Properties

Label 143.4.n.a.25.12
Level $143$
Weight $4$
Character 143.25
Analytic conductor $8.437$
Analytic rank $0$
Dimension $160$
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] = [143,4,Mod(25,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.25");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 143.n (of order \(10\), degree \(4\), 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: \(8.43727313082\)
Analytic rank: \(0\)
Dimension: \(160\)
Relative dimension: \(40\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 25.12
Character \(\chi\) \(=\) 143.25
Dual form 143.4.n.a.103.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.38497 - 1.90624i) q^{2} +(-0.928232 - 2.85681i) q^{3} +(0.756503 - 2.32828i) q^{4} +(7.86101 - 10.8197i) q^{5} +(-4.16020 + 5.72602i) q^{6} +(-12.3082 - 3.99917i) q^{7} +(-23.4134 + 7.60747i) q^{8} +(14.5437 - 10.5666i) q^{9} +O(q^{10})\) \(q+(-1.38497 - 1.90624i) q^{2} +(-0.928232 - 2.85681i) q^{3} +(0.756503 - 2.32828i) q^{4} +(7.86101 - 10.8197i) q^{5} +(-4.16020 + 5.72602i) q^{6} +(-12.3082 - 3.99917i) q^{7} +(-23.4134 + 7.60747i) q^{8} +(14.5437 - 10.5666i) q^{9} -31.5123 q^{10} +(5.26848 - 36.1005i) q^{11} -7.35365 q^{12} +(45.2544 - 12.2082i) q^{13} +(9.42303 + 29.0011i) q^{14} +(-38.2068 - 12.4141i) q^{15} +(31.0841 + 22.5839i) q^{16} +(84.5701 + 61.4438i) q^{17} +(-40.2852 - 13.0895i) q^{18} +(-126.227 + 41.0136i) q^{19} +(-19.2445 - 26.4878i) q^{20} +38.8742i q^{21} +(-76.1130 + 39.9550i) q^{22} -96.3465 q^{23} +(43.4662 + 59.8260i) q^{24} +(-16.6444 - 51.2261i) q^{25} +(-85.9476 - 69.3580i) q^{26} +(-109.301 - 79.4116i) q^{27} +(-18.6223 + 25.6314i) q^{28} +(-26.8636 + 82.6777i) q^{29} +(29.2508 + 90.0246i) q^{30} +(-19.2997 - 26.5637i) q^{31} +106.415i q^{32} +(-108.022 + 18.4586i) q^{33} -246.309i q^{34} +(-140.025 + 101.734i) q^{35} +(-13.5997 - 41.8555i) q^{36} +(165.962 + 53.9243i) q^{37} +(253.002 + 183.817i) q^{38} +(-76.8830 - 117.951i) q^{39} +(-101.742 + 313.129i) q^{40} +(85.4150 - 27.7530i) q^{41} +(74.1037 - 53.8395i) q^{42} +243.311 q^{43} +(-80.0662 - 39.5766i) q^{44} -240.424i q^{45} +(133.437 + 183.660i) q^{46} +(284.931 - 92.5796i) q^{47} +(35.6646 - 109.764i) q^{48} +(-141.995 - 103.166i) q^{49} +(-74.5975 + 102.675i) q^{50} +(97.0322 - 298.634i) q^{51} +(5.81110 - 114.600i) q^{52} +(15.4371 - 11.2157i) q^{53} +318.336i q^{54} +(-349.182 - 340.789i) q^{55} +318.600 q^{56} +(234.336 + 322.535i) q^{57} +(194.809 - 63.2973i) q^{58} +(237.585 + 77.1959i) q^{59} +(-57.8070 + 79.5646i) q^{60} +(-468.587 - 340.448i) q^{61} +(-23.9075 + 73.5799i) q^{62} +(-221.264 + 71.8932i) q^{63} +(451.525 - 328.052i) q^{64} +(223.656 - 585.610i) q^{65} +(184.794 + 180.353i) q^{66} -671.282i q^{67} +(207.036 - 150.420i) q^{68} +(89.4320 + 275.243i) q^{69} +(387.859 + 126.023i) q^{70} +(-232.650 + 320.215i) q^{71} +(-260.133 + 358.042i) q^{72} +(267.819 + 87.0198i) q^{73} +(-127.059 - 391.047i) q^{74} +(-130.893 + 95.0994i) q^{75} +324.918i q^{76} +(-209.217 + 423.261i) q^{77} +(-118.363 + 309.916i) q^{78} +(982.682 - 713.960i) q^{79} +(488.705 - 158.790i) q^{80} +(24.5836 - 75.6607i) q^{81} +(-171.201 - 124.385i) q^{82} +(110.645 - 152.289i) q^{83} +(90.5099 + 29.4084i) q^{84} +(1329.61 - 432.017i) q^{85} +(-336.978 - 463.810i) q^{86} +261.130 q^{87} +(151.280 + 885.314i) q^{88} +64.9589i q^{89} +(-458.307 + 332.979i) q^{90} +(-605.821 - 30.7197i) q^{91} +(-72.8864 + 224.321i) q^{92} +(-57.9729 + 79.7928i) q^{93} +(-571.099 - 414.928i) q^{94} +(-548.513 + 1688.15i) q^{95} +(304.006 - 98.7774i) q^{96} +(-27.8646 - 38.3524i) q^{97} +413.558i q^{98} +(-304.837 - 580.706i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 160 q - 6 q^{3} + 146 q^{4} - 426 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 160 q - 6 q^{3} + 146 q^{4} - 426 q^{9} + 184 q^{10} + 84 q^{12} - 39 q^{13} - 158 q^{14} - 634 q^{16} - 116 q^{17} - 1026 q^{22} + 184 q^{23} + 506 q^{25} - 450 q^{26} - 210 q^{27} + 188 q^{29} - 1424 q^{30} + 1762 q^{35} + 1086 q^{36} - 418 q^{38} + 529 q^{39} - 1190 q^{40} + 1444 q^{42} + 4288 q^{43} - 2128 q^{48} + 902 q^{49} + 350 q^{51} - 1746 q^{52} - 2866 q^{53} + 486 q^{55} - 6436 q^{56} + 570 q^{61} + 1702 q^{62} + 5834 q^{64} + 810 q^{65} + 3954 q^{66} - 3112 q^{68} + 4656 q^{69} + 5140 q^{74} - 854 q^{75} - 144 q^{77} - 4904 q^{78} - 1730 q^{79} + 1622 q^{81} + 5578 q^{82} - 8556 q^{87} - 3538 q^{88} - 12996 q^{90} + 5315 q^{91} + 9394 q^{92} + 4646 q^{94} + 1922 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38497 1.90624i −0.489660 0.673959i 0.490665 0.871348i \(-0.336754\pi\)
−0.980325 + 0.197389i \(0.936754\pi\)
\(3\) −0.928232 2.85681i −0.178638 0.549793i 0.821143 0.570723i \(-0.193337\pi\)
−0.999781 + 0.0209307i \(0.993337\pi\)
\(4\) 0.756503 2.32828i 0.0945629 0.291035i
\(5\) 7.86101 10.8197i 0.703110 0.967747i −0.296808 0.954937i \(-0.595922\pi\)
0.999918 0.0128103i \(-0.00407777\pi\)
\(6\) −4.16020 + 5.72602i −0.283066 + 0.389606i
\(7\) −12.3082 3.99917i −0.664579 0.215935i −0.0427473 0.999086i \(-0.513611\pi\)
−0.621831 + 0.783151i \(0.713611\pi\)
\(8\) −23.4134 + 7.60747i −1.03474 + 0.336206i
\(9\) 14.5437 10.5666i 0.538657 0.391357i
\(10\) −31.5123 −0.996507
\(11\) 5.26848 36.1005i 0.144410 0.989518i
\(12\) −7.35365 −0.176901
\(13\) 45.2544 12.2082i 0.965486 0.260457i
\(14\) 9.42303 + 29.0011i 0.179886 + 0.553634i
\(15\) −38.2068 12.4141i −0.657663 0.213688i
\(16\) 31.0841 + 22.5839i 0.485689 + 0.352874i
\(17\) 84.5701 + 61.4438i 1.20654 + 0.876606i 0.994912 0.100743i \(-0.0321220\pi\)
0.211632 + 0.977349i \(0.432122\pi\)
\(18\) −40.2852 13.0895i −0.527518 0.171401i
\(19\) −126.227 + 41.0136i −1.52413 + 0.495219i −0.946945 0.321397i \(-0.895848\pi\)
−0.577182 + 0.816616i \(0.695848\pi\)
\(20\) −19.2445 26.4878i −0.215160 0.296142i
\(21\) 38.8742i 0.403955i
\(22\) −76.1130 + 39.9550i −0.737606 + 0.387201i
\(23\) −96.3465 −0.873462 −0.436731 0.899592i \(-0.643864\pi\)
−0.436731 + 0.899592i \(0.643864\pi\)
\(24\) 43.4662 + 59.8260i 0.369687 + 0.508831i
\(25\) −16.6444 51.2261i −0.133155 0.409809i
\(26\) −85.9476 69.3580i −0.648297 0.523163i
\(27\) −109.301 79.4116i −0.779071 0.566029i
\(28\) −18.6223 + 25.6314i −0.125689 + 0.172996i
\(29\) −26.8636 + 82.6777i −0.172015 + 0.529409i −0.999485 0.0321021i \(-0.989780\pi\)
0.827469 + 0.561511i \(0.189780\pi\)
\(30\) 29.2508 + 90.0246i 0.178014 + 0.547872i
\(31\) −19.2997 26.5637i −0.111817 0.153903i 0.749440 0.662072i \(-0.230323\pi\)
−0.861257 + 0.508169i \(0.830323\pi\)
\(32\) 106.415i 0.587863i
\(33\) −108.022 + 18.4586i −0.569827 + 0.0973706i
\(34\) 246.309i 1.24240i
\(35\) −140.025 + 101.734i −0.676242 + 0.491318i
\(36\) −13.5997 41.8555i −0.0629615 0.193776i
\(37\) 165.962 + 53.9243i 0.737405 + 0.239597i 0.653553 0.756881i \(-0.273278\pi\)
0.0838518 + 0.996478i \(0.473278\pi\)
\(38\) 253.002 + 183.817i 1.08006 + 0.784710i
\(39\) −76.8830 117.951i −0.315670 0.484289i
\(40\) −101.742 + 313.129i −0.402170 + 1.23775i
\(41\) 85.4150 27.7530i 0.325355 0.105714i −0.141785 0.989897i \(-0.545284\pi\)
0.467141 + 0.884183i \(0.345284\pi\)
\(42\) 74.1037 53.8395i 0.272249 0.197800i
\(43\) 243.311 0.862897 0.431448 0.902138i \(-0.358003\pi\)
0.431448 + 0.902138i \(0.358003\pi\)
\(44\) −80.0662 39.5766i −0.274328 0.135600i
\(45\) 240.424i 0.796451i
\(46\) 133.437 + 183.660i 0.427700 + 0.588678i
\(47\) 284.931 92.5796i 0.884285 0.287322i 0.168550 0.985693i \(-0.446092\pi\)
0.715736 + 0.698371i \(0.246092\pi\)
\(48\) 35.6646 109.764i 0.107245 0.330065i
\(49\) −141.995 103.166i −0.413980 0.300774i
\(50\) −74.5975 + 102.675i −0.210994 + 0.290408i
\(51\) 97.0322 298.634i 0.266416 0.819945i
\(52\) 5.81110 114.600i 0.0154972 0.305619i
\(53\) 15.4371 11.2157i 0.0400086 0.0290679i −0.567601 0.823304i \(-0.692128\pi\)
0.607610 + 0.794236i \(0.292128\pi\)
\(54\) 318.336i 0.802224i
\(55\) −349.182 340.789i −0.856068 0.835492i
\(56\) 318.600 0.760262
\(57\) 234.336 + 322.535i 0.544535 + 0.749488i
\(58\) 194.809 63.2973i 0.441029 0.143299i
\(59\) 237.585 + 77.1959i 0.524252 + 0.170340i 0.559174 0.829050i \(-0.311118\pi\)
−0.0349220 + 0.999390i \(0.511118\pi\)
\(60\) −57.8070 + 79.5646i −0.124381 + 0.171196i
\(61\) −468.587 340.448i −0.983548 0.714589i −0.0250492 0.999686i \(-0.507974\pi\)
−0.958499 + 0.285097i \(0.907974\pi\)
\(62\) −23.9075 + 73.5799i −0.0489720 + 0.150720i
\(63\) −221.264 + 71.8932i −0.442487 + 0.143773i
\(64\) 451.525 328.052i 0.881885 0.640727i
\(65\) 223.656 585.610i 0.426786 1.11748i
\(66\) 184.794 + 180.353i 0.344645 + 0.336361i
\(67\) 671.282i 1.22403i −0.790845 0.612016i \(-0.790359\pi\)
0.790845 0.612016i \(-0.209641\pi\)
\(68\) 207.036 150.420i 0.369217 0.268252i
\(69\) 89.4320 + 275.243i 0.156034 + 0.480223i
\(70\) 387.859 + 126.023i 0.662257 + 0.215180i
\(71\) −232.650 + 320.215i −0.388879 + 0.535246i −0.957910 0.287070i \(-0.907319\pi\)
0.569030 + 0.822317i \(0.307319\pi\)
\(72\) −260.133 + 358.042i −0.425791 + 0.586051i
\(73\) 267.819 + 87.0198i 0.429396 + 0.139519i 0.515738 0.856746i \(-0.327518\pi\)
−0.0863423 + 0.996266i \(0.527518\pi\)
\(74\) −127.059 391.047i −0.199599 0.614302i
\(75\) −130.893 + 95.0994i −0.201523 + 0.146415i
\(76\) 324.918i 0.490403i
\(77\) −209.217 + 423.261i −0.309643 + 0.626429i
\(78\) −118.363 + 309.916i −0.171820 + 0.449886i
\(79\) 982.682 713.960i 1.39950 1.01680i 0.404752 0.914427i \(-0.367358\pi\)
0.994747 0.102369i \(-0.0326421\pi\)
\(80\) 488.705 158.790i 0.682986 0.221915i
\(81\) 24.5836 75.6607i 0.0337224 0.103787i
\(82\) −171.201 124.385i −0.230561 0.167512i
\(83\) 110.645 152.289i 0.146323 0.201397i −0.729564 0.683913i \(-0.760277\pi\)
0.875887 + 0.482516i \(0.160277\pi\)
\(84\) 90.5099 + 29.4084i 0.117565 + 0.0381991i
\(85\) 1329.61 432.017i 1.69667 0.551280i
\(86\) −336.978 463.810i −0.422526 0.581557i
\(87\) 261.130 0.321794
\(88\) 151.280 + 885.314i 0.183256 + 1.07244i
\(89\) 64.9589i 0.0773666i 0.999252 + 0.0386833i \(0.0123163\pi\)
−0.999252 + 0.0386833i \(0.987684\pi\)
\(90\) −458.307 + 332.979i −0.536775 + 0.389990i
\(91\) −605.821 30.7197i −0.697883 0.0353879i
\(92\) −72.8864 + 224.321i −0.0825971 + 0.254208i
\(93\) −57.9729 + 79.7928i −0.0646398 + 0.0889691i
\(94\) −571.099 414.928i −0.626642 0.455282i
\(95\) −548.513 + 1688.15i −0.592381 + 1.82316i
\(96\) 304.006 98.7774i 0.323202 0.105015i
\(97\) −27.8646 38.3524i −0.0291673 0.0401453i 0.794184 0.607677i \(-0.207898\pi\)
−0.823352 + 0.567532i \(0.807898\pi\)
\(98\) 413.558i 0.426283i
\(99\) −304.837 580.706i −0.309468 0.589526i
\(100\) −131.860 −0.131860
\(101\) −1036.54 + 753.093i −1.02119 + 0.741937i −0.966526 0.256568i \(-0.917408\pi\)
−0.0546620 + 0.998505i \(0.517408\pi\)
\(102\) −703.657 + 228.632i −0.683063 + 0.221941i
\(103\) 237.201 730.029i 0.226914 0.698368i −0.771178 0.636619i \(-0.780332\pi\)
0.998092 0.0617487i \(-0.0196677\pi\)
\(104\) −966.686 + 630.106i −0.911455 + 0.594106i
\(105\) 420.609 + 305.590i 0.390926 + 0.284024i
\(106\) −42.7599 13.8935i −0.0391812 0.0127307i
\(107\) −379.386 1167.63i −0.342772 1.05494i −0.962766 0.270337i \(-0.912865\pi\)
0.619993 0.784607i \(-0.287135\pi\)
\(108\) −267.579 + 194.407i −0.238405 + 0.173211i
\(109\) 1798.21i 1.58016i −0.613002 0.790081i \(-0.710038\pi\)
0.613002 0.790081i \(-0.289962\pi\)
\(110\) −166.022 + 1137.61i −0.143905 + 0.986062i
\(111\) 524.175i 0.448221i
\(112\) −292.272 402.277i −0.246581 0.339390i
\(113\) 548.979 + 1689.58i 0.457023 + 1.40657i 0.868744 + 0.495262i \(0.164928\pi\)
−0.411721 + 0.911310i \(0.635072\pi\)
\(114\) 290.284 893.402i 0.238487 0.733989i
\(115\) −757.380 + 1042.44i −0.614140 + 0.845291i
\(116\) 172.174 + 125.092i 0.137810 + 0.100125i
\(117\) 529.169 655.739i 0.418134 0.518146i
\(118\) −181.893 559.808i −0.141903 0.436733i
\(119\) −795.179 1094.47i −0.612554 0.843109i
\(120\) 988.990 0.752350
\(121\) −1275.49 380.389i −0.958292 0.285792i
\(122\) 1364.75i 1.01278i
\(123\) −158.570 218.253i −0.116242 0.159993i
\(124\) −76.4480 + 24.8395i −0.0553648 + 0.0179891i
\(125\) 904.827 + 293.996i 0.647442 + 0.210367i
\(126\) 443.490 + 322.214i 0.313565 + 0.227819i
\(127\) 1205.85 + 876.104i 0.842537 + 0.612139i 0.923078 0.384612i \(-0.125665\pi\)
−0.0805412 + 0.996751i \(0.525665\pi\)
\(128\) −441.045 143.304i −0.304557 0.0989565i
\(129\) −225.849 695.092i −0.154146 0.474414i
\(130\) −1426.07 + 384.708i −0.962113 + 0.259547i
\(131\) −893.062 −0.595628 −0.297814 0.954624i \(-0.596257\pi\)
−0.297814 + 0.954624i \(0.596257\pi\)
\(132\) −38.7425 + 265.470i −0.0255462 + 0.175047i
\(133\) 1717.64 1.11984
\(134\) −1279.63 + 929.704i −0.824948 + 0.599360i
\(135\) −1718.43 + 558.351i −1.09555 + 0.355964i
\(136\) −2447.51 795.243i −1.54318 0.501408i
\(137\) −18.2290 + 25.0901i −0.0113680 + 0.0156466i −0.814663 0.579934i \(-0.803078\pi\)
0.803295 + 0.595581i \(0.203078\pi\)
\(138\) 400.821 551.682i 0.247247 0.340307i
\(139\) −772.027 + 2376.05i −0.471097 + 1.44989i 0.380053 + 0.924965i \(0.375906\pi\)
−0.851150 + 0.524923i \(0.824094\pi\)
\(140\) 130.935 + 402.978i 0.0790433 + 0.243270i
\(141\) −528.964 728.056i −0.315935 0.434847i
\(142\) 932.620 0.551153
\(143\) −202.299 1698.02i −0.118301 0.992978i
\(144\) 690.715 0.399719
\(145\) 683.377 + 940.587i 0.391389 + 0.538700i
\(146\) −205.040 631.049i −0.116228 0.357712i
\(147\) −162.919 + 501.414i −0.0914106 + 0.281333i
\(148\) 251.101 345.611i 0.139462 0.191953i
\(149\) −1487.19 + 2046.94i −0.817687 + 1.12545i 0.172404 + 0.985026i \(0.444846\pi\)
−0.990091 + 0.140424i \(0.955154\pi\)
\(150\) 362.566 + 117.805i 0.197356 + 0.0641248i
\(151\) 2502.89 813.238i 1.34889 0.438281i 0.456571 0.889687i \(-0.349078\pi\)
0.892318 + 0.451407i \(0.149078\pi\)
\(152\) 2643.39 1920.53i 1.41057 1.02484i
\(153\) 1879.22 0.992980
\(154\) 1096.60 187.384i 0.573808 0.0980509i
\(155\) −439.128 −0.227559
\(156\) −332.785 + 89.7745i −0.170796 + 0.0460751i
\(157\) −744.911 2292.60i −0.378665 1.16541i −0.940973 0.338483i \(-0.890086\pi\)
0.562308 0.826928i \(-0.309914\pi\)
\(158\) −2721.97 884.421i −1.37056 0.445321i
\(159\) −46.3704 33.6901i −0.0231284 0.0168038i
\(160\) 1151.38 + 836.525i 0.568903 + 0.413332i
\(161\) 1185.85 + 385.306i 0.580484 + 0.188611i
\(162\) −178.275 + 57.9252i −0.0864607 + 0.0280928i
\(163\) −431.516 593.930i −0.207355 0.285400i 0.692655 0.721269i \(-0.256441\pi\)
−0.900010 + 0.435869i \(0.856441\pi\)
\(164\) 219.865i 0.104686i
\(165\) −649.447 + 1313.88i −0.306420 + 0.619911i
\(166\) −443.540 −0.207382
\(167\) 1199.03 + 1650.32i 0.555591 + 0.764705i 0.990758 0.135645i \(-0.0433106\pi\)
−0.435167 + 0.900350i \(0.643311\pi\)
\(168\) −295.734 910.177i −0.135812 0.417986i
\(169\) 1898.92 1104.95i 0.864325 0.502934i
\(170\) −2665.00 1936.24i −1.20233 0.873544i
\(171\) −1402.43 + 1930.28i −0.627174 + 0.863231i
\(172\) 184.065 566.495i 0.0815980 0.251133i
\(173\) −487.393 1500.04i −0.214195 0.659226i −0.999210 0.0397480i \(-0.987344\pi\)
0.785014 0.619478i \(-0.212656\pi\)
\(174\) −361.656 497.777i −0.157570 0.216876i
\(175\) 697.063i 0.301103i
\(176\) 979.056 1003.17i 0.419313 0.429640i
\(177\) 750.389i 0.318659i
\(178\) 123.827 89.9659i 0.0521419 0.0378833i
\(179\) 1020.07 + 3139.47i 0.425944 + 1.31092i 0.902088 + 0.431553i \(0.142034\pi\)
−0.476144 + 0.879368i \(0.657966\pi\)
\(180\) −559.773 181.881i −0.231795 0.0753147i
\(181\) −3858.79 2803.57i −1.58465 1.15131i −0.911111 0.412161i \(-0.864774\pi\)
−0.673537 0.739153i \(-0.735226\pi\)
\(182\) 780.484 + 1197.39i 0.317875 + 0.487673i
\(183\) −537.637 + 1654.68i −0.217176 + 0.668400i
\(184\) 2255.80 732.954i 0.903803 0.293663i
\(185\) 1888.07 1371.77i 0.750346 0.545158i
\(186\) 232.395 0.0916131
\(187\) 2663.70 2729.30i 1.04165 1.06731i
\(188\) 733.434i 0.284528i
\(189\) 1027.71 + 1414.52i 0.395529 + 0.544399i
\(190\) 3977.70 1292.43i 1.51880 0.493489i
\(191\) 0.289707 0.891627i 0.000109751 0.000337779i −0.951002 0.309186i \(-0.899943\pi\)
0.951111 + 0.308848i \(0.0999435\pi\)
\(192\) −1356.30 985.411i −0.509805 0.370395i
\(193\) −216.630 + 298.166i −0.0807947 + 0.111204i −0.847501 0.530793i \(-0.821894\pi\)
0.766707 + 0.641998i \(0.221894\pi\)
\(194\) −34.5174 + 106.234i −0.0127743 + 0.0393151i
\(195\) −1880.58 95.3595i −0.690620 0.0350197i
\(196\) −347.618 + 252.559i −0.126683 + 0.0920405i
\(197\) 1403.57i 0.507614i 0.967255 + 0.253807i \(0.0816828\pi\)
−0.967255 + 0.253807i \(0.918317\pi\)
\(198\) −684.777 + 1385.35i −0.245783 + 0.497236i
\(199\) 2135.37 0.760664 0.380332 0.924850i \(-0.375810\pi\)
0.380332 + 0.924850i \(0.375810\pi\)
\(200\) 779.402 + 1072.76i 0.275560 + 0.379276i
\(201\) −1917.72 + 623.106i −0.672964 + 0.218659i
\(202\) 2871.16 + 932.897i 1.00007 + 0.324942i
\(203\) 661.284 910.179i 0.228636 0.314690i
\(204\) −621.899 451.836i −0.213439 0.155073i
\(205\) 371.167 1142.33i 0.126456 0.389191i
\(206\) −1720.13 + 558.904i −0.581782 + 0.189032i
\(207\) −1401.24 + 1018.06i −0.470497 + 0.341836i
\(208\) 1682.40 + 642.542i 0.560834 + 0.214194i
\(209\) 815.586 + 4772.92i 0.269929 + 1.57966i
\(210\) 1225.02i 0.402544i
\(211\) −2679.22 + 1946.57i −0.874148 + 0.635106i −0.931697 0.363237i \(-0.881672\pi\)
0.0575487 + 0.998343i \(0.481672\pi\)
\(212\) −14.4351 44.4267i −0.00467645 0.0143926i
\(213\) 1130.74 + 367.401i 0.363743 + 0.118187i
\(214\) −1700.35 + 2340.33i −0.543148 + 0.747579i
\(215\) 1912.67 2632.56i 0.606711 0.835066i
\(216\) 3163.22 + 1027.79i 0.996435 + 0.323761i
\(217\) 131.311 + 404.134i 0.0410782 + 0.126426i
\(218\) −3427.84 + 2490.47i −1.06496 + 0.773742i
\(219\) 845.882i 0.261002i
\(220\) −1057.61 + 555.185i −0.324109 + 0.170139i
\(221\) 4577.29 + 1748.16i 1.39322 + 0.532098i
\(222\) −999.206 + 725.966i −0.302083 + 0.219476i
\(223\) 2166.76 704.022i 0.650659 0.211412i 0.0349541 0.999389i \(-0.488872\pi\)
0.615705 + 0.787977i \(0.288872\pi\)
\(224\) 425.569 1309.77i 0.126940 0.390681i
\(225\) −783.359 569.144i −0.232106 0.168635i
\(226\) 2460.44 3386.51i 0.724186 0.996757i
\(227\) 1898.37 + 616.818i 0.555063 + 0.180351i 0.573099 0.819486i \(-0.305741\pi\)
−0.0180354 + 0.999837i \(0.505741\pi\)
\(228\) 928.227 301.599i 0.269620 0.0876048i
\(229\) 3394.71 + 4672.42i 0.979602 + 1.34831i 0.937043 + 0.349213i \(0.113551\pi\)
0.0425590 + 0.999094i \(0.486449\pi\)
\(230\) 3036.10 0.870412
\(231\) 1403.38 + 204.808i 0.399720 + 0.0583349i
\(232\) 2140.13i 0.605631i
\(233\) 4310.92 3132.07i 1.21209 0.880638i 0.216675 0.976244i \(-0.430479\pi\)
0.995419 + 0.0956061i \(0.0304789\pi\)
\(234\) −1982.88 100.547i −0.553953 0.0280896i
\(235\) 1238.15 3810.65i 0.343695 1.05778i
\(236\) 359.467 494.764i 0.0991496 0.136468i
\(237\) −2951.80 2144.61i −0.809031 0.587795i
\(238\) −985.031 + 3031.61i −0.268278 + 0.825673i
\(239\) −6661.51 + 2164.46i −1.80292 + 0.585803i −0.999948 0.0102174i \(-0.996748\pi\)
−0.802969 + 0.596021i \(0.796748\pi\)
\(240\) −907.263 1248.74i −0.244015 0.335858i
\(241\) 3315.33i 0.886139i −0.896487 0.443069i \(-0.853889\pi\)
0.896487 0.443069i \(-0.146111\pi\)
\(242\) 1041.39 + 2958.22i 0.276625 + 0.785790i
\(243\) −3886.75 −1.02607
\(244\) −1147.15 + 833.450i −0.300977 + 0.218673i
\(245\) −2232.45 + 725.367i −0.582147 + 0.189151i
\(246\) −196.429 + 604.546i −0.0509100 + 0.156685i
\(247\) −5211.62 + 3397.04i −1.34254 + 0.875095i
\(248\) 653.954 + 475.126i 0.167444 + 0.121655i
\(249\) −537.765 174.730i −0.136865 0.0444703i
\(250\) −692.728 2132.00i −0.175248 0.539357i
\(251\) 9.88428 7.18135i 0.00248562 0.00180591i −0.586542 0.809919i \(-0.699511\pi\)
0.589027 + 0.808113i \(0.299511\pi\)
\(252\) 569.552i 0.142375i
\(253\) −507.599 + 3478.15i −0.126136 + 0.864307i
\(254\) 3512.03i 0.867576i
\(255\) −2468.38 3397.43i −0.606180 0.834335i
\(256\) −1042.08 3207.18i −0.254413 0.783004i
\(257\) 1406.42 4328.51i 0.341362 1.05060i −0.622141 0.782905i \(-0.713737\pi\)
0.963503 0.267699i \(-0.0862631\pi\)
\(258\) −1012.22 + 1393.20i −0.244256 + 0.336190i
\(259\) −1827.03 1327.42i −0.438326 0.318462i
\(260\) −1194.26 963.748i −0.284866 0.229881i
\(261\) 482.928 + 1486.30i 0.114531 + 0.352489i
\(262\) 1236.86 + 1702.40i 0.291655 + 0.401429i
\(263\) 4555.18 1.06800 0.534001 0.845484i \(-0.320688\pi\)
0.534001 + 0.845484i \(0.320688\pi\)
\(264\) 2388.75 1253.96i 0.556883 0.292332i
\(265\) 255.193i 0.0591561i
\(266\) −2378.88 3274.24i −0.548339 0.754724i
\(267\) 185.575 60.2969i 0.0425356 0.0138206i
\(268\) −1562.93 507.827i −0.356236 0.115748i
\(269\) −2516.48 1828.33i −0.570380 0.414405i 0.264863 0.964286i \(-0.414673\pi\)
−0.835243 + 0.549881i \(0.814673\pi\)
\(270\) 3444.32 + 2502.44i 0.776350 + 0.564052i
\(271\) −5437.70 1766.82i −1.21888 0.396038i −0.372207 0.928150i \(-0.621399\pi\)
−0.846674 + 0.532111i \(0.821399\pi\)
\(272\) 1241.14 + 3819.85i 0.276674 + 0.851516i
\(273\) 474.583 + 1759.23i 0.105213 + 0.390012i
\(274\) 73.0744 0.0161116
\(275\) −1936.98 + 330.986i −0.424742 + 0.0725789i
\(276\) 708.498 0.154517
\(277\) −1828.18 + 1328.25i −0.396552 + 0.288112i −0.768135 0.640288i \(-0.778815\pi\)
0.371583 + 0.928400i \(0.378815\pi\)
\(278\) 5598.57 1819.09i 1.20784 0.392452i
\(279\) −561.379 182.403i −0.120462 0.0391405i
\(280\) 2504.51 3447.17i 0.534547 0.735741i
\(281\) 2927.36 4029.17i 0.621466 0.855375i −0.375993 0.926623i \(-0.622698\pi\)
0.997459 + 0.0712481i \(0.0226982\pi\)
\(282\) −655.256 + 2016.67i −0.138368 + 0.425854i
\(283\) 179.582 + 552.696i 0.0377210 + 0.116093i 0.968144 0.250394i \(-0.0805603\pi\)
−0.930423 + 0.366487i \(0.880560\pi\)
\(284\) 569.548 + 783.916i 0.119002 + 0.163792i
\(285\) 5331.86 1.10818
\(286\) −2956.67 + 2737.34i −0.611299 + 0.565952i
\(287\) −1162.29 −0.239052
\(288\) 1124.44 + 1547.66i 0.230064 + 0.316656i
\(289\) 1858.56 + 5720.07i 0.378295 + 1.16427i
\(290\) 846.535 2605.37i 0.171415 0.527560i
\(291\) −83.7004 + 115.204i −0.0168612 + 0.0232074i
\(292\) 405.212 557.727i 0.0812098 0.111776i
\(293\) 2681.07 + 871.131i 0.534572 + 0.173693i 0.563848 0.825878i \(-0.309320\pi\)
−0.0292764 + 0.999571i \(0.509320\pi\)
\(294\) 1181.46 383.878i 0.234367 0.0761505i
\(295\) 2702.89 1963.77i 0.533453 0.387576i
\(296\) −4295.96 −0.843573
\(297\) −3442.64 + 3527.43i −0.672601 + 0.689165i
\(298\) 5961.68 1.15890
\(299\) −4360.10 + 1176.21i −0.843315 + 0.227499i
\(300\) 122.397 + 376.698i 0.0235553 + 0.0724956i
\(301\) −2994.71 973.040i −0.573463 0.186329i
\(302\) −5016.65 3644.81i −0.955880 0.694488i
\(303\) 3113.60 + 2262.16i 0.590335 + 0.428903i
\(304\) −4849.89 1575.83i −0.915001 0.297302i
\(305\) −7367.13 + 2393.73i −1.38308 + 0.449391i
\(306\) −2602.66 3582.25i −0.486223 0.669228i
\(307\) 4140.36i 0.769716i −0.922976 0.384858i \(-0.874250\pi\)
0.922976 0.384858i \(-0.125750\pi\)
\(308\) 827.195 + 807.313i 0.153032 + 0.149354i
\(309\) −2305.73 −0.424493
\(310\) 608.178 + 837.085i 0.111426 + 0.153365i
\(311\) −571.430 1758.68i −0.104189 0.320661i 0.885350 0.464925i \(-0.153919\pi\)
−0.989539 + 0.144264i \(0.953919\pi\)
\(312\) 2697.40 + 2176.75i 0.489456 + 0.394981i
\(313\) 4944.36 + 3592.29i 0.892881 + 0.648716i 0.936628 0.350326i \(-0.113929\pi\)
−0.0437463 + 0.999043i \(0.513929\pi\)
\(314\) −3338.58 + 4595.16i −0.600022 + 0.825860i
\(315\) −961.495 + 2959.18i −0.171981 + 0.529304i
\(316\) −918.895 2828.07i −0.163582 0.503454i
\(317\) 2226.27 + 3064.20i 0.394447 + 0.542910i 0.959339 0.282255i \(-0.0910824\pi\)
−0.564892 + 0.825165i \(0.691082\pi\)
\(318\) 135.053i 0.0238157i
\(319\) 2843.17 + 1405.37i 0.499019 + 0.246664i
\(320\) 7464.20i 1.30394i
\(321\) −2983.53 + 2167.66i −0.518768 + 0.376907i
\(322\) −907.876 2794.15i −0.157124 0.483578i
\(323\) −13195.0 4287.33i −2.27304 0.738555i
\(324\) −157.561 114.475i −0.0270167 0.0196288i
\(325\) −1378.61 2115.01i −0.235296 0.360983i
\(326\) −534.541 + 1645.15i −0.0908144 + 0.279498i
\(327\) −5137.15 + 1669.16i −0.868761 + 0.282278i
\(328\) −1788.72 + 1299.58i −0.301115 + 0.218773i
\(329\) −3877.22 −0.649720
\(330\) 3404.04 581.674i 0.567836 0.0970305i
\(331\) 1299.67i 0.215820i 0.994161 + 0.107910i \(0.0344158\pi\)
−0.994161 + 0.107910i \(0.965584\pi\)
\(332\) −270.869 372.819i −0.0447767 0.0616298i
\(333\) 2983.50 969.399i 0.490976 0.159528i
\(334\) 1485.30 4571.29i 0.243329 0.748891i
\(335\) −7263.10 5276.95i −1.18455 0.860629i
\(336\) −877.932 + 1208.37i −0.142545 + 0.196196i
\(337\) −3247.72 + 9995.44i −0.524969 + 1.61569i 0.239410 + 0.970919i \(0.423046\pi\)
−0.764378 + 0.644768i \(0.776954\pi\)
\(338\) −4736.24 2089.49i −0.762182 0.336253i
\(339\) 4317.23 3136.65i 0.691681 0.502535i
\(340\) 3422.53i 0.545919i
\(341\) −1060.64 + 556.777i −0.168437 + 0.0884199i
\(342\) 5621.92 0.888884
\(343\) 3944.28 + 5428.83i 0.620907 + 0.854605i
\(344\) −5696.73 + 1850.98i −0.892870 + 0.290111i
\(345\) 3681.09 + 1196.06i 0.574444 + 0.186648i
\(346\) −2184.42 + 3006.60i −0.339408 + 0.467155i
\(347\) −1069.79 777.244i −0.165502 0.120244i 0.501952 0.864896i \(-0.332616\pi\)
−0.667453 + 0.744652i \(0.732616\pi\)
\(348\) 197.545 607.982i 0.0304297 0.0936531i
\(349\) 7163.78 2327.65i 1.09876 0.357010i 0.297137 0.954835i \(-0.403968\pi\)
0.801627 + 0.597825i \(0.203968\pi\)
\(350\) 1328.77 965.410i 0.202931 0.147438i
\(351\) −5915.81 2259.36i −0.899608 0.343578i
\(352\) 3841.61 + 560.642i 0.581701 + 0.0848930i
\(353\) 10836.3i 1.63387i 0.576728 + 0.816936i \(0.304329\pi\)
−0.576728 + 0.816936i \(0.695671\pi\)
\(354\) −1430.42 + 1039.26i −0.214763 + 0.156035i
\(355\) 1635.78 + 5034.42i 0.244559 + 0.752674i
\(356\) 151.242 + 49.1416i 0.0225163 + 0.00731601i
\(357\) −2388.58 + 3287.60i −0.354109 + 0.487389i
\(358\) 4571.82 6292.57i 0.674939 0.928974i
\(359\) 11578.5 + 3762.08i 1.70220 + 0.553078i 0.989004 0.147887i \(-0.0472472\pi\)
0.713195 + 0.700965i \(0.247247\pi\)
\(360\) 1829.02 + 5629.14i 0.267772 + 0.824116i
\(361\) 8702.03 6322.40i 1.26870 0.921767i
\(362\) 11238.6i 1.63174i
\(363\) 97.2510 + 3996.91i 0.0140616 + 0.577915i
\(364\) −529.830 + 1387.28i −0.0762929 + 0.199762i
\(365\) 3046.86 2213.67i 0.436931 0.317449i
\(366\) 3898.83 1266.81i 0.556817 0.180921i
\(367\) −2889.59 + 8893.25i −0.410996 + 1.26492i 0.504788 + 0.863244i \(0.331571\pi\)
−0.915784 + 0.401672i \(0.868429\pi\)
\(368\) −2994.85 2175.88i −0.424231 0.308222i
\(369\) 948.996 1306.18i 0.133883 0.184274i
\(370\) −5229.84 1699.28i −0.734829 0.238760i
\(371\) −234.856 + 76.3095i −0.0328656 + 0.0106787i
\(372\) 141.923 + 195.340i 0.0197806 + 0.0272256i
\(373\) −86.3592 −0.0119880 −0.00599398 0.999982i \(-0.501908\pi\)
−0.00599398 + 0.999982i \(0.501908\pi\)
\(374\) −8891.87 1297.67i −1.22938 0.179415i
\(375\) 2857.81i 0.393538i
\(376\) −5966.90 + 4335.21i −0.818402 + 0.594604i
\(377\) −206.354 + 4069.49i −0.0281903 + 0.555939i
\(378\) 1273.08 3918.14i 0.173228 0.533141i
\(379\) 4887.30 6726.79i 0.662384 0.911694i −0.337173 0.941443i \(-0.609471\pi\)
0.999557 + 0.0297490i \(0.00947081\pi\)
\(380\) 3515.53 + 2554.18i 0.474586 + 0.344807i
\(381\) 1383.55 4258.12i 0.186040 0.572572i
\(382\) −2.10089 + 0.682622i −0.000281390 + 9.14292e-5i
\(383\) −1362.30 1875.05i −0.181751 0.250158i 0.708414 0.705797i \(-0.249411\pi\)
−0.890165 + 0.455639i \(0.849411\pi\)
\(384\) 1393.00i 0.185121i
\(385\) 2934.92 + 5590.93i 0.388513 + 0.740105i
\(386\) 868.402 0.114509
\(387\) 3538.65 2570.98i 0.464805 0.337701i
\(388\) −110.375 + 35.8629i −0.0144418 + 0.00469243i
\(389\) −167.108 + 514.306i −0.0217808 + 0.0670343i −0.961356 0.275308i \(-0.911220\pi\)
0.939575 + 0.342342i \(0.111220\pi\)
\(390\) 2422.76 + 3716.91i 0.314567 + 0.482598i
\(391\) −8148.03 5919.89i −1.05387 0.765683i
\(392\) 4109.42 + 1335.23i 0.529482 + 0.172039i
\(393\) 828.970 + 2551.31i 0.106402 + 0.327472i
\(394\) 2675.54 1943.89i 0.342111 0.248558i
\(395\) 16244.8i 2.06928i
\(396\) −1582.65 + 270.440i −0.200837 + 0.0343185i
\(397\) 7613.80i 0.962533i 0.876574 + 0.481266i \(0.159823\pi\)
−0.876574 + 0.481266i \(0.840177\pi\)
\(398\) −2957.41 4070.53i −0.372467 0.512656i
\(399\) −1594.37 4906.96i −0.200046 0.615678i
\(400\) 639.511 1968.21i 0.0799389 0.246027i
\(401\) 9030.35 12429.2i 1.12457 1.54784i 0.326588 0.945167i \(-0.394101\pi\)
0.797986 0.602676i \(-0.205899\pi\)
\(402\) 3843.78 + 2792.67i 0.476891 + 0.346482i
\(403\) −1197.69 966.513i −0.148043 0.119468i
\(404\) 969.261 + 2983.08i 0.119363 + 0.367361i
\(405\) −625.377 860.758i −0.0767290 0.105608i
\(406\) −2650.88 −0.324042
\(407\) 2821.06 5707.20i 0.343574 0.695075i
\(408\) 7730.22i 0.937997i
\(409\) 1778.27 + 2447.58i 0.214987 + 0.295905i 0.902867 0.429920i \(-0.141458\pi\)
−0.687880 + 0.725825i \(0.741458\pi\)
\(410\) −2691.62 + 874.562i −0.324219 + 0.105345i
\(411\) 88.5982 + 28.7873i 0.0106332 + 0.00345492i
\(412\) −1520.27 1104.54i −0.181792 0.132079i
\(413\) −2615.51 1900.28i −0.311625 0.226408i
\(414\) 3881.34 + 1261.12i 0.460767 + 0.149712i
\(415\) −777.953 2394.29i −0.0920198 0.283208i
\(416\) 1299.13 + 4815.72i 0.153113 + 0.567573i
\(417\) 7504.55 0.881293
\(418\) 7968.80 8165.05i 0.932456 0.955420i
\(419\) 13631.4 1.58935 0.794677 0.607033i \(-0.207640\pi\)
0.794677 + 0.607033i \(0.207640\pi\)
\(420\) 1029.69 748.114i 0.119628 0.0869148i
\(421\) 20.9177 6.79658i 0.00242154 0.000786805i −0.307806 0.951449i \(-0.599595\pi\)
0.310228 + 0.950662i \(0.399595\pi\)
\(422\) 7421.27 + 2411.32i 0.856071 + 0.278154i
\(423\) 3165.70 4357.21i 0.363881 0.500839i
\(424\) −276.112 + 380.036i −0.0316255 + 0.0435287i
\(425\) 1739.91 5354.89i 0.198583 0.611177i
\(426\) −865.688 2664.31i −0.0984571 0.303020i
\(427\) 4405.94 + 6064.25i 0.499340 + 0.687283i
\(428\) −3005.57 −0.339439
\(429\) −4663.14 + 2154.09i −0.524799 + 0.242425i
\(430\) −7667.29 −0.859883
\(431\) −33.0621 45.5061i −0.00369500 0.00508574i 0.807165 0.590325i \(-0.201000\pi\)
−0.810860 + 0.585239i \(0.801000\pi\)
\(432\) −1604.09 4936.88i −0.178650 0.549828i
\(433\) 885.094 2724.04i 0.0982330 0.302330i −0.889850 0.456254i \(-0.849191\pi\)
0.988083 + 0.153924i \(0.0491910\pi\)
\(434\) 588.516 810.023i 0.0650914 0.0895907i
\(435\) 2052.74 2825.36i 0.226256 0.311415i
\(436\) −4186.74 1360.35i −0.459882 0.149425i
\(437\) 12161.5 3951.51i 1.33127 0.432555i
\(438\) −1612.46 + 1171.52i −0.175905 + 0.127802i
\(439\) 12323.2 1.33975 0.669877 0.742472i \(-0.266347\pi\)
0.669877 + 0.742472i \(0.266347\pi\)
\(440\) 10768.1 + 5322.64i 1.16670 + 0.576698i
\(441\) −3155.25 −0.340703
\(442\) −3006.98 11146.6i −0.323592 1.19952i
\(443\) 472.218 + 1453.34i 0.0506451 + 0.155869i 0.973180 0.230043i \(-0.0738867\pi\)
−0.922535 + 0.385912i \(0.873887\pi\)
\(444\) −1220.42 396.540i −0.130448 0.0423850i
\(445\) 702.838 + 510.642i 0.0748713 + 0.0543972i
\(446\) −4342.93 3155.32i −0.461084 0.334997i
\(447\) 7228.18 + 2348.58i 0.764834 + 0.248510i
\(448\) −6869.38 + 2232.00i −0.724437 + 0.235384i
\(449\) −799.912 1100.98i −0.0840762 0.115721i 0.764907 0.644141i \(-0.222785\pi\)
−0.848983 + 0.528420i \(0.822785\pi\)
\(450\) 2281.52i 0.239004i
\(451\) −551.890 3229.74i −0.0576219 0.337211i
\(452\) 4349.12 0.452578
\(453\) −4646.53 6395.39i −0.481927 0.663315i
\(454\) −1453.38 4473.04i −0.150243 0.462401i
\(455\) −5094.74 + 6313.34i −0.524935 + 0.650493i
\(456\) −7940.27 5768.94i −0.815432 0.592446i
\(457\) −9677.95 + 13320.6i −0.990625 + 1.36348i −0.0597207 + 0.998215i \(0.519021\pi\)
−0.930904 + 0.365263i \(0.880979\pi\)
\(458\) 4205.21 12942.3i 0.429032 1.32042i
\(459\) −4364.22 13431.7i −0.443801 1.36588i
\(460\) 1854.14 + 2552.00i 0.187934 + 0.258669i
\(461\) 6218.34i 0.628237i −0.949384 0.314118i \(-0.898291\pi\)
0.949384 0.314118i \(-0.101709\pi\)
\(462\) −1553.22 2958.83i −0.156412 0.297960i
\(463\) 5055.65i 0.507464i −0.967275 0.253732i \(-0.918342\pi\)
0.967275 0.253732i \(-0.0816581\pi\)
\(464\) −2702.22 + 1963.28i −0.270361 + 0.196429i
\(465\) 407.613 + 1254.50i 0.0406507 + 0.125110i
\(466\) −11941.0 3879.86i −1.18703 0.385689i
\(467\) 11288.1 + 8201.28i 1.11852 + 0.812655i 0.983985 0.178253i \(-0.0570446\pi\)
0.134539 + 0.990908i \(0.457045\pi\)
\(468\) −1126.42 1728.12i −0.111259 0.170689i
\(469\) −2684.57 + 8262.25i −0.264311 + 0.813466i
\(470\) −8978.83 + 2917.40i −0.881197 + 0.286318i
\(471\) −5858.07 + 4256.13i −0.573090 + 0.416374i
\(472\) −6149.93 −0.599732
\(473\) 1281.88 8783.63i 0.124611 0.853852i
\(474\) 8597.08i 0.833074i
\(475\) 4201.93 + 5783.46i 0.405890 + 0.558659i
\(476\) −3149.79 + 1023.43i −0.303299 + 0.0985477i
\(477\) 106.001 326.237i 0.0101749 0.0313153i
\(478\) 13352.0 + 9700.76i 1.27762 + 0.928248i
\(479\) −3143.26 + 4326.33i −0.299832 + 0.412683i −0.932176 0.362004i \(-0.882093\pi\)
0.632345 + 0.774687i \(0.282093\pi\)
\(480\) 1321.04 4065.75i 0.125619 0.386615i
\(481\) 8168.82 + 414.221i 0.774358 + 0.0392658i
\(482\) −6319.84 + 4591.63i −0.597222 + 0.433907i
\(483\) 3745.39i 0.352839i
\(484\) −1850.56 + 2681.92i −0.173794 + 0.251871i
\(485\) −634.007 −0.0593583
\(486\) 5383.03 + 7409.10i 0.502426 + 0.691530i
\(487\) −12108.8 + 3934.40i −1.12670 + 0.366088i −0.812322 0.583209i \(-0.801797\pi\)
−0.314381 + 0.949297i \(0.601797\pi\)
\(488\) 13561.2 + 4406.29i 1.25796 + 0.408736i
\(489\) −1296.20 + 1784.06i −0.119869 + 0.164986i
\(490\) 4474.60 + 3250.99i 0.412534 + 0.299724i
\(491\) −3227.63 + 9933.62i −0.296662 + 0.913031i 0.685997 + 0.727605i \(0.259367\pi\)
−0.982658 + 0.185426i \(0.940633\pi\)
\(492\) −628.111 + 204.086i −0.0575558 + 0.0187010i
\(493\) −7351.89 + 5341.46i −0.671628 + 0.487966i
\(494\) 13693.5 + 5229.82i 1.24717 + 0.476317i
\(495\) −8679.41 1266.67i −0.788102 0.115015i
\(496\) 1261.57i 0.114206i
\(497\) 4144.08 3010.85i 0.374019 0.271741i
\(498\) 411.708 + 1267.11i 0.0370464 + 0.114017i
\(499\) −16165.0 5252.34i −1.45019 0.471196i −0.525134 0.851020i \(-0.675985\pi\)
−0.925059 + 0.379824i \(0.875985\pi\)
\(500\) 1369.01 1884.28i 0.122448 0.168535i
\(501\) 3601.67 4957.28i 0.321179 0.442065i
\(502\) −27.3788 8.89592i −0.00243422 0.000790925i
\(503\) 267.168 + 822.260i 0.0236828 + 0.0728882i 0.962199 0.272346i \(-0.0877995\pi\)
−0.938517 + 0.345234i \(0.887800\pi\)
\(504\) 4633.63 3366.53i 0.409520 0.297534i
\(505\) 17135.2i 1.50991i
\(506\) 7333.22 3849.52i 0.644272 0.338206i
\(507\) −4919.26 4399.20i −0.430911 0.385356i
\(508\) 2952.04 2144.79i 0.257826 0.187322i
\(509\) 20399.3 6628.14i 1.77639 0.577185i 0.777716 0.628616i \(-0.216378\pi\)
0.998677 + 0.0514313i \(0.0163783\pi\)
\(510\) −3057.71 + 9410.67i −0.265486 + 0.817081i
\(511\) −2948.36 2142.11i −0.255240 0.185443i
\(512\) −6851.08 + 9429.70i −0.591363 + 0.813941i
\(513\) 17053.6 + 5541.06i 1.46771 + 0.476888i
\(514\) −10199.1 + 3313.87i −0.875216 + 0.284375i
\(515\) −6034.09 8305.22i −0.516299 0.710624i
\(516\) −1789.22 −0.152647
\(517\) −1841.02 10773.9i −0.156611 0.916508i
\(518\) 5321.21i 0.451352i
\(519\) −3832.91 + 2784.77i −0.324174 + 0.235526i
\(520\) −781.534 + 15412.6i −0.0659087 + 1.29978i
\(521\) −4999.79 + 15387.8i −0.420431 + 1.29395i 0.486870 + 0.873474i \(0.338138\pi\)
−0.907302 + 0.420480i \(0.861862\pi\)
\(522\) 2164.41 2979.06i 0.181482 0.249789i
\(523\) 3798.03 + 2759.43i 0.317545 + 0.230710i 0.735127 0.677929i \(-0.237122\pi\)
−0.417582 + 0.908639i \(0.637122\pi\)
\(524\) −675.604 + 2079.30i −0.0563243 + 0.173348i
\(525\) 1991.37 647.036i 0.165544 0.0537885i
\(526\) −6308.78 8683.29i −0.522958 0.719790i
\(527\) 3432.34i 0.283710i
\(528\) −3774.65 1865.80i −0.311118 0.153785i
\(529\) −2884.35 −0.237063
\(530\) −486.460 + 353.434i −0.0398688 + 0.0289664i
\(531\) 4271.07 1387.75i 0.349056 0.113415i
\(532\) 1299.40 3999.14i 0.105895 0.325911i
\(533\) 3526.59 2298.71i 0.286592 0.186807i
\(534\) −371.956 270.242i −0.0301425 0.0218998i
\(535\) −15615.8 5073.89i −1.26193 0.410025i
\(536\) 5106.76 + 15717.0i 0.411527 + 1.26655i
\(537\) 8021.98 5828.31i 0.644644 0.468362i
\(538\) 7329.19i 0.587331i
\(539\) −4472.42 + 4582.57i −0.357404 + 0.366206i
\(540\) 4423.37i 0.352503i
\(541\) −13865.2 19083.7i −1.10187 1.51659i −0.832888 0.553442i \(-0.813314\pi\)
−0.268978 0.963146i \(-0.586686\pi\)
\(542\) 4163.06 + 12812.6i 0.329924 + 1.01540i
\(543\) −4427.41 + 13626.2i −0.349905 + 1.07690i
\(544\) −6538.51 + 8999.49i −0.515324 + 0.709283i
\(545\) −19456.2 14135.8i −1.52920 1.11103i
\(546\) 2696.24 3341.15i 0.211334 0.261882i
\(547\) −2832.00 8715.99i −0.221366 0.681296i −0.998640 0.0521331i \(-0.983398\pi\)
0.777274 0.629163i \(-0.216602\pi\)
\(548\) 44.6263 + 61.4229i 0.00347873 + 0.00478806i
\(549\) −10412.4 −0.809454
\(550\) 3313.59 + 3233.94i 0.256894 + 0.250720i
\(551\) 11537.9i 0.892072i
\(552\) −4187.81 5764.03i −0.322908 0.444445i
\(553\) −14950.3 + 4857.63i −1.14964 + 0.373540i
\(554\) 5063.95 + 1645.38i 0.388351 + 0.126183i
\(555\) −5671.44 4120.54i −0.433765 0.315148i
\(556\) 4948.07 + 3594.99i 0.377419 + 0.274211i
\(557\) −12996.7 4222.89i −0.988668 0.321238i −0.230340 0.973110i \(-0.573984\pi\)
−0.758329 + 0.651873i \(0.773984\pi\)
\(558\) 429.787 + 1322.75i 0.0326063 + 0.100352i
\(559\) 11010.9 2970.38i 0.833114 0.224747i
\(560\) −6650.09 −0.501817
\(561\) −10269.6 5076.26i −0.772877 0.382032i
\(562\) −11734.9 −0.880795
\(563\) −7461.67 + 5421.22i −0.558564 + 0.405821i −0.830933 0.556372i \(-0.812193\pi\)
0.272369 + 0.962193i \(0.412193\pi\)
\(564\) −2095.28 + 680.798i −0.156431 + 0.0508276i
\(565\) 22596.4 + 7342.01i 1.68254 + 0.546691i
\(566\) 804.859 1107.79i 0.0597716 0.0822686i
\(567\) −605.159 + 832.930i −0.0448224 + 0.0616927i
\(568\) 3011.09 9267.19i 0.222434 0.684582i
\(569\) −2526.23 7774.95i −0.186125 0.572834i 0.813841 0.581088i \(-0.197373\pi\)
−0.999966 + 0.00825362i \(0.997373\pi\)
\(570\) −7384.46 10163.8i −0.542633 0.746870i
\(571\) −13990.3 −1.02535 −0.512675 0.858582i \(-0.671346\pi\)
−0.512675 + 0.858582i \(0.671346\pi\)
\(572\) −4106.51 813.552i −0.300178 0.0594691i
\(573\) −2.81612 −0.000205314
\(574\) 1609.73 + 2215.61i 0.117054 + 0.161111i
\(575\) 1603.63 + 4935.45i 0.116306 + 0.357952i
\(576\) 3100.45 9542.20i 0.224280 0.690264i
\(577\) −6829.32 + 9399.75i −0.492735 + 0.678192i −0.980890 0.194565i \(-0.937670\pi\)
0.488154 + 0.872757i \(0.337670\pi\)
\(578\) 8329.81 11465.0i 0.599437 0.825054i
\(579\) 1052.88 + 342.103i 0.0755723 + 0.0245549i
\(580\) 2706.92 879.533i 0.193791 0.0629666i
\(581\) −1970.86 + 1431.92i −0.140732 + 0.102248i
\(582\) 335.529 0.0238971
\(583\) −323.563 616.378i −0.0229856 0.0437869i
\(584\) −6932.56 −0.491218
\(585\) −2935.13 10880.2i −0.207441 0.768962i
\(586\) −2052.60 6317.26i −0.144697 0.445330i
\(587\) 3676.54 + 1194.58i 0.258513 + 0.0839958i 0.435406 0.900234i \(-0.356605\pi\)
−0.176893 + 0.984230i \(0.556605\pi\)
\(588\) 1044.18 + 758.643i 0.0732336 + 0.0532073i
\(589\) 3525.61 + 2561.51i 0.246639 + 0.179194i
\(590\) −7486.84 2432.62i −0.522421 0.169745i
\(591\) 4009.71 1302.84i 0.279082 0.0906793i
\(592\) 3940.96 + 5424.26i 0.273602 + 0.376581i
\(593\) 20857.4i 1.44437i 0.691700 + 0.722185i \(0.256862\pi\)
−0.691700 + 0.722185i \(0.743138\pi\)
\(594\) 11492.1 + 1677.15i 0.793815 + 0.115849i
\(595\) −18092.8 −1.24661
\(596\) 3640.78 + 5011.11i 0.250222 + 0.344401i
\(597\) −1982.12 6100.33i −0.135884 0.418207i
\(598\) 8280.75 + 6682.41i 0.566263 + 0.456963i
\(599\) 21270.2 + 15453.7i 1.45088 + 1.05412i 0.985625 + 0.168945i \(0.0540361\pi\)
0.465252 + 0.885178i \(0.345964\pi\)
\(600\) 2341.19 3222.37i 0.159298 0.219254i
\(601\) −777.825 + 2393.90i −0.0527923 + 0.162478i −0.973977 0.226649i \(-0.927223\pi\)
0.921184 + 0.389127i \(0.127223\pi\)
\(602\) 2292.72 + 7056.28i 0.155223 + 0.477728i
\(603\) −7093.20 9762.95i −0.479034 0.659333i
\(604\) 6442.64i 0.434018i
\(605\) −14142.3 + 10810.2i −0.950358 + 0.726441i
\(606\) 9068.29i 0.607878i
\(607\) 22265.6 16176.9i 1.48885 1.08171i 0.514281 0.857622i \(-0.328059\pi\)
0.974568 0.224091i \(-0.0719413\pi\)
\(608\) −4364.44 13432.4i −0.291121 0.895977i
\(609\) −3214.03 1044.30i −0.213857 0.0694864i
\(610\) 14766.3 + 10728.3i 0.980112 + 0.712093i
\(611\) 11764.1 7668.12i 0.778930 0.507723i
\(612\) 1421.64 4375.34i 0.0938990 0.288991i
\(613\) 2341.34 760.747i 0.154267 0.0501244i −0.230865 0.972986i \(-0.574156\pi\)
0.385133 + 0.922861i \(0.374156\pi\)
\(614\) −7892.54 + 5734.26i −0.518757 + 0.376899i
\(615\) −3607.96 −0.236564
\(616\) 1678.53 11501.6i 0.109789 0.752293i
\(617\) 13863.2i 0.904556i −0.891877 0.452278i \(-0.850612\pi\)
0.891877 0.452278i \(-0.149388\pi\)
\(618\) 3193.36 + 4395.28i 0.207857 + 0.286091i
\(619\) −3488.44 + 1133.46i −0.226514 + 0.0735990i −0.420075 0.907489i \(-0.637996\pi\)
0.193561 + 0.981088i \(0.437996\pi\)
\(620\) −332.202 + 1022.41i −0.0215186 + 0.0662275i
\(621\) 10530.7 + 7651.03i 0.680490 + 0.494405i
\(622\) −2561.06 + 3525.00i −0.165095 + 0.227234i
\(623\) 259.781 799.525i 0.0167061 0.0514162i
\(624\) 273.959 5402.72i 0.0175755 0.346606i
\(625\) 15740.8 11436.3i 1.00741 0.731925i
\(626\) 14400.4i 0.919416i
\(627\) 12878.3 6760.35i 0.820268 0.430594i
\(628\) −5901.34 −0.374983
\(629\) 10722.1 + 14757.7i 0.679679 + 0.935498i
\(630\) 6972.56 2265.52i 0.440942 0.143271i
\(631\) 1685.34 + 547.600i 0.106327 + 0.0345477i 0.361697 0.932296i \(-0.382197\pi\)
−0.255370 + 0.966843i \(0.582197\pi\)
\(632\) −17576.5 + 24192.0i −1.10626 + 1.52263i
\(633\) 8047.91 + 5847.15i 0.505333 + 0.367146i
\(634\) 2757.80 8487.63i 0.172754 0.531682i
\(635\) 18958.4 6159.97i 1.18479 0.384962i
\(636\) −113.519 + 82.4765i −0.00707756 + 0.00514215i
\(637\) −7685.37 2935.19i −0.478030 0.182569i
\(638\) −1258.72 7366.18i −0.0781082 0.457100i
\(639\) 7115.44i 0.440505i
\(640\) −5017.58 + 3645.48i −0.309902 + 0.225157i
\(641\) −3954.62 12171.1i −0.243679 0.749966i −0.995851 0.0909993i \(-0.970994\pi\)
0.752172 0.658966i \(-0.229006\pi\)
\(642\) 8264.20 + 2685.20i 0.508040 + 0.165072i
\(643\) −12942.2 + 17813.4i −0.793764 + 1.09252i 0.199865 + 0.979824i \(0.435950\pi\)
−0.993629 + 0.112700i \(0.964050\pi\)
\(644\) 1794.20 2469.50i 0.109785 0.151105i
\(645\) −9296.12 3020.49i −0.567495 0.184390i
\(646\) 10102.0 + 31090.8i 0.615260 + 1.89358i
\(647\) −11489.9 + 8347.90i −0.698167 + 0.507248i −0.879335 0.476204i \(-0.842012\pi\)
0.181167 + 0.983452i \(0.442012\pi\)
\(648\) 1958.49i 0.118730i
\(649\) 4038.52 8170.21i 0.244261 0.494158i
\(650\) −2122.40 + 5557.18i −0.128073 + 0.335339i
\(651\) 1032.64 750.260i 0.0621698 0.0451690i
\(652\) −1709.28 + 555.378i −0.102669 + 0.0333593i
\(653\) 8350.10 25699.0i 0.500405 1.54009i −0.307955 0.951401i \(-0.599645\pi\)
0.808361 0.588688i \(-0.200355\pi\)
\(654\) 10296.6 + 7480.93i 0.615641 + 0.447290i
\(655\) −7020.37 + 9662.71i −0.418792 + 0.576417i
\(656\) 3281.82 + 1066.33i 0.195325 + 0.0634651i
\(657\) 4814.60 1564.36i 0.285899 0.0928941i
\(658\) 5369.82 + 7390.92i 0.318142 + 0.437885i
\(659\) 1957.86 0.115732 0.0578661 0.998324i \(-0.481570\pi\)
0.0578661 + 0.998324i \(0.481570\pi\)
\(660\) 2567.76 + 2506.04i 0.151439 + 0.147799i
\(661\) 12936.0i 0.761198i −0.924740 0.380599i \(-0.875718\pi\)
0.924740 0.380599i \(-0.124282\pi\)
\(662\) 2477.49 1800.00i 0.145454 0.105678i
\(663\) 745.356 14699.1i 0.0436610 0.861035i
\(664\) −1432.03 + 4407.34i −0.0836951 + 0.257587i
\(665\) 13502.4 18584.4i 0.787368 1.08372i
\(666\) −5979.97 4344.70i −0.347927 0.252784i
\(667\) 2588.22 7965.71i 0.150249 0.462419i
\(668\) 4749.48 1543.20i 0.275094 0.0893834i
\(669\) −4022.51 5536.51i −0.232465 0.319961i
\(670\) 21153.7i 1.21976i
\(671\) −14759.1 + 15122.6i −0.849133 + 0.870045i
\(672\) −4136.78 −0.237470
\(673\) −4827.35 + 3507.27i −0.276494 + 0.200885i −0.717387 0.696675i \(-0.754662\pi\)
0.440893 + 0.897560i \(0.354662\pi\)
\(674\) 23551.7 7652.43i 1.34596 0.437330i
\(675\) −2248.71 + 6920.80i −0.128226 + 0.394640i
\(676\) −1136.08 5257.11i −0.0646382 0.299107i
\(677\) 19306.9 + 14027.3i 1.09605 + 0.796326i 0.980411 0.196965i \(-0.0631086\pi\)
0.115639 + 0.993291i \(0.463109\pi\)
\(678\) −11958.4 3885.54i −0.677377 0.220093i
\(679\) 189.585 + 583.483i 0.0107152 + 0.0329779i
\(680\) −27844.2 + 20230.0i −1.57026 + 1.14086i
\(681\) 5995.83i 0.337387i
\(682\) 2530.31 + 1250.73i 0.142068 + 0.0702241i
\(683\) 3289.66i 0.184298i 0.995745 + 0.0921490i \(0.0293736\pi\)
−0.995745 + 0.0921490i \(0.970626\pi\)
\(684\) 3433.29 + 4725.52i 0.191923 + 0.264159i
\(685\) 128.170 + 394.466i 0.00714908 + 0.0220026i
\(686\) 4885.99 15037.5i 0.271936 0.836932i
\(687\) 10197.1 14035.1i 0.566294 0.779437i
\(688\) 7563.10 + 5494.91i 0.419100 + 0.304494i
\(689\) 561.675 696.020i 0.0310568 0.0384852i
\(690\) −2818.21 8673.55i −0.155489 0.478546i
\(691\) 6387.32 + 8791.40i 0.351643 + 0.483995i 0.947797 0.318875i \(-0.103305\pi\)
−0.596154 + 0.802870i \(0.703305\pi\)
\(692\) −3861.23 −0.212112
\(693\) 1429.65 + 8366.52i 0.0783664 + 0.458611i
\(694\) 3115.73i 0.170420i
\(695\) 19639.4 + 27031.3i 1.07189 + 1.47533i
\(696\) −6113.94 + 1986.54i −0.332971 + 0.108189i
\(697\) 8928.80 + 2901.14i 0.485226 + 0.157659i
\(698\) −14358.7 10432.2i −0.778631 0.565709i
\(699\) −12949.2 9408.18i −0.700695 0.509084i
\(700\) 1622.96 + 527.330i 0.0876313 + 0.0284731i
\(701\) −6461.11 19885.2i −0.348121 1.07141i −0.959892 0.280371i \(-0.909543\pi\)
0.611771 0.791035i \(-0.290457\pi\)
\(702\) 3886.30 + 14406.1i 0.208945 + 0.774536i
\(703\) −23160.5 −1.24255
\(704\) −9463.98 18028.6i −0.506658 0.965168i
\(705\) −12035.6 −0.642959
\(706\) 20656.6 15007.9i 1.10116 0.800042i
\(707\) 15769.7 5123.89i 0.838870 0.272565i
\(708\) −1747.11 567.671i −0.0927409 0.0301333i
\(709\) 8762.34 12060.3i 0.464142 0.638836i −0.511220 0.859450i \(-0.670806\pi\)
0.975361 + 0.220614i \(0.0708061\pi\)
\(710\) 7331.33 10090.7i 0.387521 0.533377i
\(711\) 6747.71 20767.3i 0.355919 1.09541i
\(712\) −494.173 1520.91i −0.0260111 0.0800540i
\(713\) 1859.46 + 2559.32i 0.0976679 + 0.134428i
\(714\) 9575.06 0.501874
\(715\) −19962.4 11159.3i −1.04413 0.583687i
\(716\) 8081.24 0.421802
\(717\) 12366.9 + 17021.5i 0.644140 + 0.886583i
\(718\) −8864.40 27281.8i −0.460747 1.41803i
\(719\) −10114.9 + 31130.3i −0.524646 + 1.61469i 0.240369 + 0.970682i \(0.422732\pi\)
−0.765015 + 0.644013i \(0.777268\pi\)
\(720\) 5429.72 7473.36i 0.281047 0.386828i
\(721\) −5839.02 + 8036.72i −0.301604 + 0.415122i
\(722\) −24104.1 7831.89i −1.24247 0.403702i
\(723\) −9471.27 + 3077.40i −0.487193 + 0.158298i
\(724\) −9446.68 + 6863.41i −0.484921 + 0.352316i
\(725\) 4682.38 0.239861
\(726\) 7484.39 5720.97i 0.382606 0.292459i
\(727\) 26471.9 1.35047 0.675234 0.737604i \(-0.264043\pi\)
0.675234 + 0.737604i \(0.264043\pi\)
\(728\) 14418.0 3889.52i 0.734022 0.198015i
\(729\) 2944.05 + 9060.85i 0.149573 + 0.460339i
\(730\) −8439.61 2742.19i −0.427896 0.139032i
\(731\) 20576.8 + 14949.9i 1.04112 + 0.756420i
\(732\) 3445.82 + 2503.54i 0.173991 + 0.126412i
\(733\) −12469.7 4051.66i −0.628349 0.204163i −0.0225052 0.999747i \(-0.507164\pi\)
−0.605843 + 0.795584i \(0.707164\pi\)
\(734\) 20954.7 6808.60i 1.05375 0.342384i
\(735\) 4144.46 + 5704.37i 0.207988 + 0.286270i
\(736\) 10252.7i 0.513476i
\(737\) −24233.6 3536.63i −1.21120 0.176762i
\(738\) −3804.23 −0.189750
\(739\) 12922.7 + 17786.5i 0.643259 + 0.885370i 0.998784 0.0492969i \(-0.0156981\pi\)
−0.355525 + 0.934667i \(0.615698\pi\)
\(740\) −1765.52 5433.71i −0.0877050 0.269928i
\(741\) 14542.3 + 11735.3i 0.720950 + 0.581792i
\(742\) 470.733 + 342.008i 0.0232900 + 0.0169212i
\(743\) −16104.7 + 22166.2i −0.795185 + 1.09448i 0.198258 + 0.980150i \(0.436472\pi\)
−0.993443 + 0.114328i \(0.963528\pi\)
\(744\) 750.320 2309.25i 0.0369732 0.113792i
\(745\) 10456.6 + 32182.0i 0.514228 + 1.58263i
\(746\) 119.605 + 164.622i 0.00587003 + 0.00807940i
\(747\) 3384.00i 0.165748i
\(748\) −4339.48 8266.57i −0.212122 0.404085i
\(749\) 15888.6i 0.775110i
\(750\) −5447.69 + 3957.98i −0.265229 + 0.192700i
\(751\) 10619.2 + 32682.4i 0.515977 + 1.58801i 0.781498 + 0.623908i \(0.214456\pi\)
−0.265521 + 0.964105i \(0.585544\pi\)
\(752\) 10947.6 + 3557.10i 0.530876 + 0.172492i
\(753\) −29.6906 21.5715i −0.00143690 0.00104397i
\(754\) 8043.23 5242.75i 0.388484 0.253222i
\(755\) 10876.2 33473.5i 0.524272 1.61354i
\(756\) 4070.87 1322.71i 0.195841 0.0636327i
\(757\) 12226.3 8882.95i 0.587019 0.426494i −0.254229 0.967144i \(-0.581822\pi\)
0.841248 + 0.540650i \(0.181822\pi\)
\(758\) −19591.7 −0.938787
\(759\) 10407.6 1778.42i 0.497722 0.0850496i
\(760\) 43698.1i 2.08565i
\(761\) −16035.5 22071.0i −0.763847 1.05135i −0.996884 0.0788778i \(-0.974866\pi\)
0.233037 0.972468i \(-0.425134\pi\)
\(762\) −10033.2 + 3259.98i −0.476987 + 0.154982i
\(763\) −7191.36 + 22132.7i −0.341212 + 1.05014i
\(764\) −1.85679 1.34904i −8.79271e−5 6.38827e-5i
\(765\) 14772.6 20332.7i 0.698174 0.960954i
\(766\) −1687.56 + 5193.77i −0.0796005 + 0.244985i
\(767\) 11694.2 + 592.983i 0.550524 + 0.0279157i
\(768\) −8195.01 + 5954.02i −0.385042 + 0.279749i
\(769\) 27744.9i 1.30105i 0.759486 + 0.650524i \(0.225451\pi\)
−0.759486 + 0.650524i \(0.774549\pi\)
\(770\) 6592.91 13337.9i 0.308561 0.624241i
\(771\) −13671.2 −0.638595
\(772\) 530.331 + 729.938i 0.0247241 + 0.0340298i
\(773\) 13819.4 4490.21i 0.643015 0.208928i 0.0306833 0.999529i \(-0.490232\pi\)
0.612332 + 0.790601i \(0.290232\pi\)
\(774\) −9801.83 3184.81i −0.455193 0.147901i
\(775\) −1039.53 + 1430.78i −0.0481818 + 0.0663165i
\(776\) 944.171 + 685.980i 0.0436775 + 0.0317336i
\(777\) −2096.26 + 6451.64i −0.0967864 + 0.297878i
\(778\) 1211.83 393.748i 0.0558436 0.0181447i
\(779\) −9643.40 + 7006.34i −0.443531 + 0.322244i
\(780\) −1644.69 + 4306.36i −0.0754990 + 0.197683i
\(781\) 10334.2 + 10085.8i 0.473478 + 0.462098i
\(782\) 23731.0i 1.08519i
\(783\) 9501.78 6903.45i 0.433673 0.315082i
\(784\) −2083.91 6413.62i −0.0949303 0.292165i
\(785\) −30661.1 9962.40i −1.39407 0.452960i
\(786\) 3715.32 5113.70i 0.168602 0.232060i
\(787\) −22139.3 + 30472.2i −1.00277 + 1.38020i −0.0791629 + 0.996862i \(0.525225\pi\)
−0.923609 + 0.383336i \(0.874775\pi\)
\(788\) 3267.89 + 1061.80i 0.147733 + 0.0480014i
\(789\) −4228.27 13013.3i −0.190786 0.587180i
\(790\) −30966.6 + 22498.5i −1.39461 + 1.01324i
\(791\) 22991.1i 1.03346i
\(792\) 11555.0 + 11277.2i 0.518420 + 0.505959i
\(793\) −25361.9 9686.20i −1.13572 0.433754i
\(794\) 14513.8 10544.9i 0.648708 0.471314i
\(795\) −729.036 + 236.878i −0.0325236 + 0.0105676i
\(796\) 1615.41 4971.72i 0.0719305 0.221379i
\(797\) 29869.4 + 21701.4i 1.32751 + 0.964496i 0.999806 + 0.0197168i \(0.00627646\pi\)
0.327709 + 0.944779i \(0.393724\pi\)
\(798\) −7145.72 + 9835.25i −0.316987 + 0.436296i
\(799\) 29785.1 + 9677.75i 1.31880 + 0.428503i
\(800\) 5451.20 1771.20i 0.240911 0.0782768i
\(801\) 686.397 + 944.744i 0.0302780 + 0.0416740i
\(802\) −36199.9 −1.59384
\(803\) 4552.45 9209.94i 0.200065 0.404747i
\(804\) 4936.37i 0.216533i
\(805\) 13490.9 9801.69i 0.590672 0.429148i
\(806\) −183.647 + 3621.68i −0.00802565 + 0.158273i
\(807\) −2887.30 + 8886.20i −0.125945 + 0.387619i
\(808\) 18539.9 25518.0i 0.807216 1.11104i
\(809\) −21393.3 15543.1i −0.929724 0.675484i 0.0162012 0.999869i \(-0.494843\pi\)
−0.945925 + 0.324385i \(0.894843\pi\)
\(810\) −774.688 + 2384.24i −0.0336046 + 0.103424i
\(811\) −20335.6 + 6607.44i −0.880493 + 0.286090i −0.714162 0.699980i \(-0.753192\pi\)
−0.166331 + 0.986070i \(0.553192\pi\)
\(812\) −1618.89 2228.20i −0.0699652 0.0962988i
\(813\) 17174.5i 0.740879i
\(814\) −14786.4 + 2526.66i −0.636687 + 0.108796i
\(815\) −9818.32 −0.421989
\(816\) 9760.50 7091.42i 0.418733 0.304227i
\(817\) −30712.3 + 9979.04i −1.31516 + 0.427323i
\(818\) 2202.84 6779.64i 0.0941570 0.289785i
\(819\) −9135.51 + 5954.72i −0.389769 + 0.254059i
\(820\) −2378.88 1728.36i −0.101310 0.0736060i
\(821\) 4860.87 + 1579.39i 0.206633 + 0.0671390i 0.410505 0.911859i \(-0.365353\pi\)
−0.203872 + 0.978998i \(0.565353\pi\)
\(822\) −67.8301 208.759i −0.00287816 0.00885806i
\(823\) 18117.7 13163.3i 0.767367 0.557524i −0.133794 0.991009i \(-0.542716\pi\)
0.901161 + 0.433485i \(0.142716\pi\)
\(824\) 18897.0i 0.798916i
\(825\) 2743.53 + 5226.33i 0.115779 + 0.220555i
\(826\) 7617.63i 0.320885i
\(827\) −7497.15 10318.9i −0.315238 0.433887i 0.621768 0.783201i \(-0.286415\pi\)
−0.937006 + 0.349314i \(0.886415\pi\)
\(828\) 1310.28 + 4032.63i 0.0549945 + 0.169256i
\(829\) −2829.22 + 8707.44i −0.118532 + 0.364803i −0.992667 0.120879i \(-0.961429\pi\)
0.874135 + 0.485682i \(0.161429\pi\)
\(830\) −3486.67 + 4798.99i −0.145812 + 0.200693i
\(831\) 5491.54 + 3989.83i 0.229241 + 0.166553i
\(832\) 16428.6 20358.1i 0.684565 0.848305i
\(833\) −5669.67 17449.4i −0.235825 0.725795i
\(834\) −10393.6 14305.5i −0.431534 0.593956i
\(835\) 27281.6 1.13068
\(836\) 11729.7 + 1711.82i 0.485262 + 0.0708189i
\(837\) 4436.06i 0.183193i
\(838\) −18879.1 25984.9i −0.778243 1.07116i
\(839\) −10725.5 + 3484.94i −0.441343 + 0.143401i −0.521255 0.853401i \(-0.674536\pi\)
0.0799121 + 0.996802i \(0.474536\pi\)
\(840\) −12172.7 3955.14i −0.499996 0.162458i
\(841\) 13617.2 + 9893.45i 0.558332 + 0.405652i
\(842\) −41.9263 30.4612i −0.00171600 0.00124675i
\(843\) −14227.8 4622.90i −0.581296 0.188875i
\(844\) 2505.31 + 7710.56i 0.102176 + 0.314465i
\(845\) 2972.19 29231.8i 0.121002 1.19007i
\(846\) −12690.3 −0.515723
\(847\) 14177.7 + 9782.77i 0.575148 + 0.396859i
\(848\) 733.145 0.0296890
\(849\) 1412.25 1026.06i 0.0570888 0.0414774i
\(850\) −12617.4 + 4099.66i −0.509147 + 0.165432i
\(851\) −15989.8 5195.42i −0.644095 0.209279i
\(852\) 1710.82 2354.75i 0.0687932 0.0946858i
\(853\) −15020.3 + 20673.6i −0.602912 + 0.829837i −0.995971 0.0896764i \(-0.971417\pi\)
0.393059 + 0.919513i \(0.371417\pi\)
\(854\) 5457.87 16797.6i 0.218694 0.673070i
\(855\) 9860.64 + 30347.9i 0.394417 + 1.21389i
\(856\) 17765.4 + 24452.0i 0.709357 + 0.976347i
\(857\) −11712.6 −0.466856 −0.233428 0.972374i \(-0.574994\pi\)
−0.233428 + 0.972374i \(0.574994\pi\)
\(858\) 10564.5 + 5905.75i 0.420358 + 0.234987i
\(859\) 13886.5 0.551573 0.275786 0.961219i \(-0.411062\pi\)
0.275786 + 0.961219i \(0.411062\pi\)
\(860\) −4682.39 6444.76i −0.185661 0.255540i
\(861\) 1078.88 + 3320.44i 0.0427038 + 0.131429i
\(862\) −40.9558 + 126.049i −0.00161828 + 0.00498056i
\(863\) −19461.4 + 26786.4i −0.767642 + 1.05657i 0.228898 + 0.973451i \(0.426488\pi\)
−0.996540 + 0.0831182i \(0.973512\pi\)
\(864\) 8450.55 11631.2i 0.332747 0.457987i
\(865\) −20061.5 6518.36i −0.788567 0.256221i
\(866\) −6418.51 + 2085.50i −0.251859 + 0.0818339i
\(867\) 14616.0 10619.1i 0.572531 0.415968i
\(868\) 1040.27 0.0406787
\(869\) −20597.1 39236.8i −0.804036 1.53166i
\(870\) −8228.81 −0.320670
\(871\) −8195.12 30378.5i −0.318807 1.18179i
\(872\) 13679.9 + 42102.3i 0.531260 + 1.63505i
\(873\) −810.512 263.351i −0.0314223 0.0102097i
\(874\) −24375.8 17710.1i −0.943393 0.685415i
\(875\) −9961.02 7237.11i −0.384850 0.279610i
\(876\) −1969.45 639.912i −0.0759606 0.0246811i
\(877\) 36502.7 11860.4i 1.40548 0.456669i 0.494524 0.869164i \(-0.335343\pi\)
0.910960 + 0.412495i \(0.135343\pi\)
\(878\) −17067.2 23490.9i −0.656024 0.902940i
\(879\) 8467.90i 0.324932i
\(880\) −3157.66 18479.0i −0.120960 0.707873i
\(881\) −6570.59 −0.251270 −0.125635 0.992077i \(-0.540097\pi\)
−0.125635 + 0.992077i \(0.540097\pi\)
\(882\) 4369.92 + 6014.68i 0.166829 + 0.229620i
\(883\) 702.044 + 2160.67i 0.0267561 + 0.0823469i 0.963543 0.267554i \(-0.0862153\pi\)
−0.936787 + 0.349901i \(0.886215\pi\)
\(884\) 7532.92 9334.70i 0.286606 0.355158i
\(885\) −8119.02 5898.81i −0.308382 0.224052i
\(886\) 2116.41 2912.99i 0.0802508 0.110456i
\(887\) 191.647 589.829i 0.00725465 0.0223275i −0.947364 0.320159i \(-0.896264\pi\)
0.954618 + 0.297832i \(0.0962635\pi\)
\(888\) 3987.65 + 12272.7i 0.150695 + 0.463790i
\(889\) −11338.2 15605.6i −0.427750 0.588747i
\(890\) 2047.00i 0.0770963i
\(891\) −2601.87 1286.10i −0.0978292 0.0483568i
\(892\) 5577.41i 0.209356i
\(893\) −32168.9 + 23372.0i −1.20548 + 0.875829i
\(894\) −5533.83 17031.4i −0.207023 0.637153i
\(895\) 41987.0 + 13642.4i 1.56813 + 0.509515i
\(896\) 4855.36 + 3527.63i 0.181034 + 0.131529i
\(897\) 7407.40 + 11364.2i 0.275726 + 0.423008i
\(898\) −990.894 + 3049.66i −0.0368224 + 0.113328i
\(899\) 2714.69 882.056i 0.100712 0.0327233i
\(900\) −1917.74 + 1393.32i −0.0710273 + 0.0516044i
\(901\) 1994.66 0.0737532
\(902\) −5392.32 + 5525.12i −0.199052 + 0.203954i
\(903\) 9458.51i 0.348571i
\(904\) −25706.9 35382.5i −0.945796 1.30178i
\(905\) −60667.9 + 19712.2i −2.22836 + 0.724039i
\(906\) −5755.90 + 17714.8i −0.211067 + 0.649598i
\(907\) 23721.0 + 17234.3i 0.868405 + 0.630933i 0.930158 0.367158i \(-0.119669\pi\)
−0.0617536 + 0.998091i \(0.519669\pi\)
\(908\) 2872.25 3953.31i 0.104977 0.144488i
\(909\) −7117.55 + 21905.6i −0.259708 + 0.799298i
\(910\) 19090.8 + 968.050i 0.695445 + 0.0352643i
\(911\) −18124.1 + 13168.0i −0.659143 + 0.478896i −0.866374 0.499396i \(-0.833555\pi\)
0.207230 + 0.978292i \(0.433555\pi\)
\(912\) 15317.9i 0.556171i
\(913\) −4914.79 4796.66i −0.178155 0.173873i
\(914\) 38795.9 1.40400
\(915\) 13676.8 + 18824.5i 0.494144 + 0.680131i
\(916\) 13446.8 4369.13i 0.485038 0.157598i
\(917\) 10992.0 + 3571.50i 0.395841 + 0.128617i
\(918\) −19559.8 + 26921.7i −0.703235 + 0.967919i
\(919\) −9307.98 6762.64i −0.334104 0.242741i 0.408066 0.912953i \(-0.366203\pi\)
−0.742170 + 0.670211i \(0.766203\pi\)
\(920\) 9802.48 30168.9i 0.351281 1.08113i
\(921\) −11828.2 + 3843.22i −0.423184 + 0.137501i
\(922\) −11853.7 + 8612.20i −0.423406 + 0.307622i
\(923\) −6619.19 + 17331.4i −0.236049 + 0.618059i
\(924\) 1538.51 3112.51i 0.0547762 0.110816i
\(925\) 9399.11i 0.334098i
\(926\) −9637.30 + 7001.91i −0.342010 + 0.248485i
\(927\) −4264.17 13123.8i −0.151083 0.464985i
\(928\) −8798.11 2858.68i −0.311220 0.101121i
\(929\) −6761.78 + 9306.79i −0.238802 + 0.328682i −0.911550 0.411189i \(-0.865114\pi\)
0.672748 + 0.739871i \(0.265114\pi\)
\(930\) 1826.86 2514.46i 0.0644141 0.0886584i
\(931\) 22154.8 + 7198.52i 0.779907 + 0.253407i
\(932\) −4031.10 12406.4i −0.141677 0.436037i
\(933\) −4493.79 + 3264.93i −0.157685 + 0.114565i
\(934\) 32876.4i 1.15176i
\(935\) −8590.99 50275.7i −0.300487 1.75849i
\(936\) −7401.12 + 19378.7i −0.258454 + 0.676724i
\(937\) −27882.3 + 20257.7i −0.972120 + 0.706286i −0.955934 0.293583i \(-0.905152\pi\)
−0.0161860 + 0.999869i \(0.505152\pi\)
\(938\) 19467.9 6325.51i 0.677665 0.220187i
\(939\) 5672.96 17459.6i 0.197156 0.606785i
\(940\) −7935.57 5765.53i −0.275351 0.200054i
\(941\) 14100.3 19407.3i 0.488475 0.672329i −0.491631 0.870804i \(-0.663599\pi\)
0.980106 + 0.198475i \(0.0635989\pi\)
\(942\) 16226.5 + 5272.30i 0.561239 + 0.182358i
\(943\) −8229.43 + 2673.90i −0.284186 + 0.0923376i
\(944\) 5641.72 + 7765.16i 0.194515 + 0.267727i
\(945\) 23383.6 0.804941
\(946\) −18519.1 + 9721.48i −0.636478 + 0.334115i
\(947\) 270.862i 0.00929443i 0.999989 + 0.00464722i \(0.00147926\pi\)
−0.999989 + 0.00464722i \(0.998521\pi\)
\(948\) −7226.30 + 5250.21i −0.247573 + 0.179872i
\(949\) 13182.4 + 668.445i 0.450914 + 0.0228648i
\(950\) 5205.15 16019.8i 0.177766 0.547106i
\(951\) 6687.32 9204.30i 0.228024 0.313849i
\(952\) 26944.0 + 19576.0i 0.917290 + 0.666450i
\(953\) −14775.2 + 45473.4i −0.502220 + 1.54567i 0.303175 + 0.952935i \(0.401953\pi\)
−0.805395 + 0.592739i \(0.798047\pi\)
\(954\) −768.696 + 249.765i −0.0260875 + 0.00847634i
\(955\) −7.36978 10.1436i −0.000249718 0.000343707i
\(956\) 17147.3i 0.580106i
\(957\) 1375.76 9426.91i 0.0464701 0.318421i
\(958\) 12600.4 0.424947
\(959\) 324.705 235.912i 0.0109336 0.00794369i
\(960\) −21323.8 + 6928.52i −0.716898 + 0.232934i
\(961\) 8872.77 27307.6i 0.297834 0.916639i
\(962\) −10524.0 16145.5i −0.352709 0.541113i
\(963\) −17855.6 12972.9i −0.597497 0.434107i
\(964\) −7719.02 2508.06i −0.257897 0.0837958i
\(965\) 1523.15 + 4687.76i 0.0508102 + 0.156378i
\(966\) −7139.64 + 5187.25i −0.237799 + 0.172771i
\(967\) 41044.1i 1.36493i −0.730917 0.682466i \(-0.760907\pi\)
0.730917 0.682466i \(-0.239093\pi\)
\(968\) 32757.3 797.036i 1.08766 0.0264646i
\(969\) 41675.3i 1.38163i
\(970\) 878.079 + 1208.57i 0.0290654 + 0.0400051i
\(971\) 13393.2 + 41220.0i 0.442644 + 1.36232i 0.885047 + 0.465502i \(0.154126\pi\)
−0.442402 + 0.896817i \(0.645874\pi\)
\(972\) −2940.34 + 9049.43i −0.0970282 + 0.298622i
\(973\) 19004.5 26157.4i 0.626162 0.861838i
\(974\) 24270.3 + 17633.4i 0.798430 + 0.580093i
\(975\) −4762.50 + 5901.63i −0.156433 + 0.193850i
\(976\) −6876.95 21165.1i −0.225539 0.694137i
\(977\) 5644.27 + 7768.67i 0.184827 + 0.254393i 0.891369 0.453279i \(-0.149746\pi\)
−0.706542 + 0.707671i \(0.749746\pi\)
\(978\) 5196.05 0.169889
\(979\) 2345.04 + 342.234i 0.0765556 + 0.0111725i
\(980\) 5746.50i 0.187312i
\(981\) −19001.1 26152.7i −0.618408 0.851165i
\(982\) 23406.1 7605.10i 0.760609 0.247137i
\(983\) 9713.33 + 3156.05i 0.315165 + 0.102403i 0.462328 0.886709i \(-0.347014\pi\)
−0.147163 + 0.989112i \(0.547014\pi\)
\(984\) 5373.01 + 3903.72i 0.174070 + 0.126470i
\(985\) 15186.2 + 11033.4i 0.491242 + 0.356908i
\(986\) 20364.3 + 6616.75i 0.657738 + 0.213712i
\(987\) 3598.96 + 11076.5i 0.116065 + 0.357211i
\(988\) 3966.65 + 14704.0i 0.127729 + 0.473477i
\(989\) −23442.1 −0.753708
\(990\) 9606.13 + 18299.4i 0.308387 + 0.587467i
\(991\) −19662.3 −0.630267 −0.315133 0.949047i \(-0.602049\pi\)
−0.315133 + 0.949047i \(0.602049\pi\)
\(992\) 2826.77 2053.77i 0.0904738 0.0657330i
\(993\) 3712.91 1206.40i 0.118656 0.0385537i
\(994\) −11478.8 3729.70i −0.366285 0.119013i
\(995\) 16786.1 23104.1i 0.534830 0.736130i
\(996\) −813.642 + 1119.88i −0.0258848 + 0.0356273i
\(997\) 1677.16 5161.77i 0.0532760 0.163967i −0.920878 0.389850i \(-0.872527\pi\)
0.974154 + 0.225883i \(0.0725268\pi\)
\(998\) 12375.8 + 38088.8i 0.392534 + 1.20810i
\(999\) −13857.5 19073.3i −0.438872 0.604055i
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 143.4.n.a.25.12 160
11.4 even 5 inner 143.4.n.a.103.29 yes 160
13.12 even 2 inner 143.4.n.a.25.29 yes 160
143.103 even 10 inner 143.4.n.a.103.12 yes 160
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.4.n.a.25.12 160 1.1 even 1 trivial
143.4.n.a.25.29 yes 160 13.12 even 2 inner
143.4.n.a.103.12 yes 160 143.103 even 10 inner
143.4.n.a.103.29 yes 160 11.4 even 5 inner