Properties

Label 120.4.m.b.59.7
Level $120$
Weight $4$
Character 120.59
Analytic conductor $7.080$
Analytic rank $0$
Dimension $64$
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [120,4,Mod(59,120)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(120, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("120.59");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 120.m (of order \(2\), degree \(1\), 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: \(7.08022920069\)
Analytic rank: \(0\)
Dimension: \(64\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 59.7
Character \(\chi\) \(=\) 120.59
Dual form 120.4.m.b.59.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.73183 + 0.732884i) q^{2} +(-2.64167 - 4.47455i) q^{3} +(6.92576 - 4.00422i) q^{4} +(10.4671 + 3.92924i) q^{5} +(10.4959 + 10.2877i) q^{6} +4.10158 q^{7} +(-15.9854 + 16.0146i) q^{8} +(-13.0432 + 23.6406i) q^{9} +O(q^{10})\) \(q+(-2.73183 + 0.732884i) q^{2} +(-2.64167 - 4.47455i) q^{3} +(6.92576 - 4.00422i) q^{4} +(10.4671 + 3.92924i) q^{5} +(10.4959 + 10.2877i) q^{6} +4.10158 q^{7} +(-15.9854 + 16.0146i) q^{8} +(-13.0432 + 23.6406i) q^{9} +(-31.4741 - 3.06281i) q^{10} -5.96978i q^{11} +(-36.2127 - 20.4118i) q^{12} +33.0570 q^{13} +(-11.2048 + 3.00598i) q^{14} +(-10.0691 - 57.2155i) q^{15} +(31.9324 - 55.4646i) q^{16} +50.6136 q^{17} +(18.3059 - 74.1410i) q^{18} +74.1386 q^{19} +(88.2265 - 14.6998i) q^{20} +(-10.8350 - 18.3527i) q^{21} +(4.37515 + 16.3084i) q^{22} -184.927i q^{23} +(113.886 + 29.2219i) q^{24} +(94.1221 + 82.2559i) q^{25} +(-90.3061 + 24.2270i) q^{26} +(140.237 - 4.08828i) q^{27} +(28.4065 - 16.4236i) q^{28} -98.3905 q^{29} +(69.4395 + 148.923i) q^{30} -192.624i q^{31} +(-46.5846 + 174.922i) q^{32} +(-26.7121 + 15.7702i) q^{33} +(-138.268 + 37.0939i) q^{34} +(42.9318 + 16.1161i) q^{35} +(4.32825 + 215.957i) q^{36} +350.946 q^{37} +(-202.534 + 54.3350i) q^{38} +(-87.3258 - 147.915i) q^{39} +(-230.246 + 104.817i) q^{40} -292.535i q^{41} +(43.0498 + 42.1956i) q^{42} +80.8246i q^{43} +(-23.9043 - 41.3453i) q^{44} +(-229.414 + 196.199i) q^{45} +(135.530 + 505.188i) q^{46} -63.1702i q^{47} +(-332.534 + 3.63627i) q^{48} -326.177 q^{49} +(-317.409 - 155.728i) q^{50} +(-133.705 - 226.473i) q^{51} +(228.945 - 132.368i) q^{52} -178.821i q^{53} +(-380.106 + 113.946i) q^{54} +(23.4567 - 62.4865i) q^{55} +(-65.5652 + 65.6852i) q^{56} +(-195.850 - 331.737i) q^{57} +(268.786 - 72.1088i) q^{58} +479.870i q^{59} +(-298.840 - 355.942i) q^{60} +635.627i q^{61} +(141.171 + 526.215i) q^{62} +(-53.4975 + 96.9635i) q^{63} +(-0.936778 - 511.999i) q^{64} +(346.013 + 129.889i) q^{65} +(61.4150 - 62.6582i) q^{66} +288.505i q^{67} +(350.538 - 202.668i) q^{68} +(-827.464 + 488.515i) q^{69} +(-129.093 - 12.5624i) q^{70} +1062.20 q^{71} +(-170.095 - 586.784i) q^{72} +980.889i q^{73} +(-958.725 + 257.203i) q^{74} +(119.418 - 638.447i) q^{75} +(513.467 - 296.868i) q^{76} -24.4855i q^{77} +(346.964 + 340.079i) q^{78} -804.239i q^{79} +(552.175 - 455.086i) q^{80} +(-388.752 - 616.695i) q^{81} +(214.394 + 799.156i) q^{82} -300.045 q^{83} +(-148.529 - 83.7206i) q^{84} +(529.780 + 198.873i) q^{85} +(-59.2350 - 220.799i) q^{86} +(259.915 + 440.253i) q^{87} +(95.6038 + 95.4290i) q^{88} +1112.49i q^{89} +(482.928 - 704.117i) q^{90} +135.586 q^{91} +(-740.488 - 1280.76i) q^{92} +(-861.905 + 508.849i) q^{93} +(46.2964 + 172.570i) q^{94} +(776.020 + 291.309i) q^{95} +(905.760 - 253.642i) q^{96} -1217.88i q^{97} +(891.059 - 239.050i) q^{98} +(141.129 + 77.8648i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9} - 72 q^{10} - 128 q^{16} + 672 q^{19} - 416 q^{24} + 496 q^{25} - 248 q^{30} + 240 q^{34} - 608 q^{36} - 1344 q^{40} + 336 q^{46} + 3520 q^{49} - 544 q^{51} - 952 q^{54} - 2064 q^{60} + 2176 q^{64} - 176 q^{66} + 672 q^{70} - 1600 q^{75} + 2304 q^{76} - 2304 q^{81} - 736 q^{84} - 1432 q^{90} - 2752 q^{91} + 4496 q^{94} + 640 q^{96} + 256 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.73183 + 0.732884i −0.965847 + 0.259114i
\(3\) −2.64167 4.47455i −0.508390 0.861127i
\(4\) 6.92576 4.00422i 0.865720 0.500528i
\(5\) 10.4671 + 3.92924i 0.936210 + 0.351442i
\(6\) 10.4959 + 10.2877i 0.714156 + 0.699986i
\(7\) 4.10158 0.221464 0.110732 0.993850i \(-0.464680\pi\)
0.110732 + 0.993850i \(0.464680\pi\)
\(8\) −15.9854 + 16.0146i −0.706460 + 0.707753i
\(9\) −13.0432 + 23.6406i −0.483080 + 0.875576i
\(10\) −31.4741 3.06281i −0.995299 0.0968547i
\(11\) 5.96978i 0.163632i −0.996647 0.0818162i \(-0.973928\pi\)
0.996647 0.0818162i \(-0.0260720\pi\)
\(12\) −36.2127 20.4118i −0.871142 0.491032i
\(13\) 33.0570 0.705259 0.352630 0.935763i \(-0.385288\pi\)
0.352630 + 0.935763i \(0.385288\pi\)
\(14\) −11.2048 + 3.00598i −0.213901 + 0.0573844i
\(15\) −10.0691 57.2155i −0.173323 0.984865i
\(16\) 31.9324 55.4646i 0.498943 0.866635i
\(17\) 50.6136 0.722095 0.361047 0.932547i \(-0.382419\pi\)
0.361047 + 0.932547i \(0.382419\pi\)
\(18\) 18.3059 74.1410i 0.239708 0.970845i
\(19\) 74.1386 0.895188 0.447594 0.894237i \(-0.352281\pi\)
0.447594 + 0.894237i \(0.352281\pi\)
\(20\) 88.2265 14.6998i 0.986402 0.164349i
\(21\) −10.8350 18.3527i −0.112590 0.190709i
\(22\) 4.37515 + 16.3084i 0.0423994 + 0.158044i
\(23\) 184.927i 1.67652i −0.545273 0.838259i \(-0.683574\pi\)
0.545273 0.838259i \(-0.316426\pi\)
\(24\) 113.886 + 29.2219i 0.968622 + 0.248537i
\(25\) 94.1221 + 82.2559i 0.752977 + 0.658047i
\(26\) −90.3061 + 24.2270i −0.681173 + 0.182742i
\(27\) 140.237 4.08828i 0.999575 0.0291404i
\(28\) 28.4065 16.4236i 0.191726 0.110849i
\(29\) −98.3905 −0.630023 −0.315011 0.949088i \(-0.602008\pi\)
−0.315011 + 0.949088i \(0.602008\pi\)
\(30\) 69.4395 + 148.923i 0.422595 + 0.906319i
\(31\) 192.624i 1.11601i −0.829838 0.558004i \(-0.811567\pi\)
0.829838 0.558004i \(-0.188433\pi\)
\(32\) −46.5846 + 174.922i −0.257346 + 0.966319i
\(33\) −26.7121 + 15.7702i −0.140908 + 0.0831890i
\(34\) −138.268 + 37.0939i −0.697433 + 0.187105i
\(35\) 42.9318 + 16.1161i 0.207337 + 0.0778319i
\(36\) 4.32825 + 215.957i 0.0200382 + 0.999799i
\(37\) 350.946 1.55933 0.779665 0.626196i \(-0.215389\pi\)
0.779665 + 0.626196i \(0.215389\pi\)
\(38\) −202.534 + 54.3350i −0.864614 + 0.231955i
\(39\) −87.3258 147.915i −0.358547 0.607318i
\(40\) −230.246 + 104.817i −0.910129 + 0.414326i
\(41\) 292.535i 1.11430i −0.830412 0.557150i \(-0.811895\pi\)
0.830412 0.557150i \(-0.188105\pi\)
\(42\) 43.0498 + 42.1956i 0.158160 + 0.155022i
\(43\) 80.8246i 0.286643i 0.989676 + 0.143321i \(0.0457782\pi\)
−0.989676 + 0.143321i \(0.954222\pi\)
\(44\) −23.9043 41.3453i −0.0819026 0.141660i
\(45\) −229.414 + 196.199i −0.759979 + 0.649948i
\(46\) 135.530 + 505.188i 0.434408 + 1.61926i
\(47\) 63.1702i 0.196049i −0.995184 0.0980246i \(-0.968748\pi\)
0.995184 0.0980246i \(-0.0312524\pi\)
\(48\) −332.534 + 3.63627i −0.999940 + 0.0109344i
\(49\) −326.177 −0.950954
\(50\) −317.409 155.728i −0.897769 0.440466i
\(51\) −133.705 226.473i −0.367105 0.621815i
\(52\) 228.945 132.368i 0.610557 0.353002i
\(53\) 178.821i 0.463453i −0.972781 0.231726i \(-0.925563\pi\)
0.972781 0.231726i \(-0.0744374\pi\)
\(54\) −380.106 + 113.946i −0.957886 + 0.287149i
\(55\) 23.4567 62.4865i 0.0575073 0.153194i
\(56\) −65.5652 + 65.6852i −0.156456 + 0.156742i
\(57\) −195.850 331.737i −0.455104 0.770871i
\(58\) 268.786 72.1088i 0.608506 0.163247i
\(59\) 479.870i 1.05888i 0.848348 + 0.529439i \(0.177598\pi\)
−0.848348 + 0.529439i \(0.822402\pi\)
\(60\) −298.840 355.942i −0.643002 0.765865i
\(61\) 635.627i 1.33416i 0.744986 + 0.667080i \(0.232456\pi\)
−0.744986 + 0.667080i \(0.767544\pi\)
\(62\) 141.171 + 526.215i 0.289173 + 1.07789i
\(63\) −53.4975 + 96.9635i −0.106985 + 0.193909i
\(64\) −0.936778 511.999i −0.00182965 0.999998i
\(65\) 346.013 + 129.889i 0.660271 + 0.247858i
\(66\) 61.4150 62.6582i 0.114540 0.116859i
\(67\) 288.505i 0.526067i 0.964787 + 0.263033i \(0.0847229\pi\)
−0.964787 + 0.263033i \(0.915277\pi\)
\(68\) 350.538 202.668i 0.625132 0.361429i
\(69\) −827.464 + 488.515i −1.44369 + 0.852324i
\(70\) −129.093 12.5624i −0.220423 0.0214499i
\(71\) 1062.20 1.77549 0.887743 0.460340i \(-0.152273\pi\)
0.887743 + 0.460340i \(0.152273\pi\)
\(72\) −170.095 586.784i −0.278415 0.960461i
\(73\) 980.889i 1.57266i 0.617805 + 0.786332i \(0.288022\pi\)
−0.617805 + 0.786332i \(0.711978\pi\)
\(74\) −958.725 + 257.203i −1.50607 + 0.404044i
\(75\) 119.418 638.447i 0.183857 0.982953i
\(76\) 513.467 296.868i 0.774982 0.448067i
\(77\) 24.4855i 0.0362387i
\(78\) 346.964 + 340.079i 0.503665 + 0.493672i
\(79\) 804.239i 1.14537i −0.819777 0.572683i \(-0.805903\pi\)
0.819777 0.572683i \(-0.194097\pi\)
\(80\) 552.175 455.086i 0.771687 0.636002i
\(81\) −388.752 616.695i −0.533267 0.845947i
\(82\) 214.394 + 799.156i 0.288730 + 1.07624i
\(83\) −300.045 −0.396798 −0.198399 0.980121i \(-0.563574\pi\)
−0.198399 + 0.980121i \(0.563574\pi\)
\(84\) −148.529 83.7206i −0.192927 0.108746i
\(85\) 529.780 + 198.873i 0.676032 + 0.253775i
\(86\) −59.2350 220.799i −0.0742730 0.276853i
\(87\) 259.915 + 440.253i 0.320297 + 0.542530i
\(88\) 95.6038 + 95.4290i 0.115811 + 0.115600i
\(89\) 1112.49i 1.32499i 0.749066 + 0.662495i \(0.230502\pi\)
−0.749066 + 0.662495i \(0.769498\pi\)
\(90\) 482.928 704.117i 0.565613 0.824671i
\(91\) 135.586 0.156190
\(92\) −740.488 1280.76i −0.839144 1.45139i
\(93\) −861.905 + 508.849i −0.961026 + 0.567367i
\(94\) 46.2964 + 172.570i 0.0507990 + 0.189354i
\(95\) 776.020 + 291.309i 0.838083 + 0.314607i
\(96\) 905.760 253.642i 0.962956 0.269659i
\(97\) 1217.88i 1.27481i −0.770529 0.637405i \(-0.780008\pi\)
0.770529 0.637405i \(-0.219992\pi\)
\(98\) 891.059 239.050i 0.918476 0.246405i
\(99\) 141.129 + 77.8648i 0.143273 + 0.0790475i
\(100\) 981.238 + 192.799i 0.981238 + 0.192799i
\(101\) 461.131 0.454300 0.227150 0.973860i \(-0.427059\pi\)
0.227150 + 0.973860i \(0.427059\pi\)
\(102\) 531.236 + 520.696i 0.515688 + 0.505456i
\(103\) −1363.74 −1.30460 −0.652299 0.757962i \(-0.726195\pi\)
−0.652299 + 0.757962i \(0.726195\pi\)
\(104\) −528.428 + 529.396i −0.498237 + 0.499150i
\(105\) −41.2994 234.674i −0.0383848 0.218112i
\(106\) 131.055 + 488.509i 0.120087 + 0.447624i
\(107\) 626.784 0.566295 0.283147 0.959076i \(-0.408621\pi\)
0.283147 + 0.959076i \(0.408621\pi\)
\(108\) 954.875 589.853i 0.850767 0.525543i
\(109\) 472.473i 0.415181i −0.978216 0.207590i \(-0.933438\pi\)
0.978216 0.207590i \(-0.0665621\pi\)
\(110\) −18.2843 + 187.893i −0.0158486 + 0.162863i
\(111\) −927.084 1570.33i −0.792747 1.34278i
\(112\) 130.973 227.492i 0.110498 0.191929i
\(113\) −507.424 −0.422429 −0.211214 0.977440i \(-0.567742\pi\)
−0.211214 + 0.977440i \(0.567742\pi\)
\(114\) 778.152 + 762.713i 0.639304 + 0.626619i
\(115\) 726.622 1935.65i 0.589199 1.56957i
\(116\) −681.429 + 393.978i −0.545424 + 0.315344i
\(117\) −431.168 + 781.487i −0.340697 + 0.617508i
\(118\) −351.689 1310.92i −0.274370 1.02271i
\(119\) 207.596 0.159918
\(120\) 1077.24 + 753.356i 0.819487 + 0.573098i
\(121\) 1295.36 0.973224
\(122\) −465.841 1736.42i −0.345699 1.28859i
\(123\) −1308.96 + 772.781i −0.959555 + 0.566499i
\(124\) −771.309 1334.07i −0.558594 0.966152i
\(125\) 661.986 + 1230.81i 0.473679 + 0.880698i
\(126\) 75.0830 304.095i 0.0530867 0.215008i
\(127\) −2049.23 −1.43181 −0.715903 0.698199i \(-0.753985\pi\)
−0.715903 + 0.698199i \(0.753985\pi\)
\(128\) 377.795 + 1398.01i 0.260880 + 0.965371i
\(129\) 361.654 213.512i 0.246836 0.145726i
\(130\) −1040.44 101.248i −0.701944 0.0683077i
\(131\) 1677.53i 1.11883i 0.828888 + 0.559415i \(0.188974\pi\)
−0.828888 + 0.559415i \(0.811026\pi\)
\(132\) −121.854 + 216.182i −0.0803487 + 0.142547i
\(133\) 304.085 0.198252
\(134\) −211.440 788.145i −0.136311 0.508100i
\(135\) 1483.94 + 508.231i 0.946053 + 0.324011i
\(136\) −809.077 + 810.559i −0.510131 + 0.511065i
\(137\) −1839.77 −1.14731 −0.573657 0.819096i \(-0.694476\pi\)
−0.573657 + 0.819096i \(0.694476\pi\)
\(138\) 1902.46 1940.97i 1.17354 1.19730i
\(139\) −1598.25 −0.975264 −0.487632 0.873049i \(-0.662139\pi\)
−0.487632 + 0.873049i \(0.662139\pi\)
\(140\) 361.868 60.2923i 0.218453 0.0363973i
\(141\) −282.658 + 166.875i −0.168823 + 0.0996694i
\(142\) −2901.74 + 778.466i −1.71485 + 0.460052i
\(143\) 197.343i 0.115403i
\(144\) 894.715 + 1478.33i 0.517775 + 0.855517i
\(145\) −1029.87 386.600i −0.589833 0.221417i
\(146\) −718.878 2679.62i −0.407498 1.51895i
\(147\) 861.652 + 1459.50i 0.483455 + 0.818892i
\(148\) 2430.57 1405.27i 1.34994 0.780489i
\(149\) 533.530 0.293346 0.146673 0.989185i \(-0.453144\pi\)
0.146673 + 0.989185i \(0.453144\pi\)
\(150\) 141.677 + 1831.65i 0.0771191 + 0.997022i
\(151\) 3056.41i 1.64720i 0.567173 + 0.823599i \(0.308037\pi\)
−0.567173 + 0.823599i \(0.691963\pi\)
\(152\) −1185.13 + 1187.30i −0.632414 + 0.633572i
\(153\) −660.162 + 1196.53i −0.348830 + 0.632249i
\(154\) 17.9450 + 66.8901i 0.00938994 + 0.0350011i
\(155\) 756.866 2016.22i 0.392213 1.04482i
\(156\) −1197.08 674.754i −0.614381 0.346305i
\(157\) 1429.75 0.726794 0.363397 0.931634i \(-0.381617\pi\)
0.363397 + 0.931634i \(0.381617\pi\)
\(158\) 589.414 + 2197.04i 0.296780 + 1.10625i
\(159\) −800.145 + 472.387i −0.399092 + 0.235615i
\(160\) −1174.92 + 1647.90i −0.580535 + 0.814235i
\(161\) 758.491i 0.371289i
\(162\) 1513.97 + 1399.80i 0.734251 + 0.678878i
\(163\) 600.115i 0.288372i 0.989551 + 0.144186i \(0.0460564\pi\)
−0.989551 + 0.144186i \(0.953944\pi\)
\(164\) −1171.38 2026.03i −0.557739 0.964673i
\(165\) −341.564 + 60.1105i −0.161156 + 0.0283612i
\(166\) 819.671 219.898i 0.383246 0.102816i
\(167\) 1087.44i 0.503883i −0.967742 0.251942i \(-0.918931\pi\)
0.967742 0.251942i \(-0.0810691\pi\)
\(168\) 467.113 + 119.856i 0.214515 + 0.0550421i
\(169\) −1104.23 −0.502609
\(170\) −1593.02 155.020i −0.718700 0.0699383i
\(171\) −967.002 + 1752.68i −0.432447 + 0.783805i
\(172\) 323.640 + 559.772i 0.143473 + 0.248152i
\(173\) 374.343i 0.164513i −0.996611 0.0822567i \(-0.973787\pi\)
0.996611 0.0822567i \(-0.0262127\pi\)
\(174\) −1032.70 1012.21i −0.449935 0.441007i
\(175\) 386.049 + 337.379i 0.166757 + 0.145734i
\(176\) −331.111 190.629i −0.141809 0.0816433i
\(177\) 2147.20 1267.66i 0.911829 0.538322i
\(178\) −815.329 3039.14i −0.343323 1.27974i
\(179\) 1886.45i 0.787708i −0.919173 0.393854i \(-0.871142\pi\)
0.919173 0.393854i \(-0.128858\pi\)
\(180\) −803.242 + 2277.46i −0.332612 + 0.943064i
\(181\) 986.271i 0.405022i −0.979280 0.202511i \(-0.935090\pi\)
0.979280 0.202511i \(-0.0649101\pi\)
\(182\) −370.397 + 99.3688i −0.150855 + 0.0404709i
\(183\) 2844.15 1679.12i 1.14888 0.678273i
\(184\) 2961.53 + 2956.12i 1.18656 + 1.18439i
\(185\) 3673.41 + 1378.95i 1.45986 + 0.548015i
\(186\) 1981.65 2021.76i 0.781191 0.797005i
\(187\) 302.152i 0.118158i
\(188\) −252.947 437.501i −0.0981281 0.169724i
\(189\) 575.191 16.7684i 0.221370 0.00645355i
\(190\) −2333.45 227.073i −0.890979 0.0867031i
\(191\) −3513.46 −1.33102 −0.665510 0.746389i \(-0.731786\pi\)
−0.665510 + 0.746389i \(0.731786\pi\)
\(192\) −2288.49 + 1356.72i −0.860196 + 0.509964i
\(193\) 3049.07i 1.13719i 0.822619 + 0.568593i \(0.192512\pi\)
−0.822619 + 0.568593i \(0.807488\pi\)
\(194\) 892.561 + 3327.02i 0.330320 + 1.23127i
\(195\) −332.856 1891.37i −0.122238 0.694585i
\(196\) −2259.02 + 1306.09i −0.823260 + 0.475979i
\(197\) 3893.24i 1.40803i −0.710186 0.704014i \(-0.751389\pi\)
0.710186 0.704014i \(-0.248611\pi\)
\(198\) −442.606 109.282i −0.158862 0.0392239i
\(199\) 2888.21i 1.02884i 0.857537 + 0.514422i \(0.171994\pi\)
−0.857537 + 0.514422i \(0.828006\pi\)
\(200\) −2821.87 + 192.441i −0.997683 + 0.0680382i
\(201\) 1290.93 762.134i 0.453010 0.267447i
\(202\) −1259.73 + 337.956i −0.438784 + 0.117715i
\(203\) −403.556 −0.139528
\(204\) −1832.86 1033.12i −0.629047 0.354572i
\(205\) 1149.44 3062.01i 0.391612 1.04322i
\(206\) 3725.51 999.466i 1.26004 0.338039i
\(207\) 4371.77 + 2412.03i 1.46792 + 0.809892i
\(208\) 1055.59 1833.50i 0.351884 0.611202i
\(209\) 442.591i 0.146482i
\(210\) 284.811 + 610.820i 0.0935897 + 0.200717i
\(211\) −1800.81 −0.587550 −0.293775 0.955875i \(-0.594912\pi\)
−0.293775 + 0.955875i \(0.594912\pi\)
\(212\) −716.041 1238.47i −0.231971 0.401220i
\(213\) −2805.97 4752.85i −0.902638 1.52892i
\(214\) −1712.27 + 459.360i −0.546954 + 0.146735i
\(215\) −317.579 + 846.003i −0.100738 + 0.268358i
\(216\) −2176.26 + 2311.19i −0.685535 + 0.728039i
\(217\) 790.062i 0.247156i
\(218\) 346.268 + 1290.71i 0.107579 + 0.401001i
\(219\) 4389.04 2591.19i 1.35426 0.799526i
\(220\) −87.7544 526.693i −0.0268927 0.161407i
\(221\) 1673.14 0.509264
\(222\) 3683.50 + 3610.42i 1.11361 + 1.09151i
\(223\) −3394.93 −1.01947 −0.509734 0.860332i \(-0.670256\pi\)
−0.509734 + 0.860332i \(0.670256\pi\)
\(224\) −191.070 + 717.458i −0.0569929 + 0.214005i
\(225\) −3172.22 + 1152.22i −0.939918 + 0.341399i
\(226\) 1386.19 371.883i 0.408001 0.109457i
\(227\) −1666.84 −0.487366 −0.243683 0.969855i \(-0.578356\pi\)
−0.243683 + 0.969855i \(0.578356\pi\)
\(228\) −2684.76 1513.30i −0.779835 0.439566i
\(229\) 5278.56i 1.52322i −0.648037 0.761609i \(-0.724410\pi\)
0.648037 0.761609i \(-0.275590\pi\)
\(230\) −566.396 + 5820.40i −0.162379 + 1.66864i
\(231\) −109.562 + 64.6826i −0.0312061 + 0.0184234i
\(232\) 1572.81 1575.69i 0.445086 0.445901i
\(233\) −469.587 −0.132033 −0.0660165 0.997819i \(-0.521029\pi\)
−0.0660165 + 0.997819i \(0.521029\pi\)
\(234\) 605.138 2450.88i 0.169056 0.684698i
\(235\) 248.211 661.211i 0.0689000 0.183543i
\(236\) 1921.51 + 3323.47i 0.529998 + 0.916692i
\(237\) −3598.61 + 2124.53i −0.986306 + 0.582292i
\(238\) −567.116 + 152.144i −0.154456 + 0.0414370i
\(239\) −130.148 −0.0352242 −0.0176121 0.999845i \(-0.505606\pi\)
−0.0176121 + 0.999845i \(0.505606\pi\)
\(240\) −3494.97 1268.55i −0.939996 0.341184i
\(241\) 5560.04 1.48611 0.743057 0.669228i \(-0.233375\pi\)
0.743057 + 0.669228i \(0.233375\pi\)
\(242\) −3538.70 + 949.350i −0.939986 + 0.252176i
\(243\) −1732.48 + 3368.59i −0.457360 + 0.889281i
\(244\) 2545.19 + 4402.20i 0.667784 + 1.15501i
\(245\) −3414.14 1281.63i −0.890292 0.334205i
\(246\) 3009.50 3070.42i 0.779995 0.795785i
\(247\) 2450.80 0.631340
\(248\) 3084.80 + 3079.16i 0.789859 + 0.788415i
\(249\) 792.619 + 1342.57i 0.201728 + 0.341693i
\(250\) −2710.47 2877.21i −0.685702 0.727883i
\(251\) 6537.02i 1.64388i 0.569576 + 0.821939i \(0.307107\pi\)
−0.569576 + 0.821939i \(0.692893\pi\)
\(252\) 17.7527 + 885.763i 0.00443775 + 0.221420i
\(253\) −1103.97 −0.274332
\(254\) 5598.13 1501.85i 1.38291 0.371001i
\(255\) −509.636 2895.88i −0.125155 0.711166i
\(256\) −2056.65 3542.23i −0.502111 0.864803i
\(257\) 2769.77 0.672270 0.336135 0.941814i \(-0.390880\pi\)
0.336135 + 0.941814i \(0.390880\pi\)
\(258\) −831.496 + 848.328i −0.200646 + 0.204708i
\(259\) 1439.43 0.345336
\(260\) 2916.51 485.931i 0.695670 0.115908i
\(261\) 1283.32 2326.01i 0.304351 0.551633i
\(262\) −1229.44 4582.73i −0.289904 1.08062i
\(263\) 2001.24i 0.469207i 0.972091 + 0.234604i \(0.0753792\pi\)
−0.972091 + 0.234604i \(0.924621\pi\)
\(264\) 174.448 679.876i 0.0406687 0.158498i
\(265\) 702.632 1871.75i 0.162877 0.433889i
\(266\) −830.708 + 222.859i −0.191481 + 0.0513698i
\(267\) 4977.91 2938.84i 1.14098 0.673611i
\(268\) 1155.24 + 1998.12i 0.263311 + 0.455427i
\(269\) 2476.45 0.561307 0.280654 0.959809i \(-0.409449\pi\)
0.280654 + 0.959809i \(0.409449\pi\)
\(270\) −4426.34 300.844i −0.997698 0.0678102i
\(271\) 1616.36i 0.362313i −0.983454 0.181156i \(-0.942016\pi\)
0.983454 0.181156i \(-0.0579840\pi\)
\(272\) 1616.21 2807.27i 0.360284 0.625792i
\(273\) −358.173 606.686i −0.0794052 0.134499i
\(274\) 5025.93 1348.34i 1.10813 0.297285i
\(275\) 491.049 561.888i 0.107678 0.123211i
\(276\) −3774.69 + 6696.69i −0.823224 + 1.46048i
\(277\) 5749.66 1.24716 0.623580 0.781759i \(-0.285677\pi\)
0.623580 + 0.781759i \(0.285677\pi\)
\(278\) 4366.14 1171.33i 0.941956 0.252704i
\(279\) 4553.74 + 2512.43i 0.977151 + 0.539122i
\(280\) −944.373 + 429.915i −0.201561 + 0.0917584i
\(281\) 7754.89i 1.64633i −0.567804 0.823164i \(-0.692207\pi\)
0.567804 0.823164i \(-0.307793\pi\)
\(282\) 649.873 663.028i 0.137232 0.140010i
\(283\) 4931.44i 1.03584i 0.855428 + 0.517922i \(0.173294\pi\)
−0.855428 + 0.517922i \(0.826706\pi\)
\(284\) 7356.52 4253.27i 1.53707 0.888680i
\(285\) −746.512 4241.88i −0.155156 0.881639i
\(286\) 144.630 + 539.107i 0.0299025 + 0.111462i
\(287\) 1199.86i 0.246778i
\(288\) −3527.65 3382.83i −0.721767 0.692136i
\(289\) −2351.26 −0.478579
\(290\) 3096.75 + 301.352i 0.627061 + 0.0610207i
\(291\) −5449.44 + 3217.22i −1.09777 + 0.648100i
\(292\) 3927.70 + 6793.41i 0.787162 + 1.36149i
\(293\) 688.926i 0.137363i 0.997639 + 0.0686817i \(0.0218793\pi\)
−0.997639 + 0.0686817i \(0.978121\pi\)
\(294\) −3423.53 3355.60i −0.679129 0.665655i
\(295\) −1885.53 + 5022.87i −0.372134 + 0.991332i
\(296\) −5610.00 + 5620.28i −1.10160 + 1.10362i
\(297\) −24.4061 837.181i −0.00476831 0.163563i
\(298\) −1457.51 + 391.016i −0.283327 + 0.0760099i
\(299\) 6113.13i 1.18238i
\(300\) −1729.42 4899.91i −0.332827 0.942988i
\(301\) 331.508i 0.0634811i
\(302\) −2239.99 8349.58i −0.426811 1.59094i
\(303\) −1218.16 2063.35i −0.230961 0.391210i
\(304\) 2367.42 4112.07i 0.446648 0.775801i
\(305\) −2497.53 + 6653.20i −0.468880 + 1.24905i
\(306\) 926.528 3752.55i 0.173092 0.701042i
\(307\) 6625.29i 1.23168i −0.787872 0.615839i \(-0.788817\pi\)
0.787872 0.615839i \(-0.211183\pi\)
\(308\) −98.0454 169.581i −0.0181385 0.0313726i
\(309\) 3602.56 + 6102.14i 0.663244 + 1.12343i
\(310\) −589.971 + 6062.67i −0.108091 + 1.11076i
\(311\) −5355.88 −0.976540 −0.488270 0.872693i \(-0.662372\pi\)
−0.488270 + 0.872693i \(0.662372\pi\)
\(312\) 3764.74 + 965.989i 0.683130 + 0.175283i
\(313\) 57.6042i 0.0104025i −0.999986 0.00520125i \(-0.998344\pi\)
0.999986 0.00520125i \(-0.00165562\pi\)
\(314\) −3905.84 + 1047.84i −0.701971 + 0.188322i
\(315\) −940.959 + 804.726i −0.168308 + 0.143940i
\(316\) −3220.35 5569.97i −0.573288 0.991567i
\(317\) 7806.30i 1.38311i 0.722325 + 0.691554i \(0.243074\pi\)
−0.722325 + 0.691554i \(0.756926\pi\)
\(318\) 1839.65 1876.89i 0.324411 0.330978i
\(319\) 587.370i 0.103092i
\(320\) 2001.96 5362.85i 0.349729 0.936851i
\(321\) −1655.76 2804.58i −0.287898 0.487652i
\(322\) 555.886 + 2072.07i 0.0962059 + 0.358608i
\(323\) 3752.43 0.646410
\(324\) −5161.79 2714.44i −0.885080 0.465438i
\(325\) 3111.40 + 2719.14i 0.531044 + 0.464094i
\(326\) −439.815 1639.41i −0.0747212 0.278523i
\(327\) −2114.10 + 1248.12i −0.357523 + 0.211074i
\(328\) 4684.84 + 4676.28i 0.788650 + 0.787208i
\(329\) 259.097i 0.0434179i
\(330\) 889.039 414.538i 0.148303 0.0691502i
\(331\) −6218.44 −1.03262 −0.516308 0.856403i \(-0.672694\pi\)
−0.516308 + 0.856403i \(0.672694\pi\)
\(332\) −2078.04 + 1201.45i −0.343516 + 0.198608i
\(333\) −4577.45 + 8296.57i −0.753282 + 1.36531i
\(334\) 796.966 + 2970.69i 0.130563 + 0.486674i
\(335\) −1133.61 + 3019.82i −0.184882 + 0.492509i
\(336\) −1363.91 + 14.9144i −0.221451 + 0.00242157i
\(337\) 8547.36i 1.38162i 0.723038 + 0.690808i \(0.242745\pi\)
−0.723038 + 0.690808i \(0.757255\pi\)
\(338\) 3016.57 809.274i 0.485444 0.130233i
\(339\) 1340.45 + 2270.49i 0.214758 + 0.363765i
\(340\) 4465.46 744.009i 0.712276 0.118675i
\(341\) −1149.92 −0.182615
\(342\) 1357.17 5496.72i 0.214583 0.869089i
\(343\) −2744.68 −0.432067
\(344\) −1294.38 1292.01i −0.202872 0.202501i
\(345\) −10580.7 + 1862.05i −1.65114 + 0.290579i
\(346\) 274.350 + 1022.64i 0.0426276 + 0.158895i
\(347\) −11848.5 −1.83303 −0.916517 0.399996i \(-0.869012\pi\)
−0.916517 + 0.399996i \(0.869012\pi\)
\(348\) 3562.98 + 2008.33i 0.548839 + 0.309361i
\(349\) 3765.09i 0.577480i 0.957408 + 0.288740i \(0.0932363\pi\)
−0.957408 + 0.288740i \(0.906764\pi\)
\(350\) −1301.88 638.732i −0.198824 0.0975475i
\(351\) 4635.80 135.146i 0.704960 0.0205515i
\(352\) 1044.25 + 278.100i 0.158121 + 0.0421101i
\(353\) −7721.18 −1.16418 −0.582092 0.813123i \(-0.697766\pi\)
−0.582092 + 0.813123i \(0.697766\pi\)
\(354\) −4936.74 + 5036.68i −0.741200 + 0.756204i
\(355\) 11118.2 + 4173.63i 1.66223 + 0.623980i
\(356\) 4454.67 + 7704.87i 0.663195 + 1.14707i
\(357\) −548.399 928.897i −0.0813007 0.137710i
\(358\) 1382.55 + 5153.45i 0.204106 + 0.760805i
\(359\) 1277.28 0.187778 0.0938892 0.995583i \(-0.470070\pi\)
0.0938892 + 0.995583i \(0.470070\pi\)
\(360\) 525.207 6810.30i 0.0768913 0.997039i
\(361\) −1362.46 −0.198639
\(362\) 722.822 + 2694.32i 0.104947 + 0.391189i
\(363\) −3421.92 5796.16i −0.494777 0.838070i
\(364\) 939.036 542.917i 0.135217 0.0781774i
\(365\) −3854.15 + 10267.1i −0.552700 + 1.47234i
\(366\) −6539.12 + 6671.49i −0.933894 + 0.952798i
\(367\) −4874.49 −0.693315 −0.346657 0.937992i \(-0.612683\pi\)
−0.346657 + 0.937992i \(0.612683\pi\)
\(368\) −10256.9 5905.15i −1.45293 0.836487i
\(369\) 6915.70 + 3815.58i 0.975655 + 0.538296i
\(370\) −11045.7 1074.88i −1.55200 0.151029i
\(371\) 733.449i 0.102638i
\(372\) −3931.80 + 6975.43i −0.547996 + 0.972202i
\(373\) 9969.36 1.38390 0.691949 0.721946i \(-0.256752\pi\)
0.691949 + 0.721946i \(0.256752\pi\)
\(374\) 221.442 + 825.428i 0.0306164 + 0.114123i
\(375\) 3758.58 6213.49i 0.517580 0.855635i
\(376\) 1011.65 + 1009.80i 0.138755 + 0.138501i
\(377\) −3252.50 −0.444330
\(378\) −1559.03 + 467.356i −0.212138 + 0.0635932i
\(379\) −3910.73 −0.530028 −0.265014 0.964245i \(-0.585377\pi\)
−0.265014 + 0.964245i \(0.585377\pi\)
\(380\) 6540.99 1089.82i 0.883015 0.147123i
\(381\) 5413.38 + 9169.36i 0.727916 + 1.23297i
\(382\) 9598.16 2574.96i 1.28556 0.344886i
\(383\) 2301.53i 0.307056i 0.988144 + 0.153528i \(0.0490636\pi\)
−0.988144 + 0.153528i \(0.950936\pi\)
\(384\) 5257.44 5383.53i 0.698679 0.715436i
\(385\) 96.2095 256.293i 0.0127358 0.0339270i
\(386\) −2234.61 8329.53i −0.294660 1.09835i
\(387\) −1910.74 1054.21i −0.250978 0.138471i
\(388\) −4876.65 8434.71i −0.638078 1.10363i
\(389\) −13438.1 −1.75152 −0.875758 0.482751i \(-0.839638\pi\)
−0.875758 + 0.482751i \(0.839638\pi\)
\(390\) 2295.46 + 4922.96i 0.298039 + 0.639190i
\(391\) 9359.82i 1.21060i
\(392\) 5214.06 5223.61i 0.671810 0.673041i
\(393\) 7506.20 4431.49i 0.963455 0.568801i
\(394\) 2853.29 + 10635.6i 0.364839 + 1.35994i
\(395\) 3160.05 8418.08i 0.402530 1.07230i
\(396\) 1289.21 25.8387i 0.163599 0.00327890i
\(397\) −10501.3 −1.32757 −0.663786 0.747922i \(-0.731051\pi\)
−0.663786 + 0.747922i \(0.731051\pi\)
\(398\) −2116.73 7890.10i −0.266588 0.993706i
\(399\) −803.293 1360.64i −0.100789 0.170720i
\(400\) 7567.83 2593.82i 0.945979 0.324228i
\(401\) 13566.8i 1.68951i −0.535155 0.844754i \(-0.679747\pi\)
0.535155 0.844754i \(-0.320253\pi\)
\(402\) −2968.04 + 3028.12i −0.368239 + 0.375694i
\(403\) 6367.58i 0.787076i
\(404\) 3193.69 1846.47i 0.393297 0.227390i
\(405\) −1645.97 7982.54i −0.201948 0.979396i
\(406\) 1102.45 295.760i 0.134762 0.0361535i
\(407\) 2095.07i 0.255157i
\(408\) 5764.20 + 1479.03i 0.699437 + 0.179467i
\(409\) −7673.26 −0.927674 −0.463837 0.885921i \(-0.653528\pi\)
−0.463837 + 0.885921i \(0.653528\pi\)
\(410\) −895.981 + 9207.28i −0.107925 + 1.10906i
\(411\) 4860.06 + 8232.13i 0.583282 + 0.987983i
\(412\) −9444.96 + 5460.73i −1.12942 + 0.652988i
\(413\) 1968.22i 0.234504i
\(414\) −13710.7 3385.25i −1.62764 0.401874i
\(415\) −3140.61 1178.95i −0.371486 0.139451i
\(416\) −1539.95 + 5782.42i −0.181496 + 0.681506i
\(417\) 4222.05 + 7151.44i 0.495814 + 0.839827i
\(418\) 324.368 + 1209.08i 0.0379554 + 0.141479i
\(419\) 1239.80i 0.144554i 0.997385 + 0.0722768i \(0.0230265\pi\)
−0.997385 + 0.0722768i \(0.976973\pi\)
\(420\) −1225.72 1459.92i −0.142402 0.169612i
\(421\) 1701.96i 0.197027i 0.995136 + 0.0985134i \(0.0314087\pi\)
−0.995136 + 0.0985134i \(0.968591\pi\)
\(422\) 4919.51 1319.79i 0.567483 0.152242i
\(423\) 1493.38 + 823.939i 0.171656 + 0.0947075i
\(424\) 2863.76 + 2858.52i 0.328010 + 0.327411i
\(425\) 4763.86 + 4163.27i 0.543721 + 0.475172i
\(426\) 11148.7 + 10927.5i 1.26797 + 1.24282i
\(427\) 2607.07i 0.295469i
\(428\) 4340.96 2509.79i 0.490253 0.283446i
\(429\) −883.021 + 521.315i −0.0993769 + 0.0586698i
\(430\) 247.551 2543.88i 0.0277627 0.285295i
\(431\) 9669.03 1.08061 0.540303 0.841471i \(-0.318310\pi\)
0.540303 + 0.841471i \(0.318310\pi\)
\(432\) 4251.33 7908.71i 0.473477 0.880806i
\(433\) 11871.2i 1.31753i −0.752348 0.658766i \(-0.771079\pi\)
0.752348 0.658766i \(-0.228921\pi\)
\(434\) 579.023 + 2158.31i 0.0640415 + 0.238715i
\(435\) 990.708 + 5629.46i 0.109197 + 0.620487i
\(436\) −1891.89 3272.24i −0.207810 0.359430i
\(437\) 13710.2i 1.50080i
\(438\) −10091.1 + 10295.3i −1.10084 + 1.12313i
\(439\) 16373.4i 1.78009i −0.455868 0.890047i \(-0.650671\pi\)
0.455868 0.890047i \(-0.349329\pi\)
\(440\) 625.734 + 1374.52i 0.0677971 + 0.148926i
\(441\) 4254.38 7711.01i 0.459387 0.832632i
\(442\) −4570.72 + 1226.21i −0.491871 + 0.131957i
\(443\) 13008.8 1.39519 0.697594 0.716493i \(-0.254254\pi\)
0.697594 + 0.716493i \(0.254254\pi\)
\(444\) −12708.7 7163.45i −1.35840 0.765681i
\(445\) −4371.26 + 11644.6i −0.465657 + 1.24047i
\(446\) 9274.36 2488.09i 0.984650 0.264158i
\(447\) −1409.41 2387.31i −0.149134 0.252608i
\(448\) −3.84227 2100.00i −0.000405201 0.221464i
\(449\) 9615.94i 1.01070i 0.862914 + 0.505350i \(0.168637\pi\)
−0.862914 + 0.505350i \(0.831363\pi\)
\(450\) 7821.53 5472.54i 0.819356 0.573285i
\(451\) −1746.37 −0.182336
\(452\) −3514.30 + 2031.84i −0.365705 + 0.211437i
\(453\) 13676.0 8074.02i 1.41845 0.837418i
\(454\) 4553.52 1221.60i 0.470721 0.126283i
\(455\) 1419.20 + 532.750i 0.146226 + 0.0548917i
\(456\) 8443.37 + 2166.47i 0.867099 + 0.222487i
\(457\) 3926.38i 0.401900i 0.979601 + 0.200950i \(0.0644030\pi\)
−0.979601 + 0.200950i \(0.935597\pi\)
\(458\) 3868.57 + 14420.1i 0.394687 + 1.47120i
\(459\) 7097.88 206.923i 0.721788 0.0210421i
\(460\) −2718.38 16315.4i −0.275533 1.65372i
\(461\) 360.528 0.0364240 0.0182120 0.999834i \(-0.494203\pi\)
0.0182120 + 0.999834i \(0.494203\pi\)
\(462\) 251.898 256.998i 0.0253666 0.0258801i
\(463\) 14036.6 1.40894 0.704468 0.709735i \(-0.251185\pi\)
0.704468 + 0.709735i \(0.251185\pi\)
\(464\) −3141.84 + 5457.19i −0.314346 + 0.546000i
\(465\) −11021.1 + 1939.56i −1.09912 + 0.193430i
\(466\) 1282.83 344.153i 0.127524 0.0342115i
\(467\) 4186.44 0.414829 0.207415 0.978253i \(-0.433495\pi\)
0.207415 + 0.978253i \(0.433495\pi\)
\(468\) 143.079 + 7138.89i 0.0141321 + 0.705118i
\(469\) 1183.32i 0.116505i
\(470\) −193.478 + 1988.22i −0.0189883 + 0.195128i
\(471\) −3776.93 6397.49i −0.369494 0.625862i
\(472\) −7684.95 7670.90i −0.749424 0.748054i
\(473\) 482.505 0.0469040
\(474\) 8273.73 8441.22i 0.801741 0.817970i
\(475\) 6978.08 + 6098.34i 0.674056 + 0.589076i
\(476\) 1437.76 831.260i 0.138444 0.0800435i
\(477\) 4227.44 + 2332.40i 0.405788 + 0.223885i
\(478\) 355.543 95.3836i 0.0340212 0.00912708i
\(479\) 3466.07 0.330624 0.165312 0.986241i \(-0.447137\pi\)
0.165312 + 0.986241i \(0.447137\pi\)
\(480\) 10477.3 + 904.041i 0.996298 + 0.0859659i
\(481\) 11601.2 1.09973
\(482\) −15189.1 + 4074.86i −1.43536 + 0.385072i
\(483\) −3393.91 + 2003.68i −0.319727 + 0.188759i
\(484\) 8971.37 5186.92i 0.842540 0.487126i
\(485\) 4785.33 12747.7i 0.448022 1.19349i
\(486\) 2264.04 10472.1i 0.211315 0.977418i
\(487\) −2368.19 −0.220355 −0.110178 0.993912i \(-0.535142\pi\)
−0.110178 + 0.993912i \(0.535142\pi\)
\(488\) −10179.3 10160.7i −0.944256 0.942530i
\(489\) 2685.25 1585.31i 0.248325 0.146605i
\(490\) 10266.1 + 999.020i 0.946483 + 0.0921043i
\(491\) 19310.1i 1.77485i 0.460953 + 0.887424i \(0.347508\pi\)
−0.460953 + 0.887424i \(0.652492\pi\)
\(492\) −5971.18 + 10593.5i −0.547157 + 0.970713i
\(493\) −4979.90 −0.454936
\(494\) −6695.17 + 1796.15i −0.609777 + 0.163589i
\(495\) 1171.27 + 1369.55i 0.106353 + 0.124357i
\(496\) −10683.8 6150.94i −0.967172 0.556825i
\(497\) 4356.68 0.393207
\(498\) −3149.24 3086.76i −0.283375 0.277753i
\(499\) −2257.79 −0.202551 −0.101275 0.994858i \(-0.532292\pi\)
−0.101275 + 0.994858i \(0.532292\pi\)
\(500\) 9513.21 + 5873.58i 0.850887 + 0.525349i
\(501\) −4865.79 + 2872.65i −0.433907 + 0.256169i
\(502\) −4790.88 17858.0i −0.425951 1.58773i
\(503\) 171.197i 0.0151755i 0.999971 + 0.00758776i \(0.00241528\pi\)
−0.999971 + 0.00758776i \(0.997585\pi\)
\(504\) −697.658 2406.74i −0.0616591 0.212708i
\(505\) 4826.73 + 1811.90i 0.425320 + 0.159660i
\(506\) 3015.86 809.083i 0.264963 0.0710833i
\(507\) 2917.02 + 4940.94i 0.255521 + 0.432810i
\(508\) −14192.5 + 8205.57i −1.23954 + 0.716660i
\(509\) 872.727 0.0759979 0.0379989 0.999278i \(-0.487902\pi\)
0.0379989 + 0.999278i \(0.487902\pi\)
\(510\) 3514.58 + 7537.55i 0.305154 + 0.654448i
\(511\) 4023.19i 0.348289i
\(512\) 8214.45 + 8169.49i 0.709045 + 0.705163i
\(513\) 10396.9 303.099i 0.894808 0.0260861i
\(514\) −7566.53 + 2029.92i −0.649310 + 0.174194i
\(515\) −14274.5 5358.48i −1.22138 0.458491i
\(516\) 1649.78 2926.87i 0.140751 0.249706i
\(517\) −377.112 −0.0320800
\(518\) −3932.28 + 1054.94i −0.333542 + 0.0894813i
\(519\) −1675.02 + 988.892i −0.141667 + 0.0836368i
\(520\) −7611.26 + 3464.94i −0.641877 + 0.292207i
\(521\) 783.069i 0.0658481i 0.999458 + 0.0329240i \(0.0104819\pi\)
−0.999458 + 0.0329240i \(0.989518\pi\)
\(522\) −1801.13 + 7294.78i −0.151021 + 0.611655i
\(523\) 10952.6i 0.915727i −0.889023 0.457863i \(-0.848615\pi\)
0.889023 0.457863i \(-0.151385\pi\)
\(524\) 6717.22 + 11618.2i 0.560006 + 0.968593i
\(525\) 489.804 2618.64i 0.0407177 0.217689i
\(526\) −1466.67 5467.03i −0.121578 0.453182i
\(527\) 9749.40i 0.805864i
\(528\) 21.7077 + 1985.15i 0.00178922 + 0.163623i
\(529\) −22030.9 −1.81071
\(530\) −547.697 + 5628.24i −0.0448876 + 0.461274i
\(531\) −11344.4 6259.03i −0.927128 0.511523i
\(532\) 2106.02 1217.63i 0.171631 0.0992308i
\(533\) 9670.35i 0.785871i
\(534\) −11445.0 + 11676.6i −0.927475 + 0.946250i
\(535\) 6560.64 + 2462.79i 0.530170 + 0.199020i
\(536\) −4620.30 4611.85i −0.372325 0.371645i
\(537\) −8441.00 + 4983.37i −0.678317 + 0.400463i
\(538\) −6765.23 + 1814.95i −0.542137 + 0.145442i
\(539\) 1947.20i 0.155607i
\(540\) 12312.5 2422.14i 0.981194 0.193023i
\(541\) 8779.37i 0.697698i 0.937179 + 0.348849i \(0.113427\pi\)
−0.937179 + 0.348849i \(0.886573\pi\)
\(542\) 1184.60 + 4415.61i 0.0938801 + 0.349939i
\(543\) −4413.12 + 2605.40i −0.348775 + 0.205909i
\(544\) −2357.82 + 8853.46i −0.185828 + 0.697774i
\(545\) 1856.46 4945.44i 0.145912 0.388696i
\(546\) 1423.10 + 1394.86i 0.111544 + 0.109331i
\(547\) 4135.81i 0.323281i 0.986850 + 0.161640i \(0.0516784\pi\)
−0.986850 + 0.161640i \(0.948322\pi\)
\(548\) −12741.8 + 7366.85i −0.993253 + 0.574263i
\(549\) −15026.6 8290.59i −1.16816 0.644506i
\(550\) −929.663 + 1894.86i −0.0720745 + 0.146904i
\(551\) −7294.54 −0.563989
\(552\) 5403.91 21060.6i 0.416677 1.62391i
\(553\) 3298.65i 0.253658i
\(554\) −15707.1 + 4213.83i −1.20457 + 0.323156i
\(555\) −3533.73 20079.6i −0.270267 1.53573i
\(556\) −11069.1 + 6399.75i −0.844306 + 0.488147i
\(557\) 13645.6i 1.03803i 0.854765 + 0.519015i \(0.173701\pi\)
−0.854765 + 0.519015i \(0.826299\pi\)
\(558\) −14281.3 3526.15i −1.08347 0.267516i
\(559\) 2671.82i 0.202157i
\(560\) 2264.79 1866.57i 0.170901 0.140852i
\(561\) −1351.99 + 798.186i −0.101749 + 0.0600703i
\(562\) 5683.43 + 21185.0i 0.426586 + 1.59010i
\(563\) 10861.6 0.813076 0.406538 0.913634i \(-0.366736\pi\)
0.406538 + 0.913634i \(0.366736\pi\)
\(564\) −1289.42 + 2287.56i −0.0962665 + 0.170787i
\(565\) −5311.28 1993.79i −0.395482 0.148459i
\(566\) −3614.18 13471.9i −0.268401 1.00047i
\(567\) −1594.50 2529.42i −0.118100 0.187347i
\(568\) −16979.6 + 17010.7i −1.25431 + 1.25661i
\(569\) 4479.34i 0.330024i 0.986292 + 0.165012i \(0.0527663\pi\)
−0.986292 + 0.165012i \(0.947234\pi\)
\(570\) 5148.15 + 11041.0i 0.378302 + 0.811325i
\(571\) 9122.59 0.668596 0.334298 0.942467i \(-0.391501\pi\)
0.334298 + 0.942467i \(0.391501\pi\)
\(572\) −790.206 1366.75i −0.0577626 0.0999069i
\(573\) 9281.40 + 15721.1i 0.676677 + 1.14618i
\(574\) 879.355 + 3277.80i 0.0639435 + 0.238350i
\(575\) 15211.3 17405.7i 1.10323 1.26238i
\(576\) 12116.2 + 6655.94i 0.876459 + 0.481477i
\(577\) 12703.2i 0.916533i −0.888815 0.458267i \(-0.848471\pi\)
0.888815 0.458267i \(-0.151529\pi\)
\(578\) 6423.24 1723.20i 0.462234 0.124006i
\(579\) 13643.2 8054.64i 0.979262 0.578134i
\(580\) −8680.65 + 1446.32i −0.621456 + 0.103543i
\(581\) −1230.66 −0.0878765
\(582\) 12529.1 12782.7i 0.892349 0.910413i
\(583\) −1067.52 −0.0758359
\(584\) −15708.6 15679.9i −1.11306 1.11102i
\(585\) −7583.75 + 6485.77i −0.535982 + 0.458382i
\(586\) −504.903 1882.03i −0.0355927 0.132672i
\(587\) 584.550 0.0411021 0.0205511 0.999789i \(-0.493458\pi\)
0.0205511 + 0.999789i \(0.493458\pi\)
\(588\) 11811.7 + 6657.87i 0.828415 + 0.466949i
\(589\) 14280.9i 0.999038i
\(590\) 1469.75 15103.5i 0.102557 1.05390i
\(591\) −17420.5 + 10284.6i −1.21249 + 0.715827i
\(592\) 11206.6 19465.1i 0.778018 1.35137i
\(593\) 9207.43 0.637612 0.318806 0.947820i \(-0.396718\pi\)
0.318806 + 0.947820i \(0.396718\pi\)
\(594\) 680.230 + 2269.15i 0.0469868 + 0.156741i
\(595\) 2172.93 + 815.694i 0.149717 + 0.0562020i
\(596\) 3695.11 2136.38i 0.253955 0.146828i
\(597\) 12923.5 7629.71i 0.885966 0.523054i
\(598\) 4480.21 + 16700.0i 0.306371 + 1.14200i
\(599\) −14077.4 −0.960246 −0.480123 0.877201i \(-0.659408\pi\)
−0.480123 + 0.877201i \(0.659408\pi\)
\(600\) 8315.54 + 12118.2i 0.565801 + 0.824542i
\(601\) 9056.37 0.614670 0.307335 0.951601i \(-0.400563\pi\)
0.307335 + 0.951601i \(0.400563\pi\)
\(602\) −242.957 905.623i −0.0164488 0.0613130i
\(603\) −6820.41 3763.01i −0.460611 0.254132i
\(604\) 12238.5 + 21168.0i 0.824469 + 1.42601i
\(605\) 13558.7 + 5089.79i 0.911142 + 0.342032i
\(606\) 4839.99 + 4743.96i 0.324441 + 0.318004i
\(607\) 21455.8 1.43470 0.717350 0.696713i \(-0.245355\pi\)
0.717350 + 0.696713i \(0.245355\pi\)
\(608\) −3453.72 + 12968.5i −0.230373 + 0.865037i
\(609\) 1066.06 + 1805.73i 0.0709344 + 0.120151i
\(610\) 1946.81 20005.8i 0.129220 1.32789i
\(611\) 2088.22i 0.138266i
\(612\) 219.069 + 10930.4i 0.0144695 + 0.721950i
\(613\) −9740.71 −0.641800 −0.320900 0.947113i \(-0.603985\pi\)
−0.320900 + 0.947113i \(0.603985\pi\)
\(614\) 4855.57 + 18099.1i 0.319145 + 1.18961i
\(615\) −16737.5 + 2945.58i −1.09744 + 0.193134i
\(616\) 392.126 + 391.409i 0.0256481 + 0.0256012i
\(617\) 3739.84 0.244020 0.122010 0.992529i \(-0.461066\pi\)
0.122010 + 0.992529i \(0.461066\pi\)
\(618\) −14313.7 14029.7i −0.931687 0.913201i
\(619\) −21751.2 −1.41237 −0.706183 0.708029i \(-0.749585\pi\)
−0.706183 + 0.708029i \(0.749585\pi\)
\(620\) −2831.53 16994.5i −0.183414 1.10083i
\(621\) −756.032 25933.5i −0.0488543 1.67581i
\(622\) 14631.3 3925.24i 0.943188 0.253035i
\(623\) 4562.98i 0.293438i
\(624\) −10992.6 + 120.204i −0.705217 + 0.00771157i
\(625\) 2092.94 + 15484.2i 0.133948 + 0.990988i
\(626\) 42.2172 + 157.365i 0.00269543 + 0.0100472i
\(627\) −1980.40 + 1169.18i −0.126139 + 0.0744698i
\(628\) 9902.12 5725.05i 0.629200 0.363781i
\(629\) 17762.7 1.12598
\(630\) 1980.77 2887.99i 0.125263 0.182635i
\(631\) 5974.16i 0.376906i 0.982082 + 0.188453i \(0.0603472\pi\)
−0.982082 + 0.188453i \(0.939653\pi\)
\(632\) 12879.6 + 12856.0i 0.810637 + 0.809155i
\(633\) 4757.15 + 8057.82i 0.298704 + 0.505955i
\(634\) −5721.11 21325.5i −0.358382 1.33587i
\(635\) −21449.5 8051.91i −1.34047 0.503197i
\(636\) −3650.07 + 6475.60i −0.227570 + 0.403733i
\(637\) −10782.4 −0.670669
\(638\) −430.474 1604.59i −0.0267126 0.0995712i
\(639\) −13854.4 + 25110.9i −0.857702 + 1.55457i
\(640\) −1538.67 + 16117.6i −0.0950335 + 0.995474i
\(641\) 7044.53i 0.434075i 0.976163 + 0.217038i \(0.0696394\pi\)
−0.976163 + 0.217038i \(0.930361\pi\)
\(642\) 6578.67 + 6448.14i 0.404423 + 0.396399i
\(643\) 2177.00i 0.133519i −0.997769 0.0667595i \(-0.978734\pi\)
0.997769 0.0667595i \(-0.0212660\pi\)
\(644\) −3037.17 5253.13i −0.185840 0.321432i
\(645\) 4624.42 813.834i 0.282304 0.0496817i
\(646\) −10251.0 + 2750.09i −0.624333 + 0.167494i
\(647\) 15827.7i 0.961747i 0.876790 + 0.480873i \(0.159680\pi\)
−0.876790 + 0.480873i \(0.840320\pi\)
\(648\) 16090.5 + 3632.38i 0.975453 + 0.220206i
\(649\) 2864.72 0.173267
\(650\) −10492.6 5147.92i −0.633160 0.310643i
\(651\) −3535.17 + 2087.08i −0.212833 + 0.125652i
\(652\) 2403.00 + 4156.26i 0.144338 + 0.249650i
\(653\) 18484.0i 1.10771i 0.832613 + 0.553856i \(0.186844\pi\)
−0.832613 + 0.553856i \(0.813156\pi\)
\(654\) 4860.64 4959.03i 0.290621 0.296504i
\(655\) −6591.43 + 17559.0i −0.393204 + 1.04746i
\(656\) −16225.4 9341.34i −0.965691 0.555973i
\(657\) −23188.8 12793.9i −1.37699 0.759722i
\(658\) 189.888 + 707.809i 0.0112502 + 0.0419350i
\(659\) 11168.2i 0.660169i 0.943951 + 0.330084i \(0.107077\pi\)
−0.943951 + 0.330084i \(0.892923\pi\)
\(660\) −2124.89 + 1784.01i −0.125320 + 0.105216i
\(661\) 6525.85i 0.384003i 0.981395 + 0.192002i \(0.0614979\pi\)
−0.981395 + 0.192002i \(0.938502\pi\)
\(662\) 16987.7 4557.39i 0.997350 0.267565i
\(663\) −4419.87 7486.53i −0.258905 0.438541i
\(664\) 4796.32 4805.11i 0.280321 0.280835i
\(665\) 3182.90 + 1194.82i 0.185606 + 0.0696742i
\(666\) 6424.39 26019.5i 0.373784 1.51387i
\(667\) 18195.0i 1.05624i
\(668\) −4354.35 7531.34i −0.252208 0.436222i
\(669\) 8968.28 + 15190.8i 0.518287 + 0.877892i
\(670\) 883.637 9080.43i 0.0509520 0.523593i
\(671\) 3794.55 0.218312
\(672\) 3715.04 1040.33i 0.213260 0.0597198i
\(673\) 10707.9i 0.613313i −0.951820 0.306656i \(-0.900790\pi\)
0.951820 0.306656i \(-0.0992103\pi\)
\(674\) −6264.22 23349.9i −0.357995 1.33443i
\(675\) 13535.6 + 11150.5i 0.771833 + 0.635826i
\(676\) −7647.65 + 4421.59i −0.435119 + 0.251570i
\(677\) 5626.13i 0.319394i −0.987166 0.159697i \(-0.948948\pi\)
0.987166 0.159697i \(-0.0510517\pi\)
\(678\) −5325.88 5220.20i −0.301680 0.295694i
\(679\) 4995.21i 0.282325i
\(680\) −11653.6 + 5305.17i −0.657199 + 0.299182i
\(681\) 4403.24 + 7458.35i 0.247772 + 0.419684i
\(682\) 3141.39 842.759i 0.176378 0.0473181i
\(683\) 8947.12 0.501247 0.250624 0.968085i \(-0.419364\pi\)
0.250624 + 0.968085i \(0.419364\pi\)
\(684\) 320.891 + 16010.7i 0.0179380 + 0.895008i
\(685\) −19257.1 7228.90i −1.07413 0.403215i
\(686\) 7497.99 2011.53i 0.417310 0.111954i
\(687\) −23619.2 + 13944.2i −1.31168 + 0.774388i
\(688\) 4482.91 + 2580.92i 0.248414 + 0.143018i
\(689\) 5911.30i 0.326854i
\(690\) 27539.9 12841.2i 1.51946 0.708488i
\(691\) −2216.99 −0.122053 −0.0610263 0.998136i \(-0.519437\pi\)
−0.0610263 + 0.998136i \(0.519437\pi\)
\(692\) −1498.96 2592.61i −0.0823435 0.142423i
\(693\) 578.851 + 319.368i 0.0317298 + 0.0175062i
\(694\) 32368.2 8683.60i 1.77043 0.474964i
\(695\) −16729.1 6279.91i −0.913052 0.342749i
\(696\) −11205.3 2875.16i −0.610254 0.156584i
\(697\) 14806.3i 0.804631i
\(698\) −2759.37 10285.6i −0.149633 0.557757i
\(699\) 1240.49 + 2101.19i 0.0671242 + 0.113697i
\(700\) 4024.62 + 790.778i 0.217309 + 0.0426980i
\(701\) 34614.1 1.86499 0.932493 0.361188i \(-0.117629\pi\)
0.932493 + 0.361188i \(0.117629\pi\)
\(702\) −12565.2 + 3766.70i −0.675558 + 0.202514i
\(703\) 26018.7 1.39589
\(704\) −3056.52 + 5.59236i −0.163632 + 0.000299389i
\(705\) −3614.31 + 636.069i −0.193082 + 0.0339798i
\(706\) 21092.9 5658.73i 1.12442 0.301656i
\(707\) 1891.37 0.100611
\(708\) 9795.03 17377.4i 0.519943 0.922432i
\(709\) 21114.8i 1.11845i −0.829015 0.559226i \(-0.811098\pi\)
0.829015 0.559226i \(-0.188902\pi\)
\(710\) −33431.7 3253.31i −1.76714 0.171964i
\(711\) 19012.7 + 10489.8i 1.00286 + 0.553304i
\(712\) −17816.2 17783.6i −0.937766 0.936052i
\(713\) −35621.3 −1.87101
\(714\) 2178.91 + 2135.67i 0.114207 + 0.111941i
\(715\) 775.409 2065.62i 0.0405576 0.108042i
\(716\) −7553.76 13065.1i −0.394270 0.681935i
\(717\) 343.809 + 582.355i 0.0179076 + 0.0303325i
\(718\) −3489.32 + 936.101i −0.181365 + 0.0486560i
\(719\) 26234.0 1.36073 0.680363 0.732875i \(-0.261822\pi\)
0.680363 + 0.732875i \(0.261822\pi\)
\(720\) 3556.38 + 18989.5i 0.184081 + 0.982911i
\(721\) −5593.50 −0.288922
\(722\) 3722.02 998.528i 0.191855 0.0514700i
\(723\) −14687.8 24878.7i −0.755525 1.27973i
\(724\) −3949.25 6830.68i −0.202725 0.350636i
\(725\) −9260.72 8093.20i −0.474393 0.414585i
\(726\) 13596.0 + 13326.2i 0.695034 + 0.681244i
\(727\) −1445.23 −0.0737287 −0.0368643 0.999320i \(-0.511737\pi\)
−0.0368643 + 0.999320i \(0.511737\pi\)
\(728\) −2167.39 + 2171.36i −0.110342 + 0.110544i
\(729\) 19649.6 1146.65i 0.998302 0.0582560i
\(730\) 3004.28 30872.6i 0.152320 1.56527i
\(731\) 4090.83i 0.206983i
\(732\) 12974.3 23017.8i 0.655115 1.16224i
\(733\) −19855.7 −1.00053 −0.500265 0.865872i \(-0.666764\pi\)
−0.500265 + 0.865872i \(0.666764\pi\)
\(734\) 13316.3 3572.44i 0.669636 0.179647i
\(735\) 3284.32 + 18662.4i 0.164822 + 0.936561i
\(736\) 32347.8 + 8614.74i 1.62005 + 0.431445i
\(737\) 1722.31 0.0860815
\(738\) −21688.9 5355.12i −1.08181 0.267106i
\(739\) −6549.70 −0.326028 −0.163014 0.986624i \(-0.552122\pi\)
−0.163014 + 0.986624i \(0.552122\pi\)
\(740\) 30962.8 5158.84i 1.53813 0.256274i
\(741\) −6474.21 10966.2i −0.320966 0.543664i
\(742\) 537.533 + 2003.66i 0.0265950 + 0.0991328i
\(743\) 22234.5i 1.09785i 0.835870 + 0.548927i \(0.184963\pi\)
−0.835870 + 0.548927i \(0.815037\pi\)
\(744\) 5628.83 21937.2i 0.277370 1.08099i
\(745\) 5584.54 + 2096.37i 0.274633 + 0.103094i
\(746\) −27234.6 + 7306.39i −1.33663 + 0.358587i
\(747\) 3913.53 7093.23i 0.191685 0.347427i
\(748\) −1209.89 2092.63i −0.0591414 0.102292i
\(749\) 2570.80 0.125414
\(750\) −5714.03 + 19728.8i −0.278196 + 0.960524i
\(751\) 9278.78i 0.450849i 0.974261 + 0.225424i \(0.0723769\pi\)
−0.974261 + 0.225424i \(0.927623\pi\)
\(752\) −3503.71 2017.17i −0.169903 0.0978174i
\(753\) 29250.2 17268.7i 1.41559 0.835730i
\(754\) 8885.27 2383.70i 0.429154 0.115132i
\(755\) −12009.4 + 31991.8i −0.578895 + 1.54212i
\(756\) 3916.49 2419.33i 0.188415 0.116389i
\(757\) −990.407 −0.0475521 −0.0237761 0.999717i \(-0.507569\pi\)
−0.0237761 + 0.999717i \(0.507569\pi\)
\(758\) 10683.4 2866.11i 0.511926 0.137337i
\(759\) 2916.33 + 4939.77i 0.139468 + 0.236235i
\(760\) −17070.1 + 7770.99i −0.814736 + 0.370899i
\(761\) 10150.9i 0.483533i 0.970334 + 0.241766i \(0.0777268\pi\)
−0.970334 + 0.241766i \(0.922273\pi\)
\(762\) −21508.5 21081.7i −1.02253 1.00225i
\(763\) 1937.88i 0.0919477i
\(764\) −24333.4 + 14068.7i −1.15229 + 0.666213i
\(765\) −11611.5 + 9930.36i −0.548777 + 0.469324i
\(766\) −1686.75 6287.38i −0.0795625 0.296569i
\(767\) 15863.1i 0.746784i
\(768\) −10416.9 + 18560.0i −0.489437 + 0.872038i
\(769\) 10878.0 0.510103 0.255051 0.966927i \(-0.417908\pi\)
0.255051 + 0.966927i \(0.417908\pi\)
\(770\) −74.9945 + 770.659i −0.00350989 + 0.0360683i