Properties

Label 9196.2.a.n.1.6
Level $9196$
Weight $2$
Character 9196.1
Self dual yes
Analytic conductor $73.430$
Analytic rank $0$
Dimension $6$
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] = [9196,2,Mod(1,9196)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9196, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("9196.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9196 = 2^{2} \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9196.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: \(73.4304296988\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.744786576.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} - 17x^{4} + 13x^{3} + 69x^{2} - 21x - 30 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 836)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(3.27915\) of defining polynomial
Character \(\chi\) \(=\) 9196.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.27915 q^{3} +3.53478 q^{5} +2.34459 q^{7} +7.75283 q^{9} +O(q^{10})\) \(q+3.27915 q^{3} +3.53478 q^{5} +2.34459 q^{7} +7.75283 q^{9} +5.44101 q^{13} +11.5911 q^{15} -3.37635 q^{17} +1.00000 q^{19} +7.68827 q^{21} -5.78459 q^{23} +7.49465 q^{25} +15.5853 q^{27} -9.19463 q^{29} -9.59107 q^{31} +8.28761 q^{35} -6.58617 q^{37} +17.8419 q^{39} -2.37145 q^{41} -1.18026 q^{43} +27.4045 q^{45} +1.69320 q^{47} -1.50289 q^{49} -11.0716 q^{51} +2.51125 q^{53} +3.27915 q^{57} -4.83925 q^{59} +7.62786 q^{61} +18.1772 q^{63} +19.2328 q^{65} +2.22139 q^{67} -18.9686 q^{69} +11.0379 q^{71} +14.9944 q^{73} +24.5761 q^{75} +5.18195 q^{79} +27.8479 q^{81} +4.24982 q^{83} -11.9347 q^{85} -30.1506 q^{87} +6.09139 q^{89} +12.7569 q^{91} -31.4506 q^{93} +3.53478 q^{95} -6.16698 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{3} + 5 q^{5} + 2 q^{7} + 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{3} + 5 q^{5} + 2 q^{7} + 17 q^{9} - 8 q^{13} + 9 q^{15} + 2 q^{17} + 6 q^{19} - 18 q^{21} + 5 q^{23} + 13 q^{25} + 7 q^{27} - 10 q^{29} + 3 q^{31} + 4 q^{35} + 7 q^{37} + 10 q^{39} - 6 q^{41} - 16 q^{43} + 42 q^{45} + 12 q^{49} - 8 q^{51} + 20 q^{53} + q^{57} + 15 q^{59} - 24 q^{61} + 20 q^{63} + 28 q^{65} + 25 q^{67} - 33 q^{69} - 9 q^{71} + 26 q^{73} + 28 q^{75} + 16 q^{79} + 58 q^{81} + 2 q^{83} - 12 q^{85} + 36 q^{87} + 7 q^{89} + 8 q^{91} - 55 q^{93} + 5 q^{95} + 37 q^{97}+O(q^{100}) \) 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
\(3\) 3.27915 1.89322 0.946609 0.322383i \(-0.104484\pi\)
0.946609 + 0.322383i \(0.104484\pi\)
\(4\) 0 0
\(5\) 3.53478 1.58080 0.790400 0.612591i \(-0.209873\pi\)
0.790400 + 0.612591i \(0.209873\pi\)
\(6\) 0 0
\(7\) 2.34459 0.886172 0.443086 0.896479i \(-0.353884\pi\)
0.443086 + 0.896479i \(0.353884\pi\)
\(8\) 0 0
\(9\) 7.75283 2.58428
\(10\) 0 0
\(11\) 0 0
\(12\) 0 0
\(13\) 5.44101 1.50906 0.754532 0.656263i \(-0.227864\pi\)
0.754532 + 0.656263i \(0.227864\pi\)
\(14\) 0 0
\(15\) 11.5911 2.99280
\(16\) 0 0
\(17\) −3.37635 −0.818886 −0.409443 0.912336i \(-0.634277\pi\)
−0.409443 + 0.912336i \(0.634277\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 7.68827 1.67772
\(22\) 0 0
\(23\) −5.78459 −1.20617 −0.603086 0.797676i \(-0.706062\pi\)
−0.603086 + 0.797676i \(0.706062\pi\)
\(24\) 0 0
\(25\) 7.49465 1.49893
\(26\) 0 0
\(27\) 15.5853 2.99938
\(28\) 0 0
\(29\) −9.19463 −1.70740 −0.853700 0.520766i \(-0.825647\pi\)
−0.853700 + 0.520766i \(0.825647\pi\)
\(30\) 0 0
\(31\) −9.59107 −1.72261 −0.861304 0.508091i \(-0.830351\pi\)
−0.861304 + 0.508091i \(0.830351\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 8.28761 1.40086
\(36\) 0 0
\(37\) −6.58617 −1.08276 −0.541380 0.840778i \(-0.682098\pi\)
−0.541380 + 0.840778i \(0.682098\pi\)
\(38\) 0 0
\(39\) 17.8419 2.85699
\(40\) 0 0
\(41\) −2.37145 −0.370359 −0.185179 0.982705i \(-0.559287\pi\)
−0.185179 + 0.982705i \(0.559287\pi\)
\(42\) 0 0
\(43\) −1.18026 −0.179988 −0.0899941 0.995942i \(-0.528685\pi\)
−0.0899941 + 0.995942i \(0.528685\pi\)
\(44\) 0 0
\(45\) 27.4045 4.08523
\(46\) 0 0
\(47\) 1.69320 0.246979 0.123490 0.992346i \(-0.460591\pi\)
0.123490 + 0.992346i \(0.460591\pi\)
\(48\) 0 0
\(49\) −1.50289 −0.214698
\(50\) 0 0
\(51\) −11.0716 −1.55033
\(52\) 0 0
\(53\) 2.51125 0.344947 0.172474 0.985014i \(-0.444824\pi\)
0.172474 + 0.985014i \(0.444824\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 3.27915 0.434334
\(58\) 0 0
\(59\) −4.83925 −0.630016 −0.315008 0.949089i \(-0.602007\pi\)
−0.315008 + 0.949089i \(0.602007\pi\)
\(60\) 0 0
\(61\) 7.62786 0.976647 0.488324 0.872663i \(-0.337609\pi\)
0.488324 + 0.872663i \(0.337609\pi\)
\(62\) 0 0
\(63\) 18.1772 2.29012
\(64\) 0 0
\(65\) 19.2328 2.38553
\(66\) 0 0
\(67\) 2.22139 0.271386 0.135693 0.990751i \(-0.456674\pi\)
0.135693 + 0.990751i \(0.456674\pi\)
\(68\) 0 0
\(69\) −18.9686 −2.28355
\(70\) 0 0
\(71\) 11.0379 1.30996 0.654978 0.755648i \(-0.272678\pi\)
0.654978 + 0.755648i \(0.272678\pi\)
\(72\) 0 0
\(73\) 14.9944 1.75496 0.877482 0.479610i \(-0.159222\pi\)
0.877482 + 0.479610i \(0.159222\pi\)
\(74\) 0 0
\(75\) 24.5761 2.83780
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 5.18195 0.583015 0.291507 0.956569i \(-0.405843\pi\)
0.291507 + 0.956569i \(0.405843\pi\)
\(80\) 0 0
\(81\) 27.8479 3.09421
\(82\) 0 0
\(83\) 4.24982 0.466478 0.233239 0.972419i \(-0.425068\pi\)
0.233239 + 0.972419i \(0.425068\pi\)
\(84\) 0 0
\(85\) −11.9347 −1.29450
\(86\) 0 0
\(87\) −30.1506 −3.23248
\(88\) 0 0
\(89\) 6.09139 0.645686 0.322843 0.946453i \(-0.395361\pi\)
0.322843 + 0.946453i \(0.395361\pi\)
\(90\) 0 0
\(91\) 12.7569 1.33729
\(92\) 0 0
\(93\) −31.4506 −3.26127
\(94\) 0 0
\(95\) 3.53478 0.362661
\(96\) 0 0
\(97\) −6.16698 −0.626162 −0.313081 0.949726i \(-0.601361\pi\)
−0.313081 + 0.949726i \(0.601361\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −6.86510 −0.683103 −0.341551 0.939863i \(-0.610952\pi\)
−0.341551 + 0.939863i \(0.610952\pi\)
\(102\) 0 0
\(103\) 12.8156 1.26276 0.631380 0.775473i \(-0.282489\pi\)
0.631380 + 0.775473i \(0.282489\pi\)
\(104\) 0 0
\(105\) 27.1763 2.65214
\(106\) 0 0
\(107\) −3.49076 −0.337465 −0.168732 0.985662i \(-0.553967\pi\)
−0.168732 + 0.985662i \(0.553967\pi\)
\(108\) 0 0
\(109\) −19.9904 −1.91473 −0.957366 0.288877i \(-0.906718\pi\)
−0.957366 + 0.288877i \(0.906718\pi\)
\(110\) 0 0
\(111\) −21.5971 −2.04990
\(112\) 0 0
\(113\) 14.0212 1.31900 0.659502 0.751703i \(-0.270767\pi\)
0.659502 + 0.751703i \(0.270767\pi\)
\(114\) 0 0
\(115\) −20.4473 −1.90672
\(116\) 0 0
\(117\) 42.1832 3.89984
\(118\) 0 0
\(119\) −7.91617 −0.725674
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) −7.77636 −0.701171
\(124\) 0 0
\(125\) 8.81804 0.788710
\(126\) 0 0
\(127\) 5.54742 0.492254 0.246127 0.969238i \(-0.420842\pi\)
0.246127 + 0.969238i \(0.420842\pi\)
\(128\) 0 0
\(129\) −3.87026 −0.340757
\(130\) 0 0
\(131\) 11.6672 1.01937 0.509685 0.860361i \(-0.329762\pi\)
0.509685 + 0.860361i \(0.329762\pi\)
\(132\) 0 0
\(133\) 2.34459 0.203302
\(134\) 0 0
\(135\) 55.0904 4.74143
\(136\) 0 0
\(137\) −2.82797 −0.241610 −0.120805 0.992676i \(-0.538548\pi\)
−0.120805 + 0.992676i \(0.538548\pi\)
\(138\) 0 0
\(139\) −15.4993 −1.31464 −0.657318 0.753614i \(-0.728309\pi\)
−0.657318 + 0.753614i \(0.728309\pi\)
\(140\) 0 0
\(141\) 5.55227 0.467585
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −32.5010 −2.69906
\(146\) 0 0
\(147\) −4.92820 −0.406471
\(148\) 0 0
\(149\) 0.234586 0.0192180 0.00960900 0.999954i \(-0.496941\pi\)
0.00960900 + 0.999954i \(0.496941\pi\)
\(150\) 0 0
\(151\) −17.3110 −1.40875 −0.704375 0.709828i \(-0.748773\pi\)
−0.704375 + 0.709828i \(0.748773\pi\)
\(152\) 0 0
\(153\) −26.1763 −2.11623
\(154\) 0 0
\(155\) −33.9023 −2.72310
\(156\) 0 0
\(157\) −10.8360 −0.864806 −0.432403 0.901680i \(-0.642334\pi\)
−0.432403 + 0.901680i \(0.642334\pi\)
\(158\) 0 0
\(159\) 8.23478 0.653060
\(160\) 0 0
\(161\) −13.5625 −1.06888
\(162\) 0 0
\(163\) −8.95716 −0.701579 −0.350789 0.936454i \(-0.614087\pi\)
−0.350789 + 0.936454i \(0.614087\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 14.1193 1.09258 0.546291 0.837596i \(-0.316039\pi\)
0.546291 + 0.837596i \(0.316039\pi\)
\(168\) 0 0
\(169\) 16.6046 1.27728
\(170\) 0 0
\(171\) 7.75283 0.592874
\(172\) 0 0
\(173\) −2.56411 −0.194946 −0.0974729 0.995238i \(-0.531076\pi\)
−0.0974729 + 0.995238i \(0.531076\pi\)
\(174\) 0 0
\(175\) 17.5719 1.32831
\(176\) 0 0
\(177\) −15.8686 −1.19276
\(178\) 0 0
\(179\) 0.455979 0.0340815 0.0170407 0.999855i \(-0.494576\pi\)
0.0170407 + 0.999855i \(0.494576\pi\)
\(180\) 0 0
\(181\) −8.41804 −0.625708 −0.312854 0.949801i \(-0.601285\pi\)
−0.312854 + 0.949801i \(0.601285\pi\)
\(182\) 0 0
\(183\) 25.0129 1.84901
\(184\) 0 0
\(185\) −23.2807 −1.71163
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 36.5411 2.65797
\(190\) 0 0
\(191\) 17.9694 1.30022 0.650110 0.759840i \(-0.274723\pi\)
0.650110 + 0.759840i \(0.274723\pi\)
\(192\) 0 0
\(193\) −17.2504 −1.24171 −0.620854 0.783926i \(-0.713214\pi\)
−0.620854 + 0.783926i \(0.713214\pi\)
\(194\) 0 0
\(195\) 63.0671 4.51633
\(196\) 0 0
\(197\) 6.88359 0.490435 0.245218 0.969468i \(-0.421141\pi\)
0.245218 + 0.969468i \(0.421141\pi\)
\(198\) 0 0
\(199\) −15.0531 −1.06708 −0.533542 0.845773i \(-0.679140\pi\)
−0.533542 + 0.845773i \(0.679140\pi\)
\(200\) 0 0
\(201\) 7.28429 0.513794
\(202\) 0 0
\(203\) −21.5576 −1.51305
\(204\) 0 0
\(205\) −8.38256 −0.585464
\(206\) 0 0
\(207\) −44.8470 −3.11708
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −19.2475 −1.32505 −0.662526 0.749039i \(-0.730516\pi\)
−0.662526 + 0.749039i \(0.730516\pi\)
\(212\) 0 0
\(213\) 36.1949 2.48003
\(214\) 0 0
\(215\) −4.17196 −0.284525
\(216\) 0 0
\(217\) −22.4871 −1.52653
\(218\) 0 0
\(219\) 49.1690 3.32253
\(220\) 0 0
\(221\) −18.3708 −1.23575
\(222\) 0 0
\(223\) −15.6477 −1.04785 −0.523923 0.851765i \(-0.675532\pi\)
−0.523923 + 0.851765i \(0.675532\pi\)
\(224\) 0 0
\(225\) 58.1048 3.87365
\(226\) 0 0
\(227\) 25.9837 1.72460 0.862300 0.506398i \(-0.169023\pi\)
0.862300 + 0.506398i \(0.169023\pi\)
\(228\) 0 0
\(229\) −19.9887 −1.32089 −0.660445 0.750874i \(-0.729632\pi\)
−0.660445 + 0.750874i \(0.729632\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −16.7578 −1.09784 −0.548920 0.835875i \(-0.684961\pi\)
−0.548920 + 0.835875i \(0.684961\pi\)
\(234\) 0 0
\(235\) 5.98510 0.390425
\(236\) 0 0
\(237\) 16.9924 1.10377
\(238\) 0 0
\(239\) 6.69553 0.433098 0.216549 0.976272i \(-0.430520\pi\)
0.216549 + 0.976272i \(0.430520\pi\)
\(240\) 0 0
\(241\) −9.95052 −0.640969 −0.320485 0.947254i \(-0.603846\pi\)
−0.320485 + 0.947254i \(0.603846\pi\)
\(242\) 0 0
\(243\) 44.5618 2.85864
\(244\) 0 0
\(245\) −5.31238 −0.339395
\(246\) 0 0
\(247\) 5.44101 0.346203
\(248\) 0 0
\(249\) 13.9358 0.883145
\(250\) 0 0
\(251\) 2.64146 0.166728 0.0833639 0.996519i \(-0.473434\pi\)
0.0833639 + 0.996519i \(0.473434\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −39.1355 −2.45076
\(256\) 0 0
\(257\) −2.24328 −0.139932 −0.0699659 0.997549i \(-0.522289\pi\)
−0.0699659 + 0.997549i \(0.522289\pi\)
\(258\) 0 0
\(259\) −15.4419 −0.959512
\(260\) 0 0
\(261\) −71.2844 −4.41239
\(262\) 0 0
\(263\) 8.31828 0.512927 0.256464 0.966554i \(-0.417443\pi\)
0.256464 + 0.966554i \(0.417443\pi\)
\(264\) 0 0
\(265\) 8.87672 0.545293
\(266\) 0 0
\(267\) 19.9746 1.22243
\(268\) 0 0
\(269\) −31.0749 −1.89467 −0.947334 0.320248i \(-0.896234\pi\)
−0.947334 + 0.320248i \(0.896234\pi\)
\(270\) 0 0
\(271\) 23.9002 1.45184 0.725918 0.687781i \(-0.241415\pi\)
0.725918 + 0.687781i \(0.241415\pi\)
\(272\) 0 0
\(273\) 41.8320 2.53179
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.66668 0.100141 0.0500705 0.998746i \(-0.484055\pi\)
0.0500705 + 0.998746i \(0.484055\pi\)
\(278\) 0 0
\(279\) −74.3580 −4.45170
\(280\) 0 0
\(281\) −13.3003 −0.793432 −0.396716 0.917941i \(-0.629850\pi\)
−0.396716 + 0.917941i \(0.629850\pi\)
\(282\) 0 0
\(283\) −13.2362 −0.786811 −0.393406 0.919365i \(-0.628703\pi\)
−0.393406 + 0.919365i \(0.628703\pi\)
\(284\) 0 0
\(285\) 11.5911 0.686596
\(286\) 0 0
\(287\) −5.56009 −0.328202
\(288\) 0 0
\(289\) −5.60024 −0.329426
\(290\) 0 0
\(291\) −20.2225 −1.18546
\(292\) 0 0
\(293\) 8.08113 0.472105 0.236052 0.971740i \(-0.424146\pi\)
0.236052 + 0.971740i \(0.424146\pi\)
\(294\) 0 0
\(295\) −17.1057 −0.995930
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −31.4740 −1.82019
\(300\) 0 0
\(301\) −2.76723 −0.159501
\(302\) 0 0
\(303\) −22.5117 −1.29326
\(304\) 0 0
\(305\) 26.9628 1.54388
\(306\) 0 0
\(307\) 4.12730 0.235557 0.117779 0.993040i \(-0.462423\pi\)
0.117779 + 0.993040i \(0.462423\pi\)
\(308\) 0 0
\(309\) 42.0244 2.39068
\(310\) 0 0
\(311\) 10.7342 0.608682 0.304341 0.952563i \(-0.401564\pi\)
0.304341 + 0.952563i \(0.401564\pi\)
\(312\) 0 0
\(313\) 7.22131 0.408172 0.204086 0.978953i \(-0.434578\pi\)
0.204086 + 0.978953i \(0.434578\pi\)
\(314\) 0 0
\(315\) 64.2525 3.62022
\(316\) 0 0
\(317\) 17.7601 0.997506 0.498753 0.866744i \(-0.333792\pi\)
0.498753 + 0.866744i \(0.333792\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −11.4467 −0.638895
\(322\) 0 0
\(323\) −3.37635 −0.187865
\(324\) 0 0
\(325\) 40.7785 2.26198
\(326\) 0 0
\(327\) −65.5515 −3.62501
\(328\) 0 0
\(329\) 3.96987 0.218866
\(330\) 0 0
\(331\) 5.86554 0.322399 0.161200 0.986922i \(-0.448464\pi\)
0.161200 + 0.986922i \(0.448464\pi\)
\(332\) 0 0
\(333\) −51.0615 −2.79815
\(334\) 0 0
\(335\) 7.85213 0.429008
\(336\) 0 0
\(337\) 6.27598 0.341874 0.170937 0.985282i \(-0.445320\pi\)
0.170937 + 0.985282i \(0.445320\pi\)
\(338\) 0 0
\(339\) 45.9776 2.49716
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −19.9358 −1.07643
\(344\) 0 0
\(345\) −67.0496 −3.60983
\(346\) 0 0
\(347\) 12.8165 0.688025 0.344012 0.938965i \(-0.388214\pi\)
0.344012 + 0.938965i \(0.388214\pi\)
\(348\) 0 0
\(349\) −8.94535 −0.478834 −0.239417 0.970917i \(-0.576956\pi\)
−0.239417 + 0.970917i \(0.576956\pi\)
\(350\) 0 0
\(351\) 84.7996 4.52627
\(352\) 0 0
\(353\) 33.8419 1.80122 0.900611 0.434626i \(-0.143119\pi\)
0.900611 + 0.434626i \(0.143119\pi\)
\(354\) 0 0
\(355\) 39.0165 2.07078
\(356\) 0 0
\(357\) −25.9583 −1.37386
\(358\) 0 0
\(359\) 2.70804 0.142925 0.0714625 0.997443i \(-0.477233\pi\)
0.0714625 + 0.997443i \(0.477233\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 53.0019 2.77425
\(366\) 0 0
\(367\) 22.5295 1.17603 0.588016 0.808850i \(-0.299909\pi\)
0.588016 + 0.808850i \(0.299909\pi\)
\(368\) 0 0
\(369\) −18.3855 −0.957111
\(370\) 0 0
\(371\) 5.88786 0.305683
\(372\) 0 0
\(373\) −25.5197 −1.32136 −0.660680 0.750668i \(-0.729732\pi\)
−0.660680 + 0.750668i \(0.729732\pi\)
\(374\) 0 0
\(375\) 28.9157 1.49320
\(376\) 0 0
\(377\) −50.0281 −2.57658
\(378\) 0 0
\(379\) −12.0860 −0.620818 −0.310409 0.950603i \(-0.600466\pi\)
−0.310409 + 0.950603i \(0.600466\pi\)
\(380\) 0 0
\(381\) 18.1908 0.931944
\(382\) 0 0
\(383\) 19.4116 0.991885 0.495943 0.868355i \(-0.334823\pi\)
0.495943 + 0.868355i \(0.334823\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −9.15037 −0.465139
\(388\) 0 0
\(389\) 11.2668 0.571250 0.285625 0.958342i \(-0.407799\pi\)
0.285625 + 0.958342i \(0.407799\pi\)
\(390\) 0 0
\(391\) 19.5308 0.987716
\(392\) 0 0
\(393\) 38.2586 1.92989
\(394\) 0 0
\(395\) 18.3170 0.921630
\(396\) 0 0
\(397\) 11.9391 0.599204 0.299602 0.954064i \(-0.403146\pi\)
0.299602 + 0.954064i \(0.403146\pi\)
\(398\) 0 0
\(399\) 7.68827 0.384895
\(400\) 0 0
\(401\) 9.90453 0.494608 0.247304 0.968938i \(-0.420455\pi\)
0.247304 + 0.968938i \(0.420455\pi\)
\(402\) 0 0
\(403\) −52.1851 −2.59953
\(404\) 0 0
\(405\) 98.4362 4.89134
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −11.1425 −0.550960 −0.275480 0.961307i \(-0.588837\pi\)
−0.275480 + 0.961307i \(0.588837\pi\)
\(410\) 0 0
\(411\) −9.27336 −0.457421
\(412\) 0 0
\(413\) −11.3461 −0.558303
\(414\) 0 0
\(415\) 15.0222 0.737409
\(416\) 0 0
\(417\) −50.8246 −2.48889
\(418\) 0 0
\(419\) −7.88093 −0.385009 −0.192504 0.981296i \(-0.561661\pi\)
−0.192504 + 0.981296i \(0.561661\pi\)
\(420\) 0 0
\(421\) 37.8040 1.84245 0.921226 0.389027i \(-0.127189\pi\)
0.921226 + 0.389027i \(0.127189\pi\)
\(422\) 0 0
\(423\) 13.1271 0.638262
\(424\) 0 0
\(425\) −25.3046 −1.22745
\(426\) 0 0
\(427\) 17.8842 0.865478
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 9.80267 0.472178 0.236089 0.971731i \(-0.424134\pi\)
0.236089 + 0.971731i \(0.424134\pi\)
\(432\) 0 0
\(433\) −22.1855 −1.06617 −0.533083 0.846063i \(-0.678967\pi\)
−0.533083 + 0.846063i \(0.678967\pi\)
\(434\) 0 0
\(435\) −106.576 −5.10991
\(436\) 0 0
\(437\) −5.78459 −0.276715
\(438\) 0 0
\(439\) −18.9073 −0.902396 −0.451198 0.892424i \(-0.649003\pi\)
−0.451198 + 0.892424i \(0.649003\pi\)
\(440\) 0 0
\(441\) −11.6516 −0.554840
\(442\) 0 0
\(443\) 4.46822 0.212292 0.106146 0.994351i \(-0.466149\pi\)
0.106146 + 0.994351i \(0.466149\pi\)
\(444\) 0 0
\(445\) 21.5317 1.02070
\(446\) 0 0
\(447\) 0.769242 0.0363839
\(448\) 0 0
\(449\) −28.6131 −1.35033 −0.675167 0.737665i \(-0.735929\pi\)
−0.675167 + 0.737665i \(0.735929\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −56.7654 −2.66707
\(454\) 0 0
\(455\) 45.0930 2.11399
\(456\) 0 0
\(457\) 14.8196 0.693232 0.346616 0.938007i \(-0.387331\pi\)
0.346616 + 0.938007i \(0.387331\pi\)
\(458\) 0 0
\(459\) −52.6213 −2.45615
\(460\) 0 0
\(461\) −36.4495 −1.69762 −0.848811 0.528697i \(-0.822681\pi\)
−0.848811 + 0.528697i \(0.822681\pi\)
\(462\) 0 0
\(463\) −32.9591 −1.53174 −0.765871 0.642995i \(-0.777692\pi\)
−0.765871 + 0.642995i \(0.777692\pi\)
\(464\) 0 0
\(465\) −111.171 −5.15542
\(466\) 0 0
\(467\) 6.28650 0.290905 0.145452 0.989365i \(-0.453536\pi\)
0.145452 + 0.989365i \(0.453536\pi\)
\(468\) 0 0
\(469\) 5.20826 0.240495
\(470\) 0 0
\(471\) −35.5329 −1.63727
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 7.49465 0.343878
\(476\) 0 0
\(477\) 19.4693 0.891439
\(478\) 0 0
\(479\) 18.8832 0.862797 0.431399 0.902161i \(-0.358020\pi\)
0.431399 + 0.902161i \(0.358020\pi\)
\(480\) 0 0
\(481\) −35.8354 −1.63396
\(482\) 0 0
\(483\) −44.4735 −2.02362
\(484\) 0 0
\(485\) −21.7989 −0.989837
\(486\) 0 0
\(487\) 24.5268 1.11142 0.555708 0.831377i \(-0.312447\pi\)
0.555708 + 0.831377i \(0.312447\pi\)
\(488\) 0 0
\(489\) −29.3719 −1.32824
\(490\) 0 0
\(491\) 34.8056 1.57075 0.785377 0.619017i \(-0.212469\pi\)
0.785377 + 0.619017i \(0.212469\pi\)
\(492\) 0 0
\(493\) 31.0443 1.39816
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 25.8794 1.16085
\(498\) 0 0
\(499\) −9.63700 −0.431411 −0.215706 0.976458i \(-0.569205\pi\)
−0.215706 + 0.976458i \(0.569205\pi\)
\(500\) 0 0
\(501\) 46.2992 2.06850
\(502\) 0 0
\(503\) −32.1848 −1.43505 −0.717524 0.696534i \(-0.754724\pi\)
−0.717524 + 0.696534i \(0.754724\pi\)
\(504\) 0 0
\(505\) −24.2666 −1.07985
\(506\) 0 0
\(507\) 54.4490 2.41816
\(508\) 0 0
\(509\) 13.3645 0.592371 0.296185 0.955131i \(-0.404285\pi\)
0.296185 + 0.955131i \(0.404285\pi\)
\(510\) 0 0
\(511\) 35.1558 1.55520
\(512\) 0 0
\(513\) 15.5853 0.688106
\(514\) 0 0
\(515\) 45.3004 1.99617
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −8.40811 −0.369075
\(520\) 0 0
\(521\) 15.8705 0.695298 0.347649 0.937625i \(-0.386980\pi\)
0.347649 + 0.937625i \(0.386980\pi\)
\(522\) 0 0
\(523\) 17.2073 0.752423 0.376211 0.926534i \(-0.377227\pi\)
0.376211 + 0.926534i \(0.377227\pi\)
\(524\) 0 0
\(525\) 57.6209 2.51478
\(526\) 0 0
\(527\) 32.3828 1.41062
\(528\) 0 0
\(529\) 10.4615 0.454849
\(530\) 0 0
\(531\) −37.5179 −1.62814
\(532\) 0 0
\(533\) −12.9031 −0.558896
\(534\) 0 0
\(535\) −12.3391 −0.533465
\(536\) 0 0
\(537\) 1.49522 0.0645237
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −35.0905 −1.50866 −0.754330 0.656496i \(-0.772038\pi\)
−0.754330 + 0.656496i \(0.772038\pi\)
\(542\) 0 0
\(543\) −27.6040 −1.18460
\(544\) 0 0
\(545\) −70.6616 −3.02681
\(546\) 0 0
\(547\) 2.78485 0.119072 0.0595358 0.998226i \(-0.481038\pi\)
0.0595358 + 0.998226i \(0.481038\pi\)
\(548\) 0 0
\(549\) 59.1375 2.52393
\(550\) 0 0
\(551\) −9.19463 −0.391704
\(552\) 0 0
\(553\) 12.1496 0.516652
\(554\) 0 0
\(555\) −76.3408 −3.24049
\(556\) 0 0
\(557\) −2.49963 −0.105913 −0.0529564 0.998597i \(-0.516864\pi\)
−0.0529564 + 0.998597i \(0.516864\pi\)
\(558\) 0 0
\(559\) −6.42181 −0.271614
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −6.06488 −0.255604 −0.127802 0.991800i \(-0.540792\pi\)
−0.127802 + 0.991800i \(0.540792\pi\)
\(564\) 0 0
\(565\) 49.5618 2.08508
\(566\) 0 0
\(567\) 65.2920 2.74201
\(568\) 0 0
\(569\) 14.9447 0.626513 0.313256 0.949669i \(-0.398580\pi\)
0.313256 + 0.949669i \(0.398580\pi\)
\(570\) 0 0
\(571\) −27.3521 −1.14465 −0.572325 0.820027i \(-0.693958\pi\)
−0.572325 + 0.820027i \(0.693958\pi\)
\(572\) 0 0
\(573\) 58.9244 2.46160
\(574\) 0 0
\(575\) −43.3535 −1.80797
\(576\) 0 0
\(577\) −1.83560 −0.0764170 −0.0382085 0.999270i \(-0.512165\pi\)
−0.0382085 + 0.999270i \(0.512165\pi\)
\(578\) 0 0
\(579\) −56.5666 −2.35083
\(580\) 0 0
\(581\) 9.96409 0.413380
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 149.108 6.16487
\(586\) 0 0
\(587\) 31.1835 1.28708 0.643540 0.765412i \(-0.277465\pi\)
0.643540 + 0.765412i \(0.277465\pi\)
\(588\) 0 0
\(589\) −9.59107 −0.395193
\(590\) 0 0
\(591\) 22.5723 0.928501
\(592\) 0 0
\(593\) −20.4998 −0.841827 −0.420913 0.907101i \(-0.638290\pi\)
−0.420913 + 0.907101i \(0.638290\pi\)
\(594\) 0 0
\(595\) −27.9819 −1.14715
\(596\) 0 0
\(597\) −49.3613 −2.02023
\(598\) 0 0
\(599\) −21.8573 −0.893065 −0.446532 0.894768i \(-0.647341\pi\)
−0.446532 + 0.894768i \(0.647341\pi\)
\(600\) 0 0
\(601\) −2.12818 −0.0868102 −0.0434051 0.999058i \(-0.513821\pi\)
−0.0434051 + 0.999058i \(0.513821\pi\)
\(602\) 0 0
\(603\) 17.2221 0.701338
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 11.3933 0.462439 0.231219 0.972902i \(-0.425729\pi\)
0.231219 + 0.972902i \(0.425729\pi\)
\(608\) 0 0
\(609\) −70.6908 −2.86454
\(610\) 0 0
\(611\) 9.21273 0.372707
\(612\) 0 0
\(613\) 44.3930 1.79302 0.896508 0.443028i \(-0.146096\pi\)
0.896508 + 0.443028i \(0.146096\pi\)
\(614\) 0 0
\(615\) −27.4877 −1.10841
\(616\) 0 0
\(617\) 37.3951 1.50547 0.752736 0.658323i \(-0.228734\pi\)
0.752736 + 0.658323i \(0.228734\pi\)
\(618\) 0 0
\(619\) −15.6910 −0.630673 −0.315337 0.948980i \(-0.602117\pi\)
−0.315337 + 0.948980i \(0.602117\pi\)
\(620\) 0 0
\(621\) −90.1544 −3.61777
\(622\) 0 0
\(623\) 14.2818 0.572189
\(624\) 0 0
\(625\) −6.30344 −0.252138
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 22.2372 0.886657
\(630\) 0 0
\(631\) −7.72618 −0.307574 −0.153787 0.988104i \(-0.549147\pi\)
−0.153787 + 0.988104i \(0.549147\pi\)
\(632\) 0 0
\(633\) −63.1154 −2.50861
\(634\) 0 0
\(635\) 19.6089 0.778155
\(636\) 0 0
\(637\) −8.17723 −0.323994
\(638\) 0 0
\(639\) 85.5749 3.38529
\(640\) 0 0
\(641\) −7.26960 −0.287132 −0.143566 0.989641i \(-0.545857\pi\)
−0.143566 + 0.989641i \(0.545857\pi\)
\(642\) 0 0
\(643\) −6.00629 −0.236865 −0.118432 0.992962i \(-0.537787\pi\)
−0.118432 + 0.992962i \(0.537787\pi\)
\(644\) 0 0
\(645\) −13.6805 −0.538669
\(646\) 0 0
\(647\) 46.0802 1.81160 0.905801 0.423704i \(-0.139270\pi\)
0.905801 + 0.423704i \(0.139270\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −73.7388 −2.89005
\(652\) 0 0
\(653\) −37.2226 −1.45663 −0.728317 0.685240i \(-0.759697\pi\)
−0.728317 + 0.685240i \(0.759697\pi\)
\(654\) 0 0
\(655\) 41.2410 1.61142
\(656\) 0 0
\(657\) 116.249 4.53531
\(658\) 0 0
\(659\) −34.9204 −1.36030 −0.680152 0.733071i \(-0.738086\pi\)
−0.680152 + 0.733071i \(0.738086\pi\)
\(660\) 0 0
\(661\) −18.6194 −0.724211 −0.362105 0.932137i \(-0.617942\pi\)
−0.362105 + 0.932137i \(0.617942\pi\)
\(662\) 0 0
\(663\) −60.2405 −2.33955
\(664\) 0 0
\(665\) 8.28761 0.321380
\(666\) 0 0
\(667\) 53.1872 2.05942
\(668\) 0 0
\(669\) −51.3111 −1.98380
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 39.6581 1.52871 0.764355 0.644796i \(-0.223058\pi\)
0.764355 + 0.644796i \(0.223058\pi\)
\(674\) 0 0
\(675\) 116.806 4.49587
\(676\) 0 0
\(677\) 43.8777 1.68636 0.843179 0.537632i \(-0.180681\pi\)
0.843179 + 0.537632i \(0.180681\pi\)
\(678\) 0 0
\(679\) −14.4591 −0.554888
\(680\) 0 0
\(681\) 85.2046 3.26505
\(682\) 0 0
\(683\) −5.57257 −0.213228 −0.106614 0.994300i \(-0.534001\pi\)
−0.106614 + 0.994300i \(0.534001\pi\)
\(684\) 0 0
\(685\) −9.99626 −0.381937
\(686\) 0 0
\(687\) −65.5460 −2.50073
\(688\) 0 0
\(689\) 13.6638 0.520547
\(690\) 0 0
\(691\) −3.03739 −0.115548 −0.0577739 0.998330i \(-0.518400\pi\)
−0.0577739 + 0.998330i \(0.518400\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −54.7866 −2.07818
\(696\) 0 0
\(697\) 8.00687 0.303282
\(698\) 0 0
\(699\) −54.9514 −2.07845
\(700\) 0 0
\(701\) −6.85374 −0.258862 −0.129431 0.991588i \(-0.541315\pi\)
−0.129431 + 0.991588i \(0.541315\pi\)
\(702\) 0 0
\(703\) −6.58617 −0.248402
\(704\) 0 0
\(705\) 19.6260 0.739159
\(706\) 0 0
\(707\) −16.0959 −0.605347
\(708\) 0 0
\(709\) 22.4947 0.844804 0.422402 0.906409i \(-0.361187\pi\)
0.422402 + 0.906409i \(0.361187\pi\)
\(710\) 0 0
\(711\) 40.1748 1.50667
\(712\) 0 0
\(713\) 55.4805 2.07776
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 21.9557 0.819949
\(718\) 0 0
\(719\) 16.5930 0.618816 0.309408 0.950929i \(-0.399869\pi\)
0.309408 + 0.950929i \(0.399869\pi\)
\(720\) 0 0
\(721\) 30.0474 1.11902
\(722\) 0 0
\(723\) −32.6293 −1.21350
\(724\) 0 0
\(725\) −68.9105 −2.55927
\(726\) 0 0
\(727\) 12.7104 0.471402 0.235701 0.971826i \(-0.424261\pi\)
0.235701 + 0.971826i \(0.424261\pi\)
\(728\) 0 0
\(729\) 62.5811 2.31782
\(730\) 0 0
\(731\) 3.98498 0.147390
\(732\) 0 0
\(733\) 19.8202 0.732077 0.366039 0.930600i \(-0.380714\pi\)
0.366039 + 0.930600i \(0.380714\pi\)
\(734\) 0 0
\(735\) −17.4201 −0.642550
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 48.1166 1.77000 0.885000 0.465592i \(-0.154158\pi\)
0.885000 + 0.465592i \(0.154158\pi\)
\(740\) 0 0
\(741\) 17.8419 0.655438
\(742\) 0 0
\(743\) −35.5155 −1.30294 −0.651468 0.758676i \(-0.725847\pi\)
−0.651468 + 0.758676i \(0.725847\pi\)
\(744\) 0 0
\(745\) 0.829208 0.0303798
\(746\) 0 0
\(747\) 32.9481 1.20551
\(748\) 0 0
\(749\) −8.18441 −0.299052
\(750\) 0 0
\(751\) −8.43033 −0.307627 −0.153814 0.988100i \(-0.549156\pi\)
−0.153814 + 0.988100i \(0.549156\pi\)
\(752\) 0 0
\(753\) 8.66176 0.315652
\(754\) 0 0
\(755\) −61.1906 −2.22695
\(756\) 0 0
\(757\) −39.6118 −1.43972 −0.719858 0.694121i \(-0.755793\pi\)
−0.719858 + 0.694121i \(0.755793\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 40.8269 1.47998 0.739988 0.672621i \(-0.234831\pi\)
0.739988 + 0.672621i \(0.234831\pi\)
\(762\) 0 0
\(763\) −46.8693 −1.69678
\(764\) 0 0
\(765\) −92.5274 −3.34534
\(766\) 0 0
\(767\) −26.3304 −0.950735
\(768\) 0 0
\(769\) 7.64570 0.275711 0.137856 0.990452i \(-0.455979\pi\)
0.137856 + 0.990452i \(0.455979\pi\)
\(770\) 0 0
\(771\) −7.35604 −0.264921
\(772\) 0 0
\(773\) −12.7578 −0.458867 −0.229433 0.973324i \(-0.573687\pi\)
−0.229433 + 0.973324i \(0.573687\pi\)
\(774\) 0 0
\(775\) −71.8817 −2.58207
\(776\) 0 0
\(777\) −50.6363 −1.81657
\(778\) 0 0
\(779\) −2.37145 −0.0849662
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −143.301 −5.12115
\(784\) 0 0
\(785\) −38.3028 −1.36709
\(786\) 0 0
\(787\) −27.0124 −0.962889 −0.481445 0.876476i \(-0.659888\pi\)
−0.481445 + 0.876476i \(0.659888\pi\)
\(788\) 0 0
\(789\) 27.2769 0.971084
\(790\) 0 0
\(791\) 32.8740 1.16886
\(792\) 0 0
\(793\) 41.5033 1.47382
\(794\) 0 0
\(795\) 29.1081 1.03236
\(796\) 0 0
\(797\) −17.2729 −0.611837 −0.305919 0.952058i \(-0.598964\pi\)
−0.305919 + 0.952058i \(0.598964\pi\)
\(798\) 0 0
\(799\) −5.71685 −0.202248
\(800\) 0 0
\(801\) 47.2255 1.66863
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −47.9405 −1.68968
\(806\) 0 0
\(807\) −101.899 −3.58702
\(808\) 0 0
\(809\) 38.7686 1.36303 0.681515 0.731804i \(-0.261321\pi\)
0.681515 + 0.731804i \(0.261321\pi\)
\(810\) 0 0
\(811\) −15.4408 −0.542199 −0.271100 0.962551i \(-0.587387\pi\)
−0.271100 + 0.962551i \(0.587387\pi\)
\(812\) 0 0
\(813\) 78.3725 2.74864
\(814\) 0 0
\(815\) −31.6616 −1.10906
\(816\) 0 0
\(817\) −1.18026 −0.0412921
\(818\) 0 0
\(819\) 98.9025 3.45593
\(820\) 0 0
\(821\) −34.9424 −1.21950 −0.609750 0.792594i \(-0.708730\pi\)
−0.609750 + 0.792594i \(0.708730\pi\)
\(822\) 0 0
\(823\) −20.9332 −0.729684 −0.364842 0.931069i \(-0.618877\pi\)
−0.364842 + 0.931069i \(0.618877\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −31.8329 −1.10694 −0.553470 0.832869i \(-0.686697\pi\)
−0.553470 + 0.832869i \(0.686697\pi\)
\(828\) 0 0
\(829\) −15.1128 −0.524891 −0.262445 0.964947i \(-0.584529\pi\)
−0.262445 + 0.964947i \(0.584529\pi\)
\(830\) 0 0
\(831\) 5.46529 0.189589
\(832\) 0 0
\(833\) 5.07428 0.175813
\(834\) 0 0
\(835\) 49.9085 1.72715
\(836\) 0 0
\(837\) −149.479 −5.16676
\(838\) 0 0
\(839\) 39.0512 1.34820 0.674099 0.738641i \(-0.264532\pi\)
0.674099 + 0.738641i \(0.264532\pi\)
\(840\) 0 0
\(841\) 55.5412 1.91521
\(842\) 0 0
\(843\) −43.6139 −1.50214
\(844\) 0 0
\(845\) 58.6935 2.01912
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −43.4036 −1.48961
\(850\) 0 0
\(851\) 38.0983 1.30599
\(852\) 0 0
\(853\) 14.8573 0.508703 0.254351 0.967112i \(-0.418138\pi\)
0.254351 + 0.967112i \(0.418138\pi\)
\(854\) 0 0
\(855\) 27.4045 0.937216
\(856\) 0 0
\(857\) −42.3513 −1.44669 −0.723347 0.690485i \(-0.757397\pi\)
−0.723347 + 0.690485i \(0.757397\pi\)
\(858\) 0 0
\(859\) 23.9371 0.816723 0.408361 0.912820i \(-0.366100\pi\)
0.408361 + 0.912820i \(0.366100\pi\)
\(860\) 0 0
\(861\) −18.2324 −0.621358
\(862\) 0 0
\(863\) −41.0021 −1.39573 −0.697865 0.716230i \(-0.745866\pi\)
−0.697865 + 0.716230i \(0.745866\pi\)
\(864\) 0 0
\(865\) −9.06357 −0.308171
\(866\) 0 0
\(867\) −18.3640 −0.623676
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 12.0866 0.409540
\(872\) 0 0
\(873\) −47.8116 −1.61818
\(874\) 0 0
\(875\) 20.6747 0.698933
\(876\) 0 0
\(877\) 1.31855 0.0445242 0.0222621 0.999752i \(-0.492913\pi\)
0.0222621 + 0.999752i \(0.492913\pi\)
\(878\) 0 0
\(879\) 26.4992 0.893797
\(880\) 0 0
\(881\) −25.5816 −0.861865 −0.430933 0.902384i \(-0.641815\pi\)
−0.430933 + 0.902384i \(0.641815\pi\)
\(882\) 0 0
\(883\) −23.2089 −0.781040 −0.390520 0.920594i \(-0.627705\pi\)
−0.390520 + 0.920594i \(0.627705\pi\)
\(884\) 0 0
\(885\) −56.0920 −1.88551
\(886\) 0 0
\(887\) 33.6865 1.13108 0.565540 0.824721i \(-0.308668\pi\)
0.565540 + 0.824721i \(0.308668\pi\)
\(888\) 0 0
\(889\) 13.0064 0.436222
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1.69320 0.0566609
\(894\) 0 0
\(895\) 1.61179 0.0538760
\(896\) 0 0
\(897\) −103.208 −3.44602
\(898\) 0 0
\(899\) 88.1863 2.94118
\(900\) 0 0
\(901\) −8.47887 −0.282472
\(902\) 0 0
\(903\) −9.07417 −0.301969
\(904\) 0 0
\(905\) −29.7559 −0.989119
\(906\) 0 0
\(907\) 40.5536 1.34656 0.673280 0.739388i \(-0.264885\pi\)
0.673280 + 0.739388i \(0.264885\pi\)
\(908\) 0 0
\(909\) −53.2240 −1.76533
\(910\) 0 0
\(911\) −14.4247 −0.477911 −0.238956 0.971031i \(-0.576805\pi\)
−0.238956 + 0.971031i \(0.576805\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 88.4150 2.92291
\(916\) 0 0
\(917\) 27.3549 0.903337
\(918\) 0 0
\(919\) −39.7419 −1.31096 −0.655482 0.755211i \(-0.727534\pi\)
−0.655482 + 0.755211i \(0.727534\pi\)
\(920\) 0 0
\(921\) 13.5340 0.445962
\(922\) 0 0
\(923\) 60.0573 1.97681
\(924\) 0 0
\(925\) −49.3611 −1.62298
\(926\) 0 0
\(927\) 99.3574 3.26332
\(928\) 0 0
\(929\) −20.4506 −0.670964 −0.335482 0.942047i \(-0.608899\pi\)
−0.335482 + 0.942047i \(0.608899\pi\)
\(930\) 0 0
\(931\) −1.50289 −0.0492552
\(932\) 0 0
\(933\) 35.1991 1.15237
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 8.32869 0.272086 0.136043 0.990703i \(-0.456561\pi\)
0.136043 + 0.990703i \(0.456561\pi\)
\(938\) 0 0
\(939\) 23.6798 0.772760
\(940\) 0 0
\(941\) −51.0299 −1.66353 −0.831763 0.555131i \(-0.812668\pi\)
−0.831763 + 0.555131i \(0.812668\pi\)
\(942\) 0 0
\(943\) 13.7179 0.446716
\(944\) 0 0
\(945\) 129.165 4.20172
\(946\) 0 0
\(947\) −22.5652 −0.733270 −0.366635 0.930365i \(-0.619490\pi\)
−0.366635 + 0.930365i \(0.619490\pi\)
\(948\) 0 0
\(949\) 81.5848 2.64835
\(950\) 0 0
\(951\) 58.2380 1.88850
\(952\) 0 0
\(953\) −34.1812 −1.10724 −0.553619 0.832770i \(-0.686754\pi\)
−0.553619 + 0.832770i \(0.686754\pi\)
\(954\) 0 0
\(955\) 63.5178 2.05539
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −6.63045 −0.214108
\(960\) 0 0
\(961\) 60.9886 1.96738
\(962\) 0 0
\(963\) −27.0633 −0.872103
\(964\) 0 0
\(965\) −60.9762 −1.96289
\(966\) 0 0
\(967\) −22.0673 −0.709636 −0.354818 0.934935i \(-0.615457\pi\)
−0.354818 + 0.934935i \(0.615457\pi\)
\(968\) 0 0
\(969\) −11.0716 −0.355670
\(970\) 0 0
\(971\) 13.2403 0.424902 0.212451 0.977172i \(-0.431855\pi\)
0.212451 + 0.977172i \(0.431855\pi\)
\(972\) 0 0
\(973\) −36.3396 −1.16499
\(974\) 0 0
\(975\) 133.719 4.28243
\(976\) 0 0
\(977\) 6.65904 0.213041 0.106521 0.994310i \(-0.466029\pi\)
0.106521 + 0.994310i \(0.466029\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −154.982 −4.94820
\(982\) 0 0
\(983\) 30.9907 0.988449 0.494225 0.869334i \(-0.335452\pi\)
0.494225 + 0.869334i \(0.335452\pi\)
\(984\) 0 0
\(985\) 24.3319 0.775280
\(986\) 0 0
\(987\) 13.0178 0.414361
\(988\) 0 0
\(989\) 6.82733 0.217097
\(990\) 0 0
\(991\) 59.2229 1.88128 0.940639 0.339408i \(-0.110227\pi\)
0.940639 + 0.339408i \(0.110227\pi\)
\(992\) 0 0
\(993\) 19.2340 0.610373
\(994\) 0 0
\(995\) −53.2093 −1.68685
\(996\) 0 0
\(997\) 28.5785 0.905092 0.452546 0.891741i \(-0.350516\pi\)
0.452546 + 0.891741i \(0.350516\pi\)
\(998\) 0 0
\(999\) −102.647 −3.24761
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 9196.2.a.n.1.6 6
11.10 odd 2 836.2.a.e.1.6 6
33.32 even 2 7524.2.a.q.1.1 6
44.43 even 2 3344.2.a.w.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
836.2.a.e.1.6 6 11.10 odd 2
3344.2.a.w.1.1 6 44.43 even 2
7524.2.a.q.1.1 6 33.32 even 2
9196.2.a.n.1.6 6 1.1 even 1 trivial