Properties

Label 4598.2.a.br.1.4
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: \( x^{4} - x^{3} - 8x^{2} + 7x - 1 \) Copy content Toggle raw display
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 1.4
Root \(2.94749\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.94749 q^{3} +1.00000 q^{4} +2.36624 q^{5} -2.94749 q^{6} +1.66073 q^{7} -1.00000 q^{8} +5.68769 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.94749 q^{3} +1.00000 q^{4} +2.36624 q^{5} -2.94749 q^{6} +1.66073 q^{7} -1.00000 q^{8} +5.68769 q^{9} -2.36624 q^{10} +2.94749 q^{12} +0.633765 q^{13} -1.66073 q^{14} +6.97445 q^{15} +1.00000 q^{16} -0.581254 q^{17} -5.68769 q^{18} +1.00000 q^{19} +2.36624 q^{20} +4.89498 q^{21} +3.60822 q^{23} -2.94749 q^{24} +0.599069 q^{25} -0.633765 q^{26} +7.92194 q^{27} +1.66073 q^{28} -9.13696 q^{29} -6.97445 q^{30} +1.02555 q^{31} -1.00000 q^{32} +0.581254 q^{34} +3.92967 q^{35} +5.68769 q^{36} +2.15895 q^{37} -1.00000 q^{38} +1.86801 q^{39} -2.36624 q^{40} +4.40093 q^{41} -4.89498 q^{42} +9.58267 q^{43} +13.4584 q^{45} -3.60822 q^{46} +8.73247 q^{47} +2.94749 q^{48} -4.24198 q^{49} -0.599069 q^{50} -1.71324 q^{51} +0.633765 q^{52} -12.5302 q^{53} -7.92194 q^{54} -1.66073 q^{56} +2.94749 q^{57} +9.13696 q^{58} +6.47623 q^{59} +6.97445 q^{60} +1.32146 q^{61} -1.02555 q^{62} +9.44571 q^{63} +1.00000 q^{64} +1.49964 q^{65} -0.393199 q^{67} -0.581254 q^{68} +10.6352 q^{69} -3.92967 q^{70} -0.312308 q^{71} -5.68769 q^{72} -9.31372 q^{73} -2.15895 q^{74} +1.76575 q^{75} +1.00000 q^{76} -1.86801 q^{78} +11.2704 q^{79} +2.36624 q^{80} +6.28676 q^{81} -4.40093 q^{82} -6.90413 q^{83} +4.89498 q^{84} -1.37538 q^{85} -9.58267 q^{86} -26.9311 q^{87} +0.519595 q^{89} -13.4584 q^{90} +1.05251 q^{91} +3.60822 q^{92} +3.02279 q^{93} -8.73247 q^{94} +2.36624 q^{95} -2.94749 q^{96} -8.37894 q^{97} +4.24198 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + q^{3} + 4 q^{4} + 3 q^{5} - q^{6} + q^{7} - 4 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} + q^{3} + 4 q^{4} + 3 q^{5} - q^{6} + q^{7} - 4 q^{8} + 5 q^{9} - 3 q^{10} + q^{12} + 9 q^{13} - q^{14} + 5 q^{15} + 4 q^{16} + 2 q^{17} - 5 q^{18} + 4 q^{19} + 3 q^{20} - 2 q^{21} - 2 q^{23} - q^{24} + 15 q^{25} - 9 q^{26} - 2 q^{27} + q^{28} - 5 q^{29} - 5 q^{30} + 27 q^{31} - 4 q^{32} - 2 q^{34} - 12 q^{35} + 5 q^{36} + 6 q^{37} - 4 q^{38} - 2 q^{39} - 3 q^{40} + 5 q^{41} + 2 q^{42} - q^{43} + 11 q^{45} + 2 q^{46} + 22 q^{47} + q^{48} - 7 q^{49} - 15 q^{50} - 12 q^{51} + 9 q^{52} + 2 q^{54} - q^{56} + q^{57} + 5 q^{58} + 5 q^{60} - 6 q^{61} - 27 q^{62} + 30 q^{63} + 4 q^{64} - 26 q^{65} + 17 q^{67} + 2 q^{68} + 14 q^{69} + 12 q^{70} - 19 q^{71} - 5 q^{72} - 20 q^{73} - 6 q^{74} + 23 q^{75} + 4 q^{76} + 2 q^{78} - 12 q^{79} + 3 q^{80} + 20 q^{81} - 5 q^{82} + 23 q^{83} - 2 q^{84} + 30 q^{85} + q^{86} - 45 q^{87} + 16 q^{89} - 11 q^{90} + 15 q^{91} - 2 q^{92} - 12 q^{93} - 22 q^{94} + 3 q^{95} - q^{96} + 8 q^{97} + 7 q^{98}+O(q^{100}) \) 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
\(3\) 2.94749 1.70173 0.850867 0.525381i \(-0.176077\pi\)
0.850867 + 0.525381i \(0.176077\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.36624 1.05821 0.529106 0.848556i \(-0.322527\pi\)
0.529106 + 0.848556i \(0.322527\pi\)
\(6\) −2.94749 −1.20331
\(7\) 1.66073 0.627696 0.313848 0.949473i \(-0.398382\pi\)
0.313848 + 0.949473i \(0.398382\pi\)
\(8\) −1.00000 −0.353553
\(9\) 5.68769 1.89590
\(10\) −2.36624 −0.748269
\(11\) 0 0
\(12\) 2.94749 0.850867
\(13\) 0.633765 0.175775 0.0878874 0.996130i \(-0.471988\pi\)
0.0878874 + 0.996130i \(0.471988\pi\)
\(14\) −1.66073 −0.443848
\(15\) 6.97445 1.80080
\(16\) 1.00000 0.250000
\(17\) −0.581254 −0.140975 −0.0704874 0.997513i \(-0.522455\pi\)
−0.0704874 + 0.997513i \(0.522455\pi\)
\(18\) −5.68769 −1.34060
\(19\) 1.00000 0.229416
\(20\) 2.36624 0.529106
\(21\) 4.89498 1.06817
\(22\) 0 0
\(23\) 3.60822 0.752365 0.376183 0.926546i \(-0.377237\pi\)
0.376183 + 0.926546i \(0.377237\pi\)
\(24\) −2.94749 −0.601654
\(25\) 0.599069 0.119814
\(26\) −0.633765 −0.124291
\(27\) 7.92194 1.52458
\(28\) 1.66073 0.313848
\(29\) −9.13696 −1.69669 −0.848345 0.529443i \(-0.822401\pi\)
−0.848345 + 0.529443i \(0.822401\pi\)
\(30\) −6.97445 −1.27335
\(31\) 1.02555 0.184194 0.0920969 0.995750i \(-0.470643\pi\)
0.0920969 + 0.995750i \(0.470643\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 0.581254 0.0996842
\(35\) 3.92967 0.664236
\(36\) 5.68769 0.947949
\(37\) 2.15895 0.354929 0.177464 0.984127i \(-0.443211\pi\)
0.177464 + 0.984127i \(0.443211\pi\)
\(38\) −1.00000 −0.162221
\(39\) 1.86801 0.299122
\(40\) −2.36624 −0.374135
\(41\) 4.40093 0.687310 0.343655 0.939096i \(-0.388335\pi\)
0.343655 + 0.939096i \(0.388335\pi\)
\(42\) −4.89498 −0.755312
\(43\) 9.58267 1.46134 0.730672 0.682729i \(-0.239207\pi\)
0.730672 + 0.682729i \(0.239207\pi\)
\(44\) 0 0
\(45\) 13.4584 2.00626
\(46\) −3.60822 −0.532003
\(47\) 8.73247 1.27376 0.636881 0.770962i \(-0.280224\pi\)
0.636881 + 0.770962i \(0.280224\pi\)
\(48\) 2.94749 0.425433
\(49\) −4.24198 −0.605997
\(50\) −0.599069 −0.0847212
\(51\) −1.71324 −0.239901
\(52\) 0.633765 0.0878874
\(53\) −12.5302 −1.72115 −0.860575 0.509324i \(-0.829895\pi\)
−0.860575 + 0.509324i \(0.829895\pi\)
\(54\) −7.92194 −1.07804
\(55\) 0 0
\(56\) −1.66073 −0.221924
\(57\) 2.94749 0.390404
\(58\) 9.13696 1.19974
\(59\) 6.47623 0.843134 0.421567 0.906797i \(-0.361480\pi\)
0.421567 + 0.906797i \(0.361480\pi\)
\(60\) 6.97445 0.900398
\(61\) 1.32146 0.169195 0.0845976 0.996415i \(-0.473040\pi\)
0.0845976 + 0.996415i \(0.473040\pi\)
\(62\) −1.02555 −0.130245
\(63\) 9.44571 1.19005
\(64\) 1.00000 0.125000
\(65\) 1.49964 0.186007
\(66\) 0 0
\(67\) −0.393199 −0.0480369 −0.0240184 0.999712i \(-0.507646\pi\)
−0.0240184 + 0.999712i \(0.507646\pi\)
\(68\) −0.581254 −0.0704874
\(69\) 10.6352 1.28033
\(70\) −3.92967 −0.469686
\(71\) −0.312308 −0.0370642 −0.0185321 0.999828i \(-0.505899\pi\)
−0.0185321 + 0.999828i \(0.505899\pi\)
\(72\) −5.68769 −0.670301
\(73\) −9.31372 −1.09009 −0.545044 0.838407i \(-0.683487\pi\)
−0.545044 + 0.838407i \(0.683487\pi\)
\(74\) −2.15895 −0.250973
\(75\) 1.76575 0.203891
\(76\) 1.00000 0.114708
\(77\) 0 0
\(78\) −1.86801 −0.211511
\(79\) 11.2704 1.26801 0.634007 0.773327i \(-0.281409\pi\)
0.634007 + 0.773327i \(0.281409\pi\)
\(80\) 2.36624 0.264553
\(81\) 6.28676 0.698529
\(82\) −4.40093 −0.486001
\(83\) −6.90413 −0.757826 −0.378913 0.925432i \(-0.623702\pi\)
−0.378913 + 0.925432i \(0.623702\pi\)
\(84\) 4.89498 0.534086
\(85\) −1.37538 −0.149181
\(86\) −9.58267 −1.03333
\(87\) −26.9311 −2.88732
\(88\) 0 0
\(89\) 0.519595 0.0550769 0.0275385 0.999621i \(-0.491233\pi\)
0.0275385 + 0.999621i \(0.491233\pi\)
\(90\) −13.4584 −1.41864
\(91\) 1.05251 0.110333
\(92\) 3.60822 0.376183
\(93\) 3.02279 0.313449
\(94\) −8.73247 −0.900686
\(95\) 2.36624 0.242771
\(96\) −2.94749 −0.300827
\(97\) −8.37894 −0.850753 −0.425376 0.905017i \(-0.639858\pi\)
−0.425376 + 0.905017i \(0.639858\pi\)
\(98\) 4.24198 0.428505
\(99\) 0 0
\(100\) 0.599069 0.0599069
\(101\) −16.5379 −1.64558 −0.822791 0.568344i \(-0.807584\pi\)
−0.822791 + 0.568344i \(0.807584\pi\)
\(102\) 1.71324 0.169636
\(103\) 2.79627 0.275525 0.137762 0.990465i \(-0.456009\pi\)
0.137762 + 0.990465i \(0.456009\pi\)
\(104\) −0.633765 −0.0621457
\(105\) 11.5827 1.13035
\(106\) 12.5302 1.21704
\(107\) 18.9681 1.83372 0.916859 0.399210i \(-0.130716\pi\)
0.916859 + 0.399210i \(0.130716\pi\)
\(108\) 7.92194 0.762289
\(109\) 17.0732 1.63531 0.817656 0.575707i \(-0.195273\pi\)
0.817656 + 0.575707i \(0.195273\pi\)
\(110\) 0 0
\(111\) 6.36348 0.603995
\(112\) 1.66073 0.156924
\(113\) 21.1114 1.98599 0.992997 0.118137i \(-0.0376922\pi\)
0.992997 + 0.118137i \(0.0376922\pi\)
\(114\) −2.94749 −0.276058
\(115\) 8.53789 0.796162
\(116\) −9.13696 −0.848345
\(117\) 3.60466 0.333251
\(118\) −6.47623 −0.596185
\(119\) −0.965305 −0.0884893
\(120\) −6.97445 −0.636677
\(121\) 0 0
\(122\) −1.32146 −0.119639
\(123\) 12.9717 1.16962
\(124\) 1.02555 0.0920969
\(125\) −10.4136 −0.931424
\(126\) −9.44571 −0.841491
\(127\) 4.62745 0.410620 0.205310 0.978697i \(-0.434180\pi\)
0.205310 + 0.978697i \(0.434180\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 28.2448 2.48682
\(130\) −1.49964 −0.131527
\(131\) −15.7763 −1.37838 −0.689191 0.724579i \(-0.742034\pi\)
−0.689191 + 0.724579i \(0.742034\pi\)
\(132\) 0 0
\(133\) 1.66073 0.144003
\(134\) 0.393199 0.0339672
\(135\) 18.7452 1.61333
\(136\) 0.581254 0.0498421
\(137\) −20.6366 −1.76310 −0.881552 0.472087i \(-0.843501\pi\)
−0.881552 + 0.472087i \(0.843501\pi\)
\(138\) −10.6352 −0.905327
\(139\) −9.56721 −0.811480 −0.405740 0.913989i \(-0.632986\pi\)
−0.405740 + 0.913989i \(0.632986\pi\)
\(140\) 3.92967 0.332118
\(141\) 25.7389 2.16760
\(142\) 0.312308 0.0262083
\(143\) 0 0
\(144\) 5.68769 0.473974
\(145\) −21.6202 −1.79546
\(146\) 9.31372 0.770809
\(147\) −12.5032 −1.03125
\(148\) 2.15895 0.177464
\(149\) 18.3096 1.49998 0.749988 0.661451i \(-0.230059\pi\)
0.749988 + 0.661451i \(0.230059\pi\)
\(150\) −1.76575 −0.144173
\(151\) 6.25562 0.509075 0.254538 0.967063i \(-0.418077\pi\)
0.254538 + 0.967063i \(0.418077\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −3.30599 −0.267274
\(154\) 0 0
\(155\) 2.42669 0.194916
\(156\) 1.86801 0.149561
\(157\) −6.15619 −0.491318 −0.245659 0.969356i \(-0.579004\pi\)
−0.245659 + 0.969356i \(0.579004\pi\)
\(158\) −11.2704 −0.896622
\(159\) −36.9325 −2.92894
\(160\) −2.36624 −0.187067
\(161\) 5.99227 0.472257
\(162\) −6.28676 −0.493935
\(163\) −11.8439 −0.927685 −0.463842 0.885918i \(-0.653530\pi\)
−0.463842 + 0.885918i \(0.653530\pi\)
\(164\) 4.40093 0.343655
\(165\) 0 0
\(166\) 6.90413 0.535864
\(167\) −4.89142 −0.378509 −0.189255 0.981928i \(-0.560607\pi\)
−0.189255 + 0.981928i \(0.560607\pi\)
\(168\) −4.89498 −0.377656
\(169\) −12.5983 −0.969103
\(170\) 1.37538 0.105487
\(171\) 5.68769 0.434949
\(172\) 9.58267 0.730672
\(173\) −18.1206 −1.37768 −0.688840 0.724913i \(-0.741880\pi\)
−0.688840 + 0.724913i \(0.741880\pi\)
\(174\) 26.9311 2.04164
\(175\) 0.994891 0.0752067
\(176\) 0 0
\(177\) 19.0886 1.43479
\(178\) −0.519595 −0.0389453
\(179\) 3.07947 0.230171 0.115085 0.993356i \(-0.463286\pi\)
0.115085 + 0.993356i \(0.463286\pi\)
\(180\) 13.4584 1.00313
\(181\) 0.0693910 0.00515779 0.00257889 0.999997i \(-0.499179\pi\)
0.00257889 + 0.999997i \(0.499179\pi\)
\(182\) −1.05251 −0.0780173
\(183\) 3.89498 0.287925
\(184\) −3.60822 −0.266001
\(185\) 5.10858 0.375590
\(186\) −3.02279 −0.221642
\(187\) 0 0
\(188\) 8.73247 0.636881
\(189\) 13.1562 0.956972
\(190\) −2.36624 −0.171665
\(191\) 13.6776 0.989677 0.494838 0.868985i \(-0.335227\pi\)
0.494838 + 0.868985i \(0.335227\pi\)
\(192\) 2.94749 0.212717
\(193\) 5.61830 0.404414 0.202207 0.979343i \(-0.435189\pi\)
0.202207 + 0.979343i \(0.435189\pi\)
\(194\) 8.37894 0.601573
\(195\) 4.42016 0.316534
\(196\) −4.24198 −0.302999
\(197\) 5.46494 0.389361 0.194680 0.980867i \(-0.437633\pi\)
0.194680 + 0.980867i \(0.437633\pi\)
\(198\) 0 0
\(199\) −13.5571 −0.961039 −0.480519 0.876984i \(-0.659552\pi\)
−0.480519 + 0.876984i \(0.659552\pi\)
\(200\) −0.599069 −0.0423606
\(201\) −1.15895 −0.0817459
\(202\) 16.5379 1.16360
\(203\) −15.1740 −1.06501
\(204\) −1.71324 −0.119951
\(205\) 10.4136 0.727320
\(206\) −2.79627 −0.194826
\(207\) 20.5224 1.42641
\(208\) 0.633765 0.0439437
\(209\) 0 0
\(210\) −11.5827 −0.799280
\(211\) 14.3562 0.988318 0.494159 0.869371i \(-0.335476\pi\)
0.494159 + 0.869371i \(0.335476\pi\)
\(212\) −12.5302 −0.860575
\(213\) −0.920526 −0.0630734
\(214\) −18.9681 −1.29664
\(215\) 22.6749 1.54641
\(216\) −7.92194 −0.539020
\(217\) 1.70316 0.115618
\(218\) −17.0732 −1.15634
\(219\) −27.4521 −1.85504
\(220\) 0 0
\(221\) −0.368378 −0.0247798
\(222\) −6.36348 −0.427089
\(223\) −5.16251 −0.345707 −0.172854 0.984948i \(-0.555299\pi\)
−0.172854 + 0.984948i \(0.555299\pi\)
\(224\) −1.66073 −0.110962
\(225\) 3.40732 0.227155
\(226\) −21.1114 −1.40431
\(227\) −18.3435 −1.21750 −0.608751 0.793361i \(-0.708329\pi\)
−0.608751 + 0.793361i \(0.708329\pi\)
\(228\) 2.94749 0.195202
\(229\) 18.3344 1.21157 0.605785 0.795629i \(-0.292859\pi\)
0.605785 + 0.795629i \(0.292859\pi\)
\(230\) −8.53789 −0.562972
\(231\) 0 0
\(232\) 9.13696 0.599871
\(233\) −14.6429 −0.959289 −0.479645 0.877463i \(-0.659234\pi\)
−0.479645 + 0.877463i \(0.659234\pi\)
\(234\) −3.60466 −0.235644
\(235\) 20.6631 1.34791
\(236\) 6.47623 0.421567
\(237\) 33.2193 2.15782
\(238\) 0.965305 0.0625714
\(239\) −12.5868 −0.814175 −0.407088 0.913389i \(-0.633456\pi\)
−0.407088 + 0.913389i \(0.633456\pi\)
\(240\) 6.97445 0.450199
\(241\) −2.79627 −0.180124 −0.0900619 0.995936i \(-0.528706\pi\)
−0.0900619 + 0.995936i \(0.528706\pi\)
\(242\) 0 0
\(243\) −5.23567 −0.335868
\(244\) 1.32146 0.0845976
\(245\) −10.0375 −0.641274
\(246\) −12.9717 −0.827045
\(247\) 0.633765 0.0403255
\(248\) −1.02555 −0.0651223
\(249\) −20.3498 −1.28962
\(250\) 10.4136 0.658616
\(251\) −1.72891 −0.109128 −0.0545640 0.998510i \(-0.517377\pi\)
−0.0545640 + 0.998510i \(0.517377\pi\)
\(252\) 9.44571 0.595024
\(253\) 0 0
\(254\) −4.62745 −0.290352
\(255\) −4.05393 −0.253867
\(256\) 1.00000 0.0625000
\(257\) 21.5414 1.34372 0.671859 0.740679i \(-0.265496\pi\)
0.671859 + 0.740679i \(0.265496\pi\)
\(258\) −28.2448 −1.75845
\(259\) 3.58543 0.222788
\(260\) 1.49964 0.0930035
\(261\) −51.9682 −3.21675
\(262\) 15.7763 0.974664
\(263\) −22.7920 −1.40541 −0.702707 0.711479i \(-0.748026\pi\)
−0.702707 + 0.711479i \(0.748026\pi\)
\(264\) 0 0
\(265\) −29.6493 −1.82134
\(266\) −1.66073 −0.101826
\(267\) 1.53150 0.0937263
\(268\) −0.393199 −0.0240184
\(269\) −18.6429 −1.13668 −0.568339 0.822794i \(-0.692414\pi\)
−0.568339 + 0.822794i \(0.692414\pi\)
\(270\) −18.7452 −1.14080
\(271\) −3.33571 −0.202630 −0.101315 0.994854i \(-0.532305\pi\)
−0.101315 + 0.994854i \(0.532305\pi\)
\(272\) −0.581254 −0.0352437
\(273\) 3.10226 0.187758
\(274\) 20.6366 1.24670
\(275\) 0 0
\(276\) 10.6352 0.640163
\(277\) 23.5883 1.41728 0.708641 0.705570i \(-0.249309\pi\)
0.708641 + 0.705570i \(0.249309\pi\)
\(278\) 9.56721 0.573803
\(279\) 5.83300 0.349212
\(280\) −3.92967 −0.234843
\(281\) 31.6366 1.88728 0.943641 0.330972i \(-0.107377\pi\)
0.943641 + 0.330972i \(0.107377\pi\)
\(282\) −25.7389 −1.53273
\(283\) 6.06757 0.360680 0.180340 0.983604i \(-0.442280\pi\)
0.180340 + 0.983604i \(0.442280\pi\)
\(284\) −0.312308 −0.0185321
\(285\) 6.97445 0.413131
\(286\) 0 0
\(287\) 7.30875 0.431422
\(288\) −5.68769 −0.335150
\(289\) −16.6621 −0.980126
\(290\) 21.6202 1.26958
\(291\) −24.6968 −1.44775
\(292\) −9.31372 −0.545044
\(293\) 16.8312 0.983288 0.491644 0.870796i \(-0.336396\pi\)
0.491644 + 0.870796i \(0.336396\pi\)
\(294\) 12.5032 0.729201
\(295\) 15.3243 0.892215
\(296\) −2.15895 −0.125486
\(297\) 0 0
\(298\) −18.3096 −1.06064
\(299\) 2.28676 0.132247
\(300\) 1.76575 0.101946
\(301\) 15.9142 0.917280
\(302\) −6.25562 −0.359971
\(303\) −48.7453 −2.80034
\(304\) 1.00000 0.0573539
\(305\) 3.12688 0.179044
\(306\) 3.30599 0.188991
\(307\) −5.10858 −0.291562 −0.145781 0.989317i \(-0.546570\pi\)
−0.145781 + 0.989317i \(0.546570\pi\)
\(308\) 0 0
\(309\) 8.24198 0.468870
\(310\) −2.42669 −0.137827
\(311\) −24.5635 −1.39287 −0.696435 0.717620i \(-0.745231\pi\)
−0.696435 + 0.717620i \(0.745231\pi\)
\(312\) −1.86801 −0.105756
\(313\) −24.2868 −1.37277 −0.686387 0.727237i \(-0.740804\pi\)
−0.686387 + 0.727237i \(0.740804\pi\)
\(314\) 6.15619 0.347414
\(315\) 22.3508 1.25932
\(316\) 11.2704 0.634007
\(317\) −28.6225 −1.60760 −0.803801 0.594898i \(-0.797192\pi\)
−0.803801 + 0.594898i \(0.797192\pi\)
\(318\) 36.9325 2.07107
\(319\) 0 0
\(320\) 2.36624 0.132277
\(321\) 55.9084 3.12050
\(322\) −5.99227 −0.333936
\(323\) −0.581254 −0.0323418
\(324\) 6.28676 0.349264
\(325\) 0.379669 0.0210602
\(326\) 11.8439 0.655972
\(327\) 50.3229 2.78287
\(328\) −4.40093 −0.243001
\(329\) 14.5023 0.799535
\(330\) 0 0
\(331\) −2.40960 −0.132444 −0.0662218 0.997805i \(-0.521094\pi\)
−0.0662218 + 0.997805i \(0.521094\pi\)
\(332\) −6.90413 −0.378913
\(333\) 12.2794 0.672909
\(334\) 4.89142 0.267647
\(335\) −0.930401 −0.0508332
\(336\) 4.89498 0.267043
\(337\) −17.5195 −0.954346 −0.477173 0.878809i \(-0.658338\pi\)
−0.477173 + 0.878809i \(0.658338\pi\)
\(338\) 12.5983 0.685259
\(339\) 62.2257 3.37963
\(340\) −1.37538 −0.0745906
\(341\) 0 0
\(342\) −5.68769 −0.307555
\(343\) −18.6699 −1.00808
\(344\) −9.58267 −0.516663
\(345\) 25.1653 1.35486
\(346\) 18.1206 0.974167
\(347\) −32.1534 −1.72609 −0.863043 0.505130i \(-0.831445\pi\)
−0.863043 + 0.505130i \(0.831445\pi\)
\(348\) −26.9311 −1.44366
\(349\) −0.407455 −0.0218106 −0.0109053 0.999941i \(-0.503471\pi\)
−0.0109053 + 0.999941i \(0.503471\pi\)
\(350\) −0.994891 −0.0531792
\(351\) 5.02065 0.267982
\(352\) 0 0
\(353\) 3.94158 0.209789 0.104895 0.994483i \(-0.466549\pi\)
0.104895 + 0.994483i \(0.466549\pi\)
\(354\) −19.0886 −1.01455
\(355\) −0.738995 −0.0392218
\(356\) 0.519595 0.0275385
\(357\) −2.84522 −0.150585
\(358\) −3.07947 −0.162755
\(359\) 20.0781 1.05968 0.529842 0.848097i \(-0.322251\pi\)
0.529842 + 0.848097i \(0.322251\pi\)
\(360\) −13.4584 −0.709321
\(361\) 1.00000 0.0526316
\(362\) −0.0693910 −0.00364711
\(363\) 0 0
\(364\) 1.05251 0.0551666
\(365\) −22.0385 −1.15355
\(366\) −3.89498 −0.203594
\(367\) −20.5918 −1.07488 −0.537442 0.843301i \(-0.680609\pi\)
−0.537442 + 0.843301i \(0.680609\pi\)
\(368\) 3.60822 0.188091
\(369\) 25.0311 1.30307
\(370\) −5.10858 −0.265582
\(371\) −20.8092 −1.08036
\(372\) 3.02279 0.156724
\(373\) 20.8813 1.08119 0.540597 0.841282i \(-0.318198\pi\)
0.540597 + 0.841282i \(0.318198\pi\)
\(374\) 0 0
\(375\) −30.6941 −1.58504
\(376\) −8.73247 −0.450343
\(377\) −5.79068 −0.298235
\(378\) −13.1562 −0.676681
\(379\) −0.753845 −0.0387224 −0.0193612 0.999813i \(-0.506163\pi\)
−0.0193612 + 0.999813i \(0.506163\pi\)
\(380\) 2.36624 0.121385
\(381\) 13.6394 0.698765
\(382\) −13.6776 −0.699807
\(383\) −18.3142 −0.935812 −0.467906 0.883778i \(-0.654991\pi\)
−0.467906 + 0.883778i \(0.654991\pi\)
\(384\) −2.94749 −0.150413
\(385\) 0 0
\(386\) −5.61830 −0.285964
\(387\) 54.5033 2.77056
\(388\) −8.37894 −0.425376
\(389\) −26.1206 −1.32436 −0.662182 0.749343i \(-0.730370\pi\)
−0.662182 + 0.749343i \(0.730370\pi\)
\(390\) −4.42016 −0.223824
\(391\) −2.09729 −0.106065
\(392\) 4.24198 0.214252
\(393\) −46.5005 −2.34564
\(394\) −5.46494 −0.275320
\(395\) 26.6683 1.34183
\(396\) 0 0
\(397\) −34.9079 −1.75198 −0.875988 0.482332i \(-0.839790\pi\)
−0.875988 + 0.482332i \(0.839790\pi\)
\(398\) 13.5571 0.679557
\(399\) 4.89498 0.245055
\(400\) 0.599069 0.0299535
\(401\) 6.35353 0.317280 0.158640 0.987336i \(-0.449289\pi\)
0.158640 + 0.987336i \(0.449289\pi\)
\(402\) 1.15895 0.0578031
\(403\) 0.649956 0.0323766
\(404\) −16.5379 −0.822791
\(405\) 14.8760 0.739192
\(406\) 15.1740 0.753073
\(407\) 0 0
\(408\) 1.71324 0.0848180
\(409\) −26.1816 −1.29460 −0.647299 0.762237i \(-0.724101\pi\)
−0.647299 + 0.762237i \(0.724101\pi\)
\(410\) −10.4136 −0.514293
\(411\) −60.8261 −3.00033
\(412\) 2.79627 0.137762
\(413\) 10.7553 0.529232
\(414\) −20.5224 −1.00862
\(415\) −16.3368 −0.801941
\(416\) −0.633765 −0.0310729
\(417\) −28.1992 −1.38092
\(418\) 0 0
\(419\) 8.15060 0.398183 0.199091 0.979981i \(-0.436201\pi\)
0.199091 + 0.979981i \(0.436201\pi\)
\(420\) 11.5827 0.565176
\(421\) 10.9531 0.533820 0.266910 0.963721i \(-0.413997\pi\)
0.266910 + 0.963721i \(0.413997\pi\)
\(422\) −14.3562 −0.698847
\(423\) 49.6676 2.41492
\(424\) 12.5302 0.608518
\(425\) −0.348211 −0.0168907
\(426\) 0.920526 0.0445996
\(427\) 2.19458 0.106203
\(428\) 18.9681 0.916859
\(429\) 0 0
\(430\) −22.6749 −1.09348
\(431\) −17.8510 −0.859852 −0.429926 0.902864i \(-0.641460\pi\)
−0.429926 + 0.902864i \(0.641460\pi\)
\(432\) 7.92194 0.381145
\(433\) 39.4138 1.89411 0.947054 0.321074i \(-0.104044\pi\)
0.947054 + 0.321074i \(0.104044\pi\)
\(434\) −1.70316 −0.0817541
\(435\) −63.7253 −3.05539
\(436\) 17.0732 0.817656
\(437\) 3.60822 0.172604
\(438\) 27.4521 1.31171
\(439\) −16.9993 −0.811331 −0.405666 0.914022i \(-0.632960\pi\)
−0.405666 + 0.914022i \(0.632960\pi\)
\(440\) 0 0
\(441\) −24.1271 −1.14891
\(442\) 0.368378 0.0175220
\(443\) 16.2668 0.772859 0.386430 0.922319i \(-0.373708\pi\)
0.386430 + 0.922319i \(0.373708\pi\)
\(444\) 6.36348 0.301997
\(445\) 1.22948 0.0582831
\(446\) 5.16251 0.244452
\(447\) 53.9672 2.55256
\(448\) 1.66073 0.0784620
\(449\) 16.5534 0.781201 0.390601 0.920560i \(-0.372267\pi\)
0.390601 + 0.920560i \(0.372267\pi\)
\(450\) −3.40732 −0.160623
\(451\) 0 0
\(452\) 21.1114 0.992997
\(453\) 18.4384 0.866311
\(454\) 18.3435 0.860904
\(455\) 2.49049 0.116756
\(456\) −2.94749 −0.138029
\(457\) 11.5805 0.541714 0.270857 0.962620i \(-0.412693\pi\)
0.270857 + 0.962620i \(0.412693\pi\)
\(458\) −18.3344 −0.856709
\(459\) −4.60466 −0.214927
\(460\) 8.53789 0.398081
\(461\) 5.42648 0.252736 0.126368 0.991983i \(-0.459668\pi\)
0.126368 + 0.991983i \(0.459668\pi\)
\(462\) 0 0
\(463\) 26.9168 1.25093 0.625466 0.780252i \(-0.284909\pi\)
0.625466 + 0.780252i \(0.284909\pi\)
\(464\) −9.13696 −0.424173
\(465\) 7.15263 0.331695
\(466\) 14.6429 0.678320
\(467\) 12.5581 0.581118 0.290559 0.956857i \(-0.406159\pi\)
0.290559 + 0.956857i \(0.406159\pi\)
\(468\) 3.60466 0.166625
\(469\) −0.652996 −0.0301526
\(470\) −20.6631 −0.953117
\(471\) −18.1453 −0.836092
\(472\) −6.47623 −0.298093
\(473\) 0 0
\(474\) −33.2193 −1.52581
\(475\) 0.599069 0.0274872
\(476\) −0.965305 −0.0442447
\(477\) −71.2677 −3.26312
\(478\) 12.5868 0.575709
\(479\) −40.2322 −1.83826 −0.919128 0.393960i \(-0.871105\pi\)
−0.919128 + 0.393960i \(0.871105\pi\)
\(480\) −6.97445 −0.318339
\(481\) 1.36827 0.0623875
\(482\) 2.79627 0.127367
\(483\) 17.6621 0.803655
\(484\) 0 0
\(485\) −19.8265 −0.900277
\(486\) 5.23567 0.237495
\(487\) −14.2795 −0.647066 −0.323533 0.946217i \(-0.604871\pi\)
−0.323533 + 0.946217i \(0.604871\pi\)
\(488\) −1.32146 −0.0598195
\(489\) −34.9097 −1.57867
\(490\) 10.0375 0.453449
\(491\) −14.0094 −0.632233 −0.316117 0.948720i \(-0.602379\pi\)
−0.316117 + 0.948720i \(0.602379\pi\)
\(492\) 12.9717 0.584809
\(493\) 5.31089 0.239191
\(494\) −0.633765 −0.0285144
\(495\) 0 0
\(496\) 1.02555 0.0460484
\(497\) −0.518659 −0.0232651
\(498\) 20.3498 0.911898
\(499\) 18.1506 0.812533 0.406266 0.913755i \(-0.366831\pi\)
0.406266 + 0.913755i \(0.366831\pi\)
\(500\) −10.4136 −0.465712
\(501\) −14.4174 −0.644122
\(502\) 1.72891 0.0771651
\(503\) 29.8672 1.33171 0.665855 0.746081i \(-0.268067\pi\)
0.665855 + 0.746081i \(0.268067\pi\)
\(504\) −9.44571 −0.420745
\(505\) −39.1325 −1.74138
\(506\) 0 0
\(507\) −37.1335 −1.64916
\(508\) 4.62745 0.205310
\(509\) 24.2045 1.07285 0.536423 0.843949i \(-0.319775\pi\)
0.536423 + 0.843949i \(0.319775\pi\)
\(510\) 4.05393 0.179511
\(511\) −15.4676 −0.684245
\(512\) −1.00000 −0.0441942
\(513\) 7.92194 0.349762
\(514\) −21.5414 −0.950153
\(515\) 6.61664 0.291564
\(516\) 28.2448 1.24341
\(517\) 0 0
\(518\) −3.58543 −0.157535
\(519\) −53.4102 −2.34445
\(520\) −1.49964 −0.0657634
\(521\) −6.36899 −0.279031 −0.139515 0.990220i \(-0.544554\pi\)
−0.139515 + 0.990220i \(0.544554\pi\)
\(522\) 51.9682 2.27459
\(523\) 21.2749 0.930284 0.465142 0.885236i \(-0.346003\pi\)
0.465142 + 0.885236i \(0.346003\pi\)
\(524\) −15.7763 −0.689191
\(525\) 2.93243 0.127982
\(526\) 22.7920 0.993778
\(527\) −0.596103 −0.0259667
\(528\) 0 0
\(529\) −9.98077 −0.433946
\(530\) 29.6493 1.28788
\(531\) 36.8348 1.59849
\(532\) 1.66073 0.0720017
\(533\) 2.78915 0.120812
\(534\) −1.53150 −0.0662745
\(535\) 44.8831 1.94046
\(536\) 0.393199 0.0169836
\(537\) 9.07672 0.391689
\(538\) 18.6429 0.803753
\(539\) 0 0
\(540\) 18.7452 0.806664
\(541\) 34.2668 1.47324 0.736622 0.676304i \(-0.236420\pi\)
0.736622 + 0.676304i \(0.236420\pi\)
\(542\) 3.33571 0.143281
\(543\) 0.204529 0.00877718
\(544\) 0.581254 0.0249211
\(545\) 40.3991 1.73051
\(546\) −3.10226 −0.132765
\(547\) 31.2732 1.33715 0.668573 0.743647i \(-0.266906\pi\)
0.668573 + 0.743647i \(0.266906\pi\)
\(548\) −20.6366 −0.881552
\(549\) 7.51604 0.320777
\(550\) 0 0
\(551\) −9.13696 −0.389248
\(552\) −10.6352 −0.452663
\(553\) 18.7170 0.795928
\(554\) −23.5883 −1.00217
\(555\) 15.0575 0.639155
\(556\) −9.56721 −0.405740
\(557\) −24.7198 −1.04741 −0.523707 0.851899i \(-0.675451\pi\)
−0.523707 + 0.851899i \(0.675451\pi\)
\(558\) −5.83300 −0.246931
\(559\) 6.07316 0.256867
\(560\) 3.92967 0.166059
\(561\) 0 0
\(562\) −31.6366 −1.33451
\(563\) −8.94251 −0.376882 −0.188441 0.982085i \(-0.560343\pi\)
−0.188441 + 0.982085i \(0.560343\pi\)
\(564\) 25.7389 1.08380
\(565\) 49.9546 2.10160
\(566\) −6.06757 −0.255039
\(567\) 10.4406 0.438464
\(568\) 0.312308 0.0131042
\(569\) 0.764409 0.0320457 0.0160228 0.999872i \(-0.494900\pi\)
0.0160228 + 0.999872i \(0.494900\pi\)
\(570\) −6.97445 −0.292128
\(571\) −4.11866 −0.172361 −0.0861804 0.996280i \(-0.527466\pi\)
−0.0861804 + 0.996280i \(0.527466\pi\)
\(572\) 0 0
\(573\) 40.3146 1.68417
\(574\) −7.30875 −0.305061
\(575\) 2.16157 0.0901438
\(576\) 5.68769 0.236987
\(577\) 26.8538 1.11794 0.558968 0.829189i \(-0.311197\pi\)
0.558968 + 0.829189i \(0.311197\pi\)
\(578\) 16.6621 0.693054
\(579\) 16.5599 0.688205
\(580\) −21.6202 −0.897730
\(581\) −11.4659 −0.475685
\(582\) 24.6968 1.02372
\(583\) 0 0
\(584\) 9.31372 0.385405
\(585\) 8.52947 0.352650
\(586\) −16.8312 −0.695289
\(587\) 11.4832 0.473964 0.236982 0.971514i \(-0.423842\pi\)
0.236982 + 0.971514i \(0.423842\pi\)
\(588\) −12.5032 −0.515623
\(589\) 1.02555 0.0422570
\(590\) −15.3243 −0.630891
\(591\) 16.1079 0.662589
\(592\) 2.15895 0.0887322
\(593\) −32.3508 −1.32849 −0.664245 0.747515i \(-0.731247\pi\)
−0.664245 + 0.747515i \(0.731247\pi\)
\(594\) 0 0
\(595\) −2.28414 −0.0936405
\(596\) 18.3096 0.749988
\(597\) −39.9595 −1.63543
\(598\) −2.28676 −0.0935126
\(599\) 6.06380 0.247760 0.123880 0.992297i \(-0.460466\pi\)
0.123880 + 0.992297i \(0.460466\pi\)
\(600\) −1.76575 −0.0720864
\(601\) 23.0923 0.941953 0.470976 0.882146i \(-0.343902\pi\)
0.470976 + 0.882146i \(0.343902\pi\)
\(602\) −15.9142 −0.648615
\(603\) −2.23639 −0.0910730
\(604\) 6.25562 0.254538
\(605\) 0 0
\(606\) 48.7453 1.98014
\(607\) 11.1808 0.453815 0.226907 0.973916i \(-0.427139\pi\)
0.226907 + 0.973916i \(0.427139\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −44.7252 −1.81236
\(610\) −3.12688 −0.126604
\(611\) 5.53433 0.223895
\(612\) −3.30599 −0.133637
\(613\) 33.8355 1.36660 0.683302 0.730136i \(-0.260543\pi\)
0.683302 + 0.730136i \(0.260543\pi\)
\(614\) 5.10858 0.206166
\(615\) 30.6941 1.23770
\(616\) 0 0
\(617\) 24.9927 1.00617 0.503085 0.864237i \(-0.332198\pi\)
0.503085 + 0.864237i \(0.332198\pi\)
\(618\) −8.24198 −0.331541
\(619\) 7.68493 0.308884 0.154442 0.988002i \(-0.450642\pi\)
0.154442 + 0.988002i \(0.450642\pi\)
\(620\) 2.42669 0.0974581
\(621\) 28.5841 1.14704
\(622\) 24.5635 0.984907
\(623\) 0.862906 0.0345716
\(624\) 1.86801 0.0747804
\(625\) −27.6365 −1.10546
\(626\) 24.2868 0.970697
\(627\) 0 0
\(628\) −6.15619 −0.245659
\(629\) −1.25490 −0.0500360
\(630\) −22.3508 −0.890476
\(631\) 25.7004 1.02312 0.511558 0.859249i \(-0.329068\pi\)
0.511558 + 0.859249i \(0.329068\pi\)
\(632\) −11.2704 −0.448311
\(633\) 42.3146 1.68185
\(634\) 28.6225 1.13675
\(635\) 10.9496 0.434523
\(636\) −36.9325 −1.46447
\(637\) −2.68842 −0.106519
\(638\) 0 0
\(639\) −1.77631 −0.0702699
\(640\) −2.36624 −0.0935337
\(641\) 4.03846 0.159510 0.0797548 0.996815i \(-0.474586\pi\)
0.0797548 + 0.996815i \(0.474586\pi\)
\(642\) −55.9084 −2.20653
\(643\) 5.44194 0.214609 0.107305 0.994226i \(-0.465778\pi\)
0.107305 + 0.994226i \(0.465778\pi\)
\(644\) 5.99227 0.236128
\(645\) 66.8339 2.63158
\(646\) 0.581254 0.0228691
\(647\) −32.4046 −1.27395 −0.636977 0.770882i \(-0.719816\pi\)
−0.636977 + 0.770882i \(0.719816\pi\)
\(648\) −6.28676 −0.246967
\(649\) 0 0
\(650\) −0.379669 −0.0148918
\(651\) 5.02003 0.196751
\(652\) −11.8439 −0.463842
\(653\) 24.7672 0.969217 0.484609 0.874731i \(-0.338962\pi\)
0.484609 + 0.874731i \(0.338962\pi\)
\(654\) −50.3229 −1.96778
\(655\) −37.3305 −1.45862
\(656\) 4.40093 0.171827
\(657\) −52.9736 −2.06670
\(658\) −14.5023 −0.565357
\(659\) −27.5600 −1.07358 −0.536792 0.843715i \(-0.680364\pi\)
−0.536792 + 0.843715i \(0.680364\pi\)
\(660\) 0 0
\(661\) −7.53372 −0.293028 −0.146514 0.989209i \(-0.546805\pi\)
−0.146514 + 0.989209i \(0.546805\pi\)
\(662\) 2.40960 0.0936517
\(663\) −1.08579 −0.0421686
\(664\) 6.90413 0.267932
\(665\) 3.92967 0.152386
\(666\) −12.2794 −0.475818
\(667\) −32.9681 −1.27653
\(668\) −4.89142 −0.189255
\(669\) −15.2164 −0.588301
\(670\) 0.930401 0.0359445
\(671\) 0 0
\(672\) −4.89498 −0.188828
\(673\) −8.79534 −0.339035 −0.169518 0.985527i \(-0.554221\pi\)
−0.169518 + 0.985527i \(0.554221\pi\)
\(674\) 17.5195 0.674824
\(675\) 4.74579 0.182666
\(676\) −12.5983 −0.484552
\(677\) 15.8310 0.608434 0.304217 0.952603i \(-0.401605\pi\)
0.304217 + 0.952603i \(0.401605\pi\)
\(678\) −62.2257 −2.38976
\(679\) −13.9151 −0.534014
\(680\) 1.37538 0.0527435
\(681\) −54.0673 −2.07186
\(682\) 0 0
\(683\) 38.6640 1.47944 0.739719 0.672916i \(-0.234958\pi\)
0.739719 + 0.672916i \(0.234958\pi\)
\(684\) 5.68769 0.217474
\(685\) −48.8310 −1.86574
\(686\) 18.6699 0.712819
\(687\) 54.0404 2.06177
\(688\) 9.58267 0.365336
\(689\) −7.94117 −0.302535
\(690\) −25.1653 −0.958028
\(691\) −27.4678 −1.04492 −0.522462 0.852663i \(-0.674986\pi\)
−0.522462 + 0.852663i \(0.674986\pi\)
\(692\) −18.1206 −0.688840
\(693\) 0 0
\(694\) 32.1534 1.22053
\(695\) −22.6383 −0.858718
\(696\) 26.9311 1.02082
\(697\) −2.55806 −0.0968933
\(698\) 0.407455 0.0154224
\(699\) −43.1598 −1.63245
\(700\) 0.994891 0.0376034
\(701\) −1.50892 −0.0569911 −0.0284955 0.999594i \(-0.509072\pi\)
−0.0284955 + 0.999594i \(0.509072\pi\)
\(702\) −5.02065 −0.189492
\(703\) 2.15895 0.0814263
\(704\) 0 0
\(705\) 60.9042 2.29378
\(706\) −3.94158 −0.148343
\(707\) −27.4649 −1.03293
\(708\) 19.0886 0.717394
\(709\) 16.2959 0.612006 0.306003 0.952031i \(-0.401008\pi\)
0.306003 + 0.952031i \(0.401008\pi\)
\(710\) 0.738995 0.0277340
\(711\) 64.1023 2.40403
\(712\) −0.519595 −0.0194726
\(713\) 3.70040 0.138581
\(714\) 2.84522 0.106480
\(715\) 0 0
\(716\) 3.07947 0.115085
\(717\) −37.0996 −1.38551
\(718\) −20.0781 −0.749309
\(719\) 40.6785 1.51705 0.758526 0.651643i \(-0.225920\pi\)
0.758526 + 0.651643i \(0.225920\pi\)
\(720\) 13.4584 0.501566
\(721\) 4.64385 0.172946
\(722\) −1.00000 −0.0372161
\(723\) −8.24198 −0.306523
\(724\) 0.0693910 0.00257889
\(725\) −5.47367 −0.203287
\(726\) 0 0
\(727\) 27.7545 1.02936 0.514679 0.857383i \(-0.327911\pi\)
0.514679 + 0.857383i \(0.327911\pi\)
\(728\) −1.05251 −0.0390087
\(729\) −34.2924 −1.27009
\(730\) 22.0385 0.815680
\(731\) −5.56996 −0.206013
\(732\) 3.89498 0.143963
\(733\) −6.89854 −0.254803 −0.127402 0.991851i \(-0.540664\pi\)
−0.127402 + 0.991851i \(0.540664\pi\)
\(734\) 20.5918 0.760058
\(735\) −29.5855 −1.09128
\(736\) −3.60822 −0.133001
\(737\) 0 0
\(738\) −25.0311 −0.921409
\(739\) 49.2039 1.80999 0.904997 0.425418i \(-0.139873\pi\)
0.904997 + 0.425418i \(0.139873\pi\)
\(740\) 5.10858 0.187795
\(741\) 1.86801 0.0686232
\(742\) 20.8092 0.763929
\(743\) 10.4046 0.381709 0.190854 0.981618i \(-0.438874\pi\)
0.190854 + 0.981618i \(0.438874\pi\)
\(744\) −3.02279 −0.110821
\(745\) 43.3247 1.58729
\(746\) −20.8813 −0.764520
\(747\) −39.2685 −1.43676
\(748\) 0 0
\(749\) 31.5009 1.15102
\(750\) 30.6941 1.12079
\(751\) 37.7103 1.37607 0.688035 0.725677i \(-0.258474\pi\)
0.688035 + 0.725677i \(0.258474\pi\)
\(752\) 8.73247 0.318440
\(753\) −5.09595 −0.185707
\(754\) 5.79068 0.210884
\(755\) 14.8023 0.538710
\(756\) 13.1562 0.478486
\(757\) 14.3972 0.523274 0.261637 0.965166i \(-0.415738\pi\)
0.261637 + 0.965166i \(0.415738\pi\)
\(758\) 0.753845 0.0273809
\(759\) 0 0
\(760\) −2.36624 −0.0858324
\(761\) −39.7311 −1.44025 −0.720126 0.693843i \(-0.755916\pi\)
−0.720126 + 0.693843i \(0.755916\pi\)
\(762\) −13.6394 −0.494102
\(763\) 28.3539 1.02648
\(764\) 13.6776 0.494838
\(765\) −7.82276 −0.282832
\(766\) 18.3142 0.661719
\(767\) 4.10441 0.148202
\(768\) 2.94749 0.106358
\(769\) −2.27170 −0.0819197 −0.0409598 0.999161i \(-0.513042\pi\)
−0.0409598 + 0.999161i \(0.513042\pi\)
\(770\) 0 0
\(771\) 63.4932 2.28665
\(772\) 5.61830 0.202207
\(773\) 3.64157 0.130978 0.0654891 0.997853i \(-0.479139\pi\)
0.0654891 + 0.997853i \(0.479139\pi\)
\(774\) −54.5033 −1.95908
\(775\) 0.614374 0.0220690
\(776\) 8.37894 0.300786
\(777\) 10.5680 0.379125
\(778\) 26.1206 0.936467
\(779\) 4.40093 0.157680
\(780\) 4.42016 0.158267
\(781\) 0 0
\(782\) 2.09729 0.0749989
\(783\) −72.3825 −2.58674
\(784\) −4.24198 −0.151499
\(785\) −14.5670 −0.519918
\(786\) 46.5005 1.65862
\(787\) 0.279643 0.00996821 0.00498410 0.999988i \(-0.498414\pi\)
0.00498410 + 0.999988i \(0.498414\pi\)
\(788\) 5.46494 0.194680
\(789\) −67.1791 −2.39164
\(790\) −26.6683 −0.948816
\(791\) 35.0603 1.24660
\(792\) 0 0
\(793\) 0.837492 0.0297402
\(794\) 34.9079 1.23883
\(795\) −87.3910 −3.09944
\(796\) −13.5571 −0.480519
\(797\) −3.66014 −0.129649 −0.0648243 0.997897i \(-0.520649\pi\)
−0.0648243 + 0.997897i \(0.520649\pi\)
\(798\) −4.89498 −0.173280
\(799\) −5.07578 −0.179568
\(800\) −0.599069 −0.0211803
\(801\) 2.95530 0.104420
\(802\) −6.35353 −0.224351
\(803\) 0 0
\(804\) −1.15895 −0.0408730
\(805\) 14.1791 0.499748
\(806\) −0.649956 −0.0228937
\(807\) −54.9498 −1.93432
\(808\) 16.5379 0.581801
\(809\) −27.0990 −0.952749 −0.476375 0.879242i \(-0.658049\pi\)
−0.476375 + 0.879242i \(0.658049\pi\)
\(810\) −14.8760 −0.522688
\(811\) −31.4212 −1.10335 −0.551673 0.834060i \(-0.686010\pi\)
−0.551673 + 0.834060i \(0.686010\pi\)
\(812\) −15.1740 −0.532503
\(813\) −9.83198 −0.344823
\(814\) 0 0
\(815\) −28.0254 −0.981687
\(816\) −1.71324 −0.0599754
\(817\) 9.58267 0.335255
\(818\) 26.1816 0.915418
\(819\) 5.98636 0.209180
\(820\) 10.4136 0.363660
\(821\) 20.1304 0.702557 0.351279 0.936271i \(-0.385747\pi\)
0.351279 + 0.936271i \(0.385747\pi\)
\(822\) 60.8261 2.12156
\(823\) −7.23922 −0.252344 −0.126172 0.992008i \(-0.540269\pi\)
−0.126172 + 0.992008i \(0.540269\pi\)
\(824\) −2.79627 −0.0974128
\(825\) 0 0
\(826\) −10.7553 −0.374223
\(827\) −23.1088 −0.803571 −0.401786 0.915734i \(-0.631610\pi\)
−0.401786 + 0.915734i \(0.631610\pi\)
\(828\) 20.5224 0.713204
\(829\) 21.7081 0.753955 0.376977 0.926223i \(-0.376963\pi\)
0.376977 + 0.926223i \(0.376963\pi\)
\(830\) 16.3368 0.567058
\(831\) 69.5261 2.41183
\(832\) 0.633765 0.0219718
\(833\) 2.46567 0.0854303
\(834\) 28.1992 0.976460
\(835\) −11.5742 −0.400543
\(836\) 0 0
\(837\) 8.12433 0.280818
\(838\) −8.15060 −0.281558
\(839\) −21.1935 −0.731681 −0.365841 0.930678i \(-0.619218\pi\)
−0.365841 + 0.930678i \(0.619218\pi\)
\(840\) −11.5827 −0.399640
\(841\) 54.4840 1.87876
\(842\) −10.9531 −0.377468
\(843\) 93.2485 3.21165
\(844\) 14.3562 0.494159
\(845\) −29.8106 −1.02552
\(846\) −49.6676 −1.70761
\(847\) 0 0
\(848\) −12.5302 −0.430287
\(849\) 17.8841 0.613780
\(850\) 0.348211 0.0119435
\(851\) 7.78996 0.267036
\(852\) −0.920526 −0.0315367
\(853\) −30.5835 −1.04716 −0.523579 0.851977i \(-0.675404\pi\)
−0.523579 + 0.851977i \(0.675404\pi\)
\(854\) −2.19458 −0.0750970
\(855\) 13.4584 0.460268
\(856\) −18.9681 −0.648318
\(857\) −48.3757 −1.65248 −0.826241 0.563317i \(-0.809525\pi\)
−0.826241 + 0.563317i \(0.809525\pi\)
\(858\) 0 0
\(859\) −57.0941 −1.94802 −0.974012 0.226495i \(-0.927273\pi\)
−0.974012 + 0.226495i \(0.927273\pi\)
\(860\) 22.6749 0.773206
\(861\) 21.5425 0.734165
\(862\) 17.8510 0.608007
\(863\) 3.31963 0.113002 0.0565008 0.998403i \(-0.482006\pi\)
0.0565008 + 0.998403i \(0.482006\pi\)
\(864\) −7.92194 −0.269510
\(865\) −42.8775 −1.45788
\(866\) −39.4138 −1.33934
\(867\) −49.1115 −1.66791
\(868\) 1.70316 0.0578089
\(869\) 0 0
\(870\) 63.7253 2.16049
\(871\) −0.249195 −0.00844367
\(872\) −17.0732 −0.578170
\(873\) −47.6568 −1.61294
\(874\) −3.60822 −0.122050
\(875\) −17.2942 −0.584651
\(876\) −27.4521 −0.927521
\(877\) −4.46676 −0.150832 −0.0754159 0.997152i \(-0.524028\pi\)
−0.0754159 + 0.997152i \(0.524028\pi\)
\(878\) 16.9993 0.573698
\(879\) 49.6097 1.67329
\(880\) 0 0
\(881\) 6.10320 0.205622 0.102811 0.994701i \(-0.467216\pi\)
0.102811 + 0.994701i \(0.467216\pi\)
\(882\) 24.1271 0.812401
\(883\) 6.98526 0.235073 0.117536 0.993069i \(-0.462500\pi\)
0.117536 + 0.993069i \(0.462500\pi\)
\(884\) −0.368378 −0.0123899
\(885\) 45.1682 1.51831
\(886\) −16.2668 −0.546494
\(887\) −39.3670 −1.32182 −0.660908 0.750467i \(-0.729829\pi\)
−0.660908 + 0.750467i \(0.729829\pi\)
\(888\) −6.36348 −0.213544
\(889\) 7.68493 0.257744
\(890\) −1.22948 −0.0412124
\(891\) 0 0
\(892\) −5.16251 −0.172854
\(893\) 8.73247 0.292221
\(894\) −53.9672 −1.80493
\(895\) 7.28676 0.243570
\(896\) −1.66073 −0.0554810
\(897\) 6.74020 0.225049
\(898\) −16.5534 −0.552393
\(899\) −9.37039 −0.312520
\(900\) 3.40732 0.113577
\(901\) 7.28320 0.242639
\(902\) 0 0
\(903\) 46.9070 1.56097
\(904\) −21.1114 −0.702155
\(905\) 0.164195 0.00545804
\(906\) −18.4384 −0.612574
\(907\) 56.7300 1.88369 0.941844 0.336050i \(-0.109091\pi\)
0.941844 + 0.336050i \(0.109091\pi\)
\(908\) −18.3435 −0.608751
\(909\) −94.0624 −3.11985
\(910\) −2.49049 −0.0825589
\(911\) −47.8355 −1.58486 −0.792431 0.609962i \(-0.791185\pi\)
−0.792431 + 0.609962i \(0.791185\pi\)
\(912\) 2.94749 0.0976011
\(913\) 0 0
\(914\) −11.5805 −0.383050
\(915\) 9.21643 0.304686
\(916\) 18.3344 0.605785
\(917\) −26.2002 −0.865206
\(918\) 4.60466 0.151976
\(919\) 0.295588 0.00975054 0.00487527 0.999988i \(-0.498448\pi\)
0.00487527 + 0.999988i \(0.498448\pi\)
\(920\) −8.53789 −0.281486
\(921\) −15.0575 −0.496161
\(922\) −5.42648 −0.178712
\(923\) −0.197930 −0.00651495
\(924\) 0 0
\(925\) 1.29336 0.0425254
\(926\) −26.9168 −0.884542
\(927\) 15.9043 0.522367
\(928\) 9.13696 0.299935
\(929\) −18.6254 −0.611080 −0.305540 0.952179i \(-0.598837\pi\)
−0.305540 + 0.952179i \(0.598837\pi\)
\(930\) −7.15263 −0.234544
\(931\) −4.24198 −0.139025
\(932\) −14.6429 −0.479645
\(933\) −72.4007 −2.37029
\(934\) −12.5581 −0.410912
\(935\) 0 0
\(936\) −3.60466 −0.117822
\(937\) −50.5786 −1.65233 −0.826165 0.563428i \(-0.809482\pi\)
−0.826165 + 0.563428i \(0.809482\pi\)
\(938\) 0.652996 0.0213211
\(939\) −71.5852 −2.33609
\(940\) 20.6631 0.673955
\(941\) 47.1169 1.53597 0.767983 0.640470i \(-0.221261\pi\)
0.767983 + 0.640470i \(0.221261\pi\)
\(942\) 18.1453 0.591206
\(943\) 15.8795 0.517108
\(944\) 6.47623 0.210783
\(945\) 31.1306 1.01268
\(946\) 0 0
\(947\) 8.28227 0.269138 0.134569 0.990904i \(-0.457035\pi\)
0.134569 + 0.990904i \(0.457035\pi\)
\(948\) 33.2193 1.07891
\(949\) −5.90271 −0.191610
\(950\) −0.599069 −0.0194364
\(951\) −84.3646 −2.73571
\(952\) 0.965305 0.0312857
\(953\) −10.0765 −0.326410 −0.163205 0.986592i \(-0.552183\pi\)
−0.163205 + 0.986592i \(0.552183\pi\)
\(954\) 71.2677 2.30738
\(955\) 32.3644 1.04729
\(956\) −12.5868 −0.407088
\(957\) 0 0
\(958\) 40.2322 1.29984
\(959\) −34.2718 −1.10669
\(960\) 6.97445 0.225099
\(961\) −29.9483 −0.966073
\(962\) −1.36827 −0.0441147
\(963\) 107.885 3.47654
\(964\) −2.79627 −0.0900619
\(965\) 13.2942 0.427956
\(966\) −17.6621 −0.568270
\(967\) 48.6402 1.56416 0.782082 0.623175i \(-0.214158\pi\)
0.782082 + 0.623175i \(0.214158\pi\)
\(968\) 0 0
\(969\) −1.71324 −0.0550372
\(970\) 19.8265 0.636592
\(971\) −4.89578 −0.157113 −0.0785565 0.996910i \(-0.525031\pi\)
−0.0785565 + 0.996910i \(0.525031\pi\)
\(972\) −5.23567 −0.167934
\(973\) −15.8885 −0.509363
\(974\) 14.2795 0.457545
\(975\) 1.11907 0.0358389
\(976\) 1.32146 0.0422988
\(977\) −36.1052 −1.15511 −0.577553 0.816353i \(-0.695992\pi\)
−0.577553 + 0.816353i \(0.695992\pi\)
\(978\) 34.9097 1.11629
\(979\) 0 0
\(980\) −10.0375 −0.320637
\(981\) 97.1069 3.10038
\(982\) 14.0094 0.447057
\(983\) −18.7371 −0.597621 −0.298811 0.954312i \(-0.596590\pi\)
−0.298811 + 0.954312i \(0.596590\pi\)
\(984\) −12.9717 −0.413523
\(985\) 12.9313 0.412027
\(986\) −5.31089 −0.169133
\(987\) 42.7453 1.36060
\(988\) 0.633765 0.0201627
\(989\) 34.5764 1.09946
\(990\) 0 0
\(991\) −8.60669 −0.273400 −0.136700 0.990612i \(-0.543650\pi\)
−0.136700 + 0.990612i \(0.543650\pi\)
\(992\) −1.02555 −0.0325612
\(993\) −7.10226 −0.225384
\(994\) 0.518659 0.0164509
\(995\) −32.0793 −1.01698
\(996\) −20.3498 −0.644809
\(997\) −13.3500 −0.422798 −0.211399 0.977400i \(-0.567802\pi\)
−0.211399 + 0.977400i \(0.567802\pi\)
\(998\) −18.1506 −0.574547
\(999\) 17.1031 0.541117
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.1.4 4
11.10 odd 2 4598.2.a.bu.1.4 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.br.1.4 4 1.1 even 1 trivial
4598.2.a.bu.1.4 yes 4 11.10 odd 2