Properties

Label 4598.2.a.cd.1.8
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $0$
Dimension $10$
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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \( x^{10} - 2x^{9} - 19x^{8} + 36x^{7} + 118x^{6} - 220x^{5} - 270x^{4} + 512x^{3} + 176x^{2} - 392x + 44 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 418)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(2.10092\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.10092 q^{3} +1.00000 q^{4} +2.46005 q^{5} +2.10092 q^{6} +3.09995 q^{7} +1.00000 q^{8} +1.41386 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.10092 q^{3} +1.00000 q^{4} +2.46005 q^{5} +2.10092 q^{6} +3.09995 q^{7} +1.00000 q^{8} +1.41386 q^{9} +2.46005 q^{10} +2.10092 q^{12} +3.97832 q^{13} +3.09995 q^{14} +5.16836 q^{15} +1.00000 q^{16} +2.14576 q^{17} +1.41386 q^{18} +1.00000 q^{19} +2.46005 q^{20} +6.51275 q^{21} -2.55940 q^{23} +2.10092 q^{24} +1.05183 q^{25} +3.97832 q^{26} -3.33234 q^{27} +3.09995 q^{28} -6.50365 q^{29} +5.16836 q^{30} +1.48635 q^{31} +1.00000 q^{32} +2.14576 q^{34} +7.62603 q^{35} +1.41386 q^{36} -1.74921 q^{37} +1.00000 q^{38} +8.35814 q^{39} +2.46005 q^{40} -5.48529 q^{41} +6.51275 q^{42} -4.59472 q^{43} +3.47817 q^{45} -2.55940 q^{46} -3.40634 q^{47} +2.10092 q^{48} +2.60971 q^{49} +1.05183 q^{50} +4.50808 q^{51} +3.97832 q^{52} -11.7609 q^{53} -3.33234 q^{54} +3.09995 q^{56} +2.10092 q^{57} -6.50365 q^{58} -6.65028 q^{59} +5.16836 q^{60} +6.34059 q^{61} +1.48635 q^{62} +4.38291 q^{63} +1.00000 q^{64} +9.78686 q^{65} +14.1154 q^{67} +2.14576 q^{68} -5.37710 q^{69} +7.62603 q^{70} -15.9696 q^{71} +1.41386 q^{72} +3.17623 q^{73} -1.74921 q^{74} +2.20981 q^{75} +1.00000 q^{76} +8.35814 q^{78} -7.25669 q^{79} +2.46005 q^{80} -11.2426 q^{81} -5.48529 q^{82} -11.2166 q^{83} +6.51275 q^{84} +5.27868 q^{85} -4.59472 q^{86} -13.6636 q^{87} -4.63686 q^{89} +3.47817 q^{90} +12.3326 q^{91} -2.55940 q^{92} +3.12270 q^{93} -3.40634 q^{94} +2.46005 q^{95} +2.10092 q^{96} -5.47081 q^{97} +2.60971 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9} - 3 q^{10} + 2 q^{12} + 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} + 12 q^{17} + 12 q^{18} + 10 q^{19} - 3 q^{20} - q^{21} + 14 q^{23} + 2 q^{24} + 5 q^{25} + 11 q^{26} + 2 q^{27} + 11 q^{28} + 16 q^{29} + q^{30} + 12 q^{31} + 10 q^{32} + 12 q^{34} - 12 q^{35} + 12 q^{36} - q^{37} + 10 q^{38} + 11 q^{39} - 3 q^{40} - 5 q^{41} - q^{42} + 22 q^{43} - 2 q^{45} + 14 q^{46} + 8 q^{47} + 2 q^{48} - 3 q^{49} + 5 q^{50} + 8 q^{51} + 11 q^{52} + 2 q^{53} + 2 q^{54} + 11 q^{56} + 2 q^{57} + 16 q^{58} - 7 q^{59} + q^{60} + 35 q^{61} + 12 q^{62} + 38 q^{63} + 10 q^{64} + 4 q^{65} + 9 q^{67} + 12 q^{68} + 6 q^{69} - 12 q^{70} - 4 q^{71} + 12 q^{72} + 5 q^{73} - q^{74} - 15 q^{75} + 10 q^{76} + 11 q^{78} + 18 q^{79} - 3 q^{80} - 6 q^{81} - 5 q^{82} + 7 q^{83} - q^{84} + 35 q^{85} + 22 q^{86} + 8 q^{87} + 22 q^{89} - 2 q^{90} + 11 q^{91} + 14 q^{92} - 64 q^{93} + 8 q^{94} - 3 q^{95} + 2 q^{96} + 32 q^{97} - 3 q^{98}+O(q^{100}) \) 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
\(3\) 2.10092 1.21297 0.606483 0.795096i \(-0.292580\pi\)
0.606483 + 0.795096i \(0.292580\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.46005 1.10017 0.550083 0.835110i \(-0.314596\pi\)
0.550083 + 0.835110i \(0.314596\pi\)
\(6\) 2.10092 0.857697
\(7\) 3.09995 1.17167 0.585836 0.810430i \(-0.300766\pi\)
0.585836 + 0.810430i \(0.300766\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.41386 0.471288
\(10\) 2.46005 0.777935
\(11\) 0 0
\(12\) 2.10092 0.606483
\(13\) 3.97832 1.10339 0.551694 0.834047i \(-0.313982\pi\)
0.551694 + 0.834047i \(0.313982\pi\)
\(14\) 3.09995 0.828497
\(15\) 5.16836 1.33447
\(16\) 1.00000 0.250000
\(17\) 2.14576 0.520424 0.260212 0.965551i \(-0.416208\pi\)
0.260212 + 0.965551i \(0.416208\pi\)
\(18\) 1.41386 0.333251
\(19\) 1.00000 0.229416
\(20\) 2.46005 0.550083
\(21\) 6.51275 1.42120
\(22\) 0 0
\(23\) −2.55940 −0.533672 −0.266836 0.963742i \(-0.585978\pi\)
−0.266836 + 0.963742i \(0.585978\pi\)
\(24\) 2.10092 0.428848
\(25\) 1.05183 0.210366
\(26\) 3.97832 0.780213
\(27\) −3.33234 −0.641310
\(28\) 3.09995 0.585836
\(29\) −6.50365 −1.20770 −0.603849 0.797099i \(-0.706367\pi\)
−0.603849 + 0.797099i \(0.706367\pi\)
\(30\) 5.16836 0.943609
\(31\) 1.48635 0.266956 0.133478 0.991052i \(-0.457385\pi\)
0.133478 + 0.991052i \(0.457385\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 2.14576 0.367995
\(35\) 7.62603 1.28903
\(36\) 1.41386 0.235644
\(37\) −1.74921 −0.287569 −0.143784 0.989609i \(-0.545927\pi\)
−0.143784 + 0.989609i \(0.545927\pi\)
\(38\) 1.00000 0.162221
\(39\) 8.35814 1.33837
\(40\) 2.46005 0.388968
\(41\) −5.48529 −0.856659 −0.428329 0.903623i \(-0.640898\pi\)
−0.428329 + 0.903623i \(0.640898\pi\)
\(42\) 6.51275 1.00494
\(43\) −4.59472 −0.700689 −0.350344 0.936621i \(-0.613935\pi\)
−0.350344 + 0.936621i \(0.613935\pi\)
\(44\) 0 0
\(45\) 3.47817 0.518495
\(46\) −2.55940 −0.377363
\(47\) −3.40634 −0.496866 −0.248433 0.968649i \(-0.579916\pi\)
−0.248433 + 0.968649i \(0.579916\pi\)
\(48\) 2.10092 0.303242
\(49\) 2.60971 0.372815
\(50\) 1.05183 0.148751
\(51\) 4.50808 0.631257
\(52\) 3.97832 0.551694
\(53\) −11.7609 −1.61548 −0.807742 0.589536i \(-0.799311\pi\)
−0.807742 + 0.589536i \(0.799311\pi\)
\(54\) −3.33234 −0.453475
\(55\) 0 0
\(56\) 3.09995 0.414249
\(57\) 2.10092 0.278274
\(58\) −6.50365 −0.853971
\(59\) −6.65028 −0.865793 −0.432896 0.901444i \(-0.642508\pi\)
−0.432896 + 0.901444i \(0.642508\pi\)
\(60\) 5.16836 0.667233
\(61\) 6.34059 0.811829 0.405915 0.913911i \(-0.366953\pi\)
0.405915 + 0.913911i \(0.366953\pi\)
\(62\) 1.48635 0.188766
\(63\) 4.38291 0.552195
\(64\) 1.00000 0.125000
\(65\) 9.78686 1.21391
\(66\) 0 0
\(67\) 14.1154 1.72447 0.862236 0.506506i \(-0.169063\pi\)
0.862236 + 0.506506i \(0.169063\pi\)
\(68\) 2.14576 0.260212
\(69\) −5.37710 −0.647326
\(70\) 7.62603 0.911485
\(71\) −15.9696 −1.89524 −0.947619 0.319404i \(-0.896517\pi\)
−0.947619 + 0.319404i \(0.896517\pi\)
\(72\) 1.41386 0.166626
\(73\) 3.17623 0.371749 0.185875 0.982573i \(-0.440488\pi\)
0.185875 + 0.982573i \(0.440488\pi\)
\(74\) −1.74921 −0.203342
\(75\) 2.20981 0.255167
\(76\) 1.00000 0.114708
\(77\) 0 0
\(78\) 8.35814 0.946373
\(79\) −7.25669 −0.816442 −0.408221 0.912883i \(-0.633851\pi\)
−0.408221 + 0.912883i \(0.633851\pi\)
\(80\) 2.46005 0.275042
\(81\) −11.2426 −1.24918
\(82\) −5.48529 −0.605749
\(83\) −11.2166 −1.23118 −0.615588 0.788068i \(-0.711082\pi\)
−0.615588 + 0.788068i \(0.711082\pi\)
\(84\) 6.51275 0.710600
\(85\) 5.27868 0.572553
\(86\) −4.59472 −0.495462
\(87\) −13.6636 −1.46490
\(88\) 0 0
\(89\) −4.63686 −0.491506 −0.245753 0.969332i \(-0.579035\pi\)
−0.245753 + 0.969332i \(0.579035\pi\)
\(90\) 3.47817 0.366632
\(91\) 12.3326 1.29281
\(92\) −2.55940 −0.266836
\(93\) 3.12270 0.323809
\(94\) −3.40634 −0.351338
\(95\) 2.46005 0.252395
\(96\) 2.10092 0.214424
\(97\) −5.47081 −0.555477 −0.277738 0.960657i \(-0.589585\pi\)
−0.277738 + 0.960657i \(0.589585\pi\)
\(98\) 2.60971 0.263620
\(99\) 0 0
\(100\) 1.05183 0.105183
\(101\) 5.80492 0.577611 0.288806 0.957388i \(-0.406742\pi\)
0.288806 + 0.957388i \(0.406742\pi\)
\(102\) 4.50808 0.446366
\(103\) −9.56301 −0.942271 −0.471136 0.882061i \(-0.656156\pi\)
−0.471136 + 0.882061i \(0.656156\pi\)
\(104\) 3.97832 0.390107
\(105\) 16.0217 1.56356
\(106\) −11.7609 −1.14232
\(107\) 14.5663 1.40818 0.704090 0.710111i \(-0.251355\pi\)
0.704090 + 0.710111i \(0.251355\pi\)
\(108\) −3.33234 −0.320655
\(109\) 3.38080 0.323822 0.161911 0.986805i \(-0.448234\pi\)
0.161911 + 0.986805i \(0.448234\pi\)
\(110\) 0 0
\(111\) −3.67496 −0.348811
\(112\) 3.09995 0.292918
\(113\) 11.3668 1.06930 0.534650 0.845074i \(-0.320444\pi\)
0.534650 + 0.845074i \(0.320444\pi\)
\(114\) 2.10092 0.196769
\(115\) −6.29625 −0.587128
\(116\) −6.50365 −0.603849
\(117\) 5.62481 0.520014
\(118\) −6.65028 −0.612208
\(119\) 6.65177 0.609766
\(120\) 5.16836 0.471805
\(121\) 0 0
\(122\) 6.34059 0.574050
\(123\) −11.5242 −1.03910
\(124\) 1.48635 0.133478
\(125\) −9.71268 −0.868729
\(126\) 4.38291 0.390461
\(127\) 13.3466 1.18432 0.592160 0.805820i \(-0.298275\pi\)
0.592160 + 0.805820i \(0.298275\pi\)
\(128\) 1.00000 0.0883883
\(129\) −9.65314 −0.849912
\(130\) 9.78686 0.858364
\(131\) 4.58757 0.400818 0.200409 0.979712i \(-0.435773\pi\)
0.200409 + 0.979712i \(0.435773\pi\)
\(132\) 0 0
\(133\) 3.09995 0.268800
\(134\) 14.1154 1.21939
\(135\) −8.19772 −0.705548
\(136\) 2.14576 0.183998
\(137\) −13.6371 −1.16509 −0.582546 0.812798i \(-0.697943\pi\)
−0.582546 + 0.812798i \(0.697943\pi\)
\(138\) −5.37710 −0.457729
\(139\) 5.78982 0.491086 0.245543 0.969386i \(-0.421034\pi\)
0.245543 + 0.969386i \(0.421034\pi\)
\(140\) 7.62603 0.644517
\(141\) −7.15646 −0.602682
\(142\) −15.9696 −1.34014
\(143\) 0 0
\(144\) 1.41386 0.117822
\(145\) −15.9993 −1.32867
\(146\) 3.17623 0.262866
\(147\) 5.48278 0.452212
\(148\) −1.74921 −0.143784
\(149\) 10.3503 0.847926 0.423963 0.905679i \(-0.360639\pi\)
0.423963 + 0.905679i \(0.360639\pi\)
\(150\) 2.20981 0.180430
\(151\) 12.1731 0.990632 0.495316 0.868713i \(-0.335052\pi\)
0.495316 + 0.868713i \(0.335052\pi\)
\(152\) 1.00000 0.0811107
\(153\) 3.03382 0.245270
\(154\) 0 0
\(155\) 3.65649 0.293696
\(156\) 8.35814 0.669186
\(157\) 3.72389 0.297199 0.148599 0.988897i \(-0.452524\pi\)
0.148599 + 0.988897i \(0.452524\pi\)
\(158\) −7.25669 −0.577312
\(159\) −24.7087 −1.95953
\(160\) 2.46005 0.194484
\(161\) −7.93402 −0.625289
\(162\) −11.2426 −0.883301
\(163\) −19.8920 −1.55806 −0.779032 0.626984i \(-0.784289\pi\)
−0.779032 + 0.626984i \(0.784289\pi\)
\(164\) −5.48529 −0.428329
\(165\) 0 0
\(166\) −11.2166 −0.870573
\(167\) 21.9867 1.70138 0.850690 0.525667i \(-0.176184\pi\)
0.850690 + 0.525667i \(0.176184\pi\)
\(168\) 6.51275 0.502470
\(169\) 2.82705 0.217465
\(170\) 5.27868 0.404856
\(171\) 1.41386 0.108121
\(172\) −4.59472 −0.350344
\(173\) 25.4819 1.93735 0.968675 0.248333i \(-0.0798828\pi\)
0.968675 + 0.248333i \(0.0798828\pi\)
\(174\) −13.6636 −1.03584
\(175\) 3.26062 0.246480
\(176\) 0 0
\(177\) −13.9717 −1.05018
\(178\) −4.63686 −0.347547
\(179\) 22.7884 1.70329 0.851643 0.524122i \(-0.175607\pi\)
0.851643 + 0.524122i \(0.175607\pi\)
\(180\) 3.47817 0.259248
\(181\) −1.54547 −0.114874 −0.0574368 0.998349i \(-0.518293\pi\)
−0.0574368 + 0.998349i \(0.518293\pi\)
\(182\) 12.3326 0.914154
\(183\) 13.3211 0.984722
\(184\) −2.55940 −0.188682
\(185\) −4.30315 −0.316374
\(186\) 3.12270 0.228967
\(187\) 0 0
\(188\) −3.40634 −0.248433
\(189\) −10.3301 −0.751405
\(190\) 2.46005 0.178471
\(191\) 7.14404 0.516925 0.258462 0.966021i \(-0.416784\pi\)
0.258462 + 0.966021i \(0.416784\pi\)
\(192\) 2.10092 0.151621
\(193\) 12.0980 0.870833 0.435417 0.900229i \(-0.356601\pi\)
0.435417 + 0.900229i \(0.356601\pi\)
\(194\) −5.47081 −0.392781
\(195\) 20.5614 1.47243
\(196\) 2.60971 0.186408
\(197\) −18.2516 −1.30037 −0.650186 0.759775i \(-0.725309\pi\)
−0.650186 + 0.759775i \(0.725309\pi\)
\(198\) 0 0
\(199\) 23.9705 1.69923 0.849613 0.527406i \(-0.176835\pi\)
0.849613 + 0.527406i \(0.176835\pi\)
\(200\) 1.05183 0.0743756
\(201\) 29.6554 2.09173
\(202\) 5.80492 0.408433
\(203\) −20.1610 −1.41503
\(204\) 4.50808 0.315629
\(205\) −13.4941 −0.942467
\(206\) −9.56301 −0.666286
\(207\) −3.61865 −0.251513
\(208\) 3.97832 0.275847
\(209\) 0 0
\(210\) 16.0217 1.10560
\(211\) −20.7466 −1.42826 −0.714129 0.700015i \(-0.753177\pi\)
−0.714129 + 0.700015i \(0.753177\pi\)
\(212\) −11.7609 −0.807742
\(213\) −33.5508 −2.29886
\(214\) 14.5663 0.995734
\(215\) −11.3032 −0.770874
\(216\) −3.33234 −0.226737
\(217\) 4.60761 0.312785
\(218\) 3.38080 0.228977
\(219\) 6.67300 0.450920
\(220\) 0 0
\(221\) 8.53654 0.574230
\(222\) −3.67496 −0.246647
\(223\) 28.3845 1.90077 0.950384 0.311080i \(-0.100691\pi\)
0.950384 + 0.311080i \(0.100691\pi\)
\(224\) 3.09995 0.207124
\(225\) 1.48715 0.0991430
\(226\) 11.3668 0.756109
\(227\) 8.50634 0.564585 0.282293 0.959328i \(-0.408905\pi\)
0.282293 + 0.959328i \(0.408905\pi\)
\(228\) 2.10092 0.139137
\(229\) −1.70730 −0.112822 −0.0564109 0.998408i \(-0.517966\pi\)
−0.0564109 + 0.998408i \(0.517966\pi\)
\(230\) −6.29625 −0.415162
\(231\) 0 0
\(232\) −6.50365 −0.426986
\(233\) −9.95632 −0.652260 −0.326130 0.945325i \(-0.605745\pi\)
−0.326130 + 0.945325i \(0.605745\pi\)
\(234\) 5.62481 0.367705
\(235\) −8.37977 −0.546636
\(236\) −6.65028 −0.432896
\(237\) −15.2457 −0.990317
\(238\) 6.65177 0.431170
\(239\) −16.2786 −1.05297 −0.526487 0.850183i \(-0.676491\pi\)
−0.526487 + 0.850183i \(0.676491\pi\)
\(240\) 5.16836 0.333616
\(241\) 5.95144 0.383366 0.191683 0.981457i \(-0.438605\pi\)
0.191683 + 0.981457i \(0.438605\pi\)
\(242\) 0 0
\(243\) −13.6227 −0.873899
\(244\) 6.34059 0.405915
\(245\) 6.42000 0.410159
\(246\) −11.5242 −0.734753
\(247\) 3.97832 0.253135
\(248\) 1.48635 0.0943832
\(249\) −23.5651 −1.49338
\(250\) −9.71268 −0.614284
\(251\) −21.0594 −1.32926 −0.664630 0.747173i \(-0.731411\pi\)
−0.664630 + 0.747173i \(0.731411\pi\)
\(252\) 4.38291 0.276098
\(253\) 0 0
\(254\) 13.3466 0.837441
\(255\) 11.0901 0.694488
\(256\) 1.00000 0.0625000
\(257\) 1.27738 0.0796811 0.0398405 0.999206i \(-0.487315\pi\)
0.0398405 + 0.999206i \(0.487315\pi\)
\(258\) −9.65314 −0.600978
\(259\) −5.42248 −0.336936
\(260\) 9.78686 0.606955
\(261\) −9.19528 −0.569174
\(262\) 4.58757 0.283421
\(263\) −8.85896 −0.546267 −0.273134 0.961976i \(-0.588060\pi\)
−0.273134 + 0.961976i \(0.588060\pi\)
\(264\) 0 0
\(265\) −28.9324 −1.77730
\(266\) 3.09995 0.190070
\(267\) −9.74167 −0.596181
\(268\) 14.1154 0.862236
\(269\) 26.0234 1.58667 0.793337 0.608783i \(-0.208342\pi\)
0.793337 + 0.608783i \(0.208342\pi\)
\(270\) −8.19772 −0.498897
\(271\) −17.0826 −1.03770 −0.518848 0.854867i \(-0.673639\pi\)
−0.518848 + 0.854867i \(0.673639\pi\)
\(272\) 2.14576 0.130106
\(273\) 25.9098 1.56813
\(274\) −13.6371 −0.823845
\(275\) 0 0
\(276\) −5.37710 −0.323663
\(277\) −8.49406 −0.510359 −0.255179 0.966894i \(-0.582135\pi\)
−0.255179 + 0.966894i \(0.582135\pi\)
\(278\) 5.78982 0.347251
\(279\) 2.10150 0.125813
\(280\) 7.62603 0.455742
\(281\) −29.4238 −1.75527 −0.877637 0.479325i \(-0.840881\pi\)
−0.877637 + 0.479325i \(0.840881\pi\)
\(282\) −7.15646 −0.426161
\(283\) 17.0589 1.01405 0.507024 0.861932i \(-0.330745\pi\)
0.507024 + 0.861932i \(0.330745\pi\)
\(284\) −15.9696 −0.947619
\(285\) 5.16836 0.306147
\(286\) 0 0
\(287\) −17.0041 −1.00372
\(288\) 1.41386 0.0833128
\(289\) −12.3957 −0.729159
\(290\) −15.9993 −0.939510
\(291\) −11.4937 −0.673775
\(292\) 3.17623 0.185875
\(293\) −20.5142 −1.19845 −0.599227 0.800579i \(-0.704525\pi\)
−0.599227 + 0.800579i \(0.704525\pi\)
\(294\) 5.48278 0.319762
\(295\) −16.3600 −0.952516
\(296\) −1.74921 −0.101671
\(297\) 0 0
\(298\) 10.3503 0.599575
\(299\) −10.1821 −0.588847
\(300\) 2.20981 0.127584
\(301\) −14.2434 −0.820977
\(302\) 12.1731 0.700483
\(303\) 12.1957 0.700623
\(304\) 1.00000 0.0573539
\(305\) 15.5982 0.893147
\(306\) 3.03382 0.173432
\(307\) −5.64603 −0.322236 −0.161118 0.986935i \(-0.551510\pi\)
−0.161118 + 0.986935i \(0.551510\pi\)
\(308\) 0 0
\(309\) −20.0911 −1.14294
\(310\) 3.65649 0.207674
\(311\) 8.41613 0.477235 0.238617 0.971114i \(-0.423306\pi\)
0.238617 + 0.971114i \(0.423306\pi\)
\(312\) 8.35814 0.473186
\(313\) 31.3766 1.77351 0.886756 0.462239i \(-0.152954\pi\)
0.886756 + 0.462239i \(0.152954\pi\)
\(314\) 3.72389 0.210151
\(315\) 10.7822 0.607507
\(316\) −7.25669 −0.408221
\(317\) 7.20289 0.404555 0.202277 0.979328i \(-0.435166\pi\)
0.202277 + 0.979328i \(0.435166\pi\)
\(318\) −24.7087 −1.38560
\(319\) 0 0
\(320\) 2.46005 0.137521
\(321\) 30.6027 1.70808
\(322\) −7.93402 −0.442146
\(323\) 2.14576 0.119393
\(324\) −11.2426 −0.624588
\(325\) 4.18452 0.232115
\(326\) −19.8920 −1.10172
\(327\) 7.10279 0.392785
\(328\) −5.48529 −0.302875
\(329\) −10.5595 −0.582164
\(330\) 0 0
\(331\) 20.4083 1.12174 0.560870 0.827904i \(-0.310467\pi\)
0.560870 + 0.827904i \(0.310467\pi\)
\(332\) −11.2166 −0.615588
\(333\) −2.47315 −0.135528
\(334\) 21.9867 1.20306
\(335\) 34.7246 1.89721
\(336\) 6.51275 0.355300
\(337\) 32.1119 1.74925 0.874623 0.484803i \(-0.161109\pi\)
0.874623 + 0.484803i \(0.161109\pi\)
\(338\) 2.82705 0.153771
\(339\) 23.8807 1.29702
\(340\) 5.27868 0.286277
\(341\) 0 0
\(342\) 1.41386 0.0764530
\(343\) −13.6097 −0.734855
\(344\) −4.59472 −0.247731
\(345\) −13.2279 −0.712167
\(346\) 25.4819 1.36991
\(347\) −1.12968 −0.0606444 −0.0303222 0.999540i \(-0.509653\pi\)
−0.0303222 + 0.999540i \(0.509653\pi\)
\(348\) −13.6636 −0.732448
\(349\) 21.1559 1.13245 0.566225 0.824251i \(-0.308403\pi\)
0.566225 + 0.824251i \(0.308403\pi\)
\(350\) 3.26062 0.174288
\(351\) −13.2571 −0.707614
\(352\) 0 0
\(353\) −0.0272714 −0.00145151 −0.000725755 1.00000i \(-0.500231\pi\)
−0.000725755 1.00000i \(0.500231\pi\)
\(354\) −13.9717 −0.742588
\(355\) −39.2858 −2.08508
\(356\) −4.63686 −0.245753
\(357\) 13.9748 0.739626
\(358\) 22.7884 1.20441
\(359\) −15.1154 −0.797758 −0.398879 0.917004i \(-0.630601\pi\)
−0.398879 + 0.917004i \(0.630601\pi\)
\(360\) 3.47817 0.183316
\(361\) 1.00000 0.0526316
\(362\) −1.54547 −0.0812279
\(363\) 0 0
\(364\) 12.3326 0.646404
\(365\) 7.81367 0.408986
\(366\) 13.3211 0.696304
\(367\) 21.4714 1.12080 0.560399 0.828223i \(-0.310648\pi\)
0.560399 + 0.828223i \(0.310648\pi\)
\(368\) −2.55940 −0.133418
\(369\) −7.75546 −0.403733
\(370\) −4.30315 −0.223710
\(371\) −36.4582 −1.89282
\(372\) 3.12270 0.161904
\(373\) 18.3417 0.949697 0.474848 0.880068i \(-0.342503\pi\)
0.474848 + 0.880068i \(0.342503\pi\)
\(374\) 0 0
\(375\) −20.4056 −1.05374
\(376\) −3.40634 −0.175669
\(377\) −25.8736 −1.33256
\(378\) −10.3301 −0.531323
\(379\) 12.3232 0.633003 0.316501 0.948592i \(-0.397492\pi\)
0.316501 + 0.948592i \(0.397492\pi\)
\(380\) 2.46005 0.126198
\(381\) 28.0402 1.43654
\(382\) 7.14404 0.365521
\(383\) 28.7507 1.46909 0.734546 0.678558i \(-0.237395\pi\)
0.734546 + 0.678558i \(0.237395\pi\)
\(384\) 2.10092 0.107212
\(385\) 0 0
\(386\) 12.0980 0.615772
\(387\) −6.49631 −0.330226
\(388\) −5.47081 −0.277738
\(389\) 2.72988 0.138410 0.0692052 0.997602i \(-0.477954\pi\)
0.0692052 + 0.997602i \(0.477954\pi\)
\(390\) 20.5614 1.04117
\(391\) −5.49187 −0.277736
\(392\) 2.60971 0.131810
\(393\) 9.63812 0.486179
\(394\) −18.2516 −0.919502
\(395\) −17.8518 −0.898222
\(396\) 0 0
\(397\) 7.21330 0.362025 0.181013 0.983481i \(-0.442062\pi\)
0.181013 + 0.983481i \(0.442062\pi\)
\(398\) 23.9705 1.20153
\(399\) 6.51275 0.326045
\(400\) 1.05183 0.0525915
\(401\) −1.18981 −0.0594164 −0.0297082 0.999559i \(-0.509458\pi\)
−0.0297082 + 0.999559i \(0.509458\pi\)
\(402\) 29.6554 1.47908
\(403\) 5.91317 0.294556
\(404\) 5.80492 0.288806
\(405\) −27.6573 −1.37430
\(406\) −20.1610 −1.00057
\(407\) 0 0
\(408\) 4.50808 0.223183
\(409\) −11.7792 −0.582442 −0.291221 0.956656i \(-0.594061\pi\)
−0.291221 + 0.956656i \(0.594061\pi\)
\(410\) −13.4941 −0.666425
\(411\) −28.6504 −1.41322
\(412\) −9.56301 −0.471136
\(413\) −20.6156 −1.01443
\(414\) −3.61865 −0.177847
\(415\) −27.5932 −1.35450
\(416\) 3.97832 0.195053
\(417\) 12.1640 0.595672
\(418\) 0 0
\(419\) 20.0798 0.980963 0.490482 0.871452i \(-0.336821\pi\)
0.490482 + 0.871452i \(0.336821\pi\)
\(420\) 16.0217 0.781778
\(421\) 0.885182 0.0431412 0.0215706 0.999767i \(-0.493133\pi\)
0.0215706 + 0.999767i \(0.493133\pi\)
\(422\) −20.7466 −1.00993
\(423\) −4.81611 −0.234167
\(424\) −11.7609 −0.571160
\(425\) 2.25698 0.109480
\(426\) −33.5508 −1.62554
\(427\) 19.6555 0.951198
\(428\) 14.5663 0.704090
\(429\) 0 0
\(430\) −11.3032 −0.545090
\(431\) 20.3046 0.978038 0.489019 0.872273i \(-0.337355\pi\)
0.489019 + 0.872273i \(0.337355\pi\)
\(432\) −3.33234 −0.160327
\(433\) −36.1713 −1.73828 −0.869140 0.494566i \(-0.835327\pi\)
−0.869140 + 0.494566i \(0.835327\pi\)
\(434\) 4.60761 0.221172
\(435\) −33.6132 −1.61163
\(436\) 3.38080 0.161911
\(437\) −2.55940 −0.122433
\(438\) 6.67300 0.318848
\(439\) −21.4914 −1.02573 −0.512864 0.858470i \(-0.671416\pi\)
−0.512864 + 0.858470i \(0.671416\pi\)
\(440\) 0 0
\(441\) 3.68977 0.175703
\(442\) 8.53654 0.406042
\(443\) −24.5995 −1.16876 −0.584379 0.811481i \(-0.698662\pi\)
−0.584379 + 0.811481i \(0.698662\pi\)
\(444\) −3.67496 −0.174406
\(445\) −11.4069 −0.540739
\(446\) 28.3845 1.34405
\(447\) 21.7451 1.02851
\(448\) 3.09995 0.146459
\(449\) 35.2701 1.66450 0.832251 0.554400i \(-0.187052\pi\)
0.832251 + 0.554400i \(0.187052\pi\)
\(450\) 1.48715 0.0701047
\(451\) 0 0
\(452\) 11.3668 0.534650
\(453\) 25.5747 1.20160
\(454\) 8.50634 0.399222
\(455\) 30.3388 1.42230
\(456\) 2.10092 0.0983846
\(457\) 7.37055 0.344780 0.172390 0.985029i \(-0.444851\pi\)
0.172390 + 0.985029i \(0.444851\pi\)
\(458\) −1.70730 −0.0797770
\(459\) −7.15042 −0.333753
\(460\) −6.29625 −0.293564
\(461\) 36.4875 1.69939 0.849696 0.527272i \(-0.176785\pi\)
0.849696 + 0.527272i \(0.176785\pi\)
\(462\) 0 0
\(463\) −16.2208 −0.753844 −0.376922 0.926245i \(-0.623018\pi\)
−0.376922 + 0.926245i \(0.623018\pi\)
\(464\) −6.50365 −0.301924
\(465\) 7.68199 0.356244
\(466\) −9.95632 −0.461217
\(467\) 4.27354 0.197756 0.0988779 0.995100i \(-0.468475\pi\)
0.0988779 + 0.995100i \(0.468475\pi\)
\(468\) 5.62481 0.260007
\(469\) 43.7571 2.02052
\(470\) −8.37977 −0.386530
\(471\) 7.82359 0.360492
\(472\) −6.65028 −0.306104
\(473\) 0 0
\(474\) −15.2457 −0.700260
\(475\) 1.05183 0.0482613
\(476\) 6.65177 0.304883
\(477\) −16.6283 −0.761359
\(478\) −16.2786 −0.744564
\(479\) 39.1936 1.79080 0.895402 0.445260i \(-0.146889\pi\)
0.895402 + 0.445260i \(0.146889\pi\)
\(480\) 5.16836 0.235902
\(481\) −6.95893 −0.317300
\(482\) 5.95144 0.271081
\(483\) −16.6687 −0.758454
\(484\) 0 0
\(485\) −13.4585 −0.611117
\(486\) −13.6227 −0.617940
\(487\) 3.27438 0.148376 0.0741882 0.997244i \(-0.476363\pi\)
0.0741882 + 0.997244i \(0.476363\pi\)
\(488\) 6.34059 0.287025
\(489\) −41.7916 −1.88988
\(490\) 6.42000 0.290026
\(491\) −40.6503 −1.83452 −0.917260 0.398288i \(-0.869604\pi\)
−0.917260 + 0.398288i \(0.869604\pi\)
\(492\) −11.5242 −0.519549
\(493\) −13.9553 −0.628515
\(494\) 3.97832 0.178993
\(495\) 0 0
\(496\) 1.48635 0.0667390
\(497\) −49.5049 −2.22060
\(498\) −23.5651 −1.05598
\(499\) −14.1445 −0.633195 −0.316598 0.948560i \(-0.602540\pi\)
−0.316598 + 0.948560i \(0.602540\pi\)
\(500\) −9.71268 −0.434364
\(501\) 46.1923 2.06372
\(502\) −21.0594 −0.939928
\(503\) 27.7402 1.23688 0.618438 0.785834i \(-0.287766\pi\)
0.618438 + 0.785834i \(0.287766\pi\)
\(504\) 4.38291 0.195230
\(505\) 14.2804 0.635468
\(506\) 0 0
\(507\) 5.93940 0.263778
\(508\) 13.3466 0.592160
\(509\) 4.86817 0.215778 0.107889 0.994163i \(-0.465591\pi\)
0.107889 + 0.994163i \(0.465591\pi\)
\(510\) 11.0901 0.491077
\(511\) 9.84616 0.435568
\(512\) 1.00000 0.0441942
\(513\) −3.33234 −0.147127
\(514\) 1.27738 0.0563430
\(515\) −23.5254 −1.03666
\(516\) −9.65314 −0.424956
\(517\) 0 0
\(518\) −5.42248 −0.238250
\(519\) 53.5353 2.34994
\(520\) 9.78686 0.429182
\(521\) 18.6548 0.817281 0.408641 0.912695i \(-0.366003\pi\)
0.408641 + 0.912695i \(0.366003\pi\)
\(522\) −9.19528 −0.402466
\(523\) 8.39239 0.366974 0.183487 0.983022i \(-0.441262\pi\)
0.183487 + 0.983022i \(0.441262\pi\)
\(524\) 4.58757 0.200409
\(525\) 6.85031 0.298972
\(526\) −8.85896 −0.386269
\(527\) 3.18935 0.138930
\(528\) 0 0
\(529\) −16.4495 −0.715194
\(530\) −28.9324 −1.25674
\(531\) −9.40259 −0.408038
\(532\) 3.09995 0.134400
\(533\) −21.8223 −0.945227
\(534\) −9.74167 −0.421563
\(535\) 35.8338 1.54923
\(536\) 14.1154 0.609693
\(537\) 47.8766 2.06603
\(538\) 26.0234 1.12195
\(539\) 0 0
\(540\) −8.19772 −0.352774
\(541\) 32.0199 1.37664 0.688322 0.725405i \(-0.258347\pi\)
0.688322 + 0.725405i \(0.258347\pi\)
\(542\) −17.0826 −0.733762
\(543\) −3.24690 −0.139338
\(544\) 2.14576 0.0919989
\(545\) 8.31693 0.356258
\(546\) 25.9098 1.10884
\(547\) −25.7176 −1.09961 −0.549803 0.835295i \(-0.685297\pi\)
−0.549803 + 0.835295i \(0.685297\pi\)
\(548\) −13.6371 −0.582546
\(549\) 8.96474 0.382606
\(550\) 0 0
\(551\) −6.50365 −0.277065
\(552\) −5.37710 −0.228864
\(553\) −22.4954 −0.956602
\(554\) −8.49406 −0.360878
\(555\) −9.04057 −0.383751
\(556\) 5.78982 0.245543
\(557\) −37.3111 −1.58092 −0.790461 0.612512i \(-0.790159\pi\)
−0.790461 + 0.612512i \(0.790159\pi\)
\(558\) 2.10150 0.0889634
\(559\) −18.2793 −0.773131
\(560\) 7.62603 0.322259
\(561\) 0 0
\(562\) −29.4238 −1.24117
\(563\) −0.758990 −0.0319876 −0.0159938 0.999872i \(-0.505091\pi\)
−0.0159938 + 0.999872i \(0.505091\pi\)
\(564\) −7.15646 −0.301341
\(565\) 27.9629 1.17641
\(566\) 17.0589 0.717041
\(567\) −34.8515 −1.46362
\(568\) −15.9696 −0.670068
\(569\) 31.2487 1.31001 0.655007 0.755623i \(-0.272666\pi\)
0.655007 + 0.755623i \(0.272666\pi\)
\(570\) 5.16836 0.216479
\(571\) 20.5848 0.861445 0.430723 0.902484i \(-0.358259\pi\)
0.430723 + 0.902484i \(0.358259\pi\)
\(572\) 0 0
\(573\) 15.0091 0.627012
\(574\) −17.0041 −0.709739
\(575\) −2.69206 −0.112267
\(576\) 1.41386 0.0589110
\(577\) 12.5133 0.520934 0.260467 0.965483i \(-0.416124\pi\)
0.260467 + 0.965483i \(0.416124\pi\)
\(578\) −12.3957 −0.515593
\(579\) 25.4169 1.05629
\(580\) −15.9993 −0.664334
\(581\) −34.7708 −1.44254
\(582\) −11.4937 −0.476431
\(583\) 0 0
\(584\) 3.17623 0.131433
\(585\) 13.8373 0.572102
\(586\) −20.5142 −0.847435
\(587\) 12.0214 0.496178 0.248089 0.968737i \(-0.420197\pi\)
0.248089 + 0.968737i \(0.420197\pi\)
\(588\) 5.48278 0.226106
\(589\) 1.48635 0.0612439
\(590\) −16.3600 −0.673531
\(591\) −38.3451 −1.57731
\(592\) −1.74921 −0.0718922
\(593\) 33.2839 1.36680 0.683402 0.730042i \(-0.260500\pi\)
0.683402 + 0.730042i \(0.260500\pi\)
\(594\) 0 0
\(595\) 16.3637 0.670844
\(596\) 10.3503 0.423963
\(597\) 50.3602 2.06110
\(598\) −10.1821 −0.416378
\(599\) −14.8580 −0.607081 −0.303541 0.952819i \(-0.598169\pi\)
−0.303541 + 0.952819i \(0.598169\pi\)
\(600\) 2.20981 0.0902152
\(601\) −30.9531 −1.26260 −0.631301 0.775538i \(-0.717479\pi\)
−0.631301 + 0.775538i \(0.717479\pi\)
\(602\) −14.2434 −0.580518
\(603\) 19.9573 0.812724
\(604\) 12.1731 0.495316
\(605\) 0 0
\(606\) 12.1957 0.495415
\(607\) −29.4283 −1.19446 −0.597229 0.802071i \(-0.703732\pi\)
−0.597229 + 0.802071i \(0.703732\pi\)
\(608\) 1.00000 0.0405554
\(609\) −42.3567 −1.71638
\(610\) 15.5982 0.631551
\(611\) −13.5515 −0.548236
\(612\) 3.03382 0.122635
\(613\) −21.5787 −0.871554 −0.435777 0.900055i \(-0.643526\pi\)
−0.435777 + 0.900055i \(0.643526\pi\)
\(614\) −5.64603 −0.227855
\(615\) −28.3500 −1.14318
\(616\) 0 0
\(617\) −21.8270 −0.878721 −0.439360 0.898311i \(-0.644795\pi\)
−0.439360 + 0.898311i \(0.644795\pi\)
\(618\) −20.0911 −0.808183
\(619\) 41.5379 1.66955 0.834775 0.550592i \(-0.185598\pi\)
0.834775 + 0.550592i \(0.185598\pi\)
\(620\) 3.65649 0.146848
\(621\) 8.52881 0.342249
\(622\) 8.41613 0.337456
\(623\) −14.3740 −0.575884
\(624\) 8.35814 0.334593
\(625\) −29.1528 −1.16611
\(626\) 31.3766 1.25406
\(627\) 0 0
\(628\) 3.72389 0.148599
\(629\) −3.75340 −0.149658
\(630\) 10.7822 0.429572
\(631\) 1.40462 0.0559171 0.0279585 0.999609i \(-0.491099\pi\)
0.0279585 + 0.999609i \(0.491099\pi\)
\(632\) −7.25669 −0.288656
\(633\) −43.5870 −1.73243
\(634\) 7.20289 0.286063
\(635\) 32.8333 1.30295
\(636\) −24.7087 −0.979765
\(637\) 10.3822 0.411360
\(638\) 0 0
\(639\) −22.5788 −0.893203
\(640\) 2.46005 0.0972419
\(641\) −12.6801 −0.500832 −0.250416 0.968138i \(-0.580567\pi\)
−0.250416 + 0.968138i \(0.580567\pi\)
\(642\) 30.6027 1.20779
\(643\) 4.42309 0.174429 0.0872147 0.996190i \(-0.472203\pi\)
0.0872147 + 0.996190i \(0.472203\pi\)
\(644\) −7.93402 −0.312644
\(645\) −23.7472 −0.935044
\(646\) 2.14576 0.0844239
\(647\) −24.5901 −0.966736 −0.483368 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(648\) −11.2426 −0.441650
\(649\) 0 0
\(650\) 4.18452 0.164130
\(651\) 9.68022 0.379398
\(652\) −19.8920 −0.779032
\(653\) 19.5368 0.764533 0.382267 0.924052i \(-0.375144\pi\)
0.382267 + 0.924052i \(0.375144\pi\)
\(654\) 7.10279 0.277741
\(655\) 11.2856 0.440967
\(656\) −5.48529 −0.214165
\(657\) 4.49076 0.175201
\(658\) −10.5595 −0.411652
\(659\) −35.3980 −1.37891 −0.689456 0.724328i \(-0.742150\pi\)
−0.689456 + 0.724328i \(0.742150\pi\)
\(660\) 0 0
\(661\) −26.3898 −1.02644 −0.513222 0.858256i \(-0.671548\pi\)
−0.513222 + 0.858256i \(0.671548\pi\)
\(662\) 20.4083 0.793190
\(663\) 17.9346 0.696522
\(664\) −11.2166 −0.435287
\(665\) 7.62603 0.295725
\(666\) −2.47315 −0.0958326
\(667\) 16.6455 0.644514
\(668\) 21.9867 0.850690
\(669\) 59.6336 2.30557
\(670\) 34.7246 1.34153
\(671\) 0 0
\(672\) 6.51275 0.251235
\(673\) 4.02795 0.155266 0.0776331 0.996982i \(-0.475264\pi\)
0.0776331 + 0.996982i \(0.475264\pi\)
\(674\) 32.1119 1.23690
\(675\) −3.50506 −0.134910
\(676\) 2.82705 0.108733
\(677\) −21.6069 −0.830419 −0.415210 0.909726i \(-0.636292\pi\)
−0.415210 + 0.909726i \(0.636292\pi\)
\(678\) 23.8807 0.917135
\(679\) −16.9593 −0.650837
\(680\) 5.27868 0.202428
\(681\) 17.8711 0.684823
\(682\) 0 0
\(683\) 3.73163 0.142787 0.0713935 0.997448i \(-0.477255\pi\)
0.0713935 + 0.997448i \(0.477255\pi\)
\(684\) 1.41386 0.0540605
\(685\) −33.5478 −1.28180
\(686\) −13.6097 −0.519621
\(687\) −3.58691 −0.136849
\(688\) −4.59472 −0.175172
\(689\) −46.7887 −1.78251
\(690\) −13.2279 −0.503578
\(691\) 42.4147 1.61353 0.806765 0.590872i \(-0.201216\pi\)
0.806765 + 0.590872i \(0.201216\pi\)
\(692\) 25.4819 0.968675
\(693\) 0 0
\(694\) −1.12968 −0.0428820
\(695\) 14.2432 0.540277
\(696\) −13.6636 −0.517919
\(697\) −11.7701 −0.445826
\(698\) 21.1559 0.800763
\(699\) −20.9174 −0.791170
\(700\) 3.26062 0.123240
\(701\) 51.9082 1.96054 0.980272 0.197654i \(-0.0633322\pi\)
0.980272 + 0.197654i \(0.0633322\pi\)
\(702\) −13.2571 −0.500358
\(703\) −1.74921 −0.0659728
\(704\) 0 0
\(705\) −17.6052 −0.663051
\(706\) −0.0272714 −0.00102637
\(707\) 17.9950 0.676771
\(708\) −13.9717 −0.525089
\(709\) −42.1161 −1.58170 −0.790852 0.612008i \(-0.790362\pi\)
−0.790852 + 0.612008i \(0.790362\pi\)
\(710\) −39.2858 −1.47437
\(711\) −10.2600 −0.384779
\(712\) −4.63686 −0.173774
\(713\) −3.80416 −0.142467
\(714\) 13.9748 0.522995
\(715\) 0 0
\(716\) 22.7884 0.851643
\(717\) −34.2000 −1.27722
\(718\) −15.1154 −0.564100
\(719\) −6.37162 −0.237621 −0.118811 0.992917i \(-0.537908\pi\)
−0.118811 + 0.992917i \(0.537908\pi\)
\(720\) 3.47817 0.129624
\(721\) −29.6449 −1.10403
\(722\) 1.00000 0.0372161
\(723\) 12.5035 0.465010
\(724\) −1.54547 −0.0574368
\(725\) −6.84074 −0.254059
\(726\) 0 0
\(727\) −36.8358 −1.36616 −0.683082 0.730342i \(-0.739361\pi\)
−0.683082 + 0.730342i \(0.739361\pi\)
\(728\) 12.3326 0.457077
\(729\) 5.10748 0.189166
\(730\) 7.81367 0.289197
\(731\) −9.85919 −0.364655
\(732\) 13.3211 0.492361
\(733\) 7.23710 0.267308 0.133654 0.991028i \(-0.457329\pi\)
0.133654 + 0.991028i \(0.457329\pi\)
\(734\) 21.4714 0.792524
\(735\) 13.4879 0.497509
\(736\) −2.55940 −0.0943408
\(737\) 0 0
\(738\) −7.75546 −0.285482
\(739\) −19.6497 −0.722825 −0.361413 0.932406i \(-0.617705\pi\)
−0.361413 + 0.932406i \(0.617705\pi\)
\(740\) −4.30315 −0.158187
\(741\) 8.35814 0.307044
\(742\) −36.4582 −1.33842
\(743\) −7.72331 −0.283341 −0.141670 0.989914i \(-0.545247\pi\)
−0.141670 + 0.989914i \(0.545247\pi\)
\(744\) 3.12270 0.114484
\(745\) 25.4621 0.932860
\(746\) 18.3417 0.671537
\(747\) −15.8587 −0.580239
\(748\) 0 0
\(749\) 45.1549 1.64992
\(750\) −20.4056 −0.745106
\(751\) −45.4390 −1.65809 −0.829046 0.559181i \(-0.811116\pi\)
−0.829046 + 0.559181i \(0.811116\pi\)
\(752\) −3.40634 −0.124217
\(753\) −44.2442 −1.61235
\(754\) −25.8736 −0.942261
\(755\) 29.9464 1.08986
\(756\) −10.3301 −0.375702
\(757\) −0.394649 −0.0143438 −0.00717189 0.999974i \(-0.502283\pi\)
−0.00717189 + 0.999974i \(0.502283\pi\)
\(758\) 12.3232 0.447601
\(759\) 0 0
\(760\) 2.46005 0.0892353
\(761\) −37.5003 −1.35938 −0.679692 0.733498i \(-0.737886\pi\)
−0.679692 + 0.733498i \(0.737886\pi\)
\(762\) 28.0402 1.01579
\(763\) 10.4803 0.379413
\(764\) 7.14404 0.258462
\(765\) 7.46334 0.269838
\(766\) 28.7507 1.03881
\(767\) −26.4570 −0.955305
\(768\) 2.10092 0.0758104
\(769\) −0.388213 −0.0139993 −0.00699965 0.999976i \(-0.502228\pi\)
−0.00699965 + 0.999976i \(0.502228\pi\)
\(770\) 0 0
\(771\) 2.68368 0.0966505
\(772\) 12.0980 0.435417
\(773\) −32.5057 −1.16915 −0.584574 0.811341i \(-0.698738\pi\)
−0.584574 + 0.811341i \(0.698738\pi\)
\(774\) −6.49631 −0.233505
\(775\) 1.56339 0.0561585
\(776\) −5.47081 −0.196391
\(777\) −11.3922 −0.408693
\(778\) 2.72988 0.0978709
\(779\) −5.48529 −0.196531
\(780\) 20.5614 0.736216
\(781\) 0 0
\(782\) −5.49187 −0.196389
\(783\) 21.6724 0.774508
\(784\) 2.60971 0.0932038
\(785\) 9.16094 0.326968
\(786\) 9.63812 0.343781
\(787\) 11.8225 0.421425 0.210713 0.977548i \(-0.432422\pi\)
0.210713 + 0.977548i \(0.432422\pi\)
\(788\) −18.2516 −0.650186
\(789\) −18.6120 −0.662604
\(790\) −17.8518 −0.635139
\(791\) 35.2366 1.25287
\(792\) 0 0
\(793\) 25.2249 0.895763
\(794\) 7.21330 0.255991
\(795\) −60.7846 −2.15581
\(796\) 23.9705 0.849613
\(797\) 27.4045 0.970719 0.485359 0.874315i \(-0.338689\pi\)
0.485359 + 0.874315i \(0.338689\pi\)
\(798\) 6.51275 0.230549
\(799\) −7.30921 −0.258581
\(800\) 1.05183 0.0371878
\(801\) −6.55589 −0.231641
\(802\) −1.18981 −0.0420137
\(803\) 0 0
\(804\) 29.6554 1.04586
\(805\) −19.5181 −0.687922
\(806\) 5.91317 0.208283
\(807\) 54.6731 1.92458
\(808\) 5.80492 0.204216
\(809\) −9.23218 −0.324586 −0.162293 0.986743i \(-0.551889\pi\)
−0.162293 + 0.986743i \(0.551889\pi\)
\(810\) −27.6573 −0.971778
\(811\) 28.3825 0.996646 0.498323 0.866992i \(-0.333949\pi\)
0.498323 + 0.866992i \(0.333949\pi\)
\(812\) −20.1610 −0.707513
\(813\) −35.8892 −1.25869
\(814\) 0 0
\(815\) −48.9353 −1.71413
\(816\) 4.50808 0.157814
\(817\) −4.59472 −0.160749
\(818\) −11.7792 −0.411849
\(819\) 17.4366 0.609285
\(820\) −13.4941 −0.471233
\(821\) −29.3170 −1.02317 −0.511584 0.859233i \(-0.670941\pi\)
−0.511584 + 0.859233i \(0.670941\pi\)
\(822\) −28.6504 −0.999296
\(823\) −19.1547 −0.667692 −0.333846 0.942628i \(-0.608347\pi\)
−0.333846 + 0.942628i \(0.608347\pi\)
\(824\) −9.56301 −0.333143
\(825\) 0 0
\(826\) −20.6156 −0.717307
\(827\) 19.0633 0.662896 0.331448 0.943473i \(-0.392463\pi\)
0.331448 + 0.943473i \(0.392463\pi\)
\(828\) −3.61865 −0.125757
\(829\) −3.45420 −0.119969 −0.0599847 0.998199i \(-0.519105\pi\)
−0.0599847 + 0.998199i \(0.519105\pi\)
\(830\) −27.5932 −0.957775
\(831\) −17.8453 −0.619048
\(832\) 3.97832 0.137923
\(833\) 5.59981 0.194022
\(834\) 12.1640 0.421203
\(835\) 54.0883 1.87180
\(836\) 0 0
\(837\) −4.95302 −0.171202
\(838\) 20.0798 0.693646
\(839\) 16.7961 0.579865 0.289932 0.957047i \(-0.406367\pi\)
0.289932 + 0.957047i \(0.406367\pi\)
\(840\) 16.0217 0.552800
\(841\) 13.2975 0.458533
\(842\) 0.885182 0.0305054
\(843\) −61.8170 −2.12909
\(844\) −20.7466 −0.714129
\(845\) 6.95466 0.239248
\(846\) −4.81611 −0.165581
\(847\) 0 0
\(848\) −11.7609 −0.403871
\(849\) 35.8395 1.23001
\(850\) 2.25698 0.0774138
\(851\) 4.47694 0.153467
\(852\) −33.5508 −1.14943
\(853\) 5.53724 0.189592 0.0947958 0.995497i \(-0.469780\pi\)
0.0947958 + 0.995497i \(0.469780\pi\)
\(854\) 19.6555 0.672598
\(855\) 3.47817 0.118951
\(856\) 14.5663 0.497867
\(857\) −26.5793 −0.907932 −0.453966 0.891019i \(-0.649991\pi\)
−0.453966 + 0.891019i \(0.649991\pi\)
\(858\) 0 0
\(859\) 19.7426 0.673610 0.336805 0.941574i \(-0.390654\pi\)
0.336805 + 0.941574i \(0.390654\pi\)
\(860\) −11.3032 −0.385437
\(861\) −35.7243 −1.21748
\(862\) 20.3046 0.691577
\(863\) −22.8417 −0.777539 −0.388770 0.921335i \(-0.627100\pi\)
−0.388770 + 0.921335i \(0.627100\pi\)
\(864\) −3.33234 −0.113369
\(865\) 62.6866 2.13141
\(866\) −36.1713 −1.22915
\(867\) −26.0424 −0.884445
\(868\) 4.60761 0.156392
\(869\) 0 0
\(870\) −33.6132 −1.13959
\(871\) 56.1557 1.90276
\(872\) 3.38080 0.114488
\(873\) −7.73499 −0.261790
\(874\) −2.55940 −0.0865730
\(875\) −30.1089 −1.01787
\(876\) 6.67300 0.225460
\(877\) −39.1209 −1.32102 −0.660510 0.750817i \(-0.729660\pi\)
−0.660510 + 0.750817i \(0.729660\pi\)
\(878\) −21.4914 −0.725300
\(879\) −43.0987 −1.45368
\(880\) 0 0
\(881\) 39.7517 1.33927 0.669635 0.742691i \(-0.266451\pi\)
0.669635 + 0.742691i \(0.266451\pi\)
\(882\) 3.68977 0.124241
\(883\) −24.1017 −0.811088 −0.405544 0.914075i \(-0.632918\pi\)
−0.405544 + 0.914075i \(0.632918\pi\)
\(884\) 8.53654 0.287115
\(885\) −34.3710 −1.15537
\(886\) −24.5995 −0.826437
\(887\) 40.9484 1.37491 0.687457 0.726225i \(-0.258727\pi\)
0.687457 + 0.726225i \(0.258727\pi\)
\(888\) −3.67496 −0.123323
\(889\) 41.3739 1.38764
\(890\) −11.4069 −0.382360
\(891\) 0 0
\(892\) 28.3845 0.950384
\(893\) −3.40634 −0.113989
\(894\) 21.7451 0.727264
\(895\) 56.0606 1.87390
\(896\) 3.09995 0.103562
\(897\) −21.3918 −0.714252
\(898\) 35.2701 1.17698
\(899\) −9.66669 −0.322402
\(900\) 1.48715 0.0495715
\(901\) −25.2361 −0.840737
\(902\) 0 0
\(903\) −29.9243 −0.995818
\(904\) 11.3668 0.378054
\(905\) −3.80192 −0.126380
\(906\) 25.5747 0.849662
\(907\) −54.8992 −1.82290 −0.911449 0.411413i \(-0.865035\pi\)
−0.911449 + 0.411413i \(0.865035\pi\)
\(908\) 8.50634 0.282293
\(909\) 8.20737 0.272221
\(910\) 30.3388 1.00572
\(911\) 46.8459 1.55207 0.776037 0.630687i \(-0.217227\pi\)
0.776037 + 0.630687i \(0.217227\pi\)
\(912\) 2.10092 0.0695684
\(913\) 0 0
\(914\) 7.37055 0.243796
\(915\) 32.7705 1.08336
\(916\) −1.70730 −0.0564109
\(917\) 14.2213 0.469627
\(918\) −7.15042 −0.235999
\(919\) 1.76516 0.0582272 0.0291136 0.999576i \(-0.490732\pi\)
0.0291136 + 0.999576i \(0.490732\pi\)
\(920\) −6.29625 −0.207581
\(921\) −11.8619 −0.390861
\(922\) 36.4875 1.20165
\(923\) −63.5320 −2.09118
\(924\) 0 0
\(925\) −1.83988 −0.0604947
\(926\) −16.2208 −0.533048
\(927\) −13.5208 −0.444081
\(928\) −6.50365 −0.213493
\(929\) −28.8886 −0.947805 −0.473902 0.880577i \(-0.657155\pi\)
−0.473902 + 0.880577i \(0.657155\pi\)
\(930\) 7.68199 0.251902
\(931\) 2.60971 0.0855297
\(932\) −9.95632 −0.326130
\(933\) 17.6816 0.578870
\(934\) 4.27354 0.139835
\(935\) 0 0
\(936\) 5.62481 0.183853
\(937\) −25.1445 −0.821436 −0.410718 0.911762i \(-0.634722\pi\)
−0.410718 + 0.911762i \(0.634722\pi\)
\(938\) 43.7571 1.42872
\(939\) 65.9198 2.15121
\(940\) −8.37977 −0.273318
\(941\) 0.744662 0.0242753 0.0121376 0.999926i \(-0.496136\pi\)
0.0121376 + 0.999926i \(0.496136\pi\)
\(942\) 7.82359 0.254906
\(943\) 14.0391 0.457175
\(944\) −6.65028 −0.216448
\(945\) −25.4125 −0.826670
\(946\) 0 0
\(947\) 54.6088 1.77455 0.887273 0.461244i \(-0.152597\pi\)
0.887273 + 0.461244i \(0.152597\pi\)
\(948\) −15.2457 −0.495158
\(949\) 12.6361 0.410184
\(950\) 1.05183 0.0341259
\(951\) 15.1327 0.490712
\(952\) 6.65177 0.215585
\(953\) −29.4684 −0.954574 −0.477287 0.878747i \(-0.658380\pi\)
−0.477287 + 0.878747i \(0.658380\pi\)
\(954\) −16.6283 −0.538362
\(955\) 17.5747 0.568703
\(956\) −16.2786 −0.526487
\(957\) 0 0
\(958\) 39.1936 1.26629
\(959\) −42.2742 −1.36511
\(960\) 5.16836 0.166808
\(961\) −28.7908 −0.928734
\(962\) −6.95893 −0.224365
\(963\) 20.5948 0.663659
\(964\) 5.95144 0.191683
\(965\) 29.7616 0.958061
\(966\) −16.6687 −0.536308
\(967\) 30.8647 0.992541 0.496271 0.868168i \(-0.334702\pi\)
0.496271 + 0.868168i \(0.334702\pi\)
\(968\) 0 0
\(969\) 4.50808 0.144820
\(970\) −13.4585 −0.432125
\(971\) −10.8297 −0.347541 −0.173771 0.984786i \(-0.555595\pi\)
−0.173771 + 0.984786i \(0.555595\pi\)
\(972\) −13.6227 −0.436949
\(973\) 17.9482 0.575392
\(974\) 3.27438 0.104918
\(975\) 8.79134 0.281548
\(976\) 6.34059 0.202957
\(977\) 5.53214 0.176989 0.0884945 0.996077i \(-0.471794\pi\)
0.0884945 + 0.996077i \(0.471794\pi\)
\(978\) −41.7916 −1.33635
\(979\) 0 0
\(980\) 6.42000 0.205079
\(981\) 4.77999 0.152613
\(982\) −40.6503 −1.29720
\(983\) 22.2474 0.709583 0.354791 0.934945i \(-0.384552\pi\)
0.354791 + 0.934945i \(0.384552\pi\)
\(984\) −11.5242 −0.367377
\(985\) −44.8998 −1.43063
\(986\) −13.9553 −0.444427
\(987\) −22.1847 −0.706146
\(988\) 3.97832 0.126567
\(989\) 11.7597 0.373938
\(990\) 0 0
\(991\) −8.28887 −0.263305 −0.131652 0.991296i \(-0.542028\pi\)
−0.131652 + 0.991296i \(0.542028\pi\)
\(992\) 1.48635 0.0471916
\(993\) 42.8761 1.36063
\(994\) −49.5049 −1.57020
\(995\) 58.9686 1.86943
\(996\) −23.5651 −0.746688
\(997\) 27.5534 0.872624 0.436312 0.899795i \(-0.356284\pi\)
0.436312 + 0.899795i \(0.356284\pi\)
\(998\) −14.1445 −0.447736
\(999\) 5.82898 0.184421
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.cd.1.8 10
11.7 odd 10 418.2.f.h.115.2 20
11.8 odd 10 418.2.f.h.229.2 yes 20
11.10 odd 2 4598.2.a.cc.1.8 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.f.h.115.2 20 11.7 odd 10
418.2.f.h.229.2 yes 20 11.8 odd 10
4598.2.a.cc.1.8 10 11.10 odd 2
4598.2.a.cd.1.8 10 1.1 even 1 trivial