Properties

Label 322.4.e.b.93.10
Level $322$
Weight $4$
Character 322.93
Analytic conductor $18.999$
Analytic rank $0$
Dimension $22$
Inner twists $2$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [322,4,Mod(93,322)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(322, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("322.93"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: \( N \) \(=\) \( 322 = 2 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 322.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [22,-22,6,-44,27] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(18.9986150218\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 93.10
Character \(\chi\) \(=\) 322.93
Dual form 322.4.e.b.277.10

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(3.73605 + 6.47103i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.65469 - 4.59806i) q^{5} -14.9442 q^{6} +(9.31488 - 16.0073i) q^{7} +8.00000 q^{8} +(-14.4162 + 24.9695i) q^{9} +(5.30939 + 9.19613i) q^{10} +(-7.53617 - 13.0530i) q^{11} +(14.9442 - 25.8841i) q^{12} +19.5834 q^{13} +(18.4105 + 32.1411i) q^{14} +39.6723 q^{15} +(-8.00000 + 13.8564i) q^{16} +(57.4595 + 99.5228i) q^{17} +(-28.8323 - 49.9390i) q^{18} +(-25.9174 + 44.8903i) q^{19} -21.2376 q^{20} +(138.384 + 0.472845i) q^{21} +30.1447 q^{22} +(11.5000 - 19.9186i) q^{23} +(29.8884 + 51.7682i) q^{24} +(48.4052 + 83.8403i) q^{25} +(-19.5834 + 33.9194i) q^{26} -13.6912 q^{27} +(-74.0806 - 0.253126i) q^{28} +227.585 q^{29} +(-39.6723 + 68.7144i) q^{30} +(89.0122 + 154.174i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(56.3110 - 97.5336i) q^{33} -229.838 q^{34} +(-48.8744 - 85.3248i) q^{35} +115.329 q^{36} +(-10.3699 + 17.9612i) q^{37} +(-51.8349 - 89.7806i) q^{38} +(73.1644 + 126.725i) q^{39} +(21.2376 - 36.7845i) q^{40} -107.492 q^{41} +(-139.203 + 239.216i) q^{42} +138.795 q^{43} +(-30.1447 + 52.2121i) q^{44} +(76.5410 + 132.573i) q^{45} +(23.0000 + 39.8372i) q^{46} +(-10.7254 + 18.5769i) q^{47} -119.554 q^{48} +(-169.466 - 298.212i) q^{49} -193.621 q^{50} +(-429.343 + 743.644i) q^{51} +(-39.1667 - 67.8387i) q^{52} +(-214.602 - 371.701i) q^{53} +(13.6912 - 23.7139i) q^{54} -80.0249 q^{55} +(74.5190 - 128.058i) q^{56} -387.316 q^{57} +(-227.585 + 394.189i) q^{58} +(-64.2821 - 111.340i) q^{59} +(-79.3446 - 137.429i) q^{60} +(-112.966 + 195.662i) q^{61} -356.049 q^{62} +(265.409 + 463.351i) q^{63} +64.0000 q^{64} +(51.9878 - 90.0455i) q^{65} +(112.622 + 195.067i) q^{66} +(-239.358 - 414.580i) q^{67} +(229.838 - 398.091i) q^{68} +171.858 q^{69} +(196.661 + 0.671971i) q^{70} +652.010 q^{71} +(-115.329 + 199.756i) q^{72} +(258.209 + 447.231i) q^{73} +(-20.7398 - 35.9223i) q^{74} +(-361.689 + 626.463i) q^{75} +207.340 q^{76} +(-279.142 - 0.953799i) q^{77} -292.658 q^{78} +(174.698 - 302.586i) q^{79} +(42.4751 + 73.5690i) q^{80} +(338.085 + 585.581i) q^{81} +(107.492 - 186.181i) q^{82} +373.014 q^{83} +(-275.131 - 480.324i) q^{84} +610.150 q^{85} +(-138.795 + 240.399i) q^{86} +(850.269 + 1472.71i) q^{87} +(-60.2894 - 104.424i) q^{88} +(-448.347 + 776.560i) q^{89} -306.164 q^{90} +(182.417 - 313.476i) q^{91} -92.0000 q^{92} +(-665.108 + 1152.00i) q^{93} +(-21.4507 - 37.1537i) q^{94} +(137.606 + 238.340i) q^{95} +(119.554 - 207.073i) q^{96} -1294.92 q^{97} +(685.984 + 4.68793i) q^{98} +434.570 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q - 22 q^{2} + 6 q^{3} - 44 q^{4} + 27 q^{5} - 24 q^{6} + q^{7} + 176 q^{8} - 59 q^{9} + 54 q^{10} - 56 q^{11} + 24 q^{12} - 206 q^{13} - 64 q^{14} + 124 q^{15} - 176 q^{16} + 157 q^{17} - 118 q^{18}+ \cdots + 202 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).

\(n\) \(185\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.353553 + 0.612372i
\(3\) 3.73605 + 6.47103i 0.719003 + 1.24535i 0.961395 + 0.275172i \(0.0887348\pi\)
−0.242392 + 0.970178i \(0.577932\pi\)
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) 2.65469 4.59806i 0.237443 0.411263i −0.722537 0.691332i \(-0.757024\pi\)
0.959980 + 0.280069i \(0.0903574\pi\)
\(6\) −14.9442 −1.01682
\(7\) 9.31488 16.0073i 0.502956 0.864312i
\(8\) 8.00000 0.353553
\(9\) −14.4162 + 24.9695i −0.533932 + 0.924797i
\(10\) 5.30939 + 9.19613i 0.167898 + 0.290807i
\(11\) −7.53617 13.0530i −0.206567 0.357785i 0.744064 0.668109i \(-0.232896\pi\)
−0.950631 + 0.310324i \(0.899563\pi\)
\(12\) 14.9442 25.8841i 0.359502 0.622675i
\(13\) 19.5834 0.417804 0.208902 0.977937i \(-0.433011\pi\)
0.208902 + 0.977937i \(0.433011\pi\)
\(14\) 18.4105 + 32.1411i 0.351459 + 0.613577i
\(15\) 39.6723 0.682889
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 57.4595 + 99.5228i 0.819763 + 1.41987i 0.905856 + 0.423585i \(0.139228\pi\)
−0.0860930 + 0.996287i \(0.527438\pi\)
\(18\) −28.8323 49.9390i −0.377547 0.653930i
\(19\) −25.9174 + 44.8903i −0.312940 + 0.542029i −0.978998 0.203872i \(-0.934647\pi\)
0.666057 + 0.745901i \(0.267981\pi\)
\(20\) −21.2376 −0.237443
\(21\) 138.384 + 0.472845i 1.43800 + 0.00491349i
\(22\) 30.1447 0.292130
\(23\) 11.5000 19.9186i 0.104257 0.180579i
\(24\) 29.8884 + 51.7682i 0.254206 + 0.440298i
\(25\) 48.4052 + 83.8403i 0.387242 + 0.670722i
\(26\) −19.5834 + 33.9194i −0.147716 + 0.255851i
\(27\) −13.6912 −0.0975881
\(28\) −74.0806 0.253126i −0.499997 0.00170844i
\(29\) 227.585 1.45729 0.728646 0.684890i \(-0.240150\pi\)
0.728646 + 0.684890i \(0.240150\pi\)
\(30\) −39.6723 + 68.7144i −0.241438 + 0.418183i
\(31\) 89.0122 + 154.174i 0.515712 + 0.893239i 0.999834 + 0.0182383i \(0.00580574\pi\)
−0.484122 + 0.875000i \(0.660861\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) 56.3110 97.5336i 0.297045 0.514497i
\(34\) −229.838 −1.15932
\(35\) −48.8744 85.3248i −0.236036 0.412072i
\(36\) 115.329 0.533932
\(37\) −10.3699 + 17.9612i −0.0460756 + 0.0798054i −0.888143 0.459566i \(-0.848005\pi\)
0.842068 + 0.539372i \(0.181338\pi\)
\(38\) −51.8349 89.7806i −0.221282 0.383272i
\(39\) 73.1644 + 126.725i 0.300402 + 0.520312i
\(40\) 21.2376 36.7845i 0.0839488 0.145404i
\(41\) −107.492 −0.409449 −0.204724 0.978820i \(-0.565630\pi\)
−0.204724 + 0.978820i \(0.565630\pi\)
\(42\) −139.203 + 239.216i −0.511418 + 0.878853i
\(43\) 138.795 0.492232 0.246116 0.969240i \(-0.420846\pi\)
0.246116 + 0.969240i \(0.420846\pi\)
\(44\) −30.1447 + 52.2121i −0.103284 + 0.178893i
\(45\) 76.5410 + 132.573i 0.253557 + 0.439173i
\(46\) 23.0000 + 39.8372i 0.0737210 + 0.127688i
\(47\) −10.7254 + 18.5769i −0.0332863 + 0.0576535i −0.882189 0.470896i \(-0.843931\pi\)
0.848902 + 0.528550i \(0.177264\pi\)
\(48\) −119.554 −0.359502
\(49\) −169.466 298.212i −0.494070 0.869422i
\(50\) −193.621 −0.547642
\(51\) −429.343 + 743.644i −1.17883 + 2.04179i
\(52\) −39.1667 67.8387i −0.104451 0.180914i
\(53\) −214.602 371.701i −0.556185 0.963341i −0.997810 0.0661410i \(-0.978931\pi\)
0.441625 0.897200i \(-0.354402\pi\)
\(54\) 13.6912 23.7139i 0.0345026 0.0597603i
\(55\) −80.0249 −0.196192
\(56\) 74.5190 128.058i 0.177822 0.305580i
\(57\) −387.316 −0.900021
\(58\) −227.585 + 394.189i −0.515231 + 0.892406i
\(59\) −64.2821 111.340i −0.141844 0.245682i 0.786347 0.617785i \(-0.211970\pi\)
−0.928191 + 0.372104i \(0.878637\pi\)
\(60\) −79.3446 137.429i −0.170722 0.295700i
\(61\) −112.966 + 195.662i −0.237111 + 0.410688i −0.959884 0.280397i \(-0.909534\pi\)
0.722773 + 0.691085i \(0.242867\pi\)
\(62\) −356.049 −0.729326
\(63\) 265.409 + 463.351i 0.530769 + 0.926616i
\(64\) 64.0000 0.125000
\(65\) 51.9878 90.0455i 0.0992046 0.171827i
\(66\) 112.622 + 195.067i 0.210043 + 0.363805i
\(67\) −239.358 414.580i −0.436451 0.755955i 0.560962 0.827842i \(-0.310431\pi\)
−0.997413 + 0.0718863i \(0.977098\pi\)
\(68\) 229.838 398.091i 0.409882 0.709936i
\(69\) 171.858 0.299845
\(70\) 196.661 + 0.671971i 0.335793 + 0.00114737i
\(71\) 652.010 1.08985 0.544925 0.838485i \(-0.316558\pi\)
0.544925 + 0.838485i \(0.316558\pi\)
\(72\) −115.329 + 199.756i −0.188773 + 0.326965i
\(73\) 258.209 + 447.231i 0.413987 + 0.717047i 0.995322 0.0966178i \(-0.0308025\pi\)
−0.581334 + 0.813665i \(0.697469\pi\)
\(74\) −20.7398 35.9223i −0.0325804 0.0564309i
\(75\) −361.689 + 626.463i −0.556856 + 0.964503i
\(76\) 207.340 0.312940
\(77\) −279.142 0.953799i −0.413132 0.00141163i
\(78\) −292.658 −0.424833
\(79\) 174.698 302.586i 0.248799 0.430932i −0.714394 0.699744i \(-0.753298\pi\)
0.963193 + 0.268812i \(0.0866309\pi\)
\(80\) 42.4751 + 73.5690i 0.0593608 + 0.102816i
\(81\) 338.085 + 585.581i 0.463766 + 0.803265i
\(82\) 107.492 186.181i 0.144762 0.250735i
\(83\) 373.014 0.493297 0.246649 0.969105i \(-0.420671\pi\)
0.246649 + 0.969105i \(0.420671\pi\)
\(84\) −275.131 480.324i −0.357372 0.623900i
\(85\) 610.150 0.778588
\(86\) −138.795 + 240.399i −0.174030 + 0.301430i
\(87\) 850.269 + 1472.71i 1.04780 + 1.81484i
\(88\) −60.2894 104.424i −0.0730326 0.126496i
\(89\) −448.347 + 776.560i −0.533985 + 0.924890i 0.465226 + 0.885192i \(0.345973\pi\)
−0.999212 + 0.0396981i \(0.987360\pi\)
\(90\) −306.164 −0.358583
\(91\) 182.417 313.476i 0.210137 0.361113i
\(92\) −92.0000 −0.104257
\(93\) −665.108 + 1152.00i −0.741597 + 1.28448i
\(94\) −21.4507 37.1537i −0.0235369 0.0407672i
\(95\) 137.606 + 238.340i 0.148611 + 0.257402i
\(96\) 119.554 207.073i 0.127103 0.220149i
\(97\) −1294.92 −1.35546 −0.677729 0.735312i \(-0.737036\pi\)
−0.677729 + 0.735312i \(0.737036\pi\)
\(98\) 685.984 + 4.68793i 0.707090 + 0.00483216i
\(99\) 434.570 0.441171
\(100\) 193.621 335.361i 0.193621 0.335361i
\(101\) −154.615 267.801i −0.152325 0.263834i 0.779757 0.626082i \(-0.215343\pi\)
−0.932082 + 0.362248i \(0.882009\pi\)
\(102\) −858.687 1487.29i −0.833555 1.44376i
\(103\) −308.814 + 534.882i −0.295421 + 0.511684i −0.975083 0.221842i \(-0.928793\pi\)
0.679662 + 0.733526i \(0.262127\pi\)
\(104\) 156.667 0.147716
\(105\) 369.543 635.045i 0.343463 0.590229i
\(106\) 858.407 0.786564
\(107\) 612.602 1061.06i 0.553481 0.958657i −0.444539 0.895759i \(-0.646633\pi\)
0.998020 0.0628975i \(-0.0200341\pi\)
\(108\) 27.3825 + 47.4278i 0.0243970 + 0.0422569i
\(109\) −78.6223 136.178i −0.0690886 0.119665i 0.829412 0.558638i \(-0.188676\pi\)
−0.898500 + 0.438973i \(0.855342\pi\)
\(110\) 80.0249 138.607i 0.0693643 0.120143i
\(111\) −154.970 −0.132514
\(112\) 147.284 + 257.129i 0.124259 + 0.216932i
\(113\) −1226.97 −1.02145 −0.510723 0.859745i \(-0.670622\pi\)
−0.510723 + 0.859745i \(0.670622\pi\)
\(114\) 387.316 670.850i 0.318205 0.551148i
\(115\) −61.0580 105.755i −0.0495103 0.0857543i
\(116\) −455.170 788.378i −0.364323 0.631026i
\(117\) −282.317 + 488.987i −0.223079 + 0.386383i
\(118\) 257.128 0.200598
\(119\) 2128.32 + 7.27224i 1.63952 + 0.00560206i
\(120\) 317.378 0.241438
\(121\) 551.912 955.940i 0.414660 0.718212i
\(122\) −225.931 391.324i −0.167663 0.290400i
\(123\) −401.595 695.583i −0.294395 0.509907i
\(124\) 356.049 616.695i 0.257856 0.446619i
\(125\) 1177.68 0.842677
\(126\) −1067.96 3.64910i −0.755089 0.00258006i
\(127\) 1229.19 0.858840 0.429420 0.903105i \(-0.358718\pi\)
0.429420 + 0.903105i \(0.358718\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) 518.544 + 898.145i 0.353917 + 0.613002i
\(130\) 103.976 + 180.091i 0.0701482 + 0.121500i
\(131\) 1210.47 2096.59i 0.807321 1.39832i −0.107393 0.994217i \(-0.534250\pi\)
0.914713 0.404104i \(-0.132417\pi\)
\(132\) −450.488 −0.297045
\(133\) 477.154 + 833.016i 0.311087 + 0.543095i
\(134\) 957.432 0.617235
\(135\) −36.3460 + 62.9532i −0.0231716 + 0.0401344i
\(136\) 459.676 + 796.182i 0.289830 + 0.502001i
\(137\) −1601.35 2773.63i −0.998635 1.72969i −0.544556 0.838724i \(-0.683302\pi\)
−0.454078 0.890962i \(-0.650031\pi\)
\(138\) −171.858 + 297.667i −0.106011 + 0.183617i
\(139\) −1710.35 −1.04367 −0.521833 0.853048i \(-0.674752\pi\)
−0.521833 + 0.853048i \(0.674752\pi\)
\(140\) −197.825 + 339.955i −0.119423 + 0.205225i
\(141\) −160.282 −0.0957317
\(142\) −652.010 + 1129.32i −0.385320 + 0.667395i
\(143\) −147.584 255.622i −0.0863046 0.149484i
\(144\) −230.659 399.512i −0.133483 0.231199i
\(145\) 604.169 1046.45i 0.346024 0.599331i
\(146\) −1032.84 −0.585466
\(147\) 1296.60 2210.75i 0.727497 1.24041i
\(148\) 82.9591 0.0460756
\(149\) 1323.72 2292.75i 0.727807 1.26060i −0.230001 0.973191i \(-0.573873\pi\)
0.957808 0.287409i \(-0.0927939\pi\)
\(150\) −723.377 1252.93i −0.393757 0.682007i
\(151\) 505.407 + 875.391i 0.272381 + 0.471777i 0.969471 0.245206i \(-0.0788557\pi\)
−0.697090 + 0.716983i \(0.745522\pi\)
\(152\) −207.340 + 359.123i −0.110641 + 0.191636i
\(153\) −3313.38 −1.75079
\(154\) 280.794 482.534i 0.146929 0.252492i
\(155\) 945.200 0.489809
\(156\) 292.658 506.898i 0.150201 0.260156i
\(157\) −38.3946 66.5013i −0.0195173 0.0338050i 0.856102 0.516807i \(-0.172880\pi\)
−0.875619 + 0.483002i \(0.839546\pi\)
\(158\) 349.397 + 605.173i 0.175927 + 0.304715i
\(159\) 1603.53 2777.39i 0.799798 1.38529i
\(160\) −169.900 −0.0839488
\(161\) −211.721 369.623i −0.103640 0.180934i
\(162\) −1352.34 −0.655864
\(163\) −1074.61 + 1861.27i −0.516379 + 0.894394i 0.483440 + 0.875377i \(0.339387\pi\)
−0.999819 + 0.0190171i \(0.993946\pi\)
\(164\) 214.984 + 372.362i 0.102362 + 0.177296i
\(165\) −298.977 517.843i −0.141063 0.244328i
\(166\) −373.014 + 646.080i −0.174407 + 0.302082i
\(167\) −2071.34 −0.959791 −0.479896 0.877326i \(-0.659325\pi\)
−0.479896 + 0.877326i \(0.659325\pi\)
\(168\) 1107.08 + 3.78276i 0.508409 + 0.00173718i
\(169\) −1813.49 −0.825440
\(170\) −610.150 + 1056.81i −0.275273 + 0.476786i
\(171\) −747.260 1294.29i −0.334178 0.578813i
\(172\) −277.589 480.799i −0.123058 0.213143i
\(173\) −1560.93 + 2703.60i −0.685983 + 1.18816i 0.287144 + 0.957887i \(0.407294\pi\)
−0.973127 + 0.230270i \(0.926039\pi\)
\(174\) −3401.08 −1.48181
\(175\) 1792.94 + 6.12630i 0.774479 + 0.00264631i
\(176\) 241.157 0.103284
\(177\) 480.322 831.943i 0.203973 0.353292i
\(178\) −896.694 1553.12i −0.377585 0.653996i
\(179\) 1534.64 + 2658.08i 0.640808 + 1.10991i 0.985253 + 0.171106i \(0.0547340\pi\)
−0.344444 + 0.938807i \(0.611933\pi\)
\(180\) 306.164 530.291i 0.126778 0.219587i
\(181\) 1108.70 0.455300 0.227650 0.973743i \(-0.426896\pi\)
0.227650 + 0.973743i \(0.426896\pi\)
\(182\) 360.540 + 629.431i 0.146841 + 0.256355i
\(183\) −1688.18 −0.681934
\(184\) 92.0000 159.349i 0.0368605 0.0638442i
\(185\) 55.0578 + 95.3628i 0.0218807 + 0.0378985i
\(186\) −1330.22 2304.00i −0.524388 0.908267i
\(187\) 866.049 1500.04i 0.338673 0.586598i
\(188\) 85.8028 0.0332863
\(189\) −127.532 + 219.159i −0.0490825 + 0.0843466i
\(190\) −550.423 −0.210168
\(191\) 1590.31 2754.50i 0.602465 1.04350i −0.389982 0.920822i \(-0.627519\pi\)
0.992447 0.122677i \(-0.0391479\pi\)
\(192\) 239.107 + 414.146i 0.0898754 + 0.155669i
\(193\) 406.163 + 703.494i 0.151483 + 0.262376i 0.931773 0.363042i \(-0.118262\pi\)
−0.780290 + 0.625418i \(0.784928\pi\)
\(194\) 1294.92 2242.87i 0.479227 0.830045i
\(195\) 776.917 0.285314
\(196\) −694.104 + 1183.47i −0.252953 + 0.431294i
\(197\) −3772.40 −1.36433 −0.682164 0.731199i \(-0.738961\pi\)
−0.682164 + 0.731199i \(0.738961\pi\)
\(198\) −434.570 + 752.698i −0.155978 + 0.270161i
\(199\) 762.138 + 1320.06i 0.271490 + 0.470235i 0.969244 0.246103i \(-0.0791503\pi\)
−0.697754 + 0.716338i \(0.745817\pi\)
\(200\) 387.242 + 670.722i 0.136911 + 0.237136i
\(201\) 1788.51 3097.78i 0.627620 1.08707i
\(202\) 618.460 0.215419
\(203\) 2119.93 3643.02i 0.732954 1.25956i
\(204\) 3434.75 1.17883
\(205\) −285.358 + 494.254i −0.0972207 + 0.168391i
\(206\) −617.628 1069.76i −0.208894 0.361815i
\(207\) 331.572 + 574.299i 0.111332 + 0.192833i
\(208\) −156.667 + 271.355i −0.0522254 + 0.0904571i
\(209\) 781.273 0.258573
\(210\) 730.388 + 1275.11i 0.240008 + 0.419005i
\(211\) 910.563 0.297089 0.148544 0.988906i \(-0.452541\pi\)
0.148544 + 0.988906i \(0.452541\pi\)
\(212\) −858.407 + 1486.80i −0.278092 + 0.481670i
\(213\) 2435.94 + 4219.18i 0.783606 + 1.35725i
\(214\) 1225.20 + 2122.11i 0.391370 + 0.677873i
\(215\) 368.457 638.187i 0.116877 0.202437i
\(216\) −109.530 −0.0345026
\(217\) 3297.04 + 11.2656i 1.03142 + 0.00352424i
\(218\) 314.489 0.0977060
\(219\) −1929.36 + 3341.76i −0.595316 + 1.03112i
\(220\) 160.050 + 277.214i 0.0490480 + 0.0849536i
\(221\) 1125.25 + 1948.99i 0.342500 + 0.593228i
\(222\) 154.970 268.415i 0.0468508 0.0811480i
\(223\) 1289.30 0.387166 0.193583 0.981084i \(-0.437989\pi\)
0.193583 + 0.981084i \(0.437989\pi\)
\(224\) −592.645 2.02501i −0.176776 0.000604024i
\(225\) −2791.27 −0.827042
\(226\) 1226.97 2125.17i 0.361136 0.625506i
\(227\) −706.968 1224.50i −0.206710 0.358032i 0.743966 0.668217i \(-0.232942\pi\)
−0.950676 + 0.310185i \(0.899609\pi\)
\(228\) 774.631 + 1341.70i 0.225005 + 0.389721i
\(229\) 399.583 692.098i 0.115306 0.199717i −0.802596 0.596523i \(-0.796548\pi\)
0.917902 + 0.396807i \(0.129882\pi\)
\(230\) 244.232 0.0700181
\(231\) −1036.72 1809.90i −0.295286 0.515509i
\(232\) 1820.68 0.515231
\(233\) −777.205 + 1346.16i −0.218525 + 0.378497i −0.954357 0.298667i \(-0.903458\pi\)
0.735832 + 0.677164i \(0.236791\pi\)
\(234\) −564.634 977.974i −0.157740 0.273214i
\(235\) 56.9451 + 98.6318i 0.0158072 + 0.0273788i
\(236\) −257.128 + 445.359i −0.0709222 + 0.122841i
\(237\) 2610.73 0.715548
\(238\) −2140.91 + 3679.08i −0.583087 + 1.00201i
\(239\) −6967.81 −1.88582 −0.942908 0.333052i \(-0.891922\pi\)
−0.942908 + 0.333052i \(0.891922\pi\)
\(240\) −317.378 + 549.715i −0.0853612 + 0.147850i
\(241\) 2529.12 + 4380.57i 0.675996 + 1.17086i 0.976177 + 0.216977i \(0.0696197\pi\)
−0.300181 + 0.953882i \(0.597047\pi\)
\(242\) 1103.82 + 1911.88i 0.293209 + 0.507853i
\(243\) −2711.04 + 4695.66i −0.715692 + 1.23961i
\(244\) 903.725 0.237111
\(245\) −1821.08 12.4450i −0.474875 0.00324523i
\(246\) 1606.38 0.416337
\(247\) −507.551 + 879.103i −0.130748 + 0.226462i
\(248\) 712.097 + 1233.39i 0.182332 + 0.315808i
\(249\) 1393.60 + 2413.79i 0.354682 + 0.614328i
\(250\) −1177.68 + 2039.80i −0.297931 + 0.516032i
\(251\) −3363.38 −0.845796 −0.422898 0.906177i \(-0.638987\pi\)
−0.422898 + 0.906177i \(0.638987\pi\)
\(252\) 1074.28 1846.11i 0.268544 0.461484i
\(253\) −346.664 −0.0861445
\(254\) −1229.19 + 2129.01i −0.303646 + 0.525930i
\(255\) 2279.55 + 3948.30i 0.559808 + 0.969615i
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 3510.14 6079.75i 0.851972 1.47566i −0.0274543 0.999623i \(-0.508740\pi\)
0.879426 0.476035i \(-0.157927\pi\)
\(258\) −2074.18 −0.500514
\(259\) 190.915 + 333.300i 0.0458027 + 0.0799623i
\(260\) −415.903 −0.0992046
\(261\) −3280.90 + 5682.69i −0.778095 + 1.34770i
\(262\) 2420.93 + 4193.18i 0.570862 + 0.988762i
\(263\) 559.283 + 968.707i 0.131129 + 0.227122i 0.924112 0.382122i \(-0.124807\pi\)
−0.792983 + 0.609244i \(0.791473\pi\)
\(264\) 450.488 780.269i 0.105021 0.181902i
\(265\) −2278.81 −0.528249
\(266\) −1919.98 6.56037i −0.442562 0.00151219i
\(267\) −6700.19 −1.53575
\(268\) −957.432 + 1658.32i −0.218226 + 0.377978i
\(269\) 1392.93 + 2412.63i 0.315720 + 0.546843i 0.979590 0.201005i \(-0.0644207\pi\)
−0.663871 + 0.747848i \(0.731087\pi\)
\(270\) −72.6921 125.906i −0.0163848 0.0283793i
\(271\) 1344.77 2329.21i 0.301435 0.522100i −0.675026 0.737794i \(-0.735868\pi\)
0.976461 + 0.215693i \(0.0692011\pi\)
\(272\) −1838.70 −0.409882
\(273\) 2710.03 + 9.25990i 0.600801 + 0.00205287i
\(274\) 6405.42 1.41228
\(275\) 729.580 1263.67i 0.159983 0.277099i
\(276\) −343.717 595.335i −0.0749613 0.129837i
\(277\) 415.418 + 719.525i 0.0901085 + 0.156072i 0.907557 0.419930i \(-0.137945\pi\)
−0.817448 + 0.576002i \(0.804612\pi\)
\(278\) 1710.35 2962.41i 0.368992 0.639113i
\(279\) −5132.85 −1.10142
\(280\) −390.995 682.599i −0.0834515 0.145690i
\(281\) −8850.37 −1.87889 −0.939447 0.342695i \(-0.888660\pi\)
−0.939447 + 0.342695i \(0.888660\pi\)
\(282\) 160.282 277.616i 0.0338463 0.0586235i
\(283\) 278.788 + 482.874i 0.0585590 + 0.101427i 0.893819 0.448428i \(-0.148016\pi\)
−0.835260 + 0.549856i \(0.814683\pi\)
\(284\) −1304.02 2258.63i −0.272463 0.471919i
\(285\) −1028.20 + 1780.90i −0.213704 + 0.370146i
\(286\) 590.334 0.122053
\(287\) −1001.27 + 1720.65i −0.205935 + 0.353891i
\(288\) 922.634 0.188773
\(289\) −4146.69 + 7182.28i −0.844024 + 1.46189i
\(290\) 1208.34 + 2092.90i 0.244676 + 0.423791i
\(291\) −4837.90 8379.48i −0.974579 1.68802i
\(292\) 1032.84 1788.92i 0.206994 0.358523i
\(293\) −263.506 −0.0525400 −0.0262700 0.999655i \(-0.508363\pi\)
−0.0262700 + 0.999655i \(0.508363\pi\)
\(294\) 2532.54 + 4456.54i 0.502383 + 0.884049i
\(295\) −682.597 −0.134720
\(296\) −82.9591 + 143.689i −0.0162902 + 0.0282155i
\(297\) 103.179 + 178.712i 0.0201585 + 0.0349156i
\(298\) 2647.44 + 4585.50i 0.514638 + 0.891378i
\(299\) 225.209 390.073i 0.0435590 0.0754465i
\(300\) 2893.51 0.556856
\(301\) 1292.86 2221.73i 0.247571 0.425442i
\(302\) −2021.63 −0.385204
\(303\) 1155.30 2001.04i 0.219044 0.379395i
\(304\) −414.679 718.245i −0.0782351 0.135507i
\(305\) 599.778 + 1038.85i 0.112601 + 0.195030i
\(306\) 3313.38 5738.94i 0.618998 1.07214i
\(307\) 6200.77 1.15276 0.576379 0.817182i \(-0.304465\pi\)
0.576379 + 0.817182i \(0.304465\pi\)
\(308\) 554.980 + 968.884i 0.102672 + 0.179244i
\(309\) −4614.98 −0.849635
\(310\) −945.200 + 1637.14i −0.173173 + 0.299945i
\(311\) −4212.12 7295.61i −0.767999 1.33021i −0.938647 0.344880i \(-0.887919\pi\)
0.170648 0.985332i \(-0.445414\pi\)
\(312\) 585.315 + 1013.80i 0.106208 + 0.183958i
\(313\) 1210.55 2096.74i 0.218609 0.378642i −0.735774 0.677227i \(-0.763181\pi\)
0.954383 + 0.298585i \(0.0965148\pi\)
\(314\) 153.578 0.0276017
\(315\) 2835.10 + 9.68724i 0.507111 + 0.00173274i
\(316\) −1397.59 −0.248799
\(317\) 516.132 893.966i 0.0914474 0.158392i −0.816673 0.577101i \(-0.804184\pi\)
0.908120 + 0.418709i \(0.137517\pi\)
\(318\) 3207.05 + 5554.77i 0.565542 + 0.979548i
\(319\) −1715.12 2970.67i −0.301029 0.521398i
\(320\) 169.900 294.276i 0.0296804 0.0514079i
\(321\) 9154.85 1.59182
\(322\) 851.927 + 2.91095i 0.147441 + 0.000503791i
\(323\) −5956.81 −1.02615
\(324\) 1352.34 2342.32i 0.231883 0.401633i
\(325\) 947.936 + 1641.87i 0.161791 + 0.280230i
\(326\) −2149.22 3722.55i −0.365135 0.632432i
\(327\) 587.474 1017.53i 0.0993498 0.172079i
\(328\) −859.934 −0.144762
\(329\) 197.460 + 344.725i 0.0330891 + 0.0577669i
\(330\) 1195.91 0.199493
\(331\) −907.676 + 1572.14i −0.150726 + 0.261066i −0.931495 0.363755i \(-0.881495\pi\)
0.780768 + 0.624821i \(0.214828\pi\)
\(332\) −746.029 1292.16i −0.123324 0.213604i
\(333\) −298.988 517.862i −0.0492025 0.0852212i
\(334\) 2071.34 3587.67i 0.339337 0.587750i
\(335\) −2541.69 −0.414529
\(336\) −1113.63 + 1913.73i −0.180814 + 0.310722i
\(337\) −8160.36 −1.31906 −0.659530 0.751678i \(-0.729245\pi\)
−0.659530 + 0.751678i \(0.729245\pi\)
\(338\) 1813.49 3141.06i 0.291837 0.505477i
\(339\) −4584.02 7939.75i −0.734424 1.27206i
\(340\) −1220.30 2113.62i −0.194647 0.337139i
\(341\) 1341.62 2323.76i 0.213058 0.369028i
\(342\) 2989.04 0.472599
\(343\) −6352.12 65.1156i −0.999947 0.0102505i
\(344\) 1110.36 0.174030
\(345\) 456.231 790.216i 0.0711961 0.123315i
\(346\) −3121.85 5407.21i −0.485063 0.840154i
\(347\) 2846.90 + 4930.97i 0.440431 + 0.762848i 0.997721 0.0674692i \(-0.0214924\pi\)
−0.557291 + 0.830317i \(0.688159\pi\)
\(348\) 3401.08 5890.84i 0.523899 0.907420i
\(349\) 4560.60 0.699494 0.349747 0.936844i \(-0.386267\pi\)
0.349747 + 0.936844i \(0.386267\pi\)
\(350\) −1803.55 + 3099.34i −0.275440 + 0.473334i
\(351\) −268.120 −0.0407727
\(352\) −241.157 + 417.697i −0.0365163 + 0.0632481i
\(353\) −4290.24 7430.92i −0.646874 1.12042i −0.983865 0.178911i \(-0.942742\pi\)
0.336991 0.941508i \(-0.390591\pi\)
\(354\) 960.645 + 1663.89i 0.144231 + 0.249815i
\(355\) 1730.89 2997.99i 0.258777 0.448216i
\(356\) 3586.78 0.533985
\(357\) 7904.44 + 13799.6i 1.17184 + 2.04580i
\(358\) −6138.58 −0.906240
\(359\) −994.576 + 1722.66i −0.146217 + 0.253254i −0.929826 0.367999i \(-0.880043\pi\)
0.783610 + 0.621254i \(0.213376\pi\)
\(360\) 612.328 + 1060.58i 0.0896458 + 0.155271i
\(361\) 2086.07 + 3613.18i 0.304137 + 0.526780i
\(362\) −1108.70 + 1920.33i −0.160973 + 0.278813i
\(363\) 8247.89 1.19257
\(364\) −1450.75 4.95705i −0.208901 0.000713791i
\(365\) 2741.86 0.393194
\(366\) 1688.18 2924.02i 0.241100 0.417598i
\(367\) 57.4441 + 99.4961i 0.00817046 + 0.0141516i 0.870082 0.492907i \(-0.164066\pi\)
−0.861911 + 0.507059i \(0.830733\pi\)
\(368\) 184.000 + 318.697i 0.0260643 + 0.0451447i
\(369\) 1549.62 2684.02i 0.218618 0.378657i
\(370\) −220.231 −0.0309440
\(371\) −7948.91 27.1606i −1.11236 0.00380083i
\(372\) 5320.87 0.741597
\(373\) −6284.35 + 10884.8i −0.872363 + 1.51098i −0.0128183 + 0.999918i \(0.504080\pi\)
−0.859545 + 0.511060i \(0.829253\pi\)
\(374\) 1732.10 + 3000.08i 0.239478 + 0.414788i
\(375\) 4399.86 + 7620.79i 0.605888 + 1.04943i
\(376\) −85.8028 + 148.615i −0.0117685 + 0.0203836i
\(377\) 4456.88 0.608862
\(378\) −252.063 440.052i −0.0342982 0.0598778i
\(379\) −12075.5 −1.63662 −0.818308 0.574781i \(-0.805087\pi\)
−0.818308 + 0.574781i \(0.805087\pi\)
\(380\) 550.423 953.360i 0.0743055 0.128701i
\(381\) 4592.31 + 7954.11i 0.617509 + 1.06956i
\(382\) 3180.62 + 5508.99i 0.426007 + 0.737865i
\(383\) 6114.01 10589.8i 0.815695 1.41283i −0.0931328 0.995654i \(-0.529688\pi\)
0.908828 0.417171i \(-0.136979\pi\)
\(384\) −956.429 −0.127103
\(385\) −745.422 + 1280.98i −0.0986759 + 0.169571i
\(386\) −1624.65 −0.214229
\(387\) −2000.89 + 3465.64i −0.262818 + 0.455215i
\(388\) 2589.84 + 4485.74i 0.338865 + 0.586931i
\(389\) −1568.78 2717.21i −0.204474 0.354159i 0.745491 0.666516i \(-0.232215\pi\)
−0.949965 + 0.312356i \(0.898882\pi\)
\(390\) −776.917 + 1345.66i −0.100874 + 0.174718i
\(391\) 2643.14 0.341865
\(392\) −1355.73 2385.69i −0.174680 0.307387i
\(393\) 18089.5 2.32187
\(394\) 3772.40 6533.99i 0.482363 0.835477i
\(395\) −927.541 1606.55i −0.118151 0.204644i
\(396\) −869.141 1505.40i −0.110293 0.191033i
\(397\) −7744.89 + 13414.5i −0.979106 + 1.69586i −0.313445 + 0.949606i \(0.601483\pi\)
−0.665661 + 0.746254i \(0.731850\pi\)
\(398\) −3048.55 −0.383945
\(399\) −3607.80 + 6199.87i −0.452671 + 0.777899i
\(400\) −1548.97 −0.193621
\(401\) 3026.26 5241.64i 0.376869 0.652755i −0.613736 0.789511i \(-0.710334\pi\)
0.990605 + 0.136756i \(0.0436675\pi\)
\(402\) 3577.01 + 6195.57i 0.443794 + 0.768674i
\(403\) 1743.16 + 3019.24i 0.215466 + 0.373198i
\(404\) −618.460 + 1071.20i −0.0761623 + 0.131917i
\(405\) 3590.05 0.440472
\(406\) 4189.96 + 7314.84i 0.512178 + 0.894161i
\(407\) 312.597 0.0380709
\(408\) −3434.75 + 5949.16i −0.416778 + 0.721880i
\(409\) −5960.88 10324.6i −0.720652 1.24821i −0.960739 0.277454i \(-0.910509\pi\)
0.240087 0.970751i \(-0.422824\pi\)
\(410\) −570.716 988.508i −0.0687454 0.119071i
\(411\) 11965.5 20724.8i 1.43604 2.48730i
\(412\) 2470.51 0.295421
\(413\) −2381.03 8.13572i −0.283687 0.000969329i
\(414\) −1326.29 −0.157448
\(415\) 990.239 1715.14i 0.117130 0.202875i
\(416\) −313.334 542.710i −0.0369290 0.0639629i
\(417\) −6389.94 11067.7i −0.750400 1.29973i
\(418\) −781.273 + 1353.20i −0.0914194 + 0.158343i
\(419\) −7468.53 −0.870792 −0.435396 0.900239i \(-0.643392\pi\)
−0.435396 + 0.900239i \(0.643392\pi\)
\(420\) −2938.95 10.0421i −0.341443 0.00116667i
\(421\) 6039.59 0.699172 0.349586 0.936904i \(-0.386322\pi\)
0.349586 + 0.936904i \(0.386322\pi\)
\(422\) −910.563 + 1577.14i −0.105037 + 0.181929i
\(423\) −309.237 535.614i −0.0355452 0.0615660i
\(424\) −1716.81 2973.61i −0.196641 0.340592i
\(425\) −5562.68 + 9634.84i −0.634893 + 1.09967i
\(426\) −9743.78 −1.10819
\(427\) 2079.76 + 3630.84i 0.235706 + 0.411496i
\(428\) −4900.81 −0.553481
\(429\) 1102.76 1910.03i 0.124107 0.214959i
\(430\) 736.915 + 1276.37i 0.0826446 + 0.143145i
\(431\) −6776.07 11736.5i −0.757289 1.31166i −0.944228 0.329292i \(-0.893190\pi\)
0.186939 0.982372i \(-0.440143\pi\)
\(432\) 109.530 189.711i 0.0121985 0.0211284i
\(433\) 2807.93 0.311641 0.155821 0.987785i \(-0.450198\pi\)
0.155821 + 0.987785i \(0.450198\pi\)
\(434\) −3316.55 + 5699.37i −0.366819 + 0.630365i
\(435\) 9028.82 0.995169
\(436\) −314.489 + 544.711i −0.0345443 + 0.0598324i
\(437\) 596.101 + 1032.48i 0.0652526 + 0.113021i
\(438\) −3858.73 6683.51i −0.420952 0.729111i
\(439\) 7949.37 13768.7i 0.864243 1.49691i −0.00355438 0.999994i \(-0.501131\pi\)
0.867797 0.496919i \(-0.165535\pi\)
\(440\) −640.199 −0.0693643
\(441\) 9889.25 + 67.5819i 1.06784 + 0.00729747i
\(442\) −4501.00 −0.484368
\(443\) 4597.32 7962.79i 0.493059 0.854004i −0.506909 0.862000i \(-0.669212\pi\)
0.999968 + 0.00799607i \(0.00254525\pi\)
\(444\) 309.939 + 536.831i 0.0331285 + 0.0573803i
\(445\) 2380.45 + 4123.06i 0.253582 + 0.439217i
\(446\) −1289.30 + 2233.14i −0.136884 + 0.237090i
\(447\) 19781.9 2.09318
\(448\) 596.152 1024.47i 0.0628695 0.108039i
\(449\) −11231.7 −1.18053 −0.590265 0.807209i \(-0.700977\pi\)
−0.590265 + 0.807209i \(0.700977\pi\)
\(450\) 2791.27 4834.62i 0.292404 0.506458i
\(451\) 810.076 + 1403.09i 0.0845787 + 0.146495i
\(452\) 2453.94 + 4250.34i 0.255362 + 0.442299i
\(453\) −3776.46 + 6541.01i −0.391685 + 0.678419i
\(454\) 2827.87 0.292332
\(455\) −957.124 1670.95i −0.0986169 0.172165i
\(456\) −3098.52 −0.318205
\(457\) 4875.98 8445.45i 0.499100 0.864467i −0.500899 0.865506i \(-0.666997\pi\)
0.999999 + 0.00103874i \(0.000330643\pi\)
\(458\) 799.165 + 1384.20i 0.0815339 + 0.141221i
\(459\) −786.692 1362.59i −0.0799992 0.138563i
\(460\) −244.232 + 423.022i −0.0247551 + 0.0428772i
\(461\) −6728.85 −0.679813 −0.339906 0.940459i \(-0.610395\pi\)
−0.339906 + 0.940459i \(0.610395\pi\)
\(462\) 4171.56 + 14.2538i 0.420083 + 0.00143538i
\(463\) −7665.18 −0.769398 −0.384699 0.923042i \(-0.625695\pi\)
−0.384699 + 0.923042i \(0.625695\pi\)
\(464\) −1820.68 + 3153.51i −0.182162 + 0.315513i
\(465\) 3531.32 + 6116.42i 0.352174 + 0.609983i
\(466\) −1554.41 2692.32i −0.154521 0.267638i
\(467\) 8377.96 14511.1i 0.830163 1.43788i −0.0677464 0.997703i \(-0.521581\pi\)
0.897909 0.440181i \(-0.145086\pi\)
\(468\) 2258.53 0.223079
\(469\) −8865.89 30.2938i −0.872897 0.00298260i
\(470\) −227.780 −0.0223547
\(471\) 286.888 496.905i 0.0280660 0.0486118i
\(472\) −514.257 890.719i −0.0501496 0.0868616i
\(473\) −1045.98 1811.69i −0.101679 0.176113i
\(474\) −2610.73 + 4521.91i −0.252985 + 0.438182i
\(475\) −5018.16 −0.484734
\(476\) −4231.44 7387.25i −0.407454 0.711332i
\(477\) 12374.9 1.18786
\(478\) 6967.81 12068.6i 0.666737 1.15482i
\(479\) −2759.29 4779.22i −0.263205 0.455884i 0.703887 0.710312i \(-0.251446\pi\)
−0.967092 + 0.254428i \(0.918113\pi\)
\(480\) −634.757 1099.43i −0.0603595 0.104546i
\(481\) −203.077 + 351.740i −0.0192506 + 0.0333430i
\(482\) −10116.5 −0.956003
\(483\) 1600.84 2750.98i 0.150809 0.259160i
\(484\) −4415.30 −0.414660
\(485\) −3437.62 + 5954.14i −0.321844 + 0.557450i
\(486\) −5422.08 9391.31i −0.506071 0.876540i
\(487\) −1976.96 3424.19i −0.183952 0.318614i 0.759271 0.650775i \(-0.225556\pi\)
−0.943223 + 0.332161i \(0.892222\pi\)
\(488\) −903.725 + 1565.30i −0.0838313 + 0.145200i
\(489\) −16059.2 −1.48511
\(490\) 1842.63 3141.75i 0.169881 0.289653i
\(491\) 12730.6 1.17011 0.585053 0.810995i \(-0.301074\pi\)
0.585053 + 0.810995i \(0.301074\pi\)
\(492\) −1606.38 + 2782.33i −0.147197 + 0.254954i
\(493\) 13076.9 + 22649.9i 1.19464 + 2.06917i
\(494\) −1015.10 1758.21i −0.0924525 0.160133i
\(495\) 1153.65 1998.18i 0.104753 0.181438i
\(496\) −2848.39 −0.257856
\(497\) 6073.40 10436.9i 0.548147 0.941971i
\(498\) −5574.40 −0.501596
\(499\) 9009.94 15605.7i 0.808297 1.40001i −0.105745 0.994393i \(-0.533723\pi\)
0.914042 0.405619i \(-0.132944\pi\)
\(500\) −2355.35 4079.59i −0.210669 0.364890i
\(501\) −7738.63 13403.7i −0.690093 1.19528i
\(502\) 3363.38 5825.55i 0.299034 0.517942i
\(503\) −10200.1 −0.904175 −0.452087 0.891974i \(-0.649320\pi\)
−0.452087 + 0.891974i \(0.649320\pi\)
\(504\) 2123.27 + 3706.81i 0.187655 + 0.327608i
\(505\) −1641.82 −0.144674
\(506\) 346.664 600.439i 0.0304567 0.0527525i
\(507\) −6775.30 11735.2i −0.593494 1.02796i
\(508\) −2458.37 4258.03i −0.214710 0.371889i
\(509\) −6186.28 + 10714.9i −0.538707 + 0.933068i 0.460267 + 0.887781i \(0.347754\pi\)
−0.998974 + 0.0452876i \(0.985580\pi\)
\(510\) −9118.20 −0.791688
\(511\) 9564.14 + 32.6797i 0.827970 + 0.00282909i
\(512\) 512.000 0.0441942
\(513\) 354.842 614.604i 0.0305393 0.0528956i
\(514\) 7020.29 + 12159.5i 0.602435 + 1.04345i
\(515\) 1639.61 + 2839.89i 0.140291 + 0.242992i
\(516\) 2074.18 3592.58i 0.176958 0.306501i
\(517\) 323.312 0.0275034
\(518\) −768.208 2.62488i −0.0651604 0.000222646i
\(519\) −23326.8 −1.97290
\(520\) 415.903 720.364i 0.0350741 0.0607501i
\(521\) −5830.30 10098.4i −0.490269 0.849171i 0.509668 0.860371i \(-0.329768\pi\)
−0.999937 + 0.0112002i \(0.996435\pi\)
\(522\) −6561.80 11365.4i −0.550196 0.952967i
\(523\) 1992.69 3451.44i 0.166605 0.288568i −0.770619 0.637296i \(-0.780053\pi\)
0.937224 + 0.348728i \(0.113386\pi\)
\(524\) −9683.74 −0.807321
\(525\) 6658.88 + 11625.1i 0.553557 + 0.966400i
\(526\) −2237.13 −0.185444
\(527\) −10229.2 + 17717.5i −0.845523 + 1.46449i
\(528\) 900.976 + 1560.54i 0.0742613 + 0.128624i
\(529\) −264.500 458.127i −0.0217391 0.0376533i
\(530\) 2278.81 3947.01i 0.186764 0.323485i
\(531\) 3706.80 0.302941
\(532\) 1931.34 3318.94i 0.157395 0.270478i
\(533\) −2105.05 −0.171069
\(534\) 6700.19 11605.1i 0.542969 0.940451i
\(535\) −3252.54 5633.56i −0.262840 0.455253i
\(536\) −1914.86 3316.64i −0.154309 0.267271i
\(537\) −11467.0 + 19861.5i −0.921487 + 1.59606i
\(538\) −5571.73 −0.446495
\(539\) −2615.44 + 4459.42i −0.209008 + 0.356365i
\(540\) 290.768 0.0231716
\(541\) −4283.59 + 7419.40i −0.340418 + 0.589621i −0.984510 0.175326i \(-0.943902\pi\)
0.644092 + 0.764948i \(0.277235\pi\)
\(542\) 2689.54 + 4658.41i 0.213147 + 0.369181i
\(543\) 4142.17 + 7174.45i 0.327362 + 0.567008i
\(544\) 1838.70 3184.73i 0.144915 0.251000i
\(545\) −834.873 −0.0656184
\(546\) −2726.07 + 4684.65i −0.213672 + 0.367188i
\(547\) −14381.3 −1.12413 −0.562067 0.827091i \(-0.689994\pi\)
−0.562067 + 0.827091i \(0.689994\pi\)
\(548\) −6405.42 + 11094.5i −0.499317 + 0.864843i
\(549\) −3257.06 5641.39i −0.253202 0.438559i
\(550\) 1459.16 + 2527.34i 0.113125 + 0.195938i
\(551\) −5898.42 + 10216.4i −0.456046 + 0.789894i
\(552\) 1374.87 0.106011
\(553\) −3216.29 5615.00i −0.247325 0.431780i
\(554\) −1661.67 −0.127433
\(555\) −411.397 + 712.561i −0.0314646 + 0.0544982i
\(556\) 3420.69 + 5924.81i 0.260917 + 0.451921i
\(557\) 879.823 + 1523.90i 0.0669287 + 0.115924i 0.897548 0.440917i \(-0.145347\pi\)
−0.830619 + 0.556841i \(0.812013\pi\)
\(558\) 5132.85 8890.36i 0.389411 0.674479i
\(559\) 2718.07 0.205656
\(560\) 1573.29 + 5.37577i 0.118721 + 0.000405657i
\(561\) 12942.4 0.974027
\(562\) 8850.37 15329.3i 0.664289 1.15058i
\(563\) 6298.53 + 10909.4i 0.471495 + 0.816653i 0.999468 0.0326082i \(-0.0103814\pi\)
−0.527974 + 0.849261i \(0.677048\pi\)
\(564\) 320.564 + 555.233i 0.0239329 + 0.0414530i
\(565\) −3257.23 + 5641.68i −0.242535 + 0.420084i
\(566\) −1115.15 −0.0828149
\(567\) 12522.8 + 42.7890i 0.927526 + 0.00316926i
\(568\) 5216.08 0.385320
\(569\) 3214.85 5568.29i 0.236860 0.410254i −0.722951 0.690899i \(-0.757215\pi\)
0.959812 + 0.280645i \(0.0905483\pi\)
\(570\) −2056.41 3561.80i −0.151111 0.261733i
\(571\) 2545.07 + 4408.19i 0.186529 + 0.323077i 0.944091 0.329686i \(-0.106943\pi\)
−0.757562 + 0.652763i \(0.773610\pi\)
\(572\) −590.334 + 1022.49i −0.0431523 + 0.0747420i
\(573\) 23765.9 1.73270
\(574\) −1978.98 3454.91i −0.143904 0.251228i
\(575\) 2226.64 0.161491
\(576\) −922.634 + 1598.05i −0.0667415 + 0.115600i
\(577\) 6374.46 + 11040.9i 0.459917 + 0.796600i 0.998956 0.0456809i \(-0.0145457\pi\)
−0.539039 + 0.842281i \(0.681212\pi\)
\(578\) −8293.38 14364.6i −0.596815 1.03371i
\(579\) −3034.89 + 5256.58i −0.217834 + 0.377299i
\(580\) −4833.35 −0.346024
\(581\) 3474.58 5970.95i 0.248107 0.426363i
\(582\) 19351.6 1.37826
\(583\) −3234.55 + 5602.40i −0.229779 + 0.397989i
\(584\) 2065.67 + 3577.85i 0.146367 + 0.253514i
\(585\) 1498.93 + 2596.22i 0.105937 + 0.183488i
\(586\) 263.506 456.406i 0.0185757 0.0321740i
\(587\) 7455.98 0.524261 0.262131 0.965032i \(-0.415575\pi\)
0.262131 + 0.965032i \(0.415575\pi\)
\(588\) −10251.5 70.0573i −0.718987 0.00491346i
\(589\) −9227.87 −0.645548
\(590\) 682.597 1182.29i 0.0476306 0.0824987i
\(591\) −14093.9 24411.3i −0.980956 1.69907i
\(592\) −165.918 287.379i −0.0115189 0.0199513i
\(593\) −4502.80 + 7799.08i −0.311817 + 0.540084i −0.978756 0.205029i \(-0.934271\pi\)
0.666938 + 0.745113i \(0.267604\pi\)
\(594\) −412.718 −0.0285084
\(595\) 5683.47 9766.84i 0.391596 0.672943i
\(596\) −10589.8 −0.727807
\(597\) −5694.77 + 9863.64i −0.390405 + 0.676201i
\(598\) 450.417 + 780.146i 0.0308009 + 0.0533487i
\(599\) 7098.17 + 12294.4i 0.484179 + 0.838623i 0.999835 0.0181728i \(-0.00578489\pi\)
−0.515656 + 0.856796i \(0.672452\pi\)
\(600\) −2893.51 + 5011.70i −0.196878 + 0.341003i
\(601\) 4208.80 0.285658 0.142829 0.989747i \(-0.454380\pi\)
0.142829 + 0.989747i \(0.454380\pi\)
\(602\) 2555.29 + 4461.02i 0.172999 + 0.302022i
\(603\) 13802.5 0.932140
\(604\) 2021.63 3501.57i 0.136190 0.235889i
\(605\) −2930.32 5075.46i −0.196916 0.341069i
\(606\) 2310.60 + 4002.08i 0.154887 + 0.268273i
\(607\) 6715.91 11632.3i 0.449078 0.777825i −0.549248 0.835659i \(-0.685086\pi\)
0.998326 + 0.0578336i \(0.0184193\pi\)
\(608\) 1658.72 0.110641
\(609\) 31494.2 + 107.612i 2.09558 + 0.00716039i
\(610\) −2399.11 −0.159241
\(611\) −210.038 + 363.797i −0.0139071 + 0.0240878i
\(612\) 6626.76 + 11477.9i 0.437698 + 0.758115i
\(613\) −13887.1 24053.1i −0.914999 1.58482i −0.806903 0.590684i \(-0.798858\pi\)
−0.108096 0.994140i \(-0.534475\pi\)
\(614\) −6200.77 + 10740.1i −0.407562 + 0.705917i
\(615\) −4264.44 −0.279608
\(616\) −2233.14 7.63039i −0.146064 0.000499086i
\(617\) 10560.5 0.689061 0.344530 0.938775i \(-0.388038\pi\)
0.344530 + 0.938775i \(0.388038\pi\)
\(618\) 4614.98 7993.38i 0.300391 0.520293i
\(619\) 10219.4 + 17700.6i 0.663577 + 1.14935i 0.979669 + 0.200620i \(0.0642956\pi\)
−0.316093 + 0.948728i \(0.602371\pi\)
\(620\) −1890.40 3274.27i −0.122452 0.212093i
\(621\) −157.449 + 272.710i −0.0101743 + 0.0176223i
\(622\) 16848.5 1.08611
\(623\) 8254.31 + 14410.4i 0.530822 + 0.926709i
\(624\) −2341.26 −0.150201
\(625\) −2924.28 + 5065.00i −0.187154 + 0.324160i
\(626\) 2421.11 + 4193.48i 0.154580 + 0.267740i
\(627\) 2918.88 + 5055.64i 0.185915 + 0.322014i
\(628\) −153.578 + 266.005i −0.00975866 + 0.0169025i
\(629\) −2383.39 −0.151085
\(630\) −2851.88 + 4900.85i −0.180352 + 0.309928i
\(631\) −15693.6 −0.990099 −0.495049 0.868865i \(-0.664850\pi\)
−0.495049 + 0.868865i \(0.664850\pi\)
\(632\) 1397.59 2420.69i 0.0879636 0.152357i
\(633\) 3401.91 + 5892.28i 0.213608 + 0.369980i
\(634\) 1032.26 + 1787.93i 0.0646631 + 0.112000i
\(635\) 3263.12 5651.88i 0.203926 0.353210i
\(636\) −12828.2 −0.799798
\(637\) −3318.71 5839.99i −0.206424 0.363248i
\(638\) 6860.48 0.425719
\(639\) −9399.49 + 16280.4i −0.581906 + 1.00789i
\(640\) 339.801 + 588.552i 0.0209872 + 0.0363509i
\(641\) 6949.46 + 12036.8i 0.428217 + 0.741693i 0.996715 0.0809913i \(-0.0258086\pi\)
−0.568498 + 0.822685i \(0.692475\pi\)
\(642\) −9154.85 + 15856.7i −0.562793 + 0.974786i
\(643\) 18032.4 1.10595 0.552977 0.833196i \(-0.313492\pi\)
0.552977 + 0.833196i \(0.313492\pi\)
\(644\) −856.969 + 1472.67i −0.0524368 + 0.0901107i
\(645\) 5506.30 0.336140
\(646\) 5956.81 10317.5i 0.362798 0.628385i
\(647\) 1011.50 + 1751.97i 0.0614624 + 0.106456i 0.895119 0.445827i \(-0.147090\pi\)
−0.833657 + 0.552283i \(0.813757\pi\)
\(648\) 2704.68 + 4684.64i 0.163966 + 0.283997i
\(649\) −968.882 + 1678.15i −0.0586008 + 0.101500i
\(650\) −3791.75 −0.228807
\(651\) 12245.0 + 21377.3i 0.737204 + 1.28701i
\(652\) 8596.86 0.516379
\(653\) 76.5213 132.539i 0.00458577 0.00794279i −0.863723 0.503966i \(-0.831874\pi\)
0.868309 + 0.496023i \(0.165207\pi\)
\(654\) 1174.95 + 2035.07i 0.0702509 + 0.121678i
\(655\) −6426.84 11131.6i −0.383385 0.664043i
\(656\) 859.934 1489.45i 0.0511811 0.0886482i
\(657\) −14889.5 −0.884164
\(658\) −794.541 2.71486i −0.0470736 0.000160846i
\(659\) −5171.29 −0.305683 −0.152841 0.988251i \(-0.548842\pi\)
−0.152841 + 0.988251i \(0.548842\pi\)
\(660\) −1195.91 + 2071.37i −0.0705313 + 0.122164i
\(661\) 2213.22 + 3833.40i 0.130233 + 0.225570i 0.923766 0.382957i \(-0.125094\pi\)
−0.793533 + 0.608527i \(0.791761\pi\)
\(662\) −1815.35 3144.28i −0.106580 0.184601i
\(663\) −8407.99 + 14563.1i −0.492517 + 0.853065i
\(664\) 2984.12 0.174407
\(665\) 5096.96 + 17.4158i 0.297220 + 0.00101557i
\(666\) 1195.95 0.0695828
\(667\) 2617.23 4533.17i 0.151933 0.263156i
\(668\) 4142.68 + 7175.33i 0.239948 + 0.415602i
\(669\) 4816.90 + 8343.12i 0.278374 + 0.482158i
\(670\) 2541.69 4402.33i 0.146558 0.253846i
\(671\) 3405.31 0.195917
\(672\) −2201.05 3842.59i −0.126350 0.220582i
\(673\) 19846.7 1.13675 0.568377 0.822768i \(-0.307571\pi\)
0.568377 + 0.822768i \(0.307571\pi\)
\(674\) 8160.36 14134.2i 0.466358 0.807756i
\(675\) −662.727 1147.88i −0.0377902 0.0654545i
\(676\) 3626.98 + 6282.12i 0.206360 + 0.357426i
\(677\) 11868.9 20557.5i 0.673792 1.16704i −0.303028 0.952982i \(-0.597998\pi\)
0.976820 0.214061i \(-0.0686692\pi\)
\(678\) 18336.1 1.03863
\(679\) −12062.0 + 20728.2i −0.681736 + 1.17154i
\(680\) 4881.20 0.275273
\(681\) 5282.54 9149.62i 0.297250 0.514852i
\(682\) 2683.24 + 4647.51i 0.150655 + 0.260942i
\(683\) 2366.81 + 4099.44i 0.132597 + 0.229664i 0.924677 0.380753i \(-0.124335\pi\)
−0.792080 + 0.610417i \(0.791002\pi\)
\(684\) −2989.04 + 5177.17i −0.167089 + 0.289406i
\(685\) −17004.4 −0.948475
\(686\) 6464.90 10937.1i 0.359812 0.608716i
\(687\) 5971.45 0.331623
\(688\) −1110.36 + 1923.20i −0.0615290 + 0.106571i
\(689\) −4202.62 7279.15i −0.232376 0.402487i
\(690\) 912.463 + 1580.43i 0.0503433 + 0.0871971i
\(691\) 137.772 238.628i 0.00758480 0.0131373i −0.862208 0.506554i \(-0.830919\pi\)
0.869793 + 0.493417i \(0.164252\pi\)
\(692\) 12487.4 0.685983
\(693\) 4047.97 6956.29i 0.221890 0.381310i
\(694\) −11387.6 −0.622863
\(695\) −4540.44 + 7864.28i −0.247811 + 0.429222i
\(696\) 6802.15 + 11781.7i 0.370453 + 0.641643i
\(697\) −6176.43 10697.9i −0.335651 0.581365i
\(698\) −4560.60 + 7899.20i −0.247309 + 0.428351i
\(699\) −11614.7 −0.628481
\(700\) −3564.66 6223.19i −0.192474 0.336021i
\(701\) 15236.5 0.820933 0.410467 0.911876i \(-0.365366\pi\)
0.410467 + 0.911876i \(0.365366\pi\)
\(702\) 268.120 464.398i 0.0144153 0.0249681i
\(703\) −537.522 931.015i −0.0288379 0.0499487i
\(704\) −482.315 835.394i −0.0258209 0.0447231i
\(705\) −425.499 + 736.987i −0.0227308 + 0.0393709i
\(706\) 17161.0 0.914819
\(707\) −5726.99 19.5685i −0.304647 0.00104095i
\(708\) −3842.58 −0.203973
\(709\) −10131.4 + 17548.0i −0.536659 + 0.929521i 0.462422 + 0.886660i \(0.346981\pi\)
−0.999081 + 0.0428611i \(0.986353\pi\)
\(710\) 3461.78 + 5995.97i 0.182983 + 0.316936i
\(711\) 5036.96 + 8724.26i 0.265683 + 0.460176i
\(712\) −3586.78 + 6212.48i −0.188792 + 0.326998i
\(713\) 4094.56 0.215067
\(714\) −31806.0 108.678i −1.66710 0.00569631i
\(715\) −1567.16 −0.0819697
\(716\) 6138.58 10632.3i 0.320404 0.554956i
\(717\) −26032.1 45088.9i −1.35591 2.34850i
\(718\) −1989.15 3445.31i −0.103391 0.179078i
\(719\) −2009.28 + 3480.18i −0.104219 + 0.180513i −0.913419 0.407021i \(-0.866568\pi\)
0.809200 + 0.587534i \(0.199901\pi\)
\(720\) −2449.31 −0.126778
\(721\) 5685.43 + 9925.63i 0.293671 + 0.512690i
\(722\) −8344.29 −0.430114
\(723\) −18897.9 + 32732.0i −0.972087 + 1.68370i
\(724\) −2217.41 3840.66i −0.113825 0.197151i
\(725\) 11016.3 + 19080.8i 0.564324 + 0.977438i
\(726\) −8247.89 + 14285.8i −0.421636 + 0.730295i
\(727\) 31658.7 1.61507 0.807536 0.589819i \(-0.200801\pi\)
0.807536 + 0.589819i \(0.200801\pi\)
\(728\) 1459.33 2507.81i 0.0742946 0.127673i
\(729\) −22257.7 −1.13081
\(730\) −2741.86 + 4749.05i −0.139015 + 0.240781i
\(731\) 7975.08 + 13813.2i 0.403514 + 0.698907i
\(732\) 3376.36 + 5848.03i 0.170483 + 0.295286i
\(733\) −17998.9 + 31175.0i −0.906963 + 1.57091i −0.0887026 + 0.996058i \(0.528272\pi\)
−0.818260 + 0.574848i \(0.805061\pi\)
\(734\) −229.776 −0.0115548
\(735\) −6723.11 11830.7i −0.337395 0.593719i
\(736\) −736.000 −0.0368605
\(737\) −3607.68 + 6248.69i −0.180313 + 0.312311i
\(738\) 3099.24 + 5368.04i 0.154586 + 0.267751i
\(739\) −4080.24 7067.19i −0.203104 0.351787i 0.746423 0.665472i \(-0.231770\pi\)
−0.949527 + 0.313685i \(0.898436\pi\)
\(740\) 220.231 381.451i 0.0109403 0.0189492i
\(741\) −7584.94 −0.376032
\(742\) 7995.95 13740.8i 0.395607 0.679837i
\(743\) −2264.67 −0.111821 −0.0559104 0.998436i \(-0.517806\pi\)
−0.0559104 + 0.998436i \(0.517806\pi\)
\(744\) −5320.87 + 9216.01i −0.262194 + 0.454133i
\(745\) −7028.14 12173.1i −0.345626 0.598641i
\(746\) −12568.7 21769.6i −0.616854 1.06842i
\(747\) −5377.43 + 9313.99i −0.263387 + 0.456200i
\(748\) −6928.39 −0.338673
\(749\) −11278.3 19689.7i −0.550202 0.960542i
\(750\) −17599.5 −0.856855
\(751\) 10088.6 17473.9i 0.490195 0.849043i −0.509741 0.860328i \(-0.670259\pi\)
0.999936 + 0.0112846i \(0.00359209\pi\)
\(752\) −171.606 297.230i −0.00832156 0.0144134i
\(753\) −12565.8 21764.6i −0.608130 1.05331i
\(754\) −4456.88 + 7719.54i −0.215265 + 0.372850i
\(755\) 5366.81 0.258700
\(756\) 1014.25 + 3.46560i 0.0487938 + 0.000166723i
\(757\) 2404.49 0.115446 0.0577231 0.998333i \(-0.481616\pi\)
0.0577231 + 0.998333i \(0.481616\pi\)
\(758\) 12075.5 20915.4i 0.578631 1.00222i
\(759\) −1295.15 2243.27i −0.0619382 0.107280i
\(760\) 1100.85 + 1906.72i 0.0525419 + 0.0910053i
\(761\) −18198.3 + 31520.4i −0.866871 + 1.50147i −0.00169435 + 0.999999i \(0.500539\pi\)
−0.865177 + 0.501467i \(0.832794\pi\)
\(762\) −18369.2 −0.873290
\(763\) −2912.19 9.95066i −0.138176 0.000472134i
\(764\) −12722.5 −0.602465
\(765\) −8796.01 + 15235.1i −0.415713 + 0.720036i
\(766\) 12228.0 + 21179.5i 0.576783 + 0.999018i
\(767\) −1258.86 2180.41i −0.0592631 0.102647i
\(768\) 956.429 1656.58i 0.0449377 0.0778344i
\(769\) −29050.2 −1.36226 −0.681129 0.732163i \(-0.738511\pi\)
−0.681129 + 0.732163i \(0.738511\pi\)
\(770\) −1473.30 2572.09i −0.0689534 0.120379i
\(771\) 52456.3 2.45028
\(772\) 1624.65 2813.98i 0.0757415 0.131188i
\(773\) 15384.7 + 26647.1i 0.715847 + 1.23988i 0.962632 + 0.270813i \(0.0872926\pi\)
−0.246785 + 0.969070i \(0.579374\pi\)
\(774\) −4001.77 6931.27i −0.185841 0.321886i
\(775\) −8617.31 + 14925.6i −0.399410 + 0.691798i
\(776\) −10359.4 −0.479227
\(777\) −1443.52 + 2480.64i −0.0666488 + 0.114534i
\(778\) 6275.12 0.289170
\(779\) 2785.91 4825.34i 0.128133 0.221933i
\(780\) −1553.83 2691.32i −0.0713284 0.123544i
\(781\) −4913.66 8510.71i −0.225128 0.389932i
\(782\) −2643.14 + 4578.05i −0.120868 + 0.209349i
\(783\) −3115.92 −0.142214
\(784\) 5487.87 + 37.5034i 0.249994 + 0.00170843i
\(785\) −407.703 −0.0185370
\(786\) −18089.5 + 31331.9i −0.820903 + 1.42185i
\(787\) −5586.24 9675.66i −0.253022 0.438246i 0.711335 0.702854i \(-0.248091\pi\)
−0.964356 + 0.264607i \(0.914758\pi\)
\(788\) 7544.81 + 13068.0i 0.341082 + 0.590771i
\(789\) −4179.02 + 7238.28i −0.188564 + 0.326603i
\(790\) 3710.16 0.167091
\(791\) −11429.1 + 19640.4i −0.513743 + 0.882849i
\(792\) 3476.56 0.155978
\(793\) −2212.25 + 3831.72i −0.0990658 + 0.171587i
\(794\) −15489.8 26829.1i −0.692332 1.19915i
\(795\) −8513.74 14746.2i −0.379813 0.657855i
\(796\) 3048.55 5280.25i 0.135745 0.235117i
\(797\) −7065.60 −0.314023 −0.157012 0.987597i \(-0.550186\pi\)
−0.157012 + 0.987597i \(0.550186\pi\)
\(798\) −7130.69 12448.8i −0.316320 0.552232i
\(799\) −2465.09 −0.109147
\(800\) 1548.97 2682.89i 0.0684553 0.118568i
\(801\) −12926.9 22390.0i −0.570224 0.987656i
\(802\) 6052.52 + 10483.3i 0.266486 + 0.461568i
\(803\) 3891.81 6740.82i 0.171032 0.296237i
\(804\) −14308.1 −0.627620
\(805\) −2261.61 7.72767i −0.0990200 0.000338341i
\(806\) −6972.63 −0.304715
\(807\) −10408.1 + 18027.4i −0.454007 + 0.786363i
\(808\) −1236.92 2142.41i −0.0538549 0.0932794i
\(809\) −18934.6 32795.7i −0.822875 1.42526i −0.903532 0.428520i \(-0.859035\pi\)
0.0806569 0.996742i \(-0.474298\pi\)
\(810\) −3590.05 + 6218.15i −0.155730 + 0.269733i
\(811\) 33563.4 1.45323 0.726616 0.687044i \(-0.241092\pi\)
0.726616 + 0.687044i \(0.241092\pi\)
\(812\) −16859.6 57.6076i −0.728642 0.00248969i
\(813\) 20096.5 0.866931
\(814\) −312.597 + 541.434i −0.0134601 + 0.0233136i
\(815\) 5705.51 + 9882.23i 0.245221 + 0.424735i
\(816\) −6869.49 11898.3i −0.294706 0.510446i
\(817\) −3597.20 + 6230.54i −0.154039 + 0.266804i
\(818\) 23843.5 1.01916
\(819\) 5197.61 + 9073.98i 0.221757 + 0.387143i
\(820\) 2282.86 0.0972207
\(821\) 8951.76 15504.9i 0.380534 0.659105i −0.610604 0.791936i \(-0.709073\pi\)
0.991139 + 0.132831i \(0.0424067\pi\)
\(822\) 23931.0 + 41449.7i 1.01544 + 1.75879i
\(823\) −3317.99 5746.93i −0.140532 0.243409i 0.787165 0.616743i \(-0.211548\pi\)
−0.927697 + 0.373334i \(0.878215\pi\)
\(824\) −2470.51 + 4279.05i −0.104447 + 0.180908i
\(825\) 10903.0 0.460113
\(826\) 2395.12 4115.93i 0.100892 0.173379i
\(827\) 30086.7 1.26508 0.632538 0.774529i \(-0.282013\pi\)
0.632538 + 0.774529i \(0.282013\pi\)
\(828\) 1326.29 2297.20i 0.0556662 0.0964167i
\(829\) −9482.65 16424.4i −0.397281 0.688111i 0.596108 0.802904i \(-0.296713\pi\)
−0.993389 + 0.114793i \(0.963380\pi\)
\(830\) 1980.48 + 3430.29i 0.0828234 + 0.143454i
\(831\) −3104.05 + 5376.37i −0.129577 + 0.224433i
\(832\) 1253.34 0.0522254
\(833\) 19941.4 34000.8i 0.829447 1.41424i
\(834\) 25559.8 1.06123
\(835\) −5498.77 + 9524.16i −0.227896 + 0.394727i
\(836\) −1562.55 2706.41i −0.0646433 0.111965i
\(837\) −1218.69 2110.83i −0.0503273 0.0871695i
\(838\) 7468.53 12935.9i 0.307871 0.533249i
\(839\) −5909.42 −0.243166 −0.121583 0.992581i \(-0.538797\pi\)
−0.121583 + 0.992581i \(0.538797\pi\)
\(840\) 2956.34 5080.36i 0.121433 0.208678i
\(841\) 27405.9 1.12370
\(842\) −6039.59 + 10460.9i −0.247195 + 0.428154i
\(843\) −33065.4 57271.0i −1.35093 2.33988i
\(844\) −1821.13 3154.28i −0.0742722 0.128643i
\(845\) −4814.27 + 8338.55i −0.195995 + 0.339473i
\(846\) 1236.95 0.0502685
\(847\) −10161.0 17739.1i −0.412203 0.719625i
\(848\) 6867.25 0.278092
\(849\) −2083.13 + 3608.09i −0.0842082 + 0.145853i
\(850\) −11125.4 19269.7i −0.448937 0.777582i
\(851\) 238.507 + 413.107i 0.00960744 + 0.0166406i
\(852\) 9743.78 16876.7i 0.391803 0.678623i
\(853\) −4235.96 −0.170031 −0.0850156 0.996380i \(-0.527094\pi\)
−0.0850156 + 0.996380i \(0.527094\pi\)
\(854\) −8368.56 28.5945i −0.335323 0.00114576i
\(855\) −7934.98 −0.317393
\(856\) 4900.81 8488.46i 0.195685 0.338936i
\(857\) −11282.5 19541.9i −0.449712 0.778924i 0.548655 0.836049i \(-0.315140\pi\)
−0.998367 + 0.0571249i \(0.981807\pi\)
\(858\) 2205.52 + 3820.07i 0.0877566 + 0.151999i
\(859\) 1670.45 2893.31i 0.0663505 0.114923i −0.830942 0.556359i \(-0.812198\pi\)
0.897292 + 0.441437i \(0.145531\pi\)
\(860\) −2947.66 −0.116877
\(861\) −14875.2 50.8270i −0.588787 0.00201182i
\(862\) 27104.3 1.07097
\(863\) 24944.2 43204.6i 0.983905 1.70417i 0.337202 0.941432i \(-0.390520\pi\)
0.646703 0.762741i \(-0.276147\pi\)
\(864\) 219.060 + 379.423i 0.00862565 + 0.0149401i
\(865\) 8287.56 + 14354.5i 0.325764 + 0.564239i
\(866\) −2807.93 + 4863.48i −0.110182 + 0.190840i
\(867\) −61969.0 −2.42742
\(868\) −6555.05 11443.8i −0.256328 0.447498i
\(869\) −5266.22 −0.205575
\(870\) −9028.82 + 15638.4i −0.351846 + 0.609414i
\(871\) −4687.43 8118.87i −0.182351 0.315841i
\(872\) −628.979 1089.42i −0.0244265 0.0423079i
\(873\) 18667.8 32333.6i 0.723722 1.25352i
\(874\) −2384.40 −0.0922811
\(875\) 10969.9 18851.4i 0.423830 0.728336i
\(876\) 15434.9 0.595316
\(877\) −20594.0 + 35669.9i −0.792942 + 1.37342i 0.131196 + 0.991356i \(0.458118\pi\)
−0.924138 + 0.382059i \(0.875215\pi\)
\(878\) 15898.7 + 27537.4i 0.611112 + 1.05848i
\(879\) −984.473 1705.16i −0.0377764 0.0654307i
\(880\) 640.199 1108.86i 0.0245240 0.0424768i
\(881\) 19351.1 0.740018 0.370009 0.929028i \(-0.379355\pi\)
0.370009 + 0.929028i \(0.379355\pi\)
\(882\) −10006.3 + 17061.1i −0.382007 + 0.651335i
\(883\) −31330.1 −1.19404 −0.597022 0.802225i \(-0.703649\pi\)
−0.597022 + 0.802225i \(0.703649\pi\)
\(884\) 4501.00 7795.96i 0.171250 0.296614i
\(885\) −2550.22 4417.11i −0.0968640 0.167773i
\(886\) 9194.64 + 15925.6i 0.348646 + 0.603872i
\(887\) 9419.34 16314.8i 0.356562 0.617583i −0.630822 0.775927i \(-0.717282\pi\)
0.987384 + 0.158344i \(0.0506156\pi\)
\(888\) −1239.76 −0.0468508
\(889\) 11449.7 19675.9i 0.431959 0.742306i
\(890\) −9521.79 −0.358619
\(891\) 5095.73 8826.07i 0.191598 0.331857i
\(892\) −2578.61 4466.28i −0.0967916 0.167648i
\(893\) −555.948 962.929i −0.0208332 0.0360842i
\(894\) −19781.9 + 34263.3i −0.740052 + 1.28181i
\(895\) 16296.0 0.608622
\(896\) 1178.27 + 2057.03i 0.0439324 + 0.0766971i
\(897\) 3365.56 0.125276
\(898\) 11231.7 19453.9i 0.417381 0.722924i
\(899\) 20257.8 + 35087.6i 0.751543 + 1.30171i
\(900\) 5582.54 + 9669.24i 0.206761 + 0.358120i
\(901\) 24661.8 42715.5i 0.911880 1.57942i
\(902\) −3240.31 −0.119612
\(903\) 19207.0 + 65.6284i 0.707829 + 0.00241858i
\(904\) −9815.75 −0.361136
\(905\) 2943.27 5097.89i 0.108108 0.187248i
\(906\) −7552.91 13082.0i −0.276963 0.479714i
\(907\) 14377.3 + 24902.2i 0.526339 + 0.911646i 0.999529 + 0.0306853i \(0.00976897\pi\)
−0.473190 + 0.880960i \(0.656898\pi\)
\(908\) −2827.87 + 4898.02i −0.103355 + 0.179016i
\(909\) 8915.82 0.325324
\(910\) 3851.29 + 13.1595i 0.140296 + 0.000479375i
\(911\) 7679.37 0.279285 0.139643 0.990202i \(-0.455405\pi\)
0.139643 + 0.990202i \(0.455405\pi\)
\(912\) 3098.52 5366.80i 0.112503 0.194860i
\(913\) −2811.10 4868.97i −0.101899 0.176494i
\(914\) 9751.96 + 16890.9i 0.352917 + 0.611270i
\(915\) −4481.60 + 7762.36i −0.161920 + 0.280454i
\(916\) −3196.66 −0.115306
\(917\) −22285.4 38905.8i −0.802538 1.40107i
\(918\) 3146.77 0.113136
\(919\) −22968.5 + 39782.6i −0.824440 + 1.42797i 0.0779068 + 0.996961i \(0.475176\pi\)
−0.902347 + 0.431011i \(0.858157\pi\)
\(920\) −488.464 846.044i −0.0175045 0.0303187i
\(921\) 23166.4 + 40125.4i 0.828837 + 1.43559i
\(922\) 6728.85 11654.7i 0.240350 0.416299i
\(923\) 12768.6 0.455344
\(924\) −4196.24 + 7211.09i −0.149401 + 0.256740i
\(925\) −2007.83 −0.0713696
\(926\) 7665.18 13276.5i 0.272023 0.471158i
\(927\) −8903.82 15421.9i −0.315469 0.546409i
\(928\) −3641.36 6307.02i −0.128808 0.223101i
\(929\) 17842.4 30903.9i 0.630129 1.09142i −0.357396 0.933953i \(-0.616335\pi\)
0.987525 0.157463i \(-0.0503315\pi\)
\(930\) −14125.3 −0.498049
\(931\) 17778.9 + 121.499i 0.625866 + 0.00427709i
\(932\) 6217.64 0.218525
\(933\) 31473.4 54513.5i 1.10439 1.91285i
\(934\) 16755.9 + 29022.1i 0.587014 + 1.01674i
\(935\) −4598.19 7964.30i −0.160831 0.278567i
\(936\) −2258.53 + 3911.90i −0.0788702 + 0.136607i
\(937\) 4161.99 0.145108 0.0725540 0.997364i \(-0.476885\pi\)
0.0725540 + 0.997364i \(0.476885\pi\)
\(938\) 8918.36 15325.9i 0.310442 0.533484i
\(939\) 18090.8 0.628722
\(940\) 227.780 394.527i 0.00790359 0.0136894i
\(941\) 15330.8 + 26553.8i 0.531106 + 0.919903i 0.999341 + 0.0362989i \(0.0115568\pi\)
−0.468235 + 0.883604i \(0.655110\pi\)
\(942\) 573.776 + 993.810i 0.0198457 + 0.0343737i
\(943\) −1236.16 + 2141.08i −0.0426880 + 0.0739377i
\(944\) 2057.03 0.0709222
\(945\) 669.150 + 1168.20i 0.0230343 + 0.0402134i
\(946\) 4183.92 0.143796
\(947\) −4582.68 + 7937.43i −0.157251 + 0.272367i −0.933877 0.357596i \(-0.883597\pi\)
0.776625 + 0.629963i \(0.216930\pi\)
\(948\) −5221.45 9043.82i −0.178887 0.309842i
\(949\) 5056.60 + 8758.29i 0.172965 + 0.299585i
\(950\) 5018.16 8691.70i 0.171379 0.296838i
\(951\) 7713.18 0.263004
\(952\) 17026.5 + 58.1779i 0.579657 + 0.00198063i
\(953\) −27150.4 −0.922862 −0.461431 0.887176i \(-0.652664\pi\)
−0.461431 + 0.887176i \(0.652664\pi\)
\(954\) −12374.9 + 21434.0i −0.419972 + 0.727412i
\(955\) −8443.57 14624.7i −0.286102 0.495543i
\(956\) 13935.6 + 24137.2i 0.471454 + 0.816583i
\(957\) 12815.5 22197.2i 0.432882 0.749773i
\(958\) 11037.1 0.372227
\(959\) −59314.7 202.672i −1.99726 0.00682442i
\(960\) 2539.03 0.0853612
\(961\) −950.839 + 1646.90i −0.0319170 + 0.0552818i
\(962\) −406.154 703.480i −0.0136122 0.0235770i
\(963\) 17662.7 + 30592.7i 0.591042 + 1.02371i
\(964\) 10116.5 17522.3i 0.337998 0.585430i
\(965\) 4312.95 0.143874
\(966\) 3164.01 + 5523.72i 0.105383 + 0.183978i
\(967\) −34024.7 −1.13150 −0.565750 0.824577i \(-0.691413\pi\)
−0.565750 + 0.824577i \(0.691413\pi\)
\(968\) 4415.30 7647.52i 0.146604 0.253926i
\(969\) −22255.0 38546.7i −0.737804 1.27791i
\(970\) −6875.24 11908.3i −0.227578 0.394177i
\(971\) −9397.19 + 16276.4i −0.310577 + 0.537935i −0.978487 0.206307i \(-0.933856\pi\)
0.667911 + 0.744242i \(0.267189\pi\)
\(972\) 21688.3 0.715692
\(973\) −15931.7 + 27378.0i −0.524919 + 0.902053i
\(974\) 7907.83 0.260147
\(975\) −7083.08 + 12268.3i −0.232656 + 0.402973i
\(976\) −1807.45 3130.59i −0.0592777 0.102672i
\(977\) 30213.5 + 52331.3i 0.989371 + 1.71364i 0.620616 + 0.784115i \(0.286883\pi\)
0.368756 + 0.929526i \(0.379784\pi\)
\(978\) 16059.2 27815.3i 0.525067 0.909442i
\(979\) 13515.3 0.441216
\(980\) 3599.04 + 6333.29i 0.117314 + 0.206438i
\(981\) 4533.73 0.147554
\(982\) −12730.6 + 22050.0i −0.413695 + 0.716541i
\(983\) −19469.3 33721.8i −0.631713 1.09416i −0.987201 0.159478i \(-0.949019\pi\)
0.355489 0.934681i \(-0.384314\pi\)
\(984\) −3212.76 5564.66i −0.104084 0.180279i
\(985\) −10014.6 + 17345.8i −0.323950 + 0.561098i
\(986\) −52307.7 −1.68947
\(987\) −1493.01 + 2565.68i −0.0481489 + 0.0827421i
\(988\) 4060.40 0.130748
\(989\) 1596.14 2764.59i 0.0513188 0.0888867i
\(990\) 2307.30 + 3996.37i 0.0740716 + 0.128296i
\(991\) 15799.8 + 27366.0i 0.506455 + 0.877205i 0.999972 + 0.00746941i \(0.00237761\pi\)
−0.493517 + 0.869736i \(0.664289\pi\)
\(992\) 2848.39 4933.56i 0.0911658 0.157904i
\(993\) −13564.5 −0.433491
\(994\) 12003.9 + 20956.4i 0.383038 + 0.668707i
\(995\) 8092.97 0.257854
\(996\) 5574.40 9655.15i 0.177341 0.307164i
\(997\) −19353.3 33520.9i −0.614770 1.06481i −0.990425 0.138053i \(-0.955916\pi\)
0.375655 0.926760i \(-0.377418\pi\)
\(998\) 18019.9 + 31211.4i 0.571552 + 0.989958i
\(999\) 141.977 245.911i 0.00449644 0.00778805i
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 322.4.e.b.93.10 22
7.2 even 3 2254.4.a.w.1.2 11
7.4 even 3 inner 322.4.e.b.277.10 yes 22
7.5 odd 6 2254.4.a.x.1.10 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
322.4.e.b.93.10 22 1.1 even 1 trivial
322.4.e.b.277.10 yes 22 7.4 even 3 inner
2254.4.a.w.1.2 11 7.2 even 3
2254.4.a.x.1.10 11 7.5 odd 6