Properties

Label 4598.2.a.br.1.2
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $0$
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: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.33452.1
Defining polynomial: \(x^{4} - x^{3} - 8 x^{2} + 7 x - 1\)
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 \(0.180986\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.180986 q^{3} +1.00000 q^{4} +4.08332 q^{5} -0.180986 q^{6} -3.52528 q^{7} -1.00000 q^{8} -2.96724 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.180986 q^{3} +1.00000 q^{4} +4.08332 q^{5} -0.180986 q^{6} -3.52528 q^{7} -1.00000 q^{8} -2.96724 q^{9} -4.08332 q^{10} +0.180986 q^{12} -1.08332 q^{13} +3.52528 q^{14} +0.739025 q^{15} +1.00000 q^{16} +3.90234 q^{17} +2.96724 q^{18} +1.00000 q^{19} +4.08332 q^{20} -0.638028 q^{21} -4.34430 q^{23} -0.180986 q^{24} +11.6735 q^{25} +1.08332 q^{26} -1.07999 q^{27} -3.52528 q^{28} +6.06565 q^{29} -0.739025 q^{30} +7.26098 q^{31} -1.00000 q^{32} -3.90234 q^{34} -14.3949 q^{35} -2.96724 q^{36} +0.754105 q^{37} -1.00000 q^{38} -0.196066 q^{39} -4.08332 q^{40} -6.67351 q^{41} +0.638028 q^{42} -4.60527 q^{43} -12.1162 q^{45} +4.34430 q^{46} +12.1666 q^{47} +0.180986 q^{48} +5.42762 q^{49} -11.6735 q^{50} +0.706269 q^{51} -1.08332 q^{52} +4.42429 q^{53} +1.07999 q^{54} +3.52528 q^{56} +0.180986 q^{57} -6.06565 q^{58} -3.54036 q^{59} +0.739025 q^{60} -9.05057 q^{61} -7.26098 q^{62} +10.4604 q^{63} +1.00000 q^{64} -4.42355 q^{65} +1.35864 q^{67} +3.90234 q^{68} -0.786258 q^{69} +14.3949 q^{70} -8.96724 q^{71} +2.96724 q^{72} -8.26431 q^{73} -0.754105 q^{74} +2.11274 q^{75} +1.00000 q^{76} +0.196066 q^{78} -11.5725 q^{79} +4.08332 q^{80} +8.70627 q^{81} +6.67351 q^{82} +17.6558 q^{83} -0.638028 q^{84} +15.9345 q^{85} +4.60527 q^{86} +1.09780 q^{87} +12.2965 q^{89} +12.1162 q^{90} +3.81901 q^{91} -4.34430 q^{92} +1.31414 q^{93} -12.1666 q^{94} +4.08332 q^{95} -0.180986 q^{96} +16.4933 q^{97} -5.42762 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + q^{3} + 4 q^{4} + 3 q^{5} - q^{6} + q^{7} - 4 q^{8} + 5 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{2} + q^{3} + 4 q^{4} + 3 q^{5} - q^{6} + q^{7} - 4 q^{8} + 5 q^{9} - 3 q^{10} + q^{12} + 9 q^{13} - q^{14} + 5 q^{15} + 4 q^{16} + 2 q^{17} - 5 q^{18} + 4 q^{19} + 3 q^{20} - 2 q^{21} - 2 q^{23} - q^{24} + 15 q^{25} - 9 q^{26} - 2 q^{27} + q^{28} - 5 q^{29} - 5 q^{30} + 27 q^{31} - 4 q^{32} - 2 q^{34} - 12 q^{35} + 5 q^{36} + 6 q^{37} - 4 q^{38} - 2 q^{39} - 3 q^{40} + 5 q^{41} + 2 q^{42} - q^{43} + 11 q^{45} + 2 q^{46} + 22 q^{47} + q^{48} - 7 q^{49} - 15 q^{50} - 12 q^{51} + 9 q^{52} + 2 q^{54} - q^{56} + q^{57} + 5 q^{58} + 5 q^{60} - 6 q^{61} - 27 q^{62} + 30 q^{63} + 4 q^{64} - 26 q^{65} + 17 q^{67} + 2 q^{68} + 14 q^{69} + 12 q^{70} - 19 q^{71} - 5 q^{72} - 20 q^{73} - 6 q^{74} + 23 q^{75} + 4 q^{76} + 2 q^{78} - 12 q^{79} + 3 q^{80} + 20 q^{81} - 5 q^{82} + 23 q^{83} - 2 q^{84} + 30 q^{85} + q^{86} - 45 q^{87} + 16 q^{89} - 11 q^{90} + 15 q^{91} - 2 q^{92} - 12 q^{93} - 22 q^{94} + 3 q^{95} - q^{96} + 8 q^{97} + 7 q^{98} + O(q^{100}) \)

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
\(3\) 0.180986 0.104492 0.0522462 0.998634i \(-0.483362\pi\)
0.0522462 + 0.998634i \(0.483362\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.08332 1.82612 0.913058 0.407829i \(-0.133714\pi\)
0.913058 + 0.407829i \(0.133714\pi\)
\(6\) −0.180986 −0.0738873
\(7\) −3.52528 −1.33243 −0.666216 0.745759i \(-0.732087\pi\)
−0.666216 + 0.745759i \(0.732087\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.96724 −0.989081
\(10\) −4.08332 −1.29126
\(11\) 0 0
\(12\) 0.180986 0.0522462
\(13\) −1.08332 −0.300459 −0.150230 0.988651i \(-0.548001\pi\)
−0.150230 + 0.988651i \(0.548001\pi\)
\(14\) 3.52528 0.942171
\(15\) 0.739025 0.190815
\(16\) 1.00000 0.250000
\(17\) 3.90234 0.946455 0.473228 0.880940i \(-0.343089\pi\)
0.473228 + 0.880940i \(0.343089\pi\)
\(18\) 2.96724 0.699386
\(19\) 1.00000 0.229416
\(20\) 4.08332 0.913058
\(21\) −0.638028 −0.139229
\(22\) 0 0
\(23\) −4.34430 −0.905848 −0.452924 0.891549i \(-0.649619\pi\)
−0.452924 + 0.891549i \(0.649619\pi\)
\(24\) −0.180986 −0.0369437
\(25\) 11.6735 2.33470
\(26\) 1.08332 0.212457
\(27\) −1.07999 −0.207844
\(28\) −3.52528 −0.666216
\(29\) 6.06565 1.12636 0.563181 0.826334i \(-0.309577\pi\)
0.563181 + 0.826334i \(0.309577\pi\)
\(30\) −0.739025 −0.134927
\(31\) 7.26098 1.30411 0.652055 0.758172i \(-0.273907\pi\)
0.652055 + 0.758172i \(0.273907\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −3.90234 −0.669245
\(35\) −14.3949 −2.43318
\(36\) −2.96724 −0.494541
\(37\) 0.754105 0.123974 0.0619870 0.998077i \(-0.480256\pi\)
0.0619870 + 0.998077i \(0.480256\pi\)
\(38\) −1.00000 −0.162221
\(39\) −0.196066 −0.0313957
\(40\) −4.08332 −0.645630
\(41\) −6.67351 −1.04223 −0.521114 0.853487i \(-0.674483\pi\)
−0.521114 + 0.853487i \(0.674483\pi\)
\(42\) 0.638028 0.0984498
\(43\) −4.60527 −0.702297 −0.351149 0.936320i \(-0.614209\pi\)
−0.351149 + 0.936320i \(0.614209\pi\)
\(44\) 0 0
\(45\) −12.1162 −1.80618
\(46\) 4.34430 0.640532
\(47\) 12.1666 1.77469 0.887344 0.461109i \(-0.152548\pi\)
0.887344 + 0.461109i \(0.152548\pi\)
\(48\) 0.180986 0.0261231
\(49\) 5.42762 0.775374
\(50\) −11.6735 −1.65088
\(51\) 0.706269 0.0988974
\(52\) −1.08332 −0.150230
\(53\) 4.42429 0.607722 0.303861 0.952716i \(-0.401724\pi\)
0.303861 + 0.952716i \(0.401724\pi\)
\(54\) 1.07999 0.146968
\(55\) 0 0
\(56\) 3.52528 0.471086
\(57\) 0.180986 0.0239722
\(58\) −6.06565 −0.796458
\(59\) −3.54036 −0.460916 −0.230458 0.973082i \(-0.574022\pi\)
−0.230458 + 0.973082i \(0.574022\pi\)
\(60\) 0.739025 0.0954077
\(61\) −9.05057 −1.15881 −0.579403 0.815041i \(-0.696714\pi\)
−0.579403 + 0.815041i \(0.696714\pi\)
\(62\) −7.26098 −0.922145
\(63\) 10.4604 1.31788
\(64\) 1.00000 0.125000
\(65\) −4.42355 −0.548674
\(66\) 0 0
\(67\) 1.35864 0.165984 0.0829921 0.996550i \(-0.473552\pi\)
0.0829921 + 0.996550i \(0.473552\pi\)
\(68\) 3.90234 0.473228
\(69\) −0.786258 −0.0946543
\(70\) 14.3949 1.72052
\(71\) −8.96724 −1.06422 −0.532108 0.846676i \(-0.678600\pi\)
−0.532108 + 0.846676i \(0.678600\pi\)
\(72\) 2.96724 0.349693
\(73\) −8.26431 −0.967264 −0.483632 0.875271i \(-0.660683\pi\)
−0.483632 + 0.875271i \(0.660683\pi\)
\(74\) −0.754105 −0.0876629
\(75\) 2.11274 0.243959
\(76\) 1.00000 0.114708
\(77\) 0 0
\(78\) 0.196066 0.0222001
\(79\) −11.5725 −1.30201 −0.651005 0.759074i \(-0.725652\pi\)
−0.651005 + 0.759074i \(0.725652\pi\)
\(80\) 4.08332 0.456529
\(81\) 8.70627 0.967363
\(82\) 6.67351 0.736966
\(83\) 17.6558 1.93798 0.968990 0.247100i \(-0.0794777\pi\)
0.968990 + 0.247100i \(0.0794777\pi\)
\(84\) −0.638028 −0.0696145
\(85\) 15.9345 1.72834
\(86\) 4.60527 0.496599
\(87\) 1.09780 0.117696
\(88\) 0 0
\(89\) 12.2965 1.30342 0.651711 0.758467i \(-0.274051\pi\)
0.651711 + 0.758467i \(0.274051\pi\)
\(90\) 12.1162 1.27716
\(91\) 3.81901 0.400341
\(92\) −4.34430 −0.452924
\(93\) 1.31414 0.136270
\(94\) −12.1666 −1.25489
\(95\) 4.08332 0.418940
\(96\) −0.180986 −0.0184718
\(97\) 16.4933 1.67464 0.837319 0.546715i \(-0.184122\pi\)
0.837319 + 0.546715i \(0.184122\pi\)
\(98\) −5.42762 −0.548272
\(99\) 0 0
\(100\) 11.6735 1.16735
\(101\) 9.73916 0.969082 0.484541 0.874768i \(-0.338987\pi\)
0.484541 + 0.874768i \(0.338987\pi\)
\(102\) −0.706269 −0.0699310
\(103\) −7.88799 −0.777227 −0.388613 0.921401i \(-0.627046\pi\)
−0.388613 + 0.921401i \(0.627046\pi\)
\(104\) 1.08332 0.106228
\(105\) −2.60527 −0.254248
\(106\) −4.42429 −0.429725
\(107\) 12.3510 1.19401 0.597006 0.802237i \(-0.296357\pi\)
0.597006 + 0.802237i \(0.296357\pi\)
\(108\) −1.07999 −0.103922
\(109\) 15.9890 1.53147 0.765734 0.643158i \(-0.222376\pi\)
0.765734 + 0.643158i \(0.222376\pi\)
\(110\) 0 0
\(111\) 0.136483 0.0129544
\(112\) −3.52528 −0.333108
\(113\) −0.326620 −0.0307259 −0.0153629 0.999882i \(-0.504890\pi\)
−0.0153629 + 0.999882i \(0.504890\pi\)
\(114\) −0.180986 −0.0169509
\(115\) −17.7392 −1.65419
\(116\) 6.06565 0.563181
\(117\) 3.21448 0.297179
\(118\) 3.54036 0.325917
\(119\) −13.7568 −1.26109
\(120\) −0.739025 −0.0674634
\(121\) 0 0
\(122\) 9.05057 0.819400
\(123\) −1.20781 −0.108905
\(124\) 7.26098 0.652055
\(125\) 27.2501 2.43732
\(126\) −10.4604 −0.931884
\(127\) 2.52862 0.224378 0.112189 0.993687i \(-0.464214\pi\)
0.112189 + 0.993687i \(0.464214\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.833491 −0.0733848
\(130\) 4.42355 0.387971
\(131\) 12.6080 1.10157 0.550783 0.834648i \(-0.314329\pi\)
0.550783 + 0.834648i \(0.314329\pi\)
\(132\) 0 0
\(133\) −3.52528 −0.305681
\(134\) −1.35864 −0.117369
\(135\) −4.40994 −0.379547
\(136\) −3.90234 −0.334622
\(137\) 0.489194 0.0417947 0.0208973 0.999782i \(-0.493348\pi\)
0.0208973 + 0.999782i \(0.493348\pi\)
\(138\) 0.786258 0.0669307
\(139\) −14.0245 −1.18954 −0.594770 0.803896i \(-0.702757\pi\)
−0.594770 + 0.803896i \(0.702757\pi\)
\(140\) −14.3949 −1.21659
\(141\) 2.20199 0.185441
\(142\) 8.96724 0.752514
\(143\) 0 0
\(144\) −2.96724 −0.247270
\(145\) 24.7680 2.05687
\(146\) 8.26431 0.683959
\(147\) 0.982324 0.0810207
\(148\) 0.754105 0.0619870
\(149\) 19.0204 1.55821 0.779106 0.626892i \(-0.215673\pi\)
0.779106 + 0.626892i \(0.215673\pi\)
\(150\) −2.11274 −0.172505
\(151\) 13.9043 1.13152 0.565759 0.824571i \(-0.308583\pi\)
0.565759 + 0.824571i \(0.308583\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −11.5792 −0.936121
\(154\) 0 0
\(155\) 29.6489 2.38146
\(156\) −0.196066 −0.0156979
\(157\) 3.19273 0.254808 0.127404 0.991851i \(-0.459336\pi\)
0.127404 + 0.991851i \(0.459336\pi\)
\(158\) 11.5725 0.920660
\(159\) 0.800735 0.0635024
\(160\) −4.08332 −0.322815
\(161\) 15.3149 1.20698
\(162\) −8.70627 −0.684029
\(163\) 6.15998 0.482487 0.241243 0.970465i \(-0.422445\pi\)
0.241243 + 0.970465i \(0.422445\pi\)
\(164\) −6.67351 −0.521114
\(165\) 0 0
\(166\) −17.6558 −1.37036
\(167\) −6.92075 −0.535544 −0.267772 0.963482i \(-0.586287\pi\)
−0.267772 + 0.963482i \(0.586287\pi\)
\(168\) 0.638028 0.0492249
\(169\) −11.8264 −0.909724
\(170\) −15.9345 −1.22212
\(171\) −2.96724 −0.226911
\(172\) −4.60527 −0.351149
\(173\) 22.3444 1.69882 0.849408 0.527737i \(-0.176959\pi\)
0.849408 + 0.527737i \(0.176959\pi\)
\(174\) −1.09780 −0.0832239
\(175\) −41.1524 −3.11083
\(176\) 0 0
\(177\) −0.640757 −0.0481622
\(178\) −12.2965 −0.921659
\(179\) 2.37705 0.177669 0.0888346 0.996046i \(-0.471686\pi\)
0.0888346 + 0.996046i \(0.471686\pi\)
\(180\) −12.1162 −0.903089
\(181\) −25.5137 −1.89642 −0.948208 0.317650i \(-0.897106\pi\)
−0.948208 + 0.317650i \(0.897106\pi\)
\(182\) −3.81901 −0.283084
\(183\) −1.63803 −0.121086
\(184\) 4.34430 0.320266
\(185\) 3.07925 0.226391
\(186\) −1.31414 −0.0963572
\(187\) 0 0
\(188\) 12.1666 0.887344
\(189\) 3.80727 0.276938
\(190\) −4.08332 −0.296235
\(191\) −19.8580 −1.43687 −0.718436 0.695593i \(-0.755142\pi\)
−0.718436 + 0.695593i \(0.755142\pi\)
\(192\) 0.180986 0.0130616
\(193\) 22.5464 1.62293 0.811464 0.584403i \(-0.198671\pi\)
0.811464 + 0.584403i \(0.198671\pi\)
\(194\) −16.4933 −1.18415
\(195\) −0.800601 −0.0573323
\(196\) 5.42762 0.387687
\(197\) 12.3333 0.878710 0.439355 0.898313i \(-0.355207\pi\)
0.439355 + 0.898313i \(0.355207\pi\)
\(198\) 0 0
\(199\) 6.86625 0.486735 0.243368 0.969934i \(-0.421748\pi\)
0.243368 + 0.969934i \(0.421748\pi\)
\(200\) −11.6735 −0.825442
\(201\) 0.245895 0.0173441
\(202\) −9.73916 −0.685245
\(203\) −21.3831 −1.50080
\(204\) 0.706269 0.0494487
\(205\) −27.2501 −1.90323
\(206\) 7.88799 0.549582
\(207\) 12.8906 0.895958
\(208\) −1.08332 −0.0751148
\(209\) 0 0
\(210\) 2.60527 0.179781
\(211\) −8.80740 −0.606326 −0.303163 0.952939i \(-0.598043\pi\)
−0.303163 + 0.952939i \(0.598043\pi\)
\(212\) 4.42429 0.303861
\(213\) −1.62295 −0.111203
\(214\) −12.3510 −0.844294
\(215\) −18.8048 −1.28248
\(216\) 1.07999 0.0734839
\(217\) −25.5970 −1.73764
\(218\) −15.9890 −1.08291
\(219\) −1.49573 −0.101072
\(220\) 0 0
\(221\) −4.22748 −0.284371
\(222\) −0.136483 −0.00916011
\(223\) 3.80467 0.254780 0.127390 0.991853i \(-0.459340\pi\)
0.127390 + 0.991853i \(0.459340\pi\)
\(224\) 3.52528 0.235543
\(225\) −34.6382 −2.30921
\(226\) 0.326620 0.0217265
\(227\) 5.58353 0.370592 0.185296 0.982683i \(-0.440676\pi\)
0.185296 + 0.982683i \(0.440676\pi\)
\(228\) 0.180986 0.0119861
\(229\) 13.4343 0.887762 0.443881 0.896086i \(-0.353601\pi\)
0.443881 + 0.896086i \(0.353601\pi\)
\(230\) 17.7392 1.16969
\(231\) 0 0
\(232\) −6.06565 −0.398229
\(233\) 6.10113 0.399698 0.199849 0.979827i \(-0.435955\pi\)
0.199849 + 0.979827i \(0.435955\pi\)
\(234\) −3.21448 −0.210137
\(235\) 49.6803 3.24079
\(236\) −3.54036 −0.230458
\(237\) −2.09447 −0.136050
\(238\) 13.7568 0.891723
\(239\) 3.36137 0.217429 0.108714 0.994073i \(-0.465327\pi\)
0.108714 + 0.994073i \(0.465327\pi\)
\(240\) 0.739025 0.0477039
\(241\) 7.88799 0.508110 0.254055 0.967190i \(-0.418236\pi\)
0.254055 + 0.967190i \(0.418236\pi\)
\(242\) 0 0
\(243\) 4.81568 0.308926
\(244\) −9.05057 −0.579403
\(245\) 22.1627 1.41592
\(246\) 1.20781 0.0770074
\(247\) −1.08332 −0.0689301
\(248\) −7.26098 −0.461072
\(249\) 3.19546 0.202504
\(250\) −27.2501 −1.72345
\(251\) −12.7254 −0.803221 −0.401611 0.915811i \(-0.631549\pi\)
−0.401611 + 0.915811i \(0.631549\pi\)
\(252\) 10.4604 0.658942
\(253\) 0 0
\(254\) −2.52862 −0.158659
\(255\) 2.88392 0.180598
\(256\) 1.00000 0.0625000
\(257\) −12.2979 −0.767124 −0.383562 0.923515i \(-0.625303\pi\)
−0.383562 + 0.923515i \(0.625303\pi\)
\(258\) 0.833491 0.0518909
\(259\) −2.65843 −0.165187
\(260\) −4.42355 −0.274337
\(261\) −17.9982 −1.11406
\(262\) −12.6080 −0.778925
\(263\) −7.82369 −0.482429 −0.241215 0.970472i \(-0.577546\pi\)
−0.241215 + 0.970472i \(0.577546\pi\)
\(264\) 0 0
\(265\) 18.0658 1.10977
\(266\) 3.52528 0.216149
\(267\) 2.22549 0.136198
\(268\) 1.35864 0.0829921
\(269\) 2.10113 0.128108 0.0640541 0.997946i \(-0.479597\pi\)
0.0640541 + 0.997946i \(0.479597\pi\)
\(270\) 4.40994 0.268381
\(271\) −16.0841 −0.977037 −0.488518 0.872554i \(-0.662463\pi\)
−0.488518 + 0.872554i \(0.662463\pi\)
\(272\) 3.90234 0.236614
\(273\) 0.691189 0.0418327
\(274\) −0.489194 −0.0295533
\(275\) 0 0
\(276\) −0.786258 −0.0473272
\(277\) −2.06431 −0.124032 −0.0620161 0.998075i \(-0.519753\pi\)
−0.0620161 + 0.998075i \(0.519753\pi\)
\(278\) 14.0245 0.841132
\(279\) −21.5451 −1.28987
\(280\) 14.3949 0.860258
\(281\) 10.5108 0.627022 0.313511 0.949585i \(-0.398495\pi\)
0.313511 + 0.949585i \(0.398495\pi\)
\(282\) −2.20199 −0.131127
\(283\) 16.4480 0.977733 0.488867 0.872358i \(-0.337410\pi\)
0.488867 + 0.872358i \(0.337410\pi\)
\(284\) −8.96724 −0.532108
\(285\) 0.739025 0.0437761
\(286\) 0 0
\(287\) 23.5260 1.38870
\(288\) 2.96724 0.174847
\(289\) −1.77178 −0.104222
\(290\) −24.7680 −1.45443
\(291\) 2.98505 0.174987
\(292\) −8.26431 −0.483632
\(293\) 25.4166 1.48485 0.742427 0.669927i \(-0.233675\pi\)
0.742427 + 0.669927i \(0.233675\pi\)
\(294\) −0.982324 −0.0572903
\(295\) −14.4564 −0.841686
\(296\) −0.754105 −0.0438315
\(297\) 0 0
\(298\) −19.0204 −1.10182
\(299\) 4.70627 0.272171
\(300\) 2.11274 0.121979
\(301\) 16.2349 0.935763
\(302\) −13.9043 −0.800104
\(303\) 1.76265 0.101262
\(304\) 1.00000 0.0573539
\(305\) −36.9564 −2.11612
\(306\) 11.5792 0.661938
\(307\) −3.07925 −0.175742 −0.0878711 0.996132i \(-0.528006\pi\)
−0.0878711 + 0.996132i \(0.528006\pi\)
\(308\) 0 0
\(309\) −1.42762 −0.0812143
\(310\) −29.6489 −1.68394
\(311\) 22.8309 1.29462 0.647311 0.762226i \(-0.275894\pi\)
0.647311 + 0.762226i \(0.275894\pi\)
\(312\) 0.196066 0.0111001
\(313\) 0.646443 0.0365391 0.0182696 0.999833i \(-0.494184\pi\)
0.0182696 + 0.999833i \(0.494184\pi\)
\(314\) −3.19273 −0.180176
\(315\) 42.7131 2.40661
\(316\) −11.5725 −0.651005
\(317\) −16.4376 −0.923228 −0.461614 0.887081i \(-0.652730\pi\)
−0.461614 + 0.887081i \(0.652730\pi\)
\(318\) −0.800735 −0.0449030
\(319\) 0 0
\(320\) 4.08332 0.228265
\(321\) 2.23535 0.124765
\(322\) −15.3149 −0.853464
\(323\) 3.90234 0.217132
\(324\) 8.70627 0.483682
\(325\) −12.6462 −0.701483
\(326\) −6.15998 −0.341170
\(327\) 2.89379 0.160027
\(328\) 6.67351 0.368483
\(329\) −42.8909 −2.36465
\(330\) 0 0
\(331\) −25.9201 −1.42470 −0.712350 0.701824i \(-0.752369\pi\)
−0.712350 + 0.701824i \(0.752369\pi\)
\(332\) 17.6558 0.968990
\(333\) −2.23761 −0.122620
\(334\) 6.92075 0.378686
\(335\) 5.54776 0.303107
\(336\) −0.638028 −0.0348073
\(337\) 30.1177 1.64061 0.820307 0.571923i \(-0.193802\pi\)
0.820307 + 0.571923i \(0.193802\pi\)
\(338\) 11.8264 0.643272
\(339\) −0.0591138 −0.00321062
\(340\) 15.9345 0.864169
\(341\) 0 0
\(342\) 2.96724 0.160450
\(343\) 5.54309 0.299299
\(344\) 4.60527 0.248300
\(345\) −3.21054 −0.172850
\(346\) −22.3444 −1.20124
\(347\) −14.8604 −0.797750 −0.398875 0.917005i \(-0.630599\pi\)
−0.398875 + 0.917005i \(0.630599\pi\)
\(348\) 1.09780 0.0588482
\(349\) −21.7760 −1.16564 −0.582821 0.812601i \(-0.698051\pi\)
−0.582821 + 0.812601i \(0.698051\pi\)
\(350\) 41.1524 2.19969
\(351\) 1.16997 0.0624486
\(352\) 0 0
\(353\) −25.4658 −1.35541 −0.677705 0.735334i \(-0.737025\pi\)
−0.677705 + 0.735334i \(0.737025\pi\)
\(354\) 0.640757 0.0340558
\(355\) −36.6161 −1.94338
\(356\) 12.2965 0.651711
\(357\) −2.48980 −0.131774
\(358\) −2.37705 −0.125631
\(359\) 1.72728 0.0911622 0.0455811 0.998961i \(-0.485486\pi\)
0.0455811 + 0.998961i \(0.485486\pi\)
\(360\) 12.1162 0.638580
\(361\) 1.00000 0.0526316
\(362\) 25.5137 1.34097
\(363\) 0 0
\(364\) 3.81901 0.200171
\(365\) −33.7458 −1.76634
\(366\) 1.63803 0.0856211
\(367\) 12.6231 0.658919 0.329460 0.944170i \(-0.393133\pi\)
0.329460 + 0.944170i \(0.393133\pi\)
\(368\) −4.34430 −0.226462
\(369\) 19.8019 1.03085
\(370\) −3.07925 −0.160083
\(371\) −15.5969 −0.809748
\(372\) 1.31414 0.0681348
\(373\) −1.96997 −0.102001 −0.0510007 0.998699i \(-0.516241\pi\)
−0.0510007 + 0.998699i \(0.516241\pi\)
\(374\) 0 0
\(375\) 4.93189 0.254682
\(376\) −12.1666 −0.627447
\(377\) −6.57104 −0.338426
\(378\) −3.80727 −0.195825
\(379\) −12.1837 −0.625835 −0.312918 0.949780i \(-0.601306\pi\)
−0.312918 + 0.949780i \(0.601306\pi\)
\(380\) 4.08332 0.209470
\(381\) 0.457644 0.0234458
\(382\) 19.8580 1.01602
\(383\) 36.3472 1.85725 0.928627 0.371016i \(-0.120990\pi\)
0.928627 + 0.371016i \(0.120990\pi\)
\(384\) −0.180986 −0.00923591
\(385\) 0 0
\(386\) −22.5464 −1.14758
\(387\) 13.6650 0.694629
\(388\) 16.4933 0.837319
\(389\) 14.3444 0.727291 0.363646 0.931537i \(-0.381532\pi\)
0.363646 + 0.931537i \(0.381532\pi\)
\(390\) 0.800601 0.0405400
\(391\) −16.9529 −0.857345
\(392\) −5.42762 −0.274136
\(393\) 2.28187 0.115105
\(394\) −12.3333 −0.621342
\(395\) −47.2543 −2.37762
\(396\) 0 0
\(397\) −34.8468 −1.74891 −0.874456 0.485105i \(-0.838781\pi\)
−0.874456 + 0.485105i \(0.838781\pi\)
\(398\) −6.86625 −0.344174
\(399\) −0.638028 −0.0319413
\(400\) 11.6735 0.583676
\(401\) 34.6599 1.73083 0.865417 0.501053i \(-0.167054\pi\)
0.865417 + 0.501053i \(0.167054\pi\)
\(402\) −0.245895 −0.0122641
\(403\) −7.86597 −0.391832
\(404\) 9.73916 0.484541
\(405\) 35.5505 1.76652
\(406\) 21.3831 1.06123
\(407\) 0 0
\(408\) −0.706269 −0.0349655
\(409\) 36.3459 1.79719 0.898595 0.438780i \(-0.144589\pi\)
0.898595 + 0.438780i \(0.144589\pi\)
\(410\) 27.2501 1.34579
\(411\) 0.0885374 0.00436723
\(412\) −7.88799 −0.388613
\(413\) 12.4808 0.614139
\(414\) −12.8906 −0.633538
\(415\) 72.0945 3.53898
\(416\) 1.08332 0.0531142
\(417\) −2.53824 −0.124298
\(418\) 0 0
\(419\) 10.2663 0.501542 0.250771 0.968046i \(-0.419316\pi\)
0.250771 + 0.968046i \(0.419316\pi\)
\(420\) −2.60527 −0.127124
\(421\) −3.27805 −0.159762 −0.0798811 0.996804i \(-0.525454\pi\)
−0.0798811 + 0.996804i \(0.525454\pi\)
\(422\) 8.80740 0.428737
\(423\) −36.1014 −1.75531
\(424\) −4.42429 −0.214862
\(425\) 45.5540 2.20969
\(426\) 1.62295 0.0786321
\(427\) 31.9058 1.54403
\(428\) 12.3510 0.597006
\(429\) 0 0
\(430\) 18.8048 0.906848
\(431\) 15.2775 0.735893 0.367946 0.929847i \(-0.380061\pi\)
0.367946 + 0.929847i \(0.380061\pi\)
\(432\) −1.07999 −0.0519610
\(433\) 33.8113 1.62487 0.812435 0.583052i \(-0.198142\pi\)
0.812435 + 0.583052i \(0.198142\pi\)
\(434\) 25.5970 1.22869
\(435\) 4.48266 0.214927
\(436\) 15.9890 0.765734
\(437\) −4.34430 −0.207816
\(438\) 1.49573 0.0714685
\(439\) −5.15290 −0.245935 −0.122967 0.992411i \(-0.539241\pi\)
−0.122967 + 0.992411i \(0.539241\pi\)
\(440\) 0 0
\(441\) −16.1051 −0.766908
\(442\) 4.22748 0.201081
\(443\) 0.986260 0.0468586 0.0234293 0.999725i \(-0.492542\pi\)
0.0234293 + 0.999725i \(0.492542\pi\)
\(444\) 0.136483 0.00647718
\(445\) 50.2104 2.38020
\(446\) −3.80467 −0.180156
\(447\) 3.44243 0.162821
\(448\) −3.52528 −0.166554
\(449\) −28.3689 −1.33881 −0.669406 0.742897i \(-0.733451\pi\)
−0.669406 + 0.742897i \(0.733451\pi\)
\(450\) 34.6382 1.63286
\(451\) 0 0
\(452\) −0.326620 −0.0153629
\(453\) 2.51649 0.118235
\(454\) −5.58353 −0.262048
\(455\) 15.5943 0.731070
\(456\) −0.180986 −0.00847546
\(457\) −4.74943 −0.222169 −0.111085 0.993811i \(-0.535432\pi\)
−0.111085 + 0.993811i \(0.535432\pi\)
\(458\) −13.4343 −0.627743
\(459\) −4.21448 −0.196715
\(460\) −17.7392 −0.827093
\(461\) 0.587462 0.0273608 0.0136804 0.999906i \(-0.495645\pi\)
0.0136804 + 0.999906i \(0.495645\pi\)
\(462\) 0 0
\(463\) −24.2324 −1.12618 −0.563088 0.826397i \(-0.690387\pi\)
−0.563088 + 0.826397i \(0.690387\pi\)
\(464\) 6.06565 0.281591
\(465\) 5.36604 0.248844
\(466\) −6.10113 −0.282629
\(467\) 36.0423 1.66784 0.833919 0.551887i \(-0.186092\pi\)
0.833919 + 0.551887i \(0.186092\pi\)
\(468\) 3.21448 0.148589
\(469\) −4.78959 −0.221163
\(470\) −49.6803 −2.29158
\(471\) 0.577841 0.0266255
\(472\) 3.54036 0.162958
\(473\) 0 0
\(474\) 2.09447 0.0962020
\(475\) 11.6735 0.535618
\(476\) −13.7568 −0.630543
\(477\) −13.1279 −0.601087
\(478\) −3.36137 −0.153745
\(479\) −10.3904 −0.474749 −0.237374 0.971418i \(-0.576287\pi\)
−0.237374 + 0.971418i \(0.576287\pi\)
\(480\) −0.739025 −0.0337317
\(481\) −0.816938 −0.0372492
\(482\) −7.88799 −0.359288
\(483\) 2.77178 0.126120
\(484\) 0 0
\(485\) 67.3473 3.05808
\(486\) −4.81568 −0.218444
\(487\) 27.5903 1.25024 0.625118 0.780530i \(-0.285051\pi\)
0.625118 + 0.780530i \(0.285051\pi\)
\(488\) 9.05057 0.409700
\(489\) 1.11487 0.0504162
\(490\) −22.1627 −1.00121
\(491\) −27.0436 −1.22046 −0.610231 0.792224i \(-0.708923\pi\)
−0.610231 + 0.792224i \(0.708923\pi\)
\(492\) −1.20781 −0.0544525
\(493\) 23.6702 1.06605
\(494\) 1.08332 0.0487409
\(495\) 0 0
\(496\) 7.26098 0.326027
\(497\) 31.6121 1.41800
\(498\) −3.19546 −0.143192
\(499\) 20.2663 0.907244 0.453622 0.891194i \(-0.350132\pi\)
0.453622 + 0.891194i \(0.350132\pi\)
\(500\) 27.2501 1.21866
\(501\) −1.25256 −0.0559602
\(502\) 12.7254 0.567963
\(503\) −43.4573 −1.93767 −0.968833 0.247716i \(-0.920320\pi\)
−0.968833 + 0.247716i \(0.920320\pi\)
\(504\) −10.4604 −0.465942
\(505\) 39.7681 1.76966
\(506\) 0 0
\(507\) −2.14042 −0.0950593
\(508\) 2.52862 0.112189
\(509\) 19.3824 0.859109 0.429554 0.903041i \(-0.358671\pi\)
0.429554 + 0.903041i \(0.358671\pi\)
\(510\) −2.88392 −0.127702
\(511\) 29.1340 1.28881
\(512\) −1.00000 −0.0441942
\(513\) −1.07999 −0.0476827
\(514\) 12.2979 0.542439
\(515\) −32.2092 −1.41931
\(516\) −0.833491 −0.0366924
\(517\) 0 0
\(518\) 2.65843 0.116805
\(519\) 4.04403 0.177513
\(520\) 4.42355 0.193985
\(521\) −16.0302 −0.702294 −0.351147 0.936320i \(-0.614208\pi\)
−0.351147 + 0.936320i \(0.614208\pi\)
\(522\) 17.9982 0.787762
\(523\) 34.7772 1.52070 0.760351 0.649512i \(-0.225027\pi\)
0.760351 + 0.649512i \(0.225027\pi\)
\(524\) 12.6080 0.550783
\(525\) −7.44802 −0.325058
\(526\) 7.82369 0.341129
\(527\) 28.3348 1.23428
\(528\) 0 0
\(529\) −4.12709 −0.179439
\(530\) −18.0658 −0.784727
\(531\) 10.5051 0.455883
\(532\) −3.52528 −0.152840
\(533\) 7.22956 0.313147
\(534\) −2.22549 −0.0963064
\(535\) 50.4329 2.18041
\(536\) −1.35864 −0.0586843
\(537\) 0.430214 0.0185651
\(538\) −2.10113 −0.0905862
\(539\) 0 0
\(540\) −4.40994 −0.189774
\(541\) 18.9863 0.816283 0.408142 0.912919i \(-0.366177\pi\)
0.408142 + 0.912919i \(0.366177\pi\)
\(542\) 16.0841 0.690869
\(543\) −4.61762 −0.198161
\(544\) −3.90234 −0.167311
\(545\) 65.2882 2.79664
\(546\) −0.691189 −0.0295802
\(547\) −10.9784 −0.469402 −0.234701 0.972068i \(-0.575411\pi\)
−0.234701 + 0.972068i \(0.575411\pi\)
\(548\) 0.489194 0.0208973
\(549\) 26.8552 1.14615
\(550\) 0 0
\(551\) 6.06565 0.258405
\(552\) 0.786258 0.0334654
\(553\) 40.7964 1.73484
\(554\) 2.06431 0.0877039
\(555\) 0.557302 0.0236562
\(556\) −14.0245 −0.594770
\(557\) −27.3905 −1.16057 −0.580287 0.814412i \(-0.697059\pi\)
−0.580287 + 0.814412i \(0.697059\pi\)
\(558\) 21.5451 0.912076
\(559\) 4.98899 0.211012
\(560\) −14.3949 −0.608294
\(561\) 0 0
\(562\) −10.5108 −0.443372
\(563\) −23.4427 −0.987992 −0.493996 0.869464i \(-0.664464\pi\)
−0.493996 + 0.869464i \(0.664464\pi\)
\(564\) 2.20199 0.0927207
\(565\) −1.33370 −0.0561090
\(566\) −16.4480 −0.691362
\(567\) −30.6921 −1.28895
\(568\) 8.96724 0.376257
\(569\) −16.5370 −0.693268 −0.346634 0.938000i \(-0.612675\pi\)
−0.346634 + 0.938000i \(0.612675\pi\)
\(570\) −0.739025 −0.0309543
\(571\) −26.9700 −1.12866 −0.564329 0.825550i \(-0.690865\pi\)
−0.564329 + 0.825550i \(0.690865\pi\)
\(572\) 0 0
\(573\) −3.59402 −0.150142
\(574\) −23.5260 −0.981957
\(575\) −50.7132 −2.11489
\(576\) −2.96724 −0.123635
\(577\) 1.66931 0.0694943 0.0347472 0.999396i \(-0.488937\pi\)
0.0347472 + 0.999396i \(0.488937\pi\)
\(578\) 1.77178 0.0736964
\(579\) 4.08059 0.169584
\(580\) 24.7680 1.02843
\(581\) −62.2418 −2.58223
\(582\) −2.98505 −0.123734
\(583\) 0 0
\(584\) 8.26431 0.341979
\(585\) 13.1257 0.542683
\(586\) −25.4166 −1.04995
\(587\) −19.7023 −0.813202 −0.406601 0.913606i \(-0.633286\pi\)
−0.406601 + 0.913606i \(0.633286\pi\)
\(588\) 0.982324 0.0405104
\(589\) 7.26098 0.299183
\(590\) 14.4564 0.595162
\(591\) 2.23215 0.0918186
\(592\) 0.754105 0.0309935
\(593\) −25.3604 −1.04142 −0.520712 0.853732i \(-0.674334\pi\)
−0.520712 + 0.853732i \(0.674334\pi\)
\(594\) 0 0
\(595\) −56.1736 −2.30289
\(596\) 19.0204 0.779106
\(597\) 1.24270 0.0508602
\(598\) −4.70627 −0.192454
\(599\) −8.05463 −0.329103 −0.164552 0.986368i \(-0.552618\pi\)
−0.164552 + 0.986368i \(0.552618\pi\)
\(600\) −2.11274 −0.0862525
\(601\) −31.5522 −1.28704 −0.643521 0.765428i \(-0.722527\pi\)
−0.643521 + 0.765428i \(0.722527\pi\)
\(602\) −16.2349 −0.661684
\(603\) −4.03142 −0.164172
\(604\) 13.9043 0.565759
\(605\) 0 0
\(606\) −1.76265 −0.0716029
\(607\) −35.8403 −1.45471 −0.727356 0.686260i \(-0.759251\pi\)
−0.727356 + 0.686260i \(0.759251\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −3.87005 −0.156822
\(610\) 36.9564 1.49632
\(611\) −13.1804 −0.533221
\(612\) −11.5792 −0.468061
\(613\) 19.3522 0.781629 0.390814 0.920470i \(-0.372193\pi\)
0.390814 + 0.920470i \(0.372193\pi\)
\(614\) 3.07925 0.124269
\(615\) −4.93189 −0.198873
\(616\) 0 0
\(617\) −19.2966 −0.776852 −0.388426 0.921480i \(-0.626981\pi\)
−0.388426 + 0.921480i \(0.626981\pi\)
\(618\) 1.42762 0.0574272
\(619\) −8.91408 −0.358287 −0.179144 0.983823i \(-0.557333\pi\)
−0.179144 + 0.983823i \(0.557333\pi\)
\(620\) 29.6489 1.19073
\(621\) 4.69179 0.188275
\(622\) −22.8309 −0.915435
\(623\) −43.3485 −1.73672
\(624\) −0.196066 −0.00784893
\(625\) 52.9033 2.11613
\(626\) −0.646443 −0.0258371
\(627\) 0 0
\(628\) 3.19273 0.127404
\(629\) 2.94277 0.117336
\(630\) −42.7131 −1.70173
\(631\) −9.54383 −0.379934 −0.189967 0.981790i \(-0.560838\pi\)
−0.189967 + 0.981790i \(0.560838\pi\)
\(632\) 11.5725 0.460330
\(633\) −1.59402 −0.0633565
\(634\) 16.4376 0.652821
\(635\) 10.3251 0.409741
\(636\) 0.800735 0.0317512
\(637\) −5.87985 −0.232968
\(638\) 0 0
\(639\) 26.6080 1.05260
\(640\) −4.08332 −0.161407
\(641\) 15.7458 0.621923 0.310961 0.950423i \(-0.399349\pi\)
0.310961 + 0.950423i \(0.399349\pi\)
\(642\) −2.23535 −0.0882224
\(643\) −18.0423 −0.711518 −0.355759 0.934578i \(-0.615778\pi\)
−0.355759 + 0.934578i \(0.615778\pi\)
\(644\) 15.3149 0.603491
\(645\) −3.40341 −0.134009
\(646\) −3.90234 −0.153535
\(647\) 13.5850 0.534081 0.267041 0.963685i \(-0.413954\pi\)
0.267041 + 0.963685i \(0.413954\pi\)
\(648\) −8.70627 −0.342015
\(649\) 0 0
\(650\) 12.6462 0.496023
\(651\) −4.63270 −0.181570
\(652\) 6.15998 0.241243
\(653\) −11.9429 −0.467362 −0.233681 0.972313i \(-0.575077\pi\)
−0.233681 + 0.972313i \(0.575077\pi\)
\(654\) −2.89379 −0.113156
\(655\) 51.4825 2.01159
\(656\) −6.67351 −0.260557
\(657\) 24.5222 0.956703
\(658\) 42.8909 1.67206
\(659\) 12.2721 0.478054 0.239027 0.971013i \(-0.423172\pi\)
0.239027 + 0.971013i \(0.423172\pi\)
\(660\) 0 0
\(661\) 16.9831 0.660564 0.330282 0.943882i \(-0.392856\pi\)
0.330282 + 0.943882i \(0.392856\pi\)
\(662\) 25.9201 1.00742
\(663\) −0.765116 −0.0297146
\(664\) −17.6558 −0.685179
\(665\) −14.3949 −0.558209
\(666\) 2.23761 0.0867057
\(667\) −26.3510 −1.02031
\(668\) −6.92075 −0.267772
\(669\) 0.688593 0.0266225
\(670\) −5.54776 −0.214329
\(671\) 0 0
\(672\) 0.638028 0.0246124
\(673\) 45.7965 1.76533 0.882663 0.470006i \(-0.155748\pi\)
0.882663 + 0.470006i \(0.155748\pi\)
\(674\) −30.1177 −1.16009
\(675\) −12.6073 −0.485254
\(676\) −11.8264 −0.454862
\(677\) −7.64483 −0.293815 −0.146907 0.989150i \(-0.546932\pi\)
−0.146907 + 0.989150i \(0.546932\pi\)
\(678\) 0.0591138 0.00227025
\(679\) −58.1434 −2.23134
\(680\) −15.9345 −0.611060
\(681\) 1.01054 0.0387240
\(682\) 0 0
\(683\) −39.5426 −1.51306 −0.756528 0.653961i \(-0.773106\pi\)
−0.756528 + 0.653961i \(0.773106\pi\)
\(684\) −2.96724 −0.113455
\(685\) 1.99754 0.0763220
\(686\) −5.54309 −0.211636
\(687\) 2.43142 0.0927645
\(688\) −4.60527 −0.175574
\(689\) −4.79292 −0.182596
\(690\) 3.21054 0.122223
\(691\) −14.9274 −0.567866 −0.283933 0.958844i \(-0.591639\pi\)
−0.283933 + 0.958844i \(0.591639\pi\)
\(692\) 22.3444 0.849408
\(693\) 0 0
\(694\) 14.8604 0.564094
\(695\) −57.2664 −2.17224
\(696\) −1.09780 −0.0416119
\(697\) −26.0423 −0.986422
\(698\) 21.7760 0.824233
\(699\) 1.10422 0.0417655
\(700\) −41.1524 −1.55542
\(701\) −35.9728 −1.35867 −0.679337 0.733827i \(-0.737732\pi\)
−0.679337 + 0.733827i \(0.737732\pi\)
\(702\) −1.16997 −0.0441579
\(703\) 0.754105 0.0284416
\(704\) 0 0
\(705\) 8.99145 0.338638
\(706\) 25.4658 0.958419
\(707\) −34.3333 −1.29124
\(708\) −0.640757 −0.0240811
\(709\) −0.311540 −0.0117001 −0.00585007 0.999983i \(-0.501862\pi\)
−0.00585007 + 0.999983i \(0.501862\pi\)
\(710\) 36.6161 1.37418
\(711\) 34.3385 1.28779
\(712\) −12.2965 −0.460829
\(713\) −31.5438 −1.18133
\(714\) 2.48980 0.0931783
\(715\) 0 0
\(716\) 2.37705 0.0888346
\(717\) 0.608362 0.0227197
\(718\) −1.72728 −0.0644614
\(719\) −35.7163 −1.33199 −0.665996 0.745955i \(-0.731993\pi\)
−0.665996 + 0.745955i \(0.731993\pi\)
\(720\) −12.1162 −0.451545
\(721\) 27.8074 1.03560
\(722\) −1.00000 −0.0372161
\(723\) 1.42762 0.0530937
\(724\) −25.5137 −0.948208
\(725\) 70.8074 2.62972
\(726\) 0 0
\(727\) 17.6337 0.653997 0.326999 0.945025i \(-0.393963\pi\)
0.326999 + 0.945025i \(0.393963\pi\)
\(728\) −3.81901 −0.141542
\(729\) −25.2472 −0.935083
\(730\) 33.7458 1.24899
\(731\) −17.9713 −0.664693
\(732\) −1.63803 −0.0605432
\(733\) 6.19680 0.228884 0.114442 0.993430i \(-0.463492\pi\)
0.114442 + 0.993430i \(0.463492\pi\)
\(734\) −12.6231 −0.465926
\(735\) 4.01114 0.147953
\(736\) 4.34430 0.160133
\(737\) 0 0
\(738\) −19.8019 −0.728920
\(739\) 5.18257 0.190644 0.0953219 0.995446i \(-0.469612\pi\)
0.0953219 + 0.995446i \(0.469612\pi\)
\(740\) 3.07925 0.113196
\(741\) −0.196066 −0.00720267
\(742\) 15.5969 0.572579
\(743\) 51.1819 1.87768 0.938840 0.344353i \(-0.111902\pi\)
0.938840 + 0.344353i \(0.111902\pi\)
\(744\) −1.31414 −0.0481786
\(745\) 77.6664 2.84548
\(746\) 1.96997 0.0721258
\(747\) −52.3892 −1.91682
\(748\) 0 0
\(749\) −43.5406 −1.59094
\(750\) −4.93189 −0.180087
\(751\) −32.0673 −1.17015 −0.585075 0.810979i \(-0.698935\pi\)
−0.585075 + 0.810979i \(0.698935\pi\)
\(752\) 12.1666 0.443672
\(753\) −2.30313 −0.0839305
\(754\) 6.57104 0.239303
\(755\) 56.7758 2.06628
\(756\) 3.80727 0.138469
\(757\) −21.1762 −0.769661 −0.384830 0.922987i \(-0.625740\pi\)
−0.384830 + 0.922987i \(0.625740\pi\)
\(758\) 12.1837 0.442532
\(759\) 0 0
\(760\) −4.08332 −0.148118
\(761\) −25.5169 −0.924986 −0.462493 0.886623i \(-0.653045\pi\)
−0.462493 + 0.886623i \(0.653045\pi\)
\(762\) −0.457644 −0.0165787
\(763\) −56.3657 −2.04058
\(764\) −19.8580 −0.718436
\(765\) −47.2815 −1.70947
\(766\) −36.3472 −1.31328
\(767\) 3.83535 0.138486
\(768\) 0.180986 0.00653078
\(769\) 2.92274 0.105397 0.0526984 0.998610i \(-0.483218\pi\)
0.0526984 + 0.998610i \(0.483218\pi\)
\(770\) 0 0
\(771\) −2.22576 −0.0801587
\(772\) 22.5464 0.811464
\(773\) −34.7509 −1.24990 −0.624952 0.780663i \(-0.714881\pi\)
−0.624952 + 0.780663i \(0.714881\pi\)
\(774\) −13.6650 −0.491177
\(775\) 84.7611 3.04471
\(776\) −16.4933 −0.592074
\(777\) −0.481140 −0.0172608
\(778\) −14.3444 −0.514273
\(779\) −6.67351 −0.239103
\(780\) −0.800601 −0.0286661
\(781\) 0 0
\(782\) 16.9529 0.606234
\(783\) −6.55083 −0.234108
\(784\) 5.42762 0.193843
\(785\) 13.0370 0.465309
\(786\) −2.28187 −0.0813918
\(787\) 17.8238 0.635351 0.317675 0.948200i \(-0.397098\pi\)
0.317675 + 0.948200i \(0.397098\pi\)
\(788\) 12.3333 0.439355
\(789\) −1.41598 −0.0504102
\(790\) 47.2543 1.68123
\(791\) 1.15143 0.0409401
\(792\) 0 0
\(793\) 9.80467 0.348174
\(794\) 34.8468 1.23667
\(795\) 3.26966 0.115963
\(796\) 6.86625 0.243368
\(797\) −46.0418 −1.63088 −0.815441 0.578840i \(-0.803506\pi\)
−0.815441 + 0.578840i \(0.803506\pi\)
\(798\) 0.638028 0.0225859
\(799\) 47.4783 1.67966
\(800\) −11.6735 −0.412721
\(801\) −36.4866 −1.28919
\(802\) −34.6599 −1.22388
\(803\) 0 0
\(804\) 0.245895 0.00867205
\(805\) 62.5355 2.20409
\(806\) 7.86597 0.277067
\(807\) 0.380276 0.0133863
\(808\) −9.73916 −0.342622
\(809\) 53.4229 1.87825 0.939125 0.343575i \(-0.111638\pi\)
0.939125 + 0.343575i \(0.111638\pi\)
\(810\) −35.5505 −1.24912
\(811\) −42.7552 −1.50134 −0.750669 0.660678i \(-0.770269\pi\)
−0.750669 + 0.660678i \(0.770269\pi\)
\(812\) −21.3831 −0.750400
\(813\) −2.91099 −0.102093
\(814\) 0 0
\(815\) 25.1532 0.881077
\(816\) 0.706269 0.0247244
\(817\) −4.60527 −0.161118
\(818\) −36.3459 −1.27080
\(819\) −11.3319 −0.395970
\(820\) −27.2501 −0.951615
\(821\) −27.5151 −0.960285 −0.480143 0.877190i \(-0.659415\pi\)
−0.480143 + 0.877190i \(0.659415\pi\)
\(822\) −0.0885374 −0.00308810
\(823\) 10.3745 0.361631 0.180815 0.983517i \(-0.442126\pi\)
0.180815 + 0.983517i \(0.442126\pi\)
\(824\) 7.88799 0.274791
\(825\) 0 0
\(826\) −12.4808 −0.434262
\(827\) −53.1407 −1.84788 −0.923941 0.382534i \(-0.875051\pi\)
−0.923941 + 0.382534i \(0.875051\pi\)
\(828\) 12.8906 0.447979
\(829\) −22.8587 −0.793916 −0.396958 0.917837i \(-0.629934\pi\)
−0.396958 + 0.917837i \(0.629934\pi\)
\(830\) −72.0945 −2.50244
\(831\) −0.373611 −0.0129604
\(832\) −1.08332 −0.0375574
\(833\) 21.1804 0.733857
\(834\) 2.53824 0.0878919
\(835\) −28.2596 −0.977965
\(836\) 0 0
\(837\) −7.84177 −0.271051
\(838\) −10.2663 −0.354643
\(839\) 52.4169 1.80963 0.904816 0.425803i \(-0.140008\pi\)
0.904816 + 0.425803i \(0.140008\pi\)
\(840\) 2.60527 0.0898904
\(841\) 7.79205 0.268691
\(842\) 3.27805 0.112969
\(843\) 1.90231 0.0655191
\(844\) −8.80740 −0.303163
\(845\) −48.2911 −1.66126
\(846\) 36.1014 1.24119
\(847\) 0 0
\(848\) 4.42429 0.151931
\(849\) 2.97687 0.102166
\(850\) −45.5540 −1.56249
\(851\) −3.27606 −0.112302
\(852\) −1.62295 −0.0556013
\(853\) −0.889115 −0.0304427 −0.0152214 0.999884i \(-0.504845\pi\)
−0.0152214 + 0.999884i \(0.504845\pi\)
\(854\) −31.9058 −1.09179
\(855\) −12.1162 −0.414366
\(856\) −12.3510 −0.422147
\(857\) −35.7742 −1.22202 −0.611012 0.791621i \(-0.709237\pi\)
−0.611012 + 0.791621i \(0.709237\pi\)
\(858\) 0 0
\(859\) 33.5139 1.14348 0.571740 0.820435i \(-0.306268\pi\)
0.571740 + 0.820435i \(0.306268\pi\)
\(860\) −18.8048 −0.641238
\(861\) 4.25789 0.145108
\(862\) −15.2775 −0.520355
\(863\) 28.9111 0.984146 0.492073 0.870554i \(-0.336239\pi\)
0.492073 + 0.870554i \(0.336239\pi\)
\(864\) 1.07999 0.0367420
\(865\) 91.2395 3.10224
\(866\) −33.8113 −1.14896
\(867\) −0.320668 −0.0108905
\(868\) −25.5970 −0.868818
\(869\) 0 0
\(870\) −4.48266 −0.151977
\(871\) −1.47184 −0.0498715
\(872\) −15.9890 −0.541455
\(873\) −48.9395 −1.65635
\(874\) 4.34430 0.146948
\(875\) −96.0643 −3.24757
\(876\) −1.49573 −0.0505359
\(877\) 24.6284 0.831642 0.415821 0.909446i \(-0.363494\pi\)
0.415821 + 0.909446i \(0.363494\pi\)
\(878\) 5.15290 0.173902
\(879\) 4.60006 0.155156
\(880\) 0 0
\(881\) 47.5997 1.60368 0.801838 0.597542i \(-0.203856\pi\)
0.801838 + 0.597542i \(0.203856\pi\)
\(882\) 16.1051 0.542286
\(883\) 37.4768 1.26120 0.630598 0.776110i \(-0.282810\pi\)
0.630598 + 0.776110i \(0.282810\pi\)
\(884\) −4.22748 −0.142186
\(885\) −2.61642 −0.0879499
\(886\) −0.986260 −0.0331340
\(887\) −25.5777 −0.858815 −0.429408 0.903111i \(-0.641278\pi\)
−0.429408 + 0.903111i \(0.641278\pi\)
\(888\) −0.136483 −0.00458006
\(889\) −8.91408 −0.298969
\(890\) −50.2104 −1.68306
\(891\) 0 0
\(892\) 3.80467 0.127390
\(893\) 12.1666 0.407141
\(894\) −3.44243 −0.115132
\(895\) 9.70627 0.324445
\(896\) 3.52528 0.117771
\(897\) 0.851770 0.0284398
\(898\) 28.3689 0.946683
\(899\) 44.0425 1.46890
\(900\) −34.6382 −1.15461
\(901\) 17.2650 0.575182
\(902\) 0 0
\(903\) 2.93829 0.0977802
\(904\) 0.326620 0.0108632
\(905\) −104.181 −3.46308
\(906\) −2.51649 −0.0836048
\(907\) −33.4531 −1.11079 −0.555396 0.831586i \(-0.687433\pi\)
−0.555396 + 0.831586i \(0.687433\pi\)
\(908\) 5.58353 0.185296
\(909\) −28.8985 −0.958501
\(910\) −15.5943 −0.516945
\(911\) −33.3522 −1.10501 −0.552504 0.833510i \(-0.686328\pi\)
−0.552504 + 0.833510i \(0.686328\pi\)
\(912\) 0.180986 0.00599305
\(913\) 0 0
\(914\) 4.74943 0.157097
\(915\) −6.68859 −0.221118
\(916\) 13.4343 0.443881
\(917\) −44.4468 −1.46776
\(918\) 4.21448 0.139099
\(919\) −54.4174 −1.79506 −0.897532 0.440949i \(-0.854642\pi\)
−0.897532 + 0.440949i \(0.854642\pi\)
\(920\) 17.7392 0.584843
\(921\) −0.557302 −0.0183637
\(922\) −0.587462 −0.0193470
\(923\) 9.71441 0.319754
\(924\) 0 0
\(925\) 8.80305 0.289443
\(926\) 24.2324 0.796327
\(927\) 23.4056 0.768741
\(928\) −6.06565 −0.199115
\(929\) −20.4289 −0.670250 −0.335125 0.942174i \(-0.608778\pi\)
−0.335125 + 0.942174i \(0.608778\pi\)
\(930\) −5.36604 −0.175959
\(931\) 5.42762 0.177883
\(932\) 6.10113 0.199849
\(933\) 4.13208 0.135278
\(934\) −36.0423 −1.17934
\(935\) 0 0
\(936\) −3.21448 −0.105069
\(937\) −10.7981 −0.352759 −0.176380 0.984322i \(-0.556439\pi\)
−0.176380 + 0.984322i \(0.556439\pi\)
\(938\) 4.78959 0.156386
\(939\) 0.116997 0.00381806
\(940\) 49.6803 1.62039
\(941\) −45.1998 −1.47347 −0.736736 0.676181i \(-0.763634\pi\)
−0.736736 + 0.676181i \(0.763634\pi\)
\(942\) −0.577841 −0.0188271
\(943\) 28.9917 0.944100
\(944\) −3.54036 −0.115229
\(945\) 15.5463 0.505721
\(946\) 0 0
\(947\) −25.6435 −0.833301 −0.416651 0.909067i \(-0.636796\pi\)
−0.416651 + 0.909067i \(0.636796\pi\)
\(948\) −2.09447 −0.0680251
\(949\) 8.95290 0.290623
\(950\) −11.6735 −0.378739
\(951\) −2.97498 −0.0964704
\(952\) 13.7568 0.445862
\(953\) 30.6312 0.992242 0.496121 0.868253i \(-0.334757\pi\)
0.496121 + 0.868253i \(0.334757\pi\)
\(954\) 13.1279 0.425033
\(955\) −81.0865 −2.62390
\(956\) 3.36137 0.108714
\(957\) 0 0
\(958\) 10.3904 0.335698
\(959\) −1.72455 −0.0556886
\(960\) 0.739025 0.0238519
\(961\) 21.7218 0.700702
\(962\) 0.816938 0.0263391
\(963\) −36.6483 −1.18098
\(964\) 7.88799 0.254055
\(965\) 92.0643 2.96365
\(966\) −2.77178 −0.0891806
\(967\) −7.40068 −0.237990 −0.118995 0.992895i \(-0.537967\pi\)
−0.118995 + 0.992895i \(0.537967\pi\)
\(968\) 0 0
\(969\) 0.706269 0.0226886
\(970\) −67.3473 −2.16239
\(971\) 16.1436 0.518074 0.259037 0.965867i \(-0.416595\pi\)
0.259037 + 0.965867i \(0.416595\pi\)
\(972\) 4.81568 0.154463
\(973\) 49.4402 1.58498
\(974\) −27.5903 −0.884051
\(975\) −2.28878 −0.0732997
\(976\) −9.05057 −0.289702
\(977\) 13.0674 0.418063 0.209032 0.977909i \(-0.432969\pi\)
0.209032 + 0.977909i \(0.432969\pi\)
\(978\) −1.11487 −0.0356496
\(979\) 0 0
\(980\) 22.1627 0.707962
\(981\) −47.4432 −1.51475
\(982\) 27.0436 0.862997
\(983\) 33.2009 1.05894 0.529472 0.848327i \(-0.322390\pi\)
0.529472 + 0.848327i \(0.322390\pi\)
\(984\) 1.20781 0.0385037
\(985\) 50.3608 1.60463
\(986\) −23.6702 −0.753812
\(987\) −7.76265 −0.247088
\(988\) −1.08332 −0.0344650
\(989\) 20.0067 0.636175
\(990\) 0 0
\(991\) −4.31422 −0.137046 −0.0685228 0.997650i \(-0.521829\pi\)
−0.0685228 + 0.997650i \(0.521829\pi\)
\(992\) −7.26098 −0.230536
\(993\) −4.69119 −0.148870
\(994\) −31.6121 −1.00267
\(995\) 28.0371 0.888836
\(996\) 3.19546 0.101252
\(997\) −49.2187 −1.55877 −0.779386 0.626545i \(-0.784469\pi\)
−0.779386 + 0.626545i \(0.784469\pi\)
\(998\) −20.2663 −0.641519
\(999\) −0.814425 −0.0257673
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.br.1.2 4
11.10 odd 2 4598.2.a.bu.1.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.br.1.2 4 1.1 even 1 trivial
4598.2.a.bu.1.2 yes 4 11.10 odd 2