Properties

Label 69.4.g.a.5.4
Level $69$
Weight $4$
Character 69.5
Analytic conductor $4.071$
Analytic rank $0$
Dimension $220$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [69,4,Mod(5,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 69.g (of order \(22\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.07113179040\)
Analytic rank: \(0\)
Dimension: \(220\)
Relative dimension: \(22\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.4
Character \(\chi\) \(=\) 69.5
Dual form 69.4.g.a.14.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.17465 + 4.00049i) q^{2} +(4.31812 + 2.89031i) q^{3} +(-7.89411 - 5.07323i) q^{4} +(-0.800687 + 5.56890i) q^{5} +(-16.6349 + 13.8795i) q^{6} +(-5.95353 + 2.71889i) q^{7} +(4.36018 - 3.77812i) q^{8} +(10.2923 + 24.9614i) q^{9} +O(q^{10})\) \(q+(-1.17465 + 4.00049i) q^{2} +(4.31812 + 2.89031i) q^{3} +(-7.89411 - 5.07323i) q^{4} +(-0.800687 + 5.56890i) q^{5} +(-16.6349 + 13.8795i) q^{6} +(-5.95353 + 2.71889i) q^{7} +(4.36018 - 3.77812i) q^{8} +(10.2923 + 24.9614i) q^{9} +(-21.3378 - 9.74465i) q^{10} +(5.86916 - 1.72334i) q^{11} +(-19.4245 - 44.7232i) q^{12} +(10.1423 - 22.2086i) q^{13} +(-3.88357 - 27.0108i) q^{14} +(-19.5533 + 21.7329i) q^{15} +(-21.1925 - 46.4052i) q^{16} +(-5.56809 + 3.57839i) q^{17} +(-111.948 + 11.8533i) q^{18} +(20.8258 - 32.4055i) q^{19} +(34.5730 - 39.8994i) q^{20} +(-33.5665 - 5.46705i) q^{21} +25.5038i q^{22} +(50.7872 + 97.9166i) q^{23} +(29.7477 - 3.71210i) q^{24} +(89.5651 + 26.2987i) q^{25} +(76.9317 + 66.6617i) q^{26} +(-27.7027 + 137.534i) q^{27} +(60.7913 + 8.74048i) q^{28} +(103.555 + 161.135i) q^{29} +(-63.9741 - 103.751i) q^{30} +(-41.0835 - 47.4128i) q^{31} +(256.222 - 36.8392i) q^{32} +(30.3247 + 9.52207i) q^{33} +(-7.77477 - 26.4784i) q^{34} +(-10.3743 - 35.3316i) q^{35} +(45.3865 - 249.263i) q^{36} +(251.132 - 36.1073i) q^{37} +(105.175 + 121.379i) q^{38} +(107.986 - 66.5850i) q^{39} +(17.5488 + 27.3065i) q^{40} +(-349.514 - 50.2525i) q^{41} +(61.2998 - 127.860i) q^{42} +(259.004 + 224.428i) q^{43} +(-55.0746 - 16.1714i) q^{44} +(-147.248 + 37.3304i) q^{45} +(-451.372 + 88.1562i) q^{46} -112.534i q^{47} +(42.6133 - 261.636i) q^{48} +(-196.565 + 226.848i) q^{49} +(-210.415 + 327.413i) q^{50} +(-34.3863 - 0.641557i) q^{51} +(-192.734 + 123.863i) q^{52} +(-300.933 - 658.951i) q^{53} +(-517.662 - 272.379i) q^{54} +(4.89775 + 34.0646i) q^{55} +(-15.6862 + 34.3480i) q^{56} +(183.590 - 79.7381i) q^{57} +(-766.259 + 224.994i) q^{58} +(398.645 + 182.055i) q^{59} +(264.612 - 72.3637i) q^{60} +(369.846 - 320.474i) q^{61} +(237.933 - 108.661i) q^{62} +(-129.142 - 120.625i) q^{63} +(-95.5148 + 664.320i) q^{64} +(115.557 + 74.2638i) q^{65} +(-73.7139 + 110.129i) q^{66} +(186.577 - 635.422i) q^{67} +62.1091 q^{68} +(-63.7036 + 569.606i) q^{69} +153.530 q^{70} +(181.547 - 618.292i) q^{71} +(139.183 + 69.9506i) q^{72} +(196.952 + 126.574i) q^{73} +(-150.545 + 1047.06i) q^{74} +(310.741 + 372.431i) q^{75} +(-328.802 + 150.159i) q^{76} +(-30.2566 + 26.2175i) q^{77} +(139.527 + 510.209i) q^{78} +(-620.492 - 283.369i) q^{79} +(275.394 - 80.8631i) q^{80} +(-517.138 + 513.818i) q^{81} +(611.591 - 1339.20i) q^{82} +(-76.5729 - 532.576i) q^{83} +(237.241 + 213.448i) q^{84} +(-15.4694 - 33.8733i) q^{85} +(-1202.06 + 772.517i) q^{86} +(-18.5660 + 995.104i) q^{87} +(19.0796 - 29.6884i) q^{88} +(-242.580 + 279.952i) q^{89} +(23.6252 - 632.915i) q^{90} +159.796i q^{91} +(95.8338 - 1030.62i) q^{92} +(-40.3656 - 323.478i) q^{93} +(450.192 + 132.188i) q^{94} +(163.788 + 141.923i) q^{95} +(1212.87 + 581.485i) q^{96} +(1778.54 + 255.715i) q^{97} +(-676.609 - 1052.82i) q^{98} +(103.424 + 128.765i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 220 q - 5 q^{3} + 50 q^{4} - 32 q^{6} - 22 q^{7} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 220 q - 5 q^{3} + 50 q^{4} - 32 q^{6} - 22 q^{7} - 5 q^{9} - 22 q^{10} + 4 q^{12} + 30 q^{13} + 363 q^{15} + 162 q^{16} - 78 q^{18} - 22 q^{19} - 671 q^{21} - 1258 q^{24} - 632 q^{25} - 269 q^{27} - 22 q^{28} + 1485 q^{30} - 138 q^{31} + 957 q^{33} + 1892 q^{34} - 518 q^{36} + 1166 q^{37} - 401 q^{39} - 2332 q^{40} - 11 q^{42} - 1738 q^{43} - 4326 q^{46} + 1706 q^{48} - 3212 q^{49} - 11 q^{51} - 346 q^{52} - 2307 q^{54} - 1030 q^{55} - 2123 q^{57} + 8656 q^{58} - 451 q^{60} + 506 q^{61} + 2079 q^{63} + 2524 q^{64} + 5742 q^{66} + 1430 q^{67} + 4875 q^{69} + 8092 q^{70} + 6445 q^{72} - 114 q^{73} + 9349 q^{75} + 1034 q^{76} + 6684 q^{78} - 1870 q^{79} - 5497 q^{81} - 4220 q^{82} - 16753 q^{84} - 958 q^{85} - 3785 q^{87} + 1386 q^{88} - 18700 q^{90} - 14746 q^{93} - 6900 q^{94} - 10367 q^{96} + 12650 q^{97} - 4631 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.17465 + 4.00049i −0.415302 + 1.41439i 0.440812 + 0.897600i \(0.354691\pi\)
−0.856113 + 0.516788i \(0.827128\pi\)
\(3\) 4.31812 + 2.89031i 0.831022 + 0.556240i
\(4\) −7.89411 5.07323i −0.986763 0.634154i
\(5\) −0.800687 + 5.56890i −0.0716156 + 0.498097i 0.922170 + 0.386785i \(0.126414\pi\)
−0.993785 + 0.111312i \(0.964495\pi\)
\(6\) −16.6349 + 13.8795i −1.13186 + 0.944380i
\(7\) −5.95353 + 2.71889i −0.321460 + 0.146806i −0.569609 0.821916i \(-0.692905\pi\)
0.248148 + 0.968722i \(0.420178\pi\)
\(8\) 4.36018 3.77812i 0.192695 0.166971i
\(9\) 10.2923 + 24.9614i 0.381195 + 0.924495i
\(10\) −21.3378 9.74465i −0.674761 0.308153i
\(11\) 5.86916 1.72334i 0.160874 0.0472370i −0.200304 0.979734i \(-0.564193\pi\)
0.361178 + 0.932497i \(0.382375\pi\)
\(12\) −19.4245 44.7232i −0.467280 1.07587i
\(13\) 10.1423 22.2086i 0.216383 0.473813i −0.770049 0.637985i \(-0.779768\pi\)
0.986432 + 0.164172i \(0.0524954\pi\)
\(14\) −3.88357 27.0108i −0.0741376 0.515638i
\(15\) −19.5533 + 21.7329i −0.336576 + 0.374095i
\(16\) −21.1925 46.4052i −0.331133 0.725081i
\(17\) −5.56809 + 3.57839i −0.0794388 + 0.0510522i −0.579757 0.814789i \(-0.696853\pi\)
0.500318 + 0.865841i \(0.333216\pi\)
\(18\) −111.948 + 11.8533i −1.46590 + 0.155213i
\(19\) 20.8258 32.4055i 0.251461 0.391281i −0.692458 0.721458i \(-0.743472\pi\)
0.943919 + 0.330177i \(0.107108\pi\)
\(20\) 34.5730 39.8994i 0.386538 0.446089i
\(21\) −33.5665 5.46705i −0.348800 0.0568099i
\(22\) 25.5038i 0.247156i
\(23\) 50.7872 + 97.9166i 0.460429 + 0.887696i
\(24\) 29.7477 3.71210i 0.253009 0.0315721i
\(25\) 89.5651 + 26.2987i 0.716521 + 0.210389i
\(26\) 76.9317 + 66.6617i 0.580291 + 0.502825i
\(27\) −27.7027 + 137.534i −0.197459 + 0.980311i
\(28\) 60.7913 + 8.74048i 0.410303 + 0.0589927i
\(29\) 103.555 + 161.135i 0.663093 + 1.03179i 0.996045 + 0.0888486i \(0.0283187\pi\)
−0.332953 + 0.942944i \(0.608045\pi\)
\(30\) −63.9741 103.751i −0.389334 0.631411i
\(31\) −41.0835 47.4128i −0.238026 0.274697i 0.624151 0.781304i \(-0.285445\pi\)
−0.862177 + 0.506607i \(0.830900\pi\)
\(32\) 256.222 36.8392i 1.41544 0.203510i
\(33\) 30.3247 + 9.52207i 0.159965 + 0.0502297i
\(34\) −7.77477 26.4784i −0.0392165 0.133559i
\(35\) −10.3743 35.3316i −0.0501021 0.170632i
\(36\) 45.3865 249.263i 0.210123 1.15399i
\(37\) 251.132 36.1073i 1.11583 0.160433i 0.440363 0.897820i \(-0.354850\pi\)
0.675470 + 0.737387i \(0.263941\pi\)
\(38\) 105.175 + 121.379i 0.448991 + 0.518163i
\(39\) 107.986 66.5850i 0.443372 0.273388i
\(40\) 17.5488 + 27.3065i 0.0693678 + 0.107938i
\(41\) −349.514 50.2525i −1.33134 0.191418i −0.560344 0.828260i \(-0.689331\pi\)
−0.770994 + 0.636842i \(0.780240\pi\)
\(42\) 61.2998 127.860i 0.225208 0.469745i
\(43\) 259.004 + 224.428i 0.918550 + 0.795928i 0.979340 0.202222i \(-0.0648163\pi\)
−0.0607892 + 0.998151i \(0.519362\pi\)
\(44\) −55.0746 16.1714i −0.188700 0.0554074i
\(45\) −147.248 + 37.3304i −0.487788 + 0.123664i
\(46\) −451.372 + 88.1562i −1.44676 + 0.282564i
\(47\) 112.534i 0.349251i −0.984635 0.174626i \(-0.944129\pi\)
0.984635 0.174626i \(-0.0558715\pi\)
\(48\) 42.6133 261.636i 0.128140 0.786748i
\(49\) −196.565 + 226.848i −0.573076 + 0.661365i
\(50\) −210.415 + 327.413i −0.595144 + 0.926063i
\(51\) −34.3863 0.641557i −0.0944126 0.00176149i
\(52\) −192.734 + 123.863i −0.513989 + 0.330321i
\(53\) −300.933 658.951i −0.779930 1.70781i −0.703458 0.710737i \(-0.748362\pi\)
−0.0764717 0.997072i \(-0.524365\pi\)
\(54\) −517.662 272.379i −1.30453 0.686408i
\(55\) 4.89775 + 34.0646i 0.0120075 + 0.0835140i
\(56\) −15.6862 + 34.3480i −0.0374314 + 0.0819633i
\(57\) 183.590 79.7381i 0.426616 0.185291i
\(58\) −766.259 + 224.994i −1.73474 + 0.509365i
\(59\) 398.645 + 182.055i 0.879648 + 0.401722i 0.803451 0.595371i \(-0.202995\pi\)
0.0761968 + 0.997093i \(0.475722\pi\)
\(60\) 264.612 72.3637i 0.569354 0.155702i
\(61\) 369.846 320.474i 0.776294 0.672663i −0.173746 0.984791i \(-0.555587\pi\)
0.950040 + 0.312128i \(0.101042\pi\)
\(62\) 237.933 108.661i 0.487380 0.222579i
\(63\) −129.142 120.625i −0.258261 0.241227i
\(64\) −95.5148 + 664.320i −0.186552 + 1.29750i
\(65\) 115.557 + 74.2638i 0.220509 + 0.141712i
\(66\) −73.7139 + 110.129i −0.137478 + 0.205392i
\(67\) 186.577 635.422i 0.340208 1.15864i −0.594757 0.803905i \(-0.702752\pi\)
0.934966 0.354738i \(-0.115430\pi\)
\(68\) 62.1091 0.110762
\(69\) −63.7036 + 569.606i −0.111145 + 0.993804i
\(70\) 153.530 0.262148
\(71\) 181.547 618.292i 0.303460 1.03349i −0.656726 0.754129i \(-0.728059\pi\)
0.960186 0.279361i \(-0.0901225\pi\)
\(72\) 139.183 + 69.9506i 0.227818 + 0.114497i
\(73\) 196.952 + 126.574i 0.315775 + 0.202936i 0.688921 0.724837i \(-0.258085\pi\)
−0.373146 + 0.927772i \(0.621721\pi\)
\(74\) −150.545 + 1047.06i −0.236494 + 1.64485i
\(75\) 310.741 + 372.431i 0.478418 + 0.573395i
\(76\) −328.802 + 150.159i −0.496265 + 0.226637i
\(77\) −30.2566 + 26.2175i −0.0447800 + 0.0388021i
\(78\) 139.527 + 510.209i 0.202543 + 0.740639i
\(79\) −620.492 283.369i −0.883681 0.403563i −0.0787235 0.996896i \(-0.525084\pi\)
−0.804957 + 0.593333i \(0.797812\pi\)
\(80\) 275.394 80.8631i 0.384875 0.113010i
\(81\) −517.138 + 513.818i −0.709381 + 0.704826i
\(82\) 611.591 1339.20i 0.823646 1.80353i
\(83\) −76.5729 532.576i −0.101265 0.704311i −0.975691 0.219152i \(-0.929671\pi\)
0.874426 0.485159i \(-0.161238\pi\)
\(84\) 237.241 + 213.448i 0.308157 + 0.277251i
\(85\) −15.4694 33.8733i −0.0197399 0.0432244i
\(86\) −1202.06 + 772.517i −1.50723 + 0.968636i
\(87\) −18.5660 + 995.104i −0.0228791 + 1.22628i
\(88\) 19.0796 29.6884i 0.0231124 0.0359636i
\(89\) −242.580 + 279.952i −0.288915 + 0.333426i −0.881590 0.472016i \(-0.843526\pi\)
0.592675 + 0.805442i \(0.298072\pi\)
\(90\) 23.6252 632.915i 0.0276702 0.741279i
\(91\) 159.796i 0.184078i
\(92\) 95.8338 1030.62i 0.108602 1.16793i
\(93\) −40.3656 323.478i −0.0450077 0.360678i
\(94\) 450.192 + 132.188i 0.493976 + 0.145045i
\(95\) 163.788 + 141.923i 0.176888 + 0.153274i
\(96\) 1212.87 + 581.485i 1.28946 + 0.618204i
\(97\) 1778.54 + 255.715i 1.86168 + 0.267670i 0.979233 0.202738i \(-0.0649840\pi\)
0.882449 + 0.470407i \(0.155893\pi\)
\(98\) −676.609 1052.82i −0.697427 1.08522i
\(99\) 103.424 + 128.765i 0.104995 + 0.130721i
\(100\) −573.617 661.989i −0.573617 0.661989i
\(101\) −900.406 + 129.459i −0.887067 + 0.127541i −0.570761 0.821116i \(-0.693352\pi\)
−0.316306 + 0.948657i \(0.602443\pi\)
\(102\) 42.9584 136.809i 0.0417012 0.132805i
\(103\) −422.908 1440.29i −0.404567 1.37783i −0.870134 0.492816i \(-0.835968\pi\)
0.465566 0.885013i \(-0.345851\pi\)
\(104\) −39.6844 135.153i −0.0374171 0.127431i
\(105\) 57.3217 182.551i 0.0532764 0.169668i
\(106\) 2989.62 429.842i 2.73941 0.393868i
\(107\) −653.187 753.818i −0.590149 0.681068i 0.379606 0.925148i \(-0.376060\pi\)
−0.969755 + 0.244080i \(0.921514\pi\)
\(108\) 916.430 945.164i 0.816514 0.842116i
\(109\) −228.473 355.510i −0.200768 0.312401i 0.726241 0.687440i \(-0.241266\pi\)
−0.927009 + 0.375039i \(0.877629\pi\)
\(110\) −142.028 20.4206i −0.123108 0.0177002i
\(111\) 1188.78 + 569.932i 1.01652 + 0.487348i
\(112\) 252.341 + 218.655i 0.212892 + 0.184472i
\(113\) 174.861 + 51.3437i 0.145571 + 0.0427435i 0.353706 0.935357i \(-0.384921\pi\)
−0.208135 + 0.978100i \(0.566739\pi\)
\(114\) 103.337 + 828.115i 0.0848985 + 0.680352i
\(115\) −585.952 + 204.429i −0.475133 + 0.165766i
\(116\) 1797.37i 1.43864i
\(117\) 658.745 + 24.5894i 0.520522 + 0.0194299i
\(118\) −1196.58 + 1380.93i −0.933509 + 1.07733i
\(119\) 23.4205 36.4431i 0.0180417 0.0280734i
\(120\) −3.14626 + 168.634i −0.00239344 + 0.128284i
\(121\) −1088.23 + 699.364i −0.817604 + 0.525442i
\(122\) 847.612 + 1856.01i 0.629010 + 1.37734i
\(123\) −1364.00 1227.20i −0.999897 0.899615i
\(124\) 83.7807 + 582.708i 0.0606753 + 0.422006i
\(125\) −510.317 + 1117.44i −0.365153 + 0.799575i
\(126\) 634.255 374.941i 0.448444 0.265099i
\(127\) −1527.06 + 448.384i −1.06696 + 0.313288i −0.767652 0.640867i \(-0.778575\pi\)
−0.299311 + 0.954156i \(0.596757\pi\)
\(128\) −661.693 302.185i −0.456922 0.208669i
\(129\) 469.743 + 1717.71i 0.320609 + 1.17237i
\(130\) −432.831 + 375.050i −0.292014 + 0.253031i
\(131\) −1520.35 + 694.319i −1.01400 + 0.463076i −0.851903 0.523699i \(-0.824551\pi\)
−0.162092 + 0.986776i \(0.551824\pi\)
\(132\) −191.079 229.012i −0.125994 0.151007i
\(133\) −35.8799 + 249.550i −0.0233924 + 0.162697i
\(134\) 2322.84 + 1492.80i 1.49748 + 0.962373i
\(135\) −743.731 264.395i −0.474149 0.168559i
\(136\) −10.7583 + 36.6393i −0.00678320 + 0.0231014i
\(137\) 2268.78 1.41485 0.707427 0.706787i \(-0.249856\pi\)
0.707427 + 0.706787i \(0.249856\pi\)
\(138\) −2203.87 923.933i −1.35947 0.569931i
\(139\) −1100.89 −0.671774 −0.335887 0.941902i \(-0.609036\pi\)
−0.335887 + 0.941902i \(0.609036\pi\)
\(140\) −97.3496 + 331.542i −0.0587682 + 0.200146i
\(141\) 325.258 485.936i 0.194267 0.290235i
\(142\) 2260.22 + 1452.55i 1.33573 + 0.858420i
\(143\) 21.2540 147.825i 0.0124290 0.0864456i
\(144\) 940.217 1006.61i 0.544107 0.582528i
\(145\) −980.258 + 447.669i −0.561421 + 0.256392i
\(146\) −737.707 + 639.227i −0.418172 + 0.362348i
\(147\) −1504.45 + 411.424i −0.844116 + 0.230841i
\(148\) −2165.64 989.016i −1.20280 0.549302i
\(149\) 619.140 181.796i 0.340415 0.0999550i −0.107057 0.994253i \(-0.534143\pi\)
0.447472 + 0.894298i \(0.352324\pi\)
\(150\) −1854.92 + 805.642i −1.00969 + 0.438536i
\(151\) 720.740 1578.20i 0.388431 0.850544i −0.609883 0.792492i \(-0.708784\pi\)
0.998314 0.0580529i \(-0.0184892\pi\)
\(152\) −31.6278 219.976i −0.0168773 0.117384i
\(153\) −146.630 102.157i −0.0774792 0.0539799i
\(154\) −69.3420 151.838i −0.0362840 0.0794509i
\(155\) 296.932 190.827i 0.153872 0.0988876i
\(156\) −1190.25 22.2069i −0.610874 0.0113973i
\(157\) −1578.68 + 2456.48i −0.802500 + 1.24871i 0.162563 + 0.986698i \(0.448024\pi\)
−0.965063 + 0.262017i \(0.915612\pi\)
\(158\) 1862.48 2149.41i 0.937789 1.08227i
\(159\) 605.106 3715.21i 0.301812 1.85305i
\(160\) 1456.37i 0.719602i
\(161\) −568.587 444.865i −0.278329 0.217765i
\(162\) −1448.07 2672.36i −0.702290 1.29605i
\(163\) −822.969 241.645i −0.395460 0.116117i 0.0779556 0.996957i \(-0.475161\pi\)
−0.473415 + 0.880839i \(0.656979\pi\)
\(164\) 2504.16 + 2169.86i 1.19233 + 1.03316i
\(165\) −77.3080 + 161.251i −0.0364753 + 0.0760810i
\(166\) 2220.51 + 319.262i 1.03822 + 0.149274i
\(167\) −1196.97 1862.53i −0.554638 0.863034i 0.444831 0.895614i \(-0.353264\pi\)
−0.999469 + 0.0325809i \(0.989627\pi\)
\(168\) −167.011 + 102.981i −0.0766975 + 0.0472925i
\(169\) 1048.37 + 1209.89i 0.477184 + 0.550699i
\(170\) 153.681 22.0960i 0.0693341 0.00996873i
\(171\) 1023.23 + 186.313i 0.457593 + 0.0833200i
\(172\) −906.026 3085.64i −0.401650 1.36790i
\(173\) −930.813 3170.06i −0.409066 1.39315i −0.864389 0.502824i \(-0.832294\pi\)
0.455323 0.890327i \(-0.349524\pi\)
\(174\) −3959.10 1243.17i −1.72493 0.541636i
\(175\) −604.732 + 86.9473i −0.261219 + 0.0375577i
\(176\) −204.354 235.837i −0.0875214 0.101005i
\(177\) 1195.20 + 1938.34i 0.507553 + 0.823134i
\(178\) −835.001 1299.29i −0.351606 0.547110i
\(179\) 1684.16 + 242.145i 0.703239 + 0.101110i 0.484652 0.874707i \(-0.338946\pi\)
0.218587 + 0.975818i \(0.429855\pi\)
\(180\) 1351.78 + 452.334i 0.559753 + 0.187306i
\(181\) 3066.67 + 2657.28i 1.25936 + 1.09124i 0.991814 + 0.127692i \(0.0407569\pi\)
0.267542 + 0.963546i \(0.413789\pi\)
\(182\) −639.261 187.704i −0.260358 0.0764481i
\(183\) 2523.31 314.874i 1.01928 0.127192i
\(184\) 591.382 + 235.054i 0.236942 + 0.0941761i
\(185\) 1427.44i 0.567283i
\(186\) 1341.49 + 218.491i 0.528831 + 0.0861320i
\(187\) −26.5132 + 30.5978i −0.0103681 + 0.0119654i
\(188\) −570.912 + 888.357i −0.221479 + 0.344628i
\(189\) −209.010 894.132i −0.0804404 0.344119i
\(190\) −760.157 + 488.523i −0.290251 + 0.186533i
\(191\) −647.824 1418.54i −0.245418 0.537391i 0.746332 0.665573i \(-0.231813\pi\)
−0.991751 + 0.128183i \(0.959086\pi\)
\(192\) −2332.53 + 2592.55i −0.876750 + 0.974483i
\(193\) −27.7346 192.898i −0.0103439 0.0719436i 0.983996 0.178193i \(-0.0570250\pi\)
−0.994340 + 0.106249i \(0.966116\pi\)
\(194\) −3112.15 + 6814.65i −1.15175 + 2.52198i
\(195\) 284.343 + 654.674i 0.104421 + 0.240422i
\(196\) 2702.56 793.543i 0.984898 0.289192i
\(197\) 1921.54 + 877.538i 0.694945 + 0.317371i 0.731385 0.681965i \(-0.238874\pi\)
−0.0364399 + 0.999336i \(0.511602\pi\)
\(198\) −636.610 + 262.492i −0.228495 + 0.0942147i
\(199\) 1818.12 1575.41i 0.647654 0.561195i −0.267872 0.963455i \(-0.586320\pi\)
0.915526 + 0.402259i \(0.131775\pi\)
\(200\) 489.880 223.721i 0.173199 0.0790971i
\(201\) 2642.22 2204.56i 0.927204 0.773621i
\(202\) 539.763 3754.14i 0.188008 1.30762i
\(203\) −1054.62 677.766i −0.364631 0.234334i
\(204\) 268.194 + 179.514i 0.0920459 + 0.0616103i
\(205\) 559.702 1906.17i 0.190689 0.649428i
\(206\) 6258.65 2.11680
\(207\) −1921.41 + 2275.50i −0.645157 + 0.764050i
\(208\) −1245.54 −0.415204
\(209\) 66.3840 226.083i 0.0219707 0.0748253i
\(210\) 662.960 + 443.748i 0.217850 + 0.145817i
\(211\) −2486.59 1598.03i −0.811297 0.521389i 0.0679871 0.997686i \(-0.478342\pi\)
−0.879284 + 0.476297i \(0.841979\pi\)
\(212\) −967.416 + 6728.53i −0.313408 + 2.17980i
\(213\) 2570.99 2145.13i 0.827050 0.690056i
\(214\) 3782.91 1727.60i 1.20838 0.551851i
\(215\) −1457.20 + 1262.67i −0.462233 + 0.400527i
\(216\) 398.830 + 704.337i 0.125634 + 0.221871i
\(217\) 373.502 + 170.572i 0.116843 + 0.0533604i
\(218\) 1690.59 496.403i 0.525235 0.154223i
\(219\) 484.627 + 1115.81i 0.149535 + 0.344291i
\(220\) 134.154 293.757i 0.0411122 0.0900231i
\(221\) 22.9977 + 159.953i 0.00699998 + 0.0486859i
\(222\) −3676.41 + 4086.23i −1.11146 + 1.23536i
\(223\) 913.615 + 2000.54i 0.274351 + 0.600744i 0.995783 0.0917411i \(-0.0292432\pi\)
−0.721432 + 0.692485i \(0.756516\pi\)
\(224\) −1425.27 + 915.963i −0.425132 + 0.273216i
\(225\) 265.377 + 2506.34i 0.0786302 + 0.742619i
\(226\) −410.800 + 639.218i −0.120912 + 0.188142i
\(227\) 2174.04 2508.97i 0.635665 0.733597i −0.342937 0.939358i \(-0.611422\pi\)
0.978602 + 0.205762i \(0.0659672\pi\)
\(228\) −1853.81 301.935i −0.538472 0.0877022i
\(229\) 590.818i 0.170491i 0.996360 + 0.0852454i \(0.0271674\pi\)
−0.996360 + 0.0852454i \(0.972833\pi\)
\(230\) −129.526 2584.23i −0.0371334 0.740865i
\(231\) −206.428 + 25.7594i −0.0587965 + 0.00733699i
\(232\) 1060.30 + 311.334i 0.300054 + 0.0881037i
\(233\) 1934.90 + 1676.60i 0.544032 + 0.471406i 0.882988 0.469396i \(-0.155528\pi\)
−0.338956 + 0.940802i \(0.610074\pi\)
\(234\) −872.165 + 2606.42i −0.243655 + 0.728150i
\(235\) 626.692 + 90.1047i 0.173961 + 0.0250118i
\(236\) −2223.34 3459.58i −0.613250 0.954236i
\(237\) −1860.33 3017.03i −0.509880 0.826908i
\(238\) 118.279 + 136.502i 0.0322139 + 0.0371768i
\(239\) 4028.68 579.236i 1.09035 0.156769i 0.426391 0.904539i \(-0.359785\pi\)
0.663958 + 0.747770i \(0.268876\pi\)
\(240\) 1422.90 + 446.798i 0.382700 + 0.120169i
\(241\) 122.537 + 417.321i 0.0327522 + 0.111544i 0.974247 0.225484i \(-0.0723965\pi\)
−0.941495 + 0.337028i \(0.890578\pi\)
\(242\) −1519.51 5174.97i −0.403627 1.37463i
\(243\) −3718.16 + 724.038i −0.981563 + 0.191140i
\(244\) −4545.44 + 653.536i −1.19259 + 0.171469i
\(245\) −1105.91 1276.29i −0.288383 0.332812i
\(246\) 6511.61 4015.13i 1.68766 1.04063i
\(247\) −508.461 791.180i −0.130982 0.203812i
\(248\) −358.263 51.5104i −0.0917327 0.0131892i
\(249\) 1208.66 2521.05i 0.307613 0.641626i
\(250\) −3870.86 3354.12i −0.979259 0.848533i
\(251\) −3746.93 1100.20i −0.942247 0.276669i −0.225692 0.974199i \(-0.572464\pi\)
−0.716555 + 0.697530i \(0.754282\pi\)
\(252\) 407.507 + 1607.39i 0.101867 + 0.401811i
\(253\) 466.822 + 487.164i 0.116003 + 0.121058i
\(254\) 6635.67i 1.63921i
\(255\) 31.1054 190.980i 0.00763881 0.0469005i
\(256\) −1529.94 + 1765.64i −0.373520 + 0.431065i
\(257\) −2121.50 + 3301.12i −0.514925 + 0.801239i −0.997200 0.0747808i \(-0.976174\pi\)
0.482275 + 0.876020i \(0.339811\pi\)
\(258\) −7423.45 138.502i −1.79133 0.0334215i
\(259\) −1396.95 + 897.765i −0.335144 + 0.215384i
\(260\) −535.460 1172.49i −0.127722 0.279673i
\(261\) −2956.33 + 4243.32i −0.701119 + 1.00634i
\(262\) −991.743 6897.72i −0.233855 1.62650i
\(263\) −1612.03 + 3529.85i −0.377954 + 0.827603i 0.621084 + 0.783744i \(0.286693\pi\)
−0.999038 + 0.0438592i \(0.986035\pi\)
\(264\) 168.197 73.0523i 0.0392113 0.0170305i
\(265\) 3910.58 1148.25i 0.906510 0.266175i
\(266\) −956.178 436.672i −0.220402 0.100654i
\(267\) −1856.64 + 507.737i −0.425559 + 0.116378i
\(268\) −4696.50 + 4069.54i −1.07046 + 0.927562i
\(269\) 220.223 100.572i 0.0499153 0.0227955i −0.390301 0.920687i \(-0.627629\pi\)
0.440216 + 0.897892i \(0.354902\pi\)
\(270\) 1931.33 2664.72i 0.435323 0.600628i
\(271\) 332.232 2310.73i 0.0744711 0.517958i −0.918105 0.396336i \(-0.870281\pi\)
0.992577 0.121622i \(-0.0388095\pi\)
\(272\) 284.058 + 182.553i 0.0633218 + 0.0406945i
\(273\) −461.858 + 690.016i −0.102392 + 0.152973i
\(274\) −2665.02 + 9076.23i −0.587591 + 2.00115i
\(275\) 570.993 0.125208
\(276\) 3392.63 4173.35i 0.739899 0.910166i
\(277\) 3703.65 0.803360 0.401680 0.915780i \(-0.368426\pi\)
0.401680 + 0.915780i \(0.368426\pi\)
\(278\) 1293.17 4404.12i 0.278989 0.950149i
\(279\) 760.647 1513.48i 0.163221 0.324767i
\(280\) −178.721 114.857i −0.0381450 0.0245143i
\(281\) −645.895 + 4492.30i −0.137121 + 0.953695i 0.798828 + 0.601559i \(0.205454\pi\)
−0.935949 + 0.352136i \(0.885456\pi\)
\(282\) 1561.92 + 1872.00i 0.329826 + 0.395304i
\(283\) 952.250 434.878i 0.200019 0.0913456i −0.312887 0.949790i \(-0.601296\pi\)
0.512906 + 0.858445i \(0.328569\pi\)
\(284\) −4569.89 + 3959.83i −0.954835 + 0.827369i
\(285\) 297.055 + 1086.24i 0.0617404 + 0.225766i
\(286\) 566.405 + 258.669i 0.117106 + 0.0534804i
\(287\) 2217.47 651.108i 0.456074 0.133915i
\(288\) 3556.67 + 6016.50i 0.727703 + 1.23099i
\(289\) −2022.74 + 4429.17i −0.411711 + 0.901521i
\(290\) −639.435 4447.37i −0.129479 0.900547i
\(291\) 6940.84 + 6244.73i 1.39821 + 1.25798i
\(292\) −912.626 1998.37i −0.182902 0.400500i
\(293\) −6777.83 + 4355.85i −1.35142 + 0.868503i −0.997761 0.0668731i \(-0.978698\pi\)
−0.353655 + 0.935376i \(0.615061\pi\)
\(294\) 121.307 6501.83i 0.0240638 1.28978i
\(295\) −1333.04 + 2074.25i −0.263093 + 0.409381i
\(296\) 958.563 1106.24i 0.188228 0.217226i
\(297\) 74.4259 + 854.949i 0.0145408 + 0.167034i
\(298\) 2690.41i 0.522991i
\(299\) 2689.69 134.812i 0.520231 0.0260748i
\(300\) −563.594 4516.47i −0.108464 0.869196i
\(301\) −2152.18 631.937i −0.412125 0.121011i
\(302\) 5466.96 + 4737.15i 1.04168 + 0.902624i
\(303\) −4262.23 2043.43i −0.808115 0.387432i
\(304\) −1945.14 279.668i −0.366978 0.0527634i
\(305\) 1488.55 + 2316.24i 0.279457 + 0.434843i
\(306\) 580.918 466.592i 0.108526 0.0871676i
\(307\) 5251.60 + 6060.67i 0.976302 + 1.12671i 0.991924 + 0.126835i \(0.0404819\pi\)
−0.0156214 + 0.999878i \(0.504973\pi\)
\(308\) 371.857 53.4649i 0.0687938 0.00989106i
\(309\) 2336.72 7441.69i 0.430199 1.37004i
\(310\) 414.609 + 1412.03i 0.0759620 + 0.258703i
\(311\) 686.944 + 2339.52i 0.125251 + 0.426565i 0.998113 0.0614013i \(-0.0195569\pi\)
−0.872862 + 0.487967i \(0.837739\pi\)
\(312\) 219.271 698.305i 0.0397877 0.126711i
\(313\) −9435.50 + 1356.62i −1.70392 + 0.244986i −0.924408 0.381404i \(-0.875441\pi\)
−0.779509 + 0.626391i \(0.784532\pi\)
\(314\) −7972.72 9201.01i −1.43289 1.65364i
\(315\) 775.149 622.598i 0.138650 0.111363i
\(316\) 3460.63 + 5384.84i 0.616062 + 0.958611i
\(317\) −4477.61 643.783i −0.793337 0.114065i −0.266281 0.963895i \(-0.585795\pi\)
−0.527056 + 0.849831i \(0.676704\pi\)
\(318\) 14151.9 + 6784.80i 2.49559 + 1.19646i
\(319\) 885.471 + 767.265i 0.155413 + 0.134666i
\(320\) −3623.05 1063.82i −0.632922 0.185843i
\(321\) −641.773 5142.98i −0.111590 0.894247i
\(322\) 2447.57 1752.07i 0.423595 0.303227i
\(323\) 254.960i 0.0439205i
\(324\) 6689.06 1432.57i 1.14696 0.245639i
\(325\) 1492.46 1722.39i 0.254728 0.293972i
\(326\) 1933.40 3008.43i 0.328470 0.511109i
\(327\) 40.9620 2195.49i 0.00692723 0.371287i
\(328\) −1713.80 + 1101.39i −0.288503 + 0.185410i
\(329\) 305.968 + 669.976i 0.0512722 + 0.112270i
\(330\) −554.273 498.684i −0.0924598 0.0831868i
\(331\) −85.1328 592.112i −0.0141369 0.0983245i 0.981531 0.191301i \(-0.0612708\pi\)
−0.995668 + 0.0929770i \(0.970362\pi\)
\(332\) −2097.41 + 4592.69i −0.346718 + 0.759206i
\(333\) 3486.01 + 5896.97i 0.573669 + 0.970426i
\(334\) 8857.05 2600.66i 1.45101 0.426054i
\(335\) 3389.21 + 1547.80i 0.552753 + 0.252434i
\(336\) 457.659 + 1673.52i 0.0743075 + 0.271720i
\(337\) 9046.32 7838.68i 1.46227 1.26706i 0.565362 0.824843i \(-0.308736\pi\)
0.896906 0.442220i \(-0.145809\pi\)
\(338\) −6071.61 + 2772.81i −0.977078 + 0.446216i
\(339\) 606.670 + 727.109i 0.0971970 + 0.116493i
\(340\) −49.7299 + 345.879i −0.00793231 + 0.0551704i
\(341\) −322.834 207.473i −0.0512681 0.0329480i
\(342\) −1947.28 + 3874.57i −0.307886 + 0.612611i
\(343\) 1185.95 4038.98i 0.186692 0.635815i
\(344\) 1977.22 0.309897
\(345\) −3121.07 810.835i −0.487052 0.126533i
\(346\) 13775.2 2.14034
\(347\) 1757.94 5987.00i 0.271963 0.926223i −0.704348 0.709854i \(-0.748761\pi\)
0.976312 0.216368i \(-0.0694211\pi\)
\(348\) 5194.96 7761.27i 0.800227 1.19554i
\(349\) −10504.0 6750.48i −1.61107 1.03537i −0.961399 0.275157i \(-0.911270\pi\)
−0.649672 0.760215i \(-0.725094\pi\)
\(350\) 362.516 2521.36i 0.0553638 0.385063i
\(351\) 2773.47 + 2010.15i 0.421757 + 0.305681i
\(352\) 1440.32 657.773i 0.218095 0.0996007i
\(353\) 2675.84 2318.63i 0.403458 0.349598i −0.429372 0.903128i \(-0.641265\pi\)
0.832829 + 0.553530i \(0.186720\pi\)
\(354\) −9158.27 + 2504.52i −1.37502 + 0.376028i
\(355\) 3297.84 + 1506.07i 0.493046 + 0.225167i
\(356\) 3335.22 979.308i 0.496534 0.145796i
\(357\) 206.464 89.6729i 0.0306085 0.0132941i
\(358\) −2946.99 + 6453.02i −0.435066 + 0.952661i
\(359\) −1501.83 10445.4i −0.220789 1.53562i −0.735064 0.677998i \(-0.762848\pi\)
0.514274 0.857626i \(-0.328061\pi\)
\(360\) −500.990 + 719.088i −0.0733458 + 0.105276i
\(361\) 2232.93 + 4889.42i 0.325547 + 0.712848i
\(362\) −14232.7 + 9146.80i −2.06645 + 1.32802i
\(363\) −6720.49 125.386i −0.971719 0.0181297i
\(364\) 810.681 1261.44i 0.116734 0.181642i
\(365\) −862.573 + 995.463i −0.123696 + 0.142753i
\(366\) −1704.35 + 10464.3i −0.243410 + 1.49448i
\(367\) 12875.1i 1.83127i −0.402014 0.915634i \(-0.631690\pi\)
0.402014 0.915634i \(-0.368310\pi\)
\(368\) 3467.53 4431.89i 0.491188 0.627794i
\(369\) −2342.92 9241.55i −0.330535 1.30378i
\(370\) −5710.46 1676.74i −0.802359 0.235594i
\(371\) 3583.22 + 3104.88i 0.501433 + 0.434494i
\(372\) −1322.43 + 2758.35i −0.184314 + 0.384446i
\(373\) −9959.38 1431.94i −1.38251 0.198775i −0.589396 0.807845i \(-0.700634\pi\)
−0.793117 + 0.609069i \(0.791543\pi\)
\(374\) −91.2627 142.008i −0.0126179 0.0196338i
\(375\) −5433.35 + 3350.26i −0.748206 + 0.461351i
\(376\) −425.168 490.670i −0.0583147 0.0672988i
\(377\) 4628.87 665.531i 0.632358 0.0909194i
\(378\) 3822.48 + 214.151i 0.520125 + 0.0291395i
\(379\) 2714.52 + 9244.81i 0.367904 + 1.25297i 0.910689 + 0.413094i \(0.135552\pi\)
−0.542785 + 0.839872i \(0.682630\pi\)
\(380\) −572.952 1951.29i −0.0773469 0.263419i
\(381\) −7889.97 2477.48i −1.06093 0.333137i
\(382\) 6435.81 925.329i 0.862001 0.123937i
\(383\) 762.074 + 879.480i 0.101671 + 0.117335i 0.804305 0.594217i \(-0.202538\pi\)
−0.702633 + 0.711552i \(0.747993\pi\)
\(384\) −1983.86 3217.37i −0.263642 0.427567i
\(385\) −121.777 189.488i −0.0161203 0.0250837i
\(386\) 804.266 + 115.636i 0.106052 + 0.0152480i
\(387\) −2936.29 + 8774.95i −0.385685 + 1.15260i
\(388\) −12742.7 11041.6i −1.66730 1.44472i
\(389\) 9331.91 + 2740.10i 1.21631 + 0.357142i 0.826069 0.563569i \(-0.190572\pi\)
0.390246 + 0.920711i \(0.372390\pi\)
\(390\) −2953.02 + 368.497i −0.383416 + 0.0478450i
\(391\) −633.172 363.471i −0.0818948 0.0470116i
\(392\) 1731.75i 0.223128i
\(393\) −8571.83 1396.12i −1.10023 0.179198i
\(394\) −5767.72 + 6656.31i −0.737497 + 0.851117i
\(395\) 2074.87 3228.57i 0.264299 0.411258i
\(396\) −163.184 1541.18i −0.0207078 0.195573i
\(397\) 8198.20 5268.66i 1.03641 0.666062i 0.0923156 0.995730i \(-0.470573\pi\)
0.944097 + 0.329668i \(0.106937\pi\)
\(398\) 4166.76 + 9123.93i 0.524776 + 1.14910i
\(399\) −876.210 + 973.884i −0.109938 + 0.122193i
\(400\) −677.716 4713.62i −0.0847145 0.589202i
\(401\) −2415.81 + 5289.89i −0.300847 + 0.658764i −0.998326 0.0578418i \(-0.981578\pi\)
0.697478 + 0.716606i \(0.254305\pi\)
\(402\) 5715.64 + 13159.8i 0.709130 + 1.63271i
\(403\) −1469.66 + 431.530i −0.181660 + 0.0533401i
\(404\) 7764.67 + 3546.01i 0.956205 + 0.436684i
\(405\) −2447.33 3291.30i −0.300269 0.403817i
\(406\) 3950.21 3422.88i 0.482872 0.418411i
\(407\) 1411.71 644.705i 0.171931 0.0785181i
\(408\) −152.354 + 127.118i −0.0184869 + 0.0154247i
\(409\) 45.1998 314.371i 0.00546451 0.0380065i −0.986907 0.161292i \(-0.948434\pi\)
0.992371 + 0.123285i \(0.0393430\pi\)
\(410\) 6968.16 + 4478.17i 0.839349 + 0.539417i
\(411\) 9796.85 + 6557.47i 1.17577 + 0.786997i
\(412\) −3968.46 + 13515.3i −0.474544 + 1.61615i
\(413\) −2868.33 −0.341747
\(414\) −6846.14 10359.5i −0.812728 1.22981i
\(415\) 3027.18 0.358068
\(416\) 1780.55 6063.98i 0.209852 0.714690i
\(417\) −4753.79 3181.92i −0.558259 0.373668i
\(418\) 826.466 + 531.137i 0.0967076 + 0.0621502i
\(419\) −685.441 + 4767.35i −0.0799188 + 0.555848i 0.910043 + 0.414514i \(0.136048\pi\)
−0.989962 + 0.141334i \(0.954861\pi\)
\(420\) −1378.63 + 1150.27i −0.160167 + 0.133637i
\(421\) −1909.21 + 871.906i −0.221019 + 0.100936i −0.522848 0.852426i \(-0.675130\pi\)
0.301828 + 0.953362i \(0.402403\pi\)
\(422\) 9313.79 8070.44i 1.07438 0.930955i
\(423\) 2809.01 1158.23i 0.322881 0.133133i
\(424\) −3801.72 1736.19i −0.435442 0.198860i
\(425\) −592.813 + 174.066i −0.0676604 + 0.0198669i
\(426\) 5561.56 + 12805.0i 0.632532 + 1.45635i
\(427\) −1330.56 + 2913.52i −0.150797 + 0.330199i
\(428\) 1332.03 + 9264.48i 0.150435 + 1.04630i
\(429\) 519.035 576.894i 0.0584132 0.0649247i
\(430\) −3339.60 7312.70i −0.374534 0.820115i
\(431\) −6317.20 + 4059.82i −0.706006 + 0.453723i −0.843744 0.536746i \(-0.819653\pi\)
0.137738 + 0.990469i \(0.456017\pi\)
\(432\) 6969.37 1629.14i 0.776190 0.181440i
\(433\) 2865.74 4459.17i 0.318057 0.494906i −0.645008 0.764176i \(-0.723146\pi\)
0.963065 + 0.269270i \(0.0867824\pi\)
\(434\) −1121.11 + 1293.83i −0.123997 + 0.143101i
\(435\) −5526.77 900.159i −0.609169 0.0992168i
\(436\) 3965.53i 0.435584i
\(437\) 4230.72 + 393.401i 0.463119 + 0.0430639i
\(438\) −5033.07 + 628.057i −0.549062 + 0.0685154i
\(439\) −10861.2 3189.14i −1.18082 0.346719i −0.368328 0.929696i \(-0.620069\pi\)
−0.812488 + 0.582977i \(0.801888\pi\)
\(440\) 150.055 + 130.024i 0.0162582 + 0.0140878i
\(441\) −7685.54 2571.75i −0.829882 0.277697i
\(442\) −666.904 95.8864i −0.0717679 0.0103187i
\(443\) 368.204 + 572.937i 0.0394897 + 0.0614471i 0.860437 0.509557i \(-0.170191\pi\)
−0.820947 + 0.571004i \(0.806554\pi\)
\(444\) −6492.94 10530.1i −0.694012 1.12553i
\(445\) −1364.80 1575.06i −0.145388 0.167786i
\(446\) −9076.31 + 1304.98i −0.963623 + 0.138548i
\(447\) 3198.96 + 1004.49i 0.338492 + 0.106288i
\(448\) −1237.56 4214.74i −0.130512 0.444482i
\(449\) −1719.39 5855.72i −0.180720 0.615475i −0.999164 0.0408886i \(-0.986981\pi\)
0.818444 0.574586i \(-0.194837\pi\)
\(450\) −10338.3 1882.43i −1.08301 0.197197i
\(451\) −2137.95 + 307.391i −0.223220 + 0.0320942i
\(452\) −1119.89 1292.42i −0.116538 0.134492i
\(453\) 7673.73 4731.70i 0.795901 0.490761i
\(454\) 7483.40 + 11644.4i 0.773597 + 1.20374i
\(455\) −889.886 127.946i −0.0916890 0.0131829i
\(456\) 499.226 1041.30i 0.0512684 0.106937i
\(457\) −5746.48 4979.35i −0.588204 0.509681i 0.309138 0.951017i \(-0.399959\pi\)
−0.897342 + 0.441336i \(0.854505\pi\)
\(458\) −2363.56 694.005i −0.241140 0.0708051i
\(459\) −337.899 864.932i −0.0343611 0.0879554i
\(460\) 5662.68 + 1358.89i 0.573965 + 0.137736i
\(461\) 6866.71i 0.693741i 0.937913 + 0.346871i \(0.112756\pi\)
−0.937913 + 0.346871i \(0.887244\pi\)
\(462\) 139.431 856.073i 0.0140409 0.0862081i
\(463\) −280.507 + 323.722i −0.0281561 + 0.0324938i −0.769653 0.638462i \(-0.779571\pi\)
0.741497 + 0.670956i \(0.234116\pi\)
\(464\) 5282.89 8220.34i 0.528561 0.822456i
\(465\) 1833.74 + 34.2126i 0.182876 + 0.00341198i
\(466\) −8980.05 + 5771.13i −0.892688 + 0.573696i
\(467\) −1335.37 2924.06i −0.132321 0.289742i 0.831861 0.554984i \(-0.187275\pi\)
−0.964182 + 0.265242i \(0.914548\pi\)
\(468\) −5075.46 3536.08i −0.501310 0.349264i
\(469\) 616.849 + 4290.28i 0.0607323 + 0.422403i
\(470\) −1096.61 + 2401.23i −0.107623 + 0.235661i
\(471\) −13916.9 + 6044.48i −1.36148 + 0.591327i
\(472\) 2425.99 712.336i 0.236579 0.0694659i
\(473\) 1906.90 + 870.851i 0.185368 + 0.0846549i
\(474\) 14254.8 3898.29i 1.38132 0.377752i
\(475\) 2717.49 2354.72i 0.262499 0.227456i
\(476\) −369.768 + 168.868i −0.0356057 + 0.0162606i
\(477\) 13351.0 14293.8i 1.28155 1.37205i
\(478\) −2415.06 + 16797.1i −0.231092 + 1.60728i
\(479\) −15485.2 9951.73i −1.47711 0.949283i −0.997416 0.0718482i \(-0.977110\pi\)
−0.479697 0.877434i \(-0.659253\pi\)
\(480\) −4209.36 + 6288.79i −0.400271 + 0.598005i
\(481\) 1745.17 5943.51i 0.165432 0.563411i
\(482\) −1813.43 −0.171368
\(483\) −1169.43 3564.37i −0.110168 0.335785i
\(484\) 12138.6 1.13999
\(485\) −2848.10 + 9699.75i −0.266651 + 0.908130i
\(486\) 1471.03 15724.9i 0.137299 1.46769i
\(487\) 4788.44 + 3077.35i 0.445555 + 0.286341i 0.744117 0.668050i \(-0.232871\pi\)
−0.298562 + 0.954390i \(0.596507\pi\)
\(488\) 401.809 2794.65i 0.0372727 0.259237i
\(489\) −2855.25 3422.09i −0.264046 0.316466i
\(490\) 6404.82 2924.99i 0.590491 0.269668i
\(491\) −3244.68 + 2811.53i −0.298228 + 0.258416i −0.791102 0.611685i \(-0.790492\pi\)
0.492873 + 0.870101i \(0.335947\pi\)
\(492\) 4541.67 + 16607.5i 0.416167 + 1.52180i
\(493\) −1153.21 526.652i −0.105351 0.0481120i
\(494\) 3762.37 1104.73i 0.342666 0.100616i
\(495\) −799.889 + 472.856i −0.0726310 + 0.0429360i
\(496\) −1329.54 + 2911.28i −0.120359 + 0.263549i
\(497\) 600.221 + 4174.63i 0.0541722 + 0.376776i
\(498\) 8665.68 + 7796.57i 0.779755 + 0.701552i
\(499\) 6671.15 + 14607.8i 0.598480 + 1.31049i 0.930180 + 0.367104i \(0.119651\pi\)
−0.331700 + 0.943385i \(0.607622\pi\)
\(500\) 9697.53 6232.22i 0.867374 0.557427i
\(501\) 214.601 11502.2i 0.0191370 1.02571i
\(502\) 8802.66 13697.2i 0.782633 1.21780i
\(503\) 8772.20 10123.7i 0.777600 0.897399i −0.219333 0.975650i \(-0.570388\pi\)
0.996934 + 0.0782513i \(0.0249336\pi\)
\(504\) −1018.82 38.0301i −0.0900432 0.00336110i
\(505\) 5117.93i 0.450980i
\(506\) −2497.25 + 1295.27i −0.219400 + 0.113798i
\(507\) 1030.05 + 8254.55i 0.0902294 + 0.723072i
\(508\) 14329.5 + 4207.52i 1.25151 + 0.367477i
\(509\) 7183.82 + 6224.82i 0.625574 + 0.542063i 0.908928 0.416952i \(-0.136902\pi\)
−0.283354 + 0.959015i \(0.591447\pi\)
\(510\) 727.476 + 348.772i 0.0631631 + 0.0302821i
\(511\) −1516.70 218.069i −0.131301 0.0188783i
\(512\) −8412.52 13090.1i −0.726142 1.12990i
\(513\) 3879.93 + 3761.97i 0.333924 + 0.323772i
\(514\) −10714.1 12364.7i −0.919413 1.06106i
\(515\) 8359.47 1201.91i 0.715266 0.102840i
\(516\) 5006.12 15942.9i 0.427097 1.36017i
\(517\) −193.935 660.481i −0.0164976 0.0561855i
\(518\) −1950.57 6643.05i −0.165450 0.563473i
\(519\) 5143.08 16379.0i 0.434983 1.38528i
\(520\) 784.426 112.783i 0.0661526 0.00951131i
\(521\) 4814.95 + 5556.75i 0.404888 + 0.467266i 0.921174 0.389150i \(-0.127231\pi\)
−0.516286 + 0.856416i \(0.672686\pi\)
\(522\) −13502.7 16811.2i −1.13218 1.40959i
\(523\) 10619.2 + 16523.9i 0.887853 + 1.38153i 0.924087 + 0.382183i \(0.124828\pi\)
−0.0362333 + 0.999343i \(0.511536\pi\)
\(524\) 15524.2 + 2232.05i 1.29423 + 0.186083i
\(525\) −2862.61 1372.41i −0.237970 0.114089i
\(526\) −12227.6 10595.2i −1.01359 0.878278i
\(527\) 398.418 + 116.986i 0.0329324 + 0.00966981i
\(528\) −200.783 1609.02i −0.0165492 0.132620i
\(529\) −7008.31 + 9945.83i −0.576010 + 0.817443i
\(530\) 16993.0i 1.39270i
\(531\) −441.381 + 11824.5i −0.0360721 + 0.966364i
\(532\) 1549.27 1787.95i 0.126258 0.145709i
\(533\) −4660.93 + 7252.54i −0.378775 + 0.589386i
\(534\) 149.704 8023.88i 0.0121317 0.650238i
\(535\) 4720.93 3033.96i 0.381502 0.245177i
\(536\) −1587.19 3475.46i −0.127903 0.280069i
\(537\) 6572.51 + 5913.34i 0.528165 + 0.475194i
\(538\) 143.654 + 999.136i 0.0115118 + 0.0800666i
\(539\) −762.735 + 1670.16i −0.0609523 + 0.133467i
\(540\) 4529.75 + 5860.28i 0.360980 + 0.467012i
\(541\) −4558.79 + 1338.58i −0.362287 + 0.106377i −0.457810 0.889050i \(-0.651366\pi\)
0.0955225 + 0.995427i \(0.469548\pi\)
\(542\) 8853.79 + 4043.39i 0.701666 + 0.320440i
\(543\) 5561.87 + 20338.0i 0.439563 + 1.60735i
\(544\) −1294.84 + 1121.99i −0.102051 + 0.0884280i
\(545\) 2162.74 987.689i 0.169984 0.0776292i
\(546\) −2217.88 2658.19i −0.173840 0.208352i
\(547\) −2362.99 + 16434.9i −0.184706 + 1.28466i 0.660748 + 0.750608i \(0.270239\pi\)
−0.845454 + 0.534048i \(0.820670\pi\)
\(548\) −17910.0 11510.0i −1.39613 0.897235i
\(549\) 11806.0 + 5933.46i 0.917793 + 0.461264i
\(550\) −670.717 + 2284.25i −0.0519991 + 0.177093i
\(551\) 7378.27 0.570463
\(552\) 1874.28 + 2724.26i 0.144519 + 0.210059i
\(553\) 4464.56 0.343314
\(554\) −4350.49 + 14816.4i −0.333637 + 1.13626i
\(555\) −4125.74 + 6163.85i −0.315545 + 0.471425i
\(556\) 8690.58 + 5585.09i 0.662882 + 0.426009i
\(557\) −1762.65 + 12259.5i −0.134086 + 0.932590i 0.806064 + 0.591829i \(0.201594\pi\)
−0.940150 + 0.340761i \(0.889315\pi\)
\(558\) 5161.19 + 4820.78i 0.391560 + 0.365734i
\(559\) 7611.14 3475.89i 0.575880 0.262996i
\(560\) −1419.71 + 1230.19i −0.107132 + 0.0928301i
\(561\) −202.924 + 55.4939i −0.0152718 + 0.00417639i
\(562\) −17212.7 7860.78i −1.29195 0.590013i
\(563\) −16024.0 + 4705.06i −1.19952 + 0.352211i −0.819669 0.572837i \(-0.805843\pi\)
−0.379850 + 0.925048i \(0.624024\pi\)
\(564\) −5032.89 + 2185.92i −0.375750 + 0.163198i
\(565\) −425.937 + 932.671i −0.0317156 + 0.0694474i
\(566\) 621.165 + 4320.30i 0.0461299 + 0.320840i
\(567\) 1681.79 4465.07i 0.124565 0.330715i
\(568\) −1544.40 3381.77i −0.114088 0.249817i
\(569\) 17472.2 11228.7i 1.28730 0.827295i 0.295527 0.955335i \(-0.404505\pi\)
0.991769 + 0.128040i \(0.0408686\pi\)
\(570\) −4694.43 87.5856i −0.344961 0.00643606i
\(571\) −5586.27 + 8692.41i −0.409419 + 0.637068i −0.983326 0.181852i \(-0.941791\pi\)
0.573907 + 0.818921i \(0.305427\pi\)
\(572\) −917.730 + 1059.12i −0.0670843 + 0.0774194i
\(573\) 1302.62 7997.81i 0.0949701 0.583095i
\(574\) 9635.80i 0.700680i
\(575\) 1973.69 + 10105.5i 0.143145 + 0.732922i
\(576\) −17565.4 + 4453.18i −1.27064 + 0.322134i
\(577\) −6773.71 1988.94i −0.488723 0.143502i 0.0280810 0.999606i \(-0.491060\pi\)
−0.516804 + 0.856104i \(0.672879\pi\)
\(578\) −15342.9 13294.7i −1.10412 0.956722i
\(579\) 437.774 913.118i 0.0314218 0.0655404i
\(580\) 10009.4 + 1439.13i 0.716582 + 0.103029i
\(581\) 1903.89 + 2962.52i 0.135950 + 0.211542i
\(582\) −33135.0 + 20431.4i −2.35995 + 1.45517i
\(583\) −2901.82 3348.88i −0.206142 0.237901i
\(584\) 1336.96 192.226i 0.0947324 0.0136205i
\(585\) −664.385 + 3648.80i −0.0469554 + 0.257879i
\(586\) −9463.95 32231.3i −0.667154 2.27212i
\(587\) −7320.98 24933.0i −0.514769 1.75314i −0.647577 0.762000i \(-0.724218\pi\)
0.132809 0.991142i \(-0.457600\pi\)
\(588\) 13963.5 + 4384.61i 0.979332 + 0.307514i
\(589\) −2392.03 + 343.923i −0.167338 + 0.0240596i
\(590\) −6732.15 7769.32i −0.469760 0.542132i
\(591\) 5761.08 + 9343.15i 0.400980 + 0.650298i
\(592\) −6997.69 10888.6i −0.485816 0.755945i
\(593\) −8630.36 1240.86i −0.597650 0.0859291i −0.163151 0.986601i \(-0.552166\pi\)
−0.434500 + 0.900672i \(0.643075\pi\)
\(594\) −3507.64 706.526i −0.242290 0.0488032i
\(595\) 184.195 + 159.606i 0.0126912 + 0.0109970i
\(596\) −5809.85 1705.93i −0.399296 0.117244i
\(597\) 12404.3 1547.88i 0.850374 0.106115i
\(598\) −2620.14 + 10918.5i −0.179173 + 0.746637i
\(599\) 1735.17i 0.118359i 0.998247 + 0.0591796i \(0.0188485\pi\)
−0.998247 + 0.0591796i \(0.981152\pi\)
\(600\) 2761.98 + 449.850i 0.187929 + 0.0306084i
\(601\) −7930.81 + 9152.64i −0.538277 + 0.621205i −0.958111 0.286396i \(-0.907543\pi\)
0.419834 + 0.907601i \(0.362088\pi\)
\(602\) 5056.12 7867.47i 0.342312 0.532648i
\(603\) 17781.3 1882.72i 1.20085 0.127148i
\(604\) −13696.2 + 8802.00i −0.922665 + 0.592961i
\(605\) −3023.35 6620.22i −0.203168 0.444877i
\(606\) 13181.4 14650.7i 0.883591 0.982087i
\(607\) −2555.82 17776.1i −0.170902 1.18865i −0.876984 0.480520i \(-0.840448\pi\)
0.706082 0.708130i \(-0.250461\pi\)
\(608\) 4142.24 9070.23i 0.276299 0.605011i
\(609\) −2595.04 5974.86i −0.172671 0.397559i
\(610\) −11014.6 + 3234.18i −0.731096 + 0.214669i
\(611\) −2499.23 1141.36i −0.165480 0.0755720i
\(612\) 639.243 + 1550.33i 0.0422220 + 0.102399i
\(613\) 6721.41 5824.14i 0.442864 0.383743i −0.404689 0.914454i \(-0.632620\pi\)
0.847553 + 0.530711i \(0.178075\pi\)
\(614\) −30414.5 + 13889.8i −1.99907 + 0.912944i
\(615\) 7926.27 6613.35i 0.519704 0.433620i
\(616\) −32.8715 + 228.626i −0.00215005 + 0.0149539i
\(617\) −18828.4 12100.3i −1.22853 0.789527i −0.244866 0.969557i \(-0.578744\pi\)
−0.983661 + 0.180030i \(0.942380\pi\)
\(618\) 27025.6 + 18089.4i 1.75911 + 1.17745i
\(619\) 6192.21 21088.7i 0.402078 1.36935i −0.471156 0.882050i \(-0.656163\pi\)
0.873234 0.487301i \(-0.162019\pi\)
\(620\) −3312.12 −0.214545
\(621\) −14873.8 + 4272.41i −0.961135 + 0.276080i
\(622\) −10166.1 −0.655346
\(623\) 683.049 2326.25i 0.0439258 0.149598i
\(624\) −5378.38 3599.98i −0.345044 0.230953i
\(625\) 4001.68 + 2571.72i 0.256108 + 0.164590i
\(626\) 5656.27 39340.2i 0.361134 2.51174i
\(627\) 940.103 784.383i 0.0598790 0.0499605i
\(628\) 24924.6 11382.7i 1.58376 0.723277i
\(629\) −1269.12 + 1099.70i −0.0804500 + 0.0697103i
\(630\) 1580.17 + 3832.31i 0.0999294 + 0.242354i
\(631\) 12247.4 + 5593.19i 0.772679 + 0.352871i 0.762425 0.647077i \(-0.224009\pi\)
0.0102540 + 0.999947i \(0.496736\pi\)
\(632\) −3776.06 + 1108.75i −0.237664 + 0.0697844i
\(633\) −6118.57 14087.5i −0.384189 0.884562i
\(634\) 7835.08 17156.4i 0.490806 1.07471i
\(635\) −1274.31 8863.03i −0.0796370 0.553888i
\(636\) −23624.9 + 26258.4i −1.47294 + 1.63713i
\(637\) 3044.36 + 6666.21i 0.189359 + 0.414639i
\(638\) −4109.55 + 2641.05i −0.255014 + 0.163887i
\(639\) 17301.9 1831.97i 1.07113 0.113414i
\(640\) 2212.65 3442.95i 0.136660 0.212648i
\(641\) −983.212 + 1134.69i −0.0605843 + 0.0699180i −0.785233 0.619201i \(-0.787457\pi\)
0.724648 + 0.689119i \(0.242002\pi\)
\(642\) 21328.3 + 3473.80i 1.31116 + 0.213551i
\(643\) 18820.0i 1.15426i 0.816654 + 0.577128i \(0.195827\pi\)
−0.816654 + 0.577128i \(0.804173\pi\)
\(644\) 2231.59 + 6396.38i 0.136548 + 0.391386i
\(645\) −9941.84 + 1240.60i −0.606914 + 0.0757345i
\(646\) −1019.96 299.489i −0.0621207 0.0182403i
\(647\) −6420.95 5563.79i −0.390160 0.338076i 0.437588 0.899176i \(-0.355833\pi\)
−0.827748 + 0.561100i \(0.810378\pi\)
\(648\) −313.553 + 4194.15i −0.0190085 + 0.254262i
\(649\) 2653.46 + 381.509i 0.160489 + 0.0230748i
\(650\) 5137.28 + 7993.77i 0.310001 + 0.482371i
\(651\) 1119.82 + 1816.09i 0.0674180 + 0.109336i
\(652\) 5270.68 + 6082.69i 0.316589 + 0.365363i
\(653\) 6687.77 961.557i 0.400785 0.0576242i 0.0610249 0.998136i \(-0.480563\pi\)
0.339760 + 0.940512i \(0.389654\pi\)
\(654\) 8734.93 + 2742.80i 0.522267 + 0.163994i
\(655\) −2649.27 9022.59i −0.158039 0.538232i
\(656\) 5075.10 + 17284.2i 0.302057 + 1.02871i
\(657\) −1132.36 + 6218.93i −0.0672415 + 0.369290i
\(658\) −3039.64 + 437.034i −0.180087 + 0.0258926i
\(659\) −1809.47 2088.24i −0.106960 0.123439i 0.699745 0.714393i \(-0.253297\pi\)
−0.806705 + 0.590954i \(0.798751\pi\)
\(660\) 1428.34 880.730i 0.0842396 0.0519430i
\(661\) −14356.1 22338.5i −0.844762 1.31448i −0.947496 0.319767i \(-0.896396\pi\)
0.102734 0.994709i \(-0.467241\pi\)
\(662\) 2468.74 + 354.951i 0.144940 + 0.0208392i
\(663\) −363.006 + 757.166i −0.0212639 + 0.0443528i
\(664\) −2346.01 2032.83i −0.137113 0.118809i
\(665\) −1360.99 399.623i −0.0793639 0.0233033i
\(666\) −27685.6 + 7018.86i −1.61080 + 0.408371i
\(667\) −10518.5 + 18323.3i −0.610611 + 1.06369i
\(668\) 20775.5i 1.20334i
\(669\) −1837.07 + 11279.2i −0.106166 + 0.651836i
\(670\) −10173.1 + 11740.4i −0.586599 + 0.676971i
\(671\) 1618.40 2518.28i 0.0931113 0.144884i
\(672\) −8801.88 164.220i −0.505267 0.00942695i
\(673\) 14424.6 9270.11i 0.826191 0.530961i −0.0578743 0.998324i \(-0.518432\pi\)
0.884066 + 0.467363i \(0.154796\pi\)
\(674\) 20732.3 + 45397.5i 1.18484 + 2.59443i
\(675\) −6098.16 + 11589.7i −0.347731 + 0.660870i
\(676\) −2137.93 14869.6i −0.121639 0.846018i
\(677\) 4081.83 8937.95i 0.231724 0.507405i −0.757674 0.652633i \(-0.773664\pi\)
0.989398 + 0.145228i \(0.0463915\pi\)
\(678\) −3621.42 + 1572.88i −0.205132 + 0.0890945i
\(679\) −11283.8 + 3313.23i −0.637753 + 0.187261i
\(680\) −195.427 89.2484i −0.0110210 0.00503312i
\(681\) 16639.5 4550.41i 0.936307 0.256053i
\(682\) 1209.21 1047.79i 0.0678930 0.0588296i
\(683\) 8301.20 3791.03i 0.465061 0.212386i −0.169082 0.985602i \(-0.554080\pi\)
0.634143 + 0.773216i \(0.281353\pi\)
\(684\) −7132.28 6661.87i −0.398698 0.372402i
\(685\) −1816.58 + 12634.6i −0.101326 + 0.704735i
\(686\) 14764.8 + 9488.78i 0.821755 + 0.528110i
\(687\) −1707.65 + 2551.22i −0.0948337 + 0.141682i
\(688\) 4925.67 16775.3i 0.272950 0.929582i
\(689\) −17686.6 −0.977945
\(690\) 6909.91 11533.4i 0.381240 0.636330i
\(691\) −13858.5 −0.762958 −0.381479 0.924378i \(-0.624585\pi\)
−0.381479 + 0.924378i \(0.624585\pi\)
\(692\) −8734.51 + 29747.0i −0.479821 + 1.63412i
\(693\) −965.834 485.409i −0.0529423 0.0266077i
\(694\) 21886.0 + 14065.3i 1.19709 + 0.769324i
\(695\) 881.472 6130.77i 0.0481095 0.334609i
\(696\) 3678.67 + 4408.98i 0.200344 + 0.240118i
\(697\) 2125.95 970.887i 0.115532 0.0527618i
\(698\) 39343.7 34091.5i 2.13350 1.84869i
\(699\) 3509.23 + 12832.2i 0.189888 + 0.694361i
\(700\) 5214.92 + 2381.57i 0.281579 + 0.128593i
\(701\) −11319.2 + 3323.62i −0.609873 + 0.179075i −0.572062 0.820210i \(-0.693856\pi\)
−0.0378104 + 0.999285i \(0.512038\pi\)
\(702\) −11299.5 + 8734.01i −0.607508 + 0.469578i
\(703\) 4059.94 8890.03i 0.217815 0.476947i
\(704\) 584.258 + 4063.60i 0.0312785 + 0.217547i
\(705\) 2445.70 + 2200.41i 0.130653 + 0.117549i
\(706\) 6132.47 + 13428.2i 0.326910 + 0.715834i
\(707\) 5008.61 3218.84i 0.266433 0.171226i
\(708\) 398.614 21365.0i 0.0211594 1.13411i
\(709\) 4899.27 7623.41i 0.259515 0.403813i −0.686907 0.726745i \(-0.741032\pi\)
0.946422 + 0.322932i \(0.104669\pi\)
\(710\) −9898.85 + 11423.9i −0.523236 + 0.603846i
\(711\) 687.009 18404.8i 0.0362375 0.970794i
\(712\) 2137.14i 0.112490i
\(713\) 2555.99 6430.72i 0.134253 0.337773i
\(714\) 116.212 + 931.293i 0.00609124 + 0.0488134i
\(715\) 806.203 + 236.722i 0.0421682 + 0.0123817i
\(716\) −12066.4 10455.6i −0.629811 0.545734i
\(717\) 19070.5 + 9142.90i 0.993305 + 0.476217i
\(718\) 43551.0 + 6261.69i 2.26366 + 0.325465i
\(719\) 14192.5 + 22084.0i 0.736150 + 1.14547i 0.984258 + 0.176739i \(0.0565549\pi\)
−0.248108 + 0.968732i \(0.579809\pi\)
\(720\) 4852.88 + 6041.95i 0.251189 + 0.312736i
\(721\) 6433.79 + 7424.99i 0.332326 + 0.383525i
\(722\) −22183.0 + 3189.44i −1.14344 + 0.164402i
\(723\) −677.059 + 2156.21i −0.0348272 + 0.110913i
\(724\) −10727.6 36534.8i −0.550673 1.87542i
\(725\) 5037.28 + 17155.4i 0.258041 + 0.878808i
\(726\) 8395.83 26738.0i 0.429199 1.36686i
\(727\) 2822.26 405.780i 0.143978 0.0207009i −0.0699490 0.997551i \(-0.522284\pi\)
0.213927 + 0.976850i \(0.431375\pi\)
\(728\) 603.727 + 696.738i 0.0307357 + 0.0354709i
\(729\) −18148.1 7620.13i −0.922020 0.387142i
\(730\) −2969.12 4620.04i −0.150537 0.234240i
\(731\) −2245.24 322.817i −0.113602 0.0163336i
\(732\) −21516.7 10315.7i −1.08645 0.520872i
\(733\) 15255.9 + 13219.3i 0.768743 + 0.666120i 0.948210 0.317644i \(-0.102892\pi\)
−0.179467 + 0.983764i \(0.557437\pi\)
\(734\) 51506.8 + 15123.7i 2.59012 + 0.760528i
\(735\) −1086.58 8707.56i −0.0545296 0.436984i
\(736\) 16620.0 + 23217.5i 0.832366 + 1.16278i
\(737\) 4050.92i 0.202466i
\(738\) 39722.8 + 1482.76i 1.98133 + 0.0739583i
\(739\) −4022.18 + 4641.85i −0.200214 + 0.231060i −0.846974 0.531634i \(-0.821578\pi\)
0.646760 + 0.762694i \(0.276124\pi\)
\(740\) 7241.73 11268.4i 0.359745 0.559774i
\(741\) 91.1600 4886.02i 0.00451936 0.242230i
\(742\) −16630.1 + 10687.5i −0.822789 + 0.528775i
\(743\) −15602.5 34164.6i −0.770389 1.68692i −0.725796 0.687910i \(-0.758528\pi\)
−0.0445929 0.999005i \(-0.514199\pi\)
\(744\) −1398.14 1257.92i −0.0688955 0.0619858i
\(745\) 516.666 + 3593.49i 0.0254083 + 0.176718i
\(746\) 17427.3 38160.4i 0.855305 1.87286i
\(747\) 12505.7 7392.78i 0.612531 0.362099i
\(748\) 364.528 107.035i 0.0178188 0.00523207i
\(749\) 5938.31 + 2711.94i 0.289694 + 0.132299i
\(750\) −7020.40 25671.5i −0.341798 1.24985i
\(751\) −6507.21 + 5638.53i −0.316180 + 0.273972i −0.798463 0.602044i \(-0.794353\pi\)
0.482283 + 0.876016i \(0.339808\pi\)
\(752\) −5222.17 + 2384.88i −0.253235 + 0.115649i
\(753\) −12999.8 15580.5i −0.629134 0.754033i
\(754\) −2774.85 + 19299.5i −0.134024 + 0.932159i
\(755\) 8211.76 + 5277.38i 0.395836 + 0.254389i
\(756\) −2886.20 + 8118.73i −0.138849 + 0.390576i
\(757\) −2542.95 + 8660.50i −0.122094 + 0.415814i −0.997744 0.0671321i \(-0.978615\pi\)
0.875650 + 0.482946i \(0.160433\pi\)
\(758\) −40172.4 −1.92497
\(759\) 607.738 + 3452.89i 0.0290639 + 0.165128i
\(760\) 1250.35 0.0596776
\(761\) 6921.45 23572.3i 0.329701 1.12286i −0.613240 0.789897i \(-0.710134\pi\)
0.942940 0.332961i \(-0.108048\pi\)
\(762\) 19179.1 28653.6i 0.911792 1.36222i
\(763\) 2326.81 + 1495.35i 0.110401 + 0.0709506i
\(764\) −2082.58 + 14484.6i −0.0986190 + 0.685910i
\(765\) 686.308 734.770i 0.0324360 0.0347264i
\(766\) −4413.52 + 2015.59i −0.208182 + 0.0950733i
\(767\) 8086.40 7006.90i 0.380682 0.329863i
\(768\) −11709.7 + 3202.26i −0.550179 + 0.150458i
\(769\) −26710.3 12198.2i −1.25254 0.572014i −0.324988 0.945718i \(-0.605360\pi\)
−0.927548 + 0.373705i \(0.878087\pi\)
\(770\) 901.091 264.584i 0.0421728 0.0123831i
\(771\) −18702.2 + 8122.85i −0.873595 + 0.379426i
\(772\) −759.678 + 1663.46i −0.0354163 + 0.0775509i
\(773\) 190.979 + 1328.29i 0.00888621 + 0.0618049i 0.993782 0.111343i \(-0.0355152\pi\)
−0.984896 + 0.173148i \(0.944606\pi\)
\(774\) −31655.0 22054.1i −1.47005 1.02418i
\(775\) −2432.75 5326.97i −0.112757 0.246904i
\(776\) 8720.87 5604.56i 0.403429 0.259268i
\(777\) −8627.01 160.957i −0.398317 0.00743153i
\(778\) −21923.5 + 34113.6i −1.01028 + 1.57202i
\(779\) −8907.35 + 10279.6i −0.409678 + 0.472794i
\(780\) 1076.69 6610.60i 0.0494251 0.303458i
\(781\) 3941.72i 0.180596i
\(782\) 2197.82 2106.05i 0.100504 0.0963070i
\(783\) −25030.2 + 9778.45i −1.14241 + 0.446300i
\(784\) 14692.6 + 4314.15i 0.669308 + 0.196526i
\(785\) −12415.8 10758.4i −0.564510 0.489151i
\(786\) 15654.1 32651.6i 0.710384 1.48174i
\(787\) 776.043 + 111.578i 0.0351499 + 0.00505379i 0.159867 0.987139i \(-0.448893\pi\)
−0.124717 + 0.992192i \(0.539802\pi\)
\(788\) −10716.9 16675.8i −0.484484 0.753872i
\(789\) −17163.3 + 10583.0i −0.774434 + 0.477524i
\(790\) 10478.6 + 12092.9i 0.471914 + 0.544617i
\(791\) −1180.64 + 169.750i −0.0530703 + 0.00763036i
\(792\) 937.436 + 170.691i 0.0420585 + 0.00765815i
\(793\) −3366.17 11464.1i −0.150739 0.513371i
\(794\) 11447.2 + 38985.7i 0.511646 + 1.74251i
\(795\) 20205.1 + 6344.50i 0.901387 + 0.283039i
\(796\) −22344.9 + 3212.71i −0.994966 + 0.143054i
\(797\) 8202.00 + 9465.62i 0.364529 + 0.420689i 0.908152 0.418640i \(-0.137493\pi\)
−0.543623 + 0.839330i \(0.682948\pi\)
\(798\) −2866.77 4649.25i −0.127171 0.206242i
\(799\) 402.691 + 626.600i 0.0178300 + 0.0277441i
\(800\) 23917.4 + 3438.80i 1.05701 + 0.151975i
\(801\) −9484.69 3173.78i −0.418383 0.140000i
\(802\) −18324.4 15878.2i −0.806805 0.699101i
\(803\) 1374.07 + 403.465i 0.0603861 + 0.0177310i
\(804\) −32042.2 + 3998.43i −1.40553 + 0.175390i
\(805\) 2932.67 2810.21i 0.128401 0.123040i
\(806\) 6386.25i 0.279089i
\(807\) 1241.63 + 202.228i 0.0541605 + 0.00882125i
\(808\) −3436.82 + 3966.30i −0.149637 + 0.172691i
\(809\) −21017.8 + 32704.3i −0.913406 + 1.42129i −0.00648931 + 0.999979i \(0.502066\pi\)
−0.906917 + 0.421309i \(0.861571\pi\)
\(810\) 16041.6 5924.41i 0.695856 0.256991i
\(811\) −14225.6 + 9142.25i −0.615942 + 0.395842i −0.811081 0.584934i \(-0.801121\pi\)
0.195139 + 0.980776i \(0.437484\pi\)
\(812\) 4886.85 + 10700.7i 0.211201 + 0.462465i
\(813\) 8113.33 9017.74i 0.349996 0.389011i
\(814\) 920.875 + 6404.83i 0.0396519 + 0.275785i
\(815\) 2004.64 4389.55i 0.0861589 0.188662i
\(816\) 698.961 + 1609.30i 0.0299859 + 0.0690401i
\(817\) 12666.7 3719.27i 0.542412 0.159266i
\(818\) 1204.55 + 550.098i 0.0514865 + 0.0235131i
\(819\) −3988.72 + 1644.66i −0.170179 + 0.0701698i
\(820\) −14088.8 + 12208.0i −0.600002 + 0.519905i
\(821\) 9631.03 4398.34i 0.409410 0.186971i −0.200055 0.979785i \(-0.564112\pi\)
0.609464 + 0.792814i \(0.291385\pi\)
\(822\) −37741.0 + 31489.5i −1.60142 + 1.33616i
\(823\) 4030.60 28033.5i 0.170714 1.18735i −0.706665 0.707548i \(-0.749801\pi\)
0.877380 0.479797i \(-0.159290\pi\)
\(824\) −7285.56 4682.15i −0.308015 0.197949i
\(825\) 2465.61 + 1650.34i 0.104051 + 0.0696456i
\(826\) 3369.29 11474.8i 0.141928 0.483363i
\(827\) −25557.7 −1.07464 −0.537320 0.843378i \(-0.680563\pi\)
−0.537320 + 0.843378i \(0.680563\pi\)
\(828\) 26712.0 8215.27i 1.12114 0.344807i
\(829\) −6703.51 −0.280847 −0.140424 0.990092i \(-0.544846\pi\)
−0.140424 + 0.990092i \(0.544846\pi\)
\(830\) −3555.87 + 12110.2i −0.148706 + 0.506447i
\(831\) 15992.8 + 10704.7i 0.667610 + 0.446861i
\(832\) 13784.9 + 8859.02i 0.574405 + 0.369148i
\(833\) 282.740 1966.50i 0.0117603 0.0817948i
\(834\) 18313.3 15279.9i 0.760357 0.634410i
\(835\) 11330.6 5174.52i 0.469596 0.214457i
\(836\) −1671.01 + 1447.94i −0.0691307 + 0.0599021i
\(837\) 7658.99 4336.90i 0.316289 0.179098i
\(838\) −18266.6 8342.07i −0.752994 0.343881i
\(839\) 32132.2 9434.86i 1.32220 0.388233i 0.456914 0.889511i \(-0.348955\pi\)
0.865287 + 0.501277i \(0.167136\pi\)
\(840\) −439.766 1012.52i −0.0180635 0.0415897i
\(841\) −5109.21 + 11187.6i −0.209488 + 0.458715i
\(842\) −1245.40 8661.95i −0.0509731 0.354526i
\(843\) −15773.2 + 17531.4i −0.644433 + 0.716269i
\(844\) 11522.2 + 25230.1i 0.469917 + 1.02898i
\(845\) −7577.16 + 4869.54i −0.308476 + 0.198245i
\(846\) 1333.90 + 12597.9i 0.0542085 + 0.511969i
\(847\) 4577.33 7122.46i 0.185689 0.288938i
\(848\) −24201.2 + 27929.7i −0.980038 + 1.13102i
\(849\) 5368.85 + 874.439i 0.217030 + 0.0353483i
\(850\) 2576.01i 0.103949i
\(851\) 16289.8 + 22756.2i 0.656178 + 0.916654i
\(852\) −31178.4 + 3890.64i −1.25370 + 0.156445i
\(853\) −7792.56 2288.10i −0.312793 0.0918442i 0.121568 0.992583i \(-0.461208\pi\)
−0.434361 + 0.900739i \(0.643026\pi\)
\(854\) −10092.6 8745.26i −0.404403 0.350418i
\(855\) −1856.85 + 5549.09i −0.0742723 + 0.221959i
\(856\) −5696.03 818.965i −0.227437 0.0327005i
\(857\) 17096.6 + 26602.8i 0.681455 + 1.06036i 0.993885 + 0.110424i \(0.0352209\pi\)
−0.312429 + 0.949941i \(0.601143\pi\)
\(858\) 1698.17 + 2754.05i 0.0675695 + 0.109582i
\(859\) −19906.7 22973.5i −0.790696 0.912511i 0.207137 0.978312i \(-0.433585\pi\)
−0.997833 + 0.0658005i \(0.979040\pi\)
\(860\) 17909.1 2574.94i 0.710110 0.102098i
\(861\) 11457.2 + 3597.61i 0.453496 + 0.142400i
\(862\) −8820.76 30040.8i −0.348534 1.18700i
\(863\) 5380.31 + 18323.7i 0.212222 + 0.722763i 0.994948 + 0.100396i \(0.0320109\pi\)
−0.782725 + 0.622368i \(0.786171\pi\)
\(864\) −2031.42 + 36259.8i −0.0799888 + 1.42776i
\(865\) 18399.0 2645.38i 0.723220 0.103983i
\(866\) 14472.6 + 16702.3i 0.567899 + 0.655390i
\(867\) −21536.1 + 13279.4i −0.843602 + 0.520174i
\(868\) −2083.11 3241.38i −0.0814577 0.126751i
\(869\) −4130.10 593.819i −0.161225 0.0231806i
\(870\) 10093.1 21052.4i 0.393320 0.820396i
\(871\) −12219.5 10588.3i −0.475365 0.411906i
\(872\) −2339.34 686.893i −0.0908488 0.0266756i
\(873\) 11922.2 + 47026.6i 0.462205 + 1.82315i
\(874\) −6543.42 + 16462.9i −0.253243 + 0.637145i
\(875\) 8040.20i 0.310638i
\(876\) 1835.08 11267.0i 0.0707781 0.434561i
\(877\) −19407.4 + 22397.3i −0.747253 + 0.862376i −0.994299 0.106628i \(-0.965995\pi\)
0.247046 + 0.969004i \(0.420540\pi\)
\(878\) 25516.3 39704.1i 0.980790 1.52614i
\(879\) −41857.2 780.944i −1.60615 0.0299665i
\(880\) 1476.98 949.196i 0.0565783 0.0363607i
\(881\) −13992.3 30638.9i −0.535089 1.17168i −0.963404 0.268052i \(-0.913620\pi\)
0.428316 0.903629i \(-0.359107\pi\)
\(882\) 19316.1 27725.0i 0.737422 1.05845i
\(883\) −4772.76 33195.3i −0.181898 1.26513i −0.852269 0.523104i \(-0.824774\pi\)
0.670370 0.742027i \(-0.266135\pi\)
\(884\) 629.932 1379.36i 0.0239671 0.0524806i
\(885\) −11751.4 + 5103.95i −0.446350 + 0.193862i
\(886\) −2724.54 + 799.998i −0.103310 + 0.0303346i
\(887\) 11406.3 + 5209.08i 0.431777 + 0.197186i 0.619434 0.785049i \(-0.287362\pi\)
−0.187657 + 0.982235i \(0.560089\pi\)
\(888\) 7336.56 2006.34i 0.277251 0.0758201i
\(889\) 7872.27 6821.36i 0.296994 0.257346i
\(890\) 7904.17 3609.71i 0.297695 0.135953i
\(891\) −2149.68 + 3906.88i −0.0808273 + 0.146897i
\(892\) 2937.02 20427.4i 0.110245 0.766772i
\(893\) −3646.73 2343.61i −0.136655 0.0878231i
\(894\) −7776.11 + 11617.5i −0.290908 + 0.434617i
\(895\) −2696.96 + 9185.01i −0.100726 + 0.343040i
\(896\) 4761.02 0.177516
\(897\) 12004.1 + 7191.91i 0.446827 + 0.267704i
\(898\) 25445.4 0.945573
\(899\) 3385.46 11529.8i 0.125597 0.427743i
\(900\) 10620.3 21131.6i 0.393346 0.782653i
\(901\) 4033.60 + 2592.24i 0.149144 + 0.0958491i
\(902\) 1281.63 8913.94i 0.0473100 0.329048i
\(903\) −7466.87 8949.23i −0.275174 0.329803i
\(904\) 956.407 436.777i 0.0351876 0.0160697i
\(905\) −17253.6 + 14950.3i −0.633733 + 0.549132i
\(906\) 9915.18 + 36256.8i 0.363587 + 1.32953i
\(907\) 41082.9 + 18761.9i 1.50401 + 0.686857i 0.985727 0.168353i \(-0.0538450\pi\)
0.518281 + 0.855211i \(0.326572\pi\)
\(908\) −29890.7 + 8776.70i −1.09246 + 0.320777i
\(909\) −12498.7 21142.9i −0.456056 0.771470i
\(910\) 1557.15 3409.69i 0.0567243 0.124209i
\(911\) 197.058 + 1370.57i 0.00716665 + 0.0498451i 0.993091 0.117347i \(-0.0374390\pi\)
−0.985924 + 0.167192i \(0.946530\pi\)
\(912\) −7591.00 6829.68i −0.275617 0.247975i
\(913\) −1367.23 2993.81i −0.0495604 0.108522i
\(914\) 26670.0 17139.8i 0.965169 0.620276i
\(915\) −266.877 + 14304.2i −0.00964229 + 0.516809i
\(916\) 2997.36 4663.98i 0.108117 0.168234i
\(917\) 7163.66 8267.30i 0.257977 0.297721i
\(918\) 3857.07 335.769i 0.138673 0.0120719i
\(919\) 16113.1i 0.578369i −0.957273 0.289185i \(-0.906616\pi\)
0.957273 0.289185i \(-0.0933841\pi\)
\(920\) −1782.50 + 3105.14i −0.0638776 + 0.111276i
\(921\) 5159.84 + 41349.4i 0.184606 + 1.47938i
\(922\) −27470.2 8065.99i −0.981219 0.288112i
\(923\) −11890.1 10302.8i −0.424017 0.367413i
\(924\) 1760.25 + 843.912i 0.0626710 + 0.0300462i
\(925\) 23442.2 + 3370.48i 0.833271 + 0.119806i
\(926\) −965.550 1502.43i −0.0342656 0.0533183i
\(927\) 31599.0 25380.3i 1.11958 0.899242i
\(928\) 32469.2 + 37471.4i 1.14855 + 1.32550i
\(929\) 37610.2 5407.53i 1.32826 0.190974i 0.558602 0.829436i \(-0.311338\pi\)
0.769654 + 0.638461i \(0.220429\pi\)
\(930\) −2290.87 + 7295.66i −0.0807747 + 0.257241i
\(931\) 3257.52 + 11094.1i 0.114673 + 0.390541i
\(932\) −6768.51 23051.4i −0.237886 0.810166i
\(933\) −3795.61 + 12087.8i −0.133186 + 0.424155i
\(934\) 13266.3 1907.40i 0.464760 0.0668224i
\(935\) −149.168 172.149i −0.00521743 0.00602124i
\(936\) 2965.15 2381.60i 0.103546 0.0831679i
\(937\) 12203.4 + 18988.8i 0.425472 + 0.662047i 0.986125 0.166004i \(-0.0530864\pi\)
−0.560654 + 0.828051i \(0.689450\pi\)
\(938\) −17887.8 2571.88i −0.622663 0.0895255i
\(939\) −44664.7 21413.4i −1.55226 0.744197i
\(940\) −4490.05 3890.65i −0.155797 0.134999i
\(941\) −51988.7 15265.3i −1.80105 0.528835i −0.803278 0.595605i \(-0.796912\pi\)
−0.997768 + 0.0667700i \(0.978731\pi\)
\(942\) −7833.41 62774.6i −0.270941 2.17124i
\(943\) −12830.3 36775.4i −0.443066 1.26996i
\(944\) 22357.4i 0.770839i
\(945\) 5146.68 448.035i 0.177166 0.0154228i
\(946\) −5723.77 + 6605.58i −0.196719 + 0.227025i
\(947\) −28813.5 + 44834.7i −0.988715 + 1.53847i −0.153792 + 0.988103i \(0.549148\pi\)
−0.834923 + 0.550367i \(0.814488\pi\)
\(948\) −620.443 + 33254.7i −0.0212564 + 1.13931i
\(949\) 4808.59 3090.29i 0.164482 0.105706i
\(950\) 6227.92 + 13637.2i 0.212695 + 0.465738i
\(951\) −17474.1 15721.6i −0.595833 0.536076i
\(952\) −35.5684 247.384i −0.00121090 0.00842201i
\(953\) 15486.8 33911.5i 0.526410 1.15268i −0.440546 0.897730i \(-0.645215\pi\)
0.966955 0.254946i \(-0.0820577\pi\)
\(954\) 41499.4 + 70200.9i 1.40838 + 2.38243i
\(955\) 8418.39 2471.86i 0.285249 0.0837566i
\(956\) −34741.4 15865.9i −1.17533 0.536756i
\(957\) 1605.94 + 5872.42i 0.0542451 + 0.198358i
\(958\) 58001.5 50258.6i 1.95610 1.69497i
\(959\) −13507.2 + 6168.55i −0.454819 + 0.207709i
\(960\) −12570.0 15065.5i −0.422599 0.506495i
\(961\) 3679.57 25592.0i 0.123513 0.859052i
\(962\) 21727.0 + 13963.1i 0.728177 + 0.467971i
\(963\) 12093.5 24062.9i 0.404682 0.805209i
\(964\) 1149.85 3916.04i 0.0384173 0.130837i
\(965\) 1096.44 0.0365757
\(966\) 15632.9 491.418i 0.520684 0.0163676i
\(967\) 36860.2 1.22579 0.612897 0.790163i \(-0.290004\pi\)
0.612897 + 0.790163i \(0.290004\pi\)
\(968\) −2102.61 + 7160.82i −0.0698144 + 0.237766i
\(969\) −736.911 + 1100.95i −0.0244303 + 0.0364989i
\(970\) −35458.3 22787.6i −1.17371 0.754296i
\(971\) 5440.44 37839.1i 0.179806 1.25058i −0.677403 0.735612i \(-0.736895\pi\)
0.857209 0.514968i \(-0.172196\pi\)
\(972\) 33024.7 + 13147.4i 1.08978 + 0.433852i
\(973\) 6554.21 2993.21i 0.215949 0.0986205i
\(974\) −17935.6 + 15541.3i −0.590036 + 0.511269i
\(975\) 11422.8 3123.81i 0.375204 0.102607i
\(976\) −22709.6 10371.1i −0.744792 0.340135i
\(977\) 19251.4 5652.72i 0.630406 0.185104i 0.0491062 0.998794i \(-0.484363\pi\)
0.581299 + 0.813690i \(0.302545\pi\)
\(978\) 17043.9 7402.64i 0.557265 0.242035i
\(979\) −941.288 + 2061.13i −0.0307290 + 0.0672871i
\(980\) 2255.26 + 15685.7i 0.0735118 + 0.511286i
\(981\) 6522.52 9361.99i 0.212281 0.304695i
\(982\) −7436.13 16282.9i −0.241646 0.529131i
\(983\) 14485.6 9309.31i 0.470008 0.302056i −0.284114 0.958791i \(-0.591699\pi\)
0.754122 + 0.656735i \(0.228063\pi\)
\(984\) −10583.8 197.465i −0.342884 0.00639731i
\(985\) −6425.47 + 9998.23i −0.207850 + 0.323422i
\(986\) 3461.48 3994.76i 0.111801 0.129026i
\(987\) −615.230 + 3777.37i −0.0198409 + 0.121819i
\(988\) 8825.20i 0.284177i
\(989\) −8821.13 + 36758.8i −0.283615 + 1.18186i
\(990\) −952.068 3755.39i −0.0305643 0.120560i
\(991\) −16873.6 4954.53i −0.540875 0.158815i −0.000127189 1.00000i \(-0.500040\pi\)
−0.540748 + 0.841185i \(0.681859\pi\)
\(992\) −12273.1 10634.7i −0.392815 0.340376i
\(993\) 1343.77 2802.87i 0.0429439 0.0895733i
\(994\) −17405.6 2502.55i −0.555405 0.0798551i
\(995\) 7317.56 + 11386.3i 0.233148 + 0.362785i
\(996\) −22331.1 + 13769.6i −0.710431 + 0.438059i
\(997\) 17820.7 + 20566.2i 0.566086 + 0.653298i 0.964554 0.263884i \(-0.0850037\pi\)
−0.398469 + 0.917182i \(0.630458\pi\)
\(998\) −66274.6 + 9528.85i −2.10209 + 0.302235i
\(999\) −1991.06 + 35539.4i −0.0630574 + 1.12554i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 69.4.g.a.5.4 220
3.2 odd 2 inner 69.4.g.a.5.19 yes 220
23.14 odd 22 inner 69.4.g.a.14.19 yes 220
69.14 even 22 inner 69.4.g.a.14.4 yes 220
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.4.g.a.5.4 220 1.1 even 1 trivial
69.4.g.a.5.19 yes 220 3.2 odd 2 inner
69.4.g.a.14.4 yes 220 69.14 even 22 inner
69.4.g.a.14.19 yes 220 23.14 odd 22 inner