Properties

Label 1075.2.a.p.1.2
Level $1075$
Weight $2$
Character 1075.1
Self dual yes
Analytic conductor $8.584$
Analytic rank $1$
Dimension $6$
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] = [1075,2,Mod(1,1075)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1075, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1075.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1075.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: \(8.58391821729\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.32503921.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} - 5x^{4} + 13x^{3} + 9x^{2} - 11x - 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 215)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.840555\) of defining polynomial
Character \(\chi\) \(=\) 1075.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.84056 q^{2} -0.291442 q^{3} +1.38764 q^{4} +0.536415 q^{6} -5.13977 q^{7} +1.12707 q^{8} -2.91506 q^{9} +O(q^{10})\) \(q-1.84056 q^{2} -0.291442 q^{3} +1.38764 q^{4} +0.536415 q^{6} -5.13977 q^{7} +1.12707 q^{8} -2.91506 q^{9} +5.03950 q^{11} -0.404418 q^{12} +1.68111 q^{13} +9.46004 q^{14} -4.84973 q^{16} +7.47071 q^{17} +5.36533 q^{18} -0.608281 q^{19} +1.49795 q^{21} -9.27547 q^{22} +1.48871 q^{23} -0.328477 q^{24} -3.09418 q^{26} +1.72390 q^{27} -7.13218 q^{28} -5.51410 q^{29} +1.88966 q^{31} +6.67205 q^{32} -1.46872 q^{33} -13.7503 q^{34} -4.04507 q^{36} -5.08289 q^{37} +1.11957 q^{38} -0.489946 q^{39} -6.85633 q^{41} -2.75705 q^{42} -1.00000 q^{43} +6.99303 q^{44} -2.74005 q^{46} -8.54354 q^{47} +1.41342 q^{48} +19.4173 q^{49} -2.17728 q^{51} +2.33278 q^{52} -9.18537 q^{53} -3.17293 q^{54} -5.79291 q^{56} +0.177279 q^{57} +10.1490 q^{58} +7.44326 q^{59} -8.51814 q^{61} -3.47803 q^{62} +14.9828 q^{63} -2.58081 q^{64} +2.70326 q^{66} +4.71055 q^{67} +10.3667 q^{68} -0.433871 q^{69} +3.25011 q^{71} -3.28549 q^{72} -6.48385 q^{73} +9.35534 q^{74} -0.844077 q^{76} -25.9019 q^{77} +0.901773 q^{78} -3.22785 q^{79} +8.24277 q^{81} +12.6195 q^{82} +6.51534 q^{83} +2.07862 q^{84} +1.84056 q^{86} +1.60704 q^{87} +5.67989 q^{88} -11.5677 q^{89} -8.64053 q^{91} +2.06579 q^{92} -0.550728 q^{93} +15.7249 q^{94} -1.94452 q^{96} -1.06878 q^{97} -35.7386 q^{98} -14.6904 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} - 4 q^{3} + 7 q^{4} - 8 q^{7} - 9 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} - 4 q^{3} + 7 q^{4} - 8 q^{7} - 9 q^{8} + 8 q^{9} - 5 q^{12} - 6 q^{13} - 4 q^{14} + 5 q^{16} - 6 q^{17} + 11 q^{18} + 6 q^{19} - 12 q^{21} + q^{22} - 32 q^{26} - 10 q^{27} + 10 q^{28} - 10 q^{29} - 11 q^{32} - 6 q^{33} + 14 q^{34} - 41 q^{36} - 28 q^{37} + 6 q^{38} + 8 q^{39} - 6 q^{41} - 5 q^{42} - 6 q^{43} + 4 q^{44} - 8 q^{46} + 6 q^{47} + 32 q^{48} + 20 q^{49} - 8 q^{51} + 16 q^{52} + 4 q^{53} - 5 q^{54} - 35 q^{56} - 4 q^{57} + 26 q^{58} - 20 q^{59} - 8 q^{61} - 2 q^{62} + 2 q^{63} + 17 q^{64} - 35 q^{66} - 22 q^{67} - 22 q^{68} - 42 q^{69} + 8 q^{71} + 2 q^{72} - 34 q^{73} + 45 q^{74} - 16 q^{76} - 8 q^{77} + 26 q^{78} - 16 q^{79} + 46 q^{81} - 22 q^{82} + 14 q^{83} + 37 q^{84} + 3 q^{86} + 2 q^{87} - 20 q^{88} + 24 q^{91} - 46 q^{92} - 30 q^{93} + 12 q^{94} - 23 q^{96} - 34 q^{97} - 32 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.84056 −1.30147 −0.650735 0.759305i \(-0.725539\pi\)
−0.650735 + 0.759305i \(0.725539\pi\)
\(3\) −0.291442 −0.168264 −0.0841320 0.996455i \(-0.526812\pi\)
−0.0841320 + 0.996455i \(0.526812\pi\)
\(4\) 1.38764 0.693822
\(5\) 0 0
\(6\) 0.536415 0.218991
\(7\) −5.13977 −1.94265 −0.971326 0.237752i \(-0.923589\pi\)
−0.971326 + 0.237752i \(0.923589\pi\)
\(8\) 1.12707 0.398481
\(9\) −2.91506 −0.971687
\(10\) 0 0
\(11\) 5.03950 1.51947 0.759733 0.650236i \(-0.225330\pi\)
0.759733 + 0.650236i \(0.225330\pi\)
\(12\) −0.404418 −0.116745
\(13\) 1.68111 0.466256 0.233128 0.972446i \(-0.425104\pi\)
0.233128 + 0.972446i \(0.425104\pi\)
\(14\) 9.46004 2.52830
\(15\) 0 0
\(16\) −4.84973 −1.21243
\(17\) 7.47071 1.81191 0.905957 0.423370i \(-0.139153\pi\)
0.905957 + 0.423370i \(0.139153\pi\)
\(18\) 5.36533 1.26462
\(19\) −0.608281 −0.139549 −0.0697746 0.997563i \(-0.522228\pi\)
−0.0697746 + 0.997563i \(0.522228\pi\)
\(20\) 0 0
\(21\) 1.49795 0.326878
\(22\) −9.27547 −1.97754
\(23\) 1.48871 0.310417 0.155208 0.987882i \(-0.450395\pi\)
0.155208 + 0.987882i \(0.450395\pi\)
\(24\) −0.328477 −0.0670501
\(25\) 0 0
\(26\) −3.09418 −0.606818
\(27\) 1.72390 0.331764
\(28\) −7.13218 −1.34785
\(29\) −5.51410 −1.02394 −0.511972 0.859002i \(-0.671085\pi\)
−0.511972 + 0.859002i \(0.671085\pi\)
\(30\) 0 0
\(31\) 1.88966 0.339394 0.169697 0.985496i \(-0.445721\pi\)
0.169697 + 0.985496i \(0.445721\pi\)
\(32\) 6.67205 1.17946
\(33\) −1.46872 −0.255671
\(34\) −13.7503 −2.35815
\(35\) 0 0
\(36\) −4.04507 −0.674178
\(37\) −5.08289 −0.835622 −0.417811 0.908534i \(-0.637203\pi\)
−0.417811 + 0.908534i \(0.637203\pi\)
\(38\) 1.11957 0.181619
\(39\) −0.489946 −0.0784542
\(40\) 0 0
\(41\) −6.85633 −1.07078 −0.535389 0.844605i \(-0.679835\pi\)
−0.535389 + 0.844605i \(0.679835\pi\)
\(42\) −2.75705 −0.425422
\(43\) −1.00000 −0.152499
\(44\) 6.99303 1.05424
\(45\) 0 0
\(46\) −2.74005 −0.403998
\(47\) −8.54354 −1.24620 −0.623102 0.782141i \(-0.714128\pi\)
−0.623102 + 0.782141i \(0.714128\pi\)
\(48\) 1.41342 0.204009
\(49\) 19.4173 2.77390
\(50\) 0 0
\(51\) −2.17728 −0.304880
\(52\) 2.33278 0.323499
\(53\) −9.18537 −1.26171 −0.630854 0.775902i \(-0.717295\pi\)
−0.630854 + 0.775902i \(0.717295\pi\)
\(54\) −3.17293 −0.431781
\(55\) 0 0
\(56\) −5.79291 −0.774110
\(57\) 0.177279 0.0234811
\(58\) 10.1490 1.33263
\(59\) 7.44326 0.969030 0.484515 0.874783i \(-0.338996\pi\)
0.484515 + 0.874783i \(0.338996\pi\)
\(60\) 0 0
\(61\) −8.51814 −1.09064 −0.545318 0.838229i \(-0.683591\pi\)
−0.545318 + 0.838229i \(0.683591\pi\)
\(62\) −3.47803 −0.441711
\(63\) 14.9828 1.88765
\(64\) −2.58081 −0.322602
\(65\) 0 0
\(66\) 2.70326 0.332748
\(67\) 4.71055 0.575485 0.287743 0.957708i \(-0.407095\pi\)
0.287743 + 0.957708i \(0.407095\pi\)
\(68\) 10.3667 1.25715
\(69\) −0.433871 −0.0522320
\(70\) 0 0
\(71\) 3.25011 0.385717 0.192858 0.981227i \(-0.438224\pi\)
0.192858 + 0.981227i \(0.438224\pi\)
\(72\) −3.28549 −0.387199
\(73\) −6.48385 −0.758877 −0.379438 0.925217i \(-0.623883\pi\)
−0.379438 + 0.925217i \(0.623883\pi\)
\(74\) 9.35534 1.08754
\(75\) 0 0
\(76\) −0.844077 −0.0968223
\(77\) −25.9019 −2.95179
\(78\) 0.901773 0.102106
\(79\) −3.22785 −0.363162 −0.181581 0.983376i \(-0.558121\pi\)
−0.181581 + 0.983376i \(0.558121\pi\)
\(80\) 0 0
\(81\) 8.24277 0.915863
\(82\) 12.6195 1.39359
\(83\) 6.51534 0.715152 0.357576 0.933884i \(-0.383603\pi\)
0.357576 + 0.933884i \(0.383603\pi\)
\(84\) 2.07862 0.226796
\(85\) 0 0
\(86\) 1.84056 0.198472
\(87\) 1.60704 0.172293
\(88\) 5.67989 0.605478
\(89\) −11.5677 −1.22617 −0.613087 0.790016i \(-0.710072\pi\)
−0.613087 + 0.790016i \(0.710072\pi\)
\(90\) 0 0
\(91\) −8.64053 −0.905773
\(92\) 2.06579 0.215374
\(93\) −0.550728 −0.0571078
\(94\) 15.7249 1.62190
\(95\) 0 0
\(96\) −1.94452 −0.198461
\(97\) −1.06878 −0.108518 −0.0542591 0.998527i \(-0.517280\pi\)
−0.0542591 + 0.998527i \(0.517280\pi\)
\(98\) −35.7386 −3.61014
\(99\) −14.6904 −1.47644
\(100\) 0 0
\(101\) −15.7267 −1.56487 −0.782433 0.622735i \(-0.786022\pi\)
−0.782433 + 0.622735i \(0.786022\pi\)
\(102\) 4.00740 0.396792
\(103\) −16.4707 −1.62290 −0.811451 0.584421i \(-0.801322\pi\)
−0.811451 + 0.584421i \(0.801322\pi\)
\(104\) 1.89474 0.185794
\(105\) 0 0
\(106\) 16.9062 1.64207
\(107\) −2.13751 −0.206641 −0.103320 0.994648i \(-0.532947\pi\)
−0.103320 + 0.994648i \(0.532947\pi\)
\(108\) 2.39216 0.230185
\(109\) −1.91506 −0.183430 −0.0917148 0.995785i \(-0.529235\pi\)
−0.0917148 + 0.995785i \(0.529235\pi\)
\(110\) 0 0
\(111\) 1.48137 0.140605
\(112\) 24.9265 2.35534
\(113\) −10.3309 −0.971853 −0.485926 0.874000i \(-0.661518\pi\)
−0.485926 + 0.874000i \(0.661518\pi\)
\(114\) −0.326291 −0.0305599
\(115\) 0 0
\(116\) −7.65161 −0.710434
\(117\) −4.90054 −0.453055
\(118\) −13.6997 −1.26116
\(119\) −38.3978 −3.51992
\(120\) 0 0
\(121\) 14.3965 1.30877
\(122\) 15.6781 1.41943
\(123\) 1.99822 0.180174
\(124\) 2.62218 0.235479
\(125\) 0 0
\(126\) −27.5766 −2.45672
\(127\) −12.1166 −1.07517 −0.537587 0.843208i \(-0.680664\pi\)
−0.537587 + 0.843208i \(0.680664\pi\)
\(128\) −8.59397 −0.759607
\(129\) 0.291442 0.0256600
\(130\) 0 0
\(131\) −0.00984495 −0.000860157 0 −0.000430079 1.00000i \(-0.500137\pi\)
−0.000430079 1.00000i \(0.500137\pi\)
\(132\) −2.03806 −0.177390
\(133\) 3.12643 0.271095
\(134\) −8.67003 −0.748976
\(135\) 0 0
\(136\) 8.42005 0.722013
\(137\) −7.64961 −0.653551 −0.326775 0.945102i \(-0.605962\pi\)
−0.326775 + 0.945102i \(0.605962\pi\)
\(138\) 0.798564 0.0679783
\(139\) 10.8055 0.916509 0.458255 0.888821i \(-0.348475\pi\)
0.458255 + 0.888821i \(0.348475\pi\)
\(140\) 0 0
\(141\) 2.48995 0.209691
\(142\) −5.98200 −0.501999
\(143\) 8.47195 0.708460
\(144\) 14.1373 1.17811
\(145\) 0 0
\(146\) 11.9339 0.987655
\(147\) −5.65901 −0.466747
\(148\) −7.05324 −0.579773
\(149\) −3.39172 −0.277860 −0.138930 0.990302i \(-0.544366\pi\)
−0.138930 + 0.990302i \(0.544366\pi\)
\(150\) 0 0
\(151\) 0.387678 0.0315488 0.0157744 0.999876i \(-0.494979\pi\)
0.0157744 + 0.999876i \(0.494979\pi\)
\(152\) −0.685578 −0.0556077
\(153\) −21.7776 −1.76061
\(154\) 47.6738 3.84167
\(155\) 0 0
\(156\) −0.679871 −0.0544332
\(157\) 20.2046 1.61250 0.806252 0.591573i \(-0.201493\pi\)
0.806252 + 0.591573i \(0.201493\pi\)
\(158\) 5.94104 0.472644
\(159\) 2.67700 0.212300
\(160\) 0 0
\(161\) −7.65161 −0.603032
\(162\) −15.1713 −1.19197
\(163\) −10.9097 −0.854510 −0.427255 0.904131i \(-0.640519\pi\)
−0.427255 + 0.904131i \(0.640519\pi\)
\(164\) −9.51415 −0.742930
\(165\) 0 0
\(166\) −11.9918 −0.930748
\(167\) −1.54073 −0.119225 −0.0596127 0.998222i \(-0.518987\pi\)
−0.0596127 + 0.998222i \(0.518987\pi\)
\(168\) 1.68830 0.130255
\(169\) −10.1739 −0.782605
\(170\) 0 0
\(171\) 1.77318 0.135598
\(172\) −1.38764 −0.105807
\(173\) 6.99994 0.532196 0.266098 0.963946i \(-0.414266\pi\)
0.266098 + 0.963946i \(0.414266\pi\)
\(174\) −2.95785 −0.224234
\(175\) 0 0
\(176\) −24.4402 −1.84225
\(177\) −2.16928 −0.163053
\(178\) 21.2910 1.59583
\(179\) −11.8268 −0.883974 −0.441987 0.897021i \(-0.645726\pi\)
−0.441987 + 0.897021i \(0.645726\pi\)
\(180\) 0 0
\(181\) −1.74546 −0.129739 −0.0648694 0.997894i \(-0.520663\pi\)
−0.0648694 + 0.997894i \(0.520663\pi\)
\(182\) 15.9034 1.17884
\(183\) 2.48254 0.183515
\(184\) 1.67788 0.123695
\(185\) 0 0
\(186\) 1.01364 0.0743240
\(187\) 37.6486 2.75314
\(188\) −11.8554 −0.864644
\(189\) −8.86044 −0.644502
\(190\) 0 0
\(191\) 21.9963 1.59159 0.795797 0.605564i \(-0.207052\pi\)
0.795797 + 0.605564i \(0.207052\pi\)
\(192\) 0.752158 0.0542823
\(193\) −15.1264 −1.08882 −0.544412 0.838818i \(-0.683247\pi\)
−0.544412 + 0.838818i \(0.683247\pi\)
\(194\) 1.96715 0.141233
\(195\) 0 0
\(196\) 26.9443 1.92459
\(197\) 14.5354 1.03560 0.517802 0.855501i \(-0.326750\pi\)
0.517802 + 0.855501i \(0.326750\pi\)
\(198\) 27.0386 1.92155
\(199\) −7.46791 −0.529386 −0.264693 0.964333i \(-0.585271\pi\)
−0.264693 + 0.964333i \(0.585271\pi\)
\(200\) 0 0
\(201\) −1.37285 −0.0968335
\(202\) 28.9459 2.03662
\(203\) 28.3412 1.98917
\(204\) −3.02129 −0.211532
\(205\) 0 0
\(206\) 30.3151 2.11216
\(207\) −4.33967 −0.301628
\(208\) −8.15294 −0.565304
\(209\) −3.06543 −0.212040
\(210\) 0 0
\(211\) −8.81738 −0.607014 −0.303507 0.952829i \(-0.598157\pi\)
−0.303507 + 0.952829i \(0.598157\pi\)
\(212\) −12.7460 −0.875401
\(213\) −0.947218 −0.0649023
\(214\) 3.93421 0.268937
\(215\) 0 0
\(216\) 1.94296 0.132202
\(217\) −9.71245 −0.659324
\(218\) 3.52478 0.238728
\(219\) 1.88966 0.127692
\(220\) 0 0
\(221\) 12.5591 0.844816
\(222\) −2.72654 −0.182993
\(223\) 3.76333 0.252011 0.126006 0.992030i \(-0.459784\pi\)
0.126006 + 0.992030i \(0.459784\pi\)
\(224\) −34.2928 −2.29129
\(225\) 0 0
\(226\) 19.0147 1.26484
\(227\) 21.9658 1.45792 0.728960 0.684556i \(-0.240004\pi\)
0.728960 + 0.684556i \(0.240004\pi\)
\(228\) 0.245999 0.0162917
\(229\) −14.2515 −0.941765 −0.470883 0.882196i \(-0.656064\pi\)
−0.470883 + 0.882196i \(0.656064\pi\)
\(230\) 0 0
\(231\) 7.54889 0.496681
\(232\) −6.21481 −0.408022
\(233\) 16.5427 1.08375 0.541875 0.840459i \(-0.317715\pi\)
0.541875 + 0.840459i \(0.317715\pi\)
\(234\) 9.01972 0.589637
\(235\) 0 0
\(236\) 10.3286 0.672335
\(237\) 0.940731 0.0611071
\(238\) 70.6732 4.58106
\(239\) −9.08775 −0.587838 −0.293919 0.955830i \(-0.594960\pi\)
−0.293919 + 0.955830i \(0.594960\pi\)
\(240\) 0 0
\(241\) −3.24141 −0.208797 −0.104399 0.994536i \(-0.533292\pi\)
−0.104399 + 0.994536i \(0.533292\pi\)
\(242\) −26.4976 −1.70333
\(243\) −7.57398 −0.485871
\(244\) −11.8202 −0.756708
\(245\) 0 0
\(246\) −3.67784 −0.234490
\(247\) −1.02259 −0.0650657
\(248\) 2.12979 0.135242
\(249\) −1.89884 −0.120334
\(250\) 0 0
\(251\) 8.88255 0.560661 0.280331 0.959903i \(-0.409556\pi\)
0.280331 + 0.959903i \(0.409556\pi\)
\(252\) 20.7907 1.30969
\(253\) 7.50233 0.471667
\(254\) 22.3013 1.39931
\(255\) 0 0
\(256\) 20.9793 1.31121
\(257\) −20.4758 −1.27724 −0.638622 0.769520i \(-0.720495\pi\)
−0.638622 + 0.769520i \(0.720495\pi\)
\(258\) −0.536415 −0.0333957
\(259\) 26.1249 1.62332
\(260\) 0 0
\(261\) 16.0740 0.994953
\(262\) 0.0181202 0.00111947
\(263\) −14.6293 −0.902083 −0.451041 0.892503i \(-0.648947\pi\)
−0.451041 + 0.892503i \(0.648947\pi\)
\(264\) −1.65536 −0.101880
\(265\) 0 0
\(266\) −5.75436 −0.352822
\(267\) 3.37131 0.206321
\(268\) 6.53657 0.399284
\(269\) −12.5266 −0.763762 −0.381881 0.924211i \(-0.624724\pi\)
−0.381881 + 0.924211i \(0.624724\pi\)
\(270\) 0 0
\(271\) 2.66641 0.161973 0.0809863 0.996715i \(-0.474193\pi\)
0.0809863 + 0.996715i \(0.474193\pi\)
\(272\) −36.2309 −2.19682
\(273\) 2.51821 0.152409
\(274\) 14.0795 0.850576
\(275\) 0 0
\(276\) −0.602059 −0.0362397
\(277\) 4.83731 0.290646 0.145323 0.989384i \(-0.453578\pi\)
0.145323 + 0.989384i \(0.453578\pi\)
\(278\) −19.8881 −1.19281
\(279\) −5.50849 −0.329785
\(280\) 0 0
\(281\) −27.6927 −1.65201 −0.826004 0.563664i \(-0.809391\pi\)
−0.826004 + 0.563664i \(0.809391\pi\)
\(282\) −4.58288 −0.272907
\(283\) 4.82203 0.286640 0.143320 0.989676i \(-0.454222\pi\)
0.143320 + 0.989676i \(0.454222\pi\)
\(284\) 4.50999 0.267619
\(285\) 0 0
\(286\) −15.5931 −0.922039
\(287\) 35.2400 2.08015
\(288\) −19.4494 −1.14607
\(289\) 38.8115 2.28303
\(290\) 0 0
\(291\) 0.311488 0.0182597
\(292\) −8.99727 −0.526525
\(293\) 28.1922 1.64700 0.823502 0.567314i \(-0.192017\pi\)
0.823502 + 0.567314i \(0.192017\pi\)
\(294\) 10.4157 0.607457
\(295\) 0 0
\(296\) −5.72880 −0.332979
\(297\) 8.68757 0.504104
\(298\) 6.24265 0.361627
\(299\) 2.50268 0.144734
\(300\) 0 0
\(301\) 5.13977 0.296252
\(302\) −0.713543 −0.0410598
\(303\) 4.58342 0.263311
\(304\) 2.95000 0.169194
\(305\) 0 0
\(306\) 40.0828 2.29138
\(307\) −5.79727 −0.330868 −0.165434 0.986221i \(-0.552902\pi\)
−0.165434 + 0.986221i \(0.552902\pi\)
\(308\) −35.9426 −2.04802
\(309\) 4.80024 0.273076
\(310\) 0 0
\(311\) −15.0774 −0.854959 −0.427479 0.904025i \(-0.640598\pi\)
−0.427479 + 0.904025i \(0.640598\pi\)
\(312\) −0.552206 −0.0312625
\(313\) 0.780361 0.0441086 0.0220543 0.999757i \(-0.492979\pi\)
0.0220543 + 0.999757i \(0.492979\pi\)
\(314\) −37.1877 −2.09862
\(315\) 0 0
\(316\) −4.47911 −0.251970
\(317\) −21.4989 −1.20750 −0.603750 0.797174i \(-0.706327\pi\)
−0.603750 + 0.797174i \(0.706327\pi\)
\(318\) −4.92717 −0.276302
\(319\) −27.7883 −1.55585
\(320\) 0 0
\(321\) 0.622960 0.0347702
\(322\) 14.0832 0.784827
\(323\) −4.54429 −0.252851
\(324\) 11.4380 0.635446
\(325\) 0 0
\(326\) 20.0798 1.11212
\(327\) 0.558129 0.0308646
\(328\) −7.72760 −0.426685
\(329\) 43.9119 2.42094
\(330\) 0 0
\(331\) 17.6324 0.969163 0.484581 0.874746i \(-0.338972\pi\)
0.484581 + 0.874746i \(0.338972\pi\)
\(332\) 9.04098 0.496188
\(333\) 14.8169 0.811963
\(334\) 2.83580 0.155168
\(335\) 0 0
\(336\) −7.26463 −0.396318
\(337\) −26.9345 −1.46722 −0.733608 0.679573i \(-0.762165\pi\)
−0.733608 + 0.679573i \(0.762165\pi\)
\(338\) 18.7256 1.01854
\(339\) 3.01087 0.163528
\(340\) 0 0
\(341\) 9.52296 0.515697
\(342\) −3.26363 −0.176477
\(343\) −63.8219 −3.44606
\(344\) −1.12707 −0.0607678
\(345\) 0 0
\(346\) −12.8838 −0.692636
\(347\) −11.4381 −0.614028 −0.307014 0.951705i \(-0.599330\pi\)
−0.307014 + 0.951705i \(0.599330\pi\)
\(348\) 2.23000 0.119541
\(349\) 9.05483 0.484694 0.242347 0.970190i \(-0.422083\pi\)
0.242347 + 0.970190i \(0.422083\pi\)
\(350\) 0 0
\(351\) 2.89806 0.154687
\(352\) 33.6238 1.79215
\(353\) −9.57877 −0.509827 −0.254913 0.966964i \(-0.582047\pi\)
−0.254913 + 0.966964i \(0.582047\pi\)
\(354\) 3.99268 0.212208
\(355\) 0 0
\(356\) −16.0518 −0.850746
\(357\) 11.1907 0.592276
\(358\) 21.7678 1.15047
\(359\) 1.30335 0.0687879 0.0343940 0.999408i \(-0.489050\pi\)
0.0343940 + 0.999408i \(0.489050\pi\)
\(360\) 0 0
\(361\) −18.6300 −0.980526
\(362\) 3.21261 0.168851
\(363\) −4.19575 −0.220220
\(364\) −11.9900 −0.628446
\(365\) 0 0
\(366\) −4.56926 −0.238839
\(367\) 17.4149 0.909053 0.454526 0.890733i \(-0.349809\pi\)
0.454526 + 0.890733i \(0.349809\pi\)
\(368\) −7.21983 −0.376359
\(369\) 19.9866 1.04046
\(370\) 0 0
\(371\) 47.2107 2.45106
\(372\) −0.764214 −0.0396226
\(373\) −13.5500 −0.701591 −0.350796 0.936452i \(-0.614089\pi\)
−0.350796 + 0.936452i \(0.614089\pi\)
\(374\) −69.2944 −3.58313
\(375\) 0 0
\(376\) −9.62921 −0.496589
\(377\) −9.26982 −0.477420
\(378\) 16.3081 0.838800
\(379\) 8.25854 0.424213 0.212106 0.977247i \(-0.431968\pi\)
0.212106 + 0.977247i \(0.431968\pi\)
\(380\) 0 0
\(381\) 3.53128 0.180913
\(382\) −40.4853 −2.07141
\(383\) 17.7331 0.906118 0.453059 0.891481i \(-0.350333\pi\)
0.453059 + 0.891481i \(0.350333\pi\)
\(384\) 2.50464 0.127815
\(385\) 0 0
\(386\) 27.8410 1.41707
\(387\) 2.91506 0.148181
\(388\) −1.48309 −0.0752923
\(389\) −25.0836 −1.27179 −0.635894 0.771776i \(-0.719368\pi\)
−0.635894 + 0.771776i \(0.719368\pi\)
\(390\) 0 0
\(391\) 11.1217 0.562448
\(392\) 21.8847 1.10535
\(393\) 0.00286923 0.000144734 0
\(394\) −26.7532 −1.34781
\(395\) 0 0
\(396\) −20.3851 −1.02439
\(397\) 1.18706 0.0595770 0.0297885 0.999556i \(-0.490517\pi\)
0.0297885 + 0.999556i \(0.490517\pi\)
\(398\) 13.7451 0.688980
\(399\) −0.911171 −0.0456156
\(400\) 0 0
\(401\) 34.8646 1.74105 0.870527 0.492121i \(-0.163778\pi\)
0.870527 + 0.492121i \(0.163778\pi\)
\(402\) 2.52681 0.126026
\(403\) 3.17674 0.158244
\(404\) −21.8231 −1.08574
\(405\) 0 0
\(406\) −52.1636 −2.58884
\(407\) −25.6152 −1.26970
\(408\) −2.45396 −0.121489
\(409\) 27.2193 1.34591 0.672954 0.739684i \(-0.265025\pi\)
0.672954 + 0.739684i \(0.265025\pi\)
\(410\) 0 0
\(411\) 2.22942 0.109969
\(412\) −22.8554 −1.12600
\(413\) −38.2567 −1.88249
\(414\) 7.98740 0.392560
\(415\) 0 0
\(416\) 11.2165 0.549932
\(417\) −3.14917 −0.154216
\(418\) 5.64209 0.275964
\(419\) 1.70123 0.0831104 0.0415552 0.999136i \(-0.486769\pi\)
0.0415552 + 0.999136i \(0.486769\pi\)
\(420\) 0 0
\(421\) −12.3991 −0.604293 −0.302147 0.953261i \(-0.597703\pi\)
−0.302147 + 0.953261i \(0.597703\pi\)
\(422\) 16.2289 0.790009
\(423\) 24.9049 1.21092
\(424\) −10.3526 −0.502767
\(425\) 0 0
\(426\) 1.74341 0.0844683
\(427\) 43.7813 2.11873
\(428\) −2.96610 −0.143372
\(429\) −2.46908 −0.119208
\(430\) 0 0
\(431\) −15.2271 −0.733465 −0.366733 0.930326i \(-0.619524\pi\)
−0.366733 + 0.930326i \(0.619524\pi\)
\(432\) −8.36044 −0.402242
\(433\) −5.77913 −0.277727 −0.138864 0.990312i \(-0.544345\pi\)
−0.138864 + 0.990312i \(0.544345\pi\)
\(434\) 17.8763 0.858090
\(435\) 0 0
\(436\) −2.65742 −0.127268
\(437\) −0.905551 −0.0433184
\(438\) −3.47803 −0.166187
\(439\) 7.89384 0.376753 0.188376 0.982097i \(-0.439678\pi\)
0.188376 + 0.982097i \(0.439678\pi\)
\(440\) 0 0
\(441\) −56.6025 −2.69536
\(442\) −23.1157 −1.09950
\(443\) −28.7110 −1.36410 −0.682050 0.731306i \(-0.738911\pi\)
−0.682050 + 0.731306i \(0.738911\pi\)
\(444\) 2.05561 0.0975549
\(445\) 0 0
\(446\) −6.92662 −0.327985
\(447\) 0.988489 0.0467539
\(448\) 13.2648 0.626703
\(449\) −9.97648 −0.470819 −0.235410 0.971896i \(-0.575643\pi\)
−0.235410 + 0.971896i \(0.575643\pi\)
\(450\) 0 0
\(451\) −34.5525 −1.62701
\(452\) −14.3357 −0.674293
\(453\) −0.112986 −0.00530853
\(454\) −40.4292 −1.89744
\(455\) 0 0
\(456\) 0.199806 0.00935678
\(457\) 12.5755 0.588255 0.294128 0.955766i \(-0.404971\pi\)
0.294128 + 0.955766i \(0.404971\pi\)
\(458\) 26.2307 1.22568
\(459\) 12.8787 0.601128
\(460\) 0 0
\(461\) 24.2571 1.12977 0.564883 0.825171i \(-0.308921\pi\)
0.564883 + 0.825171i \(0.308921\pi\)
\(462\) −13.8942 −0.646414
\(463\) 26.4560 1.22951 0.614757 0.788716i \(-0.289254\pi\)
0.614757 + 0.788716i \(0.289254\pi\)
\(464\) 26.7419 1.24146
\(465\) 0 0
\(466\) −30.4478 −1.41047
\(467\) −4.66803 −0.216011 −0.108005 0.994150i \(-0.534446\pi\)
−0.108005 + 0.994150i \(0.534446\pi\)
\(468\) −6.80021 −0.314340
\(469\) −24.2112 −1.11797
\(470\) 0 0
\(471\) −5.88847 −0.271326
\(472\) 8.38912 0.386140
\(473\) −5.03950 −0.231716
\(474\) −1.73147 −0.0795289
\(475\) 0 0
\(476\) −53.2824 −2.44220
\(477\) 26.7759 1.22599
\(478\) 16.7265 0.765052
\(479\) −20.2163 −0.923707 −0.461853 0.886956i \(-0.652815\pi\)
−0.461853 + 0.886956i \(0.652815\pi\)
\(480\) 0 0
\(481\) −8.54490 −0.389614
\(482\) 5.96599 0.271743
\(483\) 2.23000 0.101469
\(484\) 19.9772 0.908057
\(485\) 0 0
\(486\) 13.9403 0.632346
\(487\) 23.6802 1.07305 0.536527 0.843883i \(-0.319736\pi\)
0.536527 + 0.843883i \(0.319736\pi\)
\(488\) −9.60059 −0.434598
\(489\) 3.17953 0.143783
\(490\) 0 0
\(491\) 0.723299 0.0326420 0.0163210 0.999867i \(-0.494805\pi\)
0.0163210 + 0.999867i \(0.494805\pi\)
\(492\) 2.77282 0.125008
\(493\) −41.1943 −1.85530
\(494\) 1.88213 0.0846810
\(495\) 0 0
\(496\) −9.16437 −0.411492
\(497\) −16.7048 −0.749314
\(498\) 3.49493 0.156611
\(499\) −0.367937 −0.0164711 −0.00823556 0.999966i \(-0.502621\pi\)
−0.00823556 + 0.999966i \(0.502621\pi\)
\(500\) 0 0
\(501\) 0.449034 0.0200614
\(502\) −16.3488 −0.729683
\(503\) 9.38700 0.418546 0.209273 0.977857i \(-0.432890\pi\)
0.209273 + 0.977857i \(0.432890\pi\)
\(504\) 16.8867 0.752193
\(505\) 0 0
\(506\) −13.8085 −0.613861
\(507\) 2.96509 0.131684
\(508\) −16.8135 −0.745979
\(509\) −13.6908 −0.606836 −0.303418 0.952858i \(-0.598128\pi\)
−0.303418 + 0.952858i \(0.598128\pi\)
\(510\) 0 0
\(511\) 33.3255 1.47423
\(512\) −21.4256 −0.946888
\(513\) −1.04861 −0.0462974
\(514\) 37.6868 1.66229
\(515\) 0 0
\(516\) 0.404418 0.0178035
\(517\) −43.0551 −1.89356
\(518\) −48.0843 −2.11270
\(519\) −2.04008 −0.0895494
\(520\) 0 0
\(521\) −7.85102 −0.343960 −0.171980 0.985100i \(-0.555016\pi\)
−0.171980 + 0.985100i \(0.555016\pi\)
\(522\) −29.5850 −1.29490
\(523\) 6.26463 0.273933 0.136967 0.990576i \(-0.456265\pi\)
0.136967 + 0.990576i \(0.456265\pi\)
\(524\) −0.0136613 −0.000596796 0
\(525\) 0 0
\(526\) 26.9261 1.17403
\(527\) 14.1171 0.614952
\(528\) 7.12290 0.309984
\(529\) −20.7838 −0.903641
\(530\) 0 0
\(531\) −21.6976 −0.941594
\(532\) 4.33837 0.188092
\(533\) −11.5263 −0.499257
\(534\) −6.20509 −0.268520
\(535\) 0 0
\(536\) 5.30914 0.229320
\(537\) 3.44682 0.148741
\(538\) 23.0560 0.994013
\(539\) 97.8533 4.21484
\(540\) 0 0
\(541\) −37.2677 −1.60226 −0.801131 0.598488i \(-0.795768\pi\)
−0.801131 + 0.598488i \(0.795768\pi\)
\(542\) −4.90767 −0.210802
\(543\) 0.508699 0.0218304
\(544\) 49.8450 2.13709
\(545\) 0 0
\(546\) −4.63491 −0.198356
\(547\) 41.7401 1.78468 0.892339 0.451366i \(-0.149063\pi\)
0.892339 + 0.451366i \(0.149063\pi\)
\(548\) −10.6149 −0.453448
\(549\) 24.8309 1.05976
\(550\) 0 0
\(551\) 3.35412 0.142890
\(552\) −0.489006 −0.0208135
\(553\) 16.5904 0.705497
\(554\) −8.90334 −0.378267
\(555\) 0 0
\(556\) 14.9942 0.635894
\(557\) 13.6095 0.576652 0.288326 0.957532i \(-0.406901\pi\)
0.288326 + 0.957532i \(0.406901\pi\)
\(558\) 10.1387 0.429205
\(559\) −1.68111 −0.0711034
\(560\) 0 0
\(561\) −10.9724 −0.463255
\(562\) 50.9700 2.15004
\(563\) −41.4317 −1.74614 −0.873068 0.487598i \(-0.837873\pi\)
−0.873068 + 0.487598i \(0.837873\pi\)
\(564\) 3.45516 0.145488
\(565\) 0 0
\(566\) −8.87522 −0.373053
\(567\) −42.3660 −1.77920
\(568\) 3.66312 0.153701
\(569\) 1.50042 0.0629007 0.0314504 0.999505i \(-0.489987\pi\)
0.0314504 + 0.999505i \(0.489987\pi\)
\(570\) 0 0
\(571\) 42.5501 1.78066 0.890332 0.455311i \(-0.150472\pi\)
0.890332 + 0.455311i \(0.150472\pi\)
\(572\) 11.7561 0.491545
\(573\) −6.41063 −0.267808
\(574\) −64.8611 −2.70725
\(575\) 0 0
\(576\) 7.52323 0.313468
\(577\) −14.1072 −0.587290 −0.293645 0.955915i \(-0.594868\pi\)
−0.293645 + 0.955915i \(0.594868\pi\)
\(578\) −71.4348 −2.97129
\(579\) 4.40847 0.183210
\(580\) 0 0
\(581\) −33.4874 −1.38929
\(582\) −0.573310 −0.0237645
\(583\) −46.2896 −1.91712
\(584\) −7.30778 −0.302398
\(585\) 0 0
\(586\) −51.8892 −2.14352
\(587\) −41.2458 −1.70240 −0.851198 0.524845i \(-0.824123\pi\)
−0.851198 + 0.524845i \(0.824123\pi\)
\(588\) −7.85269 −0.323839
\(589\) −1.14945 −0.0473621
\(590\) 0 0
\(591\) −4.23622 −0.174255
\(592\) 24.6506 1.01314
\(593\) −6.83172 −0.280545 −0.140273 0.990113i \(-0.544798\pi\)
−0.140273 + 0.990113i \(0.544798\pi\)
\(594\) −15.9900 −0.656076
\(595\) 0 0
\(596\) −4.70650 −0.192786
\(597\) 2.17646 0.0890767
\(598\) −4.60632 −0.188367
\(599\) −0.441871 −0.0180543 −0.00902717 0.999959i \(-0.502873\pi\)
−0.00902717 + 0.999959i \(0.502873\pi\)
\(600\) 0 0
\(601\) −22.3310 −0.910899 −0.455450 0.890262i \(-0.650521\pi\)
−0.455450 + 0.890262i \(0.650521\pi\)
\(602\) −9.46004 −0.385562
\(603\) −13.7315 −0.559192
\(604\) 0.537959 0.0218893
\(605\) 0 0
\(606\) −8.43604 −0.342691
\(607\) −21.6504 −0.878763 −0.439381 0.898301i \(-0.644802\pi\)
−0.439381 + 0.898301i \(0.644802\pi\)
\(608\) −4.05848 −0.164593
\(609\) −8.25983 −0.334705
\(610\) 0 0
\(611\) −14.3626 −0.581050
\(612\) −30.2195 −1.22155
\(613\) 25.4719 1.02880 0.514399 0.857551i \(-0.328015\pi\)
0.514399 + 0.857551i \(0.328015\pi\)
\(614\) 10.6702 0.430614
\(615\) 0 0
\(616\) −29.1933 −1.17623
\(617\) −33.9269 −1.36585 −0.682923 0.730490i \(-0.739292\pi\)
−0.682923 + 0.730490i \(0.739292\pi\)
\(618\) −8.83510 −0.355400
\(619\) −36.1265 −1.45205 −0.726024 0.687670i \(-0.758634\pi\)
−0.726024 + 0.687670i \(0.758634\pi\)
\(620\) 0 0
\(621\) 2.56638 0.102985
\(622\) 27.7507 1.11270
\(623\) 59.4553 2.38203
\(624\) 2.37611 0.0951204
\(625\) 0 0
\(626\) −1.43630 −0.0574060
\(627\) 0.893394 0.0356787
\(628\) 28.0368 1.11879
\(629\) −37.9728 −1.51407
\(630\) 0 0
\(631\) −7.67874 −0.305686 −0.152843 0.988251i \(-0.548843\pi\)
−0.152843 + 0.988251i \(0.548843\pi\)
\(632\) −3.63803 −0.144713
\(633\) 2.56975 0.102139
\(634\) 39.5699 1.57152
\(635\) 0 0
\(636\) 3.71473 0.147298
\(637\) 32.6426 1.29335
\(638\) 51.1459 2.02489
\(639\) −9.47427 −0.374796
\(640\) 0 0
\(641\) 9.35930 0.369670 0.184835 0.982770i \(-0.440825\pi\)
0.184835 + 0.982770i \(0.440825\pi\)
\(642\) −1.14659 −0.0452524
\(643\) −5.80473 −0.228916 −0.114458 0.993428i \(-0.536513\pi\)
−0.114458 + 0.993428i \(0.536513\pi\)
\(644\) −10.6177 −0.418397
\(645\) 0 0
\(646\) 8.36402 0.329078
\(647\) 26.8056 1.05384 0.526919 0.849915i \(-0.323347\pi\)
0.526919 + 0.849915i \(0.323347\pi\)
\(648\) 9.29022 0.364954
\(649\) 37.5103 1.47241
\(650\) 0 0
\(651\) 2.83061 0.110941
\(652\) −15.1387 −0.592878
\(653\) 7.24374 0.283469 0.141735 0.989905i \(-0.454732\pi\)
0.141735 + 0.989905i \(0.454732\pi\)
\(654\) −1.02727 −0.0401694
\(655\) 0 0
\(656\) 33.2514 1.29825
\(657\) 18.9008 0.737391
\(658\) −80.8222 −3.15078
\(659\) 30.2151 1.17701 0.588507 0.808492i \(-0.299716\pi\)
0.588507 + 0.808492i \(0.299716\pi\)
\(660\) 0 0
\(661\) −1.97273 −0.0767304 −0.0383652 0.999264i \(-0.512215\pi\)
−0.0383652 + 0.999264i \(0.512215\pi\)
\(662\) −32.4534 −1.26134
\(663\) −3.66025 −0.142152
\(664\) 7.34328 0.284975
\(665\) 0 0
\(666\) −27.2714 −1.05674
\(667\) −8.20888 −0.317849
\(668\) −2.13799 −0.0827212
\(669\) −1.09679 −0.0424044
\(670\) 0 0
\(671\) −42.9272 −1.65718
\(672\) 9.99437 0.385541
\(673\) 51.0499 1.96783 0.983915 0.178638i \(-0.0571691\pi\)
0.983915 + 0.178638i \(0.0571691\pi\)
\(674\) 49.5744 1.90954
\(675\) 0 0
\(676\) −14.1177 −0.542989
\(677\) −18.6165 −0.715490 −0.357745 0.933819i \(-0.616454\pi\)
−0.357745 + 0.933819i \(0.616454\pi\)
\(678\) −5.54167 −0.212827
\(679\) 5.49329 0.210813
\(680\) 0 0
\(681\) −6.40175 −0.245316
\(682\) −17.5275 −0.671164
\(683\) −5.53670 −0.211856 −0.105928 0.994374i \(-0.533781\pi\)
−0.105928 + 0.994374i \(0.533781\pi\)
\(684\) 2.46054 0.0940810
\(685\) 0 0
\(686\) 117.468 4.48494
\(687\) 4.15348 0.158465
\(688\) 4.84973 0.184894
\(689\) −15.4416 −0.588279
\(690\) 0 0
\(691\) −18.0622 −0.687120 −0.343560 0.939131i \(-0.611633\pi\)
−0.343560 + 0.939131i \(0.611633\pi\)
\(692\) 9.71343 0.369249
\(693\) 75.5055 2.86822
\(694\) 21.0524 0.799139
\(695\) 0 0
\(696\) 1.81126 0.0686555
\(697\) −51.2217 −1.94016
\(698\) −16.6659 −0.630815
\(699\) −4.82124 −0.182356
\(700\) 0 0
\(701\) −25.7231 −0.971547 −0.485774 0.874085i \(-0.661462\pi\)
−0.485774 + 0.874085i \(0.661462\pi\)
\(702\) −5.33404 −0.201320
\(703\) 3.09182 0.116610
\(704\) −13.0060 −0.490182
\(705\) 0 0
\(706\) 17.6303 0.663524
\(707\) 80.8317 3.03999
\(708\) −3.01019 −0.113130
\(709\) 22.8874 0.859556 0.429778 0.902935i \(-0.358592\pi\)
0.429778 + 0.902935i \(0.358592\pi\)
\(710\) 0 0
\(711\) 9.40938 0.352879
\(712\) −13.0377 −0.488607
\(713\) 2.81316 0.105354
\(714\) −20.5971 −0.770828
\(715\) 0 0
\(716\) −16.4113 −0.613321
\(717\) 2.64855 0.0989119
\(718\) −2.39888 −0.0895254
\(719\) 33.5392 1.25080 0.625400 0.780304i \(-0.284936\pi\)
0.625400 + 0.780304i \(0.284936\pi\)
\(720\) 0 0
\(721\) 84.6554 3.15273
\(722\) 34.2895 1.27612
\(723\) 0.944682 0.0351331
\(724\) −2.42207 −0.0900157
\(725\) 0 0
\(726\) 7.72251 0.286609
\(727\) −47.3713 −1.75690 −0.878452 0.477831i \(-0.841423\pi\)
−0.878452 + 0.477831i \(0.841423\pi\)
\(728\) −9.73852 −0.360934
\(729\) −22.5209 −0.834109
\(730\) 0 0
\(731\) −7.47071 −0.276314
\(732\) 3.44489 0.127327
\(733\) 28.8063 1.06399 0.531993 0.846749i \(-0.321443\pi\)
0.531993 + 0.846749i \(0.321443\pi\)
\(734\) −32.0532 −1.18310
\(735\) 0 0
\(736\) 9.93272 0.366125
\(737\) 23.7388 0.874430
\(738\) −36.7865 −1.35413
\(739\) −44.3061 −1.62982 −0.814912 0.579584i \(-0.803215\pi\)
−0.814912 + 0.579584i \(0.803215\pi\)
\(740\) 0 0
\(741\) 0.298025 0.0109482
\(742\) −86.8939 −3.18998
\(743\) 8.81533 0.323403 0.161702 0.986840i \(-0.448302\pi\)
0.161702 + 0.986840i \(0.448302\pi\)
\(744\) −0.620711 −0.0227564
\(745\) 0 0
\(746\) 24.9395 0.913099
\(747\) −18.9926 −0.694904
\(748\) 52.2429 1.91019
\(749\) 10.9863 0.401431
\(750\) 0 0
\(751\) 4.39589 0.160408 0.0802041 0.996778i \(-0.474443\pi\)
0.0802041 + 0.996778i \(0.474443\pi\)
\(752\) 41.4339 1.51094
\(753\) −2.58875 −0.0943392
\(754\) 17.0616 0.621347
\(755\) 0 0
\(756\) −12.2951 −0.447170
\(757\) −3.60759 −0.131120 −0.0655600 0.997849i \(-0.520883\pi\)
−0.0655600 + 0.997849i \(0.520883\pi\)
\(758\) −15.2003 −0.552100
\(759\) −2.18649 −0.0793647
\(760\) 0 0
\(761\) 11.6606 0.422696 0.211348 0.977411i \(-0.432215\pi\)
0.211348 + 0.977411i \(0.432215\pi\)
\(762\) −6.49952 −0.235453
\(763\) 9.84298 0.356340
\(764\) 30.5230 1.10428
\(765\) 0 0
\(766\) −32.6387 −1.17928
\(767\) 12.5130 0.451816
\(768\) −6.11425 −0.220629
\(769\) −1.46086 −0.0526800 −0.0263400 0.999653i \(-0.508385\pi\)
−0.0263400 + 0.999653i \(0.508385\pi\)
\(770\) 0 0
\(771\) 5.96750 0.214914
\(772\) −20.9901 −0.755450
\(773\) −11.5351 −0.414887 −0.207444 0.978247i \(-0.566514\pi\)
−0.207444 + 0.978247i \(0.566514\pi\)
\(774\) −5.36533 −0.192853
\(775\) 0 0
\(776\) −1.20460 −0.0432425
\(777\) −7.61389 −0.273147
\(778\) 46.1677 1.65519
\(779\) 4.17057 0.149426
\(780\) 0 0
\(781\) 16.3789 0.586083
\(782\) −20.4701 −0.732009
\(783\) −9.50575 −0.339708
\(784\) −94.1686 −3.36316
\(785\) 0 0
\(786\) −0.00528098 −0.000188366 0
\(787\) 1.47008 0.0524028 0.0262014 0.999657i \(-0.491659\pi\)
0.0262014 + 0.999657i \(0.491659\pi\)
\(788\) 20.1700 0.718525
\(789\) 4.26360 0.151788
\(790\) 0 0
\(791\) 53.0987 1.88797
\(792\) −16.5572 −0.588335
\(793\) −14.3199 −0.508516
\(794\) −2.18486 −0.0775377
\(795\) 0 0
\(796\) −10.3628 −0.367300
\(797\) 43.1788 1.52947 0.764735 0.644345i \(-0.222870\pi\)
0.764735 + 0.644345i \(0.222870\pi\)
\(798\) 1.67706 0.0593673
\(799\) −63.8263 −2.25801
\(800\) 0 0
\(801\) 33.7206 1.19146
\(802\) −64.1702 −2.26593
\(803\) −32.6753 −1.15309
\(804\) −1.90503 −0.0671852
\(805\) 0 0
\(806\) −5.84696 −0.205950
\(807\) 3.65079 0.128514
\(808\) −17.7252 −0.623569
\(809\) −21.8926 −0.769704 −0.384852 0.922978i \(-0.625748\pi\)
−0.384852 + 0.922978i \(0.625748\pi\)
\(810\) 0 0
\(811\) 41.6105 1.46114 0.730572 0.682836i \(-0.239254\pi\)
0.730572 + 0.682836i \(0.239254\pi\)
\(812\) 39.3276 1.38013
\(813\) −0.777102 −0.0272542
\(814\) 47.1462 1.65247
\(815\) 0 0
\(816\) 10.5592 0.369647
\(817\) 0.608281 0.0212810
\(818\) −50.0987 −1.75166
\(819\) 25.1877 0.880128
\(820\) 0 0
\(821\) −14.9071 −0.520262 −0.260131 0.965573i \(-0.583766\pi\)
−0.260131 + 0.965573i \(0.583766\pi\)
\(822\) −4.10337 −0.143121
\(823\) 26.2455 0.914860 0.457430 0.889246i \(-0.348770\pi\)
0.457430 + 0.889246i \(0.348770\pi\)
\(824\) −18.5637 −0.646696
\(825\) 0 0
\(826\) 70.4136 2.45000
\(827\) 6.14518 0.213689 0.106844 0.994276i \(-0.465925\pi\)
0.106844 + 0.994276i \(0.465925\pi\)
\(828\) −6.02192 −0.209276
\(829\) 23.4428 0.814200 0.407100 0.913384i \(-0.366540\pi\)
0.407100 + 0.913384i \(0.366540\pi\)
\(830\) 0 0
\(831\) −1.40979 −0.0489052
\(832\) −4.33864 −0.150415
\(833\) 145.061 5.02606
\(834\) 5.79622 0.200707
\(835\) 0 0
\(836\) −4.25372 −0.147118
\(837\) 3.25759 0.112599
\(838\) −3.13120 −0.108166
\(839\) 37.5665 1.29694 0.648470 0.761240i \(-0.275409\pi\)
0.648470 + 0.761240i \(0.275409\pi\)
\(840\) 0 0
\(841\) 1.40533 0.0484598
\(842\) 22.8212 0.786469
\(843\) 8.07082 0.277974
\(844\) −12.2354 −0.421159
\(845\) 0 0
\(846\) −45.8389 −1.57598
\(847\) −73.9948 −2.54249
\(848\) 44.5466 1.52974
\(849\) −1.40534 −0.0482312
\(850\) 0 0
\(851\) −7.56693 −0.259391
\(852\) −1.31440 −0.0450307
\(853\) −22.1842 −0.759571 −0.379786 0.925075i \(-0.624002\pi\)
−0.379786 + 0.925075i \(0.624002\pi\)
\(854\) −80.5820 −2.75746
\(855\) 0 0
\(856\) −2.40913 −0.0823425
\(857\) 24.9840 0.853437 0.426718 0.904385i \(-0.359670\pi\)
0.426718 + 0.904385i \(0.359670\pi\)
\(858\) 4.54448 0.155146
\(859\) −18.7825 −0.640850 −0.320425 0.947274i \(-0.603826\pi\)
−0.320425 + 0.947274i \(0.603826\pi\)
\(860\) 0 0
\(861\) −10.2704 −0.350015
\(862\) 28.0264 0.954583
\(863\) −35.7173 −1.21583 −0.607916 0.794001i \(-0.707994\pi\)
−0.607916 + 0.794001i \(0.707994\pi\)
\(864\) 11.5019 0.391304
\(865\) 0 0
\(866\) 10.6368 0.361454
\(867\) −11.3113 −0.384152
\(868\) −13.4774 −0.457454
\(869\) −16.2667 −0.551811
\(870\) 0 0
\(871\) 7.91895 0.268324
\(872\) −2.15842 −0.0730932
\(873\) 3.11556 0.105446
\(874\) 1.66672 0.0563776
\(875\) 0 0
\(876\) 2.62218 0.0885953
\(877\) 42.4124 1.43216 0.716082 0.698016i \(-0.245934\pi\)
0.716082 + 0.698016i \(0.245934\pi\)
\(878\) −14.5291 −0.490332
\(879\) −8.21638 −0.277132
\(880\) 0 0
\(881\) −26.5019 −0.892873 −0.446437 0.894815i \(-0.647307\pi\)
−0.446437 + 0.894815i \(0.647307\pi\)
\(882\) 104.180 3.50793
\(883\) 9.84464 0.331299 0.165649 0.986185i \(-0.447028\pi\)
0.165649 + 0.986185i \(0.447028\pi\)
\(884\) 17.4276 0.586152
\(885\) 0 0
\(886\) 52.8441 1.77533
\(887\) −48.1046 −1.61519 −0.807597 0.589735i \(-0.799232\pi\)
−0.807597 + 0.589735i \(0.799232\pi\)
\(888\) 1.66961 0.0560285
\(889\) 62.2765 2.08869
\(890\) 0 0
\(891\) 41.5394 1.39162
\(892\) 5.22216 0.174851
\(893\) 5.19687 0.173907
\(894\) −1.81937 −0.0608488
\(895\) 0 0
\(896\) 44.1711 1.47565
\(897\) −0.729386 −0.0243535
\(898\) 18.3623 0.612757
\(899\) −10.4198 −0.347520
\(900\) 0 0
\(901\) −68.6212 −2.28610
\(902\) 63.5957 2.11751
\(903\) −1.49795 −0.0498485
\(904\) −11.6437 −0.387265
\(905\) 0 0
\(906\) 0.207956 0.00690889
\(907\) 44.8522 1.48929 0.744646 0.667459i \(-0.232618\pi\)
0.744646 + 0.667459i \(0.232618\pi\)
\(908\) 30.4807 1.01154
\(909\) 45.8443 1.52056
\(910\) 0 0
\(911\) −49.9719 −1.65564 −0.827822 0.560991i \(-0.810420\pi\)
−0.827822 + 0.560991i \(0.810420\pi\)
\(912\) −0.859753 −0.0284693
\(913\) 32.8340 1.08665
\(914\) −23.1458 −0.765596
\(915\) 0 0
\(916\) −19.7760 −0.653417
\(917\) 0.0506008 0.00167099
\(918\) −23.7040 −0.782350
\(919\) 12.3429 0.407155 0.203577 0.979059i \(-0.434743\pi\)
0.203577 + 0.979059i \(0.434743\pi\)
\(920\) 0 0
\(921\) 1.68957 0.0556732
\(922\) −44.6466 −1.47036
\(923\) 5.46379 0.179843
\(924\) 10.4752 0.344608
\(925\) 0 0
\(926\) −48.6937 −1.60018
\(927\) 48.0130 1.57695
\(928\) −36.7904 −1.20770
\(929\) 20.2913 0.665735 0.332867 0.942974i \(-0.391984\pi\)
0.332867 + 0.942974i \(0.391984\pi\)
\(930\) 0 0
\(931\) −11.8112 −0.387095
\(932\) 22.9554 0.751930
\(933\) 4.39417 0.143859
\(934\) 8.59177 0.281131
\(935\) 0 0
\(936\) −5.52328 −0.180534
\(937\) 5.50728 0.179915 0.0899576 0.995946i \(-0.471327\pi\)
0.0899576 + 0.995946i \(0.471327\pi\)
\(938\) 44.5620 1.45500
\(939\) −0.227430 −0.00742190
\(940\) 0 0
\(941\) 29.3989 0.958378 0.479189 0.877712i \(-0.340931\pi\)
0.479189 + 0.877712i \(0.340931\pi\)
\(942\) 10.8381 0.353123
\(943\) −10.2071 −0.332388
\(944\) −36.0978 −1.17488
\(945\) 0 0
\(946\) 9.27547 0.301572
\(947\) 10.8670 0.353130 0.176565 0.984289i \(-0.443501\pi\)
0.176565 + 0.984289i \(0.443501\pi\)
\(948\) 1.30540 0.0423974
\(949\) −10.9001 −0.353831
\(950\) 0 0
\(951\) 6.26568 0.203179
\(952\) −43.2772 −1.40262
\(953\) −51.5990 −1.67146 −0.835728 0.549144i \(-0.814954\pi\)
−0.835728 + 0.549144i \(0.814954\pi\)
\(954\) −49.2826 −1.59558
\(955\) 0 0
\(956\) −12.6106 −0.407855
\(957\) 8.09868 0.261793
\(958\) 37.2092 1.20218
\(959\) 39.3173 1.26962
\(960\) 0 0
\(961\) −27.4292 −0.884812
\(962\) 15.7274 0.507070
\(963\) 6.23097 0.200790
\(964\) −4.49792 −0.144868
\(965\) 0 0
\(966\) −4.10444 −0.132058
\(967\) 49.7367 1.59942 0.799712 0.600383i \(-0.204985\pi\)
0.799712 + 0.600383i \(0.204985\pi\)
\(968\) 16.2260 0.521522
\(969\) 1.32440 0.0425457
\(970\) 0 0
\(971\) 23.7725 0.762896 0.381448 0.924390i \(-0.375426\pi\)
0.381448 + 0.924390i \(0.375426\pi\)
\(972\) −10.5100 −0.337108
\(973\) −55.5377 −1.78046
\(974\) −43.5848 −1.39655
\(975\) 0 0
\(976\) 41.3107 1.32232
\(977\) −40.5334 −1.29678 −0.648389 0.761309i \(-0.724557\pi\)
−0.648389 + 0.761309i \(0.724557\pi\)
\(978\) −5.85210 −0.187130
\(979\) −58.2954 −1.86313
\(980\) 0 0
\(981\) 5.58252 0.178236
\(982\) −1.33127 −0.0424826
\(983\) −60.6697 −1.93506 −0.967532 0.252749i \(-0.918665\pi\)
−0.967532 + 0.252749i \(0.918665\pi\)
\(984\) 2.25215 0.0717958
\(985\) 0 0
\(986\) 75.8203 2.41461
\(987\) −12.7978 −0.407357
\(988\) −1.41899 −0.0451440
\(989\) −1.48871 −0.0473381
\(990\) 0 0
\(991\) −35.5820 −1.13030 −0.565150 0.824988i \(-0.691182\pi\)
−0.565150 + 0.824988i \(0.691182\pi\)
\(992\) 12.6079 0.400302
\(993\) −5.13881 −0.163075
\(994\) 30.7461 0.975209
\(995\) 0 0
\(996\) −2.63492 −0.0834906
\(997\) −0.728331 −0.0230665 −0.0115332 0.999933i \(-0.503671\pi\)
−0.0115332 + 0.999933i \(0.503671\pi\)
\(998\) 0.677208 0.0214366
\(999\) −8.76238 −0.277229
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 1075.2.a.p.1.2 6
3.2 odd 2 9675.2.a.cl.1.5 6
5.2 odd 4 1075.2.b.k.474.3 12
5.3 odd 4 1075.2.b.k.474.10 12
5.4 even 2 215.2.a.d.1.5 6
15.14 odd 2 1935.2.a.z.1.2 6
20.19 odd 2 3440.2.a.x.1.4 6
215.214 odd 2 9245.2.a.n.1.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
215.2.a.d.1.5 6 5.4 even 2
1075.2.a.p.1.2 6 1.1 even 1 trivial
1075.2.b.k.474.3 12 5.2 odd 4
1075.2.b.k.474.10 12 5.3 odd 4
1935.2.a.z.1.2 6 15.14 odd 2
3440.2.a.x.1.4 6 20.19 odd 2
9245.2.a.n.1.2 6 215.214 odd 2
9675.2.a.cl.1.5 6 3.2 odd 2