Properties

Label 115.4.e.a.22.11
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 22.11
Character \(\chi\) \(=\) 115.22
Dual form 115.4.e.a.68.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.84990 - 1.84990i) q^{2} +(-5.85544 + 5.85544i) q^{3} -1.15573i q^{4} +(-10.6129 - 3.51653i) q^{5} +21.6640 q^{6} +(-7.25929 + 7.25929i) q^{7} +(-16.9372 + 16.9372i) q^{8} -41.5723i q^{9} +O(q^{10})\) \(q+(-1.84990 - 1.84990i) q^{2} +(-5.85544 + 5.85544i) q^{3} -1.15573i q^{4} +(-10.6129 - 3.51653i) q^{5} +21.6640 q^{6} +(-7.25929 + 7.25929i) q^{7} +(-16.9372 + 16.9372i) q^{8} -41.5723i q^{9} +(13.1276 + 26.1381i) q^{10} +0.503049i q^{11} +(6.76730 + 6.76730i) q^{12} +(-4.59644 + 4.59644i) q^{13} +26.8579 q^{14} +(82.7341 - 41.5524i) q^{15} +53.4185 q^{16} +(74.8926 - 74.8926i) q^{17} +(-76.9047 + 76.9047i) q^{18} +133.354 q^{19} +(-4.06416 + 12.2657i) q^{20} -85.0127i q^{21} +(0.930591 - 0.930591i) q^{22} +(-71.2984 + 84.1638i) q^{23} -198.349i q^{24} +(100.268 + 74.6413i) q^{25} +17.0059 q^{26} +(85.3275 + 85.3275i) q^{27} +(8.38978 + 8.38978i) q^{28} -150.499i q^{29} +(-229.918 - 76.1821i) q^{30} -122.391 q^{31} +(36.6787 + 36.6787i) q^{32} +(-2.94557 - 2.94557i) q^{33} -277.088 q^{34} +(102.570 - 51.5147i) q^{35} -48.0464 q^{36} +(53.1409 - 53.1409i) q^{37} +(-246.692 - 246.692i) q^{38} -53.8283i q^{39} +(239.313 - 120.193i) q^{40} -134.778 q^{41} +(-157.265 + 157.265i) q^{42} +(300.444 + 300.444i) q^{43} +0.581389 q^{44} +(-146.191 + 441.204i) q^{45} +(287.590 - 23.7997i) q^{46} +(31.8091 + 31.8091i) q^{47} +(-312.789 + 312.789i) q^{48} +237.605i q^{49} +(-47.4068 - 323.565i) q^{50} +877.058i q^{51} +(5.31224 + 5.31224i) q^{52} +(-189.294 - 189.294i) q^{53} -315.695i q^{54} +(1.76899 - 5.33882i) q^{55} -245.904i q^{56} +(-780.847 + 780.847i) q^{57} +(-278.409 + 278.409i) q^{58} +213.925i q^{59} +(-48.0234 - 95.6183i) q^{60} -205.810i q^{61} +(226.412 + 226.412i) q^{62} +(301.786 + 301.786i) q^{63} -563.052i q^{64} +(64.9451 - 32.6181i) q^{65} +10.8980i q^{66} +(710.343 - 710.343i) q^{67} +(-86.5555 - 86.5555i) q^{68} +(-75.3326 - 910.299i) q^{69} +(-285.041 - 94.4468i) q^{70} +449.783 q^{71} +(704.119 + 704.119i) q^{72} +(365.998 - 365.998i) q^{73} -196.611 q^{74} +(-1024.17 + 150.055i) q^{75} -154.121i q^{76} +(-3.65178 - 3.65178i) q^{77} +(-99.5771 + 99.5771i) q^{78} +625.818 q^{79} +(-566.926 - 187.848i) q^{80} +123.193 q^{81} +(249.326 + 249.326i) q^{82} +(-819.106 - 819.106i) q^{83} -98.2517 q^{84} +(-1058.19 + 531.466i) q^{85} -1111.58i q^{86} +(881.240 + 881.240i) q^{87} +(-8.52024 - 8.52024i) q^{88} -397.018 q^{89} +(1086.62 - 545.746i) q^{90} -66.7338i q^{91} +(97.2706 + 82.4016i) q^{92} +(716.655 - 716.655i) q^{93} -117.688i q^{94} +(-1415.28 - 468.944i) q^{95} -429.540 q^{96} +(-1055.44 + 1055.44i) q^{97} +(439.547 - 439.547i) q^{98} +20.9129 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.84990 1.84990i −0.654039 0.654039i 0.299924 0.953963i \(-0.403039\pi\)
−0.953963 + 0.299924i \(0.903039\pi\)
\(3\) −5.85544 + 5.85544i −1.12688 + 1.12688i −0.136198 + 0.990682i \(0.543488\pi\)
−0.990682 + 0.136198i \(0.956512\pi\)
\(4\) 1.15573i 0.144466i
\(5\) −10.6129 3.51653i −0.949248 0.314528i
\(6\) 21.6640 1.47405
\(7\) −7.25929 + 7.25929i −0.391965 + 0.391965i −0.875387 0.483422i \(-0.839394\pi\)
0.483422 + 0.875387i \(0.339394\pi\)
\(8\) −16.9372 + 16.9372i −0.748525 + 0.748525i
\(9\) 41.5723i 1.53972i
\(10\) 13.1276 + 26.1381i 0.415132 + 0.826559i
\(11\) 0.503049i 0.0137886i 0.999976 + 0.00689432i \(0.00219455\pi\)
−0.999976 + 0.00689432i \(0.997805\pi\)
\(12\) 6.76730 + 6.76730i 0.162796 + 0.162796i
\(13\) −4.59644 + 4.59644i −0.0980633 + 0.0980633i −0.754436 0.656373i \(-0.772090\pi\)
0.656373 + 0.754436i \(0.272090\pi\)
\(14\) 26.8579 0.512721
\(15\) 82.7341 41.5524i 1.42412 0.715253i
\(16\) 53.4185 0.834663
\(17\) 74.8926 74.8926i 1.06848 1.06848i 0.0710011 0.997476i \(-0.477381\pi\)
0.997476 0.0710011i \(-0.0226194\pi\)
\(18\) −76.9047 + 76.9047i −1.00703 + 1.00703i
\(19\) 133.354 1.61019 0.805093 0.593149i \(-0.202116\pi\)
0.805093 + 0.593149i \(0.202116\pi\)
\(20\) −4.06416 + 12.2657i −0.0454387 + 0.137134i
\(21\) 85.0127i 0.883395i
\(22\) 0.930591 0.930591i 0.00901831 0.00901831i
\(23\) −71.2984 + 84.1638i −0.646380 + 0.763016i
\(24\) 198.349i 1.68700i
\(25\) 100.268 + 74.6413i 0.802144 + 0.597131i
\(26\) 17.0059 0.128274
\(27\) 85.3275 + 85.3275i 0.608196 + 0.608196i
\(28\) 8.38978 + 8.38978i 0.0566257 + 0.0566257i
\(29\) 150.499i 0.963691i −0.876256 0.481846i \(-0.839967\pi\)
0.876256 0.481846i \(-0.160033\pi\)
\(30\) −229.918 76.1821i −1.39924 0.463629i
\(31\) −122.391 −0.709101 −0.354550 0.935037i \(-0.615366\pi\)
−0.354550 + 0.935037i \(0.615366\pi\)
\(32\) 36.6787 + 36.6787i 0.202623 + 0.202623i
\(33\) −2.94557 2.94557i −0.0155381 0.0155381i
\(34\) −277.088 −1.39765
\(35\) 102.570 51.5147i 0.495356 0.248788i
\(36\) −48.0464 −0.222437
\(37\) 53.1409 53.1409i 0.236117 0.236117i −0.579123 0.815240i \(-0.696605\pi\)
0.815240 + 0.579123i \(0.196605\pi\)
\(38\) −246.692 246.692i −1.05312 1.05312i
\(39\) 53.8283i 0.221011i
\(40\) 239.313 120.193i 0.945969 0.475104i
\(41\) −134.778 −0.513385 −0.256692 0.966493i \(-0.582633\pi\)
−0.256692 + 0.966493i \(0.582633\pi\)
\(42\) −157.265 + 157.265i −0.577774 + 0.577774i
\(43\) 300.444 + 300.444i 1.06552 + 1.06552i 0.997698 + 0.0678196i \(0.0216042\pi\)
0.0678196 + 0.997698i \(0.478396\pi\)
\(44\) 0.581389 0.00199199
\(45\) −146.191 + 441.204i −0.484284 + 1.46157i
\(46\) 287.590 23.7997i 0.921800 0.0762844i
\(47\) 31.8091 + 31.8091i 0.0987200 + 0.0987200i 0.754742 0.656022i \(-0.227762\pi\)
−0.656022 + 0.754742i \(0.727762\pi\)
\(48\) −312.789 + 312.789i −0.940565 + 0.940565i
\(49\) 237.605i 0.692727i
\(50\) −47.4068 323.565i −0.134087 0.915180i
\(51\) 877.058i 2.40809i
\(52\) 5.31224 + 5.31224i 0.0141668 + 0.0141668i
\(53\) −189.294 189.294i −0.490594 0.490594i 0.417899 0.908493i \(-0.362767\pi\)
−0.908493 + 0.417899i \(0.862767\pi\)
\(54\) 315.695i 0.795567i
\(55\) 1.76899 5.33882i 0.00433692 0.0130888i
\(56\) 245.904i 0.586791i
\(57\) −780.847 + 780.847i −1.81449 + 1.81449i
\(58\) −278.409 + 278.409i −0.630291 + 0.630291i
\(59\) 213.925i 0.472044i 0.971748 + 0.236022i \(0.0758438\pi\)
−0.971748 + 0.236022i \(0.924156\pi\)
\(60\) −48.0234 95.6183i −0.103330 0.205738i
\(61\) 205.810i 0.431987i −0.976395 0.215994i \(-0.930701\pi\)
0.976395 0.215994i \(-0.0692990\pi\)
\(62\) 226.412 + 226.412i 0.463780 + 0.463780i
\(63\) 301.786 + 301.786i 0.603515 + 0.603515i
\(64\) 563.052i 1.09971i
\(65\) 64.9451 32.6181i 0.123930 0.0622427i
\(66\) 10.8980i 0.0203251i
\(67\) 710.343 710.343i 1.29526 1.29526i 0.363767 0.931490i \(-0.381490\pi\)
0.931490 0.363767i \(-0.118510\pi\)
\(68\) −86.5555 86.5555i −0.154359 0.154359i
\(69\) −75.3326 910.299i −0.131435 1.58822i
\(70\) −285.041 94.4468i −0.486699 0.161265i
\(71\) 449.783 0.751823 0.375912 0.926656i \(-0.377330\pi\)
0.375912 + 0.926656i \(0.377330\pi\)
\(72\) 704.119 + 704.119i 1.15252 + 1.15252i
\(73\) 365.998 365.998i 0.586807 0.586807i −0.349959 0.936765i \(-0.613804\pi\)
0.936765 + 0.349959i \(0.113804\pi\)
\(74\) −196.611 −0.308859
\(75\) −1024.17 + 150.055i −1.57681 + 0.231025i
\(76\) 154.121i 0.232617i
\(77\) −3.65178 3.65178i −0.00540466 0.00540466i
\(78\) −99.5771 + 99.5771i −0.144550 + 0.144550i
\(79\) 625.818 0.891266 0.445633 0.895216i \(-0.352979\pi\)
0.445633 + 0.895216i \(0.352979\pi\)
\(80\) −566.926 187.848i −0.792303 0.262525i
\(81\) 123.193 0.168990
\(82\) 249.326 + 249.326i 0.335774 + 0.335774i
\(83\) −819.106 819.106i −1.08324 1.08324i −0.996206 0.0870306i \(-0.972262\pi\)
−0.0870306 0.996206i \(-0.527738\pi\)
\(84\) −98.2517 −0.127621
\(85\) −1058.19 + 531.466i −1.35032 + 0.678184i
\(86\) 1111.58i 1.39378i
\(87\) 881.240 + 881.240i 1.08596 + 1.08596i
\(88\) −8.52024 8.52024i −0.0103211 0.0103211i
\(89\) −397.018 −0.472852 −0.236426 0.971649i \(-0.575976\pi\)
−0.236426 + 0.971649i \(0.575976\pi\)
\(90\) 1086.62 545.746i 1.27267 0.639185i
\(91\) 66.7338i 0.0768747i
\(92\) 97.2706 + 82.4016i 0.110230 + 0.0933800i
\(93\) 716.655 716.655i 0.799072 0.799072i
\(94\) 117.688i 0.129133i
\(95\) −1415.28 468.944i −1.52847 0.506449i
\(96\) −429.540 −0.456664
\(97\) −1055.44 + 1055.44i −1.10478 + 1.10478i −0.110951 + 0.993826i \(0.535390\pi\)
−0.993826 + 0.110951i \(0.964610\pi\)
\(98\) 439.547 439.547i 0.453070 0.453070i
\(99\) 20.9129 0.0212306
\(100\) 86.2652 115.883i 0.0862652 0.115883i
\(101\) 391.120 0.385326 0.192663 0.981265i \(-0.438288\pi\)
0.192663 + 0.981265i \(0.438288\pi\)
\(102\) 1622.47 1622.47i 1.57499 1.57499i
\(103\) 1072.57 + 1072.57i 1.02605 + 1.02605i 0.999652 + 0.0263981i \(0.00840375\pi\)
0.0263981 + 0.999652i \(0.491596\pi\)
\(104\) 155.702i 0.146806i
\(105\) −298.950 + 902.232i −0.277853 + 0.838561i
\(106\) 700.350i 0.641736i
\(107\) 848.627 848.627i 0.766728 0.766728i −0.210801 0.977529i \(-0.567607\pi\)
0.977529 + 0.210801i \(0.0676073\pi\)
\(108\) 98.6155 98.6155i 0.0878637 0.0878637i
\(109\) 1503.89 1.32152 0.660762 0.750595i \(-0.270233\pi\)
0.660762 + 0.750595i \(0.270233\pi\)
\(110\) −13.1487 + 6.60383i −0.0113971 + 0.00572410i
\(111\) 622.327i 0.532150i
\(112\) −387.780 + 387.780i −0.327159 + 0.327159i
\(113\) 710.245 + 710.245i 0.591277 + 0.591277i 0.937976 0.346700i \(-0.112698\pi\)
−0.346700 + 0.937976i \(0.612698\pi\)
\(114\) 2888.98 2.37349
\(115\) 1052.65 642.500i 0.853565 0.520986i
\(116\) −173.937 −0.139221
\(117\) 191.085 + 191.085i 0.150990 + 0.150990i
\(118\) 395.739 395.739i 0.308735 0.308735i
\(119\) 1087.33i 0.837611i
\(120\) −697.502 + 2105.07i −0.530608 + 1.60138i
\(121\) 1330.75 0.999810
\(122\) −380.727 + 380.727i −0.282536 + 0.282536i
\(123\) 789.184 789.184i 0.578523 0.578523i
\(124\) 141.451i 0.102441i
\(125\) −801.657 1144.76i −0.573619 0.819122i
\(126\) 1116.55i 0.789444i
\(127\) −1844.31 1844.31i −1.28863 1.28863i −0.935619 0.353012i \(-0.885158\pi\)
−0.353012 0.935619i \(-0.614842\pi\)
\(128\) −748.160 + 748.160i −0.516630 + 0.516630i
\(129\) −3518.46 −2.40142
\(130\) −180.482 59.8018i −0.121764 0.0403459i
\(131\) 2266.15 1.51141 0.755704 0.654913i \(-0.227295\pi\)
0.755704 + 0.654913i \(0.227295\pi\)
\(132\) −3.40429 + 3.40429i −0.00224474 + 0.00224474i
\(133\) −968.056 + 968.056i −0.631136 + 0.631136i
\(134\) −2628.13 −1.69430
\(135\) −605.517 1205.63i −0.386034 0.768623i
\(136\) 2536.94i 1.59956i
\(137\) 592.705 592.705i 0.369622 0.369622i −0.497717 0.867339i \(-0.665828\pi\)
0.867339 + 0.497717i \(0.165828\pi\)
\(138\) −1544.61 + 1823.32i −0.952794 + 1.12472i
\(139\) 1031.29i 0.629299i 0.949208 + 0.314650i \(0.101887\pi\)
−0.949208 + 0.314650i \(0.898113\pi\)
\(140\) −59.5371 118.543i −0.0359414 0.0715622i
\(141\) −372.513 −0.222491
\(142\) −832.055 832.055i −0.491722 0.491722i
\(143\) −2.31223 2.31223i −0.00135216 0.00135216i
\(144\) 2220.73i 1.28514i
\(145\) −529.236 + 1597.24i −0.303108 + 0.914782i
\(146\) −1354.12 −0.767589
\(147\) −1391.28 1391.28i −0.780620 0.780620i
\(148\) −61.4165 61.4165i −0.0341109 0.0341109i
\(149\) −540.563 −0.297213 −0.148606 0.988896i \(-0.547479\pi\)
−0.148606 + 0.988896i \(0.547479\pi\)
\(150\) 2172.20 + 1617.03i 1.18240 + 0.880198i
\(151\) 2797.30 1.50756 0.753778 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(152\) −2258.64 + 2258.64i −1.20526 + 1.20526i
\(153\) −3113.46 3113.46i −1.64515 1.64515i
\(154\) 13.5109i 0.00706972i
\(155\) 1298.93 + 430.393i 0.673113 + 0.223032i
\(156\) −62.2110 −0.0319286
\(157\) −491.173 + 491.173i −0.249681 + 0.249681i −0.820840 0.571159i \(-0.806494\pi\)
0.571159 + 0.820840i \(0.306494\pi\)
\(158\) −1157.70 1157.70i −0.582923 0.582923i
\(159\) 2216.80 1.10568
\(160\) −260.286 518.250i −0.128609 0.256070i
\(161\) −93.3938 1128.54i −0.0457171 0.552434i
\(162\) −227.896 227.896i −0.110526 0.110526i
\(163\) −439.096 + 439.096i −0.210998 + 0.210998i −0.804691 0.593693i \(-0.797669\pi\)
0.593693 + 0.804691i \(0.297669\pi\)
\(164\) 155.767i 0.0741667i
\(165\) 20.9029 + 41.6193i 0.00986237 + 0.0196367i
\(166\) 3030.53i 1.41696i
\(167\) −468.862 468.862i −0.217255 0.217255i 0.590085 0.807341i \(-0.299094\pi\)
−0.807341 + 0.590085i \(0.799094\pi\)
\(168\) 1439.88 + 1439.88i 0.661243 + 0.661243i
\(169\) 2154.75i 0.980767i
\(170\) 2940.71 + 974.388i 1.32672 + 0.439601i
\(171\) 5543.84i 2.47923i
\(172\) 347.232 347.232i 0.153931 0.153931i
\(173\) 1158.88 1158.88i 0.509293 0.509293i −0.405016 0.914309i \(-0.632734\pi\)
0.914309 + 0.405016i \(0.132734\pi\)
\(174\) 3260.42i 1.42053i
\(175\) −1269.72 + 186.031i −0.548466 + 0.0803580i
\(176\) 26.8721i 0.0115089i
\(177\) −1252.62 1252.62i −0.531937 0.531937i
\(178\) 734.445 + 734.445i 0.309264 + 0.309264i
\(179\) 371.700i 0.155208i −0.996984 0.0776039i \(-0.975273\pi\)
0.996984 0.0776039i \(-0.0247269\pi\)
\(180\) 509.912 + 168.957i 0.211148 + 0.0699627i
\(181\) 2549.93i 1.04715i −0.851979 0.523576i \(-0.824597\pi\)
0.851979 0.523576i \(-0.175403\pi\)
\(182\) −123.451 + 123.451i −0.0502790 + 0.0502790i
\(183\) 1205.11 + 1205.11i 0.486797 + 0.486797i
\(184\) −217.904 2633.09i −0.0873049 1.05497i
\(185\) −750.852 + 377.108i −0.298399 + 0.149868i
\(186\) −2651.48 −1.04525
\(187\) 37.6746 + 37.6746i 0.0147328 + 0.0147328i
\(188\) 36.7628 36.7628i 0.0142617 0.0142617i
\(189\) −1238.83 −0.476783
\(190\) 1750.62 + 3485.62i 0.668439 + 1.33091i
\(191\) 3346.43i 1.26774i 0.773438 + 0.633872i \(0.218535\pi\)
−0.773438 + 0.633872i \(0.781465\pi\)
\(192\) 3296.91 + 3296.91i 1.23924 + 1.23924i
\(193\) −1459.17 + 1459.17i −0.544215 + 0.544215i −0.924762 0.380547i \(-0.875736\pi\)
0.380547 + 0.924762i \(0.375736\pi\)
\(194\) 3904.91 1.44513
\(195\) −189.289 + 571.276i −0.0695142 + 0.209794i
\(196\) 274.608 0.100076
\(197\) −2542.11 2542.11i −0.919380 0.919380i 0.0776046 0.996984i \(-0.475273\pi\)
−0.996984 + 0.0776046i \(0.975273\pi\)
\(198\) −38.6869 38.6869i −0.0138856 0.0138856i
\(199\) −1564.86 −0.557436 −0.278718 0.960373i \(-0.589909\pi\)
−0.278718 + 0.960373i \(0.589909\pi\)
\(200\) −2962.47 + 434.044i −1.04739 + 0.153458i
\(201\) 8318.74i 2.91920i
\(202\) −723.534 723.534i −0.252018 0.252018i
\(203\) 1092.52 + 1092.52i 0.377733 + 0.377733i
\(204\) 1013.64 0.347888
\(205\) 1430.39 + 473.951i 0.487329 + 0.161474i
\(206\) 3968.28i 1.34215i
\(207\) 3498.89 + 2964.04i 1.17483 + 0.995242i
\(208\) −245.535 + 245.535i −0.0818498 + 0.0818498i
\(209\) 67.0836i 0.0222023i
\(210\) 2222.07 1116.01i 0.730178 0.366725i
\(211\) −137.567 −0.0448840 −0.0224420 0.999748i \(-0.507144\pi\)
−0.0224420 + 0.999748i \(0.507144\pi\)
\(212\) −218.772 + 218.772i −0.0708743 + 0.0708743i
\(213\) −2633.68 + 2633.68i −0.847215 + 0.847215i
\(214\) −3139.75 −1.00294
\(215\) −2132.06 4245.10i −0.676305 1.34658i
\(216\) −2890.42 −0.910500
\(217\) 888.474 888.474i 0.277943 0.277943i
\(218\) −2782.04 2782.04i −0.864329 0.864329i
\(219\) 4286.16i 1.32252i
\(220\) −6.17023 2.04447i −0.00189089 0.000626538i
\(221\) 688.478i 0.209557i
\(222\) 1151.24 1151.24i 0.348047 0.348047i
\(223\) 3435.79 3435.79i 1.03174 1.03174i 0.0322582 0.999480i \(-0.489730\pi\)
0.999480 0.0322582i \(-0.0102699\pi\)
\(224\) −532.523 −0.158842
\(225\) 3103.02 4168.38i 0.919412 1.23507i
\(226\) 2627.77i 0.773436i
\(227\) 2524.56 2524.56i 0.738153 0.738153i −0.234067 0.972220i \(-0.575204\pi\)
0.972220 + 0.234067i \(0.0752035\pi\)
\(228\) 902.447 + 902.447i 0.262132 + 0.262132i
\(229\) −1964.53 −0.566900 −0.283450 0.958987i \(-0.591479\pi\)
−0.283450 + 0.958987i \(0.591479\pi\)
\(230\) −3135.86 758.734i −0.899010 0.217519i
\(231\) 42.7656 0.0121808
\(232\) 2549.04 + 2549.04i 0.721347 + 0.721347i
\(233\) 2236.36 2236.36i 0.628793 0.628793i −0.318971 0.947764i \(-0.603337\pi\)
0.947764 + 0.318971i \(0.103337\pi\)
\(234\) 706.976i 0.197506i
\(235\) −225.730 449.446i −0.0626596 0.124760i
\(236\) 247.239 0.0681944
\(237\) −3664.44 + 3664.44i −1.00435 + 1.00435i
\(238\) 2011.46 2011.46i 0.547830 0.547830i
\(239\) 3196.23i 0.865050i 0.901622 + 0.432525i \(0.142377\pi\)
−0.901622 + 0.432525i \(0.857623\pi\)
\(240\) 4419.53 2219.67i 1.18866 0.596996i
\(241\) 1965.34i 0.525305i −0.964891 0.262652i \(-0.915403\pi\)
0.964891 0.262652i \(-0.0845972\pi\)
\(242\) −2461.75 2461.75i −0.653915 0.653915i
\(243\) −3025.19 + 3025.19i −0.798627 + 0.798627i
\(244\) −237.860 −0.0624075
\(245\) 835.547 2521.69i 0.217882 0.657570i
\(246\) −2919.82 −0.756753
\(247\) −612.954 + 612.954i −0.157900 + 0.157900i
\(248\) 2072.97 2072.97i 0.530780 0.530780i
\(249\) 9592.46 2.44135
\(250\) −634.703 + 3600.68i −0.160568 + 0.910907i
\(251\) 1985.68i 0.499343i −0.968331 0.249671i \(-0.919677\pi\)
0.968331 0.249671i \(-0.0803226\pi\)
\(252\) 348.783 348.783i 0.0871875 0.0871875i
\(253\) −42.3385 35.8666i −0.0105209 0.00891270i
\(254\) 6823.59i 1.68563i
\(255\) 3084.20 9308.14i 0.757413 2.28588i
\(256\) −1736.37 −0.423918
\(257\) 4227.41 + 4227.41i 1.02607 + 1.02607i 0.999651 + 0.0264141i \(0.00840885\pi\)
0.0264141 + 0.999651i \(0.491591\pi\)
\(258\) 6508.80 + 6508.80i 1.57062 + 1.57062i
\(259\) 771.531i 0.185099i
\(260\) −37.6977 75.0590i −0.00899197 0.0179037i
\(261\) −6256.61 −1.48381
\(262\) −4192.15 4192.15i −0.988520 0.988520i
\(263\) −3980.50 3980.50i −0.933263 0.933263i 0.0646449 0.997908i \(-0.479409\pi\)
−0.997908 + 0.0646449i \(0.979409\pi\)
\(264\) 99.7795 0.0232614
\(265\) 1343.30 + 2674.62i 0.311390 + 0.620002i
\(266\) 3581.62 0.825575
\(267\) 2324.72 2324.72i 0.532848 0.532848i
\(268\) −820.964 820.964i −0.187121 0.187121i
\(269\) 7753.02i 1.75729i 0.477479 + 0.878643i \(0.341551\pi\)
−0.477479 + 0.878643i \(0.658449\pi\)
\(270\) −1110.15 + 3350.44i −0.250228 + 0.755191i
\(271\) −5540.81 −1.24199 −0.620997 0.783813i \(-0.713272\pi\)
−0.620997 + 0.783813i \(0.713272\pi\)
\(272\) 4000.64 4000.64i 0.891819 0.891819i
\(273\) 390.755 + 390.755i 0.0866286 + 0.0866286i
\(274\) −2192.89 −0.483494
\(275\) −37.5483 + 50.4397i −0.00823362 + 0.0110605i
\(276\) −1052.06 + 87.0641i −0.229444 + 0.0189878i
\(277\) −2648.85 2648.85i −0.574563 0.574563i 0.358837 0.933400i \(-0.383173\pi\)
−0.933400 + 0.358837i \(0.883173\pi\)
\(278\) 1907.78 1907.78i 0.411586 0.411586i
\(279\) 5088.09i 1.09181i
\(280\) −864.730 + 2609.76i −0.184562 + 0.557011i
\(281\) 485.195i 0.103005i −0.998673 0.0515023i \(-0.983599\pi\)
0.998673 0.0515023i \(-0.0164009\pi\)
\(282\) 689.112 + 689.112i 0.145518 + 0.145518i
\(283\) −3114.36 3114.36i −0.654167 0.654167i 0.299827 0.953994i \(-0.403071\pi\)
−0.953994 + 0.299827i \(0.903071\pi\)
\(284\) 519.828i 0.108613i
\(285\) 11032.9 5541.19i 2.29310 1.15169i
\(286\) 8.55481i 0.00176873i
\(287\) 978.392 978.392i 0.201229 0.201229i
\(288\) 1524.82 1524.82i 0.311982 0.311982i
\(289\) 6304.79i 1.28329i
\(290\) 3933.77 1975.70i 0.796547 0.400059i
\(291\) 12360.1i 2.48990i
\(292\) −422.995 422.995i −0.0847737 0.0847737i
\(293\) 5460.39 + 5460.39i 1.08874 + 1.08874i 0.995659 + 0.0930762i \(0.0296700\pi\)
0.0930762 + 0.995659i \(0.470330\pi\)
\(294\) 5147.48i 1.02111i
\(295\) 752.273 2270.36i 0.148471 0.448087i
\(296\) 1800.12i 0.353478i
\(297\) −42.9239 + 42.9239i −0.00838619 + 0.00838619i
\(298\) 999.989 + 999.989i 0.194389 + 0.194389i
\(299\) −59.1351 714.572i −0.0114377 0.138210i
\(300\) 173.423 + 1183.66i 0.0333753 + 0.227796i
\(301\) −4362.02 −0.835291
\(302\) −5174.73 5174.73i −0.986001 0.986001i
\(303\) −2290.18 + 2290.18i −0.434216 + 0.434216i
\(304\) 7123.57 1.34396
\(305\) −723.736 + 2184.24i −0.135872 + 0.410063i
\(306\) 11519.2i 2.15199i
\(307\) 7130.23 + 7130.23i 1.32555 + 1.32555i 0.909209 + 0.416340i \(0.136687\pi\)
0.416340 + 0.909209i \(0.363313\pi\)
\(308\) −4.22047 + 4.22047i −0.000780791 + 0.000780791i
\(309\) −12560.7 −2.31247
\(310\) −1606.71 3199.07i −0.294370 0.586114i
\(311\) −1853.34 −0.337921 −0.168961 0.985623i \(-0.554041\pi\)
−0.168961 + 0.985623i \(0.554041\pi\)
\(312\) 911.701 + 911.701i 0.165432 + 0.165432i
\(313\) −1356.77 1356.77i −0.245013 0.245013i 0.573907 0.818920i \(-0.305427\pi\)
−0.818920 + 0.573907i \(0.805427\pi\)
\(314\) 1817.24 0.326602
\(315\) −2141.59 4264.07i −0.383063 0.762708i
\(316\) 723.276i 0.128758i
\(317\) 309.563 + 309.563i 0.0548480 + 0.0548480i 0.733999 0.679151i \(-0.237652\pi\)
−0.679151 + 0.733999i \(0.737652\pi\)
\(318\) −4100.85 4100.85i −0.723159 0.723159i
\(319\) 75.7086 0.0132880
\(320\) −1979.99 + 5975.62i −0.345890 + 1.04390i
\(321\) 9938.17i 1.72802i
\(322\) −1914.93 + 2260.47i −0.331412 + 0.391214i
\(323\) 9987.23 9987.23i 1.72045 1.72045i
\(324\) 142.378i 0.0244133i
\(325\) −803.960 + 117.791i −0.137217 + 0.0201043i
\(326\) 1624.57 0.276002
\(327\) −8805.92 + 8805.92i −1.48920 + 1.48920i
\(328\) 2282.76 2282.76i 0.384282 0.384282i
\(329\) −461.824 −0.0773896
\(330\) 38.3233 115.660i 0.00639282 0.0192936i
\(331\) −3448.22 −0.572602 −0.286301 0.958140i \(-0.592426\pi\)
−0.286301 + 0.958140i \(0.592426\pi\)
\(332\) −946.665 + 946.665i −0.156491 + 0.156491i
\(333\) −2209.19 2209.19i −0.363553 0.363553i
\(334\) 1734.70i 0.284187i
\(335\) −10036.8 + 5040.87i −1.63692 + 0.822125i
\(336\) 4541.25i 0.737337i
\(337\) 3720.80 3720.80i 0.601438 0.601438i −0.339256 0.940694i \(-0.610175\pi\)
0.940694 + 0.339256i \(0.110175\pi\)
\(338\) 3986.07 3986.07i 0.641460 0.641460i
\(339\) −8317.60 −1.33260
\(340\) 614.231 + 1222.98i 0.0979746 + 0.195075i
\(341\) 61.5688i 0.00977754i
\(342\) −10255.6 + 10255.6i −1.62151 + 1.62151i
\(343\) −4214.78 4214.78i −0.663490 0.663490i
\(344\) −10177.3 −1.59513
\(345\) −2401.60 + 9925.84i −0.374776 + 1.54895i
\(346\) −4287.61 −0.666195
\(347\) 2049.87 + 2049.87i 0.317126 + 0.317126i 0.847662 0.530536i \(-0.178009\pi\)
−0.530536 + 0.847662i \(0.678009\pi\)
\(348\) 1018.48 1018.48i 0.156885 0.156885i
\(349\) 11825.7i 1.81379i −0.421352 0.906897i \(-0.638444\pi\)
0.421352 0.906897i \(-0.361556\pi\)
\(350\) 2692.99 + 2004.71i 0.411276 + 0.306161i
\(351\) −784.405 −0.119283
\(352\) −18.4512 + 18.4512i −0.00279390 + 0.00279390i
\(353\) −5463.27 + 5463.27i −0.823740 + 0.823740i −0.986642 0.162902i \(-0.947915\pi\)
0.162902 + 0.986642i \(0.447915\pi\)
\(354\) 4634.46i 0.695815i
\(355\) −4773.51 1581.68i −0.713667 0.236470i
\(356\) 458.846i 0.0683112i
\(357\) −6366.82 6366.82i −0.943887 0.943887i
\(358\) −687.609 + 687.609i −0.101512 + 0.101512i
\(359\) 5814.63 0.854831 0.427416 0.904055i \(-0.359424\pi\)
0.427416 + 0.904055i \(0.359424\pi\)
\(360\) −4996.70 9948.81i −0.731525 1.45652i
\(361\) 10924.3 1.59270
\(362\) −4717.11 + 4717.11i −0.684879 + 0.684879i
\(363\) −7792.11 + 7792.11i −1.12667 + 1.12667i
\(364\) −77.1262 −0.0111058
\(365\) −5171.36 + 2597.27i −0.741592 + 0.372458i
\(366\) 4458.65i 0.636769i
\(367\) −4200.09 + 4200.09i −0.597392 + 0.597392i −0.939618 0.342226i \(-0.888819\pi\)
0.342226 + 0.939618i \(0.388819\pi\)
\(368\) −3808.65 + 4495.90i −0.539510 + 0.636861i
\(369\) 5603.03i 0.790467i
\(370\) 2086.62 + 691.389i 0.293184 + 0.0971448i
\(371\) 2748.28 0.384591
\(372\) −828.259 828.259i −0.115439 0.115439i
\(373\) 4490.67 + 4490.67i 0.623373 + 0.623373i 0.946392 0.323019i \(-0.104698\pi\)
−0.323019 + 0.946392i \(0.604698\pi\)
\(374\) 139.389i 0.0192717i
\(375\) 11397.1 + 2009.01i 1.56945 + 0.276652i
\(376\) −1077.52 −0.147789
\(377\) 691.761 + 691.761i 0.0945027 + 0.0945027i
\(378\) 2291.72 + 2291.72i 0.311834 + 0.311834i
\(379\) 11193.1 1.51702 0.758511 0.651660i \(-0.225927\pi\)
0.758511 + 0.651660i \(0.225927\pi\)
\(380\) −541.972 + 1635.68i −0.0731647 + 0.220812i
\(381\) 21598.5 2.90426
\(382\) 6190.56 6190.56i 0.829153 0.829153i
\(383\) 10128.5 + 10128.5i 1.35128 + 1.35128i 0.884231 + 0.467050i \(0.154683\pi\)
0.467050 + 0.884231i \(0.345317\pi\)
\(384\) 8761.62i 1.16436i
\(385\) 25.9144 + 51.5976i 0.00343045 + 0.00683028i
\(386\) 5398.65 0.711875
\(387\) 12490.2 12490.2i 1.64059 1.64059i
\(388\) 1219.80 + 1219.80i 0.159603 + 0.159603i
\(389\) 5091.74 0.663654 0.331827 0.943340i \(-0.392335\pi\)
0.331827 + 0.943340i \(0.392335\pi\)
\(390\) 1406.97 706.637i 0.182679 0.0917486i
\(391\) 963.524 + 11643.0i 0.124623 + 1.50591i
\(392\) −4024.37 4024.37i −0.518524 0.518524i
\(393\) −13269.3 + 13269.3i −1.70318 + 1.70318i
\(394\) 9405.30i 1.20262i
\(395\) −6641.75 2200.71i −0.846032 0.280328i
\(396\) 24.1697i 0.00306710i
\(397\) −7017.86 7017.86i −0.887195 0.887195i 0.107058 0.994253i \(-0.465857\pi\)
−0.994253 + 0.107058i \(0.965857\pi\)
\(398\) 2894.83 + 2894.83i 0.364585 + 0.364585i
\(399\) 11336.8i 1.42243i
\(400\) 5356.16 + 3987.22i 0.669520 + 0.498403i
\(401\) 4694.52i 0.584621i −0.956323 0.292310i \(-0.905576\pi\)
0.956323 0.292310i \(-0.0944240\pi\)
\(402\) 15388.9 15388.9i 1.90927 1.90927i
\(403\) 562.564 562.564i 0.0695368 0.0695368i
\(404\) 452.029i 0.0556665i
\(405\) −1307.44 433.214i −0.160413 0.0531520i
\(406\) 4042.11i 0.494104i
\(407\) 26.7325 + 26.7325i 0.00325573 + 0.00325573i
\(408\) −14854.9 14854.9i −1.80252 1.80252i
\(409\) 9665.07i 1.16848i −0.811582 0.584238i \(-0.801393\pi\)
0.811582 0.584238i \(-0.198607\pi\)
\(410\) −1769.31 3522.84i −0.213122 0.424343i
\(411\) 6941.10i 0.833039i
\(412\) 1239.60 1239.60i 0.148229 0.148229i
\(413\) −1552.94 1552.94i −0.185025 0.185025i
\(414\) −989.411 11955.8i −0.117456 1.41931i
\(415\) 5812.69 + 11573.5i 0.687552 + 1.36897i
\(416\) −337.183 −0.0397398
\(417\) −6038.64 6038.64i −0.709145 0.709145i
\(418\) 124.098 124.098i 0.0145211 0.0145211i
\(419\) −2184.46 −0.254697 −0.127348 0.991858i \(-0.540647\pi\)
−0.127348 + 0.991858i \(0.540647\pi\)
\(420\) 1042.74 + 345.505i 0.121144 + 0.0401403i
\(421\) 9809.98i 1.13565i −0.823149 0.567825i \(-0.807785\pi\)
0.823149 0.567825i \(-0.192215\pi\)
\(422\) 254.486 + 254.486i 0.0293559 + 0.0293559i
\(423\) 1322.38 1322.38i 0.152001 0.152001i
\(424\) 6412.21 0.734445
\(425\) 13099.4 1919.25i 1.49509 0.219052i
\(426\) 9744.09 1.10822
\(427\) 1494.03 + 1494.03i 0.169324 + 0.169324i
\(428\) −980.783 980.783i −0.110766 0.110766i
\(429\) 27.0783 0.00304744
\(430\) −3908.92 + 11797.1i −0.438383 + 1.32304i
\(431\) 14369.3i 1.60591i 0.596041 + 0.802954i \(0.296740\pi\)
−0.596041 + 0.802954i \(0.703260\pi\)
\(432\) 4558.06 + 4558.06i 0.507639 + 0.507639i
\(433\) −3589.57 3589.57i −0.398392 0.398392i 0.479273 0.877666i \(-0.340900\pi\)
−0.877666 + 0.479273i \(0.840900\pi\)
\(434\) −3287.18 −0.363571
\(435\) −6253.62 12451.4i −0.689283 1.37242i
\(436\) 1738.09i 0.190916i
\(437\) −9507.93 + 11223.6i −1.04079 + 1.22860i
\(438\) 7928.98 7928.98i 0.864980 0.864980i
\(439\) 3913.40i 0.425459i 0.977111 + 0.212730i \(0.0682354\pi\)
−0.977111 + 0.212730i \(0.931765\pi\)
\(440\) 60.4629 + 120.386i 0.00655104 + 0.0130436i
\(441\) 9877.81 1.06660
\(442\) 1273.62 1273.62i 0.137058 0.137058i
\(443\) 6616.32 6616.32i 0.709596 0.709596i −0.256854 0.966450i \(-0.582686\pi\)
0.966450 + 0.256854i \(0.0826861\pi\)
\(444\) 719.241 0.0768777
\(445\) 4213.52 + 1396.13i 0.448854 + 0.148725i
\(446\) −12711.7 −1.34959
\(447\) 3165.24 3165.24i 0.334923 0.334923i
\(448\) 4087.36 + 4087.36i 0.431048 + 0.431048i
\(449\) 2465.92i 0.259185i 0.991567 + 0.129592i \(0.0413669\pi\)
−0.991567 + 0.129592i \(0.958633\pi\)
\(450\) −13451.4 + 1970.81i −1.40912 + 0.206455i
\(451\) 67.7999i 0.00707888i
\(452\) 820.851 820.851i 0.0854195 0.0854195i
\(453\) −16379.4 + 16379.4i −1.69884 + 1.69884i
\(454\) −9340.37 −0.965562
\(455\) −234.671 + 708.240i −0.0241793 + 0.0729732i
\(456\) 26450.7i 2.71638i
\(457\) 116.177 116.177i 0.0118917 0.0118917i −0.701136 0.713028i \(-0.747323\pi\)
0.713028 + 0.701136i \(0.247323\pi\)
\(458\) 3634.20 + 3634.20i 0.370775 + 0.370775i
\(459\) 12780.8 1.29969
\(460\) −742.556 1216.58i −0.0752649 0.123311i
\(461\) −3362.71 −0.339734 −0.169867 0.985467i \(-0.554334\pi\)
−0.169867 + 0.985467i \(0.554334\pi\)
\(462\) −79.1121 79.1121i −0.00796672 0.00796672i
\(463\) 1782.49 1782.49i 0.178919 0.178919i −0.611966 0.790884i \(-0.709621\pi\)
0.790884 + 0.611966i \(0.209621\pi\)
\(464\) 8039.45i 0.804358i
\(465\) −10125.9 + 5085.66i −1.00985 + 0.507187i
\(466\) −8274.09 −0.822511
\(467\) 7735.30 7735.30i 0.766482 0.766482i −0.211004 0.977485i \(-0.567673\pi\)
0.977485 + 0.211004i \(0.0676732\pi\)
\(468\) 220.842 220.842i 0.0218129 0.0218129i
\(469\) 10313.2i 1.01539i
\(470\) −413.852 + 1249.01i −0.0406161 + 0.122580i
\(471\) 5752.07i 0.562720i
\(472\) −3623.28 3623.28i −0.353337 0.353337i
\(473\) −151.138 + 151.138i −0.0146920 + 0.0146920i
\(474\) 13557.7 1.31377
\(475\) 13371.1 + 9953.73i 1.29160 + 0.961491i
\(476\) 1256.66 0.121006
\(477\) −7869.39 + 7869.39i −0.755376 + 0.755376i
\(478\) 5912.71 5912.71i 0.565777 0.565777i
\(479\) −5001.62 −0.477098 −0.238549 0.971130i \(-0.576672\pi\)
−0.238549 + 0.971130i \(0.576672\pi\)
\(480\) 4558.67 + 1510.49i 0.433487 + 0.143634i
\(481\) 488.518i 0.0463087i
\(482\) −3635.68 + 3635.68i −0.343570 + 0.343570i
\(483\) 7154.99 + 6061.27i 0.674044 + 0.571009i
\(484\) 1537.98i 0.144439i
\(485\) 14912.7 7489.79i 1.39619 0.701224i
\(486\) 11192.6 1.04467
\(487\) 9743.25 + 9743.25i 0.906589 + 0.906589i 0.995995 0.0894065i \(-0.0284970\pi\)
−0.0894065 + 0.995995i \(0.528497\pi\)
\(488\) 3485.84 + 3485.84i 0.323353 + 0.323353i
\(489\) 5142.21i 0.475539i
\(490\) −6210.55 + 3119.19i −0.572580 + 0.287573i
\(491\) −5576.92 −0.512593 −0.256296 0.966598i \(-0.582502\pi\)
−0.256296 + 0.966598i \(0.582502\pi\)
\(492\) −912.083 912.083i −0.0835770 0.0835770i
\(493\) −11271.3 11271.3i −1.02968 1.02968i
\(494\) 2267.81 0.206546
\(495\) −221.947 73.5410i −0.0201531 0.00667762i
\(496\) −6537.95 −0.591861
\(497\) −3265.11 + 3265.11i −0.294688 + 0.294688i
\(498\) −17745.1 17745.1i −1.59674 1.59674i
\(499\) 9649.45i 0.865669i −0.901473 0.432834i \(-0.857513\pi\)
0.901473 0.432834i \(-0.142487\pi\)
\(500\) −1323.03 + 926.499i −0.118335 + 0.0828686i
\(501\) 5490.79 0.489641
\(502\) −3673.31 + 3673.31i −0.326590 + 0.326590i
\(503\) 3329.89 + 3329.89i 0.295174 + 0.295174i 0.839120 0.543946i \(-0.183070\pi\)
−0.543946 + 0.839120i \(0.683070\pi\)
\(504\) −10222.8 −0.903492
\(505\) −4150.92 1375.39i −0.365770 0.121196i
\(506\) 11.9724 + 144.672i 0.00105186 + 0.0127104i
\(507\) −12617.0 12617.0i −1.10521 1.10521i
\(508\) −2131.52 + 2131.52i −0.186164 + 0.186164i
\(509\) 14272.2i 1.24284i 0.783478 + 0.621419i \(0.213443\pi\)
−0.783478 + 0.621419i \(0.786557\pi\)
\(510\) −22924.6 + 11513.7i −1.99043 + 0.999675i
\(511\) 5313.78i 0.460015i
\(512\) 9197.39 + 9197.39i 0.793889 + 0.793889i
\(513\) 11378.8 + 11378.8i 0.979308 + 0.979308i
\(514\) 15640.6i 1.34217i
\(515\) −7611.34 15154.8i −0.651254 1.29670i
\(516\) 4066.39i 0.346924i
\(517\) −16.0016 + 16.0016i −0.00136121 + 0.00136121i
\(518\) 1427.26 1427.26i 0.121062 0.121062i
\(519\) 13571.5i 1.14782i
\(520\) −547.530 + 1652.45i −0.0461745 + 0.139355i
\(521\) 9927.43i 0.834796i 0.908724 + 0.417398i \(0.137058\pi\)
−0.908724 + 0.417398i \(0.862942\pi\)
\(522\) 11574.1 + 11574.1i 0.970470 + 0.970470i
\(523\) 10057.5 + 10057.5i 0.840887 + 0.840887i 0.988974 0.148088i \(-0.0473117\pi\)
−0.148088 + 0.988974i \(0.547312\pi\)
\(524\) 2619.06i 0.218347i
\(525\) 6345.46 8524.05i 0.527502 0.708610i
\(526\) 14727.1i 1.22078i
\(527\) −9166.20 + 9166.20i −0.757658 + 0.757658i
\(528\) −157.348 157.348i −0.0129691 0.0129691i
\(529\) −2000.08 12001.5i −0.164386 0.986396i
\(530\) 2462.80 7432.75i 0.201844 0.609166i
\(531\) 8893.35 0.726814
\(532\) 1118.81 + 1118.81i 0.0911778 + 0.0911778i
\(533\) 619.498 619.498i 0.0503442 0.0503442i
\(534\) −8600.99 −0.697006
\(535\) −11990.6 + 6022.18i −0.968972 + 0.486657i
\(536\) 24062.4i 1.93907i
\(537\) 2176.47 + 2176.47i 0.174900 + 0.174900i
\(538\) 14342.3 14342.3i 1.14933 1.14933i
\(539\) −119.527 −0.00955176
\(540\) −1393.38 + 699.813i −0.111040 + 0.0557688i
\(541\) −8573.49 −0.681337 −0.340668 0.940184i \(-0.610653\pi\)
−0.340668 + 0.940184i \(0.610653\pi\)
\(542\) 10250.0 + 10250.0i 0.812312 + 0.812312i
\(543\) 14930.9 + 14930.9i 1.18002 + 1.18002i
\(544\) 5493.92 0.432996
\(545\) −15960.6 5288.47i −1.25445 0.415657i
\(546\) 1445.72i 0.113317i
\(547\) 10840.7 + 10840.7i 0.847378 + 0.847378i 0.989805 0.142427i \(-0.0454906\pi\)
−0.142427 + 0.989805i \(0.545491\pi\)
\(548\) −685.007 685.007i −0.0533979 0.0533979i
\(549\) −8555.98 −0.665138
\(550\) 162.769 23.8479i 0.0126191 0.00184887i
\(551\) 20069.7i 1.55172i
\(552\) 16693.8 + 14142.0i 1.28720 + 1.09044i
\(553\) −4542.99 + 4542.99i −0.349345 + 0.349345i
\(554\) 9800.23i 0.751574i
\(555\) 2188.43 6604.70i 0.167376 0.505142i
\(556\) 1191.89 0.0909125
\(557\) 11350.7 11350.7i 0.863455 0.863455i −0.128282 0.991738i \(-0.540946\pi\)
0.991738 + 0.128282i \(0.0409464\pi\)
\(558\) 9412.47 9412.47i 0.714089 0.714089i
\(559\) −2761.94 −0.208976
\(560\) 5479.12 2751.84i 0.413455 0.207654i
\(561\) −441.203 −0.0332043
\(562\) −897.562 + 897.562i −0.0673690 + 0.0673690i
\(563\) −11657.3 11657.3i −0.872637 0.872637i 0.120122 0.992759i \(-0.461671\pi\)
−0.992759 + 0.120122i \(0.961671\pi\)
\(564\) 430.524i 0.0321425i
\(565\) −5040.17 10035.4i −0.375295 0.747241i
\(566\) 11522.5i 0.855701i
\(567\) −894.297 + 894.297i −0.0662380 + 0.0662380i
\(568\) −7618.07 + 7618.07i −0.562759 + 0.562759i
\(569\) 20010.6 1.47432 0.737162 0.675716i \(-0.236166\pi\)
0.737162 + 0.675716i \(0.236166\pi\)
\(570\) −30660.5 10159.2i −2.25303 0.746529i
\(571\) 9517.11i 0.697511i −0.937214 0.348756i \(-0.886604\pi\)
0.937214 0.348756i \(-0.113396\pi\)
\(572\) −2.67232 + 2.67232i −0.000195341 + 0.000195341i
\(573\) −19594.8 19594.8i −1.42859 1.42859i
\(574\) −3619.86 −0.263223
\(575\) −13431.0 + 3117.13i −0.974110 + 0.226075i
\(576\) −23407.4 −1.69324
\(577\) −9261.46 9261.46i −0.668214 0.668214i 0.289088 0.957302i \(-0.406648\pi\)
−0.957302 + 0.289088i \(0.906648\pi\)
\(578\) −11663.2 + 11663.2i −0.839320 + 0.839320i
\(579\) 17088.2i 1.22653i
\(580\) 1845.97 + 611.654i 0.132155 + 0.0437889i
\(581\) 11892.3 0.849181
\(582\) −22865.0 + 22865.0i −1.62849 + 1.62849i
\(583\) 95.2241 95.2241i 0.00676463 0.00676463i
\(584\) 12398.0i 0.878479i
\(585\) −1356.01 2699.92i −0.0958361 0.190817i
\(586\) 20202.4i 1.42415i
\(587\) 14419.3 + 14419.3i 1.01388 + 1.01388i 0.999902 + 0.0139823i \(0.00445086\pi\)
0.0139823 + 0.999902i \(0.495549\pi\)
\(588\) −1607.95 + 1607.95i −0.112773 + 0.112773i
\(589\) −16321.4 −1.14178
\(590\) −5591.58 + 2808.32i −0.390172 + 0.195960i
\(591\) 29770.3 2.07206
\(592\) 2838.71 2838.71i 0.197078 0.197078i
\(593\) −10401.8 + 10401.8i −0.720319 + 0.720319i −0.968670 0.248351i \(-0.920111\pi\)
0.248351 + 0.968670i \(0.420111\pi\)
\(594\) 158.810 0.0109698
\(595\) 3823.64 11539.8i 0.263452 0.795101i
\(596\) 624.745i 0.0429372i
\(597\) 9162.92 9162.92i 0.628163 0.628163i
\(598\) −1212.49 + 1431.28i −0.0829140 + 0.0978754i
\(599\) 2357.32i 0.160797i 0.996763 + 0.0803987i \(0.0256193\pi\)
−0.996763 + 0.0803987i \(0.974381\pi\)
\(600\) 14805.1 19888.1i 1.00736 1.35321i
\(601\) 2597.15 0.176273 0.0881363 0.996108i \(-0.471909\pi\)
0.0881363 + 0.996108i \(0.471909\pi\)
\(602\) 8069.30 + 8069.30i 0.546313 + 0.546313i
\(603\) −29530.6 29530.6i −1.99433 1.99433i
\(604\) 3232.92i 0.217791i
\(605\) −14123.1 4679.62i −0.949068 0.314468i
\(606\) 8473.21 0.567988
\(607\) 956.512 + 956.512i 0.0639599 + 0.0639599i 0.738363 0.674403i \(-0.235599\pi\)
−0.674403 + 0.738363i \(0.735599\pi\)
\(608\) 4891.25 + 4891.25i 0.326261 + 0.326261i
\(609\) −12794.4 −0.851319
\(610\) 5379.47 2701.79i 0.357063 0.179331i
\(611\) −292.418 −0.0193616
\(612\) −3598.32 + 3598.32i −0.237669 + 0.237669i
\(613\) 10533.3 + 10533.3i 0.694025 + 0.694025i 0.963115 0.269090i \(-0.0867229\pi\)
−0.269090 + 0.963115i \(0.586723\pi\)
\(614\) 26380.4i 1.73392i
\(615\) −11150.7 + 5600.35i −0.731124 + 0.367200i
\(616\) 123.702 0.00809105
\(617\) −4250.50 + 4250.50i −0.277340 + 0.277340i −0.832046 0.554706i \(-0.812831\pi\)
0.554706 + 0.832046i \(0.312831\pi\)
\(618\) 23236.0 + 23236.0i 1.51244 + 1.51244i
\(619\) −19672.0 −1.27736 −0.638679 0.769473i \(-0.720519\pi\)
−0.638679 + 0.769473i \(0.720519\pi\)
\(620\) 497.418 1501.21i 0.0322206 0.0972420i
\(621\) −13265.2 + 1097.77i −0.857188 + 0.0709374i
\(622\) 3428.50 + 3428.50i 0.221014 + 0.221014i
\(623\) 2882.07 2882.07i 0.185342 0.185342i
\(624\) 2875.43i 0.184470i
\(625\) 4482.34 + 14968.3i 0.286870 + 0.957970i
\(626\) 5019.78i 0.320496i
\(627\) −392.804 392.804i −0.0250193 0.0250193i
\(628\) 567.663 + 567.663i 0.0360704 + 0.0360704i
\(629\) 7959.72i 0.504570i
\(630\) −3926.38 + 11849.8i −0.248303 + 0.749379i
\(631\) 3946.36i 0.248973i −0.992221 0.124487i \(-0.960272\pi\)
0.992221 0.124487i \(-0.0397284\pi\)
\(632\) −10599.6 + 10599.6i −0.667135 + 0.667135i
\(633\) 805.516 805.516i 0.0505788 0.0505788i
\(634\) 1145.32i 0.0717455i
\(635\) 13087.9 + 26059.1i 0.817920 + 1.62854i
\(636\) 2562.02i 0.159734i
\(637\) −1092.14 1092.14i −0.0679311 0.0679311i
\(638\) −140.053 140.053i −0.00869086 0.00869086i
\(639\) 18698.5i 1.15759i
\(640\) 10571.1 5309.23i 0.652905 0.327915i
\(641\) 17277.0i 1.06459i −0.846559 0.532295i \(-0.821330\pi\)
0.846559 0.532295i \(-0.178670\pi\)
\(642\) 18384.6 18384.6i 1.13019 1.13019i
\(643\) −6563.82 6563.82i −0.402569 0.402569i 0.476569 0.879137i \(-0.341880\pi\)
−0.879137 + 0.476569i \(0.841880\pi\)
\(644\) −1304.29 + 107.938i −0.0798080 + 0.00660458i
\(645\) 37341.1 + 12372.8i 2.27954 + 0.755314i
\(646\) −36950.8 −2.25048
\(647\) −15122.2 15122.2i −0.918881 0.918881i 0.0780670 0.996948i \(-0.475125\pi\)
−0.996948 + 0.0780670i \(0.975125\pi\)
\(648\) −2086.55 + 2086.55i −0.126493 + 0.126493i
\(649\) −107.615 −0.00650885
\(650\) 1705.15 + 1269.34i 0.102895 + 0.0765966i
\(651\) 10404.8i 0.626416i
\(652\) 507.477 + 507.477i 0.0304821 + 0.0304821i
\(653\) 5336.67 5336.67i 0.319816 0.319816i −0.528880 0.848697i \(-0.677388\pi\)
0.848697 + 0.528880i \(0.177388\pi\)
\(654\) 32580.2 1.94799
\(655\) −24050.5 7968.99i −1.43470 0.475380i
\(656\) −7199.63 −0.428503
\(657\) −15215.4 15215.4i −0.903516 0.903516i
\(658\) 854.328 + 854.328i 0.0506158 + 0.0506158i
\(659\) 25483.4 1.50636 0.753180 0.657815i \(-0.228519\pi\)
0.753180 + 0.657815i \(0.228519\pi\)
\(660\) 48.1007 24.1581i 0.00283684 0.00142478i
\(661\) 11464.6i 0.674618i −0.941394 0.337309i \(-0.890483\pi\)
0.941394 0.337309i \(-0.109517\pi\)
\(662\) 6378.87 + 6378.87i 0.374504 + 0.374504i
\(663\) −4031.34 4031.34i −0.236145 0.236145i
\(664\) 27746.7 1.62166
\(665\) 13678.1 6869.70i 0.797615 0.400595i
\(666\) 8173.58i 0.475555i
\(667\) 12666.6 + 10730.4i 0.735311 + 0.622911i
\(668\) −541.878 + 541.878i −0.0313860 + 0.0313860i
\(669\) 40236.1i 2.32529i
\(670\) 27892.1 + 9241.90i 1.60831 + 0.532904i
\(671\) 103.532 0.00595651
\(672\) 3118.15 3118.15i 0.178996 0.178996i
\(673\) 8366.16 8366.16i 0.479186 0.479186i −0.425686 0.904871i \(-0.639967\pi\)
0.904871 + 0.425686i \(0.139967\pi\)
\(674\) −13766.2 −0.786728
\(675\) 2186.66 + 14924.6i 0.124688 + 0.851033i
\(676\) 2490.30 0.141688
\(677\) 23927.8 23927.8i 1.35838 1.35838i 0.482454 0.875921i \(-0.339745\pi\)
0.875921 0.482454i \(-0.160255\pi\)
\(678\) 15386.7 + 15386.7i 0.871569 + 0.871569i
\(679\) 15323.4i 0.866068i
\(680\) 8921.23 26924.3i 0.503108 1.51838i
\(681\) 29564.8i 1.66362i
\(682\) −113.896 + 113.896i −0.00639489 + 0.00639489i
\(683\) −13609.0 + 13609.0i −0.762420 + 0.762420i −0.976759 0.214339i \(-0.931240\pi\)
0.214339 + 0.976759i \(0.431240\pi\)
\(684\) −6407.18 −0.358165
\(685\) −8374.60 + 4206.06i −0.467120 + 0.234606i
\(686\) 15593.9i 0.867896i
\(687\) 11503.2 11503.2i 0.638828 0.638828i
\(688\) 16049.2 + 16049.2i 0.889348 + 0.889348i
\(689\) 1740.15 0.0962186
\(690\) 22804.5 13919.1i 1.25819 0.767958i
\(691\) −23724.8 −1.30613 −0.653063 0.757303i \(-0.726516\pi\)
−0.653063 + 0.757303i \(0.726516\pi\)
\(692\) −1339.35 1339.35i −0.0735756 0.0735756i
\(693\) −151.813 + 151.813i −0.00832165 + 0.00832165i
\(694\) 7584.12i 0.414826i
\(695\) 3626.55 10945.0i 0.197932 0.597361i
\(696\) −29851.5 −1.62574
\(697\) −10093.9 + 10093.9i −0.548540 + 0.548540i
\(698\) −21876.3 + 21876.3i −1.18629 + 1.18629i
\(699\) 26189.8i 1.41715i
\(700\) 215.002 + 1467.45i 0.0116090 + 0.0792349i
\(701\) 5842.52i 0.314792i −0.987536 0.157396i \(-0.949690\pi\)
0.987536 0.157396i \(-0.0503099\pi\)
\(702\) 1451.07 + 1451.07i 0.0780159 + 0.0780159i
\(703\) 7086.56 7086.56i 0.380191 0.380191i
\(704\) 283.243 0.0151635
\(705\) 3953.45 + 1309.95i 0.211199 + 0.0699798i
\(706\) 20213.0 1.07752
\(707\) −2839.25 + 2839.25i −0.151034 + 0.151034i
\(708\) −1447.69 + 1447.69i −0.0768469 + 0.0768469i
\(709\) −555.625 −0.0294315 −0.0147157 0.999892i \(-0.504684\pi\)
−0.0147157 + 0.999892i \(0.504684\pi\)
\(710\) 5904.58 + 11756.5i 0.312106 + 0.621426i
\(711\) 26016.7i 1.37230i
\(712\) 6724.38 6724.38i 0.353942 0.353942i
\(713\) 8726.30 10300.9i 0.458349 0.541055i
\(714\) 23556.0i 1.23468i
\(715\) 16.4085 + 32.6706i 0.000858242 + 0.00170883i
\(716\) −429.585 −0.0224223
\(717\) −18715.3 18715.3i −0.974808 0.974808i
\(718\) −10756.5 10756.5i −0.559093 0.559093i
\(719\) 16315.0i 0.846239i 0.906074 + 0.423120i \(0.139065\pi\)
−0.906074 + 0.423120i \(0.860935\pi\)
\(720\) −7809.27 + 23568.4i −0.404214 + 1.21992i
\(721\) −15572.1 −0.804351
\(722\) −20208.9 20208.9i −1.04169 1.04169i
\(723\) 11507.9 + 11507.9i 0.591955 + 0.591955i
\(724\) −2947.03 −0.151278
\(725\) 11233.5 15090.3i 0.575449 0.773019i
\(726\) 28829.3 1.47377
\(727\) −10929.0 + 10929.0i −0.557544 + 0.557544i −0.928607 0.371064i \(-0.878993\pi\)
0.371064 + 0.928607i \(0.378993\pi\)
\(728\) 1130.28 + 1130.28i 0.0575427 + 0.0575427i
\(729\) 32101.5i 1.63092i
\(730\) 14371.2 + 4761.81i 0.728632 + 0.241428i
\(731\) 45002.0 2.27696
\(732\) 1392.78 1392.78i 0.0703258 0.0703258i
\(733\) −14665.6 14665.6i −0.739001 0.739001i 0.233383 0.972385i \(-0.425020\pi\)
−0.972385 + 0.233383i \(0.925020\pi\)
\(734\) 15539.5 0.781435
\(735\) 9873.09 + 19658.1i 0.495475 + 0.986529i
\(736\) −5702.15 + 471.887i −0.285576 + 0.0236331i
\(737\) 357.337 + 357.337i 0.0178598 + 0.0178598i
\(738\) 10365.1 10365.1i 0.516996 0.516996i
\(739\) 5318.71i 0.264752i −0.991200 0.132376i \(-0.957739\pi\)
0.991200 0.132376i \(-0.0422607\pi\)
\(740\) 435.835 + 867.782i 0.0216508 + 0.0431085i
\(741\) 7178.23i 0.355869i
\(742\) −5084.04 5084.04i −0.251538 0.251538i
\(743\) −2074.70 2074.70i −0.102441 0.102441i 0.654029 0.756470i \(-0.273077\pi\)
−0.756470 + 0.654029i \(0.773077\pi\)
\(744\) 24276.3i 1.19625i
\(745\) 5736.95 + 1900.91i 0.282128 + 0.0934817i
\(746\) 16614.6i 0.815421i
\(747\) −34052.2 + 34052.2i −1.66788 + 1.66788i
\(748\) 43.5417 43.5417i 0.00212840 0.00212840i
\(749\) 12320.9i 0.601061i
\(750\) −17367.1 24800.0i −0.845541 1.20742i
\(751\) 27699.5i 1.34590i 0.739689 + 0.672949i \(0.234973\pi\)
−0.739689 + 0.672949i \(0.765027\pi\)
\(752\) 1699.20 + 1699.20i 0.0823980 + 0.0823980i
\(753\) 11627.0 + 11627.0i 0.562699 + 0.562699i
\(754\) 2559.38i 0.123617i
\(755\) −29687.5 9836.80i −1.43105 0.474169i
\(756\) 1431.76i 0.0688790i
\(757\) 20005.6 20005.6i 0.960523 0.960523i −0.0387265 0.999250i \(-0.512330\pi\)
0.999250 + 0.0387265i \(0.0123301\pi\)
\(758\) −20706.2 20706.2i −0.992192 0.992192i
\(759\) 457.925 37.8960i 0.0218994 0.00181230i
\(760\) 31913.4 16028.2i 1.52318 0.765005i
\(761\) 19931.3 0.949420 0.474710 0.880142i \(-0.342553\pi\)
0.474710 + 0.880142i \(0.342553\pi\)
\(762\) −39955.1 39955.1i −1.89950 1.89950i
\(763\) −10917.1 + 10917.1i −0.517991 + 0.517991i
\(764\) 3867.56 0.183146
\(765\) 22094.3 + 43991.5i 1.04421 + 2.07910i
\(766\) 37473.3i 1.76758i
\(767\) −983.291 983.291i −0.0462902 0.0462902i
\(768\) 10167.2 10167.2i 0.477704 0.477704i
\(769\) −17879.5 −0.838429 −0.419214 0.907887i \(-0.637694\pi\)
−0.419214 + 0.907887i \(0.637694\pi\)
\(770\) 47.5114 143.390i 0.00222363 0.00671092i
\(771\) −49506.7 −2.31250
\(772\) 1686.41 + 1686.41i 0.0786206 +