Properties

Label 6034.2.a.p.1.11
Level $6034$
Weight $2$
Character 6034.1
Self dual yes
Analytic conductor $48.182$
Analytic rank $0$
Dimension $27$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6034,2,Mod(1,6034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6034, 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("6034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6034.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: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(27\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 6034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.394534 q^{3} +1.00000 q^{4} +4.36123 q^{5} +0.394534 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.84434 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.394534 q^{3} +1.00000 q^{4} +4.36123 q^{5} +0.394534 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.84434 q^{9} -4.36123 q^{10} -1.35764 q^{11} -0.394534 q^{12} -3.09098 q^{13} -1.00000 q^{14} -1.72065 q^{15} +1.00000 q^{16} -3.52186 q^{17} +2.84434 q^{18} +3.98583 q^{19} +4.36123 q^{20} -0.394534 q^{21} +1.35764 q^{22} -0.903008 q^{23} +0.394534 q^{24} +14.0203 q^{25} +3.09098 q^{26} +2.30579 q^{27} +1.00000 q^{28} +2.54612 q^{29} +1.72065 q^{30} -5.16014 q^{31} -1.00000 q^{32} +0.535636 q^{33} +3.52186 q^{34} +4.36123 q^{35} -2.84434 q^{36} -9.36407 q^{37} -3.98583 q^{38} +1.21950 q^{39} -4.36123 q^{40} -0.259660 q^{41} +0.394534 q^{42} +7.42347 q^{43} -1.35764 q^{44} -12.4048 q^{45} +0.903008 q^{46} -8.45701 q^{47} -0.394534 q^{48} +1.00000 q^{49} -14.0203 q^{50} +1.38949 q^{51} -3.09098 q^{52} +14.4498 q^{53} -2.30579 q^{54} -5.92099 q^{55} -1.00000 q^{56} -1.57255 q^{57} -2.54612 q^{58} +7.10247 q^{59} -1.72065 q^{60} +8.93330 q^{61} +5.16014 q^{62} -2.84434 q^{63} +1.00000 q^{64} -13.4805 q^{65} -0.535636 q^{66} -8.46286 q^{67} -3.52186 q^{68} +0.356268 q^{69} -4.36123 q^{70} +3.07426 q^{71} +2.84434 q^{72} +7.04932 q^{73} +9.36407 q^{74} -5.53150 q^{75} +3.98583 q^{76} -1.35764 q^{77} -1.21950 q^{78} +10.4298 q^{79} +4.36123 q^{80} +7.62331 q^{81} +0.259660 q^{82} +5.97823 q^{83} -0.394534 q^{84} -15.3596 q^{85} -7.42347 q^{86} -1.00453 q^{87} +1.35764 q^{88} +16.5792 q^{89} +12.4048 q^{90} -3.09098 q^{91} -0.903008 q^{92} +2.03585 q^{93} +8.45701 q^{94} +17.3831 q^{95} +0.394534 q^{96} -7.70375 q^{97} -1.00000 q^{98} +3.86160 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 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
\(3\) −0.394534 −0.227784 −0.113892 0.993493i \(-0.536332\pi\)
−0.113892 + 0.993493i \(0.536332\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.36123 1.95040 0.975201 0.221322i \(-0.0710373\pi\)
0.975201 + 0.221322i \(0.0710373\pi\)
\(6\) 0.394534 0.161068
\(7\) 1.00000 0.377964
\(8\) −1.00000 −0.353553
\(9\) −2.84434 −0.948114
\(10\) −4.36123 −1.37914
\(11\) −1.35764 −0.409344 −0.204672 0.978831i \(-0.565613\pi\)
−0.204672 + 0.978831i \(0.565613\pi\)
\(12\) −0.394534 −0.113892
\(13\) −3.09098 −0.857284 −0.428642 0.903474i \(-0.641008\pi\)
−0.428642 + 0.903474i \(0.641008\pi\)
\(14\) −1.00000 −0.267261
\(15\) −1.72065 −0.444271
\(16\) 1.00000 0.250000
\(17\) −3.52186 −0.854176 −0.427088 0.904210i \(-0.640460\pi\)
−0.427088 + 0.904210i \(0.640460\pi\)
\(18\) 2.84434 0.670418
\(19\) 3.98583 0.914413 0.457206 0.889361i \(-0.348850\pi\)
0.457206 + 0.889361i \(0.348850\pi\)
\(20\) 4.36123 0.975201
\(21\) −0.394534 −0.0860944
\(22\) 1.35764 0.289450
\(23\) −0.903008 −0.188290 −0.0941451 0.995558i \(-0.530012\pi\)
−0.0941451 + 0.995558i \(0.530012\pi\)
\(24\) 0.394534 0.0805339
\(25\) 14.0203 2.80407
\(26\) 3.09098 0.606191
\(27\) 2.30579 0.443750
\(28\) 1.00000 0.188982
\(29\) 2.54612 0.472803 0.236402 0.971655i \(-0.424032\pi\)
0.236402 + 0.971655i \(0.424032\pi\)
\(30\) 1.72065 0.314147
\(31\) −5.16014 −0.926789 −0.463395 0.886152i \(-0.653369\pi\)
−0.463395 + 0.886152i \(0.653369\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.535636 0.0932423
\(34\) 3.52186 0.603993
\(35\) 4.36123 0.737182
\(36\) −2.84434 −0.474057
\(37\) −9.36407 −1.53944 −0.769722 0.638380i \(-0.779605\pi\)
−0.769722 + 0.638380i \(0.779605\pi\)
\(38\) −3.98583 −0.646587
\(39\) 1.21950 0.195276
\(40\) −4.36123 −0.689571
\(41\) −0.259660 −0.0405521 −0.0202760 0.999794i \(-0.506455\pi\)
−0.0202760 + 0.999794i \(0.506455\pi\)
\(42\) 0.394534 0.0608779
\(43\) 7.42347 1.13207 0.566034 0.824382i \(-0.308477\pi\)
0.566034 + 0.824382i \(0.308477\pi\)
\(44\) −1.35764 −0.204672
\(45\) −12.4048 −1.84920
\(46\) 0.903008 0.133141
\(47\) −8.45701 −1.23358 −0.616791 0.787127i \(-0.711568\pi\)
−0.616791 + 0.787127i \(0.711568\pi\)
\(48\) −0.394534 −0.0569461
\(49\) 1.00000 0.142857
\(50\) −14.0203 −1.98277
\(51\) 1.38949 0.194568
\(52\) −3.09098 −0.428642
\(53\) 14.4498 1.98484 0.992418 0.122906i \(-0.0392213\pi\)
0.992418 + 0.122906i \(0.0392213\pi\)
\(54\) −2.30579 −0.313779
\(55\) −5.92099 −0.798386
\(56\) −1.00000 −0.133631
\(57\) −1.57255 −0.208289
\(58\) −2.54612 −0.334322
\(59\) 7.10247 0.924663 0.462332 0.886707i \(-0.347013\pi\)
0.462332 + 0.886707i \(0.347013\pi\)
\(60\) −1.72065 −0.222136
\(61\) 8.93330 1.14379 0.571896 0.820326i \(-0.306208\pi\)
0.571896 + 0.820326i \(0.306208\pi\)
\(62\) 5.16014 0.655339
\(63\) −2.84434 −0.358354
\(64\) 1.00000 0.125000
\(65\) −13.4805 −1.67205
\(66\) −0.535636 −0.0659323
\(67\) −8.46286 −1.03390 −0.516952 0.856015i \(-0.672933\pi\)
−0.516952 + 0.856015i \(0.672933\pi\)
\(68\) −3.52186 −0.427088
\(69\) 0.356268 0.0428896
\(70\) −4.36123 −0.521267
\(71\) 3.07426 0.364847 0.182424 0.983220i \(-0.441606\pi\)
0.182424 + 0.983220i \(0.441606\pi\)
\(72\) 2.84434 0.335209
\(73\) 7.04932 0.825061 0.412530 0.910944i \(-0.364645\pi\)
0.412530 + 0.910944i \(0.364645\pi\)
\(74\) 9.36407 1.08855
\(75\) −5.53150 −0.638722
\(76\) 3.98583 0.457206
\(77\) −1.35764 −0.154718
\(78\) −1.21950 −0.138081
\(79\) 10.4298 1.17344 0.586722 0.809788i \(-0.300418\pi\)
0.586722 + 0.809788i \(0.300418\pi\)
\(80\) 4.36123 0.487600
\(81\) 7.62331 0.847035
\(82\) 0.259660 0.0286747
\(83\) 5.97823 0.656196 0.328098 0.944644i \(-0.393592\pi\)
0.328098 + 0.944644i \(0.393592\pi\)
\(84\) −0.394534 −0.0430472
\(85\) −15.3596 −1.66599
\(86\) −7.42347 −0.800493
\(87\) −1.00453 −0.107697
\(88\) 1.35764 0.144725
\(89\) 16.5792 1.75739 0.878697 0.477380i \(-0.158413\pi\)
0.878697 + 0.477380i \(0.158413\pi\)
\(90\) 12.4048 1.30758
\(91\) −3.09098 −0.324023
\(92\) −0.903008 −0.0941451
\(93\) 2.03585 0.211108
\(94\) 8.45701 0.872274
\(95\) 17.3831 1.78347
\(96\) 0.394534 0.0402670
\(97\) −7.70375 −0.782198 −0.391099 0.920349i \(-0.627905\pi\)
−0.391099 + 0.920349i \(0.627905\pi\)
\(98\) −1.00000 −0.101015
\(99\) 3.86160 0.388105
\(100\) 14.0203 1.40203
\(101\) −16.4046 −1.63232 −0.816161 0.577824i \(-0.803902\pi\)
−0.816161 + 0.577824i \(0.803902\pi\)
\(102\) −1.38949 −0.137580
\(103\) 10.8336 1.06746 0.533731 0.845654i \(-0.320789\pi\)
0.533731 + 0.845654i \(0.320789\pi\)
\(104\) 3.09098 0.303096
\(105\) −1.72065 −0.167919
\(106\) −14.4498 −1.40349
\(107\) 17.4950 1.69130 0.845651 0.533736i \(-0.179212\pi\)
0.845651 + 0.533736i \(0.179212\pi\)
\(108\) 2.30579 0.221875
\(109\) 8.89206 0.851705 0.425853 0.904793i \(-0.359974\pi\)
0.425853 + 0.904793i \(0.359974\pi\)
\(110\) 5.92099 0.564544
\(111\) 3.69445 0.350661
\(112\) 1.00000 0.0944911
\(113\) 7.02869 0.661203 0.330602 0.943770i \(-0.392748\pi\)
0.330602 + 0.943770i \(0.392748\pi\)
\(114\) 1.57255 0.147283
\(115\) −3.93823 −0.367241
\(116\) 2.54612 0.236402
\(117\) 8.79181 0.812803
\(118\) −7.10247 −0.653836
\(119\) −3.52186 −0.322848
\(120\) 1.72065 0.157074
\(121\) −9.15681 −0.832437
\(122\) −8.93330 −0.808783
\(123\) 0.102445 0.00923713
\(124\) −5.16014 −0.463395
\(125\) 39.3397 3.51865
\(126\) 2.84434 0.253394
\(127\) 20.9612 1.86001 0.930003 0.367552i \(-0.119804\pi\)
0.930003 + 0.367552i \(0.119804\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.92881 −0.257867
\(130\) 13.4805 1.18232
\(131\) 16.5111 1.44258 0.721290 0.692633i \(-0.243549\pi\)
0.721290 + 0.692633i \(0.243549\pi\)
\(132\) 0.535636 0.0466211
\(133\) 3.98583 0.345615
\(134\) 8.46286 0.731080
\(135\) 10.0561 0.865491
\(136\) 3.52186 0.301997
\(137\) −1.63908 −0.140036 −0.0700179 0.997546i \(-0.522306\pi\)
−0.0700179 + 0.997546i \(0.522306\pi\)
\(138\) −0.356268 −0.0303275
\(139\) −14.4616 −1.22662 −0.613310 0.789843i \(-0.710162\pi\)
−0.613310 + 0.789843i \(0.710162\pi\)
\(140\) 4.36123 0.368591
\(141\) 3.33658 0.280991
\(142\) −3.07426 −0.257986
\(143\) 4.19645 0.350924
\(144\) −2.84434 −0.237029
\(145\) 11.1042 0.922156
\(146\) −7.04932 −0.583406
\(147\) −0.394534 −0.0325406
\(148\) −9.36407 −0.769722
\(149\) 23.3780 1.91520 0.957601 0.288097i \(-0.0930225\pi\)
0.957601 + 0.288097i \(0.0930225\pi\)
\(150\) 5.53150 0.451645
\(151\) 5.96165 0.485152 0.242576 0.970132i \(-0.422008\pi\)
0.242576 + 0.970132i \(0.422008\pi\)
\(152\) −3.98583 −0.323294
\(153\) 10.0174 0.809856
\(154\) 1.35764 0.109402
\(155\) −22.5046 −1.80761
\(156\) 1.21950 0.0976380
\(157\) 19.5839 1.56297 0.781483 0.623926i \(-0.214463\pi\)
0.781483 + 0.623926i \(0.214463\pi\)
\(158\) −10.4298 −0.829750
\(159\) −5.70095 −0.452115
\(160\) −4.36123 −0.344786
\(161\) −0.903008 −0.0711670
\(162\) −7.62331 −0.598944
\(163\) 3.94704 0.309156 0.154578 0.987981i \(-0.450598\pi\)
0.154578 + 0.987981i \(0.450598\pi\)
\(164\) −0.259660 −0.0202760
\(165\) 2.33603 0.181860
\(166\) −5.97823 −0.464001
\(167\) −17.9985 −1.39277 −0.696384 0.717670i \(-0.745209\pi\)
−0.696384 + 0.717670i \(0.745209\pi\)
\(168\) 0.394534 0.0304390
\(169\) −3.44584 −0.265064
\(170\) 15.3596 1.17803
\(171\) −11.3371 −0.866968
\(172\) 7.42347 0.566034
\(173\) −15.2602 −1.16021 −0.580105 0.814542i \(-0.696988\pi\)
−0.580105 + 0.814542i \(0.696988\pi\)
\(174\) 1.00453 0.0761534
\(175\) 14.0203 1.05984
\(176\) −1.35764 −0.102336
\(177\) −2.80217 −0.210624
\(178\) −16.5792 −1.24267
\(179\) 23.3598 1.74599 0.872997 0.487726i \(-0.162173\pi\)
0.872997 + 0.487726i \(0.162173\pi\)
\(180\) −12.4048 −0.924602
\(181\) −3.89088 −0.289207 −0.144603 0.989490i \(-0.546191\pi\)
−0.144603 + 0.989490i \(0.546191\pi\)
\(182\) 3.09098 0.229119
\(183\) −3.52449 −0.260538
\(184\) 0.903008 0.0665706
\(185\) −40.8389 −3.00253
\(186\) −2.03585 −0.149276
\(187\) 4.78142 0.349652
\(188\) −8.45701 −0.616791
\(189\) 2.30579 0.167722
\(190\) −17.3831 −1.26110
\(191\) −6.48366 −0.469141 −0.234571 0.972099i \(-0.575368\pi\)
−0.234571 + 0.972099i \(0.575368\pi\)
\(192\) −0.394534 −0.0284731
\(193\) −24.9775 −1.79792 −0.898962 0.438028i \(-0.855677\pi\)
−0.898962 + 0.438028i \(0.855677\pi\)
\(194\) 7.70375 0.553097
\(195\) 5.31851 0.380866
\(196\) 1.00000 0.0714286
\(197\) −6.06704 −0.432259 −0.216129 0.976365i \(-0.569343\pi\)
−0.216129 + 0.976365i \(0.569343\pi\)
\(198\) −3.86160 −0.274432
\(199\) 16.3363 1.15805 0.579025 0.815310i \(-0.303434\pi\)
0.579025 + 0.815310i \(0.303434\pi\)
\(200\) −14.0203 −0.991387
\(201\) 3.33889 0.235507
\(202\) 16.4046 1.15423
\(203\) 2.54612 0.178703
\(204\) 1.38949 0.0972839
\(205\) −1.13244 −0.0790929
\(206\) −10.8336 −0.754810
\(207\) 2.56846 0.178521
\(208\) −3.09098 −0.214321
\(209\) −5.41133 −0.374310
\(210\) 1.72065 0.118736
\(211\) 11.3837 0.783683 0.391842 0.920033i \(-0.371838\pi\)
0.391842 + 0.920033i \(0.371838\pi\)
\(212\) 14.4498 0.992418
\(213\) −1.21290 −0.0831065
\(214\) −17.4950 −1.19593
\(215\) 32.3754 2.20799
\(216\) −2.30579 −0.156889
\(217\) −5.16014 −0.350293
\(218\) −8.89206 −0.602246
\(219\) −2.78120 −0.187936
\(220\) −5.92099 −0.399193
\(221\) 10.8860 0.732271
\(222\) −3.69445 −0.247955
\(223\) −5.11012 −0.342199 −0.171100 0.985254i \(-0.554732\pi\)
−0.171100 + 0.985254i \(0.554732\pi\)
\(224\) −1.00000 −0.0668153
\(225\) −39.8786 −2.65857
\(226\) −7.02869 −0.467541
\(227\) 2.63322 0.174773 0.0873864 0.996174i \(-0.472149\pi\)
0.0873864 + 0.996174i \(0.472149\pi\)
\(228\) −1.57255 −0.104144
\(229\) 18.2735 1.20755 0.603773 0.797156i \(-0.293663\pi\)
0.603773 + 0.797156i \(0.293663\pi\)
\(230\) 3.93823 0.259679
\(231\) 0.535636 0.0352423
\(232\) −2.54612 −0.167161
\(233\) −18.5926 −1.21804 −0.609022 0.793154i \(-0.708438\pi\)
−0.609022 + 0.793154i \(0.708438\pi\)
\(234\) −8.79181 −0.574739
\(235\) −36.8830 −2.40598
\(236\) 7.10247 0.462332
\(237\) −4.11491 −0.267292
\(238\) 3.52186 0.228288
\(239\) −17.6002 −1.13846 −0.569232 0.822177i \(-0.692759\pi\)
−0.569232 + 0.822177i \(0.692759\pi\)
\(240\) −1.72065 −0.111068
\(241\) 14.6839 0.945874 0.472937 0.881096i \(-0.343194\pi\)
0.472937 + 0.881096i \(0.343194\pi\)
\(242\) 9.15681 0.588622
\(243\) −9.92504 −0.636691
\(244\) 8.93330 0.571896
\(245\) 4.36123 0.278629
\(246\) −0.102445 −0.00653164
\(247\) −12.3201 −0.783911
\(248\) 5.16014 0.327669
\(249\) −2.35862 −0.149471
\(250\) −39.3397 −2.48806
\(251\) −20.5652 −1.29807 −0.649033 0.760761i \(-0.724826\pi\)
−0.649033 + 0.760761i \(0.724826\pi\)
\(252\) −2.84434 −0.179177
\(253\) 1.22596 0.0770755
\(254\) −20.9612 −1.31522
\(255\) 6.05990 0.379485
\(256\) 1.00000 0.0625000
\(257\) −11.0028 −0.686334 −0.343167 0.939274i \(-0.611500\pi\)
−0.343167 + 0.939274i \(0.611500\pi\)
\(258\) 2.92881 0.182340
\(259\) −9.36407 −0.581855
\(260\) −13.4805 −0.836024
\(261\) −7.24205 −0.448271
\(262\) −16.5111 −1.02006
\(263\) 0.890541 0.0549131 0.0274566 0.999623i \(-0.491259\pi\)
0.0274566 + 0.999623i \(0.491259\pi\)
\(264\) −0.535636 −0.0329661
\(265\) 63.0190 3.87123
\(266\) −3.98583 −0.244387
\(267\) −6.54107 −0.400307
\(268\) −8.46286 −0.516952
\(269\) −8.01173 −0.488484 −0.244242 0.969714i \(-0.578539\pi\)
−0.244242 + 0.969714i \(0.578539\pi\)
\(270\) −10.0561 −0.611994
\(271\) −4.76535 −0.289475 −0.144737 0.989470i \(-0.546234\pi\)
−0.144737 + 0.989470i \(0.546234\pi\)
\(272\) −3.52186 −0.213544
\(273\) 1.21950 0.0738074
\(274\) 1.63908 0.0990203
\(275\) −19.0346 −1.14783
\(276\) 0.356268 0.0214448
\(277\) −20.6479 −1.24061 −0.620305 0.784360i \(-0.712991\pi\)
−0.620305 + 0.784360i \(0.712991\pi\)
\(278\) 14.4616 0.867351
\(279\) 14.6772 0.878702
\(280\) −4.36123 −0.260633
\(281\) −27.4714 −1.63880 −0.819402 0.573219i \(-0.805694\pi\)
−0.819402 + 0.573219i \(0.805694\pi\)
\(282\) −3.33658 −0.198690
\(283\) 26.4442 1.57195 0.785973 0.618261i \(-0.212162\pi\)
0.785973 + 0.618261i \(0.212162\pi\)
\(284\) 3.07426 0.182424
\(285\) −6.85824 −0.406247
\(286\) −4.19645 −0.248141
\(287\) −0.259660 −0.0153273
\(288\) 2.84434 0.167605
\(289\) −4.59653 −0.270384
\(290\) −11.1042 −0.652063
\(291\) 3.03939 0.178172
\(292\) 7.04932 0.412530
\(293\) −6.05329 −0.353637 −0.176818 0.984243i \(-0.556581\pi\)
−0.176818 + 0.984243i \(0.556581\pi\)
\(294\) 0.394534 0.0230097
\(295\) 30.9755 1.80346
\(296\) 9.36407 0.544275
\(297\) −3.13044 −0.181647
\(298\) −23.3780 −1.35425
\(299\) 2.79118 0.161418
\(300\) −5.53150 −0.319361
\(301\) 7.42347 0.427882
\(302\) −5.96165 −0.343054
\(303\) 6.47219 0.371818
\(304\) 3.98583 0.228603
\(305\) 38.9602 2.23085
\(306\) −10.0174 −0.572655
\(307\) 14.3662 0.819924 0.409962 0.912103i \(-0.365542\pi\)
0.409962 + 0.912103i \(0.365542\pi\)
\(308\) −1.35764 −0.0773588
\(309\) −4.27421 −0.243151
\(310\) 22.5046 1.27817
\(311\) 5.12859 0.290816 0.145408 0.989372i \(-0.453551\pi\)
0.145408 + 0.989372i \(0.453551\pi\)
\(312\) −1.21950 −0.0690405
\(313\) −1.99777 −0.112920 −0.0564602 0.998405i \(-0.517981\pi\)
−0.0564602 + 0.998405i \(0.517981\pi\)
\(314\) −19.5839 −1.10518
\(315\) −12.4048 −0.698933
\(316\) 10.4298 0.586722
\(317\) 31.6073 1.77524 0.887622 0.460573i \(-0.152356\pi\)
0.887622 + 0.460573i \(0.152356\pi\)
\(318\) 5.70095 0.319693
\(319\) −3.45672 −0.193539
\(320\) 4.36123 0.243800
\(321\) −6.90236 −0.385252
\(322\) 0.903008 0.0503227
\(323\) −14.0375 −0.781069
\(324\) 7.62331 0.423517
\(325\) −43.3366 −2.40388
\(326\) −3.94704 −0.218606
\(327\) −3.50822 −0.194005
\(328\) 0.259660 0.0143373
\(329\) −8.45701 −0.466250
\(330\) −2.33603 −0.128594
\(331\) −3.66999 −0.201721 −0.100861 0.994901i \(-0.532160\pi\)
−0.100861 + 0.994901i \(0.532160\pi\)
\(332\) 5.97823 0.328098
\(333\) 26.6346 1.45957
\(334\) 17.9985 0.984835
\(335\) −36.9085 −2.01653
\(336\) −0.394534 −0.0215236
\(337\) 3.64064 0.198318 0.0991592 0.995072i \(-0.468385\pi\)
0.0991592 + 0.995072i \(0.468385\pi\)
\(338\) 3.44584 0.187429
\(339\) −2.77306 −0.150612
\(340\) −15.3596 −0.832993
\(341\) 7.00563 0.379376
\(342\) 11.3371 0.613039
\(343\) 1.00000 0.0539949
\(344\) −7.42347 −0.400247
\(345\) 1.55376 0.0836519
\(346\) 15.2602 0.820392
\(347\) −20.9412 −1.12418 −0.562091 0.827075i \(-0.690003\pi\)
−0.562091 + 0.827075i \(0.690003\pi\)
\(348\) −1.00453 −0.0538486
\(349\) 17.5132 0.937460 0.468730 0.883341i \(-0.344712\pi\)
0.468730 + 0.883341i \(0.344712\pi\)
\(350\) −14.0203 −0.749418
\(351\) −7.12716 −0.380420
\(352\) 1.35764 0.0723626
\(353\) 18.2425 0.970951 0.485475 0.874250i \(-0.338647\pi\)
0.485475 + 0.874250i \(0.338647\pi\)
\(354\) 2.80217 0.148934
\(355\) 13.4075 0.711599
\(356\) 16.5792 0.878697
\(357\) 1.38949 0.0735397
\(358\) −23.3598 −1.23460
\(359\) 25.9880 1.37159 0.685796 0.727793i \(-0.259454\pi\)
0.685796 + 0.727793i \(0.259454\pi\)
\(360\) 12.4048 0.653792
\(361\) −3.11314 −0.163850
\(362\) 3.89088 0.204500
\(363\) 3.61267 0.189616
\(364\) −3.09098 −0.162011
\(365\) 30.7437 1.60920
\(366\) 3.52449 0.184228
\(367\) 16.2164 0.846491 0.423246 0.906015i \(-0.360891\pi\)
0.423246 + 0.906015i \(0.360891\pi\)
\(368\) −0.903008 −0.0470725
\(369\) 0.738562 0.0384480
\(370\) 40.8389 2.12311
\(371\) 14.4498 0.750198
\(372\) 2.03585 0.105554
\(373\) −26.3843 −1.36613 −0.683063 0.730359i \(-0.739353\pi\)
−0.683063 + 0.730359i \(0.739353\pi\)
\(374\) −4.78142 −0.247241
\(375\) −15.5209 −0.801494
\(376\) 8.45701 0.436137
\(377\) −7.87002 −0.405327
\(378\) −2.30579 −0.118597
\(379\) −12.7881 −0.656880 −0.328440 0.944525i \(-0.606523\pi\)
−0.328440 + 0.944525i \(0.606523\pi\)
\(380\) 17.3831 0.891736
\(381\) −8.26991 −0.423680
\(382\) 6.48366 0.331733
\(383\) −8.81531 −0.450441 −0.225221 0.974308i \(-0.572310\pi\)
−0.225221 + 0.974308i \(0.572310\pi\)
\(384\) 0.394534 0.0201335
\(385\) −5.92099 −0.301762
\(386\) 24.9775 1.27132
\(387\) −21.1149 −1.07333
\(388\) −7.70375 −0.391099
\(389\) −15.9743 −0.809928 −0.404964 0.914333i \(-0.632716\pi\)
−0.404964 + 0.914333i \(0.632716\pi\)
\(390\) −5.31851 −0.269313
\(391\) 3.18026 0.160833
\(392\) −1.00000 −0.0505076
\(393\) −6.51419 −0.328597
\(394\) 6.06704 0.305653
\(395\) 45.4868 2.28869
\(396\) 3.86160 0.194053
\(397\) −30.9786 −1.55477 −0.777386 0.629024i \(-0.783455\pi\)
−0.777386 + 0.629024i \(0.783455\pi\)
\(398\) −16.3363 −0.818864
\(399\) −1.57255 −0.0787258
\(400\) 14.0203 0.701016
\(401\) −4.67504 −0.233460 −0.116730 0.993164i \(-0.537241\pi\)
−0.116730 + 0.993164i \(0.537241\pi\)
\(402\) −3.33889 −0.166529
\(403\) 15.9499 0.794521
\(404\) −16.4046 −0.816161
\(405\) 33.2470 1.65206
\(406\) −2.54612 −0.126362
\(407\) 12.7131 0.630163
\(408\) −1.38949 −0.0687901
\(409\) −15.6899 −0.775813 −0.387907 0.921699i \(-0.626802\pi\)
−0.387907 + 0.921699i \(0.626802\pi\)
\(410\) 1.13244 0.0559271
\(411\) 0.646672 0.0318980
\(412\) 10.8336 0.533731
\(413\) 7.10247 0.349490
\(414\) −2.56846 −0.126233
\(415\) 26.0724 1.27985
\(416\) 3.09098 0.151548
\(417\) 5.70561 0.279405
\(418\) 5.41133 0.264677
\(419\) −17.6854 −0.863987 −0.431993 0.901877i \(-0.642190\pi\)
−0.431993 + 0.901877i \(0.642190\pi\)
\(420\) −1.72065 −0.0839593
\(421\) 24.2089 1.17987 0.589935 0.807451i \(-0.299153\pi\)
0.589935 + 0.807451i \(0.299153\pi\)
\(422\) −11.3837 −0.554148
\(423\) 24.0546 1.16958
\(424\) −14.4498 −0.701746
\(425\) −49.3776 −2.39516
\(426\) 1.21290 0.0587652
\(427\) 8.93330 0.432313
\(428\) 17.4950 0.845651
\(429\) −1.65564 −0.0799351
\(430\) −32.3754 −1.56128
\(431\) −1.00000 −0.0481683
\(432\) 2.30579 0.110938
\(433\) −15.1216 −0.726698 −0.363349 0.931653i \(-0.618367\pi\)
−0.363349 + 0.931653i \(0.618367\pi\)
\(434\) 5.16014 0.247695
\(435\) −4.38100 −0.210053
\(436\) 8.89206 0.425853
\(437\) −3.59924 −0.172175
\(438\) 2.78120 0.132891
\(439\) −9.71123 −0.463492 −0.231746 0.972776i \(-0.574444\pi\)
−0.231746 + 0.972776i \(0.574444\pi\)
\(440\) 5.92099 0.282272
\(441\) −2.84434 −0.135445
\(442\) −10.8860 −0.517794
\(443\) 18.4989 0.878908 0.439454 0.898265i \(-0.355172\pi\)
0.439454 + 0.898265i \(0.355172\pi\)
\(444\) 3.69445 0.175331
\(445\) 72.3058 3.42762
\(446\) 5.11012 0.241971
\(447\) −9.22343 −0.436253
\(448\) 1.00000 0.0472456
\(449\) −4.48720 −0.211764 −0.105882 0.994379i \(-0.533767\pi\)
−0.105882 + 0.994379i \(0.533767\pi\)
\(450\) 39.8786 1.87990
\(451\) 0.352525 0.0165998
\(452\) 7.02869 0.330602
\(453\) −2.35207 −0.110510
\(454\) −2.63322 −0.123583
\(455\) −13.4805 −0.631975
\(456\) 1.57255 0.0736413
\(457\) −20.0945 −0.939980 −0.469990 0.882672i \(-0.655742\pi\)
−0.469990 + 0.882672i \(0.655742\pi\)
\(458\) −18.2735 −0.853864
\(459\) −8.12067 −0.379040
\(460\) −3.93823 −0.183621
\(461\) 10.5920 0.493319 0.246660 0.969102i \(-0.420667\pi\)
0.246660 + 0.969102i \(0.420667\pi\)
\(462\) −0.535636 −0.0249200
\(463\) −27.8033 −1.29213 −0.646064 0.763284i \(-0.723586\pi\)
−0.646064 + 0.763284i \(0.723586\pi\)
\(464\) 2.54612 0.118201
\(465\) 8.87882 0.411746
\(466\) 18.5926 0.861287
\(467\) 30.3975 1.40663 0.703314 0.710879i \(-0.251703\pi\)
0.703314 + 0.710879i \(0.251703\pi\)
\(468\) 8.79181 0.406402
\(469\) −8.46286 −0.390779
\(470\) 36.8830 1.70128
\(471\) −7.72652 −0.356019
\(472\) −7.10247 −0.326918
\(473\) −10.0784 −0.463406
\(474\) 4.11491 0.189004
\(475\) 55.8827 2.56407
\(476\) −3.52186 −0.161424
\(477\) −41.1003 −1.88185
\(478\) 17.6002 0.805015
\(479\) 25.6190 1.17056 0.585280 0.810831i \(-0.300985\pi\)
0.585280 + 0.810831i \(0.300985\pi\)
\(480\) 1.72065 0.0785368
\(481\) 28.9442 1.31974
\(482\) −14.6839 −0.668834
\(483\) 0.356268 0.0162107
\(484\) −9.15681 −0.416219
\(485\) −33.5978 −1.52560
\(486\) 9.92504 0.450209
\(487\) 9.16834 0.415457 0.207728 0.978187i \(-0.433393\pi\)
0.207728 + 0.978187i \(0.433393\pi\)
\(488\) −8.93330 −0.404392
\(489\) −1.55724 −0.0704209
\(490\) −4.36123 −0.197020
\(491\) 20.2230 0.912650 0.456325 0.889813i \(-0.349165\pi\)
0.456325 + 0.889813i \(0.349165\pi\)
\(492\) 0.102445 0.00461857
\(493\) −8.96708 −0.403857
\(494\) 12.3201 0.554309
\(495\) 16.8413 0.756961
\(496\) −5.16014 −0.231697
\(497\) 3.07426 0.137899
\(498\) 2.35862 0.105692
\(499\) −30.2185 −1.35277 −0.676384 0.736549i \(-0.736454\pi\)
−0.676384 + 0.736549i \(0.736454\pi\)
\(500\) 39.3397 1.75933
\(501\) 7.10103 0.317251
\(502\) 20.5652 0.917871
\(503\) 2.33522 0.104122 0.0520611 0.998644i \(-0.483421\pi\)
0.0520611 + 0.998644i \(0.483421\pi\)
\(504\) 2.84434 0.126697
\(505\) −71.5444 −3.18368
\(506\) −1.22596 −0.0545006
\(507\) 1.35950 0.0603775
\(508\) 20.9612 0.930003
\(509\) 5.10020 0.226063 0.113031 0.993591i \(-0.463944\pi\)
0.113031 + 0.993591i \(0.463944\pi\)
\(510\) −6.05990 −0.268337
\(511\) 7.04932 0.311844
\(512\) −1.00000 −0.0441942
\(513\) 9.19050 0.405771
\(514\) 11.0028 0.485312
\(515\) 47.2477 2.08198
\(516\) −2.92881 −0.128934
\(517\) 11.4816 0.504960
\(518\) 9.36407 0.411434
\(519\) 6.02066 0.264278
\(520\) 13.4805 0.591158
\(521\) 11.8819 0.520558 0.260279 0.965533i \(-0.416186\pi\)
0.260279 + 0.965533i \(0.416186\pi\)
\(522\) 7.24205 0.316976
\(523\) −13.4111 −0.586428 −0.293214 0.956047i \(-0.594725\pi\)
−0.293214 + 0.956047i \(0.594725\pi\)
\(524\) 16.5111 0.721290
\(525\) −5.53150 −0.241414
\(526\) −0.890541 −0.0388294
\(527\) 18.1733 0.791641
\(528\) 0.535636 0.0233106
\(529\) −22.1846 −0.964547
\(530\) −63.0190 −2.73737
\(531\) −20.2019 −0.876687
\(532\) 3.98583 0.172808
\(533\) 0.802604 0.0347647
\(534\) 6.54107 0.283060
\(535\) 76.2996 3.29872
\(536\) 8.46286 0.365540
\(537\) −9.21624 −0.397710
\(538\) 8.01173 0.345410
\(539\) −1.35764 −0.0584778
\(540\) 10.0561 0.432745
\(541\) −11.2452 −0.483471 −0.241735 0.970342i \(-0.577717\pi\)
−0.241735 + 0.970342i \(0.577717\pi\)
\(542\) 4.76535 0.204689
\(543\) 1.53508 0.0658768
\(544\) 3.52186 0.150998
\(545\) 38.7803 1.66117
\(546\) −1.21950 −0.0521897
\(547\) −28.5990 −1.22280 −0.611402 0.791320i \(-0.709394\pi\)
−0.611402 + 0.791320i \(0.709394\pi\)
\(548\) −1.63908 −0.0700179
\(549\) −25.4094 −1.08445
\(550\) 19.0346 0.811637
\(551\) 10.1484 0.432337
\(552\) −0.356268 −0.0151638
\(553\) 10.4298 0.443520
\(554\) 20.6479 0.877244
\(555\) 16.1123 0.683930
\(556\) −14.4616 −0.613310
\(557\) −14.1575 −0.599874 −0.299937 0.953959i \(-0.596966\pi\)
−0.299937 + 0.953959i \(0.596966\pi\)
\(558\) −14.6772 −0.621336
\(559\) −22.9458 −0.970504
\(560\) 4.36123 0.184296
\(561\) −1.88643 −0.0796453
\(562\) 27.4714 1.15881
\(563\) 4.75532 0.200413 0.100206 0.994967i \(-0.468050\pi\)
0.100206 + 0.994967i \(0.468050\pi\)
\(564\) 3.33658 0.140495
\(565\) 30.6537 1.28961
\(566\) −26.4442 −1.11153
\(567\) 7.62331 0.320149
\(568\) −3.07426 −0.128993
\(569\) −1.94720 −0.0816309 −0.0408155 0.999167i \(-0.512996\pi\)
−0.0408155 + 0.999167i \(0.512996\pi\)
\(570\) 6.85824 0.287260
\(571\) 6.19322 0.259178 0.129589 0.991568i \(-0.458634\pi\)
0.129589 + 0.991568i \(0.458634\pi\)
\(572\) 4.19645 0.175462
\(573\) 2.55803 0.106863
\(574\) 0.259660 0.0108380
\(575\) −12.6605 −0.527978
\(576\) −2.84434 −0.118514
\(577\) −5.67958 −0.236444 −0.118222 0.992987i \(-0.537719\pi\)
−0.118222 + 0.992987i \(0.537719\pi\)
\(578\) 4.59653 0.191190
\(579\) 9.85449 0.409539
\(580\) 11.1042 0.461078
\(581\) 5.97823 0.248019
\(582\) −3.03939 −0.125987
\(583\) −19.6177 −0.812482
\(584\) −7.04932 −0.291703
\(585\) 38.3431 1.58529
\(586\) 6.05329 0.250059
\(587\) 43.8327 1.80917 0.904584 0.426295i \(-0.140181\pi\)
0.904584 + 0.426295i \(0.140181\pi\)
\(588\) −0.394534 −0.0162703
\(589\) −20.5675 −0.847468
\(590\) −30.9755 −1.27524
\(591\) 2.39365 0.0984618
\(592\) −9.36407 −0.384861
\(593\) −11.1452 −0.457678 −0.228839 0.973464i \(-0.573493\pi\)
−0.228839 + 0.973464i \(0.573493\pi\)
\(594\) 3.13044 0.128444
\(595\) −15.3596 −0.629683
\(596\) 23.3780 0.957601
\(597\) −6.44523 −0.263786
\(598\) −2.79118 −0.114140
\(599\) −14.4273 −0.589484 −0.294742 0.955577i \(-0.595234\pi\)
−0.294742 + 0.955577i \(0.595234\pi\)
\(600\) 5.53150 0.225822
\(601\) −18.8864 −0.770394 −0.385197 0.922834i \(-0.625866\pi\)
−0.385197 + 0.922834i \(0.625866\pi\)
\(602\) −7.42347 −0.302558
\(603\) 24.0713 0.980258
\(604\) 5.96165 0.242576
\(605\) −39.9349 −1.62359
\(606\) −6.47219 −0.262915
\(607\) −9.84799 −0.399718 −0.199859 0.979825i \(-0.564048\pi\)
−0.199859 + 0.979825i \(0.564048\pi\)
\(608\) −3.98583 −0.161647
\(609\) −1.00453 −0.0407057
\(610\) −38.9602 −1.57745
\(611\) 26.1405 1.05753
\(612\) 10.0174 0.404928
\(613\) 32.0775 1.29560 0.647798 0.761812i \(-0.275690\pi\)
0.647798 + 0.761812i \(0.275690\pi\)
\(614\) −14.3662 −0.579774
\(615\) 0.446785 0.0180161
\(616\) 1.35764 0.0547010
\(617\) 29.0669 1.17019 0.585096 0.810964i \(-0.301057\pi\)
0.585096 + 0.810964i \(0.301057\pi\)
\(618\) 4.27421 0.171934
\(619\) 3.16253 0.127113 0.0635565 0.997978i \(-0.479756\pi\)
0.0635565 + 0.997978i \(0.479756\pi\)
\(620\) −22.5046 −0.903805
\(621\) −2.08215 −0.0835538
\(622\) −5.12859 −0.205638
\(623\) 16.5792 0.664233
\(624\) 1.21950 0.0488190
\(625\) 101.468 4.05872
\(626\) 1.99777 0.0798468
\(627\) 2.13496 0.0852619
\(628\) 19.5839 0.781483
\(629\) 32.9789 1.31495
\(630\) 12.4048 0.494220
\(631\) −38.8808 −1.54782 −0.773909 0.633296i \(-0.781701\pi\)
−0.773909 + 0.633296i \(0.781701\pi\)
\(632\) −10.4298 −0.414875
\(633\) −4.49124 −0.178511
\(634\) −31.6073 −1.25529
\(635\) 91.4166 3.62776
\(636\) −5.70095 −0.226057
\(637\) −3.09098 −0.122469
\(638\) 3.45672 0.136853
\(639\) −8.74424 −0.345917
\(640\) −4.36123 −0.172393
\(641\) 31.6863 1.25153 0.625767 0.780010i \(-0.284786\pi\)
0.625767 + 0.780010i \(0.284786\pi\)
\(642\) 6.90236 0.272415
\(643\) −19.9290 −0.785923 −0.392961 0.919555i \(-0.628549\pi\)
−0.392961 + 0.919555i \(0.628549\pi\)
\(644\) −0.903008 −0.0355835
\(645\) −12.7732 −0.502945
\(646\) 14.0375 0.552299
\(647\) −37.0848 −1.45795 −0.728977 0.684538i \(-0.760004\pi\)
−0.728977 + 0.684538i \(0.760004\pi\)
\(648\) −7.62331 −0.299472
\(649\) −9.64262 −0.378506
\(650\) 43.3366 1.69980
\(651\) 2.03585 0.0797914
\(652\) 3.94704 0.154578
\(653\) −21.6565 −0.847485 −0.423743 0.905783i \(-0.639284\pi\)
−0.423743 + 0.905783i \(0.639284\pi\)
\(654\) 3.50822 0.137182
\(655\) 72.0086 2.81361
\(656\) −0.259660 −0.0101380
\(657\) −20.0507 −0.782252
\(658\) 8.45701 0.329689
\(659\) −1.11710 −0.0435160 −0.0217580 0.999763i \(-0.506926\pi\)
−0.0217580 + 0.999763i \(0.506926\pi\)
\(660\) 2.33603 0.0909299
\(661\) −10.2585 −0.399009 −0.199505 0.979897i \(-0.563933\pi\)
−0.199505 + 0.979897i \(0.563933\pi\)
\(662\) 3.66999 0.142638
\(663\) −4.29490 −0.166800
\(664\) −5.97823 −0.232000
\(665\) 17.3831 0.674089
\(666\) −26.6346 −1.03207
\(667\) −2.29917 −0.0890242
\(668\) −17.9985 −0.696384
\(669\) 2.01612 0.0779476
\(670\) 36.9085 1.42590
\(671\) −12.1282 −0.468205
\(672\) 0.394534 0.0152195
\(673\) 28.6171 1.10311 0.551555 0.834139i \(-0.314035\pi\)
0.551555 + 0.834139i \(0.314035\pi\)
\(674\) −3.64064 −0.140232
\(675\) 32.3280 1.24430
\(676\) −3.44584 −0.132532
\(677\) −9.77999 −0.375875 −0.187938 0.982181i \(-0.560180\pi\)
−0.187938 + 0.982181i \(0.560180\pi\)
\(678\) 2.77306 0.106499
\(679\) −7.70375 −0.295643
\(680\) 15.3596 0.589015
\(681\) −1.03889 −0.0398105
\(682\) −7.00563 −0.268259
\(683\) 22.4568 0.859286 0.429643 0.902999i \(-0.358639\pi\)
0.429643 + 0.902999i \(0.358639\pi\)
\(684\) −11.3371 −0.433484
\(685\) −7.14839 −0.273126
\(686\) −1.00000 −0.0381802
\(687\) −7.20951 −0.275060
\(688\) 7.42347 0.283017
\(689\) −44.6641 −1.70157
\(690\) −1.55376 −0.0591508
\(691\) 48.9818 1.86335 0.931677 0.363287i \(-0.118346\pi\)
0.931677 + 0.363287i \(0.118346\pi\)
\(692\) −15.2602 −0.580105
\(693\) 3.86160 0.146690
\(694\) 20.9412 0.794917
\(695\) −63.0705 −2.39240
\(696\) 1.00453 0.0380767
\(697\) 0.914485 0.0346386
\(698\) −17.5132 −0.662885
\(699\) 7.33542 0.277451
\(700\) 14.0203 0.529919
\(701\) 1.43535 0.0542124 0.0271062 0.999633i \(-0.491371\pi\)
0.0271062 + 0.999633i \(0.491371\pi\)
\(702\) 7.12716 0.268997
\(703\) −37.3236 −1.40769
\(704\) −1.35764 −0.0511681
\(705\) 14.5516 0.548045
\(706\) −18.2425 −0.686566
\(707\) −16.4046 −0.616960
\(708\) −2.80217 −0.105312
\(709\) 8.47048 0.318116 0.159058 0.987269i \(-0.449154\pi\)
0.159058 + 0.987269i \(0.449154\pi\)
\(710\) −13.4075 −0.503176
\(711\) −29.6659 −1.11256
\(712\) −16.5792 −0.621333
\(713\) 4.65965 0.174505
\(714\) −1.38949 −0.0520004
\(715\) 18.3017 0.684444
\(716\) 23.3598 0.872997
\(717\) 6.94389 0.259324
\(718\) −25.9880 −0.969863
\(719\) −17.9697 −0.670158 −0.335079 0.942190i \(-0.608763\pi\)
−0.335079 + 0.942190i \(0.608763\pi\)
\(720\) −12.4048 −0.462301
\(721\) 10.8336 0.403463
\(722\) 3.11314 0.115859
\(723\) −5.79331 −0.215455
\(724\) −3.89088 −0.144603
\(725\) 35.6975 1.32577
\(726\) −3.61267 −0.134079
\(727\) 43.2500 1.60405 0.802027 0.597287i \(-0.203755\pi\)
0.802027 + 0.597287i \(0.203755\pi\)
\(728\) 3.09098 0.114559
\(729\) −18.9542 −0.702007
\(730\) −30.7437 −1.13788
\(731\) −26.1444 −0.966985
\(732\) −3.52449 −0.130269
\(733\) −28.3661 −1.04772 −0.523862 0.851803i \(-0.675509\pi\)
−0.523862 + 0.851803i \(0.675509\pi\)
\(734\) −16.2164 −0.598560
\(735\) −1.72065 −0.0634673
\(736\) 0.903008 0.0332853
\(737\) 11.4895 0.423223
\(738\) −0.738562 −0.0271869
\(739\) 34.1770 1.25722 0.628610 0.777721i \(-0.283624\pi\)
0.628610 + 0.777721i \(0.283624\pi\)
\(740\) −40.8389 −1.50127
\(741\) 4.86071 0.178563
\(742\) −14.4498 −0.530470
\(743\) −39.2682 −1.44061 −0.720305 0.693657i \(-0.755998\pi\)
−0.720305 + 0.693657i \(0.755998\pi\)
\(744\) −2.03585 −0.0746380
\(745\) 101.957 3.73541
\(746\) 26.3843 0.965998
\(747\) −17.0041 −0.622149
\(748\) 4.78142 0.174826
\(749\) 17.4950 0.639252
\(750\) 15.5209 0.566742
\(751\) 13.7769 0.502727 0.251363 0.967893i \(-0.419121\pi\)
0.251363 + 0.967893i \(0.419121\pi\)
\(752\) −8.45701 −0.308395
\(753\) 8.11368 0.295679
\(754\) 7.87002 0.286609
\(755\) 26.0001 0.946241
\(756\) 2.30579 0.0838609
\(757\) 34.6043 1.25771 0.628857 0.777521i \(-0.283523\pi\)
0.628857 + 0.777521i \(0.283523\pi\)
\(758\) 12.7881 0.464485
\(759\) −0.483684 −0.0175566
\(760\) −17.3831 −0.630552
\(761\) −28.1535 −1.02056 −0.510282 0.860007i \(-0.670459\pi\)
−0.510282 + 0.860007i \(0.670459\pi\)
\(762\) 8.26991 0.299587
\(763\) 8.89206 0.321914
\(764\) −6.48366 −0.234571
\(765\) 43.6880 1.57954
\(766\) 8.81531 0.318510
\(767\) −21.9536 −0.792699
\(768\) −0.394534 −0.0142365
\(769\) −47.7602 −1.72228 −0.861138 0.508372i \(-0.830248\pi\)
−0.861138 + 0.508372i \(0.830248\pi\)
\(770\) 5.92099 0.213378
\(771\) 4.34097 0.156336
\(772\) −24.9775 −0.898962
\(773\) 38.5450 1.38637 0.693183 0.720762i \(-0.256208\pi\)
0.693183 + 0.720762i \(0.256208\pi\)
\(774\) 21.1149 0.758959
\(775\) −72.3469 −2.59878
\(776\) 7.70375 0.276549
\(777\) 3.69445 0.132537
\(778\) 15.9743 0.572705
\(779\) −1.03496 −0.0370813
\(780\) 5.31851 0.190433
\(781\) −4.17374 −0.149348
\(782\) −3.18026 −0.113726
\(783\) 5.87083 0.209806
\(784\) 1.00000 0.0357143
\(785\) 85.4100 3.04841
\(786\) 6.51419 0.232353
\(787\) 45.8605 1.63475 0.817375 0.576107i \(-0.195429\pi\)
0.817375 + 0.576107i \(0.195429\pi\)
\(788\) −6.06704 −0.216129
\(789\) −0.351349 −0.0125083
\(790\) −45.4868 −1.61835
\(791\) 7.02869 0.249911
\(792\) −3.86160 −0.137216
\(793\) −27.6127 −0.980554
\(794\) 30.9786 1.09939
\(795\) −24.8632 −0.881805
\(796\) 16.3363 0.579025
\(797\) 25.9398 0.918833 0.459417 0.888221i \(-0.348058\pi\)
0.459417 + 0.888221i \(0.348058\pi\)
\(798\) 1.57255 0.0556676
\(799\) 29.7844 1.05370
\(800\) −14.0203 −0.495693
\(801\) −47.1570 −1.66621
\(802\) 4.67504 0.165081
\(803\) −9.57045 −0.337734
\(804\) 3.33889 0.117754
\(805\) −3.93823 −0.138804
\(806\) −15.9499 −0.561811
\(807\) 3.16090 0.111269
\(808\) 16.4046 0.577113
\(809\) −9.18215 −0.322827 −0.161414 0.986887i \(-0.551605\pi\)
−0.161414 + 0.986887i \(0.551605\pi\)
\(810\) −33.2470 −1.16818
\(811\) 0.639239 0.0224467 0.0112234 0.999937i \(-0.496427\pi\)
0.0112234 + 0.999937i \(0.496427\pi\)
\(812\) 2.54612 0.0893514
\(813\) 1.88009 0.0659378
\(814\) −12.7131 −0.445592
\(815\) 17.2139 0.602978
\(816\) 1.38949 0.0486420
\(817\) 29.5887 1.03518
\(818\) 15.6899 0.548583
\(819\) 8.79181 0.307211
\(820\) −1.13244 −0.0395464
\(821\) −48.8106 −1.70350 −0.851751 0.523947i \(-0.824459\pi\)
−0.851751 + 0.523947i \(0.824459\pi\)
\(822\) −0.646672 −0.0225553
\(823\) 27.7749 0.968172 0.484086 0.875020i \(-0.339152\pi\)
0.484086 + 0.875020i \(0.339152\pi\)
\(824\) −10.8336 −0.377405
\(825\) 7.50979 0.261457
\(826\) −7.10247 −0.247127
\(827\) 39.4657 1.37236 0.686178 0.727434i \(-0.259287\pi\)
0.686178 + 0.727434i \(0.259287\pi\)
\(828\) 2.56846 0.0892603
\(829\) −14.3461 −0.498262 −0.249131 0.968470i \(-0.580145\pi\)
−0.249131 + 0.968470i \(0.580145\pi\)
\(830\) −26.0724 −0.904988
\(831\) 8.14629 0.282592
\(832\) −3.09098 −0.107160
\(833\) −3.52186 −0.122025
\(834\) −5.70561 −0.197569
\(835\) −78.4957 −2.71646
\(836\) −5.41133 −0.187155
\(837\) −11.8982 −0.411263
\(838\) 17.6854 0.610931
\(839\) 42.7812 1.47697 0.738486 0.674269i \(-0.235541\pi\)
0.738486 + 0.674269i \(0.235541\pi\)
\(840\) 1.72065 0.0593682
\(841\) −22.5173 −0.776457
\(842\) −24.2089 −0.834294
\(843\) 10.8384 0.373294
\(844\) 11.3837 0.391842
\(845\) −15.0281 −0.516982
\(846\) −24.0546 −0.827016
\(847\) −9.15681 −0.314632
\(848\) 14.4498 0.496209
\(849\) −10.4332 −0.358065
\(850\) 49.3776 1.69364
\(851\) 8.45583 0.289862
\(852\) −1.21290 −0.0415533
\(853\) 16.2227 0.555455 0.277727 0.960660i \(-0.410419\pi\)
0.277727 + 0.960660i \(0.410419\pi\)
\(854\) −8.93330 −0.305691
\(855\) −49.4436 −1.69093
\(856\) −17.4950 −0.597966
\(857\) −26.5321 −0.906318 −0.453159 0.891430i \(-0.649703\pi\)
−0.453159 + 0.891430i \(0.649703\pi\)
\(858\) 1.65564 0.0565227
\(859\) −27.0108 −0.921598 −0.460799 0.887505i \(-0.652437\pi\)
−0.460799 + 0.887505i \(0.652437\pi\)
\(860\) 32.3754 1.10399
\(861\) 0.102445 0.00349131
\(862\) 1.00000 0.0340601
\(863\) 23.6051 0.803528 0.401764 0.915743i \(-0.368397\pi\)
0.401764 + 0.915743i \(0.368397\pi\)
\(864\) −2.30579 −0.0784447
\(865\) −66.5531 −2.26287
\(866\) 15.1216 0.513853
\(867\) 1.81349 0.0615893
\(868\) −5.16014 −0.175147
\(869\) −14.1599 −0.480343
\(870\) 4.38100 0.148530
\(871\) 26.1585 0.886349
\(872\) −8.89206 −0.301123
\(873\) 21.9121 0.741613
\(874\) 3.59924 0.121746
\(875\) 39.3397 1.32993
\(876\) −2.78120 −0.0939680
\(877\) −37.5779 −1.26891 −0.634457 0.772958i \(-0.718776\pi\)
−0.634457 + 0.772958i \(0.718776\pi\)
\(878\) 9.71123 0.327738
\(879\) 2.38823 0.0805529
\(880\) −5.92099 −0.199597
\(881\) −26.0606 −0.878003 −0.439001 0.898486i \(-0.644668\pi\)
−0.439001 + 0.898486i \(0.644668\pi\)
\(882\) 2.84434 0.0957740
\(883\) −45.9346 −1.54582 −0.772911 0.634515i \(-0.781200\pi\)
−0.772911 + 0.634515i \(0.781200\pi\)
\(884\) 10.8860 0.366135
\(885\) −12.2209 −0.410801
\(886\) −18.4989 −0.621482
\(887\) 27.1187 0.910556 0.455278 0.890349i \(-0.349540\pi\)
0.455278 + 0.890349i \(0.349540\pi\)
\(888\) −3.69445 −0.123977
\(889\) 20.9612 0.703016
\(890\) −72.3058 −2.42370
\(891\) −10.3497 −0.346729
\(892\) −5.11012 −0.171100
\(893\) −33.7082 −1.12800
\(894\) 9.22343 0.308478
\(895\) 101.877 3.40539
\(896\) −1.00000 −0.0334077
\(897\) −1.10122 −0.0367685
\(898\) 4.48720 0.149740
\(899\) −13.1384 −0.438189
\(900\) −39.8786 −1.32929
\(901\) −50.8902 −1.69540
\(902\) −0.352525 −0.0117378
\(903\) −2.92881 −0.0974647
\(904\) −7.02869 −0.233771
\(905\) −16.9690 −0.564069
\(906\) 2.35207 0.0781424
\(907\) −38.5684 −1.28064 −0.640321 0.768107i \(-0.721199\pi\)
−0.640321 + 0.768107i \(0.721199\pi\)
\(908\) 2.63322 0.0873864
\(909\) 46.6604 1.54763
\(910\) 13.4805 0.446874
\(911\) 19.9873 0.662209 0.331105 0.943594i \(-0.392579\pi\)
0.331105 + 0.943594i \(0.392579\pi\)
\(912\) −1.57255 −0.0520722
\(913\) −8.11630 −0.268610
\(914\) 20.0945 0.664666
\(915\) −15.3711 −0.508154
\(916\) 18.2735 0.603773
\(917\) 16.5111 0.545244
\(918\) 8.12067 0.268022
\(919\) 17.3188 0.571294 0.285647 0.958335i \(-0.407792\pi\)
0.285647 + 0.958335i \(0.407792\pi\)
\(920\) 3.93823 0.129839
\(921\) −5.66797 −0.186766
\(922\) −10.5920 −0.348829
\(923\) −9.50247 −0.312778
\(924\) 0.535636 0.0176211
\(925\) −131.287 −4.31670
\(926\) 27.8033 0.913672
\(927\) −30.8144 −1.01208
\(928\) −2.54612 −0.0835806
\(929\) −54.0384 −1.77294 −0.886471 0.462784i \(-0.846850\pi\)
−0.886471 + 0.462784i \(0.846850\pi\)
\(930\) −8.87882 −0.291148
\(931\) 3.98583 0.130630
\(932\) −18.5926 −0.609022
\(933\) −2.02340 −0.0662433
\(934\) −30.3975 −0.994636
\(935\) 20.8529 0.681962
\(936\) −8.79181 −0.287369
\(937\) −18.9391 −0.618712 −0.309356 0.950946i \(-0.600114\pi\)
−0.309356 + 0.950946i \(0.600114\pi\)
\(938\) 8.46286 0.276322
\(939\) 0.788187 0.0257215
\(940\) −36.8830 −1.20299
\(941\) 17.2105 0.561048 0.280524 0.959847i \(-0.409492\pi\)
0.280524 + 0.959847i \(0.409492\pi\)
\(942\) 7.72652 0.251744
\(943\) 0.234475 0.00763556
\(944\) 7.10247 0.231166
\(945\) 10.0561 0.327125
\(946\) 10.0784 0.327677
\(947\) 33.9255 1.10243 0.551215 0.834363i \(-0.314165\pi\)
0.551215 + 0.834363i \(0.314165\pi\)
\(948\) −4.11491 −0.133646
\(949\) −21.7893 −0.707311
\(950\) −55.8827 −1.81307
\(951\) −12.4702 −0.404373
\(952\) 3.52186 0.114144
\(953\) −0.934417 −0.0302688 −0.0151344 0.999885i \(-0.504818\pi\)
−0.0151344 + 0.999885i \(0.504818\pi\)
\(954\) 41.1003 1.33067
\(955\) −28.2767 −0.915013
\(956\) −17.6002 −0.569232
\(957\) 1.36380 0.0440853
\(958\) −25.6190 −0.827711
\(959\) −1.63908 −0.0529286
\(960\) −1.72065 −0.0555339
\(961\) −4.37292 −0.141062
\(962\) −28.9442 −0.933197
\(963\) −49.7617 −1.60355
\(964\) 14.6839 0.472937
\(965\) −108.933 −3.50667
\(966\) −0.356268 −0.0114627
\(967\) 11.1288 0.357878 0.178939 0.983860i \(-0.442734\pi\)
0.178939 + 0.983860i \(0.442734\pi\)
\(968\) 9.15681 0.294311
\(969\) 5.53828 0.177915
\(970\) 33.5978 1.07876
\(971\) 19.2648 0.618238 0.309119 0.951023i \(-0.399966\pi\)
0.309119 + 0.951023i \(0.399966\pi\)
\(972\) −9.92504 −0.318346
\(973\) −14.4616 −0.463619
\(974\) −9.16834 −0.293772
\(975\) 17.0978 0.547566
\(976\) 8.93330 0.285948
\(977\) 29.5133 0.944216 0.472108 0.881541i \(-0.343493\pi\)
0.472108 + 0.881541i \(0.343493\pi\)
\(978\) 1.55724 0.0497951
\(979\) −22.5087 −0.719380
\(980\) 4.36123 0.139314
\(981\) −25.2921 −0.807514
\(982\) −20.2230 −0.645341
\(983\) −1.11612 −0.0355986 −0.0177993 0.999842i \(-0.505666\pi\)
−0.0177993 + 0.999842i \(0.505666\pi\)
\(984\) −0.102445 −0.00326582
\(985\) −26.4598 −0.843078
\(986\) 8.96708 0.285570
\(987\) 3.33658 0.106205
\(988\) −12.3201 −0.391956
\(989\) −6.70345 −0.213157
\(990\) −16.8413 −0.535252
\(991\) 55.4777 1.76231 0.881153 0.472831i \(-0.156768\pi\)
0.881153 + 0.472831i \(0.156768\pi\)
\(992\) 5.16014 0.163835
\(993\) 1.44794 0.0459489
\(994\) −3.07426 −0.0975095
\(995\) 71.2463 2.25866
\(996\) −2.35862 −0.0747356
\(997\) 6.33246 0.200551 0.100276 0.994960i \(-0.468028\pi\)
0.100276 + 0.994960i \(0.468028\pi\)
\(998\) 30.2185 0.956551
\(999\) −21.5916 −0.683128
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 6034.2.a.p.1.11 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6034.2.a.p.1.11 27 1.1 even 1 trivial