Properties

Label 8007.2.a.i.1.5
Level $8007$
Weight $2$
Character 8007.1
Self dual yes
Analytic conductor $63.936$
Analytic rank $0$
Dimension $63$
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] = [8007,2,Mod(1,8007)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("8007.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8007.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: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(63\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 8007.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.34343 q^{2} +1.00000 q^{3} +3.49167 q^{4} +2.63222 q^{5} -2.34343 q^{6} +1.69426 q^{7} -3.49562 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.34343 q^{2} +1.00000 q^{3} +3.49167 q^{4} +2.63222 q^{5} -2.34343 q^{6} +1.69426 q^{7} -3.49562 q^{8} +1.00000 q^{9} -6.16842 q^{10} -1.32194 q^{11} +3.49167 q^{12} +4.21493 q^{13} -3.97037 q^{14} +2.63222 q^{15} +1.20841 q^{16} +1.00000 q^{17} -2.34343 q^{18} +0.200368 q^{19} +9.19083 q^{20} +1.69426 q^{21} +3.09787 q^{22} -3.01962 q^{23} -3.49562 q^{24} +1.92857 q^{25} -9.87740 q^{26} +1.00000 q^{27} +5.91578 q^{28} +5.81319 q^{29} -6.16842 q^{30} -8.08840 q^{31} +4.15942 q^{32} -1.32194 q^{33} -2.34343 q^{34} +4.45965 q^{35} +3.49167 q^{36} -3.41483 q^{37} -0.469548 q^{38} +4.21493 q^{39} -9.20123 q^{40} +2.29353 q^{41} -3.97037 q^{42} +0.581734 q^{43} -4.61576 q^{44} +2.63222 q^{45} +7.07628 q^{46} +8.80652 q^{47} +1.20841 q^{48} -4.12949 q^{49} -4.51946 q^{50} +1.00000 q^{51} +14.7171 q^{52} +0.940952 q^{53} -2.34343 q^{54} -3.47962 q^{55} -5.92248 q^{56} +0.200368 q^{57} -13.6228 q^{58} -0.347504 q^{59} +9.19083 q^{60} +5.96624 q^{61} +18.9546 q^{62} +1.69426 q^{63} -12.1641 q^{64} +11.0946 q^{65} +3.09787 q^{66} -0.333659 q^{67} +3.49167 q^{68} -3.01962 q^{69} -10.4509 q^{70} +5.17052 q^{71} -3.49562 q^{72} -8.65040 q^{73} +8.00242 q^{74} +1.92857 q^{75} +0.699618 q^{76} -2.23970 q^{77} -9.87740 q^{78} +5.40248 q^{79} +3.18078 q^{80} +1.00000 q^{81} -5.37474 q^{82} +4.12163 q^{83} +5.91578 q^{84} +2.63222 q^{85} -1.36325 q^{86} +5.81319 q^{87} +4.62098 q^{88} +11.1722 q^{89} -6.16842 q^{90} +7.14118 q^{91} -10.5435 q^{92} -8.08840 q^{93} -20.6375 q^{94} +0.527412 q^{95} +4.15942 q^{96} -16.3073 q^{97} +9.67718 q^{98} -1.32194 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34343 −1.65706 −0.828528 0.559948i \(-0.810821\pi\)
−0.828528 + 0.559948i \(0.810821\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.49167 1.74583
\(5\) 2.63222 1.17716 0.588582 0.808438i \(-0.299687\pi\)
0.588582 + 0.808438i \(0.299687\pi\)
\(6\) −2.34343 −0.956702
\(7\) 1.69426 0.640369 0.320184 0.947355i \(-0.396255\pi\)
0.320184 + 0.947355i \(0.396255\pi\)
\(8\) −3.49562 −1.23589
\(9\) 1.00000 0.333333
\(10\) −6.16842 −1.95063
\(11\) −1.32194 −0.398579 −0.199289 0.979941i \(-0.563863\pi\)
−0.199289 + 0.979941i \(0.563863\pi\)
\(12\) 3.49167 1.00796
\(13\) 4.21493 1.16901 0.584506 0.811389i \(-0.301288\pi\)
0.584506 + 0.811389i \(0.301288\pi\)
\(14\) −3.97037 −1.06113
\(15\) 2.63222 0.679636
\(16\) 1.20841 0.302101
\(17\) 1.00000 0.242536
\(18\) −2.34343 −0.552352
\(19\) 0.200368 0.0459676 0.0229838 0.999736i \(-0.492683\pi\)
0.0229838 + 0.999736i \(0.492683\pi\)
\(20\) 9.19083 2.05513
\(21\) 1.69426 0.369717
\(22\) 3.09787 0.660467
\(23\) −3.01962 −0.629635 −0.314818 0.949152i \(-0.601943\pi\)
−0.314818 + 0.949152i \(0.601943\pi\)
\(24\) −3.49562 −0.713540
\(25\) 1.92857 0.385713
\(26\) −9.87740 −1.93712
\(27\) 1.00000 0.192450
\(28\) 5.91578 1.11798
\(29\) 5.81319 1.07948 0.539741 0.841831i \(-0.318522\pi\)
0.539741 + 0.841831i \(0.318522\pi\)
\(30\) −6.16842 −1.12619
\(31\) −8.08840 −1.45272 −0.726360 0.687315i \(-0.758789\pi\)
−0.726360 + 0.687315i \(0.758789\pi\)
\(32\) 4.15942 0.735289
\(33\) −1.32194 −0.230120
\(34\) −2.34343 −0.401895
\(35\) 4.45965 0.753819
\(36\) 3.49167 0.581945
\(37\) −3.41483 −0.561395 −0.280698 0.959796i \(-0.590566\pi\)
−0.280698 + 0.959796i \(0.590566\pi\)
\(38\) −0.469548 −0.0761708
\(39\) 4.21493 0.674929
\(40\) −9.20123 −1.45484
\(41\) 2.29353 0.358190 0.179095 0.983832i \(-0.442683\pi\)
0.179095 + 0.983832i \(0.442683\pi\)
\(42\) −3.97037 −0.612642
\(43\) 0.581734 0.0887136 0.0443568 0.999016i \(-0.485876\pi\)
0.0443568 + 0.999016i \(0.485876\pi\)
\(44\) −4.61576 −0.695852
\(45\) 2.63222 0.392388
\(46\) 7.07628 1.04334
\(47\) 8.80652 1.28456 0.642282 0.766469i \(-0.277988\pi\)
0.642282 + 0.766469i \(0.277988\pi\)
\(48\) 1.20841 0.174418
\(49\) −4.12949 −0.589928
\(50\) −4.51946 −0.639149
\(51\) 1.00000 0.140028
\(52\) 14.7171 2.04090
\(53\) 0.940952 0.129250 0.0646249 0.997910i \(-0.479415\pi\)
0.0646249 + 0.997910i \(0.479415\pi\)
\(54\) −2.34343 −0.318901
\(55\) −3.47962 −0.469192
\(56\) −5.92248 −0.791424
\(57\) 0.200368 0.0265394
\(58\) −13.6228 −1.78876
\(59\) −0.347504 −0.0452412 −0.0226206 0.999744i \(-0.507201\pi\)
−0.0226206 + 0.999744i \(0.507201\pi\)
\(60\) 9.19083 1.18653
\(61\) 5.96624 0.763898 0.381949 0.924183i \(-0.375253\pi\)
0.381949 + 0.924183i \(0.375253\pi\)
\(62\) 18.9546 2.40724
\(63\) 1.69426 0.213456
\(64\) −12.1641 −1.52052
\(65\) 11.0946 1.37612
\(66\) 3.09787 0.381321
\(67\) −0.333659 −0.0407629 −0.0203815 0.999792i \(-0.506488\pi\)
−0.0203815 + 0.999792i \(0.506488\pi\)
\(68\) 3.49167 0.423427
\(69\) −3.01962 −0.363520
\(70\) −10.4509 −1.24912
\(71\) 5.17052 0.613628 0.306814 0.951770i \(-0.400737\pi\)
0.306814 + 0.951770i \(0.400737\pi\)
\(72\) −3.49562 −0.411963
\(73\) −8.65040 −1.01245 −0.506226 0.862401i \(-0.668960\pi\)
−0.506226 + 0.862401i \(0.668960\pi\)
\(74\) 8.00242 0.930263
\(75\) 1.92857 0.222692
\(76\) 0.699618 0.0802517
\(77\) −2.23970 −0.255237
\(78\) −9.87740 −1.11840
\(79\) 5.40248 0.607827 0.303913 0.952700i \(-0.401707\pi\)
0.303913 + 0.952700i \(0.401707\pi\)
\(80\) 3.18078 0.355623
\(81\) 1.00000 0.111111
\(82\) −5.37474 −0.593540
\(83\) 4.12163 0.452408 0.226204 0.974080i \(-0.427368\pi\)
0.226204 + 0.974080i \(0.427368\pi\)
\(84\) 5.91578 0.645465
\(85\) 2.63222 0.285504
\(86\) −1.36325 −0.147003
\(87\) 5.81319 0.623239
\(88\) 4.62098 0.492599
\(89\) 11.1722 1.18425 0.592126 0.805845i \(-0.298289\pi\)
0.592126 + 0.805845i \(0.298289\pi\)
\(90\) −6.16842 −0.650208
\(91\) 7.14118 0.748599
\(92\) −10.5435 −1.09924
\(93\) −8.08840 −0.838728
\(94\) −20.6375 −2.12859
\(95\) 0.527412 0.0541113
\(96\) 4.15942 0.424519
\(97\) −16.3073 −1.65576 −0.827879 0.560907i \(-0.810452\pi\)
−0.827879 + 0.560907i \(0.810452\pi\)
\(98\) 9.67718 0.977543
\(99\) −1.32194 −0.132860
\(100\) 6.73392 0.673392
\(101\) 12.5834 1.25210 0.626049 0.779783i \(-0.284671\pi\)
0.626049 + 0.779783i \(0.284671\pi\)
\(102\) −2.34343 −0.232034
\(103\) 13.9393 1.37348 0.686738 0.726905i \(-0.259042\pi\)
0.686738 + 0.726905i \(0.259042\pi\)
\(104\) −14.7338 −1.44477
\(105\) 4.45965 0.435218
\(106\) −2.20506 −0.214174
\(107\) −20.2486 −1.95751 −0.978755 0.205035i \(-0.934269\pi\)
−0.978755 + 0.205035i \(0.934269\pi\)
\(108\) 3.49167 0.335986
\(109\) 10.7016 1.02502 0.512512 0.858680i \(-0.328715\pi\)
0.512512 + 0.858680i \(0.328715\pi\)
\(110\) 8.15426 0.777478
\(111\) −3.41483 −0.324122
\(112\) 2.04735 0.193456
\(113\) 6.67043 0.627502 0.313751 0.949505i \(-0.398414\pi\)
0.313751 + 0.949505i \(0.398414\pi\)
\(114\) −0.469548 −0.0439772
\(115\) −7.94831 −0.741183
\(116\) 20.2977 1.88460
\(117\) 4.21493 0.389671
\(118\) 0.814351 0.0749671
\(119\) 1.69426 0.155312
\(120\) −9.20123 −0.839953
\(121\) −9.25248 −0.841135
\(122\) −13.9815 −1.26582
\(123\) 2.29353 0.206801
\(124\) −28.2420 −2.53621
\(125\) −8.08468 −0.723116
\(126\) −3.97037 −0.353709
\(127\) 17.4233 1.54607 0.773035 0.634364i \(-0.218738\pi\)
0.773035 + 0.634364i \(0.218738\pi\)
\(128\) 20.1869 1.78429
\(129\) 0.581734 0.0512188
\(130\) −25.9995 −2.28030
\(131\) −6.85121 −0.598593 −0.299296 0.954160i \(-0.596752\pi\)
−0.299296 + 0.954160i \(0.596752\pi\)
\(132\) −4.61576 −0.401750
\(133\) 0.339475 0.0294362
\(134\) 0.781906 0.0675464
\(135\) 2.63222 0.226545
\(136\) −3.49562 −0.299747
\(137\) 10.3764 0.886512 0.443256 0.896395i \(-0.353823\pi\)
0.443256 + 0.896395i \(0.353823\pi\)
\(138\) 7.07628 0.602373
\(139\) 6.74346 0.571973 0.285986 0.958234i \(-0.407679\pi\)
0.285986 + 0.958234i \(0.407679\pi\)
\(140\) 15.5716 1.31604
\(141\) 8.80652 0.741643
\(142\) −12.1168 −1.01682
\(143\) −5.57187 −0.465943
\(144\) 1.20841 0.100700
\(145\) 15.3016 1.27073
\(146\) 20.2716 1.67769
\(147\) −4.12949 −0.340595
\(148\) −11.9235 −0.980102
\(149\) 7.13928 0.584872 0.292436 0.956285i \(-0.405534\pi\)
0.292436 + 0.956285i \(0.405534\pi\)
\(150\) −4.51946 −0.369013
\(151\) 17.3354 1.41073 0.705367 0.708842i \(-0.250782\pi\)
0.705367 + 0.708842i \(0.250782\pi\)
\(152\) −0.700410 −0.0568107
\(153\) 1.00000 0.0808452
\(154\) 5.24858 0.422943
\(155\) −21.2904 −1.71009
\(156\) 14.7171 1.17831
\(157\) 1.00000 0.0798087
\(158\) −12.6603 −1.00720
\(159\) 0.940952 0.0746224
\(160\) 10.9485 0.865555
\(161\) −5.11602 −0.403199
\(162\) −2.34343 −0.184117
\(163\) 21.3736 1.67411 0.837053 0.547122i \(-0.184276\pi\)
0.837053 + 0.547122i \(0.184276\pi\)
\(164\) 8.00825 0.625340
\(165\) −3.47962 −0.270888
\(166\) −9.65875 −0.749664
\(167\) −22.2209 −1.71950 −0.859752 0.510712i \(-0.829382\pi\)
−0.859752 + 0.510712i \(0.829382\pi\)
\(168\) −5.92248 −0.456929
\(169\) 4.76566 0.366589
\(170\) −6.16842 −0.473096
\(171\) 0.200368 0.0153225
\(172\) 2.03122 0.154879
\(173\) 8.90582 0.677097 0.338548 0.940949i \(-0.390064\pi\)
0.338548 + 0.940949i \(0.390064\pi\)
\(174\) −13.6228 −1.03274
\(175\) 3.26749 0.246999
\(176\) −1.59743 −0.120411
\(177\) −0.347504 −0.0261200
\(178\) −26.1813 −1.96237
\(179\) 20.6630 1.54443 0.772214 0.635362i \(-0.219149\pi\)
0.772214 + 0.635362i \(0.219149\pi\)
\(180\) 9.19083 0.685044
\(181\) 10.7691 0.800458 0.400229 0.916415i \(-0.368931\pi\)
0.400229 + 0.916415i \(0.368931\pi\)
\(182\) −16.7349 −1.24047
\(183\) 5.96624 0.441037
\(184\) 10.5555 0.778158
\(185\) −8.98858 −0.660854
\(186\) 18.9546 1.38982
\(187\) −1.32194 −0.0966696
\(188\) 30.7495 2.24263
\(189\) 1.69426 0.123239
\(190\) −1.23595 −0.0896655
\(191\) 16.4057 1.18707 0.593536 0.804808i \(-0.297732\pi\)
0.593536 + 0.804808i \(0.297732\pi\)
\(192\) −12.1641 −0.877870
\(193\) 10.1229 0.728664 0.364332 0.931269i \(-0.381297\pi\)
0.364332 + 0.931269i \(0.381297\pi\)
\(194\) 38.2151 2.74368
\(195\) 11.0946 0.794502
\(196\) −14.4188 −1.02992
\(197\) 9.56610 0.681556 0.340778 0.940144i \(-0.389309\pi\)
0.340778 + 0.940144i \(0.389309\pi\)
\(198\) 3.09787 0.220156
\(199\) −18.9114 −1.34059 −0.670297 0.742093i \(-0.733833\pi\)
−0.670297 + 0.742093i \(0.733833\pi\)
\(200\) −6.74154 −0.476699
\(201\) −0.333659 −0.0235345
\(202\) −29.4884 −2.07480
\(203\) 9.84904 0.691267
\(204\) 3.49167 0.244466
\(205\) 6.03708 0.421648
\(206\) −32.6657 −2.27593
\(207\) −3.01962 −0.209878
\(208\) 5.09335 0.353160
\(209\) −0.264874 −0.0183217
\(210\) −10.4509 −0.721180
\(211\) 11.1000 0.764158 0.382079 0.924130i \(-0.375208\pi\)
0.382079 + 0.924130i \(0.375208\pi\)
\(212\) 3.28549 0.225649
\(213\) 5.17052 0.354278
\(214\) 47.4513 3.24370
\(215\) 1.53125 0.104430
\(216\) −3.49562 −0.237847
\(217\) −13.7038 −0.930277
\(218\) −25.0784 −1.69852
\(219\) −8.65040 −0.584540
\(220\) −12.1497 −0.819132
\(221\) 4.21493 0.283527
\(222\) 8.00242 0.537088
\(223\) −11.8262 −0.791943 −0.395971 0.918263i \(-0.629592\pi\)
−0.395971 + 0.918263i \(0.629592\pi\)
\(224\) 7.04713 0.470856
\(225\) 1.92857 0.128571
\(226\) −15.6317 −1.03981
\(227\) −10.0902 −0.669710 −0.334855 0.942270i \(-0.608687\pi\)
−0.334855 + 0.942270i \(0.608687\pi\)
\(228\) 0.699618 0.0463333
\(229\) −2.86997 −0.189653 −0.0948266 0.995494i \(-0.530230\pi\)
−0.0948266 + 0.995494i \(0.530230\pi\)
\(230\) 18.6263 1.22818
\(231\) −2.23970 −0.147361
\(232\) −20.3207 −1.33412
\(233\) 21.0685 1.38024 0.690121 0.723694i \(-0.257557\pi\)
0.690121 + 0.723694i \(0.257557\pi\)
\(234\) −9.87740 −0.645706
\(235\) 23.1807 1.51214
\(236\) −1.21337 −0.0789835
\(237\) 5.40248 0.350929
\(238\) −3.97037 −0.257361
\(239\) 27.0493 1.74967 0.874836 0.484419i \(-0.160969\pi\)
0.874836 + 0.484419i \(0.160969\pi\)
\(240\) 3.18078 0.205319
\(241\) 15.2582 0.982868 0.491434 0.870915i \(-0.336473\pi\)
0.491434 + 0.870915i \(0.336473\pi\)
\(242\) 21.6826 1.39381
\(243\) 1.00000 0.0641500
\(244\) 20.8321 1.33364
\(245\) −10.8697 −0.694441
\(246\) −5.37474 −0.342681
\(247\) 0.844537 0.0537366
\(248\) 28.2740 1.79540
\(249\) 4.12163 0.261198
\(250\) 18.9459 1.19824
\(251\) −31.1231 −1.96447 −0.982236 0.187648i \(-0.939914\pi\)
−0.982236 + 0.187648i \(0.939914\pi\)
\(252\) 5.91578 0.372659
\(253\) 3.99175 0.250959
\(254\) −40.8303 −2.56192
\(255\) 2.63222 0.164836
\(256\) −22.9785 −1.43615
\(257\) 3.94888 0.246324 0.123162 0.992387i \(-0.460696\pi\)
0.123162 + 0.992387i \(0.460696\pi\)
\(258\) −1.36325 −0.0848724
\(259\) −5.78560 −0.359500
\(260\) 38.7387 2.40247
\(261\) 5.81319 0.359827
\(262\) 16.0553 0.991902
\(263\) 14.1209 0.870733 0.435366 0.900253i \(-0.356619\pi\)
0.435366 + 0.900253i \(0.356619\pi\)
\(264\) 4.62098 0.284402
\(265\) 2.47679 0.152148
\(266\) −0.795535 −0.0487774
\(267\) 11.1722 0.683728
\(268\) −1.16503 −0.0711653
\(269\) 23.8881 1.45648 0.728241 0.685321i \(-0.240338\pi\)
0.728241 + 0.685321i \(0.240338\pi\)
\(270\) −6.16842 −0.375398
\(271\) −17.5817 −1.06801 −0.534005 0.845481i \(-0.679314\pi\)
−0.534005 + 0.845481i \(0.679314\pi\)
\(272\) 1.20841 0.0732703
\(273\) 7.14118 0.432204
\(274\) −24.3163 −1.46900
\(275\) −2.54944 −0.153737
\(276\) −10.5435 −0.634645
\(277\) −16.3152 −0.980286 −0.490143 0.871642i \(-0.663055\pi\)
−0.490143 + 0.871642i \(0.663055\pi\)
\(278\) −15.8028 −0.947790
\(279\) −8.08840 −0.484240
\(280\) −15.5892 −0.931635
\(281\) 15.5401 0.927045 0.463522 0.886085i \(-0.346585\pi\)
0.463522 + 0.886085i \(0.346585\pi\)
\(282\) −20.6375 −1.22894
\(283\) −5.24539 −0.311806 −0.155903 0.987772i \(-0.549829\pi\)
−0.155903 + 0.987772i \(0.549829\pi\)
\(284\) 18.0537 1.07129
\(285\) 0.527412 0.0312412
\(286\) 13.0573 0.772094
\(287\) 3.88583 0.229374
\(288\) 4.15942 0.245096
\(289\) 1.00000 0.0588235
\(290\) −35.8582 −2.10567
\(291\) −16.3073 −0.955952
\(292\) −30.2043 −1.76757
\(293\) −14.5139 −0.847910 −0.423955 0.905683i \(-0.639358\pi\)
−0.423955 + 0.905683i \(0.639358\pi\)
\(294\) 9.67718 0.564385
\(295\) −0.914706 −0.0532562
\(296\) 11.9370 0.693821
\(297\) −1.32194 −0.0767065
\(298\) −16.7304 −0.969166
\(299\) −12.7275 −0.736051
\(300\) 6.73392 0.388783
\(301\) 0.985607 0.0568094
\(302\) −40.6243 −2.33766
\(303\) 12.5834 0.722900
\(304\) 0.242126 0.0138869
\(305\) 15.7044 0.899233
\(306\) −2.34343 −0.133965
\(307\) −15.7810 −0.900667 −0.450334 0.892860i \(-0.648695\pi\)
−0.450334 + 0.892860i \(0.648695\pi\)
\(308\) −7.82029 −0.445602
\(309\) 13.9393 0.792977
\(310\) 49.8926 2.83371
\(311\) 17.2449 0.977867 0.488933 0.872321i \(-0.337386\pi\)
0.488933 + 0.872321i \(0.337386\pi\)
\(312\) −14.7338 −0.834137
\(313\) −1.31450 −0.0742997 −0.0371499 0.999310i \(-0.511828\pi\)
−0.0371499 + 0.999310i \(0.511828\pi\)
\(314\) −2.34343 −0.132247
\(315\) 4.45965 0.251273
\(316\) 18.8637 1.06116
\(317\) 25.3157 1.42187 0.710937 0.703256i \(-0.248271\pi\)
0.710937 + 0.703256i \(0.248271\pi\)
\(318\) −2.20506 −0.123653
\(319\) −7.68467 −0.430259
\(320\) −32.0186 −1.78990
\(321\) −20.2486 −1.13017
\(322\) 11.9890 0.668123
\(323\) 0.200368 0.0111488
\(324\) 3.49167 0.193982
\(325\) 8.12878 0.450904
\(326\) −50.0875 −2.77409
\(327\) 10.7016 0.591798
\(328\) −8.01732 −0.442682
\(329\) 14.9205 0.822595
\(330\) 8.15426 0.448877
\(331\) −8.93826 −0.491291 −0.245646 0.969360i \(-0.579000\pi\)
−0.245646 + 0.969360i \(0.579000\pi\)
\(332\) 14.3914 0.789828
\(333\) −3.41483 −0.187132
\(334\) 52.0731 2.84931
\(335\) −0.878263 −0.0479846
\(336\) 2.04735 0.111692
\(337\) −21.3670 −1.16394 −0.581968 0.813212i \(-0.697717\pi\)
−0.581968 + 0.813212i \(0.697717\pi\)
\(338\) −11.1680 −0.607459
\(339\) 6.67043 0.362288
\(340\) 9.19083 0.498443
\(341\) 10.6924 0.579023
\(342\) −0.469548 −0.0253903
\(343\) −18.8562 −1.01814
\(344\) −2.03352 −0.109640
\(345\) −7.94831 −0.427922
\(346\) −20.8702 −1.12199
\(347\) −8.11833 −0.435815 −0.217907 0.975969i \(-0.569923\pi\)
−0.217907 + 0.975969i \(0.569923\pi\)
\(348\) 20.2977 1.08807
\(349\) −23.8501 −1.27667 −0.638334 0.769759i \(-0.720376\pi\)
−0.638334 + 0.769759i \(0.720376\pi\)
\(350\) −7.65713 −0.409291
\(351\) 4.21493 0.224976
\(352\) −5.49849 −0.293071
\(353\) 13.0359 0.693833 0.346916 0.937896i \(-0.387229\pi\)
0.346916 + 0.937896i \(0.387229\pi\)
\(354\) 0.814351 0.0432823
\(355\) 13.6099 0.722340
\(356\) 39.0096 2.06751
\(357\) 1.69426 0.0896696
\(358\) −48.4224 −2.55920
\(359\) 12.7269 0.671698 0.335849 0.941916i \(-0.390977\pi\)
0.335849 + 0.941916i \(0.390977\pi\)
\(360\) −9.20123 −0.484947
\(361\) −18.9599 −0.997887
\(362\) −25.2365 −1.32640
\(363\) −9.25248 −0.485629
\(364\) 24.9346 1.30693
\(365\) −22.7697 −1.19182
\(366\) −13.9815 −0.730823
\(367\) −33.8498 −1.76695 −0.883473 0.468482i \(-0.844801\pi\)
−0.883473 + 0.468482i \(0.844801\pi\)
\(368\) −3.64893 −0.190214
\(369\) 2.29353 0.119397
\(370\) 21.0641 1.09507
\(371\) 1.59421 0.0827675
\(372\) −28.2420 −1.46428
\(373\) 30.4444 1.57635 0.788175 0.615451i \(-0.211026\pi\)
0.788175 + 0.615451i \(0.211026\pi\)
\(374\) 3.09787 0.160187
\(375\) −8.08468 −0.417491
\(376\) −30.7843 −1.58758
\(377\) 24.5022 1.26193
\(378\) −3.97037 −0.204214
\(379\) −26.8570 −1.37955 −0.689775 0.724024i \(-0.742291\pi\)
−0.689775 + 0.724024i \(0.742291\pi\)
\(380\) 1.84155 0.0944693
\(381\) 17.4233 0.892624
\(382\) −38.4455 −1.96704
\(383\) 19.4573 0.994219 0.497110 0.867688i \(-0.334395\pi\)
0.497110 + 0.867688i \(0.334395\pi\)
\(384\) 20.1869 1.03016
\(385\) −5.89538 −0.300456
\(386\) −23.7224 −1.20744
\(387\) 0.581734 0.0295712
\(388\) −56.9397 −2.89068
\(389\) −14.8086 −0.750826 −0.375413 0.926858i \(-0.622499\pi\)
−0.375413 + 0.926858i \(0.622499\pi\)
\(390\) −25.9995 −1.31653
\(391\) −3.01962 −0.152709
\(392\) 14.4351 0.729084
\(393\) −6.85121 −0.345598
\(394\) −22.4175 −1.12938
\(395\) 14.2205 0.715511
\(396\) −4.61576 −0.231951
\(397\) 7.40718 0.371756 0.185878 0.982573i \(-0.440487\pi\)
0.185878 + 0.982573i \(0.440487\pi\)
\(398\) 44.3176 2.22144
\(399\) 0.339475 0.0169950
\(400\) 2.33049 0.116525
\(401\) −20.7838 −1.03789 −0.518947 0.854806i \(-0.673676\pi\)
−0.518947 + 0.854806i \(0.673676\pi\)
\(402\) 0.781906 0.0389979
\(403\) −34.0921 −1.69825
\(404\) 43.9372 2.18596
\(405\) 2.63222 0.130796
\(406\) −23.0805 −1.14547
\(407\) 4.51419 0.223760
\(408\) −3.49562 −0.173059
\(409\) −4.19752 −0.207554 −0.103777 0.994601i \(-0.533093\pi\)
−0.103777 + 0.994601i \(0.533093\pi\)
\(410\) −14.1475 −0.698694
\(411\) 10.3764 0.511828
\(412\) 48.6713 2.39786
\(413\) −0.588761 −0.0289710
\(414\) 7.07628 0.347780
\(415\) 10.8490 0.532558
\(416\) 17.5317 0.859562
\(417\) 6.74346 0.330228
\(418\) 0.620713 0.0303601
\(419\) −26.6237 −1.30065 −0.650325 0.759656i \(-0.725367\pi\)
−0.650325 + 0.759656i \(0.725367\pi\)
\(420\) 15.5716 0.759817
\(421\) 2.43007 0.118435 0.0592173 0.998245i \(-0.481140\pi\)
0.0592173 + 0.998245i \(0.481140\pi\)
\(422\) −26.0122 −1.26625
\(423\) 8.80652 0.428188
\(424\) −3.28921 −0.159738
\(425\) 1.92857 0.0935493
\(426\) −12.1168 −0.587059
\(427\) 10.1083 0.489177
\(428\) −70.7015 −3.41749
\(429\) −5.57187 −0.269013
\(430\) −3.58838 −0.173047
\(431\) −38.5352 −1.85618 −0.928088 0.372360i \(-0.878549\pi\)
−0.928088 + 0.372360i \(0.878549\pi\)
\(432\) 1.20841 0.0581394
\(433\) −9.47365 −0.455274 −0.227637 0.973746i \(-0.573100\pi\)
−0.227637 + 0.973746i \(0.573100\pi\)
\(434\) 32.1140 1.54152
\(435\) 15.3016 0.733655
\(436\) 37.3663 1.78952
\(437\) −0.605036 −0.0289428
\(438\) 20.2716 0.968615
\(439\) −5.98904 −0.285841 −0.142921 0.989734i \(-0.545649\pi\)
−0.142921 + 0.989734i \(0.545649\pi\)
\(440\) 12.1634 0.579869
\(441\) −4.12949 −0.196643
\(442\) −9.87740 −0.469820
\(443\) −2.36813 −0.112513 −0.0562567 0.998416i \(-0.517917\pi\)
−0.0562567 + 0.998416i \(0.517917\pi\)
\(444\) −11.9235 −0.565862
\(445\) 29.4077 1.39406
\(446\) 27.7139 1.31229
\(447\) 7.13928 0.337676
\(448\) −20.6092 −0.973691
\(449\) −7.35402 −0.347058 −0.173529 0.984829i \(-0.555517\pi\)
−0.173529 + 0.984829i \(0.555517\pi\)
\(450\) −4.51946 −0.213050
\(451\) −3.03190 −0.142767
\(452\) 23.2909 1.09551
\(453\) 17.3354 0.814488
\(454\) 23.6457 1.10975
\(455\) 18.7971 0.881223
\(456\) −0.700410 −0.0327997
\(457\) 6.92939 0.324143 0.162072 0.986779i \(-0.448182\pi\)
0.162072 + 0.986779i \(0.448182\pi\)
\(458\) 6.72559 0.314266
\(459\) 1.00000 0.0466760
\(460\) −27.7528 −1.29398
\(461\) −10.3910 −0.483955 −0.241978 0.970282i \(-0.577796\pi\)
−0.241978 + 0.970282i \(0.577796\pi\)
\(462\) 5.24858 0.244186
\(463\) 9.57768 0.445113 0.222556 0.974920i \(-0.428560\pi\)
0.222556 + 0.974920i \(0.428560\pi\)
\(464\) 7.02469 0.326113
\(465\) −21.2904 −0.987320
\(466\) −49.3725 −2.28714
\(467\) 14.8538 0.687354 0.343677 0.939088i \(-0.388327\pi\)
0.343677 + 0.939088i \(0.388327\pi\)
\(468\) 14.7171 0.680300
\(469\) −0.565304 −0.0261033
\(470\) −54.3223 −2.50570
\(471\) 1.00000 0.0460776
\(472\) 1.21474 0.0559130
\(473\) −0.769015 −0.0353593
\(474\) −12.6603 −0.581509
\(475\) 0.386423 0.0177303
\(476\) 5.91578 0.271149
\(477\) 0.940952 0.0430832
\(478\) −63.3881 −2.89931
\(479\) −24.2328 −1.10723 −0.553613 0.832774i \(-0.686751\pi\)
−0.553613 + 0.832774i \(0.686751\pi\)
\(480\) 10.9485 0.499729
\(481\) −14.3933 −0.656278
\(482\) −35.7566 −1.62867
\(483\) −5.11602 −0.232787
\(484\) −32.3066 −1.46848
\(485\) −42.9244 −1.94910
\(486\) −2.34343 −0.106300
\(487\) −33.5072 −1.51836 −0.759178 0.650883i \(-0.774399\pi\)
−0.759178 + 0.650883i \(0.774399\pi\)
\(488\) −20.8557 −0.944093
\(489\) 21.3736 0.966546
\(490\) 25.4724 1.15073
\(491\) 5.11611 0.230887 0.115443 0.993314i \(-0.463171\pi\)
0.115443 + 0.993314i \(0.463171\pi\)
\(492\) 8.00825 0.361040
\(493\) 5.81319 0.261813
\(494\) −1.97911 −0.0890446
\(495\) −3.47962 −0.156397
\(496\) −9.77407 −0.438868
\(497\) 8.76019 0.392948
\(498\) −9.65875 −0.432819
\(499\) 17.9381 0.803021 0.401511 0.915854i \(-0.368485\pi\)
0.401511 + 0.915854i \(0.368485\pi\)
\(500\) −28.2290 −1.26244
\(501\) −22.2209 −0.992756
\(502\) 72.9348 3.25524
\(503\) −27.3128 −1.21782 −0.608909 0.793240i \(-0.708393\pi\)
−0.608909 + 0.793240i \(0.708393\pi\)
\(504\) −5.92248 −0.263808
\(505\) 33.1223 1.47392
\(506\) −9.35439 −0.415853
\(507\) 4.76566 0.211651
\(508\) 60.8364 2.69918
\(509\) 23.1250 1.02500 0.512499 0.858688i \(-0.328720\pi\)
0.512499 + 0.858688i \(0.328720\pi\)
\(510\) −6.16842 −0.273142
\(511\) −14.6560 −0.648343
\(512\) 13.4745 0.595495
\(513\) 0.200368 0.00884646
\(514\) −9.25392 −0.408173
\(515\) 36.6912 1.61681
\(516\) 2.03122 0.0894195
\(517\) −11.6417 −0.512000
\(518\) 13.5582 0.595711
\(519\) 8.90582 0.390922
\(520\) −38.7826 −1.70073
\(521\) −4.75568 −0.208350 −0.104175 0.994559i \(-0.533220\pi\)
−0.104175 + 0.994559i \(0.533220\pi\)
\(522\) −13.6228 −0.596254
\(523\) −7.81714 −0.341820 −0.170910 0.985287i \(-0.554671\pi\)
−0.170910 + 0.985287i \(0.554671\pi\)
\(524\) −23.9221 −1.04504
\(525\) 3.26749 0.142605
\(526\) −33.0914 −1.44285
\(527\) −8.08840 −0.352336
\(528\) −1.59743 −0.0695194
\(529\) −13.8819 −0.603560
\(530\) −5.80419 −0.252118
\(531\) −0.347504 −0.0150804
\(532\) 1.18533 0.0513907
\(533\) 9.66709 0.418728
\(534\) −26.1813 −1.13298
\(535\) −53.2988 −2.30431
\(536\) 1.16634 0.0503784
\(537\) 20.6630 0.891676
\(538\) −55.9801 −2.41347
\(539\) 5.45893 0.235133
\(540\) 9.19083 0.395510
\(541\) 5.59802 0.240678 0.120339 0.992733i \(-0.461602\pi\)
0.120339 + 0.992733i \(0.461602\pi\)
\(542\) 41.2014 1.76975
\(543\) 10.7691 0.462145
\(544\) 4.15942 0.178334
\(545\) 28.1688 1.20662
\(546\) −16.7349 −0.716186
\(547\) 27.8189 1.18945 0.594725 0.803929i \(-0.297261\pi\)
0.594725 + 0.803929i \(0.297261\pi\)
\(548\) 36.2308 1.54770
\(549\) 5.96624 0.254633
\(550\) 5.97444 0.254751
\(551\) 1.16478 0.0496212
\(552\) 10.5555 0.449270
\(553\) 9.15319 0.389233
\(554\) 38.2336 1.62439
\(555\) −8.98858 −0.381544
\(556\) 23.5459 0.998569
\(557\) 19.2020 0.813616 0.406808 0.913514i \(-0.366642\pi\)
0.406808 + 0.913514i \(0.366642\pi\)
\(558\) 18.9546 0.802412
\(559\) 2.45197 0.103707
\(560\) 5.38907 0.227730
\(561\) −1.32194 −0.0558122
\(562\) −36.4172 −1.53616
\(563\) −27.9107 −1.17630 −0.588149 0.808753i \(-0.700143\pi\)
−0.588149 + 0.808753i \(0.700143\pi\)
\(564\) 30.7495 1.29479
\(565\) 17.5580 0.738672
\(566\) 12.2922 0.516680
\(567\) 1.69426 0.0711521
\(568\) −18.0742 −0.758375
\(569\) −26.9919 −1.13156 −0.565780 0.824556i \(-0.691425\pi\)
−0.565780 + 0.824556i \(0.691425\pi\)
\(570\) −1.23595 −0.0517684
\(571\) 5.03627 0.210761 0.105381 0.994432i \(-0.466394\pi\)
0.105381 + 0.994432i \(0.466394\pi\)
\(572\) −19.4551 −0.813460
\(573\) 16.4057 0.685356
\(574\) −9.10618 −0.380085
\(575\) −5.82355 −0.242859
\(576\) −12.1641 −0.506839
\(577\) −9.76393 −0.406478 −0.203239 0.979129i \(-0.565147\pi\)
−0.203239 + 0.979129i \(0.565147\pi\)
\(578\) −2.34343 −0.0974739
\(579\) 10.1229 0.420694
\(580\) 53.4280 2.21848
\(581\) 6.98310 0.289708
\(582\) 38.2151 1.58407
\(583\) −1.24388 −0.0515162
\(584\) 30.2385 1.25128
\(585\) 11.0946 0.458706
\(586\) 34.0123 1.40503
\(587\) −28.0390 −1.15729 −0.578647 0.815578i \(-0.696419\pi\)
−0.578647 + 0.815578i \(0.696419\pi\)
\(588\) −14.4188 −0.594622
\(589\) −1.62066 −0.0667780
\(590\) 2.14355 0.0882485
\(591\) 9.56610 0.393497
\(592\) −4.12650 −0.169598
\(593\) 20.0367 0.822810 0.411405 0.911453i \(-0.365038\pi\)
0.411405 + 0.911453i \(0.365038\pi\)
\(594\) 3.09787 0.127107
\(595\) 4.45965 0.182828
\(596\) 24.9280 1.02109
\(597\) −18.9114 −0.773992
\(598\) 29.8260 1.21968
\(599\) 2.39580 0.0978898 0.0489449 0.998801i \(-0.484414\pi\)
0.0489449 + 0.998801i \(0.484414\pi\)
\(600\) −6.74154 −0.275222
\(601\) 6.14181 0.250530 0.125265 0.992123i \(-0.460022\pi\)
0.125265 + 0.992123i \(0.460022\pi\)
\(602\) −2.30970 −0.0941364
\(603\) −0.333659 −0.0135876
\(604\) 60.5294 2.46291
\(605\) −24.3545 −0.990153
\(606\) −29.4884 −1.19788
\(607\) −31.3457 −1.27228 −0.636141 0.771573i \(-0.719470\pi\)
−0.636141 + 0.771573i \(0.719470\pi\)
\(608\) 0.833415 0.0337994
\(609\) 9.84904 0.399103
\(610\) −36.8022 −1.49008
\(611\) 37.1189 1.50167
\(612\) 3.49167 0.141142
\(613\) 29.5265 1.19257 0.596283 0.802775i \(-0.296644\pi\)
0.596283 + 0.802775i \(0.296644\pi\)
\(614\) 36.9816 1.49246
\(615\) 6.03708 0.243438
\(616\) 7.82914 0.315445
\(617\) −2.38840 −0.0961535 −0.0480767 0.998844i \(-0.515309\pi\)
−0.0480767 + 0.998844i \(0.515309\pi\)
\(618\) −32.6657 −1.31401
\(619\) 20.6316 0.829255 0.414627 0.909991i \(-0.363912\pi\)
0.414627 + 0.909991i \(0.363912\pi\)
\(620\) −74.3391 −2.98553
\(621\) −3.01962 −0.121173
\(622\) −40.4122 −1.62038
\(623\) 18.9286 0.758358
\(624\) 5.09335 0.203897
\(625\) −30.9235 −1.23694
\(626\) 3.08043 0.123119
\(627\) −0.264874 −0.0105780
\(628\) 3.49167 0.139333
\(629\) −3.41483 −0.136158
\(630\) −10.4509 −0.416373
\(631\) 43.2137 1.72031 0.860154 0.510034i \(-0.170367\pi\)
0.860154 + 0.510034i \(0.170367\pi\)
\(632\) −18.8850 −0.751206
\(633\) 11.1000 0.441187
\(634\) −59.3257 −2.35612
\(635\) 45.8620 1.81998
\(636\) 3.28549 0.130278
\(637\) −17.4055 −0.689633
\(638\) 18.0085 0.712963
\(639\) 5.17052 0.204543
\(640\) 53.1364 2.10040
\(641\) −39.6883 −1.56759 −0.783797 0.621017i \(-0.786720\pi\)
−0.783797 + 0.621017i \(0.786720\pi\)
\(642\) 47.4513 1.87275
\(643\) −47.1409 −1.85905 −0.929527 0.368754i \(-0.879784\pi\)
−0.929527 + 0.368754i \(0.879784\pi\)
\(644\) −17.8634 −0.703918
\(645\) 1.53125 0.0602929
\(646\) −0.469548 −0.0184741
\(647\) −9.83543 −0.386671 −0.193335 0.981133i \(-0.561931\pi\)
−0.193335 + 0.981133i \(0.561931\pi\)
\(648\) −3.49562 −0.137321
\(649\) 0.459378 0.0180322
\(650\) −19.0492 −0.747173
\(651\) −13.7038 −0.537095
\(652\) 74.6294 2.92271
\(653\) 41.3384 1.61769 0.808847 0.588018i \(-0.200092\pi\)
0.808847 + 0.588018i \(0.200092\pi\)
\(654\) −25.0784 −0.980642
\(655\) −18.0339 −0.704641
\(656\) 2.77152 0.108210
\(657\) −8.65040 −0.337484
\(658\) −34.9652 −1.36309
\(659\) −32.6987 −1.27376 −0.636880 0.770963i \(-0.719775\pi\)
−0.636880 + 0.770963i \(0.719775\pi\)
\(660\) −12.1497 −0.472926
\(661\) 18.6623 0.725879 0.362939 0.931813i \(-0.381773\pi\)
0.362939 + 0.931813i \(0.381773\pi\)
\(662\) 20.9462 0.814097
\(663\) 4.21493 0.163694
\(664\) −14.4076 −0.559125
\(665\) 0.893571 0.0346512
\(666\) 8.00242 0.310088
\(667\) −17.5536 −0.679680
\(668\) −77.5879 −3.00197
\(669\) −11.8262 −0.457228
\(670\) 2.05815 0.0795132
\(671\) −7.88699 −0.304474
\(672\) 7.04713 0.271849
\(673\) −6.58598 −0.253871 −0.126935 0.991911i \(-0.540514\pi\)
−0.126935 + 0.991911i \(0.540514\pi\)
\(674\) 50.0721 1.92871
\(675\) 1.92857 0.0742306
\(676\) 16.6401 0.640004
\(677\) 23.7157 0.911467 0.455734 0.890116i \(-0.349377\pi\)
0.455734 + 0.890116i \(0.349377\pi\)
\(678\) −15.6317 −0.600332
\(679\) −27.6288 −1.06030
\(680\) −9.20123 −0.352851
\(681\) −10.0902 −0.386657
\(682\) −25.0568 −0.959474
\(683\) 16.5588 0.633606 0.316803 0.948491i \(-0.397391\pi\)
0.316803 + 0.948491i \(0.397391\pi\)
\(684\) 0.699618 0.0267506
\(685\) 27.3128 1.04357
\(686\) 44.1882 1.68712
\(687\) −2.86997 −0.109496
\(688\) 0.702970 0.0268005
\(689\) 3.96605 0.151095
\(690\) 18.6263 0.709091
\(691\) −46.2055 −1.75774 −0.878869 0.477063i \(-0.841701\pi\)
−0.878869 + 0.477063i \(0.841701\pi\)
\(692\) 31.0962 1.18210
\(693\) −2.23970 −0.0850792
\(694\) 19.0248 0.722170
\(695\) 17.7502 0.673305
\(696\) −20.3207 −0.770254
\(697\) 2.29353 0.0868738
\(698\) 55.8911 2.11551
\(699\) 21.0685 0.796883
\(700\) 11.4090 0.431219
\(701\) 17.3662 0.655910 0.327955 0.944693i \(-0.393640\pi\)
0.327955 + 0.944693i \(0.393640\pi\)
\(702\) −9.87740 −0.372799
\(703\) −0.684223 −0.0258060
\(704\) 16.0802 0.606046
\(705\) 23.1807 0.873035
\(706\) −30.5488 −1.14972
\(707\) 21.3196 0.801805
\(708\) −1.21337 −0.0456012
\(709\) −16.4449 −0.617600 −0.308800 0.951127i \(-0.599927\pi\)
−0.308800 + 0.951127i \(0.599927\pi\)
\(710\) −31.8939 −1.19696
\(711\) 5.40248 0.202609
\(712\) −39.0538 −1.46360
\(713\) 24.4239 0.914683
\(714\) −3.97037 −0.148588
\(715\) −14.6664 −0.548492
\(716\) 72.1485 2.69631
\(717\) 27.0493 1.01017
\(718\) −29.8245 −1.11304
\(719\) 1.35352 0.0504779 0.0252389 0.999681i \(-0.491965\pi\)
0.0252389 + 0.999681i \(0.491965\pi\)
\(720\) 3.18078 0.118541
\(721\) 23.6167 0.879531
\(722\) 44.4311 1.65355
\(723\) 15.2582 0.567459
\(724\) 37.6020 1.39747
\(725\) 11.2111 0.416371
\(726\) 21.6826 0.804715
\(727\) 34.9133 1.29486 0.647431 0.762124i \(-0.275844\pi\)
0.647431 + 0.762124i \(0.275844\pi\)
\(728\) −24.9628 −0.925184
\(729\) 1.00000 0.0370370
\(730\) 53.3593 1.97491
\(731\) 0.581734 0.0215162
\(732\) 20.8321 0.769977
\(733\) −33.8932 −1.25187 −0.625937 0.779874i \(-0.715283\pi\)
−0.625937 + 0.779874i \(0.715283\pi\)
\(734\) 79.3247 2.92793
\(735\) −10.8697 −0.400936
\(736\) −12.5599 −0.462964
\(737\) 0.441076 0.0162472
\(738\) −5.37474 −0.197847
\(739\) −21.7263 −0.799215 −0.399608 0.916686i \(-0.630854\pi\)
−0.399608 + 0.916686i \(0.630854\pi\)
\(740\) −31.3851 −1.15374
\(741\) 0.844537 0.0310249
\(742\) −3.73593 −0.137150
\(743\) −6.63705 −0.243490 −0.121745 0.992561i \(-0.538849\pi\)
−0.121745 + 0.992561i \(0.538849\pi\)
\(744\) 28.2740 1.03657
\(745\) 18.7921 0.688490
\(746\) −71.3443 −2.61210
\(747\) 4.12163 0.150803
\(748\) −4.61576 −0.168769
\(749\) −34.3064 −1.25353
\(750\) 18.9459 0.691806
\(751\) 4.82655 0.176123 0.0880617 0.996115i \(-0.471933\pi\)
0.0880617 + 0.996115i \(0.471933\pi\)
\(752\) 10.6418 0.388068
\(753\) −31.1231 −1.13419
\(754\) −57.4192 −2.09108
\(755\) 45.6305 1.66066
\(756\) 5.91578 0.215155
\(757\) 26.5789 0.966028 0.483014 0.875613i \(-0.339542\pi\)
0.483014 + 0.875613i \(0.339542\pi\)
\(758\) 62.9374 2.28599
\(759\) 3.99175 0.144891
\(760\) −1.84363 −0.0668755
\(761\) 16.2352 0.588526 0.294263 0.955724i \(-0.404926\pi\)
0.294263 + 0.955724i \(0.404926\pi\)
\(762\) −40.8303 −1.47913
\(763\) 18.1312 0.656394
\(764\) 57.2831 2.07243
\(765\) 2.63222 0.0951680
\(766\) −45.5967 −1.64748
\(767\) −1.46471 −0.0528875
\(768\) −22.9785 −0.829164
\(769\) −24.8260 −0.895249 −0.447624 0.894222i \(-0.647730\pi\)
−0.447624 + 0.894222i \(0.647730\pi\)
\(770\) 13.8154 0.497873
\(771\) 3.94888 0.142215
\(772\) 35.3459 1.27213
\(773\) 3.20794 0.115382 0.0576909 0.998334i \(-0.481626\pi\)
0.0576909 + 0.998334i \(0.481626\pi\)
\(774\) −1.36325 −0.0490011
\(775\) −15.5990 −0.560334
\(776\) 57.0042 2.04633
\(777\) −5.78560 −0.207557
\(778\) 34.7029 1.24416
\(779\) 0.459550 0.0164651
\(780\) 38.7387 1.38707
\(781\) −6.83510 −0.244579
\(782\) 7.07628 0.253047
\(783\) 5.81319 0.207746
\(784\) −4.99010 −0.178218
\(785\) 2.63222 0.0939479
\(786\) 16.0553 0.572675
\(787\) 27.9067 0.994766 0.497383 0.867531i \(-0.334294\pi\)
0.497383 + 0.867531i \(0.334294\pi\)
\(788\) 33.4016 1.18988
\(789\) 14.1209 0.502718
\(790\) −33.3248 −1.18564
\(791\) 11.3014 0.401833
\(792\) 4.62098 0.164200
\(793\) 25.1473 0.893007
\(794\) −17.3582 −0.616020
\(795\) 2.47679 0.0878427
\(796\) −66.0323 −2.34045
\(797\) 35.3877 1.25350 0.626749 0.779222i \(-0.284385\pi\)
0.626749 + 0.779222i \(0.284385\pi\)
\(798\) −0.795535 −0.0281617
\(799\) 8.80652 0.311552
\(800\) 8.02173 0.283611
\(801\) 11.1722 0.394751
\(802\) 48.7055 1.71985
\(803\) 11.4353 0.403542
\(804\) −1.16503 −0.0410873
\(805\) −13.4665 −0.474631
\(806\) 79.8924 2.81409
\(807\) 23.8881 0.840901
\(808\) −43.9869 −1.54745
\(809\) −15.1711 −0.533388 −0.266694 0.963781i \(-0.585931\pi\)
−0.266694 + 0.963781i \(0.585931\pi\)
\(810\) −6.16842 −0.216736
\(811\) −40.8498 −1.43443 −0.717216 0.696851i \(-0.754584\pi\)
−0.717216 + 0.696851i \(0.754584\pi\)
\(812\) 34.3896 1.20684
\(813\) −17.5817 −0.616616
\(814\) −10.5787 −0.370783
\(815\) 56.2598 1.97070
\(816\) 1.20841 0.0423026
\(817\) 0.116561 0.00407795
\(818\) 9.83659 0.343928
\(819\) 7.14118 0.249533
\(820\) 21.0795 0.736127
\(821\) −53.0547 −1.85162 −0.925811 0.377987i \(-0.876616\pi\)
−0.925811 + 0.377987i \(0.876616\pi\)
\(822\) −24.3163 −0.848128
\(823\) 20.5826 0.717463 0.358732 0.933441i \(-0.383209\pi\)
0.358732 + 0.933441i \(0.383209\pi\)
\(824\) −48.7263 −1.69746
\(825\) −2.54944 −0.0887602
\(826\) 1.37972 0.0480066
\(827\) −23.5729 −0.819710 −0.409855 0.912151i \(-0.634421\pi\)
−0.409855 + 0.912151i \(0.634421\pi\)
\(828\) −10.5435 −0.366413
\(829\) 21.1595 0.734900 0.367450 0.930043i \(-0.380231\pi\)
0.367450 + 0.930043i \(0.380231\pi\)
\(830\) −25.4239 −0.882477
\(831\) −16.3152 −0.565968
\(832\) −51.2710 −1.77750
\(833\) −4.12949 −0.143078
\(834\) −15.8028 −0.547207
\(835\) −58.4902 −2.02414
\(836\) −0.924850 −0.0319866
\(837\) −8.08840 −0.279576
\(838\) 62.3907 2.15525
\(839\) −31.9427 −1.10278 −0.551392 0.834246i \(-0.685903\pi\)
−0.551392 + 0.834246i \(0.685903\pi\)
\(840\) −15.5892 −0.537880
\(841\) 4.79318 0.165282
\(842\) −5.69471 −0.196253
\(843\) 15.5401 0.535230
\(844\) 38.7577 1.33409
\(845\) 12.5443 0.431536
\(846\) −20.6375 −0.709531
\(847\) −15.6761 −0.538637
\(848\) 1.13705 0.0390465
\(849\) −5.24539 −0.180021
\(850\) −4.51946 −0.155016
\(851\) 10.3115 0.353474
\(852\) 18.0537 0.618511
\(853\) 9.13920 0.312920 0.156460 0.987684i \(-0.449992\pi\)
0.156460 + 0.987684i \(0.449992\pi\)
\(854\) −23.6882 −0.810593
\(855\) 0.527412 0.0180371
\(856\) 70.7815 2.41926
\(857\) −27.9302 −0.954079 −0.477040 0.878882i \(-0.658290\pi\)
−0.477040 + 0.878882i \(0.658290\pi\)
\(858\) 13.0573 0.445769
\(859\) 29.9001 1.02018 0.510090 0.860121i \(-0.329612\pi\)
0.510090 + 0.860121i \(0.329612\pi\)
\(860\) 5.34661 0.182318
\(861\) 3.88583 0.132429
\(862\) 90.3046 3.07579
\(863\) 10.0814 0.343173 0.171587 0.985169i \(-0.445111\pi\)
0.171587 + 0.985169i \(0.445111\pi\)
\(864\) 4.15942 0.141506
\(865\) 23.4420 0.797054
\(866\) 22.2008 0.754415
\(867\) 1.00000 0.0339618
\(868\) −47.8492 −1.62411
\(869\) −7.14174 −0.242267
\(870\) −35.8582 −1.21571
\(871\) −1.40635 −0.0476523
\(872\) −37.4086 −1.26681
\(873\) −16.3073 −0.551919
\(874\) 1.41786 0.0479598
\(875\) −13.6975 −0.463061
\(876\) −30.2043 −1.02051
\(877\) 40.4003 1.36422 0.682110 0.731249i \(-0.261062\pi\)
0.682110 + 0.731249i \(0.261062\pi\)
\(878\) 14.0349 0.473655
\(879\) −14.5139 −0.489541
\(880\) −4.20479 −0.141744
\(881\) 27.0800 0.912350 0.456175 0.889890i \(-0.349219\pi\)
0.456175 + 0.889890i \(0.349219\pi\)
\(882\) 9.67718 0.325848
\(883\) −1.84057 −0.0619403 −0.0309701 0.999520i \(-0.509860\pi\)
−0.0309701 + 0.999520i \(0.509860\pi\)
\(884\) 14.7171 0.494991
\(885\) −0.914706 −0.0307475
\(886\) 5.54956 0.186441
\(887\) −8.19905 −0.275297 −0.137649 0.990481i \(-0.543954\pi\)
−0.137649 + 0.990481i \(0.543954\pi\)
\(888\) 11.9370 0.400578
\(889\) 29.5196 0.990055
\(890\) −68.9149 −2.31003
\(891\) −1.32194 −0.0442865
\(892\) −41.2933 −1.38260
\(893\) 1.76454 0.0590482
\(894\) −16.7304 −0.559548
\(895\) 54.3896 1.81804
\(896\) 34.2019 1.14260
\(897\) −12.7275 −0.424959
\(898\) 17.2336 0.575094
\(899\) −47.0194 −1.56819
\(900\) 6.73392 0.224464
\(901\) 0.940952 0.0313477
\(902\) 7.10506 0.236573
\(903\) 0.985607 0.0327989
\(904\) −23.3173 −0.775522
\(905\) 28.3465 0.942270
\(906\) −40.6243 −1.34965
\(907\) 54.7096 1.81660 0.908302 0.418316i \(-0.137380\pi\)
0.908302 + 0.418316i \(0.137380\pi\)
\(908\) −35.2316 −1.16920
\(909\) 12.5834 0.417366
\(910\) −44.0498 −1.46024
\(911\) −21.7271 −0.719852 −0.359926 0.932981i \(-0.617198\pi\)
−0.359926 + 0.932981i \(0.617198\pi\)
\(912\) 0.242126 0.00801758
\(913\) −5.44853 −0.180320
\(914\) −16.2385 −0.537123
\(915\) 15.7044 0.519173
\(916\) −10.0210 −0.331103
\(917\) −11.6077 −0.383320
\(918\) −2.34343 −0.0773447
\(919\) 53.7107 1.77175 0.885875 0.463923i \(-0.153559\pi\)
0.885875 + 0.463923i \(0.153559\pi\)
\(920\) 27.7842 0.916019
\(921\) −15.7810 −0.520000
\(922\) 24.3505 0.801941
\(923\) 21.7934 0.717338
\(924\) −7.82029 −0.257269
\(925\) −6.58573 −0.216538
\(926\) −22.4446 −0.737576
\(927\) 13.9393 0.457825
\(928\) 24.1795 0.793732
\(929\) −21.9632 −0.720591 −0.360295 0.932838i \(-0.617324\pi\)
−0.360295 + 0.932838i \(0.617324\pi\)
\(930\) 49.8926 1.63604
\(931\) −0.827418 −0.0271175
\(932\) 73.5641 2.40967
\(933\) 17.2449 0.564572
\(934\) −34.8090 −1.13898
\(935\) −3.47962 −0.113796
\(936\) −14.7338 −0.481589
\(937\) −34.3407 −1.12186 −0.560931 0.827863i \(-0.689557\pi\)
−0.560931 + 0.827863i \(0.689557\pi\)
\(938\) 1.32475 0.0432546
\(939\) −1.31450 −0.0428970
\(940\) 80.9392 2.63995
\(941\) −37.7683 −1.23121 −0.615607 0.788054i \(-0.711089\pi\)
−0.615607 + 0.788054i \(0.711089\pi\)
\(942\) −2.34343 −0.0763531
\(943\) −6.92561 −0.225529
\(944\) −0.419925 −0.0136674
\(945\) 4.45965 0.145073
\(946\) 1.80213 0.0585924
\(947\) −25.9868 −0.844457 −0.422229 0.906489i \(-0.638752\pi\)
−0.422229 + 0.906489i \(0.638752\pi\)
\(948\) 18.8637 0.612664
\(949\) −36.4608 −1.18357
\(950\) −0.905556 −0.0293801
\(951\) 25.3157 0.820919
\(952\) −5.92248 −0.191949
\(953\) −15.7304 −0.509559 −0.254779 0.966999i \(-0.582003\pi\)
−0.254779 + 0.966999i \(0.582003\pi\)
\(954\) −2.20506 −0.0713913
\(955\) 43.1833 1.39738
\(956\) 94.4471 3.05464
\(957\) −7.68467 −0.248410
\(958\) 56.7879 1.83473
\(959\) 17.5802 0.567695
\(960\) −32.0186 −1.03340
\(961\) 34.4222 1.11039
\(962\) 33.7297 1.08749
\(963\) −20.2486 −0.652503
\(964\) 53.2766 1.71592
\(965\) 26.6457 0.857757
\(966\) 11.9890 0.385741
\(967\) 50.1371 1.61230 0.806150 0.591711i \(-0.201547\pi\)
0.806150 + 0.591711i \(0.201547\pi\)
\(968\) 32.3432 1.03955
\(969\) 0.200368 0.00643674
\(970\) 100.590 3.22976
\(971\) 38.1545 1.22443 0.612217 0.790689i \(-0.290278\pi\)
0.612217 + 0.790689i \(0.290278\pi\)
\(972\) 3.49167 0.111995
\(973\) 11.4251 0.366273
\(974\) 78.5218 2.51600
\(975\) 8.12878 0.260329
\(976\) 7.20963 0.230775
\(977\) 23.0721 0.738141 0.369071 0.929401i \(-0.379676\pi\)
0.369071 + 0.929401i \(0.379676\pi\)
\(978\) −50.0875 −1.60162
\(979\) −14.7690 −0.472018
\(980\) −37.9535 −1.21238
\(981\) 10.7016 0.341675
\(982\) −11.9892 −0.382592
\(983\) −40.6354 −1.29607 −0.648034 0.761612i \(-0.724408\pi\)
−0.648034 + 0.761612i \(0.724408\pi\)
\(984\) −8.01732 −0.255583
\(985\) 25.1801 0.802303
\(986\) −13.6228 −0.433839
\(987\) 14.9205 0.474925
\(988\) 2.94884 0.0938152
\(989\) −1.75662 −0.0558572
\(990\) 8.15426 0.259159
\(991\) −38.1690 −1.21248 −0.606239 0.795282i \(-0.707323\pi\)
−0.606239 + 0.795282i \(0.707323\pi\)
\(992\) −33.6431 −1.06817
\(993\) −8.93826 −0.283647
\(994\) −20.5289 −0.651137
\(995\) −49.7789 −1.57810
\(996\) 14.3914 0.456008
\(997\) −53.7168 −1.70123 −0.850615 0.525789i \(-0.823770\pi\)
−0.850615 + 0.525789i \(0.823770\pi\)
\(998\) −42.0368 −1.33065
\(999\) −3.41483 −0.108041
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 8007.2.a.i.1.5 63
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.i.1.5 63 1.1 even 1 trivial