Properties

Label 4598.2.a.be.1.1
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $1$
Dimension $2$
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: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 418)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.23607 q^{3} +1.00000 q^{4} +3.85410 q^{5} -3.23607 q^{6} -3.85410 q^{7} +1.00000 q^{8} +7.47214 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.23607 q^{3} +1.00000 q^{4} +3.85410 q^{5} -3.23607 q^{6} -3.85410 q^{7} +1.00000 q^{8} +7.47214 q^{9} +3.85410 q^{10} -3.23607 q^{12} -4.00000 q^{13} -3.85410 q^{14} -12.4721 q^{15} +1.00000 q^{16} +1.61803 q^{17} +7.47214 q^{18} +1.00000 q^{19} +3.85410 q^{20} +12.4721 q^{21} +0.854102 q^{23} -3.23607 q^{24} +9.85410 q^{25} -4.00000 q^{26} -14.4721 q^{27} -3.85410 q^{28} -5.70820 q^{29} -12.4721 q^{30} -2.76393 q^{31} +1.00000 q^{32} +1.61803 q^{34} -14.8541 q^{35} +7.47214 q^{36} -3.23607 q^{37} +1.00000 q^{38} +12.9443 q^{39} +3.85410 q^{40} +0.472136 q^{41} +12.4721 q^{42} -7.61803 q^{43} +28.7984 q^{45} +0.854102 q^{46} -0.854102 q^{47} -3.23607 q^{48} +7.85410 q^{49} +9.85410 q^{50} -5.23607 q^{51} -4.00000 q^{52} +11.2361 q^{53} -14.4721 q^{54} -3.85410 q^{56} -3.23607 q^{57} -5.70820 q^{58} +6.94427 q^{59} -12.4721 q^{60} -1.14590 q^{61} -2.76393 q^{62} -28.7984 q^{63} +1.00000 q^{64} -15.4164 q^{65} -9.23607 q^{67} +1.61803 q^{68} -2.76393 q^{69} -14.8541 q^{70} -2.76393 q^{71} +7.47214 q^{72} -10.9443 q^{73} -3.23607 q^{74} -31.8885 q^{75} +1.00000 q^{76} +12.9443 q^{78} -9.23607 q^{79} +3.85410 q^{80} +24.4164 q^{81} +0.472136 q^{82} +2.14590 q^{83} +12.4721 q^{84} +6.23607 q^{85} -7.61803 q^{86} +18.4721 q^{87} -14.1803 q^{89} +28.7984 q^{90} +15.4164 q^{91} +0.854102 q^{92} +8.94427 q^{93} -0.854102 q^{94} +3.85410 q^{95} -3.23607 q^{96} +16.9443 q^{97} +7.85410 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} - q^{7} + 2 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} - q^{7} + 2 q^{8} + 6 q^{9} + q^{10} - 2 q^{12} - 8 q^{13} - q^{14} - 16 q^{15} + 2 q^{16} + q^{17} + 6 q^{18} + 2 q^{19} + q^{20} + 16 q^{21} - 5 q^{23} - 2 q^{24} + 13 q^{25} - 8 q^{26} - 20 q^{27} - q^{28} + 2 q^{29} - 16 q^{30} - 10 q^{31} + 2 q^{32} + q^{34} - 23 q^{35} + 6 q^{36} - 2 q^{37} + 2 q^{38} + 8 q^{39} + q^{40} - 8 q^{41} + 16 q^{42} - 13 q^{43} + 33 q^{45} - 5 q^{46} + 5 q^{47} - 2 q^{48} + 9 q^{49} + 13 q^{50} - 6 q^{51} - 8 q^{52} + 18 q^{53} - 20 q^{54} - q^{56} - 2 q^{57} + 2 q^{58} - 4 q^{59} - 16 q^{60} - 9 q^{61} - 10 q^{62} - 33 q^{63} + 2 q^{64} - 4 q^{65} - 14 q^{67} + q^{68} - 10 q^{69} - 23 q^{70} - 10 q^{71} + 6 q^{72} - 4 q^{73} - 2 q^{74} - 28 q^{75} + 2 q^{76} + 8 q^{78} - 14 q^{79} + q^{80} + 22 q^{81} - 8 q^{82} + 11 q^{83} + 16 q^{84} + 8 q^{85} - 13 q^{86} + 28 q^{87} - 6 q^{89} + 33 q^{90} + 4 q^{91} - 5 q^{92} + 5 q^{94} + q^{95} - 2 q^{96} + 16 q^{97} + 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) −3.23607 −1.86834 −0.934172 0.356822i \(-0.883860\pi\)
−0.934172 + 0.356822i \(0.883860\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.85410 1.72361 0.861803 0.507242i \(-0.169335\pi\)
0.861803 + 0.507242i \(0.169335\pi\)
\(6\) −3.23607 −1.32112
\(7\) −3.85410 −1.45671 −0.728357 0.685198i \(-0.759716\pi\)
−0.728357 + 0.685198i \(0.759716\pi\)
\(8\) 1.00000 0.353553
\(9\) 7.47214 2.49071
\(10\) 3.85410 1.21877
\(11\) 0 0
\(12\) −3.23607 −0.934172
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) −3.85410 −1.03005
\(15\) −12.4721 −3.22029
\(16\) 1.00000 0.250000
\(17\) 1.61803 0.392431 0.196215 0.980561i \(-0.437135\pi\)
0.196215 + 0.980561i \(0.437135\pi\)
\(18\) 7.47214 1.76120
\(19\) 1.00000 0.229416
\(20\) 3.85410 0.861803
\(21\) 12.4721 2.72164
\(22\) 0 0
\(23\) 0.854102 0.178093 0.0890463 0.996027i \(-0.471618\pi\)
0.0890463 + 0.996027i \(0.471618\pi\)
\(24\) −3.23607 −0.660560
\(25\) 9.85410 1.97082
\(26\) −4.00000 −0.784465
\(27\) −14.4721 −2.78516
\(28\) −3.85410 −0.728357
\(29\) −5.70820 −1.05999 −0.529993 0.848002i \(-0.677806\pi\)
−0.529993 + 0.848002i \(0.677806\pi\)
\(30\) −12.4721 −2.27709
\(31\) −2.76393 −0.496417 −0.248208 0.968707i \(-0.579842\pi\)
−0.248208 + 0.968707i \(0.579842\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 1.61803 0.277491
\(35\) −14.8541 −2.51080
\(36\) 7.47214 1.24536
\(37\) −3.23607 −0.532006 −0.266003 0.963972i \(-0.585703\pi\)
−0.266003 + 0.963972i \(0.585703\pi\)
\(38\) 1.00000 0.162221
\(39\) 12.9443 2.07274
\(40\) 3.85410 0.609387
\(41\) 0.472136 0.0737352 0.0368676 0.999320i \(-0.488262\pi\)
0.0368676 + 0.999320i \(0.488262\pi\)
\(42\) 12.4721 1.92449
\(43\) −7.61803 −1.16174 −0.580870 0.813997i \(-0.697287\pi\)
−0.580870 + 0.813997i \(0.697287\pi\)
\(44\) 0 0
\(45\) 28.7984 4.29301
\(46\) 0.854102 0.125930
\(47\) −0.854102 −0.124584 −0.0622918 0.998058i \(-0.519841\pi\)
−0.0622918 + 0.998058i \(0.519841\pi\)
\(48\) −3.23607 −0.467086
\(49\) 7.85410 1.12201
\(50\) 9.85410 1.39358
\(51\) −5.23607 −0.733196
\(52\) −4.00000 −0.554700
\(53\) 11.2361 1.54339 0.771696 0.635991i \(-0.219409\pi\)
0.771696 + 0.635991i \(0.219409\pi\)
\(54\) −14.4721 −1.96941
\(55\) 0 0
\(56\) −3.85410 −0.515026
\(57\) −3.23607 −0.428628
\(58\) −5.70820 −0.749524
\(59\) 6.94427 0.904067 0.452034 0.892001i \(-0.350699\pi\)
0.452034 + 0.892001i \(0.350699\pi\)
\(60\) −12.4721 −1.61015
\(61\) −1.14590 −0.146717 −0.0733586 0.997306i \(-0.523372\pi\)
−0.0733586 + 0.997306i \(0.523372\pi\)
\(62\) −2.76393 −0.351020
\(63\) −28.7984 −3.62825
\(64\) 1.00000 0.125000
\(65\) −15.4164 −1.91217
\(66\) 0 0
\(67\) −9.23607 −1.12837 −0.564183 0.825650i \(-0.690809\pi\)
−0.564183 + 0.825650i \(0.690809\pi\)
\(68\) 1.61803 0.196215
\(69\) −2.76393 −0.332738
\(70\) −14.8541 −1.77540
\(71\) −2.76393 −0.328018 −0.164009 0.986459i \(-0.552443\pi\)
−0.164009 + 0.986459i \(0.552443\pi\)
\(72\) 7.47214 0.880600
\(73\) −10.9443 −1.28093 −0.640465 0.767987i \(-0.721258\pi\)
−0.640465 + 0.767987i \(0.721258\pi\)
\(74\) −3.23607 −0.376185
\(75\) −31.8885 −3.68217
\(76\) 1.00000 0.114708
\(77\) 0 0
\(78\) 12.9443 1.46565
\(79\) −9.23607 −1.03914 −0.519569 0.854428i \(-0.673908\pi\)
−0.519569 + 0.854428i \(0.673908\pi\)
\(80\) 3.85410 0.430902
\(81\) 24.4164 2.71293
\(82\) 0.472136 0.0521387
\(83\) 2.14590 0.235543 0.117771 0.993041i \(-0.462425\pi\)
0.117771 + 0.993041i \(0.462425\pi\)
\(84\) 12.4721 1.36082
\(85\) 6.23607 0.676397
\(86\) −7.61803 −0.821474
\(87\) 18.4721 1.98042
\(88\) 0 0
\(89\) −14.1803 −1.50311 −0.751557 0.659669i \(-0.770697\pi\)
−0.751557 + 0.659669i \(0.770697\pi\)
\(90\) 28.7984 3.03562
\(91\) 15.4164 1.61608
\(92\) 0.854102 0.0890463
\(93\) 8.94427 0.927478
\(94\) −0.854102 −0.0880939
\(95\) 3.85410 0.395423
\(96\) −3.23607 −0.330280
\(97\) 16.9443 1.72043 0.860215 0.509931i \(-0.170329\pi\)
0.860215 + 0.509931i \(0.170329\pi\)
\(98\) 7.85410 0.793384
\(99\) 0 0
\(100\) 9.85410 0.985410
\(101\) 3.56231 0.354463 0.177231 0.984169i \(-0.443286\pi\)
0.177231 + 0.984169i \(0.443286\pi\)
\(102\) −5.23607 −0.518448
\(103\) −6.94427 −0.684239 −0.342120 0.939656i \(-0.611145\pi\)
−0.342120 + 0.939656i \(0.611145\pi\)
\(104\) −4.00000 −0.392232
\(105\) 48.0689 4.69104
\(106\) 11.2361 1.09134
\(107\) −2.47214 −0.238990 −0.119495 0.992835i \(-0.538128\pi\)
−0.119495 + 0.992835i \(0.538128\pi\)
\(108\) −14.4721 −1.39258
\(109\) 0.944272 0.0904448 0.0452224 0.998977i \(-0.485600\pi\)
0.0452224 + 0.998977i \(0.485600\pi\)
\(110\) 0 0
\(111\) 10.4721 0.993971
\(112\) −3.85410 −0.364178
\(113\) −7.52786 −0.708162 −0.354081 0.935215i \(-0.615206\pi\)
−0.354081 + 0.935215i \(0.615206\pi\)
\(114\) −3.23607 −0.303086
\(115\) 3.29180 0.306962
\(116\) −5.70820 −0.529993
\(117\) −29.8885 −2.76320
\(118\) 6.94427 0.639272
\(119\) −6.23607 −0.571659
\(120\) −12.4721 −1.13855
\(121\) 0 0
\(122\) −1.14590 −0.103745
\(123\) −1.52786 −0.137763
\(124\) −2.76393 −0.248208
\(125\) 18.7082 1.67331
\(126\) −28.7984 −2.56556
\(127\) −2.29180 −0.203364 −0.101682 0.994817i \(-0.532422\pi\)
−0.101682 + 0.994817i \(0.532422\pi\)
\(128\) 1.00000 0.0883883
\(129\) 24.6525 2.17053
\(130\) −15.4164 −1.35211
\(131\) 13.8541 1.21044 0.605219 0.796059i \(-0.293085\pi\)
0.605219 + 0.796059i \(0.293085\pi\)
\(132\) 0 0
\(133\) −3.85410 −0.334193
\(134\) −9.23607 −0.797875
\(135\) −55.7771 −4.80053
\(136\) 1.61803 0.138745
\(137\) −9.56231 −0.816963 −0.408481 0.912767i \(-0.633942\pi\)
−0.408481 + 0.912767i \(0.633942\pi\)
\(138\) −2.76393 −0.235282
\(139\) 14.0902 1.19511 0.597556 0.801827i \(-0.296138\pi\)
0.597556 + 0.801827i \(0.296138\pi\)
\(140\) −14.8541 −1.25540
\(141\) 2.76393 0.232765
\(142\) −2.76393 −0.231944
\(143\) 0 0
\(144\) 7.47214 0.622678
\(145\) −22.0000 −1.82700
\(146\) −10.9443 −0.905754
\(147\) −25.4164 −2.09631
\(148\) −3.23607 −0.266003
\(149\) −3.52786 −0.289014 −0.144507 0.989504i \(-0.546160\pi\)
−0.144507 + 0.989504i \(0.546160\pi\)
\(150\) −31.8885 −2.60369
\(151\) −10.7639 −0.875956 −0.437978 0.898986i \(-0.644305\pi\)
−0.437978 + 0.898986i \(0.644305\pi\)
\(152\) 1.00000 0.0811107
\(153\) 12.0902 0.977432
\(154\) 0 0
\(155\) −10.6525 −0.855627
\(156\) 12.9443 1.03637
\(157\) −22.3262 −1.78183 −0.890914 0.454172i \(-0.849935\pi\)
−0.890914 + 0.454172i \(0.849935\pi\)
\(158\) −9.23607 −0.734782
\(159\) −36.3607 −2.88359
\(160\) 3.85410 0.304694
\(161\) −3.29180 −0.259430
\(162\) 24.4164 1.91833
\(163\) 17.2705 1.35273 0.676365 0.736566i \(-0.263554\pi\)
0.676365 + 0.736566i \(0.263554\pi\)
\(164\) 0.472136 0.0368676
\(165\) 0 0
\(166\) 2.14590 0.166554
\(167\) 6.29180 0.486874 0.243437 0.969917i \(-0.421725\pi\)
0.243437 + 0.969917i \(0.421725\pi\)
\(168\) 12.4721 0.962246
\(169\) 3.00000 0.230769
\(170\) 6.23607 0.478285
\(171\) 7.47214 0.571409
\(172\) −7.61803 −0.580870
\(173\) 4.00000 0.304114 0.152057 0.988372i \(-0.451410\pi\)
0.152057 + 0.988372i \(0.451410\pi\)
\(174\) 18.4721 1.40037
\(175\) −37.9787 −2.87092
\(176\) 0 0
\(177\) −22.4721 −1.68911
\(178\) −14.1803 −1.06286
\(179\) −21.1246 −1.57893 −0.789464 0.613797i \(-0.789641\pi\)
−0.789464 + 0.613797i \(0.789641\pi\)
\(180\) 28.7984 2.14650
\(181\) −5.41641 −0.402598 −0.201299 0.979530i \(-0.564516\pi\)
−0.201299 + 0.979530i \(0.564516\pi\)
\(182\) 15.4164 1.14274
\(183\) 3.70820 0.274118
\(184\) 0.854102 0.0629652
\(185\) −12.4721 −0.916970
\(186\) 8.94427 0.655826
\(187\) 0 0
\(188\) −0.854102 −0.0622918
\(189\) 55.7771 4.05719
\(190\) 3.85410 0.279606
\(191\) −13.3820 −0.968285 −0.484143 0.874989i \(-0.660868\pi\)
−0.484143 + 0.874989i \(0.660868\pi\)
\(192\) −3.23607 −0.233543
\(193\) −18.4721 −1.32965 −0.664827 0.746998i \(-0.731495\pi\)
−0.664827 + 0.746998i \(0.731495\pi\)
\(194\) 16.9443 1.21653
\(195\) 49.8885 3.57259
\(196\) 7.85410 0.561007
\(197\) −10.9443 −0.779747 −0.389874 0.920868i \(-0.627481\pi\)
−0.389874 + 0.920868i \(0.627481\pi\)
\(198\) 0 0
\(199\) 26.6180 1.88690 0.943451 0.331511i \(-0.107559\pi\)
0.943451 + 0.331511i \(0.107559\pi\)
\(200\) 9.85410 0.696790
\(201\) 29.8885 2.10818
\(202\) 3.56231 0.250643
\(203\) 22.0000 1.54410
\(204\) −5.23607 −0.366598
\(205\) 1.81966 0.127091
\(206\) −6.94427 −0.483830
\(207\) 6.38197 0.443577
\(208\) −4.00000 −0.277350
\(209\) 0 0
\(210\) 48.0689 3.31707
\(211\) 14.9443 1.02881 0.514403 0.857549i \(-0.328014\pi\)
0.514403 + 0.857549i \(0.328014\pi\)
\(212\) 11.2361 0.771696
\(213\) 8.94427 0.612851
\(214\) −2.47214 −0.168992
\(215\) −29.3607 −2.00238
\(216\) −14.4721 −0.984704
\(217\) 10.6525 0.723137
\(218\) 0.944272 0.0639542
\(219\) 35.4164 2.39322
\(220\) 0 0
\(221\) −6.47214 −0.435363
\(222\) 10.4721 0.702844
\(223\) −10.6525 −0.713343 −0.356671 0.934230i \(-0.616088\pi\)
−0.356671 + 0.934230i \(0.616088\pi\)
\(224\) −3.85410 −0.257513
\(225\) 73.6312 4.90875
\(226\) −7.52786 −0.500746
\(227\) −26.1803 −1.73765 −0.868825 0.495119i \(-0.835124\pi\)
−0.868825 + 0.495119i \(0.835124\pi\)
\(228\) −3.23607 −0.214314
\(229\) −10.8541 −0.717259 −0.358630 0.933480i \(-0.616756\pi\)
−0.358630 + 0.933480i \(0.616756\pi\)
\(230\) 3.29180 0.217055
\(231\) 0 0
\(232\) −5.70820 −0.374762
\(233\) −0.326238 −0.0213726 −0.0106863 0.999943i \(-0.503402\pi\)
−0.0106863 + 0.999943i \(0.503402\pi\)
\(234\) −29.8885 −1.95388
\(235\) −3.29180 −0.214733
\(236\) 6.94427 0.452034
\(237\) 29.8885 1.94147
\(238\) −6.23607 −0.404224
\(239\) −15.3262 −0.991372 −0.495686 0.868502i \(-0.665083\pi\)
−0.495686 + 0.868502i \(0.665083\pi\)
\(240\) −12.4721 −0.805073
\(241\) −19.5279 −1.25790 −0.628950 0.777446i \(-0.716515\pi\)
−0.628950 + 0.777446i \(0.716515\pi\)
\(242\) 0 0
\(243\) −35.5967 −2.28353
\(244\) −1.14590 −0.0733586
\(245\) 30.2705 1.93391
\(246\) −1.52786 −0.0974131
\(247\) −4.00000 −0.254514
\(248\) −2.76393 −0.175510
\(249\) −6.94427 −0.440075
\(250\) 18.7082 1.18321
\(251\) −12.3820 −0.781543 −0.390771 0.920488i \(-0.627792\pi\)
−0.390771 + 0.920488i \(0.627792\pi\)
\(252\) −28.7984 −1.81413
\(253\) 0 0
\(254\) −2.29180 −0.143800
\(255\) −20.1803 −1.26374
\(256\) 1.00000 0.0625000
\(257\) −18.1803 −1.13406 −0.567029 0.823698i \(-0.691907\pi\)
−0.567029 + 0.823698i \(0.691907\pi\)
\(258\) 24.6525 1.53480
\(259\) 12.4721 0.774981
\(260\) −15.4164 −0.956085
\(261\) −42.6525 −2.64012
\(262\) 13.8541 0.855909
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 0 0
\(265\) 43.3050 2.66020
\(266\) −3.85410 −0.236310
\(267\) 45.8885 2.80833
\(268\) −9.23607 −0.564183
\(269\) 19.7082 1.20163 0.600815 0.799388i \(-0.294843\pi\)
0.600815 + 0.799388i \(0.294843\pi\)
\(270\) −55.7771 −3.39449
\(271\) 28.0902 1.70636 0.853178 0.521620i \(-0.174672\pi\)
0.853178 + 0.521620i \(0.174672\pi\)
\(272\) 1.61803 0.0981077
\(273\) −49.8885 −3.01939
\(274\) −9.56231 −0.577680
\(275\) 0 0
\(276\) −2.76393 −0.166369
\(277\) −20.4721 −1.23005 −0.615026 0.788507i \(-0.710854\pi\)
−0.615026 + 0.788507i \(0.710854\pi\)
\(278\) 14.0902 0.845072
\(279\) −20.6525 −1.23643
\(280\) −14.8541 −0.887702
\(281\) −4.00000 −0.238620 −0.119310 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) 2.76393 0.164590
\(283\) −9.85410 −0.585766 −0.292883 0.956148i \(-0.594615\pi\)
−0.292883 + 0.956148i \(0.594615\pi\)
\(284\) −2.76393 −0.164009
\(285\) −12.4721 −0.738786
\(286\) 0 0
\(287\) −1.81966 −0.107411
\(288\) 7.47214 0.440300
\(289\) −14.3820 −0.845998
\(290\) −22.0000 −1.29188
\(291\) −54.8328 −3.21436
\(292\) −10.9443 −0.640465
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) −25.4164 −1.48232
\(295\) 26.7639 1.55826
\(296\) −3.23607 −0.188093
\(297\) 0 0
\(298\) −3.52786 −0.204364
\(299\) −3.41641 −0.197576
\(300\) −31.8885 −1.84109
\(301\) 29.3607 1.69232
\(302\) −10.7639 −0.619395
\(303\) −11.5279 −0.662258
\(304\) 1.00000 0.0573539
\(305\) −4.41641 −0.252883
\(306\) 12.0902 0.691149
\(307\) −1.52786 −0.0871998 −0.0435999 0.999049i \(-0.513883\pi\)
−0.0435999 + 0.999049i \(0.513883\pi\)
\(308\) 0 0
\(309\) 22.4721 1.27840
\(310\) −10.6525 −0.605020
\(311\) 5.43769 0.308343 0.154172 0.988044i \(-0.450729\pi\)
0.154172 + 0.988044i \(0.450729\pi\)
\(312\) 12.9443 0.732825
\(313\) −15.5066 −0.876484 −0.438242 0.898857i \(-0.644399\pi\)
−0.438242 + 0.898857i \(0.644399\pi\)
\(314\) −22.3262 −1.25994
\(315\) −110.992 −6.25368
\(316\) −9.23607 −0.519569
\(317\) −8.47214 −0.475843 −0.237921 0.971284i \(-0.576466\pi\)
−0.237921 + 0.971284i \(0.576466\pi\)
\(318\) −36.3607 −2.03901
\(319\) 0 0
\(320\) 3.85410 0.215451
\(321\) 8.00000 0.446516
\(322\) −3.29180 −0.183445
\(323\) 1.61803 0.0900298
\(324\) 24.4164 1.35647
\(325\) −39.4164 −2.18643
\(326\) 17.2705 0.956525
\(327\) −3.05573 −0.168982
\(328\) 0.472136 0.0260693
\(329\) 3.29180 0.181483
\(330\) 0 0
\(331\) −10.4721 −0.575601 −0.287800 0.957690i \(-0.592924\pi\)
−0.287800 + 0.957690i \(0.592924\pi\)
\(332\) 2.14590 0.117771
\(333\) −24.1803 −1.32507
\(334\) 6.29180 0.344272
\(335\) −35.5967 −1.94486
\(336\) 12.4721 0.680411
\(337\) 26.1803 1.42613 0.713067 0.701096i \(-0.247306\pi\)
0.713067 + 0.701096i \(0.247306\pi\)
\(338\) 3.00000 0.163178
\(339\) 24.3607 1.32309
\(340\) 6.23607 0.338198
\(341\) 0 0
\(342\) 7.47214 0.404047
\(343\) −3.29180 −0.177740
\(344\) −7.61803 −0.410737
\(345\) −10.6525 −0.573510
\(346\) 4.00000 0.215041
\(347\) 3.79837 0.203907 0.101954 0.994789i \(-0.467491\pi\)
0.101954 + 0.994789i \(0.467491\pi\)
\(348\) 18.4721 0.990210
\(349\) 9.67376 0.517825 0.258912 0.965901i \(-0.416636\pi\)
0.258912 + 0.965901i \(0.416636\pi\)
\(350\) −37.9787 −2.03005
\(351\) 57.8885 3.08986
\(352\) 0 0
\(353\) −33.9230 −1.80554 −0.902769 0.430125i \(-0.858469\pi\)
−0.902769 + 0.430125i \(0.858469\pi\)
\(354\) −22.4721 −1.19438
\(355\) −10.6525 −0.565375
\(356\) −14.1803 −0.751557
\(357\) 20.1803 1.06806
\(358\) −21.1246 −1.11647
\(359\) −2.20163 −0.116197 −0.0580987 0.998311i \(-0.518504\pi\)
−0.0580987 + 0.998311i \(0.518504\pi\)
\(360\) 28.7984 1.51781
\(361\) 1.00000 0.0526316
\(362\) −5.41641 −0.284680
\(363\) 0 0
\(364\) 15.4164 0.808039
\(365\) −42.1803 −2.20782
\(366\) 3.70820 0.193831
\(367\) 9.09017 0.474503 0.237252 0.971448i \(-0.423753\pi\)
0.237252 + 0.971448i \(0.423753\pi\)
\(368\) 0.854102 0.0445231
\(369\) 3.52786 0.183653
\(370\) −12.4721 −0.648395
\(371\) −43.3050 −2.24828
\(372\) 8.94427 0.463739
\(373\) −18.4721 −0.956451 −0.478225 0.878237i \(-0.658720\pi\)
−0.478225 + 0.878237i \(0.658720\pi\)
\(374\) 0 0
\(375\) −60.5410 −3.12632
\(376\) −0.854102 −0.0440469
\(377\) 22.8328 1.17595
\(378\) 55.7771 2.86886
\(379\) 7.88854 0.405207 0.202604 0.979261i \(-0.435060\pi\)
0.202604 + 0.979261i \(0.435060\pi\)
\(380\) 3.85410 0.197711
\(381\) 7.41641 0.379954
\(382\) −13.3820 −0.684681
\(383\) −18.6525 −0.953097 −0.476548 0.879148i \(-0.658112\pi\)
−0.476548 + 0.879148i \(0.658112\pi\)
\(384\) −3.23607 −0.165140
\(385\) 0 0
\(386\) −18.4721 −0.940207
\(387\) −56.9230 −2.89356
\(388\) 16.9443 0.860215
\(389\) 2.27051 0.115119 0.0575597 0.998342i \(-0.481668\pi\)
0.0575597 + 0.998342i \(0.481668\pi\)
\(390\) 49.8885 2.52620
\(391\) 1.38197 0.0698890
\(392\) 7.85410 0.396692
\(393\) −44.8328 −2.26152
\(394\) −10.9443 −0.551364
\(395\) −35.5967 −1.79107
\(396\) 0 0
\(397\) 16.5623 0.831238 0.415619 0.909539i \(-0.363565\pi\)
0.415619 + 0.909539i \(0.363565\pi\)
\(398\) 26.6180 1.33424
\(399\) 12.4721 0.624388
\(400\) 9.85410 0.492705
\(401\) −19.2361 −0.960603 −0.480302 0.877103i \(-0.659473\pi\)
−0.480302 + 0.877103i \(0.659473\pi\)
\(402\) 29.8885 1.49071
\(403\) 11.0557 0.550725
\(404\) 3.56231 0.177231
\(405\) 94.1033 4.67603
\(406\) 22.0000 1.09184
\(407\) 0 0
\(408\) −5.23607 −0.259224
\(409\) 29.5279 1.46006 0.730029 0.683416i \(-0.239506\pi\)
0.730029 + 0.683416i \(0.239506\pi\)
\(410\) 1.81966 0.0898666
\(411\) 30.9443 1.52637
\(412\) −6.94427 −0.342120
\(413\) −26.7639 −1.31697
\(414\) 6.38197 0.313657
\(415\) 8.27051 0.405983
\(416\) −4.00000 −0.196116
\(417\) −45.5967 −2.23288
\(418\) 0 0
\(419\) −28.7426 −1.40417 −0.702085 0.712093i \(-0.747747\pi\)
−0.702085 + 0.712093i \(0.747747\pi\)
\(420\) 48.0689 2.34552
\(421\) 24.4721 1.19270 0.596349 0.802725i \(-0.296617\pi\)
0.596349 + 0.802725i \(0.296617\pi\)
\(422\) 14.9443 0.727476
\(423\) −6.38197 −0.310302
\(424\) 11.2361 0.545672
\(425\) 15.9443 0.773411
\(426\) 8.94427 0.433351
\(427\) 4.41641 0.213725
\(428\) −2.47214 −0.119495
\(429\) 0 0
\(430\) −29.3607 −1.41590
\(431\) 10.5836 0.509794 0.254897 0.966968i \(-0.417958\pi\)
0.254897 + 0.966968i \(0.417958\pi\)
\(432\) −14.4721 −0.696291
\(433\) 11.8885 0.571327 0.285663 0.958330i \(-0.407786\pi\)
0.285663 + 0.958330i \(0.407786\pi\)
\(434\) 10.6525 0.511335
\(435\) 71.1935 3.41347
\(436\) 0.944272 0.0452224
\(437\) 0.854102 0.0408572
\(438\) 35.4164 1.69226
\(439\) 18.3607 0.876307 0.438154 0.898900i \(-0.355633\pi\)
0.438154 + 0.898900i \(0.355633\pi\)
\(440\) 0 0
\(441\) 58.6869 2.79462
\(442\) −6.47214 −0.307848
\(443\) −21.2705 −1.01059 −0.505296 0.862946i \(-0.668617\pi\)
−0.505296 + 0.862946i \(0.668617\pi\)
\(444\) 10.4721 0.496986
\(445\) −54.6525 −2.59078
\(446\) −10.6525 −0.504409
\(447\) 11.4164 0.539978
\(448\) −3.85410 −0.182089
\(449\) 15.7082 0.741316 0.370658 0.928769i \(-0.379132\pi\)
0.370658 + 0.928769i \(0.379132\pi\)
\(450\) 73.6312 3.47101
\(451\) 0 0
\(452\) −7.52786 −0.354081
\(453\) 34.8328 1.63659
\(454\) −26.1803 −1.22870
\(455\) 59.4164 2.78548
\(456\) −3.23607 −0.151543
\(457\) 11.0902 0.518776 0.259388 0.965773i \(-0.416479\pi\)
0.259388 + 0.965773i \(0.416479\pi\)
\(458\) −10.8541 −0.507179
\(459\) −23.4164 −1.09298
\(460\) 3.29180 0.153481
\(461\) −30.6869 −1.42923 −0.714616 0.699517i \(-0.753399\pi\)
−0.714616 + 0.699517i \(0.753399\pi\)
\(462\) 0 0
\(463\) −12.2148 −0.567669 −0.283835 0.958873i \(-0.591607\pi\)
−0.283835 + 0.958873i \(0.591607\pi\)
\(464\) −5.70820 −0.264997
\(465\) 34.4721 1.59861
\(466\) −0.326238 −0.0151127
\(467\) 9.27051 0.428988 0.214494 0.976725i \(-0.431190\pi\)
0.214494 + 0.976725i \(0.431190\pi\)
\(468\) −29.8885 −1.38160
\(469\) 35.5967 1.64371
\(470\) −3.29180 −0.151839
\(471\) 72.2492 3.32907
\(472\) 6.94427 0.319636
\(473\) 0 0
\(474\) 29.8885 1.37283
\(475\) 9.85410 0.452137
\(476\) −6.23607 −0.285830
\(477\) 83.9574 3.84415
\(478\) −15.3262 −0.701006
\(479\) 19.9098 0.909703 0.454852 0.890567i \(-0.349692\pi\)
0.454852 + 0.890567i \(0.349692\pi\)
\(480\) −12.4721 −0.569273
\(481\) 12.9443 0.590208
\(482\) −19.5279 −0.889470
\(483\) 10.6525 0.484704
\(484\) 0 0
\(485\) 65.3050 2.96535
\(486\) −35.5967 −1.61470
\(487\) 21.4164 0.970470 0.485235 0.874384i \(-0.338734\pi\)
0.485235 + 0.874384i \(0.338734\pi\)
\(488\) −1.14590 −0.0518724
\(489\) −55.8885 −2.52737
\(490\) 30.2705 1.36748
\(491\) −23.7426 −1.07149 −0.535745 0.844380i \(-0.679969\pi\)
−0.535745 + 0.844380i \(0.679969\pi\)
\(492\) −1.52786 −0.0688814
\(493\) −9.23607 −0.415972
\(494\) −4.00000 −0.179969
\(495\) 0 0
\(496\) −2.76393 −0.124104
\(497\) 10.6525 0.477829
\(498\) −6.94427 −0.311180
\(499\) −20.0344 −0.896865 −0.448432 0.893817i \(-0.648018\pi\)
−0.448432 + 0.893817i \(0.648018\pi\)
\(500\) 18.7082 0.836656
\(501\) −20.3607 −0.909648
\(502\) −12.3820 −0.552634
\(503\) 24.9443 1.11221 0.556105 0.831112i \(-0.312295\pi\)
0.556105 + 0.831112i \(0.312295\pi\)
\(504\) −28.7984 −1.28278
\(505\) 13.7295 0.610954
\(506\) 0 0
\(507\) −9.70820 −0.431156
\(508\) −2.29180 −0.101682
\(509\) 23.2361 1.02992 0.514960 0.857214i \(-0.327807\pi\)
0.514960 + 0.857214i \(0.327807\pi\)
\(510\) −20.1803 −0.893600
\(511\) 42.1803 1.86595
\(512\) 1.00000 0.0441942
\(513\) −14.4721 −0.638960
\(514\) −18.1803 −0.801900
\(515\) −26.7639 −1.17936
\(516\) 24.6525 1.08526
\(517\) 0 0
\(518\) 12.4721 0.547994
\(519\) −12.9443 −0.568190
\(520\) −15.4164 −0.676054
\(521\) −23.4164 −1.02589 −0.512946 0.858421i \(-0.671446\pi\)
−0.512946 + 0.858421i \(0.671446\pi\)
\(522\) −42.6525 −1.86685
\(523\) −29.4164 −1.28629 −0.643145 0.765745i \(-0.722371\pi\)
−0.643145 + 0.765745i \(0.722371\pi\)
\(524\) 13.8541 0.605219
\(525\) 122.902 5.36387
\(526\) −16.0000 −0.697633
\(527\) −4.47214 −0.194809
\(528\) 0 0
\(529\) −22.2705 −0.968283
\(530\) 43.3050 1.88105
\(531\) 51.8885 2.25177
\(532\) −3.85410 −0.167097
\(533\) −1.88854 −0.0818019
\(534\) 45.8885 1.98579
\(535\) −9.52786 −0.411925
\(536\) −9.23607 −0.398937
\(537\) 68.3607 2.94998
\(538\) 19.7082 0.849681
\(539\) 0 0
\(540\) −55.7771 −2.40026
\(541\) 14.8541 0.638628 0.319314 0.947649i \(-0.396548\pi\)
0.319314 + 0.947649i \(0.396548\pi\)
\(542\) 28.0902 1.20658
\(543\) 17.5279 0.752193
\(544\) 1.61803 0.0693726
\(545\) 3.63932 0.155891
\(546\) −49.8885 −2.13503
\(547\) −43.3050 −1.85159 −0.925793 0.378031i \(-0.876601\pi\)
−0.925793 + 0.378031i \(0.876601\pi\)
\(548\) −9.56231 −0.408481
\(549\) −8.56231 −0.365430
\(550\) 0 0
\(551\) −5.70820 −0.243178
\(552\) −2.76393 −0.117641
\(553\) 35.5967 1.51373
\(554\) −20.4721 −0.869778
\(555\) 40.3607 1.71322
\(556\) 14.0902 0.597556
\(557\) 28.1459 1.19258 0.596290 0.802769i \(-0.296641\pi\)
0.596290 + 0.802769i \(0.296641\pi\)
\(558\) −20.6525 −0.874289
\(559\) 30.4721 1.28883
\(560\) −14.8541 −0.627700
\(561\) 0 0
\(562\) −4.00000 −0.168730
\(563\) 32.9443 1.38844 0.694218 0.719765i \(-0.255750\pi\)
0.694218 + 0.719765i \(0.255750\pi\)
\(564\) 2.76393 0.116383
\(565\) −29.0132 −1.22059
\(566\) −9.85410 −0.414199
\(567\) −94.1033 −3.95197
\(568\) −2.76393 −0.115972
\(569\) 14.1803 0.594471 0.297235 0.954804i \(-0.403935\pi\)
0.297235 + 0.954804i \(0.403935\pi\)
\(570\) −12.4721 −0.522400
\(571\) 14.2148 0.594870 0.297435 0.954742i \(-0.403869\pi\)
0.297435 + 0.954742i \(0.403869\pi\)
\(572\) 0 0
\(573\) 43.3050 1.80909
\(574\) −1.81966 −0.0759511
\(575\) 8.41641 0.350988
\(576\) 7.47214 0.311339
\(577\) 39.3050 1.63629 0.818143 0.575014i \(-0.195004\pi\)
0.818143 + 0.575014i \(0.195004\pi\)
\(578\) −14.3820 −0.598211
\(579\) 59.7771 2.48425
\(580\) −22.0000 −0.913500
\(581\) −8.27051 −0.343119
\(582\) −54.8328 −2.27289
\(583\) 0 0
\(584\) −10.9443 −0.452877
\(585\) −115.193 −4.76266
\(586\) −24.0000 −0.991431
\(587\) 33.5279 1.38384 0.691922 0.721973i \(-0.256764\pi\)
0.691922 + 0.721973i \(0.256764\pi\)
\(588\) −25.4164 −1.04815
\(589\) −2.76393 −0.113886
\(590\) 26.7639 1.10185
\(591\) 35.4164 1.45684
\(592\) −3.23607 −0.133002
\(593\) 10.7426 0.441148 0.220574 0.975370i \(-0.429207\pi\)
0.220574 + 0.975370i \(0.429207\pi\)
\(594\) 0 0
\(595\) −24.0344 −0.985316
\(596\) −3.52786 −0.144507
\(597\) −86.1378 −3.52538
\(598\) −3.41641 −0.139707
\(599\) 29.4164 1.20192 0.600961 0.799278i \(-0.294785\pi\)
0.600961 + 0.799278i \(0.294785\pi\)
\(600\) −31.8885 −1.30184
\(601\) 29.3050 1.19537 0.597687 0.801730i \(-0.296087\pi\)
0.597687 + 0.801730i \(0.296087\pi\)
\(602\) 29.3607 1.19665
\(603\) −69.0132 −2.81043
\(604\) −10.7639 −0.437978
\(605\) 0 0
\(606\) −11.5279 −0.468287
\(607\) −9.23607 −0.374880 −0.187440 0.982276i \(-0.560019\pi\)
−0.187440 + 0.982276i \(0.560019\pi\)
\(608\) 1.00000 0.0405554
\(609\) −71.1935 −2.88491
\(610\) −4.41641 −0.178815
\(611\) 3.41641 0.138213
\(612\) 12.0902 0.488716
\(613\) −2.27051 −0.0917050 −0.0458525 0.998948i \(-0.514600\pi\)
−0.0458525 + 0.998948i \(0.514600\pi\)
\(614\) −1.52786 −0.0616596
\(615\) −5.88854 −0.237449
\(616\) 0 0
\(617\) 2.36068 0.0950374 0.0475187 0.998870i \(-0.484869\pi\)
0.0475187 + 0.998870i \(0.484869\pi\)
\(618\) 22.4721 0.903962
\(619\) 34.2705 1.37745 0.688724 0.725024i \(-0.258171\pi\)
0.688724 + 0.725024i \(0.258171\pi\)
\(620\) −10.6525 −0.427814
\(621\) −12.3607 −0.496017
\(622\) 5.43769 0.218032
\(623\) 54.6525 2.18961
\(624\) 12.9443 0.518186
\(625\) 22.8328 0.913313
\(626\) −15.5066 −0.619767
\(627\) 0 0
\(628\) −22.3262 −0.890914
\(629\) −5.23607 −0.208776
\(630\) −110.992 −4.42202
\(631\) −13.5279 −0.538536 −0.269268 0.963065i \(-0.586782\pi\)
−0.269268 + 0.963065i \(0.586782\pi\)
\(632\) −9.23607 −0.367391
\(633\) −48.3607 −1.92216
\(634\) −8.47214 −0.336472
\(635\) −8.83282 −0.350520
\(636\) −36.3607 −1.44179
\(637\) −31.4164 −1.24476
\(638\) 0 0
\(639\) −20.6525 −0.816999
\(640\) 3.85410 0.152347
\(641\) 2.11146 0.0833975 0.0416988 0.999130i \(-0.486723\pi\)
0.0416988 + 0.999130i \(0.486723\pi\)
\(642\) 8.00000 0.315735
\(643\) 29.3262 1.15651 0.578257 0.815855i \(-0.303733\pi\)
0.578257 + 0.815855i \(0.303733\pi\)
\(644\) −3.29180 −0.129715
\(645\) 95.0132 3.74114
\(646\) 1.61803 0.0636607
\(647\) −33.3050 −1.30935 −0.654676 0.755909i \(-0.727195\pi\)
−0.654676 + 0.755909i \(0.727195\pi\)
\(648\) 24.4164 0.959167
\(649\) 0 0
\(650\) −39.4164 −1.54604
\(651\) −34.4721 −1.35107
\(652\) 17.2705 0.676365
\(653\) 27.6180 1.08078 0.540389 0.841416i \(-0.318277\pi\)
0.540389 + 0.841416i \(0.318277\pi\)
\(654\) −3.05573 −0.119488
\(655\) 53.3951 2.08632
\(656\) 0.472136 0.0184338
\(657\) −81.7771 −3.19043
\(658\) 3.29180 0.128328
\(659\) 29.4164 1.14590 0.572950 0.819590i \(-0.305799\pi\)
0.572950 + 0.819590i \(0.305799\pi\)
\(660\) 0 0
\(661\) −19.4164 −0.755211 −0.377605 0.925967i \(-0.623252\pi\)
−0.377605 + 0.925967i \(0.623252\pi\)
\(662\) −10.4721 −0.407011
\(663\) 20.9443 0.813408
\(664\) 2.14590 0.0832770
\(665\) −14.8541 −0.576017
\(666\) −24.1803 −0.936969
\(667\) −4.87539 −0.188776
\(668\) 6.29180 0.243437
\(669\) 34.4721 1.33277
\(670\) −35.5967 −1.37522
\(671\) 0 0
\(672\) 12.4721 0.481123
\(673\) −24.6525 −0.950283 −0.475142 0.879909i \(-0.657603\pi\)
−0.475142 + 0.879909i \(0.657603\pi\)
\(674\) 26.1803 1.00843
\(675\) −142.610 −5.48906
\(676\) 3.00000 0.115385
\(677\) −17.4164 −0.669367 −0.334683 0.942331i \(-0.608629\pi\)
−0.334683 + 0.942331i \(0.608629\pi\)
\(678\) 24.3607 0.935566
\(679\) −65.3050 −2.50617
\(680\) 6.23607 0.239142
\(681\) 84.7214 3.24653
\(682\) 0 0
\(683\) −9.70820 −0.371474 −0.185737 0.982599i \(-0.559467\pi\)
−0.185737 + 0.982599i \(0.559467\pi\)
\(684\) 7.47214 0.285704
\(685\) −36.8541 −1.40812
\(686\) −3.29180 −0.125681
\(687\) 35.1246 1.34009
\(688\) −7.61803 −0.290435
\(689\) −44.9443 −1.71224
\(690\) −10.6525 −0.405533
\(691\) 14.2148 0.540756 0.270378 0.962754i \(-0.412851\pi\)
0.270378 + 0.962754i \(0.412851\pi\)
\(692\) 4.00000 0.152057
\(693\) 0 0
\(694\) 3.79837 0.144184
\(695\) 54.3050 2.05990
\(696\) 18.4721 0.700185
\(697\) 0.763932 0.0289360
\(698\) 9.67376 0.366157
\(699\) 1.05573 0.0399313
\(700\) −37.9787 −1.43546
\(701\) 42.0902 1.58972 0.794862 0.606790i \(-0.207543\pi\)
0.794862 + 0.606790i \(0.207543\pi\)
\(702\) 57.8885 2.18486
\(703\) −3.23607 −0.122051
\(704\) 0 0
\(705\) 10.6525 0.401195
\(706\) −33.9230 −1.27671
\(707\) −13.7295 −0.516351
\(708\) −22.4721 −0.844555
\(709\) 46.0344 1.72886 0.864430 0.502753i \(-0.167680\pi\)
0.864430 + 0.502753i \(0.167680\pi\)
\(710\) −10.6525 −0.399780
\(711\) −69.0132 −2.58820
\(712\) −14.1803 −0.531431
\(713\) −2.36068 −0.0884082
\(714\) 20.1803 0.755230
\(715\) 0 0
\(716\) −21.1246 −0.789464
\(717\) 49.5967 1.85222
\(718\) −2.20163 −0.0821640
\(719\) −8.72949 −0.325555 −0.162778 0.986663i \(-0.552045\pi\)
−0.162778 + 0.986663i \(0.552045\pi\)
\(720\) 28.7984 1.07325
\(721\) 26.7639 0.996741
\(722\) 1.00000 0.0372161
\(723\) 63.1935 2.35019
\(724\) −5.41641 −0.201299
\(725\) −56.2492 −2.08904
\(726\) 0 0
\(727\) 34.1591 1.26689 0.633445 0.773788i \(-0.281640\pi\)
0.633445 + 0.773788i \(0.281640\pi\)
\(728\) 15.4164 0.571370
\(729\) 41.9443 1.55349
\(730\) −42.1803 −1.56116
\(731\) −12.3262 −0.455902
\(732\) 3.70820 0.137059
\(733\) 20.7984 0.768205 0.384103 0.923290i \(-0.374511\pi\)
0.384103 + 0.923290i \(0.374511\pi\)
\(734\) 9.09017 0.335524
\(735\) −97.9574 −3.61321
\(736\) 0.854102 0.0314826
\(737\) 0 0
\(738\) 3.52786 0.129862
\(739\) −46.2148 −1.70004 −0.850019 0.526752i \(-0.823410\pi\)
−0.850019 + 0.526752i \(0.823410\pi\)
\(740\) −12.4721 −0.458485
\(741\) 12.9443 0.475520
\(742\) −43.3050 −1.58977
\(743\) 3.41641 0.125336 0.0626679 0.998034i \(-0.480039\pi\)
0.0626679 + 0.998034i \(0.480039\pi\)
\(744\) 8.94427 0.327913
\(745\) −13.5967 −0.498146
\(746\) −18.4721 −0.676313
\(747\) 16.0344 0.586670
\(748\) 0 0
\(749\) 9.52786 0.348141
\(750\) −60.5410 −2.21065
\(751\) −37.8885 −1.38257 −0.691286 0.722581i \(-0.742956\pi\)
−0.691286 + 0.722581i \(0.742956\pi\)
\(752\) −0.854102 −0.0311459
\(753\) 40.0689 1.46019
\(754\) 22.8328 0.831522
\(755\) −41.4853 −1.50980
\(756\) 55.7771 2.02859
\(757\) 30.3607 1.10348 0.551739 0.834017i \(-0.313965\pi\)
0.551739 + 0.834017i \(0.313965\pi\)
\(758\) 7.88854 0.286525
\(759\) 0 0
\(760\) 3.85410 0.139803
\(761\) −31.5279 −1.14288 −0.571442 0.820642i \(-0.693616\pi\)
−0.571442 + 0.820642i \(0.693616\pi\)
\(762\) 7.41641 0.268668
\(763\) −3.63932 −0.131752
\(764\) −13.3820 −0.484143
\(765\) 46.5967 1.68471
\(766\) −18.6525 −0.673941
\(767\) −27.7771 −1.00297
\(768\) −3.23607 −0.116772
\(769\) −13.2705 −0.478547 −0.239273 0.970952i \(-0.576909\pi\)
−0.239273 + 0.970952i \(0.576909\pi\)
\(770\) 0 0
\(771\) 58.8328 2.11881
\(772\) −18.4721 −0.664827
\(773\) 14.3607 0.516518 0.258259 0.966076i \(-0.416851\pi\)
0.258259 + 0.966076i \(0.416851\pi\)
\(774\) −56.9230 −2.04605
\(775\) −27.2361 −0.978348
\(776\) 16.9443 0.608264
\(777\) −40.3607 −1.44793
\(778\) 2.27051 0.0814017
\(779\) 0.472136 0.0169160
\(780\) 49.8885 1.78630
\(781\) 0 0
\(782\) 1.38197 0.0494190
\(783\) 82.6099 2.95224
\(784\) 7.85410 0.280504
\(785\) −86.0476 −3.07117
\(786\) −44.8328 −1.59913
\(787\) 17.4164 0.620828 0.310414 0.950601i \(-0.399532\pi\)
0.310414 + 0.950601i \(0.399532\pi\)
\(788\) −10.9443 −0.389874
\(789\) 51.7771 1.84331
\(790\) −35.5967 −1.26648
\(791\) 29.0132 1.03159
\(792\) 0 0
\(793\) 4.58359 0.162768
\(794\) 16.5623 0.587774
\(795\) −140.138 −4.97017
\(796\) 26.6180 0.943451
\(797\) 34.0000 1.20434 0.602171 0.798367i \(-0.294303\pi\)
0.602171 + 0.798367i \(0.294303\pi\)
\(798\) 12.4721 0.441509
\(799\) −1.38197 −0.0488904
\(800\) 9.85410 0.348395
\(801\) −105.957 −3.74382
\(802\) −19.2361 −0.679249
\(803\) 0 0
\(804\) 29.8885 1.05409
\(805\) −12.6869 −0.447155
\(806\) 11.0557 0.389421
\(807\) −63.7771 −2.24506
\(808\) 3.56231 0.125321
\(809\) 35.0902 1.23370 0.616852 0.787079i \(-0.288408\pi\)
0.616852 + 0.787079i \(0.288408\pi\)
\(810\) 94.1033 3.30645
\(811\) −12.7639 −0.448202 −0.224101 0.974566i \(-0.571945\pi\)
−0.224101 + 0.974566i \(0.571945\pi\)
\(812\) 22.0000 0.772049
\(813\) −90.9017 −3.18806
\(814\) 0 0
\(815\) 66.5623 2.33158
\(816\) −5.23607 −0.183299
\(817\) −7.61803 −0.266521
\(818\) 29.5279 1.03242
\(819\) 115.193 4.02519
\(820\) 1.81966 0.0635453
\(821\) 47.6180 1.66188 0.830940 0.556361i \(-0.187803\pi\)
0.830940 + 0.556361i \(0.187803\pi\)
\(822\) 30.9443 1.07931
\(823\) −1.74265 −0.0607448 −0.0303724 0.999539i \(-0.509669\pi\)
−0.0303724 + 0.999539i \(0.509669\pi\)
\(824\) −6.94427 −0.241915
\(825\) 0 0
\(826\) −26.7639 −0.931236
\(827\) −12.0689 −0.419676 −0.209838 0.977736i \(-0.567294\pi\)
−0.209838 + 0.977736i \(0.567294\pi\)
\(828\) 6.38197 0.221789
\(829\) 42.3607 1.47125 0.735624 0.677391i \(-0.236889\pi\)
0.735624 + 0.677391i \(0.236889\pi\)
\(830\) 8.27051 0.287074
\(831\) 66.2492 2.29816
\(832\) −4.00000 −0.138675
\(833\) 12.7082 0.440313
\(834\) −45.5967 −1.57889
\(835\) 24.2492 0.839179
\(836\) 0 0
\(837\) 40.0000 1.38260
\(838\) −28.7426 −0.992898
\(839\) 23.0132 0.794502 0.397251 0.917710i \(-0.369964\pi\)
0.397251 + 0.917710i \(0.369964\pi\)
\(840\) 48.0689 1.65853
\(841\) 3.58359 0.123572
\(842\) 24.4721 0.843365
\(843\) 12.9443 0.445824
\(844\) 14.9443 0.514403
\(845\) 11.5623 0.397755
\(846\) −6.38197 −0.219417
\(847\) 0 0
\(848\) 11.2361 0.385848
\(849\) 31.8885 1.09441
\(850\) 15.9443 0.546884
\(851\) −2.76393 −0.0947464
\(852\) 8.94427 0.306426
\(853\) 6.85410 0.234680 0.117340 0.993092i \(-0.462563\pi\)
0.117340 + 0.993092i \(0.462563\pi\)
\(854\) 4.41641 0.151126
\(855\) 28.7984 0.984884
\(856\) −2.47214 −0.0844959
\(857\) 26.8328 0.916592 0.458296 0.888800i \(-0.348460\pi\)
0.458296 + 0.888800i \(0.348460\pi\)
\(858\) 0 0
\(859\) 7.03444 0.240012 0.120006 0.992773i \(-0.461709\pi\)
0.120006 + 0.992773i \(0.461709\pi\)
\(860\) −29.3607 −1.00119
\(861\) 5.88854 0.200681
\(862\) 10.5836 0.360479
\(863\) −18.7639 −0.638732 −0.319366 0.947632i \(-0.603470\pi\)
−0.319366 + 0.947632i \(0.603470\pi\)
\(864\) −14.4721 −0.492352
\(865\) 15.4164 0.524174
\(866\) 11.8885 0.403989
\(867\) 46.5410 1.58062
\(868\) 10.6525 0.361569
\(869\) 0 0
\(870\) 71.1935 2.41369
\(871\) 36.9443 1.25181
\(872\) 0.944272 0.0319771
\(873\) 126.610 4.28510
\(874\) 0.854102 0.0288904
\(875\) −72.1033 −2.43754
\(876\) 35.4164 1.19661
\(877\) 32.6525 1.10260 0.551298 0.834308i \(-0.314133\pi\)
0.551298 + 0.834308i \(0.314133\pi\)
\(878\) 18.3607 0.619643
\(879\) 77.6656 2.61960
\(880\) 0 0
\(881\) 5.41641 0.182483 0.0912417 0.995829i \(-0.470916\pi\)
0.0912417 + 0.995829i \(0.470916\pi\)
\(882\) 58.6869 1.97609
\(883\) 28.0344 0.943434 0.471717 0.881750i \(-0.343634\pi\)
0.471717 + 0.881750i \(0.343634\pi\)
\(884\) −6.47214 −0.217681
\(885\) −86.6099 −2.91136
\(886\) −21.2705 −0.714597
\(887\) −35.3050 −1.18542 −0.592712 0.805414i \(-0.701943\pi\)
−0.592712 + 0.805414i \(0.701943\pi\)
\(888\) 10.4721 0.351422
\(889\) 8.83282 0.296243
\(890\) −54.6525 −1.83196
\(891\) 0 0
\(892\) −10.6525 −0.356671
\(893\) −0.854102 −0.0285814
\(894\) 11.4164 0.381822
\(895\) −81.4164 −2.72145
\(896\) −3.85410 −0.128757
\(897\) 11.0557 0.369140
\(898\) 15.7082 0.524190
\(899\) 15.7771 0.526195
\(900\) 73.6312 2.45437
\(901\) 18.1803 0.605675
\(902\) 0 0
\(903\) −95.0132 −3.16184
\(904\) −7.52786 −0.250373
\(905\) −20.8754 −0.693921
\(906\) 34.8328 1.15724
\(907\) 17.3475 0.576015 0.288008 0.957628i \(-0.407007\pi\)
0.288008 + 0.957628i \(0.407007\pi\)
\(908\) −26.1803 −0.868825
\(909\) 26.6180 0.882864
\(910\) 59.4164 1.96963
\(911\) 23.5967 0.781795 0.390898 0.920434i \(-0.372165\pi\)
0.390898 + 0.920434i \(0.372165\pi\)
\(912\) −3.23607 −0.107157
\(913\) 0 0
\(914\) 11.0902 0.366830
\(915\) 14.2918 0.472472
\(916\) −10.8541 −0.358630
\(917\) −53.3951 −1.76326
\(918\) −23.4164 −0.772857
\(919\) 39.6312 1.30731 0.653656 0.756792i \(-0.273234\pi\)
0.653656 + 0.756792i \(0.273234\pi\)
\(920\) 3.29180 0.108527
\(921\) 4.94427 0.162919
\(922\) −30.6869 −1.01062
\(923\) 11.0557 0.363904
\(924\) 0 0
\(925\) −31.8885 −1.04849
\(926\) −12.2148 −0.401403
\(927\) −51.8885 −1.70424
\(928\) −5.70820 −0.187381
\(929\) −49.6180 −1.62791 −0.813957 0.580925i \(-0.802691\pi\)
−0.813957 + 0.580925i \(0.802691\pi\)
\(930\) 34.4721 1.13039
\(931\) 7.85410 0.257408
\(932\) −0.326238 −0.0106863
\(933\) −17.5967 −0.576092
\(934\) 9.27051 0.303340
\(935\) 0 0
\(936\) −29.8885 −0.976938
\(937\) −8.49342 −0.277468 −0.138734 0.990330i \(-0.544303\pi\)
−0.138734 + 0.990330i \(0.544303\pi\)
\(938\) 35.5967 1.16228
\(939\) 50.1803 1.63757
\(940\) −3.29180 −0.107367
\(941\) 20.7639 0.676885 0.338442 0.940987i \(-0.390100\pi\)
0.338442 + 0.940987i \(0.390100\pi\)
\(942\) 72.2492 2.35401
\(943\) 0.403252 0.0131317
\(944\) 6.94427 0.226017
\(945\) 214.971 6.99299
\(946\) 0 0
\(947\) −1.49342 −0.0485297 −0.0242649 0.999706i \(-0.507724\pi\)
−0.0242649 + 0.999706i \(0.507724\pi\)
\(948\) 29.8885 0.970735
\(949\) 43.7771 1.42106
\(950\) 9.85410 0.319709
\(951\) 27.4164 0.889038
\(952\) −6.23607 −0.202112
\(953\) 23.0132 0.745469 0.372735 0.927938i \(-0.378420\pi\)
0.372735 + 0.927938i \(0.378420\pi\)
\(954\) 83.9574 2.71822
\(955\) −51.5755 −1.66894
\(956\) −15.3262 −0.495686
\(957\) 0 0
\(958\) 19.9098 0.643257
\(959\) 36.8541 1.19008
\(960\) −12.4721 −0.402536
\(961\) −23.3607 −0.753570
\(962\) 12.9443 0.417340
\(963\) −18.4721 −0.595256
\(964\) −19.5279 −0.628950
\(965\) −71.1935 −2.29180
\(966\) 10.6525 0.342738
\(967\) −48.8541 −1.57104 −0.785521 0.618835i \(-0.787605\pi\)
−0.785521 + 0.618835i \(0.787605\pi\)
\(968\) 0 0
\(969\) −5.23607 −0.168207
\(970\) 65.3050 2.09682
\(971\) −32.9443 −1.05723 −0.528616 0.848861i \(-0.677289\pi\)
−0.528616 + 0.848861i \(0.677289\pi\)
\(972\) −35.5967 −1.14177
\(973\) −54.3050 −1.74094
\(974\) 21.4164 0.686226
\(975\) 127.554 4.08500
\(976\) −1.14590 −0.0366793
\(977\) 6.83282 0.218601 0.109301 0.994009i \(-0.465139\pi\)
0.109301 + 0.994009i \(0.465139\pi\)
\(978\) −55.8885 −1.78712
\(979\) 0 0
\(980\) 30.2705 0.966956
\(981\) 7.05573 0.225272
\(982\) −23.7426 −0.757658
\(983\) 0.583592 0.0186137 0.00930685 0.999957i \(-0.497037\pi\)
0.00930685 + 0.999957i \(0.497037\pi\)
\(984\) −1.52786 −0.0487065
\(985\) −42.1803 −1.34398
\(986\) −9.23607 −0.294136
\(987\) −10.6525 −0.339072
\(988\) −4.00000 −0.127257
\(989\) −6.50658 −0.206897
\(990\) 0 0
\(991\) 12.9443 0.411188 0.205594 0.978637i \(-0.434087\pi\)
0.205594 + 0.978637i \(0.434087\pi\)
\(992\) −2.76393 −0.0877549
\(993\) 33.8885 1.07542
\(994\) 10.6525 0.337876
\(995\) 102.589 3.25228
\(996\) −6.94427 −0.220038
\(997\) 39.9230 1.26437 0.632187 0.774816i \(-0.282158\pi\)
0.632187 + 0.774816i \(0.282158\pi\)
\(998\) −20.0344 −0.634179
\(999\) 46.8328 1.48172
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.be.1.1 2
11.5 even 5 418.2.f.a.267.1 yes 4
11.9 even 5 418.2.f.a.191.1 4
11.10 odd 2 4598.2.a.v.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.f.a.191.1 4 11.9 even 5
418.2.f.a.267.1 yes 4 11.5 even 5
4598.2.a.v.1.1 2 11.10 odd 2
4598.2.a.be.1.1 2 1.1 even 1 trivial