Properties

Label 245.4.e.h.116.2
Level $245$
Weight $4$
Character 245.116
Analytic conductor $14.455$
Analytic rank $0$
Dimension $4$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [245,4,Mod(116,245)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(245, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("245.116");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.e (of order \(3\), degree \(2\), not 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: \(14.4554679514\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 116.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 245.116
Dual form 245.4.e.h.226.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.29289 - 2.23936i) q^{2} +(-3.32843 + 5.76500i) q^{3} +(0.656854 - 1.13770i) q^{4} +(2.50000 + 4.33013i) q^{5} +17.2132 q^{6} -24.0833 q^{8} +(-8.65685 - 14.9941i) q^{9} +O(q^{10})\) \(q+(-1.29289 - 2.23936i) q^{2} +(-3.32843 + 5.76500i) q^{3} +(0.656854 - 1.13770i) q^{4} +(2.50000 + 4.33013i) q^{5} +17.2132 q^{6} -24.0833 q^{8} +(-8.65685 - 14.9941i) q^{9} +(6.46447 - 11.1968i) q^{10} +(-19.1274 + 33.1297i) q^{11} +(4.37258 + 7.57354i) q^{12} +19.3431 q^{13} -33.2843 q^{15} +(25.8823 + 44.8294i) q^{16} +(43.6127 - 75.5394i) q^{17} +(-22.3848 + 38.7716i) q^{18} +(22.1127 + 38.3003i) q^{19} +6.56854 q^{20} +98.9188 q^{22} +(-109.083 - 188.938i) q^{23} +(80.1594 - 138.840i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-25.0086 - 43.3162i) q^{26} -64.4802 q^{27} -46.9411 q^{29} +(43.0330 + 74.5354i) q^{30} +(-97.2792 + 168.493i) q^{31} +(-29.4071 + 50.9345i) q^{32} +(-127.328 - 220.539i) q^{33} -225.546 q^{34} -22.7452 q^{36} +(-183.426 - 317.704i) q^{37} +(57.1787 - 99.0364i) q^{38} +(-64.3823 + 111.513i) q^{39} +(-60.2082 - 104.284i) q^{40} -339.362 q^{41} -226.167 q^{43} +(25.1279 + 43.5227i) q^{44} +(43.2843 - 74.9706i) q^{45} +(-282.066 + 488.553i) q^{46} +(-5.83810 - 10.1119i) q^{47} -344.589 q^{48} +64.6447 q^{50} +(290.323 + 502.855i) q^{51} +(12.7056 - 22.0068i) q^{52} +(104.510 - 181.016i) q^{53} +(83.3661 + 144.394i) q^{54} -191.274 q^{55} -294.402 q^{57} +(60.6899 + 105.118i) q^{58} +(308.000 - 533.472i) q^{59} +(-21.8629 + 37.8677i) q^{60} +(-160.368 - 277.765i) q^{61} +503.087 q^{62} +566.197 q^{64} +(48.3579 + 83.7583i) q^{65} +(-329.244 + 570.268i) q^{66} +(-7.25483 + 12.5657i) q^{67} +(-57.2944 - 99.2368i) q^{68} +1452.30 q^{69} -952.000 q^{71} +(208.485 + 361.107i) q^{72} +(-412.245 + 714.029i) q^{73} +(-474.302 + 821.514i) q^{74} +(-83.2107 - 144.125i) q^{75} +58.0993 q^{76} +332.958 q^{78} +(-78.1375 - 135.338i) q^{79} +(-129.411 + 224.147i) q^{80} +(448.353 - 776.570i) q^{81} +(438.759 + 759.954i) q^{82} -1036.53 q^{83} +436.127 q^{85} +(292.409 + 506.468i) q^{86} +(156.240 - 270.616i) q^{87} +(460.651 - 797.870i) q^{88} +(85.1127 + 147.420i) q^{89} -223.848 q^{90} -286.607 q^{92} +(-647.574 - 1121.63i) q^{93} +(-15.0961 + 26.1472i) q^{94} +(-110.563 + 191.502i) q^{95} +(-195.759 - 339.064i) q^{96} +1059.87 q^{97} +662.333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{2} - 2 q^{3} - 20 q^{4} + 10 q^{5} - 16 q^{6} + 96 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 8 q^{2} - 2 q^{3} - 20 q^{4} + 10 q^{5} - 16 q^{6} + 96 q^{8} - 12 q^{9} + 40 q^{10} + 14 q^{11} + 108 q^{12} + 100 q^{13} - 20 q^{15} - 168 q^{16} + 50 q^{17} - 16 q^{18} - 36 q^{19} - 200 q^{20} - 368 q^{22} - 244 q^{23} + 496 q^{24} - 50 q^{25} - 216 q^{26} + 172 q^{27} - 52 q^{29} - 40 q^{30} + 120 q^{31} - 672 q^{32} - 498 q^{33} - 48 q^{34} - 272 q^{36} - 564 q^{37} - 320 q^{38} + 14 q^{39} + 240 q^{40} - 656 q^{41} - 520 q^{43} + 1164 q^{44} + 60 q^{45} - 704 q^{46} + 350 q^{47} - 2736 q^{48} + 400 q^{50} + 754 q^{51} - 628 q^{52} + 56 q^{53} - 648 q^{54} + 140 q^{55} - 1336 q^{57} + 8 q^{58} + 1232 q^{59} - 540 q^{60} - 336 q^{61} - 2400 q^{62} + 4256 q^{64} + 250 q^{65} - 1976 q^{66} + 152 q^{67} - 908 q^{68} + 2664 q^{69} - 3808 q^{71} + 800 q^{72} - 676 q^{73} - 2016 q^{74} - 50 q^{75} + 3536 q^{76} - 880 q^{78} - 1014 q^{79} + 840 q^{80} + 1454 q^{81} + 816 q^{82} - 752 q^{83} + 500 q^{85} + 768 q^{86} + 410 q^{87} + 4688 q^{88} + 216 q^{89} - 160 q^{90} + 528 q^{92} - 2760 q^{93} + 1928 q^{94} + 180 q^{95} + 2464 q^{96} + 5484 q^{97} + 1880 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.29289 2.23936i −0.457107 0.791732i 0.541700 0.840572i \(-0.317781\pi\)
−0.998807 + 0.0488398i \(0.984448\pi\)
\(3\) −3.32843 + 5.76500i −0.640556 + 1.10948i 0.344753 + 0.938694i \(0.387963\pi\)
−0.985309 + 0.170782i \(0.945371\pi\)
\(4\) 0.656854 1.13770i 0.0821068 0.142213i
\(5\) 2.50000 + 4.33013i 0.223607 + 0.387298i
\(6\) 17.2132 1.17121
\(7\) 0 0
\(8\) −24.0833 −1.06434
\(9\) −8.65685 14.9941i −0.320624 0.555337i
\(10\) 6.46447 11.1968i 0.204424 0.354073i
\(11\) −19.1274 + 33.1297i −0.524285 + 0.908088i 0.475315 + 0.879815i \(0.342334\pi\)
−0.999600 + 0.0282725i \(0.990999\pi\)
\(12\) 4.37258 + 7.57354i 0.105188 + 0.182191i
\(13\) 19.3431 0.412679 0.206339 0.978480i \(-0.433845\pi\)
0.206339 + 0.978480i \(0.433845\pi\)
\(14\) 0 0
\(15\) −33.2843 −0.572931
\(16\) 25.8823 + 44.8294i 0.404410 + 0.700459i
\(17\) 43.6127 75.5394i 0.622214 1.07771i −0.366859 0.930277i \(-0.619567\pi\)
0.989073 0.147429i \(-0.0470998\pi\)
\(18\) −22.3848 + 38.7716i −0.293119 + 0.507697i
\(19\) 22.1127 + 38.3003i 0.267000 + 0.462458i 0.968086 0.250619i \(-0.0806343\pi\)
−0.701086 + 0.713077i \(0.747301\pi\)
\(20\) 6.56854 0.0734385
\(21\) 0 0
\(22\) 98.9188 0.958617
\(23\) −109.083 188.938i −0.988932 1.71288i −0.622959 0.782255i \(-0.714069\pi\)
−0.365973 0.930625i \(-0.619264\pi\)
\(24\) 80.1594 138.840i 0.681769 1.18086i
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) −25.0086 43.3162i −0.188638 0.326731i
\(27\) −64.4802 −0.459601
\(28\) 0 0
\(29\) −46.9411 −0.300578 −0.150289 0.988642i \(-0.548020\pi\)
−0.150289 + 0.988642i \(0.548020\pi\)
\(30\) 43.0330 + 74.5354i 0.261891 + 0.453608i
\(31\) −97.2792 + 168.493i −0.563609 + 0.976199i 0.433569 + 0.901120i \(0.357254\pi\)
−0.997178 + 0.0750783i \(0.976079\pi\)
\(32\) −29.4071 + 50.9345i −0.162453 + 0.281376i
\(33\) −127.328 220.539i −0.671668 1.16336i
\(34\) −225.546 −1.13767
\(35\) 0 0
\(36\) −22.7452 −0.105302
\(37\) −183.426 317.704i −0.815003 1.41163i −0.909326 0.416085i \(-0.863402\pi\)
0.0943225 0.995542i \(-0.469932\pi\)
\(38\) 57.1787 99.0364i 0.244095 0.422785i
\(39\) −64.3823 + 111.513i −0.264344 + 0.457857i
\(40\) −60.2082 104.284i −0.237994 0.412217i
\(41\) −339.362 −1.29267 −0.646336 0.763053i \(-0.723699\pi\)
−0.646336 + 0.763053i \(0.723699\pi\)
\(42\) 0 0
\(43\) −226.167 −0.802095 −0.401047 0.916057i \(-0.631354\pi\)
−0.401047 + 0.916057i \(0.631354\pi\)
\(44\) 25.1279 + 43.5227i 0.0860947 + 0.149120i
\(45\) 43.2843 74.9706i 0.143388 0.248354i
\(46\) −282.066 + 488.553i −0.904095 + 1.56594i
\(47\) −5.83810 10.1119i −0.0181186 0.0313823i 0.856824 0.515609i \(-0.172434\pi\)
−0.874943 + 0.484227i \(0.839101\pi\)
\(48\) −344.589 −1.03619
\(49\) 0 0
\(50\) 64.6447 0.182843
\(51\) 290.323 + 502.855i 0.797126 + 1.38066i
\(52\) 12.7056 22.0068i 0.0338837 0.0586883i
\(53\) 104.510 181.016i 0.270859 0.469141i −0.698223 0.715880i \(-0.746026\pi\)
0.969082 + 0.246739i \(0.0793591\pi\)
\(54\) 83.3661 + 144.394i 0.210087 + 0.363881i
\(55\) −191.274 −0.468935
\(56\) 0 0
\(57\) −294.402 −0.684114
\(58\) 60.6899 + 105.118i 0.137396 + 0.237977i
\(59\) 308.000 533.472i 0.679630 1.17715i −0.295462 0.955354i \(-0.595474\pi\)
0.975092 0.221800i \(-0.0711931\pi\)
\(60\) −21.8629 + 37.8677i −0.0470415 + 0.0814783i
\(61\) −160.368 277.765i −0.336606 0.583018i 0.647186 0.762332i \(-0.275946\pi\)
−0.983792 + 0.179314i \(0.942612\pi\)
\(62\) 503.087 1.03052
\(63\) 0 0
\(64\) 566.197 1.10585
\(65\) 48.3579 + 83.7583i 0.0922778 + 0.159830i
\(66\) −329.244 + 570.268i −0.614048 + 1.06356i
\(67\) −7.25483 + 12.5657i −0.0132286 + 0.0229127i −0.872564 0.488500i \(-0.837544\pi\)
0.859335 + 0.511413i \(0.170878\pi\)
\(68\) −57.2944 99.2368i −0.102176 0.176974i
\(69\) 1452.30 2.53387
\(70\) 0 0
\(71\) −952.000 −1.59129 −0.795645 0.605763i \(-0.792868\pi\)
−0.795645 + 0.605763i \(0.792868\pi\)
\(72\) 208.485 + 361.107i 0.341253 + 0.591068i
\(73\) −412.245 + 714.029i −0.660953 + 1.14480i 0.319412 + 0.947616i \(0.396515\pi\)
−0.980366 + 0.197189i \(0.936819\pi\)
\(74\) −474.302 + 821.514i −0.745087 + 1.29053i
\(75\) −83.2107 144.125i −0.128111 0.221895i
\(76\) 58.0993 0.0876901
\(77\) 0 0
\(78\) 332.958 0.483334
\(79\) −78.1375 135.338i −0.111280 0.192743i 0.805006 0.593266i \(-0.202162\pi\)
−0.916287 + 0.400523i \(0.868829\pi\)
\(80\) −129.411 + 224.147i −0.180858 + 0.313255i
\(81\) 448.353 776.570i 0.615024 1.06525i
\(82\) 438.759 + 759.954i 0.590889 + 1.02345i
\(83\) −1036.53 −1.37077 −0.685384 0.728182i \(-0.740366\pi\)
−0.685384 + 0.728182i \(0.740366\pi\)
\(84\) 0 0
\(85\) 436.127 0.556525
\(86\) 292.409 + 506.468i 0.366643 + 0.635044i
\(87\) 156.240 270.616i 0.192537 0.333483i
\(88\) 460.651 797.870i 0.558017 0.966514i
\(89\) 85.1127 + 147.420i 0.101370 + 0.175578i 0.912249 0.409635i \(-0.134344\pi\)
−0.810879 + 0.585213i \(0.801011\pi\)
\(90\) −223.848 −0.262174
\(91\) 0 0
\(92\) −286.607 −0.324792
\(93\) −647.574 1121.63i −0.722046 1.25062i
\(94\) −15.0961 + 26.1472i −0.0165643 + 0.0286901i
\(95\) −110.563 + 191.502i −0.119406 + 0.206817i
\(96\) −195.759 339.064i −0.208120 0.360475i
\(97\) 1059.87 1.10942 0.554710 0.832044i \(-0.312829\pi\)
0.554710 + 0.832044i \(0.312829\pi\)
\(98\) 0 0
\(99\) 662.333 0.672394
\(100\) 16.4214 + 28.4426i 0.0164214 + 0.0284426i
\(101\) 120.917 209.434i 0.119125 0.206331i −0.800296 0.599605i \(-0.795324\pi\)
0.919421 + 0.393274i \(0.128658\pi\)
\(102\) 750.714 1300.28i 0.728743 1.26222i
\(103\) 839.788 + 1454.56i 0.803367 + 1.39147i 0.917388 + 0.397994i \(0.130294\pi\)
−0.114021 + 0.993478i \(0.536373\pi\)
\(104\) −465.846 −0.439230
\(105\) 0 0
\(106\) −540.479 −0.495245
\(107\) −753.441 1305.00i −0.680728 1.17905i −0.974759 0.223259i \(-0.928330\pi\)
0.294031 0.955796i \(-0.405003\pi\)
\(108\) −42.3541 + 73.3595i −0.0377364 + 0.0653613i
\(109\) 626.205 1084.62i 0.550271 0.953097i −0.447984 0.894042i \(-0.647858\pi\)
0.998255 0.0590556i \(-0.0188089\pi\)
\(110\) 247.297 + 428.331i 0.214353 + 0.371271i
\(111\) 2442.09 2.08822
\(112\) 0 0
\(113\) 1370.20 1.14069 0.570345 0.821405i \(-0.306810\pi\)
0.570345 + 0.821405i \(0.306810\pi\)
\(114\) 380.630 + 659.271i 0.312713 + 0.541635i
\(115\) 545.416 944.689i 0.442264 0.766023i
\(116\) −30.8335 + 53.4052i −0.0246795 + 0.0427461i
\(117\) −167.451 290.033i −0.132315 0.229176i
\(118\) −1592.84 −1.24265
\(119\) 0 0
\(120\) 801.594 0.609793
\(121\) −66.2162 114.690i −0.0497492 0.0861681i
\(122\) −414.676 + 718.240i −0.307730 + 0.533003i
\(123\) 1129.54 1956.43i 0.828028 1.43419i
\(124\) 127.797 + 221.350i 0.0925522 + 0.160305i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 1213.49 0.847873 0.423936 0.905692i \(-0.360648\pi\)
0.423936 + 0.905692i \(0.360648\pi\)
\(128\) −496.775 860.440i −0.343040 0.594163i
\(129\) 752.779 1303.85i 0.513787 0.889905i
\(130\) 125.043 216.581i 0.0843616 0.146119i
\(131\) 991.209 + 1716.83i 0.661087 + 1.14504i 0.980330 + 0.197363i \(0.0632378\pi\)
−0.319244 + 0.947673i \(0.603429\pi\)
\(132\) −334.545 −0.220594
\(133\) 0 0
\(134\) 37.5189 0.0241876
\(135\) −161.201 279.208i −0.102770 0.178003i
\(136\) −1050.34 + 1819.24i −0.662247 + 1.14705i
\(137\) −1105.47 + 1914.74i −0.689394 + 1.19407i 0.282640 + 0.959226i \(0.408790\pi\)
−0.972034 + 0.234840i \(0.924543\pi\)
\(138\) −1877.67 3252.22i −1.15825 2.00614i
\(139\) 528.039 0.322213 0.161107 0.986937i \(-0.448494\pi\)
0.161107 + 0.986937i \(0.448494\pi\)
\(140\) 0 0
\(141\) 77.7267 0.0464239
\(142\) 1230.83 + 2131.87i 0.727390 + 1.25988i
\(143\) −369.984 + 640.832i −0.216361 + 0.374749i
\(144\) 448.118 776.163i 0.259327 0.449168i
\(145\) −117.353 203.261i −0.0672112 0.116413i
\(146\) 2131.95 1.20851
\(147\) 0 0
\(148\) −481.938 −0.267669
\(149\) 164.186 + 284.378i 0.0902727 + 0.156357i 0.907626 0.419780i \(-0.137893\pi\)
−0.817353 + 0.576137i \(0.804559\pi\)
\(150\) −215.165 + 372.677i −0.117121 + 0.202860i
\(151\) −514.714 + 891.512i −0.277396 + 0.480465i −0.970737 0.240145i \(-0.922805\pi\)
0.693340 + 0.720610i \(0.256138\pi\)
\(152\) −532.546 922.397i −0.284179 0.492212i
\(153\) −1510.20 −0.797987
\(154\) 0 0
\(155\) −972.792 −0.504107
\(156\) 84.5795 + 146.496i 0.0434088 + 0.0751863i
\(157\) −262.549 + 454.749i −0.133463 + 0.231165i −0.925009 0.379944i \(-0.875943\pi\)
0.791546 + 0.611109i \(0.209276\pi\)
\(158\) −202.047 + 349.956i −0.101734 + 0.176209i
\(159\) 695.706 + 1205.00i 0.347000 + 0.601022i
\(160\) −294.071 −0.145302
\(161\) 0 0
\(162\) −2318.69 −1.12453
\(163\) −501.313 868.299i −0.240895 0.417242i 0.720075 0.693897i \(-0.244108\pi\)
−0.960969 + 0.276655i \(0.910774\pi\)
\(164\) −222.912 + 386.094i −0.106137 + 0.183835i
\(165\) 636.642 1102.70i 0.300379 0.520272i
\(166\) 1340.12 + 2321.16i 0.626587 + 1.08528i
\(167\) −359.422 −0.166544 −0.0832722 0.996527i \(-0.526537\pi\)
−0.0832722 + 0.996527i \(0.526537\pi\)
\(168\) 0 0
\(169\) −1822.84 −0.829696
\(170\) −563.866 976.644i −0.254391 0.440619i
\(171\) 382.853 663.121i 0.171213 0.296550i
\(172\) −148.558 + 257.311i −0.0658574 + 0.114068i
\(173\) −1646.83 2852.39i −0.723733 1.25354i −0.959493 0.281732i \(-0.909091\pi\)
0.235760 0.971811i \(-0.424242\pi\)
\(174\) −808.007 −0.352039
\(175\) 0 0
\(176\) −1980.24 −0.848104
\(177\) 2050.31 + 3551.24i 0.870683 + 1.50807i
\(178\) 220.083 381.195i 0.0926738 0.160516i
\(179\) −1489.41 + 2579.74i −0.621921 + 1.07720i 0.367207 + 0.930139i \(0.380314\pi\)
−0.989128 + 0.147059i \(0.953019\pi\)
\(180\) −56.8629 98.4895i −0.0235462 0.0407832i
\(181\) 1462.31 0.600514 0.300257 0.953858i \(-0.402928\pi\)
0.300257 + 0.953858i \(0.402928\pi\)
\(182\) 0 0
\(183\) 2135.09 0.862460
\(184\) 2627.08 + 4550.24i 1.05256 + 1.82309i
\(185\) 917.132 1588.52i 0.364480 0.631299i
\(186\) −1674.49 + 2900.30i −0.660104 + 1.14333i
\(187\) 1668.40 + 2889.75i 0.652434 + 1.13005i
\(188\) −15.3391 −0.00595064
\(189\) 0 0
\(190\) 571.787 0.218325
\(191\) 187.461 + 324.693i 0.0710169 + 0.123005i 0.899347 0.437235i \(-0.144042\pi\)
−0.828330 + 0.560240i \(0.810709\pi\)
\(192\) −1884.54 + 3264.13i −0.708361 + 1.22692i
\(193\) −366.514 + 634.821i −0.136696 + 0.236764i −0.926244 0.376925i \(-0.876982\pi\)
0.789548 + 0.613688i \(0.210315\pi\)
\(194\) −1370.30 2373.43i −0.507124 0.878364i
\(195\) −643.823 −0.236436
\(196\) 0 0
\(197\) −2093.24 −0.757043 −0.378521 0.925593i \(-0.623567\pi\)
−0.378521 + 0.925593i \(0.623567\pi\)
\(198\) −856.326 1483.20i −0.307356 0.532356i
\(199\) −1432.52 + 2481.20i −0.510295 + 0.883856i 0.489634 + 0.871928i \(0.337130\pi\)
−0.999929 + 0.0119283i \(0.996203\pi\)
\(200\) 301.041 521.418i 0.106434 0.184349i
\(201\) −48.2944 83.6483i −0.0169474 0.0293537i
\(202\) −625.330 −0.217812
\(203\) 0 0
\(204\) 762.801 0.261798
\(205\) −848.406 1469.48i −0.289050 0.500649i
\(206\) 2171.51 3761.17i 0.734449 1.27210i
\(207\) −1888.64 + 3271.21i −0.634151 + 1.09838i
\(208\) 500.644 + 867.141i 0.166891 + 0.289065i
\(209\) −1691.84 −0.559936
\(210\) 0 0
\(211\) 5643.65 1.84135 0.920674 0.390331i \(-0.127640\pi\)
0.920674 + 0.390331i \(0.127640\pi\)
\(212\) −137.295 237.802i −0.0444787 0.0770393i
\(213\) 3168.66 5488.28i 1.01931 1.76550i
\(214\) −1948.24 + 3374.44i −0.622330 + 1.07791i
\(215\) −565.416 979.330i −0.179354 0.310650i
\(216\) 1552.89 0.489172
\(217\) 0 0
\(218\) −3238.46 −1.00613
\(219\) −2744.25 4753.19i −0.846755 1.46662i
\(220\) −125.639 + 217.614i −0.0385027 + 0.0666887i
\(221\) 843.607 1461.17i 0.256774 0.444746i
\(222\) −3157.36 5468.70i −0.954540 1.65331i
\(223\) −6369.16 −1.91260 −0.956302 0.292381i \(-0.905552\pi\)
−0.956302 + 0.292381i \(0.905552\pi\)
\(224\) 0 0
\(225\) 432.843 0.128250
\(226\) −1771.53 3068.37i −0.521417 0.903120i
\(227\) 507.837 879.600i 0.148486 0.257185i −0.782182 0.623050i \(-0.785893\pi\)
0.930668 + 0.365865i \(0.119227\pi\)
\(228\) −193.379 + 334.943i −0.0561704 + 0.0972900i
\(229\) −2054.18 3557.94i −0.592768 1.02670i −0.993858 0.110665i \(-0.964702\pi\)
0.401090 0.916039i \(-0.368632\pi\)
\(230\) −2820.66 −0.808647
\(231\) 0 0
\(232\) 1130.50 0.319917
\(233\) −304.215 526.916i −0.0855357 0.148152i 0.820084 0.572244i \(-0.193927\pi\)
−0.905619 + 0.424092i \(0.860593\pi\)
\(234\) −432.992 + 749.964i −0.120964 + 0.209516i
\(235\) 29.1905 50.5594i 0.00810288 0.0140346i
\(236\) −404.622 700.826i −0.111605 0.193305i
\(237\) 1040.30 0.285126
\(238\) 0 0
\(239\) −5054.44 −1.36797 −0.683985 0.729496i \(-0.739755\pi\)
−0.683985 + 0.729496i \(0.739755\pi\)
\(240\) −861.472 1492.11i −0.231699 0.401315i
\(241\) −2.43391 + 4.21565i −0.000650547 + 0.00112678i −0.866350 0.499437i \(-0.833540\pi\)
0.865700 + 0.500563i \(0.166874\pi\)
\(242\) −171.221 + 296.563i −0.0454814 + 0.0787761i
\(243\) 2114.14 + 3661.79i 0.558115 + 0.966683i
\(244\) −421.352 −0.110551
\(245\) 0 0
\(246\) −5841.52 −1.51399
\(247\) 427.729 + 740.849i 0.110185 + 0.190846i
\(248\) 2342.80 4057.85i 0.599871 1.03901i
\(249\) 3450.01 5975.59i 0.878054 1.52083i
\(250\) 161.612 + 279.920i 0.0408849 + 0.0708147i
\(251\) −547.921 −0.137787 −0.0688934 0.997624i \(-0.521947\pi\)
−0.0688934 + 0.997624i \(0.521947\pi\)
\(252\) 0 0
\(253\) 8345.92 2.07393
\(254\) −1568.91 2717.44i −0.387568 0.671288i
\(255\) −1451.62 + 2514.27i −0.356485 + 0.617451i
\(256\) 980.232 1697.81i 0.239314 0.414505i
\(257\) 887.306 + 1536.86i 0.215364 + 0.373022i 0.953385 0.301756i \(-0.0975728\pi\)
−0.738021 + 0.674778i \(0.764239\pi\)
\(258\) −3893.05 −0.939421
\(259\) 0 0
\(260\) 127.056 0.0303065
\(261\) 406.362 + 703.840i 0.0963724 + 0.166922i
\(262\) 2563.06 4439.34i 0.604374 1.04681i
\(263\) 599.547 1038.45i 0.140569 0.243473i −0.787142 0.616772i \(-0.788440\pi\)
0.927711 + 0.373299i \(0.121774\pi\)
\(264\) 3066.48 + 5311.31i 0.714883 + 1.23821i
\(265\) 1045.10 0.242263
\(266\) 0 0
\(267\) −1133.17 −0.259733
\(268\) 9.53074 + 16.5077i 0.00217232 + 0.00376257i
\(269\) −1625.15 + 2814.84i −0.368353 + 0.638006i −0.989308 0.145840i \(-0.953411\pi\)
0.620955 + 0.783846i \(0.286745\pi\)
\(270\) −416.830 + 721.971i −0.0939536 + 0.162732i
\(271\) 448.071 + 776.082i 0.100437 + 0.173962i 0.911865 0.410491i \(-0.134643\pi\)
−0.811428 + 0.584453i \(0.801309\pi\)
\(272\) 4515.18 1.00652
\(273\) 0 0
\(274\) 5717.04 1.26051
\(275\) −478.185 828.241i −0.104857 0.181618i
\(276\) 953.951 1652.29i 0.208048 0.360349i
\(277\) 193.281 334.772i 0.0419246 0.0726156i −0.844302 0.535868i \(-0.819984\pi\)
0.886226 + 0.463253i \(0.153318\pi\)
\(278\) −682.698 1182.47i −0.147286 0.255107i
\(279\) 3368.53 0.722826
\(280\) 0 0
\(281\) −3335.10 −0.708025 −0.354013 0.935241i \(-0.615183\pi\)
−0.354013 + 0.935241i \(0.615183\pi\)
\(282\) −100.492 174.058i −0.0212207 0.0367553i
\(283\) −2706.13 + 4687.15i −0.568419 + 0.984531i 0.428303 + 0.903635i \(0.359111\pi\)
−0.996723 + 0.0808959i \(0.974222\pi\)
\(284\) −625.325 + 1083.10i −0.130656 + 0.226302i
\(285\) −736.005 1274.80i −0.152973 0.264956i
\(286\) 1913.40 0.395601
\(287\) 0 0
\(288\) 1018.29 0.208345
\(289\) −1347.63 2334.17i −0.274300 0.475101i
\(290\) −303.449 + 525.590i −0.0614454 + 0.106427i
\(291\) −3527.71 + 6110.17i −0.710646 + 1.23088i
\(292\) 541.569 + 938.026i 0.108538 + 0.187992i
\(293\) 282.211 0.0562695 0.0281347 0.999604i \(-0.491043\pi\)
0.0281347 + 0.999604i \(0.491043\pi\)
\(294\) 0 0
\(295\) 3080.00 0.607880
\(296\) 4417.51 + 7651.34i 0.867440 + 1.50245i
\(297\) 1233.34 2136.21i 0.240962 0.417358i
\(298\) 424.550 735.341i 0.0825285 0.142944i
\(299\) −2110.01 3654.65i −0.408111 0.706869i
\(300\) −218.629 −0.0420752
\(301\) 0 0
\(302\) 2661.88 0.507199
\(303\) 804.925 + 1394.17i 0.152613 + 0.264333i
\(304\) −1144.65 + 1982.60i −0.215955 + 0.374045i
\(305\) 801.838 1388.82i 0.150535 0.260734i
\(306\) 1952.52 + 3381.87i 0.364765 + 0.631792i
\(307\) 1919.67 0.356878 0.178439 0.983951i \(-0.442895\pi\)
0.178439 + 0.983951i \(0.442895\pi\)
\(308\) 0 0
\(309\) −11180.7 −2.05841
\(310\) 1257.72 + 2178.43i 0.230431 + 0.399118i
\(311\) −606.654 + 1050.76i −0.110612 + 0.191585i −0.916017 0.401139i \(-0.868614\pi\)
0.805405 + 0.592724i \(0.201948\pi\)
\(312\) 1550.53 2685.60i 0.281352 0.487315i
\(313\) 717.001 + 1241.88i 0.129480 + 0.224266i 0.923475 0.383658i \(-0.125336\pi\)
−0.793995 + 0.607924i \(0.792002\pi\)
\(314\) 1357.79 0.244028
\(315\) 0 0
\(316\) −205.300 −0.0365475
\(317\) −3248.48 5626.52i −0.575560 0.996899i −0.995981 0.0895699i \(-0.971451\pi\)
0.420420 0.907329i \(-0.361883\pi\)
\(318\) 1798.95 3115.87i 0.317232 0.549463i
\(319\) 897.862 1555.14i 0.157588 0.272951i
\(320\) 1415.49 + 2451.70i 0.247276 + 0.428295i
\(321\) 10031.1 1.74418
\(322\) 0 0
\(323\) 3857.58 0.664524
\(324\) −589.005 1020.19i −0.100995 0.174929i
\(325\) −241.789 + 418.791i −0.0412679 + 0.0714781i
\(326\) −1296.29 + 2245.24i −0.220229 + 0.381448i
\(327\) 4168.55 + 7220.15i 0.704959 + 1.22102i
\(328\) 8172.96 1.37584
\(329\) 0 0
\(330\) −3292.44 −0.549221
\(331\) 4841.94 + 8386.49i 0.804039 + 1.39264i 0.916938 + 0.399031i \(0.130653\pi\)
−0.112898 + 0.993607i \(0.536013\pi\)
\(332\) −680.848 + 1179.26i −0.112549 + 0.194941i
\(333\) −3175.79 + 5500.63i −0.522619 + 0.905204i
\(334\) 464.695 + 804.875i 0.0761286 + 0.131859i
\(335\) −72.5483 −0.0118321
\(336\) 0 0
\(337\) 29.1319 0.00470895 0.00235447 0.999997i \(-0.499251\pi\)
0.00235447 + 0.999997i \(0.499251\pi\)
\(338\) 2356.74 + 4082.00i 0.379260 + 0.656897i
\(339\) −4560.62 + 7899.23i −0.730676 + 1.26557i
\(340\) 286.472 496.184i 0.0456945 0.0791451i
\(341\) −3721.40 6445.65i −0.590983 1.02361i
\(342\) −1979.95 −0.313051
\(343\) 0 0
\(344\) 5446.83 0.853701
\(345\) 3630.76 + 6288.66i 0.566590 + 0.981362i
\(346\) −4258.34 + 7375.66i −0.661647 + 1.14601i
\(347\) 3924.29 6797.07i 0.607110 1.05154i −0.384605 0.923081i \(-0.625662\pi\)
0.991714 0.128463i \(-0.0410045\pi\)
\(348\) −205.254 355.510i −0.0316171 0.0547625i
\(349\) −10269.6 −1.57513 −0.787567 0.616229i \(-0.788659\pi\)
−0.787567 + 0.616229i \(0.788659\pi\)
\(350\) 0 0
\(351\) −1247.25 −0.189668
\(352\) −1124.96 1948.49i −0.170343 0.295043i
\(353\) −1399.97 + 2424.81i −0.211084 + 0.365609i −0.952054 0.305930i \(-0.901033\pi\)
0.740970 + 0.671538i \(0.234366\pi\)
\(354\) 5301.67 9182.76i 0.795990 1.37869i
\(355\) −2380.00 4122.28i −0.355823 0.616304i
\(356\) 223.627 0.0332927
\(357\) 0 0
\(358\) 7702.60 1.13714
\(359\) 1581.65 + 2739.49i 0.232524 + 0.402743i 0.958550 0.284924i \(-0.0919683\pi\)
−0.726026 + 0.687667i \(0.758635\pi\)
\(360\) −1042.43 + 1805.54i −0.152613 + 0.264334i
\(361\) 2451.56 4246.22i 0.357422 0.619073i
\(362\) −1890.62 3274.64i −0.274499 0.475446i
\(363\) 881.583 0.127469
\(364\) 0 0
\(365\) −4122.45 −0.591175
\(366\) −2760.44 4781.22i −0.394236 0.682837i
\(367\) −1591.42 + 2756.42i −0.226353 + 0.392055i −0.956725 0.290995i \(-0.906014\pi\)
0.730371 + 0.683050i \(0.239347\pi\)
\(368\) 5646.64 9780.27i 0.799868 1.38541i
\(369\) 2937.81 + 5088.44i 0.414462 + 0.717869i
\(370\) −4743.02 −0.666426
\(371\) 0 0
\(372\) −1701.45 −0.237139
\(373\) 1307.57 + 2264.78i 0.181510 + 0.314385i 0.942395 0.334502i \(-0.108568\pi\)
−0.760885 + 0.648887i \(0.775235\pi\)
\(374\) 4314.12 7472.27i 0.596464 1.03311i
\(375\) 416.053 720.626i 0.0572931 0.0992345i
\(376\) 140.600 + 243.527i 0.0192843 + 0.0334015i
\(377\) −907.989 −0.124042
\(378\) 0 0
\(379\) −672.434 −0.0911362 −0.0455681 0.998961i \(-0.514510\pi\)
−0.0455681 + 0.998961i \(0.514510\pi\)
\(380\) 145.248 + 251.577i 0.0196081 + 0.0339622i
\(381\) −4039.01 + 6995.78i −0.543110 + 0.940694i
\(382\) 484.735 839.586i 0.0649246 0.112453i
\(383\) −584.928 1013.13i −0.0780377 0.135165i 0.824366 0.566058i \(-0.191532\pi\)
−0.902403 + 0.430893i \(0.858199\pi\)
\(384\) 6613.92 0.878946
\(385\) 0 0
\(386\) 1895.45 0.249938
\(387\) 1957.89 + 3391.17i 0.257171 + 0.445433i
\(388\) 696.182 1205.82i 0.0910910 0.157774i
\(389\) 561.110 971.871i 0.0731347 0.126673i −0.827139 0.561998i \(-0.810033\pi\)
0.900274 + 0.435325i \(0.143366\pi\)
\(390\) 832.394 + 1441.75i 0.108077 + 0.187194i
\(391\) −19029.7 −2.46131
\(392\) 0 0
\(393\) −13196.7 −1.69385
\(394\) 2706.34 + 4687.52i 0.346049 + 0.599375i
\(395\) 390.688 676.691i 0.0497661 0.0861975i
\(396\) 435.056 753.540i 0.0552081 0.0956232i
\(397\) 992.963 + 1719.86i 0.125530 + 0.217424i 0.921940 0.387333i \(-0.126604\pi\)
−0.796410 + 0.604757i \(0.793270\pi\)
\(398\) 7408.38 0.933037
\(399\) 0 0
\(400\) −1294.11 −0.161764
\(401\) 2086.19 + 3613.38i 0.259799 + 0.449984i 0.966188 0.257839i \(-0.0830105\pi\)
−0.706389 + 0.707824i \(0.749677\pi\)
\(402\) −124.879 + 216.297i −0.0154935 + 0.0268356i
\(403\) −1881.69 + 3259.18i −0.232589 + 0.402856i
\(404\) −158.849 275.135i −0.0195620 0.0338824i
\(405\) 4483.53 0.550095
\(406\) 0 0
\(407\) 14033.9 1.70918
\(408\) −6991.93 12110.4i −0.848412 1.46949i
\(409\) 5850.40 10133.2i 0.707295 1.22507i −0.258562 0.965995i \(-0.583249\pi\)
0.965857 0.259076i \(-0.0834180\pi\)
\(410\) −2193.80 + 3799.77i −0.264253 + 0.457700i
\(411\) −7358.98 12746.1i −0.883192 1.52973i
\(412\) 2206.47 0.263848
\(413\) 0 0
\(414\) 9767.22 1.15950
\(415\) −2591.32 4488.30i −0.306513 0.530896i
\(416\) −568.825 + 985.234i −0.0670408 + 0.116118i
\(417\) −1757.54 + 3044.15i −0.206396 + 0.357488i
\(418\) 2187.36 + 3788.62i 0.255951 + 0.443320i
\(419\) 2733.20 0.318677 0.159339 0.987224i \(-0.449064\pi\)
0.159339 + 0.987224i \(0.449064\pi\)
\(420\) 0 0
\(421\) 13549.4 1.56854 0.784272 0.620417i \(-0.213037\pi\)
0.784272 + 0.620417i \(0.213037\pi\)
\(422\) −7296.63 12638.1i −0.841693 1.45786i
\(423\) −101.079 + 175.074i −0.0116185 + 0.0201239i
\(424\) −2516.93 + 4359.46i −0.288286 + 0.499325i
\(425\) 1090.32 + 1888.49i 0.124443 + 0.215541i
\(426\) −16387.0 −1.86374
\(427\) 0 0
\(428\) −1979.60 −0.223569
\(429\) −2462.93 4265.92i −0.277183 0.480095i
\(430\) −1462.05 + 2532.34i −0.163968 + 0.284000i
\(431\) 3214.63 5567.90i 0.359265 0.622265i −0.628573 0.777750i \(-0.716361\pi\)
0.987838 + 0.155485i \(0.0496942\pi\)
\(432\) −1668.89 2890.61i −0.185867 0.321932i
\(433\) 8022.03 0.890333 0.445166 0.895448i \(-0.353145\pi\)
0.445166 + 0.895448i \(0.353145\pi\)
\(434\) 0 0
\(435\) 1562.40 0.172210
\(436\) −822.651 1424.87i −0.0903620 0.156512i
\(437\) 4824.25 8355.85i 0.528090 0.914678i
\(438\) −7096.05 + 12290.7i −0.774115 + 1.34081i
\(439\) 2784.94 + 4823.66i 0.302774 + 0.524421i 0.976763 0.214321i \(-0.0687538\pi\)
−0.673989 + 0.738741i \(0.735420\pi\)
\(440\) 4606.51 0.499106
\(441\) 0 0
\(442\) −4362.77 −0.469493
\(443\) 2743.11 + 4751.20i 0.294196 + 0.509563i 0.974798 0.223091i \(-0.0716148\pi\)
−0.680601 + 0.732654i \(0.738281\pi\)
\(444\) 1604.09 2778.37i 0.171457 0.296972i
\(445\) −425.563 + 737.098i −0.0453340 + 0.0785208i
\(446\) 8234.65 + 14262.8i 0.874264 + 1.51427i
\(447\) −2185.92 −0.231299
\(448\) 0 0
\(449\) −7232.67 −0.760203 −0.380101 0.924945i \(-0.624111\pi\)
−0.380101 + 0.924945i \(0.624111\pi\)
\(450\) −559.619 969.289i −0.0586238 0.101539i
\(451\) 6491.13 11243.0i 0.677728 1.17386i
\(452\) 900.024 1558.89i 0.0936583 0.162221i
\(453\) −3426.38 5934.66i −0.355376 0.615529i
\(454\) −2626.32 −0.271496
\(455\) 0 0
\(456\) 7090.16 0.728130
\(457\) 1450.25 + 2511.91i 0.148446 + 0.257117i 0.930653 0.365902i \(-0.119239\pi\)
−0.782207 + 0.623019i \(0.785906\pi\)
\(458\) −5311.66 + 9200.07i −0.541916 + 0.938627i
\(459\) −2812.16 + 4870.80i −0.285970 + 0.495315i
\(460\) −716.518 1241.05i −0.0726257 0.125791i
\(461\) 6073.57 0.613611 0.306805 0.951772i \(-0.400740\pi\)
0.306805 + 0.951772i \(0.400740\pi\)
\(462\) 0 0
\(463\) −18922.8 −1.89939 −0.949693 0.313183i \(-0.898605\pi\)
−0.949693 + 0.313183i \(0.898605\pi\)
\(464\) −1214.94 2104.34i −0.121557 0.210542i
\(465\) 3237.87 5608.15i 0.322909 0.559294i
\(466\) −786.636 + 1362.49i −0.0781979 + 0.135443i
\(467\) 3388.35 + 5868.80i 0.335748 + 0.581532i 0.983628 0.180210i \(-0.0576777\pi\)
−0.647880 + 0.761742i \(0.724344\pi\)
\(468\) −439.963 −0.0434558
\(469\) 0 0
\(470\) −150.961 −0.0148155
\(471\) −1747.75 3027.19i −0.170981 0.296148i
\(472\) −7417.64 + 12847.7i −0.723358 + 1.25289i
\(473\) 4325.98 7492.82i 0.420526 0.728373i
\(474\) −1345.00 2329.60i −0.130333 0.225743i
\(475\) −1105.63 −0.106800
\(476\) 0 0
\(477\) −3618.90 −0.347375
\(478\) 6534.86 + 11318.7i 0.625308 + 1.08307i
\(479\) −1198.66 + 2076.14i −0.114338 + 0.198040i −0.917515 0.397701i \(-0.869808\pi\)
0.803177 + 0.595741i \(0.203141\pi\)
\(480\) 978.793 1695.32i 0.0930741 0.161209i
\(481\) −3548.04 6145.39i −0.336334 0.582548i
\(482\) 12.5871 0.00118948
\(483\) 0 0
\(484\) −173.977 −0.0163390
\(485\) 2649.68 + 4589.38i 0.248074 + 0.429677i
\(486\) 5466.70 9468.61i 0.510236 0.883755i
\(487\) −2793.08 + 4837.76i −0.259890 + 0.450143i −0.966212 0.257747i \(-0.917020\pi\)
0.706322 + 0.707891i \(0.250353\pi\)
\(488\) 3862.17 + 6689.48i 0.358263 + 0.620530i
\(489\) 6674.33 0.617227
\(490\) 0 0
\(491\) 537.392 0.0493934 0.0246967 0.999695i \(-0.492138\pi\)
0.0246967 + 0.999695i \(0.492138\pi\)
\(492\) −1483.89 2570.17i −0.135973 0.235513i
\(493\) −2047.23 + 3545.90i −0.187023 + 0.323934i
\(494\) 1106.02 1915.68i 0.100733 0.174474i
\(495\) 1655.83 + 2867.99i 0.150352 + 0.260417i
\(496\) −10071.2 −0.911716
\(497\) 0 0
\(498\) −17842.0 −1.60546
\(499\) −299.482 518.719i −0.0268671 0.0465351i 0.852279 0.523087i \(-0.175220\pi\)
−0.879146 + 0.476552i \(0.841886\pi\)
\(500\) −82.1068 + 142.213i −0.00734385 + 0.0127199i
\(501\) 1196.31 2072.07i 0.106681 0.184777i
\(502\) 708.403 + 1226.99i 0.0629832 + 0.109090i
\(503\) 4426.76 0.392405 0.196202 0.980563i \(-0.437139\pi\)
0.196202 + 0.980563i \(0.437139\pi\)
\(504\) 0 0
\(505\) 1209.17 0.106549
\(506\) −10790.4 18689.5i −0.948006 1.64200i
\(507\) 6067.20 10508.7i 0.531467 0.920528i
\(508\) 797.086 1380.59i 0.0696161 0.120579i
\(509\) −8863.84 15352.6i −0.771872 1.33692i −0.936536 0.350571i \(-0.885987\pi\)
0.164665 0.986350i \(-0.447346\pi\)
\(510\) 7507.14 0.651808
\(511\) 0 0
\(512\) −13017.7 −1.12365
\(513\) −1425.83 2469.61i −0.122713 0.212546i
\(514\) 2294.38 3973.99i 0.196889 0.341022i
\(515\) −4198.94 + 7272.78i −0.359277 + 0.622286i
\(516\) −988.932 1712.88i −0.0843707 0.146134i
\(517\) 446.671 0.0379972
\(518\) 0 0
\(519\) 21925.4 1.85437
\(520\) −1164.62 2017.17i −0.0982149 0.170113i
\(521\) −4331.40 + 7502.20i −0.364226 + 0.630858i −0.988652 0.150226i \(-0.952000\pi\)
0.624425 + 0.781084i \(0.285333\pi\)
\(522\) 1050.77 1819.98i 0.0881050 0.152602i
\(523\) 3885.20 + 6729.36i 0.324833 + 0.562628i 0.981479 0.191572i \(-0.0613584\pi\)
−0.656645 + 0.754200i \(0.728025\pi\)
\(524\) 2604.32 0.217119
\(525\) 0 0
\(526\) −3100.60 −0.257020
\(527\) 8485.22 + 14696.8i 0.701370 + 1.21481i
\(528\) 6591.09 11416.1i 0.543259 0.940951i
\(529\) −17714.8 + 30683.0i −1.45597 + 2.52182i
\(530\) −1351.20 2340.34i −0.110740 0.191808i
\(531\) −10665.2 −0.871624
\(532\) 0 0
\(533\) −6564.34 −0.533458
\(534\) 1465.06 + 2537.56i 0.118726 + 0.205639i
\(535\) 3767.20 6524.99i 0.304431 0.527289i
\(536\) 174.720 302.624i 0.0140798 0.0243869i
\(537\) −9914.79 17172.9i −0.796750 1.38001i
\(538\) 8404.56 0.673506
\(539\) 0 0
\(540\) −423.541 −0.0337524
\(541\) −10820.5 18741.6i −0.859906 1.48940i −0.872018 0.489474i \(-0.837189\pi\)
0.0121123 0.999927i \(-0.496144\pi\)
\(542\) 1158.62 2006.78i 0.0918208 0.159038i
\(543\) −4867.21 + 8430.25i −0.384663 + 0.666255i
\(544\) 2565.04 + 4442.79i 0.202161 + 0.350152i
\(545\) 6262.05 0.492177
\(546\) 0 0
\(547\) 7489.29 0.585409 0.292705 0.956203i \(-0.405445\pi\)
0.292705 + 0.956203i \(0.405445\pi\)
\(548\) 1452.27 + 2515.41i 0.113208 + 0.196082i
\(549\) −2776.56 + 4809.14i −0.215848 + 0.373860i
\(550\) −1236.49 + 2141.66i −0.0958617 + 0.166037i
\(551\) −1037.99 1797.86i −0.0802542 0.139004i
\(552\) −34976.2 −2.69689
\(553\) 0 0
\(554\) −999.566 −0.0766561
\(555\) 6105.21 + 10574.5i 0.466940 + 0.808764i
\(556\) 346.844 600.752i 0.0264559 0.0458230i
\(557\) −12648.9 + 21908.6i −0.962214 + 1.66660i −0.245293 + 0.969449i \(0.578884\pi\)
−0.716921 + 0.697154i \(0.754449\pi\)
\(558\) −4355.15 7543.34i −0.330409 0.572285i
\(559\) −4374.77 −0.331007
\(560\) 0 0
\(561\) −22212.5 −1.67168
\(562\) 4311.92 + 7468.47i 0.323643 + 0.560566i
\(563\) −7830.65 + 13563.1i −0.586186 + 1.01530i 0.408541 + 0.912740i \(0.366038\pi\)
−0.994726 + 0.102563i \(0.967296\pi\)
\(564\) 51.0551 88.4300i 0.00381172 0.00660209i
\(565\) 3425.51 + 5933.16i 0.255066 + 0.441787i
\(566\) 13994.9 1.03931
\(567\) 0 0
\(568\) 22927.3 1.69367
\(569\) 4991.37 + 8645.31i 0.367749 + 0.636960i 0.989213 0.146482i \(-0.0467952\pi\)
−0.621464 + 0.783443i \(0.713462\pi\)
\(570\) −1903.15 + 3296.36i −0.139850 + 0.242227i
\(571\) 5791.81 10031.7i 0.424483 0.735226i −0.571889 0.820331i \(-0.693789\pi\)
0.996372 + 0.0851049i \(0.0271226\pi\)
\(572\) 486.052 + 841.866i 0.0355294 + 0.0615388i
\(573\) −2495.81 −0.181961
\(574\) 0 0
\(575\) 5454.16 0.395573
\(576\) −4901.48 8489.62i −0.354563 0.614122i
\(577\) 297.689 515.613i 0.0214783 0.0372015i −0.855086 0.518485i \(-0.826496\pi\)
0.876565 + 0.481284i \(0.159829\pi\)
\(578\) −3484.70 + 6035.67i −0.250769 + 0.434344i
\(579\) −2439.83 4225.91i −0.175122 0.303321i
\(580\) −308.335 −0.0220740
\(581\) 0 0
\(582\) 18243.8 1.29936
\(583\) 3998.00 + 6924.74i 0.284014 + 0.491927i
\(584\) 9928.20 17196.1i 0.703479 1.21846i
\(585\) 837.254 1450.17i 0.0591730 0.102491i
\(586\) −364.869 631.972i −0.0257212 0.0445504i
\(587\) −15750.3 −1.10747 −0.553736 0.832693i \(-0.686798\pi\)
−0.553736 + 0.832693i \(0.686798\pi\)
\(588\) 0 0
\(589\) −8604.42 −0.601934
\(590\) −3982.11 6897.22i −0.277866 0.481278i
\(591\) 6967.21 12067.6i 0.484928 0.839920i
\(592\) 9494.98 16445.8i 0.659191 1.14175i
\(593\) 208.939 + 361.893i 0.0144690 + 0.0250610i 0.873169 0.487417i \(-0.162061\pi\)
−0.858700 + 0.512478i \(0.828728\pi\)
\(594\) −6378.31 −0.440581
\(595\) 0 0
\(596\) 431.385 0.0296480
\(597\) −9536.08 16517.0i −0.653745 1.13232i
\(598\) −5456.04 + 9450.15i −0.373101 + 0.646229i
\(599\) 9998.67 17318.2i 0.682028 1.18131i −0.292333 0.956316i \(-0.594432\pi\)
0.974361 0.224990i \(-0.0722350\pi\)
\(600\) 2003.98 + 3471.00i 0.136354 + 0.236172i
\(601\) −15992.6 −1.08545 −0.542723 0.839912i \(-0.682607\pi\)
−0.542723 + 0.839912i \(0.682607\pi\)
\(602\) 0 0
\(603\) 251.216 0.0169657
\(604\) 676.185 + 1171.19i 0.0455523 + 0.0788988i
\(605\) 331.081 573.449i 0.0222485 0.0385356i
\(606\) 2081.36 3605.03i 0.139521 0.241657i
\(607\) −7079.59 12262.2i −0.473396 0.819947i 0.526140 0.850398i \(-0.323639\pi\)
−0.999536 + 0.0304515i \(0.990306\pi\)
\(608\) −2601.08 −0.173499
\(609\) 0 0
\(610\) −4146.76 −0.275242
\(611\) −112.927 195.596i −0.00747716 0.0129508i
\(612\) −991.978 + 1718.16i −0.0655202 + 0.113484i
\(613\) 2314.70 4009.18i 0.152512 0.264159i −0.779638 0.626230i \(-0.784597\pi\)
0.932150 + 0.362071i \(0.117930\pi\)
\(614\) −2481.93 4298.84i −0.163131 0.282552i
\(615\) 11295.4 0.740611
\(616\) 0 0
\(617\) −23165.3 −1.51151 −0.755753 0.654857i \(-0.772729\pi\)
−0.755753 + 0.654857i \(0.772729\pi\)
\(618\) 14455.4 + 25037.6i 0.940912 + 1.62971i
\(619\) −6185.30 + 10713.3i −0.401629 + 0.695641i −0.993923 0.110081i \(-0.964889\pi\)
0.592294 + 0.805722i \(0.298222\pi\)
\(620\) −638.983 + 1106.75i −0.0413906 + 0.0716906i
\(621\) 7033.71 + 12182.7i 0.454514 + 0.787241i
\(622\) 3137.36 0.202245
\(623\) 0 0
\(624\) −6665.43 −0.427613
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) 1854.01 3211.24i 0.118373 0.205027i
\(627\) 5631.15 9753.44i 0.358671 0.621236i
\(628\) 344.913 + 597.407i 0.0219165 + 0.0379604i
\(629\) −31998.9 −2.02842
\(630\) 0 0
\(631\) 13980.2 0.882002 0.441001 0.897507i \(-0.354623\pi\)
0.441001 + 0.897507i \(0.354623\pi\)
\(632\) 1881.81 + 3259.38i 0.118440 + 0.205145i
\(633\) −18784.5 + 32535.6i −1.17949 + 2.04293i
\(634\) −8399.86 + 14549.0i −0.526185 + 0.911379i
\(635\) 3033.73 + 5254.57i 0.189590 + 0.328380i
\(636\) 1827.91 0.113964
\(637\) 0 0
\(638\) −4643.36 −0.288139
\(639\) 8241.33 + 14274.4i 0.510206 + 0.883703i
\(640\) 2483.88 4302.20i 0.153412 0.265718i
\(641\) 8030.47 13909.2i 0.494828 0.857067i −0.505155 0.863029i \(-0.668564\pi\)
0.999982 + 0.00596217i \(0.00189783\pi\)
\(642\) −12969.1 22463.2i −0.797275 1.38092i
\(643\) −4502.17 −0.276125 −0.138063 0.990424i \(-0.544087\pi\)
−0.138063 + 0.990424i \(0.544087\pi\)
\(644\) 0 0
\(645\) 7527.79 0.459545
\(646\) −4987.44 8638.49i −0.303759 0.526125i
\(647\) −14707.4 + 25474.0i −0.893675 + 1.54789i −0.0582393 + 0.998303i \(0.518549\pi\)
−0.835436 + 0.549588i \(0.814785\pi\)
\(648\) −10797.8 + 18702.3i −0.654595 + 1.13379i
\(649\) 11782.5 + 20407.9i 0.712640 + 1.23433i
\(650\) 1250.43 0.0754553
\(651\) 0 0
\(652\) −1317.16 −0.0791164
\(653\) −6506.82 11270.1i −0.389941 0.675398i 0.602500 0.798119i \(-0.294171\pi\)
−0.992441 + 0.122721i \(0.960838\pi\)
\(654\) 10779.0 18669.8i 0.644483 1.11628i
\(655\) −4956.05 + 8584.13i −0.295647 + 0.512076i
\(656\) −8783.46 15213.4i −0.522769 0.905463i
\(657\) 14275.0 0.847671
\(658\) 0 0
\(659\) 23474.2 1.38759 0.693797 0.720171i \(-0.255937\pi\)
0.693797 + 0.720171i \(0.255937\pi\)
\(660\) −836.362 1448.62i −0.0493263 0.0854356i
\(661\) 4633.18 8024.91i 0.272632 0.472213i −0.696903 0.717166i \(-0.745439\pi\)
0.969535 + 0.244953i \(0.0787724\pi\)
\(662\) 12520.2 21685.7i 0.735064 1.27317i
\(663\) 5615.77 + 9726.79i 0.328957 + 0.569770i
\(664\) 24963.0 1.45896
\(665\) 0 0
\(666\) 16423.8 0.955572
\(667\) 5120.49 + 8868.95i 0.297251 + 0.514853i
\(668\) −236.088 + 408.916i −0.0136744 + 0.0236848i
\(669\) 21199.3 36718.2i 1.22513 2.12199i
\(670\) 93.7973 + 162.462i 0.00540851 + 0.00936782i
\(671\) 12269.7 0.705909
\(672\) 0 0
\(673\) −25067.2 −1.43576 −0.717882 0.696164i \(-0.754888\pi\)
−0.717882 + 0.696164i \(0.754888\pi\)
\(674\) −37.6644 65.2367i −0.00215249 0.00372822i
\(675\) 806.003 1396.04i 0.0459601 0.0796052i
\(676\) −1197.34 + 2073.86i −0.0681237 + 0.117994i
\(677\) 11204.8 + 19407.3i 0.636093 + 1.10174i 0.986283 + 0.165066i \(0.0527838\pi\)
−0.350190 + 0.936679i \(0.613883\pi\)
\(678\) 23585.6 1.33599
\(679\) 0 0
\(680\) −10503.4 −0.592332
\(681\) 3380.60 + 5855.37i 0.190227 + 0.329483i
\(682\) −9622.75 + 16667.1i −0.540284 + 0.935800i
\(683\) 4378.77 7584.24i 0.245313 0.424895i −0.716907 0.697169i \(-0.754443\pi\)
0.962220 + 0.272275i \(0.0877759\pi\)
\(684\) −502.957 871.147i −0.0281156 0.0486976i
\(685\) −11054.7 −0.616613
\(686\) 0 0
\(687\) 27348.7 1.51880
\(688\) −5853.70 10138.9i −0.324375 0.561834i
\(689\) 2021.55 3501.42i 0.111778 0.193604i
\(690\) 9388.36 16261.1i 0.517984 0.897174i
\(691\) −4234.21 7333.87i −0.233107 0.403753i 0.725614 0.688102i \(-0.241556\pi\)
−0.958721 + 0.284349i \(0.908223\pi\)
\(692\) −4326.90 −0.237694
\(693\) 0 0
\(694\) −20294.8 −1.11006
\(695\) 1320.10 + 2286.47i 0.0720491 + 0.124793i
\(696\) −3762.77 + 6517.31i −0.204925 + 0.354940i
\(697\) −14800.5 + 25635.2i −0.804318 + 1.39312i
\(698\) 13277.6 + 22997.4i 0.720004 + 1.24708i
\(699\) 4050.23 0.219162
\(700\) 0 0
\(701\) 15996.9 0.861906 0.430953 0.902374i \(-0.358177\pi\)
0.430953 + 0.902374i \(0.358177\pi\)
\(702\) 1612.56 + 2793.04i 0.0866983 + 0.150166i
\(703\) 8112.11 14050.6i 0.435212 0.753809i
\(704\) −10829.9 + 18757.9i −0.579782 + 1.00421i
\(705\) 194.317 + 336.566i 0.0103807 + 0.0179799i
\(706\) 7240.03 0.385952
\(707\) 0 0
\(708\) 5387.02 0.285956
\(709\) −9951.48 17236.5i −0.527131 0.913017i −0.999500 0.0316164i \(-0.989935\pi\)
0.472369 0.881401i \(-0.343399\pi\)
\(710\) −6154.17 + 10659.3i −0.325299 + 0.563434i
\(711\) −1352.85 + 2343.21i −0.0713584 + 0.123596i
\(712\) −2049.79 3550.34i −0.107892 0.186875i
\(713\) 42446.1 2.22948
\(714\) 0 0
\(715\) −3699.84 −0.193519
\(716\) 1956.65 + 3389.02i 0.102128 + 0.176891i
\(717\) 16823.3 29138.9i 0.876261 1.51773i
\(718\) 4089.80 7083.73i 0.212576 0.368193i
\(719\) 5536.53 + 9589.56i 0.287174 + 0.497399i 0.973134 0.230240i \(-0.0739510\pi\)
−0.685960 + 0.727639i \(0.740618\pi\)
\(720\) 4481.18 0.231949
\(721\) 0 0
\(722\) −12678.4 −0.653520
\(723\) −16.2022 28.0630i −0.000833424 0.00144353i
\(724\) 960.528 1663.68i 0.0493062 0.0854009i
\(725\) 586.764 1016.31i 0.0300578 0.0520616i
\(726\) −1139.79 1974.18i −0.0582667 0.100921i
\(727\) 31652.7 1.61476 0.807382 0.590029i \(-0.200884\pi\)
0.807382 + 0.590029i \(0.200884\pi\)
\(728\) 0 0
\(729\) −3935.94 −0.199967
\(730\) 5329.88 + 9231.63i 0.270230 + 0.468052i
\(731\) −9863.73 + 17084.5i −0.499074 + 0.864422i
\(732\) 1402.44 2429.10i 0.0708138 0.122653i
\(733\) −8479.15 14686.3i −0.427264 0.740043i 0.569365 0.822085i \(-0.307189\pi\)
−0.996629 + 0.0820419i \(0.973856\pi\)
\(734\) 8230.16 0.413870
\(735\) 0 0
\(736\) 12831.3 0.642618
\(737\) −277.532 480.700i −0.0138712 0.0240255i
\(738\) 7596.55 13157.6i 0.378906 0.656285i
\(739\) 5808.30 10060.3i 0.289123 0.500775i −0.684478 0.729034i \(-0.739970\pi\)
0.973601 + 0.228258i \(0.0733031\pi\)
\(740\) −1204.84 2086.85i −0.0598526 0.103668i
\(741\) −5694.66 −0.282319
\(742\) 0 0
\(743\) 15928.0 0.786464 0.393232 0.919439i \(-0.371357\pi\)
0.393232 + 0.919439i \(0.371357\pi\)
\(744\) 15595.7 + 27012.5i 0.768502 + 1.33108i
\(745\) −820.929 + 1421.89i −0.0403712 + 0.0699249i
\(746\) 3381.10 5856.23i 0.165939 0.287415i
\(747\) 8973.07 + 15541.8i 0.439501 + 0.761239i
\(748\) 4383.57 0.214277
\(749\) 0 0
\(750\) −2151.65 −0.104756
\(751\) −12786.0 22145.9i −0.621260 1.07605i −0.989251 0.146225i \(-0.953288\pi\)
0.367991 0.929829i \(-0.380046\pi\)
\(752\) 302.206 523.436i 0.0146547 0.0253827i
\(753\) 1823.71 3158.77i 0.0882601 0.152871i
\(754\) 1173.93 + 2033.31i 0.0567004 + 0.0982080i
\(755\) −5147.14 −0.248111
\(756\) 0 0
\(757\) 6202.41 0.297794 0.148897 0.988853i \(-0.452428\pi\)
0.148897 + 0.988853i \(0.452428\pi\)
\(758\) 869.385 + 1505.82i 0.0416590 + 0.0721555i
\(759\) −27778.8 + 48114.3i −1.32847 + 2.30097i
\(760\) 2662.73 4611.98i 0.127089 0.220124i
\(761\) 14599.5 + 25287.1i 0.695444 + 1.20454i 0.970031 + 0.242982i \(0.0781257\pi\)
−0.274587 + 0.961562i \(0.588541\pi\)
\(762\) 20888.1 0.993037
\(763\) 0 0
\(764\) 492.539 0.0233239
\(765\) −3775.49 6539.34i −0.178435 0.309059i
\(766\) −1512.50 + 2619.73i −0.0713431 + 0.123570i
\(767\) 5957.69 10319.0i 0.280469 0.485786i
\(768\) 6525.26 + 11302.1i 0.306589 + 0.531027i
\(769\) 21838.2 1.02407 0.512033 0.858966i \(-0.328892\pi\)
0.512033 + 0.858966i \(0.328892\pi\)
\(770\) 0 0
\(771\) −11813.3 −0.551812
\(772\) 481.492 + 833.969i