Properties

Label 121.4.c.c.81.1
Level $121$
Weight $4$
Character 121.81
Analytic conductor $7.139$
Analytic rank $0$
Dimension $8$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [121,4,Mod(3,121)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(121, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("121.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 121 = 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 121.c (of order \(5\), degree \(4\), not 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: \(7.13923111069\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.324000000.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 11)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 81.1
Root \(0.535233 - 1.64728i\) of defining polynomial
Character \(\chi\) \(=\) 121.81
Dual form 121.4.c.c.3.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.21028 - 1.60586i) q^{2} +(-2.44995 + 7.54017i) q^{3} +(-0.165602 - 0.509670i) q^{4} +(-12.0191 + 8.73238i) q^{5} +(17.5235 - 12.7316i) q^{6} +(0.949237 + 2.92145i) q^{7} +(-7.20643 + 22.1791i) q^{8} +(-29.0084 - 21.0759i) q^{9} +O(q^{10})\) \(q+(-2.21028 - 1.60586i) q^{2} +(-2.44995 + 7.54017i) q^{3} +(-0.165602 - 0.509670i) q^{4} +(-12.0191 + 8.73238i) q^{5} +(17.5235 - 12.7316i) q^{6} +(0.949237 + 2.92145i) q^{7} +(-7.20643 + 22.1791i) q^{8} +(-29.0084 - 21.0759i) q^{9} +40.5885 q^{10} +4.24871 q^{12} +(-4.33551 - 3.14993i) q^{13} +(2.59336 - 7.98156i) q^{14} +(-36.3974 - 112.020i) q^{15} +(48.0763 - 34.9295i) q^{16} +(33.3440 - 24.2258i) q^{17} +(30.2718 + 93.1669i) q^{18} +(43.2386 - 133.075i) q^{19} +(6.44101 + 4.67967i) q^{20} -24.3538 q^{21} -111.354 q^{23} +(-149.579 - 108.675i) q^{24} +(29.5769 - 91.0283i) q^{25} +(4.52432 + 13.9244i) q^{26} +(56.8054 - 41.2716i) q^{27} +(1.33178 - 0.967595i) q^{28} +(-7.72383 - 23.7715i) q^{29} +(-99.4397 + 306.044i) q^{30} +(-25.4820 - 18.5137i) q^{31} +24.2102 q^{32} -112.603 q^{34} +(-36.9202 - 26.8241i) q^{35} +(-5.93788 + 18.2749i) q^{36} +(4.06159 + 12.5003i) q^{37} +(-309.268 + 224.697i) q^{38} +(34.3728 - 24.9733i) q^{39} +(-107.062 - 329.502i) q^{40} +(80.6756 - 248.294i) q^{41} +(53.8287 + 39.1088i) q^{42} -57.7128 q^{43} +532.697 q^{45} +(246.123 + 178.819i) q^{46} +(-106.254 + 327.017i) q^{47} +(145.590 + 448.079i) q^{48} +(269.859 - 196.064i) q^{49} +(-211.552 + 153.701i) q^{50} +(100.976 + 310.771i) q^{51} +(-0.887457 + 2.73131i) q^{52} +(277.489 + 201.607i) q^{53} -191.832 q^{54} -71.6359 q^{56} +(897.474 + 652.053i) q^{57} +(-21.1019 + 64.9450i) q^{58} +(27.3076 + 84.0442i) q^{59} +(-51.0656 + 37.1013i) q^{60} +(-597.619 + 434.195i) q^{61} +(26.5917 + 81.8408i) q^{62} +(34.0362 - 104.753i) q^{63} +(-438.122 - 318.314i) q^{64} +79.6152 q^{65} +342.359 q^{67} +(-17.8690 - 12.9826i) q^{68} +(272.811 - 839.627i) q^{69} +(38.5281 + 118.577i) q^{70} +(167.761 - 121.886i) q^{71} +(676.492 - 491.500i) q^{72} +(-312.293 - 961.138i) q^{73} +(11.0965 - 34.1515i) q^{74} +(613.907 + 446.029i) q^{75} -74.9845 q^{76} -116.077 q^{78} +(-1047.05 - 760.727i) q^{79} +(-272.816 + 839.641i) q^{80} +(-127.142 - 391.304i) q^{81} +(-577.041 + 419.245i) q^{82} +(-357.461 + 259.711i) q^{83} +(4.03304 + 12.4124i) q^{84} +(-189.215 + 582.344i) q^{85} +(127.561 + 92.6787i) q^{86} +198.164 q^{87} -1489.11 q^{89} +(-1177.41 - 855.437i) q^{90} +(5.08695 - 15.6560i) q^{91} +(18.4404 + 56.7537i) q^{92} +(202.026 - 146.781i) q^{93} +(759.995 - 552.168i) q^{94} +(642.370 + 1977.01i) q^{95} +(-59.3139 + 182.549i) q^{96} +(-1089.27 - 791.403i) q^{97} -911.314 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} + 26 q^{6} - 20 q^{7} + 12 q^{8} - 44 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} + 26 q^{6} - 20 q^{7} + 12 q^{8} - 44 q^{9} + 200 q^{10} - 160 q^{12} - 80 q^{13} + 4 q^{14} + 194 q^{15} + 8 q^{16} + 124 q^{17} - 92 q^{18} - 72 q^{19} - 88 q^{20} + 304 q^{21} - 392 q^{23} - 252 q^{24} - 136 q^{25} + 40 q^{26} + 182 q^{27} + 128 q^{28} - 144 q^{29} + 266 q^{30} + 34 q^{31} - 416 q^{32} - 208 q^{34} + 172 q^{35} + 80 q^{36} - 54 q^{37} - 432 q^{38} - 400 q^{39} + 492 q^{40} - 536 q^{41} + 140 q^{42} - 240 q^{43} + 1712 q^{45} + 314 q^{46} + 272 q^{47} - 776 q^{48} + 390 q^{49} - 232 q^{50} + 164 q^{51} + 560 q^{52} + 492 q^{53} - 440 q^{54} + 480 q^{56} + 1512 q^{57} + 192 q^{58} - 634 q^{59} - 632 q^{60} - 840 q^{61} - 134 q^{62} - 248 q^{63} - 224 q^{64} - 3520 q^{65} + 3016 q^{67} - 640 q^{68} - 962 q^{69} - 284 q^{70} + 678 q^{71} + 744 q^{72} + 400 q^{73} - 6 q^{74} + 520 q^{75} + 1728 q^{76} - 1760 q^{78} - 316 q^{79} + 1544 q^{80} + 1294 q^{81} - 512 q^{82} - 468 q^{83} + 736 q^{84} - 452 q^{85} + 156 q^{86} + 4800 q^{87} - 7368 q^{89} - 1532 q^{90} - 1280 q^{91} + 40 q^{92} + 638 q^{93} + 992 q^{94} - 2952 q^{95} + 952 q^{96} - 2194 q^{97} - 3480 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.21028 1.60586i −0.781450 0.567757i 0.123964 0.992287i \(-0.460439\pi\)
−0.905414 + 0.424530i \(0.860439\pi\)
\(3\) −2.44995 + 7.54017i −0.471493 + 1.45111i 0.379137 + 0.925341i \(0.376221\pi\)
−0.850630 + 0.525766i \(0.823779\pi\)
\(4\) −0.165602 0.509670i −0.0207002 0.0637087i
\(5\) −12.0191 + 8.73238i −1.07502 + 0.781048i −0.976808 0.214118i \(-0.931312\pi\)
−0.0982119 + 0.995166i \(0.531312\pi\)
\(6\) 17.5235 12.7316i 1.19232 0.866274i
\(7\) 0.949237 + 2.92145i 0.0512540 + 0.157744i 0.973407 0.229081i \(-0.0735720\pi\)
−0.922153 + 0.386824i \(0.873572\pi\)
\(8\) −7.20643 + 22.1791i −0.318482 + 0.980188i
\(9\) −29.0084 21.0759i −1.07439 0.780588i
\(10\) 40.5885 1.28352
\(11\) 0 0
\(12\) 4.24871 0.102208
\(13\) −4.33551 3.14993i −0.0924964 0.0672026i 0.540576 0.841295i \(-0.318206\pi\)
−0.633072 + 0.774093i \(0.718206\pi\)
\(14\) 2.59336 7.98156i 0.0495076 0.152369i
\(15\) −36.3974 112.020i −0.626519 1.92823i
\(16\) 48.0763 34.9295i 0.751193 0.545774i
\(17\) 33.3440 24.2258i 0.475712 0.345625i −0.323951 0.946074i \(-0.605011\pi\)
0.799663 + 0.600449i \(0.205011\pi\)
\(18\) 30.2718 + 93.1669i 0.396396 + 1.21998i
\(19\) 43.2386 133.075i 0.522085 1.60681i −0.247924 0.968779i \(-0.579748\pi\)
0.770009 0.638033i \(-0.220252\pi\)
\(20\) 6.44101 + 4.67967i 0.0720127 + 0.0523203i
\(21\) −24.3538 −0.253069
\(22\) 0 0
\(23\) −111.354 −1.00952 −0.504758 0.863261i \(-0.668418\pi\)
−0.504758 + 0.863261i \(0.668418\pi\)
\(24\) −149.579 108.675i −1.27219 0.924304i
\(25\) 29.5769 91.0283i 0.236615 0.728226i
\(26\) 4.52432 + 13.9244i 0.0341266 + 0.105031i
\(27\) 56.8054 41.2716i 0.404897 0.294175i
\(28\) 1.33178 0.967595i 0.00898867 0.00653065i
\(29\) −7.72383 23.7715i −0.0494579 0.152216i 0.923277 0.384134i \(-0.125500\pi\)
−0.972735 + 0.231918i \(0.925500\pi\)
\(30\) −99.4397 + 306.044i −0.605171 + 1.86252i
\(31\) −25.4820 18.5137i −0.147635 0.107263i 0.511516 0.859274i \(-0.329084\pi\)
−0.659151 + 0.752011i \(0.729084\pi\)
\(32\) 24.2102 0.133744
\(33\) 0 0
\(34\) −112.603 −0.567976
\(35\) −36.9202 26.8241i −0.178304 0.129546i
\(36\) −5.93788 + 18.2749i −0.0274902 + 0.0846061i
\(37\) 4.06159 + 12.5003i 0.0180465 + 0.0555415i 0.959674 0.281114i \(-0.0907041\pi\)
−0.941628 + 0.336656i \(0.890704\pi\)
\(38\) −309.268 + 224.697i −1.32026 + 0.959227i
\(39\) 34.3728 24.9733i 0.141130 0.102537i
\(40\) −107.062 329.502i −0.423199 1.30247i
\(41\) 80.6756 248.294i 0.307303 0.945781i −0.671505 0.741000i \(-0.734352\pi\)
0.978808 0.204781i \(-0.0656482\pi\)
\(42\) 53.8287 + 39.1088i 0.197761 + 0.143681i
\(43\) −57.7128 −0.204677 −0.102339 0.994750i \(-0.532633\pi\)
−0.102339 + 0.994750i \(0.532633\pi\)
\(44\) 0 0
\(45\) 532.697 1.76466
\(46\) 246.123 + 178.819i 0.788887 + 0.573160i
\(47\) −106.254 + 327.017i −0.329761 + 1.01490i 0.639484 + 0.768804i \(0.279148\pi\)
−0.969245 + 0.246097i \(0.920852\pi\)
\(48\) 145.590 + 448.079i 0.437793 + 1.34739i
\(49\) 269.859 196.064i 0.786761 0.571615i
\(50\) −211.552 + 153.701i −0.598359 + 0.434733i
\(51\) 100.976 + 310.771i 0.277243 + 0.853268i
\(52\) −0.887457 + 2.73131i −0.00236669 + 0.00728394i
\(53\) 277.489 + 201.607i 0.719170 + 0.522507i 0.886119 0.463458i \(-0.153392\pi\)
−0.166949 + 0.985966i \(0.553392\pi\)
\(54\) −191.832 −0.483426
\(55\) 0 0
\(56\) −71.6359 −0.170942
\(57\) 897.474 + 652.053i 2.08550 + 1.51520i
\(58\) −21.1019 + 64.9450i −0.0477727 + 0.147029i
\(59\) 27.3076 + 84.0442i 0.0602568 + 0.185451i 0.976654 0.214819i \(-0.0689162\pi\)
−0.916397 + 0.400270i \(0.868916\pi\)
\(60\) −51.0656 + 37.1013i −0.109876 + 0.0798294i
\(61\) −597.619 + 434.195i −1.25438 + 0.911361i −0.998468 0.0553387i \(-0.982376\pi\)
−0.255913 + 0.966700i \(0.582376\pi\)
\(62\) 26.5917 + 81.8408i 0.0544702 + 0.167642i
\(63\) 34.0362 104.753i 0.0680661 0.209486i
\(64\) −438.122 318.314i −0.855707 0.621708i
\(65\) 79.6152 0.151924
\(66\) 0 0
\(67\) 342.359 0.624266 0.312133 0.950038i \(-0.398957\pi\)
0.312133 + 0.950038i \(0.398957\pi\)
\(68\) −17.8690 12.9826i −0.0318666 0.0231525i
\(69\) 272.811 839.627i 0.475980 1.46492i
\(70\) 38.5281 + 118.577i 0.0657855 + 0.202467i
\(71\) 167.761 121.886i 0.280417 0.203735i −0.438682 0.898642i \(-0.644555\pi\)
0.719099 + 0.694908i \(0.244555\pi\)
\(72\) 676.492 491.500i 1.10730 0.804498i
\(73\) −312.293 961.138i −0.500700 1.54100i −0.807882 0.589344i \(-0.799386\pi\)
0.307182 0.951651i \(-0.400614\pi\)
\(74\) 11.0965 34.1515i 0.0174316 0.0536490i
\(75\) 613.907 + 446.029i 0.945171 + 0.686707i
\(76\) −74.9845 −0.113175
\(77\) 0 0
\(78\) −116.077 −0.168502
\(79\) −1047.05 760.727i −1.49117 1.08340i −0.973738 0.227673i \(-0.926888\pi\)
−0.517432 0.855725i \(-0.673112\pi\)
\(80\) −272.816 + 839.641i −0.381272 + 1.17343i
\(81\) −127.142 391.304i −0.174406 0.536768i
\(82\) −577.041 + 419.245i −0.777116 + 0.564607i
\(83\) −357.461 + 259.711i −0.472728 + 0.343457i −0.798504 0.601990i \(-0.794375\pi\)
0.325775 + 0.945447i \(0.394375\pi\)
\(84\) 4.03304 + 12.4124i 0.00523857 + 0.0161227i
\(85\) −189.215 + 582.344i −0.241450 + 0.743107i
\(86\) 127.561 + 92.6787i 0.159945 + 0.116207i
\(87\) 198.164 0.244200
\(88\) 0 0
\(89\) −1489.11 −1.77355 −0.886773 0.462205i \(-0.847058\pi\)
−0.886773 + 0.462205i \(0.847058\pi\)
\(90\) −1177.41 855.437i −1.37900 1.00190i
\(91\) 5.08695 15.6560i 0.00585997 0.0180351i
\(92\) 18.4404 + 56.7537i 0.0208972 + 0.0643150i
\(93\) 202.026 146.781i 0.225259 0.163661i
\(94\) 759.995 552.168i 0.833909 0.605870i
\(95\) 642.370 + 1977.01i 0.693745 + 2.13513i
\(96\) −59.3139 + 182.549i −0.0630593 + 0.194077i
\(97\) −1089.27 791.403i −1.14019 0.828400i −0.153048 0.988219i \(-0.548909\pi\)
−0.987146 + 0.159819i \(0.948909\pi\)
\(98\) −911.314 −0.939353
\(99\) 0 0
\(100\) −51.2923 −0.0512923
\(101\) 130.625 + 94.9046i 0.128690 + 0.0934986i 0.650268 0.759705i \(-0.274657\pi\)
−0.521578 + 0.853203i \(0.674657\pi\)
\(102\) 275.871 849.042i 0.267797 0.824193i
\(103\) −10.7412 33.0580i −0.0102753 0.0316243i 0.945787 0.324786i \(-0.105292\pi\)
−0.956063 + 0.293162i \(0.905292\pi\)
\(104\) 101.106 73.4580i 0.0953297 0.0692611i
\(105\) 292.711 212.667i 0.272054 0.197659i
\(106\) −289.573 891.215i −0.265338 0.816627i
\(107\) 257.158 791.450i 0.232340 0.715068i −0.765123 0.643884i \(-0.777322\pi\)
0.997463 0.0711847i \(-0.0226780\pi\)
\(108\) −30.4419 22.1174i −0.0271229 0.0197060i
\(109\) 1044.26 0.917629 0.458815 0.888532i \(-0.348274\pi\)
0.458815 + 0.888532i \(0.348274\pi\)
\(110\) 0 0
\(111\) −104.205 −0.0891055
\(112\) 147.681 + 107.296i 0.124594 + 0.0905228i
\(113\) 91.1853 280.639i 0.0759114 0.233631i −0.905899 0.423493i \(-0.860804\pi\)
0.981811 + 0.189861i \(0.0608039\pi\)
\(114\) −936.559 2882.43i −0.769446 2.36811i
\(115\) 1338.37 972.384i 1.08525 0.788480i
\(116\) −10.8365 + 7.87321i −0.00867368 + 0.00630180i
\(117\) 59.3788 + 182.749i 0.0469194 + 0.144403i
\(118\) 74.6058 229.613i 0.0582036 0.179132i
\(119\) 102.426 + 74.4167i 0.0789022 + 0.0573258i
\(120\) 2746.80 2.08956
\(121\) 0 0
\(122\) 2018.16 1.49767
\(123\) 1674.53 + 1216.62i 1.22754 + 0.891858i
\(124\) −5.21603 + 16.0533i −0.00377752 + 0.0116260i
\(125\) −134.454 413.807i −0.0962075 0.296096i
\(126\) −243.448 + 176.875i −0.172127 + 0.125058i
\(127\) 1065.96 774.469i 0.744796 0.541126i −0.149414 0.988775i \(-0.547739\pi\)
0.894209 + 0.447649i \(0.147739\pi\)
\(128\) 397.351 + 1222.92i 0.274385 + 0.844469i
\(129\) 141.393 435.164i 0.0965039 0.297008i
\(130\) −175.972 127.851i −0.118721 0.0862559i
\(131\) −1600.71 −1.06759 −0.533797 0.845612i \(-0.679235\pi\)
−0.533797 + 0.845612i \(0.679235\pi\)
\(132\) 0 0
\(133\) 429.815 0.280223
\(134\) −756.708 549.780i −0.487833 0.354431i
\(135\) −322.351 + 992.093i −0.205508 + 0.632487i
\(136\) 297.016 + 914.121i 0.187271 + 0.576362i
\(137\) −1303.87 + 947.320i −0.813120 + 0.590766i −0.914734 0.404058i \(-0.867600\pi\)
0.101613 + 0.994824i \(0.467600\pi\)
\(138\) −1951.31 + 1417.71i −1.20367 + 0.874518i
\(139\) −9.84588 30.3025i −0.00600803 0.0184908i 0.948008 0.318248i \(-0.103094\pi\)
−0.954016 + 0.299757i \(0.903094\pi\)
\(140\) −7.55738 + 23.2592i −0.00456225 + 0.0140412i
\(141\) −2205.45 1602.35i −1.31725 0.957037i
\(142\) −566.529 −0.334803
\(143\) 0 0
\(144\) −2130.79 −1.23310
\(145\) 300.415 + 218.264i 0.172056 + 0.125006i
\(146\) −853.199 + 2625.88i −0.483639 + 1.48849i
\(147\) 817.215 + 2515.13i 0.458522 + 1.41119i
\(148\) 5.69842 4.14014i 0.00316491 0.00229944i
\(149\) 1964.57 1427.34i 1.08016 0.784782i 0.102449 0.994738i \(-0.467332\pi\)
0.977711 + 0.209956i \(0.0673320\pi\)
\(150\) −640.643 1971.70i −0.348722 1.07326i
\(151\) −796.237 + 2450.57i −0.429118 + 1.32069i 0.469877 + 0.882732i \(0.344298\pi\)
−0.898995 + 0.437958i \(0.855702\pi\)
\(152\) 2639.88 + 1917.99i 1.40870 + 1.02348i
\(153\) −1477.84 −0.780889
\(154\) 0 0
\(155\) 467.939 0.242489
\(156\) −18.4203 13.3832i −0.00945389 0.00686865i
\(157\) 765.109 2354.76i 0.388932 1.19701i −0.544656 0.838660i \(-0.683340\pi\)
0.933587 0.358350i \(-0.116660\pi\)
\(158\) 1092.65 + 3362.83i 0.550168 + 1.69324i
\(159\) −2199.99 + 1598.38i −1.09730 + 0.797233i
\(160\) −290.985 + 211.413i −0.143777 + 0.104460i
\(161\) −105.701 325.315i −0.0517418 0.159245i
\(162\) −347.359 + 1069.06i −0.168464 + 0.518478i
\(163\) 2204.66 + 1601.78i 1.05940 + 0.769699i 0.973977 0.226646i \(-0.0727760\pi\)
0.0854225 + 0.996345i \(0.472776\pi\)
\(164\) −139.908 −0.0666157
\(165\) 0 0
\(166\) 1207.15 0.564414
\(167\) −2214.52 1608.94i −1.02614 0.745531i −0.0586043 0.998281i \(-0.518665\pi\)
−0.967532 + 0.252750i \(0.918665\pi\)
\(168\) 175.504 540.147i 0.0805979 0.248055i
\(169\) −670.036 2062.16i −0.304978 0.938625i
\(170\) 1353.38 983.288i 0.610585 0.443616i
\(171\) −4058.95 + 2949.00i −1.81518 + 1.31880i
\(172\) 9.55734 + 29.4145i 0.00423686 + 0.0130397i
\(173\) 713.031 2194.48i 0.313357 0.964413i −0.663069 0.748558i \(-0.730746\pi\)
0.976426 0.215854i \(-0.0692536\pi\)
\(174\) −437.998 318.224i −0.190830 0.138646i
\(175\) 294.010 0.127001
\(176\) 0 0
\(177\) −700.610 −0.297520
\(178\) 3291.35 + 2391.31i 1.38594 + 1.00694i
\(179\) −405.478 + 1247.93i −0.169312 + 0.521089i −0.999328 0.0366506i \(-0.988331\pi\)
0.830016 + 0.557739i \(0.188331\pi\)
\(180\) −88.2156 271.500i −0.0365289 0.112424i
\(181\) 649.781 472.094i 0.266839 0.193870i −0.446318 0.894875i \(-0.647265\pi\)
0.713157 + 0.701005i \(0.247265\pi\)
\(182\) −36.3849 + 26.4352i −0.0148188 + 0.0107665i
\(183\) −1809.77 5569.90i −0.731050 2.24994i
\(184\) 802.464 2469.73i 0.321513 0.989516i
\(185\) −157.974 114.775i −0.0627810 0.0456130i
\(186\) −682.242 −0.268949
\(187\) 0 0
\(188\) 184.267 0.0714842
\(189\) 174.495 + 126.778i 0.0671568 + 0.0487922i
\(190\) 1754.99 5401.30i 0.670106 2.06238i
\(191\) 530.967 + 1634.15i 0.201149 + 0.619073i 0.999850 + 0.0173442i \(0.00552110\pi\)
−0.798701 + 0.601729i \(0.794479\pi\)
\(192\) 3473.52 2523.66i 1.30562 0.948591i
\(193\) −1084.23 + 787.740i −0.404377 + 0.293797i −0.771321 0.636446i \(-0.780404\pi\)
0.366945 + 0.930243i \(0.380404\pi\)
\(194\) 1136.71 + 3498.44i 0.420676 + 1.29471i
\(195\) −195.053 + 600.312i −0.0716311 + 0.220458i
\(196\) −144.617 105.070i −0.0527030 0.0382910i
\(197\) −3518.33 −1.27244 −0.636220 0.771508i \(-0.719503\pi\)
−0.636220 + 0.771508i \(0.719503\pi\)
\(198\) 0 0
\(199\) 823.692 0.293417 0.146709 0.989180i \(-0.453132\pi\)
0.146709 + 0.989180i \(0.453132\pi\)
\(200\) 1805.78 + 1311.98i 0.638441 + 0.463855i
\(201\) −838.762 + 2581.44i −0.294337 + 0.905876i
\(202\) −136.314 419.531i −0.0474802 0.146129i
\(203\) 62.1156 45.1296i 0.0214762 0.0156033i
\(204\) 141.669 102.928i 0.0486216 0.0353256i
\(205\) 1198.55 + 3688.76i 0.408343 + 1.25675i
\(206\) −29.3455 + 90.3161i −0.00992522 + 0.0305467i
\(207\) 3230.20 + 2346.88i 1.08461 + 0.788016i
\(208\) −318.461 −0.106160
\(209\) 0 0
\(210\) −988.484 −0.324819
\(211\) 86.8424 + 63.0947i 0.0283340 + 0.0205859i 0.601862 0.798600i \(-0.294426\pi\)
−0.573528 + 0.819186i \(0.694426\pi\)
\(212\) 56.8005 174.814i 0.0184013 0.0566334i
\(213\) 508.032 + 1563.56i 0.163426 + 0.502974i
\(214\) −1839.35 + 1336.36i −0.587547 + 0.426878i
\(215\) 693.655 503.970i 0.220032 0.159863i
\(216\) 506.003 + 1557.32i 0.159394 + 0.490564i
\(217\) 29.8985 92.0182i 0.00935320 0.0287862i
\(218\) −2308.09 1676.93i −0.717082 0.520990i
\(219\) 8012.24 2.47222
\(220\) 0 0
\(221\) −220.873 −0.0672285
\(222\) 230.322 + 167.339i 0.0696315 + 0.0505903i
\(223\) −1215.57 + 3741.15i −0.365026 + 1.12344i 0.584938 + 0.811078i \(0.301119\pi\)
−0.949965 + 0.312358i \(0.898881\pi\)
\(224\) 22.9813 + 70.7290i 0.00685491 + 0.0210972i
\(225\) −2776.48 + 2017.23i −0.822661 + 0.597698i
\(226\) −652.212 + 473.860i −0.191967 + 0.139472i
\(227\) −547.548 1685.18i −0.160097 0.492728i 0.838545 0.544833i \(-0.183407\pi\)
−0.998642 + 0.0521050i \(0.983407\pi\)
\(228\) 183.708 565.396i 0.0533613 0.164229i
\(229\) −1549.57 1125.83i −0.447154 0.324876i 0.341317 0.939948i \(-0.389127\pi\)
−0.788471 + 0.615072i \(0.789127\pi\)
\(230\) −4519.68 −1.29573
\(231\) 0 0
\(232\) 582.892 0.164952
\(233\) −3556.70 2584.09i −1.00003 0.726564i −0.0379350 0.999280i \(-0.512078\pi\)
−0.962095 + 0.272716i \(0.912078\pi\)
\(234\) 162.226 499.280i 0.0453207 0.139483i
\(235\) −1578.56 4858.30i −0.438186 1.34860i
\(236\) 38.3126 27.8357i 0.0105675 0.00767776i
\(237\) 8301.23 6031.19i 2.27520 1.65303i
\(238\) −106.887 328.963i −0.0291110 0.0895945i
\(239\) −1262.18 + 3884.58i −0.341604 + 1.05135i 0.621772 + 0.783198i \(0.286413\pi\)
−0.963377 + 0.268152i \(0.913587\pi\)
\(240\) −5662.65 4114.16i −1.52301 1.10653i
\(241\) 3908.58 1.04471 0.522353 0.852730i \(-0.325054\pi\)
0.522353 + 0.852730i \(0.325054\pi\)
\(242\) 0 0
\(243\) 5157.80 1.36162
\(244\) 320.263 + 232.685i 0.0840276 + 0.0610496i
\(245\) −1531.35 + 4713.02i −0.399325 + 1.22900i
\(246\) −1747.45 5378.11i −0.452901 1.39389i
\(247\) −606.638 + 440.748i −0.156273 + 0.113539i
\(248\) 594.252 431.749i 0.152157 0.110549i
\(249\) −1082.50 3331.59i −0.275505 0.847917i
\(250\) −367.335 + 1130.54i −0.0929293 + 0.286007i
\(251\) −885.786 643.561i −0.222750 0.161838i 0.470813 0.882233i \(-0.343960\pi\)
−0.693564 + 0.720395i \(0.743960\pi\)
\(252\) −59.0258 −0.0147551
\(253\) 0 0
\(254\) −3599.76 −0.889249
\(255\) −3927.40 2853.43i −0.964485 0.700739i
\(256\) −253.197 + 779.261i −0.0618158 + 0.190249i
\(257\) 242.016 + 744.847i 0.0587413 + 0.180787i 0.976122 0.217224i \(-0.0697004\pi\)
−0.917380 + 0.398012i \(0.869700\pi\)
\(258\) −1011.33 + 734.775i −0.244042 + 0.177307i
\(259\) −32.6636 + 23.7315i −0.00783636 + 0.00569345i
\(260\) −13.1844 40.5775i −0.00314486 0.00967888i
\(261\) −276.949 + 852.361i −0.0656809 + 0.202145i
\(262\) 3538.02 + 2570.52i 0.834272 + 0.606134i
\(263\) 6180.06 1.44897 0.724484 0.689292i \(-0.242078\pi\)
0.724484 + 0.689292i \(0.242078\pi\)
\(264\) 0 0
\(265\) −5095.67 −1.18122
\(266\) −950.010 690.223i −0.218981 0.159099i
\(267\) 3648.25 11228.2i 0.836215 2.57360i
\(268\) −56.6952 174.490i −0.0129224 0.0397712i
\(269\) −798.471 + 580.123i −0.180980 + 0.131490i −0.674587 0.738195i \(-0.735678\pi\)
0.493607 + 0.869685i \(0.335678\pi\)
\(270\) 2305.65 1675.15i 0.519693 0.377579i
\(271\) 1414.37 + 4352.98i 0.317036 + 0.975736i 0.974908 + 0.222607i \(0.0714565\pi\)
−0.657873 + 0.753129i \(0.728543\pi\)
\(272\) 756.860 2329.38i 0.168718 0.519262i
\(273\) 105.586 + 76.7129i 0.0234079 + 0.0170069i
\(274\) 4403.18 0.970825
\(275\) 0 0
\(276\) −473.110 −0.103181
\(277\) −459.389 333.766i −0.0996462 0.0723972i 0.536846 0.843680i \(-0.319615\pi\)
−0.636493 + 0.771283i \(0.719615\pi\)
\(278\) −26.8994 + 82.7880i −0.00580331 + 0.0178608i
\(279\) 348.999 + 1074.11i 0.0748890 + 0.230485i
\(280\) 860.998 625.551i 0.183766 0.133514i
\(281\) −4296.70 + 3121.74i −0.912170 + 0.662730i −0.941563 0.336838i \(-0.890643\pi\)
0.0293930 + 0.999568i \(0.490643\pi\)
\(282\) 2301.49 + 7083.27i 0.486000 + 1.49575i
\(283\) −1461.17 + 4497.01i −0.306917 + 0.944593i 0.672038 + 0.740517i \(0.265419\pi\)
−0.978955 + 0.204076i \(0.934581\pi\)
\(284\) −89.9029 65.3183i −0.0187844 0.0136476i
\(285\) −16480.8 −3.42539
\(286\) 0 0
\(287\) 801.960 0.164941
\(288\) −702.301 510.252i −0.143693 0.104399i
\(289\) −993.271 + 3056.97i −0.202172 + 0.622221i
\(290\) −313.498 964.849i −0.0634802 0.195372i
\(291\) 8635.98 6274.40i 1.73969 1.26396i
\(292\) −438.146 + 318.332i −0.0878102 + 0.0637979i
\(293\) 719.675 + 2214.93i 0.143494 + 0.441630i 0.996814 0.0797574i \(-0.0254146\pi\)
−0.853320 + 0.521388i \(0.825415\pi\)
\(294\) 2232.67 6871.46i 0.442898 1.36310i
\(295\) −1062.12 771.674i −0.209623 0.152300i
\(296\) −306.515 −0.0601886
\(297\) 0 0
\(298\) −6634.36 −1.28966
\(299\) 482.776 + 350.757i 0.0933767 + 0.0678421i
\(300\) 125.664 386.753i 0.0241840 0.0744306i
\(301\) −54.7832 168.605i −0.0104905 0.0322865i
\(302\) 5695.17 4137.78i 1.08517 0.788419i
\(303\) −1035.62 + 752.423i −0.196353 + 0.142659i
\(304\) −2569.48 7908.05i −0.484769 1.49197i
\(305\) 3391.27 10437.3i 0.636668 1.95946i
\(306\) 3266.42 + 2373.20i 0.610226 + 0.443355i
\(307\) −1678.07 −0.311962 −0.155981 0.987760i \(-0.549854\pi\)
−0.155981 + 0.987760i \(0.549854\pi\)
\(308\) 0 0
\(309\) 275.578 0.0507349
\(310\) −1034.27 751.443i −0.189493 0.137675i
\(311\) 1104.03 3397.85i 0.201298 0.619531i −0.798547 0.601932i \(-0.794398\pi\)
0.999845 0.0175989i \(-0.00560221\pi\)
\(312\) 306.181 + 942.327i 0.0555579 + 0.170990i
\(313\) −5812.27 + 4222.86i −1.04961 + 0.762589i −0.972139 0.234405i \(-0.924686\pi\)
−0.0774746 + 0.996994i \(0.524686\pi\)
\(314\) −5472.52 + 3976.02i −0.983541 + 0.714585i
\(315\) 505.656 + 1556.25i 0.0904460 + 0.278364i
\(316\) −214.326 + 659.627i −0.0381544 + 0.117427i
\(317\) 12.7078 + 9.23273i 0.00225154 + 0.00163584i 0.588910 0.808198i \(-0.299557\pi\)
−0.586659 + 0.809834i \(0.699557\pi\)
\(318\) 7429.36 1.31012
\(319\) 0 0
\(320\) 8045.47 1.40549
\(321\) 5337.64 + 3878.02i 0.928094 + 0.674299i
\(322\) −288.781 + 888.777i −0.0499787 + 0.153819i
\(323\) −1782.10 5484.73i −0.306992 0.944825i
\(324\) −178.381 + 129.601i −0.0305865 + 0.0222224i
\(325\) −414.964 + 301.489i −0.0708248 + 0.0514572i
\(326\) −2300.67 7080.74i −0.390866 1.20296i
\(327\) −2558.38 + 7873.87i −0.432656 + 1.33158i
\(328\) 4925.56 + 3578.63i 0.829172 + 0.602429i
\(329\) −1056.23 −0.176996
\(330\) 0 0
\(331\) −1318.95 −0.219022 −0.109511 0.993986i \(-0.534928\pi\)
−0.109511 + 0.993986i \(0.534928\pi\)
\(332\) 191.563 + 139.179i 0.0316668 + 0.0230073i
\(333\) 145.634 448.216i 0.0239661 0.0737600i
\(334\) 2310.96 + 7112.41i 0.378594 + 1.16519i
\(335\) −4114.84 + 2989.61i −0.671098 + 0.487581i
\(336\) −1170.84 + 850.667i −0.190103 + 0.138118i
\(337\) −73.9116 227.477i −0.0119472 0.0367698i 0.944905 0.327344i \(-0.106154\pi\)
−0.956852 + 0.290574i \(0.906154\pi\)
\(338\) −1830.57 + 5633.92i −0.294586 + 0.906642i
\(339\) 1892.67 + 1375.10i 0.303232 + 0.220311i
\(340\) 328.137 0.0523404
\(341\) 0 0
\(342\) 13707.1 2.16723
\(343\) 1681.35 + 1221.57i 0.264678 + 0.192300i
\(344\) 415.904 1280.02i 0.0651861 0.200622i
\(345\) 4052.99 + 12473.8i 0.632481 + 1.94658i
\(346\) −5100.02 + 3705.38i −0.792425 + 0.575730i
\(347\) 4743.10 3446.06i 0.733784 0.533125i −0.156975 0.987603i \(-0.550174\pi\)
0.890758 + 0.454478i \(0.150174\pi\)
\(348\) −32.8163 100.998i −0.00505500 0.0155577i
\(349\) 1079.00 3320.83i 0.165495 0.509341i −0.833577 0.552403i \(-0.813711\pi\)
0.999072 + 0.0430615i \(0.0137111\pi\)
\(350\) −649.844 472.139i −0.0992446 0.0721054i
\(351\) −376.283 −0.0572208
\(352\) 0 0
\(353\) −10916.7 −1.64600 −0.822999 0.568043i \(-0.807701\pi\)
−0.822999 + 0.568043i \(0.807701\pi\)
\(354\) 1548.54 + 1125.08i 0.232497 + 0.168919i
\(355\) −951.984 + 2929.91i −0.142327 + 0.438037i
\(356\) 246.600 + 758.956i 0.0367128 + 0.112990i
\(357\) −812.053 + 589.991i −0.120388 + 0.0874668i
\(358\) 2900.22 2107.13i 0.428161 0.311077i
\(359\) −3553.92 10937.8i −0.522476 1.60802i −0.769254 0.638943i \(-0.779372\pi\)
0.246778 0.969072i \(-0.420628\pi\)
\(360\) −3838.85 + 11814.8i −0.562014 + 1.72970i
\(361\) −10290.3 7476.31i −1.50026 1.09000i
\(362\) −2194.31 −0.318592
\(363\) 0 0
\(364\) −8.82180 −0.00127030
\(365\) 12146.5 + 8824.94i 1.74185 + 1.26553i
\(366\) −4944.39 + 15217.3i −0.706140 + 2.17328i
\(367\) 2091.12 + 6435.80i 0.297427 + 0.915385i 0.982396 + 0.186813i \(0.0598157\pi\)
−0.684969 + 0.728572i \(0.740184\pi\)
\(368\) −5353.48 + 3889.53i −0.758342 + 0.550967i
\(369\) −7573.29 + 5502.31i −1.06843 + 0.776258i
\(370\) 164.854 + 507.368i 0.0231631 + 0.0712887i
\(371\) −325.584 + 1002.04i −0.0455619 + 0.140225i
\(372\) −108.265 78.6595i −0.0150895 0.0109632i
\(373\) −5310.22 −0.737139 −0.368569 0.929600i \(-0.620152\pi\)
−0.368569 + 0.929600i \(0.620152\pi\)
\(374\) 0 0
\(375\) 3449.58 0.475028
\(376\) −6487.24 4713.25i −0.889770 0.646456i
\(377\) −41.3919 + 127.391i −0.00565462 + 0.0174031i
\(378\) −182.094 560.428i −0.0247775 0.0762574i
\(379\) 678.172 492.721i 0.0919139 0.0667794i −0.540879 0.841100i \(-0.681908\pi\)
0.632793 + 0.774321i \(0.281908\pi\)
\(380\) 901.246 654.793i 0.121666 0.0883952i
\(381\) 3228.07 + 9934.96i 0.434065 + 1.33592i
\(382\) 1450.63 4464.58i 0.194295 0.597978i
\(383\) 2291.27 + 1664.70i 0.305688 + 0.222095i 0.730044 0.683400i \(-0.239500\pi\)
−0.424356 + 0.905495i \(0.639500\pi\)
\(384\) −10194.5 −1.35479
\(385\) 0 0
\(386\) 3661.45 0.482806
\(387\) 1674.16 + 1216.35i 0.219903 + 0.159769i
\(388\) −222.969 + 686.227i −0.0291740 + 0.0897884i
\(389\) 961.431 + 2958.98i 0.125312 + 0.385671i 0.993958 0.109763i \(-0.0350090\pi\)
−0.868646 + 0.495434i \(0.835009\pi\)
\(390\) 1395.14 1013.63i 0.181143 0.131608i
\(391\) −3712.98 + 2697.64i −0.480239 + 0.348914i
\(392\) 2403.81 + 7398.16i 0.309721 + 0.953223i
\(393\) 3921.66 12069.6i 0.503363 1.54919i
\(394\) 7776.48 + 5649.94i 0.994348 + 0.722436i
\(395\) 19227.5 2.44922
\(396\) 0 0
\(397\) 14208.7 1.79626 0.898131 0.439728i \(-0.144925\pi\)
0.898131 + 0.439728i \(0.144925\pi\)
\(398\) −1820.59 1322.73i −0.229291 0.166590i
\(399\) −1053.03 + 3240.88i −0.132123 + 0.406634i
\(400\) −1757.62 5409.41i −0.219703 0.676177i
\(401\) 5065.81 3680.52i 0.630859 0.458346i −0.225839 0.974165i \(-0.572512\pi\)
0.856698 + 0.515819i \(0.172512\pi\)
\(402\) 5999.33 4358.77i 0.744327 0.540785i
\(403\) 52.1603 + 160.533i 0.00644737 + 0.0198429i
\(404\) 26.7383 82.2919i 0.00329277 0.0101341i
\(405\) 4945.15 + 3592.86i 0.606732 + 0.440816i
\(406\) −209.764 −0.0256415
\(407\) 0 0
\(408\) −7620.30 −0.924660
\(409\) 3391.80 + 2464.29i 0.410059 + 0.297925i 0.773625 0.633643i \(-0.218441\pi\)
−0.363567 + 0.931568i \(0.618441\pi\)
\(410\) 3274.50 10077.9i 0.394429 1.21393i
\(411\) −3948.53 12152.3i −0.473884 1.45847i
\(412\) −15.0699 + 10.9489i −0.00180204 + 0.00130926i
\(413\) −219.610 + 159.556i −0.0261653 + 0.0190102i
\(414\) −3370.88 10374.5i −0.400168 1.23159i
\(415\) 2028.46 6242.97i 0.239936 0.738446i
\(416\) −104.964 76.2606i −0.0123708 0.00898794i
\(417\) 252.608 0.0296649
\(418\) 0 0
\(419\) −9287.15 −1.08283 −0.541416 0.840755i \(-0.682112\pi\)
−0.541416 + 0.840755i \(0.682112\pi\)
\(420\) −156.863 113.968i −0.0182241 0.0132406i
\(421\) 4062.34 12502.6i 0.470276 1.44736i −0.381947 0.924184i \(-0.624746\pi\)
0.852224 0.523178i \(-0.175254\pi\)
\(422\) −90.6245 278.913i −0.0104539 0.0321737i
\(423\) 9974.44 7246.85i 1.14651 0.832988i
\(424\) −6471.18 + 4701.58i −0.741198 + 0.538512i
\(425\) −1219.02 3751.77i −0.139132 0.428206i
\(426\) 1387.97 4271.73i 0.157857 0.485835i
\(427\) −1835.76 1333.76i −0.208053 0.151160i
\(428\) −445.964 −0.0503656
\(429\) 0 0
\(430\) −2342.47 −0.262707
\(431\) −3972.00 2885.83i −0.443909 0.322519i 0.343277 0.939234i \(-0.388463\pi\)
−0.787186 + 0.616715i \(0.788463\pi\)
\(432\) 1289.40 3968.37i 0.143603 0.441964i
\(433\) −3628.88 11168.5i −0.402755 1.23955i −0.922755 0.385386i \(-0.874068\pi\)
0.520000 0.854166i \(-0.325932\pi\)
\(434\) −213.852 + 155.373i −0.0236526 + 0.0171846i
\(435\) −2381.75 + 1730.44i −0.262520 + 0.190732i
\(436\) −172.931 532.226i −0.0189951 0.0584610i
\(437\) −4814.78 + 14818.4i −0.527053 + 1.62210i
\(438\) −17709.3 12866.5i −1.93192 1.40362i
\(439\) −11824.2 −1.28551 −0.642754 0.766073i \(-0.722208\pi\)
−0.642754 + 0.766073i \(0.722208\pi\)
\(440\) 0 0
\(441\) −11960.4 −1.29148
\(442\) 488.189 + 354.690i 0.0525357 + 0.0381695i
\(443\) 3121.72 9607.68i 0.334803 1.03042i −0.632016 0.774955i \(-0.717772\pi\)
0.966819 0.255462i \(-0.0822275\pi\)
\(444\) 17.2565 + 53.1102i 0.00184450 + 0.00567680i
\(445\) 17897.8 13003.5i 1.90660 1.38522i
\(446\) 8694.52 6316.94i 0.923088 0.670663i
\(447\) 5949.32 + 18310.1i 0.629515 + 1.93745i
\(448\) 514.058 1582.11i 0.0542120 0.166847i
\(449\) 279.316 + 202.935i 0.0293580 + 0.0213299i 0.602368 0.798219i \(-0.294224\pi\)
−0.573009 + 0.819549i \(0.694224\pi\)
\(450\) 9376.17 0.982216
\(451\) 0 0
\(452\) −158.134 −0.0164557
\(453\) −16526.9 12007.5i −1.71414 1.24539i
\(454\) −1495.93 + 4603.99i −0.154642 + 0.475939i
\(455\) 75.5738 + 232.592i 0.00778671 + 0.0239650i
\(456\) −20929.5 + 15206.2i −2.14938 + 1.56161i
\(457\) 8549.00 6211.21i 0.875067 0.635773i −0.0568749 0.998381i \(-0.518114\pi\)
0.931942 + 0.362608i \(0.118114\pi\)
\(458\) 1617.05 + 4976.77i 0.164978 + 0.507749i
\(459\) 894.281 2752.31i 0.0909400 0.279885i
\(460\) −717.231 521.099i −0.0726980 0.0528182i
\(461\) 4733.96 0.478270 0.239135 0.970986i \(-0.423136\pi\)
0.239135 + 0.970986i \(0.423136\pi\)
\(462\) 0 0
\(463\) 3431.20 0.344409 0.172204 0.985061i \(-0.444911\pi\)
0.172204 + 0.985061i \(0.444911\pi\)
\(464\) −1201.66 873.058i −0.120228 0.0873506i
\(465\) −1146.43 + 3528.34i −0.114332 + 0.351877i
\(466\) 3711.59 + 11423.1i 0.368962 + 1.13555i
\(467\) −4139.71 + 3007.67i −0.410199 + 0.298027i −0.773682 0.633574i \(-0.781587\pi\)
0.363483 + 0.931601i \(0.381587\pi\)
\(468\) 83.3085 60.5272i 0.00822850 0.00597835i
\(469\) 324.980 + 1000.19i 0.0319961 + 0.0984739i
\(470\) −4312.70 + 13273.1i −0.423255 + 1.30265i
\(471\) 15880.8 + 11538.1i 1.55361 + 1.12876i
\(472\) −2060.82 −0.200968
\(473\) 0 0
\(474\) −28033.2 −2.71648
\(475\) −10834.7 7871.87i −1.04659 0.760392i
\(476\) 20.9661 64.5269i 0.00201886 0.00621341i
\(477\) −3800.46 11696.6i −0.364804 1.12275i
\(478\) 9027.85 6559.12i 0.863858 0.627630i
\(479\) −9357.81 + 6798.85i −0.892629 + 0.648533i −0.936562 0.350502i \(-0.886011\pi\)
0.0439333 + 0.999034i \(0.486011\pi\)
\(480\) −881.191 2712.03i −0.0837931 0.257889i
\(481\) 21.7660 66.9889i 0.00206329 0.00635017i
\(482\) −8639.05 6276.64i −0.816386 0.593139i
\(483\) 2711.89 0.255477
\(484\) 0 0
\(485\) 20002.9 1.87275
\(486\) −11400.2 8282.71i −1.06404 0.773068i
\(487\) −5663.21 + 17429.6i −0.526950 + 1.62179i 0.233477 + 0.972362i \(0.424990\pi\)
−0.760427 + 0.649423i \(0.775010\pi\)
\(488\) −5323.37 16383.7i −0.493807 1.51978i
\(489\) −17479.0 + 12699.2i −1.61641 + 1.17439i
\(490\) 10953.2 7957.94i 1.00982 0.733679i
\(491\) −2353.96 7244.75i −0.216360 0.665888i −0.999054 0.0434814i \(-0.986155\pi\)
0.782694 0.622407i \(-0.213845\pi\)
\(492\) 342.767 1054.93i 0.0314088 0.0966665i
\(493\) −833.427 605.520i −0.0761372 0.0553169i
\(494\) 2048.62 0.186582
\(495\) 0 0
\(496\) −1871.75 −0.169444
\(497\) 515.328 + 374.408i 0.0465103 + 0.0337917i
\(498\) −2957.45 + 9102.09i −0.266117 + 0.819024i
\(499\) 3989.14 + 12277.3i 0.357872 + 1.10142i 0.954325 + 0.298770i \(0.0965763\pi\)
−0.596453 + 0.802648i \(0.703424\pi\)
\(500\) −188.639 + 137.054i −0.0168724 + 0.0122585i
\(501\) 17557.2 12756.0i 1.56566 1.13752i
\(502\) 924.363 + 2844.90i 0.0821839 + 0.252936i
\(503\) 3141.36 9668.11i 0.278462 0.857017i −0.709821 0.704382i \(-0.751224\pi\)
0.988283 0.152635i \(-0.0487759\pi\)
\(504\) 2078.04 + 1509.79i 0.183658 + 0.133435i
\(505\) −2398.74 −0.211371
\(506\) 0 0
\(507\) 17190.6 1.50584
\(508\) −571.249 415.037i −0.0498919 0.0362486i
\(509\) 1993.14 6134.25i 0.173564 0.534177i −0.826001 0.563669i \(-0.809389\pi\)
0.999565 + 0.0294928i \(0.00938922\pi\)
\(510\) 4098.44 + 12613.7i 0.355847 + 1.09519i
\(511\) 2511.48 1824.70i 0.217419 0.157964i
\(512\) 10133.3 7362.24i 0.874670 0.635485i
\(513\) −3036.02 9343.89i −0.261293 0.804177i
\(514\) 661.199 2034.96i 0.0567398 0.174627i
\(515\) 417.774 + 303.530i 0.0357462 + 0.0259712i
\(516\) −245.205 −0.0209197
\(517\) 0 0
\(518\) 110.305 0.00935623
\(519\) 14799.9 + 10752.7i 1.25172 + 0.909428i
\(520\) −573.742 + 1765.80i −0.0483851 + 0.148914i
\(521\) −5972.50 18381.5i −0.502227 1.54569i −0.805383 0.592754i \(-0.798041\pi\)
0.303157 0.952941i \(-0.401959\pi\)
\(522\) 1980.90 1439.21i 0.166096 0.120675i
\(523\) −5063.71 + 3679.00i −0.423367 + 0.307594i −0.778991 0.627035i \(-0.784268\pi\)
0.355624 + 0.934629i \(0.384268\pi\)
\(524\) 265.081 + 815.835i 0.0220994 + 0.0680151i
\(525\) −720.310 + 2216.89i −0.0598799 + 0.184291i
\(526\) −13659.6 9924.30i −1.13230 0.822662i
\(527\) −1298.18 −0.107305
\(528\) 0 0
\(529\) 232.675 0.0191235
\(530\) 11262.8 + 8182.93i 0.923069 + 0.670649i
\(531\) 979.153 3013.52i 0.0800219 0.246282i
\(532\) −71.1781 219.064i −0.00580068 0.0178527i
\(533\) −1131.88 + 822.358i −0.0919834 + 0.0668298i
\(534\) −26094.5 + 18958.8i −2.11464 + 1.53638i
\(535\) 3820.44 + 11758.1i 0.308733 + 0.950181i
\(536\) −2467.19 + 7593.22i −0.198818 + 0.611898i
\(537\) −8416.22 6114.75i −0.676326 0.491379i
\(538\) 2696.44 0.216081
\(539\) 0 0
\(540\) 559.022 0.0445490
\(541\) 11332.8 + 8233.79i 0.900623 + 0.654341i 0.938626 0.344937i \(-0.112100\pi\)
−0.0380030 + 0.999278i \(0.512100\pi\)
\(542\) 3864.12 11892.6i 0.306233 0.942489i
\(543\) 1967.74 + 6056.07i 0.155513 + 0.478620i
\(544\) 807.265 586.512i 0.0636235 0.0462252i
\(545\) −12551.0 + 9118.84i −0.986470 + 0.716712i
\(546\) −110.185 339.113i −0.00863638 0.0265801i
\(547\) −1529.46 + 4707.20i −0.119552 + 0.367944i −0.992869 0.119208i \(-0.961964\pi\)
0.873317 + 0.487152i \(0.161964\pi\)
\(548\) 698.744 + 507.667i 0.0544687 + 0.0395738i
\(549\) 26487.0 2.05909
\(550\) 0 0
\(551\) −3497.35 −0.270404
\(552\) 16656.2 + 12101.4i 1.28430 + 0.933100i
\(553\) 1228.53 3781.02i 0.0944707 0.290751i
\(554\) 479.395 + 1475.43i 0.0367645 + 0.113150i
\(555\) 1252.45 909.958i 0.0957901 0.0695956i
\(556\) −13.8138 + 10.0363i −0.00105366 + 0.000765528i
\(557\) −1174.75 3615.51i −0.0893641 0.275034i 0.896380 0.443287i \(-0.146188\pi\)
−0.985744 + 0.168252i \(0.946188\pi\)
\(558\) 953.483 2934.52i 0.0723372 0.222631i
\(559\) 250.214 + 181.791i 0.0189319 + 0.0137548i
\(560\) −2711.94 −0.204644
\(561\) 0 0
\(562\) 14510.0 1.08908
\(563\) 8009.36 + 5819.14i 0.599564 + 0.435608i 0.845724 0.533621i \(-0.179169\pi\)
−0.246160 + 0.969229i \(0.579169\pi\)
\(564\) −451.444 + 1389.40i −0.0337043 + 0.103731i
\(565\) 1354.69 + 4169.29i 0.100871 + 0.310449i
\(566\) 10451.2 7593.21i 0.776139 0.563898i
\(567\) 1022.49 742.880i 0.0757327 0.0550230i
\(568\) 1494.36 + 4599.15i 0.110390 + 0.339747i
\(569\) 1646.80 5068.33i 0.121331 0.373419i −0.871884 0.489713i \(-0.837102\pi\)
0.993215 + 0.116294i \(0.0371015\pi\)
\(570\) 36427.1 + 26465.8i 2.67678 + 1.94479i
\(571\) −16962.6 −1.24319 −0.621597 0.783337i \(-0.713516\pi\)
−0.621597 + 0.783337i \(0.713516\pi\)
\(572\) 0 0
\(573\) −13622.6 −0.993181
\(574\) −1772.55 1287.83i −0.128893 0.0936466i
\(575\) −3293.50 + 10136.3i −0.238867 + 0.735156i
\(576\) 6000.49 + 18467.6i 0.434063 + 1.33591i
\(577\) 12529.2 9103.01i 0.903983 0.656782i −0.0355028 0.999370i \(-0.511303\pi\)
0.939486 + 0.342587i \(0.111303\pi\)
\(578\) 7104.47 5161.70i 0.511258 0.371451i
\(579\) −3283.38 10105.2i −0.235670 0.725317i
\(580\) 61.4935 189.257i 0.00440238 0.0135491i
\(581\) −1098.05 797.778i −0.0784074 0.0569663i
\(582\) −29163.7 −2.07710
\(583\) 0 0
\(584\) 23567.7 1.66993
\(585\) −2309.51 1677.96i −0.163225 0.118590i
\(586\) 1966.19 6051.30i 0.138605 0.426582i
\(587\) 3425.19 + 10541.7i 0.240839 + 0.741228i 0.996293 + 0.0860254i \(0.0274166\pi\)
−0.755453 + 0.655202i \(0.772583\pi\)
\(588\) 1146.55 833.019i 0.0804133 0.0584237i
\(589\) −3565.51 + 2590.50i −0.249430 + 0.181222i
\(590\) 1108.37 + 3411.22i 0.0773407 + 0.238030i
\(591\) 8619.73 26528.8i 0.599946 1.84644i
\(592\) 631.896 + 459.099i 0.0438695 + 0.0318731i
\(593\) 4349.68 0.301214 0.150607 0.988594i \(-0.451877\pi\)
0.150607 + 0.988594i \(0.451877\pi\)
\(594\) 0 0
\(595\) −1880.90 −0.129596
\(596\) −1052.81 764.911i −0.0723570 0.0525705i
\(597\) −2018.00 + 6210.78i −0.138344 + 0.425779i
\(598\) −503.801 1550.54i −0.0344514 0.106031i
\(599\) −10666.0 + 7749.31i −0.727548 + 0.528595i −0.888787 0.458321i \(-0.848451\pi\)
0.161239 + 0.986915i \(0.448451\pi\)
\(600\) −14316.6 + 10401.6i −0.974123 + 0.707742i
\(601\) −5798.71 17846.6i −0.393568 1.21128i −0.930071 0.367379i \(-0.880255\pi\)
0.536503 0.843898i \(-0.319745\pi\)
\(602\) −149.670 + 460.638i −0.0101331 + 0.0311864i
\(603\) −9931.30 7215.51i −0.670703 0.487294i
\(604\) 1380.84 0.0930223
\(605\) 0 0
\(606\) 3497.29 0.234435
\(607\) −17694.3 12855.7i −1.18318 0.859629i −0.190652 0.981658i \(-0.561060\pi\)
−0.992527 + 0.122028i \(0.961060\pi\)
\(608\) 1046.82 3221.77i 0.0698257 0.214901i
\(609\) 188.105 + 578.927i 0.0125162 + 0.0385210i
\(610\) −24256.4 + 17623.3i −1.61002 + 1.16975i
\(611\) 1490.75 1083.09i 0.0987057 0.0717139i
\(612\) 244.732 + 753.208i 0.0161646 + 0.0497494i
\(613\) −1090.17 + 3355.19i −0.0718294 + 0.221068i −0.980526 0.196389i \(-0.937079\pi\)
0.908697 + 0.417457i \(0.137079\pi\)
\(614\) 3708.99 + 2694.74i 0.243783 + 0.177119i
\(615\) −30750.2 −2.01621
\(616\) 0 0
\(617\) −22728.1 −1.48298 −0.741490 0.670963i \(-0.765881\pi\)
−0.741490 + 0.670963i \(0.765881\pi\)
\(618\) −609.103 442.540i −0.0396468 0.0288051i
\(619\) −6626.35 + 20393.8i −0.430267 + 1.32423i 0.467592 + 0.883944i \(0.345121\pi\)
−0.897860 + 0.440282i \(0.854879\pi\)
\(620\) −77.4914 238.494i −0.00501956 0.0154486i
\(621\) −6325.50 + 4595.75i −0.408750 + 0.296974i
\(622\) −7896.67 + 5737.26i −0.509047 + 0.369845i
\(623\) −1413.52 4350.37i −0.0909013 0.279766i
\(624\) 780.213 2401.25i 0.0500537 0.154050i
\(625\) 14908.7 + 10831.8i 0.954156 + 0.693235i
\(626\) 19628.0 1.25319
\(627\) 0 0
\(628\) −1326.85 −0.0843109
\(629\) 438.259 + 318.414i 0.0277815 + 0.0201844i
\(630\) 1381.48 4251.75i 0.0873642 0.268879i
\(631\) 6653.74 + 20478.1i 0.419780 + 1.29195i 0.907905 + 0.419177i \(0.137681\pi\)
−0.488124 + 0.872774i \(0.662319\pi\)
\(632\) 24417.7 17740.5i 1.53684 1.11658i
\(633\) −688.504 + 500.228i −0.0432316 + 0.0314096i
\(634\) −13.2612 40.8138i −0.000830709 0.00255666i
\(635\) −6048.97 + 18616.8i −0.378025 + 1.16344i
\(636\) 1178.97 + 856.571i 0.0735050 + 0.0534045i
\(637\) −1787.56 −0.111187
\(638\) 0 0
\(639\) −7435.33 −0.460309
\(640\) −15454.8 11228.6i −0.954540 0.693514i
\(641\) 6226.16 19162.1i 0.383648 1.18075i −0.553808 0.832644i \(-0.686826\pi\)
0.937456 0.348103i \(-0.113174\pi\)
\(642\) −5570.10 17143.0i −0.342421 1.05386i
\(643\) −23356.1 + 16969.2i −1.43246 + 1.04074i −0.442911 + 0.896566i \(0.646054\pi\)
−0.989552 + 0.144179i \(0.953946\pi\)
\(644\) −148.299 + 107.745i −0.00907421 + 0.00659280i
\(645\) 2100.60 + 6464.98i 0.128234 + 0.394664i
\(646\) −4868.78 + 14984.6i −0.296532 + 0.912631i
\(647\) 1286.35 + 934.591i 0.0781636 + 0.0567891i 0.626181 0.779678i \(-0.284617\pi\)
−0.548017 + 0.836467i \(0.684617\pi\)
\(648\) 9595.02 0.581679
\(649\) 0 0
\(650\) 1401.33 0.0845612
\(651\) 620.583 + 450.880i 0.0373619 + 0.0271450i
\(652\) 451.282 1388.90i 0.0271067 0.0834259i
\(653\) 6189.01 + 19047.8i 0.370896 + 1.14150i 0.946206 + 0.323564i \(0.104881\pi\)
−0.575311 + 0.817935i \(0.695119\pi\)
\(654\) 18299.0 13295.0i 1.09411 0.794919i
\(655\) 19239.1 13978.0i 1.14769 0.833842i
\(656\) −4794.20 14755.0i −0.285338 0.878182i
\(657\) −11197.7 + 34462.9i −0.664937 + 2.04646i
\(658\) 2334.55 + 1696.15i 0.138313 + 0.100491i
\(659\) −10520.7 −0.621897 −0.310948 0.950427i \(-0.600647\pi\)
−0.310948 + 0.950427i \(0.600647\pi\)
\(660\) 0 0
\(661\) 3295.83 0.193938 0.0969690 0.995287i \(-0.469085\pi\)
0.0969690 + 0.995287i \(0.469085\pi\)
\(662\) 2915.25 + 2118.05i 0.171155 + 0.124351i
\(663\) 541.127 1665.42i 0.0316978 0.0975557i
\(664\) −3184.13 9799.76i −0.186097 0.572748i
\(665\) −5165.99 + 3753.31i −0.301246 + 0.218868i
\(666\) −1041.66 + 756.813i −0.0606060 + 0.0440329i
\(667\) 860.078 + 2647.05i 0.0499286 + 0.153664i
\(668\) −453.301 + 1395.12i −0.0262556 + 0.0808064i
\(669\) −25230.8 18331.3i −1.45812 1.05938i
\(670\) 13895.8 0.801257
\(671\) 0 0
\(672\) −589.612 −0.0338464
\(673\) 960.819 + 698.076i 0.0550325 + 0.0399834i 0.614961 0.788557i \(-0.289172\pi\)
−0.559929 + 0.828541i \(0.689172\pi\)
\(674\) −201.930 + 621.477i −0.0115402 + 0.0355169i
\(675\) −2076.75 6391.59i −0.118421 0.364463i
\(676\) −940.060 + 682.994i −0.0534855 + 0.0388595i
\(677\) −10696.3 + 7771.33i −0.607227 + 0.441177i −0.848437 0.529297i \(-0.822456\pi\)
0.241210 + 0.970473i \(0.422456\pi\)
\(678\) −1975.10 6078.72i −0.111878 0.344324i
\(679\) 1278.07 3933.49i 0.0722353 0.222317i
\(680\) −11552.3 8393.24i −0.651487 0.473333i
\(681\) 14048.0 0.790485
\(682\) 0 0
\(683\) −13831.4 −0.774882 −0.387441 0.921894i \(-0.626641\pi\)
−0.387441 + 0.921894i \(0.626641\pi\)
\(684\) 2175.18 + 1580.36i 0.121594 + 0.0883432i
\(685\) 7399.02 22771.8i 0.412704 1.27017i
\(686\) −1754.58 5400.03i −0.0976532 0.300546i
\(687\) 12285.3 8925.78i 0.682260 0.495691i
\(688\) −2774.62 + 2015.88i −0.153752 + 0.111707i
\(689\) −568.005 1748.14i −0.0314068 0.0966602i
\(690\) 11073.0 34079.2i 0.610930 1.88025i
\(691\) 7942.18 + 5770.33i 0.437243 + 0.317675i 0.784538 0.620080i \(-0.212900\pi\)
−0.347296 + 0.937756i \(0.612900\pi\)
\(692\) −1236.54 −0.0679280
\(693\) 0 0
\(694\) −16017.4 −0.876101
\(695\) 382.951 + 278.230i 0.0209010 + 0.0151854i
\(696\) −1428.06 + 4395.11i −0.0777735 + 0.239362i
\(697\) −3325.08 10233.5i −0.180698 0.556130i
\(698\) −7717.68 + 5607.22i −0.418508 + 0.304064i
\(699\) 28198.2 20487.2i 1.52583 1.10858i
\(700\) −48.6886 149.848i −0.00262894 0.00809104i
\(701\) 9254.98 28483.9i 0.498653 1.53470i −0.312532 0.949907i \(-0.601177\pi\)
0.811185 0.584789i \(-0.198823\pi\)
\(702\) 831.689 + 604.258i 0.0447152 + 0.0324875i
\(703\) 1839.09 0.0986667
\(704\) 0 0
\(705\) 40499.8 2.16356
\(706\) 24128.9 + 17530.7i 1.28627 + 0.934527i
\(707\) −153.265 + 471.702i −0.00815294 + 0.0250922i
\(708\) 116.022 + 357.080i 0.00615873 + 0.0189546i
\(709\) −9147.95 + 6646.38i −0.484568 + 0.352059i −0.803091 0.595856i \(-0.796813\pi\)
0.318524 + 0.947915i \(0.396813\pi\)
\(710\) 6809.16 4947.15i 0.359920 0.261497i
\(711\) 14340.3 + 44135.0i 0.756405 + 2.32798i
\(712\) 10731.2 33027.2i 0.564843 1.73841i
\(713\) 2837.51 + 2061.57i 0.149040 + 0.108284i
\(714\) 2742.30 0.143737
\(715\) 0 0
\(716\) 703.181 0.0367027
\(717\) −26198.1 19034.1i −1.36456 0.991409i
\(718\) −9709.49 + 29882.8i −0.504673 + 1.55322i
\(719\) −10081.2 31026.7i −0.522900 1.60932i −0.768431 0.639933i \(-0.778962\pi\)
0.245531 0.969389i \(-0.421038\pi\)
\(720\) 25610.1 18606.9i 1.32560 0.963106i
\(721\) 86.3813 62.7597i 0.00446187 0.00324174i
\(722\) 10738.4 + 33049.4i 0.553521 + 1.70356i
\(723\) −9575.83 + 29471.4i −0.492571 + 1.51598i
\(724\) −348.217 252.994i −0.0178748 0.0129868i
\(725\) −2392.33 −0.122550
\(726\) 0 0
\(727\) −502.545 −0.0256373 −0.0128187 0.999918i \(-0.504080\pi\)
−0.0128187 + 0.999918i \(0.504080\pi\)
\(728\) 310.578 + 225.648i 0.0158115 + 0.0114877i
\(729\) −9203.52 + 28325.5i −0.467587 + 1.43909i
\(730\) −12675.5 39011.1i −0.642658 1.97790i
\(731\) −1924.37 + 1398.14i −0.0973673 + 0.0707415i
\(732\) −2539.11 + 1844.77i −0.128208 + 0.0931485i
\(733\) 2667.24 + 8208.93i 0.134402 + 0.413647i 0.995497 0.0947978i \(-0.0302204\pi\)
−0.861094 + 0.508445i \(0.830220\pi\)
\(734\) 5713.05 17582.9i 0.287292 0.884194i
\(735\) −31785.2 23093.3i −1.59512 1.15893i
\(736\) −2695.90 −0.135017
\(737\) 0 0
\(738\) 25575.0 1.27565
\(739\) 14851.5 + 10790.3i 0.739273 + 0.537113i 0.892483 0.451080i \(-0.148961\pi\)
−0.153210 + 0.988194i \(0.548961\pi\)
\(740\) −32.3365 + 99.5214i −0.00160637 + 0.00494389i
\(741\) −1837.08 5653.96i −0.0910755 0.280302i
\(742\) 2328.77 1691.95i 0.115218 0.0837108i
\(743\) −9046.95 + 6572.99i −0.446703 + 0.324549i −0.788293 0.615300i \(-0.789035\pi\)
0.341590 + 0.939849i \(0.389035\pi\)
\(744\) 1799.58 + 5538.53i 0.0886770 + 0.272920i
\(745\) −11148.2 + 34310.7i −0.548241 + 1.68731i
\(746\) 11737.0 + 8527.47i 0.576037 + 0.418516i
\(747\) 15843.0 0.775991
\(748\) 0 0
\(749\) 2556.29 0.124706
\(750\) −7624.52 5539.54i −0.371211 0.269701i
\(751\) 5170.90 15914.4i 0.251250 0.773269i −0.743295 0.668964i \(-0.766738\pi\)
0.994545 0.104305i \(-0.0332618\pi\)
\(752\) 6314.23 + 19433.2i 0.306192 + 0.942361i
\(753\) 7022.69 5102.29i 0.339869 0.246929i
\(754\) 296.060 215.100i 0.0142995 0.0103892i
\(755\) −11829.2 36406.6i −0.570211 1.75493i
\(756\) 35.7182 109.929i 0.00171833 0.00528848i
\(757\) 19742.0 + 14343.4i 0.947865 + 0.688664i 0.950301 0.311333i \(-0.100775\pi\)
−0.00243609 + 0.999997i \(0.500775\pi\)
\(758\) −2290.19 −0.109741
\(759\) 0 0
\(760\) −48477.6 −2.31377
\(761\) −6851.83 4978.15i −0.326385 0.237132i 0.412510 0.910953i \(-0.364652\pi\)
−0.738895 + 0.673821i \(0.764652\pi\)
\(762\) 8819.24 27142.8i 0.419275 1.29039i
\(763\) 991.247 + 3050.74i 0.0470322 + 0.144750i
\(764\) 744.947 541.236i 0.0352765 0.0256299i
\(765\) 17762.2 12905.0i 0.839471 0.609911i
\(766\) −2391.06 7358.91i −0.112784 0.347113i
\(767\) 146.341 450.391i 0.00688927 0.0212030i
\(768\)