Properties

Label 294.4.a.n.1.2
Level $294$
Weight $4$
Character 294.1
Self dual yes
Analytic conductor $17.347$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 294.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(17.3465615417\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{1345}) \)
Defining polynomial: \(x^{2} - x - 336\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-17.8371\) of defining polynomial
Character \(\chi\) \(=\) 294.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +20.8371 q^{5} +6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +20.8371 q^{5} +6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} +41.6742 q^{10} +15.1629 q^{11} +12.0000 q^{12} +2.16288 q^{13} +62.5114 q^{15} +16.0000 q^{16} -119.348 q^{17} +18.0000 q^{18} -33.5114 q^{19} +83.3485 q^{20} +30.3258 q^{22} +0.651517 q^{23} +24.0000 q^{24} +309.186 q^{25} +4.32576 q^{26} +27.0000 q^{27} -163.208 q^{29} +125.023 q^{30} -223.326 q^{31} +32.0000 q^{32} +45.4886 q^{33} -238.697 q^{34} +36.0000 q^{36} +168.534 q^{37} -67.0227 q^{38} +6.48864 q^{39} +166.697 q^{40} -323.023 q^{41} +221.557 q^{43} +60.6515 q^{44} +187.534 q^{45} +1.30303 q^{46} +508.045 q^{47} +48.0000 q^{48} +618.371 q^{50} -358.045 q^{51} +8.65152 q^{52} -176.511 q^{53} +54.0000 q^{54} +315.951 q^{55} -100.534 q^{57} -326.417 q^{58} +454.928 q^{59} +250.045 q^{60} +38.6515 q^{61} -446.652 q^{62} +64.0000 q^{64} +45.0682 q^{65} +90.9773 q^{66} +141.792 q^{67} -477.394 q^{68} +1.95455 q^{69} +602.742 q^{71} +72.0000 q^{72} -1102.30 q^{73} +337.068 q^{74} +927.557 q^{75} -134.045 q^{76} +12.9773 q^{78} -116.303 q^{79} +333.394 q^{80} +81.0000 q^{81} -646.045 q^{82} -568.928 q^{83} -2486.88 q^{85} +443.114 q^{86} -489.625 q^{87} +121.303 q^{88} -383.159 q^{89} +375.068 q^{90} +2.60607 q^{92} -669.977 q^{93} +1016.09 q^{94} -698.280 q^{95} +96.0000 q^{96} +334.701 q^{97} +136.466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 4q^{2} + 6q^{3} + 8q^{4} + 5q^{5} + 12q^{6} + 16q^{8} + 18q^{9} + O(q^{10}) \) \( 2q + 4q^{2} + 6q^{3} + 8q^{4} + 5q^{5} + 12q^{6} + 16q^{8} + 18q^{9} + 10q^{10} + 67q^{11} + 24q^{12} + 41q^{13} + 15q^{15} + 32q^{16} - 92q^{17} + 36q^{18} + 43q^{19} + 20q^{20} + 134q^{22} + 148q^{23} + 48q^{24} + 435q^{25} + 82q^{26} + 54q^{27} + 77q^{29} + 30q^{30} - 520q^{31} + 64q^{32} + 201q^{33} - 184q^{34} + 72q^{36} + 7q^{37} + 86q^{38} + 123q^{39} + 40q^{40} - 426q^{41} - 107q^{43} + 268q^{44} + 45q^{45} + 296q^{46} + 576q^{47} + 96q^{48} + 870q^{50} - 276q^{51} + 164q^{52} - 243q^{53} + 108q^{54} - 505q^{55} + 129q^{57} + 154q^{58} - 7q^{59} + 60q^{60} + 224q^{61} - 1040q^{62} + 128q^{64} - 570q^{65} + 402q^{66} + 687q^{67} - 368q^{68} + 444q^{69} + 472q^{71} + 144q^{72} - 921q^{73} + 14q^{74} + 1305q^{75} + 172q^{76} + 246q^{78} - 526q^{79} + 80q^{80} + 162q^{81} - 852q^{82} - 221q^{83} - 2920q^{85} - 214q^{86} + 231q^{87} + 536q^{88} + 774q^{89} + 90q^{90} + 592q^{92} - 1560q^{93} + 1152q^{94} - 1910q^{95} + 192q^{96} + 1953q^{97} + 603q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) 3.00000 0.577350
\(4\) 4.00000 0.500000
\(5\) 20.8371 1.86373 0.931864 0.362807i \(-0.118182\pi\)
0.931864 + 0.362807i \(0.118182\pi\)
\(6\) 6.00000 0.408248
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) 41.6742 1.31786
\(11\) 15.1629 0.415616 0.207808 0.978170i \(-0.433367\pi\)
0.207808 + 0.978170i \(0.433367\pi\)
\(12\) 12.0000 0.288675
\(13\) 2.16288 0.0461442 0.0230721 0.999734i \(-0.492655\pi\)
0.0230721 + 0.999734i \(0.492655\pi\)
\(14\) 0 0
\(15\) 62.5114 1.07602
\(16\) 16.0000 0.250000
\(17\) −119.348 −1.70272 −0.851361 0.524581i \(-0.824222\pi\)
−0.851361 + 0.524581i \(0.824222\pi\)
\(18\) 18.0000 0.235702
\(19\) −33.5114 −0.404633 −0.202317 0.979320i \(-0.564847\pi\)
−0.202317 + 0.979320i \(0.564847\pi\)
\(20\) 83.3485 0.931864
\(21\) 0 0
\(22\) 30.3258 0.293885
\(23\) 0.651517 0.00590655 0.00295327 0.999996i \(-0.499060\pi\)
0.00295327 + 0.999996i \(0.499060\pi\)
\(24\) 24.0000 0.204124
\(25\) 309.186 2.47348
\(26\) 4.32576 0.0326289
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −163.208 −1.04507 −0.522535 0.852618i \(-0.675014\pi\)
−0.522535 + 0.852618i \(0.675014\pi\)
\(30\) 125.023 0.760864
\(31\) −223.326 −1.29389 −0.646943 0.762538i \(-0.723953\pi\)
−0.646943 + 0.762538i \(0.723953\pi\)
\(32\) 32.0000 0.176777
\(33\) 45.4886 0.239956
\(34\) −238.697 −1.20401
\(35\) 0 0
\(36\) 36.0000 0.166667
\(37\) 168.534 0.748833 0.374417 0.927261i \(-0.377843\pi\)
0.374417 + 0.927261i \(0.377843\pi\)
\(38\) −67.0227 −0.286119
\(39\) 6.48864 0.0266414
\(40\) 166.697 0.658928
\(41\) −323.023 −1.23043 −0.615216 0.788359i \(-0.710931\pi\)
−0.615216 + 0.788359i \(0.710931\pi\)
\(42\) 0 0
\(43\) 221.557 0.785746 0.392873 0.919593i \(-0.371481\pi\)
0.392873 + 0.919593i \(0.371481\pi\)
\(44\) 60.6515 0.207808
\(45\) 187.534 0.621243
\(46\) 1.30303 0.00417656
\(47\) 508.045 1.57672 0.788362 0.615211i \(-0.210929\pi\)
0.788362 + 0.615211i \(0.210929\pi\)
\(48\) 48.0000 0.144338
\(49\) 0 0
\(50\) 618.371 1.74902
\(51\) −358.045 −0.983066
\(52\) 8.65152 0.0230721
\(53\) −176.511 −0.457466 −0.228733 0.973489i \(-0.573458\pi\)
−0.228733 + 0.973489i \(0.573458\pi\)
\(54\) 54.0000 0.136083
\(55\) 315.951 0.774596
\(56\) 0 0
\(57\) −100.534 −0.233615
\(58\) −326.417 −0.738976
\(59\) 454.928 1.00384 0.501920 0.864914i \(-0.332627\pi\)
0.501920 + 0.864914i \(0.332627\pi\)
\(60\) 250.045 0.538012
\(61\) 38.6515 0.0811282 0.0405641 0.999177i \(-0.487085\pi\)
0.0405641 + 0.999177i \(0.487085\pi\)
\(62\) −446.652 −0.914916
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 45.0682 0.0860003
\(66\) 90.9773 0.169675
\(67\) 141.792 0.258546 0.129273 0.991609i \(-0.458736\pi\)
0.129273 + 0.991609i \(0.458736\pi\)
\(68\) −477.394 −0.851361
\(69\) 1.95455 0.00341015
\(70\) 0 0
\(71\) 602.742 1.00750 0.503749 0.863850i \(-0.331954\pi\)
0.503749 + 0.863850i \(0.331954\pi\)
\(72\) 72.0000 0.117851
\(73\) −1102.30 −1.76732 −0.883660 0.468129i \(-0.844928\pi\)
−0.883660 + 0.468129i \(0.844928\pi\)
\(74\) 337.068 0.529505
\(75\) 927.557 1.42807
\(76\) −134.045 −0.202317
\(77\) 0 0
\(78\) 12.9773 0.0188383
\(79\) −116.303 −0.165634 −0.0828172 0.996565i \(-0.526392\pi\)
−0.0828172 + 0.996565i \(0.526392\pi\)
\(80\) 333.394 0.465932
\(81\) 81.0000 0.111111
\(82\) −646.045 −0.870046
\(83\) −568.928 −0.752385 −0.376193 0.926542i \(-0.622767\pi\)
−0.376193 + 0.926542i \(0.622767\pi\)
\(84\) 0 0
\(85\) −2486.88 −3.17341
\(86\) 443.114 0.555607
\(87\) −489.625 −0.603371
\(88\) 121.303 0.146943
\(89\) −383.159 −0.456346 −0.228173 0.973621i \(-0.573275\pi\)
−0.228173 + 0.973621i \(0.573275\pi\)
\(90\) 375.068 0.439285
\(91\) 0 0
\(92\) 2.60607 0.00295327
\(93\) −669.977 −0.747026
\(94\) 1016.09 1.11491
\(95\) −698.280 −0.754127
\(96\) 96.0000 0.102062
\(97\) 334.701 0.350348 0.175174 0.984538i \(-0.443951\pi\)
0.175174 + 0.984538i \(0.443951\pi\)
\(98\) 0 0
\(99\) 136.466 0.138539
\(100\) 1236.74 1.23674
\(101\) −14.7424 −0.0145240 −0.00726201 0.999974i \(-0.502312\pi\)
−0.00726201 + 0.999974i \(0.502312\pi\)
\(102\) −716.091 −0.695133
\(103\) −841.420 −0.804928 −0.402464 0.915436i \(-0.631846\pi\)
−0.402464 + 0.915436i \(0.631846\pi\)
\(104\) 17.3030 0.0163144
\(105\) 0 0
\(106\) −353.023 −0.323477
\(107\) −715.670 −0.646603 −0.323301 0.946296i \(-0.604793\pi\)
−0.323301 + 0.946296i \(0.604793\pi\)
\(108\) 108.000 0.0962250
\(109\) 600.019 0.527260 0.263630 0.964624i \(-0.415080\pi\)
0.263630 + 0.964624i \(0.415080\pi\)
\(110\) 631.901 0.547722
\(111\) 505.602 0.432339
\(112\) 0 0
\(113\) 622.644 0.518349 0.259174 0.965831i \(-0.416550\pi\)
0.259174 + 0.965831i \(0.416550\pi\)
\(114\) −201.068 −0.165191
\(115\) 13.5757 0.0110082
\(116\) −652.833 −0.522535
\(117\) 19.4659 0.0153814
\(118\) 909.856 0.709822
\(119\) 0 0
\(120\) 500.091 0.380432
\(121\) −1101.09 −0.827263
\(122\) 77.3030 0.0573663
\(123\) −969.068 −0.710390
\(124\) −893.303 −0.646943
\(125\) 3837.90 2.74618
\(126\) 0 0
\(127\) −180.076 −0.125820 −0.0629100 0.998019i \(-0.520038\pi\)
−0.0629100 + 0.998019i \(0.520038\pi\)
\(128\) 128.000 0.0883883
\(129\) 664.670 0.453651
\(130\) 90.1363 0.0608114
\(131\) 217.860 0.145302 0.0726508 0.997357i \(-0.476854\pi\)
0.0726508 + 0.997357i \(0.476854\pi\)
\(132\) 181.955 0.119978
\(133\) 0 0
\(134\) 283.583 0.182820
\(135\) 562.602 0.358675
\(136\) −954.788 −0.602003
\(137\) −2601.86 −1.62257 −0.811283 0.584654i \(-0.801230\pi\)
−0.811283 + 0.584654i \(0.801230\pi\)
\(138\) 3.90910 0.00241134
\(139\) −2651.55 −1.61800 −0.808998 0.587811i \(-0.799990\pi\)
−0.808998 + 0.587811i \(0.799990\pi\)
\(140\) 0 0
\(141\) 1524.14 0.910322
\(142\) 1205.48 0.712409
\(143\) 32.7955 0.0191783
\(144\) 144.000 0.0833333
\(145\) −3400.79 −1.94773
\(146\) −2204.60 −1.24968
\(147\) 0 0
\(148\) 674.136 0.374417
\(149\) 581.023 0.319458 0.159729 0.987161i \(-0.448938\pi\)
0.159729 + 0.987161i \(0.448938\pi\)
\(150\) 1855.11 1.00980
\(151\) −615.390 −0.331654 −0.165827 0.986155i \(-0.553029\pi\)
−0.165827 + 0.986155i \(0.553029\pi\)
\(152\) −268.091 −0.143059
\(153\) −1074.14 −0.567574
\(154\) 0 0
\(155\) −4653.47 −2.41145
\(156\) 25.9546 0.0133207
\(157\) −306.932 −0.156024 −0.0780122 0.996952i \(-0.524857\pi\)
−0.0780122 + 0.996952i \(0.524857\pi\)
\(158\) −232.606 −0.117121
\(159\) −529.534 −0.264118
\(160\) 666.788 0.329464
\(161\) 0 0
\(162\) 162.000 0.0785674
\(163\) 3514.50 1.68882 0.844408 0.535701i \(-0.179953\pi\)
0.844408 + 0.535701i \(0.179953\pi\)
\(164\) −1292.09 −0.615216
\(165\) 947.852 0.447213
\(166\) −1137.86 −0.532017
\(167\) 1123.30 0.520502 0.260251 0.965541i \(-0.416195\pi\)
0.260251 + 0.965541i \(0.416195\pi\)
\(168\) 0 0
\(169\) −2192.32 −0.997871
\(170\) −4973.76 −2.24394
\(171\) −301.602 −0.134878
\(172\) 886.227 0.392873
\(173\) 1530.60 0.672655 0.336327 0.941745i \(-0.390815\pi\)
0.336327 + 0.941745i \(0.390815\pi\)
\(174\) −979.250 −0.426648
\(175\) 0 0
\(176\) 242.606 0.103904
\(177\) 1364.78 0.579568
\(178\) −766.318 −0.322685
\(179\) 3413.43 1.42532 0.712659 0.701511i \(-0.247491\pi\)
0.712659 + 0.701511i \(0.247491\pi\)
\(180\) 750.136 0.310621
\(181\) 1286.71 0.528399 0.264200 0.964468i \(-0.414892\pi\)
0.264200 + 0.964468i \(0.414892\pi\)
\(182\) 0 0
\(183\) 115.955 0.0468394
\(184\) 5.21213 0.00208828
\(185\) 3511.77 1.39562
\(186\) −1339.95 −0.528227
\(187\) −1809.67 −0.707679
\(188\) 2032.18 0.788362
\(189\) 0 0
\(190\) −1396.56 −0.533248
\(191\) 1055.30 0.399783 0.199891 0.979818i \(-0.435941\pi\)
0.199891 + 0.979818i \(0.435941\pi\)
\(192\) 192.000 0.0721688
\(193\) −4770.84 −1.77934 −0.889670 0.456604i \(-0.849066\pi\)
−0.889670 + 0.456604i \(0.849066\pi\)
\(194\) 669.402 0.247733
\(195\) 135.205 0.0496523
\(196\) 0 0
\(197\) 1622.31 0.586725 0.293363 0.956001i \(-0.405226\pi\)
0.293363 + 0.956001i \(0.405226\pi\)
\(198\) 272.932 0.0979617
\(199\) −3550.14 −1.26464 −0.632318 0.774709i \(-0.717896\pi\)
−0.632318 + 0.774709i \(0.717896\pi\)
\(200\) 2473.48 0.874509
\(201\) 425.375 0.149272
\(202\) −29.4848 −0.0102700
\(203\) 0 0
\(204\) −1432.18 −0.491533
\(205\) −6730.86 −2.29319
\(206\) −1682.84 −0.569170
\(207\) 5.86365 0.00196885
\(208\) 34.6061 0.0115361
\(209\) −508.129 −0.168172
\(210\) 0 0
\(211\) 4653.39 1.51826 0.759129 0.650941i \(-0.225625\pi\)
0.759129 + 0.650941i \(0.225625\pi\)
\(212\) −706.045 −0.228733
\(213\) 1808.23 0.581679
\(214\) −1431.34 −0.457217
\(215\) 4616.61 1.46442
\(216\) 216.000 0.0680414
\(217\) 0 0
\(218\) 1200.04 0.372829
\(219\) −3306.90 −1.02036
\(220\) 1263.80 0.387298
\(221\) −258.136 −0.0785707
\(222\) 1011.20 0.305710
\(223\) −4649.53 −1.39621 −0.698107 0.715993i \(-0.745974\pi\)
−0.698107 + 0.715993i \(0.745974\pi\)
\(224\) 0 0
\(225\) 2782.67 0.824495
\(226\) 1245.29 0.366528
\(227\) 4151.72 1.21392 0.606958 0.794734i \(-0.292389\pi\)
0.606958 + 0.794734i \(0.292389\pi\)
\(228\) −402.136 −0.116808
\(229\) 4263.63 1.23034 0.615172 0.788393i \(-0.289087\pi\)
0.615172 + 0.788393i \(0.289087\pi\)
\(230\) 27.1515 0.00778398
\(231\) 0 0
\(232\) −1305.67 −0.369488
\(233\) 3049.90 0.857535 0.428768 0.903415i \(-0.358948\pi\)
0.428768 + 0.903415i \(0.358948\pi\)
\(234\) 38.9318 0.0108763
\(235\) 10586.2 2.93859
\(236\) 1819.71 0.501920
\(237\) −348.909 −0.0956290
\(238\) 0 0
\(239\) 3987.20 1.07912 0.539562 0.841946i \(-0.318590\pi\)
0.539562 + 0.841946i \(0.318590\pi\)
\(240\) 1000.18 0.269006
\(241\) −624.648 −0.166959 −0.0834795 0.996509i \(-0.526603\pi\)
−0.0834795 + 0.996509i \(0.526603\pi\)
\(242\) −2202.17 −0.584963
\(243\) 243.000 0.0641500
\(244\) 154.606 0.0405641
\(245\) 0 0
\(246\) −1938.14 −0.502321
\(247\) −72.4810 −0.0186715
\(248\) −1786.61 −0.457458
\(249\) −1706.78 −0.434390
\(250\) 7675.80 1.94184
\(251\) −1328.78 −0.334152 −0.167076 0.985944i \(-0.553432\pi\)
−0.167076 + 0.985944i \(0.553432\pi\)
\(252\) 0 0
\(253\) 9.87887 0.00245486
\(254\) −360.152 −0.0889682
\(255\) −7460.64 −1.83217
\(256\) 256.000 0.0625000
\(257\) −3226.18 −0.783049 −0.391525 0.920168i \(-0.628052\pi\)
−0.391525 + 0.920168i \(0.628052\pi\)
\(258\) 1329.34 0.320780
\(259\) 0 0
\(260\) 180.273 0.0430001
\(261\) −1468.87 −0.348357
\(262\) 435.720 0.102744
\(263\) 3250.61 0.762135 0.381067 0.924547i \(-0.375557\pi\)
0.381067 + 0.924547i \(0.375557\pi\)
\(264\) 363.909 0.0848373
\(265\) −3677.99 −0.852593
\(266\) 0 0
\(267\) −1149.48 −0.263471
\(268\) 567.167 0.129273
\(269\) 2826.04 0.640546 0.320273 0.947325i \(-0.396225\pi\)
0.320273 + 0.947325i \(0.396225\pi\)
\(270\) 1125.20 0.253621
\(271\) −2396.77 −0.537245 −0.268622 0.963246i \(-0.586568\pi\)
−0.268622 + 0.963246i \(0.586568\pi\)
\(272\) −1909.58 −0.425680
\(273\) 0 0
\(274\) −5203.71 −1.14733
\(275\) 4688.14 1.02802
\(276\) 7.81820 0.00170507
\(277\) 1820.47 0.394878 0.197439 0.980315i \(-0.436738\pi\)
0.197439 + 0.980315i \(0.436738\pi\)
\(278\) −5303.10 −1.14410
\(279\) −2009.93 −0.431296
\(280\) 0 0
\(281\) 3083.81 0.654679 0.327339 0.944907i \(-0.393848\pi\)
0.327339 + 0.944907i \(0.393848\pi\)
\(282\) 3048.27 0.643695
\(283\) 2554.77 0.536626 0.268313 0.963332i \(-0.413534\pi\)
0.268313 + 0.963332i \(0.413534\pi\)
\(284\) 2410.97 0.503749
\(285\) −2094.84 −0.435395
\(286\) 65.5910 0.0135611
\(287\) 0 0
\(288\) 288.000 0.0589256
\(289\) 9331.06 1.89926
\(290\) −6801.58 −1.37725
\(291\) 1004.10 0.202273
\(292\) −4409.20 −0.883660
\(293\) −1846.47 −0.368163 −0.184081 0.982911i \(-0.558931\pi\)
−0.184081 + 0.982911i \(0.558931\pi\)
\(294\) 0 0
\(295\) 9479.39 1.87089
\(296\) 1348.27 0.264753
\(297\) 409.398 0.0799854
\(298\) 1162.05 0.225891
\(299\) 1.40915 0.000272553 0
\(300\) 3710.23 0.714034
\(301\) 0 0
\(302\) −1230.78 −0.234515
\(303\) −44.2272 −0.00838544
\(304\) −536.182 −0.101158
\(305\) 805.386 0.151201
\(306\) −2148.27 −0.401335
\(307\) 7041.50 1.30905 0.654527 0.756039i \(-0.272868\pi\)
0.654527 + 0.756039i \(0.272868\pi\)
\(308\) 0 0
\(309\) −2524.26 −0.464726
\(310\) −9306.93 −1.70516
\(311\) −2685.99 −0.489738 −0.244869 0.969556i \(-0.578745\pi\)
−0.244869 + 0.969556i \(0.578745\pi\)
\(312\) 51.9091 0.00941915
\(313\) 2219.19 0.400754 0.200377 0.979719i \(-0.435783\pi\)
0.200377 + 0.979719i \(0.435783\pi\)
\(314\) −613.864 −0.110326
\(315\) 0 0
\(316\) −465.212 −0.0828172
\(317\) 2221.26 0.393560 0.196780 0.980448i \(-0.436952\pi\)
0.196780 + 0.980448i \(0.436952\pi\)
\(318\) −1059.07 −0.186760
\(319\) −2474.71 −0.434348
\(320\) 1333.58 0.232966
\(321\) −2147.01 −0.373316
\(322\) 0 0
\(323\) 3999.53 0.688978
\(324\) 324.000 0.0555556
\(325\) 668.731 0.114137
\(326\) 7029.00 1.19417
\(327\) 1800.06 0.304414
\(328\) −2584.18 −0.435023
\(329\) 0 0
\(330\) 1895.70 0.316228
\(331\) 4154.06 0.689812 0.344906 0.938637i \(-0.387911\pi\)
0.344906 + 0.938637i \(0.387911\pi\)
\(332\) −2275.71 −0.376193
\(333\) 1516.81 0.249611
\(334\) 2246.61 0.368050
\(335\) 2954.53 0.481860
\(336\) 0 0
\(337\) −254.167 −0.0410841 −0.0205420 0.999789i \(-0.506539\pi\)
−0.0205420 + 0.999789i \(0.506539\pi\)
\(338\) −4384.64 −0.705601
\(339\) 1867.93 0.299269
\(340\) −9947.52 −1.58671
\(341\) −3386.26 −0.537761
\(342\) −603.205 −0.0953730
\(343\) 0 0
\(344\) 1772.45 0.277803
\(345\) 40.7272 0.00635559
\(346\) 3061.20 0.475639
\(347\) −6224.64 −0.962986 −0.481493 0.876450i \(-0.659905\pi\)
−0.481493 + 0.876450i \(0.659905\pi\)
\(348\) −1958.50 −0.301686
\(349\) 9732.21 1.49270 0.746352 0.665552i \(-0.231804\pi\)
0.746352 + 0.665552i \(0.231804\pi\)
\(350\) 0 0
\(351\) 58.3977 0.00888046
\(352\) 485.212 0.0734713
\(353\) 1425.61 0.214951 0.107476 0.994208i \(-0.465723\pi\)
0.107476 + 0.994208i \(0.465723\pi\)
\(354\) 2729.57 0.409816
\(355\) 12559.4 1.87770
\(356\) −1532.64 −0.228173
\(357\) 0 0
\(358\) 6826.86 1.00785
\(359\) −5766.49 −0.847754 −0.423877 0.905720i \(-0.639331\pi\)
−0.423877 + 0.905720i \(0.639331\pi\)
\(360\) 1500.27 0.219643
\(361\) −5735.99 −0.836272
\(362\) 2573.42 0.373635
\(363\) −3303.26 −0.477621
\(364\) 0 0
\(365\) −22968.7 −3.29381
\(366\) 231.909 0.0331204
\(367\) 11545.3 1.64213 0.821065 0.570834i \(-0.193380\pi\)
0.821065 + 0.570834i \(0.193380\pi\)
\(368\) 10.4243 0.00147664
\(369\) −2907.20 −0.410144
\(370\) 7023.53 0.986854
\(371\) 0 0
\(372\) −2679.91 −0.373513
\(373\) −6479.57 −0.899463 −0.449731 0.893164i \(-0.648480\pi\)
−0.449731 + 0.893164i \(0.648480\pi\)
\(374\) −3619.33 −0.500404
\(375\) 11513.7 1.58551
\(376\) 4064.36 0.557456
\(377\) −353.000 −0.0482239
\(378\) 0 0
\(379\) 611.996 0.0829449 0.0414725 0.999140i \(-0.486795\pi\)
0.0414725 + 0.999140i \(0.486795\pi\)
\(380\) −2793.12 −0.377063
\(381\) −540.227 −0.0726422
\(382\) 2110.59 0.282689
\(383\) 4360.81 0.581794 0.290897 0.956754i \(-0.406046\pi\)
0.290897 + 0.956754i \(0.406046\pi\)
\(384\) 384.000 0.0510310
\(385\) 0 0
\(386\) −9541.68 −1.25818
\(387\) 1994.01 0.261915
\(388\) 1338.80 0.175174
\(389\) −13146.9 −1.71356 −0.856781 0.515681i \(-0.827539\pi\)
−0.856781 + 0.515681i \(0.827539\pi\)
\(390\) 270.409 0.0351095
\(391\) −77.7575 −0.0100572
\(392\) 0 0
\(393\) 653.580 0.0838899
\(394\) 3244.62 0.414877
\(395\) −2423.42 −0.308697
\(396\) 545.864 0.0692694
\(397\) −8478.04 −1.07179 −0.535895 0.844285i \(-0.680026\pi\)
−0.535895 + 0.844285i \(0.680026\pi\)
\(398\) −7100.27 −0.894232
\(399\) 0 0
\(400\) 4946.97 0.618371
\(401\) 2803.00 0.349065 0.174533 0.984651i \(-0.444159\pi\)
0.174533 + 0.984651i \(0.444159\pi\)
\(402\) 850.750 0.105551
\(403\) −483.027 −0.0597054
\(404\) −58.9697 −0.00726201
\(405\) 1687.81 0.207081
\(406\) 0 0
\(407\) 2555.46 0.311227
\(408\) −2864.36 −0.347566
\(409\) −6385.39 −0.771973 −0.385987 0.922504i \(-0.626139\pi\)
−0.385987 + 0.922504i \(0.626139\pi\)
\(410\) −13461.7 −1.62153
\(411\) −7805.57 −0.936789
\(412\) −3365.68 −0.402464
\(413\) 0 0
\(414\) 11.7273 0.00139219
\(415\) −11854.8 −1.40224
\(416\) 69.2121 0.00815722
\(417\) −7954.65 −0.934151
\(418\) −1016.26 −0.118916
\(419\) 4831.66 0.563346 0.281673 0.959510i \(-0.409111\pi\)
0.281673 + 0.959510i \(0.409111\pi\)
\(420\) 0 0
\(421\) 7475.37 0.865385 0.432693 0.901542i \(-0.357564\pi\)
0.432693 + 0.901542i \(0.357564\pi\)
\(422\) 9306.77 1.07357
\(423\) 4572.41 0.525575
\(424\) −1412.09 −0.161739
\(425\) −36900.8 −4.21165
\(426\) 3616.45 0.411309
\(427\) 0 0
\(428\) −2862.68 −0.323301
\(429\) 98.3864 0.0110726
\(430\) 9233.21 1.03550
\(431\) 6991.93 0.781414 0.390707 0.920515i \(-0.372231\pi\)
0.390707 + 0.920515i \(0.372231\pi\)
\(432\) 432.000 0.0481125
\(433\) −7699.26 −0.854510 −0.427255 0.904131i \(-0.640519\pi\)
−0.427255 + 0.904131i \(0.640519\pi\)
\(434\) 0 0
\(435\) −10202.4 −1.12452
\(436\) 2400.08 0.263630
\(437\) −21.8332 −0.00238999
\(438\) −6613.80 −0.721505
\(439\) 9412.32 1.02329 0.511646 0.859196i \(-0.329036\pi\)
0.511646 + 0.859196i \(0.329036\pi\)
\(440\) 2527.61 0.273861
\(441\) 0 0
\(442\) −516.273 −0.0555579
\(443\) −6258.18 −0.671185 −0.335593 0.942007i \(-0.608937\pi\)
−0.335593 + 0.942007i \(0.608937\pi\)
\(444\) 2022.41 0.216170
\(445\) −7983.93 −0.850505
\(446\) −9299.07 −0.987273
\(447\) 1743.07 0.184439
\(448\) 0 0
\(449\) −11633.8 −1.22279 −0.611396 0.791325i \(-0.709392\pi\)
−0.611396 + 0.791325i \(0.709392\pi\)
\(450\) 5565.34 0.583006
\(451\) −4897.95 −0.511387
\(452\) 2490.58 0.259174
\(453\) −1846.17 −0.191480
\(454\) 8303.43 0.858369
\(455\) 0 0
\(456\) −804.273 −0.0825954
\(457\) −13104.6 −1.34138 −0.670688 0.741740i \(-0.734001\pi\)
−0.670688 + 0.741740i \(0.734001\pi\)
\(458\) 8527.26 0.869985
\(459\) −3222.41 −0.327689
\(460\) 54.3029 0.00550410
\(461\) −2594.63 −0.262134 −0.131067 0.991373i \(-0.541840\pi\)
−0.131067 + 0.991373i \(0.541840\pi\)
\(462\) 0 0
\(463\) −14136.2 −1.41893 −0.709465 0.704741i \(-0.751063\pi\)
−0.709465 + 0.704741i \(0.751063\pi\)
\(464\) −2611.33 −0.261267
\(465\) −13960.4 −1.39225
\(466\) 6099.80 0.606369
\(467\) 15590.2 1.54482 0.772409 0.635125i \(-0.219052\pi\)
0.772409 + 0.635125i \(0.219052\pi\)
\(468\) 77.8637 0.00769070
\(469\) 0 0
\(470\) 21172.4 2.07789
\(471\) −920.795 −0.0900807
\(472\) 3639.42 0.354911
\(473\) 3359.44 0.326569
\(474\) −697.818 −0.0676199
\(475\) −10361.2 −1.00085
\(476\) 0 0
\(477\) −1588.60 −0.152489
\(478\) 7974.41 0.763056
\(479\) −8453.51 −0.806369 −0.403184 0.915119i \(-0.632097\pi\)
−0.403184 + 0.915119i \(0.632097\pi\)
\(480\) 2000.36 0.190216
\(481\) 364.519 0.0345543
\(482\) −1249.30 −0.118058
\(483\) 0 0
\(484\) −4404.35 −0.413632
\(485\) 6974.20 0.652953
\(486\) 486.000 0.0453609
\(487\) −4011.07 −0.373221 −0.186611 0.982434i \(-0.559750\pi\)
−0.186611 + 0.982434i \(0.559750\pi\)
\(488\) 309.212 0.0286831
\(489\) 10543.5 0.975038
\(490\) 0 0
\(491\) 13927.9 1.28016 0.640079 0.768309i \(-0.278902\pi\)
0.640079 + 0.768309i \(0.278902\pi\)
\(492\) −3876.27 −0.355195
\(493\) 19478.7 1.77946
\(494\) −144.962 −0.0132027
\(495\) 2843.56 0.258199
\(496\) −3573.21 −0.323472
\(497\) 0 0
\(498\) −3413.57 −0.307160
\(499\) −3947.55 −0.354141 −0.177071 0.984198i \(-0.556662\pi\)
−0.177071 + 0.984198i \(0.556662\pi\)
\(500\) 15351.6 1.37309
\(501\) 3369.91 0.300512
\(502\) −2657.57 −0.236281
\(503\) −13725.3 −1.21666 −0.608331 0.793684i \(-0.708161\pi\)
−0.608331 + 0.793684i \(0.708161\pi\)
\(504\) 0 0
\(505\) −307.190 −0.0270688
\(506\) 19.7577 0.00173585
\(507\) −6576.97 −0.576121
\(508\) −720.303 −0.0629100
\(509\) 7830.10 0.681853 0.340926 0.940090i \(-0.389259\pi\)
0.340926 + 0.940090i \(0.389259\pi\)
\(510\) −14921.3 −1.29554
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) −904.807 −0.0778717
\(514\) −6452.36 −0.553700
\(515\) −17532.8 −1.50017
\(516\) 2658.68 0.226825
\(517\) 7703.43 0.655312
\(518\) 0 0
\(519\) 4591.80 0.388357
\(520\) 360.545 0.0304057
\(521\) −5907.39 −0.496751 −0.248376 0.968664i \(-0.579897\pi\)
−0.248376 + 0.968664i \(0.579897\pi\)
\(522\) −2937.75 −0.246325
\(523\) 7908.06 0.661176 0.330588 0.943775i \(-0.392753\pi\)
0.330588 + 0.943775i \(0.392753\pi\)
\(524\) 871.439 0.0726508
\(525\) 0 0
\(526\) 6501.23 0.538911
\(527\) 26653.6 2.20313
\(528\) 727.818 0.0599891
\(529\) −12166.6 −0.999965
\(530\) −7355.98 −0.602874
\(531\) 4094.35 0.334613
\(532\) 0 0
\(533\) −698.659 −0.0567773
\(534\) −2298.95 −0.186302
\(535\) −14912.5 −1.20509
\(536\) 1134.33 0.0914100
\(537\) 10240.3 0.822908
\(538\) 5652.08 0.452934
\(539\) 0 0
\(540\) 2250.41 0.179337
\(541\) −3941.04 −0.313195 −0.156598 0.987662i \(-0.550053\pi\)
−0.156598 + 0.987662i \(0.550053\pi\)
\(542\) −4793.54 −0.379889
\(543\) 3860.12 0.305071
\(544\) −3819.15 −0.301001
\(545\) 12502.7 0.982670
\(546\) 0 0
\(547\) −1828.71 −0.142943 −0.0714717 0.997443i \(-0.522770\pi\)
−0.0714717 + 0.997443i \(0.522770\pi\)
\(548\) −10407.4 −0.811283
\(549\) 347.864 0.0270427
\(550\) 9376.29 0.726920
\(551\) 5469.33 0.422870
\(552\) 15.6364 0.00120567
\(553\) 0 0
\(554\) 3640.93 0.279221
\(555\) 10535.3 0.805763
\(556\) −10606.2 −0.808998
\(557\) 22532.0 1.71402 0.857011 0.515298i \(-0.172319\pi\)
0.857011 + 0.515298i \(0.172319\pi\)
\(558\) −4019.86 −0.304972
\(559\) 479.201 0.0362577
\(560\) 0 0
\(561\) −5429.00 −0.408579
\(562\) 6167.62 0.462928
\(563\) 23355.7 1.74836 0.874179 0.485604i \(-0.161400\pi\)
0.874179 + 0.485604i \(0.161400\pi\)
\(564\) 6096.55 0.455161
\(565\) 12974.1 0.966062
\(566\) 5109.54 0.379452
\(567\) 0 0
\(568\) 4821.94 0.356204
\(569\) −20887.6 −1.53894 −0.769468 0.638686i \(-0.779478\pi\)
−0.769468 + 0.638686i \(0.779478\pi\)
\(570\) −4189.68 −0.307871
\(571\) 23745.3 1.74029 0.870147 0.492792i \(-0.164024\pi\)
0.870147 + 0.492792i \(0.164024\pi\)
\(572\) 131.182 0.00958914
\(573\) 3165.89 0.230815
\(574\) 0 0
\(575\) 201.440 0.0146098
\(576\) 576.000 0.0416667
\(577\) 2454.39 0.177084 0.0885422 0.996072i \(-0.471779\pi\)
0.0885422 + 0.996072i \(0.471779\pi\)
\(578\) 18662.1 1.34298
\(579\) −14312.5 −1.02730
\(580\) −13603.2 −0.973863
\(581\) 0 0
\(582\) 2008.20 0.143029
\(583\) −2676.42 −0.190130
\(584\) −8818.39 −0.624842
\(585\) 405.614 0.0286668
\(586\) −3692.93 −0.260330
\(587\) 18567.5 1.30556 0.652780 0.757547i \(-0.273603\pi\)
0.652780 + 0.757547i \(0.273603\pi\)
\(588\) 0 0
\(589\) 7483.95 0.523550
\(590\) 18958.8 1.32292
\(591\) 4866.93 0.338746
\(592\) 2696.55 0.187208
\(593\) 17112.9 1.18507 0.592533 0.805546i \(-0.298128\pi\)
0.592533 + 0.805546i \(0.298128\pi\)
\(594\) 818.795 0.0565582
\(595\) 0 0
\(596\) 2324.09 0.159729
\(597\) −10650.4 −0.730138
\(598\) 2.81830 0.000192724 0
\(599\) 23264.8 1.58694 0.793469 0.608611i \(-0.208273\pi\)
0.793469 + 0.608611i \(0.208273\pi\)
\(600\) 7420.45 0.504898
\(601\) 25322.3 1.71867 0.859334 0.511416i \(-0.170879\pi\)
0.859334 + 0.511416i \(0.170879\pi\)
\(602\) 0 0
\(603\) 1276.13 0.0861821
\(604\) −2461.56 −0.165827
\(605\) −22943.5 −1.54179
\(606\) −88.4545 −0.00592940
\(607\) −21734.4 −1.45333 −0.726665 0.686992i \(-0.758931\pi\)
−0.726665 + 0.686992i \(0.758931\pi\)
\(608\) −1072.36 −0.0715297
\(609\) 0 0
\(610\) 1610.77 0.106915
\(611\) 1098.84 0.0727567
\(612\) −4296.55 −0.283787
\(613\) −13572.4 −0.894262 −0.447131 0.894468i \(-0.647554\pi\)
−0.447131 + 0.894468i \(0.647554\pi\)
\(614\) 14083.0 0.925641
\(615\) −20192.6 −1.32397
\(616\) 0 0
\(617\) −8497.12 −0.554427 −0.277213 0.960808i \(-0.589411\pi\)
−0.277213 + 0.960808i \(0.589411\pi\)
\(618\) −5048.52 −0.328611
\(619\) −22982.9 −1.49235 −0.746173 0.665752i \(-0.768111\pi\)
−0.746173 + 0.665752i \(0.768111\pi\)
\(620\) −18613.9 −1.20573
\(621\) 17.5910 0.00113672
\(622\) −5371.98 −0.346297
\(623\) 0 0
\(624\) 103.818 0.00666034
\(625\) 41322.5 2.64464
\(626\) 4438.38 0.283376
\(627\) −1524.39 −0.0970943
\(628\) −1227.73 −0.0780122
\(629\) −20114.3 −1.27505
\(630\) 0 0
\(631\) −15717.9 −0.991635 −0.495817 0.868427i \(-0.665131\pi\)
−0.495817 + 0.868427i \(0.665131\pi\)
\(632\) −930.424 −0.0585606
\(633\) 13960.2 0.876566
\(634\) 4442.52 0.278289
\(635\) −3752.26 −0.234494
\(636\) −2118.14 −0.132059
\(637\) 0 0
\(638\) −4949.42 −0.307131
\(639\) 5424.68 0.335833
\(640\) 2667.15 0.164732
\(641\) 29107.4 1.79356 0.896780 0.442478i \(-0.145900\pi\)
0.896780 + 0.442478i \(0.145900\pi\)
\(642\) −4294.02 −0.263974
\(643\) −3112.26 −0.190880 −0.0954398 0.995435i \(-0.530426\pi\)
−0.0954398 + 0.995435i \(0.530426\pi\)
\(644\) 0 0
\(645\) 13849.8 0.845482
\(646\) 7999.06 0.487181
\(647\) −7857.59 −0.477456 −0.238728 0.971087i \(-0.576730\pi\)
−0.238728 + 0.971087i \(0.576730\pi\)
\(648\) 648.000 0.0392837
\(649\) 6898.02 0.417213
\(650\) 1337.46 0.0807071
\(651\) 0 0
\(652\) 14058.0 0.844408
\(653\) −19522.0 −1.16992 −0.584958 0.811063i \(-0.698889\pi\)
−0.584958 + 0.811063i \(0.698889\pi\)
\(654\) 3600.11 0.215253
\(655\) 4539.57 0.270803
\(656\) −5168.36 −0.307608
\(657\) −9920.69 −0.589107
\(658\) 0 0
\(659\) 664.061 0.0392536 0.0196268 0.999807i \(-0.493752\pi\)
0.0196268 + 0.999807i \(0.493752\pi\)
\(660\) 3791.41 0.223607
\(661\) 15921.6 0.936883 0.468442 0.883494i \(-0.344816\pi\)
0.468442 + 0.883494i \(0.344816\pi\)
\(662\) 8308.11 0.487770
\(663\) −774.409 −0.0453628
\(664\) −4551.42 −0.266008
\(665\) 0 0
\(666\) 3033.61 0.176502
\(667\) −106.333 −0.00617276
\(668\) 4493.21 0.260251
\(669\) −13948.6 −0.806105
\(670\) 5909.06 0.340727
\(671\) 586.068 0.0337182
\(672\) 0 0
\(673\) 24631.0 1.41078 0.705391 0.708819i \(-0.250771\pi\)
0.705391 + 0.708819i \(0.250771\pi\)
\(674\) −508.333 −0.0290508
\(675\) 8348.01 0.476022
\(676\) −8769.29 −0.498935
\(677\) 17092.8 0.970353 0.485177 0.874416i \(-0.338755\pi\)
0.485177 + 0.874416i \(0.338755\pi\)
\(678\) 3735.86 0.211615
\(679\) 0 0
\(680\) −19895.0 −1.12197
\(681\) 12455.1 0.700855
\(682\) −6772.52 −0.380254
\(683\) −19163.6 −1.07361 −0.536804 0.843707i \(-0.680368\pi\)
−0.536804 + 0.843707i \(0.680368\pi\)
\(684\) −1206.41 −0.0674389
\(685\) −54215.2 −3.02402
\(686\) 0 0
\(687\) 12790.9 0.710339
\(688\) 3544.91 0.196437
\(689\) −381.773 −0.0211094
\(690\) 81.4544 0.00449408
\(691\) 8095.87 0.445704 0.222852 0.974852i \(-0.428463\pi\)
0.222852 + 0.974852i \(0.428463\pi\)
\(692\) 6122.39 0.336327
\(693\) 0 0
\(694\) −12449.3 −0.680934
\(695\) −55250.7 −3.01551
\(696\) −3917.00 −0.213324
\(697\) 38552.3 2.09508
\(698\) 19464.4 1.05550
\(699\) 9149.70 0.495098
\(700\) 0 0
\(701\) 12354.7 0.665664 0.332832 0.942986i \(-0.391996\pi\)
0.332832 + 0.942986i \(0.391996\pi\)
\(702\) 116.795 0.00627943
\(703\) −5647.81 −0.303003
\(704\) 970.424 0.0519520
\(705\) 31758.6 1.69659
\(706\) 2851.23 0.151993
\(707\) 0 0
\(708\) 5459.14 0.289784
\(709\) 3828.82 0.202813 0.101406 0.994845i \(-0.467666\pi\)
0.101406 + 0.994845i \(0.467666\pi\)
\(710\) 25118.8 1.32774
\(711\) −1046.73 −0.0552114
\(712\) −3065.27 −0.161343
\(713\) −145.500 −0.00764241
\(714\) 0 0
\(715\) 683.363 0.0357431
\(716\) 13653.7 0.712659
\(717\) 11961.6 0.623033
\(718\) −11533.0 −0.599453
\(719\) 1223.00 0.0634356 0.0317178 0.999497i \(-0.489902\pi\)
0.0317178 + 0.999497i \(0.489902\pi\)
\(720\) 3000.55 0.155311
\(721\) 0 0
\(722\) −11472.0 −0.591333
\(723\) −1873.94 −0.0963938
\(724\) 5146.83 0.264200
\(725\) −50461.7 −2.58496
\(726\) −6606.52 −0.337729
\(727\) 6368.21 0.324875 0.162437 0.986719i \(-0.448064\pi\)
0.162437 + 0.986719i \(0.448064\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −45937.5 −2.32907
\(731\) −26442.5 −1.33791
\(732\) 463.818 0.0234197
\(733\) −25154.0 −1.26751 −0.633753 0.773535i \(-0.718487\pi\)
−0.633753 + 0.773535i \(0.718487\pi\)
\(734\) 23090.7 1.16116
\(735\) 0 0
\(736\) 20.8485 0.00104414
\(737\) 2149.97 0.107456
\(738\) −5814.41 −0.290015
\(739\) −10739.1 −0.534566 −0.267283 0.963618i \(-0.586126\pi\)
−0.267283 + 0.963618i \(0.586126\pi\)
\(740\) 14047.1 0.697811
\(741\) −217.443 −0.0107800
\(742\) 0 0
\(743\) 28166.3 1.39074 0.695370 0.718652i \(-0.255240\pi\)
0.695370 + 0.718652i \(0.255240\pi\)
\(744\) −5359.82 −0.264114
\(745\) 12106.8 0.595383
\(746\) −12959.1 −0.636016
\(747\) −5120.35 −0.250795
\(748\) −7238.67 −0.353839
\(749\) 0 0
\(750\) 23027.4 1.12112
\(751\) 28657.0 1.39242 0.696211 0.717837i \(-0.254868\pi\)
0.696211 + 0.717837i \(0.254868\pi\)
\(752\) 8128.73 0.394181
\(753\) −3986.35 −0.192923
\(754\) −706.000 −0.0340995
\(755\) −12823.0 −0.618113
\(756\) 0 0
\(757\) −23604.1 −1.13330 −0.566648 0.823960i \(-0.691760\pi\)
−0.566648 + 0.823960i \(0.691760\pi\)
\(758\) 1223.99 0.0586509
\(759\) 29.6366 0.00141731
\(760\) −5586.24 −0.266624
\(761\) 4630.97 0.220595 0.110297 0.993899i \(-0.464820\pi\)
0.110297 + 0.993899i \(0.464820\pi\)
\(762\) −1080.45 −0.0513658
\(763\) 0 0
\(764\) 4221.18 0.199891
\(765\) −22381.9 −1.05780
\(766\) 8721.62 0.411390
\(767\) 983.954 0.0463214
\(768\) 768.000 0.0360844
\(769\) 33276.8 1.56046 0.780228 0.625495i \(-0.215103\pi\)
0.780228 + 0.625495i \(0.215103\pi\)
\(770\) 0 0
\(771\) −9678.55 −0.452094
\(772\) −19083.4 −0.889670
\(773\) −22938.8 −1.06734 −0.533668 0.845694i \(-0.679187\pi\)
−0.533668 + 0.845694i \(0.679187\pi\)
\(774\) 3988.02 0.185202
\(775\) −69049.1 −3.20041
\(776\) 2677.61 0.123867
\(777\) 0 0
\(778\) −26293.8 −1.21167
\(779\) 10824.9 0.497873
\(780\) 540.818 0.0248261
\(781\) 9139.31 0.418733
\(782\) −155.515 −0.00711152
\(783\) −4406.62 −0.201124
\(784\) 0 0
\(785\) −6395.58 −0.290787
\(786\) 1307.16 0.0593191
\(787\) −13514.5 −0.612120 −0.306060 0.952012i \(-0.599011\pi\)
−0.306060 + 0.952012i \(0.599011\pi\)
\(788\) 6489.24 0.293363
\(789\) 9751.84 0.440019
\(790\) −4846.84 −0.218282
\(791\) 0 0
\(792\) 1091.73 0.0489809
\(793\) 83.5986 0.00374360
\(794\) −16956.1 −0.757870
\(795\) −11034.0 −0.492245
\(796\) −14200.5 −0.632318
\(797\) 10473.4 0.465480 0.232740 0.972539i \(-0.425231\pi\)
0.232740 + 0.972539i \(0.425231\pi\)
\(798\) 0 0
\(799\) −60634.5 −2.68472
\(800\) 9893.94 0.437254
\(801\) −3448.43 −0.152115
\(802\) 5606.00 0.246826
\(803\) −16714.0 −0.734527
\(804\) 1701.50 0.0746359
\(805\) 0 0
\(806\) −966.053 −0.0422181
\(807\) 8478.12 0.369819
\(808\) −117.939 −0.00513501
\(809\) 23568.0 1.02423 0.512117 0.858916i \(-0.328861\pi\)
0.512117 + 0.858916i \(0.328861\pi\)
\(810\) 3375.61 0.146428
\(811\) −6704.22 −0.290280 −0.145140 0.989411i \(-0.546363\pi\)
−0.145140 + 0.989411i \(0.546363\pi\)
\(812\) 0 0
\(813\) −7190.31 −0.310178
\(814\) 5110.92 0.220071
\(815\) 73232.1 3.14749
\(816\) −5728.73 −0.245767
\(817\) −7424.67 −0.317939
\(818\) −12770.8 −0.545867
\(819\) 0 0
\(820\) −26923.5 −1.14659
\(821\) 24539.4 1.04316 0.521579 0.853203i \(-0.325343\pi\)
0.521579 + 0.853203i \(0.325343\pi\)
\(822\) −15611.1 −0.662410
\(823\) −31117.0 −1.31795 −0.658973 0.752167i \(-0.729009\pi\)
−0.658973 + 0.752167i \(0.729009\pi\)
\(824\) −6731.36 −0.284585
\(825\) 14064.4 0.593528
\(826\) 0 0
\(827\) 31244.9 1.31377 0.656887 0.753989i \(-0.271873\pi\)
0.656887 + 0.753989i \(0.271873\pi\)
\(828\) 23.4546 0.000984425 0
\(829\) 4231.50 0.177281 0.0886405 0.996064i \(-0.471748\pi\)
0.0886405 + 0.996064i \(0.471748\pi\)
\(830\) −23709.6 −0.991535
\(831\) 5461.40 0.227983
\(832\) 138.424 0.00576803
\(833\) 0 0
\(834\) −15909.3 −0.660544
\(835\) 23406.4 0.970074
\(836\) −2032.51 −0.0840861
\(837\) −6029.80 −0.249009
\(838\) 9663.32 0.398346
\(839\) −38670.4 −1.59124 −0.795621 0.605795i \(-0.792855\pi\)
−0.795621 + 0.605795i \(0.792855\pi\)
\(840\) 0 0
\(841\) 2247.96 0.0921710
\(842\) 14950.7 0.611920
\(843\) 9251.43 0.377979
\(844\) 18613.5 0.759129
\(845\) −45681.7 −1.85976
\(846\) 9144.82 0.371637
\(847\) 0 0
\(848\) −2824.18 −0.114367
\(849\) 7664.31 0.309821
\(850\) −73801.7 −2.97809
\(851\) 109.803 0.00442302
\(852\) 7232.91 0.290840
\(853\) −19944.4 −0.800565 −0.400282 0.916392i \(-0.631088\pi\)
−0.400282 + 0.916392i \(0.631088\pi\)
\(854\) 0 0
\(855\) −6284.52 −0.251376
\(856\) −5725.36 −0.228609
\(857\) 13882.2 0.553334 0.276667 0.960966i \(-0.410770\pi\)
0.276667 + 0.960966i \(0.410770\pi\)
\(858\) 196.773 0.00782950
\(859\) −4157.16 −0.165123 −0.0825614 0.996586i \(-0.526310\pi\)
−0.0825614 + 0.996586i \(0.526310\pi\)
\(860\) 18466.4 0.732209
\(861\) 0 0
\(862\) 13983.9 0.552543
\(863\) −16237.9 −0.640493 −0.320246 0.947334i \(-0.603766\pi\)
−0.320246 + 0.947334i \(0.603766\pi\)
\(864\) 864.000 0.0340207
\(865\) 31893.3 1.25365
\(866\) −15398.5 −0.604230
\(867\) 27993.2 1.09654
\(868\) 0 0
\(869\) −1763.49 −0.0688403
\(870\) −20404.8 −0.795156
\(871\) 306.678 0.0119304
\(872\) 4800.15 0.186415
\(873\) 3012.31 0.116783
\(874\) −43.6664 −0.00168998
\(875\) 0 0
\(876\) −13227.6 −0.510181
\(877\) −16489.4 −0.634900 −0.317450 0.948275i \(-0.602827\pi\)
−0.317450 + 0.948275i \(0.602827\pi\)
\(878\) 18824.6 0.723577
\(879\) −5539.40 −0.212559
\(880\) 5055.21 0.193649
\(881\) 45411.7 1.73662 0.868309 0.496023i \(-0.165207\pi\)
0.868309 + 0.496023i \(0.165207\pi\)
\(882\) 0 0
\(883\) −2206.85 −0.0841070 −0.0420535 0.999115i \(-0.513390\pi\)
−0.0420535 + 0.999115i \(0.513390\pi\)
\(884\) −1032.55 −0.0392854
\(885\) 28438.2 1.08016
\(886\) −12516.4 −0.474600
\(887\) 28146.2 1.06545 0.532727 0.846287i \(-0.321167\pi\)
0.532727 + 0.846287i \(0.321167\pi\)
\(888\) 4044.82 0.152855
\(889\) 0 0
\(890\) −15967.9 −0.601398
\(891\) 1228.19 0.0461796
\(892\) −18598.1 −0.698107
\(893\) −17025.3 −0.637995
\(894\) 3486.14 0.130418
\(895\) 71126.1 2.65641
\(896\) 0 0
\(897\) 4.22746 0.000157359 0
\(898\) −23267.6 −0.864644
\(899\) 36448.6 1.35220
\(900\) 11130.7 0.412247
\(901\) 21066.4 0.778937
\(902\) −9795.91 −0.361605
\(903\) 0 0
\(904\) 4981.15 0.183264
\(905\) 26811.3 0.984793
\(906\) −3692.34 −0.135397
\(907\) −5042.25 −0.184592 −0.0922960 0.995732i \(-0.529421\pi\)
−0.0922960 + 0.995732i \(0.529421\pi\)
\(908\) 16606.9 0.606958
\(909\) −132.682 −0.00484134
\(910\) 0 0
\(911\) 29647.3 1.07822 0.539110 0.842235i \(-0.318761\pi\)
0.539110 + 0.842235i \(0.318761\pi\)
\(912\) −1608.55 −0.0584038
\(913\) −8626.59 −0.312704
\(914\) −26209.3 −0.948496
\(915\) 2416.16 0.0872959
\(916\) 17054.5 0.615172
\(917\) 0 0
\(918\) −6444.82 −0.231711
\(919\) −11891.3 −0.426830 −0.213415 0.976962i \(-0.568459\pi\)
−0.213415 + 0.976962i \(0.568459\pi\)
\(920\) 108.606 0.00389199
\(921\) 21124.5 0.755782
\(922\) −5189.26 −0.185357
\(923\) 1303.66 0.0464902
\(924\) 0 0
\(925\) 52108.3 1.85223
\(926\) −28272.4 −1.00333
\(927\) −7572.78 −0.268309
\(928\) −5222.67 −0.184744
\(929\) −39188.5 −1.38400 −0.691999 0.721898i \(-0.743270\pi\)
−0.691999 + 0.721898i \(0.743270\pi\)
\(930\) −27920.8 −0.984472
\(931\) 0 0
\(932\) 12199.6 0.428768
\(933\) −8057.98 −0.282751
\(934\) 31180.5 1.09235
\(935\) −37708.2 −1.31892
\(936\) 155.727 0.00543815
\(937\) 9716.23 0.338757 0.169379 0.985551i \(-0.445824\pi\)
0.169379 + 0.985551i \(0.445824\pi\)
\(938\) 0 0
\(939\) 6657.57 0.231375
\(940\) 42344.8 1.46929
\(941\) −6995.87 −0.242358 −0.121179 0.992631i \(-0.538667\pi\)
−0.121179 + 0.992631i \(0.538667\pi\)
\(942\) −1841.59 −0.0636967
\(943\) −210.455 −0.00726760
\(944\) 7278.85 0.250960
\(945\) 0 0
\(946\) 6718.88 0.230919
\(947\) 14979.2 0.514002 0.257001 0.966411i \(-0.417266\pi\)
0.257001 + 0.966411i \(0.417266\pi\)
\(948\) −1395.64 −0.0478145
\(949\) −2384.14 −0.0815516
\(950\) −20722.5 −0.707711
\(951\) 6663.78 0.227222
\(952\) 0 0
\(953\) 29393.3 0.999100 0.499550 0.866285i \(-0.333499\pi\)
0.499550 + 0.866285i \(0.333499\pi\)
\(954\) −3177.20 −0.107826
\(955\) 21989.3 0.745087
\(956\) 15948.8 0.539562
\(957\) −7424.12 −0.250771
\(958\) −16907.0 −0.570189
\(959\) 0 0
\(960\) 4000.73 0.134503
\(961\) 20083.4 0.674143
\(962\) 729.038 0.0244336
\(963\) −6441.03 −0.215534
\(964\) −2498.59 −0.0834795
\(965\) −99410.6 −3.31621
\(966\) 0 0
\(967\) −7133.95 −0.237241 −0.118621 0.992940i \(-0.537847\pi\)
−0.118621 + 0.992940i \(0.537847\pi\)
\(968\) −8808.70 −0.292482
\(969\) 11998.6 0.397781
\(970\) 13948.4 0.461707
\(971\) −9688.13 −0.320192 −0.160096 0.987101i \(-0.551180\pi\)
−0.160096 + 0.987101i \(0.551180\pi\)
\(972\) 972.000 0.0320750
\(973\) 0 0
\(974\) −8022.14 −0.263907
\(975\) 2006.19 0.0658970
\(976\) 618.424 0.0202820
\(977\) 21305.7 0.697676 0.348838 0.937183i \(-0.386576\pi\)
0.348838 + 0.937183i \(0.386576\pi\)
\(978\) 21087.0 0.689456
\(979\) −5809.79 −0.189665
\(980\) 0 0
\(981\) 5400.17 0.175753
\(982\) 27855.8 0.905208
\(983\) −37280.8 −1.20964 −0.604818 0.796364i \(-0.706754\pi\)
−0.604818 + 0.796364i \(0.706754\pi\)
\(984\) −7752.55 −0.251161
\(985\) 33804.3 1.09350
\(986\) 38957.3 1.25827
\(987\) 0 0
\(988\) −289.924 −0.00933574
\(989\) 144.348 0.00464105
\(990\) 5687.11 0.182574
\(991\) −51397.1 −1.64751 −0.823755 0.566946i \(-0.808125\pi\)
−0.823755 + 0.566946i \(0.808125\pi\)
\(992\) −7146.42 −0.228729
\(993\) 12462.2 0.398263
\(994\) 0 0
\(995\) −73974.6 −2.35694
\(996\) −6827.14 −0.217195
\(997\) −34373.8 −1.09191 −0.545953 0.837816i \(-0.683832\pi\)
−0.545953 + 0.837816i \(0.683832\pi\)
\(998\) −7895.10 −0.250416
\(999\) 4550.42 0.144113
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 294.4.a.n.1.2 2
3.2 odd 2 882.4.a.v.1.1 2
4.3 odd 2 2352.4.a.bq.1.2 2
7.2 even 3 42.4.e.c.25.1 4
7.3 odd 6 294.4.e.l.79.2 4
7.4 even 3 42.4.e.c.37.1 yes 4
7.5 odd 6 294.4.e.l.67.2 4
7.6 odd 2 294.4.a.m.1.1 2
21.2 odd 6 126.4.g.g.109.2 4
21.5 even 6 882.4.g.bf.361.1 4
21.11 odd 6 126.4.g.g.37.2 4
21.17 even 6 882.4.g.bf.667.1 4
21.20 even 2 882.4.a.z.1.2 2
28.11 odd 6 336.4.q.j.289.1 4
28.23 odd 6 336.4.q.j.193.1 4
28.27 even 2 2352.4.a.ca.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.4.e.c.25.1 4 7.2 even 3
42.4.e.c.37.1 yes 4 7.4 even 3
126.4.g.g.37.2 4 21.11 odd 6
126.4.g.g.109.2 4 21.2 odd 6
294.4.a.m.1.1 2 7.6 odd 2
294.4.a.n.1.2 2 1.1 even 1 trivial
294.4.e.l.67.2 4 7.5 odd 6
294.4.e.l.79.2 4 7.3 odd 6
336.4.q.j.193.1 4 28.23 odd 6
336.4.q.j.289.1 4 28.11 odd 6
882.4.a.v.1.1 2 3.2 odd 2
882.4.a.z.1.2 2 21.20 even 2
882.4.g.bf.361.1 4 21.5 even 6
882.4.g.bf.667.1 4 21.17 even 6
2352.4.a.bq.1.2 2 4.3 odd 2
2352.4.a.ca.1.1 2 28.27 even 2