Properties

Label 1003.2.a.j.1.10
Level $1003$
Weight $2$
Character 1003.1
Self dual yes
Analytic conductor $8.009$
Analytic rank $0$
Dimension $22$
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] = [1003,2,Mod(1,1003)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1003, 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("1003.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1003 = 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1003.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: \(8.00899532273\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 1003.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.0191532 q^{2} +1.86649 q^{3} -1.99963 q^{4} -3.05402 q^{5} -0.0357493 q^{6} -1.55451 q^{7} +0.0766058 q^{8} +0.483795 q^{9} +O(q^{10})\) \(q-0.0191532 q^{2} +1.86649 q^{3} -1.99963 q^{4} -3.05402 q^{5} -0.0357493 q^{6} -1.55451 q^{7} +0.0766058 q^{8} +0.483795 q^{9} +0.0584943 q^{10} +1.27925 q^{11} -3.73230 q^{12} +3.24016 q^{13} +0.0297738 q^{14} -5.70031 q^{15} +3.99780 q^{16} -1.00000 q^{17} -0.00926623 q^{18} +6.72577 q^{19} +6.10692 q^{20} -2.90148 q^{21} -0.0245017 q^{22} +8.38656 q^{23} +0.142984 q^{24} +4.32704 q^{25} -0.0620595 q^{26} -4.69648 q^{27} +3.10845 q^{28} +5.42429 q^{29} +0.109179 q^{30} +0.0319668 q^{31} -0.229782 q^{32} +2.38771 q^{33} +0.0191532 q^{34} +4.74750 q^{35} -0.967412 q^{36} -5.26718 q^{37} -0.128820 q^{38} +6.04774 q^{39} -0.233956 q^{40} +3.84825 q^{41} +0.0555726 q^{42} -1.23767 q^{43} -2.55803 q^{44} -1.47752 q^{45} -0.160630 q^{46} +7.94885 q^{47} +7.46186 q^{48} -4.58350 q^{49} -0.0828767 q^{50} -1.86649 q^{51} -6.47914 q^{52} +7.06796 q^{53} +0.0899526 q^{54} -3.90685 q^{55} -0.119084 q^{56} +12.5536 q^{57} -0.103893 q^{58} +1.00000 q^{59} +11.3985 q^{60} -6.33365 q^{61} -0.000612267 q^{62} -0.752063 q^{63} -7.99120 q^{64} -9.89552 q^{65} -0.0457323 q^{66} +6.61210 q^{67} +1.99963 q^{68} +15.6535 q^{69} -0.0909299 q^{70} -1.04893 q^{71} +0.0370615 q^{72} +4.13553 q^{73} +0.100883 q^{74} +8.07639 q^{75} -13.4491 q^{76} -1.98860 q^{77} -0.115834 q^{78} +5.60337 q^{79} -12.2094 q^{80} -10.2173 q^{81} -0.0737064 q^{82} -2.78891 q^{83} +5.80189 q^{84} +3.05402 q^{85} +0.0237053 q^{86} +10.1244 q^{87} +0.0979979 q^{88} -4.28437 q^{89} +0.0282992 q^{90} -5.03686 q^{91} -16.7701 q^{92} +0.0596658 q^{93} -0.152246 q^{94} -20.5407 q^{95} -0.428887 q^{96} -5.05989 q^{97} +0.0877888 q^{98} +0.618894 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0191532 −0.0135434 −0.00677168 0.999977i \(-0.502156\pi\)
−0.00677168 + 0.999977i \(0.502156\pi\)
\(3\) 1.86649 1.07762 0.538810 0.842427i \(-0.318874\pi\)
0.538810 + 0.842427i \(0.318874\pi\)
\(4\) −1.99963 −0.999817
\(5\) −3.05402 −1.36580 −0.682900 0.730512i \(-0.739281\pi\)
−0.682900 + 0.730512i \(0.739281\pi\)
\(6\) −0.0357493 −0.0145946
\(7\) −1.55451 −0.587549 −0.293774 0.955875i \(-0.594911\pi\)
−0.293774 + 0.955875i \(0.594911\pi\)
\(8\) 0.0766058 0.0270842
\(9\) 0.483795 0.161265
\(10\) 0.0584943 0.0184975
\(11\) 1.27925 0.385708 0.192854 0.981227i \(-0.438226\pi\)
0.192854 + 0.981227i \(0.438226\pi\)
\(12\) −3.73230 −1.07742
\(13\) 3.24016 0.898659 0.449330 0.893366i \(-0.351663\pi\)
0.449330 + 0.893366i \(0.351663\pi\)
\(14\) 0.0297738 0.00795739
\(15\) −5.70031 −1.47181
\(16\) 3.99780 0.999450
\(17\) −1.00000 −0.242536
\(18\) −0.00926623 −0.00218407
\(19\) 6.72577 1.54300 0.771499 0.636230i \(-0.219507\pi\)
0.771499 + 0.636230i \(0.219507\pi\)
\(20\) 6.10692 1.36555
\(21\) −2.90148 −0.633154
\(22\) −0.0245017 −0.00522379
\(23\) 8.38656 1.74872 0.874360 0.485278i \(-0.161282\pi\)
0.874360 + 0.485278i \(0.161282\pi\)
\(24\) 0.142984 0.0291865
\(25\) 4.32704 0.865408
\(26\) −0.0620595 −0.0121709
\(27\) −4.69648 −0.903838
\(28\) 3.10845 0.587441
\(29\) 5.42429 1.00727 0.503633 0.863918i \(-0.331997\pi\)
0.503633 + 0.863918i \(0.331997\pi\)
\(30\) 0.109179 0.0199333
\(31\) 0.0319668 0.00574141 0.00287070 0.999996i \(-0.499086\pi\)
0.00287070 + 0.999996i \(0.499086\pi\)
\(32\) −0.229782 −0.0406202
\(33\) 2.38771 0.415647
\(34\) 0.0191532 0.00328475
\(35\) 4.74750 0.802474
\(36\) −0.967412 −0.161235
\(37\) −5.26718 −0.865919 −0.432960 0.901413i \(-0.642531\pi\)
−0.432960 + 0.901413i \(0.642531\pi\)
\(38\) −0.128820 −0.0208974
\(39\) 6.04774 0.968413
\(40\) −0.233956 −0.0369917
\(41\) 3.84825 0.600996 0.300498 0.953782i \(-0.402847\pi\)
0.300498 + 0.953782i \(0.402847\pi\)
\(42\) 0.0555726 0.00857504
\(43\) −1.23767 −0.188743 −0.0943714 0.995537i \(-0.530084\pi\)
−0.0943714 + 0.995537i \(0.530084\pi\)
\(44\) −2.55803 −0.385637
\(45\) −1.47752 −0.220256
\(46\) −0.160630 −0.0236835
\(47\) 7.94885 1.15946 0.579729 0.814809i \(-0.303158\pi\)
0.579729 + 0.814809i \(0.303158\pi\)
\(48\) 7.46186 1.07703
\(49\) −4.58350 −0.654786
\(50\) −0.0828767 −0.0117205
\(51\) −1.86649 −0.261361
\(52\) −6.47914 −0.898495
\(53\) 7.06796 0.970859 0.485429 0.874276i \(-0.338663\pi\)
0.485429 + 0.874276i \(0.338663\pi\)
\(54\) 0.0899526 0.0122410
\(55\) −3.90685 −0.526800
\(56\) −0.119084 −0.0159133
\(57\) 12.5536 1.66277
\(58\) −0.103893 −0.0136418
\(59\) 1.00000 0.130189
\(60\) 11.3985 1.47154
\(61\) −6.33365 −0.810941 −0.405470 0.914108i \(-0.632892\pi\)
−0.405470 + 0.914108i \(0.632892\pi\)
\(62\) −0.000612267 0 −7.77580e−5 0
\(63\) −0.752063 −0.0947511
\(64\) −7.99120 −0.998900
\(65\) −9.89552 −1.22739
\(66\) −0.0457323 −0.00562926
\(67\) 6.61210 0.807796 0.403898 0.914804i \(-0.367655\pi\)
0.403898 + 0.914804i \(0.367655\pi\)
\(68\) 1.99963 0.242491
\(69\) 15.6535 1.88446
\(70\) −0.0909299 −0.0108682
\(71\) −1.04893 −0.124485 −0.0622427 0.998061i \(-0.519825\pi\)
−0.0622427 + 0.998061i \(0.519825\pi\)
\(72\) 0.0370615 0.00436774
\(73\) 4.13553 0.484027 0.242014 0.970273i \(-0.422192\pi\)
0.242014 + 0.970273i \(0.422192\pi\)
\(74\) 0.100883 0.0117275
\(75\) 8.07639 0.932581
\(76\) −13.4491 −1.54272
\(77\) −1.98860 −0.226622
\(78\) −0.115834 −0.0131156
\(79\) 5.60337 0.630429 0.315214 0.949021i \(-0.397924\pi\)
0.315214 + 0.949021i \(0.397924\pi\)
\(80\) −12.2094 −1.36505
\(81\) −10.2173 −1.13526
\(82\) −0.0737064 −0.00813951
\(83\) −2.78891 −0.306122 −0.153061 0.988217i \(-0.548913\pi\)
−0.153061 + 0.988217i \(0.548913\pi\)
\(84\) 5.80189 0.633038
\(85\) 3.05402 0.331255
\(86\) 0.0237053 0.00255621
\(87\) 10.1244 1.08545
\(88\) 0.0979979 0.0104466
\(89\) −4.28437 −0.454142 −0.227071 0.973878i \(-0.572915\pi\)
−0.227071 + 0.973878i \(0.572915\pi\)
\(90\) 0.0282992 0.00298300
\(91\) −5.03686 −0.528006
\(92\) −16.7701 −1.74840
\(93\) 0.0596658 0.00618706
\(94\) −0.152246 −0.0157030
\(95\) −20.5407 −2.10743
\(96\) −0.428887 −0.0437731
\(97\) −5.05989 −0.513754 −0.256877 0.966444i \(-0.582694\pi\)
−0.256877 + 0.966444i \(0.582694\pi\)
\(98\) 0.0877888 0.00886801
\(99\) 0.618894 0.0622012
\(100\) −8.65250 −0.865250
\(101\) 3.67012 0.365190 0.182595 0.983188i \(-0.441550\pi\)
0.182595 + 0.983188i \(0.441550\pi\)
\(102\) 0.0357493 0.00353971
\(103\) 16.0220 1.57869 0.789345 0.613950i \(-0.210420\pi\)
0.789345 + 0.613950i \(0.210420\pi\)
\(104\) 0.248215 0.0243395
\(105\) 8.86117 0.864762
\(106\) −0.135374 −0.0131487
\(107\) −17.8627 −1.72685 −0.863424 0.504478i \(-0.831685\pi\)
−0.863424 + 0.504478i \(0.831685\pi\)
\(108\) 9.39123 0.903672
\(109\) 7.36384 0.705328 0.352664 0.935750i \(-0.385276\pi\)
0.352664 + 0.935750i \(0.385276\pi\)
\(110\) 0.0748288 0.00713465
\(111\) −9.83115 −0.933132
\(112\) −6.21461 −0.587226
\(113\) −5.86956 −0.552162 −0.276081 0.961134i \(-0.589036\pi\)
−0.276081 + 0.961134i \(0.589036\pi\)
\(114\) −0.240442 −0.0225195
\(115\) −25.6127 −2.38840
\(116\) −10.8466 −1.00708
\(117\) 1.56757 0.144922
\(118\) −0.0191532 −0.00176320
\(119\) 1.55451 0.142502
\(120\) −0.436677 −0.0398629
\(121\) −9.36352 −0.851229
\(122\) 0.121310 0.0109829
\(123\) 7.18273 0.647645
\(124\) −0.0639219 −0.00574036
\(125\) 2.05523 0.183825
\(126\) 0.0144044 0.00128325
\(127\) 13.3973 1.18882 0.594411 0.804161i \(-0.297385\pi\)
0.594411 + 0.804161i \(0.297385\pi\)
\(128\) 0.612622 0.0541486
\(129\) −2.31010 −0.203393
\(130\) 0.189531 0.0166230
\(131\) 20.9107 1.82697 0.913487 0.406868i \(-0.133379\pi\)
0.913487 + 0.406868i \(0.133379\pi\)
\(132\) −4.77454 −0.415571
\(133\) −10.4553 −0.906587
\(134\) −0.126643 −0.0109403
\(135\) 14.3431 1.23446
\(136\) −0.0766058 −0.00656889
\(137\) 0.638567 0.0545565 0.0272782 0.999628i \(-0.491316\pi\)
0.0272782 + 0.999628i \(0.491316\pi\)
\(138\) −0.299814 −0.0255219
\(139\) −9.45404 −0.801881 −0.400940 0.916104i \(-0.631317\pi\)
−0.400940 + 0.916104i \(0.631317\pi\)
\(140\) −9.49326 −0.802327
\(141\) 14.8365 1.24946
\(142\) 0.0200904 0.00168595
\(143\) 4.14498 0.346620
\(144\) 1.93412 0.161176
\(145\) −16.5659 −1.37572
\(146\) −0.0792087 −0.00655535
\(147\) −8.55508 −0.705611
\(148\) 10.5324 0.865760
\(149\) 13.3088 1.09030 0.545148 0.838340i \(-0.316473\pi\)
0.545148 + 0.838340i \(0.316473\pi\)
\(150\) −0.154689 −0.0126303
\(151\) 12.2023 0.993010 0.496505 0.868034i \(-0.334616\pi\)
0.496505 + 0.868034i \(0.334616\pi\)
\(152\) 0.515233 0.0417910
\(153\) −0.483795 −0.0391125
\(154\) 0.0380881 0.00306923
\(155\) −0.0976273 −0.00784161
\(156\) −12.0933 −0.968236
\(157\) 10.2953 0.821652 0.410826 0.911714i \(-0.365240\pi\)
0.410826 + 0.911714i \(0.365240\pi\)
\(158\) −0.107323 −0.00853812
\(159\) 13.1923 1.04622
\(160\) 0.701760 0.0554790
\(161\) −13.0370 −1.02746
\(162\) 0.195695 0.0153752
\(163\) −4.22266 −0.330744 −0.165372 0.986231i \(-0.552883\pi\)
−0.165372 + 0.986231i \(0.552883\pi\)
\(164\) −7.69509 −0.600886
\(165\) −7.29211 −0.567690
\(166\) 0.0534166 0.00414593
\(167\) 20.6542 1.59827 0.799135 0.601152i \(-0.205291\pi\)
0.799135 + 0.601152i \(0.205291\pi\)
\(168\) −0.222270 −0.0171485
\(169\) −2.50135 −0.192411
\(170\) −0.0584943 −0.00448631
\(171\) 3.25390 0.248832
\(172\) 2.47488 0.188708
\(173\) 4.03662 0.306899 0.153449 0.988157i \(-0.450962\pi\)
0.153449 + 0.988157i \(0.450962\pi\)
\(174\) −0.193915 −0.0147006
\(175\) −6.72642 −0.508470
\(176\) 5.11418 0.385496
\(177\) 1.86649 0.140294
\(178\) 0.0820594 0.00615062
\(179\) 25.9761 1.94155 0.970773 0.239998i \(-0.0771467\pi\)
0.970773 + 0.239998i \(0.0771467\pi\)
\(180\) 2.95450 0.220215
\(181\) −7.58334 −0.563665 −0.281832 0.959464i \(-0.590942\pi\)
−0.281832 + 0.959464i \(0.590942\pi\)
\(182\) 0.0964720 0.00715098
\(183\) −11.8217 −0.873886
\(184\) 0.642460 0.0473627
\(185\) 16.0861 1.18267
\(186\) −0.00114279 −8.37936e−5 0
\(187\) −1.27925 −0.0935480
\(188\) −15.8948 −1.15925
\(189\) 7.30071 0.531049
\(190\) 0.393419 0.0285416
\(191\) −13.5965 −0.983811 −0.491906 0.870649i \(-0.663699\pi\)
−0.491906 + 0.870649i \(0.663699\pi\)
\(192\) −14.9155 −1.07643
\(193\) −10.9354 −0.787150 −0.393575 0.919293i \(-0.628762\pi\)
−0.393575 + 0.919293i \(0.628762\pi\)
\(194\) 0.0969132 0.00695796
\(195\) −18.4699 −1.32266
\(196\) 9.16533 0.654666
\(197\) 4.27287 0.304429 0.152215 0.988347i \(-0.451359\pi\)
0.152215 + 0.988347i \(0.451359\pi\)
\(198\) −0.0118538 −0.000842414 0
\(199\) −2.43533 −0.172636 −0.0863179 0.996268i \(-0.527510\pi\)
−0.0863179 + 0.996268i \(0.527510\pi\)
\(200\) 0.331477 0.0234389
\(201\) 12.3414 0.870497
\(202\) −0.0702946 −0.00494591
\(203\) −8.43210 −0.591818
\(204\) 3.73230 0.261313
\(205\) −11.7526 −0.820840
\(206\) −0.306872 −0.0213808
\(207\) 4.05738 0.282007
\(208\) 12.9535 0.898165
\(209\) 8.60394 0.595147
\(210\) −0.169720 −0.0117118
\(211\) 19.8832 1.36881 0.684407 0.729100i \(-0.260061\pi\)
0.684407 + 0.729100i \(0.260061\pi\)
\(212\) −14.1333 −0.970681
\(213\) −1.95783 −0.134148
\(214\) 0.342127 0.0233873
\(215\) 3.77987 0.257785
\(216\) −0.359778 −0.0244798
\(217\) −0.0496927 −0.00337336
\(218\) −0.141041 −0.00955252
\(219\) 7.71893 0.521597
\(220\) 7.81227 0.526703
\(221\) −3.24016 −0.217957
\(222\) 0.188298 0.0126377
\(223\) −9.57676 −0.641307 −0.320654 0.947197i \(-0.603903\pi\)
−0.320654 + 0.947197i \(0.603903\pi\)
\(224\) 0.357199 0.0238663
\(225\) 2.09340 0.139560
\(226\) 0.112421 0.00747813
\(227\) 12.9958 0.862558 0.431279 0.902219i \(-0.358062\pi\)
0.431279 + 0.902219i \(0.358062\pi\)
\(228\) −25.1026 −1.66246
\(229\) −15.4677 −1.02213 −0.511067 0.859541i \(-0.670750\pi\)
−0.511067 + 0.859541i \(0.670750\pi\)
\(230\) 0.490566 0.0323470
\(231\) −3.71171 −0.244213
\(232\) 0.415532 0.0272810
\(233\) −3.30958 −0.216818 −0.108409 0.994106i \(-0.534576\pi\)
−0.108409 + 0.994106i \(0.534576\pi\)
\(234\) −0.0300241 −0.00196274
\(235\) −24.2759 −1.58359
\(236\) −1.99963 −0.130165
\(237\) 10.4587 0.679362
\(238\) −0.0297738 −0.00192995
\(239\) 0.398777 0.0257947 0.0128974 0.999917i \(-0.495895\pi\)
0.0128974 + 0.999917i \(0.495895\pi\)
\(240\) −22.7887 −1.47100
\(241\) −3.25734 −0.209824 −0.104912 0.994482i \(-0.533456\pi\)
−0.104912 + 0.994482i \(0.533456\pi\)
\(242\) 0.179342 0.0115285
\(243\) −4.98113 −0.319540
\(244\) 12.6650 0.810792
\(245\) 13.9981 0.894307
\(246\) −0.137572 −0.00877130
\(247\) 21.7926 1.38663
\(248\) 0.00244884 0.000155502 0
\(249\) −5.20548 −0.329884
\(250\) −0.0393643 −0.00248961
\(251\) −24.9075 −1.57215 −0.786074 0.618132i \(-0.787890\pi\)
−0.786074 + 0.618132i \(0.787890\pi\)
\(252\) 1.50385 0.0947337
\(253\) 10.7285 0.674495
\(254\) −0.256602 −0.0161007
\(255\) 5.70031 0.356967
\(256\) 15.9707 0.998166
\(257\) 22.6703 1.41414 0.707068 0.707145i \(-0.250017\pi\)
0.707068 + 0.707145i \(0.250017\pi\)
\(258\) 0.0442458 0.00275463
\(259\) 8.18787 0.508770
\(260\) 19.7874 1.22716
\(261\) 2.62424 0.162437
\(262\) −0.400507 −0.0247434
\(263\) 6.08012 0.374916 0.187458 0.982273i \(-0.439975\pi\)
0.187458 + 0.982273i \(0.439975\pi\)
\(264\) 0.182912 0.0112575
\(265\) −21.5857 −1.32600
\(266\) 0.200252 0.0122782
\(267\) −7.99675 −0.489393
\(268\) −13.2218 −0.807648
\(269\) −3.85797 −0.235225 −0.117612 0.993060i \(-0.537524\pi\)
−0.117612 + 0.993060i \(0.537524\pi\)
\(270\) −0.274717 −0.0167188
\(271\) 0.470992 0.0286107 0.0143054 0.999898i \(-0.495446\pi\)
0.0143054 + 0.999898i \(0.495446\pi\)
\(272\) −3.99780 −0.242402
\(273\) −9.40126 −0.568990
\(274\) −0.0122306 −0.000738879 0
\(275\) 5.53536 0.333795
\(276\) −31.3012 −1.88411
\(277\) −31.5468 −1.89546 −0.947731 0.319070i \(-0.896630\pi\)
−0.947731 + 0.319070i \(0.896630\pi\)
\(278\) 0.181075 0.0108602
\(279\) 0.0154654 0.000925888 0
\(280\) 0.363686 0.0217344
\(281\) 7.89501 0.470977 0.235489 0.971877i \(-0.424331\pi\)
0.235489 + 0.971877i \(0.424331\pi\)
\(282\) −0.284166 −0.0169218
\(283\) −10.5762 −0.628687 −0.314344 0.949309i \(-0.601784\pi\)
−0.314344 + 0.949309i \(0.601784\pi\)
\(284\) 2.09748 0.124463
\(285\) −38.3390 −2.27101
\(286\) −0.0793896 −0.00469441
\(287\) −5.98214 −0.353114
\(288\) −0.111168 −0.00655061
\(289\) 1.00000 0.0588235
\(290\) 0.317290 0.0186319
\(291\) −9.44425 −0.553632
\(292\) −8.26954 −0.483938
\(293\) −18.8541 −1.10147 −0.550734 0.834680i \(-0.685652\pi\)
−0.550734 + 0.834680i \(0.685652\pi\)
\(294\) 0.163857 0.00955635
\(295\) −3.05402 −0.177812
\(296\) −0.403497 −0.0234528
\(297\) −6.00797 −0.348618
\(298\) −0.254906 −0.0147663
\(299\) 27.1738 1.57150
\(300\) −16.1498 −0.932410
\(301\) 1.92397 0.110896
\(302\) −0.233713 −0.0134487
\(303\) 6.85025 0.393537
\(304\) 26.8883 1.54215
\(305\) 19.3431 1.10758
\(306\) 0.00926623 0.000529715 0
\(307\) −18.9909 −1.08387 −0.541933 0.840421i \(-0.682308\pi\)
−0.541933 + 0.840421i \(0.682308\pi\)
\(308\) 3.97648 0.226581
\(309\) 29.9049 1.70123
\(310\) 0.00186988 0.000106202 0
\(311\) −5.90441 −0.334809 −0.167404 0.985888i \(-0.553539\pi\)
−0.167404 + 0.985888i \(0.553539\pi\)
\(312\) 0.463292 0.0262287
\(313\) −19.8488 −1.12192 −0.560959 0.827843i \(-0.689568\pi\)
−0.560959 + 0.827843i \(0.689568\pi\)
\(314\) −0.197187 −0.0111279
\(315\) 2.29682 0.129411
\(316\) −11.2047 −0.630313
\(317\) −2.89777 −0.162755 −0.0813774 0.996683i \(-0.525932\pi\)
−0.0813774 + 0.996683i \(0.525932\pi\)
\(318\) −0.252675 −0.0141693
\(319\) 6.93902 0.388510
\(320\) 24.4053 1.36430
\(321\) −33.3405 −1.86089
\(322\) 0.249700 0.0139152
\(323\) −6.72577 −0.374232
\(324\) 20.4309 1.13505
\(325\) 14.0203 0.777707
\(326\) 0.0808775 0.00447939
\(327\) 13.7446 0.760076
\(328\) 0.294798 0.0162775
\(329\) −12.3566 −0.681239
\(330\) 0.139667 0.00768844
\(331\) −18.0331 −0.991189 −0.495594 0.868554i \(-0.665050\pi\)
−0.495594 + 0.868554i \(0.665050\pi\)
\(332\) 5.57679 0.306066
\(333\) −2.54823 −0.139642
\(334\) −0.395594 −0.0216459
\(335\) −20.1935 −1.10329
\(336\) −11.5995 −0.632806
\(337\) −18.3604 −1.00016 −0.500078 0.865980i \(-0.666695\pi\)
−0.500078 + 0.865980i \(0.666695\pi\)
\(338\) 0.0479088 0.00260589
\(339\) −10.9555 −0.595021
\(340\) −6.10692 −0.331194
\(341\) 0.0408935 0.00221451
\(342\) −0.0623226 −0.00337002
\(343\) 18.0067 0.972268
\(344\) −0.0948126 −0.00511196
\(345\) −47.8060 −2.57379
\(346\) −0.0773143 −0.00415644
\(347\) 17.3667 0.932292 0.466146 0.884708i \(-0.345642\pi\)
0.466146 + 0.884708i \(0.345642\pi\)
\(348\) −20.2451 −1.08525
\(349\) −10.6426 −0.569688 −0.284844 0.958574i \(-0.591942\pi\)
−0.284844 + 0.958574i \(0.591942\pi\)
\(350\) 0.128833 0.00688639
\(351\) −15.2174 −0.812242
\(352\) −0.293949 −0.0156675
\(353\) 1.48876 0.0792388 0.0396194 0.999215i \(-0.487385\pi\)
0.0396194 + 0.999215i \(0.487385\pi\)
\(354\) −0.0357493 −0.00190006
\(355\) 3.20346 0.170022
\(356\) 8.56717 0.454059
\(357\) 2.90148 0.153563
\(358\) −0.497526 −0.0262951
\(359\) −21.1583 −1.11669 −0.558346 0.829608i \(-0.688564\pi\)
−0.558346 + 0.829608i \(0.688564\pi\)
\(360\) −0.113187 −0.00596546
\(361\) 26.2360 1.38084
\(362\) 0.145245 0.00763392
\(363\) −17.4769 −0.917302
\(364\) 10.0719 0.527910
\(365\) −12.6300 −0.661084
\(366\) 0.226424 0.0118354
\(367\) 14.9663 0.781232 0.390616 0.920554i \(-0.372262\pi\)
0.390616 + 0.920554i \(0.372262\pi\)
\(368\) 33.5278 1.74776
\(369\) 1.86176 0.0969196
\(370\) −0.308100 −0.0160174
\(371\) −10.9872 −0.570427
\(372\) −0.119310 −0.00618592
\(373\) −22.2215 −1.15059 −0.575294 0.817947i \(-0.695112\pi\)
−0.575294 + 0.817947i \(0.695112\pi\)
\(374\) 0.0245017 0.00126695
\(375\) 3.83607 0.198094
\(376\) 0.608928 0.0314031
\(377\) 17.5756 0.905188
\(378\) −0.139832 −0.00719219
\(379\) 2.57221 0.132126 0.0660629 0.997815i \(-0.478956\pi\)
0.0660629 + 0.997815i \(0.478956\pi\)
\(380\) 41.0738 2.10704
\(381\) 25.0060 1.28110
\(382\) 0.260417 0.0133241
\(383\) 33.8756 1.73096 0.865480 0.500943i \(-0.167013\pi\)
0.865480 + 0.500943i \(0.167013\pi\)
\(384\) 1.14345 0.0583516
\(385\) 6.07324 0.309521
\(386\) 0.209449 0.0106607
\(387\) −0.598778 −0.0304376
\(388\) 10.1179 0.513660
\(389\) −22.8193 −1.15698 −0.578492 0.815688i \(-0.696358\pi\)
−0.578492 + 0.815688i \(0.696358\pi\)
\(390\) 0.353758 0.0179132
\(391\) −8.38656 −0.424127
\(392\) −0.351123 −0.0177344
\(393\) 39.0296 1.96878
\(394\) −0.0818392 −0.00412300
\(395\) −17.1128 −0.861039
\(396\) −1.23756 −0.0621898
\(397\) −38.0344 −1.90889 −0.954447 0.298381i \(-0.903553\pi\)
−0.954447 + 0.298381i \(0.903553\pi\)
\(398\) 0.0466443 0.00233807
\(399\) −19.5147 −0.976956
\(400\) 17.2986 0.864932
\(401\) −2.13057 −0.106396 −0.0531978 0.998584i \(-0.516941\pi\)
−0.0531978 + 0.998584i \(0.516941\pi\)
\(402\) −0.236378 −0.0117895
\(403\) 0.103578 0.00515957
\(404\) −7.33889 −0.365123
\(405\) 31.2039 1.55054
\(406\) 0.161502 0.00801520
\(407\) −6.73804 −0.333992
\(408\) −0.142984 −0.00707877
\(409\) 34.2649 1.69429 0.847144 0.531363i \(-0.178320\pi\)
0.847144 + 0.531363i \(0.178320\pi\)
\(410\) 0.225101 0.0111169
\(411\) 1.19188 0.0587912
\(412\) −32.0380 −1.57840
\(413\) −1.55451 −0.0764924
\(414\) −0.0777118 −0.00381933
\(415\) 8.51738 0.418102
\(416\) −0.744532 −0.0365037
\(417\) −17.6459 −0.864123
\(418\) −0.164793 −0.00806030
\(419\) −12.4579 −0.608607 −0.304303 0.952575i \(-0.598424\pi\)
−0.304303 + 0.952575i \(0.598424\pi\)
\(420\) −17.7191 −0.864603
\(421\) −6.29159 −0.306633 −0.153317 0.988177i \(-0.548995\pi\)
−0.153317 + 0.988177i \(0.548995\pi\)
\(422\) −0.380827 −0.0185384
\(423\) 3.84561 0.186980
\(424\) 0.541447 0.0262950
\(425\) −4.32704 −0.209892
\(426\) 0.0374987 0.00181682
\(427\) 9.84571 0.476467
\(428\) 35.7188 1.72653
\(429\) 7.73657 0.373525
\(430\) −0.0723966 −0.00349127
\(431\) 34.4498 1.65939 0.829694 0.558219i \(-0.188515\pi\)
0.829694 + 0.558219i \(0.188515\pi\)
\(432\) −18.7756 −0.903340
\(433\) 12.1163 0.582274 0.291137 0.956681i \(-0.405967\pi\)
0.291137 + 0.956681i \(0.405967\pi\)
\(434\) 0.000951774 0 4.56866e−5 0
\(435\) −30.9201 −1.48251
\(436\) −14.7250 −0.705199
\(437\) 56.4061 2.69827
\(438\) −0.147842 −0.00706418
\(439\) −25.1601 −1.20082 −0.600412 0.799691i \(-0.704997\pi\)
−0.600412 + 0.799691i \(0.704997\pi\)
\(440\) −0.299288 −0.0142680
\(441\) −2.21748 −0.105594
\(442\) 0.0620595 0.00295187
\(443\) −18.8947 −0.897713 −0.448856 0.893604i \(-0.648169\pi\)
−0.448856 + 0.893604i \(0.648169\pi\)
\(444\) 19.6587 0.932961
\(445\) 13.0846 0.620267
\(446\) 0.183426 0.00868546
\(447\) 24.8407 1.17493
\(448\) 12.4224 0.586902
\(449\) −22.2605 −1.05054 −0.525270 0.850936i \(-0.676036\pi\)
−0.525270 + 0.850936i \(0.676036\pi\)
\(450\) −0.0400953 −0.00189011
\(451\) 4.92287 0.231809
\(452\) 11.7370 0.552061
\(453\) 22.7755 1.07009
\(454\) −0.248910 −0.0116819
\(455\) 15.3827 0.721151
\(456\) 0.961680 0.0450348
\(457\) 2.89748 0.135538 0.0677692 0.997701i \(-0.478412\pi\)
0.0677692 + 0.997701i \(0.478412\pi\)
\(458\) 0.296256 0.0138431
\(459\) 4.69648 0.219213
\(460\) 51.2161 2.38796
\(461\) 26.3573 1.22758 0.613790 0.789469i \(-0.289644\pi\)
0.613790 + 0.789469i \(0.289644\pi\)
\(462\) 0.0710912 0.00330746
\(463\) −22.3854 −1.04034 −0.520170 0.854063i \(-0.674131\pi\)
−0.520170 + 0.854063i \(0.674131\pi\)
\(464\) 21.6852 1.00671
\(465\) −0.182221 −0.00845028
\(466\) 0.0633891 0.00293644
\(467\) −40.8398 −1.88984 −0.944920 0.327303i \(-0.893860\pi\)
−0.944920 + 0.327303i \(0.893860\pi\)
\(468\) −3.13457 −0.144896
\(469\) −10.2786 −0.474620
\(470\) 0.464962 0.0214471
\(471\) 19.2160 0.885428
\(472\) 0.0766058 0.00352607
\(473\) −1.58329 −0.0727996
\(474\) −0.200317 −0.00920085
\(475\) 29.1027 1.33532
\(476\) −3.10845 −0.142475
\(477\) 3.41944 0.156566
\(478\) −0.00763786 −0.000349348 0
\(479\) 24.9826 1.14149 0.570743 0.821129i \(-0.306655\pi\)
0.570743 + 0.821129i \(0.306655\pi\)
\(480\) 1.30983 0.0597853
\(481\) −17.0665 −0.778166
\(482\) 0.0623886 0.00284172
\(483\) −24.3334 −1.10721
\(484\) 18.7236 0.851073
\(485\) 15.4530 0.701685
\(486\) 0.0954047 0.00432764
\(487\) 14.8054 0.670898 0.335449 0.942058i \(-0.391112\pi\)
0.335449 + 0.942058i \(0.391112\pi\)
\(488\) −0.485194 −0.0219637
\(489\) −7.88157 −0.356417
\(490\) −0.268109 −0.0121119
\(491\) −9.65823 −0.435870 −0.217935 0.975963i \(-0.569932\pi\)
−0.217935 + 0.975963i \(0.569932\pi\)
\(492\) −14.3628 −0.647526
\(493\) −5.42429 −0.244298
\(494\) −0.417398 −0.0187796
\(495\) −1.89012 −0.0849544
\(496\) 0.127797 0.00573825
\(497\) 1.63058 0.0731413
\(498\) 0.0997016 0.00446774
\(499\) 29.2660 1.31013 0.655063 0.755574i \(-0.272642\pi\)
0.655063 + 0.755574i \(0.272642\pi\)
\(500\) −4.10971 −0.183792
\(501\) 38.5509 1.72233
\(502\) 0.477059 0.0212922
\(503\) 18.5421 0.826749 0.413375 0.910561i \(-0.364350\pi\)
0.413375 + 0.910561i \(0.364350\pi\)
\(504\) −0.0576124 −0.00256626
\(505\) −11.2086 −0.498777
\(506\) −0.205485 −0.00913494
\(507\) −4.66874 −0.207346
\(508\) −26.7898 −1.18860
\(509\) 32.8543 1.45624 0.728120 0.685450i \(-0.240395\pi\)
0.728120 + 0.685450i \(0.240395\pi\)
\(510\) −0.109179 −0.00483454
\(511\) −6.42871 −0.284390
\(512\) −1.53113 −0.0676672
\(513\) −31.5875 −1.39462
\(514\) −0.434210 −0.0191522
\(515\) −48.9314 −2.15617
\(516\) 4.61935 0.203356
\(517\) 10.1686 0.447213
\(518\) −0.156824 −0.00689045
\(519\) 7.53433 0.330720
\(520\) −0.758055 −0.0332429
\(521\) 12.9195 0.566012 0.283006 0.959118i \(-0.408668\pi\)
0.283006 + 0.959118i \(0.408668\pi\)
\(522\) −0.0502627 −0.00219994
\(523\) 30.3367 1.32653 0.663267 0.748383i \(-0.269170\pi\)
0.663267 + 0.748383i \(0.269170\pi\)
\(524\) −41.8137 −1.82664
\(525\) −12.5548 −0.547937
\(526\) −0.116454 −0.00507763
\(527\) −0.0319668 −0.00139250
\(528\) 9.54558 0.415418
\(529\) 47.3344 2.05802
\(530\) 0.413435 0.0179585
\(531\) 0.483795 0.0209949
\(532\) 20.9067 0.906421
\(533\) 12.4690 0.540091
\(534\) 0.153163 0.00662803
\(535\) 54.5529 2.35853
\(536\) 0.506525 0.0218786
\(537\) 48.4843 2.09225
\(538\) 0.0738926 0.00318574
\(539\) −5.86344 −0.252556
\(540\) −28.6810 −1.23423
\(541\) −12.0883 −0.519717 −0.259858 0.965647i \(-0.583676\pi\)
−0.259858 + 0.965647i \(0.583676\pi\)
\(542\) −0.00902100 −0.000387485 0
\(543\) −14.1542 −0.607417
\(544\) 0.229782 0.00985184
\(545\) −22.4893 −0.963337
\(546\) 0.180064 0.00770604
\(547\) −27.1223 −1.15967 −0.579833 0.814736i \(-0.696882\pi\)
−0.579833 + 0.814736i \(0.696882\pi\)
\(548\) −1.27690 −0.0545465
\(549\) −3.06419 −0.130776
\(550\) −0.106020 −0.00452071
\(551\) 36.4825 1.55421
\(552\) 1.19915 0.0510390
\(553\) −8.71049 −0.370408
\(554\) 0.604222 0.0256709
\(555\) 30.0245 1.27447
\(556\) 18.9046 0.801734
\(557\) 27.1148 1.14889 0.574445 0.818543i \(-0.305218\pi\)
0.574445 + 0.818543i \(0.305218\pi\)
\(558\) −0.000296212 0 −1.25396e−5 0
\(559\) −4.01025 −0.169615
\(560\) 18.9796 0.802032
\(561\) −2.38771 −0.100809
\(562\) −0.151215 −0.00637861
\(563\) 13.3183 0.561299 0.280650 0.959810i \(-0.409450\pi\)
0.280650 + 0.959810i \(0.409450\pi\)
\(564\) −29.6675 −1.24923
\(565\) 17.9258 0.754143
\(566\) 0.202567 0.00851454
\(567\) 15.8829 0.667020
\(568\) −0.0803544 −0.00337160
\(569\) 26.0910 1.09379 0.546896 0.837200i \(-0.315809\pi\)
0.546896 + 0.837200i \(0.315809\pi\)
\(570\) 0.734315 0.0307571
\(571\) 27.7143 1.15981 0.579903 0.814685i \(-0.303090\pi\)
0.579903 + 0.814685i \(0.303090\pi\)
\(572\) −8.28843 −0.346557
\(573\) −25.3778 −1.06017
\(574\) 0.114577 0.00478236
\(575\) 36.2890 1.51336
\(576\) −3.86610 −0.161088
\(577\) 32.2828 1.34395 0.671976 0.740573i \(-0.265446\pi\)
0.671976 + 0.740573i \(0.265446\pi\)
\(578\) −0.0191532 −0.000796669 0
\(579\) −20.4109 −0.848248
\(580\) 33.1257 1.37547
\(581\) 4.33538 0.179862
\(582\) 0.180888 0.00749804
\(583\) 9.04168 0.374468
\(584\) 0.316806 0.0131095
\(585\) −4.78740 −0.197935
\(586\) 0.361117 0.0149176
\(587\) −30.3876 −1.25423 −0.627114 0.778927i \(-0.715764\pi\)
−0.627114 + 0.778927i \(0.715764\pi\)
\(588\) 17.1070 0.705481
\(589\) 0.215002 0.00885898
\(590\) 0.0584943 0.00240817
\(591\) 7.97528 0.328059
\(592\) −21.0571 −0.865443
\(593\) −2.55216 −0.104805 −0.0524024 0.998626i \(-0.516688\pi\)
−0.0524024 + 0.998626i \(0.516688\pi\)
\(594\) 0.115072 0.00472146
\(595\) −4.74750 −0.194629
\(596\) −26.6126 −1.09010
\(597\) −4.54552 −0.186036
\(598\) −0.520466 −0.0212834
\(599\) −6.54443 −0.267398 −0.133699 0.991022i \(-0.542686\pi\)
−0.133699 + 0.991022i \(0.542686\pi\)
\(600\) 0.618699 0.0252583
\(601\) −31.2786 −1.27588 −0.637940 0.770086i \(-0.720213\pi\)
−0.637940 + 0.770086i \(0.720213\pi\)
\(602\) −0.0368501 −0.00150190
\(603\) 3.19890 0.130269
\(604\) −24.4001 −0.992828
\(605\) 28.5964 1.16261
\(606\) −0.131204 −0.00532981
\(607\) −30.7224 −1.24698 −0.623492 0.781830i \(-0.714286\pi\)
−0.623492 + 0.781830i \(0.714286\pi\)
\(608\) −1.54546 −0.0626768
\(609\) −15.7385 −0.637754
\(610\) −0.370482 −0.0150004
\(611\) 25.7556 1.04196
\(612\) 0.967412 0.0391053
\(613\) −5.41588 −0.218745 −0.109373 0.994001i \(-0.534884\pi\)
−0.109373 + 0.994001i \(0.534884\pi\)
\(614\) 0.363736 0.0146792
\(615\) −21.9362 −0.884554
\(616\) −0.152339 −0.00613790
\(617\) 2.64249 0.106382 0.0531912 0.998584i \(-0.483061\pi\)
0.0531912 + 0.998584i \(0.483061\pi\)
\(618\) −0.572774 −0.0230404
\(619\) 47.3007 1.90117 0.950587 0.310459i \(-0.100483\pi\)
0.950587 + 0.310459i \(0.100483\pi\)
\(620\) 0.195219 0.00784017
\(621\) −39.3873 −1.58056
\(622\) 0.113088 0.00453443
\(623\) 6.66009 0.266831
\(624\) 24.1776 0.967881
\(625\) −27.9119 −1.11648
\(626\) 0.380168 0.0151946
\(627\) 16.0592 0.641342
\(628\) −20.5868 −0.821501
\(629\) 5.26718 0.210016
\(630\) −0.0439914 −0.00175266
\(631\) −35.1144 −1.39788 −0.698942 0.715178i \(-0.746345\pi\)
−0.698942 + 0.715178i \(0.746345\pi\)
\(632\) 0.429251 0.0170747
\(633\) 37.1118 1.47506
\(634\) 0.0555016 0.00220425
\(635\) −40.9158 −1.62369
\(636\) −26.3797 −1.04602
\(637\) −14.8513 −0.588430
\(638\) −0.132904 −0.00526174
\(639\) −0.507469 −0.0200752
\(640\) −1.87096 −0.0739562
\(641\) −32.5758 −1.28667 −0.643333 0.765587i \(-0.722449\pi\)
−0.643333 + 0.765587i \(0.722449\pi\)
\(642\) 0.638578 0.0252027
\(643\) −33.1924 −1.30898 −0.654489 0.756071i \(-0.727116\pi\)
−0.654489 + 0.756071i \(0.727116\pi\)
\(644\) 26.0692 1.02727
\(645\) 7.05509 0.277794
\(646\) 0.128820 0.00506836
\(647\) −37.6793 −1.48133 −0.740664 0.671876i \(-0.765489\pi\)
−0.740664 + 0.671876i \(0.765489\pi\)
\(648\) −0.782707 −0.0307476
\(649\) 1.27925 0.0502149
\(650\) −0.268534 −0.0105328
\(651\) −0.0927510 −0.00363520
\(652\) 8.44377 0.330684
\(653\) 32.2777 1.26312 0.631562 0.775326i \(-0.282414\pi\)
0.631562 + 0.775326i \(0.282414\pi\)
\(654\) −0.263252 −0.0102940
\(655\) −63.8616 −2.49528
\(656\) 15.3845 0.600665
\(657\) 2.00075 0.0780566
\(658\) 0.236668 0.00922627
\(659\) −36.2590 −1.41245 −0.706225 0.707987i \(-0.749603\pi\)
−0.706225 + 0.707987i \(0.749603\pi\)
\(660\) 14.5816 0.567586
\(661\) −5.70626 −0.221948 −0.110974 0.993823i \(-0.535397\pi\)
−0.110974 + 0.993823i \(0.535397\pi\)
\(662\) 0.345392 0.0134240
\(663\) −6.04774 −0.234875
\(664\) −0.213647 −0.00829110
\(665\) 31.9306 1.23822
\(666\) 0.0488069 0.00189123
\(667\) 45.4911 1.76142
\(668\) −41.3008 −1.59798
\(669\) −17.8749 −0.691085
\(670\) 0.386770 0.0149422
\(671\) −8.10231 −0.312786
\(672\) 0.666708 0.0257188
\(673\) 39.5766 1.52557 0.762783 0.646655i \(-0.223833\pi\)
0.762783 + 0.646655i \(0.223833\pi\)
\(674\) 0.351661 0.0135455
\(675\) −20.3219 −0.782189
\(676\) 5.00177 0.192376
\(677\) −43.4891 −1.67142 −0.835711 0.549170i \(-0.814944\pi\)
−0.835711 + 0.549170i \(0.814944\pi\)
\(678\) 0.209833 0.00805859
\(679\) 7.86564 0.301856
\(680\) 0.233956 0.00897179
\(681\) 24.2565 0.929510
\(682\) −0.000783242 0 −2.99919e−5 0
\(683\) 12.3529 0.472670 0.236335 0.971672i \(-0.424054\pi\)
0.236335 + 0.971672i \(0.424054\pi\)
\(684\) −6.50660 −0.248786
\(685\) −1.95020 −0.0745132
\(686\) −0.344885 −0.0131678
\(687\) −28.8703 −1.10147
\(688\) −4.94795 −0.188639
\(689\) 22.9013 0.872471
\(690\) 0.915638 0.0348577
\(691\) −11.3531 −0.431892 −0.215946 0.976405i \(-0.569284\pi\)
−0.215946 + 0.976405i \(0.569284\pi\)
\(692\) −8.07177 −0.306843
\(693\) −0.962076 −0.0365463
\(694\) −0.332628 −0.0126264
\(695\) 28.8728 1.09521
\(696\) 0.775588 0.0293986
\(697\) −3.84825 −0.145763
\(698\) 0.203841 0.00771549
\(699\) −6.17731 −0.233647
\(700\) 13.4504 0.508376
\(701\) 48.2615 1.82281 0.911406 0.411508i \(-0.134998\pi\)
0.911406 + 0.411508i \(0.134998\pi\)
\(702\) 0.291461 0.0110005
\(703\) −35.4259 −1.33611
\(704\) −10.2227 −0.385284
\(705\) −45.3109 −1.70651
\(706\) −0.0285146 −0.00107316
\(707\) −5.70523 −0.214567
\(708\) −3.73230 −0.140268
\(709\) 14.0407 0.527309 0.263654 0.964617i \(-0.415072\pi\)
0.263654 + 0.964617i \(0.415072\pi\)
\(710\) −0.0613566 −0.00230267
\(711\) 2.71088 0.101666
\(712\) −0.328208 −0.0123001
\(713\) 0.268092 0.0100401
\(714\) −0.0555726 −0.00207975
\(715\) −12.6588 −0.473414
\(716\) −51.9427 −1.94119
\(717\) 0.744314 0.0277969
\(718\) 0.405249 0.0151238
\(719\) −47.0040 −1.75295 −0.876476 0.481445i \(-0.840112\pi\)
−0.876476 + 0.481445i \(0.840112\pi\)
\(720\) −5.90683 −0.220134
\(721\) −24.9063 −0.927558
\(722\) −0.502505 −0.0187013
\(723\) −6.07981 −0.226111
\(724\) 15.1639 0.563561
\(725\) 23.4711 0.871696
\(726\) 0.334740 0.0124234
\(727\) −14.5747 −0.540545 −0.270273 0.962784i \(-0.587114\pi\)
−0.270273 + 0.962784i \(0.587114\pi\)
\(728\) −0.385853 −0.0143007
\(729\) 21.3547 0.790916
\(730\) 0.241905 0.00895330
\(731\) 1.23767 0.0457768
\(732\) 23.6391 0.873725
\(733\) 32.0936 1.18540 0.592701 0.805422i \(-0.298061\pi\)
0.592701 + 0.805422i \(0.298061\pi\)
\(734\) −0.286652 −0.0105805
\(735\) 26.1274 0.963723
\(736\) −1.92708 −0.0710333
\(737\) 8.45852 0.311574
\(738\) −0.0356588 −0.00131262
\(739\) −20.7196 −0.762182 −0.381091 0.924537i \(-0.624452\pi\)
−0.381091 + 0.924537i \(0.624452\pi\)
\(740\) −32.1662 −1.18245
\(741\) 40.6757 1.49426
\(742\) 0.210440 0.00772550
\(743\) −47.3465 −1.73698 −0.868488 0.495710i \(-0.834908\pi\)
−0.868488 + 0.495710i \(0.834908\pi\)
\(744\) 0.00457075 0.000167572 0
\(745\) −40.6452 −1.48913
\(746\) 0.425614 0.0155828
\(747\) −1.34926 −0.0493668
\(748\) 2.55803 0.0935308
\(749\) 27.7677 1.01461
\(750\) −0.0734731 −0.00268286
\(751\) −32.0162 −1.16829 −0.584144 0.811650i \(-0.698570\pi\)
−0.584144 + 0.811650i \(0.698570\pi\)
\(752\) 31.7779 1.15882
\(753\) −46.4897 −1.69418
\(754\) −0.336629 −0.0122593
\(755\) −37.2661 −1.35625
\(756\) −14.5988 −0.530951
\(757\) −0.251509 −0.00914126 −0.00457063 0.999990i \(-0.501455\pi\)
−0.00457063 + 0.999990i \(0.501455\pi\)
\(758\) −0.0492662 −0.00178943
\(759\) 20.0247 0.726850
\(760\) −1.57353 −0.0570781
\(761\) 4.65013 0.168567 0.0842835 0.996442i \(-0.473140\pi\)
0.0842835 + 0.996442i \(0.473140\pi\)
\(762\) −0.478946 −0.0173504
\(763\) −11.4472 −0.414415
\(764\) 27.1881 0.983631
\(765\) 1.47752 0.0534198
\(766\) −0.648826 −0.0234430
\(767\) 3.24016 0.116995
\(768\) 29.8091 1.07564
\(769\) 38.1782 1.37674 0.688371 0.725359i \(-0.258326\pi\)
0.688371 + 0.725359i \(0.258326\pi\)
\(770\) −0.116322 −0.00419195
\(771\) 42.3140 1.52390
\(772\) 21.8669 0.787005
\(773\) 26.5983 0.956673 0.478337 0.878177i \(-0.341240\pi\)
0.478337 + 0.878177i \(0.341240\pi\)
\(774\) 0.0114685 0.000412227 0
\(775\) 0.138322 0.00496866
\(776\) −0.387617 −0.0139146
\(777\) 15.2826 0.548261
\(778\) 0.437062 0.0156694
\(779\) 25.8825 0.927336
\(780\) 36.9331 1.32242
\(781\) −1.34185 −0.0480151
\(782\) 0.160630 0.00574410
\(783\) −25.4751 −0.910404
\(784\) −18.3239 −0.654426
\(785\) −31.4420 −1.12221
\(786\) −0.747543 −0.0266640
\(787\) −44.3438 −1.58069 −0.790343 0.612665i \(-0.790098\pi\)
−0.790343 + 0.612665i \(0.790098\pi\)
\(788\) −8.54417 −0.304374
\(789\) 11.3485 0.404017
\(790\) 0.327765 0.0116614
\(791\) 9.12429 0.324422
\(792\) 0.0474109 0.00168467
\(793\) −20.5221 −0.728759
\(794\) 0.728482 0.0258528
\(795\) −40.2895 −1.42892
\(796\) 4.86976 0.172604
\(797\) 19.6861 0.697318 0.348659 0.937250i \(-0.386637\pi\)
0.348659 + 0.937250i \(0.386637\pi\)
\(798\) 0.373769 0.0132313
\(799\) −7.94885 −0.281210
\(800\) −0.994278 −0.0351530
\(801\) −2.07276 −0.0732373
\(802\) 0.0408072 0.00144095
\(803\) 5.29037 0.186693
\(804\) −24.6783 −0.870338
\(805\) 39.8152 1.40330
\(806\) −0.00198384 −6.98780e−5 0
\(807\) −7.20088 −0.253483
\(808\) 0.281152 0.00989091
\(809\) 18.9912 0.667695 0.333848 0.942627i \(-0.391653\pi\)
0.333848 + 0.942627i \(0.391653\pi\)
\(810\) −0.597655 −0.0209995
\(811\) −26.4131 −0.927488 −0.463744 0.885969i \(-0.653494\pi\)
−0.463744 + 0.885969i \(0.653494\pi\)
\(812\) 16.8611 0.591709
\(813\) 0.879103 0.0308315
\(814\) 0.129055 0.00452338
\(815\) 12.8961 0.451731
\(816\) −7.46186 −0.261217
\(817\) −8.32428 −0.291230
\(818\) −0.656282 −0.0229464
\(819\) −2.43681 −0.0851489
\(820\) 23.5010 0.820689
\(821\) 7.22225 0.252058 0.126029 0.992027i \(-0.459777\pi\)
0.126029 + 0.992027i \(0.459777\pi\)
\(822\) −0.0228284 −0.000796230 0
\(823\) −23.0573 −0.803728 −0.401864 0.915699i \(-0.631638\pi\)
−0.401864 + 0.915699i \(0.631638\pi\)
\(824\) 1.22737 0.0427576
\(825\) 10.3317 0.359704
\(826\) 0.0297738 0.00103596
\(827\) 43.0813 1.49808 0.749042 0.662523i \(-0.230514\pi\)
0.749042 + 0.662523i \(0.230514\pi\)
\(828\) −8.11327 −0.281955
\(829\) 33.1999 1.15308 0.576539 0.817069i \(-0.304403\pi\)
0.576539 + 0.817069i \(0.304403\pi\)
\(830\) −0.163135 −0.00566251
\(831\) −58.8818 −2.04259
\(832\) −25.8928 −0.897671
\(833\) 4.58350 0.158809
\(834\) 0.337975 0.0117031
\(835\) −63.0783 −2.18292
\(836\) −17.2047 −0.595038
\(837\) −0.150131 −0.00518930
\(838\) 0.238608 0.00824258
\(839\) −48.6889 −1.68093 −0.840463 0.541869i \(-0.817717\pi\)
−0.840463 + 0.541869i \(0.817717\pi\)
\(840\) 0.678818 0.0234214
\(841\) 0.422909 0.0145831
\(842\) 0.120504 0.00415285
\(843\) 14.7360 0.507534
\(844\) −39.7591 −1.36856
\(845\) 7.63916 0.262795
\(846\) −0.0736558 −0.00253234
\(847\) 14.5557 0.500139
\(848\) 28.2563 0.970325
\(849\) −19.7403 −0.677486
\(850\) 0.0828767 0.00284265
\(851\) −44.1735 −1.51425
\(852\) 3.91493 0.134123
\(853\) 33.3026 1.14026 0.570129 0.821555i \(-0.306893\pi\)
0.570129 + 0.821555i \(0.306893\pi\)
\(854\) −0.188577 −0.00645297
\(855\) −9.93746 −0.339854
\(856\) −1.36838 −0.0467704
\(857\) −10.6484 −0.363742 −0.181871 0.983322i \(-0.558215\pi\)
−0.181871 + 0.983322i \(0.558215\pi\)
\(858\) −0.148180 −0.00505879
\(859\) 37.4215 1.27681 0.638403 0.769702i \(-0.279595\pi\)
0.638403 + 0.769702i \(0.279595\pi\)
\(860\) −7.55835 −0.257737
\(861\) −11.1656 −0.380523
\(862\) −0.659824 −0.0224737
\(863\) 13.6271 0.463872 0.231936 0.972731i \(-0.425494\pi\)
0.231936 + 0.972731i \(0.425494\pi\)
\(864\) 1.07917 0.0367140
\(865\) −12.3279 −0.419162
\(866\) −0.232067 −0.00788594
\(867\) 1.86649 0.0633894
\(868\) 0.0993671 0.00337274
\(869\) 7.16811 0.243161
\(870\) 0.592219 0.0200781
\(871\) 21.4243 0.725934
\(872\) 0.564113 0.0191033
\(873\) −2.44795 −0.0828505
\(874\) −1.08036 −0.0365437
\(875\) −3.19487 −0.108006
\(876\) −15.4350 −0.521502
\(877\) 3.20321 0.108165 0.0540823 0.998536i \(-0.482777\pi\)
0.0540823 + 0.998536i \(0.482777\pi\)
\(878\) 0.481896 0.0162632
\(879\) −35.1911 −1.18697
\(880\) −15.6188 −0.526510
\(881\) −33.8961 −1.14199 −0.570994 0.820954i \(-0.693442\pi\)
−0.570994 + 0.820954i \(0.693442\pi\)
\(882\) 0.0424718 0.00143010
\(883\) 44.2816 1.49019 0.745097 0.666956i \(-0.232403\pi\)
0.745097 + 0.666956i \(0.232403\pi\)
\(884\) 6.47914 0.217917
\(885\) −5.70031 −0.191614
\(886\) 0.361894 0.0121581
\(887\) 3.37449 0.113304 0.0566521 0.998394i \(-0.481957\pi\)
0.0566521 + 0.998394i \(0.481957\pi\)
\(888\) −0.753123 −0.0252732
\(889\) −20.8263 −0.698491
\(890\) −0.250611 −0.00840051
\(891\) −13.0705 −0.437879
\(892\) 19.1500 0.641189
\(893\) 53.4622 1.78904
\(894\) −0.475779 −0.0159124
\(895\) −79.3316 −2.65176
\(896\) −0.952326 −0.0318150
\(897\) 50.7198 1.69348
\(898\) 0.426361 0.0142278
\(899\) 0.173397 0.00578312
\(900\) −4.18603 −0.139534
\(901\) −7.06796 −0.235468
\(902\) −0.0942888 −0.00313947
\(903\) 3.59107 0.119503
\(904\) −0.449643 −0.0149549
\(905\) 23.1597 0.769853
\(906\) −0.436224 −0.0144926
\(907\) 4.18661 0.139014 0.0695070 0.997581i \(-0.477857\pi\)
0.0695070 + 0.997581i \(0.477857\pi\)
\(908\) −25.9867 −0.862400
\(909\) 1.77559 0.0588924
\(910\) −0.294628 −0.00976681
\(911\) −27.0651 −0.896706 −0.448353 0.893857i \(-0.647989\pi\)
−0.448353 + 0.893857i \(0.647989\pi\)
\(912\) 50.1868 1.66185
\(913\) −3.56771 −0.118074
\(914\) −0.0554960 −0.00183565
\(915\) 36.1037 1.19355
\(916\) 30.9297 1.02195
\(917\) −32.5058 −1.07344
\(918\) −0.0899526 −0.00296888
\(919\) −34.6546 −1.14315 −0.571575 0.820550i \(-0.693668\pi\)
−0.571575 + 0.820550i \(0.693668\pi\)
\(920\) −1.96208 −0.0646880
\(921\) −35.4463 −1.16800
\(922\) −0.504826 −0.0166256
\(923\) −3.39871 −0.111870
\(924\) 7.42207 0.244168
\(925\) −22.7913 −0.749373
\(926\) 0.428753 0.0140897
\(927\) 7.75134 0.254587
\(928\) −1.24641 −0.0409153
\(929\) 19.6352 0.644211 0.322105 0.946704i \(-0.395609\pi\)
0.322105 + 0.946704i \(0.395609\pi\)
\(930\) 0.00349011 0.000114445 0
\(931\) −30.8276 −1.01033
\(932\) 6.61795 0.216778
\(933\) −11.0205 −0.360796
\(934\) 0.782213 0.0255948
\(935\) 3.90685 0.127768
\(936\) 0.120085 0.00392511
\(937\) 28.0019 0.914783 0.457392 0.889265i \(-0.348784\pi\)
0.457392 + 0.889265i \(0.348784\pi\)
\(938\) 0.196867 0.00642795
\(939\) −37.0476 −1.20900
\(940\) 48.5430 1.58330
\(941\) 3.62509 0.118175 0.0590873 0.998253i \(-0.481181\pi\)
0.0590873 + 0.998253i \(0.481181\pi\)
\(942\) −0.368049 −0.0119917
\(943\) 32.2736 1.05097
\(944\) 3.99780 0.130117
\(945\) −22.2965 −0.725306
\(946\) 0.0303250 0.000985952 0
\(947\) −9.48566 −0.308243 −0.154121 0.988052i \(-0.549255\pi\)
−0.154121 + 0.988052i \(0.549255\pi\)
\(948\) −20.9135 −0.679238
\(949\) 13.3998 0.434975
\(950\) −0.557410 −0.0180848
\(951\) −5.40866 −0.175388
\(952\) 0.119084 0.00385955
\(953\) −12.6228 −0.408894 −0.204447 0.978878i \(-0.565540\pi\)
−0.204447 + 0.978878i \(0.565540\pi\)
\(954\) −0.0654933 −0.00212042
\(955\) 41.5241 1.34369
\(956\) −0.797408 −0.0257900
\(957\) 12.9516 0.418667
\(958\) −0.478498 −0.0154596
\(959\) −0.992658 −0.0320546
\(960\) 45.5523 1.47019
\(961\) −30.9990 −0.999967
\(962\) 0.326879 0.0105390
\(963\) −8.64186 −0.278480
\(964\) 6.51349 0.209785
\(965\) 33.3970 1.07509
\(966\) 0.466063 0.0149953
\(967\) 23.8248 0.766153 0.383077 0.923717i \(-0.374865\pi\)
0.383077 + 0.923717i \(0.374865\pi\)
\(968\) −0.717300 −0.0230549
\(969\) −12.5536 −0.403280
\(970\) −0.295975 −0.00950318
\(971\) 29.7437 0.954519 0.477260 0.878762i \(-0.341630\pi\)
0.477260 + 0.878762i \(0.341630\pi\)
\(972\) 9.96044 0.319481
\(973\) 14.6964 0.471144
\(974\) −0.283572 −0.00908622
\(975\) 26.1688 0.838073
\(976\) −25.3207 −0.810494
\(977\) 58.8180 1.88175 0.940877 0.338747i \(-0.110003\pi\)
0.940877 + 0.338747i \(0.110003\pi\)
\(978\) 0.150957 0.00482708
\(979\) −5.48078 −0.175166
\(980\) −27.9911 −0.894143
\(981\) 3.56259 0.113745
\(982\) 0.184986 0.00590314
\(983\) 53.6016 1.70963 0.854813 0.518936i \(-0.173672\pi\)
0.854813 + 0.518936i \(0.173672\pi\)
\(984\) 0.550239 0.0175410
\(985\) −13.0494 −0.415790
\(986\) 0.103893 0.00330861
\(987\) −23.0634 −0.734117
\(988\) −43.5772 −1.38638
\(989\) −10.3798 −0.330058
\(990\) 0.0362018 0.00115057
\(991\) −29.3965 −0.933811 −0.466905 0.884307i \(-0.654631\pi\)
−0.466905 + 0.884307i \(0.654631\pi\)
\(992\) −0.00734541 −0.000233217 0
\(993\) −33.6586 −1.06812
\(994\) −0.0312308 −0.000990580 0
\(995\) 7.43754 0.235786
\(996\) 10.4090 0.329823
\(997\) −22.9518 −0.726890 −0.363445 0.931616i \(-0.618400\pi\)
−0.363445 + 0.931616i \(0.618400\pi\)
\(998\) −0.560538 −0.0177435
\(999\) 24.7372 0.782650
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 1003.2.a.j.1.10 22
3.2 odd 2 9027.2.a.s.1.13 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1003.2.a.j.1.10 22 1.1 even 1 trivial
9027.2.a.s.1.13 22 3.2 odd 2