Properties

Label 6032.2.a.bc.1.7
Level $6032$
Weight $2$
Character 6032.1
Self dual yes
Analytic conductor $48.166$
Analytic rank $0$
Dimension $11$
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] = [6032,2,Mod(1,6032)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6032, 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("6032.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6032 = 2^{4} \cdot 13 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6032.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: \(48.1657624992\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - 5x^{10} - 9x^{9} + 65x^{8} + 19x^{7} - 298x^{6} + 17x^{5} + 541x^{4} - 60x^{3} - 287x^{2} + 16x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 3016)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-0.224040\) of defining polynomial
Character \(\chi\) \(=\) 6032.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.22404 q^{3} -3.27866 q^{5} -0.601962 q^{7} -1.50173 q^{9} +O(q^{10})\) \(q+1.22404 q^{3} -3.27866 q^{5} -0.601962 q^{7} -1.50173 q^{9} -0.827372 q^{11} +1.00000 q^{13} -4.01321 q^{15} +2.70818 q^{17} +2.59408 q^{19} -0.736826 q^{21} -2.76786 q^{23} +5.74961 q^{25} -5.51029 q^{27} -1.00000 q^{29} -7.65930 q^{31} -1.01274 q^{33} +1.97363 q^{35} -0.225685 q^{37} +1.22404 q^{39} +4.73068 q^{41} -2.77861 q^{43} +4.92365 q^{45} +5.82952 q^{47} -6.63764 q^{49} +3.31492 q^{51} -12.2897 q^{53} +2.71267 q^{55} +3.17526 q^{57} +9.83353 q^{59} +10.9144 q^{61} +0.903982 q^{63} -3.27866 q^{65} -2.31721 q^{67} -3.38797 q^{69} -7.35144 q^{71} +2.82727 q^{73} +7.03776 q^{75} +0.498046 q^{77} +3.87837 q^{79} -2.23965 q^{81} +12.8866 q^{83} -8.87921 q^{85} -1.22404 q^{87} +6.09649 q^{89} -0.601962 q^{91} -9.37529 q^{93} -8.50511 q^{95} -0.349662 q^{97} +1.24248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q + 6 q^{3} - 2 q^{5} + 3 q^{7} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 11 q + 6 q^{3} - 2 q^{5} + 3 q^{7} + 11 q^{9} + 13 q^{11} + 11 q^{13} + 8 q^{15} - 6 q^{17} + 12 q^{19} + q^{21} + 13 q^{23} + 11 q^{25} + 24 q^{27} - 11 q^{29} + 11 q^{31} + 17 q^{33} + 4 q^{35} + 11 q^{37} + 6 q^{39} - 9 q^{41} + 30 q^{43} - 16 q^{45} + q^{47} - 4 q^{49} + 13 q^{51} - 9 q^{53} + q^{55} + 2 q^{57} + 9 q^{59} - 5 q^{61} + 6 q^{63} - 2 q^{65} + 25 q^{67} + 26 q^{71} + 10 q^{73} + 41 q^{75} - 8 q^{77} + 14 q^{79} + 3 q^{81} + 6 q^{83} + 19 q^{85} - 6 q^{87} - 11 q^{89} + 3 q^{91} - 3 q^{93} + 31 q^{95} + 12 q^{97} + 35 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.22404 0.706700 0.353350 0.935491i \(-0.385042\pi\)
0.353350 + 0.935491i \(0.385042\pi\)
\(4\) 0 0
\(5\) −3.27866 −1.46626 −0.733131 0.680088i \(-0.761942\pi\)
−0.733131 + 0.680088i \(0.761942\pi\)
\(6\) 0 0
\(7\) −0.601962 −0.227520 −0.113760 0.993508i \(-0.536290\pi\)
−0.113760 + 0.993508i \(0.536290\pi\)
\(8\) 0 0
\(9\) −1.50173 −0.500575
\(10\) 0 0
\(11\) −0.827372 −0.249462 −0.124731 0.992191i \(-0.539807\pi\)
−0.124731 + 0.992191i \(0.539807\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −4.01321 −1.03621
\(16\) 0 0
\(17\) 2.70818 0.656831 0.328415 0.944533i \(-0.393485\pi\)
0.328415 + 0.944533i \(0.393485\pi\)
\(18\) 0 0
\(19\) 2.59408 0.595123 0.297562 0.954703i \(-0.403827\pi\)
0.297562 + 0.954703i \(0.403827\pi\)
\(20\) 0 0
\(21\) −0.736826 −0.160789
\(22\) 0 0
\(23\) −2.76786 −0.577139 −0.288569 0.957459i \(-0.593180\pi\)
−0.288569 + 0.957459i \(0.593180\pi\)
\(24\) 0 0
\(25\) 5.74961 1.14992
\(26\) 0 0
\(27\) −5.51029 −1.06046
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) −7.65930 −1.37565 −0.687826 0.725876i \(-0.741435\pi\)
−0.687826 + 0.725876i \(0.741435\pi\)
\(32\) 0 0
\(33\) −1.01274 −0.176295
\(34\) 0 0
\(35\) 1.97363 0.333604
\(36\) 0 0
\(37\) −0.225685 −0.0371024 −0.0185512 0.999828i \(-0.505905\pi\)
−0.0185512 + 0.999828i \(0.505905\pi\)
\(38\) 0 0
\(39\) 1.22404 0.196003
\(40\) 0 0
\(41\) 4.73068 0.738808 0.369404 0.929269i \(-0.379562\pi\)
0.369404 + 0.929269i \(0.379562\pi\)
\(42\) 0 0
\(43\) −2.77861 −0.423734 −0.211867 0.977298i \(-0.567954\pi\)
−0.211867 + 0.977298i \(0.567954\pi\)
\(44\) 0 0
\(45\) 4.92365 0.733974
\(46\) 0 0
\(47\) 5.82952 0.850323 0.425161 0.905118i \(-0.360217\pi\)
0.425161 + 0.905118i \(0.360217\pi\)
\(48\) 0 0
\(49\) −6.63764 −0.948235
\(50\) 0 0
\(51\) 3.31492 0.464182
\(52\) 0 0
\(53\) −12.2897 −1.68812 −0.844060 0.536249i \(-0.819841\pi\)
−0.844060 + 0.536249i \(0.819841\pi\)
\(54\) 0 0
\(55\) 2.71267 0.365776
\(56\) 0 0
\(57\) 3.17526 0.420574
\(58\) 0 0
\(59\) 9.83353 1.28022 0.640108 0.768285i \(-0.278890\pi\)
0.640108 + 0.768285i \(0.278890\pi\)
\(60\) 0 0
\(61\) 10.9144 1.39745 0.698724 0.715391i \(-0.253752\pi\)
0.698724 + 0.715391i \(0.253752\pi\)
\(62\) 0 0
\(63\) 0.903982 0.113891
\(64\) 0 0
\(65\) −3.27866 −0.406668
\(66\) 0 0
\(67\) −2.31721 −0.283092 −0.141546 0.989932i \(-0.545207\pi\)
−0.141546 + 0.989932i \(0.545207\pi\)
\(68\) 0 0
\(69\) −3.38797 −0.407864
\(70\) 0 0
\(71\) −7.35144 −0.872455 −0.436228 0.899836i \(-0.643686\pi\)
−0.436228 + 0.899836i \(0.643686\pi\)
\(72\) 0 0
\(73\) 2.82727 0.330906 0.165453 0.986218i \(-0.447091\pi\)
0.165453 + 0.986218i \(0.447091\pi\)
\(74\) 0 0
\(75\) 7.03776 0.812650
\(76\) 0 0
\(77\) 0.498046 0.0567577
\(78\) 0 0
\(79\) 3.87837 0.436350 0.218175 0.975910i \(-0.429990\pi\)
0.218175 + 0.975910i \(0.429990\pi\)
\(80\) 0 0
\(81\) −2.23965 −0.248850
\(82\) 0 0
\(83\) 12.8866 1.41449 0.707246 0.706967i \(-0.249937\pi\)
0.707246 + 0.706967i \(0.249937\pi\)
\(84\) 0 0
\(85\) −8.87921 −0.963085
\(86\) 0 0
\(87\) −1.22404 −0.131231
\(88\) 0 0
\(89\) 6.09649 0.646227 0.323114 0.946360i \(-0.395270\pi\)
0.323114 + 0.946360i \(0.395270\pi\)
\(90\) 0 0
\(91\) −0.601962 −0.0631028
\(92\) 0 0
\(93\) −9.37529 −0.972173
\(94\) 0 0
\(95\) −8.50511 −0.872606
\(96\) 0 0
\(97\) −0.349662 −0.0355028 −0.0177514 0.999842i \(-0.505651\pi\)
−0.0177514 + 0.999842i \(0.505651\pi\)
\(98\) 0 0
\(99\) 1.24248 0.124874
\(100\) 0 0
\(101\) −8.06282 −0.802281 −0.401140 0.916017i \(-0.631386\pi\)
−0.401140 + 0.916017i \(0.631386\pi\)
\(102\) 0 0
\(103\) 11.0253 1.08636 0.543178 0.839618i \(-0.317221\pi\)
0.543178 + 0.839618i \(0.317221\pi\)
\(104\) 0 0
\(105\) 2.41580 0.235758
\(106\) 0 0
\(107\) −7.10422 −0.686791 −0.343396 0.939191i \(-0.611577\pi\)
−0.343396 + 0.939191i \(0.611577\pi\)
\(108\) 0 0
\(109\) 4.85946 0.465452 0.232726 0.972542i \(-0.425235\pi\)
0.232726 + 0.972542i \(0.425235\pi\)
\(110\) 0 0
\(111\) −0.276248 −0.0262203
\(112\) 0 0
\(113\) 5.87435 0.552613 0.276306 0.961070i \(-0.410890\pi\)
0.276306 + 0.961070i \(0.410890\pi\)
\(114\) 0 0
\(115\) 9.07487 0.846236
\(116\) 0 0
\(117\) −1.50173 −0.138835
\(118\) 0 0
\(119\) −1.63022 −0.149442
\(120\) 0 0
\(121\) −10.3155 −0.937769
\(122\) 0 0
\(123\) 5.79054 0.522116
\(124\) 0 0
\(125\) −2.45773 −0.219826
\(126\) 0 0
\(127\) 19.3798 1.71968 0.859840 0.510564i \(-0.170563\pi\)
0.859840 + 0.510564i \(0.170563\pi\)
\(128\) 0 0
\(129\) −3.40113 −0.299453
\(130\) 0 0
\(131\) 18.2164 1.59157 0.795787 0.605576i \(-0.207057\pi\)
0.795787 + 0.605576i \(0.207057\pi\)
\(132\) 0 0
\(133\) −1.56154 −0.135403
\(134\) 0 0
\(135\) 18.0664 1.55491
\(136\) 0 0
\(137\) −1.20370 −0.102839 −0.0514194 0.998677i \(-0.516375\pi\)
−0.0514194 + 0.998677i \(0.516375\pi\)
\(138\) 0 0
\(139\) 10.8228 0.917974 0.458987 0.888443i \(-0.348212\pi\)
0.458987 + 0.888443i \(0.348212\pi\)
\(140\) 0 0
\(141\) 7.13557 0.600923
\(142\) 0 0
\(143\) −0.827372 −0.0691883
\(144\) 0 0
\(145\) 3.27866 0.272278
\(146\) 0 0
\(147\) −8.12474 −0.670117
\(148\) 0 0
\(149\) −10.9856 −0.899972 −0.449986 0.893036i \(-0.648571\pi\)
−0.449986 + 0.893036i \(0.648571\pi\)
\(150\) 0 0
\(151\) −4.21821 −0.343273 −0.171637 0.985160i \(-0.554905\pi\)
−0.171637 + 0.985160i \(0.554905\pi\)
\(152\) 0 0
\(153\) −4.06694 −0.328793
\(154\) 0 0
\(155\) 25.1122 2.01706
\(156\) 0 0
\(157\) 6.93213 0.553244 0.276622 0.960979i \(-0.410785\pi\)
0.276622 + 0.960979i \(0.410785\pi\)
\(158\) 0 0
\(159\) −15.0431 −1.19299
\(160\) 0 0
\(161\) 1.66615 0.131311
\(162\) 0 0
\(163\) 19.5223 1.52911 0.764554 0.644560i \(-0.222959\pi\)
0.764554 + 0.644560i \(0.222959\pi\)
\(164\) 0 0
\(165\) 3.32042 0.258494
\(166\) 0 0
\(167\) −0.0763064 −0.00590477 −0.00295238 0.999996i \(-0.500940\pi\)
−0.00295238 + 0.999996i \(0.500940\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −3.89560 −0.297904
\(172\) 0 0
\(173\) 0.843567 0.0641352 0.0320676 0.999486i \(-0.489791\pi\)
0.0320676 + 0.999486i \(0.489791\pi\)
\(174\) 0 0
\(175\) −3.46105 −0.261631
\(176\) 0 0
\(177\) 12.0366 0.904729
\(178\) 0 0
\(179\) 14.2736 1.06686 0.533430 0.845844i \(-0.320903\pi\)
0.533430 + 0.845844i \(0.320903\pi\)
\(180\) 0 0
\(181\) 10.3154 0.766740 0.383370 0.923595i \(-0.374763\pi\)
0.383370 + 0.923595i \(0.374763\pi\)
\(182\) 0 0
\(183\) 13.3597 0.987576
\(184\) 0 0
\(185\) 0.739945 0.0544018
\(186\) 0 0
\(187\) −2.24067 −0.163854
\(188\) 0 0
\(189\) 3.31699 0.241275
\(190\) 0 0
\(191\) 2.42264 0.175296 0.0876481 0.996151i \(-0.472065\pi\)
0.0876481 + 0.996151i \(0.472065\pi\)
\(192\) 0 0
\(193\) 18.5027 1.33186 0.665928 0.746016i \(-0.268036\pi\)
0.665928 + 0.746016i \(0.268036\pi\)
\(194\) 0 0
\(195\) −4.01321 −0.287392
\(196\) 0 0
\(197\) −7.70796 −0.549169 −0.274585 0.961563i \(-0.588540\pi\)
−0.274585 + 0.961563i \(0.588540\pi\)
\(198\) 0 0
\(199\) 8.31700 0.589576 0.294788 0.955563i \(-0.404751\pi\)
0.294788 + 0.955563i \(0.404751\pi\)
\(200\) 0 0
\(201\) −2.83635 −0.200061
\(202\) 0 0
\(203\) 0.601962 0.0422495
\(204\) 0 0
\(205\) −15.5103 −1.08329
\(206\) 0 0
\(207\) 4.15656 0.288901
\(208\) 0 0
\(209\) −2.14627 −0.148461
\(210\) 0 0
\(211\) −2.75591 −0.189725 −0.0948623 0.995490i \(-0.530241\pi\)
−0.0948623 + 0.995490i \(0.530241\pi\)
\(212\) 0 0
\(213\) −8.99846 −0.616564
\(214\) 0 0
\(215\) 9.11012 0.621305
\(216\) 0 0
\(217\) 4.61061 0.312989
\(218\) 0 0
\(219\) 3.46069 0.233852
\(220\) 0 0
\(221\) 2.70818 0.182172
\(222\) 0 0
\(223\) 11.8675 0.794709 0.397354 0.917665i \(-0.369928\pi\)
0.397354 + 0.917665i \(0.369928\pi\)
\(224\) 0 0
\(225\) −8.63434 −0.575623
\(226\) 0 0
\(227\) 24.5666 1.63054 0.815270 0.579081i \(-0.196589\pi\)
0.815270 + 0.579081i \(0.196589\pi\)
\(228\) 0 0
\(229\) 12.8212 0.847246 0.423623 0.905839i \(-0.360758\pi\)
0.423623 + 0.905839i \(0.360758\pi\)
\(230\) 0 0
\(231\) 0.609629 0.0401106
\(232\) 0 0
\(233\) −1.73990 −0.113985 −0.0569924 0.998375i \(-0.518151\pi\)
−0.0569924 + 0.998375i \(0.518151\pi\)
\(234\) 0 0
\(235\) −19.1130 −1.24680
\(236\) 0 0
\(237\) 4.74728 0.308369
\(238\) 0 0
\(239\) 1.66422 0.107650 0.0538248 0.998550i \(-0.482859\pi\)
0.0538248 + 0.998550i \(0.482859\pi\)
\(240\) 0 0
\(241\) 17.9604 1.15693 0.578466 0.815707i \(-0.303652\pi\)
0.578466 + 0.815707i \(0.303652\pi\)
\(242\) 0 0
\(243\) 13.7895 0.884594
\(244\) 0 0
\(245\) 21.7626 1.39036
\(246\) 0 0
\(247\) 2.59408 0.165058
\(248\) 0 0
\(249\) 15.7738 0.999622
\(250\) 0 0
\(251\) −12.3300 −0.778260 −0.389130 0.921183i \(-0.627224\pi\)
−0.389130 + 0.921183i \(0.627224\pi\)
\(252\) 0 0
\(253\) 2.29005 0.143974
\(254\) 0 0
\(255\) −10.8685 −0.680612
\(256\) 0 0
\(257\) −27.6115 −1.72236 −0.861178 0.508303i \(-0.830273\pi\)
−0.861178 + 0.508303i \(0.830273\pi\)
\(258\) 0 0
\(259\) 0.135854 0.00844155
\(260\) 0 0
\(261\) 1.50173 0.0929544
\(262\) 0 0
\(263\) −14.7647 −0.910433 −0.455217 0.890381i \(-0.650438\pi\)
−0.455217 + 0.890381i \(0.650438\pi\)
\(264\) 0 0
\(265\) 40.2937 2.47522
\(266\) 0 0
\(267\) 7.46236 0.456689
\(268\) 0 0
\(269\) −19.4044 −1.18311 −0.591554 0.806265i \(-0.701486\pi\)
−0.591554 + 0.806265i \(0.701486\pi\)
\(270\) 0 0
\(271\) 15.7055 0.954041 0.477021 0.878892i \(-0.341717\pi\)
0.477021 + 0.878892i \(0.341717\pi\)
\(272\) 0 0
\(273\) −0.736826 −0.0445947
\(274\) 0 0
\(275\) −4.75707 −0.286862
\(276\) 0 0
\(277\) 22.1155 1.32879 0.664395 0.747382i \(-0.268689\pi\)
0.664395 + 0.747382i \(0.268689\pi\)
\(278\) 0 0
\(279\) 11.5022 0.688617
\(280\) 0 0
\(281\) −27.6693 −1.65061 −0.825307 0.564684i \(-0.808998\pi\)
−0.825307 + 0.564684i \(0.808998\pi\)
\(282\) 0 0
\(283\) −5.45624 −0.324340 −0.162170 0.986763i \(-0.551849\pi\)
−0.162170 + 0.986763i \(0.551849\pi\)
\(284\) 0 0
\(285\) −10.4106 −0.616671
\(286\) 0 0
\(287\) −2.84769 −0.168094
\(288\) 0 0
\(289\) −9.66575 −0.568574
\(290\) 0 0
\(291\) −0.428001 −0.0250898
\(292\) 0 0
\(293\) 4.54294 0.265402 0.132701 0.991156i \(-0.457635\pi\)
0.132701 + 0.991156i \(0.457635\pi\)
\(294\) 0 0
\(295\) −32.2408 −1.87713
\(296\) 0 0
\(297\) 4.55906 0.264544
\(298\) 0 0
\(299\) −2.76786 −0.160069
\(300\) 0 0
\(301\) 1.67262 0.0964081
\(302\) 0 0
\(303\) −9.86922 −0.566972
\(304\) 0 0
\(305\) −35.7847 −2.04902
\(306\) 0 0
\(307\) 5.63926 0.321850 0.160925 0.986967i \(-0.448552\pi\)
0.160925 + 0.986967i \(0.448552\pi\)
\(308\) 0 0
\(309\) 13.4954 0.767728
\(310\) 0 0
\(311\) −5.42432 −0.307585 −0.153792 0.988103i \(-0.549149\pi\)
−0.153792 + 0.988103i \(0.549149\pi\)
\(312\) 0 0
\(313\) 20.4594 1.15643 0.578217 0.815883i \(-0.303749\pi\)
0.578217 + 0.815883i \(0.303749\pi\)
\(314\) 0 0
\(315\) −2.96385 −0.166994
\(316\) 0 0
\(317\) −8.27849 −0.464966 −0.232483 0.972600i \(-0.574685\pi\)
−0.232483 + 0.972600i \(0.574685\pi\)
\(318\) 0 0
\(319\) 0.827372 0.0463239
\(320\) 0 0
\(321\) −8.69586 −0.485355
\(322\) 0 0
\(323\) 7.02525 0.390895
\(324\) 0 0
\(325\) 5.74961 0.318931
\(326\) 0 0
\(327\) 5.94818 0.328935
\(328\) 0 0
\(329\) −3.50915 −0.193466
\(330\) 0 0
\(331\) 24.1014 1.32473 0.662366 0.749181i \(-0.269553\pi\)
0.662366 + 0.749181i \(0.269553\pi\)
\(332\) 0 0
\(333\) 0.338917 0.0185725
\(334\) 0 0
\(335\) 7.59733 0.415087
\(336\) 0 0
\(337\) −21.3743 −1.16433 −0.582165 0.813071i \(-0.697794\pi\)
−0.582165 + 0.813071i \(0.697794\pi\)
\(338\) 0 0
\(339\) 7.19044 0.390531
\(340\) 0 0
\(341\) 6.33709 0.343173
\(342\) 0 0
\(343\) 8.20934 0.443263
\(344\) 0 0
\(345\) 11.1080 0.598035
\(346\) 0 0
\(347\) 11.4461 0.614460 0.307230 0.951635i \(-0.400598\pi\)
0.307230 + 0.951635i \(0.400598\pi\)
\(348\) 0 0
\(349\) 18.9218 1.01286 0.506431 0.862280i \(-0.330964\pi\)
0.506431 + 0.862280i \(0.330964\pi\)
\(350\) 0 0
\(351\) −5.51029 −0.294118
\(352\) 0 0
\(353\) 14.2270 0.757229 0.378615 0.925554i \(-0.376401\pi\)
0.378615 + 0.925554i \(0.376401\pi\)
\(354\) 0 0
\(355\) 24.1029 1.27925
\(356\) 0 0
\(357\) −1.99546 −0.105611
\(358\) 0 0
\(359\) −18.7948 −0.991952 −0.495976 0.868336i \(-0.665190\pi\)
−0.495976 + 0.868336i \(0.665190\pi\)
\(360\) 0 0
\(361\) −12.2707 −0.645828
\(362\) 0 0
\(363\) −12.6265 −0.662721
\(364\) 0 0
\(365\) −9.26964 −0.485195
\(366\) 0 0
\(367\) −18.7747 −0.980032 −0.490016 0.871713i \(-0.663009\pi\)
−0.490016 + 0.871713i \(0.663009\pi\)
\(368\) 0 0
\(369\) −7.10418 −0.369829
\(370\) 0 0
\(371\) 7.39793 0.384081
\(372\) 0 0
\(373\) −33.5892 −1.73918 −0.869591 0.493773i \(-0.835617\pi\)
−0.869591 + 0.493773i \(0.835617\pi\)
\(374\) 0 0
\(375\) −3.00836 −0.155351
\(376\) 0 0
\(377\) −1.00000 −0.0515026
\(378\) 0 0
\(379\) 8.40087 0.431524 0.215762 0.976446i \(-0.430777\pi\)
0.215762 + 0.976446i \(0.430777\pi\)
\(380\) 0 0
\(381\) 23.7217 1.21530
\(382\) 0 0
\(383\) −4.27010 −0.218192 −0.109096 0.994031i \(-0.534796\pi\)
−0.109096 + 0.994031i \(0.534796\pi\)
\(384\) 0 0
\(385\) −1.63292 −0.0832216
\(386\) 0 0
\(387\) 4.17271 0.212111
\(388\) 0 0
\(389\) 15.2951 0.775491 0.387746 0.921766i \(-0.373254\pi\)
0.387746 + 0.921766i \(0.373254\pi\)
\(390\) 0 0
\(391\) −7.49587 −0.379082
\(392\) 0 0
\(393\) 22.2976 1.12477
\(394\) 0 0
\(395\) −12.7158 −0.639803
\(396\) 0 0
\(397\) −10.9177 −0.547944 −0.273972 0.961738i \(-0.588338\pi\)
−0.273972 + 0.961738i \(0.588338\pi\)
\(398\) 0 0
\(399\) −1.91139 −0.0956890
\(400\) 0 0
\(401\) 20.1764 1.00756 0.503779 0.863832i \(-0.331942\pi\)
0.503779 + 0.863832i \(0.331942\pi\)
\(402\) 0 0
\(403\) −7.65930 −0.381537
\(404\) 0 0
\(405\) 7.34304 0.364879
\(406\) 0 0
\(407\) 0.186725 0.00925564
\(408\) 0 0
\(409\) 22.4756 1.11135 0.555673 0.831401i \(-0.312461\pi\)
0.555673 + 0.831401i \(0.312461\pi\)
\(410\) 0 0
\(411\) −1.47337 −0.0726762
\(412\) 0 0
\(413\) −5.91941 −0.291275
\(414\) 0 0
\(415\) −42.2509 −2.07402
\(416\) 0 0
\(417\) 13.2475 0.648733
\(418\) 0 0
\(419\) 5.43850 0.265688 0.132844 0.991137i \(-0.457589\pi\)
0.132844 + 0.991137i \(0.457589\pi\)
\(420\) 0 0
\(421\) 26.4707 1.29010 0.645051 0.764140i \(-0.276836\pi\)
0.645051 + 0.764140i \(0.276836\pi\)
\(422\) 0 0
\(423\) −8.75434 −0.425650
\(424\) 0 0
\(425\) 15.5710 0.755304
\(426\) 0 0
\(427\) −6.57006 −0.317948
\(428\) 0 0
\(429\) −1.01274 −0.0488954
\(430\) 0 0
\(431\) −10.0342 −0.483328 −0.241664 0.970360i \(-0.577693\pi\)
−0.241664 + 0.970360i \(0.577693\pi\)
\(432\) 0 0
\(433\) 20.9045 1.00461 0.502304 0.864691i \(-0.332486\pi\)
0.502304 + 0.864691i \(0.332486\pi\)
\(434\) 0 0
\(435\) 4.01321 0.192419
\(436\) 0 0
\(437\) −7.18006 −0.343469
\(438\) 0 0
\(439\) −19.1346 −0.913244 −0.456622 0.889661i \(-0.650941\pi\)
−0.456622 + 0.889661i \(0.650941\pi\)
\(440\) 0 0
\(441\) 9.96791 0.474663
\(442\) 0 0
\(443\) 1.99943 0.0949959 0.0474979 0.998871i \(-0.484875\pi\)
0.0474979 + 0.998871i \(0.484875\pi\)
\(444\) 0 0
\(445\) −19.9883 −0.947538
\(446\) 0 0
\(447\) −13.4468 −0.636010
\(448\) 0 0
\(449\) −24.7572 −1.16836 −0.584182 0.811623i \(-0.698585\pi\)
−0.584182 + 0.811623i \(0.698585\pi\)
\(450\) 0 0
\(451\) −3.91403 −0.184305
\(452\) 0 0
\(453\) −5.16326 −0.242591
\(454\) 0 0
\(455\) 1.97363 0.0925252
\(456\) 0 0
\(457\) 8.22345 0.384677 0.192338 0.981329i \(-0.438393\pi\)
0.192338 + 0.981329i \(0.438393\pi\)
\(458\) 0 0
\(459\) −14.9229 −0.696540
\(460\) 0 0
\(461\) 2.64673 0.123271 0.0616353 0.998099i \(-0.480368\pi\)
0.0616353 + 0.998099i \(0.480368\pi\)
\(462\) 0 0
\(463\) −5.12629 −0.238239 −0.119119 0.992880i \(-0.538007\pi\)
−0.119119 + 0.992880i \(0.538007\pi\)
\(464\) 0 0
\(465\) 30.7384 1.42546
\(466\) 0 0
\(467\) 16.3745 0.757722 0.378861 0.925454i \(-0.376316\pi\)
0.378861 + 0.925454i \(0.376316\pi\)
\(468\) 0 0
\(469\) 1.39487 0.0644091
\(470\) 0 0
\(471\) 8.48521 0.390978
\(472\) 0 0
\(473\) 2.29894 0.105706
\(474\) 0 0
\(475\) 14.9150 0.684346
\(476\) 0 0
\(477\) 18.4557 0.845030
\(478\) 0 0
\(479\) 23.3991 1.06913 0.534566 0.845127i \(-0.320475\pi\)
0.534566 + 0.845127i \(0.320475\pi\)
\(480\) 0 0
\(481\) −0.225685 −0.0102904
\(482\) 0 0
\(483\) 2.03943 0.0927973
\(484\) 0 0
\(485\) 1.14642 0.0520564
\(486\) 0 0
\(487\) −10.7683 −0.487958 −0.243979 0.969780i \(-0.578453\pi\)
−0.243979 + 0.969780i \(0.578453\pi\)
\(488\) 0 0
\(489\) 23.8961 1.08062
\(490\) 0 0
\(491\) 25.9891 1.17287 0.586436 0.809995i \(-0.300530\pi\)
0.586436 + 0.809995i \(0.300530\pi\)
\(492\) 0 0
\(493\) −2.70818 −0.121970
\(494\) 0 0
\(495\) −4.07369 −0.183099
\(496\) 0 0
\(497\) 4.42529 0.198501
\(498\) 0 0
\(499\) 18.2986 0.819160 0.409580 0.912274i \(-0.365675\pi\)
0.409580 + 0.912274i \(0.365675\pi\)
\(500\) 0 0
\(501\) −0.0934021 −0.00417290
\(502\) 0 0
\(503\) −26.0611 −1.16201 −0.581003 0.813901i \(-0.697340\pi\)
−0.581003 + 0.813901i \(0.697340\pi\)
\(504\) 0 0
\(505\) 26.4352 1.17635
\(506\) 0 0
\(507\) 1.22404 0.0543615
\(508\) 0 0
\(509\) −44.4586 −1.97059 −0.985296 0.170858i \(-0.945346\pi\)
−0.985296 + 0.170858i \(0.945346\pi\)
\(510\) 0 0
\(511\) −1.70191 −0.0752879
\(512\) 0 0
\(513\) −14.2942 −0.631102
\(514\) 0 0
\(515\) −36.1482 −1.59288
\(516\) 0 0
\(517\) −4.82318 −0.212123
\(518\) 0 0
\(519\) 1.03256 0.0453244
\(520\) 0 0
\(521\) −30.4671 −1.33479 −0.667394 0.744705i \(-0.732590\pi\)
−0.667394 + 0.744705i \(0.732590\pi\)
\(522\) 0 0
\(523\) −21.1943 −0.926761 −0.463381 0.886159i \(-0.653364\pi\)
−0.463381 + 0.886159i \(0.653364\pi\)
\(524\) 0 0
\(525\) −4.23646 −0.184894
\(526\) 0 0
\(527\) −20.7428 −0.903570
\(528\) 0 0
\(529\) −15.3390 −0.666911
\(530\) 0 0
\(531\) −14.7673 −0.640844
\(532\) 0 0
\(533\) 4.73068 0.204909
\(534\) 0 0
\(535\) 23.2923 1.00702
\(536\) 0 0
\(537\) 17.4715 0.753950
\(538\) 0 0
\(539\) 5.49180 0.236548
\(540\) 0 0
\(541\) 19.1472 0.823203 0.411601 0.911364i \(-0.364970\pi\)
0.411601 + 0.911364i \(0.364970\pi\)
\(542\) 0 0
\(543\) 12.6265 0.541855
\(544\) 0 0
\(545\) −15.9325 −0.682474
\(546\) 0 0
\(547\) −20.6301 −0.882078 −0.441039 0.897488i \(-0.645390\pi\)
−0.441039 + 0.897488i \(0.645390\pi\)
\(548\) 0 0
\(549\) −16.3905 −0.699527
\(550\) 0 0
\(551\) −2.59408 −0.110512
\(552\) 0 0
\(553\) −2.33463 −0.0992785
\(554\) 0 0
\(555\) 0.905722 0.0384458
\(556\) 0 0
\(557\) −5.91634 −0.250683 −0.125342 0.992114i \(-0.540003\pi\)
−0.125342 + 0.992114i \(0.540003\pi\)
\(558\) 0 0
\(559\) −2.77861 −0.117523
\(560\) 0 0
\(561\) −2.74267 −0.115796
\(562\) 0 0
\(563\) −10.1661 −0.428451 −0.214225 0.976784i \(-0.568723\pi\)
−0.214225 + 0.976784i \(0.568723\pi\)
\(564\) 0 0
\(565\) −19.2600 −0.810274
\(566\) 0 0
\(567\) 1.34818 0.0566183
\(568\) 0 0
\(569\) −37.8937 −1.58859 −0.794294 0.607534i \(-0.792159\pi\)
−0.794294 + 0.607534i \(0.792159\pi\)
\(570\) 0 0
\(571\) 28.6930 1.20076 0.600382 0.799713i \(-0.295015\pi\)
0.600382 + 0.799713i \(0.295015\pi\)
\(572\) 0 0
\(573\) 2.96541 0.123882
\(574\) 0 0
\(575\) −15.9141 −0.663665
\(576\) 0 0
\(577\) 42.2707 1.75975 0.879875 0.475204i \(-0.157626\pi\)
0.879875 + 0.475204i \(0.157626\pi\)
\(578\) 0 0
\(579\) 22.6481 0.941223
\(580\) 0 0
\(581\) −7.75727 −0.321826
\(582\) 0 0
\(583\) 10.1681 0.421122
\(584\) 0 0
\(585\) 4.92365 0.203568
\(586\) 0 0
\(587\) 11.2525 0.464440 0.232220 0.972663i \(-0.425401\pi\)
0.232220 + 0.972663i \(0.425401\pi\)
\(588\) 0 0
\(589\) −19.8689 −0.818682
\(590\) 0 0
\(591\) −9.43485 −0.388098
\(592\) 0 0
\(593\) −23.6952 −0.973047 −0.486523 0.873668i \(-0.661735\pi\)
−0.486523 + 0.873668i \(0.661735\pi\)
\(594\) 0 0
\(595\) 5.34495 0.219121
\(596\) 0 0
\(597\) 10.1803 0.416654
\(598\) 0 0
\(599\) −4.45553 −0.182048 −0.0910240 0.995849i \(-0.529014\pi\)
−0.0910240 + 0.995849i \(0.529014\pi\)
\(600\) 0 0
\(601\) −23.2125 −0.946857 −0.473428 0.880832i \(-0.656984\pi\)
−0.473428 + 0.880832i \(0.656984\pi\)
\(602\) 0 0
\(603\) 3.47981 0.141709
\(604\) 0 0
\(605\) 33.8209 1.37501
\(606\) 0 0
\(607\) −38.3209 −1.55540 −0.777698 0.628638i \(-0.783613\pi\)
−0.777698 + 0.628638i \(0.783613\pi\)
\(608\) 0 0
\(609\) 0.736826 0.0298577
\(610\) 0 0
\(611\) 5.82952 0.235837
\(612\) 0 0
\(613\) −11.1580 −0.450666 −0.225333 0.974282i \(-0.572347\pi\)
−0.225333 + 0.974282i \(0.572347\pi\)
\(614\) 0 0
\(615\) −18.9852 −0.765558
\(616\) 0 0
\(617\) −3.05538 −0.123005 −0.0615026 0.998107i \(-0.519589\pi\)
−0.0615026 + 0.998107i \(0.519589\pi\)
\(618\) 0 0
\(619\) 2.47159 0.0993416 0.0496708 0.998766i \(-0.484183\pi\)
0.0496708 + 0.998766i \(0.484183\pi\)
\(620\) 0 0
\(621\) 15.2517 0.612030
\(622\) 0 0
\(623\) −3.66986 −0.147030
\(624\) 0 0
\(625\) −20.6900 −0.827601
\(626\) 0 0
\(627\) −2.62712 −0.104917
\(628\) 0 0
\(629\) −0.611196 −0.0243700
\(630\) 0 0
\(631\) −21.6543 −0.862044 −0.431022 0.902341i \(-0.641847\pi\)
−0.431022 + 0.902341i \(0.641847\pi\)
\(632\) 0 0
\(633\) −3.37334 −0.134078
\(634\) 0 0
\(635\) −63.5398 −2.52150
\(636\) 0 0
\(637\) −6.63764 −0.262993
\(638\) 0 0
\(639\) 11.0398 0.436729
\(640\) 0 0
\(641\) 11.1650 0.440989 0.220495 0.975388i \(-0.429233\pi\)
0.220495 + 0.975388i \(0.429233\pi\)
\(642\) 0 0
\(643\) −38.1880 −1.50599 −0.752995 0.658027i \(-0.771391\pi\)
−0.752995 + 0.658027i \(0.771391\pi\)
\(644\) 0 0
\(645\) 11.1512 0.439076
\(646\) 0 0
\(647\) 40.1272 1.57756 0.788782 0.614674i \(-0.210712\pi\)
0.788782 + 0.614674i \(0.210712\pi\)
\(648\) 0 0
\(649\) −8.13598 −0.319365
\(650\) 0 0
\(651\) 5.64357 0.221189
\(652\) 0 0
\(653\) −33.2910 −1.30278 −0.651389 0.758744i \(-0.725813\pi\)
−0.651389 + 0.758744i \(0.725813\pi\)
\(654\) 0 0
\(655\) −59.7254 −2.33366
\(656\) 0 0
\(657\) −4.24578 −0.165643
\(658\) 0 0
\(659\) 23.5133 0.915948 0.457974 0.888965i \(-0.348575\pi\)
0.457974 + 0.888965i \(0.348575\pi\)
\(660\) 0 0
\(661\) 17.2981 0.672818 0.336409 0.941716i \(-0.390788\pi\)
0.336409 + 0.941716i \(0.390788\pi\)
\(662\) 0 0
\(663\) 3.31492 0.128741
\(664\) 0 0
\(665\) 5.11976 0.198536
\(666\) 0 0
\(667\) 2.76786 0.107172
\(668\) 0 0
\(669\) 14.5263 0.561621
\(670\) 0 0
\(671\) −9.03028 −0.348610
\(672\) 0 0
\(673\) −20.2017 −0.778719 −0.389359 0.921086i \(-0.627304\pi\)
−0.389359 + 0.921086i \(0.627304\pi\)
\(674\) 0 0
\(675\) −31.6821 −1.21944
\(676\) 0 0
\(677\) −12.2741 −0.471732 −0.235866 0.971786i \(-0.575793\pi\)
−0.235866 + 0.971786i \(0.575793\pi\)
\(678\) 0 0
\(679\) 0.210483 0.00807761
\(680\) 0 0
\(681\) 30.0705 1.15230
\(682\) 0 0
\(683\) 26.4703 1.01286 0.506429 0.862282i \(-0.330965\pi\)
0.506429 + 0.862282i \(0.330965\pi\)
\(684\) 0 0
\(685\) 3.94652 0.150789
\(686\) 0 0
\(687\) 15.6936 0.598749
\(688\) 0 0
\(689\) −12.2897 −0.468200
\(690\) 0 0
\(691\) 28.6836 1.09118 0.545588 0.838054i \(-0.316306\pi\)
0.545588 + 0.838054i \(0.316306\pi\)
\(692\) 0 0
\(693\) −0.747929 −0.0284115
\(694\) 0 0
\(695\) −35.4841 −1.34599
\(696\) 0 0
\(697\) 12.8115 0.485272
\(698\) 0 0
\(699\) −2.12971 −0.0805531
\(700\) 0 0
\(701\) −8.08141 −0.305231 −0.152615 0.988286i \(-0.548770\pi\)
−0.152615 + 0.988286i \(0.548770\pi\)
\(702\) 0 0
\(703\) −0.585446 −0.0220805
\(704\) 0 0
\(705\) −23.3951 −0.881111
\(706\) 0 0
\(707\) 4.85351 0.182535
\(708\) 0 0
\(709\) −14.8243 −0.556737 −0.278368 0.960474i \(-0.589794\pi\)
−0.278368 + 0.960474i \(0.589794\pi\)
\(710\) 0 0
\(711\) −5.82424 −0.218426
\(712\) 0 0
\(713\) 21.1999 0.793941
\(714\) 0 0
\(715\) 2.71267 0.101448
\(716\) 0 0
\(717\) 2.03708 0.0760760
\(718\) 0 0
\(719\) −27.0604 −1.00918 −0.504591 0.863359i \(-0.668357\pi\)
−0.504591 + 0.863359i \(0.668357\pi\)
\(720\) 0 0
\(721\) −6.63682 −0.247168
\(722\) 0 0
\(723\) 21.9843 0.817604
\(724\) 0 0
\(725\) −5.74961 −0.213535
\(726\) 0 0
\(727\) 18.9983 0.704609 0.352304 0.935885i \(-0.385398\pi\)
0.352304 + 0.935885i \(0.385398\pi\)
\(728\) 0 0
\(729\) 23.5978 0.873993
\(730\) 0 0
\(731\) −7.52498 −0.278322
\(732\) 0 0
\(733\) −14.8868 −0.549855 −0.274928 0.961465i \(-0.588654\pi\)
−0.274928 + 0.961465i \(0.588654\pi\)
\(734\) 0 0
\(735\) 26.6383 0.982567
\(736\) 0 0
\(737\) 1.91719 0.0706206
\(738\) 0 0
\(739\) 19.5322 0.718502 0.359251 0.933241i \(-0.383032\pi\)
0.359251 + 0.933241i \(0.383032\pi\)
\(740\) 0 0
\(741\) 3.17526 0.116646
\(742\) 0 0
\(743\) −7.94584 −0.291505 −0.145752 0.989321i \(-0.546560\pi\)
−0.145752 + 0.989321i \(0.546560\pi\)
\(744\) 0 0
\(745\) 36.0179 1.31959
\(746\) 0 0
\(747\) −19.3522 −0.708060
\(748\) 0 0
\(749\) 4.27647 0.156259
\(750\) 0 0
\(751\) 41.5062 1.51458 0.757291 0.653077i \(-0.226522\pi\)
0.757291 + 0.653077i \(0.226522\pi\)
\(752\) 0 0
\(753\) −15.0924 −0.549996
\(754\) 0 0
\(755\) 13.8301 0.503328
\(756\) 0 0
\(757\) −0.188655 −0.00685679 −0.00342839 0.999994i \(-0.501091\pi\)
−0.00342839 + 0.999994i \(0.501091\pi\)
\(758\) 0 0
\(759\) 2.80311 0.101747
\(760\) 0 0
\(761\) 40.1966 1.45712 0.728562 0.684980i \(-0.240189\pi\)
0.728562 + 0.684980i \(0.240189\pi\)
\(762\) 0 0
\(763\) −2.92521 −0.105900
\(764\) 0 0
\(765\) 13.3341 0.482096
\(766\) 0 0
\(767\) 9.83353 0.355068
\(768\) 0 0
\(769\) 30.0868 1.08496 0.542480 0.840069i \(-0.317486\pi\)
0.542480 + 0.840069i \(0.317486\pi\)
\(770\) 0 0
\(771\) −33.7976 −1.21719
\(772\) 0 0
\(773\) 16.3747 0.588957 0.294479 0.955658i \(-0.404854\pi\)
0.294479 + 0.955658i \(0.404854\pi\)
\(774\) 0 0
\(775\) −44.0380 −1.58189
\(776\) 0 0
\(777\) 0.166291 0.00596564
\(778\) 0 0
\(779\) 12.2718 0.439682
\(780\) 0 0
\(781\) 6.08237 0.217644
\(782\) 0 0
\(783\) 5.51029 0.196922
\(784\) 0 0
\(785\) −22.7281 −0.811201
\(786\) 0 0
\(787\) −49.3784 −1.76015 −0.880075 0.474834i \(-0.842508\pi\)
−0.880075 + 0.474834i \(0.842508\pi\)
\(788\) 0 0
\(789\) −18.0726 −0.643403
\(790\) 0 0
\(791\) −3.53614 −0.125731
\(792\) 0 0
\(793\) 10.9144 0.387582
\(794\) 0 0
\(795\) 49.3212 1.74924
\(796\) 0 0
\(797\) 36.4158 1.28991 0.644956 0.764220i \(-0.276876\pi\)
0.644956 + 0.764220i \(0.276876\pi\)
\(798\) 0 0
\(799\) 15.7874 0.558518
\(800\) 0 0
\(801\) −9.15526 −0.323485
\(802\) 0 0
\(803\) −2.33920 −0.0825486
\(804\) 0 0
\(805\) −5.46273 −0.192536
\(806\) 0 0
\(807\) −23.7518 −0.836103
\(808\) 0 0
\(809\) 29.2602 1.02873 0.514367 0.857570i \(-0.328027\pi\)
0.514367 + 0.857570i \(0.328027\pi\)
\(810\) 0 0
\(811\) 0.304733 0.0107006 0.00535032 0.999986i \(-0.498297\pi\)
0.00535032 + 0.999986i \(0.498297\pi\)
\(812\) 0 0
\(813\) 19.2242 0.674221
\(814\) 0 0
\(815\) −64.0071 −2.24207
\(816\) 0 0
\(817\) −7.20795 −0.252174
\(818\) 0 0
\(819\) 0.903982 0.0315877
\(820\) 0 0
\(821\) 0.799463 0.0279015 0.0139507 0.999903i \(-0.495559\pi\)
0.0139507 + 0.999903i \(0.495559\pi\)
\(822\) 0 0
\(823\) 17.0421 0.594049 0.297024 0.954870i \(-0.404006\pi\)
0.297024 + 0.954870i \(0.404006\pi\)
\(824\) 0 0
\(825\) −5.82284 −0.202725
\(826\) 0 0
\(827\) −1.03107 −0.0358537 −0.0179268 0.999839i \(-0.505707\pi\)
−0.0179268 + 0.999839i \(0.505707\pi\)
\(828\) 0 0
\(829\) 4.74405 0.164768 0.0823838 0.996601i \(-0.473747\pi\)
0.0823838 + 0.996601i \(0.473747\pi\)
\(830\) 0 0
\(831\) 27.0702 0.939055
\(832\) 0 0
\(833\) −17.9759 −0.622829
\(834\) 0 0
\(835\) 0.250183 0.00865793
\(836\) 0 0
\(837\) 42.2050 1.45882
\(838\) 0 0
\(839\) −13.4304 −0.463668 −0.231834 0.972755i \(-0.574473\pi\)
−0.231834 + 0.972755i \(0.574473\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −33.8684 −1.16649
\(844\) 0 0
\(845\) −3.27866 −0.112789
\(846\) 0 0
\(847\) 6.20951 0.213361
\(848\) 0 0
\(849\) −6.67866 −0.229211
\(850\) 0 0
\(851\) 0.624665 0.0214132
\(852\) 0 0
\(853\) 3.41618 0.116968 0.0584839 0.998288i \(-0.481373\pi\)
0.0584839 + 0.998288i \(0.481373\pi\)
\(854\) 0 0
\(855\) 12.7723 0.436805
\(856\) 0 0
\(857\) 50.4323 1.72273 0.861367 0.507983i \(-0.169609\pi\)
0.861367 + 0.507983i \(0.169609\pi\)
\(858\) 0 0
\(859\) −0.273275 −0.00932403 −0.00466202 0.999989i \(-0.501484\pi\)
−0.00466202 + 0.999989i \(0.501484\pi\)
\(860\) 0 0
\(861\) −3.48569 −0.118792
\(862\) 0 0
\(863\) −5.64202 −0.192057 −0.0960284 0.995379i \(-0.530614\pi\)
−0.0960284 + 0.995379i \(0.530614\pi\)
\(864\) 0 0
\(865\) −2.76577 −0.0940390
\(866\) 0 0
\(867\) −11.8313 −0.401811
\(868\) 0 0
\(869\) −3.20885 −0.108853
\(870\) 0 0
\(871\) −2.31721 −0.0785155
\(872\) 0 0
\(873\) 0.525097 0.0177718
\(874\) 0 0
\(875\) 1.47946 0.0500148
\(876\) 0 0
\(877\) −11.5694 −0.390669 −0.195335 0.980737i \(-0.562579\pi\)
−0.195335 + 0.980737i \(0.562579\pi\)
\(878\) 0 0
\(879\) 5.56075 0.187559
\(880\) 0 0
\(881\) −44.9099 −1.51305 −0.756526 0.653964i \(-0.773105\pi\)
−0.756526 + 0.653964i \(0.773105\pi\)
\(882\) 0 0
\(883\) −35.2202 −1.18525 −0.592627 0.805477i \(-0.701909\pi\)
−0.592627 + 0.805477i \(0.701909\pi\)
\(884\) 0 0
\(885\) −39.4640 −1.32657
\(886\) 0 0
\(887\) −38.3479 −1.28760 −0.643798 0.765196i \(-0.722642\pi\)
−0.643798 + 0.765196i \(0.722642\pi\)
\(888\) 0 0
\(889\) −11.6659 −0.391262
\(890\) 0 0
\(891\) 1.85302 0.0620785
\(892\) 0 0
\(893\) 15.1223 0.506047
\(894\) 0 0
\(895\) −46.7984 −1.56430
\(896\) 0 0
\(897\) −3.38797 −0.113121
\(898\) 0 0
\(899\) 7.65930 0.255452
\(900\) 0 0
\(901\) −33.2827 −1.10881
\(902\) 0 0
\(903\) 2.04735 0.0681316
\(904\) 0 0
\(905\) −33.8208 −1.12424
\(906\) 0 0
\(907\) 47.7790 1.58648 0.793238 0.608912i \(-0.208394\pi\)
0.793238 + 0.608912i \(0.208394\pi\)
\(908\) 0 0
\(909\) 12.1081 0.401602
\(910\) 0 0
\(911\) 42.9606 1.42335 0.711674 0.702510i \(-0.247937\pi\)
0.711674 + 0.702510i \(0.247937\pi\)
\(912\) 0 0
\(913\) −10.6620 −0.352862
\(914\) 0 0
\(915\) −43.8019 −1.44805
\(916\) 0 0
\(917\) −10.9656 −0.362115
\(918\) 0 0
\(919\) 16.0897 0.530749 0.265374 0.964145i \(-0.414504\pi\)
0.265374 + 0.964145i \(0.414504\pi\)
\(920\) 0 0
\(921\) 6.90269 0.227451
\(922\) 0 0
\(923\) −7.35144 −0.241976
\(924\) 0 0
\(925\) −1.29760 −0.0426649
\(926\) 0 0
\(927\) −16.5570 −0.543803
\(928\) 0 0
\(929\) −1.21769 −0.0399511 −0.0199756 0.999800i \(-0.506359\pi\)
−0.0199756 + 0.999800i \(0.506359\pi\)
\(930\) 0 0
\(931\) −17.2186 −0.564316
\(932\) 0 0
\(933\) −6.63958 −0.217370
\(934\) 0 0
\(935\) 7.34640 0.240253
\(936\) 0 0
\(937\) −9.85548 −0.321965 −0.160982 0.986957i \(-0.551466\pi\)
−0.160982 + 0.986957i \(0.551466\pi\)
\(938\) 0 0
\(939\) 25.0431 0.817252
\(940\) 0 0
\(941\) 31.3188 1.02096 0.510481 0.859889i \(-0.329467\pi\)
0.510481 + 0.859889i \(0.329467\pi\)
\(942\) 0 0
\(943\) −13.0939 −0.426395
\(944\) 0 0
\(945\) −10.8753 −0.353773
\(946\) 0 0
\(947\) 8.90100 0.289243 0.144622 0.989487i \(-0.453803\pi\)
0.144622 + 0.989487i \(0.453803\pi\)
\(948\) 0 0
\(949\) 2.82727 0.0917769
\(950\) 0 0
\(951\) −10.1332 −0.328592
\(952\) 0 0
\(953\) −34.6383 −1.12205 −0.561023 0.827800i \(-0.689592\pi\)
−0.561023 + 0.827800i \(0.689592\pi\)
\(954\) 0 0
\(955\) −7.94302 −0.257030
\(956\) 0 0
\(957\) 1.01274 0.0327371
\(958\) 0 0
\(959\) 0.724580 0.0233979
\(960\) 0 0
\(961\) 27.6649 0.892416
\(962\) 0 0
\(963\) 10.6686 0.343790
\(964\) 0 0
\(965\) −60.6642 −1.95285
\(966\) 0 0
\(967\) 58.8955 1.89395 0.946976 0.321306i \(-0.104122\pi\)
0.946976 + 0.321306i \(0.104122\pi\)
\(968\) 0 0
\(969\) 8.59918 0.276246
\(970\) 0 0
\(971\) 7.25044 0.232678 0.116339 0.993210i \(-0.462884\pi\)
0.116339 + 0.993210i \(0.462884\pi\)
\(972\) 0 0
\(973\) −6.51489 −0.208858
\(974\) 0 0
\(975\) 7.03776 0.225389
\(976\) 0 0
\(977\) 18.2906 0.585167 0.292584 0.956240i \(-0.405485\pi\)
0.292584 + 0.956240i \(0.405485\pi\)
\(978\) 0 0
\(979\) −5.04407 −0.161209
\(980\) 0 0
\(981\) −7.29758 −0.232994
\(982\) 0 0
\(983\) −21.4487 −0.684109 −0.342054 0.939680i \(-0.611123\pi\)
−0.342054 + 0.939680i \(0.611123\pi\)
\(984\) 0 0
\(985\) 25.2718 0.805226
\(986\) 0 0
\(987\) −4.29534 −0.136722
\(988\) 0 0
\(989\) 7.69081 0.244553
\(990\) 0 0
\(991\) 56.1990 1.78522 0.892609 0.450831i \(-0.148872\pi\)
0.892609 + 0.450831i \(0.148872\pi\)
\(992\) 0 0
\(993\) 29.5011 0.936188
\(994\) 0 0
\(995\) −27.2686 −0.864473
\(996\) 0 0
\(997\) 45.2578 1.43333 0.716664 0.697418i \(-0.245668\pi\)
0.716664 + 0.697418i \(0.245668\pi\)
\(998\) 0 0
\(999\) 1.24359 0.0393455
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 6032.2.a.bc.1.7 11
4.3 odd 2 3016.2.a.i.1.5 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3016.2.a.i.1.5 11 4.3 odd 2
6032.2.a.bc.1.7 11 1.1 even 1 trivial