Properties

Label 4598.2.a.bv.1.3
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: 4.4.258228.1
Defining polynomial: \(x^{4} - 2 x^{3} - 12 x^{2} + 6 x + 24\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.48761\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.48761 q^{3} +1.00000 q^{4} +1.48761 q^{5} +2.48761 q^{6} +4.90325 q^{7} +1.00000 q^{8} +3.18819 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.48761 q^{3} +1.00000 q^{4} +1.48761 q^{5} +2.48761 q^{6} +4.90325 q^{7} +1.00000 q^{8} +3.18819 q^{9} +1.48761 q^{10} +2.48761 q^{12} -3.09144 q^{13} +4.90325 q^{14} +3.70058 q^{15} +1.00000 q^{16} -5.90325 q^{17} +3.18819 q^{18} +1.00000 q^{19} +1.48761 q^{20} +12.1974 q^{21} +2.09144 q^{23} +2.48761 q^{24} -2.78703 q^{25} -3.09144 q^{26} +0.468133 q^{27} +4.90325 q^{28} -0.700580 q^{29} +3.70058 q^{30} +4.97521 q^{31} +1.00000 q^{32} -5.90325 q^{34} +7.29411 q^{35} +3.18819 q^{36} +9.31889 q^{37} +1.00000 q^{38} -7.69028 q^{39} +1.48761 q^{40} -6.48229 q^{41} +12.1974 q^{42} +0.792340 q^{43} +4.74277 q^{45} +2.09144 q^{46} -2.18819 q^{47} +2.48761 q^{48} +17.0419 q^{49} -2.78703 q^{50} -14.6850 q^{51} -3.09144 q^{52} -5.29942 q^{53} +0.468133 q^{54} +4.90325 q^{56} +2.48761 q^{57} -0.700580 q^{58} -0.603830 q^{59} +3.70058 q^{60} +5.11123 q^{61} +4.97521 q^{62} +15.6325 q^{63} +1.00000 q^{64} -4.59884 q^{65} -11.8731 q^{67} -5.90325 q^{68} +5.20267 q^{69} +7.29411 q^{70} +9.45751 q^{71} +3.18819 q^{72} +1.90325 q^{73} +9.31889 q^{74} -6.93303 q^{75} +1.00000 q^{76} -7.69028 q^{78} +14.4823 q^{79} +1.48761 q^{80} -8.40003 q^{81} -6.48229 q^{82} -7.48761 q^{83} +12.1974 q^{84} -8.78171 q^{85} +0.792340 q^{86} -1.74277 q^{87} +3.50708 q^{89} +4.74277 q^{90} -15.1581 q^{91} +2.09144 q^{92} +12.3764 q^{93} -2.18819 q^{94} +1.48761 q^{95} +2.48761 q^{96} -10.0000 q^{97} +17.0419 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 3 q^{7} + 4 q^{8} + 16 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 3 q^{7} + 4 q^{8} + 16 q^{9} - 2 q^{10} + 2 q^{12} + q^{13} + 3 q^{14} + 26 q^{15} + 4 q^{16} - 7 q^{17} + 16 q^{18} + 4 q^{19} - 2 q^{20} - 9 q^{21} - 5 q^{23} + 2 q^{24} + 8 q^{25} + q^{26} + 8 q^{27} + 3 q^{28} - 14 q^{29} + 26 q^{30} + 4 q^{31} + 4 q^{32} - 7 q^{34} - 12 q^{35} + 16 q^{36} + 12 q^{37} + 4 q^{38} + 5 q^{39} - 2 q^{40} + 12 q^{41} - 9 q^{42} + 14 q^{43} - 2 q^{45} - 5 q^{46} - 12 q^{47} + 2 q^{48} + 23 q^{49} + 8 q^{50} + 7 q^{51} + q^{52} - 10 q^{53} + 8 q^{54} + 3 q^{56} + 2 q^{57} - 14 q^{58} + 3 q^{59} + 26 q^{60} + 6 q^{61} + 4 q^{62} - 18 q^{63} + 4 q^{64} + 4 q^{65} + 15 q^{67} - 7 q^{68} - 7 q^{69} - 12 q^{70} - 16 q^{71} + 16 q^{72} - 9 q^{73} + 12 q^{74} - 44 q^{75} + 4 q^{76} + 5 q^{78} + 20 q^{79} - 2 q^{80} + 52 q^{81} + 12 q^{82} - 22 q^{83} - 9 q^{84} + 14 q^{85} + 14 q^{86} + 14 q^{87} - 8 q^{89} - 2 q^{90} - 18 q^{91} - 5 q^{92} + 56 q^{93} - 12 q^{94} - 2 q^{95} + 2 q^{96} - 40 q^{97} + 23 q^{98} + O(q^{100}) \)

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
\(3\) 2.48761 1.43622 0.718110 0.695929i \(-0.245007\pi\)
0.718110 + 0.695929i \(0.245007\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.48761 0.665278 0.332639 0.943054i \(-0.392061\pi\)
0.332639 + 0.943054i \(0.392061\pi\)
\(6\) 2.48761 1.01556
\(7\) 4.90325 1.85325 0.926627 0.375981i \(-0.122694\pi\)
0.926627 + 0.375981i \(0.122694\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.18819 1.06273
\(10\) 1.48761 0.470422
\(11\) 0 0
\(12\) 2.48761 0.718110
\(13\) −3.09144 −0.857410 −0.428705 0.903444i \(-0.641030\pi\)
−0.428705 + 0.903444i \(0.641030\pi\)
\(14\) 4.90325 1.31045
\(15\) 3.70058 0.955486
\(16\) 1.00000 0.250000
\(17\) −5.90325 −1.43175 −0.715874 0.698229i \(-0.753972\pi\)
−0.715874 + 0.698229i \(0.753972\pi\)
\(18\) 3.18819 0.751463
\(19\) 1.00000 0.229416
\(20\) 1.48761 0.332639
\(21\) 12.1974 2.66168
\(22\) 0 0
\(23\) 2.09144 0.436095 0.218047 0.975938i \(-0.430031\pi\)
0.218047 + 0.975938i \(0.430031\pi\)
\(24\) 2.48761 0.507781
\(25\) −2.78703 −0.557405
\(26\) −3.09144 −0.606281
\(27\) 0.468133 0.0900922
\(28\) 4.90325 0.926627
\(29\) −0.700580 −0.130094 −0.0650472 0.997882i \(-0.520720\pi\)
−0.0650472 + 0.997882i \(0.520720\pi\)
\(30\) 3.70058 0.675630
\(31\) 4.97521 0.893575 0.446787 0.894640i \(-0.352568\pi\)
0.446787 + 0.894640i \(0.352568\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −5.90325 −1.01240
\(35\) 7.29411 1.23293
\(36\) 3.18819 0.531364
\(37\) 9.31889 1.53202 0.766008 0.642831i \(-0.222240\pi\)
0.766008 + 0.642831i \(0.222240\pi\)
\(38\) 1.00000 0.162221
\(39\) −7.69028 −1.23143
\(40\) 1.48761 0.235211
\(41\) −6.48229 −1.01236 −0.506182 0.862427i \(-0.668944\pi\)
−0.506182 + 0.862427i \(0.668944\pi\)
\(42\) 12.1974 1.88209
\(43\) 0.792340 0.120831 0.0604154 0.998173i \(-0.480757\pi\)
0.0604154 + 0.998173i \(0.480757\pi\)
\(44\) 0 0
\(45\) 4.74277 0.707010
\(46\) 2.09144 0.308365
\(47\) −2.18819 −0.319180 −0.159590 0.987183i \(-0.551017\pi\)
−0.159590 + 0.987183i \(0.551017\pi\)
\(48\) 2.48761 0.359055
\(49\) 17.0419 2.43455
\(50\) −2.78703 −0.394145
\(51\) −14.6850 −2.05631
\(52\) −3.09144 −0.428705
\(53\) −5.29942 −0.727931 −0.363966 0.931412i \(-0.618577\pi\)
−0.363966 + 0.931412i \(0.618577\pi\)
\(54\) 0.468133 0.0637048
\(55\) 0 0
\(56\) 4.90325 0.655224
\(57\) 2.48761 0.329492
\(58\) −0.700580 −0.0919906
\(59\) −0.603830 −0.0786119 −0.0393060 0.999227i \(-0.512515\pi\)
−0.0393060 + 0.999227i \(0.512515\pi\)
\(60\) 3.70058 0.477743
\(61\) 5.11123 0.654426 0.327213 0.944951i \(-0.393890\pi\)
0.327213 + 0.944951i \(0.393890\pi\)
\(62\) 4.97521 0.631853
\(63\) 15.6325 1.96951
\(64\) 1.00000 0.125000
\(65\) −4.59884 −0.570416
\(66\) 0 0
\(67\) −11.8731 −1.45054 −0.725268 0.688467i \(-0.758284\pi\)
−0.725268 + 0.688467i \(0.758284\pi\)
\(68\) −5.90325 −0.715874
\(69\) 5.20267 0.626328
\(70\) 7.29411 0.871813
\(71\) 9.45751 1.12240 0.561200 0.827680i \(-0.310340\pi\)
0.561200 + 0.827680i \(0.310340\pi\)
\(72\) 3.18819 0.375731
\(73\) 1.90325 0.222759 0.111379 0.993778i \(-0.464473\pi\)
0.111379 + 0.993778i \(0.464473\pi\)
\(74\) 9.31889 1.08330
\(75\) −6.93303 −0.800557
\(76\) 1.00000 0.114708
\(77\) 0 0
\(78\) −7.69028 −0.870752
\(79\) 14.4823 1.62939 0.814693 0.579893i \(-0.196906\pi\)
0.814693 + 0.579893i \(0.196906\pi\)
\(80\) 1.48761 0.166319
\(81\) −8.40003 −0.933336
\(82\) −6.48229 −0.715850
\(83\) −7.48761 −0.821872 −0.410936 0.911664i \(-0.634798\pi\)
−0.410936 + 0.911664i \(0.634798\pi\)
\(84\) 12.1974 1.33084
\(85\) −8.78171 −0.952511
\(86\) 0.792340 0.0854403
\(87\) −1.74277 −0.186844
\(88\) 0 0
\(89\) 3.50708 0.371750 0.185875 0.982573i \(-0.440488\pi\)
0.185875 + 0.982573i \(0.440488\pi\)
\(90\) 4.74277 0.499931
\(91\) −15.1581 −1.58900
\(92\) 2.09144 0.218047
\(93\) 12.3764 1.28337
\(94\) −2.18819 −0.225694
\(95\) 1.48761 0.152625
\(96\) 2.48761 0.253890
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 17.0419 1.72149
\(99\) 0 0
\(100\) −2.78703 −0.278703
\(101\) −6.08645 −0.605624 −0.302812 0.953050i \(-0.597925\pi\)
−0.302812 + 0.953050i \(0.597925\pi\)
\(102\) −14.6850 −1.45403
\(103\) 17.5071 1.72502 0.862512 0.506037i \(-0.168890\pi\)
0.862512 + 0.506037i \(0.168890\pi\)
\(104\) −3.09144 −0.303140
\(105\) 18.1449 1.77076
\(106\) −5.29942 −0.514725
\(107\) −11.7424 −1.13518 −0.567592 0.823310i \(-0.692125\pi\)
−0.567592 + 0.823310i \(0.692125\pi\)
\(108\) 0.468133 0.0450461
\(109\) 2.60383 0.249402 0.124701 0.992194i \(-0.460203\pi\)
0.124701 + 0.992194i \(0.460203\pi\)
\(110\) 0 0
\(111\) 23.1817 2.20031
\(112\) 4.90325 0.463314
\(113\) 12.4823 1.17424 0.587118 0.809502i \(-0.300263\pi\)
0.587118 + 0.809502i \(0.300263\pi\)
\(114\) 2.48761 0.232986
\(115\) 3.11123 0.290124
\(116\) −0.700580 −0.0650472
\(117\) −9.85607 −0.911194
\(118\) −0.603830 −0.0555870
\(119\) −28.9451 −2.65339
\(120\) 3.70058 0.337815
\(121\) 0 0
\(122\) 5.11123 0.462749
\(123\) −16.1254 −1.45398
\(124\) 4.97521 0.446787
\(125\) −11.5840 −1.03611
\(126\) 15.6325 1.39265
\(127\) −18.7817 −1.66661 −0.833304 0.552815i \(-0.813553\pi\)
−0.833304 + 0.552815i \(0.813553\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.97103 0.173540
\(130\) −4.59884 −0.403345
\(131\) −9.98937 −0.872776 −0.436388 0.899759i \(-0.643742\pi\)
−0.436388 + 0.899759i \(0.643742\pi\)
\(132\) 0 0
\(133\) 4.90325 0.425166
\(134\) −11.8731 −1.02568
\(135\) 0.696398 0.0599364
\(136\) −5.90325 −0.506200
\(137\) 10.6956 0.913786 0.456893 0.889522i \(-0.348962\pi\)
0.456893 + 0.889522i \(0.348962\pi\)
\(138\) 5.20267 0.442881
\(139\) −8.32680 −0.706270 −0.353135 0.935572i \(-0.614884\pi\)
−0.353135 + 0.935572i \(0.614884\pi\)
\(140\) 7.29411 0.616465
\(141\) −5.44335 −0.458412
\(142\) 9.45751 0.793656
\(143\) 0 0
\(144\) 3.18819 0.265682
\(145\) −1.04219 −0.0865489
\(146\) 1.90325 0.157514
\(147\) 42.3934 3.49655
\(148\) 9.31889 0.766008
\(149\) −23.3410 −1.91217 −0.956083 0.293096i \(-0.905314\pi\)
−0.956083 + 0.293096i \(0.905314\pi\)
\(150\) −6.93303 −0.566079
\(151\) −3.32421 −0.270520 −0.135260 0.990810i \(-0.543187\pi\)
−0.135260 + 0.990810i \(0.543187\pi\)
\(152\) 1.00000 0.0811107
\(153\) −18.8207 −1.52156
\(154\) 0 0
\(155\) 7.40116 0.594475
\(156\) −7.69028 −0.615715
\(157\) 22.9177 1.82903 0.914517 0.404547i \(-0.132571\pi\)
0.914517 + 0.404547i \(0.132571\pi\)
\(158\) 14.4823 1.15215
\(159\) −13.1829 −1.04547
\(160\) 1.48761 0.117606
\(161\) 10.2548 0.808194
\(162\) −8.40003 −0.659968
\(163\) −20.4053 −1.59827 −0.799135 0.601152i \(-0.794709\pi\)
−0.799135 + 0.601152i \(0.794709\pi\)
\(164\) −6.48229 −0.506182
\(165\) 0 0
\(166\) −7.48761 −0.581151
\(167\) −14.7817 −1.14384 −0.571922 0.820308i \(-0.693802\pi\)
−0.571922 + 0.820308i \(0.693802\pi\)
\(168\) 12.1974 0.941047
\(169\) −3.44302 −0.264848
\(170\) −8.78171 −0.673527
\(171\) 3.18819 0.243807
\(172\) 0.792340 0.0604154
\(173\) −18.2640 −1.38859 −0.694293 0.719692i \(-0.744283\pi\)
−0.694293 + 0.719692i \(0.744283\pi\)
\(174\) −1.74277 −0.132119
\(175\) −13.6655 −1.03301
\(176\) 0 0
\(177\) −1.50209 −0.112904
\(178\) 3.50708 0.262867
\(179\) −15.6262 −1.16796 −0.583979 0.811769i \(-0.698505\pi\)
−0.583979 + 0.811769i \(0.698505\pi\)
\(180\) 4.74277 0.353505
\(181\) 22.6378 1.68265 0.841327 0.540527i \(-0.181775\pi\)
0.841327 + 0.540527i \(0.181775\pi\)
\(182\) −15.1581 −1.12359
\(183\) 12.7147 0.939901
\(184\) 2.09144 0.154183
\(185\) 13.8628 1.01922
\(186\) 12.3764 0.907480
\(187\) 0 0
\(188\) −2.18819 −0.159590
\(189\) 2.29537 0.166964
\(190\) 1.48761 0.107922
\(191\) 13.5021 0.976977 0.488489 0.872570i \(-0.337548\pi\)
0.488489 + 0.872570i \(0.337548\pi\)
\(192\) 2.48761 0.179528
\(193\) 8.00000 0.575853 0.287926 0.957653i \(-0.407034\pi\)
0.287926 + 0.957653i \(0.407034\pi\)
\(194\) −10.0000 −0.717958
\(195\) −11.4401 −0.819243
\(196\) 17.0419 1.21728
\(197\) 13.3806 0.953325 0.476663 0.879086i \(-0.341846\pi\)
0.476663 + 0.879086i \(0.341846\pi\)
\(198\) 0 0
\(199\) −24.6354 −1.74636 −0.873178 0.487401i \(-0.837945\pi\)
−0.873178 + 0.487401i \(0.837945\pi\)
\(200\) −2.78703 −0.197073
\(201\) −29.5357 −2.08329
\(202\) −6.08645 −0.428241
\(203\) −3.43512 −0.241098
\(204\) −14.6850 −1.02815
\(205\) −9.64310 −0.673503
\(206\) 17.5071 1.21978
\(207\) 6.66789 0.463450
\(208\) −3.09144 −0.214353
\(209\) 0 0
\(210\) 18.1449 1.25211
\(211\) −21.4522 −1.47683 −0.738415 0.674347i \(-0.764425\pi\)
−0.738415 + 0.674347i \(0.764425\pi\)
\(212\) −5.29942 −0.363966
\(213\) 23.5266 1.61201
\(214\) −11.7424 −0.802697
\(215\) 1.17869 0.0803860
\(216\) 0.468133 0.0318524
\(217\) 24.3947 1.65602
\(218\) 2.60383 0.176354
\(219\) 4.73454 0.319930
\(220\) 0 0
\(221\) 18.2495 1.22760
\(222\) 23.1817 1.55586
\(223\) −7.26401 −0.486434 −0.243217 0.969972i \(-0.578203\pi\)
−0.243217 + 0.969972i \(0.578203\pi\)
\(224\) 4.90325 0.327612
\(225\) −8.88556 −0.592371
\(226\) 12.4823 0.830310
\(227\) 6.44302 0.427638 0.213819 0.976873i \(-0.431410\pi\)
0.213819 + 0.976873i \(0.431410\pi\)
\(228\) 2.48761 0.164746
\(229\) −14.1333 −0.933955 −0.466977 0.884269i \(-0.654657\pi\)
−0.466977 + 0.884269i \(0.654657\pi\)
\(230\) 3.11123 0.205149
\(231\) 0 0
\(232\) −0.700580 −0.0459953
\(233\) −24.1776 −1.58392 −0.791962 0.610570i \(-0.790940\pi\)
−0.791962 + 0.610570i \(0.790940\pi\)
\(234\) −9.85607 −0.644312
\(235\) −3.25516 −0.212343
\(236\) −0.603830 −0.0393060
\(237\) 36.0262 2.34016
\(238\) −28.9451 −1.87623
\(239\) 28.1581 1.82140 0.910698 0.413074i \(-0.135545\pi\)
0.910698 + 0.413074i \(0.135545\pi\)
\(240\) 3.70058 0.238871
\(241\) −17.7843 −1.14559 −0.572794 0.819699i \(-0.694140\pi\)
−0.572794 + 0.819699i \(0.694140\pi\)
\(242\) 0 0
\(243\) −22.3004 −1.43057
\(244\) 5.11123 0.327213
\(245\) 25.3516 1.61965
\(246\) −16.1254 −1.02812
\(247\) −3.09144 −0.196703
\(248\) 4.97521 0.315926
\(249\) −18.6262 −1.18039
\(250\) −11.5840 −0.732639
\(251\) 1.20766 0.0762268 0.0381134 0.999273i \(-0.487865\pi\)
0.0381134 + 0.999273i \(0.487865\pi\)
\(252\) 15.6325 0.984753
\(253\) 0 0
\(254\) −18.7817 −1.17847
\(255\) −21.8454 −1.36801
\(256\) 1.00000 0.0625000
\(257\) −16.4053 −1.02334 −0.511669 0.859183i \(-0.670972\pi\)
−0.511669 + 0.859183i \(0.670972\pi\)
\(258\) 1.97103 0.122711
\(259\) 45.6929 2.83922
\(260\) −4.59884 −0.285208
\(261\) −2.23358 −0.138255
\(262\) −9.98937 −0.617146
\(263\) 27.1776 1.67584 0.837920 0.545793i \(-0.183772\pi\)
0.837920 + 0.545793i \(0.183772\pi\)
\(264\) 0 0
\(265\) −7.88345 −0.484277
\(266\) 4.90325 0.300638
\(267\) 8.72423 0.533915
\(268\) −11.8731 −0.725268
\(269\) 9.23922 0.563325 0.281663 0.959514i \(-0.409114\pi\)
0.281663 + 0.959514i \(0.409114\pi\)
\(270\) 0.696398 0.0423814
\(271\) −17.0613 −1.03640 −0.518201 0.855259i \(-0.673398\pi\)
−0.518201 + 0.855259i \(0.673398\pi\)
\(272\) −5.90325 −0.357937
\(273\) −37.7074 −2.28215
\(274\) 10.6956 0.646144
\(275\) 0 0
\(276\) 5.20267 0.313164
\(277\) −21.6705 −1.30205 −0.651026 0.759055i \(-0.725661\pi\)
−0.651026 + 0.759055i \(0.725661\pi\)
\(278\) −8.32680 −0.499408
\(279\) 15.8619 0.949627
\(280\) 7.29411 0.435906
\(281\) 0.675793 0.0403144 0.0201572 0.999797i \(-0.493583\pi\)
0.0201572 + 0.999797i \(0.493583\pi\)
\(282\) −5.44335 −0.324147
\(283\) −2.64841 −0.157432 −0.0787160 0.996897i \(-0.525082\pi\)
−0.0787160 + 0.996897i \(0.525082\pi\)
\(284\) 9.45751 0.561200
\(285\) 3.70058 0.219203
\(286\) 0 0
\(287\) −31.7843 −1.87617
\(288\) 3.18819 0.187866
\(289\) 17.8484 1.04990
\(290\) −1.04219 −0.0611993
\(291\) −24.8761 −1.45826
\(292\) 1.90325 0.111379
\(293\) 1.70589 0.0996593 0.0498297 0.998758i \(-0.484132\pi\)
0.0498297 + 0.998758i \(0.484132\pi\)
\(294\) 42.3934 2.47244
\(295\) −0.898261 −0.0522988
\(296\) 9.31889 0.541650
\(297\) 0 0
\(298\) −23.3410 −1.35211
\(299\) −6.46554 −0.373912
\(300\) −6.93303 −0.400278
\(301\) 3.88504 0.223930
\(302\) −3.32421 −0.191287
\(303\) −15.1407 −0.869810
\(304\) 1.00000 0.0573539
\(305\) 7.60351 0.435375
\(306\) −18.8207 −1.07591
\(307\) 14.3136 0.816919 0.408460 0.912776i \(-0.366066\pi\)
0.408460 + 0.912776i \(0.366066\pi\)
\(308\) 0 0
\(309\) 43.5507 2.47751
\(310\) 7.40116 0.420358
\(311\) 22.1805 1.25774 0.628870 0.777511i \(-0.283518\pi\)
0.628870 + 0.777511i \(0.283518\pi\)
\(312\) −7.69028 −0.435376
\(313\) 10.4873 0.592776 0.296388 0.955068i \(-0.404218\pi\)
0.296388 + 0.955068i \(0.404218\pi\)
\(314\) 22.9177 1.29332
\(315\) 23.2550 1.31027
\(316\) 14.4823 0.814693
\(317\) 30.2785 1.70061 0.850305 0.526291i \(-0.176418\pi\)
0.850305 + 0.526291i \(0.176418\pi\)
\(318\) −13.1829 −0.739259
\(319\) 0 0
\(320\) 1.48761 0.0831597
\(321\) −29.2106 −1.63038
\(322\) 10.2548 0.571480
\(323\) −5.90325 −0.328466
\(324\) −8.40003 −0.466668
\(325\) 8.61592 0.477925
\(326\) −20.4053 −1.13015
\(327\) 6.47730 0.358196
\(328\) −6.48229 −0.357925
\(329\) −10.7292 −0.591521
\(330\) 0 0
\(331\) 4.62330 0.254120 0.127060 0.991895i \(-0.459446\pi\)
0.127060 + 0.991895i \(0.459446\pi\)
\(332\) −7.48761 −0.410936
\(333\) 29.7104 1.62812
\(334\) −14.7817 −0.808819
\(335\) −17.6626 −0.965010
\(336\) 12.1974 0.665420
\(337\) 25.8728 1.40938 0.704691 0.709514i \(-0.251086\pi\)
0.704691 + 0.709514i \(0.251086\pi\)
\(338\) −3.44302 −0.187276
\(339\) 31.0510 1.68646
\(340\) −8.78171 −0.476255
\(341\) 0 0
\(342\) 3.18819 0.172397
\(343\) 49.2378 2.65859
\(344\) 0.792340 0.0427201
\(345\) 7.73953 0.416682
\(346\) −18.2640 −0.981879
\(347\) 30.4911 1.63685 0.818425 0.574613i \(-0.194848\pi\)
0.818425 + 0.574613i \(0.194848\pi\)
\(348\) −1.74277 −0.0934221
\(349\) 29.6967 1.58963 0.794815 0.606852i \(-0.207568\pi\)
0.794815 + 0.606852i \(0.207568\pi\)
\(350\) −13.6655 −0.730451
\(351\) −1.44720 −0.0772460
\(352\) 0 0
\(353\) −9.53977 −0.507751 −0.253875 0.967237i \(-0.581705\pi\)
−0.253875 + 0.967237i \(0.581705\pi\)
\(354\) −1.50209 −0.0798352
\(355\) 14.0690 0.746708
\(356\) 3.50708 0.185875
\(357\) −72.0041 −3.81086
\(358\) −15.6262 −0.825871
\(359\) 16.6956 0.881160 0.440580 0.897713i \(-0.354773\pi\)
0.440580 + 0.897713i \(0.354773\pi\)
\(360\) 4.74277 0.249966
\(361\) 1.00000 0.0526316
\(362\) 22.6378 1.18982
\(363\) 0 0
\(364\) −15.1581 −0.794500
\(365\) 2.83129 0.148196
\(366\) 12.7147 0.664610
\(367\) 0.198813 0.0103780 0.00518898 0.999987i \(-0.498348\pi\)
0.00518898 + 0.999987i \(0.498348\pi\)
\(368\) 2.09144 0.109024
\(369\) −20.6668 −1.07587
\(370\) 13.8628 0.720695
\(371\) −25.9844 −1.34904
\(372\) 12.3764 0.641685
\(373\) 15.4427 0.799593 0.399796 0.916604i \(-0.369081\pi\)
0.399796 + 0.916604i \(0.369081\pi\)
\(374\) 0 0
\(375\) −28.8165 −1.48808
\(376\) −2.18819 −0.112847
\(377\) 2.16580 0.111544
\(378\) 2.29537 0.118061
\(379\) 20.9791 1.07762 0.538811 0.842427i \(-0.318874\pi\)
0.538811 + 0.842427i \(0.318874\pi\)
\(380\) 1.48761 0.0763126
\(381\) −46.7215 −2.39362
\(382\) 13.5021 0.690827
\(383\) −25.3310 −1.29435 −0.647176 0.762340i \(-0.724050\pi\)
−0.647176 + 0.762340i \(0.724050\pi\)
\(384\) 2.48761 0.126945
\(385\) 0 0
\(386\) 8.00000 0.407189
\(387\) 2.52613 0.128410
\(388\) −10.0000 −0.507673
\(389\) −4.46282 −0.226274 −0.113137 0.993579i \(-0.536090\pi\)
−0.113137 + 0.993579i \(0.536090\pi\)
\(390\) −11.4401 −0.579292
\(391\) −12.3463 −0.624378
\(392\) 17.0419 0.860744
\(393\) −24.8496 −1.25350
\(394\) 13.3806 0.674103
\(395\) 21.5440 1.08399
\(396\) 0 0
\(397\) 29.9398 1.50264 0.751318 0.659941i \(-0.229419\pi\)
0.751318 + 0.659941i \(0.229419\pi\)
\(398\) −24.6354 −1.23486
\(399\) 12.1974 0.610632
\(400\) −2.78703 −0.139351
\(401\) −18.2888 −0.913299 −0.456649 0.889647i \(-0.650951\pi\)
−0.456649 + 0.889647i \(0.650951\pi\)
\(402\) −29.5357 −1.47311
\(403\) −15.3806 −0.766160
\(404\) −6.08645 −0.302812
\(405\) −12.4959 −0.620928
\(406\) −3.43512 −0.170482
\(407\) 0 0
\(408\) −14.6850 −0.727014
\(409\) 25.5634 1.26403 0.632015 0.774956i \(-0.282228\pi\)
0.632015 + 0.774956i \(0.282228\pi\)
\(410\) −9.64310 −0.476239
\(411\) 26.6064 1.31240
\(412\) 17.5071 0.862512
\(413\) −2.96073 −0.145688
\(414\) 6.66789 0.327709
\(415\) −11.1386 −0.546773
\(416\) −3.09144 −0.151570
\(417\) −20.7138 −1.01436
\(418\) 0 0
\(419\) −27.6103 −1.34885 −0.674425 0.738343i \(-0.735608\pi\)
−0.674425 + 0.738343i \(0.735608\pi\)
\(420\) 18.1449 0.885379
\(421\) −18.5242 −0.902812 −0.451406 0.892319i \(-0.649077\pi\)
−0.451406 + 0.892319i \(0.649077\pi\)
\(422\) −21.4522 −1.04428
\(423\) −6.97634 −0.339201
\(424\) −5.29942 −0.257363
\(425\) 16.4525 0.798064
\(426\) 23.5266 1.13987
\(427\) 25.0617 1.21282
\(428\) −11.7424 −0.567592
\(429\) 0 0
\(430\) 1.17869 0.0568415
\(431\) 13.8835 0.668742 0.334371 0.942441i \(-0.391476\pi\)
0.334371 + 0.942441i \(0.391476\pi\)
\(432\) 0.468133 0.0225231
\(433\) 5.02479 0.241476 0.120738 0.992684i \(-0.461474\pi\)
0.120738 + 0.992684i \(0.461474\pi\)
\(434\) 24.3947 1.17098
\(435\) −2.59255 −0.124303
\(436\) 2.60383 0.124701
\(437\) 2.09144 0.100047
\(438\) 4.73454 0.226225
\(439\) −8.23245 −0.392913 −0.196457 0.980513i \(-0.562943\pi\)
−0.196457 + 0.980513i \(0.562943\pi\)
\(440\) 0 0
\(441\) 54.3326 2.58727
\(442\) 18.2495 0.868041
\(443\) −20.1722 −0.958412 −0.479206 0.877702i \(-0.659075\pi\)
−0.479206 + 0.877702i \(0.659075\pi\)
\(444\) 23.1817 1.10016
\(445\) 5.21715 0.247317
\(446\) −7.26401 −0.343961
\(447\) −58.0631 −2.74629
\(448\) 4.90325 0.231657
\(449\) −10.7923 −0.509322 −0.254661 0.967030i \(-0.581964\pi\)
−0.254661 + 0.967030i \(0.581964\pi\)
\(450\) −8.88556 −0.418869
\(451\) 0 0
\(452\) 12.4823 0.587118
\(453\) −8.26932 −0.388527
\(454\) 6.44302 0.302386
\(455\) −22.5493 −1.05713
\(456\) 2.48761 0.116493
\(457\) 8.27431 0.387056 0.193528 0.981095i \(-0.438007\pi\)
0.193528 + 0.981095i \(0.438007\pi\)
\(458\) −14.1333 −0.660406
\(459\) −2.76351 −0.128989
\(460\) 3.11123 0.145062
\(461\) 17.6209 0.820687 0.410344 0.911931i \(-0.365409\pi\)
0.410344 + 0.911931i \(0.365409\pi\)
\(462\) 0 0
\(463\) 2.53977 0.118033 0.0590166 0.998257i \(-0.481204\pi\)
0.0590166 + 0.998257i \(0.481204\pi\)
\(464\) −0.700580 −0.0325236
\(465\) 18.4112 0.853798
\(466\) −24.1776 −1.12000
\(467\) −10.8213 −0.500750 −0.250375 0.968149i \(-0.580554\pi\)
−0.250375 + 0.968149i \(0.580554\pi\)
\(468\) −9.85607 −0.455597
\(469\) −58.2170 −2.68821
\(470\) −3.25516 −0.150149
\(471\) 57.0103 2.62690
\(472\) −0.603830 −0.0277935
\(473\) 0 0
\(474\) 36.0262 1.65474
\(475\) −2.78703 −0.127878
\(476\) −28.9451 −1.32670
\(477\) −16.8955 −0.773594
\(478\) 28.1581 1.28792
\(479\) 9.96459 0.455294 0.227647 0.973744i \(-0.426897\pi\)
0.227647 + 0.973744i \(0.426897\pi\)
\(480\) 3.70058 0.168908
\(481\) −28.8088 −1.31357
\(482\) −17.7843 −0.810053
\(483\) 25.5100 1.16074
\(484\) 0 0
\(485\) −14.8761 −0.675487
\(486\) −22.3004 −1.01156
\(487\) 8.36639 0.379118 0.189559 0.981869i \(-0.439294\pi\)
0.189559 + 0.981869i \(0.439294\pi\)
\(488\) 5.11123 0.231375
\(489\) −50.7605 −2.29547
\(490\) 25.3516 1.14527
\(491\) −4.27722 −0.193028 −0.0965142 0.995332i \(-0.530769\pi\)
−0.0965142 + 0.995332i \(0.530769\pi\)
\(492\) −16.1254 −0.726989
\(493\) 4.13570 0.186262
\(494\) −3.09144 −0.139090
\(495\) 0 0
\(496\) 4.97521 0.223394
\(497\) 46.3725 2.08009
\(498\) −18.6262 −0.834661
\(499\) 2.08645 0.0934022 0.0467011 0.998909i \(-0.485129\pi\)
0.0467011 + 0.998909i \(0.485129\pi\)
\(500\) −11.5840 −0.518054
\(501\) −36.7711 −1.64281
\(502\) 1.20766 0.0539005
\(503\) 7.55166 0.336712 0.168356 0.985726i \(-0.446154\pi\)
0.168356 + 0.985726i \(0.446154\pi\)
\(504\) 15.6325 0.696326
\(505\) −9.05424 −0.402908
\(506\) 0 0
\(507\) −8.56488 −0.380380
\(508\) −18.7817 −0.833304
\(509\) −23.3578 −1.03532 −0.517659 0.855587i \(-0.673196\pi\)
−0.517659 + 0.855587i \(0.673196\pi\)
\(510\) −21.8454 −0.967333
\(511\) 9.33211 0.412828
\(512\) 1.00000 0.0441942
\(513\) 0.468133 0.0206686
\(514\) −16.4053 −0.723609
\(515\) 26.0436 1.14762
\(516\) 1.97103 0.0867698
\(517\) 0 0
\(518\) 45.6929 2.00763
\(519\) −45.4337 −1.99432
\(520\) −4.59884 −0.201673
\(521\) −15.0538 −0.659517 −0.329759 0.944065i \(-0.606967\pi\)
−0.329759 + 0.944065i \(0.606967\pi\)
\(522\) −2.23358 −0.0977611
\(523\) −18.6027 −0.813439 −0.406720 0.913553i \(-0.633327\pi\)
−0.406720 + 0.913553i \(0.633327\pi\)
\(524\) −9.98937 −0.436388
\(525\) −33.9944 −1.48364
\(526\) 27.1776 1.18500
\(527\) −29.3699 −1.27937
\(528\) 0 0
\(529\) −18.6259 −0.809821
\(530\) −7.88345 −0.342435
\(531\) −1.92512 −0.0835432
\(532\) 4.90325 0.212583
\(533\) 20.0396 0.868011
\(534\) 8.72423 0.377535
\(535\) −17.4681 −0.755213
\(536\) −11.8731 −0.512842
\(537\) −38.8719 −1.67745
\(538\) 9.23922 0.398331
\(539\) 0 0
\(540\) 0.696398 0.0299682
\(541\) 0.549267 0.0236148 0.0118074 0.999930i \(-0.496241\pi\)
0.0118074 + 0.999930i \(0.496241\pi\)
\(542\) −17.0613 −0.732847
\(543\) 56.3139 2.41666
\(544\) −5.90325 −0.253100
\(545\) 3.87347 0.165921
\(546\) −37.7074 −1.61373
\(547\) 40.5059 1.73191 0.865955 0.500123i \(-0.166712\pi\)
0.865955 + 0.500123i \(0.166712\pi\)
\(548\) 10.6956 0.456893
\(549\) 16.2956 0.695478
\(550\) 0 0
\(551\) −0.700580 −0.0298457
\(552\) 5.20267 0.221440
\(553\) 71.0103 3.01967
\(554\) −21.6705 −0.920690
\(555\) 34.4853 1.46382
\(556\) −8.32680 −0.353135
\(557\) 41.5924 1.76233 0.881163 0.472812i \(-0.156761\pi\)
0.881163 + 0.472812i \(0.156761\pi\)
\(558\) 15.8619 0.671488
\(559\) −2.44947 −0.103602
\(560\) 7.29411 0.308232
\(561\) 0 0
\(562\) 0.675793 0.0285066
\(563\) 7.87879 0.332051 0.166026 0.986121i \(-0.446907\pi\)
0.166026 + 0.986121i \(0.446907\pi\)
\(564\) −5.44335 −0.229206
\(565\) 18.5687 0.781193
\(566\) −2.64841 −0.111321
\(567\) −41.1874 −1.72971
\(568\) 9.45751 0.396828
\(569\) 7.38055 0.309409 0.154704 0.987961i \(-0.450557\pi\)
0.154704 + 0.987961i \(0.450557\pi\)
\(570\) 3.70058 0.155000
\(571\) 2.68464 0.112349 0.0561743 0.998421i \(-0.482110\pi\)
0.0561743 + 0.998421i \(0.482110\pi\)
\(572\) 0 0
\(573\) 33.5879 1.40315
\(574\) −31.7843 −1.32665
\(575\) −5.82889 −0.243081
\(576\) 3.18819 0.132841
\(577\) 6.42355 0.267416 0.133708 0.991021i \(-0.457312\pi\)
0.133708 + 0.991021i \(0.457312\pi\)
\(578\) 17.8484 0.742394
\(579\) 19.9009 0.827051
\(580\) −1.04219 −0.0432745
\(581\) −36.7136 −1.52314
\(582\) −24.8761 −1.03115
\(583\) 0 0
\(584\) 1.90325 0.0787571
\(585\) −14.6620 −0.606197
\(586\) 1.70589 0.0704698
\(587\) −20.8392 −0.860125 −0.430063 0.902799i \(-0.641509\pi\)
−0.430063 + 0.902799i \(0.641509\pi\)
\(588\) 42.3934 1.74828
\(589\) 4.97521 0.205000
\(590\) −0.898261 −0.0369808
\(591\) 33.2856 1.36918
\(592\) 9.31889 0.383004
\(593\) 5.11383 0.210000 0.105000 0.994472i \(-0.466516\pi\)
0.105000 + 0.994472i \(0.466516\pi\)
\(594\) 0 0
\(595\) −43.0589 −1.76524
\(596\) −23.3410 −0.956083
\(597\) −61.2832 −2.50815
\(598\) −6.46554 −0.264396
\(599\) −19.4797 −0.795919 −0.397960 0.917403i \(-0.630282\pi\)
−0.397960 + 0.917403i \(0.630282\pi\)
\(600\) −6.93303 −0.283040
\(601\) 33.3020 1.35842 0.679209 0.733945i \(-0.262323\pi\)
0.679209 + 0.733945i \(0.262323\pi\)
\(602\) 3.88504 0.158343
\(603\) −37.8538 −1.54153
\(604\) −3.32421 −0.135260
\(605\) 0 0
\(606\) −15.1407 −0.615048
\(607\) −7.07051 −0.286983 −0.143492 0.989652i \(-0.545833\pi\)
−0.143492 + 0.989652i \(0.545833\pi\)
\(608\) 1.00000 0.0405554
\(609\) −8.54522 −0.346270
\(610\) 7.60351 0.307857
\(611\) 6.76464 0.273668
\(612\) −18.8207 −0.760780
\(613\) −31.2552 −1.26238 −0.631192 0.775627i \(-0.717434\pi\)
−0.631192 + 0.775627i \(0.717434\pi\)
\(614\) 14.3136 0.577649
\(615\) −23.9882 −0.967299
\(616\) 0 0
\(617\) 41.7410 1.68043 0.840214 0.542254i \(-0.182429\pi\)
0.840214 + 0.542254i \(0.182429\pi\)
\(618\) 43.5507 1.75187
\(619\) −8.82131 −0.354558 −0.177279 0.984161i \(-0.556730\pi\)
−0.177279 + 0.984161i \(0.556730\pi\)
\(620\) 7.40116 0.297238
\(621\) 0.979070 0.0392887
\(622\) 22.1805 0.889356
\(623\) 17.1961 0.688947
\(624\) −7.69028 −0.307857
\(625\) −3.29735 −0.131894
\(626\) 10.4873 0.419156
\(627\) 0 0
\(628\) 22.9177 0.914517
\(629\) −55.0118 −2.19346
\(630\) 23.2550 0.926500
\(631\) −29.1623 −1.16093 −0.580466 0.814285i \(-0.697129\pi\)
−0.580466 + 0.814285i \(0.697129\pi\)
\(632\) 14.4823 0.576075
\(633\) −53.3646 −2.12105
\(634\) 30.2785 1.20251
\(635\) −27.9398 −1.10876
\(636\) −13.1829 −0.522735
\(637\) −52.6838 −2.08741
\(638\) 0 0
\(639\) 30.1523 1.19281
\(640\) 1.48761 0.0588028
\(641\) −39.8735 −1.57491 −0.787454 0.616374i \(-0.788601\pi\)
−0.787454 + 0.616374i \(0.788601\pi\)
\(642\) −29.2106 −1.15285
\(643\) −11.2366 −0.443129 −0.221565 0.975146i \(-0.571116\pi\)
−0.221565 + 0.975146i \(0.571116\pi\)
\(644\) 10.2548 0.404097
\(645\) 2.93212 0.115452
\(646\) −5.90325 −0.232260
\(647\) −10.7022 −0.420746 −0.210373 0.977621i \(-0.567468\pi\)
−0.210373 + 0.977621i \(0.567468\pi\)
\(648\) −8.40003 −0.329984
\(649\) 0 0
\(650\) 8.61592 0.337944
\(651\) 60.6844 2.37841
\(652\) −20.4053 −0.799135
\(653\) −33.6024 −1.31496 −0.657481 0.753471i \(-0.728378\pi\)
−0.657481 + 0.753471i \(0.728378\pi\)
\(654\) 6.47730 0.253283
\(655\) −14.8603 −0.580638
\(656\) −6.48229 −0.253091
\(657\) 6.06792 0.236732
\(658\) −10.7292 −0.418269
\(659\) 6.17529 0.240555 0.120278 0.992740i \(-0.461622\pi\)
0.120278 + 0.992740i \(0.461622\pi\)
\(660\) 0 0
\(661\) 22.0114 0.856146 0.428073 0.903744i \(-0.359193\pi\)
0.428073 + 0.903744i \(0.359193\pi\)
\(662\) 4.62330 0.179690
\(663\) 45.3976 1.76310
\(664\) −7.48761 −0.290575
\(665\) 7.29411 0.282853
\(666\) 29.7104 1.15125
\(667\) −1.46522 −0.0567335
\(668\) −14.7817 −0.571922
\(669\) −18.0700 −0.698626
\(670\) −17.6626 −0.682365
\(671\) 0 0
\(672\) 12.1974 0.470523
\(673\) 6.63620 0.255807 0.127903 0.991787i \(-0.459175\pi\)
0.127903 + 0.991787i \(0.459175\pi\)
\(674\) 25.8728 0.996584
\(675\) −1.30470 −0.0502179
\(676\) −3.44302 −0.132424
\(677\) 26.2521 1.00895 0.504475 0.863426i \(-0.331686\pi\)
0.504475 + 0.863426i \(0.331686\pi\)
\(678\) 31.0510 1.19251
\(679\) −49.0325 −1.88169
\(680\) −8.78171 −0.336763
\(681\) 16.0277 0.614183
\(682\) 0 0
\(683\) 36.5776 1.39960 0.699801 0.714338i \(-0.253272\pi\)
0.699801 + 0.714338i \(0.253272\pi\)
\(684\) 3.18819 0.121903
\(685\) 15.9108 0.607922
\(686\) 49.2378 1.87991
\(687\) −35.1581 −1.34136
\(688\) 0.792340 0.0302077
\(689\) 16.3828 0.624136
\(690\) 7.73953 0.294639
\(691\) −17.1660 −0.653025 −0.326513 0.945193i \(-0.605874\pi\)
−0.326513 + 0.945193i \(0.605874\pi\)
\(692\) −18.2640 −0.694293
\(693\) 0 0
\(694\) 30.4911 1.15743
\(695\) −12.3870 −0.469866
\(696\) −1.74277 −0.0660594
\(697\) 38.2666 1.44945
\(698\) 29.6967 1.12404
\(699\) −60.1443 −2.27486
\(700\) −13.6655 −0.516507
\(701\) 5.67838 0.214470 0.107235 0.994234i \(-0.465800\pi\)
0.107235 + 0.994234i \(0.465800\pi\)
\(702\) −1.44720 −0.0546212
\(703\) 9.31889 0.351469
\(704\) 0 0
\(705\) −8.09756 −0.304972
\(706\) −9.53977 −0.359034
\(707\) −29.8434 −1.12238
\(708\) −1.50209 −0.0564520
\(709\) 5.39118 0.202470 0.101235 0.994863i \(-0.467721\pi\)
0.101235 + 0.994863i \(0.467721\pi\)
\(710\) 14.0690 0.528002
\(711\) 46.1722 1.73159
\(712\) 3.50708 0.131433
\(713\) 10.4053 0.389683
\(714\) −72.0041 −2.69468
\(715\) 0 0
\(716\) −15.6262 −0.583979
\(717\) 70.0462 2.61592
\(718\) 16.6956 0.623074
\(719\) −44.4507 −1.65773 −0.828866 0.559447i \(-0.811014\pi\)
−0.828866 + 0.559447i \(0.811014\pi\)
\(720\) 4.74277 0.176752
\(721\) 85.8416 3.19691
\(722\) 1.00000 0.0372161
\(723\) −44.2404 −1.64532
\(724\) 22.6378 0.841327
\(725\) 1.95253 0.0725153
\(726\) 0 0
\(727\) −9.35690 −0.347028 −0.173514 0.984831i \(-0.555512\pi\)
−0.173514 + 0.984831i \(0.555512\pi\)
\(728\) −15.1581 −0.561796
\(729\) −30.2744 −1.12128
\(730\) 2.83129 0.104791
\(731\) −4.67738 −0.172999
\(732\) 12.7147 0.469950
\(733\) 5.76690 0.213005 0.106503 0.994312i \(-0.466035\pi\)
0.106503 + 0.994312i \(0.466035\pi\)
\(734\) 0.198813 0.00733833
\(735\) 63.0648 2.32618
\(736\) 2.09144 0.0770914
\(737\) 0 0
\(738\) −20.6668 −0.760754
\(739\) −21.1843 −0.779278 −0.389639 0.920968i \(-0.627400\pi\)
−0.389639 + 0.920968i \(0.627400\pi\)
\(740\) 13.8628 0.509608
\(741\) −7.69028 −0.282509
\(742\) −25.9844 −0.953917
\(743\) −21.8117 −0.800193 −0.400097 0.916473i \(-0.631023\pi\)
−0.400097 + 0.916473i \(0.631023\pi\)
\(744\) 12.3764 0.453740
\(745\) −34.7222 −1.27212
\(746\) 15.4427 0.565397
\(747\) −23.8719 −0.873427
\(748\) 0 0
\(749\) −57.5761 −2.10379
\(750\) −28.8165 −1.05223
\(751\) −0.530276 −0.0193500 −0.00967502 0.999953i \(-0.503080\pi\)
−0.00967502 + 0.999953i \(0.503080\pi\)
\(752\) −2.18819 −0.0797949
\(753\) 3.00418 0.109478
\(754\) 2.16580 0.0788737
\(755\) −4.94511 −0.179971
\(756\) 2.29537 0.0834819
\(757\) 6.70589 0.243730 0.121865 0.992547i \(-0.461113\pi\)
0.121865 + 0.992547i \(0.461113\pi\)
\(758\) 20.9791 0.761994
\(759\) 0 0
\(760\) 1.48761 0.0539612
\(761\) −46.5357 −1.68692 −0.843459 0.537193i \(-0.819485\pi\)
−0.843459 + 0.537193i \(0.819485\pi\)
\(762\) −46.7215 −1.69254
\(763\) 12.7672 0.462205
\(764\) 13.5021 0.488489
\(765\) −27.9977 −1.01226
\(766\) −25.3310 −0.915246
\(767\) 1.86670 0.0674027
\(768\) 2.48761 0.0897638
\(769\) 19.5882 0.706369 0.353185 0.935554i \(-0.385099\pi\)
0.353185 + 0.935554i \(0.385099\pi\)
\(770\) 0 0
\(771\) −40.8100 −1.46974
\(772\) 8.00000 0.287926
\(773\) 28.5348 1.02632 0.513162 0.858292i \(-0.328474\pi\)
0.513162 + 0.858292i \(0.328474\pi\)
\(774\) 2.52613 0.0907998
\(775\) −13.8661 −0.498083
\(776\) −10.0000 −0.358979
\(777\) 113.666 4.07774
\(778\) −4.46282 −0.160000
\(779\) −6.48229 −0.232252
\(780\) −11.4401 −0.409622
\(781\) 0 0
\(782\) −12.3463 −0.441502
\(783\) −0.327964 −0.0117205
\(784\) 17.0419 0.608638
\(785\) 34.0926 1.21682
\(786\) −24.8496 −0.886357
\(787\) 22.0811 0.787107 0.393554 0.919302i \(-0.371246\pi\)
0.393554 + 0.919302i \(0.371246\pi\)
\(788\) 13.3806 0.476663
\(789\) 67.6071 2.40688
\(790\) 21.5440 0.766499
\(791\) 61.2038 2.17616
\(792\) 0 0
\(793\) −15.8011 −0.561112
\(794\) 29.9398 1.06252
\(795\) −19.6109 −0.695528
\(796\) −24.6354 −0.873178
\(797\) 40.8484 1.44692 0.723462 0.690365i \(-0.242550\pi\)
0.723462 + 0.690365i \(0.242550\pi\)
\(798\) 12.1974 0.431782
\(799\) 12.9174 0.456985
\(800\) −2.78703 −0.0985363
\(801\) 11.1812 0.395069
\(802\) −18.2888 −0.645800
\(803\) 0 0
\(804\) −29.5357 −1.04164
\(805\) 15.2552 0.537674
\(806\) −15.3806 −0.541757
\(807\) 22.9835 0.809059
\(808\) −6.08645 −0.214120
\(809\) 5.16340 0.181535 0.0907677 0.995872i \(-0.471068\pi\)
0.0907677 + 0.995872i \(0.471068\pi\)
\(810\) −12.4959 −0.439062
\(811\) −33.6162 −1.18043 −0.590213 0.807248i \(-0.700956\pi\)
−0.590213 + 0.807248i \(0.700956\pi\)
\(812\) −3.43512 −0.120549
\(813\) −42.4419 −1.48850
\(814\) 0 0
\(815\) −30.3551 −1.06329
\(816\) −14.6850 −0.514077
\(817\) 0.792340 0.0277205
\(818\) 25.5634 0.893804
\(819\) −48.3268 −1.68867
\(820\) −9.64310 −0.336752
\(821\) 38.4026 1.34026 0.670130 0.742243i \(-0.266238\pi\)
0.670130 + 0.742243i \(0.266238\pi\)
\(822\) 26.6064 0.928005
\(823\) 42.0589 1.46608 0.733041 0.680184i \(-0.238100\pi\)
0.733041 + 0.680184i \(0.238100\pi\)
\(824\) 17.5071 0.609888
\(825\) 0 0
\(826\) −2.96073 −0.103017
\(827\) 46.2094 1.60686 0.803430 0.595399i \(-0.203006\pi\)
0.803430 + 0.595399i \(0.203006\pi\)
\(828\) 6.66789 0.231725
\(829\) −20.8484 −0.724094 −0.362047 0.932160i \(-0.617922\pi\)
−0.362047 + 0.932160i \(0.617922\pi\)
\(830\) −11.1386 −0.386627
\(831\) −53.9076 −1.87003
\(832\) −3.09144 −0.107176
\(833\) −100.602 −3.48567
\(834\) −20.7138 −0.717260
\(835\) −21.9894 −0.760974
\(836\) 0 0
\(837\) 2.32906 0.0805041
\(838\) −27.6103 −0.953781
\(839\) 53.8522 1.85919 0.929593 0.368589i \(-0.120159\pi\)
0.929593 + 0.368589i \(0.120159\pi\)
\(840\) 18.1449 0.626057
\(841\) −28.5092 −0.983075
\(842\) −18.5242 −0.638385
\(843\) 1.68111 0.0579004
\(844\) −21.4522 −0.738415
\(845\) −5.12186 −0.176197
\(846\) −6.97634 −0.239852
\(847\) 0 0
\(848\) −5.29942 −0.181983
\(849\) −6.58821 −0.226107
\(850\) 16.4525 0.564317
\(851\) 19.4899 0.668104
\(852\) 23.5266 0.806006
\(853\) 7.61300 0.260664 0.130332 0.991470i \(-0.458396\pi\)
0.130332 + 0.991470i \(0.458396\pi\)
\(854\) 25.0617 0.857592
\(855\) 4.74277 0.162199
\(856\) −11.7424 −0.401348
\(857\) −45.9688 −1.57026 −0.785132 0.619329i \(-0.787405\pi\)
−0.785132 + 0.619329i \(0.787405\pi\)
\(858\) 0 0
\(859\) 35.5813 1.21402 0.607009 0.794695i \(-0.292369\pi\)
0.607009 + 0.794695i \(0.292369\pi\)
\(860\) 1.17869 0.0401930
\(861\) −79.0668 −2.69459
\(862\) 13.8835 0.472872
\(863\) 4.29783 0.146300 0.0731499 0.997321i \(-0.476695\pi\)
0.0731499 + 0.997321i \(0.476695\pi\)
\(864\) 0.468133 0.0159262
\(865\) −27.1697 −0.923796
\(866\) 5.02479 0.170749
\(867\) 44.3997 1.50789
\(868\) 24.3947 0.828011
\(869\) 0 0
\(870\) −2.59255 −0.0878957
\(871\) 36.7051 1.24370
\(872\) 2.60383 0.0881768
\(873\) −31.8819 −1.07904
\(874\) 2.09144 0.0707439
\(875\) −56.7994 −1.92017
\(876\) 4.73454 0.159965
\(877\) −7.43836 −0.251175 −0.125588 0.992083i \(-0.540082\pi\)
−0.125588 + 0.992083i \(0.540082\pi\)
\(878\) −8.23245 −0.277832
\(879\) 4.24359 0.143133
\(880\) 0 0
\(881\) 1.71380 0.0577393 0.0288697 0.999583i \(-0.490809\pi\)
0.0288697 + 0.999583i \(0.490809\pi\)
\(882\) 54.3326 1.82947
\(883\) 9.92418 0.333975 0.166988 0.985959i \(-0.446596\pi\)
0.166988 + 0.985959i \(0.446596\pi\)
\(884\) 18.2495 0.613798
\(885\) −2.23452 −0.0751126
\(886\) −20.1722 −0.677700
\(887\) −7.22441 −0.242572 −0.121286 0.992618i \(-0.538702\pi\)
−0.121286 + 0.992618i \(0.538702\pi\)
\(888\) 23.1817 0.777928
\(889\) −92.0914 −3.08865
\(890\) 5.21715 0.174879
\(891\) 0 0
\(892\) −7.26401 −0.243217
\(893\) −2.18819 −0.0732249
\(894\) −58.0631 −1.94192
\(895\) −23.2457 −0.777017
\(896\) 4.90325 0.163806
\(897\) −16.0837 −0.537020
\(898\) −10.7923 −0.360145
\(899\) −3.48553 −0.116249
\(900\) −8.88556 −0.296185
\(901\) 31.2838 1.04221
\(902\) 0 0
\(903\) 9.66446 0.321613
\(904\) 12.4823 0.415155
\(905\) 33.6761 1.11943
\(906\) −8.26932 −0.274730
\(907\) 26.1673 0.868869 0.434435 0.900703i \(-0.356948\pi\)
0.434435 + 0.900703i \(0.356948\pi\)
\(908\) 6.44302 0.213819
\(909\) −19.4047 −0.643614
\(910\) −22.5493 −0.747501
\(911\) 45.0705 1.49325 0.746626 0.665244i \(-0.231672\pi\)
0.746626 + 0.665244i \(0.231672\pi\)
\(912\) 2.48761 0.0823729
\(913\) 0 0
\(914\) 8.27431 0.273690
\(915\) 18.9145 0.625295
\(916\) −14.1333 −0.466977
\(917\) −48.9804 −1.61748
\(918\) −2.76351 −0.0912093
\(919\) −25.4024 −0.837949 −0.418974 0.907998i \(-0.637610\pi\)
−0.418974 + 0.907998i \(0.637610\pi\)
\(920\) 3.11123 0.102574
\(921\) 35.6066 1.17328
\(922\) 17.6209 0.580314
\(923\) −29.2373 −0.962357
\(924\) 0 0
\(925\) −25.9720 −0.853954
\(926\) 2.53977 0.0834621
\(927\) 55.8158 1.83323
\(928\) −0.700580 −0.0229977
\(929\) 24.9398 0.818248 0.409124 0.912479i \(-0.365834\pi\)
0.409124 + 0.912479i \(0.365834\pi\)
\(930\) 18.4112 0.603726
\(931\) 17.0419 0.558524
\(932\) −24.1776 −0.791962
\(933\) 55.1763 1.80639
\(934\) −10.8213 −0.354084
\(935\) 0 0
\(936\) −9.85607 −0.322156
\(937\) −16.0288 −0.523639 −0.261820 0.965117i \(-0.584323\pi\)
−0.261820 + 0.965117i \(0.584323\pi\)
\(938\) −58.2170 −1.90085
\(939\) 26.0882 0.851357
\(940\) −3.25516 −0.106172
\(941\) −35.9569 −1.17216 −0.586080 0.810253i \(-0.699330\pi\)
−0.586080 + 0.810253i \(0.699330\pi\)
\(942\) 57.0103 1.85750
\(943\) −13.5573 −0.441487
\(944\) −0.603830 −0.0196530
\(945\) 3.41461 0.111077
\(946\) 0 0
\(947\) −39.1771 −1.27308 −0.636542 0.771242i \(-0.719636\pi\)
−0.636542 + 0.771242i \(0.719636\pi\)
\(948\) 36.0262 1.17008
\(949\) −5.88378 −0.190995
\(950\) −2.78703 −0.0904231
\(951\) 75.3210 2.44245
\(952\) −28.9451 −0.938116
\(953\) 34.0670 1.10354 0.551769 0.833997i \(-0.313953\pi\)
0.551769 + 0.833997i \(0.313953\pi\)
\(954\) −16.8955 −0.547013
\(955\) 20.0858 0.649961
\(956\) 28.1581 0.910698
\(957\) 0 0
\(958\) 9.96459 0.321941
\(959\) 52.4432 1.69348
\(960\) 3.70058 0.119436
\(961\) −6.24726 −0.201524
\(962\) −28.8088 −0.928832
\(963\) −37.4371 −1.20639
\(964\) −17.7843 −0.572794
\(965\) 11.9009 0.383102
\(966\) 25.5100 0.820771
\(967\) 4.50980 0.145025 0.0725127 0.997367i \(-0.476898\pi\)
0.0725127 + 0.997367i \(0.476898\pi\)
\(968\) 0 0
\(969\) −14.6850 −0.471749
\(970\) −14.8761 −0.477642
\(971\) −1.82970 −0.0587178 −0.0293589 0.999569i \(-0.509347\pi\)
−0.0293589 + 0.999569i \(0.509347\pi\)
\(972\) −22.3004 −0.715284
\(973\) −40.8284 −1.30890
\(974\) 8.36639 0.268077
\(975\) 21.4330 0.686406
\(976\) 5.11123 0.163607
\(977\) −27.8902 −0.892287 −0.446144 0.894961i \(-0.647203\pi\)
−0.446144 + 0.894961i \(0.647203\pi\)
\(978\) −50.7605 −1.62314
\(979\) 0 0
\(980\) 25.3516 0.809827
\(981\) 8.30149 0.265046
\(982\) −4.27722 −0.136492
\(983\) 46.1790 1.47288 0.736441 0.676502i \(-0.236505\pi\)
0.736441 + 0.676502i \(0.236505\pi\)
\(984\) −16.1254 −0.514059
\(985\) 19.9050 0.634226
\(986\) 4.13570 0.131707
\(987\) −26.6901 −0.849555
\(988\) −3.09144 −0.0983517
\(989\) 1.65713 0.0526937
\(990\) 0 0
\(991\) 36.2782 1.15241 0.576207 0.817304i \(-0.304532\pi\)
0.576207 + 0.817304i \(0.304532\pi\)
\(992\) 4.97521 0.157963
\(993\) 11.5010 0.364972
\(994\) 46.3725 1.47085
\(995\) −36.6478 −1.16181
\(996\) −18.6262 −0.590194
\(997\) −44.0469 −1.39498 −0.697489 0.716596i \(-0.745699\pi\)
−0.697489 + 0.716596i \(0.745699\pi\)
\(998\) 2.08645 0.0660453
\(999\) 4.36248 0.138023
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.bv.1.3 yes 4
11.10 odd 2 4598.2.a.bs.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.bs.1.3 4 11.10 odd 2
4598.2.a.bv.1.3 yes 4 1.1 even 1 trivial