Properties

Label 4923.2.a.l.1.8
Level $4923$
Weight $2$
Character 4923.1
Self dual yes
Analytic conductor $39.310$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 4923 = 3^{2} \cdot 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4923.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(39.3103529151\)
Analytic rank: \(0\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \(x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} - 137 x^{10} - 7703 x^{9} + 2068 x^{8} + 11068 x^{7} - 4274 x^{6} - 9021 x^{5} + 4048 x^{4} + 3834 x^{3} - 1851 x^{2} - 654 x + 328\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 547)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-0.735255\) of defining polynomial
Character \(\chi\) \(=\) 4923.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.735255 q^{2} -1.45940 q^{4} -0.962787 q^{5} -3.25298 q^{7} +2.54354 q^{8} +O(q^{10})\) \(q-0.735255 q^{2} -1.45940 q^{4} -0.962787 q^{5} -3.25298 q^{7} +2.54354 q^{8} +0.707894 q^{10} +0.883096 q^{11} -4.48154 q^{13} +2.39177 q^{14} +1.04865 q^{16} +3.18294 q^{17} +4.12466 q^{19} +1.40509 q^{20} -0.649301 q^{22} -3.73970 q^{23} -4.07304 q^{25} +3.29508 q^{26} +4.74740 q^{28} -6.33388 q^{29} -8.47939 q^{31} -5.85811 q^{32} -2.34028 q^{34} +3.13193 q^{35} +11.0375 q^{37} -3.03268 q^{38} -2.44889 q^{40} -1.41138 q^{41} -9.31097 q^{43} -1.28879 q^{44} +2.74963 q^{46} +5.82191 q^{47} +3.58188 q^{49} +2.99473 q^{50} +6.54036 q^{52} +7.06826 q^{53} -0.850233 q^{55} -8.27409 q^{56} +4.65702 q^{58} -12.9274 q^{59} -3.04777 q^{61} +6.23452 q^{62} +2.20991 q^{64} +4.31477 q^{65} -9.15218 q^{67} -4.64518 q^{68} -2.30277 q^{70} +4.57601 q^{71} -14.4453 q^{73} -8.11538 q^{74} -6.01952 q^{76} -2.87269 q^{77} +7.20620 q^{79} -1.00962 q^{80} +1.03773 q^{82} -7.39056 q^{83} -3.06450 q^{85} +6.84594 q^{86} +2.24619 q^{88} -0.838265 q^{89} +14.5784 q^{91} +5.45771 q^{92} -4.28059 q^{94} -3.97117 q^{95} +0.475381 q^{97} -2.63360 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q + 4q^{2} + 16q^{4} + 27q^{5} - 11q^{7} + 12q^{8} + O(q^{10}) \) \( 18q + 4q^{2} + 16q^{4} + 27q^{5} - 11q^{7} + 12q^{8} - 5q^{10} - 2q^{11} - 25q^{13} + 7q^{14} + 8q^{16} + 30q^{17} + 4q^{19} + 41q^{20} - 24q^{22} + 26q^{23} + 31q^{25} + 18q^{26} - 16q^{28} + 18q^{29} - 5q^{31} + 28q^{32} + 5q^{34} + 9q^{35} - 18q^{37} + 45q^{38} + 7q^{40} + 17q^{41} + 8q^{43} - 12q^{44} + 30q^{46} + 52q^{47} + 29q^{49} - 13q^{50} - 14q^{52} + 60q^{53} + 11q^{55} - 7q^{56} + 14q^{58} + 8q^{59} - 26q^{61} - 4q^{62} + 44q^{64} + 6q^{65} + 12q^{67} + 61q^{68} + 35q^{70} + q^{71} - 2q^{73} - 16q^{74} + 66q^{76} + 73q^{77} + 18q^{79} + 32q^{80} + 44q^{82} + 43q^{83} + 51q^{85} - 4q^{86} - 17q^{88} + 28q^{89} - q^{91} + 68q^{92} + 78q^{94} + 18q^{95} - 34q^{97} - 34q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.735255 −0.519904 −0.259952 0.965622i \(-0.583707\pi\)
−0.259952 + 0.965622i \(0.583707\pi\)
\(3\) 0 0
\(4\) −1.45940 −0.729700
\(5\) −0.962787 −0.430571 −0.215286 0.976551i \(-0.569068\pi\)
−0.215286 + 0.976551i \(0.569068\pi\)
\(6\) 0 0
\(7\) −3.25298 −1.22951 −0.614755 0.788718i \(-0.710745\pi\)
−0.614755 + 0.788718i \(0.710745\pi\)
\(8\) 2.54354 0.899278
\(9\) 0 0
\(10\) 0.707894 0.223856
\(11\) 0.883096 0.266263 0.133132 0.991098i \(-0.457497\pi\)
0.133132 + 0.991098i \(0.457497\pi\)
\(12\) 0 0
\(13\) −4.48154 −1.24296 −0.621478 0.783431i \(-0.713468\pi\)
−0.621478 + 0.783431i \(0.713468\pi\)
\(14\) 2.39177 0.639228
\(15\) 0 0
\(16\) 1.04865 0.262161
\(17\) 3.18294 0.771977 0.385988 0.922504i \(-0.373860\pi\)
0.385988 + 0.922504i \(0.373860\pi\)
\(18\) 0 0
\(19\) 4.12466 0.946261 0.473131 0.880992i \(-0.343124\pi\)
0.473131 + 0.880992i \(0.343124\pi\)
\(20\) 1.40509 0.314188
\(21\) 0 0
\(22\) −0.649301 −0.138431
\(23\) −3.73970 −0.779781 −0.389890 0.920861i \(-0.627487\pi\)
−0.389890 + 0.920861i \(0.627487\pi\)
\(24\) 0 0
\(25\) −4.07304 −0.814608
\(26\) 3.29508 0.646218
\(27\) 0 0
\(28\) 4.74740 0.897174
\(29\) −6.33388 −1.17617 −0.588086 0.808798i \(-0.700119\pi\)
−0.588086 + 0.808798i \(0.700119\pi\)
\(30\) 0 0
\(31\) −8.47939 −1.52294 −0.761472 0.648198i \(-0.775523\pi\)
−0.761472 + 0.648198i \(0.775523\pi\)
\(32\) −5.85811 −1.03558
\(33\) 0 0
\(34\) −2.34028 −0.401354
\(35\) 3.13193 0.529392
\(36\) 0 0
\(37\) 11.0375 1.81455 0.907276 0.420535i \(-0.138158\pi\)
0.907276 + 0.420535i \(0.138158\pi\)
\(38\) −3.03268 −0.491965
\(39\) 0 0
\(40\) −2.44889 −0.387203
\(41\) −1.41138 −0.220421 −0.110210 0.993908i \(-0.535152\pi\)
−0.110210 + 0.993908i \(0.535152\pi\)
\(42\) 0 0
\(43\) −9.31097 −1.41991 −0.709955 0.704247i \(-0.751285\pi\)
−0.709955 + 0.704247i \(0.751285\pi\)
\(44\) −1.28879 −0.194292
\(45\) 0 0
\(46\) 2.74963 0.405411
\(47\) 5.82191 0.849213 0.424606 0.905378i \(-0.360413\pi\)
0.424606 + 0.905378i \(0.360413\pi\)
\(48\) 0 0
\(49\) 3.58188 0.511697
\(50\) 2.99473 0.423518
\(51\) 0 0
\(52\) 6.54036 0.906985
\(53\) 7.06826 0.970900 0.485450 0.874264i \(-0.338656\pi\)
0.485450 + 0.874264i \(0.338656\pi\)
\(54\) 0 0
\(55\) −0.850233 −0.114645
\(56\) −8.27409 −1.10567
\(57\) 0 0
\(58\) 4.65702 0.611497
\(59\) −12.9274 −1.68301 −0.841503 0.540252i \(-0.818329\pi\)
−0.841503 + 0.540252i \(0.818329\pi\)
\(60\) 0 0
\(61\) −3.04777 −0.390227 −0.195114 0.980781i \(-0.562508\pi\)
−0.195114 + 0.980781i \(0.562508\pi\)
\(62\) 6.23452 0.791784
\(63\) 0 0
\(64\) 2.20991 0.276239
\(65\) 4.31477 0.535182
\(66\) 0 0
\(67\) −9.15218 −1.11812 −0.559059 0.829128i \(-0.688837\pi\)
−0.559059 + 0.829128i \(0.688837\pi\)
\(68\) −4.64518 −0.563311
\(69\) 0 0
\(70\) −2.30277 −0.275233
\(71\) 4.57601 0.543072 0.271536 0.962428i \(-0.412468\pi\)
0.271536 + 0.962428i \(0.412468\pi\)
\(72\) 0 0
\(73\) −14.4453 −1.69070 −0.845349 0.534215i \(-0.820607\pi\)
−0.845349 + 0.534215i \(0.820607\pi\)
\(74\) −8.11538 −0.943393
\(75\) 0 0
\(76\) −6.01952 −0.690486
\(77\) −2.87269 −0.327374
\(78\) 0 0
\(79\) 7.20620 0.810761 0.405381 0.914148i \(-0.367139\pi\)
0.405381 + 0.914148i \(0.367139\pi\)
\(80\) −1.00962 −0.112879
\(81\) 0 0
\(82\) 1.03773 0.114598
\(83\) −7.39056 −0.811219 −0.405610 0.914046i \(-0.632941\pi\)
−0.405610 + 0.914046i \(0.632941\pi\)
\(84\) 0 0
\(85\) −3.06450 −0.332391
\(86\) 6.84594 0.738217
\(87\) 0 0
\(88\) 2.24619 0.239445
\(89\) −0.838265 −0.0888559 −0.0444280 0.999013i \(-0.514147\pi\)
−0.0444280 + 0.999013i \(0.514147\pi\)
\(90\) 0 0
\(91\) 14.5784 1.52823
\(92\) 5.45771 0.569006
\(93\) 0 0
\(94\) −4.28059 −0.441509
\(95\) −3.97117 −0.407433
\(96\) 0 0
\(97\) 0.475381 0.0482676 0.0241338 0.999709i \(-0.492317\pi\)
0.0241338 + 0.999709i \(0.492317\pi\)
\(98\) −2.63360 −0.266033
\(99\) 0 0
\(100\) 5.94419 0.594419
\(101\) 3.07939 0.306411 0.153205 0.988194i \(-0.451040\pi\)
0.153205 + 0.988194i \(0.451040\pi\)
\(102\) 0 0
\(103\) −3.71378 −0.365929 −0.182965 0.983119i \(-0.558569\pi\)
−0.182965 + 0.983119i \(0.558569\pi\)
\(104\) −11.3990 −1.11776
\(105\) 0 0
\(106\) −5.19698 −0.504775
\(107\) −16.1036 −1.55680 −0.778398 0.627771i \(-0.783968\pi\)
−0.778398 + 0.627771i \(0.783968\pi\)
\(108\) 0 0
\(109\) 2.61098 0.250087 0.125043 0.992151i \(-0.460093\pi\)
0.125043 + 0.992151i \(0.460093\pi\)
\(110\) 0.625139 0.0596046
\(111\) 0 0
\(112\) −3.41122 −0.322330
\(113\) 12.2204 1.14960 0.574798 0.818295i \(-0.305081\pi\)
0.574798 + 0.818295i \(0.305081\pi\)
\(114\) 0 0
\(115\) 3.60053 0.335751
\(116\) 9.24367 0.858253
\(117\) 0 0
\(118\) 9.50495 0.875002
\(119\) −10.3540 −0.949154
\(120\) 0 0
\(121\) −10.2201 −0.929104
\(122\) 2.24089 0.202881
\(123\) 0 0
\(124\) 12.3748 1.11129
\(125\) 8.73541 0.781318
\(126\) 0 0
\(127\) 5.90845 0.524290 0.262145 0.965028i \(-0.415570\pi\)
0.262145 + 0.965028i \(0.415570\pi\)
\(128\) 10.0914 0.891959
\(129\) 0 0
\(130\) −3.17246 −0.278243
\(131\) −4.91027 −0.429012 −0.214506 0.976723i \(-0.568814\pi\)
−0.214506 + 0.976723i \(0.568814\pi\)
\(132\) 0 0
\(133\) −13.4174 −1.16344
\(134\) 6.72919 0.581314
\(135\) 0 0
\(136\) 8.09595 0.694222
\(137\) 8.29905 0.709036 0.354518 0.935049i \(-0.384645\pi\)
0.354518 + 0.935049i \(0.384645\pi\)
\(138\) 0 0
\(139\) 21.0776 1.78778 0.893889 0.448288i \(-0.147966\pi\)
0.893889 + 0.448288i \(0.147966\pi\)
\(140\) −4.57073 −0.386297
\(141\) 0 0
\(142\) −3.36453 −0.282345
\(143\) −3.95763 −0.330954
\(144\) 0 0
\(145\) 6.09818 0.506426
\(146\) 10.6210 0.879001
\(147\) 0 0
\(148\) −16.1081 −1.32408
\(149\) 20.9236 1.71413 0.857063 0.515212i \(-0.172287\pi\)
0.857063 + 0.515212i \(0.172287\pi\)
\(150\) 0 0
\(151\) −12.2666 −0.998241 −0.499121 0.866533i \(-0.666344\pi\)
−0.499121 + 0.866533i \(0.666344\pi\)
\(152\) 10.4912 0.850952
\(153\) 0 0
\(154\) 2.11216 0.170203
\(155\) 8.16385 0.655736
\(156\) 0 0
\(157\) 9.63793 0.769191 0.384595 0.923085i \(-0.374341\pi\)
0.384595 + 0.923085i \(0.374341\pi\)
\(158\) −5.29840 −0.421518
\(159\) 0 0
\(160\) 5.64011 0.445890
\(161\) 12.1652 0.958749
\(162\) 0 0
\(163\) 11.8440 0.927693 0.463847 0.885915i \(-0.346469\pi\)
0.463847 + 0.885915i \(0.346469\pi\)
\(164\) 2.05977 0.160841
\(165\) 0 0
\(166\) 5.43395 0.421756
\(167\) 18.8572 1.45922 0.729609 0.683865i \(-0.239702\pi\)
0.729609 + 0.683865i \(0.239702\pi\)
\(168\) 0 0
\(169\) 7.08424 0.544941
\(170\) 2.25319 0.172812
\(171\) 0 0
\(172\) 13.5884 1.03611
\(173\) 15.1822 1.15428 0.577140 0.816645i \(-0.304169\pi\)
0.577140 + 0.816645i \(0.304169\pi\)
\(174\) 0 0
\(175\) 13.2495 1.00157
\(176\) 0.926054 0.0698040
\(177\) 0 0
\(178\) 0.616339 0.0461966
\(179\) 2.57897 0.192761 0.0963806 0.995345i \(-0.469273\pi\)
0.0963806 + 0.995345i \(0.469273\pi\)
\(180\) 0 0
\(181\) −9.50776 −0.706706 −0.353353 0.935490i \(-0.614959\pi\)
−0.353353 + 0.935490i \(0.614959\pi\)
\(182\) −10.7188 −0.794532
\(183\) 0 0
\(184\) −9.51208 −0.701240
\(185\) −10.6268 −0.781295
\(186\) 0 0
\(187\) 2.81084 0.205549
\(188\) −8.49649 −0.619670
\(189\) 0 0
\(190\) 2.91982 0.211826
\(191\) −6.20885 −0.449257 −0.224628 0.974444i \(-0.572117\pi\)
−0.224628 + 0.974444i \(0.572117\pi\)
\(192\) 0 0
\(193\) −19.6307 −1.41305 −0.706526 0.707687i \(-0.749739\pi\)
−0.706526 + 0.707687i \(0.749739\pi\)
\(194\) −0.349526 −0.0250945
\(195\) 0 0
\(196\) −5.22739 −0.373385
\(197\) −26.3638 −1.87834 −0.939171 0.343449i \(-0.888405\pi\)
−0.939171 + 0.343449i \(0.888405\pi\)
\(198\) 0 0
\(199\) −5.17965 −0.367176 −0.183588 0.983003i \(-0.558771\pi\)
−0.183588 + 0.983003i \(0.558771\pi\)
\(200\) −10.3600 −0.732559
\(201\) 0 0
\(202\) −2.26414 −0.159304
\(203\) 20.6040 1.44612
\(204\) 0 0
\(205\) 1.35886 0.0949069
\(206\) 2.73058 0.190248
\(207\) 0 0
\(208\) −4.69955 −0.325855
\(209\) 3.64247 0.251955
\(210\) 0 0
\(211\) 11.3624 0.782217 0.391109 0.920344i \(-0.372092\pi\)
0.391109 + 0.920344i \(0.372092\pi\)
\(212\) −10.3154 −0.708466
\(213\) 0 0
\(214\) 11.8403 0.809385
\(215\) 8.96448 0.611373
\(216\) 0 0
\(217\) 27.5833 1.87248
\(218\) −1.91974 −0.130021
\(219\) 0 0
\(220\) 1.24083 0.0836567
\(221\) −14.2645 −0.959534
\(222\) 0 0
\(223\) 18.9951 1.27201 0.636003 0.771686i \(-0.280587\pi\)
0.636003 + 0.771686i \(0.280587\pi\)
\(224\) 19.0563 1.27325
\(225\) 0 0
\(226\) −8.98510 −0.597680
\(227\) −11.7708 −0.781254 −0.390627 0.920549i \(-0.627742\pi\)
−0.390627 + 0.920549i \(0.627742\pi\)
\(228\) 0 0
\(229\) 6.31464 0.417283 0.208641 0.977992i \(-0.433096\pi\)
0.208641 + 0.977992i \(0.433096\pi\)
\(230\) −2.64731 −0.174558
\(231\) 0 0
\(232\) −16.1105 −1.05771
\(233\) −20.7839 −1.36160 −0.680799 0.732470i \(-0.738367\pi\)
−0.680799 + 0.732470i \(0.738367\pi\)
\(234\) 0 0
\(235\) −5.60526 −0.365647
\(236\) 18.8663 1.22809
\(237\) 0 0
\(238\) 7.61287 0.493469
\(239\) 23.8405 1.54212 0.771058 0.636765i \(-0.219728\pi\)
0.771058 + 0.636765i \(0.219728\pi\)
\(240\) 0 0
\(241\) 1.62031 0.104374 0.0521868 0.998637i \(-0.483381\pi\)
0.0521868 + 0.998637i \(0.483381\pi\)
\(242\) 7.51442 0.483045
\(243\) 0 0
\(244\) 4.44792 0.284749
\(245\) −3.44859 −0.220322
\(246\) 0 0
\(247\) −18.4848 −1.17616
\(248\) −21.5677 −1.36955
\(249\) 0 0
\(250\) −6.42276 −0.406211
\(251\) 10.7109 0.676064 0.338032 0.941135i \(-0.390239\pi\)
0.338032 + 0.941135i \(0.390239\pi\)
\(252\) 0 0
\(253\) −3.30251 −0.207627
\(254\) −4.34422 −0.272581
\(255\) 0 0
\(256\) −11.8396 −0.739972
\(257\) 28.7954 1.79621 0.898105 0.439781i \(-0.144944\pi\)
0.898105 + 0.439781i \(0.144944\pi\)
\(258\) 0 0
\(259\) −35.9047 −2.23101
\(260\) −6.29698 −0.390522
\(261\) 0 0
\(262\) 3.61030 0.223045
\(263\) 27.1652 1.67508 0.837539 0.546378i \(-0.183994\pi\)
0.837539 + 0.546378i \(0.183994\pi\)
\(264\) 0 0
\(265\) −6.80523 −0.418042
\(266\) 9.86523 0.604876
\(267\) 0 0
\(268\) 13.3567 0.815890
\(269\) 19.2182 1.17176 0.585878 0.810399i \(-0.300750\pi\)
0.585878 + 0.810399i \(0.300750\pi\)
\(270\) 0 0
\(271\) −9.73786 −0.591533 −0.295766 0.955260i \(-0.595575\pi\)
−0.295766 + 0.955260i \(0.595575\pi\)
\(272\) 3.33778 0.202382
\(273\) 0 0
\(274\) −6.10192 −0.368631
\(275\) −3.59689 −0.216900
\(276\) 0 0
\(277\) −26.8931 −1.61585 −0.807925 0.589285i \(-0.799409\pi\)
−0.807925 + 0.589285i \(0.799409\pi\)
\(278\) −15.4974 −0.929474
\(279\) 0 0
\(280\) 7.96619 0.476071
\(281\) 4.21282 0.251316 0.125658 0.992074i \(-0.459896\pi\)
0.125658 + 0.992074i \(0.459896\pi\)
\(282\) 0 0
\(283\) 31.3587 1.86408 0.932039 0.362357i \(-0.118028\pi\)
0.932039 + 0.362357i \(0.118028\pi\)
\(284\) −6.67822 −0.396280
\(285\) 0 0
\(286\) 2.90987 0.172064
\(287\) 4.59120 0.271010
\(288\) 0 0
\(289\) −6.86888 −0.404052
\(290\) −4.48372 −0.263293
\(291\) 0 0
\(292\) 21.0815 1.23370
\(293\) 15.8890 0.928244 0.464122 0.885771i \(-0.346370\pi\)
0.464122 + 0.885771i \(0.346370\pi\)
\(294\) 0 0
\(295\) 12.4463 0.724654
\(296\) 28.0743 1.63179
\(297\) 0 0
\(298\) −15.3842 −0.891181
\(299\) 16.7596 0.969234
\(300\) 0 0
\(301\) 30.2884 1.74579
\(302\) 9.01908 0.518990
\(303\) 0 0
\(304\) 4.32530 0.248073
\(305\) 2.93436 0.168021
\(306\) 0 0
\(307\) −13.7030 −0.782070 −0.391035 0.920376i \(-0.627883\pi\)
−0.391035 + 0.920376i \(0.627883\pi\)
\(308\) 4.19241 0.238884
\(309\) 0 0
\(310\) −6.00251 −0.340920
\(311\) −6.49422 −0.368253 −0.184127 0.982903i \(-0.558946\pi\)
−0.184127 + 0.982903i \(0.558946\pi\)
\(312\) 0 0
\(313\) 8.26403 0.467111 0.233555 0.972344i \(-0.424964\pi\)
0.233555 + 0.972344i \(0.424964\pi\)
\(314\) −7.08634 −0.399905
\(315\) 0 0
\(316\) −10.5167 −0.591612
\(317\) 28.1441 1.58073 0.790364 0.612638i \(-0.209892\pi\)
0.790364 + 0.612638i \(0.209892\pi\)
\(318\) 0 0
\(319\) −5.59343 −0.313172
\(320\) −2.12768 −0.118941
\(321\) 0 0
\(322\) −8.94450 −0.498457
\(323\) 13.1285 0.730492
\(324\) 0 0
\(325\) 18.2535 1.01252
\(326\) −8.70836 −0.482312
\(327\) 0 0
\(328\) −3.58991 −0.198220
\(329\) −18.9386 −1.04412
\(330\) 0 0
\(331\) −1.78319 −0.0980130 −0.0490065 0.998798i \(-0.515606\pi\)
−0.0490065 + 0.998798i \(0.515606\pi\)
\(332\) 10.7858 0.591947
\(333\) 0 0
\(334\) −13.8649 −0.758653
\(335\) 8.81160 0.481429
\(336\) 0 0
\(337\) 17.5528 0.956160 0.478080 0.878316i \(-0.341333\pi\)
0.478080 + 0.878316i \(0.341333\pi\)
\(338\) −5.20873 −0.283317
\(339\) 0 0
\(340\) 4.47232 0.242546
\(341\) −7.48811 −0.405504
\(342\) 0 0
\(343\) 11.1191 0.600374
\(344\) −23.6829 −1.27689
\(345\) 0 0
\(346\) −11.1628 −0.600115
\(347\) −14.8308 −0.796160 −0.398080 0.917351i \(-0.630323\pi\)
−0.398080 + 0.917351i \(0.630323\pi\)
\(348\) 0 0
\(349\) −34.3697 −1.83977 −0.919884 0.392190i \(-0.871718\pi\)
−0.919884 + 0.392190i \(0.871718\pi\)
\(350\) −9.74178 −0.520720
\(351\) 0 0
\(352\) −5.17327 −0.275736
\(353\) 16.1758 0.860949 0.430474 0.902603i \(-0.358346\pi\)
0.430474 + 0.902603i \(0.358346\pi\)
\(354\) 0 0
\(355\) −4.40572 −0.233831
\(356\) 1.22336 0.0648381
\(357\) 0 0
\(358\) −1.89620 −0.100217
\(359\) −17.7167 −0.935053 −0.467526 0.883979i \(-0.654855\pi\)
−0.467526 + 0.883979i \(0.654855\pi\)
\(360\) 0 0
\(361\) −1.98721 −0.104590
\(362\) 6.99063 0.367419
\(363\) 0 0
\(364\) −21.2757 −1.11515
\(365\) 13.9078 0.727966
\(366\) 0 0
\(367\) 7.29148 0.380612 0.190306 0.981725i \(-0.439052\pi\)
0.190306 + 0.981725i \(0.439052\pi\)
\(368\) −3.92162 −0.204428
\(369\) 0 0
\(370\) 7.81338 0.406198
\(371\) −22.9929 −1.19373
\(372\) 0 0
\(373\) 19.4135 1.00520 0.502598 0.864520i \(-0.332378\pi\)
0.502598 + 0.864520i \(0.332378\pi\)
\(374\) −2.06669 −0.106866
\(375\) 0 0
\(376\) 14.8083 0.763678
\(377\) 28.3856 1.46193
\(378\) 0 0
\(379\) 21.5543 1.10717 0.553586 0.832792i \(-0.313259\pi\)
0.553586 + 0.832792i \(0.313259\pi\)
\(380\) 5.79552 0.297304
\(381\) 0 0
\(382\) 4.56509 0.233571
\(383\) 8.69462 0.444274 0.222137 0.975015i \(-0.428697\pi\)
0.222137 + 0.975015i \(0.428697\pi\)
\(384\) 0 0
\(385\) 2.76579 0.140958
\(386\) 14.4336 0.734652
\(387\) 0 0
\(388\) −0.693771 −0.0352209
\(389\) −20.0986 −1.01904 −0.509520 0.860459i \(-0.670177\pi\)
−0.509520 + 0.860459i \(0.670177\pi\)
\(390\) 0 0
\(391\) −11.9032 −0.601973
\(392\) 9.11066 0.460158
\(393\) 0 0
\(394\) 19.3841 0.976558
\(395\) −6.93804 −0.349091
\(396\) 0 0
\(397\) −22.3318 −1.12080 −0.560402 0.828221i \(-0.689353\pi\)
−0.560402 + 0.828221i \(0.689353\pi\)
\(398\) 3.80836 0.190896
\(399\) 0 0
\(400\) −4.27118 −0.213559
\(401\) 1.95708 0.0977321 0.0488661 0.998805i \(-0.484439\pi\)
0.0488661 + 0.998805i \(0.484439\pi\)
\(402\) 0 0
\(403\) 38.0008 1.89295
\(404\) −4.49406 −0.223588
\(405\) 0 0
\(406\) −15.1492 −0.751842
\(407\) 9.74716 0.483149
\(408\) 0 0
\(409\) 14.4716 0.715576 0.357788 0.933803i \(-0.383531\pi\)
0.357788 + 0.933803i \(0.383531\pi\)
\(410\) −0.999110 −0.0493425
\(411\) 0 0
\(412\) 5.41989 0.267019
\(413\) 42.0526 2.06927
\(414\) 0 0
\(415\) 7.11554 0.349288
\(416\) 26.2534 1.28718
\(417\) 0 0
\(418\) −2.67814 −0.130992
\(419\) 4.92102 0.240408 0.120204 0.992749i \(-0.461645\pi\)
0.120204 + 0.992749i \(0.461645\pi\)
\(420\) 0 0
\(421\) 16.7810 0.817857 0.408928 0.912566i \(-0.365903\pi\)
0.408928 + 0.912566i \(0.365903\pi\)
\(422\) −8.35424 −0.406678
\(423\) 0 0
\(424\) 17.9784 0.873109
\(425\) −12.9643 −0.628859
\(426\) 0 0
\(427\) 9.91435 0.479789
\(428\) 23.5016 1.13599
\(429\) 0 0
\(430\) −6.59119 −0.317855
\(431\) −10.5214 −0.506800 −0.253400 0.967362i \(-0.581549\pi\)
−0.253400 + 0.967362i \(0.581549\pi\)
\(432\) 0 0
\(433\) −11.8135 −0.567721 −0.283860 0.958866i \(-0.591615\pi\)
−0.283860 + 0.958866i \(0.591615\pi\)
\(434\) −20.2808 −0.973508
\(435\) 0 0
\(436\) −3.81047 −0.182488
\(437\) −15.4250 −0.737876
\(438\) 0 0
\(439\) 8.18885 0.390833 0.195416 0.980720i \(-0.437394\pi\)
0.195416 + 0.980720i \(0.437394\pi\)
\(440\) −2.16260 −0.103098
\(441\) 0 0
\(442\) 10.4880 0.498866
\(443\) 15.7119 0.746496 0.373248 0.927732i \(-0.378244\pi\)
0.373248 + 0.927732i \(0.378244\pi\)
\(444\) 0 0
\(445\) 0.807071 0.0382588
\(446\) −13.9663 −0.661321
\(447\) 0 0
\(448\) −7.18881 −0.339639
\(449\) −9.89465 −0.466957 −0.233479 0.972362i \(-0.575011\pi\)
−0.233479 + 0.972362i \(0.575011\pi\)
\(450\) 0 0
\(451\) −1.24639 −0.0586900
\(452\) −17.8344 −0.838860
\(453\) 0 0
\(454\) 8.65453 0.406177
\(455\) −14.0359 −0.658012
\(456\) 0 0
\(457\) 19.4319 0.908985 0.454492 0.890751i \(-0.349821\pi\)
0.454492 + 0.890751i \(0.349821\pi\)
\(458\) −4.64287 −0.216947
\(459\) 0 0
\(460\) −5.25461 −0.244998
\(461\) −28.4760 −1.32626 −0.663130 0.748504i \(-0.730772\pi\)
−0.663130 + 0.748504i \(0.730772\pi\)
\(462\) 0 0
\(463\) −10.8095 −0.502361 −0.251181 0.967940i \(-0.580819\pi\)
−0.251181 + 0.967940i \(0.580819\pi\)
\(464\) −6.64200 −0.308347
\(465\) 0 0
\(466\) 15.2815 0.707901
\(467\) −26.3662 −1.22008 −0.610041 0.792369i \(-0.708847\pi\)
−0.610041 + 0.792369i \(0.708847\pi\)
\(468\) 0 0
\(469\) 29.7719 1.37474
\(470\) 4.12130 0.190101
\(471\) 0 0
\(472\) −32.8814 −1.51349
\(473\) −8.22248 −0.378070
\(474\) 0 0
\(475\) −16.7999 −0.770832
\(476\) 15.1107 0.692597
\(477\) 0 0
\(478\) −17.5289 −0.801752
\(479\) 0.194030 0.00886547 0.00443274 0.999990i \(-0.498589\pi\)
0.00443274 + 0.999990i \(0.498589\pi\)
\(480\) 0 0
\(481\) −49.4650 −2.25541
\(482\) −1.19134 −0.0542642
\(483\) 0 0
\(484\) 14.9153 0.677967
\(485\) −0.457691 −0.0207827
\(486\) 0 0
\(487\) −2.65682 −0.120392 −0.0601959 0.998187i \(-0.519173\pi\)
−0.0601959 + 0.998187i \(0.519173\pi\)
\(488\) −7.75214 −0.350923
\(489\) 0 0
\(490\) 2.53559 0.114546
\(491\) −11.0398 −0.498219 −0.249109 0.968475i \(-0.580138\pi\)
−0.249109 + 0.968475i \(0.580138\pi\)
\(492\) 0 0
\(493\) −20.1604 −0.907978
\(494\) 13.5911 0.611491
\(495\) 0 0
\(496\) −8.89187 −0.399257
\(497\) −14.8857 −0.667713
\(498\) 0 0
\(499\) 30.9966 1.38760 0.693799 0.720168i \(-0.255935\pi\)
0.693799 + 0.720168i \(0.255935\pi\)
\(500\) −12.7484 −0.570128
\(501\) 0 0
\(502\) −7.87523 −0.351489
\(503\) 37.0982 1.65413 0.827063 0.562109i \(-0.190010\pi\)
0.827063 + 0.562109i \(0.190010\pi\)
\(504\) 0 0
\(505\) −2.96480 −0.131932
\(506\) 2.42819 0.107946
\(507\) 0 0
\(508\) −8.62279 −0.382575
\(509\) 8.10275 0.359148 0.179574 0.983744i \(-0.442528\pi\)
0.179574 + 0.983744i \(0.442528\pi\)
\(510\) 0 0
\(511\) 46.9904 2.07873
\(512\) −11.4776 −0.507244
\(513\) 0 0
\(514\) −21.1720 −0.933857
\(515\) 3.57558 0.157559
\(516\) 0 0
\(517\) 5.14130 0.226114
\(518\) 26.3992 1.15991
\(519\) 0 0
\(520\) 10.9748 0.481277
\(521\) −9.96721 −0.436671 −0.218336 0.975874i \(-0.570063\pi\)
−0.218336 + 0.975874i \(0.570063\pi\)
\(522\) 0 0
\(523\) −7.12073 −0.311368 −0.155684 0.987807i \(-0.549758\pi\)
−0.155684 + 0.987807i \(0.549758\pi\)
\(524\) 7.16604 0.313050
\(525\) 0 0
\(526\) −19.9734 −0.870879
\(527\) −26.9894 −1.17568
\(528\) 0 0
\(529\) −9.01467 −0.391942
\(530\) 5.00358 0.217342
\(531\) 0 0
\(532\) 19.5814 0.848961
\(533\) 6.32517 0.273974
\(534\) 0 0
\(535\) 15.5044 0.670312
\(536\) −23.2790 −1.00550
\(537\) 0 0
\(538\) −14.1303 −0.609201
\(539\) 3.16314 0.136246
\(540\) 0 0
\(541\) 39.1006 1.68107 0.840533 0.541760i \(-0.182242\pi\)
0.840533 + 0.541760i \(0.182242\pi\)
\(542\) 7.15981 0.307540
\(543\) 0 0
\(544\) −18.6460 −0.799441
\(545\) −2.51382 −0.107680
\(546\) 0 0
\(547\) −1.00000 −0.0427569
\(548\) −12.1116 −0.517383
\(549\) 0 0
\(550\) 2.64463 0.112767
\(551\) −26.1251 −1.11297
\(552\) 0 0
\(553\) −23.4416 −0.996840
\(554\) 19.7733 0.840087
\(555\) 0 0
\(556\) −30.7606 −1.30454
\(557\) −39.1227 −1.65768 −0.828841 0.559485i \(-0.810999\pi\)
−0.828841 + 0.559485i \(0.810999\pi\)
\(558\) 0 0
\(559\) 41.7275 1.76489
\(560\) 3.28428 0.138786
\(561\) 0 0
\(562\) −3.09750 −0.130660
\(563\) −32.3381 −1.36289 −0.681445 0.731869i \(-0.738648\pi\)
−0.681445 + 0.731869i \(0.738648\pi\)
\(564\) 0 0
\(565\) −11.7656 −0.494983
\(566\) −23.0566 −0.969142
\(567\) 0 0
\(568\) 11.6393 0.488373
\(569\) −0.316254 −0.0132581 −0.00662903 0.999978i \(-0.502110\pi\)
−0.00662903 + 0.999978i \(0.502110\pi\)
\(570\) 0 0
\(571\) 4.67642 0.195702 0.0978511 0.995201i \(-0.468803\pi\)
0.0978511 + 0.995201i \(0.468803\pi\)
\(572\) 5.77577 0.241497
\(573\) 0 0
\(574\) −3.37570 −0.140899
\(575\) 15.2319 0.635216
\(576\) 0 0
\(577\) 38.4107 1.59906 0.799529 0.600627i \(-0.205082\pi\)
0.799529 + 0.600627i \(0.205082\pi\)
\(578\) 5.05038 0.210068
\(579\) 0 0
\(580\) −8.89968 −0.369539
\(581\) 24.0413 0.997403
\(582\) 0 0
\(583\) 6.24195 0.258515
\(584\) −36.7423 −1.52041
\(585\) 0 0
\(586\) −11.6825 −0.482598
\(587\) −6.56995 −0.271171 −0.135586 0.990766i \(-0.543292\pi\)
−0.135586 + 0.990766i \(0.543292\pi\)
\(588\) 0 0
\(589\) −34.9746 −1.44110
\(590\) −9.15125 −0.376751
\(591\) 0 0
\(592\) 11.5744 0.475706
\(593\) 0.570902 0.0234441 0.0117221 0.999931i \(-0.496269\pi\)
0.0117221 + 0.999931i \(0.496269\pi\)
\(594\) 0 0
\(595\) 9.96874 0.408679
\(596\) −30.5359 −1.25080
\(597\) 0 0
\(598\) −12.3226 −0.503909
\(599\) −8.95352 −0.365831 −0.182915 0.983129i \(-0.558553\pi\)
−0.182915 + 0.983129i \(0.558553\pi\)
\(600\) 0 0
\(601\) −12.7284 −0.519202 −0.259601 0.965716i \(-0.583591\pi\)
−0.259601 + 0.965716i \(0.583591\pi\)
\(602\) −22.2697 −0.907646
\(603\) 0 0
\(604\) 17.9019 0.728416
\(605\) 9.83982 0.400046
\(606\) 0 0
\(607\) 26.7859 1.08721 0.543603 0.839342i \(-0.317060\pi\)
0.543603 + 0.839342i \(0.317060\pi\)
\(608\) −24.1627 −0.979926
\(609\) 0 0
\(610\) −2.15750 −0.0873547
\(611\) −26.0911 −1.05553
\(612\) 0 0
\(613\) 31.3273 1.26530 0.632649 0.774439i \(-0.281968\pi\)
0.632649 + 0.774439i \(0.281968\pi\)
\(614\) 10.0752 0.406602
\(615\) 0 0
\(616\) −7.30682 −0.294400
\(617\) 31.6103 1.27258 0.636292 0.771448i \(-0.280467\pi\)
0.636292 + 0.771448i \(0.280467\pi\)
\(618\) 0 0
\(619\) 7.99712 0.321431 0.160716 0.987001i \(-0.448620\pi\)
0.160716 + 0.987001i \(0.448620\pi\)
\(620\) −11.9143 −0.478490
\(621\) 0 0
\(622\) 4.77491 0.191457
\(623\) 2.72686 0.109249
\(624\) 0 0
\(625\) 11.9549 0.478195
\(626\) −6.07617 −0.242853
\(627\) 0 0
\(628\) −14.0656 −0.561278
\(629\) 35.1317 1.40079
\(630\) 0 0
\(631\) −44.2164 −1.76023 −0.880113 0.474764i \(-0.842534\pi\)
−0.880113 + 0.474764i \(0.842534\pi\)
\(632\) 18.3293 0.729100
\(633\) 0 0
\(634\) −20.6931 −0.821827
\(635\) −5.68858 −0.225744
\(636\) 0 0
\(637\) −16.0523 −0.636017
\(638\) 4.11260 0.162819
\(639\) 0 0
\(640\) −9.71583 −0.384052
\(641\) 16.8320 0.664824 0.332412 0.943134i \(-0.392138\pi\)
0.332412 + 0.943134i \(0.392138\pi\)
\(642\) 0 0
\(643\) −12.4597 −0.491362 −0.245681 0.969351i \(-0.579012\pi\)
−0.245681 + 0.969351i \(0.579012\pi\)
\(644\) −17.7538 −0.699599
\(645\) 0 0
\(646\) −9.65283 −0.379786
\(647\) 48.1533 1.89310 0.946551 0.322555i \(-0.104542\pi\)
0.946551 + 0.322555i \(0.104542\pi\)
\(648\) 0 0
\(649\) −11.4161 −0.448123
\(650\) −13.4210 −0.526415
\(651\) 0 0
\(652\) −17.2851 −0.676938
\(653\) 12.7505 0.498967 0.249484 0.968379i \(-0.419739\pi\)
0.249484 + 0.968379i \(0.419739\pi\)
\(654\) 0 0
\(655\) 4.72754 0.184720
\(656\) −1.48004 −0.0577858
\(657\) 0 0
\(658\) 13.9247 0.542840
\(659\) 29.8939 1.16450 0.582250 0.813010i \(-0.302172\pi\)
0.582250 + 0.813010i \(0.302172\pi\)
\(660\) 0 0
\(661\) 22.0815 0.858872 0.429436 0.903097i \(-0.358712\pi\)
0.429436 + 0.903097i \(0.358712\pi\)
\(662\) 1.31110 0.0509574
\(663\) 0 0
\(664\) −18.7982 −0.729512
\(665\) 12.9181 0.500943
\(666\) 0 0
\(667\) 23.6868 0.917157
\(668\) −27.5203 −1.06479
\(669\) 0 0
\(670\) −6.47878 −0.250297
\(671\) −2.69148 −0.103903
\(672\) 0 0
\(673\) 24.6133 0.948772 0.474386 0.880317i \(-0.342670\pi\)
0.474386 + 0.880317i \(0.342670\pi\)
\(674\) −12.9058 −0.497112
\(675\) 0 0
\(676\) −10.3387 −0.397644
\(677\) −15.1930 −0.583913 −0.291956 0.956432i \(-0.594306\pi\)
−0.291956 + 0.956432i \(0.594306\pi\)
\(678\) 0 0
\(679\) −1.54640 −0.0593456
\(680\) −7.79467 −0.298912
\(681\) 0 0
\(682\) 5.50568 0.210823
\(683\) 23.5519 0.901189 0.450594 0.892729i \(-0.351212\pi\)
0.450594 + 0.892729i \(0.351212\pi\)
\(684\) 0 0
\(685\) −7.99022 −0.305291
\(686\) −8.17537 −0.312137
\(687\) 0 0
\(688\) −9.76391 −0.372245
\(689\) −31.6767 −1.20679
\(690\) 0 0
\(691\) −37.0300 −1.40869 −0.704343 0.709860i \(-0.748758\pi\)
−0.704343 + 0.709860i \(0.748758\pi\)
\(692\) −22.1569 −0.842278
\(693\) 0 0
\(694\) 10.9044 0.413927
\(695\) −20.2932 −0.769766
\(696\) 0 0
\(697\) −4.49235 −0.170160
\(698\) 25.2705 0.956503
\(699\) 0 0
\(700\) −19.3363 −0.730845
\(701\) −35.5829 −1.34395 −0.671973 0.740576i \(-0.734553\pi\)
−0.671973 + 0.740576i \(0.734553\pi\)
\(702\) 0 0
\(703\) 45.5259 1.71704
\(704\) 1.95157 0.0735524
\(705\) 0 0
\(706\) −11.8933 −0.447611
\(707\) −10.0172 −0.376736
\(708\) 0 0
\(709\) 40.5125 1.52148 0.760739 0.649058i \(-0.224837\pi\)
0.760739 + 0.649058i \(0.224837\pi\)
\(710\) 3.23933 0.121570
\(711\) 0 0
\(712\) −2.13216 −0.0799062
\(713\) 31.7103 1.18756
\(714\) 0 0
\(715\) 3.81036 0.142499
\(716\) −3.76375 −0.140658
\(717\) 0 0
\(718\) 13.0263 0.486138
\(719\) −6.36743 −0.237465 −0.118733 0.992926i \(-0.537883\pi\)
−0.118733 + 0.992926i \(0.537883\pi\)
\(720\) 0 0
\(721\) 12.0808 0.449914
\(722\) 1.46111 0.0543767
\(723\) 0 0
\(724\) 13.8756 0.515683
\(725\) 25.7982 0.958120
\(726\) 0 0
\(727\) −35.1164 −1.30240 −0.651198 0.758908i \(-0.725733\pi\)
−0.651198 + 0.758908i \(0.725733\pi\)
\(728\) 37.0807 1.37430
\(729\) 0 0
\(730\) −10.2258 −0.378473
\(731\) −29.6363 −1.09614
\(732\) 0 0
\(733\) 26.1891 0.967315 0.483658 0.875257i \(-0.339308\pi\)
0.483658 + 0.875257i \(0.339308\pi\)
\(734\) −5.36110 −0.197882
\(735\) 0 0
\(736\) 21.9075 0.807523
\(737\) −8.08225 −0.297714
\(738\) 0 0
\(739\) 15.8483 0.582988 0.291494 0.956573i \(-0.405848\pi\)
0.291494 + 0.956573i \(0.405848\pi\)
\(740\) 15.5087 0.570110
\(741\) 0 0
\(742\) 16.9057 0.620626
\(743\) −13.1980 −0.484189 −0.242095 0.970253i \(-0.577834\pi\)
−0.242095 + 0.970253i \(0.577834\pi\)
\(744\) 0 0
\(745\) −20.1449 −0.738054
\(746\) −14.2739 −0.522605
\(747\) 0 0
\(748\) −4.10214 −0.149989
\(749\) 52.3848 1.91410
\(750\) 0 0
\(751\) −17.3729 −0.633945 −0.316973 0.948435i \(-0.602666\pi\)
−0.316973 + 0.948435i \(0.602666\pi\)
\(752\) 6.10512 0.222631
\(753\) 0 0
\(754\) −20.8707 −0.760064
\(755\) 11.8101 0.429814
\(756\) 0 0
\(757\) −38.7514 −1.40844 −0.704222 0.709980i \(-0.748704\pi\)
−0.704222 + 0.709980i \(0.748704\pi\)
\(758\) −15.8479 −0.575623
\(759\) 0 0
\(760\) −10.1008 −0.366396
\(761\) 29.0280 1.05226 0.526132 0.850403i \(-0.323642\pi\)
0.526132 + 0.850403i \(0.323642\pi\)
\(762\) 0 0
\(763\) −8.49347 −0.307484
\(764\) 9.06120 0.327823
\(765\) 0 0
\(766\) −6.39277 −0.230980
\(767\) 57.9348 2.09190
\(768\) 0 0
\(769\) −8.49451 −0.306320 −0.153160 0.988201i \(-0.548945\pi\)
−0.153160 + 0.988201i \(0.548945\pi\)
\(770\) −2.03356 −0.0732845
\(771\) 0 0
\(772\) 28.6491 1.03110
\(773\) 30.2676 1.08865 0.544325 0.838875i \(-0.316786\pi\)
0.544325 + 0.838875i \(0.316786\pi\)
\(774\) 0 0
\(775\) 34.5369 1.24060
\(776\) 1.20915 0.0434060
\(777\) 0 0
\(778\) 14.7776 0.529803
\(779\) −5.82147 −0.208576
\(780\) 0 0
\(781\) 4.04105 0.144600
\(782\) 8.75192 0.312968
\(783\) 0 0
\(784\) 3.75612 0.134147
\(785\) −9.27927 −0.331191
\(786\) 0 0
\(787\) −25.5339 −0.910185 −0.455093 0.890444i \(-0.650394\pi\)
−0.455093 + 0.890444i \(0.650394\pi\)
\(788\) 38.4753 1.37063
\(789\) 0 0
\(790\) 5.10123 0.181494
\(791\) −39.7526 −1.41344
\(792\) 0 0
\(793\) 13.6587 0.485036
\(794\) 16.4196 0.582710
\(795\) 0 0
\(796\) 7.55918 0.267928
\(797\) 48.5429 1.71948 0.859738 0.510735i \(-0.170627\pi\)
0.859738 + 0.510735i \(0.170627\pi\)
\(798\) 0 0
\(799\) 18.5308 0.655573
\(800\) 23.8603 0.843589
\(801\) 0 0
\(802\) −1.43896 −0.0508113
\(803\) −12.7566 −0.450171
\(804\) 0 0
\(805\) −11.7125 −0.412810
\(806\) −27.9403 −0.984154
\(807\) 0 0
\(808\) 7.83256 0.275549
\(809\) −30.1082 −1.05855 −0.529274 0.848451i \(-0.677536\pi\)
−0.529274 + 0.848451i \(0.677536\pi\)
\(810\) 0 0
\(811\) −26.6166 −0.934634 −0.467317 0.884090i \(-0.654779\pi\)
−0.467317 + 0.884090i \(0.654779\pi\)
\(812\) −30.0695 −1.05523
\(813\) 0 0
\(814\) −7.16665 −0.251191
\(815\) −11.4032 −0.399438
\(816\) 0 0
\(817\) −38.4046 −1.34361
\(818\) −10.6403 −0.372031
\(819\) 0 0
\(820\) −1.98312 −0.0692536
\(821\) 52.7820 1.84210 0.921052 0.389440i \(-0.127332\pi\)
0.921052 + 0.389440i \(0.127332\pi\)
\(822\) 0 0
\(823\) −20.7992 −0.725014 −0.362507 0.931981i \(-0.618079\pi\)
−0.362507 + 0.931981i \(0.618079\pi\)
\(824\) −9.44615 −0.329072
\(825\) 0 0
\(826\) −30.9194 −1.07582
\(827\) −12.6722 −0.440654 −0.220327 0.975426i \(-0.570713\pi\)
−0.220327 + 0.975426i \(0.570713\pi\)
\(828\) 0 0
\(829\) 24.4262 0.848357 0.424179 0.905579i \(-0.360563\pi\)
0.424179 + 0.905579i \(0.360563\pi\)
\(830\) −5.23174 −0.181596
\(831\) 0 0
\(832\) −9.90383 −0.343354
\(833\) 11.4009 0.395018
\(834\) 0 0
\(835\) −18.1555 −0.628297
\(836\) −5.31581 −0.183851
\(837\) 0 0
\(838\) −3.61821 −0.124989
\(839\) −41.6208 −1.43691 −0.718455 0.695574i \(-0.755150\pi\)
−0.718455 + 0.695574i \(0.755150\pi\)
\(840\) 0 0
\(841\) 11.1181 0.383383
\(842\) −12.3383 −0.425207
\(843\) 0 0
\(844\) −16.5822 −0.570784
\(845\) −6.82061 −0.234636
\(846\) 0 0
\(847\) 33.2459 1.14234
\(848\) 7.41210 0.254533
\(849\) 0 0
\(850\) 9.53204 0.326946
\(851\) −41.2769 −1.41495
\(852\) 0 0
\(853\) 11.9436 0.408942 0.204471 0.978873i \(-0.434453\pi\)
0.204471 + 0.978873i \(0.434453\pi\)
\(854\) −7.28958 −0.249444
\(855\) 0 0
\(856\) −40.9603 −1.39999
\(857\) 17.0803 0.583452 0.291726 0.956502i \(-0.405771\pi\)
0.291726 + 0.956502i \(0.405771\pi\)
\(858\) 0 0
\(859\) −45.1499 −1.54049 −0.770247 0.637745i \(-0.779867\pi\)
−0.770247 + 0.637745i \(0.779867\pi\)
\(860\) −13.0828 −0.446118
\(861\) 0 0
\(862\) 7.73595 0.263487
\(863\) 42.9192 1.46099 0.730494 0.682919i \(-0.239290\pi\)
0.730494 + 0.682919i \(0.239290\pi\)
\(864\) 0 0
\(865\) −14.6172 −0.497000
\(866\) 8.68594 0.295160
\(867\) 0 0
\(868\) −40.2550 −1.36634
\(869\) 6.36377 0.215876
\(870\) 0 0
\(871\) 41.0159 1.38977
\(872\) 6.64114 0.224897
\(873\) 0 0
\(874\) 11.3413 0.383625
\(875\) −28.4161 −0.960640
\(876\) 0 0
\(877\) −22.1529 −0.748050 −0.374025 0.927419i \(-0.622023\pi\)
−0.374025 + 0.927419i \(0.622023\pi\)
\(878\) −6.02090 −0.203196
\(879\) 0 0
\(880\) −0.891593 −0.0300556
\(881\) 8.84872 0.298121 0.149060 0.988828i \(-0.452375\pi\)
0.149060 + 0.988828i \(0.452375\pi\)
\(882\) 0 0
\(883\) 14.6632 0.493455 0.246728 0.969085i \(-0.420645\pi\)
0.246728 + 0.969085i \(0.420645\pi\)
\(884\) 20.8176 0.700172
\(885\) 0 0
\(886\) −11.5523 −0.388107
\(887\) −17.3973 −0.584143 −0.292072 0.956396i \(-0.594345\pi\)
−0.292072 + 0.956396i \(0.594345\pi\)
\(888\) 0 0
\(889\) −19.2201 −0.644621
\(890\) −0.593403 −0.0198909
\(891\) 0 0
\(892\) −27.7214 −0.928183
\(893\) 24.0134 0.803577
\(894\) 0 0
\(895\) −2.48300 −0.0829975
\(896\) −32.8270 −1.09667
\(897\) 0 0
\(898\) 7.27509 0.242773
\(899\) 53.7075 1.79124
\(900\) 0 0
\(901\) 22.4979 0.749512
\(902\) 0.916412 0.0305132
\(903\) 0 0
\(904\) 31.0830 1.03381
\(905\) 9.15395 0.304288
\(906\) 0 0
\(907\) −33.7438 −1.12045 −0.560223 0.828342i \(-0.689285\pi\)
−0.560223 + 0.828342i \(0.689285\pi\)
\(908\) 17.1783 0.570081
\(909\) 0 0
\(910\) 10.3199 0.342103
\(911\) −12.1001 −0.400895 −0.200447 0.979704i \(-0.564240\pi\)
−0.200447 + 0.979704i \(0.564240\pi\)
\(912\) 0 0
\(913\) −6.52657 −0.215998
\(914\) −14.2874 −0.472585
\(915\) 0 0
\(916\) −9.21557 −0.304491
\(917\) 15.9730 0.527475
\(918\) 0 0
\(919\) −31.4919 −1.03882 −0.519412 0.854524i \(-0.673849\pi\)
−0.519412 + 0.854524i \(0.673849\pi\)
\(920\) 9.15811 0.301934
\(921\) 0 0
\(922\) 20.9371 0.689528
\(923\) −20.5076 −0.675015
\(924\) 0 0
\(925\) −44.9562 −1.47815
\(926\) 7.94777 0.261180
\(927\) 0 0
\(928\) 37.1046 1.21802
\(929\) −28.6545 −0.940123 −0.470061 0.882634i \(-0.655768\pi\)
−0.470061 + 0.882634i \(0.655768\pi\)
\(930\) 0 0
\(931\) 14.7740 0.484199
\(932\) 30.3320 0.993558
\(933\) 0 0
\(934\) 19.3859 0.634326
\(935\) −2.70624 −0.0885036
\(936\) 0 0
\(937\) 6.14354 0.200701 0.100350 0.994952i \(-0.468004\pi\)
0.100350 + 0.994952i \(0.468004\pi\)
\(938\) −21.8899 −0.714731
\(939\) 0 0
\(940\) 8.18031 0.266812
\(941\) 25.9528 0.846038 0.423019 0.906121i \(-0.360970\pi\)
0.423019 + 0.906121i \(0.360970\pi\)
\(942\) 0 0
\(943\) 5.27814 0.171880
\(944\) −13.5563 −0.441219
\(945\) 0 0
\(946\) 6.04562 0.196560
\(947\) −45.1337 −1.46665 −0.733324 0.679880i \(-0.762032\pi\)
−0.733324 + 0.679880i \(0.762032\pi\)
\(948\) 0 0
\(949\) 64.7374 2.10146
\(950\) 12.3522 0.400759
\(951\) 0 0
\(952\) −26.3360 −0.853553
\(953\) 6.09060 0.197294 0.0986469 0.995122i \(-0.468549\pi\)
0.0986469 + 0.995122i \(0.468549\pi\)
\(954\) 0 0
\(955\) 5.97781 0.193437
\(956\) −34.7929 −1.12528
\(957\) 0 0
\(958\) −0.142662 −0.00460920
\(959\) −26.9966 −0.871767
\(960\) 0 0
\(961\) 40.9000 1.31936
\(962\) 36.3694 1.17260
\(963\) 0 0
\(964\) −2.36468 −0.0761614
\(965\) 18.9002 0.608420
\(966\) 0 0
\(967\) −32.8474 −1.05630 −0.528151 0.849150i \(-0.677115\pi\)
−0.528151 + 0.849150i \(0.677115\pi\)
\(968\) −25.9954 −0.835523
\(969\) 0 0
\(970\) 0.336519 0.0108050
\(971\) −45.3642 −1.45581 −0.727903 0.685680i \(-0.759505\pi\)
−0.727903 + 0.685680i \(0.759505\pi\)
\(972\) 0 0
\(973\) −68.5650 −2.19809
\(974\) 1.95344 0.0625922
\(975\) 0 0
\(976\) −3.19603 −0.102303
\(977\) −9.96515 −0.318813 −0.159407 0.987213i \(-0.550958\pi\)
−0.159407 + 0.987213i \(0.550958\pi\)
\(978\) 0 0
\(979\) −0.740268 −0.0236591
\(980\) 5.03286 0.160769
\(981\) 0 0
\(982\) 8.11707 0.259026
\(983\) 8.37150 0.267009 0.133505 0.991048i \(-0.457377\pi\)
0.133505 + 0.991048i \(0.457377\pi\)
\(984\) 0 0
\(985\) 25.3827 0.808761
\(986\) 14.8230 0.472062
\(987\) 0 0
\(988\) 26.9768 0.858245
\(989\) 34.8202 1.10722
\(990\) 0 0
\(991\) 28.8111 0.915215 0.457608 0.889154i \(-0.348706\pi\)
0.457608 + 0.889154i \(0.348706\pi\)
\(992\) 49.6732 1.57712
\(993\) 0 0
\(994\) 10.9448 0.347147
\(995\) 4.98690 0.158095
\(996\) 0 0
\(997\) 12.3708 0.391788 0.195894 0.980625i \(-0.437239\pi\)
0.195894 + 0.980625i \(0.437239\pi\)
\(998\) −22.7904 −0.721418
\(999\) 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 4923.2.a.l.1.8 18
3.2 odd 2 547.2.a.b.1.11 18
12.11 even 2 8752.2.a.s.1.6 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.2.a.b.1.11 18 3.2 odd 2
4923.2.a.l.1.8 18 1.1 even 1 trivial
8752.2.a.s.1.6 18 12.11 even 2