Properties

Label 735.4.a.e.1.1
Level $735$
Weight $4$
Character 735.1
Self dual yes
Analytic conductor $43.366$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 735.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(43.3664038542\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 15)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 735.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.00000 q^{3} -7.00000 q^{4} -5.00000 q^{5} -3.00000 q^{6} -15.0000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.00000 q^{3} -7.00000 q^{4} -5.00000 q^{5} -3.00000 q^{6} -15.0000 q^{8} +9.00000 q^{9} -5.00000 q^{10} +52.0000 q^{11} +21.0000 q^{12} -22.0000 q^{13} +15.0000 q^{15} +41.0000 q^{16} +14.0000 q^{17} +9.00000 q^{18} +20.0000 q^{19} +35.0000 q^{20} +52.0000 q^{22} -168.000 q^{23} +45.0000 q^{24} +25.0000 q^{25} -22.0000 q^{26} -27.0000 q^{27} +230.000 q^{29} +15.0000 q^{30} +288.000 q^{31} +161.000 q^{32} -156.000 q^{33} +14.0000 q^{34} -63.0000 q^{36} -34.0000 q^{37} +20.0000 q^{38} +66.0000 q^{39} +75.0000 q^{40} -122.000 q^{41} -188.000 q^{43} -364.000 q^{44} -45.0000 q^{45} -168.000 q^{46} -256.000 q^{47} -123.000 q^{48} +25.0000 q^{50} -42.0000 q^{51} +154.000 q^{52} -338.000 q^{53} -27.0000 q^{54} -260.000 q^{55} -60.0000 q^{57} +230.000 q^{58} -100.000 q^{59} -105.000 q^{60} -742.000 q^{61} +288.000 q^{62} -167.000 q^{64} +110.000 q^{65} -156.000 q^{66} -84.0000 q^{67} -98.0000 q^{68} +504.000 q^{69} -328.000 q^{71} -135.000 q^{72} +38.0000 q^{73} -34.0000 q^{74} -75.0000 q^{75} -140.000 q^{76} +66.0000 q^{78} -240.000 q^{79} -205.000 q^{80} +81.0000 q^{81} -122.000 q^{82} -1212.00 q^{83} -70.0000 q^{85} -188.000 q^{86} -690.000 q^{87} -780.000 q^{88} -330.000 q^{89} -45.0000 q^{90} +1176.00 q^{92} -864.000 q^{93} -256.000 q^{94} -100.000 q^{95} -483.000 q^{96} -866.000 q^{97} +468.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.353553 0.176777 0.984251i \(-0.443433\pi\)
0.176777 + 0.984251i \(0.443433\pi\)
\(3\) −3.00000 −0.577350
\(4\) −7.00000 −0.875000
\(5\) −5.00000 −0.447214
\(6\) −3.00000 −0.204124
\(7\) 0 0
\(8\) −15.0000 −0.662913
\(9\) 9.00000 0.333333
\(10\) −5.00000 −0.158114
\(11\) 52.0000 1.42533 0.712663 0.701506i \(-0.247489\pi\)
0.712663 + 0.701506i \(0.247489\pi\)
\(12\) 21.0000 0.505181
\(13\) −22.0000 −0.469362 −0.234681 0.972072i \(-0.575405\pi\)
−0.234681 + 0.972072i \(0.575405\pi\)
\(14\) 0 0
\(15\) 15.0000 0.258199
\(16\) 41.0000 0.640625
\(17\) 14.0000 0.199735 0.0998676 0.995001i \(-0.468158\pi\)
0.0998676 + 0.995001i \(0.468158\pi\)
\(18\) 9.00000 0.117851
\(19\) 20.0000 0.241490 0.120745 0.992684i \(-0.461472\pi\)
0.120745 + 0.992684i \(0.461472\pi\)
\(20\) 35.0000 0.391312
\(21\) 0 0
\(22\) 52.0000 0.503929
\(23\) −168.000 −1.52306 −0.761531 0.648129i \(-0.775552\pi\)
−0.761531 + 0.648129i \(0.775552\pi\)
\(24\) 45.0000 0.382733
\(25\) 25.0000 0.200000
\(26\) −22.0000 −0.165944
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) 230.000 1.47276 0.736378 0.676570i \(-0.236535\pi\)
0.736378 + 0.676570i \(0.236535\pi\)
\(30\) 15.0000 0.0912871
\(31\) 288.000 1.66859 0.834296 0.551317i \(-0.185875\pi\)
0.834296 + 0.551317i \(0.185875\pi\)
\(32\) 161.000 0.889408
\(33\) −156.000 −0.822913
\(34\) 14.0000 0.0706171
\(35\) 0 0
\(36\) −63.0000 −0.291667
\(37\) −34.0000 −0.151069 −0.0755347 0.997143i \(-0.524066\pi\)
−0.0755347 + 0.997143i \(0.524066\pi\)
\(38\) 20.0000 0.0853797
\(39\) 66.0000 0.270986
\(40\) 75.0000 0.296464
\(41\) −122.000 −0.464712 −0.232356 0.972631i \(-0.574643\pi\)
−0.232356 + 0.972631i \(0.574643\pi\)
\(42\) 0 0
\(43\) −188.000 −0.666738 −0.333369 0.942796i \(-0.608185\pi\)
−0.333369 + 0.942796i \(0.608185\pi\)
\(44\) −364.000 −1.24716
\(45\) −45.0000 −0.149071
\(46\) −168.000 −0.538484
\(47\) −256.000 −0.794499 −0.397249 0.917711i \(-0.630035\pi\)
−0.397249 + 0.917711i \(0.630035\pi\)
\(48\) −123.000 −0.369865
\(49\) 0 0
\(50\) 25.0000 0.0707107
\(51\) −42.0000 −0.115317
\(52\) 154.000 0.410691
\(53\) −338.000 −0.875998 −0.437999 0.898976i \(-0.644313\pi\)
−0.437999 + 0.898976i \(0.644313\pi\)
\(54\) −27.0000 −0.0680414
\(55\) −260.000 −0.637425
\(56\) 0 0
\(57\) −60.0000 −0.139424
\(58\) 230.000 0.520698
\(59\) −100.000 −0.220659 −0.110330 0.993895i \(-0.535191\pi\)
−0.110330 + 0.993895i \(0.535191\pi\)
\(60\) −105.000 −0.225924
\(61\) −742.000 −1.55743 −0.778716 0.627376i \(-0.784129\pi\)
−0.778716 + 0.627376i \(0.784129\pi\)
\(62\) 288.000 0.589936
\(63\) 0 0
\(64\) −167.000 −0.326172
\(65\) 110.000 0.209905
\(66\) −156.000 −0.290944
\(67\) −84.0000 −0.153168 −0.0765838 0.997063i \(-0.524401\pi\)
−0.0765838 + 0.997063i \(0.524401\pi\)
\(68\) −98.0000 −0.174768
\(69\) 504.000 0.879340
\(70\) 0 0
\(71\) −328.000 −0.548260 −0.274130 0.961693i \(-0.588390\pi\)
−0.274130 + 0.961693i \(0.588390\pi\)
\(72\) −135.000 −0.220971
\(73\) 38.0000 0.0609255 0.0304628 0.999536i \(-0.490302\pi\)
0.0304628 + 0.999536i \(0.490302\pi\)
\(74\) −34.0000 −0.0534111
\(75\) −75.0000 −0.115470
\(76\) −140.000 −0.211304
\(77\) 0 0
\(78\) 66.0000 0.0958081
\(79\) −240.000 −0.341799 −0.170899 0.985288i \(-0.554667\pi\)
−0.170899 + 0.985288i \(0.554667\pi\)
\(80\) −205.000 −0.286496
\(81\) 81.0000 0.111111
\(82\) −122.000 −0.164301
\(83\) −1212.00 −1.60282 −0.801411 0.598114i \(-0.795917\pi\)
−0.801411 + 0.598114i \(0.795917\pi\)
\(84\) 0 0
\(85\) −70.0000 −0.0893243
\(86\) −188.000 −0.235727
\(87\) −690.000 −0.850296
\(88\) −780.000 −0.944867
\(89\) −330.000 −0.393033 −0.196516 0.980501i \(-0.562963\pi\)
−0.196516 + 0.980501i \(0.562963\pi\)
\(90\) −45.0000 −0.0527046
\(91\) 0 0
\(92\) 1176.00 1.33268
\(93\) −864.000 −0.963362
\(94\) −256.000 −0.280898
\(95\) −100.000 −0.107998
\(96\) −483.000 −0.513500
\(97\) −866.000 −0.906484 −0.453242 0.891387i \(-0.649733\pi\)
−0.453242 + 0.891387i \(0.649733\pi\)
\(98\) 0 0
\(99\) 468.000 0.475109
\(100\) −175.000 −0.175000
\(101\) 1218.00 1.19996 0.599978 0.800017i \(-0.295176\pi\)
0.599978 + 0.800017i \(0.295176\pi\)
\(102\) −42.0000 −0.0407708
\(103\) 88.0000 0.0841835 0.0420917 0.999114i \(-0.486598\pi\)
0.0420917 + 0.999114i \(0.486598\pi\)
\(104\) 330.000 0.311146
\(105\) 0 0
\(106\) −338.000 −0.309712
\(107\) 36.0000 0.0325257 0.0162629 0.999868i \(-0.494823\pi\)
0.0162629 + 0.999868i \(0.494823\pi\)
\(108\) 189.000 0.168394
\(109\) −970.000 −0.852378 −0.426189 0.904634i \(-0.640144\pi\)
−0.426189 + 0.904634i \(0.640144\pi\)
\(110\) −260.000 −0.225364
\(111\) 102.000 0.0872199
\(112\) 0 0
\(113\) 1042.00 0.867461 0.433731 0.901043i \(-0.357197\pi\)
0.433731 + 0.901043i \(0.357197\pi\)
\(114\) −60.0000 −0.0492940
\(115\) 840.000 0.681134
\(116\) −1610.00 −1.28866
\(117\) −198.000 −0.156454
\(118\) −100.000 −0.0780148
\(119\) 0 0
\(120\) −225.000 −0.171163
\(121\) 1373.00 1.03156
\(122\) −742.000 −0.550635
\(123\) 366.000 0.268302
\(124\) −2016.00 −1.46002
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 1936.00 1.35269 0.676347 0.736583i \(-0.263562\pi\)
0.676347 + 0.736583i \(0.263562\pi\)
\(128\) −1455.00 −1.00473
\(129\) 564.000 0.384941
\(130\) 110.000 0.0742126
\(131\) −732.000 −0.488207 −0.244104 0.969749i \(-0.578494\pi\)
−0.244104 + 0.969749i \(0.578494\pi\)
\(132\) 1092.00 0.720048
\(133\) 0 0
\(134\) −84.0000 −0.0541529
\(135\) 135.000 0.0860663
\(136\) −210.000 −0.132407
\(137\) −2214.00 −1.38069 −0.690346 0.723479i \(-0.742542\pi\)
−0.690346 + 0.723479i \(0.742542\pi\)
\(138\) 504.000 0.310894
\(139\) −20.0000 −0.0122042 −0.00610208 0.999981i \(-0.501942\pi\)
−0.00610208 + 0.999981i \(0.501942\pi\)
\(140\) 0 0
\(141\) 768.000 0.458704
\(142\) −328.000 −0.193839
\(143\) −1144.00 −0.668994
\(144\) 369.000 0.213542
\(145\) −1150.00 −0.658637
\(146\) 38.0000 0.0215404
\(147\) 0 0
\(148\) 238.000 0.132186
\(149\) −1330.00 −0.731261 −0.365630 0.930760i \(-0.619147\pi\)
−0.365630 + 0.930760i \(0.619147\pi\)
\(150\) −75.0000 −0.0408248
\(151\) −1208.00 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) −300.000 −0.160087
\(153\) 126.000 0.0665784
\(154\) 0 0
\(155\) −1440.00 −0.746217
\(156\) −462.000 −0.237113
\(157\) 3514.00 1.78629 0.893146 0.449768i \(-0.148493\pi\)
0.893146 + 0.449768i \(0.148493\pi\)
\(158\) −240.000 −0.120844
\(159\) 1014.00 0.505757
\(160\) −805.000 −0.397755
\(161\) 0 0
\(162\) 81.0000 0.0392837
\(163\) −2068.00 −0.993732 −0.496866 0.867827i \(-0.665516\pi\)
−0.496866 + 0.867827i \(0.665516\pi\)
\(164\) 854.000 0.406623
\(165\) 780.000 0.368018
\(166\) −1212.00 −0.566683
\(167\) 24.0000 0.0111208 0.00556041 0.999985i \(-0.498230\pi\)
0.00556041 + 0.999985i \(0.498230\pi\)
\(168\) 0 0
\(169\) −1713.00 −0.779700
\(170\) −70.0000 −0.0315809
\(171\) 180.000 0.0804967
\(172\) 1316.00 0.583396
\(173\) 618.000 0.271593 0.135797 0.990737i \(-0.456641\pi\)
0.135797 + 0.990737i \(0.456641\pi\)
\(174\) −690.000 −0.300625
\(175\) 0 0
\(176\) 2132.00 0.913100
\(177\) 300.000 0.127398
\(178\) −330.000 −0.138958
\(179\) 3340.00 1.39466 0.697328 0.716752i \(-0.254372\pi\)
0.697328 + 0.716752i \(0.254372\pi\)
\(180\) 315.000 0.130437
\(181\) 178.000 0.0730974 0.0365487 0.999332i \(-0.488364\pi\)
0.0365487 + 0.999332i \(0.488364\pi\)
\(182\) 0 0
\(183\) 2226.00 0.899184
\(184\) 2520.00 1.00966
\(185\) 170.000 0.0675603
\(186\) −864.000 −0.340600
\(187\) 728.000 0.284688
\(188\) 1792.00 0.695186
\(189\) 0 0
\(190\) −100.000 −0.0381830
\(191\) −1888.00 −0.715240 −0.357620 0.933867i \(-0.616412\pi\)
−0.357620 + 0.933867i \(0.616412\pi\)
\(192\) 501.000 0.188315
\(193\) 1922.00 0.716832 0.358416 0.933562i \(-0.383317\pi\)
0.358416 + 0.933562i \(0.383317\pi\)
\(194\) −866.000 −0.320491
\(195\) −330.000 −0.121189
\(196\) 0 0
\(197\) 2526.00 0.913554 0.456777 0.889581i \(-0.349004\pi\)
0.456777 + 0.889581i \(0.349004\pi\)
\(198\) 468.000 0.167976
\(199\) 1160.00 0.413217 0.206609 0.978424i \(-0.433757\pi\)
0.206609 + 0.978424i \(0.433757\pi\)
\(200\) −375.000 −0.132583
\(201\) 252.000 0.0884314
\(202\) 1218.00 0.424248
\(203\) 0 0
\(204\) 294.000 0.100903
\(205\) 610.000 0.207826
\(206\) 88.0000 0.0297634
\(207\) −1512.00 −0.507687
\(208\) −902.000 −0.300685
\(209\) 1040.00 0.344202
\(210\) 0 0
\(211\) −4468.00 −1.45777 −0.728886 0.684635i \(-0.759961\pi\)
−0.728886 + 0.684635i \(0.759961\pi\)
\(212\) 2366.00 0.766498
\(213\) 984.000 0.316538
\(214\) 36.0000 0.0114996
\(215\) 940.000 0.298174
\(216\) 405.000 0.127578
\(217\) 0 0
\(218\) −970.000 −0.301361
\(219\) −114.000 −0.0351754
\(220\) 1820.00 0.557747
\(221\) −308.000 −0.0937481
\(222\) 102.000 0.0308369
\(223\) −6032.00 −1.81136 −0.905678 0.423965i \(-0.860638\pi\)
−0.905678 + 0.423965i \(0.860638\pi\)
\(224\) 0 0
\(225\) 225.000 0.0666667
\(226\) 1042.00 0.306694
\(227\) −2636.00 −0.770738 −0.385369 0.922763i \(-0.625926\pi\)
−0.385369 + 0.922763i \(0.625926\pi\)
\(228\) 420.000 0.121996
\(229\) −4830.00 −1.39378 −0.696889 0.717179i \(-0.745433\pi\)
−0.696889 + 0.717179i \(0.745433\pi\)
\(230\) 840.000 0.240817
\(231\) 0 0
\(232\) −3450.00 −0.976309
\(233\) 2682.00 0.754093 0.377046 0.926194i \(-0.376940\pi\)
0.377046 + 0.926194i \(0.376940\pi\)
\(234\) −198.000 −0.0553148
\(235\) 1280.00 0.355311
\(236\) 700.000 0.193077
\(237\) 720.000 0.197338
\(238\) 0 0
\(239\) 2320.00 0.627901 0.313950 0.949439i \(-0.398347\pi\)
0.313950 + 0.949439i \(0.398347\pi\)
\(240\) 615.000 0.165409
\(241\) −2002.00 −0.535104 −0.267552 0.963543i \(-0.586215\pi\)
−0.267552 + 0.963543i \(0.586215\pi\)
\(242\) 1373.00 0.364710
\(243\) −243.000 −0.0641500
\(244\) 5194.00 1.36275
\(245\) 0 0
\(246\) 366.000 0.0948590
\(247\) −440.000 −0.113346
\(248\) −4320.00 −1.10613
\(249\) 3636.00 0.925390
\(250\) −125.000 −0.0316228
\(251\) −132.000 −0.0331943 −0.0165971 0.999862i \(-0.505283\pi\)
−0.0165971 + 0.999862i \(0.505283\pi\)
\(252\) 0 0
\(253\) −8736.00 −2.17086
\(254\) 1936.00 0.478250
\(255\) 210.000 0.0515714
\(256\) −119.000 −0.0290527
\(257\) 7614.00 1.84805 0.924024 0.382335i \(-0.124880\pi\)
0.924024 + 0.382335i \(0.124880\pi\)
\(258\) 564.000 0.136097
\(259\) 0 0
\(260\) −770.000 −0.183667
\(261\) 2070.00 0.490919
\(262\) −732.000 −0.172607
\(263\) −4888.00 −1.14603 −0.573017 0.819543i \(-0.694227\pi\)
−0.573017 + 0.819543i \(0.694227\pi\)
\(264\) 2340.00 0.545519
\(265\) 1690.00 0.391758
\(266\) 0 0
\(267\) 990.000 0.226918
\(268\) 588.000 0.134022
\(269\) −1270.00 −0.287856 −0.143928 0.989588i \(-0.545973\pi\)
−0.143928 + 0.989588i \(0.545973\pi\)
\(270\) 135.000 0.0304290
\(271\) −1072.00 −0.240293 −0.120146 0.992756i \(-0.538336\pi\)
−0.120146 + 0.992756i \(0.538336\pi\)
\(272\) 574.000 0.127955
\(273\) 0 0
\(274\) −2214.00 −0.488148
\(275\) 1300.00 0.285065
\(276\) −3528.00 −0.769423
\(277\) −5394.00 −1.17001 −0.585007 0.811028i \(-0.698908\pi\)
−0.585007 + 0.811028i \(0.698908\pi\)
\(278\) −20.0000 −0.00431482
\(279\) 2592.00 0.556197
\(280\) 0 0
\(281\) 2442.00 0.518425 0.259213 0.965820i \(-0.416537\pi\)
0.259213 + 0.965820i \(0.416537\pi\)
\(282\) 768.000 0.162176
\(283\) −2772.00 −0.582255 −0.291128 0.956684i \(-0.594030\pi\)
−0.291128 + 0.956684i \(0.594030\pi\)
\(284\) 2296.00 0.479727
\(285\) 300.000 0.0623525
\(286\) −1144.00 −0.236525
\(287\) 0 0
\(288\) 1449.00 0.296469
\(289\) −4717.00 −0.960106
\(290\) −1150.00 −0.232863
\(291\) 2598.00 0.523359
\(292\) −266.000 −0.0533098
\(293\) −4542.00 −0.905619 −0.452810 0.891607i \(-0.649578\pi\)
−0.452810 + 0.891607i \(0.649578\pi\)
\(294\) 0 0
\(295\) 500.000 0.0986818
\(296\) 510.000 0.100146
\(297\) −1404.00 −0.274304
\(298\) −1330.00 −0.258540
\(299\) 3696.00 0.714867
\(300\) 525.000 0.101036
\(301\) 0 0
\(302\) −1208.00 −0.230174
\(303\) −3654.00 −0.692795
\(304\) 820.000 0.154705
\(305\) 3710.00 0.696505
\(306\) 126.000 0.0235390
\(307\) −5116.00 −0.951093 −0.475546 0.879691i \(-0.657750\pi\)
−0.475546 + 0.879691i \(0.657750\pi\)
\(308\) 0 0
\(309\) −264.000 −0.0486034
\(310\) −1440.00 −0.263827
\(311\) 2808.00 0.511984 0.255992 0.966679i \(-0.417598\pi\)
0.255992 + 0.966679i \(0.417598\pi\)
\(312\) −990.000 −0.179640
\(313\) 7318.00 1.32153 0.660763 0.750594i \(-0.270233\pi\)
0.660763 + 0.750594i \(0.270233\pi\)
\(314\) 3514.00 0.631549
\(315\) 0 0
\(316\) 1680.00 0.299074
\(317\) 2246.00 0.397943 0.198971 0.980005i \(-0.436240\pi\)
0.198971 + 0.980005i \(0.436240\pi\)
\(318\) 1014.00 0.178812
\(319\) 11960.0 2.09916
\(320\) 835.000 0.145868
\(321\) −108.000 −0.0187787
\(322\) 0 0
\(323\) 280.000 0.0482341
\(324\) −567.000 −0.0972222
\(325\) −550.000 −0.0938723
\(326\) −2068.00 −0.351337
\(327\) 2910.00 0.492120
\(328\) 1830.00 0.308064
\(329\) 0 0
\(330\) 780.000 0.130114
\(331\) 1332.00 0.221188 0.110594 0.993866i \(-0.464725\pi\)
0.110594 + 0.993866i \(0.464725\pi\)
\(332\) 8484.00 1.40247
\(333\) −306.000 −0.0503564
\(334\) 24.0000 0.00393180
\(335\) 420.000 0.0684987
\(336\) 0 0
\(337\) −11534.0 −1.86438 −0.932191 0.361966i \(-0.882106\pi\)
−0.932191 + 0.361966i \(0.882106\pi\)
\(338\) −1713.00 −0.275665
\(339\) −3126.00 −0.500829
\(340\) 490.000 0.0781588
\(341\) 14976.0 2.37829
\(342\) 180.000 0.0284599
\(343\) 0 0
\(344\) 2820.00 0.441989
\(345\) −2520.00 −0.393253
\(346\) 618.000 0.0960228
\(347\) 11956.0 1.84966 0.924830 0.380382i \(-0.124207\pi\)
0.924830 + 0.380382i \(0.124207\pi\)
\(348\) 4830.00 0.744009
\(349\) −4870.00 −0.746949 −0.373474 0.927640i \(-0.621834\pi\)
−0.373474 + 0.927640i \(0.621834\pi\)
\(350\) 0 0
\(351\) 594.000 0.0903287
\(352\) 8372.00 1.26770
\(353\) −10722.0 −1.61664 −0.808321 0.588742i \(-0.799623\pi\)
−0.808321 + 0.588742i \(0.799623\pi\)
\(354\) 300.000 0.0450419
\(355\) 1640.00 0.245189
\(356\) 2310.00 0.343904
\(357\) 0 0
\(358\) 3340.00 0.493085
\(359\) 120.000 0.0176417 0.00882083 0.999961i \(-0.497192\pi\)
0.00882083 + 0.999961i \(0.497192\pi\)
\(360\) 675.000 0.0988212
\(361\) −6459.00 −0.941682
\(362\) 178.000 0.0258438
\(363\) −4119.00 −0.595569
\(364\) 0 0
\(365\) −190.000 −0.0272467
\(366\) 2226.00 0.317910
\(367\) −3936.00 −0.559830 −0.279915 0.960025i \(-0.590306\pi\)
−0.279915 + 0.960025i \(0.590306\pi\)
\(368\) −6888.00 −0.975711
\(369\) −1098.00 −0.154904
\(370\) 170.000 0.0238862
\(371\) 0 0
\(372\) 6048.00 0.842941
\(373\) 3022.00 0.419499 0.209750 0.977755i \(-0.432735\pi\)
0.209750 + 0.977755i \(0.432735\pi\)
\(374\) 728.000 0.100652
\(375\) 375.000 0.0516398
\(376\) 3840.00 0.526683
\(377\) −5060.00 −0.691255
\(378\) 0 0
\(379\) −13340.0 −1.80799 −0.903997 0.427539i \(-0.859381\pi\)
−0.903997 + 0.427539i \(0.859381\pi\)
\(380\) 700.000 0.0944980
\(381\) −5808.00 −0.780979
\(382\) −1888.00 −0.252876
\(383\) 1008.00 0.134481 0.0672407 0.997737i \(-0.478580\pi\)
0.0672407 + 0.997737i \(0.478580\pi\)
\(384\) 4365.00 0.580079
\(385\) 0 0
\(386\) 1922.00 0.253438
\(387\) −1692.00 −0.222246
\(388\) 6062.00 0.793174
\(389\) 9630.00 1.25517 0.627584 0.778549i \(-0.284044\pi\)
0.627584 + 0.778549i \(0.284044\pi\)
\(390\) −330.000 −0.0428467
\(391\) −2352.00 −0.304209
\(392\) 0 0
\(393\) 2196.00 0.281867
\(394\) 2526.00 0.322990
\(395\) 1200.00 0.152857
\(396\) −3276.00 −0.415720
\(397\) −7126.00 −0.900866 −0.450433 0.892810i \(-0.648730\pi\)
−0.450433 + 0.892810i \(0.648730\pi\)
\(398\) 1160.00 0.146094
\(399\) 0 0
\(400\) 1025.00 0.128125
\(401\) −8718.00 −1.08568 −0.542838 0.839837i \(-0.682650\pi\)
−0.542838 + 0.839837i \(0.682650\pi\)
\(402\) 252.000 0.0312652
\(403\) −6336.00 −0.783173
\(404\) −8526.00 −1.04996
\(405\) −405.000 −0.0496904
\(406\) 0 0
\(407\) −1768.00 −0.215323
\(408\) 630.000 0.0764452
\(409\) 10870.0 1.31415 0.657074 0.753826i \(-0.271794\pi\)
0.657074 + 0.753826i \(0.271794\pi\)
\(410\) 610.000 0.0734774
\(411\) 6642.00 0.797143
\(412\) −616.000 −0.0736605
\(413\) 0 0
\(414\) −1512.00 −0.179495
\(415\) 6060.00 0.716804
\(416\) −3542.00 −0.417454
\(417\) 60.0000 0.00704607
\(418\) 1040.00 0.121694
\(419\) 9700.00 1.13097 0.565484 0.824759i \(-0.308689\pi\)
0.565484 + 0.824759i \(0.308689\pi\)
\(420\) 0 0
\(421\) 862.000 0.0997893 0.0498947 0.998754i \(-0.484111\pi\)
0.0498947 + 0.998754i \(0.484111\pi\)
\(422\) −4468.00 −0.515400
\(423\) −2304.00 −0.264833
\(424\) 5070.00 0.580710
\(425\) 350.000 0.0399470
\(426\) 984.000 0.111913
\(427\) 0 0
\(428\) −252.000 −0.0284600
\(429\) 3432.00 0.386244
\(430\) 940.000 0.105421
\(431\) 15792.0 1.76490 0.882452 0.470402i \(-0.155891\pi\)
0.882452 + 0.470402i \(0.155891\pi\)
\(432\) −1107.00 −0.123288
\(433\) −11602.0 −1.28766 −0.643830 0.765169i \(-0.722655\pi\)
−0.643830 + 0.765169i \(0.722655\pi\)
\(434\) 0 0
\(435\) 3450.00 0.380264
\(436\) 6790.00 0.745830
\(437\) −3360.00 −0.367805
\(438\) −114.000 −0.0124364
\(439\) 440.000 0.0478361 0.0239181 0.999714i \(-0.492386\pi\)
0.0239181 + 0.999714i \(0.492386\pi\)
\(440\) 3900.00 0.422557
\(441\) 0 0
\(442\) −308.000 −0.0331449
\(443\) −10188.0 −1.09266 −0.546328 0.837571i \(-0.683975\pi\)
−0.546328 + 0.837571i \(0.683975\pi\)
\(444\) −714.000 −0.0763174
\(445\) 1650.00 0.175770
\(446\) −6032.00 −0.640411
\(447\) 3990.00 0.422194
\(448\) 0 0
\(449\) −13310.0 −1.39897 −0.699485 0.714647i \(-0.746587\pi\)
−0.699485 + 0.714647i \(0.746587\pi\)
\(450\) 225.000 0.0235702
\(451\) −6344.00 −0.662367
\(452\) −7294.00 −0.759029
\(453\) 3624.00 0.375873
\(454\) −2636.00 −0.272497
\(455\) 0 0
\(456\) 900.000 0.0924262
\(457\) 3226.00 0.330210 0.165105 0.986276i \(-0.447204\pi\)
0.165105 + 0.986276i \(0.447204\pi\)
\(458\) −4830.00 −0.492775
\(459\) −378.000 −0.0384391
\(460\) −5880.00 −0.595992
\(461\) −6582.00 −0.664977 −0.332488 0.943107i \(-0.607888\pi\)
−0.332488 + 0.943107i \(0.607888\pi\)
\(462\) 0 0
\(463\) 15072.0 1.51286 0.756431 0.654073i \(-0.226941\pi\)
0.756431 + 0.654073i \(0.226941\pi\)
\(464\) 9430.00 0.943484
\(465\) 4320.00 0.430828
\(466\) 2682.00 0.266612
\(467\) −476.000 −0.0471663 −0.0235831 0.999722i \(-0.507507\pi\)
−0.0235831 + 0.999722i \(0.507507\pi\)
\(468\) 1386.00 0.136897
\(469\) 0 0
\(470\) 1280.00 0.125621
\(471\) −10542.0 −1.03132
\(472\) 1500.00 0.146278
\(473\) −9776.00 −0.950319
\(474\) 720.000 0.0697694
\(475\) 500.000 0.0482980
\(476\) 0 0
\(477\) −3042.00 −0.291999
\(478\) 2320.00 0.221997
\(479\) 19680.0 1.87725 0.938624 0.344941i \(-0.112101\pi\)
0.938624 + 0.344941i \(0.112101\pi\)
\(480\) 2415.00 0.229644
\(481\) 748.000 0.0709062
\(482\) −2002.00 −0.189188
\(483\) 0 0
\(484\) −9611.00 −0.902611
\(485\) 4330.00 0.405392
\(486\) −243.000 −0.0226805
\(487\) −5944.00 −0.553077 −0.276538 0.961003i \(-0.589187\pi\)
−0.276538 + 0.961003i \(0.589187\pi\)
\(488\) 11130.0 1.03244
\(489\) 6204.00 0.573731
\(490\) 0 0
\(491\) 10772.0 0.990089 0.495044 0.868868i \(-0.335152\pi\)
0.495044 + 0.868868i \(0.335152\pi\)
\(492\) −2562.00 −0.234764
\(493\) 3220.00 0.294161
\(494\) −440.000 −0.0400740
\(495\) −2340.00 −0.212475
\(496\) 11808.0 1.06894
\(497\) 0 0
\(498\) 3636.00 0.327175
\(499\) 8140.00 0.730253 0.365127 0.930958i \(-0.381026\pi\)
0.365127 + 0.930958i \(0.381026\pi\)
\(500\) 875.000 0.0782624
\(501\) −72.0000 −0.00642060
\(502\) −132.000 −0.0117360
\(503\) 13768.0 1.22045 0.610223 0.792229i \(-0.291080\pi\)
0.610223 + 0.792229i \(0.291080\pi\)
\(504\) 0 0
\(505\) −6090.00 −0.536637
\(506\) −8736.00 −0.767515
\(507\) 5139.00 0.450160
\(508\) −13552.0 −1.18361
\(509\) −22150.0 −1.92884 −0.964422 0.264368i \(-0.914837\pi\)
−0.964422 + 0.264368i \(0.914837\pi\)
\(510\) 210.000 0.0182332
\(511\) 0 0
\(512\) 11521.0 0.994455
\(513\) −540.000 −0.0464748
\(514\) 7614.00 0.653384
\(515\) −440.000 −0.0376480
\(516\) −3948.00 −0.336824
\(517\) −13312.0 −1.13242
\(518\) 0 0
\(519\) −1854.00 −0.156805
\(520\) −1650.00 −0.139149
\(521\) −1562.00 −0.131348 −0.0656741 0.997841i \(-0.520920\pi\)
−0.0656741 + 0.997841i \(0.520920\pi\)
\(522\) 2070.00 0.173566
\(523\) 668.000 0.0558501 0.0279250 0.999610i \(-0.491110\pi\)
0.0279250 + 0.999610i \(0.491110\pi\)
\(524\) 5124.00 0.427181
\(525\) 0 0
\(526\) −4888.00 −0.405184
\(527\) 4032.00 0.333276
\(528\) −6396.00 −0.527178
\(529\) 16057.0 1.31972
\(530\) 1690.00 0.138507
\(531\) −900.000 −0.0735531
\(532\) 0 0
\(533\) 2684.00 0.218118
\(534\) 990.000 0.0802275
\(535\) −180.000 −0.0145459
\(536\) 1260.00 0.101537
\(537\) −10020.0 −0.805205
\(538\) −1270.00 −0.101772
\(539\) 0 0
\(540\) −945.000 −0.0753080
\(541\) −6138.00 −0.487788 −0.243894 0.969802i \(-0.578425\pi\)
−0.243894 + 0.969802i \(0.578425\pi\)
\(542\) −1072.00 −0.0849564
\(543\) −534.000 −0.0422028
\(544\) 2254.00 0.177646
\(545\) 4850.00 0.381195
\(546\) 0 0
\(547\) −10484.0 −0.819494 −0.409747 0.912199i \(-0.634383\pi\)
−0.409747 + 0.912199i \(0.634383\pi\)
\(548\) 15498.0 1.20811
\(549\) −6678.00 −0.519144
\(550\) 1300.00 0.100786
\(551\) 4600.00 0.355656
\(552\) −7560.00 −0.582926
\(553\) 0 0
\(554\) −5394.00 −0.413663
\(555\) −510.000 −0.0390059
\(556\) 140.000 0.0106786
\(557\) 3606.00 0.274311 0.137155 0.990550i \(-0.456204\pi\)
0.137155 + 0.990550i \(0.456204\pi\)
\(558\) 2592.00 0.196645
\(559\) 4136.00 0.312941
\(560\) 0 0
\(561\) −2184.00 −0.164365
\(562\) 2442.00 0.183291
\(563\) −12252.0 −0.917159 −0.458579 0.888654i \(-0.651641\pi\)
−0.458579 + 0.888654i \(0.651641\pi\)
\(564\) −5376.00 −0.401366
\(565\) −5210.00 −0.387940
\(566\) −2772.00 −0.205858
\(567\) 0 0
\(568\) 4920.00 0.363448
\(569\) −14550.0 −1.07200 −0.536000 0.844218i \(-0.680065\pi\)
−0.536000 + 0.844218i \(0.680065\pi\)
\(570\) 300.000 0.0220449
\(571\) −25468.0 −1.86655 −0.933277 0.359157i \(-0.883064\pi\)
−0.933277 + 0.359157i \(0.883064\pi\)
\(572\) 8008.00 0.585369
\(573\) 5664.00 0.412944
\(574\) 0 0
\(575\) −4200.00 −0.304612
\(576\) −1503.00 −0.108724
\(577\) −12866.0 −0.928282 −0.464141 0.885761i \(-0.653637\pi\)
−0.464141 + 0.885761i \(0.653637\pi\)
\(578\) −4717.00 −0.339449
\(579\) −5766.00 −0.413863
\(580\) 8050.00 0.576307
\(581\) 0 0
\(582\) 2598.00 0.185035
\(583\) −17576.0 −1.24858
\(584\) −570.000 −0.0403883
\(585\) 990.000 0.0699683
\(586\) −4542.00 −0.320185
\(587\) 14844.0 1.04374 0.521872 0.853024i \(-0.325234\pi\)
0.521872 + 0.853024i \(0.325234\pi\)
\(588\) 0 0
\(589\) 5760.00 0.402948
\(590\) 500.000 0.0348893
\(591\) −7578.00 −0.527440
\(592\) −1394.00 −0.0967788
\(593\) −20402.0 −1.41283 −0.706416 0.707797i \(-0.749689\pi\)
−0.706416 + 0.707797i \(0.749689\pi\)
\(594\) −1404.00 −0.0969812
\(595\) 0 0
\(596\) 9310.00 0.639853
\(597\) −3480.00 −0.238571
\(598\) 3696.00 0.252744
\(599\) 10760.0 0.733959 0.366980 0.930229i \(-0.380392\pi\)
0.366980 + 0.930229i \(0.380392\pi\)
\(600\) 1125.00 0.0765466
\(601\) −14282.0 −0.969343 −0.484671 0.874696i \(-0.661061\pi\)
−0.484671 + 0.874696i \(0.661061\pi\)
\(602\) 0 0
\(603\) −756.000 −0.0510559
\(604\) 8456.00 0.569652
\(605\) −6865.00 −0.461326
\(606\) −3654.00 −0.244940
\(607\) −11056.0 −0.739290 −0.369645 0.929173i \(-0.620521\pi\)
−0.369645 + 0.929173i \(0.620521\pi\)
\(608\) 3220.00 0.214783
\(609\) 0 0
\(610\) 3710.00 0.246252
\(611\) 5632.00 0.372907
\(612\) −882.000 −0.0582561
\(613\) −16418.0 −1.08176 −0.540878 0.841101i \(-0.681908\pi\)
−0.540878 + 0.841101i \(0.681908\pi\)
\(614\) −5116.00 −0.336262
\(615\) −1830.00 −0.119988
\(616\) 0 0
\(617\) −10374.0 −0.676891 −0.338445 0.940986i \(-0.609901\pi\)
−0.338445 + 0.940986i \(0.609901\pi\)
\(618\) −264.000 −0.0171839
\(619\) 5260.00 0.341546 0.170773 0.985310i \(-0.445373\pi\)
0.170773 + 0.985310i \(0.445373\pi\)
\(620\) 10080.0 0.652940
\(621\) 4536.00 0.293113
\(622\) 2808.00 0.181014
\(623\) 0 0
\(624\) 2706.00 0.173600
\(625\) 625.000 0.0400000
\(626\) 7318.00 0.467230
\(627\) −3120.00 −0.198725
\(628\) −24598.0 −1.56300
\(629\) −476.000 −0.0301739
\(630\) 0 0
\(631\) 21352.0 1.34708 0.673542 0.739149i \(-0.264772\pi\)
0.673542 + 0.739149i \(0.264772\pi\)
\(632\) 3600.00 0.226583
\(633\) 13404.0 0.841645
\(634\) 2246.00 0.140694
\(635\) −9680.00 −0.604943
\(636\) −7098.00 −0.442538
\(637\) 0 0
\(638\) 11960.0 0.742164
\(639\) −2952.00 −0.182753
\(640\) 7275.00 0.449328
\(641\) −29118.0 −1.79422 −0.897108 0.441812i \(-0.854336\pi\)
−0.897108 + 0.441812i \(0.854336\pi\)
\(642\) −108.000 −0.00663928
\(643\) −5772.00 −0.354005 −0.177003 0.984210i \(-0.556640\pi\)
−0.177003 + 0.984210i \(0.556640\pi\)
\(644\) 0 0
\(645\) −2820.00 −0.172151
\(646\) 280.000 0.0170533
\(647\) 14264.0 0.866732 0.433366 0.901218i \(-0.357326\pi\)
0.433366 + 0.901218i \(0.357326\pi\)
\(648\) −1215.00 −0.0736570
\(649\) −5200.00 −0.314511
\(650\) −550.000 −0.0331889
\(651\) 0 0
\(652\) 14476.0 0.869515
\(653\) 6902.00 0.413623 0.206812 0.978381i \(-0.433691\pi\)
0.206812 + 0.978381i \(0.433691\pi\)
\(654\) 2910.00 0.173991
\(655\) 3660.00 0.218333
\(656\) −5002.00 −0.297706
\(657\) 342.000 0.0203085
\(658\) 0 0
\(659\) 20140.0 1.19051 0.595253 0.803539i \(-0.297052\pi\)
0.595253 + 0.803539i \(0.297052\pi\)
\(660\) −5460.00 −0.322015
\(661\) 3218.00 0.189358 0.0946790 0.995508i \(-0.469818\pi\)
0.0946790 + 0.995508i \(0.469818\pi\)
\(662\) 1332.00 0.0782019
\(663\) 924.000 0.0541255
\(664\) 18180.0 1.06253
\(665\) 0 0
\(666\) −306.000 −0.0178037
\(667\) −38640.0 −2.24310
\(668\) −168.000 −0.00973071
\(669\) 18096.0 1.04579
\(670\) 420.000 0.0242179
\(671\) −38584.0 −2.21985
\(672\) 0 0
\(673\) −7518.00 −0.430606 −0.215303 0.976547i \(-0.569074\pi\)
−0.215303 + 0.976547i \(0.569074\pi\)
\(674\) −11534.0 −0.659159
\(675\) −675.000 −0.0384900
\(676\) 11991.0 0.682237
\(677\) 18114.0 1.02833 0.514164 0.857692i \(-0.328102\pi\)
0.514164 + 0.857692i \(0.328102\pi\)
\(678\) −3126.00 −0.177070
\(679\) 0 0
\(680\) 1050.00 0.0592142
\(681\) 7908.00 0.444986
\(682\) 14976.0 0.840851
\(683\) −23868.0 −1.33716 −0.668582 0.743638i \(-0.733099\pi\)
−0.668582 + 0.743638i \(0.733099\pi\)
\(684\) −1260.00 −0.0704347
\(685\) 11070.0 0.617464
\(686\) 0 0
\(687\) 14490.0 0.804699
\(688\) −7708.00 −0.427129
\(689\) 7436.00 0.411160
\(690\) −2520.00 −0.139036
\(691\) −172.000 −0.00946916 −0.00473458 0.999989i \(-0.501507\pi\)
−0.00473458 + 0.999989i \(0.501507\pi\)
\(692\) −4326.00 −0.237644
\(693\) 0 0
\(694\) 11956.0 0.653953
\(695\) 100.000 0.00545787
\(696\) 10350.0 0.563672
\(697\) −1708.00 −0.0928194
\(698\) −4870.00 −0.264086
\(699\) −8046.00 −0.435376
\(700\) 0 0
\(701\) −22138.0 −1.19278 −0.596391 0.802694i \(-0.703399\pi\)
−0.596391 + 0.802694i \(0.703399\pi\)
\(702\) 594.000 0.0319360
\(703\) −680.000 −0.0364818
\(704\) −8684.00 −0.464901
\(705\) −3840.00 −0.205139
\(706\) −10722.0 −0.571569
\(707\) 0 0
\(708\) −2100.00 −0.111473
\(709\) 3070.00 0.162618 0.0813091 0.996689i \(-0.474090\pi\)
0.0813091 + 0.996689i \(0.474090\pi\)
\(710\) 1640.00 0.0866875
\(711\) −2160.00 −0.113933
\(712\) 4950.00 0.260546
\(713\) −48384.0 −2.54137
\(714\) 0 0
\(715\) 5720.00 0.299183
\(716\) −23380.0 −1.22032
\(717\) −6960.00 −0.362519
\(718\) 120.000 0.00623727
\(719\) −15600.0 −0.809154 −0.404577 0.914504i \(-0.632581\pi\)
−0.404577 + 0.914504i \(0.632581\pi\)
\(720\) −1845.00 −0.0954987
\(721\) 0 0
\(722\) −6459.00 −0.332935
\(723\) 6006.00 0.308943
\(724\) −1246.00 −0.0639603
\(725\) 5750.00 0.294551
\(726\) −4119.00 −0.210565
\(727\) −20696.0 −1.05581 −0.527904 0.849304i \(-0.677022\pi\)
−0.527904 + 0.849304i \(0.677022\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −190.000 −0.00963317
\(731\) −2632.00 −0.133171
\(732\) −15582.0 −0.786786
\(733\) 30778.0 1.55090 0.775451 0.631408i \(-0.217522\pi\)
0.775451 + 0.631408i \(0.217522\pi\)
\(734\) −3936.00 −0.197930
\(735\) 0 0
\(736\) −27048.0 −1.35462
\(737\) −4368.00 −0.218314
\(738\) −1098.00 −0.0547669
\(739\) 11740.0 0.584388 0.292194 0.956359i \(-0.405615\pi\)
0.292194 + 0.956359i \(0.405615\pi\)
\(740\) −1190.00 −0.0591152
\(741\) 1320.00 0.0654405
\(742\) 0 0
\(743\) 2632.00 0.129958 0.0649789 0.997887i \(-0.479302\pi\)
0.0649789 + 0.997887i \(0.479302\pi\)
\(744\) 12960.0 0.638625
\(745\) 6650.00 0.327030
\(746\) 3022.00 0.148315
\(747\) −10908.0 −0.534274
\(748\) −5096.00 −0.249102
\(749\) 0 0
\(750\) 375.000 0.0182574
\(751\) −20528.0 −0.997440 −0.498720 0.866763i \(-0.666196\pi\)
−0.498720 + 0.866763i \(0.666196\pi\)
\(752\) −10496.0 −0.508976
\(753\) 396.000 0.0191647
\(754\) −5060.00 −0.244396
\(755\) 6040.00 0.291150
\(756\) 0 0
\(757\) 21646.0 1.03928 0.519642 0.854384i \(-0.326066\pi\)
0.519642 + 0.854384i \(0.326066\pi\)
\(758\) −13340.0 −0.639222
\(759\) 26208.0 1.25335
\(760\) 1500.00 0.0715931
\(761\) −18282.0 −0.870857 −0.435428 0.900223i \(-0.643403\pi\)
−0.435428 + 0.900223i \(0.643403\pi\)
\(762\) −5808.00 −0.276118
\(763\) 0 0
\(764\) 13216.0 0.625835
\(765\) −630.000 −0.0297748
\(766\) 1008.00 0.0475464
\(767\) 2200.00 0.103569
\(768\) 357.000 0.0167736
\(769\) 24190.0 1.13435 0.567174 0.823598i \(-0.308037\pi\)
0.567174 + 0.823598i \(0.308037\pi\)
\(770\) 0 0
\(771\) −22842.0 −1.06697
\(772\) −13454.0 −0.627228
\(773\) 25698.0 1.19572 0.597861 0.801600i \(-0.296018\pi\)
0.597861 + 0.801600i \(0.296018\pi\)
\(774\) −1692.00 −0.0785758
\(775\) 7200.00 0.333718
\(776\) 12990.0 0.600920
\(777\) 0 0
\(778\) 9630.00 0.443769
\(779\) −2440.00 −0.112223
\(780\) 2310.00 0.106040
\(781\) −17056.0 −0.781449
\(782\) −2352.00 −0.107554
\(783\) −6210.00 −0.283432
\(784\) 0 0
\(785\) −17570.0 −0.798854
\(786\) 2196.00 0.0996549
\(787\) −33436.0 −1.51444 −0.757220 0.653160i \(-0.773443\pi\)
−0.757220 + 0.653160i \(0.773443\pi\)
\(788\) −17682.0 −0.799359
\(789\) 14664.0 0.661663
\(790\) 1200.00 0.0540431
\(791\) 0 0
\(792\) −7020.00 −0.314956
\(793\) 16324.0 0.730999
\(794\) −7126.00 −0.318504
\(795\) −5070.00 −0.226182
\(796\) −8120.00 −0.361565
\(797\) 37594.0 1.67083 0.835413 0.549623i \(-0.185229\pi\)
0.835413 + 0.549623i \(0.185229\pi\)
\(798\) 0 0
\(799\) −3584.00 −0.158689
\(800\) 4025.00 0.177882
\(801\) −2970.00 −0.131011
\(802\) −8718.00 −0.383844
\(803\) 1976.00 0.0868388
\(804\) −1764.00 −0.0773775
\(805\) 0 0
\(806\) −6336.00 −0.276893
\(807\) 3810.00 0.166194
\(808\) −18270.0 −0.795466
\(809\) 4730.00 0.205560 0.102780 0.994704i \(-0.467226\pi\)
0.102780 + 0.994704i \(0.467226\pi\)
\(810\) −405.000 −0.0175682
\(811\) 8748.00 0.378772 0.189386 0.981903i \(-0.439350\pi\)
0.189386 + 0.981903i \(0.439350\pi\)
\(812\) 0 0
\(813\) 3216.00 0.138733
\(814\) −1768.00 −0.0761282
\(815\) 10340.0 0.444410
\(816\) −1722.00 −0.0738751
\(817\) −3760.00 −0.161011
\(818\) 10870.0 0.464622
\(819\) 0 0
\(820\) −4270.00 −0.181847
\(821\) 44142.0 1.87645 0.938226 0.346024i \(-0.112468\pi\)
0.938226 + 0.346024i \(0.112468\pi\)
\(822\) 6642.00 0.281833
\(823\) 3992.00 0.169079 0.0845397 0.996420i \(-0.473058\pi\)
0.0845397 + 0.996420i \(0.473058\pi\)
\(824\) −1320.00 −0.0558063
\(825\) −3900.00 −0.164583
\(826\) 0 0
\(827\) −14444.0 −0.607336 −0.303668 0.952778i \(-0.598211\pi\)
−0.303668 + 0.952778i \(0.598211\pi\)
\(828\) 10584.0 0.444226
\(829\) −42150.0 −1.76590 −0.882949 0.469468i \(-0.844446\pi\)
−0.882949 + 0.469468i \(0.844446\pi\)
\(830\) 6060.00 0.253429
\(831\) 16182.0 0.675508
\(832\) 3674.00 0.153093
\(833\) 0 0
\(834\) 60.0000 0.00249116
\(835\) −120.000 −0.00497338
\(836\) −7280.00 −0.301177
\(837\) −7776.00 −0.321121
\(838\) 9700.00 0.399858
\(839\) −13400.0 −0.551394 −0.275697 0.961245i \(-0.588909\pi\)
−0.275697 + 0.961245i \(0.588909\pi\)
\(840\) 0 0
\(841\) 28511.0 1.16901
\(842\) 862.000 0.0352809
\(843\) −7326.00 −0.299313
\(844\) 31276.0 1.27555
\(845\) 8565.00 0.348692
\(846\) −2304.00 −0.0936326
\(847\) 0 0
\(848\) −13858.0 −0.561186
\(849\) 8316.00 0.336165
\(850\) 350.000 0.0141234
\(851\) 5712.00 0.230088
\(852\) −6888.00 −0.276971
\(853\) 8658.00 0.347531 0.173766 0.984787i \(-0.444406\pi\)
0.173766 + 0.984787i \(0.444406\pi\)
\(854\) 0 0
\(855\) −900.000 −0.0359992
\(856\) −540.000 −0.0215617
\(857\) −42826.0 −1.70701 −0.853505 0.521084i \(-0.825528\pi\)
−0.853505 + 0.521084i \(0.825528\pi\)
\(858\) 3432.00 0.136558
\(859\) 35900.0 1.42595 0.712976 0.701189i \(-0.247347\pi\)
0.712976 + 0.701189i \(0.247347\pi\)
\(860\) −6580.00 −0.260902
\(861\) 0 0
\(862\) 15792.0 0.623988
\(863\) −3088.00 −0.121804 −0.0609019 0.998144i \(-0.519398\pi\)
−0.0609019 + 0.998144i \(0.519398\pi\)
\(864\) −4347.00 −0.171167
\(865\) −3090.00 −0.121460
\(866\) −11602.0 −0.455256
\(867\) 14151.0 0.554317
\(868\) 0 0
\(869\) −12480.0 −0.487175
\(870\) 3450.00 0.134444
\(871\) 1848.00 0.0718910
\(872\) 14550.0 0.565052
\(873\) −7794.00 −0.302161
\(874\) −3360.00 −0.130039
\(875\) 0 0
\(876\) 798.000 0.0307784
\(877\) −35274.0 −1.35817 −0.679087 0.734058i \(-0.737624\pi\)
−0.679087 + 0.734058i \(0.737624\pi\)
\(878\) 440.000 0.0169126
\(879\) 13626.0 0.522860
\(880\) −10660.0 −0.408351
\(881\) −25042.0 −0.957646 −0.478823 0.877911i \(-0.658936\pi\)
−0.478823 + 0.877911i \(0.658936\pi\)
\(882\) 0 0
\(883\) 12572.0 0.479141 0.239570 0.970879i \(-0.422993\pi\)
0.239570 + 0.970879i \(0.422993\pi\)
\(884\) 2156.00 0.0820296
\(885\) −1500.00 −0.0569740
\(886\) −10188.0 −0.386312
\(887\) 21864.0 0.827645 0.413823 0.910358i \(-0.364193\pi\)
0.413823 + 0.910358i \(0.364193\pi\)
\(888\) −1530.00 −0.0578192
\(889\) 0 0
\(890\) 1650.00 0.0621440
\(891\) 4212.00 0.158370
\(892\) 42224.0 1.58494
\(893\) −5120.00 −0.191864
\(894\) 3990.00 0.149268
\(895\) −16700.0 −0.623709
\(896\) 0 0
\(897\) −11088.0 −0.412729
\(898\) −13310.0 −0.494611
\(899\) 66240.0 2.45743
\(900\) −1575.00 −0.0583333
\(901\) −4732.00 −0.174968
\(902\) −6344.00 −0.234182
\(903\) 0 0
\(904\) −15630.0 −0.575051
\(905\) −890.000 −0.0326902
\(906\) 3624.00 0.132891
\(907\) 31236.0 1.14352 0.571761 0.820420i \(-0.306260\pi\)
0.571761 + 0.820420i \(0.306260\pi\)
\(908\) 18452.0 0.674396
\(909\) 10962.0 0.399985
\(910\) 0 0
\(911\) 8272.00 0.300838 0.150419 0.988622i \(-0.451938\pi\)
0.150419 + 0.988622i \(0.451938\pi\)
\(912\) −2460.00 −0.0893188
\(913\) −63024.0 −2.28455
\(914\) 3226.00 0.116747
\(915\) −11130.0 −0.402127
\(916\) 33810.0 1.21956
\(917\) 0 0
\(918\) −378.000 −0.0135903
\(919\) 20200.0 0.725067 0.362533 0.931971i \(-0.381912\pi\)
0.362533 + 0.931971i \(0.381912\pi\)
\(920\) −12600.0 −0.451532
\(921\) 15348.0 0.549114
\(922\) −6582.00 −0.235105
\(923\) 7216.00 0.257332
\(924\) 0 0
\(925\) −850.000 −0.0302139
\(926\) 15072.0 0.534878
\(927\) 792.000 0.0280612
\(928\) 37030.0 1.30988
\(929\) −31010.0 −1.09516 −0.547581 0.836753i \(-0.684451\pi\)
−0.547581 + 0.836753i \(0.684451\pi\)
\(930\) 4320.00 0.152321
\(931\) 0 0
\(932\) −18774.0 −0.659831
\(933\) −8424.00 −0.295594
\(934\) −476.000 −0.0166758
\(935\) −3640.00 −0.127316
\(936\) 2970.00 0.103715
\(937\) 39174.0 1.36580 0.682902 0.730510i \(-0.260717\pi\)
0.682902 + 0.730510i \(0.260717\pi\)
\(938\) 0 0
\(939\) −21954.0 −0.762984
\(940\) −8960.00 −0.310897
\(941\) 4138.00 0.143353 0.0716764 0.997428i \(-0.477165\pi\)
0.0716764 + 0.997428i \(0.477165\pi\)
\(942\) −10542.0 −0.364625
\(943\) 20496.0 0.707785
\(944\) −4100.00 −0.141360
\(945\) 0 0
\(946\) −9776.00 −0.335989
\(947\) 23676.0 0.812425 0.406213 0.913779i \(-0.366849\pi\)
0.406213 + 0.913779i \(0.366849\pi\)
\(948\) −5040.00 −0.172670
\(949\) −836.000 −0.0285961
\(950\) 500.000 0.0170759
\(951\) −6738.00 −0.229752
\(952\) 0 0
\(953\) 18922.0 0.643173 0.321586 0.946880i \(-0.395784\pi\)
0.321586 + 0.946880i \(0.395784\pi\)
\(954\) −3042.00 −0.103237
\(955\) 9440.00 0.319865
\(956\) −16240.0 −0.549413
\(957\) −35880.0 −1.21195
\(958\) 19680.0 0.663708
\(959\) 0 0
\(960\) −2505.00 −0.0842172
\(961\) 53153.0 1.78420
\(962\) 748.000 0.0250691
\(963\) 324.000 0.0108419
\(964\) 14014.0 0.468216
\(965\) −9610.00 −0.320577
\(966\) 0 0
\(967\) 39656.0 1.31877 0.659385 0.751805i \(-0.270817\pi\)
0.659385 + 0.751805i \(0.270817\pi\)
\(968\) −20595.0 −0.683831
\(969\) −840.000 −0.0278480
\(970\) 4330.00 0.143328
\(971\) 33228.0 1.09818 0.549092 0.835762i \(-0.314974\pi\)
0.549092 + 0.835762i \(0.314974\pi\)
\(972\) 1701.00 0.0561313
\(973\) 0 0
\(974\) −5944.00 −0.195542
\(975\) 1650.00 0.0541972
\(976\) −30422.0 −0.997730
\(977\) −974.000 −0.0318946 −0.0159473 0.999873i \(-0.505076\pi\)
−0.0159473 + 0.999873i \(0.505076\pi\)
\(978\) 6204.00 0.202845
\(979\) −17160.0 −0.560200
\(980\) 0 0
\(981\) −8730.00 −0.284126
\(982\) 10772.0 0.350049
\(983\) 13608.0 0.441534 0.220767 0.975327i \(-0.429144\pi\)
0.220767 + 0.975327i \(0.429144\pi\)
\(984\) −5490.00 −0.177861
\(985\) −12630.0 −0.408554
\(986\) 3220.00 0.104002
\(987\) 0 0
\(988\) 3080.00 0.0991780
\(989\) 31584.0 1.01548
\(990\) −2340.00 −0.0751213
\(991\) 13472.0 0.431839 0.215919 0.976411i \(-0.430725\pi\)
0.215919 + 0.976411i \(0.430725\pi\)
\(992\) 46368.0 1.48406
\(993\) −3996.00 −0.127703
\(994\) 0 0
\(995\) −5800.00 −0.184796
\(996\) −25452.0 −0.809716
\(997\) 3234.00 0.102730 0.0513650 0.998680i \(-0.483643\pi\)
0.0513650 + 0.998680i \(0.483643\pi\)
\(998\) 8140.00 0.258184
\(999\) 918.000 0.0290733
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 735.4.a.e.1.1 1
3.2 odd 2 2205.4.a.l.1.1 1
7.6 odd 2 15.4.a.a.1.1 1
21.20 even 2 45.4.a.c.1.1 1
28.27 even 2 240.4.a.e.1.1 1
35.13 even 4 75.4.b.b.49.1 2
35.27 even 4 75.4.b.b.49.2 2
35.34 odd 2 75.4.a.b.1.1 1
56.13 odd 2 960.4.a.b.1.1 1
56.27 even 2 960.4.a.ba.1.1 1
63.13 odd 6 405.4.e.g.136.1 2
63.20 even 6 405.4.e.i.271.1 2
63.34 odd 6 405.4.e.g.271.1 2
63.41 even 6 405.4.e.i.136.1 2
77.76 even 2 1815.4.a.e.1.1 1
84.83 odd 2 720.4.a.n.1.1 1
105.62 odd 4 225.4.b.e.199.1 2
105.83 odd 4 225.4.b.e.199.2 2
105.104 even 2 225.4.a.f.1.1 1
140.27 odd 4 1200.4.f.b.49.2 2
140.83 odd 4 1200.4.f.b.49.1 2
140.139 even 2 1200.4.a.t.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.4.a.a.1.1 1 7.6 odd 2
45.4.a.c.1.1 1 21.20 even 2
75.4.a.b.1.1 1 35.34 odd 2
75.4.b.b.49.1 2 35.13 even 4
75.4.b.b.49.2 2 35.27 even 4
225.4.a.f.1.1 1 105.104 even 2
225.4.b.e.199.1 2 105.62 odd 4
225.4.b.e.199.2 2 105.83 odd 4
240.4.a.e.1.1 1 28.27 even 2
405.4.e.g.136.1 2 63.13 odd 6
405.4.e.g.271.1 2 63.34 odd 6
405.4.e.i.136.1 2 63.41 even 6
405.4.e.i.271.1 2 63.20 even 6
720.4.a.n.1.1 1 84.83 odd 2
735.4.a.e.1.1 1 1.1 even 1 trivial
960.4.a.b.1.1 1 56.13 odd 2
960.4.a.ba.1.1 1 56.27 even 2
1200.4.a.t.1.1 1 140.139 even 2
1200.4.f.b.49.1 2 140.83 odd 4
1200.4.f.b.49.2 2 140.27 odd 4
1815.4.a.e.1.1 1 77.76 even 2
2205.4.a.l.1.1 1 3.2 odd 2