Properties

Label 2151.4.a.h.1.15
Level $2151$
Weight $4$
Character 2151.1
Self dual yes
Analytic conductor $126.913$
Analytic rank $0$
Dimension $59$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2151.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(126.913108422\)
Analytic rank: \(0\)
Dimension: \(59\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.96448 q^{2} +0.788155 q^{4} +20.3046 q^{5} -25.7042 q^{7} +21.3794 q^{8} +O(q^{10})\) \(q-2.96448 q^{2} +0.788155 q^{4} +20.3046 q^{5} -25.7042 q^{7} +21.3794 q^{8} -60.1925 q^{10} -49.6129 q^{11} +51.2572 q^{13} +76.1995 q^{14} -69.6841 q^{16} -127.732 q^{17} -97.6252 q^{19} +16.0031 q^{20} +147.077 q^{22} -175.901 q^{23} +287.275 q^{25} -151.951 q^{26} -20.2589 q^{28} -16.4948 q^{29} -289.775 q^{31} +35.5420 q^{32} +378.659 q^{34} -521.912 q^{35} +86.9503 q^{37} +289.408 q^{38} +434.099 q^{40} -88.5567 q^{41} -346.091 q^{43} -39.1027 q^{44} +521.456 q^{46} +346.909 q^{47} +317.704 q^{49} -851.622 q^{50} +40.3986 q^{52} -234.823 q^{53} -1007.37 q^{55} -549.539 q^{56} +48.8985 q^{58} +427.583 q^{59} +170.020 q^{61} +859.034 q^{62} +452.109 q^{64} +1040.75 q^{65} +724.407 q^{67} -100.672 q^{68} +1547.20 q^{70} -29.5053 q^{71} -1203.07 q^{73} -257.763 q^{74} -76.9438 q^{76} +1275.26 q^{77} +1204.60 q^{79} -1414.90 q^{80} +262.525 q^{82} +191.594 q^{83} -2593.54 q^{85} +1025.98 q^{86} -1060.69 q^{88} +1007.77 q^{89} -1317.52 q^{91} -138.637 q^{92} -1028.41 q^{94} -1982.24 q^{95} +58.7645 q^{97} -941.828 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.96448 −1.04810 −0.524051 0.851687i \(-0.675580\pi\)
−0.524051 + 0.851687i \(0.675580\pi\)
\(3\) 0 0
\(4\) 0.788155 0.0985194
\(5\) 20.3046 1.81610 0.908048 0.418867i \(-0.137573\pi\)
0.908048 + 0.418867i \(0.137573\pi\)
\(6\) 0 0
\(7\) −25.7042 −1.38789 −0.693947 0.720026i \(-0.744130\pi\)
−0.693947 + 0.720026i \(0.744130\pi\)
\(8\) 21.3794 0.944844
\(9\) 0 0
\(10\) −60.1925 −1.90345
\(11\) −49.6129 −1.35990 −0.679948 0.733260i \(-0.737998\pi\)
−0.679948 + 0.733260i \(0.737998\pi\)
\(12\) 0 0
\(13\) 51.2572 1.09355 0.546776 0.837279i \(-0.315855\pi\)
0.546776 + 0.837279i \(0.315855\pi\)
\(14\) 76.1995 1.45466
\(15\) 0 0
\(16\) −69.6841 −1.08881
\(17\) −127.732 −1.82232 −0.911162 0.412048i \(-0.864813\pi\)
−0.911162 + 0.412048i \(0.864813\pi\)
\(18\) 0 0
\(19\) −97.6252 −1.17878 −0.589388 0.807850i \(-0.700631\pi\)
−0.589388 + 0.807850i \(0.700631\pi\)
\(20\) 16.0031 0.178921
\(21\) 0 0
\(22\) 147.077 1.42531
\(23\) −175.901 −1.59469 −0.797346 0.603522i \(-0.793763\pi\)
−0.797346 + 0.603522i \(0.793763\pi\)
\(24\) 0 0
\(25\) 287.275 2.29820
\(26\) −151.951 −1.14616
\(27\) 0 0
\(28\) −20.2589 −0.136734
\(29\) −16.4948 −0.105621 −0.0528104 0.998605i \(-0.516818\pi\)
−0.0528104 + 0.998605i \(0.516818\pi\)
\(30\) 0 0
\(31\) −289.775 −1.67888 −0.839438 0.543455i \(-0.817116\pi\)
−0.839438 + 0.543455i \(0.817116\pi\)
\(32\) 35.5420 0.196344
\(33\) 0 0
\(34\) 378.659 1.90998
\(35\) −521.912 −2.52055
\(36\) 0 0
\(37\) 86.9503 0.386339 0.193170 0.981165i \(-0.438123\pi\)
0.193170 + 0.981165i \(0.438123\pi\)
\(38\) 289.408 1.23548
\(39\) 0 0
\(40\) 434.099 1.71593
\(41\) −88.5567 −0.337323 −0.168661 0.985674i \(-0.553944\pi\)
−0.168661 + 0.985674i \(0.553944\pi\)
\(42\) 0 0
\(43\) −346.091 −1.22741 −0.613703 0.789537i \(-0.710321\pi\)
−0.613703 + 0.789537i \(0.710321\pi\)
\(44\) −39.1027 −0.133976
\(45\) 0 0
\(46\) 521.456 1.67140
\(47\) 346.909 1.07664 0.538319 0.842741i \(-0.319060\pi\)
0.538319 + 0.842741i \(0.319060\pi\)
\(48\) 0 0
\(49\) 317.704 0.926250
\(50\) −851.622 −2.40875
\(51\) 0 0
\(52\) 40.3986 0.107736
\(53\) −234.823 −0.608592 −0.304296 0.952578i \(-0.598421\pi\)
−0.304296 + 0.952578i \(0.598421\pi\)
\(54\) 0 0
\(55\) −1007.37 −2.46970
\(56\) −549.539 −1.31134
\(57\) 0 0
\(58\) 48.8985 0.110701
\(59\) 427.583 0.943501 0.471751 0.881732i \(-0.343622\pi\)
0.471751 + 0.881732i \(0.343622\pi\)
\(60\) 0 0
\(61\) 170.020 0.356866 0.178433 0.983952i \(-0.442897\pi\)
0.178433 + 0.983952i \(0.442897\pi\)
\(62\) 859.034 1.75964
\(63\) 0 0
\(64\) 452.109 0.883025
\(65\) 1040.75 1.98600
\(66\) 0 0
\(67\) 724.407 1.32090 0.660451 0.750869i \(-0.270365\pi\)
0.660451 + 0.750869i \(0.270365\pi\)
\(68\) −100.672 −0.179534
\(69\) 0 0
\(70\) 1547.20 2.64179
\(71\) −29.5053 −0.0493189 −0.0246594 0.999696i \(-0.507850\pi\)
−0.0246594 + 0.999696i \(0.507850\pi\)
\(72\) 0 0
\(73\) −1203.07 −1.92888 −0.964442 0.264294i \(-0.914861\pi\)
−0.964442 + 0.264294i \(0.914861\pi\)
\(74\) −257.763 −0.404923
\(75\) 0 0
\(76\) −76.9438 −0.116132
\(77\) 1275.26 1.88739
\(78\) 0 0
\(79\) 1204.60 1.71555 0.857775 0.514025i \(-0.171846\pi\)
0.857775 + 0.514025i \(0.171846\pi\)
\(80\) −1414.90 −1.97739
\(81\) 0 0
\(82\) 262.525 0.353549
\(83\) 191.594 0.253376 0.126688 0.991943i \(-0.459565\pi\)
0.126688 + 0.991943i \(0.459565\pi\)
\(84\) 0 0
\(85\) −2593.54 −3.30951
\(86\) 1025.98 1.28645
\(87\) 0 0
\(88\) −1060.69 −1.28489
\(89\) 1007.77 1.20026 0.600132 0.799901i \(-0.295115\pi\)
0.600132 + 0.799901i \(0.295115\pi\)
\(90\) 0 0
\(91\) −1317.52 −1.51774
\(92\) −138.637 −0.157108
\(93\) 0 0
\(94\) −1028.41 −1.12843
\(95\) −1982.24 −2.14077
\(96\) 0 0
\(97\) 58.7645 0.0615116 0.0307558 0.999527i \(-0.490209\pi\)
0.0307558 + 0.999527i \(0.490209\pi\)
\(98\) −941.828 −0.970806
\(99\) 0 0
\(100\) 226.417 0.226417
\(101\) −145.304 −0.143151 −0.0715755 0.997435i \(-0.522803\pi\)
−0.0715755 + 0.997435i \(0.522803\pi\)
\(102\) 0 0
\(103\) 1887.96 1.80608 0.903038 0.429561i \(-0.141332\pi\)
0.903038 + 0.429561i \(0.141332\pi\)
\(104\) 1095.85 1.03324
\(105\) 0 0
\(106\) 696.127 0.637867
\(107\) 971.749 0.877967 0.438984 0.898495i \(-0.355339\pi\)
0.438984 + 0.898495i \(0.355339\pi\)
\(108\) 0 0
\(109\) 1672.48 1.46968 0.734838 0.678243i \(-0.237258\pi\)
0.734838 + 0.678243i \(0.237258\pi\)
\(110\) 2986.33 2.58850
\(111\) 0 0
\(112\) 1791.17 1.51116
\(113\) −62.9425 −0.0523994 −0.0261997 0.999657i \(-0.508341\pi\)
−0.0261997 + 0.999657i \(0.508341\pi\)
\(114\) 0 0
\(115\) −3571.59 −2.89611
\(116\) −13.0004 −0.0104057
\(117\) 0 0
\(118\) −1267.56 −0.988886
\(119\) 3283.24 2.52919
\(120\) 0 0
\(121\) 1130.44 0.849317
\(122\) −504.021 −0.374032
\(123\) 0 0
\(124\) −228.388 −0.165402
\(125\) 3294.93 2.35766
\(126\) 0 0
\(127\) 802.101 0.560432 0.280216 0.959937i \(-0.409594\pi\)
0.280216 + 0.959937i \(0.409594\pi\)
\(128\) −1624.60 −1.12184
\(129\) 0 0
\(130\) −3085.30 −2.08153
\(131\) −366.963 −0.244746 −0.122373 0.992484i \(-0.539050\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(132\) 0 0
\(133\) 2509.37 1.63602
\(134\) −2147.49 −1.38444
\(135\) 0 0
\(136\) −2730.83 −1.72181
\(137\) 1591.63 0.992568 0.496284 0.868160i \(-0.334697\pi\)
0.496284 + 0.868160i \(0.334697\pi\)
\(138\) 0 0
\(139\) −1268.70 −0.774168 −0.387084 0.922044i \(-0.626518\pi\)
−0.387084 + 0.922044i \(0.626518\pi\)
\(140\) −411.347 −0.248323
\(141\) 0 0
\(142\) 87.4681 0.0516912
\(143\) −2543.02 −1.48712
\(144\) 0 0
\(145\) −334.919 −0.191817
\(146\) 3566.48 2.02167
\(147\) 0 0
\(148\) 68.5303 0.0380619
\(149\) −241.701 −0.132892 −0.0664459 0.997790i \(-0.521166\pi\)
−0.0664459 + 0.997790i \(0.521166\pi\)
\(150\) 0 0
\(151\) −211.546 −0.114009 −0.0570045 0.998374i \(-0.518155\pi\)
−0.0570045 + 0.998374i \(0.518155\pi\)
\(152\) −2087.17 −1.11376
\(153\) 0 0
\(154\) −3780.48 −1.97818
\(155\) −5883.76 −3.04900
\(156\) 0 0
\(157\) −2178.32 −1.10732 −0.553658 0.832744i \(-0.686768\pi\)
−0.553658 + 0.832744i \(0.686768\pi\)
\(158\) −3571.03 −1.79807
\(159\) 0 0
\(160\) 721.666 0.356579
\(161\) 4521.39 2.21326
\(162\) 0 0
\(163\) −598.892 −0.287784 −0.143892 0.989593i \(-0.545962\pi\)
−0.143892 + 0.989593i \(0.545962\pi\)
\(164\) −69.7964 −0.0332328
\(165\) 0 0
\(166\) −567.977 −0.265564
\(167\) −421.028 −0.195091 −0.0975453 0.995231i \(-0.531099\pi\)
−0.0975453 + 0.995231i \(0.531099\pi\)
\(168\) 0 0
\(169\) 430.298 0.195857
\(170\) 7688.50 3.46871
\(171\) 0 0
\(172\) −272.774 −0.120923
\(173\) 4319.92 1.89848 0.949241 0.314551i \(-0.101854\pi\)
0.949241 + 0.314551i \(0.101854\pi\)
\(174\) 0 0
\(175\) −7384.17 −3.18966
\(176\) 3457.23 1.48067
\(177\) 0 0
\(178\) −2987.52 −1.25800
\(179\) −2.38961 −0.000997808 0 −0.000498904 1.00000i \(-0.500159\pi\)
−0.000498904 1.00000i \(0.500159\pi\)
\(180\) 0 0
\(181\) −1432.19 −0.588143 −0.294072 0.955783i \(-0.595010\pi\)
−0.294072 + 0.955783i \(0.595010\pi\)
\(182\) 3905.77 1.59074
\(183\) 0 0
\(184\) −3760.66 −1.50674
\(185\) 1765.49 0.701628
\(186\) 0 0
\(187\) 6337.14 2.47817
\(188\) 273.418 0.106070
\(189\) 0 0
\(190\) 5876.30 2.24375
\(191\) −3769.31 −1.42795 −0.713973 0.700173i \(-0.753106\pi\)
−0.713973 + 0.700173i \(0.753106\pi\)
\(192\) 0 0
\(193\) −2778.74 −1.03636 −0.518182 0.855270i \(-0.673391\pi\)
−0.518182 + 0.855270i \(0.673391\pi\)
\(194\) −174.206 −0.0644705
\(195\) 0 0
\(196\) 250.400 0.0912536
\(197\) 2904.23 1.05034 0.525172 0.850996i \(-0.324001\pi\)
0.525172 + 0.850996i \(0.324001\pi\)
\(198\) 0 0
\(199\) −3462.83 −1.23354 −0.616768 0.787145i \(-0.711558\pi\)
−0.616768 + 0.787145i \(0.711558\pi\)
\(200\) 6141.77 2.17144
\(201\) 0 0
\(202\) 430.750 0.150037
\(203\) 423.984 0.146590
\(204\) 0 0
\(205\) −1798.10 −0.612610
\(206\) −5596.81 −1.89295
\(207\) 0 0
\(208\) −3571.81 −1.19067
\(209\) 4843.47 1.60301
\(210\) 0 0
\(211\) −2056.51 −0.670975 −0.335487 0.942045i \(-0.608901\pi\)
−0.335487 + 0.942045i \(0.608901\pi\)
\(212\) −185.077 −0.0599581
\(213\) 0 0
\(214\) −2880.73 −0.920200
\(215\) −7027.23 −2.22908
\(216\) 0 0
\(217\) 7448.43 2.33010
\(218\) −4958.04 −1.54037
\(219\) 0 0
\(220\) −793.962 −0.243313
\(221\) −6547.17 −1.99281
\(222\) 0 0
\(223\) 359.449 0.107939 0.0539697 0.998543i \(-0.482813\pi\)
0.0539697 + 0.998543i \(0.482813\pi\)
\(224\) −913.578 −0.272505
\(225\) 0 0
\(226\) 186.592 0.0549199
\(227\) −3911.17 −1.14358 −0.571792 0.820398i \(-0.693752\pi\)
−0.571792 + 0.820398i \(0.693752\pi\)
\(228\) 0 0
\(229\) −2409.64 −0.695342 −0.347671 0.937617i \(-0.613027\pi\)
−0.347671 + 0.937617i \(0.613027\pi\)
\(230\) 10587.9 3.03542
\(231\) 0 0
\(232\) −352.648 −0.0997952
\(233\) −102.677 −0.0288696 −0.0144348 0.999896i \(-0.504595\pi\)
−0.0144348 + 0.999896i \(0.504595\pi\)
\(234\) 0 0
\(235\) 7043.84 1.95528
\(236\) 337.002 0.0929531
\(237\) 0 0
\(238\) −9733.10 −2.65085
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) −1694.91 −0.453023 −0.226511 0.974009i \(-0.572732\pi\)
−0.226511 + 0.974009i \(0.572732\pi\)
\(242\) −3351.17 −0.890171
\(243\) 0 0
\(244\) 134.002 0.0351582
\(245\) 6450.84 1.68216
\(246\) 0 0
\(247\) −5003.99 −1.28905
\(248\) −6195.22 −1.58628
\(249\) 0 0
\(250\) −9767.75 −2.47107
\(251\) −7693.01 −1.93458 −0.967288 0.253681i \(-0.918359\pi\)
−0.967288 + 0.253681i \(0.918359\pi\)
\(252\) 0 0
\(253\) 8726.96 2.16861
\(254\) −2377.81 −0.587391
\(255\) 0 0
\(256\) 1199.24 0.292784
\(257\) 1383.71 0.335851 0.167925 0.985800i \(-0.446293\pi\)
0.167925 + 0.985800i \(0.446293\pi\)
\(258\) 0 0
\(259\) −2234.98 −0.536198
\(260\) 820.276 0.195659
\(261\) 0 0
\(262\) 1087.86 0.256519
\(263\) 7580.93 1.77742 0.888708 0.458473i \(-0.151604\pi\)
0.888708 + 0.458473i \(0.151604\pi\)
\(264\) 0 0
\(265\) −4767.97 −1.10526
\(266\) −7438.99 −1.71471
\(267\) 0 0
\(268\) 570.945 0.130134
\(269\) 773.031 0.175214 0.0876069 0.996155i \(-0.472078\pi\)
0.0876069 + 0.996155i \(0.472078\pi\)
\(270\) 0 0
\(271\) 6402.73 1.43520 0.717598 0.696458i \(-0.245242\pi\)
0.717598 + 0.696458i \(0.245242\pi\)
\(272\) 8900.87 1.98417
\(273\) 0 0
\(274\) −4718.35 −1.04031
\(275\) −14252.6 −3.12531
\(276\) 0 0
\(277\) 2367.03 0.513434 0.256717 0.966487i \(-0.417359\pi\)
0.256717 + 0.966487i \(0.417359\pi\)
\(278\) 3761.03 0.811408
\(279\) 0 0
\(280\) −11158.2 −2.38153
\(281\) 3994.73 0.848063 0.424032 0.905647i \(-0.360615\pi\)
0.424032 + 0.905647i \(0.360615\pi\)
\(282\) 0 0
\(283\) 5609.87 1.17835 0.589173 0.808007i \(-0.299454\pi\)
0.589173 + 0.808007i \(0.299454\pi\)
\(284\) −23.2548 −0.00485886
\(285\) 0 0
\(286\) 7538.73 1.55865
\(287\) 2276.28 0.468168
\(288\) 0 0
\(289\) 11402.4 2.32086
\(290\) 992.862 0.201044
\(291\) 0 0
\(292\) −948.205 −0.190032
\(293\) −3906.04 −0.778817 −0.389409 0.921065i \(-0.627321\pi\)
−0.389409 + 0.921065i \(0.627321\pi\)
\(294\) 0 0
\(295\) 8681.88 1.71349
\(296\) 1858.94 0.365030
\(297\) 0 0
\(298\) 716.517 0.139284
\(299\) −9016.19 −1.74388
\(300\) 0 0
\(301\) 8895.99 1.70351
\(302\) 627.124 0.119493
\(303\) 0 0
\(304\) 6802.92 1.28347
\(305\) 3452.18 0.648103
\(306\) 0 0
\(307\) −2829.34 −0.525991 −0.262995 0.964797i \(-0.584710\pi\)
−0.262995 + 0.964797i \(0.584710\pi\)
\(308\) 1005.10 0.185945
\(309\) 0 0
\(310\) 17442.3 3.19567
\(311\) 7494.76 1.36652 0.683262 0.730174i \(-0.260561\pi\)
0.683262 + 0.730174i \(0.260561\pi\)
\(312\) 0 0
\(313\) 3199.49 0.577782 0.288891 0.957362i \(-0.406713\pi\)
0.288891 + 0.957362i \(0.406713\pi\)
\(314\) 6457.58 1.16058
\(315\) 0 0
\(316\) 949.414 0.169015
\(317\) 1703.90 0.301895 0.150947 0.988542i \(-0.451768\pi\)
0.150947 + 0.988542i \(0.451768\pi\)
\(318\) 0 0
\(319\) 818.354 0.143633
\(320\) 9179.87 1.60366
\(321\) 0 0
\(322\) −13403.6 −2.31973
\(323\) 12469.8 2.14811
\(324\) 0 0
\(325\) 14724.9 2.51320
\(326\) 1775.41 0.301628
\(327\) 0 0
\(328\) −1893.29 −0.318717
\(329\) −8917.02 −1.49426
\(330\) 0 0
\(331\) −449.298 −0.0746092 −0.0373046 0.999304i \(-0.511877\pi\)
−0.0373046 + 0.999304i \(0.511877\pi\)
\(332\) 151.006 0.0249624
\(333\) 0 0
\(334\) 1248.13 0.204475
\(335\) 14708.8 2.39888
\(336\) 0 0
\(337\) −10616.9 −1.71615 −0.858073 0.513528i \(-0.828338\pi\)
−0.858073 + 0.513528i \(0.828338\pi\)
\(338\) −1275.61 −0.205278
\(339\) 0 0
\(340\) −2044.11 −0.326051
\(341\) 14376.6 2.28310
\(342\) 0 0
\(343\) 650.215 0.102357
\(344\) −7399.22 −1.15971
\(345\) 0 0
\(346\) −12806.3 −1.98980
\(347\) 2930.04 0.453293 0.226647 0.973977i \(-0.427224\pi\)
0.226647 + 0.973977i \(0.427224\pi\)
\(348\) 0 0
\(349\) −6874.66 −1.05442 −0.527209 0.849735i \(-0.676762\pi\)
−0.527209 + 0.849735i \(0.676762\pi\)
\(350\) 21890.2 3.34309
\(351\) 0 0
\(352\) −1763.34 −0.267007
\(353\) 10603.9 1.59883 0.799415 0.600780i \(-0.205143\pi\)
0.799415 + 0.600780i \(0.205143\pi\)
\(354\) 0 0
\(355\) −599.093 −0.0895678
\(356\) 794.280 0.118249
\(357\) 0 0
\(358\) 7.08395 0.00104581
\(359\) 75.6572 0.0111227 0.00556133 0.999985i \(-0.498230\pi\)
0.00556133 + 0.999985i \(0.498230\pi\)
\(360\) 0 0
\(361\) 2671.67 0.389513
\(362\) 4245.71 0.616435
\(363\) 0 0
\(364\) −1038.41 −0.149526
\(365\) −24427.8 −3.50304
\(366\) 0 0
\(367\) −3790.84 −0.539184 −0.269592 0.962975i \(-0.586889\pi\)
−0.269592 + 0.962975i \(0.586889\pi\)
\(368\) 12257.5 1.73632
\(369\) 0 0
\(370\) −5233.76 −0.735379
\(371\) 6035.92 0.844661
\(372\) 0 0
\(373\) −1797.32 −0.249495 −0.124747 0.992189i \(-0.539812\pi\)
−0.124747 + 0.992189i \(0.539812\pi\)
\(374\) −18786.4 −2.59738
\(375\) 0 0
\(376\) 7416.71 1.01725
\(377\) −845.475 −0.115502
\(378\) 0 0
\(379\) 13319.4 1.80520 0.902602 0.430475i \(-0.141654\pi\)
0.902602 + 0.430475i \(0.141654\pi\)
\(380\) −1562.31 −0.210907
\(381\) 0 0
\(382\) 11174.0 1.49663
\(383\) −1097.73 −0.146452 −0.0732260 0.997315i \(-0.523329\pi\)
−0.0732260 + 0.997315i \(0.523329\pi\)
\(384\) 0 0
\(385\) 25893.6 3.42768
\(386\) 8237.54 1.08622
\(387\) 0 0
\(388\) 46.3155 0.00606009
\(389\) 7483.53 0.975398 0.487699 0.873012i \(-0.337836\pi\)
0.487699 + 0.873012i \(0.337836\pi\)
\(390\) 0 0
\(391\) 22468.2 2.90605
\(392\) 6792.31 0.875162
\(393\) 0 0
\(394\) −8609.54 −1.10087
\(395\) 24458.9 3.11560
\(396\) 0 0
\(397\) 4426.81 0.559635 0.279818 0.960053i \(-0.409726\pi\)
0.279818 + 0.960053i \(0.409726\pi\)
\(398\) 10265.5 1.29287
\(399\) 0 0
\(400\) −20018.5 −2.50231
\(401\) 7266.49 0.904915 0.452458 0.891786i \(-0.350547\pi\)
0.452458 + 0.891786i \(0.350547\pi\)
\(402\) 0 0
\(403\) −14853.1 −1.83594
\(404\) −114.522 −0.0141031
\(405\) 0 0
\(406\) −1256.89 −0.153642
\(407\) −4313.86 −0.525381
\(408\) 0 0
\(409\) 553.982 0.0669747 0.0334874 0.999439i \(-0.489339\pi\)
0.0334874 + 0.999439i \(0.489339\pi\)
\(410\) 5330.45 0.642078
\(411\) 0 0
\(412\) 1488.00 0.177933
\(413\) −10990.7 −1.30948
\(414\) 0 0
\(415\) 3890.23 0.460154
\(416\) 1821.78 0.214712
\(417\) 0 0
\(418\) −14358.4 −1.68012
\(419\) 13106.6 1.52816 0.764079 0.645123i \(-0.223194\pi\)
0.764079 + 0.645123i \(0.223194\pi\)
\(420\) 0 0
\(421\) 11133.5 1.28887 0.644434 0.764660i \(-0.277093\pi\)
0.644434 + 0.764660i \(0.277093\pi\)
\(422\) 6096.47 0.703250
\(423\) 0 0
\(424\) −5020.36 −0.575024
\(425\) −36694.2 −4.18807
\(426\) 0 0
\(427\) −4370.22 −0.495292
\(428\) 765.889 0.0864968
\(429\) 0 0
\(430\) 20832.1 2.33631
\(431\) −14193.7 −1.58628 −0.793138 0.609042i \(-0.791554\pi\)
−0.793138 + 0.609042i \(0.791554\pi\)
\(432\) 0 0
\(433\) 8641.86 0.959125 0.479562 0.877508i \(-0.340795\pi\)
0.479562 + 0.877508i \(0.340795\pi\)
\(434\) −22080.7 −2.44219
\(435\) 0 0
\(436\) 1318.17 0.144792
\(437\) 17172.4 1.87978
\(438\) 0 0
\(439\) −6963.77 −0.757090 −0.378545 0.925583i \(-0.623575\pi\)
−0.378545 + 0.925583i \(0.623575\pi\)
\(440\) −21536.9 −2.33348
\(441\) 0 0
\(442\) 19409.0 2.08867
\(443\) 5282.31 0.566524 0.283262 0.959043i \(-0.408583\pi\)
0.283262 + 0.959043i \(0.408583\pi\)
\(444\) 0 0
\(445\) 20462.3 2.17979
\(446\) −1065.58 −0.113132
\(447\) 0 0
\(448\) −11621.1 −1.22554
\(449\) −6696.11 −0.703806 −0.351903 0.936036i \(-0.614465\pi\)
−0.351903 + 0.936036i \(0.614465\pi\)
\(450\) 0 0
\(451\) 4393.55 0.458724
\(452\) −49.6084 −0.00516236
\(453\) 0 0
\(454\) 11594.6 1.19859
\(455\) −26751.7 −2.75635
\(456\) 0 0
\(457\) −9008.10 −0.922059 −0.461030 0.887385i \(-0.652520\pi\)
−0.461030 + 0.887385i \(0.652520\pi\)
\(458\) 7143.33 0.728790
\(459\) 0 0
\(460\) −2814.97 −0.285323
\(461\) −5976.41 −0.603794 −0.301897 0.953341i \(-0.597620\pi\)
−0.301897 + 0.953341i \(0.597620\pi\)
\(462\) 0 0
\(463\) −17279.0 −1.73440 −0.867198 0.497964i \(-0.834081\pi\)
−0.867198 + 0.497964i \(0.834081\pi\)
\(464\) 1149.42 0.115001
\(465\) 0 0
\(466\) 304.385 0.0302583
\(467\) −11059.4 −1.09586 −0.547932 0.836523i \(-0.684585\pi\)
−0.547932 + 0.836523i \(0.684585\pi\)
\(468\) 0 0
\(469\) −18620.3 −1.83327
\(470\) −20881.3 −2.04933
\(471\) 0 0
\(472\) 9141.46 0.891462
\(473\) 17170.6 1.66914
\(474\) 0 0
\(475\) −28045.3 −2.70906
\(476\) 2587.70 0.249175
\(477\) 0 0
\(478\) 708.511 0.0677961
\(479\) −3287.38 −0.313579 −0.156789 0.987632i \(-0.550114\pi\)
−0.156789 + 0.987632i \(0.550114\pi\)
\(480\) 0 0
\(481\) 4456.83 0.422482
\(482\) 5024.52 0.474815
\(483\) 0 0
\(484\) 890.962 0.0836742
\(485\) 1193.19 0.111711
\(486\) 0 0
\(487\) 998.298 0.0928896 0.0464448 0.998921i \(-0.485211\pi\)
0.0464448 + 0.998921i \(0.485211\pi\)
\(488\) 3634.92 0.337183
\(489\) 0 0
\(490\) −19123.4 −1.76308
\(491\) −12962.9 −1.19147 −0.595733 0.803183i \(-0.703138\pi\)
−0.595733 + 0.803183i \(0.703138\pi\)
\(492\) 0 0
\(493\) 2106.91 0.192475
\(494\) 14834.2 1.35106
\(495\) 0 0
\(496\) 20192.7 1.82798
\(497\) 758.410 0.0684494
\(498\) 0 0
\(499\) −21620.5 −1.93961 −0.969807 0.243873i \(-0.921582\pi\)
−0.969807 + 0.243873i \(0.921582\pi\)
\(500\) 2596.91 0.232275
\(501\) 0 0
\(502\) 22805.8 2.02763
\(503\) −10796.7 −0.957058 −0.478529 0.878072i \(-0.658830\pi\)
−0.478529 + 0.878072i \(0.658830\pi\)
\(504\) 0 0
\(505\) −2950.33 −0.259976
\(506\) −25870.9 −2.27293
\(507\) 0 0
\(508\) 632.180 0.0552135
\(509\) 12066.0 1.05072 0.525359 0.850880i \(-0.323931\pi\)
0.525359 + 0.850880i \(0.323931\pi\)
\(510\) 0 0
\(511\) 30923.9 2.67709
\(512\) 9441.70 0.814977
\(513\) 0 0
\(514\) −4101.99 −0.352006
\(515\) 38334.1 3.28001
\(516\) 0 0
\(517\) −17211.2 −1.46411
\(518\) 6625.57 0.561990
\(519\) 0 0
\(520\) 22250.7 1.87646
\(521\) 13033.5 1.09599 0.547994 0.836482i \(-0.315392\pi\)
0.547994 + 0.836482i \(0.315392\pi\)
\(522\) 0 0
\(523\) −11294.2 −0.944283 −0.472141 0.881523i \(-0.656519\pi\)
−0.472141 + 0.881523i \(0.656519\pi\)
\(524\) −289.224 −0.0241122
\(525\) 0 0
\(526\) −22473.5 −1.86291
\(527\) 37013.5 3.05946
\(528\) 0 0
\(529\) 18774.2 1.54304
\(530\) 14134.6 1.15843
\(531\) 0 0
\(532\) 1977.77 0.161179
\(533\) −4539.17 −0.368880
\(534\) 0 0
\(535\) 19730.9 1.59447
\(536\) 15487.4 1.24805
\(537\) 0 0
\(538\) −2291.64 −0.183642
\(539\) −15762.2 −1.25960
\(540\) 0 0
\(541\) −15543.5 −1.23525 −0.617624 0.786474i \(-0.711905\pi\)
−0.617624 + 0.786474i \(0.711905\pi\)
\(542\) −18980.8 −1.50423
\(543\) 0 0
\(544\) −4539.85 −0.357802
\(545\) 33959.0 2.66907
\(546\) 0 0
\(547\) 18479.4 1.44447 0.722233 0.691650i \(-0.243116\pi\)
0.722233 + 0.691650i \(0.243116\pi\)
\(548\) 1254.45 0.0977872
\(549\) 0 0
\(550\) 42251.4 3.27565
\(551\) 1610.30 0.124503
\(552\) 0 0
\(553\) −30963.3 −2.38100
\(554\) −7017.03 −0.538132
\(555\) 0 0
\(556\) −999.929 −0.0762706
\(557\) 1232.15 0.0937304 0.0468652 0.998901i \(-0.485077\pi\)
0.0468652 + 0.998901i \(0.485077\pi\)
\(558\) 0 0
\(559\) −17739.7 −1.34223
\(560\) 36368.9 2.74441
\(561\) 0 0
\(562\) −11842.3 −0.888858
\(563\) 21917.7 1.64071 0.820356 0.571853i \(-0.193775\pi\)
0.820356 + 0.571853i \(0.193775\pi\)
\(564\) 0 0
\(565\) −1278.02 −0.0951623
\(566\) −16630.3 −1.23503
\(567\) 0 0
\(568\) −630.806 −0.0465987
\(569\) 16714.5 1.23147 0.615736 0.787952i \(-0.288859\pi\)
0.615736 + 0.787952i \(0.288859\pi\)
\(570\) 0 0
\(571\) −15191.2 −1.11337 −0.556684 0.830725i \(-0.687926\pi\)
−0.556684 + 0.830725i \(0.687926\pi\)
\(572\) −2004.29 −0.146510
\(573\) 0 0
\(574\) −6747.98 −0.490688
\(575\) −50532.0 −3.66492
\(576\) 0 0
\(577\) −10638.4 −0.767563 −0.383781 0.923424i \(-0.625378\pi\)
−0.383781 + 0.923424i \(0.625378\pi\)
\(578\) −33802.2 −2.43250
\(579\) 0 0
\(580\) −263.968 −0.0188977
\(581\) −4924.77 −0.351659
\(582\) 0 0
\(583\) 11650.2 0.827621
\(584\) −25720.9 −1.82250
\(585\) 0 0
\(586\) 11579.4 0.816281
\(587\) 7932.26 0.557750 0.278875 0.960327i \(-0.410038\pi\)
0.278875 + 0.960327i \(0.410038\pi\)
\(588\) 0 0
\(589\) 28289.4 1.97902
\(590\) −25737.3 −1.79591
\(591\) 0 0
\(592\) −6059.05 −0.420651
\(593\) 20361.1 1.41000 0.704999 0.709208i \(-0.250947\pi\)
0.704999 + 0.709208i \(0.250947\pi\)
\(594\) 0 0
\(595\) 66664.7 4.59325
\(596\) −190.498 −0.0130924
\(597\) 0 0
\(598\) 26728.3 1.82776
\(599\) 7549.97 0.514997 0.257499 0.966279i \(-0.417102\pi\)
0.257499 + 0.966279i \(0.417102\pi\)
\(600\) 0 0
\(601\) 14106.0 0.957398 0.478699 0.877979i \(-0.341109\pi\)
0.478699 + 0.877979i \(0.341109\pi\)
\(602\) −26372.0 −1.78545
\(603\) 0 0
\(604\) −166.731 −0.0112321
\(605\) 22953.1 1.54244
\(606\) 0 0
\(607\) −3652.23 −0.244216 −0.122108 0.992517i \(-0.538965\pi\)
−0.122108 + 0.992517i \(0.538965\pi\)
\(608\) −3469.80 −0.231446
\(609\) 0 0
\(610\) −10233.9 −0.679278
\(611\) 17781.6 1.17736
\(612\) 0 0
\(613\) −22961.7 −1.51291 −0.756454 0.654046i \(-0.773070\pi\)
−0.756454 + 0.654046i \(0.773070\pi\)
\(614\) 8387.54 0.551292
\(615\) 0 0
\(616\) 27264.2 1.78329
\(617\) 6976.88 0.455233 0.227616 0.973751i \(-0.426907\pi\)
0.227616 + 0.973751i \(0.426907\pi\)
\(618\) 0 0
\(619\) −17452.2 −1.13322 −0.566610 0.823986i \(-0.691745\pi\)
−0.566610 + 0.823986i \(0.691745\pi\)
\(620\) −4637.32 −0.300386
\(621\) 0 0
\(622\) −22218.1 −1.43226
\(623\) −25903.9 −1.66584
\(624\) 0 0
\(625\) 30992.6 1.98353
\(626\) −9484.83 −0.605575
\(627\) 0 0
\(628\) −1716.85 −0.109092
\(629\) −11106.3 −0.704035
\(630\) 0 0
\(631\) 12015.3 0.758034 0.379017 0.925390i \(-0.376262\pi\)
0.379017 + 0.925390i \(0.376262\pi\)
\(632\) 25753.7 1.62093
\(633\) 0 0
\(634\) −5051.19 −0.316417
\(635\) 16286.3 1.01780
\(636\) 0 0
\(637\) 16284.6 1.01290
\(638\) −2425.99 −0.150542
\(639\) 0 0
\(640\) −32986.9 −2.03738
\(641\) 3224.56 0.198693 0.0993467 0.995053i \(-0.468325\pi\)
0.0993467 + 0.995053i \(0.468325\pi\)
\(642\) 0 0
\(643\) 20969.8 1.28611 0.643055 0.765820i \(-0.277667\pi\)
0.643055 + 0.765820i \(0.277667\pi\)
\(644\) 3563.56 0.218049
\(645\) 0 0
\(646\) −36966.6 −2.25144
\(647\) −19896.6 −1.20899 −0.604493 0.796610i \(-0.706624\pi\)
−0.604493 + 0.796610i \(0.706624\pi\)
\(648\) 0 0
\(649\) −21213.6 −1.28306
\(650\) −43651.7 −2.63410
\(651\) 0 0
\(652\) −472.020 −0.0283523
\(653\) 18417.7 1.10374 0.551869 0.833931i \(-0.313915\pi\)
0.551869 + 0.833931i \(0.313915\pi\)
\(654\) 0 0
\(655\) −7451.03 −0.444482
\(656\) 6170.99 0.367281
\(657\) 0 0
\(658\) 26434.3 1.56614
\(659\) −26225.4 −1.55022 −0.775110 0.631826i \(-0.782306\pi\)
−0.775110 + 0.631826i \(0.782306\pi\)
\(660\) 0 0
\(661\) 24662.9 1.45125 0.725623 0.688092i \(-0.241552\pi\)
0.725623 + 0.688092i \(0.241552\pi\)
\(662\) 1331.94 0.0781981
\(663\) 0 0
\(664\) 4096.16 0.239401
\(665\) 50951.7 2.97116
\(666\) 0 0
\(667\) 2901.45 0.168433
\(668\) −331.835 −0.0192202
\(669\) 0 0
\(670\) −43603.9 −2.51428
\(671\) −8435.19 −0.485301
\(672\) 0 0
\(673\) −20312.4 −1.16343 −0.581713 0.813394i \(-0.697617\pi\)
−0.581713 + 0.813394i \(0.697617\pi\)
\(674\) 31473.7 1.79870
\(675\) 0 0
\(676\) 339.141 0.0192957
\(677\) −13110.5 −0.744278 −0.372139 0.928177i \(-0.621375\pi\)
−0.372139 + 0.928177i \(0.621375\pi\)
\(678\) 0 0
\(679\) −1510.49 −0.0853716
\(680\) −55448.2 −3.12697
\(681\) 0 0
\(682\) −42619.2 −2.39292
\(683\) −2293.08 −0.128466 −0.0642330 0.997935i \(-0.520460\pi\)
−0.0642330 + 0.997935i \(0.520460\pi\)
\(684\) 0 0
\(685\) 32317.3 1.80260
\(686\) −1927.55 −0.107280
\(687\) 0 0
\(688\) 24117.0 1.33642
\(689\) −12036.3 −0.665527
\(690\) 0 0
\(691\) 5086.75 0.280042 0.140021 0.990149i \(-0.455283\pi\)
0.140021 + 0.990149i \(0.455283\pi\)
\(692\) 3404.77 0.187037
\(693\) 0 0
\(694\) −8686.05 −0.475098
\(695\) −25760.3 −1.40596
\(696\) 0 0
\(697\) 11311.5 0.614711
\(698\) 20379.8 1.10514
\(699\) 0 0
\(700\) −5819.87 −0.314243
\(701\) 32271.2 1.73875 0.869376 0.494151i \(-0.164521\pi\)
0.869376 + 0.494151i \(0.164521\pi\)
\(702\) 0 0
\(703\) −8488.54 −0.455407
\(704\) −22430.4 −1.20082
\(705\) 0 0
\(706\) −31435.0 −1.67574
\(707\) 3734.91 0.198678
\(708\) 0 0
\(709\) 2369.04 0.125488 0.0627441 0.998030i \(-0.480015\pi\)
0.0627441 + 0.998030i \(0.480015\pi\)
\(710\) 1776.00 0.0938762
\(711\) 0 0
\(712\) 21545.5 1.13406
\(713\) 50971.8 2.67729
\(714\) 0 0
\(715\) −51634.8 −2.70075
\(716\) −1.88338 −9.83034e−5 0
\(717\) 0 0
\(718\) −224.284 −0.0116577
\(719\) 1461.76 0.0758200 0.0379100 0.999281i \(-0.487930\pi\)
0.0379100 + 0.999281i \(0.487930\pi\)
\(720\) 0 0
\(721\) −48528.3 −2.50664
\(722\) −7920.12 −0.408250
\(723\) 0 0
\(724\) −1128.79 −0.0579435
\(725\) −4738.54 −0.242738
\(726\) 0 0
\(727\) 12826.8 0.654359 0.327179 0.944962i \(-0.393902\pi\)
0.327179 + 0.944962i \(0.393902\pi\)
\(728\) −28167.8 −1.43402
\(729\) 0 0
\(730\) 72415.7 3.67154
\(731\) 44206.9 2.23673
\(732\) 0 0
\(733\) −23659.8 −1.19222 −0.596108 0.802904i \(-0.703287\pi\)
−0.596108 + 0.802904i \(0.703287\pi\)
\(734\) 11237.9 0.565120
\(735\) 0 0
\(736\) −6251.89 −0.313108
\(737\) −35939.9 −1.79629
\(738\) 0 0
\(739\) 23944.7 1.19191 0.595953 0.803019i \(-0.296774\pi\)
0.595953 + 0.803019i \(0.296774\pi\)
\(740\) 1391.48 0.0691240
\(741\) 0 0
\(742\) −17893.4 −0.885291
\(743\) 13425.5 0.662900 0.331450 0.943473i \(-0.392462\pi\)
0.331450 + 0.943473i \(0.392462\pi\)
\(744\) 0 0
\(745\) −4907.63 −0.241344
\(746\) 5328.11 0.261496
\(747\) 0 0
\(748\) 4994.65 0.244148
\(749\) −24978.0 −1.21853
\(750\) 0 0
\(751\) −9964.72 −0.484178 −0.242089 0.970254i \(-0.577833\pi\)
−0.242089 + 0.970254i \(0.577833\pi\)
\(752\) −24174.1 −1.17226
\(753\) 0 0
\(754\) 2506.40 0.121058
\(755\) −4295.35 −0.207051
\(756\) 0 0
\(757\) −23792.0 −1.14232 −0.571159 0.820839i \(-0.693506\pi\)
−0.571159 + 0.820839i \(0.693506\pi\)
\(758\) −39485.2 −1.89204
\(759\) 0 0
\(760\) −42379.0 −2.02269
\(761\) −25279.5 −1.20418 −0.602091 0.798428i \(-0.705665\pi\)
−0.602091 + 0.798428i \(0.705665\pi\)
\(762\) 0 0
\(763\) −42989.7 −2.03975
\(764\) −2970.80 −0.140680
\(765\) 0 0
\(766\) 3254.19 0.153497
\(767\) 21916.7 1.03177
\(768\) 0 0
\(769\) −17553.0 −0.823116 −0.411558 0.911384i \(-0.635015\pi\)
−0.411558 + 0.911384i \(0.635015\pi\)
\(770\) −76761.0 −3.59256
\(771\) 0 0
\(772\) −2190.08 −0.102102
\(773\) 29507.6 1.37298 0.686490 0.727139i \(-0.259150\pi\)
0.686490 + 0.727139i \(0.259150\pi\)
\(774\) 0 0
\(775\) −83245.2 −3.85840
\(776\) 1256.35 0.0581189
\(777\) 0 0
\(778\) −22184.8 −1.02232
\(779\) 8645.36 0.397628
\(780\) 0 0
\(781\) 1463.85 0.0670685
\(782\) −66606.5 −3.04583
\(783\) 0 0
\(784\) −22138.9 −1.00851
\(785\) −44229.7 −2.01099
\(786\) 0 0
\(787\) −21920.3 −0.992851 −0.496426 0.868079i \(-0.665354\pi\)
−0.496426 + 0.868079i \(0.665354\pi\)
\(788\) 2288.98 0.103479
\(789\) 0 0
\(790\) −72508.1 −3.26547
\(791\) 1617.88 0.0727248
\(792\) 0 0
\(793\) 8714.75 0.390252
\(794\) −13123.2 −0.586555
\(795\) 0 0
\(796\) −2729.25 −0.121527
\(797\) −12991.8 −0.577408 −0.288704 0.957418i \(-0.593224\pi\)
−0.288704 + 0.957418i \(0.593224\pi\)
\(798\) 0 0
\(799\) −44311.4 −1.96198
\(800\) 10210.3 0.451238
\(801\) 0 0
\(802\) −21541.4 −0.948444
\(803\) 59687.7 2.62308
\(804\) 0 0
\(805\) 91804.8 4.01950
\(806\) 44031.6 1.92425
\(807\) 0 0
\(808\) −3106.50 −0.135255
\(809\) 14922.2 0.648502 0.324251 0.945971i \(-0.394888\pi\)
0.324251 + 0.945971i \(0.394888\pi\)
\(810\) 0 0
\(811\) −1662.46 −0.0719812 −0.0359906 0.999352i \(-0.511459\pi\)
−0.0359906 + 0.999352i \(0.511459\pi\)
\(812\) 334.165 0.0144420
\(813\) 0 0
\(814\) 12788.4 0.550653
\(815\) −12160.2 −0.522644
\(816\) 0 0
\(817\) 33787.2 1.44684
\(818\) −1642.27 −0.0701964
\(819\) 0 0
\(820\) −1417.19 −0.0603540
\(821\) −776.061 −0.0329899 −0.0164950 0.999864i \(-0.505251\pi\)
−0.0164950 + 0.999864i \(0.505251\pi\)
\(822\) 0 0
\(823\) 6659.13 0.282044 0.141022 0.990006i \(-0.454961\pi\)
0.141022 + 0.990006i \(0.454961\pi\)
\(824\) 40363.3 1.70646
\(825\) 0 0
\(826\) 32581.6 1.37247
\(827\) −26721.8 −1.12359 −0.561794 0.827277i \(-0.689889\pi\)
−0.561794 + 0.827277i \(0.689889\pi\)
\(828\) 0 0
\(829\) 16455.6 0.689416 0.344708 0.938710i \(-0.387978\pi\)
0.344708 + 0.938710i \(0.387978\pi\)
\(830\) −11532.5 −0.482289
\(831\) 0 0
\(832\) 23173.8 0.965634
\(833\) −40580.9 −1.68793
\(834\) 0 0
\(835\) −8548.79 −0.354303
\(836\) 3817.40 0.157928
\(837\) 0 0
\(838\) −38854.2 −1.60167
\(839\) −11792.2 −0.485235 −0.242617 0.970122i \(-0.578006\pi\)
−0.242617 + 0.970122i \(0.578006\pi\)
\(840\) 0 0
\(841\) −24116.9 −0.988844
\(842\) −33005.0 −1.35087
\(843\) 0 0
\(844\) −1620.84 −0.0661040
\(845\) 8737.01 0.355695
\(846\) 0 0
\(847\) −29057.0 −1.17876
\(848\) 16363.4 0.662643
\(849\) 0 0
\(850\) 108779. 4.38952
\(851\) −15294.7 −0.616092
\(852\) 0 0
\(853\) 29560.6 1.18656 0.593281 0.804996i \(-0.297832\pi\)
0.593281 + 0.804996i \(0.297832\pi\)
\(854\) 12955.4 0.519117
\(855\) 0 0
\(856\) 20775.4 0.829543
\(857\) 6745.76 0.268881 0.134440 0.990922i \(-0.457076\pi\)
0.134440 + 0.990922i \(0.457076\pi\)
\(858\) 0 0
\(859\) −22311.2 −0.886202 −0.443101 0.896472i \(-0.646122\pi\)
−0.443101 + 0.896472i \(0.646122\pi\)
\(860\) −5538.55 −0.219608
\(861\) 0 0
\(862\) 42076.9 1.66258
\(863\) −18773.2 −0.740497 −0.370248 0.928933i \(-0.620727\pi\)
−0.370248 + 0.928933i \(0.620727\pi\)
\(864\) 0 0
\(865\) 87714.0 3.44782
\(866\) −25618.6 −1.00526
\(867\) 0 0
\(868\) 5870.52 0.229560
\(869\) −59763.9 −2.33297
\(870\) 0 0
\(871\) 37131.1 1.44448
\(872\) 35756.6 1.38861
\(873\) 0 0
\(874\) −50907.2 −1.97021
\(875\) −84693.3 −3.27218
\(876\) 0 0
\(877\) −12134.1 −0.467207 −0.233604 0.972332i \(-0.575052\pi\)
−0.233604 + 0.972332i \(0.575052\pi\)
\(878\) 20644.0 0.793508
\(879\) 0 0
\(880\) 70197.5 2.68904
\(881\) 13766.4 0.526449 0.263224 0.964735i \(-0.415214\pi\)
0.263224 + 0.964735i \(0.415214\pi\)
\(882\) 0 0
\(883\) −51432.3 −1.96018 −0.980088 0.198563i \(-0.936373\pi\)
−0.980088 + 0.198563i \(0.936373\pi\)
\(884\) −5160.19 −0.196330
\(885\) 0 0
\(886\) −15659.3 −0.593775
\(887\) 49720.0 1.88211 0.941056 0.338250i \(-0.109835\pi\)
0.941056 + 0.338250i \(0.109835\pi\)
\(888\) 0 0
\(889\) −20617.3 −0.777821
\(890\) −60660.2 −2.28465
\(891\) 0 0
\(892\) 283.301 0.0106341
\(893\) −33867.1 −1.26911
\(894\) 0 0
\(895\) −48.5199 −0.00181211
\(896\) 41759.1 1.55700
\(897\) 0 0
\(898\) 19850.5 0.737661
\(899\) 4779.78 0.177324
\(900\) 0 0
\(901\) 29994.3 1.10905
\(902\) −13024.6 −0.480790
\(903\) 0 0
\(904\) −1345.67 −0.0495093
\(905\) −29080.0 −1.06812
\(906\) 0 0
\(907\) −29374.9 −1.07539 −0.537695 0.843139i \(-0.680705\pi\)
−0.537695 + 0.843139i \(0.680705\pi\)
\(908\) −3082.61 −0.112665
\(909\) 0 0
\(910\) 79305.0 2.88894
\(911\) 1836.71 0.0667981 0.0333990 0.999442i \(-0.489367\pi\)
0.0333990 + 0.999442i \(0.489367\pi\)
\(912\) 0 0
\(913\) −9505.54 −0.344565
\(914\) 26704.3 0.966413
\(915\) 0 0
\(916\) −1899.17 −0.0685047
\(917\) 9432.49 0.339682
\(918\) 0 0
\(919\) 41798.7 1.50034 0.750170 0.661245i \(-0.229972\pi\)
0.750170 + 0.661245i \(0.229972\pi\)
\(920\) −76358.5 −2.73638
\(921\) 0 0
\(922\) 17717.0 0.632838
\(923\) −1512.36 −0.0539328
\(924\) 0 0
\(925\) 24978.7 0.887885
\(926\) 51223.4 1.81782
\(927\) 0 0
\(928\) −586.258 −0.0207380
\(929\) 20108.8 0.710170 0.355085 0.934834i \(-0.384452\pi\)
0.355085 + 0.934834i \(0.384452\pi\)
\(930\) 0 0
\(931\) −31015.9 −1.09184
\(932\) −80.9256 −0.00284421
\(933\) 0 0
\(934\) 32785.4 1.14858
\(935\) 128673. 4.50059
\(936\) 0 0
\(937\) −7701.92 −0.268528 −0.134264 0.990946i \(-0.542867\pi\)
−0.134264 + 0.990946i \(0.542867\pi\)
\(938\) 55199.5 1.92146
\(939\) 0 0
\(940\) 5551.64 0.192633
\(941\) 7997.14 0.277045 0.138523 0.990359i \(-0.455765\pi\)
0.138523 + 0.990359i \(0.455765\pi\)
\(942\) 0 0
\(943\) 15577.2 0.537926
\(944\) −29795.7 −1.02730
\(945\) 0 0
\(946\) −50901.9 −1.74943
\(947\) −9984.70 −0.342618 −0.171309 0.985217i \(-0.554800\pi\)
−0.171309 + 0.985217i \(0.554800\pi\)
\(948\) 0 0
\(949\) −61665.9 −2.10934
\(950\) 83139.7 2.83938
\(951\) 0 0
\(952\) 70193.6 2.38969
\(953\) −26566.4 −0.903010 −0.451505 0.892269i \(-0.649113\pi\)
−0.451505 + 0.892269i \(0.649113\pi\)
\(954\) 0 0
\(955\) −76534.2 −2.59328
\(956\) −188.369 −0.00637269
\(957\) 0 0
\(958\) 9745.38 0.328663
\(959\) −40911.4 −1.37758
\(960\) 0 0
\(961\) 54178.7 1.81863
\(962\) −13212.2 −0.442805
\(963\) 0 0
\(964\) −1335.85 −0.0446315
\(965\) −56421.2 −1.88214
\(966\) 0 0
\(967\) 31596.9 1.05076 0.525382 0.850867i \(-0.323923\pi\)
0.525382 + 0.850867i \(0.323923\pi\)
\(968\) 24168.1 0.802472
\(969\) 0 0
\(970\) −3537.18 −0.117085
\(971\) −23395.4 −0.773218 −0.386609 0.922244i \(-0.626354\pi\)
−0.386609 + 0.922244i \(0.626354\pi\)
\(972\) 0 0
\(973\) 32610.8 1.07446
\(974\) −2959.44 −0.0973578
\(975\) 0 0
\(976\) −11847.7 −0.388561
\(977\) −31837.4 −1.04255 −0.521274 0.853390i \(-0.674543\pi\)
−0.521274 + 0.853390i \(0.674543\pi\)
\(978\) 0 0
\(979\) −49998.4 −1.63223
\(980\) 5084.26 0.165725
\(981\) 0 0
\(982\) 38428.4 1.24878
\(983\) 24432.7 0.792758 0.396379 0.918087i \(-0.370267\pi\)
0.396379 + 0.918087i \(0.370267\pi\)
\(984\) 0 0
\(985\) 58969.1 1.90753
\(986\) −6245.89 −0.201734
\(987\) 0 0
\(988\) −3943.92 −0.126997
\(989\) 60877.8 1.95733
\(990\) 0 0
\(991\) −14624.1 −0.468767 −0.234384 0.972144i \(-0.575307\pi\)
−0.234384 + 0.972144i \(0.575307\pi\)
\(992\) −10299.2 −0.329637
\(993\) 0 0
\(994\) −2248.29 −0.0717420
\(995\) −70311.3 −2.24022
\(996\) 0 0
\(997\) 8431.79 0.267841 0.133920 0.990992i \(-0.457243\pi\)
0.133920 + 0.990992i \(0.457243\pi\)
\(998\) 64093.7 2.03292
\(999\) 0 0
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 2151.4.a.h.1.15 yes 59
3.2 odd 2 2151.4.a.g.1.45 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.45 59 3.2 odd 2
2151.4.a.h.1.15 yes 59 1.1 even 1 trivial