Properties

Label 245.4.e.i.226.2
Level $245$
Weight $4$
Character 245.226
Analytic conductor $14.455$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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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 226.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 245.226
Dual form 245.4.e.i.116.2

$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

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

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 −0.998807 0.0488398i \(-0.984448\pi\)
0.541700 + 0.840572i \(0.317781\pi\)
\(3\) 3.32843 + 5.76500i 0.640556 + 1.10948i 0.985309 + 0.170782i \(0.0546294\pi\)
−0.344753 + 0.938694i \(0.612037\pi\)
\(4\) 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 −0.999600 0.0282725i \(-0.990999\pi\)
0.475315 0.879815i \(-0.342334\pi\)
\(12\) −4.37258 + 7.57354i −0.105188 + 0.182191i
\(13\) −19.3431 −0.412679 −0.206339 0.978480i \(-0.566155\pi\)
−0.206339 + 0.978480i \(0.566155\pi\)
\(14\) 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 −0.989073 0.147429i \(-0.952900\pi\)
0.366859 0.930277i \(-0.380433\pi\)
\(18\) −22.3848 38.7716i −0.293119 0.507697i
\(19\) −22.1127 + 38.3003i −0.267000 + 0.462458i −0.968086 0.250619i \(-0.919366\pi\)
0.701086 + 0.713077i \(0.252699\pi\)
\(20\) −6.56854 −0.0734385
\(21\) 0 0
\(22\) 98.9188 0.958617
\(23\) −109.083 + 188.938i −0.988932 + 1.71288i −0.365973 + 0.930625i \(0.619264\pi\)
−0.622959 + 0.782255i \(0.714069\pi\)
\(24\) −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 0.997178 + 0.0750783i \(0.0239207\pi\)
−0.433569 + 0.901120i \(0.642746\pi\)
\(32\) −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 0.0943225 + 0.995542i \(0.469932\pi\)
−0.909326 + 0.416085i \(0.863402\pi\)
\(38\) −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 \(-0.276301\pi\)
0.646336 + 0.763053i \(0.276301\pi\)
\(42\) 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 \(-0.827566\pi\)
0.874943 + 0.484227i \(0.160899\pi\)
\(48\) 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 0.969082 0.246739i \(-0.0793591\pi\)
−0.698223 + 0.715880i \(0.746026\pi\)
\(54\) −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 −0.975092 0.221800i \(-0.928807\pi\)
0.295462 0.955354i \(-0.404526\pi\)
\(60\) −21.8629 37.8677i −0.0470415 0.0814783i
\(61\) 160.368 277.765i 0.336606 0.583018i −0.647186 0.762332i \(-0.724054\pi\)
0.983792 + 0.179314i \(0.0573877\pi\)
\(62\) −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 0.859335 0.511413i \(-0.170878\pi\)
−0.872564 + 0.488500i \(0.837544\pi\)
\(68\) 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 0.980366 + 0.197189i \(0.0631812\pi\)
−0.319412 + 0.947616i \(0.603485\pi\)
\(74\) −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 −0.916287 0.400523i \(-0.868829\pi\)
0.805006 + 0.593266i \(0.202162\pi\)
\(80\) 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 \(-0.259634\pi\)
0.685384 + 0.728182i \(0.259634\pi\)
\(84\) 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 \(-0.865656\pi\)
0.810879 + 0.585213i \(0.198989\pi\)
\(90\) 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 \(-0.687171\pi\)
−0.554710 + 0.832044i \(0.687171\pi\)
\(98\) 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 \(-0.204676\pi\)
−0.919421 + 0.393274i \(0.871342\pi\)
\(102\) 750.714 + 1300.28i 0.728743 + 1.26222i
\(103\) −839.788 + 1454.56i −0.803367 + 1.39147i 0.114021 + 0.993478i \(0.463627\pi\)
−0.917388 + 0.397994i \(0.869706\pi\)
\(104\) 465.846 0.439230
\(105\) 0 0
\(106\) −540.479 −0.495245
\(107\) −753.441 + 1305.00i −0.680728 + 1.17905i 0.294031 + 0.955796i \(0.405003\pi\)
−0.974759 + 0.223259i \(0.928330\pi\)
\(108\) 42.3541 + 73.3595i 0.0377364 + 0.0653613i
\(109\) 626.205 + 1084.62i 0.550271 + 0.953097i 0.998255 + 0.0590556i \(0.0188089\pi\)
−0.447984 + 0.894042i \(0.647858\pi\)
\(110\) −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 0.319244 + 0.947673i \(0.396571\pi\)
−0.980330 + 0.197363i \(0.936762\pi\)
\(132\) 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 −0.972034 0.234840i \(-0.924543\pi\)
0.282640 0.959226i \(-0.408790\pi\)
\(138\) 1877.67 3252.22i 1.15825 2.00614i
\(139\) −528.039 −0.322213 −0.161107 0.986937i \(-0.551506\pi\)
−0.161107 + 0.986937i \(0.551506\pi\)
\(140\) 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 −0.817353 0.576137i \(-0.804559\pi\)
0.907626 + 0.419780i \(0.137893\pi\)
\(150\) 215.165 + 372.677i 0.117121 + 0.202860i
\(151\) −514.714 891.512i −0.277396 0.480465i 0.693340 0.720610i \(-0.256138\pi\)
−0.970737 + 0.240145i \(0.922805\pi\)
\(152\) 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 \(-0.124057\pi\)
−0.791546 + 0.611109i \(0.790724\pi\)
\(158\) −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 −0.960969 0.276655i \(-0.910774\pi\)
0.720075 + 0.693897i \(0.244108\pi\)
\(164\) 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 \(-0.473463\pi\)
0.0832722 + 0.996527i \(0.473463\pi\)
\(168\) 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 −0.235760 0.971811i \(-0.575758\pi\)
0.959493 0.281732i \(-0.0909088\pi\)
\(174\) 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 −0.989128 0.147059i \(-0.953019\pi\)
0.367207 0.930139i \(-0.380314\pi\)
\(180\) 56.8629 98.4895i 0.0235462 0.0407832i
\(181\) −1462.31 −0.600514 −0.300257 0.953858i \(-0.597072\pi\)
−0.300257 + 0.953858i \(0.597072\pi\)
\(182\) 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 −0.828330 0.560240i \(-0.810709\pi\)
0.899347 + 0.437235i \(0.144042\pi\)
\(192\) 1884.54 + 3264.13i 0.708361 + 1.22692i
\(193\) −366.514 634.821i −0.136696 0.236764i 0.789548 0.613688i \(-0.210315\pi\)
−0.926244 + 0.376925i \(0.876982\pi\)
\(194\) 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 0.999929 + 0.0119283i \(0.00379699\pi\)
−0.489634 + 0.871928i \(0.662870\pi\)
\(200\) 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 \(-0.0944477\pi\)
0.956302 + 0.292381i \(0.0944477\pi\)
\(224\) 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 \(-0.214107\pi\)
−0.930668 + 0.365865i \(0.880773\pi\)
\(228\) −193.379 334.943i −0.0561704 0.0972900i
\(229\) 2054.18 3557.94i 0.592768 1.02670i −0.401090 0.916039i \(-0.631368\pi\)
0.993858 0.110665i \(-0.0352982\pi\)
\(230\) 2820.66 0.808647
\(231\) 0 0
\(232\) 1130.50 0.319917
\(233\) −304.215 + 526.916i −0.0855357 + 0.148152i −0.905619 0.424092i \(-0.860593\pi\)
0.820084 + 0.572244i \(0.193927\pi\)
\(234\) 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 \(-0.166460\pi\)
−0.865700 + 0.500563i \(0.833126\pi\)
\(242\) −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 \(-0.478053\pi\)
0.0688934 + 0.997624i \(0.478053\pi\)
\(252\) 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 \(-0.902427\pi\)
0.738021 + 0.674778i \(0.235761\pi\)
\(258\) 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 0.927711 0.373299i \(-0.121774\pi\)
−0.787142 + 0.616772i \(0.788440\pi\)
\(264\) −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 \(-0.0465885\pi\)
−0.620955 + 0.783846i \(0.713255\pi\)
\(270\) −416.830 721.971i −0.0939536 0.162732i
\(271\) −448.071 + 776.082i −0.100437 + 0.173962i −0.911865 0.410491i \(-0.865357\pi\)
0.811428 + 0.584453i \(0.198691\pi\)
\(272\) −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 0.886226 0.463253i \(-0.153318\pi\)
−0.844302 + 0.535868i \(0.819984\pi\)
\(278\) 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 0.996723 + 0.0808959i \(0.0257781\pi\)
−0.428303 + 0.903635i \(0.640889\pi\)
\(284\) −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 \(-0.508957\pi\)
−0.0281347 + 0.999604i \(0.508957\pi\)
\(294\) 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 \(-0.557105\pi\)
−0.178439 + 0.983951i \(0.557105\pi\)
\(308\) 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 \(-0.131386\pi\)
−0.805405 + 0.592724i \(0.798052\pi\)
\(312\) 1550.53 + 2685.60i 0.281352 + 0.487315i
\(313\) −717.001 + 1241.88i −0.129480 + 0.224266i −0.923475 0.383658i \(-0.874664\pi\)
0.793995 + 0.607924i \(0.207998\pi\)
\(314\) −1357.79 −0.244028
\(315\) 0 0
\(316\) −205.300 −0.0365475
\(317\) −3248.48 + 5626.52i −0.575560 + 0.996899i 0.420420 + 0.907329i \(0.361883\pi\)
−0.995981 + 0.0895699i \(0.971451\pi\)
\(318\) −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 −0.112898 0.993607i \(-0.536013\pi\)
0.916938 0.399031i \(-0.130653\pi\)
\(332\) 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 0.991714 + 0.128463i \(0.0410045\pi\)
−0.384605 + 0.923081i \(0.625662\pi\)
\(348\) 205.254 355.510i 0.0316171 0.0547625i
\(349\) 10269.6 1.57513 0.787567 0.616229i \(-0.211341\pi\)
0.787567 + 0.616229i \(0.211341\pi\)
\(350\) 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 \(-0.0989672\pi\)
−0.740970 + 0.671538i \(0.765634\pi\)
\(354\) 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 −0.726026 0.687667i \(-0.758635\pi\)
0.958550 + 0.284924i \(0.0919683\pi\)
\(360\) 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 \(-0.0939864\pi\)
−0.730371 + 0.683050i \(0.760653\pi\)
\(368\) 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 −0.760885 0.648887i \(-0.775235\pi\)
0.942395 + 0.334502i \(0.108568\pi\)
\(374\) −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 \(-0.808468\pi\)
0.902403 + 0.430893i \(0.141801\pi\)
\(384\) −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 0.900274 0.435325i \(-0.143366\pi\)
−0.827139 + 0.561998i \(0.810033\pi\)
\(390\) −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 \(-0.873396\pi\)
0.796410 + 0.604757i \(0.206730\pi\)
\(398\) −7408.38 −0.933037
\(399\) 0 0
\(400\) −1294.11 −0.161764
\(401\) 2086.19 3613.38i 0.259799 0.449984i −0.706389 0.707824i \(-0.749677\pi\)
0.966188 + 0.257839i \(0.0830105\pi\)
\(402\) 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 −0.965857 0.259076i \(-0.916582\pi\)
0.258562 0.965995i \(-0.416751\pi\)
\(410\) −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 \(-0.550936\pi\)
−0.159339 + 0.987224i \(0.550936\pi\)
\(420\) 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 0.987838 0.155485i \(-0.0496942\pi\)
−0.628573 + 0.777750i \(0.716361\pi\)
\(432\) 1668.89 2890.61i 0.185867 0.321932i
\(433\) −8022.03 −0.890333 −0.445166 0.895448i \(-0.646855\pi\)
−0.445166 + 0.895448i \(0.646855\pi\)
\(434\) 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 \(-0.931246\pi\)
0.673989 + 0.738741i \(0.264580\pi\)
\(440\) −4606.51 −0.499106
\(441\) 0 0
\(442\) −4362.77 −0.469493
\(443\) 2743.11 4751.20i 0.294196 0.509563i −0.680601 0.732654i \(-0.738281\pi\)
0.974798 + 0.223091i \(0.0716148\pi\)
\(444\) −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 −0.782207 0.623019i \(-0.785906\pi\)
0.930653 + 0.365902i \(0.119239\pi\)
\(458\) 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 \(-0.599260\pi\)
−0.306805 + 0.951772i \(0.599260\pi\)
\(462\) 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 \(-0.942322\pi\)
0.647880 + 0.761742i \(0.275656\pi\)
\(468\) 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 \(-0.130192\pi\)
−0.803177 + 0.595741i \(0.796859\pi\)
\(480\) 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 0.706322 0.707891i \(-0.250353\pi\)
−0.966212 + 0.257747i \(0.917020\pi\)
\(488\) −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 −0.879146 0.476552i \(-0.841886\pi\)
0.852279 + 0.523087i \(0.175220\pi\)
\(500\) 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 \(-0.562861\pi\)
−0.196202 + 0.980563i \(0.562861\pi\)
\(504\) 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 −0.164665 0.986350i \(-0.552654\pi\)
0.936536 0.350571i \(-0.114013\pi\)
\(510\) −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 \(-0.0480001\pi\)
−0.624425 + 0.781084i \(0.714667\pi\)
\(522\) 1050.77 + 1819.98i 0.0881050 + 0.152602i
\(523\) −3885.20 + 6729.36i −0.324833 + 0.562628i −0.981479 0.191572i \(-0.938642\pi\)
0.656645 + 0.754200i \(0.271975\pi\)
\(524\) −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 0.0121123 + 0.999927i \(0.496144\pi\)
−0.872018 + 0.489474i \(0.837189\pi\)
\(542\) −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 −0.716921 0.697154i \(-0.754449\pi\)
−0.245293 0.969449i \(-0.578884\pi\)
\(558\) 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 0.994726 + 0.102563i \(0.0327044\pi\)
−0.408541 + 0.912740i \(0.633962\pi\)
\(564\) 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 −0.621464 0.783443i \(-0.713462\pi\)
0.989213 + 0.146482i \(0.0467952\pi\)
\(570\) 1903.15 + 3296.36i 0.139850 + 0.242227i
\(571\) 5791.81 + 10031.7i 0.424483 + 0.735226i 0.996372 0.0851049i \(-0.0271226\pi\)
−0.571889 + 0.820331i \(0.693789\pi\)
\(572\) −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 \(-0.173504\pi\)
−0.876565 + 0.481284i \(0.840171\pi\)
\(578\) −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 \(-0.313202\pi\)
0.553736 + 0.832693i \(0.313202\pi\)
\(588\) 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 \(-0.837939\pi\)
0.858700 + 0.512478i \(0.171272\pi\)
\(594\) 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 0.974361 + 0.224990i \(0.0722350\pi\)
−0.292333 + 0.956316i \(0.594432\pi\)
\(600\) −2003.98 + 3471.00i −0.136354 + 0.236172i
\(601\) 15992.6 1.08545 0.542723 0.839912i \(-0.317393\pi\)
0.542723 + 0.839912i \(0.317393\pi\)
\(602\) 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 \(-0.676361\pi\)
0.999536 + 0.0304515i \(0.00969450\pi\)
\(608\) 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 0.932150 0.362071i \(-0.117930\pi\)
−0.779638 + 0.626230i \(0.784597\pi\)
\(614\) 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 \(-0.0351109\pi\)
−0.592294 + 0.805722i \(0.701778\pi\)
\(620\) −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 0.999982 0.00596217i \(-0.00189783\pi\)
−0.505155 + 0.863029i \(0.668564\pi\)
\(642\) 12969.1 22463.2i 0.797275 1.38092i
\(643\) 4502.17 0.276125 0.138063 0.990424i \(-0.455913\pi\)
0.138063 + 0.990424i \(0.455913\pi\)
\(644\) 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 0.835436 + 0.549588i \(0.185215\pi\)
0.0582393 + 0.998303i \(0.481451\pi\)
\(648\) −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 −0.992441 0.122721i \(-0.960838\pi\)
0.602500 + 0.798119i \(0.294171\pi\)
\(654\) −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 \(-0.254561\pi\)
−0.969535 + 0.244953i \(0.921228\pi\)
\(662\) 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 0.350190 + 0.936679i \(0.386117\pi\)
−0.986283 + 0.165066i \(0.947216\pi\)
\(678\) −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 0.962220 0.272275i \(-0.0877759\pi\)
−0.716907 + 0.697169i \(0.754443\pi\)
\(684\) 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 \(-0.758444\pi\)
0.958721 + 0.284349i \(0.0917774\pi\)
\(692\) 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 0.472369 + 0.881401i \(0.343399\pi\)
−0.999500 + 0.0316164i \(0.989935\pi\)
\(710\) 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 \(-0.926049\pi\)
0.685960 + 0.727639i \(0.259382\pi\)
\(720\) −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 \(-0.799116\pi\)
−0.807382 + 0.590029i \(0.799116\pi\)
\(728\) 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 \(-0.692811\pi\)
0.996629 + 0.0820419i \(0.0261441\pi\)
\(734\) −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 0.973601 0.228258i \(-0.0733031\pi\)
−0.684478 + 0.729034i \(0.739970\pi\)
\(740\) 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 0.367991 + 0.929829i \(0.380046\pi\)
−0.989251 + 0.146225i \(0.953288\pi\)
\(752\) −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 0.274587 + 0.961562i \(0.411459\pi\)
−0.970031 + 0.242982i \(0.921874\pi\)
\(762\) −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 \(-0.671108\pi\)
−0.512033 + 0.858966i \(0.671108\pi\)
\(770\) 0 0
\(771\) −11813.3 −0.551812
\(772\) 481.492