Properties

Label 8006.2.a.a.1.15
Level $8006$
Weight $2$
Character 8006.1
Self dual yes
Analytic conductor $63.928$
Analytic rank $1$
Dimension $69$
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] = [8006,2,Mod(1,8006)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8006, 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("8006.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8006 = 2 \cdot 4003 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8006.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: \(63.9282318582\)
Analytic rank: \(1\)
Dimension: \(69\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 8006.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.10040 q^{3} +1.00000 q^{4} -0.571471 q^{5} -2.10040 q^{6} +3.01756 q^{7} +1.00000 q^{8} +1.41167 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.10040 q^{3} +1.00000 q^{4} -0.571471 q^{5} -2.10040 q^{6} +3.01756 q^{7} +1.00000 q^{8} +1.41167 q^{9} -0.571471 q^{10} -1.18938 q^{11} -2.10040 q^{12} -5.61973 q^{13} +3.01756 q^{14} +1.20032 q^{15} +1.00000 q^{16} -0.461237 q^{17} +1.41167 q^{18} +2.18243 q^{19} -0.571471 q^{20} -6.33808 q^{21} -1.18938 q^{22} +0.111126 q^{23} -2.10040 q^{24} -4.67342 q^{25} -5.61973 q^{26} +3.33612 q^{27} +3.01756 q^{28} +3.20738 q^{29} +1.20032 q^{30} +10.6915 q^{31} +1.00000 q^{32} +2.49816 q^{33} -0.461237 q^{34} -1.72445 q^{35} +1.41167 q^{36} -2.75061 q^{37} +2.18243 q^{38} +11.8037 q^{39} -0.571471 q^{40} -3.60037 q^{41} -6.33808 q^{42} +3.85351 q^{43} -1.18938 q^{44} -0.806729 q^{45} +0.111126 q^{46} -2.93386 q^{47} -2.10040 q^{48} +2.10567 q^{49} -4.67342 q^{50} +0.968781 q^{51} -5.61973 q^{52} -8.95066 q^{53} +3.33612 q^{54} +0.679695 q^{55} +3.01756 q^{56} -4.58398 q^{57} +3.20738 q^{58} +12.8394 q^{59} +1.20032 q^{60} -1.89738 q^{61} +10.6915 q^{62} +4.25980 q^{63} +1.00000 q^{64} +3.21151 q^{65} +2.49816 q^{66} +0.845266 q^{67} -0.461237 q^{68} -0.233408 q^{69} -1.72445 q^{70} -9.80424 q^{71} +1.41167 q^{72} -7.90337 q^{73} -2.75061 q^{74} +9.81604 q^{75} +2.18243 q^{76} -3.58902 q^{77} +11.8037 q^{78} -1.47331 q^{79} -0.571471 q^{80} -11.2422 q^{81} -3.60037 q^{82} -7.00283 q^{83} -6.33808 q^{84} +0.263584 q^{85} +3.85351 q^{86} -6.73677 q^{87} -1.18938 q^{88} -16.8609 q^{89} -0.806729 q^{90} -16.9579 q^{91} +0.111126 q^{92} -22.4564 q^{93} -2.93386 q^{94} -1.24720 q^{95} -2.10040 q^{96} -12.0645 q^{97} +2.10567 q^{98} -1.67901 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69 q + 69 q^{2} - 15 q^{3} + 69 q^{4} - 9 q^{5} - 15 q^{6} - 29 q^{7} + 69 q^{8} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 69 q + 69 q^{2} - 15 q^{3} + 69 q^{4} - 9 q^{5} - 15 q^{6} - 29 q^{7} + 69 q^{8} + 40 q^{9} - 9 q^{10} - 48 q^{11} - 15 q^{12} - 30 q^{13} - 29 q^{14} - 51 q^{15} + 69 q^{16} - 37 q^{17} + 40 q^{18} - 72 q^{19} - 9 q^{20} - 38 q^{21} - 48 q^{22} - 75 q^{23} - 15 q^{24} + 18 q^{25} - 30 q^{26} - 48 q^{27} - 29 q^{28} - 27 q^{29} - 51 q^{30} - 61 q^{31} + 69 q^{32} - 29 q^{33} - 37 q^{34} - 64 q^{35} + 40 q^{36} - 42 q^{37} - 72 q^{38} - 68 q^{39} - 9 q^{40} - 49 q^{41} - 38 q^{42} - 95 q^{43} - 48 q^{44} - 20 q^{45} - 75 q^{46} - 62 q^{47} - 15 q^{48} - 4 q^{49} + 18 q^{50} - 76 q^{51} - 30 q^{52} - 28 q^{53} - 48 q^{54} - 76 q^{55} - 29 q^{56} - 44 q^{57} - 27 q^{58} - 68 q^{59} - 51 q^{60} - 62 q^{61} - 61 q^{62} - 91 q^{63} + 69 q^{64} - 79 q^{65} - 29 q^{66} - 116 q^{67} - 37 q^{68} - 23 q^{69} - 64 q^{70} - 89 q^{71} + 40 q^{72} - 60 q^{73} - 42 q^{74} - 47 q^{75} - 72 q^{76} + 5 q^{77} - 68 q^{78} - 170 q^{79} - 9 q^{80} - 3 q^{81} - 49 q^{82} - 82 q^{83} - 38 q^{84} - 81 q^{85} - 95 q^{86} - 51 q^{87} - 48 q^{88} - 78 q^{89} - 20 q^{90} - 85 q^{91} - 75 q^{92} - 21 q^{93} - 62 q^{94} - 70 q^{95} - 15 q^{96} - 60 q^{97} - 4 q^{98} - 148 q^{99}+O(q^{100}) \) 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
\(3\) −2.10040 −1.21267 −0.606333 0.795211i \(-0.707360\pi\)
−0.606333 + 0.795211i \(0.707360\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.571471 −0.255570 −0.127785 0.991802i \(-0.540787\pi\)
−0.127785 + 0.991802i \(0.540787\pi\)
\(6\) −2.10040 −0.857484
\(7\) 3.01756 1.14053 0.570265 0.821461i \(-0.306840\pi\)
0.570265 + 0.821461i \(0.306840\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.41167 0.470557
\(10\) −0.571471 −0.180715
\(11\) −1.18938 −0.358611 −0.179305 0.983793i \(-0.557385\pi\)
−0.179305 + 0.983793i \(0.557385\pi\)
\(12\) −2.10040 −0.606333
\(13\) −5.61973 −1.55863 −0.779316 0.626631i \(-0.784433\pi\)
−0.779316 + 0.626631i \(0.784433\pi\)
\(14\) 3.01756 0.806477
\(15\) 1.20032 0.309920
\(16\) 1.00000 0.250000
\(17\) −0.461237 −0.111866 −0.0559332 0.998435i \(-0.517813\pi\)
−0.0559332 + 0.998435i \(0.517813\pi\)
\(18\) 1.41167 0.332734
\(19\) 2.18243 0.500685 0.250342 0.968157i \(-0.419457\pi\)
0.250342 + 0.968157i \(0.419457\pi\)
\(20\) −0.571471 −0.127785
\(21\) −6.33808 −1.38308
\(22\) −1.18938 −0.253576
\(23\) 0.111126 0.0231713 0.0115856 0.999933i \(-0.496312\pi\)
0.0115856 + 0.999933i \(0.496312\pi\)
\(24\) −2.10040 −0.428742
\(25\) −4.67342 −0.934684
\(26\) −5.61973 −1.10212
\(27\) 3.33612 0.642037
\(28\) 3.01756 0.570265
\(29\) 3.20738 0.595595 0.297798 0.954629i \(-0.403748\pi\)
0.297798 + 0.954629i \(0.403748\pi\)
\(30\) 1.20032 0.219147
\(31\) 10.6915 1.92025 0.960125 0.279572i \(-0.0901924\pi\)
0.960125 + 0.279572i \(0.0901924\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.49816 0.434875
\(34\) −0.461237 −0.0791015
\(35\) −1.72445 −0.291485
\(36\) 1.41167 0.235278
\(37\) −2.75061 −0.452197 −0.226099 0.974104i \(-0.572597\pi\)
−0.226099 + 0.974104i \(0.572597\pi\)
\(38\) 2.18243 0.354038
\(39\) 11.8037 1.89010
\(40\) −0.571471 −0.0903575
\(41\) −3.60037 −0.562283 −0.281142 0.959666i \(-0.590713\pi\)
−0.281142 + 0.959666i \(0.590713\pi\)
\(42\) −6.33808 −0.977986
\(43\) 3.85351 0.587655 0.293828 0.955858i \(-0.405071\pi\)
0.293828 + 0.955858i \(0.405071\pi\)
\(44\) −1.18938 −0.179305
\(45\) −0.806729 −0.120260
\(46\) 0.111126 0.0163846
\(47\) −2.93386 −0.427948 −0.213974 0.976839i \(-0.568641\pi\)
−0.213974 + 0.976839i \(0.568641\pi\)
\(48\) −2.10040 −0.303166
\(49\) 2.10567 0.300810
\(50\) −4.67342 −0.660922
\(51\) 0.968781 0.135656
\(52\) −5.61973 −0.779316
\(53\) −8.95066 −1.22947 −0.614734 0.788735i \(-0.710736\pi\)
−0.614734 + 0.788735i \(0.710736\pi\)
\(54\) 3.33612 0.453989
\(55\) 0.679695 0.0916500
\(56\) 3.01756 0.403238
\(57\) −4.58398 −0.607163
\(58\) 3.20738 0.421150
\(59\) 12.8394 1.67154 0.835772 0.549076i \(-0.185020\pi\)
0.835772 + 0.549076i \(0.185020\pi\)
\(60\) 1.20032 0.154960
\(61\) −1.89738 −0.242935 −0.121467 0.992595i \(-0.538760\pi\)
−0.121467 + 0.992595i \(0.538760\pi\)
\(62\) 10.6915 1.35782
\(63\) 4.25980 0.536684
\(64\) 1.00000 0.125000
\(65\) 3.21151 0.398339
\(66\) 2.49816 0.307503
\(67\) 0.845266 0.103266 0.0516329 0.998666i \(-0.483557\pi\)
0.0516329 + 0.998666i \(0.483557\pi\)
\(68\) −0.461237 −0.0559332
\(69\) −0.233408 −0.0280990
\(70\) −1.72445 −0.206111
\(71\) −9.80424 −1.16355 −0.581775 0.813350i \(-0.697642\pi\)
−0.581775 + 0.813350i \(0.697642\pi\)
\(72\) 1.41167 0.166367
\(73\) −7.90337 −0.925020 −0.462510 0.886614i \(-0.653051\pi\)
−0.462510 + 0.886614i \(0.653051\pi\)
\(74\) −2.75061 −0.319752
\(75\) 9.81604 1.13346
\(76\) 2.18243 0.250342
\(77\) −3.58902 −0.409006
\(78\) 11.8037 1.33650
\(79\) −1.47331 −0.165760 −0.0828800 0.996560i \(-0.526412\pi\)
−0.0828800 + 0.996560i \(0.526412\pi\)
\(80\) −0.571471 −0.0638924
\(81\) −11.2422 −1.24913
\(82\) −3.60037 −0.397594
\(83\) −7.00283 −0.768660 −0.384330 0.923196i \(-0.625568\pi\)
−0.384330 + 0.923196i \(0.625568\pi\)
\(84\) −6.33808 −0.691541
\(85\) 0.263584 0.0285897
\(86\) 3.85351 0.415535
\(87\) −6.73677 −0.722258
\(88\) −1.18938 −0.126788
\(89\) −16.8609 −1.78725 −0.893626 0.448812i \(-0.851847\pi\)
−0.893626 + 0.448812i \(0.851847\pi\)
\(90\) −0.806729 −0.0850367
\(91\) −16.9579 −1.77767
\(92\) 0.111126 0.0115856
\(93\) −22.4564 −2.32862
\(94\) −2.93386 −0.302605
\(95\) −1.24720 −0.127960
\(96\) −2.10040 −0.214371
\(97\) −12.0645 −1.22496 −0.612481 0.790485i \(-0.709828\pi\)
−0.612481 + 0.790485i \(0.709828\pi\)
\(98\) 2.10567 0.212705
\(99\) −1.67901 −0.168747
\(100\) −4.67342 −0.467342
\(101\) 3.12601 0.311050 0.155525 0.987832i \(-0.450293\pi\)
0.155525 + 0.987832i \(0.450293\pi\)
\(102\) 0.968781 0.0959236
\(103\) 15.3458 1.51207 0.756033 0.654533i \(-0.227135\pi\)
0.756033 + 0.654533i \(0.227135\pi\)
\(104\) −5.61973 −0.551060
\(105\) 3.62203 0.353474
\(106\) −8.95066 −0.869364
\(107\) 16.8821 1.63205 0.816025 0.578016i \(-0.196173\pi\)
0.816025 + 0.578016i \(0.196173\pi\)
\(108\) 3.33612 0.321019
\(109\) −4.32579 −0.414335 −0.207168 0.978305i \(-0.566425\pi\)
−0.207168 + 0.978305i \(0.566425\pi\)
\(110\) 0.679695 0.0648063
\(111\) 5.77737 0.548364
\(112\) 3.01756 0.285133
\(113\) 6.63395 0.624070 0.312035 0.950071i \(-0.398989\pi\)
0.312035 + 0.950071i \(0.398989\pi\)
\(114\) −4.58398 −0.429329
\(115\) −0.0635051 −0.00592188
\(116\) 3.20738 0.297798
\(117\) −7.93320 −0.733425
\(118\) 12.8394 1.18196
\(119\) −1.39181 −0.127587
\(120\) 1.20032 0.109573
\(121\) −9.58538 −0.871398
\(122\) −1.89738 −0.171781
\(123\) 7.56221 0.681862
\(124\) 10.6915 0.960125
\(125\) 5.52808 0.494447
\(126\) 4.25980 0.379493
\(127\) −10.1188 −0.897902 −0.448951 0.893556i \(-0.648202\pi\)
−0.448951 + 0.893556i \(0.648202\pi\)
\(128\) 1.00000 0.0883883
\(129\) −8.09391 −0.712629
\(130\) 3.21151 0.281668
\(131\) 1.88162 0.164398 0.0821988 0.996616i \(-0.473806\pi\)
0.0821988 + 0.996616i \(0.473806\pi\)
\(132\) 2.49816 0.217437
\(133\) 6.58562 0.571046
\(134\) 0.845266 0.0730199
\(135\) −1.90650 −0.164085
\(136\) −0.461237 −0.0395507
\(137\) 17.6989 1.51212 0.756060 0.654502i \(-0.227122\pi\)
0.756060 + 0.654502i \(0.227122\pi\)
\(138\) −0.233408 −0.0198690
\(139\) −14.8737 −1.26157 −0.630784 0.775958i \(-0.717267\pi\)
−0.630784 + 0.775958i \(0.717267\pi\)
\(140\) −1.72445 −0.145742
\(141\) 6.16228 0.518958
\(142\) −9.80424 −0.822754
\(143\) 6.68397 0.558942
\(144\) 1.41167 0.117639
\(145\) −1.83292 −0.152216
\(146\) −7.90337 −0.654088
\(147\) −4.42274 −0.364782
\(148\) −2.75061 −0.226099
\(149\) 18.7464 1.53576 0.767882 0.640592i \(-0.221311\pi\)
0.767882 + 0.640592i \(0.221311\pi\)
\(150\) 9.81604 0.801476
\(151\) −20.4397 −1.66336 −0.831680 0.555256i \(-0.812620\pi\)
−0.831680 + 0.555256i \(0.812620\pi\)
\(152\) 2.18243 0.177019
\(153\) −0.651114 −0.0526395
\(154\) −3.58902 −0.289211
\(155\) −6.10988 −0.490758
\(156\) 11.8037 0.945049
\(157\) 1.38318 0.110390 0.0551948 0.998476i \(-0.482422\pi\)
0.0551948 + 0.998476i \(0.482422\pi\)
\(158\) −1.47331 −0.117210
\(159\) 18.7999 1.49093
\(160\) −0.571471 −0.0451788
\(161\) 0.335328 0.0264276
\(162\) −11.2422 −0.883270
\(163\) 10.4329 0.817165 0.408582 0.912721i \(-0.366023\pi\)
0.408582 + 0.912721i \(0.366023\pi\)
\(164\) −3.60037 −0.281142
\(165\) −1.42763 −0.111141
\(166\) −7.00283 −0.543525
\(167\) 2.57038 0.198902 0.0994512 0.995042i \(-0.468291\pi\)
0.0994512 + 0.995042i \(0.468291\pi\)
\(168\) −6.33808 −0.488993
\(169\) 18.5813 1.42933
\(170\) 0.263584 0.0202159
\(171\) 3.08088 0.235600
\(172\) 3.85351 0.293828
\(173\) −2.17575 −0.165419 −0.0827094 0.996574i \(-0.526357\pi\)
−0.0827094 + 0.996574i \(0.526357\pi\)
\(174\) −6.73677 −0.510713
\(175\) −14.1023 −1.06604
\(176\) −1.18938 −0.0896527
\(177\) −26.9678 −2.02702
\(178\) −16.8609 −1.26378
\(179\) −21.0627 −1.57430 −0.787151 0.616761i \(-0.788445\pi\)
−0.787151 + 0.616761i \(0.788445\pi\)
\(180\) −0.806729 −0.0601300
\(181\) −10.3419 −0.768704 −0.384352 0.923187i \(-0.625575\pi\)
−0.384352 + 0.923187i \(0.625575\pi\)
\(182\) −16.9579 −1.25700
\(183\) 3.98526 0.294599
\(184\) 0.111126 0.00819229
\(185\) 1.57189 0.115568
\(186\) −22.4564 −1.64658
\(187\) 0.548585 0.0401165
\(188\) −2.93386 −0.213974
\(189\) 10.0670 0.732263
\(190\) −1.24720 −0.0904812
\(191\) 0.655753 0.0474486 0.0237243 0.999719i \(-0.492448\pi\)
0.0237243 + 0.999719i \(0.492448\pi\)
\(192\) −2.10040 −0.151583
\(193\) 2.17573 0.156613 0.0783063 0.996929i \(-0.475049\pi\)
0.0783063 + 0.996929i \(0.475049\pi\)
\(194\) −12.0645 −0.866179
\(195\) −6.74545 −0.483052
\(196\) 2.10567 0.150405
\(197\) 1.28802 0.0917673 0.0458837 0.998947i \(-0.485390\pi\)
0.0458837 + 0.998947i \(0.485390\pi\)
\(198\) −1.67901 −0.119322
\(199\) −19.2438 −1.36416 −0.682079 0.731279i \(-0.738924\pi\)
−0.682079 + 0.731279i \(0.738924\pi\)
\(200\) −4.67342 −0.330461
\(201\) −1.77540 −0.125227
\(202\) 3.12601 0.219946
\(203\) 9.67846 0.679295
\(204\) 0.968781 0.0678282
\(205\) 2.05751 0.143703
\(206\) 15.3458 1.06919
\(207\) 0.156873 0.0109034
\(208\) −5.61973 −0.389658
\(209\) −2.59574 −0.179551
\(210\) 3.62203 0.249944
\(211\) −1.76956 −0.121822 −0.0609108 0.998143i \(-0.519401\pi\)
−0.0609108 + 0.998143i \(0.519401\pi\)
\(212\) −8.95066 −0.614734
\(213\) 20.5928 1.41100
\(214\) 16.8821 1.15403
\(215\) −2.20217 −0.150187
\(216\) 3.33612 0.226995
\(217\) 32.2622 2.19010
\(218\) −4.32579 −0.292979
\(219\) 16.6002 1.12174
\(220\) 0.679695 0.0458250
\(221\) 2.59203 0.174359
\(222\) 5.77737 0.387752
\(223\) −12.4006 −0.830406 −0.415203 0.909729i \(-0.636289\pi\)
−0.415203 + 0.909729i \(0.636289\pi\)
\(224\) 3.01756 0.201619
\(225\) −6.59733 −0.439822
\(226\) 6.63395 0.441284
\(227\) 3.76542 0.249920 0.124960 0.992162i \(-0.460120\pi\)
0.124960 + 0.992162i \(0.460120\pi\)
\(228\) −4.58398 −0.303581
\(229\) 17.4343 1.15209 0.576044 0.817419i \(-0.304596\pi\)
0.576044 + 0.817419i \(0.304596\pi\)
\(230\) −0.0635051 −0.00418740
\(231\) 7.53836 0.495988
\(232\) 3.20738 0.210575
\(233\) 5.72024 0.374745 0.187373 0.982289i \(-0.440003\pi\)
0.187373 + 0.982289i \(0.440003\pi\)
\(234\) −7.93320 −0.518610
\(235\) 1.67662 0.109371
\(236\) 12.8394 0.835772
\(237\) 3.09453 0.201011
\(238\) −1.39181 −0.0902176
\(239\) −0.915196 −0.0591991 −0.0295996 0.999562i \(-0.509423\pi\)
−0.0295996 + 0.999562i \(0.509423\pi\)
\(240\) 1.20032 0.0774801
\(241\) −8.57289 −0.552228 −0.276114 0.961125i \(-0.589047\pi\)
−0.276114 + 0.961125i \(0.589047\pi\)
\(242\) −9.58538 −0.616172
\(243\) 13.6047 0.872743
\(244\) −1.89738 −0.121467
\(245\) −1.20333 −0.0768779
\(246\) 7.56221 0.482149
\(247\) −12.2647 −0.780383
\(248\) 10.6915 0.678911
\(249\) 14.7087 0.932128
\(250\) 5.52808 0.349627
\(251\) −4.67991 −0.295393 −0.147697 0.989033i \(-0.547186\pi\)
−0.147697 + 0.989033i \(0.547186\pi\)
\(252\) 4.25980 0.268342
\(253\) −0.132170 −0.00830947
\(254\) −10.1188 −0.634913
\(255\) −0.553630 −0.0346697
\(256\) 1.00000 0.0625000
\(257\) −25.2913 −1.57763 −0.788813 0.614634i \(-0.789304\pi\)
−0.788813 + 0.614634i \(0.789304\pi\)
\(258\) −8.09391 −0.503905
\(259\) −8.30012 −0.515745
\(260\) 3.21151 0.199170
\(261\) 4.52776 0.280261
\(262\) 1.88162 0.116247
\(263\) −18.0309 −1.11183 −0.555917 0.831238i \(-0.687633\pi\)
−0.555917 + 0.831238i \(0.687633\pi\)
\(264\) 2.49816 0.153751
\(265\) 5.11504 0.314214
\(266\) 6.58562 0.403791
\(267\) 35.4146 2.16734
\(268\) 0.845266 0.0516329
\(269\) −7.97505 −0.486247 −0.243124 0.969995i \(-0.578172\pi\)
−0.243124 + 0.969995i \(0.578172\pi\)
\(270\) −1.90650 −0.116026
\(271\) −29.9244 −1.81778 −0.908890 0.417037i \(-0.863069\pi\)
−0.908890 + 0.417037i \(0.863069\pi\)
\(272\) −0.461237 −0.0279666
\(273\) 35.6183 2.15572
\(274\) 17.6989 1.06923
\(275\) 5.55846 0.335188
\(276\) −0.233408 −0.0140495
\(277\) −14.1989 −0.853129 −0.426564 0.904457i \(-0.640276\pi\)
−0.426564 + 0.904457i \(0.640276\pi\)
\(278\) −14.8737 −0.892063
\(279\) 15.0929 0.903586
\(280\) −1.72445 −0.103056
\(281\) −25.5686 −1.52529 −0.762647 0.646815i \(-0.776100\pi\)
−0.762647 + 0.646815i \(0.776100\pi\)
\(282\) 6.16228 0.366958
\(283\) −5.66128 −0.336528 −0.168264 0.985742i \(-0.553816\pi\)
−0.168264 + 0.985742i \(0.553816\pi\)
\(284\) −9.80424 −0.581775
\(285\) 2.61961 0.155172
\(286\) 6.68397 0.395232
\(287\) −10.8643 −0.641301
\(288\) 1.41167 0.0831834
\(289\) −16.7873 −0.987486
\(290\) −1.83292 −0.107633
\(291\) 25.3402 1.48547
\(292\) −7.90337 −0.462510
\(293\) 32.9911 1.92736 0.963680 0.267058i \(-0.0860516\pi\)
0.963680 + 0.267058i \(0.0860516\pi\)
\(294\) −4.42274 −0.257939
\(295\) −7.33733 −0.427196
\(296\) −2.75061 −0.159876
\(297\) −3.96791 −0.230241
\(298\) 18.7464 1.08595
\(299\) −0.624496 −0.0361155
\(300\) 9.81604 0.566729
\(301\) 11.6282 0.670239
\(302\) −20.4397 −1.17617
\(303\) −6.56587 −0.377200
\(304\) 2.18243 0.125171
\(305\) 1.08430 0.0620868
\(306\) −0.651114 −0.0372217
\(307\) 22.6839 1.29464 0.647319 0.762219i \(-0.275890\pi\)
0.647319 + 0.762219i \(0.275890\pi\)
\(308\) −3.58902 −0.204503
\(309\) −32.2323 −1.83363
\(310\) −6.10988 −0.347018
\(311\) 0.327113 0.0185489 0.00927445 0.999957i \(-0.497048\pi\)
0.00927445 + 0.999957i \(0.497048\pi\)
\(312\) 11.8037 0.668251
\(313\) −2.76056 −0.156036 −0.0780181 0.996952i \(-0.524859\pi\)
−0.0780181 + 0.996952i \(0.524859\pi\)
\(314\) 1.38318 0.0780573
\(315\) −2.43435 −0.137160
\(316\) −1.47331 −0.0828800
\(317\) −21.5671 −1.21133 −0.605664 0.795720i \(-0.707093\pi\)
−0.605664 + 0.795720i \(0.707093\pi\)
\(318\) 18.7999 1.05425
\(319\) −3.81478 −0.213587
\(320\) −0.571471 −0.0319462
\(321\) −35.4590 −1.97913
\(322\) 0.335328 0.0186871
\(323\) −1.00662 −0.0560098
\(324\) −11.2422 −0.624567
\(325\) 26.2634 1.45683
\(326\) 10.4329 0.577823
\(327\) 9.08587 0.502450
\(328\) −3.60037 −0.198797
\(329\) −8.85311 −0.488088
\(330\) −1.42763 −0.0785884
\(331\) −0.419719 −0.0230698 −0.0115349 0.999933i \(-0.503672\pi\)
−0.0115349 + 0.999933i \(0.503672\pi\)
\(332\) −7.00283 −0.384330
\(333\) −3.88295 −0.212784
\(334\) 2.57038 0.140645
\(335\) −0.483045 −0.0263916
\(336\) −6.33808 −0.345770
\(337\) −24.3871 −1.32845 −0.664225 0.747532i \(-0.731238\pi\)
−0.664225 + 0.747532i \(0.731238\pi\)
\(338\) 18.5813 1.01069
\(339\) −13.9339 −0.756788
\(340\) 0.263584 0.0142948
\(341\) −12.7162 −0.688622
\(342\) 3.08088 0.166595
\(343\) −14.7689 −0.797448
\(344\) 3.85351 0.207768
\(345\) 0.133386 0.00718126
\(346\) −2.17575 −0.116969
\(347\) −21.5409 −1.15638 −0.578188 0.815904i \(-0.696240\pi\)
−0.578188 + 0.815904i \(0.696240\pi\)
\(348\) −6.73677 −0.361129
\(349\) −12.6704 −0.678234 −0.339117 0.940744i \(-0.610128\pi\)
−0.339117 + 0.940744i \(0.610128\pi\)
\(350\) −14.1023 −0.753801
\(351\) −18.7481 −1.00070
\(352\) −1.18938 −0.0633940
\(353\) −0.181780 −0.00967518 −0.00483759 0.999988i \(-0.501540\pi\)
−0.00483759 + 0.999988i \(0.501540\pi\)
\(354\) −26.9678 −1.43332
\(355\) 5.60284 0.297368
\(356\) −16.8609 −0.893626
\(357\) 2.92335 0.154720
\(358\) −21.0627 −1.11320
\(359\) −3.44057 −0.181587 −0.0907933 0.995870i \(-0.528940\pi\)
−0.0907933 + 0.995870i \(0.528940\pi\)
\(360\) −0.806729 −0.0425183
\(361\) −14.2370 −0.749315
\(362\) −10.3419 −0.543556
\(363\) 20.1331 1.05671
\(364\) −16.9579 −0.888834
\(365\) 4.51655 0.236407
\(366\) 3.98526 0.208313
\(367\) 1.92925 0.100706 0.0503531 0.998731i \(-0.483965\pi\)
0.0503531 + 0.998731i \(0.483965\pi\)
\(368\) 0.111126 0.00579282
\(369\) −5.08254 −0.264586
\(370\) 1.57189 0.0817188
\(371\) −27.0091 −1.40224
\(372\) −22.4564 −1.16431
\(373\) −19.7154 −1.02083 −0.510413 0.859930i \(-0.670507\pi\)
−0.510413 + 0.859930i \(0.670507\pi\)
\(374\) 0.548585 0.0283666
\(375\) −11.6112 −0.599598
\(376\) −2.93386 −0.151302
\(377\) −18.0246 −0.928314
\(378\) 10.0670 0.517788
\(379\) 8.07357 0.414712 0.207356 0.978266i \(-0.433514\pi\)
0.207356 + 0.978266i \(0.433514\pi\)
\(380\) −1.24720 −0.0639799
\(381\) 21.2536 1.08885
\(382\) 0.655753 0.0335513
\(383\) 3.38074 0.172748 0.0863740 0.996263i \(-0.472472\pi\)
0.0863740 + 0.996263i \(0.472472\pi\)
\(384\) −2.10040 −0.107185
\(385\) 2.05102 0.104530
\(386\) 2.17573 0.110742
\(387\) 5.43989 0.276525
\(388\) −12.0645 −0.612481
\(389\) −13.5165 −0.685314 −0.342657 0.939461i \(-0.611327\pi\)
−0.342657 + 0.939461i \(0.611327\pi\)
\(390\) −6.74545 −0.341569
\(391\) −0.0512552 −0.00259209
\(392\) 2.10567 0.106352
\(393\) −3.95214 −0.199359
\(394\) 1.28802 0.0648893
\(395\) 0.841953 0.0423632
\(396\) −1.67901 −0.0843733
\(397\) −16.7146 −0.838883 −0.419441 0.907782i \(-0.637774\pi\)
−0.419441 + 0.907782i \(0.637774\pi\)
\(398\) −19.2438 −0.964605
\(399\) −13.8324 −0.692488
\(400\) −4.67342 −0.233671
\(401\) −12.8696 −0.642677 −0.321339 0.946964i \(-0.604133\pi\)
−0.321339 + 0.946964i \(0.604133\pi\)
\(402\) −1.77540 −0.0885487
\(403\) −60.0833 −2.99296
\(404\) 3.12601 0.155525
\(405\) 6.42459 0.319241
\(406\) 9.67846 0.480334
\(407\) 3.27151 0.162163
\(408\) 0.968781 0.0479618
\(409\) 12.6660 0.626295 0.313147 0.949705i \(-0.398617\pi\)
0.313147 + 0.949705i \(0.398617\pi\)
\(410\) 2.05751 0.101613
\(411\) −37.1747 −1.83369
\(412\) 15.3458 0.756033
\(413\) 38.7436 1.90645
\(414\) 0.156873 0.00770987
\(415\) 4.00191 0.196446
\(416\) −5.61973 −0.275530
\(417\) 31.2406 1.52986
\(418\) −2.59574 −0.126962
\(419\) −0.334875 −0.0163597 −0.00817985 0.999967i \(-0.502604\pi\)
−0.00817985 + 0.999967i \(0.502604\pi\)
\(420\) 3.62203 0.176737
\(421\) 9.64771 0.470201 0.235100 0.971971i \(-0.424458\pi\)
0.235100 + 0.971971i \(0.424458\pi\)
\(422\) −1.76956 −0.0861409
\(423\) −4.14165 −0.201374
\(424\) −8.95066 −0.434682
\(425\) 2.15555 0.104560
\(426\) 20.5928 0.997725
\(427\) −5.72546 −0.277075
\(428\) 16.8821 0.816025
\(429\) −14.0390 −0.677809
\(430\) −2.20217 −0.106198
\(431\) 26.9205 1.29672 0.648358 0.761336i \(-0.275456\pi\)
0.648358 + 0.761336i \(0.275456\pi\)
\(432\) 3.33612 0.160509
\(433\) 15.0759 0.724501 0.362251 0.932081i \(-0.382008\pi\)
0.362251 + 0.932081i \(0.382008\pi\)
\(434\) 32.2622 1.54864
\(435\) 3.84987 0.184587
\(436\) −4.32579 −0.207168
\(437\) 0.242524 0.0116015
\(438\) 16.6002 0.793189
\(439\) 8.36521 0.399250 0.199625 0.979872i \(-0.436028\pi\)
0.199625 + 0.979872i \(0.436028\pi\)
\(440\) 0.679695 0.0324032
\(441\) 2.97251 0.141548
\(442\) 2.59203 0.123290
\(443\) 3.00833 0.142930 0.0714650 0.997443i \(-0.477233\pi\)
0.0714650 + 0.997443i \(0.477233\pi\)
\(444\) 5.77737 0.274182
\(445\) 9.63552 0.456768
\(446\) −12.4006 −0.587186
\(447\) −39.3748 −1.86237
\(448\) 3.01756 0.142566
\(449\) −9.96365 −0.470214 −0.235107 0.971970i \(-0.575544\pi\)
−0.235107 + 0.971970i \(0.575544\pi\)
\(450\) −6.59733 −0.311001
\(451\) 4.28220 0.201641
\(452\) 6.63395 0.312035
\(453\) 42.9315 2.01710
\(454\) 3.76542 0.176720
\(455\) 9.69093 0.454318
\(456\) −4.58398 −0.214664
\(457\) 36.3378 1.69981 0.849905 0.526936i \(-0.176659\pi\)
0.849905 + 0.526936i \(0.176659\pi\)
\(458\) 17.4343 0.814649
\(459\) −1.53874 −0.0718224
\(460\) −0.0635051 −0.00296094
\(461\) −17.0377 −0.793526 −0.396763 0.917921i \(-0.629867\pi\)
−0.396763 + 0.917921i \(0.629867\pi\)
\(462\) 7.53836 0.350716
\(463\) 25.8486 1.20128 0.600642 0.799518i \(-0.294912\pi\)
0.600642 + 0.799518i \(0.294912\pi\)
\(464\) 3.20738 0.148899
\(465\) 12.8332 0.595125
\(466\) 5.72024 0.264985
\(467\) 11.2437 0.520297 0.260149 0.965569i \(-0.416228\pi\)
0.260149 + 0.965569i \(0.416228\pi\)
\(468\) −7.93320 −0.366712
\(469\) 2.55064 0.117778
\(470\) 1.67662 0.0773366
\(471\) −2.90522 −0.133866
\(472\) 12.8394 0.590980
\(473\) −4.58328 −0.210739
\(474\) 3.09453 0.142137
\(475\) −10.1994 −0.467982
\(476\) −1.39181 −0.0637935
\(477\) −12.6354 −0.578534
\(478\) −0.915196 −0.0418601
\(479\) 20.0928 0.918065 0.459033 0.888419i \(-0.348196\pi\)
0.459033 + 0.888419i \(0.348196\pi\)
\(480\) 1.20032 0.0547867
\(481\) 15.4577 0.704809
\(482\) −8.57289 −0.390484
\(483\) −0.704323 −0.0320478
\(484\) −9.58538 −0.435699
\(485\) 6.89450 0.313063
\(486\) 13.6047 0.617122
\(487\) −15.9412 −0.722363 −0.361182 0.932495i \(-0.617627\pi\)
−0.361182 + 0.932495i \(0.617627\pi\)
\(488\) −1.89738 −0.0858904
\(489\) −21.9132 −0.990947
\(490\) −1.20333 −0.0543608
\(491\) −1.33619 −0.0603014 −0.0301507 0.999545i \(-0.509599\pi\)
−0.0301507 + 0.999545i \(0.509599\pi\)
\(492\) 7.56221 0.340931
\(493\) −1.47936 −0.0666271
\(494\) −12.2647 −0.551814
\(495\) 0.959504 0.0431265
\(496\) 10.6915 0.480062
\(497\) −29.5849 −1.32706
\(498\) 14.7087 0.659114
\(499\) −22.7132 −1.01678 −0.508391 0.861126i \(-0.669760\pi\)
−0.508391 + 0.861126i \(0.669760\pi\)
\(500\) 5.52808 0.247223
\(501\) −5.39883 −0.241202
\(502\) −4.67991 −0.208875
\(503\) −25.0145 −1.11534 −0.557672 0.830062i \(-0.688305\pi\)
−0.557672 + 0.830062i \(0.688305\pi\)
\(504\) 4.25980 0.189747
\(505\) −1.78643 −0.0794949
\(506\) −0.132170 −0.00587568
\(507\) −39.0282 −1.73330
\(508\) −10.1188 −0.448951
\(509\) 4.74486 0.210312 0.105156 0.994456i \(-0.466466\pi\)
0.105156 + 0.994456i \(0.466466\pi\)
\(510\) −0.553630 −0.0245152
\(511\) −23.8489 −1.05501
\(512\) 1.00000 0.0441942
\(513\) 7.28087 0.321458
\(514\) −25.2913 −1.11555
\(515\) −8.76968 −0.386438
\(516\) −8.09391 −0.356315
\(517\) 3.48947 0.153467
\(518\) −8.30012 −0.364687
\(519\) 4.56993 0.200598
\(520\) 3.21151 0.140834
\(521\) −23.5110 −1.03003 −0.515017 0.857180i \(-0.672215\pi\)
−0.515017 + 0.857180i \(0.672215\pi\)
\(522\) 4.52776 0.198175
\(523\) 38.5322 1.68489 0.842447 0.538780i \(-0.181114\pi\)
0.842447 + 0.538780i \(0.181114\pi\)
\(524\) 1.88162 0.0821988
\(525\) 29.6205 1.29274
\(526\) −18.0309 −0.786185
\(527\) −4.93131 −0.214811
\(528\) 2.49816 0.108719
\(529\) −22.9877 −0.999463
\(530\) 5.11504 0.222183
\(531\) 18.1250 0.786556
\(532\) 6.58562 0.285523
\(533\) 20.2331 0.876393
\(534\) 35.4146 1.53254
\(535\) −9.64761 −0.417103
\(536\) 0.845266 0.0365099
\(537\) 44.2401 1.90910
\(538\) −7.97505 −0.343829
\(539\) −2.50443 −0.107874
\(540\) −1.90650 −0.0820426
\(541\) −21.0405 −0.904604 −0.452302 0.891865i \(-0.649397\pi\)
−0.452302 + 0.891865i \(0.649397\pi\)
\(542\) −29.9244 −1.28536
\(543\) 21.7220 0.932181
\(544\) −0.461237 −0.0197754
\(545\) 2.47206 0.105892
\(546\) 35.6183 1.52432
\(547\) −22.0336 −0.942087 −0.471044 0.882110i \(-0.656123\pi\)
−0.471044 + 0.882110i \(0.656123\pi\)
\(548\) 17.6989 0.756060
\(549\) −2.67848 −0.114315
\(550\) 5.55846 0.237013
\(551\) 6.99989 0.298205
\(552\) −0.233408 −0.00993450
\(553\) −4.44579 −0.189054
\(554\) −14.1989 −0.603253
\(555\) −3.30160 −0.140145
\(556\) −14.8737 −0.630784
\(557\) −20.2363 −0.857440 −0.428720 0.903437i \(-0.641035\pi\)
−0.428720 + 0.903437i \(0.641035\pi\)
\(558\) 15.0929 0.638932
\(559\) −21.6557 −0.915939
\(560\) −1.72445 −0.0728712
\(561\) −1.15225 −0.0486479
\(562\) −25.5686 −1.07855
\(563\) 13.6164 0.573865 0.286932 0.957951i \(-0.407364\pi\)
0.286932 + 0.957951i \(0.407364\pi\)
\(564\) 6.16228 0.259479
\(565\) −3.79111 −0.159493
\(566\) −5.66128 −0.237961
\(567\) −33.9240 −1.42467
\(568\) −9.80424 −0.411377
\(569\) −20.2814 −0.850242 −0.425121 0.905137i \(-0.639768\pi\)
−0.425121 + 0.905137i \(0.639768\pi\)
\(570\) 2.61961 0.109723
\(571\) −39.9276 −1.67092 −0.835459 0.549552i \(-0.814798\pi\)
−0.835459 + 0.549552i \(0.814798\pi\)
\(572\) 6.68397 0.279471
\(573\) −1.37734 −0.0575393
\(574\) −10.8643 −0.453469
\(575\) −0.519337 −0.0216578
\(576\) 1.41167 0.0588196
\(577\) −12.3279 −0.513216 −0.256608 0.966516i \(-0.582605\pi\)
−0.256608 + 0.966516i \(0.582605\pi\)
\(578\) −16.7873 −0.698258
\(579\) −4.56990 −0.189919
\(580\) −1.83292 −0.0761081
\(581\) −21.1315 −0.876681
\(582\) 25.3402 1.05038
\(583\) 10.6457 0.440900
\(584\) −7.90337 −0.327044
\(585\) 4.53360 0.187441
\(586\) 32.9911 1.36285
\(587\) 10.7811 0.444985 0.222493 0.974934i \(-0.428581\pi\)
0.222493 + 0.974934i \(0.428581\pi\)
\(588\) −4.42274 −0.182391
\(589\) 23.3335 0.961440
\(590\) −7.33733 −0.302073
\(591\) −2.70535 −0.111283
\(592\) −2.75061 −0.113049
\(593\) −38.5134 −1.58156 −0.790779 0.612102i \(-0.790324\pi\)
−0.790779 + 0.612102i \(0.790324\pi\)
\(594\) −3.96791 −0.162805
\(595\) 0.795379 0.0326074
\(596\) 18.7464 0.767882
\(597\) 40.4196 1.65427
\(598\) −0.624496 −0.0255375
\(599\) 6.36495 0.260065 0.130032 0.991510i \(-0.458492\pi\)
0.130032 + 0.991510i \(0.458492\pi\)
\(600\) 9.81604 0.400738
\(601\) −3.31049 −0.135038 −0.0675189 0.997718i \(-0.521508\pi\)
−0.0675189 + 0.997718i \(0.521508\pi\)
\(602\) 11.6282 0.473930
\(603\) 1.19324 0.0485924
\(604\) −20.4397 −0.831680
\(605\) 5.47777 0.222703
\(606\) −6.56587 −0.266720
\(607\) −0.296238 −0.0120239 −0.00601197 0.999982i \(-0.501914\pi\)
−0.00601197 + 0.999982i \(0.501914\pi\)
\(608\) 2.18243 0.0885094
\(609\) −20.3286 −0.823757
\(610\) 1.08430 0.0439020
\(611\) 16.4875 0.667013
\(612\) −0.651114 −0.0263197
\(613\) 41.5640 1.67876 0.839378 0.543549i \(-0.182920\pi\)
0.839378 + 0.543549i \(0.182920\pi\)
\(614\) 22.6839 0.915448
\(615\) −4.32158 −0.174263
\(616\) −3.58902 −0.144606
\(617\) 22.9112 0.922370 0.461185 0.887304i \(-0.347424\pi\)
0.461185 + 0.887304i \(0.347424\pi\)
\(618\) −32.2323 −1.29657
\(619\) −1.82194 −0.0732301 −0.0366151 0.999329i \(-0.511658\pi\)
−0.0366151 + 0.999329i \(0.511658\pi\)
\(620\) −6.10988 −0.245379
\(621\) 0.370729 0.0148768
\(622\) 0.327113 0.0131161
\(623\) −50.8788 −2.03842
\(624\) 11.8037 0.472525
\(625\) 20.2080 0.808319
\(626\) −2.76056 −0.110334
\(627\) 5.45208 0.217735
\(628\) 1.38318 0.0551948
\(629\) 1.26868 0.0505857
\(630\) −2.43435 −0.0969869
\(631\) 39.0695 1.55533 0.777665 0.628678i \(-0.216404\pi\)
0.777665 + 0.628678i \(0.216404\pi\)
\(632\) −1.47331 −0.0586050
\(633\) 3.71678 0.147729
\(634\) −21.5671 −0.856539
\(635\) 5.78263 0.229477
\(636\) 18.7999 0.745466
\(637\) −11.8333 −0.468852
\(638\) −3.81478 −0.151029
\(639\) −13.8404 −0.547516
\(640\) −0.571471 −0.0225894
\(641\) −8.79739 −0.347476 −0.173738 0.984792i \(-0.555585\pi\)
−0.173738 + 0.984792i \(0.555585\pi\)
\(642\) −35.4590 −1.39946
\(643\) 1.70336 0.0671738 0.0335869 0.999436i \(-0.489307\pi\)
0.0335869 + 0.999436i \(0.489307\pi\)
\(644\) 0.335328 0.0132138
\(645\) 4.62544 0.182126
\(646\) −1.00662 −0.0396049
\(647\) −21.6115 −0.849637 −0.424819 0.905278i \(-0.639662\pi\)
−0.424819 + 0.905278i \(0.639662\pi\)
\(648\) −11.2422 −0.441635
\(649\) −15.2709 −0.599434
\(650\) 26.2634 1.03013
\(651\) −67.7635 −2.65586
\(652\) 10.4329 0.408582
\(653\) 2.80818 0.109893 0.0549463 0.998489i \(-0.482501\pi\)
0.0549463 + 0.998489i \(0.482501\pi\)
\(654\) 9.08587 0.355286
\(655\) −1.07529 −0.0420151
\(656\) −3.60037 −0.140571
\(657\) −11.1570 −0.435274
\(658\) −8.85311 −0.345130
\(659\) 29.6050 1.15325 0.576623 0.817011i \(-0.304370\pi\)
0.576623 + 0.817011i \(0.304370\pi\)
\(660\) −1.42763 −0.0555704
\(661\) −6.83459 −0.265835 −0.132917 0.991127i \(-0.542434\pi\)
−0.132917 + 0.991127i \(0.542434\pi\)
\(662\) −0.419719 −0.0163128
\(663\) −5.44428 −0.211439
\(664\) −7.00283 −0.271762
\(665\) −3.76349 −0.145942
\(666\) −3.88295 −0.150461
\(667\) 0.356422 0.0138007
\(668\) 2.57038 0.0994512
\(669\) 26.0462 1.00700
\(670\) −0.483045 −0.0186617
\(671\) 2.25670 0.0871190
\(672\) −6.33808 −0.244497
\(673\) −10.2477 −0.395020 −0.197510 0.980301i \(-0.563286\pi\)
−0.197510 + 0.980301i \(0.563286\pi\)
\(674\) −24.3871 −0.939356
\(675\) −15.5911 −0.600102
\(676\) 18.5813 0.714667
\(677\) 7.34302 0.282215 0.141108 0.989994i \(-0.454934\pi\)
0.141108 + 0.989994i \(0.454934\pi\)
\(678\) −13.9339 −0.535130
\(679\) −36.4053 −1.39711
\(680\) 0.263584 0.0101080
\(681\) −7.90888 −0.303069
\(682\) −12.7162 −0.486929
\(683\) 3.12947 0.119746 0.0598730 0.998206i \(-0.480930\pi\)
0.0598730 + 0.998206i \(0.480930\pi\)
\(684\) 3.08088 0.117800
\(685\) −10.1144 −0.386452
\(686\) −14.7689 −0.563881
\(687\) −36.6189 −1.39710
\(688\) 3.85351 0.146914
\(689\) 50.3002 1.91629
\(690\) 0.133386 0.00507792
\(691\) 29.9139 1.13798 0.568989 0.822345i \(-0.307335\pi\)
0.568989 + 0.822345i \(0.307335\pi\)
\(692\) −2.17575 −0.0827094
\(693\) −5.06651 −0.192461
\(694\) −21.5409 −0.817681
\(695\) 8.49987 0.322419
\(696\) −6.73677 −0.255357
\(697\) 1.66062 0.0629006
\(698\) −12.6704 −0.479584
\(699\) −12.0148 −0.454440
\(700\) −14.1023 −0.533018
\(701\) −35.7472 −1.35015 −0.675077 0.737747i \(-0.735890\pi\)
−0.675077 + 0.737747i \(0.735890\pi\)
\(702\) −18.7481 −0.707602
\(703\) −6.00302 −0.226408
\(704\) −1.18938 −0.0448263
\(705\) −3.52156 −0.132630
\(706\) −0.181780 −0.00684139
\(707\) 9.43294 0.354762
\(708\) −26.9678 −1.01351
\(709\) −32.8622 −1.23416 −0.617082 0.786898i \(-0.711686\pi\)
−0.617082 + 0.786898i \(0.711686\pi\)
\(710\) 5.60284 0.210271
\(711\) −2.07982 −0.0779995
\(712\) −16.8609 −0.631889
\(713\) 1.18810 0.0444947
\(714\) 2.92335 0.109404
\(715\) −3.81970 −0.142849
\(716\) −21.0627 −0.787151
\(717\) 1.92228 0.0717887
\(718\) −3.44057 −0.128401
\(719\) 33.5746 1.25212 0.626061 0.779774i \(-0.284666\pi\)
0.626061 + 0.779774i \(0.284666\pi\)
\(720\) −0.806729 −0.0300650
\(721\) 46.3069 1.72456
\(722\) −14.2370 −0.529846
\(723\) 18.0065 0.669668
\(724\) −10.3419 −0.384352
\(725\) −14.9894 −0.556694
\(726\) 20.1331 0.747210
\(727\) −13.6317 −0.505573 −0.252786 0.967522i \(-0.581347\pi\)
−0.252786 + 0.967522i \(0.581347\pi\)
\(728\) −16.9579 −0.628500
\(729\) 5.15129 0.190789
\(730\) 4.51655 0.167165
\(731\) −1.77738 −0.0657389
\(732\) 3.98526 0.147299
\(733\) 42.5900 1.57310 0.786549 0.617528i \(-0.211866\pi\)
0.786549 + 0.617528i \(0.211866\pi\)
\(734\) 1.92925 0.0712100
\(735\) 2.52747 0.0932271
\(736\) 0.111126 0.00409614
\(737\) −1.00534 −0.0370322
\(738\) −5.08254 −0.187091
\(739\) 18.8417 0.693105 0.346552 0.938031i \(-0.387352\pi\)
0.346552 + 0.938031i \(0.387352\pi\)
\(740\) 1.57189 0.0577839
\(741\) 25.7607 0.946343
\(742\) −27.0091 −0.991537
\(743\) 1.11868 0.0410406 0.0205203 0.999789i \(-0.493468\pi\)
0.0205203 + 0.999789i \(0.493468\pi\)
\(744\) −22.4564 −0.823291
\(745\) −10.7130 −0.392494
\(746\) −19.7154 −0.721832
\(747\) −9.88568 −0.361698
\(748\) 0.548585 0.0200582
\(749\) 50.9426 1.86140
\(750\) −11.6112 −0.423980
\(751\) −8.51148 −0.310588 −0.155294 0.987868i \(-0.549633\pi\)
−0.155294 + 0.987868i \(0.549633\pi\)
\(752\) −2.93386 −0.106987
\(753\) 9.82967 0.358213
\(754\) −18.0246 −0.656417
\(755\) 11.6807 0.425104
\(756\) 10.0670 0.366132
\(757\) 16.1593 0.587321 0.293661 0.955910i \(-0.405126\pi\)
0.293661 + 0.955910i \(0.405126\pi\)
\(758\) 8.07357 0.293245
\(759\) 0.277610 0.0100766
\(760\) −1.24720 −0.0452406
\(761\) 28.7713 1.04296 0.521480 0.853264i \(-0.325380\pi\)
0.521480 + 0.853264i \(0.325380\pi\)
\(762\) 21.2536 0.769937
\(763\) −13.0533 −0.472562
\(764\) 0.655753 0.0237243
\(765\) 0.372093 0.0134531
\(766\) 3.38074 0.122151
\(767\) −72.1538 −2.60532
\(768\) −2.10040 −0.0757916
\(769\) −19.9712 −0.720178 −0.360089 0.932918i \(-0.617254\pi\)
−0.360089 + 0.932918i \(0.617254\pi\)
\(770\) 2.05102 0.0739136
\(771\) 53.1217 1.91313
\(772\) 2.17573 0.0783063
\(773\) 12.3630 0.444665 0.222332 0.974971i \(-0.428633\pi\)
0.222332 + 0.974971i \(0.428633\pi\)
\(774\) 5.43989 0.195533
\(775\) −49.9659 −1.79483
\(776\) −12.0645 −0.433089
\(777\) 17.4336 0.625426
\(778\) −13.5165 −0.484590
\(779\) −7.85757 −0.281527
\(780\) −6.74545 −0.241526
\(781\) 11.6609 0.417261
\(782\) −0.0512552 −0.00183288
\(783\) 10.7002 0.382395
\(784\) 2.10567 0.0752024
\(785\) −0.790446 −0.0282122
\(786\) −3.95214 −0.140968
\(787\) −2.28758 −0.0815436 −0.0407718 0.999168i \(-0.512982\pi\)
−0.0407718 + 0.999168i \(0.512982\pi\)
\(788\) 1.28802 0.0458837
\(789\) 37.8721 1.34828
\(790\) 0.841953 0.0299553
\(791\) 20.0184 0.711771
\(792\) −1.67901 −0.0596609
\(793\) 10.6628 0.378646
\(794\) −16.7146 −0.593180
\(795\) −10.7436 −0.381037
\(796\) −19.2438 −0.682079
\(797\) −17.0454 −0.603779 −0.301890 0.953343i \(-0.597617\pi\)
−0.301890 + 0.953343i \(0.597617\pi\)
\(798\) −13.8324 −0.489663
\(799\) 1.35321 0.0478730
\(800\) −4.67342 −0.165230
\(801\) −23.8020 −0.841004
\(802\) −12.8696 −0.454442
\(803\) 9.40009 0.331722
\(804\) −1.77540 −0.0626134
\(805\) −0.191630 −0.00675408
\(806\) −60.0833 −2.11634
\(807\) 16.7508 0.589655
\(808\) 3.12601 0.109973
\(809\) −2.04016 −0.0717283 −0.0358642 0.999357i \(-0.511418\pi\)
−0.0358642 + 0.999357i \(0.511418\pi\)
\(810\) 6.42459 0.225737
\(811\) 8.41659 0.295546 0.147773 0.989021i \(-0.452789\pi\)
0.147773 + 0.989021i \(0.452789\pi\)
\(812\) 9.67846 0.339647
\(813\) 62.8532 2.20436
\(814\) 3.27151 0.114666
\(815\) −5.96208 −0.208843
\(816\) 0.968781 0.0339141
\(817\) 8.41004 0.294230
\(818\) 12.6660 0.442857
\(819\) −23.9389 −0.836493
\(820\) 2.05751 0.0718513
\(821\) −25.0850 −0.875472 −0.437736 0.899104i \(-0.644220\pi\)
−0.437736 + 0.899104i \(0.644220\pi\)
\(822\) −37.1747 −1.29662
\(823\) 15.3427 0.534813 0.267407 0.963584i \(-0.413833\pi\)
0.267407 + 0.963584i \(0.413833\pi\)
\(824\) 15.3458 0.534596
\(825\) −11.6750 −0.406470
\(826\) 38.7436 1.34806
\(827\) −24.1699 −0.840470 −0.420235 0.907415i \(-0.638052\pi\)
−0.420235 + 0.907415i \(0.638052\pi\)
\(828\) 0.156873 0.00545170
\(829\) −8.91433 −0.309607 −0.154804 0.987945i \(-0.549475\pi\)
−0.154804 + 0.987945i \(0.549475\pi\)
\(830\) 4.00191 0.138908
\(831\) 29.8233 1.03456
\(832\) −5.61973 −0.194829
\(833\) −0.971212 −0.0336505
\(834\) 31.2406 1.08177
\(835\) −1.46890 −0.0508334
\(836\) −2.59574 −0.0897754
\(837\) 35.6682 1.23287
\(838\) −0.334875 −0.0115681
\(839\) 37.9865 1.31144 0.655719 0.755005i \(-0.272365\pi\)
0.655719 + 0.755005i \(0.272365\pi\)
\(840\) 3.62203 0.124972
\(841\) −18.7127 −0.645266
\(842\) 9.64771 0.332482
\(843\) 53.7042 1.84967
\(844\) −1.76956 −0.0609108
\(845\) −10.6187 −0.365294
\(846\) −4.14165 −0.142393
\(847\) −28.9245 −0.993856
\(848\) −8.95066 −0.307367
\(849\) 11.8909 0.408096
\(850\) 2.15555 0.0739349
\(851\) −0.305663 −0.0104780
\(852\) 20.5928 0.705498
\(853\) −50.5354 −1.73030 −0.865150 0.501513i \(-0.832777\pi\)
−0.865150 + 0.501513i \(0.832777\pi\)
\(854\) −5.72546 −0.195921
\(855\) −1.76063 −0.0602123
\(856\) 16.8821 0.577017
\(857\) 56.5372 1.93127 0.965637 0.259894i \(-0.0836877\pi\)
0.965637 + 0.259894i \(0.0836877\pi\)
\(858\) −14.0390 −0.479284
\(859\) 24.4426 0.833969 0.416985 0.908914i \(-0.363087\pi\)
0.416985 + 0.908914i \(0.363087\pi\)
\(860\) −2.20217 −0.0750934
\(861\) 22.8194 0.777684
\(862\) 26.9205 0.916916
\(863\) −17.3511 −0.590639 −0.295319 0.955399i \(-0.595426\pi\)
−0.295319 + 0.955399i \(0.595426\pi\)
\(864\) 3.33612 0.113497
\(865\) 1.24338 0.0422760
\(866\) 15.0759 0.512300
\(867\) 35.2599 1.19749
\(868\) 32.2622 1.09505
\(869\) 1.75232 0.0594433
\(870\) 3.84987 0.130523
\(871\) −4.75017 −0.160953
\(872\) −4.32579 −0.146490
\(873\) −17.0311 −0.576414
\(874\) 0.242524 0.00820351
\(875\) 16.6813 0.563931
\(876\) 16.6002 0.560869
\(877\) −1.59693 −0.0539245 −0.0269622 0.999636i \(-0.508583\pi\)
−0.0269622 + 0.999636i \(0.508583\pi\)
\(878\) 8.36521 0.282312
\(879\) −69.2944 −2.33724
\(880\) 0.679695 0.0229125
\(881\) 23.6990 0.798438 0.399219 0.916856i \(-0.369281\pi\)
0.399219 + 0.916856i \(0.369281\pi\)
\(882\) 2.97251 0.100090
\(883\) −34.6138 −1.16485 −0.582423 0.812886i \(-0.697895\pi\)
−0.582423 + 0.812886i \(0.697895\pi\)
\(884\) 2.59203 0.0871793
\(885\) 15.4113 0.518046
\(886\) 3.00833 0.101067
\(887\) −18.9605 −0.636631 −0.318316 0.947985i \(-0.603117\pi\)
−0.318316 + 0.947985i \(0.603117\pi\)
\(888\) 5.77737 0.193876
\(889\) −30.5342 −1.02408
\(890\) 9.63552 0.322983
\(891\) 13.3712 0.447952
\(892\) −12.4006 −0.415203
\(893\) −6.40296 −0.214267
\(894\) −39.3748 −1.31689
\(895\) 12.0367 0.402344
\(896\) 3.01756 0.100810
\(897\) 1.31169 0.0437960
\(898\) −9.96365 −0.332491
\(899\) 34.2917 1.14369
\(900\) −6.59733 −0.219911
\(901\) 4.12837 0.137536
\(902\) 4.28220 0.142582
\(903\) −24.4239 −0.812775
\(904\) 6.63395 0.220642
\(905\) 5.91007 0.196457
\(906\) 42.9315 1.42630
\(907\) 4.62771 0.153661 0.0768304 0.997044i \(-0.475520\pi\)
0.0768304 + 0.997044i \(0.475520\pi\)
\(908\) 3.76542 0.124960
\(909\) 4.41290 0.146367
\(910\) 9.69093 0.321251
\(911\) −18.6525 −0.617985 −0.308993 0.951064i \(-0.599992\pi\)
−0.308993 + 0.951064i \(0.599992\pi\)
\(912\) −4.58398 −0.151791
\(913\) 8.32900 0.275650
\(914\) 36.3378 1.20195
\(915\) −2.27746 −0.0752905
\(916\) 17.4343 0.576044
\(917\) 5.67789 0.187501
\(918\) −1.53874 −0.0507861
\(919\) 16.1258 0.531940 0.265970 0.963981i \(-0.414308\pi\)
0.265970 + 0.963981i \(0.414308\pi\)
\(920\) −0.0635051 −0.00209370
\(921\) −47.6452 −1.56996
\(922\) −17.0377 −0.561108
\(923\) 55.0972 1.81355
\(924\) 7.53836 0.247994
\(925\) 12.8547 0.422661
\(926\) 25.8486 0.849436
\(927\) 21.6632 0.711513
\(928\) 3.20738 0.105287
\(929\) −53.3143 −1.74918 −0.874592 0.484859i \(-0.838871\pi\)
−0.874592 + 0.484859i \(0.838871\pi\)
\(930\) 12.8332 0.420817
\(931\) 4.59548 0.150611
\(932\) 5.72024 0.187373
\(933\) −0.687068 −0.0224936
\(934\) 11.2437 0.367906
\(935\) −0.313500 −0.0102526
\(936\) −7.93320 −0.259305
\(937\) 42.4663 1.38731 0.693656 0.720306i \(-0.255999\pi\)
0.693656 + 0.720306i \(0.255999\pi\)
\(938\) 2.55064 0.0832814
\(939\) 5.79828 0.189220
\(940\) 1.67662 0.0546853
\(941\) 26.2983 0.857299 0.428650 0.903471i \(-0.358990\pi\)
0.428650 + 0.903471i \(0.358990\pi\)
\(942\) −2.90522 −0.0946573
\(943\) −0.400093 −0.0130288
\(944\) 12.8394 0.417886
\(945\) −5.75297 −0.187144
\(946\) −4.58328 −0.149015
\(947\) 17.9840 0.584400 0.292200 0.956357i \(-0.405613\pi\)
0.292200 + 0.956357i \(0.405613\pi\)
\(948\) 3.09453 0.100506
\(949\) 44.4148 1.44177
\(950\) −10.1994 −0.330913
\(951\) 45.2995 1.46894
\(952\) −1.39181 −0.0451088
\(953\) 20.9575 0.678879 0.339440 0.940628i \(-0.389763\pi\)
0.339440 + 0.940628i \(0.389763\pi\)
\(954\) −12.6354 −0.409085
\(955\) −0.374744 −0.0121264
\(956\) −0.915196 −0.0295996
\(957\) 8.01256 0.259009
\(958\) 20.0928 0.649170
\(959\) 53.4075 1.72462
\(960\) 1.20032 0.0387401
\(961\) 83.3081 2.68736
\(962\) 15.4577 0.498375
\(963\) 23.8319 0.767972
\(964\) −8.57289 −0.276114
\(965\) −1.24337 −0.0400254
\(966\) −0.704323 −0.0226612
\(967\) −6.51940 −0.209650 −0.104825 0.994491i \(-0.533428\pi\)
−0.104825 + 0.994491i \(0.533428\pi\)
\(968\) −9.58538 −0.308086
\(969\) 2.11430 0.0679211
\(970\) 6.89450 0.221369
\(971\) 4.25646 0.136596 0.0682982 0.997665i \(-0.478243\pi\)
0.0682982 + 0.997665i \(0.478243\pi\)
\(972\) 13.6047 0.436371
\(973\) −44.8822 −1.43886
\(974\) −15.9412 −0.510788
\(975\) −55.1635 −1.76665
\(976\) −1.89738 −0.0607337
\(977\) −30.4906 −0.975482 −0.487741 0.872988i \(-0.662179\pi\)
−0.487741 + 0.872988i \(0.662179\pi\)
\(978\) −21.9132 −0.700706
\(979\) 20.0540 0.640928
\(980\) −1.20333 −0.0384389
\(981\) −6.10658 −0.194968
\(982\) −1.33619 −0.0426396
\(983\) 24.1118 0.769048 0.384524 0.923115i \(-0.374366\pi\)
0.384524 + 0.923115i \(0.374366\pi\)
\(984\) 7.56221 0.241074
\(985\) −0.736064 −0.0234529
\(986\) −1.47936 −0.0471125
\(987\) 18.5950 0.591887
\(988\) −12.2647 −0.390192
\(989\) 0.428224 0.0136167
\(990\) 0.959504 0.0304951
\(991\) −22.7615 −0.723043 −0.361522 0.932364i \(-0.617743\pi\)
−0.361522 + 0.932364i \(0.617743\pi\)
\(992\) 10.6915 0.339455
\(993\) 0.881577 0.0279760
\(994\) −29.5849 −0.938376
\(995\) 10.9973 0.348637
\(996\) 14.7087 0.466064
\(997\) 32.8062 1.03898 0.519491 0.854476i \(-0.326122\pi\)
0.519491 + 0.854476i \(0.326122\pi\)
\(998\) −22.7132 −0.718973
\(999\) −9.17637 −0.290328
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 8006.2.a.a.1.15 69
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8006.2.a.a.1.15 69 1.1 even 1 trivial