Properties

Label 124.2.d.b.123.4
Level $124$
Weight $2$
Character 124.123
Analytic conductor $0.990$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [124,2,Mod(123,124)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(124, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("124.123");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 124.d (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(0.990144985064\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{6}, \sqrt{-7})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{3} - 7x^{2} + 8x + 58 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 123.4
Root \(2.94949 + 1.32288i\) of defining polynomial
Character \(\chi\) \(=\) 124.123
Dual form 124.2.d.b.123.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 1.32288i) q^{2} +2.44949 q^{3} +(-1.50000 + 1.32288i) q^{4} -2.00000 q^{5} +(1.22474 + 3.24037i) q^{6} +(-2.50000 - 1.32288i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(0.500000 + 1.32288i) q^{2} +2.44949 q^{3} +(-1.50000 + 1.32288i) q^{4} -2.00000 q^{5} +(1.22474 + 3.24037i) q^{6} +(-2.50000 - 1.32288i) q^{8} +3.00000 q^{9} +(-1.00000 - 2.64575i) q^{10} +2.44949 q^{11} +(-3.67423 + 3.24037i) q^{12} -6.48074i q^{13} -4.89898 q^{15} +(0.500000 - 3.96863i) q^{16} +(1.50000 + 3.96863i) q^{18} +5.29150i q^{19} +(3.00000 - 2.64575i) q^{20} +(1.22474 + 3.24037i) q^{22} -4.89898 q^{23} +(-6.12372 - 3.24037i) q^{24} -1.00000 q^{25} +(8.57321 - 3.24037i) q^{26} +6.48074i q^{29} +(-2.44949 - 6.48074i) q^{30} +(4.89898 - 2.64575i) q^{31} +(5.50000 - 1.32288i) q^{32} +6.00000 q^{33} +(-4.50000 + 3.96863i) q^{36} -6.48074i q^{37} +(-7.00000 + 2.64575i) q^{38} -15.8745i q^{39} +(5.00000 + 2.64575i) q^{40} -8.00000 q^{41} +2.44949 q^{43} +(-3.67423 + 3.24037i) q^{44} -6.00000 q^{45} +(-2.44949 - 6.48074i) q^{46} +10.5830i q^{47} +(1.22474 - 9.72111i) q^{48} +7.00000 q^{49} +(-0.500000 - 1.32288i) q^{50} +(8.57321 + 9.72111i) q^{52} +6.48074i q^{53} -4.89898 q^{55} +12.9615i q^{57} +(-8.57321 + 3.24037i) q^{58} -5.29150i q^{59} +(7.34847 - 6.48074i) q^{60} +6.48074i q^{61} +(5.94949 + 5.15787i) q^{62} +(4.50000 + 6.61438i) q^{64} +12.9615i q^{65} +(3.00000 + 7.93725i) q^{66} +5.29150i q^{67} -12.0000 q^{69} +5.29150i q^{71} +(-7.50000 - 3.96863i) q^{72} -12.9615i q^{73} +(8.57321 - 3.24037i) q^{74} -2.44949 q^{75} +(-7.00000 - 7.93725i) q^{76} +(21.0000 - 7.93725i) q^{78} -9.79796 q^{79} +(-1.00000 + 7.93725i) q^{80} -9.00000 q^{81} +(-4.00000 - 10.5830i) q^{82} +12.2474 q^{83} +(1.22474 + 3.24037i) q^{86} +15.8745i q^{87} +(-6.12372 - 3.24037i) q^{88} -12.9615i q^{89} +(-3.00000 - 7.93725i) q^{90} +(7.34847 - 6.48074i) q^{92} +(12.0000 - 6.48074i) q^{93} +(-14.0000 + 5.29150i) q^{94} -10.5830i q^{95} +(13.4722 - 3.24037i) q^{96} +4.00000 q^{97} +(3.50000 + 9.26013i) q^{98} +7.34847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 6 q^{4} - 8 q^{5} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 6 q^{4} - 8 q^{5} - 10 q^{8} + 12 q^{9} - 4 q^{10} + 2 q^{16} + 6 q^{18} + 12 q^{20} - 4 q^{25} + 22 q^{32} + 24 q^{33} - 18 q^{36} - 28 q^{38} + 20 q^{40} - 32 q^{41} - 24 q^{45} + 28 q^{49} - 2 q^{50} + 14 q^{62} + 18 q^{64} + 12 q^{66} - 48 q^{69} - 30 q^{72} - 28 q^{76} + 84 q^{78} - 4 q^{80} - 36 q^{81} - 16 q^{82} - 12 q^{90} + 48 q^{93} - 56 q^{94} + 16 q^{97} + 14 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).

\(n\) \(63\) \(65\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 1.32288i 0.353553 + 0.935414i
\(3\) 2.44949 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(4\) −1.50000 + 1.32288i −0.750000 + 0.661438i
\(5\) −2.00000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 1.22474 + 3.24037i 0.500000 + 1.32288i
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) −2.50000 1.32288i −0.883883 0.467707i
\(9\) 3.00000 1.00000
\(10\) −1.00000 2.64575i −0.316228 0.836660i
\(11\) 2.44949 0.738549 0.369274 0.929320i \(-0.379606\pi\)
0.369274 + 0.929320i \(0.379606\pi\)
\(12\) −3.67423 + 3.24037i −1.06066 + 0.935414i
\(13\) 6.48074i 1.79743i −0.438529 0.898717i \(-0.644500\pi\)
0.438529 0.898717i \(-0.355500\pi\)
\(14\) 0 0
\(15\) −4.89898 −1.26491
\(16\) 0.500000 3.96863i 0.125000 0.992157i
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 1.50000 + 3.96863i 0.353553 + 0.935414i
\(19\) 5.29150i 1.21395i 0.794719 + 0.606977i \(0.207618\pi\)
−0.794719 + 0.606977i \(0.792382\pi\)
\(20\) 3.00000 2.64575i 0.670820 0.591608i
\(21\) 0 0
\(22\) 1.22474 + 3.24037i 0.261116 + 0.690849i
\(23\) −4.89898 −1.02151 −0.510754 0.859727i \(-0.670634\pi\)
−0.510754 + 0.859727i \(0.670634\pi\)
\(24\) −6.12372 3.24037i −1.25000 0.661438i
\(25\) −1.00000 −0.200000
\(26\) 8.57321 3.24037i 1.68135 0.635489i
\(27\) 0 0
\(28\) 0 0
\(29\) 6.48074i 1.20344i 0.798706 + 0.601722i \(0.205518\pi\)
−0.798706 + 0.601722i \(0.794482\pi\)
\(30\) −2.44949 6.48074i −0.447214 1.18322i
\(31\) 4.89898 2.64575i 0.879883 0.475191i
\(32\) 5.50000 1.32288i 0.972272 0.233854i
\(33\) 6.00000 1.04447
\(34\) 0 0
\(35\) 0 0
\(36\) −4.50000 + 3.96863i −0.750000 + 0.661438i
\(37\) 6.48074i 1.06543i −0.846296 0.532714i \(-0.821172\pi\)
0.846296 0.532714i \(-0.178828\pi\)
\(38\) −7.00000 + 2.64575i −1.13555 + 0.429198i
\(39\) 15.8745i 2.54196i
\(40\) 5.00000 + 2.64575i 0.790569 + 0.418330i
\(41\) −8.00000 −1.24939 −0.624695 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) 2.44949 0.373544 0.186772 0.982403i \(-0.440197\pi\)
0.186772 + 0.982403i \(0.440197\pi\)
\(44\) −3.67423 + 3.24037i −0.553912 + 0.488504i
\(45\) −6.00000 −0.894427
\(46\) −2.44949 6.48074i −0.361158 0.955533i
\(47\) 10.5830i 1.54369i 0.635811 + 0.771845i \(0.280666\pi\)
−0.635811 + 0.771845i \(0.719334\pi\)
\(48\) 1.22474 9.72111i 0.176777 1.40312i
\(49\) 7.00000 1.00000
\(50\) −0.500000 1.32288i −0.0707107 0.187083i
\(51\) 0 0
\(52\) 8.57321 + 9.72111i 1.18889 + 1.34808i
\(53\) 6.48074i 0.890198i 0.895481 + 0.445099i \(0.146832\pi\)
−0.895481 + 0.445099i \(0.853168\pi\)
\(54\) 0 0
\(55\) −4.89898 −0.660578
\(56\) 0 0
\(57\) 12.9615i 1.71679i
\(58\) −8.57321 + 3.24037i −1.12572 + 0.425481i
\(59\) 5.29150i 0.688895i −0.938806 0.344447i \(-0.888066\pi\)
0.938806 0.344447i \(-0.111934\pi\)
\(60\) 7.34847 6.48074i 0.948683 0.836660i
\(61\) 6.48074i 0.829774i 0.909873 + 0.414887i \(0.136179\pi\)
−0.909873 + 0.414887i \(0.863821\pi\)
\(62\) 5.94949 + 5.15787i 0.755586 + 0.655050i
\(63\) 0 0
\(64\) 4.50000 + 6.61438i 0.562500 + 0.826797i
\(65\) 12.9615i 1.60767i
\(66\) 3.00000 + 7.93725i 0.369274 + 0.977008i
\(67\) 5.29150i 0.646460i 0.946320 + 0.323230i \(0.104769\pi\)
−0.946320 + 0.323230i \(0.895231\pi\)
\(68\) 0 0
\(69\) −12.0000 −1.44463
\(70\) 0 0
\(71\) 5.29150i 0.627986i 0.949425 + 0.313993i \(0.101667\pi\)
−0.949425 + 0.313993i \(0.898333\pi\)
\(72\) −7.50000 3.96863i −0.883883 0.467707i
\(73\) 12.9615i 1.51703i −0.651658 0.758513i \(-0.725926\pi\)
0.651658 0.758513i \(-0.274074\pi\)
\(74\) 8.57321 3.24037i 0.996616 0.376685i
\(75\) −2.44949 −0.282843
\(76\) −7.00000 7.93725i −0.802955 0.910465i
\(77\) 0 0
\(78\) 21.0000 7.93725i 2.37778 0.898717i
\(79\) −9.79796 −1.10236 −0.551178 0.834388i \(-0.685822\pi\)
−0.551178 + 0.834388i \(0.685822\pi\)
\(80\) −1.00000 + 7.93725i −0.111803 + 0.887412i
\(81\) −9.00000 −1.00000
\(82\) −4.00000 10.5830i −0.441726 1.16870i
\(83\) 12.2474 1.34433 0.672166 0.740400i \(-0.265364\pi\)
0.672166 + 0.740400i \(0.265364\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.22474 + 3.24037i 0.132068 + 0.349418i
\(87\) 15.8745i 1.70193i
\(88\) −6.12372 3.24037i −0.652791 0.345425i
\(89\) 12.9615i 1.37391i −0.726698 0.686957i \(-0.758946\pi\)
0.726698 0.686957i \(-0.241054\pi\)
\(90\) −3.00000 7.93725i −0.316228 0.836660i
\(91\) 0 0
\(92\) 7.34847 6.48074i 0.766131 0.675664i
\(93\) 12.0000 6.48074i 1.24434 0.672022i
\(94\) −14.0000 + 5.29150i −1.44399 + 0.545777i
\(95\) 10.5830i 1.08579i
\(96\) 13.4722 3.24037i 1.37500 0.330719i
\(97\) 4.00000 0.406138 0.203069 0.979164i \(-0.434908\pi\)
0.203069 + 0.979164i \(0.434908\pi\)
\(98\) 3.50000 + 9.26013i 0.353553 + 0.935414i
\(99\) 7.34847 0.738549
\(100\) 1.50000 1.32288i 0.150000 0.132288i
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 0 0
\(103\) 5.29150i 0.521387i −0.965422 0.260694i \(-0.916049\pi\)
0.965422 0.260694i \(-0.0839512\pi\)
\(104\) −8.57321 + 16.2019i −0.840673 + 1.58872i
\(105\) 0 0
\(106\) −8.57321 + 3.24037i −0.832704 + 0.314733i
\(107\) 5.29150i 0.511549i 0.966736 + 0.255774i \(0.0823304\pi\)
−0.966736 + 0.255774i \(0.917670\pi\)
\(108\) 0 0
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) −2.44949 6.48074i −0.233550 0.617914i
\(111\) 15.8745i 1.50674i
\(112\) 0 0
\(113\) −4.00000 −0.376288 −0.188144 0.982141i \(-0.560247\pi\)
−0.188144 + 0.982141i \(0.560247\pi\)
\(114\) −17.1464 + 6.48074i −1.60591 + 0.606977i
\(115\) 9.79796 0.913664
\(116\) −8.57321 9.72111i −0.796003 0.902583i
\(117\) 19.4422i 1.79743i
\(118\) 7.00000 2.64575i 0.644402 0.243561i
\(119\) 0 0
\(120\) 12.2474 + 6.48074i 1.11803 + 0.591608i
\(121\) −5.00000 −0.454545
\(122\) −8.57321 + 3.24037i −0.776182 + 0.293369i
\(123\) −19.5959 −1.76690
\(124\) −3.84847 + 10.4494i −0.345603 + 0.938381i
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) −9.79796 −0.869428 −0.434714 0.900568i \(-0.643151\pi\)
−0.434714 + 0.900568i \(0.643151\pi\)
\(128\) −6.50000 + 9.26013i −0.574524 + 0.818488i
\(129\) 6.00000 0.528271
\(130\) −17.1464 + 6.48074i −1.50384 + 0.568399i
\(131\) 5.29150i 0.462321i 0.972916 + 0.231160i \(0.0742522\pi\)
−0.972916 + 0.231160i \(0.925748\pi\)
\(132\) −9.00000 + 7.93725i −0.783349 + 0.690849i
\(133\) 0 0
\(134\) −7.00000 + 2.64575i −0.604708 + 0.228558i
\(135\) 0 0
\(136\) 0 0
\(137\) 12.9615i 1.10737i −0.832725 0.553687i \(-0.813220\pi\)
0.832725 0.553687i \(-0.186780\pi\)
\(138\) −6.00000 15.8745i −0.510754 1.35133i
\(139\) 7.34847 0.623289 0.311645 0.950199i \(-0.399120\pi\)
0.311645 + 0.950199i \(0.399120\pi\)
\(140\) 0 0
\(141\) 25.9230i 2.18311i
\(142\) −7.00000 + 2.64575i −0.587427 + 0.222027i
\(143\) 15.8745i 1.32749i
\(144\) 1.50000 11.9059i 0.125000 0.992157i
\(145\) 12.9615i 1.07639i
\(146\) 17.1464 6.48074i 1.41905 0.536350i
\(147\) 17.1464 1.41421
\(148\) 8.57321 + 9.72111i 0.704714 + 0.799070i
\(149\) 2.00000 0.163846 0.0819232 0.996639i \(-0.473894\pi\)
0.0819232 + 0.996639i \(0.473894\pi\)
\(150\) −1.22474 3.24037i −0.100000 0.264575i
\(151\) 4.89898 0.398673 0.199337 0.979931i \(-0.436121\pi\)
0.199337 + 0.979931i \(0.436121\pi\)
\(152\) 7.00000 13.2288i 0.567775 1.07299i
\(153\) 0 0
\(154\) 0 0
\(155\) −9.79796 + 5.29150i −0.786991 + 0.425024i
\(156\) 21.0000 + 23.8118i 1.68135 + 1.90647i
\(157\) 6.00000 0.478852 0.239426 0.970915i \(-0.423041\pi\)
0.239426 + 0.970915i \(0.423041\pi\)
\(158\) −4.89898 12.9615i −0.389742 1.03116i
\(159\) 15.8745i 1.25893i
\(160\) −11.0000 + 2.64575i −0.869626 + 0.209165i
\(161\) 0 0
\(162\) −4.50000 11.9059i −0.353553 0.935414i
\(163\) 15.8745i 1.24339i −0.783260 0.621694i \(-0.786445\pi\)
0.783260 0.621694i \(-0.213555\pi\)
\(164\) 12.0000 10.5830i 0.937043 0.826394i
\(165\) −12.0000 −0.934199
\(166\) 6.12372 + 16.2019i 0.475293 + 1.25751i
\(167\) −4.89898 −0.379094 −0.189547 0.981872i \(-0.560702\pi\)
−0.189547 + 0.981872i \(0.560702\pi\)
\(168\) 0 0
\(169\) −29.0000 −2.23077
\(170\) 0 0
\(171\) 15.8745i 1.21395i
\(172\) −3.67423 + 3.24037i −0.280158 + 0.247076i
\(173\) 2.00000 0.152057 0.0760286 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) −21.0000 + 7.93725i −1.59201 + 0.601722i
\(175\) 0 0
\(176\) 1.22474 9.72111i 0.0923186 0.732756i
\(177\) 12.9615i 0.974245i
\(178\) 17.1464 6.48074i 1.28518 0.485752i
\(179\) 12.2474 0.915417 0.457709 0.889102i \(-0.348670\pi\)
0.457709 + 0.889102i \(0.348670\pi\)
\(180\) 9.00000 7.93725i 0.670820 0.591608i
\(181\) 6.48074i 0.481710i 0.970561 + 0.240855i \(0.0774278\pi\)
−0.970561 + 0.240855i \(0.922572\pi\)
\(182\) 0 0
\(183\) 15.8745i 1.17348i
\(184\) 12.2474 + 6.48074i 0.902894 + 0.477767i
\(185\) 12.9615i 0.952947i
\(186\) 14.5732 + 12.6341i 1.06856 + 0.926380i
\(187\) 0 0
\(188\) −14.0000 15.8745i −1.02105 1.15777i
\(189\) 0 0
\(190\) 14.0000 5.29150i 1.01567 0.383886i
\(191\) 10.5830i 0.765759i −0.923798 0.382880i \(-0.874932\pi\)
0.923798 0.382880i \(-0.125068\pi\)
\(192\) 11.0227 + 16.2019i 0.795495 + 1.16927i
\(193\) 6.00000 0.431889 0.215945 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) 2.00000 + 5.29150i 0.143592 + 0.379908i
\(195\) 31.7490i 2.27359i
\(196\) −10.5000 + 9.26013i −0.750000 + 0.661438i
\(197\) 6.48074i 0.461734i −0.972985 0.230867i \(-0.925844\pi\)
0.972985 0.230867i \(-0.0741562\pi\)
\(198\) 3.67423 + 9.72111i 0.261116 + 0.690849i
\(199\) 14.6969 1.04184 0.520919 0.853606i \(-0.325589\pi\)
0.520919 + 0.853606i \(0.325589\pi\)
\(200\) 2.50000 + 1.32288i 0.176777 + 0.0935414i
\(201\) 12.9615i 0.914232i
\(202\) 1.00000 + 2.64575i 0.0703598 + 0.186154i
\(203\) 0 0
\(204\) 0 0
\(205\) 16.0000 1.11749
\(206\) 7.00000 2.64575i 0.487713 0.184338i
\(207\) −14.6969 −1.02151
\(208\) −25.7196 3.24037i −1.78334 0.224679i
\(209\) 12.9615i 0.896564i
\(210\) 0 0
\(211\) 15.8745i 1.09285i 0.837509 + 0.546423i \(0.184011\pi\)
−0.837509 + 0.546423i \(0.815989\pi\)
\(212\) −8.57321 9.72111i −0.588811 0.667649i
\(213\) 12.9615i 0.888106i
\(214\) −7.00000 + 2.64575i −0.478510 + 0.180860i
\(215\) −4.89898 −0.334108
\(216\) 0 0
\(217\) 0 0
\(218\) 7.00000 + 18.5203i 0.474100 + 1.25435i
\(219\) 31.7490i 2.14540i
\(220\) 7.34847 6.48074i 0.495434 0.436931i
\(221\) 0 0
\(222\) 21.0000 7.93725i 1.40943 0.532714i
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) −3.00000 −0.200000
\(226\) −2.00000 5.29150i −0.133038 0.351986i
\(227\) 26.4575i 1.75605i −0.478618 0.878023i \(-0.658862\pi\)
0.478618 0.878023i \(-0.341138\pi\)
\(228\) −17.1464 19.4422i −1.13555 1.28759i
\(229\) 6.48074i 0.428259i −0.976805 0.214130i \(-0.931308\pi\)
0.976805 0.214130i \(-0.0686915\pi\)
\(230\) 4.89898 + 12.9615i 0.323029 + 0.854655i
\(231\) 0 0
\(232\) 8.57321 16.2019i 0.562859 1.06370i
\(233\) −16.0000 −1.04819 −0.524097 0.851658i \(-0.675597\pi\)
−0.524097 + 0.851658i \(0.675597\pi\)
\(234\) 25.7196 9.72111i 1.68135 0.635489i
\(235\) 21.1660i 1.38072i
\(236\) 7.00000 + 7.93725i 0.455661 + 0.516671i
\(237\) −24.0000 −1.55897
\(238\) 0 0
\(239\) −19.5959 −1.26755 −0.633777 0.773516i \(-0.718496\pi\)
−0.633777 + 0.773516i \(0.718496\pi\)
\(240\) −2.44949 + 19.4422i −0.158114 + 1.25499i
\(241\) 25.9230i 1.66984i 0.550368 + 0.834922i \(0.314488\pi\)
−0.550368 + 0.834922i \(0.685512\pi\)
\(242\) −2.50000 6.61438i −0.160706 0.425188i
\(243\) −22.0454 −1.41421
\(244\) −8.57321 9.72111i −0.548844 0.622330i
\(245\) −14.0000 −0.894427
\(246\) −9.79796 25.9230i −0.624695 1.65279i
\(247\) 34.2929 2.18200
\(248\) −15.7474 + 0.133638i −0.999964 + 0.00848599i
\(249\) 30.0000 1.90117
\(250\) 6.00000 + 15.8745i 0.379473 + 1.00399i
\(251\) −7.34847 −0.463831 −0.231916 0.972736i \(-0.574499\pi\)
−0.231916 + 0.972736i \(0.574499\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) −4.89898 12.9615i −0.307389 0.813276i
\(255\) 0 0
\(256\) −15.5000 3.96863i −0.968750 0.248039i
\(257\) 10.0000 0.623783 0.311891 0.950118i \(-0.399037\pi\)
0.311891 + 0.950118i \(0.399037\pi\)
\(258\) 3.00000 + 7.93725i 0.186772 + 0.494152i
\(259\) 0 0
\(260\) −17.1464 19.4422i −1.06338 1.20576i
\(261\) 19.4422i 1.20344i
\(262\) −7.00000 + 2.64575i −0.432461 + 0.163455i
\(263\) −4.89898 −0.302084 −0.151042 0.988527i \(-0.548263\pi\)
−0.151042 + 0.988527i \(0.548263\pi\)
\(264\) −15.0000 7.93725i −0.923186 0.488504i
\(265\) 12.9615i 0.796217i
\(266\) 0 0
\(267\) 31.7490i 1.94301i
\(268\) −7.00000 7.93725i −0.427593 0.484845i
\(269\) 6.48074i 0.395138i −0.980289 0.197569i \(-0.936695\pi\)
0.980289 0.197569i \(-0.0633046\pi\)
\(270\) 0 0
\(271\) −29.3939 −1.78555 −0.892775 0.450502i \(-0.851245\pi\)
−0.892775 + 0.450502i \(0.851245\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 17.1464 6.48074i 1.03585 0.391516i
\(275\) −2.44949 −0.147710
\(276\) 18.0000 15.8745i 1.08347 0.955533i
\(277\) 6.48074i 0.389390i 0.980864 + 0.194695i \(0.0623717\pi\)
−0.980864 + 0.194695i \(0.937628\pi\)
\(278\) 3.67423 + 9.72111i 0.220366 + 0.583033i
\(279\) 14.6969 7.93725i 0.879883 0.475191i
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) −34.2929 + 12.9615i −2.04211 + 0.771845i
\(283\) 15.8745i 0.943642i 0.881694 + 0.471821i \(0.156403\pi\)
−0.881694 + 0.471821i \(0.843597\pi\)
\(284\) −7.00000 7.93725i −0.415374 0.470989i
\(285\) 25.9230i 1.53554i
\(286\) 21.0000 7.93725i 1.24176 0.469340i
\(287\) 0 0
\(288\) 16.5000 3.96863i 0.972272 0.233854i
\(289\) 17.0000 1.00000
\(290\) 17.1464 6.48074i 1.00687 0.380562i
\(291\) 9.79796 0.574367
\(292\) 17.1464 + 19.4422i 1.00342 + 1.13777i
\(293\) 22.0000 1.28525 0.642627 0.766179i \(-0.277845\pi\)
0.642627 + 0.766179i \(0.277845\pi\)
\(294\) 8.57321 + 22.6826i 0.500000 + 1.32288i
\(295\) 10.5830i 0.616166i
\(296\) −8.57321 + 16.2019i −0.498308 + 0.941714i
\(297\) 0 0
\(298\) 1.00000 + 2.64575i 0.0579284 + 0.153264i
\(299\) 31.7490i 1.83609i
\(300\) 3.67423 3.24037i 0.212132 0.187083i
\(301\) 0 0
\(302\) 2.44949 + 6.48074i 0.140952 + 0.372925i
\(303\) 4.89898 0.281439
\(304\) 21.0000 + 2.64575i 1.20443 + 0.151744i
\(305\) 12.9615i 0.742172i
\(306\) 0 0
\(307\) 26.4575i 1.51001i 0.655719 + 0.755005i \(0.272366\pi\)
−0.655719 + 0.755005i \(0.727634\pi\)
\(308\) 0 0
\(309\) 12.9615i 0.737353i
\(310\) −11.8990 10.3157i −0.675817 0.585894i
\(311\) 5.29150i 0.300054i −0.988682 0.150027i \(-0.952064\pi\)
0.988682 0.150027i \(-0.0479360\pi\)
\(312\) −21.0000 + 39.6863i −1.18889 + 2.24679i
\(313\) 12.9615i 0.732626i −0.930492 0.366313i \(-0.880620\pi\)
0.930492 0.366313i \(-0.119380\pi\)
\(314\) 3.00000 + 7.93725i 0.169300 + 0.447925i
\(315\) 0 0
\(316\) 14.6969 12.9615i 0.826767 0.729140i
\(317\) −14.0000 −0.786318 −0.393159 0.919470i \(-0.628618\pi\)
−0.393159 + 0.919470i \(0.628618\pi\)
\(318\) −21.0000 + 7.93725i −1.17762 + 0.445099i
\(319\) 15.8745i 0.888802i
\(320\) −9.00000 13.2288i −0.503115 0.739510i
\(321\) 12.9615i 0.723439i
\(322\) 0 0
\(323\) 0 0
\(324\) 13.5000 11.9059i 0.750000 0.661438i
\(325\) 6.48074i 0.359487i
\(326\) 21.0000 7.93725i 1.16308 0.439604i
\(327\) 34.2929 1.89640
\(328\) 20.0000 + 10.5830i 1.10432 + 0.584349i
\(329\) 0 0
\(330\) −6.00000 15.8745i −0.330289 0.873863i
\(331\) −12.2474 −0.673181 −0.336590 0.941651i \(-0.609274\pi\)
−0.336590 + 0.941651i \(0.609274\pi\)
\(332\) −18.3712 + 16.2019i −1.00825 + 0.889192i
\(333\) 19.4422i 1.06543i
\(334\) −2.44949 6.48074i −0.134030 0.354610i
\(335\) 10.5830i 0.578211i
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) −14.5000 38.3634i −0.788696 2.08669i
\(339\) −9.79796 −0.532152
\(340\) 0 0
\(341\) 12.0000 6.48074i 0.649836 0.350952i
\(342\) −21.0000 + 7.93725i −1.13555 + 0.429198i
\(343\) 0 0
\(344\) −6.12372 3.24037i −0.330169 0.174709i
\(345\) 24.0000 1.29212
\(346\) 1.00000 + 2.64575i 0.0537603 + 0.142236i
\(347\) −22.0454 −1.18346 −0.591730 0.806136i \(-0.701555\pi\)
−0.591730 + 0.806136i \(0.701555\pi\)
\(348\) −21.0000 23.8118i −1.12572 1.27644i
\(349\) −18.0000 −0.963518 −0.481759 0.876304i \(-0.660002\pi\)
−0.481759 + 0.876304i \(0.660002\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 13.4722 3.24037i 0.718070 0.172712i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 17.1464 6.48074i 0.911322 0.344447i
\(355\) 10.5830i 0.561688i
\(356\) 17.1464 + 19.4422i 0.908759 + 1.03044i
\(357\) 0 0
\(358\) 6.12372 + 16.2019i 0.323649 + 0.856294i
\(359\) 21.1660i 1.11710i 0.829471 + 0.558550i \(0.188642\pi\)
−0.829471 + 0.558550i \(0.811358\pi\)
\(360\) 15.0000 + 7.93725i 0.790569 + 0.418330i
\(361\) −9.00000 −0.473684
\(362\) −8.57321 + 3.24037i −0.450598 + 0.170310i
\(363\) −12.2474 −0.642824
\(364\) 0 0
\(365\) 25.9230i 1.35687i
\(366\) −21.0000 + 7.93725i −1.09769 + 0.414887i
\(367\) 19.5959 1.02290 0.511449 0.859313i \(-0.329109\pi\)
0.511449 + 0.859313i \(0.329109\pi\)
\(368\) −2.44949 + 19.4422i −0.127688 + 1.01350i
\(369\) −24.0000 −1.24939
\(370\) −17.1464 + 6.48074i −0.891400 + 0.336918i
\(371\) 0 0
\(372\) −9.42679 + 25.5956i −0.488756 + 1.32707i
\(373\) −26.0000 −1.34623 −0.673114 0.739538i \(-0.735044\pi\)
−0.673114 + 0.739538i \(0.735044\pi\)
\(374\) 0 0
\(375\) 29.3939 1.51789
\(376\) 14.0000 26.4575i 0.721995 1.36444i
\(377\) 42.0000 2.16311
\(378\) 0 0
\(379\) 15.8745i 0.815419i −0.913112 0.407709i \(-0.866328\pi\)
0.913112 0.407709i \(-0.133672\pi\)
\(380\) 14.0000 + 15.8745i 0.718185 + 0.814345i
\(381\) −24.0000 −1.22956
\(382\) 14.0000 5.29150i 0.716302 0.270737i
\(383\) 29.3939 1.50196 0.750978 0.660327i \(-0.229582\pi\)
0.750978 + 0.660327i \(0.229582\pi\)
\(384\) −15.9217 + 22.6826i −0.812500 + 1.15752i
\(385\) 0 0
\(386\) 3.00000 + 7.93725i 0.152696 + 0.403996i
\(387\) 7.34847 0.373544
\(388\) −6.00000 + 5.29150i −0.304604 + 0.268635i
\(389\) 19.4422i 0.985760i −0.870097 0.492880i \(-0.835944\pi\)
0.870097 0.492880i \(-0.164056\pi\)
\(390\) −42.0000 + 15.8745i −2.12675 + 0.803837i
\(391\) 0 0
\(392\) −17.5000 9.26013i −0.883883 0.467707i
\(393\) 12.9615i 0.653820i
\(394\) 8.57321 3.24037i 0.431912 0.163247i
\(395\) 19.5959 0.985978
\(396\) −11.0227 + 9.72111i −0.553912 + 0.488504i
\(397\) 10.0000 0.501886 0.250943 0.968002i \(-0.419259\pi\)
0.250943 + 0.968002i \(0.419259\pi\)
\(398\) 7.34847 + 19.4422i 0.368345 + 0.974551i
\(399\) 0 0
\(400\) −0.500000 + 3.96863i −0.0250000 + 0.198431i
\(401\) 25.9230i 1.29453i −0.762265 0.647265i \(-0.775913\pi\)
0.762265 0.647265i \(-0.224087\pi\)
\(402\) −17.1464 + 6.48074i −0.855186 + 0.323230i
\(403\) −17.1464 31.7490i −0.854124 1.58153i
\(404\) −3.00000 + 2.64575i −0.149256 + 0.131631i
\(405\) 18.0000 0.894427
\(406\) 0 0
\(407\) 15.8745i 0.786870i
\(408\) 0 0
\(409\) 38.8844i 1.92271i 0.275308 + 0.961356i \(0.411220\pi\)
−0.275308 + 0.961356i \(0.588780\pi\)
\(410\) 8.00000 + 21.1660i 0.395092 + 1.04531i
\(411\) 31.7490i 1.56606i
\(412\) 7.00000 + 7.93725i 0.344865 + 0.391040i
\(413\) 0 0
\(414\) −7.34847 19.4422i −0.361158 0.955533i
\(415\) −24.4949 −1.20241
\(416\) −8.57321 35.6441i −0.420336 1.74759i
\(417\) 18.0000 0.881464
\(418\) −17.1464 + 6.48074i −0.838659 + 0.316983i
\(419\) 37.0405i 1.80955i 0.425892 + 0.904774i \(0.359960\pi\)
−0.425892 + 0.904774i \(0.640040\pi\)
\(420\) 0 0
\(421\) 18.0000 0.877266 0.438633 0.898666i \(-0.355463\pi\)
0.438633 + 0.898666i \(0.355463\pi\)
\(422\) −21.0000 + 7.93725i −1.02226 + 0.386379i
\(423\) 31.7490i 1.54369i
\(424\) 8.57321 16.2019i 0.416352 0.786831i
\(425\) 0 0
\(426\) −17.1464 + 6.48074i −0.830747 + 0.313993i
\(427\) 0 0
\(428\) −7.00000 7.93725i −0.338358 0.383662i
\(429\) 38.8844i 1.87736i
\(430\) −2.44949 6.48074i −0.118125 0.312529i
\(431\) 10.5830i 0.509765i 0.966972 + 0.254883i \(0.0820369\pi\)
−0.966972 + 0.254883i \(0.917963\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 31.7490i 1.52225i
\(436\) −21.0000 + 18.5203i −1.00572 + 0.886960i
\(437\) 25.9230i 1.24006i
\(438\) 42.0000 15.8745i 2.00684 0.758513i
\(439\) 21.1660i 1.01020i 0.863061 + 0.505099i \(0.168544\pi\)
−0.863061 + 0.505099i \(0.831456\pi\)
\(440\) 12.2474 + 6.48074i 0.583874 + 0.308957i
\(441\) 21.0000 1.00000
\(442\) 0 0
\(443\) 5.29150i 0.251407i 0.992068 + 0.125703i \(0.0401188\pi\)
−0.992068 + 0.125703i \(0.959881\pi\)
\(444\) 21.0000 + 23.8118i 0.996616 + 1.13006i
\(445\) 25.9230i 1.22887i
\(446\) 0 0
\(447\) 4.89898 0.231714
\(448\) 0 0
\(449\) 25.9230i 1.22338i −0.791097 0.611690i \(-0.790490\pi\)
0.791097 0.611690i \(-0.209510\pi\)
\(450\) −1.50000 3.96863i −0.0707107 0.187083i
\(451\) −19.5959 −0.922736
\(452\) 6.00000 5.29150i 0.282216 0.248891i
\(453\) 12.0000 0.563809
\(454\) 35.0000 13.2288i 1.64263 0.620856i
\(455\) 0 0
\(456\) 17.1464 32.4037i 0.802955 1.51744i
\(457\) 12.9615i 0.606313i 0.952941 + 0.303156i \(0.0980404\pi\)
−0.952941 + 0.303156i \(0.901960\pi\)
\(458\) 8.57321 3.24037i 0.400600 0.151413i
\(459\) 0 0
\(460\) −14.6969 + 12.9615i −0.685248 + 0.604332i
\(461\) 6.48074i 0.301838i −0.988546 0.150919i \(-0.951777\pi\)
0.988546 0.150919i \(-0.0482233\pi\)
\(462\) 0 0
\(463\) 9.79796 0.455350 0.227675 0.973737i \(-0.426888\pi\)
0.227675 + 0.973737i \(0.426888\pi\)
\(464\) 25.7196 + 3.24037i 1.19400 + 0.150430i
\(465\) −24.0000 + 12.9615i −1.11297 + 0.601074i
\(466\) −8.00000 21.1660i −0.370593 0.980497i
\(467\) 5.29150i 0.244862i −0.992477 0.122431i \(-0.960931\pi\)
0.992477 0.122431i \(-0.0390689\pi\)
\(468\) 25.7196 + 29.1633i 1.18889 + 1.34808i
\(469\) 0 0
\(470\) 28.0000 10.5830i 1.29154 0.488158i
\(471\) 14.6969 0.677199
\(472\) −7.00000 + 13.2288i −0.322201 + 0.608903i
\(473\) 6.00000 0.275880
\(474\) −12.0000 31.7490i −0.551178 1.45828i
\(475\) 5.29150i 0.242791i
\(476\) 0 0
\(477\) 19.4422i 0.890198i
\(478\) −9.79796 25.9230i −0.448148 1.18569i
\(479\) 5.29150i 0.241775i −0.992666 0.120887i \(-0.961426\pi\)
0.992666 0.120887i \(-0.0385740\pi\)
\(480\) −26.9444 + 6.48074i −1.22984 + 0.295804i
\(481\) −42.0000 −1.91504
\(482\) −34.2929 + 12.9615i −1.56200 + 0.590379i
\(483\) 0 0
\(484\) 7.50000 6.61438i 0.340909 0.300654i
\(485\) −8.00000 −0.363261
\(486\) −11.0227 29.1633i −0.500000 1.32288i
\(487\) 4.89898 0.221994 0.110997 0.993821i \(-0.464596\pi\)
0.110997 + 0.993821i \(0.464596\pi\)
\(488\) 8.57321 16.2019i 0.388091 0.733423i
\(489\) 38.8844i 1.75842i
\(490\) −7.00000 18.5203i −0.316228 0.836660i
\(491\) 7.34847 0.331632 0.165816 0.986157i \(-0.446974\pi\)
0.165816 + 0.986157i \(0.446974\pi\)
\(492\) 29.3939 25.9230i 1.32518 1.16870i
\(493\) 0 0
\(494\) 17.1464 + 45.3652i 0.771454 + 2.04108i
\(495\) −14.6969 −0.660578
\(496\) −8.05051 20.7651i −0.361479 0.932380i
\(497\) 0 0
\(498\) 15.0000 + 39.6863i 0.672166 + 1.77838i
\(499\) −22.0454 −0.986888 −0.493444 0.869778i \(-0.664262\pi\)
−0.493444 + 0.869778i \(0.664262\pi\)
\(500\) −18.0000 + 15.8745i −0.804984 + 0.709930i
\(501\) −12.0000 −0.536120
\(502\) −3.67423 9.72111i −0.163989 0.433874i
\(503\) 5.29150i 0.235936i 0.993017 + 0.117968i \(0.0376381\pi\)
−0.993017 + 0.117968i \(0.962362\pi\)
\(504\) 0 0
\(505\) −4.00000 −0.177998
\(506\) −6.00000 15.8745i −0.266733 0.705708i
\(507\) −71.0352 −3.15478
\(508\) 14.6969 12.9615i 0.652071 0.575073i
\(509\) 19.4422i 0.861761i 0.902409 + 0.430881i \(0.141797\pi\)
−0.902409 + 0.430881i \(0.858203\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −2.50000 22.4889i −0.110485 0.993878i
\(513\) 0 0
\(514\) 5.00000 + 13.2288i 0.220541 + 0.583495i
\(515\) 10.5830i 0.466343i
\(516\) −9.00000 + 7.93725i −0.396203 + 0.349418i
\(517\) 25.9230i 1.14009i
\(518\) 0 0
\(519\) 4.89898 0.215041
\(520\) 17.1464 32.4037i 0.751921 1.42100i
\(521\) −26.0000 −1.13908 −0.569540 0.821963i \(-0.692879\pi\)
−0.569540 + 0.821963i \(0.692879\pi\)
\(522\) −25.7196 + 9.72111i −1.12572 + 0.425481i
\(523\) 2.44949 0.107109 0.0535544 0.998565i \(-0.482945\pi\)
0.0535544 + 0.998565i \(0.482945\pi\)
\(524\) −7.00000 7.93725i −0.305796 0.346741i
\(525\) 0 0
\(526\) −2.44949 6.48074i −0.106803 0.282574i
\(527\) 0 0
\(528\) 3.00000 23.8118i 0.130558 1.03627i
\(529\) 1.00000 0.0434783
\(530\) 17.1464 6.48074i 0.744793 0.281505i
\(531\) 15.8745i 0.688895i
\(532\) 0 0
\(533\) 51.8459i 2.24570i
\(534\) 42.0000 15.8745i 1.81752 0.686957i
\(535\) 10.5830i 0.457543i
\(536\) 7.00000 13.2288i 0.302354 0.571395i
\(537\) 30.0000 1.29460
\(538\) 8.57321 3.24037i 0.369618 0.139702i
\(539\) 17.1464 0.738549
\(540\) 0 0
\(541\) −6.00000 −0.257960 −0.128980 0.991647i \(-0.541170\pi\)
−0.128980 + 0.991647i \(0.541170\pi\)
\(542\) −14.6969 38.8844i −0.631288 1.67023i
\(543\) 15.8745i 0.681240i
\(544\) 0 0
\(545\) −28.0000 −1.19939
\(546\) 0 0
\(547\) 5.29150i 0.226248i 0.993581 + 0.113124i \(0.0360858\pi\)
−0.993581 + 0.113124i \(0.963914\pi\)
\(548\) 17.1464 + 19.4422i 0.732459 + 0.830531i
\(549\) 19.4422i 0.829774i
\(550\) −1.22474 3.24037i −0.0522233 0.138170i
\(551\) −34.2929 −1.46092
\(552\) 30.0000 + 15.8745i 1.27688 + 0.675664i
\(553\) 0 0
\(554\) −8.57321 + 3.24037i −0.364241 + 0.137670i
\(555\) 31.7490i 1.34767i
\(556\) −11.0227 + 9.72111i −0.467467 + 0.412267i
\(557\) 19.4422i 0.823793i −0.911231 0.411897i \(-0.864866\pi\)
0.911231 0.411897i \(-0.135134\pi\)
\(558\) 17.8485 + 15.4736i 0.755586 + 0.655050i
\(559\) 15.8745i 0.671420i
\(560\) 0 0
\(561\) 0 0
\(562\) −5.00000 13.2288i −0.210912 0.558021i
\(563\) 26.4575i 1.11505i −0.830160 0.557526i \(-0.811751\pi\)
0.830160 0.557526i \(-0.188249\pi\)
\(564\) −34.2929 38.8844i −1.44399 1.63733i
\(565\) 8.00000 0.336563
\(566\) −21.0000 + 7.93725i −0.882696 + 0.333628i
\(567\) 0 0
\(568\) 7.00000 13.2288i 0.293713 0.555066i
\(569\) 12.9615i 0.543374i 0.962386 + 0.271687i \(0.0875815\pi\)
−0.962386 + 0.271687i \(0.912419\pi\)
\(570\) 34.2929 12.9615i 1.43637 0.542897i
\(571\) −46.5403 −1.94765 −0.973826 0.227297i \(-0.927011\pi\)
−0.973826 + 0.227297i \(0.927011\pi\)
\(572\) 21.0000 + 23.8118i 0.878054 + 0.995620i
\(573\) 25.9230i 1.08295i
\(574\) 0 0
\(575\) 4.89898 0.204302
\(576\) 13.5000 + 19.8431i 0.562500 + 0.826797i
\(577\) −12.0000 −0.499567 −0.249783 0.968302i \(-0.580359\pi\)
−0.249783 + 0.968302i \(0.580359\pi\)
\(578\) 8.50000 + 22.4889i 0.353553 + 0.935414i
\(579\) 14.6969 0.610784
\(580\) 17.1464 + 19.4422i 0.711967 + 0.807294i
\(581\) 0 0
\(582\) 4.89898 + 12.9615i 0.203069 + 0.537271i
\(583\) 15.8745i 0.657455i
\(584\) −17.1464 + 32.4037i −0.709524 + 1.34087i
\(585\) 38.8844i 1.60767i
\(586\) 11.0000 + 29.1033i 0.454406 + 1.20224i
\(587\) 41.6413 1.71872 0.859361 0.511370i \(-0.170862\pi\)
0.859361 + 0.511370i \(0.170862\pi\)
\(588\) −25.7196 + 22.6826i −1.06066 + 0.935414i
\(589\) 14.0000 + 25.9230i 0.576860 + 1.06814i
\(590\) −14.0000 + 5.29150i −0.576371 + 0.217848i
\(591\) 15.8745i 0.652990i
\(592\) −25.7196 3.24037i −1.05707 0.133178i
\(593\) −4.00000 −0.164260 −0.0821302 0.996622i \(-0.526172\pi\)
−0.0821302 + 0.996622i \(0.526172\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −3.00000 + 2.64575i −0.122885 + 0.108374i
\(597\) 36.0000 1.47338
\(598\) −42.0000 + 15.8745i −1.71751 + 0.649157i
\(599\) 21.1660i 0.864820i −0.901677 0.432410i \(-0.857663\pi\)
0.901677 0.432410i \(-0.142337\pi\)
\(600\) 6.12372 + 3.24037i 0.250000 + 0.132288i
\(601\) 12.9615i 0.528710i −0.964425 0.264355i \(-0.914841\pi\)
0.964425 0.264355i \(-0.0851590\pi\)
\(602\) 0 0
\(603\) 15.8745i 0.646460i
\(604\) −7.34847 + 6.48074i −0.299005 + 0.263698i
\(605\) 10.0000 0.406558
\(606\) 2.44949 + 6.48074i 0.0995037 + 0.263262i
\(607\) 37.0405i 1.50343i −0.659489 0.751714i \(-0.729227\pi\)
0.659489 0.751714i \(-0.270773\pi\)
\(608\) 7.00000 + 29.1033i 0.283887 + 1.18029i
\(609\) 0 0
\(610\) 17.1464 6.48074i 0.694239 0.262398i
\(611\) 68.5857 2.77468
\(612\) 0 0
\(613\) 6.48074i 0.261755i −0.991399 0.130877i \(-0.958221\pi\)
0.991399 0.130877i \(-0.0417794\pi\)
\(614\) −35.0000 + 13.2288i −1.41249 + 0.533869i
\(615\) 39.1918 1.58037
\(616\) 0 0
\(617\) −10.0000 −0.402585 −0.201292 0.979531i \(-0.564514\pi\)
−0.201292 + 0.979531i \(0.564514\pi\)
\(618\) 17.1464 6.48074i 0.689730 0.260694i
\(619\) −17.1464 −0.689173 −0.344587 0.938755i \(-0.611981\pi\)
−0.344587 + 0.938755i \(0.611981\pi\)
\(620\) 7.69694 20.8987i 0.309116 0.839313i
\(621\) 0 0
\(622\) 7.00000 2.64575i 0.280674 0.106085i
\(623\) 0 0
\(624\) −63.0000 7.93725i −2.52202 0.317744i
\(625\) −19.0000 −0.760000
\(626\) 17.1464 6.48074i 0.685309 0.259022i
\(627\) 31.7490i 1.26793i
\(628\) −9.00000 + 7.93725i −0.359139 + 0.316731i
\(629\) 0 0
\(630\) 0 0
\(631\) 14.6969 0.585076 0.292538 0.956254i \(-0.405500\pi\)
0.292538 + 0.956254i \(0.405500\pi\)
\(632\) 24.4949 + 12.9615i 0.974355 + 0.515580i
\(633\) 38.8844i 1.54552i
\(634\) −7.00000 18.5203i −0.278006 0.735533i
\(635\) 19.5959 0.777640
\(636\) −21.0000 23.8118i −0.832704 0.944198i
\(637\) 45.3652i 1.79743i
\(638\) −21.0000 + 7.93725i −0.831398 + 0.314239i
\(639\) 15.8745i 0.627986i
\(640\) 13.0000 18.5203i 0.513870 0.732078i
\(641\) 25.9230i 1.02390i 0.859017 + 0.511948i \(0.171076\pi\)
−0.859017 + 0.511948i \(0.828924\pi\)
\(642\) −17.1464 + 6.48074i −0.676716 + 0.255774i
\(643\) 22.0454 0.869386 0.434693 0.900579i \(-0.356857\pi\)
0.434693 + 0.900579i \(0.356857\pi\)
\(644\) 0 0
\(645\) −12.0000 −0.472500
\(646\) 0 0
\(647\) −34.2929 −1.34819 −0.674096 0.738644i \(-0.735466\pi\)
−0.674096 + 0.738644i \(0.735466\pi\)
\(648\) 22.5000 + 11.9059i 0.883883 + 0.467707i
\(649\) 12.9615i 0.508783i
\(650\) −8.57321 + 3.24037i −0.336269 + 0.127098i
\(651\) 0 0
\(652\) 21.0000 + 23.8118i 0.822423 + 0.932541i
\(653\) −14.0000 −0.547862 −0.273931 0.961749i \(-0.588324\pi\)
−0.273931 + 0.961749i \(0.588324\pi\)
\(654\) 17.1464 + 45.3652i 0.670478 + 1.77392i
\(655\) 10.5830i 0.413512i
\(656\) −4.00000 + 31.7490i −0.156174 + 1.23959i
\(657\) 38.8844i 1.51703i
\(658\) 0 0
\(659\) 26.4575i 1.03064i 0.856998 + 0.515319i \(0.172327\pi\)
−0.856998 + 0.515319i \(0.827673\pi\)
\(660\) 18.0000 15.8745i 0.700649 0.617914i
\(661\) 2.00000 0.0777910 0.0388955 0.999243i \(-0.487616\pi\)
0.0388955 + 0.999243i \(0.487616\pi\)
\(662\) −6.12372 16.2019i −0.238005 0.629703i
\(663\) 0 0
\(664\) −30.6186 16.2019i −1.18823 0.628754i
\(665\) 0 0
\(666\) 25.7196 9.72111i 0.996616 0.376685i
\(667\) 31.7490i 1.22933i
\(668\) 7.34847 6.48074i 0.284321 0.250747i
\(669\) 0 0
\(670\) 14.0000 5.29150i 0.540867 0.204429i
\(671\) 15.8745i 0.612829i
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 43.5000 38.3634i 1.67308 1.47552i
\(677\) 32.4037i 1.24538i 0.782470 + 0.622688i \(0.213959\pi\)
−0.782470 + 0.622688i \(0.786041\pi\)
\(678\) −4.89898 12.9615i −0.188144 0.497783i
\(679\) 0 0
\(680\) 0 0
\(681\) 64.8074i 2.48343i
\(682\) 14.5732 + 12.6341i 0.558037 + 0.483786i
\(683\) 5.29150i 0.202474i −0.994862 0.101237i \(-0.967720\pi\)
0.994862 0.101237i \(-0.0322800\pi\)
\(684\) −21.0000 23.8118i −0.802955 0.910465i
\(685\) 25.9230i 0.990465i
\(686\) 0 0
\(687\) 15.8745i 0.605650i
\(688\) 1.22474 9.72111i 0.0466930 0.370614i
\(689\) 42.0000 1.60007
\(690\) 12.0000 + 31.7490i 0.456832 + 1.20866i
\(691\) 47.6235i 1.81168i −0.423615 0.905842i \(-0.639239\pi\)
0.423615 0.905842i \(-0.360761\pi\)
\(692\) −3.00000 + 2.64575i −0.114043 + 0.100576i
\(693\) 0 0
\(694\) −11.0227 29.1633i −0.418416 1.10702i
\(695\) −14.6969 −0.557487
\(696\) 21.0000 39.6863i 0.796003 1.50430i
\(697\) 0 0
\(698\) −9.00000 23.8118i −0.340655 0.901288i
\(699\) −39.1918 −1.48237
\(700\) 0 0
\(701\) 38.0000 1.43524 0.717620 0.696435i \(-0.245231\pi\)
0.717620 + 0.696435i \(0.245231\pi\)
\(702\) 0 0
\(703\) 34.2929 1.29338
\(704\) 11.0227 + 16.2019i 0.415434 + 0.610630i
\(705\) 51.8459i 1.95263i
\(706\) 0 0
\(707\) 0 0
\(708\) 17.1464 + 19.4422i 0.644402 + 0.730683i
\(709\) 19.4422i 0.730168i −0.930975 0.365084i \(-0.881040\pi\)
0.930975 0.365084i \(-0.118960\pi\)
\(710\) 14.0000 5.29150i 0.525411 0.198587i
\(711\) −29.3939 −1.10236
\(712\) −17.1464 + 32.4037i −0.642590 + 1.21438i
\(713\) −24.0000 + 12.9615i −0.898807 + 0.485411i
\(714\) 0 0
\(715\) 31.7490i 1.18735i
\(716\) −18.3712 + 16.2019i −0.686563 + 0.605492i
\(717\) −48.0000 −1.79259
\(718\) −28.0000 + 10.5830i −1.04495 + 0.394954i
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) −3.00000 + 23.8118i −0.111803 + 0.887412i
\(721\) 0 0
\(722\) −4.50000 11.9059i −0.167473 0.443091i
\(723\) 63.4980i 2.36152i
\(724\) −8.57321 9.72111i −0.318621 0.361282i
\(725\) 6.48074i 0.240689i
\(726\) −6.12372 16.2019i −0.227273 0.601307i
\(727\) 47.6235i 1.76626i 0.469130 + 0.883129i \(0.344568\pi\)
−0.469130 + 0.883129i \(0.655432\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) −34.2929 + 12.9615i −1.26924 + 0.479726i
\(731\) 0 0
\(732\) −21.0000 23.8118i −0.776182 0.880108i
\(733\) 30.0000 1.10808 0.554038 0.832492i \(-0.313086\pi\)
0.554038 + 0.832492i \(0.313086\pi\)
\(734\) 9.79796 + 25.9230i 0.361649 + 0.956834i
\(735\) −34.2929 −1.26491
\(736\) −26.9444 + 6.48074i −0.993183 + 0.238883i
\(737\) 12.9615i 0.477442i
\(738\) −12.0000 31.7490i −0.441726 1.16870i
\(739\) −36.7423 −1.35159 −0.675795 0.737090i \(-0.736199\pi\)
−0.675795 + 0.737090i \(0.736199\pi\)
\(740\) −17.1464 19.4422i −0.630315 0.714710i
\(741\) 84.0000 3.08582
\(742\) 0 0
\(743\) 14.6969 0.539178 0.269589 0.962975i \(-0.413112\pi\)
0.269589 + 0.962975i \(0.413112\pi\)
\(744\) −38.5732 + 0.327344i −1.41416 + 0.0120010i
\(745\) −4.00000 −0.146549
\(746\) −13.0000 34.3948i −0.475964 1.25928i
\(747\) 36.7423 1.34433
\(748\) 0 0
\(749\) 0 0
\(750\) 14.6969 + 38.8844i 0.536656 + 1.41986i
\(751\) 10.5830i 0.386179i 0.981181 + 0.193090i \(0.0618508\pi\)
−0.981181 + 0.193090i \(0.938149\pi\)
\(752\) 42.0000 + 5.29150i 1.53158 + 0.192961i
\(753\) −18.0000 −0.655956
\(754\) 21.0000 + 55.5608i 0.764775 + 2.02340i
\(755\) −9.79796 −0.356584
\(756\) 0 0
\(757\) 32.4037i 1.17773i −0.808230 0.588866i \(-0.799574\pi\)
0.808230 0.588866i \(-0.200426\pi\)
\(758\) 21.0000 7.93725i 0.762754 0.288294i
\(759\) −29.3939 −1.06693
\(760\) −14.0000 + 26.4575i −0.507833 + 0.959715i
\(761\) 12.9615i 0.469853i −0.972013 0.234927i \(-0.924515\pi\)
0.972013 0.234927i \(-0.0754850\pi\)
\(762\) −12.0000 31.7490i −0.434714 1.15015i
\(763\) 0 0
\(764\) 14.0000 + 15.8745i 0.506502 + 0.574320i
\(765\) 0 0
\(766\) 14.6969 + 38.8844i 0.531022 + 1.40495i
\(767\) −34.2929 −1.23824
\(768\) −37.9671 9.72111i −1.37002 0.350780i
\(769\) 36.0000 1.29819 0.649097 0.760706i \(-0.275147\pi\)
0.649097 + 0.760706i \(0.275147\pi\)
\(770\) 0 0
\(771\) 24.4949 0.882162
\(772\) −9.00000 + 7.93725i −0.323917 + 0.285668i
\(773\) 19.4422i 0.699288i −0.936883 0.349644i \(-0.886303\pi\)
0.936883 0.349644i \(-0.113697\pi\)
\(774\) 3.67423 + 9.72111i 0.132068 + 0.349418i
\(775\) −4.89898 + 2.64575i −0.175977 + 0.0950382i
\(776\) −10.0000 5.29150i −0.358979 0.189954i
\(777\) 0 0
\(778\) 25.7196 9.72111i 0.922094 0.348519i
\(779\) 42.3320i 1.51670i
\(780\) −42.0000 47.6235i −1.50384 1.70520i
\(781\) 12.9615i 0.463798i
\(782\) 0 0
\(783\) 0 0
\(784\) 3.50000 27.7804i 0.125000 0.992157i
\(785\) −12.0000 −0.428298
\(786\) −17.1464 + 6.48074i −0.611593 + 0.231160i
\(787\) 31.8434 1.13509 0.567547 0.823341i \(-0.307893\pi\)
0.567547 + 0.823341i \(0.307893\pi\)
\(788\) 8.57321 + 9.72111i 0.305408 + 0.346300i
\(789\) −12.0000 −0.427211
\(790\) 9.79796 + 25.9230i 0.348596 + 0.922298i
\(791\) 0 0
\(792\) −18.3712 9.72111i −0.652791 0.345425i
\(793\) 42.0000 1.49146
\(794\) 5.00000 + 13.2288i 0.177443 + 0.469471i
\(795\) 31.7490i 1.12602i
\(796\) −22.0454 + 19.4422i −0.781379 + 0.689111i
\(797\) 45.3652i 1.60692i −0.595361 0.803459i \(-0.702991\pi\)
0.595361 0.803459i \(-0.297009\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −5.50000 + 1.32288i −0.194454 + 0.0467707i
\(801\) 38.8844i 1.37391i
\(802\) 34.2929 12.9615i 1.21092 0.457686i
\(803\) 31.7490i 1.12040i
\(804\) −17.1464 19.4422i −0.604708 0.685674i
\(805\) 0 0
\(806\) 33.4268 38.5571i 1.17741 1.35812i
\(807\) 15.8745i 0.558809i
\(808\) −5.00000 2.64575i −0.175899 0.0930772i
\(809\) 12.9615i 0.455701i −0.973696 0.227851i \(-0.926830\pi\)
0.973696 0.227851i \(-0.0731698\pi\)
\(810\) 9.00000 + 23.8118i 0.316228 + 0.836660i
\(811\) 5.29150i 0.185810i −0.995675 0.0929049i \(-0.970385\pi\)
0.995675 0.0929049i \(-0.0296153\pi\)
\(812\) 0 0
\(813\) −72.0000 −2.52515
\(814\) 21.0000 7.93725i 0.736050 0.278201i
\(815\) 31.7490i 1.11212i
\(816\) 0 0
\(817\) 12.9615i 0.453465i
\(818\) −51.4393 + 19.4422i −1.79853 + 0.679781i
\(819\) 0 0
\(820\) −24.0000 + 21.1660i −0.838116 + 0.739149i
\(821\) 19.4422i 0.678538i 0.940689 + 0.339269i \(0.110180\pi\)
−0.940689 + 0.339269i \(0.889820\pi\)
\(822\) 42.0000 15.8745i 1.46492 0.553687i
\(823\) 53.8888 1.87844 0.939222 0.343310i \(-0.111548\pi\)
0.939222 + 0.343310i \(0.111548\pi\)
\(824\) −7.00000 + 13.2288i −0.243857 + 0.460846i
\(825\) −6.00000 −0.208893
\(826\) 0 0
\(827\) −26.9444 −0.936948 −0.468474 0.883477i \(-0.655196\pi\)
−0.468474 + 0.883477i \(0.655196\pi\)
\(828\) 22.0454 19.4422i 0.766131 0.675664i
\(829\) 19.4422i 0.675256i 0.941280 + 0.337628i \(0.109625\pi\)
−0.941280 + 0.337628i \(0.890375\pi\)
\(830\) −12.2474 32.4037i −0.425115 1.12475i
\(831\) 15.8745i 0.550681i
\(832\) 42.8661 29.1633i 1.48611 1.01106i
\(833\) 0 0
\(834\) 9.00000 + 23.8118i 0.311645 + 0.824534i
\(835\) 9.79796 0.339072
\(836\) −17.1464 19.4422i −0.593022 0.672423i
\(837\) 0 0
\(838\) −49.0000 + 18.5203i −1.69268 + 0.639772i
\(839\) 42.3320i 1.46146i −0.682665 0.730732i \(-0.739179\pi\)
0.682665 0.730732i \(-0.260821\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) 9.00000 + 23.8118i 0.310160 + 0.820608i
\(843\) −24.4949 −0.843649
\(844\) −21.0000 23.8118i −0.722850 0.819635i
\(845\) 58.0000 1.99526
\(846\) −42.0000 + 15.8745i −1.44399 + 0.545777i
\(847\) 0 0
\(848\) 25.7196 + 3.24037i 0.883216 + 0.111275i
\(849\) 38.8844i 1.33451i
\(850\) 0 0
\(851\) 31.7490i 1.08834i
\(852\) −17.1464 19.4422i −0.587427 0.666080i
\(853\) 18.0000 0.616308 0.308154 0.951336i \(-0.400289\pi\)
0.308154 + 0.951336i \(0.400289\pi\)
\(854\) 0 0
\(855\) 31.7490i 1.08579i
\(856\) 7.00000 13.2288i 0.239255 0.452150i
\(857\) 22.0000 0.751506 0.375753 0.926720i \(-0.377384\pi\)
0.375753 + 0.926720i \(0.377384\pi\)
\(858\) 51.4393 19.4422i 1.75611 0.663747i
\(859\) 12.2474 0.417878 0.208939 0.977929i \(-0.432999\pi\)
0.208939 + 0.977929i \(0.432999\pi\)
\(860\) 7.34847 6.48074i 0.250581 0.220991i
\(861\) 0 0
\(862\) −14.0000 + 5.29150i −0.476842 + 0.180229i
\(863\) 9.79796 0.333526 0.166763 0.985997i \(-0.446668\pi\)
0.166763 + 0.985997i \(0.446668\pi\)
\(864\) 0 0
\(865\) −4.00000 −0.136004
\(866\) 0 0
\(867\) 41.6413 1.41421
\(868\) 0 0
\(869\) −24.0000 −0.814144
\(870\) 42.0000 15.8745i 1.42393 0.538196i
\(871\) 34.2929 1.16197
\(872\) −35.0000 18.5203i −1.18525 0.627175i
\(873\) 12.0000 0.406138
\(874\) 34.2929 12.9615i 1.15997 0.438429i
\(875\) 0 0
\(876\) 42.0000 + 47.6235i 1.41905 + 1.60905i
\(877\) −30.0000 −1.01303 −0.506514 0.862232i \(-0.669066\pi\)
−0.506514 + 0.862232i \(0.669066\pi\)
\(878\) −28.0000 + 10.5830i −0.944954 + 0.357159i
\(879\) 53.8888 1.81762
\(880\) −2.44949 + 19.4422i −0.0825723 + 0.655397i
\(881\) 25.9230i 0.873367i −0.899615 0.436683i \(-0.856153\pi\)
0.899615 0.436683i \(-0.143847\pi\)
\(882\) 10.5000 + 27.7804i 0.353553 + 0.935414i
\(883\) −26.9444 −0.906751 −0.453375 0.891320i \(-0.649780\pi\)
−0.453375 + 0.891320i \(0.649780\pi\)
\(884\) 0 0
\(885\) 25.9230i 0.871391i
\(886\) −7.00000 + 2.64575i −0.235170 + 0.0888858i
\(887\) 21.1660i 0.710685i −0.934736 0.355343i \(-0.884364\pi\)
0.934736 0.355343i \(-0.115636\pi\)
\(888\) −21.0000 + 39.6863i −0.704714 + 1.33178i
\(889\) 0 0
\(890\) −34.2929 + 12.9615i −1.14950 + 0.434470i
\(891\) −22.0454 −0.738549
\(892\) 0 0
\(893\) −56.0000 −1.87397
\(894\) 2.44949 + 6.48074i 0.0819232 + 0.216748i
\(895\) −24.4949 −0.818774
\(896\) 0 0
\(897\) 77.7689i 2.59663i
\(898\) 34.2929 12.9615i 1.14437 0.432530i
\(899\) 17.1464 + 31.7490i 0.571865 + 1.05889i
\(900\) 4.50000 3.96863i 0.150000 0.132288i
\(901\) 0 0
\(902\) −9.79796 25.9230i −0.326236 0.863140i
\(903\) 0 0
\(904\) 10.0000 + 5.29150i 0.332595 + 0.175993i
\(905\) 12.9615i 0.430854i
\(906\) 6.00000 + 15.8745i 0.199337 + 0.527395i
\(907\) 37.0405i 1.22991i 0.788562 + 0.614955i \(0.210826\pi\)
−0.788562 + 0.614955i \(0.789174\pi\)
\(908\) 35.0000 + 39.6863i 1.16152 + 1.31704i
\(909\) 6.00000 0.199007
\(910\) 0 0
\(911\) −48.9898 −1.62310 −0.811552 0.584280i \(-0.801377\pi\)
−0.811552 + 0.584280i \(0.801377\pi\)
\(912\) 51.4393 + 6.48074i 1.70332 + 0.214599i
\(913\) 30.0000 0.992855
\(914\) −17.1464 + 6.48074i −0.567153 + 0.214364i
\(915\) 31.7490i 1.04959i
\(916\) 8.57321 + 9.72111i 0.283267 + 0.321195i
\(917\) 0 0
\(918\) 0 0
\(919\) 5.29150i 0.174551i 0.996184 + 0.0872753i \(0.0278160\pi\)
−0.996184 + 0.0872753i \(0.972184\pi\)
\(920\) −24.4949 12.9615i −0.807573 0.427327i
\(921\) 64.8074i 2.13548i
\(922\) 8.57321 3.24037i 0.282344 0.106716i
\(923\) 34.2929 1.12876
\(924\) 0 0
\(925\) 6.48074i 0.213085i
\(926\) 4.89898 + 12.9615i 0.160990 + 0.425941i
\(927\) 15.8745i 0.521387i
\(928\) 8.57321 + 35.6441i 0.281430 + 1.17007i
\(929\) 51.8459i 1.70101i 0.525967 + 0.850505i \(0.323703\pi\)
−0.525967 + 0.850505i \(0.676297\pi\)
\(930\) −29.1464 25.2683i −0.955749 0.828579i
\(931\) 37.0405i 1.21395i
\(932\) 24.0000 21.1660i 0.786146 0.693316i
\(933\) 12.9615i 0.424340i
\(934\) 7.00000 2.64575i 0.229047 0.0865716i
\(935\) 0 0
\(936\) −25.7196 + 48.6056i −0.840673 + 1.58872i
\(937\) 6.00000 0.196011 0.0980057 0.995186i \(-0.468754\pi\)
0.0980057 + 0.995186i \(0.468754\pi\)
\(938\) 0 0
\(939\) 31.7490i 1.03609i
\(940\) 28.0000 + 31.7490i 0.913259 + 1.03554i
\(941\) 6.48074i 0.211266i −0.994405 0.105633i \(-0.966313\pi\)
0.994405 0.105633i \(-0.0336869\pi\)
\(942\) 7.34847 + 19.4422i 0.239426 + 0.633462i
\(943\) 39.1918 1.27626
\(944\) −21.0000 2.64575i −0.683492 0.0861119i
\(945\) 0 0
\(946\) 3.00000 + 7.93725i 0.0975384 + 0.258062i
\(947\) −26.9444 −0.875575 −0.437787 0.899078i \(-0.644238\pi\)
−0.437787 + 0.899078i \(0.644238\pi\)
\(948\) 36.0000 31.7490i 1.16923 1.03116i
\(949\) −84.0000 −2.72676
\(950\) 7.00000 2.64575i 0.227110 0.0858395i
\(951\) −34.2929 −1.11202
\(952\) 0 0
\(953\) 12.9615i 0.419864i 0.977716 + 0.209932i \(0.0673242\pi\)
−0.977716 + 0.209932i \(0.932676\pi\)
\(954\) −25.7196 + 9.72111i −0.832704 + 0.314733i
\(955\) 21.1660i 0.684916i
\(956\) 29.3939 25.9230i 0.950666 0.838409i
\(957\) 38.8844i 1.25696i
\(958\) 7.00000 2.64575i 0.226160 0.0854803i
\(959\) 0 0
\(960\) −22.0454 32.4037i −0.711512 1.04583i
\(961\) 17.0000 25.9230i 0.548387 0.836225i
\(962\) −21.0000 55.5608i −0.677067 1.79135i
\(963\) 15.8745i 0.511549i
\(964\) −34.2929 38.8844i −1.10450 1.25238i
\(965\) −12.0000 −0.386294
\(966\) 0 0
\(967\) −14.6969 −0.472622 −0.236311 0.971678i \(-0.575938\pi\)
−0.236311 + 0.971678i \(0.575938\pi\)
\(968\) 12.5000 + 6.61438i 0.401765 + 0.212594i
\(969\) 0 0
\(970\) −4.00000 10.5830i −0.128432 0.339800i
\(971\) 26.4575i 0.849062i 0.905413 + 0.424531i \(0.139561\pi\)
−0.905413 + 0.424531i \(0.860439\pi\)
\(972\) 33.0681 29.1633i 1.06066 0.935414i
\(973\) 0 0
\(974\) 2.44949 + 6.48074i 0.0784867 + 0.207656i
\(975\) 15.8745i 0.508391i
\(976\) 25.7196 + 3.24037i 0.823266 + 0.103722i
\(977\) 10.0000 0.319928 0.159964 0.987123i \(-0.448862\pi\)
0.159964 + 0.987123i \(0.448862\pi\)
\(978\) 51.4393 19.4422i 1.64485 0.621694i
\(979\) 31.7490i 1.01470i
\(980\) 21.0000 18.5203i 0.670820 0.591608i
\(981\) 42.0000 1.34096
\(982\) 3.67423 + 9.72111i 0.117250 + 0.310213i
\(983\) −53.8888 −1.71878 −0.859392 0.511316i \(-0.829158\pi\)
−0.859392 + 0.511316i \(0.829158\pi\)
\(984\) 48.9898 + 25.9230i 1.56174 + 0.826394i
\(985\) 12.9615i 0.412987i
\(986\) 0 0
\(987\) 0 0
\(988\) −51.4393 + 45.3652i −1.63650 + 1.44326i
\(989\) −12.0000 −0.381578
\(990\) −7.34847 19.4422i −0.233550 0.617914i
\(991\) −29.3939 −0.933727 −0.466864 0.884329i \(-0.654616\pi\)
−0.466864 + 0.884329i \(0.654616\pi\)
\(992\) 23.4444 21.0324i 0.744360 0.667779i
\(993\) −30.0000 −0.952021
\(994\) 0 0
\(995\) −29.3939 −0.931849
\(996\) −45.0000 + 39.6863i −1.42588 + 1.25751i
\(997\) −58.0000 −1.83688 −0.918439 0.395562i \(-0.870550\pi\)
−0.918439 + 0.395562i \(0.870550\pi\)
\(998\) −11.0227 29.1633i −0.348918 0.923149i
\(999\) 0 0
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 124.2.d.b.123.4 yes 4
3.2 odd 2 1116.2.g.b.991.1 4
4.3 odd 2 inner 124.2.d.b.123.1 4
8.3 odd 2 1984.2.h.e.1983.4 4
8.5 even 2 1984.2.h.e.1983.2 4
12.11 even 2 1116.2.g.b.991.4 4
31.30 odd 2 inner 124.2.d.b.123.3 yes 4
93.92 even 2 1116.2.g.b.991.2 4
124.123 even 2 inner 124.2.d.b.123.2 yes 4
248.61 odd 2 1984.2.h.e.1983.3 4
248.123 even 2 1984.2.h.e.1983.1 4
372.371 odd 2 1116.2.g.b.991.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
124.2.d.b.123.1 4 4.3 odd 2 inner
124.2.d.b.123.2 yes 4 124.123 even 2 inner
124.2.d.b.123.3 yes 4 31.30 odd 2 inner
124.2.d.b.123.4 yes 4 1.1 even 1 trivial
1116.2.g.b.991.1 4 3.2 odd 2
1116.2.g.b.991.2 4 93.92 even 2
1116.2.g.b.991.3 4 372.371 odd 2
1116.2.g.b.991.4 4 12.11 even 2
1984.2.h.e.1983.1 4 248.123 even 2
1984.2.h.e.1983.2 4 8.5 even 2
1984.2.h.e.1983.3 4 248.61 odd 2
1984.2.h.e.1983.4 4 8.3 odd 2