Properties

Label 112.4.j.b.27.9
Level $112$
Weight $4$
Character 112.27
Analytic conductor $6.608$
Analytic rank $0$
Dimension $88$
Inner twists $4$

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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] = [112,4,Mod(27,112)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 2])) 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("112.27"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 112.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [88] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.60821392064\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(44\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 27.9
Character \(\chi\) \(=\) 112.27
Dual form 112.4.j.b.83.9

$q$-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+(-2.35605 + 1.56494i) q^{2} +(-4.79702 + 4.79702i) q^{3} +(3.10192 - 7.37415i) q^{4} +(2.04624 - 2.04624i) q^{5} +(3.79496 - 18.8091i) q^{6} +(13.3740 - 12.8115i) q^{7} +(4.23184 + 22.2282i) q^{8} -19.0229i q^{9} +(-1.61879 + 8.02329i) q^{10} +(34.5515 - 34.5515i) q^{11} +(20.4940 + 50.2540i) q^{12} +(-7.32563 - 7.32563i) q^{13} +(-11.4606 + 51.1141i) q^{14} +19.6317i q^{15} +(-44.7562 - 45.7480i) q^{16} +133.707i q^{17} +(29.7697 + 44.8188i) q^{18} +(-13.6735 + 13.6735i) q^{19} +(-8.74201 - 21.4366i) q^{20} +(-2.69841 + 125.613i) q^{21} +(-27.3339 + 135.476i) q^{22} +129.773 q^{23} +(-126.929 - 86.3288i) q^{24} +116.626i q^{25} +(28.7237 + 5.79535i) q^{26} +(-38.2664 - 38.2664i) q^{27} +(-52.9889 - 138.362i) q^{28} +(85.7909 - 85.7909i) q^{29} +(-30.7225 - 46.2533i) q^{30} +239.073 q^{31} +(177.041 + 37.7438i) q^{32} +331.489i q^{33} +(-209.244 - 315.021i) q^{34} +(1.15105 - 53.5820i) q^{35} +(-140.278 - 59.0074i) q^{36} +(-50.7975 - 50.7975i) q^{37} +(10.8172 - 53.6135i) q^{38} +70.2824 q^{39} +(54.1436 + 36.8248i) q^{40} +118.276 q^{41} +(-190.219 - 300.172i) q^{42} +(-75.4750 + 75.4750i) q^{43} +(-147.612 - 361.964i) q^{44} +(-38.9254 - 38.9254i) q^{45} +(-305.751 + 203.087i) q^{46} +169.043 q^{47} +(434.151 + 4.75794i) q^{48} +(14.7299 - 342.684i) q^{49} +(-182.512 - 274.776i) q^{50} +(-641.398 - 641.398i) q^{51} +(-76.7438 + 31.2968i) q^{52} +(482.264 + 482.264i) q^{53} +(150.042 + 30.2728i) q^{54} -141.401i q^{55} +(341.373 + 243.064i) q^{56} -131.184i q^{57} +(-67.8698 + 336.385i) q^{58} +(285.231 + 285.231i) q^{59} +(144.767 + 60.8961i) q^{60} +(-313.070 - 313.070i) q^{61} +(-563.267 + 374.135i) q^{62} +(-243.712 - 254.413i) q^{63} +(-476.183 + 188.132i) q^{64} -29.9800 q^{65} +(-518.760 - 781.003i) q^{66} +(-58.2711 - 58.2711i) q^{67} +(985.979 + 414.750i) q^{68} +(-622.523 + 622.523i) q^{69} +(81.1407 + 128.043i) q^{70} -374.109 q^{71} +(422.844 - 80.5018i) q^{72} +610.003 q^{73} +(199.176 + 40.1862i) q^{74} +(-559.457 - 559.457i) q^{75} +(58.4162 + 143.244i) q^{76} +(19.4359 - 904.751i) q^{77} +(-165.589 + 109.988i) q^{78} +460.899i q^{79} +(-185.193 - 2.02957i) q^{80} +880.748 q^{81} +(-278.664 + 185.095i) q^{82} +(875.405 - 875.405i) q^{83} +(917.917 + 409.539i) q^{84} +(273.598 + 273.598i) q^{85} +(59.7088 - 295.937i) q^{86} +823.082i q^{87} +(914.233 + 621.800i) q^{88} -633.231 q^{89} +(152.626 + 30.7941i) q^{90} +(-191.826 - 4.12080i) q^{91} +(402.545 - 956.964i) q^{92} +(-1146.84 + 1146.84i) q^{93} +(-398.272 + 264.542i) q^{94} +55.9584i q^{95} +(-1030.33 + 668.211i) q^{96} +946.138i q^{97} +(501.575 + 830.430i) q^{98} +(-657.269 - 657.269i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q - 4 q^{2} + 24 q^{4} - 4 q^{7} + 80 q^{8} + 112 q^{11} - 24 q^{14} + 240 q^{16} + 68 q^{18} + 52 q^{21} - 120 q^{22} + 160 q^{23} + 96 q^{28} + 528 q^{29} - 552 q^{30} - 984 q^{32} + 476 q^{35} + 32 q^{36}+ \cdots + 7592 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\) \(85\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.35605 + 1.56494i −0.832989 + 0.553290i
\(3\) −4.79702 + 4.79702i −0.923188 + 0.923188i −0.997253 0.0740657i \(-0.976403\pi\)
0.0740657 + 0.997253i \(0.476403\pi\)
\(4\) 3.10192 7.37415i 0.387740 0.921769i
\(5\) 2.04624 2.04624i 0.183021 0.183021i −0.609650 0.792671i \(-0.708690\pi\)
0.792671 + 0.609650i \(0.208690\pi\)
\(6\) 3.79496 18.8091i 0.258214 1.27980i
\(7\) 13.3740 12.8115i 0.722130 0.691757i
\(8\) 4.23184 + 22.2282i 0.187023 + 0.982356i
\(9\) 19.0229i 0.704551i
\(10\) −1.61879 + 8.02329i −0.0511908 + 0.253719i
\(11\) 34.5515 34.5515i 0.947061 0.947061i −0.0516064 0.998668i \(-0.516434\pi\)
0.998668 + 0.0516064i \(0.0164341\pi\)
\(12\) 20.4940 + 50.2540i 0.493009 + 1.20892i
\(13\) −7.32563 7.32563i −0.156290 0.156290i 0.624631 0.780920i \(-0.285250\pi\)
−0.780920 + 0.624631i \(0.785250\pi\)
\(14\) −11.4606 + 51.1141i −0.218784 + 0.975773i
\(15\) 19.6317i 0.337926i
\(16\) −44.7562 45.7480i −0.699315 0.714813i
\(17\) 133.707i 1.90758i 0.300477 + 0.953789i \(0.402854\pi\)
−0.300477 + 0.953789i \(0.597146\pi\)
\(18\) 29.7697 + 44.8188i 0.389821 + 0.586883i
\(19\) −13.6735 + 13.6735i −0.165100 + 0.165100i −0.784822 0.619722i \(-0.787246\pi\)
0.619722 + 0.784822i \(0.287246\pi\)
\(20\) −8.74201 21.4366i −0.0977387 0.239668i
\(21\) −2.69841 + 125.613i −0.0280401 + 1.30528i
\(22\) −27.3339 + 135.476i −0.264891 + 1.31289i
\(23\) 129.773 1.17650 0.588250 0.808679i \(-0.299817\pi\)
0.588250 + 0.808679i \(0.299817\pi\)
\(24\) −126.929 86.3288i −1.07956 0.734242i
\(25\) 116.626i 0.933006i
\(26\) 28.7237 + 5.79535i 0.216661 + 0.0437139i
\(27\) −38.2664 38.2664i −0.272755 0.272755i
\(28\) −52.9889 138.362i −0.357641 0.933859i
\(29\) 85.7909 85.7909i 0.549344 0.549344i −0.376907 0.926251i \(-0.623012\pi\)
0.926251 + 0.376907i \(0.123012\pi\)
\(30\) −30.7225 46.2533i −0.186971 0.281489i
\(31\) 239.073 1.38512 0.692560 0.721360i \(-0.256483\pi\)
0.692560 + 0.721360i \(0.256483\pi\)
\(32\) 177.041 + 37.7438i 0.978021 + 0.208507i
\(33\) 331.489i 1.74863i
\(34\) −209.244 315.021i −1.05544 1.58899i
\(35\) 1.15105 53.5820i 0.00555893 0.258772i
\(36\) −140.278 59.0074i −0.649433 0.273183i
\(37\) −50.7975 50.7975i −0.225704 0.225704i 0.585191 0.810895i \(-0.301019\pi\)
−0.810895 + 0.585191i \(0.801019\pi\)
\(38\) 10.8172 53.6135i 0.0461783 0.228875i
\(39\) 70.2824 0.288569
\(40\) 54.1436 + 36.8248i 0.214021 + 0.145563i
\(41\) 118.276 0.450527 0.225264 0.974298i \(-0.427676\pi\)
0.225264 + 0.974298i \(0.427676\pi\)
\(42\) −190.219 300.172i −0.698843 1.10280i
\(43\) −75.4750 + 75.4750i −0.267671 + 0.267671i −0.828161 0.560490i \(-0.810613\pi\)
0.560490 + 0.828161i \(0.310613\pi\)
\(44\) −147.612 361.964i −0.505758 1.24018i
\(45\) −38.9254 38.9254i −0.128948 0.128948i
\(46\) −305.751 + 203.087i −0.980011 + 0.650946i
\(47\) 169.043 0.524625 0.262313 0.964983i \(-0.415515\pi\)
0.262313 + 0.964983i \(0.415515\pi\)
\(48\) 434.151 + 4.75794i 1.30551 + 0.0143073i
\(49\) 14.7299 342.684i 0.0429442 0.999077i
\(50\) −182.512 274.776i −0.516223 0.777184i
\(51\) −641.398 641.398i −1.76105 1.76105i
\(52\) −76.7438 + 31.2968i −0.204662 + 0.0834631i
\(53\) 482.264 + 482.264i 1.24989 + 1.24989i 0.955769 + 0.294118i \(0.0950257\pi\)
0.294118 + 0.955769i \(0.404974\pi\)
\(54\) 150.042 + 30.2728i 0.378114 + 0.0762891i
\(55\) 141.401i 0.346665i
\(56\) 341.373 + 243.064i 0.814606 + 0.580014i
\(57\) 131.184i 0.304837i
\(58\) −67.8698 + 336.385i −0.153651 + 0.761544i
\(59\) 285.231 + 285.231i 0.629389 + 0.629389i 0.947914 0.318525i \(-0.103188\pi\)
−0.318525 + 0.947914i \(0.603188\pi\)
\(60\) 144.767 + 60.8961i 0.311490 + 0.131027i
\(61\) −313.070 313.070i −0.657124 0.657124i 0.297575 0.954699i \(-0.403822\pi\)
−0.954699 + 0.297575i \(0.903822\pi\)
\(62\) −563.267 + 374.135i −1.15379 + 0.766373i
\(63\) −243.712 254.413i −0.487378 0.508778i
\(64\) −476.183 + 188.132i −0.930045 + 0.367446i
\(65\) −29.9800 −0.0572086
\(66\) −518.760 781.003i −0.967500 1.45659i
\(67\) −58.2711 58.2711i −0.106253 0.106253i 0.651982 0.758235i \(-0.273938\pi\)
−0.758235 + 0.651982i \(0.773938\pi\)
\(68\) 985.979 + 414.750i 1.75835 + 0.739644i
\(69\) −622.523 + 622.523i −1.08613 + 1.08613i
\(70\) 81.1407 + 128.043i 0.138545 + 0.218629i
\(71\) −374.109 −0.625331 −0.312666 0.949863i \(-0.601222\pi\)
−0.312666 + 0.949863i \(0.601222\pi\)
\(72\) 422.844 80.5018i 0.692120 0.131767i
\(73\) 610.003 0.978020 0.489010 0.872278i \(-0.337358\pi\)
0.489010 + 0.872278i \(0.337358\pi\)
\(74\) 199.176 + 40.1862i 0.312889 + 0.0631291i
\(75\) −559.457 559.457i −0.861340 0.861340i
\(76\) 58.4162 + 143.244i 0.0881683 + 0.216200i
\(77\) 19.4359 904.751i 0.0287652 1.33904i
\(78\) −165.589 + 109.988i −0.240375 + 0.159662i
\(79\) 460.899i 0.656395i 0.944609 + 0.328198i \(0.106441\pi\)
−0.944609 + 0.328198i \(0.893559\pi\)
\(80\) −185.193 2.02957i −0.258816 0.00283641i
\(81\) 880.748 1.20816
\(82\) −278.664 + 185.095i −0.375284 + 0.249272i
\(83\) 875.405 875.405i 1.15769 1.15769i 0.172717 0.984971i \(-0.444745\pi\)
0.984971 0.172717i \(-0.0552548\pi\)
\(84\) 917.917 + 409.539i 1.19230 + 0.531957i
\(85\) 273.598 + 273.598i 0.349128 + 0.349128i
\(86\) 59.7088 295.937i 0.0748670 0.371066i
\(87\) 823.082i 1.01430i
\(88\) 914.233 + 621.800i 1.10747 + 0.753229i
\(89\) −633.231 −0.754184 −0.377092 0.926176i \(-0.623076\pi\)
−0.377092 + 0.926176i \(0.623076\pi\)
\(90\) 152.626 + 30.7941i 0.178758 + 0.0360665i
\(91\) −191.826 4.12080i −0.220976 0.00474700i
\(92\) 402.545 956.964i 0.456176 1.08446i
\(93\) −1146.84 + 1146.84i −1.27873 + 1.27873i
\(94\) −398.272 + 264.542i −0.437007 + 0.290270i
\(95\) 55.9584i 0.0604338i
\(96\) −1030.33 + 668.211i −1.09539 + 0.710406i
\(97\) 946.138i 0.990368i 0.868788 + 0.495184i \(0.164899\pi\)
−0.868788 + 0.495184i \(0.835101\pi\)
\(98\) 501.575 + 830.430i 0.517008 + 0.855981i
\(99\) −657.269 657.269i −0.667253 0.667253i
\(100\) 860.016 + 361.764i 0.860016 + 0.361764i
\(101\) 141.100 141.100i 0.139010 0.139010i −0.634178 0.773187i \(-0.718661\pi\)
0.773187 + 0.634178i \(0.218661\pi\)
\(102\) 2514.91 + 507.414i 2.44131 + 0.492564i
\(103\) 891.445i 0.852784i −0.904539 0.426392i \(-0.859784\pi\)
0.904539 0.426392i \(-0.140216\pi\)
\(104\) 131.834 193.836i 0.124302 0.182762i
\(105\) 251.512 + 262.556i 0.233763 + 0.244027i
\(106\) −1890.95 381.522i −1.73269 0.349591i
\(107\) −727.560 + 727.560i −0.657345 + 0.657345i −0.954751 0.297406i \(-0.903878\pi\)
0.297406 + 0.954751i \(0.403878\pi\)
\(108\) −400.882 + 163.483i −0.357175 + 0.145659i
\(109\) −1136.70 + 1136.70i −0.998867 + 0.998867i −0.999999 0.00113245i \(-0.999640\pi\)
0.00113245 + 0.999999i \(0.499640\pi\)
\(110\) 221.285 + 333.149i 0.191806 + 0.288768i
\(111\) 487.353 0.416735
\(112\) −1184.67 38.4413i −0.999474 0.0324318i
\(113\) −556.606 −0.463373 −0.231686 0.972791i \(-0.574424\pi\)
−0.231686 + 0.972791i \(0.574424\pi\)
\(114\) 205.295 + 309.075i 0.168663 + 0.253926i
\(115\) 265.546 265.546i 0.215325 0.215325i
\(116\) −366.519 898.752i −0.293366 0.719371i
\(117\) −139.355 + 139.355i −0.110114 + 0.110114i
\(118\) −1118.39 225.648i −0.872509 0.176039i
\(119\) 1713.00 + 1788.21i 1.31958 + 1.37752i
\(120\) −436.378 + 83.0784i −0.331964 + 0.0631999i
\(121\) 1056.61i 0.793849i
\(122\) 1227.55 + 247.672i 0.910957 + 0.183796i
\(123\) −567.373 + 567.373i −0.415921 + 0.415921i
\(124\) 741.584 1762.96i 0.537066 1.27676i
\(125\) 494.425 + 494.425i 0.353781 + 0.353781i
\(126\) 972.338 + 218.014i 0.687482 + 0.154144i
\(127\) 1588.68i 1.11002i −0.831843 0.555011i \(-0.812714\pi\)
0.831843 0.555011i \(-0.187286\pi\)
\(128\) 827.494 1188.45i 0.571413 0.820663i
\(129\) 724.111i 0.494220i
\(130\) 70.6343 46.9169i 0.0476541 0.0316530i
\(131\) 1500.21 1500.21i 1.00057 1.00057i 0.000565274 1.00000i \(-0.499820\pi\)
1.00000 0.000565274i \(-0.000179932\pi\)
\(132\) 2444.45 + 1028.25i 1.61183 + 0.678014i
\(133\) −7.69157 + 358.047i −0.00501461 + 0.233433i
\(134\) 228.480 + 46.0986i 0.147296 + 0.0297188i
\(135\) −156.605 −0.0998399
\(136\) −2972.07 + 565.829i −1.87392 + 0.356760i
\(137\) 2259.10i 1.40882i −0.709795 0.704408i \(-0.751212\pi\)
0.709795 0.704408i \(-0.248788\pi\)
\(138\) 492.482 2440.91i 0.303789 1.50568i
\(139\) −2145.82 2145.82i −1.30940 1.30940i −0.921850 0.387547i \(-0.873323\pi\)
−0.387547 0.921850i \(-0.626677\pi\)
\(140\) −391.551 174.695i −0.236372 0.105460i
\(141\) −810.901 + 810.901i −0.484328 + 0.484328i
\(142\) 881.418 585.458i 0.520894 0.345990i
\(143\) −506.223 −0.296031
\(144\) −870.259 + 851.392i −0.503622 + 0.492703i
\(145\) 351.098i 0.201083i
\(146\) −1437.20 + 954.618i −0.814679 + 0.541129i
\(147\) 1573.20 + 1714.52i 0.882690 + 0.961982i
\(148\) −532.158 + 217.019i −0.295561 + 0.120533i
\(149\) −1085.99 1085.99i −0.597100 0.597100i 0.342440 0.939540i \(-0.388747\pi\)
−0.939540 + 0.342440i \(0.888747\pi\)
\(150\) 2193.62 + 442.590i 1.19406 + 0.240915i
\(151\) 257.765 0.138918 0.0694590 0.997585i \(-0.477873\pi\)
0.0694590 + 0.997585i \(0.477873\pi\)
\(152\) −361.800 246.072i −0.193065 0.131310i
\(153\) 2543.50 1.34399
\(154\) 1370.09 + 2162.05i 0.716915 + 1.13132i
\(155\) 489.200 489.200i 0.253507 0.253507i
\(156\) 218.010 518.273i 0.111890 0.265994i
\(157\) −1532.56 1532.56i −0.779053 0.779053i 0.200617 0.979670i \(-0.435705\pi\)
−0.979670 + 0.200617i \(0.935705\pi\)
\(158\) −721.280 1085.90i −0.363177 0.546770i
\(159\) −4626.86 −2.30776
\(160\) 439.501 285.035i 0.217160 0.140838i
\(161\) 1735.59 1662.59i 0.849586 0.813852i
\(162\) −2075.08 + 1378.32i −1.00638 + 0.668462i
\(163\) −177.457 177.457i −0.0852729 0.0852729i 0.663184 0.748457i \(-0.269205\pi\)
−0.748457 + 0.663184i \(0.769205\pi\)
\(164\) 366.883 872.186i 0.174687 0.415282i
\(165\) 678.306 + 678.306i 0.320037 + 0.320037i
\(166\) −692.539 + 3432.45i −0.323804 + 1.60488i
\(167\) 1722.29i 0.798054i 0.916939 + 0.399027i \(0.130652\pi\)
−0.916939 + 0.399027i \(0.869348\pi\)
\(168\) −2803.56 + 471.592i −1.28750 + 0.216572i
\(169\) 2089.67i 0.951147i
\(170\) −1072.77 216.445i −0.483988 0.0976504i
\(171\) 260.108 + 260.108i 0.116322 + 0.116322i
\(172\) 322.447 + 790.682i 0.142944 + 0.350517i
\(173\) 1795.20 + 1795.20i 0.788939 + 0.788939i 0.981320 0.192381i \(-0.0616210\pi\)
−0.192381 + 0.981320i \(0.561621\pi\)
\(174\) −1288.08 1939.22i −0.561200 0.844896i
\(175\) 1494.15 + 1559.76i 0.645414 + 0.673752i
\(176\) −3127.06 34.2700i −1.33927 0.0146773i
\(177\) −2736.52 −1.16209
\(178\) 1491.92 990.969i 0.628226 0.417282i
\(179\) −953.910 953.910i −0.398316 0.398316i 0.479323 0.877639i \(-0.340882\pi\)
−0.877639 + 0.479323i \(0.840882\pi\)
\(180\) −407.785 + 166.298i −0.168858 + 0.0688619i
\(181\) −1780.34 + 1780.34i −0.731114 + 0.731114i −0.970840 0.239727i \(-0.922942\pi\)
0.239727 + 0.970840i \(0.422942\pi\)
\(182\) 458.399 290.487i 0.186697 0.118310i
\(183\) 3003.61 1.21330
\(184\) 549.178 + 2884.61i 0.220032 + 1.15574i
\(185\) −207.888 −0.0826173
\(186\) 907.271 4496.74i 0.357658 1.77267i
\(187\) 4619.79 + 4619.79i 1.80659 + 1.80659i
\(188\) 524.356 1246.55i 0.203418 0.483583i
\(189\) −1002.03 21.5256i −0.385645 0.00828442i
\(190\) −87.5715 131.841i −0.0334374 0.0503406i
\(191\) 2064.00i 0.781916i 0.920409 + 0.390958i \(0.127856\pi\)
−0.920409 + 0.390958i \(0.872144\pi\)
\(192\) 1381.79 3186.74i 0.519385 1.19783i
\(193\) 1142.67 0.426172 0.213086 0.977033i \(-0.431649\pi\)
0.213086 + 0.977033i \(0.431649\pi\)
\(194\) −1480.65 2229.15i −0.547961 0.824965i
\(195\) 143.815 143.815i 0.0528143 0.0528143i
\(196\) −2481.31 1171.60i −0.904267 0.426967i
\(197\) 837.511 + 837.511i 0.302894 + 0.302894i 0.842145 0.539251i \(-0.181292\pi\)
−0.539251 + 0.842145i \(0.681292\pi\)
\(198\) 2577.14 + 519.970i 0.924998 + 0.186630i
\(199\) 2165.33i 0.771338i 0.922637 + 0.385669i \(0.126029\pi\)
−0.922637 + 0.385669i \(0.873971\pi\)
\(200\) −2592.38 + 493.542i −0.916544 + 0.174493i
\(201\) 559.056 0.196183
\(202\) −111.625 + 553.251i −0.0388808 + 0.192706i
\(203\) 48.2590 2246.48i 0.0166853 0.776710i
\(204\) −6719.33 + 2740.20i −2.30611 + 0.940453i
\(205\) 242.021 242.021i 0.0824561 0.0824561i
\(206\) 1395.06 + 2100.29i 0.471837 + 0.710359i
\(207\) 2468.65i 0.828904i
\(208\) −7.26595 + 663.000i −0.00242213 + 0.221013i
\(209\) 944.877i 0.312720i
\(210\) −1003.46 224.991i −0.329739 0.0739328i
\(211\) 130.423 + 130.423i 0.0425531 + 0.0425531i 0.728063 0.685510i \(-0.240421\pi\)
−0.685510 + 0.728063i \(0.740421\pi\)
\(212\) 5052.23 2060.34i 1.63674 0.667476i
\(213\) 1794.61 1794.61i 0.577298 0.577298i
\(214\) 575.578 2852.76i 0.183858 0.911263i
\(215\) 308.880i 0.0979789i
\(216\) 688.656 1012.53i 0.216931 0.318954i
\(217\) 3197.37 3062.89i 1.00024 0.958167i
\(218\) 899.254 4457.00i 0.279381 1.38471i
\(219\) −2926.20 + 2926.20i −0.902896 + 0.902896i
\(220\) −1042.72 438.616i −0.319545 0.134416i
\(221\) 979.491 979.491i 0.298134 0.298134i
\(222\) −1148.23 + 762.679i −0.347135 + 0.230575i
\(223\) 1221.92 0.366933 0.183466 0.983026i \(-0.441268\pi\)
0.183466 + 0.983026i \(0.441268\pi\)
\(224\) 2851.30 1763.37i 0.850495 0.525984i
\(225\) 2218.56 0.657351
\(226\) 1311.39 871.056i 0.385984 0.256380i
\(227\) −3515.16 + 3515.16i −1.02780 + 1.02780i −0.0281934 + 0.999602i \(0.508975\pi\)
−0.999602 + 0.0281934i \(0.991025\pi\)
\(228\) −967.369 406.922i −0.280989 0.118198i
\(229\) 3345.39 3345.39i 0.965369 0.965369i −0.0340515 0.999420i \(-0.510841\pi\)
0.999420 + 0.0340515i \(0.0108410\pi\)
\(230\) −210.075 + 1041.20i −0.0602259 + 0.298500i
\(231\) 4246.88 + 4433.34i 1.20963 + 1.26274i
\(232\) 2270.03 + 1543.92i 0.642391 + 0.436911i
\(233\) 537.847i 0.151225i −0.997137 0.0756127i \(-0.975909\pi\)
0.997137 0.0756127i \(-0.0240913\pi\)
\(234\) 110.244 546.408i 0.0307987 0.152649i
\(235\) 345.902 345.902i 0.0960177 0.0960177i
\(236\) 2988.10 1218.57i 0.824191 0.336112i
\(237\) −2210.95 2210.95i −0.605976 0.605976i
\(238\) −6834.34 1532.37i −1.86136 0.417347i
\(239\) 6403.30i 1.73303i 0.499149 + 0.866516i \(0.333646\pi\)
−0.499149 + 0.866516i \(0.666354\pi\)
\(240\) 898.113 878.642i 0.241554 0.236317i
\(241\) 1648.67i 0.440664i −0.975425 0.220332i \(-0.929286\pi\)
0.975425 0.220332i \(-0.0707140\pi\)
\(242\) 1653.54 + 2489.43i 0.439229 + 0.661268i
\(243\) −3191.77 + 3191.77i −0.842603 + 0.842603i
\(244\) −3279.75 + 1337.51i −0.860509 + 0.350923i
\(245\) −671.072 731.354i −0.174993 0.190712i
\(246\) 448.853 2224.66i 0.116333 0.576583i
\(247\) 200.333 0.0516069
\(248\) 1011.72 + 5314.15i 0.259049 + 1.36068i
\(249\) 8398.68i 2.13753i
\(250\) −1938.63 391.143i −0.490440 0.0989521i
\(251\) −3775.90 3775.90i −0.949534 0.949534i 0.0492528 0.998786i \(-0.484316\pi\)
−0.998786 + 0.0492528i \(0.984316\pi\)
\(252\) −2632.05 + 1008.00i −0.657951 + 0.251977i
\(253\) 4483.84 4483.84i 1.11422 1.11422i
\(254\) 2486.20 + 3743.01i 0.614165 + 0.924636i
\(255\) −2624.91 −0.644620
\(256\) −89.7669 + 4095.02i −0.0219157 + 0.999760i
\(257\) 6959.86i 1.68928i 0.535337 + 0.844638i \(0.320185\pi\)
−0.535337 + 0.844638i \(0.679815\pi\)
\(258\) 1133.19 + 1706.04i 0.273447 + 0.411680i
\(259\) −1330.16 28.5745i −0.319120 0.00685534i
\(260\) −92.9956 + 221.077i −0.0221821 + 0.0527331i
\(261\) −1631.99 1631.99i −0.387041 0.387041i
\(262\) −1186.83 + 5882.31i −0.279856 + 1.38706i
\(263\) −4461.40 −1.04602 −0.523008 0.852328i \(-0.675190\pi\)
−0.523008 + 0.852328i \(0.675190\pi\)
\(264\) −7368.39 + 1402.81i −1.71778 + 0.327034i
\(265\) 1973.66 0.457512
\(266\) −542.201 855.613i −0.124979 0.197222i
\(267\) 3037.62 3037.62i 0.696253 0.696253i
\(268\) −610.452 + 248.948i −0.139139 + 0.0567421i
\(269\) −2252.15 2252.15i −0.510469 0.510469i 0.404201 0.914670i \(-0.367550\pi\)
−0.914670 + 0.404201i \(0.867550\pi\)
\(270\) 368.968 245.077i 0.0831655 0.0552405i
\(271\) 6670.05 1.49512 0.747559 0.664196i \(-0.231226\pi\)
0.747559 + 0.664196i \(0.231226\pi\)
\(272\) 6116.85 5984.24i 1.36356 1.33400i
\(273\) 939.960 900.425i 0.208384 0.199620i
\(274\) 3535.36 + 5322.55i 0.779485 + 1.17353i
\(275\) 4029.60 + 4029.60i 0.883614 + 0.883614i
\(276\) 2659.56 + 6521.59i 0.580025 + 1.42230i
\(277\) −1517.50 1517.50i −0.329161 0.329161i 0.523106 0.852267i \(-0.324773\pi\)
−0.852267 + 0.523106i \(0.824773\pi\)
\(278\) 8413.74 + 1697.57i 1.81519 + 0.366236i
\(279\) 4547.85i 0.975888i
\(280\) 1195.90 201.165i 0.255245 0.0429353i
\(281\) 559.278i 0.118732i −0.998236 0.0593661i \(-0.981092\pi\)
0.998236 0.0593661i \(-0.0189079\pi\)
\(282\) 641.509 3179.53i 0.135466 0.671413i
\(283\) 25.8379 + 25.8379i 0.00542721 + 0.00542721i 0.709815 0.704388i \(-0.248778\pi\)
−0.704388 + 0.709815i \(0.748778\pi\)
\(284\) −1160.45 + 2758.73i −0.242466 + 0.576411i
\(285\) −268.434 268.434i −0.0557917 0.0557917i
\(286\) 1192.69 792.209i 0.246591 0.163791i
\(287\) 1581.83 1515.30i 0.325339 0.311655i
\(288\) 717.995 3367.82i 0.146904 0.689066i
\(289\) −12964.7 −2.63885
\(290\) 549.447 + 827.203i 0.111257 + 0.167500i
\(291\) −4538.65 4538.65i −0.914296 0.914296i
\(292\) 1892.18 4498.25i 0.379217 0.901508i
\(293\) −3862.53 + 3862.53i −0.770142 + 0.770142i −0.978131 0.207989i \(-0.933308\pi\)
0.207989 + 0.978131i \(0.433308\pi\)
\(294\) −6389.66 1577.52i −1.26753 0.312936i
\(295\) 1167.30 0.230383
\(296\) 914.168 1344.10i 0.179510 0.263933i
\(297\) −2644.33 −0.516631
\(298\) 4258.16 + 859.135i 0.827747 + 0.167008i
\(299\) −950.667 950.667i −0.183875 0.183875i
\(300\) −5860.91 + 2390.13i −1.12793 + 0.459980i
\(301\) −42.4561 + 1976.36i −0.00812999 + 0.378456i
\(302\) −607.307 + 403.387i −0.115717 + 0.0768620i
\(303\) 1353.72i 0.256664i
\(304\) 1237.51 + 13.5621i 0.233473 + 0.00255868i
\(305\) −1281.23 −0.240535
\(306\) −5992.61 + 3980.43i −1.11952 + 0.743614i
\(307\) 2044.42 2044.42i 0.380069 0.380069i −0.491058 0.871127i \(-0.663390\pi\)
0.871127 + 0.491058i \(0.163390\pi\)
\(308\) −6611.48 2949.79i −1.22313 0.545713i
\(309\) 4276.28 + 4276.28i 0.787279 + 0.787279i
\(310\) −387.010 + 1918.15i −0.0709054 + 0.351431i
\(311\) 9371.35i 1.70868i −0.519711 0.854342i \(-0.673960\pi\)
0.519711 0.854342i \(-0.326040\pi\)
\(312\) 297.424 + 1562.25i 0.0539690 + 0.283477i
\(313\) −8978.95 −1.62147 −0.810735 0.585413i \(-0.800932\pi\)
−0.810735 + 0.585413i \(0.800932\pi\)
\(314\) 6009.14 + 1212.42i 1.07998 + 0.217900i
\(315\) −1019.28 21.8962i −0.182318 0.00391655i
\(316\) 3398.74 + 1429.67i 0.605045 + 0.254511i
\(317\) −1767.75 + 1767.75i −0.313207 + 0.313207i −0.846151 0.532944i \(-0.821086\pi\)
0.532944 + 0.846151i \(0.321086\pi\)
\(318\) 10901.1 7240.76i 1.92234 1.27686i
\(319\) 5928.41i 1.04052i
\(320\) −589.422 + 1359.35i −0.102968 + 0.237469i
\(321\) 6980.25i 1.21371i
\(322\) −1487.27 + 6633.22i −0.257399 + 1.14800i
\(323\) −1828.24 1828.24i −0.314942 0.314942i
\(324\) 2732.01 6494.77i 0.468451 1.11364i
\(325\) 854.357 854.357i 0.145819 0.145819i
\(326\) 695.806 + 140.387i 0.118212 + 0.0238507i
\(327\) 10905.6i 1.84428i
\(328\) 500.525 + 2629.06i 0.0842588 + 0.442578i
\(329\) 2260.78 2165.69i 0.378848 0.362913i
\(330\) −2659.63 536.612i −0.443660 0.0895138i
\(331\) 4730.32 4730.32i 0.785504 0.785504i −0.195250 0.980754i \(-0.562552\pi\)
0.980754 + 0.195250i \(0.0625518\pi\)
\(332\) −3739.93 9170.80i −0.618239 1.51600i
\(333\) −966.314 + 966.314i −0.159020 + 0.159020i
\(334\) −2695.29 4057.80i −0.441555 0.664770i
\(335\) −238.473 −0.0388931
\(336\) 5867.31 5498.50i 0.952643 0.892761i
\(337\) 1717.91 0.277688 0.138844 0.990314i \(-0.455661\pi\)
0.138844 + 0.990314i \(0.455661\pi\)
\(338\) 3270.21 + 4923.36i 0.526260 + 0.792295i
\(339\) 2670.05 2670.05i 0.427780 0.427780i
\(340\) 2866.23 1168.87i 0.457186 0.186444i
\(341\) 8260.32 8260.32i 1.31179 1.31179i
\(342\) −1019.88 205.773i −0.161254 0.0325350i
\(343\) −4193.30 4771.78i −0.660108 0.751171i
\(344\) −1997.07 1358.27i −0.313008 0.212887i
\(345\) 2547.66i 0.397570i
\(346\) −7038.96 1420.19i −1.09369 0.220665i
\(347\) −7793.80 + 7793.80i −1.20574 + 1.20574i −0.233352 + 0.972392i \(0.574969\pi\)
−0.972392 + 0.233352i \(0.925031\pi\)
\(348\) 6069.53 + 2553.13i 0.934946 + 0.393283i
\(349\) 4211.57 + 4211.57i 0.645960 + 0.645960i 0.952014 0.306054i \(-0.0990088\pi\)
−0.306054 + 0.952014i \(0.599009\pi\)
\(350\) −5961.23 1336.60i −0.910403 0.204127i
\(351\) 560.652i 0.0852574i
\(352\) 7421.13 4812.92i 1.12371 0.728777i
\(353\) 7172.87i 1.08151i 0.841180 + 0.540755i \(0.181862\pi\)
−0.841180 + 0.540755i \(0.818138\pi\)
\(354\) 6447.38 4282.50i 0.968007 0.642972i
\(355\) −765.516 + 765.516i −0.114449 + 0.114449i
\(356\) −1964.23 + 4669.54i −0.292427 + 0.695183i
\(357\) −16795.4 360.798i −2.48993 0.0534887i
\(358\) 3740.27 + 754.644i 0.552177 + 0.111408i
\(359\) −12810.1 −1.88326 −0.941630 0.336650i \(-0.890706\pi\)
−0.941630 + 0.336650i \(0.890706\pi\)
\(360\) 700.514 1029.97i 0.102557 0.150789i
\(361\) 6485.07i 0.945484i
\(362\) 1408.44 6980.69i 0.204491 1.01353i
\(363\) 5068.60 + 5068.60i 0.732872 + 0.732872i
\(364\) −625.415 + 1401.77i −0.0900568 + 0.201848i
\(365\) 1248.21 1248.21i 0.178998 0.178998i
\(366\) −7076.65 + 4700.48i −1.01066 + 0.671305i
\(367\) 5502.08 0.782578 0.391289 0.920268i \(-0.372029\pi\)
0.391289 + 0.920268i \(0.372029\pi\)
\(368\) −5808.13 5936.85i −0.822744 0.840977i
\(369\) 2249.95i 0.317419i
\(370\) 489.793 325.332i 0.0688193 0.0457114i
\(371\) 12628.3 + 271.282i 1.76720 + 0.0379630i
\(372\) 4899.55 + 12014.4i 0.682877 + 1.67450i
\(373\) −5026.12 5026.12i −0.697702 0.697702i 0.266213 0.963914i \(-0.414228\pi\)
−0.963914 + 0.266213i \(0.914228\pi\)
\(374\) −18114.2 3654.75i −2.50444 0.505301i
\(375\) −4743.53 −0.653213
\(376\) 715.361 + 3757.51i 0.0981169 + 0.515369i
\(377\) −1256.94 −0.171713
\(378\) 2394.51 1517.40i 0.325821 0.206473i
\(379\) 6001.11 6001.11i 0.813342 0.813342i −0.171792 0.985133i \(-0.554956\pi\)
0.985133 + 0.171792i \(0.0549556\pi\)
\(380\) 412.645 + 173.578i 0.0557060 + 0.0234326i
\(381\) 7620.96 + 7620.96i 1.02476 + 1.02476i
\(382\) −3230.04 4862.88i −0.432626 0.651327i
\(383\) −12452.4 −1.66133 −0.830665 0.556773i \(-0.812039\pi\)
−0.830665 + 0.556773i \(0.812039\pi\)
\(384\) 1731.50 + 9670.52i 0.230104 + 1.28515i
\(385\) −1811.57 1891.11i −0.239808 0.250337i
\(386\) −2692.19 + 1788.21i −0.354997 + 0.235797i
\(387\) 1435.75 + 1435.75i 0.188588 + 0.188588i
\(388\) 6976.96 + 2934.84i 0.912891 + 0.384005i
\(389\) 7568.58 + 7568.58i 0.986483 + 0.986483i 0.999910 0.0134265i \(-0.00427393\pi\)
−0.0134265 + 0.999910i \(0.504274\pi\)
\(390\) −113.773 + 563.896i −0.0147721 + 0.0732154i
\(391\) 17351.6i 2.24426i
\(392\) 7679.56 1122.76i 0.989481 0.144664i
\(393\) 14393.1i 1.84742i
\(394\) −3283.87 662.561i −0.419896 0.0847191i
\(395\) 943.111 + 943.111i 0.120134 + 0.120134i
\(396\) −6885.60 + 2808.01i −0.873773 + 0.356332i
\(397\) −746.476 746.476i −0.0943692 0.0943692i 0.658346 0.752715i \(-0.271256\pi\)
−0.752715 + 0.658346i \(0.771256\pi\)
\(398\) −3388.62 5101.62i −0.426774 0.642516i
\(399\) −1680.66 1754.46i −0.210873 0.220132i
\(400\) 5335.40 5219.73i 0.666925 0.652466i
\(401\) 8402.79 1.04642 0.523211 0.852203i \(-0.324734\pi\)
0.523211 + 0.852203i \(0.324734\pi\)
\(402\) −1317.16 + 874.889i −0.163418 + 0.108546i
\(403\) −1751.36 1751.36i −0.216480 0.216480i
\(404\) −602.811 1478.17i −0.0742351 0.182034i
\(405\) 1802.22 1802.22i 0.221119 0.221119i
\(406\) 3401.91 + 5368.34i 0.415848 + 0.656223i
\(407\) −3510.26 −0.427511
\(408\) 11542.8 16971.4i 1.40062 2.05934i
\(409\) −8430.15 −1.01918 −0.509589 0.860418i \(-0.670203\pi\)
−0.509589 + 0.860418i \(0.670203\pi\)
\(410\) −191.465 + 948.963i −0.0230628 + 0.114307i
\(411\) 10837.0 + 10837.0i 1.30060 + 1.30060i
\(412\) −6573.65 2765.19i −0.786069 0.330658i
\(413\) 7468.95 + 160.448i 0.889886 + 0.0191165i
\(414\) 3863.29 + 5816.26i 0.458624 + 0.690468i
\(415\) 3582.58i 0.423764i
\(416\) −1020.44 1573.43i −0.120267 0.185442i
\(417\) 20587.1 2.41764
\(418\) −1478.68 2226.18i −0.173025 0.260492i
\(419\) −8672.14 + 8672.14i −1.01113 + 1.01113i −0.0111887 + 0.999937i \(0.503562\pi\)
−0.999937 + 0.0111887i \(0.996438\pi\)
\(420\) 2716.30 1040.26i 0.315575 0.120856i
\(421\) 10398.8 + 10398.8i 1.20382 + 1.20382i 0.972997 + 0.230818i \(0.0741403\pi\)
0.230818 + 0.972997i \(0.425860\pi\)
\(422\) −511.387 103.179i −0.0589904 0.0119020i
\(423\) 3215.68i 0.369625i
\(424\) −8678.97 + 12760.7i −0.994076 + 1.46159i
\(425\) −15593.7 −1.77978
\(426\) −1419.73 + 7036.64i −0.161469 + 0.800296i
\(427\) −8197.92 176.108i −0.929099 0.0199589i
\(428\) 3108.31 + 7621.97i 0.351041 + 0.860799i
\(429\) 2428.36 2428.36i 0.273293 0.273293i
\(430\) −483.379 727.736i −0.0542107 0.0816153i
\(431\) 12243.6i 1.36834i −0.729322 0.684170i \(-0.760165\pi\)
0.729322 0.684170i \(-0.239835\pi\)
\(432\) −37.9547 + 3463.28i −0.00422707 + 0.385710i
\(433\) 8787.77i 0.975320i −0.873034 0.487660i \(-0.837851\pi\)
0.873034 0.487660i \(-0.162149\pi\)
\(434\) −2739.92 + 12220.0i −0.303042 + 1.35156i
\(435\) 1684.22 + 1684.22i 0.185638 + 0.185638i
\(436\) 4856.26 + 11908.2i 0.533424 + 1.30802i
\(437\) −1774.44 + 1774.44i −0.194240 + 0.194240i
\(438\) 2314.93 11473.6i 0.252538 1.25167i
\(439\) 6163.76i 0.670115i −0.942198 0.335057i \(-0.891244\pi\)
0.942198 0.335057i \(-0.108756\pi\)
\(440\) 3143.10 598.388i 0.340548 0.0648342i
\(441\) −6518.83 280.204i −0.703901 0.0302564i
\(442\) −774.882 + 3840.57i −0.0833877 + 0.413297i
\(443\) 705.371 705.371i 0.0756505 0.0756505i −0.668269 0.743920i \(-0.732965\pi\)
0.743920 + 0.668269i \(0.232965\pi\)
\(444\) 1511.73 3593.82i 0.161585 0.384133i
\(445\) −1295.74 + 1295.74i −0.138032 + 0.138032i
\(446\) −2878.91 + 1912.24i −0.305651 + 0.203020i
\(447\) 10419.1 1.10247
\(448\) −3958.23 + 8616.72i −0.417431 + 0.908709i
\(449\) 1808.14 0.190048 0.0950240 0.995475i \(-0.469707\pi\)
0.0950240 + 0.995475i \(0.469707\pi\)
\(450\) −5227.03 + 3471.91i −0.547566 + 0.363706i
\(451\) 4086.62 4086.62i 0.426677 0.426677i
\(452\) −1726.55 + 4104.50i −0.179668 + 0.427123i
\(453\) −1236.51 + 1236.51i −0.128247 + 0.128247i
\(454\) 2780.87 13782.9i 0.287473 1.42481i
\(455\) −400.954 + 384.089i −0.0413121 + 0.0395745i
\(456\) 2915.98 555.149i 0.299458 0.0570115i
\(457\) 13173.0i 1.34838i −0.738560 0.674188i \(-0.764494\pi\)
0.738560 0.674188i \(-0.235506\pi\)
\(458\) −2646.56 + 13117.2i −0.270012 + 1.33827i
\(459\) 5116.51 5116.51i 0.520301 0.520301i
\(460\) −1134.48 2781.88i −0.114990 0.281969i
\(461\) −2780.05 2780.05i −0.280867 0.280867i 0.552588 0.833455i \(-0.313640\pi\)
−0.833455 + 0.552588i \(0.813640\pi\)
\(462\) −16943.8 3799.06i −1.70627 0.382572i
\(463\) 3630.01i 0.364365i −0.983265 0.182182i \(-0.941684\pi\)
0.983265 0.182182i \(-0.0583161\pi\)
\(464\) −7764.44 85.0920i −0.776843 0.00851357i
\(465\) 4693.41i 0.468068i
\(466\) 841.699 + 1267.19i 0.0836716 + 0.125969i
\(467\) −39.0209 + 39.0209i −0.00386654 + 0.00386654i −0.709037 0.705171i \(-0.750870\pi\)
0.705171 + 0.709037i \(0.250870\pi\)
\(468\) 595.355 + 1459.89i 0.0588040 + 0.144195i
\(469\) −1525.86 32.7786i −0.150230 0.00322723i
\(470\) −273.645 + 1356.28i −0.0268560 + 0.133107i
\(471\) 14703.4 1.43842
\(472\) −5133.12 + 7547.23i −0.500574 + 0.735994i
\(473\) 5215.55i 0.507001i
\(474\) 8669.09 + 1749.09i 0.840052 + 0.169491i
\(475\) −1594.68 1594.68i −0.154040 0.154040i
\(476\) 18500.1 7085.01i 1.78141 0.682229i
\(477\) 9174.04 9174.04i 0.880609 0.880609i
\(478\) −10020.8 15086.5i −0.958870 1.44360i
\(479\) −1088.16 −0.103798 −0.0518990 0.998652i \(-0.516527\pi\)
−0.0518990 + 0.998652i \(0.516527\pi\)
\(480\) −740.976 + 3475.62i −0.0704599 + 0.330499i
\(481\) 744.247i 0.0705504i
\(482\) 2580.06 + 3884.34i 0.243815 + 0.367068i
\(483\) −350.181 + 16301.1i −0.0329892 + 1.53567i
\(484\) −7791.63 3277.53i −0.731746 0.307807i
\(485\) 1936.03 + 1936.03i 0.181259 + 0.181259i
\(486\) 2525.03 12514.9i 0.235675 1.16808i
\(487\) −17740.1 −1.65068 −0.825339 0.564638i \(-0.809016\pi\)
−0.825339 + 0.564638i \(0.809016\pi\)
\(488\) 5634.12 8283.85i 0.522632 0.768426i
\(489\) 1702.53 0.157446
\(490\) 2725.60 + 672.916i 0.251286 + 0.0620393i
\(491\) 5821.10 5821.10i 0.535036 0.535036i −0.387031 0.922067i \(-0.626499\pi\)
0.922067 + 0.387031i \(0.126499\pi\)
\(492\) 2423.95 + 5943.84i 0.222114 + 0.544653i
\(493\) 11470.9 + 11470.9i 1.04792 + 1.04792i
\(494\) −471.995 + 313.510i −0.0429880 + 0.0285536i
\(495\) −2689.86 −0.244243
\(496\) −10700.0 10937.1i −0.968636 0.990102i
\(497\) −5003.34 + 4792.90i −0.451571 + 0.432577i
\(498\) −13143.4 19787.7i −1.18267 1.78054i
\(499\) 4283.85 + 4283.85i 0.384312 + 0.384312i 0.872653 0.488341i \(-0.162398\pi\)
−0.488341 + 0.872653i \(0.662398\pi\)
\(500\) 5179.63 2112.30i 0.463280 0.188930i
\(501\) −8261.88 8261.88i −0.736753 0.736753i
\(502\) 14805.3 + 2987.14i 1.31632 + 0.265583i
\(503\) 743.585i 0.0659142i −0.999457 0.0329571i \(-0.989508\pi\)
0.999457 0.0329571i \(-0.0104925\pi\)
\(504\) 4623.78 6493.91i 0.408650 0.573932i
\(505\) 577.449i 0.0508834i
\(506\) −3547.20 + 17581.1i −0.311645 + 1.54462i
\(507\) 10024.2 + 10024.2i 0.878087 + 0.878087i
\(508\) −11715.2 4927.97i −1.02318 0.430400i
\(509\) 6189.71 + 6189.71i 0.539006 + 0.539006i 0.923237 0.384231i \(-0.125533\pi\)
−0.384231 + 0.923237i \(0.625533\pi\)
\(510\) 6184.41 4107.83i 0.536961 0.356662i
\(511\) 8158.20 7815.06i 0.706258 0.676552i
\(512\) −6196.96 9788.53i −0.534902 0.844914i
\(513\) 1046.47 0.0900638
\(514\) −10891.8 16397.8i −0.934660 1.40715i
\(515\) −1824.11 1824.11i −0.156078 0.156078i
\(516\) −5339.70 2246.13i −0.455557 0.191629i
\(517\) 5840.68 5840.68i 0.496852 0.496852i
\(518\) 3178.64 2014.30i 0.269616 0.170856i
\(519\) −17223.2 −1.45668
\(520\) −126.871 666.401i −0.0106993 0.0561992i
\(521\) 11779.3 0.990521 0.495260 0.868745i \(-0.335073\pi\)
0.495260 + 0.868745i \(0.335073\pi\)
\(522\) 6399.01 + 1291.08i 0.536547 + 0.108255i
\(523\) −1261.69 1261.69i −0.105488 0.105488i 0.652393 0.757881i \(-0.273765\pi\)
−0.757881 + 0.652393i \(0.773765\pi\)
\(524\) −6409.25 15716.3i −0.534331 1.31025i
\(525\) −14649.7 314.705i −1.21784 0.0261616i
\(526\) 10511.3 6981.83i 0.871319 0.578750i
\(527\) 31965.8i 2.64222i
\(528\) 15165.0 14836.2i 1.24994 1.22284i
\(529\) 4673.97 0.384151
\(530\) −4650.03 + 3088.65i −0.381102 + 0.253137i
\(531\) 5425.92 5425.92i 0.443437 0.443437i
\(532\) 2616.43 + 1167.35i 0.213227 + 0.0951337i
\(533\) −866.447 866.447i −0.0704127 0.0704127i
\(534\) −2403.08 + 11910.5i −0.194741 + 0.965201i
\(535\) 2977.53i 0.240616i
\(536\) 1048.67 1541.85i 0.0845064 0.124250i
\(537\) 9151.86 0.735441
\(538\) 8830.67 + 1781.69i 0.707653 + 0.142777i
\(539\) −11331.3 12349.2i −0.905517 0.986858i
\(540\) −485.775 + 1154.83i −0.0387119 + 0.0920293i
\(541\) 3180.80 3180.80i 0.252778 0.252778i −0.569330 0.822109i \(-0.692797\pi\)
0.822109 + 0.569330i \(0.192797\pi\)
\(542\) −15715.0 + 10438.2i −1.24542 + 0.827234i
\(543\) 17080.7i 1.34991i
\(544\) −5046.62 + 23671.7i −0.397743 + 1.86565i
\(545\) 4651.94i 0.365628i
\(546\) −805.479 + 3592.43i −0.0631343 + 0.281578i
\(547\) −2706.48 2706.48i −0.211555 0.211555i 0.593373 0.804928i \(-0.297796\pi\)
−0.804928 + 0.593373i \(0.797796\pi\)
\(548\) −16658.9 7007.55i −1.29860 0.546255i
\(549\) −5955.50 + 5955.50i −0.462977 + 0.462977i
\(550\) −15800.0 3187.84i −1.22494 0.247145i
\(551\) 2346.12i 0.181394i
\(552\) −16472.0 11203.1i −1.27010 0.863835i
\(553\) 5904.82 + 6164.09i 0.454066 + 0.474003i
\(554\) 5950.09 + 1200.50i 0.456309 + 0.0920659i
\(555\) 997.242 997.242i 0.0762713 0.0762713i
\(556\) −22479.8 + 9167.44i −1.71467 + 0.699256i
\(557\) −1976.55 + 1976.55i −0.150358 + 0.150358i −0.778278 0.627920i \(-0.783906\pi\)
0.627920 + 0.778278i \(0.283906\pi\)
\(558\) 7117.12 + 10715.0i 0.539949 + 0.812903i
\(559\) 1105.80 0.0836682
\(560\) −2502.79 + 2345.47i −0.188861 + 0.176989i
\(561\) −44322.5 −3.33565
\(562\) 875.237 + 1317.69i 0.0656933 + 0.0989025i
\(563\) −1969.01 + 1969.01i −0.147396 + 0.147396i −0.776954 0.629558i \(-0.783236\pi\)
0.629558 + 0.776954i \(0.283236\pi\)
\(564\) 3464.36 + 8495.06i 0.258645 + 0.634231i
\(565\) −1138.95 + 1138.95i −0.0848071 + 0.0848071i
\(566\) −101.310 20.4405i −0.00752363 0.00151798i
\(567\) 11779.2 11283.7i 0.872448 0.835752i
\(568\) −1583.17 8315.75i −0.116951 0.614298i
\(569\) 12025.5i 0.886004i 0.896521 + 0.443002i \(0.146087\pi\)
−0.896521 + 0.443002i \(0.853913\pi\)
\(570\) 1052.53 + 212.360i 0.0773429 + 0.0156049i
\(571\) −3067.62 + 3067.62i −0.224826 + 0.224826i −0.810527 0.585701i \(-0.800819\pi\)
0.585701 + 0.810527i \(0.300819\pi\)
\(572\) −1570.26 + 3732.96i −0.114783 + 0.272873i
\(573\) −9901.06 9901.06i −0.721855 0.721855i
\(574\) −1355.51 + 6045.58i −0.0985681 + 0.439613i
\(575\) 15134.8i 1.09768i
\(576\) 3578.81 + 9058.37i 0.258884 + 0.655264i
\(577\) 4574.91i 0.330080i −0.986287 0.165040i \(-0.947225\pi\)
0.986287 0.165040i \(-0.0527753\pi\)
\(578\) 30545.4 20289.0i 2.19813 1.46005i
\(579\) −5481.42 + 5481.42i −0.393437 + 0.393437i
\(580\) −2589.05 1089.08i −0.185352 0.0779681i
\(581\) 492.431 22923.0i 0.0351626 1.63684i
\(582\) 17796.0 + 3590.55i 1.26747 + 0.255727i
\(583\) 33325.9 2.36744
\(584\) 2581.43 + 13559.2i 0.182912 + 0.960763i
\(585\) 570.306i 0.0403064i
\(586\) 3055.68 15145.0i 0.215408 1.06763i
\(587\) 1826.09 + 1826.09i 0.128400 + 0.128400i 0.768386 0.639986i \(-0.221060\pi\)
−0.639986 + 0.768386i \(0.721060\pi\)
\(588\) 17523.1 6282.72i 1.22898 0.440638i
\(589\) −3268.95 + 3268.95i −0.228684 + 0.228684i
\(590\) −2750.23 + 1826.76i −0.191907 + 0.127469i
\(591\) −8035.12 −0.559257
\(592\) −50.3836 + 4597.39i −0.00349789 + 0.319175i
\(593\) 5705.55i 0.395107i −0.980292 0.197554i \(-0.936700\pi\)
0.980292 0.197554i \(-0.0632997\pi\)
\(594\) 6230.16 4138.22i 0.430348 0.285847i
\(595\) 7164.31 + 153.904i 0.493627 + 0.0106041i
\(596\) −11376.9 + 4639.61i −0.781908 + 0.318869i
\(597\) −10387.1 10387.1i −0.712090 0.712090i
\(598\) 3727.55 + 752.079i 0.254901 + 0.0514294i
\(599\) 10497.7 0.716070 0.358035 0.933708i \(-0.383447\pi\)
0.358035 + 0.933708i \(0.383447\pi\)
\(600\) 10068.2 14803.2i 0.685052 1.00723i
\(601\) −9375.74 −0.636347 −0.318173 0.948033i \(-0.603069\pi\)
−0.318173 + 0.948033i \(0.603069\pi\)
\(602\) −2992.85 4722.83i −0.202624 0.319748i
\(603\) −1108.48 + 1108.48i −0.0748606 + 0.0748606i
\(604\) 799.566 1900.80i 0.0538641 0.128050i
\(605\) −2162.09 2162.09i −0.145291 0.145291i
\(606\) −2118.49 3189.43i −0.142010 0.213798i
\(607\) 5702.60 0.381320 0.190660 0.981656i \(-0.438937\pi\)
0.190660 + 0.981656i \(0.438937\pi\)
\(608\) −2936.85 + 1904.67i −0.195896 + 0.127047i
\(609\) 10544.9 + 11007.9i 0.701646 + 0.732453i
\(610\) 3018.65 2005.06i 0.200363 0.133086i
\(611\) −1238.34 1238.34i −0.0819934 0.0819934i
\(612\) 7889.73 18756.2i 0.521117 1.23884i
\(613\) 7424.25 + 7424.25i 0.489172 + 0.489172i 0.908045 0.418873i \(-0.137575\pi\)
−0.418873 + 0.908045i \(0.637575\pi\)
\(614\) −1617.35 + 8016.15i −0.106305 + 0.526882i
\(615\) 2321.96i 0.152245i
\(616\) 20193.2 3396.74i 1.32079 0.222173i
\(617\) 22808.8i 1.48825i −0.668043 0.744123i \(-0.732868\pi\)
0.668043 0.744123i \(-0.267132\pi\)
\(618\) −16767.3 3383.00i −1.09139 0.220201i
\(619\) −15749.6 15749.6i −1.02267 1.02267i −0.999737 0.0229291i \(-0.992701\pi\)
−0.0229291 0.999737i \(-0.507299\pi\)
\(620\) −2089.98 5124.90i −0.135380 0.331969i
\(621\) −4965.94 4965.94i −0.320896 0.320896i
\(622\) 14665.6 + 22079.4i 0.945398 + 1.42331i
\(623\) −8468.86 + 8112.65i −0.544619 + 0.521712i
\(624\) −3145.57 3215.28i −0.201801 0.206273i
\(625\) −12554.8 −0.803507
\(626\) 21154.8 14051.5i 1.35067 0.897144i
\(627\) −4532.60 4532.60i −0.288699 0.288699i
\(628\) −16055.2 + 6547.44i −1.02018 + 0.416037i
\(629\) 6792.00 6792.00i 0.430548 0.430548i
\(630\) 2435.75 1543.53i 0.154036 0.0976122i
\(631\) −7632.20 −0.481510 −0.240755 0.970586i \(-0.577395\pi\)
−0.240755 + 0.970586i \(0.577395\pi\)
\(632\) −10244.9 + 1950.45i −0.644814 + 0.122761i
\(633\) −1251.29 −0.0785689
\(634\) 1398.48 6931.32i 0.0876036 0.434193i
\(635\) −3250.83 3250.83i −0.203158 0.203158i
\(636\) −14352.1 + 34119.2i −0.894811 + 2.12722i
\(637\) −2618.28 + 2402.47i −0.162857 + 0.149434i
\(638\) 9277.61 + 13967.6i 0.575712 + 0.866745i
\(639\) 7116.62i 0.440578i
\(640\) −738.596 4125.10i −0.0456181 0.254780i
\(641\) 18811.7 1.15915 0.579576 0.814918i \(-0.303218\pi\)
0.579576 + 0.814918i \(0.303218\pi\)
\(642\) 10923.7 + 16445.8i 0.671531 + 1.01100i
\(643\) −14360.3 + 14360.3i −0.880740 + 0.880740i −0.993610 0.112869i \(-0.963996\pi\)
0.112869 + 0.993610i \(0.463996\pi\)
\(644\) −6876.51 17955.7i −0.420765 1.09868i
\(645\) −1481.71 1481.71i −0.0904529 0.0904529i
\(646\) 7168.52 + 1446.33i 0.436597 + 0.0880887i
\(647\) 13880.5i 0.843430i −0.906728 0.421715i \(-0.861428\pi\)
0.906728 0.421715i \(-0.138572\pi\)
\(648\) 3727.18 + 19577.4i 0.225953 + 1.18684i
\(649\) 19710.4 1.19214
\(650\) −675.888 + 3349.92i −0.0407854 + 0.202146i
\(651\) −645.117 + 30030.6i −0.0388389 + 1.80797i
\(652\) −1859.05 + 758.136i −0.111666 + 0.0455382i
\(653\) 6926.86 6926.86i 0.415113 0.415113i −0.468402 0.883515i \(-0.655170\pi\)
0.883515 + 0.468402i \(0.155170\pi\)
\(654\) 17066.6 + 25694.1i 1.02042 + 1.53627i
\(655\) 6139.59i 0.366250i
\(656\) −5293.59 5410.90i −0.315061 0.322043i
\(657\) 11604.0i 0.689065i
\(658\) −1937.33 + 8640.46i −0.114780 + 0.511915i
\(659\) −21306.6 21306.6i −1.25947 1.25947i −0.951348 0.308118i \(-0.900301\pi\)
−0.308118 0.951348i \(-0.599699\pi\)
\(660\) 7105.98 2897.88i 0.419091 0.170909i
\(661\) 9192.89 9192.89i 0.540941 0.540941i −0.382864 0.923805i \(-0.625062\pi\)
0.923805 + 0.382864i \(0.125062\pi\)
\(662\) −3742.18 + 18547.5i −0.219704 + 1.08893i
\(663\) 9397.29i 0.550468i
\(664\) 23163.2 + 15754.1i 1.35378 + 0.920748i
\(665\) 716.912 + 748.389i 0.0418055 + 0.0436410i
\(666\) 764.457 3788.91i 0.0444777 0.220446i
\(667\) 11133.3 11133.3i 0.646303 0.646303i
\(668\) 12700.4 + 5342.41i 0.735621 + 0.309437i
\(669\) −5861.59 + 5861.59i −0.338748 + 0.338748i
\(670\) 561.855 373.197i 0.0323975 0.0215192i
\(671\) −21634.1 −1.24467
\(672\) −5218.83 + 22136.7i −0.299584 + 1.27075i
\(673\) −24859.6 −1.42388 −0.711938 0.702242i \(-0.752182\pi\)
−0.711938 + 0.702242i \(0.752182\pi\)
\(674\) −4047.49 + 2688.43i −0.231311 + 0.153642i
\(675\) 4462.85 4462.85i 0.254482 0.254482i
\(676\) −15409.5 6481.99i −0.876738 0.368798i
\(677\) −11098.7 + 11098.7i −0.630070 + 0.630070i −0.948086 0.318016i \(-0.896984\pi\)
0.318016 + 0.948086i \(0.396984\pi\)
\(678\) −2112.30 + 10469.3i −0.119649 + 0.593022i
\(679\) 12121.5 + 12653.7i 0.685094 + 0.715175i
\(680\) −4923.75 + 7239.40i −0.277673 + 0.408262i
\(681\) 33724.7i 1.89770i
\(682\) −6534.80 + 32388.6i −0.366907 + 1.81851i
\(683\) −5129.88 + 5129.88i −0.287393 + 0.287393i −0.836048 0.548656i \(-0.815140\pi\)
0.548656 + 0.836048i \(0.315140\pi\)
\(684\) 2724.91 1111.24i 0.152324 0.0621191i
\(685\) −4622.66 4622.66i −0.257844 0.257844i
\(686\) 17347.2 + 4680.26i 0.965478 + 0.260486i
\(687\) 32095.8i 1.78243i
\(688\) 6830.81 + 74.8601i 0.378521 + 0.00414828i
\(689\) 7065.77i 0.390688i
\(690\) −3986.94 6002.42i −0.219972 0.331171i
\(691\) −1243.53 + 1243.53i −0.0684606 + 0.0684606i −0.740508 0.672047i \(-0.765415\pi\)
0.672047 + 0.740508i \(0.265415\pi\)
\(692\) 18806.6 7669.51i 1.03312 0.421316i
\(693\) −17211.0 369.726i −0.943420 0.0202666i
\(694\) 6165.73 30559.4i 0.337245 1.67150i
\(695\) −8781.73 −0.479295
\(696\) −18295.6 + 3483.15i −0.996399 + 0.189696i
\(697\) 15814.4i 0.859416i
\(698\) −16513.5 3331.80i −0.895481 0.180674i
\(699\) 2580.07 + 2580.07i 0.139609 + 0.139609i
\(700\) 16136.6 6179.87i 0.871296 0.333682i
\(701\) 8513.11 8513.11i 0.458681 0.458681i −0.439541 0.898223i \(-0.644859\pi\)
0.898223 + 0.439541i \(0.144859\pi\)
\(702\) −877.387 1320.92i −0.0471721 0.0710185i
\(703\) 1389.15 0.0745276
\(704\) −9952.59 + 22953.1i −0.532816 + 1.22880i
\(705\) 3318.60i 0.177285i
\(706\) −11225.1 16899.6i −0.598389 0.900886i
\(707\) 79.3713 3694.78i 0.00422216 0.196544i
\(708\) −8488.48 + 20179.5i −0.450588 + 1.07118i
\(709\) 20499.4 + 20499.4i 1.08585 + 1.08585i 0.995950 + 0.0899043i \(0.0286561\pi\)
0.0899043 + 0.995950i \(0.471344\pi\)
\(710\) 605.605 3001.58i 0.0320112 0.158658i
\(711\) 8767.63 0.462464
\(712\) −2679.73 14075.6i −0.141049 0.740877i
\(713\) 31025.1 1.62959
\(714\) 40135.3 25433.7i 2.10368 1.33310i
\(715\) −1035.85 + 1035.85i −0.0541801 + 0.0541801i
\(716\) −9993.23 + 4075.32i −0.521598 + 0.212712i
\(717\) −30716.8 30716.8i −1.59991 1.59991i
\(718\) 30181.2 20047.0i 1.56873 1.04199i
\(719\) 14074.7 0.730037 0.365018 0.931000i \(-0.381063\pi\)
0.365018 + 0.931000i \(0.381063\pi\)
\(720\) −38.6083 + 3522.91i −0.00199840 + 0.182349i
\(721\) −11420.8 11922.2i −0.589919 0.615821i
\(722\) −10148.8 15279.1i −0.523127 0.787577i
\(723\) 7908.69 + 7908.69i 0.406815 + 0.406815i
\(724\) 7606.02 + 18651.0i 0.390436 + 0.957400i
\(725\) 10005.4 + 10005.4i 0.512541 + 0.512541i
\(726\) −19873.9 4009.80i −1.01596 0.204983i
\(727\) 95.2264i 0.00485798i −0.999997 0.00242899i \(-0.999227\pi\)
0.999997 0.00242899i \(-0.000773172\pi\)
\(728\) −720.178 4281.37i −0.0366642 0.217965i
\(729\) 6841.84i 0.347602i
\(730\) −987.469 + 4894.23i −0.0500656 + 0.248142i
\(731\) −10091.6 10091.6i −0.510602 0.510602i
\(732\) 9316.96 22149.1i 0.470444 1.11838i
\(733\) −13958.3 13958.3i −0.703357 0.703357i 0.261772 0.965130i \(-0.415693\pi\)
−0.965130 + 0.261772i \(0.915693\pi\)
\(734\) −12963.2 + 8610.42i −0.651878 + 0.432993i
\(735\) 6727.47 + 289.173i 0.337614 + 0.0145120i
\(736\) 22975.1 + 4898.11i 1.15064 + 0.245308i
\(737\) −4026.71 −0.201256
\(738\) 3521.04 + 5300.99i 0.175625 + 0.264407i
\(739\) 22132.3 + 22132.3i 1.10169 + 1.10169i 0.994207 + 0.107485i \(0.0342797\pi\)
0.107485 + 0.994207i \(0.465720\pi\)
\(740\) −644.851 + 1533.00i −0.0320340 + 0.0761541i
\(741\) −961.004 + 961.004i −0.0476428 + 0.0476428i
\(742\) −30177.5 + 19123.5i −1.49306 + 0.946151i
\(743\) −5532.55 −0.273176 −0.136588 0.990628i \(-0.543614\pi\)
−0.136588 + 0.990628i \(0.543614\pi\)
\(744\) −30345.3 20638.9i −1.49531 1.01701i
\(745\) −4444.40 −0.218564
\(746\) 19707.4 + 3976.20i 0.967209 + 0.195146i
\(747\) −16652.7 16652.7i −0.815651 0.815651i
\(748\) 48397.3 19736.8i 2.36575 0.964773i
\(749\) −409.266 + 19051.6i −0.0199656 + 0.929412i
\(750\) 11176.0 7423.35i 0.544119 0.361417i
\(751\) 36330.7i 1.76528i −0.470048 0.882641i \(-0.655764\pi\)
0.470048 0.882641i \(-0.344236\pi\)
\(752\) −7565.70 7733.37i −0.366879 0.375009i
\(753\) 36226.2 1.75320
\(754\) 2961.42 1967.04i 0.143035 0.0950073i
\(755\) 527.449 527.449i 0.0254250 0.0254250i
\(756\) −3266.94 + 7322.34i −0.157166 + 0.352263i
\(757\) 15674.3 + 15674.3i 0.752564 + 0.752564i 0.974957 0.222393i \(-0.0713869\pi\)
−0.222393 + 0.974957i \(0.571387\pi\)
\(758\) −4747.52 + 23530.3i −0.227490 + 1.12752i
\(759\) 43018.2i 2.05726i
\(760\) −1243.85 + 236.807i −0.0593674 + 0.0113025i
\(761\) 16656.7 0.793437 0.396718 0.917940i \(-0.370149\pi\)
0.396718 + 0.917940i \(0.370149\pi\)
\(762\) −29881.7 6028.99i −1.42060 0.286624i
\(763\) −639.417 + 29765.2i −0.0303387 + 1.41229i
\(764\) 15220.3 + 6402.37i 0.720745 + 0.303180i
\(765\) 5204.62 5204.62i 0.245978 0.245978i
\(766\) 29338.5 19487.3i 1.38387 0.919198i
\(767\) 4179.00i 0.196734i
\(768\) −19213.3 20074.5i −0.902734 0.943198i
\(769\) 9190.37i 0.430966i 0.976508 + 0.215483i \(0.0691327\pi\)
−0.976508 + 0.215483i \(0.930867\pi\)
\(770\) 7227.61 + 1620.55i 0.338266 + 0.0758447i
\(771\) −33386.6 33386.6i −1.55952 1.55952i
\(772\) 3544.47 8426.23i 0.165244 0.392832i
\(773\) −3285.14 + 3285.14i −0.152857 + 0.152857i −0.779393 0.626536i \(-0.784472\pi\)
0.626536 + 0.779393i \(0.284472\pi\)
\(774\) −5629.57 1135.83i −0.261435 0.0527476i
\(775\) 27882.0i 1.29233i
\(776\) −21030.9 + 4003.90i −0.972894 + 0.185221i
\(777\) 6517.88 6243.74i 0.300937 0.288279i
\(778\) −29676.3 5987.55i −1.36754 0.275918i
\(779\) −1617.24 + 1617.24i −0.0743822 + 0.0743822i
\(780\) −614.410 1506.61i −0.0282044 0.0691608i
\(781\) −12926.0 + 12926.0i −0.592227 + 0.592227i
\(782\) −27154.2 40881.2i −1.24173 1.86945i
\(783\) −6565.83 −0.299672
\(784\) −16336.4 + 14663.3i −0.744185 + 0.667973i
\(785\) −6271.96 −0.285167
\(786\) −22524.3 33910.8i −1.02216 1.53888i
\(787\) −11875.1 + 11875.1i −0.537867 + 0.537867i −0.922902 0.385035i \(-0.874189\pi\)
0.385035 + 0.922902i \(0.374189\pi\)
\(788\) 8773.83 3578.04i 0.396643 0.161754i
\(789\) 21401.5 21401.5i 0.965668 0.965668i
\(790\) −3697.93 746.101i −0.166540 0.0336014i
\(791\) −7444.08 + 7130.98i −0.334616 + 0.320541i
\(792\) 11828.4 17391.3i 0.530688 0.780271i
\(793\) 4586.87i 0.205403i
\(794\) 2926.92 + 590.542i 0.130822 + 0.0263949i
\(795\) −9467.67 + 9467.67i −0.422369 + 0.422369i
\(796\) 15967.5 + 6716.68i 0.710995 + 0.299079i
\(797\) 27267.4 + 27267.4i 1.21187 + 1.21187i 0.970411 + 0.241460i \(0.0776263\pi\)
0.241460 + 0.970411i \(0.422374\pi\)
\(798\) 6705.35 + 1503.44i 0.297452 + 0.0666934i
\(799\) 22602.3i 1.00076i
\(800\) −4401.90 + 20647.5i −0.194538 + 0.912500i
\(801\) 12045.9i 0.531361i
\(802\) −19797.4 + 13149.9i −0.871658 + 0.578975i
\(803\) 21076.5 21076.5i 0.926244 0.926244i
\(804\) 1734.15 4122.56i 0.0760679 0.180835i
\(805\) 149.375 6953.48i 0.00654008 0.304445i
\(806\) 6867.05 + 1385.51i 0.300101 + 0.0605490i
\(807\) 21607.3 0.942518
\(808\) 3733.51 + 2539.28i 0.162555 + 0.110559i
\(809\) 37899.6i 1.64707i −0.567265 0.823535i \(-0.691999\pi\)
0.567265 0.823535i \(-0.308001\pi\)
\(810\) −1425.75 + 7066.49i −0.0618466 + 0.306532i
\(811\) 2453.46 + 2453.46i 0.106230 + 0.106230i 0.758224 0.651994i \(-0.226067\pi\)
−0.651994 + 0.758224i \(0.726067\pi\)
\(812\) −16416.2 7324.28i −0.709478 0.316542i
\(813\) −31996.4 + 31996.4i −1.38027 + 1.38027i
\(814\) 8270.34 5493.35i 0.356112 0.236538i
\(815\) −726.238 −0.0312135
\(816\) −636.172 + 58049.2i −0.0272923 + 2.49035i
\(817\) 2064.01i 0.0883850i
\(818\) 19861.8 13192.7i 0.848964 0.563902i
\(819\) −78.3895 + 3649.08i −0.00334451 + 0.155689i
\(820\) −1033.97 2535.43i −0.0440340 0.107977i
\(821\) −16123.1 16123.1i −0.685385 0.685385i 0.275823 0.961208i \(-0.411050\pi\)
−0.961208 + 0.275823i \(0.911050\pi\)
\(822\) −42491.6 8573.19i −1.80300 0.363776i
\(823\) 24632.9 1.04332 0.521658 0.853155i \(-0.325314\pi\)
0.521658 + 0.853155i \(0.325314\pi\)
\(824\) 19815.2 3772.45i 0.837737 0.159490i
\(825\) −38660.1 −1.63148
\(826\) −17848.3 + 11310.4i −0.751842 + 0.476441i
\(827\) 1089.80 1089.80i 0.0458236 0.0458236i −0.683824 0.729647i \(-0.739684\pi\)
0.729647 + 0.683824i \(0.239684\pi\)
\(828\) −18204.2 7657.56i −0.764058 0.321399i
\(829\) 4055.04 + 4055.04i 0.169888 + 0.169888i 0.786930 0.617042i \(-0.211669\pi\)
−0.617042 + 0.786930i \(0.711669\pi\)
\(830\) 5606.53 + 8440.73i 0.234464 + 0.352990i
\(831\) 14559.0 0.607755
\(832\) 4866.53 + 2110.15i 0.202784 + 0.0879284i
\(833\) 45819.4 + 1969.49i 1.90582 + 0.0819194i
\(834\) −48504.2 + 32217.6i −2.01386 + 1.33766i
\(835\) 3524.22 + 3524.22i 0.146061 + 0.146061i
\(836\) 6967.67 + 2930.93i 0.288256 + 0.121254i
\(837\) −9148.46 9148.46i −0.377798 0.377798i
\(838\) 6860.59 34003.4i 0.282810 1.40170i
\(839\) 35349.1i 1.45457i −0.686335 0.727285i \(-0.740782\pi\)
0.686335 0.727285i \(-0.259218\pi\)
\(840\) −4771.77 + 6701.75i −0.196002 + 0.275277i
\(841\) 9668.83i 0.396442i
\(842\) −40773.5 8226.55i −1.66882 0.336705i
\(843\) 2682.87 + 2682.87i 0.109612 + 0.109612i
\(844\) 1366.32 557.197i 0.0557236 0.0227246i
\(845\) −4275.97 4275.97i −0.174080 0.174080i
\(846\) 5032.34 + 7576.29i 0.204510 + 0.307894i
\(847\) −13536.8 14131.2i −0.549151 0.573263i
\(848\) 478.335 43646.9i 0.0193704 1.76750i
\(849\) −247.890 −0.0100207
\(850\) 36739.6 24403.3i 1.48254 0.984736i
\(851\) −6592.13 6592.13i −0.265541 0.265541i
\(852\) −7666.98 18800.4i −0.308294 0.755977i
\(853\) −28356.9 + 28356.9i −1.13824 + 1.13824i −0.149477 + 0.988765i \(0.547759\pi\)
−0.988765 + 0.149477i \(0.952241\pi\)
\(854\) 19590.3 12414.3i 0.784972 0.497436i
\(855\) 1064.49 0.0425787
\(856\) −19251.3 13093.4i −0.768685 0.522808i
\(857\) 5617.28 0.223900 0.111950 0.993714i \(-0.464290\pi\)
0.111950 + 0.993714i \(0.464290\pi\)
\(858\) −1921.09 + 9521.59i −0.0764395 + 0.378860i
\(859\) −26923.7 26923.7i −1.06941 1.06941i −0.997404 0.0720059i \(-0.977060\pi\)
−0.0720059 0.997404i \(-0.522940\pi\)
\(860\) 2277.73 + 958.122i 0.0903139 + 0.0379903i
\(861\) −319.158 + 14857.0i −0.0126328 + 0.588066i
\(862\) 19160.6 + 28846.6i 0.757089 + 1.13981i
\(863\) 7764.09i 0.306249i 0.988207 + 0.153124i \(0.0489335\pi\)
−0.988207 + 0.153124i \(0.951067\pi\)
\(864\) −5330.40 8219.04i −0.209889 0.323631i
\(865\) 7346.82 0.288785
\(866\) 13752.3 + 20704.4i 0.539635 + 0.812430i
\(867\) 62191.9 62191.9i 2.43616 2.43616i
\(868\) −12668.2 33078.7i −0.495376 1.29351i
\(869\) 15924.8 + 15924.8i 0.621646 + 0.621646i
\(870\) −6603.83 1332.40i −0.257346 0.0519226i
\(871\) 853.745i 0.0332124i
\(872\) −30077.2 20456.5i −1.16805 0.794432i
\(873\) 17998.3 0.697765
\(874\) 1403.77 6957.57i 0.0543287 0.269271i
\(875\) 12946.8 + 278.123i 0.500207 + 0.0107455i
\(876\) 12501.4 + 30655.1i 0.482172 + 1.18235i
\(877\) 15619.2 15619.2i 0.601396 0.601396i −0.339287 0.940683i \(-0.610186\pi\)
0.940683 + 0.339287i \(0.110186\pi\)
\(878\) 9645.93 + 14522.1i 0.370768 + 0.558198i
\(879\) 37057.3i 1.42197i
\(880\) −6468.84 + 6328.59i −0.247801 + 0.242428i
\(881\) 45320.9i 1.73314i 0.499053 + 0.866571i \(0.333681\pi\)
−0.499053 + 0.866571i \(0.666319\pi\)
\(882\) 15797.2 9541.41i 0.603082 0.364258i
\(883\) −5998.33 5998.33i −0.228607 0.228607i 0.583504 0.812110i \(-0.301681\pi\)
−0.812110 + 0.583504i \(0.801681\pi\)
\(884\) −4184.61 10261.2i −0.159212 0.390410i
\(885\) −5599.59 + 5599.59i −0.212687 + 0.212687i
\(886\) −558.023 + 2765.75i −0.0211593 + 0.104873i
\(887\) 25507.8i 0.965578i 0.875737 + 0.482789i \(0.160376\pi\)
−0.875737 + 0.482789i \(0.839624\pi\)
\(888\) 2062.40 + 10833.0i 0.0779388 + 0.409381i
\(889\) −20353.5 21247.1i −0.767866 0.801581i
\(890\) 1025.07 5080.59i 0.0386073 0.191350i
\(891\) 30431.2 30431.2i 1.14420 1.14420i
\(892\) 3790.31 9010.65i 0.142275 0.338227i
\(893\) −2311.40 + 2311.40i −0.0866158 + 0.0866158i
\(894\) −24547.8 + 16305.2i −0.918346 + 0.609986i
\(895\) −3903.86 −0.145801
\(896\) −4158.87 26495.8i −0.155065 0.987904i
\(897\) 9120.74 0.339501
\(898\) −4260.07 + 2829.64i −0.158308 + 0.105152i
\(899\) 20510.3 20510.3i 0.760907 0.760907i
\(900\) 6881.79 16360.0i 0.254881 0.605925i
\(901\) −64482.2 + 64482.2i −2.38426 + 2.38426i
\(902\) −3232.95 + 16023.6i −0.119341 + 0.591493i
\(903\) −9276.96 9684.29i −0.341880 0.356891i
\(904\) −2355.47 12372.3i −0.0866612 0.455197i
\(905\) 7286.01i 0.267619i
\(906\) 978.207 4848.32i 0.0358706 0.177787i
\(907\) −26334.9 + 26334.9i −0.964096 + 0.964096i −0.999377 0.0352818i \(-0.988767\pi\)
0.0352818 + 0.999377i \(0.488767\pi\)
\(908\) 15017.6 + 36825.1i 0.548873 + 1.34591i
\(909\) −2684.13 2684.13i −0.0979393 0.0979393i
\(910\) 343.589 1532.40i 0.0125163 0.0558227i
\(911\) 16395.8i 0.596285i −0.954521 0.298142i \(-0.903633\pi\)
0.954521 0.298142i \(-0.0963671\pi\)
\(912\) −6001.40 + 5871.29i −0.217902 + 0.213177i
\(913\) 60493.1i 2.19280i
\(914\) 20615.0 + 31036.3i 0.746043 + 1.12318i
\(915\) 6146.11 6146.11i 0.222059 0.222059i
\(916\) −14292.3 35046.5i −0.515535 1.26416i
\(917\) 843.896 39283.9i 0.0303903 1.41469i
\(918\) −4047.70 + 20061.8i −0.145527 + 0.721282i
\(919\) −26851.4 −0.963815 −0.481908 0.876222i \(-0.660056\pi\)
−0.481908 + 0.876222i \(0.660056\pi\)
\(920\) 7026.36 + 4778.86i 0.251796 + 0.171255i
\(921\) 19614.3i 0.701750i
\(922\) 10900.5 + 2199.31i 0.389360 + 0.0785581i
\(923\) 2740.58 + 2740.58i 0.0977327 + 0.0977327i
\(924\) 45865.6 17565.2i 1.63297 0.625383i
\(925\) 5924.29 5924.29i 0.210583 0.210583i
\(926\) 5680.75 + 8552.48i 0.201599 + 0.303512i
\(927\) −16957.9 −0.600830
\(928\) 18426.6 11950.4i 0.651812 0.422728i
\(929\) 19627.5i 0.693171i 0.938018 + 0.346585i \(0.112659\pi\)
−0.938018 + 0.346585i \(0.887341\pi\)
\(930\) −7344.91 11057.9i −0.258978 0.389896i
\(931\) 4484.26 + 4887.08i 0.157858 + 0.172038i
\(932\) −3966.16 1668.36i −0.139395 0.0586361i
\(933\) 44954.6 + 44954.6i 1.57744 + 1.57744i
\(934\) 30.8697 153.001i 0.00108146 0.00536010i
\(935\) 18906.4 0.661290
\(936\) −3687.32 2507.87i −0.128765 0.0875772i
\(937\) −4230.42 −0.147494 −0.0737469 0.997277i \(-0.523496\pi\)
−0.0737469 + 0.997277i \(0.523496\pi\)
\(938\) 3646.30 2310.65i 0.126925 0.0804324i
\(939\) 43072.2 43072.2i 1.49692 1.49692i
\(940\) −1477.77 3623.69i −0.0512762 0.125736i
\(941\) 3133.94 + 3133.94i 0.108569 + 0.108569i 0.759305 0.650735i \(-0.225539\pi\)
−0.650735 + 0.759305i \(0.725539\pi\)
\(942\) −34642.0 + 23010.0i −1.19819 + 0.795866i
\(943\) 15349.0 0.530045
\(944\) 282.908 25814.7i 0.00975409 0.890038i
\(945\) −2094.44 + 2006.35i −0.0720974 + 0.0690650i
\(946\) −8162.03 12288.1i −0.280519 0.422326i
\(947\) 273.354 + 273.354i 0.00937997 + 0.00937997i 0.711781 0.702401i \(-0.247889\pi\)
−0.702401 + 0.711781i \(0.747889\pi\)
\(948\) −23162.0 + 9445.67i −0.793531 + 0.323609i
\(949\) −4468.65 4468.65i −0.152854 0.152854i
\(950\) 6252.71 + 1261.56i 0.213542 + 0.0430846i
\(951\) 16959.9i 0.578298i
\(952\) −32499.5 + 45644.2i −1.10642 + 1.55392i
\(953\) 20906.0i 0.710610i −0.934750 0.355305i \(-0.884377\pi\)
0.934750 0.355305i \(-0.115623\pi\)
\(954\) −7257.64 + 35971.3i −0.246305 + 1.22077i
\(955\) 4223.44 + 4223.44i 0.143107 + 0.143107i
\(956\) 47218.9 + 19862.5i 1.59746 + 0.671966i
\(957\) 28438.7 + 28438.7i 0.960599 + 0.960599i
\(958\) 2563.76 1702.91i 0.0864626 0.0574304i
\(959\) −28942.5 30213.3i −0.974559 1.01735i
\(960\) −3693.36 9348.30i −0.124169 0.314287i
\(961\) 27364.8 0.918558
\(962\) −1164.70 1753.48i −0.0390348 0.0587677i
\(963\) 13840.3 + 13840.3i 0.463133 + 0.463133i
\(964\) −12157.5 5114.03i −0.406190 0.170863i
\(965\) 2338.18 2338.18i 0.0779986 0.0779986i
\(966\) −24685.2 38954.2i −0.822189 1.29744i
\(967\) 9771.57 0.324956 0.162478 0.986712i \(-0.448051\pi\)
0.162478 + 0.986712i \(0.448051\pi\)
\(968\) 23486.6 4471.42i 0.779842 0.148468i
\(969\) 17540.3 0.581501
\(970\) −7591.13 1531.60i −0.251275 0.0506977i
\(971\) 9977.45 + 9977.45i 0.329754 + 0.329754i 0.852493 0.522739i \(-0.175090\pi\)
−0.522739 + 0.852493i \(0.675090\pi\)
\(972\) 13636.0 + 33437.3i 0.449974 + 1.10340i
\(973\) −56189.5 1207.06i −1.85134 0.0397705i
\(974\) 41796.5 27762.2i 1.37500 0.913304i
\(975\) 8196.74i 0.269237i
\(976\) −310.520 + 28334.2i −0.0101839 + 0.929258i
\(977\) 15291.4 0.500732 0.250366 0.968151i \(-0.419449\pi\)
0.250366 + 0.968151i \(0.419449\pi\)
\(978\) −4011.24 + 2664.36i −0.131150 + 0.0871132i
\(979\) −21879.1 + 21879.1i −0.714258 + 0.714258i
\(980\) −7474.73 + 2679.99i −0.243644 + 0.0873562i
\(981\) 21623.4 + 21623.4i 0.703753 + 0.703753i
\(982\) −4605.11 + 22824.5i −0.149649 + 0.741709i
\(983\) 14778.2i 0.479504i 0.970834 + 0.239752i \(0.0770661\pi\)
−0.970834 + 0.239752i \(0.922934\pi\)
\(984\) −15012.7 10210.6i −0.486369 0.330796i
\(985\) 3427.50 0.110872
\(986\) −44977.2 9074.69i −1.45270 0.293101i
\(987\) −456.147 + 21233.9i −0.0147106 + 0.684785i
\(988\) 621.418 1477.29i 0.0200101 0.0475696i
\(989\) −9794.60 + 9794.60i −0.314914 + 0.314914i
\(990\) 6337.44 4209.48i 0.203452 0.135137i
\(991\) 7672.15i 0.245927i 0.992411 + 0.122964i \(0.0392398\pi\)
−0.992411 + 0.122964i \(0.960760\pi\)
\(992\) 42325.6 + 9023.51i 1.35468 + 0.288807i
\(993\) 45382.9i 1.45033i
\(994\) 4287.51 19122.2i 0.136812 0.610182i
\(995\) 4430.79 + 4430.79i 0.141171 + 0.141171i
\(996\) 61933.1 + 26052.0i 1.97031 + 0.828805i
\(997\) −28731.6 + 28731.6i −0.912677 + 0.912677i −0.996482 0.0838054i \(-0.973293\pi\)
0.0838054 + 0.996482i \(0.473293\pi\)
\(998\) −16796.9 3388.98i −0.532763 0.107491i
\(999\) 3887.68i 0.123124i
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 112.4.j.b.27.9 88
4.3 odd 2 448.4.j.b.335.37 88
7.6 odd 2 inner 112.4.j.b.27.10 yes 88
16.3 odd 4 inner 112.4.j.b.83.10 yes 88
16.13 even 4 448.4.j.b.111.8 88
28.27 even 2 448.4.j.b.335.8 88
112.13 odd 4 448.4.j.b.111.37 88
112.83 even 4 inner 112.4.j.b.83.9 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.4.j.b.27.9 88 1.1 even 1 trivial
112.4.j.b.27.10 yes 88 7.6 odd 2 inner
112.4.j.b.83.9 yes 88 112.83 even 4 inner
112.4.j.b.83.10 yes 88 16.3 odd 4 inner
448.4.j.b.111.8 88 16.13 even 4
448.4.j.b.111.37 88 112.13 odd 4
448.4.j.b.335.8 88 28.27 even 2
448.4.j.b.335.37 88 4.3 odd 2