Properties

Label 115.4.e.a.22.1
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 22.1
Character \(\chi\) \(=\) 115.22
Dual form 115.4.e.a.68.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.71645 - 3.71645i) q^{2} +(3.49413 - 3.49413i) q^{3} +19.6239i q^{4} +(-10.7999 + 2.89187i) q^{5} -25.9715 q^{6} +(2.69551 - 2.69551i) q^{7} +(43.1997 - 43.1997i) q^{8} +2.58205i q^{9} +O(q^{10})\) \(q+(-3.71645 - 3.71645i) q^{2} +(3.49413 - 3.49413i) q^{3} +19.6239i q^{4} +(-10.7999 + 2.89187i) q^{5} -25.9715 q^{6} +(2.69551 - 2.69551i) q^{7} +(43.1997 - 43.1997i) q^{8} +2.58205i q^{9} +(50.8846 + 29.3896i) q^{10} +70.6258i q^{11} +(68.5686 + 68.5686i) q^{12} +(31.0634 - 31.0634i) q^{13} -20.0354 q^{14} +(-27.6316 + 47.8408i) q^{15} -164.107 q^{16} +(-34.9841 + 34.9841i) q^{17} +(9.59606 - 9.59606i) q^{18} +117.583 q^{19} +(-56.7499 - 211.936i) q^{20} -18.8370i q^{21} +(262.477 - 262.477i) q^{22} +(-98.5389 + 49.5690i) q^{23} -301.891i q^{24} +(108.274 - 62.4636i) q^{25} -230.891 q^{26} +(103.364 + 103.364i) q^{27} +(52.8965 + 52.8965i) q^{28} -97.5091i q^{29} +(280.489 - 75.1063i) q^{30} -87.2021 q^{31} +(264.298 + 264.298i) q^{32} +(246.776 + 246.776i) q^{33} +260.033 q^{34} +(-21.3161 + 36.9062i) q^{35} -50.6700 q^{36} +(-155.647 + 155.647i) q^{37} +(-436.992 - 436.992i) q^{38} -217.079i q^{39} +(-341.623 + 591.479i) q^{40} +181.541 q^{41} +(-70.0065 + 70.0065i) q^{42} +(76.7114 + 76.7114i) q^{43} -1385.96 q^{44} +(-7.46696 - 27.8858i) q^{45} +(550.435 + 181.994i) q^{46} +(78.8226 + 78.8226i) q^{47} +(-573.413 + 573.413i) q^{48} +328.468i q^{49} +(-634.538 - 170.252i) q^{50} +244.479i q^{51} +(609.586 + 609.586i) q^{52} +(424.580 + 424.580i) q^{53} -768.291i q^{54} +(-204.241 - 762.749i) q^{55} -232.891i q^{56} +(410.852 - 410.852i) q^{57} +(-362.387 + 362.387i) q^{58} +558.444i q^{59} +(-938.824 - 542.240i) q^{60} +61.6086i q^{61} +(324.082 + 324.082i) q^{62} +(6.95995 + 6.95995i) q^{63} -651.639i q^{64} +(-245.649 + 425.312i) q^{65} -1834.26i q^{66} +(-371.522 + 371.522i) q^{67} +(-686.526 - 686.526i) q^{68} +(-171.107 + 517.509i) q^{69} +(216.380 - 57.9399i) q^{70} -93.0234 q^{71} +(111.544 + 111.544i) q^{72} +(240.796 - 240.796i) q^{73} +1156.91 q^{74} +(160.068 - 596.581i) q^{75} +2307.45i q^{76} +(190.373 + 190.373i) q^{77} +(-806.763 + 806.763i) q^{78} +567.099 q^{79} +(1772.34 - 474.577i) q^{80} +652.618 q^{81} +(-674.686 - 674.686i) q^{82} +(-722.376 - 722.376i) q^{83} +369.655 q^{84} +(276.654 - 478.994i) q^{85} -570.187i q^{86} +(-340.710 - 340.710i) q^{87} +(3051.01 + 3051.01i) q^{88} -0.0871278 q^{89} +(-75.8855 + 131.387i) q^{90} -167.463i q^{91} +(-972.740 - 1933.72i) q^{92} +(-304.696 + 304.696i) q^{93} -585.880i q^{94} +(-1269.88 + 340.036i) q^{95} +1846.98 q^{96} +(-169.555 + 169.555i) q^{97} +(1220.73 - 1220.73i) q^{98} -182.360 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.71645 3.71645i −1.31396 1.31396i −0.918469 0.395493i \(-0.870574\pi\)
−0.395493 0.918469i \(-0.629426\pi\)
\(3\) 3.49413 3.49413i 0.672446 0.672446i −0.285833 0.958279i \(-0.592270\pi\)
0.958279 + 0.285833i \(0.0922703\pi\)
\(4\) 19.6239i 2.45299i
\(5\) −10.7999 + 2.89187i −0.965969 + 0.258657i
\(6\) −25.9715 −1.76714
\(7\) 2.69551 2.69551i 0.145544 0.145544i −0.630580 0.776124i \(-0.717183\pi\)
0.776124 + 0.630580i \(0.217183\pi\)
\(8\) 43.1997 43.1997i 1.90918 1.90918i
\(9\) 2.58205i 0.0956316i
\(10\) 50.8846 + 29.3896i 1.60911 + 0.929382i
\(11\) 70.6258i 1.93586i 0.251217 + 0.967931i \(0.419169\pi\)
−0.251217 + 0.967931i \(0.580831\pi\)
\(12\) 68.5686 + 68.5686i 1.64951 + 1.64951i
\(13\) 31.0634 31.0634i 0.662725 0.662725i −0.293296 0.956022i \(-0.594752\pi\)
0.956022 + 0.293296i \(0.0947522\pi\)
\(14\) −20.0354 −0.382478
\(15\) −27.6316 + 47.8408i −0.475630 + 0.823495i
\(16\) −164.107 −2.56417
\(17\) −34.9841 + 34.9841i −0.499112 + 0.499112i −0.911161 0.412050i \(-0.864813\pi\)
0.412050 + 0.911161i \(0.364813\pi\)
\(18\) 9.59606 9.59606i 0.125656 0.125656i
\(19\) 117.583 1.41976 0.709880 0.704323i \(-0.248749\pi\)
0.709880 + 0.704323i \(0.248749\pi\)
\(20\) −56.7499 211.936i −0.634483 2.36951i
\(21\) 18.8370i 0.195741i
\(22\) 262.477 262.477i 2.54365 2.54365i
\(23\) −98.5389 + 49.5690i −0.893338 + 0.449385i
\(24\) 301.891i 2.56764i
\(25\) 108.274 62.4636i 0.866193 0.499709i
\(26\) −230.891 −1.74159
\(27\) 103.364 + 103.364i 0.736754 + 0.736754i
\(28\) 52.8965 + 52.8965i 0.357018 + 0.357018i
\(29\) 97.5091i 0.624379i −0.950020 0.312189i \(-0.898938\pi\)
0.950020 0.312189i \(-0.101062\pi\)
\(30\) 280.489 75.1063i 1.70700 0.457082i
\(31\) −87.2021 −0.505224 −0.252612 0.967568i \(-0.581290\pi\)
−0.252612 + 0.967568i \(0.581290\pi\)
\(32\) 264.298 + 264.298i 1.46005 + 1.46005i
\(33\) 246.776 + 246.776i 1.30176 + 1.30176i
\(34\) 260.033 1.31163
\(35\) −21.3161 + 36.9062i −0.102945 + 0.178237i
\(36\) −50.6700 −0.234583
\(37\) −155.647 + 155.647i −0.691572 + 0.691572i −0.962578 0.271006i \(-0.912644\pi\)
0.271006 + 0.962578i \(0.412644\pi\)
\(38\) −436.992 436.992i −1.86551 1.86551i
\(39\) 217.079i 0.891295i
\(40\) −341.623 + 591.479i −1.35038 + 2.33803i
\(41\) 181.541 0.691509 0.345755 0.938325i \(-0.387623\pi\)
0.345755 + 0.938325i \(0.387623\pi\)
\(42\) −70.0065 + 70.0065i −0.257196 + 0.257196i
\(43\) 76.7114 + 76.7114i 0.272055 + 0.272055i 0.829927 0.557872i \(-0.188382\pi\)
−0.557872 + 0.829927i \(0.688382\pi\)
\(44\) −1385.96 −4.74865
\(45\) −7.46696 27.8858i −0.0247358 0.0923772i
\(46\) 550.435 + 181.994i 1.76429 + 0.583337i
\(47\) 78.8226 + 78.8226i 0.244627 + 0.244627i 0.818761 0.574134i \(-0.194661\pi\)
−0.574134 + 0.818761i \(0.694661\pi\)
\(48\) −573.413 + 573.413i −1.72427 + 1.72427i
\(49\) 328.468i 0.957634i
\(50\) −634.538 170.252i −1.79474 0.481546i
\(51\) 244.479i 0.671252i
\(52\) 609.586 + 609.586i 1.62566 + 1.62566i
\(53\) 424.580 + 424.580i 1.10039 + 1.10039i 0.994364 + 0.106024i \(0.0338121\pi\)
0.106024 + 0.994364i \(0.466188\pi\)
\(54\) 768.291i 1.93613i
\(55\) −204.241 762.749i −0.500724 1.86998i
\(56\) 232.891i 0.555738i
\(57\) 410.852 410.852i 0.954713 0.954713i
\(58\) −362.387 + 362.387i −0.820410 + 0.820410i
\(59\) 558.444i 1.23226i 0.787646 + 0.616129i \(0.211300\pi\)
−0.787646 + 0.616129i \(0.788700\pi\)
\(60\) −938.824 542.240i −2.02003 1.16672i
\(61\) 61.6086i 0.129314i 0.997908 + 0.0646571i \(0.0205954\pi\)
−0.997908 + 0.0646571i \(0.979405\pi\)
\(62\) 324.082 + 324.082i 0.663846 + 0.663846i
\(63\) 6.95995 + 6.95995i 0.0139186 + 0.0139186i
\(64\) 651.639i 1.27273i
\(65\) −245.649 + 425.312i −0.468754 + 0.811591i
\(66\) 1834.26i 3.42093i
\(67\) −371.522 + 371.522i −0.677442 + 0.677442i −0.959421 0.281979i \(-0.909009\pi\)
0.281979 + 0.959421i \(0.409009\pi\)
\(68\) −686.526 686.526i −1.22432 1.22432i
\(69\) −171.107 + 517.509i −0.298534 + 0.902910i
\(70\) 216.380 57.9399i 0.369462 0.0989307i
\(71\) −93.0234 −0.155491 −0.0777454 0.996973i \(-0.524772\pi\)
−0.0777454 + 0.996973i \(0.524772\pi\)
\(72\) 111.544 + 111.544i 0.182577 + 0.182577i
\(73\) 240.796 240.796i 0.386070 0.386070i −0.487213 0.873283i \(-0.661987\pi\)
0.873283 + 0.487213i \(0.161987\pi\)
\(74\) 1156.91 1.81740
\(75\) 160.068 596.581i 0.246441 0.918496i
\(76\) 2307.45i 3.48266i
\(77\) 190.373 + 190.373i 0.281753 + 0.281753i
\(78\) −806.763 + 806.763i −1.17113 + 1.17113i
\(79\) 567.099 0.807641 0.403820 0.914838i \(-0.367682\pi\)
0.403820 + 0.914838i \(0.367682\pi\)
\(80\) 1772.34 474.577i 2.47691 0.663241i
\(81\) 652.618 0.895223
\(82\) −674.686 674.686i −0.908617 0.908617i
\(83\) −722.376 722.376i −0.955314 0.955314i 0.0437293 0.999043i \(-0.486076\pi\)
−0.999043 + 0.0437293i \(0.986076\pi\)
\(84\) 369.655 0.480151
\(85\) 276.654 478.994i 0.353028 0.611225i
\(86\) 570.187i 0.714940i
\(87\) −340.710 340.710i −0.419861 0.419861i
\(88\) 3051.01 + 3051.01i 3.69590 + 3.69590i
\(89\) −0.0871278 −0.000103770 −5.18850e−5 1.00000i \(-0.500017\pi\)
−5.18850e−5 1.00000i \(0.500017\pi\)
\(90\) −75.8855 + 131.387i −0.0888782 + 0.153882i
\(91\) 167.463i 0.192911i
\(92\) −972.740 1933.72i −1.10234 2.19135i
\(93\) −304.696 + 304.696i −0.339736 + 0.339736i
\(94\) 585.880i 0.642861i
\(95\) −1269.88 + 340.036i −1.37144 + 0.367231i
\(96\) 1846.98 1.96361
\(97\) −169.555 + 169.555i −0.177482 + 0.177482i −0.790257 0.612775i \(-0.790053\pi\)
0.612775 + 0.790257i \(0.290053\pi\)
\(98\) 1220.73 1220.73i 1.25829 1.25829i
\(99\) −182.360 −0.185129
\(100\) 1225.78 + 2124.76i 1.22578 + 2.12476i
\(101\) 497.288 0.489921 0.244961 0.969533i \(-0.421225\pi\)
0.244961 + 0.969533i \(0.421225\pi\)
\(102\) 908.591 908.591i 0.881999 0.881999i
\(103\) −1081.77 1081.77i −1.03485 1.03485i −0.999370 0.0354803i \(-0.988704\pi\)
−0.0354803 0.999370i \(-0.511296\pi\)
\(104\) 2683.86i 2.53052i
\(105\) 54.4741 + 203.437i 0.0506298 + 0.189080i
\(106\) 3155.86i 2.89173i
\(107\) 368.897 368.897i 0.333295 0.333295i −0.520541 0.853837i \(-0.674270\pi\)
0.853837 + 0.520541i \(0.174270\pi\)
\(108\) −2028.40 + 2028.40i −1.80725 + 1.80725i
\(109\) −644.222 −0.566104 −0.283052 0.959105i \(-0.591347\pi\)
−0.283052 + 0.959105i \(0.591347\pi\)
\(110\) −2075.67 + 3593.76i −1.79915 + 3.11502i
\(111\) 1087.70i 0.930090i
\(112\) −442.353 + 442.353i −0.373200 + 0.373200i
\(113\) −909.217 909.217i −0.756920 0.756920i 0.218841 0.975761i \(-0.429772\pi\)
−0.975761 + 0.218841i \(0.929772\pi\)
\(114\) −3053.81 −2.50891
\(115\) 920.859 820.301i 0.746701 0.665160i
\(116\) 1913.51 1.53160
\(117\) 80.2073 + 80.2073i 0.0633775 + 0.0633775i
\(118\) 2075.43 2075.43i 1.61914 1.61914i
\(119\) 188.600i 0.145285i
\(120\) 873.030 + 3260.38i 0.664137 + 2.48026i
\(121\) −3657.00 −2.74756
\(122\) 228.965 228.965i 0.169914 0.169914i
\(123\) 634.327 634.327i 0.465003 0.465003i
\(124\) 1711.25i 1.23931i
\(125\) −988.709 + 987.714i −0.707463 + 0.706750i
\(126\) 51.7326i 0.0365770i
\(127\) 1255.84 + 1255.84i 0.877465 + 0.877465i 0.993272 0.115807i \(-0.0369453\pi\)
−0.115807 + 0.993272i \(0.536945\pi\)
\(128\) −307.398 + 307.398i −0.212269 + 0.212269i
\(129\) 536.080 0.365885
\(130\) 2493.59 667.706i 1.68232 0.450475i
\(131\) 825.793 0.550762 0.275381 0.961335i \(-0.411196\pi\)
0.275381 + 0.961335i \(0.411196\pi\)
\(132\) −4842.72 + 4842.72i −3.19321 + 3.19321i
\(133\) 316.947 316.947i 0.206638 0.206638i
\(134\) 2761.48 1.78026
\(135\) −1415.23 817.399i −0.902248 0.521115i
\(136\) 3022.61i 1.90578i
\(137\) 14.1324 14.1324i 0.00881322 0.00881322i −0.702686 0.711500i \(-0.748016\pi\)
0.711500 + 0.702686i \(0.248016\pi\)
\(138\) 2559.20 1287.38i 1.57865 0.794126i
\(139\) 2328.20i 1.42069i 0.703855 + 0.710344i \(0.251461\pi\)
−0.703855 + 0.710344i \(0.748539\pi\)
\(140\) −724.246 418.306i −0.437214 0.252523i
\(141\) 550.834 0.328997
\(142\) 345.716 + 345.716i 0.204309 + 0.204309i
\(143\) 2193.88 + 2193.88i 1.28294 + 1.28294i
\(144\) 423.733i 0.245216i
\(145\) 281.984 + 1053.09i 0.161500 + 0.603131i
\(146\) −1789.81 −1.01456
\(147\) 1147.71 + 1147.71i 0.643958 + 0.643958i
\(148\) −3054.40 3054.40i −1.69642 1.69642i
\(149\) −3245.89 −1.78465 −0.892326 0.451391i \(-0.850928\pi\)
−0.892326 + 0.451391i \(0.850928\pi\)
\(150\) −2812.04 + 1622.28i −1.53068 + 0.883055i
\(151\) −1903.09 −1.02564 −0.512819 0.858497i \(-0.671399\pi\)
−0.512819 + 0.858497i \(0.671399\pi\)
\(152\) 5079.56 5079.56i 2.71057 2.71057i
\(153\) −90.3309 90.3309i −0.0477308 0.0477308i
\(154\) 1415.02i 0.740425i
\(155\) 941.771 252.177i 0.488031 0.130680i
\(156\) 4259.95 2.18634
\(157\) 666.703 666.703i 0.338909 0.338909i −0.517048 0.855957i \(-0.672969\pi\)
0.855957 + 0.517048i \(0.172969\pi\)
\(158\) −2107.59 2107.59i −1.06121 1.06121i
\(159\) 2967.08 1.47990
\(160\) −3618.70 2090.07i −1.78802 1.03271i
\(161\) −131.999 + 399.227i −0.0646147 + 0.195425i
\(162\) −2425.42 2425.42i −1.17629 1.17629i
\(163\) 1276.65 1276.65i 0.613466 0.613466i −0.330382 0.943847i \(-0.607177\pi\)
0.943847 + 0.330382i \(0.107177\pi\)
\(164\) 3562.54i 1.69627i
\(165\) −3378.79 1951.50i −1.59417 0.920753i
\(166\) 5369.34i 2.51049i
\(167\) 913.251 + 913.251i 0.423171 + 0.423171i 0.886294 0.463123i \(-0.153271\pi\)
−0.463123 + 0.886294i \(0.653271\pi\)
\(168\) −813.751 813.751i −0.373704 0.373704i
\(169\) 267.133i 0.121590i
\(170\) −2808.32 + 751.983i −1.26699 + 0.339261i
\(171\) 303.606i 0.135774i
\(172\) −1505.38 + 1505.38i −0.667349 + 0.667349i
\(173\) 2515.97 2515.97i 1.10570 1.10570i 0.111988 0.993710i \(-0.464278\pi\)
0.993710 0.111988i \(-0.0357217\pi\)
\(174\) 2532.46i 1.10336i
\(175\) 123.483 460.226i 0.0533396 0.198799i
\(176\) 11590.2i 4.96389i
\(177\) 1951.28 + 1951.28i 0.828627 + 0.828627i
\(178\) 0.323806 + 0.323806i 0.000136350 + 0.000136350i
\(179\) 3856.80i 1.61045i −0.592969 0.805225i \(-0.702044\pi\)
0.592969 0.805225i \(-0.297956\pi\)
\(180\) 547.229 146.531i 0.226600 0.0606766i
\(181\) 2450.67i 1.00639i −0.864172 0.503196i \(-0.832157\pi\)
0.864172 0.503196i \(-0.167843\pi\)
\(182\) −622.369 + 622.369i −0.253478 + 0.253478i
\(183\) 215.269 + 215.269i 0.0869569 + 0.0869569i
\(184\) −2115.48 + 6398.22i −0.847584 + 2.56349i
\(185\) 1230.85 2131.07i 0.489157 0.846917i
\(186\) 2264.77 0.892801
\(187\) −2470.78 2470.78i −0.966211 0.966211i
\(188\) −1546.81 + 1546.81i −0.600068 + 0.600068i
\(189\) 557.236 0.214460
\(190\) 5983.17 + 3455.73i 2.28455 + 1.31950i
\(191\) 4205.73i 1.59328i −0.604456 0.796639i \(-0.706609\pi\)
0.604456 0.796639i \(-0.293391\pi\)
\(192\) −2276.91 2276.91i −0.855844 0.855844i
\(193\) −1539.23 + 1539.23i −0.574073 + 0.574073i −0.933264 0.359191i \(-0.883053\pi\)
0.359191 + 0.933264i \(0.383053\pi\)
\(194\) 1260.29 0.466409
\(195\) 627.765 + 2344.43i 0.230539 + 0.860963i
\(196\) −6445.84 −2.34907
\(197\) −1526.16 1526.16i −0.551951 0.551951i 0.375053 0.927004i \(-0.377625\pi\)
−0.927004 + 0.375053i \(0.877625\pi\)
\(198\) 677.729 + 677.729i 0.243253 + 0.243253i
\(199\) 4868.55 1.73428 0.867142 0.498061i \(-0.165955\pi\)
0.867142 + 0.498061i \(0.165955\pi\)
\(200\) 1979.00 7375.82i 0.699682 2.60775i
\(201\) 2596.29i 0.911086i
\(202\) −1848.14 1848.14i −0.643738 0.643738i
\(203\) −262.837 262.837i −0.0908746 0.0908746i
\(204\) −4797.63 −1.64657
\(205\) −1960.61 + 524.992i −0.667977 + 0.178864i
\(206\) 8040.65i 2.71951i
\(207\) −127.990 254.433i −0.0429754 0.0854313i
\(208\) −5097.72 + 5097.72i −1.69934 + 1.69934i
\(209\) 8304.41i 2.74846i
\(210\) 553.611 958.511i 0.181918 0.314969i
\(211\) 1523.81 0.497174 0.248587 0.968610i \(-0.420034\pi\)
0.248587 + 0.968610i \(0.420034\pi\)
\(212\) −8331.93 + 8331.93i −2.69924 + 2.69924i
\(213\) −325.036 + 325.036i −0.104559 + 0.104559i
\(214\) −2741.97 −0.875875
\(215\) −1050.31 606.633i −0.333166 0.192428i
\(216\) 8930.56 2.81318
\(217\) −235.054 + 235.054i −0.0735324 + 0.0735324i
\(218\) 2394.22 + 2394.22i 0.743839 + 0.743839i
\(219\) 1682.75i 0.519222i
\(220\) 14968.1 4008.01i 4.58705 1.22827i
\(221\) 2173.45i 0.661548i
\(222\) 4042.38 4042.38i 1.22210 1.22210i
\(223\) −1390.89 + 1390.89i −0.417673 + 0.417673i −0.884401 0.466728i \(-0.845433\pi\)
0.466728 + 0.884401i \(0.345433\pi\)
\(224\) 1424.84 0.425004
\(225\) 161.284 + 279.570i 0.0477880 + 0.0828354i
\(226\) 6758.11i 1.98913i
\(227\) 329.537 329.537i 0.0963530 0.0963530i −0.657287 0.753640i \(-0.728296\pi\)
0.753640 + 0.657287i \(0.228296\pi\)
\(228\) 8062.52 + 8062.52i 2.34190 + 2.34190i
\(229\) 3621.72 1.04511 0.522555 0.852605i \(-0.324979\pi\)
0.522555 + 0.852605i \(0.324979\pi\)
\(230\) −6470.93 373.720i −1.85513 0.107141i
\(231\) 1330.38 0.378928
\(232\) −4212.36 4212.36i −1.19205 1.19205i
\(233\) −83.9472 + 83.9472i −0.0236033 + 0.0236033i −0.718810 0.695207i \(-0.755313\pi\)
0.695207 + 0.718810i \(0.255313\pi\)
\(234\) 596.172i 0.166551i
\(235\) −1079.22 623.329i −0.299576 0.173028i
\(236\) −10958.9 −3.02272
\(237\) 1981.52 1981.52i 0.543095 0.543095i
\(238\) 700.923 700.923i 0.190900 0.190900i
\(239\) 3144.38i 0.851017i −0.904954 0.425509i \(-0.860095\pi\)
0.904954 0.425509i \(-0.139905\pi\)
\(240\) 4534.54 7851.01i 1.21960 2.11159i
\(241\) 5266.92i 1.40777i −0.710314 0.703885i \(-0.751447\pi\)
0.710314 0.703885i \(-0.248553\pi\)
\(242\) 13591.1 + 13591.1i 3.61019 + 3.61019i
\(243\) −510.485 + 510.485i −0.134764 + 0.134764i
\(244\) −1209.00 −0.317207
\(245\) −949.888 3547.41i −0.247699 0.925045i
\(246\) −4714.89 −1.22199
\(247\) 3652.53 3652.53i 0.940911 0.940911i
\(248\) −3767.10 + 3767.10i −0.964562 + 0.964562i
\(249\) −5048.16 −1.28480
\(250\) 7345.27 + 3.70004i 1.85822 + 0.000936044i
\(251\) 875.069i 0.220055i 0.993929 + 0.110028i \(0.0350939\pi\)
−0.993929 + 0.110028i \(0.964906\pi\)
\(252\) −136.582 + 136.582i −0.0341422 + 0.0341422i
\(253\) −3500.85 6959.39i −0.869948 1.72938i
\(254\) 9334.54i 2.30591i
\(255\) −707.001 2640.34i −0.173624 0.648409i
\(256\) −2928.25 −0.714906
\(257\) 2903.41 + 2903.41i 0.704707 + 0.704707i 0.965417 0.260710i \(-0.0839567\pi\)
−0.260710 + 0.965417i \(0.583957\pi\)
\(258\) −1992.31 1992.31i −0.480759 0.480759i
\(259\) 839.095i 0.201308i
\(260\) −8346.28 4820.60i −1.99083 1.14985i
\(261\) 251.774 0.0597103
\(262\) −3069.01 3069.01i −0.723681 0.723681i
\(263\) 2424.48 + 2424.48i 0.568440 + 0.568440i 0.931691 0.363251i \(-0.118333\pi\)
−0.363251 + 0.931691i \(0.618333\pi\)
\(264\) 21321.3 4.97059
\(265\) −5813.24 3357.58i −1.34756 0.778318i
\(266\) −2355.83 −0.543028
\(267\) −0.304436 + 0.304436i −6.97798e−5 + 6.97798e-5i
\(268\) −7290.71 7290.71i −1.66176 1.66176i
\(269\) 2056.18i 0.466051i 0.972471 + 0.233026i \(0.0748626\pi\)
−0.972471 + 0.233026i \(0.925137\pi\)
\(270\) 2221.80 + 8297.44i 0.500794 + 1.87024i
\(271\) 3036.18 0.680572 0.340286 0.940322i \(-0.389476\pi\)
0.340286 + 0.940322i \(0.389476\pi\)
\(272\) 5741.15 5741.15i 1.27981 1.27981i
\(273\) −585.140 585.140i −0.129723 0.129723i
\(274\) −105.044 −0.0231605
\(275\) 4411.54 + 7646.95i 0.967368 + 1.67683i
\(276\) −10155.6 3357.79i −2.21483 0.732302i
\(277\) 77.5156 + 77.5156i 0.0168139 + 0.0168139i 0.715464 0.698650i \(-0.246215\pi\)
−0.698650 + 0.715464i \(0.746215\pi\)
\(278\) 8652.64 8652.64i 1.86673 1.86673i
\(279\) 225.160i 0.0483154i
\(280\) 673.490 + 2515.19i 0.143745 + 0.536826i
\(281\) 3619.73i 0.768451i 0.923239 + 0.384226i \(0.125532\pi\)
−0.923239 + 0.384226i \(0.874468\pi\)
\(282\) −2047.14 2047.14i −0.432289 0.432289i
\(283\) 5080.30 + 5080.30i 1.06711 + 1.06711i 0.997580 + 0.0695306i \(0.0221501\pi\)
0.0695306 + 0.997580i \(0.477850\pi\)
\(284\) 1825.49i 0.381418i
\(285\) −3249.01 + 5625.27i −0.675280 + 1.16917i
\(286\) 16306.8i 3.37148i
\(287\) 489.345 489.345i 0.100645 0.100645i
\(288\) −682.431 + 682.431i −0.139627 + 0.139627i
\(289\) 2465.22i 0.501775i
\(290\) 2865.76 4961.71i 0.580286 1.00470i
\(291\) 1184.90i 0.238694i
\(292\) 4725.37 + 4725.37i 0.947025 + 0.947025i
\(293\) −3393.79 3393.79i −0.676679 0.676679i 0.282568 0.959247i \(-0.408814\pi\)
−0.959247 + 0.282568i \(0.908814\pi\)
\(294\) 8530.82i 1.69227i
\(295\) −1614.95 6031.12i −0.318732 1.19032i
\(296\) 13447.8i 2.64066i
\(297\) −7300.14 + 7300.14i −1.42625 + 1.42625i
\(298\) 12063.2 + 12063.2i 2.34497 + 2.34497i
\(299\) −1521.17 + 4600.73i −0.294219 + 0.889857i
\(300\) 11707.3 + 3141.16i 2.25306 + 0.604517i
\(301\) 413.553 0.0791920
\(302\) 7072.74 + 7072.74i 1.34765 + 1.34765i
\(303\) 1737.59 1737.59i 0.329446 0.329446i
\(304\) −19296.3 −3.64051
\(305\) −178.164 665.364i −0.0334480 0.124914i
\(306\) 671.419i 0.125433i
\(307\) −4008.91 4008.91i −0.745279 0.745279i 0.228310 0.973589i \(-0.426680\pi\)
−0.973589 + 0.228310i \(0.926680\pi\)
\(308\) −3735.86 + 3735.86i −0.691138 + 0.691138i
\(309\) −7559.67 −1.39176
\(310\) −4437.24 2562.84i −0.812963 0.469546i
\(311\) −3301.67 −0.601996 −0.300998 0.953625i \(-0.597320\pi\)
−0.300998 + 0.953625i \(0.597320\pi\)
\(312\) −9377.76 9377.76i −1.70164 1.70164i
\(313\) −2091.05 2091.05i −0.377614 0.377614i 0.492627 0.870241i \(-0.336037\pi\)
−0.870241 + 0.492627i \(0.836037\pi\)
\(314\) −4955.53 −0.890627
\(315\) −95.2939 55.0393i −0.0170451 0.00984480i
\(316\) 11128.7i 1.98114i
\(317\) 986.304 + 986.304i 0.174752 + 0.174752i 0.789064 0.614312i \(-0.210566\pi\)
−0.614312 + 0.789064i \(0.710566\pi\)
\(318\) −11027.0 11027.0i −1.94454 1.94454i
\(319\) 6886.66 1.20871
\(320\) 1884.46 + 7037.61i 0.329201 + 1.22942i
\(321\) 2577.95i 0.448247i
\(322\) 1974.27 993.138i 0.341683 0.171880i
\(323\) −4113.55 + 4113.55i −0.708619 + 0.708619i
\(324\) 12806.9i 2.19597i
\(325\) 1423.03 5303.69i 0.242878 0.905218i
\(326\) −9489.20 −1.61214
\(327\) −2251.00 + 2251.00i −0.380674 + 0.380674i
\(328\) 7842.50 7842.50i 1.32021 1.32021i
\(329\) 424.935 0.0712079
\(330\) 5304.44 + 19809.8i 0.884848 + 3.30452i
\(331\) 8190.61 1.36011 0.680056 0.733161i \(-0.261956\pi\)
0.680056 + 0.733161i \(0.261956\pi\)
\(332\) 14175.9 14175.9i 2.34338 2.34338i
\(333\) −401.888 401.888i −0.0661361 0.0661361i
\(334\) 6788.10i 1.11206i
\(335\) 2937.99 5086.78i 0.479163 0.829613i
\(336\) 3091.28i 0.501914i
\(337\) −4426.61 + 4426.61i −0.715527 + 0.715527i −0.967686 0.252159i \(-0.918859\pi\)
0.252159 + 0.967686i \(0.418859\pi\)
\(338\) 992.787 992.787i 0.159765 0.159765i
\(339\) −6353.85 −1.01798
\(340\) 9399.74 + 5429.05i 1.49933 + 0.865974i
\(341\) 6158.72i 0.978045i
\(342\) 1128.34 1128.34i 0.178402 0.178402i
\(343\) 1809.95 + 1809.95i 0.284922 + 0.284922i
\(344\) 6627.82 1.03880
\(345\) 351.364 6083.85i 0.0548314 0.949401i
\(346\) −18700.9 −2.90569
\(347\) −3775.87 3775.87i −0.584148 0.584148i 0.351892 0.936040i \(-0.385538\pi\)
−0.936040 + 0.351892i \(0.885538\pi\)
\(348\) 6686.07 6686.07i 1.02992 1.02992i
\(349\) 6013.63i 0.922355i 0.887308 + 0.461178i \(0.152573\pi\)
−0.887308 + 0.461178i \(0.847427\pi\)
\(350\) −2169.32 + 1251.49i −0.331300 + 0.191128i
\(351\) 6421.65 0.976531
\(352\) −18666.2 + 18666.2i −2.82646 + 2.82646i
\(353\) 737.448 737.448i 0.111191 0.111191i −0.649322 0.760513i \(-0.724947\pi\)
0.760513 + 0.649322i \(0.224947\pi\)
\(354\) 14503.6i 2.17757i
\(355\) 1004.64 269.012i 0.150199 0.0402188i
\(356\) 1.70979i 0.000254547i
\(357\) 658.995 + 658.995i 0.0976967 + 0.0976967i
\(358\) −14333.6 + 14333.6i −2.11607 + 2.11607i
\(359\) 2769.18 0.407108 0.203554 0.979064i \(-0.434751\pi\)
0.203554 + 0.979064i \(0.434751\pi\)
\(360\) −1527.23 882.088i −0.223589 0.129139i
\(361\) 6966.82 1.01572
\(362\) −9107.79 + 9107.79i −1.32236 + 1.32236i
\(363\) −12778.1 + 12778.1i −1.84759 + 1.84759i
\(364\) 3286.29 0.473210
\(365\) −1904.22 + 3296.92i −0.273072 + 0.472791i
\(366\) 1600.07i 0.228516i
\(367\) 6500.70 6500.70i 0.924615 0.924615i −0.0727364 0.997351i \(-0.523173\pi\)
0.997351 + 0.0727364i \(0.0231732\pi\)
\(368\) 16170.9 8134.64i 2.29068 1.15230i
\(369\) 468.747i 0.0661301i
\(370\) −12494.4 + 3345.62i −1.75555 + 0.470083i
\(371\) 2288.92 0.320310
\(372\) −5979.33 5979.33i −0.833370 0.833370i
\(373\) −3083.94 3083.94i −0.428098 0.428098i 0.459882 0.887980i \(-0.347892\pi\)
−0.887980 + 0.459882i \(0.847892\pi\)
\(374\) 18365.1i 2.53913i
\(375\) −3.47871 + 6905.89i −0.000479040 + 0.950983i
\(376\) 6810.23 0.934071
\(377\) −3028.96 3028.96i −0.413792 0.413792i
\(378\) −2070.94 2070.94i −0.281792 0.281792i
\(379\) −12579.9 −1.70498 −0.852489 0.522746i \(-0.824908\pi\)
−0.852489 + 0.522746i \(0.824908\pi\)
\(380\) −6672.83 24920.1i −0.900814 3.36414i
\(381\) 8776.17 1.18010
\(382\) −15630.4 + 15630.4i −2.09351 + 2.09351i
\(383\) 4263.99 + 4263.99i 0.568876 + 0.568876i 0.931813 0.362938i \(-0.118226\pi\)
−0.362938 + 0.931813i \(0.618226\pi\)
\(384\) 2148.18i 0.285479i
\(385\) −2606.53 1505.47i −0.345042 0.199287i
\(386\) 11440.9 1.50862
\(387\) −198.073 + 198.073i −0.0260171 + 0.0260171i
\(388\) −3327.34 3327.34i −0.435362 0.435362i
\(389\) 8556.72 1.11528 0.557639 0.830084i \(-0.311707\pi\)
0.557639 + 0.830084i \(0.311707\pi\)
\(390\) 6379.88 11046.0i 0.828353 1.43419i
\(391\) 1713.17 5181.43i 0.221582 0.670169i
\(392\) 14189.7 + 14189.7i 1.82829 + 1.82829i
\(393\) 2885.43 2885.43i 0.370358 0.370358i
\(394\) 11343.8i 1.45049i
\(395\) −6124.59 + 1639.98i −0.780156 + 0.208902i
\(396\) 3578.61i 0.454121i
\(397\) −9370.46 9370.46i −1.18461 1.18461i −0.978537 0.206072i \(-0.933932\pi\)
−0.206072 0.978537i \(-0.566068\pi\)
\(398\) −18093.7 18093.7i −2.27878 2.27878i
\(399\) 2214.91i 0.277905i
\(400\) −17768.6 + 10250.7i −2.22107 + 1.28134i
\(401\) 5100.76i 0.635211i 0.948223 + 0.317605i \(0.102879\pi\)
−0.948223 + 0.317605i \(0.897121\pi\)
\(402\) 9648.98 9648.98i 1.19713 1.19713i
\(403\) −2708.79 + 2708.79i −0.334825 + 0.334825i
\(404\) 9758.75i 1.20177i
\(405\) −7048.18 + 1887.29i −0.864758 + 0.231556i
\(406\) 1953.64i 0.238811i
\(407\) −10992.7 10992.7i −1.33879 1.33879i
\(408\) 10561.4 + 10561.4i 1.28154 + 1.28154i
\(409\) 2575.73i 0.311398i −0.987805 0.155699i \(-0.950237\pi\)
0.987805 0.155699i \(-0.0497630\pi\)
\(410\) 9237.62 + 5335.41i 1.11272 + 0.642676i
\(411\) 98.7608i 0.0118528i
\(412\) 21228.5 21228.5i 2.53848 2.53848i
\(413\) 1505.29 + 1505.29i 0.179348 + 0.179348i
\(414\) −469.917 + 1421.25i −0.0557854 + 0.168722i
\(415\) 9890.58 + 5712.54i 1.16990 + 0.675706i
\(416\) 16420.0 1.93523
\(417\) 8135.05 + 8135.05i 0.955337 + 0.955337i
\(418\) 30862.9 30862.9i 3.61137 3.61137i
\(419\) 10481.2 1.22205 0.611026 0.791610i \(-0.290757\pi\)
0.611026 + 0.791610i \(0.290757\pi\)
\(420\) −3992.23 + 1069.00i −0.463811 + 0.124194i
\(421\) 2808.97i 0.325180i 0.986694 + 0.162590i \(0.0519847\pi\)
−0.986694 + 0.162590i \(0.948015\pi\)
\(422\) −5663.17 5663.17i −0.653267 0.653267i
\(423\) −203.524 + 203.524i −0.0233940 + 0.0233940i
\(424\) 36683.5 4.20167
\(425\) −1602.64 + 5973.11i −0.182917 + 0.681738i
\(426\) 2415.96 0.274774
\(427\) 166.067 + 166.067i 0.0188209 + 0.0188209i
\(428\) 7239.21 + 7239.21i 0.817571 + 0.817571i
\(429\) 15331.4 1.72542
\(430\) 1648.91 + 6157.94i 0.184924 + 0.690610i
\(431\) 10490.7i 1.17243i −0.810155 0.586215i \(-0.800617\pi\)
0.810155 0.586215i \(-0.199383\pi\)
\(432\) −16962.7 16962.7i −1.88916 1.88916i
\(433\) 8920.14 + 8920.14i 0.990010 + 0.990010i 0.999951 0.00994052i \(-0.00316422\pi\)
−0.00994052 + 0.999951i \(0.503164\pi\)
\(434\) 1747.13 0.193237
\(435\) 4664.91 + 2694.33i 0.514173 + 0.296973i
\(436\) 12642.2i 1.38865i
\(437\) −11586.5 + 5828.49i −1.26833 + 0.638019i
\(438\) −6253.85 + 6253.85i −0.682238 + 0.682238i
\(439\) 3758.92i 0.408664i −0.978902 0.204332i \(-0.934498\pi\)
0.978902 0.204332i \(-0.0655022\pi\)
\(440\) −41773.7 24127.4i −4.52609 2.61416i
\(441\) −848.123 −0.0915800
\(442\) 8077.51 8077.51i 0.869249 0.869249i
\(443\) 10017.5 10017.5i 1.07437 1.07437i 0.0773688 0.997003i \(-0.475348\pi\)
0.997003 0.0773688i \(-0.0246519\pi\)
\(444\) −21345.0 −2.28150
\(445\) 0.940969 0.251962i 0.000100239 2.68408e-5i
\(446\) 10338.4 1.09761
\(447\) −11341.6 + 11341.6i −1.20008 + 1.20008i
\(448\) −1756.50 1756.50i −0.185239 0.185239i
\(449\) 9423.08i 0.990429i 0.868771 + 0.495214i \(0.164911\pi\)
−0.868771 + 0.495214i \(0.835089\pi\)
\(450\) 439.600 1638.41i 0.0460510 0.171634i
\(451\) 12821.5i 1.33867i
\(452\) 17842.4 17842.4i 1.85672 1.85672i
\(453\) −6649.66 + 6649.66i −0.689687 + 0.689687i
\(454\) −2449.41 −0.253208
\(455\) 484.283 + 1808.58i 0.0498979 + 0.186346i
\(456\) 35497.3i 3.64543i
\(457\) 7207.79 7207.79i 0.737781 0.737781i −0.234367 0.972148i \(-0.575302\pi\)
0.972148 + 0.234367i \(0.0753017\pi\)
\(458\) −13459.9 13459.9i −1.37324 1.37324i
\(459\) −7232.18 −0.735445
\(460\) 16097.5 + 18070.9i 1.63163 + 1.83165i
\(461\) −4267.00 −0.431093 −0.215547 0.976494i \(-0.569153\pi\)
−0.215547 + 0.976494i \(0.569153\pi\)
\(462\) −4944.27 4944.27i −0.497896 0.497896i
\(463\) −3214.21 + 3214.21i −0.322629 + 0.322629i −0.849775 0.527146i \(-0.823262\pi\)
0.527146 + 0.849775i \(0.323262\pi\)
\(464\) 16001.9i 1.60102i
\(465\) 2409.53 4171.81i 0.240300 0.416050i
\(466\) 623.970 0.0620276
\(467\) 1387.00 1387.00i 0.137436 0.137436i −0.635042 0.772478i \(-0.719017\pi\)
0.772478 + 0.635042i \(0.219017\pi\)
\(468\) −1573.98 + 1573.98i −0.155464 + 0.155464i
\(469\) 2002.88i 0.197195i
\(470\) 1694.29 + 6327.42i 0.166280 + 0.620984i
\(471\) 4659.10i 0.455796i
\(472\) 24124.6 + 24124.6i 2.35259 + 2.35259i
\(473\) −5417.80 + 5417.80i −0.526661 + 0.526661i
\(474\) −14728.4 −1.42721
\(475\) 12731.2 7344.68i 1.22979 0.709467i
\(476\) −3701.08 −0.356384
\(477\) −1096.29 + 1096.29i −0.105232 + 0.105232i
\(478\) −11685.9 + 11685.9i −1.11820 + 1.11820i
\(479\) 2424.10 0.231231 0.115616 0.993294i \(-0.463116\pi\)
0.115616 + 0.993294i \(0.463116\pi\)
\(480\) −19947.2 + 5341.24i −1.89679 + 0.507902i
\(481\) 9669.83i 0.916645i
\(482\) −19574.2 + 19574.2i −1.84975 + 1.84975i
\(483\) 933.730 + 1856.17i 0.0879632 + 0.174863i
\(484\) 71764.8i 6.73974i
\(485\) 1340.84 2321.51i 0.125535 0.217349i
\(486\) 3794.38 0.354149
\(487\) 10961.4 + 10961.4i 1.01993 + 1.01993i 0.999797 + 0.0201342i \(0.00640935\pi\)
0.0201342 + 0.999797i \(0.493591\pi\)
\(488\) 2661.47 + 2661.47i 0.246883 + 0.246883i
\(489\) 8921.57i 0.825046i
\(490\) −9653.56 + 16714.0i −0.890007 + 1.54094i
\(491\) 18504.0 1.70076 0.850382 0.526165i \(-0.176371\pi\)
0.850382 + 0.526165i \(0.176371\pi\)
\(492\) 12448.0 + 12448.0i 1.14065 + 1.14065i
\(493\) 3411.27 + 3411.27i 0.311635 + 0.311635i
\(494\) −27148.9 −2.47264
\(495\) 1969.46 527.360i 0.178829 0.0478850i
\(496\) 14310.5 1.29548
\(497\) −250.746 + 250.746i −0.0226308 + 0.0226308i
\(498\) 18761.2 + 18761.2i 1.68817 + 1.68817i
\(499\) 9355.71i 0.839317i −0.907682 0.419658i \(-0.862150\pi\)
0.907682 0.419658i \(-0.137850\pi\)
\(500\) −19382.8 19402.4i −1.73365 1.73540i
\(501\) 6382.05 0.569119
\(502\) 3252.15 3252.15i 0.289144 0.289144i
\(503\) 6245.76 + 6245.76i 0.553648 + 0.553648i 0.927492 0.373844i \(-0.121960\pi\)
−0.373844 + 0.927492i \(0.621960\pi\)
\(504\) 601.336 0.0531461
\(505\) −5370.65 + 1438.09i −0.473249 + 0.126721i
\(506\) −12853.4 + 38874.9i −1.12926 + 3.41542i
\(507\) 933.400 + 933.400i 0.0817628 + 0.0817628i
\(508\) −24644.6 + 24644.6i −2.15241 + 2.15241i
\(509\) 12044.2i 1.04882i 0.851465 + 0.524412i \(0.175715\pi\)
−0.851465 + 0.524412i \(0.824285\pi\)
\(510\) −7185.13 + 12440.2i −0.623849 + 1.08012i
\(511\) 1298.14i 0.112380i
\(512\) 13341.9 + 13341.9i 1.15163 + 1.15163i
\(513\) 12153.8 + 12153.8i 1.04601 + 1.04601i
\(514\) 21580.7i 1.85192i
\(515\) 14811.3 + 8554.60i 1.26731 + 0.731963i
\(516\) 10520.0i 0.897513i
\(517\) −5566.91 + 5566.91i −0.473564 + 0.473564i
\(518\) 3118.45 3118.45i 0.264511 0.264511i
\(519\) 17582.3i 1.48704i
\(520\) 7761.37 + 28985.3i 0.654536 + 2.44440i
\(521\) 4570.82i 0.384359i 0.981360 + 0.192180i \(0.0615556\pi\)
−0.981360 + 0.192180i \(0.938444\pi\)
\(522\) −935.703 935.703i −0.0784571 0.0784571i
\(523\) 7280.41 + 7280.41i 0.608700 + 0.608700i 0.942606 0.333906i \(-0.108367\pi\)
−0.333906 + 0.942606i \(0.608367\pi\)
\(524\) 16205.3i 1.35102i
\(525\) −1176.63 2039.56i −0.0978136 0.169550i
\(526\) 18020.9i 1.49382i
\(527\) 3050.69 3050.69i 0.252163 0.252163i
\(528\) −40497.7 40497.7i −3.33795 3.33795i
\(529\) 7252.82 9768.96i 0.596106 0.802906i
\(530\) 9126.33 + 34082.8i 0.747967 + 2.79333i
\(531\) −1441.93 −0.117843
\(532\) 6219.75 + 6219.75i 0.506880 + 0.506880i
\(533\) 5639.27 5639.27i 0.458281 0.458281i
\(534\) 2.26284 0.000183376
\(535\) −2917.23 + 5050.84i −0.235744 + 0.408162i
\(536\) 32099.2i 2.58671i
\(537\) −13476.2 13476.2i −1.08294 1.08294i
\(538\) 7641.70 7641.70i 0.612373 0.612373i
\(539\) −23198.3 −1.85385
\(540\) 16040.6 27772.3i 1.27829 2.21321i
\(541\) −13636.4 −1.08369 −0.541844 0.840479i \(-0.682273\pi\)
−0.541844 + 0.840479i \(0.682273\pi\)
\(542\) −11283.8 11283.8i −0.894246 0.894246i
\(543\) −8562.98 8562.98i −0.676745 0.676745i
\(544\) −18492.5 −1.45746
\(545\) 6957.51 1863.01i 0.546839 0.146427i
\(546\) 4349.28i 0.340901i
\(547\) −11863.1 11863.1i −0.927294 0.927294i 0.0702367 0.997530i \(-0.477625\pi\)
−0.997530 + 0.0702367i \(0.977625\pi\)
\(548\) 277.333 + 277.333i 0.0216187 + 0.0216187i
\(549\) −159.077 −0.0123665
\(550\) 12024.2 44814.7i 0.932207 3.47438i
\(551\) 11465.4i 0.886468i
\(552\) 14964.5 + 29748.0i 1.15386 + 2.29377i
\(553\) 1528.62 1528.62i 0.117547 0.117547i
\(554\) 576.165i 0.0441858i
\(555\) −3145.49 11747.0i −0.240574 0.898439i
\(556\) −45688.5 −3.48494
\(557\) 737.647 737.647i 0.0561133 0.0561133i −0.678493 0.734607i \(-0.737367\pi\)
0.734607 + 0.678493i \(0.237367\pi\)
\(558\) −836.796 + 836.796i −0.0634846 + 0.0634846i
\(559\) 4765.83 0.360596
\(560\) 3498.12 6056.58i 0.263969 0.457031i
\(561\) −17266.5 −1.29945
\(562\) 13452.5 13452.5i 1.00972 1.00972i
\(563\) −11444.6 11444.6i −0.856721 0.856721i 0.134229 0.990950i \(-0.457144\pi\)
−0.990950 + 0.134229i \(0.957144\pi\)
\(564\) 10809.5i 0.807027i
\(565\) 12448.8 + 7190.08i 0.926944 + 0.535379i
\(566\) 37761.3i 2.80428i
\(567\) 1759.14 1759.14i 0.130294 0.130294i
\(568\) −4018.58 + 4018.58i −0.296859 + 0.296859i
\(569\) 4441.18 0.327212 0.163606 0.986526i \(-0.447687\pi\)
0.163606 + 0.986526i \(0.447687\pi\)
\(570\) 32980.8 8831.24i 2.42353 0.648947i
\(571\) 3443.25i 0.252357i 0.992008 + 0.126178i \(0.0402711\pi\)
−0.992008 + 0.126178i \(0.959729\pi\)
\(572\) −43052.5 + 43052.5i −3.14705 + 3.14705i
\(573\) −14695.4 14695.4i −1.07139 1.07139i
\(574\) −3637.25 −0.264487
\(575\) −7572.95 + 11522.1i −0.549241 + 0.835664i
\(576\) 1682.57 0.121713
\(577\) 6922.03 + 6922.03i 0.499424 + 0.499424i 0.911259 0.411834i \(-0.135112\pi\)
−0.411834 + 0.911259i \(0.635112\pi\)
\(578\) 9161.86 9161.86i 0.659313 0.659313i
\(579\) 10756.5i 0.772066i
\(580\) −20665.7 + 5533.63i −1.47947 + 0.396158i
\(581\) −3894.35 −0.278080
\(582\) 4403.61 4403.61i 0.313635 0.313635i
\(583\) −29986.3 + 29986.3i −2.13020 + 2.13020i
\(584\) 20804.7i 1.47415i
\(585\) −1098.18 634.278i −0.0776137 0.0448277i
\(586\) 25225.6i 1.77826i
\(587\) −4271.56 4271.56i −0.300352 0.300352i 0.540800 0.841151i \(-0.318122\pi\)
−0.841151 + 0.540800i \(0.818122\pi\)
\(588\) −22522.6 + 22522.6i −1.57962 + 1.57962i
\(589\) −10253.5 −0.717298
\(590\) −16412.5 + 28416.2i −1.14524 + 1.98284i
\(591\) −10665.2 −0.742315
\(592\) 25542.7 25542.7i 1.77331 1.77331i
\(593\) 12386.4 12386.4i 0.857752 0.857752i −0.133321 0.991073i \(-0.542564\pi\)
0.991073 + 0.133321i \(0.0425640\pi\)
\(594\) 54261.1 3.74808
\(595\) −545.408 2036.86i −0.0375791 0.140341i
\(596\) 63697.0i 4.37774i
\(597\) 17011.4 17011.4i 1.16621 1.16621i
\(598\) 22751.7 11445.0i 1.55583 0.782646i
\(599\) 14988.3i 1.02238i −0.859468 0.511189i \(-0.829205\pi\)
0.859468 0.511189i \(-0.170795\pi\)
\(600\) −18857.2 32687.0i −1.28307 2.22407i
\(601\) 12090.1 0.820578 0.410289 0.911956i \(-0.365428\pi\)
0.410289 + 0.911956i \(0.365428\pi\)
\(602\) −1536.95 1536.95i −0.104055 0.104055i
\(603\) −959.288 959.288i −0.0647848 0.0647848i
\(604\) 37346.1i 2.51588i
\(605\) 39495.1 10575.6i 2.65406 0.710675i
\(606\) −12915.3 −0.865758
\(607\) −5162.54 5162.54i −0.345208 0.345208i 0.513113 0.858321i \(-0.328492\pi\)
−0.858321 + 0.513113i \(0.828492\pi\)
\(608\) 31077.0 + 31077.0i 2.07292 + 2.07292i
\(609\) −1836.78 −0.122217
\(610\) −1810.65 + 3134.93i −0.120182 + 0.208081i
\(611\) 4896.99 0.324241
\(612\) 1772.65 1772.65i 0.117083 0.117083i
\(613\) 103.785 + 103.785i 0.00683825 + 0.00683825i 0.710518 0.703679i \(-0.248461\pi\)
−0.703679 + 0.710518i \(0.748461\pi\)
\(614\) 29797.8i 1.95854i
\(615\) −5016.26 + 8685.04i −0.328902 + 0.569455i
\(616\) 16448.1 1.07583
\(617\) 6895.43 6895.43i 0.449918 0.449918i −0.445409 0.895327i \(-0.646942\pi\)
0.895327 + 0.445409i \(0.146942\pi\)
\(618\) 28095.1 + 28095.1i 1.82872 + 1.82872i
\(619\) −8092.22 −0.525450 −0.262725 0.964871i \(-0.584621\pi\)
−0.262725 + 0.964871i \(0.584621\pi\)
\(620\) 4948.71 + 18481.2i 0.320556 + 1.19714i
\(621\) −15309.0 5061.70i −0.989256 0.327084i
\(622\) 12270.5 + 12270.5i 0.791000 + 0.791000i
\(623\) −0.234854 + 0.234854i −1.51031e−5 + 1.51031e-5i
\(624\) 35624.3i 2.28544i
\(625\) 7821.59 13526.4i 0.500582 0.865689i
\(626\) 15542.5i 0.992340i
\(627\) 29016.7 + 29016.7i 1.84819 + 1.84819i
\(628\) 13083.3 + 13083.3i 0.831341 + 0.831341i
\(629\) 10890.3i 0.690343i
\(630\) 149.604 + 558.705i 0.00946090 + 0.0353323i
\(631\) 2106.26i 0.132882i −0.997790 0.0664412i \(-0.978836\pi\)
0.997790 0.0664412i \(-0.0211645\pi\)
\(632\) 24498.5 24498.5i 1.54193 1.54193i
\(633\) 5324.41 5324.41i 0.334323 0.334323i
\(634\) 7331.09i 0.459235i
\(635\) −17194.7 9931.20i −1.07457 0.620642i
\(636\) 58225.8i 3.63019i
\(637\) 10203.3 + 10203.3i 0.634648 + 0.634648i
\(638\) −25593.9 25593.9i −1.58820 1.58820i
\(639\) 240.191i 0.0148698i
\(640\) 2430.90 4208.82i 0.150141 0.259950i
\(641\) 26795.9i 1.65113i 0.564308 + 0.825564i \(0.309143\pi\)
−0.564308 + 0.825564i \(0.690857\pi\)
\(642\) −9580.81 + 9580.81i −0.588979 + 0.588979i
\(643\) −20053.2 20053.2i −1.22989 1.22989i −0.964003 0.265891i \(-0.914334\pi\)
−0.265891 0.964003i \(-0.585666\pi\)
\(644\) −7834.40 2590.33i −0.479377 0.158499i
\(645\) −5789.59 + 1550.27i −0.353434 + 0.0946387i
\(646\) 30575.6 1.86220
\(647\) −6591.04 6591.04i −0.400496 0.400496i 0.477912 0.878408i \(-0.341394\pi\)
−0.878408 + 0.477912i \(0.841394\pi\)
\(648\) 28192.9 28192.9i 1.70914 1.70914i
\(649\) −39440.5 −2.38548
\(650\) −24999.5 + 14422.3i −1.50856 + 0.870289i
\(651\) 1642.62i 0.0988932i
\(652\) 25052.9 + 25052.9i 1.50483 + 1.50483i
\(653\) −10440.2 + 10440.2i −0.625661 + 0.625661i −0.946973 0.321313i \(-0.895876\pi\)
0.321313 + 0.946973i \(0.395876\pi\)
\(654\) 16731.4 1.00038
\(655\) −8918.45 + 2388.09i −0.532020 + 0.142458i
\(656\) −29792.1 −1.77315
\(657\) 621.749 + 621.749i 0.0369204 + 0.0369204i
\(658\) −1579.25 1579.25i −0.0935645 0.0935645i
\(659\) 12239.6 0.723500 0.361750 0.932275i \(-0.382179\pi\)
0.361750 + 0.932275i \(0.382179\pi\)
\(660\) 38296.2 66305.2i 2.25860 3.91049i
\(661\) 26289.5i 1.54696i −0.633819 0.773481i \(-0.718514\pi\)
0.633819 0.773481i \(-0.281486\pi\)
\(662\) −30440.0 30440.0i −1.78713 1.78713i
\(663\) 7594.33 + 7594.33i 0.444856 + 0.444856i
\(664\) −62412.9 −3.64772
\(665\) −2506.42 + 4339.56i −0.146157 + 0.253054i
\(666\) 2987.19i 0.173801i
\(667\) 4833.43 + 9608.44i 0.280587 + 0.557781i
\(668\) −17921.6 + 17921.6i −1.03803 + 1.03803i
\(669\) 9719.94i 0.561726i
\(670\) −29823.6 + 7985.84i −1.71968 + 0.460478i
\(671\) −4351.15 −0.250334
\(672\) 4978.57 4978.57i 0.285792 0.285792i
\(673\) −10979.3 + 10979.3i −0.628855 + 0.628855i −0.947780 0.318925i \(-0.896678\pi\)
0.318925 + 0.947780i \(0.396678\pi\)
\(674\) 32902.5 1.88035
\(675\) 17648.1 + 4735.14i 1.00633 + 0.270008i
\(676\) −5242.21 −0.298259
\(677\) −8582.49 + 8582.49i −0.487226 + 0.487226i −0.907430 0.420204i \(-0.861959\pi\)
0.420204 + 0.907430i \(0.361959\pi\)
\(678\) 23613.7 + 23613.7i 1.33758 + 1.33758i
\(679\) 914.078i 0.0516629i
\(680\) −8741.00 32643.8i −0.492944 1.84093i
\(681\) 2302.89i 0.129584i
\(682\) −22888.5 + 22888.5i −1.28511 + 1.28511i
\(683\) −9534.15 + 9534.15i −0.534135 + 0.534135i −0.921800 0.387665i \(-0.873282\pi\)
0.387665 + 0.921800i \(0.373282\pi\)
\(684\) −5957.94 −0.333052
\(685\) −111.759 + 193.497i −0.00623370 + 0.0107929i
\(686\) 13453.2i 0.748753i
\(687\) 12654.8 12654.8i 0.702781 0.702781i
\(688\) −12588.9 12588.9i −0.697597 0.697597i
\(689\) 26377.8 1.45851
\(690\) −23916.1 + 21304.5i −1.31952 + 1.17543i
\(691\) 12617.6 0.694641 0.347321 0.937746i \(-0.387092\pi\)
0.347321 + 0.937746i \(0.387092\pi\)
\(692\) 49373.2 + 49373.2i 2.71227 + 2.71227i
\(693\) −491.552 + 491.552i −0.0269445 + 0.0269445i
\(694\) 28065.6i 1.53510i
\(695\) −6732.86 25144.3i −0.367471 1.37234i
\(696\) −29437.1 −1.60318
\(697\) −6351.04 + 6351.04i −0.345140 + 0.345140i
\(698\) 22349.3 22349.3i 1.21194 1.21194i
\(699\) 586.645i 0.0317439i
\(700\) 9031.44 + 2423.22i 0.487652 + 0.130841i
\(701\) 6706.27i 0.361330i −0.983545 0.180665i \(-0.942175\pi\)
0.983545 0.180665i \(-0.0578250\pi\)
\(702\) −23865.7 23865.7i −1.28312 1.28312i
\(703\) −18301.4 + 18301.4i −0.981866 + 0.981866i
\(704\) 46022.5 2.46383
\(705\) −5948.93 + 1592.94i −0.317801 + 0.0850973i
\(706\) −5481.37 −0.292201
\(707\) 1340.45 1340.45i 0.0713051 0.0713051i
\(708\) −38291.7 + 38291.7i −2.03261 + 2.03261i
\(709\) 5259.88 0.278616 0.139308 0.990249i \(-0.455512\pi\)
0.139308 + 0.990249i \(0.455512\pi\)
\(710\) −4733.46 2733.92i −0.250202 0.144510i
\(711\) 1464.28i 0.0772359i
\(712\) −3.76390 + 3.76390i −0.000198115 + 0.000198115i
\(713\) 8592.80 4322.52i 0.451336 0.227040i
\(714\) 4898.24i 0.256739i
\(715\) −30038.0 17349.2i −1.57113 0.907443i
\(716\) 75685.6 3.95042
\(717\) −10986.9 10986.9i −0.572263 0.572263i
\(718\) −10291.5 10291.5i −0.534925 0.534925i
\(719\) 2675.11i 0.138755i −0.997590 0.0693775i \(-0.977899\pi\)
0.997590 0.0693775i \(-0.0221013\pi\)
\(720\) 1225.38 + 4576.26i 0.0634268 + 0.236871i
\(721\) −5831.83 −0.301233
\(722\) −25891.8 25891.8i −1.33462 1.33462i
\(723\) −18403.3 18403.3i −0.946649 0.946649i
\(724\) 48091.8 2.46867
\(725\) −6090.77 10557.7i −0.312008 0.540833i
\(726\) 94977.9 4.85532
\(727\) −19936.7 + 19936.7i −1.01707 + 1.01707i −0.0172198 + 0.999852i \(0.505482\pi\)
−0.999852 + 0.0172198i \(0.994518\pi\)
\(728\) −7234.37 7234.37i −0.368302 0.368302i
\(729\) 21188.1i 1.07647i
\(730\) 19329.7 5175.91i 0.980035 0.262423i
\(731\) −5367.36 −0.271572
\(732\) −4224.42 + 4224.42i −0.213304 + 0.213304i
\(733\) 3876.87 + 3876.87i 0.195356 + 0.195356i 0.798006 0.602650i \(-0.205889\pi\)
−0.602650 + 0.798006i \(0.705889\pi\)
\(734\) −48319.0 −2.42982
\(735\) −15714.2 9076.10i −0.788607 0.455479i
\(736\) −39144.6 12942.6i −1.96045 0.648195i
\(737\) −26239.0 26239.0i −1.31143 1.31143i
\(738\) 1742.07 1742.07i 0.0868925 0.0868925i
\(739\) 14307.0i 0.712168i −0.934454 0.356084i \(-0.884112\pi\)
0.934454 0.356084i \(-0.115888\pi\)
\(740\) 41820.0 + 24154.2i 2.07748 + 1.19990i
\(741\) 25524.9i 1.26542i
\(742\) −8506.65 8506.65i −0.420875 0.420875i
\(743\) 17115.6 + 17115.6i 0.845103 + 0.845103i 0.989517 0.144415i \(-0.0461299\pi\)
−0.144415 + 0.989517i \(0.546130\pi\)
\(744\) 26325.5i 1.29723i
\(745\) 35055.1 9386.68i 1.72392 0.461613i
\(746\) 22922.6i 1.12501i
\(747\) 1865.21 1865.21i 0.0913582 0.0913582i
\(748\) 48486.5 48486.5i 2.37011 2.37011i
\(749\) 1988.73i 0.0970183i
\(750\) 25678.3 25652.4i 1.25018 1.24893i
\(751\) 12144.0i 0.590069i −0.955487 0.295034i \(-0.904669\pi\)
0.955487 0.295034i \(-0.0953311\pi\)
\(752\) −12935.4 12935.4i −0.627266 0.627266i
\(753\) 3057.61 + 3057.61i 0.147975 + 0.147975i
\(754\) 22513.9i 1.08741i
\(755\) 20553.1 5503.50i 0.990735 0.265288i
\(756\) 10935.2i 0.526069i
\(757\) 18568.1 18568.1i 0.891504 0.891504i −0.103160 0.994665i \(-0.532896\pi\)
0.994665 + 0.103160i \(0.0328955\pi\)
\(758\) 46752.5 + 46752.5i 2.24028 + 2.24028i
\(759\) −36549.5 12084.6i −1.74791 0.577921i
\(760\) −40169.1 + 69548.0i −1.91722 + 3.31944i
\(761\) −3136.39 −0.149401 −0.0747005 0.997206i \(-0.523800\pi\)
−0.0747005 + 0.997206i \(0.523800\pi\)
\(762\) −32616.2 32616.2i −1.55060 1.55060i
\(763\) −1736.51 + 1736.51i −0.0823930 + 0.0823930i
\(764\) 82533.0 3.90830
\(765\) 1236.79 + 714.336i 0.0584524 + 0.0337606i
\(766\) 31693.7i 1.49496i
\(767\) 17347.1 + 17347.1i 0.816648 + 0.816648i
\(768\) −10231.7 + 10231.7i −0.480736 + 0.480736i
\(769\) −3823.32 −0.179288 −0.0896440 0.995974i \(-0.528573\pi\)
−0.0896440 + 0.995974i \(0.528573\pi\)
\(770\) 4092.05 + 15282.0i 0.191516 + 0.715228i
\(771\) 20289.8 0.947755
\(772\) −30205.7 30205.7i −1.40820 1.40820i