Properties

Label 19.4.e.a.9.3
Level $19$
Weight $4$
Character 19.9
Analytic conductor $1.121$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [19,4,Mod(4,19)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(19, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("19.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 19.e (of order \(9\), degree \(6\), 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: \(1.12103629011\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 9.3
Character \(\chi\) \(=\) 19.9
Dual form 19.4.e.a.17.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.477474 + 2.70789i) q^{2} +(-4.62264 + 3.87886i) q^{3} +(0.412858 - 0.150268i) q^{4} +(5.11043 + 1.86004i) q^{5} +(-12.7107 - 10.6656i) q^{6} +(11.7392 - 20.3328i) q^{7} +(11.6027 + 20.0964i) q^{8} +(1.63479 - 9.27135i) q^{9} +O(q^{10})\) \(q+(0.477474 + 2.70789i) q^{2} +(-4.62264 + 3.87886i) q^{3} +(0.412858 - 0.150268i) q^{4} +(5.11043 + 1.86004i) q^{5} +(-12.7107 - 10.6656i) q^{6} +(11.7392 - 20.3328i) q^{7} +(11.6027 + 20.0964i) q^{8} +(1.63479 - 9.27135i) q^{9} +(-2.59670 + 14.7266i) q^{10} +(-23.6008 - 40.8778i) q^{11} +(-1.32563 + 2.29605i) q^{12} +(-14.0615 - 11.7990i) q^{13} +(60.6643 + 22.0800i) q^{14} +(-30.8385 + 11.2243i) q^{15} +(-46.1865 + 38.7550i) q^{16} +(16.8867 + 95.7695i) q^{17} +25.8864 q^{18} +(-25.4519 - 78.8112i) q^{19} +2.38939 q^{20} +(24.6022 + 139.526i) q^{21} +(99.4237 - 83.4264i) q^{22} +(84.7939 - 30.8625i) q^{23} +(-131.586 - 47.8935i) q^{24} +(-73.0988 - 61.3372i) q^{25} +(25.2364 - 43.7108i) q^{26} +(-53.0596 - 91.9020i) q^{27} +(1.79124 - 10.1586i) q^{28} +(16.0833 - 91.2129i) q^{29} +(-45.1188 - 78.1481i) q^{30} +(-142.156 + 246.222i) q^{31} +(15.2136 + 12.7658i) q^{32} +(267.657 + 97.4192i) q^{33} +(-251.270 + 91.4549i) q^{34} +(97.8122 - 82.0742i) q^{35} +(-0.718252 - 4.07341i) q^{36} +232.514 q^{37} +(201.259 - 106.551i) q^{38} +110.768 q^{39} +(21.9144 + 124.283i) q^{40} +(-197.399 + 165.638i) q^{41} +(-366.074 + 133.240i) q^{42} +(-75.7804 - 27.5818i) q^{43} +(-15.8864 - 13.3303i) q^{44} +(25.5996 - 44.3398i) q^{45} +(124.059 + 214.877i) q^{46} +(-85.6235 + 485.595i) q^{47} +(63.1782 - 358.301i) q^{48} +(-104.116 - 180.335i) q^{49} +(131.192 - 227.230i) q^{50} +(-449.538 - 377.207i) q^{51} +(-7.57843 - 2.75832i) q^{52} +(-106.793 + 38.8693i) q^{53} +(223.526 - 187.560i) q^{54} +(-44.5757 - 252.802i) q^{55} +544.824 q^{56} +(423.353 + 265.591i) q^{57} +254.674 q^{58} +(-31.3837 - 177.986i) q^{59} +(-11.0453 + 9.26810i) q^{60} +(259.591 - 94.4833i) q^{61} +(-734.617 - 267.379i) q^{62} +(-169.322 - 142.078i) q^{63} +(-268.473 + 465.008i) q^{64} +(-49.9138 - 86.4532i) q^{65} +(-136.001 + 771.301i) q^{66} +(26.9102 - 152.615i) q^{67} +(21.3629 + 37.0017i) q^{68} +(-272.261 + 471.570i) q^{69} +(268.951 + 225.676i) q^{70} +(-577.366 - 210.144i) q^{71} +(205.289 - 74.7191i) q^{72} +(368.338 - 309.072i) q^{73} +(111.019 + 629.622i) q^{74} +575.828 q^{75} +(-22.3508 - 28.7132i) q^{76} -1108.22 q^{77} +(52.8889 + 299.948i) q^{78} +(975.594 - 818.621i) q^{79} +(-308.119 + 112.146i) q^{80} +(840.609 + 305.957i) q^{81} +(-542.782 - 455.448i) q^{82} +(-154.093 + 266.896i) q^{83} +(31.1235 + 53.9075i) q^{84} +(-91.8370 + 520.834i) q^{85} +(38.5053 - 218.375i) q^{86} +(279.455 + 484.029i) q^{87} +(547.665 - 948.584i) q^{88} +(32.1471 + 26.9746i) q^{89} +(132.290 + 48.1498i) q^{90} +(-404.979 + 147.400i) q^{91} +(30.3702 - 25.4836i) q^{92} +(-297.922 - 1689.60i) q^{93} -1355.82 q^{94} +(16.5219 - 450.101i) q^{95} -119.844 q^{96} +(98.6409 + 559.420i) q^{97} +(438.614 - 368.041i) q^{98} +(-417.574 + 151.985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 6 q^{2} - 3 q^{3} - 24 q^{4} - 6 q^{5} + 42 q^{6} + 3 q^{7} - 75 q^{8} - 51 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 6 q^{2} - 3 q^{3} - 24 q^{4} - 6 q^{5} + 42 q^{6} + 3 q^{7} - 75 q^{8} - 51 q^{9} + 75 q^{10} + 39 q^{11} - 219 q^{12} - 156 q^{13} + 93 q^{14} - 192 q^{15} + 504 q^{16} + 12 q^{17} + 264 q^{18} + 546 q^{19} - 198 q^{20} + 453 q^{21} - 6 q^{22} + 6 q^{23} + 192 q^{24} - 498 q^{25} - 639 q^{26} - 870 q^{27} - 1368 q^{28} - 630 q^{29} - 522 q^{30} - 591 q^{31} + 147 q^{32} + 1506 q^{33} - 408 q^{34} + 2001 q^{35} + 1059 q^{36} - 72 q^{37} + 2934 q^{38} + 336 q^{39} + 2886 q^{40} - 477 q^{41} + 237 q^{42} + 588 q^{43} - 3423 q^{44} - 1569 q^{45} - 1728 q^{46} - 1242 q^{47} - 4599 q^{48} - 639 q^{49} - 1788 q^{50} + 9 q^{51} + 2733 q^{52} - 300 q^{53} + 3777 q^{54} + 315 q^{55} + 4638 q^{56} + 3342 q^{57} - 2820 q^{58} + 2097 q^{59} + 1116 q^{60} - 2316 q^{61} - 1320 q^{62} - 2979 q^{63} - 1785 q^{64} - 2433 q^{65} - 1590 q^{66} + 57 q^{67} - 438 q^{68} - 1767 q^{69} - 213 q^{70} - 792 q^{71} - 1686 q^{72} + 4068 q^{73} + 4287 q^{74} + 1332 q^{75} + 5538 q^{76} + 3786 q^{77} + 2121 q^{78} + 1824 q^{79} - 2739 q^{80} + 1536 q^{81} + 2205 q^{82} + 1071 q^{83} - 1437 q^{84} - 2394 q^{85} - 5256 q^{86} + 759 q^{87} + 1101 q^{88} - 3006 q^{89} - 3822 q^{90} - 3285 q^{91} - 1452 q^{92} - 135 q^{93} - 1086 q^{94} - 3078 q^{95} - 1590 q^{96} - 2535 q^{97} - 2403 q^{98} + 492 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/19\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.477474 + 2.70789i 0.168813 + 0.957383i 0.945046 + 0.326938i \(0.106017\pi\)
−0.776233 + 0.630446i \(0.782872\pi\)
\(3\) −4.62264 + 3.87886i −0.889628 + 0.746487i −0.968136 0.250427i \(-0.919429\pi\)
0.0785074 + 0.996914i \(0.474985\pi\)
\(4\) 0.412858 0.150268i 0.0516073 0.0187835i
\(5\) 5.11043 + 1.86004i 0.457091 + 0.166367i 0.560296 0.828293i \(-0.310688\pi\)
−0.103205 + 0.994660i \(0.532910\pi\)
\(6\) −12.7107 10.6656i −0.864854 0.725699i
\(7\) 11.7392 20.3328i 0.633856 1.09787i −0.352900 0.935661i \(-0.614805\pi\)
0.986756 0.162210i \(-0.0518621\pi\)
\(8\) 11.6027 + 20.0964i 0.512771 + 0.888146i
\(9\) 1.63479 9.27135i 0.0605477 0.343383i
\(10\) −2.59670 + 14.7266i −0.0821148 + 0.465696i
\(11\) −23.6008 40.8778i −0.646901 1.12046i −0.983859 0.178945i \(-0.942732\pi\)
0.336959 0.941519i \(-0.390602\pi\)
\(12\) −1.32563 + 2.29605i −0.0318896 + 0.0552345i
\(13\) −14.0615 11.7990i −0.299997 0.251728i 0.480346 0.877079i \(-0.340511\pi\)
−0.780343 + 0.625351i \(0.784956\pi\)
\(14\) 60.6643 + 22.0800i 1.15809 + 0.421509i
\(15\) −30.8385 + 11.2243i −0.530832 + 0.193207i
\(16\) −46.1865 + 38.7550i −0.721663 + 0.605547i
\(17\) 16.8867 + 95.7695i 0.240920 + 1.36632i 0.829780 + 0.558090i \(0.188466\pi\)
−0.588861 + 0.808235i \(0.700423\pi\)
\(18\) 25.8864 0.338971
\(19\) −25.4519 78.8112i −0.307320 0.951606i
\(20\) 2.38939 0.0267142
\(21\) 24.6022 + 139.526i 0.255650 + 1.44986i
\(22\) 99.4237 83.4264i 0.963509 0.808480i
\(23\) 84.7939 30.8625i 0.768728 0.279794i 0.0722640 0.997386i \(-0.476978\pi\)
0.696464 + 0.717591i \(0.254755\pi\)
\(24\) −131.586 47.8935i −1.11916 0.407343i
\(25\) −73.0988 61.3372i −0.584791 0.490698i
\(26\) 25.2364 43.7108i 0.190357 0.329707i
\(27\) −53.0596 91.9020i −0.378197 0.655057i
\(28\) 1.79124 10.1586i 0.0120897 0.0685641i
\(29\) 16.0833 91.2129i 0.102986 0.584062i −0.889020 0.457869i \(-0.848613\pi\)
0.992006 0.126193i \(-0.0402760\pi\)
\(30\) −45.1188 78.1481i −0.274584 0.475594i
\(31\) −142.156 + 246.222i −0.823613 + 1.42654i 0.0793624 + 0.996846i \(0.474712\pi\)
−0.902975 + 0.429693i \(0.858622\pi\)
\(32\) 15.2136 + 12.7658i 0.0840443 + 0.0705215i
\(33\) 267.657 + 97.4192i 1.41191 + 0.513894i
\(34\) −251.270 + 91.4549i −1.26743 + 0.461305i
\(35\) 97.8122 82.0742i 0.472380 0.396374i
\(36\) −0.718252 4.07341i −0.00332524 0.0188584i
\(37\) 232.514 1.03311 0.516555 0.856254i \(-0.327214\pi\)
0.516555 + 0.856254i \(0.327214\pi\)
\(38\) 201.259 106.551i 0.859173 0.454866i
\(39\) 110.768 0.454798
\(40\) 21.9144 + 124.283i 0.0866245 + 0.491272i
\(41\) −197.399 + 165.638i −0.751918 + 0.630934i −0.936009 0.351975i \(-0.885510\pi\)
0.184092 + 0.982909i \(0.441066\pi\)
\(42\) −366.074 + 133.240i −1.34492 + 0.489510i
\(43\) −75.7804 27.5818i −0.268754 0.0978184i 0.204128 0.978944i \(-0.434564\pi\)
−0.472882 + 0.881126i \(0.656786\pi\)
\(44\) −15.8864 13.3303i −0.0544310 0.0456730i
\(45\) 25.5996 44.3398i 0.0848036 0.146884i
\(46\) 124.059 + 214.877i 0.397641 + 0.688735i
\(47\) −85.6235 + 485.595i −0.265734 + 1.50705i 0.501205 + 0.865329i \(0.332890\pi\)
−0.766938 + 0.641721i \(0.778221\pi\)
\(48\) 63.1782 358.301i 0.189979 1.07742i
\(49\) −104.116 180.335i −0.303547 0.525758i
\(50\) 131.192 227.230i 0.371066 0.642705i
\(51\) −449.538 377.207i −1.23427 1.03568i
\(52\) −7.57843 2.75832i −0.0202104 0.00735597i
\(53\) −106.793 + 38.8693i −0.276775 + 0.100738i −0.476679 0.879078i \(-0.658159\pi\)
0.199903 + 0.979816i \(0.435937\pi\)
\(54\) 223.526 187.560i 0.563296 0.472662i
\(55\) −44.5757 252.802i −0.109283 0.619777i
\(56\) 544.824 1.30009
\(57\) 423.353 + 265.591i 0.983762 + 0.617166i
\(58\) 254.674 0.576557
\(59\) −31.3837 177.986i −0.0692509 0.392741i −0.999656 0.0262097i \(-0.991656\pi\)
0.930406 0.366532i \(-0.119455\pi\)
\(60\) −11.0453 + 9.26810i −0.0237657 + 0.0199418i
\(61\) 259.591 94.4833i 0.544872 0.198317i −0.0548947 0.998492i \(-0.517482\pi\)
0.599767 + 0.800175i \(0.295260\pi\)
\(62\) −734.617 267.379i −1.50478 0.547695i
\(63\) −169.322 142.078i −0.338612 0.284129i
\(64\) −268.473 + 465.008i −0.524361 + 0.908219i
\(65\) −49.9138 86.4532i −0.0952468 0.164972i
\(66\) −136.001 + 771.301i −0.253645 + 1.43849i
\(67\) 26.9102 152.615i 0.0490686 0.278282i −0.950394 0.311047i \(-0.899320\pi\)
0.999463 + 0.0327652i \(0.0104314\pi\)
\(68\) 21.3629 + 37.0017i 0.0380976 + 0.0659869i
\(69\) −272.261 + 471.570i −0.475020 + 0.822758i
\(70\) 268.951 + 225.676i 0.459225 + 0.385336i
\(71\) −577.366 210.144i −0.965080 0.351261i −0.189058 0.981966i \(-0.560543\pi\)
−0.776022 + 0.630705i \(0.782766\pi\)
\(72\) 205.289 74.7191i 0.336022 0.122302i
\(73\) 368.338 309.072i 0.590557 0.495536i −0.297838 0.954616i \(-0.596265\pi\)
0.888395 + 0.459080i \(0.151821\pi\)
\(74\) 111.019 + 629.622i 0.174402 + 0.989082i
\(75\) 575.828 0.886545
\(76\) −22.3508 28.7132i −0.0337344 0.0433372i
\(77\) −1108.22 −1.64017
\(78\) 52.8889 + 299.948i 0.0767755 + 0.435416i
\(79\) 975.594 818.621i 1.38940 1.16585i 0.423824 0.905745i \(-0.360688\pi\)
0.965581 0.260104i \(-0.0837568\pi\)
\(80\) −308.119 + 112.146i −0.430609 + 0.156729i
\(81\) 840.609 + 305.957i 1.15310 + 0.419694i
\(82\) −542.782 455.448i −0.730979 0.613364i
\(83\) −154.093 + 266.896i −0.203781 + 0.352960i −0.949744 0.313028i \(-0.898657\pi\)
0.745962 + 0.665988i \(0.231990\pi\)
\(84\) 31.1235 + 53.9075i 0.0404269 + 0.0700214i
\(85\) −91.8370 + 520.834i −0.117190 + 0.664616i
\(86\) 38.5053 218.375i 0.0482807 0.273813i
\(87\) 279.455 + 484.029i 0.344376 + 0.596476i
\(88\) 547.665 948.584i 0.663424 1.14908i
\(89\) 32.1471 + 26.9746i 0.0382875 + 0.0321270i 0.661731 0.749742i \(-0.269822\pi\)
−0.623443 + 0.781869i \(0.714267\pi\)
\(90\) 132.290 + 48.1498i 0.154940 + 0.0563937i
\(91\) −404.979 + 147.400i −0.466520 + 0.169799i
\(92\) 30.3702 25.4836i 0.0344164 0.0288788i
\(93\) −297.922 1689.60i −0.332183 1.88390i
\(94\) −1355.82 −1.48768
\(95\) 16.5219 450.101i 0.0178433 0.486098i
\(96\) −119.844 −0.127412
\(97\) 98.6409 + 559.420i 0.103252 + 0.585572i 0.991904 + 0.126990i \(0.0405316\pi\)
−0.888652 + 0.458583i \(0.848357\pi\)
\(98\) 438.614 368.041i 0.452110 0.379365i
\(99\) −417.574 + 151.985i −0.423917 + 0.154293i
\(100\) −39.3965 14.3391i −0.0393965 0.0143391i
\(101\) −5.35419 4.49270i −0.00527487 0.00442614i 0.640146 0.768253i \(-0.278874\pi\)
−0.645421 + 0.763827i \(0.723318\pi\)
\(102\) 806.792 1397.41i 0.783180 1.35651i
\(103\) 439.531 + 761.289i 0.420468 + 0.728273i 0.995985 0.0895173i \(-0.0285324\pi\)
−0.575517 + 0.817790i \(0.695199\pi\)
\(104\) 73.9669 419.487i 0.0697409 0.395520i
\(105\) −133.797 + 758.800i −0.124355 + 0.705250i
\(106\) −156.244 270.623i −0.143168 0.247974i
\(107\) −426.585 + 738.867i −0.385416 + 0.667560i −0.991827 0.127591i \(-0.959275\pi\)
0.606411 + 0.795152i \(0.292609\pi\)
\(108\) −35.7160 29.9693i −0.0318220 0.0267018i
\(109\) 496.022 + 180.537i 0.435874 + 0.158645i 0.550632 0.834748i \(-0.314387\pi\)
−0.114757 + 0.993394i \(0.536609\pi\)
\(110\) 663.275 241.412i 0.574916 0.209252i
\(111\) −1074.83 + 901.889i −0.919084 + 0.771203i
\(112\) 245.809 + 1394.05i 0.207382 + 1.17612i
\(113\) −387.539 −0.322625 −0.161312 0.986903i \(-0.551573\pi\)
−0.161312 + 0.986903i \(0.551573\pi\)
\(114\) −517.052 + 1273.20i −0.424793 + 1.04602i
\(115\) 490.739 0.397927
\(116\) −7.06626 40.0748i −0.00565592 0.0320763i
\(117\) −132.381 + 111.080i −0.104603 + 0.0877726i
\(118\) 466.980 169.967i 0.364314 0.132599i
\(119\) 2145.50 + 780.899i 1.65276 + 0.601554i
\(120\) −583.379 489.513i −0.443791 0.372385i
\(121\) −448.495 + 776.815i −0.336961 + 0.583633i
\(122\) 379.798 + 657.830i 0.281847 + 0.488173i
\(123\) 270.022 1531.37i 0.197943 1.12259i
\(124\) −21.6911 + 123.016i −0.0157090 + 0.0890901i
\(125\) −599.377 1038.15i −0.428879 0.742841i
\(126\) 303.884 526.343i 0.214859 0.372146i
\(127\) −437.956 367.489i −0.306002 0.256767i 0.476835 0.878993i \(-0.341784\pi\)
−0.782837 + 0.622226i \(0.786228\pi\)
\(128\) −1238.08 450.625i −0.854937 0.311172i
\(129\) 457.292 166.441i 0.312111 0.113599i
\(130\) 210.273 176.440i 0.141863 0.119037i
\(131\) −7.61560 43.1902i −0.00507922 0.0288057i 0.982163 0.188032i \(-0.0602110\pi\)
−0.987242 + 0.159227i \(0.949100\pi\)
\(132\) 125.143 0.0825177
\(133\) −1901.24 407.668i −1.23954 0.265784i
\(134\) 426.114 0.274706
\(135\) −100.216 568.352i −0.0638904 0.362340i
\(136\) −1728.70 + 1450.55i −1.08996 + 0.914584i
\(137\) 1958.25 712.743i 1.22120 0.444480i 0.350624 0.936516i \(-0.385970\pi\)
0.870575 + 0.492036i \(0.163747\pi\)
\(138\) −1406.96 512.090i −0.867885 0.315884i
\(139\) 1763.12 + 1479.43i 1.07587 + 0.902762i 0.995571 0.0940092i \(-0.0299683\pi\)
0.0802982 + 0.996771i \(0.474413\pi\)
\(140\) 28.0494 48.5831i 0.0169329 0.0293287i
\(141\) −1487.75 2576.85i −0.888588 1.53908i
\(142\) 293.369 1663.78i 0.173373 0.983249i
\(143\) −150.455 + 853.270i −0.0879835 + 0.498979i
\(144\) 283.806 + 491.567i 0.164240 + 0.284472i
\(145\) 251.853 436.221i 0.144243 0.249836i
\(146\) 1012.80 + 849.844i 0.574111 + 0.481737i
\(147\) 1180.79 + 429.771i 0.662515 + 0.241136i
\(148\) 95.9953 34.9394i 0.0533160 0.0194054i
\(149\) −286.850 + 240.696i −0.157716 + 0.132339i −0.718231 0.695805i \(-0.755048\pi\)
0.560515 + 0.828144i \(0.310603\pi\)
\(150\) 274.943 + 1559.28i 0.149660 + 0.848764i
\(151\) −496.496 −0.267578 −0.133789 0.991010i \(-0.542714\pi\)
−0.133789 + 0.991010i \(0.542714\pi\)
\(152\) 1288.51 1425.92i 0.687580 0.760901i
\(153\) 915.519 0.483760
\(154\) −529.144 3000.92i −0.276881 1.57027i
\(155\) −1184.46 + 993.882i −0.613795 + 0.515035i
\(156\) 45.7315 16.6449i 0.0234709 0.00854269i
\(157\) −2592.46 943.577i −1.31784 0.479654i −0.415073 0.909788i \(-0.636244\pi\)
−0.902765 + 0.430134i \(0.858466\pi\)
\(158\) 2682.56 + 2250.93i 1.35071 + 1.13338i
\(159\) 342.895 593.912i 0.171028 0.296228i
\(160\) 54.0034 + 93.5366i 0.0266834 + 0.0462170i
\(161\) 367.889 2086.40i 0.180085 1.02131i
\(162\) −427.128 + 2422.36i −0.207150 + 1.17481i
\(163\) 1856.68 + 3215.87i 0.892188 + 1.54531i 0.837247 + 0.546825i \(0.184164\pi\)
0.0549404 + 0.998490i \(0.482503\pi\)
\(164\) −56.6079 + 98.0477i −0.0269533 + 0.0466844i
\(165\) 1186.64 + 995.708i 0.559877 + 0.469793i
\(166\) −796.301 289.830i −0.372319 0.135513i
\(167\) −1406.58 + 511.954i −0.651764 + 0.237223i −0.646677 0.762764i \(-0.723842\pi\)
−0.00508752 + 0.999987i \(0.501619\pi\)
\(168\) −2518.53 + 2113.30i −1.15660 + 0.970502i
\(169\) −322.995 1831.80i −0.147017 0.833772i
\(170\) −1454.21 −0.656075
\(171\) −772.294 + 107.134i −0.345373 + 0.0479109i
\(172\) −35.4312 −0.0157070
\(173\) 98.3955 + 558.029i 0.0432420 + 0.245238i 0.998765 0.0496780i \(-0.0158195\pi\)
−0.955523 + 0.294916i \(0.904708\pi\)
\(174\) −1177.27 + 987.843i −0.512921 + 0.430392i
\(175\) −2105.28 + 766.259i −0.909395 + 0.330993i
\(176\) 2674.26 + 973.350i 1.14534 + 0.416869i
\(177\) 835.456 + 701.031i 0.354784 + 0.297699i
\(178\) −57.6949 + 99.9304i −0.0242945 + 0.0420792i
\(179\) −1443.68 2500.53i −0.602826 1.04413i −0.992391 0.123127i \(-0.960708\pi\)
0.389565 0.920999i \(-0.372626\pi\)
\(180\) 3.90614 22.1528i 0.00161748 0.00917320i
\(181\) 404.469 2293.86i 0.166099 0.941995i −0.781825 0.623498i \(-0.785711\pi\)
0.947924 0.318497i \(-0.103178\pi\)
\(182\) −592.510 1026.26i −0.241317 0.417974i
\(183\) −833.508 + 1443.68i −0.336692 + 0.583168i
\(184\) 1604.06 + 1345.97i 0.642680 + 0.539273i
\(185\) 1188.25 + 432.486i 0.472225 + 0.171876i
\(186\) 4432.99 1613.48i 1.74754 0.636054i
\(187\) 3516.30 2950.53i 1.37507 1.15382i
\(188\) 37.6191 + 213.348i 0.0145939 + 0.0827661i
\(189\) −2491.51 −0.958891
\(190\) 1226.71 170.172i 0.468395 0.0649767i
\(191\) 2368.42 0.897239 0.448620 0.893723i \(-0.351916\pi\)
0.448620 + 0.893723i \(0.351916\pi\)
\(192\) −562.648 3190.94i −0.211488 1.19941i
\(193\) −2094.11 + 1757.17i −0.781022 + 0.655355i −0.943506 0.331356i \(-0.892494\pi\)
0.162484 + 0.986711i \(0.448049\pi\)
\(194\) −1467.75 + 534.217i −0.543187 + 0.197704i
\(195\) 566.073 + 206.034i 0.207884 + 0.0756635i
\(196\) −70.0839 58.8074i −0.0255408 0.0214313i
\(197\) −1088.18 + 1884.79i −0.393552 + 0.681652i −0.992915 0.118825i \(-0.962087\pi\)
0.599363 + 0.800477i \(0.295420\pi\)
\(198\) −610.938 1058.18i −0.219280 0.379805i
\(199\) 896.373 5083.58i 0.319308 1.81088i −0.227673 0.973738i \(-0.573112\pi\)
0.546981 0.837145i \(-0.315777\pi\)
\(200\) 384.517 2180.70i 0.135947 0.770995i
\(201\) 467.576 + 809.866i 0.164081 + 0.284197i
\(202\) 9.60925 16.6437i 0.00334705 0.00579726i
\(203\) −1665.81 1397.78i −0.575947 0.483277i
\(204\) −242.277 88.1818i −0.0831510 0.0302645i
\(205\) −1316.89 + 479.309i −0.448661 + 0.163299i
\(206\) −1851.62 + 1553.70i −0.626256 + 0.525491i
\(207\) −147.517 836.608i −0.0495319 0.280909i
\(208\) 1106.72 0.368930
\(209\) −2620.94 + 2900.42i −0.867436 + 0.959936i
\(210\) −2118.63 −0.696187
\(211\) 610.668 + 3463.27i 0.199242 + 1.12996i 0.906246 + 0.422750i \(0.138935\pi\)
−0.707004 + 0.707209i \(0.749954\pi\)
\(212\) −38.2494 + 32.0950i −0.0123914 + 0.0103976i
\(213\) 3484.07 1268.10i 1.12077 0.407928i
\(214\) −2204.45 802.355i −0.704174 0.256298i
\(215\) −335.967 281.910i −0.106571 0.0894237i
\(216\) 1231.27 2132.62i 0.387858 0.671789i
\(217\) 3337.59 + 5780.88i 1.04410 + 1.80844i
\(218\) −252.037 + 1429.38i −0.0783033 + 0.444080i
\(219\) −503.847 + 2857.46i −0.155465 + 0.881686i
\(220\) −56.3914 97.6728i −0.0172814 0.0299323i
\(221\) 892.533 1545.91i 0.271666 0.470540i
\(222\) −2955.42 2479.89i −0.893490 0.749727i
\(223\) −1988.21 723.650i −0.597043 0.217306i 0.0257814 0.999668i \(-0.491793\pi\)
−0.622824 + 0.782362i \(0.714015\pi\)
\(224\) 438.160 159.477i 0.130695 0.0475693i
\(225\) −688.180 + 577.451i −0.203905 + 0.171097i
\(226\) −185.040 1049.41i −0.0544631 0.308875i
\(227\) −1257.38 −0.367644 −0.183822 0.982960i \(-0.558847\pi\)
−0.183822 + 0.982960i \(0.558847\pi\)
\(228\) 214.694 + 46.0352i 0.0623618 + 0.0133717i
\(229\) 1823.23 0.526125 0.263063 0.964779i \(-0.415267\pi\)
0.263063 + 0.964779i \(0.415267\pi\)
\(230\) 234.315 + 1328.87i 0.0671751 + 0.380969i
\(231\) 5122.88 4298.61i 1.45914 1.22436i
\(232\) 2019.66 735.098i 0.571541 0.208024i
\(233\) 6446.27 + 2346.25i 1.81248 + 0.659691i 0.996685 + 0.0813561i \(0.0259251\pi\)
0.815800 + 0.578334i \(0.196297\pi\)
\(234\) −364.002 305.434i −0.101690 0.0853283i
\(235\) −1340.80 + 2322.34i −0.372188 + 0.644649i
\(236\) −39.7025 68.7668i −0.0109509 0.0189675i
\(237\) −1334.51 + 7568.38i −0.365763 + 2.07434i
\(238\) −1090.17 + 6182.64i −0.296912 + 1.68387i
\(239\) −1965.93 3405.09i −0.532072 0.921576i −0.999299 0.0374388i \(-0.988080\pi\)
0.467227 0.884138i \(-0.345253\pi\)
\(240\) 989.324 1713.56i 0.266086 0.460874i
\(241\) 2081.75 + 1746.80i 0.556420 + 0.466892i 0.877108 0.480293i \(-0.159470\pi\)
−0.320688 + 0.947185i \(0.603914\pi\)
\(242\) −2317.67 843.565i −0.615644 0.224076i
\(243\) −2380.17 + 866.312i −0.628346 + 0.228699i
\(244\) 92.9763 78.0164i 0.0243942 0.0204692i
\(245\) −196.649 1115.25i −0.0512793 0.290819i
\(246\) 4275.71 1.10817
\(247\) −572.002 + 1408.51i −0.147351 + 0.362840i
\(248\) −6597.57 −1.68930
\(249\) −322.938 1831.47i −0.0821901 0.466123i
\(250\) 2525.01 2118.74i 0.638783 0.536003i
\(251\) −3027.38 + 1101.88i −0.761302 + 0.277091i −0.693354 0.720597i \(-0.743868\pi\)
−0.0679486 + 0.997689i \(0.521645\pi\)
\(252\) −91.2557 33.2143i −0.0228118 0.00830281i
\(253\) −3262.79 2737.81i −0.810790 0.680334i
\(254\) 786.006 1361.40i 0.194167 0.336307i
\(255\) −1595.71 2763.85i −0.391871 0.678741i
\(256\) −116.826 + 662.555i −0.0285220 + 0.161756i
\(257\) 1218.62 6911.11i 0.295779 1.67744i −0.368241 0.929730i \(-0.620040\pi\)
0.664020 0.747715i \(-0.268849\pi\)
\(258\) 669.048 + 1158.82i 0.161446 + 0.279633i
\(259\) 2729.52 4727.67i 0.654843 1.13422i
\(260\) −33.5984 28.1924i −0.00801418 0.00672470i
\(261\) −819.374 298.228i −0.194322 0.0707273i
\(262\) 113.318 41.2444i 0.0267207 0.00972553i
\(263\) −107.382 + 90.1044i −0.0251767 + 0.0211258i −0.655289 0.755378i \(-0.727453\pi\)
0.630112 + 0.776504i \(0.283009\pi\)
\(264\) 1147.76 + 6509.28i 0.267575 + 1.51749i
\(265\) −618.055 −0.143271
\(266\) 196.126 5343.00i 0.0452077 1.23158i
\(267\) −253.235 −0.0580440
\(268\) −11.8231 67.0521i −0.00269481 0.0152831i
\(269\) 2625.17 2202.78i 0.595016 0.499278i −0.294823 0.955552i \(-0.595261\pi\)
0.889839 + 0.456274i \(0.150816\pi\)
\(270\) 1491.18 542.746i 0.336113 0.122335i
\(271\) −3006.87 1094.41i −0.674001 0.245316i −0.0177312 0.999843i \(-0.505644\pi\)
−0.656269 + 0.754527i \(0.727867\pi\)
\(272\) −4491.49 3768.81i −1.00124 0.840138i
\(273\) 1300.33 2252.23i 0.288276 0.499309i
\(274\) 2865.04 + 4962.40i 0.631691 + 1.09412i
\(275\) −782.138 + 4435.72i −0.171508 + 0.972670i
\(276\) −41.5432 + 235.603i −0.00906018 + 0.0513828i
\(277\) −818.845 1418.28i −0.177616 0.307640i 0.763447 0.645870i \(-0.223505\pi\)
−0.941063 + 0.338230i \(0.890172\pi\)
\(278\) −3164.30 + 5480.72i −0.682669 + 1.18242i
\(279\) 2050.41 + 1720.50i 0.439982 + 0.369189i
\(280\) 2784.29 + 1013.40i 0.594260 + 0.216293i
\(281\) 1120.25 407.736i 0.237823 0.0865605i −0.220359 0.975419i \(-0.570723\pi\)
0.458182 + 0.888858i \(0.348501\pi\)
\(282\) 6267.48 5259.04i 1.32349 1.11054i
\(283\) −419.567 2379.48i −0.0881295 0.499807i −0.996637 0.0819395i \(-0.973889\pi\)
0.908508 0.417868i \(-0.137223\pi\)
\(284\) −269.948 −0.0564031
\(285\) 1669.50 + 2144.74i 0.346992 + 0.445767i
\(286\) −2382.40 −0.492567
\(287\) 1050.58 + 5958.15i 0.216076 + 1.22543i
\(288\) 143.227 120.182i 0.0293046 0.0245895i
\(289\) −4269.93 + 1554.13i −0.869108 + 0.316329i
\(290\) 1301.49 + 473.705i 0.263539 + 0.0959203i
\(291\) −2625.89 2203.39i −0.528978 0.443865i
\(292\) 105.627 182.952i 0.0211691 0.0366660i
\(293\) 888.642 + 1539.17i 0.177184 + 0.306892i 0.940915 0.338643i \(-0.109968\pi\)
−0.763731 + 0.645535i \(0.776634\pi\)
\(294\) −599.978 + 3402.65i −0.119019 + 0.674988i
\(295\) 170.677 967.958i 0.0336854 0.191040i
\(296\) 2697.79 + 4672.71i 0.529749 + 0.917552i
\(297\) −2504.50 + 4337.92i −0.489312 + 0.847514i
\(298\) −788.741 661.833i −0.153324 0.128654i
\(299\) −1556.48 566.512i −0.301049 0.109573i
\(300\) 237.735 86.5286i 0.0457522 0.0166524i
\(301\) −1450.42 + 1217.04i −0.277743 + 0.233054i
\(302\) −237.064 1344.46i −0.0451705 0.256175i
\(303\) 42.1771 0.00799673
\(304\) 4229.86 + 2653.62i 0.798024 + 0.500643i
\(305\) 1502.36 0.282049
\(306\) 437.136 + 2479.12i 0.0816648 + 0.463144i
\(307\) 4825.96 4049.46i 0.897173 0.752817i −0.0724631 0.997371i \(-0.523086\pi\)
0.969636 + 0.244554i \(0.0786415\pi\)
\(308\) −457.536 + 166.529i −0.0846445 + 0.0308081i
\(309\) −4984.73 1814.29i −0.917706 0.334018i
\(310\) −3256.87 2732.84i −0.596703 0.500693i
\(311\) −2076.83 + 3597.17i −0.378669 + 0.655874i −0.990869 0.134829i \(-0.956952\pi\)
0.612200 + 0.790703i \(0.290285\pi\)
\(312\) 1285.21 + 2226.05i 0.233207 + 0.403927i
\(313\) 58.6545 332.646i 0.0105922 0.0600712i −0.979054 0.203603i \(-0.934735\pi\)
0.989646 + 0.143532i \(0.0458459\pi\)
\(314\) 1317.27 7470.62i 0.236745 1.34265i
\(315\) −601.036 1041.03i −0.107507 0.186207i
\(316\) 279.769 484.575i 0.0498046 0.0862641i
\(317\) −4068.20 3413.63i −0.720799 0.604822i 0.206808 0.978382i \(-0.433693\pi\)
−0.927606 + 0.373560i \(0.878137\pi\)
\(318\) 1771.97 + 644.945i 0.312476 + 0.113732i
\(319\) −4108.16 + 1495.25i −0.721043 + 0.262438i
\(320\) −2236.95 + 1877.02i −0.390779 + 0.327902i
\(321\) −894.010 5070.18i −0.155448 0.881588i
\(322\) 5825.40 1.00819
\(323\) 7117.91 3768.38i 1.22616 0.649159i
\(324\) 393.028 0.0673916
\(325\) 304.162 + 1724.99i 0.0519135 + 0.294416i
\(326\) −7821.70 + 6563.18i −1.32885 + 1.11503i
\(327\) −2993.21 + 1089.44i −0.506193 + 0.184239i
\(328\) −5619.10 2045.18i −0.945923 0.344288i
\(329\) 8868.38 + 7441.46i 1.48611 + 1.24699i
\(330\) −2129.68 + 3688.71i −0.355257 + 0.615324i
\(331\) −2795.49 4841.93i −0.464212 0.804038i 0.534954 0.844881i \(-0.320329\pi\)
−0.999166 + 0.0408431i \(0.986996\pi\)
\(332\) −23.5124 + 133.345i −0.00388678 + 0.0220430i
\(333\) 380.111 2155.72i 0.0625525 0.354753i
\(334\) −2057.92 3564.42i −0.337139 0.583942i
\(335\) 421.393 729.875i 0.0687259 0.119037i
\(336\) −6543.63 5490.76i −1.06245 0.891504i
\(337\) 8251.69 + 3003.37i 1.33382 + 0.485472i 0.907862 0.419270i \(-0.137714\pi\)
0.425961 + 0.904742i \(0.359936\pi\)
\(338\) 4806.08 1749.27i 0.773422 0.281502i
\(339\) 1791.45 1503.21i 0.287016 0.240835i
\(340\) 40.3490 + 228.830i 0.00643597 + 0.0365002i
\(341\) 13420.0 2.13118
\(342\) −658.858 2040.13i −0.104172 0.322567i
\(343\) 3164.11 0.498093
\(344\) −324.960 1842.94i −0.0509322 0.288851i
\(345\) −2268.51 + 1903.51i −0.354007 + 0.297047i
\(346\) −1464.10 + 532.888i −0.227487 + 0.0827984i
\(347\) 1363.50 + 496.273i 0.210941 + 0.0767762i 0.445329 0.895367i \(-0.353087\pi\)
−0.234389 + 0.972143i \(0.575309\pi\)
\(348\) 188.109 + 157.842i 0.0289762 + 0.0243139i
\(349\) 3391.17 5873.67i 0.520129 0.900890i −0.479597 0.877489i \(-0.659217\pi\)
0.999726 0.0234010i \(-0.00744943\pi\)
\(350\) −3080.16 5335.00i −0.470404 0.814764i
\(351\) −338.254 + 1918.33i −0.0514378 + 0.291718i
\(352\) 162.782 923.182i 0.0246486 0.139789i
\(353\) −5155.16 8928.99i −0.777284 1.34630i −0.933502 0.358573i \(-0.883263\pi\)
0.156218 0.987723i \(-0.450070\pi\)
\(354\) −1499.41 + 2597.05i −0.225120 + 0.389919i
\(355\) −2559.71 2147.85i −0.382691 0.321116i
\(356\) 17.3256 + 6.30601i 0.00257937 + 0.000938813i
\(357\) −12946.9 + 4712.28i −1.91939 + 0.698601i
\(358\) 6081.84 5103.27i 0.897864 0.753398i
\(359\) 1862.89 + 10565.0i 0.273870 + 1.55320i 0.742528 + 0.669815i \(0.233627\pi\)
−0.468657 + 0.883380i \(0.655262\pi\)
\(360\) 1188.10 0.173939
\(361\) −5563.40 + 4011.79i −0.811109 + 0.584895i
\(362\) 6404.63 0.929890
\(363\) −939.926 5330.59i −0.135905 0.770753i
\(364\) −145.049 + 121.711i −0.0208864 + 0.0175257i
\(365\) 2457.25 894.366i 0.352379 0.128256i
\(366\) −4307.30 1567.73i −0.615153 0.223897i
\(367\) 2814.42 + 2361.58i 0.400304 + 0.335895i 0.820611 0.571487i \(-0.193633\pi\)
−0.420307 + 0.907382i \(0.638078\pi\)
\(368\) −2720.25 + 4711.62i −0.385334 + 0.667419i
\(369\) 1212.98 + 2100.94i 0.171125 + 0.296398i
\(370\) −603.768 + 3424.14i −0.0848336 + 0.481115i
\(371\) −463.333 + 2627.69i −0.0648384 + 0.367717i
\(372\) −376.892 652.796i −0.0525294 0.0909836i
\(373\) −1353.85 + 2344.94i −0.187935 + 0.325513i −0.944562 0.328334i \(-0.893513\pi\)
0.756626 + 0.653847i \(0.226846\pi\)
\(374\) 9668.65 + 8112.96i 1.33678 + 1.12169i
\(375\) 6797.55 + 2474.11i 0.936064 + 0.340699i
\(376\) −10752.2 + 3913.48i −1.47474 + 0.536762i
\(377\) −1302.38 + 1092.83i −0.177920 + 0.149293i
\(378\) −1189.63 6746.72i −0.161873 0.918026i
\(379\) −12094.2 −1.63915 −0.819573 0.572974i \(-0.805790\pi\)
−0.819573 + 0.572974i \(0.805790\pi\)
\(380\) −60.8145 188.310i −0.00820979 0.0254214i
\(381\) 3449.95 0.463901
\(382\) 1130.86 + 6413.41i 0.151465 + 0.859002i
\(383\) −4039.50 + 3389.54i −0.538926 + 0.452213i −0.871170 0.490981i \(-0.836639\pi\)
0.332244 + 0.943193i \(0.392194\pi\)
\(384\) 7471.12 2719.26i 0.992862 0.361372i
\(385\) −5663.46 2061.33i −0.749705 0.272870i
\(386\) −5758.09 4831.61i −0.759273 0.637105i
\(387\) −379.606 + 657.497i −0.0498616 + 0.0863629i
\(388\) 124.788 + 216.139i 0.0163277 + 0.0282803i
\(389\) −1156.94 + 6561.34i −0.150795 + 0.855201i 0.811735 + 0.584026i \(0.198523\pi\)
−0.962530 + 0.271175i \(0.912588\pi\)
\(390\) −287.631 + 1631.24i −0.0373456 + 0.211797i
\(391\) 4387.58 + 7599.51i 0.567492 + 0.982925i
\(392\) 2416.06 4184.74i 0.311300 0.539187i
\(393\) 202.733 + 170.113i 0.0260217 + 0.0218348i
\(394\) −5623.37 2046.74i −0.719038 0.261709i
\(395\) 6508.38 2368.86i 0.829043 0.301747i
\(396\) −149.561 + 125.496i −0.0189790 + 0.0159253i
\(397\) 1129.71 + 6406.89i 0.142817 + 0.809956i 0.969094 + 0.246692i \(0.0793435\pi\)
−0.826277 + 0.563264i \(0.809545\pi\)
\(398\) 14193.8 1.78761
\(399\) 10370.0 5490.14i 1.30113 0.688849i
\(400\) 5753.30 0.719163
\(401\) −593.766 3367.41i −0.0739432 0.419353i −0.999199 0.0400098i \(-0.987261\pi\)
0.925256 0.379343i \(-0.123850\pi\)
\(402\) −1969.77 + 1652.83i −0.244386 + 0.205064i
\(403\) 4904.11 1784.95i 0.606181 0.220632i
\(404\) −2.88563 1.05028i −0.000355360 0.000129341i
\(405\) 3726.78 + 3127.14i 0.457248 + 0.383676i
\(406\) 2989.66 5178.24i 0.365454 0.632985i
\(407\) −5487.51 9504.65i −0.668319 1.15756i
\(408\) 2364.67 13410.7i 0.286933 1.62728i
\(409\) 230.257 1305.85i 0.0278373 0.157873i −0.967720 0.252026i \(-0.918903\pi\)
0.995558 + 0.0941529i \(0.0300142\pi\)
\(410\) −1926.70 3337.14i −0.232080 0.401974i
\(411\) −6287.64 + 10890.5i −0.754614 + 1.30703i
\(412\) 295.861 + 248.257i 0.0353787 + 0.0296863i
\(413\) −3987.37 1451.28i −0.475074 0.172913i
\(414\) 2195.01 798.917i 0.260576 0.0948421i
\(415\) −1283.92 + 1077.34i −0.151868 + 0.127432i
\(416\) −63.3035 359.012i −0.00746084 0.0423126i
\(417\) −13888.8 −1.63102
\(418\) −9105.46 5712.33i −1.06546 0.668420i
\(419\) −2455.32 −0.286277 −0.143139 0.989703i \(-0.545719\pi\)
−0.143139 + 0.989703i \(0.545719\pi\)
\(420\) 58.7842 + 333.382i 0.00682947 + 0.0387318i
\(421\) −715.441 + 600.326i −0.0828230 + 0.0694967i −0.683259 0.730176i \(-0.739438\pi\)
0.600436 + 0.799673i \(0.294994\pi\)
\(422\) −9086.58 + 3307.24i −1.04817 + 0.381503i
\(423\) 4362.15 + 1587.69i 0.501406 + 0.182497i
\(424\) −2020.22 1695.16i −0.231392 0.194161i
\(425\) 4639.83 8036.42i 0.529564 0.917233i
\(426\) 5097.43 + 8829.00i 0.579745 + 1.00415i
\(427\) 1126.27 6387.37i 0.127644 0.723903i
\(428\) −65.0910 + 369.149i −0.00735115 + 0.0416904i
\(429\) −2614.22 4527.96i −0.294209 0.509585i
\(430\) 602.965 1044.37i 0.0676223 0.117125i
\(431\) 807.361 + 677.456i 0.0902302 + 0.0757121i 0.686787 0.726859i \(-0.259021\pi\)
−0.596557 + 0.802571i \(0.703465\pi\)
\(432\) 6012.30 + 2188.30i 0.669599 + 0.243714i
\(433\) 8600.27 3130.24i 0.954509 0.347413i 0.182630 0.983182i \(-0.441539\pi\)
0.771879 + 0.635769i \(0.219317\pi\)
\(434\) −14060.4 + 11798.0i −1.55511 + 1.30489i
\(435\) 527.817 + 2993.40i 0.0581767 + 0.329937i
\(436\) 231.916 0.0254742
\(437\) −4590.48 5897.20i −0.502499 0.645541i
\(438\) −7978.26 −0.870356
\(439\) 281.660 + 1597.38i 0.0306217 + 0.173664i 0.996283 0.0861398i \(-0.0274532\pi\)
−0.965661 + 0.259804i \(0.916342\pi\)
\(440\) 4563.21 3828.99i 0.494415 0.414864i
\(441\) −1842.16 + 670.491i −0.198916 + 0.0723994i
\(442\) 4612.32 + 1678.75i 0.496348 + 0.180656i
\(443\) −7978.73 6694.95i −0.855713 0.718028i 0.105327 0.994438i \(-0.466411\pi\)
−0.961040 + 0.276409i \(0.910855\pi\)
\(444\) −308.227 + 533.865i −0.0329455 + 0.0570633i
\(445\) 114.111 + 197.647i 0.0121560 + 0.0210547i
\(446\) 1010.24 5729.38i 0.107257 0.608283i
\(447\) 392.381 2225.30i 0.0415190 0.235466i
\(448\) 6303.30 + 10917.6i 0.664738 + 1.15136i
\(449\) 6677.63 11566.0i 0.701864 1.21566i −0.265947 0.963988i \(-0.585685\pi\)
0.967811 0.251677i \(-0.0809820\pi\)
\(450\) −1892.26 1587.80i −0.198227 0.166332i
\(451\) 11429.7 + 4160.07i 1.19335 + 0.434346i
\(452\) −159.998 + 58.2347i −0.0166498 + 0.00606002i
\(453\) 2295.12 1925.84i 0.238045 0.199743i
\(454\) −600.366 3404.85i −0.0620630 0.351977i
\(455\) −2343.79 −0.241491
\(456\) −425.415 + 11589.5i −0.0436884 + 1.19019i
\(457\) −17571.0 −1.79855 −0.899275 0.437384i \(-0.855905\pi\)
−0.899275 + 0.437384i \(0.855905\pi\)
\(458\) 870.546 + 4937.11i 0.0888165 + 0.503703i
\(459\) 7905.40 6633.42i 0.803905 0.674557i
\(460\) 202.606 73.7424i 0.0205359 0.00747447i
\(461\) 9777.28 + 3558.64i 0.987794 + 0.359528i 0.784866 0.619666i \(-0.212732\pi\)
0.202928 + 0.979194i \(0.434954\pi\)
\(462\) 14086.2 + 11819.7i 1.41851 + 1.19027i
\(463\) −2012.85 + 3486.36i −0.202041 + 0.349946i −0.949186 0.314716i \(-0.898091\pi\)
0.747145 + 0.664661i \(0.231424\pi\)
\(464\) 2792.13 + 4836.11i 0.279356 + 0.483859i
\(465\) 1620.22 9188.72i 0.161583 0.916380i
\(466\) −3275.46 + 18576.0i −0.325607 + 1.84661i
\(467\) 3336.14 + 5778.36i 0.330574 + 0.572571i 0.982624 0.185605i \(-0.0594244\pi\)
−0.652051 + 0.758175i \(0.726091\pi\)
\(468\) −37.9625 + 65.7530i −0.00374961 + 0.00649452i
\(469\) −2787.20 2338.74i −0.274415 0.230262i
\(470\) −6928.83 2521.89i −0.680006 0.247502i
\(471\) 15644.0 5693.95i 1.53044 0.557035i
\(472\) 3212.74 2695.81i 0.313302 0.262891i
\(473\) 660.995 + 3748.69i 0.0642549 + 0.364408i
\(474\) −21131.5 −2.04769
\(475\) −2973.55 + 7322.15i −0.287233 + 0.707291i
\(476\) 1003.13 0.0965935
\(477\) 185.788 + 1053.65i 0.0178336 + 0.101139i
\(478\) 8281.92 6949.35i 0.792481 0.664971i
\(479\) −5473.84 + 1992.31i −0.522142 + 0.190044i −0.589626 0.807676i \(-0.700725\pi\)
0.0674844 + 0.997720i \(0.478503\pi\)
\(480\) −612.453 222.915i −0.0582386 0.0211971i
\(481\) −3269.50 2743.44i −0.309930 0.260062i
\(482\) −3736.15 + 6471.20i −0.353064 + 0.611525i
\(483\) 6392.24 + 11071.7i 0.602188 + 1.04302i
\(484\) −68.4341 + 388.109i −0.00642694 + 0.0364490i
\(485\) −536.449 + 3042.35i −0.0502245 + 0.284838i
\(486\) −3482.35 6031.60i −0.325026 0.562961i
\(487\) −1435.60 + 2486.53i −0.133579 + 0.231366i −0.925054 0.379836i \(-0.875980\pi\)
0.791475 + 0.611202i \(0.209314\pi\)
\(488\) 4910.73 + 4120.59i 0.455529 + 0.382234i
\(489\) −21056.7 7664.00i −1.94727 0.708749i
\(490\) 2926.08 1065.01i 0.269769 0.0981879i
\(491\) −8671.93 + 7276.61i −0.797064 + 0.668816i −0.947483 0.319806i \(-0.896382\pi\)
0.150419 + 0.988622i \(0.451938\pi\)
\(492\) −118.635 672.814i −0.0108709 0.0616520i
\(493\) 9007.01 0.822830
\(494\) −4087.22 876.388i −0.372252 0.0798190i
\(495\) −2416.68 −0.219438
\(496\) −2976.64 16881.4i −0.269466 1.52822i
\(497\) −11050.6 + 9272.57i −0.997360 + 0.836885i
\(498\) 4805.22 1748.96i 0.432384 0.157375i
\(499\) 702.905 + 255.837i 0.0630588 + 0.0229515i 0.373357 0.927688i \(-0.378207\pi\)
−0.310298 + 0.950639i \(0.600429\pi\)
\(500\) −403.459 338.542i −0.0360864 0.0302801i
\(501\) 4516.33 7822.51i 0.402744 0.697573i
\(502\) −4429.26 7671.71i −0.393800 0.682082i
\(503\) 571.219 3239.54i 0.0506350 0.287165i −0.948967 0.315375i \(-0.897870\pi\)
0.999602 + 0.0282100i \(0.00898071\pi\)
\(504\) 890.672 5051.25i 0.0787177 0.446430i
\(505\) −19.0056 32.9187i −0.00167473 0.00290072i
\(506\) 5855.78 10142.5i 0.514469 0.891086i
\(507\) 8598.38 + 7214.90i 0.753190 + 0.632001i
\(508\) −236.035 85.9099i −0.0206149 0.00750322i
\(509\) −1780.26 + 647.963i −0.155027 + 0.0564253i −0.418368 0.908278i \(-0.637398\pi\)
0.263341 + 0.964703i \(0.415176\pi\)
\(510\) 6722.29 5640.67i 0.583663 0.489751i
\(511\) −1960.33 11117.6i −0.169707 0.962454i
\(512\) −12390.2 −1.06948
\(513\) −5892.43 + 6520.77i −0.507129 + 0.561207i
\(514\) 19296.4 1.65589
\(515\) 830.159 + 4708.06i 0.0710314 + 0.402839i
\(516\) 163.786 137.433i 0.0139734 0.0117251i
\(517\) 21870.8 7960.33i 1.86050 0.677166i
\(518\) 14105.3 + 5133.90i 1.19643 + 0.435465i
\(519\) −2619.36 2197.91i −0.221536 0.185891i
\(520\) 1158.27 2006.18i 0.0976796 0.169186i
\(521\) −6557.36 11357.7i −0.551407 0.955065i −0.998173 0.0604141i \(-0.980758\pi\)
0.446767 0.894651i \(-0.352575\pi\)
\(522\) 416.338 2361.17i 0.0349092 0.197980i
\(523\) −892.891 + 5063.83i −0.0746527 + 0.423377i 0.924461 + 0.381277i \(0.124516\pi\)
−0.999113 + 0.0420993i \(0.986595\pi\)
\(524\) −9.63427 16.6870i −0.000803197 0.00139118i
\(525\) 6759.75 11708.2i 0.561942 0.973312i
\(526\) −295.265 247.757i −0.0244756 0.0205375i
\(527\) −25981.1 9456.34i −2.14754 0.781641i
\(528\) −16137.6 + 5873.61i −1.33011 + 0.484122i
\(529\) −3082.95 + 2586.90i −0.253386 + 0.212616i
\(530\) −295.105 1673.62i −0.0241859 0.137165i
\(531\) −1701.47 −0.139054
\(532\) −846.202 + 117.387i −0.0689615 + 0.00956647i
\(533\) 4730.10 0.384397
\(534\) −120.913 685.733i −0.00979855 0.0555704i
\(535\) −3554.36 + 2982.46i −0.287230 + 0.241015i
\(536\) 3379.25 1229.95i 0.272316 0.0991149i
\(537\) 16372.8 + 5959.23i 1.31572 + 0.478882i
\(538\) 7218.33 + 6056.90i 0.578447 + 0.485375i
\(539\) −4914.46 + 8512.10i −0.392729 + 0.680226i
\(540\) −126.780 219.589i −0.0101032 0.0174993i
\(541\) −3801.70 + 21560.5i −0.302122 + 1.71342i 0.334632 + 0.942349i \(0.391388\pi\)
−0.636753 + 0.771068i \(0.719723\pi\)
\(542\) 1527.84 8664.82i 0.121082 0.686689i
\(543\) 7027.83 + 12172.6i 0.555420 + 0.962016i
\(544\) −965.662 + 1672.57i −0.0761073 + 0.131822i
\(545\) 2199.08 + 1845.25i 0.172841 + 0.145031i
\(546\) 6719.67 + 2445.76i 0.526695 + 0.191701i
\(547\) 16584.9 6036.43i 1.29638 0.471845i 0.400565 0.916268i \(-0.368814\pi\)
0.895817 + 0.444424i \(0.146591\pi\)
\(548\) 701.375 588.523i 0.0546738 0.0458768i
\(549\) −451.612 2561.22i −0.0351080 0.199108i
\(550\) −12384.9 −0.960171
\(551\) −7597.94 + 1054.00i −0.587447 + 0.0814918i
\(552\) −12635.8 −0.974306
\(553\) −5192.22 29446.5i −0.399269 2.26437i
\(554\) 3449.57 2894.53i 0.264546 0.221980i
\(555\) −7170.39 + 2609.81i −0.548408 + 0.199604i
\(556\) 950.230 + 345.855i 0.0724797 + 0.0263805i
\(557\) 5123.81 + 4299.39i 0.389772 + 0.327057i 0.816524 0.577311i \(-0.195898\pi\)
−0.426753 + 0.904368i \(0.640342\pi\)
\(558\) −3679.90 + 6373.78i −0.279181 + 0.483555i
\(559\) 740.150 + 1281.98i 0.0560018 + 0.0969980i
\(560\) −1336.81 + 7581.43i −0.100876 + 0.572097i
\(561\) −4809.93 + 27278.5i −0.361988 + 2.05294i
\(562\) 1638.99 + 2838.82i 0.123019 + 0.213075i
\(563\) −3043.88 + 5272.16i −0.227859 + 0.394663i −0.957173 0.289516i \(-0.906506\pi\)
0.729315 + 0.684178i \(0.239839\pi\)
\(564\) −1001.45 840.314i −0.0747669 0.0627369i
\(565\) −1980.49 720.839i −0.147469 0.0536742i
\(566\) 6243.04 2272.28i 0.463630 0.168748i
\(567\) 16089.0 13500.3i 1.19167 0.999928i
\(568\) −2475.85 14041.2i −0.182895 1.03725i
\(569\) 15509.6 1.14270 0.571350 0.820706i \(-0.306420\pi\)
0.571350 + 0.820706i \(0.306420\pi\)
\(570\) −5010.58 + 5544.88i −0.368193 + 0.407456i
\(571\) −5985.24 −0.438660 −0.219330 0.975651i \(-0.570387\pi\)
−0.219330 + 0.975651i \(0.570387\pi\)
\(572\) 66.1029 + 374.888i 0.00483199 + 0.0274036i
\(573\) −10948.4 + 9186.76i −0.798209 + 0.669777i
\(574\) −15632.4 + 5689.72i −1.13673 + 0.413736i
\(575\) −8091.35 2945.01i −0.586840 0.213592i
\(576\) 3872.36 + 3249.29i 0.280119 + 0.235047i
\(577\) −6754.38 + 11698.9i −0.487328 + 0.844077i −0.999894 0.0145707i \(-0.995362\pi\)
0.512566 + 0.858648i \(0.328695\pi\)
\(578\) −6247.18 10820.4i −0.449565 0.778669i
\(579\) 2864.52 16245.5i 0.205605 1.16605i
\(580\) 38.4292 217.943i 0.00275118 0.0156027i
\(581\) 3617.84 + 6266.28i 0.258336 + 0.447451i
\(582\) 4712.73 8162.69i 0.335651 0.581365i
\(583\) 4109.28 + 3448.10i 0.291919 + 0.244949i
\(584\) 10485.0 + 3816.21i 0.742929 + 0.270404i
\(585\) −883.136 + 321.435i −0.0624157 + 0.0227175i
\(586\) −3743.60 + 3141.26i −0.263903 + 0.221441i
\(587\) 308.492 + 1749.54i 0.0216914 + 0.123018i 0.993731 0.111800i \(-0.0356617\pi\)
−0.972039 + 0.234818i \(0.924551\pi\)
\(588\) 552.078 0.0387200
\(589\) 23023.2 + 4936.67i 1.61062 + 0.345351i
\(590\) 2702.62 0.188585
\(591\) −2280.54 12933.6i −0.158729 0.900198i
\(592\) −10739.0 + 9011.09i −0.745558 + 0.625597i
\(593\) −8376.07 + 3048.64i −0.580040 + 0.211117i −0.615343 0.788259i \(-0.710983\pi\)
0.0353030 + 0.999377i \(0.488760\pi\)
\(594\) −12942.4 4710.66i −0.893998 0.325389i
\(595\) 9511.94 + 7981.46i 0.655381 + 0.549930i
\(596\) −82.2595 + 142.478i −0.00565349 + 0.00979213i
\(597\) 15574.9 + 26976.5i 1.06773 + 1.84937i
\(598\) 790.874 4485.27i 0.0540823 0.306716i
\(599\) 3509.08 19901.0i 0.239361 1.35748i −0.593872 0.804559i \(-0.702402\pi\)
0.833233 0.552922i \(-0.186487\pi\)
\(600\) 6681.15 + 11572.1i 0.454595 + 0.787382i
\(601\) −3014.26 + 5220.85i −0.204583 + 0.354347i −0.950000 0.312251i \(-0.898917\pi\)
0.745417 + 0.666598i \(0.232250\pi\)
\(602\) −3988.16 3346.46i −0.270009 0.226564i
\(603\) −1370.96 498.987i −0.0925864 0.0336987i
\(604\) −204.982 + 74.6074i −0.0138090 + 0.00502605i
\(605\) −3736.91 + 3135.64i −0.251119 + 0.210714i
\(606\) 20.1385 + 114.211i 0.00134995 + 0.00765594i
\(607\) −3058.64 −0.204524 −0.102262 0.994757i \(-0.532608\pi\)
−0.102262 + 0.994757i \(0.532608\pi\)
\(608\) 618.868 1523.92i 0.0412803 0.101650i
\(609\) 13122.3 0.873138
\(610\) 717.339 + 4068.23i 0.0476135 + 0.270029i
\(611\) 6933.55 5817.94i 0.459086 0.385219i
\(612\) 377.979 137.573i 0.0249655 0.00908671i
\(613\) −17448.7 6350.79i −1.14966 0.418444i −0.304270 0.952586i \(-0.598413\pi\)
−0.845395 + 0.534142i \(0.820635\pi\)
\(614\) 13269.8 + 11134.6i 0.872189 + 0.731853i
\(615\) 4228.34 7323.70i 0.277241 0.480196i
\(616\) −12858.3 22271.2i −0.841030 1.45671i
\(617\) 4417.45 25052.6i 0.288233 1.63465i −0.405271 0.914197i \(-0.632823\pi\)
0.693504 0.720453i \(-0.256066\pi\)
\(618\) 2532.83 14364.4i 0.164863 0.934983i
\(619\) −4466.62 7736.41i −0.290030 0.502346i 0.683787 0.729682i \(-0.260332\pi\)
−0.973816 + 0.227336i \(0.926999\pi\)
\(620\) −339.666 + 588.319i −0.0220021 + 0.0381088i
\(621\) −7335.46 6155.18i −0.474012 0.397744i
\(622\) −10732.4 3906.26i −0.691847 0.251812i
\(623\) 925.851 336.982i 0.0595400 0.0216708i
\(624\) −5115.99 + 4292.83i −0.328211 + 0.275402i
\(625\) 939.203 + 5326.49i 0.0601090 + 0.340895i
\(626\) 928.776 0.0592993
\(627\) 865.329 23573.9i 0.0551163 1.50151i
\(628\) −1212.11 −0.0770196
\(629\) 3926.41 + 22267.8i 0.248897 + 1.41156i
\(630\) 2532.00 2124.60i 0.160123 0.134359i
\(631\) 2045.40 744.466i 0.129043 0.0469679i −0.276691 0.960959i \(-0.589238\pi\)
0.405735 + 0.913991i \(0.367016\pi\)
\(632\) 27770.9 + 10107.8i 1.74789 + 0.636180i
\(633\) −16256.4 13640.8i −1.02075 0.856512i
\(634\) 7301.27 12646.2i 0.457367 0.792182i
\(635\) −1554.60 2692.64i −0.0971533 0.168274i
\(636\) 52.3211 296.728i 0.00326205 0.0185000i
\(637\) −663.741 + 3764.26i −0.0412847 + 0.234137i
\(638\) −6010.50 10410.5i −0.372975 0.646012i
\(639\) −2892.19 + 5009.42i −0.179050 + 0.310124i
\(640\) −5488.95 4605.77i −0.339015 0.284467i
\(641\) 15117.7 + 5502.41i 0.931536 + 0.339051i 0.762818 0.646613i \(-0.223815\pi\)
0.168718 + 0.985664i \(0.446037\pi\)
\(642\) 13302.6 4841.76i 0.817777 0.297646i
\(643\) −11391.2 + 9558.35i −0.698639 + 0.586228i −0.921386 0.388648i \(-0.872942\pi\)
0.222747 + 0.974876i \(0.428498\pi\)
\(644\) −161.634 916.670i −0.00989015 0.0560898i
\(645\) 2646.55 0.161562
\(646\) 13603.0 + 17475.2i 0.828486 + 1.06432i
\(647\) −17908.3 −1.08817 −0.544086 0.839029i \(-0.683124\pi\)
−0.544086 + 0.839029i \(0.683124\pi\)
\(648\) 3604.68 + 20443.2i 0.218527 + 1.23933i
\(649\) −6534.97 + 5483.49i −0.395254 + 0.331658i
\(650\) −4525.85 + 1647.28i −0.273105 + 0.0994022i
\(651\) −37851.7 13776.9i −2.27884 0.829430i
\(652\) 1249.79 + 1048.70i 0.0750698 + 0.0629910i
\(653\) −7139.51 + 12366.0i −0.427857 + 0.741070i −0.996682 0.0813882i \(-0.974065\pi\)
0.568825 + 0.822458i \(0.307398\pi\)
\(654\) −4379.26 7585.11i −0.261839 0.453519i
\(655\) 41.4167 234.886i 0.00247067 0.0140118i
\(656\) 2697.88 15300.4i 0.160571 0.910644i
\(657\) −2263.36 3920.25i −0.134402 0.232791i
\(658\) −15916.2 + 27567.7i −0.942977 + 1.63328i
\(659\) 14665.1 + 12305.5i 0.866876 + 0.727395i 0.963438 0.267932i \(-0.0863402\pi\)
−0.0965620 + 0.995327i \(0.530785\pi\)
\(660\) 639.537 + 232.772i 0.0377181 + 0.0137283i
\(661\) 2596.82 945.165i 0.152806 0.0556167i −0.264485 0.964390i \(-0.585202\pi\)
0.417291 + 0.908773i \(0.362980\pi\)
\(662\) 11776.6 9881.77i 0.691408 0.580160i
\(663\) 1870.51 + 10608.2i 0.109570 + 0.621401i
\(664\) −7151.56 −0.417973
\(665\) −8957.88 5619.75i −0.522363 0.327706i
\(666\) 6018.94 0.350194
\(667\) −1451.29 8230.67i −0.0842491 0.477800i
\(668\) −503.788 + 422.729i −0.0291799 + 0.0244848i
\(669\) 11997.7 4366.82i 0.693362 0.252363i
\(670\) 2177.62 + 792.590i 0.125566 + 0.0457021i
\(671\) −9988.81 8381.61i −0.574685 0.482218i
\(672\) −1406.87 + 2436.77i −0.0807605 + 0.139881i
\(673\) 10446.1 + 18093.1i 0.598315 + 1.03631i 0.993070 + 0.117526i \(0.0374964\pi\)
−0.394754 + 0.918787i \(0.629170\pi\)
\(674\) −4192.83 + 23778.7i −0.239617 + 1.35893i
\(675\) −1758.41 + 9972.46i −0.100269 + 0.568652i
\(676\) −408.612 707.737i −0.0232483 0.0402672i
\(677\) 12848.3 22253.9i 0.729395 1.26335i −0.227745 0.973721i \(-0.573135\pi\)
0.957139 0.289628i \(-0.0935315\pi\)
\(678\) 4925.89 + 4133.31i 0.279023 + 0.234128i
\(679\) 12532.6 + 4561.48i 0.708330 + 0.257811i
\(680\) −11532.5 + 4197.47i −0.650367 + 0.236714i
\(681\) 5812.42 4877.20i 0.327067 0.274442i
\(682\) 6407.69 + 36339.8i 0.359770 + 2.04036i
\(683\) 26695.9 1.49559 0.747796 0.663929i \(-0.231112\pi\)
0.747796 + 0.663929i \(0.231112\pi\)
\(684\) −302.749 + 160.282i −0.0169238 + 0.00895987i
\(685\) 11333.2 0.632146
\(686\) 1510.78 + 8568.05i 0.0840843 + 0.476866i
\(687\) −8428.16 + 7072.06i −0.468056 + 0.392745i
\(688\) 4568.96 1662.97i 0.253183 0.0921512i
\(689\) 1960.29 + 713.486i 0.108390 + 0.0394509i
\(690\) −6237.64 5234.00i −0.344149 0.288775i
\(691\) 16838.1 29164.4i 0.926991 1.60560i 0.138664 0.990340i \(-0.455719\pi\)
0.788327 0.615256i \(-0.210947\pi\)
\(692\) 124.477 + 215.601i 0.00683803 + 0.0118438i
\(693\) −1811.70 + 10274.7i −0.0993084 + 0.563206i
\(694\) −692.818 + 3929.16i −0.0378948 + 0.214912i
\(695\) 6258.49 + 10840.0i 0.341580 + 0.591634i
\(696\) −6484.85 + 11232.1i −0.353172 + 0.611711i
\(697\) −19196.5 16107.8i −1.04321 0.875359i
\(698\) 17524.4 + 6378.38i 0.950301 + 0.345881i
\(699\) −38899.6 + 14158.3i −2.10489 + 0.766116i
\(700\) −754.037 + 632.712i −0.0407142 + 0.0341633i
\(701\) −2244.79 12730.8i −0.120948 0.685930i −0.983632 0.180187i \(-0.942330\pi\)
0.862684 0.505743i \(-0.168782\pi\)
\(702\) −5356.15 −0.287970
\(703\) −5917.93 18324.7i −0.317495 0.983114i
\(704\) 25344.7 1.35684
\(705\) −2809.97 15936.1i −0.150113 0.851332i
\(706\) 21717.3 18223.0i 1.15771 0.971431i
\(707\) −154.203 + 56.1254i −0.00820284 + 0.00298559i
\(708\) 450.267 + 163.884i 0.0239012 + 0.00869934i
\(709\) −11565.1 9704.25i −0.612603 0.514035i 0.282866 0.959160i \(-0.408715\pi\)
−0.895469 + 0.445125i \(0.853159\pi\)
\(710\) 4593.95 7956.96i 0.242828 0.420590i
\(711\) −5994.83 10383.3i −0.316208 0.547688i
\(712\) −169.101 + 959.020i −0.00890075 + 0.0504787i
\(713\) −4454.97 + 25265.4i −0.233997 + 1.32706i
\(714\) −18942.1 32808.8i −0.992846 1.71966i
\(715\) −2356.01 + 4080.73i −0.123230 + 0.213441i
\(716\) −971.786 815.425i −0.0507226 0.0425613i
\(717\) 22295.6 + 8114.95i 1.16129 + 0.422675i
\(718\) −27719.3 + 10089.0i −1.44077 + 0.524398i
\(719\) −8869.03 + 7442.00i −0.460027 + 0.386008i −0.843141 0.537693i \(-0.819296\pi\)
0.383114 + 0.923701i \(0.374852\pi\)
\(720\) 536.036 + 3040.01i 0.0277457 + 0.157354i
\(721\) 20638.9 1.06607
\(722\) −13519.9 13149.5i −0.696894 0.677805i
\(723\) −16398.8 −0.843536
\(724\) −177.705 1007.82i −0.00912205 0.0517337i
\(725\) −6770.41 + 5681.05i −0.346823 + 0.291019i
\(726\) 13985.9 5090.43i 0.714964 0.260225i
\(727\) 3836.36 + 1396.32i 0.195712 + 0.0712334i 0.438017 0.898967i \(-0.355681\pi\)
−0.242305 + 0.970200i \(0.577903\pi\)
\(728\) −7661.06 6428.39i −0.390024 0.327269i
\(729\) −4434.14 + 7680.15i −0.225278 + 0.390192i
\(730\) 3595.12 + 6226.93i 0.182276 + 0.315711i
\(731\) 1361.81 7723.22i 0.0689035 0.390771i
\(732\) −127.182 + 721.284i −0.00642182 + 0.0364200i
\(733\) −17806.4 30841.6i −0.897263 1.55411i −0.830978 0.556305i \(-0.812219\pi\)
−0.0662848 0.997801i \(-0.521115\pi\)
\(734\) −5051.08 + 8748.74i −0.254004 + 0.439948i
\(735\) 5234.94 + 4392.63i 0.262712 + 0.220442i
\(736\) 1684.01 + 612.928i 0.0843387 + 0.0306968i
\(737\) −6873.66 + 2501.81i −0.343548 + 0.125041i
\(738\) −5109.95 + 4287.76i −0.254878 + 0.213868i
\(739\) 505.438 + 2866.48i 0.0251594 + 0.142686i 0.994800 0.101849i \(-0.0324758\pi\)
−0.969640 + 0.244535i \(0.921365\pi\)
\(740\) 555.566 0.0275987
\(741\) −2819.27 8729.77i −0.139768 0.432788i
\(742\) −7336.73 −0.362991
\(743\) 6796.69 + 38546.0i 0.335594 + 1.90325i 0.421287 + 0.906927i \(0.361578\pi\)
−0.0856930 + 0.996322i \(0.527310\pi\)
\(744\) 30498.2 25591.1i 1.50285 1.26104i
\(745\) −1913.63 + 696.505i −0.0941075 + 0.0342523i
\(746\) −6996.27 2546.44i −0.343367 0.124975i
\(747\) 2222.58 + 1864.97i 0.108862 + 0.0913461i
\(748\) 1008.36 1746.54i 0.0492907 0.0853740i
\(749\) 10015.5 + 17347.4i 0.488597 + 0.846274i
\(750\) −3453.95 + 19588.3i −0.168161 + 0.953686i
\(751\) 3986.93 22611.0i 0.193722 1.09865i −0.720505 0.693449i \(-0.756090\pi\)
0.914227 0.405202i \(-0.132799\pi\)
\(752\) −14864.6 25746.3i −0.720820 1.24850i
\(753\) 9720.49 16836.4i 0.470431 0.814810i
\(754\) −3581.10 3004.90i −0.172966 0.145135i
\(755\) −2537.31 923.504i −0.122307 0.0445162i
\(756\) −1028.64 + 374.394i −0.0494857 + 0.0180113i
\(757\) 7376.48 6189.60i 0.354165 0.297180i −0.448295 0.893886i \(-0.647969\pi\)
0.802460 + 0.596706i \(0.203524\pi\)
\(758\) −5774.66 32749.7i −0.276709 1.56929i
\(759\) 25702.3 1.22916
\(760\) 9237.12 4890.35i 0.440876 0.233410i
\(761\) 18187.4 0.866350 0.433175 0.901310i \(-0.357393\pi\)
0.433175 + 0.901310i \(0.357393\pi\)
\(762\) 1647.26 + 9342.09i 0.0783123 + 0.444131i
\(763\) 9493.73 7966.18i 0.450454 0.377975i
\(764\) 977.820 355.897i 0.0463040 0.0168533i
\(765\) 4678.70 + 1702.91i 0.221122 + 0.0804820i
\(766\) −11107.3 9320.09i −0.523918 0.439620i
\(767\) −1658.75 + 2873.05i −0.0780888 + 0.135254i
\(768\) −2029.91 3515.91i −0.0953751 0.165194i
\(769\) −2426.76 + 13762.9i −0.113799 + 0.645385i 0.873539 + 0.486754i \(0.161819\pi\)
−0.987338 + 0.158631i \(0.949292\pi\)
\(770\) 2877.70 16320.2i 0.134682 0.763819i
\(771\) 21174.0 + 36674.4i 0.989057 + 1.71310i
\(772\) −600.524 + 1040.14i −0.0279965 + 0.0484914i
\(773\) −15491.5 12998.9i −0.720816 0.604837i 0.206795 0.978384i \(-0.433697\pi\)
−0.927611 + 0.373548i \(0.878141\pi\)
\(774\) −1961.68 713.993i −0.0910996 0.0331576i
\(775\) 25494.0 9279.05i 1.18164 0.430082i
\(776\) −10097.9 + 8473.11i −0.467129 + 0.391968i
\(777\) 5720.36 + 32441.8i 0.264114 + 1.49787i
\(778\) −18319.8 −0.844211
\(779\) 18078.3 + 11341.5i 0.831480 + 0.521631i
\(780\) 264.668 0.0121495
\(781\) 5036.07 + 28561.0i 0.230736 + 1.30857i
\(782\) −18483.7 + 15509.6i −0.845236 + 0.709237i
\(783\) −9236.02 + 3361.64i −0.421543 + 0.153429i
\(784\) 11797.7 + 4294.00i 0.537430 + 0.195608i
\(785\) −11493.5 9644.17i −0.522573 0.438491i
\(786\) −363.848 + 630.203i −0.0165115 + 0.0285987i
\(787\) 3258.28 + 5643.50i 0.147579 + 0.255615i 0.930332 0.366718i \(-0.119518\pi\)
−0.782753 + 0.622333i \(0.786185\pi\)
\(788\) −166.041 + 941.667i −0.00750632 + 0.0425705i
\(789\) 146.888 833.041i 0.00662781 0.0375882i
\(790\) 9522.18 + 16492.9i 0.428840 + 0.742774i
\(791\) −4549.38 + 7879.76i −0.204497 + 0.354200i
\(792\) −7899.34 6628.33i −0.354407 0.297383i
\(793\) −4765.05 1734.34i −0.213382 0.0776647i
\(794\) −16809.7 + 6118.24i −0.751329 + 0.273461i
\(795\) 2857.05 2397.35i 0.127458 0.106950i
\(796\) −393.825 2233.49i −0.0175361 0.0994524i
\(797\) −21628.0 −0.961235 −0.480618 0.876930i \(-0.659587\pi\)
−0.480618 + 0.876930i \(0.659587\pi\)
\(798\) 19818.1 + 25459.5i 0.879140 + 1.12940i
\(799\) −47951.1 −2.12314
\(800\) −329.083 1866.32i −0.0145436 0.0824806i
\(801\) 302.645 253.949i 0.0133501 0.0112021i
\(802\) 8835.07 3215.70i 0.388999 0.141584i
\(803\) −21327.2 7762.48i −0.937262 0.341136i
\(804\) 314.740 + 264.098i 0.0138060 + 0.0115846i
\(805\) 5760.87 9978.12i 0.252229 0.436873i
\(806\) 7175.03 + 12427.5i 0.313560 + 0.543102i
\(807\) −3590.96 + 20365.3i −0.156639 + 0.888344i
\(808\) 28.1643 159.728i 0.00122626 0.00695446i
\(809\) −11239.6 19467.5i −0.488459 0.846035i 0.511453 0.859311i \(-0.329107\pi\)
−0.999912 + 0.0132758i \(0.995774\pi\)
\(810\) −6688.51 + 11584.8i −0.290136 + 0.502531i
\(811\) 320.403 + 268.850i 0.0138728 + 0.0116407i 0.649698 0.760193i \(-0.274895\pi\)
−0.635825 + 0.771833i \(0.719340\pi\)
\(812\) −897.786 326.768i −0.0388007 0.0141223i
\(813\) 18144.7 6604.14i 0.782735 0.284892i
\(814\) 23117.4 19397.8i 0.995411 0.835249i
\(815\) 3506.79 + 19888.0i 0.150721 + 0.854780i
\(816\) 35381.2 1.51788
\(817\) −244.996 + 6674.36i −0.0104912 + 0.285809i
\(818\) 3646.04 0.155844
\(819\) 704.544 + 3995.67i 0.0300595 + 0.170476i
\(820\) −471.664 + 395.773i −0.0200868 + 0.0168549i
\(821\) −35130.4 + 12786.4i −1.49338 + 0.543544i −0.954336 0.298737i \(-0.903435\pi\)
−0.539039 + 0.842281i \(0.681213\pi\)
\(822\) −32492.5 11826.3i −1.37872 0.501812i
\(823\) 10803.6 + 9065.33i 0.457583 + 0.383958i 0.842241 0.539101i \(-0.181236\pi\)
−0.384658 + 0.923059i \(0.625680\pi\)
\(824\) −10199.5 + 17666.0i −0.431208 + 0.746875i
\(825\) −13590.0 23538.6i −0.573507 0.993343i
\(826\) 2026.05 11490.3i 0.0853455 0.484018i
\(827\) 7514.64 42617.7i 0.315973 1.79197i −0.250737 0.968055i \(-0.580673\pi\)
0.566710 0.823917i \(-0.308216\pi\)
\(828\) −186.619 323.233i −0.00783267 0.0135666i
\(829\) −13342.5 + 23109.9i −0.558993 + 0.968204i 0.438588 + 0.898688i \(0.355479\pi\)
−0.997581 + 0.0695155i \(0.977855\pi\)
\(830\) −3530.34 2962.31i −0.147639 0.123883i
\(831\) 9286.54 + 3380.02i 0.387661 + 0.141097i
\(832\) 9261.78 3371.01i 0.385931 0.140467i
\(833\) 15512.4 13016.5i 0.645226 0.541409i
\(834\) −6631.53 37609.3i −0.275337 1.56151i
\(835\) −8140.50 −0.337381
\(836\) −646.234 + 1591.31i −0.0267350 + 0.0658331i
\(837\) 30171.0 1.24595
\(838\) −1172.35 6648.73i −0.0483272 0.274077i
\(839\) 23549.6 19760.5i 0.969039 0.813120i −0.0133609 0.999911i \(-0.504253\pi\)
0.982400 + 0.186791i \(0.0598086\pi\)
\(840\) −16801.6 + 6115.28i −0.690131 + 0.251187i
\(841\) 14857.0 + 5407.52i 0.609170 + 0.221720i
\(842\) −1967.22 1650.69i −0.0805166 0.0675614i
\(843\) −3596.94 + 6230.09i −0.146958 + 0.254538i
\(844\) 772.538 + 1338.08i 0.0315069 + 0.0545716i
\(845\) 1756.58 9962.06i 0.0715127 0.405568i
\(846\) −2216.48 + 12570.3i −0.0900759 + 0.510846i
\(847\) 10529.9 + 18238.3i 0.427169 + 0.739878i
\(848\) 3425.99 5933.99i 0.138737 0.240299i
\(849\) 11169.2 + 9372.05i 0.451502 + 0.378855i
\(850\) 23977.1 + 8726.97i 0.967540 + 0.352156i
\(851\) 19715.8 7175.95i 0.794181 0.289058i
\(852\) 1247.87 1047.09i 0.0501777 0.0421041i
\(853\) −1637.01 9283.93i −0.0657093 0.372656i −0.999875 0.0158164i \(-0.994965\pi\)
0.934166 0.356840i \(-0.116146\pi\)
\(854\) 17834.1 0.714601
\(855\) −4146.03 889.000i −0.165838 0.0355592i
\(856\) −19798.1 −0.790521
\(857\) −6156.15 34913.3i −0.245379 1.39162i −0.819610 0.572922i \(-0.805810\pi\)
0.574230 0.818694i \(-0.305301\pi\)
\(858\) 11013.0 9240.99i 0.438202 0.367695i
\(859\) −2974.86 + 1082.76i −0.118162 + 0.0430074i −0.400424 0.916330i \(-0.631137\pi\)
0.282263 + 0.959337i \(0.408915\pi\)
\(860\) −181.069 65.9037i −0.00717953 0.00261314i
\(861\) −27967.3 23467.3i −1.10699 0.928878i
\(862\) −1448.98 + 2509.71i −0.0572535 + 0.0991660i
\(863\) 8473.77 + 14677.0i 0.334241 + 0.578923i 0.983339 0.181782i \(-0.0581866\pi\)
−0.649097 + 0.760705i \(0.724853\pi\)
\(864\) 365.968 2075.51i 0.0144103 0.0817249i
\(865\) −535.115 + 3034.79i −0.0210340 + 0.119290i
\(866\) 12582.7 + 21794.0i 0.493740 + 0.855183i
\(867\) 13710.1 23746.6i 0.537047 0.930193i
\(868\) 2246.63 + 1885.15i 0.0878522 + 0.0737167i
\(869\) −56488.2 20560.0i −2.20510 0.802590i
\(870\) −7853.77 + 2858.54i −0.306055 + 0.111395i
\(871\) −2179.11 + 1828.49i −0.0847718 + 0.0711320i
\(872\) 2127.03 + 12063.0i 0.0826037 + 0.468469i
\(873\) 5347.84 0.207327
\(874\) 13777.1 15246.3i 0.533202 0.590060i
\(875\) −28144.8 −1.08739
\(876\) 221.367 + 1255.44i 0.00853803 + 0.0484216i
\(877\) −13543.5 + 11364.3i −0.521472 + 0.437567i −0.865145 0.501522i \(-0.832774\pi\)
0.343672 + 0.939090i \(0.388329\pi\)
\(878\) −4191.03 + 1525.41i −0.161094 + 0.0586334i
\(879\) −10078.1 3668.13i −0.386719 0.140754i
\(880\) 11856.1 + 9948.47i 0.454170 + 0.381094i
\(881\) −13438.4 + 23276.0i −0.513907 + 0.890113i 0.485963 + 0.873980i \(0.338469\pi\)
−0.999870 + 0.0161337i \(0.994864\pi\)
\(882\) −2695.20 4668.22i −0.102893 0.178217i
\(883\) −6839.72 + 38790.0i −0.260674 + 1.47835i 0.520403 + 0.853921i \(0.325782\pi\)
−0.781077 + 0.624434i \(0.785330\pi\)
\(884\) 136.188 772.362i 0.00518157 0.0293861i
\(885\) 2965.59 + 5136.56i 0.112641 + 0.195100i
\(886\) 14319.5 24802.2i 0.542973 0.940457i
\(887\) 12259.4 + 10286.9i 0.464072 + 0.389402i 0.844627 0.535356i \(-0.179823\pi\)
−0.380555 + 0.924758i \(0.624267\pi\)
\(888\) −30595.7 11135.9i −1.15622 0.420830i
\(889\) −12613.3 + 4590.88i −0.475858 + 0.173198i
\(890\) −480.721 + 403.373i −0.0181054 + 0.0151922i
\(891\) −7332.21 41583.0i −0.275688 1.56351i
\(892\) −929.591 −0.0348935
\(893\) 40449.6 5611.25i 1.51578 0.210272i
\(894\) 6213.22 0.232440
\(895\) −2726.74 15464.1i −0.101838 0.577551i
\(896\) −23696.5 + 19883.8i −0.883533 + 0.741372i
\(897\) 9392.47 3418.58i 0.349616 0.127250i
\(898\) 34507.8 + 12559.8i 1.28234 + 0.466734i
\(899\) 20172.2 + 16926.5i 0.748367 + 0.627955i
\(900\) −197.348 + 341.817i −0.00730919 + 0.0126599i
\(901\) −5525.87 9571.10i −0.204321 0.353895i
\(902\) −5807.62 + 32936.7i −0.214382 + 1.21582i
\(903\) 1984.02 11251.9i 0.0731163 0.414663i
\(904\) −4496.49 7788.15i −0.165433 0.286538i
\(905\) 6333.69 10970.3i 0.232640 0.402944i
\(906\) 6310.81 + 5295.40i 0.231416 + 0.194181i
\(907\) −3270.13 1190.23i −0.119717 0.0435733i 0.281467 0.959571i \(-0.409179\pi\)
−0.401184 + 0.915998i \(0.631401\pi\)
\(908\) −519.120 + 188.944i −0.0189731 + 0.00690565i
\(909\) −50.4064 + 42.2960i −0.00183925 + 0.00154331i
\(910\) −1119.10 6346.71i −0.0407667 0.231199i
\(911\) −18185.1 −0.661359 −0.330680 0.943743i \(-0.607278\pi\)
−0.330680 + 0.943743i \(0.607278\pi\)
\(912\) −29846.2 + 4140.32i −1.08367 + 0.150329i
\(913\) 14546.8 0.527305
\(914\) −8389.70 47580.3i −0.303618 1.72190i
\(915\) −6944.89 + 5827.45i −0.250919 + 0.210546i
\(916\) 752.737 273.974i 0.0271519 0.00988247i
\(917\) −967.581 352.171i −0.0348444 0.0126823i
\(918\) 21737.2 + 18239.7i 0.781519 + 0.655772i
\(919\) −8934.27 + 15474.6i −0.320690 + 0.555452i −0.980631 0.195866i \(-0.937248\pi\)
0.659940 + 0.751318i \(0.270582\pi\)
\(920\) 5693.89 + 9862.11i 0.204046 + 0.353418i
\(921\) −6601.40 + 37438.4i −0.236182 + 1.33945i
\(922\) −4968.00 + 28174.9i −0.177454 + 1.00639i
\(923\) 5639.15 + 9767.30i 0.201100 + 0.348315i
\(924\) 1469.08 2544.52i 0.0523043 0.0905937i
\(925\) −16996.5 14261.8i −0.604153 0.506944i
\(926\) −10401.8 3785.93i −0.369139 0.134356i
\(927\) 7776.72 2830.49i 0.275535 0.100287i
\(928\) 1409.09 1182.36i 0.0498443 0.0418244i
\(929\) 2814.85 + 15963.8i 0.0994105 + 0.563785i 0.993306 + 0.115510i \(0.0368503\pi\)
−0.893896 + 0.448275i \(0.852039\pi\)
\(930\) 25655.7 0.904604
\(931\) −11562.4 + 12795.4i −0.407029 + 0.450433i
\(932\) 3013.96 0.105929
\(933\) −4352.48 24684.2i −0.152727 0.866156i
\(934\) −14054.2 + 11792.9i −0.492365 + 0.413143i
\(935\) 23457.9 8537.99i 0.820488 0.298633i
\(936\) −3768.29 1371.55i −0.131592 0.0478957i
\(937\) 14567.9 + 12223.9i 0.507910 + 0.426187i 0.860393 0.509631i \(-0.170218\pi\)
−0.352483 + 0.935818i \(0.614662\pi\)
\(938\) 5002.22 8664.10i 0.174124 0.301592i
\(939\) 1019.15 + 1765.22i 0.0354193 + 0.0613479i
\(940\) −204.588 + 1160.27i −0.00709885 + 0.0402596i
\(941\) −6801.96 + 38575.8i −0.235640 + 1.33638i 0.605620 + 0.795754i \(0.292925\pi\)
−0.841261 + 0.540630i \(0.818186\pi\)
\(942\) 22888.2 + 39643.5i 0.791654 + 1.37118i
\(943\) −11626.3 + 20137.3i −0.401489 + 0.695399i
\(944\) 8347.34 + 7004.25i 0.287799 + 0.241492i
\(945\) −12732.7 4634.31i −0.438300 0.159528i
\(946\) −9835.43 + 3579.80i −0.338031 + 0.123033i
\(947\) 36536.0 30657.4i 1.25371 1.05199i 0.257385 0.966309i \(-0.417139\pi\)
0.996323 0.0856775i \(-0.0273055\pi\)
\(948\) 586.323 + 3325.20i 0.0200874 + 0.113921i
\(949\) −8826.14 −0.301906
\(950\) −21247.4 4555.90i −0.725638 0.155593i
\(951\) 32046.8 1.09273
\(952\) 9200.31 + 52177.5i 0.313218 + 1.77635i
\(953\) 8730.52 7325.78i 0.296757 0.249009i −0.482236 0.876041i \(-0.660175\pi\)
0.778993 + 0.627033i \(0.215731\pi\)
\(954\) −2764.47 + 1006.19i −0.0938187 + 0.0341472i
\(955\) 12103.6 + 4405.36i 0.410120 + 0.149271i
\(956\) −1323.32 1110.40i −0.0447692 0.0375658i
\(957\) 13190.7 22847.0i 0.445553 0.771721i
\(958\) −8008.58 13871.3i −0.270089 0.467808i
\(959\) 8496.09 48183.7i 0.286082 1.62245i
\(960\) 3059.91 17353.6i 0.102873 0.583422i
\(961\) −25521.2 44204.0i −0.856675 1.48381i
\(962\) 5867.83 10163.4i 0.196659 0.340624i
\(963\) 6152.92 + 5162.91i 0.205893 + 0.172765i
\(964\) 1121.95 + 408.358i 0.0374852 + 0.0136435i
\(965\) −13970.2 + 5084.74i −0.466028 + 0.169620i
\(966\) −26928.8 + 22595.9i −0.896914 + 0.752600i
\(967\) −1305.96 7406.47i −0.0434300 0.246304i 0.955362 0.295437i \(-0.0954653\pi\)
−0.998792 + 0.0491331i \(0.984354\pi\)
\(968\) −20815.0 −0.691135
\(969\) −18286.5 + 45029.2i −0.606241 + 1.49283i
\(970\) −8494.50 −0.281177
\(971\) 84.9728 + 481.905i 0.00280835 + 0.0159269i 0.986180 0.165679i \(-0.0529816\pi\)
−0.983371 + 0.181606i \(0.941870\pi\)
\(972\) −852.495 + 715.328i −0.0281315 + 0.0236051i
\(973\) 50778.7 18481.9i 1.67306 0.608945i
\(974\) −7418.70 2700.19i −0.244056 0.0888291i
\(975\) −8097.02 6794.21i −0.265961 0.223168i
\(976\) −8327.87 + 14424.3i −0.273124 + 0.473064i
\(977\) −8975.95 15546.8i −0.293926 0.509096i 0.680808 0.732462i \(-0.261629\pi\)
−0.974735 + 0.223366i \(0.928295\pi\)
\(978\) 10699.3 60678.5i 0.349821 1.98393i
\(979\) 343.965 1950.72i 0.0112290 0.0636827i
\(980\) −248.775 430.890i −0.00810899 0.0140452i
\(981\) 2484.72 4303.65i 0.0808674 0.140066i
\(982\) −23844.9 20008.2i −0.774868 0.650192i
\(983\) 17320.0 + 6303.96i 0.561976 + 0.204542i 0.607359 0.794427i \(-0.292229\pi\)
−0.0453837 + 0.998970i \(0.514451\pi\)
\(984\) 33908.1 12341.5i 1.09853 0.399831i
\(985\) −9066.86 + 7608.00i −0.293294 + 0.246102i
\(986\) 4300.61 + 24390.0i 0.138904 + 0.787764i
\(987\) −69859.7 −2.25295
\(988\) −24.5009 + 667.470i −0.000788944 + 0.0214930i
\(989\) −7276.96 −0.233968
\(990\) −1153.90 6544.11i −0.0370439 0.210086i
\(991\) 10549.6 8852.13i 0.338161 0.283751i −0.457854 0.889027i \(-0.651382\pi\)
0.796015 + 0.605276i \(0.206937\pi\)
\(992\) −5305.92 + 1931.20i −0.169822 + 0.0618100i
\(993\) 31703.7 + 11539.2i 1.01318 + 0.368767i
\(994\) −30385.5 25496.4i −0.969587 0.813580i
\(995\) 14036.5 24312.0i 0.447224 0.774616i
\(996\) −408.539 707.610i −0.0129970 0.0225115i
\(997\) 6089.47 34535.1i 0.193436 1.09703i −0.721193 0.692734i \(-0.756406\pi\)
0.914629 0.404295i \(-0.132483\pi\)
\(998\) −357.158 + 2025.54i −0.0113283 + 0.0642460i
\(999\) −12337.1 21368.5i −0.390720 0.676746i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 19.4.e.a.9.3 24
3.2 odd 2 171.4.u.b.28.2 24
19.6 even 9 361.4.a.n.1.9 12
19.13 odd 18 361.4.a.m.1.4 12
19.17 even 9 inner 19.4.e.a.17.3 yes 24
57.17 odd 18 171.4.u.b.55.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
19.4.e.a.9.3 24 1.1 even 1 trivial
19.4.e.a.17.3 yes 24 19.17 even 9 inner
171.4.u.b.28.2 24 3.2 odd 2
171.4.u.b.55.2 24 57.17 odd 18
361.4.a.m.1.4 12 19.13 odd 18
361.4.a.n.1.9 12 19.6 even 9