Properties

Label 1003.2.a.g.1.3
Level $1003$
Weight $2$
Character 1003.1
Self dual yes
Analytic conductor $8.009$
Analytic rank $1$
Dimension $10$
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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 3x^{9} - 10x^{8} + 34x^{7} + 28x^{6} - 129x^{5} - 3x^{4} + 178x^{3} - 56x^{2} - 56x + 15 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.08521\) 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)
 
\(f(q)\) \(=\) \(q-1.86330 q^{2} +1.08521 q^{3} +1.47190 q^{4} +0.335552 q^{5} -2.02208 q^{6} -1.78229 q^{7} +0.984011 q^{8} -1.82232 q^{9} +O(q^{10})\) \(q-1.86330 q^{2} +1.08521 q^{3} +1.47190 q^{4} +0.335552 q^{5} -2.02208 q^{6} -1.78229 q^{7} +0.984011 q^{8} -1.82232 q^{9} -0.625236 q^{10} -2.96686 q^{11} +1.59732 q^{12} +5.83034 q^{13} +3.32094 q^{14} +0.364145 q^{15} -4.77731 q^{16} -1.00000 q^{17} +3.39553 q^{18} +0.660752 q^{19} +0.493900 q^{20} -1.93416 q^{21} +5.52816 q^{22} +2.34383 q^{23} +1.06786 q^{24} -4.88740 q^{25} -10.8637 q^{26} -5.23323 q^{27} -2.62335 q^{28} -5.05539 q^{29} -0.678513 q^{30} -3.22725 q^{31} +6.93356 q^{32} -3.21967 q^{33} +1.86330 q^{34} -0.598051 q^{35} -2.68227 q^{36} +7.16306 q^{37} -1.23118 q^{38} +6.32716 q^{39} +0.330187 q^{40} -10.1061 q^{41} +3.60392 q^{42} -4.53751 q^{43} -4.36692 q^{44} -0.611483 q^{45} -4.36726 q^{46} +3.42798 q^{47} -5.18439 q^{48} -3.82345 q^{49} +9.10672 q^{50} -1.08521 q^{51} +8.58168 q^{52} -3.90662 q^{53} +9.75110 q^{54} -0.995537 q^{55} -1.75379 q^{56} +0.717055 q^{57} +9.41972 q^{58} -1.00000 q^{59} +0.535985 q^{60} +1.20369 q^{61} +6.01335 q^{62} +3.24789 q^{63} -3.36470 q^{64} +1.95639 q^{65} +5.99922 q^{66} +7.89572 q^{67} -1.47190 q^{68} +2.54355 q^{69} +1.11435 q^{70} +4.37632 q^{71} -1.79318 q^{72} -15.3323 q^{73} -13.3470 q^{74} -5.30387 q^{75} +0.972560 q^{76} +5.28780 q^{77} -11.7894 q^{78} +0.0651189 q^{79} -1.60304 q^{80} -0.212211 q^{81} +18.8308 q^{82} -17.7551 q^{83} -2.84689 q^{84} -0.335552 q^{85} +8.45476 q^{86} -5.48616 q^{87} -2.91942 q^{88} -10.4873 q^{89} +1.13938 q^{90} -10.3914 q^{91} +3.44988 q^{92} -3.50225 q^{93} -6.38736 q^{94} +0.221717 q^{95} +7.52437 q^{96} +4.30637 q^{97} +7.12425 q^{98} +5.40656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9} + 4 q^{10} + 12 q^{11} - 24 q^{12} - 11 q^{13} - 12 q^{14} + 9 q^{15} - 3 q^{16} - 10 q^{17} - 22 q^{18} - 5 q^{19} - 36 q^{20} - 10 q^{21} + 6 q^{22} - 7 q^{23} + 35 q^{24} + 2 q^{25} + q^{26} - 31 q^{27} - 4 q^{28} + 10 q^{29} - 9 q^{30} + 13 q^{31} - 15 q^{32} - 9 q^{33} + q^{34} - 8 q^{35} + 40 q^{36} + 12 q^{37} - 50 q^{38} + 24 q^{39} + 5 q^{40} - 29 q^{41} - 17 q^{42} - 18 q^{43} - 6 q^{44} - 14 q^{45} + 11 q^{46} - 18 q^{47} - 43 q^{48} - 9 q^{49} - 31 q^{50} + 7 q^{51} - 68 q^{52} + 19 q^{54} - 27 q^{55} - 7 q^{56} + 20 q^{57} + 23 q^{58} - 10 q^{59} + 38 q^{60} + 8 q^{61} - 46 q^{62} + 39 q^{63} - 20 q^{64} + 58 q^{65} - 34 q^{66} - 6 q^{67} - 15 q^{68} + 6 q^{69} + 73 q^{70} + 8 q^{71} - 70 q^{72} - 41 q^{73} - 10 q^{74} + 10 q^{75} + 12 q^{76} - 22 q^{77} - 43 q^{78} + 3 q^{79} - 15 q^{80} + 26 q^{81} + 8 q^{82} - 22 q^{84} + 12 q^{85} - 29 q^{86} - 28 q^{87} + 33 q^{88} - 45 q^{89} + 56 q^{90} - 14 q^{91} + 36 q^{92} - 19 q^{93} + 15 q^{94} - 17 q^{95} + 90 q^{96} - 5 q^{97} + 30 q^{98} + 14 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.86330 −1.31755 −0.658777 0.752338i \(-0.728926\pi\)
−0.658777 + 0.752338i \(0.728926\pi\)
\(3\) 1.08521 0.626547 0.313273 0.949663i \(-0.398574\pi\)
0.313273 + 0.949663i \(0.398574\pi\)
\(4\) 1.47190 0.735950
\(5\) 0.335552 0.150064 0.0750318 0.997181i \(-0.476094\pi\)
0.0750318 + 0.997181i \(0.476094\pi\)
\(6\) −2.02208 −0.825510
\(7\) −1.78229 −0.673641 −0.336821 0.941569i \(-0.609352\pi\)
−0.336821 + 0.941569i \(0.609352\pi\)
\(8\) 0.984011 0.347900
\(9\) −1.82232 −0.607439
\(10\) −0.625236 −0.197717
\(11\) −2.96686 −0.894542 −0.447271 0.894399i \(-0.647604\pi\)
−0.447271 + 0.894399i \(0.647604\pi\)
\(12\) 1.59732 0.461107
\(13\) 5.83034 1.61705 0.808523 0.588464i \(-0.200267\pi\)
0.808523 + 0.588464i \(0.200267\pi\)
\(14\) 3.32094 0.887559
\(15\) 0.364145 0.0940219
\(16\) −4.77731 −1.19433
\(17\) −1.00000 −0.242536
\(18\) 3.39553 0.800334
\(19\) 0.660752 0.151587 0.0757934 0.997124i \(-0.475851\pi\)
0.0757934 + 0.997124i \(0.475851\pi\)
\(20\) 0.493900 0.110439
\(21\) −1.93416 −0.422068
\(22\) 5.52816 1.17861
\(23\) 2.34383 0.488722 0.244361 0.969684i \(-0.421422\pi\)
0.244361 + 0.969684i \(0.421422\pi\)
\(24\) 1.06786 0.217976
\(25\) −4.88740 −0.977481
\(26\) −10.8637 −2.13055
\(27\) −5.23323 −1.00714
\(28\) −2.62335 −0.495766
\(29\) −5.05539 −0.938762 −0.469381 0.882996i \(-0.655523\pi\)
−0.469381 + 0.882996i \(0.655523\pi\)
\(30\) −0.678513 −0.123879
\(31\) −3.22725 −0.579632 −0.289816 0.957082i \(-0.593594\pi\)
−0.289816 + 0.957082i \(0.593594\pi\)
\(32\) 6.93356 1.22569
\(33\) −3.21967 −0.560472
\(34\) 1.86330 0.319554
\(35\) −0.598051 −0.101089
\(36\) −2.68227 −0.447045
\(37\) 7.16306 1.17760 0.588800 0.808279i \(-0.299600\pi\)
0.588800 + 0.808279i \(0.299600\pi\)
\(38\) −1.23118 −0.199724
\(39\) 6.32716 1.01316
\(40\) 0.330187 0.0522072
\(41\) −10.1061 −1.57831 −0.789157 0.614192i \(-0.789482\pi\)
−0.789157 + 0.614192i \(0.789482\pi\)
\(42\) 3.60392 0.556097
\(43\) −4.53751 −0.691964 −0.345982 0.938241i \(-0.612454\pi\)
−0.345982 + 0.938241i \(0.612454\pi\)
\(44\) −4.36692 −0.658338
\(45\) −0.611483 −0.0911545
\(46\) −4.36726 −0.643918
\(47\) 3.42798 0.500022 0.250011 0.968243i \(-0.419566\pi\)
0.250011 + 0.968243i \(0.419566\pi\)
\(48\) −5.18439 −0.748302
\(49\) −3.82345 −0.546207
\(50\) 9.10672 1.28788
\(51\) −1.08521 −0.151960
\(52\) 8.58168 1.19007
\(53\) −3.90662 −0.536616 −0.268308 0.963333i \(-0.586464\pi\)
−0.268308 + 0.963333i \(0.586464\pi\)
\(54\) 9.75110 1.32696
\(55\) −0.995537 −0.134238
\(56\) −1.75379 −0.234360
\(57\) 0.717055 0.0949763
\(58\) 9.41972 1.23687
\(59\) −1.00000 −0.130189
\(60\) 0.535985 0.0691954
\(61\) 1.20369 0.154116 0.0770580 0.997027i \(-0.475447\pi\)
0.0770580 + 0.997027i \(0.475447\pi\)
\(62\) 6.01335 0.763696
\(63\) 3.24789 0.409196
\(64\) −3.36470 −0.420588
\(65\) 1.95639 0.242660
\(66\) 5.99922 0.738453
\(67\) 7.89572 0.964616 0.482308 0.876002i \(-0.339799\pi\)
0.482308 + 0.876002i \(0.339799\pi\)
\(68\) −1.47190 −0.178494
\(69\) 2.54355 0.306207
\(70\) 1.11435 0.133190
\(71\) 4.37632 0.519374 0.259687 0.965693i \(-0.416381\pi\)
0.259687 + 0.965693i \(0.416381\pi\)
\(72\) −1.79318 −0.211328
\(73\) −15.3323 −1.79451 −0.897254 0.441515i \(-0.854441\pi\)
−0.897254 + 0.441515i \(0.854441\pi\)
\(74\) −13.3470 −1.55155
\(75\) −5.30387 −0.612438
\(76\) 0.972560 0.111560
\(77\) 5.28780 0.602600
\(78\) −11.7894 −1.33489
\(79\) 0.0651189 0.00732645 0.00366323 0.999993i \(-0.498834\pi\)
0.00366323 + 0.999993i \(0.498834\pi\)
\(80\) −1.60304 −0.179225
\(81\) −0.212211 −0.0235789
\(82\) 18.8308 2.07951
\(83\) −17.7551 −1.94888 −0.974439 0.224652i \(-0.927875\pi\)
−0.974439 + 0.224652i \(0.927875\pi\)
\(84\) −2.84689 −0.310621
\(85\) −0.335552 −0.0363958
\(86\) 8.45476 0.911700
\(87\) −5.48616 −0.588179
\(88\) −2.91942 −0.311211
\(89\) −10.4873 −1.11166 −0.555828 0.831297i \(-0.687599\pi\)
−0.555828 + 0.831297i \(0.687599\pi\)
\(90\) 1.13938 0.120101
\(91\) −10.3914 −1.08931
\(92\) 3.44988 0.359675
\(93\) −3.50225 −0.363166
\(94\) −6.38736 −0.658806
\(95\) 0.221717 0.0227477
\(96\) 7.52437 0.767953
\(97\) 4.30637 0.437246 0.218623 0.975809i \(-0.429844\pi\)
0.218623 + 0.975809i \(0.429844\pi\)
\(98\) 7.12425 0.719658
\(99\) 5.40656 0.543380
\(100\) −7.19377 −0.719377
\(101\) −16.9163 −1.68324 −0.841620 0.540071i \(-0.818397\pi\)
−0.841620 + 0.540071i \(0.818397\pi\)
\(102\) 2.02208 0.200216
\(103\) 1.32193 0.130254 0.0651268 0.997877i \(-0.479255\pi\)
0.0651268 + 0.997877i \(0.479255\pi\)
\(104\) 5.73712 0.562571
\(105\) −0.649011 −0.0633370
\(106\) 7.27922 0.707020
\(107\) 5.87500 0.567957 0.283979 0.958831i \(-0.408346\pi\)
0.283979 + 0.958831i \(0.408346\pi\)
\(108\) −7.70279 −0.741202
\(109\) 9.54324 0.914076 0.457038 0.889447i \(-0.348910\pi\)
0.457038 + 0.889447i \(0.348910\pi\)
\(110\) 1.85499 0.176866
\(111\) 7.77344 0.737822
\(112\) 8.51454 0.804548
\(113\) −15.5885 −1.46644 −0.733222 0.679989i \(-0.761984\pi\)
−0.733222 + 0.679989i \(0.761984\pi\)
\(114\) −1.33609 −0.125136
\(115\) 0.786477 0.0733394
\(116\) −7.44103 −0.690882
\(117\) −10.6247 −0.982257
\(118\) 1.86330 0.171531
\(119\) 1.78229 0.163382
\(120\) 0.358323 0.0327102
\(121\) −2.19774 −0.199795
\(122\) −2.24283 −0.203056
\(123\) −10.9673 −0.988888
\(124\) −4.75019 −0.426580
\(125\) −3.31774 −0.296748
\(126\) −6.05181 −0.539138
\(127\) 5.88880 0.522547 0.261273 0.965265i \(-0.415858\pi\)
0.261273 + 0.965265i \(0.415858\pi\)
\(128\) −7.59766 −0.671544
\(129\) −4.92416 −0.433548
\(130\) −3.64534 −0.319718
\(131\) 9.61177 0.839785 0.419892 0.907574i \(-0.362068\pi\)
0.419892 + 0.907574i \(0.362068\pi\)
\(132\) −4.73903 −0.412480
\(133\) −1.17765 −0.102115
\(134\) −14.7121 −1.27093
\(135\) −1.75602 −0.151134
\(136\) −0.984011 −0.0843782
\(137\) −20.5821 −1.75845 −0.879223 0.476410i \(-0.841938\pi\)
−0.879223 + 0.476410i \(0.841938\pi\)
\(138\) −4.73940 −0.403445
\(139\) 1.51139 0.128194 0.0640971 0.997944i \(-0.479583\pi\)
0.0640971 + 0.997944i \(0.479583\pi\)
\(140\) −0.880271 −0.0743965
\(141\) 3.72008 0.313287
\(142\) −8.15442 −0.684303
\(143\) −17.2978 −1.44652
\(144\) 8.70577 0.725481
\(145\) −1.69635 −0.140874
\(146\) 28.5687 2.36436
\(147\) −4.14925 −0.342225
\(148\) 10.5433 0.866655
\(149\) −9.99932 −0.819177 −0.409588 0.912270i \(-0.634328\pi\)
−0.409588 + 0.912270i \(0.634328\pi\)
\(150\) 9.88271 0.806920
\(151\) −11.6818 −0.950648 −0.475324 0.879811i \(-0.657669\pi\)
−0.475324 + 0.879811i \(0.657669\pi\)
\(152\) 0.650187 0.0527371
\(153\) 1.82232 0.147326
\(154\) −9.85277 −0.793959
\(155\) −1.08291 −0.0869816
\(156\) 9.31294 0.745632
\(157\) −1.38132 −0.110241 −0.0551206 0.998480i \(-0.517554\pi\)
−0.0551206 + 0.998480i \(0.517554\pi\)
\(158\) −0.121336 −0.00965300
\(159\) −4.23951 −0.336215
\(160\) 2.32657 0.183932
\(161\) −4.17738 −0.329223
\(162\) 0.395413 0.0310665
\(163\) 6.47260 0.506973 0.253487 0.967339i \(-0.418423\pi\)
0.253487 + 0.967339i \(0.418423\pi\)
\(164\) −14.8752 −1.16156
\(165\) −1.08037 −0.0841065
\(166\) 33.0832 2.56775
\(167\) −4.61493 −0.357114 −0.178557 0.983930i \(-0.557143\pi\)
−0.178557 + 0.983930i \(0.557143\pi\)
\(168\) −1.90323 −0.146838
\(169\) 20.9929 1.61484
\(170\) 0.625236 0.0479534
\(171\) −1.20410 −0.0920798
\(172\) −6.67876 −0.509251
\(173\) 16.8344 1.27990 0.639948 0.768418i \(-0.278956\pi\)
0.639948 + 0.768418i \(0.278956\pi\)
\(174\) 10.2224 0.774957
\(175\) 8.71076 0.658472
\(176\) 14.1736 1.06838
\(177\) −1.08521 −0.0815695
\(178\) 19.5411 1.46467
\(179\) 5.62749 0.420618 0.210309 0.977635i \(-0.432553\pi\)
0.210309 + 0.977635i \(0.432553\pi\)
\(180\) −0.900041 −0.0670851
\(181\) −11.9052 −0.884904 −0.442452 0.896792i \(-0.645891\pi\)
−0.442452 + 0.896792i \(0.645891\pi\)
\(182\) 19.3622 1.43522
\(183\) 1.30625 0.0965610
\(184\) 2.30635 0.170027
\(185\) 2.40358 0.176715
\(186\) 6.52576 0.478492
\(187\) 2.96686 0.216958
\(188\) 5.04564 0.367991
\(189\) 9.32712 0.678448
\(190\) −0.413126 −0.0299713
\(191\) −25.4738 −1.84322 −0.921611 0.388115i \(-0.873126\pi\)
−0.921611 + 0.388115i \(0.873126\pi\)
\(192\) −3.65141 −0.263518
\(193\) 10.9178 0.785881 0.392940 0.919564i \(-0.371458\pi\)
0.392940 + 0.919564i \(0.371458\pi\)
\(194\) −8.02408 −0.576095
\(195\) 2.12309 0.152038
\(196\) −5.62774 −0.401981
\(197\) 12.7677 0.909662 0.454831 0.890578i \(-0.349700\pi\)
0.454831 + 0.890578i \(0.349700\pi\)
\(198\) −10.0741 −0.715932
\(199\) 8.19687 0.581061 0.290530 0.956866i \(-0.406168\pi\)
0.290530 + 0.956866i \(0.406168\pi\)
\(200\) −4.80926 −0.340066
\(201\) 8.56853 0.604377
\(202\) 31.5203 2.21776
\(203\) 9.01016 0.632389
\(204\) −1.59732 −0.111835
\(205\) −3.39114 −0.236847
\(206\) −2.46316 −0.171616
\(207\) −4.27120 −0.296869
\(208\) −27.8534 −1.93128
\(209\) −1.96036 −0.135601
\(210\) 1.20931 0.0834500
\(211\) 21.1312 1.45473 0.727367 0.686249i \(-0.240744\pi\)
0.727367 + 0.686249i \(0.240744\pi\)
\(212\) −5.75015 −0.394922
\(213\) 4.74923 0.325412
\(214\) −10.9469 −0.748315
\(215\) −1.52257 −0.103839
\(216\) −5.14956 −0.350383
\(217\) 5.75189 0.390464
\(218\) −17.7819 −1.20435
\(219\) −16.6388 −1.12434
\(220\) −1.46533 −0.0987926
\(221\) −5.83034 −0.392191
\(222\) −14.4843 −0.972121
\(223\) −20.0111 −1.34004 −0.670020 0.742343i \(-0.733714\pi\)
−0.670020 + 0.742343i \(0.733714\pi\)
\(224\) −12.3576 −0.825676
\(225\) 8.90640 0.593760
\(226\) 29.0461 1.93212
\(227\) 11.1459 0.739778 0.369889 0.929076i \(-0.379396\pi\)
0.369889 + 0.929076i \(0.379396\pi\)
\(228\) 1.05543 0.0698978
\(229\) 20.2955 1.34116 0.670581 0.741836i \(-0.266045\pi\)
0.670581 + 0.741836i \(0.266045\pi\)
\(230\) −1.46545 −0.0966286
\(231\) 5.73838 0.377557
\(232\) −4.97456 −0.326596
\(233\) −5.04130 −0.330267 −0.165133 0.986271i \(-0.552805\pi\)
−0.165133 + 0.986271i \(0.552805\pi\)
\(234\) 19.7971 1.29418
\(235\) 1.15027 0.0750351
\(236\) −1.47190 −0.0958125
\(237\) 0.0706678 0.00459037
\(238\) −3.32094 −0.215265
\(239\) 24.7860 1.60327 0.801637 0.597812i \(-0.203963\pi\)
0.801637 + 0.597812i \(0.203963\pi\)
\(240\) −1.73963 −0.112293
\(241\) 11.3279 0.729697 0.364848 0.931067i \(-0.381121\pi\)
0.364848 + 0.931067i \(0.381121\pi\)
\(242\) 4.09506 0.263241
\(243\) 15.4694 0.992363
\(244\) 1.77170 0.113422
\(245\) −1.28297 −0.0819658
\(246\) 20.4354 1.30291
\(247\) 3.85241 0.245123
\(248\) −3.17565 −0.201654
\(249\) −19.2681 −1.22106
\(250\) 6.18196 0.390982
\(251\) 9.31329 0.587850 0.293925 0.955829i \(-0.405038\pi\)
0.293925 + 0.955829i \(0.405038\pi\)
\(252\) 4.78057 0.301148
\(253\) −6.95381 −0.437182
\(254\) −10.9726 −0.688484
\(255\) −0.364145 −0.0228037
\(256\) 20.8861 1.30538
\(257\) 17.0007 1.06048 0.530238 0.847849i \(-0.322103\pi\)
0.530238 + 0.847849i \(0.322103\pi\)
\(258\) 9.17520 0.571223
\(259\) −12.7666 −0.793280
\(260\) 2.87960 0.178585
\(261\) 9.21252 0.570241
\(262\) −17.9097 −1.10646
\(263\) −9.94021 −0.612940 −0.306470 0.951880i \(-0.599148\pi\)
−0.306470 + 0.951880i \(0.599148\pi\)
\(264\) −3.16819 −0.194989
\(265\) −1.31088 −0.0805265
\(266\) 2.19432 0.134542
\(267\) −11.3810 −0.696504
\(268\) 11.6217 0.709909
\(269\) 4.02855 0.245625 0.122813 0.992430i \(-0.460809\pi\)
0.122813 + 0.992430i \(0.460809\pi\)
\(270\) 3.27200 0.199128
\(271\) 15.7817 0.958670 0.479335 0.877632i \(-0.340878\pi\)
0.479335 + 0.877632i \(0.340878\pi\)
\(272\) 4.77731 0.289667
\(273\) −11.2768 −0.682504
\(274\) 38.3507 2.31685
\(275\) 14.5002 0.874398
\(276\) 3.74385 0.225353
\(277\) 15.7930 0.948909 0.474454 0.880280i \(-0.342645\pi\)
0.474454 + 0.880280i \(0.342645\pi\)
\(278\) −2.81617 −0.168903
\(279\) 5.88108 0.352091
\(280\) −0.588488 −0.0351689
\(281\) −7.57142 −0.451673 −0.225837 0.974165i \(-0.572512\pi\)
−0.225837 + 0.974165i \(0.572512\pi\)
\(282\) −6.93163 −0.412773
\(283\) 15.7493 0.936200 0.468100 0.883675i \(-0.344939\pi\)
0.468100 + 0.883675i \(0.344939\pi\)
\(284\) 6.44151 0.382233
\(285\) 0.240610 0.0142525
\(286\) 32.2311 1.90586
\(287\) 18.0120 1.06322
\(288\) −12.6351 −0.744533
\(289\) 1.00000 0.0588235
\(290\) 3.16081 0.185609
\(291\) 4.67332 0.273955
\(292\) −22.5676 −1.32067
\(293\) 2.58099 0.150783 0.0753916 0.997154i \(-0.475979\pi\)
0.0753916 + 0.997154i \(0.475979\pi\)
\(294\) 7.73132 0.450899
\(295\) −0.335552 −0.0195366
\(296\) 7.04853 0.409688
\(297\) 15.5263 0.900925
\(298\) 18.6318 1.07931
\(299\) 13.6653 0.790286
\(300\) −7.80676 −0.450723
\(301\) 8.08715 0.466135
\(302\) 21.7667 1.25253
\(303\) −18.3578 −1.05463
\(304\) −3.15662 −0.181044
\(305\) 0.403899 0.0231272
\(306\) −3.39553 −0.194109
\(307\) −15.8745 −0.906005 −0.453002 0.891509i \(-0.649647\pi\)
−0.453002 + 0.891509i \(0.649647\pi\)
\(308\) 7.78311 0.443484
\(309\) 1.43457 0.0816100
\(310\) 2.01779 0.114603
\(311\) −6.04920 −0.343018 −0.171509 0.985183i \(-0.554864\pi\)
−0.171509 + 0.985183i \(0.554864\pi\)
\(312\) 6.22599 0.352477
\(313\) 28.0638 1.58626 0.793130 0.609053i \(-0.208450\pi\)
0.793130 + 0.609053i \(0.208450\pi\)
\(314\) 2.57381 0.145249
\(315\) 1.08984 0.0614054
\(316\) 0.0958485 0.00539190
\(317\) −24.9206 −1.39968 −0.699840 0.714300i \(-0.746745\pi\)
−0.699840 + 0.714300i \(0.746745\pi\)
\(318\) 7.89949 0.442981
\(319\) 14.9986 0.839762
\(320\) −1.12903 −0.0631149
\(321\) 6.37561 0.355852
\(322\) 7.78372 0.433770
\(323\) −0.660752 −0.0367652
\(324\) −0.312353 −0.0173529
\(325\) −28.4953 −1.58063
\(326\) −12.0604 −0.667965
\(327\) 10.3564 0.572712
\(328\) −9.94455 −0.549096
\(329\) −6.10964 −0.336835
\(330\) 2.01305 0.110815
\(331\) −6.25862 −0.344005 −0.172003 0.985097i \(-0.555024\pi\)
−0.172003 + 0.985097i \(0.555024\pi\)
\(332\) −26.1338 −1.43428
\(333\) −13.0534 −0.715320
\(334\) 8.59901 0.470517
\(335\) 2.64943 0.144754
\(336\) 9.24007 0.504087
\(337\) −14.5926 −0.794910 −0.397455 0.917622i \(-0.630107\pi\)
−0.397455 + 0.917622i \(0.630107\pi\)
\(338\) −39.1162 −2.12764
\(339\) −16.9168 −0.918796
\(340\) −0.493900 −0.0267855
\(341\) 9.57481 0.518505
\(342\) 2.24360 0.121320
\(343\) 19.2905 1.04159
\(344\) −4.46496 −0.240734
\(345\) 0.853494 0.0459506
\(346\) −31.3676 −1.68633
\(347\) −29.6944 −1.59408 −0.797038 0.603929i \(-0.793601\pi\)
−0.797038 + 0.603929i \(0.793601\pi\)
\(348\) −8.07509 −0.432870
\(349\) 28.5347 1.52743 0.763714 0.645555i \(-0.223374\pi\)
0.763714 + 0.645555i \(0.223374\pi\)
\(350\) −16.2308 −0.867572
\(351\) −30.5115 −1.62859
\(352\) −20.5709 −1.09643
\(353\) 9.76145 0.519549 0.259775 0.965669i \(-0.416352\pi\)
0.259775 + 0.965669i \(0.416352\pi\)
\(354\) 2.02208 0.107472
\(355\) 1.46849 0.0779391
\(356\) −15.4363 −0.818123
\(357\) 1.93416 0.102367
\(358\) −10.4857 −0.554188
\(359\) 22.9107 1.20918 0.604590 0.796537i \(-0.293337\pi\)
0.604590 + 0.796537i \(0.293337\pi\)
\(360\) −0.601706 −0.0317127
\(361\) −18.5634 −0.977021
\(362\) 22.1829 1.16591
\(363\) −2.38501 −0.125181
\(364\) −15.2950 −0.801677
\(365\) −5.14478 −0.269290
\(366\) −2.43394 −0.127224
\(367\) −7.95154 −0.415067 −0.207533 0.978228i \(-0.566544\pi\)
−0.207533 + 0.978228i \(0.566544\pi\)
\(368\) −11.1972 −0.583694
\(369\) 18.4166 0.958729
\(370\) −4.47861 −0.232832
\(371\) 6.96272 0.361486
\(372\) −5.15496 −0.267272
\(373\) 9.27783 0.480388 0.240194 0.970725i \(-0.422789\pi\)
0.240194 + 0.970725i \(0.422789\pi\)
\(374\) −5.52816 −0.285854
\(375\) −3.60045 −0.185926
\(376\) 3.37317 0.173958
\(377\) −29.4747 −1.51802
\(378\) −17.3793 −0.893893
\(379\) 7.95324 0.408531 0.204265 0.978916i \(-0.434519\pi\)
0.204265 + 0.978916i \(0.434519\pi\)
\(380\) 0.326345 0.0167411
\(381\) 6.39059 0.327400
\(382\) 47.4655 2.42855
\(383\) −20.2576 −1.03511 −0.517557 0.855648i \(-0.673159\pi\)
−0.517557 + 0.855648i \(0.673159\pi\)
\(384\) −8.24506 −0.420754
\(385\) 1.77433 0.0904284
\(386\) −20.3432 −1.03544
\(387\) 8.26878 0.420326
\(388\) 6.33855 0.321791
\(389\) 5.39968 0.273775 0.136887 0.990587i \(-0.456290\pi\)
0.136887 + 0.990587i \(0.456290\pi\)
\(390\) −3.95596 −0.200318
\(391\) −2.34383 −0.118532
\(392\) −3.76232 −0.190026
\(393\) 10.4308 0.526164
\(394\) −23.7901 −1.19853
\(395\) 0.0218508 0.00109943
\(396\) 7.95791 0.399900
\(397\) 6.75805 0.339177 0.169588 0.985515i \(-0.445756\pi\)
0.169588 + 0.985515i \(0.445756\pi\)
\(398\) −15.2733 −0.765579
\(399\) −1.27800 −0.0639799
\(400\) 23.3486 1.16743
\(401\) 7.86655 0.392837 0.196418 0.980520i \(-0.437069\pi\)
0.196418 + 0.980520i \(0.437069\pi\)
\(402\) −15.9658 −0.796300
\(403\) −18.8160 −0.937292
\(404\) −24.8992 −1.23878
\(405\) −0.0712078 −0.00353834
\(406\) −16.7887 −0.833207
\(407\) −21.2518 −1.05341
\(408\) −1.06786 −0.0528669
\(409\) −29.2041 −1.44405 −0.722024 0.691868i \(-0.756788\pi\)
−0.722024 + 0.691868i \(0.756788\pi\)
\(410\) 6.31872 0.312059
\(411\) −22.3359 −1.10175
\(412\) 1.94575 0.0958601
\(413\) 1.78229 0.0877006
\(414\) 7.95854 0.391141
\(415\) −5.95777 −0.292456
\(416\) 40.4250 1.98200
\(417\) 1.64017 0.0803197
\(418\) 3.65274 0.178661
\(419\) 25.2775 1.23488 0.617442 0.786616i \(-0.288169\pi\)
0.617442 + 0.786616i \(0.288169\pi\)
\(420\) −0.955280 −0.0466129
\(421\) −26.9567 −1.31379 −0.656894 0.753983i \(-0.728130\pi\)
−0.656894 + 0.753983i \(0.728130\pi\)
\(422\) −39.3739 −1.91669
\(423\) −6.24686 −0.303733
\(424\) −3.84416 −0.186689
\(425\) 4.88740 0.237074
\(426\) −8.84926 −0.428748
\(427\) −2.14531 −0.103819
\(428\) 8.64741 0.417988
\(429\) −18.7718 −0.906310
\(430\) 2.83701 0.136813
\(431\) −22.9758 −1.10671 −0.553353 0.832947i \(-0.686652\pi\)
−0.553353 + 0.832947i \(0.686652\pi\)
\(432\) 25.0008 1.20285
\(433\) 15.9134 0.764751 0.382376 0.924007i \(-0.375106\pi\)
0.382376 + 0.924007i \(0.375106\pi\)
\(434\) −10.7175 −0.514457
\(435\) −1.84090 −0.0882642
\(436\) 14.0467 0.672714
\(437\) 1.54869 0.0740838
\(438\) 31.0031 1.48138
\(439\) 6.10811 0.291524 0.145762 0.989320i \(-0.453437\pi\)
0.145762 + 0.989320i \(0.453437\pi\)
\(440\) −0.979619 −0.0467015
\(441\) 6.96754 0.331788
\(442\) 10.8637 0.516734
\(443\) 3.55001 0.168666 0.0843330 0.996438i \(-0.473124\pi\)
0.0843330 + 0.996438i \(0.473124\pi\)
\(444\) 11.4417 0.543000
\(445\) −3.51905 −0.166819
\(446\) 37.2867 1.76558
\(447\) −10.8514 −0.513253
\(448\) 5.99686 0.283325
\(449\) −32.8083 −1.54832 −0.774161 0.632989i \(-0.781828\pi\)
−0.774161 + 0.632989i \(0.781828\pi\)
\(450\) −16.5953 −0.782311
\(451\) 29.9835 1.41187
\(452\) −22.9447 −1.07923
\(453\) −12.6772 −0.595626
\(454\) −20.7682 −0.974698
\(455\) −3.48684 −0.163466
\(456\) 0.705590 0.0330423
\(457\) −7.85695 −0.367533 −0.183766 0.982970i \(-0.558829\pi\)
−0.183766 + 0.982970i \(0.558829\pi\)
\(458\) −37.8166 −1.76705
\(459\) 5.23323 0.244266
\(460\) 1.15762 0.0539741
\(461\) 10.5628 0.491957 0.245978 0.969275i \(-0.420891\pi\)
0.245978 + 0.969275i \(0.420891\pi\)
\(462\) −10.6923 −0.497452
\(463\) −32.3816 −1.50490 −0.752450 0.658649i \(-0.771128\pi\)
−0.752450 + 0.658649i \(0.771128\pi\)
\(464\) 24.1512 1.12119
\(465\) −1.17519 −0.0544981
\(466\) 9.39348 0.435144
\(467\) 4.58631 0.212229 0.106115 0.994354i \(-0.466159\pi\)
0.106115 + 0.994354i \(0.466159\pi\)
\(468\) −15.6385 −0.722892
\(469\) −14.0724 −0.649805
\(470\) −2.14329 −0.0988628
\(471\) −1.49902 −0.0690712
\(472\) −0.984011 −0.0452928
\(473\) 13.4622 0.618991
\(474\) −0.131676 −0.00604806
\(475\) −3.22936 −0.148173
\(476\) 2.62335 0.120241
\(477\) 7.11910 0.325961
\(478\) −46.1838 −2.11240
\(479\) −0.613626 −0.0280373 −0.0140186 0.999902i \(-0.504462\pi\)
−0.0140186 + 0.999902i \(0.504462\pi\)
\(480\) 2.52482 0.115242
\(481\) 41.7631 1.90423
\(482\) −21.1074 −0.961416
\(483\) −4.53333 −0.206274
\(484\) −3.23486 −0.147039
\(485\) 1.44501 0.0656147
\(486\) −28.8242 −1.30749
\(487\) 10.6801 0.483962 0.241981 0.970281i \(-0.422203\pi\)
0.241981 + 0.970281i \(0.422203\pi\)
\(488\) 1.18444 0.0536170
\(489\) 7.02414 0.317642
\(490\) 2.39056 0.107994
\(491\) 38.8940 1.75526 0.877630 0.479338i \(-0.159123\pi\)
0.877630 + 0.479338i \(0.159123\pi\)
\(492\) −16.1428 −0.727772
\(493\) 5.05539 0.227683
\(494\) −7.17821 −0.322963
\(495\) 1.81418 0.0815415
\(496\) 15.4176 0.692270
\(497\) −7.79986 −0.349872
\(498\) 35.9022 1.60882
\(499\) −35.7847 −1.60194 −0.800970 0.598704i \(-0.795683\pi\)
−0.800970 + 0.598704i \(0.795683\pi\)
\(500\) −4.88338 −0.218392
\(501\) −5.00817 −0.223749
\(502\) −17.3535 −0.774524
\(503\) 17.2649 0.769802 0.384901 0.922958i \(-0.374236\pi\)
0.384901 + 0.922958i \(0.374236\pi\)
\(504\) 3.19596 0.142359
\(505\) −5.67632 −0.252593
\(506\) 12.9571 0.576011
\(507\) 22.7818 1.01177
\(508\) 8.66773 0.384568
\(509\) 16.2983 0.722411 0.361206 0.932486i \(-0.382365\pi\)
0.361206 + 0.932486i \(0.382365\pi\)
\(510\) 0.678513 0.0300451
\(511\) 27.3265 1.20885
\(512\) −23.7219 −1.04837
\(513\) −3.45787 −0.152669
\(514\) −31.6775 −1.39723
\(515\) 0.443577 0.0195463
\(516\) −7.24786 −0.319069
\(517\) −10.1703 −0.447290
\(518\) 23.7881 1.04519
\(519\) 18.2689 0.801915
\(520\) 1.92511 0.0844214
\(521\) −33.4699 −1.46634 −0.733172 0.680044i \(-0.761961\pi\)
−0.733172 + 0.680044i \(0.761961\pi\)
\(522\) −17.1657 −0.751323
\(523\) 1.80809 0.0790621 0.0395311 0.999218i \(-0.487414\pi\)
0.0395311 + 0.999218i \(0.487414\pi\)
\(524\) 14.1476 0.618039
\(525\) 9.45301 0.412563
\(526\) 18.5216 0.807581
\(527\) 3.22725 0.140581
\(528\) 15.3814 0.669388
\(529\) −17.5065 −0.761151
\(530\) 2.44256 0.106098
\(531\) 1.82232 0.0790818
\(532\) −1.73338 −0.0751516
\(533\) −58.9223 −2.55221
\(534\) 21.2062 0.917682
\(535\) 1.97137 0.0852297
\(536\) 7.76948 0.335590
\(537\) 6.10701 0.263537
\(538\) −7.50642 −0.323625
\(539\) 11.3436 0.488605
\(540\) −2.58469 −0.111227
\(541\) 6.67089 0.286804 0.143402 0.989665i \(-0.454196\pi\)
0.143402 + 0.989665i \(0.454196\pi\)
\(542\) −29.4061 −1.26310
\(543\) −12.9196 −0.554434
\(544\) −6.93356 −0.297274
\(545\) 3.20226 0.137170
\(546\) 21.0121 0.899236
\(547\) −2.92387 −0.125016 −0.0625078 0.998044i \(-0.519910\pi\)
−0.0625078 + 0.998044i \(0.519910\pi\)
\(548\) −30.2948 −1.29413
\(549\) −2.19350 −0.0936161
\(550\) −27.0184 −1.15207
\(551\) −3.34036 −0.142304
\(552\) 2.50288 0.106530
\(553\) −0.116061 −0.00493540
\(554\) −29.4271 −1.25024
\(555\) 2.60840 0.110720
\(556\) 2.22461 0.0943445
\(557\) −15.5279 −0.657940 −0.328970 0.944340i \(-0.606702\pi\)
−0.328970 + 0.944340i \(0.606702\pi\)
\(558\) −10.9582 −0.463899
\(559\) −26.4552 −1.11894
\(560\) 2.85707 0.120733
\(561\) 3.21967 0.135935
\(562\) 14.1079 0.595104
\(563\) −26.3223 −1.10935 −0.554677 0.832066i \(-0.687158\pi\)
−0.554677 + 0.832066i \(0.687158\pi\)
\(564\) 5.47558 0.230564
\(565\) −5.23076 −0.220060
\(566\) −29.3458 −1.23349
\(567\) 0.378220 0.0158838
\(568\) 4.30635 0.180690
\(569\) 21.2835 0.892251 0.446125 0.894970i \(-0.352804\pi\)
0.446125 + 0.894970i \(0.352804\pi\)
\(570\) −0.448329 −0.0187784
\(571\) 14.0880 0.589563 0.294782 0.955565i \(-0.404753\pi\)
0.294782 + 0.955565i \(0.404753\pi\)
\(572\) −25.4607 −1.06456
\(573\) −27.6445 −1.15486
\(574\) −33.5619 −1.40085
\(575\) −11.4552 −0.477716
\(576\) 6.13155 0.255481
\(577\) −22.5707 −0.939630 −0.469815 0.882765i \(-0.655679\pi\)
−0.469815 + 0.882765i \(0.655679\pi\)
\(578\) −1.86330 −0.0775032
\(579\) 11.8481 0.492391
\(580\) −2.49685 −0.103676
\(581\) 31.6447 1.31284
\(582\) −8.70782 −0.360951
\(583\) 11.5904 0.480025
\(584\) −15.0871 −0.624310
\(585\) −3.56516 −0.147401
\(586\) −4.80917 −0.198665
\(587\) 41.4964 1.71274 0.856371 0.516361i \(-0.172714\pi\)
0.856371 + 0.516361i \(0.172714\pi\)
\(588\) −6.10728 −0.251860
\(589\) −2.13241 −0.0878645
\(590\) 0.625236 0.0257406
\(591\) 13.8557 0.569946
\(592\) −34.2202 −1.40644
\(593\) −12.0523 −0.494928 −0.247464 0.968897i \(-0.579597\pi\)
−0.247464 + 0.968897i \(0.579597\pi\)
\(594\) −28.9301 −1.18702
\(595\) 0.598051 0.0245177
\(596\) −14.7180 −0.602873
\(597\) 8.89533 0.364062
\(598\) −25.4627 −1.04125
\(599\) −7.94051 −0.324441 −0.162220 0.986755i \(-0.551866\pi\)
−0.162220 + 0.986755i \(0.551866\pi\)
\(600\) −5.21906 −0.213067
\(601\) −34.8574 −1.42186 −0.710932 0.703261i \(-0.751727\pi\)
−0.710932 + 0.703261i \(0.751727\pi\)
\(602\) −15.0688 −0.614159
\(603\) −14.3885 −0.585945
\(604\) −17.1944 −0.699629
\(605\) −0.737458 −0.0299819
\(606\) 34.2062 1.38953
\(607\) 40.2138 1.63223 0.816115 0.577890i \(-0.196124\pi\)
0.816115 + 0.577890i \(0.196124\pi\)
\(608\) 4.58136 0.185799
\(609\) 9.77792 0.396221
\(610\) −0.752587 −0.0304714
\(611\) 19.9863 0.808559
\(612\) 2.68227 0.108424
\(613\) 13.0768 0.528166 0.264083 0.964500i \(-0.414931\pi\)
0.264083 + 0.964500i \(0.414931\pi\)
\(614\) 29.5790 1.19371
\(615\) −3.68010 −0.148396
\(616\) 5.20325 0.209645
\(617\) −13.5140 −0.544055 −0.272027 0.962289i \(-0.587694\pi\)
−0.272027 + 0.962289i \(0.587694\pi\)
\(618\) −2.67304 −0.107526
\(619\) 42.1820 1.69544 0.847718 0.530447i \(-0.177976\pi\)
0.847718 + 0.530447i \(0.177976\pi\)
\(620\) −1.59394 −0.0640141
\(621\) −12.2658 −0.492209
\(622\) 11.2715 0.451945
\(623\) 18.6914 0.748857
\(624\) −30.2268 −1.21004
\(625\) 23.3237 0.932950
\(626\) −52.2914 −2.08998
\(627\) −2.12740 −0.0849603
\(628\) −2.03316 −0.0811319
\(629\) −7.16306 −0.285610
\(630\) −2.03070 −0.0809050
\(631\) −24.2876 −0.966876 −0.483438 0.875379i \(-0.660612\pi\)
−0.483438 + 0.875379i \(0.660612\pi\)
\(632\) 0.0640777 0.00254887
\(633\) 22.9318 0.911459
\(634\) 46.4346 1.84415
\(635\) 1.97600 0.0784152
\(636\) −6.24013 −0.247437
\(637\) −22.2920 −0.883243
\(638\) −27.9470 −1.10643
\(639\) −7.97504 −0.315488
\(640\) −2.54941 −0.100774
\(641\) 0.958607 0.0378627 0.0189313 0.999821i \(-0.493974\pi\)
0.0189313 + 0.999821i \(0.493974\pi\)
\(642\) −11.8797 −0.468854
\(643\) −35.7827 −1.41113 −0.705566 0.708644i \(-0.749307\pi\)
−0.705566 + 0.708644i \(0.749307\pi\)
\(644\) −6.14868 −0.242292
\(645\) −1.65231 −0.0650597
\(646\) 1.23118 0.0484402
\(647\) 49.7798 1.95705 0.978524 0.206135i \(-0.0660885\pi\)
0.978524 + 0.206135i \(0.0660885\pi\)
\(648\) −0.208817 −0.00820312
\(649\) 2.96686 0.116459
\(650\) 53.0953 2.08257
\(651\) 6.24202 0.244644
\(652\) 9.52702 0.373107
\(653\) 34.6089 1.35435 0.677176 0.735821i \(-0.263204\pi\)
0.677176 + 0.735821i \(0.263204\pi\)
\(654\) −19.2972 −0.754579
\(655\) 3.22525 0.126021
\(656\) 48.2802 1.88502
\(657\) 27.9403 1.09005
\(658\) 11.3841 0.443799
\(659\) 38.8265 1.51247 0.756233 0.654302i \(-0.227038\pi\)
0.756233 + 0.654302i \(0.227038\pi\)
\(660\) −1.59019 −0.0618982
\(661\) −40.7428 −1.58471 −0.792356 0.610058i \(-0.791146\pi\)
−0.792356 + 0.610058i \(0.791146\pi\)
\(662\) 11.6617 0.453245
\(663\) −6.32716 −0.245726
\(664\) −17.4712 −0.678015
\(665\) −0.395163 −0.0153238
\(666\) 24.3224 0.942474
\(667\) −11.8490 −0.458794
\(668\) −6.79271 −0.262818
\(669\) −21.7162 −0.839598
\(670\) −4.93669 −0.190721
\(671\) −3.57117 −0.137863
\(672\) −13.4106 −0.517325
\(673\) 27.1195 1.04538 0.522690 0.852523i \(-0.324928\pi\)
0.522690 + 0.852523i \(0.324928\pi\)
\(674\) 27.1905 1.04734
\(675\) 25.5769 0.984456
\(676\) 30.8995 1.18844
\(677\) 50.8005 1.95242 0.976210 0.216827i \(-0.0695707\pi\)
0.976210 + 0.216827i \(0.0695707\pi\)
\(678\) 31.5212 1.21056
\(679\) −7.67520 −0.294547
\(680\) −0.330187 −0.0126621
\(681\) 12.0956 0.463506
\(682\) −17.8408 −0.683158
\(683\) −11.4679 −0.438807 −0.219404 0.975634i \(-0.570411\pi\)
−0.219404 + 0.975634i \(0.570411\pi\)
\(684\) −1.77231 −0.0677661
\(685\) −6.90637 −0.263879
\(686\) −35.9441 −1.37235
\(687\) 22.0249 0.840301
\(688\) 21.6771 0.826431
\(689\) −22.7769 −0.867732
\(690\) −1.59032 −0.0605424
\(691\) 3.16212 0.120293 0.0601464 0.998190i \(-0.480843\pi\)
0.0601464 + 0.998190i \(0.480843\pi\)
\(692\) 24.7786 0.941939
\(693\) −9.63604 −0.366043
\(694\) 55.3296 2.10028
\(695\) 0.507150 0.0192373
\(696\) −5.39845 −0.204628
\(697\) 10.1061 0.382797
\(698\) −53.1688 −2.01247
\(699\) −5.47088 −0.206928
\(700\) 12.8214 0.484602
\(701\) 30.4979 1.15189 0.575945 0.817488i \(-0.304634\pi\)
0.575945 + 0.817488i \(0.304634\pi\)
\(702\) 56.8523 2.14575
\(703\) 4.73301 0.178509
\(704\) 9.98260 0.376233
\(705\) 1.24828 0.0470130
\(706\) −18.1885 −0.684535
\(707\) 30.1498 1.13390
\(708\) −1.59732 −0.0600310
\(709\) −44.4812 −1.67052 −0.835262 0.549852i \(-0.814684\pi\)
−0.835262 + 0.549852i \(0.814684\pi\)
\(710\) −2.73623 −0.102689
\(711\) −0.118667 −0.00445037
\(712\) −10.3197 −0.386745
\(713\) −7.56413 −0.283279
\(714\) −3.60392 −0.134873
\(715\) −5.80432 −0.217069
\(716\) 8.28310 0.309554
\(717\) 26.8980 1.00453
\(718\) −42.6896 −1.59316
\(719\) 7.93928 0.296085 0.148043 0.988981i \(-0.452703\pi\)
0.148043 + 0.988981i \(0.452703\pi\)
\(720\) 2.92124 0.108868
\(721\) −2.35606 −0.0877442
\(722\) 34.5893 1.28728
\(723\) 12.2932 0.457189
\(724\) −17.5232 −0.651245
\(725\) 24.7077 0.917622
\(726\) 4.44401 0.164933
\(727\) −46.0250 −1.70697 −0.853487 0.521114i \(-0.825516\pi\)
−0.853487 + 0.521114i \(0.825516\pi\)
\(728\) −10.2252 −0.378971
\(729\) 17.4242 0.645341
\(730\) 9.58629 0.354805
\(731\) 4.53751 0.167826
\(732\) 1.92267 0.0710640
\(733\) −19.9668 −0.737491 −0.368745 0.929530i \(-0.620213\pi\)
−0.368745 + 0.929530i \(0.620213\pi\)
\(734\) 14.8161 0.546873
\(735\) −1.39229 −0.0513554
\(736\) 16.2511 0.599022
\(737\) −23.4255 −0.862889
\(738\) −34.3157 −1.26318
\(739\) 47.7707 1.75727 0.878636 0.477492i \(-0.158454\pi\)
0.878636 + 0.477492i \(0.158454\pi\)
\(740\) 3.53783 0.130053
\(741\) 4.18068 0.153581
\(742\) −12.9737 −0.476278
\(743\) −12.5372 −0.459945 −0.229972 0.973197i \(-0.573864\pi\)
−0.229972 + 0.973197i \(0.573864\pi\)
\(744\) −3.44625 −0.126346
\(745\) −3.35530 −0.122929
\(746\) −17.2874 −0.632937
\(747\) 32.3555 1.18382
\(748\) 4.36692 0.159670
\(749\) −10.4709 −0.382600
\(750\) 6.70873 0.244968
\(751\) 14.9786 0.546576 0.273288 0.961932i \(-0.411889\pi\)
0.273288 + 0.961932i \(0.411889\pi\)
\(752\) −16.3765 −0.597190
\(753\) 10.1069 0.368315
\(754\) 54.9202 2.00008
\(755\) −3.91984 −0.142658
\(756\) 13.7286 0.499304
\(757\) −17.1376 −0.622878 −0.311439 0.950266i \(-0.600811\pi\)
−0.311439 + 0.950266i \(0.600811\pi\)
\(758\) −14.8193 −0.538261
\(759\) −7.54635 −0.273915
\(760\) 0.218172 0.00791392
\(761\) −9.58584 −0.347486 −0.173743 0.984791i \(-0.555586\pi\)
−0.173743 + 0.984791i \(0.555586\pi\)
\(762\) −11.9076 −0.431367
\(763\) −17.0088 −0.615759
\(764\) −37.4949 −1.35652
\(765\) 0.611483 0.0221082
\(766\) 37.7461 1.36382
\(767\) −5.83034 −0.210522
\(768\) 22.6659 0.817884
\(769\) −28.3985 −1.02408 −0.512038 0.858963i \(-0.671109\pi\)
−0.512038 + 0.858963i \(0.671109\pi\)
\(770\) −3.30612 −0.119144
\(771\) 18.4494 0.664438
\(772\) 16.0699 0.578369
\(773\) −17.5482 −0.631165 −0.315582 0.948898i \(-0.602200\pi\)
−0.315582 + 0.948898i \(0.602200\pi\)
\(774\) −15.4072 −0.553802
\(775\) 15.7729 0.566579
\(776\) 4.23752 0.152118
\(777\) −13.8545 −0.497027
\(778\) −10.0612 −0.360713
\(779\) −6.67765 −0.239252
\(780\) 3.12498 0.111892
\(781\) −12.9839 −0.464602
\(782\) 4.36726 0.156173
\(783\) 26.4560 0.945461
\(784\) 18.2658 0.652351
\(785\) −0.463504 −0.0165432
\(786\) −19.4358 −0.693250
\(787\) −37.2633 −1.32829 −0.664146 0.747603i \(-0.731205\pi\)
−0.664146 + 0.747603i \(0.731205\pi\)
\(788\) 18.7928 0.669466
\(789\) −10.7872 −0.384035
\(790\) −0.0407147 −0.00144856
\(791\) 27.7832 0.987857
\(792\) 5.32011 0.189042
\(793\) 7.01790 0.249213
\(794\) −12.5923 −0.446884
\(795\) −1.42258 −0.0504536
\(796\) 12.0650 0.427632
\(797\) −40.9410 −1.45020 −0.725102 0.688642i \(-0.758207\pi\)
−0.725102 + 0.688642i \(0.758207\pi\)
\(798\) 2.38130 0.0842971
\(799\) −3.42798 −0.121273
\(800\) −33.8871 −1.19809
\(801\) 19.1113 0.675263
\(802\) −14.6578 −0.517584
\(803\) 45.4887 1.60526
\(804\) 12.6120 0.444791
\(805\) −1.40173 −0.0494044
\(806\) 35.0599 1.23493
\(807\) 4.37183 0.153896
\(808\) −16.6459 −0.585600
\(809\) −38.5922 −1.35683 −0.678414 0.734680i \(-0.737332\pi\)
−0.678414 + 0.734680i \(0.737332\pi\)
\(810\) 0.132682 0.00466196
\(811\) −52.3127 −1.83695 −0.918474 0.395481i \(-0.870578\pi\)
−0.918474 + 0.395481i \(0.870578\pi\)
\(812\) 13.2620 0.465407
\(813\) 17.1265 0.600652
\(814\) 39.5986 1.38793
\(815\) 2.17190 0.0760782
\(816\) 5.18439 0.181490
\(817\) −2.99817 −0.104893
\(818\) 54.4161 1.90261
\(819\) 18.9363 0.661689
\(820\) −4.99142 −0.174308
\(821\) 46.8691 1.63574 0.817871 0.575402i \(-0.195154\pi\)
0.817871 + 0.575402i \(0.195154\pi\)
\(822\) 41.6186 1.45161
\(823\) −30.8025 −1.07371 −0.536854 0.843675i \(-0.680387\pi\)
−0.536854 + 0.843675i \(0.680387\pi\)
\(824\) 1.30079 0.0453153
\(825\) 15.7358 0.547851
\(826\) −3.32094 −0.115550
\(827\) 31.4859 1.09487 0.547435 0.836848i \(-0.315604\pi\)
0.547435 + 0.836848i \(0.315604\pi\)
\(828\) −6.28678 −0.218481
\(829\) −3.11446 −0.108170 −0.0540849 0.998536i \(-0.517224\pi\)
−0.0540849 + 0.998536i \(0.517224\pi\)
\(830\) 11.1011 0.385326
\(831\) 17.1387 0.594536
\(832\) −19.6174 −0.680110
\(833\) 3.82345 0.132475
\(834\) −3.05614 −0.105826
\(835\) −1.54855 −0.0535898
\(836\) −2.88545 −0.0997954
\(837\) 16.8890 0.583768
\(838\) −47.0996 −1.62703
\(839\) −31.2075 −1.07740 −0.538701 0.842497i \(-0.681085\pi\)
−0.538701 + 0.842497i \(0.681085\pi\)
\(840\) −0.638634 −0.0220350
\(841\) −3.44304 −0.118725
\(842\) 50.2285 1.73099
\(843\) −8.21659 −0.282995
\(844\) 31.1031 1.07061
\(845\) 7.04423 0.242329
\(846\) 11.6398 0.400184
\(847\) 3.91701 0.134590
\(848\) 18.6631 0.640895
\(849\) 17.0913 0.586573
\(850\) −9.10672 −0.312358
\(851\) 16.7890 0.575519
\(852\) 6.99039 0.239487
\(853\) −16.3030 −0.558206 −0.279103 0.960261i \(-0.590037\pi\)
−0.279103 + 0.960261i \(0.590037\pi\)
\(854\) 3.99737 0.136787
\(855\) −0.404038 −0.0138178
\(856\) 5.78106 0.197593
\(857\) −40.9532 −1.39894 −0.699468 0.714664i \(-0.746580\pi\)
−0.699468 + 0.714664i \(0.746580\pi\)
\(858\) 34.9775 1.19411
\(859\) −9.97437 −0.340321 −0.170161 0.985416i \(-0.554429\pi\)
−0.170161 + 0.985416i \(0.554429\pi\)
\(860\) −2.24107 −0.0764200
\(861\) 19.5469 0.666156
\(862\) 42.8109 1.45815
\(863\) 28.9286 0.984742 0.492371 0.870385i \(-0.336130\pi\)
0.492371 + 0.870385i \(0.336130\pi\)
\(864\) −36.2849 −1.23444
\(865\) 5.64883 0.192066
\(866\) −29.6516 −1.00760
\(867\) 1.08521 0.0368557
\(868\) 8.46621 0.287362
\(869\) −0.193199 −0.00655382
\(870\) 3.43015 0.116293
\(871\) 46.0348 1.55983
\(872\) 9.39065 0.318007
\(873\) −7.84758 −0.265600
\(874\) −2.88568 −0.0976095
\(875\) 5.91317 0.199902
\(876\) −24.4906 −0.827460
\(877\) −41.3086 −1.39489 −0.697447 0.716637i \(-0.745681\pi\)
−0.697447 + 0.716637i \(0.745681\pi\)
\(878\) −11.3813 −0.384099
\(879\) 2.80092 0.0944728
\(880\) 4.75599 0.160324
\(881\) −25.6855 −0.865365 −0.432683 0.901546i \(-0.642433\pi\)
−0.432683 + 0.901546i \(0.642433\pi\)
\(882\) −12.9826 −0.437148
\(883\) −24.4200 −0.821799 −0.410900 0.911681i \(-0.634785\pi\)
−0.410900 + 0.911681i \(0.634785\pi\)
\(884\) −8.58168 −0.288633
\(885\) −0.364145 −0.0122406
\(886\) −6.61474 −0.222227
\(887\) −11.7041 −0.392984 −0.196492 0.980505i \(-0.562955\pi\)
−0.196492 + 0.980505i \(0.562955\pi\)
\(888\) 7.64915 0.256689
\(889\) −10.4955 −0.352009
\(890\) 6.55706 0.219793
\(891\) 0.629599 0.0210924
\(892\) −29.4543 −0.986202
\(893\) 2.26504 0.0757967
\(894\) 20.2194 0.676238
\(895\) 1.88832 0.0631195
\(896\) 13.5412 0.452380
\(897\) 14.8298 0.495151
\(898\) 61.1319 2.04000
\(899\) 16.3150 0.544136
\(900\) 13.1093 0.436978
\(901\) 3.90662 0.130148
\(902\) −55.8684 −1.86021
\(903\) 8.77626 0.292056
\(904\) −15.3393 −0.510176
\(905\) −3.99481 −0.132792
\(906\) 23.6214 0.784769
\(907\) 24.1452 0.801728 0.400864 0.916138i \(-0.368710\pi\)
0.400864 + 0.916138i \(0.368710\pi\)
\(908\) 16.4056 0.544440
\(909\) 30.8269 1.02247
\(910\) 6.49705 0.215375
\(911\) 25.2852 0.837737 0.418868 0.908047i \(-0.362427\pi\)
0.418868 + 0.908047i \(0.362427\pi\)
\(912\) −3.42559 −0.113433
\(913\) 52.6770 1.74335
\(914\) 14.6399 0.484244
\(915\) 0.438316 0.0144903
\(916\) 29.8729 0.987028
\(917\) −17.1309 −0.565714
\(918\) −9.75110 −0.321834
\(919\) 18.3380 0.604914 0.302457 0.953163i \(-0.402193\pi\)
0.302457 + 0.953163i \(0.402193\pi\)
\(920\) 0.773902 0.0255148
\(921\) −17.2272 −0.567655
\(922\) −19.6816 −0.648180
\(923\) 25.5155 0.839852
\(924\) 8.44631 0.277863
\(925\) −35.0088 −1.15108
\(926\) 60.3367 1.98279
\(927\) −2.40898 −0.0791211
\(928\) −35.0518 −1.15063
\(929\) 35.7491 1.17289 0.586445 0.809989i \(-0.300527\pi\)
0.586445 + 0.809989i \(0.300527\pi\)
\(930\) 2.18973 0.0718042
\(931\) −2.52635 −0.0827978
\(932\) −7.42029 −0.243060
\(933\) −6.56465 −0.214917
\(934\) −8.54569 −0.279623
\(935\) 0.995537 0.0325575
\(936\) −10.4549 −0.341728
\(937\) 20.7094 0.676548 0.338274 0.941048i \(-0.390157\pi\)
0.338274 + 0.941048i \(0.390157\pi\)
\(938\) 26.2212 0.856154
\(939\) 30.4551 0.993866
\(940\) 1.69308 0.0552220
\(941\) −17.2905 −0.563655 −0.281828 0.959465i \(-0.590941\pi\)
−0.281828 + 0.959465i \(0.590941\pi\)
\(942\) 2.79313 0.0910051
\(943\) −23.6871 −0.771357
\(944\) 4.77731 0.155488
\(945\) 3.12974 0.101810
\(946\) −25.0841 −0.815554
\(947\) −12.8393 −0.417221 −0.208610 0.977999i \(-0.566894\pi\)
−0.208610 + 0.977999i \(0.566894\pi\)
\(948\) 0.104016 0.00337828
\(949\) −89.3925 −2.90180
\(950\) 6.01728 0.195226
\(951\) −27.0441 −0.876965
\(952\) 1.75379 0.0568407
\(953\) 31.1210 1.00811 0.504054 0.863672i \(-0.331841\pi\)
0.504054 + 0.863672i \(0.331841\pi\)
\(954\) −13.2650 −0.429472
\(955\) −8.54781 −0.276600
\(956\) 36.4825 1.17993
\(957\) 16.2767 0.526150
\(958\) 1.14337 0.0369406
\(959\) 36.6832 1.18456
\(960\) −1.22524 −0.0395444
\(961\) −20.5848 −0.664027
\(962\) −77.8174 −2.50893
\(963\) −10.7061 −0.344999
\(964\) 16.6736 0.537020
\(965\) 3.66349 0.117932
\(966\) 8.44698 0.271777
\(967\) −11.3986 −0.366554 −0.183277 0.983061i \(-0.558671\pi\)
−0.183277 + 0.983061i \(0.558671\pi\)
\(968\) −2.16260 −0.0695087
\(969\) −0.717055 −0.0230351
\(970\) −2.69250 −0.0864509
\(971\) −58.6062 −1.88076 −0.940381 0.340122i \(-0.889532\pi\)
−0.940381 + 0.340122i \(0.889532\pi\)
\(972\) 22.7694 0.730329
\(973\) −2.69373 −0.0863569
\(974\) −19.9003 −0.637646
\(975\) −30.9234 −0.990340
\(976\) −5.75038 −0.184065
\(977\) 13.0114 0.416272 0.208136 0.978100i \(-0.433260\pi\)
0.208136 + 0.978100i \(0.433260\pi\)
\(978\) −13.0881 −0.418511
\(979\) 31.1145 0.994422
\(980\) −1.88840 −0.0603228
\(981\) −17.3908 −0.555245
\(982\) −72.4713 −2.31265
\(983\) −7.81190 −0.249161 −0.124580 0.992210i \(-0.539758\pi\)
−0.124580 + 0.992210i \(0.539758\pi\)
\(984\) −10.7919 −0.344034
\(985\) 4.28424 0.136507
\(986\) −9.41972 −0.299985
\(987\) −6.63025 −0.211043
\(988\) 5.67036 0.180398
\(989\) −10.6351 −0.338178
\(990\) −3.38037 −0.107435
\(991\) 56.6951 1.80098 0.900489 0.434879i \(-0.143209\pi\)
0.900489 + 0.434879i \(0.143209\pi\)
\(992\) −22.3763 −0.710450
\(993\) −6.79193 −0.215535
\(994\) 14.5335 0.460975
\(995\) 2.75048 0.0871960
\(996\) −28.3607 −0.898642
\(997\) −13.1729 −0.417189 −0.208594 0.978002i \(-0.566889\pi\)
−0.208594 + 0.978002i \(0.566889\pi\)
\(998\) 66.6777 2.11064
\(999\) −37.4860 −1.18600
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.g.1.3 10
3.2 odd 2 9027.2.a.j.1.8 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1003.2.a.g.1.3 10 1.1 even 1 trivial
9027.2.a.j.1.8 10 3.2 odd 2