Properties

Label 4022.2.a.d.1.9
Level $4022$
Weight $2$
Character 4022.1
Self dual yes
Analytic conductor $32.116$
Analytic rank $1$
Dimension $37$
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] = [4022,2,Mod(1,4022)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4022, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4022.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4022 = 2 \cdot 2011 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4022.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: \(32.1158316930\)
Analytic rank: \(1\)
Dimension: \(37\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 4022.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.94782 q^{3} +1.00000 q^{4} +3.45647 q^{5} +1.94782 q^{6} -2.39115 q^{7} -1.00000 q^{8} +0.794011 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.94782 q^{3} +1.00000 q^{4} +3.45647 q^{5} +1.94782 q^{6} -2.39115 q^{7} -1.00000 q^{8} +0.794011 q^{9} -3.45647 q^{10} +0.977749 q^{11} -1.94782 q^{12} -5.92195 q^{13} +2.39115 q^{14} -6.73259 q^{15} +1.00000 q^{16} -3.06365 q^{17} -0.794011 q^{18} +5.80636 q^{19} +3.45647 q^{20} +4.65754 q^{21} -0.977749 q^{22} -1.03892 q^{23} +1.94782 q^{24} +6.94720 q^{25} +5.92195 q^{26} +4.29687 q^{27} -2.39115 q^{28} +3.53785 q^{29} +6.73259 q^{30} +3.73582 q^{31} -1.00000 q^{32} -1.90448 q^{33} +3.06365 q^{34} -8.26495 q^{35} +0.794011 q^{36} +0.629177 q^{37} -5.80636 q^{38} +11.5349 q^{39} -3.45647 q^{40} +7.85266 q^{41} -4.65754 q^{42} -9.12530 q^{43} +0.977749 q^{44} +2.74448 q^{45} +1.03892 q^{46} +6.49858 q^{47} -1.94782 q^{48} -1.28239 q^{49} -6.94720 q^{50} +5.96745 q^{51} -5.92195 q^{52} -7.59890 q^{53} -4.29687 q^{54} +3.37956 q^{55} +2.39115 q^{56} -11.3097 q^{57} -3.53785 q^{58} -7.49169 q^{59} -6.73259 q^{60} +5.09242 q^{61} -3.73582 q^{62} -1.89860 q^{63} +1.00000 q^{64} -20.4691 q^{65} +1.90448 q^{66} +2.93883 q^{67} -3.06365 q^{68} +2.02363 q^{69} +8.26495 q^{70} -0.869517 q^{71} -0.794011 q^{72} -7.50447 q^{73} -0.629177 q^{74} -13.5319 q^{75} +5.80636 q^{76} -2.33795 q^{77} -11.5349 q^{78} +9.44928 q^{79} +3.45647 q^{80} -10.7516 q^{81} -7.85266 q^{82} +8.38779 q^{83} +4.65754 q^{84} -10.5894 q^{85} +9.12530 q^{86} -6.89111 q^{87} -0.977749 q^{88} -14.6218 q^{89} -2.74448 q^{90} +14.1603 q^{91} -1.03892 q^{92} -7.27671 q^{93} -6.49858 q^{94} +20.0695 q^{95} +1.94782 q^{96} -13.1082 q^{97} +1.28239 q^{98} +0.776344 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.94782 −1.12458 −0.562288 0.826942i \(-0.690079\pi\)
−0.562288 + 0.826942i \(0.690079\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.45647 1.54578 0.772891 0.634539i \(-0.218810\pi\)
0.772891 + 0.634539i \(0.218810\pi\)
\(6\) 1.94782 0.795195
\(7\) −2.39115 −0.903771 −0.451886 0.892076i \(-0.649248\pi\)
−0.451886 + 0.892076i \(0.649248\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.794011 0.264670
\(10\) −3.45647 −1.09303
\(11\) 0.977749 0.294803 0.147401 0.989077i \(-0.452909\pi\)
0.147401 + 0.989077i \(0.452909\pi\)
\(12\) −1.94782 −0.562288
\(13\) −5.92195 −1.64245 −0.821227 0.570602i \(-0.806710\pi\)
−0.821227 + 0.570602i \(0.806710\pi\)
\(14\) 2.39115 0.639063
\(15\) −6.73259 −1.73835
\(16\) 1.00000 0.250000
\(17\) −3.06365 −0.743045 −0.371523 0.928424i \(-0.621164\pi\)
−0.371523 + 0.928424i \(0.621164\pi\)
\(18\) −0.794011 −0.187150
\(19\) 5.80636 1.33207 0.666035 0.745921i \(-0.267990\pi\)
0.666035 + 0.745921i \(0.267990\pi\)
\(20\) 3.45647 0.772891
\(21\) 4.65754 1.01636
\(22\) −0.977749 −0.208457
\(23\) −1.03892 −0.216630 −0.108315 0.994117i \(-0.534545\pi\)
−0.108315 + 0.994117i \(0.534545\pi\)
\(24\) 1.94782 0.397598
\(25\) 6.94720 1.38944
\(26\) 5.92195 1.16139
\(27\) 4.29687 0.826934
\(28\) −2.39115 −0.451886
\(29\) 3.53785 0.656962 0.328481 0.944510i \(-0.393463\pi\)
0.328481 + 0.944510i \(0.393463\pi\)
\(30\) 6.73259 1.22920
\(31\) 3.73582 0.670973 0.335486 0.942045i \(-0.391099\pi\)
0.335486 + 0.942045i \(0.391099\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.90448 −0.331528
\(34\) 3.06365 0.525412
\(35\) −8.26495 −1.39703
\(36\) 0.794011 0.132335
\(37\) 0.629177 0.103436 0.0517180 0.998662i \(-0.483530\pi\)
0.0517180 + 0.998662i \(0.483530\pi\)
\(38\) −5.80636 −0.941915
\(39\) 11.5349 1.84706
\(40\) −3.45647 −0.546516
\(41\) 7.85266 1.22638 0.613190 0.789936i \(-0.289886\pi\)
0.613190 + 0.789936i \(0.289886\pi\)
\(42\) −4.65754 −0.718674
\(43\) −9.12530 −1.39160 −0.695798 0.718238i \(-0.744949\pi\)
−0.695798 + 0.718238i \(0.744949\pi\)
\(44\) 0.977749 0.147401
\(45\) 2.74448 0.409123
\(46\) 1.03892 0.153180
\(47\) 6.49858 0.947916 0.473958 0.880547i \(-0.342825\pi\)
0.473958 + 0.880547i \(0.342825\pi\)
\(48\) −1.94782 −0.281144
\(49\) −1.28239 −0.183198
\(50\) −6.94720 −0.982482
\(51\) 5.96745 0.835611
\(52\) −5.92195 −0.821227
\(53\) −7.59890 −1.04379 −0.521894 0.853010i \(-0.674774\pi\)
−0.521894 + 0.853010i \(0.674774\pi\)
\(54\) −4.29687 −0.584730
\(55\) 3.37956 0.455700
\(56\) 2.39115 0.319531
\(57\) −11.3097 −1.49801
\(58\) −3.53785 −0.464543
\(59\) −7.49169 −0.975335 −0.487667 0.873030i \(-0.662152\pi\)
−0.487667 + 0.873030i \(0.662152\pi\)
\(60\) −6.73259 −0.869174
\(61\) 5.09242 0.652018 0.326009 0.945367i \(-0.394296\pi\)
0.326009 + 0.945367i \(0.394296\pi\)
\(62\) −3.73582 −0.474449
\(63\) −1.89860 −0.239201
\(64\) 1.00000 0.125000
\(65\) −20.4691 −2.53887
\(66\) 1.90448 0.234426
\(67\) 2.93883 0.359035 0.179517 0.983755i \(-0.442546\pi\)
0.179517 + 0.983755i \(0.442546\pi\)
\(68\) −3.06365 −0.371523
\(69\) 2.02363 0.243616
\(70\) 8.26495 0.987851
\(71\) −0.869517 −0.103193 −0.0515964 0.998668i \(-0.516431\pi\)
−0.0515964 + 0.998668i \(0.516431\pi\)
\(72\) −0.794011 −0.0935751
\(73\) −7.50447 −0.878331 −0.439166 0.898406i \(-0.644726\pi\)
−0.439166 + 0.898406i \(0.644726\pi\)
\(74\) −0.629177 −0.0731403
\(75\) −13.5319 −1.56253
\(76\) 5.80636 0.666035
\(77\) −2.33795 −0.266434
\(78\) −11.5349 −1.30607
\(79\) 9.44928 1.06313 0.531563 0.847019i \(-0.321605\pi\)
0.531563 + 0.847019i \(0.321605\pi\)
\(80\) 3.45647 0.386445
\(81\) −10.7516 −1.19462
\(82\) −7.85266 −0.867181
\(83\) 8.38779 0.920680 0.460340 0.887743i \(-0.347728\pi\)
0.460340 + 0.887743i \(0.347728\pi\)
\(84\) 4.65754 0.508179
\(85\) −10.5894 −1.14859
\(86\) 9.12530 0.984007
\(87\) −6.89111 −0.738804
\(88\) −0.977749 −0.104228
\(89\) −14.6218 −1.54991 −0.774956 0.632015i \(-0.782228\pi\)
−0.774956 + 0.632015i \(0.782228\pi\)
\(90\) −2.74448 −0.289293
\(91\) 14.1603 1.48440
\(92\) −1.03892 −0.108315
\(93\) −7.27671 −0.754559
\(94\) −6.49858 −0.670278
\(95\) 20.0695 2.05909
\(96\) 1.94782 0.198799
\(97\) −13.1082 −1.33094 −0.665468 0.746426i \(-0.731768\pi\)
−0.665468 + 0.746426i \(0.731768\pi\)
\(98\) 1.28239 0.129540
\(99\) 0.776344 0.0780255
\(100\) 6.94720 0.694720
\(101\) −12.8622 −1.27983 −0.639917 0.768444i \(-0.721031\pi\)
−0.639917 + 0.768444i \(0.721031\pi\)
\(102\) −5.96745 −0.590866
\(103\) 4.69253 0.462369 0.231184 0.972910i \(-0.425740\pi\)
0.231184 + 0.972910i \(0.425740\pi\)
\(104\) 5.92195 0.580695
\(105\) 16.0987 1.57107
\(106\) 7.59890 0.738070
\(107\) −11.1173 −1.07475 −0.537375 0.843343i \(-0.680584\pi\)
−0.537375 + 0.843343i \(0.680584\pi\)
\(108\) 4.29687 0.413467
\(109\) 6.23740 0.597435 0.298717 0.954342i \(-0.403441\pi\)
0.298717 + 0.954342i \(0.403441\pi\)
\(110\) −3.37956 −0.322229
\(111\) −1.22553 −0.116322
\(112\) −2.39115 −0.225943
\(113\) −9.62327 −0.905281 −0.452640 0.891693i \(-0.649518\pi\)
−0.452640 + 0.891693i \(0.649518\pi\)
\(114\) 11.3097 1.05925
\(115\) −3.59100 −0.334862
\(116\) 3.53785 0.328481
\(117\) −4.70210 −0.434709
\(118\) 7.49169 0.689666
\(119\) 7.32567 0.671543
\(120\) 6.73259 0.614599
\(121\) −10.0440 −0.913091
\(122\) −5.09242 −0.461046
\(123\) −15.2956 −1.37916
\(124\) 3.73582 0.335486
\(125\) 6.73043 0.601988
\(126\) 1.89860 0.169141
\(127\) 17.6938 1.57007 0.785037 0.619449i \(-0.212644\pi\)
0.785037 + 0.619449i \(0.212644\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 17.7745 1.56495
\(130\) 20.4691 1.79526
\(131\) −4.91795 −0.429683 −0.214842 0.976649i \(-0.568924\pi\)
−0.214842 + 0.976649i \(0.568924\pi\)
\(132\) −1.90448 −0.165764
\(133\) −13.8839 −1.20389
\(134\) −2.93883 −0.253876
\(135\) 14.8520 1.27826
\(136\) 3.06365 0.262706
\(137\) −4.47013 −0.381909 −0.190954 0.981599i \(-0.561158\pi\)
−0.190954 + 0.981599i \(0.561158\pi\)
\(138\) −2.02363 −0.172263
\(139\) 9.71261 0.823813 0.411906 0.911226i \(-0.364863\pi\)
0.411906 + 0.911226i \(0.364863\pi\)
\(140\) −8.26495 −0.698516
\(141\) −12.6581 −1.06600
\(142\) 0.869517 0.0729683
\(143\) −5.79019 −0.484200
\(144\) 0.794011 0.0661676
\(145\) 12.2285 1.01552
\(146\) 7.50447 0.621074
\(147\) 2.49786 0.206020
\(148\) 0.629177 0.0517180
\(149\) 7.33772 0.601129 0.300565 0.953761i \(-0.402825\pi\)
0.300565 + 0.953761i \(0.402825\pi\)
\(150\) 13.5319 1.10488
\(151\) −5.72157 −0.465614 −0.232807 0.972523i \(-0.574791\pi\)
−0.232807 + 0.972523i \(0.574791\pi\)
\(152\) −5.80636 −0.470958
\(153\) −2.43258 −0.196662
\(154\) 2.33795 0.188397
\(155\) 12.9127 1.03718
\(156\) 11.5349 0.923532
\(157\) 10.0393 0.801224 0.400612 0.916248i \(-0.368798\pi\)
0.400612 + 0.916248i \(0.368798\pi\)
\(158\) −9.44928 −0.751744
\(159\) 14.8013 1.17382
\(160\) −3.45647 −0.273258
\(161\) 2.48422 0.195784
\(162\) 10.7516 0.844724
\(163\) −20.7645 −1.62640 −0.813201 0.581983i \(-0.802277\pi\)
−0.813201 + 0.581983i \(0.802277\pi\)
\(164\) 7.85266 0.613190
\(165\) −6.58279 −0.512469
\(166\) −8.38779 −0.651019
\(167\) 11.8093 0.913831 0.456915 0.889510i \(-0.348954\pi\)
0.456915 + 0.889510i \(0.348954\pi\)
\(168\) −4.65754 −0.359337
\(169\) 22.0695 1.69765
\(170\) 10.5894 0.812172
\(171\) 4.61031 0.352559
\(172\) −9.12530 −0.695798
\(173\) −1.56209 −0.118764 −0.0593818 0.998235i \(-0.518913\pi\)
−0.0593818 + 0.998235i \(0.518913\pi\)
\(174\) 6.89111 0.522413
\(175\) −16.6118 −1.25573
\(176\) 0.977749 0.0737006
\(177\) 14.5925 1.09684
\(178\) 14.6218 1.09595
\(179\) −11.1537 −0.833666 −0.416833 0.908983i \(-0.636860\pi\)
−0.416833 + 0.908983i \(0.636860\pi\)
\(180\) 2.74448 0.204561
\(181\) 16.5708 1.23169 0.615847 0.787865i \(-0.288814\pi\)
0.615847 + 0.787865i \(0.288814\pi\)
\(182\) −14.1603 −1.04963
\(183\) −9.91914 −0.733244
\(184\) 1.03892 0.0765902
\(185\) 2.17473 0.159890
\(186\) 7.27671 0.533554
\(187\) −2.99549 −0.219052
\(188\) 6.49858 0.473958
\(189\) −10.2745 −0.747359
\(190\) −20.0695 −1.45599
\(191\) −17.7089 −1.28137 −0.640686 0.767803i \(-0.721350\pi\)
−0.640686 + 0.767803i \(0.721350\pi\)
\(192\) −1.94782 −0.140572
\(193\) −13.2164 −0.951335 −0.475667 0.879625i \(-0.657793\pi\)
−0.475667 + 0.879625i \(0.657793\pi\)
\(194\) 13.1082 0.941114
\(195\) 39.8701 2.85516
\(196\) −1.28239 −0.0915990
\(197\) 12.1174 0.863328 0.431664 0.902034i \(-0.357927\pi\)
0.431664 + 0.902034i \(0.357927\pi\)
\(198\) −0.776344 −0.0551724
\(199\) −8.59925 −0.609585 −0.304792 0.952419i \(-0.598587\pi\)
−0.304792 + 0.952419i \(0.598587\pi\)
\(200\) −6.94720 −0.491241
\(201\) −5.72431 −0.403762
\(202\) 12.8622 0.904979
\(203\) −8.45954 −0.593744
\(204\) 5.96745 0.417805
\(205\) 27.1425 1.89571
\(206\) −4.69253 −0.326944
\(207\) −0.824914 −0.0573355
\(208\) −5.92195 −0.410613
\(209\) 5.67716 0.392697
\(210\) −16.0987 −1.11091
\(211\) −15.1078 −1.04006 −0.520031 0.854147i \(-0.674080\pi\)
−0.520031 + 0.854147i \(0.674080\pi\)
\(212\) −7.59890 −0.521894
\(213\) 1.69367 0.116048
\(214\) 11.1173 0.759963
\(215\) −31.5414 −2.15110
\(216\) −4.29687 −0.292365
\(217\) −8.93291 −0.606406
\(218\) −6.23740 −0.422450
\(219\) 14.6174 0.987750
\(220\) 3.37956 0.227850
\(221\) 18.1428 1.22042
\(222\) 1.22553 0.0822519
\(223\) 12.4181 0.831576 0.415788 0.909461i \(-0.363506\pi\)
0.415788 + 0.909461i \(0.363506\pi\)
\(224\) 2.39115 0.159766
\(225\) 5.51615 0.367743
\(226\) 9.62327 0.640130
\(227\) 4.51477 0.299656 0.149828 0.988712i \(-0.452128\pi\)
0.149828 + 0.988712i \(0.452128\pi\)
\(228\) −11.3097 −0.749006
\(229\) −29.4052 −1.94315 −0.971576 0.236729i \(-0.923925\pi\)
−0.971576 + 0.236729i \(0.923925\pi\)
\(230\) 3.59100 0.236783
\(231\) 4.55391 0.299625
\(232\) −3.53785 −0.232271
\(233\) −3.90158 −0.255601 −0.127800 0.991800i \(-0.540792\pi\)
−0.127800 + 0.991800i \(0.540792\pi\)
\(234\) 4.70210 0.307386
\(235\) 22.4622 1.46527
\(236\) −7.49169 −0.487667
\(237\) −18.4055 −1.19557
\(238\) −7.32567 −0.474852
\(239\) −24.4116 −1.57905 −0.789526 0.613717i \(-0.789674\pi\)
−0.789526 + 0.613717i \(0.789674\pi\)
\(240\) −6.73259 −0.434587
\(241\) −26.1321 −1.68332 −0.841660 0.540008i \(-0.818421\pi\)
−0.841660 + 0.540008i \(0.818421\pi\)
\(242\) 10.0440 0.645653
\(243\) 8.05154 0.516507
\(244\) 5.09242 0.326009
\(245\) −4.43253 −0.283184
\(246\) 15.2956 0.975211
\(247\) −34.3850 −2.18786
\(248\) −3.73582 −0.237225
\(249\) −16.3379 −1.03537
\(250\) −6.73043 −0.425670
\(251\) 21.9976 1.38848 0.694238 0.719745i \(-0.255741\pi\)
0.694238 + 0.719745i \(0.255741\pi\)
\(252\) −1.89860 −0.119601
\(253\) −1.01580 −0.0638630
\(254\) −17.6938 −1.11021
\(255\) 20.6263 1.29167
\(256\) 1.00000 0.0625000
\(257\) −14.0947 −0.879206 −0.439603 0.898192i \(-0.644881\pi\)
−0.439603 + 0.898192i \(0.644881\pi\)
\(258\) −17.7745 −1.10659
\(259\) −1.50446 −0.0934825
\(260\) −20.4691 −1.26944
\(261\) 2.80909 0.173879
\(262\) 4.91795 0.303832
\(263\) −14.0607 −0.867018 −0.433509 0.901149i \(-0.642725\pi\)
−0.433509 + 0.901149i \(0.642725\pi\)
\(264\) 1.90448 0.117213
\(265\) −26.2654 −1.61347
\(266\) 13.8839 0.851276
\(267\) 28.4808 1.74299
\(268\) 2.93883 0.179517
\(269\) −32.4136 −1.97629 −0.988145 0.153526i \(-0.950937\pi\)
−0.988145 + 0.153526i \(0.950937\pi\)
\(270\) −14.8520 −0.903865
\(271\) −1.57480 −0.0956621 −0.0478310 0.998855i \(-0.515231\pi\)
−0.0478310 + 0.998855i \(0.515231\pi\)
\(272\) −3.06365 −0.185761
\(273\) −27.5817 −1.66932
\(274\) 4.47013 0.270050
\(275\) 6.79262 0.409610
\(276\) 2.02363 0.121808
\(277\) −0.196864 −0.0118284 −0.00591420 0.999983i \(-0.501883\pi\)
−0.00591420 + 0.999983i \(0.501883\pi\)
\(278\) −9.71261 −0.582524
\(279\) 2.96628 0.177587
\(280\) 8.26495 0.493925
\(281\) −13.1151 −0.782378 −0.391189 0.920310i \(-0.627936\pi\)
−0.391189 + 0.920310i \(0.627936\pi\)
\(282\) 12.6581 0.753778
\(283\) 15.0768 0.896223 0.448111 0.893978i \(-0.352097\pi\)
0.448111 + 0.893978i \(0.352097\pi\)
\(284\) −0.869517 −0.0515964
\(285\) −39.0918 −2.31560
\(286\) 5.79019 0.342381
\(287\) −18.7769 −1.10837
\(288\) −0.794011 −0.0467876
\(289\) −7.61402 −0.447884
\(290\) −12.2285 −0.718081
\(291\) 25.5324 1.49674
\(292\) −7.50447 −0.439166
\(293\) 23.4079 1.36751 0.683753 0.729714i \(-0.260347\pi\)
0.683753 + 0.729714i \(0.260347\pi\)
\(294\) −2.49786 −0.145678
\(295\) −25.8948 −1.50765
\(296\) −0.629177 −0.0365702
\(297\) 4.20127 0.243782
\(298\) −7.33772 −0.425062
\(299\) 6.15243 0.355804
\(300\) −13.5319 −0.781265
\(301\) 21.8200 1.25768
\(302\) 5.72157 0.329239
\(303\) 25.0532 1.43927
\(304\) 5.80636 0.333017
\(305\) 17.6018 1.00788
\(306\) 2.43258 0.139061
\(307\) −21.3899 −1.22078 −0.610392 0.792100i \(-0.708988\pi\)
−0.610392 + 0.792100i \(0.708988\pi\)
\(308\) −2.33795 −0.133217
\(309\) −9.14021 −0.519969
\(310\) −12.9127 −0.733395
\(311\) 3.11928 0.176878 0.0884391 0.996082i \(-0.471812\pi\)
0.0884391 + 0.996082i \(0.471812\pi\)
\(312\) −11.5349 −0.653036
\(313\) −17.3323 −0.979679 −0.489840 0.871813i \(-0.662945\pi\)
−0.489840 + 0.871813i \(0.662945\pi\)
\(314\) −10.0393 −0.566551
\(315\) −6.56247 −0.369753
\(316\) 9.44928 0.531563
\(317\) −15.4248 −0.866341 −0.433171 0.901312i \(-0.642605\pi\)
−0.433171 + 0.901312i \(0.642605\pi\)
\(318\) −14.8013 −0.830016
\(319\) 3.45913 0.193674
\(320\) 3.45647 0.193223
\(321\) 21.6545 1.20864
\(322\) −2.48422 −0.138440
\(323\) −17.7887 −0.989788
\(324\) −10.7516 −0.597310
\(325\) −41.1410 −2.28209
\(326\) 20.7645 1.15004
\(327\) −12.1494 −0.671861
\(328\) −7.85266 −0.433591
\(329\) −15.5391 −0.856699
\(330\) 6.58279 0.362371
\(331\) 17.1044 0.940140 0.470070 0.882629i \(-0.344229\pi\)
0.470070 + 0.882629i \(0.344229\pi\)
\(332\) 8.38779 0.460340
\(333\) 0.499574 0.0273765
\(334\) −11.8093 −0.646176
\(335\) 10.1580 0.554989
\(336\) 4.65754 0.254090
\(337\) 22.4924 1.22524 0.612621 0.790377i \(-0.290115\pi\)
0.612621 + 0.790377i \(0.290115\pi\)
\(338\) −22.0695 −1.20042
\(339\) 18.7444 1.01806
\(340\) −10.5894 −0.574293
\(341\) 3.65269 0.197804
\(342\) −4.61031 −0.249297
\(343\) 19.8045 1.06934
\(344\) 9.12530 0.492003
\(345\) 6.99462 0.376578
\(346\) 1.56209 0.0839785
\(347\) 8.55698 0.459363 0.229681 0.973266i \(-0.426232\pi\)
0.229681 + 0.973266i \(0.426232\pi\)
\(348\) −6.89111 −0.369402
\(349\) 27.2249 1.45731 0.728657 0.684878i \(-0.240145\pi\)
0.728657 + 0.684878i \(0.240145\pi\)
\(350\) 16.6118 0.887939
\(351\) −25.4459 −1.35820
\(352\) −0.977749 −0.0521142
\(353\) 30.4965 1.62317 0.811584 0.584236i \(-0.198606\pi\)
0.811584 + 0.584236i \(0.198606\pi\)
\(354\) −14.5925 −0.775581
\(355\) −3.00546 −0.159513
\(356\) −14.6218 −0.774956
\(357\) −14.2691 −0.755201
\(358\) 11.1537 0.589491
\(359\) −12.0849 −0.637814 −0.318907 0.947786i \(-0.603316\pi\)
−0.318907 + 0.947786i \(0.603316\pi\)
\(360\) −2.74448 −0.144647
\(361\) 14.7138 0.774409
\(362\) −16.5708 −0.870940
\(363\) 19.5639 1.02684
\(364\) 14.1603 0.742201
\(365\) −25.9390 −1.35771
\(366\) 9.91914 0.518482
\(367\) −23.9765 −1.25157 −0.625783 0.779997i \(-0.715220\pi\)
−0.625783 + 0.779997i \(0.715220\pi\)
\(368\) −1.03892 −0.0541574
\(369\) 6.23510 0.324586
\(370\) −2.17473 −0.113059
\(371\) 18.1701 0.943346
\(372\) −7.27671 −0.377280
\(373\) −17.4513 −0.903592 −0.451796 0.892121i \(-0.649217\pi\)
−0.451796 + 0.892121i \(0.649217\pi\)
\(374\) 2.99549 0.154893
\(375\) −13.1097 −0.676981
\(376\) −6.49858 −0.335139
\(377\) −20.9510 −1.07903
\(378\) 10.2745 0.528462
\(379\) −18.6880 −0.959937 −0.479969 0.877286i \(-0.659352\pi\)
−0.479969 + 0.877286i \(0.659352\pi\)
\(380\) 20.0695 1.02954
\(381\) −34.4644 −1.76567
\(382\) 17.7089 0.906067
\(383\) −7.52543 −0.384532 −0.192266 0.981343i \(-0.561584\pi\)
−0.192266 + 0.981343i \(0.561584\pi\)
\(384\) 1.94782 0.0993994
\(385\) −8.08105 −0.411849
\(386\) 13.2164 0.672695
\(387\) −7.24559 −0.368314
\(388\) −13.1082 −0.665468
\(389\) 7.36501 0.373421 0.186710 0.982415i \(-0.440217\pi\)
0.186710 + 0.982415i \(0.440217\pi\)
\(390\) −39.8701 −2.01890
\(391\) 3.18289 0.160966
\(392\) 1.28239 0.0647702
\(393\) 9.57929 0.483211
\(394\) −12.1174 −0.610465
\(395\) 32.6612 1.64336
\(396\) 0.776344 0.0390128
\(397\) 21.1057 1.05926 0.529632 0.848228i \(-0.322330\pi\)
0.529632 + 0.848228i \(0.322330\pi\)
\(398\) 8.59925 0.431042
\(399\) 27.0433 1.35386
\(400\) 6.94720 0.347360
\(401\) 3.15705 0.157655 0.0788277 0.996888i \(-0.474882\pi\)
0.0788277 + 0.996888i \(0.474882\pi\)
\(402\) 5.72431 0.285503
\(403\) −22.1233 −1.10204
\(404\) −12.8622 −0.639917
\(405\) −37.1625 −1.84662
\(406\) 8.45954 0.419840
\(407\) 0.615178 0.0304932
\(408\) −5.96745 −0.295433
\(409\) −25.4041 −1.25615 −0.628077 0.778151i \(-0.716158\pi\)
−0.628077 + 0.778151i \(0.716158\pi\)
\(410\) −27.1425 −1.34047
\(411\) 8.70701 0.429485
\(412\) 4.69253 0.231184
\(413\) 17.9138 0.881479
\(414\) 0.824914 0.0405423
\(415\) 28.9922 1.42317
\(416\) 5.92195 0.290348
\(417\) −18.9184 −0.926440
\(418\) −5.67716 −0.277679
\(419\) −25.8634 −1.26351 −0.631754 0.775169i \(-0.717665\pi\)
−0.631754 + 0.775169i \(0.717665\pi\)
\(420\) 16.0987 0.785534
\(421\) −18.3138 −0.892559 −0.446280 0.894894i \(-0.647251\pi\)
−0.446280 + 0.894894i \(0.647251\pi\)
\(422\) 15.1078 0.735435
\(423\) 5.15995 0.250885
\(424\) 7.59890 0.369035
\(425\) −21.2838 −1.03242
\(426\) −1.69367 −0.0820583
\(427\) −12.1768 −0.589275
\(428\) −11.1173 −0.537375
\(429\) 11.2783 0.544519
\(430\) 31.5414 1.52106
\(431\) −6.22975 −0.300077 −0.150038 0.988680i \(-0.547940\pi\)
−0.150038 + 0.988680i \(0.547940\pi\)
\(432\) 4.29687 0.206733
\(433\) −27.8348 −1.33765 −0.668827 0.743418i \(-0.733203\pi\)
−0.668827 + 0.743418i \(0.733203\pi\)
\(434\) 8.93291 0.428793
\(435\) −23.8189 −1.14203
\(436\) 6.23740 0.298717
\(437\) −6.03234 −0.288566
\(438\) −14.6174 −0.698445
\(439\) −15.9019 −0.758958 −0.379479 0.925200i \(-0.623897\pi\)
−0.379479 + 0.925200i \(0.623897\pi\)
\(440\) −3.37956 −0.161114
\(441\) −1.01823 −0.0484871
\(442\) −18.1428 −0.862966
\(443\) 0.277743 0.0131959 0.00659797 0.999978i \(-0.497900\pi\)
0.00659797 + 0.999978i \(0.497900\pi\)
\(444\) −1.22553 −0.0581608
\(445\) −50.5400 −2.39583
\(446\) −12.4181 −0.588013
\(447\) −14.2926 −0.676015
\(448\) −2.39115 −0.112971
\(449\) 23.1883 1.09432 0.547162 0.837027i \(-0.315708\pi\)
0.547162 + 0.837027i \(0.315708\pi\)
\(450\) −5.51615 −0.260034
\(451\) 7.67793 0.361540
\(452\) −9.62327 −0.452640
\(453\) 11.1446 0.523619
\(454\) −4.51477 −0.211888
\(455\) 48.9447 2.29456
\(456\) 11.3097 0.529627
\(457\) −10.6967 −0.500368 −0.250184 0.968198i \(-0.580491\pi\)
−0.250184 + 0.968198i \(0.580491\pi\)
\(458\) 29.4052 1.37402
\(459\) −13.1641 −0.614449
\(460\) −3.59100 −0.167431
\(461\) −26.2415 −1.22219 −0.611094 0.791558i \(-0.709270\pi\)
−0.611094 + 0.791558i \(0.709270\pi\)
\(462\) −4.55391 −0.211867
\(463\) 8.58195 0.398837 0.199419 0.979914i \(-0.436095\pi\)
0.199419 + 0.979914i \(0.436095\pi\)
\(464\) 3.53785 0.164241
\(465\) −25.1517 −1.16638
\(466\) 3.90158 0.180737
\(467\) −2.85203 −0.131976 −0.0659881 0.997820i \(-0.521020\pi\)
−0.0659881 + 0.997820i \(0.521020\pi\)
\(468\) −4.70210 −0.217354
\(469\) −7.02718 −0.324485
\(470\) −22.4622 −1.03610
\(471\) −19.5548 −0.901037
\(472\) 7.49169 0.344833
\(473\) −8.92226 −0.410246
\(474\) 18.4055 0.845393
\(475\) 40.3379 1.85083
\(476\) 7.32567 0.335771
\(477\) −6.03361 −0.276260
\(478\) 24.4116 1.11656
\(479\) 8.83196 0.403543 0.201771 0.979433i \(-0.435330\pi\)
0.201771 + 0.979433i \(0.435330\pi\)
\(480\) 6.73259 0.307299
\(481\) −3.72596 −0.169889
\(482\) 26.1321 1.19029
\(483\) −4.83881 −0.220174
\(484\) −10.0440 −0.456546
\(485\) −45.3081 −2.05734
\(486\) −8.05154 −0.365225
\(487\) −6.17488 −0.279811 −0.139905 0.990165i \(-0.544680\pi\)
−0.139905 + 0.990165i \(0.544680\pi\)
\(488\) −5.09242 −0.230523
\(489\) 40.4456 1.82901
\(490\) 4.43253 0.200241
\(491\) 16.0000 0.722070 0.361035 0.932552i \(-0.382424\pi\)
0.361035 + 0.932552i \(0.382424\pi\)
\(492\) −15.2956 −0.689578
\(493\) −10.8388 −0.488153
\(494\) 34.3850 1.54705
\(495\) 2.68341 0.120610
\(496\) 3.73582 0.167743
\(497\) 2.07915 0.0932626
\(498\) 16.3379 0.732120
\(499\) 33.0280 1.47853 0.739267 0.673412i \(-0.235172\pi\)
0.739267 + 0.673412i \(0.235172\pi\)
\(500\) 6.73043 0.300994
\(501\) −23.0024 −1.02767
\(502\) −21.9976 −0.981801
\(503\) 15.6359 0.697171 0.348586 0.937277i \(-0.386662\pi\)
0.348586 + 0.937277i \(0.386662\pi\)
\(504\) 1.89860 0.0845705
\(505\) −44.4577 −1.97834
\(506\) 1.01580 0.0451580
\(507\) −42.9875 −1.90914
\(508\) 17.6938 0.785037
\(509\) 12.7332 0.564391 0.282195 0.959357i \(-0.408937\pi\)
0.282195 + 0.959357i \(0.408937\pi\)
\(510\) −20.6263 −0.913349
\(511\) 17.9443 0.793810
\(512\) −1.00000 −0.0441942
\(513\) 24.9492 1.10153
\(514\) 14.0947 0.621693
\(515\) 16.2196 0.714721
\(516\) 17.7745 0.782477
\(517\) 6.35399 0.279448
\(518\) 1.50446 0.0661021
\(519\) 3.04267 0.133559
\(520\) 20.4691 0.897628
\(521\) −14.2619 −0.624825 −0.312413 0.949947i \(-0.601137\pi\)
−0.312413 + 0.949947i \(0.601137\pi\)
\(522\) −2.80909 −0.122951
\(523\) −19.6422 −0.858894 −0.429447 0.903092i \(-0.641291\pi\)
−0.429447 + 0.903092i \(0.641291\pi\)
\(524\) −4.91795 −0.214842
\(525\) 32.3569 1.41217
\(526\) 14.0607 0.613074
\(527\) −11.4453 −0.498563
\(528\) −1.90448 −0.0828819
\(529\) −21.9206 −0.953072
\(530\) 26.2654 1.14089
\(531\) −5.94848 −0.258142
\(532\) −13.8839 −0.601943
\(533\) −46.5031 −2.01427
\(534\) −28.4808 −1.23248
\(535\) −38.4266 −1.66133
\(536\) −2.93883 −0.126938
\(537\) 21.7254 0.937520
\(538\) 32.4136 1.39745
\(539\) −1.25385 −0.0540072
\(540\) 14.8520 0.639129
\(541\) −34.0235 −1.46278 −0.731392 0.681957i \(-0.761129\pi\)
−0.731392 + 0.681957i \(0.761129\pi\)
\(542\) 1.57480 0.0676433
\(543\) −32.2769 −1.38513
\(544\) 3.06365 0.131353
\(545\) 21.5594 0.923503
\(546\) 27.5817 1.18039
\(547\) 20.3929 0.871939 0.435970 0.899961i \(-0.356405\pi\)
0.435970 + 0.899961i \(0.356405\pi\)
\(548\) −4.47013 −0.190954
\(549\) 4.04344 0.172570
\(550\) −6.79262 −0.289638
\(551\) 20.5420 0.875120
\(552\) −2.02363 −0.0861314
\(553\) −22.5947 −0.960823
\(554\) 0.196864 0.00836394
\(555\) −4.23599 −0.179808
\(556\) 9.71261 0.411906
\(557\) 10.1574 0.430383 0.215192 0.976572i \(-0.430962\pi\)
0.215192 + 0.976572i \(0.430962\pi\)
\(558\) −2.96628 −0.125573
\(559\) 54.0396 2.28563
\(560\) −8.26495 −0.349258
\(561\) 5.83467 0.246340
\(562\) 13.1151 0.553225
\(563\) −11.8407 −0.499027 −0.249514 0.968371i \(-0.580271\pi\)
−0.249514 + 0.968371i \(0.580271\pi\)
\(564\) −12.6581 −0.533002
\(565\) −33.2625 −1.39937
\(566\) −15.0768 −0.633725
\(567\) 25.7087 1.07966
\(568\) 0.869517 0.0364841
\(569\) 1.10203 0.0461995 0.0230998 0.999733i \(-0.492646\pi\)
0.0230998 + 0.999733i \(0.492646\pi\)
\(570\) 39.0918 1.63738
\(571\) −13.9479 −0.583703 −0.291852 0.956464i \(-0.594271\pi\)
−0.291852 + 0.956464i \(0.594271\pi\)
\(572\) −5.79019 −0.242100
\(573\) 34.4938 1.44100
\(574\) 18.7769 0.783733
\(575\) −7.21758 −0.300994
\(576\) 0.794011 0.0330838
\(577\) −10.5434 −0.438928 −0.219464 0.975621i \(-0.570431\pi\)
−0.219464 + 0.975621i \(0.570431\pi\)
\(578\) 7.61402 0.316702
\(579\) 25.7431 1.06985
\(580\) 12.2285 0.507760
\(581\) −20.0565 −0.832084
\(582\) −25.5324 −1.05835
\(583\) −7.42982 −0.307712
\(584\) 7.50447 0.310537
\(585\) −16.2527 −0.671965
\(586\) −23.4079 −0.966972
\(587\) −4.23027 −0.174602 −0.0873010 0.996182i \(-0.527824\pi\)
−0.0873010 + 0.996182i \(0.527824\pi\)
\(588\) 2.49786 0.103010
\(589\) 21.6915 0.893782
\(590\) 25.8948 1.06607
\(591\) −23.6025 −0.970878
\(592\) 0.629177 0.0258590
\(593\) 11.4230 0.469087 0.234543 0.972106i \(-0.424640\pi\)
0.234543 + 0.972106i \(0.424640\pi\)
\(594\) −4.20127 −0.172380
\(595\) 25.3210 1.03806
\(596\) 7.33772 0.300565
\(597\) 16.7498 0.685524
\(598\) −6.15243 −0.251592
\(599\) −31.8719 −1.30225 −0.651125 0.758971i \(-0.725702\pi\)
−0.651125 + 0.758971i \(0.725702\pi\)
\(600\) 13.5319 0.552438
\(601\) 14.7214 0.600500 0.300250 0.953860i \(-0.402930\pi\)
0.300250 + 0.953860i \(0.402930\pi\)
\(602\) −21.8200 −0.889317
\(603\) 2.33346 0.0950259
\(604\) −5.72157 −0.232807
\(605\) −34.7168 −1.41144
\(606\) −25.0532 −1.01772
\(607\) 8.87986 0.360423 0.180211 0.983628i \(-0.442322\pi\)
0.180211 + 0.983628i \(0.442322\pi\)
\(608\) −5.80636 −0.235479
\(609\) 16.4777 0.667710
\(610\) −17.6018 −0.712677
\(611\) −38.4843 −1.55691
\(612\) −2.43258 −0.0983310
\(613\) −12.0865 −0.488168 −0.244084 0.969754i \(-0.578487\pi\)
−0.244084 + 0.969754i \(0.578487\pi\)
\(614\) 21.3899 0.863224
\(615\) −52.8688 −2.13187
\(616\) 2.33795 0.0941986
\(617\) 45.3182 1.82444 0.912221 0.409699i \(-0.134366\pi\)
0.912221 + 0.409699i \(0.134366\pi\)
\(618\) 9.14021 0.367673
\(619\) 10.0733 0.404879 0.202439 0.979295i \(-0.435113\pi\)
0.202439 + 0.979295i \(0.435113\pi\)
\(620\) 12.9127 0.518588
\(621\) −4.46411 −0.179138
\(622\) −3.11928 −0.125072
\(623\) 34.9631 1.40077
\(624\) 11.5349 0.461766
\(625\) −11.4724 −0.458898
\(626\) 17.3323 0.692738
\(627\) −11.0581 −0.441618
\(628\) 10.0393 0.400612
\(629\) −1.92758 −0.0768577
\(630\) 6.56247 0.261455
\(631\) −6.91807 −0.275404 −0.137702 0.990474i \(-0.543972\pi\)
−0.137702 + 0.990474i \(0.543972\pi\)
\(632\) −9.44928 −0.375872
\(633\) 29.4273 1.16963
\(634\) 15.4248 0.612596
\(635\) 61.1582 2.42699
\(636\) 14.8013 0.586910
\(637\) 7.59423 0.300894
\(638\) −3.45913 −0.136948
\(639\) −0.690407 −0.0273121
\(640\) −3.45647 −0.136629
\(641\) 24.8111 0.979979 0.489990 0.871728i \(-0.337001\pi\)
0.489990 + 0.871728i \(0.337001\pi\)
\(642\) −21.6545 −0.854636
\(643\) −4.43907 −0.175060 −0.0875300 0.996162i \(-0.527897\pi\)
−0.0875300 + 0.996162i \(0.527897\pi\)
\(644\) 2.48422 0.0978918
\(645\) 61.4370 2.41908
\(646\) 17.7887 0.699886
\(647\) −23.1463 −0.909973 −0.454987 0.890498i \(-0.650356\pi\)
−0.454987 + 0.890498i \(0.650356\pi\)
\(648\) 10.7516 0.422362
\(649\) −7.32499 −0.287531
\(650\) 41.1410 1.61368
\(651\) 17.3997 0.681949
\(652\) −20.7645 −0.813201
\(653\) −9.62947 −0.376830 −0.188415 0.982089i \(-0.560335\pi\)
−0.188415 + 0.982089i \(0.560335\pi\)
\(654\) 12.1494 0.475077
\(655\) −16.9988 −0.664196
\(656\) 7.85266 0.306595
\(657\) −5.95863 −0.232468
\(658\) 15.5391 0.605778
\(659\) −5.29072 −0.206097 −0.103048 0.994676i \(-0.532860\pi\)
−0.103048 + 0.994676i \(0.532860\pi\)
\(660\) −6.58279 −0.256235
\(661\) −36.7220 −1.42832 −0.714159 0.699983i \(-0.753191\pi\)
−0.714159 + 0.699983i \(0.753191\pi\)
\(662\) −17.1044 −0.664780
\(663\) −35.3390 −1.37245
\(664\) −8.38779 −0.325509
\(665\) −47.9893 −1.86094
\(666\) −0.499574 −0.0193581
\(667\) −3.67554 −0.142318
\(668\) 11.8093 0.456915
\(669\) −24.1882 −0.935171
\(670\) −10.1580 −0.392437
\(671\) 4.97912 0.192217
\(672\) −4.65754 −0.179669
\(673\) 38.3598 1.47866 0.739330 0.673343i \(-0.235142\pi\)
0.739330 + 0.673343i \(0.235142\pi\)
\(674\) −22.4924 −0.866376
\(675\) 29.8512 1.14897
\(676\) 22.0695 0.848827
\(677\) 29.6043 1.13779 0.568894 0.822411i \(-0.307372\pi\)
0.568894 + 0.822411i \(0.307372\pi\)
\(678\) −18.7444 −0.719875
\(679\) 31.3437 1.20286
\(680\) 10.5894 0.406086
\(681\) −8.79396 −0.336985
\(682\) −3.65269 −0.139869
\(683\) 27.8840 1.06695 0.533477 0.845815i \(-0.320885\pi\)
0.533477 + 0.845815i \(0.320885\pi\)
\(684\) 4.61031 0.176280
\(685\) −15.4509 −0.590347
\(686\) −19.8045 −0.756138
\(687\) 57.2761 2.18522
\(688\) −9.12530 −0.347899
\(689\) 45.0003 1.71437
\(690\) −6.99462 −0.266281
\(691\) −18.6111 −0.708001 −0.354001 0.935245i \(-0.615179\pi\)
−0.354001 + 0.935245i \(0.615179\pi\)
\(692\) −1.56209 −0.0593818
\(693\) −1.85636 −0.0705172
\(694\) −8.55698 −0.324818
\(695\) 33.5714 1.27343
\(696\) 6.89111 0.261207
\(697\) −24.0578 −0.911255
\(698\) −27.2249 −1.03048
\(699\) 7.59958 0.287443
\(700\) −16.6118 −0.627867
\(701\) −14.0763 −0.531656 −0.265828 0.964021i \(-0.585645\pi\)
−0.265828 + 0.964021i \(0.585645\pi\)
\(702\) 25.4459 0.960393
\(703\) 3.65323 0.137784
\(704\) 0.977749 0.0368503
\(705\) −43.7523 −1.64781
\(706\) −30.4965 −1.14775
\(707\) 30.7554 1.15668
\(708\) 14.5925 0.548419
\(709\) −1.87960 −0.0705900 −0.0352950 0.999377i \(-0.511237\pi\)
−0.0352950 + 0.999377i \(0.511237\pi\)
\(710\) 3.00546 0.112793
\(711\) 7.50283 0.281378
\(712\) 14.6218 0.547977
\(713\) −3.88121 −0.145353
\(714\) 14.2691 0.534007
\(715\) −20.0136 −0.748467
\(716\) −11.1537 −0.416833
\(717\) 47.5494 1.77576
\(718\) 12.0849 0.451003
\(719\) −33.8694 −1.26312 −0.631558 0.775329i \(-0.717584\pi\)
−0.631558 + 0.775329i \(0.717584\pi\)
\(720\) 2.74448 0.102281
\(721\) −11.2206 −0.417875
\(722\) −14.7138 −0.547590
\(723\) 50.9008 1.89302
\(724\) 16.5708 0.615847
\(725\) 24.5781 0.912809
\(726\) −19.5639 −0.726086
\(727\) −25.7838 −0.956266 −0.478133 0.878287i \(-0.658686\pi\)
−0.478133 + 0.878287i \(0.658686\pi\)
\(728\) −14.1603 −0.524815
\(729\) 16.5718 0.613769
\(730\) 25.9390 0.960044
\(731\) 27.9568 1.03402
\(732\) −9.91914 −0.366622
\(733\) −12.3942 −0.457788 −0.228894 0.973451i \(-0.573511\pi\)
−0.228894 + 0.973451i \(0.573511\pi\)
\(734\) 23.9765 0.884990
\(735\) 8.63378 0.318462
\(736\) 1.03892 0.0382951
\(737\) 2.87344 0.105844
\(738\) −6.23510 −0.229517
\(739\) 14.3947 0.529519 0.264760 0.964314i \(-0.414707\pi\)
0.264760 + 0.964314i \(0.414707\pi\)
\(740\) 2.17473 0.0799448
\(741\) 66.9758 2.46042
\(742\) −18.1701 −0.667046
\(743\) 43.5855 1.59900 0.799498 0.600668i \(-0.205099\pi\)
0.799498 + 0.600668i \(0.205099\pi\)
\(744\) 7.27671 0.266777
\(745\) 25.3626 0.929214
\(746\) 17.4513 0.638936
\(747\) 6.66000 0.243677
\(748\) −2.99549 −0.109526
\(749\) 26.5832 0.971328
\(750\) 13.1097 0.478698
\(751\) −34.7991 −1.26984 −0.634918 0.772579i \(-0.718966\pi\)
−0.634918 + 0.772579i \(0.718966\pi\)
\(752\) 6.49858 0.236979
\(753\) −42.8474 −1.56145
\(754\) 20.9510 0.762990
\(755\) −19.7764 −0.719738
\(756\) −10.2745 −0.373679
\(757\) 28.3582 1.03070 0.515349 0.856981i \(-0.327662\pi\)
0.515349 + 0.856981i \(0.327662\pi\)
\(758\) 18.6880 0.678778
\(759\) 1.97860 0.0718188
\(760\) −20.0695 −0.727997
\(761\) −5.87340 −0.212911 −0.106455 0.994317i \(-0.533950\pi\)
−0.106455 + 0.994317i \(0.533950\pi\)
\(762\) 34.4644 1.24851
\(763\) −14.9146 −0.539944
\(764\) −17.7089 −0.640686
\(765\) −8.40813 −0.303997
\(766\) 7.52543 0.271905
\(767\) 44.3654 1.60194
\(768\) −1.94782 −0.0702860
\(769\) −16.8641 −0.608136 −0.304068 0.952650i \(-0.598345\pi\)
−0.304068 + 0.952650i \(0.598345\pi\)
\(770\) 8.08105 0.291221
\(771\) 27.4541 0.988734
\(772\) −13.2164 −0.475667
\(773\) 29.0197 1.04376 0.521882 0.853018i \(-0.325230\pi\)
0.521882 + 0.853018i \(0.325230\pi\)
\(774\) 7.24559 0.260438
\(775\) 25.9535 0.932275
\(776\) 13.1082 0.470557
\(777\) 2.93042 0.105128
\(778\) −7.36501 −0.264048
\(779\) 45.5953 1.63362
\(780\) 39.8701 1.42758
\(781\) −0.850170 −0.0304215
\(782\) −3.18289 −0.113820
\(783\) 15.2017 0.543264
\(784\) −1.28239 −0.0457995
\(785\) 34.7006 1.23852
\(786\) −9.57929 −0.341682
\(787\) −52.5340 −1.87263 −0.936317 0.351156i \(-0.885789\pi\)
−0.936317 + 0.351156i \(0.885789\pi\)
\(788\) 12.1174 0.431664
\(789\) 27.3877 0.975027
\(790\) −32.6612 −1.16203
\(791\) 23.0107 0.818166
\(792\) −0.776344 −0.0275862
\(793\) −30.1571 −1.07091
\(794\) −21.1057 −0.749013
\(795\) 51.1603 1.81447
\(796\) −8.59925 −0.304792
\(797\) −37.8357 −1.34021 −0.670105 0.742267i \(-0.733751\pi\)
−0.670105 + 0.742267i \(0.733751\pi\)
\(798\) −27.0433 −0.957324
\(799\) −19.9094 −0.704344
\(800\) −6.94720 −0.245620
\(801\) −11.6099 −0.410216
\(802\) −3.15705 −0.111479
\(803\) −7.33749 −0.258934
\(804\) −5.72431 −0.201881
\(805\) 8.58662 0.302639
\(806\) 22.1233 0.779261
\(807\) 63.1358 2.22249
\(808\) 12.8622 0.452489
\(809\) 17.3244 0.609093 0.304547 0.952497i \(-0.401495\pi\)
0.304547 + 0.952497i \(0.401495\pi\)
\(810\) 37.1625 1.30576
\(811\) 52.0696 1.82841 0.914206 0.405249i \(-0.132815\pi\)
0.914206 + 0.405249i \(0.132815\pi\)
\(812\) −8.45954 −0.296872
\(813\) 3.06742 0.107579
\(814\) −0.615178 −0.0215620
\(815\) −71.7719 −2.51406
\(816\) 5.96745 0.208903
\(817\) −52.9848 −1.85370
\(818\) 25.4041 0.888235
\(819\) 11.2434 0.392877
\(820\) 27.1425 0.947857
\(821\) 21.2633 0.742094 0.371047 0.928614i \(-0.378999\pi\)
0.371047 + 0.928614i \(0.378999\pi\)
\(822\) −8.70701 −0.303692
\(823\) −20.8761 −0.727696 −0.363848 0.931458i \(-0.618537\pi\)
−0.363848 + 0.931458i \(0.618537\pi\)
\(824\) −4.69253 −0.163472
\(825\) −13.2308 −0.460638
\(826\) −17.9138 −0.623300
\(827\) 45.9878 1.59915 0.799577 0.600564i \(-0.205057\pi\)
0.799577 + 0.600564i \(0.205057\pi\)
\(828\) −0.824914 −0.0286677
\(829\) −31.4132 −1.09103 −0.545513 0.838102i \(-0.683665\pi\)
−0.545513 + 0.838102i \(0.683665\pi\)
\(830\) −28.9922 −1.00633
\(831\) 0.383455 0.0133019
\(832\) −5.92195 −0.205307
\(833\) 3.92879 0.136124
\(834\) 18.9184 0.655092
\(835\) 40.8185 1.41258
\(836\) 5.67716 0.196349
\(837\) 16.0523 0.554850
\(838\) 25.8634 0.893435
\(839\) 46.5165 1.60593 0.802964 0.596027i \(-0.203255\pi\)
0.802964 + 0.596027i \(0.203255\pi\)
\(840\) −16.0987 −0.555457
\(841\) −16.4836 −0.568400
\(842\) 18.3138 0.631135
\(843\) 25.5458 0.879844
\(844\) −15.1078 −0.520031
\(845\) 76.2826 2.62420
\(846\) −5.15995 −0.177403
\(847\) 24.0168 0.825226
\(848\) −7.59890 −0.260947
\(849\) −29.3669 −1.00787
\(850\) 21.2838 0.730028
\(851\) −0.653664 −0.0224073
\(852\) 1.69367 0.0580240
\(853\) 20.9271 0.716530 0.358265 0.933620i \(-0.383368\pi\)
0.358265 + 0.933620i \(0.383368\pi\)
\(854\) 12.1768 0.416680
\(855\) 15.9354 0.544980
\(856\) 11.1173 0.379982
\(857\) 34.5692 1.18086 0.590431 0.807088i \(-0.298958\pi\)
0.590431 + 0.807088i \(0.298958\pi\)
\(858\) −11.2783 −0.385033
\(859\) −38.4860 −1.31313 −0.656563 0.754272i \(-0.727990\pi\)
−0.656563 + 0.754272i \(0.727990\pi\)
\(860\) −31.5414 −1.07555
\(861\) 36.5741 1.24644
\(862\) 6.22975 0.212186
\(863\) −9.71330 −0.330645 −0.165322 0.986240i \(-0.552866\pi\)
−0.165322 + 0.986240i \(0.552866\pi\)
\(864\) −4.29687 −0.146183
\(865\) −5.39932 −0.183582
\(866\) 27.8348 0.945864
\(867\) 14.8308 0.503679
\(868\) −8.93291 −0.303203
\(869\) 9.23903 0.313412
\(870\) 23.8189 0.807537
\(871\) −17.4036 −0.589698
\(872\) −6.23740 −0.211225
\(873\) −10.4081 −0.352259
\(874\) 6.03234 0.204047
\(875\) −16.0935 −0.544059
\(876\) 14.6174 0.493875
\(877\) −30.8135 −1.04050 −0.520248 0.854015i \(-0.674161\pi\)
−0.520248 + 0.854015i \(0.674161\pi\)
\(878\) 15.9019 0.536665
\(879\) −45.5945 −1.53786
\(880\) 3.37956 0.113925
\(881\) −13.7664 −0.463802 −0.231901 0.972739i \(-0.574495\pi\)
−0.231901 + 0.972739i \(0.574495\pi\)
\(882\) 1.01823 0.0342855
\(883\) −36.2822 −1.22099 −0.610496 0.792019i \(-0.709030\pi\)
−0.610496 + 0.792019i \(0.709030\pi\)
\(884\) 18.1428 0.610209
\(885\) 50.4385 1.69547
\(886\) −0.277743 −0.00933094
\(887\) −13.7336 −0.461128 −0.230564 0.973057i \(-0.574057\pi\)
−0.230564 + 0.973057i \(0.574057\pi\)
\(888\) 1.22553 0.0411259
\(889\) −42.3087 −1.41899
\(890\) 50.5400 1.69410
\(891\) −10.5124 −0.352177
\(892\) 12.4181 0.415788
\(893\) 37.7331 1.26269
\(894\) 14.2926 0.478015
\(895\) −38.5524 −1.28867
\(896\) 2.39115 0.0798828
\(897\) −11.9838 −0.400129
\(898\) −23.1883 −0.773804
\(899\) 13.2168 0.440804
\(900\) 5.51615 0.183872
\(901\) 23.2804 0.775582
\(902\) −7.67793 −0.255647
\(903\) −42.5015 −1.41436
\(904\) 9.62327 0.320065
\(905\) 57.2764 1.90393
\(906\) −11.1446 −0.370254
\(907\) 45.4762 1.51001 0.755006 0.655717i \(-0.227634\pi\)
0.755006 + 0.655717i \(0.227634\pi\)
\(908\) 4.51477 0.149828
\(909\) −10.2127 −0.338734
\(910\) −48.9447 −1.62250
\(911\) −18.1413 −0.601048 −0.300524 0.953774i \(-0.597162\pi\)
−0.300524 + 0.953774i \(0.597162\pi\)
\(912\) −11.3097 −0.374503
\(913\) 8.20116 0.271419
\(914\) 10.6967 0.353814
\(915\) −34.2852 −1.13343
\(916\) −29.4052 −0.971576
\(917\) 11.7596 0.388335
\(918\) 13.1641 0.434481
\(919\) 54.6117 1.80147 0.900737 0.434365i \(-0.143027\pi\)
0.900737 + 0.434365i \(0.143027\pi\)
\(920\) 3.59100 0.118392
\(921\) 41.6636 1.37286
\(922\) 26.2415 0.864217
\(923\) 5.14924 0.169489
\(924\) 4.55391 0.149813
\(925\) 4.37102 0.143718
\(926\) −8.58195 −0.282020
\(927\) 3.72592 0.122375
\(928\) −3.53785 −0.116136
\(929\) 37.5139 1.23079 0.615396 0.788218i \(-0.288996\pi\)
0.615396 + 0.788218i \(0.288996\pi\)
\(930\) 25.1517 0.824758
\(931\) −7.44599 −0.244032
\(932\) −3.90158 −0.127800
\(933\) −6.07581 −0.198913
\(934\) 2.85203 0.0933213
\(935\) −10.3538 −0.338606
\(936\) 4.70210 0.153693
\(937\) −26.8071 −0.875751 −0.437876 0.899036i \(-0.644269\pi\)
−0.437876 + 0.899036i \(0.644269\pi\)
\(938\) 7.02718 0.229446
\(939\) 33.7602 1.10172
\(940\) 22.4622 0.732635
\(941\) 21.7970 0.710561 0.355281 0.934760i \(-0.384385\pi\)
0.355281 + 0.934760i \(0.384385\pi\)
\(942\) 19.5548 0.637129
\(943\) −8.15828 −0.265670
\(944\) −7.49169 −0.243834
\(945\) −35.5135 −1.15525
\(946\) 8.92226 0.290088
\(947\) 27.3554 0.888932 0.444466 0.895796i \(-0.353393\pi\)
0.444466 + 0.895796i \(0.353393\pi\)
\(948\) −18.4055 −0.597783
\(949\) 44.4411 1.44262
\(950\) −40.3379 −1.30873
\(951\) 30.0447 0.974266
\(952\) −7.32567 −0.237426
\(953\) −24.9250 −0.807401 −0.403701 0.914891i \(-0.632276\pi\)
−0.403701 + 0.914891i \(0.632276\pi\)
\(954\) 6.03361 0.195345
\(955\) −61.2104 −1.98072
\(956\) −24.4116 −0.789526
\(957\) −6.73777 −0.217801
\(958\) −8.83196 −0.285348
\(959\) 10.6888 0.345158
\(960\) −6.73259 −0.217293
\(961\) −17.0437 −0.549796
\(962\) 3.72596 0.120130
\(963\) −8.82726 −0.284455
\(964\) −26.1321 −0.841660
\(965\) −45.6820 −1.47056
\(966\) 4.83881 0.155686
\(967\) 21.7212 0.698507 0.349253 0.937028i \(-0.386435\pi\)
0.349253 + 0.937028i \(0.386435\pi\)
\(968\) 10.0440 0.322827
\(969\) 34.6492 1.11309
\(970\) 45.3081 1.45476
\(971\) 44.0353 1.41316 0.706580 0.707633i \(-0.250237\pi\)
0.706580 + 0.707633i \(0.250237\pi\)
\(972\) 8.05154 0.258253
\(973\) −23.2243 −0.744538
\(974\) 6.17488 0.197856
\(975\) 80.1353 2.56638
\(976\) 5.09242 0.163005
\(977\) 39.2032 1.25422 0.627111 0.778930i \(-0.284237\pi\)
0.627111 + 0.778930i \(0.284237\pi\)
\(978\) −40.4456 −1.29331
\(979\) −14.2965 −0.456918
\(980\) −4.43253 −0.141592
\(981\) 4.95257 0.158123
\(982\) −16.0000 −0.510580
\(983\) 24.5197 0.782056 0.391028 0.920379i \(-0.372120\pi\)
0.391028 + 0.920379i \(0.372120\pi\)
\(984\) 15.2956 0.487605
\(985\) 41.8834 1.33452
\(986\) 10.8388 0.345176
\(987\) 30.2674 0.963423
\(988\) −34.3850 −1.09393
\(989\) 9.48046 0.301461
\(990\) −2.68341 −0.0852844
\(991\) −19.3469 −0.614575 −0.307288 0.951617i \(-0.599421\pi\)
−0.307288 + 0.951617i \(0.599421\pi\)
\(992\) −3.73582 −0.118612
\(993\) −33.3162 −1.05726
\(994\) −2.07915 −0.0659466
\(995\) −29.7231 −0.942285
\(996\) −16.3379 −0.517687
\(997\) −32.0044 −1.01359 −0.506794 0.862067i \(-0.669170\pi\)
−0.506794 + 0.862067i \(0.669170\pi\)
\(998\) −33.0280 −1.04548
\(999\) 2.70349 0.0855348
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 4022.2.a.d.1.9 37
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4022.2.a.d.1.9 37 1.1 even 1 trivial