Properties

Label 21.4.g.a.17.3
Level $21$
Weight $4$
Character 21.17
Analytic conductor $1.239$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [21,4,Mod(5,21)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(21, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 21.g (of order \(6\), 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: \(1.23904011012\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.3
Root \(-2.23014 - 2.00661i\) of defining polynomial
Character \(\chi\) \(=\) 21.17
Dual form 21.4.g.a.5.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.65310 + 0.954416i) q^{2} +(-3.47555 + 3.86271i) q^{3} +(-2.17818 + 3.77272i) q^{4} +(0.623706 + 1.08029i) q^{5} +(2.05878 - 9.70256i) q^{6} +(10.0808 + 15.5363i) q^{7} -23.5862i q^{8} +(-2.84113 - 26.8501i) q^{9} +O(q^{10})\) \(q+(-1.65310 + 0.954416i) q^{2} +(-3.47555 + 3.86271i) q^{3} +(-2.17818 + 3.77272i) q^{4} +(0.623706 + 1.08029i) q^{5} +(2.05878 - 9.70256i) q^{6} +(10.0808 + 15.5363i) q^{7} -23.5862i q^{8} +(-2.84113 - 26.8501i) q^{9} +(-2.06209 - 1.19055i) q^{10} +(35.2392 + 20.3453i) q^{11} +(-7.00257 - 21.5260i) q^{12} +19.5973i q^{13} +(-31.4927 - 16.0617i) q^{14} +(-6.34057 - 1.34540i) q^{15} +(5.08559 + 8.80850i) q^{16} +(-52.3592 + 90.6889i) q^{17} +(30.3228 + 41.6742i) q^{18} +(35.0345 - 20.2272i) q^{19} -5.43418 q^{20} +(-95.0487 - 15.0578i) q^{21} -77.6716 q^{22} +(69.6324 - 40.2023i) q^{23} +(91.1068 + 81.9750i) q^{24} +(61.7220 - 106.906i) q^{25} +(-18.7040 - 32.3962i) q^{26} +(113.589 + 82.3444i) q^{27} +(-80.5720 + 4.19132i) q^{28} -211.712i q^{29} +(11.7656 - 3.82746i) q^{30} +(-86.6242 - 50.0125i) q^{31} +(146.596 + 84.6373i) q^{32} +(-201.064 + 65.4076i) q^{33} -199.890i q^{34} +(-10.4962 + 20.5803i) q^{35} +(107.486 + 47.7656i) q^{36} +(94.9875 + 164.523i) q^{37} +(-38.6103 + 66.8750i) q^{38} +(-75.6987 - 68.1113i) q^{39} +(25.4799 - 14.7109i) q^{40} -186.753 q^{41} +(171.496 - 65.8241i) q^{42} +158.618 q^{43} +(-153.515 + 88.6317i) q^{44} +(27.2339 - 19.8158i) q^{45} +(-76.7393 + 132.916i) q^{46} +(179.034 + 310.097i) q^{47} +(-51.6999 - 10.9702i) q^{48} +(-139.753 + 313.238i) q^{49} +235.634i q^{50} +(-168.328 - 517.442i) q^{51} +(-73.9351 - 42.6865i) q^{52} +(-366.460 - 211.576i) q^{53} +(-266.364 - 27.7123i) q^{54} +50.7580i q^{55} +(366.442 - 237.769i) q^{56} +(-43.6323 + 205.629i) q^{57} +(202.061 + 349.980i) q^{58} +(312.781 - 541.753i) q^{59} +(18.8867 - 20.9907i) q^{60} +(699.575 - 403.900i) q^{61} +190.931 q^{62} +(388.510 - 314.812i) q^{63} -404.486 q^{64} +(-21.1708 + 12.2229i) q^{65} +(269.952 - 300.023i) q^{66} +(-149.272 + 258.547i) q^{67} +(-228.096 - 395.074i) q^{68} +(-86.7208 + 408.695i) q^{69} +(-2.29089 - 44.0390i) q^{70} +455.386i q^{71} +(-633.292 + 67.0114i) q^{72} +(-434.467 - 250.840i) q^{73} +(-314.047 - 181.315i) q^{74} +(198.428 + 609.970i) q^{75} +176.234i q^{76} +(39.1491 + 752.584i) q^{77} +(190.144 + 40.3465i) q^{78} +(30.9561 + 53.6176i) q^{79} +(-6.34382 + 10.9878i) q^{80} +(-712.856 + 152.569i) q^{81} +(308.720 - 178.240i) q^{82} -73.1180 q^{83} +(263.842 - 325.794i) q^{84} -130.627 q^{85} +(-262.211 + 151.388i) q^{86} +(817.783 + 735.816i) q^{87} +(479.870 - 831.158i) q^{88} +(57.3723 + 99.3717i) q^{89} +(-26.1077 + 58.7498i) q^{90} +(-304.469 + 197.557i) q^{91} +350.271i q^{92} +(494.251 - 160.784i) q^{93} +(-591.922 - 341.746i) q^{94} +(43.7025 + 25.2316i) q^{95} +(-836.432 + 272.098i) q^{96} -1416.51i q^{97} +(-67.9336 - 651.195i) q^{98} +(446.156 - 1003.98i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{3} + 14 q^{4} - 56 q^{7} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{3} + 14 q^{4} - 56 q^{7} - 3 q^{9} + 30 q^{10} - 192 q^{12} + 6 q^{15} + 134 q^{16} + 66 q^{18} + 300 q^{19} + 357 q^{21} - 268 q^{22} + 414 q^{24} - 42 q^{25} - 602 q^{28} - 822 q^{30} - 930 q^{31} - 855 q^{33} + 852 q^{36} + 764 q^{37} - 426 q^{39} + 2298 q^{40} + 966 q^{42} - 1012 q^{43} + 2367 q^{45} + 608 q^{46} - 336 q^{49} - 1341 q^{51} - 3000 q^{52} - 4158 q^{54} + 270 q^{57} + 2870 q^{58} - 918 q^{60} + 2358 q^{61} + 1071 q^{63} - 548 q^{64} + 2934 q^{66} + 792 q^{67} - 4242 q^{70} - 2712 q^{72} - 2904 q^{73} - 2418 q^{75} + 4296 q^{78} + 1674 q^{79} + 837 q^{81} + 5040 q^{82} + 3864 q^{84} + 348 q^{85} + 1638 q^{87} - 554 q^{88} - 1218 q^{91} - 1479 q^{93} - 1356 q^{94} - 4410 q^{96} - 3354 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.65310 + 0.954416i −0.584458 + 0.337437i −0.762903 0.646513i \(-0.776227\pi\)
0.178445 + 0.983950i \(0.442893\pi\)
\(3\) −3.47555 + 3.86271i −0.668870 + 0.743380i
\(4\) −2.17818 + 3.77272i −0.272273 + 0.471590i
\(5\) 0.623706 + 1.08029i 0.0557859 + 0.0966240i 0.892570 0.450909i \(-0.148900\pi\)
−0.836784 + 0.547533i \(0.815567\pi\)
\(6\) 2.05878 9.70256i 0.140082 0.660175i
\(7\) 10.0808 + 15.5363i 0.544314 + 0.838881i
\(8\) 23.5862i 1.04237i
\(9\) −2.84113 26.8501i −0.105227 0.994448i
\(10\) −2.06209 1.19055i −0.0652090 0.0376484i
\(11\) 35.2392 + 20.3453i 0.965910 + 0.557668i 0.897987 0.440022i \(-0.145029\pi\)
0.0679230 + 0.997691i \(0.478363\pi\)
\(12\) −7.00257 21.5260i −0.168456 0.517834i
\(13\) 19.5973i 0.418101i 0.977905 + 0.209050i \(0.0670373\pi\)
−0.977905 + 0.209050i \(0.932963\pi\)
\(14\) −31.4927 16.0617i −0.601198 0.306619i
\(15\) −6.34057 1.34540i −0.109142 0.0231588i
\(16\) 5.08559 + 8.80850i 0.0794623 + 0.137633i
\(17\) −52.3592 + 90.6889i −0.746999 + 1.29384i 0.202256 + 0.979333i \(0.435173\pi\)
−0.949255 + 0.314507i \(0.898161\pi\)
\(18\) 30.3228 + 41.6742i 0.397064 + 0.545706i
\(19\) 35.0345 20.2272i 0.423025 0.244234i −0.273346 0.961916i \(-0.588130\pi\)
0.696371 + 0.717682i \(0.254797\pi\)
\(20\) −5.43418 −0.0607559
\(21\) −95.0487 15.0578i −0.987683 0.156470i
\(22\) −77.6716 −0.752711
\(23\) 69.6324 40.2023i 0.631276 0.364467i −0.149970 0.988691i \(-0.547918\pi\)
0.781246 + 0.624223i \(0.214584\pi\)
\(24\) 91.1068 + 81.9750i 0.774879 + 0.697212i
\(25\) 61.7220 106.906i 0.493776 0.855245i
\(26\) −18.7040 32.3962i −0.141083 0.244362i
\(27\) 113.589 + 82.3444i 0.809636 + 0.586933i
\(28\) −80.5720 + 4.19132i −0.543810 + 0.0282888i
\(29\) 211.712i 1.35565i −0.735222 0.677827i \(-0.762922\pi\)
0.735222 0.677827i \(-0.237078\pi\)
\(30\) 11.7656 3.82746i 0.0716034 0.0232932i
\(31\) −86.6242 50.0125i −0.501876 0.289758i 0.227612 0.973752i \(-0.426908\pi\)
−0.729488 + 0.683994i \(0.760242\pi\)
\(32\) 146.596 + 84.6373i 0.809837 + 0.467560i
\(33\) −201.064 + 65.4076i −1.06063 + 0.345030i
\(34\) 199.890i 1.00826i
\(35\) −10.4962 + 20.5803i −0.0506910 + 0.0993916i
\(36\) 107.486 + 47.7656i 0.497622 + 0.221137i
\(37\) 94.9875 + 164.523i 0.422050 + 0.731012i 0.996140 0.0877801i \(-0.0279773\pi\)
−0.574090 + 0.818792i \(0.694644\pi\)
\(38\) −38.6103 + 66.8750i −0.164827 + 0.285488i
\(39\) −75.6987 68.1113i −0.310808 0.279655i
\(40\) 25.4799 14.7109i 0.100718 0.0581497i
\(41\) −186.753 −0.711362 −0.355681 0.934607i \(-0.615751\pi\)
−0.355681 + 0.934607i \(0.615751\pi\)
\(42\) 171.496 65.8241i 0.630058 0.241830i
\(43\) 158.618 0.562536 0.281268 0.959629i \(-0.409245\pi\)
0.281268 + 0.959629i \(0.409245\pi\)
\(44\) −153.515 + 88.6317i −0.525982 + 0.303676i
\(45\) 27.2339 19.8158i 0.0902174 0.0656437i
\(46\) −76.7393 + 132.916i −0.245969 + 0.426032i
\(47\) 179.034 + 310.097i 0.555635 + 0.962388i 0.997854 + 0.0654808i \(0.0208581\pi\)
−0.442219 + 0.896907i \(0.645809\pi\)
\(48\) −51.6999 10.9702i −0.155463 0.0329877i
\(49\) −139.753 + 313.238i −0.407444 + 0.913230i
\(50\) 235.634i 0.666473i
\(51\) −168.328 517.442i −0.462170 1.42071i
\(52\) −73.9351 42.6865i −0.197172 0.113837i
\(53\) −366.460 211.576i −0.949758 0.548343i −0.0567521 0.998388i \(-0.518074\pi\)
−0.893006 + 0.450045i \(0.851408\pi\)
\(54\) −266.364 27.7123i −0.671251 0.0698364i
\(55\) 50.7580i 0.124440i
\(56\) 366.442 237.769i 0.874427 0.567379i
\(57\) −43.6323 + 205.629i −0.101390 + 0.477829i
\(58\) 202.061 + 349.980i 0.457447 + 0.792322i
\(59\) 312.781 541.753i 0.690180 1.19543i −0.281599 0.959532i \(-0.590865\pi\)
0.971779 0.235895i \(-0.0758020\pi\)
\(60\) 18.8867 20.9907i 0.0406378 0.0451647i
\(61\) 699.575 403.900i 1.46838 0.847772i 0.469011 0.883192i \(-0.344611\pi\)
0.999372 + 0.0354209i \(0.0112772\pi\)
\(62\) 190.931 0.391101
\(63\) 388.510 314.812i 0.776948 0.629565i
\(64\) −404.486 −0.790012
\(65\) −21.1708 + 12.2229i −0.0403986 + 0.0233241i
\(66\) 269.952 300.023i 0.503466 0.559550i
\(67\) −149.272 + 258.547i −0.272187 + 0.471441i −0.969421 0.245402i \(-0.921080\pi\)
0.697235 + 0.716843i \(0.254413\pi\)
\(68\) −228.096 395.074i −0.406775 0.704555i
\(69\) −86.7208 + 408.695i −0.151304 + 0.713059i
\(70\) −2.29089 44.0390i −0.00391162 0.0751952i
\(71\) 455.386i 0.761189i 0.924742 + 0.380594i \(0.124281\pi\)
−0.924742 + 0.380594i \(0.875719\pi\)
\(72\) −633.292 + 67.0114i −1.03659 + 0.109686i
\(73\) −434.467 250.840i −0.696582 0.402172i 0.109491 0.993988i \(-0.465078\pi\)
−0.806073 + 0.591816i \(0.798411\pi\)
\(74\) −314.047 181.315i −0.493341 0.284831i
\(75\) 198.428 + 609.970i 0.305500 + 0.939110i
\(76\) 176.234i 0.265993i
\(77\) 39.1491 + 752.584i 0.0579410 + 1.11383i
\(78\) 190.144 + 40.3465i 0.276020 + 0.0585685i
\(79\) 30.9561 + 53.6176i 0.0440865 + 0.0763601i 0.887227 0.461334i \(-0.152629\pi\)
−0.843140 + 0.537694i \(0.819296\pi\)
\(80\) −6.34382 + 10.9878i −0.00886576 + 0.0153559i
\(81\) −712.856 + 152.569i −0.977855 + 0.209285i
\(82\) 308.720 178.240i 0.415761 0.240040i
\(83\) −73.1180 −0.0966957 −0.0483478 0.998831i \(-0.515396\pi\)
−0.0483478 + 0.998831i \(0.515396\pi\)
\(84\) 263.842 325.794i 0.342709 0.423179i
\(85\) −130.627 −0.166688
\(86\) −262.211 + 151.388i −0.328779 + 0.189820i
\(87\) 817.783 + 735.816i 1.00777 + 0.906755i
\(88\) 479.870 831.158i 0.581298 1.00684i
\(89\) 57.3723 + 99.3717i 0.0683309 + 0.118353i 0.898167 0.439655i \(-0.144899\pi\)
−0.829836 + 0.558008i \(0.811566\pi\)
\(90\) −26.1077 + 58.7498i −0.0305777 + 0.0688086i
\(91\) −304.469 + 197.557i −0.350737 + 0.227578i
\(92\) 350.271i 0.396938i
\(93\) 494.251 160.784i 0.551090 0.179274i
\(94\) −591.922 341.746i −0.649490 0.374983i
\(95\) 43.7025 + 25.2316i 0.0471977 + 0.0272496i
\(96\) −836.432 + 272.098i −0.889250 + 0.289280i
\(97\) 1416.51i 1.48273i −0.671101 0.741366i \(-0.734178\pi\)
0.671101 0.741366i \(-0.265822\pi\)
\(98\) −67.9336 651.195i −0.0700238 0.671231i
\(99\) 446.156 1003.98i 0.452933 1.01923i
\(100\) 268.883 + 465.720i 0.268883 + 0.465720i
\(101\) 120.406 208.549i 0.118622 0.205459i −0.800600 0.599199i \(-0.795486\pi\)
0.919222 + 0.393740i \(0.128819\pi\)
\(102\) 772.117 + 694.727i 0.749520 + 0.674394i
\(103\) −960.453 + 554.518i −0.918799 + 0.530469i −0.883252 0.468899i \(-0.844651\pi\)
−0.0355471 + 0.999368i \(0.511317\pi\)
\(104\) 462.226 0.435817
\(105\) −43.0157 112.072i −0.0399800 0.104163i
\(106\) 807.725 0.740124
\(107\) 924.644 533.843i 0.835408 0.482323i −0.0202926 0.999794i \(-0.506460\pi\)
0.855701 + 0.517471i \(0.173126\pi\)
\(108\) −558.079 + 249.178i −0.497233 + 0.222011i
\(109\) −5.04376 + 8.73604i −0.00443215 + 0.00767671i −0.868233 0.496157i \(-0.834744\pi\)
0.863801 + 0.503833i \(0.168077\pi\)
\(110\) −48.4442 83.9079i −0.0419907 0.0727300i
\(111\) −965.640 204.899i −0.825716 0.175208i
\(112\) −85.5845 + 167.808i −0.0722051 + 0.141575i
\(113\) 884.294i 0.736171i −0.929792 0.368086i \(-0.880013\pi\)
0.929792 0.368086i \(-0.119987\pi\)
\(114\) −124.127 381.568i −0.101979 0.313484i
\(115\) 86.8602 + 50.1487i 0.0704326 + 0.0406643i
\(116\) 798.731 + 461.148i 0.639313 + 0.369108i
\(117\) 526.189 55.6784i 0.415780 0.0439954i
\(118\) 1194.09i 0.931569i
\(119\) −1936.79 + 100.751i −1.49198 + 0.0776122i
\(120\) −31.7330 + 149.550i −0.0241401 + 0.113767i
\(121\) 162.366 + 281.226i 0.121988 + 0.211289i
\(122\) −770.976 + 1335.37i −0.572139 + 0.990973i
\(123\) 649.067 721.372i 0.475808 0.528812i
\(124\) 377.366 217.873i 0.273294 0.157787i
\(125\) 309.912 0.221755
\(126\) −341.783 + 891.215i −0.241655 + 0.630125i
\(127\) −840.132 −0.587005 −0.293503 0.955958i \(-0.594821\pi\)
−0.293503 + 0.955958i \(0.594821\pi\)
\(128\) −504.115 + 291.051i −0.348108 + 0.200980i
\(129\) −551.285 + 612.697i −0.376263 + 0.418178i
\(130\) 23.3315 40.4114i 0.0157408 0.0272639i
\(131\) −258.951 448.517i −0.172707 0.299138i 0.766658 0.642056i \(-0.221918\pi\)
−0.939366 + 0.342918i \(0.888585\pi\)
\(132\) 191.189 901.027i 0.126067 0.594124i
\(133\) 667.434 + 340.400i 0.435142 + 0.221928i
\(134\) 569.871i 0.367383i
\(135\) −18.1098 + 174.067i −0.0115455 + 0.110973i
\(136\) 2139.01 + 1234.96i 1.34866 + 0.778651i
\(137\) 950.957 + 549.035i 0.593034 + 0.342389i 0.766296 0.642487i \(-0.222097\pi\)
−0.173262 + 0.984876i \(0.555431\pi\)
\(138\) −246.707 758.380i −0.152182 0.467808i
\(139\) 828.268i 0.505416i 0.967543 + 0.252708i \(0.0813212\pi\)
−0.967543 + 0.252708i \(0.918679\pi\)
\(140\) −54.7811 84.4270i −0.0330703 0.0509670i
\(141\) −1820.06 386.197i −1.08707 0.230664i
\(142\) −434.628 752.797i −0.256853 0.444883i
\(143\) −398.714 + 690.592i −0.233162 + 0.403848i
\(144\) 222.060 161.575i 0.128507 0.0935039i
\(145\) 228.710 132.046i 0.130989 0.0756264i
\(146\) 957.621 0.542830
\(147\) −724.230 1628.50i −0.406350 0.913717i
\(148\) −827.601 −0.459651
\(149\) 773.007 446.296i 0.425015 0.245382i −0.272206 0.962239i \(-0.587753\pi\)
0.697221 + 0.716857i \(0.254420\pi\)
\(150\) −910.186 818.956i −0.495442 0.445783i
\(151\) −712.518 + 1234.12i −0.383999 + 0.665106i −0.991630 0.129113i \(-0.958787\pi\)
0.607630 + 0.794220i \(0.292120\pi\)
\(152\) −477.083 826.332i −0.254583 0.440950i
\(153\) 2583.76 + 1148.19i 1.36526 + 0.606705i
\(154\) −782.996 1206.73i −0.409712 0.631436i
\(155\) 124.772i 0.0646577i
\(156\) 421.851 137.231i 0.216507 0.0704314i
\(157\) −244.872 141.377i −0.124477 0.0718670i 0.436468 0.899720i \(-0.356229\pi\)
−0.560946 + 0.827853i \(0.689562\pi\)
\(158\) −102.347 59.0900i −0.0515334 0.0297528i
\(159\) 2090.91 680.189i 1.04289 0.339261i
\(160\) 211.155i 0.104333i
\(161\) 1326.55 + 676.557i 0.649358 + 0.331181i
\(162\) 1032.81 932.572i 0.500894 0.452283i
\(163\) −1158.07 2005.83i −0.556484 0.963858i −0.997786 0.0664997i \(-0.978817\pi\)
0.441303 0.897358i \(-0.354516\pi\)
\(164\) 406.781 704.565i 0.193685 0.335471i
\(165\) −196.064 176.412i −0.0925063 0.0832342i
\(166\) 120.871 69.7849i 0.0565145 0.0326287i
\(167\) −2344.70 −1.08646 −0.543229 0.839585i \(-0.682798\pi\)
−0.543229 + 0.839585i \(0.682798\pi\)
\(168\) −355.155 + 2241.84i −0.163100 + 1.02953i
\(169\) 1812.95 0.825192
\(170\) 215.939 124.672i 0.0974221 0.0562467i
\(171\) −642.640 883.213i −0.287391 0.394977i
\(172\) −345.499 + 598.423i −0.153163 + 0.265287i
\(173\) 516.901 + 895.298i 0.227163 + 0.393458i 0.956966 0.290199i \(-0.0937216\pi\)
−0.729803 + 0.683657i \(0.760388\pi\)
\(174\) −2054.15 435.869i −0.894969 0.189903i
\(175\) 2283.13 118.767i 0.986218 0.0513026i
\(176\) 413.872i 0.177255i
\(177\) 1005.55 + 3091.07i 0.427016 + 1.31265i
\(178\) −189.684 109.514i −0.0798730 0.0461147i
\(179\) −125.472 72.4412i −0.0523922 0.0302486i 0.473575 0.880753i \(-0.342963\pi\)
−0.525967 + 0.850505i \(0.676297\pi\)
\(180\) 15.4392 + 145.908i 0.00639316 + 0.0604186i
\(181\) 2057.17i 0.844797i −0.906410 0.422398i \(-0.861188\pi\)
0.906410 0.422398i \(-0.138812\pi\)
\(182\) 314.766 617.171i 0.128198 0.251361i
\(183\) −871.257 + 4106.03i −0.351941 + 1.65862i
\(184\) −948.219 1642.36i −0.379911 0.658025i
\(185\) −118.489 + 205.228i −0.0470889 + 0.0815604i
\(186\) −663.589 + 737.511i −0.261595 + 0.290736i
\(187\) −3690.19 + 2130.53i −1.44307 + 0.833155i
\(188\) −1559.88 −0.605137
\(189\) −134.257 + 2594.85i −0.0516706 + 0.998664i
\(190\) −96.3259 −0.0367801
\(191\) −2553.66 + 1474.36i −0.967417 + 0.558538i −0.898448 0.439080i \(-0.855304\pi\)
−0.0689690 + 0.997619i \(0.521971\pi\)
\(192\) 1405.81 1562.41i 0.528415 0.587279i
\(193\) 1135.40 1966.57i 0.423460 0.733455i −0.572815 0.819685i \(-0.694149\pi\)
0.996275 + 0.0862300i \(0.0274820\pi\)
\(194\) 1351.94 + 2341.63i 0.500329 + 0.866594i
\(195\) 26.3662 124.258i 0.00968270 0.0456323i
\(196\) −877.352 1209.54i −0.319735 0.440794i
\(197\) 495.849i 0.179329i −0.995972 0.0896645i \(-0.971421\pi\)
0.995972 0.0896645i \(-0.0285795\pi\)
\(198\) 220.675 + 2085.49i 0.0792055 + 0.748532i
\(199\) 727.207 + 419.853i 0.259047 + 0.149561i 0.623900 0.781504i \(-0.285547\pi\)
−0.364853 + 0.931065i \(0.618881\pi\)
\(200\) −2521.50 1455.79i −0.891484 0.514699i
\(201\) −479.890 1475.19i −0.168402 0.517670i
\(202\) 459.668i 0.160109i
\(203\) 3289.22 2134.24i 1.13723 0.737902i
\(204\) 2318.81 + 492.028i 0.795831 + 0.168867i
\(205\) −116.479 201.747i −0.0396840 0.0687347i
\(206\) 1058.48 1833.34i 0.357999 0.620073i
\(207\) −1277.27 1755.42i −0.428871 0.589420i
\(208\) −172.623 + 99.6638i −0.0575444 + 0.0332233i
\(209\) 1646.12 0.544805
\(210\) 178.072 + 144.211i 0.0585150 + 0.0473880i
\(211\) 4001.71 1.30564 0.652818 0.757514i \(-0.273586\pi\)
0.652818 + 0.757514i \(0.273586\pi\)
\(212\) 1596.43 921.701i 0.517186 0.298598i
\(213\) −1759.03 1582.72i −0.565852 0.509136i
\(214\) −1019.02 + 1764.99i −0.325507 + 0.563795i
\(215\) 98.9311 + 171.354i 0.0313816 + 0.0543545i
\(216\) 1942.19 2679.13i 0.611803 0.843943i
\(217\) −96.2355 1849.99i −0.0301055 0.578734i
\(218\) 19.2554i 0.00598228i
\(219\) 2478.93 806.416i 0.764889 0.248825i
\(220\) −191.496 110.560i −0.0586848 0.0338817i
\(221\) −1777.26 1026.10i −0.540955 0.312321i
\(222\) 1791.85 582.905i 0.541718 0.176225i
\(223\) 3040.54i 0.913047i 0.889711 + 0.456523i \(0.150905\pi\)
−0.889711 + 0.456523i \(0.849095\pi\)
\(224\) 162.862 + 3130.78i 0.0485788 + 0.933856i
\(225\) −3045.79 1353.51i −0.902455 0.401040i
\(226\) 843.984 + 1461.82i 0.248411 + 0.430261i
\(227\) 2198.24 3807.46i 0.642741 1.11326i −0.342078 0.939672i \(-0.611131\pi\)
0.984818 0.173588i \(-0.0555360\pi\)
\(228\) −680.742 612.510i −0.197734 0.177914i
\(229\) −1717.81 + 991.778i −0.495703 + 0.286194i −0.726937 0.686704i \(-0.759057\pi\)
0.231234 + 0.972898i \(0.425724\pi\)
\(230\) −191.451 −0.0548865
\(231\) −3043.08 2464.42i −0.866754 0.701935i
\(232\) −4993.49 −1.41310
\(233\) −3787.78 + 2186.87i −1.06500 + 0.614879i −0.926812 0.375526i \(-0.877462\pi\)
−0.138191 + 0.990406i \(0.544129\pi\)
\(234\) −816.701 + 594.245i −0.228160 + 0.166013i
\(235\) −223.329 + 386.818i −0.0619932 + 0.107375i
\(236\) 1362.59 + 2360.07i 0.375834 + 0.650964i
\(237\) −314.699 66.7758i −0.0862527 0.0183019i
\(238\) 3105.55 2015.06i 0.845810 0.548810i
\(239\) 3826.41i 1.03561i 0.855500 + 0.517803i \(0.173250\pi\)
−0.855500 + 0.517803i \(0.826750\pi\)
\(240\) −20.3946 62.6931i −0.00548526 0.0168618i
\(241\) 2979.03 + 1719.94i 0.796250 + 0.459715i 0.842158 0.539231i \(-0.181285\pi\)
−0.0459083 + 0.998946i \(0.514618\pi\)
\(242\) −536.813 309.929i −0.142594 0.0823264i
\(243\) 1888.24 3283.82i 0.498479 0.866902i
\(244\) 3519.07i 0.923300i
\(245\) −425.553 + 44.3943i −0.110970 + 0.0115765i
\(246\) −384.483 + 1811.98i −0.0996493 + 0.469624i
\(247\) 396.398 + 686.582i 0.102114 + 0.176867i
\(248\) −1179.61 + 2043.14i −0.302036 + 0.523142i
\(249\) 254.125 282.434i 0.0646768 0.0718816i
\(250\) −512.314 + 295.785i −0.129606 + 0.0748282i
\(251\) −2046.61 −0.514664 −0.257332 0.966323i \(-0.582843\pi\)
−0.257332 + 0.966323i \(0.582843\pi\)
\(252\) 341.453 + 2151.46i 0.0853552 + 0.537814i
\(253\) 3271.72 0.813008
\(254\) 1388.82 801.835i 0.343080 0.198077i
\(255\) 454.000 504.575i 0.111493 0.123913i
\(256\) 2173.51 3764.63i 0.530642 0.919099i
\(257\) −3025.57 5240.44i −0.734357 1.27194i −0.955005 0.296590i \(-0.904150\pi\)
0.220648 0.975354i \(-0.429183\pi\)
\(258\) 326.560 1539.00i 0.0788014 0.371372i
\(259\) −1598.53 + 3134.29i −0.383505 + 0.751950i
\(260\) 106.495i 0.0254021i
\(261\) −5684.49 + 601.501i −1.34813 + 0.142651i
\(262\) 856.143 + 494.294i 0.201880 + 0.116556i
\(263\) 5433.69 + 3137.14i 1.27398 + 0.735530i 0.975734 0.218960i \(-0.0702665\pi\)
0.298242 + 0.954490i \(0.403600\pi\)
\(264\) 1542.72 + 4742.33i 0.359650 + 1.10557i
\(265\) 527.844i 0.122359i
\(266\) −1428.22 + 74.2951i −0.329209 + 0.0171253i
\(267\) −583.245 123.758i −0.133685 0.0283666i
\(268\) −650.284 1126.32i −0.148218 0.256721i
\(269\) −1668.18 + 2889.37i −0.378106 + 0.654899i −0.990787 0.135432i \(-0.956758\pi\)
0.612681 + 0.790331i \(0.290091\pi\)
\(270\) −136.195 305.034i −0.0306985 0.0687548i
\(271\) 2462.26 1421.59i 0.551925 0.318654i −0.197973 0.980207i \(-0.563436\pi\)
0.749898 + 0.661553i \(0.230103\pi\)
\(272\) −1065.11 −0.237433
\(273\) 295.091 1862.70i 0.0654202 0.412951i
\(274\) −2096.03 −0.462138
\(275\) 4350.06 2511.51i 0.953886 0.550726i
\(276\) −1353.00 1217.39i −0.295076 0.265500i
\(277\) −3174.17 + 5497.82i −0.688510 + 1.19253i 0.283809 + 0.958881i \(0.408402\pi\)
−0.972320 + 0.233654i \(0.924932\pi\)
\(278\) −790.512 1369.21i −0.170546 0.295394i
\(279\) −1096.73 + 2467.96i −0.235339 + 0.529580i
\(280\) 485.411 + 247.566i 0.103603 + 0.0528390i
\(281\) 3735.88i 0.793110i −0.918011 0.396555i \(-0.870206\pi\)
0.918011 0.396555i \(-0.129794\pi\)
\(282\) 3377.32 1098.67i 0.713179 0.232003i
\(283\) −4777.96 2758.56i −1.00361 0.579432i −0.0942927 0.995545i \(-0.530059\pi\)
−0.909313 + 0.416112i \(0.863392\pi\)
\(284\) −1718.05 991.914i −0.358969 0.207251i
\(285\) −249.353 + 81.1164i −0.0518259 + 0.0168594i
\(286\) 1522.15i 0.314709i
\(287\) −1882.62 2901.44i −0.387205 0.596748i
\(288\) 1856.02 4176.59i 0.379747 0.854541i
\(289\) −3026.48 5242.01i −0.616014 1.06697i
\(290\) −252.054 + 436.570i −0.0510383 + 0.0884008i
\(291\) 5471.58 + 4923.16i 1.10223 + 0.991755i
\(292\) 1892.70 1092.75i 0.379321 0.219001i
\(293\) 7574.50 1.51026 0.755131 0.655574i \(-0.227573\pi\)
0.755131 + 0.655574i \(0.227573\pi\)
\(294\) 2751.49 + 2000.85i 0.545816 + 0.396912i
\(295\) 780.333 0.154009
\(296\) 3880.48 2240.40i 0.761988 0.439934i
\(297\) 2327.45 + 5212.75i 0.454721 + 1.01843i
\(298\) −851.904 + 1475.54i −0.165602 + 0.286831i
\(299\) 787.855 + 1364.61i 0.152384 + 0.263937i
\(300\) −2733.46 580.012i −0.526055 0.111623i
\(301\) 1599.01 + 2464.34i 0.306196 + 0.471901i
\(302\) 2720.15i 0.518302i
\(303\) 387.088 + 1189.91i 0.0733915 + 0.225606i
\(304\) 356.343 + 205.735i 0.0672291 + 0.0388148i
\(305\) 872.657 + 503.829i 0.163830 + 0.0945874i
\(306\) −5367.06 + 567.912i −1.00266 + 0.106096i
\(307\) 10635.6i 1.97723i −0.150480 0.988613i \(-0.548082\pi\)
0.150480 0.988613i \(-0.451918\pi\)
\(308\) −2924.57 1491.57i −0.541047 0.275941i
\(309\) 1196.16 5637.21i 0.220217 1.03783i
\(310\) 119.085 + 206.261i 0.0218179 + 0.0377897i
\(311\) −2885.59 + 4997.99i −0.526132 + 0.911287i 0.473405 + 0.880845i \(0.343025\pi\)
−0.999537 + 0.0304419i \(0.990309\pi\)
\(312\) −1606.49 + 1785.45i −0.291505 + 0.323978i
\(313\) −2030.41 + 1172.26i −0.366664 + 0.211694i −0.672000 0.740551i \(-0.734565\pi\)
0.305336 + 0.952245i \(0.401231\pi\)
\(314\) 539.730 0.0970023
\(315\) 582.404 + 223.354i 0.104174 + 0.0399509i
\(316\) −269.712 −0.0480142
\(317\) −6852.10 + 3956.06i −1.21405 + 0.700929i −0.963638 0.267211i \(-0.913898\pi\)
−0.250407 + 0.968141i \(0.580565\pi\)
\(318\) −2807.29 + 3120.01i −0.495047 + 0.550193i
\(319\) 4307.36 7460.56i 0.756005 1.30944i
\(320\) −252.280 436.962i −0.0440715 0.0763341i
\(321\) −1151.56 + 5427.03i −0.200230 + 0.943637i
\(322\) −2838.63 + 147.664i −0.491275 + 0.0255559i
\(323\) 4236.32i 0.729769i
\(324\) 977.130 3021.73i 0.167546 0.518129i
\(325\) 2095.06 + 1209.58i 0.357579 + 0.206448i
\(326\) 3828.79 + 2210.55i 0.650482 + 0.375556i
\(327\) −16.2150 49.8451i −0.00274218 0.00842949i
\(328\) 4404.78i 0.741505i
\(329\) −3012.94 + 5907.57i −0.504889 + 0.989953i
\(330\) 492.482 + 104.500i 0.0821523 + 0.0174319i
\(331\) 2440.02 + 4226.23i 0.405182 + 0.701797i 0.994343 0.106220i \(-0.0338747\pi\)
−0.589160 + 0.808016i \(0.700541\pi\)
\(332\) 159.264 275.854i 0.0263276 0.0456007i
\(333\) 4147.59 3017.86i 0.682543 0.496629i
\(334\) 3876.02 2237.82i 0.634989 0.366611i
\(335\) −372.407 −0.0607367
\(336\) −350.743 913.814i −0.0569482 0.148371i
\(337\) −4136.39 −0.668616 −0.334308 0.942464i \(-0.608503\pi\)
−0.334308 + 0.942464i \(0.608503\pi\)
\(338\) −2996.97 + 1730.30i −0.482290 + 0.278450i
\(339\) 3415.77 + 3073.41i 0.547255 + 0.492403i
\(340\) 284.529 492.819i 0.0453846 0.0786085i
\(341\) −2035.04 3524.80i −0.323178 0.559761i
\(342\) 1905.30 + 846.691i 0.301248 + 0.133871i
\(343\) −6275.39 + 986.454i −0.987869 + 0.155287i
\(344\) 3741.20i 0.586373i
\(345\) −495.597 + 161.222i −0.0773393 + 0.0251591i
\(346\) −1708.97 986.676i −0.265535 0.153306i
\(347\) 2009.83 + 1160.38i 0.310933 + 0.179517i 0.647344 0.762198i \(-0.275880\pi\)
−0.336411 + 0.941715i \(0.609213\pi\)
\(348\) −4557.31 + 1482.53i −0.702004 + 0.228368i
\(349\) 226.795i 0.0347853i −0.999849 0.0173926i \(-0.994463\pi\)
0.999849 0.0173926i \(-0.00553653\pi\)
\(350\) −3660.88 + 2375.39i −0.559092 + 0.362771i
\(351\) −1613.73 + 2226.03i −0.245397 + 0.338509i
\(352\) 3443.95 + 5965.10i 0.521486 + 0.903241i
\(353\) 742.854 1286.66i 0.112006 0.194000i −0.804573 0.593854i \(-0.797606\pi\)
0.916579 + 0.399854i \(0.130939\pi\)
\(354\) −4612.44 4150.13i −0.692509 0.623098i
\(355\) −491.949 + 284.027i −0.0735491 + 0.0424636i
\(356\) −499.869 −0.0744185
\(357\) 6342.25 7831.45i 0.940245 1.16102i
\(358\) 276.556 0.0408280
\(359\) 9419.94 5438.60i 1.38486 0.799550i 0.392131 0.919909i \(-0.371738\pi\)
0.992730 + 0.120359i \(0.0384045\pi\)
\(360\) −467.380 642.344i −0.0684252 0.0940402i
\(361\) −2611.22 + 4522.77i −0.380700 + 0.659392i
\(362\) 1963.39 + 3400.70i 0.285066 + 0.493748i
\(363\) −1650.61 350.241i −0.238662 0.0506416i
\(364\) −82.1386 1578.99i −0.0118276 0.227367i
\(365\) 625.800i 0.0897421i
\(366\) −2478.59 7619.21i −0.353983 1.08815i
\(367\) −3299.69 1905.08i −0.469325 0.270965i 0.246632 0.969109i \(-0.420676\pi\)
−0.715957 + 0.698144i \(0.754009\pi\)
\(368\) 708.243 + 408.904i 0.100325 + 0.0579229i
\(369\) 530.587 + 5014.32i 0.0748544 + 0.707413i
\(370\) 452.349i 0.0635581i
\(371\) −407.121 7826.30i −0.0569721 1.09521i
\(372\) −469.976 + 2214.89i −0.0655030 + 0.308700i
\(373\) 4869.55 + 8434.30i 0.675967 + 1.17081i 0.976185 + 0.216938i \(0.0696070\pi\)
−0.300219 + 0.953870i \(0.597060\pi\)
\(374\) 4066.83 7043.95i 0.562274 0.973888i
\(375\) −1077.11 + 1197.10i −0.148325 + 0.164848i
\(376\) 7314.00 4222.74i 1.00317 0.579179i
\(377\) 4148.98 0.566800
\(378\) −2254.63 4417.67i −0.306787 0.601113i
\(379\) 320.171 0.0433933 0.0216967 0.999765i \(-0.493093\pi\)
0.0216967 + 0.999765i \(0.493093\pi\)
\(380\) −190.384 + 109.918i −0.0257013 + 0.0148386i
\(381\) 2919.92 3245.19i 0.392630 0.436368i
\(382\) 2814.30 4874.51i 0.376943 0.652884i
\(383\) −2185.13 3784.75i −0.291527 0.504939i 0.682644 0.730751i \(-0.260830\pi\)
−0.974171 + 0.225812i \(0.927497\pi\)
\(384\) 627.829 2958.81i 0.0834343 0.393206i
\(385\) −788.592 + 511.683i −0.104391 + 0.0677346i
\(386\) 4334.57i 0.571564i
\(387\) −450.654 4258.92i −0.0591939 0.559413i
\(388\) 5344.11 + 3085.42i 0.699242 + 0.403708i
\(389\) −11877.4 6857.42i −1.54809 0.893791i −0.998288 0.0584981i \(-0.981369\pi\)
−0.549805 0.835293i \(-0.685298\pi\)
\(390\) 75.0078 + 230.575i 0.00973889 + 0.0299375i
\(391\) 8419.84i 1.08903i
\(392\) 7388.10 + 3296.25i 0.951927 + 0.424709i
\(393\) 2632.49 + 558.587i 0.337892 + 0.0716971i
\(394\) 473.246 + 819.687i 0.0605122 + 0.104810i
\(395\) −38.6150 + 66.8832i −0.00491882 + 0.00851964i
\(396\) 2815.93 + 3870.07i 0.357337 + 0.491107i
\(397\) −2181.61 + 1259.55i −0.275798 + 0.159232i −0.631520 0.775360i \(-0.717568\pi\)
0.355722 + 0.934592i \(0.384235\pi\)
\(398\) −1602.86 −0.201869
\(399\) −3634.57 + 1395.03i −0.456030 + 0.175035i
\(400\) 1255.57 0.156946
\(401\) −2268.96 + 1309.98i −0.282560 + 0.163136i −0.634582 0.772856i \(-0.718828\pi\)
0.352022 + 0.935992i \(0.385494\pi\)
\(402\) 2201.25 + 1980.61i 0.273105 + 0.245731i
\(403\) 980.109 1697.60i 0.121148 0.209835i
\(404\) 524.530 + 908.513i 0.0645950 + 0.111882i
\(405\) −609.431 674.933i −0.0747725 0.0828091i
\(406\) −3400.45 + 6667.38i −0.415669 + 0.815016i
\(407\) 7730.22i 0.941456i
\(408\) −12204.5 + 3970.22i −1.48091 + 0.481753i
\(409\) −12058.7 6962.09i −1.45786 0.841694i −0.458952 0.888461i \(-0.651775\pi\)
−0.998906 + 0.0467669i \(0.985108\pi\)
\(410\) 385.101 + 222.338i 0.0463872 + 0.0267817i
\(411\) −5425.86 + 1765.08i −0.651187 + 0.211836i
\(412\) 4831.36i 0.577729i
\(413\) 11569.9 601.863i 1.37850 0.0717088i
\(414\) 3786.85 + 1682.83i 0.449549 + 0.199774i
\(415\) −45.6041 78.9886i −0.00539426 0.00934313i
\(416\) −1658.66 + 2872.89i −0.195487 + 0.338593i
\(417\) −3199.36 2878.69i −0.375716 0.338057i
\(418\) −2721.19 + 1571.08i −0.318416 + 0.183837i
\(419\) −15171.1 −1.76887 −0.884433 0.466666i \(-0.845455\pi\)
−0.884433 + 0.466666i \(0.845455\pi\)
\(420\) 516.512 + 81.8265i 0.0600076 + 0.00950648i
\(421\) −1052.53 −0.121846 −0.0609228 0.998142i \(-0.519404\pi\)
−0.0609228 + 0.998142i \(0.519404\pi\)
\(422\) −6615.22 + 3819.30i −0.763090 + 0.440570i
\(423\) 7817.47 5688.11i 0.898577 0.653819i
\(424\) −4990.27 + 8643.40i −0.571578 + 0.990002i
\(425\) 6463.43 + 11195.0i 0.737700 + 1.27773i
\(426\) 4418.41 + 937.541i 0.502518 + 0.106629i
\(427\) 13327.4 + 6797.16i 1.51044 + 0.770345i
\(428\) 4651.23i 0.525294i
\(429\) −1281.81 3940.30i −0.144258 0.443449i
\(430\) −327.085 188.843i −0.0366824 0.0211786i
\(431\) −6923.58 3997.33i −0.773776 0.446740i 0.0604442 0.998172i \(-0.480748\pi\)
−0.834220 + 0.551432i \(0.814082\pi\)
\(432\) −147.665 + 1419.32i −0.0164456 + 0.158072i
\(433\) 12889.4i 1.43055i −0.698845 0.715273i \(-0.746303\pi\)
0.698845 0.715273i \(-0.253697\pi\)
\(434\) 1924.74 + 2966.36i 0.212882 + 0.328087i
\(435\) −284.838 + 1342.38i −0.0313953 + 0.147959i
\(436\) −21.9724 38.0574i −0.00241351 0.00418032i
\(437\) 1626.36 2816.94i 0.178030 0.308358i
\(438\) −3328.26 + 3699.02i −0.363083 + 0.403529i
\(439\) 12456.7 7191.89i 1.35427 0.781891i 0.365430 0.930839i \(-0.380922\pi\)
0.988845 + 0.148948i \(0.0475888\pi\)
\(440\) 1197.19 0.129713
\(441\) 8807.53 + 2862.44i 0.951034 + 0.309085i
\(442\) 3917.30 0.421554
\(443\) −3432.16 + 1981.56i −0.368097 + 0.212521i −0.672627 0.739982i \(-0.734834\pi\)
0.304530 + 0.952503i \(0.401501\pi\)
\(444\) 2876.37 3196.79i 0.307447 0.341695i
\(445\) −71.5668 + 123.957i −0.00762380 + 0.0132048i
\(446\) −2901.94 5026.30i −0.308096 0.533637i
\(447\) −962.710 + 4537.03i −0.101867 + 0.480076i
\(448\) −4077.56 6284.22i −0.430015 0.662726i
\(449\) 13479.1i 1.41675i −0.705838 0.708373i \(-0.749430\pi\)
0.705838 0.708373i \(-0.250570\pi\)
\(450\) 6326.79 669.465i 0.662773 0.0701308i
\(451\) −6581.00 3799.54i −0.687112 0.396704i
\(452\) 3336.19 + 1926.15i 0.347171 + 0.200439i
\(453\) −2290.65 7041.49i −0.237581 0.730327i
\(454\) 8392.13i 0.867538i
\(455\) −403.318 205.698i −0.0415557 0.0211940i
\(456\) 4850.01 + 1029.12i 0.498076 + 0.105686i
\(457\) −1989.79 3446.42i −0.203673 0.352772i 0.746036 0.665905i \(-0.231955\pi\)
−0.949709 + 0.313134i \(0.898621\pi\)
\(458\) 1893.14 3279.01i 0.193145 0.334537i
\(459\) −13415.1 + 5989.74i −1.36419 + 0.609101i
\(460\) −378.395 + 218.466i −0.0383538 + 0.0221436i
\(461\) 9053.72 0.914694 0.457347 0.889288i \(-0.348800\pi\)
0.457347 + 0.889288i \(0.348800\pi\)
\(462\) 7382.59 + 1169.56i 0.743440 + 0.117777i
\(463\) −5736.10 −0.575764 −0.287882 0.957666i \(-0.592951\pi\)
−0.287882 + 0.957666i \(0.592951\pi\)
\(464\) 1864.87 1076.68i 0.186582 0.107723i
\(465\) 481.960 + 433.652i 0.0480653 + 0.0432476i
\(466\) 4174.37 7230.23i 0.414966 0.718742i
\(467\) 6196.30 + 10732.3i 0.613984 + 1.06345i 0.990562 + 0.137067i \(0.0437675\pi\)
−0.376578 + 0.926385i \(0.622899\pi\)
\(468\) −936.077 + 2106.44i −0.0924576 + 0.208056i
\(469\) −5521.65 + 287.234i −0.543638 + 0.0282798i
\(470\) 852.596i 0.0836752i
\(471\) 1397.17 454.509i 0.136684 0.0444643i
\(472\) −12777.9 7377.32i −1.24608 0.719425i
\(473\) 5589.57 + 3227.14i 0.543359 + 0.313709i
\(474\) 583.959 189.967i 0.0565868 0.0184081i
\(475\) 4993.85i 0.482387i
\(476\) 3838.58 7526.44i 0.369624 0.724735i
\(477\) −4639.67 + 10440.6i −0.445359 + 1.00219i
\(478\) −3651.98 6325.42i −0.349452 0.605268i
\(479\) 4133.87 7160.07i 0.394324 0.682989i −0.598691 0.800980i \(-0.704312\pi\)
0.993015 + 0.117991i \(0.0376455\pi\)
\(480\) −815.632 733.880i −0.0775590 0.0697851i
\(481\) −3224.21 + 1861.50i −0.305637 + 0.176460i
\(482\) −6566.17 −0.620499
\(483\) −7223.82 + 2772.67i −0.680529 + 0.261202i
\(484\) −1414.65 −0.132856
\(485\) 1530.24 883.487i 0.143268 0.0827156i
\(486\) 12.6949 + 7230.63i 0.00118488 + 0.674873i
\(487\) −470.075 + 814.194i −0.0437395 + 0.0757590i −0.887066 0.461642i \(-0.847260\pi\)
0.843327 + 0.537401i \(0.180594\pi\)
\(488\) −9526.46 16500.3i −0.883694 1.53060i
\(489\) 11772.9 + 2498.08i 1.08873 + 0.231017i
\(490\) 661.109 479.542i 0.0609507 0.0442112i
\(491\) 1057.30i 0.0971801i 0.998819 + 0.0485900i \(0.0154728\pi\)
−0.998819 + 0.0485900i \(0.984527\pi\)
\(492\) 1307.75 + 4020.03i 0.119833 + 0.368368i
\(493\) 19199.9 + 11085.1i 1.75400 + 1.01267i
\(494\) −1310.57 756.658i −0.119363 0.0689142i
\(495\) 1362.86 144.210i 0.123749 0.0130944i
\(496\) 1017.37i 0.0920995i
\(497\) −7075.02 + 4590.68i −0.638547 + 0.414326i
\(498\) −150.534 + 709.431i −0.0135454 + 0.0638361i
\(499\) 3086.65 + 5346.23i 0.276909 + 0.479620i 0.970615 0.240638i \(-0.0773568\pi\)
−0.693706 + 0.720258i \(0.744023\pi\)
\(500\) −675.044 + 1169.21i −0.0603778 + 0.104577i
\(501\) 8149.12 9056.91i 0.726699 0.807651i
\(502\) 3383.24 1953.31i 0.300800 0.173667i
\(503\) −4284.28 −0.379775 −0.189887 0.981806i \(-0.560812\pi\)
−0.189887 + 0.981806i \(0.560812\pi\)
\(504\) −7425.23 9163.49i −0.656242 0.809869i
\(505\) 300.390 0.0264697
\(506\) −5408.46 + 3122.58i −0.475169 + 0.274339i
\(507\) −6300.98 + 7002.89i −0.551946 + 0.613431i
\(508\) 1829.96 3169.58i 0.159826 0.276826i
\(509\) 7550.52 + 13077.9i 0.657507 + 1.13884i 0.981259 + 0.192693i \(0.0617223\pi\)
−0.323752 + 0.946142i \(0.604944\pi\)
\(510\) −268.932 + 1267.42i −0.0233500 + 0.110043i
\(511\) −482.673 9278.68i −0.0417851 0.803258i
\(512\) 3640.92i 0.314272i
\(513\) 5645.13 + 587.315i 0.485845 + 0.0505470i
\(514\) 10003.1 + 5775.30i 0.858401 + 0.495598i
\(515\) −1198.08 691.712i −0.102512 0.0591854i
\(516\) −1110.74 3414.41i −0.0947624 0.291301i
\(517\) 14570.1i 1.23944i
\(518\) −348.892 6706.94i −0.0295935 0.568892i
\(519\) −5254.79 1115.01i −0.444431 0.0943037i
\(520\) 288.293 + 499.338i 0.0243125 + 0.0421104i
\(521\) −6894.00 + 11940.8i −0.579715 + 1.00410i 0.415796 + 0.909458i \(0.363503\pi\)
−0.995512 + 0.0946385i \(0.969830\pi\)
\(522\) 8822.93 6419.71i 0.739788 0.538281i
\(523\) −832.513 + 480.652i −0.0696047 + 0.0401863i −0.534398 0.845233i \(-0.679462\pi\)
0.464794 + 0.885419i \(0.346128\pi\)
\(524\) 2256.17 0.188094
\(525\) −7476.36 + 9231.85i −0.621514 + 0.767449i
\(526\) −11976.5 −0.992780
\(527\) 9071.15 5237.23i 0.749802 0.432898i
\(528\) −1598.67 1438.43i −0.131767 0.118560i
\(529\) −2851.06 + 4938.17i −0.234327 + 0.405866i
\(530\) 503.783 + 872.577i 0.0412885 + 0.0715138i
\(531\) −15434.8 6859.02i −1.26142 0.560557i
\(532\) −2738.03 + 1776.59i −0.223136 + 0.144784i
\(533\) 3659.84i 0.297421i
\(534\) 1082.28 352.073i 0.0877054 0.0285313i
\(535\) 1153.41 + 665.922i 0.0932080 + 0.0538137i
\(536\) 6098.14 + 3520.76i 0.491417 + 0.283720i
\(537\) 715.903 232.889i 0.0575298 0.0187149i
\(538\) 6368.54i 0.510348i
\(539\) −11297.7 + 8194.92i −0.902834 + 0.654880i
\(540\) −617.261 447.474i −0.0491902 0.0356596i
\(541\) 597.846 + 1035.50i 0.0475109 + 0.0822913i 0.888803 0.458290i \(-0.151538\pi\)
−0.841292 + 0.540581i \(0.818204\pi\)
\(542\) −2713.57 + 4700.04i −0.215051 + 0.372480i
\(543\) 7946.26 + 7149.79i 0.628005 + 0.565059i
\(544\) −15351.3 + 8863.09i −1.20989 + 0.698533i
\(545\) −12.5833 −0.000989006
\(546\) 1289.97 + 3360.86i 0.101109 + 0.263428i
\(547\) 18601.8 1.45403 0.727014 0.686622i \(-0.240907\pi\)
0.727014 + 0.686622i \(0.240907\pi\)
\(548\) −4142.71 + 2391.80i −0.322934 + 0.186446i
\(549\) −12832.3 17636.1i −0.997578 1.37102i
\(550\) −4794.05 + 8303.53i −0.371671 + 0.643753i
\(551\) −4282.34 7417.24i −0.331096 0.573475i
\(552\) 9639.56 + 2045.41i 0.743274 + 0.157715i
\(553\) −520.955 + 1021.45i −0.0400601 + 0.0785473i
\(554\) 12117.9i 0.929315i
\(555\) −380.925 1170.97i −0.0291340 0.0895582i
\(556\) −3124.83 1804.12i −0.238349 0.137611i
\(557\) 5908.09 + 3411.04i 0.449432 + 0.259480i 0.707590 0.706623i \(-0.249782\pi\)
−0.258158 + 0.966103i \(0.583116\pi\)
\(558\) −542.458 5126.51i −0.0411543 0.388929i
\(559\) 3108.49i 0.235197i
\(560\) −234.661 + 12.2070i −0.0177076 + 0.000921141i
\(561\) 4595.80 21658.9i 0.345873 1.63002i
\(562\) 3565.58 + 6175.77i 0.267624 + 0.463539i
\(563\) −5679.80 + 9837.71i −0.425178 + 0.736430i −0.996437 0.0843399i \(-0.973122\pi\)
0.571259 + 0.820770i \(0.306455\pi\)
\(564\) 5421.43 6025.36i 0.404758 0.449847i
\(565\) 955.293 551.539i 0.0711318 0.0410680i
\(566\) 10531.2 0.782087
\(567\) −9556.55 9537.12i −0.707826 0.706387i
\(568\) 10740.8 0.793443
\(569\) 18467.2 10662.1i 1.36061 0.785549i 0.370905 0.928671i \(-0.379047\pi\)
0.989705 + 0.143122i \(0.0457141\pi\)
\(570\) 334.785 372.079i 0.0246011 0.0273416i
\(571\) 7384.00 12789.5i 0.541175 0.937343i −0.457662 0.889126i \(-0.651313\pi\)
0.998837 0.0482163i \(-0.0153537\pi\)
\(572\) −1736.94 3008.47i −0.126967 0.219913i
\(573\) 3180.36 14988.3i 0.231870 1.09275i
\(574\) 5881.34 + 2999.56i 0.427670 + 0.218117i
\(575\) 9925.45i 0.719861i
\(576\) 1149.20 + 10860.5i 0.0831305 + 0.785626i
\(577\) 16718.5 + 9652.44i 1.20624 + 0.696424i 0.961936 0.273275i \(-0.0881068\pi\)
0.244305 + 0.969698i \(0.421440\pi\)
\(578\) 10006.1 + 5777.04i 0.720069 + 0.415732i
\(579\) 3650.16 + 11220.6i 0.261996 + 0.805377i
\(580\) 1150.48i 0.0823640i
\(581\) −737.091 1135.98i −0.0526328 0.0811162i
\(582\) −13743.8 2916.29i −0.978863 0.207705i
\(583\) −8609.17 14911.5i −0.611587 1.05930i
\(584\) −5916.35 + 10247.4i −0.419213 + 0.726099i
\(585\) 388.336 + 533.710i 0.0274457 + 0.0377200i
\(586\) −12521.4 + 7229.22i −0.882684 + 0.509618i
\(587\) 4397.46 0.309204 0.154602 0.987977i \(-0.450590\pi\)
0.154602 + 0.987977i \(0.450590\pi\)
\(588\) 7721.38 + 814.854i 0.541538 + 0.0571497i
\(589\) −4046.45 −0.283075
\(590\) −1289.97 + 744.762i −0.0900119 + 0.0519684i
\(591\) 1915.32 + 1723.35i 0.133310 + 0.119948i
\(592\) −966.135 + 1673.40i −0.0670742 + 0.116176i
\(593\) −10970.1 19000.8i −0.759677 1.31580i −0.943015 0.332749i \(-0.892024\pi\)
0.183339 0.983050i \(-0.441309\pi\)
\(594\) −8822.62 6395.82i −0.609422 0.441791i
\(595\) −1316.83 2029.46i −0.0907307 0.139832i
\(596\) 3888.46i 0.267244i
\(597\) −4149.21 + 1349.77i −0.284449 + 0.0925335i
\(598\) −2604.80 1503.88i −0.178124 0.102840i
\(599\) −4765.07 2751.12i −0.325034 0.187659i 0.328600 0.944469i \(-0.393423\pi\)
−0.653634 + 0.756810i \(0.726757\pi\)
\(600\) 14386.9 4680.17i 0.978903 0.318445i
\(601\) 5814.58i 0.394645i −0.980339 0.197322i \(-0.936775\pi\)
0.980339 0.197322i \(-0.0632246\pi\)
\(602\) −4995.31 2547.68i −0.338196 0.172484i
\(603\) 7366.11 + 3273.41i 0.497465 + 0.221067i
\(604\) −3103.99 5376.27i −0.209105 0.362181i
\(605\) −202.537 + 350.804i −0.0136104 + 0.0235739i
\(606\) −1775.56 1597.60i −0.119022 0.107092i
\(607\) −11510.7 + 6645.69i −0.769693 + 0.444382i −0.832765 0.553627i \(-0.813244\pi\)
0.0630721 + 0.998009i \(0.479910\pi\)
\(608\) 6847.90 0.456775
\(609\) −3187.91 + 20123.0i −0.212119 + 1.33896i
\(610\) −1923.45 −0.127669
\(611\) −6077.05 + 3508.59i −0.402375 + 0.232311i
\(612\) −9959.72 + 7246.85i −0.657839 + 0.478655i
\(613\) −9797.17 + 16969.2i −0.645520 + 1.11807i 0.338661 + 0.940909i \(0.390026\pi\)
−0.984181 + 0.177166i \(0.943307\pi\)
\(614\) 10150.8 + 17581.7i 0.667189 + 1.15561i
\(615\) 1184.12 + 251.257i 0.0776394 + 0.0164743i
\(616\) 17750.6 923.379i 1.16103 0.0603961i
\(617\) 348.388i 0.0227319i 0.999935 + 0.0113660i \(0.00361797\pi\)
−0.999935 + 0.0113660i \(0.996382\pi\)
\(618\) 3402.88 + 10460.5i 0.221495 + 0.680878i
\(619\) 5867.68 + 3387.71i 0.381005 + 0.219973i 0.678255 0.734826i \(-0.262736\pi\)
−0.297251 + 0.954799i \(0.596070\pi\)
\(620\) 470.731 + 271.777i 0.0304920 + 0.0176045i
\(621\) 11219.9 + 1167.31i 0.725022 + 0.0754307i
\(622\) 11016.2i 0.710145i
\(623\) −965.508 + 1893.10i −0.0620903 + 0.121742i
\(624\) 214.986 1013.18i 0.0137922 0.0649994i
\(625\) −7521.95 13028.4i −0.481405 0.833818i
\(626\) 2237.65 3875.72i 0.142866 0.247452i
\(627\) −5721.16 + 6358.48i −0.364404 + 0.404997i
\(628\) 1066.75 615.890i 0.0677836 0.0391349i
\(629\) −19893.9 −1.26108
\(630\) −1175.94 + 186.631i −0.0743662 + 0.0118025i
\(631\) −7326.82 −0.462244 −0.231122 0.972925i \(-0.574240\pi\)
−0.231122 + 0.972925i \(0.574240\pi\)
\(632\) 1264.64 730.138i 0.0795957 0.0459546i
\(633\) −13908.2 + 15457.5i −0.873301 + 0.970584i
\(634\) 7551.46 13079.5i 0.473039 0.819327i
\(635\) −523.995 907.586i −0.0327466 0.0567188i
\(636\) −1988.21 + 9369.98i −0.123959 + 0.584189i
\(637\) −6138.62 2738.79i −0.381822 0.170353i
\(638\) 16444.0i 1.02042i
\(639\) 12227.2 1293.81i 0.756963 0.0800975i
\(640\) −628.838 363.060i −0.0388391 0.0224238i
\(641\) −2433.38 1404.91i −0.149942 0.0865689i 0.423152 0.906059i \(-0.360924\pi\)
−0.573094 + 0.819490i \(0.694257\pi\)
\(642\) −3276.01 10070.5i −0.201392 0.619081i
\(643\) 27485.5i 1.68573i 0.538128 + 0.842863i \(0.319132\pi\)
−0.538128 + 0.842863i \(0.680868\pi\)
\(644\) −5441.92 + 3531.03i −0.332984 + 0.216059i
\(645\) −1005.73 213.405i −0.0613962 0.0130276i
\(646\) −4043.21 7003.05i −0.246251 0.426519i
\(647\) 14659.9 25391.7i 0.890790 1.54289i 0.0518595 0.998654i \(-0.483485\pi\)
0.838930 0.544239i \(-0.183181\pi\)
\(648\) 3598.53 + 16813.6i 0.218153 + 1.01929i
\(649\) 22044.3 12727.3i 1.33330 0.769783i
\(650\) −4617.78 −0.278653
\(651\) 7480.44 + 6057.99i 0.450356 + 0.364718i
\(652\) 10089.9 0.606061
\(653\) −14500.6 + 8371.91i −0.868992 + 0.501713i −0.867013 0.498285i \(-0.833963\pi\)
−0.00197863 + 0.999998i \(0.500630\pi\)
\(654\) 74.3780 + 66.9229i 0.00444711 + 0.00400137i
\(655\) 323.019 559.485i 0.0192693 0.0333754i
\(656\) −949.747 1645.01i −0.0565265 0.0979068i
\(657\) −5500.69 + 12378.1i −0.326640 + 0.735034i
\(658\) −657.599 12641.4i −0.0389603 0.748954i
\(659\) 9520.47i 0.562769i 0.959595 + 0.281385i \(0.0907937\pi\)
−0.959595 + 0.281385i \(0.909206\pi\)
\(660\) 1092.62 355.437i 0.0644394 0.0209626i
\(661\) −20217.5 11672.6i −1.18966 0.686853i −0.231434 0.972851i \(-0.574342\pi\)
−0.958230 + 0.285998i \(0.907675\pi\)
\(662\) −8067.16 4657.58i −0.473624 0.273447i
\(663\) 10140.5 3298.77i 0.594002 0.193233i
\(664\) 1724.58i 0.100793i
\(665\) 48.5515 + 933.331i 0.00283120 + 0.0544256i
\(666\) −3976.08 + 8947.34i −0.231337 + 0.520574i
\(667\) −8511.31 14742.0i −0.494092 0.855792i
\(668\) 5107.19 8845.91i 0.295813 0.512363i
\(669\) −11744.7 10567.5i −0.678740 0.610709i
\(670\) 615.625 355.431i 0.0354980 0.0204948i
\(671\) 32869.9 1.89110
\(672\) −12659.3 10252.1i −0.726703 0.588516i
\(673\) −12283.5 −0.703559 −0.351780 0.936083i \(-0.614423\pi\)
−0.351780 + 0.936083i \(0.614423\pi\)
\(674\) 6837.85 3947.84i 0.390778 0.225616i
\(675\) 15814.0 7060.82i 0.901750 0.402624i
\(676\) −3948.93 + 6839.74i −0.224677 + 0.389152i
\(677\) −6495.88 11251.2i −0.368769 0.638727i 0.620604 0.784124i \(-0.286887\pi\)
−0.989373 + 0.145397i \(0.953554\pi\)
\(678\) −8579.91 1820.57i −0.486002 0.103125i
\(679\) 22007.4 14279.6i 1.24384 0.807072i
\(680\) 3081.00i 0.173751i
\(681\) 7067.05 + 21724.2i 0.397665 + 1.22243i
\(682\) 6728.24 + 3884.55i 0.377768 + 0.218104i
\(683\) 7366.62 + 4253.12i 0.412703 + 0.238274i 0.691950 0.721945i \(-0.256752\pi\)
−0.279248 + 0.960219i \(0.590085\pi\)
\(684\) 4731.90 500.703i 0.264516 0.0279896i
\(685\) 1369.74i 0.0764018i
\(686\) 9432.34 7620.03i 0.524968 0.424102i
\(687\) 2139.38 10082.4i 0.118810 0.559923i
\(688\) 806.667 + 1397.19i 0.0447004 + 0.0774234i
\(689\) 4146.31 7181.62i 0.229263 0.397095i
\(690\) 665.397 739.520i 0.0367119 0.0408015i
\(691\) −22372.0 + 12916.5i −1.23165 + 0.711093i −0.967374 0.253354i \(-0.918466\pi\)
−0.264276 + 0.964447i \(0.585133\pi\)
\(692\) −4503.61 −0.247401
\(693\) 20095.7 3189.34i 1.10155 0.174824i
\(694\) −4429.93 −0.242303
\(695\) −894.770 + 516.595i −0.0488353 + 0.0281951i
\(696\) 17355.1 19288.4i 0.945177 1.05047i
\(697\) 9778.22 16936.4i 0.531387 0.920389i
\(698\) 216.457 + 374.914i 0.0117378 + 0.0203305i
\(699\) 4717.33 22231.7i 0.255259 1.20298i
\(700\) −4524.99 + 8872.30i −0.244327 + 0.479059i
\(701\) 22607.8i 1.21810i 0.793134 + 0.609048i \(0.208448\pi\)
−0.793134 + 0.609048i \(0.791552\pi\)
\(702\) 543.086 5220.01i 0.0291987 0.280650i
\(703\) 6655.69 + 3842.67i 0.357076 + 0.206158i
\(704\) −14253.8 8229.41i −0.763080 0.440565i
\(705\) −717.975 2207.06i −0.0383553 0.117905i
\(706\) 2835.96i 0.151180i
\(707\) 4453.86 231.688i 0.236923 0.0123246i
\(708\) −13852.0 2939.26i −0.735298 0.156023i
\(709\) 5472.41 + 9478.50i 0.289874 + 0.502077i 0.973779 0.227494i \(-0.0730532\pi\)
−0.683905 + 0.729571i \(0.739720\pi\)
\(710\) 542.159 939.048i 0.0286576 0.0496364i
\(711\) 1351.69 983.509i 0.0712971 0.0518769i
\(712\) 2343.80 1353.19i 0.123368 0.0712263i
\(713\) −8042.46 −0.422430
\(714\) −3009.89 + 18999.3i −0.157762 + 0.995841i
\(715\) −994.720 −0.0520285
\(716\) 546.601 315.580i 0.0285299 0.0164718i
\(717\) −14780.3 13298.9i −0.769849 0.692685i
\(718\) −10381.4 + 17981.1i −0.539595 + 0.934607i
\(719\) 12885.3 + 22317.9i 0.668344 + 1.15761i 0.978367 + 0.206877i \(0.0663299\pi\)
−0.310023 + 0.950729i \(0.600337\pi\)
\(720\) 313.048 + 139.114i 0.0162036 + 0.00720068i
\(721\) −18297.3 9331.88i −0.945116 0.482021i
\(722\) 9968.76i 0.513849i
\(723\) −16997.4 + 5529.40i −0.874330 + 0.284427i
\(724\) 7761.13 + 4480.89i 0.398398 + 0.230015i
\(725\) −22633.2 13067.3i −1.15942 0.669389i
\(726\) 3062.89 996.381i 0.156576 0.0509355i
\(727\) 15593.1i 0.795485i 0.917497 + 0.397742i \(0.130206\pi\)
−0.917497 + 0.397742i \(0.869794\pi\)
\(728\) 4659.63 + 7181.28i 0.237221 + 0.365599i
\(729\) 6121.81 + 18706.8i 0.311020 + 0.950403i
\(730\) 597.273 + 1034.51i 0.0302823 + 0.0524505i
\(731\) −8305.13 + 14384.9i −0.420214 + 0.727832i
\(732\) −13593.2 12230.7i −0.686363 0.617568i
\(733\) 692.858 400.022i 0.0349131 0.0201571i −0.482442 0.875928i \(-0.660250\pi\)
0.517355 + 0.855771i \(0.326917\pi\)
\(734\) 7272.94 0.365734
\(735\) 1307.55 1798.08i 0.0656185 0.0902358i
\(736\) 13610.4 0.681641
\(737\) −10520.5 + 6073.99i −0.525815 + 0.303580i
\(738\) −5662.86 7782.76i −0.282456 0.388194i
\(739\) 454.445 787.122i 0.0226211 0.0391810i −0.854493 0.519463i \(-0.826132\pi\)
0.877114 + 0.480282i \(0.159466\pi\)
\(740\) −516.179 894.048i −0.0256421 0.0444133i
\(741\) −4029.77 855.076i −0.199781 0.0423914i
\(742\) 8142.55 + 12549.1i 0.402860 + 0.620877i
\(743\) 8109.00i 0.400391i 0.979756 + 0.200195i \(0.0641577\pi\)
−0.979756 + 0.200195i \(0.935842\pi\)
\(744\) −3792.28 11657.5i −0.186870 0.574442i
\(745\) 964.258 + 556.715i 0.0474197 + 0.0273778i
\(746\) −16099.7 9295.14i −0.790148 0.456192i
\(747\) 207.737 + 1963.22i 0.0101750 + 0.0961588i
\(748\) 18562.8i 0.907382i
\(749\) 17615.1 + 8983.95i 0.859337 + 0.438273i
\(750\) 638.041 3006.94i 0.0310639 0.146397i
\(751\) 10382.2 + 17982.5i 0.504463 + 0.873756i 0.999987 + 0.00516122i \(0.00164288\pi\)
−0.495524 + 0.868594i \(0.665024\pi\)
\(752\) −1820.99 + 3154.05i −0.0883041 + 0.152947i
\(753\) 7113.09 7905.46i 0.344243 0.382591i
\(754\) −6858.67 + 3959.85i −0.331271 + 0.191259i
\(755\) −1777.61 −0.0856870
\(756\) −9497.21 6158.57i −0.456892 0.296276i
\(757\) 23295.6 1.11848 0.559242 0.829005i \(-0.311092\pi\)
0.559242 + 0.829005i \(0.311092\pi\)
\(758\) −529.273 + 305.576i −0.0253616 + 0.0146425i
\(759\) −11371.0 + 12637.7i −0.543796 + 0.604374i
\(760\) 595.119 1030.78i 0.0284042 0.0491976i
\(761\) 5014.38 + 8685.16i 0.238858 + 0.413715i 0.960387 0.278670i \(-0.0898935\pi\)
−0.721529 + 0.692385i \(0.756560\pi\)
\(762\) −1729.65 + 8151.43i −0.0822290 + 0.387526i
\(763\) −186.571 + 9.70535i −0.00885233 + 0.000460494i
\(764\) 12845.7i 0.608299i
\(765\) 371.128 + 3507.35i 0.0175401 + 0.165763i
\(766\) 7224.45 + 4171.04i 0.340770 + 0.196744i
\(767\) 10616.9 + 6129.66i 0.499809 + 0.288565i
\(768\) 6987.55 + 21479.8i 0.328309 + 1.00923i
\(769\) 13500.3i 0.633074i −0.948580 0.316537i \(-0.897480\pi\)
0.948580 0.316537i \(-0.102520\pi\)
\(770\) 815.259 1598.51i 0.0381557 0.0748132i
\(771\) 30757.8 + 6526.49i 1.43673 + 0.304858i
\(772\) 4946.21 + 8567.09i 0.230593 + 0.399399i
\(773\) 11644.9 20169.5i 0.541833 0.938482i −0.456966 0.889484i \(-0.651064\pi\)
0.998799 0.0489979i \(-0.0156028\pi\)
\(774\) 4809.75 + 6610.29i 0.223363 + 0.306979i
\(775\) −10693.2 + 6173.74i −0.495629 + 0.286151i
\(776\) −33410.2 −1.54556
\(777\) −6551.10 17068.0i −0.302470 0.788046i
\(778\) 26179.3 1.20639
\(779\) −6542.79 + 3777.48i −0.300924 + 0.173739i
\(780\) 411.360 + 370.129i 0.0188834 + 0.0169907i
\(781\) −9264.99 + 16047.4i −0.424491 + 0.735240i
\(782\) −8036.02 13918.8i −0.367478 0.636490i
\(783\) 17433.3 24048.1i 0.795677 1.09759i
\(784\) −3469.88 + 361.983i −0.158067 + 0.0164898i
\(785\) 352.711i 0.0160367i
\(786\) −4884.88 + 1589.09i −0.221677 + 0.0721132i
\(787\) −20635.4 11913.8i −0.934653 0.539622i −0.0463726 0.998924i \(-0.514766\pi\)
−0.888280 + 0.459302i \(0.848099\pi\)
\(788\) 1870.70 + 1080.05i 0.0845698 + 0.0488264i
\(789\) −31002.9 + 10085.5i −1.39890 + 0.455074i
\(790\) 147.419i 0.00663916i
\(791\) 13738.7 8914.42i 0.617560 0.400709i
\(792\) −23680.1 10523.1i −1.06242 0.472125i
\(793\) 7915.34 + 13709.8i 0.354454 + 0.613932i
\(794\) 2404.27 4164.32i 0.107461 0.186129i
\(795\) 2038.91 + 1834.55i 0.0909594 + 0.0818424i
\(796\) −3167.98 + 1829.03i −0.141063 + 0.0814426i
\(797\) −12609.3 −0.560406 −0.280203 0.959941i \(-0.590402\pi\)
−0.280203 + 0.959941i \(0.590402\pi\)
\(798\) 4676.85 5775.00i 0.207467 0.256182i
\(799\) −37496.4 −1.66023
\(800\) 18096.4 10448.0i 0.799756 0.461739i
\(801\) 2505.14 1822.78i 0.110505 0.0804054i
\(802\) 2500.54 4331.06i 0.110096 0.190692i
\(803\) −10206.8 17678.8i −0.448557 0.776924i
\(804\) 6610.76 + 1402.74i 0.289980 + 0.0615307i
\(805\) 96.4977 + 1855.03i 0.00422497 + 0.0812188i
\(806\) 3741.73i 0.163519i
\(807\) −5362.97 16485.8i −0.233935 0.719118i
\(808\) −4918.87 2839.91i −0.214165 0.123648i
\(809\) 30281.4 + 17483.0i 1.31599 + 0.759789i 0.983082 0.183169i \(-0.0586354\pi\)
0.332912 + 0.942958i \(0.391969\pi\)
\(810\) 1651.61 + 534.079i 0.0716442 + 0.0231674i
\(811\) 5691.42i 0.246428i 0.992380 + 0.123214i \(0.0393201\pi\)
−0.992380 + 0.123214i \(0.960680\pi\)
\(812\) 887.354 + 17058.1i 0.0383498 + 0.737218i
\(813\) −3066.52 + 14451.8i −0.132285 + 0.623428i
\(814\) −7377.84 12778.8i −0.317682 0.550241i
\(815\) 1444.59 2502.10i 0.0620879 0.107539i
\(816\) 3701.84 4114.22i 0.158812 0.176503i
\(817\) 5557.12 3208.40i 0.237967 0.137390i
\(818\) 26578.9 1.13607
\(819\) 6169.47 + 7613.75i 0.263222 + 0.324842i
\(820\) 1014.85 0.0432195
\(821\) 10487.0 6054.70i 0.445798 0.257382i −0.260256 0.965540i \(-0.583807\pi\)
0.706054 + 0.708158i \(0.250474\pi\)
\(822\) 7284.86 8096.37i 0.309110 0.343544i
\(823\) 15861.0 27472.0i 0.671784 1.16356i −0.305614 0.952155i \(-0.598862\pi\)
0.977398 0.211408i \(-0.0678049\pi\)
\(824\) 13079.0 + 22653.5i 0.552946 + 0.957731i
\(825\) −5417.61 + 25531.9i −0.228627 + 1.07746i
\(826\) −18551.8 + 12037.5i −0.781476 + 0.507066i
\(827\) 36401.9i 1.53061i −0.643666 0.765307i \(-0.722587\pi\)
0.643666 0.765307i \(-0.277413\pi\)
\(828\) 9404.82 995.165i 0.394735 0.0417686i
\(829\) 27287.8 + 15754.6i 1.14324 + 0.660049i 0.947230 0.320554i \(-0.103869\pi\)
0.196007 + 0.980602i \(0.437202\pi\)
\(830\) 150.776 + 87.0505i 0.00630543 + 0.00364044i
\(831\) −10204.5 31368.9i −0.425983 1.30948i
\(832\) 7926.83i 0.330305i
\(833\) −21089.8 29075.0i −0.877214 1.20935i
\(834\) 8036.32 + 1705.22i 0.333663 + 0.0707998i
\(835\) −1462.40 2532.96i −0.0606090 0.104978i
\(836\) −3585.54 + 6210.34i −0.148336 + 0.256925i
\(837\) −5721.28 12813.9i −0.236268 0.529166i
\(838\) 25079.2 14479.5i 1.03383 0.596881i
\(839\) −13781.4 −0.567090 −0.283545 0.958959i \(-0.591510\pi\)
−0.283545 + 0.958959i \(0.591510\pi\)
\(840\) −2643.35 + 1014.58i −0.108576 + 0.0416741i
\(841\) −20433.0 −0.837796
\(842\) 1739.93 1004.55i 0.0712136 0.0411152i
\(843\) 14430.6 + 12984.2i 0.589582 + 0.530487i
\(844\) −8716.46 + 15097.4i −0.355489 + 0.615726i
\(845\) 1130.74 + 1958.51i 0.0460341 + 0.0797334i
\(846\) −7494.20 + 16864.1i −0.304558 + 0.685343i
\(847\) −2732.43 + 5357.56i −0.110847 + 0.217341i
\(848\) 4303.95i 0.174290i
\(849\) 27261.6 8868.40i 1.10202 0.358496i
\(850\) −21369.3 12337.6i −0.862309 0.497854i
\(851\) 13228.4 + 7637.43i 0.532860 + 0.307647i
\(852\) 9802.63 3188.87i 0.394170 0.128227i
\(853\) 11376.3i 0.456645i −0.973586 0.228322i \(-0.926676\pi\)
0.973586 0.228322i \(-0.0733240\pi\)
\(854\) −28518.8 + 1483.54i −1.14273 + 0.0594444i
\(855\) 553.308 1245.10i 0.0221318 0.0498030i
\(856\) −12591.3 21808.8i −0.502761 0.870807i
\(857\) −21559.6 + 37342.3i −0.859349 + 1.48844i 0.0132022 + 0.999913i \(0.495797\pi\)
−0.872551 + 0.488523i \(0.837536\pi\)
\(858\) 5879.65 + 5290.32i 0.233948 + 0.210499i
\(859\) 32325.9 18663.4i 1.28399 0.741311i 0.306413 0.951899i \(-0.400871\pi\)
0.977575 + 0.210588i \(0.0675378\pi\)
\(860\) −861.960 −0.0341774
\(861\) 17750.6 + 2812.07i 0.702600 + 0.111307i
\(862\) 15260.5 0.602986
\(863\) −30262.7 + 17472.2i −1.19369 + 0.689176i −0.959141 0.282929i \(-0.908694\pi\)
−0.234547 + 0.972105i \(0.575361\pi\)
\(864\) 9682.26 + 21685.2i 0.381247 + 0.853873i
\(865\) −644.788 + 1116.80i −0.0253450 + 0.0438988i
\(866\) 12301.9 + 21307.5i 0.482719 + 0.836093i
\(867\) 30767.1 + 6528.45i 1.20520 + 0.255730i
\(868\) 7189.11 + 3666.54i 0.281122 + 0.143376i
\(869\) 2519.25i 0.0983426i
\(870\) −810.319 2490.93i −0.0315775 0.0970694i
\(871\) −5066.82 2925.33i −0.197110 0.113801i
\(872\) 206.050 + 118.963i 0.00800200 + 0.00461995i
\(873\) −38033.5 + 4024.49i −1.47450 + 0.156023i
\(874\) 6208.89i 0.240296i
\(875\) 3124.17 + 4814.88i 0.120704 + 0.186026i
\(876\) −2357.18 + 11108.8i −0.0909152 + 0.428462i
\(877\) −2054.59 3558.66i −0.0791092 0.137021i 0.823757 0.566944i \(-0.191874\pi\)
−0.902866 + 0.429922i \(0.858541\pi\)
\(878\) −13728.1 + 23777.8i −0.527678 + 0.913964i
\(879\) −26325.5 + 29258.1i −1.01017 + 1.12270i
\(880\) −447.102 + 258.134i −0.0171271 + 0.00988831i
\(881\) 15697.6 0.600301 0.300151 0.953892i \(-0.402963\pi\)
0.300151 + 0.953892i \(0.402963\pi\)
\(882\) −17291.6 + 3674.15i −0.660136 + 0.140267i
\(883\) −44102.6 −1.68083 −0.840413 0.541946i \(-0.817688\pi\)
−0.840413 + 0.541946i \(0.817688\pi\)
\(884\) 7742.37 4470.06i 0.294575 0.170073i
\(885\) −2712.09 + 3014.20i −0.103012 + 0.114487i
\(886\) 3782.46 6551.42i 0.143425 0.248419i
\(887\) −14164.5 24533.5i −0.536185 0.928699i −0.999105 0.0422991i \(-0.986532\pi\)
0.462920 0.886400i \(-0.346802\pi\)
\(888\) −4832.79 + 22775.8i −0.182633 + 0.860704i
\(889\) −8469.24 13052.5i −0.319515 0.492428i
\(890\) 273.218i 0.0102902i
\(891\) −28224.5 9126.89i −1.06123 0.343168i
\(892\) −11471.1 6622.84i −0.430584 0.248598i
\(893\) 12544.8 + 7242.73i 0.470095 + 0.271409i
\(894\) −2738.76 8418.97i −0.102458 0.314958i
\(895\) 180.728i 0.00674979i
\(896\) −9603.75 4898.04i −0.358079 0.182625i
\(897\) −8009.31 1699.49i −0.298131 0.0632602i
\(898\) 12864.7 + 22282.3i 0.478062 + 0.828028i
\(899\) −10588.3 + 18339.4i −0.392812 + 0.680370i
\(900\) 11740.7 8542.72i 0.434840 0.316397i
\(901\) 38375.1 22155.9i 1.41894 0.819223i
\(902\) 14505.4 0.535450
\(903\) −15076.5 2388.43i −0.555607 0.0880201i
\(904\) −20857.1 −0.767365
\(905\) 2222.34 1283.07i 0.0816277 0.0471278i
\(906\) 10507.2 + 9454.03i 0.385295 + 0.346677i
\(907\) −7102.79 + 12302.4i −0.260027 + 0.450380i −0.966249 0.257611i \(-0.917065\pi\)
0.706222 + 0.707991i \(0.250398\pi\)
\(908\) 9576.32 + 16586.7i 0.350002 + 0.606220i
\(909\) −5941.64 2640.39i −0.216800 0.0963434i
\(910\) 863.045 44.8952i 0.0314392 0.00163545i
\(911\) 17955.9i 0.653025i −0.945193 0.326512i \(-0.894127\pi\)
0.945193 0.326512i \(-0.105873\pi\)
\(912\) −2033.18 + 661.410i −0.0738216 + 0.0240148i
\(913\) −2576.62 1487.61i −0.0933993 0.0539241i
\(914\) 6578.63 + 3798.17i 0.238076 + 0.137453i
\(915\) −4979.11 + 1619.74i −0.179895 + 0.0585214i
\(916\) 8641.09i 0.311692i
\(917\) 4357.84 8544.57i 0.156934 0.307706i
\(918\) 16459.8 22705.2i 0.591781 0.816323i
\(919\) 21121.3 + 36583.1i 0.758135 + 1.31313i 0.943800 + 0.330516i \(0.107223\pi\)
−0.185665 + 0.982613i \(0.559444\pi\)
\(920\) 1182.82 2048.70i 0.0423874 0.0734171i
\(921\) 41082.5 + 36964.7i 1.46983 + 1.32251i
\(922\) −14966.7 + 8641.01i −0.534600 + 0.308651i
\(923\) −8924.34 −0.318254
\(924\) 15926.0 6112.75i 0.567019 0.217635i
\(925\) 23451.3 0.833593
\(926\) 9482.32 5474.62i 0.336510 0.194284i
\(927\) 17617.6 + 24212.8i 0.624206 + 0.857878i
\(928\) 17918.7 31036.2i 0.633849 1.09786i
\(929\) −22338.1 38690.6i −0.788900 1.36641i −0.926642 0.375946i \(-0.877318\pi\)
0.137742 0.990468i \(-0.456016\pi\)
\(930\) −1210.61 256.879i −0.0426854 0.00905741i
\(931\) 1439.74 + 13801.0i 0.0506826 + 0.485831i
\(932\) 19053.6i 0.669660i
\(933\) −9276.80 28517.0i −0.325519 1.00065i
\(934\) −20486.2 11827.7i −0.717696 0.414362i
\(935\) −4603.19 2657.65i −0.161006 0.0929566i
\(936\) −1313.24 12410.8i −0.0458597 0.433398i
\(937\) 15309.3i 0.533761i −0.963730 0.266880i \(-0.914007\pi\)
0.963730 0.266880i \(-0.0859929\pi\)
\(938\) 8853.68 5744.78i 0.308191 0.199972i
\(939\) 2528.70 11917.2i 0.0878817 0.414166i
\(940\) −972.904 1685.12i −0.0337581 0.0584708i
\(941\) 21192.2 36706.0i 0.734162 1.27161i −0.220928 0.975290i \(-0.570909\pi\)
0.955090 0.296316i \(-0.0957582\pi\)
\(942\) −1875.86 + 2084.82i −0.0648819 + 0.0721096i
\(943\) −13004.0 + 7507.87i −0.449066 + 0.259268i
\(944\) 6362.70 0.219373
\(945\) −2886.93 + 1473.39i −0.0993775 + 0.0507188i
\(946\) −12320.1 −0.423427
\(947\) 10648.1 6147.69i 0.365383 0.210954i −0.306057 0.952013i \(-0.599010\pi\)
0.671439 + 0.741060i \(0.265676\pi\)
\(948\) 937.398 1041.82i 0.0321153 0.0356928i
\(949\) 4915.78 8514.37i 0.168148 0.291242i
\(950\) 4766.21 + 8255.32i 0.162775 + 0.281935i
\(951\) 8533.67 40217.2i 0.290981 1.37133i
\(952\) 2376.34 + 45681.6i 0.0809008 + 1.55520i
\(953\) 1322.78i 0.0449621i 0.999747 + 0.0224811i \(0.00715655\pi\)
−0.999747 + 0.0224811i \(0.992843\pi\)
\(954\) −2294.85 21687.5i −0.0778810 0.736015i
\(955\) −3185.47 1839.13i −0.107936 0.0623171i
\(956\) −14436.0 8334.62i −0.488382 0.281967i
\(957\) 13847.6 + 42567.6i 0.467742 + 1.43784i
\(958\) 15781.7i 0.532238i
\(959\) 1056.47 + 20309.1i 0.0355737 + 0.683852i
\(960\) 2564.67 + 544.197i 0.0862234 + 0.0182957i
\(961\) −9893.00 17135.2i −0.332080 0.575180i
\(962\) 3553.29 6154.47i 0.119088 0.206266i
\(963\) −16960.8 23310.1i −0.567553 0.780017i
\(964\) −12977.7 + 7492.70i −0.433594 + 0.250336i
\(965\) 2832.62 0.0944925
\(966\) 9295.40 11478.0i 0.309601 0.382297i
\(967\) 36887.2 1.22669 0.613346 0.789814i \(-0.289823\pi\)
0.613346 + 0.789814i \(0.289823\pi\)
\(968\) 6633.06 3829.60i 0.220242 0.127157i
\(969\) −16363.7 14723.5i −0.542495 0.488120i
\(970\) −1686.43 + 2920.98i −0.0558226 + 0.0966875i
\(971\) 3409.79 + 5905.93i 0.112693 + 0.195191i 0.916855 0.399220i \(-0.130719\pi\)
−0.804162 + 0.594410i \(0.797386\pi\)
\(972\) 8276.02 + 14276.5i 0.273100 + 0.471111i
\(973\) −12868.2 + 8349.64i −0.423984 + 0.275105i
\(974\) 1794.59i 0.0590373i
\(975\) −11953.8 + 3888.65i −0.392643 + 0.127730i
\(976\) 7115.50 + 4108.14i 0.233362 + 0.134732i
\(977\) 42700.8 + 24653.3i 1.39828 + 0.807298i 0.994213 0.107431i \(-0.0342624\pi\)
0.404068 + 0.914729i \(0.367596\pi\)
\(978\) −21845.9 + 7106.65i −0.714269 + 0.232357i
\(979\) 4669.03i 0.152424i
\(980\) 759.444 1702.19i 0.0247546 0.0554842i
\(981\) 248.894 + 110.605i 0.00810047 + 0.00359975i
\(982\) −1009.11 1747.82i −0.0327921 0.0567977i
\(983\) −9765.55 + 16914.4i −0.316859 + 0.548816i −0.979831 0.199828i \(-0.935962\pi\)
0.662972 + 0.748644i \(0.269295\pi\)
\(984\) −17014.4 15309.0i −0.551220 0.495970i
\(985\) 535.661 309.264i 0.0173275 0.0100040i
\(986\) −42319.1 −1.36685
\(987\) −12347.6 32170.1i −0.398206 1.03747i
\(988\) −3453.71 −0.111212
\(989\) 11045.0 6376.81i 0.355116 0.205026i
\(990\) −2115.30 + 1539.13i −0.0679077 + 0.0494107i
\(991\) −9285.39 + 16082.8i −0.297639 + 0.515526i −0.975595 0.219576i \(-0.929533\pi\)
0.677956 + 0.735102i \(0.262866\pi\)
\(992\) −8465.85 14663.3i −0.270959 0.469314i
\(993\) −24805.1 5263.39i −0.792716 0.168206i
\(994\) 7314.27 14341.3i 0.233395 0.457625i
\(995\) 1047.46i 0.0333735i
\(996\) 512.014 + 1573.94i 0.0162889 + 0.0500723i
\(997\) 19389.3 + 11194.4i 0.615913 + 0.355598i 0.775276 0.631622i \(-0.217611\pi\)
−0.159363 + 0.987220i \(0.550944\pi\)
\(998\) −10205.1 5891.89i −0.323683 0.186878i
\(999\) −2758.05 + 26509.7i −0.0873481 + 0.839569i
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 21.4.g.a.17.3 yes 12
3.2 odd 2 inner 21.4.g.a.17.4 yes 12
4.3 odd 2 336.4.bc.d.17.5 12
7.2 even 3 147.4.g.d.68.4 12
7.3 odd 6 147.4.c.a.146.5 12
7.4 even 3 147.4.c.a.146.6 12
7.5 odd 6 inner 21.4.g.a.5.4 yes 12
7.6 odd 2 147.4.g.d.80.3 12
12.11 even 2 336.4.bc.d.17.3 12
21.2 odd 6 147.4.g.d.68.3 12
21.5 even 6 inner 21.4.g.a.5.3 12
21.11 odd 6 147.4.c.a.146.7 12
21.17 even 6 147.4.c.a.146.8 12
21.20 even 2 147.4.g.d.80.4 12
28.19 even 6 336.4.bc.d.257.3 12
84.47 odd 6 336.4.bc.d.257.5 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.4.g.a.5.3 12 21.5 even 6 inner
21.4.g.a.5.4 yes 12 7.5 odd 6 inner
21.4.g.a.17.3 yes 12 1.1 even 1 trivial
21.4.g.a.17.4 yes 12 3.2 odd 2 inner
147.4.c.a.146.5 12 7.3 odd 6
147.4.c.a.146.6 12 7.4 even 3
147.4.c.a.146.7 12 21.11 odd 6
147.4.c.a.146.8 12 21.17 even 6
147.4.g.d.68.3 12 21.2 odd 6
147.4.g.d.68.4 12 7.2 even 3
147.4.g.d.80.3 12 7.6 odd 2
147.4.g.d.80.4 12 21.20 even 2
336.4.bc.d.17.3 12 12.11 even 2
336.4.bc.d.17.5 12 4.3 odd 2
336.4.bc.d.257.3 12 28.19 even 6
336.4.bc.d.257.5 12 84.47 odd 6