Properties

Label 930.4.a.c.1.1
Level $930$
Weight $4$
Character 930.1
Self dual yes
Analytic conductor $54.872$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 930.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(54.8717763053\)
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 \(\chi\) \(=\) 930.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} +26.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} +26.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} -48.0000 q^{11} +12.0000 q^{12} -88.0000 q^{13} +52.0000 q^{14} -15.0000 q^{15} +16.0000 q^{16} -54.0000 q^{17} +18.0000 q^{18} -160.000 q^{19} -20.0000 q^{20} +78.0000 q^{21} -96.0000 q^{22} -48.0000 q^{23} +24.0000 q^{24} +25.0000 q^{25} -176.000 q^{26} +27.0000 q^{27} +104.000 q^{28} -120.000 q^{29} -30.0000 q^{30} +31.0000 q^{31} +32.0000 q^{32} -144.000 q^{33} -108.000 q^{34} -130.000 q^{35} +36.0000 q^{36} -304.000 q^{37} -320.000 q^{38} -264.000 q^{39} -40.0000 q^{40} +162.000 q^{41} +156.000 q^{42} +272.000 q^{43} -192.000 q^{44} -45.0000 q^{45} -96.0000 q^{46} +96.0000 q^{47} +48.0000 q^{48} +333.000 q^{49} +50.0000 q^{50} -162.000 q^{51} -352.000 q^{52} +582.000 q^{53} +54.0000 q^{54} +240.000 q^{55} +208.000 q^{56} -480.000 q^{57} -240.000 q^{58} +30.0000 q^{59} -60.0000 q^{60} -478.000 q^{61} +62.0000 q^{62} +234.000 q^{63} +64.0000 q^{64} +440.000 q^{65} -288.000 q^{66} -334.000 q^{67} -216.000 q^{68} -144.000 q^{69} -260.000 q^{70} +1062.00 q^{71} +72.0000 q^{72} +212.000 q^{73} -608.000 q^{74} +75.0000 q^{75} -640.000 q^{76} -1248.00 q^{77} -528.000 q^{78} -640.000 q^{79} -80.0000 q^{80} +81.0000 q^{81} +324.000 q^{82} +972.000 q^{83} +312.000 q^{84} +270.000 q^{85} +544.000 q^{86} -360.000 q^{87} -384.000 q^{88} +120.000 q^{89} -90.0000 q^{90} -2288.00 q^{91} -192.000 q^{92} +93.0000 q^{93} +192.000 q^{94} +800.000 q^{95} +96.0000 q^{96} +86.0000 q^{97} +666.000 q^{98} -432.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) 3.00000 0.577350
\(4\) 4.00000 0.500000
\(5\) −5.00000 −0.447214
\(6\) 6.00000 0.408248
\(7\) 26.0000 1.40387 0.701934 0.712242i \(-0.252320\pi\)
0.701934 + 0.712242i \(0.252320\pi\)
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) −10.0000 −0.316228
\(11\) −48.0000 −1.31569 −0.657843 0.753155i \(-0.728531\pi\)
−0.657843 + 0.753155i \(0.728531\pi\)
\(12\) 12.0000 0.288675
\(13\) −88.0000 −1.87745 −0.938723 0.344671i \(-0.887990\pi\)
−0.938723 + 0.344671i \(0.887990\pi\)
\(14\) 52.0000 0.992685
\(15\) −15.0000 −0.258199
\(16\) 16.0000 0.250000
\(17\) −54.0000 −0.770407 −0.385204 0.922832i \(-0.625869\pi\)
−0.385204 + 0.922832i \(0.625869\pi\)
\(18\) 18.0000 0.235702
\(19\) −160.000 −1.93192 −0.965961 0.258688i \(-0.916710\pi\)
−0.965961 + 0.258688i \(0.916710\pi\)
\(20\) −20.0000 −0.223607
\(21\) 78.0000 0.810524
\(22\) −96.0000 −0.930330
\(23\) −48.0000 −0.435161 −0.217580 0.976042i \(-0.569816\pi\)
−0.217580 + 0.976042i \(0.569816\pi\)
\(24\) 24.0000 0.204124
\(25\) 25.0000 0.200000
\(26\) −176.000 −1.32756
\(27\) 27.0000 0.192450
\(28\) 104.000 0.701934
\(29\) −120.000 −0.768395 −0.384197 0.923251i \(-0.625522\pi\)
−0.384197 + 0.923251i \(0.625522\pi\)
\(30\) −30.0000 −0.182574
\(31\) 31.0000 0.179605
\(32\) 32.0000 0.176777
\(33\) −144.000 −0.759612
\(34\) −108.000 −0.544760
\(35\) −130.000 −0.627829
\(36\) 36.0000 0.166667
\(37\) −304.000 −1.35074 −0.675369 0.737480i \(-0.736016\pi\)
−0.675369 + 0.737480i \(0.736016\pi\)
\(38\) −320.000 −1.36608
\(39\) −264.000 −1.08394
\(40\) −40.0000 −0.158114
\(41\) 162.000 0.617077 0.308538 0.951212i \(-0.400160\pi\)
0.308538 + 0.951212i \(0.400160\pi\)
\(42\) 156.000 0.573127
\(43\) 272.000 0.964642 0.482321 0.875995i \(-0.339794\pi\)
0.482321 + 0.875995i \(0.339794\pi\)
\(44\) −192.000 −0.657843
\(45\) −45.0000 −0.149071
\(46\) −96.0000 −0.307705
\(47\) 96.0000 0.297937 0.148969 0.988842i \(-0.452405\pi\)
0.148969 + 0.988842i \(0.452405\pi\)
\(48\) 48.0000 0.144338
\(49\) 333.000 0.970845
\(50\) 50.0000 0.141421
\(51\) −162.000 −0.444795
\(52\) −352.000 −0.938723
\(53\) 582.000 1.50837 0.754187 0.656659i \(-0.228031\pi\)
0.754187 + 0.656659i \(0.228031\pi\)
\(54\) 54.0000 0.136083
\(55\) 240.000 0.588393
\(56\) 208.000 0.496342
\(57\) −480.000 −1.11540
\(58\) −240.000 −0.543337
\(59\) 30.0000 0.0661978 0.0330989 0.999452i \(-0.489462\pi\)
0.0330989 + 0.999452i \(0.489462\pi\)
\(60\) −60.0000 −0.129099
\(61\) −478.000 −1.00331 −0.501653 0.865069i \(-0.667274\pi\)
−0.501653 + 0.865069i \(0.667274\pi\)
\(62\) 62.0000 0.127000
\(63\) 234.000 0.467956
\(64\) 64.0000 0.125000
\(65\) 440.000 0.839620
\(66\) −288.000 −0.537127
\(67\) −334.000 −0.609024 −0.304512 0.952509i \(-0.598493\pi\)
−0.304512 + 0.952509i \(0.598493\pi\)
\(68\) −216.000 −0.385204
\(69\) −144.000 −0.251240
\(70\) −260.000 −0.443942
\(71\) 1062.00 1.77516 0.887579 0.460656i \(-0.152386\pi\)
0.887579 + 0.460656i \(0.152386\pi\)
\(72\) 72.0000 0.117851
\(73\) 212.000 0.339900 0.169950 0.985453i \(-0.445639\pi\)
0.169950 + 0.985453i \(0.445639\pi\)
\(74\) −608.000 −0.955116
\(75\) 75.0000 0.115470
\(76\) −640.000 −0.965961
\(77\) −1248.00 −1.84705
\(78\) −528.000 −0.766464
\(79\) −640.000 −0.911464 −0.455732 0.890117i \(-0.650622\pi\)
−0.455732 + 0.890117i \(0.650622\pi\)
\(80\) −80.0000 −0.111803
\(81\) 81.0000 0.111111
\(82\) 324.000 0.436339
\(83\) 972.000 1.28543 0.642716 0.766105i \(-0.277808\pi\)
0.642716 + 0.766105i \(0.277808\pi\)
\(84\) 312.000 0.405262
\(85\) 270.000 0.344537
\(86\) 544.000 0.682105
\(87\) −360.000 −0.443633
\(88\) −384.000 −0.465165
\(89\) 120.000 0.142921 0.0714605 0.997443i \(-0.477234\pi\)
0.0714605 + 0.997443i \(0.477234\pi\)
\(90\) −90.0000 −0.105409
\(91\) −2288.00 −2.63569
\(92\) −192.000 −0.217580
\(93\) 93.0000 0.103695
\(94\) 192.000 0.210673
\(95\) 800.000 0.863982
\(96\) 96.0000 0.102062
\(97\) 86.0000 0.0900204 0.0450102 0.998987i \(-0.485668\pi\)
0.0450102 + 0.998987i \(0.485668\pi\)
\(98\) 666.000 0.686491
\(99\) −432.000 −0.438562
\(100\) 100.000 0.100000
\(101\) 1722.00 1.69649 0.848245 0.529605i \(-0.177660\pi\)
0.848245 + 0.529605i \(0.177660\pi\)
\(102\) −324.000 −0.314517
\(103\) −1258.00 −1.20344 −0.601721 0.798707i \(-0.705518\pi\)
−0.601721 + 0.798707i \(0.705518\pi\)
\(104\) −704.000 −0.663778
\(105\) −390.000 −0.362477
\(106\) 1164.00 1.06658
\(107\) −1884.00 −1.70218 −0.851090 0.525021i \(-0.824058\pi\)
−0.851090 + 0.525021i \(0.824058\pi\)
\(108\) 108.000 0.0962250
\(109\) −70.0000 −0.0615118 −0.0307559 0.999527i \(-0.509791\pi\)
−0.0307559 + 0.999527i \(0.509791\pi\)
\(110\) 480.000 0.416056
\(111\) −912.000 −0.779849
\(112\) 416.000 0.350967
\(113\) −2178.00 −1.81318 −0.906589 0.422016i \(-0.861323\pi\)
−0.906589 + 0.422016i \(0.861323\pi\)
\(114\) −960.000 −0.788704
\(115\) 240.000 0.194610
\(116\) −480.000 −0.384197
\(117\) −792.000 −0.625816
\(118\) 60.0000 0.0468089
\(119\) −1404.00 −1.08155
\(120\) −120.000 −0.0912871
\(121\) 973.000 0.731029
\(122\) −956.000 −0.709444
\(123\) 486.000 0.356269
\(124\) 124.000 0.0898027
\(125\) −125.000 −0.0894427
\(126\) 468.000 0.330895
\(127\) −2464.00 −1.72161 −0.860806 0.508934i \(-0.830040\pi\)
−0.860806 + 0.508934i \(0.830040\pi\)
\(128\) 128.000 0.0883883
\(129\) 816.000 0.556936
\(130\) 880.000 0.593701
\(131\) −1458.00 −0.972413 −0.486206 0.873844i \(-0.661620\pi\)
−0.486206 + 0.873844i \(0.661620\pi\)
\(132\) −576.000 −0.379806
\(133\) −4160.00 −2.71216
\(134\) −668.000 −0.430645
\(135\) −135.000 −0.0860663
\(136\) −432.000 −0.272380
\(137\) 966.000 0.602416 0.301208 0.953559i \(-0.402610\pi\)
0.301208 + 0.953559i \(0.402610\pi\)
\(138\) −288.000 −0.177654
\(139\) 980.000 0.598004 0.299002 0.954253i \(-0.403346\pi\)
0.299002 + 0.954253i \(0.403346\pi\)
\(140\) −520.000 −0.313914
\(141\) 288.000 0.172014
\(142\) 2124.00 1.25523
\(143\) 4224.00 2.47013
\(144\) 144.000 0.0833333
\(145\) 600.000 0.343636
\(146\) 424.000 0.240346
\(147\) 999.000 0.560518
\(148\) −1216.00 −0.675369
\(149\) −30.0000 −0.0164946 −0.00824730 0.999966i \(-0.502625\pi\)
−0.00824730 + 0.999966i \(0.502625\pi\)
\(150\) 150.000 0.0816497
\(151\) 1832.00 0.987325 0.493662 0.869654i \(-0.335658\pi\)
0.493662 + 0.869654i \(0.335658\pi\)
\(152\) −1280.00 −0.683038
\(153\) −486.000 −0.256802
\(154\) −2496.00 −1.30606
\(155\) −155.000 −0.0803219
\(156\) −1056.00 −0.541972
\(157\) 3566.00 1.81272 0.906362 0.422501i \(-0.138848\pi\)
0.906362 + 0.422501i \(0.138848\pi\)
\(158\) −1280.00 −0.644502
\(159\) 1746.00 0.870860
\(160\) −160.000 −0.0790569
\(161\) −1248.00 −0.610908
\(162\) 162.000 0.0785674
\(163\) −1798.00 −0.863989 −0.431995 0.901876i \(-0.642190\pi\)
−0.431995 + 0.901876i \(0.642190\pi\)
\(164\) 648.000 0.308538
\(165\) 720.000 0.339709
\(166\) 1944.00 0.908938
\(167\) −864.000 −0.400349 −0.200175 0.979760i \(-0.564151\pi\)
−0.200175 + 0.979760i \(0.564151\pi\)
\(168\) 624.000 0.286563
\(169\) 5547.00 2.52481
\(170\) 540.000 0.243624
\(171\) −1440.00 −0.643974
\(172\) 1088.00 0.482321
\(173\) 1482.00 0.651297 0.325648 0.945491i \(-0.394417\pi\)
0.325648 + 0.945491i \(0.394417\pi\)
\(174\) −720.000 −0.313696
\(175\) 650.000 0.280774
\(176\) −768.000 −0.328921
\(177\) 90.0000 0.0382193
\(178\) 240.000 0.101060
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) −180.000 −0.0745356
\(181\) −358.000 −0.147016 −0.0735081 0.997295i \(-0.523419\pi\)
−0.0735081 + 0.997295i \(0.523419\pi\)
\(182\) −4576.00 −1.86371
\(183\) −1434.00 −0.579259
\(184\) −384.000 −0.153852
\(185\) 1520.00 0.604068
\(186\) 186.000 0.0733236
\(187\) 2592.00 1.01361
\(188\) 384.000 0.148969
\(189\) 702.000 0.270175
\(190\) 1600.00 0.610927
\(191\) 1722.00 0.652354 0.326177 0.945309i \(-0.394240\pi\)
0.326177 + 0.945309i \(0.394240\pi\)
\(192\) 192.000 0.0721688
\(193\) −418.000 −0.155898 −0.0779490 0.996957i \(-0.524837\pi\)
−0.0779490 + 0.996957i \(0.524837\pi\)
\(194\) 172.000 0.0636540
\(195\) 1320.00 0.484755
\(196\) 1332.00 0.485423
\(197\) −54.0000 −0.0195296 −0.00976482 0.999952i \(-0.503108\pi\)
−0.00976482 + 0.999952i \(0.503108\pi\)
\(198\) −864.000 −0.310110
\(199\) −1720.00 −0.612701 −0.306351 0.951919i \(-0.599108\pi\)
−0.306351 + 0.951919i \(0.599108\pi\)
\(200\) 200.000 0.0707107
\(201\) −1002.00 −0.351620
\(202\) 3444.00 1.19960
\(203\) −3120.00 −1.07872
\(204\) −648.000 −0.222397
\(205\) −810.000 −0.275965
\(206\) −2516.00 −0.850961
\(207\) −432.000 −0.145054
\(208\) −1408.00 −0.469362
\(209\) 7680.00 2.54180
\(210\) −780.000 −0.256310
\(211\) −2488.00 −0.811758 −0.405879 0.913927i \(-0.633035\pi\)
−0.405879 + 0.913927i \(0.633035\pi\)
\(212\) 2328.00 0.754187
\(213\) 3186.00 1.02489
\(214\) −3768.00 −1.20362
\(215\) −1360.00 −0.431401
\(216\) 216.000 0.0680414
\(217\) 806.000 0.252142
\(218\) −140.000 −0.0434954
\(219\) 636.000 0.196242
\(220\) 960.000 0.294196
\(221\) 4752.00 1.44640
\(222\) −1824.00 −0.551436
\(223\) −3148.00 −0.945317 −0.472658 0.881246i \(-0.656706\pi\)
−0.472658 + 0.881246i \(0.656706\pi\)
\(224\) 832.000 0.248171
\(225\) 225.000 0.0666667
\(226\) −4356.00 −1.28211
\(227\) 1536.00 0.449110 0.224555 0.974461i \(-0.427907\pi\)
0.224555 + 0.974461i \(0.427907\pi\)
\(228\) −1920.00 −0.557698
\(229\) −2770.00 −0.799331 −0.399665 0.916661i \(-0.630874\pi\)
−0.399665 + 0.916661i \(0.630874\pi\)
\(230\) 480.000 0.137610
\(231\) −3744.00 −1.06639
\(232\) −960.000 −0.271668
\(233\) −2598.00 −0.730475 −0.365237 0.930914i \(-0.619012\pi\)
−0.365237 + 0.930914i \(0.619012\pi\)
\(234\) −1584.00 −0.442518
\(235\) −480.000 −0.133241
\(236\) 120.000 0.0330989
\(237\) −1920.00 −0.526234
\(238\) −2808.00 −0.764771
\(239\) −5340.00 −1.44525 −0.722627 0.691238i \(-0.757066\pi\)
−0.722627 + 0.691238i \(0.757066\pi\)
\(240\) −240.000 −0.0645497
\(241\) 3002.00 0.802389 0.401195 0.915993i \(-0.368595\pi\)
0.401195 + 0.915993i \(0.368595\pi\)
\(242\) 1946.00 0.516916
\(243\) 243.000 0.0641500
\(244\) −1912.00 −0.501653
\(245\) −1665.00 −0.434175
\(246\) 972.000 0.251921
\(247\) 14080.0 3.62708
\(248\) 248.000 0.0635001
\(249\) 2916.00 0.742145
\(250\) −250.000 −0.0632456
\(251\) 2352.00 0.591462 0.295731 0.955271i \(-0.404437\pi\)
0.295731 + 0.955271i \(0.404437\pi\)
\(252\) 936.000 0.233978
\(253\) 2304.00 0.572535
\(254\) −4928.00 −1.21736
\(255\) 810.000 0.198918
\(256\) 256.000 0.0625000
\(257\) −294.000 −0.0713588 −0.0356794 0.999363i \(-0.511360\pi\)
−0.0356794 + 0.999363i \(0.511360\pi\)
\(258\) 1632.00 0.393813
\(259\) −7904.00 −1.89626
\(260\) 1760.00 0.419810
\(261\) −1080.00 −0.256132
\(262\) −2916.00 −0.687600
\(263\) −2448.00 −0.573955 −0.286977 0.957937i \(-0.592650\pi\)
−0.286977 + 0.957937i \(0.592650\pi\)
\(264\) −1152.00 −0.268563
\(265\) −2910.00 −0.674566
\(266\) −8320.00 −1.91779
\(267\) 360.000 0.0825155
\(268\) −1336.00 −0.304512
\(269\) −8400.00 −1.90393 −0.951965 0.306208i \(-0.900940\pi\)
−0.951965 + 0.306208i \(0.900940\pi\)
\(270\) −270.000 −0.0608581
\(271\) −3688.00 −0.826679 −0.413340 0.910577i \(-0.635638\pi\)
−0.413340 + 0.910577i \(0.635638\pi\)
\(272\) −864.000 −0.192602
\(273\) −6864.00 −1.52171
\(274\) 1932.00 0.425972
\(275\) −1200.00 −0.263137
\(276\) −576.000 −0.125620
\(277\) −9124.00 −1.97909 −0.989545 0.144223i \(-0.953932\pi\)
−0.989545 + 0.144223i \(0.953932\pi\)
\(278\) 1960.00 0.422852
\(279\) 279.000 0.0598684
\(280\) −1040.00 −0.221971
\(281\) 6702.00 1.42280 0.711402 0.702786i \(-0.248061\pi\)
0.711402 + 0.702786i \(0.248061\pi\)
\(282\) 576.000 0.121632
\(283\) 6482.00 1.36154 0.680768 0.732499i \(-0.261646\pi\)
0.680768 + 0.732499i \(0.261646\pi\)
\(284\) 4248.00 0.887579
\(285\) 2400.00 0.498820
\(286\) 8448.00 1.74665
\(287\) 4212.00 0.866294
\(288\) 288.000 0.0589256
\(289\) −1997.00 −0.406473
\(290\) 1200.00 0.242988
\(291\) 258.000 0.0519733
\(292\) 848.000 0.169950
\(293\) 4062.00 0.809913 0.404957 0.914336i \(-0.367287\pi\)
0.404957 + 0.914336i \(0.367287\pi\)
\(294\) 1998.00 0.396346
\(295\) −150.000 −0.0296045
\(296\) −2432.00 −0.477558
\(297\) −1296.00 −0.253204
\(298\) −60.0000 −0.0116634
\(299\) 4224.00 0.816991
\(300\) 300.000 0.0577350
\(301\) 7072.00 1.35423
\(302\) 3664.00 0.698144
\(303\) 5166.00 0.979468
\(304\) −2560.00 −0.482980
\(305\) 2390.00 0.448692
\(306\) −972.000 −0.181587
\(307\) 5006.00 0.930643 0.465322 0.885142i \(-0.345939\pi\)
0.465322 + 0.885142i \(0.345939\pi\)
\(308\) −4992.00 −0.923525
\(309\) −3774.00 −0.694807
\(310\) −310.000 −0.0567962
\(311\) −438.000 −0.0798608 −0.0399304 0.999202i \(-0.512714\pi\)
−0.0399304 + 0.999202i \(0.512714\pi\)
\(312\) −2112.00 −0.383232
\(313\) 10292.0 1.85859 0.929294 0.369340i \(-0.120416\pi\)
0.929294 + 0.369340i \(0.120416\pi\)
\(314\) 7132.00 1.28179
\(315\) −1170.00 −0.209276
\(316\) −2560.00 −0.455732
\(317\) −8874.00 −1.57228 −0.786141 0.618047i \(-0.787924\pi\)
−0.786141 + 0.618047i \(0.787924\pi\)
\(318\) 3492.00 0.615791
\(319\) 5760.00 1.01097
\(320\) −320.000 −0.0559017
\(321\) −5652.00 −0.982754
\(322\) −2496.00 −0.431977
\(323\) 8640.00 1.48837
\(324\) 324.000 0.0555556
\(325\) −2200.00 −0.375489
\(326\) −3596.00 −0.610933
\(327\) −210.000 −0.0355138
\(328\) 1296.00 0.218170
\(329\) 2496.00 0.418264
\(330\) 1440.00 0.240210
\(331\) −9508.00 −1.57887 −0.789436 0.613832i \(-0.789627\pi\)
−0.789436 + 0.613832i \(0.789627\pi\)
\(332\) 3888.00 0.642716
\(333\) −2736.00 −0.450246
\(334\) −1728.00 −0.283090
\(335\) 1670.00 0.272364
\(336\) 1248.00 0.202631
\(337\) −3304.00 −0.534066 −0.267033 0.963687i \(-0.586043\pi\)
−0.267033 + 0.963687i \(0.586043\pi\)
\(338\) 11094.0 1.78531
\(339\) −6534.00 −1.04684
\(340\) 1080.00 0.172268
\(341\) −1488.00 −0.236304
\(342\) −2880.00 −0.455358
\(343\) −260.000 −0.0409291
\(344\) 2176.00 0.341052
\(345\) 720.000 0.112358
\(346\) 2964.00 0.460536
\(347\) −5724.00 −0.885534 −0.442767 0.896637i \(-0.646003\pi\)
−0.442767 + 0.896637i \(0.646003\pi\)
\(348\) −1440.00 −0.221816
\(349\) 10010.0 1.53531 0.767655 0.640864i \(-0.221424\pi\)
0.767655 + 0.640864i \(0.221424\pi\)
\(350\) 1300.00 0.198537
\(351\) −2376.00 −0.361315
\(352\) −1536.00 −0.232583
\(353\) −7758.00 −1.16974 −0.584868 0.811129i \(-0.698854\pi\)
−0.584868 + 0.811129i \(0.698854\pi\)
\(354\) 180.000 0.0270251
\(355\) −5310.00 −0.793875
\(356\) 480.000 0.0714605
\(357\) −4212.00 −0.624433
\(358\) 0 0
\(359\) 8730.00 1.28343 0.641716 0.766943i \(-0.278223\pi\)
0.641716 + 0.766943i \(0.278223\pi\)
\(360\) −360.000 −0.0527046
\(361\) 18741.0 2.73232
\(362\) −716.000 −0.103956
\(363\) 2919.00 0.422060
\(364\) −9152.00 −1.31784
\(365\) −1060.00 −0.152008
\(366\) −2868.00 −0.409598
\(367\) −5404.00 −0.768628 −0.384314 0.923202i \(-0.625562\pi\)
−0.384314 + 0.923202i \(0.625562\pi\)
\(368\) −768.000 −0.108790
\(369\) 1458.00 0.205692
\(370\) 3040.00 0.427141
\(371\) 15132.0 2.11756
\(372\) 372.000 0.0518476
\(373\) −9538.00 −1.32402 −0.662009 0.749496i \(-0.730296\pi\)
−0.662009 + 0.749496i \(0.730296\pi\)
\(374\) 5184.00 0.716733
\(375\) −375.000 −0.0516398
\(376\) 768.000 0.105337
\(377\) 10560.0 1.44262
\(378\) 1404.00 0.191042
\(379\) −5440.00 −0.737293 −0.368646 0.929570i \(-0.620179\pi\)
−0.368646 + 0.929570i \(0.620179\pi\)
\(380\) 3200.00 0.431991
\(381\) −7392.00 −0.993973
\(382\) 3444.00 0.461284
\(383\) 6672.00 0.890139 0.445070 0.895496i \(-0.353179\pi\)
0.445070 + 0.895496i \(0.353179\pi\)
\(384\) 384.000 0.0510310
\(385\) 6240.00 0.826026
\(386\) −836.000 −0.110236
\(387\) 2448.00 0.321547
\(388\) 344.000 0.0450102
\(389\) −10440.0 −1.36074 −0.680371 0.732867i \(-0.738182\pi\)
−0.680371 + 0.732867i \(0.738182\pi\)
\(390\) 2640.00 0.342773
\(391\) 2592.00 0.335251
\(392\) 2664.00 0.343246
\(393\) −4374.00 −0.561423
\(394\) −108.000 −0.0138095
\(395\) 3200.00 0.407619
\(396\) −1728.00 −0.219281
\(397\) −6334.00 −0.800741 −0.400371 0.916353i \(-0.631119\pi\)
−0.400371 + 0.916353i \(0.631119\pi\)
\(398\) −3440.00 −0.433245
\(399\) −12480.0 −1.56587
\(400\) 400.000 0.0500000
\(401\) 10212.0 1.27173 0.635864 0.771801i \(-0.280644\pi\)
0.635864 + 0.771801i \(0.280644\pi\)
\(402\) −2004.00 −0.248633
\(403\) −2728.00 −0.337199
\(404\) 6888.00 0.848245
\(405\) −405.000 −0.0496904
\(406\) −6240.00 −0.762773
\(407\) 14592.0 1.77715
\(408\) −1296.00 −0.157259
\(409\) 8030.00 0.970802 0.485401 0.874292i \(-0.338674\pi\)
0.485401 + 0.874292i \(0.338674\pi\)
\(410\) −1620.00 −0.195137
\(411\) 2898.00 0.347805
\(412\) −5032.00 −0.601721
\(413\) 780.000 0.0929329
\(414\) −864.000 −0.102568
\(415\) −4860.00 −0.574863
\(416\) −2816.00 −0.331889
\(417\) 2940.00 0.345258
\(418\) 15360.0 1.79733
\(419\) 7530.00 0.877958 0.438979 0.898497i \(-0.355340\pi\)
0.438979 + 0.898497i \(0.355340\pi\)
\(420\) −1560.00 −0.181239
\(421\) −4078.00 −0.472089 −0.236045 0.971742i \(-0.575851\pi\)
−0.236045 + 0.971742i \(0.575851\pi\)
\(422\) −4976.00 −0.574000
\(423\) 864.000 0.0993123
\(424\) 4656.00 0.533291
\(425\) −1350.00 −0.154081
\(426\) 6372.00 0.724705
\(427\) −12428.0 −1.40851
\(428\) −7536.00 −0.851090
\(429\) 12672.0 1.42613
\(430\) −2720.00 −0.305047
\(431\) 15882.0 1.77496 0.887481 0.460843i \(-0.152453\pi\)
0.887481 + 0.460843i \(0.152453\pi\)
\(432\) 432.000 0.0481125
\(433\) 4772.00 0.529625 0.264813 0.964300i \(-0.414690\pi\)
0.264813 + 0.964300i \(0.414690\pi\)
\(434\) 1612.00 0.178291
\(435\) 1800.00 0.198399
\(436\) −280.000 −0.0307559
\(437\) 7680.00 0.840696
\(438\) 1272.00 0.138764
\(439\) −1960.00 −0.213088 −0.106544 0.994308i \(-0.533979\pi\)
−0.106544 + 0.994308i \(0.533979\pi\)
\(440\) 1920.00 0.208028
\(441\) 2997.00 0.323615
\(442\) 9504.00 1.02276
\(443\) −4128.00 −0.442725 −0.221363 0.975192i \(-0.571050\pi\)
−0.221363 + 0.975192i \(0.571050\pi\)
\(444\) −3648.00 −0.389924
\(445\) −600.000 −0.0639162
\(446\) −6296.00 −0.668440
\(447\) −90.0000 −0.00952316
\(448\) 1664.00 0.175484
\(449\) −14820.0 −1.55768 −0.778841 0.627222i \(-0.784192\pi\)
−0.778841 + 0.627222i \(0.784192\pi\)
\(450\) 450.000 0.0471405
\(451\) −7776.00 −0.811879
\(452\) −8712.00 −0.906589
\(453\) 5496.00 0.570032
\(454\) 3072.00 0.317569
\(455\) 11440.0 1.17872
\(456\) −3840.00 −0.394352
\(457\) 8516.00 0.871689 0.435844 0.900022i \(-0.356450\pi\)
0.435844 + 0.900022i \(0.356450\pi\)
\(458\) −5540.00 −0.565212
\(459\) −1458.00 −0.148265
\(460\) 960.000 0.0973048
\(461\) 13692.0 1.38330 0.691649 0.722234i \(-0.256885\pi\)
0.691649 + 0.722234i \(0.256885\pi\)
\(462\) −7488.00 −0.754055
\(463\) −4288.00 −0.430411 −0.215205 0.976569i \(-0.569042\pi\)
−0.215205 + 0.976569i \(0.569042\pi\)
\(464\) −1920.00 −0.192099
\(465\) −465.000 −0.0463739
\(466\) −5196.00 −0.516524
\(467\) −324.000 −0.0321048 −0.0160524 0.999871i \(-0.505110\pi\)
−0.0160524 + 0.999871i \(0.505110\pi\)
\(468\) −3168.00 −0.312908
\(469\) −8684.00 −0.854989
\(470\) −960.000 −0.0942160
\(471\) 10698.0 1.04658
\(472\) 240.000 0.0234044
\(473\) −13056.0 −1.26917
\(474\) −3840.00 −0.372103
\(475\) −4000.00 −0.386384
\(476\) −5616.00 −0.540775
\(477\) 5238.00 0.502791
\(478\) −10680.0 −1.02195
\(479\) −8970.00 −0.855636 −0.427818 0.903865i \(-0.640718\pi\)
−0.427818 + 0.903865i \(0.640718\pi\)
\(480\) −480.000 −0.0456435
\(481\) 26752.0 2.53594
\(482\) 6004.00 0.567375
\(483\) −3744.00 −0.352708
\(484\) 3892.00 0.365515
\(485\) −430.000 −0.0402583
\(486\) 486.000 0.0453609
\(487\) 14216.0 1.32277 0.661384 0.750047i \(-0.269969\pi\)
0.661384 + 0.750047i \(0.269969\pi\)
\(488\) −3824.00 −0.354722
\(489\) −5394.00 −0.498824
\(490\) −3330.00 −0.307008
\(491\) −8268.00 −0.759938 −0.379969 0.924999i \(-0.624065\pi\)
−0.379969 + 0.924999i \(0.624065\pi\)
\(492\) 1944.00 0.178135
\(493\) 6480.00 0.591977
\(494\) 28160.0 2.56473
\(495\) 2160.00 0.196131
\(496\) 496.000 0.0449013
\(497\) 27612.0 2.49209
\(498\) 5832.00 0.524775
\(499\) −11860.0 −1.06398 −0.531990 0.846750i \(-0.678556\pi\)
−0.531990 + 0.846750i \(0.678556\pi\)
\(500\) −500.000 −0.0447214
\(501\) −2592.00 −0.231142
\(502\) 4704.00 0.418227
\(503\) −3768.00 −0.334010 −0.167005 0.985956i \(-0.553410\pi\)
−0.167005 + 0.985956i \(0.553410\pi\)
\(504\) 1872.00 0.165447
\(505\) −8610.00 −0.758693
\(506\) 4608.00 0.404843
\(507\) 16641.0 1.45770
\(508\) −9856.00 −0.860806
\(509\) −3420.00 −0.297817 −0.148908 0.988851i \(-0.547576\pi\)
−0.148908 + 0.988851i \(0.547576\pi\)
\(510\) 1620.00 0.140656
\(511\) 5512.00 0.477175
\(512\) 512.000 0.0441942
\(513\) −4320.00 −0.371799
\(514\) −588.000 −0.0504583
\(515\) 6290.00 0.538195
\(516\) 3264.00 0.278468
\(517\) −4608.00 −0.391992
\(518\) −15808.0 −1.34086
\(519\) 4446.00 0.376026
\(520\) 3520.00 0.296850
\(521\) −15198.0 −1.27800 −0.638999 0.769208i \(-0.720651\pi\)
−0.638999 + 0.769208i \(0.720651\pi\)
\(522\) −2160.00 −0.181112
\(523\) −208.000 −0.0173904 −0.00869522 0.999962i \(-0.502768\pi\)
−0.00869522 + 0.999962i \(0.502768\pi\)
\(524\) −5832.00 −0.486206
\(525\) 1950.00 0.162105
\(526\) −4896.00 −0.405847
\(527\) −1674.00 −0.138369
\(528\) −2304.00 −0.189903
\(529\) −9863.00 −0.810635
\(530\) −5820.00 −0.476990
\(531\) 270.000 0.0220659
\(532\) −16640.0 −1.35608
\(533\) −14256.0 −1.15853
\(534\) 720.000 0.0583473
\(535\) 9420.00 0.761238
\(536\) −2672.00 −0.215322
\(537\) 0 0
\(538\) −16800.0 −1.34628
\(539\) −15984.0 −1.27733
\(540\) −540.000 −0.0430331
\(541\) −22918.0 −1.82130 −0.910649 0.413182i \(-0.864417\pi\)
−0.910649 + 0.413182i \(0.864417\pi\)
\(542\) −7376.00 −0.584550
\(543\) −1074.00 −0.0848798
\(544\) −1728.00 −0.136190
\(545\) 350.000 0.0275089
\(546\) −13728.0 −1.07601
\(547\) 23906.0 1.86864 0.934321 0.356434i \(-0.116007\pi\)
0.934321 + 0.356434i \(0.116007\pi\)
\(548\) 3864.00 0.301208
\(549\) −4302.00 −0.334435
\(550\) −2400.00 −0.186066
\(551\) 19200.0 1.48448
\(552\) −1152.00 −0.0888268
\(553\) −16640.0 −1.27957
\(554\) −18248.0 −1.39943
\(555\) 4560.00 0.348759
\(556\) 3920.00 0.299002
\(557\) 18846.0 1.43363 0.716814 0.697265i \(-0.245600\pi\)
0.716814 + 0.697265i \(0.245600\pi\)
\(558\) 558.000 0.0423334
\(559\) −23936.0 −1.81106
\(560\) −2080.00 −0.156957
\(561\) 7776.00 0.585210
\(562\) 13404.0 1.00607
\(563\) 19452.0 1.45614 0.728068 0.685505i \(-0.240419\pi\)
0.728068 + 0.685505i \(0.240419\pi\)
\(564\) 1152.00 0.0860070
\(565\) 10890.0 0.810877
\(566\) 12964.0 0.962752
\(567\) 2106.00 0.155985
\(568\) 8496.00 0.627613
\(569\) 23940.0 1.76383 0.881913 0.471412i \(-0.156256\pi\)
0.881913 + 0.471412i \(0.156256\pi\)
\(570\) 4800.00 0.352719
\(571\) −9628.00 −0.705638 −0.352819 0.935692i \(-0.614777\pi\)
−0.352819 + 0.935692i \(0.614777\pi\)
\(572\) 16896.0 1.23507
\(573\) 5166.00 0.376637
\(574\) 8424.00 0.612563
\(575\) −1200.00 −0.0870321
\(576\) 576.000 0.0416667
\(577\) −23374.0 −1.68643 −0.843217 0.537573i \(-0.819341\pi\)
−0.843217 + 0.537573i \(0.819341\pi\)
\(578\) −3994.00 −0.287420
\(579\) −1254.00 −0.0900077
\(580\) 2400.00 0.171818
\(581\) 25272.0 1.80458
\(582\) 516.000 0.0367507
\(583\) −27936.0 −1.98455
\(584\) 1696.00 0.120173
\(585\) 3960.00 0.279873
\(586\) 8124.00 0.572695
\(587\) −11244.0 −0.790613 −0.395306 0.918549i \(-0.629362\pi\)
−0.395306 + 0.918549i \(0.629362\pi\)
\(588\) 3996.00 0.280259
\(589\) −4960.00 −0.346983
\(590\) −300.000 −0.0209336
\(591\) −162.000 −0.0112754
\(592\) −4864.00 −0.337684
\(593\) −5298.00 −0.366885 −0.183442 0.983030i \(-0.558724\pi\)
−0.183442 + 0.983030i \(0.558724\pi\)
\(594\) −2592.00 −0.179042
\(595\) 7020.00 0.483684
\(596\) −120.000 −0.00824730
\(597\) −5160.00 −0.353743
\(598\) 8448.00 0.577700
\(599\) −2430.00 −0.165755 −0.0828774 0.996560i \(-0.526411\pi\)
−0.0828774 + 0.996560i \(0.526411\pi\)
\(600\) 600.000 0.0408248
\(601\) 2702.00 0.183389 0.0916946 0.995787i \(-0.470772\pi\)
0.0916946 + 0.995787i \(0.470772\pi\)
\(602\) 14144.0 0.957585
\(603\) −3006.00 −0.203008
\(604\) 7328.00 0.493662
\(605\) −4865.00 −0.326926
\(606\) 10332.0 0.692589
\(607\) 8366.00 0.559416 0.279708 0.960085i \(-0.409762\pi\)
0.279708 + 0.960085i \(0.409762\pi\)
\(608\) −5120.00 −0.341519
\(609\) −9360.00 −0.622802
\(610\) 4780.00 0.317273
\(611\) −8448.00 −0.559361
\(612\) −1944.00 −0.128401
\(613\) −6028.00 −0.397176 −0.198588 0.980083i \(-0.563635\pi\)
−0.198588 + 0.980083i \(0.563635\pi\)
\(614\) 10012.0 0.658064
\(615\) −2430.00 −0.159329
\(616\) −9984.00 −0.653031
\(617\) −5634.00 −0.367612 −0.183806 0.982963i \(-0.558842\pi\)
−0.183806 + 0.982963i \(0.558842\pi\)
\(618\) −7548.00 −0.491303
\(619\) −10420.0 −0.676600 −0.338300 0.941038i \(-0.609852\pi\)
−0.338300 + 0.941038i \(0.609852\pi\)
\(620\) −620.000 −0.0401610
\(621\) −1296.00 −0.0837467
\(622\) −876.000 −0.0564701
\(623\) 3120.00 0.200642
\(624\) −4224.00 −0.270986
\(625\) 625.000 0.0400000
\(626\) 20584.0 1.31422
\(627\) 23040.0 1.46751
\(628\) 14264.0 0.906362
\(629\) 16416.0 1.04062
\(630\) −2340.00 −0.147981
\(631\) −7408.00 −0.467366 −0.233683 0.972313i \(-0.575078\pi\)
−0.233683 + 0.972313i \(0.575078\pi\)
\(632\) −5120.00 −0.322251
\(633\) −7464.00 −0.468669
\(634\) −17748.0 −1.11177
\(635\) 12320.0 0.769928
\(636\) 6984.00 0.435430
\(637\) −29304.0 −1.82271
\(638\) 11520.0 0.714861
\(639\) 9558.00 0.591719
\(640\) −640.000 −0.0395285
\(641\) −13428.0 −0.827417 −0.413708 0.910409i \(-0.635767\pi\)
−0.413708 + 0.910409i \(0.635767\pi\)
\(642\) −11304.0 −0.694912
\(643\) −5848.00 −0.358667 −0.179333 0.983788i \(-0.557394\pi\)
−0.179333 + 0.983788i \(0.557394\pi\)
\(644\) −4992.00 −0.305454
\(645\) −4080.00 −0.249070
\(646\) 17280.0 1.05243
\(647\) 9456.00 0.574581 0.287290 0.957844i \(-0.407246\pi\)
0.287290 + 0.957844i \(0.407246\pi\)
\(648\) 648.000 0.0392837
\(649\) −1440.00 −0.0870954
\(650\) −4400.00 −0.265511
\(651\) 2418.00 0.145574
\(652\) −7192.00 −0.431995
\(653\) −378.000 −0.0226528 −0.0113264 0.999936i \(-0.503605\pi\)
−0.0113264 + 0.999936i \(0.503605\pi\)
\(654\) −420.000 −0.0251121
\(655\) 7290.00 0.434876
\(656\) 2592.00 0.154269
\(657\) 1908.00 0.113300
\(658\) 4992.00 0.295757
\(659\) 6330.00 0.374176 0.187088 0.982343i \(-0.440095\pi\)
0.187088 + 0.982343i \(0.440095\pi\)
\(660\) 2880.00 0.169854
\(661\) 2702.00 0.158995 0.0794974 0.996835i \(-0.474668\pi\)
0.0794974 + 0.996835i \(0.474668\pi\)
\(662\) −19016.0 −1.11643
\(663\) 14256.0 0.835079
\(664\) 7776.00 0.454469
\(665\) 20800.0 1.21292
\(666\) −5472.00 −0.318372
\(667\) 5760.00 0.334375
\(668\) −3456.00 −0.200175
\(669\) −9444.00 −0.545779
\(670\) 3340.00 0.192590
\(671\) 22944.0 1.32003
\(672\) 2496.00 0.143282
\(673\) 2312.00 0.132424 0.0662118 0.997806i \(-0.478909\pi\)
0.0662118 + 0.997806i \(0.478909\pi\)
\(674\) −6608.00 −0.377642
\(675\) 675.000 0.0384900
\(676\) 22188.0 1.26240
\(677\) 6486.00 0.368209 0.184104 0.982907i \(-0.441062\pi\)
0.184104 + 0.982907i \(0.441062\pi\)
\(678\) −13068.0 −0.740226
\(679\) 2236.00 0.126377
\(680\) 2160.00 0.121812
\(681\) 4608.00 0.259294
\(682\) −2976.00 −0.167092
\(683\) 9552.00 0.535135 0.267567 0.963539i \(-0.413780\pi\)
0.267567 + 0.963539i \(0.413780\pi\)
\(684\) −5760.00 −0.321987
\(685\) −4830.00 −0.269408
\(686\) −520.000 −0.0289412
\(687\) −8310.00 −0.461494
\(688\) 4352.00 0.241161
\(689\) −51216.0 −2.83189
\(690\) 1440.00 0.0794491
\(691\) −26548.0 −1.46155 −0.730777 0.682617i \(-0.760842\pi\)
−0.730777 + 0.682617i \(0.760842\pi\)
\(692\) 5928.00 0.325648
\(693\) −11232.0 −0.615683
\(694\) −11448.0 −0.626167
\(695\) −4900.00 −0.267435
\(696\) −2880.00 −0.156848
\(697\) −8748.00 −0.475400
\(698\) 20020.0 1.08563
\(699\) −7794.00 −0.421740
\(700\) 2600.00 0.140387
\(701\) −20658.0 −1.11304 −0.556521 0.830834i \(-0.687864\pi\)
−0.556521 + 0.830834i \(0.687864\pi\)
\(702\) −4752.00 −0.255488
\(703\) 48640.0 2.60952
\(704\) −3072.00 −0.164461
\(705\) −1440.00 −0.0769270
\(706\) −15516.0 −0.827128
\(707\) 44772.0 2.38165
\(708\) 360.000 0.0191096
\(709\) −23530.0 −1.24639 −0.623193 0.782068i \(-0.714165\pi\)
−0.623193 + 0.782068i \(0.714165\pi\)
\(710\) −10620.0 −0.561354
\(711\) −5760.00 −0.303821
\(712\) 960.000 0.0505302
\(713\) −1488.00 −0.0781571
\(714\) −8424.00 −0.441541
\(715\) −21120.0 −1.10468
\(716\) 0 0
\(717\) −16020.0 −0.834418
\(718\) 17460.0 0.907523
\(719\) 120.000 0.00622426 0.00311213 0.999995i \(-0.499009\pi\)
0.00311213 + 0.999995i \(0.499009\pi\)
\(720\) −720.000 −0.0372678
\(721\) −32708.0 −1.68947
\(722\) 37482.0 1.93204
\(723\) 9006.00 0.463260
\(724\) −1432.00 −0.0735081
\(725\) −3000.00 −0.153679
\(726\) 5838.00 0.298441
\(727\) 24626.0 1.25630 0.628148 0.778094i \(-0.283813\pi\)
0.628148 + 0.778094i \(0.283813\pi\)
\(728\) −18304.0 −0.931856
\(729\) 729.000 0.0370370
\(730\) −2120.00 −0.107486
\(731\) −14688.0 −0.743167
\(732\) −5736.00 −0.289629
\(733\) −26998.0 −1.36043 −0.680214 0.733013i \(-0.738113\pi\)
−0.680214 + 0.733013i \(0.738113\pi\)
\(734\) −10808.0 −0.543502
\(735\) −4995.00 −0.250671
\(736\) −1536.00 −0.0769262
\(737\) 16032.0 0.801284
\(738\) 2916.00 0.145446
\(739\) 3620.00 0.180195 0.0900973 0.995933i \(-0.471282\pi\)
0.0900973 + 0.995933i \(0.471282\pi\)
\(740\) 6080.00 0.302034
\(741\) 42240.0 2.09410
\(742\) 30264.0 1.49734
\(743\) 20952.0 1.03453 0.517264 0.855826i \(-0.326951\pi\)
0.517264 + 0.855826i \(0.326951\pi\)
\(744\) 744.000 0.0366618
\(745\) 150.000 0.00737661
\(746\) −19076.0 −0.936222
\(747\) 8748.00 0.428477
\(748\) 10368.0 0.506807
\(749\) −48984.0 −2.38963
\(750\) −750.000 −0.0365148
\(751\) 8672.00 0.421366 0.210683 0.977554i \(-0.432431\pi\)
0.210683 + 0.977554i \(0.432431\pi\)
\(752\) 1536.00 0.0744843
\(753\) 7056.00 0.341481
\(754\) 21120.0 1.02009
\(755\) −9160.00 −0.441545
\(756\) 2808.00 0.135087
\(757\) 21176.0 1.01672 0.508359 0.861146i \(-0.330252\pi\)
0.508359 + 0.861146i \(0.330252\pi\)
\(758\) −10880.0 −0.521345
\(759\) 6912.00 0.330553
\(760\) 6400.00 0.305464
\(761\) 27132.0 1.29242 0.646212 0.763158i \(-0.276352\pi\)
0.646212 + 0.763158i \(0.276352\pi\)
\(762\) −14784.0 −0.702845
\(763\) −1820.00 −0.0863544
\(764\) 6888.00 0.326177
\(765\) 2430.00 0.114846
\(766\) 13344.0 0.629423
\(767\) −2640.00 −0.124283
\(768\) 768.000 0.0360844
\(769\) −6850.00 −0.321219 −0.160609 0.987018i \(-0.551346\pi\)
−0.160609 + 0.987018i \(0.551346\pi\)
\(770\) 12480.0 0.584088
\(771\) −882.000 −0.0411990
\(772\) −1672.00 −0.0779490
\(773\) 7422.00 0.345344 0.172672 0.984979i \(-0.444760\pi\)
0.172672 + 0.984979i \(0.444760\pi\)
\(774\) 4896.00 0.227368
\(775\) 775.000 0.0359211
\(776\) 688.000 0.0318270
\(777\) −23712.0 −1.09480
\(778\) −20880.0 −0.962191
\(779\) −25920.0 −1.19214
\(780\) 5280.00 0.242377
\(781\) −50976.0 −2.33555
\(782\) 5184.00 0.237058
\(783\) −3240.00 −0.147878
\(784\) 5328.00 0.242711
\(785\) −17830.0 −0.810675
\(786\) −8748.00 −0.396986
\(787\) −1204.00 −0.0545336 −0.0272668 0.999628i \(-0.508680\pi\)
−0.0272668 + 0.999628i \(0.508680\pi\)
\(788\) −216.000 −0.00976482
\(789\) −7344.00 −0.331373
\(790\) 6400.00 0.288230
\(791\) −56628.0 −2.54546
\(792\) −3456.00 −0.155055
\(793\) 42064.0 1.88365
\(794\) −12668.0 −0.566210
\(795\) −8730.00 −0.389461
\(796\) −6880.00 −0.306351
\(797\) 37266.0 1.65625 0.828124 0.560545i \(-0.189408\pi\)
0.828124 + 0.560545i \(0.189408\pi\)
\(798\) −24960.0 −1.10724
\(799\) −5184.00 −0.229533
\(800\) 800.000 0.0353553
\(801\) 1080.00 0.0476404
\(802\) 20424.0 0.899248
\(803\) −10176.0 −0.447202
\(804\) −4008.00 −0.175810
\(805\) 6240.00 0.273206
\(806\) −5456.00 −0.238436
\(807\) −25200.0 −1.09923
\(808\) 13776.0 0.599799
\(809\) −25860.0 −1.12384 −0.561922 0.827190i \(-0.689938\pi\)
−0.561922 + 0.827190i \(0.689938\pi\)
\(810\) −810.000 −0.0351364
\(811\) −5128.00 −0.222033 −0.111016 0.993819i \(-0.535411\pi\)
−0.111016 + 0.993819i \(0.535411\pi\)
\(812\) −12480.0 −0.539362
\(813\) −11064.0 −0.477283
\(814\) 29184.0 1.25663
\(815\) 8990.00 0.386388
\(816\) −2592.00 −0.111199
\(817\) −43520.0 −1.86361
\(818\) 16060.0 0.686461
\(819\) −20592.0 −0.878563
\(820\) −3240.00 −0.137983
\(821\) 8592.00 0.365241 0.182621 0.983183i \(-0.441542\pi\)
0.182621 + 0.983183i \(0.441542\pi\)
\(822\) 5796.00 0.245935
\(823\) 39392.0 1.66843 0.834216 0.551438i \(-0.185921\pi\)
0.834216 + 0.551438i \(0.185921\pi\)
\(824\) −10064.0 −0.425481
\(825\) −3600.00 −0.151922
\(826\) 1560.00 0.0657135
\(827\) −22044.0 −0.926898 −0.463449 0.886123i \(-0.653388\pi\)
−0.463449 + 0.886123i \(0.653388\pi\)
\(828\) −1728.00 −0.0725268
\(829\) −21310.0 −0.892795 −0.446397 0.894835i \(-0.647293\pi\)
−0.446397 + 0.894835i \(0.647293\pi\)
\(830\) −9720.00 −0.406489
\(831\) −27372.0 −1.14263
\(832\) −5632.00 −0.234681
\(833\) −17982.0 −0.747946
\(834\) 5880.00 0.244134
\(835\) 4320.00 0.179042
\(836\) 30720.0 1.27090
\(837\) 837.000 0.0345651
\(838\) 15060.0 0.620810
\(839\) −14070.0 −0.578963 −0.289482 0.957184i \(-0.593483\pi\)
−0.289482 + 0.957184i \(0.593483\pi\)
\(840\) −3120.00 −0.128155
\(841\) −9989.00 −0.409570
\(842\) −8156.00 −0.333817
\(843\) 20106.0 0.821456
\(844\) −9952.00 −0.405879
\(845\) −27735.0 −1.12913
\(846\) 1728.00 0.0702244
\(847\) 25298.0 1.02627
\(848\) 9312.00 0.377094
\(849\) 19446.0 0.786084
\(850\) −2700.00 −0.108952
\(851\) 14592.0 0.587788
\(852\) 12744.0 0.512444
\(853\) −22918.0 −0.919927 −0.459963 0.887938i \(-0.652137\pi\)
−0.459963 + 0.887938i \(0.652137\pi\)
\(854\) −24856.0 −0.995966
\(855\) 7200.00 0.287994
\(856\) −15072.0 −0.601811
\(857\) −25914.0 −1.03291 −0.516456 0.856314i \(-0.672749\pi\)
−0.516456 + 0.856314i \(0.672749\pi\)
\(858\) 25344.0 1.00843
\(859\) −31900.0 −1.26707 −0.633535 0.773714i \(-0.718397\pi\)
−0.633535 + 0.773714i \(0.718397\pi\)
\(860\) −5440.00 −0.215701
\(861\) 12636.0 0.500155
\(862\) 31764.0 1.25509
\(863\) 7752.00 0.305772 0.152886 0.988244i \(-0.451143\pi\)
0.152886 + 0.988244i \(0.451143\pi\)
\(864\) 864.000 0.0340207
\(865\) −7410.00 −0.291269
\(866\) 9544.00 0.374502
\(867\) −5991.00 −0.234677
\(868\) 3224.00 0.126071
\(869\) 30720.0 1.19920
\(870\) 3600.00 0.140289
\(871\) 29392.0 1.14341
\(872\) −560.000 −0.0217477
\(873\) 774.000 0.0300068
\(874\) 15360.0 0.594462
\(875\) −3250.00 −0.125566
\(876\) 2544.00 0.0981208
\(877\) 28706.0 1.10528 0.552641 0.833419i \(-0.313620\pi\)
0.552641 + 0.833419i \(0.313620\pi\)
\(878\) −3920.00 −0.150676
\(879\) 12186.0 0.467604
\(880\) 3840.00 0.147098
\(881\) −43608.0 −1.66764 −0.833820 0.552036i \(-0.813851\pi\)
−0.833820 + 0.552036i \(0.813851\pi\)
\(882\) 5994.00 0.228830
\(883\) −32668.0 −1.24503 −0.622517 0.782606i \(-0.713890\pi\)
−0.622517 + 0.782606i \(0.713890\pi\)
\(884\) 19008.0 0.723199
\(885\) −450.000 −0.0170922
\(886\) −8256.00 −0.313054
\(887\) 32316.0 1.22330 0.611649 0.791129i \(-0.290507\pi\)
0.611649 + 0.791129i \(0.290507\pi\)
\(888\) −7296.00 −0.275718
\(889\) −64064.0 −2.41692
\(890\) −1200.00 −0.0451956
\(891\) −3888.00 −0.146187
\(892\) −12592.0 −0.472658
\(893\) −15360.0 −0.575591
\(894\) −180.000 −0.00673389
\(895\) 0 0
\(896\) 3328.00 0.124086
\(897\) 12672.0 0.471690
\(898\) −29640.0 −1.10145
\(899\) −3720.00 −0.138008
\(900\) 900.000 0.0333333
\(901\) −31428.0 −1.16206
\(902\) −15552.0 −0.574085
\(903\) 21216.0 0.781865
\(904\) −17424.0 −0.641055
\(905\) 1790.00 0.0657476
\(906\) 10992.0 0.403074
\(907\) 45206.0 1.65495 0.827476 0.561502i \(-0.189776\pi\)
0.827476 + 0.561502i \(0.189776\pi\)
\(908\) 6144.00 0.224555
\(909\) 15498.0 0.565496
\(910\) 22880.0 0.833478
\(911\) −1368.00 −0.0497518 −0.0248759 0.999691i \(-0.507919\pi\)
−0.0248759 + 0.999691i \(0.507919\pi\)
\(912\) −7680.00 −0.278849
\(913\) −46656.0 −1.69122
\(914\) 17032.0 0.616377
\(915\) 7170.00 0.259052
\(916\) −11080.0 −0.399665
\(917\) −37908.0 −1.36514
\(918\) −2916.00 −0.104839
\(919\) −8260.00 −0.296488 −0.148244 0.988951i \(-0.547362\pi\)
−0.148244 + 0.988951i \(0.547362\pi\)
\(920\) 1920.00 0.0688049
\(921\) 15018.0 0.537307
\(922\) 27384.0 0.978139
\(923\) −93456.0 −3.33276
\(924\) −14976.0 −0.533197
\(925\) −7600.00 −0.270148
\(926\) −8576.00 −0.304346
\(927\) −11322.0 −0.401147
\(928\) −3840.00 −0.135834
\(929\) 9120.00 0.322086 0.161043 0.986947i \(-0.448514\pi\)
0.161043 + 0.986947i \(0.448514\pi\)
\(930\) −930.000 −0.0327913
\(931\) −53280.0 −1.87560
\(932\) −10392.0 −0.365237
\(933\) −1314.00 −0.0461076
\(934\) −648.000 −0.0227015
\(935\) −12960.0 −0.453302
\(936\) −6336.00 −0.221259
\(937\) −27274.0 −0.950910 −0.475455 0.879740i \(-0.657717\pi\)
−0.475455 + 0.879740i \(0.657717\pi\)
\(938\) −17368.0 −0.604569
\(939\) 30876.0 1.07306
\(940\) −1920.00 −0.0666207
\(941\) 49392.0 1.71109 0.855544 0.517731i \(-0.173223\pi\)
0.855544 + 0.517731i \(0.173223\pi\)
\(942\) 21396.0 0.740042
\(943\) −7776.00 −0.268527
\(944\) 480.000 0.0165494
\(945\) −3510.00 −0.120826
\(946\) −26112.0 −0.897436
\(947\) −25164.0 −0.863485 −0.431742 0.901997i \(-0.642101\pi\)
−0.431742 + 0.901997i \(0.642101\pi\)
\(948\) −7680.00 −0.263117
\(949\) −18656.0 −0.638145
\(950\) −8000.00 −0.273215
\(951\) −26622.0 −0.907758
\(952\) −11232.0 −0.382386
\(953\) −21138.0 −0.718496 −0.359248 0.933242i \(-0.616967\pi\)
−0.359248 + 0.933242i \(0.616967\pi\)
\(954\) 10476.0 0.355527
\(955\) −8610.00 −0.291741
\(956\) −21360.0 −0.722627
\(957\) 17280.0 0.583681
\(958\) −17940.0 −0.605026
\(959\) 25116.0 0.845712
\(960\) −960.000 −0.0322749
\(961\) 961.000 0.0322581
\(962\) 53504.0 1.79318
\(963\) −16956.0 −0.567393
\(964\) 12008.0 0.401195
\(965\) 2090.00 0.0697197
\(966\) −7488.00 −0.249402
\(967\) 21356.0 0.710199 0.355100 0.934828i \(-0.384447\pi\)
0.355100 + 0.934828i \(0.384447\pi\)
\(968\) 7784.00 0.258458
\(969\) 25920.0 0.859309
\(970\) −860.000 −0.0284669
\(971\) 31242.0 1.03255 0.516274 0.856424i \(-0.327319\pi\)
0.516274 + 0.856424i \(0.327319\pi\)
\(972\) 972.000 0.0320750
\(973\) 25480.0 0.839518
\(974\) 28432.0 0.935339
\(975\) −6600.00 −0.216789
\(976\) −7648.00 −0.250826
\(977\) 7686.00 0.251686 0.125843 0.992050i \(-0.459836\pi\)
0.125843 + 0.992050i \(0.459836\pi\)
\(978\) −10788.0 −0.352722
\(979\) −5760.00 −0.188039
\(980\) −6660.00 −0.217088
\(981\) −630.000 −0.0205039
\(982\) −16536.0 −0.537357
\(983\) −35928.0 −1.16574 −0.582871 0.812564i \(-0.698071\pi\)
−0.582871 + 0.812564i \(0.698071\pi\)
\(984\) 3888.00 0.125960
\(985\) 270.000 0.00873392
\(986\) 12960.0 0.418591
\(987\) 7488.00 0.241485
\(988\) 56320.0 1.81354
\(989\) −13056.0 −0.419774
\(990\) 4320.00 0.138685
\(991\) −8968.00 −0.287465 −0.143733 0.989617i \(-0.545911\pi\)
−0.143733 + 0.989617i \(0.545911\pi\)
\(992\) 992.000 0.0317500
\(993\) −28524.0 −0.911563
\(994\) 55224.0 1.76217
\(995\) 8600.00 0.274008
\(996\) 11664.0 0.371072
\(997\) 34526.0 1.09674 0.548370 0.836236i \(-0.315249\pi\)
0.548370 + 0.836236i \(0.315249\pi\)
\(998\) −23720.0 −0.752348
\(999\) −8208.00 −0.259950
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 930.4.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.4.a.c.1.1 1 1.1 even 1 trivial