Properties

Label 1045.4.a.a.1.1
Level $1045$
Weight $4$
Character 1045.1
Self dual yes
Analytic conductor $61.657$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(61.6569959560\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1045.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.00000 q^{2} -1.00000 q^{3} +17.0000 q^{4} -5.00000 q^{5} +5.00000 q^{6} -2.00000 q^{7} -45.0000 q^{8} -26.0000 q^{9} +O(q^{10})\) \(q-5.00000 q^{2} -1.00000 q^{3} +17.0000 q^{4} -5.00000 q^{5} +5.00000 q^{6} -2.00000 q^{7} -45.0000 q^{8} -26.0000 q^{9} +25.0000 q^{10} -11.0000 q^{11} -17.0000 q^{12} -7.00000 q^{13} +10.0000 q^{14} +5.00000 q^{15} +89.0000 q^{16} +14.0000 q^{17} +130.000 q^{18} +19.0000 q^{19} -85.0000 q^{20} +2.00000 q^{21} +55.0000 q^{22} +55.0000 q^{23} +45.0000 q^{24} +25.0000 q^{25} +35.0000 q^{26} +53.0000 q^{27} -34.0000 q^{28} -26.0000 q^{29} -25.0000 q^{30} +261.000 q^{31} -85.0000 q^{32} +11.0000 q^{33} -70.0000 q^{34} +10.0000 q^{35} -442.000 q^{36} -126.000 q^{37} -95.0000 q^{38} +7.00000 q^{39} +225.000 q^{40} -381.000 q^{41} -10.0000 q^{42} +387.000 q^{43} -187.000 q^{44} +130.000 q^{45} -275.000 q^{46} +189.000 q^{47} -89.0000 q^{48} -339.000 q^{49} -125.000 q^{50} -14.0000 q^{51} -119.000 q^{52} -404.000 q^{53} -265.000 q^{54} +55.0000 q^{55} +90.0000 q^{56} -19.0000 q^{57} +130.000 q^{58} +746.000 q^{59} +85.0000 q^{60} +79.0000 q^{61} -1305.00 q^{62} +52.0000 q^{63} -287.000 q^{64} +35.0000 q^{65} -55.0000 q^{66} +537.000 q^{67} +238.000 q^{68} -55.0000 q^{69} -50.0000 q^{70} -824.000 q^{71} +1170.00 q^{72} +169.000 q^{73} +630.000 q^{74} -25.0000 q^{75} +323.000 q^{76} +22.0000 q^{77} -35.0000 q^{78} -338.000 q^{79} -445.000 q^{80} +649.000 q^{81} +1905.00 q^{82} +601.000 q^{83} +34.0000 q^{84} -70.0000 q^{85} -1935.00 q^{86} +26.0000 q^{87} +495.000 q^{88} -762.000 q^{89} -650.000 q^{90} +14.0000 q^{91} +935.000 q^{92} -261.000 q^{93} -945.000 q^{94} -95.0000 q^{95} +85.0000 q^{96} +866.000 q^{97} +1695.00 q^{98} +286.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.00000 −1.76777 −0.883883 0.467707i \(-0.845080\pi\)
−0.883883 + 0.467707i \(0.845080\pi\)
\(3\) −1.00000 −0.192450 −0.0962250 0.995360i \(-0.530677\pi\)
−0.0962250 + 0.995360i \(0.530677\pi\)
\(4\) 17.0000 2.12500
\(5\) −5.00000 −0.447214
\(6\) 5.00000 0.340207
\(7\) −2.00000 −0.107990 −0.0539949 0.998541i \(-0.517195\pi\)
−0.0539949 + 0.998541i \(0.517195\pi\)
\(8\) −45.0000 −1.98874
\(9\) −26.0000 −0.962963
\(10\) 25.0000 0.790569
\(11\) −11.0000 −0.301511
\(12\) −17.0000 −0.408956
\(13\) −7.00000 −0.149342 −0.0746712 0.997208i \(-0.523791\pi\)
−0.0746712 + 0.997208i \(0.523791\pi\)
\(14\) 10.0000 0.190901
\(15\) 5.00000 0.0860663
\(16\) 89.0000 1.39062
\(17\) 14.0000 0.199735 0.0998676 0.995001i \(-0.468158\pi\)
0.0998676 + 0.995001i \(0.468158\pi\)
\(18\) 130.000 1.70229
\(19\) 19.0000 0.229416
\(20\) −85.0000 −0.950329
\(21\) 2.00000 0.0207827
\(22\) 55.0000 0.533002
\(23\) 55.0000 0.498621 0.249311 0.968424i \(-0.419796\pi\)
0.249311 + 0.968424i \(0.419796\pi\)
\(24\) 45.0000 0.382733
\(25\) 25.0000 0.200000
\(26\) 35.0000 0.264002
\(27\) 53.0000 0.377772
\(28\) −34.0000 −0.229478
\(29\) −26.0000 −0.166485 −0.0832427 0.996529i \(-0.526528\pi\)
−0.0832427 + 0.996529i \(0.526528\pi\)
\(30\) −25.0000 −0.152145
\(31\) 261.000 1.51216 0.756080 0.654479i \(-0.227112\pi\)
0.756080 + 0.654479i \(0.227112\pi\)
\(32\) −85.0000 −0.469563
\(33\) 11.0000 0.0580259
\(34\) −70.0000 −0.353085
\(35\) 10.0000 0.0482945
\(36\) −442.000 −2.04630
\(37\) −126.000 −0.559845 −0.279923 0.960023i \(-0.590309\pi\)
−0.279923 + 0.960023i \(0.590309\pi\)
\(38\) −95.0000 −0.405554
\(39\) 7.00000 0.0287410
\(40\) 225.000 0.889391
\(41\) −381.000 −1.45127 −0.725637 0.688078i \(-0.758455\pi\)
−0.725637 + 0.688078i \(0.758455\pi\)
\(42\) −10.0000 −0.0367389
\(43\) 387.000 1.37249 0.686244 0.727372i \(-0.259258\pi\)
0.686244 + 0.727372i \(0.259258\pi\)
\(44\) −187.000 −0.640712
\(45\) 130.000 0.430650
\(46\) −275.000 −0.881446
\(47\) 189.000 0.586563 0.293282 0.956026i \(-0.405253\pi\)
0.293282 + 0.956026i \(0.405253\pi\)
\(48\) −89.0000 −0.267626
\(49\) −339.000 −0.988338
\(50\) −125.000 −0.353553
\(51\) −14.0000 −0.0384391
\(52\) −119.000 −0.317353
\(53\) −404.000 −1.04705 −0.523525 0.852010i \(-0.675383\pi\)
−0.523525 + 0.852010i \(0.675383\pi\)
\(54\) −265.000 −0.667814
\(55\) 55.0000 0.134840
\(56\) 90.0000 0.214763
\(57\) −19.0000 −0.0441511
\(58\) 130.000 0.294308
\(59\) 746.000 1.64612 0.823059 0.567956i \(-0.192266\pi\)
0.823059 + 0.567956i \(0.192266\pi\)
\(60\) 85.0000 0.182891
\(61\) 79.0000 0.165818 0.0829091 0.996557i \(-0.473579\pi\)
0.0829091 + 0.996557i \(0.473579\pi\)
\(62\) −1305.00 −2.67315
\(63\) 52.0000 0.103990
\(64\) −287.000 −0.560547
\(65\) 35.0000 0.0667879
\(66\) −55.0000 −0.102576
\(67\) 537.000 0.979179 0.489589 0.871953i \(-0.337147\pi\)
0.489589 + 0.871953i \(0.337147\pi\)
\(68\) 238.000 0.424437
\(69\) −55.0000 −0.0959597
\(70\) −50.0000 −0.0853735
\(71\) −824.000 −1.37734 −0.688668 0.725077i \(-0.741804\pi\)
−0.688668 + 0.725077i \(0.741804\pi\)
\(72\) 1170.00 1.91508
\(73\) 169.000 0.270958 0.135479 0.990780i \(-0.456743\pi\)
0.135479 + 0.990780i \(0.456743\pi\)
\(74\) 630.000 0.989676
\(75\) −25.0000 −0.0384900
\(76\) 323.000 0.487508
\(77\) 22.0000 0.0325602
\(78\) −35.0000 −0.0508073
\(79\) −338.000 −0.481367 −0.240683 0.970604i \(-0.577372\pi\)
−0.240683 + 0.970604i \(0.577372\pi\)
\(80\) −445.000 −0.621906
\(81\) 649.000 0.890261
\(82\) 1905.00 2.56551
\(83\) 601.000 0.794799 0.397400 0.917646i \(-0.369913\pi\)
0.397400 + 0.917646i \(0.369913\pi\)
\(84\) 34.0000 0.0441631
\(85\) −70.0000 −0.0893243
\(86\) −1935.00 −2.42624
\(87\) 26.0000 0.0320401
\(88\) 495.000 0.599627
\(89\) −762.000 −0.907549 −0.453774 0.891117i \(-0.649923\pi\)
−0.453774 + 0.891117i \(0.649923\pi\)
\(90\) −650.000 −0.761289
\(91\) 14.0000 0.0161275
\(92\) 935.000 1.05957
\(93\) −261.000 −0.291015
\(94\) −945.000 −1.03691
\(95\) −95.0000 −0.102598
\(96\) 85.0000 0.0903675
\(97\) 866.000 0.906484 0.453242 0.891387i \(-0.350267\pi\)
0.453242 + 0.891387i \(0.350267\pi\)
\(98\) 1695.00 1.74715
\(99\) 286.000 0.290344
\(100\) 425.000 0.425000
\(101\) 1006.00 0.991096 0.495548 0.868580i \(-0.334967\pi\)
0.495548 + 0.868580i \(0.334967\pi\)
\(102\) 70.0000 0.0679513
\(103\) 2002.00 1.91517 0.957587 0.288144i \(-0.0930383\pi\)
0.957587 + 0.288144i \(0.0930383\pi\)
\(104\) 315.000 0.297003
\(105\) −10.0000 −0.00929429
\(106\) 2020.00 1.85094
\(107\) 1144.00 1.03359 0.516797 0.856108i \(-0.327124\pi\)
0.516797 + 0.856108i \(0.327124\pi\)
\(108\) 901.000 0.802766
\(109\) 766.000 0.673115 0.336557 0.941663i \(-0.390737\pi\)
0.336557 + 0.941663i \(0.390737\pi\)
\(110\) −275.000 −0.238366
\(111\) 126.000 0.107742
\(112\) −178.000 −0.150173
\(113\) −2042.00 −1.69996 −0.849979 0.526817i \(-0.823385\pi\)
−0.849979 + 0.526817i \(0.823385\pi\)
\(114\) 95.0000 0.0780488
\(115\) −275.000 −0.222990
\(116\) −442.000 −0.353782
\(117\) 182.000 0.143811
\(118\) −3730.00 −2.90995
\(119\) −28.0000 −0.0215694
\(120\) −225.000 −0.171163
\(121\) 121.000 0.0909091
\(122\) −395.000 −0.293128
\(123\) 381.000 0.279298
\(124\) 4437.00 3.21334
\(125\) −125.000 −0.0894427
\(126\) −260.000 −0.183830
\(127\) −171.000 −0.119479 −0.0597394 0.998214i \(-0.519027\pi\)
−0.0597394 + 0.998214i \(0.519027\pi\)
\(128\) 2115.00 1.46048
\(129\) −387.000 −0.264135
\(130\) −175.000 −0.118066
\(131\) −1900.00 −1.26720 −0.633602 0.773659i \(-0.718424\pi\)
−0.633602 + 0.773659i \(0.718424\pi\)
\(132\) 187.000 0.123305
\(133\) −38.0000 −0.0247746
\(134\) −2685.00 −1.73096
\(135\) −265.000 −0.168945
\(136\) −630.000 −0.397221
\(137\) 324.000 0.202052 0.101026 0.994884i \(-0.467787\pi\)
0.101026 + 0.994884i \(0.467787\pi\)
\(138\) 275.000 0.169634
\(139\) 178.000 0.108617 0.0543085 0.998524i \(-0.482705\pi\)
0.0543085 + 0.998524i \(0.482705\pi\)
\(140\) 170.000 0.102626
\(141\) −189.000 −0.112884
\(142\) 4120.00 2.43481
\(143\) 77.0000 0.0450284
\(144\) −2314.00 −1.33912
\(145\) 130.000 0.0744546
\(146\) −845.000 −0.478991
\(147\) 339.000 0.190206
\(148\) −2142.00 −1.18967
\(149\) −1491.00 −0.819782 −0.409891 0.912135i \(-0.634433\pi\)
−0.409891 + 0.912135i \(0.634433\pi\)
\(150\) 125.000 0.0680414
\(151\) −860.000 −0.463482 −0.231741 0.972778i \(-0.574442\pi\)
−0.231741 + 0.972778i \(0.574442\pi\)
\(152\) −855.000 −0.456248
\(153\) −364.000 −0.192338
\(154\) −110.000 −0.0575588
\(155\) −1305.00 −0.676259
\(156\) 119.000 0.0610745
\(157\) 1733.00 0.880946 0.440473 0.897766i \(-0.354811\pi\)
0.440473 + 0.897766i \(0.354811\pi\)
\(158\) 1690.00 0.850944
\(159\) 404.000 0.201505
\(160\) 425.000 0.209995
\(161\) −110.000 −0.0538461
\(162\) −3245.00 −1.57377
\(163\) −3980.00 −1.91250 −0.956250 0.292549i \(-0.905496\pi\)
−0.956250 + 0.292549i \(0.905496\pi\)
\(164\) −6477.00 −3.08396
\(165\) −55.0000 −0.0259500
\(166\) −3005.00 −1.40502
\(167\) 1059.00 0.490706 0.245353 0.969434i \(-0.421096\pi\)
0.245353 + 0.969434i \(0.421096\pi\)
\(168\) −90.0000 −0.0413313
\(169\) −2148.00 −0.977697
\(170\) 350.000 0.157905
\(171\) −494.000 −0.220919
\(172\) 6579.00 2.91654
\(173\) 971.000 0.426727 0.213363 0.976973i \(-0.431558\pi\)
0.213363 + 0.976973i \(0.431558\pi\)
\(174\) −130.000 −0.0566395
\(175\) −50.0000 −0.0215980
\(176\) −979.000 −0.419289
\(177\) −746.000 −0.316795
\(178\) 3810.00 1.60433
\(179\) −2202.00 −0.919470 −0.459735 0.888056i \(-0.652056\pi\)
−0.459735 + 0.888056i \(0.652056\pi\)
\(180\) 2210.00 0.915132
\(181\) 1097.00 0.450494 0.225247 0.974302i \(-0.427681\pi\)
0.225247 + 0.974302i \(0.427681\pi\)
\(182\) −70.0000 −0.0285096
\(183\) −79.0000 −0.0319117
\(184\) −2475.00 −0.991627
\(185\) 630.000 0.250370
\(186\) 1305.00 0.514448
\(187\) −154.000 −0.0602224
\(188\) 3213.00 1.24645
\(189\) −106.000 −0.0407956
\(190\) 475.000 0.181369
\(191\) −3022.00 −1.14484 −0.572419 0.819961i \(-0.693995\pi\)
−0.572419 + 0.819961i \(0.693995\pi\)
\(192\) 287.000 0.107877
\(193\) 658.000 0.245409 0.122704 0.992443i \(-0.460843\pi\)
0.122704 + 0.992443i \(0.460843\pi\)
\(194\) −4330.00 −1.60245
\(195\) −35.0000 −0.0128533
\(196\) −5763.00 −2.10022
\(197\) 426.000 0.154067 0.0770336 0.997028i \(-0.475455\pi\)
0.0770336 + 0.997028i \(0.475455\pi\)
\(198\) −1430.00 −0.513261
\(199\) −1276.00 −0.454539 −0.227269 0.973832i \(-0.572980\pi\)
−0.227269 + 0.973832i \(0.572980\pi\)
\(200\) −1125.00 −0.397748
\(201\) −537.000 −0.188443
\(202\) −5030.00 −1.75203
\(203\) 52.0000 0.0179787
\(204\) −238.000 −0.0816830
\(205\) 1905.00 0.649029
\(206\) −10010.0 −3.38558
\(207\) −1430.00 −0.480154
\(208\) −623.000 −0.207679
\(209\) −209.000 −0.0691714
\(210\) 50.0000 0.0164301
\(211\) 4489.00 1.46462 0.732312 0.680970i \(-0.238441\pi\)
0.732312 + 0.680970i \(0.238441\pi\)
\(212\) −6868.00 −2.22498
\(213\) 824.000 0.265068
\(214\) −5720.00 −1.82715
\(215\) −1935.00 −0.613795
\(216\) −2385.00 −0.751290
\(217\) −522.000 −0.163298
\(218\) −3830.00 −1.18991
\(219\) −169.000 −0.0521459
\(220\) 935.000 0.286535
\(221\) −98.0000 −0.0298289
\(222\) −630.000 −0.190463
\(223\) −750.000 −0.225218 −0.112609 0.993639i \(-0.535921\pi\)
−0.112609 + 0.993639i \(0.535921\pi\)
\(224\) 170.000 0.0507080
\(225\) −650.000 −0.192593
\(226\) 10210.0 3.00513
\(227\) −2016.00 −0.589456 −0.294728 0.955581i \(-0.595229\pi\)
−0.294728 + 0.955581i \(0.595229\pi\)
\(228\) −323.000 −0.0938210
\(229\) −6680.00 −1.92763 −0.963814 0.266576i \(-0.914108\pi\)
−0.963814 + 0.266576i \(0.914108\pi\)
\(230\) 1375.00 0.394195
\(231\) −22.0000 −0.00626621
\(232\) 1170.00 0.331096
\(233\) −6423.00 −1.80594 −0.902972 0.429700i \(-0.858619\pi\)
−0.902972 + 0.429700i \(0.858619\pi\)
\(234\) −910.000 −0.254225
\(235\) −945.000 −0.262319
\(236\) 12682.0 3.49800
\(237\) 338.000 0.0926391
\(238\) 140.000 0.0381296
\(239\) −5440.00 −1.47232 −0.736160 0.676808i \(-0.763363\pi\)
−0.736160 + 0.676808i \(0.763363\pi\)
\(240\) 445.000 0.119686
\(241\) −155.000 −0.0414292 −0.0207146 0.999785i \(-0.506594\pi\)
−0.0207146 + 0.999785i \(0.506594\pi\)
\(242\) −605.000 −0.160706
\(243\) −2080.00 −0.549103
\(244\) 1343.00 0.352364
\(245\) 1695.00 0.441998
\(246\) −1905.00 −0.493733
\(247\) −133.000 −0.0342615
\(248\) −11745.0 −3.00729
\(249\) −601.000 −0.152959
\(250\) 625.000 0.158114
\(251\) −6609.00 −1.66198 −0.830989 0.556289i \(-0.812225\pi\)
−0.830989 + 0.556289i \(0.812225\pi\)
\(252\) 884.000 0.220979
\(253\) −605.000 −0.150340
\(254\) 855.000 0.211211
\(255\) 70.0000 0.0171905
\(256\) −8279.00 −2.02124
\(257\) −2505.00 −0.608006 −0.304003 0.952671i \(-0.598323\pi\)
−0.304003 + 0.952671i \(0.598323\pi\)
\(258\) 1935.00 0.466930
\(259\) 252.000 0.0604576
\(260\) 595.000 0.141924
\(261\) 676.000 0.160319
\(262\) 9500.00 2.24012
\(263\) 442.000 0.103631 0.0518154 0.998657i \(-0.483499\pi\)
0.0518154 + 0.998657i \(0.483499\pi\)
\(264\) −495.000 −0.115398
\(265\) 2020.00 0.468255
\(266\) 190.000 0.0437957
\(267\) 762.000 0.174658
\(268\) 9129.00 2.08076
\(269\) 1226.00 0.277883 0.138942 0.990301i \(-0.455630\pi\)
0.138942 + 0.990301i \(0.455630\pi\)
\(270\) 1325.00 0.298655
\(271\) 8264.00 1.85241 0.926203 0.377024i \(-0.123053\pi\)
0.926203 + 0.377024i \(0.123053\pi\)
\(272\) 1246.00 0.277757
\(273\) −14.0000 −0.00310373
\(274\) −1620.00 −0.357182
\(275\) −275.000 −0.0603023
\(276\) −935.000 −0.203914
\(277\) −8128.00 −1.76305 −0.881524 0.472140i \(-0.843482\pi\)
−0.881524 + 0.472140i \(0.843482\pi\)
\(278\) −890.000 −0.192010
\(279\) −6786.00 −1.45615
\(280\) −450.000 −0.0960452
\(281\) 886.000 0.188094 0.0940468 0.995568i \(-0.470020\pi\)
0.0940468 + 0.995568i \(0.470020\pi\)
\(282\) 945.000 0.199553
\(283\) 5621.00 1.18068 0.590342 0.807153i \(-0.298993\pi\)
0.590342 + 0.807153i \(0.298993\pi\)
\(284\) −14008.0 −2.92684
\(285\) 95.0000 0.0197450
\(286\) −385.000 −0.0795997
\(287\) 762.000 0.156723
\(288\) 2210.00 0.452172
\(289\) −4717.00 −0.960106
\(290\) −650.000 −0.131618
\(291\) −866.000 −0.174453
\(292\) 2873.00 0.575786
\(293\) −386.000 −0.0769637 −0.0384818 0.999259i \(-0.512252\pi\)
−0.0384818 + 0.999259i \(0.512252\pi\)
\(294\) −1695.00 −0.336239
\(295\) −3730.00 −0.736166
\(296\) 5670.00 1.11339
\(297\) −583.000 −0.113903
\(298\) 7455.00 1.44918
\(299\) −385.000 −0.0744653
\(300\) −425.000 −0.0817913
\(301\) −774.000 −0.148215
\(302\) 4300.00 0.819328
\(303\) −1006.00 −0.190737
\(304\) 1691.00 0.319031
\(305\) −395.000 −0.0741562
\(306\) 1820.00 0.340008
\(307\) 2480.00 0.461046 0.230523 0.973067i \(-0.425956\pi\)
0.230523 + 0.973067i \(0.425956\pi\)
\(308\) 374.000 0.0691903
\(309\) −2002.00 −0.368575
\(310\) 6525.00 1.19547
\(311\) 8242.00 1.50277 0.751384 0.659865i \(-0.229387\pi\)
0.751384 + 0.659865i \(0.229387\pi\)
\(312\) −315.000 −0.0571582
\(313\) −510.000 −0.0920987 −0.0460494 0.998939i \(-0.514663\pi\)
−0.0460494 + 0.998939i \(0.514663\pi\)
\(314\) −8665.00 −1.55731
\(315\) −260.000 −0.0465058
\(316\) −5746.00 −1.02290
\(317\) −8748.00 −1.54996 −0.774979 0.631987i \(-0.782240\pi\)
−0.774979 + 0.631987i \(0.782240\pi\)
\(318\) −2020.00 −0.356214
\(319\) 286.000 0.0501973
\(320\) 1435.00 0.250684
\(321\) −1144.00 −0.198915
\(322\) 550.000 0.0951873
\(323\) 266.000 0.0458224
\(324\) 11033.0 1.89180
\(325\) −175.000 −0.0298685
\(326\) 19900.0 3.38086
\(327\) −766.000 −0.129541
\(328\) 17145.0 2.88620
\(329\) −378.000 −0.0633429
\(330\) 275.000 0.0458735
\(331\) 6742.00 1.11956 0.559779 0.828642i \(-0.310886\pi\)
0.559779 + 0.828642i \(0.310886\pi\)
\(332\) 10217.0 1.68895
\(333\) 3276.00 0.539110
\(334\) −5295.00 −0.867454
\(335\) −2685.00 −0.437902
\(336\) 178.000 0.0289009
\(337\) 2244.00 0.362725 0.181363 0.983416i \(-0.441949\pi\)
0.181363 + 0.983416i \(0.441949\pi\)
\(338\) 10740.0 1.72834
\(339\) 2042.00 0.327157
\(340\) −1190.00 −0.189814
\(341\) −2871.00 −0.455934
\(342\) 2470.00 0.390533
\(343\) 1364.00 0.214720
\(344\) −17415.0 −2.72952
\(345\) 275.000 0.0429145
\(346\) −4855.00 −0.754354
\(347\) −1623.00 −0.251087 −0.125544 0.992088i \(-0.540067\pi\)
−0.125544 + 0.992088i \(0.540067\pi\)
\(348\) 442.000 0.0680853
\(349\) −8637.00 −1.32472 −0.662361 0.749185i \(-0.730445\pi\)
−0.662361 + 0.749185i \(0.730445\pi\)
\(350\) 250.000 0.0381802
\(351\) −371.000 −0.0564174
\(352\) 935.000 0.141579
\(353\) −68.0000 −0.0102529 −0.00512645 0.999987i \(-0.501632\pi\)
−0.00512645 + 0.999987i \(0.501632\pi\)
\(354\) 3730.00 0.560021
\(355\) 4120.00 0.615963
\(356\) −12954.0 −1.92854
\(357\) 28.0000 0.00415103
\(358\) 11010.0 1.62541
\(359\) 9785.00 1.43853 0.719265 0.694735i \(-0.244479\pi\)
0.719265 + 0.694735i \(0.244479\pi\)
\(360\) −5850.00 −0.856450
\(361\) 361.000 0.0526316
\(362\) −5485.00 −0.796368
\(363\) −121.000 −0.0174955
\(364\) 238.000 0.0342709
\(365\) −845.000 −0.121176
\(366\) 395.000 0.0564125
\(367\) −9159.00 −1.30271 −0.651357 0.758772i \(-0.725800\pi\)
−0.651357 + 0.758772i \(0.725800\pi\)
\(368\) 4895.00 0.693395
\(369\) 9906.00 1.39752
\(370\) −3150.00 −0.442596
\(371\) 808.000 0.113071
\(372\) −4437.00 −0.618408
\(373\) 2773.00 0.384934 0.192467 0.981303i \(-0.438351\pi\)
0.192467 + 0.981303i \(0.438351\pi\)
\(374\) 770.000 0.106459
\(375\) 125.000 0.0172133
\(376\) −8505.00 −1.16652
\(377\) 182.000 0.0248633
\(378\) 530.000 0.0721171
\(379\) −8326.00 −1.12844 −0.564219 0.825625i \(-0.690823\pi\)
−0.564219 + 0.825625i \(0.690823\pi\)
\(380\) −1615.00 −0.218020
\(381\) 171.000 0.0229937
\(382\) 15110.0 2.02381
\(383\) −6644.00 −0.886404 −0.443202 0.896422i \(-0.646157\pi\)
−0.443202 + 0.896422i \(0.646157\pi\)
\(384\) −2115.00 −0.281069
\(385\) −110.000 −0.0145613
\(386\) −3290.00 −0.433825
\(387\) −10062.0 −1.32165
\(388\) 14722.0 1.92628
\(389\) −8880.00 −1.15741 −0.578707 0.815536i \(-0.696442\pi\)
−0.578707 + 0.815536i \(0.696442\pi\)
\(390\) 175.000 0.0227217
\(391\) 770.000 0.0995923
\(392\) 15255.0 1.96555
\(393\) 1900.00 0.243874
\(394\) −2130.00 −0.272355
\(395\) 1690.00 0.215274
\(396\) 4862.00 0.616982
\(397\) −3094.00 −0.391142 −0.195571 0.980690i \(-0.562656\pi\)
−0.195571 + 0.980690i \(0.562656\pi\)
\(398\) 6380.00 0.803519
\(399\) 38.0000 0.00476787
\(400\) 2225.00 0.278125
\(401\) −6008.00 −0.748193 −0.374096 0.927390i \(-0.622047\pi\)
−0.374096 + 0.927390i \(0.622047\pi\)
\(402\) 2685.00 0.333123
\(403\) −1827.00 −0.225830
\(404\) 17102.0 2.10608
\(405\) −3245.00 −0.398137
\(406\) −260.000 −0.0317822
\(407\) 1386.00 0.168800
\(408\) 630.000 0.0764452
\(409\) −5761.00 −0.696487 −0.348243 0.937404i \(-0.613222\pi\)
−0.348243 + 0.937404i \(0.613222\pi\)
\(410\) −9525.00 −1.14733
\(411\) −324.000 −0.0388850
\(412\) 34034.0 4.06974
\(413\) −1492.00 −0.177764
\(414\) 7150.00 0.848800
\(415\) −3005.00 −0.355445
\(416\) 595.000 0.0701257
\(417\) −178.000 −0.0209034
\(418\) 1045.00 0.122279
\(419\) −5063.00 −0.590319 −0.295160 0.955448i \(-0.595373\pi\)
−0.295160 + 0.955448i \(0.595373\pi\)
\(420\) −170.000 −0.0197504
\(421\) −8537.00 −0.988285 −0.494142 0.869381i \(-0.664518\pi\)
−0.494142 + 0.869381i \(0.664518\pi\)
\(422\) −22445.0 −2.58911
\(423\) −4914.00 −0.564839
\(424\) 18180.0 2.08231
\(425\) 350.000 0.0399470
\(426\) −4120.00 −0.468579
\(427\) −158.000 −0.0179067
\(428\) 19448.0 2.19639
\(429\) −77.0000 −0.00866572
\(430\) 9675.00 1.08505
\(431\) 5936.00 0.663404 0.331702 0.943384i \(-0.392377\pi\)
0.331702 + 0.943384i \(0.392377\pi\)
\(432\) 4717.00 0.525340
\(433\) 5441.00 0.603875 0.301937 0.953328i \(-0.402367\pi\)
0.301937 + 0.953328i \(0.402367\pi\)
\(434\) 2610.00 0.288673
\(435\) −130.000 −0.0143288
\(436\) 13022.0 1.43037
\(437\) 1045.00 0.114392
\(438\) 845.000 0.0921819
\(439\) 11500.0 1.25026 0.625131 0.780520i \(-0.285046\pi\)
0.625131 + 0.780520i \(0.285046\pi\)
\(440\) −2475.00 −0.268161
\(441\) 8814.00 0.951733
\(442\) 490.000 0.0527306
\(443\) 3226.00 0.345986 0.172993 0.984923i \(-0.444656\pi\)
0.172993 + 0.984923i \(0.444656\pi\)
\(444\) 2142.00 0.228952
\(445\) 3810.00 0.405868
\(446\) 3750.00 0.398134
\(447\) 1491.00 0.157767
\(448\) 574.000 0.0605334
\(449\) 16350.0 1.71849 0.859247 0.511560i \(-0.170932\pi\)
0.859247 + 0.511560i \(0.170932\pi\)
\(450\) 3250.00 0.340459
\(451\) 4191.00 0.437575
\(452\) −34714.0 −3.61241
\(453\) 860.000 0.0891972
\(454\) 10080.0 1.04202
\(455\) −70.0000 −0.00721242
\(456\) 855.000 0.0878049
\(457\) 11851.0 1.21306 0.606528 0.795062i \(-0.292562\pi\)
0.606528 + 0.795062i \(0.292562\pi\)
\(458\) 33400.0 3.40760
\(459\) 742.000 0.0754545
\(460\) −4675.00 −0.473854
\(461\) −9891.00 −0.999284 −0.499642 0.866232i \(-0.666535\pi\)
−0.499642 + 0.866232i \(0.666535\pi\)
\(462\) 110.000 0.0110772
\(463\) −17088.0 −1.71522 −0.857610 0.514301i \(-0.828051\pi\)
−0.857610 + 0.514301i \(0.828051\pi\)
\(464\) −2314.00 −0.231519
\(465\) 1305.00 0.130146
\(466\) 32115.0 3.19249
\(467\) 4716.00 0.467303 0.233651 0.972320i \(-0.424933\pi\)
0.233651 + 0.972320i \(0.424933\pi\)
\(468\) 3094.00 0.305599
\(469\) −1074.00 −0.105741
\(470\) 4725.00 0.463719
\(471\) −1733.00 −0.169538
\(472\) −33570.0 −3.27370
\(473\) −4257.00 −0.413820
\(474\) −1690.00 −0.163764
\(475\) 475.000 0.0458831
\(476\) −476.000 −0.0458349
\(477\) 10504.0 1.00827
\(478\) 27200.0 2.60272
\(479\) 327.000 0.0311921 0.0155960 0.999878i \(-0.495035\pi\)
0.0155960 + 0.999878i \(0.495035\pi\)
\(480\) −425.000 −0.0404136
\(481\) 882.000 0.0836086
\(482\) 775.000 0.0732371
\(483\) 110.000 0.0103627
\(484\) 2057.00 0.193182
\(485\) −4330.00 −0.405392
\(486\) 10400.0 0.970686
\(487\) 14.0000 0.00130267 0.000651335 1.00000i \(-0.499793\pi\)
0.000651335 1.00000i \(0.499793\pi\)
\(488\) −3555.00 −0.329769
\(489\) 3980.00 0.368061
\(490\) −8475.00 −0.781350
\(491\) 18382.0 1.68955 0.844774 0.535123i \(-0.179735\pi\)
0.844774 + 0.535123i \(0.179735\pi\)
\(492\) 6477.00 0.593508
\(493\) −364.000 −0.0332530
\(494\) 665.000 0.0605663
\(495\) −1430.00 −0.129846
\(496\) 23229.0 2.10285
\(497\) 1648.00 0.148738
\(498\) 3005.00 0.270396
\(499\) −745.000 −0.0668352 −0.0334176 0.999441i \(-0.510639\pi\)
−0.0334176 + 0.999441i \(0.510639\pi\)
\(500\) −2125.00 −0.190066
\(501\) −1059.00 −0.0944364
\(502\) 33045.0 2.93799
\(503\) −3504.00 −0.310608 −0.155304 0.987867i \(-0.549636\pi\)
−0.155304 + 0.987867i \(0.549636\pi\)
\(504\) −2340.00 −0.206809
\(505\) −5030.00 −0.443232
\(506\) 3025.00 0.265766
\(507\) 2148.00 0.188158
\(508\) −2907.00 −0.253892
\(509\) −8085.00 −0.704050 −0.352025 0.935991i \(-0.614507\pi\)
−0.352025 + 0.935991i \(0.614507\pi\)
\(510\) −350.000 −0.0303887
\(511\) −338.000 −0.0292607
\(512\) 24475.0 2.11260
\(513\) 1007.00 0.0866669
\(514\) 12525.0 1.07481
\(515\) −10010.0 −0.856492
\(516\) −6579.00 −0.561287
\(517\) −2079.00 −0.176856
\(518\) −1260.00 −0.106875
\(519\) −971.000 −0.0821236
\(520\) −1575.00 −0.132824
\(521\) 3600.00 0.302723 0.151362 0.988478i \(-0.451634\pi\)
0.151362 + 0.988478i \(0.451634\pi\)
\(522\) −3380.00 −0.283407
\(523\) −4086.00 −0.341622 −0.170811 0.985304i \(-0.554639\pi\)
−0.170811 + 0.985304i \(0.554639\pi\)
\(524\) −32300.0 −2.69281
\(525\) 50.0000 0.00415653
\(526\) −2210.00 −0.183195
\(527\) 3654.00 0.302032
\(528\) 979.000 0.0806922
\(529\) −9142.00 −0.751377
\(530\) −10100.0 −0.827766
\(531\) −19396.0 −1.58515
\(532\) −646.000 −0.0526460
\(533\) 2667.00 0.216737
\(534\) −3810.00 −0.308754
\(535\) −5720.00 −0.462238
\(536\) −24165.0 −1.94733
\(537\) 2202.00 0.176952
\(538\) −6130.00 −0.491232
\(539\) 3729.00 0.297995
\(540\) −4505.00 −0.359008
\(541\) 105.000 0.00834437 0.00417218 0.999991i \(-0.498672\pi\)
0.00417218 + 0.999991i \(0.498672\pi\)
\(542\) −41320.0 −3.27462
\(543\) −1097.00 −0.0866976
\(544\) −1190.00 −0.0937883
\(545\) −3830.00 −0.301026
\(546\) 70.0000 0.00548667
\(547\) −2486.00 −0.194321 −0.0971606 0.995269i \(-0.530976\pi\)
−0.0971606 + 0.995269i \(0.530976\pi\)
\(548\) 5508.00 0.429361
\(549\) −2054.00 −0.159677
\(550\) 1375.00 0.106600
\(551\) −494.000 −0.0381944
\(552\) 2475.00 0.190839
\(553\) 676.000 0.0519827
\(554\) 40640.0 3.11666
\(555\) −630.000 −0.0481838
\(556\) 3026.00 0.230811
\(557\) −18568.0 −1.41248 −0.706240 0.707972i \(-0.749610\pi\)
−0.706240 + 0.707972i \(0.749610\pi\)
\(558\) 33930.0 2.57414
\(559\) −2709.00 −0.204970
\(560\) 890.000 0.0671596
\(561\) 154.000 0.0115898
\(562\) −4430.00 −0.332506
\(563\) −5682.00 −0.425342 −0.212671 0.977124i \(-0.568216\pi\)
−0.212671 + 0.977124i \(0.568216\pi\)
\(564\) −3213.00 −0.239879
\(565\) 10210.0 0.760244
\(566\) −28105.0 −2.08718
\(567\) −1298.00 −0.0961391
\(568\) 37080.0 2.73916
\(569\) 12474.0 0.919046 0.459523 0.888166i \(-0.348020\pi\)
0.459523 + 0.888166i \(0.348020\pi\)
\(570\) −475.000 −0.0349045
\(571\) −19574.0 −1.43458 −0.717291 0.696774i \(-0.754618\pi\)
−0.717291 + 0.696774i \(0.754618\pi\)
\(572\) 1309.00 0.0956854
\(573\) 3022.00 0.220324
\(574\) −3810.00 −0.277049
\(575\) 1375.00 0.0997243
\(576\) 7462.00 0.539786
\(577\) −12278.0 −0.885858 −0.442929 0.896557i \(-0.646061\pi\)
−0.442929 + 0.896557i \(0.646061\pi\)
\(578\) 23585.0 1.69724
\(579\) −658.000 −0.0472289
\(580\) 2210.00 0.158216
\(581\) −1202.00 −0.0858302
\(582\) 4330.00 0.308392
\(583\) 4444.00 0.315698
\(584\) −7605.00 −0.538865
\(585\) −910.000 −0.0643143
\(586\) 1930.00 0.136054
\(587\) 1710.00 0.120237 0.0601186 0.998191i \(-0.480852\pi\)
0.0601186 + 0.998191i \(0.480852\pi\)
\(588\) 5763.00 0.404187
\(589\) 4959.00 0.346913
\(590\) 18650.0 1.30137
\(591\) −426.000 −0.0296503
\(592\) −11214.0 −0.778535
\(593\) −18701.0 −1.29504 −0.647519 0.762049i \(-0.724194\pi\)
−0.647519 + 0.762049i \(0.724194\pi\)
\(594\) 2915.00 0.201353
\(595\) 140.000 0.00964612
\(596\) −25347.0 −1.74204
\(597\) 1276.00 0.0874761
\(598\) 1925.00 0.131637
\(599\) −6279.00 −0.428302 −0.214151 0.976801i \(-0.568698\pi\)
−0.214151 + 0.976801i \(0.568698\pi\)
\(600\) 1125.00 0.0765466
\(601\) −6349.00 −0.430917 −0.215458 0.976513i \(-0.569125\pi\)
−0.215458 + 0.976513i \(0.569125\pi\)
\(602\) 3870.00 0.262009
\(603\) −13962.0 −0.942913
\(604\) −14620.0 −0.984900
\(605\) −605.000 −0.0406558
\(606\) 5030.00 0.337178
\(607\) −22731.0 −1.51997 −0.759986 0.649940i \(-0.774794\pi\)
−0.759986 + 0.649940i \(0.774794\pi\)
\(608\) −1615.00 −0.107725
\(609\) −52.0000 −0.00346001
\(610\) 1975.00 0.131091
\(611\) −1323.00 −0.0875988
\(612\) −6188.00 −0.408717
\(613\) −20648.0 −1.36046 −0.680232 0.732997i \(-0.738121\pi\)
−0.680232 + 0.732997i \(0.738121\pi\)
\(614\) −12400.0 −0.815022
\(615\) −1905.00 −0.124906
\(616\) −990.000 −0.0647536
\(617\) −9092.00 −0.593242 −0.296621 0.954995i \(-0.595860\pi\)
−0.296621 + 0.954995i \(0.595860\pi\)
\(618\) 10010.0 0.651555
\(619\) 4531.00 0.294210 0.147105 0.989121i \(-0.453004\pi\)
0.147105 + 0.989121i \(0.453004\pi\)
\(620\) −22185.0 −1.43705
\(621\) 2915.00 0.188365
\(622\) −41210.0 −2.65654
\(623\) 1524.00 0.0980061
\(624\) 623.000 0.0399679
\(625\) 625.000 0.0400000
\(626\) 2550.00 0.162809
\(627\) 209.000 0.0133121
\(628\) 29461.0 1.87201
\(629\) −1764.00 −0.111821
\(630\) 1300.00 0.0822115
\(631\) −10714.0 −0.675939 −0.337970 0.941157i \(-0.609740\pi\)
−0.337970 + 0.941157i \(0.609740\pi\)
\(632\) 15210.0 0.957312
\(633\) −4489.00 −0.281867
\(634\) 43740.0 2.73996
\(635\) 855.000 0.0534325
\(636\) 6868.00 0.428198
\(637\) 2373.00 0.147601
\(638\) −1430.00 −0.0887371
\(639\) 21424.0 1.32632
\(640\) −10575.0 −0.653146
\(641\) −11700.0 −0.720939 −0.360470 0.932771i \(-0.617384\pi\)
−0.360470 + 0.932771i \(0.617384\pi\)
\(642\) 5720.00 0.351636
\(643\) 25296.0 1.55144 0.775721 0.631076i \(-0.217387\pi\)
0.775721 + 0.631076i \(0.217387\pi\)
\(644\) −1870.00 −0.114423
\(645\) 1935.00 0.118125
\(646\) −1330.00 −0.0810033
\(647\) 18044.0 1.09642 0.548209 0.836341i \(-0.315310\pi\)
0.548209 + 0.836341i \(0.315310\pi\)
\(648\) −29205.0 −1.77049
\(649\) −8206.00 −0.496323
\(650\) 875.000 0.0528005
\(651\) 522.000 0.0314267
\(652\) −67660.0 −4.06406
\(653\) −3877.00 −0.232341 −0.116171 0.993229i \(-0.537062\pi\)
−0.116171 + 0.993229i \(0.537062\pi\)
\(654\) 3830.00 0.228998
\(655\) 9500.00 0.566711
\(656\) −33909.0 −2.01818
\(657\) −4394.00 −0.260923
\(658\) 1890.00 0.111975
\(659\) −16215.0 −0.958493 −0.479246 0.877680i \(-0.659090\pi\)
−0.479246 + 0.877680i \(0.659090\pi\)
\(660\) −935.000 −0.0551437
\(661\) 4517.00 0.265796 0.132898 0.991130i \(-0.457572\pi\)
0.132898 + 0.991130i \(0.457572\pi\)
\(662\) −33710.0 −1.97912
\(663\) 98.0000 0.00574058
\(664\) −27045.0 −1.58065
\(665\) 190.000 0.0110795
\(666\) −16380.0 −0.953021
\(667\) −1430.00 −0.0830132
\(668\) 18003.0 1.04275
\(669\) 750.000 0.0433433
\(670\) 13425.0 0.774109
\(671\) −869.000 −0.0499961
\(672\) −170.000 −0.00975877
\(673\) 33090.0 1.89528 0.947642 0.319335i \(-0.103460\pi\)
0.947642 + 0.319335i \(0.103460\pi\)
\(674\) −11220.0 −0.641214
\(675\) 1325.00 0.0755545
\(676\) −36516.0 −2.07761
\(677\) −26169.0 −1.48561 −0.742804 0.669509i \(-0.766504\pi\)
−0.742804 + 0.669509i \(0.766504\pi\)
\(678\) −10210.0 −0.578337
\(679\) −1732.00 −0.0978911
\(680\) 3150.00 0.177643
\(681\) 2016.00 0.113441
\(682\) 14355.0 0.805984
\(683\) 5043.00 0.282526 0.141263 0.989972i \(-0.454884\pi\)
0.141263 + 0.989972i \(0.454884\pi\)
\(684\) −8398.00 −0.469453
\(685\) −1620.00 −0.0903606
\(686\) −6820.00 −0.379576
\(687\) 6680.00 0.370972
\(688\) 34443.0 1.90861
\(689\) 2828.00 0.156369
\(690\) −1375.00 −0.0758628
\(691\) −6333.00 −0.348652 −0.174326 0.984688i \(-0.555775\pi\)
−0.174326 + 0.984688i \(0.555775\pi\)
\(692\) 16507.0 0.906795
\(693\) −572.000 −0.0313542
\(694\) 8115.00 0.443863
\(695\) −890.000 −0.0485750
\(696\) −1170.00 −0.0637194
\(697\) −5334.00 −0.289870
\(698\) 43185.0 2.34180
\(699\) 6423.00 0.347554
\(700\) −850.000 −0.0458957
\(701\) 27261.0 1.46881 0.734404 0.678713i \(-0.237462\pi\)
0.734404 + 0.678713i \(0.237462\pi\)
\(702\) 1855.00 0.0997329
\(703\) −2394.00 −0.128437
\(704\) 3157.00 0.169011
\(705\) 945.000 0.0504833
\(706\) 340.000 0.0181247
\(707\) −2012.00 −0.107028
\(708\) −12682.0 −0.673190
\(709\) 19844.0 1.05114 0.525569 0.850751i \(-0.323852\pi\)
0.525569 + 0.850751i \(0.323852\pi\)
\(710\) −20600.0 −1.08888
\(711\) 8788.00 0.463538
\(712\) 34290.0 1.80488
\(713\) 14355.0 0.753996
\(714\) −140.000 −0.00733805
\(715\) −385.000 −0.0201373
\(716\) −37434.0 −1.95387
\(717\) 5440.00 0.283348
\(718\) −48925.0 −2.54299
\(719\) −28410.0 −1.47359 −0.736797 0.676114i \(-0.763663\pi\)
−0.736797 + 0.676114i \(0.763663\pi\)
\(720\) 11570.0 0.598873
\(721\) −4004.00 −0.206819
\(722\) −1805.00 −0.0930404
\(723\) 155.000 0.00797305
\(724\) 18649.0 0.957299
\(725\) −650.000 −0.0332971
\(726\) 605.000 0.0309279
\(727\) −25323.0 −1.29185 −0.645927 0.763399i \(-0.723529\pi\)
−0.645927 + 0.763399i \(0.723529\pi\)
\(728\) −630.000 −0.0320733
\(729\) −15443.0 −0.784586
\(730\) 4225.00 0.214211
\(731\) 5418.00 0.274134
\(732\) −1343.00 −0.0678124
\(733\) 20104.0 1.01304 0.506520 0.862228i \(-0.330932\pi\)
0.506520 + 0.862228i \(0.330932\pi\)
\(734\) 45795.0 2.30289
\(735\) −1695.00 −0.0850626
\(736\) −4675.00 −0.234134
\(737\) −5907.00 −0.295234
\(738\) −49530.0 −2.47049
\(739\) 9704.00 0.483041 0.241521 0.970396i \(-0.422354\pi\)
0.241521 + 0.970396i \(0.422354\pi\)
\(740\) 10710.0 0.532037
\(741\) 133.000 0.00659363
\(742\) −4040.00 −0.199883
\(743\) 413.000 0.0203923 0.0101962 0.999948i \(-0.496754\pi\)
0.0101962 + 0.999948i \(0.496754\pi\)
\(744\) 11745.0 0.578753
\(745\) 7455.00 0.366618
\(746\) −13865.0 −0.680474
\(747\) −15626.0 −0.765362
\(748\) −2618.00 −0.127973
\(749\) −2288.00 −0.111618
\(750\) −625.000 −0.0304290
\(751\) 5572.00 0.270739 0.135370 0.990795i \(-0.456778\pi\)
0.135370 + 0.990795i \(0.456778\pi\)
\(752\) 16821.0 0.815690
\(753\) 6609.00 0.319848
\(754\) −910.000 −0.0439526
\(755\) 4300.00 0.207276
\(756\) −1802.00 −0.0866906
\(757\) −17915.0 −0.860148 −0.430074 0.902794i \(-0.641512\pi\)
−0.430074 + 0.902794i \(0.641512\pi\)
\(758\) 41630.0 1.99481
\(759\) 605.000 0.0289329
\(760\) 4275.00 0.204040
\(761\) 33118.0 1.57756 0.788782 0.614673i \(-0.210712\pi\)
0.788782 + 0.614673i \(0.210712\pi\)
\(762\) −855.000 −0.0406475
\(763\) −1532.00 −0.0726895
\(764\) −51374.0 −2.43278
\(765\) 1820.00 0.0860160
\(766\) 33220.0 1.56695
\(767\) −5222.00 −0.245835
\(768\) 8279.00 0.388988
\(769\) −21758.0 −1.02030 −0.510152 0.860084i \(-0.670411\pi\)
−0.510152 + 0.860084i \(0.670411\pi\)
\(770\) 550.000 0.0257411
\(771\) 2505.00 0.117011
\(772\) 11186.0 0.521493
\(773\) 13222.0 0.615216 0.307608 0.951513i \(-0.400471\pi\)
0.307608 + 0.951513i \(0.400471\pi\)
\(774\) 50310.0 2.33638
\(775\) 6525.00 0.302432
\(776\) −38970.0 −1.80276
\(777\) −252.000 −0.0116351
\(778\) 44400.0 2.04604
\(779\) −7239.00 −0.332945
\(780\) −595.000 −0.0273134
\(781\) 9064.00 0.415282
\(782\) −3850.00 −0.176056
\(783\) −1378.00 −0.0628936
\(784\) −30171.0 −1.37441
\(785\) −8665.00 −0.393971
\(786\) −9500.00 −0.431112
\(787\) 13862.0 0.627861 0.313931 0.949446i \(-0.398354\pi\)
0.313931 + 0.949446i \(0.398354\pi\)
\(788\) 7242.00 0.327393
\(789\) −442.000 −0.0199437
\(790\) −8450.00 −0.380554
\(791\) 4084.00 0.183578
\(792\) −12870.0 −0.577419
\(793\) −553.000 −0.0247637
\(794\) 15470.0 0.691448
\(795\) −2020.00 −0.0901157
\(796\) −21692.0 −0.965895
\(797\) −4274.00 −0.189953 −0.0949767 0.995479i \(-0.530278\pi\)
−0.0949767 + 0.995479i \(0.530278\pi\)
\(798\) −190.000 −0.00842848
\(799\) 2646.00 0.117157
\(800\) −2125.00 −0.0939126
\(801\) 19812.0 0.873936
\(802\) 30040.0 1.32263
\(803\) −1859.00 −0.0816970
\(804\) −9129.00 −0.400442
\(805\) 550.000 0.0240807
\(806\) 9135.00 0.399214
\(807\) −1226.00 −0.0534786
\(808\) −45270.0 −1.97103
\(809\) −23656.0 −1.02806 −0.514030 0.857772i \(-0.671848\pi\)
−0.514030 + 0.857772i \(0.671848\pi\)
\(810\) 16225.0 0.703813
\(811\) −35621.0 −1.54232 −0.771161 0.636641i \(-0.780323\pi\)
−0.771161 + 0.636641i \(0.780323\pi\)
\(812\) 884.000 0.0382048
\(813\) −8264.00 −0.356496
\(814\) −6930.00 −0.298398
\(815\) 19900.0 0.855296
\(816\) −1246.00 −0.0534543
\(817\) 7353.00 0.314870
\(818\) 28805.0 1.23123
\(819\) −364.000 −0.0155301
\(820\) 32385.0 1.37919
\(821\) 38723.0 1.64609 0.823046 0.567974i \(-0.192273\pi\)
0.823046 + 0.567974i \(0.192273\pi\)
\(822\) 1620.00 0.0687396
\(823\) 17768.0 0.752556 0.376278 0.926507i \(-0.377204\pi\)
0.376278 + 0.926507i \(0.377204\pi\)
\(824\) −90090.0 −3.80878
\(825\) 275.000 0.0116052
\(826\) 7460.00 0.314245
\(827\) −31116.0 −1.30835 −0.654177 0.756341i \(-0.726985\pi\)
−0.654177 + 0.756341i \(0.726985\pi\)
\(828\) −24310.0 −1.02033
\(829\) 24931.0 1.04450 0.522249 0.852793i \(-0.325093\pi\)
0.522249 + 0.852793i \(0.325093\pi\)
\(830\) 15025.0 0.628344
\(831\) 8128.00 0.339299
\(832\) 2009.00 0.0837134
\(833\) −4746.00 −0.197406
\(834\) 890.000 0.0369523
\(835\) −5295.00 −0.219450
\(836\) −3553.00 −0.146989
\(837\) 13833.0 0.571253
\(838\) 25315.0 1.04355
\(839\) 10697.0 0.440169 0.220084 0.975481i \(-0.429367\pi\)
0.220084 + 0.975481i \(0.429367\pi\)
\(840\) 450.000 0.0184839
\(841\) −23713.0 −0.972283
\(842\) 42685.0 1.74706
\(843\) −886.000 −0.0361986
\(844\) 76313.0 3.11232
\(845\) 10740.0 0.437239
\(846\) 24570.0 0.998504
\(847\) −242.000 −0.00981726
\(848\) −35956.0 −1.45605
\(849\) −5621.00 −0.227223
\(850\) −1750.00 −0.0706171
\(851\) −6930.00 −0.279151
\(852\) 14008.0 0.563270
\(853\) 4338.00 0.174127 0.0870635 0.996203i \(-0.472252\pi\)
0.0870635 + 0.996203i \(0.472252\pi\)
\(854\) 790.000 0.0316549
\(855\) 2470.00 0.0987979
\(856\) −51480.0 −2.05555
\(857\) 19186.0 0.764739 0.382369 0.924010i \(-0.375108\pi\)
0.382369 + 0.924010i \(0.375108\pi\)
\(858\) 385.000 0.0153190
\(859\) −37956.0 −1.50762 −0.753808 0.657095i \(-0.771785\pi\)
−0.753808 + 0.657095i \(0.771785\pi\)
\(860\) −32895.0 −1.30431
\(861\) −762.000 −0.0301613
\(862\) −29680.0 −1.17274
\(863\) −28396.0 −1.12006 −0.560030 0.828473i \(-0.689210\pi\)
−0.560030 + 0.828473i \(0.689210\pi\)
\(864\) −4505.00 −0.177388
\(865\) −4855.00 −0.190838
\(866\) −27205.0 −1.06751
\(867\) 4717.00 0.184772
\(868\) −8874.00 −0.347008
\(869\) 3718.00 0.145138
\(870\) 650.000 0.0253300
\(871\) −3759.00 −0.146233
\(872\) −34470.0 −1.33865
\(873\) −22516.0 −0.872911
\(874\) −5225.00 −0.202218
\(875\) 250.000 0.00965891
\(876\) −2873.00 −0.110810
\(877\) 49966.0 1.92387 0.961934 0.273282i \(-0.0881094\pi\)
0.961934 + 0.273282i \(0.0881094\pi\)
\(878\) −57500.0 −2.21017
\(879\) 386.000 0.0148117
\(880\) 4895.00 0.187512
\(881\) 38733.0 1.48121 0.740606 0.671939i \(-0.234538\pi\)
0.740606 + 0.671939i \(0.234538\pi\)
\(882\) −44070.0 −1.68244
\(883\) 45426.0 1.73126 0.865632 0.500680i \(-0.166917\pi\)
0.865632 + 0.500680i \(0.166917\pi\)
\(884\) −1666.00 −0.0633865
\(885\) 3730.00 0.141675
\(886\) −16130.0 −0.611623
\(887\) 29496.0 1.11655 0.558274 0.829656i \(-0.311464\pi\)
0.558274 + 0.829656i \(0.311464\pi\)
\(888\) −5670.00 −0.214271
\(889\) 342.000 0.0129025
\(890\) −19050.0 −0.717480
\(891\) −7139.00 −0.268424
\(892\) −12750.0 −0.478589
\(893\) 3591.00 0.134567
\(894\) −7455.00 −0.278895
\(895\) 11010.0 0.411200
\(896\) −4230.00 −0.157717
\(897\) 385.000 0.0143309
\(898\) −81750.0 −3.03790
\(899\) −6786.00 −0.251753
\(900\) −11050.0 −0.409259
\(901\) −5656.00 −0.209133
\(902\) −20955.0 −0.773531
\(903\) 774.000 0.0285239
\(904\) 91890.0 3.38077
\(905\) −5485.00 −0.201467
\(906\) −4300.00 −0.157680
\(907\) 17796.0 0.651496 0.325748 0.945457i \(-0.394384\pi\)
0.325748 + 0.945457i \(0.394384\pi\)
\(908\) −34272.0 −1.25260
\(909\) −26156.0 −0.954389
\(910\) 350.000 0.0127499
\(911\) −8661.00 −0.314985 −0.157493 0.987520i \(-0.550341\pi\)
−0.157493 + 0.987520i \(0.550341\pi\)
\(912\) −1691.00 −0.0613976
\(913\) −6611.00 −0.239641
\(914\) −59255.0 −2.14440
\(915\) 395.000 0.0142714
\(916\) −113560. −4.09621
\(917\) 3800.00 0.136845
\(918\) −3710.00 −0.133386
\(919\) 40505.0 1.45390 0.726951 0.686689i \(-0.240937\pi\)
0.726951 + 0.686689i \(0.240937\pi\)
\(920\) 12375.0 0.443469
\(921\) −2480.00 −0.0887283
\(922\) 49455.0 1.76650
\(923\) 5768.00 0.205695
\(924\) −374.000 −0.0133157
\(925\) −3150.00 −0.111969
\(926\) 85440.0 3.03211
\(927\) −52052.0 −1.84424
\(928\) 2210.00 0.0781754
\(929\) 563.000 0.0198831 0.00994157 0.999951i \(-0.496835\pi\)
0.00994157 + 0.999951i \(0.496835\pi\)
\(930\) −6525.00 −0.230068
\(931\) −6441.00 −0.226740
\(932\) −109191. −3.83763
\(933\) −8242.00 −0.289208
\(934\) −23580.0 −0.826083
\(935\) 770.000 0.0269323
\(936\) −8190.00 −0.286003
\(937\) 41626.0 1.45129 0.725647 0.688067i \(-0.241541\pi\)
0.725647 + 0.688067i \(0.241541\pi\)
\(938\) 5370.00 0.186926
\(939\) 510.000 0.0177244
\(940\) −16065.0 −0.557428
\(941\) −17508.0 −0.606530 −0.303265 0.952906i \(-0.598077\pi\)
−0.303265 + 0.952906i \(0.598077\pi\)
\(942\) 8665.00 0.299704
\(943\) −20955.0 −0.723636
\(944\) 66394.0 2.28913
\(945\) 530.000 0.0182443
\(946\) 21285.0 0.731538
\(947\) 5208.00 0.178709 0.0893544 0.996000i \(-0.471520\pi\)
0.0893544 + 0.996000i \(0.471520\pi\)
\(948\) 5746.00 0.196858
\(949\) −1183.00 −0.0404655
\(950\) −2375.00 −0.0811107
\(951\) 8748.00 0.298290
\(952\) 1260.00 0.0428958
\(953\) −1334.00 −0.0453437 −0.0226718 0.999743i \(-0.507217\pi\)
−0.0226718 + 0.999743i \(0.507217\pi\)
\(954\) −52520.0 −1.78239
\(955\) 15110.0 0.511988
\(956\) −92480.0 −3.12868
\(957\) −286.000 −0.00966047
\(958\) −1635.00 −0.0551403
\(959\) −648.000 −0.0218196
\(960\) −1435.00 −0.0482442
\(961\) 38330.0 1.28663
\(962\) −4410.00 −0.147801
\(963\) −29744.0 −0.995314
\(964\) −2635.00 −0.0880370
\(965\) −3290.00 −0.109750
\(966\) −550.000 −0.0183188
\(967\) −46050.0 −1.53140 −0.765702 0.643195i \(-0.777608\pi\)
−0.765702 + 0.643195i \(0.777608\pi\)
\(968\) −5445.00 −0.180794
\(969\) −266.000 −0.00881853
\(970\) 21650.0 0.716639
\(971\) 44770.0 1.47965 0.739824 0.672801i \(-0.234909\pi\)
0.739824 + 0.672801i \(0.234909\pi\)
\(972\) −35360.0 −1.16684
\(973\) −356.000 −0.0117295
\(974\) −70.0000 −0.00230282
\(975\) 175.000 0.00574819
\(976\) 7031.00 0.230591
\(977\) 17023.0 0.557435 0.278718 0.960373i \(-0.410091\pi\)
0.278718 + 0.960373i \(0.410091\pi\)
\(978\) −19900.0 −0.650646
\(979\) 8382.00 0.273636
\(980\) 28815.0 0.939246
\(981\) −19916.0 −0.648184
\(982\) −91910.0 −2.98673
\(983\) −1698.00 −0.0550944 −0.0275472 0.999621i \(-0.508770\pi\)
−0.0275472 + 0.999621i \(0.508770\pi\)
\(984\) −17145.0 −0.555450
\(985\) −2130.00 −0.0689010
\(986\) 1820.00 0.0587836
\(987\) 378.000 0.0121903
\(988\) −2261.00 −0.0728057
\(989\) 21285.0 0.684351
\(990\) 7150.00 0.229537
\(991\) 46096.0 1.47759 0.738793 0.673932i \(-0.235396\pi\)
0.738793 + 0.673932i \(0.235396\pi\)
\(992\) −22185.0 −0.710055
\(993\) −6742.00 −0.215459
\(994\) −8240.00 −0.262935
\(995\) 6380.00 0.203276
\(996\) −10217.0 −0.325038
\(997\) −15636.0 −0.496687 −0.248344 0.968672i \(-0.579886\pi\)
−0.248344 + 0.968672i \(0.579886\pi\)
\(998\) 3725.00 0.118149
\(999\) −6678.00 −0.211494
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 1045.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.4.a.a.1.1 1 1.1 even 1 trivial