Properties

Label 115.4.e.a.22.2
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 22.2
Character \(\chi\) \(=\) 115.22
Dual form 115.4.e.a.68.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.71645 - 3.71645i) q^{2} +(3.49413 - 3.49413i) q^{3} +19.6239i q^{4} +(10.7999 - 2.89187i) q^{5} -25.9715 q^{6} +(-2.69551 + 2.69551i) q^{7} +(43.1997 - 43.1997i) q^{8} +2.58205i q^{9} +O(q^{10})\) \(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} +(-49.5690 + 98.5389i) 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} +(-1933.72 - 972.740i) 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 −0.776124 0.630580i \(-0.782817\pi\)
0.630580 + 0.776124i \(0.282817\pi\)
\(8\) 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 \(-0.580831\pi\)
0.251217 0.967931i \(-0.419169\pi\)
\(12\) 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 −0.412050 0.911161i \(-0.635187\pi\)
0.911161 + 0.412050i \(0.135187\pi\)
\(18\) 9.59606 9.59606i 0.125656 0.125656i
\(19\) −117.583 −1.41976 −0.709880 0.704323i \(-0.751251\pi\)
−0.709880 + 0.704323i \(0.751251\pi\)
\(20\) 56.7499 + 211.936i 0.634483 + 2.36951i
\(21\) 18.8370i 0.195741i
\(22\) −262.477 + 262.477i −2.54365 + 2.54365i
\(23\) −49.5690 + 98.5389i −0.449385 + 0.893338i
\(24\) 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 −0.271006 0.962578i \(-0.587356\pi\)
0.962578 + 0.271006i \(0.0873562\pi\)
\(38\) 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 0.557872 0.829927i \(-0.311618\pi\)
−0.829927 + 0.557872i \(0.811618\pi\)
\(44\) 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 \(-0.966188\pi\)
−0.106024 0.994364i \(-0.533812\pi\)
\(54\) 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 \(-0.979405\pi\)
0.997908 0.0646571i \(-0.0205954\pi\)
\(62\) 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 −0.281979 0.959421i \(-0.590991\pi\)
0.959421 + 0.281979i \(0.0909909\pi\)
\(68\) 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 \(-0.632318\pi\)
−0.403820 + 0.914838i \(0.632318\pi\)
\(80\) −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 0.999043 0.0437293i \(-0.0139239\pi\)
−0.0437293 + 0.999043i \(0.513924\pi\)
\(84\) −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 \(-0.499983\pi\)
5.18850e−5 1.00000i \(0.499983\pi\)
\(90\) 75.8855 131.387i 0.0888782 0.153882i
\(91\) 167.463i 0.192911i
\(92\) −1933.72 972.740i −2.19135 1.10234i
\(93\) −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 −0.612775 0.790257i \(-0.709947\pi\)
0.790257 + 0.612775i \(0.209947\pi\)
\(98\) 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 \(0.0112961\pi\)
0.0354803 + 0.999370i \(0.488704\pi\)
\(104\) 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 −0.853837 0.520541i \(-0.825730\pi\)
0.520541 + 0.853837i \(0.325730\pi\)
\(108\) −2028.40 + 2028.40i −1.80725 + 1.80725i
\(109\) 644.222 0.566104 0.283052 0.959105i \(-0.408653\pi\)
0.283052 + 0.959105i \(0.408653\pi\)
\(110\) −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 0.975761 0.218841i \(-0.0702275\pi\)
−0.218841 + 0.975761i \(0.570228\pi\)
\(114\) 3053.81 2.50891
\(115\) −250.377 + 1207.55i −0.203024 + 0.979174i
\(116\) 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 −0.711500 0.702686i \(-0.751984\pi\)
0.702686 + 0.711500i \(0.251984\pi\)
\(138\) 1287.38 2559.20i 0.794126 1.57865i
\(139\) 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 \(-0.149072\pi\)
0.892326 + 0.451391i \(0.149072\pi\)
\(150\) −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 −0.855957 0.517048i \(-0.827031\pi\)
0.517048 + 0.855957i \(0.327031\pi\)
\(158\) 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 \(0.167843\pi\)
−0.864172 + 0.503196i \(0.832157\pi\)
\(182\) 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 \(0.293391\pi\)
−0.604456 + 0.796639i \(0.706609\pi\)
\(192\) −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 \(-0.834045\pi\)
−0.867142 + 0.498061i \(0.834045\pi\)
\(200\) 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
\(207\) −254.433 127.990i −0.0854313 0.0429754i
\(208\) −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 −0.753640 0.657287i \(-0.771704\pi\)
0.657287 + 0.753640i \(0.271704\pi\)
\(228\) −8062.52 8062.52i −2.34190 2.34190i
\(229\) −3621.72 −1.04511 −0.522555 0.852605i \(-0.675021\pi\)
−0.522555 + 0.852605i \(0.675021\pi\)
\(230\) 5418.32 3557.29i 1.55336 1.01983i
\(231\) 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 \(0.248553\pi\)
−0.710314 + 0.703885i \(0.751447\pi\)
\(242\) 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 \(-0.964906\pi\)
0.993929 0.110028i \(-0.0350939\pi\)
\(252\) 136.582 136.582i 0.0341422 0.0341422i
\(253\) 6959.39 + 3500.85i 1.72938 + 0.869948i
\(254\) 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 0.363251 0.931691i \(-0.381667\pi\)
−0.931691 + 0.363251i \(0.881667\pi\)
\(264\) −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 \(-0.874468\pi\)
0.923239 0.384226i \(-0.125532\pi\)
\(282\) −2047.14 2047.14i −0.432289 0.432289i
\(283\) −5080.30 5080.30i −1.06711 1.06711i −0.997580 0.0695306i \(-0.977850\pi\)
−0.0695306 0.997580i \(-0.522150\pi\)
\(284\) 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 0.959247 0.282568i \(-0.0911862\pi\)
−0.282568 + 0.959247i \(0.591186\pi\)
\(294\) 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 0.870241 0.492627i \(-0.163963\pi\)
−0.492627 + 0.870241i \(0.663963\pi\)
\(314\) 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
\(322\) −993.138 + 1974.27i −0.171880 + 0.341683i
\(323\) −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 −0.252159 0.967686i \(-0.581141\pi\)
0.967686 + 0.252159i \(0.0811405\pi\)
\(338\) 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
\(345\) 3344.50 + 5094.21i 0.521919 + 0.794965i
\(346\) −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 \(-0.565249\pi\)
−0.203554 + 0.979064i \(0.565249\pi\)
\(360\) 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 −0.997351 0.0727364i \(-0.976827\pi\)
0.0727364 + 0.997351i \(0.476827\pi\)
\(368\) 8134.64 16170.9i 1.15230 2.29068i
\(369\) 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 0.887980 0.459882i \(-0.152108\pi\)
−0.459882 + 0.887980i \(0.652108\pi\)
\(374\) 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 \(-0.175092\pi\)
0.852489 + 0.522746i \(0.175092\pi\)
\(380\) −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 0.362938 0.931813i \(-0.381774\pi\)
−0.931813 + 0.362938i \(0.881774\pi\)
\(384\) 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 \(-0.688293\pi\)
−0.557639 + 0.830084i \(0.688293\pi\)
\(390\) −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 \(-0.897121\pi\)
0.948223 0.317605i \(-0.102879\pi\)
\(402\) −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 \(-0.709243\pi\)
−0.611026 + 0.791610i \(0.709243\pi\)
\(420\) −3992.23 + 1069.00i −0.463811 + 0.124194i
\(421\) 2808.97i 0.325180i −0.986694 0.162590i \(-0.948015\pi\)
0.986694 0.162590i \(-0.0519847\pi\)
\(422\) −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 \(0.199383\pi\)
−0.810155 + 0.586215i \(0.800617\pi\)
\(432\) −16962.7 16962.7i −1.88916 1.88916i
\(433\) −8920.14 8920.14i −0.990010 0.990010i 0.00994052 0.999951i \(-0.496836\pi\)
−0.999951 + 0.00994052i \(0.996836\pi\)
\(434\) −1747.13 −0.193237
\(435\) −4664.91 2694.33i −0.514173 0.296973i
\(436\) 12642.2i 1.38865i
\(437\) 5828.49 11586.5i 0.638019 1.26833i
\(438\) −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 −0.972148 0.234367i \(-0.924698\pi\)
0.234367 + 0.972148i \(0.424698\pi\)
\(458\) 13459.9 + 13459.9i 1.37324 + 1.37324i
\(459\) 7232.18 0.735445
\(460\) −23697.0 4913.39i −2.40190 0.498017i
\(461\) −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 −0.772478 0.635042i \(-0.780983\pi\)
0.635042 + 0.772478i \(0.280983\pi\)
\(468\) −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 \(-0.536884\pi\)
−0.115616 + 0.993294i \(0.536884\pi\)
\(480\) 19947.2 5341.24i 1.89679 0.507902i
\(481\) 9669.83i 0.916645i
\(482\) 19574.2 19574.2i 1.84975 1.84975i
\(483\) −1856.17 933.730i −0.174863 0.0879632i
\(484\) 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 0.373844 0.927492i \(-0.378040\pi\)
−0.927492 + 0.373844i \(0.878040\pi\)
\(504\) −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 \(-0.938444\pi\)
0.981360 0.192180i \(-0.0615556\pi\)
\(522\) −935.703 935.703i −0.0784571 0.0784571i
\(523\) −7280.41 7280.41i −0.608700 0.608700i 0.333906 0.942606i \(-0.391633\pi\)
−0.942606 + 0.333906i \(0.891633\pi\)
\(524\) 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
\(552\) 29748.0 + 14964.5i 2.29377 + 1.15386i
\(553\) 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 −0.734607 0.678493i \(-0.762633\pi\)
0.678493 + 0.734607i \(0.262633\pi\)
\(558\) −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 0.990950 0.134229i \(-0.0428557\pi\)
−0.134229 + 0.990950i \(0.542856\pi\)
\(564\) 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 \(-0.552313\pi\)
−0.163606 + 0.986526i \(0.552313\pi\)
\(570\) 32980.8 8831.24i 2.42353 0.648947i
\(571\) 3443.25i 0.252357i −0.992008 0.126178i \(-0.959729\pi\)
0.992008 0.126178i \(-0.0402711\pi\)
\(572\) 43052.5 43052.5i 3.14705 3.14705i
\(573\) 14695.4 + 14695.4i 1.07139 + 1.07139i
\(574\) 3637.25 0.264487
\(575\) 788.050 + 13765.5i 0.0571547 + 0.998365i
\(576\) 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
\(598\) 11445.0 22751.7i 0.782646 1.55583i
\(599\) 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 0.703679 0.710518i \(-0.251539\pi\)
−0.710518 + 0.703679i \(0.751539\pi\)
\(614\) 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 −0.895327 0.445409i \(-0.853058\pi\)
0.445409 + 0.895327i \(0.353058\pi\)
\(618\) −28095.1 28095.1i −1.82872 1.82872i
\(619\) 8092.22 0.525450 0.262725 0.964871i \(-0.415379\pi\)
0.262725 + 0.964871i \(0.415379\pi\)
\(620\) −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 \(0.0211645\pi\)
−0.997790 + 0.0664412i \(0.978836\pi\)
\(632\) −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 \(-0.690857\pi\)
0.564308 0.825564i \(-0.309143\pi\)
\(642\) 9580.81 9580.81i 0.588979 0.588979i
\(643\) 20053.2 + 20053.2i 1.22989 + 1.22989i 0.964003 + 0.265891i \(0.0856660\pi\)
0.265891 + 0.964003i \(0.414334\pi\)
\(644\) 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 \(-0.617821\pi\)
−0.361750 + 0.932275i \(0.617821\pi\)
\(660\) 38296.2 66305.2i 2.25860 3.91049i
\(661\) 26289.5i 1.54696i 0.633819 + 0.773481i \(0.281486\pi\)
−0.633819 + 0.773481i \(0.718514\pi\)
\(662\) −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
\(667\) 9608.44 + 4833.43i 0.557781 + 0.280587i
\(668\) −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 −0.420204 0.907430i \(-0.638041\pi\)
0.907430 + 0.420204i \(0.138041\pi\)
\(678\) −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
\(690\) 6502.68 31362.0i 0.358772 1.73033i
\(691\) 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 \(0.0578250\pi\)
−0.983545 + 0.180665i \(0.942175\pi\)
\(702\) −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 \(-0.544488\pi\)
−0.139308 + 0.990249i \(0.544488\pi\)
\(710\) 4733.46 + 2733.92i 0.250202 + 0.144510i
\(711\) 1464.28i 0.0772359i
\(712\) 3.76390 3.76390i 0.000198115 0.000198115i
\(713\) 4322.52 8592.80i 0.227040 0.451336i
\(714\) 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 \(-0.494518\pi\)
0.999852 0.0172198i \(-0.00548151\pi\)
\(728\) 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 0.602650 0.798006i \(-0.294111\pi\)
−0.798006 + 0.602650i \(0.794111\pi\)
\(734\) 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 0.144415 0.989517i \(-0.453870\pi\)
−0.989517 + 0.144415i \(0.953870\pi\)
\(744\) 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 \(0.0953311\pi\)
−0.955487 + 0.295034i \(0.904669\pi\)
\(752\) −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 −0.994665 0.103160i \(-0.967104\pi\)
0.103160 + 0.994665i \(0.467104\pi\)
\(758\) −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 \(-0.471427\pi\)
0.0896440 + 0.995974i \(0.471427\pi\)
\(770\) −4092.05 15282.0i −0.191516 0.715228i
\(771\) 20289.8 0.947755
\(772\) −30205.7 30205.7i −1.40820 1.40820i