Properties

Label 6010.2.a.h.1.19
Level $6010$
Weight $2$
Character 6010.1
Self dual yes
Analytic conductor $47.990$
Analytic rank $0$
Dimension $28$
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] = [6010,2,Mod(1,6010)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6010, 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("6010.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6010.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: \(47.9900916148\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 6010.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.25977 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.25977 q^{6} +3.22153 q^{7} +1.00000 q^{8} -1.41297 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.25977 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.25977 q^{6} +3.22153 q^{7} +1.00000 q^{8} -1.41297 q^{9} -1.00000 q^{10} +5.03908 q^{11} +1.25977 q^{12} +2.54225 q^{13} +3.22153 q^{14} -1.25977 q^{15} +1.00000 q^{16} +0.741176 q^{17} -1.41297 q^{18} +8.15755 q^{19} -1.00000 q^{20} +4.05839 q^{21} +5.03908 q^{22} -0.280998 q^{23} +1.25977 q^{24} +1.00000 q^{25} +2.54225 q^{26} -5.55934 q^{27} +3.22153 q^{28} +3.73498 q^{29} -1.25977 q^{30} -8.36407 q^{31} +1.00000 q^{32} +6.34810 q^{33} +0.741176 q^{34} -3.22153 q^{35} -1.41297 q^{36} -0.170862 q^{37} +8.15755 q^{38} +3.20265 q^{39} -1.00000 q^{40} -4.02927 q^{41} +4.05839 q^{42} -9.44017 q^{43} +5.03908 q^{44} +1.41297 q^{45} -0.280998 q^{46} +6.34766 q^{47} +1.25977 q^{48} +3.37824 q^{49} +1.00000 q^{50} +0.933714 q^{51} +2.54225 q^{52} +0.251008 q^{53} -5.55934 q^{54} -5.03908 q^{55} +3.22153 q^{56} +10.2767 q^{57} +3.73498 q^{58} +5.26832 q^{59} -1.25977 q^{60} -3.17080 q^{61} -8.36407 q^{62} -4.55193 q^{63} +1.00000 q^{64} -2.54225 q^{65} +6.34810 q^{66} -6.76837 q^{67} +0.741176 q^{68} -0.353994 q^{69} -3.22153 q^{70} -5.09804 q^{71} -1.41297 q^{72} +12.0725 q^{73} -0.170862 q^{74} +1.25977 q^{75} +8.15755 q^{76} +16.2335 q^{77} +3.20265 q^{78} -4.38753 q^{79} -1.00000 q^{80} -2.76459 q^{81} -4.02927 q^{82} -2.56246 q^{83} +4.05839 q^{84} -0.741176 q^{85} -9.44017 q^{86} +4.70523 q^{87} +5.03908 q^{88} -13.3773 q^{89} +1.41297 q^{90} +8.18992 q^{91} -0.280998 q^{92} -10.5368 q^{93} +6.34766 q^{94} -8.15755 q^{95} +1.25977 q^{96} -6.12982 q^{97} +3.37824 q^{98} -7.12008 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9} - 28 q^{10} + 4 q^{11} + 4 q^{12} + 22 q^{13} + 10 q^{14} - 4 q^{15} + 28 q^{16} + 15 q^{17} + 40 q^{18} - 11 q^{19} - 28 q^{20} + 18 q^{21} + 4 q^{22} + 23 q^{23} + 4 q^{24} + 28 q^{25} + 22 q^{26} + 19 q^{27} + 10 q^{28} + 19 q^{29} - 4 q^{30} + 7 q^{31} + 28 q^{32} + 33 q^{33} + 15 q^{34} - 10 q^{35} + 40 q^{36} + 22 q^{37} - 11 q^{38} + 8 q^{39} - 28 q^{40} + 41 q^{41} + 18 q^{42} + 7 q^{43} + 4 q^{44} - 40 q^{45} + 23 q^{46} + 51 q^{47} + 4 q^{48} + 60 q^{49} + 28 q^{50} - 5 q^{51} + 22 q^{52} + 25 q^{53} + 19 q^{54} - 4 q^{55} + 10 q^{56} + 8 q^{57} + 19 q^{58} + 32 q^{59} - 4 q^{60} + 24 q^{61} + 7 q^{62} + 33 q^{63} + 28 q^{64} - 22 q^{65} + 33 q^{66} + 3 q^{67} + 15 q^{68} + 43 q^{69} - 10 q^{70} + 8 q^{71} + 40 q^{72} + 47 q^{73} + 22 q^{74} + 4 q^{75} - 11 q^{76} + 46 q^{77} + 8 q^{78} - 22 q^{79} - 28 q^{80} + 76 q^{81} + 41 q^{82} + 36 q^{83} + 18 q^{84} - 15 q^{85} + 7 q^{86} + 72 q^{87} + 4 q^{88} + 70 q^{89} - 40 q^{90} - 21 q^{91} + 23 q^{92} + 24 q^{93} + 51 q^{94} + 11 q^{95} + 4 q^{96} + 43 q^{97} + 60 q^{98} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.25977 0.727330 0.363665 0.931530i \(-0.381525\pi\)
0.363665 + 0.931530i \(0.381525\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 1.25977 0.514300
\(7\) 3.22153 1.21762 0.608812 0.793315i \(-0.291647\pi\)
0.608812 + 0.793315i \(0.291647\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.41297 −0.470991
\(10\) −1.00000 −0.316228
\(11\) 5.03908 1.51934 0.759670 0.650309i \(-0.225361\pi\)
0.759670 + 0.650309i \(0.225361\pi\)
\(12\) 1.25977 0.363665
\(13\) 2.54225 0.705092 0.352546 0.935794i \(-0.385316\pi\)
0.352546 + 0.935794i \(0.385316\pi\)
\(14\) 3.22153 0.860990
\(15\) −1.25977 −0.325272
\(16\) 1.00000 0.250000
\(17\) 0.741176 0.179762 0.0898808 0.995953i \(-0.471351\pi\)
0.0898808 + 0.995953i \(0.471351\pi\)
\(18\) −1.41297 −0.333041
\(19\) 8.15755 1.87147 0.935735 0.352703i \(-0.114737\pi\)
0.935735 + 0.352703i \(0.114737\pi\)
\(20\) −1.00000 −0.223607
\(21\) 4.05839 0.885614
\(22\) 5.03908 1.07434
\(23\) −0.280998 −0.0585922 −0.0292961 0.999571i \(-0.509327\pi\)
−0.0292961 + 0.999571i \(0.509327\pi\)
\(24\) 1.25977 0.257150
\(25\) 1.00000 0.200000
\(26\) 2.54225 0.498575
\(27\) −5.55934 −1.06990
\(28\) 3.22153 0.608812
\(29\) 3.73498 0.693569 0.346784 0.937945i \(-0.387274\pi\)
0.346784 + 0.937945i \(0.387274\pi\)
\(30\) −1.25977 −0.230002
\(31\) −8.36407 −1.50223 −0.751115 0.660171i \(-0.770484\pi\)
−0.751115 + 0.660171i \(0.770484\pi\)
\(32\) 1.00000 0.176777
\(33\) 6.34810 1.10506
\(34\) 0.741176 0.127111
\(35\) −3.22153 −0.544538
\(36\) −1.41297 −0.235495
\(37\) −0.170862 −0.0280895 −0.0140447 0.999901i \(-0.504471\pi\)
−0.0140447 + 0.999901i \(0.504471\pi\)
\(38\) 8.15755 1.32333
\(39\) 3.20265 0.512835
\(40\) −1.00000 −0.158114
\(41\) −4.02927 −0.629267 −0.314633 0.949213i \(-0.601882\pi\)
−0.314633 + 0.949213i \(0.601882\pi\)
\(42\) 4.05839 0.626224
\(43\) −9.44017 −1.43961 −0.719806 0.694175i \(-0.755769\pi\)
−0.719806 + 0.694175i \(0.755769\pi\)
\(44\) 5.03908 0.759670
\(45\) 1.41297 0.210633
\(46\) −0.280998 −0.0414310
\(47\) 6.34766 0.925902 0.462951 0.886384i \(-0.346791\pi\)
0.462951 + 0.886384i \(0.346791\pi\)
\(48\) 1.25977 0.181833
\(49\) 3.37824 0.482606
\(50\) 1.00000 0.141421
\(51\) 0.933714 0.130746
\(52\) 2.54225 0.352546
\(53\) 0.251008 0.0344786 0.0172393 0.999851i \(-0.494512\pi\)
0.0172393 + 0.999851i \(0.494512\pi\)
\(54\) −5.55934 −0.756531
\(55\) −5.03908 −0.679469
\(56\) 3.22153 0.430495
\(57\) 10.2767 1.36118
\(58\) 3.73498 0.490427
\(59\) 5.26832 0.685877 0.342939 0.939358i \(-0.388578\pi\)
0.342939 + 0.939358i \(0.388578\pi\)
\(60\) −1.25977 −0.162636
\(61\) −3.17080 −0.405979 −0.202989 0.979181i \(-0.565066\pi\)
−0.202989 + 0.979181i \(0.565066\pi\)
\(62\) −8.36407 −1.06224
\(63\) −4.55193 −0.573489
\(64\) 1.00000 0.125000
\(65\) −2.54225 −0.315327
\(66\) 6.34810 0.781397
\(67\) −6.76837 −0.826888 −0.413444 0.910529i \(-0.635674\pi\)
−0.413444 + 0.910529i \(0.635674\pi\)
\(68\) 0.741176 0.0898808
\(69\) −0.353994 −0.0426159
\(70\) −3.22153 −0.385046
\(71\) −5.09804 −0.605026 −0.302513 0.953145i \(-0.597826\pi\)
−0.302513 + 0.953145i \(0.597826\pi\)
\(72\) −1.41297 −0.166520
\(73\) 12.0725 1.41298 0.706488 0.707725i \(-0.250278\pi\)
0.706488 + 0.707725i \(0.250278\pi\)
\(74\) −0.170862 −0.0198623
\(75\) 1.25977 0.145466
\(76\) 8.15755 0.935735
\(77\) 16.2335 1.84998
\(78\) 3.20265 0.362629
\(79\) −4.38753 −0.493636 −0.246818 0.969062i \(-0.579385\pi\)
−0.246818 + 0.969062i \(0.579385\pi\)
\(80\) −1.00000 −0.111803
\(81\) −2.76459 −0.307177
\(82\) −4.02927 −0.444959
\(83\) −2.56246 −0.281267 −0.140633 0.990062i \(-0.544914\pi\)
−0.140633 + 0.990062i \(0.544914\pi\)
\(84\) 4.05839 0.442807
\(85\) −0.741176 −0.0803919
\(86\) −9.44017 −1.01796
\(87\) 4.70523 0.504454
\(88\) 5.03908 0.537168
\(89\) −13.3773 −1.41800 −0.708998 0.705211i \(-0.750852\pi\)
−0.708998 + 0.705211i \(0.750852\pi\)
\(90\) 1.41297 0.148940
\(91\) 8.18992 0.858537
\(92\) −0.280998 −0.0292961
\(93\) −10.5368 −1.09262
\(94\) 6.34766 0.654711
\(95\) −8.15755 −0.836947
\(96\) 1.25977 0.128575
\(97\) −6.12982 −0.622389 −0.311195 0.950346i \(-0.600729\pi\)
−0.311195 + 0.950346i \(0.600729\pi\)
\(98\) 3.37824 0.341254
\(99\) −7.12008 −0.715595
\(100\) 1.00000 0.100000
\(101\) 3.15971 0.314403 0.157202 0.987567i \(-0.449753\pi\)
0.157202 + 0.987567i \(0.449753\pi\)
\(102\) 0.933714 0.0924515
\(103\) 12.8371 1.26487 0.632437 0.774612i \(-0.282055\pi\)
0.632437 + 0.774612i \(0.282055\pi\)
\(104\) 2.54225 0.249288
\(105\) −4.05839 −0.396059
\(106\) 0.251008 0.0243800
\(107\) 10.6960 1.03402 0.517011 0.855979i \(-0.327045\pi\)
0.517011 + 0.855979i \(0.327045\pi\)
\(108\) −5.55934 −0.534948
\(109\) −2.06372 −0.197668 −0.0988340 0.995104i \(-0.531511\pi\)
−0.0988340 + 0.995104i \(0.531511\pi\)
\(110\) −5.03908 −0.480457
\(111\) −0.215247 −0.0204303
\(112\) 3.22153 0.304406
\(113\) −9.93713 −0.934807 −0.467403 0.884044i \(-0.654810\pi\)
−0.467403 + 0.884044i \(0.654810\pi\)
\(114\) 10.2767 0.962498
\(115\) 0.280998 0.0262032
\(116\) 3.73498 0.346784
\(117\) −3.59212 −0.332092
\(118\) 5.26832 0.484988
\(119\) 2.38772 0.218882
\(120\) −1.25977 −0.115001
\(121\) 14.3923 1.30839
\(122\) −3.17080 −0.287070
\(123\) −5.07597 −0.457685
\(124\) −8.36407 −0.751115
\(125\) −1.00000 −0.0894427
\(126\) −4.55193 −0.405518
\(127\) 6.10582 0.541804 0.270902 0.962607i \(-0.412678\pi\)
0.270902 + 0.962607i \(0.412678\pi\)
\(128\) 1.00000 0.0883883
\(129\) −11.8925 −1.04707
\(130\) −2.54225 −0.222970
\(131\) 6.40845 0.559908 0.279954 0.960013i \(-0.409681\pi\)
0.279954 + 0.960013i \(0.409681\pi\)
\(132\) 6.34810 0.552531
\(133\) 26.2798 2.27875
\(134\) −6.76837 −0.584698
\(135\) 5.55934 0.478472
\(136\) 0.741176 0.0635553
\(137\) −8.97013 −0.766370 −0.383185 0.923672i \(-0.625173\pi\)
−0.383185 + 0.923672i \(0.625173\pi\)
\(138\) −0.353994 −0.0301340
\(139\) 2.87367 0.243741 0.121871 0.992546i \(-0.461111\pi\)
0.121871 + 0.992546i \(0.461111\pi\)
\(140\) −3.22153 −0.272269
\(141\) 7.99661 0.673436
\(142\) −5.09804 −0.427818
\(143\) 12.8106 1.07127
\(144\) −1.41297 −0.117748
\(145\) −3.73498 −0.310173
\(146\) 12.0725 0.999125
\(147\) 4.25582 0.351014
\(148\) −0.170862 −0.0140447
\(149\) −6.64556 −0.544426 −0.272213 0.962237i \(-0.587755\pi\)
−0.272213 + 0.962237i \(0.587755\pi\)
\(150\) 1.25977 0.102860
\(151\) 14.0599 1.14418 0.572090 0.820191i \(-0.306133\pi\)
0.572090 + 0.820191i \(0.306133\pi\)
\(152\) 8.15755 0.661665
\(153\) −1.04726 −0.0846661
\(154\) 16.2335 1.30814
\(155\) 8.36407 0.671818
\(156\) 3.20265 0.256417
\(157\) −21.6550 −1.72826 −0.864128 0.503271i \(-0.832130\pi\)
−0.864128 + 0.503271i \(0.832130\pi\)
\(158\) −4.38753 −0.349053
\(159\) 0.316213 0.0250773
\(160\) −1.00000 −0.0790569
\(161\) −0.905244 −0.0713432
\(162\) −2.76459 −0.217207
\(163\) 18.6235 1.45871 0.729354 0.684137i \(-0.239821\pi\)
0.729354 + 0.684137i \(0.239821\pi\)
\(164\) −4.02927 −0.314633
\(165\) −6.34810 −0.494199
\(166\) −2.56246 −0.198885
\(167\) −11.3326 −0.876941 −0.438471 0.898746i \(-0.644480\pi\)
−0.438471 + 0.898746i \(0.644480\pi\)
\(168\) 4.05839 0.313112
\(169\) −6.53699 −0.502845
\(170\) −0.741176 −0.0568456
\(171\) −11.5264 −0.881445
\(172\) −9.44017 −0.719806
\(173\) 21.3455 1.62287 0.811433 0.584445i \(-0.198688\pi\)
0.811433 + 0.584445i \(0.198688\pi\)
\(174\) 4.70523 0.356703
\(175\) 3.22153 0.243525
\(176\) 5.03908 0.379835
\(177\) 6.63689 0.498859
\(178\) −13.3773 −1.00267
\(179\) 13.5678 1.01411 0.507053 0.861915i \(-0.330735\pi\)
0.507053 + 0.861915i \(0.330735\pi\)
\(180\) 1.41297 0.105317
\(181\) 0.469172 0.0348733 0.0174366 0.999848i \(-0.494449\pi\)
0.0174366 + 0.999848i \(0.494449\pi\)
\(182\) 8.18992 0.607077
\(183\) −3.99448 −0.295281
\(184\) −0.280998 −0.0207155
\(185\) 0.170862 0.0125620
\(186\) −10.5368 −0.772598
\(187\) 3.73485 0.273119
\(188\) 6.34766 0.462951
\(189\) −17.9096 −1.30273
\(190\) −8.15755 −0.591811
\(191\) 19.0017 1.37492 0.687458 0.726224i \(-0.258727\pi\)
0.687458 + 0.726224i \(0.258727\pi\)
\(192\) 1.25977 0.0909163
\(193\) 23.2684 1.67490 0.837449 0.546515i \(-0.184046\pi\)
0.837449 + 0.546515i \(0.184046\pi\)
\(194\) −6.12982 −0.440096
\(195\) −3.20265 −0.229347
\(196\) 3.37824 0.241303
\(197\) 3.41108 0.243029 0.121515 0.992590i \(-0.461225\pi\)
0.121515 + 0.992590i \(0.461225\pi\)
\(198\) −7.12008 −0.506002
\(199\) −10.5463 −0.747606 −0.373803 0.927508i \(-0.621946\pi\)
−0.373803 + 0.927508i \(0.621946\pi\)
\(200\) 1.00000 0.0707107
\(201\) −8.52661 −0.601421
\(202\) 3.15971 0.222317
\(203\) 12.0324 0.844505
\(204\) 0.933714 0.0653731
\(205\) 4.02927 0.281417
\(206\) 12.8371 0.894401
\(207\) 0.397043 0.0275964
\(208\) 2.54225 0.176273
\(209\) 41.1066 2.84340
\(210\) −4.05839 −0.280056
\(211\) 17.4016 1.19798 0.598988 0.800758i \(-0.295570\pi\)
0.598988 + 0.800758i \(0.295570\pi\)
\(212\) 0.251008 0.0172393
\(213\) −6.42237 −0.440054
\(214\) 10.6960 0.731164
\(215\) 9.44017 0.643814
\(216\) −5.55934 −0.378265
\(217\) −26.9451 −1.82915
\(218\) −2.06372 −0.139772
\(219\) 15.2086 1.02770
\(220\) −5.03908 −0.339735
\(221\) 1.88425 0.126749
\(222\) −0.215247 −0.0144464
\(223\) −14.0516 −0.940965 −0.470483 0.882409i \(-0.655920\pi\)
−0.470483 + 0.882409i \(0.655920\pi\)
\(224\) 3.22153 0.215247
\(225\) −1.41297 −0.0941981
\(226\) −9.93713 −0.661008
\(227\) 4.38716 0.291186 0.145593 0.989345i \(-0.453491\pi\)
0.145593 + 0.989345i \(0.453491\pi\)
\(228\) 10.2767 0.680589
\(229\) −13.3580 −0.882724 −0.441362 0.897329i \(-0.645505\pi\)
−0.441362 + 0.897329i \(0.645505\pi\)
\(230\) 0.280998 0.0185285
\(231\) 20.4506 1.34555
\(232\) 3.73498 0.245214
\(233\) −5.42645 −0.355498 −0.177749 0.984076i \(-0.556882\pi\)
−0.177749 + 0.984076i \(0.556882\pi\)
\(234\) −3.59212 −0.234824
\(235\) −6.34766 −0.414076
\(236\) 5.26832 0.342939
\(237\) −5.52729 −0.359036
\(238\) 2.38772 0.154773
\(239\) −20.8299 −1.34737 −0.673686 0.739017i \(-0.735290\pi\)
−0.673686 + 0.739017i \(0.735290\pi\)
\(240\) −1.25977 −0.0813180
\(241\) −19.7899 −1.27478 −0.637390 0.770542i \(-0.719986\pi\)
−0.637390 + 0.770542i \(0.719986\pi\)
\(242\) 14.3923 0.925173
\(243\) 13.1953 0.846477
\(244\) −3.17080 −0.202989
\(245\) −3.37824 −0.215828
\(246\) −5.07597 −0.323632
\(247\) 20.7385 1.31956
\(248\) −8.36407 −0.531119
\(249\) −3.22812 −0.204574
\(250\) −1.00000 −0.0632456
\(251\) 24.9665 1.57587 0.787937 0.615756i \(-0.211149\pi\)
0.787937 + 0.615756i \(0.211149\pi\)
\(252\) −4.55193 −0.286745
\(253\) −1.41597 −0.0890215
\(254\) 6.10582 0.383113
\(255\) −0.933714 −0.0584714
\(256\) 1.00000 0.0625000
\(257\) −26.5943 −1.65891 −0.829455 0.558574i \(-0.811349\pi\)
−0.829455 + 0.558574i \(0.811349\pi\)
\(258\) −11.8925 −0.740393
\(259\) −0.550435 −0.0342024
\(260\) −2.54225 −0.157663
\(261\) −5.27743 −0.326664
\(262\) 6.40845 0.395915
\(263\) 8.11125 0.500161 0.250080 0.968225i \(-0.419543\pi\)
0.250080 + 0.968225i \(0.419543\pi\)
\(264\) 6.34810 0.390698
\(265\) −0.251008 −0.0154193
\(266\) 26.2798 1.61132
\(267\) −16.8524 −1.03135
\(268\) −6.76837 −0.413444
\(269\) −5.04811 −0.307789 −0.153894 0.988087i \(-0.549182\pi\)
−0.153894 + 0.988087i \(0.549182\pi\)
\(270\) 5.55934 0.338331
\(271\) 6.98247 0.424155 0.212078 0.977253i \(-0.431977\pi\)
0.212078 + 0.977253i \(0.431977\pi\)
\(272\) 0.741176 0.0449404
\(273\) 10.3174 0.624440
\(274\) −8.97013 −0.541905
\(275\) 5.03908 0.303868
\(276\) −0.353994 −0.0213080
\(277\) −3.01293 −0.181029 −0.0905147 0.995895i \(-0.528851\pi\)
−0.0905147 + 0.995895i \(0.528851\pi\)
\(278\) 2.87367 0.172351
\(279\) 11.8182 0.707537
\(280\) −3.22153 −0.192523
\(281\) −12.0243 −0.717312 −0.358656 0.933470i \(-0.616765\pi\)
−0.358656 + 0.933470i \(0.616765\pi\)
\(282\) 7.99661 0.476191
\(283\) −31.6802 −1.88319 −0.941596 0.336743i \(-0.890675\pi\)
−0.941596 + 0.336743i \(0.890675\pi\)
\(284\) −5.09804 −0.302513
\(285\) −10.2767 −0.608737
\(286\) 12.8106 0.757505
\(287\) −12.9804 −0.766210
\(288\) −1.41297 −0.0832602
\(289\) −16.4507 −0.967686
\(290\) −3.73498 −0.219326
\(291\) −7.72219 −0.452683
\(292\) 12.0725 0.706488
\(293\) 20.9078 1.22144 0.610722 0.791845i \(-0.290879\pi\)
0.610722 + 0.791845i \(0.290879\pi\)
\(294\) 4.25582 0.248204
\(295\) −5.26832 −0.306734
\(296\) −0.170862 −0.00993113
\(297\) −28.0140 −1.62554
\(298\) −6.64556 −0.384967
\(299\) −0.714367 −0.0413129
\(300\) 1.25977 0.0727330
\(301\) −30.4118 −1.75291
\(302\) 14.0599 0.809058
\(303\) 3.98052 0.228675
\(304\) 8.15755 0.467868
\(305\) 3.17080 0.181559
\(306\) −1.04726 −0.0598679
\(307\) −4.36711 −0.249244 −0.124622 0.992204i \(-0.539772\pi\)
−0.124622 + 0.992204i \(0.539772\pi\)
\(308\) 16.2335 0.924991
\(309\) 16.1718 0.919981
\(310\) 8.36407 0.475047
\(311\) 16.7802 0.951516 0.475758 0.879576i \(-0.342174\pi\)
0.475758 + 0.879576i \(0.342174\pi\)
\(312\) 3.20265 0.181315
\(313\) −14.3726 −0.812387 −0.406194 0.913787i \(-0.633144\pi\)
−0.406194 + 0.913787i \(0.633144\pi\)
\(314\) −21.6550 −1.22206
\(315\) 4.55193 0.256472
\(316\) −4.38753 −0.246818
\(317\) 12.3187 0.691887 0.345944 0.938255i \(-0.387559\pi\)
0.345944 + 0.938255i \(0.387559\pi\)
\(318\) 0.316213 0.0177323
\(319\) 18.8209 1.05377
\(320\) −1.00000 −0.0559017
\(321\) 13.4745 0.752075
\(322\) −0.905244 −0.0504473
\(323\) 6.04618 0.336419
\(324\) −2.76459 −0.153589
\(325\) 2.54225 0.141018
\(326\) 18.6235 1.03146
\(327\) −2.59981 −0.143770
\(328\) −4.02927 −0.222479
\(329\) 20.4492 1.12740
\(330\) −6.34810 −0.349451
\(331\) 1.64904 0.0906393 0.0453196 0.998973i \(-0.485569\pi\)
0.0453196 + 0.998973i \(0.485569\pi\)
\(332\) −2.56246 −0.140633
\(333\) 0.241423 0.0132299
\(334\) −11.3326 −0.620091
\(335\) 6.76837 0.369796
\(336\) 4.05839 0.221404
\(337\) 1.70474 0.0928629 0.0464314 0.998921i \(-0.485215\pi\)
0.0464314 + 0.998921i \(0.485215\pi\)
\(338\) −6.53699 −0.355565
\(339\) −12.5185 −0.679913
\(340\) −0.741176 −0.0401959
\(341\) −42.1472 −2.28240
\(342\) −11.5264 −0.623276
\(343\) −11.6676 −0.629991
\(344\) −9.44017 −0.508980
\(345\) 0.353994 0.0190584
\(346\) 21.3455 1.14754
\(347\) −19.5187 −1.04782 −0.523909 0.851775i \(-0.675527\pi\)
−0.523909 + 0.851775i \(0.675527\pi\)
\(348\) 4.70523 0.252227
\(349\) 1.38647 0.0742160 0.0371080 0.999311i \(-0.488185\pi\)
0.0371080 + 0.999311i \(0.488185\pi\)
\(350\) 3.22153 0.172198
\(351\) −14.1332 −0.754375
\(352\) 5.03908 0.268584
\(353\) −16.9064 −0.899836 −0.449918 0.893070i \(-0.648547\pi\)
−0.449918 + 0.893070i \(0.648547\pi\)
\(354\) 6.63689 0.352747
\(355\) 5.09804 0.270576
\(356\) −13.3773 −0.708998
\(357\) 3.00799 0.159199
\(358\) 13.5678 0.717081
\(359\) 15.8749 0.837844 0.418922 0.908022i \(-0.362408\pi\)
0.418922 + 0.908022i \(0.362408\pi\)
\(360\) 1.41297 0.0744702
\(361\) 47.5457 2.50240
\(362\) 0.469172 0.0246591
\(363\) 18.1311 0.951634
\(364\) 8.18992 0.429268
\(365\) −12.0725 −0.631902
\(366\) −3.99448 −0.208795
\(367\) −28.6903 −1.49762 −0.748810 0.662785i \(-0.769374\pi\)
−0.748810 + 0.662785i \(0.769374\pi\)
\(368\) −0.280998 −0.0146481
\(369\) 5.69325 0.296379
\(370\) 0.170862 0.00888267
\(371\) 0.808629 0.0419819
\(372\) −10.5368 −0.546309
\(373\) 7.28543 0.377225 0.188613 0.982052i \(-0.439601\pi\)
0.188613 + 0.982052i \(0.439601\pi\)
\(374\) 3.73485 0.193124
\(375\) −1.25977 −0.0650544
\(376\) 6.34766 0.327356
\(377\) 9.49524 0.489030
\(378\) −17.9096 −0.921169
\(379\) −18.5808 −0.954431 −0.477215 0.878786i \(-0.658354\pi\)
−0.477215 + 0.878786i \(0.658354\pi\)
\(380\) −8.15755 −0.418474
\(381\) 7.69195 0.394071
\(382\) 19.0017 0.972213
\(383\) 17.9746 0.918461 0.459231 0.888317i \(-0.348125\pi\)
0.459231 + 0.888317i \(0.348125\pi\)
\(384\) 1.25977 0.0642875
\(385\) −16.2335 −0.827337
\(386\) 23.2684 1.18433
\(387\) 13.3387 0.678044
\(388\) −6.12982 −0.311195
\(389\) −19.5925 −0.993380 −0.496690 0.867928i \(-0.665451\pi\)
−0.496690 + 0.867928i \(0.665451\pi\)
\(390\) −3.20265 −0.162173
\(391\) −0.208269 −0.0105326
\(392\) 3.37824 0.170627
\(393\) 8.07319 0.407238
\(394\) 3.41108 0.171848
\(395\) 4.38753 0.220761
\(396\) −7.12008 −0.357797
\(397\) −5.94922 −0.298583 −0.149291 0.988793i \(-0.547699\pi\)
−0.149291 + 0.988793i \(0.547699\pi\)
\(398\) −10.5463 −0.528637
\(399\) 33.1066 1.65740
\(400\) 1.00000 0.0500000
\(401\) −12.8074 −0.639569 −0.319785 0.947490i \(-0.603611\pi\)
−0.319785 + 0.947490i \(0.603611\pi\)
\(402\) −8.52661 −0.425269
\(403\) −21.2635 −1.05921
\(404\) 3.15971 0.157202
\(405\) 2.76459 0.137374
\(406\) 12.0324 0.597156
\(407\) −0.860985 −0.0426774
\(408\) 0.933714 0.0462257
\(409\) −4.36148 −0.215661 −0.107831 0.994169i \(-0.534390\pi\)
−0.107831 + 0.994169i \(0.534390\pi\)
\(410\) 4.02927 0.198992
\(411\) −11.3003 −0.557404
\(412\) 12.8371 0.632437
\(413\) 16.9720 0.835140
\(414\) 0.397043 0.0195136
\(415\) 2.56246 0.125786
\(416\) 2.54225 0.124644
\(417\) 3.62017 0.177280
\(418\) 41.1066 2.01059
\(419\) 35.4723 1.73294 0.866468 0.499232i \(-0.166385\pi\)
0.866468 + 0.499232i \(0.166385\pi\)
\(420\) −4.05839 −0.198029
\(421\) 25.0881 1.22272 0.611359 0.791353i \(-0.290623\pi\)
0.611359 + 0.791353i \(0.290623\pi\)
\(422\) 17.4016 0.847097
\(423\) −8.96907 −0.436091
\(424\) 0.251008 0.0121900
\(425\) 0.741176 0.0359523
\(426\) −6.42237 −0.311165
\(427\) −10.2148 −0.494329
\(428\) 10.6960 0.517011
\(429\) 16.1384 0.779170
\(430\) 9.44017 0.455246
\(431\) −13.4052 −0.645707 −0.322854 0.946449i \(-0.604642\pi\)
−0.322854 + 0.946449i \(0.604642\pi\)
\(432\) −5.55934 −0.267474
\(433\) −26.3427 −1.26595 −0.632976 0.774172i \(-0.718167\pi\)
−0.632976 + 0.774172i \(0.718167\pi\)
\(434\) −26.9451 −1.29341
\(435\) −4.70523 −0.225599
\(436\) −2.06372 −0.0988340
\(437\) −2.29226 −0.109654
\(438\) 15.2086 0.726694
\(439\) 5.64346 0.269347 0.134674 0.990890i \(-0.457001\pi\)
0.134674 + 0.990890i \(0.457001\pi\)
\(440\) −5.03908 −0.240229
\(441\) −4.77336 −0.227303
\(442\) 1.88425 0.0896248
\(443\) 3.44605 0.163727 0.0818634 0.996644i \(-0.473913\pi\)
0.0818634 + 0.996644i \(0.473913\pi\)
\(444\) −0.215247 −0.0102152
\(445\) 13.3773 0.634147
\(446\) −14.0516 −0.665363
\(447\) −8.37190 −0.395977
\(448\) 3.22153 0.152203
\(449\) −8.44176 −0.398391 −0.199196 0.979960i \(-0.563833\pi\)
−0.199196 + 0.979960i \(0.563833\pi\)
\(450\) −1.41297 −0.0666081
\(451\) −20.3038 −0.956070
\(452\) −9.93713 −0.467403
\(453\) 17.7123 0.832197
\(454\) 4.38716 0.205899
\(455\) −8.18992 −0.383949
\(456\) 10.2767 0.481249
\(457\) −29.4900 −1.37949 −0.689743 0.724055i \(-0.742276\pi\)
−0.689743 + 0.724055i \(0.742276\pi\)
\(458\) −13.3580 −0.624180
\(459\) −4.12045 −0.192326
\(460\) 0.280998 0.0131016
\(461\) 1.82175 0.0848474 0.0424237 0.999100i \(-0.486492\pi\)
0.0424237 + 0.999100i \(0.486492\pi\)
\(462\) 20.4506 0.951447
\(463\) −13.7778 −0.640311 −0.320155 0.947365i \(-0.603735\pi\)
−0.320155 + 0.947365i \(0.603735\pi\)
\(464\) 3.73498 0.173392
\(465\) 10.5368 0.488634
\(466\) −5.42645 −0.251375
\(467\) 10.3059 0.476899 0.238449 0.971155i \(-0.423361\pi\)
0.238449 + 0.971155i \(0.423361\pi\)
\(468\) −3.59212 −0.166046
\(469\) −21.8045 −1.00684
\(470\) −6.34766 −0.292796
\(471\) −27.2804 −1.25701
\(472\) 5.26832 0.242494
\(473\) −47.5698 −2.18726
\(474\) −5.52729 −0.253877
\(475\) 8.15755 0.374294
\(476\) 2.38772 0.109441
\(477\) −0.354667 −0.0162391
\(478\) −20.8299 −0.952736
\(479\) 27.5806 1.26019 0.630096 0.776517i \(-0.283016\pi\)
0.630096 + 0.776517i \(0.283016\pi\)
\(480\) −1.25977 −0.0575005
\(481\) −0.434372 −0.0198057
\(482\) −19.7899 −0.901405
\(483\) −1.14040 −0.0518901
\(484\) 14.3923 0.654196
\(485\) 6.12982 0.278341
\(486\) 13.1953 0.598549
\(487\) −2.18416 −0.0989737 −0.0494869 0.998775i \(-0.515759\pi\)
−0.0494869 + 0.998775i \(0.515759\pi\)
\(488\) −3.17080 −0.143535
\(489\) 23.4614 1.06096
\(490\) −3.37824 −0.152613
\(491\) −16.1287 −0.727878 −0.363939 0.931423i \(-0.618568\pi\)
−0.363939 + 0.931423i \(0.618568\pi\)
\(492\) −5.07597 −0.228842
\(493\) 2.76828 0.124677
\(494\) 20.7385 0.933069
\(495\) 7.12008 0.320024
\(496\) −8.36407 −0.375558
\(497\) −16.4235 −0.736694
\(498\) −3.22812 −0.144655
\(499\) −19.7758 −0.885288 −0.442644 0.896697i \(-0.645959\pi\)
−0.442644 + 0.896697i \(0.645959\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −14.2765 −0.637826
\(502\) 24.9665 1.11431
\(503\) −11.3213 −0.504791 −0.252395 0.967624i \(-0.581218\pi\)
−0.252395 + 0.967624i \(0.581218\pi\)
\(504\) −4.55193 −0.202759
\(505\) −3.15971 −0.140605
\(506\) −1.41597 −0.0629477
\(507\) −8.23512 −0.365734
\(508\) 6.10582 0.270902
\(509\) 19.3310 0.856832 0.428416 0.903582i \(-0.359072\pi\)
0.428416 + 0.903582i \(0.359072\pi\)
\(510\) −0.933714 −0.0413455
\(511\) 38.8918 1.72047
\(512\) 1.00000 0.0441942
\(513\) −45.3506 −2.00228
\(514\) −26.5943 −1.17303
\(515\) −12.8371 −0.565669
\(516\) −11.8925 −0.523537
\(517\) 31.9864 1.40676
\(518\) −0.550435 −0.0241847
\(519\) 26.8905 1.18036
\(520\) −2.54225 −0.111485
\(521\) −9.93862 −0.435419 −0.217709 0.976014i \(-0.569859\pi\)
−0.217709 + 0.976014i \(0.569859\pi\)
\(522\) −5.27743 −0.230987
\(523\) −19.5256 −0.853795 −0.426897 0.904300i \(-0.640393\pi\)
−0.426897 + 0.904300i \(0.640393\pi\)
\(524\) 6.40845 0.279954
\(525\) 4.05839 0.177123
\(526\) 8.11125 0.353667
\(527\) −6.19925 −0.270044
\(528\) 6.34810 0.276265
\(529\) −22.9210 −0.996567
\(530\) −0.251008 −0.0109031
\(531\) −7.44399 −0.323042
\(532\) 26.2798 1.13937
\(533\) −10.2434 −0.443691
\(534\) −16.8524 −0.729275
\(535\) −10.6960 −0.462428
\(536\) −6.76837 −0.292349
\(537\) 17.0924 0.737590
\(538\) −5.04811 −0.217640
\(539\) 17.0232 0.733242
\(540\) 5.55934 0.239236
\(541\) 40.1237 1.72505 0.862526 0.506013i \(-0.168881\pi\)
0.862526 + 0.506013i \(0.168881\pi\)
\(542\) 6.98247 0.299923
\(543\) 0.591050 0.0253644
\(544\) 0.741176 0.0317777
\(545\) 2.06372 0.0883999
\(546\) 10.3174 0.441545
\(547\) 6.56622 0.280751 0.140376 0.990098i \(-0.455169\pi\)
0.140376 + 0.990098i \(0.455169\pi\)
\(548\) −8.97013 −0.383185
\(549\) 4.48025 0.191212
\(550\) 5.03908 0.214867
\(551\) 30.4683 1.29799
\(552\) −0.353994 −0.0150670
\(553\) −14.1345 −0.601062
\(554\) −3.01293 −0.128007
\(555\) 0.215247 0.00913672
\(556\) 2.87367 0.121871
\(557\) −13.3385 −0.565172 −0.282586 0.959242i \(-0.591192\pi\)
−0.282586 + 0.959242i \(0.591192\pi\)
\(558\) 11.8182 0.500304
\(559\) −23.9992 −1.01506
\(560\) −3.22153 −0.136134
\(561\) 4.70506 0.198648
\(562\) −12.0243 −0.507216
\(563\) 11.4169 0.481164 0.240582 0.970629i \(-0.422662\pi\)
0.240582 + 0.970629i \(0.422662\pi\)
\(564\) 7.99661 0.336718
\(565\) 9.93713 0.418058
\(566\) −31.6802 −1.33162
\(567\) −8.90622 −0.374026
\(568\) −5.09804 −0.213909
\(569\) −45.6664 −1.91443 −0.957217 0.289371i \(-0.906554\pi\)
−0.957217 + 0.289371i \(0.906554\pi\)
\(570\) −10.2767 −0.430442
\(571\) 21.5389 0.901374 0.450687 0.892682i \(-0.351179\pi\)
0.450687 + 0.892682i \(0.351179\pi\)
\(572\) 12.8106 0.535637
\(573\) 23.9379 1.00002
\(574\) −12.9804 −0.541792
\(575\) −0.280998 −0.0117184
\(576\) −1.41297 −0.0588738
\(577\) 11.0320 0.459269 0.229634 0.973277i \(-0.426247\pi\)
0.229634 + 0.973277i \(0.426247\pi\)
\(578\) −16.4507 −0.684257
\(579\) 29.3130 1.21820
\(580\) −3.73498 −0.155087
\(581\) −8.25504 −0.342477
\(582\) −7.72219 −0.320095
\(583\) 1.26485 0.0523847
\(584\) 12.0725 0.499562
\(585\) 3.59212 0.148516
\(586\) 20.9078 0.863691
\(587\) 20.4254 0.843045 0.421523 0.906818i \(-0.361496\pi\)
0.421523 + 0.906818i \(0.361496\pi\)
\(588\) 4.25582 0.175507
\(589\) −68.2303 −2.81138
\(590\) −5.26832 −0.216893
\(591\) 4.29719 0.176763
\(592\) −0.170862 −0.00702237
\(593\) 47.7316 1.96010 0.980052 0.198743i \(-0.0636858\pi\)
0.980052 + 0.198743i \(0.0636858\pi\)
\(594\) −28.0140 −1.14943
\(595\) −2.38772 −0.0978870
\(596\) −6.64556 −0.272213
\(597\) −13.2859 −0.543756
\(598\) −0.714367 −0.0292126
\(599\) −24.1441 −0.986500 −0.493250 0.869888i \(-0.664191\pi\)
−0.493250 + 0.869888i \(0.664191\pi\)
\(600\) 1.25977 0.0514300
\(601\) −1.00000 −0.0407909
\(602\) −30.4118 −1.23949
\(603\) 9.56352 0.389457
\(604\) 14.0599 0.572090
\(605\) −14.3923 −0.585131
\(606\) 3.98052 0.161698
\(607\) −24.6591 −1.00088 −0.500441 0.865770i \(-0.666829\pi\)
−0.500441 + 0.865770i \(0.666829\pi\)
\(608\) 8.15755 0.330832
\(609\) 15.1580 0.614234
\(610\) 3.17080 0.128382
\(611\) 16.1373 0.652846
\(612\) −1.04726 −0.0423330
\(613\) −13.9250 −0.562424 −0.281212 0.959646i \(-0.590736\pi\)
−0.281212 + 0.959646i \(0.590736\pi\)
\(614\) −4.36711 −0.176242
\(615\) 5.07597 0.204683
\(616\) 16.2335 0.654068
\(617\) 14.3924 0.579415 0.289707 0.957115i \(-0.406442\pi\)
0.289707 + 0.957115i \(0.406442\pi\)
\(618\) 16.1718 0.650525
\(619\) 15.0658 0.605545 0.302772 0.953063i \(-0.402088\pi\)
0.302772 + 0.953063i \(0.402088\pi\)
\(620\) 8.36407 0.335909
\(621\) 1.56217 0.0626876
\(622\) 16.7802 0.672823
\(623\) −43.0955 −1.72658
\(624\) 3.20265 0.128209
\(625\) 1.00000 0.0400000
\(626\) −14.3726 −0.574445
\(627\) 51.7849 2.06809
\(628\) −21.6550 −0.864128
\(629\) −0.126639 −0.00504941
\(630\) 4.55193 0.181353
\(631\) −21.8634 −0.870369 −0.435185 0.900341i \(-0.643317\pi\)
−0.435185 + 0.900341i \(0.643317\pi\)
\(632\) −4.38753 −0.174527
\(633\) 21.9221 0.871325
\(634\) 12.3187 0.489238
\(635\) −6.10582 −0.242302
\(636\) 0.316213 0.0125387
\(637\) 8.58832 0.340282
\(638\) 18.8209 0.745126
\(639\) 7.20339 0.284962
\(640\) −1.00000 −0.0395285
\(641\) −38.5068 −1.52093 −0.760464 0.649380i \(-0.775028\pi\)
−0.760464 + 0.649380i \(0.775028\pi\)
\(642\) 13.4745 0.531797
\(643\) −33.2238 −1.31022 −0.655109 0.755535i \(-0.727377\pi\)
−0.655109 + 0.755535i \(0.727377\pi\)
\(644\) −0.905244 −0.0356716
\(645\) 11.8925 0.468266
\(646\) 6.04618 0.237884
\(647\) −10.0734 −0.396025 −0.198012 0.980200i \(-0.563449\pi\)
−0.198012 + 0.980200i \(0.563449\pi\)
\(648\) −2.76459 −0.108604
\(649\) 26.5475 1.04208
\(650\) 2.54225 0.0997151
\(651\) −33.9447 −1.33040
\(652\) 18.6235 0.729354
\(653\) 3.57503 0.139902 0.0699509 0.997550i \(-0.477716\pi\)
0.0699509 + 0.997550i \(0.477716\pi\)
\(654\) −2.59981 −0.101661
\(655\) −6.40845 −0.250399
\(656\) −4.02927 −0.157317
\(657\) −17.0581 −0.665498
\(658\) 20.4492 0.797192
\(659\) −17.5839 −0.684970 −0.342485 0.939523i \(-0.611269\pi\)
−0.342485 + 0.939523i \(0.611269\pi\)
\(660\) −6.34810 −0.247099
\(661\) −8.76137 −0.340778 −0.170389 0.985377i \(-0.554502\pi\)
−0.170389 + 0.985377i \(0.554502\pi\)
\(662\) 1.64904 0.0640916
\(663\) 2.37373 0.0921881
\(664\) −2.56246 −0.0994427
\(665\) −26.2798 −1.01909
\(666\) 0.241423 0.00935494
\(667\) −1.04952 −0.0406377
\(668\) −11.3326 −0.438471
\(669\) −17.7018 −0.684392
\(670\) 6.76837 0.261485
\(671\) −15.9779 −0.616820
\(672\) 4.05839 0.156556
\(673\) −29.2081 −1.12589 −0.562946 0.826494i \(-0.690332\pi\)
−0.562946 + 0.826494i \(0.690332\pi\)
\(674\) 1.70474 0.0656640
\(675\) −5.55934 −0.213979
\(676\) −6.53699 −0.251423
\(677\) 19.6789 0.756320 0.378160 0.925740i \(-0.376557\pi\)
0.378160 + 0.925740i \(0.376557\pi\)
\(678\) −12.5185 −0.480771
\(679\) −19.7474 −0.757836
\(680\) −0.741176 −0.0284228
\(681\) 5.52682 0.211788
\(682\) −42.1472 −1.61390
\(683\) 43.5775 1.66745 0.833723 0.552183i \(-0.186205\pi\)
0.833723 + 0.552183i \(0.186205\pi\)
\(684\) −11.5264 −0.440723
\(685\) 8.97013 0.342731
\(686\) −11.6676 −0.445471
\(687\) −16.8281 −0.642032
\(688\) −9.44017 −0.359903
\(689\) 0.638124 0.0243106
\(690\) 0.353994 0.0134763
\(691\) −24.1315 −0.918004 −0.459002 0.888435i \(-0.651793\pi\)
−0.459002 + 0.888435i \(0.651793\pi\)
\(692\) 21.3455 0.811433
\(693\) −22.9375 −0.871325
\(694\) −19.5187 −0.740919
\(695\) −2.87367 −0.109004
\(696\) 4.70523 0.178351
\(697\) −2.98640 −0.113118
\(698\) 1.38647 0.0524786
\(699\) −6.83609 −0.258565
\(700\) 3.22153 0.121762
\(701\) −6.48035 −0.244760 −0.122380 0.992483i \(-0.539053\pi\)
−0.122380 + 0.992483i \(0.539053\pi\)
\(702\) −14.1332 −0.533424
\(703\) −1.39381 −0.0525686
\(704\) 5.03908 0.189917
\(705\) −7.99661 −0.301170
\(706\) −16.9064 −0.636280
\(707\) 10.1791 0.382825
\(708\) 6.63689 0.249430
\(709\) −36.3625 −1.36562 −0.682812 0.730594i \(-0.739243\pi\)
−0.682812 + 0.730594i \(0.739243\pi\)
\(710\) 5.09804 0.191326
\(711\) 6.19945 0.232498
\(712\) −13.3773 −0.501337
\(713\) 2.35029 0.0880191
\(714\) 3.00799 0.112571
\(715\) −12.8106 −0.479088
\(716\) 13.5678 0.507053
\(717\) −26.2409 −0.979985
\(718\) 15.8749 0.592445
\(719\) −42.1623 −1.57239 −0.786195 0.617979i \(-0.787952\pi\)
−0.786195 + 0.617979i \(0.787952\pi\)
\(720\) 1.41297 0.0526584
\(721\) 41.3550 1.54014
\(722\) 47.5457 1.76947
\(723\) −24.9308 −0.927185
\(724\) 0.469172 0.0174366
\(725\) 3.73498 0.138714
\(726\) 18.1311 0.672907
\(727\) 16.9022 0.626870 0.313435 0.949610i \(-0.398520\pi\)
0.313435 + 0.949610i \(0.398520\pi\)
\(728\) 8.18992 0.303538
\(729\) 24.9168 0.922845
\(730\) −12.0725 −0.446822
\(731\) −6.99683 −0.258787
\(732\) −3.99448 −0.147640
\(733\) 39.0107 1.44089 0.720447 0.693510i \(-0.243937\pi\)
0.720447 + 0.693510i \(0.243937\pi\)
\(734\) −28.6903 −1.05898
\(735\) −4.25582 −0.156978
\(736\) −0.280998 −0.0103577
\(737\) −34.1064 −1.25632
\(738\) 5.69325 0.209571
\(739\) 12.1590 0.447277 0.223639 0.974672i \(-0.428206\pi\)
0.223639 + 0.974672i \(0.428206\pi\)
\(740\) 0.170862 0.00628100
\(741\) 26.1258 0.959756
\(742\) 0.808629 0.0296857
\(743\) 17.8692 0.655558 0.327779 0.944754i \(-0.393700\pi\)
0.327779 + 0.944754i \(0.393700\pi\)
\(744\) −10.5368 −0.386299
\(745\) 6.64556 0.243475
\(746\) 7.28543 0.266739
\(747\) 3.62068 0.132474
\(748\) 3.73485 0.136560
\(749\) 34.4575 1.25905
\(750\) −1.25977 −0.0460004
\(751\) 34.6934 1.26598 0.632990 0.774160i \(-0.281827\pi\)
0.632990 + 0.774160i \(0.281827\pi\)
\(752\) 6.34766 0.231475
\(753\) 31.4522 1.14618
\(754\) 9.49524 0.345796
\(755\) −14.0599 −0.511693
\(756\) −17.9096 −0.651365
\(757\) 16.6387 0.604744 0.302372 0.953190i \(-0.402222\pi\)
0.302372 + 0.953190i \(0.402222\pi\)
\(758\) −18.5808 −0.674885
\(759\) −1.78381 −0.0647480
\(760\) −8.15755 −0.295906
\(761\) −11.7680 −0.426589 −0.213295 0.976988i \(-0.568419\pi\)
−0.213295 + 0.976988i \(0.568419\pi\)
\(762\) 7.69195 0.278650
\(763\) −6.64832 −0.240685
\(764\) 19.0017 0.687458
\(765\) 1.04726 0.0378638
\(766\) 17.9746 0.649450
\(767\) 13.3934 0.483607
\(768\) 1.25977 0.0454581
\(769\) 15.7651 0.568505 0.284252 0.958750i \(-0.408255\pi\)
0.284252 + 0.958750i \(0.408255\pi\)
\(770\) −16.2335 −0.585016
\(771\) −33.5028 −1.20658
\(772\) 23.2684 0.837449
\(773\) 43.5857 1.56767 0.783834 0.620970i \(-0.213261\pi\)
0.783834 + 0.620970i \(0.213261\pi\)
\(774\) 13.3387 0.479450
\(775\) −8.36407 −0.300446
\(776\) −6.12982 −0.220048
\(777\) −0.693424 −0.0248764
\(778\) −19.5925 −0.702426
\(779\) −32.8690 −1.17765
\(780\) −3.20265 −0.114673
\(781\) −25.6894 −0.919240
\(782\) −0.208269 −0.00744770
\(783\) −20.7640 −0.742047
\(784\) 3.37824 0.120651
\(785\) 21.6550 0.772900
\(786\) 8.07319 0.287961
\(787\) 1.37031 0.0488462 0.0244231 0.999702i \(-0.492225\pi\)
0.0244231 + 0.999702i \(0.492225\pi\)
\(788\) 3.41108 0.121515
\(789\) 10.2183 0.363782
\(790\) 4.38753 0.156101
\(791\) −32.0127 −1.13824
\(792\) −7.12008 −0.253001
\(793\) −8.06094 −0.286253
\(794\) −5.94922 −0.211130
\(795\) −0.316213 −0.0112149
\(796\) −10.5463 −0.373803
\(797\) −25.8089 −0.914199 −0.457099 0.889416i \(-0.651112\pi\)
−0.457099 + 0.889416i \(0.651112\pi\)
\(798\) 33.1066 1.17196
\(799\) 4.70474 0.166442
\(800\) 1.00000 0.0353553
\(801\) 18.9018 0.667862
\(802\) −12.8074 −0.452244
\(803\) 60.8341 2.14679
\(804\) −8.52661 −0.300710
\(805\) 0.905244 0.0319057
\(806\) −21.2635 −0.748975
\(807\) −6.35948 −0.223864
\(808\) 3.15971 0.111158
\(809\) 24.4027 0.857954 0.428977 0.903315i \(-0.358874\pi\)
0.428977 + 0.903315i \(0.358874\pi\)
\(810\) 2.76459 0.0971379
\(811\) −36.2526 −1.27300 −0.636501 0.771276i \(-0.719619\pi\)
−0.636501 + 0.771276i \(0.719619\pi\)
\(812\) 12.0324 0.422253
\(813\) 8.79633 0.308501
\(814\) −0.860985 −0.0301775
\(815\) −18.6235 −0.652354
\(816\) 0.933714 0.0326865
\(817\) −77.0087 −2.69419
\(818\) −4.36148 −0.152496
\(819\) −11.5721 −0.404363
\(820\) 4.02927 0.140708
\(821\) −23.2190 −0.810348 −0.405174 0.914240i \(-0.632789\pi\)
−0.405174 + 0.914240i \(0.632789\pi\)
\(822\) −11.3003 −0.394144
\(823\) 39.9434 1.39234 0.696171 0.717876i \(-0.254886\pi\)
0.696171 + 0.717876i \(0.254886\pi\)
\(824\) 12.8371 0.447200
\(825\) 6.34810 0.221012
\(826\) 16.9720 0.590533
\(827\) −5.54040 −0.192659 −0.0963293 0.995350i \(-0.530710\pi\)
−0.0963293 + 0.995350i \(0.530710\pi\)
\(828\) 0.397043 0.0137982
\(829\) 18.3189 0.636241 0.318120 0.948050i \(-0.396948\pi\)
0.318120 + 0.948050i \(0.396948\pi\)
\(830\) 2.56246 0.0889443
\(831\) −3.79561 −0.131668
\(832\) 2.54225 0.0881365
\(833\) 2.50387 0.0867540
\(834\) 3.62017 0.125356
\(835\) 11.3326 0.392180
\(836\) 41.1066 1.42170
\(837\) 46.4987 1.60723
\(838\) 35.4723 1.22537
\(839\) −18.5585 −0.640710 −0.320355 0.947298i \(-0.603802\pi\)
−0.320355 + 0.947298i \(0.603802\pi\)
\(840\) −4.05839 −0.140028
\(841\) −15.0499 −0.518962
\(842\) 25.0881 0.864592
\(843\) −15.1479 −0.521722
\(844\) 17.4016 0.598988
\(845\) 6.53699 0.224879
\(846\) −8.96907 −0.308363
\(847\) 46.3653 1.59313
\(848\) 0.251008 0.00861964
\(849\) −39.9099 −1.36970
\(850\) 0.741176 0.0254221
\(851\) 0.0480118 0.00164582
\(852\) −6.42237 −0.220027
\(853\) 23.7844 0.814363 0.407182 0.913347i \(-0.366512\pi\)
0.407182 + 0.913347i \(0.366512\pi\)
\(854\) −10.2148 −0.349544
\(855\) 11.5264 0.394194
\(856\) 10.6960 0.365582
\(857\) 45.5725 1.55673 0.778363 0.627814i \(-0.216050\pi\)
0.778363 + 0.627814i \(0.216050\pi\)
\(858\) 16.1384 0.550957
\(859\) 9.42055 0.321425 0.160712 0.987001i \(-0.448621\pi\)
0.160712 + 0.987001i \(0.448621\pi\)
\(860\) 9.44017 0.321907
\(861\) −16.3524 −0.557287
\(862\) −13.4052 −0.456584
\(863\) −27.4099 −0.933044 −0.466522 0.884510i \(-0.654493\pi\)
−0.466522 + 0.884510i \(0.654493\pi\)
\(864\) −5.55934 −0.189133
\(865\) −21.3455 −0.725768
\(866\) −26.3427 −0.895163
\(867\) −20.7241 −0.703827
\(868\) −26.9451 −0.914576
\(869\) −22.1091 −0.750000
\(870\) −4.70523 −0.159522
\(871\) −17.2069 −0.583033
\(872\) −2.06372 −0.0698862
\(873\) 8.66127 0.293140
\(874\) −2.29226 −0.0775368
\(875\) −3.22153 −0.108908
\(876\) 15.2086 0.513850
\(877\) −17.0285 −0.575011 −0.287506 0.957779i \(-0.592826\pi\)
−0.287506 + 0.957779i \(0.592826\pi\)
\(878\) 5.64346 0.190457
\(879\) 26.3390 0.888393
\(880\) −5.03908 −0.169867
\(881\) 17.1326 0.577213 0.288607 0.957448i \(-0.406808\pi\)
0.288607 + 0.957448i \(0.406808\pi\)
\(882\) −4.77336 −0.160727
\(883\) 19.3023 0.649573 0.324786 0.945787i \(-0.394708\pi\)
0.324786 + 0.945787i \(0.394708\pi\)
\(884\) 1.88425 0.0633743
\(885\) −6.63689 −0.223097
\(886\) 3.44605 0.115772
\(887\) −5.32017 −0.178634 −0.0893168 0.996003i \(-0.528468\pi\)
−0.0893168 + 0.996003i \(0.528468\pi\)
\(888\) −0.215247 −0.00722321
\(889\) 19.6701 0.659713
\(890\) 13.3773 0.448409
\(891\) −13.9310 −0.466706
\(892\) −14.0516 −0.470483
\(893\) 51.7814 1.73280
\(894\) −8.37190 −0.279998
\(895\) −13.5678 −0.453522
\(896\) 3.22153 0.107624
\(897\) −0.899941 −0.0300481
\(898\) −8.44176 −0.281705
\(899\) −31.2396 −1.04190
\(900\) −1.41297 −0.0470991
\(901\) 0.186041 0.00619793
\(902\) −20.3038 −0.676043
\(903\) −38.3119 −1.27494
\(904\) −9.93713 −0.330504
\(905\) −0.469172 −0.0155958
\(906\) 17.7123 0.588452
\(907\) 27.5062 0.913328 0.456664 0.889639i \(-0.349044\pi\)
0.456664 + 0.889639i \(0.349044\pi\)
\(908\) 4.38716 0.145593
\(909\) −4.46459 −0.148081
\(910\) −8.18992 −0.271493
\(911\) −15.0129 −0.497400 −0.248700 0.968581i \(-0.580003\pi\)
−0.248700 + 0.968581i \(0.580003\pi\)
\(912\) 10.2767 0.340294
\(913\) −12.9124 −0.427339
\(914\) −29.4900 −0.975444
\(915\) 3.99448 0.132054
\(916\) −13.3580 −0.441362
\(917\) 20.6450 0.681757
\(918\) −4.12045 −0.135995
\(919\) −22.2628 −0.734382 −0.367191 0.930146i \(-0.619681\pi\)
−0.367191 + 0.930146i \(0.619681\pi\)
\(920\) 0.280998 0.00926424
\(921\) −5.50156 −0.181283
\(922\) 1.82175 0.0599962
\(923\) −12.9605 −0.426599
\(924\) 20.4506 0.672774
\(925\) −0.170862 −0.00561790
\(926\) −13.7778 −0.452768
\(927\) −18.1384 −0.595744
\(928\) 3.73498 0.122607
\(929\) 16.3123 0.535190 0.267595 0.963531i \(-0.413771\pi\)
0.267595 + 0.963531i \(0.413771\pi\)
\(930\) 10.5368 0.345516
\(931\) 27.5582 0.903183
\(932\) −5.42645 −0.177749
\(933\) 21.1392 0.692066
\(934\) 10.3059 0.337218
\(935\) −3.73485 −0.122143
\(936\) −3.59212 −0.117412
\(937\) −46.7438 −1.52705 −0.763527 0.645776i \(-0.776534\pi\)
−0.763527 + 0.645776i \(0.776534\pi\)
\(938\) −21.8045 −0.711942
\(939\) −18.1062 −0.590874
\(940\) −6.34766 −0.207038
\(941\) −41.4625 −1.35164 −0.675820 0.737067i \(-0.736210\pi\)
−0.675820 + 0.737067i \(0.736210\pi\)
\(942\) −27.2804 −0.888843
\(943\) 1.13222 0.0368701
\(944\) 5.26832 0.171469
\(945\) 17.9096 0.582599
\(946\) −47.5698 −1.54663
\(947\) 9.45305 0.307183 0.153591 0.988134i \(-0.450916\pi\)
0.153591 + 0.988134i \(0.450916\pi\)
\(948\) −5.52729 −0.179518
\(949\) 30.6912 0.996278
\(950\) 8.15755 0.264666
\(951\) 15.5188 0.503231
\(952\) 2.38772 0.0773865
\(953\) −11.9182 −0.386068 −0.193034 0.981192i \(-0.561833\pi\)
−0.193034 + 0.981192i \(0.561833\pi\)
\(954\) −0.354667 −0.0114828
\(955\) −19.0017 −0.614881
\(956\) −20.8299 −0.673686
\(957\) 23.7100 0.766436
\(958\) 27.5806 0.891090
\(959\) −28.8975 −0.933149
\(960\) −1.25977 −0.0406590
\(961\) 38.9576 1.25670
\(962\) −0.434372 −0.0140047
\(963\) −15.1131 −0.487014
\(964\) −19.7899 −0.637390
\(965\) −23.2684 −0.749038
\(966\) −1.14040 −0.0366918
\(967\) −5.09622 −0.163883 −0.0819417 0.996637i \(-0.526112\pi\)
−0.0819417 + 0.996637i \(0.526112\pi\)
\(968\) 14.3923 0.462587
\(969\) 7.61682 0.244688
\(970\) 6.12982 0.196817
\(971\) 26.0599 0.836301 0.418151 0.908378i \(-0.362678\pi\)
0.418151 + 0.908378i \(0.362678\pi\)
\(972\) 13.1953 0.423238
\(973\) 9.25759 0.296785
\(974\) −2.18416 −0.0699850
\(975\) 3.20265 0.102567
\(976\) −3.17080 −0.101495
\(977\) −49.9058 −1.59663 −0.798313 0.602242i \(-0.794274\pi\)
−0.798313 + 0.602242i \(0.794274\pi\)
\(978\) 23.4614 0.750214
\(979\) −67.4095 −2.15442
\(980\) −3.37824 −0.107914
\(981\) 2.91597 0.0930998
\(982\) −16.1287 −0.514687
\(983\) 38.7628 1.23634 0.618170 0.786044i \(-0.287874\pi\)
0.618170 + 0.786044i \(0.287874\pi\)
\(984\) −5.07597 −0.161816
\(985\) −3.41108 −0.108686
\(986\) 2.76828 0.0881600
\(987\) 25.7613 0.819992
\(988\) 20.7385 0.659780
\(989\) 2.65267 0.0843501
\(990\) 7.12008 0.226291
\(991\) −21.6649 −0.688207 −0.344104 0.938932i \(-0.611817\pi\)
−0.344104 + 0.938932i \(0.611817\pi\)
\(992\) −8.36407 −0.265559
\(993\) 2.07741 0.0659247
\(994\) −16.4235 −0.520921
\(995\) 10.5463 0.334339
\(996\) −3.22812 −0.102287
\(997\) −46.0481 −1.45836 −0.729179 0.684323i \(-0.760098\pi\)
−0.729179 + 0.684323i \(0.760098\pi\)
\(998\) −19.7758 −0.625993
\(999\) 0.949878 0.0300528
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 6010.2.a.h.1.19 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6010.2.a.h.1.19 28 1.1 even 1 trivial