0.489924
\(634\) 68.6869 2.72791
\(635\) 54.5967 2.16661
\(636\) −47.8328 −1.89669
\(637\) 0 0
\(638\) 34.4164 1.36256
\(639\) 54.6525 2.16202
\(640\) 2.85410 0.112818
\(641\) −47.5066 −1.87640 −0.938199 0.346098i \(-0.887507\pi\)
−0.938199 + 0.346098i \(0.887507\pi\)
\(642\) −23.1803 −0.914855
\(643\) 7.00000 0.276053 0.138027 0.990429i \(-0.455924\pi\)
0.138027 + 0.990429i \(0.455924\pi\)
\(644\) 21.7082 0.855423
\(645\) 86.1033 3.39032
\(646\) 7.14590 0.281152
\(647\) 24.7639 0.973571 0.486785 0.873522i \(-0.338169\pi\)
0.486785 + 0.873522i \(0.338169\pi\)
\(648\) 42.6525 1.67555
\(649\) −4.14590 −0.162741
\(650\) 0 0
\(651\) 12.3262 0.483103
\(652\) 18.0000 0.704934
\(653\) −0.381966 −0.0149475 −0.00747374 0.999972i \(-0.502379\pi\)
−0.00747374 + 0.999972i \(0.502379\pi\)
\(654\) 18.5623 0.725844
\(655\) 40.1246 1.56780
\(656\) −7.52786 −0.293914
\(657\) 7.70820 0.300726
\(658\) 5.85410 0.228217
\(659\) −23.8885 −0.930566 −0.465283 0.885162i \(-0.654047\pi\)
−0.465283 + 0.885162i \(0.654047\pi\)
\(660\) −61.6869 −2.40116
\(661\) 48.5410 1.88803 0.944013 0.329907i \(-0.107017\pi\)
0.944013 + 0.329907i \(0.107017\pi\)
\(662\) −26.5623 −1.03237
\(663\) 0 0
\(664\) 50.1246 1.94521
\(665\) 4.85410 0.188234
\(666\) 40.3607 1.56394
\(667\) −31.7082 −1.22775
\(668\) −69.1033 −2.67369
\(669\) 53.0689 2.05176
\(670\) 87.1033 3.36510
\(671\) 11.1246 0.429461
\(672\) −28.4164 −1.09619
\(673\) −39.2492 −1.51295 −0.756473 0.654025i \(-0.773079\pi\)
−0.756473 + 0.654025i \(0.773079\pi\)
\(674\) 30.2705 1.16598
\(675\) −4.14590 −0.159576
\(676\) 0 0
\(677\) 43.7426 1.68117 0.840583 0.541682i \(-0.182212\pi\)
0.840583 + 0.541682i \(0.182212\pi\)
\(678\) 10.0902 0.387511
\(679\) 18.8541 0.723554
\(680\) −28.7984 −1.10437
\(681\) 3.85410 0.147690
\(682\) 22.8541 0.875129
\(683\) −1.47214 −0.0563297 −0.0281649 0.999603i \(-0.508966\pi\)
−0.0281649 + 0.999603i \(0.508966\pi\)
\(684\) 34.6869 1.32629
\(685\) −6.85410 −0.261882
\(686\) 2.61803 0.0999570
\(687\) −34.3607 −1.31094
\(688\) 123.790 4.71946
\(689\) 0 0
\(690\) 80.2492 3.05504
\(691\) 5.85410 0.222701 0.111350 0.993781i \(-0.464482\pi\)
0.111350 + 0.993781i \(0.464482\pi\)
\(692\) −43.6869 −1.66073
\(693\) 7.14590 0.271450
\(694\) −80.5410 −3.05730
\(695\) −11.9443 −0.453072
\(696\) 138.700 5.25741
\(697\) 1.12461 0.0425977
\(698\) 54.2148 2.05206
\(699\) −6.85410 −0.259246
\(700\) −9.00000 −0.340168
\(701\) 11.2361 0.424380 0.212190 0.977228i \(-0.431940\pi\)
0.212190 + 0.977228i \(0.431940\pi\)
\(702\) 0 0
\(703\) −7.41641 −0.279715
\(704\) −16.1459 −0.608521
\(705\) 15.3262 0.577220
\(706\) 57.9787 2.18206
\(707\) 11.5623 0.434845
\(708\) −28.4164 −1.06795
\(709\) −23.5623 −0.884901 −0.442450 0.896793i \(-0.645891\pi\)
−0.442450 + 0.896793i \(0.645891\pi\)
\(710\) 97.1935 3.64761
\(711\) 15.4164 0.578160
\(712\) 36.6869 1.37490
\(713\) −21.0557 −0.788543
\(714\) 10.0902 0.377615
\(715\) 0 0
\(716\) −43.6869 −1.63266
\(717\) −64.6869 −2.41578
\(718\) −57.8328 −2.15830
\(719\) 8.12461 0.302997 0.151498 0.988457i \(-0.451590\pi\)
0.151498 + 0.988457i \(0.451590\pi\)
\(720\) −99.4296 −3.70552
\(721\) 8.70820 0.324310
\(722\) 40.7426 1.51628
\(723\) 64.3050 2.39153
\(724\) 47.1246 1.75137
\(725\) 13.1459 0.488226
\(726\) −51.8328 −1.92370
\(727\) −30.7082 −1.13890 −0.569452 0.822025i \(-0.692845\pi\)
−0.569452 + 0.822025i \(0.692845\pi\)
\(728\) 0 0
\(729\) −39.5623 −1.46527
\(730\) 13.7082 0.507363
\(731\) −18.4934 −0.684004
\(732\) 76.2492 2.81825
\(733\) 32.2705 1.19194 0.595969 0.803007i \(-0.296768\pi\)
0.595969 + 0.803007i \(0.296768\pi\)
\(734\) 3.70820 0.136872
\(735\) 6.85410 0.252817
\(736\) 48.5410 1.78925
\(737\) −23.5623 −0.867929
\(738\) 7.70820 0.283743
\(739\) 6.87539 0.252915 0.126458 0.991972i \(-0.459639\pi\)
0.126458 + 0.991972i \(0.459639\pi\)
\(740\) 50.8328 1.86865
\(741\) 0 0
\(742\) 9.85410 0.361755
\(743\) −39.3262 −1.44274 −0.721370 0.692550i \(-0.756487\pi\)
−0.721370 + 0.692550i \(0.756487\pi\)
\(744\) 92.1033 3.37667
\(745\) 4.85410 0.177841
\(746\) 53.8328 1.97096
\(747\) −25.8541 −0.945952
\(748\) 13.2492 0.484440
\(749\) 3.38197 0.123574
\(750\) 56.4508 2.06129
\(751\) 22.7082 0.828634 0.414317 0.910133i \(-0.364020\pi\)
0.414317 + 0.910133i \(0.364020\pi\)
\(752\) 22.0344 0.803513
\(753\) −2.00000 −0.0728841
\(754\) 0 0
\(755\) −3.38197 −0.123082
\(756\) 10.8541 0.394760
\(757\) 28.0000 1.01768 0.508839 0.860862i \(-0.330075\pi\)
0.508839 + 0.860862i \(0.330075\pi\)
\(758\) −16.0902 −0.584421
\(759\) −21.7082 −0.787958
\(760\) 36.2705 1.31567
\(761\) 28.8541 1.04596 0.522980 0.852345i \(-0.324820\pi\)
0.522980 + 0.852345i \(0.324820\pi\)
\(762\) −142.936 −5.17803
\(763\) −2.70820 −0.0980436
\(764\) 103.790 3.75500
\(765\) 14.8541 0.537051
\(766\) −57.5410 −2.07904
\(767\) 0 0
\(768\) 38.1246 1.37570
\(769\) 18.4164 0.664113 0.332056 0.943260i \(-0.392258\pi\)
0.332056 + 0.943260i \(0.392258\pi\)
\(770\) 12.7082 0.457972
\(771\) −43.8328 −1.57860
\(772\) 29.1246 1.04822
\(773\) −25.3607 −0.912160 −0.456080 0.889939i \(-0.650747\pi\)
−0.456080 + 0.889939i \(0.650747\pi\)
\(774\) −126.756 −4.55614
\(775\) 8.72949 0.313573
\(776\) 140.880 5.05731
\(777\) −10.4721 −0.375686
\(778\) 31.1246 1.11587
\(779\) −1.41641 −0.0507481
\(780\) 0 0
\(781\) −26.2918 −0.940794
\(782\) −17.2361 −0.616361
\(783\) −15.8541 −0.566579
\(784\) 9.85410 0.351932
\(785\) −38.8885 −1.38799
\(786\) −105.048 −3.74692
\(787\) −2.58359 −0.0920951 −0.0460476 0.998939i \(-0.514663\pi\)
−0.0460476 + 0.998939i \(0.514663\pi\)
\(788\) 81.5410 2.90478
\(789\) −23.5623 −0.838840
\(790\) 27.4164 0.975432
\(791\) −1.47214 −0.0523431
\(792\) 53.3951 1.89731
\(793\) 0 0
\(794\) 3.70820 0.131599
\(795\) 25.7984 0.914974
\(796\) −118.520 −4.20082
\(797\) −8.18034 −0.289763 −0.144881 0.989449i \(-0.546280\pi\)
−0.144881 + 0.989449i \(0.546280\pi\)
\(798\) −12.7082 −0.449866
\(799\) −3.29180 −0.116455
\(800\) −20.1246 −0.711512
\(801\) −18.9230 −0.668611
\(802\) 92.8115 3.27729
\(803\) −3.70820 −0.130860
\(804\) −161.498 −5.69561
\(805\) −11.7082 −0.412660
\(806\) 0 0
\(807\) 75.2492 2.64890
\(808\) 86.3951 3.03937
\(809\) −4.41641 −0.155273 −0.0776363 0.996982i \(-0.524737\pi\)
−0.0776363 + 0.996982i \(0.524737\pi\)
\(810\) −39.1246 −1.37470
\(811\) −39.2705 −1.37897 −0.689487 0.724298i \(-0.742164\pi\)
−0.689487 + 0.724298i \(0.742164\pi\)
\(812\) −34.4164 −1.20778
\(813\) −22.0344 −0.772782
\(814\) −19.4164 −0.680545
\(815\) −9.70820 −0.340064
\(816\) 37.9787 1.32952
\(817\) 23.2918 0.814877
\(818\) 37.7984 1.32159
\(819\) 0 0
\(820\) 9.70820 0.339025
\(821\) 7.36068 0.256889 0.128445 0.991717i \(-0.459002\pi\)
0.128445 + 0.991717i \(0.459002\pi\)
\(822\) 17.9443 0.625878
\(823\) −38.4164 −1.33911 −0.669556 0.742762i \(-0.733516\pi\)
−0.669556 + 0.742762i \(0.733516\pi\)
\(824\) 65.0689 2.26678
\(825\) 9.00000 0.313340
\(826\) 5.85410 0.203690
\(827\) −15.9787 −0.555634 −0.277817 0.960634i \(-0.589611\pi\)
−0.277817 + 0.960634i \(0.589611\pi\)
\(828\) −83.6656 −2.90758
\(829\) 7.56231 0.262650 0.131325 0.991339i \(-0.458077\pi\)
0.131325 + 0.991339i \(0.458077\pi\)
\(830\) −45.9787 −1.59594
\(831\) 13.0902 0.454093
\(832\) 0 0
\(833\) −1.47214 −0.0510065
\(834\) 31.2705 1.08281
\(835\) 37.2705 1.28980
\(836\) −16.6869 −0.577129
\(837\) −10.5279 −0.363896
\(838\) 31.2705 1.08022
\(839\) −13.7426 −0.474449 −0.237224 0.971455i \(-0.576238\pi\)
−0.237224 + 0.971455i \(0.576238\pi\)
\(840\) 51.2148 1.76708
\(841\) 21.2705 0.733466
\(842\) 3.70820 0.127793
\(843\) 52.8328 1.81966
\(844\) 22.8541 0.786671
\(845\) 0 0
\(846\) −22.5623 −0.775708
\(847\) 7.56231 0.259844
\(848\) 37.0902 1.27368
\(849\) −35.1246 −1.20547
\(850\) 7.14590 0.245102
\(851\) 17.8885 0.613211
\(852\) −180.207 −6.17378
\(853\) −14.1246 −0.483617 −0.241809 0.970324i \(-0.577741\pi\)
−0.241809 + 0.970324i \(0.577741\pi\)
\(854\) −15.7082 −0.537524
\(855\) −18.7082 −0.639807
\(856\) 25.2705 0.863728
\(857\) −26.4508 −0.903544 −0.451772 0.892133i \(-0.649208\pi\)
−0.451772 + 0.892133i \(0.649208\pi\)
\(858\) 0 0
\(859\) −44.2492 −1.50976 −0.754882 0.655861i \(-0.772306\pi\)
−0.754882 + 0.655861i \(0.772306\pi\)
\(860\) −159.644 −5.44383
\(861\) −2.00000 −0.0681598
\(862\) 20.4164 0.695386
\(863\) −11.8885 −0.404691 −0.202345 0.979314i \(-0.564856\pi\)
−0.202345 + 0.979314i \(0.564856\pi\)
\(864\) 24.2705 0.825700
\(865\) 23.5623 0.801142
\(866\) −2.61803 −0.0889644
\(867\) 38.8328 1.31883
\(868\) −22.8541 −0.775719
\(869\) −7.41641 −0.251584
\(870\) −127.228 −4.31343
\(871\) 0 0
\(872\) −20.2361 −0.685280
\(873\) −72.6656 −2.45936
\(874\) 21.7082 0.734291
\(875\) −8.23607 −0.278430
\(876\) −25.4164 −0.858741
\(877\) −0.708204 −0.0239143 −0.0119572 0.999929i \(-0.503806\pi\)
−0.0119572 + 0.999929i \(0.503806\pi\)
\(878\) −38.8885 −1.31242
\(879\) −17.7082 −0.597283
\(880\) 47.8328 1.61244
\(881\) −36.5967 −1.23298 −0.616488 0.787364i \(-0.711445\pi\)
−0.616488 + 0.787364i \(0.711445\pi\)
\(882\) −10.0902 −0.339754
\(883\) 29.0000 0.975928 0.487964 0.872864i \(-0.337740\pi\)
0.487964 + 0.872864i \(0.337740\pi\)
\(884\) 0 0
\(885\) 15.3262 0.515186
\(886\) 13.7082 0.460536
\(887\) 54.6525 1.83505 0.917525 0.397677i \(-0.130184\pi\)
0.917525 + 0.397677i \(0.130184\pi\)
\(888\) −78.2492 −2.62587
\(889\) 20.8541 0.699424
\(890\) −33.6525 −1.12803
\(891\) 10.5836 0.354564
\(892\) −98.3951 −3.29451
\(893\) 4.14590 0.138737
\(894\) −12.7082 −0.425026
\(895\) 23.5623 0.787601
\(896\) 1.09017 0.0364200
\(897\) 0 0
\(898\) 51.1246 1.70605
\(899\) 33.3820 1.11335
\(900\) 34.6869 1.15623
\(901\) −5.54102 −0.184598
\(902\) −3.70820 −0.123470
\(903\) 32.8885 1.09446
\(904\) −11.0000 −0.365855
\(905\) −25.4164 −0.844870
\(906\) 8.85410 0.294158
\(907\) −24.0000 −0.796907 −0.398453 0.917189i \(-0.630453\pi\)
−0.398453 + 0.917189i \(0.630453\pi\)
\(908\) −7.14590 −0.237145
\(909\) −44.5623 −1.47804
\(910\) 0 0
\(911\) −22.6869 −0.751651 −0.375826 0.926690i \(-0.622641\pi\)
−0.375826 + 0.926690i \(0.622641\pi\)
\(912\) −47.8328 −1.58390
\(913\) 12.4377 0.411628
\(914\) 40.3607 1.33501
\(915\) −41.1246 −1.35954
\(916\) 63.7082 2.10498
\(917\) 15.3262 0.506117
\(918\) −8.61803 −0.284438
\(919\) −30.0000 −0.989609 −0.494804 0.869004i \(-0.664760\pi\)
−0.494804 + 0.869004i \(0.664760\pi\)
\(920\) −87.4853 −2.88430
\(921\) −12.7082 −0.418750
\(922\) −31.9787 −1.05316
\(923\) 0 0
\(924\) −23.5623 −0.775143
\(925\) −7.41641 −0.243850
\(926\) 17.5623 0.577133
\(927\) −33.5623 −1.10233
\(928\) −76.9574 −2.52625
\(929\) −11.0689 −0.363158 −0.181579 0.983376i \(-0.558121\pi\)
−0.181579 + 0.983376i \(0.558121\pi\)
\(930\) −84.4853 −2.77038
\(931\) 1.85410 0.0607657
\(932\) 12.7082 0.416271
\(933\) −8.70820 −0.285094
\(934\) −6.14590 −0.201100
\(935\) −7.14590 −0.233696
\(936\) 0 0
\(937\) −15.8754 −0.518626 −0.259313 0.965793i \(-0.583496\pi\)
−0.259313 + 0.965793i \(0.583496\pi\)
\(938\) 33.2705 1.08632
\(939\) −65.7771 −2.14655
\(940\) −28.4164 −0.926841
\(941\) −20.3475 −0.663310 −0.331655 0.943401i \(-0.607607\pi\)
−0.331655 + 0.943401i \(0.607607\pi\)
\(942\) 101.812 3.31720
\(943\) 3.41641 0.111254
\(944\) 22.0344 0.717160
\(945\) −5.85410 −0.190434
\(946\) 60.9787 1.98259
\(947\) 36.8673 1.19802 0.599012 0.800740i \(-0.295560\pi\)
0.599012 + 0.800740i \(0.295560\pi\)
\(948\) −50.8328 −1.65097
\(949\) 0 0
\(950\) −9.00000 −0.291999
\(951\) 68.6869 2.22733
\(952\) −11.0000 −0.356512
\(953\) 26.7771 0.867395 0.433697 0.901059i \(-0.357209\pi\)
0.433697 + 0.901059i \(0.357209\pi\)
\(954\) −37.9787 −1.22961
\(955\) −55.9787 −1.81143
\(956\) 119.936 3.87901
\(957\) 34.4164 1.11252
\(958\) 65.3951 2.11282
\(959\) −2.61803 −0.0845407
\(960\) 59.6869 1.92639
\(961\) −8.83282 −0.284930
\(962\) 0 0
\(963\) −13.0344 −0.420029
\(964\) −119.228 −3.84007
\(965\) −15.7082 −0.505665
\(966\) 30.6525 0.986227
\(967\) 39.0000 1.25416 0.627078 0.778957i \(-0.284251\pi\)
0.627078 + 0.778957i \(0.284251\pi\)
\(968\) 56.5066 1.81619
\(969\) 7.14590 0.229559
\(970\) −129.228 −4.14926
\(971\) 31.5836 1.01357 0.506783 0.862074i \(-0.330835\pi\)
0.506783 + 0.862074i \(0.330835\pi\)
\(972\) 105.103 3.37119
\(973\) −4.56231 −0.146261
\(974\) 78.4853 2.51483
\(975\) 0 0
\(976\) −59.1246 −1.89253
\(977\) 22.5279 0.720730 0.360365 0.932811i \(-0.382652\pi\)
0.360365 + 0.932811i \(0.382652\pi\)
\(978\) 25.4164 0.812727
\(979\) 9.10333 0.290944
\(980\) −12.7082 −0.405949
\(981\) 10.4377 0.333250
\(982\) −32.4164 −1.03445
\(983\) −18.3820 −0.586294 −0.293147 0.956067i \(-0.594702\pi\)
−0.293147 + 0.956067i \(0.594702\pi\)
\(984\) −14.9443 −0.476406
\(985\) −43.9787 −1.40128
\(986\) 27.3262 0.870245
\(987\) 5.85410 0.186338
\(988\) 0 0
\(989\) −56.1803 −1.78643
\(990\) −48.9787 −1.55665
\(991\) −16.1459 −0.512891 −0.256446 0.966559i \(-0.582551\pi\)
−0.256446 + 0.966559i \(0.582551\pi\)
\(992\) −51.1033 −1.62253
\(993\) −26.5623 −0.842929
\(994\) 37.1246 1.17752
\(995\) 63.9230 2.02649
\(996\) 85.2492 2.70123
\(997\) 49.0000 1.55185 0.775923 0.630828i \(-0.217285\pi\)
0.775923 + 0.630828i \(0.217285\pi\)
\(998\) 38.8885 1.23100
\(999\) 8.94427 0.282984
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 1183.2.a.c.1.1 2
7.6 odd 2 8281.2.a.n.1.1 2
13.4 even 6 91.2.f.a.29.1 yes 4
13.5 odd 4 1183.2.c.c.337.4 4
13.8 odd 4 1183.2.c.c.337.1 4
13.10 even 6 91.2.f.a.22.1 4
13.12 even 2 1183.2.a.g.1.2 2
39.17 odd 6 819.2.o.c.757.2 4
39.23 odd 6 819.2.o.c.568.2 4
52.23 odd 6 1456.2.s.h.113.1 4
52.43 odd 6 1456.2.s.h.1121.1 4
91.4 even 6 637.2.h.g.471.2 4
91.10 odd 6 637.2.g.c.373.1 4
91.17 odd 6 637.2.h.f.471.2 4
91.23 even 6 637.2.h.g.165.2 4
91.30 even 6 637.2.g.b.263.1 4
91.62 odd 6 637.2.f.c.295.1 4
91.69 odd 6 637.2.f.c.393.1 4
91.75 odd 6 637.2.h.f.165.2 4
91.82 odd 6 637.2.g.c.263.1 4
91.88 even 6 637.2.g.b.373.1 4
91.90 odd 2 8281.2.a.bb.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.f.a.22.1 4 13.10 even 6
91.2.f.a.29.1 yes 4 13.4 even 6
637.2.f.c.295.1 4 91.62 odd 6
637.2.f.c.393.1 4 91.69 odd 6
637.2.g.b.263.1 4 91.30 even 6
637.2.g.b.373.1 4 91.88 even 6
637.2.g.c.263.1 4 91.82 odd 6
637.2.g.c.373.1 4 91.10 odd 6
637.2.h.f.165.2 4 91.75 odd 6
637.2.h.f.471.2 4 91.17 odd 6
637.2.h.g.165.2 4 91.23 even 6
637.2.h.g.471.2 4 91.4 even 6
819.2.o.c.568.2 4 39.23 odd 6
819.2.o.c.757.2 4 39.17 odd 6
1183.2.a.c.1.1 2 1.1 even 1 trivial
1183.2.a.g.1.2 2 13.12 even 2
1183.2.c.c.337.1 4 13.8 odd 4
1183.2.c.c.337.4 4 13.5 odd 4
1456.2.s.h.113.1 4 52.23 odd 6
1456.2.s.h.1121.1 4 52.43 odd 6
8281.2.a.n.1.1 2 7.6 odd 2
8281.2.a.bb.1.2 2 91.90 odd 2