Properties

Label 201.4.e.b.37.7
Level $201$
Weight $4$
Character 201.37
Analytic conductor $11.859$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [201,4,Mod(37,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.37");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 201.e (of order \(3\), degree \(2\), 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: \(11.8593839112\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.7
Character \(\chi\) \(=\) 201.37
Dual form 201.4.e.b.163.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.829978 - 1.43756i) q^{2} -3.00000 q^{3} +(2.62227 - 4.54191i) q^{4} -7.05463 q^{5} +(2.48993 + 4.31269i) q^{6} +(18.3944 - 31.8600i) q^{7} -21.9854 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+(-0.829978 - 1.43756i) q^{2} -3.00000 q^{3} +(2.62227 - 4.54191i) q^{4} -7.05463 q^{5} +(2.48993 + 4.31269i) q^{6} +(18.3944 - 31.8600i) q^{7} -21.9854 q^{8} +9.00000 q^{9} +(5.85519 + 10.1415i) q^{10} +(11.1840 - 19.3712i) q^{11} +(-7.86682 + 13.6257i) q^{12} +(31.4911 + 54.5442i) q^{13} -61.0677 q^{14} +21.1639 q^{15} +(-2.73081 - 4.72990i) q^{16} +(-45.1811 - 78.2560i) q^{17} +(-7.46980 - 12.9381i) q^{18} +(13.0185 + 22.5488i) q^{19} +(-18.4992 + 32.0415i) q^{20} +(-55.1831 + 95.5799i) q^{21} -37.1299 q^{22} +(-67.0215 - 116.085i) q^{23} +65.9561 q^{24} -75.2323 q^{25} +(52.2738 - 90.5409i) q^{26} -27.0000 q^{27} +(-96.4700 - 167.091i) q^{28} +(-124.991 + 216.491i) q^{29} +(-17.5656 - 30.4244i) q^{30} +(59.8781 - 103.712i) q^{31} +(-92.4745 + 160.171i) q^{32} +(-33.5520 + 58.1137i) q^{33} +(-74.9987 + 129.902i) q^{34} +(-129.765 + 224.760i) q^{35} +(23.6005 - 40.8772i) q^{36} +(66.0047 + 114.324i) q^{37} +(21.6102 - 37.4299i) q^{38} +(-94.4733 - 163.633i) q^{39} +155.099 q^{40} +(-190.750 + 330.389i) q^{41} +183.203 q^{42} -209.124 q^{43} +(-58.6550 - 101.593i) q^{44} -63.4916 q^{45} +(-111.253 + 192.696i) q^{46} +(158.666 - 274.818i) q^{47} +(8.19243 + 14.1897i) q^{48} +(-505.205 - 875.041i) q^{49} +(62.4411 + 108.151i) q^{50} +(135.543 + 234.768i) q^{51} +330.313 q^{52} +393.851 q^{53} +(22.4094 + 38.8142i) q^{54} +(-78.8989 + 136.657i) q^{55} +(-404.407 + 700.453i) q^{56} +(-39.0556 - 67.6463i) q^{57} +414.959 q^{58} -138.863 q^{59} +(55.4975 - 96.1244i) q^{60} +(64.3634 + 111.481i) q^{61} -198.790 q^{62} +(165.549 - 286.740i) q^{63} +263.314 q^{64} +(-222.158 - 384.789i) q^{65} +111.390 q^{66} +(-381.403 - 394.074i) q^{67} -473.909 q^{68} +(201.065 + 348.254i) q^{69} +430.810 q^{70} +(222.721 - 385.764i) q^{71} -197.868 q^{72} +(554.926 + 961.159i) q^{73} +(109.565 - 189.772i) q^{74} +225.697 q^{75} +136.553 q^{76} +(-411.445 - 712.643i) q^{77} +(-156.822 + 271.623i) q^{78} +(476.244 - 824.880i) q^{79} +(19.2648 + 33.3677i) q^{80} +81.0000 q^{81} +633.275 q^{82} +(290.083 + 502.438i) q^{83} +(289.410 + 501.273i) q^{84} +(318.736 + 552.067i) q^{85} +(173.568 + 300.629i) q^{86} +(374.973 - 649.473i) q^{87} +(-245.884 + 425.884i) q^{88} +525.436 q^{89} +(52.6967 + 91.2733i) q^{90} +2317.03 q^{91} -702.995 q^{92} +(-179.634 + 311.136i) q^{93} -526.758 q^{94} +(-91.8409 - 159.073i) q^{95} +(277.423 - 480.512i) q^{96} +(-743.743 - 1288.20i) q^{97} +(-838.618 + 1452.53i) q^{98} +(100.656 - 174.341i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9} + 14 q^{10} - 16 q^{11} + 270 q^{12} - 46 q^{13} + 14 q^{14} + 12 q^{15} - 346 q^{16} - 8 q^{17} + 18 q^{18} - 154 q^{19} - 180 q^{20} - 66 q^{21} + 214 q^{22} - 104 q^{23} - 144 q^{24} + 1032 q^{25} - 333 q^{26} - 972 q^{27} - 473 q^{28} + 76 q^{29} - 42 q^{30} + 498 q^{31} - 285 q^{32} + 48 q^{33} + 26 q^{34} - 392 q^{35} - 810 q^{36} - 124 q^{37} + 20 q^{38} + 138 q^{39} + 638 q^{40} - 508 q^{41} - 42 q^{42} - 1400 q^{43} - 333 q^{44} - 36 q^{45} - 1372 q^{46} + 18 q^{47} + 1038 q^{48} - 238 q^{49} - 337 q^{50} + 24 q^{51} + 3640 q^{52} + 724 q^{53} - 54 q^{54} - 178 q^{55} - 829 q^{56} + 462 q^{57} - 1472 q^{58} + 720 q^{59} + 540 q^{60} + 232 q^{61} - 3882 q^{62} + 198 q^{63} + 3628 q^{64} - 1428 q^{65} - 642 q^{66} - 1164 q^{67} + 1634 q^{68} + 312 q^{69} + 2550 q^{70} + 406 q^{71} + 432 q^{72} - 2120 q^{73} + 1375 q^{74} - 3096 q^{75} + 4190 q^{76} - 800 q^{77} + 999 q^{78} + 1306 q^{79} - 1927 q^{80} + 2916 q^{81} - 794 q^{82} - 1010 q^{83} + 1419 q^{84} + 472 q^{85} + 737 q^{86} - 228 q^{87} - 1838 q^{88} + 1904 q^{89} + 126 q^{90} + 7340 q^{91} + 7368 q^{92} - 1494 q^{93} - 9862 q^{94} + 1678 q^{95} + 855 q^{96} - 2358 q^{97} - 2610 q^{98} - 144 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.829978 1.43756i −0.293442 0.508256i 0.681180 0.732116i \(-0.261467\pi\)
−0.974621 + 0.223861i \(0.928134\pi\)
\(3\) −3.00000 −0.577350
\(4\) 2.62227 4.54191i 0.327784 0.567739i
\(5\) −7.05463 −0.630985 −0.315492 0.948928i \(-0.602170\pi\)
−0.315492 + 0.948928i \(0.602170\pi\)
\(6\) 2.48993 + 4.31269i 0.169419 + 0.293442i
\(7\) 18.3944 31.8600i 0.993202 1.72028i 0.395793 0.918340i \(-0.370470\pi\)
0.597409 0.801937i \(-0.296197\pi\)
\(8\) −21.9854 −0.971625
\(9\) 9.00000 0.333333
\(10\) 5.85519 + 10.1415i 0.185157 + 0.320702i
\(11\) 11.1840 19.3712i 0.306555 0.530968i −0.671052 0.741411i \(-0.734157\pi\)
0.977606 + 0.210442i \(0.0674904\pi\)
\(12\) −7.86682 + 13.6257i −0.189246 + 0.327784i
\(13\) 31.4911 + 54.5442i 0.671851 + 1.16368i 0.977379 + 0.211496i \(0.0678337\pi\)
−0.305528 + 0.952183i \(0.598833\pi\)
\(14\) −61.0677 −1.16579
\(15\) 21.1639 0.364299
\(16\) −2.73081 4.72990i −0.0426689 0.0739047i
\(17\) −45.1811 78.2560i −0.644590 1.11646i −0.984396 0.175968i \(-0.943695\pi\)
0.339806 0.940496i \(-0.389639\pi\)
\(18\) −7.46980 12.9381i −0.0978139 0.169419i
\(19\) 13.0185 + 22.5488i 0.157192 + 0.272265i 0.933855 0.357651i \(-0.116422\pi\)
−0.776663 + 0.629917i \(0.783089\pi\)
\(20\) −18.4992 + 32.0415i −0.206827 + 0.358235i
\(21\) −55.1831 + 95.5799i −0.573425 + 0.993202i
\(22\) −37.1299 −0.359824
\(23\) −67.0215 116.085i −0.607607 1.05241i −0.991634 0.129084i \(-0.958796\pi\)
0.384027 0.923322i \(-0.374537\pi\)
\(24\) 65.9561 0.560968
\(25\) −75.2323 −0.601858
\(26\) 52.2738 90.5409i 0.394298 0.682944i
\(27\) −27.0000 −0.192450
\(28\) −96.4700 167.091i −0.651112 1.12776i
\(29\) −124.991 + 216.491i −0.800354 + 1.38625i 0.119030 + 0.992891i \(0.462022\pi\)
−0.919383 + 0.393363i \(0.871312\pi\)
\(30\) −17.5656 30.4244i −0.106901 0.185157i
\(31\) 59.8781 103.712i 0.346917 0.600878i −0.638783 0.769387i \(-0.720562\pi\)
0.985700 + 0.168509i \(0.0538952\pi\)
\(32\) −92.4745 + 160.171i −0.510854 + 0.884825i
\(33\) −33.5520 + 58.1137i −0.176989 + 0.306555i
\(34\) −74.9987 + 129.902i −0.378299 + 0.655233i
\(35\) −129.765 + 224.760i −0.626696 + 1.08547i
\(36\) 23.6005 40.8772i 0.109261 0.189246i
\(37\) 66.0047 + 114.324i 0.293273 + 0.507964i 0.974582 0.224032i \(-0.0719221\pi\)
−0.681308 + 0.731996i \(0.738589\pi\)
\(38\) 21.6102 37.4299i 0.0922536 0.159788i
\(39\) −94.4733 163.633i −0.387893 0.671851i
\(40\) 155.099 0.613081
\(41\) −190.750 + 330.389i −0.726590 + 1.25849i 0.231726 + 0.972781i \(0.425563\pi\)
−0.958316 + 0.285710i \(0.907770\pi\)
\(42\) 183.203 0.673067
\(43\) −209.124 −0.741653 −0.370827 0.928702i \(-0.620926\pi\)
−0.370827 + 0.928702i \(0.620926\pi\)
\(44\) −58.6550 101.593i −0.200967 0.348086i
\(45\) −63.4916 −0.210328
\(46\) −111.253 + 192.696i −0.356594 + 0.617639i
\(47\) 158.666 274.818i 0.492422 0.852900i −0.507540 0.861628i \(-0.669445\pi\)
0.999962 + 0.00872796i \(0.00277823\pi\)
\(48\) 8.19243 + 14.1897i 0.0246349 + 0.0426689i
\(49\) −505.205 875.041i −1.47290 2.55114i
\(50\) 62.4411 + 108.151i 0.176610 + 0.305898i
\(51\) 135.543 + 234.768i 0.372154 + 0.644590i
\(52\) 330.313 0.880888
\(53\) 393.851 1.02075 0.510374 0.859953i \(-0.329507\pi\)
0.510374 + 0.859953i \(0.329507\pi\)
\(54\) 22.4094 + 38.8142i 0.0564729 + 0.0978139i
\(55\) −78.8989 + 136.657i −0.193431 + 0.335033i
\(56\) −404.407 + 700.453i −0.965020 + 1.67146i
\(57\) −39.0556 67.6463i −0.0907551 0.157192i
\(58\) 414.959 0.939428
\(59\) −138.863 −0.306413 −0.153206 0.988194i \(-0.548960\pi\)
−0.153206 + 0.988194i \(0.548960\pi\)
\(60\) 55.4975 96.1244i 0.119412 0.206827i
\(61\) 64.3634 + 111.481i 0.135097 + 0.233994i 0.925634 0.378419i \(-0.123532\pi\)
−0.790538 + 0.612413i \(0.790199\pi\)
\(62\) −198.790 −0.407199
\(63\) 165.549 286.740i 0.331067 0.573425i
\(64\) 263.314 0.514286
\(65\) −222.158 384.789i −0.423928 0.734264i
\(66\) 111.390 0.207744
\(67\) −381.403 394.074i −0.695460 0.718565i
\(68\) −473.909 −0.845146
\(69\) 201.065 + 348.254i 0.350802 + 0.607607i
\(70\) 430.810 0.735594
\(71\) 222.721 385.764i 0.372284 0.644814i −0.617633 0.786467i \(-0.711908\pi\)
0.989916 + 0.141652i \(0.0452415\pi\)
\(72\) −197.868 −0.323875
\(73\) 554.926 + 961.159i 0.889714 + 1.54103i 0.840213 + 0.542256i \(0.182430\pi\)
0.0495009 + 0.998774i \(0.484237\pi\)
\(74\) 109.565 189.772i 0.172117 0.298116i
\(75\) 225.697 0.347483
\(76\) 136.553 0.206101
\(77\) −411.445 712.643i −0.608941 1.05472i
\(78\) −156.822 + 271.623i −0.227648 + 0.394298i
\(79\) 476.244 824.880i 0.678249 1.17476i −0.297259 0.954797i \(-0.596072\pi\)
0.975508 0.219965i \(-0.0705943\pi\)
\(80\) 19.2648 + 33.3677i 0.0269234 + 0.0466327i
\(81\) 81.0000 0.111111
\(82\) 633.275 0.852847
\(83\) 290.083 + 502.438i 0.383623 + 0.664455i 0.991577 0.129517i \(-0.0413427\pi\)
−0.607954 + 0.793972i \(0.708009\pi\)
\(84\) 289.410 + 501.273i 0.375919 + 0.651112i
\(85\) 318.736 + 552.067i 0.406727 + 0.704471i
\(86\) 173.568 + 300.629i 0.217632 + 0.376949i
\(87\) 374.973 649.473i 0.462084 0.800354i
\(88\) −245.884 + 425.884i −0.297856 + 0.515902i
\(89\) 525.436 0.625799 0.312900 0.949786i \(-0.398700\pi\)
0.312900 + 0.949786i \(0.398700\pi\)
\(90\) 52.6967 + 91.2733i 0.0617191 + 0.106901i
\(91\) 2317.03 2.66913
\(92\) −702.995 −0.796655
\(93\) −179.634 + 311.136i −0.200293 + 0.346917i
\(94\) −526.758 −0.577989
\(95\) −91.8409 159.073i −0.0991860 0.171795i
\(96\) 277.423 480.512i 0.294942 0.510854i
\(97\) −743.743 1288.20i −0.778512 1.34842i −0.932799 0.360396i \(-0.882642\pi\)
0.154287 0.988026i \(-0.450692\pi\)
\(98\) −838.618 + 1452.53i −0.864421 + 1.49722i
\(99\) 100.656 174.341i 0.102185 0.176989i
\(100\) −197.279 + 341.698i −0.197279 + 0.341698i
\(101\) 484.923 839.911i 0.477739 0.827468i −0.521935 0.852985i \(-0.674790\pi\)
0.999674 + 0.0255166i \(0.00812308\pi\)
\(102\) 224.996 389.705i 0.218411 0.378299i
\(103\) 817.098 1415.26i 0.781661 1.35388i −0.149313 0.988790i \(-0.547706\pi\)
0.930974 0.365086i \(-0.118961\pi\)
\(104\) −692.343 1199.17i −0.652787 1.13066i
\(105\) 389.296 674.280i 0.361823 0.626696i
\(106\) −326.888 566.186i −0.299530 0.518801i
\(107\) 352.369 0.318362 0.159181 0.987249i \(-0.449115\pi\)
0.159181 + 0.987249i \(0.449115\pi\)
\(108\) −70.8014 + 122.632i −0.0630821 + 0.109261i
\(109\) −1786.30 −1.56969 −0.784845 0.619693i \(-0.787257\pi\)
−0.784845 + 0.619693i \(0.787257\pi\)
\(110\) 261.937 0.227043
\(111\) −198.014 342.971i −0.169321 0.293273i
\(112\) −200.926 −0.169515
\(113\) 378.916 656.301i 0.315446 0.546369i −0.664086 0.747656i \(-0.731179\pi\)
0.979532 + 0.201287i \(0.0645125\pi\)
\(114\) −64.8306 + 112.290i −0.0532626 + 0.0922536i
\(115\) 472.812 + 818.934i 0.383391 + 0.664052i
\(116\) 655.521 + 1135.40i 0.524686 + 0.908784i
\(117\) 283.420 + 490.898i 0.223950 + 0.387893i
\(118\) 115.253 + 199.624i 0.0899143 + 0.155736i
\(119\) −3324.31 −2.56083
\(120\) −465.296 −0.353962
\(121\) 415.337 + 719.384i 0.312048 + 0.540484i
\(122\) 106.840 185.053i 0.0792859 0.137327i
\(123\) 572.251 991.168i 0.419497 0.726590i
\(124\) −314.033 543.922i −0.227428 0.393916i
\(125\) 1412.56 1.01075
\(126\) −549.609 −0.388596
\(127\) −756.462 + 1310.23i −0.528544 + 0.915465i 0.470902 + 0.882186i \(0.343929\pi\)
−0.999446 + 0.0332799i \(0.989405\pi\)
\(128\) 521.251 + 902.833i 0.359941 + 0.623437i
\(129\) 627.371 0.428194
\(130\) −368.772 + 638.732i −0.248796 + 0.430927i
\(131\) −1940.54 −1.29424 −0.647120 0.762388i \(-0.724027\pi\)
−0.647120 + 0.762388i \(0.724027\pi\)
\(132\) 175.965 + 304.780i 0.116029 + 0.200967i
\(133\) 957.870 0.624495
\(134\) −249.951 + 875.365i −0.161138 + 0.564328i
\(135\) 190.475 0.121433
\(136\) 993.324 + 1720.49i 0.626300 + 1.08478i
\(137\) 693.301 0.432356 0.216178 0.976354i \(-0.430641\pi\)
0.216178 + 0.976354i \(0.430641\pi\)
\(138\) 333.758 578.087i 0.205880 0.356594i
\(139\) −843.314 −0.514597 −0.257298 0.966332i \(-0.582832\pi\)
−0.257298 + 0.966332i \(0.582832\pi\)
\(140\) 680.560 + 1178.76i 0.410842 + 0.711599i
\(141\) −475.999 + 824.454i −0.284300 + 0.492422i
\(142\) −739.415 −0.436974
\(143\) 1408.78 0.823836
\(144\) −24.5773 42.5691i −0.0142230 0.0246349i
\(145\) 881.765 1527.26i 0.505011 0.874705i
\(146\) 921.152 1595.48i 0.522158 0.904405i
\(147\) 1515.61 + 2625.12i 0.850380 + 1.47290i
\(148\) 692.330 0.384521
\(149\) 1043.20 0.573570 0.286785 0.957995i \(-0.407413\pi\)
0.286785 + 0.957995i \(0.407413\pi\)
\(150\) −187.323 324.454i −0.101966 0.176610i
\(151\) 866.011 + 1499.97i 0.466722 + 0.808385i 0.999277 0.0380094i \(-0.0121017\pi\)
−0.532556 + 0.846395i \(0.678768\pi\)
\(152\) −286.217 495.743i −0.152732 0.264540i
\(153\) −406.630 704.304i −0.214863 0.372154i
\(154\) −682.980 + 1182.96i −0.357377 + 0.618996i
\(155\) −422.418 + 731.649i −0.218899 + 0.379145i
\(156\) −990.939 −0.508581
\(157\) −415.941 720.430i −0.211437 0.366220i 0.740727 0.671806i \(-0.234481\pi\)
−0.952165 + 0.305586i \(0.901148\pi\)
\(158\) −1581.09 −0.796106
\(159\) −1181.55 −0.589329
\(160\) 652.373 1129.94i 0.322341 0.558311i
\(161\) −4931.27 −2.41391
\(162\) −67.2282 116.443i −0.0326046 0.0564729i
\(163\) 520.787 902.030i 0.250253 0.433450i −0.713343 0.700815i \(-0.752820\pi\)
0.963595 + 0.267365i \(0.0861530\pi\)
\(164\) 1000.40 + 1732.74i 0.476330 + 0.825027i
\(165\) 236.697 409.971i 0.111678 0.193431i
\(166\) 481.525 834.026i 0.225142 0.389958i
\(167\) 619.286 1072.63i 0.286957 0.497024i −0.686125 0.727484i \(-0.740690\pi\)
0.973082 + 0.230460i \(0.0740230\pi\)
\(168\) 1213.22 2101.36i 0.557155 0.965020i
\(169\) −884.878 + 1532.65i −0.402766 + 0.697612i
\(170\) 529.088 916.407i 0.238701 0.413442i
\(171\) 117.167 + 202.939i 0.0523975 + 0.0907551i
\(172\) −548.380 + 949.821i −0.243102 + 0.421065i
\(173\) −1524.03 2639.70i −0.669769 1.16007i −0.977968 0.208753i \(-0.933060\pi\)
0.308199 0.951322i \(-0.400274\pi\)
\(174\) −1244.88 −0.542379
\(175\) −1383.85 + 2396.90i −0.597767 + 1.03536i
\(176\) −122.165 −0.0523214
\(177\) 416.588 0.176908
\(178\) −436.101 755.348i −0.183635 0.318066i
\(179\) −3631.31 −1.51630 −0.758148 0.652083i \(-0.773896\pi\)
−0.758148 + 0.652083i \(0.773896\pi\)
\(180\) −166.492 + 288.373i −0.0689423 + 0.119412i
\(181\) 285.281 494.122i 0.117154 0.202916i −0.801485 0.598015i \(-0.795956\pi\)
0.918639 + 0.395099i \(0.129290\pi\)
\(182\) −1923.09 3330.89i −0.783235 1.35660i
\(183\) −193.090 334.442i −0.0779980 0.135097i
\(184\) 1473.49 + 2552.16i 0.590366 + 1.02254i
\(185\) −465.639 806.510i −0.185051 0.320518i
\(186\) 596.370 0.235097
\(187\) −2021.22 −0.790409
\(188\) −832.132 1441.30i −0.322816 0.559134i
\(189\) −496.648 + 860.219i −0.191142 + 0.331067i
\(190\) −152.452 + 264.054i −0.0582106 + 0.100824i
\(191\) 724.684 + 1255.19i 0.274535 + 0.475509i 0.970018 0.243034i \(-0.0781426\pi\)
−0.695482 + 0.718543i \(0.744809\pi\)
\(192\) −789.943 −0.296923
\(193\) −3563.95 −1.32922 −0.664608 0.747192i \(-0.731401\pi\)
−0.664608 + 0.747192i \(0.731401\pi\)
\(194\) −1234.58 + 2138.36i −0.456896 + 0.791366i
\(195\) 666.474 + 1154.37i 0.244755 + 0.423928i
\(196\) −5299.14 −1.93117
\(197\) 1153.29 1997.55i 0.417097 0.722434i −0.578549 0.815648i \(-0.696381\pi\)
0.995646 + 0.0932140i \(0.0297141\pi\)
\(198\) −334.169 −0.119941
\(199\) −1050.89 1820.20i −0.374350 0.648393i 0.615879 0.787840i \(-0.288801\pi\)
−0.990230 + 0.139447i \(0.955467\pi\)
\(200\) 1654.01 0.584780
\(201\) 1144.21 + 1182.22i 0.401524 + 0.414864i
\(202\) −1609.90 −0.560754
\(203\) 4598.26 + 7964.42i 1.58983 + 2.75366i
\(204\) 1421.73 0.487945
\(205\) 1345.67 2330.77i 0.458468 0.794089i
\(206\) −2712.69 −0.917487
\(207\) −603.194 1044.76i −0.202536 0.350802i
\(208\) 171.992 297.899i 0.0573342 0.0993058i
\(209\) 582.397 0.192752
\(210\) −1292.43 −0.424695
\(211\) 647.337 + 1121.22i 0.211206 + 0.365820i 0.952092 0.305811i \(-0.0989276\pi\)
−0.740886 + 0.671631i \(0.765594\pi\)
\(212\) 1032.78 1788.84i 0.334585 0.579518i
\(213\) −668.163 + 1157.29i −0.214938 + 0.372284i
\(214\) −292.458 506.553i −0.0934207 0.161809i
\(215\) 1475.29 0.467972
\(216\) 593.605 0.186989
\(217\) −2202.84 3815.43i −0.689117 1.19359i
\(218\) 1482.59 + 2567.92i 0.460612 + 0.797803i
\(219\) −1664.78 2883.48i −0.513677 0.889714i
\(220\) 413.789 + 716.703i 0.126807 + 0.219637i
\(221\) 2845.61 4928.74i 0.866137 1.50019i
\(222\) −328.695 + 569.316i −0.0993719 + 0.172117i
\(223\) 4200.35 1.26133 0.630664 0.776056i \(-0.282783\pi\)
0.630664 + 0.776056i \(0.282783\pi\)
\(224\) 3402.02 + 5892.47i 1.01476 + 1.75762i
\(225\) −677.090 −0.200619
\(226\) −1257.97 −0.370260
\(227\) 2127.89 3685.61i 0.622171 1.07763i −0.366910 0.930257i \(-0.619584\pi\)
0.989081 0.147375i \(-0.0470825\pi\)
\(228\) −409.658 −0.118992
\(229\) −1877.18 3251.37i −0.541692 0.938239i −0.998807 0.0488310i \(-0.984450\pi\)
0.457115 0.889408i \(-0.348883\pi\)
\(230\) 784.847 1359.39i 0.225006 0.389721i
\(231\) 1234.33 + 2137.93i 0.351572 + 0.608941i
\(232\) 2747.97 4759.63i 0.777644 1.34692i
\(233\) 1738.01 3010.32i 0.488672 0.846405i −0.511243 0.859436i \(-0.670815\pi\)
0.999915 + 0.0130314i \(0.00414813\pi\)
\(234\) 470.465 814.868i 0.131433 0.227648i
\(235\) −1119.33 + 1938.74i −0.310711 + 0.538167i
\(236\) −364.135 + 630.701i −0.100437 + 0.173962i
\(237\) −1428.73 + 2474.64i −0.391587 + 0.678249i
\(238\) 2759.11 + 4778.91i 0.751455 + 1.30156i
\(239\) −1167.11 + 2021.49i −0.315874 + 0.547110i −0.979623 0.200846i \(-0.935631\pi\)
0.663749 + 0.747955i \(0.268964\pi\)
\(240\) −57.7945 100.103i −0.0155442 0.0269234i
\(241\) 2639.66 0.705540 0.352770 0.935710i \(-0.385240\pi\)
0.352770 + 0.935710i \(0.385240\pi\)
\(242\) 689.440 1194.15i 0.183136 0.317201i
\(243\) −243.000 −0.0641500
\(244\) 675.114 0.177130
\(245\) 3564.03 + 6173.08i 0.929378 + 1.60973i
\(246\) −1899.82 −0.492392
\(247\) −819.935 + 1420.17i −0.211220 + 0.365843i
\(248\) −1316.44 + 2280.14i −0.337073 + 0.583828i
\(249\) −870.249 1507.32i −0.221485 0.383623i
\(250\) −1172.40 2030.65i −0.296596 0.513719i
\(251\) −380.358 658.800i −0.0956494 0.165670i 0.814230 0.580542i \(-0.197159\pi\)
−0.909879 + 0.414873i \(0.863826\pi\)
\(252\) −868.230 1503.82i −0.217037 0.375919i
\(253\) −2998.27 −0.745059
\(254\) 2511.39 0.620387
\(255\) −956.208 1656.20i −0.234824 0.406727i
\(256\) 1918.51 3322.96i 0.468386 0.811269i
\(257\) 2154.32 3731.40i 0.522891 0.905674i −0.476754 0.879037i \(-0.658187\pi\)
0.999645 0.0266375i \(-0.00847999\pi\)
\(258\) −520.705 901.887i −0.125650 0.217632i
\(259\) 4856.46 1.16512
\(260\) −2330.23 −0.555827
\(261\) −1124.92 + 1948.42i −0.266785 + 0.462084i
\(262\) 1610.60 + 2789.65i 0.379784 + 0.657805i
\(263\) 4352.34 1.02044 0.510222 0.860043i \(-0.329563\pi\)
0.510222 + 0.860043i \(0.329563\pi\)
\(264\) 737.653 1277.65i 0.171967 0.297856i
\(265\) −2778.47 −0.644076
\(266\) −795.011 1377.00i −0.183253 0.317403i
\(267\) −1576.31 −0.361305
\(268\) −2789.99 + 698.929i −0.635918 + 0.159306i
\(269\) 1774.24 0.402145 0.201073 0.979576i \(-0.435557\pi\)
0.201073 + 0.979576i \(0.435557\pi\)
\(270\) −158.090 273.820i −0.0356335 0.0617191i
\(271\) −631.572 −0.141569 −0.0707846 0.997492i \(-0.522550\pi\)
−0.0707846 + 0.997492i \(0.522550\pi\)
\(272\) −246.762 + 427.405i −0.0550079 + 0.0952765i
\(273\) −6951.10 −1.54102
\(274\) −575.425 996.665i −0.126871 0.219747i
\(275\) −841.397 + 1457.34i −0.184502 + 0.319568i
\(276\) 2108.98 0.459949
\(277\) 2997.35 0.650156 0.325078 0.945687i \(-0.394609\pi\)
0.325078 + 0.945687i \(0.394609\pi\)
\(278\) 699.932 + 1212.32i 0.151004 + 0.261547i
\(279\) 538.903 933.407i 0.115639 0.200293i
\(280\) 2852.94 4941.43i 0.608913 1.05467i
\(281\) 755.171 + 1308.00i 0.160319 + 0.277681i 0.934983 0.354692i \(-0.115414\pi\)
−0.774664 + 0.632373i \(0.782081\pi\)
\(282\) 1580.27 0.333702
\(283\) 7519.83 1.57953 0.789766 0.613408i \(-0.210202\pi\)
0.789766 + 0.613408i \(0.210202\pi\)
\(284\) −1168.07 2023.16i −0.244057 0.422720i
\(285\) 275.523 + 477.219i 0.0572651 + 0.0991860i
\(286\) −1169.26 2025.22i −0.241748 0.418719i
\(287\) 7017.46 + 12154.6i 1.44330 + 2.49987i
\(288\) −832.270 + 1441.53i −0.170285 + 0.294942i
\(289\) −1626.17 + 2816.61i −0.330993 + 0.573297i
\(290\) −2927.38 −0.592765
\(291\) 2231.23 + 3864.60i 0.449474 + 0.778512i
\(292\) 5820.67 1.16654
\(293\) 3743.75 0.746457 0.373229 0.927739i \(-0.378251\pi\)
0.373229 + 0.927739i \(0.378251\pi\)
\(294\) 2515.85 4357.59i 0.499073 0.864421i
\(295\) 979.623 0.193342
\(296\) −1451.14 2513.45i −0.284952 0.493551i
\(297\) −301.968 + 523.024i −0.0589965 + 0.102185i
\(298\) −865.830 1499.66i −0.168309 0.291520i
\(299\) 4221.16 7311.27i 0.816442 1.41412i
\(300\) 591.838 1025.09i 0.113899 0.197279i
\(301\) −3846.70 + 6662.68i −0.736611 + 1.27585i
\(302\) 1437.54 2489.89i 0.273911 0.474428i
\(303\) −1454.77 + 2519.73i −0.275823 + 0.477739i
\(304\) 71.1022 123.153i 0.0134145 0.0232345i
\(305\) −454.060 786.455i −0.0852439 0.147647i
\(306\) −674.988 + 1169.11i −0.126100 + 0.218411i
\(307\) 566.159 + 980.616i 0.105252 + 0.182302i 0.913841 0.406072i \(-0.133102\pi\)
−0.808589 + 0.588374i \(0.799768\pi\)
\(308\) −4315.68 −0.798405
\(309\) −2451.29 + 4245.77i −0.451292 + 0.781661i
\(310\) 1402.39 0.256937
\(311\) −4228.64 −0.771011 −0.385505 0.922706i \(-0.625973\pi\)
−0.385505 + 0.922706i \(0.625973\pi\)
\(312\) 2077.03 + 3597.52i 0.376887 + 0.652787i
\(313\) −7527.97 −1.35944 −0.679722 0.733470i \(-0.737900\pi\)
−0.679722 + 0.733470i \(0.737900\pi\)
\(314\) −690.443 + 1195.88i −0.124089 + 0.214929i
\(315\) −1167.89 + 2022.84i −0.208899 + 0.361823i
\(316\) −2497.69 4326.12i −0.444639 0.770137i
\(317\) 683.056 + 1183.09i 0.121023 + 0.209618i 0.920171 0.391516i \(-0.128049\pi\)
−0.799148 + 0.601134i \(0.794716\pi\)
\(318\) 980.663 + 1698.56i 0.172934 + 0.299530i
\(319\) 2795.80 + 4842.47i 0.490704 + 0.849925i
\(320\) −1857.58 −0.324506
\(321\) −1057.11 −0.183807
\(322\) 4092.85 + 7089.02i 0.708340 + 1.22688i
\(323\) 1176.38 2037.56i 0.202649 0.350999i
\(324\) 212.404 367.895i 0.0364205 0.0630821i
\(325\) −2369.15 4103.48i −0.404359 0.700370i
\(326\) −1728.97 −0.293738
\(327\) 5358.89 0.906260
\(328\) 4193.72 7263.73i 0.705973 1.22278i
\(329\) −5837.13 10110.2i −0.978150 1.69420i
\(330\) −785.812 −0.131083
\(331\) −165.605 + 286.836i −0.0274999 + 0.0476313i −0.879448 0.475995i \(-0.842088\pi\)
0.851948 + 0.523627i \(0.175421\pi\)
\(332\) 3042.71 0.502983
\(333\) 594.043 + 1028.91i 0.0977578 + 0.169321i
\(334\) −2055.98 −0.336820
\(335\) 2690.66 + 2780.05i 0.438825 + 0.453403i
\(336\) 602.778 0.0978697
\(337\) 168.929 + 292.593i 0.0273060 + 0.0472955i 0.879356 0.476166i \(-0.157974\pi\)
−0.852049 + 0.523461i \(0.824640\pi\)
\(338\) 2937.72 0.472754
\(339\) −1136.75 + 1968.90i −0.182123 + 0.315446i
\(340\) 3343.25 0.533274
\(341\) −1339.35 2319.83i −0.212698 0.368404i
\(342\) 194.492 336.870i 0.0307512 0.0532626i
\(343\) −24553.2 −3.86515
\(344\) 4597.66 0.720609
\(345\) −1418.44 2456.80i −0.221351 0.383391i
\(346\) −2529.83 + 4381.79i −0.393076 + 0.680828i
\(347\) 4207.30 7287.26i 0.650893 1.12738i −0.332014 0.943274i \(-0.607728\pi\)
0.982907 0.184105i \(-0.0589386\pi\)
\(348\) −1966.56 3406.19i −0.302928 0.524686i
\(349\) 2075.92 0.318400 0.159200 0.987246i \(-0.449109\pi\)
0.159200 + 0.987246i \(0.449109\pi\)
\(350\) 4594.26 0.701638
\(351\) −850.260 1472.69i −0.129298 0.223950i
\(352\) 2068.47 + 3582.69i 0.313209 + 0.542495i
\(353\) −2412.26 4178.15i −0.363716 0.629974i 0.624854 0.780742i \(-0.285159\pi\)
−0.988569 + 0.150768i \(0.951825\pi\)
\(354\) −345.759 598.871i −0.0519120 0.0899143i
\(355\) −1571.21 + 2721.42i −0.234905 + 0.406868i
\(356\) 1377.84 2386.48i 0.205127 0.355290i
\(357\) 9972.94 1.47850
\(358\) 3013.91 + 5220.24i 0.444944 + 0.770666i
\(359\) −7650.94 −1.12479 −0.562397 0.826867i \(-0.690121\pi\)
−0.562397 + 0.826867i \(0.690121\pi\)
\(360\) 1395.89 0.204360
\(361\) 3090.54 5352.96i 0.450581 0.780429i
\(362\) −947.109 −0.137511
\(363\) −1246.01 2158.15i −0.180161 0.312048i
\(364\) 6075.89 10523.8i 0.874900 1.51537i
\(365\) −3914.79 6780.62i −0.561396 0.972367i
\(366\) −320.521 + 555.159i −0.0457757 + 0.0792859i
\(367\) −1020.62 + 1767.77i −0.145167 + 0.251436i −0.929435 0.368986i \(-0.879705\pi\)
0.784269 + 0.620422i \(0.213038\pi\)
\(368\) −366.046 + 634.010i −0.0518518 + 0.0898100i
\(369\) −1716.75 + 2973.50i −0.242197 + 0.419497i
\(370\) −772.940 + 1338.77i −0.108603 + 0.188107i
\(371\) 7244.64 12548.1i 1.01381 1.75597i
\(372\) 942.100 + 1631.77i 0.131305 + 0.227428i
\(373\) −1118.58 + 1937.44i −0.155276 + 0.268945i −0.933159 0.359463i \(-0.882960\pi\)
0.777884 + 0.628408i \(0.216293\pi\)
\(374\) 1677.57 + 2905.64i 0.231939 + 0.401730i
\(375\) −4237.69 −0.583556
\(376\) −3488.34 + 6041.97i −0.478450 + 0.828699i
\(377\) −15744.4 −2.15087
\(378\) 1648.83 0.224356
\(379\) −961.927 1666.11i −0.130372 0.225810i 0.793448 0.608638i \(-0.208284\pi\)
−0.923820 + 0.382827i \(0.874950\pi\)
\(380\) −963.327 −0.130046
\(381\) 2269.38 3930.69i 0.305155 0.528544i
\(382\) 1202.94 2083.56i 0.161120 0.279068i
\(383\) 6090.79 + 10549.6i 0.812597 + 1.40746i 0.911040 + 0.412317i \(0.135280\pi\)
−0.0984433 + 0.995143i \(0.531386\pi\)
\(384\) −1563.75 2708.50i −0.207812 0.359941i
\(385\) 2902.59 + 5027.43i 0.384233 + 0.665511i
\(386\) 2958.00 + 5123.41i 0.390047 + 0.675582i
\(387\) −1882.11 −0.247218
\(388\) −7801.19 −1.02074
\(389\) 6383.57 + 11056.7i 0.832031 + 1.44112i 0.896425 + 0.443195i \(0.146155\pi\)
−0.0643944 + 0.997925i \(0.520512\pi\)
\(390\) 1106.32 1916.20i 0.143642 0.248796i
\(391\) −6056.22 + 10489.7i −0.783315 + 1.35674i
\(392\) 11107.1 + 19238.1i 1.43111 + 2.47875i
\(393\) 5821.61 0.747230
\(394\) −3828.81 −0.489575
\(395\) −3359.73 + 5819.22i −0.427965 + 0.741257i
\(396\) −527.895 914.340i −0.0669892 0.116029i
\(397\) 7600.70 0.960876 0.480438 0.877029i \(-0.340478\pi\)
0.480438 + 0.877029i \(0.340478\pi\)
\(398\) −1744.43 + 3021.45i −0.219700 + 0.380531i
\(399\) −2873.61 −0.360552
\(400\) 205.445 + 355.841i 0.0256806 + 0.0444801i
\(401\) 1687.67 0.210170 0.105085 0.994463i \(-0.466488\pi\)
0.105085 + 0.994463i \(0.466488\pi\)
\(402\) 749.852 2626.09i 0.0930329 0.325815i
\(403\) 7542.51 0.932305
\(404\) −2543.20 4404.95i −0.313191 0.542462i
\(405\) −571.425 −0.0701094
\(406\) 7632.91 13220.6i 0.933042 1.61608i
\(407\) 2952.79 0.359617
\(408\) −2979.97 5161.46i −0.361595 0.626300i
\(409\) 1292.30 2238.33i 0.156235 0.270607i −0.777273 0.629163i \(-0.783398\pi\)
0.933508 + 0.358557i \(0.116731\pi\)
\(410\) −4467.52 −0.538134
\(411\) −2079.90 −0.249621
\(412\) −4285.31 7422.37i −0.512432 0.887558i
\(413\) −2554.29 + 4424.15i −0.304330 + 0.527115i
\(414\) −1001.28 + 1734.26i −0.118865 + 0.205880i
\(415\) −2046.43 3544.52i −0.242061 0.419261i
\(416\) −11648.5 −1.37287
\(417\) 2529.94 0.297103
\(418\) −483.376 837.233i −0.0565615 0.0979674i
\(419\) −5793.43 10034.5i −0.675483 1.16997i −0.976327 0.216298i \(-0.930602\pi\)
0.300845 0.953673i \(-0.402731\pi\)
\(420\) −2041.68 3536.29i −0.237200 0.410842i
\(421\) 2066.75 + 3579.71i 0.239257 + 0.414405i 0.960501 0.278276i \(-0.0897629\pi\)
−0.721244 + 0.692681i \(0.756430\pi\)
\(422\) 1074.55 1861.18i 0.123953 0.214693i
\(423\) 1428.00 2473.36i 0.164141 0.284300i
\(424\) −8658.96 −0.991783
\(425\) 3399.08 + 5887.38i 0.387952 + 0.671952i
\(426\) 2218.24 0.252287
\(427\) 4735.69 0.536713
\(428\) 924.007 1600.43i 0.104354 0.180747i
\(429\) −4226.35 −0.475642
\(430\) −1224.46 2120.82i −0.137322 0.237849i
\(431\) 3637.38 6300.12i 0.406511 0.704098i −0.587985 0.808872i \(-0.700079\pi\)
0.994496 + 0.104774i \(0.0334119\pi\)
\(432\) 73.7318 + 127.707i 0.00821163 + 0.0142230i
\(433\) −919.913 + 1593.34i −0.102097 + 0.176838i −0.912549 0.408968i \(-0.865889\pi\)
0.810451 + 0.585806i \(0.199222\pi\)
\(434\) −3656.62 + 6333.44i −0.404431 + 0.700495i
\(435\) −2645.30 + 4581.79i −0.291568 + 0.505011i
\(436\) −4684.15 + 8113.19i −0.514519 + 0.891173i
\(437\) 1745.04 3022.50i 0.191022 0.330860i
\(438\) −2763.46 + 4786.45i −0.301468 + 0.522158i
\(439\) −311.820 540.088i −0.0339006 0.0587175i 0.848577 0.529071i \(-0.177460\pi\)
−0.882478 + 0.470354i \(0.844126\pi\)
\(440\) 1734.62 3004.45i 0.187943 0.325526i
\(441\) −4546.84 7875.36i −0.490967 0.850380i
\(442\) −9447.17 −1.01664
\(443\) 5584.06 9671.87i 0.598886 1.03730i −0.394099 0.919068i \(-0.628943\pi\)
0.992986 0.118234i \(-0.0377232\pi\)
\(444\) −2076.99 −0.222003
\(445\) −3706.76 −0.394870
\(446\) −3486.20 6038.27i −0.370126 0.641077i
\(447\) −3129.59 −0.331151
\(448\) 4843.50 8389.18i 0.510790 0.884713i
\(449\) −5319.52 + 9213.69i −0.559118 + 0.968420i 0.438453 + 0.898754i \(0.355527\pi\)
−0.997570 + 0.0696661i \(0.977807\pi\)
\(450\) 561.970 + 973.361i 0.0588701 + 0.101966i
\(451\) 4266.70 + 7390.15i 0.445479 + 0.771593i
\(452\) −1987.24 3442.00i −0.206796 0.358182i
\(453\) −2598.03 4499.92i −0.269462 0.466722i
\(454\) −7064.40 −0.730284
\(455\) −16345.8 −1.68418
\(456\) 858.651 + 1487.23i 0.0881799 + 0.152732i
\(457\) 114.371 198.096i 0.0117068 0.0202769i −0.860113 0.510104i \(-0.829607\pi\)
0.871819 + 0.489827i \(0.162940\pi\)
\(458\) −3116.04 + 5397.13i −0.317910 + 0.550637i
\(459\) 1219.89 + 2112.91i 0.124051 + 0.214863i
\(460\) 4959.37 0.502678
\(461\) −12161.7 −1.22869 −0.614344 0.789039i \(-0.710579\pi\)
−0.614344 + 0.789039i \(0.710579\pi\)
\(462\) 2048.94 3548.87i 0.206332 0.357377i
\(463\) −6300.68 10913.1i −0.632435 1.09541i −0.987052 0.160398i \(-0.948722\pi\)
0.354617 0.935012i \(-0.384611\pi\)
\(464\) 1365.31 0.136601
\(465\) 1267.25 2194.95i 0.126382 0.218899i
\(466\) −5770.03 −0.573587
\(467\) 3467.50 + 6005.89i 0.343591 + 0.595116i 0.985097 0.172002i \(-0.0550234\pi\)
−0.641506 + 0.767118i \(0.721690\pi\)
\(468\) 2972.82 0.293629
\(469\) −19570.9 + 4902.75i −1.92686 + 0.482704i
\(470\) 3716.08 0.364702
\(471\) 1247.82 + 2161.29i 0.122073 + 0.211437i
\(472\) 3052.94 0.297718
\(473\) −2338.84 + 4050.99i −0.227357 + 0.393794i
\(474\) 4743.27 0.459632
\(475\) −979.413 1696.39i −0.0946075 0.163865i
\(476\) −8717.25 + 15098.7i −0.839401 + 1.45388i
\(477\) 3544.66 0.340249
\(478\) 3874.69 0.370762
\(479\) −5451.10 9441.59i −0.519973 0.900620i −0.999730 0.0232189i \(-0.992609\pi\)
0.479757 0.877401i \(-0.340725\pi\)
\(480\) −1957.12 + 3389.83i −0.186104 + 0.322341i
\(481\) −4157.12 + 7200.35i −0.394072 + 0.682552i
\(482\) −2190.86 3794.67i −0.207035 0.358595i
\(483\) 14793.8 1.39367
\(484\) 4356.50 0.409138
\(485\) 5246.83 + 9087.77i 0.491229 + 0.850834i
\(486\) 201.685 + 349.328i 0.0188243 + 0.0326046i
\(487\) 5919.72 + 10253.2i 0.550817 + 0.954043i 0.998216 + 0.0597087i \(0.0190172\pi\)
−0.447399 + 0.894335i \(0.647649\pi\)
\(488\) −1415.05 2450.94i −0.131263 0.227355i
\(489\) −1562.36 + 2706.09i −0.144483 + 0.250253i
\(490\) 5916.14 10247.0i 0.545436 0.944723i
\(491\) −3578.18 −0.328882 −0.164441 0.986387i \(-0.552582\pi\)
−0.164441 + 0.986387i \(0.552582\pi\)
\(492\) −3001.20 5198.23i −0.275009 0.476330i
\(493\) 22589.0 2.06360
\(494\) 2722.11 0.247922
\(495\) −710.090 + 1229.91i −0.0644771 + 0.111678i
\(496\) −654.063 −0.0592102
\(497\) −8193.63 14191.8i −0.739506 1.28086i
\(498\) −1444.58 + 2502.08i −0.129986 + 0.225142i
\(499\) 9423.01 + 16321.1i 0.845354 + 1.46420i 0.885313 + 0.464995i \(0.153944\pi\)
−0.0399591 + 0.999201i \(0.512723\pi\)
\(500\) 3704.13 6415.74i 0.331307 0.573841i
\(501\) −1857.86 + 3217.90i −0.165675 + 0.286957i
\(502\) −631.378 + 1093.58i −0.0561350 + 0.0972287i
\(503\) 6224.16 10780.6i 0.551733 0.955630i −0.446417 0.894825i \(-0.647300\pi\)
0.998150 0.0608044i \(-0.0193666\pi\)
\(504\) −3639.66 + 6304.08i −0.321673 + 0.557155i
\(505\) −3420.95 + 5925.26i −0.301446 + 0.522120i
\(506\) 2488.50 + 4310.21i 0.218631 + 0.378680i
\(507\) 2654.63 4597.96i 0.232537 0.402766i
\(508\) 3967.30 + 6871.56i 0.346497 + 0.600150i
\(509\) 13601.2 1.18440 0.592201 0.805790i \(-0.298259\pi\)
0.592201 + 0.805790i \(0.298259\pi\)
\(510\) −1587.26 + 2749.22i −0.137814 + 0.238701i
\(511\) 40830.0 3.53466
\(512\) 1970.73 0.170107
\(513\) −351.500 608.816i −0.0302517 0.0523975i
\(514\) −7152.17 −0.613752
\(515\) −5764.32 + 9984.10i −0.493216 + 0.854276i
\(516\) 1645.14 2849.46i 0.140355 0.243102i
\(517\) −3549.04 6147.13i −0.301909 0.522921i
\(518\) −4030.76 6981.47i −0.341894 0.592178i
\(519\) 4572.10 + 7919.11i 0.386692 + 0.669769i
\(520\) 4884.22 + 8459.72i 0.411899 + 0.713429i
\(521\) 546.677 0.0459700 0.0229850 0.999736i \(-0.492683\pi\)
0.0229850 + 0.999736i \(0.492683\pi\)
\(522\) 3734.63 0.313143
\(523\) 9586.48 + 16604.3i 0.801505 + 1.38825i 0.918625 + 0.395130i \(0.129301\pi\)
−0.117120 + 0.993118i \(0.537366\pi\)
\(524\) −5088.62 + 8813.74i −0.424231 + 0.734790i
\(525\) 4151.55 7190.69i 0.345121 0.597767i
\(526\) −3612.34 6256.76i −0.299440 0.518646i
\(527\) −10821.4 −0.894477
\(528\) 366.496 0.0302078
\(529\) −2900.27 + 5023.42i −0.238372 + 0.412872i
\(530\) 2306.07 + 3994.23i 0.188999 + 0.327355i
\(531\) −1249.76 −0.102138
\(532\) 2511.80 4350.56i 0.204700 0.354550i
\(533\) −24027.8 −1.95264
\(534\) 1308.30 + 2266.04i 0.106022 + 0.183635i
\(535\) −2485.83 −0.200882
\(536\) 8385.29 + 8663.87i 0.675727 + 0.698175i
\(537\) 10893.9 0.875434
\(538\) −1472.58 2550.58i −0.118006 0.204393i
\(539\) −22600.8 −1.80610
\(540\) 499.477 865.120i 0.0398038 0.0689423i
\(541\) −18396.4 −1.46197 −0.730983 0.682395i \(-0.760938\pi\)
−0.730983 + 0.682395i \(0.760938\pi\)
\(542\) 524.191 + 907.926i 0.0415423 + 0.0719534i
\(543\) −855.844 + 1482.37i −0.0676387 + 0.117154i
\(544\) 16712.4 1.31717
\(545\) 12601.6 0.990450
\(546\) 5769.26 + 9992.66i 0.452201 + 0.783235i
\(547\) 3183.22 5513.50i 0.248820 0.430969i −0.714378 0.699760i \(-0.753290\pi\)
0.963199 + 0.268790i \(0.0866238\pi\)
\(548\) 1818.02 3148.91i 0.141719 0.245465i
\(549\) 579.271 + 1003.33i 0.0450322 + 0.0779980i
\(550\) 2793.36 0.216563
\(551\) −6508.80 −0.503238
\(552\) −4420.48 7656.49i −0.340848 0.590366i
\(553\) −17520.4 30346.3i −1.34728 2.33355i
\(554\) −2487.73 4308.88i −0.190783 0.330446i
\(555\) 1396.92 + 2419.53i 0.106839 + 0.185051i
\(556\) −2211.40 + 3830.25i −0.168677 + 0.292156i
\(557\) −4062.03 + 7035.64i −0.309001 + 0.535206i −0.978144 0.207928i \(-0.933328\pi\)
0.669143 + 0.743134i \(0.266661\pi\)
\(558\) −1789.11 −0.135733
\(559\) −6585.54 11406.5i −0.498280 0.863046i
\(560\) 1417.46 0.106962
\(561\) 6063.67 0.456343
\(562\) 1253.55 2171.22i 0.0940888 0.162967i
\(563\) −243.293 −0.0182124 −0.00910621 0.999959i \(-0.502899\pi\)
−0.00910621 + 0.999959i \(0.502899\pi\)
\(564\) 2496.40 + 4323.89i 0.186378 + 0.322816i
\(565\) −2673.11 + 4629.96i −0.199042 + 0.344750i
\(566\) −6241.29 10810.2i −0.463500 0.802806i
\(567\) 1489.94 2580.66i 0.110356 0.191142i
\(568\) −4896.61 + 8481.17i −0.361720 + 0.626518i
\(569\) −1827.11 + 3164.65i −0.134616 + 0.233162i −0.925451 0.378868i \(-0.876313\pi\)
0.790835 + 0.612030i \(0.209647\pi\)
\(570\) 457.355 792.163i 0.0336079 0.0582106i
\(571\) −4034.53 + 6988.02i −0.295692 + 0.512153i −0.975146 0.221565i \(-0.928883\pi\)
0.679454 + 0.733718i \(0.262217\pi\)
\(572\) 3694.22 6398.57i 0.270040 0.467723i
\(573\) −2174.05 3765.57i −0.158503 0.274535i
\(574\) 11648.7 20176.1i 0.847050 1.46713i
\(575\) 5042.18 + 8733.31i 0.365693 + 0.633399i
\(576\) 2369.83 0.171429
\(577\) 3483.40 6033.43i 0.251328 0.435312i −0.712564 0.701607i \(-0.752466\pi\)
0.963892 + 0.266295i \(0.0857996\pi\)
\(578\) 5398.74 0.388509
\(579\) 10691.8 0.767423
\(580\) −4624.46 8009.80i −0.331069 0.573429i
\(581\) 21343.6 1.52406
\(582\) 3703.74 6415.07i 0.263789 0.456896i
\(583\) 4404.83 7629.39i 0.312915 0.541984i
\(584\) −12200.2 21131.4i −0.864469 1.49730i
\(585\) −1999.42 3463.10i −0.141309 0.244755i
\(586\) −3107.23 5381.88i −0.219042 0.379391i
\(587\) −10197.5 17662.6i −0.717029 1.24193i −0.962172 0.272444i \(-0.912168\pi\)
0.245143 0.969487i \(-0.421165\pi\)
\(588\) 15897.4 1.11496
\(589\) 3118.10 0.218131
\(590\) −813.066 1408.27i −0.0567345 0.0982671i
\(591\) −3459.86 + 5992.65i −0.240811 + 0.417097i
\(592\) 360.493 624.392i 0.0250273 0.0433486i
\(593\) 6348.26 + 10995.5i 0.439615 + 0.761436i 0.997660 0.0683749i \(-0.0217814\pi\)
−0.558044 + 0.829811i \(0.688448\pi\)
\(594\) 1002.51 0.0692481
\(595\) 23451.8 1.61585
\(596\) 2735.54 4738.10i 0.188007 0.325638i
\(597\) 3152.67 + 5460.59i 0.216131 + 0.374350i
\(598\) −14013.9 −0.958312
\(599\) −3617.42 + 6265.56i −0.246751 + 0.427385i −0.962622 0.270847i \(-0.912696\pi\)
0.715871 + 0.698232i \(0.246030\pi\)
\(600\) −4962.03 −0.337623
\(601\) 6194.70 + 10729.5i 0.420444 + 0.728231i 0.995983 0.0895440i \(-0.0285410\pi\)
−0.575539 + 0.817774i \(0.695208\pi\)
\(602\) 12770.7 0.864610
\(603\) −3432.63 3546.67i −0.231820 0.239522i
\(604\) 9083.67 0.611936
\(605\) −2930.04 5074.98i −0.196898 0.341037i
\(606\) 4829.71 0.323752
\(607\) 1375.56 2382.54i 0.0919808 0.159315i −0.816364 0.577538i \(-0.804014\pi\)
0.908345 + 0.418223i \(0.137347\pi\)
\(608\) −4815.53 −0.321210
\(609\) −13794.8 23893.3i −0.917887 1.58983i
\(610\) −753.719 + 1305.48i −0.0500282 + 0.0866514i
\(611\) 19986.3 1.32334
\(612\) −4265.18 −0.281715
\(613\) 11746.6 + 20345.7i 0.773965 + 1.34055i 0.935374 + 0.353660i \(0.115063\pi\)
−0.161409 + 0.986888i \(0.551604\pi\)
\(614\) 939.799 1627.78i 0.0617707 0.106990i
\(615\) −4037.02 + 6992.32i −0.264696 + 0.458468i
\(616\) 9045.77 + 15667.7i 0.591663 + 1.02479i
\(617\) 25962.2 1.69400 0.847001 0.531591i \(-0.178406\pi\)
0.847001 + 0.531591i \(0.178406\pi\)
\(618\) 8138.08 0.529711
\(619\) −603.378 1045.08i −0.0391790 0.0678601i 0.845771 0.533546i \(-0.179141\pi\)
−0.884950 + 0.465686i \(0.845808\pi\)
\(620\) 2215.39 + 3837.17i 0.143503 + 0.248555i
\(621\) 1809.58 + 3134.29i 0.116934 + 0.202536i
\(622\) 3509.68 + 6078.94i 0.226247 + 0.391871i
\(623\) 9665.06 16740.4i 0.621545 1.07655i
\(624\) −515.977 + 893.698i −0.0331019 + 0.0573342i
\(625\) −561.076 −0.0359089
\(626\) 6248.05 + 10821.9i 0.398917 + 0.690945i
\(627\) −1747.19 −0.111286
\(628\) −4362.84 −0.277223
\(629\) 5964.34 10330.5i 0.378082 0.654858i
\(630\) 3877.29 0.245198
\(631\) 348.175 + 603.057i 0.0219661 + 0.0380464i 0.876800 0.480856i \(-0.159674\pi\)
−0.854833 + 0.518903i \(0.826341\pi\)
\(632\) −10470.4 + 18135.3i −0.659004 + 1.14143i
\(633\) −1942.01 3363.66i −0.121940 0.211206i
\(634\) 1133.84 1963.87i 0.0710262 0.123021i
\(635\) 5336.55 9243.18i 0.333503 0.577645i
\(636\) −3098.35 + 5366.51i −0.193173 + 0.334585i
\(637\) 31818.9 55112.0i 1.97914 3.42797i
\(638\) 4640.90 8038.28i 0.287986 0.498807i
\(639\) 2004.49 3471.88i 0.124095 0.214938i
\(640\) −3677.23 6369.15i −0.227118 0.393379i
\(641\) −6208.42 + 10753.3i −0.382555 + 0.662605i −0.991427 0.130664i \(-0.958289\pi\)
0.608871 + 0.793269i \(0.291623\pi\)
\(642\) 877.375 + 1519.66i 0.0539365 + 0.0934207i
\(643\) −23562.2 −1.44510 −0.722552 0.691316i \(-0.757031\pi\)
−0.722552 + 0.691316i \(0.757031\pi\)
\(644\) −12931.1 + 22397.4i −0.791240 + 1.37047i
\(645\) −4425.87 −0.270184
\(646\) −3905.49 −0.237863
\(647\) 10869.4 + 18826.4i 0.660467 + 1.14396i 0.980493 + 0.196554i \(0.0629750\pi\)
−0.320026 + 0.947409i \(0.603692\pi\)
\(648\) −1780.81 −0.107958
\(649\) −1553.04 + 2689.94i −0.0939323 + 0.162695i
\(650\) −3932.68 + 6811.60i −0.237311 + 0.411035i
\(651\) 6608.52 + 11446.3i 0.397862 + 0.689117i
\(652\) −2731.29 4730.74i −0.164058 0.284156i
\(653\) −9139.01 15829.2i −0.547683 0.948615i −0.998433 0.0559644i \(-0.982177\pi\)
0.450750 0.892650i \(-0.351157\pi\)
\(654\) −4447.76 7703.75i −0.265934 0.460612i
\(655\) 13689.8 0.816646
\(656\) 2083.61 0.124011
\(657\) 4994.33 + 8650.43i 0.296571 + 0.513677i
\(658\) −9689.38 + 16782.5i −0.574060 + 0.994300i
\(659\) −10944.7 + 18956.8i −0.646957 + 1.12056i 0.336889 + 0.941544i \(0.390625\pi\)
−0.983846 + 0.179018i \(0.942708\pi\)
\(660\) −1241.37 2150.11i −0.0732123 0.126807i
\(661\) −3905.06 −0.229787 −0.114893 0.993378i \(-0.536653\pi\)
−0.114893 + 0.993378i \(0.536653\pi\)
\(662\) 549.794 0.0322785
\(663\) −8536.82 + 14786.2i −0.500064 + 0.866137i
\(664\) −6377.58 11046.3i −0.372738 0.645601i
\(665\) −6757.41 −0.394047
\(666\) 986.085 1707.95i 0.0573724 0.0993719i
\(667\) 33508.4 1.94520
\(668\) −3247.87 5625.48i −0.188120 0.325833i
\(669\) −12601.0 −0.728228
\(670\) 1763.31 6175.37i 0.101675 0.356083i
\(671\) 2879.36 0.165658
\(672\) −10206.1 17677.4i −0.585874 1.01476i
\(673\) −2390.82 −0.136938 −0.0684691 0.997653i \(-0.521811\pi\)
−0.0684691 + 0.997653i \(0.521811\pi\)
\(674\) 280.414 485.692i 0.0160255 0.0277569i
\(675\) 2031.27 0.115828
\(676\) 4640.78 + 8038.07i 0.264041 + 0.457332i
\(677\) −2864.24 + 4961.01i −0.162602 + 0.281635i −0.935801 0.352528i \(-0.885322\pi\)
0.773199 + 0.634164i \(0.218655\pi\)
\(678\) 3773.90 0.213770
\(679\) −54722.7 −3.09288
\(680\) −7007.53 12137.4i −0.395186 0.684482i
\(681\) −6383.66 + 11056.8i −0.359211 + 0.622171i
\(682\) −2223.27 + 3850.81i −0.124829 + 0.216210i
\(683\) −13011.4 22536.5i −0.728944 1.26257i −0.957330 0.288997i \(-0.906678\pi\)
0.228386 0.973571i \(-0.426655\pi\)
\(684\) 1228.97 0.0687002
\(685\) −4890.98 −0.272810
\(686\) 20378.6 + 35296.7i 1.13419 + 1.96448i
\(687\) 5631.54 + 9754.11i 0.312746 + 0.541692i
\(688\) 571.077 + 989.135i 0.0316455 + 0.0548116i
\(689\) 12402.8 + 21482.3i 0.685790 + 1.18782i
\(690\) −2354.54 + 4078.18i −0.129907 + 0.225006i
\(691\) 15047.0 26062.2i 0.828388 1.43481i −0.0709141 0.997482i \(-0.522592\pi\)
0.899302 0.437328i \(-0.144075\pi\)
\(692\) −15985.7 −0.878159
\(693\) −3703.00 6413.79i −0.202980 0.351572i
\(694\) −13967.9 −0.763996
\(695\) 5949.26 0.324703
\(696\) −8243.92 + 14278.9i −0.448973 + 0.777644i
\(697\) 34473.3 1.87341
\(698\) −1722.97 2984.27i −0.0934317 0.161829i
\(699\) −5214.02 + 9030.95i −0.282135 + 0.488672i
\(700\) 7257.66 + 12570.6i 0.391877 + 0.678750i
\(701\) −357.484 + 619.181i −0.0192610 + 0.0333611i −0.875495 0.483227i \(-0.839465\pi\)
0.856234 + 0.516588i \(0.172798\pi\)
\(702\) −1411.39 + 2444.61i −0.0758826 + 0.131433i
\(703\) −1718.57 + 2976.65i −0.0922007 + 0.159696i
\(704\) 2944.91 5100.73i 0.157657 0.273069i
\(705\) 3357.99 5816.21i 0.179389 0.310711i
\(706\) −4004.24 + 6935.55i −0.213459 + 0.369721i
\(707\) −17839.7 30899.3i −0.948983 1.64369i
\(708\) 1092.41 1892.10i 0.0579875 0.100437i
\(709\) 2025.74 + 3508.69i 0.107304 + 0.185856i 0.914677 0.404185i \(-0.132445\pi\)
−0.807373 + 0.590041i \(0.799112\pi\)
\(710\) 5216.29 0.275724
\(711\) 4286.20 7423.92i 0.226083 0.391587i
\(712\) −11551.9 −0.608042
\(713\) −16052.5 −0.843156
\(714\) −8277.32 14336.7i −0.433853 0.751455i
\(715\) −9938.45 −0.519828
\(716\) −9522.29 + 16493.1i −0.497018 + 0.860860i
\(717\) 3501.32 6064.46i 0.182370 0.315874i
\(718\) 6350.12 + 10998.7i 0.330062 + 0.571683i
\(719\) 16197.3 + 28054.6i 0.840136 + 1.45516i 0.889779 + 0.456391i \(0.150858\pi\)
−0.0496436 + 0.998767i \(0.515809\pi\)
\(720\) 173.384 + 300.309i 0.00897448 + 0.0155442i
\(721\) −30060.0 52065.4i −1.55269 2.68935i
\(722\) −10260.3 −0.528877
\(723\) −7918.97 −0.407344
\(724\) −1496.17 2591.44i −0.0768022 0.133025i
\(725\) 9403.36 16287.1i 0.481699 0.834328i
\(726\) −2068.32 + 3582.44i −0.105734 + 0.183136i
\(727\) 5688.01 + 9851.92i 0.290174 + 0.502596i 0.973851 0.227189i \(-0.0729534\pi\)
−0.683677 + 0.729785i \(0.739620\pi\)
\(728\) −50940.8 −2.59340
\(729\) 729.000 0.0370370
\(730\) −6498.38 + 11255.5i −0.329474 + 0.570666i
\(731\) 9448.45 + 16365.2i 0.478062 + 0.828028i
\(732\) −2025.34 −0.102266
\(733\) 3226.28 5588.08i 0.162572 0.281583i −0.773218 0.634140i \(-0.781354\pi\)
0.935790 + 0.352557i \(0.114688\pi\)
\(734\) 3388.38 0.170392
\(735\) −10692.1 18519.3i −0.536577 0.929378i
\(736\) 24791.1 1.24159
\(737\) −11899.3 + 2980.93i −0.594732 + 0.148988i
\(738\) 5699.47 0.284282
\(739\) 9385.89 + 16256.8i 0.467206 + 0.809225i 0.999298 0.0374617i \(-0.0119272\pi\)
−0.532092 + 0.846687i \(0.678594\pi\)
\(740\) −4884.13 −0.242627
\(741\) 2459.81 4260.51i 0.121948 0.211220i
\(742\) −24051.6 −1.18997
\(743\) 7100.58 + 12298.6i 0.350599 + 0.607255i 0.986355 0.164635i \(-0.0526447\pi\)
−0.635756 + 0.771890i \(0.719311\pi\)
\(744\) 3949.33 6840.43i 0.194609 0.337073i
\(745\) −7359.36 −0.361914
\(746\) 3713.58 0.182257
\(747\) 2610.75 + 4521.95i 0.127874 + 0.221485i
\(748\) −5300.20 + 9180.21i −0.259083 + 0.448746i
\(749\) 6481.60 11226.5i 0.316198 0.547671i
\(750\) 3517.19 + 6091.95i 0.171240 + 0.296596i
\(751\) −19594.9 −0.952100 −0.476050 0.879418i \(-0.657932\pi\)
−0.476050 + 0.879418i \(0.657932\pi\)
\(752\) −1733.15 −0.0840445
\(753\) 1141.07 + 1976.40i 0.0552232 + 0.0956494i
\(754\) 13067.5 + 22633.6i 0.631156 + 1.09319i
\(755\) −6109.38 10581.8i −0.294494 0.510079i
\(756\) 2604.69 + 4511.46i 0.125306 + 0.217037i
\(757\) −8658.56 + 14997.1i −0.415721 + 0.720050i −0.995504 0.0947212i \(-0.969804\pi\)
0.579783 + 0.814771i \(0.303137\pi\)
\(758\) −1596.76 + 2765.67i −0.0765130 + 0.132524i
\(759\) 8994.82 0.430160
\(760\) 2019.15 + 3497.28i 0.0963716 + 0.166921i
\(761\) −2486.17 −0.118428 −0.0592139 0.998245i \(-0.518859\pi\)
−0.0592139 + 0.998245i \(0.518859\pi\)
\(762\) −7534.16 −0.358181
\(763\) −32857.8 + 56911.3i −1.55902 + 2.70030i
\(764\) 7601.27 0.359953
\(765\) 2868.62 + 4968.60i 0.135576 + 0.234824i
\(766\) 10110.4 17511.8i 0.476900 0.826014i
\(767\) −4372.93 7574.14i −0.205864 0.356566i
\(768\) −5755.53 + 9968.87i −0.270423 + 0.468386i
\(769\) 19368.5 33547.2i 0.908251 1.57314i 0.0917586 0.995781i \(-0.470751\pi\)
0.816493 0.577356i \(-0.195915\pi\)
\(770\) 4818.17 8345.32i 0.225500 0.390577i
\(771\) −6462.97 + 11194.2i −0.301891 + 0.522891i
\(772\) −9345.65 + 16187.1i −0.435696 + 0.754647i
\(773\) 16451.2 28494.4i 0.765472 1.32584i −0.174525 0.984653i \(-0.555839\pi\)
0.939997 0.341184i \(-0.110828\pi\)
\(774\) 1562.11 + 2705.66i 0.0725440 + 0.125650i
\(775\) −4504.76 + 7802.48i −0.208795 + 0.361643i
\(776\) 16351.5 + 28321.6i 0.756422 + 1.31016i
\(777\) −14569.4 −0.672682
\(778\) 10596.5 18353.6i 0.488305 0.845769i
\(779\) −9933.16 −0.456858
\(780\) 6990.70 0.320907
\(781\) −4981.82 8628.77i −0.228251 0.395342i
\(782\) 20106.1 0.919429
\(783\) 3374.76 5845.25i 0.154028 0.266785i
\(784\) −2759.24 + 4779.14i −0.125694 + 0.217709i
\(785\) 2934.31 + 5082.37i 0.133414 + 0.231080i
\(786\) −4831.81 8368.94i −0.219268 0.379784i
\(787\) −3535.78 6124.16i −0.160149 0.277386i 0.774773 0.632239i \(-0.217864\pi\)
−0.934922 + 0.354854i \(0.884531\pi\)
\(788\) −6048.46 10476.2i −0.273436 0.473605i
\(789\) −13057.0 −0.589153
\(790\) 11154.0 0.502331
\(791\) −13939.8 24144.5i −0.626603 1.08531i
\(792\) −2212.96 + 3832.96i −0.0992854 + 0.171967i
\(793\) −4053.75 + 7021.30i −0.181529 + 0.314418i
\(794\) −6308.41 10926.5i −0.281961 0.488371i
\(795\) 8335.41 0.371857
\(796\) −11022.9 −0.490824
\(797\) 7673.36 13290.6i 0.341034 0.590689i −0.643591 0.765370i \(-0.722556\pi\)
0.984625 + 0.174681i \(0.0558895\pi\)
\(798\) 2385.03 + 4131.00i 0.105801 + 0.183253i
\(799\) −28674.9 −1.26964
\(800\) 6957.06 12050.0i 0.307462 0.532539i
\(801\) 4728.93 0.208600
\(802\) −1400.73 2426.14i −0.0616727 0.106820i
\(803\) 24825.1 1.09098
\(804\) 8369.98 2096.79i 0.367147 0.0919751i
\(805\) 34788.3 1.52314
\(806\) −6260.12 10842.8i −0.273577 0.473850i
\(807\) −5322.71 −0.232179
\(808\) −10661.2 + 18465.8i −0.464183 + 0.803989i
\(809\) 33307.2 1.44749 0.723744 0.690069i \(-0.242420\pi\)
0.723744 + 0.690069i \(0.242420\pi\)
\(810\) 474.270 + 821.460i 0.0205730 + 0.0356335i
\(811\) −19883.6 + 34439.4i −0.860922 + 1.49116i 0.0101183 + 0.999949i \(0.496779\pi\)
−0.871040 + 0.491212i \(0.836554\pi\)
\(812\) 48231.6 2.08448
\(813\) 1894.72 0.0817351
\(814\) −2450.75 4244.82i −0.105527 0.182778i
\(815\) −3673.96 + 6363.48i −0.157906 + 0.273501i
\(816\) 740.286 1282.21i 0.0317588 0.0550079i
\(817\) −2722.48 4715.48i −0.116582 0.201926i
\(818\) −4290.32 −0.183383
\(819\) 20853.3 0.889711
\(820\) −7057.44 12223.8i −0.300557 0.520580i
\(821\) −8239.24 14270.8i −0.350245 0.606643i 0.636047 0.771650i \(-0.280568\pi\)
−0.986292 + 0.165008i \(0.947235\pi\)
\(822\) 1726.27 + 2989.99i 0.0732491 + 0.126871i
\(823\) −6870.52 11900.1i −0.290998 0.504023i 0.683048 0.730374i \(-0.260654\pi\)
−0.974046 + 0.226350i \(0.927321\pi\)
\(824\) −17964.2 + 31114.9i −0.759481 + 1.31546i
\(825\) 2524.19 4372.03i 0.106523 0.184502i
\(826\) 8480.01 0.357212
\(827\) −524.614 908.658i −0.0220588 0.0382069i 0.854785 0.518982i \(-0.173689\pi\)
−0.876844 + 0.480775i \(0.840355\pi\)
\(828\) −6326.95 −0.265552
\(829\) −37990.4 −1.59163 −0.795815 0.605540i \(-0.792957\pi\)
−0.795815 + 0.605540i \(0.792957\pi\)
\(830\) −3396.98 + 5883.74i −0.142061 + 0.246057i
\(831\) −8992.05 −0.375368
\(832\) 8292.05 + 14362.3i 0.345523 + 0.598464i
\(833\) −45651.5 + 79070.7i −1.89883 + 3.28888i
\(834\) −2099.80 3636.95i −0.0871822 0.151004i
\(835\) −4368.83 + 7567.04i −0.181065 + 0.313615i
\(836\) 1527.20 2645.19i 0.0631811 0.109433i
\(837\) −1616.71 + 2800.22i −0.0667642 + 0.115639i
\(838\) −9616.83 + 16656.8i −0.396430 + 0.686636i
\(839\) 19681.0 34088.6i 0.809851 1.40270i −0.103116 0.994669i \(-0.532881\pi\)
0.912967 0.408034i \(-0.133785\pi\)
\(840\) −8558.81 + 14824.3i −0.351556 + 0.608913i
\(841\) −19051.0 32997.4i −0.781132 1.35296i
\(842\) 3430.71 5942.16i 0.140416 0.243207i
\(843\) −2265.51 3923.99i −0.0925605 0.160319i
\(844\) 6789.97 0.276920
\(845\) 6242.48 10812.3i 0.254140 0.440183i
\(846\) −4740.82 −0.192663
\(847\) 30559.4 1.23971
\(848\) −1075.53 1862.88i −0.0435541 0.0754380i
\(849\) −22559.5 −0.911943
\(850\) 5642.32 9772.79i 0.227682 0.394358i
\(851\) 8847.48 15324.3i 0.356390 0.617285i
\(852\) 3504.21 + 6069.48i 0.140907 + 0.244057i
\(853\) −9008.62 15603.4i −0.361605 0.626319i 0.626620 0.779325i \(-0.284438\pi\)
−0.988225 + 0.153006i \(0.951105\pi\)
\(854\) −3930.52 6807.87i −0.157494 0.272787i
\(855\) −826.568 1431.66i −0.0330620 0.0572651i
\(856\) −7746.95 −0.309329
\(857\) 14541.1 0.579597 0.289798 0.957088i \(-0.406412\pi\)
0.289798 + 0.957088i \(0.406412\pi\)
\(858\) 3507.78 + 6075.66i 0.139573 + 0.241748i
\(859\) 3116.05 5397.16i 0.123770 0.214376i −0.797482 0.603343i \(-0.793835\pi\)
0.921251 + 0.388968i \(0.127168\pi\)
\(860\) 3868.61 6700.64i 0.153394 0.265686i
\(861\) −21052.4 36463.8i −0.833291 1.44330i
\(862\) −12075.8 −0.477149
\(863\) −34289.5 −1.35252 −0.676262 0.736661i \(-0.736401\pi\)
−0.676262 + 0.736661i \(0.736401\pi\)
\(864\) 2496.81 4324.60i 0.0983139 0.170285i
\(865\) 10751.5 + 18622.1i 0.422614 + 0.731990i
\(866\) 3054.03 0.119839
\(867\) 4878.51 8449.83i 0.191099 0.330993i
\(868\) −23105.8 −0.903527
\(869\) −10652.6 18450.9i −0.415841 0.720258i
\(870\) 8782.15 0.342233
\(871\) 9483.65 33213.2i 0.368934 1.29206i
\(872\) 39272.4 1.52515
\(873\) −6693.69 11593.8i −0.259504 0.449474i
\(874\) −5793.39 −0.224216
\(875\) 25983.2 45004.2i 1.00388 1.73877i
\(876\) −17462.0 −0.673500
\(877\) −5351.27 9268.66i −0.206043 0.356876i 0.744422 0.667710i \(-0.232725\pi\)
−0.950464 + 0.310833i \(0.899392\pi\)
\(878\) −517.607 + 896.522i −0.0198957 + 0.0344603i
\(879\) −11231.2 −0.430967
\(880\) 861.831 0.0330140
\(881\) 8039.73 + 13925.2i 0.307452 + 0.532523i 0.977804 0.209520i \(-0.0671902\pi\)
−0.670352 + 0.742043i \(0.733857\pi\)
\(882\) −7547.56 + 13072.8i −0.288140 + 0.499073i
\(883\) −19446.1 + 33681.6i −0.741124 + 1.28366i 0.210861 + 0.977516i \(0.432373\pi\)
−0.951984 + 0.306147i \(0.900960\pi\)
\(884\) −14923.9 25849.0i −0.567812 0.983479i
\(885\) −2938.87 −0.111626
\(886\) −18538.6 −0.702953
\(887\) 20304.4 + 35168.2i 0.768608 + 1.33127i 0.938318 + 0.345773i \(0.112383\pi\)
−0.169710 + 0.985494i \(0.554283\pi\)
\(888\) 4353.42 + 7540.34i 0.164517 + 0.284952i
\(889\) 27829.3 + 48201.7i 1.04990 + 1.81848i
\(890\) 3076.53 + 5328.70i 0.115871 + 0.200695i
\(891\) 905.904 1569.07i 0.0340616 0.0589965i
\(892\) 11014.5 19077.6i 0.413443 0.716104i
\(893\) 8262.40 0.309620
\(894\) 2597.49 + 4498.98i 0.0971734 + 0.168309i
\(895\) 25617.5 0.956760
\(896\) 38352.3 1.42998
\(897\) −12663.5 + 21933.8i −0.471373 + 0.816442i
\(898\) 17660.4 0.656274
\(899\) 14968.5 + 25926.1i 0.555313 + 0.961830i
\(900\) −1775.52 + 3075.28i −0.0657598 + 0.113899i
\(901\) −17794.6 30821.2i −0.657964 1.13963i
\(902\) 7082.54 12267.3i 0.261444 0.452835i
\(903\) 11540.1 19988.0i 0.425283 0.736611i
\(904\) −8330.60 + 14429.0i −0.306495 + 0.530865i
\(905\) −2012.55 + 3485.84i −0.0739221 + 0.128037i
\(906\) −4312.62 + 7469.68i −0.158143 + 0.273911i
\(907\) 17036.7 29508.4i 0.623697 1.08028i −0.365094 0.930971i \(-0.618963\pi\)
0.988791 0.149305i \(-0.0477035\pi\)
\(908\) −11159.8 19329.3i −0.407876 0.706461i
\(909\) 4364.31 7559.20i 0.159246 0.275823i
\(910\) 13566.7 + 23498.1i 0.494209 + 0.855996i
\(911\) 48525.8 1.76480 0.882400 0.470501i \(-0.155927\pi\)
0.882400 + 0.470501i \(0.155927\pi\)
\(912\) −213.307 + 369.458i −0.00774484 + 0.0134145i
\(913\) 12977.1 0.470406
\(914\) −379.700 −0.0137411
\(915\) 1362.18 + 2359.36i 0.0492156 + 0.0852439i
\(916\) −19689.9 −0.710233
\(917\) −35694.9 + 61825.4i −1.28544 + 2.22645i
\(918\) 2024.97 3507.34i 0.0728037 0.126100i
\(919\) −6336.79 10975.6i −0.227455 0.393964i 0.729598 0.683876i \(-0.239707\pi\)
−0.957053 + 0.289912i \(0.906374\pi\)
\(920\) −10394.9 18004.6i −0.372512 0.645210i
\(921\) −1698.48 2941.85i −0.0607673 0.105252i
\(922\) 10093.9 + 17483.2i 0.360548 + 0.624487i
\(923\) 28054.9 1.00048
\(924\) 12947.0 0.460959
\(925\) −4965.69 8600.82i −0.176509 0.305722i
\(926\) −10458.9 + 18115.3i −0.371166 + 0.642878i
\(927\) 7353.88 12737.3i 0.260554 0.451292i
\(928\) −23117.0 40039.8i −0.817728 1.41635i
\(929\) 14183.8 0.500920 0.250460 0.968127i \(-0.419418\pi\)
0.250460 + 0.968127i \(0.419418\pi\)
\(930\) −4207.17 −0.148342
\(931\) 13154.0 22783.5i 0.463058 0.802039i
\(932\) −9115.05 15787.7i −0.320358 0.554876i
\(933\) 12685.9 0.445143
\(934\) 5755.90 9969.51i 0.201648 0.349264i
\(935\) 14259.0 0.498736
\(936\) −6231.09 10792.6i −0.217596 0.376887i
\(937\) −34760.5 −1.21193 −0.605963 0.795493i \(-0.707212\pi\)
−0.605963 + 0.795493i \(0.707212\pi\)
\(938\) 23291.4 + 24065.2i 0.810758 + 0.837693i
\(939\) 22583.9 0.784875
\(940\) 5870.38 + 10167.8i 0.203692 + 0.352805i
\(941\) −50154.2 −1.73749 −0.868747 0.495257i \(-0.835074\pi\)
−0.868747 + 0.495257i \(0.835074\pi\)
\(942\) 2071.33 3587.65i 0.0716429 0.124089i
\(943\) 51137.5 1.76593
\(944\) 379.207 + 656.806i 0.0130743 + 0.0226453i
\(945\) 3503.66 6068.52i 0.120608 0.208899i
\(946\) 7764.74 0.266864
\(947\) −30040.0 −1.03080 −0.515400 0.856950i \(-0.672357\pi\)
−0.515400 + 0.856950i \(0.672357\pi\)
\(948\) 7493.06 + 12978.4i 0.256712 + 0.444639i
\(949\) −34950.4 + 60535.9i −1.19551 + 2.07068i
\(950\) −1625.78 + 2815.94i −0.0555236 + 0.0961696i
\(951\) −2049.17 3549.26i −0.0698725 0.121023i
\(952\) 73086.2 2.48817
\(953\) −18412.1 −0.625842 −0.312921 0.949779i \(-0.601307\pi\)
−0.312921 + 0.949779i \(0.601307\pi\)
\(954\) −2941.99 5095.68i −0.0998432 0.172934i
\(955\) −5112.37 8854.89i −0.173228 0.300039i
\(956\) 6120.94 + 10601.8i 0.207077 + 0.358668i
\(957\) −8387.40 14527.4i −0.283308 0.490704i
\(958\) −9048.59 + 15672.6i −0.305164 + 0.528559i
\(959\) 12752.8 22088.5i 0.429416 0.743771i
\(960\) 5572.75 0.187354
\(961\) 7724.73 + 13379.6i 0.259297 + 0.449116i
\(962\) 13801.3 0.462548
\(963\) 3171.32 0.106121
\(964\) 6921.90 11989.1i 0.231265 0.400562i
\(965\) 25142.3 0.838715
\(966\) −12278.5 21267.1i −0.408960 0.708340i
\(967\) −20195.3 + 34979.2i −0.671598 + 1.16324i 0.305852 + 0.952079i \(0.401059\pi\)
−0.977451 + 0.211164i \(0.932275\pi\)
\(968\) −9131.33 15815.9i −0.303194 0.525148i
\(969\) −3529.15 + 6112.67i −0.117000 + 0.202649i
\(970\) 8709.51 15085.3i 0.288294 0.499340i
\(971\) −716.267 + 1240.61i −0.0236726 + 0.0410022i −0.877619 0.479359i \(-0.840869\pi\)
0.853946 + 0.520361i \(0.174203\pi\)
\(972\) −637.212 + 1103.68i −0.0210274 + 0.0364205i
\(973\) −15512.2 + 26867.9i −0.511098 + 0.885248i
\(974\) 9826.47 17019.9i 0.323265 0.559912i
\(975\) 7107.44 + 12310.4i 0.233457 + 0.404359i
\(976\) 351.528 608.865i 0.0115288 0.0199685i
\(977\) 12803.7 + 22176.7i 0.419270 + 0.726198i 0.995866 0.0908319i \(-0.0289526\pi\)
−0.576596 + 0.817029i \(0.695619\pi\)
\(978\) 5186.90 0.169590
\(979\) 5876.48 10178.4i 0.191842 0.332279i
\(980\) 37383.4 1.21854
\(981\) −16076.7 −0.523230
\(982\) 2969.81 + 5143.86i 0.0965076 + 0.167156i
\(983\) −28147.9 −0.913304 −0.456652 0.889645i \(-0.650952\pi\)
−0.456652 + 0.889645i \(0.650952\pi\)
\(984\) −12581.2 + 21791.2i −0.407594 + 0.705973i
\(985\) −8136.00 + 14092.0i −0.263182 + 0.455845i
\(986\) −18748.3 32473.1i −0.605546 1.04884i
\(987\) 17511.4 + 30330.6i 0.564735 + 0.978150i
\(988\) 4300.19 + 7448.15i 0.138469 + 0.239835i
\(989\) 14015.8 + 24276.1i 0.450633 + 0.780520i
\(990\) 2357.44 0.0756811
\(991\) −31949.4 −1.02412 −0.512062 0.858948i \(-0.671118\pi\)
−0.512062 + 0.858948i \(0.671118\pi\)
\(992\) 11074.4 + 19181.4i 0.354448 + 0.613922i
\(993\) 496.815 860.509i 0.0158771 0.0274999i
\(994\) −13601.1 + 23557.7i −0.434003 + 0.751716i
\(995\) 7413.64 + 12840.8i 0.236209 + 0.409126i
\(996\) −9128.12 −0.290397
\(997\) 4309.33 0.136889 0.0684443 0.997655i \(-0.478196\pi\)
0.0684443 + 0.997655i \(0.478196\pi\)
\(998\) 15641.8 27092.4i 0.496124 0.859312i
\(999\) −1782.13 3086.74i −0.0564405 0.0977578i
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 201.4.e.b.37.7 36
67.29 even 3 inner 201.4.e.b.163.7 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.4.e.b.37.7 36 1.1 even 1 trivial
201.4.e.b.163.7 yes 36 67.29 even 3 inner