Properties

Label 115.4.e.a.68.13
Level $115$
Weight $4$
Character 115.68
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 68.13
Character \(\chi\) \(=\) 115.68
Dual form 115.4.e.a.22.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.32617 + 1.32617i) q^{2} +(2.49169 + 2.49169i) q^{3} +4.48253i q^{4} +(-3.09011 - 10.7448i) q^{5} -6.60883 q^{6} +(-19.9254 - 19.9254i) q^{7} +(-16.5540 - 16.5540i) q^{8} -14.5829i q^{9} +O(q^{10})\) \(q+(-1.32617 + 1.32617i) q^{2} +(2.49169 + 2.49169i) q^{3} +4.48253i q^{4} +(-3.09011 - 10.7448i) q^{5} -6.60883 q^{6} +(-19.9254 - 19.9254i) q^{7} +(-16.5540 - 16.5540i) q^{8} -14.5829i q^{9} +(18.3475 + 10.1515i) q^{10} +4.60762i q^{11} +(-11.1691 + 11.1691i) q^{12} +(8.15116 + 8.15116i) q^{13} +52.8491 q^{14} +(19.0732 - 34.4724i) q^{15} +8.04662 q^{16} +(-2.30353 - 2.30353i) q^{17} +(19.3395 + 19.3395i) q^{18} -21.1983 q^{19} +(48.1640 - 13.8515i) q^{20} -99.2960i q^{21} +(-6.11049 - 6.11049i) q^{22} +(-40.1668 - 102.731i) q^{23} -82.4949i q^{24} +(-105.902 + 66.4054i) q^{25} -21.6197 q^{26} +(103.612 - 103.612i) q^{27} +(89.3163 - 89.3163i) q^{28} +71.7600i q^{29} +(20.4220 + 71.0107i) q^{30} -80.9736 q^{31} +(121.761 - 121.761i) q^{32} +(-11.4808 + 11.4808i) q^{33} +6.10976 q^{34} +(-152.523 + 275.667i) q^{35} +65.3685 q^{36} +(-135.336 - 135.336i) q^{37} +(28.1125 - 28.1125i) q^{38} +40.6204i q^{39} +(-126.716 + 229.023i) q^{40} -72.5275 q^{41} +(131.684 + 131.684i) q^{42} +(-137.439 + 137.439i) q^{43} -20.6538 q^{44} +(-156.691 + 45.0629i) q^{45} +(189.507 + 82.9707i) q^{46} +(423.191 - 423.191i) q^{47} +(20.0497 + 20.0497i) q^{48} +451.044i q^{49} +(52.3799 - 228.510i) q^{50} -11.4794i q^{51} +(-36.5379 + 36.5379i) q^{52} +(-400.216 + 400.216i) q^{53} +274.814i q^{54} +(49.5080 - 14.2380i) q^{55} +659.690i q^{56} +(-52.8195 - 52.8195i) q^{57} +(-95.1662 - 95.1662i) q^{58} +553.316i q^{59} +(154.524 + 85.4962i) q^{60} -257.390i q^{61} +(107.385 - 107.385i) q^{62} +(-290.571 + 290.571i) q^{63} +387.324i q^{64} +(62.3948 - 112.771i) q^{65} -30.4509i q^{66} +(-408.295 - 408.295i) q^{67} +(10.3257 - 10.3257i) q^{68} +(155.890 - 356.057i) q^{69} +(-163.309 - 567.854i) q^{70} +494.756 q^{71} +(-241.406 + 241.406i) q^{72} +(-396.935 - 396.935i) q^{73} +358.958 q^{74} +(-429.338 - 98.4145i) q^{75} -95.0219i q^{76} +(91.8087 - 91.8087i) q^{77} +(-53.8696 - 53.8696i) q^{78} +100.503 q^{79} +(-24.8650 - 86.4595i) q^{80} +122.599 q^{81} +(96.1840 - 96.1840i) q^{82} +(461.939 - 461.939i) q^{83} +445.098 q^{84} +(-17.6329 + 31.8692i) q^{85} -364.534i q^{86} +(-178.804 + 178.804i) q^{87} +(76.2744 - 76.2744i) q^{88} +1017.99 q^{89} +(148.038 - 267.560i) q^{90} -324.831i q^{91} +(460.495 - 180.049i) q^{92} +(-201.761 - 201.761i) q^{93} +1122.45i q^{94} +(65.5049 + 227.771i) q^{95} +606.781 q^{96} +(-929.909 - 929.909i) q^{97} +(-598.163 - 598.163i) q^{98} +67.1926 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 \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.32617 + 1.32617i −0.468873 + 0.468873i −0.901549 0.432677i \(-0.857569\pi\)
0.432677 + 0.901549i \(0.357569\pi\)
\(3\) 2.49169 + 2.49169i 0.479527 + 0.479527i 0.904980 0.425454i \(-0.139885\pi\)
−0.425454 + 0.904980i \(0.639885\pi\)
\(4\) 4.48253i 0.560317i
\(5\) −3.09011 10.7448i −0.276388 0.961046i
\(6\) −6.60883 −0.449674
\(7\) −19.9254 19.9254i −1.07587 1.07587i −0.996875 0.0789964i \(-0.974828\pi\)
−0.0789964 0.996875i \(-0.525172\pi\)
\(8\) −16.5540 16.5540i −0.731590 0.731590i
\(9\) 14.5829i 0.540109i
\(10\) 18.3475 + 10.1515i 0.580199 + 0.321018i
\(11\) 4.60762i 0.126295i 0.998004 + 0.0631477i \(0.0201139\pi\)
−0.998004 + 0.0631477i \(0.979886\pi\)
\(12\) −11.1691 + 11.1691i −0.268687 + 0.268687i
\(13\) 8.15116 + 8.15116i 0.173902 + 0.173902i 0.788691 0.614789i \(-0.210759\pi\)
−0.614789 + 0.788691i \(0.710759\pi\)
\(14\) 52.8491 1.00889
\(15\) 19.0732 34.4724i 0.328312 0.593382i
\(16\) 8.04662 0.125728
\(17\) −2.30353 2.30353i −0.0328641 0.0328641i 0.690484 0.723348i \(-0.257398\pi\)
−0.723348 + 0.690484i \(0.757398\pi\)
\(18\) 19.3395 + 19.3395i 0.253242 + 0.253242i
\(19\) −21.1983 −0.255959 −0.127979 0.991777i \(-0.540849\pi\)
−0.127979 + 0.991777i \(0.540849\pi\)
\(20\) 48.1640 13.8515i 0.538490 0.154865i
\(21\) 99.2960i 1.03182i
\(22\) −6.11049 6.11049i −0.0592164 0.0592164i
\(23\) −40.1668 102.731i −0.364146 0.931342i
\(24\) 82.4949i 0.701634i
\(25\) −105.902 + 66.4054i −0.847219 + 0.531243i
\(26\) −21.6197 −0.163076
\(27\) 103.612 103.612i 0.738523 0.738523i
\(28\) 89.3163 89.3163i 0.602829 0.602829i
\(29\) 71.7600i 0.459500i 0.973250 + 0.229750i \(0.0737909\pi\)
−0.973250 + 0.229750i \(0.926209\pi\)
\(30\) 20.4220 + 71.0107i 0.124284 + 0.432157i
\(31\) −80.9736 −0.469138 −0.234569 0.972099i \(-0.575368\pi\)
−0.234569 + 0.972099i \(0.575368\pi\)
\(32\) 121.761 121.761i 0.672639 0.672639i
\(33\) −11.4808 + 11.4808i −0.0605620 + 0.0605620i
\(34\) 6.10976 0.0308181
\(35\) −152.523 + 275.667i −0.736604 + 1.33132i
\(36\) 65.3685 0.302632
\(37\) −135.336 135.336i −0.601328 0.601328i 0.339337 0.940665i \(-0.389797\pi\)
−0.940665 + 0.339337i \(0.889797\pi\)
\(38\) 28.1125 28.1125i 0.120012 0.120012i
\(39\) 40.6204i 0.166781i
\(40\) −126.716 + 229.023i −0.500889 + 0.905294i
\(41\) −72.5275 −0.276266 −0.138133 0.990414i \(-0.544110\pi\)
−0.138133 + 0.990414i \(0.544110\pi\)
\(42\) 131.684 + 131.684i 0.483791 + 0.483791i
\(43\) −137.439 + 137.439i −0.487423 + 0.487423i −0.907492 0.420069i \(-0.862006\pi\)
0.420069 + 0.907492i \(0.362006\pi\)
\(44\) −20.6538 −0.0707654
\(45\) −156.691 + 45.0629i −0.519069 + 0.149279i
\(46\) 189.507 + 82.9707i 0.607419 + 0.265943i
\(47\) 423.191 423.191i 1.31338 1.31338i 0.394468 0.918910i \(-0.370929\pi\)
0.918910 0.394468i \(-0.129071\pi\)
\(48\) 20.0497 + 20.0497i 0.0602901 + 0.0602901i
\(49\) 451.044i 1.31500i
\(50\) 52.3799 228.510i 0.148153 0.646323i
\(51\) 11.4794i 0.0315184i
\(52\) −36.5379 + 36.5379i −0.0974402 + 0.0974402i
\(53\) −400.216 + 400.216i −1.03724 + 1.03724i −0.0379650 + 0.999279i \(0.512088\pi\)
−0.999279 + 0.0379650i \(0.987912\pi\)
\(54\) 274.814i 0.692547i
\(55\) 49.5080 14.2380i 0.121376 0.0349065i
\(56\) 659.690i 1.57419i
\(57\) −52.8195 52.8195i −0.122739 0.122739i
\(58\) −95.1662 95.1662i −0.215447 0.215447i
\(59\) 553.316i 1.22094i 0.792039 + 0.610471i \(0.209020\pi\)
−0.792039 + 0.610471i \(0.790980\pi\)
\(60\) 154.524 + 85.4962i 0.332482 + 0.183959i
\(61\) 257.390i 0.540252i −0.962825 0.270126i \(-0.912935\pi\)
0.962825 0.270126i \(-0.0870654\pi\)
\(62\) 107.385 107.385i 0.219966 0.219966i
\(63\) −290.571 + 290.571i −0.581087 + 0.581087i
\(64\) 387.324i 0.756493i
\(65\) 62.3948 112.771i 0.119063 0.215192i
\(66\) 30.4509i 0.0567917i
\(67\) −408.295 408.295i −0.744494 0.744494i 0.228945 0.973439i \(-0.426472\pi\)
−0.973439 + 0.228945i \(0.926472\pi\)
\(68\) 10.3257 10.3257i 0.0184143 0.0184143i
\(69\) 155.890 356.057i 0.271986 0.621221i
\(70\) −163.309 567.854i −0.278846 0.969593i
\(71\) 494.756 0.826996 0.413498 0.910505i \(-0.364307\pi\)
0.413498 + 0.910505i \(0.364307\pi\)
\(72\) −241.406 + 241.406i −0.395138 + 0.395138i
\(73\) −396.935 396.935i −0.636408 0.636408i 0.313260 0.949667i \(-0.398579\pi\)
−0.949667 + 0.313260i \(0.898579\pi\)
\(74\) 358.958 0.563892
\(75\) −429.338 98.4145i −0.661009 0.151519i
\(76\) 95.0219i 0.143418i
\(77\) 91.8087 91.8087i 0.135878 0.135878i
\(78\) −53.8696 53.8696i −0.0781992 0.0781992i
\(79\) 100.503 0.143132 0.0715660 0.997436i \(-0.477200\pi\)
0.0715660 + 0.997436i \(0.477200\pi\)
\(80\) −24.8650 86.4595i −0.0347498 0.120831i
\(81\) 122.599 0.168174
\(82\) 96.1840 96.1840i 0.129533 0.129533i
\(83\) 461.939 461.939i 0.610896 0.610896i −0.332283 0.943180i \(-0.607819\pi\)
0.943180 + 0.332283i \(0.107819\pi\)
\(84\) 445.098 0.578145
\(85\) −17.6329 + 31.8692i −0.0225006 + 0.0406671i
\(86\) 364.534i 0.457078i
\(87\) −178.804 + 178.804i −0.220343 + 0.220343i
\(88\) 76.2744 76.2744i 0.0923964 0.0923964i
\(89\) 1017.99 1.21244 0.606219 0.795297i \(-0.292685\pi\)
0.606219 + 0.795297i \(0.292685\pi\)
\(90\) 148.038 267.560i 0.173384 0.313371i
\(91\) 324.831i 0.374192i
\(92\) 460.495 180.049i 0.521846 0.204037i
\(93\) −201.761 201.761i −0.224964 0.224964i
\(94\) 1122.45i 1.23161i
\(95\) 65.5049 + 227.771i 0.0707438 + 0.245988i
\(96\) 606.781 0.645097
\(97\) −929.909 929.909i −0.973381 0.973381i 0.0262735 0.999655i \(-0.491636\pi\)
−0.999655 + 0.0262735i \(0.991636\pi\)
\(98\) −598.163 598.163i −0.616567 0.616567i
\(99\) 67.1926 0.0682132
\(100\) −297.664 474.711i −0.297664 0.474711i
\(101\) −34.5909 −0.0340784 −0.0170392 0.999855i \(-0.505424\pi\)
−0.0170392 + 0.999855i \(0.505424\pi\)
\(102\) 15.2237 + 15.2237i 0.0147781 + 0.0147781i
\(103\) 1053.48 1053.48i 1.00779 1.00779i 0.00782110 0.999969i \(-0.497510\pi\)
0.999969 0.00782110i \(-0.00248956\pi\)
\(104\) 269.869i 0.254450i
\(105\) −1066.92 + 306.836i −0.991624 + 0.285182i
\(106\) 1061.51i 0.972671i
\(107\) 1331.60 + 1331.60i 1.20309 + 1.20309i 0.973220 + 0.229874i \(0.0738313\pi\)
0.229874 + 0.973220i \(0.426169\pi\)
\(108\) 464.444 + 464.444i 0.413807 + 0.413807i
\(109\) −1753.37 −1.54076 −0.770380 0.637586i \(-0.779933\pi\)
−0.770380 + 0.637586i \(0.779933\pi\)
\(110\) −46.7741 + 84.5383i −0.0405430 + 0.0732764i
\(111\) 674.432i 0.576705i
\(112\) −160.332 160.332i −0.135268 0.135268i
\(113\) −888.241 + 888.241i −0.739458 + 0.739458i −0.972473 0.233015i \(-0.925141\pi\)
0.233015 + 0.972473i \(0.425141\pi\)
\(114\) 140.096 0.115098
\(115\) −979.705 + 749.035i −0.794417 + 0.607373i
\(116\) −321.667 −0.257466
\(117\) 118.868 118.868i 0.0939260 0.0939260i
\(118\) −733.792 733.792i −0.572466 0.572466i
\(119\) 91.7977i 0.0707150i
\(120\) −886.393 + 254.918i −0.674302 + 0.193923i
\(121\) 1309.77 0.984049
\(122\) 341.343 + 341.343i 0.253309 + 0.253309i
\(123\) −180.716 180.716i −0.132477 0.132477i
\(124\) 362.967i 0.262866i
\(125\) 1040.76 + 932.703i 0.744710 + 0.667388i
\(126\) 770.694i 0.544912i
\(127\) 544.813 544.813i 0.380664 0.380664i −0.490678 0.871341i \(-0.663251\pi\)
0.871341 + 0.490678i \(0.163251\pi\)
\(128\) 460.427 + 460.427i 0.317940 + 0.317940i
\(129\) −684.909 −0.467464
\(130\) 66.8073 + 232.300i 0.0450722 + 0.156723i
\(131\) −768.525 −0.512568 −0.256284 0.966602i \(-0.582498\pi\)
−0.256284 + 0.966602i \(0.582498\pi\)
\(132\) −51.4629 51.4629i −0.0339339 0.0339339i
\(133\) 422.384 + 422.384i 0.275378 + 0.275378i
\(134\) 1082.94 0.698146
\(135\) −1433.46 793.119i −0.913873 0.505636i
\(136\) 76.2653i 0.0480860i
\(137\) −351.092 351.092i −0.218948 0.218948i 0.589107 0.808055i \(-0.299480\pi\)
−0.808055 + 0.589107i \(0.799480\pi\)
\(138\) 265.455 + 678.931i 0.163747 + 0.418800i
\(139\) 2093.69i 1.27758i 0.769379 + 0.638792i \(0.220566\pi\)
−0.769379 + 0.638792i \(0.779434\pi\)
\(140\) −1235.69 683.691i −0.745961 0.412732i
\(141\) 2108.92 1.25960
\(142\) −656.131 + 656.131i −0.387756 + 0.387756i
\(143\) −37.5574 + 37.5574i −0.0219630 + 0.0219630i
\(144\) 117.343i 0.0679070i
\(145\) 771.049 221.746i 0.441601 0.127000i
\(146\) 1052.81 0.596788
\(147\) −1123.86 + 1123.86i −0.630576 + 0.630576i
\(148\) 606.649 606.649i 0.336934 0.336934i
\(149\) 1621.96 0.891787 0.445894 0.895086i \(-0.352886\pi\)
0.445894 + 0.895086i \(0.352886\pi\)
\(150\) 699.891 438.862i 0.380972 0.238886i
\(151\) 432.453 0.233063 0.116531 0.993187i \(-0.462822\pi\)
0.116531 + 0.993187i \(0.462822\pi\)
\(152\) 350.916 + 350.916i 0.187257 + 0.187257i
\(153\) −33.5923 + 33.5923i −0.0177502 + 0.0177502i
\(154\) 243.508i 0.127419i
\(155\) 250.217 + 870.047i 0.129664 + 0.450863i
\(156\) −182.082 −0.0934503
\(157\) −264.445 264.445i −0.134427 0.134427i 0.636692 0.771119i \(-0.280302\pi\)
−0.771119 + 0.636692i \(0.780302\pi\)
\(158\) −133.284 + 133.284i −0.0671107 + 0.0671107i
\(159\) −1994.43 −0.994772
\(160\) −1684.55 932.043i −0.832347 0.460528i
\(161\) −1246.61 + 2847.29i −0.610230 + 1.39378i
\(162\) −162.587 + 162.587i −0.0788522 + 0.0788522i
\(163\) −435.271 435.271i −0.209160 0.209160i 0.594751 0.803910i \(-0.297251\pi\)
−0.803910 + 0.594751i \(0.797251\pi\)
\(164\) 325.107i 0.154796i
\(165\) 158.836 + 87.8819i 0.0749414 + 0.0414642i
\(166\) 1225.22i 0.572865i
\(167\) 1854.62 1854.62i 0.859369 0.859369i −0.131895 0.991264i \(-0.542106\pi\)
0.991264 + 0.131895i \(0.0421061\pi\)
\(168\) −1643.75 + 1643.75i −0.754867 + 0.754867i
\(169\) 2064.12i 0.939516i
\(170\) −18.8798 65.6483i −0.00851775 0.0296176i
\(171\) 309.133i 0.138245i
\(172\) −616.073 616.073i −0.273111 0.273111i
\(173\) 374.012 + 374.012i 0.164368 + 0.164368i 0.784498 0.620131i \(-0.212920\pi\)
−0.620131 + 0.784498i \(0.712920\pi\)
\(174\) 474.250i 0.206625i
\(175\) 3433.30 + 786.995i 1.48305 + 0.339950i
\(176\) 37.0757i 0.0158789i
\(177\) −1378.69 + 1378.69i −0.585474 + 0.585474i
\(178\) −1350.03 + 1350.03i −0.568480 + 0.568480i
\(179\) 4574.50i 1.91013i −0.296390 0.955067i \(-0.595783\pi\)
0.296390 0.955067i \(-0.404217\pi\)
\(180\) −201.996 702.373i −0.0836438 0.290843i
\(181\) 3352.54i 1.37675i 0.725353 + 0.688377i \(0.241677\pi\)
−0.725353 + 0.688377i \(0.758323\pi\)
\(182\) 430.781 + 430.781i 0.175449 + 0.175449i
\(183\) 641.336 641.336i 0.259065 0.259065i
\(184\) −1035.68 + 2365.53i −0.414955 + 0.947766i
\(185\) −1035.96 + 1872.37i −0.411704 + 0.744103i
\(186\) 535.141 0.210959
\(187\) 10.6138 10.6138i 0.00415058 0.00415058i
\(188\) 1896.97 + 1896.97i 0.735907 + 0.735907i
\(189\) −4129.02 −1.58911
\(190\) −388.935 215.193i −0.148507 0.0821672i
\(191\) 2916.40i 1.10483i −0.833568 0.552417i \(-0.813706\pi\)
0.833568 0.552417i \(-0.186294\pi\)
\(192\) −965.093 + 965.093i −0.362758 + 0.362758i
\(193\) 3016.99 + 3016.99i 1.12522 + 1.12522i 0.990944 + 0.134277i \(0.0428712\pi\)
0.134277 + 0.990944i \(0.457129\pi\)
\(194\) 2466.44 0.912784
\(195\) 436.459 125.522i 0.160284 0.0460963i
\(196\) −2021.82 −0.736815
\(197\) 2033.77 2033.77i 0.735535 0.735535i −0.236175 0.971710i \(-0.575894\pi\)
0.971710 + 0.236175i \(0.0758940\pi\)
\(198\) −89.1089 + 89.1089i −0.0319833 + 0.0319833i
\(199\) 4690.71 1.67093 0.835466 0.549542i \(-0.185198\pi\)
0.835466 + 0.549542i \(0.185198\pi\)
\(200\) 2852.38 + 653.834i 1.00847 + 0.231165i
\(201\) 2034.69i 0.714010i
\(202\) 45.8735 45.8735i 0.0159784 0.0159784i
\(203\) 1429.85 1429.85i 0.494363 0.494363i
\(204\) 51.4568 0.0176603
\(205\) 224.118 + 779.295i 0.0763565 + 0.265504i
\(206\) 2794.19i 0.945051i
\(207\) −1498.12 + 585.750i −0.503026 + 0.196678i
\(208\) 65.5893 + 65.5893i 0.0218644 + 0.0218644i
\(209\) 97.6734i 0.0323264i
\(210\) 1008.00 1821.83i 0.331232 0.598660i
\(211\) −4249.66 −1.38653 −0.693267 0.720681i \(-0.743829\pi\)
−0.693267 + 0.720681i \(0.743829\pi\)
\(212\) −1793.98 1793.98i −0.581185 0.581185i
\(213\) 1232.78 + 1232.78i 0.396566 + 0.396566i
\(214\) −3531.87 −1.12820
\(215\) 1901.45 + 1052.05i 0.603153 + 0.333718i
\(216\) −3430.38 −1.08059
\(217\) 1613.43 + 1613.43i 0.504732 + 0.504732i
\(218\) 2325.28 2325.28i 0.722420 0.722420i
\(219\) 1978.08i 0.610349i
\(220\) 63.8225 + 221.921i 0.0195587 + 0.0680088i
\(221\) 37.5530i 0.0114302i
\(222\) 894.413 + 894.413i 0.270401 + 0.270401i
\(223\) −3337.04 3337.04i −1.00209 1.00209i −0.999998 0.00208721i \(-0.999336\pi\)
−0.00208721 0.999998i \(-0.500664\pi\)
\(224\) −4852.27 −1.44735
\(225\) 968.385 + 1544.37i 0.286929 + 0.457591i
\(226\) 2355.92i 0.693423i
\(227\) 768.521 + 768.521i 0.224707 + 0.224707i 0.810477 0.585770i \(-0.199208\pi\)
−0.585770 + 0.810477i \(0.699208\pi\)
\(228\) 236.765 236.765i 0.0687727 0.0687727i
\(229\) 982.207 0.283433 0.141716 0.989907i \(-0.454738\pi\)
0.141716 + 0.989907i \(0.454738\pi\)
\(230\) 305.909 2292.61i 0.0877000 0.657261i
\(231\) 457.518 0.130314
\(232\) 1187.92 1187.92i 0.336166 0.336166i
\(233\) −1134.09 1134.09i −0.318871 0.318871i 0.529462 0.848334i \(-0.322394\pi\)
−0.848334 + 0.529462i \(0.822394\pi\)
\(234\) 315.279i 0.0880787i
\(235\) −5854.82 3239.40i −1.62522 0.899215i
\(236\) −2480.26 −0.684114
\(237\) 250.422 + 250.422i 0.0686356 + 0.0686356i
\(238\) −121.740 121.740i −0.0331563 0.0331563i
\(239\) 4320.47i 1.16932i −0.811278 0.584661i \(-0.801227\pi\)
0.811278 0.584661i \(-0.198773\pi\)
\(240\) 153.475 277.386i 0.0412781 0.0746051i
\(241\) 2223.34i 0.594265i 0.954836 + 0.297132i \(0.0960302\pi\)
−0.954836 + 0.297132i \(0.903970\pi\)
\(242\) −1736.98 + 1736.98i −0.461394 + 0.461394i
\(243\) −2492.04 2492.04i −0.657879 0.657879i
\(244\) 1153.76 0.302712
\(245\) 4846.39 1393.78i 1.26377 0.363450i
\(246\) 479.322 0.124229
\(247\) −172.790 172.790i −0.0445117 0.0445117i
\(248\) 1340.44 + 1340.44i 0.343217 + 0.343217i
\(249\) 2302.02 0.585882
\(250\) −2617.16 + 143.308i −0.662094 + 0.0362544i
\(251\) 6883.87i 1.73110i −0.500823 0.865550i \(-0.666969\pi\)
0.500823 0.865550i \(-0.333031\pi\)
\(252\) −1302.49 1302.49i −0.325593 0.325593i
\(253\) 473.344 185.073i 0.117624 0.0459899i
\(254\) 1445.03i 0.356966i
\(255\) −123.344 + 35.4726i −0.0302906 + 0.00871130i
\(256\) −4319.81 −1.05464
\(257\) −3301.66 + 3301.66i −0.801370 + 0.801370i −0.983310 0.181940i \(-0.941762\pi\)
0.181940 + 0.983310i \(0.441762\pi\)
\(258\) 908.307 908.307i 0.219181 0.219181i
\(259\) 5393.26i 1.29390i
\(260\) 505.499 + 279.687i 0.120576 + 0.0667132i
\(261\) 1046.47 0.248180
\(262\) 1019.20 1019.20i 0.240329 0.240329i
\(263\) 4285.20 4285.20i 1.00470 1.00470i 0.00471301 0.999989i \(-0.498500\pi\)
0.999989 0.00471301i \(-0.00150020\pi\)
\(264\) 380.105 0.0886130
\(265\) 5536.97 + 3063.54i 1.28352 + 0.710158i
\(266\) −1120.31 −0.258235
\(267\) 2536.53 + 2536.53i 0.581397 + 0.581397i
\(268\) 1830.19 1830.19i 0.417153 0.417153i
\(269\) 4595.54i 1.04162i −0.853673 0.520809i \(-0.825630\pi\)
0.853673 0.520809i \(-0.174370\pi\)
\(270\) 2952.83 849.207i 0.665569 0.191411i
\(271\) 240.550 0.0539202 0.0269601 0.999637i \(-0.491417\pi\)
0.0269601 + 0.999637i \(0.491417\pi\)
\(272\) −18.5357 18.5357i −0.00413195 0.00413195i
\(273\) 809.378 809.378i 0.179435 0.179435i
\(274\) 931.217 0.205317
\(275\) −305.971 487.958i −0.0670935 0.107000i
\(276\) 1596.04 + 698.784i 0.348080 + 0.152398i
\(277\) 2328.38 2328.38i 0.505051 0.505051i −0.407953 0.913003i \(-0.633757\pi\)
0.913003 + 0.407953i \(0.133757\pi\)
\(278\) −2776.59 2776.59i −0.599024 0.599024i
\(279\) 1180.83i 0.253386i
\(280\) 7088.26 2038.52i 1.51287 0.435088i
\(281\) 5657.00i 1.20096i 0.799641 + 0.600478i \(0.205023\pi\)
−0.799641 + 0.600478i \(0.794977\pi\)
\(282\) −2796.80 + 2796.80i −0.590591 + 0.590591i
\(283\) −4363.26 + 4363.26i −0.916498 + 0.916498i −0.996773 0.0802745i \(-0.974420\pi\)
0.0802745 + 0.996773i \(0.474420\pi\)
\(284\) 2217.76i 0.463380i
\(285\) −404.318 + 730.755i −0.0840342 + 0.151881i
\(286\) 99.6153i 0.0205957i
\(287\) 1445.14 + 1445.14i 0.297226 + 0.297226i
\(288\) −1775.63 1775.63i −0.363298 0.363298i
\(289\) 4902.39i 0.997840i
\(290\) −728.470 + 1316.62i −0.147508 + 0.266602i
\(291\) 4634.10i 0.933524i
\(292\) 1779.28 1779.28i 0.356590 0.356590i
\(293\) −6132.67 + 6132.67i −1.22278 + 1.22278i −0.256139 + 0.966640i \(0.582450\pi\)
−0.966640 + 0.256139i \(0.917550\pi\)
\(294\) 2980.87i 0.591320i
\(295\) 5945.28 1709.81i 1.17338 0.337453i
\(296\) 4480.71i 0.879850i
\(297\) 477.404 + 477.404i 0.0932720 + 0.0932720i
\(298\) −2151.00 + 2151.00i −0.418135 + 0.418135i
\(299\) 509.970 1164.78i 0.0986365 0.225288i
\(300\) 441.146 1924.52i 0.0848987 0.370375i
\(301\) 5477.04 1.04881
\(302\) −573.507 + 573.507i −0.109277 + 0.109277i
\(303\) −86.1898 86.1898i −0.0163415 0.0163415i
\(304\) −170.574 −0.0321813
\(305\) −2765.61 + 795.363i −0.519207 + 0.149319i
\(306\) 89.0983i 0.0166451i
\(307\) −3475.49 + 3475.49i −0.646113 + 0.646113i −0.952051 0.305938i \(-0.901030\pi\)
0.305938 + 0.952051i \(0.401030\pi\)
\(308\) 411.535 + 411.535i 0.0761344 + 0.0761344i
\(309\) 5249.89 0.966525
\(310\) −1485.66 822.001i −0.272194 0.150602i
\(311\) −2417.38 −0.440762 −0.220381 0.975414i \(-0.570730\pi\)
−0.220381 + 0.975414i \(0.570730\pi\)
\(312\) 672.430 672.430i 0.122015 0.122015i
\(313\) −4934.30 + 4934.30i −0.891064 + 0.891064i −0.994623 0.103559i \(-0.966977\pi\)
0.103559 + 0.994623i \(0.466977\pi\)
\(314\) 701.400 0.126058
\(315\) 4020.03 + 2224.24i 0.719057 + 0.397846i
\(316\) 450.506i 0.0801992i
\(317\) −4601.84 + 4601.84i −0.815348 + 0.815348i −0.985430 0.170082i \(-0.945597\pi\)
0.170082 + 0.985430i \(0.445597\pi\)
\(318\) 2644.96 2644.96i 0.466421 0.466421i
\(319\) −330.643 −0.0580327
\(320\) 4161.73 1196.88i 0.727025 0.209086i
\(321\) 6635.90i 1.15383i
\(322\) −2122.78 5429.23i −0.367384 0.939625i
\(323\) 48.8309 + 48.8309i 0.00841183 + 0.00841183i
\(324\) 549.553i 0.0942307i
\(325\) −1404.51 321.947i −0.239717 0.0549489i
\(326\) 1154.49 0.196139
\(327\) −4368.87 4368.87i −0.738835 0.738835i
\(328\) 1200.62 + 1200.62i 0.202113 + 0.202113i
\(329\) −16864.5 −2.82605
\(330\) −327.190 + 94.0968i −0.0545794 + 0.0156965i
\(331\) 3823.59 0.634935 0.317468 0.948269i \(-0.397168\pi\)
0.317468 + 0.948269i \(0.397168\pi\)
\(332\) 2070.66 + 2070.66i 0.342295 + 0.342295i
\(333\) −1973.60 + 1973.60i −0.324782 + 0.324782i
\(334\) 4919.08i 0.805869i
\(335\) −3125.38 + 5648.73i −0.509724 + 0.921263i
\(336\) 798.998i 0.129729i
\(337\) 3852.91 + 3852.91i 0.622794 + 0.622794i 0.946245 0.323451i \(-0.104843\pi\)
−0.323451 + 0.946245i \(0.604843\pi\)
\(338\) 2737.38 + 2737.38i 0.440514 + 0.440514i
\(339\) −4426.45 −0.709179
\(340\) −142.855 79.0400i −0.0227865 0.0126075i
\(341\) 373.095i 0.0592500i
\(342\) −409.963 409.963i −0.0648195 0.0648195i
\(343\) 2152.83 2152.83i 0.338897 0.338897i
\(344\) 4550.31 0.713187
\(345\) −4307.49 574.759i −0.672195 0.0896928i
\(346\) −992.009 −0.154135
\(347\) −2022.78 + 2022.78i −0.312935 + 0.312935i −0.846046 0.533111i \(-0.821023\pi\)
0.533111 + 0.846046i \(0.321023\pi\)
\(348\) −801.495 801.495i −0.123462 0.123462i
\(349\) 11306.6i 1.73418i −0.498153 0.867089i \(-0.665988\pi\)
0.498153 0.867089i \(-0.334012\pi\)
\(350\) −5596.85 + 3509.46i −0.854754 + 0.535968i
\(351\) 1689.12 0.256861
\(352\) 561.027 + 561.027i 0.0849512 + 0.0849512i
\(353\) 5114.32 + 5114.32i 0.771128 + 0.771128i 0.978304 0.207176i \(-0.0664273\pi\)
−0.207176 + 0.978304i \(0.566427\pi\)
\(354\) 3656.77i 0.549025i
\(355\) −1528.85 5316.06i −0.228572 0.794781i
\(356\) 4563.19i 0.679350i
\(357\) −228.732 + 228.732i −0.0339097 + 0.0339097i
\(358\) 6066.57 + 6066.57i 0.895610 + 0.895610i
\(359\) −8136.92 −1.19624 −0.598120 0.801406i \(-0.704085\pi\)
−0.598120 + 0.801406i \(0.704085\pi\)
\(360\) 3339.83 + 1847.89i 0.488957 + 0.270535i
\(361\) −6409.63 −0.934485
\(362\) −4446.05 4446.05i −0.645522 0.645522i
\(363\) 3263.54 + 3263.54i 0.471878 + 0.471878i
\(364\) 1456.06 0.209666
\(365\) −3038.42 + 5491.57i −0.435722 + 0.787512i
\(366\) 1701.04i 0.242937i
\(367\) 401.662 + 401.662i 0.0571296 + 0.0571296i 0.735094 0.677965i \(-0.237138\pi\)
−0.677965 + 0.735094i \(0.737138\pi\)
\(368\) −323.207 826.636i −0.0457835 0.117096i
\(369\) 1057.66i 0.149214i
\(370\) −1109.22 3856.94i −0.155853 0.541926i
\(371\) 15949.0 2.23188
\(372\) 904.402 904.402i 0.126051 0.126051i
\(373\) −6151.11 + 6151.11i −0.853867 + 0.853867i −0.990607 0.136740i \(-0.956338\pi\)
0.136740 + 0.990607i \(0.456338\pi\)
\(374\) 28.1515i 0.00389218i
\(375\) 269.256 + 4917.27i 0.0370782 + 0.677139i
\(376\) −14011.0 −1.92171
\(377\) −584.928 + 584.928i −0.0799080 + 0.0799080i
\(378\) 5475.79 5475.79i 0.745091 0.745091i
\(379\) 9829.53 1.33221 0.666107 0.745857i \(-0.267960\pi\)
0.666107 + 0.745857i \(0.267960\pi\)
\(380\) −1020.99 + 293.628i −0.137831 + 0.0396390i
\(381\) 2715.01 0.365077
\(382\) 3867.65 + 3867.65i 0.518027 + 0.518027i
\(383\) 6163.24 6163.24i 0.822263 0.822263i −0.164169 0.986432i \(-0.552494\pi\)
0.986432 + 0.164169i \(0.0524943\pi\)
\(384\) 2294.48i 0.304922i
\(385\) −1270.17 702.769i −0.168139 0.0930297i
\(386\) −8002.10 −1.05517
\(387\) 2004.26 + 2004.26i 0.263261 + 0.263261i
\(388\) 4168.35 4168.35i 0.545402 0.545402i
\(389\) −1817.57 −0.236901 −0.118450 0.992960i \(-0.537793\pi\)
−0.118450 + 0.992960i \(0.537793\pi\)
\(390\) −412.357 + 745.283i −0.0535397 + 0.0967663i
\(391\) −144.118 + 329.169i −0.0186404 + 0.0425750i
\(392\) 7466.58 7466.58i 0.962039 0.962039i
\(393\) −1914.93 1914.93i −0.245790 0.245790i
\(394\) 5394.27i 0.689745i
\(395\) −310.564 1079.88i −0.0395600 0.137556i
\(396\) 301.193i 0.0382210i
\(397\) 3671.19 3671.19i 0.464111 0.464111i −0.435890 0.900000i \(-0.643566\pi\)
0.900000 + 0.435890i \(0.143566\pi\)
\(398\) −6220.69 + 6220.69i −0.783455 + 0.783455i
\(399\) 2104.90i 0.264103i
\(400\) −852.157 + 534.339i −0.106520 + 0.0667924i
\(401\) 10481.9i 1.30534i −0.757644 0.652668i \(-0.773649\pi\)
0.757644 0.652668i \(-0.226351\pi\)
\(402\) 2698.35 + 2698.35i 0.334780 + 0.334780i
\(403\) −660.029 660.029i −0.0815841 0.0815841i
\(404\) 155.055i 0.0190947i
\(405\) −378.844 1317.30i −0.0464813 0.161623i
\(406\) 3792.45i 0.463587i
\(407\) 623.577 623.577i 0.0759449 0.0759449i
\(408\) −190.030 + 190.030i −0.0230585 + 0.0230585i
\(409\) 919.762i 0.111196i −0.998453 0.0555982i \(-0.982293\pi\)
0.998453 0.0555982i \(-0.0177066\pi\)
\(410\) −1330.70 736.261i −0.160289 0.0886862i
\(411\) 1749.63i 0.209982i
\(412\) 4722.26 + 4722.26i 0.564682 + 0.564682i
\(413\) 11025.0 11025.0i 1.31358 1.31358i
\(414\) 1209.96 2763.57i 0.143638 0.328072i
\(415\) −6390.89 3536.01i −0.755944 0.418255i
\(416\) 1984.98 0.233947
\(417\) −5216.82 + 5216.82i −0.612635 + 0.612635i
\(418\) 129.532 + 129.532i 0.0151570 + 0.0151570i
\(419\) −1057.94 −0.123350 −0.0616751 0.998096i \(-0.519644\pi\)
−0.0616751 + 0.998096i \(0.519644\pi\)
\(420\) −1375.40 4782.50i −0.159792 0.555624i
\(421\) 5665.66i 0.655885i −0.944698 0.327942i \(-0.893645\pi\)
0.944698 0.327942i \(-0.106355\pi\)
\(422\) 5635.78 5635.78i 0.650108 0.650108i
\(423\) −6171.36 6171.36i −0.709367 0.709367i
\(424\) 13250.4 1.51767
\(425\) 396.917 + 90.9828i 0.0453019 + 0.0103843i
\(426\) −3269.76 −0.371878
\(427\) −5128.60 + 5128.60i −0.581242 + 0.581242i
\(428\) −5968.96 + 5968.96i −0.674114 + 0.674114i
\(429\) −187.163 −0.0210637
\(430\) −3916.86 + 1126.45i −0.439273 + 0.126331i
\(431\) 11215.4i 1.25342i −0.779251 0.626712i \(-0.784400\pi\)
0.779251 0.626712i \(-0.215600\pi\)
\(432\) 833.726 833.726i 0.0928534 0.0928534i
\(433\) 6882.83 6882.83i 0.763898 0.763898i −0.213127 0.977025i \(-0.568365\pi\)
0.977025 + 0.213127i \(0.0683647\pi\)
\(434\) −4279.38 −0.473310
\(435\) 2473.74 + 1368.69i 0.272659 + 0.150859i
\(436\) 7859.56i 0.863313i
\(437\) 851.466 + 2177.71i 0.0932062 + 0.238385i
\(438\) 2623.28 + 2623.28i 0.286176 + 0.286176i
\(439\) 8376.24i 0.910651i 0.890325 + 0.455326i \(0.150477\pi\)
−0.890325 + 0.455326i \(0.849523\pi\)
\(440\) −1055.25 583.859i −0.114334 0.0632600i
\(441\) 6577.55 0.710242
\(442\) 49.8017 + 49.8017i 0.00535933 + 0.00535933i
\(443\) −2990.80 2990.80i −0.320761 0.320761i 0.528298 0.849059i \(-0.322830\pi\)
−0.849059 + 0.528298i \(0.822830\pi\)
\(444\) 3023.16 0.323137
\(445\) −3145.71 10938.2i −0.335103 1.16521i
\(446\) 8850.99 0.939701
\(447\) 4041.43 + 4041.43i 0.427636 + 0.427636i
\(448\) 7717.60 7717.60i 0.813889 0.813889i
\(449\) 15.1435i 0.00159168i 1.00000 0.000795841i \(0.000253324\pi\)
−1.00000 0.000795841i \(0.999747\pi\)
\(450\) −3332.34 763.853i −0.349085 0.0800186i
\(451\) 334.179i 0.0348911i
\(452\) −3981.57 3981.57i −0.414330 0.414330i
\(453\) 1077.54 + 1077.54i 0.111760 + 0.111760i
\(454\) −2038.38 −0.210718
\(455\) −3490.25 + 1003.76i −0.359616 + 0.103422i
\(456\) 1748.75i 0.179589i
\(457\) −12593.6 12593.6i −1.28907 1.28907i −0.935354 0.353714i \(-0.884919\pi\)
−0.353714 0.935354i \(-0.615081\pi\)
\(458\) −1302.58 + 1302.58i −0.132894 + 0.132894i
\(459\) −477.347 −0.0485417
\(460\) −3357.57 4391.56i −0.340321 0.445125i
\(461\) −7577.09 −0.765510 −0.382755 0.923850i \(-0.625025\pi\)
−0.382755 + 0.923850i \(0.625025\pi\)
\(462\) −606.748 + 606.748i −0.0611006 + 0.0611006i
\(463\) −9385.37 9385.37i −0.942063 0.942063i 0.0563483 0.998411i \(-0.482054\pi\)
−0.998411 + 0.0563483i \(0.982054\pi\)
\(464\) 577.426i 0.0577723i
\(465\) −1544.42 + 2791.35i −0.154024 + 0.278378i
\(466\) 3008.01 0.299020
\(467\) −13304.3 13304.3i −1.31830 1.31830i −0.915117 0.403187i \(-0.867902\pi\)
−0.403187 0.915117i \(-0.632098\pi\)
\(468\) 532.829 + 532.829i 0.0526283 + 0.0526283i
\(469\) 16270.9i 1.60196i
\(470\) 12060.5 3468.49i 1.18364 0.340403i
\(471\) 1317.83i 0.128923i
\(472\) 9159.58 9159.58i 0.893229 0.893229i
\(473\) −633.264 633.264i −0.0615592 0.0615592i
\(474\) −664.205 −0.0643627
\(475\) 2244.95 1407.68i 0.216853 0.135976i
\(476\) −411.486 −0.0396228
\(477\) 5836.33 + 5836.33i 0.560224 + 0.560224i
\(478\) 5729.69 + 5729.69i 0.548263 + 0.548263i
\(479\) 15614.9 1.48948 0.744740 0.667355i \(-0.232573\pi\)
0.744740 + 0.667355i \(0.232573\pi\)
\(480\) −1875.02 6519.75i −0.178297 0.619968i
\(481\) 2206.29i 0.209144i
\(482\) −2948.53 2948.53i −0.278634 0.278634i
\(483\) −10200.8 + 3988.40i −0.960975 + 0.375732i
\(484\) 5871.09i 0.551379i
\(485\) −7118.19 + 12865.2i −0.666434 + 1.20450i
\(486\) 6609.76 0.616923
\(487\) −10985.5 + 10985.5i −1.02218 + 1.02218i −0.0224287 + 0.999748i \(0.507140\pi\)
−0.999748 + 0.0224287i \(0.992860\pi\)
\(488\) −4260.83 + 4260.83i −0.395243 + 0.395243i
\(489\) 2169.12i 0.200595i
\(490\) −4578.76 + 8275.54i −0.422138 + 0.762961i
\(491\) 9973.79 0.916723 0.458362 0.888766i \(-0.348436\pi\)
0.458362 + 0.888766i \(0.348436\pi\)
\(492\) 810.067 810.067i 0.0742289 0.0742289i
\(493\) 165.302 165.302i 0.0151010 0.0151010i
\(494\) 458.300 0.0417406
\(495\) −207.632 721.972i −0.0188533 0.0655560i
\(496\) −651.564 −0.0589840
\(497\) −9858.21 9858.21i −0.889741 0.889741i
\(498\) −3052.87 + 3052.87i −0.274704 + 0.274704i
\(499\) 1024.74i 0.0919313i −0.998943 0.0459657i \(-0.985364\pi\)
0.998943 0.0459657i \(-0.0146365\pi\)
\(500\) −4180.87 + 4665.26i −0.373949 + 0.417274i
\(501\) 9242.27 0.824180
\(502\) 9129.20 + 9129.20i 0.811665 + 0.811665i
\(503\) −4651.86 + 4651.86i −0.412358 + 0.412358i −0.882559 0.470201i \(-0.844181\pi\)
0.470201 + 0.882559i \(0.344181\pi\)
\(504\) 9620.22 0.850235
\(505\) 106.890 + 371.673i 0.00941886 + 0.0327509i
\(506\) −382.297 + 873.175i −0.0335873 + 0.0767142i
\(507\) 5143.15 5143.15i 0.450523 0.450523i
\(508\) 2442.14 + 2442.14i 0.213292 + 0.213292i
\(509\) 4570.74i 0.398025i 0.979997 + 0.199012i \(0.0637734\pi\)
−0.979997 + 0.199012i \(0.936227\pi\)
\(510\) 116.533 210.618i 0.0101180 0.0182869i
\(511\) 15818.2i 1.36939i
\(512\) 2045.39 2045.39i 0.176552 0.176552i
\(513\) −2196.39 + 2196.39i −0.189031 + 0.189031i
\(514\) 8757.15i 0.751481i
\(515\) −14574.8 8064.08i −1.24707 0.689992i
\(516\) 3070.13i 0.261928i
\(517\) 1949.90 + 1949.90i 0.165873 + 0.165873i
\(518\) −7152.39 7152.39i −0.606675 0.606675i
\(519\) 1863.85i 0.157637i
\(520\) −2899.69 + 833.924i −0.244538 + 0.0703269i
\(521\) 2807.26i 0.236062i −0.993010 0.118031i \(-0.962342\pi\)
0.993010 0.118031i \(-0.0376582\pi\)
\(522\) −1387.80 + 1387.80i −0.116365 + 0.116365i
\(523\) −3525.14 + 3525.14i −0.294730 + 0.294730i −0.838945 0.544216i \(-0.816827\pi\)
0.544216 + 0.838945i \(0.316827\pi\)
\(524\) 3444.94i 0.287200i
\(525\) 6593.79 + 10515.7i 0.548146 + 0.874176i
\(526\) 11365.8i 0.942155i
\(527\) 186.525 + 186.525i 0.0154178 + 0.0154178i
\(528\) −92.3814 + 92.3814i −0.00761436 + 0.00761436i
\(529\) −8940.26 + 8252.74i −0.734796 + 0.678289i
\(530\) −11405.8 + 3280.19i −0.934782 + 0.268834i
\(531\) 8068.96 0.659441
\(532\) −1893.35 + 1893.35i −0.154299 + 0.154299i
\(533\) −591.184 591.184i −0.0480432 0.0480432i
\(534\) −6727.74 −0.545202
\(535\) 10193.0 18422.7i 0.823708 1.48875i
\(536\) 13517.8i 1.08933i
\(537\) 11398.2 11398.2i 0.915960 0.915960i
\(538\) 6094.48 + 6094.48i 0.488386 + 0.488386i
\(539\) −2078.24 −0.166078
\(540\) 3555.18 6425.55i 0.283316 0.512059i
\(541\) 9128.91 0.725476 0.362738 0.931891i \(-0.381842\pi\)
0.362738 + 0.931891i \(0.381842\pi\)
\(542\) −319.011 + 319.011i −0.0252817 + 0.0252817i
\(543\) −8353.50 + 8353.50i −0.660190 + 0.660190i
\(544\) −560.960 −0.0442113
\(545\) 5418.12 + 18839.7i 0.425847 + 1.48074i
\(546\) 2146.75i 0.168264i
\(547\) 9547.42 9547.42i 0.746285 0.746285i −0.227494 0.973779i \(-0.573053\pi\)
0.973779 + 0.227494i \(0.0730533\pi\)
\(548\) 1573.78 1573.78i 0.122680 0.122680i
\(549\) −3753.50 −0.291795
\(550\) 1052.89 + 241.346i 0.0816276 + 0.0187110i
\(551\) 1521.19i 0.117613i
\(552\) −8474.77 + 3313.56i −0.653461 + 0.255497i
\(553\) −2002.56 2002.56i −0.153992 0.153992i
\(554\) 6175.68i 0.473609i
\(555\) −7246.65 + 2084.07i −0.554240 + 0.159394i
\(556\) −9385.02 −0.715852
\(557\) 8292.37 + 8292.37i 0.630806 + 0.630806i 0.948270 0.317464i \(-0.102831\pi\)
−0.317464 + 0.948270i \(0.602831\pi\)
\(558\) −1565.99 1565.99i −0.118806 0.118806i
\(559\) −2240.57 −0.169528
\(560\) −1227.30 + 2218.19i −0.0926121 + 0.167385i
\(561\) 52.8926 0.00398062
\(562\) −7502.16 7502.16i −0.563095 0.563095i
\(563\) −8231.39 + 8231.39i −0.616184 + 0.616184i −0.944550 0.328366i \(-0.893502\pi\)
0.328366 + 0.944550i \(0.393502\pi\)
\(564\) 9453.32i 0.705774i
\(565\) 12288.8 + 6799.23i 0.915030 + 0.506276i
\(566\) 11572.9i 0.859442i
\(567\) −2442.83 2442.83i −0.180934 0.180934i
\(568\) −8190.18 8190.18i −0.605022 0.605022i
\(569\) 5417.98 0.399180 0.199590 0.979879i \(-0.436039\pi\)
0.199590 + 0.979879i \(0.436039\pi\)
\(570\) −432.911 1505.30i −0.0318117 0.110614i
\(571\) 1022.01i 0.0749032i −0.999298 0.0374516i \(-0.988076\pi\)
0.999298 0.0374516i \(-0.0119240\pi\)
\(572\) −168.352 168.352i −0.0123062 0.0123062i
\(573\) 7266.77 7266.77i 0.529797 0.529797i
\(574\) −3833.01 −0.278723
\(575\) 11075.6 + 8212.16i 0.803280 + 0.595601i
\(576\) 5648.33 0.408588
\(577\) 7207.93 7207.93i 0.520052 0.520052i −0.397535 0.917587i \(-0.630134\pi\)
0.917587 + 0.397535i \(0.130134\pi\)
\(578\) 6501.41 + 6501.41i 0.467860 + 0.467860i
\(579\) 15034.8i 1.07915i
\(580\) 993.986 + 3456.25i 0.0711604 + 0.247436i
\(581\) −18408.6 −1.31449
\(582\) 6145.61 + 6145.61i 0.437704 + 0.437704i
\(583\) −1844.04 1844.04i −0.130999 0.130999i
\(584\) 13141.7i 0.931179i
\(585\) −1644.53 909.899i −0.116227 0.0643072i
\(586\) 16265.9i 1.14666i
\(587\) 7673.92 7673.92i 0.539585 0.539585i −0.383822 0.923407i \(-0.625392\pi\)
0.923407 + 0.383822i \(0.125392\pi\)
\(588\) −5037.76 5037.76i −0.353323 0.353323i
\(589\) 1716.50 0.120080
\(590\) −5616.97 + 10152.0i −0.391944 + 0.708389i
\(591\) 10135.1 0.705417
\(592\) −1089.00 1089.00i −0.0756040 0.0756040i
\(593\) −3832.73 3832.73i −0.265415 0.265415i 0.561834 0.827250i \(-0.310096\pi\)
−0.827250 + 0.561834i \(0.810096\pi\)
\(594\) −1266.24 −0.0874654
\(595\) 986.350 283.665i 0.0679604 0.0195448i
\(596\) 7270.50i 0.499683i
\(597\) 11687.8 + 11687.8i 0.801256 + 0.801256i
\(598\) 868.394 + 2221.01i 0.0593834 + 0.151879i
\(599\) 5384.67i 0.367298i 0.982992 + 0.183649i \(0.0587910\pi\)
−0.982992 + 0.183649i \(0.941209\pi\)
\(600\) 5478.11 + 8736.41i 0.372738 + 0.594438i
\(601\) −2031.10 −0.137854 −0.0689270 0.997622i \(-0.521958\pi\)
−0.0689270 + 0.997622i \(0.521958\pi\)
\(602\) −7263.50 + 7263.50i −0.491758 + 0.491758i
\(603\) −5954.13 + 5954.13i −0.402108 + 0.402108i
\(604\) 1938.48i 0.130589i
\(605\) −4047.33 14073.2i −0.271979 0.945717i
\(606\) 228.605 0.0153242
\(607\) 1437.36 1437.36i 0.0961130 0.0961130i −0.657415 0.753528i \(-0.728350\pi\)
0.753528 + 0.657415i \(0.228350\pi\)
\(608\) −2581.11 + 2581.11i −0.172168 + 0.172168i
\(609\) 7125.49 0.474120
\(610\) 2612.88 4722.46i 0.173430 0.313454i
\(611\) 6899.00 0.456798
\(612\) −150.578 150.578i −0.00994571 0.00994571i
\(613\) 12486.0 12486.0i 0.822683 0.822683i −0.163809 0.986492i \(-0.552378\pi\)
0.986492 + 0.163809i \(0.0523780\pi\)
\(614\) 9218.20i 0.605889i
\(615\) −1383.33 + 2500.20i −0.0907013 + 0.163931i
\(616\) −3039.60 −0.198813
\(617\) 6660.66 + 6660.66i 0.434599 + 0.434599i 0.890190 0.455590i \(-0.150572\pi\)
−0.455590 + 0.890190i \(0.650572\pi\)
\(618\) −6962.27 + 6962.27i −0.453177 + 0.453177i
\(619\) 19059.4 1.23758 0.618789 0.785557i \(-0.287624\pi\)
0.618789 + 0.785557i \(0.287624\pi\)
\(620\) −3900.01 + 1121.61i −0.252626 + 0.0726530i
\(621\) −14805.9 6482.38i −0.956747 0.418887i
\(622\) 3205.86 3205.86i 0.206661 0.206661i
\(623\) −20283.9 20283.9i −1.30443 1.30443i
\(624\) 326.857i 0.0209692i
\(625\) 6805.65 14065.0i 0.435562 0.900159i
\(626\) 13087.5i 0.835591i
\(627\) 243.372 243.372i 0.0155013 0.0155013i
\(628\) 1185.38 1185.38i 0.0753216 0.0753216i
\(629\) 623.502i 0.0395241i
\(630\) −8280.98 + 2381.53i −0.523686 + 0.150607i
\(631\) 22728.9i 1.43395i 0.697099 + 0.716975i \(0.254474\pi\)
−0.697099 + 0.716975i \(0.745526\pi\)
\(632\) −1663.72 1663.72i −0.104714 0.104714i
\(633\) −10588.9 10588.9i −0.664880 0.664880i
\(634\) 12205.7i 0.764588i
\(635\) −7537.45 4170.38i −0.471046 0.260625i
\(636\) 8940.11i 0.557387i
\(637\) −3676.54 + 3676.54i −0.228681 + 0.228681i
\(638\) 438.489 438.489i 0.0272100 0.0272100i
\(639\) 7214.99i 0.446668i
\(640\) 3524.44 6369.97i 0.217681 0.393430i
\(641\) 21074.7i 1.29860i −0.760533 0.649299i \(-0.775062\pi\)
0.760533 0.649299i \(-0.224938\pi\)
\(642\) −8800.35 8800.35i −0.541000 0.541000i
\(643\) −5345.61 + 5345.61i −0.327854 + 0.327854i −0.851770 0.523916i \(-0.824471\pi\)
0.523916 + 0.851770i \(0.324471\pi\)
\(644\) −12763.1 5587.99i −0.780957 0.341922i
\(645\) 2116.44 + 7359.23i 0.129201 + 0.449255i
\(646\) −129.516 −0.00788816
\(647\) 937.636 937.636i 0.0569741 0.0569741i −0.678046 0.735020i \(-0.737173\pi\)
0.735020 + 0.678046i \(0.237173\pi\)
\(648\) −2029.50 2029.50i −0.123034 0.123034i
\(649\) −2549.47 −0.154199
\(650\) 2289.58 1435.66i 0.138161 0.0866329i
\(651\) 8040.36i 0.484065i
\(652\) 1951.12 1951.12i 0.117196 0.117196i
\(653\) −4374.28 4374.28i −0.262142 0.262142i 0.563782 0.825924i \(-0.309346\pi\)
−0.825924 + 0.563782i \(0.809346\pi\)
\(654\) 11587.7 0.692839
\(655\) 2374.83 + 8257.67i 0.141668 + 0.492601i
\(656\) −583.602 −0.0347345
\(657\) −5788.48 + 5788.48i −0.343729 + 0.343729i
\(658\) 22365.2 22365.2i 1.32506 1.32506i
\(659\) 12314.7 0.727938 0.363969 0.931411i \(-0.381421\pi\)
0.363969 + 0.931411i \(0.381421\pi\)
\(660\) −393.934 + 711.986i −0.0232331 + 0.0419909i
\(661\) 23116.7i 1.36026i 0.733090 + 0.680132i \(0.238078\pi\)
−0.733090 + 0.680132i \(0.761922\pi\)
\(662\) −5070.74 + 5070.74i −0.297704 + 0.297704i
\(663\) 93.5704 93.5704i 0.00548111 0.00548111i
\(664\) −15293.9 −0.893851
\(665\) 3233.23 5843.65i 0.188540 0.340763i
\(666\) 5234.66i 0.304563i
\(667\) 7371.97 2882.37i 0.427952 0.167325i
\(668\) 8313.38 + 8313.38i 0.481519 + 0.481519i
\(669\) 16629.8i 0.961053i
\(670\) −3346.40 11636.0i −0.192959 0.670951i
\(671\) 1185.95 0.0682313
\(672\) −12090.4 12090.4i −0.694041 0.694041i
\(673\) 22623.2 + 22623.2i 1.29578 + 1.29578i 0.931153 + 0.364629i \(0.118804\pi\)
0.364629 + 0.931153i \(0.381196\pi\)
\(674\) −10219.3 −0.584022
\(675\) −4092.36 + 17853.1i −0.233356 + 1.01803i
\(676\) 9252.47 0.526427
\(677\) 2565.70 + 2565.70i 0.145654 + 0.145654i 0.776174 0.630519i \(-0.217158\pi\)
−0.630519 + 0.776174i \(0.717158\pi\)
\(678\) 5870.23 5870.23i 0.332515 0.332515i
\(679\) 37057.7i 2.09447i
\(680\) 819.458 235.668i 0.0462129 0.0132904i
\(681\) 3829.84i 0.215506i
\(682\) 494.789 + 494.789i 0.0277807 + 0.0277807i
\(683\) 3974.66 + 3974.66i 0.222673 + 0.222673i 0.809623 0.586950i \(-0.199671\pi\)
−0.586950 + 0.809623i \(0.699671\pi\)
\(684\) −1385.70 −0.0774612
\(685\) −2687.51 + 4857.33i −0.149904 + 0.270933i
\(686\) 5710.04i 0.317799i
\(687\) 2447.36 + 2447.36i 0.135913 + 0.135913i
\(688\) −1105.92 + 1105.92i −0.0612829 + 0.0612829i
\(689\) −6524.46 −0.360758
\(690\) 6474.70 4950.24i 0.357229 0.273120i
\(691\) −12054.9 −0.663661 −0.331831 0.943339i \(-0.607666\pi\)
−0.331831 + 0.943339i \(0.607666\pi\)
\(692\) −1676.52 + 1676.52i −0.0920980 + 0.0920980i
\(693\) −1338.84 1338.84i −0.0733886 0.0733886i
\(694\) 5365.10i 0.293453i
\(695\) 22496.3 6469.72i 1.22782 0.353109i
\(696\) 5919.84 0.322401
\(697\) 167.070 + 167.070i 0.00907921 + 0.00907921i
\(698\) 14994.5 + 14994.5i 0.813109 + 0.813109i
\(699\) 5651.63i 0.305814i
\(700\) −3527.73 + 15389.9i −0.190480 + 0.830977i
\(701\) 4207.04i 0.226673i 0.993557 + 0.113336i \(0.0361538\pi\)
−0.993557 + 0.113336i \(0.963846\pi\)
\(702\) −2240.06 + 2240.06i −0.120435 + 0.120435i
\(703\) 2868.89 + 2868.89i 0.153915 + 0.153915i
\(704\) −1784.64 −0.0955415
\(705\) −6516.81 22660.0i −0.348138 1.21053i
\(706\) −13565.0 −0.723121
\(707\) 689.237 + 689.237i 0.0366640 + 0.0366640i
\(708\) −6180.04 6180.04i −0.328051 0.328051i
\(709\) 30617.4 1.62181 0.810904 0.585179i \(-0.198976\pi\)
0.810904 + 0.585179i \(0.198976\pi\)
\(710\) 9077.53 + 5022.50i 0.479822 + 0.265480i
\(711\) 1465.62i 0.0773068i
\(712\) −16851.9 16851.9i −0.887008 0.887008i
\(713\) 3252.45 + 8318.49i 0.170835 + 0.436928i
\(714\) 606.675i 0.0317987i
\(715\) 519.605 + 287.491i 0.0271778 + 0.0150372i
\(716\) 20505.3 1.07028
\(717\) 10765.3 10765.3i 0.560721 0.560721i
\(718\) 10791.0 10791.0i 0.560884 0.560884i
\(719\) 8132.52i 0.421825i 0.977505 + 0.210912i \(0.0676435\pi\)
−0.977505 + 0.210912i \(0.932357\pi\)
\(720\) −1260.83 + 362.604i −0.0652618 + 0.0187687i
\(721\) −41982.0 −2.16851
\(722\) 8500.28 8500.28i 0.438155 0.438155i
\(723\) −5539.87 + 5539.87i −0.284966 + 0.284966i
\(724\) −15027.9 −0.771418
\(725\) −4765.25 7599.56i −0.244106 0.389297i
\(726\) −8656.04 −0.442501
\(727\) −15804.0 15804.0i −0.806240 0.806240i 0.177823 0.984063i \(-0.443095\pi\)
−0.984063 + 0.177823i \(0.943095\pi\)
\(728\) −5377.24 + 5377.24i −0.273755 + 0.273755i
\(729\) 15729.0i 0.799115i
\(730\) −3253.30 11312.2i −0.164945 0.573541i
\(731\) 633.188 0.0320374
\(732\) 2874.81 + 2874.81i 0.145159 + 0.145159i
\(733\) −14509.7 + 14509.7i −0.731142 + 0.731142i −0.970846 0.239704i \(-0.922950\pi\)
0.239704 + 0.970846i \(0.422950\pi\)
\(734\) −1065.35 −0.0535730
\(735\) 15548.6 + 8602.85i 0.780297 + 0.431729i
\(736\) −17399.3 7617.85i −0.871396 0.381518i
\(737\) 1881.27 1881.27i 0.0940262 0.0940262i
\(738\) −1402.64 1402.64i −0.0699621 0.0699621i
\(739\) 29009.7i 1.44403i −0.691878 0.722015i \(-0.743216\pi\)
0.691878 0.722015i \(-0.256784\pi\)
\(740\) −8392.94 4643.72i −0.416933 0.230685i
\(741\) 861.081i 0.0426891i
\(742\) −21151.1 + 21151.1i −1.04647 + 1.04647i
\(743\) 8443.61 8443.61i 0.416912 0.416912i −0.467226 0.884138i \(-0.654746\pi\)
0.884138 + 0.467226i \(0.154746\pi\)
\(744\) 6679.91i 0.329163i
\(745\) −5012.04 17427.7i −0.246479 0.857049i
\(746\) 16314.9i 0.800710i
\(747\) −6736.42 6736.42i −0.329950 0.329950i
\(748\) 47.5767 + 47.5767i 0.00232564 + 0.00232564i
\(749\) 53065.5i 2.58875i
\(750\) −6878.23 6164.07i −0.334877 0.300107i
\(751\) 3782.28i 0.183778i −0.995769 0.0918891i \(-0.970709\pi\)
0.995769 0.0918891i \(-0.0292905\pi\)
\(752\) 3405.26 3405.26i 0.165129 0.165129i
\(753\) 17152.5 17152.5i 0.830108 0.830108i
\(754\) 1551.43i 0.0749334i
\(755\) −1336.33 4646.63i −0.0644158 0.223984i
\(756\) 18508.5i 0.890406i
\(757\) 6899.64 + 6899.64i 0.331270 + 0.331270i 0.853069 0.521799i \(-0.174739\pi\)
−0.521799 + 0.853069i \(0.674739\pi\)
\(758\) −13035.6 + 13035.6i −0.624639 + 0.624639i
\(759\) 1640.57 + 718.283i 0.0784573 + 0.0343505i
\(760\) 2686.16 4854.89i 0.128207 0.231718i
\(761\) −6530.74 −0.311090 −0.155545 0.987829i \(-0.549713\pi\)
−0.155545 + 0.987829i \(0.549713\pi\)
\(762\) −3600.57 + 3600.57i −0.171175 + 0.171175i
\(763\) 34936.7 + 34936.7i 1.65766 + 1.65766i
\(764\) 13072.9 0.619057
\(765\) 464.747 + 257.139i 0.0219647 + 0.0121528i
\(766\) 16347.0i 0.771073i
\(767\) −4510.17 + 4510.17i −0.212324 + 0.212324i
\(768\) −10763.6 10763.6i −0.505728 0.505728i
\(769\) −41859.0 −1.96290 −0.981452 0.191706i \(-0.938598\pi\)
−0.981452 + 0.191706i \(0.938598\pi\)
\(770\) 2616.45 752.467i 0.122455 0.0352169i
\(771\) −16453.5 −0.768556
\(772\) −13523.8