Properties

Label 69.4.g.a.5.3
Level $69$
Weight $4$
Character 69.5
Analytic conductor $4.071$
Analytic rank $0$
Dimension $220$
CM no
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [69,4,Mod(5,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 69.g (of order \(22\), degree \(10\), 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: \(4.07113179040\)
Analytic rank: \(0\)
Dimension: \(220\)
Relative dimension: \(22\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.3
Character \(\chi\) \(=\) 69.5
Dual form 69.4.g.a.14.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.20747 + 4.11226i) q^{2} +(-2.48738 + 4.56212i) q^{3} +(-8.72270 - 5.60574i) q^{4} +(2.62405 - 18.2506i) q^{5} +(-15.7572 - 15.7374i) q^{6} +(-25.3847 + 11.5928i) q^{7} +(7.67232 - 6.64810i) q^{8} +(-14.6259 - 22.6954i) q^{9} +O(q^{10})\) \(q+(-1.20747 + 4.11226i) q^{2} +(-2.48738 + 4.56212i) q^{3} +(-8.72270 - 5.60574i) q^{4} +(2.62405 - 18.2506i) q^{5} +(-15.7572 - 15.7374i) q^{6} +(-25.3847 + 11.5928i) q^{7} +(7.67232 - 6.64810i) q^{8} +(-14.6259 - 22.6954i) q^{9} +(71.8830 + 32.8279i) q^{10} +(24.0678 - 7.06695i) q^{11} +(47.2707 - 25.8504i) q^{12} +(-0.705375 + 1.54456i) q^{13} +(-17.0214 - 118.387i) q^{14} +(76.7347 + 57.3675i) q^{15} +(-16.3838 - 35.8756i) q^{16} +(-52.8295 + 33.9515i) q^{17} +(110.990 - 32.7416i) q^{18} +(-65.0758 + 101.260i) q^{19} +(-125.197 + 144.485i) q^{20} +(10.2536 - 144.644i) q^{21} +107.506i q^{22} +(-68.3459 - 86.5785i) q^{23} +(11.2455 + 51.5384i) q^{24} +(-206.264 - 60.5645i) q^{25} +(-5.49990 - 4.76569i) q^{26} +(139.919 - 10.2731i) q^{27} +(286.410 + 41.1795i) q^{28} +(-31.6852 - 49.3031i) q^{29} +(-328.565 + 246.284i) q^{30} +(-39.6835 - 45.7972i) q^{31} +(247.702 - 35.6141i) q^{32} +(-27.6254 + 127.378i) q^{33} +(-75.8274 - 258.244i) q^{34} +(144.966 + 493.708i) q^{35} +(0.352754 + 279.955i) q^{36} +(-214.251 + 30.8047i) q^{37} +(-337.830 - 389.877i) q^{38} +(-5.29192 - 7.05990i) q^{39} +(-101.200 - 157.470i) q^{40} +(-189.649 - 27.2674i) q^{41} +(582.434 + 216.819i) q^{42} +(267.774 + 232.027i) q^{43} +(-249.552 - 73.2750i) q^{44} +(-452.585 + 207.378i) q^{45} +(438.559 - 176.515i) q^{46} +230.534i q^{47} +(204.422 + 14.4911i) q^{48} +(285.374 - 329.340i) q^{49} +(498.114 - 775.081i) q^{50} +(-23.4838 - 325.465i) q^{51} +(14.8112 - 9.51855i) q^{52} +(66.7132 + 146.082i) q^{53} +(-126.703 + 587.790i) q^{54} +(-65.8213 - 457.797i) q^{55} +(-117.690 + 257.704i) q^{56} +(-300.092 - 548.755i) q^{57} +(241.006 - 70.7658i) q^{58} +(-134.973 - 61.6403i) q^{59} +(-347.747 - 930.554i) q^{60} +(34.5962 - 29.9778i) q^{61} +(236.247 - 107.890i) q^{62} +(634.379 + 406.562i) q^{63} +(-107.735 + 749.312i) q^{64} +(26.3382 + 16.9265i) q^{65} +(-490.457 - 267.409i) q^{66} +(-268.027 + 912.817i) q^{67} +651.140 q^{68} +(564.984 - 96.4490i) q^{69} -2205.30 q^{70} +(-52.4218 + 178.532i) q^{71} +(-263.096 - 76.8921i) q^{72} +(753.496 + 484.242i) q^{73} +(132.025 - 918.253i) q^{74} +(789.358 - 790.354i) q^{75} +(1135.27 - 518.462i) q^{76} +(-529.029 + 458.406i) q^{77} +(35.4220 - 13.2372i) q^{78} +(-1008.40 - 460.521i) q^{79} +(-697.745 + 204.876i) q^{80} +(-301.165 + 663.883i) q^{81} +(341.126 - 746.962i) q^{82} +(-127.413 - 886.180i) q^{83} +(-900.276 + 1204.21i) q^{84} +(481.009 + 1053.26i) q^{85} +(-1277.49 + 820.991i) q^{86} +(303.740 - 21.9162i) q^{87} +(137.674 - 214.225i) q^{88} +(426.128 - 491.778i) q^{89} +(-306.312 - 2111.55i) q^{90} -47.3854i q^{91} +(110.824 + 1138.33i) q^{92} +(307.641 - 67.1261i) q^{93} +(-948.017 - 278.363i) q^{94} +(1677.30 + 1453.39i) q^{95} +(-453.652 + 1218.63i) q^{96} +(504.434 + 72.5266i) q^{97} +(1009.75 + 1571.20i) q^{98} +(-512.401 - 442.869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 220 q - 5 q^{3} + 50 q^{4} - 32 q^{6} - 22 q^{7} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 220 q - 5 q^{3} + 50 q^{4} - 32 q^{6} - 22 q^{7} - 5 q^{9} - 22 q^{10} + 4 q^{12} + 30 q^{13} + 363 q^{15} + 162 q^{16} - 78 q^{18} - 22 q^{19} - 671 q^{21} - 1258 q^{24} - 632 q^{25} - 269 q^{27} - 22 q^{28} + 1485 q^{30} - 138 q^{31} + 957 q^{33} + 1892 q^{34} - 518 q^{36} + 1166 q^{37} - 401 q^{39} - 2332 q^{40} - 11 q^{42} - 1738 q^{43} - 4326 q^{46} + 1706 q^{48} - 3212 q^{49} - 11 q^{51} - 346 q^{52} - 2307 q^{54} - 1030 q^{55} - 2123 q^{57} + 8656 q^{58} - 451 q^{60} + 506 q^{61} + 2079 q^{63} + 2524 q^{64} + 5742 q^{66} + 1430 q^{67} + 4875 q^{69} + 8092 q^{70} + 6445 q^{72} - 114 q^{73} + 9349 q^{75} + 1034 q^{76} + 6684 q^{78} - 1870 q^{79} - 5497 q^{81} - 4220 q^{82} - 16753 q^{84} - 958 q^{85} - 3785 q^{87} + 1386 q^{88} - 18700 q^{90} - 14746 q^{93} - 6900 q^{94} - 10367 q^{96} + 12650 q^{97} - 4631 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{1}{22}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20747 + 4.11226i −0.426905 + 1.45390i 0.412780 + 0.910831i \(0.364558\pi\)
−0.839685 + 0.543074i \(0.817260\pi\)
\(3\) −2.48738 + 4.56212i −0.478696 + 0.877981i
\(4\) −8.72270 5.60574i −1.09034 0.700718i
\(5\) 2.62405 18.2506i 0.234702 1.63239i −0.442626 0.896706i \(-0.645953\pi\)
0.677328 0.735681i \(-0.263138\pi\)
\(6\) −15.7572 15.7374i −1.07214 1.07079i
\(7\) −25.3847 + 11.5928i −1.37065 + 0.625954i −0.958481 0.285155i \(-0.907955\pi\)
−0.412166 + 0.911109i \(0.635228\pi\)
\(8\) 7.67232 6.64810i 0.339072 0.293807i
\(9\) −14.6259 22.6954i −0.541700 0.840572i
\(10\) 71.8830 + 32.8279i 2.27314 + 1.03811i
\(11\) 24.0678 7.06695i 0.659701 0.193706i 0.0652893 0.997866i \(-0.479203\pi\)
0.594412 + 0.804161i \(0.297385\pi\)
\(12\) 47.2707 25.8504i 1.13716 0.621865i
\(13\) −0.705375 + 1.54456i −0.0150489 + 0.0329525i −0.917007 0.398871i \(-0.869402\pi\)
0.901958 + 0.431823i \(0.142130\pi\)
\(14\) −17.0214 118.387i −0.324941 2.26001i
\(15\) 76.7347 + 57.3675i 1.32085 + 0.987481i
\(16\) −16.3838 35.8756i −0.255998 0.560556i
\(17\) −52.8295 + 33.9515i −0.753708 + 0.484379i −0.860214 0.509933i \(-0.829670\pi\)
0.106506 + 0.994312i \(0.466034\pi\)
\(18\) 110.990 32.7416i 1.45337 0.428737i
\(19\) −65.0758 + 101.260i −0.785758 + 1.22266i 0.185032 + 0.982733i \(0.440761\pi\)
−0.970790 + 0.239931i \(0.922875\pi\)
\(20\) −125.197 + 144.485i −1.39975 + 1.61539i
\(21\) 10.2536 144.644i 0.106548 1.50304i
\(22\) 107.506i 1.04184i
\(23\) −68.3459 86.5785i −0.619613 0.784907i
\(24\) 11.2455 + 51.5384i 0.0956449 + 0.438343i
\(25\) −206.264 60.5645i −1.65011 0.484516i
\(26\) −5.49990 4.76569i −0.0414854 0.0359473i
\(27\) 139.919 10.2731i 0.997315 0.0732243i
\(28\) 286.410 + 41.1795i 1.93309 + 0.277936i
\(29\) −31.6852 49.3031i −0.202889 0.315702i 0.724867 0.688889i \(-0.241901\pi\)
−0.927756 + 0.373187i \(0.878265\pi\)
\(30\) −328.565 + 246.284i −1.99958 + 1.49884i
\(31\) −39.6835 45.7972i −0.229915 0.265336i 0.629056 0.777360i \(-0.283442\pi\)
−0.858971 + 0.512023i \(0.828896\pi\)
\(32\) 247.702 35.6141i 1.36837 0.196742i
\(33\) −27.6254 + 127.378i −0.145726 + 0.671931i
\(34\) −75.8274 258.244i −0.382479 1.30260i
\(35\) 144.966 + 493.708i 0.700105 + 2.38434i
\(36\) 0.352754 + 279.955i 0.00163312 + 1.29609i
\(37\) −214.251 + 30.8047i −0.951964 + 0.136872i −0.600762 0.799428i \(-0.705136\pi\)
−0.351202 + 0.936300i \(0.614227\pi\)
\(38\) −337.830 389.877i −1.44219 1.66438i
\(39\) −5.29192 7.05990i −0.0217278 0.0289869i
\(40\) −101.200 157.470i −0.400027 0.622454i
\(41\) −189.649 27.2674i −0.722395 0.103865i −0.228696 0.973498i \(-0.573446\pi\)
−0.493698 + 0.869633i \(0.664355\pi\)
\(42\) 582.434 + 216.819i 2.13980 + 0.796567i
\(43\) 267.774 + 232.027i 0.949654 + 0.822880i 0.984297 0.176520i \(-0.0564839\pi\)
−0.0346428 + 0.999400i \(0.511029\pi\)
\(44\) −249.552 73.2750i −0.855031 0.251060i
\(45\) −452.585 + 207.378i −1.49928 + 0.686981i
\(46\) 438.559 176.515i 1.40570 0.565778i
\(47\) 230.534i 0.715465i 0.933824 + 0.357732i \(0.116450\pi\)
−0.933824 + 0.357732i \(0.883550\pi\)
\(48\) 204.422 + 14.4911i 0.614703 + 0.0435752i
\(49\) 285.374 329.340i 0.831995 0.960174i
\(50\) 498.114 775.081i 1.40888 2.19226i
\(51\) −23.4838 325.465i −0.0644783 0.893612i
\(52\) 14.8112 9.51855i 0.0394988 0.0253843i
\(53\) 66.7132 + 146.082i 0.172901 + 0.378601i 0.976167 0.217020i \(-0.0696335\pi\)
−0.803266 + 0.595620i \(0.796906\pi\)
\(54\) −126.703 + 587.790i −0.319298 + 1.48126i
\(55\) −65.8213 457.797i −0.161370 1.12235i
\(56\) −117.690 + 257.704i −0.280838 + 0.614950i
\(57\) −300.092 548.755i −0.697336 1.27516i
\(58\) 241.006 70.7658i 0.545615 0.160207i
\(59\) −134.973 61.6403i −0.297831 0.136015i 0.260895 0.965367i \(-0.415982\pi\)
−0.558726 + 0.829352i \(0.688710\pi\)
\(60\) −347.747 930.554i −0.748232 2.00223i
\(61\) 34.5962 29.9778i 0.0726162 0.0629223i −0.617796 0.786338i \(-0.711974\pi\)
0.690413 + 0.723416i \(0.257429\pi\)
\(62\) 236.247 107.890i 0.483926 0.221002i
\(63\) 634.379 + 406.562i 1.26864 + 0.813048i
\(64\) −107.735 + 749.312i −0.210420 + 1.46350i
\(65\) 26.3382 + 16.9265i 0.0502593 + 0.0322997i
\(66\) −490.457 267.409i −0.914713 0.498723i
\(67\) −268.027 + 912.817i −0.488727 + 1.66445i 0.233157 + 0.972439i \(0.425094\pi\)
−0.721884 + 0.692014i \(0.756724\pi\)
\(68\) 651.140 1.16121
\(69\) 564.984 96.4490i 0.985740 0.168277i
\(70\) −2205.30 −3.76548
\(71\) −52.4218 + 178.532i −0.0876243 + 0.298421i −0.991632 0.129095i \(-0.958793\pi\)
0.904008 + 0.427516i \(0.140611\pi\)
\(72\) −263.096 76.8921i −0.430641 0.125859i
\(73\) 753.496 + 484.242i 1.20808 + 0.776387i 0.980336 0.197333i \(-0.0632282\pi\)
0.227746 + 0.973721i \(0.426865\pi\)
\(74\) 132.025 918.253i 0.207400 1.44250i
\(75\) 789.358 790.354i 1.21530 1.21683i
\(76\) 1135.27 518.462i 1.71348 0.782522i
\(77\) −529.029 + 458.406i −0.782967 + 0.678445i
\(78\) 35.4220 13.2372i 0.0514199 0.0192155i
\(79\) −1008.40 460.521i −1.43612 0.655856i −0.463047 0.886334i \(-0.653244\pi\)
−0.973078 + 0.230478i \(0.925971\pi\)
\(80\) −697.745 + 204.876i −0.975128 + 0.286323i
\(81\) −301.165 + 663.883i −0.413121 + 0.910676i
\(82\) 341.126 746.962i 0.459403 1.00595i
\(83\) −127.413 886.180i −0.168499 1.17194i −0.881988 0.471272i \(-0.843795\pi\)
0.713489 0.700667i \(-0.247114\pi\)
\(84\) −900.276 + 1204.21i −1.16938 + 1.56417i
\(85\) 481.009 + 1053.26i 0.613797 + 1.34403i
\(86\) −1277.49 + 820.991i −1.60180 + 1.02942i
\(87\) 303.740 21.9162i 0.374302 0.0270077i
\(88\) 137.674 214.225i 0.166774 0.259505i
\(89\) 426.128 491.778i 0.507522 0.585712i −0.442940 0.896551i \(-0.646065\pi\)
0.950463 + 0.310839i \(0.100610\pi\)
\(90\) −306.312 2111.55i −0.358757 2.47308i
\(91\) 47.3854i 0.0545862i
\(92\) 110.824 + 1138.33i 0.125590 + 1.28999i
\(93\) 307.641 67.1261i 0.343020 0.0748458i
\(94\) −948.017 278.363i −1.04022 0.305436i
\(95\) 1677.30 + 1453.39i 1.81144 + 1.56962i
\(96\) −453.652 + 1218.63i −0.482298 + 1.29558i
\(97\) 504.434 + 72.5266i 0.528015 + 0.0759171i 0.401167 0.916005i \(-0.368605\pi\)
0.126848 + 0.991922i \(0.459514\pi\)
\(98\) 1009.75 + 1571.20i 1.04082 + 1.61955i
\(99\) −512.401 442.869i −0.520184 0.449596i
\(100\) 1459.67 + 1684.55i 1.45967 + 1.68455i
\(101\) 1109.31 159.495i 1.09288 0.157132i 0.427775 0.903885i \(-0.359297\pi\)
0.665101 + 0.746753i \(0.268388\pi\)
\(102\) 1366.75 + 296.417i 1.32675 + 0.287742i
\(103\) −309.534 1054.17i −0.296109 1.00846i −0.964376 0.264534i \(-0.914782\pi\)
0.668267 0.743921i \(-0.267036\pi\)
\(104\) 4.85650 + 16.5397i 0.00457903 + 0.0155948i
\(105\) −2612.94 566.687i −2.42854 0.526695i
\(106\) −681.280 + 97.9533i −0.624262 + 0.0897553i
\(107\) 404.223 + 466.498i 0.365212 + 0.421477i 0.908379 0.418147i \(-0.137320\pi\)
−0.543167 + 0.839625i \(0.682775\pi\)
\(108\) −1278.06 694.743i −1.13872 0.618997i
\(109\) −228.582 355.681i −0.200864 0.312551i 0.726179 0.687506i \(-0.241295\pi\)
−0.927043 + 0.374955i \(0.877658\pi\)
\(110\) 1962.06 + 282.101i 1.70068 + 0.244521i
\(111\) 392.389 1054.06i 0.335531 0.901326i
\(112\) 831.799 + 720.758i 0.701765 + 0.608083i
\(113\) −1859.03 545.860i −1.54764 0.454427i −0.607243 0.794517i \(-0.707724\pi\)
−0.940393 + 0.340090i \(0.889543\pi\)
\(114\) 2618.98 571.452i 2.15166 0.469486i
\(115\) −1759.46 + 1020.17i −1.42670 + 0.827230i
\(116\) 607.675i 0.486390i
\(117\) 45.3711 6.58174i 0.0358510 0.00520070i
\(118\) 416.457 480.617i 0.324898 0.374953i
\(119\) 947.471 1474.29i 0.729870 1.13570i
\(120\) 970.118 69.9985i 0.737993 0.0532497i
\(121\) −590.391 + 379.421i −0.443569 + 0.285065i
\(122\) 81.5026 + 178.466i 0.0604828 + 0.132439i
\(123\) 596.126 797.377i 0.436999 0.584529i
\(124\) 89.4202 + 621.931i 0.0647595 + 0.450412i
\(125\) −689.143 + 1509.01i −0.493110 + 1.07976i
\(126\) −2437.88 + 2117.82i −1.72368 + 1.49739i
\(127\) 48.3083 14.1846i 0.0337533 0.00991086i −0.264812 0.964300i \(-0.585310\pi\)
0.298566 + 0.954389i \(0.403492\pi\)
\(128\) −1130.21 516.148i −0.780446 0.356418i
\(129\) −1724.59 + 644.478i −1.17707 + 0.439869i
\(130\) −101.409 + 87.8714i −0.0684166 + 0.0592833i
\(131\) 1038.90 474.449i 0.692893 0.316433i −0.0376592 0.999291i \(-0.511990\pi\)
0.730552 + 0.682857i \(0.239263\pi\)
\(132\) 955.019 956.223i 0.629725 0.630519i
\(133\) 478.044 3324.87i 0.311667 2.16769i
\(134\) −3430.11 2204.40i −2.21132 1.42113i
\(135\) 179.665 2580.58i 0.114541 1.64519i
\(136\) −179.612 + 611.703i −0.113247 + 0.385684i
\(137\) −793.420 −0.494792 −0.247396 0.968915i \(-0.579575\pi\)
−0.247396 + 0.968915i \(0.579575\pi\)
\(138\) −285.577 + 2439.82i −0.176159 + 1.50501i
\(139\) 379.810 0.231763 0.115881 0.993263i \(-0.463031\pi\)
0.115881 + 0.993263i \(0.463031\pi\)
\(140\) 1503.11 5119.11i 0.907397 3.09031i
\(141\) −1051.72 573.425i −0.628164 0.342490i
\(142\) −670.874 431.145i −0.396468 0.254795i
\(143\) −6.06154 + 42.1589i −0.00354469 + 0.0246539i
\(144\) −574.584 + 896.552i −0.332514 + 0.518838i
\(145\) −982.956 + 448.901i −0.562966 + 0.257098i
\(146\) −2901.16 + 2513.87i −1.64453 + 1.42499i
\(147\) 792.654 + 2121.10i 0.444741 + 1.19011i
\(148\) 2041.53 + 932.336i 1.13387 + 0.517821i
\(149\) 232.786 68.3522i 0.127991 0.0375814i −0.217110 0.976147i \(-0.569663\pi\)
0.345100 + 0.938566i \(0.387845\pi\)
\(150\) 2297.02 + 4200.38i 1.25034 + 2.28640i
\(151\) −85.4722 + 187.158i −0.0460638 + 0.100866i −0.931265 0.364343i \(-0.881293\pi\)
0.885201 + 0.465209i \(0.154021\pi\)
\(152\) 173.904 + 1209.53i 0.0927991 + 0.645432i
\(153\) 1543.22 + 702.418i 0.815439 + 0.371158i
\(154\) −1246.30 2729.02i −0.652142 1.42799i
\(155\) −939.961 + 604.076i −0.487093 + 0.313036i
\(156\) 6.58386 + 91.2465i 0.00337905 + 0.0468306i
\(157\) 24.7058 38.4429i 0.0125588 0.0195419i −0.834917 0.550375i \(-0.814485\pi\)
0.847476 + 0.530833i \(0.178121\pi\)
\(158\) 3111.39 3590.74i 1.56664 1.80800i
\(159\) −832.383 59.0061i −0.415171 0.0294308i
\(160\) 4614.17i 2.27989i
\(161\) 2738.63 + 1405.45i 1.34059 + 0.687982i
\(162\) −2366.41 2040.09i −1.14767 0.989411i
\(163\) 1332.49 + 391.253i 0.640297 + 0.188008i 0.585736 0.810502i \(-0.300806\pi\)
0.0545615 + 0.998510i \(0.482624\pi\)
\(164\) 1501.40 + 1300.97i 0.714875 + 0.619442i
\(165\) 2252.25 + 838.429i 1.06265 + 0.395585i
\(166\) 3798.05 + 546.078i 1.77582 + 0.255324i
\(167\) −1828.74 2845.58i −0.847380 1.31855i −0.946246 0.323448i \(-0.895158\pi\)
0.0988662 0.995101i \(-0.468478\pi\)
\(168\) −882.940 1177.92i −0.405478 0.540944i
\(169\) 1436.84 + 1658.20i 0.654001 + 0.754758i
\(170\) −4912.10 + 706.253i −2.21612 + 0.318630i
\(171\) 3249.93 4.09504i 1.45338 0.00183132i
\(172\) −1035.03 3524.98i −0.458837 1.56266i
\(173\) −567.470 1932.63i −0.249387 0.849334i −0.985091 0.172031i \(-0.944967\pi\)
0.735704 0.677303i \(-0.236851\pi\)
\(174\) −276.631 + 1275.52i −0.120525 + 0.555730i
\(175\) 5938.07 853.765i 2.56500 0.368792i
\(176\) −647.854 747.663i −0.277465 0.320212i
\(177\) 616.940 462.442i 0.261989 0.196380i
\(178\) 1507.78 + 2346.16i 0.634906 + 0.987933i
\(179\) −1129.17 162.349i −0.471496 0.0677909i −0.0975285 0.995233i \(-0.531094\pi\)
−0.373967 + 0.927442i \(0.622003\pi\)
\(180\) 5110.28 + 728.176i 2.11610 + 0.301528i
\(181\) −413.009 357.874i −0.169606 0.146965i 0.565922 0.824459i \(-0.308520\pi\)
−0.735528 + 0.677494i \(0.763066\pi\)
\(182\) 194.861 + 57.2165i 0.0793631 + 0.0233031i
\(183\) 50.7084 + 232.398i 0.0204835 + 0.0938762i
\(184\) −1099.95 209.887i −0.440705 0.0840929i
\(185\) 3991.05i 1.58610i
\(186\) −95.4263 + 1346.15i −0.0376183 + 0.530670i
\(187\) −1031.56 + 1190.48i −0.403396 + 0.465543i
\(188\) 1292.31 2010.88i 0.501339 0.780098i
\(189\) −3432.73 + 1882.84i −1.32113 + 0.724638i
\(190\) −8001.99 + 5142.56i −3.05540 + 1.96358i
\(191\) 1560.40 + 3416.79i 0.591133 + 1.29440i 0.934755 + 0.355292i \(0.115619\pi\)
−0.343622 + 0.939108i \(0.611654\pi\)
\(192\) −3150.48 2355.32i −1.18420 0.885316i
\(193\) −387.663 2696.25i −0.144583 1.00560i −0.924899 0.380213i \(-0.875851\pi\)
0.780316 0.625386i \(-0.215058\pi\)
\(194\) −907.337 + 1986.79i −0.335789 + 0.735274i
\(195\) −142.734 + 78.0554i −0.0524174 + 0.0286649i
\(196\) −4335.43 + 1273.00i −1.57997 + 0.463920i
\(197\) −2814.01 1285.11i −1.01771 0.464774i −0.164523 0.986373i \(-0.552608\pi\)
−0.853191 + 0.521599i \(0.825336\pi\)
\(198\) 2439.90 1572.38i 0.875739 0.564364i
\(199\) −336.496 + 291.576i −0.119867 + 0.103866i −0.712732 0.701437i \(-0.752542\pi\)
0.592865 + 0.805302i \(0.297997\pi\)
\(200\) −1985.16 + 906.592i −0.701860 + 0.320529i
\(201\) −3497.70 3493.29i −1.22741 1.22586i
\(202\) −683.574 + 4754.36i −0.238100 + 1.65602i
\(203\) 1375.88 + 884.226i 0.475704 + 0.305717i
\(204\) −1619.63 + 2970.58i −0.555866 + 1.01952i
\(205\) −995.295 + 3389.66i −0.339095 + 1.15485i
\(206\) 4708.80 1.59261
\(207\) −965.316 + 2817.43i −0.324126 + 0.946014i
\(208\) 66.9686 0.0223242
\(209\) −850.633 + 2896.99i −0.281529 + 0.958799i
\(210\) 5485.41 10060.8i 1.80252 3.30602i
\(211\) −2461.46 1581.88i −0.803099 0.516120i 0.0735268 0.997293i \(-0.476575\pi\)
−0.876626 + 0.481173i \(0.840211\pi\)
\(212\) 236.976 1648.20i 0.0767716 0.533958i
\(213\) −684.093 683.232i −0.220062 0.219785i
\(214\) −2406.45 + 1098.99i −0.768699 + 0.351053i
\(215\) 4937.30 4278.20i 1.56614 1.35707i
\(216\) 1005.21 1009.02i 0.316648 0.317847i
\(217\) 1538.28 + 702.507i 0.481221 + 0.219766i
\(218\) 1738.66 510.517i 0.540170 0.158608i
\(219\) −4083.40 + 2233.05i −1.25996 + 0.689019i
\(220\) −1992.15 + 4362.20i −0.610504 + 1.33682i
\(221\) −15.1753 105.547i −0.00461902 0.0321260i
\(222\) 3860.79 + 2886.35i 1.16720 + 0.872610i
\(223\) 274.385 + 600.819i 0.0823954 + 0.180421i 0.946345 0.323157i \(-0.104744\pi\)
−0.863950 + 0.503578i \(0.832017\pi\)
\(224\) −5874.98 + 3775.62i −1.75240 + 1.12620i
\(225\) 1642.26 + 5567.06i 0.486595 + 1.64950i
\(226\) 4489.44 6985.71i 1.32139 2.05612i
\(227\) −4234.57 + 4886.95i −1.23814 + 1.42889i −0.372645 + 0.927974i \(0.621549\pi\)
−0.865495 + 0.500917i \(0.832996\pi\)
\(228\) −458.566 + 6468.86i −0.133199 + 1.87900i
\(229\) 5012.24i 1.44637i −0.690656 0.723183i \(-0.742678\pi\)
0.690656 0.723183i \(-0.257322\pi\)
\(230\) −2070.72 8467.17i −0.593649 2.42743i
\(231\) −775.411 3553.73i −0.220858 1.01220i
\(232\) −570.871 167.623i −0.161550 0.0474352i
\(233\) 1514.20 + 1312.06i 0.425745 + 0.368910i 0.841219 0.540695i \(-0.181839\pi\)
−0.415474 + 0.909605i \(0.636384\pi\)
\(234\) −27.7184 + 194.525i −0.00774362 + 0.0543441i
\(235\) 4207.40 + 604.932i 1.16792 + 0.167921i
\(236\) 831.793 + 1294.30i 0.229429 + 0.356998i
\(237\) 4609.22 3454.95i 1.26330 0.946934i
\(238\) 4918.64 + 5676.41i 1.33961 + 1.54600i
\(239\) 6011.51 864.325i 1.62700 0.233927i 0.732425 0.680848i \(-0.238389\pi\)
0.894573 + 0.446921i \(0.147479\pi\)
\(240\) 800.884 3692.80i 0.215403 0.993206i
\(241\) 642.398 + 2187.81i 0.171703 + 0.584768i 0.999711 + 0.0240505i \(0.00765626\pi\)
−0.828007 + 0.560717i \(0.810526\pi\)
\(242\) −847.401 2885.98i −0.225095 0.766603i
\(243\) −2279.60 3025.28i −0.601796 0.798649i
\(244\) −469.820 + 67.5499i −0.123267 + 0.0177231i
\(245\) −5261.82 6072.47i −1.37210 1.58349i
\(246\) 2559.22 + 3414.23i 0.663293 + 0.884893i
\(247\) −110.499 171.939i −0.0284650 0.0442925i
\(248\) −608.930 87.5509i −0.155916 0.0224173i
\(249\) 4359.79 + 1622.99i 1.10960 + 0.413063i
\(250\) −5373.34 4656.02i −1.35936 1.17789i
\(251\) −3667.76 1076.95i −0.922339 0.270823i −0.214113 0.976809i \(-0.568686\pi\)
−0.708226 + 0.705986i \(0.750504\pi\)
\(252\) −3254.42 7102.49i −0.813528 1.77545i
\(253\) −2256.78 1600.76i −0.560801 0.397782i
\(254\) 215.784i 0.0533051i
\(255\) −6001.57 425.440i −1.47385 0.104479i
\(256\) −478.700 + 552.450i −0.116870 + 0.134875i
\(257\) 172.486 268.394i 0.0418654 0.0651438i −0.819690 0.572807i \(-0.805854\pi\)
0.861555 + 0.507664i \(0.169491\pi\)
\(258\) −567.869 7870.16i −0.137031 1.89913i
\(259\) 5081.60 3265.74i 1.21913 0.783488i
\(260\) −134.855 295.290i −0.0321666 0.0704351i
\(261\) −655.530 + 1440.21i −0.155465 + 0.341559i
\(262\) 696.621 + 4845.11i 0.164265 + 1.14249i
\(263\) −1675.37 + 3668.55i −0.392805 + 0.860124i 0.605144 + 0.796116i \(0.293115\pi\)
−0.997949 + 0.0640077i \(0.979612\pi\)
\(264\) 634.874 + 1160.94i 0.148007 + 0.270648i
\(265\) 2841.14 834.234i 0.658604 0.193383i
\(266\) 13095.5 + 5980.52i 3.01856 + 1.37853i
\(267\) 1183.61 + 3167.29i 0.271295 + 0.725973i
\(268\) 7454.94 6459.74i 1.69919 1.47236i
\(269\) 191.447 87.4310i 0.0433931 0.0198170i −0.393600 0.919282i \(-0.628771\pi\)
0.436993 + 0.899465i \(0.356043\pi\)
\(270\) 10395.1 + 3854.80i 2.34305 + 0.868872i
\(271\) −198.964 + 1383.82i −0.0445984 + 0.310189i 0.955296 + 0.295651i \(0.0955367\pi\)
−0.999894 + 0.0145375i \(0.995372\pi\)
\(272\) 2083.58 + 1339.04i 0.464469 + 0.298496i
\(273\) 216.178 + 117.865i 0.0479256 + 0.0261302i
\(274\) 958.031 3262.75i 0.211229 0.719380i
\(275\) −5392.32 −1.18243
\(276\) −5468.85 2325.86i −1.19270 0.507247i
\(277\) −898.964 −0.194995 −0.0974973 0.995236i \(-0.531084\pi\)
−0.0974973 + 0.995236i \(0.531084\pi\)
\(278\) −458.609 + 1561.88i −0.0989407 + 0.336961i
\(279\) −458.980 + 1570.46i −0.0984890 + 0.336993i
\(280\) 4394.44 + 2824.14i 0.937923 + 0.602766i
\(281\) −650.568 + 4524.80i −0.138113 + 0.960594i 0.796427 + 0.604735i \(0.206721\pi\)
−0.934540 + 0.355859i \(0.884188\pi\)
\(282\) 3628.00 3632.58i 0.766115 0.767080i
\(283\) −5695.76 + 2601.16i −1.19639 + 0.546372i −0.911146 0.412084i \(-0.864801\pi\)
−0.285241 + 0.958456i \(0.592074\pi\)
\(284\) 1458.07 1263.42i 0.304649 0.263980i
\(285\) −10802.6 + 4036.91i −2.24523 + 0.839039i
\(286\) −166.049 75.8323i −0.0343312 0.0156785i
\(287\) 5130.30 1506.39i 1.05516 0.309824i
\(288\) −4431.14 5100.81i −0.906623 1.04364i
\(289\) −402.677 + 881.740i −0.0819616 + 0.179471i
\(290\) −659.110 4584.21i −0.133463 0.928256i
\(291\) −1585.59 + 2120.89i −0.319412 + 0.427246i
\(292\) −3857.98 8447.80i −0.773190 1.69305i
\(293\) 2401.30 1543.22i 0.478790 0.307700i −0.278893 0.960322i \(-0.589968\pi\)
0.757683 + 0.652622i \(0.226331\pi\)
\(294\) −9679.65 + 698.432i −1.92016 + 0.138549i
\(295\) −1479.15 + 2301.60i −0.291931 + 0.454253i
\(296\) −1439.01 + 1660.71i −0.282570 + 0.326103i
\(297\) 3294.96 1236.05i 0.643747 0.241492i
\(298\) 1039.81i 0.202130i
\(299\) 181.935 44.4938i 0.0351892 0.00860582i
\(300\) −11315.9 + 2469.08i −2.17774 + 0.475175i
\(301\) −9487.22 2785.70i −1.81673 0.533439i
\(302\) −666.438 577.472i −0.126984 0.110032i
\(303\) −2031.64 + 5457.53i −0.385197 + 1.03474i
\(304\) 4698.95 + 675.607i 0.886524 + 0.127463i
\(305\) −456.331 710.065i −0.0856704 0.133306i
\(306\) −4751.92 + 5497.99i −0.887743 + 1.02712i
\(307\) −1481.68 1709.95i −0.275453 0.317889i 0.601120 0.799159i \(-0.294721\pi\)
−0.876573 + 0.481269i \(0.840176\pi\)
\(308\) 7184.27 1032.94i 1.32910 0.191095i
\(309\) 5579.20 + 1210.00i 1.02715 + 0.222765i
\(310\) −1349.15 4594.77i −0.247182 0.841824i
\(311\) −543.345 1850.46i −0.0990683 0.337396i 0.895012 0.446042i \(-0.147167\pi\)
−0.994081 + 0.108646i \(0.965349\pi\)
\(312\) −87.5362 18.9846i −0.0158839 0.00344484i
\(313\) −5133.25 + 738.049i −0.926991 + 0.133281i −0.589243 0.807956i \(-0.700574\pi\)
−0.337748 + 0.941237i \(0.609665\pi\)
\(314\) 128.256 + 148.015i 0.0230506 + 0.0266019i
\(315\) 9084.66 10511.0i 1.62496 1.88009i
\(316\) 6214.41 + 9669.81i 1.10629 + 1.72142i
\(317\) −7530.73 1082.76i −1.33428 0.191841i −0.562010 0.827130i \(-0.689972\pi\)
−0.772274 + 0.635289i \(0.780881\pi\)
\(318\) 1247.73 3351.73i 0.220028 0.591056i
\(319\) −1111.01 962.700i −0.195000 0.168968i
\(320\) 13392.7 + 3932.46i 2.33961 + 0.686972i
\(321\) −3133.68 + 683.758i −0.544875 + 0.118890i
\(322\) −9086.40 + 9564.94i −1.57256 + 1.65538i
\(323\) 7558.93i 1.30214i
\(324\) 6348.53 4102.60i 1.08857 0.703463i
\(325\) 239.039 275.865i 0.0407984 0.0470838i
\(326\) −3217.87 + 5007.11i −0.546692 + 0.850669i
\(327\) 2191.23 158.108i 0.370567 0.0267381i
\(328\) −1636.32 + 1051.60i −0.275460 + 0.177027i
\(329\) −2672.54 5852.05i −0.447848 0.980650i
\(330\) −6167.36 + 8249.46i −1.02879 + 1.37611i
\(331\) −1184.46 8238.09i −0.196688 1.36800i −0.813812 0.581129i \(-0.802611\pi\)
0.617123 0.786866i \(-0.288298\pi\)
\(332\) −3856.31 + 8444.13i −0.637477 + 1.39588i
\(333\) 3832.74 + 4411.98i 0.630730 + 0.726050i
\(334\) 13909.9 4084.32i 2.27879 0.669115i
\(335\) 15956.2 + 7286.94i 2.60233 + 1.18844i
\(336\) −5357.18 + 2001.97i −0.869817 + 0.325049i
\(337\) −4692.86 + 4066.39i −0.758566 + 0.657301i −0.945703 0.325033i \(-0.894625\pi\)
0.187137 + 0.982334i \(0.440079\pi\)
\(338\) −8553.91 + 3906.44i −1.37654 + 0.628646i
\(339\) 7114.39 7123.36i 1.13982 1.14126i
\(340\) 1708.62 11883.7i 0.272538 1.89554i
\(341\) −1278.74 821.798i −0.203073 0.130507i
\(342\) −3907.35 + 13369.5i −0.617793 + 2.11386i
\(343\) −729.445 + 2484.26i −0.114829 + 0.391072i
\(344\) 3596.99 0.563769
\(345\) −277.712 10564.4i −0.0433377 1.64860i
\(346\) 8632.67 1.34132
\(347\) −1762.94 + 6004.03i −0.272737 + 0.928856i 0.703235 + 0.710958i \(0.251738\pi\)
−0.975971 + 0.217898i \(0.930080\pi\)
\(348\) −2772.29 1511.52i −0.427041 0.232833i
\(349\) 10136.1 + 6514.06i 1.55465 + 0.999111i 0.984052 + 0.177880i \(0.0569240\pi\)
0.570596 + 0.821231i \(0.306712\pi\)
\(350\) −3659.13 + 25449.8i −0.558825 + 3.88671i
\(351\) −82.8284 + 223.360i −0.0125956 + 0.0339660i
\(352\) 5709.95 2607.65i 0.864607 0.394853i
\(353\) 2761.73 2393.05i 0.416408 0.360820i −0.421315 0.906914i \(-0.638431\pi\)
0.837724 + 0.546094i \(0.183886\pi\)
\(354\) 1156.75 + 3095.41i 0.173674 + 0.464743i
\(355\) 3120.77 + 1425.21i 0.466573 + 0.213077i
\(356\) −6473.77 + 1900.87i −0.963790 + 0.282994i
\(357\) 4369.19 + 7989.60i 0.647737 + 1.18447i
\(358\) 2031.06 4447.39i 0.299845 0.656570i
\(359\) 1108.85 + 7712.22i 0.163016 + 1.13380i 0.892907 + 0.450240i \(0.148662\pi\)
−0.729891 + 0.683564i \(0.760429\pi\)
\(360\) −2093.71 + 4599.91i −0.306522 + 0.673434i
\(361\) −3169.37 6939.96i −0.462075 1.01180i
\(362\) 1970.37 1266.28i 0.286078 0.183851i
\(363\) −262.441 3637.20i −0.0379465 0.525905i
\(364\) −265.631 + 413.329i −0.0382495 + 0.0595174i
\(365\) 10814.9 12481.1i 1.55090 1.78984i
\(366\) −1016.91 72.0870i −0.145232 0.0102952i
\(367\) 6884.85i 0.979254i 0.871932 + 0.489627i \(0.162867\pi\)
−0.871932 + 0.489627i \(0.837133\pi\)
\(368\) −1986.29 + 3870.44i −0.281365 + 0.548263i
\(369\) 2154.94 + 4702.98i 0.304016 + 0.663488i
\(370\) −16412.3 4819.08i −2.30604 0.677113i
\(371\) −3387.00 2934.85i −0.473973 0.410700i
\(372\) −3059.75 1139.03i −0.426453 0.158753i
\(373\) −194.728 27.9977i −0.0270312 0.00388650i 0.128786 0.991672i \(-0.458892\pi\)
−0.155817 + 0.987786i \(0.549801\pi\)
\(374\) −3650.00 5679.51i −0.504644 0.785242i
\(375\) −5170.14 6897.43i −0.711959 0.949818i
\(376\) 1532.61 + 1768.73i 0.210209 + 0.242594i
\(377\) 98.5013 14.1623i 0.0134564 0.00193474i
\(378\) −3597.83 16389.8i −0.489556 2.23015i
\(379\) 183.459 + 624.803i 0.0248645 + 0.0846807i 0.970991 0.239118i \(-0.0768582\pi\)
−0.946126 + 0.323798i \(0.895040\pi\)
\(380\) −6483.25 22079.9i −0.875221 2.98073i
\(381\) −55.4491 + 255.671i −0.00745602 + 0.0343790i
\(382\) −15934.9 + 2291.09i −2.13429 + 0.306865i
\(383\) −6369.67 7351.00i −0.849805 0.980727i 0.150164 0.988661i \(-0.452020\pi\)
−0.999969 + 0.00793440i \(0.997474\pi\)
\(384\) 5165.98 3872.29i 0.686524 0.514601i
\(385\) 6978.02 + 10858.0i 0.923721 + 1.43734i
\(386\) 11555.8 + 1661.47i 1.52377 + 0.219085i
\(387\) 1349.53 9470.86i 0.177262 1.24401i
\(388\) −3993.46 3460.35i −0.522518 0.452765i
\(389\) −5159.78 1515.05i −0.672523 0.197471i −0.0723967 0.997376i \(-0.523065\pi\)
−0.600126 + 0.799905i \(0.704883\pi\)
\(390\) −148.638 681.209i −0.0192989 0.0884471i
\(391\) 6550.15 + 2253.46i 0.847200 + 0.291464i
\(392\) 4424.00i 0.570014i
\(393\) −419.638 + 5919.71i −0.0538624 + 0.759822i
\(394\) 8682.55 10020.2i 1.11020 1.28124i
\(395\) −11050.9 + 17195.5i −1.40767 + 2.19038i
\(396\) 1986.91 + 6735.40i 0.252137 + 0.854714i
\(397\) −445.814 + 286.507i −0.0563595 + 0.0362201i −0.568517 0.822671i \(-0.692483\pi\)
0.512158 + 0.858891i \(0.328846\pi\)
\(398\) −792.728 1735.83i −0.0998388 0.218616i
\(399\) 13979.4 + 10451.1i 1.75400 + 1.31130i
\(400\) 1206.60 + 8392.12i 0.150826 + 1.04901i
\(401\) 6010.05 13160.2i 0.748447 1.63887i −0.0206886 0.999786i \(-0.506586\pi\)
0.769136 0.639085i \(-0.220687\pi\)
\(402\) 18588.7 10165.4i 2.30627 1.26121i
\(403\) 98.7282 28.9892i 0.0122035 0.00358326i
\(404\) −10570.3 4827.28i −1.30171 0.594471i
\(405\) 11326.0 + 7238.52i 1.38962 + 0.888111i
\(406\) −5297.50 + 4590.31i −0.647563 + 0.561117i
\(407\) −4938.86 + 2255.50i −0.601499 + 0.274695i
\(408\) −2343.90 2340.95i −0.284413 0.284054i
\(409\) −1141.48 + 7939.19i −0.138002 + 0.959823i 0.796696 + 0.604380i \(0.206579\pi\)
−0.934698 + 0.355443i \(0.884330\pi\)
\(410\) −12737.4 8185.83i −1.53428 0.986023i
\(411\) 1973.53 3619.68i 0.236855 0.434417i
\(412\) −3209.46 + 10930.4i −0.383783 + 1.30705i
\(413\) 4140.85 0.493360
\(414\) −10420.4 7371.59i −1.23704 0.875106i
\(415\) −16507.7 −1.95260
\(416\) −119.715 + 407.711i −0.0141094 + 0.0480521i
\(417\) −944.730 + 1732.74i −0.110944 + 0.203483i
\(418\) −10886.1 6996.05i −1.27382 0.818632i
\(419\) 995.739 6925.52i 0.116098 0.807479i −0.845688 0.533677i \(-0.820810\pi\)
0.961786 0.273802i \(-0.0882812\pi\)
\(420\) 19615.2 + 19590.5i 2.27887 + 2.27600i
\(421\) 4554.96 2080.18i 0.527304 0.240812i −0.133931 0.990991i \(-0.542760\pi\)
0.661235 + 0.750179i \(0.270033\pi\)
\(422\) 9477.26 8212.09i 1.09324 0.947295i
\(423\) 5232.07 3371.77i 0.601399 0.387568i
\(424\) 1483.01 + 677.268i 0.169862 + 0.0775732i
\(425\) 12953.1 3803.37i 1.47839 0.434095i
\(426\) 3635.65 1988.19i 0.413493 0.226122i
\(427\) −530.688 + 1162.04i −0.0601447 + 0.131699i
\(428\) −910.849 6335.09i −0.102868 0.715463i
\(429\) −177.257 132.519i −0.0199488 0.0149139i
\(430\) 11631.4 + 25469.3i 1.30446 + 2.85637i
\(431\) −14537.4 + 9342.64i −1.62469 + 1.04413i −0.671842 + 0.740694i \(0.734497\pi\)
−0.952853 + 0.303434i \(0.901867\pi\)
\(432\) −2660.97 4851.38i −0.296357 0.540306i
\(433\) −2323.21 + 3614.99i −0.257844 + 0.401214i −0.945907 0.324438i \(-0.894825\pi\)
0.688063 + 0.725651i \(0.258461\pi\)
\(434\) −4746.32 + 5477.54i −0.524955 + 0.605830i
\(435\) 397.041 5600.95i 0.0437625 0.617345i
\(436\) 4383.88i 0.481536i
\(437\) 13214.6 1286.53i 1.44654 0.140831i
\(438\) −4252.29 19488.4i −0.463887 2.12600i
\(439\) 14126.4 + 4147.90i 1.53581 + 0.450953i 0.936821 0.349808i \(-0.113753\pi\)
0.598984 + 0.800761i \(0.295571\pi\)
\(440\) −3548.48 3074.78i −0.384471 0.333146i
\(441\) −11648.4 1659.80i −1.25779 0.179225i
\(442\) 452.360 + 65.0395i 0.0486800 + 0.00699913i
\(443\) −8380.04 13039.6i −0.898753 1.39849i −0.917101 0.398656i \(-0.869477\pi\)
0.0183472 0.999832i \(-0.494160\pi\)
\(444\) −9331.49 + 6994.64i −0.997417 + 0.747638i
\(445\) −7857.09 9067.56i −0.836992 0.965941i
\(446\) −2802.04 + 402.872i −0.297490 + 0.0427726i
\(447\) −267.196 + 1232.02i −0.0282728 + 0.130363i
\(448\) −5951.82 20270.0i −0.627672 2.13766i
\(449\) −3215.32 10950.4i −0.337952 1.15096i −0.936733 0.350045i \(-0.886166\pi\)
0.598781 0.800913i \(-0.295652\pi\)
\(450\) −24876.2 + 31.3450i −2.60594 + 0.00328359i
\(451\) −4757.13 + 683.972i −0.496684 + 0.0714124i
\(452\) 13155.8 + 15182.6i 1.36902 + 1.57993i
\(453\) −641.236 855.467i −0.0665075 0.0887271i
\(454\) −14983.3 23314.5i −1.54890 2.41014i
\(455\) −864.815 124.342i −0.0891058 0.0128115i
\(456\) −5950.58 2215.18i −0.611100 0.227490i
\(457\) 6222.34 + 5391.69i 0.636913 + 0.551888i 0.912340 0.409434i \(-0.134274\pi\)
−0.275427 + 0.961322i \(0.588819\pi\)
\(458\) 20611.6 + 6052.12i 2.10288 + 0.617461i
\(459\) −7043.10 + 5293.20i −0.716217 + 0.538268i
\(460\) 21066.0 + 964.410i 2.13524 + 0.0977518i
\(461\) 2931.99i 0.296218i −0.988971 0.148109i \(-0.952681\pi\)
0.988971 0.148109i \(-0.0473187\pi\)
\(462\) 15550.1 + 1102.32i 1.56593 + 0.111006i
\(463\) −4676.96 + 5397.50i −0.469453 + 0.541778i −0.940260 0.340459i \(-0.889418\pi\)
0.470806 + 0.882237i \(0.343963\pi\)
\(464\) −1249.65 + 1944.50i −0.125030 + 0.194550i
\(465\) −417.832 5790.78i −0.0416699 0.577508i
\(466\) −7223.89 + 4642.51i −0.718112 + 0.461503i
\(467\) 3284.16 + 7191.32i 0.325424 + 0.712579i 0.999664 0.0259334i \(-0.00825580\pi\)
−0.674240 + 0.738513i \(0.735529\pi\)
\(468\) −432.654 196.928i −0.0427339 0.0194509i
\(469\) −3778.32 26278.8i −0.371997 2.58730i
\(470\) −7567.94 + 16571.5i −0.742730 + 1.62635i
\(471\) 113.929 + 208.333i 0.0111456 + 0.0203810i
\(472\) −1445.35 + 424.393i −0.140948 + 0.0413862i
\(473\) 8084.46 + 3692.05i 0.785885 + 0.358902i
\(474\) 8642.18 + 23126.1i 0.837444 + 2.24096i
\(475\) 19555.5 16945.0i 1.88899 1.63682i
\(476\) −16529.0 + 7548.55i −1.59161 + 0.726864i
\(477\) 2339.64 3650.66i 0.224581 0.350424i
\(478\) −3704.39 + 25764.6i −0.354466 + 2.46537i
\(479\) 2913.03 + 1872.09i 0.277870 + 0.178576i 0.672152 0.740413i \(-0.265370\pi\)
−0.394282 + 0.918990i \(0.629007\pi\)
\(480\) 21050.4 + 11477.2i 2.00170 + 1.09137i
\(481\) 103.548 352.652i 0.00981575 0.0334294i
\(482\) −9772.51 −0.923497
\(483\) −13223.9 + 8998.09i −1.24577 + 0.847675i
\(484\) 7276.74 0.683390
\(485\) 2647.31 9015.92i 0.247852 0.844107i
\(486\) 15193.3 5721.39i 1.41807 0.534007i
\(487\) 4675.72 + 3004.90i 0.435066 + 0.279600i 0.739786 0.672842i \(-0.234927\pi\)
−0.304721 + 0.952442i \(0.598563\pi\)
\(488\) 66.1377 459.998i 0.00613507 0.0426703i
\(489\) −5099.34 + 5105.77i −0.471575 + 0.472170i
\(490\) 31325.1 14305.7i 2.88801 1.31891i
\(491\) −15756.0 + 13652.7i −1.44819 + 1.25486i −0.536548 + 0.843870i \(0.680272\pi\)
−0.911639 + 0.410992i \(0.865183\pi\)
\(492\) −9669.72 + 3613.56i −0.886066 + 0.331122i
\(493\) 3347.83 + 1528.90i 0.305839 + 0.139672i
\(494\) 840.484 246.788i 0.0765489 0.0224768i
\(495\) −9427.20 + 8189.54i −0.856003 + 0.743621i
\(496\) −992.835 + 2174.01i −0.0898783 + 0.196806i
\(497\) −738.979 5139.71i −0.0666957 0.463879i
\(498\) −11938.5 + 15968.9i −1.07425 + 1.43691i
\(499\) 5144.39 + 11264.6i 0.461512 + 1.01057i 0.987140 + 0.159856i \(0.0511030\pi\)
−0.525628 + 0.850714i \(0.676170\pi\)
\(500\) 14470.3 9299.51i 1.29426 0.831773i
\(501\) 17530.7 1264.92i 1.56330 0.112799i
\(502\) 8857.42 13782.4i 0.787502 1.22538i
\(503\) 3553.97 4101.50i 0.315037 0.363573i −0.576042 0.817420i \(-0.695403\pi\)
0.891079 + 0.453848i \(0.149949\pi\)
\(504\) 7570.03 1098.14i 0.669039 0.0970539i
\(505\) 20664.2i 1.82088i
\(506\) 9307.73 7347.61i 0.817746 0.645536i
\(507\) −11138.9 + 2430.47i −0.975731 + 0.212901i
\(508\) −500.894 147.076i −0.0437472 0.0128453i
\(509\) 12488.8 + 10821.6i 1.08753 + 0.942354i 0.998558 0.0536800i \(-0.0170951\pi\)
0.0889761 + 0.996034i \(0.471641\pi\)
\(510\) 8996.23 24166.3i 0.781098 2.09824i
\(511\) −24741.0 3557.22i −2.14184 0.307950i
\(512\) −7067.72 10997.6i −0.610063 0.949276i
\(513\) −8065.12 + 14836.8i −0.694120 + 1.27692i
\(514\) 895.435 + 1033.39i 0.0768403 + 0.0886785i
\(515\) −20051.6 + 2882.98i −1.71569 + 0.246679i
\(516\) 18655.9 + 4046.03i 1.59163 + 0.345187i
\(517\) 1629.17 + 5548.45i 0.138590 + 0.471993i
\(518\) 7293.73 + 24840.2i 0.618664 + 2.10698i
\(519\) 10228.4 + 2218.30i 0.865080 + 0.187616i
\(520\) 314.604 45.2333i 0.0265314 0.00381464i
\(521\) −12066.1 13925.1i −1.01464 1.17096i −0.985203 0.171390i \(-0.945174\pi\)
−0.0294368 0.999567i \(-0.509371\pi\)
\(522\) −5131.00 4434.73i −0.430225 0.371844i
\(523\) −8507.04 13237.2i −0.711256 1.10674i −0.989261 0.146157i \(-0.953310\pi\)
0.278005 0.960580i \(-0.410327\pi\)
\(524\) −11721.6 1685.32i −0.977218 0.140503i
\(525\) −10875.2 + 29213.8i −0.904065 + 2.42856i
\(526\) −13063.1 11319.2i −1.08285 0.938293i
\(527\) 3651.35 + 1072.13i 0.301813 + 0.0886201i
\(528\) 5022.39 1095.87i 0.413961 0.0903249i
\(529\) −2824.67 + 11834.6i −0.232159 + 0.972678i
\(530\) 12690.8i 1.04010i
\(531\) 575.156 + 3964.82i 0.0470050 + 0.324028i
\(532\) −22808.2 + 26322.0i −1.85876 + 2.14512i
\(533\) 175.890 273.690i 0.0142939 0.0222417i
\(534\) −14453.9 + 1042.92i −1.17131 + 0.0845157i
\(535\) 9574.59 6153.22i 0.773730 0.497246i
\(536\) 4012.11 + 8785.29i 0.323315 + 0.707961i
\(537\) 3549.32 4747.56i 0.285222 0.381513i
\(538\) 128.373 + 892.852i 0.0102873 + 0.0715494i
\(539\) 4540.91 9943.21i 0.362877 0.794590i
\(540\) −16033.2 + 21502.5i −1.27770 + 1.71355i
\(541\) −11817.4 + 3469.89i −0.939128 + 0.275753i −0.715253 0.698865i \(-0.753689\pi\)
−0.223874 + 0.974618i \(0.571871\pi\)
\(542\) −5450.40 2489.11i −0.431946 0.197263i
\(543\) 2659.97 994.029i 0.210222 0.0785596i
\(544\) −11876.8 + 10291.3i −0.936056 + 0.811097i
\(545\) −7091.22 + 3238.45i −0.557348 + 0.254532i
\(546\) −745.722 + 746.663i −0.0584505 + 0.0585242i
\(547\) 2355.54 16383.1i 0.184123 1.28061i −0.662762 0.748831i \(-0.730616\pi\)
0.846885 0.531776i \(-0.178475\pi\)
\(548\) 6920.77 + 4447.71i 0.539490 + 0.346709i
\(549\) −1186.36 346.723i −0.0922269 0.0269541i
\(550\) 6511.07 22174.7i 0.504787 1.71915i
\(551\) 7054.36 0.545419
\(552\) 3693.53 4496.06i 0.284796 0.346675i
\(553\) 30936.7 2.37896
\(554\) 1085.47 3696.78i 0.0832442 0.283504i
\(555\) −18207.7 9927.26i −1.39256 0.759259i
\(556\) −3312.97 2129.11i −0.252700 0.162400i
\(557\) −566.475 + 3939.92i −0.0430922 + 0.299713i 0.956866 + 0.290531i \(0.0938318\pi\)
−0.999958 + 0.00918191i \(0.997077\pi\)
\(558\) −5903.95 3783.73i −0.447910 0.287058i
\(559\) −547.260 + 249.925i −0.0414072 + 0.0189101i
\(560\) 15337.0 13289.6i 1.15733 1.00283i
\(561\) −2865.25 7667.27i −0.215634 0.577027i
\(562\) −17821.6 8138.86i −1.33765 0.610885i
\(563\) −14643.4 + 4299.69i −1.09617 + 0.321866i −0.779331 0.626612i \(-0.784441\pi\)
−0.316843 + 0.948478i \(0.602623\pi\)
\(564\) 5959.41 + 10897.5i 0.444923 + 0.813596i
\(565\) −14840.5 + 32496.1i −1.10503 + 2.41969i
\(566\) −3819.22 26563.3i −0.283629 1.97268i
\(567\) −51.2682 20343.9i −0.00379729 1.50681i
\(568\) 784.704 + 1718.26i 0.0579674 + 0.126931i
\(569\) −9256.68 + 5948.91i −0.682004 + 0.438297i −0.835235 0.549893i \(-0.814668\pi\)
0.153231 + 0.988190i \(0.451032\pi\)
\(570\) −3557.05 49297.5i −0.261383 3.62254i
\(571\) −6807.14 + 10592.1i −0.498896 + 0.776298i −0.995805 0.0915051i \(-0.970832\pi\)
0.496908 + 0.867803i \(0.334469\pi\)
\(572\) 289.205 333.760i 0.0211403 0.0243972i
\(573\) −19469.1 1380.13i −1.41943 0.100621i
\(574\) 22916.0i 1.66637i
\(575\) 8853.70 + 21997.3i 0.642130 + 1.59540i
\(576\) 18581.7 8514.28i 1.34416 0.615906i
\(577\) 9431.27 + 2769.27i 0.680466 + 0.199803i 0.603658 0.797243i \(-0.293709\pi\)
0.0768074 + 0.997046i \(0.475527\pi\)
\(578\) −3139.73 2720.59i −0.225944 0.195781i
\(579\) 13264.9 + 4938.03i 0.952107 + 0.354435i
\(580\) 11090.5 + 1594.57i 0.793976 + 0.114157i
\(581\) 13507.7 + 21018.4i 0.964533 + 1.50084i
\(582\) −6807.09 9081.28i −0.484816 0.646789i
\(583\) 2637.99 + 3044.40i 0.187400 + 0.216272i
\(584\) 9000.35 1294.06i 0.637735 0.0916924i
\(585\) −1.06514 845.323i −7.52788e−5 0.0597433i
\(586\) 3446.64 + 11738.2i 0.242968 + 0.827474i
\(587\) 1406.93 + 4791.55i 0.0989268 + 0.336914i 0.994053 0.108900i \(-0.0347327\pi\)
−0.895126 + 0.445813i \(0.852915\pi\)
\(588\) 4976.28 22945.2i 0.349011 1.60926i
\(589\) 7219.86 1038.06i 0.505075 0.0726188i
\(590\) −7678.77 8861.78i −0.535814 0.618362i
\(591\) 12862.3 9641.27i 0.895238 0.671047i
\(592\) 4615.39 + 7181.69i 0.320425 + 0.498591i
\(593\) 17163.2 + 2467.70i 1.18855 + 0.170887i 0.708085 0.706128i \(-0.249560\pi\)
0.480463 + 0.877015i \(0.340469\pi\)
\(594\) 1104.42 + 15042.2i 0.0762878 + 1.03904i
\(595\) −24420.6 21160.6i −1.68260 1.45798i
\(596\) −2413.69 708.723i −0.165887 0.0487088i
\(597\) −493.211 2260.40i −0.0338120 0.154961i
\(598\) −36.7107 + 801.889i −0.00251039 + 0.0548356i
\(599\) 4735.04i 0.322986i −0.986874 0.161493i \(-0.948369\pi\)
0.986874 0.161493i \(-0.0516309\pi\)
\(600\) 801.858 11311.6i 0.0545595 0.769656i
\(601\) 18390.1 21223.3i 1.24816 1.44046i 0.395109 0.918634i \(-0.370707\pi\)
0.853054 0.521822i \(-0.174748\pi\)
\(602\) 22911.1 35650.3i 1.55114 2.41362i
\(603\) 24636.9 7267.78i 1.66384 0.490824i
\(604\) 1794.71 1153.39i 0.120903 0.0776999i
\(605\) 5375.47 + 11770.6i 0.361230 + 0.790982i
\(606\) −19989.7 14944.4i −1.33998 1.00178i
\(607\) 1591.05 + 11066.0i 0.106390 + 0.739958i 0.971270 + 0.237980i \(0.0764852\pi\)
−0.864880 + 0.501978i \(0.832606\pi\)
\(608\) −12513.1 + 27399.9i −0.834660 + 1.82765i
\(609\) −7456.28 + 4077.54i −0.496131 + 0.271314i
\(610\) 3470.98 1019.17i 0.230387 0.0676477i
\(611\) −356.073 162.613i −0.0235764 0.0107670i
\(612\) −9523.51 14777.9i −0.629028 0.976080i
\(613\) −137.466 + 119.115i −0.00905741 + 0.00784829i −0.659378 0.751812i \(-0.729180\pi\)
0.650320 + 0.759660i \(0.274635\pi\)
\(614\) 8820.86 4028.35i 0.579773 0.264774i
\(615\) −12988.4 12972.0i −0.851613 0.850541i
\(616\) −1011.35 + 7034.08i −0.0661500 + 0.460083i
\(617\) 4389.73 + 2821.11i 0.286425 + 0.184074i 0.675962 0.736937i \(-0.263729\pi\)
−0.389537 + 0.921011i \(0.627365\pi\)
\(618\) −11712.6 + 21482.1i −0.762375 + 1.39828i
\(619\) −1272.82 + 4334.83i −0.0826479 + 0.281473i −0.990439 0.137949i \(-0.955949\pi\)
0.907791 + 0.419422i \(0.137767\pi\)
\(620\) 11585.3 0.750446
\(621\) −10452.4 11411.9i −0.675424 0.737429i
\(622\) 8265.66 0.532834
\(623\) −5116.06 + 17423.7i −0.329006 + 1.12049i
\(624\) −166.576 + 305.519i −0.0106865 + 0.0196002i
\(625\) 3126.39 + 2009.21i 0.200089 + 0.128589i
\(626\) 3163.18 22000.4i 0.201959 1.40466i
\(627\) −11100.6 11086.6i −0.707040 0.706150i
\(628\) −431.002 + 196.832i −0.0273867 + 0.0125071i
\(629\) 10272.9 8901.54i 0.651206 0.564273i
\(630\) 32254.5 + 50050.2i 2.03976 + 3.16516i
\(631\) −4372.17 1996.70i −0.275837 0.125971i 0.272694 0.962101i \(-0.412085\pi\)
−0.548531 + 0.836130i \(0.684813\pi\)
\(632\) −10798.4 + 3170.68i −0.679645 + 0.199562i
\(633\) 13339.3 7294.74i 0.837584 0.458041i
\(634\) 13545.7 29661.0i 0.848532 1.85802i
\(635\) −132.115 918.879i −0.00825640 0.0574245i
\(636\) 6929.86 + 5180.82i 0.432055 + 0.323007i
\(637\) 307.387 + 673.085i 0.0191195 + 0.0418659i
\(638\) 5300.39 3406.35i 0.328910 0.211378i
\(639\) 4818.59 1421.46i 0.298310 0.0880003i
\(640\) −12385.7 + 19272.6i −0.764984 + 1.19034i
\(641\) 739.641 853.591i 0.0455758 0.0525972i −0.732504 0.680763i \(-0.761648\pi\)
0.778080 + 0.628166i \(0.216194\pi\)
\(642\) 972.028 13712.1i 0.0597552 0.842951i
\(643\) 15751.2i 0.966046i 0.875608 + 0.483023i \(0.160461\pi\)
−0.875608 + 0.483023i \(0.839539\pi\)
\(644\) −16009.7 27611.4i −0.979612 1.68951i
\(645\) 7236.72 + 33166.1i 0.441776 + 2.02467i
\(646\) 31084.3 + 9127.18i 1.89318 + 0.555889i
\(647\) −1986.02 1720.90i −0.120678 0.104568i 0.592431 0.805621i \(-0.298168\pi\)
−0.713109 + 0.701053i \(0.752714\pi\)
\(648\) 2102.92 + 7095.70i 0.127486 + 0.430163i
\(649\) −3684.12 529.697i −0.222827 0.0320376i
\(650\) 845.799 + 1316.09i 0.0510384 + 0.0794173i
\(651\) −7031.20 + 5270.40i −0.423309 + 0.317302i
\(652\) −9429.62 10882.4i −0.566399 0.653660i
\(653\) 3803.81 546.906i 0.227955 0.0327750i −0.0273906 0.999625i \(-0.508720\pi\)
0.255346 + 0.966850i \(0.417811\pi\)
\(654\) −1995.67 + 9201.83i −0.119322 + 0.550184i
\(655\) −5932.88 20205.5i −0.353919 1.20534i
\(656\) 2128.94 + 7250.52i 0.126709 + 0.431532i
\(657\) −30.4720 24183.4i −0.00180948 1.43605i
\(658\) 27292.2 3924.02i 1.61696 0.232484i
\(659\) 16585.1 + 19140.2i 0.980369 + 1.13141i 0.991321 + 0.131466i \(0.0419685\pi\)
−0.0109514 + 0.999940i \(0.503486\pi\)
\(660\) −14945.7 19938.9i −0.881454 1.17594i
\(661\) 1366.34 + 2126.07i 0.0804002 + 0.125105i 0.879125 0.476592i \(-0.158128\pi\)
−0.798725 + 0.601697i \(0.794492\pi\)
\(662\) 35307.4 + 5076.44i 2.07290 + 0.298038i
\(663\) 519.264 + 193.303i 0.0304171 + 0.0113232i
\(664\) −6868.97 5952.00i −0.401458 0.347865i
\(665\) −59426.6 17449.2i −3.46536 1.01752i
\(666\) −22771.1 + 10433.9i −1.32487 + 0.607067i
\(667\) −2103.04 + 6112.92i −0.122084 + 0.354862i
\(668\) 35072.6i 2.03144i
\(669\) −3423.51 242.686i −0.197848 0.0140251i
\(670\) −49232.4 + 56817.3i −2.83883 + 3.27618i
\(671\) 620.803 965.988i 0.0357166 0.0555761i
\(672\) −2611.55 36193.8i −0.149915 2.07768i
\(673\) −4945.26 + 3178.12i −0.283248 + 0.182032i −0.674548 0.738231i \(-0.735662\pi\)
0.391301 + 0.920263i \(0.372025\pi\)
\(674\) −11055.6 24208.3i −0.631817 1.38349i
\(675\) −29482.5 6355.19i −1.68116 0.362387i
\(676\) −3237.68 22518.6i −0.184210 1.28121i
\(677\) 9168.21 20075.6i 0.520477 1.13969i −0.448782 0.893641i \(-0.648142\pi\)
0.969259 0.246044i \(-0.0791307\pi\)
\(678\) 20702.7 + 37857.5i 1.17269 + 2.14441i
\(679\) −13645.7 + 4006.74i −0.771243 + 0.226457i
\(680\) 10692.7 + 4883.17i 0.603007 + 0.275384i
\(681\) −11761.9 31474.3i −0.661846 1.77107i
\(682\) 4923.49 4266.23i 0.276437 0.239534i
\(683\) 22084.8 10085.8i 1.23726 0.565039i 0.314079 0.949397i \(-0.398304\pi\)
0.923184 + 0.384358i \(0.125577\pi\)
\(684\) −28371.1 18182.5i −1.58596 1.01641i
\(685\) −2081.97 + 14480.4i −0.116128 + 0.807691i
\(686\) −9335.16 5999.34i −0.519560 0.333901i
\(687\) 22866.4 + 12467.3i 1.26988 + 0.692370i
\(688\) 3936.96 13408.1i 0.218162 0.742990i
\(689\) −272.689 −0.0150778
\(690\) 43778.9 + 11614.2i 2.41541 + 0.640788i
\(691\) 25319.3 1.39391 0.696955 0.717115i \(-0.254538\pi\)
0.696955 + 0.717115i \(0.254538\pi\)
\(692\) −5883.93 + 20038.8i −0.323227 + 1.10081i
\(693\) 18141.3 + 5301.94i 0.994415 + 0.290626i
\(694\) −22561.4 14499.4i −1.23404 0.793067i
\(695\) 996.638 6931.77i 0.0543952 0.378327i
\(696\) 2184.69 2187.44i 0.118980 0.119130i
\(697\) 10944.8 4998.34i 0.594785 0.271629i
\(698\) −39026.6 + 33816.7i −2.11630 + 1.83378i
\(699\) −9752.17 + 3644.37i −0.527698 + 0.197200i
\(700\) −56582.0 25840.1i −3.05514 1.39524i
\(701\) 1146.29 336.582i 0.0617616 0.0181348i −0.250706 0.968063i \(-0.580663\pi\)
0.312467 + 0.949928i \(0.398845\pi\)
\(702\) −818.502 610.312i −0.0440062 0.0328130i
\(703\) 10823.3 23699.7i 0.580665 1.27148i
\(704\) 2702.41 + 18795.7i 0.144674 + 1.00623i
\(705\) −13225.2 + 17690.0i −0.706508 + 0.945024i
\(706\) 6506.16 + 14246.5i 0.346831 + 0.759454i
\(707\) −26310.6 + 16908.8i −1.39959 + 0.899463i
\(708\) −7973.72 + 575.341i −0.423264 + 0.0305405i
\(709\) −6261.38 + 9742.90i −0.331666 + 0.516082i −0.966534 0.256538i \(-0.917418\pi\)
0.634868 + 0.772621i \(0.281054\pi\)
\(710\) −9629.08 + 11112.5i −0.508976 + 0.587389i
\(711\) 4297.05 + 29621.6i 0.226655 + 1.56244i
\(712\) 6606.02i 0.347712i
\(713\) −1252.85 + 6565.80i −0.0658059 + 0.344868i
\(714\) −38131.0 + 8320.06i −1.99862 + 0.436093i
\(715\) 753.522 + 221.254i 0.0394127 + 0.0115726i
\(716\) 8939.28 + 7745.93i 0.466588 + 0.404300i
\(717\) −11009.7 + 29575.2i −0.573454 + 1.54045i
\(718\) −33053.6 4752.39i −1.71804 0.247016i
\(719\) 3380.02 + 5259.42i 0.175318 + 0.272800i 0.917781 0.397087i \(-0.129979\pi\)
−0.742463 + 0.669887i \(0.766342\pi\)
\(720\) 14854.9 + 12839.1i 0.768903 + 0.664564i
\(721\) 20078.3 + 23171.6i 1.03711 + 1.19689i
\(722\) 32365.9 4653.51i 1.66833 0.239869i
\(723\) −11578.9 2511.20i −0.595608 0.129174i
\(724\) 1596.40 + 5436.85i 0.0819473 + 0.279087i
\(725\) 3549.49 + 12088.4i 0.181827 + 0.619246i
\(726\) 15274.0 + 3312.58i 0.780815 + 0.169341i
\(727\) −806.021 + 115.888i −0.0411192 + 0.00591205i −0.162844 0.986652i \(-0.552067\pi\)
0.121725 + 0.992564i \(0.461158\pi\)
\(728\) −315.023 363.556i −0.0160378 0.0185086i
\(729\) 19471.9 2874.81i 0.989276 0.146055i
\(730\) 38266.9 + 59544.4i 1.94017 + 3.01896i
\(731\) −22024.0 3166.58i −1.11435 0.160219i
\(732\) 860.448 2311.40i 0.0434468 0.116710i
\(733\) −5881.60 5096.43i −0.296373 0.256809i 0.493962 0.869484i \(-0.335548\pi\)
−0.790335 + 0.612674i \(0.790094\pi\)
\(734\) −28312.3 8313.24i −1.42374 0.418048i
\(735\) 40791.5 8900.56i 2.04710 0.446670i
\(736\) −20012.8 19011.6i −1.00229 0.952141i
\(737\) 23863.6i 1.19271i
\(738\) −21941.9 + 3182.99i −1.09443 + 0.158764i
\(739\) −5191.76 + 5991.61i −0.258433 + 0.298248i −0.870108 0.492862i \(-0.835951\pi\)
0.611675 + 0.791109i \(0.290496\pi\)
\(740\) 22372.8 34812.8i 1.11141 1.72938i
\(741\) 1059.26 76.4306i 0.0525140 0.00378913i
\(742\) 16158.6 10384.5i 0.799461 0.513782i
\(743\) −3231.21 7075.36i −0.159545 0.349354i 0.812931 0.582361i \(-0.197871\pi\)
−0.972475 + 0.233007i \(0.925144\pi\)
\(744\) 1914.06 2560.24i 0.0943181 0.126160i
\(745\) −636.630 4427.86i −0.0313078 0.217751i
\(746\) 350.262 766.967i 0.0171904 0.0376416i
\(747\) −18248.7 + 15852.9i −0.893822 + 0.776475i
\(748\) 15671.5 4601.57i 0.766052 0.224933i
\(749\) −15669.1 7155.85i −0.764402 0.349091i
\(750\) 34606.9 12932.5i 1.68488 0.629639i
\(751\) 20373.5 17653.8i 0.989934 0.857782i 9.83404e−5 1.00000i \(-0.499969\pi\)
0.989835 + 0.142217i \(0.0454232\pi\)
\(752\) 8270.55 3777.03i 0.401058 0.183157i
\(753\) 14036.3 14054.0i 0.679297 0.680154i
\(754\) −60.6980 + 422.164i −0.00293169 + 0.0203903i
\(755\) 3191.47 + 2051.03i 0.153840 + 0.0988673i
\(756\) 40497.4 + 2819.51i 1.94825 + 0.135641i
\(757\) 6041.58 20575.7i 0.290073 0.987897i −0.677546 0.735481i \(-0.736956\pi\)
0.967619 0.252417i \(-0.0812254\pi\)
\(758\) −2790.88 −0.133732
\(759\) 12916.3 6314.02i 0.617698 0.301956i
\(760\) 22531.0 1.07538
\(761\) 5572.34 18977.7i 0.265437 0.903994i −0.713642 0.700511i \(-0.752956\pi\)
0.979078 0.203483i \(-0.0652262\pi\)
\(762\) −984.433 536.736i −0.0468008 0.0255169i
\(763\) 9925.86 + 6378.96i 0.470957 + 0.302666i
\(764\) 5542.78 38550.9i 0.262475 1.82555i
\(765\) 16869.1 26321.6i 0.797258 1.24400i
\(766\) 37920.4 17317.7i 1.78867 0.816858i
\(767\) 190.414 164.994i 0.00896407 0.00776741i
\(768\) −1329.63 3558.04i −0.0624727 0.167174i
\(769\) −19063.1 8705.82i −0.893930 0.408244i −0.0851588 0.996367i \(-0.527140\pi\)
−0.808771 + 0.588123i \(0.799867\pi\)
\(770\) −53076.7 + 15584.7i −2.48409 + 0.729396i
\(771\) 795.407 + 1454.50i 0.0371542 + 0.0679411i
\(772\) −11733.0 + 25691.7i −0.546996 + 1.19775i
\(773\) −1185.17 8243.03i −0.0551456 0.383546i −0.998639 0.0521548i \(-0.983391\pi\)
0.943493 0.331391i \(-0.107518\pi\)
\(774\) 37317.2 + 16985.4i 1.73299 + 0.788794i
\(775\) 5411.59 + 11849.7i 0.250826 + 0.549232i
\(776\) 4352.34 2797.08i 0.201340 0.129393i
\(777\) 2258.87 + 31306.0i 0.104294 + 1.44543i
\(778\) 12460.6 19389.0i 0.574207 0.893483i
\(779\) 15102.6 17429.4i 0.694619 0.801633i
\(780\) 1682.58 + 119.275i 0.0772387 + 0.00547531i
\(781\) 4667.34i 0.213842i
\(782\) −17175.9 + 24215.0i −0.785434 + 1.10732i
\(783\) −4939.87 6572.96i −0.225462 0.299998i
\(784\) −16490.8 4842.13i −0.751220 0.220578i
\(785\) −636.779 551.772i −0.0289524 0.0250874i
\(786\) −23836.7 8873.53i −1.08171 0.402683i
\(787\) 14260.5 + 2050.35i 0.645910 + 0.0928678i 0.457482 0.889219i \(-0.348752\pi\)
0.188428 + 0.982087i \(0.439661\pi\)
\(788\) 17341.7 + 26984.2i 0.783976 + 1.21989i
\(789\) −12569.1 16768.3i −0.567138 0.756613i
\(790\) −57368.9 66207.2i −2.58366 2.98171i
\(791\) 53519.1 7694.88i 2.40571 0.345889i
\(792\) −6875.54 + 8.66345i −0.308474 + 0.000388690i
\(793\) 21.8990 + 74.5813i 0.000980653 + 0.00333980i
\(794\) −639.886 2179.25i −0.0286004 0.0974040i
\(795\) −3261.11 + 15036.7i −0.145484 + 0.670813i
\(796\) 4569.66 657.018i 0.203476 0.0292555i
\(797\) 491.082 + 566.739i 0.0218256 + 0.0251881i 0.766557 0.642176i \(-0.221968\pi\)
−0.744732 + 0.667364i \(0.767423\pi\)
\(798\) −59857.3 + 44867.5i −2.65530 + 1.99034i
\(799\) −7826.97 12179.0i −0.346556 0.539252i
\(800\) −53248.9 7656.03i −2.35329 0.338352i
\(801\) −17393.6 2478.46i −0.767258 0.109328i
\(802\) 46861.1 + 40605.4i 2.06325 + 1.78781i
\(803\) 21557.1 + 6329.74i 0.947364 + 0.278171i
\(804\) 10926.9 + 50078.1i 0.479305 + 2.19667i
\(805\) 32836.7 46293.8i 1.43769 2.02689i
\(806\) 441.000i 0.0192724i
\(807\) −77.3305 + 1090.88i −0.00337319 + 0.0475846i
\(808\) 7450.65 8598.51i 0.324397 0.374374i
\(809\) 12245.9 19055.0i 0.532191 0.828105i −0.466208 0.884675i \(-0.654380\pi\)
0.998399 + 0.0565702i \(0.0180165\pi\)
\(810\) −43442.5 + 37835.3i −1.88446 + 1.64123i
\(811\) −5026.00 + 3230.01i −0.217616 + 0.139853i −0.644908 0.764260i \(-0.723104\pi\)
0.427291 + 0.904114i \(0.359468\pi\)
\(812\) −7044.67 15425.7i −0.304457 0.666669i
\(813\) −5818.27 4349.78i −0.250991 0.187643i
\(814\) −3311.69 23033.3i −0.142598 0.991791i
\(815\) 10637.1 23292.1i 0.457181 1.00109i
\(816\) −11291.5 + 6174.86i −0.484414 + 0.264906i
\(817\) −40920.7 + 12015.4i −1.75230 + 0.514523i
\(818\) −31269.7 14280.4i −1.33658 0.610395i
\(819\) −1075.43 + 693.055i −0.0458836 + 0.0295694i
\(820\) 27683.2 23987.7i 1.17895 1.02157i
\(821\) −5907.42 + 2697.83i −0.251121 + 0.114683i −0.536999 0.843583i \(-0.680442\pi\)
0.285878 + 0.958266i \(0.407715\pi\)
\(822\) 12502.1 + 12486.3i 0.530487 + 0.529819i
\(823\) −5035.96 + 35025.9i −0.213296 + 1.48351i 0.548751 + 0.835986i \(0.315103\pi\)
−0.762047 + 0.647521i \(0.775806\pi\)
\(824\) −9383.10 6030.15i −0.396694 0.254940i
\(825\) 13412.7 24600.4i 0.566026 1.03815i
\(826\) −4999.95 + 17028.3i −0.210618 + 0.717299i
\(827\) −29957.1 −1.25963 −0.629813 0.776747i \(-0.716868\pi\)
−0.629813 + 0.776747i \(0.716868\pi\)
\(828\) 24213.9 19164.3i 1.01630 0.804354i
\(829\) −2195.26 −0.0919719 −0.0459859 0.998942i \(-0.514643\pi\)
−0.0459859 + 0.998942i \(0.514643\pi\)
\(830\) 19932.5 67884.0i 0.833577 2.83890i
\(831\) 2236.06 4101.18i 0.0933432 0.171202i
\(832\) −1081.36 694.948i −0.0450594 0.0289579i
\(833\) −3894.63 + 27087.7i −0.161994 + 1.12669i
\(834\) −5984.74 5977.21i −0.248483 0.248170i
\(835\) −56732.4 + 25908.8i −2.35126 + 1.07379i
\(836\) 23659.6 20501.2i 0.978809 0.848143i
\(837\) −6022.98 6000.26i −0.248727 0.247789i
\(838\) 27277.2 + 12457.1i 1.12444 + 0.513512i
\(839\) 4716.53 1384.90i 0.194079 0.0569869i −0.183248 0.983067i \(-0.558661\pi\)
0.377328 + 0.926080i \(0.376843\pi\)
\(840\) −23814.7 + 13023.3i −0.978197 + 0.534936i
\(841\) 8704.71 19060.7i 0.356911 0.781527i
\(842\) 3054.27 + 21242.9i 0.125009 + 0.869453i
\(843\) −19024.5 14222.8i −0.777269 0.581092i
\(844\) 12602.9 + 27596.6i 0.513995 + 1.12549i
\(845\) 34033.6 21872.1i 1.38555 0.890440i
\(846\) 7548.04 + 25587.0i 0.306746 + 1.03983i
\(847\) 10588.4 16475.8i 0.429540 0.668377i
\(848\) 4147.75 4786.76i 0.167965 0.193842i
\(849\) 2300.66 32454.8i 0.0930018 1.31195i
\(850\) 57858.9i 2.33476i
\(851\) 17310.2 + 16444.2i 0.697281 + 0.662396i
\(852\) 2137.12 + 9794.48i 0.0859350 + 0.393842i
\(853\) −31578.2 9272.21i −1.26755 0.372186i −0.422249 0.906480i \(-0.638759\pi\)
−0.845299 + 0.534294i \(0.820577\pi\)
\(854\) −4137.85 3585.46i −0.165801 0.143667i
\(855\) 8453.23 59324.0i 0.338122 2.37291i
\(856\) 6202.65 + 891.807i 0.247666 + 0.0356090i
\(857\) 17405.2 + 27083.0i 0.693757 + 1.07951i 0.992149 + 0.125064i \(0.0399136\pi\)
−0.298391 + 0.954444i \(0.596450\pi\)
\(858\) 758.984 568.915i 0.0301996 0.0226369i
\(859\) 8105.17 + 9353.86i 0.321938 + 0.371536i 0.893531 0.449001i \(-0.148220\pi\)
−0.571593 + 0.820537i \(0.693674\pi\)
\(860\) −67049.1 + 9640.20i −2.65855 + 0.382242i
\(861\) −5888.64 + 27152.0i −0.233083 + 1.07472i
\(862\) −20865.9 71062.7i −0.824472 2.80790i
\(863\) 9982.10 + 33995.9i 0.393736 + 1.34094i 0.883232 + 0.468937i \(0.155363\pi\)
−0.489495 + 0.872006i \(0.662819\pi\)
\(864\) 34292.4 7527.77i 1.35029 0.296412i
\(865\) −36760.7 + 5285.39i −1.44497 + 0.207756i
\(866\) −12060.6 13918.7i −0.473251 0.546161i
\(867\) −3021.00 4030.28i −0.118337 0.157873i
\(868\) −9479.85 14750.9i −0.370699 0.576820i
\(869\) −27524.4 3957.42i −1.07446 0.154484i
\(870\) 22553.2 + 8395.72i 0.878879 + 0.327174i
\(871\) −1220.84 1057.86i −0.0474931 0.0411530i
\(872\) −4118.36 1209.26i −0.159937 0.0469618i
\(873\) −5731.78 12509.1i −0.222212 0.484959i
\(874\) −10665.6 + 55895.3i −0.412781 + 2.16326i
\(875\) 46295.0i 1.78864i
\(876\) 48136.2 + 3412.29i 1.85659 + 0.131610i
\(877\) −22511.6 + 25979.7i −0.866774 + 1.00031i 0.133183 + 0.991091i \(0.457480\pi\)
−0.999957 + 0.00921963i \(0.997065\pi\)
\(878\) −34114.5 + 53083.2i −1.31129 + 2.04040i
\(879\) 1067.43 + 14793.6i 0.0409596 + 0.567663i
\(880\) −15345.3 + 9861.85i −0.587831 + 0.377776i
\(881\) −164.777 360.812i −0.00630135 0.0137980i 0.906455 0.422302i \(-0.138778\pi\)
−0.912757 + 0.408504i \(0.866051\pi\)
\(882\) 20890.6 45897.0i 0.797532 1.75219i
\(883\) 2213.26 + 15393.6i 0.0843514 + 0.586677i 0.987532 + 0.157417i \(0.0503165\pi\)
−0.903181 + 0.429260i \(0.858774\pi\)
\(884\) −459.298 + 1005.72i −0.0174749 + 0.0382648i
\(885\) −6820.99 12473.0i −0.259079 0.473758i
\(886\) 63740.9 18716.0i 2.41695 0.709681i
\(887\) −20696.9 9451.94i −0.783464 0.357796i −0.0168121 0.999859i \(-0.505352\pi\)
−0.766652 + 0.642062i \(0.778079\pi\)
\(888\) −3996.98 10695.7i −0.151047 0.404196i
\(889\) −1061.85 + 920.102i −0.0400601 + 0.0347123i
\(890\) 46775.4 21361.6i 1.76170 0.804542i
\(891\) −2556.77 + 18106.5i −0.0961335 + 0.680798i
\(892\) 974.659 6778.90i 0.0365852 0.254456i
\(893\) −23343.8 15002.2i −0.874773 0.562182i
\(894\) −4743.75 2586.40i −0.177466 0.0967587i
\(895\) −5925.96 + 20182.0i −0.221322 + 0.753753i
\(896\) 34673.6 1.29282
\(897\) −249.555 + 940.682i −0.00928917 + 0.0350150i
\(898\) 48913.2 1.81766
\(899\) −1000.57 + 3407.61i −0.0371198 + 0.126419i
\(900\) 16882.6 57765.9i 0.625280 2.13948i
\(901\) −8484.12 5452.41i −0.313704 0.201605i
\(902\) 2931.42 20388.5i 0.108210 0.752618i
\(903\) 36307.0 36352.8i 1.33801 1.33970i
\(904\) −17892.0 + 8171.00i −0.658273 + 0.300623i
\(905\) −7615.19 + 6598.60i −0.279710 + 0.242370i
\(906\) 4292.18 1603.98i 0.157393 0.0588176i
\(907\) −3248.18 1483.39i −0.118913 0.0543057i 0.355070 0.934840i \(-0.384457\pi\)
−0.473983 + 0.880534i \(0.657184\pi\)
\(908\) 64331.8 18889.5i 2.35124 0.690387i
\(909\) −19844.5 22843.5i −0.724092 0.833523i
\(910\) 1555.56 3406.21i 0.0566664 0.124082i
\(911\) 3556.65 + 24737.0i 0.129349 + 0.899643i 0.946382 + 0.323051i \(0.104709\pi\)
−0.817032 + 0.576592i \(0.804382\pi\)
\(912\) −14770.3 + 19756.7i −0.536285 + 0.717335i
\(913\) −9329.15 20428.0i −0.338171 0.740490i
\(914\) −29685.4 + 19077.6i −1.07429 + 0.690407i
\(915\) 4374.47 315.639i 0.158050 0.0114040i
\(916\) −28097.3 + 43720.2i −1.01349 + 1.57703i
\(917\) −20872.0 + 24087.5i −0.751639 + 0.867437i
\(918\) −13262.7 35354.4i −0.476835 1.27110i
\(919\) 15182.1i 0.544951i 0.962163 + 0.272475i \(0.0878423\pi\)
−0.962163 + 0.272475i \(0.912158\pi\)
\(920\) −6716.91 + 19524.1i −0.240706 + 0.699664i
\(921\) 11486.5 2506.32i 0.410959 0.0896699i
\(922\) 12057.1 + 3540.29i 0.430673 + 0.126457i
\(923\) −238.776 206.901i −0.00851507 0.00737835i
\(924\) −13157.6 + 35344.8i −0.468455 + 1.25840i
\(925\) 46057.9 + 6622.13i 1.63716 + 0.235388i
\(926\) −16548.7 25750.2i −0.587282 0.913828i
\(927\) −19397.7 + 22443.3i −0.687277 + 0.795182i
\(928\) −9604.36 11084.0i −0.339740 0.392081i
\(929\) −50039.0 + 7194.52i −1.76720 + 0.254085i −0.947737 0.319052i \(-0.896636\pi\)
−0.819460 + 0.573137i \(0.805726\pi\)
\(930\) 24317.7 + 5273.96i 0.857430 + 0.185957i
\(931\) 14777.9 + 50329.0i 0.520222 + 1.77171i
\(932\) −5852.84 19932.9i −0.205704 0.700563i
\(933\) 9793.54 + 2123.99i 0.343651 + 0.0745299i
\(934\) −33538.1 + 4822.05i −1.17495 + 0.168932i
\(935\) 19020.2 + 21950.5i 0.665269 + 0.767762i
\(936\) 304.346 352.129i 0.0106280 0.0122967i
\(937\) −17459.7 27167.8i −0.608733 0.947207i −0.999641 0.0267775i \(-0.991475\pi\)
0.390908 0.920430i \(-0.372161\pi\)
\(938\) 112628. + 16193.4i 3.92049 + 0.563682i
\(939\) 9401.25 25254.3i 0.326729 0.877682i
\(940\) −33308.8 28862.2i −1.15576 1.00147i
\(941\) 29943.6 + 8792.24i 1.03734 + 0.304590i 0.755691 0.654929i \(-0.227301\pi\)
0.281646 + 0.959518i \(0.409119\pi\)
\(942\) −994.284 + 216.949i −0.0343902 + 0.00750382i
\(943\) 10601.0 + 18283.1i 0.366081 + 0.631369i
\(944\) 5852.16i 0.201771i
\(945\) 25355.4 + 67590.1i 0.872817 + 2.32667i
\(946\) −24944.4 + 28787.4i −0.857307 + 0.989385i
\(947\) −16158.9 + 25143.8i −0.554482 + 0.862791i −0.999464 0.0327487i \(-0.989574\pi\)
0.444981 + 0.895540i \(0.353210\pi\)
\(948\) −59572.4 + 4298.43i −2.04095 + 0.147264i
\(949\) −1279.44 + 822.244i −0.0437642 + 0.0281256i
\(950\) 46069.4 + 100878.i 1.57336 + 3.44517i
\(951\) 23671.4 31662.9i 0.807149 1.07964i
\(952\) −2531.95 17610.1i −0.0861986 0.599525i
\(953\) −7952.51 + 17413.6i −0.270312 + 0.591900i −0.995298 0.0968636i \(-0.969119\pi\)
0.724986 + 0.688764i \(0.241846\pi\)
\(954\) 12187.4 + 14029.3i 0.413609 + 0.476117i
\(955\) 66453.2 19512.4i 2.25170 0.661160i
\(956\) −57281.8 26159.7i −1.93789 0.885007i
\(957\) 7155.47 2673.99i 0.241696 0.0903216i
\(958\) −11215.9 + 9718.66i −0.378257 + 0.327762i
\(959\) 20140.8 9197.98i 0.678185 0.309717i
\(960\) −51253.1 + 51317.7i −1.72311 + 1.72528i
\(961\) 3717.10 25853.0i 0.124772 0.867812i
\(962\) 1325.17 + 851.632i 0.0444127 + 0.0285423i
\(963\) 4675.25 15997.0i 0.156446 0.535302i
\(964\) 6660.83 22684.7i 0.222542 0.757910i
\(965\) −50225.6 −1.67546
\(966\) −21035.1 65244.9i −0.700615 2.17311i
\(967\) 38443.1 1.27843 0.639217 0.769026i \(-0.279259\pi\)
0.639217 + 0.769026i \(0.279259\pi\)
\(968\) −2007.24 + 6836.02i −0.0666478 + 0.226981i
\(969\) 34484.8 + 18801.9i 1.14325 + 0.623327i
\(970\) 33879.3 + 21772.9i 1.12144 + 0.720707i
\(971\) 5713.46 39738.0i 0.188830 1.31334i −0.646214 0.763156i \(-0.723649\pi\)
0.835044 0.550184i \(-0.185442\pi\)
\(972\) 2925.35 + 39167.5i 0.0965337 + 1.29249i
\(973\) −9641.37 + 4403.07i −0.317665 + 0.145073i
\(974\) −18002.7 + 15599.5i −0.592243 + 0.513181i
\(975\) 663.952 + 1776.70i 0.0218087 + 0.0583590i
\(976\) −1642.29 750.008i −0.0538610 0.0245975i
\(977\) 1798.85 528.190i 0.0589051 0.0172961i −0.252147 0.967689i \(-0.581137\pi\)
0.311052 + 0.950393i \(0.399319\pi\)
\(978\) −14839.0 27134.9i −0.485172 0.887197i
\(979\) 6780.60 14847.4i 0.221357 0.484705i
\(980\) 11856.6 + 82464.8i 0.386476 + 2.68800i
\(981\) −4729.11 + 10389.9i −0.153913 + 0.338150i
\(982\) −37118.5 81278.2i −1.20621 2.64123i
\(983\) 18662.7 11993.8i 0.605543 0.389159i −0.201640 0.979460i \(-0.564627\pi\)
0.807183 + 0.590301i \(0.200991\pi\)
\(984\) −727.379 10080.8i −0.0235651 0.326591i
\(985\) −30838.2 + 47985.2i −0.997551 + 1.55222i
\(986\) −10329.6 + 11921.0i −0.333634 + 0.385034i
\(987\) 33345.4 + 2363.79i 1.07537 + 0.0762314i
\(988\) 2119.20i 0.0682397i
\(989\) 1787.34 39041.6i 0.0574661 1.25526i
\(990\) −22294.5 48655.8i −0.715722 1.56200i
\(991\) −59107.3 17355.5i −1.89466 0.556322i −0.992048 0.125863i \(-0.959830\pi\)
−0.902610 0.430458i \(-0.858352\pi\)
\(992\) −11460.7 9930.76i −0.366812 0.317845i
\(993\) 40529.4 + 15087.6i 1.29523 + 0.482165i
\(994\) 22028.2 + 3167.17i 0.702908 + 0.101063i
\(995\) 4438.46 + 6906.39i 0.141416 + 0.220047i
\(996\) −28931.1 38596.7i −0.920398 1.22789i
\(997\) 16290.3 + 18800.0i 0.517471 + 0.597194i 0.952996 0.302983i \(-0.0979825\pi\)
−0.435525 + 0.900177i \(0.643437\pi\)
\(998\) −52534.9 + 7553.38i −1.66630 + 0.239577i
\(999\) −29661.4 + 6511.19i −0.939386 + 0.206211i
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 69.4.g.a.5.3 220
3.2 odd 2 inner 69.4.g.a.5.20 yes 220
23.14 odd 22 inner 69.4.g.a.14.20 yes 220
69.14 even 22 inner 69.4.g.a.14.3 yes 220
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.4.g.a.5.3 220 1.1 even 1 trivial
69.4.g.a.5.20 yes 220 3.2 odd 2 inner
69.4.g.a.14.3 yes 220 69.14 even 22 inner
69.4.g.a.14.20 yes 220 23.14 odd 22 inner