Properties

Label 147.4.o.a.101.49
Level $147$
Weight $4$
Character 147.101
Analytic conductor $8.673$
Analytic rank $0$
Dimension $648$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [147,4,Mod(5,147)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(147, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([21, 29]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("147.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.o (of order \(42\), degree \(12\), 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: \(8.67328077084\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 101.49
Character \(\chi\) \(=\) 147.101
Dual form 147.4.o.a.131.49

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.32320 + 1.69673i) q^{2} +(5.19287 + 0.184765i) q^{3} +(9.94671 + 9.22920i) q^{4} +(-7.56055 - 5.15469i) q^{5} +(22.1363 + 9.60966i) q^{6} +(16.1590 + 9.04908i) q^{7} +(11.2217 + 23.3020i) q^{8} +(26.9317 + 1.91892i) q^{9} +O(q^{10})\) \(q+(4.32320 + 1.69673i) q^{2} +(5.19287 + 0.184765i) q^{3} +(9.94671 + 9.22920i) q^{4} +(-7.56055 - 5.15469i) q^{5} +(22.1363 + 9.60966i) q^{6} +(16.1590 + 9.04908i) q^{7} +(11.2217 + 23.3020i) q^{8} +(26.9317 + 1.91892i) q^{9} +(-23.9396 - 35.1129i) q^{10} +(-4.18891 - 27.7916i) q^{11} +(49.9467 + 49.7638i) q^{12} +(-55.3068 + 44.1057i) q^{13} +(54.5048 + 66.5384i) q^{14} +(-38.3085 - 28.1646i) q^{15} +(0.864176 + 11.5316i) q^{16} +(76.7608 + 23.6776i) q^{17} +(113.175 + 53.9917i) q^{18} +(-73.4757 + 42.4212i) q^{19} +(-27.6289 - 121.050i) q^{20} +(82.2397 + 49.9763i) q^{21} +(29.0453 - 127.256i) q^{22} +(-41.5542 - 134.715i) q^{23} +(53.9672 + 123.078i) q^{24} +(-15.0766 - 38.4146i) q^{25} +(-313.937 + 96.8369i) q^{26} +(139.498 + 14.9408i) q^{27} +(77.2134 + 239.143i) q^{28} +(-275.699 + 62.9265i) q^{29} +(-117.827 - 186.760i) q^{30} +(-99.1330 - 57.2345i) q^{31} +(45.1567 - 146.394i) q^{32} +(-16.6175 - 145.092i) q^{33} +(291.677 + 232.605i) q^{34} +(-75.5258 - 151.711i) q^{35} +(250.172 + 267.645i) q^{36} +(172.357 - 159.924i) q^{37} +(-389.627 + 58.7268i) q^{38} +(-295.350 + 218.816i) q^{39} +(35.2729 - 234.020i) q^{40} +(205.165 - 98.8021i) q^{41} +(270.742 + 355.596i) q^{42} +(224.640 + 108.181i) q^{43} +(214.828 - 315.095i) q^{44} +(-193.727 - 153.333i) q^{45} +(48.9286 - 652.907i) q^{46} +(-145.063 + 369.615i) q^{47} +(2.35691 + 60.0419i) q^{48} +(179.228 + 292.449i) q^{49} -191.655i q^{50} +(394.234 + 137.137i) q^{51} +(-957.181 - 71.7308i) q^{52} +(-14.1764 + 15.2785i) q^{53} +(577.728 + 301.283i) q^{54} +(-111.587 + 231.712i) q^{55} +(-29.5308 + 478.084i) q^{56} +(-389.387 + 206.712i) q^{57} +(-1298.67 - 195.743i) q^{58} +(-237.570 + 161.972i) q^{59} +(-121.107 - 633.702i) q^{60} +(-261.381 - 281.701i) q^{61} +(-331.460 - 415.638i) q^{62} +(417.826 + 274.715i) q^{63} +(501.293 - 628.601i) q^{64} +(645.501 - 48.3736i) q^{65} +(174.341 - 655.456i) q^{66} +(-124.461 + 215.573i) q^{67} +(544.992 + 943.954i) q^{68} +(-190.895 - 707.237i) q^{69} +(-69.1007 - 784.022i) q^{70} +(240.543 + 54.9023i) q^{71} +(257.504 + 649.097i) q^{72} +(560.360 - 219.925i) q^{73} +(1016.48 - 398.940i) q^{74} +(-71.1932 - 202.268i) q^{75} +(-1122.36 - 256.170i) q^{76} +(183.800 - 486.991i) q^{77} +(-1648.13 + 444.856i) q^{78} +(311.862 + 540.161i) q^{79} +(52.9084 - 91.6400i) q^{80} +(721.635 + 103.360i) q^{81} +(1054.61 - 79.0319i) q^{82} +(-220.317 + 276.268i) q^{83} +(356.773 + 1256.11i) q^{84} +(-458.303 - 574.693i) q^{85} +(787.609 + 848.841i) q^{86} +(-1443.29 + 275.829i) q^{87} +(600.594 - 409.478i) q^{88} +(-397.542 - 59.9199i) q^{89} +(-577.356 - 991.590i) q^{90} +(-1292.82 + 212.229i) q^{91} +(829.988 - 1723.49i) q^{92} +(-504.210 - 315.527i) q^{93} +(-1254.27 + 1351.78i) q^{94} +(774.185 + 58.0171i) q^{95} +(261.541 - 751.863i) q^{96} +393.436i q^{97} +(278.632 + 1568.41i) q^{98} +(-59.4846 - 756.513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 11 q^{3} - 234 q^{4} + 14 q^{6} + 28 q^{7} - 125 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 11 q^{3} - 234 q^{4} + 14 q^{6} + 28 q^{7} - 125 q^{9} - 58 q^{10} - 207 q^{12} - 28 q^{13} - 148 q^{15} + 726 q^{16} - 81 q^{18} - 342 q^{19} - 371 q^{21} - 156 q^{22} - 428 q^{24} + 1250 q^{25} - 56 q^{27} + 700 q^{28} + 389 q^{30} + 888 q^{31} + 841 q^{33} - 532 q^{34} - 38 q^{36} + 1178 q^{37} - 180 q^{39} + 194 q^{40} + 56 q^{42} + 1296 q^{43} - 617 q^{45} - 6756 q^{46} - 2380 q^{49} + 787 q^{51} - 5204 q^{52} + 4144 q^{54} - 5698 q^{55} + 863 q^{57} - 3066 q^{58} + 2820 q^{60} + 1492 q^{61} - 1085 q^{63} + 7648 q^{64} + 2568 q^{66} + 142 q^{67} - 5474 q^{69} + 5180 q^{70} + 1278 q^{72} + 2876 q^{73} - 1754 q^{75} + 7644 q^{76} + 936 q^{78} - 992 q^{79} + 911 q^{81} + 1022 q^{82} + 7868 q^{84} + 2672 q^{85} - 196 q^{87} + 370 q^{88} - 18767 q^{90} - 2254 q^{91} - 11096 q^{93} - 3628 q^{94} - 24248 q^{96} + 10982 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{42}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.32320 + 1.69673i 1.52848 + 0.599884i 0.972828 0.231530i \(-0.0743732\pi\)
0.555653 + 0.831415i \(0.312468\pi\)
\(3\) 5.19287 + 0.184765i 0.999368 + 0.0355581i
\(4\) 9.94671 + 9.22920i 1.24334 + 1.15365i
\(5\) −7.56055 5.15469i −0.676236 0.461050i 0.175874 0.984413i \(-0.443725\pi\)
−0.852110 + 0.523363i \(0.824677\pi\)
\(6\) 22.1363 + 9.60966i 1.50618 + 0.653855i
\(7\) 16.1590 + 9.04908i 0.872505 + 0.488605i
\(8\) 11.2217 + 23.3020i 0.495932 + 1.02981i
\(9\) 26.9317 + 1.91892i 0.997471 + 0.0710712i
\(10\) −23.9396 35.1129i −0.757037 1.11037i
\(11\) −4.18891 27.7916i −0.114818 0.761771i −0.969940 0.243343i \(-0.921756\pi\)
0.855122 0.518427i \(-0.173482\pi\)
\(12\) 49.9467 + 49.7638i 1.20153 + 1.19713i
\(13\) −55.3068 + 44.1057i −1.17995 + 0.940978i −0.999095 0.0425317i \(-0.986458\pi\)
−0.180854 + 0.983510i \(0.557886\pi\)
\(14\) 54.5048 + 66.5384i 1.04050 + 1.27022i
\(15\) −38.3085 28.1646i −0.659414 0.484804i
\(16\) 0.864176 + 11.5316i 0.0135028 + 0.180182i
\(17\) 76.7608 + 23.6776i 1.09513 + 0.337803i 0.789129 0.614228i \(-0.210532\pi\)
0.306002 + 0.952031i \(0.401009\pi\)
\(18\) 113.175 + 53.9917i 1.48198 + 0.706998i
\(19\) −73.4757 + 42.4212i −0.887183 + 0.512215i −0.873020 0.487684i \(-0.837842\pi\)
−0.0141629 + 0.999900i \(0.504508\pi\)
\(20\) −27.6289 121.050i −0.308900 1.35338i
\(21\) 82.2397 + 49.9763i 0.854580 + 0.519320i
\(22\) 29.0453 127.256i 0.281477 1.23323i
\(23\) −41.5542 134.715i −0.376724 1.22131i −0.923359 0.383938i \(-0.874568\pi\)
0.546635 0.837371i \(-0.315909\pi\)
\(24\) 53.9672 + 123.078i 0.459000 + 1.04680i
\(25\) −15.0766 38.4146i −0.120613 0.307317i
\(26\) −313.937 + 96.8369i −2.36801 + 0.730434i
\(27\) 139.498 + 14.9408i 0.994313 + 0.106494i
\(28\) 77.2134 + 239.143i 0.521141 + 1.61407i
\(29\) −275.699 + 62.9265i −1.76538 + 0.402936i −0.977168 0.212469i \(-0.931850\pi\)
−0.788211 + 0.615405i \(0.788993\pi\)
\(30\) −117.827 186.760i −0.717075 1.13659i
\(31\) −99.1330 57.2345i −0.574349 0.331601i 0.184535 0.982826i \(-0.440922\pi\)
−0.758884 + 0.651225i \(0.774255\pi\)
\(32\) 45.1567 146.394i 0.249458 0.808722i
\(33\) −16.6175 145.092i −0.0876587 0.765372i
\(34\) 291.677 + 232.605i 1.47124 + 1.17328i
\(35\) −75.5258 151.711i −0.364748 0.732680i
\(36\) 250.172 + 267.645i 1.15820 + 1.23910i
\(37\) 172.357 159.924i 0.765821 0.710578i −0.197093 0.980385i \(-0.563150\pi\)
0.962915 + 0.269806i \(0.0869597\pi\)
\(38\) −389.627 + 58.7268i −1.66331 + 0.250704i
\(39\) −295.350 + 218.816i −1.21266 + 0.898426i
\(40\) 35.2729 234.020i 0.139428 0.925047i
\(41\) 205.165 98.8021i 0.781496 0.376349i −0.000206755 1.00000i \(-0.500066\pi\)
0.781703 + 0.623651i \(0.214352\pi\)
\(42\) 270.742 + 355.596i 0.994676 + 1.30642i
\(43\) 224.640 + 108.181i 0.796681 + 0.383661i 0.787514 0.616297i \(-0.211368\pi\)
0.00916690 + 0.999958i \(0.497082\pi\)
\(44\) 214.828 315.095i 0.736059 1.07960i
\(45\) −193.727 153.333i −0.641758 0.507945i
\(46\) 48.9286 652.907i 0.156829 2.09274i
\(47\) −145.063 + 369.615i −0.450205 + 1.14710i 0.508086 + 0.861307i \(0.330353\pi\)
−0.958290 + 0.285797i \(0.907742\pi\)
\(48\) 2.35691 + 60.0419i 0.00708730 + 0.180548i
\(49\) 179.228 + 292.449i 0.522531 + 0.852620i
\(50\) 191.655i 0.542082i
\(51\) 394.234 + 137.137i 1.08243 + 0.376530i
\(52\) −957.181 71.7308i −2.55264 0.191294i
\(53\) −14.1764 + 15.2785i −0.0367411 + 0.0395975i −0.751155 0.660126i \(-0.770503\pi\)
0.714414 + 0.699723i \(0.246693\pi\)
\(54\) 577.728 + 301.283i 1.45590 + 0.759248i
\(55\) −111.587 + 231.712i −0.273570 + 0.568074i
\(56\) −29.5308 + 478.084i −0.0704682 + 1.14083i
\(57\) −389.387 + 206.712i −0.904835 + 0.480345i
\(58\) −1298.67 195.743i −2.94006 0.443143i
\(59\) −237.570 + 161.972i −0.524219 + 0.357407i −0.796333 0.604859i \(-0.793230\pi\)
0.272114 + 0.962265i \(0.412277\pi\)
\(60\) −121.107 633.702i −0.260581 1.36351i
\(61\) −261.381 281.701i −0.548629 0.591282i 0.396477 0.918045i \(-0.370233\pi\)
−0.945106 + 0.326763i \(0.894042\pi\)
\(62\) −331.460 415.638i −0.678959 0.851388i
\(63\) 417.826 + 274.715i 0.835573 + 0.549379i
\(64\) 501.293 628.601i 0.979088 1.22774i
\(65\) 645.501 48.3736i 1.23176 0.0923078i
\(66\) 174.341 655.456i 0.325150 1.22244i
\(67\) −124.461 + 215.573i −0.226945 + 0.393081i −0.956901 0.290413i \(-0.906207\pi\)
0.729956 + 0.683494i \(0.239540\pi\)
\(68\) 544.992 + 943.954i 0.971912 + 1.68340i
\(69\) −190.895 707.237i −0.333058 1.23393i
\(70\) −69.1007 784.022i −0.117987 1.33869i
\(71\) 240.543 + 54.9023i 0.402073 + 0.0917705i 0.418775 0.908090i \(-0.362460\pi\)
−0.0167022 + 0.999861i \(0.505317\pi\)
\(72\) 257.504 + 649.097i 0.421488 + 1.06246i
\(73\) 560.360 219.925i 0.898426 0.352606i 0.129227 0.991615i \(-0.458750\pi\)
0.769200 + 0.639009i \(0.220655\pi\)
\(74\) 1016.48 398.940i 1.59681 0.626701i
\(75\) −71.1932 202.268i −0.109609 0.311411i
\(76\) −1122.36 256.170i −1.69399 0.386641i
\(77\) 183.800 486.991i 0.272025 0.720750i
\(78\) −1648.13 + 444.856i −2.39248 + 0.645770i
\(79\) 311.862 + 540.161i 0.444142 + 0.769277i 0.997992 0.0633396i \(-0.0201751\pi\)
−0.553850 + 0.832617i \(0.686842\pi\)
\(80\) 52.9084 91.6400i 0.0739417 0.128071i
\(81\) 721.635 + 103.360i 0.989898 + 0.141783i
\(82\) 1054.61 79.0319i 1.42027 0.106434i
\(83\) −220.317 + 276.268i −0.291360 + 0.365354i −0.905871 0.423555i \(-0.860782\pi\)
0.614510 + 0.788909i \(0.289354\pi\)
\(84\) 356.773 + 1256.11i 0.463419 + 1.63158i
\(85\) −458.303 574.693i −0.584822 0.733344i
\(86\) 787.609 + 848.841i 0.987559 + 1.06434i
\(87\) −1443.29 + 275.829i −1.77859 + 0.339908i
\(88\) 600.594 409.478i 0.727540 0.496028i
\(89\) −397.542 59.9199i −0.473476 0.0713651i −0.0920304 0.995756i \(-0.529336\pi\)
−0.381446 + 0.924391i \(0.624574\pi\)
\(90\) −577.356 991.590i −0.676207 1.16136i
\(91\) −1292.82 + 212.229i −1.48928 + 0.244480i
\(92\) 829.988 1723.49i 0.940568 1.95311i
\(93\) −504.210 315.527i −0.562195 0.351814i
\(94\) −1254.27 + 1351.78i −1.37626 + 1.48325i
\(95\) 774.185 + 58.0171i 0.836102 + 0.0626572i
\(96\) 261.541 751.863i 0.278057 0.799341i
\(97\) 393.436i 0.411828i 0.978570 + 0.205914i \(0.0660168\pi\)
−0.978570 + 0.205914i \(0.933983\pi\)
\(98\) 278.632 + 1568.41i 0.287205 + 1.61667i
\(99\) −59.4846 756.513i −0.0603882 0.768005i
\(100\) 204.573 521.244i 0.204573 0.521244i
\(101\) −100.793 + 1344.99i −0.0993000 + 1.32507i 0.695645 + 0.718386i \(0.255119\pi\)
−0.794945 + 0.606681i \(0.792500\pi\)
\(102\) 1471.66 + 1261.78i 1.42859 + 1.22485i
\(103\) 726.474 1065.54i 0.694967 1.01933i −0.302833 0.953044i \(-0.597933\pi\)
0.997801 0.0662862i \(-0.0211150\pi\)
\(104\) −1648.39 793.821i −1.55421 0.748467i
\(105\) −364.165 801.769i −0.338465 0.745187i
\(106\) −87.2109 + 41.9985i −0.0799120 + 0.0384836i
\(107\) 28.4236 188.578i 0.0256805 0.170379i −0.972314 0.233678i \(-0.924924\pi\)
0.997995 + 0.0632988i \(0.0201621\pi\)
\(108\) 1249.66 + 1436.07i 1.11341 + 1.27950i
\(109\) 561.765 84.6724i 0.493645 0.0744050i 0.102498 0.994733i \(-0.467316\pi\)
0.391147 + 0.920328i \(0.372078\pi\)
\(110\) −875.564 + 812.404i −0.758925 + 0.704179i
\(111\) 924.578 798.620i 0.790604 0.682898i
\(112\) −90.3864 + 194.160i −0.0762564 + 0.163807i
\(113\) −987.842 787.777i −0.822375 0.655822i 0.119109 0.992881i \(-0.461996\pi\)
−0.941483 + 0.337059i \(0.890568\pi\)
\(114\) −2034.13 + 232.971i −1.67117 + 0.191401i
\(115\) −380.244 + 1232.72i −0.308330 + 0.999582i
\(116\) −3323.06 1918.57i −2.65981 1.53564i
\(117\) −1574.14 + 1081.71i −1.24384 + 0.854738i
\(118\) −1301.88 + 297.146i −1.01566 + 0.231818i
\(119\) 1026.12 + 1077.22i 0.790455 + 0.829821i
\(120\) 226.406 1208.72i 0.172233 0.919504i
\(121\) 517.042 159.486i 0.388461 0.119824i
\(122\) −652.029 1661.34i −0.483868 1.23288i
\(123\) 1083.65 475.159i 0.794384 0.348322i
\(124\) −457.819 1484.21i −0.331560 1.07489i
\(125\) −338.552 + 1483.29i −0.242248 + 1.06136i
\(126\) 1340.23 + 1896.59i 0.947594 + 1.34096i
\(127\) 352.039 + 1542.38i 0.245972 + 1.07767i 0.935476 + 0.353390i \(0.114971\pi\)
−0.689504 + 0.724281i \(0.742172\pi\)
\(128\) 2172.35 1254.21i 1.50008 0.866072i
\(129\) 1146.54 + 603.275i 0.782535 + 0.411747i
\(130\) 2872.70 + 886.111i 1.93810 + 0.597824i
\(131\) 78.7208 + 1050.46i 0.0525028 + 0.700601i 0.959903 + 0.280333i \(0.0904449\pi\)
−0.907400 + 0.420268i \(0.861936\pi\)
\(132\) 1173.79 1596.55i 0.773982 1.05274i
\(133\) −1571.17 + 20.5979i −1.02434 + 0.0134290i
\(134\) −903.838 + 720.786i −0.582684 + 0.464675i
\(135\) −977.668 832.031i −0.623291 0.530443i
\(136\) 309.648 + 2054.38i 0.195236 + 1.29531i
\(137\) 1735.00 + 2544.78i 1.08198 + 1.58697i 0.771316 + 0.636452i \(0.219599\pi\)
0.310663 + 0.950520i \(0.399449\pi\)
\(138\) 374.714 3381.42i 0.231144 2.08584i
\(139\) −368.585 765.375i −0.224914 0.467038i 0.757723 0.652576i \(-0.226312\pi\)
−0.982637 + 0.185538i \(0.940597\pi\)
\(140\) 648.936 2206.07i 0.391751 1.33176i
\(141\) −821.585 + 1892.56i −0.490709 + 1.13037i
\(142\) 946.759 + 645.489i 0.559509 + 0.381467i
\(143\) 1457.44 + 1352.31i 0.852290 + 0.790809i
\(144\) 1.14545 + 312.225i 0.000662878 + 0.180686i
\(145\) 2408.80 + 945.385i 1.37959 + 0.541448i
\(146\) 2795.70 1.58475
\(147\) 876.674 + 1551.76i 0.491883 + 0.870661i
\(148\) 3190.36 1.77193
\(149\) 961.615 + 377.406i 0.528715 + 0.207505i 0.614657 0.788795i \(-0.289295\pi\)
−0.0859415 + 0.996300i \(0.527390\pi\)
\(150\) 35.4112 995.238i 0.0192754 0.541739i
\(151\) −1250.66 1160.45i −0.674024 0.625403i 0.267019 0.963691i \(-0.413961\pi\)
−0.941042 + 0.338289i \(0.890152\pi\)
\(152\) −1813.02 1236.10i −0.967469 0.659609i
\(153\) 2021.86 + 784.975i 1.06835 + 0.414781i
\(154\) 1620.89 1793.50i 0.848151 0.938469i
\(155\) 454.474 + 943.724i 0.235511 + 0.489044i
\(156\) −4957.26 549.342i −2.54422 0.281940i
\(157\) 218.318 + 320.214i 0.110979 + 0.162776i 0.877710 0.479192i \(-0.159070\pi\)
−0.766731 + 0.641969i \(0.778118\pi\)
\(158\) 431.734 + 2864.37i 0.217386 + 1.44226i
\(159\) −76.4391 + 76.7200i −0.0381259 + 0.0382660i
\(160\) −1096.03 + 874.053i −0.541554 + 0.431875i
\(161\) 547.576 2552.90i 0.268043 1.24967i
\(162\) 2944.40 + 1671.26i 1.42799 + 0.810537i
\(163\) 96.1134 + 1282.54i 0.0461851 + 0.616298i 0.971491 + 0.237076i \(0.0761892\pi\)
−0.925306 + 0.379222i \(0.876192\pi\)
\(164\) 2952.58 + 910.749i 1.40584 + 0.433644i
\(165\) −622.267 + 1182.63i −0.293596 + 0.557987i
\(166\) −1421.22 + 820.544i −0.664509 + 0.383654i
\(167\) −874.986 3833.57i −0.405440 1.77635i −0.604753 0.796413i \(-0.706728\pi\)
0.199313 0.979936i \(-0.436129\pi\)
\(168\) −241.683 + 2477.17i −0.110989 + 1.13761i
\(169\) 624.650 2736.77i 0.284320 1.24569i
\(170\) −1006.23 3262.13i −0.453968 1.47173i
\(171\) −2060.23 + 1001.48i −0.921343 + 0.447867i
\(172\) 1236.01 + 3149.29i 0.547934 + 1.39611i
\(173\) 1993.79 615.004i 0.876216 0.270277i 0.176157 0.984362i \(-0.443633\pi\)
0.700059 + 0.714085i \(0.253157\pi\)
\(174\) −6707.65 1256.42i −2.92245 0.547406i
\(175\) 103.993 757.173i 0.0449209 0.327068i
\(176\) 316.862 72.3217i 0.135707 0.0309742i
\(177\) −1263.59 + 797.206i −0.536596 + 0.338540i
\(178\) −1616.99 933.567i −0.680889 0.393111i
\(179\) −1177.85 + 3818.50i −0.491826 + 1.59446i 0.280911 + 0.959734i \(0.409363\pi\)
−0.772737 + 0.634726i \(0.781113\pi\)
\(180\) −511.808 3313.10i −0.211933 1.37191i
\(181\) 370.151 + 295.185i 0.152006 + 0.121221i 0.696540 0.717518i \(-0.254722\pi\)
−0.544534 + 0.838739i \(0.683293\pi\)
\(182\) −5949.21 1276.06i −2.42299 0.519712i
\(183\) −1305.27 1511.13i −0.527257 0.610416i
\(184\) 2672.84 2480.03i 1.07089 0.993642i
\(185\) −2127.48 + 320.666i −0.845488 + 0.127437i
\(186\) −1644.43 2219.59i −0.648256 0.874992i
\(187\) 336.493 2232.49i 0.131587 0.873024i
\(188\) −4854.15 + 2337.63i −1.88311 + 0.906859i
\(189\) 2118.96 + 1503.76i 0.815510 + 0.578743i
\(190\) 3248.51 + 1564.40i 1.24038 + 0.597334i
\(191\) −1295.45 + 1900.07i −0.490761 + 0.719815i −0.989113 0.147161i \(-0.952987\pi\)
0.498351 + 0.866975i \(0.333939\pi\)
\(192\) 2719.29 3171.62i 1.02212 1.19215i
\(193\) −104.392 + 1393.01i −0.0389342 + 0.519541i 0.943307 + 0.331920i \(0.107697\pi\)
−0.982242 + 0.187620i \(0.939923\pi\)
\(194\) −667.554 + 1700.90i −0.247049 + 0.629472i
\(195\) 3360.94 131.932i 1.23427 0.0484503i
\(196\) −916.336 + 4563.04i −0.333942 + 1.66291i
\(197\) 3864.35i 1.39758i −0.715326 0.698791i \(-0.753722\pi\)
0.715326 0.698791i \(-0.246278\pi\)
\(198\) 1026.43 3371.48i 0.368412 1.21011i
\(199\) −864.870 64.8131i −0.308086 0.0230878i −0.0802097 0.996778i \(-0.525559\pi\)
−0.227876 + 0.973690i \(0.573178\pi\)
\(200\) 725.954 782.392i 0.256663 0.276617i
\(201\) −686.140 + 1096.44i −0.240779 + 0.384762i
\(202\) −2717.84 + 5643.65i −0.946665 + 1.96577i
\(203\) −5024.45 1477.99i −1.73718 0.511008i
\(204\) 2655.66 + 5002.52i 0.911439 + 1.71690i
\(205\) −2060.45 310.563i −0.701991 0.105808i
\(206\) 4948.63 3373.92i 1.67372 1.14113i
\(207\) −860.618 3707.86i −0.288971 1.24500i
\(208\) −556.405 599.662i −0.185480 0.199899i
\(209\) 1486.74 + 1864.31i 0.492056 + 0.617018i
\(210\) −213.971 4084.09i −0.0703113 1.34204i
\(211\) 2194.50 2751.82i 0.716000 0.897835i −0.282105 0.959384i \(-0.591033\pi\)
0.998104 + 0.0615487i \(0.0196039\pi\)
\(212\) −282.017 + 21.1343i −0.0913633 + 0.00684673i
\(213\) 1238.96 + 329.544i 0.398555 + 0.106009i
\(214\) 442.846 767.033i 0.141460 0.245015i
\(215\) −1140.76 1975.86i −0.361857 0.626755i
\(216\) 1217.25 + 3418.25i 0.383443 + 1.07677i
\(217\) −1083.97 1821.92i −0.339101 0.569953i
\(218\) 2572.28 + 587.107i 0.799161 + 0.182403i
\(219\) 2950.51 1038.51i 0.910396 0.320437i
\(220\) −3248.44 + 1274.92i −0.995498 + 0.390704i
\(221\) −5289.71 + 2076.06i −1.61006 + 0.631903i
\(222\) 5352.17 1883.83i 1.61808 0.569525i
\(223\) 3180.44 + 725.914i 0.955058 + 0.217986i 0.671529 0.740978i \(-0.265638\pi\)
0.283528 + 0.958964i \(0.408495\pi\)
\(224\) 2054.42 1956.96i 0.612799 0.583728i
\(225\) −332.325 1063.50i −0.0984666 0.315112i
\(226\) −2933.99 5081.82i −0.863566 1.49574i
\(227\) 911.038 1577.96i 0.266378 0.461379i −0.701546 0.712624i \(-0.747507\pi\)
0.967924 + 0.251245i \(0.0808399\pi\)
\(228\) −5780.91 1537.63i −1.67917 0.446632i
\(229\) −6455.68 + 483.786i −1.86290 + 0.139605i −0.958135 0.286315i \(-0.907570\pi\)
−0.904761 + 0.425920i \(0.859951\pi\)
\(230\) −3735.46 + 4684.12i −1.07091 + 1.34288i
\(231\) 1044.43 2494.92i 0.297481 0.710621i
\(232\) −4560.11 5718.20i −1.29046 1.61818i
\(233\) −1947.83 2099.26i −0.547667 0.590245i 0.397186 0.917738i \(-0.369987\pi\)
−0.944854 + 0.327493i \(0.893796\pi\)
\(234\) −8640.70 + 2005.56i −2.41393 + 0.560289i
\(235\) 3002.01 2046.73i 0.833316 0.568145i
\(236\) −3857.91 581.486i −1.06410 0.160388i
\(237\) 1519.66 + 2862.61i 0.416507 + 0.784583i
\(238\) 2608.36 + 6398.08i 0.710399 + 1.74255i
\(239\) 1219.75 2532.83i 0.330121 0.685503i −0.668166 0.744012i \(-0.732920\pi\)
0.998287 + 0.0585094i \(0.0186347\pi\)
\(240\) 291.678 466.099i 0.0784489 0.125361i
\(241\) −974.052 + 1049.78i −0.260349 + 0.280590i −0.849676 0.527305i \(-0.823203\pi\)
0.589327 + 0.807895i \(0.299393\pi\)
\(242\) 2505.88 + 187.790i 0.665637 + 0.0498826i
\(243\) 3728.26 + 670.067i 0.984230 + 0.176892i
\(244\) 5214.34i 1.36809i
\(245\) 152.420 3134.94i 0.0397459 0.817485i
\(246\) 5491.04 215.547i 1.42315 0.0558650i
\(247\) 2192.69 5586.88i 0.564847 1.43921i
\(248\) 221.242 2952.27i 0.0566487 0.755924i
\(249\) −1195.12 + 1393.92i −0.304167 + 0.354763i
\(250\) −3980.37 + 5838.13i −1.00696 + 1.47694i
\(251\) −1748.87 842.211i −0.439791 0.211792i 0.200867 0.979619i \(-0.435624\pi\)
−0.640658 + 0.767826i \(0.721338\pi\)
\(252\) 1620.59 + 6588.71i 0.405110 + 1.64702i
\(253\) −3569.89 + 1719.17i −0.887103 + 0.427206i
\(254\) −1095.07 + 7265.33i −0.270516 + 1.79475i
\(255\) −2273.72 3068.98i −0.558376 0.753676i
\(256\) 5159.28 777.637i 1.25959 0.189853i
\(257\) 3037.09 2818.01i 0.737154 0.683979i −0.219367 0.975642i \(-0.570399\pi\)
0.956521 + 0.291663i \(0.0942087\pi\)
\(258\) 3933.11 + 4553.44i 0.949089 + 1.09878i
\(259\) 4232.30 1024.55i 1.01538 0.245800i
\(260\) 6867.06 + 5476.30i 1.63799 + 1.30625i
\(261\) −7545.80 + 1165.67i −1.78955 + 0.276450i
\(262\) −1442.01 + 4674.89i −0.340030 + 1.10235i
\(263\) 1976.95 + 1141.39i 0.463513 + 0.267609i 0.713520 0.700635i \(-0.247100\pi\)
−0.250007 + 0.968244i \(0.580433\pi\)
\(264\) 3194.46 2015.40i 0.744718 0.469845i
\(265\) 185.937 42.4390i 0.0431021 0.00983776i
\(266\) −6827.42 2576.80i −1.57374 0.593961i
\(267\) −2053.31 384.608i −0.470639 0.0881559i
\(268\) −3227.54 + 995.565i −0.735647 + 0.226917i
\(269\) 1904.53 + 4852.66i 0.431677 + 1.09990i 0.966893 + 0.255181i \(0.0821350\pi\)
−0.535216 + 0.844715i \(0.679770\pi\)
\(270\) −2814.92 5255.87i −0.634483 1.18467i
\(271\) −2275.26 7376.22i −0.510009 1.65341i −0.734254 0.678874i \(-0.762468\pi\)
0.224246 0.974533i \(-0.428008\pi\)
\(272\) −206.706 + 905.638i −0.0460786 + 0.201884i
\(273\) −6752.65 + 863.210i −1.49703 + 0.191369i
\(274\) 3182.95 + 13945.4i 0.701784 + 3.07472i
\(275\) −1004.45 + 579.919i −0.220256 + 0.127165i
\(276\) 4628.46 8796.49i 1.00942 1.91843i
\(277\) −6032.91 1860.91i −1.30860 0.403650i −0.439481 0.898252i \(-0.644838\pi\)
−0.869120 + 0.494602i \(0.835314\pi\)
\(278\) −294.832 3934.26i −0.0636073 0.848781i
\(279\) −2559.99 1731.65i −0.549329 0.371582i
\(280\) 2687.64 3462.35i 0.573634 0.738983i
\(281\) 4749.91 3787.93i 1.00838 0.804160i 0.0276720 0.999617i \(-0.491191\pi\)
0.980712 + 0.195457i \(0.0626192\pi\)
\(282\) −6763.03 + 6787.89i −1.42813 + 1.43338i
\(283\) −1106.46 7340.89i −0.232411 1.54194i −0.735389 0.677645i \(-0.763000\pi\)
0.502978 0.864299i \(-0.332238\pi\)
\(284\) 1885.91 + 2766.12i 0.394042 + 0.577953i
\(285\) 4009.52 + 444.317i 0.833345 + 0.0923477i
\(286\) 4006.30 + 8319.18i 0.828314 + 1.72001i
\(287\) 4209.33 + 260.006i 0.865745 + 0.0534762i
\(288\) 1497.07 3856.00i 0.306304 0.788948i
\(289\) 1272.28 + 867.423i 0.258961 + 0.176557i
\(290\) 8809.65 + 8174.16i 1.78386 + 1.65518i
\(291\) −72.6933 + 2043.06i −0.0146438 + 0.411568i
\(292\) 7603.47 + 2984.14i 1.52383 + 0.598060i
\(293\) −791.543 −0.157824 −0.0789120 0.996882i \(-0.525145\pi\)
−0.0789120 + 0.996882i \(0.525145\pi\)
\(294\) 1157.11 + 8196.05i 0.229538 + 1.62586i
\(295\) 2631.07 0.519278
\(296\) 5660.70 + 2221.66i 1.11156 + 0.436255i
\(297\) −169.118 3939.46i −0.0330412 0.769666i
\(298\) 3516.89 + 3263.20i 0.683651 + 0.634336i
\(299\) 8239.95 + 5617.90i 1.59374 + 1.08659i
\(300\) 1158.63 2668.95i 0.222978 0.513641i
\(301\) 2651.03 + 3780.88i 0.507650 + 0.724009i
\(302\) −3437.90 7138.88i −0.655063 1.36025i
\(303\) −771.914 + 6965.74i −0.146354 + 1.32070i
\(304\) −552.681 810.635i −0.104271 0.152938i
\(305\) 524.097 + 3477.15i 0.0983924 + 0.652791i
\(306\) 7409.02 + 6824.16i 1.38414 + 1.27487i
\(307\) 3915.92 3122.84i 0.727990 0.580553i −0.187801 0.982207i \(-0.560136\pi\)
0.915791 + 0.401654i \(0.131565\pi\)
\(308\) 6322.74 3147.63i 1.16971 0.582315i
\(309\) 3969.36 5398.99i 0.730773 0.993973i
\(310\) 363.534 + 4851.02i 0.0666043 + 0.888773i
\(311\) 3774.38 + 1164.24i 0.688185 + 0.212277i 0.619075 0.785332i \(-0.287508\pi\)
0.0691103 + 0.997609i \(0.477984\pi\)
\(312\) −8413.18 4426.77i −1.52661 0.803258i
\(313\) 502.065 289.867i 0.0906658 0.0523459i −0.453982 0.891011i \(-0.649997\pi\)
0.544647 + 0.838665i \(0.316663\pi\)
\(314\) 400.516 + 1754.78i 0.0719823 + 0.315375i
\(315\) −1742.92 4230.76i −0.311754 0.756751i
\(316\) −1883.25 + 8251.07i −0.335257 + 1.46886i
\(317\) −2353.70 7630.52i −0.417026 1.35196i −0.883915 0.467648i \(-0.845101\pi\)
0.466889 0.884316i \(-0.345375\pi\)
\(318\) −460.634 + 201.979i −0.0812298 + 0.0356177i
\(319\) 2903.70 + 7398.51i 0.509643 + 1.29855i
\(320\) −7030.30 + 2168.56i −1.22814 + 0.378832i
\(321\) 182.442 974.009i 0.0317226 0.169358i
\(322\) 6698.85 10107.6i 1.15936 1.74930i
\(323\) −6644.48 + 1516.56i −1.14461 + 0.261250i
\(324\) 6223.97 + 7688.21i 1.06721 + 1.31828i
\(325\) 2528.14 + 1459.62i 0.431496 + 0.249124i
\(326\) −1760.61 + 5707.76i −0.299114 + 0.969705i
\(327\) 2932.81 335.898i 0.495979 0.0568049i
\(328\) 4604.58 + 3672.03i 0.775138 + 0.618152i
\(329\) −5688.75 + 4659.93i −0.953286 + 0.780882i
\(330\) −4696.79 + 4056.93i −0.783484 + 0.676748i
\(331\) −1194.66 + 1108.48i −0.198382 + 0.184072i −0.773108 0.634274i \(-0.781299\pi\)
0.574726 + 0.818346i \(0.305109\pi\)
\(332\) −4741.16 + 714.615i −0.783750 + 0.118131i
\(333\) 4948.77 3976.30i 0.814387 0.654354i
\(334\) 2721.79 18057.9i 0.445897 2.95833i
\(335\) 2052.20 988.290i 0.334698 0.161182i
\(336\) −505.239 + 991.546i −0.0820328 + 0.160992i
\(337\) −6844.70 3296.24i −1.10639 0.532811i −0.210731 0.977544i \(-0.567584\pi\)
−0.895663 + 0.444733i \(0.853299\pi\)
\(338\) 7344.04 10771.7i 1.18184 1.73345i
\(339\) −4984.18 4273.34i −0.798535 0.684649i
\(340\) 745.355 9946.08i 0.118890 1.58648i
\(341\) −1175.38 + 2994.81i −0.186658 + 0.475596i
\(342\) −10606.0 + 833.951i −1.67692 + 0.131856i
\(343\) 249.761 + 6347.54i 0.0393173 + 0.999227i
\(344\) 6448.54i 1.01070i
\(345\) −2202.32 + 6331.10i −0.343678 + 0.987986i
\(346\) 9663.06 + 724.146i 1.50141 + 0.112515i
\(347\) 5285.83 5696.77i 0.817747 0.881322i −0.176945 0.984221i \(-0.556621\pi\)
0.994692 + 0.102899i \(0.0328119\pi\)
\(348\) −16901.7 10576.9i −2.60353 1.62925i
\(349\) 1396.40 2899.66i 0.214177 0.444743i −0.766007 0.642832i \(-0.777759\pi\)
0.980184 + 0.198089i \(0.0634736\pi\)
\(350\) 1734.30 3096.96i 0.264864 0.472969i
\(351\) −8374.17 + 5326.34i −1.27345 + 0.809969i
\(352\) −4257.69 641.743i −0.644703 0.0971734i
\(353\) −7952.89 + 5422.19i −1.19912 + 0.817547i −0.987160 0.159732i \(-0.948937\pi\)
−0.211960 + 0.977278i \(0.567985\pi\)
\(354\) −6815.41 + 1302.50i −1.02326 + 0.195556i
\(355\) −1535.63 1655.02i −0.229585 0.247434i
\(356\) −3401.23 4265.00i −0.506361 0.634957i
\(357\) 5129.47 + 5783.45i 0.760448 + 0.857403i
\(358\) −11571.1 + 14509.6i −1.70824 + 2.14206i
\(359\) −9589.67 + 718.646i −1.40981 + 0.105651i −0.757766 0.652527i \(-0.773709\pi\)
−0.652048 + 0.758178i \(0.726090\pi\)
\(360\) 1399.03 6234.88i 0.204820 0.912798i
\(361\) 169.616 293.784i 0.0247290 0.0428320i
\(362\) 1099.38 + 1904.19i 0.159620 + 0.276470i
\(363\) 2714.40 732.660i 0.392477 0.105936i
\(364\) −14818.0 9820.71i −2.13372 1.41413i
\(365\) −5370.27 1225.73i −0.770117 0.175774i
\(366\) −3078.94 8747.60i −0.439724 1.24930i
\(367\) 7803.21 3062.53i 1.10988 0.435594i 0.261614 0.965173i \(-0.415745\pi\)
0.848261 + 0.529579i \(0.177650\pi\)
\(368\) 1517.58 595.606i 0.214971 0.0843698i
\(369\) 5715.03 2267.21i 0.806267 0.319855i
\(370\) −9741.58 2223.45i −1.36876 0.312410i
\(371\) −367.333 + 118.603i −0.0514043 + 0.0165972i
\(372\) −2103.16 7791.91i −0.293129 1.08600i
\(373\) −909.413 1575.15i −0.126240 0.218655i 0.795977 0.605327i \(-0.206958\pi\)
−0.922217 + 0.386673i \(0.873624\pi\)
\(374\) 5242.65 9080.54i 0.724842 1.25546i
\(375\) −2032.12 + 7639.99i −0.279835 + 1.05207i
\(376\) −10240.6 + 767.429i −1.40457 + 0.105258i
\(377\) 12472.6 15640.1i 1.70390 2.13663i
\(378\) 6609.19 + 10096.3i 0.899312 + 1.37381i
\(379\) −6533.21 8192.38i −0.885457 1.11033i −0.993231 0.116153i \(-0.962944\pi\)
0.107774 0.994175i \(-0.465628\pi\)
\(380\) 7165.14 + 7722.18i 0.967273 + 1.04247i
\(381\) 1543.11 + 8074.43i 0.207496 + 1.08574i
\(382\) −8824.39 + 6016.37i −1.18192 + 0.805822i
\(383\) 1381.19 + 208.182i 0.184271 + 0.0277744i 0.240529 0.970642i \(-0.422679\pi\)
−0.0562585 + 0.998416i \(0.517917\pi\)
\(384\) 11512.4 6111.55i 1.52993 0.812184i
\(385\) −3899.91 + 2734.48i −0.516255 + 0.361980i
\(386\) −2814.87 + 5845.15i −0.371174 + 0.770752i
\(387\) 5842.35 + 3344.57i 0.767399 + 0.439312i
\(388\) −3631.10 + 3913.39i −0.475106 + 0.512042i
\(389\) 1859.57 + 139.356i 0.242375 + 0.0181635i 0.195364 0.980731i \(-0.437411\pi\)
0.0470115 + 0.998894i \(0.485030\pi\)
\(390\) 14753.8 + 5132.23i 1.91561 + 0.666361i
\(391\) 11324.8i 1.46475i
\(392\) −4803.41 + 7458.14i −0.618900 + 0.960952i
\(393\) 214.699 + 5469.42i 0.0275576 + 0.702025i
\(394\) 6556.76 16706.3i 0.838387 2.13618i
\(395\) 426.517 5691.47i 0.0543301 0.724984i
\(396\) 6390.34 8073.82i 0.810926 1.02456i
\(397\) −6944.31 + 10185.4i −0.877896 + 1.28764i 0.0789010 + 0.996882i \(0.474859\pi\)
−0.956797 + 0.290755i \(0.906093\pi\)
\(398\) −3629.03 1747.65i −0.457053 0.220105i
\(399\) −8162.67 183.335i −1.02417 0.0230031i
\(400\) 429.954 207.055i 0.0537443 0.0258819i
\(401\) −590.505 + 3917.74i −0.0735371 + 0.487887i 0.921500 + 0.388379i \(0.126965\pi\)
−0.995037 + 0.0995078i \(0.968273\pi\)
\(402\) −4826.68 + 3575.95i −0.598839 + 0.443662i
\(403\) 8007.10 1206.88i 0.989732 0.149178i
\(404\) −13415.8 + 12448.0i −1.65213 + 1.53295i
\(405\) −4923.17 4501.27i −0.604035 0.552271i
\(406\) −19213.9 14914.8i −2.34870 1.82317i
\(407\) −5166.54 4120.18i −0.629228 0.501793i
\(408\) 1228.38 + 10725.3i 0.149054 + 1.30143i
\(409\) −1596.38 + 5175.33i −0.192997 + 0.625681i 0.806414 + 0.591352i \(0.201406\pi\)
−0.999411 + 0.0343290i \(0.989071\pi\)
\(410\) −8380.79 4838.65i −1.00951 0.582839i
\(411\) 8539.44 + 13535.3i 1.02487 + 1.62444i
\(412\) 17060.1 3893.86i 2.04003 0.465623i
\(413\) −5304.59 + 467.526i −0.632014 + 0.0557033i
\(414\) 2570.61 17490.0i 0.305166 2.07630i
\(415\) 3089.79 953.075i 0.365475 0.112734i
\(416\) 3959.35 + 10088.3i 0.466643 + 1.18899i
\(417\) −1772.60 4042.59i −0.208164 0.474740i
\(418\) 3264.22 + 10582.3i 0.381958 + 1.23828i
\(419\) 811.971 3557.48i 0.0946716 0.414783i −0.905278 0.424820i \(-0.860338\pi\)
0.999950 + 0.0100363i \(0.00319469\pi\)
\(420\) 3777.44 11335.9i 0.438858 1.31699i
\(421\) 3352.69 + 14689.1i 0.388124 + 1.70048i 0.671109 + 0.741358i \(0.265818\pi\)
−0.282985 + 0.959124i \(0.591325\pi\)
\(422\) 14156.4 8173.18i 1.63299 0.942806i
\(423\) −4616.06 + 9676.00i −0.530592 + 1.11221i
\(424\) −515.103 158.888i −0.0589991 0.0181988i
\(425\) −247.729 3305.71i −0.0282744 0.377296i
\(426\) 4797.13 + 3526.87i 0.545591 + 0.401120i
\(427\) −1674.52 6917.28i −0.189779 0.783959i
\(428\) 2023.15 1613.40i 0.228487 0.182212i
\(429\) 7318.44 + 7291.64i 0.823631 + 0.820615i
\(430\) −1579.24 10477.6i −0.177111 1.17506i
\(431\) 3076.79 + 4512.83i 0.343861 + 0.504351i 0.958745 0.284266i \(-0.0917499\pi\)
−0.614885 + 0.788617i \(0.710798\pi\)
\(432\) −51.7401 + 1621.55i −0.00576238 + 0.180595i
\(433\) 492.041 + 1021.73i 0.0546096 + 0.113398i 0.926488 0.376325i \(-0.122812\pi\)
−0.871878 + 0.489723i \(0.837098\pi\)
\(434\) −1594.93 9715.71i −0.176404 1.07458i
\(435\) 12333.9 + 5354.32i 1.35946 + 0.590161i
\(436\) 6369.17 + 4342.43i 0.699605 + 0.476983i
\(437\) 8768.01 + 8135.53i 0.959796 + 0.890561i
\(438\) 14517.7 + 516.548i 1.58375 + 0.0563507i
\(439\) −8026.34 3150.11i −0.872611 0.342475i −0.113580 0.993529i \(-0.536232\pi\)
−0.759031 + 0.651054i \(0.774327\pi\)
\(440\) −6651.55 −0.720682
\(441\) 4265.74 + 8220.07i 0.460613 + 0.887601i
\(442\) −26390.9 −2.84002
\(443\) 9825.65 + 3856.29i 1.05379 + 0.413584i 0.828080 0.560610i \(-0.189433\pi\)
0.225714 + 0.974194i \(0.427528\pi\)
\(444\) 16567.1 + 589.468i 1.77081 + 0.0630066i
\(445\) 2696.77 + 2502.24i 0.287279 + 0.266556i
\(446\) 12518.0 + 8534.61i 1.32902 + 0.906111i
\(447\) 4923.81 + 2137.49i 0.521002 + 0.226174i
\(448\) 13788.7 5621.35i 1.45414 0.592821i
\(449\) −6959.28 14451.1i −0.731467 1.51891i −0.850476 0.526014i \(-0.823686\pi\)
0.119009 0.992893i \(-0.462028\pi\)
\(450\) 367.771 5161.60i 0.0385264 0.540711i
\(451\) −3605.28 5287.98i −0.376421 0.552109i
\(452\) −2555.22 16952.8i −0.265902 1.76414i
\(453\) −6280.12 6257.12i −0.651359 0.648974i
\(454\) 6615.97 5276.06i 0.683927 0.545414i
\(455\) 10868.4 + 5059.52i 1.11982 + 0.521305i
\(456\) −9186.38 6753.86i −0.943403 0.693593i
\(457\) 581.908 + 7765.03i 0.0595635 + 0.794820i 0.944375 + 0.328871i \(0.106668\pi\)
−0.884811 + 0.465949i \(0.845713\pi\)
\(458\) −28730.0 8862.04i −2.93115 0.904139i
\(459\) 10354.2 + 4449.84i 1.05293 + 0.452507i
\(460\) −15159.2 + 8752.18i −1.53653 + 0.887114i
\(461\) 3674.32 + 16098.3i 0.371215 + 1.62640i 0.723371 + 0.690460i \(0.242592\pi\)
−0.352156 + 0.935941i \(0.614551\pi\)
\(462\) 8748.46 9013.91i 0.880985 0.907716i
\(463\) 892.555 3910.54i 0.0895908 0.392523i −0.910174 0.414227i \(-0.864052\pi\)
0.999764 + 0.0217040i \(0.00690912\pi\)
\(464\) −963.897 3124.88i −0.0964392 0.312648i
\(465\) 2185.65 + 4984.61i 0.217973 + 0.497109i
\(466\) −4858.96 12380.4i −0.483020 1.23071i
\(467\) −16423.6 + 5066.02i −1.62740 + 0.501986i −0.968241 0.250019i \(-0.919563\pi\)
−0.659158 + 0.752005i \(0.729087\pi\)
\(468\) −25640.9 3768.59i −2.53259 0.372229i
\(469\) −3961.90 + 2357.19i −0.390072 + 0.232079i
\(470\) 16451.0 3754.84i 1.61453 0.368506i
\(471\) 1074.53 + 1703.17i 0.105121 + 0.166620i
\(472\) −6440.21 3718.26i −0.628039 0.362599i
\(473\) 2065.52 6696.26i 0.200788 0.650940i
\(474\) 1712.70 + 14954.1i 0.165964 + 1.44908i
\(475\) 2737.36 + 2182.97i 0.264418 + 0.210867i
\(476\) 264.624 + 20185.1i 0.0254812 + 1.94366i
\(477\) −411.113 + 384.274i −0.0394624 + 0.0368861i
\(478\) 9570.73 8880.34i 0.915805 0.849743i
\(479\) −18615.4 + 2805.81i −1.77569 + 0.267643i −0.953463 0.301511i \(-0.902509\pi\)
−0.822231 + 0.569153i \(0.807271\pi\)
\(480\) −5853.02 + 4336.33i −0.556568 + 0.412345i
\(481\) −2478.96 + 16446.8i −0.234992 + 1.55907i
\(482\) −5992.20 + 2885.69i −0.566260 + 0.272697i
\(483\) 3315.17 13155.7i 0.312310 1.23935i
\(484\) 6614.80 + 3185.52i 0.621225 + 0.299166i
\(485\) 2028.04 2974.59i 0.189873 0.278493i
\(486\) 14981.1 + 9222.67i 1.39826 + 0.860800i
\(487\) −33.6272 + 448.724i −0.00312894 + 0.0417528i −0.998550 0.0538373i \(-0.982855\pi\)
0.995421 + 0.0955901i \(0.0304738\pi\)
\(488\) 3631.09 9251.86i 0.336827 0.858222i
\(489\) 262.134 + 6677.84i 0.0242416 + 0.617550i
\(490\) 5978.08 13294.3i 0.551147 1.22567i
\(491\) 2627.54i 0.241505i 0.992683 + 0.120753i \(0.0385308\pi\)
−0.992683 + 0.120753i \(0.961469\pi\)
\(492\) 15164.1 + 5274.93i 1.38953 + 0.483359i
\(493\) −22652.8 1697.59i −2.06943 0.155083i
\(494\) 18958.8 20432.8i 1.72672 1.86096i
\(495\) −3449.86 + 6026.28i −0.313252 + 0.547194i
\(496\) 574.338 1192.63i 0.0519931 0.107965i
\(497\) 3390.12 + 3063.86i 0.305971 + 0.276525i
\(498\) −7531.84 + 3998.38i −0.677730 + 0.359783i
\(499\) 8900.44 + 1341.53i 0.798474 + 0.120351i 0.535591 0.844477i \(-0.320089\pi\)
0.262883 + 0.964828i \(0.415327\pi\)
\(500\) −17057.1 + 11629.3i −1.52563 + 1.04016i
\(501\) −3835.38 20068.9i −0.342020 1.78964i
\(502\) −6131.70 6608.40i −0.545161 0.587544i
\(503\) −283.393 355.363i −0.0251210 0.0315007i 0.769112 0.639114i \(-0.220699\pi\)
−0.794233 + 0.607613i \(0.792127\pi\)
\(504\) −1712.72 + 12819.0i −0.151370 + 1.13294i
\(505\) 7695.08 9649.32i 0.678072 0.850276i
\(506\) −18350.3 + 1375.16i −1.61219 + 0.120817i
\(507\) 3749.38 14096.3i 0.328434 1.23479i
\(508\) −10733.3 + 18590.7i −0.937430 + 1.62368i
\(509\) −8085.19 14004.0i −0.704066 1.21948i −0.967028 0.254672i \(-0.918033\pi\)
0.262961 0.964806i \(-0.415301\pi\)
\(510\) −4622.51 17125.7i −0.401349 1.48694i
\(511\) 11045.0 + 1516.97i 0.956167 + 0.131324i
\(512\) 4059.86 + 926.636i 0.350434 + 0.0799842i
\(513\) −10883.5 + 4819.90i −0.936686 + 0.414822i
\(514\) 17911.3 7029.69i 1.53703 0.603241i
\(515\) −10985.1 + 4311.33i −0.939923 + 0.368893i
\(516\) 5836.54 + 16582.2i 0.497944 + 1.41471i
\(517\) 10879.8 + 2483.25i 0.925521 + 0.211244i
\(518\) 20035.4 + 2751.75i 1.69943 + 0.233408i
\(519\) 10467.1 2825.25i 0.885273 0.238949i
\(520\) 8370.80 + 14498.6i 0.705930 + 1.22271i
\(521\) 2253.11 3902.51i 0.189464 0.328161i −0.755608 0.655024i \(-0.772658\pi\)
0.945072 + 0.326863i \(0.105992\pi\)
\(522\) −34599.8 7763.74i −2.90113 0.650976i
\(523\) 6002.92 449.857i 0.501892 0.0376116i 0.178621 0.983918i \(-0.442837\pi\)
0.323271 + 0.946306i \(0.395217\pi\)
\(524\) −8911.85 + 11175.1i −0.742970 + 0.931654i
\(525\) 679.923 3912.68i 0.0565224 0.325264i
\(526\) 6610.10 + 8288.81i 0.547936 + 0.687090i
\(527\) −6254.35 6740.59i −0.516971 0.557163i
\(528\) 1658.79 317.012i 0.136722 0.0261291i
\(529\) −6368.65 + 4342.07i −0.523436 + 0.356873i
\(530\) 875.851 + 132.013i 0.0717822 + 0.0108194i
\(531\) −6708.97 + 3906.31i −0.548295 + 0.319246i
\(532\) −15818.1 14295.7i −1.28910 1.16504i
\(533\) −6989.26 + 14513.3i −0.567990 + 1.17944i
\(534\) −8224.30 5146.65i −0.666480 0.417074i
\(535\) −1186.96 + 1279.24i −0.0959191 + 0.103376i
\(536\) −6419.94 481.108i −0.517349 0.0387700i
\(537\) −6821.96 + 19611.4i −0.548211 + 1.57596i
\(538\) 24210.5i 1.94013i
\(539\) 7376.84 6206.08i 0.589505 0.495946i
\(540\) −2045.60 17299.1i −0.163016 1.37858i
\(541\) −4364.22 + 11119.9i −0.346825 + 0.883697i 0.645914 + 0.763410i \(0.276477\pi\)
−0.992739 + 0.120286i \(0.961619\pi\)
\(542\) 2679.04 35749.3i 0.212315 2.83315i
\(543\) 1867.60 + 1601.25i 0.147600 + 0.126549i
\(544\) 6932.52 10168.1i 0.546378 0.801389i
\(545\) −4683.71 2255.56i −0.368125 0.177280i
\(546\) −30657.7 7725.59i −2.40298 0.605540i
\(547\) 17412.5 8385.44i 1.36107 0.655458i 0.396197 0.918166i \(-0.370330\pi\)
0.964875 + 0.262708i \(0.0846156\pi\)
\(548\) −6228.72 + 41324.9i −0.485543 + 3.22137i
\(549\) −6498.87 8088.28i −0.505219 0.628778i
\(550\) −5326.39 + 802.824i −0.412942 + 0.0622410i
\(551\) 17587.7 16319.0i 1.35982 1.26173i
\(552\) 14337.9 12384.6i 1.10555 0.954935i
\(553\) 151.427 + 11550.5i 0.0116443 + 0.888208i
\(554\) −22924.0 18281.3i −1.75803 1.40198i
\(555\) −11107.0 + 1272.09i −0.849485 + 0.0972923i
\(556\) 3397.59 11014.7i 0.259155 0.840158i
\(557\) 2225.90 + 1285.12i 0.169325 + 0.0977601i 0.582268 0.812997i \(-0.302166\pi\)
−0.412942 + 0.910757i \(0.635499\pi\)
\(558\) −8129.21 11829.9i −0.616733 0.897489i
\(559\) −17195.5 + 3924.76i −1.30106 + 0.296958i
\(560\) 1684.21 1002.04i 0.127090 0.0756142i
\(561\) 2159.85 11530.8i 0.162547 0.867793i
\(562\) 26961.9 8316.64i 2.02370 0.624228i
\(563\) 2954.41 + 7527.72i 0.221161 + 0.563509i 0.997790 0.0664496i \(-0.0211672\pi\)
−0.776629 + 0.629958i \(0.783072\pi\)
\(564\) −25638.9 + 11242.1i −1.91417 + 0.839326i
\(565\) 3407.87 + 11048.0i 0.253753 + 0.822646i
\(566\) 7672.05 33613.4i 0.569753 2.49625i
\(567\) 10725.6 + 8200.33i 0.794415 + 0.607375i
\(568\) 1419.96 + 6221.23i 0.104894 + 0.459572i
\(569\) 11358.4 6557.77i 0.836852 0.483157i −0.0193412 0.999813i \(-0.506157\pi\)
0.856193 + 0.516656i \(0.172824\pi\)
\(570\) 16580.0 + 8723.94i 1.21835 + 0.641062i
\(571\) 15309.6 + 4722.39i 1.12204 + 0.346105i 0.799630 0.600494i \(-0.205029\pi\)
0.322415 + 0.946598i \(0.395505\pi\)
\(572\) 2016.03 + 26902.0i 0.147368 + 1.96649i
\(573\) −7078.16 + 9627.48i −0.516046 + 0.701909i
\(574\) 17756.6 + 8266.15i 1.29119 + 0.601084i
\(575\) −4548.55 + 3627.34i −0.329891 + 0.263079i
\(576\) 14706.9 15967.4i 1.06387 1.15505i
\(577\) −633.491 4202.94i −0.0457064 0.303242i −0.999991 0.00434125i \(-0.998618\pi\)
0.954284 0.298901i \(-0.0966200\pi\)
\(578\) 4028.52 + 5908.75i 0.289903 + 0.425210i
\(579\) −799.474 + 7214.45i −0.0573834 + 0.517828i
\(580\) 15234.5 + 31634.8i 1.09065 + 2.26476i
\(581\) −6060.08 + 2470.56i −0.432727 + 0.176414i
\(582\) −3780.79 + 8709.21i −0.269276 + 0.620289i
\(583\) 483.998 + 329.984i 0.0343828 + 0.0234418i
\(584\) 11412.9 + 10589.6i 0.808678 + 0.750343i
\(585\) 17477.3 64.1185i 1.23521 0.00453158i
\(586\) −3421.99 1343.03i −0.241231 0.0946761i
\(587\) 2582.98 0.181620 0.0908101 0.995868i \(-0.471054\pi\)
0.0908101 + 0.995868i \(0.471054\pi\)
\(588\) −5601.50 + 23525.9i −0.392861 + 1.64999i
\(589\) 9711.82 0.679403
\(590\) 11374.6 + 4464.22i 0.793706 + 0.311507i
\(591\) 713.998 20067.1i 0.0496953 1.39670i
\(592\) 1993.14 + 1849.36i 0.138374 + 0.128392i
\(593\) 4416.95 + 3011.43i 0.305873 + 0.208540i 0.706522 0.707691i \(-0.250263\pi\)
−0.400649 + 0.916231i \(0.631215\pi\)
\(594\) 5953.07 17318.0i 0.411208 1.19624i
\(595\) −2205.28 13433.7i −0.151945 0.925594i
\(596\) 6081.75 + 12628.9i 0.417983 + 0.867952i
\(597\) −4479.18 496.364i −0.307070 0.0340282i
\(598\) 26090.8 + 38268.2i 1.78417 + 2.61690i
\(599\) −1229.31 8155.95i −0.0838536 0.556332i −0.990826 0.135143i \(-0.956851\pi\)
0.906973 0.421190i \(-0.138387\pi\)
\(600\) 3914.34 3928.73i 0.266337 0.267316i
\(601\) 14751.4 11763.9i 1.00120 0.798434i 0.0216809 0.999765i \(-0.493098\pi\)
0.979523 + 0.201331i \(0.0645268\pi\)
\(602\) 5045.77 + 20843.6i 0.341611 + 1.41116i
\(603\) −3765.62 + 5566.91i −0.254308 + 0.375957i
\(604\) −1730.00 23085.3i −0.116544 1.55518i
\(605\) −4731.23 1459.39i −0.317937 0.0980705i
\(606\) −15156.1 + 28804.5i −1.01597 + 1.93087i
\(607\) −14991.2 + 8655.17i −1.00243 + 0.578752i −0.908966 0.416871i \(-0.863127\pi\)
−0.0934622 + 0.995623i \(0.529793\pi\)
\(608\) 2892.31 + 12672.0i 0.192925 + 0.845261i
\(609\) −25818.2 8603.36i −1.71791 0.572456i
\(610\) −3634.02 + 15921.7i −0.241208 + 1.05680i
\(611\) −8279.14 26840.3i −0.548180 1.77716i
\(612\) 12866.2 + 26468.1i 0.849813 + 1.74822i
\(613\) −2532.37 6452.37i −0.166854 0.425137i 0.822852 0.568256i \(-0.192382\pi\)
−0.989705 + 0.143120i \(0.954287\pi\)
\(614\) 22227.9 6856.39i 1.46098 0.450654i
\(615\) −10642.3 1993.41i −0.697785 0.130703i
\(616\) 13410.4 1181.94i 0.877144 0.0773081i
\(617\) −3719.59 + 848.973i −0.242699 + 0.0553944i −0.342140 0.939649i \(-0.611152\pi\)
0.0994410 + 0.995043i \(0.468295\pi\)
\(618\) 26320.9 16606.0i 1.71324 1.08089i
\(619\) −11111.7 6415.35i −0.721515 0.416567i 0.0937952 0.995592i \(-0.470100\pi\)
−0.815310 + 0.579025i \(0.803433\pi\)
\(620\) −4189.30 + 13581.4i −0.271365 + 0.879744i
\(621\) −3783.99 19413.4i −0.244519 1.25448i
\(622\) 14342.0 + 11437.4i 0.924536 + 0.737293i
\(623\) −5881.68 4565.64i −0.378241 0.293609i
\(624\) −2778.54 3216.77i −0.178254 0.206368i
\(625\) 6424.18 5960.76i 0.411147 0.381489i
\(626\) 2662.35 401.285i 0.169982 0.0256207i
\(627\) 7375.96 + 9955.79i 0.469804 + 0.634125i
\(628\) −783.771 + 5199.98i −0.0498024 + 0.330417i
\(629\) 17016.9 8194.91i 1.07871 0.519479i
\(630\) −356.523 21247.7i −0.0225464 1.34369i
\(631\) −20974.8 10100.9i −1.32329 0.637261i −0.367145 0.930164i \(-0.619665\pi\)
−0.956142 + 0.292903i \(0.905379\pi\)
\(632\) −9087.24 + 13328.5i −0.571948 + 0.838893i
\(633\) 11904.2 13884.4i 0.747472 0.871808i
\(634\) 2771.40 36981.8i 0.173607 2.31662i
\(635\) 5288.90 13475.9i 0.330526 0.842165i
\(636\) −1468.38 + 57.6404i −0.0915490 + 0.00359370i
\(637\) −22811.2 8269.41i −1.41886 0.514358i
\(638\) 36912.0i 2.29053i
\(639\) 6372.88 + 1940.20i 0.394534 + 0.120114i
\(640\) −22889.2 1715.31i −1.41371 0.105943i
\(641\) −21673.7 + 23358.7i −1.33550 + 1.43933i −0.528301 + 0.849057i \(0.677171\pi\)
−0.807203 + 0.590274i \(0.799020\pi\)
\(642\) 2441.36 3901.28i 0.150082 0.239830i
\(643\) −12710.1 + 26392.8i −0.779529 + 1.61871i 0.00607609 + 0.999982i \(0.498066\pi\)
−0.785605 + 0.618728i \(0.787648\pi\)
\(644\) 29007.8 20339.3i 1.77495 1.24453i
\(645\) −5558.75 10471.1i −0.339342 0.639226i
\(646\) −31298.6 4717.50i −1.90623 0.287318i
\(647\) 6214.83 4237.20i 0.377636 0.257468i −0.359595 0.933108i \(-0.617085\pi\)
0.737231 + 0.675641i \(0.236133\pi\)
\(648\) 5689.46 + 17975.4i 0.344912 + 1.08973i
\(649\) 5496.62 + 5923.95i 0.332452 + 0.358298i
\(650\) 8453.07 + 10599.8i 0.510087 + 0.639629i
\(651\) −5292.30 9661.25i −0.318620 0.581650i
\(652\) −10880.8 + 13644.1i −0.653568 + 0.819549i
\(653\) 7272.05 544.964i 0.435800 0.0326587i 0.144976 0.989435i \(-0.453690\pi\)
0.290824 + 0.956777i \(0.406071\pi\)
\(654\) 13249.1 + 3524.04i 0.792170 + 0.210705i
\(655\) 4819.60 8347.80i 0.287508 0.497978i
\(656\) 1316.65 + 2280.50i 0.0783635 + 0.135729i
\(657\) 15513.5 4847.67i 0.921215 0.287862i
\(658\) −32500.2 + 10493.5i −1.92552 + 0.621701i
\(659\) 14930.2 + 3407.72i 0.882546 + 0.201435i 0.639695 0.768629i \(-0.279061\pi\)
0.242850 + 0.970064i \(0.421918\pi\)
\(660\) −17104.3 + 6020.28i −1.00876 + 0.355059i
\(661\) −15919.6 + 6247.96i −0.936761 + 0.367652i −0.784105 0.620628i \(-0.786878\pi\)
−0.152656 + 0.988279i \(0.548783\pi\)
\(662\) −7045.56 + 2765.18i −0.413646 + 0.162344i
\(663\) −27852.3 + 9803.33i −1.63151 + 0.574253i
\(664\) −8909.93 2033.63i −0.520742 0.118856i
\(665\) 11985.1 + 7943.16i 0.698889 + 0.463192i
\(666\) 28141.2 8793.60i 1.63731 0.511629i
\(667\) 19933.6 + 34526.0i 1.15717 + 2.00428i
\(668\) 26677.5 46206.8i 1.54519 2.67634i
\(669\) 16381.5 + 4357.21i 0.946702 + 0.251808i
\(670\) 10548.9 790.534i 0.608270 0.0455836i
\(671\) −6734.03 + 8444.21i −0.387428 + 0.485820i
\(672\) 11029.9 9782.67i 0.633167 0.561569i
\(673\) 5965.29 + 7480.24i 0.341672 + 0.428443i 0.922747 0.385407i \(-0.125939\pi\)
−0.581075 + 0.813850i \(0.697368\pi\)
\(674\) −23998.2 25863.9i −1.37148 1.47810i
\(675\) −1529.22 5584.03i −0.0871996 0.318414i
\(676\) 31471.4 21456.8i 1.79059 1.22080i
\(677\) −14698.0 2215.37i −0.834401 0.125766i −0.282073 0.959393i \(-0.591022\pi\)
−0.552328 + 0.833627i \(0.686260\pi\)
\(678\) −14296.9 26931.3i −0.809834 1.52550i
\(679\) −3560.23 + 6357.54i −0.201221 + 0.359323i
\(680\) 8248.60 17128.4i 0.465176 0.965947i
\(681\) 5022.45 8025.83i 0.282615 0.451616i
\(682\) −10162.8 + 10952.9i −0.570605 + 0.614966i
\(683\) 4960.05 + 371.704i 0.277878 + 0.0208241i 0.212940 0.977065i \(-0.431696\pi\)
0.0649380 + 0.997889i \(0.479315\pi\)
\(684\) −29735.4 9052.82i −1.66222 0.506057i
\(685\) 28183.3i 1.57201i
\(686\) −9690.28 + 27865.4i −0.539325 + 1.55088i
\(687\) −33612.9 + 1319.45i −1.86668 + 0.0732755i
\(688\) −1053.37 + 2683.95i −0.0583714 + 0.148728i
\(689\) 110.181 1470.27i 0.00609226 0.0812956i
\(690\) −20263.2 + 23633.8i −1.11798 + 1.30395i
\(691\) 14577.8 21381.7i 0.802556 1.17713i −0.178601 0.983922i \(-0.557157\pi\)
0.981157 0.193212i \(-0.0618905\pi\)
\(692\) 25507.7 + 12283.9i 1.40124 + 0.674801i
\(693\) 5884.54 12762.8i 0.322562 0.699594i
\(694\) 32517.6 15659.6i 1.77860 0.856529i
\(695\) −1158.57 + 7686.60i −0.0632331 + 0.419524i
\(696\) −22623.5 30536.4i −1.23210 1.66305i
\(697\) 18088.0 2726.32i 0.982972 0.148159i
\(698\) 10956.9 10166.5i 0.594159 0.551299i
\(699\) −9726.94 11261.1i −0.526333 0.609345i
\(700\) 8022.49 6571.60i 0.433174 0.354833i
\(701\) 19108.2 + 15238.3i 1.02954 + 0.821031i 0.984043 0.177933i \(-0.0569412\pi\)
0.0454979 + 0.998964i \(0.485513\pi\)
\(702\) −45240.5 + 8818.12i −2.43233 + 0.474100i
\(703\) −5879.90 + 19062.2i −0.315455 + 1.02268i
\(704\) −19569.7 11298.6i −1.04767 0.604873i
\(705\) 15967.2 10073.7i 0.852991 0.538155i
\(706\) −43581.9 + 9947.28i −2.32327 + 0.530270i
\(707\) −13799.7 + 20821.7i −0.734074 + 1.10761i
\(708\) −19926.2 3732.39i −1.05773 0.198124i
\(709\) −21059.6 + 6496.01i −1.11553 + 0.344094i −0.797096 0.603852i \(-0.793632\pi\)
−0.318430 + 0.947946i \(0.603156\pi\)
\(710\) −3830.72 9760.50i −0.202485 0.515923i
\(711\) 7362.46 + 15145.9i 0.388346 + 0.798898i
\(712\) −3064.83 9935.94i −0.161319 0.522985i
\(713\) −3590.97 + 15733.1i −0.188616 + 0.826380i
\(714\) 12362.7 + 33706.3i 0.647988 + 1.76670i
\(715\) −4048.32 17736.9i −0.211746 0.927721i
\(716\) −46957.5 + 27110.9i −2.45096 + 1.41506i
\(717\) 6801.96 12927.3i 0.354287 0.673331i
\(718\) −42677.3 13164.2i −2.21825 0.684240i
\(719\) −1213.56 16193.8i −0.0629460 0.839956i −0.935925 0.352198i \(-0.885434\pi\)
0.872979 0.487757i \(-0.162185\pi\)
\(720\) 1600.76 2366.50i 0.0828568 0.122492i
\(721\) 21381.3 10644.2i 1.10441 0.549807i
\(722\) 1231.76 982.294i 0.0634921 0.0506332i
\(723\) −5252.08 + 5271.39i −0.270162 + 0.271155i
\(724\) 957.458 + 6352.32i 0.0491487 + 0.326080i
\(725\) 6573.91 + 9642.15i 0.336757 + 0.493932i
\(726\) 12978.0 + 1438.17i 0.663442 + 0.0735198i
\(727\) 4397.38 + 9131.25i 0.224332 + 0.465831i 0.982508 0.186219i \(-0.0596234\pi\)
−0.758176 + 0.652050i \(0.773909\pi\)
\(728\) −19453.0 27743.8i −0.990350 1.41243i
\(729\) 19236.5 + 4168.42i 0.977318 + 0.211778i
\(730\) −21137.0 14411.0i −1.07166 0.730649i
\(731\) 14682.1 + 13623.0i 0.742868 + 0.689281i
\(732\) 963.428 27077.4i 0.0486466 1.36722i
\(733\) −8921.20 3501.31i −0.449539 0.176431i 0.129761 0.991545i \(-0.458579\pi\)
−0.579300 + 0.815114i \(0.696674\pi\)
\(734\) 38931.1 1.95773
\(735\) 1370.72 16251.2i 0.0687890 0.815555i
\(736\) −21598.0 −1.08168
\(737\) 6512.46 + 2555.95i 0.325495 + 0.127747i
\(738\) 28554.0 104.756i 1.42424 0.00522508i
\(739\) 18483.6 + 17150.3i 0.920070 + 0.853701i 0.989595 0.143880i \(-0.0459578\pi\)
−0.0695249 + 0.997580i \(0.522148\pi\)
\(740\) −24120.9 16445.3i −1.19825 0.816950i
\(741\) 12418.6 28606.8i 0.615666 1.41821i
\(742\) −1789.29 110.523i −0.0885269 0.00546822i
\(743\) 11136.5 + 23125.2i 0.549877 + 1.14183i 0.971932 + 0.235261i \(0.0755946\pi\)
−0.422055 + 0.906570i \(0.638691\pi\)
\(744\) 1694.36 15289.9i 0.0834921 0.753432i
\(745\) −5324.92 7810.22i −0.261866 0.384087i
\(746\) −1258.97 8352.71i −0.0617883 0.409939i
\(747\) −6463.65 + 7017.61i −0.316590 + 0.343723i
\(748\) 23951.1 19100.3i 1.17077 0.933660i
\(749\) 2165.76 2790.03i 0.105654 0.136109i
\(750\) −21748.2 + 29581.2i −1.05884 + 1.44020i
\(751\) 823.341 + 10986.7i 0.0400055 + 0.533837i 0.980820 + 0.194915i \(0.0624431\pi\)
−0.940815 + 0.338922i \(0.889938\pi\)
\(752\) −4387.62 1353.40i −0.212766 0.0656296i
\(753\) −8926.03 4696.62i −0.431982 0.227297i
\(754\) 80458.6 46452.8i 3.88611 2.24365i
\(755\) 3473.96 + 15220.4i 0.167457 + 0.733678i
\(756\) 7198.15 + 34513.7i 0.346289 + 1.66039i
\(757\) −5036.61 + 22066.8i −0.241821 + 1.05949i 0.697536 + 0.716550i \(0.254280\pi\)
−0.939358 + 0.342939i \(0.888577\pi\)
\(758\) −14344.1 46502.4i −0.687336 2.22829i
\(759\) −18855.6 + 8267.82i −0.901732 + 0.395392i
\(760\) 7335.72 + 18691.1i 0.350125 + 0.892103i
\(761\) −3728.99 + 1150.24i −0.177629 + 0.0547914i −0.382294 0.924041i \(-0.624866\pi\)
0.204665 + 0.978832i \(0.434390\pi\)
\(762\) −7028.95 + 37525.6i −0.334163 + 1.78400i
\(763\) 9843.78 + 3715.23i 0.467063 + 0.176278i
\(764\) −30421.6 + 6943.54i −1.44060 + 0.328807i
\(765\) −11240.1 16356.9i −0.531224 0.773054i
\(766\) 5617.94 + 3243.52i 0.264993 + 0.152994i
\(767\) 5995.31 19436.3i 0.282240 0.915000i
\(768\) 26935.1 3084.91i 1.26554 0.144944i
\(769\) −17847.4 14232.8i −0.836922 0.667423i 0.108204 0.994129i \(-0.465490\pi\)
−0.945126 + 0.326705i \(0.894062\pi\)
\(770\) −21499.8 + 5204.61i −1.00623 + 0.243586i
\(771\) 16291.9 14072.4i 0.761009 0.657335i
\(772\) −13894.8 + 12892.5i −0.647777 + 0.601049i
\(773\) −7608.72 + 1146.83i −0.354032 + 0.0533618i −0.323651 0.946177i \(-0.604910\pi\)
−0.0303814 + 0.999538i \(0.509672\pi\)
\(774\) 19582.8 + 24372.1i 0.909418 + 1.13183i
\(775\) −704.049 + 4671.06i −0.0326325 + 0.216503i
\(776\) −9167.85 + 4415.01i −0.424107 + 0.204239i
\(777\) 22167.1 4538.34i 1.02347 0.209539i
\(778\) 7802.85 + 3757.65i 0.359570 + 0.173160i
\(779\) −10883.3 + 15962.9i −0.500558 + 0.734184i
\(780\) 34647.9 + 29706.5i 1.59050 + 1.36367i
\(781\) 518.211 6915.05i 0.0237427 0.316824i
\(782\) 19215.1 48959.2i 0.878681 2.23884i
\(783\) −39399.7 + 4658.99i −1.79825 + 0.212642i
\(784\) −3217.52 + 2319.52i −0.146571 + 0.105663i
\(785\) 3546.36i 0.161242i
\(786\) −8351.94 + 24009.7i −0.379013 + 1.08956i
\(787\) 13606.2 + 1019.64i 0.616275 + 0.0461834i 0.379210 0.925310i \(-0.376196\pi\)
0.237065 + 0.971494i \(0.423815\pi\)
\(788\) 35664.9 38437.6i 1.61232 1.73767i
\(789\) 10055.1 + 6292.37i 0.453704 + 0.283922i
\(790\) 11500.8 23881.6i 0.517949 1.07553i
\(791\) −8833.90 21668.8i −0.397089 0.974024i
\(792\) 16960.8 9875.45i 0.760953 0.443067i
\(793\) 26880.8 + 4051.62i 1.20374 + 0.181434i
\(794\) −47303.5 + 32251.0i −2.11428 + 1.44149i
\(795\) 973.390 186.025i 0.0434246 0.00829892i
\(796\) −8004.44 8626.74i −0.356420 0.384129i
\(797\) −1145.04 1435.83i −0.0508901 0.0638141i 0.755735 0.654877i \(-0.227280\pi\)
−0.806625 + 0.591063i \(0.798708\pi\)
\(798\) −34977.8 14642.4i −1.55163 0.649545i
\(799\) −19886.7 + 24937.2i −0.880528 + 1.10415i
\(800\) −6304.50 + 472.457i −0.278622 + 0.0208798i
\(801\) −10591.5 2376.60i −0.467207 0.104835i
\(802\) −9200.21 + 15935.2i −0.405076 + 0.701612i
\(803\) −8459.36 14652.0i −0.371761 0.643909i
\(804\) −16944.1 + 4573.50i −0.743251 + 0.200615i
\(805\) −17299.4 + 16478.7i −0.757420 + 0.721489i
\(806\) 36664.0 + 8368.31i 1.60227 + 0.365709i
\(807\) 8993.36 + 25551.1i 0.392294 + 1.11455i
\(808\) −32472.1 + 12744.4i −1.41382 + 0.554883i
\(809\) −20403.1 + 8007.62i −0.886692 + 0.348001i −0.764590 0.644516i \(-0.777059\pi\)
−0.122102 + 0.992518i \(0.538963\pi\)
\(810\) −13646.4 27813.1i −0.591957 1.20649i
\(811\) −10517.5 2400.56i −0.455390 0.103940i −0.0113278 0.999936i \(-0.503606\pi\)
−0.444062 + 0.895996i \(0.646463\pi\)
\(812\) −36336.1 61072.8i −1.57038 2.63945i
\(813\) −10452.3 38724.1i −0.450894 1.67050i
\(814\) −15345.1 26578.6i −0.660745 1.14444i
\(815\) 5884.45 10192.2i 0.252912 0.438056i
\(816\) −1240.73 + 4664.67i −0.0532281 + 0.200118i
\(817\) −21094.7 + 1580.83i −0.903319 + 0.0676944i
\(818\) −15682.6 + 19665.3i −0.670328 + 0.840565i
\(819\) −35225.1 + 3234.88i −1.50289 + 0.138017i
\(820\) −17628.5 22105.4i −0.750747 0.941407i
\(821\) 14063.6 + 15157.0i 0.597836 + 0.644314i 0.957386 0.288812i \(-0.0932602\pi\)
−0.359550 + 0.933126i \(0.617070\pi\)
\(822\) 13952.0 + 73004.7i 0.592009 + 3.09773i
\(823\) 7821.41 5332.55i 0.331273 0.225858i −0.386248 0.922395i \(-0.626229\pi\)
0.717521 + 0.696537i \(0.245277\pi\)
\(824\) 32981.5 + 4971.17i 1.39438 + 0.210168i
\(825\) −5323.12 + 2825.85i −0.224639 + 0.119253i
\(826\) −23726.1 6979.25i −0.999437 0.293994i
\(827\) −3345.25 + 6946.48i −0.140660 + 0.292083i −0.959384 0.282104i \(-0.908968\pi\)
0.818724 + 0.574187i \(0.194682\pi\)
\(828\) 25660.2 44823.8i 1.07700 1.88132i
\(829\) 1668.99 1798.74i 0.0699232 0.0753593i −0.697121 0.716953i \(-0.745536\pi\)
0.767044 + 0.641594i \(0.221727\pi\)
\(830\) 14974.9 + 1122.21i 0.626248 + 0.0469308i
\(831\) −30984.3 10778.1i −1.29342 0.449926i
\(832\) 56875.8i 2.36997i
\(833\) 6833.22 + 26692.3i 0.284222 + 1.11024i
\(834\) −804.108 20484.5i −0.0333861 0.850506i
\(835\) −13145.5 + 33494.1i −0.544812 + 1.38816i
\(836\) −2417.93 + 32265.1i −0.100031 + 1.33482i
\(837\) −12973.8 9465.23i −0.535769 0.390880i
\(838\) 9546.39 14002.0i 0.393526 0.577196i
\(839\) 21673.2 + 10437.3i 0.891827 + 0.429481i 0.822930 0.568143i \(-0.192338\pi\)
0.0688969 + 0.997624i \(0.478052\pi\)
\(840\) 14596.3 17483.0i 0.599548 0.718118i
\(841\) 50076.4 24115.5i 2.05324 0.988787i
\(842\) −10429.1 + 69192.5i −0.426853 + 2.83198i
\(843\) 25365.5 18792.6i 1.03634 0.767795i
\(844\) 47225.2 7118.06i 1.92602 0.290300i
\(845\) −18829.9 + 17471.6i −0.766590 + 0.711292i
\(846\) −36373.7 + 33999.0i −1.47819 + 1.38169i
\(847\) 9798.10 + 2101.61i 0.397482 + 0.0852565i
\(848\) −188.437 150.274i −0.00763085 0.00608540i
\(849\) −4389.36 38324.7i −0.177435 1.54923i
\(850\) 4537.92 14711.6i 0.183117 0.593650i
\(851\) −28706.5 16573.7i −1.15634 0.667613i
\(852\) 9282.17 + 14712.5i 0.373242 + 0.591599i
\(853\) 2990.76 682.620i 0.120049 0.0274003i −0.162074 0.986779i \(-0.551818\pi\)
0.282123 + 0.959378i \(0.408961\pi\)
\(854\) 4497.47 32745.9i 0.180211 1.31211i
\(855\) 20738.8 + 3048.10i 0.829534 + 0.121921i
\(856\) 4713.21 1453.83i 0.188194 0.0580502i
\(857\) 1933.23 + 4925.80i 0.0770571 + 0.196338i 0.964211 0.265135i \(-0.0854164\pi\)
−0.887154 + 0.461473i \(0.847321\pi\)
\(858\) 19267.1 + 43940.6i 0.766630 + 1.74838i
\(859\) −4712.41 15277.3i −0.187178 0.606815i −0.999714 0.0239047i \(-0.992390\pi\)
0.812537 0.582910i \(-0.198086\pi\)
\(860\) 6888.75 30181.6i 0.273145 1.19673i
\(861\) 21810.4 + 2127.91i 0.863296 + 0.0842267i
\(862\) 5644.53 + 24730.3i 0.223032 + 0.977167i
\(863\) 21213.1 12247.4i 0.836736 0.483090i −0.0194176 0.999811i \(-0.506181\pi\)
0.856153 + 0.516722i \(0.172848\pi\)
\(864\) 8486.52 19747.1i 0.334164 0.777558i
\(865\) −18244.3 5627.63i −0.717140 0.221208i
\(866\) 393.584 + 5252.01i 0.0154440 + 0.206086i
\(867\) 6446.49 + 4739.49i 0.252519 + 0.185653i
\(868\) 6032.86 28126.3i 0.235908 1.09985i
\(869\) 13705.6 10929.8i 0.535017 0.426662i
\(870\) 44237.1 + 44075.1i 1.72388 + 1.71757i
\(871\) −2624.45 17412.1i −0.102096 0.677366i
\(872\) 8276.98 + 12140.1i 0.321438 + 0.471463i
\(873\) −754.973 + 10595.9i −0.0292691 + 0.410787i
\(874\) 24102.0 + 50048.4i 0.932796 + 1.93697i
\(875\) −18893.1 + 20905.0i −0.729947 + 0.807677i
\(876\) 38932.4 + 16901.1i 1.50160 + 0.651867i
\(877\) −11425.5 7789.77i −0.439922 0.299934i 0.323030 0.946389i \(-0.395298\pi\)
−0.762952 + 0.646455i \(0.776251\pi\)
\(878\) −29354.6 27237.0i −1.12832 1.04693i
\(879\) −4110.38 146.250i −0.157724 0.00561192i
\(880\) −2768.45 1086.54i −0.106050 0.0416217i
\(881\) 17770.3 0.679565 0.339782 0.940504i \(-0.389647\pi\)
0.339782 + 0.940504i \(0.389647\pi\)
\(882\) 4494.39 + 42774.8i 0.171580 + 1.63300i
\(883\) 23216.8 0.884834 0.442417 0.896809i \(-0.354121\pi\)
0.442417 + 0.896809i \(0.354121\pi\)
\(884\) −71775.5 28169.8i −2.73085 1.07178i
\(885\) 13662.8 + 486.131i 0.518950 + 0.0184645i
\(886\) 35935.2 + 33342.9i 1.36260 + 1.26431i
\(887\) 28410.0 + 19369.6i 1.07544 + 0.733223i 0.965418 0.260707i \(-0.0839555\pi\)
0.110022 + 0.993929i \(0.464908\pi\)
\(888\) 28984.8 + 12582.7i 1.09534 + 0.475504i
\(889\) −8268.54 + 28109.0i −0.311944 + 1.06046i
\(890\) 7413.04 + 15393.3i 0.279197 + 0.579760i
\(891\) −150.332 20488.4i −0.00565244 0.770354i
\(892\) 24935.3 + 36573.4i 0.935981 + 1.37283i
\(893\) −5020.89 33311.4i −0.188150 1.24829i
\(894\) 17659.8 + 17595.2i 0.660663 + 0.658244i
\(895\) 28588.4 22798.5i 1.06772 0.851475i
\(896\) 46452.4 608.987i 1.73199 0.0227063i
\(897\) 41750.9 + 30695.5i 1.55410 + 1.14258i
\(898\) −5566.73 74282.9i −0.206865 2.76041i
\(899\) 30932.4 + 9541.39i 1.14756 + 0.353975i
\(900\) 6509.74 13645.5i 0.241102 0.505387i
\(901\) −1449.95 + 837.129i −0.0536124 + 0.0309532i
\(902\) −6614.07 28978.1i −0.244151 1.06970i
\(903\) 13067.8 + 20123.4i 0.481584 + 0.741602i
\(904\) 7271.58 31858.9i 0.267532 1.17214i
\(905\) −1276.95 4139.78i −0.0469031 0.152056i
\(906\) −16533.5 37706.4i −0.606281 1.38268i
\(907\) −8889.99 22651.3i −0.325455 0.829245i −0.996162 0.0875234i \(-0.972105\pi\)
0.670708 0.741722i \(-0.265990\pi\)
\(908\) 23625.2 7287.40i 0.863468 0.266345i
\(909\) −5295.47 + 36029.6i −0.193223 + 1.31466i
\(910\) 38401.6 + 40314.0i 1.39890 + 1.46857i
\(911\) −24481.5 + 5587.75i −0.890350 + 0.203217i −0.643143 0.765746i \(-0.722370\pi\)
−0.247207 + 0.968963i \(0.579513\pi\)
\(912\) −2720.22 4311.63i −0.0987671 0.156549i
\(913\) 8600.82 + 4965.69i 0.311770 + 0.180000i
\(914\) −10659.4 + 34557.1i −0.385758 + 1.25060i
\(915\) 2079.11 + 18153.2i 0.0751182 + 0.655877i
\(916\) −68677.7 54768.7i −2.47727 1.97555i
\(917\) −8233.61 + 17686.7i −0.296508 + 0.636931i
\(918\) 37213.2 + 36805.9i 1.33793 + 1.32328i
\(919\) 27468.0 25486.5i 0.985946 0.914824i −0.0104247 0.999946i \(-0.503318\pi\)
0.996371 + 0.0851216i \(0.0271279\pi\)
\(920\) −32991.9 + 4972.73i −1.18229 + 0.178202i
\(921\) 20911.8 15493.0i 0.748173 0.554300i
\(922\) −11429.6 + 75830.3i −0.408257 + 2.70861i
\(923\) −15725.2 + 7572.83i −0.560780 + 0.270057i
\(924\) 33414.7 15177.0i 1.18968 0.540354i
\(925\) −8742.00 4209.93i −0.310741 0.149645i
\(926\) 10493.8 15391.6i 0.372406 0.546220i
\(927\) 21609.9 27302.8i 0.765655 0.967360i
\(928\) −3237.57 + 43202.3i −0.114524 + 1.52822i
\(929\) −3141.52 + 8004.47i −0.110947 + 0.282689i −0.975554 0.219760i \(-0.929472\pi\)
0.864607 + 0.502449i \(0.167568\pi\)
\(930\) 991.483 + 25257.9i 0.0349591 + 0.890579i
\(931\) −25574.9 13884.8i −0.900306 0.488782i
\(932\) 38857.6i 1.36569i
\(933\) 19384.7 + 6743.13i 0.680202 + 0.236613i
\(934\) −79598.2 5965.06i −2.78858 0.208975i
\(935\) −14051.9 + 15144.3i −0.491492 + 0.529702i
\(936\) −42870.6 24542.1i −1.49708 0.857034i
\(937\) 10540.3 21887.1i 0.367488 0.763097i −0.632446 0.774605i \(-0.717949\pi\)
0.999934 + 0.0115080i \(0.00366320\pi\)
\(938\) −21127.6 + 3468.31i −0.735437 + 0.120729i
\(939\) 2660.71 1412.48i 0.0924698 0.0490889i
\(940\) 48749.8 + 7347.85i 1.69154 + 0.254958i
\(941\) 42650.2 29078.4i 1.47753 1.00736i 0.486506 0.873677i \(-0.338271\pi\)
0.991024 0.133686i \(-0.0426813\pi\)
\(942\) 1755.61 + 9186.32i 0.0607226 + 0.317735i
\(943\) −21835.6 23533.2i −0.754046 0.812668i
\(944\) −2073.11 2599.59i −0.0714765 0.0896287i
\(945\) −8269.05 22291.8i −0.284648 0.767357i
\(946\) 20291.4 25444.6i 0.697389 0.874499i
\(947\) 19466.8 1458.83i 0.667989 0.0500588i 0.263580 0.964637i \(-0.415097\pi\)
0.404408 + 0.914579i \(0.367478\pi\)
\(948\) −11304.0 + 42498.7i −0.387275 + 1.45601i
\(949\) −21291.7 + 36878.4i −0.728303 + 1.26146i
\(950\) 8130.23 + 14082.0i 0.277663 + 0.480926i
\(951\) −10812.6 40059.2i −0.368689 1.36594i
\(952\) −13586.7 + 35998.9i −0.462549 + 1.22556i
\(953\) −50811.0 11597.3i −1.72710 0.394200i −0.760270 0.649607i \(-0.774933\pi\)
−0.966834 + 0.255407i \(0.917790\pi\)
\(954\) −2429.33 + 963.742i −0.0824450 + 0.0327068i
\(955\) 19588.6 7687.96i 0.663741 0.260499i
\(956\) 35508.5 13936.0i 1.20128 0.471469i
\(957\) 13711.6 + 38956.0i 0.463147 + 1.31585i
\(958\) −85238.5 19455.1i −2.87467 0.656124i
\(959\) 5008.01 + 56821.3i 0.168631 + 1.91330i
\(960\) −36908.1 + 9962.08i −1.24084 + 0.334922i
\(961\) −8343.93 14452.1i −0.280082 0.485117i
\(962\) −38622.9 + 66896.8i −1.29444 + 2.24204i
\(963\) 1127.36 5024.19i 0.0377245 0.168123i
\(964\) −19377.2 + 1452.12i −0.647405 + 0.0485163i
\(965\) 7969.82 9993.84i 0.265863 0.333381i
\(966\) 36653.8 51249.6i 1.22082 1.70697i
\(967\) −14773.6 18525.5i −0.491299 0.616070i 0.472943 0.881093i \(-0.343192\pi\)
−0.964242 + 0.265024i \(0.914620\pi\)
\(968\) 9518.43 + 10258.4i 0.316048 + 0.340618i
\(969\) −34784.1 + 6647.62i −1.15317 + 0.220384i
\(970\) 13814.7 9418.70i 0.457281 0.311769i
\(971\) −14992.3 2259.72i −0.495495 0.0746838i −0.103459 0.994634i \(-0.532991\pi\)
−0.392036 + 0.919950i \(0.628229\pi\)
\(972\) 30899.7 + 41073.8i 1.01966 + 1.35539i
\(973\) 969.964 15703.1i 0.0319585 0.517387i
\(974\) −906.740 + 1882.86i −0.0298294 + 0.0619413i
\(975\) 12858.6 + 8046.75i 0.422365 + 0.264310i
\(976\) 3022.60 3257.59i 0.0991301 0.106837i
\(977\) 1030.13 + 77.1974i 0.0337326 + 0.00252791i 0.0915857 0.995797i \(-0.470806\pi\)
−0.0578531 + 0.998325i \(0.518426\pi\)
\(978\) −10197.2 + 29314.4i −0.333406 + 0.958456i
\(979\) 11299.3i 0.368875i
\(980\) 30449.1 29775.6i 0.992509 0.970558i
\(981\) 15291.8 1202.39i 0.497685 0.0391329i
\(982\) −4458.22 + 11359.4i −0.144875 + 0.369136i
\(983\) 1922.70 25656.7i 0.0623852 0.832473i −0.874988 0.484145i \(-0.839131\pi\)
0.937373 0.348328i \(-0.113250\pi\)
\(984\) 23232.5 + 19919.1i 0.752667 + 0.645323i
\(985\) −19919.5 + 29216.6i −0.644355 + 0.945095i
\(986\) −95052.1 45774.7i −3.07006 1.47846i
\(987\) −30401.9 + 23147.3i −0.980450 + 0.746491i
\(988\) 73372.4 35334.3i 2.36264 1.13779i
\(989\) 5238.90 34757.9i 0.168440 1.11753i
\(990\) −25139.4 + 20199.3i −0.807052 + 0.648461i
\(991\) −24854.5 + 3746.21i −0.796698 + 0.120083i −0.534763 0.845002i \(-0.679599\pi\)
−0.261936 + 0.965085i \(0.584361\pi\)
\(992\) −12855.3 + 11928.0i −0.411449 + 0.381769i
\(993\) −6408.53 + 5535.48i −0.204802 + 0.176902i
\(994\) 9457.62 + 18997.8i 0.301788 + 0.606210i
\(995\) 6204.80 + 4948.16i 0.197694 + 0.157656i
\(996\) −24752.3 + 2834.90i −0.787455 + 0.0901880i
\(997\) −4882.52 + 15828.8i −0.155096 + 0.502810i −0.999456 0.0329661i \(-0.989505\pi\)
0.844360 + 0.535776i \(0.179981\pi\)
\(998\) 36202.1 + 20901.3i 1.14826 + 0.662946i
\(999\) 26433.0 19734.0i 0.837139 0.624982i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 147.4.o.a.101.49 yes 648
3.2 odd 2 inner 147.4.o.a.101.6 648
49.33 odd 42 inner 147.4.o.a.131.6 yes 648
147.131 even 42 inner 147.4.o.a.131.49 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
147.4.o.a.101.6 648 3.2 odd 2 inner
147.4.o.a.101.49 yes 648 1.1 even 1 trivial
147.4.o.a.131.6 yes 648 49.33 odd 42 inner
147.4.o.a.131.49 yes 648 147.131 even 42 inner