Properties

Label 1859.2.a.q.1.6
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $1$
Dimension $9$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1859,2,Mod(1,1859)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1859, 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("1859.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.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: \(14.8441897358\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{9} - 10x^{7} - x^{6} + 31x^{5} + 9x^{4} - 31x^{3} - 15x^{2} + 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.263492\) of defining polynomial
Character \(\chi\) \(=\) 1859.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.263492 q^{2} +1.72975 q^{3} -1.93057 q^{4} -0.976450 q^{5} +0.455775 q^{6} +0.775627 q^{7} -1.03568 q^{8} -0.00797179 q^{9} +O(q^{10})\) \(q+0.263492 q^{2} +1.72975 q^{3} -1.93057 q^{4} -0.976450 q^{5} +0.455775 q^{6} +0.775627 q^{7} -1.03568 q^{8} -0.00797179 q^{9} -0.257287 q^{10} +1.00000 q^{11} -3.33940 q^{12} +0.204372 q^{14} -1.68901 q^{15} +3.58825 q^{16} -4.83237 q^{17} -0.00210050 q^{18} +0.373766 q^{19} +1.88511 q^{20} +1.34164 q^{21} +0.263492 q^{22} +0.0494328 q^{23} -1.79146 q^{24} -4.04654 q^{25} -5.20303 q^{27} -1.49740 q^{28} -0.390176 q^{29} -0.445042 q^{30} -2.30297 q^{31} +3.01683 q^{32} +1.72975 q^{33} -1.27329 q^{34} -0.757361 q^{35} +0.0153901 q^{36} +3.31853 q^{37} +0.0984844 q^{38} +1.01129 q^{40} -2.78494 q^{41} +0.353511 q^{42} -8.64863 q^{43} -1.93057 q^{44} +0.00778405 q^{45} +0.0130252 q^{46} -7.18602 q^{47} +6.20677 q^{48} -6.39840 q^{49} -1.06623 q^{50} -8.35877 q^{51} -3.42786 q^{53} -1.37096 q^{54} -0.976450 q^{55} -0.803297 q^{56} +0.646521 q^{57} -0.102808 q^{58} +12.0408 q^{59} +3.26076 q^{60} +1.31781 q^{61} -0.606814 q^{62} -0.00618313 q^{63} -6.38159 q^{64} +0.455775 q^{66} -0.0855823 q^{67} +9.32923 q^{68} +0.0855062 q^{69} -0.199559 q^{70} -5.84251 q^{71} +0.00825618 q^{72} -7.94653 q^{73} +0.874407 q^{74} -6.99950 q^{75} -0.721582 q^{76} +0.775627 q^{77} -15.1453 q^{79} -3.50375 q^{80} -8.97602 q^{81} -0.733810 q^{82} +14.5887 q^{83} -2.59013 q^{84} +4.71856 q^{85} -2.27885 q^{86} -0.674907 q^{87} -1.03568 q^{88} -4.17837 q^{89} +0.00205104 q^{90} -0.0954335 q^{92} -3.98356 q^{93} -1.89346 q^{94} -0.364964 q^{95} +5.21835 q^{96} -14.6583 q^{97} -1.68593 q^{98} -0.00797179 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q - 5 q^{3} + 2 q^{4} - 4 q^{5} - 11 q^{6} + q^{7} + 3 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 9 q - 5 q^{3} + 2 q^{4} - 4 q^{5} - 11 q^{6} + q^{7} + 3 q^{8} + 2 q^{9} - 8 q^{10} + 9 q^{11} - 9 q^{12} + 3 q^{15} - 8 q^{16} - 8 q^{17} + 27 q^{18} - q^{19} + 12 q^{20} + 17 q^{21} - 6 q^{24} - 15 q^{25} - 23 q^{27} + 11 q^{28} - 22 q^{29} - 3 q^{30} - 6 q^{31} - 19 q^{32} - 5 q^{33} + 10 q^{34} - 15 q^{35} + 7 q^{36} - 15 q^{37} + q^{38} - 3 q^{40} + 10 q^{41} + 2 q^{42} - 19 q^{43} + 2 q^{44} - 2 q^{45} + 19 q^{46} - 2 q^{47} + 6 q^{48} - 20 q^{49} - 17 q^{50} - 2 q^{51} - 5 q^{53} - 27 q^{54} - 4 q^{55} - 16 q^{56} - 32 q^{57} - 11 q^{58} - 11 q^{59} - 6 q^{60} - 68 q^{61} - 21 q^{62} - 29 q^{63} - 23 q^{64} - 11 q^{66} + 5 q^{67} + 16 q^{68} - 34 q^{69} - 5 q^{70} - 34 q^{71} + 13 q^{72} + 26 q^{73} + q^{74} + 10 q^{75} - 11 q^{76} + q^{77} - 32 q^{79} + 8 q^{80} + 13 q^{81} - 42 q^{82} + 8 q^{83} - 13 q^{84} + 23 q^{85} + 30 q^{86} + 10 q^{87} + 3 q^{88} - 37 q^{89} + 21 q^{90} - 12 q^{92} + 20 q^{93} - 12 q^{94} - 4 q^{95} + 60 q^{96} + 3 q^{97} - 9 q^{98} + 2 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.263492 0.186317 0.0931586 0.995651i \(-0.470304\pi\)
0.0931586 + 0.995651i \(0.470304\pi\)
\(3\) 1.72975 0.998670 0.499335 0.866409i \(-0.333578\pi\)
0.499335 + 0.866409i \(0.333578\pi\)
\(4\) −1.93057 −0.965286
\(5\) −0.976450 −0.436682 −0.218341 0.975873i \(-0.570064\pi\)
−0.218341 + 0.975873i \(0.570064\pi\)
\(6\) 0.455775 0.186069
\(7\) 0.775627 0.293159 0.146580 0.989199i \(-0.453174\pi\)
0.146580 + 0.989199i \(0.453174\pi\)
\(8\) −1.03568 −0.366166
\(9\) −0.00797179 −0.00265726
\(10\) −0.257287 −0.0813613
\(11\) 1.00000 0.301511
\(12\) −3.33940 −0.964003
\(13\) 0 0
\(14\) 0.204372 0.0546206
\(15\) −1.68901 −0.436101
\(16\) 3.58825 0.897063
\(17\) −4.83237 −1.17202 −0.586010 0.810304i \(-0.699302\pi\)
−0.586010 + 0.810304i \(0.699302\pi\)
\(18\) −0.00210050 −0.000495093 0
\(19\) 0.373766 0.0857478 0.0428739 0.999080i \(-0.486349\pi\)
0.0428739 + 0.999080i \(0.486349\pi\)
\(20\) 1.88511 0.421523
\(21\) 1.34164 0.292770
\(22\) 0.263492 0.0561767
\(23\) 0.0494328 0.0103074 0.00515372 0.999987i \(-0.498360\pi\)
0.00515372 + 0.999987i \(0.498360\pi\)
\(24\) −1.79146 −0.365680
\(25\) −4.04654 −0.809309
\(26\) 0 0
\(27\) −5.20303 −1.00132
\(28\) −1.49740 −0.282983
\(29\) −0.390176 −0.0724539 −0.0362270 0.999344i \(-0.511534\pi\)
−0.0362270 + 0.999344i \(0.511534\pi\)
\(30\) −0.445042 −0.0812532
\(31\) −2.30297 −0.413625 −0.206813 0.978381i \(-0.566309\pi\)
−0.206813 + 0.978381i \(0.566309\pi\)
\(32\) 3.01683 0.533305
\(33\) 1.72975 0.301110
\(34\) −1.27329 −0.218368
\(35\) −0.757361 −0.128017
\(36\) 0.0153901 0.00256502
\(37\) 3.31853 0.545563 0.272782 0.962076i \(-0.412056\pi\)
0.272782 + 0.962076i \(0.412056\pi\)
\(38\) 0.0984844 0.0159763
\(39\) 0 0
\(40\) 1.01129 0.159898
\(41\) −2.78494 −0.434934 −0.217467 0.976068i \(-0.569779\pi\)
−0.217467 + 0.976068i \(0.569779\pi\)
\(42\) 0.353511 0.0545480
\(43\) −8.64863 −1.31890 −0.659452 0.751747i \(-0.729212\pi\)
−0.659452 + 0.751747i \(0.729212\pi\)
\(44\) −1.93057 −0.291045
\(45\) 0.00778405 0.00116038
\(46\) 0.0130252 0.00192045
\(47\) −7.18602 −1.04819 −0.524094 0.851660i \(-0.675596\pi\)
−0.524094 + 0.851660i \(0.675596\pi\)
\(48\) 6.20677 0.895870
\(49\) −6.39840 −0.914058
\(50\) −1.06623 −0.150788
\(51\) −8.35877 −1.17046
\(52\) 0 0
\(53\) −3.42786 −0.470853 −0.235426 0.971892i \(-0.575649\pi\)
−0.235426 + 0.971892i \(0.575649\pi\)
\(54\) −1.37096 −0.186564
\(55\) −0.976450 −0.131665
\(56\) −0.803297 −0.107345
\(57\) 0.646521 0.0856338
\(58\) −0.102808 −0.0134994
\(59\) 12.0408 1.56757 0.783787 0.621030i \(-0.213285\pi\)
0.783787 + 0.621030i \(0.213285\pi\)
\(60\) 3.26076 0.420962
\(61\) 1.31781 0.168729 0.0843645 0.996435i \(-0.473114\pi\)
0.0843645 + 0.996435i \(0.473114\pi\)
\(62\) −0.606814 −0.0770655
\(63\) −0.00618313 −0.000779001 0
\(64\) −6.38159 −0.797699
\(65\) 0 0
\(66\) 0.455775 0.0561020
\(67\) −0.0855823 −0.0104555 −0.00522777 0.999986i \(-0.501664\pi\)
−0.00522777 + 0.999986i \(0.501664\pi\)
\(68\) 9.32923 1.13134
\(69\) 0.0855062 0.0102937
\(70\) −0.199559 −0.0238518
\(71\) −5.84251 −0.693378 −0.346689 0.937980i \(-0.612694\pi\)
−0.346689 + 0.937980i \(0.612694\pi\)
\(72\) 0.00825618 0.000973000 0
\(73\) −7.94653 −0.930071 −0.465035 0.885292i \(-0.653958\pi\)
−0.465035 + 0.885292i \(0.653958\pi\)
\(74\) 0.874407 0.101648
\(75\) −6.99950 −0.808233
\(76\) −0.721582 −0.0827711
\(77\) 0.775627 0.0883909
\(78\) 0 0
\(79\) −15.1453 −1.70398 −0.851989 0.523559i \(-0.824604\pi\)
−0.851989 + 0.523559i \(0.824604\pi\)
\(80\) −3.50375 −0.391731
\(81\) −8.97602 −0.997336
\(82\) −0.733810 −0.0810357
\(83\) 14.5887 1.60132 0.800658 0.599121i \(-0.204483\pi\)
0.800658 + 0.599121i \(0.204483\pi\)
\(84\) −2.59013 −0.282606
\(85\) 4.71856 0.511800
\(86\) −2.27885 −0.245734
\(87\) −0.674907 −0.0723576
\(88\) −1.03568 −0.110403
\(89\) −4.17837 −0.442906 −0.221453 0.975171i \(-0.571080\pi\)
−0.221453 + 0.975171i \(0.571080\pi\)
\(90\) 0.00205104 0.000216198 0
\(91\) 0 0
\(92\) −0.0954335 −0.00994963
\(93\) −3.98356 −0.413075
\(94\) −1.89346 −0.195296
\(95\) −0.364964 −0.0374445
\(96\) 5.21835 0.532596
\(97\) −14.6583 −1.48832 −0.744161 0.668000i \(-0.767151\pi\)
−0.744161 + 0.668000i \(0.767151\pi\)
\(98\) −1.68593 −0.170305
\(99\) −0.00797179 −0.000801195 0
\(100\) 7.81215 0.781215
\(101\) −0.202281 −0.0201277 −0.0100639 0.999949i \(-0.503203\pi\)
−0.0100639 + 0.999949i \(0.503203\pi\)
\(102\) −2.20247 −0.218077
\(103\) 11.5589 1.13893 0.569467 0.822014i \(-0.307150\pi\)
0.569467 + 0.822014i \(0.307150\pi\)
\(104\) 0 0
\(105\) −1.31004 −0.127847
\(106\) −0.903214 −0.0877279
\(107\) −14.2165 −1.37436 −0.687179 0.726488i \(-0.741151\pi\)
−0.687179 + 0.726488i \(0.741151\pi\)
\(108\) 10.0448 0.966564
\(109\) 12.7076 1.21717 0.608586 0.793488i \(-0.291737\pi\)
0.608586 + 0.793488i \(0.291737\pi\)
\(110\) −0.257287 −0.0245314
\(111\) 5.74022 0.544838
\(112\) 2.78314 0.262982
\(113\) 2.41619 0.227296 0.113648 0.993521i \(-0.463746\pi\)
0.113648 + 0.993521i \(0.463746\pi\)
\(114\) 0.170353 0.0159550
\(115\) −0.0482687 −0.00450107
\(116\) 0.753264 0.0699388
\(117\) 0 0
\(118\) 3.17265 0.292066
\(119\) −3.74811 −0.343589
\(120\) 1.74927 0.159686
\(121\) 1.00000 0.0909091
\(122\) 0.347234 0.0314371
\(123\) −4.81724 −0.434356
\(124\) 4.44605 0.399267
\(125\) 8.83350 0.790092
\(126\) −0.00162921 −0.000145141 0
\(127\) 3.94265 0.349853 0.174927 0.984581i \(-0.444031\pi\)
0.174927 + 0.984581i \(0.444031\pi\)
\(128\) −7.71515 −0.681930
\(129\) −14.9600 −1.31715
\(130\) 0 0
\(131\) −15.8346 −1.38347 −0.691737 0.722150i \(-0.743154\pi\)
−0.691737 + 0.722150i \(0.743154\pi\)
\(132\) −3.33940 −0.290658
\(133\) 0.289903 0.0251378
\(134\) −0.0225503 −0.00194805
\(135\) 5.08050 0.437260
\(136\) 5.00476 0.429155
\(137\) 7.83512 0.669399 0.334700 0.942325i \(-0.391365\pi\)
0.334700 + 0.942325i \(0.391365\pi\)
\(138\) 0.0225302 0.00191790
\(139\) 1.29349 0.109712 0.0548561 0.998494i \(-0.482530\pi\)
0.0548561 + 0.998494i \(0.482530\pi\)
\(140\) 1.46214 0.123573
\(141\) −12.4300 −1.04680
\(142\) −1.53946 −0.129188
\(143\) 0 0
\(144\) −0.0286048 −0.00238373
\(145\) 0.380988 0.0316393
\(146\) −2.09385 −0.173288
\(147\) −11.0676 −0.912842
\(148\) −6.40666 −0.526624
\(149\) 13.4048 1.09816 0.549081 0.835769i \(-0.314978\pi\)
0.549081 + 0.835769i \(0.314978\pi\)
\(150\) −1.84431 −0.150588
\(151\) −19.1366 −1.55731 −0.778656 0.627451i \(-0.784098\pi\)
−0.778656 + 0.627451i \(0.784098\pi\)
\(152\) −0.387100 −0.0313980
\(153\) 0.0385226 0.00311437
\(154\) 0.204372 0.0164687
\(155\) 2.24873 0.180623
\(156\) 0 0
\(157\) 0.776709 0.0619881 0.0309940 0.999520i \(-0.490133\pi\)
0.0309940 + 0.999520i \(0.490133\pi\)
\(158\) −3.99067 −0.317480
\(159\) −5.92933 −0.470227
\(160\) −2.94578 −0.232884
\(161\) 0.0383414 0.00302172
\(162\) −2.36511 −0.185821
\(163\) 3.10254 0.243010 0.121505 0.992591i \(-0.461228\pi\)
0.121505 + 0.992591i \(0.461228\pi\)
\(164\) 5.37652 0.419836
\(165\) −1.68901 −0.131489
\(166\) 3.84401 0.298353
\(167\) −20.0392 −1.55068 −0.775339 0.631545i \(-0.782421\pi\)
−0.775339 + 0.631545i \(0.782421\pi\)
\(168\) −1.38950 −0.107202
\(169\) 0 0
\(170\) 1.24331 0.0953572
\(171\) −0.00297958 −0.000227854 0
\(172\) 16.6968 1.27312
\(173\) 15.1318 1.15045 0.575223 0.817996i \(-0.304915\pi\)
0.575223 + 0.817996i \(0.304915\pi\)
\(174\) −0.177833 −0.0134815
\(175\) −3.13861 −0.237256
\(176\) 3.58825 0.270475
\(177\) 20.8275 1.56549
\(178\) −1.10097 −0.0825210
\(179\) 5.59353 0.418080 0.209040 0.977907i \(-0.432966\pi\)
0.209040 + 0.977907i \(0.432966\pi\)
\(180\) −0.0150277 −0.00112010
\(181\) 9.81461 0.729514 0.364757 0.931103i \(-0.381152\pi\)
0.364757 + 0.931103i \(0.381152\pi\)
\(182\) 0 0
\(183\) 2.27949 0.168505
\(184\) −0.0511963 −0.00377424
\(185\) −3.24038 −0.238238
\(186\) −1.04964 −0.0769630
\(187\) −4.83237 −0.353378
\(188\) 13.8731 1.01180
\(189\) −4.03561 −0.293547
\(190\) −0.0961652 −0.00697655
\(191\) −2.45366 −0.177540 −0.0887702 0.996052i \(-0.528294\pi\)
−0.0887702 + 0.996052i \(0.528294\pi\)
\(192\) −11.0385 −0.796638
\(193\) 25.1495 1.81030 0.905149 0.425094i \(-0.139759\pi\)
0.905149 + 0.425094i \(0.139759\pi\)
\(194\) −3.86234 −0.277300
\(195\) 0 0
\(196\) 12.3526 0.882327
\(197\) 23.2584 1.65710 0.828548 0.559918i \(-0.189167\pi\)
0.828548 + 0.559918i \(0.189167\pi\)
\(198\) −0.00210050 −0.000149276 0
\(199\) −19.3989 −1.37515 −0.687577 0.726111i \(-0.741326\pi\)
−0.687577 + 0.726111i \(0.741326\pi\)
\(200\) 4.19091 0.296342
\(201\) −0.148036 −0.0104416
\(202\) −0.0532996 −0.00375014
\(203\) −0.302631 −0.0212405
\(204\) 16.1372 1.12983
\(205\) 2.71935 0.189928
\(206\) 3.04568 0.212203
\(207\) −0.000394067 0 −2.73896e−5 0
\(208\) 0 0
\(209\) 0.373766 0.0258539
\(210\) −0.345186 −0.0238201
\(211\) 21.7549 1.49767 0.748835 0.662757i \(-0.230614\pi\)
0.748835 + 0.662757i \(0.230614\pi\)
\(212\) 6.61773 0.454507
\(213\) −10.1061 −0.692457
\(214\) −3.74593 −0.256066
\(215\) 8.44496 0.575941
\(216\) 5.38865 0.366651
\(217\) −1.78624 −0.121258
\(218\) 3.34837 0.226780
\(219\) −13.7455 −0.928834
\(220\) 1.88511 0.127094
\(221\) 0 0
\(222\) 1.51250 0.101513
\(223\) 16.0649 1.07578 0.537892 0.843014i \(-0.319221\pi\)
0.537892 + 0.843014i \(0.319221\pi\)
\(224\) 2.33993 0.156343
\(225\) 0.0322582 0.00215055
\(226\) 0.636648 0.0423492
\(227\) 2.71857 0.180438 0.0902190 0.995922i \(-0.471243\pi\)
0.0902190 + 0.995922i \(0.471243\pi\)
\(228\) −1.24816 −0.0826611
\(229\) −24.2039 −1.59944 −0.799720 0.600373i \(-0.795019\pi\)
−0.799720 + 0.600373i \(0.795019\pi\)
\(230\) −0.0127184 −0.000838627 0
\(231\) 1.34164 0.0882733
\(232\) 0.404096 0.0265302
\(233\) 17.8276 1.16792 0.583962 0.811781i \(-0.301502\pi\)
0.583962 + 0.811781i \(0.301502\pi\)
\(234\) 0 0
\(235\) 7.01679 0.457725
\(236\) −23.2456 −1.51316
\(237\) −26.1975 −1.70171
\(238\) −0.987598 −0.0640165
\(239\) −8.54311 −0.552608 −0.276304 0.961070i \(-0.589110\pi\)
−0.276304 + 0.961070i \(0.589110\pi\)
\(240\) −6.06060 −0.391210
\(241\) −21.6404 −1.39398 −0.696992 0.717079i \(-0.745478\pi\)
−0.696992 + 0.717079i \(0.745478\pi\)
\(242\) 0.263492 0.0169379
\(243\) 0.0828450 0.00531451
\(244\) −2.54414 −0.162872
\(245\) 6.24772 0.399152
\(246\) −1.26931 −0.0809280
\(247\) 0 0
\(248\) 2.38513 0.151456
\(249\) 25.2348 1.59919
\(250\) 2.32756 0.147208
\(251\) 20.2272 1.27673 0.638364 0.769735i \(-0.279611\pi\)
0.638364 + 0.769735i \(0.279611\pi\)
\(252\) 0.0119370 0.000751959 0
\(253\) 0.0494328 0.00310781
\(254\) 1.03886 0.0651837
\(255\) 8.16193 0.511120
\(256\) 10.7303 0.670644
\(257\) 6.67251 0.416220 0.208110 0.978105i \(-0.433269\pi\)
0.208110 + 0.978105i \(0.433269\pi\)
\(258\) −3.94183 −0.245408
\(259\) 2.57394 0.159937
\(260\) 0 0
\(261\) 0.00311040 0.000192529 0
\(262\) −4.17229 −0.257765
\(263\) 23.7582 1.46499 0.732496 0.680771i \(-0.238355\pi\)
0.732496 + 0.680771i \(0.238355\pi\)
\(264\) −1.79146 −0.110257
\(265\) 3.34713 0.205613
\(266\) 0.0763871 0.00468360
\(267\) −7.22752 −0.442317
\(268\) 0.165223 0.0100926
\(269\) −14.5009 −0.884133 −0.442066 0.896982i \(-0.645754\pi\)
−0.442066 + 0.896982i \(0.645754\pi\)
\(270\) 1.33867 0.0814691
\(271\) 19.4590 1.18205 0.591026 0.806652i \(-0.298723\pi\)
0.591026 + 0.806652i \(0.298723\pi\)
\(272\) −17.3397 −1.05138
\(273\) 0 0
\(274\) 2.06449 0.124721
\(275\) −4.04654 −0.244016
\(276\) −0.165076 −0.00993640
\(277\) −19.6474 −1.18050 −0.590248 0.807222i \(-0.700970\pi\)
−0.590248 + 0.807222i \(0.700970\pi\)
\(278\) 0.340824 0.0204413
\(279\) 0.0183588 0.00109911
\(280\) 0.784380 0.0468757
\(281\) 9.71386 0.579480 0.289740 0.957105i \(-0.406431\pi\)
0.289740 + 0.957105i \(0.406431\pi\)
\(282\) −3.27521 −0.195036
\(283\) −8.52020 −0.506473 −0.253237 0.967404i \(-0.581495\pi\)
−0.253237 + 0.967404i \(0.581495\pi\)
\(284\) 11.2794 0.669308
\(285\) −0.631296 −0.0373947
\(286\) 0 0
\(287\) −2.16007 −0.127505
\(288\) −0.0240495 −0.00141713
\(289\) 6.35175 0.373633
\(290\) 0.100387 0.00589495
\(291\) −25.3551 −1.48634
\(292\) 15.3413 0.897784
\(293\) −9.98789 −0.583499 −0.291749 0.956495i \(-0.594237\pi\)
−0.291749 + 0.956495i \(0.594237\pi\)
\(294\) −2.91623 −0.170078
\(295\) −11.7572 −0.684531
\(296\) −3.43692 −0.199767
\(297\) −5.20303 −0.301911
\(298\) 3.53205 0.204606
\(299\) 0 0
\(300\) 13.5130 0.780176
\(301\) −6.70811 −0.386649
\(302\) −5.04234 −0.290154
\(303\) −0.349896 −0.0201010
\(304\) 1.34117 0.0769212
\(305\) −1.28678 −0.0736809
\(306\) 0.0101504 0.000580260 0
\(307\) −0.878686 −0.0501493 −0.0250746 0.999686i \(-0.507982\pi\)
−0.0250746 + 0.999686i \(0.507982\pi\)
\(308\) −1.49740 −0.0853224
\(309\) 19.9940 1.13742
\(310\) 0.592524 0.0336531
\(311\) −11.9408 −0.677101 −0.338551 0.940948i \(-0.609937\pi\)
−0.338551 + 0.940948i \(0.609937\pi\)
\(312\) 0 0
\(313\) 19.5562 1.10538 0.552691 0.833386i \(-0.313601\pi\)
0.552691 + 0.833386i \(0.313601\pi\)
\(314\) 0.204657 0.0115494
\(315\) 0.00603752 0.000340176 0
\(316\) 29.2391 1.64483
\(317\) −29.5494 −1.65966 −0.829830 0.558016i \(-0.811563\pi\)
−0.829830 + 0.558016i \(0.811563\pi\)
\(318\) −1.56233 −0.0876113
\(319\) −0.390176 −0.0218457
\(320\) 6.23131 0.348341
\(321\) −24.5909 −1.37253
\(322\) 0.0101027 0.000562999 0
\(323\) −1.80617 −0.100498
\(324\) 17.3289 0.962714
\(325\) 0 0
\(326\) 0.817495 0.0452769
\(327\) 21.9810 1.21555
\(328\) 2.88429 0.159258
\(329\) −5.57367 −0.307286
\(330\) −0.445042 −0.0244987
\(331\) 32.9803 1.81276 0.906379 0.422465i \(-0.138835\pi\)
0.906379 + 0.422465i \(0.138835\pi\)
\(332\) −28.1645 −1.54573
\(333\) −0.0264546 −0.00144970
\(334\) −5.28017 −0.288918
\(335\) 0.0835668 0.00456574
\(336\) 4.81414 0.262633
\(337\) −8.43174 −0.459306 −0.229653 0.973273i \(-0.573759\pi\)
−0.229653 + 0.973273i \(0.573759\pi\)
\(338\) 0 0
\(339\) 4.17940 0.226994
\(340\) −9.10953 −0.494034
\(341\) −2.30297 −0.124713
\(342\) −0.000785097 0 −4.24532e−5 0
\(343\) −10.3922 −0.561124
\(344\) 8.95717 0.482938
\(345\) −0.0834926 −0.00449509
\(346\) 3.98710 0.214348
\(347\) −10.5456 −0.566120 −0.283060 0.959102i \(-0.591350\pi\)
−0.283060 + 0.959102i \(0.591350\pi\)
\(348\) 1.30296 0.0698458
\(349\) 35.6573 1.90869 0.954344 0.298708i \(-0.0965558\pi\)
0.954344 + 0.298708i \(0.0965558\pi\)
\(350\) −0.826999 −0.0442049
\(351\) 0 0
\(352\) 3.01683 0.160797
\(353\) 17.7029 0.942229 0.471115 0.882072i \(-0.343852\pi\)
0.471115 + 0.882072i \(0.343852\pi\)
\(354\) 5.48788 0.291678
\(355\) 5.70492 0.302786
\(356\) 8.06663 0.427531
\(357\) −6.48329 −0.343132
\(358\) 1.47385 0.0778955
\(359\) −17.9342 −0.946533 −0.473267 0.880919i \(-0.656925\pi\)
−0.473267 + 0.880919i \(0.656925\pi\)
\(360\) −0.00806175 −0.000424892 0
\(361\) −18.8603 −0.992647
\(362\) 2.58607 0.135921
\(363\) 1.72975 0.0907882
\(364\) 0 0
\(365\) 7.75939 0.406145
\(366\) 0.600627 0.0313953
\(367\) −7.54176 −0.393676 −0.196838 0.980436i \(-0.563067\pi\)
−0.196838 + 0.980436i \(0.563067\pi\)
\(368\) 0.177377 0.00924643
\(369\) 0.0222009 0.00115573
\(370\) −0.853815 −0.0443877
\(371\) −2.65874 −0.138035
\(372\) 7.69054 0.398736
\(373\) −23.5301 −1.21834 −0.609171 0.793039i \(-0.708498\pi\)
−0.609171 + 0.793039i \(0.708498\pi\)
\(374\) −1.27329 −0.0658403
\(375\) 15.2797 0.789042
\(376\) 7.44238 0.383812
\(377\) 0 0
\(378\) −1.06335 −0.0546929
\(379\) −30.4623 −1.56475 −0.782373 0.622811i \(-0.785991\pi\)
−0.782373 + 0.622811i \(0.785991\pi\)
\(380\) 0.704589 0.0361447
\(381\) 6.81979 0.349388
\(382\) −0.646520 −0.0330788
\(383\) −31.1978 −1.59413 −0.797067 0.603891i \(-0.793616\pi\)
−0.797067 + 0.603891i \(0.793616\pi\)
\(384\) −13.3453 −0.681023
\(385\) −0.757361 −0.0385987
\(386\) 6.62669 0.337290
\(387\) 0.0689450 0.00350467
\(388\) 28.2989 1.43666
\(389\) 33.8085 1.71416 0.857079 0.515186i \(-0.172277\pi\)
0.857079 + 0.515186i \(0.172277\pi\)
\(390\) 0 0
\(391\) −0.238877 −0.0120805
\(392\) 6.62667 0.334697
\(393\) −27.3898 −1.38163
\(394\) 6.12842 0.308745
\(395\) 14.7886 0.744097
\(396\) 0.0153901 0.000773382 0
\(397\) −19.1080 −0.959004 −0.479502 0.877541i \(-0.659183\pi\)
−0.479502 + 0.877541i \(0.659183\pi\)
\(398\) −5.11147 −0.256215
\(399\) 0.501459 0.0251043
\(400\) −14.5200 −0.726001
\(401\) −21.8152 −1.08940 −0.544699 0.838632i \(-0.683356\pi\)
−0.544699 + 0.838632i \(0.683356\pi\)
\(402\) −0.0390063 −0.00194546
\(403\) 0 0
\(404\) 0.390519 0.0194290
\(405\) 8.76464 0.435518
\(406\) −0.0797410 −0.00395748
\(407\) 3.31853 0.164493
\(408\) 8.65698 0.428584
\(409\) −10.2357 −0.506123 −0.253062 0.967450i \(-0.581438\pi\)
−0.253062 + 0.967450i \(0.581438\pi\)
\(410\) 0.716529 0.0353868
\(411\) 13.5528 0.668510
\(412\) −22.3153 −1.09940
\(413\) 9.33913 0.459549
\(414\) −0.000103834 0 −5.10315e−6 0
\(415\) −14.2451 −0.699266
\(416\) 0 0
\(417\) 2.23741 0.109566
\(418\) 0.0984844 0.00481703
\(419\) −4.54655 −0.222113 −0.111057 0.993814i \(-0.535424\pi\)
−0.111057 + 0.993814i \(0.535424\pi\)
\(420\) 2.52913 0.123409
\(421\) −2.57565 −0.125529 −0.0627647 0.998028i \(-0.519992\pi\)
−0.0627647 + 0.998028i \(0.519992\pi\)
\(422\) 5.73225 0.279042
\(423\) 0.0572854 0.00278531
\(424\) 3.55015 0.172410
\(425\) 19.5544 0.948527
\(426\) −2.66287 −0.129017
\(427\) 1.02213 0.0494644
\(428\) 27.4459 1.32665
\(429\) 0 0
\(430\) 2.22518 0.107308
\(431\) −22.8922 −1.10268 −0.551340 0.834281i \(-0.685883\pi\)
−0.551340 + 0.834281i \(0.685883\pi\)
\(432\) −18.6698 −0.898251
\(433\) −14.1020 −0.677700 −0.338850 0.940840i \(-0.610038\pi\)
−0.338850 + 0.940840i \(0.610038\pi\)
\(434\) −0.470661 −0.0225925
\(435\) 0.659013 0.0315973
\(436\) −24.5330 −1.17492
\(437\) 0.0184763 0.000883841 0
\(438\) −3.62183 −0.173058
\(439\) 25.3673 1.21071 0.605357 0.795954i \(-0.293030\pi\)
0.605357 + 0.795954i \(0.293030\pi\)
\(440\) 1.01129 0.0482111
\(441\) 0.0510067 0.00242889
\(442\) 0 0
\(443\) −7.84745 −0.372844 −0.186422 0.982470i \(-0.559689\pi\)
−0.186422 + 0.982470i \(0.559689\pi\)
\(444\) −11.0819 −0.525924
\(445\) 4.07997 0.193409
\(446\) 4.23297 0.200437
\(447\) 23.1869 1.09670
\(448\) −4.94973 −0.233853
\(449\) −9.41851 −0.444487 −0.222244 0.974991i \(-0.571338\pi\)
−0.222244 + 0.974991i \(0.571338\pi\)
\(450\) 0.00849978 0.000400684 0
\(451\) −2.78494 −0.131138
\(452\) −4.66463 −0.219406
\(453\) −33.1014 −1.55524
\(454\) 0.716323 0.0336187
\(455\) 0 0
\(456\) −0.669586 −0.0313562
\(457\) 30.0349 1.40497 0.702487 0.711696i \(-0.252073\pi\)
0.702487 + 0.711696i \(0.252073\pi\)
\(458\) −6.37755 −0.298003
\(459\) 25.1430 1.17357
\(460\) 0.0931861 0.00434482
\(461\) 5.52451 0.257302 0.128651 0.991690i \(-0.458935\pi\)
0.128651 + 0.991690i \(0.458935\pi\)
\(462\) 0.353511 0.0164468
\(463\) −12.9560 −0.602116 −0.301058 0.953606i \(-0.597340\pi\)
−0.301058 + 0.953606i \(0.597340\pi\)
\(464\) −1.40005 −0.0649957
\(465\) 3.88974 0.180383
\(466\) 4.69743 0.217604
\(467\) 41.3398 1.91298 0.956490 0.291766i \(-0.0942430\pi\)
0.956490 + 0.291766i \(0.0942430\pi\)
\(468\) 0 0
\(469\) −0.0663799 −0.00306514
\(470\) 1.84887 0.0852820
\(471\) 1.34351 0.0619057
\(472\) −12.4703 −0.573993
\(473\) −8.64863 −0.397664
\(474\) −6.90285 −0.317058
\(475\) −1.51246 −0.0693965
\(476\) 7.23600 0.331661
\(477\) 0.0273261 0.00125118
\(478\) −2.25104 −0.102960
\(479\) 5.83127 0.266437 0.133219 0.991087i \(-0.457469\pi\)
0.133219 + 0.991087i \(0.457469\pi\)
\(480\) −5.09546 −0.232575
\(481\) 0 0
\(482\) −5.70209 −0.259723
\(483\) 0.0663209 0.00301771
\(484\) −1.93057 −0.0877533
\(485\) 14.3131 0.649923
\(486\) 0.0218290 0.000990184 0
\(487\) −4.92176 −0.223026 −0.111513 0.993763i \(-0.535570\pi\)
−0.111513 + 0.993763i \(0.535570\pi\)
\(488\) −1.36483 −0.0617829
\(489\) 5.36661 0.242687
\(490\) 1.64623 0.0743689
\(491\) 17.3615 0.783515 0.391758 0.920069i \(-0.371867\pi\)
0.391758 + 0.920069i \(0.371867\pi\)
\(492\) 9.30003 0.419278
\(493\) 1.88547 0.0849175
\(494\) 0 0
\(495\) 0.00778405 0.000349867 0
\(496\) −8.26363 −0.371048
\(497\) −4.53161 −0.203270
\(498\) 6.64916 0.297956
\(499\) −15.1483 −0.678131 −0.339066 0.940763i \(-0.610111\pi\)
−0.339066 + 0.940763i \(0.610111\pi\)
\(500\) −17.0537 −0.762665
\(501\) −34.6627 −1.54862
\(502\) 5.32970 0.237876
\(503\) 15.3714 0.685375 0.342687 0.939449i \(-0.388663\pi\)
0.342687 + 0.939449i \(0.388663\pi\)
\(504\) 0.00640371 0.000285244 0
\(505\) 0.197518 0.00878942
\(506\) 0.0130252 0.000579039 0
\(507\) 0 0
\(508\) −7.61157 −0.337709
\(509\) 34.3660 1.52325 0.761624 0.648019i \(-0.224402\pi\)
0.761624 + 0.648019i \(0.224402\pi\)
\(510\) 2.15060 0.0952304
\(511\) −6.16354 −0.272659
\(512\) 18.2577 0.806882
\(513\) −1.94472 −0.0858613
\(514\) 1.75816 0.0775489
\(515\) −11.2867 −0.497352
\(516\) 28.8813 1.27143
\(517\) −7.18602 −0.316041
\(518\) 0.678213 0.0297990
\(519\) 26.1741 1.14892
\(520\) 0 0
\(521\) 26.2698 1.15090 0.575451 0.817836i \(-0.304826\pi\)
0.575451 + 0.817836i \(0.304826\pi\)
\(522\) 0.000819567 0 3.58715e−5 0
\(523\) 8.63548 0.377603 0.188802 0.982015i \(-0.439540\pi\)
0.188802 + 0.982015i \(0.439540\pi\)
\(524\) 30.5698 1.33545
\(525\) −5.42900 −0.236941
\(526\) 6.26010 0.272953
\(527\) 11.1288 0.484777
\(528\) 6.20677 0.270115
\(529\) −22.9976 −0.999894
\(530\) 0.881944 0.0383092
\(531\) −0.0959864 −0.00416545
\(532\) −0.559678 −0.0242651
\(533\) 0 0
\(534\) −1.90440 −0.0824112
\(535\) 13.8817 0.600157
\(536\) 0.0886354 0.00382847
\(537\) 9.67540 0.417524
\(538\) −3.82086 −0.164729
\(539\) −6.39840 −0.275599
\(540\) −9.80828 −0.422081
\(541\) 44.0739 1.89489 0.947443 0.319925i \(-0.103658\pi\)
0.947443 + 0.319925i \(0.103658\pi\)
\(542\) 5.12730 0.220237
\(543\) 16.9768 0.728544
\(544\) −14.5784 −0.625044
\(545\) −12.4084 −0.531517
\(546\) 0 0
\(547\) 5.61458 0.240062 0.120031 0.992770i \(-0.461701\pi\)
0.120031 + 0.992770i \(0.461701\pi\)
\(548\) −15.1263 −0.646162
\(549\) −0.0105053 −0.000448357 0
\(550\) −1.06623 −0.0454643
\(551\) −0.145835 −0.00621277
\(552\) −0.0885567 −0.00376922
\(553\) −11.7471 −0.499537
\(554\) −5.17693 −0.219947
\(555\) −5.60504 −0.237921
\(556\) −2.49717 −0.105904
\(557\) 2.68740 0.113869 0.0569345 0.998378i \(-0.481867\pi\)
0.0569345 + 0.998378i \(0.481867\pi\)
\(558\) 0.00483739 0.000204783 0
\(559\) 0 0
\(560\) −2.71760 −0.114840
\(561\) −8.35877 −0.352908
\(562\) 2.55953 0.107967
\(563\) −24.8840 −1.04874 −0.524368 0.851492i \(-0.675698\pi\)
−0.524368 + 0.851492i \(0.675698\pi\)
\(564\) 23.9970 1.01046
\(565\) −2.35929 −0.0992561
\(566\) −2.24501 −0.0943647
\(567\) −6.96204 −0.292378
\(568\) 6.05094 0.253892
\(569\) 38.3160 1.60629 0.803146 0.595782i \(-0.203158\pi\)
0.803146 + 0.595782i \(0.203158\pi\)
\(570\) −0.166342 −0.00696728
\(571\) −6.29021 −0.263237 −0.131618 0.991300i \(-0.542017\pi\)
−0.131618 + 0.991300i \(0.542017\pi\)
\(572\) 0 0
\(573\) −4.24421 −0.177304
\(574\) −0.569162 −0.0237564
\(575\) −0.200032 −0.00834191
\(576\) 0.0508727 0.00211969
\(577\) −31.2456 −1.30077 −0.650385 0.759605i \(-0.725392\pi\)
−0.650385 + 0.759605i \(0.725392\pi\)
\(578\) 1.67364 0.0696141
\(579\) 43.5022 1.80789
\(580\) −0.735524 −0.0305410
\(581\) 11.3154 0.469441
\(582\) −6.68088 −0.276931
\(583\) −3.42786 −0.141967
\(584\) 8.23002 0.340561
\(585\) 0 0
\(586\) −2.63173 −0.108716
\(587\) −8.59755 −0.354859 −0.177429 0.984134i \(-0.556778\pi\)
−0.177429 + 0.984134i \(0.556778\pi\)
\(588\) 21.3668 0.881154
\(589\) −0.860771 −0.0354675
\(590\) −3.09793 −0.127540
\(591\) 40.2312 1.65489
\(592\) 11.9077 0.489404
\(593\) 29.9426 1.22959 0.614797 0.788685i \(-0.289238\pi\)
0.614797 + 0.788685i \(0.289238\pi\)
\(594\) −1.37096 −0.0562511
\(595\) 3.65984 0.150039
\(596\) −25.8789 −1.06004
\(597\) −33.5553 −1.37333
\(598\) 0 0
\(599\) −27.2184 −1.11211 −0.556057 0.831144i \(-0.687687\pi\)
−0.556057 + 0.831144i \(0.687687\pi\)
\(600\) 7.24921 0.295948
\(601\) −26.1539 −1.06684 −0.533419 0.845851i \(-0.679093\pi\)
−0.533419 + 0.845851i \(0.679093\pi\)
\(602\) −1.76753 −0.0720393
\(603\) 0.000682243 0 2.77831e−5 0
\(604\) 36.9445 1.50325
\(605\) −0.976450 −0.0396984
\(606\) −0.0921948 −0.00374516
\(607\) −14.4023 −0.584573 −0.292286 0.956331i \(-0.594416\pi\)
−0.292286 + 0.956331i \(0.594416\pi\)
\(608\) 1.12759 0.0457297
\(609\) −0.523476 −0.0212123
\(610\) −0.339057 −0.0137280
\(611\) 0 0
\(612\) −0.0743706 −0.00300625
\(613\) 23.2677 0.939774 0.469887 0.882726i \(-0.344295\pi\)
0.469887 + 0.882726i \(0.344295\pi\)
\(614\) −0.231527 −0.00934367
\(615\) 4.70380 0.189675
\(616\) −0.803297 −0.0323658
\(617\) −23.7698 −0.956934 −0.478467 0.878105i \(-0.658807\pi\)
−0.478467 + 0.878105i \(0.658807\pi\)
\(618\) 5.26827 0.211921
\(619\) −37.3418 −1.50090 −0.750448 0.660930i \(-0.770162\pi\)
−0.750448 + 0.660930i \(0.770162\pi\)
\(620\) −4.34134 −0.174353
\(621\) −0.257200 −0.0103211
\(622\) −3.14631 −0.126156
\(623\) −3.24085 −0.129842
\(624\) 0 0
\(625\) 11.6072 0.464290
\(626\) 5.15291 0.205952
\(627\) 0.646521 0.0258196
\(628\) −1.49949 −0.0598362
\(629\) −16.0364 −0.639411
\(630\) 0.00159084 6.33806e−5 0
\(631\) 6.86579 0.273323 0.136661 0.990618i \(-0.456363\pi\)
0.136661 + 0.990618i \(0.456363\pi\)
\(632\) 15.6856 0.623940
\(633\) 37.6305 1.49568
\(634\) −7.78604 −0.309223
\(635\) −3.84980 −0.152775
\(636\) 11.4470 0.453903
\(637\) 0 0
\(638\) −0.102808 −0.00407023
\(639\) 0.0465752 0.00184249
\(640\) 7.53346 0.297786
\(641\) 18.3310 0.724031 0.362016 0.932172i \(-0.382089\pi\)
0.362016 + 0.932172i \(0.382089\pi\)
\(642\) −6.47951 −0.255726
\(643\) −17.7938 −0.701720 −0.350860 0.936428i \(-0.614111\pi\)
−0.350860 + 0.936428i \(0.614111\pi\)
\(644\) −0.0740208 −0.00291683
\(645\) 14.6077 0.575176
\(646\) −0.475913 −0.0187245
\(647\) 8.89493 0.349696 0.174848 0.984595i \(-0.444057\pi\)
0.174848 + 0.984595i \(0.444057\pi\)
\(648\) 9.29624 0.365191
\(649\) 12.0408 0.472641
\(650\) 0 0
\(651\) −3.08975 −0.121097
\(652\) −5.98968 −0.234574
\(653\) 3.84991 0.150659 0.0753293 0.997159i \(-0.475999\pi\)
0.0753293 + 0.997159i \(0.475999\pi\)
\(654\) 5.79183 0.226478
\(655\) 15.4617 0.604138
\(656\) −9.99306 −0.390163
\(657\) 0.0633480 0.00247144
\(658\) −1.46862 −0.0572527
\(659\) 7.26528 0.283015 0.141508 0.989937i \(-0.454805\pi\)
0.141508 + 0.989937i \(0.454805\pi\)
\(660\) 3.26076 0.126925
\(661\) −12.0382 −0.468230 −0.234115 0.972209i \(-0.575219\pi\)
−0.234115 + 0.972209i \(0.575219\pi\)
\(662\) 8.69004 0.337748
\(663\) 0 0
\(664\) −15.1091 −0.586348
\(665\) −0.283076 −0.0109772
\(666\) −0.00697059 −0.000270105 0
\(667\) −0.0192875 −0.000746815 0
\(668\) 38.6871 1.49685
\(669\) 27.7882 1.07435
\(670\) 0.0220192 0.000850676 0
\(671\) 1.31781 0.0508737
\(672\) 4.04749 0.156135
\(673\) −19.1151 −0.736832 −0.368416 0.929661i \(-0.620100\pi\)
−0.368416 + 0.929661i \(0.620100\pi\)
\(674\) −2.22170 −0.0855766
\(675\) 21.0543 0.810381
\(676\) 0 0
\(677\) 16.8824 0.648844 0.324422 0.945912i \(-0.394830\pi\)
0.324422 + 0.945912i \(0.394830\pi\)
\(678\) 1.10124 0.0422929
\(679\) −11.3693 −0.436316
\(680\) −4.88690 −0.187404
\(681\) 4.70245 0.180198
\(682\) −0.606814 −0.0232361
\(683\) 16.5802 0.634423 0.317212 0.948355i \(-0.397253\pi\)
0.317212 + 0.948355i \(0.397253\pi\)
\(684\) 0.00575230 0.000219945 0
\(685\) −7.65061 −0.292315
\(686\) −2.73825 −0.104547
\(687\) −41.8667 −1.59731
\(688\) −31.0335 −1.18314
\(689\) 0 0
\(690\) −0.0219997 −0.000837513 0
\(691\) −18.5861 −0.707047 −0.353523 0.935426i \(-0.615017\pi\)
−0.353523 + 0.935426i \(0.615017\pi\)
\(692\) −29.2130 −1.11051
\(693\) −0.00618313 −0.000234878 0
\(694\) −2.77870 −0.105478
\(695\) −1.26303 −0.0479093
\(696\) 0.698984 0.0264949
\(697\) 13.4578 0.509752
\(698\) 9.39541 0.355621
\(699\) 30.8372 1.16637
\(700\) 6.05931 0.229020
\(701\) −51.0772 −1.92916 −0.964579 0.263793i \(-0.915026\pi\)
−0.964579 + 0.263793i \(0.915026\pi\)
\(702\) 0 0
\(703\) 1.24035 0.0467808
\(704\) −6.38159 −0.240515
\(705\) 12.1373 0.457117
\(706\) 4.66457 0.175553
\(707\) −0.156895 −0.00590064
\(708\) −40.2090 −1.51115
\(709\) 6.26174 0.235165 0.117582 0.993063i \(-0.462486\pi\)
0.117582 + 0.993063i \(0.462486\pi\)
\(710\) 1.50320 0.0564142
\(711\) 0.120735 0.00452792
\(712\) 4.32743 0.162177
\(713\) −0.113842 −0.00426342
\(714\) −1.70830 −0.0639314
\(715\) 0 0
\(716\) −10.7987 −0.403567
\(717\) −14.7774 −0.551873
\(718\) −4.72554 −0.176355
\(719\) 2.84647 0.106155 0.0530776 0.998590i \(-0.483097\pi\)
0.0530776 + 0.998590i \(0.483097\pi\)
\(720\) 0.0279311 0.00104093
\(721\) 8.96540 0.333889
\(722\) −4.96954 −0.184947
\(723\) −37.4325 −1.39213
\(724\) −18.9478 −0.704190
\(725\) 1.57887 0.0586376
\(726\) 0.455775 0.0169154
\(727\) −24.5240 −0.909545 −0.454772 0.890608i \(-0.650279\pi\)
−0.454772 + 0.890608i \(0.650279\pi\)
\(728\) 0 0
\(729\) 27.0714 1.00264
\(730\) 2.04454 0.0756718
\(731\) 41.7933 1.54578
\(732\) −4.40071 −0.162655
\(733\) −3.78597 −0.139838 −0.0699191 0.997553i \(-0.522274\pi\)
−0.0699191 + 0.997553i \(0.522274\pi\)
\(734\) −1.98719 −0.0733487
\(735\) 10.8070 0.398622
\(736\) 0.149130 0.00549701
\(737\) −0.0855823 −0.00315246
\(738\) 0.00584977 0.000215333 0
\(739\) 33.0302 1.21503 0.607517 0.794307i \(-0.292166\pi\)
0.607517 + 0.794307i \(0.292166\pi\)
\(740\) 6.25579 0.229967
\(741\) 0 0
\(742\) −0.700557 −0.0257183
\(743\) 42.2022 1.54825 0.774125 0.633033i \(-0.218190\pi\)
0.774125 + 0.633033i \(0.218190\pi\)
\(744\) 4.12567 0.151254
\(745\) −13.0891 −0.479547
\(746\) −6.20000 −0.226998
\(747\) −0.116298 −0.00425512
\(748\) 9.32923 0.341110
\(749\) −11.0267 −0.402906
\(750\) 4.02609 0.147012
\(751\) −1.51083 −0.0551311 −0.0275655 0.999620i \(-0.508775\pi\)
−0.0275655 + 0.999620i \(0.508775\pi\)
\(752\) −25.7853 −0.940291
\(753\) 34.9879 1.27503
\(754\) 0 0
\(755\) 18.6859 0.680050
\(756\) 7.79104 0.283357
\(757\) −6.97665 −0.253571 −0.126785 0.991930i \(-0.540466\pi\)
−0.126785 + 0.991930i \(0.540466\pi\)
\(758\) −8.02659 −0.291539
\(759\) 0.0855062 0.00310368
\(760\) 0.377984 0.0137109
\(761\) 39.9612 1.44859 0.724296 0.689489i \(-0.242165\pi\)
0.724296 + 0.689489i \(0.242165\pi\)
\(762\) 1.79696 0.0650970
\(763\) 9.85639 0.356825
\(764\) 4.73696 0.171377
\(765\) −0.0376154 −0.00135999
\(766\) −8.22038 −0.297015
\(767\) 0 0
\(768\) 18.5607 0.669752
\(769\) −19.8747 −0.716702 −0.358351 0.933587i \(-0.616661\pi\)
−0.358351 + 0.933587i \(0.616661\pi\)
\(770\) −0.199559 −0.00719160
\(771\) 11.5418 0.415667
\(772\) −48.5529 −1.74746
\(773\) −30.3791 −1.09266 −0.546330 0.837570i \(-0.683976\pi\)
−0.546330 + 0.837570i \(0.683976\pi\)
\(774\) 0.0181665 0.000652981 0
\(775\) 9.31906 0.334751
\(776\) 15.1812 0.544974
\(777\) 4.45227 0.159724
\(778\) 8.90827 0.319377
\(779\) −1.04091 −0.0372946
\(780\) 0 0
\(781\) −5.84251 −0.209061
\(782\) −0.0629423 −0.00225081
\(783\) 2.03010 0.0725499
\(784\) −22.9591 −0.819967
\(785\) −0.758417 −0.0270691
\(786\) −7.21701 −0.257422
\(787\) 13.9900 0.498690 0.249345 0.968415i \(-0.419785\pi\)
0.249345 + 0.968415i \(0.419785\pi\)
\(788\) −44.9021 −1.59957
\(789\) 41.0957 1.46304
\(790\) 3.89669 0.138638
\(791\) 1.87406 0.0666340
\(792\) 0.00825618 0.000293371 0
\(793\) 0 0
\(794\) −5.03481 −0.178679
\(795\) 5.78970 0.205339
\(796\) 37.4511 1.32742
\(797\) −30.6940 −1.08724 −0.543619 0.839332i \(-0.682946\pi\)
−0.543619 + 0.839332i \(0.682946\pi\)
\(798\) 0.132131 0.00467737
\(799\) 34.7255 1.22850
\(800\) −12.2077 −0.431608
\(801\) 0.0333090 0.00117692
\(802\) −5.74813 −0.202973
\(803\) −7.94653 −0.280427
\(804\) 0.285794 0.0100792
\(805\) −0.0374384 −0.00131953
\(806\) 0 0
\(807\) −25.0828 −0.882957
\(808\) 0.209498 0.00737011
\(809\) 15.6130 0.548922 0.274461 0.961598i \(-0.411501\pi\)
0.274461 + 0.961598i \(0.411501\pi\)
\(810\) 2.30941 0.0811446
\(811\) 26.9841 0.947541 0.473770 0.880648i \(-0.342893\pi\)
0.473770 + 0.880648i \(0.342893\pi\)
\(812\) 0.584251 0.0205032
\(813\) 33.6592 1.18048
\(814\) 0.874407 0.0306480
\(815\) −3.02948 −0.106118
\(816\) −29.9934 −1.04998
\(817\) −3.23256 −0.113093
\(818\) −2.69703 −0.0942994
\(819\) 0 0
\(820\) −5.24991 −0.183335
\(821\) −50.1848 −1.75146 −0.875731 0.482799i \(-0.839620\pi\)
−0.875731 + 0.482799i \(0.839620\pi\)
\(822\) 3.57105 0.124555
\(823\) −46.8136 −1.63182 −0.815910 0.578179i \(-0.803764\pi\)
−0.815910 + 0.578179i \(0.803764\pi\)
\(824\) −11.9713 −0.417039
\(825\) −6.99950 −0.243691
\(826\) 2.46079 0.0856218
\(827\) 20.8413 0.724723 0.362362 0.932038i \(-0.381971\pi\)
0.362362 + 0.932038i \(0.381971\pi\)
\(828\) 0.000760776 0 2.64388e−5 0
\(829\) −53.2741 −1.85029 −0.925144 0.379617i \(-0.876056\pi\)
−0.925144 + 0.379617i \(0.876056\pi\)
\(830\) −3.75348 −0.130285
\(831\) −33.9850 −1.17893
\(832\) 0 0
\(833\) 30.9194 1.07129
\(834\) 0.589539 0.0204141
\(835\) 19.5673 0.677153
\(836\) −0.721582 −0.0249564
\(837\) 11.9824 0.414173
\(838\) −1.19798 −0.0413835
\(839\) 0.119197 0.00411514 0.00205757 0.999998i \(-0.499345\pi\)
0.00205757 + 0.999998i \(0.499345\pi\)
\(840\) 1.35678 0.0468133
\(841\) −28.8478 −0.994750
\(842\) −0.678663 −0.0233883
\(843\) 16.8025 0.578710
\(844\) −41.9994 −1.44568
\(845\) 0 0
\(846\) 0.0150943 0.000518951 0
\(847\) 0.775627 0.0266508
\(848\) −12.3000 −0.422384
\(849\) −14.7378 −0.505800
\(850\) 5.15243 0.176727
\(851\) 0.164044 0.00562336
\(852\) 19.5105 0.668419
\(853\) −35.2244 −1.20606 −0.603030 0.797718i \(-0.706040\pi\)
−0.603030 + 0.797718i \(0.706040\pi\)
\(854\) 0.269324 0.00921608
\(855\) 0.00290941 9.94999e−5 0
\(856\) 14.7236 0.503244
\(857\) −10.9308 −0.373388 −0.186694 0.982418i \(-0.559777\pi\)
−0.186694 + 0.982418i \(0.559777\pi\)
\(858\) 0 0
\(859\) −18.6770 −0.637252 −0.318626 0.947880i \(-0.603221\pi\)
−0.318626 + 0.947880i \(0.603221\pi\)
\(860\) −16.3036 −0.555948
\(861\) −3.73638 −0.127335
\(862\) −6.03192 −0.205448
\(863\) −32.8465 −1.11811 −0.559054 0.829131i \(-0.688836\pi\)
−0.559054 + 0.829131i \(0.688836\pi\)
\(864\) −15.6967 −0.534011
\(865\) −14.7754 −0.502379
\(866\) −3.71578 −0.126267
\(867\) 10.9869 0.373136
\(868\) 3.44847 0.117049
\(869\) −15.1453 −0.513769
\(870\) 0.173645 0.00588711
\(871\) 0 0
\(872\) −13.1610 −0.445687
\(873\) 0.116853 0.00395486
\(874\) 0.00486836 0.000164675 0
\(875\) 6.85150 0.231623
\(876\) 26.5367 0.896591
\(877\) 35.5874 1.20170 0.600850 0.799362i \(-0.294829\pi\)
0.600850 + 0.799362i \(0.294829\pi\)
\(878\) 6.68408 0.225577
\(879\) −17.2765 −0.582723
\(880\) −3.50375 −0.118111
\(881\) −46.3588 −1.56187 −0.780933 0.624614i \(-0.785256\pi\)
−0.780933 + 0.624614i \(0.785256\pi\)
\(882\) 0.0134399 0.000452544 0
\(883\) −30.5731 −1.02887 −0.514434 0.857530i \(-0.671998\pi\)
−0.514434 + 0.857530i \(0.671998\pi\)
\(884\) 0 0
\(885\) −20.3370 −0.683621
\(886\) −2.06774 −0.0694672
\(887\) −43.8421 −1.47207 −0.736036 0.676942i \(-0.763305\pi\)
−0.736036 + 0.676942i \(0.763305\pi\)
\(888\) −5.94501 −0.199501
\(889\) 3.05802 0.102563
\(890\) 1.07504 0.0360354
\(891\) −8.97602 −0.300708
\(892\) −31.0144 −1.03844
\(893\) −2.68589 −0.0898799
\(894\) 6.10956 0.204334
\(895\) −5.46181 −0.182568
\(896\) −5.98408 −0.199914
\(897\) 0 0
\(898\) −2.48170 −0.0828156
\(899\) 0.898564 0.0299688
\(900\) −0.0622767 −0.00207589
\(901\) 16.5647 0.551849
\(902\) −0.733810 −0.0244332
\(903\) −11.6033 −0.386135
\(904\) −2.50239 −0.0832282
\(905\) −9.58348 −0.318566
\(906\) −8.72197 −0.289768
\(907\) −45.3727 −1.50658 −0.753289 0.657690i \(-0.771534\pi\)
−0.753289 + 0.657690i \(0.771534\pi\)
\(908\) −5.24840 −0.174174
\(909\) 0.00161254 5.34847e−5 0
\(910\) 0 0
\(911\) −46.2313 −1.53171 −0.765856 0.643013i \(-0.777684\pi\)
−0.765856 + 0.643013i \(0.777684\pi\)
\(912\) 2.31988 0.0768189
\(913\) 14.5887 0.482815
\(914\) 7.91397 0.261771
\(915\) −2.22581 −0.0735829
\(916\) 46.7274 1.54392
\(917\) −12.2817 −0.405578
\(918\) 6.62497 0.218657
\(919\) −48.2463 −1.59150 −0.795750 0.605625i \(-0.792923\pi\)
−0.795750 + 0.605625i \(0.792923\pi\)
\(920\) 0.0499906 0.00164814
\(921\) −1.51991 −0.0500826
\(922\) 1.45567 0.0479398
\(923\) 0 0
\(924\) −2.59013 −0.0852090
\(925\) −13.4286 −0.441529
\(926\) −3.41381 −0.112185
\(927\) −0.0921452 −0.00302645
\(928\) −1.17709 −0.0386400
\(929\) −3.40932 −0.111856 −0.0559280 0.998435i \(-0.517812\pi\)
−0.0559280 + 0.998435i \(0.517812\pi\)
\(930\) 1.02492 0.0336084
\(931\) −2.39151 −0.0783784
\(932\) −34.4174 −1.12738
\(933\) −20.6546 −0.676201
\(934\) 10.8927 0.356421
\(935\) 4.71856 0.154314
\(936\) 0 0
\(937\) −34.6118 −1.13072 −0.565360 0.824844i \(-0.691263\pi\)
−0.565360 + 0.824844i \(0.691263\pi\)
\(938\) −0.0174906 −0.000571088 0
\(939\) 33.8273 1.10391
\(940\) −13.5464 −0.441836
\(941\) 32.9559 1.07433 0.537165 0.843477i \(-0.319495\pi\)
0.537165 + 0.843477i \(0.319495\pi\)
\(942\) 0.354005 0.0115341
\(943\) −0.137667 −0.00448306
\(944\) 43.2053 1.40621
\(945\) 3.94057 0.128187
\(946\) −2.27885 −0.0740917
\(947\) 13.5265 0.439552 0.219776 0.975550i \(-0.429467\pi\)
0.219776 + 0.975550i \(0.429467\pi\)
\(948\) 50.5762 1.64264
\(949\) 0 0
\(950\) −0.398522 −0.0129298
\(951\) −51.1130 −1.65745
\(952\) 3.88183 0.125811
\(953\) −35.2197 −1.14088 −0.570440 0.821340i \(-0.693227\pi\)
−0.570440 + 0.821340i \(0.693227\pi\)
\(954\) 0.00720023 0.000233116 0
\(955\) 2.39588 0.0775287
\(956\) 16.4931 0.533424
\(957\) −0.674907 −0.0218166
\(958\) 1.53649 0.0496419
\(959\) 6.07713 0.196241
\(960\) 10.7786 0.347878
\(961\) −25.6963 −0.828914
\(962\) 0 0
\(963\) 0.113331 0.00365203
\(964\) 41.7784 1.34559
\(965\) −24.5572 −0.790525
\(966\) 0.0174750 0.000562250 0
\(967\) −23.4856 −0.755244 −0.377622 0.925960i \(-0.623258\pi\)
−0.377622 + 0.925960i \(0.623258\pi\)
\(968\) −1.03568 −0.0332879
\(969\) −3.12423 −0.100365
\(970\) 3.77139 0.121092
\(971\) 48.6664 1.56178 0.780890 0.624668i \(-0.214766\pi\)
0.780890 + 0.624668i \(0.214766\pi\)
\(972\) −0.159938 −0.00513002
\(973\) 1.00326 0.0321631
\(974\) −1.29685 −0.0415536
\(975\) 0 0
\(976\) 4.72865 0.151360
\(977\) 15.1199 0.483729 0.241865 0.970310i \(-0.422241\pi\)
0.241865 + 0.970310i \(0.422241\pi\)
\(978\) 1.41406 0.0452167
\(979\) −4.17837 −0.133541
\(980\) −12.0617 −0.385296
\(981\) −0.101303 −0.00323434
\(982\) 4.57463 0.145982
\(983\) −34.0595 −1.08633 −0.543165 0.839626i \(-0.682774\pi\)
−0.543165 + 0.839626i \(0.682774\pi\)
\(984\) 4.98910 0.159047
\(985\) −22.7107 −0.723624
\(986\) 0.496808 0.0158216
\(987\) −9.64104 −0.306878
\(988\) 0 0
\(989\) −0.427526 −0.0135945
\(990\) 0.00205104 6.51863e−5 0
\(991\) −9.72217 −0.308835 −0.154418 0.988006i \(-0.549350\pi\)
−0.154418 + 0.988006i \(0.549350\pi\)
\(992\) −6.94766 −0.220588
\(993\) 57.0475 1.81035
\(994\) −1.19404 −0.0378727
\(995\) 18.9421 0.600505
\(996\) −48.7175 −1.54367
\(997\) 12.5275 0.396749 0.198375 0.980126i \(-0.436434\pi\)
0.198375 + 0.980126i \(0.436434\pi\)
\(998\) −3.99146 −0.126347
\(999\) −17.2664 −0.546286
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 1859.2.a.q.1.6 9
13.12 even 2 1859.2.a.r.1.4 yes 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.2.a.q.1.6 9 1.1 even 1 trivial
1859.2.a.r.1.4 yes 9 13.12 even 2