Properties

Label 115.4.e.a.22.10
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 22.10
Character \(\chi\) \(=\) 115.22
Dual form 115.4.e.a.68.10

$q$-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} +(106.947 + 27.0068i) 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} +(-88.7724 + 351.539i) 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 \(-0.478377\pi\)
0.997694 0.0678793i \(-0.0216233\pi\)
\(8\) −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 \(-0.904132\pi\)
0.954988 0.296646i \(-0.0958681\pi\)
\(12\) 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 \(0.558231\pi\)
−0.983314 + 0.181919i \(0.941769\pi\)
\(18\) −159.481 + 159.481i −2.08833 + 2.08833i
\(19\) 0.927411 0.0111980 0.00559902 0.999984i \(-0.498218\pi\)
0.00559902 + 0.999984i \(0.498218\pi\)
\(20\) −35.7805 + 8.38649i −0.400038 + 0.0937638i
\(21\) 270.779i 2.81375i
\(22\) −51.4200 + 51.4200i −0.498308 + 0.498308i
\(23\) 106.947 + 27.0068i 0.969564 + 0.244839i
\(24\) 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 −0.880324 0.474373i \(-0.842675\pi\)
0.474373 + 0.880324i \(0.342675\pi\)
\(38\) −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 \(0.0857454\pi\)
0.266131 + 0.963937i \(0.414255\pi\)
\(44\) 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 0.498461 0.866912i \(-0.333899\pi\)
−0.866912 + 0.498461i \(0.833899\pi\)
\(54\) 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 \(-0.823134\pi\)
0.849563 0.527487i \(-0.176866\pi\)
\(62\) 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 −0.494118 0.869395i \(-0.664509\pi\)
0.869395 + 0.494118i \(0.164509\pi\)
\(68\) −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 \(-0.478323\pi\)
0.0680486 + 0.997682i \(0.478323\pi\)
\(80\) 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 0.815936 0.578142i \(-0.196222\pi\)
−0.578142 + 0.815936i \(0.696222\pi\)
\(84\) 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 \(-0.500178\pi\)
−0.000560756 1.00000i \(0.500178\pi\)
\(90\) −2142.89 1329.10i −2.50979 1.55666i
\(91\) 466.484i 0.537371i
\(92\) −88.7724 + 351.539i −0.100600 + 0.398374i
\(93\) −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 \(0.506007\pi\)
−0.999822 + 0.0188718i \(0.993993\pi\)
\(98\) −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 0.786840 0.617156i \(-0.211715\pi\)
−0.617156 + 0.786840i \(0.711715\pi\)
\(104\) 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 −0.986699 0.162557i \(-0.948026\pi\)
0.162557 + 0.986699i \(0.448026\pi\)
\(108\) 905.014 905.014i 0.806343 0.806343i
\(109\) 259.683 0.228194 0.114097 0.993470i \(-0.463603\pi\)
0.114097 + 0.993470i \(0.463603\pi\)
\(110\) −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 0.645584 0.763689i \(-0.276614\pi\)
−0.763689 + 0.645584i \(0.776614\pi\)
\(114\) −30.2296 −0.0248356
\(115\) −21.1157 + 1233.06i −0.0171221 + 0.999853i
\(116\) −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 −0.960570 0.278039i \(-0.910316\pi\)
0.278039 + 0.960570i \(0.410316\pi\)
\(138\) −3486.00 880.304i −2.15035 0.543017i
\(139\) 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 \(-0.660774\pi\)
−0.483883 + 0.875133i \(0.660774\pi\)
\(150\) 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 −0.848779 0.528748i \(-0.822662\pi\)
0.528748 + 0.848779i \(0.322662\pi\)
\(158\) −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 \(-0.910298\pi\)
0.960554 0.278092i \(-0.0897021\pi\)
\(182\) −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 \(0.00472107\pi\)
−0.999890 + 0.0148311i \(0.995279\pi\)
\(192\) −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 \(-0.250428\pi\)
0.706154 + 0.708058i \(0.250428\pi\)
\(200\) 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
\(207\) 1813.03 7179.61i 0.608765 2.41071i
\(208\) 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 −0.869448 0.494025i \(-0.835525\pi\)
0.494025 + 0.869448i \(0.335525\pi\)
\(228\) 20.9137 + 20.9137i 0.00607477 + 0.00607477i
\(229\) −5693.53 −1.64297 −0.821483 0.570233i \(-0.806853\pi\)
−0.821483 + 0.570233i \(0.806853\pi\)
\(230\) 2979.42 2879.10i 0.854163 0.825401i
\(231\) −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 \(-0.755660\pi\)
0.719568 0.694422i \(-0.244340\pi\)
\(242\) −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 \(-0.825302\pi\)
0.853135 0.521690i \(-0.174698\pi\)
\(252\) 4354.80 4354.80i 1.08860 1.08860i
\(253\) 584.561 2314.86i 0.145261 0.575234i
\(254\) 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 0.503925 0.863748i \(-0.331889\pi\)
−0.863748 + 0.503925i \(0.831889\pi\)
\(264\) 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 \(0.131410\pi\)
−0.915986 + 0.401211i \(0.868590\pi\)
\(282\) 3581.06 + 3581.06i 0.756203 + 0.756203i
\(283\) −5455.86 5455.86i −1.14600 1.14600i −0.987333 0.158665i \(-0.949281\pi\)
−0.158665 0.987333i \(-0.550719\pi\)
\(284\) 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 \(0.0609412\pi\)
0.190285 + 0.981729i \(0.439059\pi\)
\(294\) 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 0.487523 0.873110i \(-0.337900\pi\)
−0.873110 + 0.487523i \(0.837900\pi\)
\(314\) 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
\(322\) −10027.7 2532.26i −1.73548 0.438252i
\(323\) −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 −0.0544068 0.998519i \(-0.517327\pi\)
0.998519 + 0.0544068i \(0.0173268\pi\)
\(338\) 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
\(345\) 8314.50 + 8604.23i 1.29750 + 1.34271i
\(346\) 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 \(-0.771636\pi\)
−0.753500 + 0.657448i \(0.771636\pi\)
\(360\) −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 −0.858150 0.513399i \(-0.828386\pi\)
0.513399 + 0.858150i \(0.328386\pi\)
\(368\) 8501.39 + 2146.81i 1.20425 + 0.304104i
\(369\) 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 0.472647 0.881252i \(-0.343299\pi\)
−0.881252 + 0.472647i \(0.843299\pi\)
\(374\) 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 \(-0.494140\pi\)
0.0184099 + 0.999831i \(0.494140\pi\)
\(380\) −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 0.673721 0.738986i \(-0.264695\pi\)
−0.738986 + 0.673721i \(0.764695\pi\)
\(384\) 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 \(-0.887809\pi\)
−0.938527 + 0.345205i \(0.887809\pi\)
\(390\) −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 \(0.256162\pi\)
−0.693287 + 0.720662i \(0.743838\pi\)
\(402\) −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 \(-0.514803\pi\)
−0.0464873 + 0.998919i \(0.514803\pi\)
\(420\) 2270.88 + 9688.61i 0.263828 + 1.12561i
\(421\) 3641.20i 0.421523i 0.977537 + 0.210762i \(0.0675944\pi\)
−0.977537 + 0.210762i \(0.932406\pi\)
\(422\) −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 \(-0.667994\pi\)
0.503608 0.863932i \(-0.332006\pi\)
\(432\) −21886.3 21886.3i −2.43751 2.43751i
\(433\) 2548.59 + 2548.59i 0.282858 + 0.282858i 0.834248 0.551390i \(-0.185902\pi\)
−0.551390 + 0.834248i \(0.685902\pi\)
\(434\) 11008.7 1.21759
\(435\) −2909.92 + 4691.62i −0.320735 + 0.517117i
\(436\) 853.589i 0.0937603i
\(437\) 99.1837 + 25.0464i 0.0108572 + 0.00274172i
\(438\) −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 −0.145721 0.989326i \(-0.546550\pi\)
0.989326 + 0.145721i \(0.0465503\pi\)
\(458\) 13525.6 + 13525.6i 1.37994 + 1.37994i
\(459\) 44974.5 4.57349
\(460\) −4053.11 69.4080i −0.410820 0.00703514i
\(461\) −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 −0.913205 0.407501i \(-0.866400\pi\)
0.407501 + 0.913205i \(0.366400\pi\)
\(468\) 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 \(-0.311078\pi\)
0.559279 + 0.828980i \(0.311078\pi\)
\(480\) −3475.25 14827.0i −0.330464 1.40991i
\(481\) 2159.65i 0.204722i
\(482\) −12343.9 + 12343.9i −1.16650 + 1.16650i
\(483\) 7312.87 28959.0i 0.688917 2.72811i
\(484\) 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 0.0522547 0.998634i \(-0.483359\pi\)
−0.998634 + 0.0522547i \(0.983359\pi\)
\(504\) 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 \(-0.976822\pi\)
0.997350 0.0727503i \(-0.0231776\pi\)
\(522\) −8116.76 8116.76i −0.680576 0.680576i
\(523\) 11704.7 + 11704.7i 0.978604 + 0.978604i 0.999776 0.0211715i \(-0.00673959\pi\)
−0.0211715 + 0.999776i \(0.506740\pi\)
\(524\) 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
\(552\) −4148.84 + 16429.4i −0.319902 + 1.26681i
\(553\) 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 −0.177779 0.984070i \(-0.556891\pi\)
0.984070 + 0.177779i \(0.0568911\pi\)
\(558\) 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 0.832029 0.554733i \(-0.187179\pi\)
−0.554733 + 0.832029i \(0.687179\pi\)
\(564\) 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 \(-0.513955\pi\)
−0.0438257 + 0.999039i \(0.513955\pi\)
\(570\) −77.1271 329.059i −0.00566754 0.0241803i
\(571\) 13728.2i 1.00614i 0.864245 + 0.503071i \(0.167797\pi\)
−0.864245 + 0.503071i \(0.832203\pi\)
\(572\) 840.889 840.889i 0.0614673 0.0614673i
\(573\) 537.167 + 537.167i 0.0391631 + 0.0391631i
\(574\) −35308.5 −2.56750
\(575\) −13476.1 + 2916.14i −0.977378 + 0.211499i
\(576\) −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
\(598\) −6005.50 1516.54i −0.410674 0.103706i
\(599\) 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 0.611808 0.791006i \(-0.290442\pi\)
−0.791006 + 0.611808i \(0.790442\pi\)
\(614\) 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 \(0.524690\pi\)
−0.996993 + 0.0774878i \(0.975310\pi\)
\(618\) −5781.72 5781.72i −0.376334 0.376334i
\(619\) 15468.8 1.00443 0.502216 0.864742i \(-0.332518\pi\)
0.502216 + 0.864742i \(0.332518\pi\)
\(620\) 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 \(-0.951059\pi\)
0.988203 0.153147i \(-0.0489409\pi\)
\(632\) −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 \(-0.615133\pi\)
0.353867 0.935296i \(-0.384867\pi\)
\(642\) 29732.9 29732.9i 1.82783 1.82783i
\(643\) −9182.06 9182.06i −0.563150 0.563150i 0.367051 0.930201i \(-0.380367\pi\)
−0.930201 + 0.367051i \(0.880367\pi\)
\(644\) 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 \(-0.288524\pi\)
0.616564 + 0.787305i \(0.288524\pi\)
\(660\) 6558.58 + 4067.88i 0.386807 + 0.239912i
\(661\) 6421.92i 0.377888i −0.981988 0.188944i \(-0.939494\pi\)
0.981988 0.188944i \(-0.0605064\pi\)
\(662\) 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
\(667\) −1374.51 + 5443.06i −0.0797919 + 0.315976i
\(668\) −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 −0.575041 0.818125i \(-0.695014\pi\)
0.818125 + 0.575041i \(0.195014\pi\)
\(678\) 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
\(690\) 688.279 40192.3i 0.0379744 2.21753i
\(691\) 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 \(0.0446463\pi\)
−0.990180 + 0.139801i \(0.955354\pi\)
\(702\) 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 \(-0.686807\pi\)
−0.553759 + 0.832677i \(0.686807\pi\)
\(710\) 6011.55 9692.34i 0.317760 0.512320i
\(711\) 6415.38i 0.338390i
\(712\) 10.5428 10.5428i 0.000554930 0.000554930i
\(713\) −12556.5 3170.84i −0.659532 0.166548i
\(714\) 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 −0.739953 0.672658i \(-0.765152\pi\)
0.672658 + 0.739953i \(0.265152\pi\)
\(728\) 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 \(0.0534848\pi\)
0.167238 + 0.985917i \(0.446515\pi\)
\(734\) 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 0.727303 0.686316i \(-0.240773\pi\)
−0.686316 + 0.727303i \(0.740773\pi\)
\(744\) 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 \(0.170368\pi\)
−0.860153 + 0.510035i \(0.829632\pi\)
\(752\) −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 −0.997054 0.0766972i \(-0.975563\pi\)
0.0766972 + 0.997054i \(0.475563\pi\)
\(758\) −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 \(-0.386572\pi\)
0.348852 + 0.937178i \(0.386572\pi\)
\(770\) −22092.0 + 5178.06i −1.03395 + 0.242343i
\(771\) −12603.2 −0.588707
\(772\) −9181.52 9181.52i −0.428044 0.428044i<