Properties

Label 1850.2.a.z.1.2
Level $1850$
Weight $2$
Character 1850.1
Self dual yes
Analytic conductor $14.772$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1850.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.7723243739\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.892.1
Defining polynomial: \( x^{3} - x^{2} - 8x + 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 370)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.91729\) of defining polynomial
Character \(\chi\) \(=\) 1850.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.406728 q^{3} +1.00000 q^{4} +0.406728 q^{6} -2.91729 q^{7} -1.00000 q^{8} -2.83457 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.406728 q^{3} +1.00000 q^{4} +0.406728 q^{6} -2.91729 q^{7} -1.00000 q^{8} -2.83457 q^{9} +6.51056 q^{11} -0.406728 q^{12} +0.813457 q^{13} +2.91729 q^{14} +1.00000 q^{16} +2.51056 q^{17} +2.83457 q^{18} +0.406728 q^{19} +1.18654 q^{21} -6.51056 q^{22} -5.02112 q^{23} +0.406728 q^{24} -0.813457 q^{26} +2.37309 q^{27} -2.91729 q^{28} -5.32401 q^{29} -8.75186 q^{31} -1.00000 q^{32} -2.64803 q^{33} -2.51056 q^{34} -2.83457 q^{36} +1.00000 q^{37} -0.406728 q^{38} -0.330856 q^{39} +6.34513 q^{41} -1.18654 q^{42} +7.32401 q^{43} +6.51056 q^{44} +5.02112 q^{46} +5.42784 q^{47} -0.406728 q^{48} +1.51056 q^{49} -1.02112 q^{51} +0.813457 q^{52} +2.34513 q^{53} -2.37309 q^{54} +2.91729 q^{56} -0.165428 q^{57} +5.32401 q^{58} -1.42784 q^{59} -1.32401 q^{61} +8.75186 q^{62} +8.26926 q^{63} +1.00000 q^{64} +2.64803 q^{66} +5.42784 q^{67} +2.51056 q^{68} +2.04223 q^{69} +14.6480 q^{71} +2.83457 q^{72} +11.0211 q^{73} -1.00000 q^{74} +0.406728 q^{76} -18.9932 q^{77} +0.330856 q^{78} -1.75870 q^{79} +7.53851 q^{81} -6.34513 q^{82} +7.05476 q^{83} +1.18654 q^{84} -7.32401 q^{86} +2.16543 q^{87} -6.51056 q^{88} +6.00000 q^{89} -2.37309 q^{91} -5.02112 q^{92} +3.55963 q^{93} -5.42784 q^{94} +0.406728 q^{96} -2.34513 q^{97} -1.51056 q^{98} -18.4546 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{2} + 3 q^{4} + q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{2} + 3 q^{4} + q^{7} - 3 q^{8} + 11 q^{9} + 11 q^{11} - q^{14} + 3 q^{16} - q^{17} - 11 q^{18} + 6 q^{21} - 11 q^{22} + 2 q^{23} + 12 q^{27} + q^{28} - 5 q^{29} + 3 q^{31} - 3 q^{32} + 14 q^{33} + q^{34} + 11 q^{36} + 3 q^{37} - 40 q^{39} - 9 q^{41} - 6 q^{42} + 11 q^{43} + 11 q^{44} - 2 q^{46} - 2 q^{47} - 4 q^{49} + 14 q^{51} - 21 q^{53} - 12 q^{54} - q^{56} - 20 q^{57} + 5 q^{58} + 14 q^{59} + 7 q^{61} - 3 q^{62} + 37 q^{63} + 3 q^{64} - 14 q^{66} - 2 q^{67} - q^{68} - 28 q^{69} + 22 q^{71} - 11 q^{72} + 16 q^{73} - 3 q^{74} - 7 q^{77} + 40 q^{78} - 26 q^{79} + 47 q^{81} + 9 q^{82} - 2 q^{83} + 6 q^{84} - 11 q^{86} + 26 q^{87} - 11 q^{88} + 18 q^{89} - 12 q^{91} + 2 q^{92} + 18 q^{93} + 2 q^{94} + 21 q^{97} + 4 q^{98} + 19 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.406728 −0.234825 −0.117412 0.993083i \(-0.537460\pi\)
−0.117412 + 0.993083i \(0.537460\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 0.406728 0.166046
\(7\) −2.91729 −1.10263 −0.551315 0.834297i \(-0.685874\pi\)
−0.551315 + 0.834297i \(0.685874\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.83457 −0.944857
\(10\) 0 0
\(11\) 6.51056 1.96301 0.981503 0.191444i \(-0.0613171\pi\)
0.981503 + 0.191444i \(0.0613171\pi\)
\(12\) −0.406728 −0.117412
\(13\) 0.813457 0.225612 0.112806 0.993617i \(-0.464016\pi\)
0.112806 + 0.993617i \(0.464016\pi\)
\(14\) 2.91729 0.779677
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 2.51056 0.608900 0.304450 0.952528i \(-0.401527\pi\)
0.304450 + 0.952528i \(0.401527\pi\)
\(18\) 2.83457 0.668115
\(19\) 0.406728 0.0933099 0.0466550 0.998911i \(-0.485144\pi\)
0.0466550 + 0.998911i \(0.485144\pi\)
\(20\) 0 0
\(21\) 1.18654 0.258925
\(22\) −6.51056 −1.38806
\(23\) −5.02112 −1.04697 −0.523487 0.852033i \(-0.675369\pi\)
−0.523487 + 0.852033i \(0.675369\pi\)
\(24\) 0.406728 0.0830231
\(25\) 0 0
\(26\) −0.813457 −0.159532
\(27\) 2.37309 0.456701
\(28\) −2.91729 −0.551315
\(29\) −5.32401 −0.988645 −0.494322 0.869279i \(-0.664584\pi\)
−0.494322 + 0.869279i \(0.664584\pi\)
\(30\) 0 0
\(31\) −8.75186 −1.57188 −0.785940 0.618303i \(-0.787821\pi\)
−0.785940 + 0.618303i \(0.787821\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.64803 −0.460963
\(34\) −2.51056 −0.430557
\(35\) 0 0
\(36\) −2.83457 −0.472429
\(37\) 1.00000 0.164399
\(38\) −0.406728 −0.0659801
\(39\) −0.330856 −0.0529794
\(40\) 0 0
\(41\) 6.34513 0.990943 0.495471 0.868624i \(-0.334995\pi\)
0.495471 + 0.868624i \(0.334995\pi\)
\(42\) −1.18654 −0.183088
\(43\) 7.32401 1.11690 0.558451 0.829538i \(-0.311396\pi\)
0.558451 + 0.829538i \(0.311396\pi\)
\(44\) 6.51056 0.981503
\(45\) 0 0
\(46\) 5.02112 0.740323
\(47\) 5.42784 0.791732 0.395866 0.918308i \(-0.370444\pi\)
0.395866 + 0.918308i \(0.370444\pi\)
\(48\) −0.406728 −0.0587062
\(49\) 1.51056 0.215794
\(50\) 0 0
\(51\) −1.02112 −0.142985
\(52\) 0.813457 0.112806
\(53\) 2.34513 0.322128 0.161064 0.986944i \(-0.448507\pi\)
0.161064 + 0.986944i \(0.448507\pi\)
\(54\) −2.37309 −0.322936
\(55\) 0 0
\(56\) 2.91729 0.389839
\(57\) −0.165428 −0.0219115
\(58\) 5.32401 0.699077
\(59\) −1.42784 −0.185889 −0.0929447 0.995671i \(-0.529628\pi\)
−0.0929447 + 0.995671i \(0.529628\pi\)
\(60\) 0 0
\(61\) −1.32401 −0.169523 −0.0847613 0.996401i \(-0.527013\pi\)
−0.0847613 + 0.996401i \(0.527013\pi\)
\(62\) 8.75186 1.11149
\(63\) 8.26926 1.04183
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 2.64803 0.325950
\(67\) 5.42784 0.663117 0.331558 0.943435i \(-0.392426\pi\)
0.331558 + 0.943435i \(0.392426\pi\)
\(68\) 2.51056 0.304450
\(69\) 2.04223 0.245856
\(70\) 0 0
\(71\) 14.6480 1.73840 0.869201 0.494460i \(-0.164634\pi\)
0.869201 + 0.494460i \(0.164634\pi\)
\(72\) 2.83457 0.334058
\(73\) 11.0211 1.28992 0.644962 0.764215i \(-0.276873\pi\)
0.644962 + 0.764215i \(0.276873\pi\)
\(74\) −1.00000 −0.116248
\(75\) 0 0
\(76\) 0.406728 0.0466550
\(77\) −18.9932 −2.16447
\(78\) 0.330856 0.0374621
\(79\) −1.75870 −0.197869 −0.0989346 0.995094i \(-0.531543\pi\)
−0.0989346 + 0.995094i \(0.531543\pi\)
\(80\) 0 0
\(81\) 7.53851 0.837613
\(82\) −6.34513 −0.700702
\(83\) 7.05476 0.774360 0.387180 0.922004i \(-0.373449\pi\)
0.387180 + 0.922004i \(0.373449\pi\)
\(84\) 1.18654 0.129462
\(85\) 0 0
\(86\) −7.32401 −0.789769
\(87\) 2.16543 0.232158
\(88\) −6.51056 −0.694028
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) −2.37309 −0.248767
\(92\) −5.02112 −0.523487
\(93\) 3.55963 0.369116
\(94\) −5.42784 −0.559839
\(95\) 0 0
\(96\) 0.406728 0.0415115
\(97\) −2.34513 −0.238112 −0.119056 0.992888i \(-0.537987\pi\)
−0.119056 + 0.992888i \(0.537987\pi\)
\(98\) −1.51056 −0.152589
\(99\) −18.4546 −1.85476
\(100\) 0 0
\(101\) −8.20766 −0.816693 −0.408346 0.912827i \(-0.633894\pi\)
−0.408346 + 0.912827i \(0.633894\pi\)
\(102\) 1.02112 0.101105
\(103\) 8.81346 0.868416 0.434208 0.900813i \(-0.357028\pi\)
0.434208 + 0.900813i \(0.357028\pi\)
\(104\) −0.813457 −0.0797660
\(105\) 0 0
\(106\) −2.34513 −0.227779
\(107\) −15.2624 −1.47547 −0.737737 0.675089i \(-0.764105\pi\)
−0.737737 + 0.675089i \(0.764105\pi\)
\(108\) 2.37309 0.228350
\(109\) 4.30290 0.412143 0.206072 0.978537i \(-0.433932\pi\)
0.206072 + 0.978537i \(0.433932\pi\)
\(110\) 0 0
\(111\) −0.406728 −0.0386050
\(112\) −2.91729 −0.275658
\(113\) 9.15859 0.861567 0.430784 0.902455i \(-0.358237\pi\)
0.430784 + 0.902455i \(0.358237\pi\)
\(114\) 0.165428 0.0154938
\(115\) 0 0
\(116\) −5.32401 −0.494322
\(117\) −2.30580 −0.213171
\(118\) 1.42784 0.131444
\(119\) −7.32401 −0.671391
\(120\) 0 0
\(121\) 31.3874 2.85340
\(122\) 1.32401 0.119871
\(123\) −2.58074 −0.232698
\(124\) −8.75186 −0.785940
\(125\) 0 0
\(126\) −8.26926 −0.736684
\(127\) 8.61439 0.764403 0.382202 0.924079i \(-0.375166\pi\)
0.382202 + 0.924079i \(0.375166\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.97888 −0.262276
\(130\) 0 0
\(131\) 13.4278 1.17320 0.586598 0.809878i \(-0.300467\pi\)
0.586598 + 0.809878i \(0.300467\pi\)
\(132\) −2.64803 −0.230481
\(133\) −1.18654 −0.102886
\(134\) −5.42784 −0.468894
\(135\) 0 0
\(136\) −2.51056 −0.215279
\(137\) 14.6903 1.25507 0.627537 0.778587i \(-0.284063\pi\)
0.627537 + 0.778587i \(0.284063\pi\)
\(138\) −2.04223 −0.173846
\(139\) 17.3662 1.47299 0.736493 0.676445i \(-0.236481\pi\)
0.736493 + 0.676445i \(0.236481\pi\)
\(140\) 0 0
\(141\) −2.20766 −0.185918
\(142\) −14.6480 −1.22924
\(143\) 5.29606 0.442879
\(144\) −2.83457 −0.236214
\(145\) 0 0
\(146\) −11.0211 −0.912114
\(147\) −0.614387 −0.0506738
\(148\) 1.00000 0.0821995
\(149\) −0.207658 −0.0170120 −0.00850601 0.999964i \(-0.502708\pi\)
−0.00850601 + 0.999964i \(0.502708\pi\)
\(150\) 0 0
\(151\) 0.813457 0.0661982 0.0330991 0.999452i \(-0.489462\pi\)
0.0330991 + 0.999452i \(0.489462\pi\)
\(152\) −0.406728 −0.0329900
\(153\) −7.11636 −0.575323
\(154\) 18.9932 1.53051
\(155\) 0 0
\(156\) −0.330856 −0.0264897
\(157\) −5.32401 −0.424903 −0.212451 0.977172i \(-0.568145\pi\)
−0.212451 + 0.977172i \(0.568145\pi\)
\(158\) 1.75870 0.139915
\(159\) −0.953831 −0.0756437
\(160\) 0 0
\(161\) 14.6480 1.15443
\(162\) −7.53851 −0.592282
\(163\) −15.2008 −1.19062 −0.595310 0.803496i \(-0.702971\pi\)
−0.595310 + 0.803496i \(0.702971\pi\)
\(164\) 6.34513 0.495471
\(165\) 0 0
\(166\) −7.05476 −0.547555
\(167\) 12.4826 0.965933 0.482966 0.875639i \(-0.339559\pi\)
0.482966 + 0.875639i \(0.339559\pi\)
\(168\) −1.18654 −0.0915438
\(169\) −12.3383 −0.949099
\(170\) 0 0
\(171\) −1.15290 −0.0881645
\(172\) 7.32401 0.558451
\(173\) −23.0354 −1.75135 −0.875674 0.482903i \(-0.839583\pi\)
−0.875674 + 0.482903i \(0.839583\pi\)
\(174\) −2.16543 −0.164161
\(175\) 0 0
\(176\) 6.51056 0.490752
\(177\) 0.580745 0.0436514
\(178\) −6.00000 −0.449719
\(179\) 24.2835 1.81504 0.907518 0.420013i \(-0.137974\pi\)
0.907518 + 0.420013i \(0.137974\pi\)
\(180\) 0 0
\(181\) 2.16543 0.160955 0.0804775 0.996756i \(-0.474355\pi\)
0.0804775 + 0.996756i \(0.474355\pi\)
\(182\) 2.37309 0.175905
\(183\) 0.538514 0.0398081
\(184\) 5.02112 0.370162
\(185\) 0 0
\(186\) −3.55963 −0.261005
\(187\) 16.3451 1.19527
\(188\) 5.42784 0.395866
\(189\) −6.92297 −0.503572
\(190\) 0 0
\(191\) −19.3326 −1.39886 −0.699429 0.714702i \(-0.746562\pi\)
−0.699429 + 0.714702i \(0.746562\pi\)
\(192\) −0.406728 −0.0293531
\(193\) 20.0422 1.44267 0.721336 0.692586i \(-0.243529\pi\)
0.721336 + 0.692586i \(0.243529\pi\)
\(194\) 2.34513 0.168370
\(195\) 0 0
\(196\) 1.51056 0.107897
\(197\) −15.6269 −1.11337 −0.556686 0.830723i \(-0.687927\pi\)
−0.556686 + 0.830723i \(0.687927\pi\)
\(198\) 18.4546 1.31151
\(199\) 20.2835 1.43786 0.718931 0.695082i \(-0.244632\pi\)
0.718931 + 0.695082i \(0.244632\pi\)
\(200\) 0 0
\(201\) −2.20766 −0.155716
\(202\) 8.20766 0.577489
\(203\) 15.5317 1.09011
\(204\) −1.02112 −0.0714924
\(205\) 0 0
\(206\) −8.81346 −0.614063
\(207\) 14.2327 0.989242
\(208\) 0.813457 0.0564031
\(209\) 2.64803 0.183168
\(210\) 0 0
\(211\) 18.7182 1.28862 0.644308 0.764766i \(-0.277146\pi\)
0.644308 + 0.764766i \(0.277146\pi\)
\(212\) 2.34513 0.161064
\(213\) −5.95777 −0.408220
\(214\) 15.2624 1.04332
\(215\) 0 0
\(216\) −2.37309 −0.161468
\(217\) 25.5317 1.73320
\(218\) −4.30290 −0.291429
\(219\) −4.48260 −0.302906
\(220\) 0 0
\(221\) 2.04223 0.137375
\(222\) 0.406728 0.0272978
\(223\) 15.7307 1.05341 0.526704 0.850049i \(-0.323428\pi\)
0.526704 + 0.850049i \(0.323428\pi\)
\(224\) 2.91729 0.194919
\(225\) 0 0
\(226\) −9.15859 −0.609220
\(227\) −12.8836 −0.855117 −0.427559 0.903988i \(-0.640626\pi\)
−0.427559 + 0.903988i \(0.640626\pi\)
\(228\) −0.165428 −0.0109557
\(229\) 5.25383 0.347183 0.173591 0.984818i \(-0.444463\pi\)
0.173591 + 0.984818i \(0.444463\pi\)
\(230\) 0 0
\(231\) 7.72506 0.508271
\(232\) 5.32401 0.349539
\(233\) −28.3172 −1.85512 −0.927560 0.373675i \(-0.878098\pi\)
−0.927560 + 0.373675i \(0.878098\pi\)
\(234\) 2.30580 0.150735
\(235\) 0 0
\(236\) −1.42784 −0.0929447
\(237\) 0.715313 0.0464646
\(238\) 7.32401 0.474745
\(239\) 14.3788 0.930085 0.465043 0.885288i \(-0.346039\pi\)
0.465043 + 0.885288i \(0.346039\pi\)
\(240\) 0 0
\(241\) 18.2749 1.17719 0.588596 0.808427i \(-0.299681\pi\)
0.588596 + 0.808427i \(0.299681\pi\)
\(242\) −31.3874 −2.01766
\(243\) −10.1854 −0.653393
\(244\) −1.32401 −0.0847613
\(245\) 0 0
\(246\) 2.58074 0.164542
\(247\) 0.330856 0.0210519
\(248\) 8.75186 0.555744
\(249\) −2.86937 −0.181839
\(250\) 0 0
\(251\) −1.22019 −0.0770174 −0.0385087 0.999258i \(-0.512261\pi\)
−0.0385087 + 0.999258i \(0.512261\pi\)
\(252\) 8.26926 0.520914
\(253\) −32.6903 −2.05522
\(254\) −8.61439 −0.540515
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −27.1306 −1.69236 −0.846181 0.532895i \(-0.821104\pi\)
−0.846181 + 0.532895i \(0.821104\pi\)
\(258\) 2.97888 0.185457
\(259\) −2.91729 −0.181271
\(260\) 0 0
\(261\) 15.0913 0.934128
\(262\) −13.4278 −0.829575
\(263\) 20.2133 1.24641 0.623204 0.782059i \(-0.285831\pi\)
0.623204 + 0.782059i \(0.285831\pi\)
\(264\) 2.64803 0.162975
\(265\) 0 0
\(266\) 1.18654 0.0727516
\(267\) −2.44037 −0.149348
\(268\) 5.42784 0.331558
\(269\) −0.207658 −0.0126611 −0.00633057 0.999980i \(-0.502015\pi\)
−0.00633057 + 0.999980i \(0.502015\pi\)
\(270\) 0 0
\(271\) −30.6480 −1.86174 −0.930868 0.365357i \(-0.880947\pi\)
−0.930868 + 0.365357i \(0.880947\pi\)
\(272\) 2.51056 0.152225
\(273\) 0.965202 0.0584167
\(274\) −14.6903 −0.887471
\(275\) 0 0
\(276\) 2.04223 0.122928
\(277\) 16.8135 1.01022 0.505111 0.863054i \(-0.331451\pi\)
0.505111 + 0.863054i \(0.331451\pi\)
\(278\) −17.3662 −1.04156
\(279\) 24.8078 1.48520
\(280\) 0 0
\(281\) −14.2749 −0.851572 −0.425786 0.904824i \(-0.640002\pi\)
−0.425786 + 0.904824i \(0.640002\pi\)
\(282\) 2.20766 0.131464
\(283\) 13.2288 0.786369 0.393184 0.919460i \(-0.371373\pi\)
0.393184 + 0.919460i \(0.371373\pi\)
\(284\) 14.6480 0.869201
\(285\) 0 0
\(286\) −5.29606 −0.313162
\(287\) −18.5106 −1.09264
\(288\) 2.83457 0.167029
\(289\) −10.6971 −0.629241
\(290\) 0 0
\(291\) 0.953831 0.0559146
\(292\) 11.0211 0.644962
\(293\) −2.34513 −0.137004 −0.0685020 0.997651i \(-0.521822\pi\)
−0.0685020 + 0.997651i \(0.521822\pi\)
\(294\) 0.614387 0.0358318
\(295\) 0 0
\(296\) −1.00000 −0.0581238
\(297\) 15.4501 0.896507
\(298\) 0.207658 0.0120293
\(299\) −4.08446 −0.236210
\(300\) 0 0
\(301\) −21.3662 −1.23153
\(302\) −0.813457 −0.0468092
\(303\) 3.33829 0.191780
\(304\) 0.406728 0.0233275
\(305\) 0 0
\(306\) 7.11636 0.406815
\(307\) 23.2624 1.32766 0.663828 0.747885i \(-0.268931\pi\)
0.663828 + 0.747885i \(0.268931\pi\)
\(308\) −18.9932 −1.08224
\(309\) −3.58468 −0.203926
\(310\) 0 0
\(311\) −31.3999 −1.78052 −0.890262 0.455449i \(-0.849479\pi\)
−0.890262 + 0.455449i \(0.849479\pi\)
\(312\) 0.330856 0.0187310
\(313\) 8.04223 0.454574 0.227287 0.973828i \(-0.427014\pi\)
0.227287 + 0.973828i \(0.427014\pi\)
\(314\) 5.32401 0.300452
\(315\) 0 0
\(316\) −1.75870 −0.0989346
\(317\) 12.3029 0.691000 0.345500 0.938419i \(-0.387709\pi\)
0.345500 + 0.938419i \(0.387709\pi\)
\(318\) 0.953831 0.0534882
\(319\) −34.6623 −1.94072
\(320\) 0 0
\(321\) 6.20766 0.346478
\(322\) −14.6480 −0.816303
\(323\) 1.02112 0.0568164
\(324\) 7.53851 0.418806
\(325\) 0 0
\(326\) 15.2008 0.841895
\(327\) −1.75011 −0.0967814
\(328\) −6.34513 −0.350351
\(329\) −15.8346 −0.872988
\(330\) 0 0
\(331\) −6.77981 −0.372652 −0.186326 0.982488i \(-0.559658\pi\)
−0.186326 + 0.982488i \(0.559658\pi\)
\(332\) 7.05476 0.387180
\(333\) −2.83457 −0.155334
\(334\) −12.4826 −0.683018
\(335\) 0 0
\(336\) 1.18654 0.0647312
\(337\) −10.6903 −0.582336 −0.291168 0.956672i \(-0.594044\pi\)
−0.291168 + 0.956672i \(0.594044\pi\)
\(338\) 12.3383 0.671114
\(339\) −3.72506 −0.202317
\(340\) 0 0
\(341\) −56.9795 −3.08561
\(342\) 1.15290 0.0623417
\(343\) 16.0143 0.864689
\(344\) −7.32401 −0.394884
\(345\) 0 0
\(346\) 23.0354 1.23839
\(347\) −5.62691 −0.302069 −0.151034 0.988529i \(-0.548260\pi\)
−0.151034 + 0.988529i \(0.548260\pi\)
\(348\) 2.16543 0.116079
\(349\) 15.1306 0.809924 0.404962 0.914334i \(-0.367285\pi\)
0.404962 + 0.914334i \(0.367285\pi\)
\(350\) 0 0
\(351\) 1.93040 0.103037
\(352\) −6.51056 −0.347014
\(353\) −35.7816 −1.90446 −0.952230 0.305381i \(-0.901216\pi\)
−0.952230 + 0.305381i \(0.901216\pi\)
\(354\) −0.580745 −0.0308662
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) 2.97888 0.157659
\(358\) −24.2835 −1.28342
\(359\) 4.48260 0.236583 0.118291 0.992979i \(-0.462258\pi\)
0.118291 + 0.992979i \(0.462258\pi\)
\(360\) 0 0
\(361\) −18.8346 −0.991293
\(362\) −2.16543 −0.113812
\(363\) −12.7661 −0.670048
\(364\) −2.37309 −0.124384
\(365\) 0 0
\(366\) −0.538514 −0.0281486
\(367\) 21.5653 1.12570 0.562850 0.826559i \(-0.309705\pi\)
0.562850 + 0.826559i \(0.309705\pi\)
\(368\) −5.02112 −0.261744
\(369\) −17.9857 −0.936300
\(370\) 0 0
\(371\) −6.84141 −0.355188
\(372\) 3.55963 0.184558
\(373\) −16.9230 −0.876238 −0.438119 0.898917i \(-0.644355\pi\)
−0.438119 + 0.898917i \(0.644355\pi\)
\(374\) −16.3451 −0.845187
\(375\) 0 0
\(376\) −5.42784 −0.279920
\(377\) −4.33086 −0.223050
\(378\) 6.92297 0.356079
\(379\) 31.2710 1.60628 0.803142 0.595788i \(-0.203160\pi\)
0.803142 + 0.595788i \(0.203160\pi\)
\(380\) 0 0
\(381\) −3.50372 −0.179501
\(382\) 19.3326 0.989142
\(383\) −1.62691 −0.0831314 −0.0415657 0.999136i \(-0.513235\pi\)
−0.0415657 + 0.999136i \(0.513235\pi\)
\(384\) 0.406728 0.0207558
\(385\) 0 0
\(386\) −20.0422 −1.02012
\(387\) −20.7604 −1.05531
\(388\) −2.34513 −0.119056
\(389\) −31.6412 −1.60427 −0.802136 0.597141i \(-0.796303\pi\)
−0.802136 + 0.597141i \(0.796303\pi\)
\(390\) 0 0
\(391\) −12.6058 −0.637503
\(392\) −1.51056 −0.0762947
\(393\) −5.46149 −0.275496
\(394\) 15.6269 0.787273
\(395\) 0 0
\(396\) −18.4546 −0.927381
\(397\) 39.2961 1.97221 0.986106 0.166116i \(-0.0531225\pi\)
0.986106 + 0.166116i \(0.0531225\pi\)
\(398\) −20.2835 −1.01672
\(399\) 0.482601 0.0241603
\(400\) 0 0
\(401\) −9.66914 −0.482854 −0.241427 0.970419i \(-0.577615\pi\)
−0.241427 + 0.970419i \(0.577615\pi\)
\(402\) 2.20766 0.110108
\(403\) −7.11926 −0.354636
\(404\) −8.20766 −0.408346
\(405\) 0 0
\(406\) −15.5317 −0.770824
\(407\) 6.51056 0.322716
\(408\) 1.02112 0.0505527
\(409\) −26.2749 −1.29921 −0.649606 0.760271i \(-0.725066\pi\)
−0.649606 + 0.760271i \(0.725066\pi\)
\(410\) 0 0
\(411\) −5.97495 −0.294722
\(412\) 8.81346 0.434208
\(413\) 4.16543 0.204967
\(414\) −14.2327 −0.699500
\(415\) 0 0
\(416\) −0.813457 −0.0398830
\(417\) −7.06335 −0.345894
\(418\) −2.64803 −0.129519
\(419\) −30.1940 −1.47507 −0.737536 0.675308i \(-0.764011\pi\)
−0.737536 + 0.675308i \(0.764011\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) −18.7182 −0.911188
\(423\) −15.3856 −0.748074
\(424\) −2.34513 −0.113890
\(425\) 0 0
\(426\) 5.95777 0.288655
\(427\) 3.86253 0.186921
\(428\) −15.2624 −0.737737
\(429\) −2.15406 −0.103999
\(430\) 0 0
\(431\) 25.5653 1.23144 0.615719 0.787966i \(-0.288866\pi\)
0.615719 + 0.787966i \(0.288866\pi\)
\(432\) 2.37309 0.114175
\(433\) −32.0422 −1.53985 −0.769926 0.638134i \(-0.779707\pi\)
−0.769926 + 0.638134i \(0.779707\pi\)
\(434\) −25.5317 −1.22556
\(435\) 0 0
\(436\) 4.30290 0.206072
\(437\) −2.04223 −0.0976931
\(438\) 4.48260 0.214187
\(439\) 3.93840 0.187970 0.0939848 0.995574i \(-0.470039\pi\)
0.0939848 + 0.995574i \(0.470039\pi\)
\(440\) 0 0
\(441\) −4.28178 −0.203894
\(442\) −2.04223 −0.0971390
\(443\) 0.0758724 0.00360481 0.00180240 0.999998i \(-0.499426\pi\)
0.00180240 + 0.999998i \(0.499426\pi\)
\(444\) −0.406728 −0.0193025
\(445\) 0 0
\(446\) −15.7307 −0.744872
\(447\) 0.0844605 0.00399485
\(448\) −2.91729 −0.137829
\(449\) 19.2961 0.910637 0.455319 0.890329i \(-0.349525\pi\)
0.455319 + 0.890329i \(0.349525\pi\)
\(450\) 0 0
\(451\) 41.3103 1.94523
\(452\) 9.15859 0.430784
\(453\) −0.330856 −0.0155450
\(454\) 12.8836 0.604659
\(455\) 0 0
\(456\) 0.165428 0.00774688
\(457\) −3.00684 −0.140654 −0.0703271 0.997524i \(-0.522404\pi\)
−0.0703271 + 0.997524i \(0.522404\pi\)
\(458\) −5.25383 −0.245495
\(459\) 5.95777 0.278085
\(460\) 0 0
\(461\) −0.633755 −0.0295169 −0.0147585 0.999891i \(-0.504698\pi\)
−0.0147585 + 0.999891i \(0.504698\pi\)
\(462\) −7.72506 −0.359402
\(463\) −18.0422 −0.838494 −0.419247 0.907872i \(-0.637706\pi\)
−0.419247 + 0.907872i \(0.637706\pi\)
\(464\) −5.32401 −0.247161
\(465\) 0 0
\(466\) 28.3172 1.31177
\(467\) 23.4758 1.08633 0.543164 0.839626i \(-0.317226\pi\)
0.543164 + 0.839626i \(0.317226\pi\)
\(468\) −2.30580 −0.106586
\(469\) −15.8346 −0.731173
\(470\) 0 0
\(471\) 2.16543 0.0997777
\(472\) 1.42784 0.0657218
\(473\) 47.6834 2.19249
\(474\) −0.715313 −0.0328554
\(475\) 0 0
\(476\) −7.32401 −0.335696
\(477\) −6.64744 −0.304365
\(478\) −14.3788 −0.657670
\(479\) −8.19907 −0.374625 −0.187313 0.982300i \(-0.559978\pi\)
−0.187313 + 0.982300i \(0.559978\pi\)
\(480\) 0 0
\(481\) 0.813457 0.0370904
\(482\) −18.2749 −0.832401
\(483\) −5.95777 −0.271088
\(484\) 31.3874 1.42670
\(485\) 0 0
\(486\) 10.1854 0.462019
\(487\) −0.953831 −0.0432222 −0.0216111 0.999766i \(-0.506880\pi\)
−0.0216111 + 0.999766i \(0.506880\pi\)
\(488\) 1.32401 0.0599353
\(489\) 6.18260 0.279587
\(490\) 0 0
\(491\) 19.3383 0.872725 0.436362 0.899771i \(-0.356267\pi\)
0.436362 + 0.899771i \(0.356267\pi\)
\(492\) −2.58074 −0.116349
\(493\) −13.3662 −0.601985
\(494\) −0.330856 −0.0148859
\(495\) 0 0
\(496\) −8.75186 −0.392970
\(497\) −42.7325 −1.91681
\(498\) 2.86937 0.128580
\(499\) −5.63550 −0.252280 −0.126140 0.992012i \(-0.540259\pi\)
−0.126140 + 0.992012i \(0.540259\pi\)
\(500\) 0 0
\(501\) −5.07703 −0.226825
\(502\) 1.22019 0.0544595
\(503\) 33.6269 1.49935 0.749675 0.661806i \(-0.230210\pi\)
0.749675 + 0.661806i \(0.230210\pi\)
\(504\) −8.26926 −0.368342
\(505\) 0 0
\(506\) 32.6903 1.45326
\(507\) 5.01833 0.222872
\(508\) 8.61439 0.382202
\(509\) −18.6903 −0.828431 −0.414216 0.910179i \(-0.635944\pi\)
−0.414216 + 0.910179i \(0.635944\pi\)
\(510\) 0 0
\(511\) −32.1517 −1.42231
\(512\) −1.00000 −0.0441942
\(513\) 0.965202 0.0426147
\(514\) 27.1306 1.19668
\(515\) 0 0
\(516\) −2.97888 −0.131138
\(517\) 35.3383 1.55418
\(518\) 2.91729 0.128178
\(519\) 9.36915 0.411260
\(520\) 0 0
\(521\) 25.1586 1.10222 0.551109 0.834433i \(-0.314205\pi\)
0.551109 + 0.834433i \(0.314205\pi\)
\(522\) −15.0913 −0.660528
\(523\) 7.25383 0.317188 0.158594 0.987344i \(-0.449304\pi\)
0.158594 + 0.987344i \(0.449304\pi\)
\(524\) 13.4278 0.586598
\(525\) 0 0
\(526\) −20.2133 −0.881344
\(527\) −21.9720 −0.957117
\(528\) −2.64803 −0.115241
\(529\) 2.21160 0.0961564
\(530\) 0 0
\(531\) 4.04733 0.175639
\(532\) −1.18654 −0.0514432
\(533\) 5.16149 0.223569
\(534\) 2.44037 0.105605
\(535\) 0 0
\(536\) −5.42784 −0.234447
\(537\) −9.87680 −0.426215
\(538\) 0.207658 0.00895278
\(539\) 9.83457 0.423605
\(540\) 0 0
\(541\) 16.0422 0.689709 0.344855 0.938656i \(-0.387928\pi\)
0.344855 + 0.938656i \(0.387928\pi\)
\(542\) 30.6480 1.31645
\(543\) −0.880741 −0.0377962
\(544\) −2.51056 −0.107639
\(545\) 0 0
\(546\) −0.965202 −0.0413068
\(547\) −16.0143 −0.684721 −0.342360 0.939569i \(-0.611226\pi\)
−0.342360 + 0.939569i \(0.611226\pi\)
\(548\) 14.6903 0.627537
\(549\) 3.75301 0.160175
\(550\) 0 0
\(551\) −2.16543 −0.0922503
\(552\) −2.04223 −0.0869231
\(553\) 5.13063 0.218177
\(554\) −16.8135 −0.714335
\(555\) 0 0
\(556\) 17.3662 0.736493
\(557\) 10.8557 0.459970 0.229985 0.973194i \(-0.426132\pi\)
0.229985 + 0.973194i \(0.426132\pi\)
\(558\) −24.8078 −1.05020
\(559\) 5.95777 0.251987
\(560\) 0 0
\(561\) −6.64803 −0.280680
\(562\) 14.2749 0.602152
\(563\) −31.0776 −1.30977 −0.654883 0.755731i \(-0.727282\pi\)
−0.654883 + 0.755731i \(0.727282\pi\)
\(564\) −2.20766 −0.0929592
\(565\) 0 0
\(566\) −13.2288 −0.556047
\(567\) −21.9920 −0.923577
\(568\) −14.6480 −0.614618
\(569\) 30.0845 1.26121 0.630603 0.776105i \(-0.282808\pi\)
0.630603 + 0.776105i \(0.282808\pi\)
\(570\) 0 0
\(571\) 5.55673 0.232542 0.116271 0.993218i \(-0.462906\pi\)
0.116271 + 0.993218i \(0.462906\pi\)
\(572\) 5.29606 0.221439
\(573\) 7.86312 0.328487
\(574\) 18.5106 0.772616
\(575\) 0 0
\(576\) −2.83457 −0.118107
\(577\) 22.2499 0.926275 0.463137 0.886286i \(-0.346724\pi\)
0.463137 + 0.886286i \(0.346724\pi\)
\(578\) 10.6971 0.444941
\(579\) −8.15174 −0.338775
\(580\) 0 0
\(581\) −20.5807 −0.853833
\(582\) −0.953831 −0.0395376
\(583\) 15.2681 0.632340
\(584\) −11.0211 −0.456057
\(585\) 0 0
\(586\) 2.34513 0.0968764
\(587\) −45.3103 −1.87016 −0.935079 0.354440i \(-0.884672\pi\)
−0.935079 + 0.354440i \(0.884672\pi\)
\(588\) −0.614387 −0.0253369
\(589\) −3.55963 −0.146672
\(590\) 0 0
\(591\) 6.35591 0.261447
\(592\) 1.00000 0.0410997
\(593\) 0.232712 0.00955635 0.00477817 0.999989i \(-0.498479\pi\)
0.00477817 + 0.999989i \(0.498479\pi\)
\(594\) −15.4501 −0.633926
\(595\) 0 0
\(596\) −0.207658 −0.00850601
\(597\) −8.24989 −0.337645
\(598\) 4.08446 0.167026
\(599\) 43.4056 1.77350 0.886752 0.462246i \(-0.152956\pi\)
0.886752 + 0.462246i \(0.152956\pi\)
\(600\) 0 0
\(601\) 35.5317 1.44937 0.724684 0.689082i \(-0.241986\pi\)
0.724684 + 0.689082i \(0.241986\pi\)
\(602\) 21.3662 0.870823
\(603\) −15.3856 −0.626551
\(604\) 0.813457 0.0330991
\(605\) 0 0
\(606\) −3.33829 −0.135609
\(607\) −26.7325 −1.08504 −0.542519 0.840043i \(-0.682529\pi\)
−0.542519 + 0.840043i \(0.682529\pi\)
\(608\) −0.406728 −0.0164950
\(609\) −6.31717 −0.255985
\(610\) 0 0
\(611\) 4.41532 0.178625
\(612\) −7.11636 −0.287662
\(613\) −48.0565 −1.94098 −0.970492 0.241134i \(-0.922481\pi\)
−0.970492 + 0.241134i \(0.922481\pi\)
\(614\) −23.2624 −0.938795
\(615\) 0 0
\(616\) 18.9932 0.765256
\(617\) −12.9789 −0.522510 −0.261255 0.965270i \(-0.584136\pi\)
−0.261255 + 0.965270i \(0.584136\pi\)
\(618\) 3.58468 0.144197
\(619\) 25.3662 1.01956 0.509778 0.860306i \(-0.329728\pi\)
0.509778 + 0.860306i \(0.329728\pi\)
\(620\) 0 0
\(621\) −11.9155 −0.478154
\(622\) 31.3999 1.25902
\(623\) −17.5037 −0.701272
\(624\) −0.330856 −0.0132448
\(625\) 0 0
\(626\) −8.04223 −0.321432
\(627\) −1.07703 −0.0430124
\(628\) −5.32401 −0.212451
\(629\) 2.51056 0.100102
\(630\) 0 0
\(631\) −31.6075 −1.25828 −0.629138 0.777293i \(-0.716592\pi\)
−0.629138 + 0.777293i \(0.716592\pi\)
\(632\) 1.75870 0.0699573
\(633\) −7.61323 −0.302599
\(634\) −12.3029 −0.488611
\(635\) 0 0
\(636\) −0.953831 −0.0378219
\(637\) 1.22877 0.0486858
\(638\) 34.6623 1.37229
\(639\) −41.5209 −1.64254
\(640\) 0 0
\(641\) −23.8625 −0.942513 −0.471257 0.881996i \(-0.656199\pi\)
−0.471257 + 0.881996i \(0.656199\pi\)
\(642\) −6.20766 −0.244997
\(643\) −32.8277 −1.29460 −0.647300 0.762236i \(-0.724102\pi\)
−0.647300 + 0.762236i \(0.724102\pi\)
\(644\) 14.6480 0.577213
\(645\) 0 0
\(646\) −1.02112 −0.0401752
\(647\) 13.9578 0.548737 0.274368 0.961625i \(-0.411531\pi\)
0.274368 + 0.961625i \(0.411531\pi\)
\(648\) −7.53851 −0.296141
\(649\) −9.29606 −0.364902
\(650\) 0 0
\(651\) −10.3845 −0.406999
\(652\) −15.2008 −0.595310
\(653\) −28.5921 −1.11890 −0.559448 0.828865i \(-0.688987\pi\)
−0.559448 + 0.828865i \(0.688987\pi\)
\(654\) 1.75011 0.0684348
\(655\) 0 0
\(656\) 6.34513 0.247736
\(657\) −31.2401 −1.21879
\(658\) 15.8346 0.617296
\(659\) −5.62691 −0.219193 −0.109597 0.993976i \(-0.534956\pi\)
−0.109597 + 0.993976i \(0.534956\pi\)
\(660\) 0 0
\(661\) 13.3240 0.518244 0.259122 0.965845i \(-0.416567\pi\)
0.259122 + 0.965845i \(0.416567\pi\)
\(662\) 6.77981 0.263505
\(663\) −0.830633 −0.0322591
\(664\) −7.05476 −0.273778
\(665\) 0 0
\(666\) 2.83457 0.109837
\(667\) 26.7325 1.03509
\(668\) 12.4826 0.482966
\(669\) −6.39814 −0.247366
\(670\) 0 0
\(671\) −8.62007 −0.332774
\(672\) −1.18654 −0.0457719
\(673\) −29.6691 −1.14366 −0.571831 0.820372i \(-0.693767\pi\)
−0.571831 + 0.820372i \(0.693767\pi\)
\(674\) 10.6903 0.411773
\(675\) 0 0
\(676\) −12.3383 −0.474550
\(677\) 1.25383 0.0481885 0.0240943 0.999710i \(-0.492330\pi\)
0.0240943 + 0.999710i \(0.492330\pi\)
\(678\) 3.72506 0.143060
\(679\) 6.84141 0.262549
\(680\) 0 0
\(681\) 5.24014 0.200803
\(682\) 56.9795 2.18186
\(683\) 4.76045 0.182153 0.0910767 0.995844i \(-0.470969\pi\)
0.0910767 + 0.995844i \(0.470969\pi\)
\(684\) −1.15290 −0.0440823
\(685\) 0 0
\(686\) −16.0143 −0.611428
\(687\) −2.13688 −0.0815271
\(688\) 7.32401 0.279225
\(689\) 1.90766 0.0726761
\(690\) 0 0
\(691\) −20.2219 −0.769279 −0.384639 0.923067i \(-0.625674\pi\)
−0.384639 + 0.923067i \(0.625674\pi\)
\(692\) −23.0354 −0.875674
\(693\) 53.8375 2.04512
\(694\) 5.62691 0.213595
\(695\) 0 0
\(696\) −2.16543 −0.0820803
\(697\) 15.9298 0.603385
\(698\) −15.1306 −0.572703
\(699\) 11.5174 0.435628
\(700\) 0 0
\(701\) −22.0845 −0.834119 −0.417059 0.908879i \(-0.636939\pi\)
−0.417059 + 0.908879i \(0.636939\pi\)
\(702\) −1.93040 −0.0728584
\(703\) 0.406728 0.0153401
\(704\) 6.51056 0.245376
\(705\) 0 0
\(706\) 35.7816 1.34666
\(707\) 23.9441 0.900510
\(708\) 0.580745 0.0218257
\(709\) 5.59896 0.210273 0.105137 0.994458i \(-0.466472\pi\)
0.105137 + 0.994458i \(0.466472\pi\)
\(710\) 0 0
\(711\) 4.98516 0.186958
\(712\) −6.00000 −0.224860
\(713\) 43.9441 1.64572
\(714\) −2.97888 −0.111482
\(715\) 0 0
\(716\) 24.2835 0.907518
\(717\) −5.84826 −0.218407
\(718\) −4.48260 −0.167289
\(719\) 40.2921 1.50264 0.751321 0.659937i \(-0.229417\pi\)
0.751321 + 0.659937i \(0.229417\pi\)
\(720\) 0 0
\(721\) −25.7114 −0.957542
\(722\) 18.8346 0.700950
\(723\) −7.43294 −0.276434
\(724\) 2.16543 0.0804775
\(725\) 0 0
\(726\) 12.7661 0.473796
\(727\) −11.2538 −0.417381 −0.208691 0.977982i \(-0.566920\pi\)
−0.208691 + 0.977982i \(0.566920\pi\)
\(728\) 2.37309 0.0879524
\(729\) −18.4729 −0.684180
\(730\) 0 0
\(731\) 18.3874 0.680081
\(732\) 0.538514 0.0199041
\(733\) 42.2892 1.56199 0.780994 0.624539i \(-0.214713\pi\)
0.780994 + 0.624539i \(0.214713\pi\)
\(734\) −21.5653 −0.795990
\(735\) 0 0
\(736\) 5.02112 0.185081
\(737\) 35.3383 1.30170
\(738\) 17.9857 0.662064
\(739\) −29.3103 −1.07820 −0.539099 0.842242i \(-0.681235\pi\)
−0.539099 + 0.842242i \(0.681235\pi\)
\(740\) 0 0
\(741\) −0.134569 −0.00494350
\(742\) 6.84141 0.251156
\(743\) 4.39245 0.161144 0.0805718 0.996749i \(-0.474325\pi\)
0.0805718 + 0.996749i \(0.474325\pi\)
\(744\) −3.55963 −0.130502
\(745\) 0 0
\(746\) 16.9230 0.619594
\(747\) −19.9972 −0.731660
\(748\) 16.3451 0.597637
\(749\) 44.5248 1.62690
\(750\) 0 0
\(751\) 2.58074 0.0941727 0.0470864 0.998891i \(-0.485006\pi\)
0.0470864 + 0.998891i \(0.485006\pi\)
\(752\) 5.42784 0.197933
\(753\) 0.496284 0.0180856
\(754\) 4.33086 0.157720
\(755\) 0 0
\(756\) −6.92297 −0.251786
\(757\) −27.3805 −0.995162 −0.497581 0.867418i \(-0.665778\pi\)
−0.497581 + 0.867418i \(0.665778\pi\)
\(758\) −31.2710 −1.13581
\(759\) 13.2961 0.482616
\(760\) 0 0
\(761\) −42.9509 −1.55697 −0.778485 0.627663i \(-0.784011\pi\)
−0.778485 + 0.627663i \(0.784011\pi\)
\(762\) 3.50372 0.126926
\(763\) −12.5528 −0.454441
\(764\) −19.3326 −0.699429
\(765\) 0 0
\(766\) 1.62691 0.0587828
\(767\) −1.16149 −0.0419389
\(768\) −0.406728 −0.0146765
\(769\) −13.0633 −0.471076 −0.235538 0.971865i \(-0.575685\pi\)
−0.235538 + 0.971865i \(0.575685\pi\)
\(770\) 0 0
\(771\) 11.0348 0.397409
\(772\) 20.0422 0.721336
\(773\) 15.3662 0.552685 0.276343 0.961059i \(-0.410878\pi\)
0.276343 + 0.961059i \(0.410878\pi\)
\(774\) 20.7604 0.746219
\(775\) 0 0
\(776\) 2.34513 0.0841852
\(777\) 1.18654 0.0425670
\(778\) 31.6412 1.13439
\(779\) 2.58074 0.0924648
\(780\) 0 0
\(781\) 95.3668 3.41249
\(782\) 12.6058 0.450782
\(783\) −12.6343 −0.451515
\(784\) 1.51056 0.0539485
\(785\) 0 0
\(786\) 5.46149 0.194805
\(787\) −10.9316 −0.389668 −0.194834 0.980836i \(-0.562417\pi\)
−0.194834 + 0.980836i \(0.562417\pi\)
\(788\) −15.6269 −0.556686
\(789\) −8.22134 −0.292688
\(790\) 0 0
\(791\) −26.7182 −0.949990
\(792\) 18.4546 0.655757
\(793\) −1.07703 −0.0382464
\(794\) −39.2961 −1.39456
\(795\) 0 0
\(796\) 20.2835 0.718931
\(797\) 24.2921 0.860471 0.430235 0.902717i \(-0.358431\pi\)
0.430235 + 0.902717i \(0.358431\pi\)
\(798\) −0.482601 −0.0170839
\(799\) 13.6269 0.482086
\(800\) 0 0
\(801\) −17.0074 −0.600928
\(802\) 9.66914 0.341429
\(803\) 71.7536 2.53213
\(804\) −2.20766 −0.0778581
\(805\) 0 0
\(806\) 7.11926 0.250765
\(807\) 0.0844605 0.00297315
\(808\) 8.20766 0.288744
\(809\) −40.0422 −1.40781 −0.703905 0.710294i \(-0.748562\pi\)
−0.703905 + 0.710294i \(0.748562\pi\)
\(810\) 0 0
\(811\) −40.6343 −1.42686 −0.713432 0.700724i \(-0.752860\pi\)
−0.713432 + 0.700724i \(0.752860\pi\)
\(812\) 15.5317 0.545055
\(813\) 12.4654 0.437182
\(814\) −6.51056 −0.228195
\(815\) 0 0
\(816\) −1.02112 −0.0357462
\(817\) 2.97888 0.104218
\(818\) 26.2749 0.918682
\(819\) 6.72668 0.235049
\(820\) 0 0
\(821\) −41.4787 −1.44762 −0.723808 0.690002i \(-0.757610\pi\)
−0.723808 + 0.690002i \(0.757610\pi\)
\(822\) 5.97495 0.208400
\(823\) 5.27610 0.183913 0.0919566 0.995763i \(-0.470688\pi\)
0.0919566 + 0.995763i \(0.470688\pi\)
\(824\) −8.81346 −0.307031
\(825\) 0 0
\(826\) −4.16543 −0.144934
\(827\) −1.76438 −0.0613537 −0.0306768 0.999529i \(-0.509766\pi\)
−0.0306768 + 0.999529i \(0.509766\pi\)
\(828\) 14.2327 0.494621
\(829\) 16.3029 0.566223 0.283112 0.959087i \(-0.408633\pi\)
0.283112 + 0.959087i \(0.408633\pi\)
\(830\) 0 0
\(831\) −6.83851 −0.237225
\(832\) 0.813457 0.0282015
\(833\) 3.79234 0.131397
\(834\) 7.06335 0.244584
\(835\) 0 0
\(836\) 2.64803 0.0915840
\(837\) −20.7689 −0.717879
\(838\) 30.1940 1.04303
\(839\) 14.3731 0.496214 0.248107 0.968733i \(-0.420192\pi\)
0.248107 + 0.968733i \(0.420192\pi\)
\(840\) 0 0
\(841\) −0.654870 −0.0225817
\(842\) −22.0000 −0.758170
\(843\) 5.80602 0.199970
\(844\) 18.7182 0.644308
\(845\) 0 0
\(846\) 15.3856 0.528968
\(847\) −91.5659 −3.14624
\(848\) 2.34513 0.0805321
\(849\) −5.38052 −0.184659
\(850\) 0 0
\(851\) −5.02112 −0.172122
\(852\) −5.95777 −0.204110
\(853\) −43.2961 −1.48243 −0.741214 0.671268i \(-0.765750\pi\)
−0.741214 + 0.671268i \(0.765750\pi\)
\(854\) −3.86253 −0.132173
\(855\) 0 0
\(856\) 15.2624 0.521659
\(857\) 49.0776 1.67646 0.838230 0.545317i \(-0.183591\pi\)
0.838230 + 0.545317i \(0.183591\pi\)
\(858\) 2.15406 0.0735383
\(859\) 15.5374 0.530128 0.265064 0.964231i \(-0.414607\pi\)
0.265064 + 0.964231i \(0.414607\pi\)
\(860\) 0 0
\(861\) 7.52877 0.256580
\(862\) −25.5653 −0.870758
\(863\) 36.0901 1.22852 0.614261 0.789103i \(-0.289454\pi\)
0.614261 + 0.789103i \(0.289454\pi\)
\(864\) −2.37309 −0.0807340
\(865\) 0 0
\(866\) 32.0422 1.08884
\(867\) 4.35081 0.147761
\(868\) 25.5317 0.866601
\(869\) −11.4501 −0.388419
\(870\) 0 0
\(871\) 4.41532 0.149607
\(872\) −4.30290 −0.145715
\(873\) 6.64744 0.224982
\(874\) 2.04223 0.0690795
\(875\) 0 0
\(876\) −4.48260 −0.151453
\(877\) −29.3240 −0.990202 −0.495101 0.868836i \(-0.664869\pi\)
−0.495101 + 0.868836i \(0.664869\pi\)
\(878\) −3.93840 −0.132915
\(879\) 0.953831 0.0321719
\(880\) 0 0
\(881\) 23.8066 0.802065 0.401033 0.916064i \(-0.368651\pi\)
0.401033 + 0.916064i \(0.368651\pi\)
\(882\) 4.28178 0.144175
\(883\) 3.94699 0.132827 0.0664134 0.997792i \(-0.478844\pi\)
0.0664134 + 0.997792i \(0.478844\pi\)
\(884\) 2.04223 0.0686876
\(885\) 0 0
\(886\) −0.0758724 −0.00254898
\(887\) −1.96346 −0.0659264 −0.0329632 0.999457i \(-0.510494\pi\)
−0.0329632 + 0.999457i \(0.510494\pi\)
\(888\) 0.406728 0.0136489
\(889\) −25.1306 −0.842854
\(890\) 0 0
\(891\) 49.0799 1.64424
\(892\) 15.7307 0.526704
\(893\) 2.20766 0.0738765
\(894\) −0.0844605 −0.00282478
\(895\) 0 0
\(896\) 2.91729 0.0974597
\(897\) 1.66127 0.0554681
\(898\) −19.2961 −0.643918
\(899\) 46.5950 1.55403
\(900\) 0 0
\(901\) 5.88758 0.196144
\(902\) −41.3103 −1.37548
\(903\) 8.69026 0.289194
\(904\) −9.15859 −0.304610
\(905\) 0 0
\(906\) 0.330856 0.0109920
\(907\) −5.89049 −0.195590 −0.0977952 0.995207i \(-0.531179\pi\)
−0.0977952 + 0.995207i \(0.531179\pi\)
\(908\) −12.8836 −0.427559
\(909\) 23.2652 0.771658
\(910\) 0 0
\(911\) −27.9527 −0.926113 −0.463057 0.886329i \(-0.653247\pi\)
−0.463057 + 0.886329i \(0.653247\pi\)
\(912\) −0.165428 −0.00547787
\(913\) 45.9304 1.52007
\(914\) 3.00684 0.0994575
\(915\) 0 0
\(916\) 5.25383 0.173591
\(917\) −39.1729 −1.29360
\(918\) −5.95777 −0.196636
\(919\) 17.7587 0.585805 0.292903 0.956142i \(-0.405379\pi\)
0.292903 + 0.956142i \(0.405379\pi\)
\(920\) 0 0
\(921\) −9.46149 −0.311767
\(922\) 0.633755 0.0208716
\(923\) 11.9155 0.392205
\(924\) 7.72506 0.254136
\(925\) 0 0
\(926\) 18.0422 0.592904
\(927\) −24.9824 −0.820529
\(928\) 5.32401 0.174769
\(929\) 34.2892 1.12499 0.562496 0.826800i \(-0.309841\pi\)
0.562496 + 0.826800i \(0.309841\pi\)
\(930\) 0 0
\(931\) 0.614387 0.0201357
\(932\) −28.3172 −0.927560
\(933\) 12.7712 0.418111
\(934\) −23.4758 −0.768150
\(935\) 0 0
\(936\) 2.30580 0.0753675
\(937\) 14.0845 0.460119 0.230060 0.973177i \(-0.426108\pi\)
0.230060 + 0.973177i \(0.426108\pi\)
\(938\) 15.8346 0.517017
\(939\) −3.27100 −0.106745
\(940\) 0 0
\(941\) 14.2499 0.464533 0.232267 0.972652i \(-0.425386\pi\)
0.232267 + 0.972652i \(0.425386\pi\)
\(942\) −2.16543 −0.0705535
\(943\) −31.8596 −1.03749
\(944\) −1.42784 −0.0464723
\(945\) 0 0
\(946\) −47.6834 −1.55032
\(947\) 29.8203 0.969029 0.484515 0.874783i \(-0.338996\pi\)
0.484515 + 0.874783i \(0.338996\pi\)
\(948\) 0.715313 0.0232323
\(949\) 8.96520 0.291023
\(950\) 0 0
\(951\) −5.00394 −0.162264
\(952\) 7.32401 0.237373
\(953\) −8.64803 −0.280137 −0.140069 0.990142i \(-0.544732\pi\)
−0.140069 + 0.990142i \(0.544732\pi\)
\(954\) 6.64744 0.215219
\(955\) 0 0
\(956\) 14.3788 0.465043
\(957\) 14.0981 0.455728
\(958\) 8.19907 0.264900
\(959\) −42.8557 −1.38388
\(960\) 0 0
\(961\) 45.5950 1.47081
\(962\) −0.813457 −0.0262269
\(963\) 43.2624 1.39411
\(964\) 18.2749 0.588596
\(965\) 0 0
\(966\) 5.95777 0.191688
\(967\) 45.0325 1.44815 0.724074 0.689723i \(-0.242268\pi\)
0.724074 + 0.689723i \(0.242268\pi\)
\(968\) −31.3874 −1.00883
\(969\) −0.415317 −0.0133419
\(970\) 0 0
\(971\) 26.3029 0.844100 0.422050 0.906573i \(-0.361311\pi\)
0.422050 + 0.906573i \(0.361311\pi\)
\(972\) −10.1854 −0.326696
\(973\) −50.6623 −1.62416
\(974\) 0.953831 0.0305627
\(975\) 0 0
\(976\) −1.32401 −0.0423807
\(977\) −25.6549 −0.820772 −0.410386 0.911912i \(-0.634606\pi\)
−0.410386 + 0.911912i \(0.634606\pi\)
\(978\) −6.18260 −0.197698
\(979\) 39.0633 1.24847
\(980\) 0 0
\(981\) −12.1969 −0.389416
\(982\) −19.3383 −0.617110
\(983\) 55.3611 1.76575 0.882873 0.469611i \(-0.155606\pi\)
0.882873 + 0.469611i \(0.155606\pi\)
\(984\) 2.58074 0.0822711
\(985\) 0 0
\(986\) 13.3662 0.425668
\(987\) 6.44037 0.204999
\(988\) 0.330856 0.0105259
\(989\) −36.7747 −1.16937
\(990\) 0 0
\(991\) −3.24814 −0.103181 −0.0515903 0.998668i \(-0.516429\pi\)
−0.0515903 + 0.998668i \(0.516429\pi\)
\(992\) 8.75186 0.277872
\(993\) 2.75754 0.0875080
\(994\) 42.7325 1.35539
\(995\) 0 0
\(996\) −2.86937 −0.0909195
\(997\) 12.6480 0.400567 0.200284 0.979738i \(-0.435814\pi\)
0.200284 + 0.979738i \(0.435814\pi\)
\(998\) 5.63550 0.178389
\(999\) 2.37309 0.0750811
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 1850.2.a.z.1.2 3
5.2 odd 4 1850.2.b.o.149.2 6
5.3 odd 4 1850.2.b.o.149.5 6
5.4 even 2 370.2.a.g.1.2 3
15.14 odd 2 3330.2.a.bg.1.3 3
20.19 odd 2 2960.2.a.u.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.a.g.1.2 3 5.4 even 2
1850.2.a.z.1.2 3 1.1 even 1 trivial
1850.2.b.o.149.2 6 5.2 odd 4
1850.2.b.o.149.5 6 5.3 odd 4
2960.2.a.u.1.2 3 20.19 odd 2
3330.2.a.bg.1.3 3 15.14 odd 2