Properties

Label 490.4.e.l.361.1
Level $490$
Weight $4$
Character 490.361
Analytic conductor $28.911$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [490,4,Mod(361,490)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(490, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("490.361");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 490.e (of order \(3\), degree \(2\), not 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: \(28.9109359028\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 490.361
Dual form 490.4.e.l.471.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(9.00000 + 15.5885i) q^{9} +(-5.00000 + 8.66025i) q^{10} +(8.50000 - 14.7224i) q^{11} +(-6.00000 - 10.3923i) q^{12} +81.0000 q^{13} -15.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-45.5000 + 78.8083i) q^{17} +(-18.0000 + 31.1769i) q^{18} +(51.0000 + 88.3346i) q^{19} -20.0000 q^{20} +34.0000 q^{22} +(45.0000 + 77.9423i) q^{23} +(12.0000 - 20.7846i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(81.0000 + 140.296i) q^{26} -135.000 q^{27} -129.000 q^{29} +(-15.0000 - 25.9808i) q^{30} +(58.0000 - 100.459i) q^{31} +(16.0000 - 27.7128i) q^{32} +(25.5000 + 44.1673i) q^{33} -182.000 q^{34} -72.0000 q^{36} +(-157.000 - 271.932i) q^{37} +(-102.000 + 176.669i) q^{38} +(-121.500 + 210.444i) q^{39} +(-20.0000 - 34.6410i) q^{40} +124.000 q^{41} -434.000 q^{43} +(34.0000 + 58.8897i) q^{44} +(-45.0000 + 77.9423i) q^{45} +(-90.0000 + 155.885i) q^{46} +(248.500 + 430.415i) q^{47} +48.0000 q^{48} -50.0000 q^{50} +(-136.500 - 236.425i) q^{51} +(-162.000 + 280.592i) q^{52} +(292.000 - 505.759i) q^{53} +(-135.000 - 233.827i) q^{54} +85.0000 q^{55} -306.000 q^{57} +(-129.000 - 223.435i) q^{58} +(-166.000 + 287.520i) q^{59} +(30.0000 - 51.9615i) q^{60} +(110.000 + 190.526i) q^{61} +232.000 q^{62} +64.0000 q^{64} +(202.500 + 350.740i) q^{65} +(-51.0000 + 88.3346i) q^{66} +(-192.000 + 332.554i) q^{67} +(-182.000 - 315.233i) q^{68} -270.000 q^{69} -664.000 q^{71} +(-72.0000 - 124.708i) q^{72} +(115.000 - 199.186i) q^{73} +(314.000 - 543.864i) q^{74} +(-37.5000 - 64.9519i) q^{75} -408.000 q^{76} -486.000 q^{78} +(-180.500 - 312.635i) q^{79} +(40.0000 - 69.2820i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(124.000 + 214.774i) q^{82} -1172.00 q^{83} -455.000 q^{85} +(-434.000 - 751.710i) q^{86} +(193.500 - 335.152i) q^{87} +(-68.0000 + 117.779i) q^{88} +(20.0000 + 34.6410i) q^{89} -180.000 q^{90} -360.000 q^{92} +(174.000 + 301.377i) q^{93} +(-497.000 + 860.829i) q^{94} +(-255.000 + 441.673i) q^{95} +(48.0000 + 83.1384i) q^{96} +175.000 q^{97} +306.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} + 5 q^{5} - 12 q^{6} - 16 q^{8} + 18 q^{9} - 10 q^{10} + 17 q^{11} - 12 q^{12} + 162 q^{13} - 30 q^{15} - 16 q^{16} - 91 q^{17} - 36 q^{18} + 102 q^{19} - 40 q^{20} + 68 q^{22}+ \cdots + 612 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i
\(3\) −1.50000 + 2.59808i −0.288675 + 0.500000i −0.973494 0.228714i \(-0.926548\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 2.50000 + 4.33013i 0.223607 + 0.387298i
\(6\) −6.00000 −0.408248
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) 9.00000 + 15.5885i 0.333333 + 0.577350i
\(10\) −5.00000 + 8.66025i −0.158114 + 0.273861i
\(11\) 8.50000 14.7224i 0.232986 0.403544i −0.725699 0.688012i \(-0.758484\pi\)
0.958685 + 0.284468i \(0.0918170\pi\)
\(12\) −6.00000 10.3923i −0.144338 0.250000i
\(13\) 81.0000 1.72810 0.864052 0.503402i \(-0.167919\pi\)
0.864052 + 0.503402i \(0.167919\pi\)
\(14\) 0 0
\(15\) −15.0000 −0.258199
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −45.5000 + 78.8083i −0.649139 + 1.12434i 0.334189 + 0.942506i \(0.391538\pi\)
−0.983329 + 0.181837i \(0.941796\pi\)
\(18\) −18.0000 + 31.1769i −0.235702 + 0.408248i
\(19\) 51.0000 + 88.3346i 0.615800 + 1.06660i 0.990244 + 0.139347i \(0.0445005\pi\)
−0.374443 + 0.927250i \(0.622166\pi\)
\(20\) −20.0000 −0.223607
\(21\) 0 0
\(22\) 34.0000 0.329492
\(23\) 45.0000 + 77.9423i 0.407963 + 0.706613i 0.994661 0.103193i \(-0.0329059\pi\)
−0.586698 + 0.809806i \(0.699573\pi\)
\(24\) 12.0000 20.7846i 0.102062 0.176777i
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) 81.0000 + 140.296i 0.610977 + 1.05824i
\(27\) −135.000 −0.962250
\(28\) 0 0
\(29\) −129.000 −0.826024 −0.413012 0.910726i \(-0.635523\pi\)
−0.413012 + 0.910726i \(0.635523\pi\)
\(30\) −15.0000 25.9808i −0.0912871 0.158114i
\(31\) 58.0000 100.459i 0.336036 0.582031i −0.647648 0.761940i \(-0.724247\pi\)
0.983683 + 0.179909i \(0.0575804\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 25.5000 + 44.1673i 0.134515 + 0.232986i
\(34\) −182.000 −0.918022
\(35\) 0 0
\(36\) −72.0000 −0.333333
\(37\) −157.000 271.932i −0.697585 1.20825i −0.969302 0.245875i \(-0.920925\pi\)
0.271717 0.962377i \(-0.412409\pi\)
\(38\) −102.000 + 176.669i −0.435436 + 0.754198i
\(39\) −121.500 + 210.444i −0.498861 + 0.864052i
\(40\) −20.0000 34.6410i −0.0790569 0.136931i
\(41\) 124.000 0.472330 0.236165 0.971713i \(-0.424109\pi\)
0.236165 + 0.971713i \(0.424109\pi\)
\(42\) 0 0
\(43\) −434.000 −1.53917 −0.769586 0.638543i \(-0.779537\pi\)
−0.769586 + 0.638543i \(0.779537\pi\)
\(44\) 34.0000 + 58.8897i 0.116493 + 0.201772i
\(45\) −45.0000 + 77.9423i −0.149071 + 0.258199i
\(46\) −90.0000 + 155.885i −0.288473 + 0.499651i
\(47\) 248.500 + 430.415i 0.771222 + 1.33580i 0.936893 + 0.349615i \(0.113688\pi\)
−0.165671 + 0.986181i \(0.552979\pi\)
\(48\) 48.0000 0.144338
\(49\) 0 0
\(50\) −50.0000 −0.141421
\(51\) −136.500 236.425i −0.374781 0.649139i
\(52\) −162.000 + 280.592i −0.432026 + 0.748291i
\(53\) 292.000 505.759i 0.756779 1.31078i −0.187706 0.982225i \(-0.560105\pi\)
0.944485 0.328554i \(-0.106561\pi\)
\(54\) −135.000 233.827i −0.340207 0.589256i
\(55\) 85.0000 0.208389
\(56\) 0 0
\(57\) −306.000 −0.711065
\(58\) −129.000 223.435i −0.292044 0.505834i
\(59\) −166.000 + 287.520i −0.366294 + 0.634440i −0.988983 0.148029i \(-0.952707\pi\)
0.622689 + 0.782470i \(0.286040\pi\)
\(60\) 30.0000 51.9615i 0.0645497 0.111803i
\(61\) 110.000 + 190.526i 0.230886 + 0.399907i 0.958069 0.286537i \(-0.0925042\pi\)
−0.727183 + 0.686444i \(0.759171\pi\)
\(62\) 232.000 0.475226
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 202.500 + 350.740i 0.386416 + 0.669292i
\(66\) −51.0000 + 88.3346i −0.0951162 + 0.164746i
\(67\) −192.000 + 332.554i −0.350098 + 0.606387i −0.986266 0.165163i \(-0.947185\pi\)
0.636169 + 0.771550i \(0.280518\pi\)
\(68\) −182.000 315.233i −0.324570 0.562171i
\(69\) −270.000 −0.471075
\(70\) 0 0
\(71\) −664.000 −1.10989 −0.554946 0.831887i \(-0.687261\pi\)
−0.554946 + 0.831887i \(0.687261\pi\)
\(72\) −72.0000 124.708i −0.117851 0.204124i
\(73\) 115.000 199.186i 0.184380 0.319355i −0.758987 0.651105i \(-0.774306\pi\)
0.943367 + 0.331750i \(0.107639\pi\)
\(74\) 314.000 543.864i 0.493267 0.854364i
\(75\) −37.5000 64.9519i −0.0577350 0.100000i
\(76\) −408.000 −0.615800
\(77\) 0 0
\(78\) −486.000 −0.705496
\(79\) −180.500 312.635i −0.257061 0.445243i 0.708392 0.705819i \(-0.249421\pi\)
−0.965453 + 0.260576i \(0.916088\pi\)
\(80\) 40.0000 69.2820i 0.0559017 0.0968246i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 124.000 + 214.774i 0.166994 + 0.289242i
\(83\) −1172.00 −1.54992 −0.774962 0.632008i \(-0.782231\pi\)
−0.774962 + 0.632008i \(0.782231\pi\)
\(84\) 0 0
\(85\) −455.000 −0.580608
\(86\) −434.000 751.710i −0.544179 0.942546i
\(87\) 193.500 335.152i 0.238453 0.413012i
\(88\) −68.0000 + 117.779i −0.0823730 + 0.142674i
\(89\) 20.0000 + 34.6410i 0.0238202 + 0.0412578i 0.877690 0.479229i \(-0.159084\pi\)
−0.853870 + 0.520487i \(0.825750\pi\)
\(90\) −180.000 −0.210819
\(91\) 0 0
\(92\) −360.000 −0.407963
\(93\) 174.000 + 301.377i 0.194010 + 0.336036i
\(94\) −497.000 + 860.829i −0.545337 + 0.944551i
\(95\) −255.000 + 441.673i −0.275394 + 0.476997i
\(96\) 48.0000 + 83.1384i 0.0510310 + 0.0883883i
\(97\) 175.000 0.183181 0.0915905 0.995797i \(-0.470805\pi\)
0.0915905 + 0.995797i \(0.470805\pi\)
\(98\) 0 0
\(99\) 306.000 0.310648
\(100\) −50.0000 86.6025i −0.0500000 0.0866025i
\(101\) 135.000 233.827i 0.133000 0.230363i −0.791832 0.610739i \(-0.790872\pi\)
0.924832 + 0.380377i \(0.124206\pi\)
\(102\) 273.000 472.850i 0.265010 0.459011i
\(103\) 282.500 + 489.304i 0.270248 + 0.468083i 0.968925 0.247354i \(-0.0795609\pi\)
−0.698677 + 0.715437i \(0.746228\pi\)
\(104\) −648.000 −0.610977
\(105\) 0 0
\(106\) 1168.00 1.07025
\(107\) 603.000 + 1044.43i 0.544806 + 0.943631i 0.998619 + 0.0525344i \(0.0167299\pi\)
−0.453813 + 0.891097i \(0.649937\pi\)
\(108\) 270.000 467.654i 0.240563 0.416667i
\(109\) 709.500 1228.89i 0.623466 1.07987i −0.365370 0.930863i \(-0.619057\pi\)
0.988835 0.149012i \(-0.0476093\pi\)
\(110\) 85.0000 + 147.224i 0.0736767 + 0.127612i
\(111\) 942.000 0.805502
\(112\) 0 0
\(113\) −778.000 −0.647682 −0.323841 0.946111i \(-0.604974\pi\)
−0.323841 + 0.946111i \(0.604974\pi\)
\(114\) −306.000 530.008i −0.251399 0.435436i
\(115\) −225.000 + 389.711i −0.182447 + 0.316007i
\(116\) 258.000 446.869i 0.206506 0.357679i
\(117\) 729.000 + 1262.67i 0.576035 + 0.997722i
\(118\) −664.000 −0.518018
\(119\) 0 0
\(120\) 120.000 0.0912871
\(121\) 521.000 + 902.398i 0.391435 + 0.677985i
\(122\) −220.000 + 381.051i −0.163261 + 0.282777i
\(123\) −186.000 + 322.161i −0.136350 + 0.236165i
\(124\) 232.000 + 401.836i 0.168018 + 0.291015i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 316.000 0.220791 0.110396 0.993888i \(-0.464788\pi\)
0.110396 + 0.993888i \(0.464788\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 651.000 1127.57i 0.444321 0.769586i
\(130\) −405.000 + 701.481i −0.273237 + 0.473261i
\(131\) −875.000 1515.54i −0.583581 1.01079i −0.995051 0.0993684i \(-0.968318\pi\)
0.411470 0.911423i \(-0.365016\pi\)
\(132\) −204.000 −0.134515
\(133\) 0 0
\(134\) −768.000 −0.495113
\(135\) −337.500 584.567i −0.215166 0.372678i
\(136\) 364.000 630.466i 0.229505 0.397515i
\(137\) −24.0000 + 41.5692i −0.0149668 + 0.0259233i −0.873412 0.486982i \(-0.838098\pi\)
0.858445 + 0.512906i \(0.171431\pi\)
\(138\) −270.000 467.654i −0.166550 0.288473i
\(139\) 38.0000 0.0231879 0.0115939 0.999933i \(-0.496309\pi\)
0.0115939 + 0.999933i \(0.496309\pi\)
\(140\) 0 0
\(141\) −1491.00 −0.890531
\(142\) −664.000 1150.08i −0.392406 0.679667i
\(143\) 688.500 1192.52i 0.402624 0.697366i
\(144\) 144.000 249.415i 0.0833333 0.144338i
\(145\) −322.500 558.586i −0.184705 0.319918i
\(146\) 460.000 0.260753
\(147\) 0 0
\(148\) 1256.00 0.697585
\(149\) 1791.00 + 3102.10i 0.984728 + 1.70560i 0.643140 + 0.765749i \(0.277631\pi\)
0.341588 + 0.939850i \(0.389035\pi\)
\(150\) 75.0000 129.904i 0.0408248 0.0707107i
\(151\) 963.500 1668.83i 0.519262 0.899388i −0.480488 0.877001i \(-0.659540\pi\)
0.999749 0.0223862i \(-0.00712634\pi\)
\(152\) −408.000 706.677i −0.217718 0.377099i
\(153\) −1638.00 −0.865519
\(154\) 0 0
\(155\) 580.000 0.300559
\(156\) −486.000 841.777i −0.249430 0.432026i
\(157\) −1255.00 + 2173.72i −0.637961 + 1.10498i 0.347918 + 0.937525i \(0.386889\pi\)
−0.985879 + 0.167456i \(0.946445\pi\)
\(158\) 361.000 625.270i 0.181770 0.314834i
\(159\) 876.000 + 1517.28i 0.436927 + 0.756779i
\(160\) 160.000 0.0790569
\(161\) 0 0
\(162\) −162.000 −0.0785674
\(163\) 935.000 + 1619.47i 0.449294 + 0.778199i 0.998340 0.0575924i \(-0.0183424\pi\)
−0.549047 + 0.835792i \(0.685009\pi\)
\(164\) −248.000 + 429.549i −0.118083 + 0.204525i
\(165\) −127.500 + 220.836i −0.0601567 + 0.104195i
\(166\) −1172.00 2029.96i −0.547981 0.949131i
\(167\) 2019.00 0.935538 0.467769 0.883851i \(-0.345058\pi\)
0.467769 + 0.883851i \(0.345058\pi\)
\(168\) 0 0
\(169\) 4364.00 1.98635
\(170\) −455.000 788.083i −0.205276 0.355548i
\(171\) −918.000 + 1590.02i −0.410533 + 0.711065i
\(172\) 868.000 1503.42i 0.384793 0.666481i
\(173\) 626.500 + 1085.13i 0.275329 + 0.476884i 0.970218 0.242233i \(-0.0778799\pi\)
−0.694889 + 0.719117i \(0.744547\pi\)
\(174\) 774.000 0.337223
\(175\) 0 0
\(176\) −272.000 −0.116493
\(177\) −498.000 862.561i −0.211480 0.366294i
\(178\) −40.0000 + 69.2820i −0.0168434 + 0.0291736i
\(179\) −246.000 + 426.084i −0.102720 + 0.177916i −0.912804 0.408397i \(-0.866088\pi\)
0.810084 + 0.586313i \(0.199421\pi\)
\(180\) −180.000 311.769i −0.0745356 0.129099i
\(181\) 4448.00 1.82661 0.913307 0.407271i \(-0.133520\pi\)
0.913307 + 0.407271i \(0.133520\pi\)
\(182\) 0 0
\(183\) −660.000 −0.266604
\(184\) −360.000 623.538i −0.144237 0.249825i
\(185\) 785.000 1359.66i 0.311969 0.540347i
\(186\) −348.000 + 602.754i −0.137186 + 0.237613i
\(187\) 773.500 + 1339.74i 0.302481 + 0.523912i
\(188\) −1988.00 −0.771222
\(189\) 0 0
\(190\) −1020.00 −0.389466
\(191\) −1999.50 3463.24i −0.757480 1.31199i −0.944132 0.329568i \(-0.893097\pi\)
0.186651 0.982426i \(-0.440236\pi\)
\(192\) −96.0000 + 166.277i −0.0360844 + 0.0625000i
\(193\) −2440.00 + 4226.20i −0.910026 + 1.57621i −0.0960015 + 0.995381i \(0.530605\pi\)
−0.814025 + 0.580830i \(0.802728\pi\)
\(194\) 175.000 + 303.109i 0.0647643 + 0.112175i
\(195\) −1215.00 −0.446195
\(196\) 0 0
\(197\) 4712.00 1.70414 0.852071 0.523426i \(-0.175346\pi\)
0.852071 + 0.523426i \(0.175346\pi\)
\(198\) 306.000 + 530.008i 0.109831 + 0.190232i
\(199\) 1378.00 2386.77i 0.490874 0.850218i −0.509071 0.860724i \(-0.670011\pi\)
0.999945 + 0.0105065i \(0.00334438\pi\)
\(200\) 100.000 173.205i 0.0353553 0.0612372i
\(201\) −576.000 997.661i −0.202129 0.350098i
\(202\) 540.000 0.188090
\(203\) 0 0
\(204\) 1092.00 0.374781
\(205\) 310.000 + 536.936i 0.105616 + 0.182933i
\(206\) −565.000 + 978.609i −0.191094 + 0.330985i
\(207\) −810.000 + 1402.96i −0.271975 + 0.471075i
\(208\) −648.000 1122.37i −0.216013 0.374146i
\(209\) 1734.00 0.573891
\(210\) 0 0
\(211\) 697.000 0.227410 0.113705 0.993515i \(-0.463728\pi\)
0.113705 + 0.993515i \(0.463728\pi\)
\(212\) 1168.00 + 2023.04i 0.378389 + 0.655390i
\(213\) 996.000 1725.12i 0.320398 0.554946i
\(214\) −1206.00 + 2088.85i −0.385236 + 0.667248i
\(215\) −1085.00 1879.28i −0.344169 0.596119i
\(216\) 1080.00 0.340207
\(217\) 0 0
\(218\) 2838.00 0.881714
\(219\) 345.000 + 597.558i 0.106452 + 0.184380i
\(220\) −170.000 + 294.449i −0.0520973 + 0.0902351i
\(221\) −3685.50 + 6383.47i −1.12178 + 1.94298i
\(222\) 942.000 + 1631.59i 0.284788 + 0.493267i
\(223\) 707.000 0.212306 0.106153 0.994350i \(-0.466147\pi\)
0.106153 + 0.994350i \(0.466147\pi\)
\(224\) 0 0
\(225\) −450.000 −0.133333
\(226\) −778.000 1347.54i −0.228990 0.396623i
\(227\) −279.500 + 484.108i −0.0817228 + 0.141548i −0.903990 0.427554i \(-0.859376\pi\)
0.822267 + 0.569102i \(0.192709\pi\)
\(228\) 612.000 1060.02i 0.177766 0.307900i
\(229\) −1918.00 3322.07i −0.553472 0.958641i −0.998021 0.0628865i \(-0.979969\pi\)
0.444549 0.895755i \(-0.353364\pi\)
\(230\) −900.000 −0.258018
\(231\) 0 0
\(232\) 1032.00 0.292044
\(233\) 684.000 + 1184.72i 0.192319 + 0.333106i 0.946018 0.324113i \(-0.105066\pi\)
−0.753699 + 0.657219i \(0.771732\pi\)
\(234\) −1458.00 + 2525.33i −0.407318 + 0.705496i
\(235\) −1242.50 + 2152.07i −0.344901 + 0.597386i
\(236\) −664.000 1150.08i −0.183147 0.317220i
\(237\) 1083.00 0.296829
\(238\) 0 0
\(239\) −3803.00 −1.02927 −0.514635 0.857409i \(-0.672073\pi\)
−0.514635 + 0.857409i \(0.672073\pi\)
\(240\) 120.000 + 207.846i 0.0322749 + 0.0559017i
\(241\) 2825.00 4893.04i 0.755080 1.30784i −0.190255 0.981735i \(-0.560931\pi\)
0.945335 0.326102i \(-0.105735\pi\)
\(242\) −1042.00 + 1804.80i −0.276786 + 0.479408i
\(243\) −1944.00 3367.11i −0.513200 0.888889i
\(244\) −880.000 −0.230886
\(245\) 0 0
\(246\) −744.000 −0.192828
\(247\) 4131.00 + 7155.10i 1.06417 + 1.84319i
\(248\) −464.000 + 803.672i −0.118807 + 0.205779i
\(249\) 1758.00 3044.95i 0.447425 0.774962i
\(250\) −125.000 216.506i −0.0316228 0.0547723i
\(251\) 1650.00 0.414929 0.207464 0.978243i \(-0.433479\pi\)
0.207464 + 0.978243i \(0.433479\pi\)
\(252\) 0 0
\(253\) 1530.00 0.380199
\(254\) 316.000 + 547.328i 0.0780614 + 0.135206i
\(255\) 682.500 1182.12i 0.167607 0.290304i
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 2905.00 + 5031.61i 0.705093 + 1.22126i 0.966658 + 0.256071i \(0.0824281\pi\)
−0.261565 + 0.965186i \(0.584239\pi\)
\(258\) 2604.00 0.628364
\(259\) 0 0
\(260\) −1620.00 −0.386416
\(261\) −1161.00 2010.91i −0.275341 0.476905i
\(262\) 1750.00 3031.09i 0.412654 0.714738i
\(263\) 1379.00 2388.50i 0.323319 0.560004i −0.657852 0.753147i \(-0.728535\pi\)
0.981171 + 0.193143i \(0.0618681\pi\)
\(264\) −204.000 353.338i −0.0475581 0.0823730i
\(265\) 2920.00 0.676884
\(266\) 0 0
\(267\) −120.000 −0.0275052
\(268\) −768.000 1330.22i −0.175049 0.303193i
\(269\) 93.0000 161.081i 0.0210792 0.0365103i −0.855293 0.518144i \(-0.826623\pi\)
0.876373 + 0.481634i \(0.159956\pi\)
\(270\) 675.000 1169.13i 0.152145 0.263523i
\(271\) −3414.00 5913.22i −0.765261 1.32547i −0.940108 0.340875i \(-0.889277\pi\)
0.174847 0.984596i \(-0.444057\pi\)
\(272\) 1456.00 0.324570
\(273\) 0 0
\(274\) −96.0000 −0.0211663
\(275\) 212.500 + 368.061i 0.0465972 + 0.0807087i
\(276\) 540.000 935.307i 0.117769 0.203981i
\(277\) 4107.00 7113.53i 0.890851 1.54300i 0.0519939 0.998647i \(-0.483442\pi\)
0.838857 0.544352i \(-0.183224\pi\)
\(278\) 38.0000 + 65.8179i 0.00819816 + 0.0141996i
\(279\) 2088.00 0.448048
\(280\) 0 0
\(281\) 6707.00 1.42387 0.711933 0.702248i \(-0.247820\pi\)
0.711933 + 0.702248i \(0.247820\pi\)
\(282\) −1491.00 2582.49i −0.314850 0.545337i
\(283\) −2748.50 + 4760.54i −0.577319 + 0.999946i 0.418466 + 0.908232i \(0.362568\pi\)
−0.995785 + 0.0917140i \(0.970765\pi\)
\(284\) 1328.00 2300.16i 0.277473 0.480597i
\(285\) −765.000 1325.02i −0.158999 0.275394i
\(286\) 2754.00 0.569397
\(287\) 0 0
\(288\) 576.000 0.117851
\(289\) −1684.00 2916.77i −0.342764 0.593685i
\(290\) 645.000 1117.17i 0.130606 0.226216i
\(291\) −262.500 + 454.663i −0.0528798 + 0.0915905i
\(292\) 460.000 + 796.743i 0.0921899 + 0.159678i
\(293\) −313.000 −0.0624084 −0.0312042 0.999513i \(-0.509934\pi\)
−0.0312042 + 0.999513i \(0.509934\pi\)
\(294\) 0 0
\(295\) −1660.00 −0.327624
\(296\) 1256.00 + 2175.46i 0.246634 + 0.427182i
\(297\) −1147.50 + 1987.53i −0.224191 + 0.388310i
\(298\) −3582.00 + 6204.21i −0.696308 + 1.20604i
\(299\) 3645.00 + 6313.33i 0.705003 + 1.22110i
\(300\) 300.000 0.0577350
\(301\) 0 0
\(302\) 3854.00 0.734347
\(303\) 405.000 + 701.481i 0.0767876 + 0.133000i
\(304\) 816.000 1413.35i 0.153950 0.266649i
\(305\) −550.000 + 952.628i −0.103255 + 0.178844i
\(306\) −1638.00 2837.10i −0.306007 0.530020i
\(307\) −5479.00 −1.01858 −0.509288 0.860596i \(-0.670091\pi\)
−0.509288 + 0.860596i \(0.670091\pi\)
\(308\) 0 0
\(309\) −1695.00 −0.312056
\(310\) 580.000 + 1004.59i 0.106264 + 0.184054i
\(311\) 2211.00 3829.56i 0.403133 0.698247i −0.590969 0.806694i \(-0.701255\pi\)
0.994102 + 0.108447i \(0.0345879\pi\)
\(312\) 972.000 1683.55i 0.176374 0.305489i
\(313\) 137.500 + 238.157i 0.0248305 + 0.0430078i 0.878174 0.478342i \(-0.158762\pi\)
−0.853343 + 0.521350i \(0.825429\pi\)
\(314\) −5020.00 −0.902213
\(315\) 0 0
\(316\) 1444.00 0.257061
\(317\) 2053.00 + 3555.90i 0.363748 + 0.630029i 0.988574 0.150734i \(-0.0481638\pi\)
−0.624827 + 0.780763i \(0.714830\pi\)
\(318\) −1752.00 + 3034.55i −0.308954 + 0.535124i
\(319\) −1096.50 + 1899.19i −0.192452 + 0.333337i
\(320\) 160.000 + 277.128i 0.0279508 + 0.0484123i
\(321\) −3618.00 −0.629087
\(322\) 0 0
\(323\) −9282.00 −1.59896
\(324\) −162.000 280.592i −0.0277778 0.0481125i
\(325\) −1012.50 + 1753.70i −0.172810 + 0.299316i
\(326\) −1870.00 + 3238.94i −0.317699 + 0.550270i
\(327\) 2128.50 + 3686.67i 0.359958 + 0.623466i
\(328\) −992.000 −0.166994
\(329\) 0 0
\(330\) −510.000 −0.0850745
\(331\) −4130.00 7153.37i −0.685817 1.18787i −0.973179 0.230048i \(-0.926112\pi\)
0.287363 0.957822i \(-0.407222\pi\)
\(332\) 2344.00 4059.93i 0.387481 0.671137i
\(333\) 2826.00 4894.78i 0.465057 0.805502i
\(334\) 2019.00 + 3497.01i 0.330763 + 0.572898i
\(335\) −1920.00 −0.313137
\(336\) 0 0
\(337\) 9946.00 1.60769 0.803847 0.594836i \(-0.202783\pi\)
0.803847 + 0.594836i \(0.202783\pi\)
\(338\) 4364.00 + 7558.67i 0.702279 + 1.21638i
\(339\) 1167.00 2021.30i 0.186970 0.323841i
\(340\) 910.000 1576.17i 0.145152 0.251411i
\(341\) −986.000 1707.80i −0.156583 0.271210i
\(342\) −3672.00 −0.580582
\(343\) 0 0
\(344\) 3472.00 0.544179
\(345\) −675.000 1169.13i −0.105336 0.182447i
\(346\) −1253.00 + 2170.26i −0.194687 + 0.337208i
\(347\) 4399.00 7619.29i 0.680550 1.17875i −0.294264 0.955724i \(-0.595074\pi\)
0.974813 0.223022i \(-0.0715922\pi\)
\(348\) 774.000 + 1340.61i 0.119226 + 0.206506i
\(349\) 1838.00 0.281908 0.140954 0.990016i \(-0.454983\pi\)
0.140954 + 0.990016i \(0.454983\pi\)
\(350\) 0 0
\(351\) −10935.0 −1.66287
\(352\) −272.000 471.118i −0.0411865 0.0713371i
\(353\) 1132.50 1961.55i 0.170756 0.295758i −0.767928 0.640536i \(-0.778712\pi\)
0.938684 + 0.344778i \(0.112046\pi\)
\(354\) 996.000 1725.12i 0.149539 0.259009i
\(355\) −1660.00 2875.20i −0.248179 0.429859i
\(356\) −160.000 −0.0238202
\(357\) 0 0
\(358\) −984.000 −0.145268
\(359\) −2068.00 3581.88i −0.304025 0.526586i 0.673019 0.739625i \(-0.264997\pi\)
−0.977044 + 0.213039i \(0.931664\pi\)
\(360\) 360.000 623.538i 0.0527046 0.0912871i
\(361\) −1772.50 + 3070.06i −0.258420 + 0.447596i
\(362\) 4448.00 + 7704.16i 0.645806 + 1.11857i
\(363\) −3126.00 −0.451990
\(364\) 0 0
\(365\) 1150.00 0.164914
\(366\) −660.000 1143.15i −0.0942589 0.163261i
\(367\) −5015.50 + 8687.10i −0.713370 + 1.23559i 0.250214 + 0.968191i \(0.419499\pi\)
−0.963585 + 0.267403i \(0.913834\pi\)
\(368\) 720.000 1247.08i 0.101991 0.176653i
\(369\) 1116.00 + 1932.97i 0.157443 + 0.272700i
\(370\) 3140.00 0.441191
\(371\) 0 0
\(372\) −1392.00 −0.194010
\(373\) −1396.00 2417.94i −0.193786 0.335647i 0.752716 0.658345i \(-0.228743\pi\)
−0.946502 + 0.322698i \(0.895410\pi\)
\(374\) −1547.00 + 2679.48i −0.213886 + 0.370462i
\(375\) 187.500 324.760i 0.0258199 0.0447214i
\(376\) −1988.00 3443.32i −0.272668 0.472275i
\(377\) −10449.0 −1.42746
\(378\) 0 0
\(379\) 9948.00 1.34827 0.674135 0.738608i \(-0.264517\pi\)
0.674135 + 0.738608i \(0.264517\pi\)
\(380\) −1020.00 1766.69i −0.137697 0.238498i
\(381\) −474.000 + 820.992i −0.0637369 + 0.110396i
\(382\) 3999.00 6926.47i 0.535619 0.927720i
\(383\) 1350.00 + 2338.27i 0.180109 + 0.311958i 0.941918 0.335844i \(-0.109022\pi\)
−0.761808 + 0.647802i \(0.775688\pi\)
\(384\) −384.000 −0.0510310
\(385\) 0 0
\(386\) −9760.00 −1.28697
\(387\) −3906.00 6765.39i −0.513057 0.888641i
\(388\) −350.000 + 606.218i −0.0457953 + 0.0793197i
\(389\) 315.500 546.462i 0.0411221 0.0712255i −0.844732 0.535190i \(-0.820240\pi\)
0.885854 + 0.463964i \(0.153573\pi\)
\(390\) −1215.00 2104.44i −0.157754 0.273237i
\(391\) −8190.00 −1.05930
\(392\) 0 0
\(393\) 5250.00 0.673861
\(394\) 4712.00 + 8161.42i 0.602505 + 1.04357i
\(395\) 902.500 1563.18i 0.114961 0.199119i
\(396\) −612.000 + 1060.02i −0.0776620 + 0.134515i
\(397\) −6569.50 11378.7i −0.830513 1.43849i −0.897632 0.440746i \(-0.854714\pi\)
0.0671186 0.997745i \(-0.478619\pi\)
\(398\) 5512.00 0.694200
\(399\) 0 0
\(400\) 400.000 0.0500000
\(401\) 443.500 + 768.165i 0.0552303 + 0.0956616i 0.892319 0.451406i \(-0.149077\pi\)
−0.837088 + 0.547068i \(0.815744\pi\)
\(402\) 1152.00 1995.32i 0.142927 0.247556i
\(403\) 4698.00 8137.17i 0.580705 1.00581i
\(404\) 540.000 + 935.307i 0.0665000 + 0.115181i
\(405\) −405.000 −0.0496904
\(406\) 0 0
\(407\) −5338.00 −0.650110
\(408\) 1092.00 + 1891.40i 0.132505 + 0.229505i
\(409\) −2595.00 + 4494.67i −0.313727 + 0.543392i −0.979166 0.203061i \(-0.934911\pi\)
0.665439 + 0.746452i \(0.268244\pi\)
\(410\) −620.000 + 1073.87i −0.0746820 + 0.129353i
\(411\) −72.0000 124.708i −0.00864111 0.0149668i
\(412\) −2260.00 −0.270248
\(413\) 0 0
\(414\) −3240.00 −0.384631
\(415\) −2930.00 5074.91i −0.346574 0.600283i
\(416\) 1296.00 2244.74i 0.152744 0.264561i
\(417\) −57.0000 + 98.7269i −0.00669377 + 0.0115939i
\(418\) 1734.00 + 3003.38i 0.202901 + 0.351435i
\(419\) 5712.00 0.665989 0.332995 0.942929i \(-0.391941\pi\)
0.332995 + 0.942929i \(0.391941\pi\)
\(420\) 0 0
\(421\) −11155.0 −1.29136 −0.645679 0.763609i \(-0.723425\pi\)
−0.645679 + 0.763609i \(0.723425\pi\)
\(422\) 697.000 + 1207.24i 0.0804015 + 0.139259i
\(423\) −4473.00 + 7747.46i −0.514148 + 0.890531i
\(424\) −2336.00 + 4046.07i −0.267562 + 0.463431i
\(425\) −1137.50 1970.21i −0.129828 0.224869i
\(426\) 3984.00 0.453111
\(427\) 0 0
\(428\) −4824.00 −0.544806
\(429\) 2065.50 + 3577.55i 0.232455 + 0.402624i
\(430\) 2170.00 3758.55i 0.243364 0.421520i
\(431\) −4249.50 + 7360.35i −0.474922 + 0.822588i −0.999587 0.0287199i \(-0.990857\pi\)
0.524666 + 0.851308i \(0.324190\pi\)
\(432\) 1080.00 + 1870.61i 0.120281 + 0.208333i
\(433\) −5102.00 −0.566251 −0.283125 0.959083i \(-0.591371\pi\)
−0.283125 + 0.959083i \(0.591371\pi\)
\(434\) 0 0
\(435\) 1935.00 0.213279
\(436\) 2838.00 + 4915.56i 0.311733 + 0.539937i
\(437\) −4590.00 + 7950.11i −0.502447 + 0.870264i
\(438\) −690.000 + 1195.12i −0.0752728 + 0.130376i
\(439\) 7847.00 + 13591.4i 0.853114 + 1.47764i 0.878384 + 0.477955i \(0.158622\pi\)
−0.0252705 + 0.999681i \(0.508045\pi\)
\(440\) −680.000 −0.0736767
\(441\) 0 0
\(442\) −14742.0 −1.58644
\(443\) −4571.00 7917.20i −0.490236 0.849115i 0.509700 0.860352i \(-0.329756\pi\)
−0.999937 + 0.0112375i \(0.996423\pi\)
\(444\) −1884.00 + 3263.18i −0.201375 + 0.348792i
\(445\) −100.000 + 173.205i −0.0106527 + 0.0184510i
\(446\) 707.000 + 1224.56i 0.0750615 + 0.130010i
\(447\) −10746.0 −1.13707
\(448\) 0 0
\(449\) −17145.0 −1.80205 −0.901027 0.433762i \(-0.857186\pi\)
−0.901027 + 0.433762i \(0.857186\pi\)
\(450\) −450.000 779.423i −0.0471405 0.0816497i
\(451\) 1054.00 1825.58i 0.110046 0.190606i
\(452\) 1556.00 2695.07i 0.161921 0.280455i
\(453\) 2890.50 + 5006.49i 0.299796 + 0.519262i
\(454\) −1118.00 −0.115573
\(455\) 0 0
\(456\) 2448.00 0.251399
\(457\) 5092.00 + 8819.60i 0.521212 + 0.902765i 0.999696 + 0.0246688i \(0.00785311\pi\)
−0.478484 + 0.878096i \(0.658814\pi\)
\(458\) 3836.00 6644.15i 0.391364 0.677862i
\(459\) 6142.50 10639.1i 0.624635 1.08190i
\(460\) −900.000 1558.85i −0.0912233 0.158003i
\(461\) 9152.00 0.924623 0.462311 0.886718i \(-0.347020\pi\)
0.462311 + 0.886718i \(0.347020\pi\)
\(462\) 0 0
\(463\) −1084.00 −0.108807 −0.0544036 0.998519i \(-0.517326\pi\)
−0.0544036 + 0.998519i \(0.517326\pi\)
\(464\) 1032.00 + 1787.48i 0.103253 + 0.178839i
\(465\) −870.000 + 1506.88i −0.0867641 + 0.150280i
\(466\) −1368.00 + 2369.45i −0.135990 + 0.235542i
\(467\) 9641.50 + 16699.6i 0.955365 + 1.65474i 0.733531 + 0.679656i \(0.237871\pi\)
0.221834 + 0.975084i \(0.428796\pi\)
\(468\) −5832.00 −0.576035
\(469\) 0 0
\(470\) −4970.00 −0.487764
\(471\) −3765.00 6521.17i −0.368327 0.637961i
\(472\) 1328.00 2300.16i 0.129505 0.224308i
\(473\) −3689.00 + 6389.54i −0.358605 + 0.621123i
\(474\) 1083.00 + 1875.81i 0.104945 + 0.181770i
\(475\) −2550.00 −0.246320
\(476\) 0 0
\(477\) 10512.0 1.00904
\(478\) −3803.00 6586.99i −0.363902 0.630297i
\(479\) −2559.00 + 4432.32i −0.244100 + 0.422793i −0.961878 0.273479i \(-0.911826\pi\)
0.717779 + 0.696272i \(0.245159\pi\)
\(480\) −240.000 + 415.692i −0.0228218 + 0.0395285i
\(481\) −12717.0 22026.5i −1.20550 2.08799i
\(482\) 11300.0 1.06784
\(483\) 0 0
\(484\) −4168.00 −0.391435
\(485\) 437.500 + 757.772i 0.0409605 + 0.0709457i
\(486\) 3888.00 6734.21i 0.362887 0.628539i
\(487\) −1459.00 + 2527.06i −0.135757 + 0.235138i −0.925886 0.377802i \(-0.876680\pi\)
0.790129 + 0.612940i \(0.210013\pi\)
\(488\) −880.000 1524.20i −0.0816306 0.141388i
\(489\) −5610.00 −0.518800
\(490\) 0 0
\(491\) −18627.0 −1.71207 −0.856033 0.516921i \(-0.827078\pi\)
−0.856033 + 0.516921i \(0.827078\pi\)
\(492\) −744.000 1288.65i −0.0681750 0.118083i
\(493\) 5869.50 10166.3i 0.536205 0.928734i
\(494\) −8262.00 + 14310.2i −0.752480 + 1.30333i
\(495\) 765.000 + 1325.02i 0.0694630 + 0.120313i
\(496\) −1856.00 −0.168018
\(497\) 0 0
\(498\) 7032.00 0.632754
\(499\) −6421.50 11122.4i −0.576084 0.997806i −0.995923 0.0902079i \(-0.971247\pi\)
0.419839 0.907599i \(-0.362086\pi\)
\(500\) 250.000 433.013i 0.0223607 0.0387298i
\(501\) −3028.50 + 5245.52i −0.270067 + 0.467769i
\(502\) 1650.00 + 2857.88i 0.146699 + 0.254091i
\(503\) 18837.0 1.66978 0.834891 0.550415i \(-0.185531\pi\)
0.834891 + 0.550415i \(0.185531\pi\)
\(504\) 0 0
\(505\) 1350.00 0.118959
\(506\) 1530.00 + 2650.04i 0.134421 + 0.232823i
\(507\) −6546.00 + 11338.0i −0.573408 + 0.993173i
\(508\) −632.000 + 1094.66i −0.0551978 + 0.0956053i
\(509\) −3871.00 6704.77i −0.337090 0.583858i 0.646794 0.762665i \(-0.276109\pi\)
−0.983884 + 0.178807i \(0.942776\pi\)
\(510\) 2730.00 0.237032
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) −6885.00 11925.2i −0.592554 1.02633i
\(514\) −5810.00 + 10063.2i −0.498576 + 0.863559i
\(515\) −1412.50 + 2446.52i −0.120859 + 0.209333i
\(516\) 2604.00 + 4510.26i 0.222160 + 0.384793i
\(517\) 8449.00 0.718736
\(518\) 0 0
\(519\) −3759.00 −0.317923
\(520\) −1620.00 2805.92i −0.136619 0.236630i
\(521\) 307.000 531.740i 0.0258156 0.0447139i −0.852829 0.522190i \(-0.825115\pi\)
0.878645 + 0.477476i \(0.158448\pi\)
\(522\) 2322.00 4021.82i 0.194696 0.337223i
\(523\) 8918.00 + 15446.4i 0.745616 + 1.29144i 0.949907 + 0.312534i \(0.101178\pi\)
−0.204291 + 0.978910i \(0.565489\pi\)
\(524\) 7000.00 0.583581
\(525\) 0 0
\(526\) 5516.00 0.457242
\(527\) 5278.00 + 9141.76i 0.436268 + 0.755639i
\(528\) 408.000 706.677i 0.0336286 0.0582465i
\(529\) 2033.50 3522.13i 0.167132 0.289482i
\(530\) 2920.00 + 5057.59i 0.239315 + 0.414505i
\(531\) −5976.00 −0.488392
\(532\) 0 0
\(533\) 10044.0 0.816236
\(534\) −120.000 207.846i −0.00972455 0.0168434i
\(535\) −3015.00 + 5222.13i −0.243645 + 0.422005i
\(536\) 1536.00 2660.43i 0.123778 0.214390i
\(537\) −738.000 1278.25i −0.0593055 0.102720i
\(538\) 372.000 0.0298105
\(539\) 0 0
\(540\) 2700.00 0.215166
\(541\) −11731.5 20319.6i −0.932304 1.61480i −0.779372 0.626562i \(-0.784462\pi\)
−0.152932 0.988237i \(-0.548872\pi\)
\(542\) 6828.00 11826.4i 0.541121 0.937249i
\(543\) −6672.00 + 11556.2i −0.527298 + 0.913307i
\(544\) 1456.00 + 2521.87i 0.114753 + 0.198758i
\(545\) 7095.00 0.557645
\(546\) 0 0
\(547\) −1860.00 −0.145389 −0.0726946 0.997354i \(-0.523160\pi\)
−0.0726946 + 0.997354i \(0.523160\pi\)
\(548\) −96.0000 166.277i −0.00748342 0.0129617i
\(549\) −1980.00 + 3429.46i −0.153924 + 0.266604i
\(550\) −425.000 + 736.122i −0.0329492 + 0.0570697i
\(551\) −6579.00 11395.2i −0.508666 0.881035i
\(552\) 2160.00 0.166550
\(553\) 0 0
\(554\) 16428.0 1.25985
\(555\) 2355.00 + 4078.98i 0.180116 + 0.311969i
\(556\) −76.0000 + 131.636i −0.00579697 + 0.0100407i
\(557\) −5144.00 + 8909.67i −0.391307 + 0.677764i −0.992622 0.121248i \(-0.961310\pi\)
0.601315 + 0.799012i \(0.294644\pi\)
\(558\) 2088.00 + 3616.52i 0.158409 + 0.274372i
\(559\) −35154.0 −2.65985
\(560\) 0 0
\(561\) −4641.00 −0.349275
\(562\) 6707.00 + 11616.9i 0.503412 + 0.871936i
\(563\) −1178.00 + 2040.36i −0.0881826 + 0.152737i −0.906743 0.421684i \(-0.861439\pi\)
0.818560 + 0.574421i \(0.194773\pi\)
\(564\) 2982.00 5164.98i 0.222633 0.385611i
\(565\) −1945.00 3368.84i −0.144826 0.250846i
\(566\) −10994.0 −0.816453
\(567\) 0 0
\(568\) 5312.00 0.392406
\(569\) 7659.00 + 13265.8i 0.564292 + 0.977382i 0.997115 + 0.0759032i \(0.0241840\pi\)
−0.432823 + 0.901479i \(0.642483\pi\)
\(570\) 1530.00 2650.04i 0.112429 0.194733i
\(571\) 6582.00 11400.4i 0.482396 0.835534i −0.517400 0.855744i \(-0.673100\pi\)
0.999796 + 0.0202094i \(0.00643329\pi\)
\(572\) 2754.00 + 4770.07i 0.201312 + 0.348683i
\(573\) 11997.0 0.874663
\(574\) 0 0
\(575\) −2250.00 −0.163185
\(576\) 576.000 + 997.661i 0.0416667 + 0.0721688i
\(577\) 4479.50 7758.72i 0.323196 0.559792i −0.657950 0.753062i \(-0.728576\pi\)
0.981146 + 0.193270i \(0.0619094\pi\)
\(578\) 3368.00 5833.55i 0.242371 0.419799i
\(579\) −7320.00 12678.6i −0.525404 0.910026i
\(580\) 2580.00 0.184705
\(581\) 0 0
\(582\) −1050.00 −0.0747833
\(583\) −4964.00 8597.90i −0.352638 0.610787i
\(584\) −920.000 + 1593.49i −0.0651881 + 0.112909i
\(585\) −3645.00 + 6313.33i −0.257611 + 0.446195i
\(586\) −313.000 542.132i −0.0220647 0.0382172i
\(587\) −16952.0 −1.19197 −0.595983 0.802997i \(-0.703237\pi\)
−0.595983 + 0.802997i \(0.703237\pi\)
\(588\) 0 0
\(589\) 11832.0 0.827723
\(590\) −1660.00 2875.20i −0.115832 0.200628i
\(591\) −7068.00 + 12242.1i −0.491944 + 0.852071i
\(592\) −2512.00 + 4350.91i −0.174396 + 0.302063i
\(593\) 5035.50 + 8721.74i 0.348707 + 0.603978i 0.986020 0.166627i \(-0.0532875\pi\)
−0.637313 + 0.770605i \(0.719954\pi\)
\(594\) −4590.00 −0.317054
\(595\) 0 0
\(596\) −14328.0 −0.984728
\(597\) 4134.00 + 7160.30i 0.283406 + 0.490874i
\(598\) −7290.00 + 12626.7i −0.498512 + 0.863448i
\(599\) 1414.50 2449.99i 0.0964856 0.167118i −0.813742 0.581226i \(-0.802573\pi\)
0.910228 + 0.414108i \(0.135906\pi\)
\(600\) 300.000 + 519.615i 0.0204124 + 0.0353553i
\(601\) 7662.00 0.520032 0.260016 0.965604i \(-0.416272\pi\)
0.260016 + 0.965604i \(0.416272\pi\)
\(602\) 0 0
\(603\) −6912.00 −0.466797
\(604\) 3854.00 + 6675.32i 0.259631 + 0.449694i
\(605\) −2605.00 + 4511.99i −0.175055 + 0.303204i
\(606\) −810.000 + 1402.96i −0.0542970 + 0.0940452i
\(607\) 453.500 + 785.485i 0.0303245 + 0.0525236i 0.880789 0.473508i \(-0.157013\pi\)
−0.850465 + 0.526032i \(0.823679\pi\)
\(608\) 3264.00 0.217718
\(609\) 0 0
\(610\) −2200.00 −0.146025
\(611\) 20128.5 + 34863.6i 1.33275 + 2.30840i
\(612\) 3276.00 5674.20i 0.216380 0.374781i
\(613\) 14823.0 25674.2i 0.976664 1.69163i 0.302335 0.953202i \(-0.402234\pi\)
0.674329 0.738431i \(-0.264433\pi\)
\(614\) −5479.00 9489.91i −0.360121 0.623748i
\(615\) −1860.00 −0.121955
\(616\) 0 0
\(617\) 11006.0 0.718128 0.359064 0.933313i \(-0.383096\pi\)
0.359064 + 0.933313i \(0.383096\pi\)
\(618\) −1695.00 2935.83i −0.110328 0.191094i
\(619\) 10549.0 18271.4i 0.684976 1.18641i −0.288468 0.957489i \(-0.593146\pi\)
0.973444 0.228924i \(-0.0735206\pi\)
\(620\) −1160.00 + 2009.18i −0.0751399 + 0.130146i
\(621\) −6075.00 10522.2i −0.392563 0.679938i
\(622\) 8844.00 0.570116
\(623\) 0 0
\(624\) 3888.00 0.249430
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) −275.000 + 476.314i −0.0175578 + 0.0304111i
\(627\) −2601.00 + 4505.06i −0.165668 + 0.286946i
\(628\) −5020.00 8694.90i −0.318981 0.552491i
\(629\) 28574.0 1.81132
\(630\) 0 0
\(631\) 21707.0 1.36948 0.684740 0.728787i \(-0.259916\pi\)
0.684740 + 0.728787i \(0.259916\pi\)
\(632\) 1444.00 + 2501.08i 0.0908849 + 0.157417i
\(633\) −1045.50 + 1810.86i −0.0656475 + 0.113705i
\(634\) −4106.00 + 7111.80i −0.257208 + 0.445498i
\(635\) 790.000 + 1368.32i 0.0493704 + 0.0855120i
\(636\) −7008.00 −0.436927
\(637\) 0 0
\(638\) −4386.00 −0.272168
\(639\) −5976.00 10350.7i −0.369964 0.640796i
\(640\) −320.000 + 554.256i −0.0197642 + 0.0342327i
\(641\) −5545.00 + 9604.22i −0.341676 + 0.591800i −0.984744 0.174009i \(-0.944328\pi\)
0.643068 + 0.765809i \(0.277661\pi\)
\(642\) −3618.00 6266.56i −0.222416 0.385236i
\(643\) 995.000 0.0610248 0.0305124 0.999534i \(-0.490286\pi\)
0.0305124 + 0.999534i \(0.490286\pi\)
\(644\) 0 0
\(645\) 6510.00 0.397412
\(646\) −9282.00 16076.9i −0.565318 0.979159i
\(647\) −10396.0 + 18006.4i −0.631699 + 1.09413i 0.355506 + 0.934674i \(0.384309\pi\)
−0.987204 + 0.159460i \(0.949025\pi\)
\(648\) 324.000 561.184i 0.0196419 0.0340207i
\(649\) 2822.00 + 4887.85i 0.170683 + 0.295631i
\(650\) −4050.00 −0.244391
\(651\) 0 0
\(652\) −7480.00 −0.449294
\(653\) 5249.00 + 9091.53i 0.314562 + 0.544838i 0.979344 0.202199i \(-0.0648089\pi\)
−0.664782 + 0.747037i \(0.731476\pi\)
\(654\) −4257.00 + 7373.34i −0.254529 + 0.440857i
\(655\) 4375.00 7577.72i 0.260985 0.452040i
\(656\) −992.000 1718.19i −0.0590413 0.102263i
\(657\) 4140.00 0.245840
\(658\) 0 0
\(659\) −6749.00 −0.398943 −0.199472 0.979904i \(-0.563923\pi\)
−0.199472 + 0.979904i \(0.563923\pi\)
\(660\) −510.000 883.346i −0.0300784 0.0520973i
\(661\) 6200.00 10738.7i 0.364829 0.631903i −0.623920 0.781489i \(-0.714461\pi\)
0.988749 + 0.149586i \(0.0477941\pi\)
\(662\) 8260.00 14306.7i 0.484946 0.839950i
\(663\) −11056.5 19150.4i −0.647660 1.12178i
\(664\) 9376.00 0.547981
\(665\) 0 0
\(666\) 11304.0 0.657689
\(667\) −5805.00 10054.6i −0.336987 0.583679i
\(668\) −4038.00 + 6994.02i −0.233885 + 0.405100i
\(669\) −1060.50 + 1836.84i −0.0612874 + 0.106153i
\(670\) −1920.00 3325.54i −0.110711 0.191756i
\(671\) 3740.00 0.215173
\(672\) 0 0
\(673\) 16024.0 0.917801 0.458900 0.888488i \(-0.348244\pi\)
0.458900 + 0.888488i \(0.348244\pi\)
\(674\) 9946.00 + 17227.0i 0.568406 + 0.984508i
\(675\) 1687.50 2922.84i 0.0962250 0.166667i
\(676\) −8728.00 + 15117.3i −0.496586 + 0.860113i
\(677\) 9367.50 + 16225.0i 0.531791 + 0.921088i 0.999311 + 0.0371063i \(0.0118140\pi\)
−0.467521 + 0.883982i \(0.654853\pi\)
\(678\) 4668.00 0.264415
\(679\) 0 0
\(680\) 3640.00 0.205276
\(681\) −838.500 1452.32i −0.0471827 0.0817228i
\(682\) 1972.00 3415.60i 0.110721 0.191775i
\(683\) 6422.00 11123.2i 0.359782 0.623160i −0.628142 0.778098i \(-0.716184\pi\)
0.987924 + 0.154938i \(0.0495178\pi\)
\(684\) −3672.00 6360.09i −0.205267 0.355532i
\(685\) −240.000 −0.0133868
\(686\) 0 0
\(687\) 11508.0 0.639094
\(688\) 3472.00 + 6013.68i 0.192396 + 0.333240i
\(689\) 23652.0 40966.5i 1.30779 2.26516i
\(690\) 1350.00 2338.27i 0.0744835 0.129009i
\(691\) 12998.0 + 22513.2i 0.715582 + 1.23942i 0.962735 + 0.270448i \(0.0871718\pi\)
−0.247153 + 0.968977i \(0.579495\pi\)
\(692\) −5012.00 −0.275329
\(693\) 0 0
\(694\) 17596.0 0.962442
\(695\) 95.0000 + 164.545i 0.00518497 + 0.00898063i
\(696\) −1548.00 + 2681.21i −0.0843057 + 0.146022i
\(697\) −5642.00 + 9772.23i −0.306608 + 0.531061i
\(698\) 1838.00 + 3183.51i 0.0996695 + 0.172633i
\(699\) −4104.00 −0.222071
\(700\) 0 0
\(701\) 25435.0 1.37042 0.685212 0.728344i \(-0.259710\pi\)
0.685212 + 0.728344i \(0.259710\pi\)
\(702\) −10935.0 18940.0i −0.587913 1.01830i
\(703\) 16014.0 27737.1i 0.859146 1.48808i
\(704\) 544.000 942.236i 0.0291233 0.0504430i
\(705\) −3727.50 6456.22i −0.199129 0.344901i
\(706\) 4530.00 0.241486
\(707\) 0 0
\(708\) 3984.00 0.211480
\(709\) −1911.50 3310.82i −0.101252 0.175374i 0.810949 0.585117i \(-0.198952\pi\)
−0.912201 + 0.409743i \(0.865618\pi\)
\(710\) 3320.00 5750.41i 0.175489 0.303956i
\(711\) 3249.00 5627.43i 0.171374 0.296829i
\(712\) −160.000 277.128i −0.00842170 0.0145868i
\(713\) 10440.0 0.548361
\(714\) 0 0
\(715\) 6885.00 0.360118
\(716\) −984.000 1704.34i −0.0513601 0.0889582i
\(717\) 5704.50 9880.48i 0.297125 0.514635i
\(718\) 4136.00 7163.76i 0.214978 0.372353i
\(719\) 10545.0 + 18264.5i 0.546957 + 0.947357i 0.998481 + 0.0550984i \(0.0175473\pi\)
−0.451524 + 0.892259i \(0.649119\pi\)
\(720\) 1440.00 0.0745356
\(721\) 0 0
\(722\) −7090.00 −0.365460
\(723\) 8475.00 + 14679.1i 0.435946 + 0.755080i
\(724\) −8896.00 + 15408.3i −0.456654 + 0.790947i
\(725\) 1612.50 2792.93i 0.0826024 0.143072i
\(726\) −3126.00 5414.39i −0.159803 0.276786i
\(727\) 7992.00 0.407712 0.203856 0.979001i \(-0.434653\pi\)
0.203856 + 0.979001i \(0.434653\pi\)
\(728\) 0 0
\(729\) 9477.00 0.481481
\(730\) 1150.00 + 1991.86i 0.0583060 + 0.100989i
\(731\) 19747.0 34202.8i 0.999137 1.73056i
\(732\) 1320.00 2286.31i 0.0666511 0.115443i
\(733\) −18482.5 32012.6i −0.931332 1.61312i −0.781047 0.624473i \(-0.785314\pi\)
−0.150286 0.988643i \(-0.548019\pi\)
\(734\) −20062.0 −1.00886
\(735\) 0 0
\(736\) 2880.00 0.144237
\(737\) 3264.00 + 5653.41i 0.163136 + 0.282559i
\(738\) −2232.00 + 3865.94i −0.111329 + 0.192828i
\(739\) 1652.50 2862.21i 0.0822574 0.142474i −0.821962 0.569543i \(-0.807120\pi\)
0.904219 + 0.427069i \(0.140454\pi\)
\(740\) 3140.00 + 5438.64i 0.155985 + 0.270173i
\(741\) −24786.0 −1.22879
\(742\) 0 0
\(743\) −2208.00 −0.109022 −0.0545112 0.998513i \(-0.517360\pi\)
−0.0545112 + 0.998513i \(0.517360\pi\)
\(744\) −1392.00 2411.01i −0.0685930 0.118807i
\(745\) −8955.00 + 15510.5i −0.440384 + 0.762767i
\(746\) 2792.00 4835.89i 0.137027 0.237338i
\(747\) −10548.0 18269.7i −0.516641 0.894849i
\(748\) −6188.00 −0.302481
\(749\) 0 0
\(750\) 750.000 0.0365148
\(751\) 5775.50 + 10003.5i 0.280627 + 0.486060i 0.971539 0.236878i \(-0.0761242\pi\)
−0.690912 + 0.722939i \(0.742791\pi\)
\(752\) 3976.00 6886.63i 0.192806 0.333949i
\(753\) −2475.00 + 4286.83i −0.119780 + 0.207464i
\(754\) −10449.0 18098.2i −0.504682 0.874135i
\(755\) 9635.00 0.464442
\(756\) 0 0
\(757\) 9688.00 0.465147 0.232574 0.972579i \(-0.425285\pi\)
0.232574 + 0.972579i \(0.425285\pi\)
\(758\) 9948.00 + 17230.4i 0.476686 + 0.825644i
\(759\) −2295.00 + 3975.06i −0.109754 + 0.190099i
\(760\) 2040.00 3533.38i 0.0973665 0.168644i
\(761\) −3507.00 6074.30i −0.167055 0.289347i 0.770328 0.637647i \(-0.220092\pi\)
−0.937383 + 0.348300i \(0.886759\pi\)
\(762\) −1896.00 −0.0901376
\(763\) 0 0
\(764\) 15996.0 0.757480
\(765\) −4095.00 7092.75i −0.193536 0.335214i
\(766\) −2700.00 + 4676.54i −0.127356 + 0.220588i
\(767\) −13446.0 + 23289.2i −0.632995 + 1.09638i
\(768\) −384.000 665.108i −0.0180422 0.0312500i
\(769\) 6278.00 0.294396 0.147198 0.989107i \(-0.452975\pi\)
0.147198 + 0.989107i \(0.452975\pi\)
\(770\) 0 0
\(771\) −17430.0 −0.814171
\(772\) −9760.00 16904.8i −0.455013 0.788106i
\(773\) 10675.5 18490.5i 0.496728 0.860359i −0.503264 0.864132i \(-0.667868\pi\)
0.999993 + 0.00377362i \(0.00120118\pi\)
\(774\) 7812.00 13530.8i 0.362786 0.628364i
\(775\) 1450.00 + 2511.47i 0.0672071 + 0.116406i
\(776\) −1400.00 −0.0647643
\(777\) 0 0
\(778\) 1262.00 0.0581554
\(779\) 6324.00 + 10953.5i 0.290861 + 0.503786i
\(780\) 2430.00 4208.88i 0.111549 0.193208i
\(781\) −5644.00 + 9775.69i −0.258589 + 0.447890i
\(782\) −8190.00 14185.5i −0.374519 0.648686i
\(783\) 17415.0 0.794842
\(784\) 0 0
\(785\) −12550.0 −0.570610
\(786\) 5250.00 + 9093.27i 0.238246 + 0.412654i
\(787\) −12983.5 + 22488.1i −0.588071 + 1.01857i 0.406414 + 0.913689i \(0.366779\pi\)
−0.994485 + 0.104880i \(0.966554\pi\)
\(788\) −9424.00 + 16322.8i −0.426036 + 0.737915i
\(789\) 4137.00 + 7165.49i 0.186668 + 0.323319i
\(790\) 3610.00 0.162580
\(791\) 0 0
\(792\) −2448.00 −0.109831
\(793\) 8910.00 + 15432.6i 0.398995 + 0.691080i
\(794\) 13139.0 22757.4i 0.587262 1.01717i
\(795\) −4380.00 + 7586.38i −0.195399 + 0.338442i
\(796\) 5512.00 + 9547.06i 0.245437 + 0.425109i
\(797\) 8595.00 0.381996 0.190998 0.981590i \(-0.438828\pi\)
0.190998 + 0.981590i \(0.438828\pi\)
\(798\) 0 0
\(799\) −45227.0 −2.00252
\(800\) 400.000 + 692.820i 0.0176777 + 0.0306186i
\(801\) −360.000 + 623.538i −0.0158801 + 0.0275052i
\(802\) −887.000 + 1536.33i −0.0390537 + 0.0676430i
\(803\) −1955.00 3386.16i −0.0859159 0.148811i
\(804\) 4608.00 0.202129
\(805\) 0 0
\(806\) 18792.0 0.821241
\(807\) 279.000 + 483.242i 0.0121701 + 0.0210792i
\(808\) −1080.00 + 1870.61i −0.0470226 + 0.0814455i
\(809\) 6835.50 11839.4i 0.297062 0.514527i −0.678400 0.734693i \(-0.737326\pi\)
0.975463 + 0.220166i \(0.0706598\pi\)
\(810\) −405.000 701.481i −0.0175682 0.0304290i
\(811\) 11986.0 0.518971 0.259485 0.965747i \(-0.416447\pi\)
0.259485 + 0.965747i \(0.416447\pi\)
\(812\) 0 0
\(813\) 20484.0 0.883647
\(814\) −5338.00 9245.69i −0.229849 0.398110i
\(815\) −4675.00 + 8097.34i −0.200930 + 0.348021i
\(816\) −2184.00 + 3782.80i −0.0936952 + 0.162285i
\(817\) −22134.0 38337.2i −0.947822 1.64168i
\(818\) −10380.0 −0.443677
\(819\) 0 0
\(820\) −2480.00 −0.105616
\(821\) 6475.50 + 11215.9i 0.275270 + 0.476781i 0.970203 0.242293i \(-0.0778995\pi\)
−0.694933 + 0.719074i \(0.744566\pi\)
\(822\) 144.000 249.415i 0.00611019 0.0105832i
\(823\) 6394.00 11074.7i 0.270815 0.469066i −0.698256 0.715848i \(-0.746040\pi\)
0.969071 + 0.246783i \(0.0793735\pi\)
\(824\) −2260.00 3914.43i −0.0955471 0.165492i
\(825\) −1275.00 −0.0538058
\(826\) 0 0
\(827\) 24662.0 1.03698 0.518490 0.855084i \(-0.326495\pi\)
0.518490 + 0.855084i \(0.326495\pi\)
\(828\) −3240.00 5611.84i −0.135988 0.235538i
\(829\) 2062.00 3571.49i 0.0863887 0.149630i −0.819593 0.572946i \(-0.805801\pi\)
0.905982 + 0.423316i \(0.139134\pi\)
\(830\) 5860.00 10149.8i 0.245065 0.424464i
\(831\) 12321.0 + 21340.6i 0.514333 + 0.890851i
\(832\) 5184.00 0.216013
\(833\) 0 0
\(834\) −228.000 −0.00946642
\(835\) 5047.50 + 8742.53i 0.209193 + 0.362332i
\(836\) −3468.00 + 6006.75i −0.143473 + 0.248502i
\(837\) −7830.00 + 13562.0i −0.323351 + 0.560060i
\(838\) 5712.00 + 9893.47i 0.235463 + 0.407833i
\(839\) 33154.0 1.36425 0.682123 0.731237i \(-0.261057\pi\)
0.682123 + 0.731237i \(0.261057\pi\)
\(840\) 0 0
\(841\) −7748.00 −0.317684
\(842\) −11155.0 19321.0i −0.456564 0.790792i
\(843\) −10060.5 + 17425.3i −0.411034 + 0.711933i
\(844\) −1394.00 + 2414.48i −0.0568524 + 0.0984713i
\(845\) 10910.0 + 18896.7i 0.444160 + 0.769308i
\(846\) −17892.0 −0.727115
\(847\) 0 0
\(848\) −9344.00 −0.378389
\(849\) −8245.50 14281.6i −0.333315 0.577319i
\(850\) 2275.00 3940.42i 0.0918022 0.159006i
\(851\) 14130.0 24473.9i 0.569178 0.985845i
\(852\) 3984.00 + 6900.49i 0.160199 + 0.277473i
\(853\) −12050.0 −0.483686 −0.241843 0.970315i \(-0.577752\pi\)
−0.241843 + 0.970315i \(0.577752\pi\)
\(854\) 0 0
\(855\) −9180.00 −0.367192
\(856\) −4824.00 8355.41i −0.192618 0.333624i
\(857\) 7635.00 13224.2i 0.304325 0.527107i −0.672786 0.739837i \(-0.734902\pi\)
0.977111 + 0.212731i \(0.0682357\pi\)
\(858\) −4131.00 + 7155.10i −0.164371 + 0.284698i
\(859\) −6282.00 10880.7i −0.249522 0.432184i 0.713872 0.700277i \(-0.246940\pi\)
−0.963393 + 0.268093i \(0.913607\pi\)
\(860\) 8680.00 0.344169
\(861\) 0 0
\(862\) −16998.0 −0.671641
\(863\) −6488.00 11237.5i −0.255914 0.443257i 0.709229 0.704978i \(-0.249043\pi\)
−0.965143 + 0.261721i \(0.915710\pi\)
\(864\) −2160.00 + 3741.23i −0.0850517 + 0.147314i
\(865\) −3132.50 + 5425.65i −0.123131 + 0.213269i
\(866\) −5102.00 8836.92i −0.200200 0.346756i
\(867\) 10104.0 0.395790
\(868\) 0 0
\(869\) −6137.00 −0.239567
\(870\) 1935.00 + 3351.52i 0.0754053 + 0.130606i
\(871\) −15552.0 + 26936.9i −0.605005 + 1.04790i
\(872\) −5676.00 + 9831.12i −0.220428 + 0.381793i
\(873\) 1575.00 + 2727.98i 0.0610603 + 0.105760i
\(874\) −18360.0 −0.710568
\(875\) 0 0
\(876\) −2760.00 −0.106452
\(877\) 7817.00 + 13539.4i 0.300982 + 0.521316i 0.976359 0.216157i \(-0.0693522\pi\)
−0.675377 + 0.737473i \(0.736019\pi\)
\(878\) −15694.0 + 27182.8i −0.603242 + 1.04485i
\(879\) 469.500 813.198i 0.0180157 0.0312042i
\(880\) −680.000 1177.79i −0.0260486 0.0451176i
\(881\) 8896.00 0.340197 0.170099 0.985427i \(-0.445591\pi\)
0.170099 + 0.985427i \(0.445591\pi\)
\(882\) 0 0
\(883\) −33456.0 −1.27507 −0.637533 0.770423i \(-0.720045\pi\)
−0.637533 + 0.770423i \(0.720045\pi\)
\(884\) −14742.0 25533.9i −0.560890 0.971491i
\(885\) 2490.00 4312.81i 0.0945768 0.163812i
\(886\) 9142.00 15834.4i 0.346650 0.600415i
\(887\) 4144.00 + 7177.62i 0.156868 + 0.271703i 0.933738 0.357958i \(-0.116527\pi\)
−0.776870 + 0.629661i \(0.783194\pi\)
\(888\) −7536.00 −0.284788
\(889\) 0 0
\(890\) −400.000 −0.0150652
\(891\) 688.500 + 1192.52i 0.0258873 + 0.0448382i
\(892\) −1414.00 + 2449.12i −0.0530765 + 0.0919312i
\(893\) −25347.0 + 43902.3i −0.949838 + 1.64517i
\(894\) −10746.0 18612.6i −0.402013 0.696308i
\(895\) −2460.00 −0.0918757
\(896\) 0 0
\(897\) −21870.0 −0.814067
\(898\) −17145.0 29696.0i −0.637123 1.10353i
\(899\) −7482.00 + 12959.2i −0.277574 + 0.480772i
\(900\) 900.000 1558.85i 0.0333333 0.0577350i
\(901\) 26572.0 + 46024.1i 0.982510 + 1.70176i
\(902\) 4216.00 0.155629
\(903\) 0 0
\(904\) 6224.00 0.228990
\(905\) 11120.0 + 19260.4i 0.408443 + 0.707445i
\(906\) −5781.00 + 10013.0i −0.211988 + 0.367173i
\(907\) −7699.00 + 13335.1i −0.281853 + 0.488185i −0.971841 0.235636i \(-0.924283\pi\)
0.689988 + 0.723821i \(0.257616\pi\)
\(908\) −1118.00 1936.43i −0.0408614 0.0707740i
\(909\) 4860.00 0.177333
\(910\) 0 0
\(911\) 22656.0 0.823959 0.411980 0.911193i \(-0.364838\pi\)
0.411980 + 0.911193i \(0.364838\pi\)
\(912\) 2448.00 + 4240.06i 0.0888831 + 0.153950i
\(913\) −9962.00 + 17254.7i −0.361111 + 0.625462i
\(914\) −10184.0 + 17639.2i −0.368552 + 0.638351i
\(915\) −1650.00 2857.88i −0.0596146 0.103255i
\(916\) 15344.0 0.553472
\(917\) 0 0
\(918\) 24570.0 0.883367
\(919\) −4574.50 7923.27i −0.164199 0.284401i 0.772172 0.635414i \(-0.219171\pi\)
−0.936371 + 0.351013i \(0.885837\pi\)
\(920\) 1800.00 3117.69i 0.0645046 0.111725i
\(921\) 8218.50 14234.9i 0.294038 0.509288i
\(922\) 9152.00 + 15851.7i 0.326904 + 0.566214i
\(923\) −53784.0 −1.91801
\(924\) 0 0
\(925\) 7850.00 0.279034
\(926\) −1084.00 1877.54i −0.0384692 0.0666306i
\(927\) −5085.00 + 8807.48i −0.180165 + 0.312056i
\(928\) −2064.00 + 3574.95i −0.0730109 + 0.126459i
\(929\) −13636.0 23618.2i −0.481574 0.834111i 0.518202 0.855258i \(-0.326602\pi\)
−0.999776 + 0.0211469i \(0.993268\pi\)
\(930\) −3480.00 −0.122703
\(931\) 0 0
\(932\) −5472.00 −0.192319
\(933\) 6633.00 + 11488.7i 0.232749 + 0.403133i
\(934\) −19283.0 + 33399.1i −0.675545 + 1.17008i
\(935\) −3867.50 + 6698.71i −0.135274 + 0.234301i
\(936\) −5832.00 10101.3i −0.203659 0.352748i
\(937\) −44177.0 −1.54023 −0.770117 0.637902i \(-0.779802\pi\)
−0.770117 + 0.637902i \(0.779802\pi\)
\(938\) 0 0
\(939\) −825.000 −0.0286718
\(940\) −4970.00 8608.29i −0.172451 0.298693i
\(941\) −1118.00 + 1936.43i −0.0387309 + 0.0670839i −0.884741 0.466083i \(-0.845665\pi\)
0.846010 + 0.533167i \(0.178998\pi\)
\(942\) 7530.00 13042.3i 0.260447 0.451107i
\(943\) 5580.00 + 9664.84i 0.192693 + 0.333755i
\(944\) 5312.00 0.183147
\(945\) 0 0
\(946\) −14756.0 −0.507145
\(947\) 8732.00 + 15124.3i 0.299632 + 0.518979i 0.976052 0.217538i \(-0.0698026\pi\)
−0.676419 + 0.736517i \(0.736469\pi\)
\(948\) −2166.00 + 3751.62i −0.0742072 + 0.128531i
\(949\) 9315.00 16134.1i 0.318628 0.551879i
\(950\) −2550.00 4416.73i −0.0870873 0.150840i
\(951\) −12318.0 −0.420019
\(952\) 0 0
\(953\) −18336.0 −0.623254 −0.311627 0.950204i \(-0.600874\pi\)
−0.311627 + 0.950204i \(0.600874\pi\)
\(954\) 10512.0 + 18207.3i 0.356749 + 0.617907i
\(955\) 9997.50 17316.2i 0.338756 0.586742i
\(956\) 7606.00 13174.0i 0.257318 0.445687i
\(957\) −3289.50 5697.58i −0.111112 0.192452i
\(958\) −10236.0 −0.345209
\(959\) 0 0
\(960\) −960.000 −0.0322749
\(961\) 8167.50 + 14146.5i 0.274160 + 0.474859i
\(962\) 25434.0 44053.0i 0.852417 1.47643i
\(963\) −10854.0 + 18799.7i −0.363204 + 0.629087i
\(964\) 11300.0 + 19572.2i 0.377540 + 0.653918i
\(965\) −24400.0 −0.813952
\(966\) 0 0
\(967\) −46802.0 −1.55641 −0.778206 0.628009i \(-0.783870\pi\)
−0.778206 + 0.628009i \(0.783870\pi\)
\(968\) −4168.00 7219.19i −0.138393 0.239704i
\(969\) 13923.0 24115.3i 0.461580 0.799480i
\(970\) −875.000 + 1515.54i −0.0289635 + 0.0501662i
\(971\) 22512.0 + 38991.9i 0.744021 + 1.28868i 0.950651 + 0.310263i \(0.100417\pi\)
−0.206630 + 0.978419i \(0.566250\pi\)
\(972\) 15552.0 0.513200
\(973\) 0 0
\(974\) −5836.00 −0.191989
\(975\) −3037.50 5261.10i −0.0997722 0.172810i
\(976\) 1760.00 3048.41i 0.0577215 0.0999766i
\(977\) −6393.00 + 11073.0i −0.209345 + 0.362596i −0.951508 0.307623i \(-0.900467\pi\)
0.742163 + 0.670219i \(0.233800\pi\)
\(978\) −5610.00 9716.81i −0.183423 0.317699i
\(979\) 680.000 0.0221991
\(980\) 0 0
\(981\) 25542.0 0.831288
\(982\) −18627.0 32262.9i −0.605307 1.04842i
\(983\) 16769.5 29045.6i 0.544114 0.942433i −0.454548 0.890722i \(-0.650199\pi\)
0.998662 0.0517108i \(-0.0164674\pi\)
\(984\) 1488.00 2577.29i 0.0482070 0.0834970i
\(985\) 11780.0 + 20403.6i 0.381058 + 0.660012i
\(986\) 23478.0 0.758308
\(987\) 0 0
\(988\) −33048.0 −1.06417
\(989\) −19530.0 33827.0i −0.627925 1.08760i
\(990\) −1530.00 + 2650.04i −0.0491178 + 0.0850745i
\(991\) 9100.00 15761.7i 0.291696 0.505233i −0.682515 0.730872i \(-0.739114\pi\)
0.974211 + 0.225639i \(0.0724470\pi\)
\(992\) −1856.00 3214.69i −0.0594033 0.102890i
\(993\) 24780.0 0.791913
\(994\) 0 0
\(995\) 13780.0 0.439051
\(996\) 7032.00 + 12179.8i 0.223712 + 0.387481i
\(997\) −16299.5 + 28231.6i −0.517764 + 0.896793i 0.482023 + 0.876158i \(0.339902\pi\)
−0.999787 + 0.0206346i \(0.993431\pi\)
\(998\) 12843.0 22244.7i 0.407353 0.705556i
\(999\) 21195.0 + 36710.8i 0.671251 + 1.16264i
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 490.4.e.l.361.1 2
7.2 even 3 inner 490.4.e.l.471.1 2
7.3 odd 6 70.4.a.b.1.1 1
7.4 even 3 490.4.a.f.1.1 1
7.5 odd 6 490.4.e.p.471.1 2
7.6 odd 2 490.4.e.p.361.1 2
21.17 even 6 630.4.a.m.1.1 1
28.3 even 6 560.4.a.k.1.1 1
35.3 even 12 350.4.c.j.99.2 2
35.4 even 6 2450.4.a.ba.1.1 1
35.17 even 12 350.4.c.j.99.1 2
35.24 odd 6 350.4.a.t.1.1 1
56.3 even 6 2240.4.a.p.1.1 1
56.45 odd 6 2240.4.a.w.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.4.a.b.1.1 1 7.3 odd 6
350.4.a.t.1.1 1 35.24 odd 6
350.4.c.j.99.1 2 35.17 even 12
350.4.c.j.99.2 2 35.3 even 12
490.4.a.f.1.1 1 7.4 even 3
490.4.e.l.361.1 2 1.1 even 1 trivial
490.4.e.l.471.1 2 7.2 even 3 inner
490.4.e.p.361.1 2 7.6 odd 2
490.4.e.p.471.1 2 7.5 odd 6
560.4.a.k.1.1 1 28.3 even 6
630.4.a.m.1.1 1 21.17 even 6
2240.4.a.p.1.1 1 56.3 even 6
2240.4.a.w.1.1 1 56.45 odd 6
2450.4.a.ba.1.1 1 35.4 even 6