Properties

Label 1805.4.a.i.1.1
Level $1805$
Weight $4$
Character 1805.1
Self dual yes
Analytic conductor $106.498$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1805,4,Mod(1,1805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1805.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1805.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(106.498447560\)
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 \(\chi\) \(=\) 1805.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.00000 q^{2} -5.00000 q^{3} +17.0000 q^{4} +5.00000 q^{5} -25.0000 q^{6} -19.0000 q^{7} +45.0000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+5.00000 q^{2} -5.00000 q^{3} +17.0000 q^{4} +5.00000 q^{5} -25.0000 q^{6} -19.0000 q^{7} +45.0000 q^{8} -2.00000 q^{9} +25.0000 q^{10} +50.0000 q^{11} -85.0000 q^{12} -55.0000 q^{13} -95.0000 q^{14} -25.0000 q^{15} +89.0000 q^{16} +51.0000 q^{17} -10.0000 q^{18} +85.0000 q^{20} +95.0000 q^{21} +250.000 q^{22} -147.000 q^{23} -225.000 q^{24} +25.0000 q^{25} -275.000 q^{26} +145.000 q^{27} -323.000 q^{28} +165.000 q^{29} -125.000 q^{30} +70.0000 q^{31} +85.0000 q^{32} -250.000 q^{33} +255.000 q^{34} -95.0000 q^{35} -34.0000 q^{36} -210.000 q^{37} +275.000 q^{39} +225.000 q^{40} +80.0000 q^{41} +475.000 q^{42} -558.000 q^{43} +850.000 q^{44} -10.0000 q^{45} -735.000 q^{46} -464.000 q^{47} -445.000 q^{48} +18.0000 q^{49} +125.000 q^{50} -255.000 q^{51} -935.000 q^{52} -455.000 q^{53} +725.000 q^{54} +250.000 q^{55} -855.000 q^{56} +825.000 q^{58} -225.000 q^{59} -425.000 q^{60} +500.000 q^{61} +350.000 q^{62} +38.0000 q^{63} -287.000 q^{64} -275.000 q^{65} -1250.00 q^{66} -105.000 q^{67} +867.000 q^{68} +735.000 q^{69} -475.000 q^{70} +1140.00 q^{71} -90.0000 q^{72} -703.000 q^{73} -1050.00 q^{74} -125.000 q^{75} -950.000 q^{77} +1375.00 q^{78} -700.000 q^{79} +445.000 q^{80} -671.000 q^{81} +400.000 q^{82} -918.000 q^{83} +1615.00 q^{84} +255.000 q^{85} -2790.00 q^{86} -825.000 q^{87} +2250.00 q^{88} -870.000 q^{89} -50.0000 q^{90} +1045.00 q^{91} -2499.00 q^{92} -350.000 q^{93} -2320.00 q^{94} -425.000 q^{96} -1380.00 q^{97} +90.0000 q^{98} -100.000 q^{99} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.00000 1.76777 0.883883 0.467707i \(-0.154920\pi\)
0.883883 + 0.467707i \(0.154920\pi\)
\(3\) −5.00000 −0.962250 −0.481125 0.876652i \(-0.659772\pi\)
−0.481125 + 0.876652i \(0.659772\pi\)
\(4\) 17.0000 2.12500
\(5\) 5.00000 0.447214
\(6\) −25.0000 −1.70103
\(7\) −19.0000 −1.02590 −0.512952 0.858417i \(-0.671448\pi\)
−0.512952 + 0.858417i \(0.671448\pi\)
\(8\) 45.0000 1.98874
\(9\) −2.00000 −0.0740741
\(10\) 25.0000 0.790569
\(11\) 50.0000 1.37051 0.685253 0.728305i \(-0.259692\pi\)
0.685253 + 0.728305i \(0.259692\pi\)
\(12\) −85.0000 −2.04478
\(13\) −55.0000 −1.17340 −0.586702 0.809803i \(-0.699574\pi\)
−0.586702 + 0.809803i \(0.699574\pi\)
\(14\) −95.0000 −1.81356
\(15\) −25.0000 −0.430331
\(16\) 89.0000 1.39062
\(17\) 51.0000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) −10.0000 −0.130946
\(19\) 0 0
\(20\) 85.0000 0.950329
\(21\) 95.0000 0.987176
\(22\) 250.000 2.42274
\(23\) −147.000 −1.33268 −0.666340 0.745648i \(-0.732140\pi\)
−0.666340 + 0.745648i \(0.732140\pi\)
\(24\) −225.000 −1.91366
\(25\) 25.0000 0.200000
\(26\) −275.000 −2.07431
\(27\) 145.000 1.03353
\(28\) −323.000 −2.18005
\(29\) 165.000 1.05654 0.528271 0.849076i \(-0.322840\pi\)
0.528271 + 0.849076i \(0.322840\pi\)
\(30\) −125.000 −0.760726
\(31\) 70.0000 0.405560 0.202780 0.979224i \(-0.435002\pi\)
0.202780 + 0.979224i \(0.435002\pi\)
\(32\) 85.0000 0.469563
\(33\) −250.000 −1.31877
\(34\) 255.000 1.28624
\(35\) −95.0000 −0.458798
\(36\) −34.0000 −0.157407
\(37\) −210.000 −0.933075 −0.466538 0.884501i \(-0.654499\pi\)
−0.466538 + 0.884501i \(0.654499\pi\)
\(38\) 0 0
\(39\) 275.000 1.12911
\(40\) 225.000 0.889391
\(41\) 80.0000 0.304729 0.152365 0.988324i \(-0.451311\pi\)
0.152365 + 0.988324i \(0.451311\pi\)
\(42\) 475.000 1.74510
\(43\) −558.000 −1.97893 −0.989467 0.144755i \(-0.953760\pi\)
−0.989467 + 0.144755i \(0.953760\pi\)
\(44\) 850.000 2.91233
\(45\) −10.0000 −0.0331269
\(46\) −735.000 −2.35587
\(47\) −464.000 −1.44003 −0.720014 0.693959i \(-0.755865\pi\)
−0.720014 + 0.693959i \(0.755865\pi\)
\(48\) −445.000 −1.33813
\(49\) 18.0000 0.0524781
\(50\) 125.000 0.353553
\(51\) −255.000 −0.700140
\(52\) −935.000 −2.49348
\(53\) −455.000 −1.17923 −0.589614 0.807685i \(-0.700720\pi\)
−0.589614 + 0.807685i \(0.700720\pi\)
\(54\) 725.000 1.82704
\(55\) 250.000 0.612909
\(56\) −855.000 −2.04025
\(57\) 0 0
\(58\) 825.000 1.86772
\(59\) −225.000 −0.496483 −0.248242 0.968698i \(-0.579853\pi\)
−0.248242 + 0.968698i \(0.579853\pi\)
\(60\) −425.000 −0.914454
\(61\) 500.000 1.04948 0.524741 0.851262i \(-0.324162\pi\)
0.524741 + 0.851262i \(0.324162\pi\)
\(62\) 350.000 0.716936
\(63\) 38.0000 0.0759929
\(64\) −287.000 −0.560547
\(65\) −275.000 −0.524762
\(66\) −1250.00 −2.33128
\(67\) −105.000 −0.191460 −0.0957298 0.995407i \(-0.530518\pi\)
−0.0957298 + 0.995407i \(0.530518\pi\)
\(68\) 867.000 1.54616
\(69\) 735.000 1.28237
\(70\) −475.000 −0.811048
\(71\) 1140.00 1.90554 0.952768 0.303698i \(-0.0982214\pi\)
0.952768 + 0.303698i \(0.0982214\pi\)
\(72\) −90.0000 −0.147314
\(73\) −703.000 −1.12712 −0.563561 0.826074i \(-0.690569\pi\)
−0.563561 + 0.826074i \(0.690569\pi\)
\(74\) −1050.00 −1.64946
\(75\) −125.000 −0.192450
\(76\) 0 0
\(77\) −950.000 −1.40601
\(78\) 1375.00 1.99600
\(79\) −700.000 −0.996913 −0.498457 0.866915i \(-0.666100\pi\)
−0.498457 + 0.866915i \(0.666100\pi\)
\(80\) 445.000 0.621906
\(81\) −671.000 −0.920439
\(82\) 400.000 0.538690
\(83\) −918.000 −1.21402 −0.607010 0.794695i \(-0.707631\pi\)
−0.607010 + 0.794695i \(0.707631\pi\)
\(84\) 1615.00 2.09775
\(85\) 255.000 0.325396
\(86\) −2790.00 −3.49830
\(87\) −825.000 −1.01666
\(88\) 2250.00 2.72558
\(89\) −870.000 −1.03618 −0.518089 0.855327i \(-0.673356\pi\)
−0.518089 + 0.855327i \(0.673356\pi\)
\(90\) −50.0000 −0.0585607
\(91\) 1045.00 1.20380
\(92\) −2499.00 −2.83194
\(93\) −350.000 −0.390251
\(94\) −2320.00 −2.54564
\(95\) 0 0
\(96\) −425.000 −0.451837
\(97\) −1380.00 −1.44451 −0.722257 0.691625i \(-0.756895\pi\)
−0.722257 + 0.691625i \(0.756895\pi\)
\(98\) 90.0000 0.0927691
\(99\) −100.000 −0.101519
\(100\) 425.000 0.425000
\(101\) 150.000 0.147778 0.0738889 0.997266i \(-0.476459\pi\)
0.0738889 + 0.997266i \(0.476459\pi\)
\(102\) −1275.00 −1.23768
\(103\) 1250.00 1.19579 0.597894 0.801575i \(-0.296004\pi\)
0.597894 + 0.801575i \(0.296004\pi\)
\(104\) −2475.00 −2.33359
\(105\) 475.000 0.441479
\(106\) −2275.00 −2.08460
\(107\) 1205.00 1.08871 0.544354 0.838856i \(-0.316775\pi\)
0.544354 + 0.838856i \(0.316775\pi\)
\(108\) 2465.00 2.19625
\(109\) −1245.00 −1.09403 −0.547015 0.837122i \(-0.684236\pi\)
−0.547015 + 0.837122i \(0.684236\pi\)
\(110\) 1250.00 1.08348
\(111\) 1050.00 0.897852
\(112\) −1691.00 −1.42665
\(113\) 480.000 0.399598 0.199799 0.979837i \(-0.435971\pi\)
0.199799 + 0.979837i \(0.435971\pi\)
\(114\) 0 0
\(115\) −735.000 −0.595992
\(116\) 2805.00 2.24515
\(117\) 110.000 0.0869188
\(118\) −1125.00 −0.877666
\(119\) −969.000 −0.746454
\(120\) −1125.00 −0.855816
\(121\) 1169.00 0.878287
\(122\) 2500.00 1.85524
\(123\) −400.000 −0.293226
\(124\) 1190.00 0.861816
\(125\) 125.000 0.0894427
\(126\) 190.000 0.134338
\(127\) −100.000 −0.0698706 −0.0349353 0.999390i \(-0.511123\pi\)
−0.0349353 + 0.999390i \(0.511123\pi\)
\(128\) −2115.00 −1.46048
\(129\) 2790.00 1.90423
\(130\) −1375.00 −0.927658
\(131\) 1158.00 0.772328 0.386164 0.922430i \(-0.373800\pi\)
0.386164 + 0.922430i \(0.373800\pi\)
\(132\) −4250.00 −2.80239
\(133\) 0 0
\(134\) −525.000 −0.338456
\(135\) 725.000 0.462208
\(136\) 2295.00 1.44702
\(137\) 1759.00 1.09695 0.548473 0.836168i \(-0.315209\pi\)
0.548473 + 0.836168i \(0.315209\pi\)
\(138\) 3675.00 2.26693
\(139\) −2226.00 −1.35832 −0.679161 0.733989i \(-0.737656\pi\)
−0.679161 + 0.733989i \(0.737656\pi\)
\(140\) −1615.00 −0.974946
\(141\) 2320.00 1.38567
\(142\) 5700.00 3.36854
\(143\) −2750.00 −1.60816
\(144\) −178.000 −0.103009
\(145\) 825.000 0.472500
\(146\) −3515.00 −1.99249
\(147\) −90.0000 −0.0504971
\(148\) −3570.00 −1.98279
\(149\) 1736.00 0.954488 0.477244 0.878771i \(-0.341636\pi\)
0.477244 + 0.878771i \(0.341636\pi\)
\(150\) −625.000 −0.340207
\(151\) 790.000 0.425757 0.212878 0.977079i \(-0.431716\pi\)
0.212878 + 0.977079i \(0.431716\pi\)
\(152\) 0 0
\(153\) −102.000 −0.0538968
\(154\) −4750.00 −2.48549
\(155\) 350.000 0.181372
\(156\) 4675.00 2.39936
\(157\) −1944.00 −0.988204 −0.494102 0.869404i \(-0.664503\pi\)
−0.494102 + 0.869404i \(0.664503\pi\)
\(158\) −3500.00 −1.76231
\(159\) 2275.00 1.13471
\(160\) 425.000 0.209995
\(161\) 2793.00 1.36720
\(162\) −3355.00 −1.62712
\(163\) −3562.00 −1.71164 −0.855820 0.517273i \(-0.826947\pi\)
−0.855820 + 0.517273i \(0.826947\pi\)
\(164\) 1360.00 0.647550
\(165\) −1250.00 −0.589772
\(166\) −4590.00 −2.14610
\(167\) −3360.00 −1.55691 −0.778457 0.627698i \(-0.783997\pi\)
−0.778457 + 0.627698i \(0.783997\pi\)
\(168\) 4275.00 1.96323
\(169\) 828.000 0.376878
\(170\) 1275.00 0.575224
\(171\) 0 0
\(172\) −9486.00 −4.20524
\(173\) 3870.00 1.70076 0.850378 0.526173i \(-0.176374\pi\)
0.850378 + 0.526173i \(0.176374\pi\)
\(174\) −4125.00 −1.79722
\(175\) −475.000 −0.205181
\(176\) 4450.00 1.90586
\(177\) 1125.00 0.477741
\(178\) −4350.00 −1.83172
\(179\) −3340.00 −1.39466 −0.697328 0.716752i \(-0.745628\pi\)
−0.697328 + 0.716752i \(0.745628\pi\)
\(180\) −170.000 −0.0703947
\(181\) −1790.00 −0.735081 −0.367540 0.930008i \(-0.619800\pi\)
−0.367540 + 0.930008i \(0.619800\pi\)
\(182\) 5225.00 2.12804
\(183\) −2500.00 −1.00987
\(184\) −6615.00 −2.65035
\(185\) −1050.00 −0.417284
\(186\) −1750.00 −0.689872
\(187\) 2550.00 0.997190
\(188\) −7888.00 −3.06006
\(189\) −2755.00 −1.06030
\(190\) 0 0
\(191\) −1647.00 −0.623941 −0.311971 0.950092i \(-0.600989\pi\)
−0.311971 + 0.950092i \(0.600989\pi\)
\(192\) 1435.00 0.539386
\(193\) 1030.00 0.384150 0.192075 0.981380i \(-0.438478\pi\)
0.192075 + 0.981380i \(0.438478\pi\)
\(194\) −6900.00 −2.55356
\(195\) 1375.00 0.504953
\(196\) 306.000 0.111516
\(197\) −336.000 −0.121518 −0.0607589 0.998152i \(-0.519352\pi\)
−0.0607589 + 0.998152i \(0.519352\pi\)
\(198\) −500.000 −0.179462
\(199\) −875.000 −0.311694 −0.155847 0.987781i \(-0.549811\pi\)
−0.155847 + 0.987781i \(0.549811\pi\)
\(200\) 1125.00 0.397748
\(201\) 525.000 0.184232
\(202\) 750.000 0.261237
\(203\) −3135.00 −1.08391
\(204\) −4335.00 −1.48780
\(205\) 400.000 0.136279
\(206\) 6250.00 2.11387
\(207\) 294.000 0.0987170
\(208\) −4895.00 −1.63177
\(209\) 0 0
\(210\) 2375.00 0.780431
\(211\) 3935.00 1.28387 0.641935 0.766759i \(-0.278132\pi\)
0.641935 + 0.766759i \(0.278132\pi\)
\(212\) −7735.00 −2.50586
\(213\) −5700.00 −1.83360
\(214\) 6025.00 1.92458
\(215\) −2790.00 −0.885007
\(216\) 6525.00 2.05542
\(217\) −1330.00 −0.416066
\(218\) −6225.00 −1.93399
\(219\) 3515.00 1.08457
\(220\) 4250.00 1.30243
\(221\) −2805.00 −0.853777
\(222\) 5250.00 1.58719
\(223\) 5690.00 1.70866 0.854329 0.519733i \(-0.173969\pi\)
0.854329 + 0.519733i \(0.173969\pi\)
\(224\) −1615.00 −0.481726
\(225\) −50.0000 −0.0148148
\(226\) 2400.00 0.706397
\(227\) 2715.00 0.793836 0.396918 0.917854i \(-0.370080\pi\)
0.396918 + 0.917854i \(0.370080\pi\)
\(228\) 0 0
\(229\) −716.000 −0.206614 −0.103307 0.994650i \(-0.532942\pi\)
−0.103307 + 0.994650i \(0.532942\pi\)
\(230\) −3675.00 −1.05358
\(231\) 4750.00 1.35293
\(232\) 7425.00 2.10119
\(233\) 3182.00 0.894677 0.447339 0.894365i \(-0.352372\pi\)
0.447339 + 0.894365i \(0.352372\pi\)
\(234\) 550.000 0.153652
\(235\) −2320.00 −0.644000
\(236\) −3825.00 −1.05503
\(237\) 3500.00 0.959280
\(238\) −4845.00 −1.31956
\(239\) −4275.00 −1.15702 −0.578508 0.815677i \(-0.696365\pi\)
−0.578508 + 0.815677i \(0.696365\pi\)
\(240\) −2225.00 −0.598430
\(241\) 280.000 0.0748398 0.0374199 0.999300i \(-0.488086\pi\)
0.0374199 + 0.999300i \(0.488086\pi\)
\(242\) 5845.00 1.55261
\(243\) −560.000 −0.147835
\(244\) 8500.00 2.23015
\(245\) 90.0000 0.0234689
\(246\) −2000.00 −0.518355
\(247\) 0 0
\(248\) 3150.00 0.806553
\(249\) 4590.00 1.16819
\(250\) 625.000 0.158114
\(251\) 1152.00 0.289696 0.144848 0.989454i \(-0.453731\pi\)
0.144848 + 0.989454i \(0.453731\pi\)
\(252\) 646.000 0.161485
\(253\) −7350.00 −1.82644
\(254\) −500.000 −0.123515
\(255\) −1275.00 −0.313112
\(256\) −8279.00 −2.02124
\(257\) −870.000 −0.211164 −0.105582 0.994411i \(-0.533671\pi\)
−0.105582 + 0.994411i \(0.533671\pi\)
\(258\) 13950.0 3.36624
\(259\) 3990.00 0.957245
\(260\) −4675.00 −1.11512
\(261\) −330.000 −0.0782624
\(262\) 5790.00 1.36530
\(263\) −5688.00 −1.33360 −0.666801 0.745236i \(-0.732337\pi\)
−0.666801 + 0.745236i \(0.732337\pi\)
\(264\) −11250.0 −2.62269
\(265\) −2275.00 −0.527367
\(266\) 0 0
\(267\) 4350.00 0.997062
\(268\) −1785.00 −0.406852
\(269\) 1010.00 0.228925 0.114462 0.993428i \(-0.463485\pi\)
0.114462 + 0.993428i \(0.463485\pi\)
\(270\) 3625.00 0.817076
\(271\) 25.0000 0.00560384 0.00280192 0.999996i \(-0.499108\pi\)
0.00280192 + 0.999996i \(0.499108\pi\)
\(272\) 4539.00 1.01183
\(273\) −5225.00 −1.15836
\(274\) 8795.00 1.93914
\(275\) 1250.00 0.274101
\(276\) 12495.0 2.72504
\(277\) 3646.00 0.790855 0.395428 0.918497i \(-0.370596\pi\)
0.395428 + 0.918497i \(0.370596\pi\)
\(278\) −11130.0 −2.40120
\(279\) −140.000 −0.0300415
\(280\) −4275.00 −0.912429
\(281\) −6000.00 −1.27377 −0.636886 0.770958i \(-0.719778\pi\)
−0.636886 + 0.770958i \(0.719778\pi\)
\(282\) 11600.0 2.44954
\(283\) 5018.00 1.05403 0.527013 0.849857i \(-0.323312\pi\)
0.527013 + 0.849857i \(0.323312\pi\)
\(284\) 19380.0 4.04927
\(285\) 0 0
\(286\) −13750.0 −2.84285
\(287\) −1520.00 −0.312623
\(288\) −170.000 −0.0347825
\(289\) −2312.00 −0.470588
\(290\) 4125.00 0.835270
\(291\) 6900.00 1.38998
\(292\) −11951.0 −2.39513
\(293\) 7035.00 1.40269 0.701347 0.712820i \(-0.252583\pi\)
0.701347 + 0.712820i \(0.252583\pi\)
\(294\) −450.000 −0.0892671
\(295\) −1125.00 −0.222034
\(296\) −9450.00 −1.85564
\(297\) 7250.00 1.41646
\(298\) 8680.00 1.68731
\(299\) 8085.00 1.56377
\(300\) −2125.00 −0.408956
\(301\) 10602.0 2.03020
\(302\) 3950.00 0.752639
\(303\) −750.000 −0.142199
\(304\) 0 0
\(305\) 2500.00 0.469343
\(306\) −510.000 −0.0952770
\(307\) 4460.00 0.829139 0.414569 0.910018i \(-0.363932\pi\)
0.414569 + 0.910018i \(0.363932\pi\)
\(308\) −16150.0 −2.98777
\(309\) −6250.00 −1.15065
\(310\) 1750.00 0.320624
\(311\) 6825.00 1.24441 0.622203 0.782856i \(-0.286238\pi\)
0.622203 + 0.782856i \(0.286238\pi\)
\(312\) 12375.0 2.24550
\(313\) 4537.00 0.819318 0.409659 0.912239i \(-0.365648\pi\)
0.409659 + 0.912239i \(0.365648\pi\)
\(314\) −9720.00 −1.74692
\(315\) 190.000 0.0339850
\(316\) −11900.0 −2.11844
\(317\) −7845.00 −1.38997 −0.694983 0.719026i \(-0.744588\pi\)
−0.694983 + 0.719026i \(0.744588\pi\)
\(318\) 11375.0 2.00591
\(319\) 8250.00 1.44800
\(320\) −1435.00 −0.250684
\(321\) −6025.00 −1.04761
\(322\) 13965.0 2.41689
\(323\) 0 0
\(324\) −11407.0 −1.95593
\(325\) −1375.00 −0.234681
\(326\) −17810.0 −3.02578
\(327\) 6225.00 1.05273
\(328\) 3600.00 0.606027
\(329\) 8816.00 1.47733
\(330\) −6250.00 −1.04258
\(331\) −7075.00 −1.17486 −0.587428 0.809277i \(-0.699859\pi\)
−0.587428 + 0.809277i \(0.699859\pi\)
\(332\) −15606.0 −2.57979
\(333\) 420.000 0.0691167
\(334\) −16800.0 −2.75226
\(335\) −525.000 −0.0856233
\(336\) 8455.00 1.37279
\(337\) 11710.0 1.89283 0.946416 0.322950i \(-0.104675\pi\)
0.946416 + 0.322950i \(0.104675\pi\)
\(338\) 4140.00 0.666232
\(339\) −2400.00 −0.384514
\(340\) 4335.00 0.691466
\(341\) 3500.00 0.555823
\(342\) 0 0
\(343\) 6175.00 0.972066
\(344\) −25110.0 −3.93558
\(345\) 3675.00 0.573494
\(346\) 19350.0 3.00654
\(347\) −336.000 −0.0519811 −0.0259905 0.999662i \(-0.508274\pi\)
−0.0259905 + 0.999662i \(0.508274\pi\)
\(348\) −14025.0 −2.16040
\(349\) −700.000 −0.107364 −0.0536822 0.998558i \(-0.517096\pi\)
−0.0536822 + 0.998558i \(0.517096\pi\)
\(350\) −2375.00 −0.362712
\(351\) −7975.00 −1.21275
\(352\) 4250.00 0.643539
\(353\) −8923.00 −1.34539 −0.672696 0.739919i \(-0.734864\pi\)
−0.672696 + 0.739919i \(0.734864\pi\)
\(354\) 5625.00 0.844535
\(355\) 5700.00 0.852182
\(356\) −14790.0 −2.20188
\(357\) 4845.00 0.718276
\(358\) −16700.0 −2.46543
\(359\) −7521.00 −1.10569 −0.552846 0.833284i \(-0.686458\pi\)
−0.552846 + 0.833284i \(0.686458\pi\)
\(360\) −450.000 −0.0658808
\(361\) 0 0
\(362\) −8950.00 −1.29945
\(363\) −5845.00 −0.845132
\(364\) 17765.0 2.55807
\(365\) −3515.00 −0.504064
\(366\) −12500.0 −1.78521
\(367\) 4624.00 0.657686 0.328843 0.944385i \(-0.393341\pi\)
0.328843 + 0.944385i \(0.393341\pi\)
\(368\) −13083.0 −1.85326
\(369\) −160.000 −0.0225725
\(370\) −5250.00 −0.737661
\(371\) 8645.00 1.20977
\(372\) −5950.00 −0.829283
\(373\) 9015.00 1.25142 0.625709 0.780056i \(-0.284810\pi\)
0.625709 + 0.780056i \(0.284810\pi\)
\(374\) 12750.0 1.76280
\(375\) −625.000 −0.0860663
\(376\) −20880.0 −2.86384
\(377\) −9075.00 −1.23975
\(378\) −13775.0 −1.87436
\(379\) 3895.00 0.527896 0.263948 0.964537i \(-0.414975\pi\)
0.263948 + 0.964537i \(0.414975\pi\)
\(380\) 0 0
\(381\) 500.000 0.0672330
\(382\) −8235.00 −1.10298
\(383\) −9690.00 −1.29278 −0.646391 0.763006i \(-0.723723\pi\)
−0.646391 + 0.763006i \(0.723723\pi\)
\(384\) 10575.0 1.40535
\(385\) −4750.00 −0.628785
\(386\) 5150.00 0.679088
\(387\) 1116.00 0.146588
\(388\) −23460.0 −3.06959
\(389\) −5650.00 −0.736417 −0.368209 0.929743i \(-0.620029\pi\)
−0.368209 + 0.929743i \(0.620029\pi\)
\(390\) 6875.00 0.892639
\(391\) −7497.00 −0.969666
\(392\) 810.000 0.104365
\(393\) −5790.00 −0.743173
\(394\) −1680.00 −0.214815
\(395\) −3500.00 −0.445833
\(396\) −1700.00 −0.215728
\(397\) 3386.00 0.428057 0.214028 0.976827i \(-0.431342\pi\)
0.214028 + 0.976827i \(0.431342\pi\)
\(398\) −4375.00 −0.551002
\(399\) 0 0
\(400\) 2225.00 0.278125
\(401\) 11840.0 1.47447 0.737234 0.675638i \(-0.236132\pi\)
0.737234 + 0.675638i \(0.236132\pi\)
\(402\) 2625.00 0.325679
\(403\) −3850.00 −0.475886
\(404\) 2550.00 0.314028
\(405\) −3355.00 −0.411633
\(406\) −15675.0 −1.91610
\(407\) −10500.0 −1.27879
\(408\) −11475.0 −1.39239
\(409\) 6770.00 0.818472 0.409236 0.912429i \(-0.365795\pi\)
0.409236 + 0.912429i \(0.365795\pi\)
\(410\) 2000.00 0.240910
\(411\) −8795.00 −1.05554
\(412\) 21250.0 2.54105
\(413\) 4275.00 0.509344
\(414\) 1470.00 0.174509
\(415\) −4590.00 −0.542926
\(416\) −4675.00 −0.550987
\(417\) 11130.0 1.30705
\(418\) 0 0
\(419\) 4550.00 0.530506 0.265253 0.964179i \(-0.414545\pi\)
0.265253 + 0.964179i \(0.414545\pi\)
\(420\) 8075.00 0.938142
\(421\) 3085.00 0.357135 0.178567 0.983928i \(-0.442854\pi\)
0.178567 + 0.983928i \(0.442854\pi\)
\(422\) 19675.0 2.26958
\(423\) 928.000 0.106669
\(424\) −20475.0 −2.34517
\(425\) 1275.00 0.145521
\(426\) −28500.0 −3.24138
\(427\) −9500.00 −1.07667
\(428\) 20485.0 2.31350
\(429\) 13750.0 1.54745
\(430\) −13950.0 −1.56449
\(431\) −4780.00 −0.534210 −0.267105 0.963667i \(-0.586067\pi\)
−0.267105 + 0.963667i \(0.586067\pi\)
\(432\) 12905.0 1.43725
\(433\) 8570.00 0.951150 0.475575 0.879675i \(-0.342240\pi\)
0.475575 + 0.879675i \(0.342240\pi\)
\(434\) −6650.00 −0.735507
\(435\) −4125.00 −0.454663
\(436\) −21165.0 −2.32482
\(437\) 0 0
\(438\) 17575.0 1.91727
\(439\) 7220.00 0.784947 0.392474 0.919763i \(-0.371619\pi\)
0.392474 + 0.919763i \(0.371619\pi\)
\(440\) 11250.0 1.21892
\(441\) −36.0000 −0.00388727
\(442\) −14025.0 −1.50928
\(443\) −10258.0 −1.10016 −0.550082 0.835111i \(-0.685403\pi\)
−0.550082 + 0.835111i \(0.685403\pi\)
\(444\) 17850.0 1.90794
\(445\) −4350.00 −0.463393
\(446\) 28450.0 3.02051
\(447\) −8680.00 −0.918456
\(448\) 5453.00 0.575067
\(449\) −7530.00 −0.791454 −0.395727 0.918368i \(-0.629507\pi\)
−0.395727 + 0.918368i \(0.629507\pi\)
\(450\) −250.000 −0.0261891
\(451\) 4000.00 0.417633
\(452\) 8160.00 0.849146
\(453\) −3950.00 −0.409685
\(454\) 13575.0 1.40332
\(455\) 5225.00 0.538356
\(456\) 0 0
\(457\) −8819.00 −0.902703 −0.451352 0.892346i \(-0.649058\pi\)
−0.451352 + 0.892346i \(0.649058\pi\)
\(458\) −3580.00 −0.365245
\(459\) 7395.00 0.752002
\(460\) −12495.0 −1.26648
\(461\) 10232.0 1.03373 0.516867 0.856065i \(-0.327098\pi\)
0.516867 + 0.856065i \(0.327098\pi\)
\(462\) 23750.0 2.39167
\(463\) −12112.0 −1.21575 −0.607875 0.794033i \(-0.707978\pi\)
−0.607875 + 0.794033i \(0.707978\pi\)
\(464\) 14685.0 1.46925
\(465\) −1750.00 −0.174525
\(466\) 15910.0 1.58158
\(467\) −5076.00 −0.502975 −0.251487 0.967861i \(-0.580920\pi\)
−0.251487 + 0.967861i \(0.580920\pi\)
\(468\) 1870.00 0.184703
\(469\) 1995.00 0.196419
\(470\) −11600.0 −1.13844
\(471\) 9720.00 0.950900
\(472\) −10125.0 −0.987375
\(473\) −27900.0 −2.71214
\(474\) 17500.0 1.69578
\(475\) 0 0
\(476\) −16473.0 −1.58622
\(477\) 910.000 0.0873502
\(478\) −21375.0 −2.04533
\(479\) 15384.0 1.46746 0.733730 0.679442i \(-0.237778\pi\)
0.733730 + 0.679442i \(0.237778\pi\)
\(480\) −2125.00 −0.202068
\(481\) 11550.0 1.09487
\(482\) 1400.00 0.132299
\(483\) −13965.0 −1.31559
\(484\) 19873.0 1.86636
\(485\) −6900.00 −0.646006
\(486\) −2800.00 −0.261339
\(487\) 8350.00 0.776950 0.388475 0.921459i \(-0.373002\pi\)
0.388475 + 0.921459i \(0.373002\pi\)
\(488\) 22500.0 2.08715
\(489\) 17810.0 1.64703
\(490\) 450.000 0.0414876
\(491\) −8772.00 −0.806262 −0.403131 0.915142i \(-0.632078\pi\)
−0.403131 + 0.915142i \(0.632078\pi\)
\(492\) −6800.00 −0.623105
\(493\) 8415.00 0.768748
\(494\) 0 0
\(495\) −500.000 −0.0454007
\(496\) 6230.00 0.563982
\(497\) −21660.0 −1.95490
\(498\) 22950.0 2.06509
\(499\) −2786.00 −0.249937 −0.124968 0.992161i \(-0.539883\pi\)
−0.124968 + 0.992161i \(0.539883\pi\)
\(500\) 2125.00 0.190066
\(501\) 16800.0 1.49814
\(502\) 5760.00 0.512114
\(503\) −727.000 −0.0644440 −0.0322220 0.999481i \(-0.510258\pi\)
−0.0322220 + 0.999481i \(0.510258\pi\)
\(504\) 1710.00 0.151130
\(505\) 750.000 0.0660882
\(506\) −36750.0 −3.22873
\(507\) −4140.00 −0.362651
\(508\) −1700.00 −0.148475
\(509\) 2370.00 0.206382 0.103191 0.994662i \(-0.467095\pi\)
0.103191 + 0.994662i \(0.467095\pi\)
\(510\) −6375.00 −0.553509
\(511\) 13357.0 1.15632
\(512\) −24475.0 −2.11260
\(513\) 0 0
\(514\) −4350.00 −0.373288
\(515\) 6250.00 0.534773
\(516\) 47430.0 4.04649
\(517\) −23200.0 −1.97357
\(518\) 19950.0 1.69219
\(519\) −19350.0 −1.63655
\(520\) −12375.0 −1.04361
\(521\) −12460.0 −1.04776 −0.523880 0.851792i \(-0.675516\pi\)
−0.523880 + 0.851792i \(0.675516\pi\)
\(522\) −1650.00 −0.138350
\(523\) 14705.0 1.22945 0.614727 0.788740i \(-0.289266\pi\)
0.614727 + 0.788740i \(0.289266\pi\)
\(524\) 19686.0 1.64120
\(525\) 2375.00 0.197435
\(526\) −28440.0 −2.35750
\(527\) 3570.00 0.295089
\(528\) −22250.0 −1.83391
\(529\) 9442.00 0.776034
\(530\) −11375.0 −0.932261
\(531\) 450.000 0.0367765
\(532\) 0 0
\(533\) −4400.00 −0.357571
\(534\) 21750.0 1.76257
\(535\) 6025.00 0.486885
\(536\) −4725.00 −0.380763
\(537\) 16700.0 1.34201
\(538\) 5050.00 0.404686
\(539\) 900.000 0.0719216
\(540\) 12325.0 0.982192
\(541\) −11450.0 −0.909933 −0.454967 0.890508i \(-0.650349\pi\)
−0.454967 + 0.890508i \(0.650349\pi\)
\(542\) 125.000 0.00990629
\(543\) 8950.00 0.707332
\(544\) 4335.00 0.341657
\(545\) −6225.00 −0.489266
\(546\) −26125.0 −2.04770
\(547\) 12500.0 0.977078 0.488539 0.872542i \(-0.337530\pi\)
0.488539 + 0.872542i \(0.337530\pi\)
\(548\) 29903.0 2.33101
\(549\) −1000.00 −0.0777395
\(550\) 6250.00 0.484547
\(551\) 0 0
\(552\) 33075.0 2.55030
\(553\) 13300.0 1.02274
\(554\) 18230.0 1.39805
\(555\) 5250.00 0.401532
\(556\) −37842.0 −2.88644
\(557\) 8006.00 0.609022 0.304511 0.952509i \(-0.401507\pi\)
0.304511 + 0.952509i \(0.401507\pi\)
\(558\) −700.000 −0.0531064
\(559\) 30690.0 2.32209
\(560\) −8455.00 −0.638016
\(561\) −12750.0 −0.959546
\(562\) −30000.0 −2.25173
\(563\) 7280.00 0.544965 0.272483 0.962161i \(-0.412155\pi\)
0.272483 + 0.962161i \(0.412155\pi\)
\(564\) 39440.0 2.94455
\(565\) 2400.00 0.178706
\(566\) 25090.0 1.86327
\(567\) 12749.0 0.944282
\(568\) 51300.0 3.78961
\(569\) 2080.00 0.153248 0.0766240 0.997060i \(-0.475586\pi\)
0.0766240 + 0.997060i \(0.475586\pi\)
\(570\) 0 0
\(571\) 7700.00 0.564334 0.282167 0.959365i \(-0.408947\pi\)
0.282167 + 0.959365i \(0.408947\pi\)
\(572\) −46750.0 −3.41734
\(573\) 8235.00 0.600388
\(574\) −7600.00 −0.552644
\(575\) −3675.00 −0.266536
\(576\) 574.000 0.0415220
\(577\) 23171.0 1.67179 0.835894 0.548891i \(-0.184950\pi\)
0.835894 + 0.548891i \(0.184950\pi\)
\(578\) −11560.0 −0.831890
\(579\) −5150.00 −0.369649
\(580\) 14025.0 1.00406
\(581\) 17442.0 1.24547
\(582\) 34500.0 2.45717
\(583\) −22750.0 −1.61614
\(584\) −31635.0 −2.24155
\(585\) 550.000 0.0388713
\(586\) 35175.0 2.47963
\(587\) −3984.00 −0.280132 −0.140066 0.990142i \(-0.544731\pi\)
−0.140066 + 0.990142i \(0.544731\pi\)
\(588\) −1530.00 −0.107306
\(589\) 0 0
\(590\) −5625.00 −0.392504
\(591\) 1680.00 0.116931
\(592\) −18690.0 −1.29756
\(593\) −7458.00 −0.516464 −0.258232 0.966083i \(-0.583140\pi\)
−0.258232 + 0.966083i \(0.583140\pi\)
\(594\) 36250.0 2.50397
\(595\) −4845.00 −0.333825
\(596\) 29512.0 2.02829
\(597\) 4375.00 0.299928
\(598\) 40425.0 2.76438
\(599\) −22000.0 −1.50066 −0.750330 0.661063i \(-0.770106\pi\)
−0.750330 + 0.661063i \(0.770106\pi\)
\(600\) −5625.00 −0.382733
\(601\) 25270.0 1.71512 0.857558 0.514387i \(-0.171981\pi\)
0.857558 + 0.514387i \(0.171981\pi\)
\(602\) 53010.0 3.58891
\(603\) 210.000 0.0141822
\(604\) 13430.0 0.904733
\(605\) 5845.00 0.392782
\(606\) −3750.00 −0.251375
\(607\) −780.000 −0.0521569 −0.0260784 0.999660i \(-0.508302\pi\)
−0.0260784 + 0.999660i \(0.508302\pi\)
\(608\) 0 0
\(609\) 15675.0 1.04299
\(610\) 12500.0 0.829689
\(611\) 25520.0 1.68974
\(612\) −1734.00 −0.114531
\(613\) −7162.00 −0.471893 −0.235947 0.971766i \(-0.575819\pi\)
−0.235947 + 0.971766i \(0.575819\pi\)
\(614\) 22300.0 1.46572
\(615\) −2000.00 −0.131135
\(616\) −42750.0 −2.79618
\(617\) −14174.0 −0.924836 −0.462418 0.886662i \(-0.653018\pi\)
−0.462418 + 0.886662i \(0.653018\pi\)
\(618\) −31250.0 −2.03408
\(619\) 10844.0 0.704131 0.352066 0.935975i \(-0.385479\pi\)
0.352066 + 0.935975i \(0.385479\pi\)
\(620\) 5950.00 0.385416
\(621\) −21315.0 −1.37736
\(622\) 34125.0 2.19982
\(623\) 16530.0 1.06302
\(624\) 24475.0 1.57017
\(625\) 625.000 0.0400000
\(626\) 22685.0 1.44836
\(627\) 0 0
\(628\) −33048.0 −2.09993
\(629\) −10710.0 −0.678912
\(630\) 950.000 0.0600776
\(631\) −26200.0 −1.65294 −0.826470 0.562980i \(-0.809655\pi\)
−0.826470 + 0.562980i \(0.809655\pi\)
\(632\) −31500.0 −1.98260
\(633\) −19675.0 −1.23540
\(634\) −39225.0 −2.45714
\(635\) −500.000 −0.0312471
\(636\) 38675.0 2.41126
\(637\) −990.000 −0.0615781
\(638\) 41250.0 2.55972
\(639\) −2280.00 −0.141151
\(640\) −10575.0 −0.653146
\(641\) −11970.0 −0.737577 −0.368788 0.929513i \(-0.620227\pi\)
−0.368788 + 0.929513i \(0.620227\pi\)
\(642\) −30125.0 −1.85193
\(643\) −6792.00 −0.416564 −0.208282 0.978069i \(-0.566787\pi\)
−0.208282 + 0.978069i \(0.566787\pi\)
\(644\) 47481.0 2.90530
\(645\) 13950.0 0.851598
\(646\) 0 0
\(647\) 11561.0 0.702488 0.351244 0.936284i \(-0.385759\pi\)
0.351244 + 0.936284i \(0.385759\pi\)
\(648\) −30195.0 −1.83051
\(649\) −11250.0 −0.680433
\(650\) −6875.00 −0.414861
\(651\) 6650.00 0.400360
\(652\) −60554.0 −3.63724
\(653\) 20198.0 1.21043 0.605213 0.796063i \(-0.293088\pi\)
0.605213 + 0.796063i \(0.293088\pi\)
\(654\) 31125.0 1.86098
\(655\) 5790.00 0.345395
\(656\) 7120.00 0.423764
\(657\) 1406.00 0.0834905
\(658\) 44080.0 2.61158
\(659\) 8445.00 0.499197 0.249598 0.968349i \(-0.419701\pi\)
0.249598 + 0.968349i \(0.419701\pi\)
\(660\) −21250.0 −1.25327
\(661\) 3095.00 0.182120 0.0910602 0.995845i \(-0.470974\pi\)
0.0910602 + 0.995845i \(0.470974\pi\)
\(662\) −35375.0 −2.07687
\(663\) 14025.0 0.821547
\(664\) −41310.0 −2.41437
\(665\) 0 0
\(666\) 2100.00 0.122182
\(667\) −24255.0 −1.40803
\(668\) −57120.0 −3.30844
\(669\) −28450.0 −1.64416
\(670\) −2625.00 −0.151362
\(671\) 25000.0 1.43832
\(672\) 8075.00 0.463541
\(673\) 7880.00 0.451340 0.225670 0.974204i \(-0.427543\pi\)
0.225670 + 0.974204i \(0.427543\pi\)
\(674\) 58550.0 3.34609
\(675\) 3625.00 0.206706
\(676\) 14076.0 0.800865
\(677\) 3975.00 0.225660 0.112830 0.993614i \(-0.464008\pi\)
0.112830 + 0.993614i \(0.464008\pi\)
\(678\) −12000.0 −0.679730
\(679\) 26220.0 1.48193
\(680\) 11475.0 0.647127
\(681\) −13575.0 −0.763870
\(682\) 17500.0 0.982565
\(683\) −19140.0 −1.07229 −0.536143 0.844127i \(-0.680119\pi\)
−0.536143 + 0.844127i \(0.680119\pi\)
\(684\) 0 0
\(685\) 8795.00 0.490569
\(686\) 30875.0 1.71839
\(687\) 3580.00 0.198814
\(688\) −49662.0 −2.75196
\(689\) 25025.0 1.38371
\(690\) 18375.0 1.01380
\(691\) −17200.0 −0.946916 −0.473458 0.880816i \(-0.656994\pi\)
−0.473458 + 0.880816i \(0.656994\pi\)
\(692\) 65790.0 3.61410
\(693\) 1900.00 0.104149
\(694\) −1680.00 −0.0918904
\(695\) −11130.0 −0.607460
\(696\) −37125.0 −2.02187
\(697\) 4080.00 0.221723
\(698\) −3500.00 −0.189795
\(699\) −15910.0 −0.860903
\(700\) −8075.00 −0.436009
\(701\) 10400.0 0.560346 0.280173 0.959950i \(-0.409608\pi\)
0.280173 + 0.959950i \(0.409608\pi\)
\(702\) −39875.0 −2.14385
\(703\) 0 0
\(704\) −14350.0 −0.768233
\(705\) 11600.0 0.619690
\(706\) −44615.0 −2.37834
\(707\) −2850.00 −0.151606
\(708\) 19125.0 1.01520
\(709\) 10800.0 0.572077 0.286038 0.958218i \(-0.407661\pi\)
0.286038 + 0.958218i \(0.407661\pi\)
\(710\) 28500.0 1.50646
\(711\) 1400.00 0.0738454
\(712\) −39150.0 −2.06069
\(713\) −10290.0 −0.540482
\(714\) 24225.0 1.26974
\(715\) −13750.0 −0.719190
\(716\) −56780.0 −2.96364
\(717\) 21375.0 1.11334
\(718\) −37605.0 −1.95460
\(719\) 16569.0 0.859415 0.429708 0.902968i \(-0.358617\pi\)
0.429708 + 0.902968i \(0.358617\pi\)
\(720\) −890.000 −0.0460671
\(721\) −23750.0 −1.22676
\(722\) 0 0
\(723\) −1400.00 −0.0720146
\(724\) −30430.0 −1.56205
\(725\) 4125.00 0.211308
\(726\) −29225.0 −1.49400
\(727\) −371.000 −0.0189266 −0.00946329 0.999955i \(-0.503012\pi\)
−0.00946329 + 0.999955i \(0.503012\pi\)
\(728\) 47025.0 2.39404
\(729\) 20917.0 1.06269
\(730\) −17575.0 −0.891068
\(731\) −28458.0 −1.43989
\(732\) −42500.0 −2.14596
\(733\) −35318.0 −1.77967 −0.889836 0.456280i \(-0.849182\pi\)
−0.889836 + 0.456280i \(0.849182\pi\)
\(734\) 23120.0 1.16264
\(735\) −450.000 −0.0225830
\(736\) −12495.0 −0.625777
\(737\) −5250.00 −0.262397
\(738\) −800.000 −0.0399030
\(739\) −8600.00 −0.428087 −0.214043 0.976824i \(-0.568663\pi\)
−0.214043 + 0.976824i \(0.568663\pi\)
\(740\) −17850.0 −0.886728
\(741\) 0 0
\(742\) 43225.0 2.13860
\(743\) 29730.0 1.46795 0.733976 0.679176i \(-0.237663\pi\)
0.733976 + 0.679176i \(0.237663\pi\)
\(744\) −15750.0 −0.776106
\(745\) 8680.00 0.426860
\(746\) 45075.0 2.21222
\(747\) 1836.00 0.0899273
\(748\) 43350.0 2.11903
\(749\) −22895.0 −1.11691
\(750\) −3125.00 −0.152145
\(751\) −10680.0 −0.518933 −0.259467 0.965752i \(-0.583547\pi\)
−0.259467 + 0.965752i \(0.583547\pi\)
\(752\) −41296.0 −2.00254
\(753\) −5760.00 −0.278760
\(754\) −45375.0 −2.19159
\(755\) 3950.00 0.190404
\(756\) −46835.0 −2.25314
\(757\) 35444.0 1.70176 0.850881 0.525358i \(-0.176069\pi\)
0.850881 + 0.525358i \(0.176069\pi\)
\(758\) 19475.0 0.933198
\(759\) 36750.0 1.75750
\(760\) 0 0
\(761\) −14525.0 −0.691893 −0.345947 0.938254i \(-0.612442\pi\)
−0.345947 + 0.938254i \(0.612442\pi\)
\(762\) 2500.00 0.118852
\(763\) 23655.0 1.12237
\(764\) −27999.0 −1.32587
\(765\) −510.000 −0.0241034
\(766\) −48450.0 −2.28534
\(767\) 12375.0 0.582575
\(768\) 41395.0 1.94494
\(769\) 22169.0 1.03958 0.519788 0.854295i \(-0.326011\pi\)
0.519788 + 0.854295i \(0.326011\pi\)
\(770\) −23750.0 −1.11155
\(771\) 4350.00 0.203193
\(772\) 17510.0 0.816320
\(773\) 26435.0 1.23001 0.615007 0.788522i \(-0.289153\pi\)
0.615007 + 0.788522i \(0.289153\pi\)
\(774\) 5580.00 0.259133
\(775\) 1750.00 0.0811121
\(776\) −62100.0 −2.87276
\(777\) −19950.0 −0.921110
\(778\) −28250.0 −1.30181
\(779\) 0 0
\(780\) 23375.0 1.07302
\(781\) 57000.0 2.61155
\(782\) −37485.0 −1.71414
\(783\) 23925.0 1.09197
\(784\) 1602.00 0.0729774
\(785\) −9720.00 −0.441938
\(786\) −28950.0 −1.31376
\(787\) 37175.0 1.68379 0.841897 0.539638i \(-0.181439\pi\)
0.841897 + 0.539638i \(0.181439\pi\)
\(788\) −5712.00 −0.258225
\(789\) 28440.0 1.28326
\(790\) −17500.0 −0.788129
\(791\) −9120.00 −0.409949
\(792\) −4500.00 −0.201895
\(793\) −27500.0 −1.23147
\(794\) 16930.0 0.756704
\(795\) 11375.0 0.507459
\(796\) −14875.0 −0.662350
\(797\) 16205.0 0.720214 0.360107 0.932911i \(-0.382740\pi\)
0.360107 + 0.932911i \(0.382740\pi\)
\(798\) 0 0
\(799\) −23664.0 −1.04777
\(800\) 2125.00 0.0939126
\(801\) 1740.00 0.0767539
\(802\) 59200.0 2.60651
\(803\) −35150.0 −1.54473
\(804\) 8925.00 0.391493
\(805\) 13965.0 0.611431
\(806\) −19250.0 −0.841256
\(807\) −5050.00 −0.220283
\(808\) 6750.00 0.293891
\(809\) −13675.0 −0.594298 −0.297149 0.954831i \(-0.596036\pi\)
−0.297149 + 0.954831i \(0.596036\pi\)
\(810\) −16775.0 −0.727671
\(811\) −9275.00 −0.401590 −0.200795 0.979633i \(-0.564352\pi\)
−0.200795 + 0.979633i \(0.564352\pi\)
\(812\) −53295.0 −2.30331
\(813\) −125.000 −0.00539230
\(814\) −52500.0 −2.26059
\(815\) −17810.0 −0.765469
\(816\) −22695.0 −0.973632
\(817\) 0 0
\(818\) 33850.0 1.44687
\(819\) −2090.00 −0.0891703
\(820\) 6800.00 0.289593
\(821\) 9938.00 0.422459 0.211229 0.977437i \(-0.432253\pi\)
0.211229 + 0.977437i \(0.432253\pi\)
\(822\) −43975.0 −1.86594
\(823\) 8203.00 0.347435 0.173717 0.984796i \(-0.444422\pi\)
0.173717 + 0.984796i \(0.444422\pi\)
\(824\) 56250.0 2.37811
\(825\) −6250.00 −0.263754
\(826\) 21375.0 0.900401
\(827\) −31905.0 −1.34153 −0.670765 0.741670i \(-0.734034\pi\)
−0.670765 + 0.741670i \(0.734034\pi\)
\(828\) 4998.00 0.209774
\(829\) −7325.00 −0.306885 −0.153443 0.988158i \(-0.549036\pi\)
−0.153443 + 0.988158i \(0.549036\pi\)
\(830\) −22950.0 −0.959766
\(831\) −18230.0 −0.761001
\(832\) 15785.0 0.657748
\(833\) 918.000 0.0381835
\(834\) 55650.0 2.31055
\(835\) −16800.0 −0.696273
\(836\) 0 0
\(837\) 10150.0 0.419158
\(838\) 22750.0 0.937811
\(839\) −26370.0 −1.08509 −0.542547 0.840026i \(-0.682540\pi\)
−0.542547 + 0.840026i \(0.682540\pi\)
\(840\) 21375.0 0.877985
\(841\) 2836.00 0.116282
\(842\) 15425.0 0.631331
\(843\) 30000.0 1.22569
\(844\) 66895.0 2.72822
\(845\) 4140.00 0.168545
\(846\) 4640.00 0.188566
\(847\) −22211.0 −0.901038
\(848\) −40495.0 −1.63986
\(849\) −25090.0 −1.01424
\(850\) 6375.00 0.257248
\(851\) 30870.0 1.24349
\(852\) −96900.0 −3.89641
\(853\) −8898.00 −0.357165 −0.178582 0.983925i \(-0.557151\pi\)
−0.178582 + 0.983925i \(0.557151\pi\)
\(854\) −47500.0 −1.90330
\(855\) 0 0
\(856\) 54225.0 2.16515
\(857\) 33200.0 1.32333 0.661663 0.749801i \(-0.269851\pi\)
0.661663 + 0.749801i \(0.269851\pi\)
\(858\) 68750.0 2.73553
\(859\) 15450.0 0.613675 0.306838 0.951762i \(-0.400729\pi\)
0.306838 + 0.951762i \(0.400729\pi\)
\(860\) −47430.0 −1.88064
\(861\) 7600.00 0.300821
\(862\) −23900.0 −0.944359
\(863\) −18140.0 −0.715519 −0.357759 0.933814i \(-0.616459\pi\)
−0.357759 + 0.933814i \(0.616459\pi\)
\(864\) 12325.0 0.485307
\(865\) 19350.0 0.760601
\(866\) 42850.0 1.68141
\(867\) 11560.0 0.452824
\(868\) −22610.0 −0.884140
\(869\) −35000.0 −1.36628
\(870\) −20625.0 −0.803739
\(871\) 5775.00 0.224659
\(872\) −56025.0 −2.17574
\(873\) 2760.00 0.107001
\(874\) 0 0
\(875\) −2375.00 −0.0917596
\(876\) 59755.0 2.30472
\(877\) 22655.0 0.872298 0.436149 0.899875i \(-0.356342\pi\)
0.436149 + 0.899875i \(0.356342\pi\)
\(878\) 36100.0 1.38760
\(879\) −35175.0 −1.34974
\(880\) 22250.0 0.852327
\(881\) −43350.0 −1.65777 −0.828887 0.559416i \(-0.811025\pi\)
−0.828887 + 0.559416i \(0.811025\pi\)
\(882\) −180.000 −0.00687179
\(883\) 24568.0 0.936330 0.468165 0.883641i \(-0.344915\pi\)
0.468165 + 0.883641i \(0.344915\pi\)
\(884\) −47685.0 −1.81428
\(885\) 5625.00 0.213652
\(886\) −51290.0 −1.94483
\(887\) −32060.0 −1.21361 −0.606804 0.794852i \(-0.707549\pi\)
−0.606804 + 0.794852i \(0.707549\pi\)
\(888\) 47250.0 1.78559
\(889\) 1900.00 0.0716805
\(890\) −21750.0 −0.819170
\(891\) −33550.0 −1.26147
\(892\) 96730.0 3.63090
\(893\) 0 0
\(894\) −43400.0 −1.62362
\(895\) −16700.0 −0.623709
\(896\) 40185.0 1.49831
\(897\) −40425.0 −1.50474
\(898\) −37650.0 −1.39911
\(899\) 11550.0 0.428492
\(900\) −850.000 −0.0314815
\(901\) −23205.0 −0.858014
\(902\) 20000.0 0.738278
\(903\) −53010.0 −1.95356
\(904\) 21600.0 0.794696
\(905\) −8950.00 −0.328738
\(906\) −19750.0 −0.724227
\(907\) −13295.0 −0.486718 −0.243359 0.969936i \(-0.578249\pi\)
−0.243359 + 0.969936i \(0.578249\pi\)
\(908\) 46155.0 1.68690
\(909\) −300.000 −0.0109465
\(910\) 26125.0 0.951687
\(911\) −190.000 −0.00690997 −0.00345498 0.999994i \(-0.501100\pi\)
−0.00345498 + 0.999994i \(0.501100\pi\)
\(912\) 0 0
\(913\) −45900.0 −1.66382
\(914\) −44095.0 −1.59577
\(915\) −12500.0 −0.451625
\(916\) −12172.0 −0.439055
\(917\) −22002.0 −0.792334
\(918\) 36975.0 1.32936
\(919\) −2725.00 −0.0978122 −0.0489061 0.998803i \(-0.515574\pi\)
−0.0489061 + 0.998803i \(0.515574\pi\)
\(920\) −33075.0 −1.18527
\(921\) −22300.0 −0.797839
\(922\) 51160.0 1.82740
\(923\) −62700.0 −2.23596
\(924\) 80750.0 2.87498
\(925\) −5250.00 −0.186615
\(926\) −60560.0 −2.14916
\(927\) −2500.00 −0.0885769
\(928\) 14025.0 0.496113
\(929\) 16825.0 0.594198 0.297099 0.954847i \(-0.403981\pi\)
0.297099 + 0.954847i \(0.403981\pi\)
\(930\) −8750.00 −0.308520
\(931\) 0 0
\(932\) 54094.0 1.90119
\(933\) −34125.0 −1.19743
\(934\) −25380.0 −0.889142
\(935\) 12750.0 0.445957
\(936\) 4950.00 0.172859
\(937\) −19259.0 −0.671466 −0.335733 0.941957i \(-0.608984\pi\)
−0.335733 + 0.941957i \(0.608984\pi\)
\(938\) 9975.00 0.347223
\(939\) −22685.0 −0.788389
\(940\) −39440.0 −1.36850
\(941\) −11435.0 −0.396143 −0.198071 0.980188i \(-0.563468\pi\)
−0.198071 + 0.980188i \(0.563468\pi\)
\(942\) 48600.0 1.68097
\(943\) −11760.0 −0.406106
\(944\) −20025.0 −0.690422
\(945\) −13775.0 −0.474181
\(946\) −139500. −4.79444
\(947\) −20014.0 −0.686766 −0.343383 0.939195i \(-0.611573\pi\)
−0.343383 + 0.939195i \(0.611573\pi\)
\(948\) 59500.0 2.03847
\(949\) 38665.0 1.32257
\(950\) 0 0
\(951\) 39225.0 1.33750
\(952\) −43605.0 −1.48450
\(953\) −26970.0 −0.916730 −0.458365 0.888764i \(-0.651565\pi\)
−0.458365 + 0.888764i \(0.651565\pi\)
\(954\) 4550.00 0.154415
\(955\) −8235.00 −0.279035
\(956\) −72675.0 −2.45866
\(957\) −41250.0 −1.39334
\(958\) 76920.0 2.59413
\(959\) −33421.0 −1.12536
\(960\) 7175.00 0.241221
\(961\) −24891.0 −0.835521
\(962\) 57750.0 1.93548
\(963\) −2410.00 −0.0806450
\(964\) 4760.00 0.159035
\(965\) 5150.00 0.171797
\(966\) −69825.0 −2.32565
\(967\) 7024.00 0.233585 0.116792 0.993156i \(-0.462739\pi\)
0.116792 + 0.993156i \(0.462739\pi\)
\(968\) 52605.0 1.74668
\(969\) 0 0
\(970\) −34500.0 −1.14199
\(971\) 12960.0 0.428328 0.214164 0.976798i \(-0.431297\pi\)
0.214164 + 0.976798i \(0.431297\pi\)
\(972\) −9520.00 −0.314150
\(973\) 42294.0 1.39351
\(974\) 41750.0 1.37347
\(975\) 6875.00 0.225822
\(976\) 44500.0 1.45944
\(977\) 5550.00 0.181740 0.0908701 0.995863i \(-0.471035\pi\)
0.0908701 + 0.995863i \(0.471035\pi\)
\(978\) 89050.0 2.91156
\(979\) −43500.0 −1.42009
\(980\) 1530.00 0.0498715
\(981\) 2490.00 0.0810393
\(982\) −43860.0 −1.42528
\(983\) 14480.0 0.469827 0.234914 0.972016i \(-0.424519\pi\)
0.234914 + 0.972016i \(0.424519\pi\)
\(984\) −18000.0 −0.583149
\(985\) −1680.00 −0.0543444
\(986\) 42075.0 1.35897
\(987\) −44080.0 −1.42156
\(988\) 0 0
\(989\) 82026.0 2.63729
\(990\) −2500.00 −0.0802578
\(991\) −21670.0 −0.694622 −0.347311 0.937750i \(-0.612905\pi\)
−0.347311 + 0.937750i \(0.612905\pi\)
\(992\) 5950.00 0.190436
\(993\) 35375.0 1.13051
\(994\) −108300. −3.45580
\(995\) −4375.00 −0.139394
\(996\) 78030.0 2.48240
\(997\) −40686.0 −1.29242 −0.646208 0.763161i \(-0.723646\pi\)
−0.646208 + 0.763161i \(0.723646\pi\)
\(998\) −13930.0 −0.441830
\(999\) −30450.0 −0.964360
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 1805.4.a.i.1.1 yes 1
19.18 odd 2 1805.4.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1805.4.a.b.1.1 1 19.18 odd 2
1805.4.a.i.1.1 yes 1 1.1 even 1 trivial