Properties

Label 4598.2.a.bq.1.2
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4598.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7152148494\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.7488.1
Defining polynomial: \(x^{4} - 2 x^{3} - 4 x^{2} + 2 x + 1\)
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 1.2
Root \(-1.43091\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.698857 q^{3} +1.00000 q^{4} -2.43091 q^{5} +0.698857 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.51160 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.698857 q^{3} +1.00000 q^{4} -2.43091 q^{5} +0.698857 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.51160 q^{9} +2.43091 q^{10} -0.698857 q^{12} -2.86182 q^{13} -1.00000 q^{14} +1.69886 q^{15} +1.00000 q^{16} -1.90931 q^{17} +2.51160 q^{18} -1.00000 q^{19} -2.43091 q^{20} -0.698857 q^{21} +6.50318 q^{23} +0.698857 q^{24} +0.909313 q^{25} +2.86182 q^{26} +3.85182 q^{27} +1.00000 q^{28} +7.02477 q^{29} -1.69886 q^{30} +5.43679 q^{31} -1.00000 q^{32} +1.90931 q^{34} -2.43091 q^{35} -2.51160 q^{36} +0.383411 q^{37} +1.00000 q^{38} +2.00000 q^{39} +2.43091 q^{40} +7.29703 q^{41} +0.698857 q^{42} -5.17726 q^{43} +6.10547 q^{45} -6.50318 q^{46} +4.08658 q^{47} -0.698857 q^{48} -6.00000 q^{49} -0.909313 q^{50} +1.33434 q^{51} -2.86182 q^{52} -0.348640 q^{53} -3.85182 q^{54} -1.00000 q^{56} +0.698857 q^{57} -7.02477 q^{58} -1.62706 q^{59} +1.69886 q^{60} +15.1777 q^{61} -5.43679 q^{62} -2.51160 q^{63} +1.00000 q^{64} +6.95681 q^{65} -7.75224 q^{67} -1.90931 q^{68} -4.54479 q^{69} +2.43091 q^{70} -13.9384 q^{71} +2.51160 q^{72} +8.33022 q^{73} -0.383411 q^{74} -0.635480 q^{75} -1.00000 q^{76} -2.00000 q^{78} -2.46253 q^{79} -2.43091 q^{80} +4.84293 q^{81} -7.29703 q^{82} -3.11135 q^{83} -0.698857 q^{84} +4.64136 q^{85} +5.17726 q^{86} -4.90931 q^{87} -3.03750 q^{89} -6.10547 q^{90} -2.86182 q^{91} +6.50318 q^{92} -3.79954 q^{93} -4.08658 q^{94} +2.43091 q^{95} +0.698857 q^{96} -12.8059 q^{97} +6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 4 q^{7} - 4 q^{8} + O(q^{10}) \) \( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} - 2 q^{12} + 4 q^{13} - 4 q^{14} + 6 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{19} - 2 q^{20} - 2 q^{21} - 8 q^{23} + 2 q^{24} - 8 q^{25} - 4 q^{26} - 14 q^{27} + 4 q^{28} - 2 q^{29} - 6 q^{30} - 4 q^{32} - 4 q^{34} - 2 q^{35} - 10 q^{37} + 4 q^{38} + 8 q^{39} + 2 q^{40} + 2 q^{41} + 2 q^{42} - 16 q^{43} - 8 q^{45} + 8 q^{46} - 2 q^{48} - 24 q^{49} + 8 q^{50} + 4 q^{52} - 6 q^{53} + 14 q^{54} - 4 q^{56} + 2 q^{57} + 2 q^{58} + 22 q^{59} + 6 q^{60} + 2 q^{61} + 4 q^{64} + 20 q^{65} - 20 q^{67} + 4 q^{68} - 2 q^{69} + 2 q^{70} - 10 q^{71} + 10 q^{74} + 2 q^{75} - 4 q^{76} - 8 q^{78} - 6 q^{79} - 2 q^{80} + 20 q^{81} - 2 q^{82} + 34 q^{83} - 2 q^{84} + 16 q^{86} - 8 q^{87} - 2 q^{89} + 8 q^{90} + 4 q^{91} - 8 q^{92} - 40 q^{93} + 2 q^{95} + 2 q^{96} - 8 q^{97} + 24 q^{98} + O(q^{100}) \)

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
\(3\) −0.698857 −0.403485 −0.201743 0.979439i \(-0.564660\pi\)
−0.201743 + 0.979439i \(0.564660\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.43091 −1.08714 −0.543568 0.839365i \(-0.682927\pi\)
−0.543568 + 0.839365i \(0.682927\pi\)
\(6\) 0.698857 0.285307
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.51160 −0.837200
\(10\) 2.43091 0.768721
\(11\) 0 0
\(12\) −0.698857 −0.201743
\(13\) −2.86182 −0.793725 −0.396862 0.917878i \(-0.629901\pi\)
−0.396862 + 0.917878i \(0.629901\pi\)
\(14\) −1.00000 −0.267261
\(15\) 1.69886 0.438643
\(16\) 1.00000 0.250000
\(17\) −1.90931 −0.463076 −0.231538 0.972826i \(-0.574376\pi\)
−0.231538 + 0.972826i \(0.574376\pi\)
\(18\) 2.51160 0.591990
\(19\) −1.00000 −0.229416
\(20\) −2.43091 −0.543568
\(21\) −0.698857 −0.152503
\(22\) 0 0
\(23\) 6.50318 1.35601 0.678003 0.735059i \(-0.262845\pi\)
0.678003 + 0.735059i \(0.262845\pi\)
\(24\) 0.698857 0.142654
\(25\) 0.909313 0.181863
\(26\) 2.86182 0.561248
\(27\) 3.85182 0.741283
\(28\) 1.00000 0.188982
\(29\) 7.02477 1.30447 0.652234 0.758018i \(-0.273832\pi\)
0.652234 + 0.758018i \(0.273832\pi\)
\(30\) −1.69886 −0.310167
\(31\) 5.43679 0.976477 0.488238 0.872710i \(-0.337640\pi\)
0.488238 + 0.872710i \(0.337640\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 1.90931 0.327444
\(35\) −2.43091 −0.410898
\(36\) −2.51160 −0.418600
\(37\) 0.383411 0.0630323 0.0315162 0.999503i \(-0.489966\pi\)
0.0315162 + 0.999503i \(0.489966\pi\)
\(38\) 1.00000 0.162221
\(39\) 2.00000 0.320256
\(40\) 2.43091 0.384360
\(41\) 7.29703 1.13960 0.569802 0.821782i \(-0.307020\pi\)
0.569802 + 0.821782i \(0.307020\pi\)
\(42\) 0.698857 0.107836
\(43\) −5.17726 −0.789525 −0.394763 0.918783i \(-0.629173\pi\)
−0.394763 + 0.918783i \(0.629173\pi\)
\(44\) 0 0
\(45\) 6.10547 0.910149
\(46\) −6.50318 −0.958841
\(47\) 4.08658 0.596088 0.298044 0.954552i \(-0.403666\pi\)
0.298044 + 0.954552i \(0.403666\pi\)
\(48\) −0.698857 −0.100871
\(49\) −6.00000 −0.857143
\(50\) −0.909313 −0.128596
\(51\) 1.33434 0.186845
\(52\) −2.86182 −0.396862
\(53\) −0.348640 −0.0478894 −0.0239447 0.999713i \(-0.507623\pi\)
−0.0239447 + 0.999713i \(0.507623\pi\)
\(54\) −3.85182 −0.524166
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) 0.698857 0.0925659
\(58\) −7.02477 −0.922398
\(59\) −1.62706 −0.211825 −0.105913 0.994375i \(-0.533776\pi\)
−0.105913 + 0.994375i \(0.533776\pi\)
\(60\) 1.69886 0.219321
\(61\) 15.1777 1.94331 0.971655 0.236403i \(-0.0759686\pi\)
0.971655 + 0.236403i \(0.0759686\pi\)
\(62\) −5.43679 −0.690473
\(63\) −2.51160 −0.316432
\(64\) 1.00000 0.125000
\(65\) 6.95681 0.862886
\(66\) 0 0
\(67\) −7.75224 −0.947087 −0.473543 0.880771i \(-0.657025\pi\)
−0.473543 + 0.880771i \(0.657025\pi\)
\(68\) −1.90931 −0.231538
\(69\) −4.54479 −0.547129
\(70\) 2.43091 0.290549
\(71\) −13.9384 −1.65418 −0.827092 0.562067i \(-0.810006\pi\)
−0.827092 + 0.562067i \(0.810006\pi\)
\(72\) 2.51160 0.295995
\(73\) 8.33022 0.974979 0.487490 0.873129i \(-0.337913\pi\)
0.487490 + 0.873129i \(0.337913\pi\)
\(74\) −0.383411 −0.0445706
\(75\) −0.635480 −0.0733789
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) −2.46253 −0.277056 −0.138528 0.990359i \(-0.544237\pi\)
−0.138528 + 0.990359i \(0.544237\pi\)
\(80\) −2.43091 −0.271784
\(81\) 4.84293 0.538103
\(82\) −7.29703 −0.805822
\(83\) −3.11135 −0.341515 −0.170757 0.985313i \(-0.554621\pi\)
−0.170757 + 0.985313i \(0.554621\pi\)
\(84\) −0.698857 −0.0762516
\(85\) 4.64136 0.503427
\(86\) 5.17726 0.558279
\(87\) −4.90931 −0.526334
\(88\) 0 0
\(89\) −3.03750 −0.321974 −0.160987 0.986956i \(-0.551468\pi\)
−0.160987 + 0.986956i \(0.551468\pi\)
\(90\) −6.10547 −0.643573
\(91\) −2.86182 −0.300000
\(92\) 6.50318 0.678003
\(93\) −3.79954 −0.393994
\(94\) −4.08658 −0.421498
\(95\) 2.43091 0.249406
\(96\) 0.698857 0.0713268
\(97\) −12.8059 −1.30024 −0.650121 0.759831i \(-0.725282\pi\)
−0.650121 + 0.759831i \(0.725282\pi\)
\(98\) 6.00000 0.606092
\(99\) 0 0
\(100\) 0.909313 0.0909313
\(101\) −6.27684 −0.624569 −0.312285 0.949989i \(-0.601094\pi\)
−0.312285 + 0.949989i \(0.601094\pi\)
\(102\) −1.33434 −0.132119
\(103\) −15.9384 −1.57046 −0.785228 0.619206i \(-0.787454\pi\)
−0.785228 + 0.619206i \(0.787454\pi\)
\(104\) 2.86182 0.280624
\(105\) 1.69886 0.165791
\(106\) 0.348640 0.0338629
\(107\) −0.268424 −0.0259495 −0.0129748 0.999916i \(-0.504130\pi\)
−0.0129748 + 0.999916i \(0.504130\pi\)
\(108\) 3.85182 0.370642
\(109\) −1.61228 −0.154429 −0.0772143 0.997015i \(-0.524603\pi\)
−0.0772143 + 0.997015i \(0.524603\pi\)
\(110\) 0 0
\(111\) −0.267949 −0.0254326
\(112\) 1.00000 0.0944911
\(113\) 9.13565 0.859410 0.429705 0.902969i \(-0.358618\pi\)
0.429705 + 0.902969i \(0.358618\pi\)
\(114\) −0.698857 −0.0654540
\(115\) −15.8086 −1.47416
\(116\) 7.02477 0.652234
\(117\) 7.18773 0.664506
\(118\) 1.62706 0.149783
\(119\) −1.90931 −0.175026
\(120\) −1.69886 −0.155084
\(121\) 0 0
\(122\) −15.1777 −1.37413
\(123\) −5.09958 −0.459814
\(124\) 5.43679 0.488238
\(125\) 9.94408 0.889426
\(126\) 2.51160 0.223751
\(127\) 16.0782 1.42671 0.713353 0.700805i \(-0.247176\pi\)
0.713353 + 0.700805i \(0.247176\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 3.61817 0.318562
\(130\) −6.95681 −0.610153
\(131\) 2.20046 0.192255 0.0961275 0.995369i \(-0.469354\pi\)
0.0961275 + 0.995369i \(0.469354\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) 7.75224 0.669691
\(135\) −9.36342 −0.805875
\(136\) 1.90931 0.163722
\(137\) 8.08246 0.690531 0.345266 0.938505i \(-0.387789\pi\)
0.345266 + 0.938505i \(0.387789\pi\)
\(138\) 4.54479 0.386878
\(139\) −0.161382 −0.0136882 −0.00684412 0.999977i \(-0.502179\pi\)
−0.00684412 + 0.999977i \(0.502179\pi\)
\(140\) −2.43091 −0.205449
\(141\) −2.85593 −0.240513
\(142\) 13.9384 1.16968
\(143\) 0 0
\(144\) −2.51160 −0.209300
\(145\) −17.0766 −1.41813
\(146\) −8.33022 −0.689414
\(147\) 4.19314 0.345845
\(148\) 0.383411 0.0315162
\(149\) 12.8332 1.05134 0.525669 0.850689i \(-0.323815\pi\)
0.525669 + 0.850689i \(0.323815\pi\)
\(150\) 0.635480 0.0518867
\(151\) 8.17884 0.665584 0.332792 0.943000i \(-0.392009\pi\)
0.332792 + 0.943000i \(0.392009\pi\)
\(152\) 1.00000 0.0811107
\(153\) 4.79543 0.387687
\(154\) 0 0
\(155\) −13.2163 −1.06156
\(156\) 2.00000 0.160128
\(157\) −9.36041 −0.747042 −0.373521 0.927622i \(-0.621850\pi\)
−0.373521 + 0.927622i \(0.621850\pi\)
\(158\) 2.46253 0.195908
\(159\) 0.243650 0.0193227
\(160\) 2.43091 0.192180
\(161\) 6.50318 0.512522
\(162\) −4.84293 −0.380496
\(163\) −5.79954 −0.454255 −0.227128 0.973865i \(-0.572933\pi\)
−0.227128 + 0.973865i \(0.572933\pi\)
\(164\) 7.29703 0.569802
\(165\) 0 0
\(166\) 3.11135 0.241488
\(167\) −10.6791 −0.826377 −0.413189 0.910646i \(-0.635585\pi\)
−0.413189 + 0.910646i \(0.635585\pi\)
\(168\) 0.698857 0.0539180
\(169\) −4.81001 −0.370001
\(170\) −4.64136 −0.355976
\(171\) 2.51160 0.192067
\(172\) −5.17726 −0.394763
\(173\) 14.5839 1.10879 0.554396 0.832253i \(-0.312949\pi\)
0.554396 + 0.832253i \(0.312949\pi\)
\(174\) 4.90931 0.372174
\(175\) 0.909313 0.0687376
\(176\) 0 0
\(177\) 1.13708 0.0854684
\(178\) 3.03750 0.227670
\(179\) −7.52906 −0.562748 −0.281374 0.959598i \(-0.590790\pi\)
−0.281374 + 0.959598i \(0.590790\pi\)
\(180\) 6.10547 0.455075
\(181\) 0.354524 0.0263516 0.0131758 0.999913i \(-0.495806\pi\)
0.0131758 + 0.999913i \(0.495806\pi\)
\(182\) 2.86182 0.212132
\(183\) −10.6071 −0.784097
\(184\) −6.50318 −0.479421
\(185\) −0.932036 −0.0685246
\(186\) 3.79954 0.278596
\(187\) 0 0
\(188\) 4.08658 0.298044
\(189\) 3.85182 0.280179
\(190\) −2.43091 −0.176357
\(191\) −5.89659 −0.426662 −0.213331 0.976980i \(-0.568431\pi\)
−0.213331 + 0.976980i \(0.568431\pi\)
\(192\) −0.698857 −0.0504357
\(193\) −12.9095 −0.929247 −0.464623 0.885508i \(-0.653810\pi\)
−0.464623 + 0.885508i \(0.653810\pi\)
\(194\) 12.8059 0.919410
\(195\) −4.86182 −0.348162
\(196\) −6.00000 −0.428571
\(197\) −22.0309 −1.56963 −0.784817 0.619728i \(-0.787243\pi\)
−0.784817 + 0.619728i \(0.787243\pi\)
\(198\) 0 0
\(199\) −10.2235 −0.724722 −0.362361 0.932038i \(-0.618029\pi\)
−0.362361 + 0.932038i \(0.618029\pi\)
\(200\) −0.909313 −0.0642981
\(201\) 5.41771 0.382136
\(202\) 6.27684 0.441637
\(203\) 7.02477 0.493043
\(204\) 1.33434 0.0934223
\(205\) −17.7384 −1.23890
\(206\) 15.9384 1.11048
\(207\) −16.3334 −1.13525
\(208\) −2.86182 −0.198431
\(209\) 0 0
\(210\) −1.69886 −0.117232
\(211\) −10.4846 −0.721787 −0.360894 0.932607i \(-0.617528\pi\)
−0.360894 + 0.932607i \(0.617528\pi\)
\(212\) −0.348640 −0.0239447
\(213\) 9.74095 0.667439
\(214\) 0.268424 0.0183491
\(215\) 12.5854 0.858320
\(216\) −3.85182 −0.262083
\(217\) 5.43679 0.369073
\(218\) 1.61228 0.109198
\(219\) −5.82164 −0.393390
\(220\) 0 0
\(221\) 5.46410 0.367555
\(222\) 0.267949 0.0179836
\(223\) 23.0671 1.54468 0.772342 0.635207i \(-0.219085\pi\)
0.772342 + 0.635207i \(0.219085\pi\)
\(224\) −1.00000 −0.0668153
\(225\) −2.28383 −0.152255
\(226\) −9.13565 −0.607694
\(227\) 0.487299 0.0323432 0.0161716 0.999869i \(-0.494852\pi\)
0.0161716 + 0.999869i \(0.494852\pi\)
\(228\) 0.698857 0.0462829
\(229\) −29.2732 −1.93443 −0.967214 0.253963i \(-0.918266\pi\)
−0.967214 + 0.253963i \(0.918266\pi\)
\(230\) 15.8086 1.04239
\(231\) 0 0
\(232\) −7.02477 −0.461199
\(233\) −22.4082 −1.46801 −0.734005 0.679145i \(-0.762351\pi\)
−0.734005 + 0.679145i \(0.762351\pi\)
\(234\) −7.18773 −0.469877
\(235\) −9.93409 −0.648028
\(236\) −1.62706 −0.105913
\(237\) 1.72095 0.111788
\(238\) 1.90931 0.123762
\(239\) 11.6847 0.755824 0.377912 0.925842i \(-0.376642\pi\)
0.377912 + 0.925842i \(0.376642\pi\)
\(240\) 1.69886 0.109661
\(241\) −5.50571 −0.354654 −0.177327 0.984152i \(-0.556745\pi\)
−0.177327 + 0.984152i \(0.556745\pi\)
\(242\) 0 0
\(243\) −14.9400 −0.958400
\(244\) 15.1777 0.971655
\(245\) 14.5854 0.931830
\(246\) 5.09958 0.325137
\(247\) 2.86182 0.182093
\(248\) −5.43679 −0.345237
\(249\) 2.17439 0.137796
\(250\) −9.94408 −0.628919
\(251\) −6.89042 −0.434920 −0.217460 0.976069i \(-0.569777\pi\)
−0.217460 + 0.976069i \(0.569777\pi\)
\(252\) −2.51160 −0.158216
\(253\) 0 0
\(254\) −16.0782 −1.00883
\(255\) −3.24365 −0.203125
\(256\) 1.00000 0.0625000
\(257\) 4.78366 0.298397 0.149198 0.988807i \(-0.452331\pi\)
0.149198 + 0.988807i \(0.452331\pi\)
\(258\) −3.61817 −0.225257
\(259\) 0.383411 0.0238240
\(260\) 6.95681 0.431443
\(261\) −17.6434 −1.09210
\(262\) −2.20046 −0.135945
\(263\) 10.8979 0.671992 0.335996 0.941863i \(-0.390927\pi\)
0.335996 + 0.941863i \(0.390927\pi\)
\(264\) 0 0
\(265\) 0.847512 0.0520623
\(266\) 1.00000 0.0613139
\(267\) 2.12278 0.129912
\(268\) −7.75224 −0.473543
\(269\) −22.6577 −1.38147 −0.690733 0.723110i \(-0.742712\pi\)
−0.690733 + 0.723110i \(0.742712\pi\)
\(270\) 9.36342 0.569840
\(271\) 3.58655 0.217867 0.108934 0.994049i \(-0.465256\pi\)
0.108934 + 0.994049i \(0.465256\pi\)
\(272\) −1.90931 −0.115769
\(273\) 2.00000 0.121046
\(274\) −8.08246 −0.488279
\(275\) 0 0
\(276\) −4.54479 −0.273564
\(277\) 0.0186108 0.00111822 0.000559109 1.00000i \(-0.499822\pi\)
0.000559109 1.00000i \(0.499822\pi\)
\(278\) 0.161382 0.00967905
\(279\) −13.6550 −0.817506
\(280\) 2.43091 0.145275
\(281\) 21.2684 1.26877 0.634384 0.773018i \(-0.281254\pi\)
0.634384 + 0.773018i \(0.281254\pi\)
\(282\) 2.85593 0.170068
\(283\) −23.1131 −1.37393 −0.686966 0.726689i \(-0.741058\pi\)
−0.686966 + 0.726689i \(0.741058\pi\)
\(284\) −13.9384 −0.827092
\(285\) −1.69886 −0.100632
\(286\) 0 0
\(287\) 7.29703 0.430730
\(288\) 2.51160 0.147997
\(289\) −13.3545 −0.785560
\(290\) 17.0766 1.00277
\(291\) 8.94949 0.524629
\(292\) 8.33022 0.487490
\(293\) 3.69044 0.215598 0.107799 0.994173i \(-0.465620\pi\)
0.107799 + 0.994173i \(0.465620\pi\)
\(294\) −4.19314 −0.244549
\(295\) 3.95523 0.230283
\(296\) −0.383411 −0.0222853
\(297\) 0 0
\(298\) −12.8332 −0.743408
\(299\) −18.6109 −1.07630
\(300\) −0.635480 −0.0366894
\(301\) −5.17726 −0.298412
\(302\) −8.17884 −0.470639
\(303\) 4.38662 0.252005
\(304\) −1.00000 −0.0573539
\(305\) −36.8957 −2.11264
\(306\) −4.79543 −0.274136
\(307\) −18.1852 −1.03788 −0.518942 0.854809i \(-0.673674\pi\)
−0.518942 + 0.854809i \(0.673674\pi\)
\(308\) 0 0
\(309\) 11.1387 0.633656
\(310\) 13.2163 0.750638
\(311\) 30.4630 1.72740 0.863699 0.504008i \(-0.168142\pi\)
0.863699 + 0.504008i \(0.168142\pi\)
\(312\) −2.00000 −0.113228
\(313\) −11.4830 −0.649057 −0.324529 0.945876i \(-0.605206\pi\)
−0.324529 + 0.945876i \(0.605206\pi\)
\(314\) 9.36041 0.528238
\(315\) 6.10547 0.344004
\(316\) −2.46253 −0.138528
\(317\) 17.6836 0.993213 0.496606 0.867976i \(-0.334579\pi\)
0.496606 + 0.867976i \(0.334579\pi\)
\(318\) −0.243650 −0.0136632
\(319\) 0 0
\(320\) −2.43091 −0.135892
\(321\) 0.187590 0.0104703
\(322\) −6.50318 −0.362408
\(323\) 1.90931 0.106237
\(324\) 4.84293 0.269051
\(325\) −2.60229 −0.144349
\(326\) 5.79954 0.321207
\(327\) 1.12675 0.0623097
\(328\) −7.29703 −0.402911
\(329\) 4.08658 0.225300
\(330\) 0 0
\(331\) −22.1282 −1.21628 −0.608138 0.793832i \(-0.708083\pi\)
−0.608138 + 0.793832i \(0.708083\pi\)
\(332\) −3.11135 −0.170757
\(333\) −0.962974 −0.0527706
\(334\) 10.6791 0.584337
\(335\) 18.8450 1.02961
\(336\) −0.698857 −0.0381258
\(337\) −14.3793 −0.783290 −0.391645 0.920116i \(-0.628094\pi\)
−0.391645 + 0.920116i \(0.628094\pi\)
\(338\) 4.81001 0.261630
\(339\) −6.38451 −0.346759
\(340\) 4.64136 0.251713
\(341\) 0 0
\(342\) −2.51160 −0.135812
\(343\) −13.0000 −0.701934
\(344\) 5.17726 0.279139
\(345\) 11.0480 0.594803
\(346\) −14.5839 −0.784034
\(347\) 0.879129 0.0471941 0.0235971 0.999722i \(-0.492488\pi\)
0.0235971 + 0.999722i \(0.492488\pi\)
\(348\) −4.90931 −0.263167
\(349\) −6.50859 −0.348397 −0.174198 0.984711i \(-0.555733\pi\)
−0.174198 + 0.984711i \(0.555733\pi\)
\(350\) −0.909313 −0.0486048
\(351\) −11.0232 −0.588375
\(352\) 0 0
\(353\) 2.71932 0.144735 0.0723675 0.997378i \(-0.476945\pi\)
0.0723675 + 0.997378i \(0.476945\pi\)
\(354\) −1.13708 −0.0604353
\(355\) 33.8830 1.79832
\(356\) −3.03750 −0.160987
\(357\) 1.33434 0.0706206
\(358\) 7.52906 0.397923
\(359\) 23.1057 1.21947 0.609735 0.792605i \(-0.291276\pi\)
0.609735 + 0.792605i \(0.291276\pi\)
\(360\) −6.10547 −0.321786
\(361\) 1.00000 0.0526316
\(362\) −0.354524 −0.0186334
\(363\) 0 0
\(364\) −2.86182 −0.150000
\(365\) −20.2500 −1.05993
\(366\) 10.6071 0.554440
\(367\) −26.2311 −1.36925 −0.684627 0.728894i \(-0.740035\pi\)
−0.684627 + 0.728894i \(0.740035\pi\)
\(368\) 6.50318 0.339002
\(369\) −18.3272 −0.954077
\(370\) 0.932036 0.0484542
\(371\) −0.348640 −0.0181005
\(372\) −3.79954 −0.196997
\(373\) −11.4943 −0.595152 −0.297576 0.954698i \(-0.596178\pi\)
−0.297576 + 0.954698i \(0.596178\pi\)
\(374\) 0 0
\(375\) −6.94949 −0.358870
\(376\) −4.08658 −0.210749
\(377\) −20.1036 −1.03539
\(378\) −3.85182 −0.198116
\(379\) 0.416325 0.0213852 0.0106926 0.999943i \(-0.496596\pi\)
0.0106926 + 0.999943i \(0.496596\pi\)
\(380\) 2.43091 0.124703
\(381\) −11.2363 −0.575655
\(382\) 5.89659 0.301696
\(383\) 31.8396 1.62693 0.813463 0.581617i \(-0.197580\pi\)
0.813463 + 0.581617i \(0.197580\pi\)
\(384\) 0.698857 0.0356634
\(385\) 0 0
\(386\) 12.9095 0.657077
\(387\) 13.0032 0.660990
\(388\) −12.8059 −0.650121
\(389\) −3.34864 −0.169783 −0.0848914 0.996390i \(-0.527054\pi\)
−0.0848914 + 0.996390i \(0.527054\pi\)
\(390\) 4.86182 0.246188
\(391\) −12.4166 −0.627935
\(392\) 6.00000 0.303046
\(393\) −1.53781 −0.0775721
\(394\) 22.0309 1.10990
\(395\) 5.98617 0.301197
\(396\) 0 0
\(397\) 2.41230 0.121070 0.0605349 0.998166i \(-0.480719\pi\)
0.0605349 + 0.998166i \(0.480719\pi\)
\(398\) 10.2235 0.512456
\(399\) 0.698857 0.0349866
\(400\) 0.909313 0.0454656
\(401\) −32.1979 −1.60789 −0.803944 0.594705i \(-0.797269\pi\)
−0.803944 + 0.594705i \(0.797269\pi\)
\(402\) −5.41771 −0.270211
\(403\) −15.5591 −0.775054
\(404\) −6.27684 −0.312285
\(405\) −11.7727 −0.584990
\(406\) −7.02477 −0.348634
\(407\) 0 0
\(408\) −1.33434 −0.0660595
\(409\) 34.0985 1.68606 0.843032 0.537863i \(-0.180768\pi\)
0.843032 + 0.537863i \(0.180768\pi\)
\(410\) 17.7384 0.876038
\(411\) −5.64849 −0.278619
\(412\) −15.9384 −0.785228
\(413\) −1.62706 −0.0800624
\(414\) 16.3334 0.802742
\(415\) 7.56340 0.371273
\(416\) 2.86182 0.140312
\(417\) 0.112783 0.00552301
\(418\) 0 0
\(419\) 17.3423 0.847225 0.423613 0.905843i \(-0.360762\pi\)
0.423613 + 0.905843i \(0.360762\pi\)
\(420\) 1.69886 0.0828957
\(421\) −6.36356 −0.310141 −0.155071 0.987903i \(-0.549560\pi\)
−0.155071 + 0.987903i \(0.549560\pi\)
\(422\) 10.4846 0.510381
\(423\) −10.2638 −0.499045
\(424\) 0.348640 0.0169315
\(425\) −1.73616 −0.0842163
\(426\) −9.74095 −0.471950
\(427\) 15.1777 0.734502
\(428\) −0.268424 −0.0129748
\(429\) 0 0
\(430\) −12.5854 −0.606924
\(431\) 25.2529 1.21639 0.608194 0.793788i \(-0.291894\pi\)
0.608194 + 0.793788i \(0.291894\pi\)
\(432\) 3.85182 0.185321
\(433\) 7.31865 0.351712 0.175856 0.984416i \(-0.443731\pi\)
0.175856 + 0.984416i \(0.443731\pi\)
\(434\) −5.43679 −0.260974
\(435\) 11.9341 0.572196
\(436\) −1.61228 −0.0772143
\(437\) −6.50318 −0.311089
\(438\) 5.82164 0.278169
\(439\) −8.02861 −0.383185 −0.191592 0.981475i \(-0.561365\pi\)
−0.191592 + 0.981475i \(0.561365\pi\)
\(440\) 0 0
\(441\) 15.0696 0.717600
\(442\) −5.46410 −0.259901
\(443\) −33.0740 −1.57140 −0.785698 0.618611i \(-0.787696\pi\)
−0.785698 + 0.618611i \(0.787696\pi\)
\(444\) −0.267949 −0.0127163
\(445\) 7.38389 0.350030
\(446\) −23.0671 −1.09226
\(447\) −8.96858 −0.424199
\(448\) 1.00000 0.0472456
\(449\) 8.93958 0.421885 0.210942 0.977498i \(-0.432347\pi\)
0.210942 + 0.977498i \(0.432347\pi\)
\(450\) 2.28383 0.107661
\(451\) 0 0
\(452\) 9.13565 0.429705
\(453\) −5.71584 −0.268554
\(454\) −0.487299 −0.0228701
\(455\) 6.95681 0.326140
\(456\) −0.698857 −0.0327270
\(457\) 1.90520 0.0891215 0.0445608 0.999007i \(-0.485811\pi\)
0.0445608 + 0.999007i \(0.485811\pi\)
\(458\) 29.2732 1.36785
\(459\) −7.35433 −0.343271
\(460\) −15.8086 −0.737081
\(461\) −21.7813 −1.01446 −0.507229 0.861812i \(-0.669330\pi\)
−0.507229 + 0.861812i \(0.669330\pi\)
\(462\) 0 0
\(463\) −36.0716 −1.67639 −0.838196 0.545370i \(-0.816389\pi\)
−0.838196 + 0.545370i \(0.816389\pi\)
\(464\) 7.02477 0.326117
\(465\) 9.23633 0.428325
\(466\) 22.4082 1.03804
\(467\) −15.8955 −0.735555 −0.367778 0.929914i \(-0.619881\pi\)
−0.367778 + 0.929914i \(0.619881\pi\)
\(468\) 7.18773 0.332253
\(469\) −7.75224 −0.357965
\(470\) 9.93409 0.458225
\(471\) 6.54159 0.301420
\(472\) 1.62706 0.0748915
\(473\) 0 0
\(474\) −1.72095 −0.0790460
\(475\) −0.909313 −0.0417221
\(476\) −1.90931 −0.0875132
\(477\) 0.875644 0.0400930
\(478\) −11.6847 −0.534448
\(479\) 5.40799 0.247097 0.123549 0.992339i \(-0.460572\pi\)
0.123549 + 0.992339i \(0.460572\pi\)
\(480\) −1.69886 −0.0775419
\(481\) −1.09725 −0.0500303
\(482\) 5.50571 0.250778
\(483\) −4.54479 −0.206795
\(484\) 0 0
\(485\) 31.1300 1.41354
\(486\) 14.9400 0.677691
\(487\) −17.5518 −0.795347 −0.397674 0.917527i \(-0.630182\pi\)
−0.397674 + 0.917527i \(0.630182\pi\)
\(488\) −15.1777 −0.687064
\(489\) 4.05305 0.183285
\(490\) −14.5854 −0.658903
\(491\) −1.28718 −0.0580895 −0.0290448 0.999578i \(-0.509247\pi\)
−0.0290448 + 0.999578i \(0.509247\pi\)
\(492\) −5.09958 −0.229907
\(493\) −13.4125 −0.604068
\(494\) −2.86182 −0.128759
\(495\) 0 0
\(496\) 5.43679 0.244119
\(497\) −13.9384 −0.625222
\(498\) −2.17439 −0.0974367
\(499\) −34.0586 −1.52467 −0.762337 0.647180i \(-0.775948\pi\)
−0.762337 + 0.647180i \(0.775948\pi\)
\(500\) 9.94408 0.444713
\(501\) 7.46320 0.333431
\(502\) 6.89042 0.307535
\(503\) −19.2313 −0.857482 −0.428741 0.903427i \(-0.641043\pi\)
−0.428741 + 0.903427i \(0.641043\pi\)
\(504\) 2.51160 0.111876
\(505\) 15.2584 0.678991
\(506\) 0 0
\(507\) 3.36151 0.149290
\(508\) 16.0782 0.713353
\(509\) −18.7783 −0.832334 −0.416167 0.909288i \(-0.636627\pi\)
−0.416167 + 0.909288i \(0.636627\pi\)
\(510\) 3.24365 0.143631
\(511\) 8.33022 0.368507
\(512\) −1.00000 −0.0441942
\(513\) −3.85182 −0.170062
\(514\) −4.78366 −0.210998
\(515\) 38.7448 1.70730
\(516\) 3.61817 0.159281
\(517\) 0 0
\(518\) −0.383411 −0.0168461
\(519\) −10.1920 −0.447381
\(520\) −6.95681 −0.305076
\(521\) −18.2036 −0.797515 −0.398757 0.917056i \(-0.630558\pi\)
−0.398757 + 0.917056i \(0.630558\pi\)
\(522\) 17.6434 0.772231
\(523\) −34.9866 −1.52986 −0.764930 0.644114i \(-0.777226\pi\)
−0.764930 + 0.644114i \(0.777226\pi\)
\(524\) 2.20046 0.0961275
\(525\) −0.635480 −0.0277346
\(526\) −10.8979 −0.475170
\(527\) −10.3805 −0.452183
\(528\) 0 0
\(529\) 19.2913 0.838754
\(530\) −0.847512 −0.0368136
\(531\) 4.08652 0.177340
\(532\) −1.00000 −0.0433555
\(533\) −20.8828 −0.904533
\(534\) −2.12278 −0.0918616
\(535\) 0.652514 0.0282106
\(536\) 7.75224 0.334846
\(537\) 5.26173 0.227061
\(538\) 22.6577 0.976844
\(539\) 0 0
\(540\) −9.36342 −0.402937
\(541\) −26.3177 −1.13149 −0.565743 0.824582i \(-0.691411\pi\)
−0.565743 + 0.824582i \(0.691411\pi\)
\(542\) −3.58655 −0.154055
\(543\) −0.247762 −0.0106325
\(544\) 1.90931 0.0818611
\(545\) 3.91931 0.167885
\(546\) −2.00000 −0.0855921
\(547\) 45.9751 1.96575 0.982876 0.184268i \(-0.0589913\pi\)
0.982876 + 0.184268i \(0.0589913\pi\)
\(548\) 8.08246 0.345266
\(549\) −38.1204 −1.62694
\(550\) 0 0
\(551\) −7.02477 −0.299265
\(552\) 4.54479 0.193439
\(553\) −2.46253 −0.104717
\(554\) −0.0186108 −0.000790699 0
\(555\) 0.651360 0.0276487
\(556\) −0.161382 −0.00684412
\(557\) −11.7236 −0.496746 −0.248373 0.968664i \(-0.579896\pi\)
−0.248373 + 0.968664i \(0.579896\pi\)
\(558\) 13.6550 0.578064
\(559\) 14.8164 0.626666
\(560\) −2.43091 −0.102725
\(561\) 0 0
\(562\) −21.2684 −0.897154
\(563\) −3.37184 −0.142106 −0.0710530 0.997473i \(-0.522636\pi\)
−0.0710530 + 0.997473i \(0.522636\pi\)
\(564\) −2.85593 −0.120256
\(565\) −22.2079 −0.934294
\(566\) 23.1131 0.971517
\(567\) 4.84293 0.203384
\(568\) 13.9384 0.584842
\(569\) −37.3809 −1.56709 −0.783544 0.621336i \(-0.786590\pi\)
−0.783544 + 0.621336i \(0.786590\pi\)
\(570\) 1.69886 0.0711573
\(571\) −19.2610 −0.806046 −0.403023 0.915190i \(-0.632041\pi\)
−0.403023 + 0.915190i \(0.632041\pi\)
\(572\) 0 0
\(573\) 4.12087 0.172152
\(574\) −7.29703 −0.304572
\(575\) 5.91342 0.246607
\(576\) −2.51160 −0.104650
\(577\) −0.476971 −0.0198566 −0.00992829 0.999951i \(-0.503160\pi\)
−0.00992829 + 0.999951i \(0.503160\pi\)
\(578\) 13.3545 0.555475
\(579\) 9.02190 0.374937
\(580\) −17.0766 −0.709066
\(581\) −3.11135 −0.129081
\(582\) −8.94949 −0.370968
\(583\) 0 0
\(584\) −8.33022 −0.344707
\(585\) −17.4727 −0.722408
\(586\) −3.69044 −0.152451
\(587\) −26.4582 −1.09205 −0.546024 0.837770i \(-0.683859\pi\)
−0.546024 + 0.837770i \(0.683859\pi\)
\(588\) 4.19314 0.172922
\(589\) −5.43679 −0.224019
\(590\) −3.95523 −0.162834
\(591\) 15.3964 0.633324
\(592\) 0.383411 0.0157581
\(593\) 7.81097 0.320758 0.160379 0.987056i \(-0.448728\pi\)
0.160379 + 0.987056i \(0.448728\pi\)
\(594\) 0 0
\(595\) 4.64136 0.190277
\(596\) 12.8332 0.525669
\(597\) 7.14474 0.292415
\(598\) 18.6109 0.761056
\(599\) −29.5804 −1.20862 −0.604312 0.796748i \(-0.706552\pi\)
−0.604312 + 0.796748i \(0.706552\pi\)
\(600\) 0.635480 0.0259434
\(601\) 13.6808 0.558051 0.279025 0.960284i \(-0.409989\pi\)
0.279025 + 0.960284i \(0.409989\pi\)
\(602\) 5.17726 0.211009
\(603\) 19.4705 0.792901
\(604\) 8.17884 0.332792
\(605\) 0 0
\(606\) −4.38662 −0.178194
\(607\) −8.70651 −0.353386 −0.176693 0.984266i \(-0.556540\pi\)
−0.176693 + 0.984266i \(0.556540\pi\)
\(608\) 1.00000 0.0405554
\(609\) −4.90931 −0.198935
\(610\) 36.8957 1.49386
\(611\) −11.6950 −0.473130
\(612\) 4.79543 0.193844
\(613\) 43.4395 1.75451 0.877253 0.480029i \(-0.159374\pi\)
0.877253 + 0.480029i \(0.159374\pi\)
\(614\) 18.1852 0.733895
\(615\) 12.3966 0.499880
\(616\) 0 0
\(617\) −37.5815 −1.51298 −0.756488 0.654008i \(-0.773086\pi\)
−0.756488 + 0.654008i \(0.773086\pi\)
\(618\) −11.1387 −0.448063
\(619\) 46.0731 1.85183 0.925917 0.377727i \(-0.123294\pi\)
0.925917 + 0.377727i \(0.123294\pi\)
\(620\) −13.2163 −0.530781
\(621\) 25.0491 1.00518
\(622\) −30.4630 −1.22146
\(623\) −3.03750 −0.121695
\(624\) 2.00000 0.0800641
\(625\) −28.7197 −1.14879
\(626\) 11.4830 0.458953
\(627\) 0 0
\(628\) −9.36041 −0.373521
\(629\) −0.732051 −0.0291888
\(630\) −6.10547 −0.243248
\(631\) 38.3314 1.52595 0.762974 0.646429i \(-0.223738\pi\)
0.762974 + 0.646429i \(0.223738\pi\)
\(632\) 2.46253 0.0979540
\(633\) 7.32721 0.291231
\(634\) −17.6836 −0.702307
\(635\) −39.0845 −1.55102
\(636\) 0.243650 0.00966134
\(637\) 17.1709 0.680336
\(638\) 0 0
\(639\) 35.0077 1.38488
\(640\) 2.43091 0.0960901
\(641\) 20.5407 0.811308 0.405654 0.914027i \(-0.367044\pi\)
0.405654 + 0.914027i \(0.367044\pi\)
\(642\) −0.187590 −0.00740359
\(643\) 15.0492 0.593483 0.296741 0.954958i \(-0.404100\pi\)
0.296741 + 0.954958i \(0.404100\pi\)
\(644\) 6.50318 0.256261
\(645\) −8.79543 −0.346320
\(646\) −1.90931 −0.0751209
\(647\) 35.5585 1.39795 0.698975 0.715146i \(-0.253640\pi\)
0.698975 + 0.715146i \(0.253640\pi\)
\(648\) −4.84293 −0.190248
\(649\) 0 0
\(650\) 2.60229 0.102070
\(651\) −3.79954 −0.148916
\(652\) −5.79954 −0.227128
\(653\) 24.7113 0.967028 0.483514 0.875337i \(-0.339360\pi\)
0.483514 + 0.875337i \(0.339360\pi\)
\(654\) −1.12675 −0.0440596
\(655\) −5.34911 −0.209007
\(656\) 7.29703 0.284901
\(657\) −20.9222 −0.816252
\(658\) −4.08658 −0.159311
\(659\) −1.39211 −0.0542289 −0.0271144 0.999632i \(-0.508632\pi\)
−0.0271144 + 0.999632i \(0.508632\pi\)
\(660\) 0 0
\(661\) 27.7243 1.07835 0.539175 0.842194i \(-0.318736\pi\)
0.539175 + 0.842194i \(0.318736\pi\)
\(662\) 22.1282 0.860036
\(663\) −3.81863 −0.148303
\(664\) 3.11135 0.120744
\(665\) 2.43091 0.0942666
\(666\) 0.962974 0.0373145
\(667\) 45.6834 1.76887
\(668\) −10.6791 −0.413189
\(669\) −16.1206 −0.623257
\(670\) −18.8450 −0.728045
\(671\) 0 0
\(672\) 0.698857 0.0269590
\(673\) 49.5016 1.90815 0.954073 0.299574i \(-0.0968445\pi\)
0.954073 + 0.299574i \(0.0968445\pi\)
\(674\) 14.3793 0.553870
\(675\) 3.50251 0.134812
\(676\) −4.81001 −0.185000
\(677\) −28.2443 −1.08552 −0.542758 0.839889i \(-0.682620\pi\)
−0.542758 + 0.839889i \(0.682620\pi\)
\(678\) 6.38451 0.245196
\(679\) −12.8059 −0.491445
\(680\) −4.64136 −0.177988
\(681\) −0.340553 −0.0130500
\(682\) 0 0
\(683\) 28.7090 1.09852 0.549261 0.835651i \(-0.314909\pi\)
0.549261 + 0.835651i \(0.314909\pi\)
\(684\) 2.51160 0.0960334
\(685\) −19.6477 −0.750701
\(686\) 13.0000 0.496342
\(687\) 20.4578 0.780513
\(688\) −5.17726 −0.197381
\(689\) 0.997744 0.0380110
\(690\) −11.0480 −0.420589
\(691\) −33.4941 −1.27418 −0.637088 0.770791i \(-0.719861\pi\)
−0.637088 + 0.770791i \(0.719861\pi\)
\(692\) 14.5839 0.554396
\(693\) 0 0
\(694\) −0.879129 −0.0333713
\(695\) 0.392305 0.0148810
\(696\) 4.90931 0.186087
\(697\) −13.9323 −0.527724
\(698\) 6.50859 0.246354
\(699\) 15.6601 0.592320
\(700\) 0.909313 0.0343688
\(701\) 44.3759 1.67605 0.838026 0.545630i \(-0.183709\pi\)
0.838026 + 0.545630i \(0.183709\pi\)
\(702\) 11.0232 0.416044
\(703\) −0.383411 −0.0144606
\(704\) 0 0
\(705\) 6.94251 0.261470
\(706\) −2.71932 −0.102343
\(707\) −6.27684 −0.236065
\(708\) 1.13708 0.0427342
\(709\) 1.80084 0.0676319 0.0338159 0.999428i \(-0.489234\pi\)
0.0338159 + 0.999428i \(0.489234\pi\)
\(710\) −33.8830 −1.27160
\(711\) 6.18487 0.231951
\(712\) 3.03750 0.113835
\(713\) 35.3564 1.32411
\(714\) −1.33434 −0.0499363
\(715\) 0 0
\(716\) −7.52906 −0.281374
\(717\) −8.16597 −0.304964
\(718\) −23.1057 −0.862296
\(719\) −21.3837 −0.797479 −0.398740 0.917064i \(-0.630552\pi\)
−0.398740 + 0.917064i \(0.630552\pi\)
\(720\) 6.10547 0.227537
\(721\) −15.9384 −0.593577
\(722\) −1.00000 −0.0372161
\(723\) 3.84771 0.143098
\(724\) 0.354524 0.0131758
\(725\) 6.38772 0.237234
\(726\) 0 0
\(727\) −25.0005 −0.927218 −0.463609 0.886040i \(-0.653446\pi\)
−0.463609 + 0.886040i \(0.653446\pi\)
\(728\) 2.86182 0.106066
\(729\) −4.08787 −0.151403
\(730\) 20.2500 0.749486
\(731\) 9.88501 0.365610
\(732\) −10.6071 −0.392049
\(733\) −35.4714 −1.31017 −0.655083 0.755557i \(-0.727367\pi\)
−0.655083 + 0.755557i \(0.727367\pi\)
\(734\) 26.2311 0.968208
\(735\) −10.1931 −0.375980
\(736\) −6.50318 −0.239710
\(737\) 0 0
\(738\) 18.3272 0.674634
\(739\) 21.1764 0.778988 0.389494 0.921029i \(-0.372650\pi\)
0.389494 + 0.921029i \(0.372650\pi\)
\(740\) −0.932036 −0.0342623
\(741\) −2.00000 −0.0734718
\(742\) 0.348640 0.0127990
\(743\) 0.450425 0.0165245 0.00826225 0.999966i \(-0.497370\pi\)
0.00826225 + 0.999966i \(0.497370\pi\)
\(744\) 3.79954 0.139298
\(745\) −31.1963 −1.14295
\(746\) 11.4943 0.420836
\(747\) 7.81446 0.285916
\(748\) 0 0
\(749\) −0.268424 −0.00980800
\(750\) 6.94949 0.253760
\(751\) 24.8901 0.908252 0.454126 0.890938i \(-0.349952\pi\)
0.454126 + 0.890938i \(0.349952\pi\)
\(752\) 4.08658 0.149022
\(753\) 4.81542 0.175484
\(754\) 20.1036 0.732130
\(755\) −19.8820 −0.723580
\(756\) 3.85182 0.140089
\(757\) −42.0173 −1.52715 −0.763573 0.645722i \(-0.776557\pi\)
−0.763573 + 0.645722i \(0.776557\pi\)
\(758\) −0.416325 −0.0151216
\(759\) 0 0
\(760\) −2.43091 −0.0881783
\(761\) 22.7584 0.824991 0.412496 0.910960i \(-0.364657\pi\)
0.412496 + 0.910960i \(0.364657\pi\)
\(762\) 11.2363 0.407049
\(763\) −1.61228 −0.0583685
\(764\) −5.89659 −0.213331
\(765\) −11.6572 −0.421469
\(766\) −31.8396 −1.15041
\(767\) 4.65635 0.168131
\(768\) −0.698857 −0.0252178
\(769\) 15.3289 0.552775 0.276388 0.961046i \(-0.410863\pi\)
0.276388 + 0.961046i \(0.410863\pi\)
\(770\) 0 0
\(771\) −3.34309 −0.120399
\(772\) −12.9095 −0.464623
\(773\) 32.8077 1.18001 0.590006 0.807399i \(-0.299125\pi\)
0.590006 + 0.807399i \(0.299125\pi\)
\(774\) −13.0032 −0.467391
\(775\) 4.94375 0.177585
\(776\) 12.8059 0.459705
\(777\) −0.267949 −0.00961262
\(778\) 3.34864 0.120055
\(779\) −7.29703 −0.261443
\(780\) −4.86182 −0.174081
\(781\) 0 0
\(782\) 12.4166 0.444017
\(783\) 27.0582 0.966980
\(784\) −6.00000 −0.214286
\(785\) 22.7543 0.812135
\(786\) 1.53781 0.0548518
\(787\) −35.5721 −1.26801 −0.634004 0.773330i \(-0.718590\pi\)
−0.634004 + 0.773330i \(0.718590\pi\)
\(788\) −22.0309 −0.784817
\(789\) −7.61606 −0.271139
\(790\) −5.98617 −0.212978
\(791\) 9.13565 0.324826
\(792\) 0 0
\(793\) −43.4359 −1.54245
\(794\) −2.41230 −0.0856092
\(795\) −0.592290 −0.0210064
\(796\) −10.2235 −0.362361
\(797\) −8.21915 −0.291137 −0.145569 0.989348i \(-0.546501\pi\)
−0.145569 + 0.989348i \(0.546501\pi\)
\(798\) −0.698857 −0.0247393
\(799\) −7.80255 −0.276034
\(800\) −0.909313 −0.0321491
\(801\) 7.62898 0.269557
\(802\) 32.1979 1.13695
\(803\) 0 0
\(804\) 5.41771 0.191068
\(805\) −15.8086 −0.557181
\(806\) 15.5591 0.548046
\(807\) 15.8345 0.557401
\(808\) 6.27684 0.220819
\(809\) −46.9337 −1.65010 −0.825050 0.565060i \(-0.808853\pi\)
−0.825050 + 0.565060i \(0.808853\pi\)
\(810\) 11.7727 0.413651
\(811\) 43.6344 1.53221 0.766105 0.642715i \(-0.222192\pi\)
0.766105 + 0.642715i \(0.222192\pi\)
\(812\) 7.02477 0.246521
\(813\) −2.50648 −0.0879063
\(814\) 0 0
\(815\) 14.0981 0.493837
\(816\) 1.33434 0.0467111
\(817\) 5.17726 0.181129
\(818\) −34.0985 −1.19223
\(819\) 7.18773 0.251160
\(820\) −17.7384 −0.619452
\(821\) −45.3423 −1.58246 −0.791228 0.611521i \(-0.790558\pi\)
−0.791228 + 0.611521i \(0.790558\pi\)
\(822\) 5.64849 0.197014
\(823\) −19.3037 −0.672884 −0.336442 0.941704i \(-0.609224\pi\)
−0.336442 + 0.941704i \(0.609224\pi\)
\(824\) 15.9384 0.555240
\(825\) 0 0
\(826\) 1.62706 0.0566127
\(827\) −28.3611 −0.986211 −0.493106 0.869969i \(-0.664138\pi\)
−0.493106 + 0.869969i \(0.664138\pi\)
\(828\) −16.3334 −0.567624
\(829\) −19.0610 −0.662015 −0.331008 0.943628i \(-0.607389\pi\)
−0.331008 + 0.943628i \(0.607389\pi\)
\(830\) −7.56340 −0.262530
\(831\) −0.0130063 −0.000451184 0
\(832\) −2.86182 −0.0992156
\(833\) 11.4559 0.396923
\(834\) −0.112783 −0.00390535
\(835\) 25.9600 0.898383
\(836\) 0 0
\(837\) 20.9415 0.723846
\(838\) −17.3423 −0.599079
\(839\) 17.8711 0.616979 0.308489 0.951228i \(-0.400177\pi\)
0.308489 + 0.951228i \(0.400177\pi\)
\(840\) −1.69886 −0.0586161
\(841\) 20.3475 0.701636
\(842\) 6.36356 0.219303
\(843\) −14.8636 −0.511929
\(844\) −10.4846 −0.360894
\(845\) 11.6927 0.402241
\(846\) 10.2638 0.352878
\(847\) 0 0
\(848\) −0.348640 −0.0119724
\(849\) 16.1528 0.554362
\(850\) 1.73616 0.0595499
\(851\) 2.49339 0.0854722
\(852\) 9.74095 0.333719
\(853\) −57.3285 −1.96289 −0.981445 0.191743i \(-0.938586\pi\)
−0.981445 + 0.191743i \(0.938586\pi\)
\(854\) −15.1777 −0.519371
\(855\) −6.10547 −0.208803
\(856\) 0.268424 0.00917454
\(857\) 32.8463 1.12201 0.561004 0.827813i \(-0.310415\pi\)
0.561004 + 0.827813i \(0.310415\pi\)
\(858\) 0 0
\(859\) 24.3172 0.829693 0.414846 0.909891i \(-0.363835\pi\)
0.414846 + 0.909891i \(0.363835\pi\)
\(860\) 12.5854 0.429160
\(861\) −5.09958 −0.173793
\(862\) −25.2529 −0.860117
\(863\) −2.59536 −0.0883470 −0.0441735 0.999024i \(-0.514065\pi\)
−0.0441735 + 0.999024i \(0.514065\pi\)
\(864\) −3.85182 −0.131042
\(865\) −35.4520 −1.20541
\(866\) −7.31865 −0.248698
\(867\) 9.33290 0.316962
\(868\) 5.43679 0.184537
\(869\) 0 0
\(870\) −11.9341 −0.404603
\(871\) 22.1855 0.751726
\(872\) 1.61228 0.0545988
\(873\) 32.1633 1.08856
\(874\) 6.50318 0.219973
\(875\) 9.94408 0.336171
\(876\) −5.82164 −0.196695
\(877\) −20.3719 −0.687910 −0.343955 0.938986i \(-0.611767\pi\)
−0.343955 + 0.938986i \(0.611767\pi\)
\(878\) 8.02861 0.270952
\(879\) −2.57909 −0.0869905
\(880\) 0 0
\(881\) 3.78366 0.127475 0.0637374 0.997967i \(-0.479698\pi\)
0.0637374 + 0.997967i \(0.479698\pi\)
\(882\) −15.0696 −0.507420
\(883\) −31.6886 −1.06641 −0.533203 0.845988i \(-0.679012\pi\)
−0.533203 + 0.845988i \(0.679012\pi\)
\(884\) 5.46410 0.183778
\(885\) −2.76414 −0.0929156
\(886\) 33.0740 1.11114
\(887\) 42.0343 1.41137 0.705687 0.708523i \(-0.250638\pi\)
0.705687 + 0.708523i \(0.250638\pi\)
\(888\) 0.267949 0.00899179
\(889\) 16.0782 0.539244
\(890\) −7.38389 −0.247508
\(891\) 0 0
\(892\) 23.0671 0.772342
\(893\) −4.08658 −0.136752
\(894\) 8.96858 0.299954
\(895\) 18.3024 0.611783
\(896\) −1.00000 −0.0334077
\(897\) 13.0064 0.434270
\(898\) −8.93958 −0.298318
\(899\) 38.1922 1.27378
\(900\) −2.28383 −0.0761276
\(901\) 0.665663 0.0221765
\(902\) 0 0
\(903\) 3.61817 0.120405
\(904\) −9.13565 −0.303847
\(905\) −0.861816 −0.0286477
\(906\) 5.71584 0.189896
\(907\) −20.8469 −0.692211 −0.346106 0.938196i \(-0.612496\pi\)
−0.346106 + 0.938196i \(0.612496\pi\)
\(908\) 0.487299 0.0161716
\(909\) 15.7649 0.522889
\(910\) −6.95681 −0.230616
\(911\) −26.1538 −0.866513 −0.433257 0.901271i \(-0.642636\pi\)
−0.433257 + 0.901271i \(0.642636\pi\)
\(912\) 0.698857 0.0231415
\(913\) 0 0
\(914\) −1.90520 −0.0630184
\(915\) 25.7848 0.852419
\(916\) −29.2732 −0.967214
\(917\) 2.20046 0.0726656
\(918\) 7.35433 0.242729
\(919\) −41.4222 −1.36639 −0.683196 0.730235i \(-0.739411\pi\)
−0.683196 + 0.730235i \(0.739411\pi\)
\(920\) 15.8086 0.521195
\(921\) 12.7089 0.418771
\(922\) 21.7813 0.717330
\(923\) 39.8891 1.31297
\(924\) 0 0
\(925\) 0.348640 0.0114632
\(926\) 36.0716 1.18539
\(927\) 40.0309 1.31479
\(928\) −7.02477 −0.230600
\(929\) 35.8540 1.17633 0.588165 0.808741i \(-0.299850\pi\)
0.588165 + 0.808741i \(0.299850\pi\)
\(930\) −9.23633 −0.302871
\(931\) 6.00000 0.196642
\(932\) −22.4082 −0.734005
\(933\) −21.2893 −0.696980
\(934\) 15.8955 0.520116
\(935\) 0 0
\(936\) −7.18773 −0.234938
\(937\) 15.3764 0.502324 0.251162 0.967945i \(-0.419187\pi\)
0.251162 + 0.967945i \(0.419187\pi\)
\(938\) 7.75224 0.253120
\(939\) 8.02497 0.261885
\(940\) −9.93409 −0.324014
\(941\) −9.70010 −0.316214 −0.158107 0.987422i \(-0.550539\pi\)
−0.158107 + 0.987422i \(0.550539\pi\)
\(942\) −6.54159 −0.213136
\(943\) 47.4539 1.54531
\(944\) −1.62706 −0.0529563
\(945\) −9.36342 −0.304592
\(946\) 0 0
\(947\) −0.368148 −0.0119632 −0.00598161 0.999982i \(-0.501904\pi\)
−0.00598161 + 0.999982i \(0.501904\pi\)
\(948\) 1.72095 0.0558940
\(949\) −23.8396 −0.773865
\(950\) 0.909313 0.0295020
\(951\) −12.3583 −0.400747
\(952\) 1.90931 0.0618812
\(953\) −36.0925 −1.16915 −0.584575 0.811340i \(-0.698739\pi\)
−0.584575 + 0.811340i \(0.698739\pi\)
\(954\) −0.875644 −0.0283500
\(955\) 14.3341 0.463839
\(956\) 11.6847 0.377912
\(957\) 0 0
\(958\) −5.40799 −0.174724
\(959\) 8.08246 0.260996
\(960\) 1.69886 0.0548304
\(961\) −1.44129 −0.0464934
\(962\) 1.09725 0.0353768
\(963\) 0.674173 0.0217249
\(964\) −5.50571 −0.177327
\(965\) 31.3818 1.01022
\(966\) 4.54479 0.146226
\(967\) −34.0953 −1.09643 −0.548216 0.836337i \(-0.684693\pi\)
−0.548216 + 0.836337i \(0.684693\pi\)
\(968\) 0 0
\(969\) −1.33434 −0.0428651
\(970\) −31.1300 −0.999523
\(971\) −3.83183 −0.122969 −0.0614846 0.998108i \(-0.519584\pi\)
−0.0614846 + 0.998108i \(0.519584\pi\)
\(972\) −14.9400 −0.479200
\(973\) −0.161382 −0.00517367
\(974\) 17.5518 0.562395
\(975\) 1.81863 0.0582426
\(976\) 15.1777 0.485828
\(977\) −3.59086 −0.114882 −0.0574408 0.998349i \(-0.518294\pi\)
−0.0574408 + 0.998349i \(0.518294\pi\)
\(978\) −4.05305 −0.129602
\(979\) 0 0
\(980\) 14.5854 0.465915
\(981\) 4.04941 0.129288
\(982\) 1.28718 0.0410755
\(983\) −46.3130 −1.47715 −0.738577 0.674169i \(-0.764502\pi\)
−0.738577 + 0.674169i \(0.764502\pi\)
\(984\) 5.09958 0.162569
\(985\) 53.5550 1.70640
\(986\) 13.4125 0.427141
\(987\) −2.85593 −0.0909053
\(988\) 2.86182 0.0910465
\(989\) −33.6687 −1.07060
\(990\) 0 0
\(991\) −3.58292 −0.113815 −0.0569076 0.998379i \(-0.518124\pi\)
−0.0569076 + 0.998379i \(0.518124\pi\)
\(992\) −5.43679 −0.172618
\(993\) 15.4644 0.490749
\(994\) 13.9384 0.442099
\(995\) 24.8523 0.787871
\(996\) 2.17439 0.0688981
\(997\) 24.0222 0.760789 0.380395 0.924824i \(-0.375788\pi\)
0.380395 + 0.924824i \(0.375788\pi\)
\(998\) 34.0586 1.07811
\(999\) 1.47683 0.0467248
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 4598.2.a.bq.1.2 4
11.10 odd 2 4598.2.a.bt.1.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.bq.1.2 4 1.1 even 1 trivial
4598.2.a.bt.1.2 yes 4 11.10 odd 2