Properties

Label 201.4.f.a.38.19
Level $201$
Weight $4$
Character 201.38
Analytic conductor $11.859$
Analytic rank $0$
Dimension $132$
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] = [201,4,Mod(38,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.38");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 201.f (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: \(11.8593839112\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(66\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 38.19
Character \(\chi\) \(=\) 201.38
Dual form 201.4.f.a.164.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41509 + 2.45101i) q^{2} +(-3.33481 - 3.98485i) q^{3} +(-0.00495393 - 0.00858046i) q^{4} -13.4714 q^{5} +(14.4859 - 2.53472i) q^{6} +(-13.0426 + 7.53016i) q^{7} -22.6134 q^{8} +(-4.75808 + 26.5774i) q^{9} +O(q^{10})\) \(q+(-1.41509 + 2.45101i) q^{2} +(-3.33481 - 3.98485i) q^{3} +(-0.00495393 - 0.00858046i) q^{4} -13.4714 q^{5} +(14.4859 - 2.53472i) q^{6} +(-13.0426 + 7.53016i) q^{7} -22.6134 q^{8} +(-4.75808 + 26.5774i) q^{9} +(19.0632 - 33.0185i) q^{10} +(13.2779 + 22.9980i) q^{11} +(-0.0176714 + 0.0483549i) q^{12} +(8.31020 + 4.79790i) q^{13} -42.6234i q^{14} +(44.9246 + 53.6816i) q^{15} +(32.0396 - 55.4942i) q^{16} +(-35.4527 - 20.4686i) q^{17} +(-58.4084 - 49.2715i) q^{18} +(48.5460 - 84.0841i) q^{19} +(0.0667364 + 0.115591i) q^{20} +(73.5013 + 26.8613i) q^{21} -75.1577 q^{22} +(-63.8718 - 36.8764i) q^{23} +(75.4113 + 90.1110i) q^{24} +56.4790 q^{25} +(-23.5194 + 13.5789i) q^{26} +(121.774 - 69.6705i) q^{27} +(0.129225 + 0.0746078i) q^{28} +(249.019 - 143.771i) q^{29} +(-195.146 + 34.1463i) q^{30} +(92.7892 - 53.5718i) q^{31} +(0.224189 + 0.388307i) q^{32} +(47.3644 - 129.605i) q^{33} +(100.337 - 57.9298i) q^{34} +(175.703 - 101.442i) q^{35} +(0.251618 - 0.0908363i) q^{36} +(-105.443 + 182.632i) q^{37} +(137.394 + 237.973i) q^{38} +(-8.59404 - 49.1150i) q^{39} +304.634 q^{40} +(92.8379 + 160.800i) q^{41} +(-169.848 + 142.141i) q^{42} +211.707i q^{43} +(0.131556 - 0.227861i) q^{44} +(64.0980 - 358.036i) q^{45} +(180.768 - 104.367i) q^{46} +(165.401 - 95.4942i) q^{47} +(-327.982 + 57.3896i) q^{48} +(-58.0932 + 100.620i) q^{49} +(-79.9228 + 138.430i) q^{50} +(36.6636 + 209.533i) q^{51} -0.0950738i q^{52} +51.4981 q^{53} +(-1.55886 + 397.060i) q^{54} +(-178.872 - 309.816i) q^{55} +(294.938 - 170.283i) q^{56} +(-496.954 + 86.9561i) q^{57} +813.796i q^{58} -798.917i q^{59} +(0.238059 - 0.651409i) q^{60} +(-105.852 - 61.1136i) q^{61} +303.236i q^{62} +(-138.075 - 382.469i) q^{63} +511.364 q^{64} +(-111.950 - 64.6345i) q^{65} +(250.637 + 299.492i) q^{66} +(-70.0189 + 543.930i) q^{67} +0.405601i q^{68} +(66.0533 + 377.495i) q^{69} +574.198i q^{70} +(-614.652 + 354.870i) q^{71} +(107.596 - 601.006i) q^{72} +(324.458 - 561.978i) q^{73} +(-298.422 - 516.882i) q^{74} +(-188.347 - 225.060i) q^{75} -0.961974 q^{76} +(-346.358 - 199.970i) q^{77} +(132.543 + 48.4381i) q^{78} +(718.162 - 414.631i) q^{79} +(-431.618 + 747.585i) q^{80} +(-683.721 - 252.915i) q^{81} -525.496 q^{82} +(186.992 + 107.960i) q^{83} +(-0.133638 - 0.763743i) q^{84} +(477.598 + 275.741i) q^{85} +(-518.895 - 299.584i) q^{86} +(-1403.34 - 512.854i) q^{87} +(-300.258 - 520.063i) q^{88} -813.215i q^{89} +(786.843 + 663.757i) q^{90} -144.516 q^{91} +0.730732i q^{92} +(-522.910 - 191.099i) q^{93} +540.531i q^{94} +(-653.983 + 1132.73i) q^{95} +(0.799717 - 2.18829i) q^{96} +(-1605.68 - 927.039i) q^{97} +(-164.414 - 284.774i) q^{98} +(-674.406 + 243.467i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q - 258 q^{4} - 23 q^{6} - 66 q^{7} - 70 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 132 q - 258 q^{4} - 23 q^{6} - 66 q^{7} - 70 q^{9} - 18 q^{10} + 114 q^{12} - 180 q^{13} - 188 q^{15} - 738 q^{16} + 159 q^{18} - 208 q^{19} + 96 q^{21} - 324 q^{22} + 736 q^{24} + 2508 q^{25} + 1704 q^{28} - 843 q^{30} + 612 q^{31} + 146 q^{33} - 762 q^{34} + 221 q^{36} - 238 q^{37} - 394 q^{39} - 864 q^{40} - 3462 q^{46} + 951 q^{48} + 2316 q^{49} - 309 q^{51} - 376 q^{54} - 96 q^{55} - 1113 q^{57} + 122 q^{60} + 1728 q^{61} - 534 q^{63} + 900 q^{64} - 1214 q^{67} - 372 q^{69} + 578 q^{73} - 184 q^{76} - 4686 q^{78} + 4476 q^{79} + 666 q^{81} + 1368 q^{82} + 1161 q^{84} - 1908 q^{85} - 462 q^{87} + 2562 q^{88} - 1160 q^{90} - 3636 q^{91} - 1828 q^{93} - 3900 q^{96} + 1074 q^{97} + 906 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41509 + 2.45101i −0.500310 + 0.866562i 0.499690 + 0.866204i \(0.333447\pi\)
−1.00000 0.000357445i \(0.999886\pi\)
\(3\) −3.33481 3.98485i −0.641785 0.766885i
\(4\) −0.00495393 0.00858046i −0.000619241 0.00107256i
\(5\) −13.4714 −1.20492 −0.602460 0.798149i \(-0.705813\pi\)
−0.602460 + 0.798149i \(0.705813\pi\)
\(6\) 14.4859 2.53472i 0.985644 0.172466i
\(7\) −13.0426 + 7.53016i −0.704236 + 0.406591i −0.808923 0.587915i \(-0.799949\pi\)
0.104687 + 0.994505i \(0.466616\pi\)
\(8\) −22.6134 −0.999380
\(9\) −4.75808 + 26.5774i −0.176225 + 0.984350i
\(10\) 19.0632 33.0185i 0.602833 1.04414i
\(11\) 13.2779 + 22.9980i 0.363949 + 0.630378i 0.988607 0.150520i \(-0.0480949\pi\)
−0.624658 + 0.780899i \(0.714762\pi\)
\(12\) −0.0176714 + 0.0483549i −0.000425109 + 0.00116324i
\(13\) 8.31020 + 4.79790i 0.177295 + 0.102361i 0.586021 0.810296i \(-0.300694\pi\)
−0.408726 + 0.912657i \(0.634027\pi\)
\(14\) 42.6234i 0.813685i
\(15\) 44.9246 + 53.6816i 0.773299 + 0.924035i
\(16\) 32.0396 55.4942i 0.500618 0.867097i
\(17\) −35.4527 20.4686i −0.505797 0.292022i 0.225308 0.974288i \(-0.427661\pi\)
−0.731104 + 0.682266i \(0.760995\pi\)
\(18\) −58.4084 49.2715i −0.764833 0.645190i
\(19\) 48.5460 84.0841i 0.586169 1.01527i −0.408559 0.912732i \(-0.633969\pi\)
0.994729 0.102543i \(-0.0326980\pi\)
\(20\) 0.0667364 + 0.115591i 0.000746136 + 0.00129235i
\(21\) 73.5013 + 26.8613i 0.763776 + 0.279124i
\(22\) −75.1577 −0.728349
\(23\) −63.8718 36.8764i −0.579051 0.334316i 0.181705 0.983353i \(-0.441838\pi\)
−0.760756 + 0.649038i \(0.775172\pi\)
\(24\) 75.4113 + 90.1110i 0.641387 + 0.766409i
\(25\) 56.4790 0.451832
\(26\) −23.5194 + 13.5789i −0.177405 + 0.102425i
\(27\) 121.774 69.6705i 0.867982 0.496596i
\(28\) 0.129225 + 0.0746078i 0.000872184 + 0.000503555i
\(29\) 249.019 143.771i 1.59454 0.920608i 0.602026 0.798477i \(-0.294360\pi\)
0.992514 0.122131i \(-0.0389729\pi\)
\(30\) −195.146 + 34.1463i −1.18762 + 0.207808i
\(31\) 92.7892 53.5718i 0.537594 0.310380i −0.206509 0.978445i \(-0.566210\pi\)
0.744103 + 0.668064i \(0.232877\pi\)
\(32\) 0.224189 + 0.388307i 0.00123848 + 0.00214511i
\(33\) 47.3644 129.605i 0.249851 0.683674i
\(34\) 100.337 57.9298i 0.506110 0.292203i
\(35\) 175.703 101.442i 0.848548 0.489909i
\(36\) 0.251618 0.0908363i 0.00116490 0.000420539i
\(37\) −105.443 + 182.632i −0.468505 + 0.811475i −0.999352 0.0359927i \(-0.988541\pi\)
0.530847 + 0.847468i \(0.321874\pi\)
\(38\) 137.394 + 237.973i 0.586532 + 1.01590i
\(39\) −8.59404 49.1150i −0.0352859 0.201659i
\(40\) 304.634 1.20417
\(41\) 92.8379 + 160.800i 0.353630 + 0.612506i 0.986883 0.161440i \(-0.0516137\pi\)
−0.633252 + 0.773946i \(0.718280\pi\)
\(42\) −169.848 + 142.141i −0.624003 + 0.522210i
\(43\) 211.707i 0.750813i 0.926860 + 0.375407i \(0.122497\pi\)
−0.926860 + 0.375407i \(0.877503\pi\)
\(44\) 0.131556 0.227861i 0.000450745 0.000780713i
\(45\) 64.0980 358.036i 0.212337 1.18606i
\(46\) 180.768 104.367i 0.579410 0.334522i
\(47\) 165.401 95.4942i 0.513323 0.296367i −0.220876 0.975302i \(-0.570891\pi\)
0.734199 + 0.678935i \(0.237558\pi\)
\(48\) −327.982 + 57.3896i −0.986253 + 0.172572i
\(49\) −58.0932 + 100.620i −0.169368 + 0.293354i
\(50\) −79.9228 + 138.430i −0.226056 + 0.391540i
\(51\) 36.6636 + 209.533i 0.100665 + 0.575303i
\(52\) 0.0950738i 0.000253545i
\(53\) 51.4981 0.133468 0.0667341 0.997771i \(-0.478742\pi\)
0.0667341 + 0.997771i \(0.478742\pi\)
\(54\) −1.55886 + 397.060i −0.00392841 + 1.00061i
\(55\) −178.872 309.816i −0.438530 0.759555i
\(56\) 294.938 170.283i 0.703799 0.406339i
\(57\) −496.954 + 86.9561i −1.15479 + 0.202063i
\(58\) 813.796i 1.84236i
\(59\) 798.917i 1.76288i −0.472292 0.881442i \(-0.656573\pi\)
0.472292 0.881442i \(-0.343427\pi\)
\(60\) 0.238059 0.651409i 0.000512222 0.00140161i
\(61\) −105.852 61.1136i −0.222179 0.128275i 0.384780 0.923008i \(-0.374277\pi\)
−0.606959 + 0.794733i \(0.707611\pi\)
\(62\) 303.236i 0.621145i
\(63\) −138.075 382.469i −0.276123 0.764866i
\(64\) 511.364 0.998758
\(65\) −111.950 64.6345i −0.213626 0.123337i
\(66\) 250.637 + 299.492i 0.467443 + 0.558560i
\(67\) −70.0189 + 543.930i −0.127674 + 0.991816i
\(68\) 0.405601i 0.000723328i
\(69\) 66.0533 + 377.495i 0.115245 + 0.658624i
\(70\) 574.198i 0.980425i
\(71\) −614.652 + 354.870i −1.02741 + 0.593173i −0.916240 0.400629i \(-0.868792\pi\)
−0.111165 + 0.993802i \(0.535458\pi\)
\(72\) 107.596 601.006i 0.176116 0.983739i
\(73\) 324.458 561.978i 0.520205 0.901021i −0.479519 0.877531i \(-0.659189\pi\)
0.999724 0.0234899i \(-0.00747776\pi\)
\(74\) −298.422 516.882i −0.468795 0.811977i
\(75\) −188.347 225.060i −0.289979 0.346503i
\(76\) −0.961974 −0.00145192
\(77\) −346.358 199.970i −0.512612 0.295957i
\(78\) 132.543 + 48.4381i 0.192404 + 0.0703145i
\(79\) 718.162 414.631i 1.02278 0.590502i 0.107871 0.994165i \(-0.465597\pi\)
0.914908 + 0.403663i \(0.132263\pi\)
\(80\) −431.618 + 747.585i −0.603205 + 1.04478i
\(81\) −683.721 252.915i −0.937889 0.346934i
\(82\) −525.496 −0.707699
\(83\) 186.992 + 107.960i 0.247289 + 0.142773i 0.618522 0.785767i \(-0.287732\pi\)
−0.371233 + 0.928540i \(0.621065\pi\)
\(84\) −0.133638 0.763743i −0.000173585 0.000992039i
\(85\) 477.598 + 275.741i 0.609444 + 0.351863i
\(86\) −518.895 299.584i −0.650626 0.375639i
\(87\) −1403.34 512.854i −1.72935 0.631997i
\(88\) −300.258 520.063i −0.363723 0.629987i
\(89\) 813.215i 0.968546i −0.874917 0.484273i \(-0.839084\pi\)
0.874917 0.484273i \(-0.160916\pi\)
\(90\) 786.843 + 663.757i 0.921562 + 0.777402i
\(91\) −144.516 −0.166477
\(92\) 0.730732i 0.000828088i
\(93\) −522.910 191.099i −0.583046 0.213076i
\(94\) 540.531i 0.593101i
\(95\) −653.983 + 1132.73i −0.706287 + 1.22332i
\(96\) 0.799717 2.18829i 0.000850217 0.00232647i
\(97\) −1605.68 927.039i −1.68074 0.970377i −0.961169 0.275961i \(-0.911004\pi\)
−0.719574 0.694416i \(-0.755663\pi\)
\(98\) −164.414 284.774i −0.169473 0.293536i
\(99\) −674.406 + 243.467i −0.684650 + 0.247165i
\(100\) −0.279793 0.484616i −0.000279793 0.000484616i
\(101\) −515.464 892.810i −0.507827 0.879583i −0.999959 0.00906205i \(-0.997115\pi\)
0.492131 0.870521i \(-0.336218\pi\)
\(102\) −565.448 206.645i −0.548899 0.200597i
\(103\) 183.127 + 317.185i 0.175185 + 0.303429i 0.940225 0.340553i \(-0.110614\pi\)
−0.765040 + 0.643982i \(0.777281\pi\)
\(104\) −187.922 108.497i −0.177185 0.102298i
\(105\) −990.166 361.859i −0.920289 0.336322i
\(106\) −72.8744 + 126.222i −0.0667754 + 0.115658i
\(107\) 881.762i 0.796665i −0.917241 0.398332i \(-0.869589\pi\)
0.917241 0.398332i \(-0.130411\pi\)
\(108\) −1.20107 0.699738i −0.00107012 0.000623447i
\(109\) 863.351i 0.758660i 0.925261 + 0.379330i \(0.123846\pi\)
−0.925261 + 0.379330i \(0.876154\pi\)
\(110\) 1012.48 0.877602
\(111\) 1079.39 188.870i 0.922988 0.161502i
\(112\) 965.053i 0.814187i
\(113\) 122.055 + 211.406i 0.101611 + 0.175995i 0.912348 0.409415i \(-0.134267\pi\)
−0.810738 + 0.585409i \(0.800934\pi\)
\(114\) 490.105 1341.09i 0.402654 1.10179i
\(115\) 860.443 + 496.777i 0.697711 + 0.402823i
\(116\) −2.46724 1.42446i −0.00197481 0.00114016i
\(117\) −167.056 + 198.035i −0.132003 + 0.156482i
\(118\) 1958.15 + 1130.54i 1.52765 + 0.881988i
\(119\) 616.528 0.474933
\(120\) −1015.90 1213.92i −0.772819 0.923462i
\(121\) 312.894 541.949i 0.235082 0.407174i
\(122\) 299.580 172.962i 0.222317 0.128355i
\(123\) 331.167 906.183i 0.242767 0.664291i
\(124\) −0.919342 0.530782i −0.000665801 0.000384401i
\(125\) 923.075 0.660499
\(126\) 1132.82 + 202.806i 0.800950 + 0.143392i
\(127\) 949.820 + 1645.14i 0.663645 + 1.14947i 0.979651 + 0.200709i \(0.0643246\pi\)
−0.316006 + 0.948757i \(0.602342\pi\)
\(128\) −725.420 + 1256.46i −0.500927 + 0.867631i
\(129\) 843.620 706.002i 0.575788 0.481860i
\(130\) 316.839 182.927i 0.213759 0.123414i
\(131\) 2304.99i 1.53731i 0.639664 + 0.768655i \(0.279074\pi\)
−0.639664 + 0.768655i \(0.720926\pi\)
\(132\) −1.34671 + 0.235644i −0.000887998 + 0.000155380i
\(133\) 1462.24i 0.953324i
\(134\) −1234.09 941.327i −0.795593 0.606853i
\(135\) −1640.47 + 938.560i −1.04585 + 0.598359i
\(136\) 801.705 + 462.865i 0.505483 + 0.291841i
\(137\) 1277.77 0.796839 0.398420 0.917203i \(-0.369559\pi\)
0.398420 + 0.917203i \(0.369559\pi\)
\(138\) −1018.71 372.292i −0.628397 0.229649i
\(139\) 150.179i 0.0916403i −0.998950 0.0458202i \(-0.985410\pi\)
0.998950 0.0458202i \(-0.0145901\pi\)
\(140\) −1.74084 1.00507i −0.00105091 0.000606744i
\(141\) −932.110 340.642i −0.556722 0.203456i
\(142\) 2008.69i 1.18708i
\(143\) 254.824i 0.149017i
\(144\) 1322.45 + 1115.58i 0.765305 + 0.645588i
\(145\) −3354.64 + 1936.80i −1.92129 + 1.10926i
\(146\) 918.274 + 1590.50i 0.520527 + 0.901579i
\(147\) 594.687 104.057i 0.333667 0.0583843i
\(148\) 2.08943 0.00116047
\(149\) 837.187i 0.460302i −0.973155 0.230151i \(-0.926078\pi\)
0.973155 0.230151i \(-0.0739220\pi\)
\(150\) 818.152 143.158i 0.445345 0.0779256i
\(151\) 682.436 1182.01i 0.367787 0.637026i −0.621432 0.783468i \(-0.713449\pi\)
0.989219 + 0.146442i \(0.0467822\pi\)
\(152\) −1097.79 + 1901.43i −0.585806 + 1.01465i
\(153\) 712.690 844.851i 0.376586 0.446419i
\(154\) 980.254 565.950i 0.512929 0.296140i
\(155\) −1250.00 + 721.689i −0.647758 + 0.373983i
\(156\) −0.378855 + 0.317053i −0.000194440 + 0.000162722i
\(157\) 1073.18 1858.81i 0.545537 0.944897i −0.453036 0.891492i \(-0.649659\pi\)
0.998573 0.0534050i \(-0.0170074\pi\)
\(158\) 2346.96i 1.18173i
\(159\) −171.737 205.212i −0.0856578 0.102355i
\(160\) −3.02014 5.23104i −0.00149227 0.00258469i
\(161\) 1110.74 0.543718
\(162\) 1587.42 1317.91i 0.769875 0.639164i
\(163\) −1262.47 2186.67i −0.606654 1.05075i −0.991788 0.127894i \(-0.959178\pi\)
0.385134 0.922861i \(-0.374155\pi\)
\(164\) 0.919825 1.59318i 0.000437965 0.000758578i
\(165\) −638.065 + 1745.96i −0.301050 + 0.823773i
\(166\) −529.220 + 305.545i −0.247442 + 0.142861i
\(167\) −57.3562 + 33.1146i −0.0265770 + 0.0153442i −0.513230 0.858251i \(-0.671551\pi\)
0.486653 + 0.873596i \(0.338218\pi\)
\(168\) −1662.11 607.424i −0.763302 0.278951i
\(169\) −1052.46 1822.91i −0.479044 0.829729i
\(170\) −1351.69 + 780.397i −0.609822 + 0.352081i
\(171\) 2003.76 + 1690.31i 0.896088 + 0.755913i
\(172\) 1.81654 1.04878i 0.000805290 0.000464935i
\(173\) 2498.16 + 1442.31i 1.09787 + 0.633855i 0.935661 0.352901i \(-0.114805\pi\)
0.162209 + 0.986756i \(0.448138\pi\)
\(174\) 3242.86 2713.85i 1.41287 1.18240i
\(175\) −736.634 + 425.296i −0.318196 + 0.183711i
\(176\) 1701.67 0.728799
\(177\) −3183.57 + 2664.24i −1.35193 + 1.13139i
\(178\) 1993.19 + 1150.77i 0.839305 + 0.484573i
\(179\) 1303.66 0.544358 0.272179 0.962247i \(-0.412256\pi\)
0.272179 + 0.962247i \(0.412256\pi\)
\(180\) −3.38965 + 1.22369i −0.00140361 + 0.000506715i
\(181\) −195.870 339.257i −0.0804360 0.139319i 0.823001 0.568039i \(-0.192298\pi\)
−0.903437 + 0.428720i \(0.858965\pi\)
\(182\) 204.503 354.209i 0.0832899 0.144262i
\(183\) 109.467 + 625.606i 0.0442189 + 0.252711i
\(184\) 1444.36 + 833.900i 0.578692 + 0.334108i
\(185\) 1420.46 2460.32i 0.564511 0.977763i
\(186\) 1208.35 1011.23i 0.476347 0.398641i
\(187\) 1087.12i 0.425124i
\(188\) −1.63877 0.946143i −0.000635742 0.000367046i
\(189\) −1063.63 + 1825.67i −0.409352 + 0.702634i
\(190\) −1850.89 3205.83i −0.706724 1.22408i
\(191\) 635.992 1101.57i 0.240936 0.417313i −0.720045 0.693927i \(-0.755879\pi\)
0.960981 + 0.276614i \(0.0892123\pi\)
\(192\) −1705.30 2037.71i −0.640988 0.765933i
\(193\) 507.444 0.189257 0.0946286 0.995513i \(-0.469834\pi\)
0.0946286 + 0.995513i \(0.469834\pi\)
\(194\) 4544.36 2623.69i 1.68178 0.970978i
\(195\) 115.774 + 661.649i 0.0425166 + 0.242983i
\(196\) 1.15116 0.000419519
\(197\) −1281.36 2219.38i −0.463417 0.802661i 0.535712 0.844401i \(-0.320043\pi\)
−0.999129 + 0.0417397i \(0.986710\pi\)
\(198\) 357.606 1997.50i 0.128353 0.716950i
\(199\) 1983.89 3436.19i 0.706703 1.22405i −0.259370 0.965778i \(-0.583515\pi\)
0.966073 0.258268i \(-0.0831517\pi\)
\(200\) −1277.18 −0.451552
\(201\) 2400.98 1534.89i 0.842548 0.538621i
\(202\) 2917.71 1.01628
\(203\) −2165.24 + 3750.31i −0.748621 + 1.29665i
\(204\) 1.61626 1.35260i 0.000554709 0.000464221i
\(205\) −1250.66 2166.20i −0.426096 0.738020i
\(206\) −1036.56 −0.350587
\(207\) 1283.99 1522.09i 0.431127 0.511074i
\(208\) 532.511 307.445i 0.177514 0.102488i
\(209\) 2578.36 0.853343
\(210\) 2288.09 1914.84i 0.751873 0.629222i
\(211\) 225.737 390.987i 0.0736509 0.127567i −0.826848 0.562426i \(-0.809868\pi\)
0.900499 + 0.434858i \(0.143202\pi\)
\(212\) −0.255118 0.441878i −8.26490e−5 0.000143152i
\(213\) 3463.85 + 1265.88i 1.11427 + 0.407213i
\(214\) 2161.20 + 1247.77i 0.690359 + 0.398579i
\(215\) 2851.99i 0.904670i
\(216\) −2753.73 + 1575.49i −0.867443 + 0.496288i
\(217\) −806.810 + 1397.44i −0.252395 + 0.437162i
\(218\) −2116.08 1221.72i −0.657426 0.379565i
\(219\) −3321.41 + 581.173i −1.02484 + 0.179324i
\(220\) −1.77224 + 3.06961i −0.000543111 + 0.000940696i
\(221\) −196.413 340.197i −0.0597835 0.103548i
\(222\) −1064.52 + 2912.87i −0.321828 + 0.880627i
\(223\) −2029.81 −0.609535 −0.304767 0.952427i \(-0.598579\pi\)
−0.304767 + 0.952427i \(0.598579\pi\)
\(224\) −5.84803 3.37636i −0.00174437 0.00100711i
\(225\) −268.731 + 1501.07i −0.0796241 + 0.444761i
\(226\) −690.876 −0.203347
\(227\) −582.153 + 336.106i −0.170215 + 0.0982737i −0.582687 0.812696i \(-0.697999\pi\)
0.412472 + 0.910970i \(0.364665\pi\)
\(228\) 3.20800 + 3.83332i 0.000931820 + 0.00111346i
\(229\) −4310.23 2488.51i −1.24379 0.718103i −0.273926 0.961751i \(-0.588322\pi\)
−0.969864 + 0.243648i \(0.921656\pi\)
\(230\) −2435.21 + 1405.97i −0.698143 + 0.403073i
\(231\) 358.188 + 2047.04i 0.102022 + 0.583055i
\(232\) −5631.16 + 3251.15i −1.59355 + 0.920037i
\(233\) −2325.52 4027.93i −0.653864 1.13252i −0.982177 0.187956i \(-0.939814\pi\)
0.328314 0.944569i \(-0.393520\pi\)
\(234\) −248.986 689.694i −0.0695586 0.192678i
\(235\) −2228.18 + 1286.44i −0.618513 + 0.357099i
\(236\) −6.85508 + 3.95778i −0.00189079 + 0.00109165i
\(237\) −4047.18 1479.05i −1.10925 0.405379i
\(238\) −872.443 + 1511.11i −0.237614 + 0.411559i
\(239\) 2321.74 + 4021.38i 0.628373 + 1.08837i 0.987878 + 0.155231i \(0.0496122\pi\)
−0.359505 + 0.933143i \(0.617054\pi\)
\(240\) 4418.38 773.119i 1.18836 0.207936i
\(241\) 3448.91 0.921842 0.460921 0.887441i \(-0.347519\pi\)
0.460921 + 0.887441i \(0.347519\pi\)
\(242\) 885.546 + 1533.81i 0.235228 + 0.407426i
\(243\) 1272.25 + 3567.95i 0.335864 + 0.941910i
\(244\) 1.21101i 0.000317733i
\(245\) 782.598 1355.50i 0.204075 0.353468i
\(246\) 1752.43 + 2094.02i 0.454190 + 0.542723i
\(247\) 806.854 465.837i 0.207850 0.120002i
\(248\) −2098.28 + 1211.44i −0.537261 + 0.310188i
\(249\) −193.379 1105.16i −0.0492163 0.281272i
\(250\) −1306.23 + 2262.46i −0.330454 + 0.572363i
\(251\) −2978.55 + 5159.00i −0.749021 + 1.29734i 0.199271 + 0.979944i \(0.436142\pi\)
−0.948292 + 0.317398i \(0.897191\pi\)
\(252\) −2.59775 + 3.07947i −0.000649375 + 0.000769795i
\(253\) 1958.57i 0.486695i
\(254\) −5376.32 −1.32811
\(255\) −493.911 2822.70i −0.121294 0.693194i
\(256\) −7.60923 13.1796i −0.00185772 0.00321767i
\(257\) 1664.71 961.123i 0.404054 0.233281i −0.284178 0.958772i \(-0.591721\pi\)
0.688232 + 0.725491i \(0.258387\pi\)
\(258\) 536.618 + 3066.77i 0.129490 + 0.740035i
\(259\) 3176.01i 0.761960i
\(260\) 1.28078i 0.000305502i
\(261\) 2636.22 + 7302.36i 0.625202 + 1.73182i
\(262\) −5649.53 3261.76i −1.33217 0.769131i
\(263\) 7697.82i 1.80482i −0.430878 0.902410i \(-0.641796\pi\)
0.430878 0.902410i \(-0.358204\pi\)
\(264\) −1071.07 + 2930.80i −0.249696 + 0.683250i
\(265\) −693.753 −0.160818
\(266\) −3583.95 2069.20i −0.826114 0.476957i
\(267\) −3240.54 + 2711.92i −0.742764 + 0.621598i
\(268\) 5.01404 2.09380i 0.00114284 0.000477236i
\(269\) 3366.83i 0.763119i −0.924344 0.381560i \(-0.875387\pi\)
0.924344 0.381560i \(-0.124613\pi\)
\(270\) 21.0001 5348.96i 0.00473342 1.20566i
\(271\) 7537.73i 1.68961i 0.535074 + 0.844805i \(0.320284\pi\)
−0.535074 + 0.844805i \(0.679716\pi\)
\(272\) −2271.78 + 1311.61i −0.506422 + 0.292383i
\(273\) 481.933 + 575.874i 0.106842 + 0.127668i
\(274\) −1808.15 + 3131.81i −0.398666 + 0.690510i
\(275\) 749.923 + 1298.90i 0.164444 + 0.284825i
\(276\) 2.91186 2.43685i 0.000635048 0.000531454i
\(277\) 3682.50 0.798773 0.399386 0.916783i \(-0.369223\pi\)
0.399386 + 0.916783i \(0.369223\pi\)
\(278\) 368.089 + 212.516i 0.0794120 + 0.0458485i
\(279\) 982.305 + 2721.00i 0.210785 + 0.583878i
\(280\) −3973.23 + 2293.95i −0.848021 + 0.489605i
\(281\) 1159.76 2008.76i 0.246212 0.426451i −0.716260 0.697834i \(-0.754148\pi\)
0.962472 + 0.271383i \(0.0874809\pi\)
\(282\) 2153.94 1802.57i 0.454840 0.380643i
\(283\) 4335.37 0.910639 0.455320 0.890328i \(-0.349525\pi\)
0.455320 + 0.890328i \(0.349525\pi\)
\(284\) 6.08989 + 3.51600i 0.00127242 + 0.000734634i
\(285\) 6694.68 1171.42i 1.39143 0.243470i
\(286\) −624.576 360.599i −0.129133 0.0745548i
\(287\) −2421.70 1398.17i −0.498078 0.287566i
\(288\) −11.3869 + 4.11078i −0.00232979 + 0.000841077i
\(289\) −1618.57 2803.45i −0.329447 0.570618i
\(290\) 10963.0i 2.21989i
\(291\) 1660.52 + 9489.89i 0.334507 + 1.91171i
\(292\) −6.42937 −0.00128853
\(293\) 93.8585i 0.0187142i 0.999956 + 0.00935712i \(0.00297851\pi\)
−0.999956 + 0.00935712i \(0.997021\pi\)
\(294\) −586.491 + 1604.83i −0.116343 + 0.318353i
\(295\) 10762.5i 2.12413i
\(296\) 2384.42 4129.94i 0.468215 0.810972i
\(297\) 3219.19 + 1875.49i 0.628945 + 0.366421i
\(298\) 2051.95 + 1184.69i 0.398880 + 0.230294i
\(299\) −353.858 612.900i −0.0684420 0.118545i
\(300\) −0.998065 + 2.73103i −0.000192078 + 0.000525588i
\(301\) −1594.19 2761.21i −0.305274 0.528750i
\(302\) 1931.41 + 3345.31i 0.368015 + 0.637420i
\(303\) −1838.74 + 5031.40i −0.348623 + 0.953948i
\(304\) −3110.79 5388.04i −0.586894 1.01653i
\(305\) 1425.97 + 823.286i 0.267708 + 0.154561i
\(306\) 1062.21 + 2942.35i 0.198440 + 0.549682i
\(307\) 639.599 1107.82i 0.118905 0.205950i −0.800429 0.599428i \(-0.795395\pi\)
0.919334 + 0.393478i \(0.128728\pi\)
\(308\) 3.96254i 0.000733074i
\(309\) 653.242 1787.49i 0.120264 0.329083i
\(310\) 4085.01i 0.748430i
\(311\) 9190.42 1.67569 0.837847 0.545905i \(-0.183814\pi\)
0.837847 + 0.545905i \(0.183814\pi\)
\(312\) 194.340 + 1110.66i 0.0352640 + 0.201534i
\(313\) 3224.46i 0.582292i −0.956679 0.291146i \(-0.905963\pi\)
0.956679 0.291146i \(-0.0940365\pi\)
\(314\) 3037.30 + 5260.75i 0.545874 + 0.945482i
\(315\) 1860.06 + 5152.40i 0.332707 + 0.921602i
\(316\) −7.11545 4.10811i −0.00126669 0.000731326i
\(317\) −3423.34 1976.47i −0.606543 0.350188i 0.165068 0.986282i \(-0.447215\pi\)
−0.771611 + 0.636095i \(0.780549\pi\)
\(318\) 745.999 130.533i 0.131552 0.0230187i
\(319\) 6612.90 + 3817.96i 1.16066 + 0.670109i
\(320\) −6888.80 −1.20342
\(321\) −3513.69 + 2940.51i −0.610950 + 0.511287i
\(322\) −1571.80 + 2722.43i −0.272027 + 0.471165i
\(323\) −3442.17 + 1987.34i −0.592965 + 0.342348i
\(324\) 1.21698 + 7.11957i 0.000208673 + 0.00122078i
\(325\) 469.352 + 270.980i 0.0801075 + 0.0462501i
\(326\) 7146.05 1.21406
\(327\) 3440.32 2879.11i 0.581805 0.486897i
\(328\) −2099.38 3636.23i −0.353411 0.612126i
\(329\) −1438.17 + 2490.99i −0.241000 + 0.417425i
\(330\) −3376.43 4034.58i −0.563231 0.673020i
\(331\) −9446.50 + 5453.94i −1.56866 + 0.905667i −0.572335 + 0.820020i \(0.693962\pi\)
−0.996326 + 0.0856465i \(0.972704\pi\)
\(332\) 2.13930i 0.000353643i
\(333\) −4352.20 3671.38i −0.716213 0.604176i
\(334\) 187.440i 0.0307074i
\(335\) 943.254 7327.51i 0.153837 1.19506i
\(336\) 3845.59 3218.27i 0.624388 0.522533i
\(337\) −7674.62 4430.94i −1.24054 0.716228i −0.271338 0.962484i \(-0.587466\pi\)
−0.969205 + 0.246256i \(0.920800\pi\)
\(338\) 5957.30 0.958682
\(339\) 435.390 1191.37i 0.0697555 0.190874i
\(340\) 5.46401i 0.000871552i
\(341\) 2464.09 + 1422.64i 0.391314 + 0.225925i
\(342\) −6978.45 + 2519.28i −1.10337 + 0.398325i
\(343\) 6915.50i 1.08864i
\(344\) 4787.41i 0.750348i
\(345\) −889.832 5085.39i −0.138861 0.793590i
\(346\) −7070.23 + 4082.00i −1.09855 + 0.634248i
\(347\) 167.833 + 290.695i 0.0259646 + 0.0449721i 0.878716 0.477345i \(-0.158401\pi\)
−0.852751 + 0.522317i \(0.825068\pi\)
\(348\) 2.55151 + 14.5819i 0.000393033 + 0.00224619i
\(349\) −10323.1 −1.58333 −0.791664 0.610956i \(-0.790785\pi\)
−0.791664 + 0.610956i \(0.790785\pi\)
\(350\) 2407.33i 0.367649i
\(351\) 1346.24 + 5.28536i 0.204721 + 0.000803737i
\(352\) −5.95353 + 10.3118i −0.000901489 + 0.00156142i
\(353\) −205.713 + 356.305i −0.0310169 + 0.0537229i −0.881117 0.472898i \(-0.843208\pi\)
0.850100 + 0.526621i \(0.176541\pi\)
\(354\) −2025.03 11573.1i −0.304038 1.73758i
\(355\) 8280.24 4780.60i 1.23794 0.714726i
\(356\) −6.97776 + 4.02861i −0.00103882 + 0.000599764i
\(357\) −2056.01 2456.77i −0.304805 0.364219i
\(358\) −1844.79 + 3195.28i −0.272348 + 0.471720i
\(359\) 5843.17i 0.859027i 0.903060 + 0.429513i \(0.141315\pi\)
−0.903060 + 0.429513i \(0.858685\pi\)
\(360\) −1449.47 + 8096.40i −0.212205 + 1.18533i
\(361\) −1283.93 2223.83i −0.187189 0.324220i
\(362\) 1108.69 0.160972
\(363\) −3203.03 + 560.459i −0.463128 + 0.0810371i
\(364\) 0.715921 + 1.24001i 0.000103089 + 0.000178556i
\(365\) −4370.91 + 7570.64i −0.626805 + 1.08566i
\(366\) −1688.27 616.983i −0.241113 0.0881154i
\(367\) 10730.5 6195.25i 1.52623 0.881171i 0.526717 0.850041i \(-0.323423\pi\)
0.999515 0.0311298i \(-0.00991051\pi\)
\(368\) −4092.85 + 2363.01i −0.579768 + 0.334729i
\(369\) −4715.38 + 1702.30i −0.665239 + 0.240157i
\(370\) 4020.17 + 6963.13i 0.564861 + 0.978368i
\(371\) −671.671 + 387.789i −0.0939931 + 0.0542669i
\(372\) 0.950743 + 5.43350i 0.000132510 + 0.000757295i
\(373\) 7146.79 4126.20i 0.992082 0.572779i 0.0861861 0.996279i \(-0.472532\pi\)
0.905896 + 0.423500i \(0.139199\pi\)
\(374\) 2664.54 + 1538.37i 0.368396 + 0.212694i
\(375\) −3078.28 3678.32i −0.423898 0.506527i
\(376\) −3740.27 + 2159.45i −0.513005 + 0.296183i
\(377\) 2759.20 0.376939
\(378\) −2969.60 5190.44i −0.404073 0.706263i
\(379\) −7740.68 4469.08i −1.04911 0.605703i −0.126709 0.991940i \(-0.540441\pi\)
−0.922400 + 0.386237i \(0.873775\pi\)
\(380\) 12.9591 0.00174945
\(381\) 3388.15 9271.11i 0.455592 1.24665i
\(382\) 1799.97 + 3117.64i 0.241085 + 0.417572i
\(383\) −6159.47 + 10668.5i −0.821760 + 1.42333i 0.0826107 + 0.996582i \(0.473674\pi\)
−0.904371 + 0.426748i \(0.859659\pi\)
\(384\) 7425.96 1299.38i 0.986860 0.172679i
\(385\) 4665.93 + 2693.87i 0.617656 + 0.356604i
\(386\) −718.079 + 1243.75i −0.0946872 + 0.164003i
\(387\) −5626.62 1007.32i −0.739063 0.132312i
\(388\) 18.3700i 0.00240359i
\(389\) 3187.76 + 1840.46i 0.415491 + 0.239884i 0.693146 0.720797i \(-0.256224\pi\)
−0.277655 + 0.960681i \(0.589557\pi\)
\(390\) −1785.53 652.529i −0.231831 0.0847233i
\(391\) 1509.62 + 2614.73i 0.195255 + 0.338191i
\(392\) 1313.68 2275.37i 0.169263 0.293172i
\(393\) 9185.03 7686.69i 1.17894 0.986621i
\(394\) 7252.95 0.927407
\(395\) −9674.66 + 5585.67i −1.23237 + 0.711507i
\(396\) 5.43001 + 4.58060i 0.000689062 + 0.000581272i
\(397\) 14320.9 1.81045 0.905224 0.424935i \(-0.139703\pi\)
0.905224 + 0.424935i \(0.139703\pi\)
\(398\) 5614.75 + 9725.03i 0.707141 + 1.22480i
\(399\) 5826.80 4876.28i 0.731090 0.611828i
\(400\) 1809.56 3134.25i 0.226195 0.391782i
\(401\) 2872.85 0.357764 0.178882 0.983871i \(-0.442752\pi\)
0.178882 + 0.983871i \(0.442752\pi\)
\(402\) 364.421 + 8056.83i 0.0452132 + 0.999597i
\(403\) 1028.13 0.127084
\(404\) −5.10714 + 8.84583i −0.000628935 + 0.00108935i
\(405\) 9210.69 + 3407.12i 1.13008 + 0.418028i
\(406\) −6128.02 10614.0i −0.749085 1.29745i
\(407\) −5600.24 −0.682049
\(408\) −829.088 4738.24i −0.100603 0.574946i
\(409\) 5935.25 3426.72i 0.717553 0.414280i −0.0962982 0.995353i \(-0.530700\pi\)
0.813851 + 0.581073i \(0.197367\pi\)
\(410\) 7079.17 0.852720
\(411\) −4261.11 5091.71i −0.511399 0.611084i
\(412\) 1.81440 3.14263i 0.000216963 0.000375792i
\(413\) 6015.98 + 10420.0i 0.716772 + 1.24149i
\(414\) 1913.69 + 5300.95i 0.227181 + 0.629293i
\(415\) −2519.04 1454.37i −0.297964 0.172029i
\(416\) 4.30255i 0.000507091i
\(417\) −598.440 + 500.818i −0.0702776 + 0.0588133i
\(418\) −3648.61 + 6319.57i −0.426936 + 0.739474i
\(419\) −9635.69 5563.17i −1.12347 0.648636i −0.181186 0.983449i \(-0.557994\pi\)
−0.942285 + 0.334813i \(0.891327\pi\)
\(420\) 1.80030 + 10.2887i 0.000209156 + 0.00119533i
\(421\) 5843.61 10121.4i 0.676485 1.17171i −0.299547 0.954081i \(-0.596836\pi\)
0.976032 0.217625i \(-0.0698311\pi\)
\(422\) 638.875 + 1106.56i 0.0736965 + 0.127646i
\(423\) 1751.00 + 4850.30i 0.201269 + 0.557517i
\(424\) −1164.55 −0.133385
\(425\) −2002.33 1156.05i −0.228535 0.131945i
\(426\) −8004.33 + 6698.60i −0.910354 + 0.761850i
\(427\) 1840.78 0.208622
\(428\) −7.56592 + 4.36819i −0.000854468 + 0.000493328i
\(429\) 1015.44 849.791i 0.114279 0.0956370i
\(430\) 6990.24 + 4035.82i 0.783952 + 0.452615i
\(431\) −4712.21 + 2720.60i −0.526634 + 0.304052i −0.739645 0.672998i \(-0.765006\pi\)
0.213011 + 0.977050i \(0.431673\pi\)
\(432\) 35.2948 8989.99i 0.00393084 1.00123i
\(433\) 1366.12 788.729i 0.151620 0.0875379i −0.422271 0.906470i \(-0.638767\pi\)
0.573891 + 0.818932i \(0.305433\pi\)
\(434\) −2283.42 3954.99i −0.252552 0.437432i
\(435\) 18904.9 + 6908.87i 2.08373 + 0.761505i
\(436\) 7.40794 4.27698i 0.000813707 0.000469794i
\(437\) −6201.44 + 3580.40i −0.678844 + 0.391931i
\(438\) 3275.63 8963.20i 0.357341 0.977804i
\(439\) 2579.07 4467.08i 0.280392 0.485654i −0.691089 0.722770i \(-0.742869\pi\)
0.971481 + 0.237116i \(0.0762021\pi\)
\(440\) 4044.91 + 7005.98i 0.438258 + 0.759084i
\(441\) −2397.82 2022.73i −0.258916 0.218414i
\(442\) 1111.77 0.119641
\(443\) −1745.80 3023.81i −0.187235 0.324301i 0.757092 0.653308i \(-0.226619\pi\)
−0.944328 + 0.329007i \(0.893286\pi\)
\(444\) −6.96784 8.32605i −0.000744773 0.000889948i
\(445\) 10955.2i 1.16702i
\(446\) 2872.36 4975.08i 0.304956 0.528199i
\(447\) −3336.06 + 2791.86i −0.352999 + 0.295415i
\(448\) −6669.53 + 3850.66i −0.703361 + 0.406086i
\(449\) 6550.99 3782.22i 0.688553 0.397537i −0.114516 0.993421i \(-0.536532\pi\)
0.803070 + 0.595885i \(0.203199\pi\)
\(450\) −3298.85 2782.81i −0.345576 0.291517i
\(451\) −2465.39 + 4270.18i −0.257407 + 0.445842i
\(452\) 1.20931 2.09458i 0.000125843 0.000217966i
\(453\) −6985.94 + 1222.39i −0.724565 + 0.126783i
\(454\) 1902.48i 0.196669i
\(455\) 1946.83 0.200591
\(456\) 11237.8 1966.37i 1.15408 0.201938i
\(457\) −5946.10 10298.9i −0.608636 1.05419i −0.991465 0.130370i \(-0.958383\pi\)
0.382829 0.923819i \(-0.374950\pi\)
\(458\) 12198.7 7042.93i 1.24456 0.718547i
\(459\) −5743.29 22.5482i −0.584039 0.00229294i
\(460\) 9.84399i 0.000997780i
\(461\) 693.575i 0.0700716i 0.999386 + 0.0350358i \(0.0111545\pi\)
−0.999386 + 0.0350358i \(0.988845\pi\)
\(462\) −5524.19 2018.83i −0.556295 0.203300i
\(463\) 9611.63 + 5549.28i 0.964774 + 0.557012i 0.897639 0.440731i \(-0.145281\pi\)
0.0671349 + 0.997744i \(0.478614\pi\)
\(464\) 18425.5i 1.84349i
\(465\) 7044.34 + 2574.37i 0.702523 + 0.256739i
\(466\) 13163.3 1.30854
\(467\) −8781.63 5070.08i −0.870162 0.502388i −0.00275984 0.999996i \(-0.500878\pi\)
−0.867402 + 0.497608i \(0.834212\pi\)
\(468\) 2.52682 + 0.452369i 0.000249577 + 4.46811e-5i
\(469\) −3182.66 7621.54i −0.313350 0.750384i
\(470\) 7281.72i 0.714639i
\(471\) −10985.9 + 1922.29i −1.07474 + 0.188057i
\(472\) 18066.2i 1.76179i
\(473\) −4868.84 + 2811.02i −0.473297 + 0.273258i
\(474\) 9352.28 7826.66i 0.906255 0.758419i
\(475\) 2741.83 4748.99i 0.264850 0.458733i
\(476\) −3.05424 5.29010i −0.000294098 0.000509393i
\(477\) −245.032 + 1368.69i −0.0235204 + 0.131379i
\(478\) −13141.9 −1.25752
\(479\) −5371.25 3101.09i −0.512356 0.295809i 0.221445 0.975173i \(-0.428923\pi\)
−0.733802 + 0.679364i \(0.762256\pi\)
\(480\) −10.7733 + 29.4794i −0.00102444 + 0.00280321i
\(481\) −1752.50 + 1011.81i −0.166127 + 0.0959137i
\(482\) −4880.52 + 8453.30i −0.461206 + 0.798833i
\(483\) −3704.11 4426.14i −0.348950 0.416969i
\(484\) −6.20022 −0.000582290
\(485\) 21630.8 + 12488.5i 2.02516 + 1.16923i
\(486\) −10545.4 1930.67i −0.984259 0.180200i
\(487\) −4902.52 2830.47i −0.456169 0.263369i 0.254263 0.967135i \(-0.418167\pi\)
−0.710432 + 0.703766i \(0.751500\pi\)
\(488\) 2393.67 + 1381.99i 0.222042 + 0.128196i
\(489\) −4503.44 + 12322.9i −0.416467 + 1.13959i
\(490\) 2214.89 + 3836.31i 0.204201 + 0.353687i
\(491\) 15457.4i 1.42074i 0.703829 + 0.710370i \(0.251472\pi\)
−0.703829 + 0.710370i \(0.748528\pi\)
\(492\) −9.41604 + 1.64760i −0.000862821 + 0.000150975i
\(493\) −11771.2 −1.07535
\(494\) 2636.81i 0.240153i
\(495\) 9085.20 3279.84i 0.824948 0.297814i
\(496\) 6865.68i 0.621528i
\(497\) 5344.45 9256.87i 0.482357 0.835467i
\(498\) 2982.40 + 1089.93i 0.268363 + 0.0980739i
\(499\) 15935.6 + 9200.45i 1.42961 + 0.825388i 0.997090 0.0762341i \(-0.0242896\pi\)
0.432524 + 0.901622i \(0.357623\pi\)
\(500\) −4.57285 7.92041i −0.000409008 0.000708423i
\(501\) 323.229 + 118.125i 0.0288239 + 0.0105338i
\(502\) −8429.82 14600.9i −0.749485 1.29815i
\(503\) 1373.67 + 2379.27i 0.121767 + 0.210907i 0.920465 0.390826i \(-0.127810\pi\)
−0.798697 + 0.601733i \(0.794477\pi\)
\(504\) 3122.34 + 8648.92i 0.275952 + 0.764391i
\(505\) 6944.03 + 12027.4i 0.611891 + 1.05983i
\(506\) 4800.45 + 2771.54i 0.421751 + 0.243498i
\(507\) −3754.29 + 10273.0i −0.328864 + 0.899879i
\(508\) 9.41068 16.2998i 0.000821912 0.00142359i
\(509\) 18133.7i 1.57910i 0.613684 + 0.789552i \(0.289687\pi\)
−0.613684 + 0.789552i \(0.710313\pi\)
\(510\) 7617.39 + 2783.80i 0.661379 + 0.241703i
\(511\) 9772.89i 0.846042i
\(512\) −11563.6 −0.998136
\(513\) 53.4782 13621.5i 0.00460258 1.17233i
\(514\) 5440.30i 0.466851i
\(515\) −2466.98 4272.93i −0.211084 0.365608i
\(516\) −10.2371 3.74116i −0.000873374 0.000319177i
\(517\) 4392.35 + 2535.93i 0.373647 + 0.215725i
\(518\) 7784.42 + 4494.33i 0.660285 + 0.381216i
\(519\) −2583.48 14764.6i −0.218502 1.24874i
\(520\) 2531.57 + 1461.60i 0.213494 + 0.123261i
\(521\) 17105.1 1.43836 0.719182 0.694822i \(-0.244517\pi\)
0.719182 + 0.694822i \(0.244517\pi\)
\(522\) −21628.6 3872.10i −1.81352 0.324669i
\(523\) 2660.12 4607.46i 0.222407 0.385220i −0.733131 0.680087i \(-0.761942\pi\)
0.955538 + 0.294867i \(0.0952753\pi\)
\(524\) 19.7778 11.4187i 0.00164885 0.000951965i
\(525\) 4151.28 + 1517.10i 0.345098 + 0.126117i
\(526\) 18867.4 + 10893.1i 1.56399 + 0.902969i
\(527\) −4386.17 −0.362551
\(528\) −5674.76 6780.92i −0.467732 0.558905i
\(529\) −3363.77 5826.21i −0.276466 0.478854i
\(530\) 981.722 1700.39i 0.0804590 0.139359i
\(531\) 21233.2 + 3801.31i 1.73530 + 0.310665i
\(532\) 12.5467 7.24382i 0.00102249 0.000590337i
\(533\) 1781.71i 0.144792i
\(534\) −2061.27 11780.2i −0.167041 0.954642i
\(535\) 11878.6i 0.959917i
\(536\) 1583.37 12300.1i 0.127595 0.991201i
\(537\) −4347.46 5194.89i −0.349361 0.417460i
\(538\) 8252.11 + 4764.36i 0.661290 + 0.381796i
\(539\) −3085.43 −0.246565
\(540\) 16.1801 + 9.42646i 0.00128941 + 0.000751204i
\(541\) 4285.41i 0.340562i −0.985396 0.170281i \(-0.945532\pi\)
0.985396 0.170281i \(-0.0544675\pi\)
\(542\) −18475.0 10666.6i −1.46415 0.845328i
\(543\) −698.699 + 1911.87i −0.0552192 + 0.151098i
\(544\) 18.3554i 0.00144665i
\(545\) 11630.6i 0.914125i
\(546\) −2093.45 + 366.307i −0.164087 + 0.0287116i
\(547\) −9555.72 + 5517.00i −0.746935 + 0.431243i −0.824585 0.565738i \(-0.808591\pi\)
0.0776506 + 0.996981i \(0.475258\pi\)
\(548\) −6.32997 10.9638i −0.000493436 0.000854656i
\(549\) 2127.89 2522.49i 0.165421 0.196097i
\(550\) −4244.83 −0.329091
\(551\) 27918.0i 2.15853i
\(552\) −1493.69 8536.44i −0.115173 0.658216i
\(553\) −6244.48 + 10815.8i −0.480185 + 0.831705i
\(554\) −5211.07 + 9025.83i −0.399634 + 0.692186i
\(555\) −14541.0 + 2544.35i −1.11213 + 0.194598i
\(556\) −1.28860 + 0.743976i −9.82895e−5 + 5.67475e-5i
\(557\) 2163.92 1249.34i 0.164611 0.0950382i −0.415431 0.909625i \(-0.636369\pi\)
0.580042 + 0.814586i \(0.303036\pi\)
\(558\) −8059.23 1442.82i −0.611424 0.109461i
\(559\) −1015.75 + 1759.33i −0.0768543 + 0.133116i
\(560\) 13000.6i 0.981030i
\(561\) −4332.02 + 3625.35i −0.326021 + 0.272838i
\(562\) 3282.33 + 5685.15i 0.246364 + 0.426715i
\(563\) −6328.08 −0.473706 −0.236853 0.971545i \(-0.576116\pi\)
−0.236853 + 0.971545i \(0.576116\pi\)
\(564\) 1.69474 + 9.68545i 0.000126527 + 0.000723105i
\(565\) −1644.26 2847.94i −0.122433 0.212059i
\(566\) −6134.93 + 10626.0i −0.455602 + 0.789125i
\(567\) 10822.0 1849.86i 0.801555 0.137013i
\(568\) 13899.4 8024.80i 1.02677 0.592805i
\(569\) 9824.61 5672.24i 0.723847 0.417913i −0.0923197 0.995729i \(-0.529428\pi\)
0.816167 + 0.577816i \(0.196095\pi\)
\(570\) −6602.41 + 18066.4i −0.485166 + 1.32757i
\(571\) −6405.74 11095.1i −0.469478 0.813160i 0.529913 0.848052i \(-0.322225\pi\)
−0.999391 + 0.0348922i \(0.988891\pi\)
\(572\) 2.18651 1.26238i 0.000159830 9.22777e-5i
\(573\) −6510.51 + 1139.19i −0.474660 + 0.0830551i
\(574\) 6853.84 3957.07i 0.498387 0.287744i
\(575\) −3607.41 2082.74i −0.261634 0.151054i
\(576\) −2433.11 + 13590.8i −0.176006 + 0.983128i
\(577\) −7263.33 + 4193.49i −0.524049 + 0.302560i −0.738590 0.674155i \(-0.764508\pi\)
0.214541 + 0.976715i \(0.431175\pi\)
\(578\) 9161.69 0.659301
\(579\) −1692.23 2022.09i −0.121462 0.145138i
\(580\) 33.2373 + 19.1895i 0.00237949 + 0.00137380i
\(581\) −3251.82 −0.232200
\(582\) −25609.6 9359.09i −1.82397 0.666576i
\(583\) 683.788 + 1184.35i 0.0485756 + 0.0841355i
\(584\) −7337.10 + 12708.2i −0.519882 + 0.900462i
\(585\) 2250.49 2667.81i 0.159053 0.188548i
\(586\) −230.048 132.818i −0.0162170 0.00936292i
\(587\) −4333.87 + 7506.49i −0.304733 + 0.527812i −0.977202 0.212313i \(-0.931900\pi\)
0.672469 + 0.740125i \(0.265234\pi\)
\(588\) −3.83890 4.58720i −0.000269241 0.000321723i
\(589\) 10402.8i 0.727741i
\(590\) −26379.1 15230.0i −1.84069 1.06272i
\(591\) −4570.81 + 12507.2i −0.318135 + 0.870523i
\(592\) 6756.69 + 11702.9i 0.469085 + 0.812479i
\(593\) −2041.40 + 3535.81i −0.141366 + 0.244854i −0.928011 0.372552i \(-0.878483\pi\)
0.786645 + 0.617406i \(0.211816\pi\)
\(594\) −9152.29 + 5236.28i −0.632194 + 0.361695i
\(595\) −8305.51 −0.572257
\(596\) −7.18345 + 4.14736i −0.000493700 + 0.000285038i
\(597\) −20308.6 + 3553.56i −1.39225 + 0.243614i
\(598\) 2002.96 0.136969
\(599\) 12473.6 + 21604.9i 0.850846 + 1.47371i 0.880446 + 0.474147i \(0.157244\pi\)
−0.0295994 + 0.999562i \(0.509423\pi\)
\(600\) 4259.16 + 5089.38i 0.289799 + 0.346288i
\(601\) −10142.7 + 17567.7i −0.688403 + 1.19235i 0.283952 + 0.958838i \(0.408354\pi\)
−0.972354 + 0.233510i \(0.924979\pi\)
\(602\) 9023.66 0.610925
\(603\) −14123.1 4448.99i −0.953795 0.300459i
\(604\) −13.5230 −0.000910995
\(605\) −4215.13 + 7300.81i −0.283255 + 0.490612i
\(606\) −9730.01 11626.6i −0.652235 0.779373i
\(607\) 6727.77 + 11652.8i 0.449871 + 0.779199i 0.998377 0.0569472i \(-0.0181367\pi\)
−0.548506 + 0.836146i \(0.684803\pi\)
\(608\) 43.5339 0.00290384
\(609\) 22165.1 3878.40i 1.47483 0.258064i
\(610\) −4035.76 + 2330.05i −0.267874 + 0.154657i
\(611\) 1832.69 0.121346
\(612\) −10.7798 1.92988i −0.000712008 0.000127469i
\(613\) 3079.07 5333.11i 0.202875 0.351391i −0.746578 0.665298i \(-0.768305\pi\)
0.949454 + 0.313907i \(0.101638\pi\)
\(614\) 1810.18 + 3135.32i 0.118979 + 0.206077i
\(615\) −4461.29 + 12207.6i −0.292515 + 0.800417i
\(616\) 7832.32 + 4521.99i 0.512294 + 0.295773i
\(617\) 2721.97i 0.177605i −0.996049 0.0888026i \(-0.971696\pi\)
0.996049 0.0888026i \(-0.0283040\pi\)
\(618\) 3456.74 + 4130.55i 0.225001 + 0.268860i
\(619\) 180.787 313.133i 0.0117390 0.0203326i −0.860096 0.510132i \(-0.829597\pi\)
0.871835 + 0.489799i \(0.162930\pi\)
\(620\) 12.3848 + 7.15039i 0.000802237 + 0.000463172i
\(621\) −10347.1 40.6230i −0.668626 0.00262503i
\(622\) −13005.3 + 22525.8i −0.838366 + 1.45209i
\(623\) 6123.64 + 10606.5i 0.393802 + 0.682085i
\(624\) −3000.95 1096.70i −0.192522 0.0703579i
\(625\) −19495.0 −1.24768
\(626\) 7903.17 + 4562.90i 0.504592 + 0.291326i
\(627\) −8598.33 10274.4i −0.547662 0.654416i
\(628\) −21.2659 −0.00135127
\(629\) 7476.47 4316.54i 0.473937 0.273628i
\(630\) −15260.7 2732.08i −0.965081 0.172776i
\(631\) −10409.8 6010.13i −0.656750 0.379175i 0.134288 0.990942i \(-0.457125\pi\)
−0.791038 + 0.611768i \(0.790459\pi\)
\(632\) −16240.1 + 9376.21i −1.02214 + 0.590136i
\(633\) −2310.81 + 404.342i −0.145097 + 0.0253888i
\(634\) 9688.67 5593.75i 0.606918 0.350404i
\(635\) −12795.4 22162.3i −0.799639 1.38501i
\(636\) −0.910046 + 2.49019i −5.67385e−5 + 0.000155255i
\(637\) −965.533 + 557.451i −0.0600562 + 0.0346735i
\(638\) −18715.7 + 10805.5i −1.16138 + 0.670524i
\(639\) −6506.97 18024.4i −0.402835 1.11586i
\(640\) 9772.43 16926.3i 0.603577 1.04543i
\(641\) −11016.5 19081.1i −0.678821 1.17575i −0.975336 0.220724i \(-0.929158\pi\)
0.296516 0.955028i \(-0.404175\pi\)
\(642\) −2235.02 12773.2i −0.137398 0.785228i
\(643\) 8921.14 0.547147 0.273574 0.961851i \(-0.411794\pi\)
0.273574 + 0.961851i \(0.411794\pi\)
\(644\) −5.50253 9.53067i −0.000336693 0.000583169i
\(645\) −11364.8 + 9510.84i −0.693778 + 0.580603i
\(646\) 11249.0i 0.685121i
\(647\) 13547.1 23464.3i 0.823172 1.42578i −0.0801370 0.996784i \(-0.525536\pi\)
0.903309 0.428991i \(-0.141131\pi\)
\(648\) 15461.3 + 5719.27i 0.937308 + 0.346719i
\(649\) 18373.5 10608.0i 1.11128 0.641600i
\(650\) −1328.35 + 766.923i −0.0801571 + 0.0462787i
\(651\) 8259.13 1445.17i 0.497236 0.0870054i
\(652\) −12.5084 + 21.6652i −0.000751330 + 0.00130134i
\(653\) −13446.8 + 23290.5i −0.805839 + 1.39575i 0.109884 + 0.993944i \(0.464952\pi\)
−0.915723 + 0.401810i \(0.868381\pi\)
\(654\) 2188.35 + 12506.5i 0.130843 + 0.747769i
\(655\) 31051.4i 1.85233i
\(656\) 11898.0 0.708136
\(657\) 13392.1 + 11297.2i 0.795247 + 0.670846i
\(658\) −4070.29 7049.94i −0.241149 0.417683i
\(659\) −20479.3 + 11823.7i −1.21056 + 0.698918i −0.962882 0.269924i \(-0.913001\pi\)
−0.247680 + 0.968842i \(0.579668\pi\)
\(660\) 18.1420 3.17446i 0.00106997 0.000187220i
\(661\) 31195.8i 1.83567i 0.396966 + 0.917834i \(0.370063\pi\)
−0.396966 + 0.917834i \(0.629937\pi\)
\(662\) 30871.2i 1.81245i
\(663\) −700.635 + 1917.17i −0.0410413 + 0.112303i
\(664\) −4228.52 2441.33i −0.247136 0.142684i
\(665\) 19698.4i 1.14868i
\(666\) 15157.3 5471.93i 0.881883 0.318368i
\(667\) −21207.0 −1.23109
\(668\) 0.568277 + 0.328095i 3.29151e−5 + 1.90035e-5i
\(669\) 6769.04 + 8088.50i 0.391190 + 0.467443i
\(670\) 16625.0 + 12681.0i 0.958626 + 0.731209i
\(671\) 3245.84i 0.186743i
\(672\) 6.04777 + 34.5631i 0.000347170 + 0.00198408i
\(673\) 25418.0i 1.45586i −0.685652 0.727930i \(-0.740483\pi\)
0.685652 0.727930i \(-0.259517\pi\)
\(674\) 21720.5 12540.4i 1.24131 0.716671i
\(675\) 6877.70 3934.92i 0.392182 0.224378i
\(676\) −10.4276 + 18.0612i −0.000593288 + 0.00102760i
\(677\) −9590.23 16610.8i −0.544435 0.942989i −0.998642 0.0520932i \(-0.983411\pi\)
0.454207 0.890896i \(-0.349923\pi\)
\(678\) 2303.94 + 2753.04i 0.130505 + 0.155944i
\(679\) 27923.0 1.57819
\(680\) −10800.1 6235.44i −0.609066 0.351645i
\(681\) 3280.70 + 1198.94i 0.184606 + 0.0674648i
\(682\) −6973.82 + 4026.34i −0.391556 + 0.226065i
\(683\) 15900.3 27540.1i 0.890786 1.54289i 0.0518515 0.998655i \(-0.483488\pi\)
0.838935 0.544232i \(-0.183179\pi\)
\(684\) 4.57715 25.5668i 0.000255865 0.00142920i
\(685\) −17213.3 −0.960127
\(686\) 16949.9 + 9786.05i 0.943369 + 0.544655i
\(687\) 4457.45 + 25474.3i 0.247543 + 1.41471i
\(688\) 11748.5 + 6783.00i 0.651028 + 0.375871i
\(689\) 427.960 + 247.083i 0.0236632 + 0.0136620i
\(690\) 13723.5 + 5015.30i 0.757168 + 0.276709i
\(691\) 321.358 + 556.609i 0.0176918 + 0.0306431i 0.874736 0.484600i \(-0.161035\pi\)
−0.857044 + 0.515243i \(0.827702\pi\)
\(692\) 28.5805i 0.00157004i
\(693\) 6962.68 8253.83i 0.381660 0.452435i
\(694\) −949.993 −0.0519614
\(695\) 2023.12i 0.110419i
\(696\) 31734.2 + 11597.4i 1.72828 + 0.631605i
\(697\) 7601.06i 0.413071i
\(698\) 14608.1 25301.9i 0.792154 1.37205i
\(699\) −8295.51 + 22699.2i −0.448877 + 1.22828i
\(700\) 7.29847 + 4.21377i 0.000394080 + 0.000227522i
\(701\) −2606.67 4514.89i −0.140446 0.243260i 0.787219 0.616674i \(-0.211520\pi\)
−0.927665 + 0.373414i \(0.878187\pi\)
\(702\) −1918.01 + 3292.17i −0.103120 + 0.177001i
\(703\) 10237.7 + 17732.1i 0.549247 + 0.951323i
\(704\) 6789.85 + 11760.4i 0.363497 + 0.629596i
\(705\) 12556.8 + 4588.94i 0.670806 + 0.245148i
\(706\) −582.203 1008.41i −0.0310361 0.0537562i
\(707\) 13446.0 + 7763.06i 0.715260 + 0.412956i
\(708\) 38.6316 + 14.1180i 0.00205065 + 0.000749417i
\(709\) −11796.1 + 20431.5i −0.624843 + 1.08226i 0.363728 + 0.931505i \(0.381504\pi\)
−0.988571 + 0.150755i \(0.951830\pi\)
\(710\) 27059.9i 1.43034i
\(711\) 7602.76 + 21059.8i 0.401021 + 1.11083i
\(712\) 18389.5i 0.967946i
\(713\) −7902.14 −0.415060
\(714\) 8931.00 1562.73i 0.468115 0.0819098i
\(715\) 3432.84i 0.179554i
\(716\) −6.45824 11.1860i −0.000337089 0.000583855i
\(717\) 8282.02 22662.3i 0.431378 1.18039i
\(718\) −14321.6 8268.60i −0.744400 0.429779i
\(719\) 2773.23 + 1601.12i 0.143844 + 0.0830485i 0.570195 0.821509i \(-0.306868\pi\)
−0.426351 + 0.904558i \(0.640201\pi\)
\(720\) −17815.2 15028.4i −0.922131 0.777882i
\(721\) −4776.91 2757.95i −0.246743 0.142457i
\(722\) 7267.48 0.374609
\(723\) −11501.5 13743.4i −0.591624 0.706947i
\(724\) −1.94065 + 3.36131i −9.96185e−5 + 0.000172544i
\(725\) 14064.3 8120.05i 0.720464 0.415960i
\(726\) 3158.88 8643.74i 0.161484 0.441872i
\(727\) 5016.95 + 2896.54i 0.255940 + 0.147767i 0.622481 0.782635i \(-0.286125\pi\)
−0.366541 + 0.930402i \(0.619458\pi\)
\(728\) 3267.99 0.166373
\(729\) 9975.04 16968.2i 0.506785 0.862073i
\(730\) −12370.5 21426.3i −0.627193 1.08633i
\(731\) 4333.35 7505.57i 0.219254 0.379759i
\(732\) 4.82569 4.03849i 0.000243665 0.000203916i
\(733\) 548.959 316.942i 0.0276620 0.0159707i −0.486105 0.873900i \(-0.661583\pi\)
0.513767 + 0.857930i \(0.328249\pi\)
\(734\) 35067.3i 1.76343i
\(735\) −8011.28 + 1401.80i −0.402042 + 0.0703484i
\(736\) 33.0691i 0.00165617i
\(737\) −13439.0 + 5611.96i −0.671686 + 0.280488i
\(738\) 2500.35 13966.3i 0.124714 0.696623i
\(739\) 19110.0 + 11033.2i 0.951251 + 0.549205i 0.893469 0.449124i \(-0.148264\pi\)
0.0577817 + 0.998329i \(0.481597\pi\)
\(740\) −28.1475 −0.00139828
\(741\) −4547.00 1661.71i −0.225423 0.0823814i
\(742\) 2195.03i 0.108601i
\(743\) −5938.43 3428.55i −0.293216 0.169289i 0.346175 0.938170i \(-0.387480\pi\)
−0.639391 + 0.768881i \(0.720814\pi\)
\(744\) 11824.8 + 4321.40i 0.582684 + 0.212944i
\(745\) 11278.1i 0.554627i
\(746\) 23355.8i 1.14627i
\(747\) −3759.02 + 4456.08i −0.184117 + 0.218259i
\(748\) −9.32801 + 5.38553i −0.000455970 + 0.000263255i
\(749\) 6639.81 + 11500.5i 0.323916 + 0.561040i
\(750\) 13371.6 2339.74i 0.651017 0.113914i
\(751\) 12502.8 0.607504 0.303752 0.952751i \(-0.401761\pi\)
0.303752 + 0.952751i \(0.401761\pi\)
\(752\) 12238.4i 0.593467i
\(753\) 30490.7 5335.20i 1.47562 0.258201i
\(754\) −3904.51 + 6762.81i −0.188586 + 0.326641i
\(755\) −9193.37 + 15923.4i −0.443154 + 0.767565i
\(756\) 20.9342 + 0.0821879i 0.00100710 + 3.95390e-6i
\(757\) −19137.2 + 11048.9i −0.918830 + 0.530487i −0.883262 0.468880i \(-0.844658\pi\)
−0.0355685 + 0.999367i \(0.511324\pi\)
\(758\) 21907.5 12648.3i 1.04976 0.606078i
\(759\) −7804.59 + 6531.44i −0.373239 + 0.312354i
\(760\) 14788.8 25614.9i 0.705849 1.22257i
\(761\) 34934.4i 1.66409i −0.554711 0.832043i \(-0.687171\pi\)
0.554711 0.832043i \(-0.312829\pi\)
\(762\) 17929.0 + 21423.8i 0.852361 + 1.01851i
\(763\) −6501.17 11260.4i −0.308464 0.534276i
\(764\) −12.6026 −0.000596790
\(765\) −9600.95 + 11381.3i −0.453756 + 0.537899i
\(766\) −17432.4 30193.8i −0.822269 1.42421i
\(767\) 3833.12 6639.17i 0.180451 0.312551i
\(768\) −27.1433 + 74.2730i −0.00127532 + 0.00348971i
\(769\) 15072.0 8701.83i 0.706776 0.408057i −0.103090 0.994672i \(-0.532873\pi\)
0.809866 + 0.586615i \(0.199540\pi\)
\(770\) −13205.4 + 7624.14i −0.618039 + 0.356825i
\(771\) −9381.43 3428.47i −0.438215 0.160147i
\(772\) −2.51384 4.35410i −0.000117196 0.000202989i
\(773\) 10098.1 5830.15i 0.469863 0.271275i −0.246319 0.969189i \(-0.579221\pi\)
0.716182 + 0.697913i \(0.245888\pi\)
\(774\) 10431.1 12365.4i 0.484417 0.574247i
\(775\) 5240.64 3025.68i 0.242902 0.140240i
\(776\) 36309.8 + 20963.5i 1.67970 + 0.969775i
\(777\) −12655.9 + 10591.4i −0.584335 + 0.489014i
\(778\) −9021.94 + 5208.82i −0.415748 + 0.240032i
\(779\) 18027.6 0.829149
\(780\) 5.10371 4.27115i 0.000234285 0.000196066i
\(781\) −16322.6 9423.86i −0.747847 0.431770i
\(782\) −8544.97 −0.390751
\(783\) 20307.5 34856.9i 0.926861 1.59091i
\(784\) 3722.57 + 6447.67i 0.169578 + 0.293717i
\(785\) −14457.3 + 25040.7i −0.657328 + 1.13853i
\(786\) 5842.50 + 33389.9i 0.265134 + 1.51524i
\(787\) −24250.2 14000.8i −1.09838 0.634150i −0.162585 0.986695i \(-0.551983\pi\)
−0.935795 + 0.352545i \(0.885316\pi\)
\(788\) −12.6955 + 21.9893i −0.000573933 + 0.000994082i
\(789\) −30674.7 + 25670.8i −1.38409 + 1.15831i
\(790\) 31616.9i 1.42390i
\(791\) −3183.84 1838.19i −0.143116 0.0826278i
\(792\) 15250.6 5505.60i 0.684225 0.247011i
\(793\) −586.434 1015.73i −0.0262609 0.0454852i
\(794\) −20265.4 + 35100.7i −0.905784 + 1.56886i
\(795\) 2313.53 + 2764.50i 0.103211 + 0.123329i
\(796\) −39.3121 −0.00175048
\(797\) −17581.6 + 10150.7i −0.781394 + 0.451138i −0.836924 0.547319i \(-0.815649\pi\)
0.0555299 + 0.998457i \(0.482315\pi\)
\(798\) 3706.36 + 21181.9i 0.164416 + 0.939638i
\(799\) −7818.54 −0.346183
\(800\) 12.6620 + 21.9312i 0.000559586 + 0.000969231i
\(801\) 21613.2 + 3869.34i 0.953388 + 0.170682i
\(802\) −4065.34 + 7041.37i −0.178993 + 0.310024i
\(803\) 17232.5 0.757312
\(804\) −25.0644 12.9978i −0.00109944 0.000570145i
\(805\) −14963.2 −0.655137
\(806\) −1454.89 + 2519.95i −0.0635812 + 0.110126i
\(807\) −13416.3 + 11227.7i −0.585225 + 0.489758i
\(808\) 11656.4 + 20189.4i 0.507512 + 0.879037i
\(809\) −22104.3 −0.960623 −0.480312 0.877098i \(-0.659476\pi\)
−0.480312 + 0.877098i \(0.659476\pi\)
\(810\) −21384.8 + 17754.1i −0.927638 + 0.770142i
\(811\) 19310.4 11148.8i 0.836102 0.482724i −0.0198356 0.999803i \(-0.506314\pi\)
0.855937 + 0.517080i \(0.172981\pi\)
\(812\) 42.9058 0.00185431
\(813\) 30036.7 25136.9i 1.29574 1.08437i
\(814\) 7924.84 13726.2i 0.341235 0.591037i
\(815\) 17007.3 + 29457.5i 0.730969 + 1.26608i
\(816\) 12802.5 + 4678.72i 0.549238 + 0.200721i
\(817\) 17801.2 + 10277.5i 0.762282 + 0.440104i
\(818\) 19396.5i 0.829072i
\(819\) 687.618 3840.86i 0.0293374 0.163871i
\(820\) −12.3913 + 21.4624i −0.000527713 + 0.000914025i
\(821\) −18153.1 10480.7i −0.771679 0.445529i 0.0617939 0.998089i \(-0.480318\pi\)
−0.833473 + 0.552560i \(0.813651\pi\)
\(822\) 18509.7 3238.78i 0.785400 0.137428i
\(823\) −2542.07 + 4402.99i −0.107668 + 0.186487i −0.914825 0.403850i \(-0.867672\pi\)
0.807157 + 0.590337i \(0.201005\pi\)
\(824\) −4141.12 7172.63i −0.175076 0.303241i
\(825\) 2675.09 7319.93i 0.112891 0.308906i
\(826\) −34052.6 −1.43443
\(827\) −26104.2 15071.3i −1.09762 0.633712i −0.162026 0.986786i \(-0.551803\pi\)
−0.935595 + 0.353074i \(0.885136\pi\)
\(828\) −19.4210 3.47688i −0.000815128 0.000145930i
\(829\) −11104.6 −0.465234 −0.232617 0.972568i \(-0.574729\pi\)
−0.232617 + 0.972568i \(0.574729\pi\)
\(830\) 7129.34 4116.13i 0.298148 0.172136i
\(831\) −12280.4 14674.2i −0.512640 0.612567i
\(832\) 4249.54 + 2453.47i 0.177075 + 0.102234i
\(833\) 4119.12 2378.18i 0.171332 0.0989183i
\(834\) −380.662 2175.48i −0.0158048 0.0903247i
\(835\) 772.669 446.100i 0.0320231 0.0184886i
\(836\) −12.7730 22.1235i −0.000528425 0.000915259i
\(837\) 7566.97 12988.4i 0.312488 0.536372i
\(838\) 27270.7 15744.8i 1.12417 0.649037i
\(839\) 20264.5 11699.7i 0.833860 0.481429i −0.0213125 0.999773i \(-0.506784\pi\)
0.855172 + 0.518344i \(0.173451\pi\)
\(840\) 22391.0 + 8182.86i 0.919718 + 0.336114i
\(841\) 29145.8 50482.0i 1.19504 2.06987i
\(842\) 16538.5 + 28645.5i 0.676904 + 1.17243i
\(843\) −11872.2 + 2077.37i −0.485054 + 0.0848737i
\(844\) −4.47313 −0.000182431
\(845\) 14178.1 + 24557.2i 0.577210 + 0.999757i
\(846\) −14365.9 2571.89i −0.583819 0.104519i
\(847\) 9424.58i 0.382329i
\(848\) 1649.98 2857.85i 0.0668166 0.115730i
\(849\) −14457.6 17275.8i −0.584434 0.698356i
\(850\) 5666.96 3271.82i 0.228676 0.132026i
\(851\) 13469.6 7776.70i 0.542577 0.313257i
\(852\) −6.29789 35.9925i −0.000253242 0.00144728i
\(853\) 21453.4 37158.3i 0.861137 1.49153i −0.00969564 0.999953i \(-0.503086\pi\)
0.870833 0.491580i \(-0.163580\pi\)
\(854\) −2604.87 + 4511.77i −0.104376 + 0.180784i
\(855\) −26993.4 22770.8i −1.07971 0.910814i
\(856\) 19939.6i 0.796170i
\(857\) −23821.2 −0.949493 −0.474746 0.880123i \(-0.657460\pi\)
−0.474746 + 0.880123i \(0.657460\pi\)
\(858\) 645.908 + 3691.37i 0.0257004 + 0.146878i
\(859\) 5235.54 + 9068.22i 0.207956 + 0.360191i 0.951071 0.308974i \(-0.0999856\pi\)
−0.743114 + 0.669164i \(0.766652\pi\)
\(860\) −24.4714 + 14.1286i −0.000970310 + 0.000560209i
\(861\) 2504.42 + 14312.7i 0.0991292 + 0.566524i
\(862\) 15399.5i 0.608481i
\(863\) 38202.9i 1.50688i 0.657514 + 0.753442i \(0.271608\pi\)
−0.657514 + 0.753442i \(0.728392\pi\)
\(864\) 54.3541 + 31.6665i 0.00214023 + 0.00124689i
\(865\) −33653.7 19430.0i −1.32284 0.763745i
\(866\) 4464.49i 0.175184i
\(867\) −5773.69 + 15798.7i −0.226165 + 0.618862i
\(868\) 15.9875 0.000625175
\(869\) 19071.4 + 11010.9i 0.744479 + 0.429825i
\(870\) −43685.8 + 36559.5i −1.70240 + 1.42469i
\(871\) −3191.59 + 4184.23i −0.124160 + 0.162775i
\(872\) 19523.3i 0.758190i
\(873\) 32278.3 38263.9i 1.25138 1.48343i
\(874\) 20266.3i 0.784347i
\(875\) −12039.3 + 6950.91i −0.465147 + 0.268553i
\(876\) 21.4407 + 25.6201i 0.000826958 + 0.000988154i
\(877\) −13111.7 + 22710.2i −0.504848 + 0.874423i 0.495136 + 0.868815i \(0.335118\pi\)
−0.999984 + 0.00560733i \(0.998215\pi\)
\(878\) 7299.23 + 12642.6i 0.280566 + 0.485955i
\(879\) 374.012 313.000i 0.0143517 0.0120105i
\(880\) −22924.0 −0.878144
\(881\) −34462.2 19896.8i −1.31789 0.760885i −0.334502 0.942395i \(-0.608568\pi\)
−0.983389 + 0.181511i \(0.941901\pi\)
\(882\) 8350.86 3014.73i 0.318807 0.115092i
\(883\) −27025.1 + 15603.0i −1.02998 + 0.594656i −0.916978 0.398939i \(-0.869379\pi\)
−0.112998 + 0.993595i \(0.536045\pi\)
\(884\) −1.94603 + 3.37062i −7.40408e−5 + 0.000128242i
\(885\) 42887.1 35891.0i 1.62897 1.36324i
\(886\) 9881.83 0.374703
\(887\) 7932.01 + 4579.55i 0.300260 + 0.173355i 0.642560 0.766236i \(-0.277872\pi\)
−0.342300 + 0.939591i \(0.611206\pi\)
\(888\) −24408.8 + 4271.00i −0.922415 + 0.161402i
\(889\) −24776.3 14304.6i −0.934725 0.539663i
\(890\) −26851.2 15502.5i −1.01130 0.583872i
\(891\) −3261.84 19082.4i −0.122644 0.717492i
\(892\) 10.0555 + 17.4167i 0.000377449 + 0.000653761i
\(893\) 18543.4i 0.694885i
\(894\) −2122.04 12127.4i −0.0793864 0.453694i
\(895\) −17562.1 −0.655908
\(896\) 21850.1i 0.814689i
\(897\) −1262.27 + 3453.98i −0.0469854 + 0.128567i
\(898\) 21408.7i 0.795565i
\(899\) 15404.2 26680.8i 0.571477 0.989827i
\(900\) 14.2111 5.13034i 0.000526338 0.000190013i
\(901\) −1825.75 1054.10i −0.0675077 0.0389756i
\(902\) −6977.48 12085.4i −0.257566 0.446118i
\(903\) −5686.71 + 15560.7i −0.209570 + 0.573453i
\(904\) −2760.08 4780.60i −0.101547 0.175885i
\(905\) 2638.65 + 4570.27i 0.0969189 + 0.167868i
\(906\) 6889.65 18852.4i 0.252642 0.691311i
\(907\) 25027.3 + 43348.5i 0.916226 + 1.58695i 0.805096 + 0.593145i \(0.202114\pi\)
0.111131 + 0.993806i \(0.464553\pi\)
\(908\) 5.76789 + 3.33009i 0.000210808 + 0.000121710i
\(909\) 26181.2 9451.65i 0.955309 0.344875i
\(910\) −2754.94 + 4771.70i −0.100358 + 0.173824i
\(911\) 27655.8i 1.00579i 0.864347 + 0.502896i \(0.167732\pi\)
−0.864347 + 0.502896i \(0.832268\pi\)
\(912\) −11096.7 + 30364.1i −0.402902 + 1.10247i
\(913\) 5733.92i 0.207848i
\(914\) 33657.0 1.21803
\(915\) −1474.68 8427.80i −0.0532802 0.304497i
\(916\) 49.3117i 0.00177872i
\(917\) −17356.9 30063.1i −0.625056 1.08263i
\(918\) 8182.54 14044.9i 0.294187 0.504959i
\(919\) −37471.0 21633.9i −1.34500 0.776535i −0.357463 0.933927i \(-0.616358\pi\)
−0.987536 + 0.157392i \(0.949691\pi\)
\(920\) −19457.5 11233.8i −0.697278 0.402574i
\(921\) −6547.44 + 1145.66i −0.234251 + 0.0409888i
\(922\) −1699.96 981.471i −0.0607214 0.0350575i
\(923\) −6810.51 −0.242872
\(924\) 15.7901 13.2143i 0.000562184 0.000470476i
\(925\) −5955.31 + 10314.9i −0.211686 + 0.366650i
\(926\) −27202.6 + 15705.4i −0.965371 + 0.557357i
\(927\) −9301.31 + 3357.86i −0.329552 + 0.118971i
\(928\) 111.655 + 64.4639i 0.00394962 + 0.00228031i
\(929\) 46807.0 1.65306 0.826528 0.562896i \(-0.190313\pi\)
0.826528 + 0.562896i \(0.190313\pi\)
\(930\) −16278.2 + 13622.7i −0.573960 + 0.480331i
\(931\) 5640.39 + 9769.44i 0.198557 + 0.343910i
\(932\) −23.0410 + 39.9081i −0.000809799 + 0.00140261i
\(933\) −30648.3 36622.5i −1.07544 1.28507i
\(934\) 24853.6 14349.2i 0.870701 0.502699i
\(935\) 14645.1i 0.512241i
\(936\) 3777.71 4478.25i 0.131921 0.156385i
\(937\) 29640.4i 1.03341i 0.856162 + 0.516707i \(0.172842\pi\)
−0.856162 + 0.516707i \(0.827158\pi\)
\(938\) 23184.2 + 2984.45i 0.807026 + 0.103887i
\(939\) −12849.0 + 10753.0i −0.446551 + 0.373706i
\(940\) 22.0765 + 12.7459i 0.000766018 + 0.000442260i
\(941\) −49685.4 −1.72125 −0.860626 0.509238i \(-0.829927\pi\)
−0.860626 + 0.509238i \(0.829927\pi\)
\(942\) 10834.5 29646.8i 0.374742 1.02542i
\(943\) 13694.1i 0.472897i
\(944\) −44335.3 25597.0i −1.52859 0.882532i
\(945\) 14328.6 24594.3i 0.493237 0.846618i
\(946\) 15911.4i 0.546854i
\(947\) 19042.6i 0.653433i 0.945122 + 0.326716i \(0.105942\pi\)
−0.945122 + 0.326716i \(0.894058\pi\)
\(948\) 7.35848 + 42.0538i 0.000252102 + 0.00144076i
\(949\) 5392.63 3113.43i 0.184460 0.106498i
\(950\) 7759.86 + 13440.5i 0.265014 + 0.459017i
\(951\) 3540.27 + 20232.7i 0.120716 + 0.689893i
\(952\) −13941.8 −0.474639
\(953\) 33564.3i 1.14087i −0.821341 0.570437i \(-0.806774\pi\)
0.821341 0.570437i \(-0.193226\pi\)
\(954\) −3007.92 2537.39i −0.102081 0.0861123i
\(955\) −8567.71 + 14839.7i −0.290308 + 0.502829i
\(956\) 23.0035 39.8433i 0.000778229 0.00134793i
\(957\) −6838.77 39083.6i −0.230999 1.32016i
\(958\) 15201.6 8776.64i 0.512673 0.295992i
\(959\) −16665.4 + 9621.79i −0.561163 + 0.323987i
\(960\) 22972.8 + 27450.8i 0.772339 + 0.922888i
\(961\) −9155.61 + 15858.0i −0.307328 + 0.532308i
\(962\) 5727.19i 0.191946i
\(963\) 23435.0 + 4195.49i 0.784197 + 0.140392i
\(964\) −17.0857 29.5932i −0.000570843 0.000988728i
\(965\) −6835.99 −0.228040
\(966\) 16090.1 2815.42i 0.535913 0.0937729i
\(967\) 18955.1 + 32831.3i 0.630358 + 1.09181i 0.987479 + 0.157754i \(0.0504252\pi\)
−0.357121 + 0.934058i \(0.616241\pi\)
\(968\) −7075.60 + 12255.3i −0.234936 + 0.406922i
\(969\) 19398.2 + 7089.15i 0.643097 + 0.235022i
\(970\) −61218.9 + 35344.8i −2.02641 + 1.16995i
\(971\) 44964.9 25960.5i 1.48609 0.857994i 0.486215 0.873839i \(-0.338377\pi\)
0.999874 + 0.0158449i \(0.00504380\pi\)
\(972\) 24.3120 28.5919i 0.000802272 0.000943503i
\(973\) 1130.87 + 1958.73i 0.0372601 + 0.0645364i
\(974\) 13875.0 8010.73i 0.456451 0.263532i
\(975\) −485.383 2773.97i −0.0159433 0.0911159i
\(976\) −6782.90 + 3916.11i −0.222454 + 0.128434i
\(977\) 35282.9 + 20370.6i 1.15537 + 0.667055i 0.950191 0.311668i \(-0.100888\pi\)
0.205183 + 0.978724i \(0.434221\pi\)
\(978\) −23830.7 28475.9i −0.779164 0.931043i
\(979\) 18702.3 10797.8i 0.610551 0.352502i
\(980\) −15.5077 −0.000505486
\(981\) −22945.7 4107.89i −0.746787 0.133695i
\(982\) −37886.2 21873.6i −1.23116 0.710809i
\(983\) −2184.96 −0.0708948 −0.0354474 0.999372i \(-0.511286\pi\)
−0.0354474 + 0.999372i \(0.511286\pi\)
\(984\) −7488.81 + 20491.9i −0.242616 + 0.663879i
\(985\) 17261.7 + 29898.2i 0.558380 + 0.967142i
\(986\) 16657.3 28851.3i 0.538008 0.931857i
\(987\) 14722.3 2576.07i 0.474787 0.0830772i
\(988\) −7.99420 4.61545i −0.000257418 0.000148621i
\(989\) 7806.98 13522.1i 0.251009 0.434760i
\(990\) −4817.46 + 26909.1i −0.154656 + 0.863867i
\(991\) 47234.0i 1.51406i −0.653378 0.757032i \(-0.726649\pi\)
0.653378 0.757032i \(-0.273351\pi\)
\(992\) 41.6047 + 24.0205i 0.00133160 + 0.000768801i
\(993\) 53235.4 + 19455.0i 1.70128 + 0.621739i
\(994\) 15125.8 + 26198.6i 0.482656 + 0.835984i
\(995\) −26725.7 + 46290.3i −0.851521 + 1.47488i
\(996\) −8.52479 + 7.13416i −0.000271203 + 0.000226962i
\(997\) 30730.0 0.976157 0.488078 0.872800i \(-0.337698\pi\)
0.488078 + 0.872800i \(0.337698\pi\)
\(998\) −45100.7 + 26038.9i −1.43050 + 0.825899i
\(999\) −116.156 + 29586.2i −0.00367869 + 0.937004i
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 201.4.f.a.38.19 132
3.2 odd 2 inner 201.4.f.a.38.48 yes 132
67.30 odd 6 inner 201.4.f.a.164.48 yes 132
201.164 even 6 inner 201.4.f.a.164.19 yes 132
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.4.f.a.38.19 132 1.1 even 1 trivial
201.4.f.a.38.48 yes 132 3.2 odd 2 inner
201.4.f.a.164.19 yes 132 201.164 even 6 inner
201.4.f.a.164.48 yes 132 67.30 odd 6 inner