Properties

Label 4598.2.a.bs.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: 4.4.258228.1
Defining polynomial: \( x^{4} - 2x^{3} - 12x^{2} + 6x + 24 \) Copy content Toggle raw display
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 1.4
Root \(-2.34628\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +3.34628 q^{3} +1.00000 q^{4} +2.34628 q^{5} -3.34628 q^{6} +4.77567 q^{7} -1.00000 q^{8} +8.19759 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +3.34628 q^{3} +1.00000 q^{4} +2.34628 q^{5} -3.34628 q^{6} +4.77567 q^{7} -1.00000 q^{8} +8.19759 q^{9} -2.34628 q^{10} +3.34628 q^{12} -1.57808 q^{13} -4.77567 q^{14} +7.85131 q^{15} +1.00000 q^{16} -3.77567 q^{17} -8.19759 q^{18} -1.00000 q^{19} +2.34628 q^{20} +15.9807 q^{21} -2.57808 q^{23} -3.34628 q^{24} +0.505030 q^{25} +1.57808 q^{26} +17.3926 q^{27} +4.77567 q^{28} +4.85131 q^{29} -7.85131 q^{30} +6.69256 q^{31} -1.00000 q^{32} +3.77567 q^{34} +11.2051 q^{35} +8.19759 q^{36} -10.8976 q^{37} +1.00000 q^{38} -5.28070 q^{39} -2.34628 q^{40} -7.00747 q^{41} -15.9807 q^{42} -11.8487 q^{43} +19.2338 q^{45} +2.57808 q^{46} -7.19759 q^{47} +3.34628 q^{48} +15.8070 q^{49} -0.505030 q^{50} -12.6345 q^{51} -1.57808 q^{52} -1.14869 q^{53} -17.3926 q^{54} -4.77567 q^{56} -3.34628 q^{57} -4.85131 q^{58} +4.92436 q^{59} +7.85131 q^{60} +4.04890 q^{61} -6.69256 q^{62} +39.1490 q^{63} +1.00000 q^{64} -3.70262 q^{65} +10.4369 q^{67} -3.77567 q^{68} -8.62698 q^{69} -11.2051 q^{70} -2.31491 q^{71} -8.19759 q^{72} +7.77567 q^{73} +10.8976 q^{74} +1.68997 q^{75} -1.00000 q^{76} +5.28070 q^{78} -0.992527 q^{79} +2.34628 q^{80} +33.6077 q^{81} +7.00747 q^{82} +8.34628 q^{83} +15.9807 q^{84} -8.85878 q^{85} +11.8487 q^{86} +16.2338 q^{87} -11.7000 q^{89} -19.2338 q^{90} -7.53640 q^{91} -2.57808 q^{92} +22.3952 q^{93} +7.19759 q^{94} -2.34628 q^{95} -3.34628 q^{96} -10.0000 q^{97} -15.8070 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 3 q^{7} - 4 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 3 q^{7} - 4 q^{8} + 16 q^{9} + 2 q^{10} + 2 q^{12} - q^{13} + 3 q^{14} + 26 q^{15} + 4 q^{16} + 7 q^{17} - 16 q^{18} - 4 q^{19} - 2 q^{20} + 9 q^{21} - 5 q^{23} - 2 q^{24} + 8 q^{25} + q^{26} + 8 q^{27} - 3 q^{28} + 14 q^{29} - 26 q^{30} + 4 q^{31} - 4 q^{32} - 7 q^{34} + 12 q^{35} + 16 q^{36} + 12 q^{37} + 4 q^{38} - 5 q^{39} + 2 q^{40} - 12 q^{41} - 9 q^{42} - 14 q^{43} - 2 q^{45} + 5 q^{46} - 12 q^{47} + 2 q^{48} + 23 q^{49} - 8 q^{50} - 7 q^{51} - q^{52} - 10 q^{53} - 8 q^{54} + 3 q^{56} - 2 q^{57} - 14 q^{58} + 3 q^{59} + 26 q^{60} - 6 q^{61} - 4 q^{62} + 18 q^{63} + 4 q^{64} - 4 q^{65} + 15 q^{67} + 7 q^{68} - 7 q^{69} - 12 q^{70} - 16 q^{71} - 16 q^{72} + 9 q^{73} - 12 q^{74} - 44 q^{75} - 4 q^{76} + 5 q^{78} - 20 q^{79} - 2 q^{80} + 52 q^{81} + 12 q^{82} + 22 q^{83} + 9 q^{84} - 14 q^{85} + 14 q^{86} - 14 q^{87} - 8 q^{89} + 2 q^{90} - 18 q^{91} - 5 q^{92} + 56 q^{93} + 12 q^{94} + 2 q^{95} - 2 q^{96} - 40 q^{97} - 23 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 3.34628 1.93198 0.965988 0.258587i \(-0.0832570\pi\)
0.965988 + 0.258587i \(0.0832570\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.34628 1.04929 0.524644 0.851322i \(-0.324198\pi\)
0.524644 + 0.851322i \(0.324198\pi\)
\(6\) −3.34628 −1.36611
\(7\) 4.77567 1.80503 0.902517 0.430654i \(-0.141717\pi\)
0.902517 + 0.430654i \(0.141717\pi\)
\(8\) −1.00000 −0.353553
\(9\) 8.19759 2.73253
\(10\) −2.34628 −0.741959
\(11\) 0 0
\(12\) 3.34628 0.965988
\(13\) −1.57808 −0.437681 −0.218840 0.975761i \(-0.570227\pi\)
−0.218840 + 0.975761i \(0.570227\pi\)
\(14\) −4.77567 −1.27635
\(15\) 7.85131 2.02720
\(16\) 1.00000 0.250000
\(17\) −3.77567 −0.915735 −0.457867 0.889020i \(-0.651387\pi\)
−0.457867 + 0.889020i \(0.651387\pi\)
\(18\) −8.19759 −1.93219
\(19\) −1.00000 −0.229416
\(20\) 2.34628 0.524644
\(21\) 15.9807 3.48728
\(22\) 0 0
\(23\) −2.57808 −0.537567 −0.268784 0.963201i \(-0.586622\pi\)
−0.268784 + 0.963201i \(0.586622\pi\)
\(24\) −3.34628 −0.683057
\(25\) 0.505030 0.101006
\(26\) 1.57808 0.309487
\(27\) 17.3926 3.34721
\(28\) 4.77567 0.902517
\(29\) 4.85131 0.900866 0.450433 0.892810i \(-0.351270\pi\)
0.450433 + 0.892810i \(0.351270\pi\)
\(30\) −7.85131 −1.43345
\(31\) 6.69256 1.20202 0.601010 0.799242i \(-0.294765\pi\)
0.601010 + 0.799242i \(0.294765\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 3.77567 0.647522
\(35\) 11.2051 1.89400
\(36\) 8.19759 1.36627
\(37\) −10.8976 −1.79156 −0.895779 0.444499i \(-0.853382\pi\)
−0.895779 + 0.444499i \(0.853382\pi\)
\(38\) 1.00000 0.162221
\(39\) −5.28070 −0.845589
\(40\) −2.34628 −0.370979
\(41\) −7.00747 −1.09438 −0.547192 0.837007i \(-0.684303\pi\)
−0.547192 + 0.837007i \(0.684303\pi\)
\(42\) −15.9807 −2.46588
\(43\) −11.8487 −1.80691 −0.903457 0.428680i \(-0.858979\pi\)
−0.903457 + 0.428680i \(0.858979\pi\)
\(44\) 0 0
\(45\) 19.2338 2.86721
\(46\) 2.57808 0.380117
\(47\) −7.19759 −1.04988 −0.524938 0.851140i \(-0.675912\pi\)
−0.524938 + 0.851140i \(0.675912\pi\)
\(48\) 3.34628 0.482994
\(49\) 15.8070 2.25815
\(50\) −0.505030 −0.0714221
\(51\) −12.6345 −1.76918
\(52\) −1.57808 −0.218840
\(53\) −1.14869 −0.157785 −0.0788923 0.996883i \(-0.525138\pi\)
−0.0788923 + 0.996883i \(0.525138\pi\)
\(54\) −17.3926 −2.36683
\(55\) 0 0
\(56\) −4.77567 −0.638176
\(57\) −3.34628 −0.443226
\(58\) −4.85131 −0.637008
\(59\) 4.92436 0.641097 0.320549 0.947232i \(-0.396133\pi\)
0.320549 + 0.947232i \(0.396133\pi\)
\(60\) 7.85131 1.01360
\(61\) 4.04890 0.518409 0.259204 0.965823i \(-0.416540\pi\)
0.259204 + 0.965823i \(0.416540\pi\)
\(62\) −6.69256 −0.849956
\(63\) 39.1490 4.93231
\(64\) 1.00000 0.125000
\(65\) −3.70262 −0.459254
\(66\) 0 0
\(67\) 10.4369 1.27507 0.637533 0.770423i \(-0.279955\pi\)
0.637533 + 0.770423i \(0.279955\pi\)
\(68\) −3.77567 −0.457867
\(69\) −8.62698 −1.03857
\(70\) −11.2051 −1.33926
\(71\) −2.31491 −0.274730 −0.137365 0.990521i \(-0.543863\pi\)
−0.137365 + 0.990521i \(0.543863\pi\)
\(72\) −8.19759 −0.966095
\(73\) 7.77567 0.910074 0.455037 0.890473i \(-0.349626\pi\)
0.455037 + 0.890473i \(0.349626\pi\)
\(74\) 10.8976 1.26682
\(75\) 1.68997 0.195141
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) 5.28070 0.597922
\(79\) −0.992527 −0.111668 −0.0558340 0.998440i \(-0.517782\pi\)
−0.0558340 + 0.998440i \(0.517782\pi\)
\(80\) 2.34628 0.262322
\(81\) 33.6077 3.73419
\(82\) 7.00747 0.773846
\(83\) 8.34628 0.916123 0.458062 0.888920i \(-0.348544\pi\)
0.458062 + 0.888920i \(0.348544\pi\)
\(84\) 15.9807 1.74364
\(85\) −8.85878 −0.960870
\(86\) 11.8487 1.27768
\(87\) 16.2338 1.74045
\(88\) 0 0
\(89\) −11.7000 −1.24020 −0.620101 0.784522i \(-0.712908\pi\)
−0.620101 + 0.784522i \(0.712908\pi\)
\(90\) −19.2338 −2.02743
\(91\) −7.53640 −0.790029
\(92\) −2.57808 −0.268784
\(93\) 22.3952 2.32227
\(94\) 7.19759 0.742375
\(95\) −2.34628 −0.240723
\(96\) −3.34628 −0.341528
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) −15.8070 −1.59675
\(99\) 0 0
\(100\) 0.505030 0.0505030
\(101\) −1.35634 −0.134961 −0.0674805 0.997721i \(-0.521496\pi\)
−0.0674805 + 0.997721i \(0.521496\pi\)
\(102\) 12.6345 1.25100
\(103\) 2.29997 0.226622 0.113311 0.993560i \(-0.463854\pi\)
0.113311 + 0.993560i \(0.463854\pi\)
\(104\) 1.57808 0.154744
\(105\) 37.4953 3.65916
\(106\) 1.14869 0.111571
\(107\) 14.6583 1.41708 0.708538 0.705673i \(-0.249355\pi\)
0.708538 + 0.705673i \(0.249355\pi\)
\(108\) 17.3926 1.67360
\(109\) 2.92436 0.280103 0.140052 0.990144i \(-0.455273\pi\)
0.140052 + 0.990144i \(0.455273\pi\)
\(110\) 0 0
\(111\) −36.4665 −3.46125
\(112\) 4.77567 0.451259
\(113\) −1.00747 −0.0947751 −0.0473875 0.998877i \(-0.515090\pi\)
−0.0473875 + 0.998877i \(0.515090\pi\)
\(114\) 3.34628 0.313408
\(115\) −6.04890 −0.564063
\(116\) 4.85131 0.450433
\(117\) −12.9365 −1.19598
\(118\) −4.92436 −0.453324
\(119\) −18.0314 −1.65293
\(120\) −7.85131 −0.716723
\(121\) 0 0
\(122\) −4.04890 −0.366570
\(123\) −23.4490 −2.11432
\(124\) 6.69256 0.601010
\(125\) −10.5465 −0.943304
\(126\) −39.1490 −3.48767
\(127\) 1.14122 0.101267 0.0506333 0.998717i \(-0.483876\pi\)
0.0506333 + 0.998717i \(0.483876\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −39.6491 −3.49091
\(130\) 3.70262 0.324741
\(131\) −18.7075 −1.63448 −0.817241 0.576296i \(-0.804498\pi\)
−0.817241 + 0.576296i \(0.804498\pi\)
\(132\) 0 0
\(133\) −4.77567 −0.414103
\(134\) −10.4369 −0.901608
\(135\) 40.8079 3.51218
\(136\) 3.77567 0.323761
\(137\) 12.0731 1.03147 0.515735 0.856748i \(-0.327519\pi\)
0.515735 + 0.856748i \(0.327519\pi\)
\(138\) 8.62698 0.734377
\(139\) 21.7803 1.84738 0.923691 0.383139i \(-0.125157\pi\)
0.923691 + 0.383139i \(0.125157\pi\)
\(140\) 11.2051 0.947001
\(141\) −24.0852 −2.02834
\(142\) 2.31491 0.194263
\(143\) 0 0
\(144\) 8.19759 0.683133
\(145\) 11.3825 0.945268
\(146\) −7.77567 −0.643519
\(147\) 52.8948 4.36269
\(148\) −10.8976 −0.895779
\(149\) 6.38024 0.522689 0.261345 0.965246i \(-0.415834\pi\)
0.261345 + 0.965246i \(0.415834\pi\)
\(150\) −1.68997 −0.137986
\(151\) −2.54387 −0.207017 −0.103509 0.994629i \(-0.533007\pi\)
−0.103509 + 0.994629i \(0.533007\pi\)
\(152\) 1.00000 0.0811107
\(153\) −30.9514 −2.50227
\(154\) 0 0
\(155\) 15.7026 1.26126
\(156\) −5.28070 −0.422795
\(157\) −5.60024 −0.446948 −0.223474 0.974710i \(-0.571740\pi\)
−0.223474 + 0.974710i \(0.571740\pi\)
\(158\) 0.992527 0.0789612
\(159\) −3.84384 −0.304836
\(160\) −2.34628 −0.185490
\(161\) −12.3121 −0.970327
\(162\) −33.6077 −2.64047
\(163\) 7.25396 0.568174 0.284087 0.958798i \(-0.408309\pi\)
0.284087 + 0.958798i \(0.408309\pi\)
\(164\) −7.00747 −0.547192
\(165\) 0 0
\(166\) −8.34628 −0.647797
\(167\) −2.85878 −0.221219 −0.110610 0.993864i \(-0.535280\pi\)
−0.110610 + 0.993864i \(0.535280\pi\)
\(168\) −15.9807 −1.23294
\(169\) −10.5097 −0.808435
\(170\) 8.85878 0.679438
\(171\) −8.19759 −0.626885
\(172\) −11.8487 −0.903457
\(173\) −12.8663 −0.978203 −0.489102 0.872227i \(-0.662675\pi\)
−0.489102 + 0.872227i \(0.662675\pi\)
\(174\) −16.2338 −1.23068
\(175\) 2.41186 0.182319
\(176\) 0 0
\(177\) 16.4783 1.23858
\(178\) 11.7000 0.876955
\(179\) −24.9290 −1.86328 −0.931640 0.363382i \(-0.881622\pi\)
−0.931640 + 0.363382i \(0.881622\pi\)
\(180\) 19.2338 1.43361
\(181\) −17.7952 −1.32271 −0.661355 0.750073i \(-0.730018\pi\)
−0.661355 + 0.750073i \(0.730018\pi\)
\(182\) 7.53640 0.558635
\(183\) 13.5488 1.00155
\(184\) 2.57808 0.190059
\(185\) −25.5689 −1.87986
\(186\) −22.3952 −1.64209
\(187\) 0 0
\(188\) −7.19759 −0.524938
\(189\) 83.0613 6.04182
\(190\) 2.34628 0.170217
\(191\) −4.47829 −0.324038 −0.162019 0.986788i \(-0.551801\pi\)
−0.162019 + 0.986788i \(0.551801\pi\)
\(192\) 3.34628 0.241497
\(193\) −8.00000 −0.575853 −0.287926 0.957653i \(-0.592966\pi\)
−0.287926 + 0.957653i \(0.592966\pi\)
\(194\) 10.0000 0.717958
\(195\) −12.3900 −0.887267
\(196\) 15.8070 1.12907
\(197\) 12.5614 0.894963 0.447481 0.894293i \(-0.352321\pi\)
0.447481 + 0.894293i \(0.352321\pi\)
\(198\) 0 0
\(199\) −0.750666 −0.0532133 −0.0266066 0.999646i \(-0.508470\pi\)
−0.0266066 + 0.999646i \(0.508470\pi\)
\(200\) −0.505030 −0.0357110
\(201\) 34.9247 2.46340
\(202\) 1.35634 0.0954318
\(203\) 23.1683 1.62609
\(204\) −12.6345 −0.884589
\(205\) −16.4415 −1.14832
\(206\) −2.29997 −0.160246
\(207\) −21.1341 −1.46892
\(208\) −1.57808 −0.109420
\(209\) 0 0
\(210\) −37.4953 −2.58742
\(211\) −4.66867 −0.321404 −0.160702 0.987003i \(-0.551376\pi\)
−0.160702 + 0.987003i \(0.551376\pi\)
\(212\) −1.14869 −0.0788923
\(213\) −7.74635 −0.530771
\(214\) −14.6583 −1.00202
\(215\) −27.8004 −1.89597
\(216\) −17.3926 −1.18342
\(217\) 31.9615 2.16969
\(218\) −2.92436 −0.198063
\(219\) 26.0196 1.75824
\(220\) 0 0
\(221\) 5.95832 0.400800
\(222\) 36.4665 2.44747
\(223\) 23.8663 1.59820 0.799101 0.601196i \(-0.205309\pi\)
0.799101 + 0.601196i \(0.205309\pi\)
\(224\) −4.77567 −0.319088
\(225\) 4.14003 0.276002
\(226\) 1.00747 0.0670161
\(227\) −13.5097 −0.896668 −0.448334 0.893866i \(-0.647982\pi\)
−0.448334 + 0.893866i \(0.647982\pi\)
\(228\) −3.34628 −0.221613
\(229\) −8.22896 −0.543785 −0.271892 0.962328i \(-0.587649\pi\)
−0.271892 + 0.962328i \(0.587649\pi\)
\(230\) 6.04890 0.398853
\(231\) 0 0
\(232\) −4.85131 −0.318504
\(233\) 0.490085 0.0321065 0.0160533 0.999871i \(-0.494890\pi\)
0.0160533 + 0.999871i \(0.494890\pi\)
\(234\) 12.9365 0.845683
\(235\) −16.8876 −1.10162
\(236\) 4.92436 0.320549
\(237\) −3.32127 −0.215740
\(238\) 18.0314 1.16880
\(239\) −20.5364 −1.32839 −0.664195 0.747560i \(-0.731225\pi\)
−0.664195 + 0.747560i \(0.731225\pi\)
\(240\) 7.85131 0.506800
\(241\) 19.4654 1.25388 0.626938 0.779069i \(-0.284308\pi\)
0.626938 + 0.779069i \(0.284308\pi\)
\(242\) 0 0
\(243\) 60.2831 3.86716
\(244\) 4.04890 0.259204
\(245\) 37.0877 2.36945
\(246\) 23.4490 1.49505
\(247\) 1.57808 0.100411
\(248\) −6.69256 −0.424978
\(249\) 27.9290 1.76993
\(250\) 10.5465 0.667017
\(251\) −9.84872 −0.621646 −0.310823 0.950468i \(-0.600605\pi\)
−0.310823 + 0.950468i \(0.600605\pi\)
\(252\) 39.1490 2.46616
\(253\) 0 0
\(254\) −1.14122 −0.0716063
\(255\) −29.6440 −1.85638
\(256\) 1.00000 0.0625000
\(257\) 11.2540 0.702003 0.351001 0.936375i \(-0.385841\pi\)
0.351001 + 0.936375i \(0.385841\pi\)
\(258\) 39.6491 2.46845
\(259\) −52.0435 −3.23382
\(260\) −3.70262 −0.229627
\(261\) 39.7691 2.46164
\(262\) 18.7075 1.15575
\(263\) −3.49008 −0.215208 −0.107604 0.994194i \(-0.534318\pi\)
−0.107604 + 0.994194i \(0.534318\pi\)
\(264\) 0 0
\(265\) −2.69515 −0.165562
\(266\) 4.77567 0.292815
\(267\) −39.1516 −2.39604
\(268\) 10.4369 0.637533
\(269\) −20.1737 −1.23001 −0.615006 0.788522i \(-0.710846\pi\)
−0.615006 + 0.788522i \(0.710846\pi\)
\(270\) −40.8079 −2.48349
\(271\) −0.239274 −0.0145349 −0.00726743 0.999974i \(-0.502313\pi\)
−0.00726743 + 0.999974i \(0.502313\pi\)
\(272\) −3.77567 −0.228934
\(273\) −25.2189 −1.52632
\(274\) −12.0731 −0.729360
\(275\) 0 0
\(276\) −8.62698 −0.519283
\(277\) 13.1901 0.792517 0.396259 0.918139i \(-0.370308\pi\)
0.396259 + 0.918139i \(0.370308\pi\)
\(278\) −21.7803 −1.30630
\(279\) 54.8629 3.28455
\(280\) −11.2051 −0.669631
\(281\) −6.54387 −0.390375 −0.195187 0.980766i \(-0.562531\pi\)
−0.195187 + 0.980766i \(0.562531\pi\)
\(282\) 24.0852 1.43425
\(283\) −9.08774 −0.540210 −0.270105 0.962831i \(-0.587058\pi\)
−0.270105 + 0.962831i \(0.587058\pi\)
\(284\) −2.31491 −0.137365
\(285\) −7.85131 −0.465071
\(286\) 0 0
\(287\) −33.4654 −1.97540
\(288\) −8.19759 −0.483048
\(289\) −2.74430 −0.161430
\(290\) −11.3825 −0.668405
\(291\) −33.4628 −1.96162
\(292\) 7.77567 0.455037
\(293\) −20.2051 −1.18039 −0.590196 0.807260i \(-0.700950\pi\)
−0.590196 + 0.807260i \(0.700950\pi\)
\(294\) −52.8948 −3.08489
\(295\) 11.5539 0.672696
\(296\) 10.8976 0.633411
\(297\) 0 0
\(298\) −6.38024 −0.369597
\(299\) 4.06842 0.235283
\(300\) 1.68997 0.0975706
\(301\) −56.5856 −3.26154
\(302\) 2.54387 0.146383
\(303\) −4.53870 −0.260741
\(304\) −1.00000 −0.0573539
\(305\) 9.49985 0.543960
\(306\) 30.9514 1.76937
\(307\) 20.2514 1.15581 0.577904 0.816105i \(-0.303871\pi\)
0.577904 + 0.816105i \(0.303871\pi\)
\(308\) 0 0
\(309\) 7.69633 0.437829
\(310\) −15.7026 −0.891849
\(311\) 29.3897 1.66654 0.833270 0.552866i \(-0.186466\pi\)
0.833270 + 0.552866i \(0.186466\pi\)
\(312\) 5.28070 0.298961
\(313\) −0.229213 −0.0129559 −0.00647796 0.999979i \(-0.502062\pi\)
−0.00647796 + 0.999979i \(0.502062\pi\)
\(314\) 5.60024 0.316040
\(315\) 91.8545 5.17542
\(316\) −0.992527 −0.0558340
\(317\) −19.6908 −1.10595 −0.552974 0.833199i \(-0.686507\pi\)
−0.552974 + 0.833199i \(0.686507\pi\)
\(318\) 3.84384 0.215552
\(319\) 0 0
\(320\) 2.34628 0.131161
\(321\) 49.0509 2.73776
\(322\) 12.3121 0.686125
\(323\) 3.77567 0.210084
\(324\) 33.6077 1.86710
\(325\) −0.796979 −0.0442084
\(326\) −7.25396 −0.401760
\(327\) 9.78573 0.541152
\(328\) 7.00747 0.386923
\(329\) −34.3733 −1.89506
\(330\) 0 0
\(331\) −16.9707 −0.932793 −0.466396 0.884576i \(-0.654448\pi\)
−0.466396 + 0.884576i \(0.654448\pi\)
\(332\) 8.34628 0.458062
\(333\) −89.3343 −4.89549
\(334\) 2.85878 0.156426
\(335\) 24.4878 1.33791
\(336\) 15.9807 0.871821
\(337\) 8.01236 0.436461 0.218230 0.975897i \(-0.429972\pi\)
0.218230 + 0.975897i \(0.429972\pi\)
\(338\) 10.5097 0.571650
\(339\) −3.37129 −0.183103
\(340\) −8.85878 −0.480435
\(341\) 0 0
\(342\) 8.19759 0.443275
\(343\) 42.0595 2.27100
\(344\) 11.8487 0.638840
\(345\) −20.2413 −1.08976
\(346\) 12.8663 0.691694
\(347\) 27.7613 1.49030 0.745152 0.666895i \(-0.232377\pi\)
0.745152 + 0.666895i \(0.232377\pi\)
\(348\) 16.2338 0.870225
\(349\) 11.4886 0.614971 0.307486 0.951553i \(-0.400512\pi\)
0.307486 + 0.951553i \(0.400512\pi\)
\(350\) −2.41186 −0.128919
\(351\) −27.4469 −1.46501
\(352\) 0 0
\(353\) −26.2853 −1.39903 −0.699514 0.714619i \(-0.746600\pi\)
−0.699514 + 0.714619i \(0.746600\pi\)
\(354\) −16.4783 −0.875811
\(355\) −5.43143 −0.288271
\(356\) −11.7000 −0.620101
\(357\) −60.3380 −3.19343
\(358\) 24.9290 1.31754
\(359\) −18.0731 −0.953859 −0.476930 0.878942i \(-0.658250\pi\)
−0.476930 + 0.878942i \(0.658250\pi\)
\(360\) −19.2338 −1.01371
\(361\) 1.00000 0.0526316
\(362\) 17.7952 0.935297
\(363\) 0 0
\(364\) −7.53640 −0.395015
\(365\) 18.2439 0.954930
\(366\) −13.5488 −0.708205
\(367\) 33.9051 1.76983 0.884916 0.465751i \(-0.154216\pi\)
0.884916 + 0.465751i \(0.154216\pi\)
\(368\) −2.57808 −0.134392
\(369\) −57.4444 −2.99044
\(370\) 25.5689 1.32926
\(371\) −5.48576 −0.284807
\(372\) 22.3952 1.16114
\(373\) −10.9342 −0.566150 −0.283075 0.959098i \(-0.591354\pi\)
−0.283075 + 0.959098i \(0.591354\pi\)
\(374\) 0 0
\(375\) −35.2914 −1.82244
\(376\) 7.19759 0.371187
\(377\) −7.65576 −0.394292
\(378\) −83.0613 −4.27221
\(379\) −24.8395 −1.27592 −0.637960 0.770069i \(-0.720222\pi\)
−0.637960 + 0.770069i \(0.720222\pi\)
\(380\) −2.34628 −0.120362
\(381\) 3.81883 0.195645
\(382\) 4.47829 0.229129
\(383\) −2.82372 −0.144285 −0.0721426 0.997394i \(-0.522984\pi\)
−0.0721426 + 0.997394i \(0.522984\pi\)
\(384\) −3.34628 −0.170764
\(385\) 0 0
\(386\) 8.00000 0.407189
\(387\) −97.1310 −4.93744
\(388\) −10.0000 −0.507673
\(389\) −7.03884 −0.356883 −0.178442 0.983950i \(-0.557106\pi\)
−0.178442 + 0.983950i \(0.557106\pi\)
\(390\) 12.3900 0.627392
\(391\) 9.73399 0.492269
\(392\) −15.8070 −0.798376
\(393\) −62.6006 −3.15778
\(394\) −12.5614 −0.632834
\(395\) −2.32875 −0.117172
\(396\) 0 0
\(397\) 4.67761 0.234763 0.117381 0.993087i \(-0.462550\pi\)
0.117381 + 0.993087i \(0.462550\pi\)
\(398\) 0.750666 0.0376275
\(399\) −15.9807 −0.800037
\(400\) 0.505030 0.0252515
\(401\) 14.5588 0.727033 0.363516 0.931588i \(-0.381576\pi\)
0.363516 + 0.931588i \(0.381576\pi\)
\(402\) −34.9247 −1.74188
\(403\) −10.5614 −0.526101
\(404\) −1.35634 −0.0674805
\(405\) 78.8531 3.91824
\(406\) −23.1683 −1.14982
\(407\) 0 0
\(408\) 12.6345 0.625499
\(409\) 9.71757 0.480503 0.240251 0.970711i \(-0.422770\pi\)
0.240251 + 0.970711i \(0.422770\pi\)
\(410\) 16.4415 0.811987
\(411\) 40.3998 1.99278
\(412\) 2.29997 0.113311
\(413\) 23.5171 1.15720
\(414\) 21.1341 1.03868
\(415\) 19.5827 0.961277
\(416\) 1.57808 0.0773718
\(417\) 72.8830 3.56910
\(418\) 0 0
\(419\) 6.13227 0.299581 0.149790 0.988718i \(-0.452140\pi\)
0.149790 + 0.988718i \(0.452140\pi\)
\(420\) 37.4953 1.82958
\(421\) −3.79957 −0.185180 −0.0925898 0.995704i \(-0.529515\pi\)
−0.0925898 + 0.995704i \(0.529515\pi\)
\(422\) 4.66867 0.227267
\(423\) −59.0029 −2.86882
\(424\) 1.14869 0.0557853
\(425\) −1.90683 −0.0924948
\(426\) 7.74635 0.375312
\(427\) 19.3362 0.935745
\(428\) 14.6583 0.708538
\(429\) 0 0
\(430\) 27.8004 1.34066
\(431\) −8.69515 −0.418831 −0.209415 0.977827i \(-0.567156\pi\)
−0.209415 + 0.977827i \(0.567156\pi\)
\(432\) 17.3926 0.836802
\(433\) 3.30744 0.158945 0.0794727 0.996837i \(-0.474676\pi\)
0.0794727 + 0.996837i \(0.474676\pi\)
\(434\) −31.9615 −1.53420
\(435\) 38.0891 1.82623
\(436\) 2.92436 0.140052
\(437\) 2.57808 0.123326
\(438\) −26.0196 −1.24326
\(439\) −4.54128 −0.216744 −0.108372 0.994110i \(-0.534564\pi\)
−0.108372 + 0.994110i \(0.534564\pi\)
\(440\) 0 0
\(441\) 129.580 6.17046
\(442\) −5.95832 −0.283408
\(443\) 17.8637 0.848728 0.424364 0.905492i \(-0.360498\pi\)
0.424364 + 0.905492i \(0.360498\pi\)
\(444\) −36.4665 −1.73062
\(445\) −27.4516 −1.30133
\(446\) −23.8663 −1.13010
\(447\) 21.3501 1.00982
\(448\) 4.77567 0.225629
\(449\) −21.8487 −1.03110 −0.515552 0.856858i \(-0.672413\pi\)
−0.515552 + 0.856858i \(0.672413\pi\)
\(450\) −4.14003 −0.195163
\(451\) 0 0
\(452\) −1.00747 −0.0473875
\(453\) −8.51250 −0.399952
\(454\) 13.5097 0.634040
\(455\) −17.6825 −0.828968
\(456\) 3.34628 0.156704
\(457\) 5.73424 0.268237 0.134118 0.990965i \(-0.457180\pi\)
0.134118 + 0.990965i \(0.457180\pi\)
\(458\) 8.22896 0.384514
\(459\) −65.6687 −3.06515
\(460\) −6.04890 −0.282031
\(461\) −12.5752 −0.585687 −0.292844 0.956160i \(-0.594602\pi\)
−0.292844 + 0.956160i \(0.594602\pi\)
\(462\) 0 0
\(463\) 19.2853 0.896265 0.448133 0.893967i \(-0.352089\pi\)
0.448133 + 0.893967i \(0.352089\pi\)
\(464\) 4.85131 0.225216
\(465\) 52.5454 2.43673
\(466\) −0.490085 −0.0227027
\(467\) 15.8004 0.731156 0.365578 0.930781i \(-0.380871\pi\)
0.365578 + 0.930781i \(0.380871\pi\)
\(468\) −12.9365 −0.597988
\(469\) 49.8430 2.30154
\(470\) 16.8876 0.778965
\(471\) −18.7400 −0.863493
\(472\) −4.92436 −0.226662
\(473\) 0 0
\(474\) 3.32127 0.152551
\(475\) −0.505030 −0.0231724
\(476\) −18.0314 −0.826466
\(477\) −9.41649 −0.431151
\(478\) 20.5364 0.939313
\(479\) 17.0149 0.777433 0.388716 0.921357i \(-0.372919\pi\)
0.388716 + 0.921357i \(0.372919\pi\)
\(480\) −7.85131 −0.358362
\(481\) 17.1973 0.784131
\(482\) −19.4654 −0.886624
\(483\) −41.1996 −1.87465
\(484\) 0 0
\(485\) −23.4628 −1.06539
\(486\) −60.2831 −2.73449
\(487\) 12.8387 0.581775 0.290888 0.956757i \(-0.406049\pi\)
0.290888 + 0.956757i \(0.406049\pi\)
\(488\) −4.04890 −0.183285
\(489\) 24.2738 1.09770
\(490\) −37.0877 −1.67545
\(491\) 21.1654 0.955182 0.477591 0.878582i \(-0.341510\pi\)
0.477591 + 0.878582i \(0.341510\pi\)
\(492\) −23.4490 −1.05716
\(493\) −18.3170 −0.824954
\(494\) −1.57808 −0.0710012
\(495\) 0 0
\(496\) 6.69256 0.300505
\(497\) −11.0553 −0.495896
\(498\) −27.9290 −1.25153
\(499\) −5.35634 −0.239783 −0.119891 0.992787i \(-0.538255\pi\)
−0.119891 + 0.992787i \(0.538255\pi\)
\(500\) −10.5465 −0.471652
\(501\) −9.56629 −0.427390
\(502\) 9.84872 0.439570
\(503\) 13.8634 0.618139 0.309070 0.951039i \(-0.399982\pi\)
0.309070 + 0.951039i \(0.399982\pi\)
\(504\) −39.1490 −1.74384
\(505\) −3.18235 −0.141613
\(506\) 0 0
\(507\) −35.1683 −1.56188
\(508\) 1.14122 0.0506333
\(509\) 28.9902 1.28497 0.642485 0.766298i \(-0.277903\pi\)
0.642485 + 0.766298i \(0.277903\pi\)
\(510\) 29.6440 1.31266
\(511\) 37.1341 1.64271
\(512\) −1.00000 −0.0441942
\(513\) −17.3926 −0.767902
\(514\) −11.2540 −0.496391
\(515\) 5.39637 0.237792
\(516\) −39.6491 −1.74546
\(517\) 0 0
\(518\) 52.0435 2.28666
\(519\) −43.0541 −1.88987
\(520\) 3.70262 0.162371
\(521\) 24.3417 1.06643 0.533215 0.845980i \(-0.320984\pi\)
0.533215 + 0.845980i \(0.320984\pi\)
\(522\) −39.7691 −1.74064
\(523\) −37.2347 −1.62816 −0.814080 0.580753i \(-0.802758\pi\)
−0.814080 + 0.580753i \(0.802758\pi\)
\(524\) −18.7075 −0.817241
\(525\) 8.07075 0.352237
\(526\) 3.49008 0.152175
\(527\) −25.2689 −1.10073
\(528\) 0 0
\(529\) −16.3535 −0.711022
\(530\) 2.69515 0.117070
\(531\) 40.3679 1.75182
\(532\) −4.77567 −0.207052
\(533\) 11.0584 0.478991
\(534\) 39.1516 1.69425
\(535\) 34.3926 1.48692
\(536\) −10.4369 −0.450804
\(537\) −83.4194 −3.59981
\(538\) 20.1737 0.869750
\(539\) 0 0
\(540\) 40.8079 1.75609
\(541\) 4.31750 0.185624 0.0928119 0.995684i \(-0.470414\pi\)
0.0928119 + 0.995684i \(0.470414\pi\)
\(542\) 0.239274 0.0102777
\(543\) −59.5479 −2.55544
\(544\) 3.77567 0.161881
\(545\) 6.86137 0.293909
\(546\) 25.2189 1.07927
\(547\) 25.0104 1.06937 0.534683 0.845053i \(-0.320431\pi\)
0.534683 + 0.845053i \(0.320431\pi\)
\(548\) 12.0731 0.515735
\(549\) 33.1912 1.41657
\(550\) 0 0
\(551\) −4.85131 −0.206673
\(552\) 8.62698 0.367189
\(553\) −4.73998 −0.201565
\(554\) −13.1901 −0.560394
\(555\) −85.5606 −3.63185
\(556\) 21.7803 0.923691
\(557\) 31.3667 1.32905 0.664525 0.747266i \(-0.268634\pi\)
0.664525 + 0.747266i \(0.268634\pi\)
\(558\) −54.8629 −2.32253
\(559\) 18.6982 0.790852
\(560\) 11.2051 0.473500
\(561\) 0 0
\(562\) 6.54387 0.276037
\(563\) −11.4924 −0.484346 −0.242173 0.970233i \(-0.577860\pi\)
−0.242173 + 0.970233i \(0.577860\pi\)
\(564\) −24.0852 −1.01417
\(565\) −2.36381 −0.0994464
\(566\) 9.08774 0.381986
\(567\) 160.499 6.74034
\(568\) 2.31491 0.0971316
\(569\) 18.5614 0.778135 0.389067 0.921209i \(-0.372797\pi\)
0.389067 + 0.921209i \(0.372797\pi\)
\(570\) 7.85131 0.328855
\(571\) 36.2099 1.51534 0.757670 0.652638i \(-0.226338\pi\)
0.757670 + 0.652638i \(0.226338\pi\)
\(572\) 0 0
\(573\) −14.9856 −0.626033
\(574\) 33.4654 1.39682
\(575\) −1.30201 −0.0542975
\(576\) 8.19759 0.341566
\(577\) 29.5560 1.23043 0.615216 0.788359i \(-0.289069\pi\)
0.615216 + 0.788359i \(0.289069\pi\)
\(578\) 2.74430 0.114148
\(579\) −26.7702 −1.11253
\(580\) 11.3825 0.472634
\(581\) 39.8591 1.65363
\(582\) 33.4628 1.38708
\(583\) 0 0
\(584\) −7.77567 −0.321760
\(585\) −30.3526 −1.25492
\(586\) 20.2051 0.834663
\(587\) −33.4340 −1.37997 −0.689985 0.723824i \(-0.742383\pi\)
−0.689985 + 0.723824i \(0.742383\pi\)
\(588\) 52.8948 2.18134
\(589\) −6.69256 −0.275762
\(590\) −11.5539 −0.475668
\(591\) 42.0340 1.72905
\(592\) −10.8976 −0.447890
\(593\) −15.2753 −0.627280 −0.313640 0.949542i \(-0.601549\pi\)
−0.313640 + 0.949542i \(0.601549\pi\)
\(594\) 0 0
\(595\) −42.3066 −1.73440
\(596\) 6.38024 0.261345
\(597\) −2.51194 −0.102807
\(598\) −4.06842 −0.166370
\(599\) 13.3316 0.544716 0.272358 0.962196i \(-0.412196\pi\)
0.272358 + 0.962196i \(0.412196\pi\)
\(600\) −1.68997 −0.0689928
\(601\) −48.4729 −1.97725 −0.988625 0.150404i \(-0.951943\pi\)
−0.988625 + 0.150404i \(0.951943\pi\)
\(602\) 56.5856 2.30626
\(603\) 85.5571 3.48416
\(604\) −2.54387 −0.103509
\(605\) 0 0
\(606\) 4.53870 0.184372
\(607\) −43.4176 −1.76227 −0.881133 0.472869i \(-0.843219\pi\)
−0.881133 + 0.472869i \(0.843219\pi\)
\(608\) 1.00000 0.0405554
\(609\) 77.5275 3.14157
\(610\) −9.49985 −0.384638
\(611\) 11.3584 0.459511
\(612\) −30.9514 −1.25114
\(613\) 44.8876 1.81299 0.906496 0.422215i \(-0.138747\pi\)
0.906496 + 0.422215i \(0.138747\pi\)
\(614\) −20.2514 −0.817279
\(615\) −55.0178 −2.21853
\(616\) 0 0
\(617\) −17.2275 −0.693552 −0.346776 0.937948i \(-0.612724\pi\)
−0.346776 + 0.937948i \(0.612724\pi\)
\(618\) −7.69633 −0.309592
\(619\) 17.8004 0.715459 0.357730 0.933825i \(-0.383551\pi\)
0.357730 + 0.933825i \(0.383551\pi\)
\(620\) 15.7026 0.630632
\(621\) −44.8395 −1.79935
\(622\) −29.3897 −1.17842
\(623\) −55.8755 −2.23861
\(624\) −5.28070 −0.211397
\(625\) −27.2701 −1.09080
\(626\) 0.229213 0.00916121
\(627\) 0 0
\(628\) −5.60024 −0.223474
\(629\) 41.1458 1.64059
\(630\) −91.8545 −3.65957
\(631\) 14.4202 0.574059 0.287029 0.957922i \(-0.407332\pi\)
0.287029 + 0.957922i \(0.407332\pi\)
\(632\) 0.992527 0.0394806
\(633\) −15.6227 −0.620945
\(634\) 19.6908 0.782023
\(635\) 2.67761 0.106258
\(636\) −3.84384 −0.152418
\(637\) −24.9448 −0.988349
\(638\) 0 0
\(639\) −18.9767 −0.750707
\(640\) −2.34628 −0.0927449
\(641\) −29.1386 −1.15091 −0.575453 0.817835i \(-0.695174\pi\)
−0.575453 + 0.817835i \(0.695174\pi\)
\(642\) −49.0509 −1.93589
\(643\) 37.4979 1.47877 0.739386 0.673282i \(-0.235116\pi\)
0.739386 + 0.673282i \(0.235116\pi\)
\(644\) −12.3121 −0.485163
\(645\) −93.0280 −3.66297
\(646\) −3.77567 −0.148552
\(647\) 40.4294 1.58945 0.794723 0.606973i \(-0.207616\pi\)
0.794723 + 0.606973i \(0.207616\pi\)
\(648\) −33.6077 −1.32024
\(649\) 0 0
\(650\) 0.796979 0.0312601
\(651\) 106.952 4.19178
\(652\) 7.25396 0.284087
\(653\) 33.8102 1.32310 0.661548 0.749903i \(-0.269900\pi\)
0.661548 + 0.749903i \(0.269900\pi\)
\(654\) −9.78573 −0.382652
\(655\) −43.8930 −1.71504
\(656\) −7.00747 −0.273596
\(657\) 63.7418 2.48680
\(658\) 34.3733 1.34001
\(659\) 25.2586 0.983935 0.491968 0.870614i \(-0.336278\pi\)
0.491968 + 0.870614i \(0.336278\pi\)
\(660\) 0 0
\(661\) −3.42965 −0.133398 −0.0666989 0.997773i \(-0.521247\pi\)
−0.0666989 + 0.997773i \(0.521247\pi\)
\(662\) 16.9707 0.659584
\(663\) 19.9382 0.774335
\(664\) −8.34628 −0.323898
\(665\) −11.2051 −0.434514
\(666\) 89.3343 3.46163
\(667\) −12.5071 −0.484276
\(668\) −2.85878 −0.110610
\(669\) 79.8632 3.08769
\(670\) −24.4878 −0.946047
\(671\) 0 0
\(672\) −15.9807 −0.616470
\(673\) −21.4855 −0.828206 −0.414103 0.910230i \(-0.635905\pi\)
−0.414103 + 0.910230i \(0.635905\pi\)
\(674\) −8.01236 −0.308624
\(675\) 8.78378 0.338088
\(676\) −10.5097 −0.404218
\(677\) −33.2825 −1.27915 −0.639575 0.768729i \(-0.720890\pi\)
−0.639575 + 0.768729i \(0.720890\pi\)
\(678\) 3.37129 0.129473
\(679\) −47.7567 −1.83273
\(680\) 8.85878 0.339719
\(681\) −45.2071 −1.73234
\(682\) 0 0
\(683\) −29.1176 −1.11416 −0.557078 0.830460i \(-0.688077\pi\)
−0.557078 + 0.830460i \(0.688077\pi\)
\(684\) −8.19759 −0.313443
\(685\) 28.3268 1.08231
\(686\) −42.0595 −1.60584
\(687\) −27.5364 −1.05058
\(688\) −11.8487 −0.451728
\(689\) 1.81273 0.0690593
\(690\) 20.2413 0.770574
\(691\) −43.2143 −1.64395 −0.821975 0.569523i \(-0.807128\pi\)
−0.821975 + 0.569523i \(0.807128\pi\)
\(692\) −12.8663 −0.489102
\(693\) 0 0
\(694\) −27.7613 −1.05380
\(695\) 51.1027 1.93844
\(696\) −16.2338 −0.615342
\(697\) 26.4579 1.00217
\(698\) −11.4886 −0.434850
\(699\) 1.63996 0.0620290
\(700\) 2.41186 0.0911597
\(701\) −30.8680 −1.16587 −0.582935 0.812519i \(-0.698096\pi\)
−0.582935 + 0.812519i \(0.698096\pi\)
\(702\) 27.4469 1.03592
\(703\) 10.8976 0.411012
\(704\) 0 0
\(705\) −56.5105 −2.12831
\(706\) 26.2853 0.989261
\(707\) −6.47744 −0.243609
\(708\) 16.4783 0.619292
\(709\) 8.14610 0.305933 0.152967 0.988231i \(-0.451117\pi\)
0.152967 + 0.988231i \(0.451117\pi\)
\(710\) 5.43143 0.203838
\(711\) −8.13633 −0.305136
\(712\) 11.7000 0.438477
\(713\) −17.2540 −0.646166
\(714\) 60.3380 2.25809
\(715\) 0 0
\(716\) −24.9290 −0.931640
\(717\) −68.7205 −2.56642
\(718\) 18.0731 0.674480
\(719\) 43.5545 1.62431 0.812154 0.583443i \(-0.198295\pi\)
0.812154 + 0.583443i \(0.198295\pi\)
\(720\) 19.2338 0.716803
\(721\) 10.9839 0.409061
\(722\) −1.00000 −0.0372161
\(723\) 65.1366 2.42246
\(724\) −17.7952 −0.661355
\(725\) 2.45006 0.0909929
\(726\) 0 0
\(727\) −35.4415 −1.31445 −0.657226 0.753693i \(-0.728270\pi\)
−0.657226 + 0.753693i \(0.728270\pi\)
\(728\) 7.53640 0.279317
\(729\) 100.901 3.73707
\(730\) −18.2439 −0.675237
\(731\) 44.7369 1.65465
\(732\) 13.5488 0.500776
\(733\) 4.60970 0.170263 0.0851317 0.996370i \(-0.472869\pi\)
0.0851317 + 0.996370i \(0.472869\pi\)
\(734\) −33.9051 −1.25146
\(735\) 124.106 4.57772
\(736\) 2.57808 0.0950293
\(737\) 0 0
\(738\) 57.4444 2.11456
\(739\) −19.1423 −0.704162 −0.352081 0.935970i \(-0.614526\pi\)
−0.352081 + 0.935970i \(0.614526\pi\)
\(740\) −25.5689 −0.939931
\(741\) 5.28070 0.193991
\(742\) 5.48576 0.201389
\(743\) 41.0970 1.50770 0.753851 0.657045i \(-0.228194\pi\)
0.753851 + 0.657045i \(0.228194\pi\)
\(744\) −22.3952 −0.821047
\(745\) 14.9698 0.548452
\(746\) 10.9342 0.400328
\(747\) 68.4194 2.50333
\(748\) 0 0
\(749\) 70.0035 2.55787
\(750\) 35.2914 1.28866
\(751\) −38.8882 −1.41905 −0.709525 0.704681i \(-0.751090\pi\)
−0.709525 + 0.704681i \(0.751090\pi\)
\(752\) −7.19759 −0.262469
\(753\) −32.9566 −1.20100
\(754\) 7.65576 0.278806
\(755\) −5.96863 −0.217221
\(756\) 83.0613 3.02091
\(757\) 25.2051 0.916094 0.458047 0.888928i \(-0.348549\pi\)
0.458047 + 0.888928i \(0.348549\pi\)
\(758\) 24.8395 0.902212
\(759\) 0 0
\(760\) 2.34628 0.0851085
\(761\) −17.9247 −0.649769 −0.324884 0.945754i \(-0.605325\pi\)
−0.324884 + 0.945754i \(0.605325\pi\)
\(762\) −3.81883 −0.138342
\(763\) 13.9658 0.505596
\(764\) −4.47829 −0.162019
\(765\) −72.6207 −2.62561
\(766\) 2.82372 0.102025
\(767\) −7.77104 −0.280596
\(768\) 3.34628 0.120748
\(769\) 17.4101 0.627825 0.313913 0.949452i \(-0.398360\pi\)
0.313913 + 0.949452i \(0.398360\pi\)
\(770\) 0 0
\(771\) 37.6589 1.35625
\(772\) −8.00000 −0.287926
\(773\) 42.5071 1.52887 0.764437 0.644699i \(-0.223017\pi\)
0.764437 + 0.644699i \(0.223017\pi\)
\(774\) 97.1310 3.49130
\(775\) 3.37994 0.121411
\(776\) 10.0000 0.358979
\(777\) −174.152 −6.24767
\(778\) 7.03884 0.252355
\(779\) 7.00747 0.251069
\(780\) −12.3900 −0.443633
\(781\) 0 0
\(782\) −9.73399 −0.348087
\(783\) 84.3769 3.01538
\(784\) 15.8070 0.564537
\(785\) −13.1397 −0.468977
\(786\) 62.6006 2.23289
\(787\) −0.289907 −0.0103341 −0.00516703 0.999987i \(-0.501645\pi\)
−0.00516703 + 0.999987i \(0.501645\pi\)
\(788\) 12.5614 0.447481
\(789\) −11.6788 −0.415776
\(790\) 2.32875 0.0828531
\(791\) −4.81136 −0.171072
\(792\) 0 0
\(793\) −6.38949 −0.226898
\(794\) −4.67761 −0.166002
\(795\) −9.01872 −0.319861
\(796\) −0.750666 −0.0266066
\(797\) 20.2557 0.717494 0.358747 0.933435i \(-0.383204\pi\)
0.358747 + 0.933435i \(0.383204\pi\)
\(798\) 15.9807 0.565712
\(799\) 27.1757 0.961408
\(800\) −0.505030 −0.0178555
\(801\) −95.9121 −3.38889
\(802\) −14.5588 −0.514090
\(803\) 0 0
\(804\) 34.9247 1.23170
\(805\) −28.8876 −1.01815
\(806\) 10.5614 0.372010
\(807\) −67.5068 −2.37635
\(808\) 1.35634 0.0477159
\(809\) −11.8902 −0.418035 −0.209018 0.977912i \(-0.567027\pi\)
−0.209018 + 0.977912i \(0.567027\pi\)
\(810\) −78.8531 −2.77062
\(811\) 37.3725 1.31232 0.656162 0.754620i \(-0.272179\pi\)
0.656162 + 0.754620i \(0.272179\pi\)
\(812\) 23.1683 0.813047
\(813\) −0.800677 −0.0280810
\(814\) 0 0
\(815\) 17.0198 0.596179
\(816\) −12.6345 −0.442294
\(817\) 11.8487 0.414534
\(818\) −9.71757 −0.339767
\(819\) −61.7803 −2.15878
\(820\) −16.4415 −0.574162
\(821\) −15.7165 −0.548508 −0.274254 0.961657i \(-0.588431\pi\)
−0.274254 + 0.961657i \(0.588431\pi\)
\(822\) −40.3998 −1.40911
\(823\) 41.3066 1.43986 0.719929 0.694047i \(-0.244174\pi\)
0.719929 + 0.694047i \(0.244174\pi\)
\(824\) −2.29997 −0.0801232
\(825\) 0 0
\(826\) −23.5171 −0.818266
\(827\) −15.7406 −0.547354 −0.273677 0.961822i \(-0.588240\pi\)
−0.273677 + 0.961822i \(0.588240\pi\)
\(828\) −21.1341 −0.734459
\(829\) −0.255696 −0.00888069 −0.00444034 0.999990i \(-0.501413\pi\)
−0.00444034 + 0.999990i \(0.501413\pi\)
\(830\) −19.5827 −0.679726
\(831\) 44.1378 1.53112
\(832\) −1.57808 −0.0547101
\(833\) −59.6822 −2.06787
\(834\) −72.8830 −2.52373
\(835\) −6.70751 −0.232123
\(836\) 0 0
\(837\) 116.401 4.02341
\(838\) −6.13227 −0.211836
\(839\) −14.2764 −0.492875 −0.246438 0.969159i \(-0.579260\pi\)
−0.246438 + 0.969159i \(0.579260\pi\)
\(840\) −37.4953 −1.29371
\(841\) −5.46479 −0.188441
\(842\) 3.79957 0.130942
\(843\) −21.8976 −0.754194
\(844\) −4.66867 −0.160702
\(845\) −24.6586 −0.848282
\(846\) 59.0029 2.02856
\(847\) 0 0
\(848\) −1.14869 −0.0394462
\(849\) −30.4101 −1.04367
\(850\) 1.90683 0.0654037
\(851\) 28.0950 0.963083
\(852\) −7.74635 −0.265385
\(853\) 31.1027 1.06494 0.532468 0.846450i \(-0.321265\pi\)
0.532468 + 0.846450i \(0.321265\pi\)
\(854\) −19.3362 −0.661672
\(855\) −19.2338 −0.657784
\(856\) −14.6583 −0.501012
\(857\) −16.9715 −0.579736 −0.289868 0.957067i \(-0.593611\pi\)
−0.289868 + 0.957067i \(0.593611\pi\)
\(858\) 0 0
\(859\) 39.5169 1.34830 0.674149 0.738595i \(-0.264510\pi\)
0.674149 + 0.738595i \(0.264510\pi\)
\(860\) −27.8004 −0.947987
\(861\) −111.985 −3.81642
\(862\) 8.69515 0.296158
\(863\) 55.4294 1.88684 0.943420 0.331600i \(-0.107588\pi\)
0.943420 + 0.331600i \(0.107588\pi\)
\(864\) −17.3926 −0.591708
\(865\) −30.1878 −1.02642
\(866\) −3.30744 −0.112391
\(867\) −9.18321 −0.311878
\(868\) 31.9615 1.08484
\(869\) 0 0
\(870\) −38.0891 −1.29134
\(871\) −16.4702 −0.558072
\(872\) −2.92436 −0.0990314
\(873\) −81.9759 −2.77446
\(874\) −2.57808 −0.0872049
\(875\) −50.3664 −1.70270
\(876\) 26.0196 0.879120
\(877\) 23.3069 0.787018 0.393509 0.919321i \(-0.371261\pi\)
0.393509 + 0.919321i \(0.371261\pi\)
\(878\) 4.54128 0.153261
\(879\) −67.6118 −2.28049
\(880\) 0 0
\(881\) 53.8830 1.81536 0.907682 0.419659i \(-0.137850\pi\)
0.907682 + 0.419659i \(0.137850\pi\)
\(882\) −129.580 −4.36317
\(883\) 46.0638 1.55017 0.775086 0.631856i \(-0.217707\pi\)
0.775086 + 0.631856i \(0.217707\pi\)
\(884\) 5.95832 0.200400
\(885\) 38.6627 1.29963
\(886\) −17.8637 −0.600142
\(887\) −14.9246 −0.501120 −0.250560 0.968101i \(-0.580615\pi\)
−0.250560 + 0.968101i \(0.580615\pi\)
\(888\) 36.4665 1.22374
\(889\) 5.45008 0.182790
\(890\) 27.4516 0.920178
\(891\) 0 0
\(892\) 23.8663 0.799101
\(893\) 7.19759 0.240858
\(894\) −21.3501 −0.714053
\(895\) −58.4904 −1.95512
\(896\) −4.77567 −0.159544
\(897\) 13.6141 0.454561
\(898\) 21.8487 0.729101
\(899\) 32.4677 1.08286
\(900\) 4.14003 0.138001
\(901\) 4.33708 0.144489
\(902\) 0 0
\(903\) −189.351 −6.30122
\(904\) 1.00747 0.0335080
\(905\) −41.7526 −1.38790
\(906\) 8.51250 0.282809
\(907\) −14.6419 −0.486177 −0.243089 0.970004i \(-0.578161\pi\)
−0.243089 + 0.970004i \(0.578161\pi\)
\(908\) −13.5097 −0.448334
\(909\) −11.1187 −0.368785
\(910\) 17.6825 0.586169
\(911\) −5.41760 −0.179493 −0.0897465 0.995965i \(-0.528606\pi\)
−0.0897465 + 0.995965i \(0.528606\pi\)
\(912\) −3.34628 −0.110806
\(913\) 0 0
\(914\) −5.73424 −0.189672
\(915\) 31.7892 1.05092
\(916\) −8.22896 −0.271892
\(917\) −89.3409 −2.95030
\(918\) 65.6687 2.16739
\(919\) −33.1536 −1.09364 −0.546819 0.837251i \(-0.684161\pi\)
−0.546819 + 0.837251i \(0.684161\pi\)
\(920\) 6.04890 0.199426
\(921\) 67.7668 2.23299
\(922\) 12.5752 0.414143
\(923\) 3.65312 0.120244
\(924\) 0 0
\(925\) −5.50363 −0.180958
\(926\) −19.2853 −0.633755
\(927\) 18.8542 0.619253
\(928\) −4.85131 −0.159252
\(929\) −0.322385 −0.0105771 −0.00528856 0.999986i \(-0.501683\pi\)
−0.00528856 + 0.999986i \(0.501683\pi\)
\(930\) −52.5454 −1.72303
\(931\) −15.8070 −0.518055
\(932\) 0.490085 0.0160533
\(933\) 98.3463 3.21971
\(934\) −15.8004 −0.517006
\(935\) 0 0
\(936\) 12.9365 0.422842
\(937\) 2.64545 0.0864229 0.0432115 0.999066i \(-0.486241\pi\)
0.0432115 + 0.999066i \(0.486241\pi\)
\(938\) −49.8430 −1.62743
\(939\) −0.767013 −0.0250305
\(940\) −16.8876 −0.550812
\(941\) 11.1772 0.364367 0.182183 0.983265i \(-0.441684\pi\)
0.182183 + 0.983265i \(0.441684\pi\)
\(942\) 18.7400 0.610582
\(943\) 18.0658 0.588304
\(944\) 4.92436 0.160274
\(945\) 194.885 6.33961
\(946\) 0 0
\(947\) 11.6693 0.379200 0.189600 0.981861i \(-0.439281\pi\)
0.189600 + 0.981861i \(0.439281\pi\)
\(948\) −3.32127 −0.107870
\(949\) −12.2706 −0.398322
\(950\) 0.505030 0.0163853
\(951\) −65.8910 −2.13666
\(952\) 18.0314 0.584400
\(953\) −42.6900 −1.38286 −0.691432 0.722442i \(-0.743020\pi\)
−0.691432 + 0.722442i \(0.743020\pi\)
\(954\) 9.41649 0.304870
\(955\) −10.5073 −0.340009
\(956\) −20.5364 −0.664195
\(957\) 0 0
\(958\) −17.0149 −0.549728
\(959\) 57.6569 1.86184
\(960\) 7.85131 0.253400
\(961\) 13.7904 0.444850
\(962\) −17.1973 −0.554464
\(963\) 120.163 3.87220
\(964\) 19.4654 0.626938
\(965\) −18.7702 −0.604235
\(966\) 41.1996 1.32558
\(967\) 15.6705 0.503928 0.251964 0.967737i \(-0.418924\pi\)
0.251964 + 0.967737i \(0.418924\pi\)
\(968\) 0 0
\(969\) 12.6345 0.405877
\(970\) 23.4628 0.753345
\(971\) −36.0369 −1.15648 −0.578239 0.815868i \(-0.696260\pi\)
−0.578239 + 0.815868i \(0.696260\pi\)
\(972\) 60.2831 1.93358
\(973\) 104.016 3.33459
\(974\) −12.8387 −0.411377
\(975\) −2.66691 −0.0854096
\(976\) 4.04890 0.129602
\(977\) −6.06273 −0.193964 −0.0969820 0.995286i \(-0.530919\pi\)
−0.0969820 + 0.995286i \(0.530919\pi\)
\(978\) −24.2738 −0.776190
\(979\) 0 0
\(980\) 37.0877 1.18472
\(981\) 23.9727 0.765390
\(982\) −21.1654 −0.675416
\(983\) −8.49608 −0.270983 −0.135491 0.990779i \(-0.543261\pi\)
−0.135491 + 0.990779i \(0.543261\pi\)
\(984\) 23.4490 0.747526
\(985\) 29.4726 0.939074
\(986\) 18.3170 0.583331
\(987\) −115.023 −3.66122
\(988\) 1.57808 0.0502055
\(989\) 30.5470 0.971337
\(990\) 0 0
\(991\) −25.2663 −0.802611 −0.401306 0.915944i \(-0.631443\pi\)
−0.401306 + 0.915944i \(0.631443\pi\)
\(992\) −6.69256 −0.212489
\(993\) −56.7886 −1.80213
\(994\) 11.0553 0.350652
\(995\) −1.76127 −0.0558361
\(996\) 27.9290 0.884964
\(997\) 45.5853 1.44370 0.721850 0.692049i \(-0.243292\pi\)
0.721850 + 0.692049i \(0.243292\pi\)
\(998\) 5.35634 0.169552
\(999\) −189.538 −5.99671
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.bs.1.4 4
11.10 odd 2 4598.2.a.bv.1.4 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.bs.1.4 4 1.1 even 1 trivial
4598.2.a.bv.1.4 yes 4 11.10 odd 2