Properties

Label 169.4.e.f.147.2
Level $169$
Weight $4$
Character 169.147
Analytic conductor $9.971$
Analytic rank $0$
Dimension $8$
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] = [169,4,Mod(23,169)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(169, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.23");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 169.e (of order \(6\), 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: \(9.97132279097\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.1731891456.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 147.2
Root \(-1.35234 - 0.780776i\) of defining polynomial
Character \(\chi\) \(=\) 169.147
Dual form 169.4.e.f.23.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.35234 - 0.780776i) q^{2} +(-4.34233 + 7.52113i) q^{3} +(-2.78078 - 4.81645i) q^{4} +3.56155i q^{5} +(11.7446 - 6.78078i) q^{6} +(-23.5360 + 13.5885i) q^{7} +21.1771i q^{8} +(-24.2116 - 41.9358i) q^{9} +O(q^{10})\) \(q+(-1.35234 - 0.780776i) q^{2} +(-4.34233 + 7.52113i) q^{3} +(-2.78078 - 4.81645i) q^{4} +3.56155i q^{5} +(11.7446 - 6.78078i) q^{6} +(-23.5360 + 13.5885i) q^{7} +21.1771i q^{8} +(-24.2116 - 41.9358i) q^{9} +(2.78078 - 4.81645i) q^{10} +(-13.2167 - 7.63068i) q^{11} +48.3002 q^{12} +42.4384 q^{14} +(-26.7869 - 15.4654i) q^{15} +(-5.71165 + 9.89286i) q^{16} +(22.2732 + 38.5783i) q^{17} +75.6155i q^{18} +(-20.7584 + 11.9848i) q^{19} +(17.1540 - 9.90388i) q^{20} -236.024i q^{21} +(11.9157 + 20.6386i) q^{22} +(61.3693 - 106.295i) q^{23} +(-159.276 - 91.9579i) q^{24} +112.315 q^{25} +186.054 q^{27} +(130.897 + 75.5734i) q^{28} +(109.955 - 190.447i) q^{29} +(24.1501 + 41.8292i) q^{30} -27.0928i q^{31} +(162.167 - 93.6274i) q^{32} +(114.783 - 66.2699i) q^{33} -69.5616i q^{34} +(-48.3963 - 83.8249i) q^{35} +(-134.654 + 233.228i) q^{36} +(-81.5729 - 47.0961i) q^{37} +37.4299 q^{38} -75.4233 q^{40} +(-138.871 - 80.1771i) q^{41} +(-184.282 + 319.185i) q^{42} +(-75.6510 - 131.031i) q^{43} +84.8769i q^{44} +(149.357 - 86.2311i) q^{45} +(-165.985 + 95.8314i) q^{46} +466.948i q^{47} +(-49.6037 - 85.9161i) q^{48} +(197.797 - 342.594i) q^{49} +(-151.889 - 87.6932i) q^{50} -386.870 q^{51} -120.847 q^{53} +(-251.609 - 145.267i) q^{54} +(27.1771 - 47.0721i) q^{55} +(-287.766 - 498.425i) q^{56} -208.169i q^{57} +(-297.393 + 171.700i) q^{58} +(-380.733 + 219.816i) q^{59} +172.024i q^{60} +(68.6525 + 118.910i) q^{61} +(-21.1534 + 36.6388i) q^{62} +(1139.69 + 658.002i) q^{63} -201.022 q^{64} -206.968 q^{66} +(443.648 + 256.140i) q^{67} +(123.874 - 214.555i) q^{68} +(532.972 + 923.134i) q^{69} +151.147i q^{70} +(-355.693 + 205.359i) q^{71} +(888.078 - 512.732i) q^{72} -308.004i q^{73} +(73.5431 + 127.380i) q^{74} +(-487.710 + 844.739i) q^{75} +(115.449 + 66.6543i) q^{76} +414.759 q^{77} -586.462 q^{79} +(-35.2339 - 20.3423i) q^{80} +(-154.193 + 267.070i) q^{81} +(125.201 + 216.854i) q^{82} -1354.20i q^{83} +(-1136.80 + 656.329i) q^{84} +(-137.399 + 79.3272i) q^{85} +236.266i q^{86} +(954.918 + 1653.97i) q^{87} +(161.596 - 279.892i) q^{88} +(-380.949 - 219.941i) q^{89} -269.309 q^{90} -682.617 q^{92} +(203.769 + 117.646i) q^{93} +(364.582 - 631.474i) q^{94} +(-42.6847 - 73.9320i) q^{95} +1626.24i q^{96} +(1308.80 - 755.634i) q^{97} +(-534.979 + 308.870i) q^{98} +739.006i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 10 q^{3} - 14 q^{4} - 70 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 10 q^{3} - 14 q^{4} - 70 q^{9} + 14 q^{10} + 172 q^{12} + 356 q^{14} + 78 q^{16} + 38 q^{17} - 284 q^{22} + 392 q^{23} + 948 q^{25} + 1340 q^{27} + 88 q^{29} + 86 q^{30} - 214 q^{35} - 500 q^{36} + 1256 q^{38} - 356 q^{40} - 394 q^{42} + 574 q^{43} - 570 q^{48} + 766 q^{49} - 1924 q^{51} - 472 q^{53} + 36 q^{55} - 2030 q^{56} + 2116 q^{61} - 664 q^{62} - 3076 q^{64} - 3272 q^{66} + 422 q^{68} + 1592 q^{69} - 294 q^{74} - 1032 q^{75} - 3048 q^{77} - 4032 q^{79} - 244 q^{81} + 144 q^{82} + 5116 q^{87} - 2484 q^{88} - 1000 q^{90} - 3152 q^{92} + 1622 q^{94} - 292 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35234 0.780776i −0.478126 0.276046i 0.241509 0.970399i \(-0.422358\pi\)
−0.719635 + 0.694352i \(0.755691\pi\)
\(3\) −4.34233 + 7.52113i −0.835682 + 1.44744i 0.0577926 + 0.998329i \(0.481594\pi\)
−0.893474 + 0.449114i \(0.851740\pi\)
\(4\) −2.78078 4.81645i −0.347597 0.602056i
\(5\) 3.56155i 0.318555i 0.987234 + 0.159277i \(0.0509165\pi\)
−0.987234 + 0.159277i \(0.949084\pi\)
\(6\) 11.7446 6.78078i 0.799122 0.461373i
\(7\) −23.5360 + 13.5885i −1.27083 + 0.733712i −0.975144 0.221574i \(-0.928881\pi\)
−0.295683 + 0.955286i \(0.595547\pi\)
\(8\) 21.1771i 0.935904i
\(9\) −24.2116 41.9358i −0.896728 1.55318i
\(10\) 2.78078 4.81645i 0.0879359 0.152309i
\(11\) −13.2167 7.63068i −0.362272 0.209158i 0.307805 0.951450i \(-0.400406\pi\)
−0.670077 + 0.742292i \(0.733739\pi\)
\(12\) 48.3002 1.16192
\(13\) 0 0
\(14\) 42.4384 0.810154
\(15\) −26.7869 15.4654i −0.461090 0.266211i
\(16\) −5.71165 + 9.89286i −0.0892445 + 0.154576i
\(17\) 22.2732 + 38.5783i 0.317767 + 0.550389i 0.980022 0.198890i \(-0.0637336\pi\)
−0.662255 + 0.749279i \(0.730400\pi\)
\(18\) 75.6155i 0.990153i
\(19\) −20.7584 + 11.9848i −0.250647 + 0.144711i −0.620061 0.784554i \(-0.712892\pi\)
0.369413 + 0.929265i \(0.379559\pi\)
\(20\) 17.1540 9.90388i 0.191788 0.110729i
\(21\) 236.024i 2.45260i
\(22\) 11.9157 + 20.6386i 0.115474 + 0.200008i
\(23\) 61.3693 106.295i 0.556365 0.963652i −0.441431 0.897295i \(-0.645529\pi\)
0.997796 0.0663568i \(-0.0211376\pi\)
\(24\) −159.276 91.9579i −1.35467 0.782117i
\(25\) 112.315 0.898523
\(26\) 0 0
\(27\) 186.054 1.32615
\(28\) 130.897 + 75.5734i 0.883471 + 0.510072i
\(29\) 109.955 190.447i 0.704071 1.21949i −0.262955 0.964808i \(-0.584697\pi\)
0.967026 0.254678i \(-0.0819694\pi\)
\(30\) 24.1501 + 41.8292i 0.146973 + 0.254564i
\(31\) 27.0928i 0.156968i −0.996915 0.0784840i \(-0.974992\pi\)
0.996915 0.0784840i \(-0.0250080\pi\)
\(32\) 162.167 93.6274i 0.895856 0.517223i
\(33\) 114.783 66.2699i 0.605488 0.349579i
\(34\) 69.5616i 0.350874i
\(35\) −48.3963 83.8249i −0.233728 0.404828i
\(36\) −134.654 + 233.228i −0.623400 + 1.07976i
\(37\) −81.5729 47.0961i −0.362446 0.209258i 0.307707 0.951481i \(-0.400438\pi\)
−0.670153 + 0.742223i \(0.733772\pi\)
\(38\) 37.4299 0.159788
\(39\) 0 0
\(40\) −75.4233 −0.298137
\(41\) −138.871 80.1771i −0.528975 0.305404i 0.211624 0.977351i \(-0.432125\pi\)
−0.740599 + 0.671947i \(0.765458\pi\)
\(42\) −184.282 + 319.185i −0.677031 + 1.17265i
\(43\) −75.6510 131.031i −0.268295 0.464700i 0.700127 0.714018i \(-0.253127\pi\)
−0.968422 + 0.249318i \(0.919793\pi\)
\(44\) 84.8769i 0.290811i
\(45\) 149.357 86.2311i 0.494773 0.285657i
\(46\) −165.985 + 95.8314i −0.532025 + 0.307165i
\(47\) 466.948i 1.44918i 0.689181 + 0.724589i \(0.257970\pi\)
−0.689181 + 0.724589i \(0.742030\pi\)
\(48\) −49.6037 85.9161i −0.149160 0.258353i
\(49\) 197.797 342.594i 0.576667 0.998817i
\(50\) −151.889 87.6932i −0.429607 0.248034i
\(51\) −386.870 −1.06221
\(52\) 0 0
\(53\) −120.847 −0.313199 −0.156600 0.987662i \(-0.550053\pi\)
−0.156600 + 0.987662i \(0.550053\pi\)
\(54\) −251.609 145.267i −0.634068 0.366079i
\(55\) 27.1771 47.0721i 0.0666283 0.115404i
\(56\) −287.766 498.425i −0.686684 1.18937i
\(57\) 208.169i 0.483730i
\(58\) −297.393 + 171.700i −0.673269 + 0.388712i
\(59\) −380.733 + 219.816i −0.840122 + 0.485045i −0.857306 0.514808i \(-0.827863\pi\)
0.0171836 + 0.999852i \(0.494530\pi\)
\(60\) 172.024i 0.370136i
\(61\) 68.6525 + 118.910i 0.144099 + 0.249587i 0.929037 0.369988i \(-0.120638\pi\)
−0.784937 + 0.619575i \(0.787305\pi\)
\(62\) −21.1534 + 36.6388i −0.0433304 + 0.0750505i
\(63\) 1139.69 + 658.002i 2.27917 + 1.31588i
\(64\) −201.022 −0.392621
\(65\) 0 0
\(66\) −206.968 −0.386000
\(67\) 443.648 + 256.140i 0.808958 + 0.467052i 0.846594 0.532239i \(-0.178649\pi\)
−0.0376358 + 0.999292i \(0.511983\pi\)
\(68\) 123.874 214.555i 0.220910 0.382627i
\(69\) 532.972 + 923.134i 0.929887 + 1.61061i
\(70\) 151.147i 0.258078i
\(71\) −355.693 + 205.359i −0.594549 + 0.343263i −0.766894 0.641774i \(-0.778199\pi\)
0.172345 + 0.985037i \(0.444866\pi\)
\(72\) 888.078 512.732i 1.45362 0.839251i
\(73\) 308.004i 0.493823i −0.969038 0.246912i \(-0.920584\pi\)
0.969038 0.246912i \(-0.0794158\pi\)
\(74\) 73.5431 + 127.380i 0.115530 + 0.200104i
\(75\) −487.710 + 844.739i −0.750879 + 1.30056i
\(76\) 115.449 + 66.6543i 0.174248 + 0.100602i
\(77\) 414.759 0.613847
\(78\) 0 0
\(79\) −586.462 −0.835217 −0.417608 0.908627i \(-0.637132\pi\)
−0.417608 + 0.908627i \(0.637132\pi\)
\(80\) −35.2339 20.3423i −0.0492409 0.0284293i
\(81\) −154.193 + 267.070i −0.211513 + 0.366352i
\(82\) 125.201 + 216.854i 0.168611 + 0.292043i
\(83\) 1354.20i 1.79088i −0.445182 0.895440i \(-0.646861\pi\)
0.445182 0.895440i \(-0.353139\pi\)
\(84\) −1136.80 + 656.329i −1.47660 + 0.852516i
\(85\) −137.399 + 79.3272i −0.175329 + 0.101226i
\(86\) 236.266i 0.296247i
\(87\) 954.918 + 1653.97i 1.17676 + 2.03820i
\(88\) 161.596 279.892i 0.195752 0.339052i
\(89\) −380.949 219.941i −0.453714 0.261952i 0.255683 0.966761i \(-0.417700\pi\)
−0.709398 + 0.704809i \(0.751033\pi\)
\(90\) −269.309 −0.315418
\(91\) 0 0
\(92\) −682.617 −0.773563
\(93\) 203.769 + 117.646i 0.227202 + 0.131175i
\(94\) 364.582 631.474i 0.400040 0.692889i
\(95\) −42.6847 73.9320i −0.0460985 0.0798449i
\(96\) 1626.24i 1.72894i
\(97\) 1308.80 755.634i 1.36998 0.790959i 0.379056 0.925374i \(-0.376249\pi\)
0.990925 + 0.134414i \(0.0429153\pi\)
\(98\) −534.979 + 308.870i −0.551439 + 0.318374i
\(99\) 739.006i 0.750231i
\(100\) −312.324 540.961i −0.312324 0.540961i
\(101\) 168.130 291.209i 0.165639 0.286895i −0.771243 0.636541i \(-0.780365\pi\)
0.936882 + 0.349646i \(0.113698\pi\)
\(102\) 523.182 + 302.059i 0.507870 + 0.293219i
\(103\) −322.712 −0.308716 −0.154358 0.988015i \(-0.549331\pi\)
−0.154358 + 0.988015i \(0.549331\pi\)
\(104\) 0 0
\(105\) 840.611 0.781288
\(106\) 163.426 + 94.3542i 0.149749 + 0.0864574i
\(107\) −717.309 + 1242.42i −0.648083 + 1.12251i 0.335498 + 0.942041i \(0.391096\pi\)
−0.983580 + 0.180471i \(0.942238\pi\)
\(108\) −517.375 896.119i −0.460967 0.798417i
\(109\) 849.147i 0.746179i −0.927795 0.373089i \(-0.878298\pi\)
0.927795 0.373089i \(-0.121702\pi\)
\(110\) −73.5055 + 42.4384i −0.0637134 + 0.0367850i
\(111\) 708.433 409.014i 0.605779 0.349747i
\(112\) 310.452i 0.261919i
\(113\) −807.263 1398.22i −0.672044 1.16401i −0.977324 0.211751i \(-0.932083\pi\)
0.305280 0.952263i \(-0.401250\pi\)
\(114\) −162.533 + 281.516i −0.133532 + 0.231284i
\(115\) 378.574 + 218.570i 0.306976 + 0.177233i
\(116\) −1223.04 −0.978931
\(117\) 0 0
\(118\) 686.509 0.535579
\(119\) −1048.45 605.321i −0.807654 0.466300i
\(120\) 327.513 567.269i 0.249147 0.431536i
\(121\) −549.045 950.974i −0.412506 0.714481i
\(122\) 214.409i 0.159112i
\(123\) 1206.05 696.311i 0.884109 0.510441i
\(124\) −130.491 + 75.3390i −0.0945035 + 0.0545616i
\(125\) 845.211i 0.604784i
\(126\) −1027.50 1779.69i −0.726487 1.25831i
\(127\) 432.587 749.263i 0.302251 0.523514i −0.674394 0.738371i \(-0.735595\pi\)
0.976646 + 0.214857i \(0.0689285\pi\)
\(128\) −1025.49 592.066i −0.708134 0.408842i
\(129\) 1314.01 0.896836
\(130\) 0 0
\(131\) −281.400 −0.187680 −0.0938400 0.995587i \(-0.529914\pi\)
−0.0938400 + 0.995587i \(0.529914\pi\)
\(132\) −638.371 368.563i −0.420932 0.243025i
\(133\) 325.713 564.152i 0.212353 0.367806i
\(134\) −399.976 692.779i −0.257856 0.446620i
\(135\) 662.641i 0.422452i
\(136\) −816.976 + 471.681i −0.515111 + 0.297400i
\(137\) −2287.55 + 1320.72i −1.42656 + 0.823624i −0.996847 0.0793428i \(-0.974718\pi\)
−0.429711 + 0.902967i \(0.641384\pi\)
\(138\) 1664.53i 1.02677i
\(139\) 999.318 + 1730.87i 0.609791 + 1.05619i 0.991274 + 0.131814i \(0.0420801\pi\)
−0.381483 + 0.924376i \(0.624587\pi\)
\(140\) −269.159 + 466.196i −0.162486 + 0.281434i
\(141\) −3511.98 2027.64i −2.09760 1.21105i
\(142\) 641.359 0.379026
\(143\) 0 0
\(144\) 553.153 0.320112
\(145\) 678.286 + 391.609i 0.388473 + 0.224285i
\(146\) −240.482 + 416.527i −0.136318 + 0.236110i
\(147\) 1717.80 + 2975.31i 0.963820 + 1.66939i
\(148\) 523.855i 0.290950i
\(149\) 1518.13 876.491i 0.834696 0.481912i −0.0207617 0.999784i \(-0.506609\pi\)
0.855458 + 0.517872i \(0.173276\pi\)
\(150\) 1319.10 761.585i 0.718029 0.414554i
\(151\) 2794.64i 1.50613i −0.657949 0.753063i \(-0.728576\pi\)
0.657949 0.753063i \(-0.271424\pi\)
\(152\) −253.804 439.601i −0.135436 0.234582i
\(153\) 1078.54 1868.09i 0.569901 0.987098i
\(154\) −560.898 323.834i −0.293496 0.169450i
\(155\) 96.4924 0.0500030
\(156\) 0 0
\(157\) 3244.87 1.64949 0.824743 0.565508i \(-0.191320\pi\)
0.824743 + 0.565508i \(0.191320\pi\)
\(158\) 793.099 + 457.896i 0.399339 + 0.230558i
\(159\) 524.756 908.903i 0.261735 0.453338i
\(160\) 333.459 + 577.568i 0.164764 + 0.285380i
\(161\) 3335.68i 1.63285i
\(162\) 417.045 240.781i 0.202260 0.116775i
\(163\) 2841.83 1640.73i 1.36558 0.788418i 0.375221 0.926936i \(-0.377567\pi\)
0.990360 + 0.138517i \(0.0442336\pi\)
\(164\) 891.818i 0.424630i
\(165\) 236.024 + 408.805i 0.111360 + 0.192881i
\(166\) −1057.33 + 1831.35i −0.494366 + 0.856266i
\(167\) 2707.65 + 1563.26i 1.25463 + 0.724364i 0.972026 0.234872i \(-0.0754671\pi\)
0.282608 + 0.959235i \(0.408800\pi\)
\(168\) 4998.29 2.29540
\(169\) 0 0
\(170\) 247.747 0.111773
\(171\) 1005.19 + 580.346i 0.449524 + 0.259533i
\(172\) −420.737 + 728.738i −0.186517 + 0.323057i
\(173\) 48.7849 + 84.4980i 0.0214396 + 0.0371345i 0.876546 0.481318i \(-0.159842\pi\)
−0.855107 + 0.518452i \(0.826508\pi\)
\(174\) 2982.31i 1.29936i
\(175\) −2643.46 + 1526.20i −1.14187 + 0.659257i
\(176\) 150.979 87.1675i 0.0646616 0.0373324i
\(177\) 3818.06i 1.62137i
\(178\) 343.450 + 594.873i 0.144622 + 0.250492i
\(179\) −17.3575 + 30.0640i −0.00724782 + 0.0125536i −0.869627 0.493710i \(-0.835640\pi\)
0.862379 + 0.506264i \(0.168974\pi\)
\(180\) −830.654 479.579i −0.343963 0.198587i
\(181\) 1229.35 0.504843 0.252422 0.967617i \(-0.418773\pi\)
0.252422 + 0.967617i \(0.418773\pi\)
\(182\) 0 0
\(183\) −1192.45 −0.481684
\(184\) 2251.01 + 1299.62i 0.901885 + 0.520704i
\(185\) 167.735 290.526i 0.0666602 0.115459i
\(186\) −183.710 318.195i −0.0724209 0.125437i
\(187\) 679.839i 0.265854i
\(188\) 2249.03 1298.48i 0.872486 0.503730i
\(189\) −4378.97 + 2528.20i −1.68531 + 0.973014i
\(190\) 133.309i 0.0509012i
\(191\) −2140.40 3707.28i −0.810858 1.40445i −0.912265 0.409602i \(-0.865668\pi\)
0.101407 0.994845i \(-0.467666\pi\)
\(192\) 872.903 1511.91i 0.328106 0.568296i
\(193\) −409.041 236.160i −0.152557 0.0880786i 0.421778 0.906699i \(-0.361406\pi\)
−0.574335 + 0.818620i \(0.694739\pi\)
\(194\) −2359.93 −0.873365
\(195\) 0 0
\(196\) −2200.12 −0.801791
\(197\) −3883.58 2242.18i −1.40453 0.810908i −0.409681 0.912229i \(-0.634360\pi\)
−0.994854 + 0.101321i \(0.967693\pi\)
\(198\) 576.998 999.390i 0.207098 0.358705i
\(199\) −183.120 317.173i −0.0652314 0.112984i 0.831565 0.555427i \(-0.187445\pi\)
−0.896797 + 0.442443i \(0.854112\pi\)
\(200\) 2378.51i 0.840931i
\(201\) −3852.93 + 2224.49i −1.35206 + 0.780614i
\(202\) −454.739 + 262.543i −0.158393 + 0.0914480i
\(203\) 5976.49i 2.06634i
\(204\) 1075.80 + 1863.34i 0.369221 + 0.639509i
\(205\) 285.555 494.596i 0.0972879 0.168508i
\(206\) 436.418 + 251.966i 0.147605 + 0.0852199i
\(207\) −5943.41 −1.99563
\(208\) 0 0
\(209\) 365.810 0.121070
\(210\) −1136.80 656.329i −0.373554 0.215671i
\(211\) −1061.28 + 1838.19i −0.346262 + 0.599744i −0.985582 0.169197i \(-0.945883\pi\)
0.639320 + 0.768941i \(0.279216\pi\)
\(212\) 336.047 + 582.051i 0.108867 + 0.188563i
\(213\) 3566.95i 1.14743i
\(214\) 1940.10 1120.12i 0.619730 0.357801i
\(215\) 466.675 269.435i 0.148033 0.0854666i
\(216\) 3940.08i 1.24115i
\(217\) 368.152 + 637.657i 0.115169 + 0.199479i
\(218\) −662.994 + 1148.34i −0.205980 + 0.356768i
\(219\) 2316.54 + 1337.45i 0.714781 + 0.412679i
\(220\) −302.294 −0.0926392
\(221\) 0 0
\(222\) −1277.39 −0.386185
\(223\) −5132.43 2963.21i −1.54122 0.889826i −0.998762 0.0497449i \(-0.984159\pi\)
−0.542461 0.840081i \(-0.682507\pi\)
\(224\) −2544.52 + 4407.24i −0.758986 + 1.31460i
\(225\) −2719.34 4710.03i −0.805730 1.39557i
\(226\) 2521.17i 0.742060i
\(227\) 775.665 447.830i 0.226796 0.130941i −0.382297 0.924039i \(-0.624867\pi\)
0.609093 + 0.793099i \(0.291534\pi\)
\(228\) −1002.63 + 578.870i −0.291232 + 0.168143i
\(229\) 627.717i 0.181138i 0.995890 + 0.0905692i \(0.0288686\pi\)
−0.995890 + 0.0905692i \(0.971131\pi\)
\(230\) −341.309 591.164i −0.0978488 0.169479i
\(231\) −1801.02 + 3119.46i −0.512981 + 0.888509i
\(232\) 4033.11 + 2328.52i 1.14132 + 0.658942i
\(233\) −2303.72 −0.647734 −0.323867 0.946103i \(-0.604983\pi\)
−0.323867 + 0.946103i \(0.604983\pi\)
\(234\) 0 0
\(235\) −1663.06 −0.461643
\(236\) 2117.47 + 1222.52i 0.584048 + 0.337200i
\(237\) 2546.61 4410.86i 0.697976 1.20893i
\(238\) 945.240 + 1637.20i 0.257440 + 0.445900i
\(239\) 544.622i 0.147400i −0.997280 0.0737001i \(-0.976519\pi\)
0.997280 0.0737001i \(-0.0234808\pi\)
\(240\) 305.995 176.666i 0.0822995 0.0475156i
\(241\) 4699.14 2713.05i 1.25601 0.725157i 0.283713 0.958909i \(-0.408434\pi\)
0.972296 + 0.233752i \(0.0751005\pi\)
\(242\) 1714.73i 0.455483i
\(243\) 1172.61 + 2031.03i 0.309561 + 0.536175i
\(244\) 381.814 661.322i 0.100177 0.173511i
\(245\) 1220.17 + 704.464i 0.318178 + 0.183700i
\(246\) −2174.65 −0.563621
\(247\) 0 0
\(248\) 573.746 0.146907
\(249\) 10185.1 + 5880.39i 2.59220 + 1.49661i
\(250\) 659.921 1143.02i 0.166948 0.289163i
\(251\) −2610.61 4521.71i −0.656494 1.13708i −0.981517 0.191375i \(-0.938705\pi\)
0.325022 0.945706i \(-0.394628\pi\)
\(252\) 7319.02i 1.82958i
\(253\) −1622.20 + 936.580i −0.403111 + 0.232736i
\(254\) −1170.01 + 675.508i −0.289028 + 0.166871i
\(255\) 1377.86i 0.338372i
\(256\) 1728.63 + 2994.07i 0.422029 + 0.730975i
\(257\) 329.103 570.023i 0.0798789 0.138354i −0.823319 0.567579i \(-0.807880\pi\)
0.903198 + 0.429225i \(0.141213\pi\)
\(258\) −1776.99 1025.95i −0.428801 0.247568i
\(259\) 2559.87 0.614141
\(260\) 0 0
\(261\) −10648.7 −2.52544
\(262\) 380.550 + 219.711i 0.0897346 + 0.0518083i
\(263\) −1623.23 + 2811.51i −0.380580 + 0.659184i −0.991145 0.132782i \(-0.957609\pi\)
0.610565 + 0.791966i \(0.290942\pi\)
\(264\) 1403.40 + 2430.76i 0.327172 + 0.566679i
\(265\) 430.401i 0.0997711i
\(266\) −880.953 + 508.618i −0.203063 + 0.117238i
\(267\) 3308.42 1910.11i 0.758321 0.437817i
\(268\) 2849.07i 0.649384i
\(269\) 1292.90 + 2239.37i 0.293047 + 0.507572i 0.974529 0.224263i \(-0.0719976\pi\)
−0.681482 + 0.731835i \(0.738664\pi\)
\(270\) 517.375 896.119i 0.116616 0.201985i
\(271\) −856.441 494.466i −0.191974 0.110836i 0.400932 0.916108i \(-0.368686\pi\)
−0.592907 + 0.805271i \(0.702020\pi\)
\(272\) −508.867 −0.113436
\(273\) 0 0
\(274\) 4124.74 0.909433
\(275\) −1484.44 857.043i −0.325510 0.187933i
\(276\) 2964.15 5134.06i 0.646452 1.11969i
\(277\) 4071.20 + 7051.53i 0.883086 + 1.52955i 0.847892 + 0.530169i \(0.177872\pi\)
0.0351939 + 0.999381i \(0.488795\pi\)
\(278\) 3120.97i 0.673322i
\(279\) −1136.16 + 655.961i −0.243799 + 0.140758i
\(280\) 1775.17 1024.89i 0.378880 0.218747i
\(281\) 1534.21i 0.325705i 0.986650 + 0.162853i \(0.0520695\pi\)
−0.986650 + 0.162853i \(0.947930\pi\)
\(282\) 3166.27 + 5484.14i 0.668612 + 1.15807i
\(283\) −3482.50 + 6031.87i −0.731495 + 1.26699i 0.224749 + 0.974417i \(0.427844\pi\)
−0.956244 + 0.292570i \(0.905490\pi\)
\(284\) 1978.20 + 1142.12i 0.413327 + 0.238634i
\(285\) 741.403 0.154095
\(286\) 0 0
\(287\) 4357.96 0.896314
\(288\) −7852.68 4533.75i −1.60668 0.927616i
\(289\) 1464.31 2536.26i 0.298048 0.516234i
\(290\) −611.518 1059.18i −0.123826 0.214473i
\(291\) 13124.9i 2.64396i
\(292\) −1483.48 + 856.490i −0.297309 + 0.171652i
\(293\) 554.281 320.015i 0.110517 0.0638070i −0.443723 0.896164i \(-0.646342\pi\)
0.554240 + 0.832357i \(0.313009\pi\)
\(294\) 5364.87i 1.06424i
\(295\) −782.887 1356.00i −0.154513 0.267625i
\(296\) 997.358 1727.48i 0.195846 0.339214i
\(297\) −2459.03 1419.72i −0.480428 0.277375i
\(298\) −2737.37 −0.532120
\(299\) 0 0
\(300\) 5424.85 1.04401
\(301\) 3561.05 + 2055.97i 0.681912 + 0.393702i
\(302\) −2181.99 + 3779.32i −0.415760 + 0.720118i
\(303\) 1460.15 + 2529.05i 0.276843 + 0.479506i
\(304\) 273.813i 0.0516587i
\(305\) −423.503 + 244.509i −0.0795072 + 0.0459035i
\(306\) −2917.12 + 1684.20i −0.544969 + 0.314638i
\(307\) 100.406i 0.0186660i −0.999956 0.00933299i \(-0.997029\pi\)
0.999956 0.00933299i \(-0.00297083\pi\)
\(308\) −1153.35 1997.67i −0.213371 0.369570i
\(309\) 1401.32 2427.16i 0.257988 0.446849i
\(310\) −130.491 75.3390i −0.0239077 0.0138031i
\(311\) 3878.92 0.707245 0.353623 0.935388i \(-0.384950\pi\)
0.353623 + 0.935388i \(0.384950\pi\)
\(312\) 0 0
\(313\) −3789.39 −0.684311 −0.342155 0.939643i \(-0.611157\pi\)
−0.342155 + 0.939643i \(0.611157\pi\)
\(314\) −4388.19 2533.52i −0.788662 0.455334i
\(315\) −2343.51 + 4059.08i −0.419180 + 0.726041i
\(316\) 1630.82 + 2824.66i 0.290319 + 0.502847i
\(317\) 4406.81i 0.780791i −0.920647 0.390396i \(-0.872338\pi\)
0.920647 0.390396i \(-0.127662\pi\)
\(318\) −1419.30 + 819.434i −0.250284 + 0.144502i
\(319\) −2906.48 + 1678.06i −0.510130 + 0.294524i
\(320\) 715.950i 0.125071i
\(321\) −6229.58 10790.0i −1.08318 1.87613i
\(322\) 2604.42 4510.99i 0.450741 0.780706i
\(323\) −924.710 533.882i −0.159295 0.0919690i
\(324\) 1715.11 0.294086
\(325\) 0 0
\(326\) −5124.19 −0.870559
\(327\) 6386.55 + 3687.27i 1.08005 + 0.623568i
\(328\) 1697.92 2940.88i 0.285829 0.495070i
\(329\) −6345.14 10990.1i −1.06328 1.84165i
\(330\) 737.127i 0.122962i
\(331\) 3577.98 2065.75i 0.594149 0.343032i −0.172587 0.984994i \(-0.555213\pi\)
0.766736 + 0.641962i \(0.221879\pi\)
\(332\) −6522.44 + 3765.73i −1.07821 + 0.622505i
\(333\) 4561.10i 0.750591i
\(334\) −2441.11 4228.13i −0.399916 0.692674i
\(335\) −912.257 + 1580.07i −0.148782 + 0.257698i
\(336\) 2334.95 + 1348.08i 0.379113 + 0.218881i
\(337\) 4560.82 0.737221 0.368611 0.929584i \(-0.379834\pi\)
0.368611 + 0.929584i \(0.379834\pi\)
\(338\) 0 0
\(339\) 14021.6 2.24646
\(340\) 764.150 + 441.182i 0.121888 + 0.0703720i
\(341\) −206.737 + 358.078i −0.0328311 + 0.0568652i
\(342\) −906.240 1569.65i −0.143286 0.248179i
\(343\) 1429.34i 0.225007i
\(344\) 2774.86 1602.07i 0.434914 0.251098i
\(345\) −3287.79 + 1898.21i −0.513069 + 0.296220i
\(346\) 152.360i 0.0236733i
\(347\) −5034.70 8720.36i −0.778896 1.34909i −0.932579 0.360967i \(-0.882447\pi\)
0.153683 0.988120i \(-0.450887\pi\)
\(348\) 5310.82 9198.62i 0.818075 1.41695i
\(349\) −5091.64 2939.66i −0.780944 0.450878i 0.0558207 0.998441i \(-0.482222\pi\)
−0.836765 + 0.547563i \(0.815556\pi\)
\(350\) 4766.49 0.727942
\(351\) 0 0
\(352\) −2857.76 −0.432725
\(353\) −7917.69 4571.28i −1.19381 0.689249i −0.234644 0.972081i \(-0.575393\pi\)
−0.959169 + 0.282833i \(0.908726\pi\)
\(354\) −2981.05 + 5163.33i −0.447574 + 0.775220i
\(355\) −731.398 1266.82i −0.109348 0.189397i
\(356\) 2446.43i 0.364215i
\(357\) 9105.39 5257.00i 1.34988 0.779356i
\(358\) 46.9466 27.1046i 0.00693074 0.00400146i
\(359\) 2754.32i 0.404924i −0.979290 0.202462i \(-0.935106\pi\)
0.979290 0.202462i \(-0.0648942\pi\)
\(360\) 1826.12 + 3162.94i 0.267347 + 0.463059i
\(361\) −3142.23 + 5442.50i −0.458117 + 0.793483i
\(362\) −1662.50 959.845i −0.241379 0.139360i
\(363\) 9536.54 1.37889
\(364\) 0 0
\(365\) 1096.97 0.157310
\(366\) 1612.60 + 931.034i 0.230306 + 0.132967i
\(367\) −1520.09 + 2632.88i −0.216208 + 0.374483i −0.953646 0.300932i \(-0.902702\pi\)
0.737438 + 0.675415i \(0.236036\pi\)
\(368\) 701.040 + 1214.24i 0.0993049 + 0.172001i
\(369\) 7764.88i 1.09546i
\(370\) −453.672 + 261.928i −0.0637440 + 0.0368026i
\(371\) 2844.25 1642.13i 0.398022 0.229798i
\(372\) 1308.59i 0.182385i
\(373\) 2692.36 + 4663.31i 0.373740 + 0.647337i 0.990138 0.140098i \(-0.0447418\pi\)
−0.616397 + 0.787435i \(0.711408\pi\)
\(374\) −530.802 + 919.376i −0.0733880 + 0.127112i
\(375\) −6356.95 3670.18i −0.875390 0.505407i
\(376\) −9888.59 −1.35629
\(377\) 0 0
\(378\) 7895.84 1.07439
\(379\) −2965.50 1712.13i −0.401920 0.232049i 0.285392 0.958411i \(-0.407876\pi\)
−0.687312 + 0.726362i \(0.741209\pi\)
\(380\) −237.393 + 411.177i −0.0320474 + 0.0555077i
\(381\) 3756.87 + 6507.09i 0.505171 + 0.874983i
\(382\) 6684.69i 0.895336i
\(383\) 331.675 191.493i 0.0442501 0.0255478i −0.477712 0.878517i \(-0.658534\pi\)
0.521962 + 0.852969i \(0.325200\pi\)
\(384\) 8906.01 5141.89i 1.18355 0.683323i
\(385\) 1477.19i 0.195544i
\(386\) 368.776 + 638.739i 0.0486275 + 0.0842253i
\(387\) −3663.27 + 6344.97i −0.481175 + 0.833419i
\(388\) −7278.94 4202.50i −0.952403 0.549870i
\(389\) −8588.34 −1.11940 −0.559699 0.828696i \(-0.689083\pi\)
−0.559699 + 0.828696i \(0.689083\pi\)
\(390\) 0 0
\(391\) 5467.56 0.707178
\(392\) 7255.15 + 4188.76i 0.934796 + 0.539705i
\(393\) 1221.93 2116.45i 0.156841 0.271656i
\(394\) 3501.29 + 6064.41i 0.447696 + 0.775433i
\(395\) 2088.72i 0.266063i
\(396\) 3559.38 2055.01i 0.451681 0.260778i
\(397\) −6269.30 + 3619.58i −0.792562 + 0.457586i −0.840864 0.541247i \(-0.817952\pi\)
0.0483020 + 0.998833i \(0.484619\pi\)
\(398\) 571.904i 0.0720275i
\(399\) 2828.71 + 4899.46i 0.354918 + 0.614737i
\(400\) −641.505 + 1111.12i −0.0801882 + 0.138890i
\(401\) −3697.60 2134.81i −0.460472 0.265854i 0.251770 0.967787i \(-0.418987\pi\)
−0.712243 + 0.701933i \(0.752321\pi\)
\(402\) 6947.32 0.861942
\(403\) 0 0
\(404\) −1870.12 −0.230302
\(405\) −951.185 549.167i −0.116703 0.0673786i
\(406\) 4666.30 8082.27i 0.570405 0.987971i
\(407\) 718.751 + 1244.91i 0.0875360 + 0.151617i
\(408\) 8192.78i 0.994125i
\(409\) −11745.5 + 6781.26i −1.41999 + 0.819834i −0.996298 0.0859711i \(-0.972601\pi\)
−0.423696 + 0.905805i \(0.639267\pi\)
\(410\) −772.337 + 445.909i −0.0930317 + 0.0537119i
\(411\) 22939.9i 2.75315i
\(412\) 897.390 + 1554.33i 0.107309 + 0.185864i
\(413\) 5973.96 10347.2i 0.711767 1.23282i
\(414\) 8037.54 + 4640.47i 0.954163 + 0.550886i
\(415\) 4823.06 0.570494
\(416\) 0 0
\(417\) −17357.5 −2.03837
\(418\) −494.701 285.616i −0.0578867 0.0334209i
\(419\) 7288.44 12624.0i 0.849794 1.47189i −0.0315973 0.999501i \(-0.510059\pi\)
0.881392 0.472386i \(-0.156607\pi\)
\(420\) −2337.55 4048.76i −0.271573 0.470379i
\(421\) 15848.4i 1.83469i −0.398099 0.917343i \(-0.630330\pi\)
0.398099 0.917343i \(-0.369670\pi\)
\(422\) 2870.42 1657.24i 0.331114 0.191169i
\(423\) 19581.8 11305.6i 2.25083 1.29952i
\(424\) 2559.18i 0.293124i
\(425\) 2501.62 + 4332.94i 0.285521 + 0.494537i
\(426\) −2784.99 + 4823.75i −0.316745 + 0.548618i
\(427\) −3231.62 1865.77i −0.366250 0.211455i
\(428\) 7978.70 0.901087
\(429\) 0 0
\(430\) −841.474 −0.0943709
\(431\) 9261.90 + 5347.36i 1.03510 + 0.597618i 0.918443 0.395554i \(-0.129447\pi\)
0.116662 + 0.993172i \(0.462781\pi\)
\(432\) −1062.67 + 1840.61i −0.118352 + 0.204991i
\(433\) −8039.50 13924.8i −0.892272 1.54546i −0.837145 0.546981i \(-0.815777\pi\)
−0.0551273 0.998479i \(-0.517556\pi\)
\(434\) 1149.78i 0.127168i
\(435\) −5890.69 + 3400.99i −0.649280 + 0.374862i
\(436\) −4089.87 + 2361.29i −0.449241 + 0.259370i
\(437\) 2942.01i 0.322049i
\(438\) −2088.50 3617.40i −0.227837 0.394625i
\(439\) 3017.90 5227.16i 0.328101 0.568288i −0.654034 0.756465i \(-0.726925\pi\)
0.982135 + 0.188177i \(0.0602579\pi\)
\(440\) 996.849 + 575.531i 0.108007 + 0.0623577i
\(441\) −19156.0 −2.06845
\(442\) 0 0
\(443\) 10201.3 1.09409 0.547043 0.837105i \(-0.315753\pi\)
0.547043 + 0.837105i \(0.315753\pi\)
\(444\) −3939.98 2274.75i −0.421134 0.243142i
\(445\) 783.332 1356.77i 0.0834461 0.144533i
\(446\) 4627.21 + 8014.56i 0.491266 + 0.850897i
\(447\) 15224.0i 1.61090i
\(448\) 4731.26 2731.59i 0.498953 0.288071i
\(449\) −5042.47 + 2911.27i −0.529997 + 0.305994i −0.741015 0.671488i \(-0.765655\pi\)
0.211018 + 0.977482i \(0.432322\pi\)
\(450\) 8492.78i 0.889675i
\(451\) 1223.61 + 2119.36i 0.127755 + 0.221279i
\(452\) −4489.64 + 7776.28i −0.467201 + 0.809216i
\(453\) 21018.9 + 12135.3i 2.18003 + 1.25864i
\(454\) −1398.62 −0.144583
\(455\) 0 0
\(456\) 4408.40 0.452724
\(457\) 4002.42 + 2310.80i 0.409684 + 0.236531i 0.690654 0.723186i \(-0.257323\pi\)
−0.280970 + 0.959717i \(0.590656\pi\)
\(458\) 490.106 848.889i 0.0500026 0.0866070i
\(459\) 4144.02 + 7177.65i 0.421408 + 0.729900i
\(460\) 2431.18i 0.246422i
\(461\) −4440.78 + 2563.88i −0.448650 + 0.259028i −0.707260 0.706954i \(-0.750069\pi\)
0.258610 + 0.965982i \(0.416736\pi\)
\(462\) 4871.20 2812.39i 0.490539 0.283213i
\(463\) 6486.27i 0.651064i 0.945531 + 0.325532i \(0.105543\pi\)
−0.945531 + 0.325532i \(0.894457\pi\)
\(464\) 1256.04 + 2175.53i 0.125669 + 0.217665i
\(465\) −419.002 + 725.733i −0.0417866 + 0.0723764i
\(466\) 3115.43 + 1798.69i 0.309698 + 0.178804i
\(467\) −12978.0 −1.28598 −0.642990 0.765875i \(-0.722306\pi\)
−0.642990 + 0.765875i \(0.722306\pi\)
\(468\) 0 0
\(469\) −13922.3 −1.37073
\(470\) 2249.03 + 1298.48i 0.220723 + 0.127435i
\(471\) −14090.3 + 24405.1i −1.37844 + 2.38754i
\(472\) −4655.07 8062.81i −0.453955 0.786273i
\(473\) 2309.08i 0.224464i
\(474\) −6887.79 + 3976.67i −0.667440 + 0.385347i
\(475\) −2331.48 + 1346.08i −0.225212 + 0.130026i
\(476\) 6733.04i 0.648337i
\(477\) 2925.89 + 5067.80i 0.280854 + 0.486454i
\(478\) −425.228 + 736.516i −0.0406893 + 0.0704759i
\(479\) 5030.71 + 2904.48i 0.479873 + 0.277055i 0.720363 0.693597i \(-0.243975\pi\)
−0.240491 + 0.970651i \(0.577308\pi\)
\(480\) −5791.95 −0.550761
\(481\) 0 0
\(482\) −8473.14 −0.800707
\(483\) −25088.1 14484.6i −2.36345 1.36454i
\(484\) −3053.54 + 5288.89i −0.286772 + 0.496703i
\(485\) 2691.23 + 4661.35i 0.251964 + 0.436414i
\(486\) 3662.20i 0.341812i
\(487\) 4665.40 2693.57i 0.434106 0.250631i −0.266989 0.963700i \(-0.586029\pi\)
0.701094 + 0.713069i \(0.252695\pi\)
\(488\) −2518.16 + 1453.86i −0.233589 + 0.134863i
\(489\) 28498.4i 2.63547i
\(490\) −1100.06 1905.36i −0.101419 0.175664i
\(491\) 7629.53 13214.7i 0.701255 1.21461i −0.266772 0.963760i \(-0.585957\pi\)
0.968026 0.250849i \(-0.0807097\pi\)
\(492\) −6707.48 3872.57i −0.614628 0.354855i
\(493\) 9796.16 0.894922
\(494\) 0 0
\(495\) −2632.01 −0.238990
\(496\) 268.025 + 154.744i 0.0242635 + 0.0140085i
\(497\) 5581.07 9666.69i 0.503712 0.872456i
\(498\) −9182.55 15904.6i −0.826264 1.43113i
\(499\) 1856.04i 0.166509i −0.996528 0.0832544i \(-0.973469\pi\)
0.996528 0.0832544i \(-0.0265314\pi\)
\(500\) 4070.91 2350.34i 0.364114 0.210221i
\(501\) −23515.0 + 13576.4i −2.09695 + 1.21067i
\(502\) 8153.20i 0.724891i
\(503\) −524.732 908.862i −0.0465142 0.0805649i 0.841831 0.539741i \(-0.181478\pi\)
−0.888345 + 0.459176i \(0.848145\pi\)
\(504\) −13934.6 + 24135.4i −1.23154 + 2.13308i
\(505\) 1037.16 + 598.803i 0.0913919 + 0.0527651i
\(506\) 2925.04 0.256984
\(507\) 0 0
\(508\) −4811.71 −0.420246
\(509\) −477.272 275.553i −0.0415613 0.0239954i 0.479075 0.877774i \(-0.340972\pi\)
−0.520637 + 0.853778i \(0.674305\pi\)
\(510\) −1075.80 + 1863.34i −0.0934063 + 0.161784i
\(511\) 4185.32 + 7249.19i 0.362324 + 0.627564i
\(512\) 4074.36i 0.351686i
\(513\) −3862.18 + 2229.83i −0.332396 + 0.191909i
\(514\) −890.121 + 513.911i −0.0763843 + 0.0441005i
\(515\) 1149.36i 0.0983431i
\(516\) −3653.96 6328.84i −0.311738 0.539945i
\(517\) 3563.13 6171.52i 0.303107 0.524997i
\(518\) −3461.83 1998.69i −0.293637 0.169531i
\(519\) −847.361 −0.0716667
\(520\) 0 0
\(521\) −8995.30 −0.756413 −0.378206 0.925721i \(-0.623459\pi\)
−0.378206 + 0.925721i \(0.623459\pi\)
\(522\) 14400.7 + 8314.27i 1.20748 + 0.697137i
\(523\) −1331.96 + 2307.02i −0.111362 + 0.192885i −0.916320 0.400448i \(-0.868855\pi\)
0.804958 + 0.593332i \(0.202188\pi\)
\(524\) 782.512 + 1355.35i 0.0652370 + 0.112994i
\(525\) 26509.1i 2.20372i
\(526\) 4390.32 2534.76i 0.363930 0.210115i
\(527\) 1045.19 603.443i 0.0863935 0.0498793i
\(528\) 1514.04i 0.124792i
\(529\) −1448.89 2509.54i −0.119083 0.206258i
\(530\) −336.047 + 582.051i −0.0275414 + 0.0477032i
\(531\) 18436.3 + 10644.2i 1.50672 + 0.869906i
\(532\) −3622.94 −0.295253
\(533\) 0 0
\(534\) −5965.49 −0.483431
\(535\) −4424.93 2554.73i −0.357582 0.206450i
\(536\) −5424.30 + 9395.16i −0.437116 + 0.757107i
\(537\) −150.744 261.096i −0.0121137 0.0209816i
\(538\) 4037.86i 0.323577i
\(539\) −5228.46 + 3018.65i −0.417821 + 0.241229i
\(540\) 3191.57 1842.66i 0.254340 0.146843i
\(541\) 6169.23i 0.490270i −0.969489 0.245135i \(-0.921168\pi\)
0.969489 0.245135i \(-0.0788322\pi\)
\(542\) 772.135 + 1337.38i 0.0611920 + 0.105988i
\(543\) −5338.23 + 9246.08i −0.421888 + 0.730732i
\(544\) 7223.97 + 4170.76i 0.569348 + 0.328713i
\(545\) 3024.28 0.237699
\(546\) 0 0
\(547\) 5140.42 0.401807 0.200904 0.979611i \(-0.435612\pi\)
0.200904 + 0.979611i \(0.435612\pi\)
\(548\) 12722.3 + 7345.24i 0.991735 + 0.572578i
\(549\) 3324.38 5757.99i 0.258435 0.447623i
\(550\) 1338.32 + 2318.03i 0.103756 + 0.179711i
\(551\) 5271.15i 0.407547i
\(552\) −19549.3 + 11286.8i −1.50738 + 0.870285i
\(553\) 13803.0 7969.16i 1.06142 0.612809i
\(554\) 12714.8i 0.975090i
\(555\) 1456.72 + 2523.12i 0.111413 + 0.192974i
\(556\) 5557.76 9626.32i 0.423923 0.734257i
\(557\) −2406.30 1389.28i −0.183049 0.105683i 0.405675 0.914017i \(-0.367036\pi\)
−0.588724 + 0.808334i \(0.700370\pi\)
\(558\) 2048.64 0.155422
\(559\) 0 0
\(560\) 1105.69 0.0834356
\(561\) 5113.16 + 2952.08i 0.384809 + 0.222170i
\(562\) 1197.87 2074.78i 0.0899097 0.155728i
\(563\) 2453.07 + 4248.85i 0.183632 + 0.318059i 0.943115 0.332468i \(-0.107881\pi\)
−0.759483 + 0.650527i \(0.774548\pi\)
\(564\) 22553.7i 1.68383i
\(565\) 4979.84 2875.11i 0.370802 0.214083i
\(566\) 9419.08 5438.11i 0.699494 0.403853i
\(567\) 8381.04i 0.620759i
\(568\) −4348.91 7532.54i −0.321261 0.556440i
\(569\) −4681.58 + 8108.73i −0.344924 + 0.597426i −0.985340 0.170602i \(-0.945429\pi\)
0.640416 + 0.768028i \(0.278762\pi\)
\(570\) −1002.63 578.870i −0.0736766 0.0425372i
\(571\) −7199.32 −0.527640 −0.263820 0.964572i \(-0.584982\pi\)
−0.263820 + 0.964572i \(0.584982\pi\)
\(572\) 0 0
\(573\) 37177.3 2.71048
\(574\) −5893.46 3402.59i −0.428551 0.247424i
\(575\) 6892.72 11938.5i 0.499906 0.865863i
\(576\) 4867.07 + 8430.01i 0.352074 + 0.609810i
\(577\) 11449.6i 0.826086i 0.910711 + 0.413043i \(0.135534\pi\)
−0.910711 + 0.413043i \(0.864466\pi\)
\(578\) −3960.50 + 2286.60i −0.285009 + 0.164550i
\(579\) 3552.38 2050.97i 0.254978 0.147211i
\(580\) 4355.91i 0.311843i
\(581\) 18401.6 + 31872.6i 1.31399 + 2.27590i
\(582\) 10247.6 17749.3i 0.729855 1.26415i
\(583\) 1597.20 + 922.142i 0.113463 + 0.0655081i
\(584\) 6522.62 0.462171
\(585\) 0 0
\(586\) −999.439 −0.0704547
\(587\) −4710.65 2719.70i −0.331226 0.191233i 0.325160 0.945659i \(-0.394582\pi\)
−0.656385 + 0.754426i \(0.727915\pi\)
\(588\) 9553.63 16547.4i 0.670042 1.16055i
\(589\) 324.703 + 562.402i 0.0227150 + 0.0393436i
\(590\) 2445.04i 0.170611i
\(591\) 33727.5 19472.6i 2.34749 1.35532i
\(592\) 931.831 537.993i 0.0646926 0.0373503i
\(593\) 28405.8i 1.96709i −0.180651 0.983547i \(-0.557820\pi\)
0.180651 0.983547i \(-0.442180\pi\)
\(594\) 2216.97 + 3839.90i 0.153137 + 0.265241i
\(595\) 2155.88 3734.10i 0.148542 0.257282i
\(596\) −8443.14 4874.65i −0.580276 0.335022i
\(597\) 3180.67 0.218051
\(598\) 0 0
\(599\) −10482.3 −0.715020 −0.357510 0.933909i \(-0.616374\pi\)
−0.357510 + 0.933909i \(0.616374\pi\)
\(600\) −17889.1 10328.3i −1.21720 0.702750i
\(601\) −1599.77 + 2770.88i −0.108579 + 0.188064i −0.915195 0.403012i \(-0.867963\pi\)
0.806616 + 0.591076i \(0.201297\pi\)
\(602\) −3210.51 5560.77i −0.217360 0.376479i
\(603\) 24806.3i 1.67527i
\(604\) −13460.3 + 7771.28i −0.906772 + 0.523525i
\(605\) 3386.95 1955.45i 0.227602 0.131406i
\(606\) 4560.20i 0.305686i
\(607\) −5671.40 9823.15i −0.379234 0.656853i 0.611717 0.791077i \(-0.290479\pi\)
−0.990951 + 0.134224i \(0.957146\pi\)
\(608\) −2244.22 + 3887.10i −0.149696 + 0.259281i
\(609\) −44950.0 25951.9i −2.99091 1.72680i
\(610\) 763.629 0.0506859
\(611\) 0 0
\(612\) −11996.7 −0.792384
\(613\) 12458.1 + 7192.70i 0.820846 + 0.473916i 0.850708 0.525638i \(-0.176174\pi\)
−0.0298622 + 0.999554i \(0.509507\pi\)
\(614\) −78.3944 + 135.783i −0.00515267 + 0.00892469i
\(615\) 2479.95 + 4295.39i 0.162603 + 0.281637i
\(616\) 8783.39i 0.574502i
\(617\) −19101.7 + 11028.4i −1.24636 + 0.719588i −0.970382 0.241575i \(-0.922336\pi\)
−0.275981 + 0.961163i \(0.589003\pi\)
\(618\) −3790.14 + 2188.24i −0.246702 + 0.142433i
\(619\) 13621.4i 0.884477i 0.896898 + 0.442238i \(0.145815\pi\)
−0.896898 + 0.442238i \(0.854185\pi\)
\(620\) −268.324 464.751i −0.0173809 0.0301046i
\(621\) 11418.0 19776.6i 0.737824 1.27795i
\(622\) −5245.63 3028.57i −0.338152 0.195232i
\(623\) 11954.7 0.768789
\(624\) 0 0
\(625\) 11029.2 0.705866
\(626\) 5124.57 + 2958.67i 0.327187 + 0.188901i
\(627\) −1588.47 + 2751.31i −0.101176 + 0.175242i
\(628\) −9023.27 15628.8i −0.573356 0.993082i
\(629\) 4195.92i 0.265982i
\(630\) 6338.46 3659.51i 0.400842 0.231426i
\(631\) −16227.1 + 9368.74i −1.02376 + 0.591068i −0.915191 0.403021i \(-0.867960\pi\)
−0.108569 + 0.994089i \(0.534627\pi\)
\(632\) 12419.6i 0.781683i
\(633\) −9216.83 15964.0i −0.578730 1.00239i
\(634\) −3440.73 + 5959.52i −0.215534 + 0.373317i
\(635\) 2668.54 + 1540.68i 0.166768 + 0.0962836i
\(636\) −5836.91 −0.363913
\(637\) 0 0
\(638\) 5240.75 0.325209
\(639\) 17223.8 + 9944.18i 1.06630 + 0.615627i
\(640\) 2108.67 3652.33i 0.130239 0.225580i
\(641\) 14899.4 + 25806.5i 0.918081 + 1.59016i 0.802327 + 0.596884i \(0.203595\pi\)
0.115753 + 0.993278i \(0.463072\pi\)
\(642\) 19455.6i 1.19603i
\(643\) 19904.3 11491.8i 1.22076 0.704807i 0.255681 0.966761i \(-0.417700\pi\)
0.965080 + 0.261955i \(0.0843671\pi\)
\(644\) 16066.1 9275.77i 0.983064 0.567573i
\(645\) 4679.90i 0.285692i
\(646\) 833.684 + 1443.98i 0.0507753 + 0.0879455i
\(647\) −12452.7 + 21568.7i −0.756672 + 1.31059i 0.187866 + 0.982195i \(0.439843\pi\)
−0.944539 + 0.328400i \(0.893491\pi\)
\(648\) −5655.77 3265.36i −0.342870 0.197956i
\(649\) 6709.39 0.405804
\(650\) 0 0
\(651\) −6394.54 −0.384980
\(652\) −15805.0 9125.03i −0.949344 0.548104i
\(653\) −5038.92 + 8727.67i −0.301973 + 0.523033i −0.976583 0.215142i \(-0.930979\pi\)
0.674610 + 0.738175i \(0.264312\pi\)
\(654\) −5757.87 9972.93i −0.344267 0.596288i
\(655\) 1002.22i 0.0597864i
\(656\) 1586.36 915.886i 0.0944162 0.0545112i
\(657\) −12916.4 + 7457.28i −0.766996 + 0.442825i
\(658\) 19816.5i 1.17406i
\(659\) −6167.30 10682.1i −0.364558 0.631433i 0.624147 0.781307i \(-0.285447\pi\)
−0.988705 + 0.149874i \(0.952113\pi\)
\(660\) 1312.66 2273.59i 0.0774169 0.134090i
\(661\) 11041.1 + 6374.56i 0.649694 + 0.375101i 0.788339 0.615241i \(-0.210941\pi\)
−0.138645 + 0.990342i \(0.544275\pi\)
\(662\) −6451.54 −0.378771
\(663\) 0 0
\(664\) 28678.1 1.67609
\(665\) 2009.26 + 1160.04i 0.117166 + 0.0676460i
\(666\) 3561.20 6168.18i 0.207198 0.358877i
\(667\) −13495.7 23375.2i −0.783440 1.35696i
\(668\) 17388.3i 1.00715i
\(669\) 44573.4 25734.5i 2.57594 1.48722i
\(670\) 2467.37 1424.54i 0.142273 0.0821413i
\(671\) 2095.46i 0.120558i
\(672\) −22098.3 38275.3i −1.26854 2.19718i
\(673\) −6809.12 + 11793.7i −0.390004 + 0.675506i −0.992450 0.122654i \(-0.960860\pi\)
0.602446 + 0.798160i \(0.294193\pi\)
\(674\) −6167.80 3560.98i −0.352485 0.203507i
\(675\) 20896.7 1.19158
\(676\) 0 0
\(677\) 9655.67 0.548150 0.274075 0.961708i \(-0.411628\pi\)
0.274075 + 0.961708i \(0.411628\pi\)
\(678\) −18962.0 10947.7i −1.07409 0.620126i
\(679\) −20535.9 + 35569.3i −1.16067 + 2.01034i
\(680\) −1679.92 2909.70i −0.0947381 0.164091i
\(681\) 7778.51i 0.437699i
\(682\) 559.158 322.830i 0.0313948 0.0181258i
\(683\) 14130.7 8158.38i 0.791650 0.457060i −0.0488929 0.998804i \(-0.515569\pi\)
0.840543 + 0.541744i \(0.182236\pi\)
\(684\) 6455.25i 0.360852i
\(685\) −4703.80 8147.23i −0.262369 0.454437i
\(686\) 1116.00 1932.97i 0.0621123 0.107582i
\(687\) −4721.14 2725.75i −0.262188 0.151374i
\(688\) 1728.37 0.0957753
\(689\) 0 0
\(690\) 5928.30 0.327082
\(691\) 2035.89 + 1175.42i 0.112082 + 0.0647106i 0.554993 0.831855i \(-0.312721\pi\)
−0.442911 + 0.896566i \(0.646054\pi\)
\(692\) 271.320 469.940i 0.0149047 0.0258157i
\(693\) −10042.0 17393.3i −0.550454 0.953414i
\(694\) 15723.9i 0.860045i
\(695\) −6164.58 + 3559.12i −0.336455 + 0.194252i
\(696\) −35026.2 + 20222.4i −1.90756 + 1.10133i
\(697\) 7143.20i 0.388189i
\(698\) 4590.44 + 7950.87i 0.248926 + 0.431153i
\(699\) 10003.5 17326.6i 0.541299 0.937558i
\(700\) 14701.7 + 8488.05i 0.793819 + 0.458312i
\(701\) 8076.90 0.435179 0.217589 0.976040i \(-0.430181\pi\)
0.217589 + 0.976040i \(0.430181\pi\)
\(702\) 0 0
\(703\) 2257.76 0.121128
\(704\) 2656.85 + 1533.93i 0.142236 + 0.0821197i
\(705\) 7221.55 12508.1i 0.385786 0.668202i
\(706\) 7138.30 + 12363.9i 0.380529 + 0.659095i
\(707\) 9138.55i 0.486125i
\(708\) −18389.5 + 10617.2i −0.976156 + 0.563584i
\(709\) −11799.5 + 6812.44i −0.625021 + 0.360856i −0.778821 0.627246i \(-0.784182\pi\)
0.153801 + 0.988102i \(0.450849\pi\)
\(710\) 2284.23i 0.120741i
\(711\) 14199.2 + 24593.8i 0.748962 + 1.29724i
\(712\) 4657.71 8067.40i 0.245162 0.424633i
\(713\) −2879.82 1662.67i −0.151263 0.0873315i
\(714\) −16418.2 −0.860553
\(715\) 0 0
\(716\) 193.069 0.0100773
\(717\) 4096.18 + 2364.93i 0.213354 + 0.123180i
\(718\) −2150.51 + 3724.79i −0.111778 + 0.193605i
\(719\) 8117.89 + 14060.6i 0.421066 + 0.729307i 0.996044 0.0888616i \(-0.0283229\pi\)
−0.574978 + 0.818169i \(0.694990\pi\)
\(720\) 1970.09i 0.101973i
\(721\) 7595.36 4385.19i 0.392325 0.226509i
\(722\) 8498.75 4906.75i 0.438076 0.252923i
\(723\) 47123.8i 2.42400i
\(724\) −3418.54 5921.08i −0.175482 0.303944i
\(725\) 12349.6 21390.1i 0.632623 1.09574i
\(726\) −12896.7 7445.91i −0.659285 0.380638i
\(727\) −24181.2 −1.23361 −0.616803 0.787118i \(-0.711572\pi\)
−0.616803 + 0.787118i \(0.711572\pi\)
\(728\) 0 0
\(729\) −28693.9 −1.45780
\(730\) −1483.48 856.490i −0.0752139 0.0434248i
\(731\) 3369.98 5836.98i 0.170511 0.295333i
\(732\) 3315.93 + 5743.36i 0.167432 + 0.290001i
\(733\) 3053.70i 0.153876i −0.997036 0.0769379i \(-0.975486\pi\)
0.997036 0.0769379i \(-0.0245143\pi\)
\(734\) 4111.38 2373.71i 0.206749 0.119367i
\(735\) −10596.7 + 6118.03i −0.531791 + 0.307030i
\(736\) 22983.4i 1.15106i
\(737\) −3909.05 6770.67i −0.195375 0.338400i
\(738\) 6062.63 10500.8i 0.302396 0.523766i
\(739\) 6957.32 + 4016.81i 0.346318 + 0.199947i 0.663062 0.748564i \(-0.269256\pi\)
−0.316744 + 0.948511i \(0.602590\pi\)
\(740\) −1865.74 −0.0926836
\(741\) 0 0
\(742\) −5128.54 −0.253739
\(743\) −13977.3 8069.81i −0.690146 0.398456i 0.113521 0.993536i \(-0.463787\pi\)
−0.803667 + 0.595080i \(0.797120\pi\)
\(744\) −2491.40 + 4315.22i −0.122767 + 0.212639i
\(745\) 3121.67 + 5406.89i 0.153515 + 0.265897i
\(746\) 8408.53i 0.412678i
\(747\) −56789.6 + 32787.5i −2.78156 + 1.60593i
\(748\) −3274.41 + 1890.48i −0.160059 + 0.0924102i
\(749\) 38988.7i 1.90202i
\(750\) 5731.19 + 9926.71i 0.279031 + 0.483296i
\(751\) −9245.56 + 16013.8i −0.449235 + 0.778097i −0.998336 0.0576584i \(-0.981637\pi\)
0.549102 + 0.835755i \(0.314970\pi\)
\(752\) −4619.45 2667.04i −0.224008 0.129331i
\(753\) 45344.5 2.19448
\(754\) 0 0
\(755\) 9953.28 0.479784
\(756\) 24353.9 + 14060.7i 1.17162 + 0.676434i
\(757\) −80.3149 + 139.109i −0.00385613 + 0.00667902i −0.867947 0.496657i \(-0.834561\pi\)
0.864091 + 0.503336i \(0.167894\pi\)
\(758\) 2673.59 + 4630.79i 0.128112 + 0.221897i
\(759\) 16267.7i 0.777973i
\(760\) 1565.66 903.936i 0.0747271 0.0431437i
\(761\) 23208.7 13399.5i 1.10554 0.638282i 0.167867 0.985810i \(-0.446312\pi\)
0.937670 + 0.347528i \(0.112979\pi\)
\(762\) 11733.1i 0.557803i
\(763\) 11538.7 + 19985.6i 0.547481 + 0.948264i
\(764\) −11903.9 + 20618.2i −0.563703 + 0.976363i
\(765\) 6653.30 + 3841.28i 0.314445 + 0.181545i
\(766\) −598.052 −0.0282095
\(767\) 0 0
\(768\) −30025.1 −1.41073
\(769\) −4456.41 2572.91i −0.208976 0.120652i 0.391860 0.920025i \(-0.371832\pi\)
−0.600835 + 0.799373i \(0.705165\pi\)
\(770\) 1153.35 1997.67i 0.0539792 0.0934947i
\(771\) 2858.15 + 4950.45i 0.133507 + 0.231240i
\(772\) 2626.83i 0.122463i
\(773\) −11094.3 + 6405.28i −0.516214 + 0.298036i −0.735384 0.677650i \(-0.762998\pi\)
0.219170 + 0.975687i \(0.429665\pi\)
\(774\) 9908.01 5720.39i 0.460124 0.265653i
\(775\) 3042.94i 0.141039i
\(776\) 16002.1 + 27716.5i 0.740262 + 1.28217i
\(777\) −11115.8 + 19253.1i −0.513227 + 0.888934i
\(778\) 11614.4 + 6705.57i 0.535214 + 0.309006i
\(779\) 3843.64 0.176781
\(780\) 0 0
\(781\) 6268.13 0.287185
\(782\) −7394.03 4268.94i −0.338120 0.195214i
\(783\) 20457.5 35433.4i 0.933705 1.61722i
\(784\) 2259.49 + 3913.55i 0.102929 + 0.178278i
\(785\) 11556.8i 0.525452i
\(786\) −3304.95 + 1908.11i −0.149979 + 0.0865905i
\(787\) 24311.9 14036.5i 1.10118 0.635764i 0.164646 0.986353i \(-0.447352\pi\)
0.936530 + 0.350588i \(0.114018\pi\)
\(788\) 24940.0i 1.12748i
\(789\) −14097.2 24417.0i −0.636087 1.10174i
\(790\) −1630.82 + 2824.66i −0.0734455 + 0.127211i
\(791\) 37999.6 + 21939.1i 1.70810 + 0.986173i
\(792\) −15650.0 −0.702144
\(793\) 0 0
\(794\) 11304.3 0.505259
\(795\) 3237.11 + 1868.94i 0.144413 + 0.0833769i
\(796\) −1018.43 + 1763.98i −0.0453485 + 0.0785459i
\(797\) 15046.6 + 26061.4i 0.668729 + 1.15827i 0.978260 + 0.207383i \(0.0664945\pi\)
−0.309531 + 0.950889i \(0.600172\pi\)
\(798\) 8834.35i 0.391896i
\(799\) −18014.1 + 10400.4i −0.797612 + 0.460501i
\(800\) 18213.9 10515.8i 0.804947 0.464737i
\(801\) 21300.6i 0.939598i
\(802\) 3333.62 + 5774.00i 0.146776 + 0.254223i
\(803\) −2350.28 + 4070.80i −0.103287 + 0.178899i
\(804\) 21428.3 + 12371.6i 0.939946 + 0.542678i
\(805\) −11880.2 −0.520151
\(806\) 0 0
\(807\) −22456.8 −0.979575
\(808\) 6166.96 + 3560.50i 0.268506 + 0.155022i
\(809\) 12168.6 21076.6i 0.528831 0.915961i −0.470604 0.882344i \(-0.655964\pi\)
0.999435 0.0336170i \(-0.0107026\pi\)
\(810\) 857.553 + 1485.33i 0.0371992 + 0.0644309i
\(811\) 19078.7i 0.826071i −0.910715 0.413035i \(-0.864469\pi\)
0.910715 0.413035i \(-0.135531\pi\)
\(812\) 28785.4 16619.3i 1.24405 0.718254i
\(813\) 7437.89 4294.27i 0.320859 0.185248i
\(814\) 2244.74i 0.0966559i
\(815\) 5843.56 + 10121.3i 0.251155 + 0.435013i
\(816\) 2209.67 3827.25i 0.0947963 0.164192i
\(817\) 3140.78 + 1813.33i 0.134495 + 0.0776505i
\(818\) 21178.6 0.905248
\(819\) 0 0
\(820\) −3176.26 −0.135268
\(821\) 1744.10 + 1006.96i 0.0741408 + 0.0428052i 0.536612 0.843829i \(-0.319704\pi\)
−0.462471 + 0.886634i \(0.653037\pi\)
\(822\) −17911.0 + 31022.7i −0.759996 + 1.31635i
\(823\) −3846.05 6661.55i −0.162898 0.282147i 0.773009 0.634395i \(-0.218751\pi\)
−0.935907 + 0.352248i \(0.885417\pi\)
\(824\) 6834.10i 0.288929i
\(825\) 12891.9 7443.12i 0.544045 0.314105i
\(826\) −16157.7 + 9328.66i −0.680628 + 0.392961i
\(827\) 4762.76i 0.200263i −0.994974 0.100131i \(-0.968074\pi\)
0.994974 0.100131i \(-0.0319263\pi\)
\(828\) 16527.3 + 28626.1i 0.693675 + 1.20148i
\(829\) 9988.83 17301.2i 0.418488 0.724842i −0.577300 0.816532i \(-0.695894\pi\)
0.995788 + 0.0916901i \(0.0292269\pi\)
\(830\) −6522.44 3765.73i −0.272768 0.157483i
\(831\) −70714.0 −2.95191
\(832\) 0 0
\(833\) 17622.3 0.732984
\(834\) 23473.3 + 13552.3i 0.974596 + 0.562683i
\(835\) −5567.63 + 9643.43i −0.230750 + 0.399670i
\(836\) −1017.24 1761.91i −0.0420836 0.0728909i
\(837\) 5040.72i 0.208164i
\(838\) −19713.0 + 11381.3i −0.812617 + 0.469165i
\(839\) −26514.0 + 15307.9i −1.09102 + 0.629901i −0.933848 0.357670i \(-0.883571\pi\)
−0.157172 + 0.987571i \(0.550238\pi\)
\(840\) 17801.7i 0.731210i
\(841\) −11985.5 20759.5i −0.491431 0.851183i
\(842\) −12374.0 + 21432.5i −0.506458 + 0.877211i
\(843\) −11539.0 6662.04i −0.471440 0.272186i
\(844\) 11804.7 0.481439
\(845\) 0 0
\(846\) −35308.5 −1.43491
\(847\) 25844.7 + 14921.4i 1.04845 + 0.605321i
\(848\) 690.233 1195.52i 0.0279513 0.0484131i
\(849\) −30244.3 52384.7i −1.22259 2.11760i
\(850\) 7812.83i 0.315268i
\(851\) −10012.1 + 5780.51i −0.403304 + 0.232848i
\(852\) −17180.0 + 9918.89i −0.690819 + 0.398845i
\(853\) 5660.88i 0.227227i 0.993525 + 0.113614i \(0.0362426\pi\)
−0.993525 + 0.113614i \(0.963757\pi\)
\(854\) 2913.50 + 5046.34i 0.116742 + 0.202204i
\(855\) −2066.93 + 3580.03i −0.0826755 + 0.143198i
\(856\) −26310.7 15190.5i −1.05056 0.606543i
\(857\) −41346.1 −1.64802 −0.824012 0.566572i \(-0.808269\pi\)
−0.824012 + 0.566572i \(0.808269\pi\)
\(858\) 0 0
\(859\) −34810.5 −1.38268 −0.691339 0.722530i \(-0.742979\pi\)
−0.691339 + 0.722530i \(0.742979\pi\)
\(860\) −2595.44 1498.48i −0.102911 0.0594159i
\(861\) −18923.7 + 32776.8i −0.749033 + 1.29736i
\(862\) −8350.19 14462.9i −0.329940 0.571473i
\(863\) 8360.51i 0.329774i 0.986312 + 0.164887i \(0.0527260\pi\)
−0.986312 + 0.164887i \(0.947274\pi\)
\(864\) 30171.9 17419.7i 1.18804 0.685916i
\(865\) −300.944 + 173.750i −0.0118294 + 0.00682969i
\(866\) 25108.2i 0.985233i
\(867\) 12717.0 + 22026.5i 0.498146 + 0.862815i
\(868\) 2047.49 3546.36i 0.0800651 0.138677i
\(869\) 7751.11 + 4475.11i 0.302576 + 0.174692i
\(870\) 10621.6 0.413917
\(871\) 0 0
\(872\) 17982.4 0.698352
\(873\) −63376.3 36590.3i −2.45700 1.41855i
\(874\) 2297.05 3978.61i 0.0889003 0.153980i
\(875\) −11485.2 19892.9i −0.443737 0.768576i
\(876\) 14876.6i 0.573784i
\(877\) 35142.7 20289.7i 1.35312 0.781223i 0.364434 0.931229i \(-0.381263\pi\)
0.988685 + 0.150006i \(0.0479293\pi\)
\(878\) −8162.48 + 4712.61i −0.313748 + 0.181142i
\(879\) 5558.43i 0.213289i
\(880\) 310.452 + 537.718i 0.0118924 + 0.0205983i
\(881\) 5222.62 9045.84i 0.199721 0.345927i −0.748717 0.662890i \(-0.769330\pi\)
0.948438 + 0.316963i \(0.102663\pi\)
\(882\) 25905.4 + 14956.5i 0.988981 + 0.570989i
\(883\) −18227.6 −0.694685 −0.347343 0.937738i \(-0.612916\pi\)
−0.347343 + 0.937738i \(0.612916\pi\)
\(884\) 0 0
\(885\) 13598.2 0.516496
\(886\) −13795.7 7964.96i −0.523111 0.302018i
\(887\) 11758.8 20366.9i 0.445122 0.770974i −0.552938 0.833222i \(-0.686494\pi\)
0.998061 + 0.0622477i \(0.0198269\pi\)
\(888\) 8661.72 + 15002.5i 0.327329 + 0.566950i
\(889\) 23512.9i 0.887061i
\(890\) −2118.67 + 1223.21i −0.0797955 + 0.0460699i
\(891\) 4075.86 2353.20i 0.153251 0.0884794i
\(892\) 32960.1i 1.23720i
\(893\) −5596.30 9693.07i −0.209712 0.363232i
\(894\) 11886.6 20588.1i 0.444683 0.770213i
\(895\) −107.075 61.8196i −0.00399901 0.00230883i
\(896\) 32181.2 1.19989
\(897\) 0 0
\(898\) 9092.21 0.337874
\(899\) −5159.74 2978.98i −0.191420 0.110517i
\(900\) −15123.7 + 26195.1i −0.560139 + 0.970189i
\(901\) −2691.64 4662.06i −0.0995245 0.172381i
\(902\) 3821.47i 0.141065i
\(903\) −30926.5 + 17855.4i −1.13972 + 0.658019i
\(904\) 29610.2 17095.5i 1.08940 0.628968i
\(905\) 4378.38i 0.160820i
\(906\) −18949.9 32822.1i −0.694886 1.20358i
\(907\) −15282.3 + 26469.7i −0.559471 + 0.969032i 0.438070 + 0.898941i \(0.355662\pi\)
−0.997541 + 0.0700908i \(0.977671\pi\)
\(908\) −4313.90 2490.63i −0.157667 0.0910292i
\(909\) −16282.8 −0.594132
\(910\) 0 0
\(911\) −32766.5 −1.19166 −0.595831 0.803110i \(-0.703177\pi\)
−0.595831 + 0.803110i \(0.703177\pi\)
\(912\) 2059.38 + 1188.99i 0.0747730 + 0.0431702i
\(913\) −10333.5 + 17898.1i −0.374577 + 0.648786i
\(914\) −3608.44 6249.99i −0.130587 0.226183i
\(915\) 4246.96i 0.153443i
\(916\) 3023.36 1745.54i 0.109055 0.0629632i
\(917\) 6623.05 3823.82i 0.238509 0.137703i
\(918\) 12942.2i 0.465312i
\(919\) −10343.4 17915.2i −0.371269 0.643057i 0.618492 0.785791i \(-0.287744\pi\)
−0.989761 + 0.142734i \(0.954411\pi\)
\(920\) −4628.68 + 8017.10i −0.165873 + 0.287300i
\(921\) 755.165 + 435.995i 0.0270179 + 0.0155988i
\(922\) 8007.28 0.286015
\(923\) 0 0
\(924\) 20033.0 0.713242
\(925\) −9161.88 5289.62i −0.325666 0.188023i
\(926\) 5064.32 8771.67i 0.179724 0.311290i
\(927\) 7813.39 + 13533.2i 0.276834 + 0.479491i
\(928\) 41179.0i 1.45665i
\(929\) −39518.6 + 22816.1i −1.39566 + 0.805782i −0.993934 0.109979i \(-0.964922\pi\)
−0.401722 + 0.915762i \(0.631588\pi\)
\(930\) 1133.27 654.294i 0.0399585 0.0230700i
\(931\) 9482.26i 0.333801i
\(932\) 6406.14 + 11095.8i 0.225150 + 0.389972i
\(933\) −16843.5 + 29173.9i −0.591032 + 1.02370i
\(934\) 17550.8 + 10133.0i 0.614860 + 0.354990i
\(935\) 2421.28 0.0846892
\(936\) 0 0
\(937\) −17761.4 −0.619253 −0.309626 0.950858i \(-0.600204\pi\)
−0.309626 + 0.950858i \(0.600204\pi\)
\(938\) 18827.7 + 10870.2i 0.655380 + 0.378384i
\(939\) 16454.8 28500.5i 0.571866 0.990501i
\(940\) 4624.60 + 8010.04i 0.160466 + 0.277935i
\(941\) 44888.3i 1.55507i 0.628841 + 0.777534i \(0.283530\pi\)
−0.628841 + 0.777534i \(0.716470\pi\)
\(942\) 38109.9 22002.8i 1.31814 0.761029i
\(943\) −17044.8 + 9840.83i −0.588606 + 0.339832i
\(944\) 5022.05i 0.173150i
\(945\) −9004.32 15595.9i −0.309958 0.536864i
\(946\) 1802.87 3122.67i 0.0619624 0.107322i
\(947\) −13916.6 8034.78i −0.477540 0.275708i 0.241851 0.970313i \(-0.422246\pi\)
−0.719391 + 0.694606i \(0.755579\pi\)
\(948\) −28326.2 −0.970457
\(949\) 0 0
\(950\) 4203.96 0.143573
\(951\) 33144.2 + 19135.8i 1.13015 + 0.652493i
\(952\) 12818.9 22203.0i 0.436411 0.755887i
\(953\) 1756.02 + 3041.51i 0.0596883 + 0.103383i 0.894325 0.447417i \(-0.147656\pi\)
−0.834637 + 0.550800i \(0.814323\pi\)
\(954\) 9137.88i 0.310115i
\(955\) 13203.7 7623.14i 0.447393 0.258303i
\(956\) −2623.14 + 1514.47i −0.0887432 + 0.0512359i
\(957\) 29146.7i 0.984513i
\(958\) −4535.50 7855.72i −0.152960 0.264934i
\(959\) 35893.2 62168.9i 1.20861 2.09337i
\(960\) 5384.75 + 3108.89i 0.181034 + 0.104520i
\(961\) 29057.0 0.975361
\(962\) 0 0
\(963\) 69468.9 2.32461
\(964\) −26134.5 15088.8i −0.873170 0.504125i
\(965\) 841.097 1456.82i 0.0280579 0.0485977i
\(966\) 22618.5 + 39176.4i 0.753352 + 1.30484i
\(967\) 37011.9i 1.23084i 0.788199 + 0.615421i \(0.211014\pi\)
−0.788199 + 0.615421i \(0.788986\pi\)
\(968\) 20138.9 11627.2i 0.668685 0.386066i
\(969\) 8030.79 4636.58i 0.266240 0.153714i
\(970\) 8405.00i 0.278215i
\(971\) −9766.15 16915.5i −0.322771 0.559056i 0.658288 0.752766i \(-0.271281\pi\)
−0.981059 + 0.193711i \(0.937948\pi\)
\(972\) 6521.55 11295.7i 0.215205 0.372745i
\(973\) −47040.0 27158.5i −1.54988 0.894823i
\(974\) −8412.30 −0.276743
\(975\) 0 0
\(976\) −1568.47 −0.0514402
\(977\) 26155.0 + 15100.6i 0.856473 + 0.494485i 0.862830 0.505495i \(-0.168690\pi\)
−0.00635674 + 0.999980i \(0.502023\pi\)
\(978\) 22250.9 38539.7i 0.727511 1.26009i
\(979\) 3356.60 + 5813.81i 0.109579 + 0.189796i
\(980\) 7835.83i 0.255415i
\(981\) −35609.7 + 20559.2i −1.15895 + 0.669119i
\(982\) −20635.5 + 11913.9i −0.670576 + 0.387157i
\(983\) 38774.9i 1.25812i −0.777359 0.629058i \(-0.783441\pi\)
0.777359 0.629058i \(-0.216559\pi\)
\(984\) 14745.8 + 25540.5i 0.477723 + 0.827441i
\(985\) 7985.65 13831.6i 0.258319 0.447421i
\(986\) −13247.8 7648.61i −0.427886 0.247040i
\(987\) 110211. 3.55425
\(988\) 0 0
\(989\) −18570.6 −0.597079
\(990\) 3559.38 + 2055.01i 0.114267 + 0.0659722i
\(991\) 13864.5 24014.0i 0.444419 0.769757i −0.553592 0.832788i \(-0.686743\pi\)
0.998012 + 0.0630311i \(0.0200767\pi\)
\(992\) −2536.63 4393.57i −0.0811875 0.140621i
\(993\) 35880.6i 1.14666i
\(994\) −15095.1 + 8715.13i −0.481676 + 0.278096i
\(995\) 1129.63 652.192i 0.0359916 0.0207798i
\(996\) 65408.2i 2.08086i
\(997\) 24459.1 + 42364.4i 0.776958 + 1.34573i 0.933687 + 0.358090i \(0.116572\pi\)
−0.156729 + 0.987642i \(0.550095\pi\)
\(998\) −1449.16 + 2510.01i −0.0459641 + 0.0796122i
\(999\) −15177.0 8762.42i −0.480658 0.277508i
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 169.4.e.f.147.2 8
13.2 odd 12 169.4.c.j.146.1 4
13.3 even 3 inner 169.4.e.f.23.3 8
13.4 even 6 169.4.b.f.168.2 4
13.5 odd 4 169.4.c.j.22.1 4
13.6 odd 12 169.4.a.g.1.2 2
13.7 odd 12 13.4.a.b.1.1 2
13.8 odd 4 169.4.c.g.22.2 4
13.9 even 3 169.4.b.f.168.3 4
13.10 even 6 inner 169.4.e.f.23.2 8
13.11 odd 12 169.4.c.g.146.2 4
13.12 even 2 inner 169.4.e.f.147.3 8
39.20 even 12 117.4.a.d.1.2 2
39.32 even 12 1521.4.a.r.1.1 2
52.7 even 12 208.4.a.h.1.1 2
65.7 even 12 325.4.b.e.274.2 4
65.33 even 12 325.4.b.e.274.3 4
65.59 odd 12 325.4.a.f.1.2 2
91.20 even 12 637.4.a.b.1.1 2
104.59 even 12 832.4.a.z.1.2 2
104.85 odd 12 832.4.a.s.1.1 2
143.98 even 12 1573.4.a.b.1.2 2
156.59 odd 12 1872.4.a.bb.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.4.a.b.1.1 2 13.7 odd 12
117.4.a.d.1.2 2 39.20 even 12
169.4.a.g.1.2 2 13.6 odd 12
169.4.b.f.168.2 4 13.4 even 6
169.4.b.f.168.3 4 13.9 even 3
169.4.c.g.22.2 4 13.8 odd 4
169.4.c.g.146.2 4 13.11 odd 12
169.4.c.j.22.1 4 13.5 odd 4
169.4.c.j.146.1 4 13.2 odd 12
169.4.e.f.23.2 8 13.10 even 6 inner
169.4.e.f.23.3 8 13.3 even 3 inner
169.4.e.f.147.2 8 1.1 even 1 trivial
169.4.e.f.147.3 8 13.12 even 2 inner
208.4.a.h.1.1 2 52.7 even 12
325.4.a.f.1.2 2 65.59 odd 12
325.4.b.e.274.2 4 65.7 even 12
325.4.b.e.274.3 4 65.33 even 12
637.4.a.b.1.1 2 91.20 even 12
832.4.a.s.1.1 2 104.85 odd 12
832.4.a.z.1.2 2 104.59 even 12
1521.4.a.r.1.1 2 39.32 even 12
1573.4.a.b.1.2 2 143.98 even 12
1872.4.a.bb.1.2 2 156.59 odd 12