Properties

Label 6003.2.a.m.1.7
Level $6003$
Weight $2$
Character 6003.1
Self dual yes
Analytic conductor $47.934$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} - 93 x^{2} - 369 x - 108\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 2001)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-0.661934\) of defining polynomial
Character \(\chi\) \(=\) 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.661934 q^{2} -1.56184 q^{4} +1.16115 q^{5} +4.80000 q^{7} -2.35770 q^{8} +O(q^{10})\) \(q+0.661934 q^{2} -1.56184 q^{4} +1.16115 q^{5} +4.80000 q^{7} -2.35770 q^{8} +0.768607 q^{10} +0.481747 q^{11} -3.88315 q^{13} +3.17728 q^{14} +1.56304 q^{16} -7.41544 q^{17} +4.27098 q^{19} -1.81354 q^{20} +0.318884 q^{22} -1.00000 q^{23} -3.65172 q^{25} -2.57039 q^{26} -7.49685 q^{28} +1.00000 q^{29} -0.692651 q^{31} +5.75004 q^{32} -4.90853 q^{34} +5.57354 q^{35} -5.71364 q^{37} +2.82710 q^{38} -2.73766 q^{40} -6.42272 q^{41} -8.76031 q^{43} -0.752413 q^{44} -0.661934 q^{46} -0.616265 q^{47} +16.0400 q^{49} -2.41720 q^{50} +6.06488 q^{52} -6.31136 q^{53} +0.559383 q^{55} -11.3170 q^{56} +0.661934 q^{58} -1.01528 q^{59} -6.33953 q^{61} -0.458489 q^{62} +0.680055 q^{64} -4.50894 q^{65} -11.6618 q^{67} +11.5818 q^{68} +3.68932 q^{70} -6.45040 q^{71} +14.7390 q^{73} -3.78205 q^{74} -6.67060 q^{76} +2.31238 q^{77} -2.44072 q^{79} +1.81494 q^{80} -4.25142 q^{82} -11.5245 q^{83} -8.61047 q^{85} -5.79874 q^{86} -1.13582 q^{88} -1.71946 q^{89} -18.6391 q^{91} +1.56184 q^{92} -0.407926 q^{94} +4.95926 q^{95} +3.96175 q^{97} +10.6174 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + O(q^{10}) \) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + 14q^{10} - 11q^{11} - 5q^{13} - 17q^{14} + 20q^{16} - 15q^{17} - 6q^{19} - 21q^{20} - 10q^{22} - 11q^{23} + 3q^{25} + 5q^{26} + 7q^{28} + 11q^{29} + 35q^{31} - 28q^{32} + 28q^{34} - 15q^{35} - 28q^{37} + 2q^{38} - q^{40} - 10q^{41} - 6q^{43} - 18q^{44} + 2q^{46} - 15q^{47} + 22q^{49} - 15q^{50} - 36q^{52} + 7q^{53} - 12q^{55} - 56q^{56} - 2q^{58} + 20q^{59} - 20q^{61} + 11q^{62} + 36q^{64} - 11q^{65} - 39q^{67} - 35q^{68} + 38q^{70} - 49q^{71} - 3q^{73} - 37q^{74} - 18q^{76} - 25q^{77} + 41q^{79} - 51q^{80} - 19q^{82} - 13q^{83} - 62q^{86} - 40q^{88} - 34q^{89} + 2q^{91} - 18q^{92} - 14q^{94} - 25q^{95} - 11q^{97} - 53q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.661934 0.468058 0.234029 0.972230i \(-0.424809\pi\)
0.234029 + 0.972230i \(0.424809\pi\)
\(3\) 0 0
\(4\) −1.56184 −0.780922
\(5\) 1.16115 0.519284 0.259642 0.965705i \(-0.416395\pi\)
0.259642 + 0.965705i \(0.416395\pi\)
\(6\) 0 0
\(7\) 4.80000 1.81423 0.907115 0.420884i \(-0.138280\pi\)
0.907115 + 0.420884i \(0.138280\pi\)
\(8\) −2.35770 −0.833574
\(9\) 0 0
\(10\) 0.768607 0.243055
\(11\) 0.481747 0.145252 0.0726260 0.997359i \(-0.476862\pi\)
0.0726260 + 0.997359i \(0.476862\pi\)
\(12\) 0 0
\(13\) −3.88315 −1.07699 −0.538497 0.842628i \(-0.681008\pi\)
−0.538497 + 0.842628i \(0.681008\pi\)
\(14\) 3.17728 0.849164
\(15\) 0 0
\(16\) 1.56304 0.390761
\(17\) −7.41544 −1.79851 −0.899254 0.437427i \(-0.855890\pi\)
−0.899254 + 0.437427i \(0.855890\pi\)
\(18\) 0 0
\(19\) 4.27098 0.979829 0.489914 0.871771i \(-0.337028\pi\)
0.489914 + 0.871771i \(0.337028\pi\)
\(20\) −1.81354 −0.405521
\(21\) 0 0
\(22\) 0.318884 0.0679864
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) −3.65172 −0.730344
\(26\) −2.57039 −0.504095
\(27\) 0 0
\(28\) −7.49685 −1.41677
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −0.692651 −0.124404 −0.0622019 0.998064i \(-0.519812\pi\)
−0.0622019 + 0.998064i \(0.519812\pi\)
\(32\) 5.75004 1.01647
\(33\) 0 0
\(34\) −4.90853 −0.841805
\(35\) 5.57354 0.942101
\(36\) 0 0
\(37\) −5.71364 −0.939317 −0.469658 0.882848i \(-0.655623\pi\)
−0.469658 + 0.882848i \(0.655623\pi\)
\(38\) 2.82710 0.458616
\(39\) 0 0
\(40\) −2.73766 −0.432862
\(41\) −6.42272 −1.00306 −0.501530 0.865140i \(-0.667229\pi\)
−0.501530 + 0.865140i \(0.667229\pi\)
\(42\) 0 0
\(43\) −8.76031 −1.33593 −0.667967 0.744191i \(-0.732835\pi\)
−0.667967 + 0.744191i \(0.732835\pi\)
\(44\) −0.752413 −0.113431
\(45\) 0 0
\(46\) −0.661934 −0.0975968
\(47\) −0.616265 −0.0898915 −0.0449457 0.998989i \(-0.514311\pi\)
−0.0449457 + 0.998989i \(0.514311\pi\)
\(48\) 0 0
\(49\) 16.0400 2.29143
\(50\) −2.41720 −0.341843
\(51\) 0 0
\(52\) 6.06488 0.841048
\(53\) −6.31136 −0.866932 −0.433466 0.901170i \(-0.642710\pi\)
−0.433466 + 0.901170i \(0.642710\pi\)
\(54\) 0 0
\(55\) 0.559383 0.0754271
\(56\) −11.3170 −1.51229
\(57\) 0 0
\(58\) 0.661934 0.0869161
\(59\) −1.01528 −0.132178 −0.0660889 0.997814i \(-0.521052\pi\)
−0.0660889 + 0.997814i \(0.521052\pi\)
\(60\) 0 0
\(61\) −6.33953 −0.811693 −0.405847 0.913941i \(-0.633023\pi\)
−0.405847 + 0.913941i \(0.633023\pi\)
\(62\) −0.458489 −0.0582282
\(63\) 0 0
\(64\) 0.680055 0.0850069
\(65\) −4.50894 −0.559266
\(66\) 0 0
\(67\) −11.6618 −1.42472 −0.712360 0.701814i \(-0.752374\pi\)
−0.712360 + 0.701814i \(0.752374\pi\)
\(68\) 11.5818 1.40449
\(69\) 0 0
\(70\) 3.68932 0.440958
\(71\) −6.45040 −0.765522 −0.382761 0.923847i \(-0.625027\pi\)
−0.382761 + 0.923847i \(0.625027\pi\)
\(72\) 0 0
\(73\) 14.7390 1.72507 0.862533 0.506000i \(-0.168876\pi\)
0.862533 + 0.506000i \(0.168876\pi\)
\(74\) −3.78205 −0.439654
\(75\) 0 0
\(76\) −6.67060 −0.765170
\(77\) 2.31238 0.263521
\(78\) 0 0
\(79\) −2.44072 −0.274602 −0.137301 0.990529i \(-0.543843\pi\)
−0.137301 + 0.990529i \(0.543843\pi\)
\(80\) 1.81494 0.202916
\(81\) 0 0
\(82\) −4.25142 −0.469490
\(83\) −11.5245 −1.26498 −0.632488 0.774570i \(-0.717966\pi\)
−0.632488 + 0.774570i \(0.717966\pi\)
\(84\) 0 0
\(85\) −8.61047 −0.933937
\(86\) −5.79874 −0.625294
\(87\) 0 0
\(88\) −1.13582 −0.121078
\(89\) −1.71946 −0.182262 −0.0911310 0.995839i \(-0.529048\pi\)
−0.0911310 + 0.995839i \(0.529048\pi\)
\(90\) 0 0
\(91\) −18.6391 −1.95391
\(92\) 1.56184 0.162833
\(93\) 0 0
\(94\) −0.407926 −0.0420744
\(95\) 4.95926 0.508810
\(96\) 0 0
\(97\) 3.96175 0.402255 0.201127 0.979565i \(-0.435540\pi\)
0.201127 + 0.979565i \(0.435540\pi\)
\(98\) 10.6174 1.07252
\(99\) 0 0
\(100\) 5.70342 0.570342
\(101\) 18.2587 1.81681 0.908407 0.418088i \(-0.137300\pi\)
0.908407 + 0.418088i \(0.137300\pi\)
\(102\) 0 0
\(103\) 9.17157 0.903702 0.451851 0.892094i \(-0.350764\pi\)
0.451851 + 0.892094i \(0.350764\pi\)
\(104\) 9.15533 0.897754
\(105\) 0 0
\(106\) −4.17770 −0.405774
\(107\) −9.32854 −0.901824 −0.450912 0.892569i \(-0.648901\pi\)
−0.450912 + 0.892569i \(0.648901\pi\)
\(108\) 0 0
\(109\) 17.1548 1.64313 0.821566 0.570114i \(-0.193101\pi\)
0.821566 + 0.570114i \(0.193101\pi\)
\(110\) 0.370274 0.0353042
\(111\) 0 0
\(112\) 7.50261 0.708930
\(113\) −8.38650 −0.788936 −0.394468 0.918910i \(-0.629071\pi\)
−0.394468 + 0.918910i \(0.629071\pi\)
\(114\) 0 0
\(115\) −1.16115 −0.108278
\(116\) −1.56184 −0.145014
\(117\) 0 0
\(118\) −0.672045 −0.0618668
\(119\) −35.5941 −3.26290
\(120\) 0 0
\(121\) −10.7679 −0.978902
\(122\) −4.19634 −0.379919
\(123\) 0 0
\(124\) 1.08181 0.0971497
\(125\) −10.0460 −0.898540
\(126\) 0 0
\(127\) 9.39321 0.833513 0.416757 0.909018i \(-0.363167\pi\)
0.416757 + 0.909018i \(0.363167\pi\)
\(128\) −11.0499 −0.976685
\(129\) 0 0
\(130\) −2.98462 −0.261769
\(131\) 17.8413 1.55881 0.779403 0.626523i \(-0.215523\pi\)
0.779403 + 0.626523i \(0.215523\pi\)
\(132\) 0 0
\(133\) 20.5007 1.77763
\(134\) −7.71936 −0.666851
\(135\) 0 0
\(136\) 17.4834 1.49919
\(137\) −6.50179 −0.555485 −0.277743 0.960656i \(-0.589586\pi\)
−0.277743 + 0.960656i \(0.589586\pi\)
\(138\) 0 0
\(139\) 8.92280 0.756822 0.378411 0.925638i \(-0.376471\pi\)
0.378411 + 0.925638i \(0.376471\pi\)
\(140\) −8.70500 −0.735707
\(141\) 0 0
\(142\) −4.26974 −0.358308
\(143\) −1.87070 −0.156436
\(144\) 0 0
\(145\) 1.16115 0.0964287
\(146\) 9.75622 0.807431
\(147\) 0 0
\(148\) 8.92382 0.733533
\(149\) −12.3725 −1.01359 −0.506797 0.862065i \(-0.669171\pi\)
−0.506797 + 0.862065i \(0.669171\pi\)
\(150\) 0 0
\(151\) −2.18528 −0.177836 −0.0889180 0.996039i \(-0.528341\pi\)
−0.0889180 + 0.996039i \(0.528341\pi\)
\(152\) −10.0697 −0.816760
\(153\) 0 0
\(154\) 1.53064 0.123343
\(155\) −0.804275 −0.0646009
\(156\) 0 0
\(157\) 14.9914 1.19645 0.598224 0.801329i \(-0.295873\pi\)
0.598224 + 0.801329i \(0.295873\pi\)
\(158\) −1.61559 −0.128530
\(159\) 0 0
\(160\) 6.67669 0.527838
\(161\) −4.80000 −0.378293
\(162\) 0 0
\(163\) −8.88481 −0.695912 −0.347956 0.937511i \(-0.613124\pi\)
−0.347956 + 0.937511i \(0.613124\pi\)
\(164\) 10.0313 0.783312
\(165\) 0 0
\(166\) −7.62844 −0.592081
\(167\) −2.40802 −0.186338 −0.0931692 0.995650i \(-0.529700\pi\)
−0.0931692 + 0.995650i \(0.529700\pi\)
\(168\) 0 0
\(169\) 2.07889 0.159915
\(170\) −5.69956 −0.437136
\(171\) 0 0
\(172\) 13.6822 1.04326
\(173\) −18.9340 −1.43952 −0.719762 0.694221i \(-0.755749\pi\)
−0.719762 + 0.694221i \(0.755749\pi\)
\(174\) 0 0
\(175\) −17.5283 −1.32501
\(176\) 0.752991 0.0567589
\(177\) 0 0
\(178\) −1.13817 −0.0853091
\(179\) 3.18736 0.238235 0.119117 0.992880i \(-0.461994\pi\)
0.119117 + 0.992880i \(0.461994\pi\)
\(180\) 0 0
\(181\) 13.2936 0.988109 0.494054 0.869431i \(-0.335514\pi\)
0.494054 + 0.869431i \(0.335514\pi\)
\(182\) −12.3379 −0.914544
\(183\) 0 0
\(184\) 2.35770 0.173812
\(185\) −6.63442 −0.487772
\(186\) 0 0
\(187\) −3.57236 −0.261237
\(188\) 0.962510 0.0701982
\(189\) 0 0
\(190\) 3.28270 0.238152
\(191\) −21.5092 −1.55635 −0.778177 0.628045i \(-0.783855\pi\)
−0.778177 + 0.628045i \(0.783855\pi\)
\(192\) 0 0
\(193\) −2.35343 −0.169403 −0.0847017 0.996406i \(-0.526994\pi\)
−0.0847017 + 0.996406i \(0.526994\pi\)
\(194\) 2.62241 0.188278
\(195\) 0 0
\(196\) −25.0520 −1.78943
\(197\) −0.766029 −0.0545773 −0.0272886 0.999628i \(-0.508687\pi\)
−0.0272886 + 0.999628i \(0.508687\pi\)
\(198\) 0 0
\(199\) 9.77290 0.692783 0.346391 0.938090i \(-0.387407\pi\)
0.346391 + 0.938090i \(0.387407\pi\)
\(200\) 8.60967 0.608796
\(201\) 0 0
\(202\) 12.0861 0.850373
\(203\) 4.80000 0.336894
\(204\) 0 0
\(205\) −7.45778 −0.520874
\(206\) 6.07097 0.422984
\(207\) 0 0
\(208\) −6.06954 −0.420847
\(209\) 2.05753 0.142322
\(210\) 0 0
\(211\) −21.5678 −1.48479 −0.742395 0.669963i \(-0.766310\pi\)
−0.742395 + 0.669963i \(0.766310\pi\)
\(212\) 9.85736 0.677007
\(213\) 0 0
\(214\) −6.17487 −0.422105
\(215\) −10.1721 −0.693730
\(216\) 0 0
\(217\) −3.32472 −0.225697
\(218\) 11.3553 0.769080
\(219\) 0 0
\(220\) −0.873668 −0.0589027
\(221\) 28.7953 1.93698
\(222\) 0 0
\(223\) −0.944373 −0.0632399 −0.0316199 0.999500i \(-0.510067\pi\)
−0.0316199 + 0.999500i \(0.510067\pi\)
\(224\) 27.6002 1.84412
\(225\) 0 0
\(226\) −5.55131 −0.369268
\(227\) −20.2556 −1.34441 −0.672204 0.740366i \(-0.734652\pi\)
−0.672204 + 0.740366i \(0.734652\pi\)
\(228\) 0 0
\(229\) 4.15599 0.274635 0.137318 0.990527i \(-0.456152\pi\)
0.137318 + 0.990527i \(0.456152\pi\)
\(230\) −0.768607 −0.0506805
\(231\) 0 0
\(232\) −2.35770 −0.154791
\(233\) 13.3848 0.876866 0.438433 0.898764i \(-0.355534\pi\)
0.438433 + 0.898764i \(0.355534\pi\)
\(234\) 0 0
\(235\) −0.715579 −0.0466792
\(236\) 1.58570 0.103220
\(237\) 0 0
\(238\) −23.5609 −1.52723
\(239\) 22.7219 1.46976 0.734878 0.678199i \(-0.237239\pi\)
0.734878 + 0.678199i \(0.237239\pi\)
\(240\) 0 0
\(241\) 4.27597 0.275440 0.137720 0.990471i \(-0.456023\pi\)
0.137720 + 0.990471i \(0.456023\pi\)
\(242\) −7.12765 −0.458183
\(243\) 0 0
\(244\) 9.90135 0.633869
\(245\) 18.6249 1.18990
\(246\) 0 0
\(247\) −16.5849 −1.05527
\(248\) 1.63307 0.103700
\(249\) 0 0
\(250\) −6.64978 −0.420569
\(251\) −18.8353 −1.18887 −0.594437 0.804142i \(-0.702625\pi\)
−0.594437 + 0.804142i \(0.702625\pi\)
\(252\) 0 0
\(253\) −0.481747 −0.0302872
\(254\) 6.21768 0.390132
\(255\) 0 0
\(256\) −8.67443 −0.542152
\(257\) 9.25845 0.577526 0.288763 0.957401i \(-0.406756\pi\)
0.288763 + 0.957401i \(0.406756\pi\)
\(258\) 0 0
\(259\) −27.4255 −1.70414
\(260\) 7.04227 0.436743
\(261\) 0 0
\(262\) 11.8098 0.729611
\(263\) −19.7994 −1.22089 −0.610443 0.792060i \(-0.709008\pi\)
−0.610443 + 0.792060i \(0.709008\pi\)
\(264\) 0 0
\(265\) −7.32847 −0.450184
\(266\) 13.5701 0.832035
\(267\) 0 0
\(268\) 18.2140 1.11259
\(269\) 6.41447 0.391097 0.195548 0.980694i \(-0.437351\pi\)
0.195548 + 0.980694i \(0.437351\pi\)
\(270\) 0 0
\(271\) 0.0813137 0.00493946 0.00246973 0.999997i \(-0.499214\pi\)
0.00246973 + 0.999997i \(0.499214\pi\)
\(272\) −11.5907 −0.702787
\(273\) 0 0
\(274\) −4.30375 −0.259999
\(275\) −1.75920 −0.106084
\(276\) 0 0
\(277\) −32.2170 −1.93573 −0.967866 0.251465i \(-0.919088\pi\)
−0.967866 + 0.251465i \(0.919088\pi\)
\(278\) 5.90630 0.354236
\(279\) 0 0
\(280\) −13.1408 −0.785311
\(281\) 20.6489 1.23181 0.615906 0.787820i \(-0.288790\pi\)
0.615906 + 0.787820i \(0.288790\pi\)
\(282\) 0 0
\(283\) −21.0893 −1.25363 −0.626813 0.779170i \(-0.715641\pi\)
−0.626813 + 0.779170i \(0.715641\pi\)
\(284\) 10.0745 0.597813
\(285\) 0 0
\(286\) −1.23828 −0.0732208
\(287\) −30.8291 −1.81978
\(288\) 0 0
\(289\) 37.9887 2.23463
\(290\) 0.768607 0.0451342
\(291\) 0 0
\(292\) −23.0200 −1.34714
\(293\) −19.7744 −1.15523 −0.577615 0.816309i \(-0.696017\pi\)
−0.577615 + 0.816309i \(0.696017\pi\)
\(294\) 0 0
\(295\) −1.17889 −0.0686378
\(296\) 13.4711 0.782990
\(297\) 0 0
\(298\) −8.18977 −0.474420
\(299\) 3.88315 0.224569
\(300\) 0 0
\(301\) −42.0495 −2.42369
\(302\) −1.44651 −0.0832375
\(303\) 0 0
\(304\) 6.67572 0.382879
\(305\) −7.36117 −0.421499
\(306\) 0 0
\(307\) 15.8499 0.904601 0.452300 0.891866i \(-0.350603\pi\)
0.452300 + 0.891866i \(0.350603\pi\)
\(308\) −3.61158 −0.205789
\(309\) 0 0
\(310\) −0.532377 −0.0302370
\(311\) −6.50938 −0.369113 −0.184557 0.982822i \(-0.559085\pi\)
−0.184557 + 0.982822i \(0.559085\pi\)
\(312\) 0 0
\(313\) −29.9378 −1.69218 −0.846092 0.533038i \(-0.821050\pi\)
−0.846092 + 0.533038i \(0.821050\pi\)
\(314\) 9.92334 0.560007
\(315\) 0 0
\(316\) 3.81202 0.214443
\(317\) −17.5373 −0.984993 −0.492497 0.870314i \(-0.663916\pi\)
−0.492497 + 0.870314i \(0.663916\pi\)
\(318\) 0 0
\(319\) 0.481747 0.0269726
\(320\) 0.789649 0.0441427
\(321\) 0 0
\(322\) −3.17728 −0.177063
\(323\) −31.6711 −1.76223
\(324\) 0 0
\(325\) 14.1802 0.786575
\(326\) −5.88116 −0.325727
\(327\) 0 0
\(328\) 15.1429 0.836126
\(329\) −2.95807 −0.163084
\(330\) 0 0
\(331\) 4.82327 0.265111 0.132556 0.991176i \(-0.457682\pi\)
0.132556 + 0.991176i \(0.457682\pi\)
\(332\) 17.9994 0.987847
\(333\) 0 0
\(334\) −1.59395 −0.0872171
\(335\) −13.5412 −0.739835
\(336\) 0 0
\(337\) 5.34820 0.291335 0.145667 0.989334i \(-0.453467\pi\)
0.145667 + 0.989334i \(0.453467\pi\)
\(338\) 1.37609 0.0748492
\(339\) 0 0
\(340\) 13.4482 0.729332
\(341\) −0.333682 −0.0180699
\(342\) 0 0
\(343\) 43.3920 2.34295
\(344\) 20.6542 1.11360
\(345\) 0 0
\(346\) −12.5330 −0.673780
\(347\) −12.8945 −0.692211 −0.346106 0.938196i \(-0.612496\pi\)
−0.346106 + 0.938196i \(0.612496\pi\)
\(348\) 0 0
\(349\) 14.2259 0.761496 0.380748 0.924679i \(-0.375667\pi\)
0.380748 + 0.924679i \(0.375667\pi\)
\(350\) −11.6025 −0.620182
\(351\) 0 0
\(352\) 2.77006 0.147645
\(353\) 27.1279 1.44387 0.721936 0.691960i \(-0.243252\pi\)
0.721936 + 0.691960i \(0.243252\pi\)
\(354\) 0 0
\(355\) −7.48991 −0.397523
\(356\) 2.68552 0.142332
\(357\) 0 0
\(358\) 2.10982 0.111508
\(359\) −33.1581 −1.75002 −0.875010 0.484105i \(-0.839145\pi\)
−0.875010 + 0.484105i \(0.839145\pi\)
\(360\) 0 0
\(361\) −0.758770 −0.0399352
\(362\) 8.79951 0.462492
\(363\) 0 0
\(364\) 29.1114 1.52585
\(365\) 17.1142 0.895800
\(366\) 0 0
\(367\) −27.4982 −1.43539 −0.717697 0.696355i \(-0.754804\pi\)
−0.717697 + 0.696355i \(0.754804\pi\)
\(368\) −1.56304 −0.0814793
\(369\) 0 0
\(370\) −4.39155 −0.228306
\(371\) −30.2945 −1.57281
\(372\) 0 0
\(373\) 16.8037 0.870062 0.435031 0.900416i \(-0.356737\pi\)
0.435031 + 0.900416i \(0.356737\pi\)
\(374\) −2.36467 −0.122274
\(375\) 0 0
\(376\) 1.45297 0.0749312
\(377\) −3.88315 −0.199993
\(378\) 0 0
\(379\) 27.0834 1.39118 0.695591 0.718438i \(-0.255143\pi\)
0.695591 + 0.718438i \(0.255143\pi\)
\(380\) −7.74560 −0.397341
\(381\) 0 0
\(382\) −14.2377 −0.728463
\(383\) 17.5873 0.898667 0.449334 0.893364i \(-0.351661\pi\)
0.449334 + 0.893364i \(0.351661\pi\)
\(384\) 0 0
\(385\) 2.68504 0.136842
\(386\) −1.55781 −0.0792906
\(387\) 0 0
\(388\) −6.18763 −0.314129
\(389\) −6.36584 −0.322761 −0.161380 0.986892i \(-0.551595\pi\)
−0.161380 + 0.986892i \(0.551595\pi\)
\(390\) 0 0
\(391\) 7.41544 0.375015
\(392\) −37.8176 −1.91008
\(393\) 0 0
\(394\) −0.507060 −0.0255453
\(395\) −2.83405 −0.142597
\(396\) 0 0
\(397\) −14.1969 −0.712520 −0.356260 0.934387i \(-0.615948\pi\)
−0.356260 + 0.934387i \(0.615948\pi\)
\(398\) 6.46901 0.324262
\(399\) 0 0
\(400\) −5.70780 −0.285390
\(401\) −4.07996 −0.203743 −0.101872 0.994798i \(-0.532483\pi\)
−0.101872 + 0.994798i \(0.532483\pi\)
\(402\) 0 0
\(403\) 2.68967 0.133982
\(404\) −28.5173 −1.41879
\(405\) 0 0
\(406\) 3.17728 0.157686
\(407\) −2.75253 −0.136438
\(408\) 0 0
\(409\) −1.77817 −0.0879247 −0.0439624 0.999033i \(-0.513998\pi\)
−0.0439624 + 0.999033i \(0.513998\pi\)
\(410\) −4.93655 −0.243799
\(411\) 0 0
\(412\) −14.3246 −0.705720
\(413\) −4.87333 −0.239801
\(414\) 0 0
\(415\) −13.3817 −0.656882
\(416\) −22.3283 −1.09473
\(417\) 0 0
\(418\) 1.36195 0.0666150
\(419\) 12.4164 0.606578 0.303289 0.952899i \(-0.401915\pi\)
0.303289 + 0.952899i \(0.401915\pi\)
\(420\) 0 0
\(421\) 39.1062 1.90592 0.952960 0.303096i \(-0.0980202\pi\)
0.952960 + 0.303096i \(0.0980202\pi\)
\(422\) −14.2765 −0.694967
\(423\) 0 0
\(424\) 14.8803 0.722653
\(425\) 27.0791 1.31353
\(426\) 0 0
\(427\) −30.4297 −1.47260
\(428\) 14.5697 0.704254
\(429\) 0 0
\(430\) −6.73324 −0.324706
\(431\) 25.8815 1.24667 0.623333 0.781957i \(-0.285778\pi\)
0.623333 + 0.781957i \(0.285778\pi\)
\(432\) 0 0
\(433\) −25.2711 −1.21445 −0.607226 0.794529i \(-0.707718\pi\)
−0.607226 + 0.794529i \(0.707718\pi\)
\(434\) −2.20075 −0.105639
\(435\) 0 0
\(436\) −26.7931 −1.28316
\(437\) −4.27098 −0.204308
\(438\) 0 0
\(439\) −40.3513 −1.92586 −0.962931 0.269749i \(-0.913059\pi\)
−0.962931 + 0.269749i \(0.913059\pi\)
\(440\) −1.31886 −0.0628741
\(441\) 0 0
\(442\) 19.0606 0.906619
\(443\) −12.7973 −0.608018 −0.304009 0.952669i \(-0.598325\pi\)
−0.304009 + 0.952669i \(0.598325\pi\)
\(444\) 0 0
\(445\) −1.99656 −0.0946458
\(446\) −0.625112 −0.0295999
\(447\) 0 0
\(448\) 3.26426 0.154222
\(449\) −6.34149 −0.299274 −0.149637 0.988741i \(-0.547810\pi\)
−0.149637 + 0.988741i \(0.547810\pi\)
\(450\) 0 0
\(451\) −3.09413 −0.145697
\(452\) 13.0984 0.616097
\(453\) 0 0
\(454\) −13.4078 −0.629261
\(455\) −21.6429 −1.01464
\(456\) 0 0
\(457\) −33.4505 −1.56475 −0.782375 0.622808i \(-0.785992\pi\)
−0.782375 + 0.622808i \(0.785992\pi\)
\(458\) 2.75099 0.128545
\(459\) 0 0
\(460\) 1.81354 0.0845569
\(461\) −5.42683 −0.252753 −0.126376 0.991982i \(-0.540335\pi\)
−0.126376 + 0.991982i \(0.540335\pi\)
\(462\) 0 0
\(463\) 10.6646 0.495624 0.247812 0.968808i \(-0.420289\pi\)
0.247812 + 0.968808i \(0.420289\pi\)
\(464\) 1.56304 0.0725625
\(465\) 0 0
\(466\) 8.85984 0.410424
\(467\) −10.6209 −0.491479 −0.245739 0.969336i \(-0.579031\pi\)
−0.245739 + 0.969336i \(0.579031\pi\)
\(468\) 0 0
\(469\) −55.9768 −2.58477
\(470\) −0.473666 −0.0218486
\(471\) 0 0
\(472\) 2.39372 0.110180
\(473\) −4.22025 −0.194047
\(474\) 0 0
\(475\) −15.5964 −0.715612
\(476\) 55.5924 2.54807
\(477\) 0 0
\(478\) 15.0404 0.687931
\(479\) −17.4622 −0.797867 −0.398934 0.916980i \(-0.630620\pi\)
−0.398934 + 0.916980i \(0.630620\pi\)
\(480\) 0 0
\(481\) 22.1870 1.01164
\(482\) 2.83041 0.128922
\(483\) 0 0
\(484\) 16.8178 0.764446
\(485\) 4.60020 0.208884
\(486\) 0 0
\(487\) 3.98493 0.180575 0.0902873 0.995916i \(-0.471221\pi\)
0.0902873 + 0.995916i \(0.471221\pi\)
\(488\) 14.9467 0.676606
\(489\) 0 0
\(490\) 12.3285 0.556943
\(491\) −14.1616 −0.639103 −0.319552 0.947569i \(-0.603532\pi\)
−0.319552 + 0.947569i \(0.603532\pi\)
\(492\) 0 0
\(493\) −7.41544 −0.333974
\(494\) −10.9781 −0.493927
\(495\) 0 0
\(496\) −1.08264 −0.0486122
\(497\) −30.9619 −1.38883
\(498\) 0 0
\(499\) −3.75546 −0.168117 −0.0840587 0.996461i \(-0.526788\pi\)
−0.0840587 + 0.996461i \(0.526788\pi\)
\(500\) 15.6903 0.701690
\(501\) 0 0
\(502\) −12.4677 −0.556462
\(503\) 21.1293 0.942110 0.471055 0.882104i \(-0.343873\pi\)
0.471055 + 0.882104i \(0.343873\pi\)
\(504\) 0 0
\(505\) 21.2012 0.943442
\(506\) −0.318884 −0.0141761
\(507\) 0 0
\(508\) −14.6707 −0.650909
\(509\) 3.59910 0.159527 0.0797637 0.996814i \(-0.474583\pi\)
0.0797637 + 0.996814i \(0.474583\pi\)
\(510\) 0 0
\(511\) 70.7471 3.12967
\(512\) 16.3580 0.722927
\(513\) 0 0
\(514\) 6.12848 0.270316
\(515\) 10.6496 0.469278
\(516\) 0 0
\(517\) −0.296884 −0.0130569
\(518\) −18.1538 −0.797634
\(519\) 0 0
\(520\) 10.6308 0.466189
\(521\) 3.83170 0.167870 0.0839349 0.996471i \(-0.473251\pi\)
0.0839349 + 0.996471i \(0.473251\pi\)
\(522\) 0 0
\(523\) 42.0646 1.83936 0.919678 0.392674i \(-0.128450\pi\)
0.919678 + 0.392674i \(0.128450\pi\)
\(524\) −27.8654 −1.21731
\(525\) 0 0
\(526\) −13.1059 −0.571445
\(527\) 5.13631 0.223741
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −4.85096 −0.210712
\(531\) 0 0
\(532\) −32.0189 −1.38819
\(533\) 24.9404 1.08029
\(534\) 0 0
\(535\) −10.8319 −0.468303
\(536\) 27.4952 1.18761
\(537\) 0 0
\(538\) 4.24595 0.183056
\(539\) 7.72721 0.332835
\(540\) 0 0
\(541\) 32.9360 1.41603 0.708015 0.706197i \(-0.249591\pi\)
0.708015 + 0.706197i \(0.249591\pi\)
\(542\) 0.0538243 0.00231195
\(543\) 0 0
\(544\) −42.6391 −1.82813
\(545\) 19.9194 0.853252
\(546\) 0 0
\(547\) −1.89683 −0.0811024 −0.0405512 0.999177i \(-0.512911\pi\)
−0.0405512 + 0.999177i \(0.512911\pi\)
\(548\) 10.1548 0.433791
\(549\) 0 0
\(550\) −1.16448 −0.0496534
\(551\) 4.27098 0.181950
\(552\) 0 0
\(553\) −11.7154 −0.498191
\(554\) −21.3255 −0.906035
\(555\) 0 0
\(556\) −13.9360 −0.591019
\(557\) −6.32207 −0.267875 −0.133937 0.990990i \(-0.542762\pi\)
−0.133937 + 0.990990i \(0.542762\pi\)
\(558\) 0 0
\(559\) 34.0176 1.43879
\(560\) 8.71170 0.368136
\(561\) 0 0
\(562\) 13.6682 0.576559
\(563\) −35.8000 −1.50879 −0.754395 0.656420i \(-0.772070\pi\)
−0.754395 + 0.656420i \(0.772070\pi\)
\(564\) 0 0
\(565\) −9.73803 −0.409682
\(566\) −13.9597 −0.586769
\(567\) 0 0
\(568\) 15.2081 0.638119
\(569\) −6.27427 −0.263031 −0.131515 0.991314i \(-0.541984\pi\)
−0.131515 + 0.991314i \(0.541984\pi\)
\(570\) 0 0
\(571\) 17.0402 0.713109 0.356555 0.934274i \(-0.383951\pi\)
0.356555 + 0.934274i \(0.383951\pi\)
\(572\) 2.92174 0.122164
\(573\) 0 0
\(574\) −20.4068 −0.851763
\(575\) 3.65172 0.152287
\(576\) 0 0
\(577\) −37.1392 −1.54613 −0.773063 0.634329i \(-0.781277\pi\)
−0.773063 + 0.634329i \(0.781277\pi\)
\(578\) 25.1460 1.04594
\(579\) 0 0
\(580\) −1.81354 −0.0753033
\(581\) −55.3175 −2.29496
\(582\) 0 0
\(583\) −3.04048 −0.125924
\(584\) −34.7501 −1.43797
\(585\) 0 0
\(586\) −13.0893 −0.540714
\(587\) −5.01609 −0.207036 −0.103518 0.994628i \(-0.533010\pi\)
−0.103518 + 0.994628i \(0.533010\pi\)
\(588\) 0 0
\(589\) −2.95830 −0.121894
\(590\) −0.780349 −0.0321265
\(591\) 0 0
\(592\) −8.93068 −0.367049
\(593\) −0.761753 −0.0312815 −0.0156407 0.999878i \(-0.504979\pi\)
−0.0156407 + 0.999878i \(0.504979\pi\)
\(594\) 0 0
\(595\) −41.3303 −1.69438
\(596\) 19.3239 0.791538
\(597\) 0 0
\(598\) 2.57039 0.105111
\(599\) −14.8728 −0.607688 −0.303844 0.952722i \(-0.598270\pi\)
−0.303844 + 0.952722i \(0.598270\pi\)
\(600\) 0 0
\(601\) 0.810605 0.0330653 0.0165326 0.999863i \(-0.494737\pi\)
0.0165326 + 0.999863i \(0.494737\pi\)
\(602\) −27.8340 −1.13443
\(603\) 0 0
\(604\) 3.41307 0.138876
\(605\) −12.5032 −0.508328
\(606\) 0 0
\(607\) 13.0304 0.528888 0.264444 0.964401i \(-0.414812\pi\)
0.264444 + 0.964401i \(0.414812\pi\)
\(608\) 24.5583 0.995970
\(609\) 0 0
\(610\) −4.87261 −0.197286
\(611\) 2.39305 0.0968125
\(612\) 0 0
\(613\) −45.4250 −1.83470 −0.917350 0.398082i \(-0.869676\pi\)
−0.917350 + 0.398082i \(0.869676\pi\)
\(614\) 10.4916 0.423405
\(615\) 0 0
\(616\) −5.45192 −0.219664
\(617\) 18.6626 0.751326 0.375663 0.926756i \(-0.377415\pi\)
0.375663 + 0.926756i \(0.377415\pi\)
\(618\) 0 0
\(619\) 25.2424 1.01458 0.507289 0.861776i \(-0.330648\pi\)
0.507289 + 0.861776i \(0.330648\pi\)
\(620\) 1.25615 0.0504483
\(621\) 0 0
\(622\) −4.30878 −0.172766
\(623\) −8.25339 −0.330665
\(624\) 0 0
\(625\) 6.59365 0.263746
\(626\) −19.8168 −0.792039
\(627\) 0 0
\(628\) −23.4143 −0.934332
\(629\) 42.3691 1.68937
\(630\) 0 0
\(631\) 7.64426 0.304313 0.152157 0.988356i \(-0.451378\pi\)
0.152157 + 0.988356i \(0.451378\pi\)
\(632\) 5.75449 0.228901
\(633\) 0 0
\(634\) −11.6085 −0.461034
\(635\) 10.9070 0.432830
\(636\) 0 0
\(637\) −62.2858 −2.46785
\(638\) 0.318884 0.0126247
\(639\) 0 0
\(640\) −12.8307 −0.507177
\(641\) −27.0958 −1.07022 −0.535110 0.844783i \(-0.679730\pi\)
−0.535110 + 0.844783i \(0.679730\pi\)
\(642\) 0 0
\(643\) 15.6696 0.617949 0.308974 0.951070i \(-0.400014\pi\)
0.308974 + 0.951070i \(0.400014\pi\)
\(644\) 7.49685 0.295417
\(645\) 0 0
\(646\) −20.9642 −0.824825
\(647\) 28.0698 1.10354 0.551769 0.833997i \(-0.313953\pi\)
0.551769 + 0.833997i \(0.313953\pi\)
\(648\) 0 0
\(649\) −0.489106 −0.0191991
\(650\) 9.38634 0.368163
\(651\) 0 0
\(652\) 13.8767 0.543453
\(653\) 4.85411 0.189956 0.0949780 0.995479i \(-0.469722\pi\)
0.0949780 + 0.995479i \(0.469722\pi\)
\(654\) 0 0
\(655\) 20.7166 0.809463
\(656\) −10.0390 −0.391957
\(657\) 0 0
\(658\) −1.95805 −0.0763326
\(659\) 2.91789 0.113665 0.0568324 0.998384i \(-0.481900\pi\)
0.0568324 + 0.998384i \(0.481900\pi\)
\(660\) 0 0
\(661\) 5.93405 0.230808 0.115404 0.993319i \(-0.463184\pi\)
0.115404 + 0.993319i \(0.463184\pi\)
\(662\) 3.19269 0.124087
\(663\) 0 0
\(664\) 27.1713 1.05445
\(665\) 23.8045 0.923098
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 3.76096 0.145516
\(669\) 0 0
\(670\) −8.96337 −0.346285
\(671\) −3.05405 −0.117900
\(672\) 0 0
\(673\) 26.3141 1.01434 0.507168 0.861847i \(-0.330693\pi\)
0.507168 + 0.861847i \(0.330693\pi\)
\(674\) 3.54015 0.136362
\(675\) 0 0
\(676\) −3.24690 −0.124881
\(677\) −5.30262 −0.203796 −0.101898 0.994795i \(-0.532492\pi\)
−0.101898 + 0.994795i \(0.532492\pi\)
\(678\) 0 0
\(679\) 19.0164 0.729782
\(680\) 20.3009 0.778506
\(681\) 0 0
\(682\) −0.220875 −0.00845776
\(683\) 45.1373 1.72713 0.863566 0.504236i \(-0.168226\pi\)
0.863566 + 0.504236i \(0.168226\pi\)
\(684\) 0 0
\(685\) −7.54958 −0.288455
\(686\) 28.7226 1.09663
\(687\) 0 0
\(688\) −13.6928 −0.522031
\(689\) 24.5080 0.933680
\(690\) 0 0
\(691\) −4.14576 −0.157712 −0.0788561 0.996886i \(-0.525127\pi\)
−0.0788561 + 0.996886i \(0.525127\pi\)
\(692\) 29.5719 1.12416
\(693\) 0 0
\(694\) −8.53528 −0.323995
\(695\) 10.3608 0.393006
\(696\) 0 0
\(697\) 47.6273 1.80401
\(698\) 9.41661 0.356424
\(699\) 0 0
\(700\) 27.3764 1.03473
\(701\) −2.99761 −0.113218 −0.0566091 0.998396i \(-0.518029\pi\)
−0.0566091 + 0.998396i \(0.518029\pi\)
\(702\) 0 0
\(703\) −24.4028 −0.920370
\(704\) 0.327614 0.0123474
\(705\) 0 0
\(706\) 17.9569 0.675816
\(707\) 87.6420 3.29612
\(708\) 0 0
\(709\) 50.3931 1.89255 0.946277 0.323357i \(-0.104811\pi\)
0.946277 + 0.323357i \(0.104811\pi\)
\(710\) −4.95783 −0.186064
\(711\) 0 0
\(712\) 4.05397 0.151929
\(713\) 0.692651 0.0259400
\(714\) 0 0
\(715\) −2.17217 −0.0812345
\(716\) −4.97816 −0.186043
\(717\) 0 0
\(718\) −21.9485 −0.819110
\(719\) −1.37707 −0.0513561 −0.0256781 0.999670i \(-0.508174\pi\)
−0.0256781 + 0.999670i \(0.508174\pi\)
\(720\) 0 0
\(721\) 44.0235 1.63952
\(722\) −0.502255 −0.0186920
\(723\) 0 0
\(724\) −20.7626 −0.771636
\(725\) −3.65172 −0.135621
\(726\) 0 0
\(727\) 2.89494 0.107367 0.0536836 0.998558i \(-0.482904\pi\)
0.0536836 + 0.998558i \(0.482904\pi\)
\(728\) 43.9456 1.62873
\(729\) 0 0
\(730\) 11.3285 0.419286
\(731\) 64.9615 2.40269
\(732\) 0 0
\(733\) 25.9159 0.957227 0.478613 0.878026i \(-0.341140\pi\)
0.478613 + 0.878026i \(0.341140\pi\)
\(734\) −18.2020 −0.671848
\(735\) 0 0
\(736\) −5.75004 −0.211949
\(737\) −5.61805 −0.206944
\(738\) 0 0
\(739\) 2.34877 0.0864010 0.0432005 0.999066i \(-0.486245\pi\)
0.0432005 + 0.999066i \(0.486245\pi\)
\(740\) 10.3619 0.380912
\(741\) 0 0
\(742\) −20.0530 −0.736168
\(743\) −19.1323 −0.701895 −0.350947 0.936395i \(-0.614140\pi\)
−0.350947 + 0.936395i \(0.614140\pi\)
\(744\) 0 0
\(745\) −14.3664 −0.526343
\(746\) 11.1229 0.407239
\(747\) 0 0
\(748\) 5.57947 0.204006
\(749\) −44.7770 −1.63611
\(750\) 0 0
\(751\) 51.4428 1.87717 0.938587 0.345043i \(-0.112136\pi\)
0.938587 + 0.345043i \(0.112136\pi\)
\(752\) −0.963250 −0.0351261
\(753\) 0 0
\(754\) −2.57039 −0.0936081
\(755\) −2.53745 −0.0923474
\(756\) 0 0
\(757\) −42.1639 −1.53247 −0.766236 0.642560i \(-0.777872\pi\)
−0.766236 + 0.642560i \(0.777872\pi\)
\(758\) 17.9274 0.651153
\(759\) 0 0
\(760\) −11.6925 −0.424131
\(761\) 11.1416 0.403884 0.201942 0.979397i \(-0.435275\pi\)
0.201942 + 0.979397i \(0.435275\pi\)
\(762\) 0 0
\(763\) 82.3430 2.98102
\(764\) 33.5941 1.21539
\(765\) 0 0
\(766\) 11.6416 0.420628
\(767\) 3.94247 0.142355
\(768\) 0 0
\(769\) −26.0823 −0.940551 −0.470275 0.882520i \(-0.655845\pi\)
−0.470275 + 0.882520i \(0.655845\pi\)
\(770\) 1.77732 0.0640500
\(771\) 0 0
\(772\) 3.67569 0.132291
\(773\) 29.4575 1.05951 0.529756 0.848150i \(-0.322284\pi\)
0.529756 + 0.848150i \(0.322284\pi\)
\(774\) 0 0
\(775\) 2.52937 0.0908575
\(776\) −9.34063 −0.335309
\(777\) 0 0
\(778\) −4.21376 −0.151071
\(779\) −27.4313 −0.982828
\(780\) 0 0
\(781\) −3.10746 −0.111194
\(782\) 4.90853 0.175529
\(783\) 0 0
\(784\) 25.0712 0.895401
\(785\) 17.4074 0.621297
\(786\) 0 0
\(787\) 7.08437 0.252530 0.126265 0.991997i \(-0.459701\pi\)
0.126265 + 0.991997i \(0.459701\pi\)
\(788\) 1.19642 0.0426206
\(789\) 0 0
\(790\) −1.87595 −0.0667434
\(791\) −40.2552 −1.43131
\(792\) 0 0
\(793\) 24.6174 0.874188
\(794\) −9.39738 −0.333501
\(795\) 0 0
\(796\) −15.2638 −0.541009
\(797\) −37.8352 −1.34019 −0.670096 0.742275i \(-0.733747\pi\)
−0.670096 + 0.742275i \(0.733747\pi\)
\(798\) 0 0
\(799\) 4.56987 0.161671
\(800\) −20.9975 −0.742375
\(801\) 0 0
\(802\) −2.70066 −0.0953637
\(803\) 7.10045 0.250570
\(804\) 0 0
\(805\) −5.57354 −0.196442
\(806\) 1.78038 0.0627113
\(807\) 0 0
\(808\) −43.0487 −1.51445
\(809\) 45.3863 1.59570 0.797849 0.602858i \(-0.205971\pi\)
0.797849 + 0.602858i \(0.205971\pi\)
\(810\) 0 0
\(811\) −43.1196 −1.51413 −0.757067 0.653337i \(-0.773368\pi\)
−0.757067 + 0.653337i \(0.773368\pi\)
\(812\) −7.49685 −0.263088
\(813\) 0 0
\(814\) −1.82199 −0.0638607
\(815\) −10.3166 −0.361376
\(816\) 0 0
\(817\) −37.4151 −1.30899
\(818\) −1.17703 −0.0411538
\(819\) 0 0
\(820\) 11.6479 0.406762
\(821\) 41.4654 1.44715 0.723576 0.690245i \(-0.242497\pi\)
0.723576 + 0.690245i \(0.242497\pi\)
\(822\) 0 0
\(823\) 30.5317 1.06427 0.532134 0.846660i \(-0.321390\pi\)
0.532134 + 0.846660i \(0.321390\pi\)
\(824\) −21.6238 −0.753302
\(825\) 0 0
\(826\) −3.22582 −0.112241
\(827\) −53.7558 −1.86927 −0.934637 0.355604i \(-0.884275\pi\)
−0.934637 + 0.355604i \(0.884275\pi\)
\(828\) 0 0
\(829\) −26.5801 −0.923164 −0.461582 0.887098i \(-0.652718\pi\)
−0.461582 + 0.887098i \(0.652718\pi\)
\(830\) −8.85780 −0.307459
\(831\) 0 0
\(832\) −2.64076 −0.0915518
\(833\) −118.944 −4.12115
\(834\) 0 0
\(835\) −2.79609 −0.0967626
\(836\) −3.21354 −0.111143
\(837\) 0 0
\(838\) 8.21880 0.283914
\(839\) 24.9153 0.860172 0.430086 0.902788i \(-0.358483\pi\)
0.430086 + 0.902788i \(0.358483\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 25.8857 0.892081
\(843\) 0 0
\(844\) 33.6856 1.15950
\(845\) 2.41391 0.0830411
\(846\) 0 0
\(847\) −51.6860 −1.77595
\(848\) −9.86494 −0.338763
\(849\) 0 0
\(850\) 17.9246 0.614807
\(851\) 5.71364 0.195861
\(852\) 0 0
\(853\) 37.6402 1.28878 0.644388 0.764699i \(-0.277112\pi\)
0.644388 + 0.764699i \(0.277112\pi\)
\(854\) −20.1425 −0.689260
\(855\) 0 0
\(856\) 21.9939 0.751737
\(857\) 34.1351 1.16603 0.583017 0.812460i \(-0.301872\pi\)
0.583017 + 0.812460i \(0.301872\pi\)
\(858\) 0 0
\(859\) −7.59289 −0.259066 −0.129533 0.991575i \(-0.541348\pi\)
−0.129533 + 0.991575i \(0.541348\pi\)
\(860\) 15.8872 0.541749
\(861\) 0 0
\(862\) 17.1318 0.583512
\(863\) −12.6678 −0.431218 −0.215609 0.976480i \(-0.569174\pi\)
−0.215609 + 0.976480i \(0.569174\pi\)
\(864\) 0 0
\(865\) −21.9853 −0.747522
\(866\) −16.7278 −0.568434
\(867\) 0 0
\(868\) 5.19270 0.176252
\(869\) −1.17581 −0.0398865
\(870\) 0 0
\(871\) 45.2847 1.53441
\(872\) −40.4459 −1.36967
\(873\) 0 0
\(874\) −2.82710 −0.0956281
\(875\) −48.2207 −1.63016
\(876\) 0 0
\(877\) 49.7555 1.68012 0.840061 0.542492i \(-0.182519\pi\)
0.840061 + 0.542492i \(0.182519\pi\)
\(878\) −26.7099 −0.901414
\(879\) 0 0
\(880\) 0.874340 0.0294740
\(881\) 18.2360 0.614386 0.307193 0.951647i \(-0.400610\pi\)
0.307193 + 0.951647i \(0.400610\pi\)
\(882\) 0 0
\(883\) 22.6184 0.761170 0.380585 0.924746i \(-0.375723\pi\)
0.380585 + 0.924746i \(0.375723\pi\)
\(884\) −44.9737 −1.51263
\(885\) 0 0
\(886\) −8.47096 −0.284587
\(887\) 18.8293 0.632227 0.316113 0.948721i \(-0.397622\pi\)
0.316113 + 0.948721i \(0.397622\pi\)
\(888\) 0 0
\(889\) 45.0874 1.51218
\(890\) −1.32159 −0.0442997
\(891\) 0 0
\(892\) 1.47496 0.0493854
\(893\) −2.63205 −0.0880783
\(894\) 0 0
\(895\) 3.70102 0.123712
\(896\) −53.0396 −1.77193
\(897\) 0 0
\(898\) −4.19765 −0.140077
\(899\) −0.692651 −0.0231012
\(900\) 0 0
\(901\) 46.8015 1.55918
\(902\) −2.04811 −0.0681944
\(903\) 0 0
\(904\) 19.7729 0.657637
\(905\) 15.4360 0.513109
\(906\) 0 0
\(907\) −44.9004 −1.49089 −0.745446 0.666566i \(-0.767764\pi\)
−0.745446 + 0.666566i \(0.767764\pi\)
\(908\) 31.6360 1.04988
\(909\) 0 0
\(910\) −14.3262 −0.474908
\(911\) −16.6245 −0.550795 −0.275398 0.961330i \(-0.588809\pi\)
−0.275398 + 0.961330i \(0.588809\pi\)
\(912\) 0 0
\(913\) −5.55188 −0.183740
\(914\) −22.1420 −0.732393
\(915\) 0 0
\(916\) −6.49100 −0.214469
\(917\) 85.6385 2.82803
\(918\) 0 0
\(919\) 54.1293 1.78556 0.892781 0.450492i \(-0.148751\pi\)
0.892781 + 0.450492i \(0.148751\pi\)
\(920\) 2.73766 0.0902580
\(921\) 0 0
\(922\) −3.59220 −0.118303
\(923\) 25.0479 0.824462
\(924\) 0 0
\(925\) 20.8646 0.686024
\(926\) 7.05923 0.231981
\(927\) 0 0
\(928\) 5.75004 0.188754
\(929\) −56.9814 −1.86950 −0.934749 0.355309i \(-0.884376\pi\)
−0.934749 + 0.355309i \(0.884376\pi\)
\(930\) 0 0
\(931\) 68.5064 2.24521
\(932\) −20.9049 −0.684764
\(933\) 0 0
\(934\) −7.03036 −0.230040
\(935\) −4.14807 −0.135656
\(936\) 0 0
\(937\) 2.24635 0.0733850 0.0366925 0.999327i \(-0.488318\pi\)
0.0366925 + 0.999327i \(0.488318\pi\)
\(938\) −37.0529 −1.20982
\(939\) 0 0
\(940\) 1.11762 0.0364528
\(941\) −3.37208 −0.109927 −0.0549634 0.998488i \(-0.517504\pi\)
−0.0549634 + 0.998488i \(0.517504\pi\)
\(942\) 0 0
\(943\) 6.42272 0.209153
\(944\) −1.58692 −0.0516499
\(945\) 0 0
\(946\) −2.79352 −0.0908253
\(947\) 54.2976 1.76444 0.882218 0.470842i \(-0.156050\pi\)
0.882218 + 0.470842i \(0.156050\pi\)
\(948\) 0 0
\(949\) −57.2337 −1.85789
\(950\) −10.3238 −0.334948
\(951\) 0 0
\(952\) 83.9203 2.71987
\(953\) 46.6397 1.51081 0.755405 0.655258i \(-0.227440\pi\)
0.755405 + 0.655258i \(0.227440\pi\)
\(954\) 0 0
\(955\) −24.9756 −0.808190
\(956\) −35.4880 −1.14777
\(957\) 0 0
\(958\) −11.5588 −0.373448
\(959\) −31.2086 −1.00778
\(960\) 0 0
\(961\) −30.5202 −0.984524
\(962\) 14.6863 0.473505
\(963\) 0 0
\(964\) −6.67840 −0.215097
\(965\) −2.73269 −0.0879685
\(966\) 0 0
\(967\) −34.1471 −1.09810 −0.549048 0.835791i \(-0.685010\pi\)
−0.549048 + 0.835791i \(0.685010\pi\)
\(968\) 25.3876 0.815987
\(969\) 0 0
\(970\) 3.04503 0.0977700
\(971\) 24.8313 0.796873 0.398437 0.917196i \(-0.369553\pi\)
0.398437 + 0.917196i \(0.369553\pi\)
\(972\) 0 0
\(973\) 42.8294 1.37305
\(974\) 2.63776 0.0845193
\(975\) 0 0
\(976\) −9.90896 −0.317178
\(977\) 60.2384 1.92720 0.963598 0.267355i \(-0.0861495\pi\)
0.963598 + 0.267355i \(0.0861495\pi\)
\(978\) 0 0
\(979\) −0.828342 −0.0264739
\(980\) −29.0892 −0.929221
\(981\) 0 0
\(982\) −9.37403 −0.299137
\(983\) 53.8499 1.71754 0.858772 0.512357i \(-0.171228\pi\)
0.858772 + 0.512357i \(0.171228\pi\)
\(984\) 0 0
\(985\) −0.889478 −0.0283411
\(986\) −4.90853 −0.156319
\(987\) 0 0
\(988\) 25.9030 0.824083
\(989\) 8.76031 0.278562
\(990\) 0 0
\(991\) 9.34232 0.296769 0.148384 0.988930i \(-0.452593\pi\)
0.148384 + 0.988930i \(0.452593\pi\)
\(992\) −3.98277 −0.126453
\(993\) 0 0
\(994\) −20.4947 −0.650053
\(995\) 11.3479 0.359751
\(996\) 0 0
\(997\) −49.9157 −1.58085 −0.790423 0.612562i \(-0.790139\pi\)
−0.790423 + 0.612562i \(0.790139\pi\)
\(998\) −2.48586 −0.0786886
\(999\) 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 6003.2.a.m.1.7 11
3.2 odd 2 2001.2.a.l.1.5 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.l.1.5 11 3.2 odd 2
6003.2.a.m.1.7 11 1.1 even 1 trivial