Properties

Label 115.4.e.a.22.12
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 22.12
Character \(\chi\) \(=\) 115.22
Dual form 115.4.e.a.68.12

$q$-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} +(-84.1638 + 71.2984i) 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} +(82.4016 + 97.2706i) 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 −0.483422 0.875387i \(-0.660606\pi\)
0.875387 + 0.483422i \(0.160606\pi\)
\(8\) −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 \(-0.997805\pi\)
0.999976 0.00689432i \(-0.00219455\pi\)
\(12\) 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 \(0.522619\pi\)
−0.997476 + 0.0710011i \(0.977381\pi\)
\(18\) −76.9047 + 76.9047i −1.00703 + 1.00703i
\(19\) −133.354 −1.61019 −0.805093 0.593149i \(-0.797884\pi\)
−0.805093 + 0.593149i \(0.797884\pi\)
\(20\) 4.06416 12.2657i 0.0454387 0.137134i
\(21\) 85.0127i 0.883395i
\(22\) −0.930591 + 0.930591i −0.00901831 + 0.00901831i
\(23\) −84.1638 + 71.2984i −0.763016 + 0.646380i
\(24\) 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 −0.815240 0.579123i \(-0.803395\pi\)
0.579123 + 0.815240i \(0.303395\pi\)
\(38\) 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 \(-0.978396\pi\)
−0.0678196 0.997698i \(-0.521604\pi\)
\(44\) −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 0.908493 0.417899i \(-0.137233\pi\)
−0.417899 + 0.908493i \(0.637233\pi\)
\(54\) 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 \(0.0692990\pi\)
−0.976395 + 0.215994i \(0.930701\pi\)
\(62\) 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 \(0.618510\pi\)
−0.931490 + 0.363767i \(0.881490\pi\)
\(68\) 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 \(-0.647021\pi\)
−0.445633 + 0.895216i \(0.647021\pi\)
\(80\) 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 \(0.0277378\pi\)
0.0870306 + 0.996206i \(0.472262\pi\)
\(84\) 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 \(-0.424024\pi\)
0.236426 + 0.971649i \(0.424024\pi\)
\(90\) −1086.62 + 545.746i −1.27267 + 0.639185i
\(91\) 66.7338i 0.0768747i
\(92\) 82.4016 + 97.2706i 0.0933800 + 0.110230i
\(93\) 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 \(-0.464610\pi\)
0.993826 0.110951i \(-0.0353898\pi\)
\(98\) 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 \(-0.991596\pi\)
−0.0263981 0.999652i \(-0.508404\pi\)
\(104\) 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 −0.977529 0.210801i \(-0.932393\pi\)
0.210801 + 0.977529i \(0.432393\pi\)
\(108\) 98.6155 98.6155i 0.0878637 0.0878637i
\(109\) −1503.89 −1.32152 −0.660762 0.750595i \(-0.729767\pi\)
−0.660762 + 0.750595i \(0.729767\pi\)
\(110\) −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 0.346700 0.937976i \(-0.387302\pi\)
−0.937976 + 0.346700i \(0.887302\pi\)
\(114\) −2888.98 −2.37349
\(115\) −1143.95 + 460.719i −0.927596 + 0.373585i
\(116\) −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 −0.867339 0.497717i \(-0.834172\pi\)
0.497717 + 0.867339i \(0.334172\pi\)
\(138\) −1823.32 + 1544.61i −1.12472 + 0.952794i
\(139\) 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 \(-0.452521\pi\)
0.148606 + 0.988896i \(0.452521\pi\)
\(150\) 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 −0.571159 0.820840i \(-0.693506\pi\)
0.820840 + 0.571159i \(0.193506\pi\)
\(158\) 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 \(0.175403\pi\)
−0.851979 + 0.523576i \(0.824597\pi\)
\(182\) 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 \(-0.781465\pi\)
0.773438 0.633872i \(-0.218535\pi\)
\(192\) 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 \(-0.410091\pi\)
0.278718 + 0.960373i \(0.410091\pi\)
\(200\) −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
\(207\) 2964.04 + 3498.89i 0.995242 + 1.17483i
\(208\) −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 −0.972220 0.234067i \(-0.924796\pi\)
0.234067 + 0.972220i \(0.424796\pi\)
\(228\) −902.447 902.447i −0.262132 0.262132i
\(229\) 1964.53 0.566900 0.283450 0.958987i \(-0.408521\pi\)
0.283450 + 0.958987i \(0.408521\pi\)
\(230\) 2968.47 + 1263.90i 0.851023 + 0.362345i
\(231\) 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 \(0.0845972\pi\)
−0.964891 + 0.262652i \(0.915403\pi\)
\(242\) −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 \(0.0803226\pi\)
−0.968331 + 0.249671i \(0.919677\pi\)
\(252\) −348.783 + 348.783i −0.0871875 + 0.0871875i
\(253\) 35.8666 + 42.3385i 0.00891270 + 0.0105209i
\(254\) 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 0.997908 0.0646449i \(-0.0205915\pi\)
−0.0646449 + 0.997908i \(0.520591\pi\)
\(264\) −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 \(0.0164009\pi\)
−0.998673 + 0.0515023i \(0.983599\pi\)
\(282\) 689.112 + 689.112i 0.145518 + 0.145518i
\(283\) 3114.36 + 3114.36i 0.654167 + 0.654167i 0.953994 0.299827i \(-0.0969289\pi\)
−0.299827 + 0.953994i \(0.596929\pi\)
\(284\) 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 \(-0.970330\pi\)
−0.0930762 0.995659i \(-0.529670\pi\)
\(294\) 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 0.818920 0.573907i \(-0.194573\pi\)
−0.573907 + 0.818920i \(0.694573\pi\)
\(314\) −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
\(322\) 2260.47 1914.93i 0.391214 0.331412i
\(323\) 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 −0.940694 0.339256i \(-0.889825\pi\)
0.339256 + 0.940694i \(0.389825\pi\)
\(338\) 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
\(345\) 4000.60 9396.02i 0.624304 1.46627i
\(346\) −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 \(-0.640576\pi\)
−0.427416 + 0.904055i \(0.640576\pi\)
\(360\) 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 −0.342226 0.939618i \(-0.611181\pi\)
0.939618 + 0.342226i \(0.111181\pi\)
\(368\) −4495.90 + 3808.65i −0.636861 + 0.539510i
\(369\) 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 0.323019 0.946392i \(-0.395302\pi\)
−0.946392 + 0.323019i \(0.895302\pi\)
\(374\) 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 \(-0.774073\pi\)
−0.758511 + 0.651660i \(0.774073\pi\)
\(380\) −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 \(-0.845317\pi\)
−0.467050 0.884231i \(-0.654683\pi\)
\(384\) 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 \(-0.607665\pi\)
−0.331827 + 0.943340i \(0.607665\pi\)
\(390\) −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 \(0.0944240\pi\)
−0.956323 + 0.292310i \(0.905576\pi\)
\(402\) −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 \(-0.459353\pi\)
0.127348 + 0.991858i \(0.459353\pi\)
\(420\) 1042.74 + 345.505i 0.121144 + 0.0401403i
\(421\) 9809.98i 1.13565i 0.823149 + 0.567825i \(0.192215\pi\)
−0.823149 + 0.567825i \(0.807785\pi\)
\(422\) 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 \(-0.703260\pi\)
0.596041 0.802954i \(-0.296740\pi\)
\(432\) 4558.06 + 4558.06i 0.507639 + 0.507639i
\(433\) 3589.57 + 3589.57i 0.398392 + 0.398392i 0.877666 0.479273i \(-0.159100\pi\)
−0.479273 + 0.877666i \(0.659100\pi\)
\(434\) 3287.18 0.363571
\(435\) 6253.62 + 12451.4i 0.689283 + 1.37242i
\(436\) 1738.09i 0.190916i
\(437\) 11223.6 9507.93i 1.22860 1.04079i
\(438\) 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 −0.713028 0.701136i \(-0.752677\pi\)
0.701136 + 0.713028i \(0.252677\pi\)
\(458\) −3634.20 3634.20i −0.370775 0.370775i
\(459\) −12780.8 −1.29969
\(460\) 532.466 + 1322.09i 0.0539704 + 0.134006i
\(461\) −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 −0.977485 0.211004i \(-0.932327\pi\)
0.211004 + 0.977485i \(0.432327\pi\)
\(468\) 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 \(-0.423328\pi\)
0.238549 + 0.971130i \(0.423328\pi\)
\(480\) −4558.67 1510.49i −0.433487 0.143634i
\(481\) 488.518i 0.0463087i
\(482\) 3635.68 3635.68i 0.343570 0.343570i
\(483\) −6061.27 7154.99i −0.571009 0.674044i
\(484\) 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 0.543946 0.839120i \(-0.316930\pi\)
−0.839120 + 0.543946i \(0.816930\pi\)
\(504\) 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 \(-0.862942\pi\)
0.908724 0.417398i \(-0.137058\pi\)
\(522\) 11574.1 + 11574.1i 0.970470 + 0.970470i
\(523\) −10057.5 10057.5i −0.840887 0.840887i 0.148088 0.988974i \(-0.452688\pi\)
−0.988974 + 0.148088i \(0.952688\pi\)
\(524\) 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
\(552\) 14142.0 + 16693.8i 1.09044 + 1.28720i
\(553\) −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 −0.991738 0.128282i \(-0.959054\pi\)
0.128282 + 0.991738i \(0.459054\pi\)
\(558\) 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 0.992759 0.120122i \(-0.0383285\pi\)
−0.120122 + 0.992759i \(0.538329\pi\)
\(564\) 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 \(-0.763834\pi\)
−0.737162 + 0.675716i \(0.763834\pi\)
\(570\) −30660.5 10159.2i −2.25303 0.746529i
\(571\) 9517.11i 0.697511i 0.937214 + 0.348756i \(0.113396\pi\)
−0.937214 + 0.348756i \(0.886604\pi\)
\(572\) 2.67232 2.67232i 0.000195341 0.000195341i
\(573\) 19594.8 + 19594.8i 1.42859 + 1.42859i
\(574\) 3619.86 0.263223
\(575\) −13760.7 + 866.848i −0.998022 + 0.0628697i
\(576\) −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
\(598\) −1431.28 + 1212.49i −0.0978754 + 0.0829140i
\(599\) 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 0.269090 0.963115i \(-0.413277\pi\)
−0.963115 + 0.269090i \(0.913277\pi\)
\(614\) 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 −0.554706 0.832046i \(-0.687169\pi\)
0.832046 + 0.554706i \(0.187169\pi\)
\(618\) −23236.0 23236.0i −1.51244 1.51244i
\(619\) 19672.0 1.27736 0.638679 0.769473i \(-0.279481\pi\)
0.638679 + 0.769473i \(0.279481\pi\)
\(620\) −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 \(0.0397284\pi\)
−0.992221 + 0.124487i \(0.960272\pi\)
\(632\) 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 \(0.178670\pi\)
−0.846559 + 0.532295i \(0.821330\pi\)
\(642\) −18384.6 + 18384.6i −1.13019 + 1.13019i
\(643\) 6563.82 + 6563.82i 0.402569 + 0.402569i 0.879137 0.476569i \(-0.158120\pi\)
−0.476569 + 0.879137i \(0.658120\pi\)
\(644\) 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 \(-0.771481\pi\)
−0.753180 + 0.657815i \(0.771481\pi\)
\(660\) 48.1007 24.1581i 0.00283684 0.00142478i
\(661\) 11464.6i 0.674618i 0.941394 + 0.337309i \(0.109517\pi\)
−0.941394 + 0.337309i \(0.890483\pi\)
\(662\) 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
\(667\) 10730.4 + 12666.6i 0.622911 + 0.735311i
\(668\) −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 \(0.660255\pi\)
−0.875921 + 0.482454i \(0.839745\pi\)
\(678\) −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
\(690\) −24782.4 + 9981.00i −1.36732 + 0.550682i
\(691\) −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 \(0.0503099\pi\)
−0.987536 + 0.157396i \(0.949690\pi\)
\(702\) 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 \(-0.495316\pi\)
0.0147157 + 0.999892i \(0.495316\pi\)
\(710\) −5904.58 11756.5i −0.312106 0.621426i
\(711\) 26016.7i 1.37230i
\(712\) −6724.38 + 6724.38i −0.353942 + 0.353942i
\(713\) 10300.9 8726.30i 0.541055 0.458349i
\(714\) 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 −0.371064 0.928607i \(-0.621007\pi\)
0.928607 + 0.371064i \(0.121007\pi\)
\(728\) −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 0.972385 0.233383i \(-0.0749797\pi\)
−0.233383 + 0.972385i \(0.574980\pi\)
\(734\) −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 0.756470 0.654029i \(-0.226923\pi\)
−0.654029 + 0.756470i \(0.726923\pi\)
\(744\) 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 \(-0.765027\pi\)
0.739689 0.672949i \(-0.234973\pi\)
\(752\) 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 −0.999250 0.0387265i \(-0.987670\pi\)
0.0387265 + 0.999250i \(0.487670\pi\)
\(758\) 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 \(-0.362306\pi\)
0.419214 + 0.907887i \(0.362306\pi\)
\(770\) −47.5114 + 143.390i −0.00222363 + 0.00671092i
\(771\) −49506.7 −2.31250
\(772\) 1686.41 + 1686.41i 0.0786206 + 0.0786206i