Properties

Label 6045.2.a.bi.1.11
Level $6045$
Weight $2$
Character 6045.1
Self dual yes
Analytic conductor $48.270$
Analytic rank $0$
Dimension $18$
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] = [6045,2,Mod(1,6045)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6045, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("6045.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6045.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: \(48.2695680219\)
Analytic rank: \(0\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 4 x^{17} - 21 x^{16} + 97 x^{15} + 156 x^{14} - 935 x^{13} - 411 x^{12} + 4582 x^{11} - 446 x^{10} - 12159 x^{9} + 4398 x^{8} + 17347 x^{7} - 7839 x^{6} - 12832 x^{5} + \cdots - 112 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(0.925440\) of defining polynomial
Character \(\chi\) \(=\) 6045.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.925440 q^{2} +1.00000 q^{3} -1.14356 q^{4} +1.00000 q^{5} +0.925440 q^{6} -0.122708 q^{7} -2.90918 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.925440 q^{2} +1.00000 q^{3} -1.14356 q^{4} +1.00000 q^{5} +0.925440 q^{6} -0.122708 q^{7} -2.90918 q^{8} +1.00000 q^{9} +0.925440 q^{10} -1.64812 q^{11} -1.14356 q^{12} -1.00000 q^{13} -0.113559 q^{14} +1.00000 q^{15} -0.405146 q^{16} +1.77746 q^{17} +0.925440 q^{18} +7.23513 q^{19} -1.14356 q^{20} -0.122708 q^{21} -1.52524 q^{22} -9.25137 q^{23} -2.90918 q^{24} +1.00000 q^{25} -0.925440 q^{26} +1.00000 q^{27} +0.140324 q^{28} +2.07063 q^{29} +0.925440 q^{30} +1.00000 q^{31} +5.44342 q^{32} -1.64812 q^{33} +1.64493 q^{34} -0.122708 q^{35} -1.14356 q^{36} -0.846152 q^{37} +6.69568 q^{38} -1.00000 q^{39} -2.90918 q^{40} +7.40266 q^{41} -0.113559 q^{42} +1.31837 q^{43} +1.88473 q^{44} +1.00000 q^{45} -8.56159 q^{46} +3.41193 q^{47} -0.405146 q^{48} -6.98494 q^{49} +0.925440 q^{50} +1.77746 q^{51} +1.14356 q^{52} +3.60465 q^{53} +0.925440 q^{54} -1.64812 q^{55} +0.356979 q^{56} +7.23513 q^{57} +1.91624 q^{58} +12.7031 q^{59} -1.14356 q^{60} -2.15214 q^{61} +0.925440 q^{62} -0.122708 q^{63} +5.84785 q^{64} -1.00000 q^{65} -1.52524 q^{66} -1.37225 q^{67} -2.03264 q^{68} -9.25137 q^{69} -0.113559 q^{70} -1.00563 q^{71} -2.90918 q^{72} +9.62315 q^{73} -0.783062 q^{74} +1.00000 q^{75} -8.27381 q^{76} +0.202238 q^{77} -0.925440 q^{78} -1.33307 q^{79} -0.405146 q^{80} +1.00000 q^{81} +6.85072 q^{82} +11.1226 q^{83} +0.140324 q^{84} +1.77746 q^{85} +1.22007 q^{86} +2.07063 q^{87} +4.79468 q^{88} -2.66859 q^{89} +0.925440 q^{90} +0.122708 q^{91} +10.5795 q^{92} +1.00000 q^{93} +3.15754 q^{94} +7.23513 q^{95} +5.44342 q^{96} +16.1017 q^{97} -6.46414 q^{98} -1.64812 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9} + 4 q^{10} + 6 q^{11} + 22 q^{12} - 18 q^{13} + 5 q^{14} + 18 q^{15} + 30 q^{16} + 18 q^{17} + 4 q^{18} + 12 q^{19} + 22 q^{20} + 8 q^{21} + 7 q^{22} + 32 q^{23} + 9 q^{24} + 18 q^{25} - 4 q^{26} + 18 q^{27} + 10 q^{28} + 7 q^{29} + 4 q^{30} + 18 q^{31} + 22 q^{32} + 6 q^{33} + 15 q^{34} + 8 q^{35} + 22 q^{36} + 3 q^{37} + 32 q^{38} - 18 q^{39} + 9 q^{40} + 4 q^{41} + 5 q^{42} + 14 q^{43} - 5 q^{44} + 18 q^{45} + 10 q^{46} + 23 q^{47} + 30 q^{48} + 28 q^{49} + 4 q^{50} + 18 q^{51} - 22 q^{52} + 35 q^{53} + 4 q^{54} + 6 q^{55} - 7 q^{56} + 12 q^{57} - 6 q^{58} + 28 q^{59} + 22 q^{60} + 19 q^{61} + 4 q^{62} + 8 q^{63} + 43 q^{64} - 18 q^{65} + 7 q^{66} + 34 q^{67} + 55 q^{68} + 32 q^{69} + 5 q^{70} - 8 q^{71} + 9 q^{72} + 22 q^{74} + 18 q^{75} + 2 q^{76} + 21 q^{77} - 4 q^{78} + 4 q^{79} + 30 q^{80} + 18 q^{81} + 29 q^{82} + 11 q^{83} + 10 q^{84} + 18 q^{85} - 22 q^{86} + 7 q^{87} - 31 q^{88} + 17 q^{89} + 4 q^{90} - 8 q^{91} + 33 q^{92} + 18 q^{93} - 14 q^{94} + 12 q^{95} + 22 q^{96} + 32 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.925440 0.654385 0.327192 0.944958i \(-0.393897\pi\)
0.327192 + 0.944958i \(0.393897\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.14356 −0.571780
\(5\) 1.00000 0.447214
\(6\) 0.925440 0.377809
\(7\) −0.122708 −0.0463792 −0.0231896 0.999731i \(-0.507382\pi\)
−0.0231896 + 0.999731i \(0.507382\pi\)
\(8\) −2.90918 −1.02855
\(9\) 1.00000 0.333333
\(10\) 0.925440 0.292650
\(11\) −1.64812 −0.496928 −0.248464 0.968641i \(-0.579926\pi\)
−0.248464 + 0.968641i \(0.579926\pi\)
\(12\) −1.14356 −0.330118
\(13\) −1.00000 −0.277350
\(14\) −0.113559 −0.0303498
\(15\) 1.00000 0.258199
\(16\) −0.405146 −0.101287
\(17\) 1.77746 0.431098 0.215549 0.976493i \(-0.430846\pi\)
0.215549 + 0.976493i \(0.430846\pi\)
\(18\) 0.925440 0.218128
\(19\) 7.23513 1.65985 0.829926 0.557873i \(-0.188382\pi\)
0.829926 + 0.557873i \(0.188382\pi\)
\(20\) −1.14356 −0.255708
\(21\) −0.122708 −0.0267770
\(22\) −1.52524 −0.325182
\(23\) −9.25137 −1.92904 −0.964522 0.264003i \(-0.914957\pi\)
−0.964522 + 0.264003i \(0.914957\pi\)
\(24\) −2.90918 −0.593833
\(25\) 1.00000 0.200000
\(26\) −0.925440 −0.181494
\(27\) 1.00000 0.192450
\(28\) 0.140324 0.0265187
\(29\) 2.07063 0.384506 0.192253 0.981345i \(-0.438421\pi\)
0.192253 + 0.981345i \(0.438421\pi\)
\(30\) 0.925440 0.168961
\(31\) 1.00000 0.179605
\(32\) 5.44342 0.962269
\(33\) −1.64812 −0.286902
\(34\) 1.64493 0.282104
\(35\) −0.122708 −0.0207414
\(36\) −1.14356 −0.190593
\(37\) −0.846152 −0.139106 −0.0695532 0.997578i \(-0.522157\pi\)
−0.0695532 + 0.997578i \(0.522157\pi\)
\(38\) 6.69568 1.08618
\(39\) −1.00000 −0.160128
\(40\) −2.90918 −0.459981
\(41\) 7.40266 1.15610 0.578050 0.816001i \(-0.303814\pi\)
0.578050 + 0.816001i \(0.303814\pi\)
\(42\) −0.113559 −0.0175225
\(43\) 1.31837 0.201049 0.100524 0.994935i \(-0.467948\pi\)
0.100524 + 0.994935i \(0.467948\pi\)
\(44\) 1.88473 0.284134
\(45\) 1.00000 0.149071
\(46\) −8.56159 −1.26234
\(47\) 3.41193 0.497681 0.248841 0.968544i \(-0.419950\pi\)
0.248841 + 0.968544i \(0.419950\pi\)
\(48\) −0.405146 −0.0584778
\(49\) −6.98494 −0.997849
\(50\) 0.925440 0.130877
\(51\) 1.77746 0.248895
\(52\) 1.14356 0.158583
\(53\) 3.60465 0.495136 0.247568 0.968870i \(-0.420369\pi\)
0.247568 + 0.968870i \(0.420369\pi\)
\(54\) 0.925440 0.125936
\(55\) −1.64812 −0.222233
\(56\) 0.356979 0.0477033
\(57\) 7.23513 0.958316
\(58\) 1.91624 0.251615
\(59\) 12.7031 1.65381 0.826904 0.562344i \(-0.190100\pi\)
0.826904 + 0.562344i \(0.190100\pi\)
\(60\) −1.14356 −0.147633
\(61\) −2.15214 −0.275553 −0.137776 0.990463i \(-0.543996\pi\)
−0.137776 + 0.990463i \(0.543996\pi\)
\(62\) 0.925440 0.117531
\(63\) −0.122708 −0.0154597
\(64\) 5.84785 0.730981
\(65\) −1.00000 −0.124035
\(66\) −1.52524 −0.187744
\(67\) −1.37225 −0.167647 −0.0838235 0.996481i \(-0.526713\pi\)
−0.0838235 + 0.996481i \(0.526713\pi\)
\(68\) −2.03264 −0.246493
\(69\) −9.25137 −1.11373
\(70\) −0.113559 −0.0135729
\(71\) −1.00563 −0.119346 −0.0596729 0.998218i \(-0.519006\pi\)
−0.0596729 + 0.998218i \(0.519006\pi\)
\(72\) −2.90918 −0.342850
\(73\) 9.62315 1.12630 0.563152 0.826353i \(-0.309588\pi\)
0.563152 + 0.826353i \(0.309588\pi\)
\(74\) −0.783062 −0.0910292
\(75\) 1.00000 0.115470
\(76\) −8.27381 −0.949071
\(77\) 0.202238 0.0230471
\(78\) −0.925440 −0.104785
\(79\) −1.33307 −0.149982 −0.0749909 0.997184i \(-0.523893\pi\)
−0.0749909 + 0.997184i \(0.523893\pi\)
\(80\) −0.405146 −0.0452967
\(81\) 1.00000 0.111111
\(82\) 6.85072 0.756535
\(83\) 11.1226 1.22087 0.610434 0.792067i \(-0.290995\pi\)
0.610434 + 0.792067i \(0.290995\pi\)
\(84\) 0.140324 0.0153106
\(85\) 1.77746 0.192793
\(86\) 1.22007 0.131563
\(87\) 2.07063 0.221995
\(88\) 4.79468 0.511115
\(89\) −2.66859 −0.282870 −0.141435 0.989948i \(-0.545172\pi\)
−0.141435 + 0.989948i \(0.545172\pi\)
\(90\) 0.925440 0.0975499
\(91\) 0.122708 0.0128633
\(92\) 10.5795 1.10299
\(93\) 1.00000 0.103695
\(94\) 3.15754 0.325675
\(95\) 7.23513 0.742309
\(96\) 5.44342 0.555566
\(97\) 16.1017 1.63488 0.817438 0.576016i \(-0.195394\pi\)
0.817438 + 0.576016i \(0.195394\pi\)
\(98\) −6.46414 −0.652977
\(99\) −1.64812 −0.165643
\(100\) −1.14356 −0.114356
\(101\) −8.59122 −0.854858 −0.427429 0.904049i \(-0.640581\pi\)
−0.427429 + 0.904049i \(0.640581\pi\)
\(102\) 1.64493 0.162873
\(103\) −3.26439 −0.321650 −0.160825 0.986983i \(-0.551415\pi\)
−0.160825 + 0.986983i \(0.551415\pi\)
\(104\) 2.90918 0.285268
\(105\) −0.122708 −0.0119751
\(106\) 3.33588 0.324010
\(107\) 16.7289 1.61724 0.808620 0.588331i \(-0.200215\pi\)
0.808620 + 0.588331i \(0.200215\pi\)
\(108\) −1.14356 −0.110039
\(109\) −6.39717 −0.612737 −0.306369 0.951913i \(-0.599114\pi\)
−0.306369 + 0.951913i \(0.599114\pi\)
\(110\) −1.52524 −0.145426
\(111\) −0.846152 −0.0803132
\(112\) 0.0497146 0.00469759
\(113\) 13.5830 1.27778 0.638892 0.769296i \(-0.279393\pi\)
0.638892 + 0.769296i \(0.279393\pi\)
\(114\) 6.69568 0.627108
\(115\) −9.25137 −0.862695
\(116\) −2.36789 −0.219853
\(117\) −1.00000 −0.0924500
\(118\) 11.7560 1.08223
\(119\) −0.218108 −0.0199940
\(120\) −2.90918 −0.265570
\(121\) −8.28369 −0.753063
\(122\) −1.99167 −0.180318
\(123\) 7.40266 0.667475
\(124\) −1.14356 −0.102695
\(125\) 1.00000 0.0894427
\(126\) −0.113559 −0.0101166
\(127\) −18.0085 −1.59800 −0.798999 0.601332i \(-0.794637\pi\)
−0.798999 + 0.601332i \(0.794637\pi\)
\(128\) −5.47500 −0.483926
\(129\) 1.31837 0.116076
\(130\) −0.925440 −0.0811664
\(131\) −5.17806 −0.452410 −0.226205 0.974080i \(-0.572632\pi\)
−0.226205 + 0.974080i \(0.572632\pi\)
\(132\) 1.88473 0.164045
\(133\) −0.887807 −0.0769826
\(134\) −1.26993 −0.109706
\(135\) 1.00000 0.0860663
\(136\) −5.17095 −0.443406
\(137\) 5.27213 0.450428 0.225214 0.974309i \(-0.427692\pi\)
0.225214 + 0.974309i \(0.427692\pi\)
\(138\) −8.56159 −0.728811
\(139\) 14.6523 1.24280 0.621398 0.783495i \(-0.286565\pi\)
0.621398 + 0.783495i \(0.286565\pi\)
\(140\) 0.140324 0.0118595
\(141\) 3.41193 0.287336
\(142\) −0.930646 −0.0780981
\(143\) 1.64812 0.137823
\(144\) −0.405146 −0.0337622
\(145\) 2.07063 0.171956
\(146\) 8.90565 0.737037
\(147\) −6.98494 −0.576108
\(148\) 0.967626 0.0795384
\(149\) 13.7879 1.12955 0.564774 0.825246i \(-0.308963\pi\)
0.564774 + 0.825246i \(0.308963\pi\)
\(150\) 0.925440 0.0755619
\(151\) 11.0546 0.899611 0.449805 0.893127i \(-0.351493\pi\)
0.449805 + 0.893127i \(0.351493\pi\)
\(152\) −21.0483 −1.70724
\(153\) 1.77746 0.143699
\(154\) 0.187159 0.0150817
\(155\) 1.00000 0.0803219
\(156\) 1.14356 0.0915582
\(157\) 9.06646 0.723582 0.361791 0.932259i \(-0.382165\pi\)
0.361791 + 0.932259i \(0.382165\pi\)
\(158\) −1.23367 −0.0981458
\(159\) 3.60465 0.285867
\(160\) 5.44342 0.430340
\(161\) 1.13521 0.0894675
\(162\) 0.925440 0.0727094
\(163\) 8.77132 0.687023 0.343511 0.939149i \(-0.388384\pi\)
0.343511 + 0.939149i \(0.388384\pi\)
\(164\) −8.46539 −0.661036
\(165\) −1.64812 −0.128306
\(166\) 10.2933 0.798918
\(167\) 2.78486 0.215499 0.107749 0.994178i \(-0.465636\pi\)
0.107749 + 0.994178i \(0.465636\pi\)
\(168\) 0.356979 0.0275415
\(169\) 1.00000 0.0769231
\(170\) 1.64493 0.126161
\(171\) 7.23513 0.553284
\(172\) −1.50763 −0.114956
\(173\) −11.1032 −0.844163 −0.422081 0.906558i \(-0.638700\pi\)
−0.422081 + 0.906558i \(0.638700\pi\)
\(174\) 1.91624 0.145270
\(175\) −0.122708 −0.00927584
\(176\) 0.667731 0.0503321
\(177\) 12.7031 0.954826
\(178\) −2.46962 −0.185106
\(179\) −9.88354 −0.738731 −0.369365 0.929284i \(-0.620425\pi\)
−0.369365 + 0.929284i \(0.620425\pi\)
\(180\) −1.14356 −0.0852360
\(181\) −7.16446 −0.532530 −0.266265 0.963900i \(-0.585790\pi\)
−0.266265 + 0.963900i \(0.585790\pi\)
\(182\) 0.113559 0.00841753
\(183\) −2.15214 −0.159091
\(184\) 26.9139 1.98412
\(185\) −0.846152 −0.0622103
\(186\) 0.925440 0.0678565
\(187\) −2.92948 −0.214225
\(188\) −3.90175 −0.284564
\(189\) −0.122708 −0.00892568
\(190\) 6.69568 0.485756
\(191\) 11.0610 0.800347 0.400174 0.916439i \(-0.368950\pi\)
0.400174 + 0.916439i \(0.368950\pi\)
\(192\) 5.84785 0.422032
\(193\) 12.3088 0.886005 0.443002 0.896520i \(-0.353913\pi\)
0.443002 + 0.896520i \(0.353913\pi\)
\(194\) 14.9011 1.06984
\(195\) −1.00000 −0.0716115
\(196\) 7.98771 0.570551
\(197\) −1.76121 −0.125481 −0.0627405 0.998030i \(-0.519984\pi\)
−0.0627405 + 0.998030i \(0.519984\pi\)
\(198\) −1.52524 −0.108394
\(199\) 7.85890 0.557103 0.278551 0.960421i \(-0.410146\pi\)
0.278551 + 0.960421i \(0.410146\pi\)
\(200\) −2.90918 −0.205710
\(201\) −1.37225 −0.0967910
\(202\) −7.95066 −0.559406
\(203\) −0.254082 −0.0178331
\(204\) −2.03264 −0.142313
\(205\) 7.40266 0.517024
\(206\) −3.02100 −0.210483
\(207\) −9.25137 −0.643015
\(208\) 0.405146 0.0280918
\(209\) −11.9244 −0.824827
\(210\) −0.113559 −0.00783629
\(211\) 15.9547 1.09836 0.549182 0.835703i \(-0.314939\pi\)
0.549182 + 0.835703i \(0.314939\pi\)
\(212\) −4.12213 −0.283109
\(213\) −1.00563 −0.0689043
\(214\) 15.4816 1.05830
\(215\) 1.31837 0.0899118
\(216\) −2.90918 −0.197944
\(217\) −0.122708 −0.00832995
\(218\) −5.92019 −0.400966
\(219\) 9.62315 0.650272
\(220\) 1.88473 0.127068
\(221\) −1.77746 −0.119565
\(222\) −0.783062 −0.0525557
\(223\) 19.8537 1.32950 0.664750 0.747066i \(-0.268538\pi\)
0.664750 + 0.747066i \(0.268538\pi\)
\(224\) −0.667949 −0.0446292
\(225\) 1.00000 0.0666667
\(226\) 12.5703 0.836163
\(227\) 18.5763 1.23295 0.616475 0.787375i \(-0.288560\pi\)
0.616475 + 0.787375i \(0.288560\pi\)
\(228\) −8.27381 −0.547947
\(229\) −9.67200 −0.639144 −0.319572 0.947562i \(-0.603539\pi\)
−0.319572 + 0.947562i \(0.603539\pi\)
\(230\) −8.56159 −0.564534
\(231\) 0.202238 0.0133063
\(232\) −6.02383 −0.395484
\(233\) 6.15546 0.403258 0.201629 0.979462i \(-0.435377\pi\)
0.201629 + 0.979462i \(0.435377\pi\)
\(234\) −0.925440 −0.0604979
\(235\) 3.41193 0.222570
\(236\) −14.5268 −0.945615
\(237\) −1.33307 −0.0865920
\(238\) −0.201846 −0.0130838
\(239\) 2.82872 0.182975 0.0914873 0.995806i \(-0.470838\pi\)
0.0914873 + 0.995806i \(0.470838\pi\)
\(240\) −0.405146 −0.0261521
\(241\) −7.70559 −0.496361 −0.248180 0.968714i \(-0.579833\pi\)
−0.248180 + 0.968714i \(0.579833\pi\)
\(242\) −7.66606 −0.492793
\(243\) 1.00000 0.0641500
\(244\) 2.46110 0.157556
\(245\) −6.98494 −0.446252
\(246\) 6.85072 0.436786
\(247\) −7.23513 −0.460360
\(248\) −2.90918 −0.184733
\(249\) 11.1226 0.704869
\(250\) 0.925440 0.0585300
\(251\) −22.1922 −1.40076 −0.700379 0.713771i \(-0.746986\pi\)
−0.700379 + 0.713771i \(0.746986\pi\)
\(252\) 0.140324 0.00883957
\(253\) 15.2474 0.958596
\(254\) −16.6658 −1.04571
\(255\) 1.77746 0.111309
\(256\) −16.7625 −1.04765
\(257\) 16.3216 1.01811 0.509056 0.860734i \(-0.329995\pi\)
0.509056 + 0.860734i \(0.329995\pi\)
\(258\) 1.22007 0.0759581
\(259\) 0.103829 0.00645164
\(260\) 1.14356 0.0709206
\(261\) 2.07063 0.128169
\(262\) −4.79199 −0.296050
\(263\) 3.71964 0.229363 0.114681 0.993402i \(-0.463415\pi\)
0.114681 + 0.993402i \(0.463415\pi\)
\(264\) 4.79468 0.295092
\(265\) 3.60465 0.221432
\(266\) −0.821612 −0.0503763
\(267\) −2.66859 −0.163315
\(268\) 1.56925 0.0958573
\(269\) −23.2982 −1.42052 −0.710259 0.703941i \(-0.751422\pi\)
−0.710259 + 0.703941i \(0.751422\pi\)
\(270\) 0.925440 0.0563205
\(271\) −10.3204 −0.626920 −0.313460 0.949601i \(-0.601488\pi\)
−0.313460 + 0.949601i \(0.601488\pi\)
\(272\) −0.720132 −0.0436644
\(273\) 0.122708 0.00742661
\(274\) 4.87904 0.294753
\(275\) −1.64812 −0.0993856
\(276\) 10.5795 0.636811
\(277\) 10.0064 0.601225 0.300612 0.953746i \(-0.402809\pi\)
0.300612 + 0.953746i \(0.402809\pi\)
\(278\) 13.5599 0.813266
\(279\) 1.00000 0.0598684
\(280\) 0.356979 0.0213336
\(281\) −1.14620 −0.0683768 −0.0341884 0.999415i \(-0.510885\pi\)
−0.0341884 + 0.999415i \(0.510885\pi\)
\(282\) 3.15754 0.188029
\(283\) 17.3625 1.03209 0.516046 0.856561i \(-0.327403\pi\)
0.516046 + 0.856561i \(0.327403\pi\)
\(284\) 1.14999 0.0682396
\(285\) 7.23513 0.428572
\(286\) 1.52524 0.0901893
\(287\) −0.908364 −0.0536190
\(288\) 5.44342 0.320756
\(289\) −13.8406 −0.814155
\(290\) 1.91624 0.112526
\(291\) 16.1017 0.943896
\(292\) −11.0047 −0.643999
\(293\) 16.9457 0.989980 0.494990 0.868899i \(-0.335172\pi\)
0.494990 + 0.868899i \(0.335172\pi\)
\(294\) −6.46414 −0.376997
\(295\) 12.7031 0.739605
\(296\) 2.46160 0.143078
\(297\) −1.64812 −0.0956338
\(298\) 12.7599 0.739159
\(299\) 9.25137 0.535020
\(300\) −1.14356 −0.0660235
\(301\) −0.161774 −0.00932448
\(302\) 10.2304 0.588692
\(303\) −8.59122 −0.493553
\(304\) −2.93129 −0.168121
\(305\) −2.15214 −0.123231
\(306\) 1.64493 0.0940347
\(307\) −24.8948 −1.42082 −0.710410 0.703788i \(-0.751490\pi\)
−0.710410 + 0.703788i \(0.751490\pi\)
\(308\) −0.231271 −0.0131779
\(309\) −3.26439 −0.185705
\(310\) 0.925440 0.0525615
\(311\) 21.5736 1.22333 0.611664 0.791118i \(-0.290501\pi\)
0.611664 + 0.791118i \(0.290501\pi\)
\(312\) 2.90918 0.164700
\(313\) −7.07729 −0.400032 −0.200016 0.979793i \(-0.564099\pi\)
−0.200016 + 0.979793i \(0.564099\pi\)
\(314\) 8.39046 0.473501
\(315\) −0.122708 −0.00691380
\(316\) 1.52444 0.0857566
\(317\) −25.8494 −1.45185 −0.725925 0.687774i \(-0.758588\pi\)
−0.725925 + 0.687774i \(0.758588\pi\)
\(318\) 3.33588 0.187067
\(319\) −3.41265 −0.191072
\(320\) 5.84785 0.326905
\(321\) 16.7289 0.933714
\(322\) 1.05057 0.0585461
\(323\) 12.8602 0.715559
\(324\) −1.14356 −0.0635312
\(325\) −1.00000 −0.0554700
\(326\) 8.11733 0.449577
\(327\) −6.39717 −0.353764
\(328\) −21.5356 −1.18911
\(329\) −0.418670 −0.0230820
\(330\) −1.52524 −0.0839617
\(331\) −20.8358 −1.14524 −0.572621 0.819820i \(-0.694073\pi\)
−0.572621 + 0.819820i \(0.694073\pi\)
\(332\) −12.7194 −0.698069
\(333\) −0.846152 −0.0463688
\(334\) 2.57722 0.141019
\(335\) −1.37225 −0.0749740
\(336\) 0.0497146 0.00271215
\(337\) −6.66018 −0.362803 −0.181401 0.983409i \(-0.558063\pi\)
−0.181401 + 0.983409i \(0.558063\pi\)
\(338\) 0.925440 0.0503373
\(339\) 13.5830 0.737729
\(340\) −2.03264 −0.110235
\(341\) −1.64812 −0.0892509
\(342\) 6.69568 0.362061
\(343\) 1.71606 0.0926586
\(344\) −3.83536 −0.206789
\(345\) −9.25137 −0.498077
\(346\) −10.2754 −0.552407
\(347\) −8.94312 −0.480092 −0.240046 0.970762i \(-0.577163\pi\)
−0.240046 + 0.970762i \(0.577163\pi\)
\(348\) −2.36789 −0.126932
\(349\) 3.26398 0.174717 0.0873584 0.996177i \(-0.472157\pi\)
0.0873584 + 0.996177i \(0.472157\pi\)
\(350\) −0.113559 −0.00606997
\(351\) −1.00000 −0.0533761
\(352\) −8.97142 −0.478178
\(353\) −2.31856 −0.123405 −0.0617024 0.998095i \(-0.519653\pi\)
−0.0617024 + 0.998095i \(0.519653\pi\)
\(354\) 11.7560 0.624824
\(355\) −1.00563 −0.0533731
\(356\) 3.05169 0.161739
\(357\) −0.218108 −0.0115435
\(358\) −9.14662 −0.483414
\(359\) −9.13662 −0.482212 −0.241106 0.970499i \(-0.577510\pi\)
−0.241106 + 0.970499i \(0.577510\pi\)
\(360\) −2.90918 −0.153327
\(361\) 33.3471 1.75511
\(362\) −6.63028 −0.348480
\(363\) −8.28369 −0.434781
\(364\) −0.140324 −0.00735497
\(365\) 9.62315 0.503699
\(366\) −1.99167 −0.104106
\(367\) −36.6342 −1.91229 −0.956145 0.292894i \(-0.905382\pi\)
−0.956145 + 0.292894i \(0.905382\pi\)
\(368\) 3.74816 0.195386
\(369\) 7.40266 0.385367
\(370\) −0.783062 −0.0407095
\(371\) −0.442318 −0.0229640
\(372\) −1.14356 −0.0592909
\(373\) −4.57955 −0.237120 −0.118560 0.992947i \(-0.537828\pi\)
−0.118560 + 0.992947i \(0.537828\pi\)
\(374\) −2.71106 −0.140185
\(375\) 1.00000 0.0516398
\(376\) −9.92591 −0.511890
\(377\) −2.07063 −0.106643
\(378\) −0.113559 −0.00584083
\(379\) 8.56969 0.440196 0.220098 0.975478i \(-0.429362\pi\)
0.220098 + 0.975478i \(0.429362\pi\)
\(380\) −8.27381 −0.424438
\(381\) −18.0085 −0.922605
\(382\) 10.2363 0.523735
\(383\) −3.49724 −0.178701 −0.0893503 0.996000i \(-0.528479\pi\)
−0.0893503 + 0.996000i \(0.528479\pi\)
\(384\) −5.47500 −0.279395
\(385\) 0.202238 0.0103070
\(386\) 11.3910 0.579788
\(387\) 1.31837 0.0670163
\(388\) −18.4132 −0.934790
\(389\) 5.50166 0.278945 0.139473 0.990226i \(-0.455459\pi\)
0.139473 + 0.990226i \(0.455459\pi\)
\(390\) −0.925440 −0.0468615
\(391\) −16.4440 −0.831607
\(392\) 20.3204 1.02634
\(393\) −5.17806 −0.261199
\(394\) −1.62989 −0.0821129
\(395\) −1.33307 −0.0670739
\(396\) 1.88473 0.0947112
\(397\) −37.4412 −1.87912 −0.939560 0.342385i \(-0.888765\pi\)
−0.939560 + 0.342385i \(0.888765\pi\)
\(398\) 7.27294 0.364560
\(399\) −0.887807 −0.0444459
\(400\) −0.405146 −0.0202573
\(401\) −14.2887 −0.713543 −0.356772 0.934192i \(-0.616123\pi\)
−0.356772 + 0.934192i \(0.616123\pi\)
\(402\) −1.26993 −0.0633386
\(403\) −1.00000 −0.0498135
\(404\) 9.82459 0.488791
\(405\) 1.00000 0.0496904
\(406\) −0.235138 −0.0116697
\(407\) 1.39456 0.0691259
\(408\) −5.17095 −0.256000
\(409\) −4.13702 −0.204563 −0.102281 0.994756i \(-0.532614\pi\)
−0.102281 + 0.994756i \(0.532614\pi\)
\(410\) 6.85072 0.338333
\(411\) 5.27213 0.260055
\(412\) 3.73303 0.183913
\(413\) −1.55877 −0.0767022
\(414\) −8.56159 −0.420779
\(415\) 11.1226 0.545989
\(416\) −5.44342 −0.266885
\(417\) 14.6523 0.717528
\(418\) −11.0353 −0.539755
\(419\) 7.81628 0.381850 0.190925 0.981605i \(-0.438851\pi\)
0.190925 + 0.981605i \(0.438851\pi\)
\(420\) 0.140324 0.00684710
\(421\) −25.4889 −1.24225 −0.621125 0.783711i \(-0.713324\pi\)
−0.621125 + 0.783711i \(0.713324\pi\)
\(422\) 14.7651 0.718753
\(423\) 3.41193 0.165894
\(424\) −10.4866 −0.509272
\(425\) 1.77746 0.0862196
\(426\) −0.930646 −0.0450899
\(427\) 0.264084 0.0127799
\(428\) −19.1305 −0.924706
\(429\) 1.64812 0.0795722
\(430\) 1.22007 0.0588369
\(431\) −14.6779 −0.707008 −0.353504 0.935433i \(-0.615010\pi\)
−0.353504 + 0.935433i \(0.615010\pi\)
\(432\) −0.405146 −0.0194926
\(433\) 2.22019 0.106695 0.0533476 0.998576i \(-0.483011\pi\)
0.0533476 + 0.998576i \(0.483011\pi\)
\(434\) −0.113559 −0.00545099
\(435\) 2.07063 0.0992791
\(436\) 7.31555 0.350351
\(437\) −66.9349 −3.20193
\(438\) 8.90565 0.425528
\(439\) 15.2422 0.727473 0.363736 0.931502i \(-0.381501\pi\)
0.363736 + 0.931502i \(0.381501\pi\)
\(440\) 4.79468 0.228578
\(441\) −6.98494 −0.332616
\(442\) −1.64493 −0.0782416
\(443\) 38.5482 1.83148 0.915740 0.401771i \(-0.131605\pi\)
0.915740 + 0.401771i \(0.131605\pi\)
\(444\) 0.967626 0.0459215
\(445\) −2.66859 −0.126503
\(446\) 18.3734 0.870004
\(447\) 13.7879 0.652145
\(448\) −0.717576 −0.0339023
\(449\) −2.78231 −0.131305 −0.0656526 0.997843i \(-0.520913\pi\)
−0.0656526 + 0.997843i \(0.520913\pi\)
\(450\) 0.925440 0.0436257
\(451\) −12.2005 −0.574499
\(452\) −15.5330 −0.730612
\(453\) 11.0546 0.519390
\(454\) 17.1912 0.806823
\(455\) 0.122708 0.00575263
\(456\) −21.0483 −0.985676
\(457\) 38.8366 1.81670 0.908349 0.418212i \(-0.137343\pi\)
0.908349 + 0.418212i \(0.137343\pi\)
\(458\) −8.95086 −0.418246
\(459\) 1.77746 0.0829648
\(460\) 10.5795 0.493272
\(461\) −8.98963 −0.418689 −0.209344 0.977842i \(-0.567133\pi\)
−0.209344 + 0.977842i \(0.567133\pi\)
\(462\) 0.187159 0.00870741
\(463\) 24.0697 1.11861 0.559307 0.828961i \(-0.311067\pi\)
0.559307 + 0.828961i \(0.311067\pi\)
\(464\) −0.838908 −0.0389453
\(465\) 1.00000 0.0463739
\(466\) 5.69651 0.263886
\(467\) 17.9629 0.831225 0.415612 0.909542i \(-0.363567\pi\)
0.415612 + 0.909542i \(0.363567\pi\)
\(468\) 1.14356 0.0528611
\(469\) 0.168386 0.00777533
\(470\) 3.15754 0.145646
\(471\) 9.06646 0.417760
\(472\) −36.9557 −1.70102
\(473\) −2.17283 −0.0999068
\(474\) −1.23367 −0.0566645
\(475\) 7.23513 0.331971
\(476\) 0.249420 0.0114322
\(477\) 3.60465 0.165045
\(478\) 2.61781 0.119736
\(479\) 2.06291 0.0942568 0.0471284 0.998889i \(-0.484993\pi\)
0.0471284 + 0.998889i \(0.484993\pi\)
\(480\) 5.44342 0.248457
\(481\) 0.846152 0.0385812
\(482\) −7.13106 −0.324811
\(483\) 1.13521 0.0516541
\(484\) 9.47290 0.430586
\(485\) 16.1017 0.731139
\(486\) 0.925440 0.0419788
\(487\) −21.6835 −0.982572 −0.491286 0.870998i \(-0.663473\pi\)
−0.491286 + 0.870998i \(0.663473\pi\)
\(488\) 6.26095 0.283420
\(489\) 8.77132 0.396653
\(490\) −6.46414 −0.292020
\(491\) 17.3189 0.781590 0.390795 0.920478i \(-0.372200\pi\)
0.390795 + 0.920478i \(0.372200\pi\)
\(492\) −8.46539 −0.381649
\(493\) 3.68047 0.165760
\(494\) −6.69568 −0.301253
\(495\) −1.64812 −0.0740777
\(496\) −0.405146 −0.0181916
\(497\) 0.123398 0.00553516
\(498\) 10.2933 0.461256
\(499\) 10.4577 0.468152 0.234076 0.972218i \(-0.424794\pi\)
0.234076 + 0.972218i \(0.424794\pi\)
\(500\) −1.14356 −0.0511416
\(501\) 2.78486 0.124418
\(502\) −20.5375 −0.916635
\(503\) 25.9440 1.15679 0.578394 0.815758i \(-0.303680\pi\)
0.578394 + 0.815758i \(0.303680\pi\)
\(504\) 0.356979 0.0159011
\(505\) −8.59122 −0.382304
\(506\) 14.1106 0.627291
\(507\) 1.00000 0.0444116
\(508\) 20.5939 0.913704
\(509\) 25.0715 1.11128 0.555638 0.831424i \(-0.312474\pi\)
0.555638 + 0.831424i \(0.312474\pi\)
\(510\) 1.64493 0.0728389
\(511\) −1.18084 −0.0522371
\(512\) −4.56266 −0.201643
\(513\) 7.23513 0.319439
\(514\) 15.1046 0.666237
\(515\) −3.26439 −0.143846
\(516\) −1.50763 −0.0663698
\(517\) −5.62328 −0.247312
\(518\) 0.0960878 0.00422186
\(519\) −11.1032 −0.487378
\(520\) 2.90918 0.127576
\(521\) −18.3380 −0.803401 −0.401700 0.915771i \(-0.631581\pi\)
−0.401700 + 0.915771i \(0.631581\pi\)
\(522\) 1.91624 0.0838717
\(523\) −4.00266 −0.175024 −0.0875121 0.996163i \(-0.527892\pi\)
−0.0875121 + 0.996163i \(0.527892\pi\)
\(524\) 5.92143 0.258679
\(525\) −0.122708 −0.00535541
\(526\) 3.44230 0.150092
\(527\) 1.77746 0.0774275
\(528\) 0.667731 0.0290593
\(529\) 62.5878 2.72121
\(530\) 3.33588 0.144902
\(531\) 12.7031 0.551269
\(532\) 1.01526 0.0440172
\(533\) −7.40266 −0.320645
\(534\) −2.46962 −0.106871
\(535\) 16.7289 0.723252
\(536\) 3.99212 0.172433
\(537\) −9.88354 −0.426506
\(538\) −21.5611 −0.929565
\(539\) 11.5121 0.495859
\(540\) −1.14356 −0.0492110
\(541\) −15.8853 −0.682962 −0.341481 0.939889i \(-0.610928\pi\)
−0.341481 + 0.939889i \(0.610928\pi\)
\(542\) −9.55091 −0.410247
\(543\) −7.16446 −0.307456
\(544\) 9.67547 0.414832
\(545\) −6.39717 −0.274025
\(546\) 0.113559 0.00485986
\(547\) −3.75156 −0.160405 −0.0802026 0.996779i \(-0.525557\pi\)
−0.0802026 + 0.996779i \(0.525557\pi\)
\(548\) −6.02900 −0.257546
\(549\) −2.15214 −0.0918509
\(550\) −1.52524 −0.0650364
\(551\) 14.9813 0.638224
\(552\) 26.9139 1.14553
\(553\) 0.163578 0.00695603
\(554\) 9.26030 0.393432
\(555\) −0.846152 −0.0359171
\(556\) −16.7558 −0.710606
\(557\) 40.5053 1.71626 0.858132 0.513430i \(-0.171625\pi\)
0.858132 + 0.513430i \(0.171625\pi\)
\(558\) 0.925440 0.0391770
\(559\) −1.31837 −0.0557609
\(560\) 0.0497146 0.00210083
\(561\) −2.92948 −0.123683
\(562\) −1.06074 −0.0447448
\(563\) 11.3096 0.476641 0.238320 0.971187i \(-0.423403\pi\)
0.238320 + 0.971187i \(0.423403\pi\)
\(564\) −3.90175 −0.164293
\(565\) 13.5830 0.571443
\(566\) 16.0679 0.675386
\(567\) −0.122708 −0.00515324
\(568\) 2.92554 0.122753
\(569\) 17.3368 0.726798 0.363399 0.931634i \(-0.381616\pi\)
0.363399 + 0.931634i \(0.381616\pi\)
\(570\) 6.69568 0.280451
\(571\) −25.6460 −1.07325 −0.536627 0.843820i \(-0.680302\pi\)
−0.536627 + 0.843820i \(0.680302\pi\)
\(572\) −1.88473 −0.0788045
\(573\) 11.0610 0.462081
\(574\) −0.840636 −0.0350875
\(575\) −9.25137 −0.385809
\(576\) 5.84785 0.243660
\(577\) 1.31756 0.0548509 0.0274255 0.999624i \(-0.491269\pi\)
0.0274255 + 0.999624i \(0.491269\pi\)
\(578\) −12.8087 −0.532770
\(579\) 12.3088 0.511535
\(580\) −2.36789 −0.0983213
\(581\) −1.36483 −0.0566229
\(582\) 14.9011 0.617671
\(583\) −5.94090 −0.246047
\(584\) −27.9954 −1.15846
\(585\) −1.00000 −0.0413449
\(586\) 15.6822 0.647828
\(587\) −19.8016 −0.817300 −0.408650 0.912691i \(-0.634000\pi\)
−0.408650 + 0.912691i \(0.634000\pi\)
\(588\) 7.98771 0.329408
\(589\) 7.23513 0.298118
\(590\) 11.7560 0.483986
\(591\) −1.76121 −0.0724465
\(592\) 0.342815 0.0140896
\(593\) −20.9097 −0.858658 −0.429329 0.903148i \(-0.641250\pi\)
−0.429329 + 0.903148i \(0.641250\pi\)
\(594\) −1.52524 −0.0625813
\(595\) −0.218108 −0.00894157
\(596\) −15.7673 −0.645854
\(597\) 7.85890 0.321644
\(598\) 8.56159 0.350109
\(599\) −2.12689 −0.0869023 −0.0434511 0.999056i \(-0.513835\pi\)
−0.0434511 + 0.999056i \(0.513835\pi\)
\(600\) −2.90918 −0.118767
\(601\) −0.348888 −0.0142314 −0.00711571 0.999975i \(-0.502265\pi\)
−0.00711571 + 0.999975i \(0.502265\pi\)
\(602\) −0.149712 −0.00610180
\(603\) −1.37225 −0.0558823
\(604\) −12.6416 −0.514380
\(605\) −8.28369 −0.336780
\(606\) −7.95066 −0.322973
\(607\) −13.0912 −0.531354 −0.265677 0.964062i \(-0.585596\pi\)
−0.265677 + 0.964062i \(0.585596\pi\)
\(608\) 39.3838 1.59722
\(609\) −0.254082 −0.0102959
\(610\) −1.99167 −0.0806405
\(611\) −3.41193 −0.138032
\(612\) −2.03264 −0.0821645
\(613\) −4.28341 −0.173005 −0.0865026 0.996252i \(-0.527569\pi\)
−0.0865026 + 0.996252i \(0.527569\pi\)
\(614\) −23.0386 −0.929763
\(615\) 7.40266 0.298504
\(616\) −0.588345 −0.0237051
\(617\) −18.6834 −0.752167 −0.376083 0.926586i \(-0.622729\pi\)
−0.376083 + 0.926586i \(0.622729\pi\)
\(618\) −3.02100 −0.121522
\(619\) −25.3256 −1.01792 −0.508961 0.860790i \(-0.669970\pi\)
−0.508961 + 0.860790i \(0.669970\pi\)
\(620\) −1.14356 −0.0459265
\(621\) −9.25137 −0.371245
\(622\) 19.9651 0.800527
\(623\) 0.327456 0.0131193
\(624\) 0.405146 0.0162188
\(625\) 1.00000 0.0400000
\(626\) −6.54961 −0.261775
\(627\) −11.9244 −0.476214
\(628\) −10.3680 −0.413730
\(629\) −1.50400 −0.0599685
\(630\) −0.113559 −0.00452429
\(631\) −17.4282 −0.693806 −0.346903 0.937901i \(-0.612767\pi\)
−0.346903 + 0.937901i \(0.612767\pi\)
\(632\) 3.87813 0.154264
\(633\) 15.9547 0.634141
\(634\) −23.9221 −0.950068
\(635\) −18.0085 −0.714647
\(636\) −4.12213 −0.163453
\(637\) 6.98494 0.276754
\(638\) −3.15821 −0.125035
\(639\) −1.00563 −0.0397819
\(640\) −5.47500 −0.216418
\(641\) −5.63300 −0.222490 −0.111245 0.993793i \(-0.535484\pi\)
−0.111245 + 0.993793i \(0.535484\pi\)
\(642\) 15.4816 0.611008
\(643\) −5.93111 −0.233900 −0.116950 0.993138i \(-0.537312\pi\)
−0.116950 + 0.993138i \(0.537312\pi\)
\(644\) −1.29819 −0.0511557
\(645\) 1.31837 0.0519106
\(646\) 11.9013 0.468251
\(647\) −12.1864 −0.479096 −0.239548 0.970885i \(-0.576999\pi\)
−0.239548 + 0.970885i \(0.576999\pi\)
\(648\) −2.90918 −0.114283
\(649\) −20.9363 −0.821823
\(650\) −0.925440 −0.0362987
\(651\) −0.122708 −0.00480930
\(652\) −10.0305 −0.392826
\(653\) −32.9623 −1.28991 −0.644957 0.764219i \(-0.723125\pi\)
−0.644957 + 0.764219i \(0.723125\pi\)
\(654\) −5.92019 −0.231498
\(655\) −5.17806 −0.202324
\(656\) −2.99916 −0.117097
\(657\) 9.62315 0.375435
\(658\) −0.387454 −0.0151045
\(659\) −39.1020 −1.52320 −0.761599 0.648049i \(-0.775585\pi\)
−0.761599 + 0.648049i \(0.775585\pi\)
\(660\) 1.88473 0.0733630
\(661\) 24.3273 0.946221 0.473111 0.881003i \(-0.343131\pi\)
0.473111 + 0.881003i \(0.343131\pi\)
\(662\) −19.2823 −0.749429
\(663\) −1.77746 −0.0690309
\(664\) −32.3577 −1.25572
\(665\) −0.887807 −0.0344277
\(666\) −0.783062 −0.0303431
\(667\) −19.1562 −0.741729
\(668\) −3.18466 −0.123218
\(669\) 19.8537 0.767587
\(670\) −1.26993 −0.0490619
\(671\) 3.54699 0.136930
\(672\) −0.667949 −0.0257667
\(673\) 34.5179 1.33057 0.665284 0.746591i \(-0.268311\pi\)
0.665284 + 0.746591i \(0.268311\pi\)
\(674\) −6.16359 −0.237413
\(675\) 1.00000 0.0384900
\(676\) −1.14356 −0.0439831
\(677\) −27.3961 −1.05292 −0.526458 0.850201i \(-0.676480\pi\)
−0.526458 + 0.850201i \(0.676480\pi\)
\(678\) 12.5703 0.482759
\(679\) −1.97580 −0.0758242
\(680\) −5.17095 −0.198297
\(681\) 18.5763 0.711844
\(682\) −1.52524 −0.0584044
\(683\) 29.1363 1.11487 0.557434 0.830221i \(-0.311786\pi\)
0.557434 + 0.830221i \(0.311786\pi\)
\(684\) −8.27381 −0.316357
\(685\) 5.27213 0.201438
\(686\) 1.58811 0.0606344
\(687\) −9.67200 −0.369010
\(688\) −0.534131 −0.0203636
\(689\) −3.60465 −0.137326
\(690\) −8.56159 −0.325934
\(691\) −41.8367 −1.59154 −0.795771 0.605598i \(-0.792934\pi\)
−0.795771 + 0.605598i \(0.792934\pi\)
\(692\) 12.6972 0.482676
\(693\) 0.202238 0.00768237
\(694\) −8.27632 −0.314165
\(695\) 14.6523 0.555795
\(696\) −6.02383 −0.228333
\(697\) 13.1579 0.498393
\(698\) 3.02062 0.114332
\(699\) 6.15546 0.232821
\(700\) 0.140324 0.00530374
\(701\) −2.66627 −0.100704 −0.0503518 0.998732i \(-0.516034\pi\)
−0.0503518 + 0.998732i \(0.516034\pi\)
\(702\) −0.925440 −0.0349285
\(703\) −6.12202 −0.230896
\(704\) −9.63797 −0.363245
\(705\) 3.41193 0.128501
\(706\) −2.14569 −0.0807542
\(707\) 1.05421 0.0396476
\(708\) −14.5268 −0.545951
\(709\) 32.1566 1.20767 0.603833 0.797111i \(-0.293639\pi\)
0.603833 + 0.797111i \(0.293639\pi\)
\(710\) −0.930646 −0.0349265
\(711\) −1.33307 −0.0499939
\(712\) 7.76339 0.290945
\(713\) −9.25137 −0.346466
\(714\) −0.201846 −0.00755391
\(715\) 1.64812 0.0616363
\(716\) 11.3024 0.422392
\(717\) 2.82872 0.105640
\(718\) −8.45539 −0.315553
\(719\) 0.324398 0.0120980 0.00604901 0.999982i \(-0.498075\pi\)
0.00604901 + 0.999982i \(0.498075\pi\)
\(720\) −0.405146 −0.0150989
\(721\) 0.400566 0.0149179
\(722\) 30.8608 1.14852
\(723\) −7.70559 −0.286574
\(724\) 8.19300 0.304490
\(725\) 2.07063 0.0769012
\(726\) −7.66606 −0.284514
\(727\) −7.11521 −0.263888 −0.131944 0.991257i \(-0.542122\pi\)
−0.131944 + 0.991257i \(0.542122\pi\)
\(728\) −0.356979 −0.0132305
\(729\) 1.00000 0.0370370
\(730\) 8.90565 0.329613
\(731\) 2.34335 0.0866718
\(732\) 2.46110 0.0909649
\(733\) −39.5190 −1.45967 −0.729835 0.683624i \(-0.760403\pi\)
−0.729835 + 0.683624i \(0.760403\pi\)
\(734\) −33.9028 −1.25137
\(735\) −6.98494 −0.257643
\(736\) −50.3590 −1.85626
\(737\) 2.26164 0.0833085
\(738\) 6.85072 0.252178
\(739\) 10.8952 0.400788 0.200394 0.979715i \(-0.435778\pi\)
0.200394 + 0.979715i \(0.435778\pi\)
\(740\) 0.967626 0.0355706
\(741\) −7.23513 −0.265789
\(742\) −0.409339 −0.0150273
\(743\) 38.3859 1.40824 0.704121 0.710080i \(-0.251341\pi\)
0.704121 + 0.710080i \(0.251341\pi\)
\(744\) −2.90918 −0.106656
\(745\) 13.7879 0.505149
\(746\) −4.23810 −0.155168
\(747\) 11.1226 0.406956
\(748\) 3.35004 0.122489
\(749\) −2.05276 −0.0750063
\(750\) 0.925440 0.0337923
\(751\) 12.9318 0.471888 0.235944 0.971767i \(-0.424182\pi\)
0.235944 + 0.971767i \(0.424182\pi\)
\(752\) −1.38233 −0.0504084
\(753\) −22.1922 −0.808728
\(754\) −1.91624 −0.0697855
\(755\) 11.0546 0.402318
\(756\) 0.140324 0.00510353
\(757\) 41.3902 1.50435 0.752176 0.658962i \(-0.229004\pi\)
0.752176 + 0.658962i \(0.229004\pi\)
\(758\) 7.93074 0.288057
\(759\) 15.2474 0.553446
\(760\) −21.0483 −0.763501
\(761\) 46.8386 1.69790 0.848948 0.528476i \(-0.177236\pi\)
0.848948 + 0.528476i \(0.177236\pi\)
\(762\) −16.6658 −0.603739
\(763\) 0.784982 0.0284183
\(764\) −12.6490 −0.457623
\(765\) 1.77746 0.0642643
\(766\) −3.23648 −0.116939
\(767\) −12.7031 −0.458684
\(768\) −16.7625 −0.604864
\(769\) −52.8158 −1.90459 −0.952294 0.305183i \(-0.901283\pi\)
−0.952294 + 0.305183i \(0.901283\pi\)
\(770\) 0.187159 0.00674473
\(771\) 16.3216 0.587807
\(772\) −14.0758 −0.506600
\(773\) −42.0977 −1.51415 −0.757075 0.653328i \(-0.773372\pi\)
−0.757075 + 0.653328i \(0.773372\pi\)
\(774\) 1.22007 0.0438545
\(775\) 1.00000 0.0359211
\(776\) −46.8426 −1.68155
\(777\) 0.103829 0.00372486
\(778\) 5.09145 0.182537
\(779\) 53.5592 1.91896
\(780\) 1.14356 0.0409461
\(781\) 1.65740 0.0593063
\(782\) −15.2179 −0.544191
\(783\) 2.07063 0.0739983
\(784\) 2.82992 0.101069
\(785\) 9.06646 0.323596
\(786\) −4.79199 −0.170925
\(787\) 20.8820 0.744361 0.372181 0.928160i \(-0.378610\pi\)
0.372181 + 0.928160i \(0.378610\pi\)
\(788\) 2.01405 0.0717476
\(789\) 3.71964 0.132423
\(790\) −1.23367 −0.0438921
\(791\) −1.66674 −0.0592626
\(792\) 4.79468 0.170372
\(793\) 2.15214 0.0764246
\(794\) −34.6496 −1.22967
\(795\) 3.60465 0.127844
\(796\) −8.98714 −0.318541
\(797\) −26.1259 −0.925427 −0.462714 0.886508i \(-0.653124\pi\)
−0.462714 + 0.886508i \(0.653124\pi\)
\(798\) −0.821612 −0.0290847
\(799\) 6.06458 0.214549
\(800\) 5.44342 0.192454
\(801\) −2.66859 −0.0942899
\(802\) −13.2233 −0.466932
\(803\) −15.8601 −0.559692
\(804\) 1.56925 0.0553432
\(805\) 1.13521 0.0400111
\(806\) −0.925440 −0.0325972
\(807\) −23.2982 −0.820136
\(808\) 24.9934 0.879264
\(809\) −18.2401 −0.641286 −0.320643 0.947200i \(-0.603899\pi\)
−0.320643 + 0.947200i \(0.603899\pi\)
\(810\) 0.925440 0.0325166
\(811\) −10.3561 −0.363651 −0.181826 0.983331i \(-0.558201\pi\)
−0.181826 + 0.983331i \(0.558201\pi\)
\(812\) 0.290559 0.0101966
\(813\) −10.3204 −0.361952
\(814\) 1.29058 0.0452349
\(815\) 8.77132 0.307246
\(816\) −0.720132 −0.0252097
\(817\) 9.53855 0.333712
\(818\) −3.82857 −0.133863
\(819\) 0.122708 0.00428776
\(820\) −8.46539 −0.295624
\(821\) −30.3405 −1.05889 −0.529445 0.848344i \(-0.677600\pi\)
−0.529445 + 0.848344i \(0.677600\pi\)
\(822\) 4.87904 0.170176
\(823\) −27.7806 −0.968373 −0.484186 0.874965i \(-0.660884\pi\)
−0.484186 + 0.874965i \(0.660884\pi\)
\(824\) 9.49669 0.330833
\(825\) −1.64812 −0.0573803
\(826\) −1.44255 −0.0501928
\(827\) −26.7571 −0.930435 −0.465218 0.885196i \(-0.654024\pi\)
−0.465218 + 0.885196i \(0.654024\pi\)
\(828\) 10.5795 0.367663
\(829\) 5.69140 0.197671 0.0988353 0.995104i \(-0.468488\pi\)
0.0988353 + 0.995104i \(0.468488\pi\)
\(830\) 10.2933 0.357287
\(831\) 10.0064 0.347117
\(832\) −5.84785 −0.202738
\(833\) −12.4155 −0.430171
\(834\) 13.5599 0.469540
\(835\) 2.78486 0.0963740
\(836\) 13.6363 0.471620
\(837\) 1.00000 0.0345651
\(838\) 7.23350 0.249877
\(839\) 30.0221 1.03648 0.518240 0.855235i \(-0.326588\pi\)
0.518240 + 0.855235i \(0.326588\pi\)
\(840\) 0.356979 0.0123169
\(841\) −24.7125 −0.852155
\(842\) −23.5884 −0.812910
\(843\) −1.14620 −0.0394774
\(844\) −18.2451 −0.628023
\(845\) 1.00000 0.0344010
\(846\) 3.15754 0.108558
\(847\) 1.01647 0.0349264
\(848\) −1.46041 −0.0501506
\(849\) 17.3625 0.595879
\(850\) 1.64493 0.0564208
\(851\) 7.82806 0.268342
\(852\) 1.14999 0.0393982
\(853\) −51.3358 −1.75770 −0.878852 0.477095i \(-0.841690\pi\)
−0.878852 + 0.477095i \(0.841690\pi\)
\(854\) 0.244394 0.00836298
\(855\) 7.23513 0.247436
\(856\) −48.6672 −1.66341
\(857\) 2.32929 0.0795670 0.0397835 0.999208i \(-0.487333\pi\)
0.0397835 + 0.999208i \(0.487333\pi\)
\(858\) 1.52524 0.0520708
\(859\) 2.01410 0.0687201 0.0343601 0.999410i \(-0.489061\pi\)
0.0343601 + 0.999410i \(0.489061\pi\)
\(860\) −1.50763 −0.0514098
\(861\) −0.908364 −0.0309569
\(862\) −13.5835 −0.462656
\(863\) −22.5353 −0.767112 −0.383556 0.923518i \(-0.625301\pi\)
−0.383556 + 0.923518i \(0.625301\pi\)
\(864\) 5.44342 0.185189
\(865\) −11.1032 −0.377521
\(866\) 2.05465 0.0698198
\(867\) −13.8406 −0.470052
\(868\) 0.140324 0.00476290
\(869\) 2.19706 0.0745301
\(870\) 1.91624 0.0649667
\(871\) 1.37225 0.0464969
\(872\) 18.6105 0.630231
\(873\) 16.1017 0.544959
\(874\) −61.9442 −2.09529
\(875\) −0.122708 −0.00414828
\(876\) −11.0047 −0.371813
\(877\) 22.1993 0.749617 0.374809 0.927102i \(-0.377708\pi\)
0.374809 + 0.927102i \(0.377708\pi\)
\(878\) 14.1058 0.476047
\(879\) 16.9457 0.571565
\(880\) 0.667731 0.0225092
\(881\) −8.42036 −0.283689 −0.141845 0.989889i \(-0.545303\pi\)
−0.141845 + 0.989889i \(0.545303\pi\)
\(882\) −6.46414 −0.217659
\(883\) 4.60615 0.155009 0.0775046 0.996992i \(-0.475305\pi\)
0.0775046 + 0.996992i \(0.475305\pi\)
\(884\) 2.03264 0.0683650
\(885\) 12.7031 0.427011
\(886\) 35.6740 1.19849
\(887\) 41.3899 1.38974 0.694868 0.719137i \(-0.255463\pi\)
0.694868 + 0.719137i \(0.255463\pi\)
\(888\) 2.46160 0.0826060
\(889\) 2.20979 0.0741139
\(890\) −2.46962 −0.0827818
\(891\) −1.64812 −0.0552142
\(892\) −22.7039 −0.760182
\(893\) 24.6858 0.826077
\(894\) 12.7599 0.426754
\(895\) −9.88354 −0.330370
\(896\) 0.671825 0.0224441
\(897\) 9.25137 0.308894
\(898\) −2.57486 −0.0859241
\(899\) 2.07063 0.0690594
\(900\) −1.14356 −0.0381187
\(901\) 6.40712 0.213452
\(902\) −11.2908 −0.375943
\(903\) −0.161774 −0.00538349
\(904\) −39.5154 −1.31426
\(905\) −7.16446 −0.238155
\(906\) 10.2304 0.339881
\(907\) −35.2866 −1.17167 −0.585837 0.810429i \(-0.699234\pi\)
−0.585837 + 0.810429i \(0.699234\pi\)
\(908\) −21.2431 −0.704976
\(909\) −8.59122 −0.284953
\(910\) 0.113559 0.00376443
\(911\) −2.88455 −0.0955696 −0.0477848 0.998858i \(-0.515216\pi\)
−0.0477848 + 0.998858i \(0.515216\pi\)
\(912\) −2.93129 −0.0970646
\(913\) −18.3315 −0.606684
\(914\) 35.9409 1.18882
\(915\) −2.15214 −0.0711474
\(916\) 11.0605 0.365450
\(917\) 0.635389 0.0209824
\(918\) 1.64493 0.0542909
\(919\) 33.1282 1.09280 0.546399 0.837525i \(-0.315998\pi\)
0.546399 + 0.837525i \(0.315998\pi\)
\(920\) 26.9139 0.887324
\(921\) −24.8948 −0.820310
\(922\) −8.31936 −0.273984
\(923\) 1.00563 0.0331006
\(924\) −0.231271 −0.00760826
\(925\) −0.846152 −0.0278213
\(926\) 22.2751 0.732004
\(927\) −3.26439 −0.107217
\(928\) 11.2713 0.369998
\(929\) 50.1823 1.64643 0.823214 0.567731i \(-0.192179\pi\)
0.823214 + 0.567731i \(0.192179\pi\)
\(930\) 0.925440 0.0303464
\(931\) −50.5370 −1.65628
\(932\) −7.03915 −0.230575
\(933\) 21.5736 0.706289
\(934\) 16.6236 0.543941
\(935\) −2.92948 −0.0958042
\(936\) 2.90918 0.0950894
\(937\) 13.2509 0.432888 0.216444 0.976295i \(-0.430554\pi\)
0.216444 + 0.976295i \(0.430554\pi\)
\(938\) 0.155831 0.00508806
\(939\) −7.07729 −0.230959
\(940\) −3.90175 −0.127261
\(941\) 17.3318 0.564999 0.282500 0.959267i \(-0.408836\pi\)
0.282500 + 0.959267i \(0.408836\pi\)
\(942\) 8.39046 0.273376
\(943\) −68.4847 −2.23017
\(944\) −5.14663 −0.167508
\(945\) −0.122708 −0.00399168
\(946\) −2.01082 −0.0653775
\(947\) −10.5526 −0.342913 −0.171457 0.985192i \(-0.554847\pi\)
−0.171457 + 0.985192i \(0.554847\pi\)
\(948\) 1.52444 0.0495116
\(949\) −9.62315 −0.312381
\(950\) 6.69568 0.217237
\(951\) −25.8494 −0.838226
\(952\) 0.634516 0.0205648
\(953\) −37.9440 −1.22913 −0.614563 0.788868i \(-0.710668\pi\)
−0.614563 + 0.788868i \(0.710668\pi\)
\(954\) 3.33588 0.108003
\(955\) 11.0610 0.357926
\(956\) −3.23481 −0.104621
\(957\) −3.41265 −0.110315
\(958\) 1.90910 0.0616802
\(959\) −0.646931 −0.0208905
\(960\) 5.84785 0.188738
\(961\) 1.00000 0.0322581
\(962\) 0.783062 0.0252469
\(963\) 16.7289 0.539080
\(964\) 8.81181 0.283809
\(965\) 12.3088 0.396233
\(966\) 1.05057 0.0338016
\(967\) −12.9381 −0.416062 −0.208031 0.978122i \(-0.566706\pi\)
−0.208031 + 0.978122i \(0.566706\pi\)
\(968\) 24.0987 0.774562
\(969\) 12.8602 0.413128
\(970\) 14.9011 0.478446
\(971\) −24.3054 −0.779997 −0.389998 0.920816i \(-0.627524\pi\)
−0.389998 + 0.920816i \(0.627524\pi\)
\(972\) −1.14356 −0.0366797
\(973\) −1.79796 −0.0576398
\(974\) −20.0668 −0.642981
\(975\) −1.00000 −0.0320256
\(976\) 0.871930 0.0279098
\(977\) −22.8576 −0.731278 −0.365639 0.930757i \(-0.619150\pi\)
−0.365639 + 0.930757i \(0.619150\pi\)
\(978\) 8.11733 0.259564
\(979\) 4.39816 0.140566
\(980\) 7.98771 0.255158
\(981\) −6.39717 −0.204246
\(982\) 16.0276 0.511461
\(983\) 53.1225 1.69435 0.847173 0.531318i \(-0.178303\pi\)
0.847173 + 0.531318i \(0.178303\pi\)
\(984\) −21.5356 −0.686531
\(985\) −1.76121 −0.0561168
\(986\) 3.40605 0.108471
\(987\) −0.418670 −0.0133264
\(988\) 8.27381 0.263225
\(989\) −12.1967 −0.387832
\(990\) −1.52524 −0.0484753
\(991\) −8.71986 −0.276995 −0.138498 0.990363i \(-0.544227\pi\)
−0.138498 + 0.990363i \(0.544227\pi\)
\(992\) 5.44342 0.172829
\(993\) −20.8358 −0.661206
\(994\) 0.114197 0.00362212
\(995\) 7.85890 0.249144
\(996\) −12.7194 −0.403030
\(997\) 39.7224 1.25802 0.629011 0.777396i \(-0.283460\pi\)
0.629011 + 0.777396i \(0.283460\pi\)
\(998\) 9.67799 0.306352
\(999\) −0.846152 −0.0267711
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 6045.2.a.bi.1.11 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6045.2.a.bi.1.11 18 1.1 even 1 trivial