Properties

Label 1003.2.a.h.1.2
Level $1003$
Weight $2$
Character 1003.1
Self dual yes
Analytic conductor $8.009$
Analytic rank $1$
Dimension $16$
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: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6 x^{15} - 5 x^{14} + 90 x^{13} - 82 x^{12} - 456 x^{11} + 723 x^{10} + 951 x^{9} - 2105 x^{8} - 695 x^{7} + 2641 x^{6} - 151 x^{5} - 1323 x^{4} + 301 x^{3} + 179 x^{2} + \cdots - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.52760\) of defining polynomial
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)
 
\(f(q)\) \(=\) \(q-2.52760 q^{2} -0.131380 q^{3} +4.38874 q^{4} -1.05573 q^{5} +0.332076 q^{6} +3.96203 q^{7} -6.03776 q^{8} -2.98274 q^{9} +O(q^{10})\) \(q-2.52760 q^{2} -0.131380 q^{3} +4.38874 q^{4} -1.05573 q^{5} +0.332076 q^{6} +3.96203 q^{7} -6.03776 q^{8} -2.98274 q^{9} +2.66845 q^{10} -0.143171 q^{11} -0.576593 q^{12} -0.0778021 q^{13} -10.0144 q^{14} +0.138702 q^{15} +6.48355 q^{16} +1.00000 q^{17} +7.53916 q^{18} -3.11646 q^{19} -4.63331 q^{20} -0.520531 q^{21} +0.361878 q^{22} -4.34147 q^{23} +0.793242 q^{24} -3.88544 q^{25} +0.196652 q^{26} +0.786013 q^{27} +17.3883 q^{28} -9.30274 q^{29} -0.350581 q^{30} +4.72224 q^{31} -4.31225 q^{32} +0.0188098 q^{33} -2.52760 q^{34} -4.18282 q^{35} -13.0905 q^{36} +7.09149 q^{37} +7.87714 q^{38} +0.0102216 q^{39} +6.37423 q^{40} +6.54746 q^{41} +1.31569 q^{42} -10.8062 q^{43} -0.628339 q^{44} +3.14896 q^{45} +10.9735 q^{46} +1.89212 q^{47} -0.851808 q^{48} +8.69765 q^{49} +9.82082 q^{50} -0.131380 q^{51} -0.341453 q^{52} -7.03133 q^{53} -1.98672 q^{54} +0.151149 q^{55} -23.9218 q^{56} +0.409440 q^{57} +23.5136 q^{58} +1.00000 q^{59} +0.608725 q^{60} +11.8426 q^{61} -11.9359 q^{62} -11.8177 q^{63} -2.06746 q^{64} +0.0821378 q^{65} -0.0475435 q^{66} -15.3533 q^{67} +4.38874 q^{68} +0.570382 q^{69} +10.5725 q^{70} -2.35610 q^{71} +18.0091 q^{72} +1.35256 q^{73} -17.9244 q^{74} +0.510469 q^{75} -13.6773 q^{76} -0.567246 q^{77} -0.0258362 q^{78} -1.77810 q^{79} -6.84486 q^{80} +8.84495 q^{81} -16.5493 q^{82} -6.22111 q^{83} -2.28448 q^{84} -1.05573 q^{85} +27.3136 q^{86} +1.22219 q^{87} +0.864431 q^{88} +0.231814 q^{89} -7.95930 q^{90} -0.308254 q^{91} -19.0536 q^{92} -0.620408 q^{93} -4.78253 q^{94} +3.29013 q^{95} +0.566544 q^{96} +2.09622 q^{97} -21.9841 q^{98} +0.427041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9} + 12 q^{10} - 7 q^{11} - 4 q^{12} - 16 q^{13} + 11 q^{14} + 7 q^{15} + 22 q^{16} + 16 q^{17} + 11 q^{18} + q^{19} - 43 q^{20} - 8 q^{21} - 18 q^{22} - 8 q^{23} - 39 q^{24} + 23 q^{25} - 49 q^{26} - 7 q^{27} - 15 q^{28} - 39 q^{29} + q^{30} - 3 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{35} - 17 q^{36} - 28 q^{37} - 27 q^{38} - 4 q^{39} + 26 q^{40} - 31 q^{41} - 45 q^{42} + 5 q^{43} - 19 q^{44} - 79 q^{45} - 39 q^{46} - 47 q^{47} - 31 q^{48} + 35 q^{49} - 13 q^{50} - 7 q^{51} + 9 q^{52} - 36 q^{53} + 9 q^{54} + 32 q^{55} + 3 q^{56} + 6 q^{57} + 22 q^{58} + 16 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 19 q^{63} + 32 q^{64} - 19 q^{65} + 48 q^{66} + 4 q^{67} + 14 q^{68} + 14 q^{69} - 11 q^{70} - 5 q^{71} + 40 q^{72} - 35 q^{73} + 31 q^{74} - 12 q^{75} + q^{76} - 79 q^{77} + 31 q^{78} - 48 q^{79} - 127 q^{80} - 28 q^{81} - 7 q^{82} - 42 q^{83} + 28 q^{84} - 21 q^{85} + 58 q^{86} - 16 q^{87} - 2 q^{88} + 20 q^{89} - 14 q^{90} + 49 q^{91} - 21 q^{92} - 55 q^{93} - 22 q^{95} + 24 q^{96} - 2 q^{97} - 78 q^{98} - 35 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.52760 −1.78728 −0.893640 0.448785i \(-0.851857\pi\)
−0.893640 + 0.448785i \(0.851857\pi\)
\(3\) −0.131380 −0.0758523 −0.0379261 0.999281i \(-0.512075\pi\)
−0.0379261 + 0.999281i \(0.512075\pi\)
\(4\) 4.38874 2.19437
\(5\) −1.05573 −0.472136 −0.236068 0.971737i \(-0.575859\pi\)
−0.236068 + 0.971737i \(0.575859\pi\)
\(6\) 0.332076 0.135569
\(7\) 3.96203 1.49751 0.748753 0.662850i \(-0.230653\pi\)
0.748753 + 0.662850i \(0.230653\pi\)
\(8\) −6.03776 −2.13467
\(9\) −2.98274 −0.994246
\(10\) 2.66845 0.843839
\(11\) −0.143171 −0.0431676 −0.0215838 0.999767i \(-0.506871\pi\)
−0.0215838 + 0.999767i \(0.506871\pi\)
\(12\) −0.576593 −0.166448
\(13\) −0.0778021 −0.0215784 −0.0107892 0.999942i \(-0.503434\pi\)
−0.0107892 + 0.999942i \(0.503434\pi\)
\(14\) −10.0144 −2.67646
\(15\) 0.138702 0.0358126
\(16\) 6.48355 1.62089
\(17\) 1.00000 0.242536
\(18\) 7.53916 1.77700
\(19\) −3.11646 −0.714964 −0.357482 0.933920i \(-0.616365\pi\)
−0.357482 + 0.933920i \(0.616365\pi\)
\(20\) −4.63331 −1.03604
\(21\) −0.520531 −0.113589
\(22\) 0.361878 0.0771526
\(23\) −4.34147 −0.905258 −0.452629 0.891699i \(-0.649514\pi\)
−0.452629 + 0.891699i \(0.649514\pi\)
\(24\) 0.793242 0.161920
\(25\) −3.88544 −0.777088
\(26\) 0.196652 0.0385667
\(27\) 0.786013 0.151268
\(28\) 17.3883 3.28608
\(29\) −9.30274 −1.72748 −0.863738 0.503941i \(-0.831883\pi\)
−0.863738 + 0.503941i \(0.831883\pi\)
\(30\) −0.350581 −0.0640071
\(31\) 4.72224 0.848140 0.424070 0.905630i \(-0.360601\pi\)
0.424070 + 0.905630i \(0.360601\pi\)
\(32\) −4.31225 −0.762306
\(33\) 0.0188098 0.00327436
\(34\) −2.52760 −0.433479
\(35\) −4.18282 −0.707026
\(36\) −13.0905 −2.18174
\(37\) 7.09149 1.16583 0.582917 0.812532i \(-0.301911\pi\)
0.582917 + 0.812532i \(0.301911\pi\)
\(38\) 7.87714 1.27784
\(39\) 0.0102216 0.00163677
\(40\) 6.37423 1.00785
\(41\) 6.54746 1.02254 0.511270 0.859420i \(-0.329175\pi\)
0.511270 + 0.859420i \(0.329175\pi\)
\(42\) 1.31569 0.203016
\(43\) −10.8062 −1.64792 −0.823962 0.566645i \(-0.808241\pi\)
−0.823962 + 0.566645i \(0.808241\pi\)
\(44\) −0.628339 −0.0947257
\(45\) 3.14896 0.469419
\(46\) 10.9735 1.61795
\(47\) 1.89212 0.275995 0.137997 0.990433i \(-0.455933\pi\)
0.137997 + 0.990433i \(0.455933\pi\)
\(48\) −0.851808 −0.122948
\(49\) 8.69765 1.24252
\(50\) 9.82082 1.38887
\(51\) −0.131380 −0.0183969
\(52\) −0.341453 −0.0473510
\(53\) −7.03133 −0.965828 −0.482914 0.875668i \(-0.660422\pi\)
−0.482914 + 0.875668i \(0.660422\pi\)
\(54\) −1.98672 −0.270359
\(55\) 0.151149 0.0203810
\(56\) −23.9218 −3.19668
\(57\) 0.409440 0.0542317
\(58\) 23.5136 3.08748
\(59\) 1.00000 0.130189
\(60\) 0.608725 0.0785860
\(61\) 11.8426 1.51629 0.758143 0.652088i \(-0.226107\pi\)
0.758143 + 0.652088i \(0.226107\pi\)
\(62\) −11.9359 −1.51586
\(63\) −11.8177 −1.48889
\(64\) −2.06746 −0.258433
\(65\) 0.0821378 0.0101879
\(66\) −0.0475435 −0.00585220
\(67\) −15.3533 −1.87571 −0.937853 0.347032i \(-0.887189\pi\)
−0.937853 + 0.347032i \(0.887189\pi\)
\(68\) 4.38874 0.532213
\(69\) 0.570382 0.0686659
\(70\) 10.5725 1.26365
\(71\) −2.35610 −0.279617 −0.139809 0.990179i \(-0.544649\pi\)
−0.139809 + 0.990179i \(0.544649\pi\)
\(72\) 18.0091 2.12239
\(73\) 1.35256 0.158305 0.0791524 0.996863i \(-0.474779\pi\)
0.0791524 + 0.996863i \(0.474779\pi\)
\(74\) −17.9244 −2.08367
\(75\) 0.510469 0.0589439
\(76\) −13.6773 −1.56890
\(77\) −0.567246 −0.0646437
\(78\) −0.0258362 −0.00292537
\(79\) −1.77810 −0.200052 −0.100026 0.994985i \(-0.531893\pi\)
−0.100026 + 0.994985i \(0.531893\pi\)
\(80\) −6.84486 −0.765278
\(81\) 8.84495 0.982772
\(82\) −16.5493 −1.82757
\(83\) −6.22111 −0.682856 −0.341428 0.939908i \(-0.610910\pi\)
−0.341428 + 0.939908i \(0.610910\pi\)
\(84\) −2.28448 −0.249257
\(85\) −1.05573 −0.114510
\(86\) 27.3136 2.94530
\(87\) 1.22219 0.131033
\(88\) 0.864431 0.0921487
\(89\) 0.231814 0.0245723 0.0122861 0.999925i \(-0.496089\pi\)
0.0122861 + 0.999925i \(0.496089\pi\)
\(90\) −7.95930 −0.838984
\(91\) −0.308254 −0.0323138
\(92\) −19.0536 −1.98647
\(93\) −0.620408 −0.0643333
\(94\) −4.78253 −0.493280
\(95\) 3.29013 0.337560
\(96\) 0.566544 0.0578227
\(97\) 2.09622 0.212839 0.106419 0.994321i \(-0.466061\pi\)
0.106419 + 0.994321i \(0.466061\pi\)
\(98\) −21.9841 −2.22073
\(99\) 0.427041 0.0429192
\(100\) −17.0522 −1.70522
\(101\) −11.8306 −1.17719 −0.588596 0.808427i \(-0.700319\pi\)
−0.588596 + 0.808427i \(0.700319\pi\)
\(102\) 0.332076 0.0328804
\(103\) 3.23062 0.318322 0.159161 0.987253i \(-0.449121\pi\)
0.159161 + 0.987253i \(0.449121\pi\)
\(104\) 0.469751 0.0460628
\(105\) 0.549539 0.0536295
\(106\) 17.7724 1.72620
\(107\) −14.1116 −1.36422 −0.682109 0.731251i \(-0.738937\pi\)
−0.682109 + 0.731251i \(0.738937\pi\)
\(108\) 3.44960 0.331938
\(109\) −17.3998 −1.66660 −0.833298 0.552824i \(-0.813550\pi\)
−0.833298 + 0.552824i \(0.813550\pi\)
\(110\) −0.382044 −0.0364265
\(111\) −0.931680 −0.0884312
\(112\) 25.6880 2.42729
\(113\) −15.3935 −1.44810 −0.724051 0.689746i \(-0.757722\pi\)
−0.724051 + 0.689746i \(0.757722\pi\)
\(114\) −1.03490 −0.0969272
\(115\) 4.58341 0.427405
\(116\) −40.8273 −3.79072
\(117\) 0.232063 0.0214543
\(118\) −2.52760 −0.232684
\(119\) 3.96203 0.363198
\(120\) −0.837447 −0.0764481
\(121\) −10.9795 −0.998137
\(122\) −29.9332 −2.71003
\(123\) −0.860205 −0.0775621
\(124\) 20.7247 1.86113
\(125\) 9.38060 0.839027
\(126\) 29.8703 2.66106
\(127\) −8.69637 −0.771678 −0.385839 0.922566i \(-0.626088\pi\)
−0.385839 + 0.922566i \(0.626088\pi\)
\(128\) 13.8502 1.22420
\(129\) 1.41971 0.124999
\(130\) −0.207611 −0.0182087
\(131\) 8.14459 0.711596 0.355798 0.934563i \(-0.384209\pi\)
0.355798 + 0.934563i \(0.384209\pi\)
\(132\) 0.0825512 0.00718516
\(133\) −12.3475 −1.07066
\(134\) 38.8070 3.35241
\(135\) −0.829815 −0.0714191
\(136\) −6.03776 −0.517734
\(137\) −6.41725 −0.548263 −0.274131 0.961692i \(-0.588390\pi\)
−0.274131 + 0.961692i \(0.588390\pi\)
\(138\) −1.44169 −0.122725
\(139\) −12.6874 −1.07613 −0.538067 0.842902i \(-0.680845\pi\)
−0.538067 + 0.842902i \(0.680845\pi\)
\(140\) −18.3573 −1.55148
\(141\) −0.248587 −0.0209348
\(142\) 5.95526 0.499754
\(143\) 0.0111390 0.000931489 0
\(144\) −19.3387 −1.61156
\(145\) 9.82116 0.815603
\(146\) −3.41872 −0.282935
\(147\) −1.14270 −0.0942482
\(148\) 31.1227 2.55827
\(149\) −3.04529 −0.249480 −0.124740 0.992189i \(-0.539810\pi\)
−0.124740 + 0.992189i \(0.539810\pi\)
\(150\) −1.29026 −0.105349
\(151\) 4.30708 0.350505 0.175253 0.984523i \(-0.443926\pi\)
0.175253 + 0.984523i \(0.443926\pi\)
\(152\) 18.8164 1.52621
\(153\) −2.98274 −0.241140
\(154\) 1.43377 0.115536
\(155\) −4.98540 −0.400437
\(156\) 0.0448601 0.00359168
\(157\) −11.3866 −0.908748 −0.454374 0.890811i \(-0.650137\pi\)
−0.454374 + 0.890811i \(0.650137\pi\)
\(158\) 4.49432 0.357549
\(159\) 0.923777 0.0732603
\(160\) 4.55256 0.359912
\(161\) −17.2010 −1.35563
\(162\) −22.3565 −1.75649
\(163\) −11.7585 −0.920999 −0.460500 0.887660i \(-0.652330\pi\)
−0.460500 + 0.887660i \(0.652330\pi\)
\(164\) 28.7351 2.24383
\(165\) −0.0198580 −0.00154594
\(166\) 15.7244 1.22045
\(167\) −12.7938 −0.990013 −0.495007 0.868889i \(-0.664834\pi\)
−0.495007 + 0.868889i \(0.664834\pi\)
\(168\) 3.14284 0.242476
\(169\) −12.9939 −0.999534
\(170\) 2.66845 0.204661
\(171\) 9.29558 0.710851
\(172\) −47.4254 −3.61615
\(173\) 7.42598 0.564586 0.282293 0.959328i \(-0.408905\pi\)
0.282293 + 0.959328i \(0.408905\pi\)
\(174\) −3.08921 −0.234193
\(175\) −15.3942 −1.16369
\(176\) −0.928254 −0.0699698
\(177\) −0.131380 −0.00987513
\(178\) −0.585932 −0.0439175
\(179\) 18.3553 1.37194 0.685969 0.727631i \(-0.259379\pi\)
0.685969 + 0.727631i \(0.259379\pi\)
\(180\) 13.8200 1.03008
\(181\) 14.3361 1.06560 0.532798 0.846242i \(-0.321141\pi\)
0.532798 + 0.846242i \(0.321141\pi\)
\(182\) 0.779141 0.0577538
\(183\) −1.55588 −0.115014
\(184\) 26.2127 1.93243
\(185\) −7.48668 −0.550432
\(186\) 1.56814 0.114982
\(187\) −0.143171 −0.0104697
\(188\) 8.30404 0.605634
\(189\) 3.11420 0.226525
\(190\) −8.31612 −0.603314
\(191\) 9.30556 0.673327 0.336663 0.941625i \(-0.390702\pi\)
0.336663 + 0.941625i \(0.390702\pi\)
\(192\) 0.271623 0.0196027
\(193\) −12.3151 −0.886463 −0.443231 0.896407i \(-0.646168\pi\)
−0.443231 + 0.896407i \(0.646168\pi\)
\(194\) −5.29839 −0.380402
\(195\) −0.0107913 −0.000772779 0
\(196\) 38.1717 2.72655
\(197\) 8.10614 0.577538 0.288769 0.957399i \(-0.406754\pi\)
0.288769 + 0.957399i \(0.406754\pi\)
\(198\) −1.07939 −0.0767087
\(199\) 25.6544 1.81859 0.909295 0.416152i \(-0.136622\pi\)
0.909295 + 0.416152i \(0.136622\pi\)
\(200\) 23.4594 1.65883
\(201\) 2.01712 0.142277
\(202\) 29.9031 2.10397
\(203\) −36.8577 −2.58690
\(204\) −0.576593 −0.0403696
\(205\) −6.91233 −0.482778
\(206\) −8.16570 −0.568931
\(207\) 12.9495 0.900050
\(208\) −0.504433 −0.0349762
\(209\) 0.446186 0.0308633
\(210\) −1.38901 −0.0958510
\(211\) 4.75556 0.327386 0.163693 0.986511i \(-0.447659\pi\)
0.163693 + 0.986511i \(0.447659\pi\)
\(212\) −30.8587 −2.11938
\(213\) 0.309544 0.0212096
\(214\) 35.6683 2.43824
\(215\) 11.4084 0.778044
\(216\) −4.74576 −0.322908
\(217\) 18.7096 1.27009
\(218\) 43.9796 2.97867
\(219\) −0.177699 −0.0120078
\(220\) 0.663355 0.0447234
\(221\) −0.0778021 −0.00523353
\(222\) 2.35491 0.158051
\(223\) −13.5394 −0.906664 −0.453332 0.891342i \(-0.649765\pi\)
−0.453332 + 0.891342i \(0.649765\pi\)
\(224\) −17.0853 −1.14156
\(225\) 11.5893 0.772617
\(226\) 38.9086 2.58816
\(227\) 22.6419 1.50280 0.751398 0.659849i \(-0.229380\pi\)
0.751398 + 0.659849i \(0.229380\pi\)
\(228\) 1.79693 0.119004
\(229\) 26.3719 1.74270 0.871352 0.490658i \(-0.163244\pi\)
0.871352 + 0.490658i \(0.163244\pi\)
\(230\) −11.5850 −0.763892
\(231\) 0.0745249 0.00490338
\(232\) 56.1678 3.68759
\(233\) 16.3691 1.07238 0.536189 0.844098i \(-0.319863\pi\)
0.536189 + 0.844098i \(0.319863\pi\)
\(234\) −0.586562 −0.0383448
\(235\) −1.99757 −0.130307
\(236\) 4.38874 0.285683
\(237\) 0.233607 0.0151744
\(238\) −10.0144 −0.649137
\(239\) 7.70132 0.498157 0.249078 0.968483i \(-0.419872\pi\)
0.249078 + 0.968483i \(0.419872\pi\)
\(240\) 0.899278 0.0580481
\(241\) −16.7487 −1.07888 −0.539440 0.842024i \(-0.681364\pi\)
−0.539440 + 0.842024i \(0.681364\pi\)
\(242\) 27.7517 1.78395
\(243\) −3.52009 −0.225814
\(244\) 51.9740 3.32729
\(245\) −9.18235 −0.586639
\(246\) 2.17425 0.138625
\(247\) 0.242467 0.0154278
\(248\) −28.5118 −1.81050
\(249\) 0.817330 0.0517962
\(250\) −23.7104 −1.49958
\(251\) −23.6645 −1.49369 −0.746845 0.664998i \(-0.768432\pi\)
−0.746845 + 0.664998i \(0.768432\pi\)
\(252\) −51.8648 −3.26717
\(253\) 0.621571 0.0390778
\(254\) 21.9809 1.37920
\(255\) 0.138702 0.00868583
\(256\) −30.8728 −1.92955
\(257\) −7.53649 −0.470113 −0.235057 0.971982i \(-0.575528\pi\)
−0.235057 + 0.971982i \(0.575528\pi\)
\(258\) −3.58846 −0.223408
\(259\) 28.0967 1.74584
\(260\) 0.360481 0.0223561
\(261\) 27.7477 1.71754
\(262\) −20.5862 −1.27182
\(263\) −7.26470 −0.447960 −0.223980 0.974594i \(-0.571905\pi\)
−0.223980 + 0.974594i \(0.571905\pi\)
\(264\) −0.113569 −0.00698969
\(265\) 7.42317 0.456002
\(266\) 31.2094 1.91357
\(267\) −0.0304558 −0.00186386
\(268\) −67.3817 −4.11599
\(269\) 4.96620 0.302795 0.151397 0.988473i \(-0.451623\pi\)
0.151397 + 0.988473i \(0.451623\pi\)
\(270\) 2.09744 0.127646
\(271\) −23.2652 −1.41326 −0.706631 0.707582i \(-0.749786\pi\)
−0.706631 + 0.707582i \(0.749786\pi\)
\(272\) 6.48355 0.393123
\(273\) 0.0404984 0.00245108
\(274\) 16.2202 0.979899
\(275\) 0.556281 0.0335450
\(276\) 2.50326 0.150678
\(277\) −17.5601 −1.05508 −0.527541 0.849529i \(-0.676886\pi\)
−0.527541 + 0.849529i \(0.676886\pi\)
\(278\) 32.0687 1.92335
\(279\) −14.0852 −0.843260
\(280\) 25.2549 1.50927
\(281\) 11.4656 0.683979 0.341989 0.939704i \(-0.388899\pi\)
0.341989 + 0.939704i \(0.388899\pi\)
\(282\) 0.628328 0.0374164
\(283\) 18.6179 1.10672 0.553359 0.832943i \(-0.313346\pi\)
0.553359 + 0.832943i \(0.313346\pi\)
\(284\) −10.3403 −0.613583
\(285\) −0.432257 −0.0256047
\(286\) −0.0281548 −0.00166483
\(287\) 25.9412 1.53126
\(288\) 12.8623 0.757920
\(289\) 1.00000 0.0588235
\(290\) −24.8239 −1.45771
\(291\) −0.275401 −0.0161443
\(292\) 5.93602 0.347379
\(293\) −12.1329 −0.708814 −0.354407 0.935091i \(-0.615317\pi\)
−0.354407 + 0.935091i \(0.615317\pi\)
\(294\) 2.88828 0.168448
\(295\) −1.05573 −0.0614668
\(296\) −42.8167 −2.48867
\(297\) −0.112534 −0.00652989
\(298\) 7.69725 0.445890
\(299\) 0.337775 0.0195340
\(300\) 2.24032 0.129345
\(301\) −42.8143 −2.46778
\(302\) −10.8866 −0.626451
\(303\) 1.55431 0.0892928
\(304\) −20.2057 −1.15888
\(305\) −12.5025 −0.715893
\(306\) 7.53916 0.430985
\(307\) −14.1309 −0.806493 −0.403246 0.915091i \(-0.632118\pi\)
−0.403246 + 0.915091i \(0.632118\pi\)
\(308\) −2.48950 −0.141852
\(309\) −0.424439 −0.0241455
\(310\) 12.6011 0.715693
\(311\) 24.8276 1.40785 0.703923 0.710276i \(-0.251430\pi\)
0.703923 + 0.710276i \(0.251430\pi\)
\(312\) −0.0617158 −0.00349397
\(313\) 4.82660 0.272816 0.136408 0.990653i \(-0.456444\pi\)
0.136408 + 0.990653i \(0.456444\pi\)
\(314\) 28.7807 1.62419
\(315\) 12.4763 0.702958
\(316\) −7.80361 −0.438988
\(317\) 8.50056 0.477439 0.238720 0.971089i \(-0.423272\pi\)
0.238720 + 0.971089i \(0.423272\pi\)
\(318\) −2.33493 −0.130937
\(319\) 1.33188 0.0745710
\(320\) 2.18268 0.122015
\(321\) 1.85398 0.103479
\(322\) 43.4772 2.42289
\(323\) −3.11646 −0.173404
\(324\) 38.8182 2.15657
\(325\) 0.302295 0.0167683
\(326\) 29.7208 1.64608
\(327\) 2.28598 0.126415
\(328\) −39.5320 −2.18279
\(329\) 7.49665 0.413304
\(330\) 0.0501930 0.00276303
\(331\) 3.12950 0.172013 0.0860065 0.996295i \(-0.472589\pi\)
0.0860065 + 0.996295i \(0.472589\pi\)
\(332\) −27.3028 −1.49844
\(333\) −21.1521 −1.15913
\(334\) 32.3375 1.76943
\(335\) 16.2089 0.885588
\(336\) −3.37489 −0.184115
\(337\) 8.50675 0.463392 0.231696 0.972788i \(-0.425573\pi\)
0.231696 + 0.972788i \(0.425573\pi\)
\(338\) 32.8434 1.78645
\(339\) 2.02240 0.109842
\(340\) −4.63331 −0.251277
\(341\) −0.676087 −0.0366122
\(342\) −23.4955 −1.27049
\(343\) 6.72615 0.363178
\(344\) 65.2451 3.51778
\(345\) −0.602168 −0.0324196
\(346\) −18.7699 −1.00907
\(347\) 10.8779 0.583957 0.291979 0.956425i \(-0.405686\pi\)
0.291979 + 0.956425i \(0.405686\pi\)
\(348\) 5.36389 0.287535
\(349\) −20.4253 −1.09334 −0.546671 0.837348i \(-0.684105\pi\)
−0.546671 + 0.837348i \(0.684105\pi\)
\(350\) 38.9103 2.07985
\(351\) −0.0611534 −0.00326413
\(352\) 0.617389 0.0329069
\(353\) −7.21912 −0.384235 −0.192117 0.981372i \(-0.561535\pi\)
−0.192117 + 0.981372i \(0.561535\pi\)
\(354\) 0.332076 0.0176496
\(355\) 2.48740 0.132017
\(356\) 1.01737 0.0539206
\(357\) −0.520531 −0.0275494
\(358\) −46.3947 −2.45204
\(359\) 5.86760 0.309680 0.154840 0.987940i \(-0.450514\pi\)
0.154840 + 0.987940i \(0.450514\pi\)
\(360\) −19.0127 −1.00206
\(361\) −9.28770 −0.488826
\(362\) −36.2359 −1.90452
\(363\) 1.44249 0.0757110
\(364\) −1.35285 −0.0709084
\(365\) −1.42793 −0.0747414
\(366\) 3.93263 0.205562
\(367\) −10.6311 −0.554939 −0.277469 0.960734i \(-0.589496\pi\)
−0.277469 + 0.960734i \(0.589496\pi\)
\(368\) −28.1481 −1.46732
\(369\) −19.5294 −1.01666
\(370\) 18.9233 0.983776
\(371\) −27.8583 −1.44633
\(372\) −2.72281 −0.141171
\(373\) 24.7657 1.28232 0.641158 0.767409i \(-0.278454\pi\)
0.641158 + 0.767409i \(0.278454\pi\)
\(374\) 0.361878 0.0187123
\(375\) −1.23242 −0.0636421
\(376\) −11.4242 −0.589158
\(377\) 0.723773 0.0372762
\(378\) −7.87144 −0.404863
\(379\) −1.70887 −0.0877790 −0.0438895 0.999036i \(-0.513975\pi\)
−0.0438895 + 0.999036i \(0.513975\pi\)
\(380\) 14.4395 0.740732
\(381\) 1.14253 0.0585336
\(382\) −23.5207 −1.20342
\(383\) 7.89067 0.403194 0.201597 0.979469i \(-0.435387\pi\)
0.201597 + 0.979469i \(0.435387\pi\)
\(384\) −1.81964 −0.0928582
\(385\) 0.598858 0.0305206
\(386\) 31.1277 1.58436
\(387\) 32.2320 1.63844
\(388\) 9.19975 0.467046
\(389\) −7.20820 −0.365470 −0.182735 0.983162i \(-0.558495\pi\)
−0.182735 + 0.983162i \(0.558495\pi\)
\(390\) 0.0272760 0.00138117
\(391\) −4.34147 −0.219557
\(392\) −52.5144 −2.65238
\(393\) −1.07004 −0.0539762
\(394\) −20.4890 −1.03222
\(395\) 1.87719 0.0944516
\(396\) 1.87417 0.0941807
\(397\) −16.3584 −0.821007 −0.410503 0.911859i \(-0.634647\pi\)
−0.410503 + 0.911859i \(0.634647\pi\)
\(398\) −64.8439 −3.25033
\(399\) 1.62221 0.0812122
\(400\) −25.1914 −1.25957
\(401\) −1.96622 −0.0981884 −0.0490942 0.998794i \(-0.515633\pi\)
−0.0490942 + 0.998794i \(0.515633\pi\)
\(402\) −5.09846 −0.254288
\(403\) −0.367400 −0.0183015
\(404\) −51.9216 −2.58319
\(405\) −9.33786 −0.464002
\(406\) 93.1614 4.62352
\(407\) −1.01529 −0.0503263
\(408\) 0.793242 0.0392713
\(409\) 33.2077 1.64201 0.821006 0.570919i \(-0.193413\pi\)
0.821006 + 0.570919i \(0.193413\pi\)
\(410\) 17.4716 0.862859
\(411\) 0.843099 0.0415870
\(412\) 14.1783 0.698517
\(413\) 3.96203 0.194959
\(414\) −32.7310 −1.60864
\(415\) 6.56780 0.322401
\(416\) 0.335502 0.0164494
\(417\) 1.66688 0.0816273
\(418\) −1.12778 −0.0551613
\(419\) −35.0489 −1.71225 −0.856125 0.516770i \(-0.827134\pi\)
−0.856125 + 0.516770i \(0.827134\pi\)
\(420\) 2.41178 0.117683
\(421\) −0.801576 −0.0390664 −0.0195332 0.999809i \(-0.506218\pi\)
−0.0195332 + 0.999809i \(0.506218\pi\)
\(422\) −12.0201 −0.585131
\(423\) −5.64372 −0.274407
\(424\) 42.4535 2.06173
\(425\) −3.88544 −0.188471
\(426\) −0.782402 −0.0379075
\(427\) 46.9206 2.27065
\(428\) −61.9320 −2.99360
\(429\) −0.00146344 −7.06556e−5 0
\(430\) −28.8357 −1.39058
\(431\) −0.544234 −0.0262148 −0.0131074 0.999914i \(-0.504172\pi\)
−0.0131074 + 0.999914i \(0.504172\pi\)
\(432\) 5.09615 0.245189
\(433\) −32.6724 −1.57014 −0.785068 0.619409i \(-0.787372\pi\)
−0.785068 + 0.619409i \(0.787372\pi\)
\(434\) −47.2904 −2.27001
\(435\) −1.29030 −0.0618654
\(436\) −76.3631 −3.65713
\(437\) 13.5300 0.647227
\(438\) 0.449151 0.0214613
\(439\) 38.8081 1.85221 0.926106 0.377264i \(-0.123135\pi\)
0.926106 + 0.377264i \(0.123135\pi\)
\(440\) −0.912604 −0.0435067
\(441\) −25.9428 −1.23537
\(442\) 0.196652 0.00935379
\(443\) −11.1198 −0.528316 −0.264158 0.964479i \(-0.585094\pi\)
−0.264158 + 0.964479i \(0.585094\pi\)
\(444\) −4.08890 −0.194051
\(445\) −0.244733 −0.0116014
\(446\) 34.2221 1.62046
\(447\) 0.400090 0.0189236
\(448\) −8.19133 −0.387004
\(449\) −22.7913 −1.07559 −0.537794 0.843076i \(-0.680742\pi\)
−0.537794 + 0.843076i \(0.680742\pi\)
\(450\) −29.2929 −1.38088
\(451\) −0.937404 −0.0441407
\(452\) −67.5582 −3.17767
\(453\) −0.565864 −0.0265866
\(454\) −57.2296 −2.68592
\(455\) 0.325432 0.0152565
\(456\) −2.47210 −0.115767
\(457\) −0.494743 −0.0231431 −0.0115715 0.999933i \(-0.503683\pi\)
−0.0115715 + 0.999933i \(0.503683\pi\)
\(458\) −66.6575 −3.11470
\(459\) 0.786013 0.0366879
\(460\) 20.1154 0.937884
\(461\) −3.13609 −0.146063 −0.0730313 0.997330i \(-0.523267\pi\)
−0.0730313 + 0.997330i \(0.523267\pi\)
\(462\) −0.188369 −0.00876370
\(463\) −7.24660 −0.336778 −0.168389 0.985721i \(-0.553857\pi\)
−0.168389 + 0.985721i \(0.553857\pi\)
\(464\) −60.3148 −2.80004
\(465\) 0.654982 0.0303741
\(466\) −41.3746 −1.91664
\(467\) −32.5522 −1.50634 −0.753168 0.657829i \(-0.771475\pi\)
−0.753168 + 0.657829i \(0.771475\pi\)
\(468\) 1.01847 0.0470786
\(469\) −60.8303 −2.80888
\(470\) 5.04904 0.232895
\(471\) 1.49597 0.0689306
\(472\) −6.03776 −0.277911
\(473\) 1.54713 0.0711370
\(474\) −0.590463 −0.0271209
\(475\) 12.1088 0.555590
\(476\) 17.3883 0.796991
\(477\) 20.9726 0.960271
\(478\) −19.4658 −0.890346
\(479\) −8.88084 −0.405776 −0.202888 0.979202i \(-0.565033\pi\)
−0.202888 + 0.979202i \(0.565033\pi\)
\(480\) −0.598116 −0.0273001
\(481\) −0.551733 −0.0251569
\(482\) 42.3340 1.92826
\(483\) 2.25987 0.102828
\(484\) −48.1862 −2.19028
\(485\) −2.21303 −0.100489
\(486\) 8.89736 0.403592
\(487\) 20.8123 0.943097 0.471548 0.881840i \(-0.343695\pi\)
0.471548 + 0.881840i \(0.343695\pi\)
\(488\) −71.5027 −3.23677
\(489\) 1.54484 0.0698599
\(490\) 23.2093 1.04849
\(491\) 22.6789 1.02349 0.511743 0.859139i \(-0.329000\pi\)
0.511743 + 0.859139i \(0.329000\pi\)
\(492\) −3.77521 −0.170200
\(493\) −9.30274 −0.418975
\(494\) −0.612858 −0.0275738
\(495\) −0.450839 −0.0202637
\(496\) 30.6169 1.37474
\(497\) −9.33492 −0.418728
\(498\) −2.06588 −0.0925742
\(499\) 12.8234 0.574055 0.287027 0.957922i \(-0.407333\pi\)
0.287027 + 0.957922i \(0.407333\pi\)
\(500\) 41.1690 1.84113
\(501\) 1.68085 0.0750948
\(502\) 59.8143 2.66964
\(503\) 42.4655 1.89344 0.946722 0.322051i \(-0.104372\pi\)
0.946722 + 0.322051i \(0.104372\pi\)
\(504\) 71.3524 3.17829
\(505\) 12.4899 0.555795
\(506\) −1.57108 −0.0698430
\(507\) 1.70715 0.0758170
\(508\) −38.1661 −1.69335
\(509\) 37.9196 1.68076 0.840379 0.542000i \(-0.182333\pi\)
0.840379 + 0.542000i \(0.182333\pi\)
\(510\) −0.350581 −0.0155240
\(511\) 5.35887 0.237062
\(512\) 50.3335 2.22445
\(513\) −2.44957 −0.108151
\(514\) 19.0492 0.840224
\(515\) −3.41065 −0.150291
\(516\) 6.23075 0.274294
\(517\) −0.270897 −0.0119140
\(518\) −71.0170 −3.12031
\(519\) −0.975625 −0.0428252
\(520\) −0.495929 −0.0217479
\(521\) −17.2911 −0.757536 −0.378768 0.925492i \(-0.623652\pi\)
−0.378768 + 0.925492i \(0.623652\pi\)
\(522\) −70.1349 −3.06972
\(523\) 35.1954 1.53899 0.769494 0.638654i \(-0.220508\pi\)
0.769494 + 0.638654i \(0.220508\pi\)
\(524\) 35.7445 1.56150
\(525\) 2.02249 0.0882688
\(526\) 18.3622 0.800631
\(527\) 4.72224 0.205704
\(528\) 0.121954 0.00530737
\(529\) −4.15167 −0.180507
\(530\) −18.7628 −0.815003
\(531\) −2.98274 −0.129440
\(532\) −54.1899 −2.34943
\(533\) −0.509406 −0.0220648
\(534\) 0.0769798 0.00333124
\(535\) 14.8980 0.644096
\(536\) 92.6997 4.00402
\(537\) −2.41152 −0.104065
\(538\) −12.5526 −0.541179
\(539\) −1.24525 −0.0536367
\(540\) −3.64184 −0.156720
\(541\) 2.03948 0.0876842 0.0438421 0.999038i \(-0.486040\pi\)
0.0438421 + 0.999038i \(0.486040\pi\)
\(542\) 58.8051 2.52590
\(543\) −1.88348 −0.0808279
\(544\) −4.31225 −0.184886
\(545\) 18.3694 0.786860
\(546\) −0.102364 −0.00438076
\(547\) 39.3632 1.68305 0.841524 0.540220i \(-0.181659\pi\)
0.841524 + 0.540220i \(0.181659\pi\)
\(548\) −28.1636 −1.20309
\(549\) −35.3233 −1.50756
\(550\) −1.40605 −0.0599544
\(551\) 28.9916 1.23508
\(552\) −3.44383 −0.146579
\(553\) −7.04488 −0.299579
\(554\) 44.3847 1.88573
\(555\) 0.983601 0.0417515
\(556\) −55.6818 −2.36144
\(557\) 8.78350 0.372169 0.186084 0.982534i \(-0.440420\pi\)
0.186084 + 0.982534i \(0.440420\pi\)
\(558\) 35.6017 1.50714
\(559\) 0.840742 0.0355596
\(560\) −27.1195 −1.14601
\(561\) 0.0188098 0.000794150 0
\(562\) −28.9803 −1.22246
\(563\) 35.9554 1.51534 0.757670 0.652638i \(-0.226338\pi\)
0.757670 + 0.652638i \(0.226338\pi\)
\(564\) −1.09099 −0.0459388
\(565\) 16.2514 0.683701
\(566\) −47.0585 −1.97802
\(567\) 35.0439 1.47171
\(568\) 14.2256 0.596891
\(569\) −18.7524 −0.786140 −0.393070 0.919509i \(-0.628587\pi\)
−0.393070 + 0.919509i \(0.628587\pi\)
\(570\) 1.09257 0.0457628
\(571\) −29.3361 −1.22768 −0.613839 0.789431i \(-0.710375\pi\)
−0.613839 + 0.789431i \(0.710375\pi\)
\(572\) 0.0488861 0.00204403
\(573\) −1.22257 −0.0510734
\(574\) −65.5688 −2.73679
\(575\) 16.8685 0.703465
\(576\) 6.16670 0.256946
\(577\) 43.0974 1.79417 0.897084 0.441860i \(-0.145681\pi\)
0.897084 + 0.441860i \(0.145681\pi\)
\(578\) −2.52760 −0.105134
\(579\) 1.61796 0.0672402
\(580\) 43.1025 1.78973
\(581\) −24.6482 −1.02258
\(582\) 0.696103 0.0288544
\(583\) 1.00668 0.0416925
\(584\) −8.16642 −0.337929
\(585\) −0.244996 −0.0101293
\(586\) 30.6672 1.26685
\(587\) −9.58551 −0.395636 −0.197818 0.980239i \(-0.563386\pi\)
−0.197818 + 0.980239i \(0.563386\pi\)
\(588\) −5.01500 −0.206815
\(589\) −14.7167 −0.606389
\(590\) 2.66845 0.109858
\(591\) −1.06498 −0.0438076
\(592\) 45.9780 1.88968
\(593\) −9.06335 −0.372187 −0.186094 0.982532i \(-0.559583\pi\)
−0.186094 + 0.982532i \(0.559583\pi\)
\(594\) 0.284440 0.0116707
\(595\) −4.18282 −0.171479
\(596\) −13.3650 −0.547450
\(597\) −3.37047 −0.137944
\(598\) −0.853759 −0.0349128
\(599\) 2.13607 0.0872775 0.0436387 0.999047i \(-0.486105\pi\)
0.0436387 + 0.999047i \(0.486105\pi\)
\(600\) −3.08209 −0.125826
\(601\) −11.4477 −0.466960 −0.233480 0.972362i \(-0.575011\pi\)
−0.233480 + 0.972362i \(0.575011\pi\)
\(602\) 108.217 4.41061
\(603\) 45.7949 1.86491
\(604\) 18.9027 0.769138
\(605\) 11.5914 0.471256
\(606\) −3.92867 −0.159591
\(607\) 34.0756 1.38309 0.691543 0.722335i \(-0.256931\pi\)
0.691543 + 0.722335i \(0.256931\pi\)
\(608\) 13.4389 0.545021
\(609\) 4.84237 0.196223
\(610\) 31.6013 1.27950
\(611\) −0.147211 −0.00595553
\(612\) −13.0905 −0.529151
\(613\) −19.8612 −0.802186 −0.401093 0.916037i \(-0.631370\pi\)
−0.401093 + 0.916037i \(0.631370\pi\)
\(614\) 35.7172 1.44143
\(615\) 0.908142 0.0366198
\(616\) 3.42490 0.137993
\(617\) −19.6163 −0.789722 −0.394861 0.918741i \(-0.629207\pi\)
−0.394861 + 0.918741i \(0.629207\pi\)
\(618\) 1.07281 0.0431547
\(619\) −16.2618 −0.653618 −0.326809 0.945090i \(-0.605973\pi\)
−0.326809 + 0.945090i \(0.605973\pi\)
\(620\) −21.8796 −0.878707
\(621\) −3.41245 −0.136937
\(622\) −62.7542 −2.51621
\(623\) 0.918454 0.0367971
\(624\) 0.0662725 0.00265302
\(625\) 9.52383 0.380953
\(626\) −12.1997 −0.487598
\(627\) −0.0586199 −0.00234105
\(628\) −49.9727 −1.99413
\(629\) 7.09149 0.282756
\(630\) −31.5349 −1.25638
\(631\) 42.1213 1.67682 0.838411 0.545038i \(-0.183485\pi\)
0.838411 + 0.545038i \(0.183485\pi\)
\(632\) 10.7357 0.427045
\(633\) −0.624786 −0.0248330
\(634\) −21.4860 −0.853318
\(635\) 9.18100 0.364337
\(636\) 4.05421 0.160760
\(637\) −0.676696 −0.0268117
\(638\) −3.36646 −0.133279
\(639\) 7.02762 0.278008
\(640\) −14.6220 −0.577987
\(641\) 50.0629 1.97736 0.988682 0.150024i \(-0.0479352\pi\)
0.988682 + 0.150024i \(0.0479352\pi\)
\(642\) −4.68611 −0.184946
\(643\) 25.7809 1.01670 0.508349 0.861151i \(-0.330256\pi\)
0.508349 + 0.861151i \(0.330256\pi\)
\(644\) −75.4907 −2.97475
\(645\) −1.49883 −0.0590164
\(646\) 7.87714 0.309922
\(647\) −30.9564 −1.21702 −0.608510 0.793546i \(-0.708233\pi\)
−0.608510 + 0.793546i \(0.708233\pi\)
\(648\) −53.4037 −2.09790
\(649\) −0.143171 −0.00561994
\(650\) −0.764080 −0.0299697
\(651\) −2.45807 −0.0963395
\(652\) −51.6051 −2.02101
\(653\) −5.83621 −0.228389 −0.114194 0.993458i \(-0.536429\pi\)
−0.114194 + 0.993458i \(0.536429\pi\)
\(654\) −5.77804 −0.225939
\(655\) −8.59846 −0.335970
\(656\) 42.4507 1.65742
\(657\) −4.03432 −0.157394
\(658\) −18.9485 −0.738689
\(659\) 43.9526 1.71215 0.856076 0.516851i \(-0.172896\pi\)
0.856076 + 0.516851i \(0.172896\pi\)
\(660\) −0.0871516 −0.00339237
\(661\) 32.5866 1.26747 0.633735 0.773550i \(-0.281521\pi\)
0.633735 + 0.773550i \(0.281521\pi\)
\(662\) −7.91012 −0.307435
\(663\) 0.0102216 0.000396976 0
\(664\) 37.5616 1.45767
\(665\) 13.0356 0.505498
\(666\) 53.4639 2.07168
\(667\) 40.3875 1.56381
\(668\) −56.1486 −2.17245
\(669\) 1.77880 0.0687725
\(670\) −40.9696 −1.58279
\(671\) −1.69551 −0.0654545
\(672\) 2.24466 0.0865897
\(673\) −12.1877 −0.469800 −0.234900 0.972020i \(-0.575476\pi\)
−0.234900 + 0.972020i \(0.575476\pi\)
\(674\) −21.5016 −0.828211
\(675\) −3.05400 −0.117549
\(676\) −57.0270 −2.19335
\(677\) −31.8860 −1.22548 −0.612740 0.790285i \(-0.709933\pi\)
−0.612740 + 0.790285i \(0.709933\pi\)
\(678\) −5.11182 −0.196318
\(679\) 8.30527 0.318727
\(680\) 6.37423 0.244441
\(681\) −2.97470 −0.113991
\(682\) 1.70887 0.0654362
\(683\) −25.1992 −0.964219 −0.482110 0.876111i \(-0.660129\pi\)
−0.482110 + 0.876111i \(0.660129\pi\)
\(684\) 40.7959 1.55987
\(685\) 6.77487 0.258854
\(686\) −17.0010 −0.649101
\(687\) −3.46474 −0.132188
\(688\) −70.0623 −2.67110
\(689\) 0.547052 0.0208410
\(690\) 1.52204 0.0579430
\(691\) 29.7311 1.13102 0.565511 0.824740i \(-0.308679\pi\)
0.565511 + 0.824740i \(0.308679\pi\)
\(692\) 32.5907 1.23891
\(693\) 1.69195 0.0642718
\(694\) −27.4950 −1.04369
\(695\) 13.3945 0.508082
\(696\) −7.37932 −0.279713
\(697\) 6.54746 0.248003
\(698\) 51.6269 1.95411
\(699\) −2.15058 −0.0813424
\(700\) −67.5612 −2.55357
\(701\) 34.7676 1.31315 0.656576 0.754260i \(-0.272004\pi\)
0.656576 + 0.754260i \(0.272004\pi\)
\(702\) 0.154571 0.00583391
\(703\) −22.1003 −0.833530
\(704\) 0.296000 0.0111559
\(705\) 0.262441 0.00988409
\(706\) 18.2470 0.686735
\(707\) −46.8733 −1.76285
\(708\) −0.576593 −0.0216697
\(709\) −16.8180 −0.631614 −0.315807 0.948823i \(-0.602275\pi\)
−0.315807 + 0.948823i \(0.602275\pi\)
\(710\) −6.28713 −0.235952
\(711\) 5.30361 0.198901
\(712\) −1.39964 −0.0524537
\(713\) −20.5015 −0.767785
\(714\) 1.31569 0.0492385
\(715\) −0.0117597 −0.000439789 0
\(716\) 80.5565 3.01054
\(717\) −1.01180 −0.0377863
\(718\) −14.8309 −0.553485
\(719\) 7.78192 0.290217 0.145108 0.989416i \(-0.453647\pi\)
0.145108 + 0.989416i \(0.453647\pi\)
\(720\) 20.4164 0.760875
\(721\) 12.7998 0.476689
\(722\) 23.4755 0.873669
\(723\) 2.20045 0.0818355
\(724\) 62.9175 2.33831
\(725\) 36.1452 1.34240
\(726\) −3.64602 −0.135317
\(727\) −19.4438 −0.721131 −0.360565 0.932734i \(-0.617416\pi\)
−0.360565 + 0.932734i \(0.617416\pi\)
\(728\) 1.86116 0.0689793
\(729\) −26.0724 −0.965644
\(730\) 3.60923 0.133584
\(731\) −10.8062 −0.399680
\(732\) −6.82834 −0.252383
\(733\) −29.9760 −1.10719 −0.553595 0.832786i \(-0.686744\pi\)
−0.553595 + 0.832786i \(0.686744\pi\)
\(734\) 26.8711 0.991831
\(735\) 1.20638 0.0444979
\(736\) 18.7215 0.690084
\(737\) 2.19815 0.0809698
\(738\) 49.3623 1.81705
\(739\) −28.4875 −1.04793 −0.523966 0.851739i \(-0.675548\pi\)
−0.523966 + 0.851739i \(0.675548\pi\)
\(740\) −32.8571 −1.20785
\(741\) −0.0318553 −0.00117023
\(742\) 70.4146 2.58500
\(743\) 12.4142 0.455431 0.227716 0.973728i \(-0.426874\pi\)
0.227716 + 0.973728i \(0.426874\pi\)
\(744\) 3.74588 0.137331
\(745\) 3.21499 0.117788
\(746\) −62.5975 −2.29186
\(747\) 18.5560 0.678927
\(748\) −0.628339 −0.0229744
\(749\) −55.9104 −2.04292
\(750\) 3.11507 0.113746
\(751\) 0.351895 0.0128408 0.00642041 0.999979i \(-0.497956\pi\)
0.00642041 + 0.999979i \(0.497956\pi\)
\(752\) 12.2677 0.447356
\(753\) 3.10904 0.113300
\(754\) −1.82940 −0.0666230
\(755\) −4.54710 −0.165486
\(756\) 13.6674 0.497079
\(757\) −7.46814 −0.271434 −0.135717 0.990748i \(-0.543334\pi\)
−0.135717 + 0.990748i \(0.543334\pi\)
\(758\) 4.31934 0.156886
\(759\) −0.0816620 −0.00296414
\(760\) −19.8650 −0.720580
\(761\) 34.3692 1.24588 0.622941 0.782269i \(-0.285938\pi\)
0.622941 + 0.782269i \(0.285938\pi\)
\(762\) −2.88785 −0.104616
\(763\) −68.9384 −2.49574
\(764\) 40.8397 1.47753
\(765\) 3.14896 0.113851
\(766\) −19.9444 −0.720621
\(767\) −0.0778021 −0.00280927
\(768\) 4.05607 0.146361
\(769\) −10.1357 −0.365504 −0.182752 0.983159i \(-0.558501\pi\)
−0.182752 + 0.983159i \(0.558501\pi\)
\(770\) −1.51367 −0.0545489
\(771\) 0.990144 0.0356592
\(772\) −54.0479 −1.94523
\(773\) 1.29325 0.0465151 0.0232575 0.999730i \(-0.492596\pi\)
0.0232575 + 0.999730i \(0.492596\pi\)
\(774\) −81.4694 −2.92836
\(775\) −18.3480 −0.659079
\(776\) −12.6565 −0.454341
\(777\) −3.69134 −0.132426
\(778\) 18.2194 0.653198
\(779\) −20.4049 −0.731080
\(780\) −0.0473600 −0.00169576
\(781\) 0.337324 0.0120704
\(782\) 10.9735 0.392410
\(783\) −7.31207 −0.261312
\(784\) 56.3916 2.01399
\(785\) 12.0211 0.429052
\(786\) 2.70462 0.0964705
\(787\) 25.8497 0.921442 0.460721 0.887545i \(-0.347591\pi\)
0.460721 + 0.887545i \(0.347591\pi\)
\(788\) 35.5757 1.26733
\(789\) 0.954436 0.0339788
\(790\) −4.74477 −0.168811
\(791\) −60.9896 −2.16854
\(792\) −2.57837 −0.0916185
\(793\) −0.921377 −0.0327191
\(794\) 41.3475 1.46737
\(795\) −0.975257 −0.0345888
\(796\) 112.590 3.99066
\(797\) 0.00206699 7.32164e−5 0 3.66082e−5 1.00000i \(-0.499988\pi\)
3.66082e−5 1.00000i \(0.499988\pi\)
\(798\) −4.10030 −0.145149
\(799\) 1.89212 0.0669386
\(800\) 16.7550 0.592379
\(801\) −0.691441 −0.0244309
\(802\) 4.96981 0.175490
\(803\) −0.193647 −0.00683364
\(804\) 8.85261 0.312207
\(805\) 18.1596 0.640041
\(806\) 0.928639 0.0327099
\(807\) −0.652460 −0.0229677
\(808\) 71.4306 2.51292
\(809\) −24.8077 −0.872192 −0.436096 0.899900i \(-0.643639\pi\)
−0.436096 + 0.899900i \(0.643639\pi\)
\(810\) 23.6023 0.829301
\(811\) 6.54547 0.229843 0.114921 0.993375i \(-0.463338\pi\)
0.114921 + 0.993375i \(0.463338\pi\)
\(812\) −161.759 −5.67662
\(813\) 3.05659 0.107199
\(814\) 2.56625 0.0899471
\(815\) 12.4138 0.434837
\(816\) −0.851808 −0.0298193
\(817\) 33.6769 1.17821
\(818\) −83.9355 −2.93474
\(819\) 0.919441 0.0321279
\(820\) −30.3364 −1.05939
\(821\) −20.2305 −0.706048 −0.353024 0.935614i \(-0.614847\pi\)
−0.353024 + 0.935614i \(0.614847\pi\)
\(822\) −2.13101 −0.0743276
\(823\) −10.1864 −0.355075 −0.177537 0.984114i \(-0.556813\pi\)
−0.177537 + 0.984114i \(0.556813\pi\)
\(824\) −19.5057 −0.679514
\(825\) −0.0730843 −0.00254447
\(826\) −10.0144 −0.348446
\(827\) −47.0412 −1.63578 −0.817891 0.575373i \(-0.804857\pi\)
−0.817891 + 0.575373i \(0.804857\pi\)
\(828\) 56.8318 1.97504
\(829\) −33.8762 −1.17657 −0.588285 0.808654i \(-0.700197\pi\)
−0.588285 + 0.808654i \(0.700197\pi\)
\(830\) −16.6007 −0.576220
\(831\) 2.30704 0.0800304
\(832\) 0.160853 0.00557657
\(833\) 8.69765 0.301356
\(834\) −4.21319 −0.145891
\(835\) 13.5068 0.467421
\(836\) 1.95819 0.0677255
\(837\) 3.71174 0.128297
\(838\) 88.5893 3.06027
\(839\) 41.1867 1.42192 0.710962 0.703231i \(-0.248260\pi\)
0.710962 + 0.703231i \(0.248260\pi\)
\(840\) −3.31799 −0.114481
\(841\) 57.5410 1.98417
\(842\) 2.02606 0.0698226
\(843\) −1.50635 −0.0518814
\(844\) 20.8709 0.718406
\(845\) 13.7181 0.471916
\(846\) 14.2650 0.490442
\(847\) −43.5011 −1.49471
\(848\) −45.5880 −1.56550
\(849\) −2.44602 −0.0839472
\(850\) 9.82082 0.336851
\(851\) −30.7875 −1.05538
\(852\) 1.35851 0.0465417
\(853\) −20.8869 −0.715155 −0.357578 0.933883i \(-0.616397\pi\)
−0.357578 + 0.933883i \(0.616397\pi\)
\(854\) −118.596 −4.05828
\(855\) −9.81360 −0.335618
\(856\) 85.2023 2.91216
\(857\) 42.8548 1.46389 0.731946 0.681362i \(-0.238612\pi\)
0.731946 + 0.681362i \(0.238612\pi\)
\(858\) 0.00369898 0.000126281 0
\(859\) −48.0358 −1.63896 −0.819481 0.573107i \(-0.805738\pi\)
−0.819481 + 0.573107i \(0.805738\pi\)
\(860\) 50.0683 1.70732
\(861\) −3.40816 −0.116150
\(862\) 1.37560 0.0468532
\(863\) 22.7316 0.773792 0.386896 0.922123i \(-0.373547\pi\)
0.386896 + 0.922123i \(0.373547\pi\)
\(864\) −3.38948 −0.115313
\(865\) −7.83981 −0.266561
\(866\) 82.5826 2.80627
\(867\) −0.131380 −0.00446190
\(868\) 82.1117 2.78705
\(869\) 0.254572 0.00863576
\(870\) 3.26137 0.110571
\(871\) 1.19452 0.0404748
\(872\) 105.056 3.55764
\(873\) −6.25247 −0.211614
\(874\) −34.1983 −1.15678
\(875\) 37.1662 1.25645
\(876\) −0.779874 −0.0263495
\(877\) −47.7357 −1.61192 −0.805959 0.591971i \(-0.798350\pi\)
−0.805959 + 0.591971i \(0.798350\pi\)
\(878\) −98.0913 −3.31042
\(879\) 1.59403 0.0537652
\(880\) 0.979984 0.0330352
\(881\) 1.96598 0.0662354 0.0331177 0.999451i \(-0.489456\pi\)
0.0331177 + 0.999451i \(0.489456\pi\)
\(882\) 65.5730 2.20796
\(883\) −47.2819 −1.59116 −0.795582 0.605846i \(-0.792835\pi\)
−0.795582 + 0.605846i \(0.792835\pi\)
\(884\) −0.341453 −0.0114843
\(885\) 0.138702 0.00466240
\(886\) 28.1063 0.944248
\(887\) 5.05234 0.169641 0.0848205 0.996396i \(-0.472968\pi\)
0.0848205 + 0.996396i \(0.472968\pi\)
\(888\) 5.62527 0.188772
\(889\) −34.4552 −1.15559
\(890\) 0.618585 0.0207350
\(891\) −1.26634 −0.0424239
\(892\) −59.4208 −1.98956
\(893\) −5.89673 −0.197326
\(894\) −1.01127 −0.0338218
\(895\) −19.3782 −0.647741
\(896\) 54.8749 1.83324
\(897\) −0.0443769 −0.00148170
\(898\) 57.6072 1.92238
\(899\) −43.9298 −1.46514
\(900\) 50.8622 1.69541
\(901\) −7.03133 −0.234248
\(902\) 2.36938 0.0788917
\(903\) 5.62494 0.187186
\(904\) 92.9426 3.09122
\(905\) −15.1350 −0.503106
\(906\) 1.43028 0.0475178
\(907\) −39.0723 −1.29738 −0.648688 0.761055i \(-0.724682\pi\)
−0.648688 + 0.761055i \(0.724682\pi\)
\(908\) 99.3694 3.29769
\(909\) 35.2877 1.17042
\(910\) −0.822561 −0.0272676
\(911\) 1.23848 0.0410328 0.0205164 0.999790i \(-0.493469\pi\)
0.0205164 + 0.999790i \(0.493469\pi\)
\(912\) 2.65462 0.0879034
\(913\) 0.890681 0.0294772
\(914\) 1.25051 0.0413632
\(915\) 1.64258 0.0543021
\(916\) 115.739 3.82414
\(917\) 32.2691 1.06562
\(918\) −1.98672 −0.0655716
\(919\) 37.5030 1.23711 0.618555 0.785742i \(-0.287718\pi\)
0.618555 + 0.785742i \(0.287718\pi\)
\(920\) −27.6735 −0.912369
\(921\) 1.85652 0.0611743
\(922\) 7.92678 0.261055
\(923\) 0.183309 0.00603370
\(924\) 0.327070 0.0107598
\(925\) −27.5536 −0.905955
\(926\) 18.3165 0.601917
\(927\) −9.63610 −0.316491
\(928\) 40.1158 1.31687
\(929\) 4.23768 0.139034 0.0695169 0.997581i \(-0.477854\pi\)
0.0695169 + 0.997581i \(0.477854\pi\)
\(930\) −1.65553 −0.0542870
\(931\) −27.1059 −0.888359
\(932\) 71.8399 2.35319
\(933\) −3.26186 −0.106788
\(934\) 82.2788 2.69224
\(935\) 0.151149 0.00494311
\(936\) −1.40114 −0.0457978
\(937\) 4.04551 0.132161 0.0660805 0.997814i \(-0.478951\pi\)
0.0660805 + 0.997814i \(0.478951\pi\)
\(938\) 153.754 5.02025
\(939\) −0.634119 −0.0206937
\(940\) −8.76681 −0.285942
\(941\) 9.64397 0.314384 0.157192 0.987568i \(-0.449756\pi\)
0.157192 + 0.987568i \(0.449756\pi\)
\(942\) −3.78121 −0.123198
\(943\) −28.4256 −0.925664
\(944\) 6.48355 0.211021
\(945\) −3.28775 −0.106950
\(946\) −3.91051 −0.127142
\(947\) −0.00195680 −6.35875e−5 0 −3.17938e−5 1.00000i \(-0.500010\pi\)
−3.17938e−5 1.00000i \(0.500010\pi\)
\(948\) 1.02524 0.0332982
\(949\) −0.105232 −0.00341597
\(950\) −30.6062 −0.992995
\(951\) −1.11680 −0.0362149
\(952\) −23.9218 −0.775309
\(953\) 6.59785 0.213725 0.106863 0.994274i \(-0.465919\pi\)
0.106863 + 0.994274i \(0.465919\pi\)
\(954\) −53.0103 −1.71627
\(955\) −9.82414 −0.317902
\(956\) 33.7991 1.09314
\(957\) −0.174983 −0.00565638
\(958\) 22.4472 0.725235
\(959\) −25.4253 −0.821026
\(960\) −0.286760 −0.00925514
\(961\) −8.70044 −0.280659
\(962\) 1.39456 0.0449623
\(963\) 42.0911 1.35637
\(964\) −73.5057 −2.36746
\(965\) 13.0014 0.418531
\(966\) −5.71203 −0.183782
\(967\) 19.7521 0.635185 0.317592 0.948227i \(-0.397126\pi\)
0.317592 + 0.948227i \(0.397126\pi\)
\(968\) 66.2916 2.13069
\(969\) 0.409440 0.0131531
\(970\) 5.59366 0.179601
\(971\) 1.06475 0.0341693 0.0170846 0.999854i \(-0.494562\pi\)
0.0170846 + 0.999854i \(0.494562\pi\)
\(972\) −15.4487 −0.495519
\(973\) −50.2680 −1.61152
\(974\) −52.6051 −1.68558
\(975\) −0.0397156 −0.00127192
\(976\) 76.7819 2.45773
\(977\) 54.5120 1.74399 0.871996 0.489513i \(-0.162825\pi\)
0.871996 + 0.489513i \(0.162825\pi\)
\(978\) −3.90472 −0.124859
\(979\) −0.0331890 −0.00106073
\(980\) −40.2989 −1.28730
\(981\) 51.8990 1.65701
\(982\) −57.3231 −1.82925
\(983\) 3.44716 0.109947 0.0549737 0.998488i \(-0.482492\pi\)
0.0549737 + 0.998488i \(0.482492\pi\)
\(984\) 5.19371 0.165570
\(985\) −8.55787 −0.272677
\(986\) 23.5136 0.748825
\(987\) −0.984910 −0.0313500
\(988\) 1.06412 0.0338543
\(989\) 46.9146 1.49180
\(990\) 1.13954 0.0362169
\(991\) −8.86662 −0.281657 −0.140829 0.990034i \(-0.544977\pi\)
−0.140829 + 0.990034i \(0.544977\pi\)
\(992\) −20.3635 −0.646542
\(993\) −0.411154 −0.0130476
\(994\) 23.5949 0.748384
\(995\) −27.0840 −0.858621
\(996\) 3.58705 0.113660
\(997\) −10.9481 −0.346729 −0.173365 0.984858i \(-0.555464\pi\)
−0.173365 + 0.984858i \(0.555464\pi\)
\(998\) −32.4124 −1.02600
\(999\) 5.57400 0.176354
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.h.1.2 16
3.2 odd 2 9027.2.a.n.1.15 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1003.2.a.h.1.2 16 1.1 even 1 trivial
9027.2.a.n.1.15 16 3.2 odd 2