Properties

Label 950.2.a.k.1.1
Level $950$
Weight $2$
Character 950.1
Self dual yes
Analytic conductor $7.586$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.257.1
Defining polynomial: \(x^{3} - x^{2} - 4 x + 3\)
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 \(0.713538\) of defining polynomial
Character \(\chi\) \(=\) 950.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.77733 q^{3} +1.00000 q^{4} +2.77733 q^{6} +4.69527 q^{7} -1.00000 q^{8} +4.71354 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.77733 q^{3} +1.00000 q^{4} +2.77733 q^{6} +4.69527 q^{7} -1.00000 q^{8} +4.71354 q^{9} +6.40880 q^{11} -2.77733 q^{12} -1.06379 q^{13} -4.69527 q^{14} +1.00000 q^{16} -1.91794 q^{17} -4.71354 q^{18} -1.00000 q^{19} -13.0403 q^{21} -6.40880 q^{22} -1.79560 q^{23} +2.77733 q^{24} +1.06379 q^{26} -4.75905 q^{27} +4.69527 q^{28} +2.93621 q^{29} -5.55465 q^{31} -1.00000 q^{32} -17.7993 q^{33} +1.91794 q^{34} +4.71354 q^{36} +11.4088 q^{37} +1.00000 q^{38} +2.95449 q^{39} -1.14585 q^{41} +13.0403 q^{42} +3.55465 q^{43} +6.40880 q^{44} +1.79560 q^{46} -10.8359 q^{47} -2.77733 q^{48} +15.0455 q^{49} +5.32674 q^{51} -1.06379 q^{52} +8.69527 q^{53} +4.75905 q^{54} -4.69527 q^{56} +2.77733 q^{57} -2.93621 q^{58} -5.63148 q^{59} -3.39053 q^{61} +5.55465 q^{62} +22.1313 q^{63} +1.00000 q^{64} +17.7993 q^{66} +8.82284 q^{67} -1.91794 q^{68} +4.98696 q^{69} -1.42708 q^{71} -4.71354 q^{72} +12.6132 q^{73} -11.4088 q^{74} -1.00000 q^{76} +30.0910 q^{77} -2.95449 q^{78} -1.96345 q^{79} -0.923174 q^{81} +1.14585 q^{82} -16.2447 q^{83} -13.0403 q^{84} -3.55465 q^{86} -8.15482 q^{87} -6.40880 q^{88} -10.0000 q^{89} -4.99477 q^{91} -1.79560 q^{92} +15.4271 q^{93} +10.8359 q^{94} +2.77733 q^{96} +14.9452 q^{97} -15.0455 q^{98} +30.2081 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 3q^{2} - 2q^{3} + 3q^{4} + 2q^{6} - 2q^{7} - 3q^{8} + 13q^{9} + O(q^{10}) \) \( 3q - 3q^{2} - 2q^{3} + 3q^{4} + 2q^{6} - 2q^{7} - 3q^{8} + 13q^{9} + 2q^{11} - 2q^{12} + 2q^{13} + 2q^{14} + 3q^{16} + 4q^{17} - 13q^{18} - 3q^{19} - 11q^{21} - 2q^{22} - 14q^{23} + 2q^{24} - 2q^{26} + 7q^{27} - 2q^{28} + 14q^{29} - 4q^{31} - 3q^{32} - 4q^{33} - 4q^{34} + 13q^{36} + 17q^{37} + 3q^{38} + 29q^{39} - 8q^{41} + 11q^{42} - 2q^{43} + 2q^{44} + 14q^{46} - 13q^{47} - 2q^{48} + 25q^{49} - 11q^{51} + 2q^{52} + 10q^{53} - 7q^{54} + 2q^{56} + 2q^{57} - 14q^{58} - 6q^{59} + 22q^{61} + 4q^{62} - 2q^{63} + 3q^{64} + 4q^{66} + 4q^{68} + 8q^{69} - 2q^{71} - 13q^{72} + 12q^{73} - 17q^{74} - 3q^{76} + 50q^{77} - 29q^{78} + 24q^{79} - q^{81} + 8q^{82} - 12q^{83} - 11q^{84} + 2q^{86} + 21q^{87} - 2q^{88} - 30q^{89} - 7q^{91} - 14q^{92} + 44q^{93} + 13q^{94} + 2q^{96} - 25q^{98} + 24q^{99} + O(q^{100}) \)

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
\(3\) −2.77733 −1.60349 −0.801745 0.597666i \(-0.796095\pi\)
−0.801745 + 0.597666i \(0.796095\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 2.77733 1.13384
\(7\) 4.69527 1.77464 0.887322 0.461151i \(-0.152563\pi\)
0.887322 + 0.461151i \(0.152563\pi\)
\(8\) −1.00000 −0.353553
\(9\) 4.71354 1.57118
\(10\) 0 0
\(11\) 6.40880 1.93233 0.966163 0.257931i \(-0.0830406\pi\)
0.966163 + 0.257931i \(0.0830406\pi\)
\(12\) −2.77733 −0.801745
\(13\) −1.06379 −0.295042 −0.147521 0.989059i \(-0.547129\pi\)
−0.147521 + 0.989059i \(0.547129\pi\)
\(14\) −4.69527 −1.25486
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −1.91794 −0.465169 −0.232584 0.972576i \(-0.574718\pi\)
−0.232584 + 0.972576i \(0.574718\pi\)
\(18\) −4.71354 −1.11099
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −13.0403 −2.84562
\(22\) −6.40880 −1.36636
\(23\) −1.79560 −0.374408 −0.187204 0.982321i \(-0.559943\pi\)
−0.187204 + 0.982321i \(0.559943\pi\)
\(24\) 2.77733 0.566919
\(25\) 0 0
\(26\) 1.06379 0.208626
\(27\) −4.75905 −0.915880
\(28\) 4.69527 0.887322
\(29\) 2.93621 0.545241 0.272620 0.962122i \(-0.412110\pi\)
0.272620 + 0.962122i \(0.412110\pi\)
\(30\) 0 0
\(31\) −5.55465 −0.997645 −0.498822 0.866704i \(-0.666234\pi\)
−0.498822 + 0.866704i \(0.666234\pi\)
\(32\) −1.00000 −0.176777
\(33\) −17.7993 −3.09847
\(34\) 1.91794 0.328924
\(35\) 0 0
\(36\) 4.71354 0.785590
\(37\) 11.4088 1.87560 0.937798 0.347182i \(-0.112861\pi\)
0.937798 + 0.347182i \(0.112861\pi\)
\(38\) 1.00000 0.162221
\(39\) 2.95449 0.473096
\(40\) 0 0
\(41\) −1.14585 −0.178951 −0.0894757 0.995989i \(-0.528519\pi\)
−0.0894757 + 0.995989i \(0.528519\pi\)
\(42\) 13.0403 2.01216
\(43\) 3.55465 0.542079 0.271040 0.962568i \(-0.412633\pi\)
0.271040 + 0.962568i \(0.412633\pi\)
\(44\) 6.40880 0.966163
\(45\) 0 0
\(46\) 1.79560 0.264747
\(47\) −10.8359 −1.58058 −0.790288 0.612736i \(-0.790069\pi\)
−0.790288 + 0.612736i \(0.790069\pi\)
\(48\) −2.77733 −0.400872
\(49\) 15.0455 2.14936
\(50\) 0 0
\(51\) 5.32674 0.745893
\(52\) −1.06379 −0.147521
\(53\) 8.69527 1.19439 0.597193 0.802097i \(-0.296283\pi\)
0.597193 + 0.802097i \(0.296283\pi\)
\(54\) 4.75905 0.647625
\(55\) 0 0
\(56\) −4.69527 −0.627431
\(57\) 2.77733 0.367866
\(58\) −2.93621 −0.385544
\(59\) −5.63148 −0.733156 −0.366578 0.930387i \(-0.619471\pi\)
−0.366578 + 0.930387i \(0.619471\pi\)
\(60\) 0 0
\(61\) −3.39053 −0.434113 −0.217056 0.976159i \(-0.569646\pi\)
−0.217056 + 0.976159i \(0.569646\pi\)
\(62\) 5.55465 0.705441
\(63\) 22.1313 2.78828
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 17.7993 2.19095
\(67\) 8.82284 1.07788 0.538941 0.842344i \(-0.318825\pi\)
0.538941 + 0.842344i \(0.318825\pi\)
\(68\) −1.91794 −0.232584
\(69\) 4.98696 0.600360
\(70\) 0 0
\(71\) −1.42708 −0.169363 −0.0846814 0.996408i \(-0.526987\pi\)
−0.0846814 + 0.996408i \(0.526987\pi\)
\(72\) −4.71354 −0.555496
\(73\) 12.6132 1.47626 0.738132 0.674656i \(-0.235708\pi\)
0.738132 + 0.674656i \(0.235708\pi\)
\(74\) −11.4088 −1.32625
\(75\) 0 0
\(76\) −1.00000 −0.114708
\(77\) 30.0910 3.42919
\(78\) −2.95449 −0.334530
\(79\) −1.96345 −0.220906 −0.110453 0.993881i \(-0.535230\pi\)
−0.110453 + 0.993881i \(0.535230\pi\)
\(80\) 0 0
\(81\) −0.923174 −0.102575
\(82\) 1.14585 0.126538
\(83\) −16.2447 −1.78309 −0.891543 0.452937i \(-0.850376\pi\)
−0.891543 + 0.452937i \(0.850376\pi\)
\(84\) −13.0403 −1.42281
\(85\) 0 0
\(86\) −3.55465 −0.383308
\(87\) −8.15482 −0.874288
\(88\) −6.40880 −0.683181
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) −4.99477 −0.523594
\(92\) −1.79560 −0.187204
\(93\) 15.4271 1.59971
\(94\) 10.8359 1.11764
\(95\) 0 0
\(96\) 2.77733 0.283460
\(97\) 14.9452 1.51745 0.758727 0.651409i \(-0.225822\pi\)
0.758727 + 0.651409i \(0.225822\pi\)
\(98\) −15.0455 −1.51983
\(99\) 30.2081 3.03603
\(100\) 0 0
\(101\) 10.5364 1.04841 0.524204 0.851592i \(-0.324363\pi\)
0.524204 + 0.851592i \(0.324363\pi\)
\(102\) −5.32674 −0.527426
\(103\) 16.9817 1.67326 0.836630 0.547769i \(-0.184523\pi\)
0.836630 + 0.547769i \(0.184523\pi\)
\(104\) 1.06379 0.104313
\(105\) 0 0
\(106\) −8.69527 −0.844559
\(107\) 1.79036 0.173081 0.0865405 0.996248i \(-0.472419\pi\)
0.0865405 + 0.996248i \(0.472419\pi\)
\(108\) −4.75905 −0.457940
\(109\) 2.41404 0.231223 0.115611 0.993295i \(-0.463117\pi\)
0.115611 + 0.993295i \(0.463117\pi\)
\(110\) 0 0
\(111\) −31.6860 −3.00750
\(112\) 4.69527 0.443661
\(113\) −7.14585 −0.672225 −0.336112 0.941822i \(-0.609112\pi\)
−0.336112 + 0.941822i \(0.609112\pi\)
\(114\) −2.77733 −0.260120
\(115\) 0 0
\(116\) 2.93621 0.272620
\(117\) −5.01420 −0.463563
\(118\) 5.63148 0.518420
\(119\) −9.00523 −0.825508
\(120\) 0 0
\(121\) 30.0728 2.73389
\(122\) 3.39053 0.306964
\(123\) 3.18239 0.286947
\(124\) −5.55465 −0.498822
\(125\) 0 0
\(126\) −22.1313 −1.97161
\(127\) −9.26295 −0.821954 −0.410977 0.911646i \(-0.634812\pi\)
−0.410977 + 0.911646i \(0.634812\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −9.87242 −0.869219
\(130\) 0 0
\(131\) 11.5181 1.00634 0.503171 0.864187i \(-0.332167\pi\)
0.503171 + 0.864187i \(0.332167\pi\)
\(132\) −17.7993 −1.54923
\(133\) −4.69527 −0.407131
\(134\) −8.82284 −0.762177
\(135\) 0 0
\(136\) 1.91794 0.164462
\(137\) −15.1041 −1.29043 −0.645214 0.764002i \(-0.723232\pi\)
−0.645214 + 0.764002i \(0.723232\pi\)
\(138\) −4.98696 −0.424518
\(139\) −0.700500 −0.0594156 −0.0297078 0.999559i \(-0.509458\pi\)
−0.0297078 + 0.999559i \(0.509458\pi\)
\(140\) 0 0
\(141\) 30.0948 2.53444
\(142\) 1.42708 0.119758
\(143\) −6.81761 −0.570117
\(144\) 4.71354 0.392795
\(145\) 0 0
\(146\) −12.6132 −1.04388
\(147\) −41.7863 −3.44648
\(148\) 11.4088 0.937798
\(149\) 12.9452 1.06051 0.530255 0.847838i \(-0.322096\pi\)
0.530255 + 0.847838i \(0.322096\pi\)
\(150\) 0 0
\(151\) 5.70830 0.464535 0.232268 0.972652i \(-0.425385\pi\)
0.232268 + 0.972652i \(0.425385\pi\)
\(152\) 1.00000 0.0811107
\(153\) −9.04028 −0.730863
\(154\) −30.0910 −2.42480
\(155\) 0 0
\(156\) 2.95449 0.236548
\(157\) −9.26295 −0.739264 −0.369632 0.929178i \(-0.620516\pi\)
−0.369632 + 0.929178i \(0.620516\pi\)
\(158\) 1.96345 0.156204
\(159\) −24.1496 −1.91519
\(160\) 0 0
\(161\) −8.43081 −0.664441
\(162\) 0.923174 0.0725314
\(163\) −4.28123 −0.335332 −0.167666 0.985844i \(-0.553623\pi\)
−0.167666 + 0.985844i \(0.553623\pi\)
\(164\) −1.14585 −0.0894757
\(165\) 0 0
\(166\) 16.2447 1.26083
\(167\) 15.2264 1.17825 0.589127 0.808040i \(-0.299472\pi\)
0.589127 + 0.808040i \(0.299472\pi\)
\(168\) 13.0403 1.00608
\(169\) −11.8684 −0.912950
\(170\) 0 0
\(171\) −4.71354 −0.360453
\(172\) 3.55465 0.271040
\(173\) 12.2630 0.932335 0.466168 0.884696i \(-0.345634\pi\)
0.466168 + 0.884696i \(0.345634\pi\)
\(174\) 8.15482 0.618215
\(175\) 0 0
\(176\) 6.40880 0.483082
\(177\) 15.6404 1.17561
\(178\) 10.0000 0.749532
\(179\) −1.57292 −0.117566 −0.0587829 0.998271i \(-0.518722\pi\)
−0.0587829 + 0.998271i \(0.518722\pi\)
\(180\) 0 0
\(181\) 11.4088 0.848010 0.424005 0.905660i \(-0.360624\pi\)
0.424005 + 0.905660i \(0.360624\pi\)
\(182\) 4.99477 0.370237
\(183\) 9.41661 0.696096
\(184\) 1.79560 0.132373
\(185\) 0 0
\(186\) −15.4271 −1.13117
\(187\) −12.2917 −0.898858
\(188\) −10.8359 −0.790288
\(189\) −22.3450 −1.62536
\(190\) 0 0
\(191\) −6.35805 −0.460053 −0.230026 0.973184i \(-0.573881\pi\)
−0.230026 + 0.973184i \(0.573881\pi\)
\(192\) −2.77733 −0.200436
\(193\) −14.4998 −1.04372 −0.521860 0.853031i \(-0.674762\pi\)
−0.521860 + 0.853031i \(0.674762\pi\)
\(194\) −14.9452 −1.07300
\(195\) 0 0
\(196\) 15.0455 1.07468
\(197\) 5.14585 0.366627 0.183313 0.983055i \(-0.441318\pi\)
0.183313 + 0.983055i \(0.441318\pi\)
\(198\) −30.2081 −2.14680
\(199\) 3.87766 0.274880 0.137440 0.990510i \(-0.456113\pi\)
0.137440 + 0.990510i \(0.456113\pi\)
\(200\) 0 0
\(201\) −24.5039 −1.72837
\(202\) −10.5364 −0.741337
\(203\) 13.7863 0.967608
\(204\) 5.32674 0.372947
\(205\) 0 0
\(206\) −16.9817 −1.18317
\(207\) −8.46362 −0.588262
\(208\) −1.06379 −0.0737604
\(209\) −6.40880 −0.443306
\(210\) 0 0
\(211\) 17.1496 1.18063 0.590313 0.807174i \(-0.299004\pi\)
0.590313 + 0.807174i \(0.299004\pi\)
\(212\) 8.69527 0.597193
\(213\) 3.96345 0.271571
\(214\) −1.79036 −0.122387
\(215\) 0 0
\(216\) 4.75905 0.323813
\(217\) −26.0806 −1.77046
\(218\) −2.41404 −0.163499
\(219\) −35.0310 −2.36717
\(220\) 0 0
\(221\) 2.04028 0.137244
\(222\) 31.6860 2.12662
\(223\) −7.84635 −0.525430 −0.262715 0.964873i \(-0.584618\pi\)
−0.262715 + 0.964873i \(0.584618\pi\)
\(224\) −4.69527 −0.313716
\(225\) 0 0
\(226\) 7.14585 0.475335
\(227\) −6.28646 −0.417247 −0.208624 0.977996i \(-0.566898\pi\)
−0.208624 + 0.977996i \(0.566898\pi\)
\(228\) 2.77733 0.183933
\(229\) −3.14585 −0.207884 −0.103942 0.994583i \(-0.533146\pi\)
−0.103942 + 0.994583i \(0.533146\pi\)
\(230\) 0 0
\(231\) −83.5726 −5.49867
\(232\) −2.93621 −0.192772
\(233\) −0.182394 −0.0119490 −0.00597451 0.999982i \(-0.501902\pi\)
−0.00597451 + 0.999982i \(0.501902\pi\)
\(234\) 5.01420 0.327789
\(235\) 0 0
\(236\) −5.63148 −0.366578
\(237\) 5.45315 0.354220
\(238\) 9.00523 0.583723
\(239\) −11.5039 −0.744126 −0.372063 0.928208i \(-0.621349\pi\)
−0.372063 + 0.928208i \(0.621349\pi\)
\(240\) 0 0
\(241\) −0.445349 −0.0286874 −0.0143437 0.999897i \(-0.504566\pi\)
−0.0143437 + 0.999897i \(0.504566\pi\)
\(242\) −30.0728 −1.93315
\(243\) 16.8411 1.08036
\(244\) −3.39053 −0.217056
\(245\) 0 0
\(246\) −3.18239 −0.202902
\(247\) 1.06379 0.0676872
\(248\) 5.55465 0.352721
\(249\) 45.1168 2.85916
\(250\) 0 0
\(251\) 13.2630 0.837150 0.418575 0.908182i \(-0.362530\pi\)
0.418575 + 0.908182i \(0.362530\pi\)
\(252\) 22.1313 1.39414
\(253\) −11.5076 −0.723479
\(254\) 9.26295 0.581209
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 23.4816 1.46474 0.732370 0.680907i \(-0.238414\pi\)
0.732370 + 0.680907i \(0.238414\pi\)
\(258\) 9.87242 0.614630
\(259\) 53.5674 3.32851
\(260\) 0 0
\(261\) 13.8399 0.856671
\(262\) −11.5181 −0.711591
\(263\) −27.9269 −1.72205 −0.861023 0.508565i \(-0.830176\pi\)
−0.861023 + 0.508565i \(0.830176\pi\)
\(264\) 17.7993 1.09547
\(265\) 0 0
\(266\) 4.69527 0.287885
\(267\) 27.7733 1.69970
\(268\) 8.82284 0.538941
\(269\) 16.4816 1.00490 0.502449 0.864607i \(-0.332432\pi\)
0.502449 + 0.864607i \(0.332432\pi\)
\(270\) 0 0
\(271\) −1.46736 −0.0891356 −0.0445678 0.999006i \(-0.514191\pi\)
−0.0445678 + 0.999006i \(0.514191\pi\)
\(272\) −1.91794 −0.116292
\(273\) 13.8721 0.839577
\(274\) 15.1041 0.912470
\(275\) 0 0
\(276\) 4.98696 0.300180
\(277\) −15.8359 −0.951486 −0.475743 0.879584i \(-0.657821\pi\)
−0.475743 + 0.879584i \(0.657821\pi\)
\(278\) 0.700500 0.0420132
\(279\) −26.1821 −1.56748
\(280\) 0 0
\(281\) −6.25515 −0.373151 −0.186576 0.982441i \(-0.559739\pi\)
−0.186576 + 0.982441i \(0.559739\pi\)
\(282\) −30.0948 −1.79212
\(283\) 16.7005 0.992742 0.496371 0.868111i \(-0.334666\pi\)
0.496371 + 0.868111i \(0.334666\pi\)
\(284\) −1.42708 −0.0846814
\(285\) 0 0
\(286\) 6.81761 0.403134
\(287\) −5.38006 −0.317575
\(288\) −4.71354 −0.277748
\(289\) −13.3215 −0.783618
\(290\) 0 0
\(291\) −41.5076 −2.43322
\(292\) 12.6132 0.738132
\(293\) −0.644516 −0.0376530 −0.0188265 0.999823i \(-0.505993\pi\)
−0.0188265 + 0.999823i \(0.505993\pi\)
\(294\) 41.7863 2.43703
\(295\) 0 0
\(296\) −11.4088 −0.663123
\(297\) −30.4998 −1.76978
\(298\) −12.9452 −0.749894
\(299\) 1.91014 0.110466
\(300\) 0 0
\(301\) 16.6900 0.961997
\(302\) −5.70830 −0.328476
\(303\) −29.2630 −1.68111
\(304\) −1.00000 −0.0573539
\(305\) 0 0
\(306\) 9.04028 0.516798
\(307\) −26.6457 −1.52075 −0.760375 0.649485i \(-0.774985\pi\)
−0.760375 + 0.649485i \(0.774985\pi\)
\(308\) 30.0910 1.71460
\(309\) −47.1638 −2.68305
\(310\) 0 0
\(311\) 11.5494 0.654907 0.327454 0.944867i \(-0.393809\pi\)
0.327454 + 0.944867i \(0.393809\pi\)
\(312\) −2.95449 −0.167265
\(313\) 23.0638 1.30364 0.651821 0.758373i \(-0.274005\pi\)
0.651821 + 0.758373i \(0.274005\pi\)
\(314\) 9.26295 0.522739
\(315\) 0 0
\(316\) −1.96345 −0.110453
\(317\) 13.9232 0.782003 0.391002 0.920390i \(-0.372129\pi\)
0.391002 + 0.920390i \(0.372129\pi\)
\(318\) 24.1496 1.35424
\(319\) 18.8176 1.05358
\(320\) 0 0
\(321\) −4.97242 −0.277534
\(322\) 8.43081 0.469831
\(323\) 1.91794 0.106717
\(324\) −0.923174 −0.0512874
\(325\) 0 0
\(326\) 4.28123 0.237115
\(327\) −6.70457 −0.370763
\(328\) 1.14585 0.0632689
\(329\) −50.8773 −2.80496
\(330\) 0 0
\(331\) −0.735546 −0.0404292 −0.0202146 0.999796i \(-0.506435\pi\)
−0.0202146 + 0.999796i \(0.506435\pi\)
\(332\) −16.2447 −0.891543
\(333\) 53.7758 2.94690
\(334\) −15.2264 −0.833152
\(335\) 0 0
\(336\) −13.0403 −0.711406
\(337\) 2.28123 0.124266 0.0621332 0.998068i \(-0.480210\pi\)
0.0621332 + 0.998068i \(0.480210\pi\)
\(338\) 11.8684 0.645553
\(339\) 19.8463 1.07791
\(340\) 0 0
\(341\) −35.5987 −1.92778
\(342\) 4.71354 0.254879
\(343\) 37.7758 2.03970
\(344\) −3.55465 −0.191654
\(345\) 0 0
\(346\) −12.2630 −0.659261
\(347\) 2.56246 0.137560 0.0687799 0.997632i \(-0.478089\pi\)
0.0687799 + 0.997632i \(0.478089\pi\)
\(348\) −8.15482 −0.437144
\(349\) −5.67176 −0.303602 −0.151801 0.988411i \(-0.548507\pi\)
−0.151801 + 0.988411i \(0.548507\pi\)
\(350\) 0 0
\(351\) 5.06262 0.270223
\(352\) −6.40880 −0.341590
\(353\) 23.6665 1.25964 0.629821 0.776740i \(-0.283128\pi\)
0.629821 + 0.776740i \(0.283128\pi\)
\(354\) −15.6404 −0.831280
\(355\) 0 0
\(356\) −10.0000 −0.529999
\(357\) 25.0105 1.32369
\(358\) 1.57292 0.0831316
\(359\) 31.9724 1.68744 0.843720 0.536784i \(-0.180361\pi\)
0.843720 + 0.536784i \(0.180361\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −11.4088 −0.599633
\(363\) −83.5218 −4.38376
\(364\) −4.99477 −0.261797
\(365\) 0 0
\(366\) −9.41661 −0.492214
\(367\) −1.14585 −0.0598128 −0.0299064 0.999553i \(-0.509521\pi\)
−0.0299064 + 0.999553i \(0.509521\pi\)
\(368\) −1.79560 −0.0936020
\(369\) −5.40100 −0.281165
\(370\) 0 0
\(371\) 40.8266 2.11961
\(372\) 15.4271 0.799857
\(373\) −32.8579 −1.70132 −0.850658 0.525719i \(-0.823796\pi\)
−0.850658 + 0.525719i \(0.823796\pi\)
\(374\) 12.2917 0.635588
\(375\) 0 0
\(376\) 10.8359 0.558818
\(377\) −3.12351 −0.160869
\(378\) 22.3450 1.14930
\(379\) −18.2865 −0.939312 −0.469656 0.882849i \(-0.655622\pi\)
−0.469656 + 0.882849i \(0.655622\pi\)
\(380\) 0 0
\(381\) 25.7262 1.31800
\(382\) 6.35805 0.325306
\(383\) −20.8542 −1.06560 −0.532799 0.846242i \(-0.678860\pi\)
−0.532799 + 0.846242i \(0.678860\pi\)
\(384\) 2.77733 0.141730
\(385\) 0 0
\(386\) 14.4998 0.738022
\(387\) 16.7550 0.851704
\(388\) 14.9452 0.758727
\(389\) −24.9086 −1.26292 −0.631459 0.775409i \(-0.717544\pi\)
−0.631459 + 0.775409i \(0.717544\pi\)
\(390\) 0 0
\(391\) 3.44385 0.174163
\(392\) −15.0455 −0.759913
\(393\) −31.9895 −1.61366
\(394\) −5.14585 −0.259244
\(395\) 0 0
\(396\) 30.2081 1.51802
\(397\) 24.7445 1.24189 0.620946 0.783853i \(-0.286749\pi\)
0.620946 + 0.783853i \(0.286749\pi\)
\(398\) −3.87766 −0.194369
\(399\) 13.0403 0.652831
\(400\) 0 0
\(401\) 15.6457 0.781308 0.390654 0.920538i \(-0.372249\pi\)
0.390654 + 0.920538i \(0.372249\pi\)
\(402\) 24.5039 1.22214
\(403\) 5.90897 0.294347
\(404\) 10.5364 0.524204
\(405\) 0 0
\(406\) −13.7863 −0.684202
\(407\) 73.1168 3.62426
\(408\) −5.32674 −0.263713
\(409\) 30.5804 1.51210 0.756052 0.654512i \(-0.227126\pi\)
0.756052 + 0.654512i \(0.227126\pi\)
\(410\) 0 0
\(411\) 41.9489 2.06919
\(412\) 16.9817 0.836630
\(413\) −26.4413 −1.30109
\(414\) 8.46362 0.415964
\(415\) 0 0
\(416\) 1.06379 0.0521565
\(417\) 1.94552 0.0952723
\(418\) 6.40880 0.313465
\(419\) 1.96345 0.0959210 0.0479605 0.998849i \(-0.484728\pi\)
0.0479605 + 0.998849i \(0.484728\pi\)
\(420\) 0 0
\(421\) −25.5949 −1.24742 −0.623710 0.781656i \(-0.714376\pi\)
−0.623710 + 0.781656i \(0.714376\pi\)
\(422\) −17.1496 −0.834829
\(423\) −51.0753 −2.48337
\(424\) −8.69527 −0.422279
\(425\) 0 0
\(426\) −3.96345 −0.192030
\(427\) −15.9194 −0.770396
\(428\) 1.79036 0.0865405
\(429\) 18.9347 0.914177
\(430\) 0 0
\(431\) −15.3540 −0.739575 −0.369788 0.929116i \(-0.620570\pi\)
−0.369788 + 0.929116i \(0.620570\pi\)
\(432\) −4.75905 −0.228970
\(433\) −16.6640 −0.800819 −0.400409 0.916336i \(-0.631132\pi\)
−0.400409 + 0.916336i \(0.631132\pi\)
\(434\) 26.0806 1.25191
\(435\) 0 0
\(436\) 2.41404 0.115611
\(437\) 1.79560 0.0858951
\(438\) 35.0310 1.67384
\(439\) −19.5987 −0.935393 −0.467697 0.883889i \(-0.654916\pi\)
−0.467697 + 0.883889i \(0.654916\pi\)
\(440\) 0 0
\(441\) 70.9176 3.37703
\(442\) −2.04028 −0.0970462
\(443\) −13.0183 −0.618517 −0.309258 0.950978i \(-0.600081\pi\)
−0.309258 + 0.950978i \(0.600081\pi\)
\(444\) −31.6860 −1.50375
\(445\) 0 0
\(446\) 7.84635 0.371535
\(447\) −35.9530 −1.70052
\(448\) 4.69527 0.221830
\(449\) 6.77359 0.319666 0.159833 0.987144i \(-0.448905\pi\)
0.159833 + 0.987144i \(0.448905\pi\)
\(450\) 0 0
\(451\) −7.34352 −0.345793
\(452\) −7.14585 −0.336112
\(453\) −15.8538 −0.744877
\(454\) 6.28646 0.295038
\(455\) 0 0
\(456\) −2.77733 −0.130060
\(457\) 27.3189 1.27793 0.638963 0.769237i \(-0.279364\pi\)
0.638963 + 0.769237i \(0.279364\pi\)
\(458\) 3.14585 0.146996
\(459\) 9.12758 0.426039
\(460\) 0 0
\(461\) −27.7993 −1.29474 −0.647372 0.762174i \(-0.724132\pi\)
−0.647372 + 0.762174i \(0.724132\pi\)
\(462\) 83.5726 3.88815
\(463\) −38.2369 −1.77702 −0.888509 0.458859i \(-0.848258\pi\)
−0.888509 + 0.458859i \(0.848258\pi\)
\(464\) 2.93621 0.136310
\(465\) 0 0
\(466\) 0.182394 0.00844923
\(467\) −23.4711 −1.08611 −0.543056 0.839696i \(-0.682733\pi\)
−0.543056 + 0.839696i \(0.682733\pi\)
\(468\) −5.01420 −0.231782
\(469\) 41.4256 1.91286
\(470\) 0 0
\(471\) 25.7262 1.18540
\(472\) 5.63148 0.259210
\(473\) 22.7811 1.04747
\(474\) −5.45315 −0.250472
\(475\) 0 0
\(476\) −9.00523 −0.412754
\(477\) 40.9855 1.87660
\(478\) 11.5039 0.526176
\(479\) −19.6900 −0.899660 −0.449830 0.893114i \(-0.648516\pi\)
−0.449830 + 0.893114i \(0.648516\pi\)
\(480\) 0 0
\(481\) −12.1365 −0.553379
\(482\) 0.445349 0.0202851
\(483\) 23.4151 1.06542
\(484\) 30.0728 1.36694
\(485\) 0 0
\(486\) −16.8411 −0.763928
\(487\) −16.3357 −0.740242 −0.370121 0.928984i \(-0.620684\pi\)
−0.370121 + 0.928984i \(0.620684\pi\)
\(488\) 3.39053 0.153482
\(489\) 11.8904 0.537701
\(490\) 0 0
\(491\) 27.1093 1.22343 0.611713 0.791080i \(-0.290481\pi\)
0.611713 + 0.791080i \(0.290481\pi\)
\(492\) 3.18239 0.143473
\(493\) −5.63148 −0.253629
\(494\) −1.06379 −0.0478621
\(495\) 0 0
\(496\) −5.55465 −0.249411
\(497\) −6.70050 −0.300558
\(498\) −45.1168 −2.02173
\(499\) −4.69003 −0.209955 −0.104977 0.994475i \(-0.533477\pi\)
−0.104977 + 0.994475i \(0.533477\pi\)
\(500\) 0 0
\(501\) −42.2887 −1.88932
\(502\) −13.2630 −0.591955
\(503\) −5.19136 −0.231471 −0.115736 0.993280i \(-0.536923\pi\)
−0.115736 + 0.993280i \(0.536923\pi\)
\(504\) −22.1313 −0.985807
\(505\) 0 0
\(506\) 11.5076 0.511577
\(507\) 32.9623 1.46391
\(508\) −9.26295 −0.410977
\(509\) −4.51811 −0.200262 −0.100131 0.994974i \(-0.531926\pi\)
−0.100131 + 0.994974i \(0.531926\pi\)
\(510\) 0 0
\(511\) 59.2223 2.61984
\(512\) −1.00000 −0.0441942
\(513\) 4.75905 0.210117
\(514\) −23.4816 −1.03573
\(515\) 0 0
\(516\) −9.87242 −0.434609
\(517\) −69.4450 −3.05419
\(518\) −53.5674 −2.35361
\(519\) −34.0582 −1.49499
\(520\) 0 0
\(521\) 14.4453 0.632862 0.316431 0.948615i \(-0.397515\pi\)
0.316431 + 0.948615i \(0.397515\pi\)
\(522\) −13.8399 −0.605758
\(523\) 18.2134 0.796415 0.398208 0.917295i \(-0.369632\pi\)
0.398208 + 0.917295i \(0.369632\pi\)
\(524\) 11.5181 0.503171
\(525\) 0 0
\(526\) 27.9269 1.21767
\(527\) 10.6535 0.464073
\(528\) −17.7993 −0.774617
\(529\) −19.7758 −0.859819
\(530\) 0 0
\(531\) −26.5442 −1.15192
\(532\) −4.69527 −0.203566
\(533\) 1.21894 0.0527981
\(534\) −27.7733 −1.20187
\(535\) 0 0
\(536\) −8.82284 −0.381089
\(537\) 4.36852 0.188516
\(538\) −16.4816 −0.710571
\(539\) 96.4237 4.15326
\(540\) 0 0
\(541\) 37.3905 1.60754 0.803772 0.594937i \(-0.202823\pi\)
0.803772 + 0.594937i \(0.202823\pi\)
\(542\) 1.46736 0.0630284
\(543\) −31.6860 −1.35977
\(544\) 1.91794 0.0822310
\(545\) 0 0
\(546\) −13.8721 −0.593671
\(547\) −29.5621 −1.26399 −0.631993 0.774974i \(-0.717763\pi\)
−0.631993 + 0.774974i \(0.717763\pi\)
\(548\) −15.1041 −0.645214
\(549\) −15.9814 −0.682069
\(550\) 0 0
\(551\) −2.93621 −0.125087
\(552\) −4.98696 −0.212259
\(553\) −9.21894 −0.392029
\(554\) 15.8359 0.672802
\(555\) 0 0
\(556\) −0.700500 −0.0297078
\(557\) −14.3723 −0.608972 −0.304486 0.952517i \(-0.598485\pi\)
−0.304486 + 0.952517i \(0.598485\pi\)
\(558\) 26.1821 1.10837
\(559\) −3.78139 −0.159936
\(560\) 0 0
\(561\) 34.1380 1.44131
\(562\) 6.25515 0.263858
\(563\) 6.39053 0.269329 0.134664 0.990891i \(-0.457004\pi\)
0.134664 + 0.990891i \(0.457004\pi\)
\(564\) 30.0948 1.26722
\(565\) 0 0
\(566\) −16.7005 −0.701974
\(567\) −4.33455 −0.182034
\(568\) 1.42708 0.0598788
\(569\) −44.9086 −1.88267 −0.941334 0.337476i \(-0.890427\pi\)
−0.941334 + 0.337476i \(0.890427\pi\)
\(570\) 0 0
\(571\) 12.4193 0.519730 0.259865 0.965645i \(-0.416322\pi\)
0.259865 + 0.965645i \(0.416322\pi\)
\(572\) −6.81761 −0.285058
\(573\) 17.6584 0.737690
\(574\) 5.38006 0.224559
\(575\) 0 0
\(576\) 4.71354 0.196397
\(577\) 4.20440 0.175032 0.0875158 0.996163i \(-0.472107\pi\)
0.0875158 + 0.996163i \(0.472107\pi\)
\(578\) 13.3215 0.554102
\(579\) 40.2708 1.67360
\(580\) 0 0
\(581\) −76.2731 −3.16434
\(582\) 41.5076 1.72055
\(583\) 55.7262 2.30795
\(584\) −12.6132 −0.521938
\(585\) 0 0
\(586\) 0.644516 0.0266247
\(587\) −24.7915 −1.02326 −0.511628 0.859207i \(-0.670957\pi\)
−0.511628 + 0.859207i \(0.670957\pi\)
\(588\) −41.7863 −1.72324
\(589\) 5.55465 0.228875
\(590\) 0 0
\(591\) −14.2917 −0.587882
\(592\) 11.4088 0.468899
\(593\) −4.67176 −0.191846 −0.0959231 0.995389i \(-0.530580\pi\)
−0.0959231 + 0.995389i \(0.530580\pi\)
\(594\) 30.4998 1.25142
\(595\) 0 0
\(596\) 12.9452 0.530255
\(597\) −10.7695 −0.440767
\(598\) −1.91014 −0.0781113
\(599\) 39.2369 1.60318 0.801588 0.597877i \(-0.203989\pi\)
0.801588 + 0.597877i \(0.203989\pi\)
\(600\) 0 0
\(601\) −42.4267 −1.73062 −0.865311 0.501235i \(-0.832879\pi\)
−0.865311 + 0.501235i \(0.832879\pi\)
\(602\) −16.6900 −0.680235
\(603\) 41.5868 1.69355
\(604\) 5.70830 0.232268
\(605\) 0 0
\(606\) 29.2630 1.18873
\(607\) 2.98173 0.121025 0.0605123 0.998167i \(-0.480727\pi\)
0.0605123 + 0.998167i \(0.480727\pi\)
\(608\) 1.00000 0.0405554
\(609\) −38.2890 −1.55155
\(610\) 0 0
\(611\) 11.5271 0.466336
\(612\) −9.04028 −0.365432
\(613\) 28.9452 1.16908 0.584542 0.811363i \(-0.301274\pi\)
0.584542 + 0.811363i \(0.301274\pi\)
\(614\) 26.6457 1.07533
\(615\) 0 0
\(616\) −30.0910 −1.21240
\(617\) 15.0365 0.605349 0.302674 0.953094i \(-0.402121\pi\)
0.302674 + 0.953094i \(0.402121\pi\)
\(618\) 47.1638 1.89721
\(619\) 8.25515 0.331803 0.165901 0.986142i \(-0.446947\pi\)
0.165901 + 0.986142i \(0.446947\pi\)
\(620\) 0 0
\(621\) 8.54535 0.342913
\(622\) −11.5494 −0.463089
\(623\) −46.9527 −1.88112
\(624\) 2.95449 0.118274
\(625\) 0 0
\(626\) −23.0638 −0.921814
\(627\) 17.7993 0.710837
\(628\) −9.26295 −0.369632
\(629\) −21.8814 −0.872468
\(630\) 0 0
\(631\) −9.09103 −0.361908 −0.180954 0.983492i \(-0.557919\pi\)
−0.180954 + 0.983492i \(0.557919\pi\)
\(632\) 1.96345 0.0781020
\(633\) −47.6300 −1.89312
\(634\) −13.9232 −0.552960
\(635\) 0 0
\(636\) −24.1496 −0.957593
\(637\) −16.0052 −0.634150
\(638\) −18.8176 −0.744996
\(639\) −6.72658 −0.266099
\(640\) 0 0
\(641\) 30.1171 1.18955 0.594777 0.803891i \(-0.297240\pi\)
0.594777 + 0.803891i \(0.297240\pi\)
\(642\) 4.97242 0.196246
\(643\) 35.3174 1.39278 0.696392 0.717662i \(-0.254788\pi\)
0.696392 + 0.717662i \(0.254788\pi\)
\(644\) −8.43081 −0.332220
\(645\) 0 0
\(646\) −1.91794 −0.0754603
\(647\) −4.12234 −0.162066 −0.0810330 0.996711i \(-0.525822\pi\)
−0.0810330 + 0.996711i \(0.525822\pi\)
\(648\) 0.923174 0.0362657
\(649\) −36.0910 −1.41670
\(650\) 0 0
\(651\) 72.4342 2.83892
\(652\) −4.28123 −0.167666
\(653\) −8.62741 −0.337617 −0.168808 0.985649i \(-0.553992\pi\)
−0.168808 + 0.985649i \(0.553992\pi\)
\(654\) 6.70457 0.262169
\(655\) 0 0
\(656\) −1.14585 −0.0447379
\(657\) 59.4528 2.31948
\(658\) 50.8773 1.98340
\(659\) −37.3853 −1.45632 −0.728162 0.685405i \(-0.759625\pi\)
−0.728162 + 0.685405i \(0.759625\pi\)
\(660\) 0 0
\(661\) −12.8997 −0.501739 −0.250869 0.968021i \(-0.580716\pi\)
−0.250869 + 0.968021i \(0.580716\pi\)
\(662\) 0.735546 0.0285878
\(663\) −5.66652 −0.220070
\(664\) 16.2447 0.630416
\(665\) 0 0
\(666\) −53.7758 −2.08377
\(667\) −5.27226 −0.204143
\(668\) 15.2264 0.589127
\(669\) 21.7919 0.842522
\(670\) 0 0
\(671\) −21.7292 −0.838848
\(672\) 13.0403 0.503040
\(673\) −10.4349 −0.402235 −0.201118 0.979567i \(-0.564457\pi\)
−0.201118 + 0.979567i \(0.564457\pi\)
\(674\) −2.28123 −0.0878696
\(675\) 0 0
\(676\) −11.8684 −0.456475
\(677\) −12.4401 −0.478112 −0.239056 0.971006i \(-0.576838\pi\)
−0.239056 + 0.971006i \(0.576838\pi\)
\(678\) −19.8463 −0.762194
\(679\) 70.1716 2.69294
\(680\) 0 0
\(681\) 17.4596 0.669052
\(682\) 35.5987 1.36314
\(683\) −17.5364 −0.671011 −0.335505 0.942038i \(-0.608907\pi\)
−0.335505 + 0.942038i \(0.608907\pi\)
\(684\) −4.71354 −0.180227
\(685\) 0 0
\(686\) −37.7758 −1.44229
\(687\) 8.73705 0.333339
\(688\) 3.55465 0.135520
\(689\) −9.24992 −0.352394
\(690\) 0 0
\(691\) −25.2734 −0.961446 −0.480723 0.876872i \(-0.659626\pi\)
−0.480723 + 0.876872i \(0.659626\pi\)
\(692\) 12.2630 0.466168
\(693\) 141.835 5.38787
\(694\) −2.56246 −0.0972695
\(695\) 0 0
\(696\) 8.15482 0.309108
\(697\) 2.19767 0.0832426
\(698\) 5.67176 0.214679
\(699\) 0.506567 0.0191601
\(700\) 0 0
\(701\) −16.0545 −0.606370 −0.303185 0.952932i \(-0.598050\pi\)
−0.303185 + 0.952932i \(0.598050\pi\)
\(702\) −5.06262 −0.191076
\(703\) −11.4088 −0.430291
\(704\) 6.40880 0.241541
\(705\) 0 0
\(706\) −23.6665 −0.890701
\(707\) 49.4711 1.86055
\(708\) 15.6404 0.587804
\(709\) 13.5076 0.507290 0.253645 0.967297i \(-0.418371\pi\)
0.253645 + 0.967297i \(0.418371\pi\)
\(710\) 0 0
\(711\) −9.25482 −0.347083
\(712\) 10.0000 0.374766
\(713\) 9.97392 0.373526
\(714\) −25.0105 −0.935993
\(715\) 0 0
\(716\) −1.57292 −0.0587829
\(717\) 31.9501 1.19320
\(718\) −31.9724 −1.19320
\(719\) 0.803402 0.0299619 0.0149809 0.999888i \(-0.495231\pi\)
0.0149809 + 0.999888i \(0.495231\pi\)
\(720\) 0 0
\(721\) 79.7337 2.96944
\(722\) −1.00000 −0.0372161
\(723\) 1.23688 0.0460000
\(724\) 11.4088 0.424005
\(725\) 0 0
\(726\) 83.5218 3.09979
\(727\) −51.6860 −1.91693 −0.958463 0.285217i \(-0.907934\pi\)
−0.958463 + 0.285217i \(0.907934\pi\)
\(728\) 4.99477 0.185118
\(729\) −44.0037 −1.62977
\(730\) 0 0
\(731\) −6.81761 −0.252158
\(732\) 9.41661 0.348048
\(733\) 22.3723 0.826338 0.413169 0.910654i \(-0.364422\pi\)
0.413169 + 0.910654i \(0.364422\pi\)
\(734\) 1.14585 0.0422940
\(735\) 0 0
\(736\) 1.79560 0.0661866
\(737\) 56.5438 2.08282
\(738\) 5.40100 0.198814
\(739\) 33.4271 1.22963 0.614817 0.788669i \(-0.289230\pi\)
0.614817 + 0.788669i \(0.289230\pi\)
\(740\) 0 0
\(741\) −2.95449 −0.108536
\(742\) −40.8266 −1.49879
\(743\) −14.4998 −0.531947 −0.265974 0.963980i \(-0.585693\pi\)
−0.265974 + 0.963980i \(0.585693\pi\)
\(744\) −15.4271 −0.565584
\(745\) 0 0
\(746\) 32.8579 1.20301
\(747\) −76.5699 −2.80155
\(748\) −12.2917 −0.449429
\(749\) 8.40623 0.307157
\(750\) 0 0
\(751\) −26.6169 −0.971266 −0.485633 0.874163i \(-0.661411\pi\)
−0.485633 + 0.874163i \(0.661411\pi\)
\(752\) −10.8359 −0.395144
\(753\) −36.8355 −1.34236
\(754\) 3.12351 0.113751
\(755\) 0 0
\(756\) −22.3450 −0.812680
\(757\) 31.0362 1.12803 0.564015 0.825764i \(-0.309256\pi\)
0.564015 + 0.825764i \(0.309256\pi\)
\(758\) 18.2865 0.664194
\(759\) 31.9605 1.16009
\(760\) 0 0
\(761\) −27.8083 −1.00805 −0.504025 0.863689i \(-0.668148\pi\)
−0.504025 + 0.863689i \(0.668148\pi\)
\(762\) −25.7262 −0.931963
\(763\) 11.3345 0.410338
\(764\) −6.35805 −0.230026
\(765\) 0 0
\(766\) 20.8542 0.753491
\(767\) 5.99070 0.216312
\(768\) −2.77733 −0.100218
\(769\) −19.2279 −0.693376 −0.346688 0.937980i \(-0.612694\pi\)
−0.346688 + 0.937980i \(0.612694\pi\)
\(770\) 0 0
\(771\) −65.2159 −2.34869
\(772\) −14.4998 −0.521860
\(773\) −6.00373 −0.215939 −0.107970 0.994154i \(-0.534435\pi\)
−0.107970 + 0.994154i \(0.534435\pi\)
\(774\) −16.7550 −0.602245
\(775\) 0 0
\(776\) −14.9452 −0.536501
\(777\) −148.774 −5.33724
\(778\) 24.9086 0.893018
\(779\) 1.14585 0.0410543
\(780\) 0 0
\(781\) −9.14585 −0.327264
\(782\) −3.44385 −0.123152
\(783\) −13.9736 −0.499375
\(784\) 15.0455 0.537340
\(785\) 0 0
\(786\) 31.9895 1.14103
\(787\) −22.2797 −0.794187 −0.397093 0.917778i \(-0.629981\pi\)
−0.397093 + 0.917778i \(0.629981\pi\)
\(788\) 5.14585 0.183313
\(789\) 77.5621 2.76128
\(790\) 0 0
\(791\) −33.5517 −1.19296
\(792\) −30.2081 −1.07340
\(793\) 3.60680 0.128081
\(794\) −24.7445 −0.878150
\(795\) 0 0
\(796\) 3.87766 0.137440
\(797\) −26.6259 −0.943138 −0.471569 0.881829i \(-0.656312\pi\)
−0.471569 + 0.881829i \(0.656312\pi\)
\(798\) −13.0403 −0.461621
\(799\) 20.7826 0.735234
\(800\) 0 0
\(801\) −47.1354 −1.66545
\(802\) −15.6457 −0.552468
\(803\) 80.8355 2.85262
\(804\) −24.5039 −0.864186
\(805\) 0 0
\(806\) −5.90897 −0.208135
\(807\) −45.7747 −1.61134
\(808\) −10.5364 −0.370669
\(809\) 0.651250 0.0228967 0.0114484 0.999934i \(-0.496356\pi\)
0.0114484 + 0.999934i \(0.496356\pi\)
\(810\) 0 0
\(811\) −13.0780 −0.459230 −0.229615 0.973281i \(-0.573747\pi\)
−0.229615 + 0.973281i \(0.573747\pi\)
\(812\) 13.7863 0.483804
\(813\) 4.07533 0.142928
\(814\) −73.1168 −2.56274
\(815\) 0 0
\(816\) 5.32674 0.186473
\(817\) −3.55465 −0.124362
\(818\) −30.5804 −1.06922
\(819\) −23.5430 −0.822660
\(820\) 0 0
\(821\) 14.6640 0.511776 0.255888 0.966706i \(-0.417632\pi\)
0.255888 + 0.966706i \(0.417632\pi\)
\(822\) −41.9489 −1.46314
\(823\) 18.2850 0.637374 0.318687 0.947860i \(-0.396758\pi\)
0.318687 + 0.947860i \(0.396758\pi\)
\(824\) −16.9817 −0.591587
\(825\) 0 0
\(826\) 26.4413 0.920010
\(827\) −40.1910 −1.39758 −0.698790 0.715327i \(-0.746278\pi\)
−0.698790 + 0.715327i \(0.746278\pi\)
\(828\) −8.46362 −0.294131
\(829\) 28.3760 0.985539 0.492769 0.870160i \(-0.335985\pi\)
0.492769 + 0.870160i \(0.335985\pi\)
\(830\) 0 0
\(831\) 43.9814 1.52570
\(832\) −1.06379 −0.0368802
\(833\) −28.8564 −0.999815
\(834\) −1.94552 −0.0673677
\(835\) 0 0
\(836\) −6.40880 −0.221653
\(837\) 26.4349 0.913723
\(838\) −1.96345 −0.0678264
\(839\) 6.93471 0.239413 0.119706 0.992809i \(-0.461805\pi\)
0.119706 + 0.992809i \(0.461805\pi\)
\(840\) 0 0
\(841\) −20.3787 −0.702712
\(842\) 25.5949 0.882060
\(843\) 17.3726 0.598344
\(844\) 17.1496 0.590313
\(845\) 0 0
\(846\) 51.0753 1.75601
\(847\) 141.200 4.85167
\(848\) 8.69527 0.298597
\(849\) −46.3827 −1.59185
\(850\) 0 0
\(851\) −20.4856 −0.702238
\(852\) 3.96345 0.135786
\(853\) −21.9739 −0.752373 −0.376186 0.926544i \(-0.622765\pi\)
−0.376186 + 0.926544i \(0.622765\pi\)
\(854\) 15.9194 0.544752
\(855\) 0 0
\(856\) −1.79036 −0.0611934
\(857\) −13.6091 −0.464879 −0.232440 0.972611i \(-0.574671\pi\)
−0.232440 + 0.972611i \(0.574671\pi\)
\(858\) −18.9347 −0.646420
\(859\) 5.17192 0.176464 0.0882319 0.996100i \(-0.471878\pi\)
0.0882319 + 0.996100i \(0.471878\pi\)
\(860\) 0 0
\(861\) 14.9422 0.509228
\(862\) 15.3540 0.522959
\(863\) −15.9635 −0.543402 −0.271701 0.962382i \(-0.587586\pi\)
−0.271701 + 0.962382i \(0.587586\pi\)
\(864\) 4.75905 0.161906
\(865\) 0 0
\(866\) 16.6640 0.566264
\(867\) 36.9982 1.25652
\(868\) −26.0806 −0.885232
\(869\) −12.5834 −0.426862
\(870\) 0 0
\(871\) −9.38563 −0.318020
\(872\) −2.41404 −0.0817496
\(873\) 70.4447 2.38419
\(874\) −1.79560 −0.0607370
\(875\) 0 0
\(876\) −35.0310 −1.18359
\(877\) 15.8866 0.536453 0.268227 0.963356i \(-0.413562\pi\)
0.268227 + 0.963356i \(0.413562\pi\)
\(878\) 19.5987 0.661423
\(879\) 1.79003 0.0603762
\(880\) 0 0
\(881\) −16.1458 −0.543967 −0.271984 0.962302i \(-0.587680\pi\)
−0.271984 + 0.962302i \(0.587680\pi\)
\(882\) −70.9176 −2.38792
\(883\) −38.2887 −1.28852 −0.644259 0.764808i \(-0.722834\pi\)
−0.644259 + 0.764808i \(0.722834\pi\)
\(884\) 2.04028 0.0686221
\(885\) 0 0
\(886\) 13.0183 0.437357
\(887\) −19.2809 −0.647389 −0.323695 0.946162i \(-0.604925\pi\)
−0.323695 + 0.946162i \(0.604925\pi\)
\(888\) 31.6860 1.06331
\(889\) −43.4920 −1.45868
\(890\) 0 0
\(891\) −5.91644 −0.198208
\(892\) −7.84635 −0.262715
\(893\) 10.8359 0.362609
\(894\) 35.9530 1.20245
\(895\) 0 0
\(896\) −4.69527 −0.156858
\(897\) −5.30507 −0.177131
\(898\) −6.77359 −0.226038
\(899\) −16.3096 −0.543957
\(900\) 0 0
\(901\) −16.6770 −0.555591
\(902\) 7.34352 0.244512
\(903\) −46.3537 −1.54255
\(904\) 7.14585 0.237667
\(905\) 0 0
\(906\) 15.8538 0.526708
\(907\) −43.0205 −1.42847 −0.714236 0.699905i \(-0.753226\pi\)
−0.714236 + 0.699905i \(0.753226\pi\)
\(908\) −6.28646 −0.208624
\(909\) 49.6636 1.64724
\(910\) 0 0
\(911\) −25.7733 −0.853906 −0.426953 0.904274i \(-0.640413\pi\)
−0.426953 + 0.904274i \(0.640413\pi\)
\(912\) 2.77733 0.0919664
\(913\) −104.109 −3.44550
\(914\) −27.3189 −0.903630
\(915\) 0 0
\(916\) −3.14585 −0.103942
\(917\) 54.0806 1.78590
\(918\) −9.12758 −0.301255
\(919\) −29.5897 −0.976074 −0.488037 0.872823i \(-0.662287\pi\)
−0.488037 + 0.872823i \(0.662287\pi\)
\(920\) 0 0
\(921\) 74.0037 2.43851
\(922\) 27.7993 0.915522
\(923\) 1.51811 0.0499691
\(924\) −83.5726 −2.74934
\(925\) 0 0
\(926\) 38.2369 1.25654
\(927\) 80.0440 2.62899
\(928\) −2.93621 −0.0963859
\(929\) −1.42334 −0.0466983 −0.0233491 0.999727i \(-0.507433\pi\)
−0.0233491 + 0.999727i \(0.507433\pi\)
\(930\) 0 0
\(931\) −15.0455 −0.493097
\(932\) −0.182394 −0.00597451
\(933\) −32.0765 −1.05014
\(934\) 23.4711 0.767998
\(935\) 0 0
\(936\) 5.01420 0.163894
\(937\) −28.2276 −0.922155 −0.461077 0.887360i \(-0.652537\pi\)
−0.461077 + 0.887360i \(0.652537\pi\)
\(938\) −41.4256 −1.35259
\(939\) −64.0556 −2.09038
\(940\) 0 0
\(941\) −15.8672 −0.517256 −0.258628 0.965977i \(-0.583270\pi\)
−0.258628 + 0.965977i \(0.583270\pi\)
\(942\) −25.7262 −0.838206
\(943\) 2.05748 0.0670009
\(944\) −5.63148 −0.183289
\(945\) 0 0
\(946\) −22.7811 −0.740676
\(947\) −43.6718 −1.41914 −0.709571 0.704634i \(-0.751111\pi\)
−0.709571 + 0.704634i \(0.751111\pi\)
\(948\) 5.45315 0.177110
\(949\) −13.4178 −0.435559
\(950\) 0 0
\(951\) −38.6692 −1.25393
\(952\) 9.00523 0.291861
\(953\) −16.0261 −0.519136 −0.259568 0.965725i \(-0.583580\pi\)
−0.259568 + 0.965725i \(0.583580\pi\)
\(954\) −40.9855 −1.32695
\(955\) 0 0
\(956\) −11.5039 −0.372063
\(957\) −52.2626 −1.68941
\(958\) 19.6900 0.636156
\(959\) −70.9176 −2.29005
\(960\) 0 0
\(961\) −0.145848 −0.00470478
\(962\) 12.1365 0.391298
\(963\) 8.43895 0.271941
\(964\) −0.445349 −0.0143437
\(965\) 0 0
\(966\) −23.4151 −0.753369
\(967\) 11.5987 0.372988 0.186494 0.982456i \(-0.440288\pi\)
0.186494 + 0.982456i \(0.440288\pi\)
\(968\) −30.0728 −0.966575
\(969\) −5.32674 −0.171120
\(970\) 0 0
\(971\) −27.0362 −0.867633 −0.433817 0.901001i \(-0.642833\pi\)
−0.433817 + 0.901001i \(0.642833\pi\)
\(972\) 16.8411 0.540179
\(973\) −3.28903 −0.105442
\(974\) 16.3357 0.523430
\(975\) 0 0
\(976\) −3.39053 −0.108528
\(977\) −14.1537 −0.452815 −0.226408 0.974033i \(-0.572698\pi\)
−0.226408 + 0.974033i \(0.572698\pi\)
\(978\) −11.8904 −0.380212
\(979\) −64.0880 −2.04826
\(980\) 0 0
\(981\) 11.3787 0.363293
\(982\) −27.1093 −0.865093
\(983\) 32.8542 1.04788 0.523942 0.851754i \(-0.324461\pi\)
0.523942 + 0.851754i \(0.324461\pi\)
\(984\) −3.18239 −0.101451
\(985\) 0 0
\(986\) 5.63148 0.179343
\(987\) 141.303 4.49772
\(988\) 1.06379 0.0338436
\(989\) −6.38273 −0.202959
\(990\) 0 0
\(991\) 47.9709 1.52385 0.761923 0.647667i \(-0.224255\pi\)
0.761923 + 0.647667i \(0.224255\pi\)
\(992\) 5.55465 0.176360
\(993\) 2.04285 0.0648279
\(994\) 6.70050 0.212527
\(995\) 0 0
\(996\) 45.1168 1.42958
\(997\) −44.1716 −1.39893 −0.699464 0.714668i \(-0.746578\pi\)
−0.699464 + 0.714668i \(0.746578\pi\)
\(998\) 4.69003 0.148460
\(999\) −54.2951 −1.71782
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 950.2.a.k.1.1 3
3.2 odd 2 8550.2.a.co.1.3 3
4.3 odd 2 7600.2.a.cb.1.3 3
5.2 odd 4 950.2.b.g.799.3 6
5.3 odd 4 950.2.b.g.799.4 6
5.4 even 2 950.2.a.m.1.3 yes 3
15.14 odd 2 8550.2.a.cj.1.1 3
20.19 odd 2 7600.2.a.bm.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.k.1.1 3 1.1 even 1 trivial
950.2.a.m.1.3 yes 3 5.4 even 2
950.2.b.g.799.3 6 5.2 odd 4
950.2.b.g.799.4 6 5.3 odd 4
7600.2.a.bm.1.1 3 20.19 odd 2
7600.2.a.cb.1.3 3 4.3 odd 2
8550.2.a.cj.1.1 3 15.14 odd 2
8550.2.a.co.1.3 3 3.2 odd 2