Properties

Label 115.4.e.a.22.9
Level $115$
Weight $4$
Character 115.22
Analytic conductor $6.785$
Analytic rank $0$
Dimension $68$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [115,4,Mod(22,115)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(115, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("115.22");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 115.e (of order \(4\), 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: \(6.78521965066\)
Analytic rank: \(0\)
Dimension: \(68\)
Relative dimension: \(34\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 22.9
Character \(\chi\) \(=\) 115.22
Dual form 115.4.e.a.68.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.37561 - 2.37561i) q^{2} +(6.86048 - 6.86048i) q^{3} +3.28704i q^{4} +(-2.55138 - 10.8853i) q^{5} -32.5957 q^{6} +(-19.7347 + 19.7347i) q^{7} +(-11.1962 + 11.1962i) q^{8} -67.1325i q^{9} +O(q^{10})\) \(q+(-2.37561 - 2.37561i) q^{2} +(6.86048 - 6.86048i) q^{3} +3.28704i q^{4} +(-2.55138 - 10.8853i) q^{5} -32.5957 q^{6} +(-19.7347 + 19.7347i) q^{7} +(-11.1962 + 11.1962i) q^{8} -67.1325i q^{9} +(-19.7982 + 31.9204i) q^{10} +21.6450i q^{11} +(22.5507 + 22.5507i) q^{12} +(11.8189 - 11.8189i) q^{13} +93.7638 q^{14} +(-92.1823 - 57.1749i) q^{15} +79.4917 q^{16} +(81.6744 - 81.6744i) q^{17} +(-159.481 + 159.481i) q^{18} -0.927411 q^{19} +(35.7805 - 8.38649i) q^{20} +270.779i q^{21} +(51.4200 - 51.4200i) q^{22} +(-27.0068 - 106.947i) q^{23} +153.622i q^{24} +(-111.981 + 55.5452i) q^{25} -56.1541 q^{26} +(-275.328 - 275.328i) q^{27} +(-64.8687 - 64.8687i) q^{28} +50.8950i q^{29} +(83.1639 + 354.815i) q^{30} -117.409 q^{31} +(-99.2720 - 99.2720i) q^{32} +(148.495 + 148.495i) q^{33} -388.053 q^{34} +(265.169 + 164.468i) q^{35} +220.667 q^{36} +(91.3643 - 91.3643i) q^{37} +(2.20317 + 2.20317i) q^{38} -162.166i q^{39} +(150.439 + 93.3082i) q^{40} +376.568 q^{41} +(643.265 - 643.265i) q^{42} +(-346.842 - 346.842i) q^{43} -71.1479 q^{44} +(-730.759 + 171.280i) q^{45} +(-189.906 + 318.222i) q^{46} +(-109.863 - 109.863i) q^{47} +(545.351 - 545.351i) q^{48} -435.916i q^{49} +(397.977 + 134.069i) q^{50} -1120.65i q^{51} +(38.8491 + 38.8491i) q^{52} +(142.165 + 142.165i) q^{53} +1308.14i q^{54} +(235.613 - 55.2246i) q^{55} -441.905i q^{56} +(-6.36249 + 6.36249i) q^{57} +(120.907 - 120.907i) q^{58} +334.266i q^{59} +(187.936 - 303.007i) q^{60} +502.616i q^{61} +(278.918 + 278.918i) q^{62} +(1324.84 + 1324.84i) q^{63} -164.271i q^{64} +(-158.807 - 98.4980i) q^{65} -705.532i q^{66} +(-205.809 + 205.809i) q^{67} +(268.467 + 268.467i) q^{68} +(-918.987 - 548.428i) q^{69} +(-239.227 - 1020.65i) q^{70} +303.641 q^{71} +(751.625 + 751.625i) q^{72} +(535.965 - 535.965i) q^{73} -434.092 q^{74} +(-387.176 + 1149.31i) q^{75} -3.04844i q^{76} +(-427.157 - 427.157i) q^{77} +(-385.244 + 385.244i) q^{78} -95.5630 q^{79} +(-202.813 - 865.293i) q^{80} -1965.19 q^{81} +(-894.579 - 894.579i) q^{82} +(-179.812 - 179.812i) q^{83} -890.061 q^{84} +(-1097.44 - 680.671i) q^{85} +1647.92i q^{86} +(349.164 + 349.164i) q^{87} +(-242.340 - 242.340i) q^{88} +0.941649 q^{89} +(2142.89 + 1329.10i) q^{90} +466.484i q^{91} +(351.539 - 88.7724i) q^{92} +(-805.483 + 805.483i) q^{93} +521.984i q^{94} +(2.36618 + 10.0952i) q^{95} -1362.11 q^{96} +(973.198 - 973.198i) q^{97} +(-1035.57 + 1035.57i) q^{98} +1453.08 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68 q - 4 q^{2} + 4 q^{3} + 32 q^{6} + 28 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 68 q - 4 q^{2} + 4 q^{3} + 32 q^{6} + 28 q^{8} + 200 q^{12} - 100 q^{13} - 832 q^{16} - 112 q^{18} - 46 q^{23} - 372 q^{25} - 312 q^{26} - 704 q^{27} - 1056 q^{31} + 560 q^{32} - 348 q^{35} + 2424 q^{36} + 2248 q^{41} - 96 q^{46} - 1412 q^{47} + 1532 q^{48} - 620 q^{50} + 112 q^{52} + 2688 q^{55} + 2044 q^{58} + 3948 q^{62} - 1836 q^{70} - 2272 q^{71} + 1128 q^{72} + 1100 q^{73} + 2828 q^{75} + 4216 q^{77} - 9180 q^{78} - 3580 q^{81} - 6516 q^{82} - 2684 q^{85} - 6304 q^{87} - 688 q^{92} - 1608 q^{93} - 8616 q^{95} - 544 q^{96} - 3612 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.37561 2.37561i −0.839905 0.839905i 0.148941 0.988846i \(-0.452413\pi\)
−0.988846 + 0.148941i \(0.952413\pi\)
\(3\) 6.86048 6.86048i 1.32030 1.32030i 0.406770 0.913531i \(-0.366655\pi\)
0.913531 0.406770i \(-0.133345\pi\)
\(4\) 3.28704i 0.410880i
\(5\) −2.55138 10.8853i −0.228202 0.973614i
\(6\) −32.5957 −2.21785
\(7\) −19.7347 + 19.7347i −1.06557 + 1.06557i −0.0678793 + 0.997694i \(0.521623\pi\)
−0.997694 + 0.0678793i \(0.978377\pi\)
\(8\) −11.1962 + 11.1962i −0.494805 + 0.494805i
\(9\) 67.1325i 2.48639i
\(10\) −19.7982 + 31.9204i −0.626075 + 1.00941i
\(11\) 21.6450i 0.593291i 0.954988 + 0.296646i \(0.0958681\pi\)
−0.954988 + 0.296646i \(0.904132\pi\)
\(12\) 22.5507 + 22.5507i 0.542485 + 0.542485i
\(13\) 11.8189 11.8189i 0.252151 0.252151i −0.569701 0.821852i \(-0.692941\pi\)
0.821852 + 0.569701i \(0.192941\pi\)
\(14\) 93.7638 1.78996
\(15\) −92.1823 57.1749i −1.58676 0.984167i
\(16\) 79.4917 1.24206
\(17\) 81.6744 81.6744i 1.16523 1.16523i 0.181919 0.983314i \(-0.441769\pi\)
0.983314 0.181919i \(-0.0582309\pi\)
\(18\) −159.481 + 159.481i −2.08833 + 2.08833i
\(19\) −0.927411 −0.0111980 −0.00559902 0.999984i \(-0.501782\pi\)
−0.00559902 + 0.999984i \(0.501782\pi\)
\(20\) 35.7805 8.38649i 0.400038 0.0937638i
\(21\) 270.779i 2.81375i
\(22\) 51.4200 51.4200i 0.498308 0.498308i
\(23\) −27.0068 106.947i −0.244839 0.969564i
\(24\) 153.622i 1.30658i
\(25\) −111.981 + 55.5452i −0.895847 + 0.444362i
\(26\) −56.1541 −0.423566
\(27\) −275.328 275.328i −1.96248 1.96248i
\(28\) −64.8687 64.8687i −0.437823 0.437823i
\(29\) 50.8950i 0.325895i 0.986635 + 0.162948i \(0.0521002\pi\)
−0.986635 + 0.162948i \(0.947900\pi\)
\(30\) 83.1639 + 354.815i 0.506119 + 2.15933i
\(31\) −117.409 −0.680235 −0.340118 0.940383i \(-0.610467\pi\)
−0.340118 + 0.940383i \(0.610467\pi\)
\(32\) −99.2720 99.2720i −0.548405 0.548405i
\(33\) 148.495 + 148.495i 0.783323 + 0.783323i
\(34\) −388.053 −1.95737
\(35\) 265.169 + 164.468i 1.28062 + 0.794290i
\(36\) 220.667 1.02161
\(37\) 91.3643 91.3643i 0.405951 0.405951i −0.474373 0.880324i \(-0.657325\pi\)
0.880324 + 0.474373i \(0.157325\pi\)
\(38\) 2.20317 + 2.20317i 0.00940528 + 0.00940528i
\(39\) 162.166i 0.665831i
\(40\) 150.439 + 93.3082i 0.594664 + 0.368833i
\(41\) 376.568 1.43439 0.717196 0.696871i \(-0.245425\pi\)
0.717196 + 0.696871i \(0.245425\pi\)
\(42\) 643.265 643.265i 2.36328 2.36328i
\(43\) −346.842 346.842i −1.23007 1.23007i −0.963937 0.266131i \(-0.914255\pi\)
−0.266131 0.963937i \(-0.585745\pi\)
\(44\) −71.1479 −0.243772
\(45\) −730.759 + 171.280i −2.42078 + 0.567399i
\(46\) −189.906 + 318.222i −0.608700 + 1.01998i
\(47\) −109.863 109.863i −0.340961 0.340961i 0.515767 0.856729i \(-0.327507\pi\)
−0.856729 + 0.515767i \(0.827507\pi\)
\(48\) 545.351 545.351i 1.63989 1.63989i
\(49\) 435.916i 1.27089i
\(50\) 397.977 + 134.069i 1.12565 + 0.379205i
\(51\) 1120.65i 3.07691i
\(52\) 38.8491 + 38.8491i 0.103604 + 0.103604i
\(53\) 142.165 + 142.165i 0.368451 + 0.368451i 0.866912 0.498461i \(-0.166101\pi\)
−0.498461 + 0.866912i \(0.666101\pi\)
\(54\) 1308.14i 3.29659i
\(55\) 235.613 55.2246i 0.577637 0.135390i
\(56\) 441.905i 1.05450i
\(57\) −6.36249 + 6.36249i −0.0147848 + 0.0147848i
\(58\) 120.907 120.907i 0.273721 0.273721i
\(59\) 334.266i 0.737588i 0.929511 + 0.368794i \(0.120229\pi\)
−0.929511 + 0.368794i \(0.879771\pi\)
\(60\) 187.936 303.007i 0.404375 0.651967i
\(61\) 502.616i 1.05497i 0.849563 + 0.527487i \(0.176866\pi\)
−0.849563 + 0.527487i \(0.823134\pi\)
\(62\) 278.918 + 278.918i 0.571333 + 0.571333i
\(63\) 1324.84 + 1324.84i 2.64943 + 2.64943i
\(64\) 164.271i 0.320841i
\(65\) −158.807 98.4980i −0.303040 0.187956i
\(66\) 705.532i 1.31583i
\(67\) −205.809 + 205.809i −0.375278 + 0.375278i −0.869395 0.494118i \(-0.835491\pi\)
0.494118 + 0.869395i \(0.335491\pi\)
\(68\) 268.467 + 268.467i 0.478771 + 0.478771i
\(69\) −918.987 548.428i −1.60338 0.956854i
\(70\) −239.227 1020.65i −0.408473 1.74273i
\(71\) 303.641 0.507543 0.253772 0.967264i \(-0.418329\pi\)
0.253772 + 0.967264i \(0.418329\pi\)
\(72\) 751.625 + 751.625i 1.23028 + 1.23028i
\(73\) 535.965 535.965i 0.859314 0.859314i −0.131943 0.991257i \(-0.542122\pi\)
0.991257 + 0.131943i \(0.0421216\pi\)
\(74\) −434.092 −0.681921
\(75\) −387.176 + 1149.31i −0.596097 + 1.76948i
\(76\) 3.04844i 0.00460105i
\(77\) −427.157 427.157i −0.632195 0.632195i
\(78\) −385.244 + 385.244i −0.559235 + 0.559235i
\(79\) −95.5630 −0.136097 −0.0680486 0.997682i \(-0.521677\pi\)
−0.0680486 + 0.997682i \(0.521677\pi\)
\(80\) −202.813 865.293i −0.283440 1.20928i
\(81\) −1965.19 −2.69573
\(82\) −894.579 894.579i −1.20475 1.20475i
\(83\) −179.812 179.812i −0.237795 0.237795i 0.578142 0.815936i \(-0.303778\pi\)
−0.815936 + 0.578142i \(0.803778\pi\)
\(84\) −890.061 −1.15611
\(85\) −1097.44 680.671i −1.40040 0.868578i
\(86\) 1647.92i 2.06628i
\(87\) 349.164 + 349.164i 0.430280 + 0.430280i
\(88\) −242.340 242.340i −0.293563 0.293563i
\(89\) 0.941649 0.00112151 0.000560756 1.00000i \(-0.499822\pi\)
0.000560756 1.00000i \(0.499822\pi\)
\(90\) 2142.89 + 1329.10i 2.50979 + 1.55666i
\(91\) 466.484i 0.537371i
\(92\) 351.539 88.7724i 0.398374 0.100600i
\(93\) −805.483 + 805.483i −0.898115 + 0.898115i
\(94\) 521.984i 0.572750i
\(95\) 2.36618 + 10.0952i 0.00255542 + 0.0109026i
\(96\) −1362.11 −1.44812
\(97\) 973.198 973.198i 1.01869 1.01869i 0.0188718 0.999822i \(-0.493993\pi\)
0.999822 0.0188718i \(-0.00600743\pi\)
\(98\) −1035.57 + 1035.57i −1.06743 + 1.06743i
\(99\) 1453.08 1.47515
\(100\) −182.579 368.086i −0.182579 0.368086i
\(101\) 1317.52 1.29800 0.649000 0.760788i \(-0.275187\pi\)
0.649000 + 0.760788i \(0.275187\pi\)
\(102\) −2662.23 + 2662.23i −2.58432 + 2.58432i
\(103\) −177.377 177.377i −0.169684 0.169684i 0.617156 0.786840i \(-0.288285\pi\)
−0.786840 + 0.617156i \(0.788285\pi\)
\(104\) 264.652i 0.249531i
\(105\) 2947.52 690.860i 2.73951 0.642105i
\(106\) 675.458i 0.618927i
\(107\) 912.174 912.174i 0.824142 0.824142i −0.162557 0.986699i \(-0.551974\pi\)
0.986699 + 0.162557i \(0.0519742\pi\)
\(108\) 905.014 905.014i 0.806343 0.806343i
\(109\) −259.683 −0.228194 −0.114097 0.993470i \(-0.536397\pi\)
−0.114097 + 0.993470i \(0.536397\pi\)
\(110\) −690.916 428.532i −0.598875 0.371445i
\(111\) 1253.61i 1.07196i
\(112\) −1568.74 + 1568.74i −1.32350 + 1.32350i
\(113\) 141.869 + 141.869i 0.118105 + 0.118105i 0.763689 0.645584i \(-0.223386\pi\)
−0.645584 + 0.763689i \(0.723386\pi\)
\(114\) 30.2296 0.0248356
\(115\) −1095.25 + 566.840i −0.888108 + 0.459635i
\(116\) −167.294 −0.133904
\(117\) −793.430 793.430i −0.626946 0.626946i
\(118\) 794.085 794.085i 0.619504 0.619504i
\(119\) 3223.64i 2.48328i
\(120\) 1672.23 391.948i 1.27211 0.298165i
\(121\) 862.495 0.648005
\(122\) 1194.02 1194.02i 0.886078 0.886078i
\(123\) 2583.44 2583.44i 1.89383 1.89383i
\(124\) 385.928i 0.279495i
\(125\) 890.334 + 1077.23i 0.637071 + 0.770805i
\(126\) 6294.59i 4.45053i
\(127\) 939.770 + 939.770i 0.656623 + 0.656623i 0.954579 0.297957i \(-0.0963051\pi\)
−0.297957 + 0.954579i \(0.596305\pi\)
\(128\) −1184.42 + 1184.42i −0.817881 + 0.817881i
\(129\) −4759.01 −3.24812
\(130\) 143.270 + 611.256i 0.0966588 + 0.412390i
\(131\) 552.479 0.368475 0.184238 0.982882i \(-0.441018\pi\)
0.184238 + 0.982882i \(0.441018\pi\)
\(132\) −488.109 + 488.109i −0.321852 + 0.321852i
\(133\) 18.3022 18.3022i 0.0119323 0.0119323i
\(134\) 977.845 0.630395
\(135\) −2294.57 + 3699.50i −1.46285 + 2.35854i
\(136\) 1828.88i 1.15313i
\(137\) 1094.47 1094.47i 0.682531 0.682531i −0.278039 0.960570i \(-0.589684\pi\)
0.960570 + 0.278039i \(0.0896844\pi\)
\(138\) 880.304 + 3486.00i 0.543017 + 2.15035i
\(139\) 847.639i 0.517236i −0.965980 0.258618i \(-0.916733\pi\)
0.965980 0.258618i \(-0.0832671\pi\)
\(140\) −540.613 + 871.622i −0.326358 + 0.526182i
\(141\) −1507.43 −0.900343
\(142\) −721.333 721.333i −0.426288 0.426288i
\(143\) 255.819 + 255.819i 0.149599 + 0.149599i
\(144\) 5336.47i 3.08824i
\(145\) 554.009 129.852i 0.317296 0.0743701i
\(146\) −2546.49 −1.44348
\(147\) −2990.59 2990.59i −1.67796 1.67796i
\(148\) 300.318 + 300.318i 0.166797 + 0.166797i
\(149\) 1760.15 0.967766 0.483883 0.875133i \(-0.339226\pi\)
0.483883 + 0.875133i \(0.339226\pi\)
\(150\) 3650.09 1810.53i 1.98686 0.985529i
\(151\) −1259.74 −0.678913 −0.339457 0.940622i \(-0.610243\pi\)
−0.339457 + 0.940622i \(0.610243\pi\)
\(152\) 10.3834 10.3834i 0.00554084 0.00554084i
\(153\) −5483.00 5483.00i −2.89722 2.89722i
\(154\) 2029.52i 1.06197i
\(155\) 299.555 + 1278.04i 0.155231 + 0.662287i
\(156\) 533.048 0.273577
\(157\) 629.567 629.567i 0.320031 0.320031i −0.528748 0.848779i \(-0.677338\pi\)
0.848779 + 0.528748i \(0.177338\pi\)
\(158\) 227.020 + 227.020i 0.114309 + 0.114309i
\(159\) 1950.64 0.972931
\(160\) −827.328 + 1333.89i −0.408788 + 0.659082i
\(161\) 2643.53 + 1577.59i 1.29403 + 0.772247i
\(162\) 4668.53 + 4668.53i 2.26416 + 2.26416i
\(163\) −414.900 + 414.900i −0.199371 + 0.199371i −0.799730 0.600359i \(-0.795024\pi\)
0.600359 + 0.799730i \(0.295024\pi\)
\(164\) 1237.80i 0.589363i
\(165\) 1237.55 1995.28i 0.583898 0.941410i
\(166\) 854.328i 0.399450i
\(167\) 344.981 + 344.981i 0.159853 + 0.159853i 0.782502 0.622649i \(-0.213943\pi\)
−0.622649 + 0.782502i \(0.713943\pi\)
\(168\) −3031.68 3031.68i −1.39226 1.39226i
\(169\) 1917.63i 0.872839i
\(170\) 990.070 + 4224.09i 0.446676 + 1.90572i
\(171\) 62.2594i 0.0278426i
\(172\) 1140.08 1140.08i 0.505410 0.505410i
\(173\) −2502.61 + 2502.61i −1.09982 + 1.09982i −0.105394 + 0.994430i \(0.533611\pi\)
−0.994430 + 0.105394i \(0.966389\pi\)
\(174\) 1658.96i 0.722788i
\(175\) 1113.74 3306.08i 0.481091 1.42809i
\(176\) 1720.60i 0.736902i
\(177\) 2293.23 + 2293.23i 0.973838 + 0.973838i
\(178\) −2.23699 2.23699i −0.000941964 0.000941964i
\(179\) 2937.46i 1.22657i −0.789862 0.613284i \(-0.789848\pi\)
0.789862 0.613284i \(-0.210152\pi\)
\(180\) −563.005 2402.03i −0.233133 0.994651i
\(181\) 1354.37i 0.556185i 0.960554 + 0.278092i \(0.0897021\pi\)
−0.960554 + 0.278092i \(0.910298\pi\)
\(182\) 1108.18 1108.18i 0.451341 0.451341i
\(183\) 3448.19 + 3448.19i 1.39288 + 1.39288i
\(184\) 1499.77 + 895.021i 0.600892 + 0.358597i
\(185\) −1227.64 761.426i −0.487879 0.302601i
\(186\) 3827.03 1.50866
\(187\) 1767.84 + 1767.84i 0.691323 + 0.691323i
\(188\) 361.125 361.125i 0.140094 0.140094i
\(189\) 10867.0 4.18233
\(190\) 18.3611 29.6033i 0.00701080 0.0113034i
\(191\) 78.2987i 0.0296623i −0.999890 0.0148311i \(-0.995279\pi\)
0.999890 0.0148311i \(-0.00472107\pi\)
\(192\) −1126.98 1126.98i −0.423606 0.423606i
\(193\) −2793.25 + 2793.25i −1.04177 + 1.04177i −0.0426851 + 0.999089i \(0.513591\pi\)
−0.999089 + 0.0426851i \(0.986409\pi\)
\(194\) −4623.88 −1.71121
\(195\) −1765.24 + 413.748i −0.648262 + 0.151944i
\(196\) 1432.87 0.522184
\(197\) 908.413 + 908.413i 0.328537 + 0.328537i 0.852030 0.523493i \(-0.175371\pi\)
−0.523493 + 0.852030i \(0.675371\pi\)
\(198\) −3451.95 3451.95i −1.23899 1.23899i
\(199\) −3964.69 −1.41231 −0.706154 0.708058i \(-0.749572\pi\)
−0.706154 + 0.708058i \(0.749572\pi\)
\(200\) 631.863 1875.65i 0.223397 0.663142i
\(201\) 2823.90i 0.990958i
\(202\) −3129.91 3129.91i −1.09020 1.09020i
\(203\) −1004.40 1004.40i −0.347265 0.347265i
\(204\) 3683.63 1.26424
\(205\) −960.769 4099.07i −0.327332 1.39654i
\(206\) 842.756i 0.285037i
\(207\) −7179.61 + 1813.03i −2.41071 + 0.608765i
\(208\) 939.503 939.503i 0.313186 0.313186i
\(209\) 20.0738i 0.00664370i
\(210\) −8643.37 5360.94i −2.84023 1.76162i
\(211\) 1368.87 0.446622 0.223311 0.974747i \(-0.428313\pi\)
0.223311 + 0.974747i \(0.428313\pi\)
\(212\) −467.303 + 467.303i −0.151389 + 0.151389i
\(213\) 2083.12 2083.12i 0.670110 0.670110i
\(214\) −4333.94 −1.38440
\(215\) −2890.57 + 4660.42i −0.916907 + 1.47832i
\(216\) 6165.23 1.94209
\(217\) 2317.03 2317.03i 0.724840 0.724840i
\(218\) 616.905 + 616.905i 0.191661 + 0.191661i
\(219\) 7353.95i 2.26911i
\(220\) 181.525 + 774.469i 0.0556292 + 0.237339i
\(221\) 1930.60i 0.587630i
\(222\) −2978.08 + 2978.08i −0.900341 + 0.900341i
\(223\) −1997.02 + 1997.02i −0.599688 + 0.599688i −0.940230 0.340541i \(-0.889390\pi\)
0.340541 + 0.940230i \(0.389390\pi\)
\(224\) 3918.20 1.16873
\(225\) 3728.89 + 7517.56i 1.10486 + 2.22742i
\(226\) 674.051i 0.198395i
\(227\) 1283.98 1283.98i 0.375422 0.375422i −0.494025 0.869448i \(-0.664475\pi\)
0.869448 + 0.494025i \(0.164475\pi\)
\(228\) −20.9137 20.9137i −0.00607477 0.00607477i
\(229\) 5693.53 1.64297 0.821483 0.570233i \(-0.193147\pi\)
0.821483 + 0.570233i \(0.193147\pi\)
\(230\) 3948.47 + 1255.29i 1.13198 + 0.359876i
\(231\) −5861.00 −1.66938
\(232\) −569.828 569.828i −0.161254 0.161254i
\(233\) 2667.79 2667.79i 0.750098 0.750098i −0.224399 0.974497i \(-0.572042\pi\)
0.974497 + 0.224399i \(0.0720419\pi\)
\(234\) 3769.76i 1.05315i
\(235\) −915.594 + 1476.20i −0.254157 + 0.409773i
\(236\) −1098.75 −0.303060
\(237\) −655.608 + 655.608i −0.179689 + 0.179689i
\(238\) 7658.10 7658.10i 2.08572 2.08572i
\(239\) 1452.22i 0.393040i −0.980500 0.196520i \(-0.937036\pi\)
0.980500 0.196520i \(-0.0629641\pi\)
\(240\) −7327.73 4544.93i −1.97085 1.22239i
\(241\) 5196.12i 1.38884i 0.719568 + 0.694422i \(0.244340\pi\)
−0.719568 + 0.694422i \(0.755660\pi\)
\(242\) −2048.95 2048.95i −0.544263 0.544263i
\(243\) −6048.30 + 6048.30i −1.59670 + 1.59670i
\(244\) −1652.12 −0.433468
\(245\) −4745.09 + 1112.19i −1.23736 + 0.290020i
\(246\) −12274.5 −3.18127
\(247\) −10.9610 + 10.9610i −0.00282360 + 0.00282360i
\(248\) 1314.53 1314.53i 0.336584 0.336584i
\(249\) −2467.20 −0.627921
\(250\) 443.998 4674.17i 0.112324 1.18248i
\(251\) 4149.09i 1.04338i 0.853135 + 0.521690i \(0.174698\pi\)
−0.853135 + 0.521690i \(0.825302\pi\)
\(252\) −4354.80 + 4354.80i −1.08860 + 1.08860i
\(253\) 2314.86 584.561i 0.575234 0.145261i
\(254\) 4465.05i 1.10300i
\(255\) −12198.7 + 2859.21i −2.99573 + 0.702159i
\(256\) 4313.27 1.05304
\(257\) −918.535 918.535i −0.222944 0.222944i 0.586793 0.809737i \(-0.300390\pi\)
−0.809737 + 0.586793i \(0.800390\pi\)
\(258\) 11305.5 + 11305.5i 2.72811 + 2.72811i
\(259\) 3606.09i 0.865142i
\(260\) 323.767 522.005i 0.0772276 0.124513i
\(261\) 3416.71 0.810302
\(262\) −1312.47 1312.47i −0.309484 0.309484i
\(263\) 1534.70 + 1534.70i 0.359823 + 0.359823i 0.863748 0.503925i \(-0.168111\pi\)
−0.503925 + 0.863748i \(0.668111\pi\)
\(264\) −3325.15 −0.775184
\(265\) 1184.80 1910.23i 0.274647 0.442810i
\(266\) −86.9576 −0.0200440
\(267\) 6.46017 6.46017i 0.00148073 0.00148073i
\(268\) −676.503 676.503i −0.154194 0.154194i
\(269\) 3177.53i 0.720214i 0.932911 + 0.360107i \(0.117260\pi\)
−0.932911 + 0.360107i \(0.882740\pi\)
\(270\) 14239.6 3337.57i 3.20960 0.752289i
\(271\) −3344.42 −0.749665 −0.374832 0.927093i \(-0.622300\pi\)
−0.374832 + 0.927093i \(0.622300\pi\)
\(272\) 6492.44 6492.44i 1.44729 1.44729i
\(273\) 3200.30 + 3200.30i 0.709492 + 0.709492i
\(274\) −5200.06 −1.14652
\(275\) −1202.28 2423.82i −0.263636 0.531499i
\(276\) 1802.70 3020.75i 0.393152 0.658796i
\(277\) 4394.13 + 4394.13i 0.953133 + 0.953133i 0.998950 0.0458168i \(-0.0145890\pi\)
−0.0458168 + 0.998950i \(0.514589\pi\)
\(278\) −2013.66 + 2013.66i −0.434429 + 0.434429i
\(279\) 7881.96i 1.69133i
\(280\) −4810.28 + 1127.47i −1.02668 + 0.240640i
\(281\) 3779.74i 0.802421i −0.915986 0.401211i \(-0.868590\pi\)
0.915986 0.401211i \(-0.131410\pi\)
\(282\) 3581.06 + 3581.06i 0.756203 + 0.756203i
\(283\) 5455.86 + 5455.86i 1.14600 + 1.14600i 0.987333 + 0.158665i \(0.0507189\pi\)
0.158665 + 0.987333i \(0.449281\pi\)
\(284\) 998.080i 0.208539i
\(285\) 85.4909 + 53.0247i 0.0177686 + 0.0110207i
\(286\) 1215.45i 0.251298i
\(287\) −7431.46 + 7431.46i −1.52845 + 1.52845i
\(288\) −6664.37 + 6664.37i −1.36355 + 1.36355i
\(289\) 8428.42i 1.71553i
\(290\) −1624.59 1007.63i −0.328962 0.204035i
\(291\) 13353.2i 2.68996i
\(292\) 1761.74 + 1761.74i 0.353075 + 0.353075i
\(293\) −5878.06 5878.06i −1.17201 1.17201i −0.981729 0.190285i \(-0.939059\pi\)
−0.190285 0.981729i \(-0.560941\pi\)
\(294\) 14209.0i 2.81865i
\(295\) 3638.59 852.839i 0.718126 0.168319i
\(296\) 2045.86i 0.401733i
\(297\) 5959.47 5959.47i 1.16432 1.16432i
\(298\) −4181.43 4181.43i −0.812831 0.812831i
\(299\) −1583.18 944.802i −0.306213 0.182740i
\(300\) −3777.83 1272.66i −0.727044 0.244924i
\(301\) 13689.6 2.62145
\(302\) 2992.64 + 2992.64i 0.570222 + 0.570222i
\(303\) 9038.81 9038.81i 1.71375 1.71375i
\(304\) −73.7215 −0.0139086
\(305\) 5471.15 1282.37i 1.02714 0.240748i
\(306\) 26051.0i 4.86678i
\(307\) 2501.93 + 2501.93i 0.465124 + 0.465124i 0.900330 0.435207i \(-0.143325\pi\)
−0.435207 + 0.900330i \(0.643325\pi\)
\(308\) 1404.08 1404.08i 0.259756 0.259756i
\(309\) −2433.78 −0.448068
\(310\) 2324.49 3747.74i 0.425878 0.686637i
\(311\) −4083.99 −0.744636 −0.372318 0.928105i \(-0.621437\pi\)
−0.372318 + 0.928105i \(0.621437\pi\)
\(312\) 1815.64 + 1815.64i 0.329456 + 0.329456i
\(313\) 2135.20 + 2135.20i 0.385586 + 0.385586i 0.873110 0.487523i \(-0.162100\pi\)
−0.487523 + 0.873110i \(0.662100\pi\)
\(314\) −2991.21 −0.537591
\(315\) 11041.1 17801.5i 1.97491 3.18412i
\(316\) 314.119i 0.0559196i
\(317\) −7371.79 7371.79i −1.30612 1.30612i −0.924190 0.381934i \(-0.875258\pi\)
−0.381934 0.924190i \(-0.624742\pi\)
\(318\) −4633.97 4633.97i −0.817170 0.817170i
\(319\) −1101.62 −0.193351
\(320\) −1788.14 + 419.117i −0.312375 + 0.0732166i
\(321\) 12515.9i 2.17623i
\(322\) −2532.26 10027.7i −0.438252 1.73548i
\(323\) −75.7457 + 75.7457i −0.0130483 + 0.0130483i
\(324\) 6459.66i 1.10762i
\(325\) −667.007 + 1979.97i −0.113843 + 0.337936i
\(326\) 1971.28 0.334905
\(327\) −1781.55 + 1781.55i −0.301284 + 0.301284i
\(328\) −4216.12 + 4216.12i −0.709744 + 0.709744i
\(329\) 4336.23 0.726638
\(330\) −7679.95 + 1800.08i −1.28111 + 0.300276i
\(331\) −2077.80 −0.345034 −0.172517 0.985007i \(-0.555190\pi\)
−0.172517 + 0.985007i \(0.555190\pi\)
\(332\) 591.050 591.050i 0.0977051 0.0977051i
\(333\) −6133.51 6133.51i −1.00935 1.00935i
\(334\) 1639.08i 0.268522i
\(335\) 2765.40 + 1715.20i 0.451015 + 0.279736i
\(336\) 21524.7i 3.49484i
\(337\) −5840.75 + 5840.75i −0.944112 + 0.944112i −0.998519 0.0544068i \(-0.982673\pi\)
0.0544068 + 0.998519i \(0.482673\pi\)
\(338\) 4555.54 4555.54i 0.733102 0.733102i
\(339\) 1946.58 0.311869
\(340\) 2237.39 3607.31i 0.356881 0.575394i
\(341\) 2541.32i 0.403578i
\(342\) 147.904 147.904i 0.0233852 0.0233852i
\(343\) 1833.66 + 1833.66i 0.288654 + 0.288654i
\(344\) 7766.59 1.21729
\(345\) −3625.13 + 11402.7i −0.565712 + 1.77943i
\(346\) 11890.4 1.84750
\(347\) −5428.08 5428.08i −0.839755 0.839755i 0.149072 0.988826i \(-0.452371\pi\)
−0.988826 + 0.149072i \(0.952371\pi\)
\(348\) −1147.72 + 1147.72i −0.176793 + 0.176793i
\(349\) 466.824i 0.0716004i 0.999359 + 0.0358002i \(0.0113980\pi\)
−0.999359 + 0.0358002i \(0.988602\pi\)
\(350\) −10499.8 + 5208.13i −1.60353 + 0.795390i
\(351\) −6508.14 −0.989683
\(352\) 2148.74 2148.74i 0.325364 0.325364i
\(353\) −6225.67 + 6225.67i −0.938694 + 0.938694i −0.998226 0.0595326i \(-0.981039\pi\)
0.0595326 + 0.998226i \(0.481039\pi\)
\(354\) 10895.6i 1.63586i
\(355\) −774.703 3305.23i −0.115823 0.494151i
\(356\) 3.09524i 0.000460807i
\(357\) 22115.7 + 22115.7i 3.27868 + 3.27868i
\(358\) −6978.25 + 6978.25i −1.03020 + 1.03020i
\(359\) 10250.7 1.50700 0.753500 0.657448i \(-0.228364\pi\)
0.753500 + 0.657448i \(0.228364\pi\)
\(360\) 6264.01 10099.4i 0.917062 1.47857i
\(361\) −6858.14 −0.999875
\(362\) 3217.45 3217.45i 0.467142 0.467142i
\(363\) 5917.13 5917.13i 0.855562 0.855562i
\(364\) −1533.35 −0.220795
\(365\) −7201.60 4466.71i −1.03274 0.640543i
\(366\) 16383.1i 2.33978i
\(367\) 2423.84 2423.84i 0.344751 0.344751i −0.513399 0.858150i \(-0.671614\pi\)
0.858150 + 0.513399i \(0.171614\pi\)
\(368\) −2146.81 8501.39i −0.304104 1.20425i
\(369\) 25280.0i 3.56646i
\(370\) 1107.53 + 4725.23i 0.155616 + 0.663928i
\(371\) −5611.17 −0.785222
\(372\) −2647.66 2647.66i −0.369018 0.369018i
\(373\) 2943.52 + 2943.52i 0.408605 + 0.408605i 0.881252 0.472647i \(-0.156701\pi\)
−0.472647 + 0.881252i \(0.656701\pi\)
\(374\) 8399.40i 1.16129i
\(375\) 13498.5 + 1282.21i 1.85882 + 0.176569i
\(376\) 2460.09 0.337419
\(377\) 601.522 + 601.522i 0.0821749 + 0.0821749i
\(378\) −25815.8 25815.8i −3.51276 3.51276i
\(379\) −271.670 −0.0368199 −0.0184099 0.999831i \(-0.505860\pi\)
−0.0184099 + 0.999831i \(0.505860\pi\)
\(380\) −33.1832 + 7.77772i −0.00447964 + 0.00104997i
\(381\) 12894.6 1.73388
\(382\) −186.007 + 186.007i −0.0249135 + 0.0249135i
\(383\) 489.187 + 489.187i 0.0652644 + 0.0652644i 0.738986 0.673721i \(-0.235305\pi\)
−0.673721 + 0.738986i \(0.735305\pi\)
\(384\) 16251.4i 2.15970i
\(385\) −3559.90 + 5739.58i −0.471246 + 0.759782i
\(386\) 13271.3 1.74998
\(387\) −23284.4 + 23284.4i −3.05843 + 3.05843i
\(388\) 3198.94 + 3198.94i 0.418561 + 0.418561i
\(389\) 14401.3 1.87705 0.938527 0.345205i \(-0.112191\pi\)
0.938527 + 0.345205i \(0.112191\pi\)
\(390\) 5176.41 + 3210.61i 0.672097 + 0.416860i
\(391\) −10940.6 6529.06i −1.41506 0.844473i
\(392\) 4880.58 + 4880.58i 0.628843 + 0.628843i
\(393\) 3790.27 3790.27i 0.486498 0.486498i
\(394\) 4316.07i 0.551879i
\(395\) 243.817 + 1040.23i 0.0310577 + 0.132506i
\(396\) 4776.33i 0.606111i
\(397\) 676.330 + 676.330i 0.0855014 + 0.0855014i 0.748564 0.663063i \(-0.230744\pi\)
−0.663063 + 0.748564i \(0.730744\pi\)
\(398\) 9418.55 + 9418.55i 1.18620 + 1.18620i
\(399\) 251.123i 0.0315085i
\(400\) −8901.55 + 4415.38i −1.11269 + 0.551923i
\(401\) 11573.9i 1.44132i −0.693287 0.720662i \(-0.743838\pi\)
0.693287 0.720662i \(-0.256162\pi\)
\(402\) 6708.49 6708.49i 0.832311 0.832311i
\(403\) −1387.64 + 1387.64i −0.171522 + 0.171522i
\(404\) 4330.74i 0.533322i
\(405\) 5013.95 + 21391.8i 0.615173 + 2.62460i
\(406\) 4772.11i 0.583339i
\(407\) 1977.58 + 1977.58i 0.240848 + 0.240848i
\(408\) 12547.0 + 12547.0i 1.52247 + 1.52247i
\(409\) 14071.5i 1.70120i 0.525816 + 0.850598i \(0.323760\pi\)
−0.525816 + 0.850598i \(0.676240\pi\)
\(410\) −7455.38 + 12020.2i −0.898037 + 1.44789i
\(411\) 15017.2i 1.80229i
\(412\) 583.045 583.045i 0.0697198 0.0697198i
\(413\) −6596.63 6596.63i −0.785954 0.785954i
\(414\) 21363.0 + 12748.9i 2.53607 + 1.51346i
\(415\) −1498.55 + 2416.09i −0.177255 + 0.285786i
\(416\) −2346.57 −0.276562
\(417\) −5815.22 5815.22i −0.682907 0.682907i
\(418\) −47.6875 + 47.6875i −0.00558007 + 0.00558007i
\(419\) 797.417 0.0929747 0.0464873 0.998919i \(-0.485197\pi\)
0.0464873 + 0.998919i \(0.485197\pi\)
\(420\) 2270.88 + 9688.61i 0.263828 + 1.12561i
\(421\) 3641.20i 0.421523i −0.977537 0.210762i \(-0.932406\pi\)
0.977537 0.210762i \(-0.0675944\pi\)
\(422\) −3251.91 3251.91i −0.375120 0.375120i
\(423\) −7375.38 + 7375.38i −0.847762 + 0.847762i
\(424\) −3183.41 −0.364622
\(425\) −4609.35 + 13682.6i −0.526086 + 1.56166i
\(426\) −9897.38 −1.12566
\(427\) −9918.98 9918.98i −1.12415 1.12415i
\(428\) 2998.35 + 2998.35i 0.338623 + 0.338623i
\(429\) 3510.09 0.395032
\(430\) 17938.2 4204.48i 2.01176 0.471530i
\(431\) 15460.6i 1.72786i 0.503608 + 0.863932i \(0.332006\pi\)
−0.503608 + 0.863932i \(0.667994\pi\)
\(432\) −21886.3 21886.3i −2.43751 2.43751i
\(433\) −2548.59 2548.59i −0.282858 0.282858i 0.551390 0.834248i \(-0.314098\pi\)
−0.834248 + 0.551390i \(0.814098\pi\)
\(434\) −11008.7 −1.21759
\(435\) 2909.92 4691.62i 0.320735 0.517117i
\(436\) 853.589i 0.0937603i
\(437\) 25.0464 + 99.1837i 0.00274172 + 0.0108572i
\(438\) −17470.1 + 17470.1i −1.90583 + 1.90583i
\(439\) 7215.24i 0.784430i 0.919874 + 0.392215i \(0.128291\pi\)
−0.919874 + 0.392215i \(0.871709\pi\)
\(440\) −2019.65 + 3256.26i −0.218826 + 0.352809i
\(441\) −29264.1 −3.15993
\(442\) −4586.35 + 4586.35i −0.493553 + 0.493553i
\(443\) −2147.30 + 2147.30i −0.230297 + 0.230297i −0.812816 0.582520i \(-0.802067\pi\)
0.582520 + 0.812816i \(0.302067\pi\)
\(444\) 4120.66 0.440445
\(445\) −2.40250 10.2502i −0.000255932 0.00109192i
\(446\) 9488.29 1.00736
\(447\) 12075.5 12075.5i 1.27774 1.27774i
\(448\) 3241.83 + 3241.83i 0.341879 + 0.341879i
\(449\) 9371.99i 0.985059i −0.870296 0.492530i \(-0.836072\pi\)
0.870296 0.492530i \(-0.163928\pi\)
\(450\) 9000.39 26717.2i 0.942850 2.79880i
\(451\) 8150.82i 0.851013i
\(452\) −466.329 + 466.329i −0.0485272 + 0.0485272i
\(453\) −8642.40 + 8642.40i −0.896369 + 0.896369i
\(454\) −6100.48 −0.630638
\(455\) 5077.83 1190.18i 0.523192 0.122629i
\(456\) 142.471i 0.0146311i
\(457\) −8241.63 + 8241.63i −0.843604 + 0.843604i −0.989326 0.145721i \(-0.953450\pi\)
0.145721 + 0.989326i \(0.453450\pi\)
\(458\) −13525.6 13525.6i −1.37994 1.37994i
\(459\) −44974.5 −4.57349
\(460\) −1863.23 3600.12i −0.188855 0.364906i
\(461\) −13985.4 −1.41294 −0.706469 0.707744i \(-0.749713\pi\)
−0.706469 + 0.707744i \(0.749713\pi\)
\(462\) 13923.5 + 13923.5i 1.40212 + 1.40212i
\(463\) 4839.39 4839.39i 0.485757 0.485757i −0.421207 0.906964i \(-0.638394\pi\)
0.906964 + 0.421207i \(0.138394\pi\)
\(464\) 4045.73i 0.404781i
\(465\) 10823.0 + 6712.86i 1.07937 + 0.669465i
\(466\) −12675.3 −1.26002
\(467\) 5103.54 5103.54i 0.505703 0.505703i −0.407501 0.913205i \(-0.633600\pi\)
0.913205 + 0.407501i \(0.133600\pi\)
\(468\) 2608.04 2608.04i 0.257600 0.257600i
\(469\) 8123.16i 0.799771i
\(470\) 5681.97 1331.78i 0.557638 0.130703i
\(471\) 8638.26i 0.845074i
\(472\) −3742.49 3742.49i −0.364962 0.364962i
\(473\) 7507.39 7507.39i 0.729789 0.729789i
\(474\) 3114.94 0.301844
\(475\) 103.852 51.5132i 0.0100317 0.00497598i
\(476\) −10596.2 −1.02033
\(477\) 9543.90 9543.90i 0.916111 0.916111i
\(478\) −3449.92 + 3449.92i −0.330116 + 0.330116i
\(479\) −11726.3 −1.11856 −0.559279 0.828980i \(-0.688922\pi\)
−0.559279 + 0.828980i \(0.688922\pi\)
\(480\) 3475.25 + 14827.0i 0.330464 + 1.40991i
\(481\) 2159.65i 0.204722i
\(482\) 12343.9 12343.9i 1.16650 1.16650i
\(483\) 28959.0 7312.87i 2.72811 0.688917i
\(484\) 2835.06i 0.266252i
\(485\) −13076.6 8110.59i −1.22428 0.759346i
\(486\) 28736.8 2.68216
\(487\) −1835.48 1835.48i −0.170788 0.170788i 0.616538 0.787325i \(-0.288535\pi\)
−0.787325 + 0.616538i \(0.788535\pi\)
\(488\) −5627.37 5627.37i −0.522006 0.522006i
\(489\) 5692.83i 0.526459i
\(490\) 13914.6 + 8630.35i 1.28285 + 0.795672i
\(491\) 11957.6 1.09906 0.549528 0.835475i \(-0.314807\pi\)
0.549528 + 0.835475i \(0.314807\pi\)
\(492\) 8491.88 + 8491.88i 0.778137 + 0.778137i
\(493\) 4156.82 + 4156.82i 0.379744 + 0.379744i
\(494\) 52.0779 0.00474311
\(495\) −3707.36 15817.3i −0.336633 1.43623i
\(496\) −9333.05 −0.844892
\(497\) −5992.26 + 5992.26i −0.540824 + 0.540824i
\(498\) 5861.10 + 5861.10i 0.527394 + 0.527394i
\(499\) 5208.35i 0.467250i −0.972327 0.233625i \(-0.924941\pi\)
0.972327 0.233625i \(-0.0750587\pi\)
\(500\) −3540.91 + 2926.56i −0.316708 + 0.261760i
\(501\) 4733.47 0.422108
\(502\) 9856.62 9856.62i 0.876340 0.876340i
\(503\) 10676.2 + 10676.2i 0.946379 + 0.946379i 0.998634 0.0522547i \(-0.0166408\pi\)
−0.0522547 + 0.998634i \(0.516641\pi\)
\(504\) −29666.2 −2.62190
\(505\) −3361.49 14341.6i −0.296207 1.26375i
\(506\) −6887.90 4110.52i −0.605147 0.361136i
\(507\) 13155.9 + 13155.9i 1.15241 + 1.15241i
\(508\) −3089.06 + 3089.06i −0.269793 + 0.269793i
\(509\) 15530.5i 1.35241i −0.736712 0.676207i \(-0.763622\pi\)
0.736712 0.676207i \(-0.236378\pi\)
\(510\) 35771.6 + 22186.9i 3.10587 + 1.92638i
\(511\) 21154.2i 1.83132i
\(512\) −771.290 771.290i −0.0665753 0.0665753i
\(513\) 255.342 + 255.342i 0.0219759 + 0.0219759i
\(514\) 4364.16i 0.374504i
\(515\) −1478.25 + 2383.36i −0.126484 + 0.203929i
\(516\) 15643.1i 1.33459i
\(517\) 2377.99 2377.99i 0.202290 0.202290i
\(518\) 8566.67 8566.67i 0.726637 0.726637i
\(519\) 34338.2i 2.90420i
\(520\) 2880.82 675.227i 0.242947 0.0569436i
\(521\) 1730.30i 0.145501i 0.997350 + 0.0727503i \(0.0231776\pi\)
−0.997350 + 0.0727503i \(0.976822\pi\)
\(522\) −8116.76 8116.76i −0.680576 0.680576i
\(523\) −11704.7 11704.7i −0.978604 0.978604i 0.0211715 0.999776i \(-0.493260\pi\)
−0.999776 + 0.0211715i \(0.993260\pi\)
\(524\) 1816.02i 0.151399i
\(525\) −15040.5 30322.1i −1.25032 2.52069i
\(526\) 7291.68i 0.604434i
\(527\) −9589.32 + 9589.32i −0.792633 + 0.792633i
\(528\) 11804.1 + 11804.1i 0.972932 + 0.972932i
\(529\) −10708.3 + 5776.58i −0.880108 + 0.474774i
\(530\) −7352.58 + 1723.35i −0.602596 + 0.141241i
\(531\) 22440.1 1.83393
\(532\) 60.1599 + 60.1599i 0.00490275 + 0.00490275i
\(533\) 4450.62 4450.62i 0.361684 0.361684i
\(534\) −30.6937 −0.00248735
\(535\) −12256.6 7602.01i −0.990467 0.614325i
\(536\) 4608.54i 0.371378i
\(537\) −20152.4 20152.4i −1.61944 1.61944i
\(538\) 7548.57 7548.57i 0.604911 0.604911i
\(539\) 9435.38 0.754009
\(540\) −12160.4 7542.35i −0.969076 0.601057i
\(541\) −18217.2 −1.44772 −0.723861 0.689946i \(-0.757634\pi\)
−0.723861 + 0.689946i \(0.757634\pi\)
\(542\) 7945.04 + 7945.04i 0.629647 + 0.629647i
\(543\) 9291.62 + 9291.62i 0.734331 + 0.734331i
\(544\) −16216.0 −1.27804
\(545\) 662.550 + 2826.74i 0.0520743 + 0.222173i
\(546\) 15205.3i 1.19181i
\(547\) 12658.7 + 12658.7i 0.989479 + 0.989479i 0.999945 0.0104661i \(-0.00333153\pi\)
−0.0104661 + 0.999945i \(0.503332\pi\)
\(548\) 3597.56 + 3597.56i 0.280438 + 0.280438i
\(549\) 33741.9 2.62308
\(550\) −2901.92 + 8614.20i −0.224979 + 0.667837i
\(551\) 47.2006i 0.00364939i
\(552\) 16429.4 4148.84i 1.26681 0.319902i
\(553\) 1885.91 1885.91i 0.145021 0.145021i
\(554\) 20877.5i 1.60108i
\(555\) −13645.9 + 3198.43i −1.04367 + 0.244623i
\(556\) 2786.22 0.212522
\(557\) −10599.2 + 10599.2i −0.806292 + 0.806292i −0.984070 0.177779i \(-0.943109\pi\)
0.177779 + 0.984070i \(0.443109\pi\)
\(558\) 18724.5 18724.5i 1.42056 1.42056i
\(559\) −8198.57 −0.620326
\(560\) 21078.8 + 13073.8i 1.59061 + 0.986554i
\(561\) 24256.5 1.82551
\(562\) −8979.19 + 8979.19i −0.673957 + 0.673957i
\(563\) −3704.30 3704.30i −0.277296 0.277296i 0.554733 0.832029i \(-0.312821\pi\)
−0.832029 + 0.554733i \(0.812821\pi\)
\(564\) 4954.98i 0.369933i
\(565\) 1182.33 1906.25i 0.0880372 0.141941i
\(566\) 25922.0i 1.92506i
\(567\) 38782.4 38782.4i 2.87250 2.87250i
\(568\) −3399.61 + 3399.61i −0.251135 + 0.251135i
\(569\) 1189.67 0.0876514 0.0438257 0.999039i \(-0.486045\pi\)
0.0438257 + 0.999039i \(0.486045\pi\)
\(570\) −77.1271 329.059i −0.00566754 0.0241803i
\(571\) 13728.2i 1.00614i −0.864245 0.503071i \(-0.832203\pi\)
0.864245 0.503071i \(-0.167797\pi\)
\(572\) −840.889 + 840.889i −0.0614673 + 0.0614673i
\(573\) −537.167 537.167i −0.0391631 0.0391631i
\(574\) 35308.5 2.56750
\(575\) 8964.63 + 10475.9i 0.650176 + 0.759784i
\(576\) −11027.9 −0.797735
\(577\) −1432.07 1432.07i −0.103324 0.103324i 0.653555 0.756879i \(-0.273277\pi\)
−0.756879 + 0.653555i \(0.773277\pi\)
\(578\) −20022.6 + 20022.6i −1.44089 + 1.44089i
\(579\) 38326.0i 2.75091i
\(580\) 426.830 + 1821.05i 0.0305572 + 0.130371i
\(581\) 7097.08 0.506775
\(582\) −31722.0 + 31722.0i −2.25931 + 2.25931i
\(583\) −3077.16 + 3077.16i −0.218599 + 0.218599i
\(584\) 12001.5i 0.850385i
\(585\) −6612.41 + 10661.1i −0.467333 + 0.753474i
\(586\) 27928.0i 1.96876i
\(587\) 7840.14 + 7840.14i 0.551273 + 0.551273i 0.926808 0.375535i \(-0.122541\pi\)
−0.375535 + 0.926808i \(0.622541\pi\)
\(588\) 9830.19 9830.19i 0.689439 0.689439i
\(589\) 108.886 0.00761730
\(590\) −10669.9 6617.87i −0.744530 0.461785i
\(591\) 12464.3 0.867535
\(592\) 7262.70 7262.70i 0.504215 0.504215i
\(593\) −3029.69 + 3029.69i −0.209805 + 0.209805i −0.804185 0.594379i \(-0.797398\pi\)
0.594379 + 0.804185i \(0.297398\pi\)
\(594\) −28314.7 −1.95584
\(595\) 35090.4 8224.72i 2.41776 0.566690i
\(596\) 5785.68i 0.397636i
\(597\) −27199.7 + 27199.7i −1.86467 + 1.86467i
\(598\) 1516.54 + 6005.50i 0.103706 + 0.410674i
\(599\) 10681.7i 0.728616i −0.931279 0.364308i \(-0.881306\pi\)
0.931279 0.364308i \(-0.118694\pi\)
\(600\) −8532.97 17202.7i −0.580595 1.17050i
\(601\) 25834.4 1.75342 0.876711 0.481017i \(-0.159732\pi\)
0.876711 + 0.481017i \(0.159732\pi\)
\(602\) −32521.2 32521.2i −2.20177 2.20177i
\(603\) 13816.5 + 13816.5i 0.933085 + 0.933085i
\(604\) 4140.80i 0.278952i
\(605\) −2200.55 9388.54i −0.147876 0.630907i
\(606\) −42945.4 −2.87877
\(607\) 7878.09 + 7878.09i 0.526790 + 0.526790i 0.919614 0.392824i \(-0.128502\pi\)
−0.392824 + 0.919614i \(0.628502\pi\)
\(608\) 92.0659 + 92.0659i 0.00614106 + 0.00614106i
\(609\) −13781.3 −0.916989
\(610\) −16043.7 9950.91i −1.06490 0.660493i
\(611\) −2596.92 −0.171948
\(612\) 18022.9 18022.9i 1.19041 1.19041i
\(613\) 2719.72 + 2719.72i 0.179198 + 0.179198i 0.791006 0.611808i \(-0.209558\pi\)
−0.611808 + 0.791006i \(0.709558\pi\)
\(614\) 11887.2i 0.781319i
\(615\) −34713.0 21530.3i −2.27603 1.41168i
\(616\) 9565.03 0.625626
\(617\) 16467.5 16467.5i 1.07448 1.07448i 0.0774878 0.996993i \(-0.475310\pi\)
0.996993 0.0774878i \(-0.0246899\pi\)
\(618\) 5781.72 + 5781.72i 0.376334 + 0.376334i
\(619\) −15468.8 −1.00443 −0.502216 0.864742i \(-0.667482\pi\)
−0.502216 + 0.864742i \(0.667482\pi\)
\(620\) −4200.96 + 984.650i −0.272120 + 0.0637814i
\(621\) −22009.8 + 36881.2i −1.42226 + 2.38324i
\(622\) 9701.96 + 9701.96i 0.625423 + 0.625423i
\(623\) −18.5831 + 18.5831i −0.00119505 + 0.00119505i
\(624\) 12890.9i 0.827001i
\(625\) 9454.46 12440.0i 0.605085 0.796161i
\(626\) 10144.8i 0.647712i
\(627\) −137.716 137.716i −0.00877168 0.00877168i
\(628\) 2069.41 + 2069.41i 0.131494 + 0.131494i
\(629\) 14924.3i 0.946056i
\(630\) −68518.8 + 16059.9i −4.33310 + 1.01562i
\(631\) 4854.93i 0.306295i 0.988203 + 0.153147i \(0.0489409\pi\)
−0.988203 + 0.153147i \(0.951059\pi\)
\(632\) 1069.94 1069.94i 0.0673415 0.0673415i
\(633\) 9391.14 9391.14i 0.589675 0.589675i
\(634\) 35025.0i 2.19404i
\(635\) 7832.00 12627.4i 0.489454 0.789140i
\(636\) 6411.84i 0.399758i
\(637\) −5152.03 5152.03i −0.320457 0.320457i
\(638\) 2617.02 + 2617.02i 0.162396 + 0.162396i
\(639\) 20384.2i 1.26195i
\(640\) 15914.7 + 9870.89i 0.982943 + 0.609658i
\(641\) 30357.5i 1.87059i 0.353867 + 0.935296i \(0.384867\pi\)
−0.353867 + 0.935296i \(0.615133\pi\)
\(642\) −29732.9 + 29732.9i −1.82783 + 1.82783i
\(643\) 9182.06 + 9182.06i 0.563150 + 0.563150i 0.930201 0.367051i \(-0.119633\pi\)
−0.367051 + 0.930201i \(0.619633\pi\)
\(644\) −5185.61 + 8689.40i −0.317301 + 0.531693i
\(645\) 12142.0 + 51803.4i 0.741228 + 3.16241i
\(646\) 359.885 0.0219187
\(647\) 4609.42 + 4609.42i 0.280085 + 0.280085i 0.833143 0.553058i \(-0.186539\pi\)
−0.553058 + 0.833143i \(0.686539\pi\)
\(648\) 22002.6 22002.6i 1.33386 1.33386i
\(649\) −7235.18 −0.437605
\(650\) 6288.19 3119.09i 0.379451 0.188217i
\(651\) 31791.9i 1.91401i
\(652\) −1363.79 1363.79i −0.0819176 0.0819176i
\(653\) 833.619 833.619i 0.0499572 0.0499572i −0.681687 0.731644i \(-0.738753\pi\)
0.731644 + 0.681687i \(0.238753\pi\)
\(654\) 8464.54 0.506100
\(655\) −1409.58 6013.91i −0.0840869 0.358753i
\(656\) 29934.1 1.78160
\(657\) −35980.6 35980.6i −2.13659 2.13659i
\(658\) −10301.2 10301.2i −0.610307 0.610307i
\(659\) −20861.1 −1.23313 −0.616564 0.787305i \(-0.711476\pi\)
−0.616564 + 0.787305i \(0.711476\pi\)
\(660\) 6558.58 + 4067.88i 0.386807 + 0.239912i
\(661\) 6421.92i 0.377888i 0.981988 + 0.188944i \(0.0605064\pi\)
−0.981988 + 0.188944i \(0.939494\pi\)
\(662\) 4936.04 + 4936.04i 0.289795 + 0.289795i
\(663\) −13244.8 13244.8i −0.775848 0.775848i
\(664\) 4026.41 0.235324
\(665\) −245.921 152.529i −0.0143405 0.00889449i
\(666\) 29141.7i 1.69552i
\(667\) 5443.06 1374.51i 0.315976 0.0797919i
\(668\) −1133.97 + 1133.97i −0.0656803 + 0.0656803i
\(669\) 27401.1i 1.58354i
\(670\) −2494.85 10644.2i −0.143858 0.613761i
\(671\) −10879.1 −0.625907
\(672\) 26880.8 26880.8i 1.54308 1.54308i
\(673\) 12621.0 12621.0i 0.722891 0.722891i −0.246302 0.969193i \(-0.579216\pi\)
0.969193 + 0.246302i \(0.0792156\pi\)
\(674\) 27750.7 1.58593
\(675\) 46124.7 + 15538.3i 2.63013 + 0.886031i
\(676\) −6303.32 −0.358632
\(677\) −4281.93 + 4281.93i −0.243084 + 0.243084i −0.818125 0.575041i \(-0.804986\pi\)
0.575041 + 0.818125i \(0.304986\pi\)
\(678\) −4624.32 4624.32i −0.261941 0.261941i
\(679\) 38411.5i 2.17098i
\(680\) 19907.9 4666.16i 1.12270 0.263146i
\(681\) 17617.5i 0.991340i
\(682\) −6037.18 + 6037.18i −0.338967 + 0.338967i
\(683\) −14893.7 + 14893.7i −0.834394 + 0.834394i −0.988114 0.153720i \(-0.950875\pi\)
0.153720 + 0.988114i \(0.450875\pi\)
\(684\) −204.649 −0.0114400
\(685\) −14706.1 9121.25i −0.820277 0.508766i
\(686\) 8712.12i 0.484884i
\(687\) 39060.4 39060.4i 2.16921 2.16921i
\(688\) −27571.1 27571.1i −1.52782 1.52782i
\(689\) 3360.47 0.185811
\(690\) 35700.3 18476.5i 1.96969 1.01940i
\(691\) 19324.8 1.06389 0.531947 0.846777i \(-0.321460\pi\)
0.531947 + 0.846777i \(0.321460\pi\)
\(692\) −8226.17 8226.17i −0.451896 0.451896i
\(693\) −28676.1 + 28676.1i −1.57188 + 1.57188i
\(694\) 25790.0i 1.41063i
\(695\) −9226.84 + 2162.65i −0.503588 + 0.118034i
\(696\) −7818.59 −0.425809
\(697\) 30756.0 30756.0i 1.67140 1.67140i
\(698\) 1108.99 1108.99i 0.0601375 0.0601375i
\(699\) 36604.7i 1.98071i
\(700\) 10867.2 + 3660.91i 0.586774 + 0.197671i
\(701\) 5189.40i 0.279602i −0.990180 0.139801i \(-0.955354\pi\)
0.990180 0.139801i \(-0.0446463\pi\)
\(702\) 15460.8 + 15460.8i 0.831239 + 0.831239i
\(703\) −84.7323 + 84.7323i −0.00454586 + 0.00454586i
\(704\) 3555.63 0.190352
\(705\) 3846.02 + 16408.9i 0.205460 + 0.876586i
\(706\) 29579.5 1.57683
\(707\) −26000.8 + 26000.8i −1.38311 + 1.38311i
\(708\) −7537.92 + 7537.92i −0.400131 + 0.400131i
\(709\) 20908.4 1.10752 0.553759 0.832677i \(-0.313193\pi\)
0.553759 + 0.832677i \(0.313193\pi\)
\(710\) −6011.55 + 9692.34i −0.317760 + 0.512320i
\(711\) 6415.38i 0.338390i
\(712\) −10.5428 + 10.5428i −0.000554930 + 0.000554930i
\(713\) 3170.84 + 12556.5i 0.166548 + 0.659532i
\(714\) 105077.i 5.50755i
\(715\) 2131.99 3437.37i 0.111513 0.179791i
\(716\) 9655.53 0.503972
\(717\) −9962.96 9962.96i −0.518931 0.518931i
\(718\) −24351.7 24351.7i −1.26574 1.26574i
\(719\) 12504.5i 0.648592i −0.945956 0.324296i \(-0.894873\pi\)
0.945956 0.324296i \(-0.105127\pi\)
\(720\) −58089.3 + 13615.4i −3.00675 + 0.704743i
\(721\) 7000.95 0.361621
\(722\) 16292.3 + 16292.3i 0.839799 + 0.839799i
\(723\) 35647.9 + 35647.9i 1.83369 + 1.83369i
\(724\) −4451.86 −0.228525
\(725\) −2826.97 5699.27i −0.144815 0.291952i
\(726\) −28113.6 −1.43718
\(727\) 1319.11 1319.11i 0.0672946 0.0672946i −0.672658 0.739953i \(-0.734848\pi\)
0.739953 + 0.672658i \(0.234848\pi\)
\(728\) −5222.82 5222.82i −0.265894 0.265894i
\(729\) 29928.4i 1.52052i
\(730\) 6497.05 + 27719.3i 0.329406 + 1.40540i
\(731\) −56656.2 −2.86663
\(732\) −11334.3 + 11334.3i −0.572308 + 0.572308i
\(733\) −22884.6 22884.6i −1.15315 1.15315i −0.985917 0.167238i \(-0.946515\pi\)
−0.167238 0.985917i \(-0.553485\pi\)
\(734\) −11516.2 −0.579116
\(735\) −24923.4 + 40183.7i −1.25077 + 2.01660i
\(736\) −7935.81 + 13297.8i −0.397443 + 0.665985i
\(737\) −4454.74 4454.74i −0.222649 0.222649i
\(738\) −60055.3 + 60055.3i −2.99548 + 2.99548i
\(739\) 8087.04i 0.402553i −0.979534 0.201277i \(-0.935491\pi\)
0.979534 0.201277i \(-0.0645090\pi\)
\(740\) 2502.84 4035.29i 0.124333 0.200460i
\(741\) 150.395i 0.00745600i
\(742\) 13329.9 + 13329.9i 0.659512 + 0.659512i
\(743\) −830.096 830.096i −0.0409869 0.0409869i 0.686316 0.727303i \(-0.259227\pi\)
−0.727303 + 0.686316i \(0.759227\pi\)
\(744\) 18036.6i 0.888783i
\(745\) −4490.81 19159.8i −0.220846 0.942230i
\(746\) 13985.3i 0.686378i
\(747\) −12071.2 + 12071.2i −0.591250 + 0.591250i
\(748\) −5810.96 + 5810.96i −0.284051 + 0.284051i
\(749\) 36002.9i 1.75637i
\(750\) −29021.0 35113.1i −1.41293 1.70953i
\(751\) 20993.8i 1.02007i −0.860153 0.510035i \(-0.829632\pi\)
0.860153 0.510035i \(-0.170368\pi\)
\(752\) −8733.21 8733.21i −0.423494 0.423494i
\(753\) 28464.8 + 28464.8i 1.37758 + 1.37758i
\(754\) 2857.96i 0.138038i
\(755\) 3214.06 + 13712.6i 0.154930 + 0.660999i
\(756\) 35720.3i 1.71843i
\(757\) 19169.0 19169.0i 0.920357 0.920357i −0.0766972 0.997054i \(-0.524437\pi\)
0.997054 + 0.0766972i \(0.0244375\pi\)
\(758\) 645.381 + 645.381i 0.0309252 + 0.0309252i
\(759\) 11870.7 19891.4i 0.567693 0.951270i
\(760\) −139.519 86.5350i −0.00665907 0.00413020i
\(761\) 15484.6 0.737601 0.368801 0.929509i \(-0.379768\pi\)
0.368801 + 0.929509i \(0.379768\pi\)
\(762\) −30632.4 30632.4i −1.45629 1.45629i
\(763\) 5124.76 5124.76i 0.243157 0.243157i
\(764\) 257.371 0.0121876
\(765\) −45695.1 + 73673.5i −2.15962 + 3.48193i
\(766\) 2324.23i 0.109632i
\(767\) 3950.65 + 3950.65i 0.185984 + 0.185984i
\(768\) 29591.1 29591.1i 1.39033 1.39033i
\(769\) −14878.5 −0.697703 −0.348852 0.937178i \(-0.613428\pi\)
−0.348852 + 0.937178i \(0.613428\pi\)
\(770\) 22092.0 5178.06i 1.03395 0.242343i
\(771\) −12603.2 −0.588707
\(772\) −9181.52 9181.52i −0.428044 0.428044i