Properties

Label 201.4.f.a.38.2
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 38.2
Character \(\chi\) \(=\) 201.38
Dual form 201.4.f.a.164.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.64802 + 4.58651i) q^{2} +(2.08276 - 4.76047i) q^{3} +(-10.0240 - 17.3621i) q^{4} -19.9728 q^{5} +(16.3187 + 22.1584i) q^{6} +(-22.9190 + 13.2323i) q^{7} +63.8072 q^{8} +(-18.3242 - 19.8299i) q^{9} +O(q^{10})\) \(q+(-2.64802 + 4.58651i) q^{2} +(2.08276 - 4.76047i) q^{3} +(-10.0240 - 17.3621i) q^{4} -19.9728 q^{5} +(16.3187 + 22.1584i) q^{6} +(-22.9190 + 13.2323i) q^{7} +63.8072 q^{8} +(-18.3242 - 19.8299i) q^{9} +(52.8883 - 91.6052i) q^{10} +(5.59972 + 9.69900i) q^{11} +(-103.530 + 11.5579i) q^{12} +(-27.1150 - 15.6548i) q^{13} -140.158i q^{14} +(-41.5985 + 95.0798i) q^{15} +(-88.7705 + 153.755i) q^{16} +(29.4712 + 17.0152i) q^{17} +(139.473 - 31.5342i) q^{18} +(45.4378 - 78.7006i) q^{19} +(200.208 + 346.770i) q^{20} +(15.2571 + 136.665i) q^{21} -59.3127 q^{22} +(138.390 + 79.8993i) q^{23} +(132.895 - 303.752i) q^{24} +273.911 q^{25} +(143.602 - 82.9087i) q^{26} +(-132.564 + 45.9310i) q^{27} +(459.482 + 265.282i) q^{28} +(-265.236 + 153.134i) q^{29} +(-325.930 - 442.565i) q^{30} +(152.420 - 87.9997i) q^{31} +(-214.904 - 372.224i) q^{32} +(57.8347 - 6.45660i) q^{33} +(-156.081 + 90.1133i) q^{34} +(457.755 - 264.285i) q^{35} +(-160.607 + 516.923i) q^{36} +(17.2119 - 29.8119i) q^{37} +(240.641 + 416.802i) q^{38} +(-130.998 + 96.4748i) q^{39} -1274.41 q^{40} +(24.4688 + 42.3812i) q^{41} +(-667.216 - 291.915i) q^{42} -58.7928i q^{43} +(112.264 - 194.446i) q^{44} +(365.985 + 396.057i) q^{45} +(-732.918 + 423.150i) q^{46} +(65.2777 - 37.6881i) q^{47} +(547.059 + 742.825i) q^{48} +(178.687 - 309.495i) q^{49} +(-725.323 + 1256.30i) q^{50} +(142.382 - 104.858i) q^{51} +627.699i q^{52} -469.309 q^{53} +(140.371 - 729.634i) q^{54} +(-111.842 - 193.716i) q^{55} +(-1462.40 + 844.315i) q^{56} +(-280.016 - 380.220i) q^{57} -1622.01i q^{58} -326.866i q^{59} +(2067.77 - 230.844i) q^{60} +(63.6744 + 36.7625i) q^{61} +932.101i q^{62} +(682.367 + 212.009i) q^{63} +855.951 q^{64} +(541.561 + 312.670i) q^{65} +(-123.534 + 282.357i) q^{66} +(319.774 - 445.542i) q^{67} -682.245i q^{68} +(668.591 - 492.389i) q^{69} +2799.33i q^{70} +(129.218 - 74.6041i) q^{71} +(-1169.22 - 1265.29i) q^{72} +(-106.110 + 183.788i) q^{73} +(91.1550 + 157.885i) q^{74} +(570.492 - 1303.95i) q^{75} -1821.88 q^{76} +(-256.680 - 148.194i) q^{77} +(-95.5956 - 856.293i) q^{78} +(-83.6573 + 48.2996i) q^{79} +(1772.99 - 3070.91i) q^{80} +(-57.4472 + 726.733i) q^{81} -259.176 q^{82} +(983.038 + 567.557i) q^{83} +(2219.86 - 1634.83i) q^{84} +(-588.621 - 339.841i) q^{85} +(269.654 + 155.685i) q^{86} +(176.567 + 1581.59i) q^{87} +(357.302 + 618.866i) q^{88} -351.119i q^{89} +(-2785.66 + 629.825i) q^{90} +828.597 q^{91} -3203.66i q^{92} +(-101.466 - 908.874i) q^{93} +399.196i q^{94} +(-907.518 + 1571.87i) q^{95} +(-2219.56 + 247.789i) q^{96} +(1049.72 + 606.059i) q^{97} +(946.333 + 1639.10i) q^{98} +(89.7195 - 288.768i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.64802 + 4.58651i −0.936217 + 1.62158i −0.163768 + 0.986499i \(0.552365\pi\)
−0.772449 + 0.635077i \(0.780968\pi\)
\(3\) 2.08276 4.76047i 0.400828 0.916153i
\(4\) −10.0240 17.3621i −1.25301 2.17027i
\(5\) −19.9728 −1.78642 −0.893209 0.449642i \(-0.851552\pi\)
−0.893209 + 0.449642i \(0.851552\pi\)
\(6\) 16.3187 + 22.1584i 1.11035 + 1.50769i
\(7\) −22.9190 + 13.2323i −1.23751 + 0.714476i −0.968584 0.248685i \(-0.920002\pi\)
−0.268925 + 0.963161i \(0.586668\pi\)
\(8\) 63.8072 2.81991
\(9\) −18.3242 19.8299i −0.678674 0.734440i
\(10\) 52.8883 91.6052i 1.67248 2.89681i
\(11\) 5.59972 + 9.69900i 0.153489 + 0.265851i 0.932508 0.361150i \(-0.117616\pi\)
−0.779019 + 0.627001i \(0.784282\pi\)
\(12\) −103.530 + 11.5579i −2.49054 + 0.278041i
\(13\) −27.1150 15.6548i −0.578488 0.333990i 0.182044 0.983290i \(-0.441729\pi\)
−0.760532 + 0.649300i \(0.775062\pi\)
\(14\) 140.158i 2.67562i
\(15\) −41.5985 + 95.0798i −0.716046 + 1.63663i
\(16\) −88.7705 + 153.755i −1.38704 + 2.40242i
\(17\) 29.4712 + 17.0152i 0.420460 + 0.242753i 0.695274 0.718745i \(-0.255283\pi\)
−0.274814 + 0.961497i \(0.588616\pi\)
\(18\) 139.473 31.5342i 1.82634 0.412927i
\(19\) 45.4378 78.7006i 0.548639 0.950271i −0.449729 0.893165i \(-0.648479\pi\)
0.998368 0.0571057i \(-0.0181872\pi\)
\(20\) 200.208 + 346.770i 2.23839 + 3.87701i
\(21\) 15.2571 + 136.665i 0.158542 + 1.42013i
\(22\) −59.3127 −0.574796
\(23\) 138.390 + 79.8993i 1.25462 + 0.724355i 0.972023 0.234884i \(-0.0754712\pi\)
0.282596 + 0.959239i \(0.408805\pi\)
\(24\) 132.895 303.752i 1.13030 2.58347i
\(25\) 273.911 2.19129
\(26\) 143.602 82.9087i 1.08318 0.625374i
\(27\) −132.564 + 45.9310i −0.944891 + 0.327386i
\(28\) 459.482 + 265.282i 3.10121 + 1.79048i
\(29\) −265.236 + 153.134i −1.69838 + 0.980562i −0.751086 + 0.660205i \(0.770470\pi\)
−0.947297 + 0.320357i \(0.896197\pi\)
\(30\) −325.930 442.565i −1.98355 2.69337i
\(31\) 152.420 87.9997i 0.883079 0.509846i 0.0114066 0.999935i \(-0.496369\pi\)
0.871672 + 0.490089i \(0.163036\pi\)
\(32\) −214.904 372.224i −1.18719 2.05627i
\(33\) 57.8347 6.45660i 0.305083 0.0340591i
\(34\) −156.081 + 90.1133i −0.787284 + 0.454538i
\(35\) 457.755 264.285i 2.21071 1.27635i
\(36\) −160.607 + 516.923i −0.743549 + 2.39316i
\(37\) 17.2119 29.8119i 0.0764762 0.132461i −0.825251 0.564766i \(-0.808966\pi\)
0.901727 + 0.432305i \(0.142300\pi\)
\(38\) 240.641 + 416.802i 1.02729 + 1.77932i
\(39\) −130.998 + 96.4748i −0.537860 + 0.396111i
\(40\) −1274.41 −5.03753
\(41\) 24.4688 + 42.3812i 0.0932046 + 0.161435i 0.908858 0.417106i \(-0.136956\pi\)
−0.815653 + 0.578541i \(0.803622\pi\)
\(42\) −667.216 291.915i −2.45128 1.07246i
\(43\) 58.7928i 0.208507i −0.994551 0.104254i \(-0.966755\pi\)
0.994551 0.104254i \(-0.0332454\pi\)
\(44\) 112.264 194.446i 0.384645 0.666225i
\(45\) 365.985 + 396.057i 1.21240 + 1.31202i
\(46\) −732.918 + 423.150i −2.34919 + 1.35631i
\(47\) 65.2777 37.6881i 0.202590 0.116965i −0.395273 0.918564i \(-0.629350\pi\)
0.597863 + 0.801598i \(0.296017\pi\)
\(48\) 547.059 + 742.825i 1.64502 + 2.23370i
\(49\) 178.687 309.495i 0.520953 0.902316i
\(50\) −725.323 + 1256.30i −2.05152 + 3.55334i
\(51\) 142.382 104.858i 0.390931 0.287904i
\(52\) 627.699i 1.67396i
\(53\) −469.309 −1.21631 −0.608157 0.793817i \(-0.708091\pi\)
−0.608157 + 0.793817i \(0.708091\pi\)
\(54\) 140.371 729.634i 0.353742 1.83872i
\(55\) −111.842 193.716i −0.274195 0.474920i
\(56\) −1462.40 + 844.315i −3.48966 + 2.01476i
\(57\) −280.016 380.220i −0.650684 0.883533i
\(58\) 1622.01i 3.67207i
\(59\) 326.866i 0.721259i −0.932709 0.360630i \(-0.882562\pi\)
0.932709 0.360630i \(-0.117438\pi\)
\(60\) 2067.77 230.844i 4.44914 0.496697i
\(61\) 63.6744 + 36.7625i 0.133650 + 0.0771631i 0.565334 0.824862i \(-0.308747\pi\)
−0.431684 + 0.902025i \(0.642080\pi\)
\(62\) 932.101i 1.90931i
\(63\) 682.367 + 212.009i 1.36461 + 0.423979i
\(64\) 855.951 1.67178
\(65\) 541.561 + 312.670i 1.03342 + 0.596646i
\(66\) −123.534 + 282.357i −0.230394 + 0.526601i
\(67\) 319.774 445.542i 0.583085 0.812411i
\(68\) 682.245i 1.21668i
\(69\) 668.591 492.389i 1.16651 0.859082i
\(70\) 2799.33i 4.77977i
\(71\) 129.218 74.6041i 0.215991 0.124703i −0.388102 0.921617i \(-0.626869\pi\)
0.604093 + 0.796914i \(0.293536\pi\)
\(72\) −1169.22 1265.29i −1.91380 2.07105i
\(73\) −106.110 + 183.788i −0.170126 + 0.294668i −0.938464 0.345377i \(-0.887751\pi\)
0.768337 + 0.640045i \(0.221084\pi\)
\(74\) 91.1550 + 157.885i 0.143197 + 0.248024i
\(75\) 570.492 1303.95i 0.878330 2.00756i
\(76\) −1821.88 −2.74979
\(77\) −256.680 148.194i −0.379888 0.219328i
\(78\) −95.5956 856.293i −0.138770 1.24303i
\(79\) −83.6573 + 48.2996i −0.119142 + 0.0687864i −0.558386 0.829581i \(-0.688579\pi\)
0.439245 + 0.898367i \(0.355246\pi\)
\(80\) 1772.99 3070.91i 2.47783 4.29173i
\(81\) −57.4472 + 726.733i −0.0788028 + 0.996890i
\(82\) −259.176 −0.349039
\(83\) 983.038 + 567.557i 1.30003 + 0.750573i 0.980409 0.196973i \(-0.0631111\pi\)
0.319621 + 0.947546i \(0.396444\pi\)
\(84\) 2219.86 1634.83i 2.88341 2.12351i
\(85\) −588.621 339.841i −0.751117 0.433658i
\(86\) 269.654 + 155.685i 0.338110 + 0.195208i
\(87\) 176.567 + 1581.59i 0.217586 + 1.94902i
\(88\) 357.302 + 618.866i 0.432824 + 0.749674i
\(89\) 351.119i 0.418186i −0.977896 0.209093i \(-0.932949\pi\)
0.977896 0.209093i \(-0.0670511\pi\)
\(90\) −2785.66 + 629.825i −3.26260 + 0.737659i
\(91\) 828.597 0.954512
\(92\) 3203.66i 3.63048i
\(93\) −101.466 908.874i −0.113134 1.01340i
\(94\) 399.196i 0.438020i
\(95\) −907.518 + 1571.87i −0.980099 + 1.69758i
\(96\) −2219.56 + 247.789i −2.35971 + 0.263436i
\(97\) 1049.72 + 606.059i 1.09880 + 0.634391i 0.935905 0.352252i \(-0.114584\pi\)
0.162893 + 0.986644i \(0.447917\pi\)
\(98\) 946.333 + 1639.10i 0.975450 + 1.68953i
\(99\) 89.7195 288.768i 0.0910823 0.293154i
\(100\) −2745.70 4755.69i −2.74570 4.75569i
\(101\) −450.651 780.551i −0.443975 0.768987i 0.554005 0.832513i \(-0.313099\pi\)
−0.997980 + 0.0635258i \(0.979765\pi\)
\(102\) 103.903 + 930.703i 0.100862 + 0.903464i
\(103\) 634.361 + 1098.75i 0.606849 + 1.05109i 0.991756 + 0.128138i \(0.0409000\pi\)
−0.384908 + 0.922955i \(0.625767\pi\)
\(104\) −1730.13 998.891i −1.63128 0.941820i
\(105\) −304.727 2729.58i −0.283222 2.53695i
\(106\) 1242.74 2152.49i 1.13873 1.97234i
\(107\) 171.267i 0.154738i −0.997003 0.0773691i \(-0.975348\pi\)
0.997003 0.0773691i \(-0.0246520\pi\)
\(108\) 2126.29 + 1841.19i 1.89447 + 1.64045i
\(109\) 1833.84i 1.61147i 0.592275 + 0.805736i \(0.298230\pi\)
−0.592275 + 0.805736i \(0.701770\pi\)
\(110\) 1184.64 1.02683
\(111\) −106.070 144.028i −0.0907005 0.123158i
\(112\) 4698.55i 3.96402i
\(113\) −346.023 599.329i −0.288063 0.498939i 0.685285 0.728275i \(-0.259678\pi\)
−0.973347 + 0.229336i \(0.926344\pi\)
\(114\) 2485.37 277.464i 2.04190 0.227955i
\(115\) −2764.02 1595.81i −2.24127 1.29400i
\(116\) 5317.47 + 3070.05i 4.25616 + 2.45730i
\(117\) 186.427 + 824.549i 0.147309 + 0.651535i
\(118\) 1499.17 + 865.547i 1.16958 + 0.675255i
\(119\) −900.600 −0.693764
\(120\) −2654.28 + 6066.77i −2.01918 + 4.61515i
\(121\) 602.786 1044.06i 0.452882 0.784415i
\(122\) −337.223 + 194.696i −0.250252 + 0.144483i
\(123\) 252.718 28.2131i 0.185258 0.0206820i
\(124\) −3055.73 1764.23i −2.21300 1.27768i
\(125\) −2974.17 −2.12814
\(126\) −2779.31 + 2568.27i −1.96508 + 1.81587i
\(127\) 85.1449 + 147.475i 0.0594912 + 0.103042i 0.894237 0.447593i \(-0.147719\pi\)
−0.834746 + 0.550635i \(0.814385\pi\)
\(128\) −547.347 + 948.033i −0.377962 + 0.654649i
\(129\) −279.881 122.451i −0.191025 0.0835755i
\(130\) −2868.13 + 1655.92i −1.93501 + 1.11718i
\(131\) 1503.32i 1.00264i 0.865263 + 0.501318i \(0.167151\pi\)
−0.865263 + 0.501318i \(0.832849\pi\)
\(132\) −691.838 939.413i −0.456188 0.619435i
\(133\) 2404.98i 1.56796i
\(134\) 1196.71 + 2646.45i 0.771493 + 1.70611i
\(135\) 2647.68 917.368i 1.68797 0.584848i
\(136\) 1880.47 + 1085.69i 1.18566 + 0.684539i
\(137\) 1624.81 1.01326 0.506632 0.862162i \(-0.330890\pi\)
0.506632 + 0.862162i \(0.330890\pi\)
\(138\) 487.902 + 4370.36i 0.300963 + 2.69587i
\(139\) 3082.76i 1.88112i 0.339622 + 0.940562i \(0.389701\pi\)
−0.339622 + 0.940562i \(0.610299\pi\)
\(140\) −9177.12 5298.41i −5.54006 3.19855i
\(141\) −43.4552 389.248i −0.0259545 0.232486i
\(142\) 790.213i 0.466995i
\(143\) 350.651i 0.205055i
\(144\) 4675.59 1057.13i 2.70578 0.611765i
\(145\) 5297.50 3058.51i 3.03402 1.75169i
\(146\) −561.963 973.348i −0.318551 0.551746i
\(147\) −1101.18 1495.24i −0.617848 0.838946i
\(148\) −690.131 −0.383300
\(149\) 1443.40i 0.793609i −0.917903 0.396805i \(-0.870119\pi\)
0.917903 0.396805i \(-0.129881\pi\)
\(150\) 4469.89 + 6069.44i 2.43310 + 3.30379i
\(151\) 1685.28 2919.00i 0.908255 1.57314i 0.0917667 0.995781i \(-0.470749\pi\)
0.816488 0.577363i \(-0.195918\pi\)
\(152\) 2899.26 5021.66i 1.54711 2.67967i
\(153\) −202.627 896.200i −0.107068 0.473552i
\(154\) 1359.39 784.843i 0.711315 0.410678i
\(155\) −3044.25 + 1757.60i −1.57755 + 0.910798i
\(156\) 2988.14 + 1307.35i 1.53361 + 0.670972i
\(157\) −137.831 + 238.730i −0.0700643 + 0.121355i −0.898929 0.438094i \(-0.855654\pi\)
0.828865 + 0.559449i \(0.188987\pi\)
\(158\) 511.593i 0.257596i
\(159\) −977.460 + 2234.13i −0.487532 + 1.11433i
\(160\) 4292.22 + 7434.34i 2.12081 + 3.67335i
\(161\) −4229.00 −2.07014
\(162\) −3181.05 2187.89i −1.54276 1.06109i
\(163\) 408.772 + 708.014i 0.196426 + 0.340221i 0.947367 0.320149i \(-0.103733\pi\)
−0.750941 + 0.660370i \(0.770400\pi\)
\(164\) 490.553 849.663i 0.233572 0.404558i
\(165\) −1155.12 + 128.956i −0.545005 + 0.0608438i
\(166\) −5206.21 + 3005.81i −2.43422 + 1.40540i
\(167\) 1748.21 1009.33i 0.810063 0.467690i −0.0369147 0.999318i \(-0.511753\pi\)
0.846978 + 0.531628i \(0.178420\pi\)
\(168\) 973.514 + 8720.20i 0.447073 + 4.00463i
\(169\) −608.352 1053.70i −0.276901 0.479607i
\(170\) 3117.36 1799.81i 1.40642 0.811995i
\(171\) −2393.23 + 541.100i −1.07026 + 0.241982i
\(172\) −1020.77 + 589.341i −0.452517 + 0.261261i
\(173\) −181.311 104.680i −0.0796811 0.0460039i 0.459630 0.888110i \(-0.347982\pi\)
−0.539311 + 0.842107i \(0.681315\pi\)
\(174\) −7721.53 3378.26i −3.36418 1.47187i
\(175\) −6277.77 + 3624.47i −2.71174 + 1.56562i
\(176\) −1988.36 −0.851581
\(177\) −1556.04 680.783i −0.660784 0.289101i
\(178\) 1610.41 + 929.770i 0.678120 + 0.391513i
\(179\) 134.646 0.0562231 0.0281116 0.999605i \(-0.491051\pi\)
0.0281116 + 0.999605i \(0.491051\pi\)
\(180\) 3207.76 10324.4i 1.32829 4.27519i
\(181\) −970.249 1680.52i −0.398442 0.690122i 0.595092 0.803658i \(-0.297116\pi\)
−0.993534 + 0.113536i \(0.963782\pi\)
\(182\) −2194.14 + 3800.37i −0.893630 + 1.54781i
\(183\) 307.625 226.553i 0.124264 0.0915152i
\(184\) 8830.25 + 5098.15i 3.53791 + 2.04261i
\(185\) −343.769 + 595.426i −0.136618 + 0.236630i
\(186\) 4437.24 + 1941.35i 1.74922 + 0.765303i
\(187\) 381.122i 0.149039i
\(188\) −1308.69 755.574i −0.507693 0.293116i
\(189\) 2430.47 2806.82i 0.935402 1.08024i
\(190\) −4806.25 8324.68i −1.83517 3.17861i
\(191\) −1075.63 + 1863.05i −0.407488 + 0.705789i −0.994608 0.103711i \(-0.966928\pi\)
0.587120 + 0.809500i \(0.300262\pi\)
\(192\) 1782.74 4074.73i 0.670095 1.53161i
\(193\) 1374.61 0.512676 0.256338 0.966587i \(-0.417484\pi\)
0.256338 + 0.966587i \(0.417484\pi\)
\(194\) −5559.39 + 3209.71i −2.05743 + 1.18786i
\(195\) 2616.40 1926.87i 0.960843 0.707620i
\(196\) −7164.65 −2.61103
\(197\) 1745.11 + 3022.62i 0.631136 + 1.09316i 0.987320 + 0.158744i \(0.0507445\pi\)
−0.356183 + 0.934416i \(0.615922\pi\)
\(198\) 1086.86 + 1176.16i 0.390099 + 0.422153i
\(199\) 1259.49 2181.51i 0.448659 0.777099i −0.549640 0.835401i \(-0.685235\pi\)
0.998299 + 0.0583019i \(0.0185686\pi\)
\(200\) 17477.5 6.17923
\(201\) −1454.97 2450.23i −0.510577 0.859832i
\(202\) 4773.34 1.66263
\(203\) 4052.63 7019.36i 1.40118 2.42691i
\(204\) −3247.81 1420.95i −1.11467 0.487680i
\(205\) −488.710 846.470i −0.166502 0.288391i
\(206\) −6719.21 −2.27257
\(207\) −951.487 4208.34i −0.319483 1.41304i
\(208\) 4814.02 2779.37i 1.60477 0.926514i
\(209\) 1017.76 0.336840
\(210\) 13326.1 + 5830.34i 4.37901 + 1.91587i
\(211\) −485.474 + 840.866i −0.158395 + 0.274349i −0.934290 0.356514i \(-0.883965\pi\)
0.775895 + 0.630862i \(0.217299\pi\)
\(212\) 4704.38 + 8148.22i 1.52405 + 2.63973i
\(213\) −86.0202 770.522i −0.0276714 0.247865i
\(214\) 785.517 + 453.519i 0.250920 + 0.144869i
\(215\) 1174.25i 0.372481i
\(216\) −8458.57 + 2930.73i −2.66450 + 0.923197i
\(217\) −2328.88 + 4033.73i −0.728545 + 1.26188i
\(218\) −8410.94 4856.06i −2.61312 1.50869i
\(219\) 653.915 + 887.920i 0.201769 + 0.273973i
\(220\) −2242.21 + 3883.63i −0.687137 + 1.19016i
\(221\) −532.741 922.734i −0.162154 0.280859i
\(222\) 941.462 105.104i 0.284625 0.0317752i
\(223\) 2852.91 0.856703 0.428351 0.903612i \(-0.359095\pi\)
0.428351 + 0.903612i \(0.359095\pi\)
\(224\) 9850.75 + 5687.33i 2.93831 + 1.69643i
\(225\) −5019.20 5431.62i −1.48717 1.60937i
\(226\) 3665.10 1.07876
\(227\) 2765.82 1596.85i 0.808696 0.466901i −0.0378066 0.999285i \(-0.512037\pi\)
0.846503 + 0.532384i \(0.178704\pi\)
\(228\) −3794.54 + 8673.01i −1.10219 + 2.51923i
\(229\) 1046.97 + 604.467i 0.302120 + 0.174429i 0.643395 0.765534i \(-0.277525\pi\)
−0.341275 + 0.939964i \(0.610859\pi\)
\(230\) 14638.4 8451.48i 4.19664 2.42293i
\(231\) −1240.08 + 913.264i −0.353208 + 0.260123i
\(232\) −16924.0 + 9771.05i −4.78928 + 2.76509i
\(233\) 264.135 + 457.496i 0.0742664 + 0.128633i 0.900767 0.434303i \(-0.143005\pi\)
−0.826501 + 0.562936i \(0.809672\pi\)
\(234\) −4275.46 1328.37i −1.19443 0.371105i
\(235\) −1303.78 + 752.735i −0.361910 + 0.208949i
\(236\) −5675.09 + 3276.51i −1.56533 + 0.903741i
\(237\) 55.6905 + 498.845i 0.0152637 + 0.136723i
\(238\) 2384.81 4130.61i 0.649514 1.12499i
\(239\) −819.001 1418.55i −0.221660 0.383927i 0.733652 0.679525i \(-0.237814\pi\)
−0.955312 + 0.295599i \(0.904481\pi\)
\(240\) −10926.3 14836.3i −2.93870 3.99032i
\(241\) 4839.72 1.29358 0.646792 0.762667i \(-0.276110\pi\)
0.646792 + 0.762667i \(0.276110\pi\)
\(242\) 3192.38 + 5529.37i 0.847992 + 1.46877i
\(243\) 3339.94 + 1787.09i 0.881718 + 0.471777i
\(244\) 1474.03i 0.386743i
\(245\) −3568.87 + 6181.46i −0.930639 + 1.61191i
\(246\) −539.802 + 1233.80i −0.139905 + 0.319773i
\(247\) −2464.09 + 1422.64i −0.634762 + 0.366480i
\(248\) 9725.49 5615.02i 2.49020 1.43772i
\(249\) 4749.28 3497.64i 1.20873 0.890176i
\(250\) 7875.66 13641.0i 1.99240 3.45094i
\(251\) −3264.94 + 5655.04i −0.821040 + 1.42208i 0.0838690 + 0.996477i \(0.473272\pi\)
−0.904909 + 0.425606i \(0.860061\pi\)
\(252\) −3159.13 13972.5i −0.789709 3.49281i
\(253\) 1789.65i 0.444722i
\(254\) −901.862 −0.222787
\(255\) −2843.76 + 2094.31i −0.698366 + 0.514316i
\(256\) 525.027 + 909.374i 0.128181 + 0.222015i
\(257\) 1270.71 733.648i 0.308424 0.178069i −0.337797 0.941219i \(-0.609682\pi\)
0.646221 + 0.763150i \(0.276348\pi\)
\(258\) 1302.76 959.425i 0.314365 0.231516i
\(259\) 911.011i 0.218562i
\(260\) 12536.9i 2.99040i
\(261\) 7896.87 + 2453.54i 1.87281 + 0.581877i
\(262\) −6894.97 3980.81i −1.62585 0.938685i
\(263\) 1224.64i 0.287126i −0.989641 0.143563i \(-0.954144\pi\)
0.989641 0.143563i \(-0.0458560\pi\)
\(264\) 3690.27 411.978i 0.860304 0.0960434i
\(265\) 9373.40 2.17284
\(266\) −11030.5 6368.45i −2.54256 1.46795i
\(267\) −1671.49 731.297i −0.383122 0.167620i
\(268\) −10941.0 1085.85i −2.49376 0.247495i
\(269\) 6608.27i 1.49782i 0.662672 + 0.748910i \(0.269422\pi\)
−0.662672 + 0.748910i \(0.730578\pi\)
\(270\) −2803.60 + 14572.8i −0.631931 + 3.28472i
\(271\) 1851.85i 0.415098i −0.978225 0.207549i \(-0.933451\pi\)
0.978225 0.207549i \(-0.0665487\pi\)
\(272\) −5232.35 + 3020.90i −1.16639 + 0.673415i
\(273\) 1725.77 3944.51i 0.382595 0.874479i
\(274\) −4302.54 + 7452.22i −0.948635 + 1.64308i
\(275\) 1533.83 + 2656.66i 0.336339 + 0.582556i
\(276\) −15250.9 6672.45i −3.32608 1.45520i
\(277\) −1095.88 −0.237708 −0.118854 0.992912i \(-0.537922\pi\)
−0.118854 + 0.992912i \(0.537922\pi\)
\(278\) −14139.1 8163.22i −3.05039 1.76114i
\(279\) −4538.00 1409.94i −0.973774 0.302549i
\(280\) 29208.1 16863.3i 6.23399 3.59920i
\(281\) −2100.12 + 3637.52i −0.445847 + 0.772229i −0.998111 0.0614402i \(-0.980431\pi\)
0.552264 + 0.833669i \(0.313764\pi\)
\(282\) 1900.36 + 831.429i 0.401294 + 0.175571i
\(283\) −7421.06 −1.55879 −0.779393 0.626535i \(-0.784472\pi\)
−0.779393 + 0.626535i \(0.784472\pi\)
\(284\) −2590.58 1495.67i −0.541276 0.312506i
\(285\) 5592.69 + 7594.04i 1.16239 + 1.57836i
\(286\) 1608.26 + 928.531i 0.332512 + 0.191976i
\(287\) −1121.60 647.557i −0.230683 0.133185i
\(288\) −3443.22 + 11082.2i −0.704491 + 2.26745i
\(289\) −1877.47 3251.87i −0.382142 0.661890i
\(290\) 32396.0i 6.55986i
\(291\) 5071.45 3734.91i 1.02163 0.752386i
\(292\) 4254.60 0.852677
\(293\) 4841.97i 0.965431i 0.875777 + 0.482715i \(0.160349\pi\)
−0.875777 + 0.482715i \(0.839651\pi\)
\(294\) 9773.86 1091.14i 1.93885 0.216452i
\(295\) 6528.41i 1.28847i
\(296\) 1098.24 1902.21i 0.215656 0.373527i
\(297\) −1187.81 1028.54i −0.232066 0.200950i
\(298\) 6620.16 + 3822.15i 1.28690 + 0.742991i
\(299\) −2501.62 4332.93i −0.483854 0.838061i
\(300\) −28357.9 + 3165.85i −5.45749 + 0.609268i
\(301\) 777.963 + 1347.47i 0.148974 + 0.258030i
\(302\) 8925.34 + 15459.1i 1.70065 + 2.94561i
\(303\) −4654.39 + 519.611i −0.882468 + 0.0985178i
\(304\) 8067.07 + 13972.6i 1.52197 + 2.63612i
\(305\) −1271.75 734.248i −0.238756 0.137846i
\(306\) 4646.99 + 1443.81i 0.868140 + 0.269729i
\(307\) −833.560 + 1443.77i −0.154963 + 0.268405i −0.933046 0.359758i \(-0.882859\pi\)
0.778082 + 0.628162i \(0.216193\pi\)
\(308\) 5942.02i 1.09928i
\(309\) 6551.77 731.432i 1.20620 0.134659i
\(310\) 18616.6i 3.41082i
\(311\) 7209.90 1.31459 0.657293 0.753635i \(-0.271701\pi\)
0.657293 + 0.753635i \(0.271701\pi\)
\(312\) −8358.64 + 6155.78i −1.51671 + 1.11700i
\(313\) 1732.91i 0.312939i −0.987683 0.156469i \(-0.949989\pi\)
0.987683 0.156469i \(-0.0500113\pi\)
\(314\) −729.958 1264.32i −0.131191 0.227229i
\(315\) −13628.7 4234.41i −2.43775 0.757404i
\(316\) 1677.17 + 968.314i 0.298570 + 0.172379i
\(317\) −487.567 281.497i −0.0863864 0.0498752i 0.456185 0.889885i \(-0.349216\pi\)
−0.542571 + 0.840010i \(0.682549\pi\)
\(318\) −7658.54 10399.2i −1.35053 1.83382i
\(319\) −2970.49 1715.02i −0.521366 0.301011i
\(320\) −17095.7 −2.98650
\(321\) −815.311 356.708i −0.141764 0.0620234i
\(322\) 11198.5 19396.4i 1.93810 3.35688i
\(323\) 2678.21 1546.27i 0.461361 0.266367i
\(324\) 13193.5 6287.39i 2.26226 1.07809i
\(325\) −7427.09 4288.03i −1.26763 0.731869i
\(326\) −4329.75 −0.735591
\(327\) 8729.96 + 3819.46i 1.47636 + 0.645923i
\(328\) 1561.29 + 2704.23i 0.262828 + 0.455232i
\(329\) −997.399 + 1727.55i −0.167138 + 0.289491i
\(330\) 2467.32 5639.44i 0.411580 0.940730i
\(331\) −8007.32 + 4623.03i −1.32967 + 0.767688i −0.985249 0.171126i \(-0.945259\pi\)
−0.344425 + 0.938814i \(0.611926\pi\)
\(332\) 22756.9i 3.76189i
\(333\) −906.560 + 204.969i −0.149187 + 0.0337305i
\(334\) 10690.9i 1.75144i
\(335\) −6386.78 + 8898.69i −1.04163 + 1.45131i
\(336\) −22367.3 9785.95i −3.63165 1.58889i
\(337\) 5120.31 + 2956.21i 0.827659 + 0.477849i 0.853050 0.521829i \(-0.174750\pi\)
−0.0253916 + 0.999678i \(0.508083\pi\)
\(338\) 6443.72 1.03696
\(339\) −3573.77 + 398.972i −0.572568 + 0.0639209i
\(340\) 13626.3i 2.17350i
\(341\) 1707.02 + 985.548i 0.271086 + 0.156511i
\(342\) 3855.57 12409.4i 0.609607 1.96206i
\(343\) 380.388i 0.0598806i
\(344\) 3751.40i 0.587971i
\(345\) −13353.6 + 9834.37i −2.08387 + 1.53468i
\(346\) 960.232 554.390i 0.149198 0.0861393i
\(347\) −1974.70 3420.28i −0.305497 0.529136i 0.671875 0.740665i \(-0.265489\pi\)
−0.977372 + 0.211528i \(0.932156\pi\)
\(348\) 25689.9 18919.5i 3.95725 2.91435i
\(349\) 7980.53 1.22403 0.612017 0.790844i \(-0.290358\pi\)
0.612017 + 0.790844i \(0.290358\pi\)
\(350\) 38390.7i 5.86306i
\(351\) 4313.52 + 829.859i 0.655951 + 0.126195i
\(352\) 2406.80 4168.70i 0.364440 0.631229i
\(353\) 4612.86 7989.70i 0.695517 1.20467i −0.274489 0.961590i \(-0.588509\pi\)
0.970006 0.243081i \(-0.0781580\pi\)
\(354\) 7242.83 5334.04i 1.08744 0.800850i
\(355\) −2580.84 + 1490.05i −0.385850 + 0.222771i
\(356\) −6096.18 + 3519.63i −0.907575 + 0.523989i
\(357\) −1875.74 + 4287.28i −0.278080 + 0.635594i
\(358\) −356.546 + 617.556i −0.0526370 + 0.0911700i
\(359\) 939.431i 0.138109i −0.997613 0.0690547i \(-0.978002\pi\)
0.997613 0.0690547i \(-0.0219983\pi\)
\(360\) 23352.5 + 25271.3i 3.41884 + 3.69976i
\(361\) −699.684 1211.89i −0.102010 0.176686i
\(362\) 10277.0 1.49211
\(363\) −3714.74 5044.07i −0.537117 0.729325i
\(364\) −8305.89 14386.2i −1.19601 2.07155i
\(365\) 2119.31 3670.75i 0.303917 0.526399i
\(366\) 224.488 + 2010.84i 0.0320606 + 0.287182i
\(367\) 8964.74 5175.79i 1.27508 0.736169i 0.299143 0.954208i \(-0.403299\pi\)
0.975940 + 0.218039i \(0.0699660\pi\)
\(368\) −24569.8 + 14185.4i −3.48041 + 2.00942i
\(369\) 392.043 1261.82i 0.0553088 0.178015i
\(370\) −1820.62 3153.40i −0.255809 0.443074i
\(371\) 10756.1 6210.04i 1.50520 0.869027i
\(372\) −14762.9 + 10872.3i −2.05758 + 1.51532i
\(373\) −1260.00 + 727.463i −0.174907 + 0.100983i −0.584898 0.811107i \(-0.698865\pi\)
0.409990 + 0.912090i \(0.365532\pi\)
\(374\) −1748.02 1009.22i −0.241679 0.139533i
\(375\) −6194.48 + 14158.4i −0.853018 + 1.94970i
\(376\) 4165.18 2404.77i 0.571285 0.329831i
\(377\) 9589.16 1.30999
\(378\) 6437.57 + 18579.9i 0.875960 + 2.52817i
\(379\) 3877.18 + 2238.49i 0.525481 + 0.303387i 0.739174 0.673514i \(-0.235216\pi\)
−0.213693 + 0.976901i \(0.568549\pi\)
\(380\) 36388.0 4.91227
\(381\) 879.388 98.1740i 0.118248 0.0132011i
\(382\) −5696.61 9866.81i −0.762994 1.32154i
\(383\) 102.787 178.032i 0.0137132 0.0237520i −0.859087 0.511829i \(-0.828968\pi\)
0.872801 + 0.488077i \(0.162301\pi\)
\(384\) 3373.09 + 4580.16i 0.448262 + 0.608673i
\(385\) 5126.60 + 2959.85i 0.678639 + 0.391812i
\(386\) −3639.99 + 6304.66i −0.479976 + 0.831343i
\(387\) −1165.85 + 1077.33i −0.153136 + 0.141509i
\(388\) 24300.6i 3.17958i
\(389\) 4985.17 + 2878.19i 0.649764 + 0.375141i 0.788366 0.615207i \(-0.210927\pi\)
−0.138602 + 0.990348i \(0.544261\pi\)
\(390\) 1909.31 + 17102.5i 0.247901 + 2.22057i
\(391\) 2719.01 + 4709.46i 0.351678 + 0.609124i
\(392\) 11401.5 19748.0i 1.46904 2.54445i
\(393\) 7156.49 + 3131.05i 0.918568 + 0.401884i
\(394\) −18484.3 −2.36352
\(395\) 1670.87 964.675i 0.212837 0.122881i
\(396\) −5912.99 + 1336.90i −0.750350 + 0.169651i
\(397\) 949.009 0.119973 0.0599867 0.998199i \(-0.480894\pi\)
0.0599867 + 0.998199i \(0.480894\pi\)
\(398\) 6670.33 + 11553.3i 0.840084 + 1.45507i
\(399\) 11448.9 + 5009.01i 1.43649 + 0.628481i
\(400\) −24315.2 + 42115.2i −3.03940 + 5.26440i
\(401\) −5215.21 −0.649464 −0.324732 0.945806i \(-0.605274\pi\)
−0.324732 + 0.945806i \(0.605274\pi\)
\(402\) 15090.8 184.976i 1.87229 0.0229496i
\(403\) −5510.49 −0.681134
\(404\) −9034.70 + 15648.6i −1.11261 + 1.92709i
\(405\) 1147.38 14514.9i 0.140775 1.78086i
\(406\) 21462.9 + 37174.8i 2.62361 + 4.54423i
\(407\) 385.527 0.0469530
\(408\) 9084.99 6690.71i 1.10239 0.811861i
\(409\) −7915.11 + 4569.79i −0.956912 + 0.552473i −0.895221 0.445622i \(-0.852982\pi\)
−0.0616904 + 0.998095i \(0.519649\pi\)
\(410\) 5176.46 0.623529
\(411\) 3384.10 7734.88i 0.406144 0.928305i
\(412\) 12717.7 22027.7i 1.52077 2.63405i
\(413\) 4325.18 + 7491.43i 0.515322 + 0.892565i
\(414\) 21821.1 + 6779.77i 2.59046 + 0.804849i
\(415\) −19634.0 11335.7i −2.32240 1.34084i
\(416\) 13457.1i 1.58603i
\(417\) 14675.4 + 6420.66i 1.72340 + 0.754007i
\(418\) −2695.04 + 4667.94i −0.315356 + 0.546212i
\(419\) −11894.5 6867.31i −1.38684 0.800692i −0.393881 0.919161i \(-0.628868\pi\)
−0.992958 + 0.118469i \(0.962201\pi\)
\(420\) −44336.7 + 32652.1i −5.15098 + 3.79347i
\(421\) −4693.20 + 8128.86i −0.543308 + 0.941037i 0.455403 + 0.890285i \(0.349495\pi\)
−0.998711 + 0.0507518i \(0.983838\pi\)
\(422\) −2571.09 4453.26i −0.296585 0.513700i
\(423\) −1943.51 603.844i −0.223397 0.0694087i
\(424\) −29945.3 −3.42989
\(425\) 8072.49 + 4660.66i 0.921349 + 0.531941i
\(426\) 3761.79 + 1645.83i 0.427839 + 0.187184i
\(427\) −1945.81 −0.220525
\(428\) −2973.56 + 1716.79i −0.335824 + 0.193888i
\(429\) −1669.26 730.322i −0.187862 0.0821918i
\(430\) −5385.73 3109.45i −0.604007 0.348723i
\(431\) −6747.28 + 3895.54i −0.754072 + 0.435364i −0.827163 0.561962i \(-0.810047\pi\)
0.0730914 + 0.997325i \(0.476714\pi\)
\(432\) 4705.70 24459.8i 0.524081 2.72412i
\(433\) 12982.6 7495.52i 1.44089 0.831897i 0.442979 0.896532i \(-0.353921\pi\)
0.997909 + 0.0646345i \(0.0205882\pi\)
\(434\) −12333.8 21362.8i −1.36415 2.36278i
\(435\) −3526.53 31588.7i −0.388699 3.48176i
\(436\) 31839.5 18382.5i 3.49733 2.01918i
\(437\) 12576.2 7260.89i 1.37667 0.794819i
\(438\) −5804.03 + 647.956i −0.633168 + 0.0706861i
\(439\) −2704.02 + 4683.50i −0.293977 + 0.509182i −0.974746 0.223315i \(-0.928312\pi\)
0.680770 + 0.732497i \(0.261645\pi\)
\(440\) −7136.31 12360.5i −0.773205 1.33923i
\(441\) −9411.53 + 2127.91i −1.01625 + 0.229771i
\(442\) 5642.84 0.607245
\(443\) −4965.16 8599.92i −0.532510 0.922335i −0.999279 0.0379558i \(-0.987915\pi\)
0.466769 0.884379i \(-0.345418\pi\)
\(444\) −1437.38 + 3285.35i −0.153637 + 0.351162i
\(445\) 7012.81i 0.747054i
\(446\) −7554.56 + 13084.9i −0.802060 + 1.38921i
\(447\) −6871.26 3006.26i −0.727068 0.318101i
\(448\) −19617.5 + 11326.2i −2.06884 + 1.19445i
\(449\) −352.889 + 203.741i −0.0370910 + 0.0214145i −0.518431 0.855120i \(-0.673484\pi\)
0.481340 + 0.876534i \(0.340150\pi\)
\(450\) 38203.1 8637.56i 4.00203 0.904841i
\(451\) −274.037 + 474.646i −0.0286118 + 0.0495570i
\(452\) −6937.09 + 12015.4i −0.721888 + 1.25035i
\(453\) −10385.8 14102.3i −1.07719 1.46266i
\(454\) 16914.0i 1.74848i
\(455\) −16549.4 −1.70516
\(456\) −17867.0 24260.8i −1.83487 2.49148i
\(457\) 3018.79 + 5228.69i 0.309000 + 0.535204i 0.978144 0.207929i \(-0.0666724\pi\)
−0.669144 + 0.743133i \(0.733339\pi\)
\(458\) −5544.78 + 3201.28i −0.565700 + 0.326607i
\(459\) −4688.36 901.972i −0.476762 0.0917221i
\(460\) 63985.8i 6.48556i
\(461\) 1881.34i 0.190071i 0.995474 + 0.0950353i \(0.0302964\pi\)
−0.995474 + 0.0950353i \(0.969704\pi\)
\(462\) −904.941 8105.97i −0.0911292 0.816285i
\(463\) −16017.0 9247.44i −1.60772 0.928218i −0.989879 0.141915i \(-0.954674\pi\)
−0.617842 0.786302i \(-0.711993\pi\)
\(464\) 54375.1i 5.44031i
\(465\) 2026.55 + 18152.7i 0.202105 + 1.81035i
\(466\) −2797.74 −0.278118
\(467\) −1198.32 691.850i −0.118740 0.0685546i 0.439454 0.898265i \(-0.355172\pi\)
−0.558194 + 0.829711i \(0.688505\pi\)
\(468\) 12447.2 11502.1i 1.22943 1.13608i
\(469\) −1433.38 + 14442.7i −0.141124 + 1.42197i
\(470\) 7973.04i 0.782487i
\(471\) 849.398 + 1153.36i 0.0830960 + 0.112832i
\(472\) 20856.4i 2.03388i
\(473\) 570.231 329.223i 0.0554318 0.0320036i
\(474\) −2435.43 1065.53i −0.235997 0.103252i
\(475\) 12445.9 21557.0i 1.20223 2.08232i
\(476\) 9027.66 + 15636.4i 0.869290 + 1.50565i
\(477\) 8599.72 + 9306.34i 0.825480 + 0.893308i
\(478\) 8674.93 0.830088
\(479\) 15595.1 + 9003.86i 1.48760 + 0.858866i 0.999900 0.0141461i \(-0.00450298\pi\)
0.487699 + 0.873012i \(0.337836\pi\)
\(480\) 44330.7 4949.03i 4.21543 0.470606i
\(481\) −933.401 + 538.899i −0.0884811 + 0.0510846i
\(482\) −12815.7 + 22197.4i −1.21107 + 2.09764i
\(483\) −8808.01 + 20132.0i −0.829768 + 1.89656i
\(484\) −24169.4 −2.26986
\(485\) −20965.9 12104.7i −1.96291 1.13329i
\(486\) −17040.7 + 10586.4i −1.59050 + 0.988087i
\(487\) 4636.64 + 2676.97i 0.431430 + 0.249086i 0.699956 0.714186i \(-0.253203\pi\)
−0.268526 + 0.963272i \(0.586536\pi\)
\(488\) 4062.89 + 2345.71i 0.376882 + 0.217593i
\(489\) 4221.86 471.324i 0.390427 0.0435869i
\(490\) −18900.9 32737.3i −1.74256 3.01820i
\(491\) 2474.99i 0.227484i −0.993510 0.113742i \(-0.963716\pi\)
0.993510 0.113742i \(-0.0362837\pi\)
\(492\) −3023.09 4104.91i −0.277015 0.376146i
\(493\) −10422.4 −0.952136
\(494\) 15068.8i 1.37242i
\(495\) −1791.95 + 5767.50i −0.162711 + 0.523696i
\(496\) 31247.1i 2.82870i
\(497\) −1974.37 + 3419.70i −0.178194 + 0.308641i
\(498\) 3465.77 + 31044.4i 0.311857 + 2.79344i
\(499\) 5672.61 + 3275.08i 0.508900 + 0.293813i 0.732381 0.680895i \(-0.238409\pi\)
−0.223482 + 0.974708i \(0.571742\pi\)
\(500\) 29813.2 + 51637.9i 2.66657 + 4.61863i
\(501\) −1163.78 10424.5i −0.103780 0.929605i
\(502\) −17291.2 29949.3i −1.53734 2.66276i
\(503\) 2101.70 + 3640.26i 0.186303 + 0.322686i 0.944015 0.329903i \(-0.107016\pi\)
−0.757712 + 0.652589i \(0.773683\pi\)
\(504\) 43539.9 + 13527.7i 3.84806 + 1.19558i
\(505\) 9000.75 + 15589.8i 0.793125 + 1.37373i
\(506\) −8208.27 4739.04i −0.721150 0.416356i
\(507\) −6283.15 + 701.444i −0.550383 + 0.0614442i
\(508\) 1706.99 2956.60i 0.149086 0.258224i
\(509\) 15816.0i 1.37727i −0.725109 0.688634i \(-0.758211\pi\)
0.725109 0.688634i \(-0.241789\pi\)
\(510\) −2075.22 18588.7i −0.180181 1.61396i
\(511\) 5616.31i 0.486205i
\(512\) −14318.7 −1.23594
\(513\) −2408.65 + 12519.9i −0.207299 + 1.07752i
\(514\) 7770.86i 0.666844i
\(515\) −12669.9 21945.0i −1.08409 1.87769i
\(516\) 679.524 + 6086.80i 0.0579736 + 0.519296i
\(517\) 731.073 + 422.085i 0.0621907 + 0.0359058i
\(518\) −4178.36 2412.38i −0.354414 0.204621i
\(519\) −875.954 + 645.103i −0.0740850 + 0.0545605i
\(520\) 34555.5 + 19950.6i 2.91415 + 1.68248i
\(521\) −5317.53 −0.447150 −0.223575 0.974687i \(-0.571773\pi\)
−0.223575 + 0.974687i \(0.571773\pi\)
\(522\) −32164.2 + 29722.0i −2.69692 + 2.49214i
\(523\) 8568.27 14840.7i 0.716375 1.24080i −0.246051 0.969257i \(-0.579133\pi\)
0.962427 0.271542i \(-0.0875334\pi\)
\(524\) 26100.8 15069.3i 2.17599 1.25631i
\(525\) 4179.10 + 37434.0i 0.347411 + 3.11192i
\(526\) 5616.80 + 3242.86i 0.465597 + 0.268813i
\(527\) 5989.34 0.495066
\(528\) −4141.28 + 9465.53i −0.341337 + 0.780178i
\(529\) 6684.30 + 11577.5i 0.549379 + 0.951553i
\(530\) −24821.0 + 42991.2i −2.03425 + 3.52343i
\(531\) −6481.70 + 5989.55i −0.529721 + 0.489500i
\(532\) 41755.7 24107.6i 3.40289 1.96466i
\(533\) 1532.22i 0.124518i
\(534\) 7780.25 5729.82i 0.630495 0.464333i
\(535\) 3420.67i 0.276427i
\(536\) 20403.9 28428.7i 1.64424 2.29092i
\(537\) 280.436 640.980i 0.0225358 0.0515090i
\(538\) −30308.9 17498.8i −2.42883 1.40228i
\(539\) 4002.38 0.319842
\(540\) −42467.9 36773.7i −3.38431 2.93053i
\(541\) 4148.64i 0.329693i 0.986319 + 0.164847i \(0.0527129\pi\)
−0.986319 + 0.164847i \(0.947287\pi\)
\(542\) 8493.51 + 4903.73i 0.673113 + 0.388622i
\(543\) −10020.9 + 1118.72i −0.791965 + 0.0884141i
\(544\) 14626.5i 1.15277i
\(545\) 36626.9i 2.87876i
\(546\) 13521.7 + 18360.4i 1.05984 + 1.43911i
\(547\) 13725.6 7924.47i 1.07288 0.619425i 0.143910 0.989591i \(-0.454032\pi\)
0.928966 + 0.370165i \(0.120699\pi\)
\(548\) −16287.2 28210.2i −1.26962 2.19905i
\(549\) −437.789 1936.30i −0.0340335 0.150527i
\(550\) −16246.4 −1.25954
\(551\) 27832.3i 2.15190i
\(552\) 42660.9 31417.9i 3.28944 2.42253i
\(553\) 1278.23 2213.95i 0.0982925 0.170248i
\(554\) 2901.92 5026.28i 0.222547 0.385462i
\(555\) 2118.52 + 2876.63i 0.162029 + 0.220011i
\(556\) 53523.3 30901.7i 4.08254 2.35706i
\(557\) 19299.1 11142.3i 1.46809 0.847604i 0.468731 0.883341i \(-0.344711\pi\)
0.999361 + 0.0357370i \(0.0113779\pi\)
\(558\) 18483.4 17080.0i 1.40227 1.29580i
\(559\) −920.391 + 1594.16i −0.0696394 + 0.120619i
\(560\) 93842.9i 7.08140i
\(561\) 1814.32 + 793.786i 0.136543 + 0.0597391i
\(562\) −11122.3 19264.5i −0.834818 1.44595i
\(563\) −3963.01 −0.296662 −0.148331 0.988938i \(-0.547390\pi\)
−0.148331 + 0.988938i \(0.547390\pi\)
\(564\) −6322.58 + 4656.31i −0.472037 + 0.347635i
\(565\) 6911.03 + 11970.2i 0.514600 + 0.891314i
\(566\) 19651.1 34036.8i 1.45936 2.52769i
\(567\) −8299.71 17416.1i −0.614735 1.28996i
\(568\) 8245.04 4760.28i 0.609075 0.351649i
\(569\) 17625.6 10176.1i 1.29860 0.749745i 0.318435 0.947945i \(-0.396843\pi\)
0.980162 + 0.198199i \(0.0635093\pi\)
\(570\) −49639.7 + 5541.72i −3.64768 + 0.407223i
\(571\) 7677.37 + 13297.6i 0.562676 + 0.974584i 0.997262 + 0.0739531i \(0.0235615\pi\)
−0.434586 + 0.900631i \(0.643105\pi\)
\(572\) −6088.05 + 3514.94i −0.445025 + 0.256935i
\(573\) 6628.72 + 9000.82i 0.483279 + 0.656221i
\(574\) 5940.05 3429.49i 0.431939 0.249380i
\(575\) 37906.5 + 21885.3i 2.74923 + 1.58727i
\(576\) −15684.6 16973.4i −1.13459 1.22782i
\(577\) −23035.1 + 13299.3i −1.66198 + 0.959547i −0.690217 + 0.723603i \(0.742485\pi\)
−0.971767 + 0.235944i \(0.924182\pi\)
\(578\) 19886.3 1.43107
\(579\) 2862.98 6543.79i 0.205495 0.469690i
\(580\) −106205. 61317.3i −7.60329 4.38976i
\(581\) −30040.3 −2.14507
\(582\) 3700.87 + 33150.4i 0.263584 + 2.36104i
\(583\) −2628.00 4551.83i −0.186691 0.323358i
\(584\) −6770.58 + 11727.0i −0.479740 + 0.830935i
\(585\) −3723.46 16468.5i −0.263156 1.16391i
\(586\) −22207.8 12821.7i −1.56552 0.903853i
\(587\) −3287.57 + 5694.24i −0.231163 + 0.400386i −0.958151 0.286264i \(-0.907586\pi\)
0.726988 + 0.686651i \(0.240920\pi\)
\(588\) −14922.3 + 34107.1i −1.04657 + 2.39210i
\(589\) 15994.1i 1.11889i
\(590\) −29942.6 17287.4i −2.08935 1.20629i
\(591\) 18023.7 2012.15i 1.25448 0.140049i
\(592\) 3055.82 + 5292.83i 0.212151 + 0.367456i
\(593\) −10405.7 + 18023.2i −0.720590 + 1.24810i 0.240174 + 0.970730i \(0.422796\pi\)
−0.960764 + 0.277369i \(0.910538\pi\)
\(594\) 7862.76 2724.29i 0.543119 0.188180i
\(595\) 17987.5 1.23935
\(596\) −25060.5 + 14468.7i −1.72235 + 0.994396i
\(597\) −7761.77 10539.3i −0.532107 0.722523i
\(598\) 26497.4 1.81197
\(599\) −5428.89 9403.11i −0.370314 0.641403i 0.619299 0.785155i \(-0.287417\pi\)
−0.989614 + 0.143752i \(0.954083\pi\)
\(600\) 36401.5 83201.1i 2.47681 5.66112i
\(601\) 7046.53 12204.9i 0.478259 0.828370i −0.521430 0.853294i \(-0.674601\pi\)
0.999689 + 0.0249246i \(0.00793455\pi\)
\(602\) −8240.25 −0.557886
\(603\) −14694.6 + 1823.11i −0.992392 + 0.123122i
\(604\) −67573.4 −4.55219
\(605\) −12039.3 + 20852.7i −0.809037 + 1.40129i
\(606\) 9941.73 22723.4i 0.666428 1.52322i
\(607\) 13921.7 + 24113.2i 0.930916 + 1.61239i 0.781760 + 0.623580i \(0.214322\pi\)
0.149156 + 0.988814i \(0.452344\pi\)
\(608\) −39059.0 −2.60535
\(609\) −24974.8 33912.1i −1.66179 2.25646i
\(610\) 6735.27 3888.61i 0.447054 0.258107i
\(611\) −2360.00 −0.156261
\(612\) −13528.8 + 12501.6i −0.893579 + 0.825730i
\(613\) −3041.69 + 5268.36i −0.200412 + 0.347124i −0.948661 0.316294i \(-0.897562\pi\)
0.748249 + 0.663418i \(0.230895\pi\)
\(614\) −4414.57 7646.26i −0.290159 0.502570i
\(615\) −5047.47 + 563.494i −0.330949 + 0.0369468i
\(616\) −16378.0 9455.85i −1.07125 0.618486i
\(617\) 20182.7i 1.31689i −0.752627 0.658447i \(-0.771213\pi\)
0.752627 0.658447i \(-0.228787\pi\)
\(618\) −13994.5 + 31986.6i −0.910909 + 2.08202i
\(619\) −4733.88 + 8199.32i −0.307384 + 0.532405i −0.977789 0.209590i \(-0.932787\pi\)
0.670405 + 0.741995i \(0.266120\pi\)
\(620\) 61031.3 + 35236.5i 3.95335 + 2.28247i
\(621\) −22015.4 4235.44i −1.42262 0.273691i
\(622\) −19092.0 + 33068.3i −1.23074 + 2.13170i
\(623\) 4646.10 + 8047.29i 0.298784 + 0.517509i
\(624\) −3204.68 28705.8i −0.205593 1.84159i
\(625\) 25163.4 1.61046
\(626\) 7948.00 + 4588.78i 0.507454 + 0.292979i
\(627\) 2119.74 4845.00i 0.135015 0.308597i
\(628\) 5526.49 0.351164
\(629\) 1014.51 585.728i 0.0643104 0.0371296i
\(630\) 55510.4 51295.5i 3.51046 3.24391i
\(631\) 14966.4 + 8640.85i 0.944220 + 0.545145i 0.891281 0.453452i \(-0.149808\pi\)
0.0529390 + 0.998598i \(0.483141\pi\)
\(632\) −5337.94 + 3081.86i −0.335968 + 0.193971i
\(633\) 2991.79 + 4062.41i 0.187856 + 0.255081i
\(634\) 2582.18 1490.82i 0.161753 0.0933881i
\(635\) −1700.58 2945.49i −0.106276 0.184076i
\(636\) 48587.5 5424.25i 3.02927 0.338185i
\(637\) −9690.17 + 5594.62i −0.602729 + 0.347986i
\(638\) 15731.9 9082.80i 0.976224 0.563623i
\(639\) −3847.21 1195.32i −0.238174 0.0740000i
\(640\) 10932.0 18934.8i 0.675198 1.16948i
\(641\) 3384.89 + 5862.80i 0.208573 + 0.361259i 0.951265 0.308374i \(-0.0997848\pi\)
−0.742692 + 0.669633i \(0.766452\pi\)
\(642\) 3795.01 2794.86i 0.233298 0.171814i
\(643\) 15442.4 0.947105 0.473553 0.880765i \(-0.342971\pi\)
0.473553 + 0.880765i \(0.342971\pi\)
\(644\) 42391.7 + 73424.6i 2.59389 + 4.49275i
\(645\) 5590.00 + 2445.69i 0.341250 + 0.149301i
\(646\) 16378.2i 0.997510i
\(647\) −1990.83 + 3448.22i −0.120970 + 0.209526i −0.920150 0.391565i \(-0.871934\pi\)
0.799180 + 0.601091i \(0.205267\pi\)
\(648\) −3665.55 + 46370.8i −0.222216 + 2.81114i
\(649\) 3170.27 1830.36i 0.191747 0.110705i
\(650\) 39334.2 22709.6i 2.37356 1.37038i
\(651\) 14352.0 + 19487.9i 0.864052 + 1.17326i
\(652\) 8195.10 14194.3i 0.492247 0.852596i
\(653\) 5785.68 10021.1i 0.346725 0.600545i −0.638941 0.769256i \(-0.720627\pi\)
0.985666 + 0.168711i \(0.0539605\pi\)
\(654\) −40635.1 + 29926.0i −2.42960 + 1.78930i
\(655\) 30025.4i 1.79113i
\(656\) −8688.44 −0.517114
\(657\) 5588.87 1263.62i 0.331876 0.0750357i
\(658\) −5282.27 9149.16i −0.312955 0.542054i
\(659\) 3652.83 2108.96i 0.215924 0.124664i −0.388137 0.921602i \(-0.626881\pi\)
0.604062 + 0.796938i \(0.293548\pi\)
\(660\) 13817.9 + 18762.7i 0.814942 + 1.10657i
\(661\) 20023.7i 1.17826i −0.808037 0.589132i \(-0.799470\pi\)
0.808037 0.589132i \(-0.200530\pi\)
\(662\) 48967.5i 2.87489i
\(663\) −5502.22 + 614.262i −0.322306 + 0.0359818i
\(664\) 62724.9 + 36214.2i 3.66596 + 2.11654i
\(665\) 48034.1i 2.80103i
\(666\) 1460.50 4700.71i 0.0849747 0.273497i
\(667\) −48941.2 −2.84110
\(668\) −35048.3 20235.1i −2.03003 1.17204i
\(669\) 5941.93 13581.2i 0.343390 0.784871i
\(670\) −23901.6 52857.0i −1.37821 3.04782i
\(671\) 823.438i 0.0473747i
\(672\) 47591.2 35048.9i 2.73195 2.01196i
\(673\) 8693.63i 0.497942i −0.968511 0.248971i \(-0.919908\pi\)
0.968511 0.248971i \(-0.0800923\pi\)
\(674\) −27117.4 + 15656.2i −1.54974 + 0.894741i
\(675\) −36310.9 + 12581.0i −2.07053 + 0.717397i
\(676\) −12196.3 + 21124.6i −0.693918 + 1.20190i
\(677\) −372.596 645.354i −0.0211522 0.0366366i 0.855256 0.518206i \(-0.173400\pi\)
−0.876408 + 0.481570i \(0.840067\pi\)
\(678\) 7633.54 17447.6i 0.432396 0.988306i
\(679\) −32078.2 −1.81303
\(680\) −37558.3 21684.3i −2.11808 1.22287i
\(681\) −1841.20 16492.5i −0.103605 0.928037i
\(682\) −9040.45 + 5219.50i −0.507590 + 0.293057i
\(683\) 3118.49 5401.39i 0.174708 0.302604i −0.765352 0.643612i \(-0.777435\pi\)
0.940060 + 0.341008i \(0.110768\pi\)
\(684\) 33384.5 + 36127.7i 1.86621 + 2.01955i
\(685\) −32452.0 −1.81011
\(686\) −1744.65 1007.28i −0.0971009 0.0560612i
\(687\) 5058.13 3725.10i 0.280902 0.206872i
\(688\) 9039.68 + 5219.06i 0.500923 + 0.289208i
\(689\) 12725.3 + 7346.96i 0.703622 + 0.406236i
\(690\) −9744.74 87288.1i −0.537646 4.81594i
\(691\) 15062.4 + 26088.8i 0.829234 + 1.43628i 0.898640 + 0.438687i \(0.144556\pi\)
−0.0694064 + 0.997588i \(0.522111\pi\)
\(692\) 4197.27i 0.230573i
\(693\) 1764.78 + 7805.47i 0.0967367 + 0.427857i
\(694\) 20916.2 1.14405
\(695\) 61571.2i 3.36047i
\(696\) 11266.2 + 100917.i 0.613572 + 5.49604i
\(697\) 1665.37i 0.0905026i
\(698\) −21132.6 + 36602.8i −1.14596 + 1.98486i
\(699\) 2728.03 304.554i 0.147616 0.0164797i
\(700\) 125857. + 72663.7i 6.79565 + 3.92347i
\(701\) 13120.5 + 22725.4i 0.706927 + 1.22443i 0.965992 + 0.258574i \(0.0832524\pi\)
−0.259065 + 0.965860i \(0.583414\pi\)
\(702\) −15228.5 + 17586.5i −0.818748 + 0.945528i
\(703\) −1564.14 2709.17i −0.0839157 0.145346i
\(704\) 4793.08 + 8301.87i 0.256600 + 0.444444i
\(705\) 867.921 + 7774.36i 0.0463656 + 0.415318i
\(706\) 24429.9 + 42313.8i 1.30231 + 2.25567i
\(707\) 20656.9 + 11926.3i 1.09885 + 0.634419i
\(708\) 3777.90 + 33840.3i 0.200540 + 1.79632i
\(709\) 7643.63 13239.2i 0.404884 0.701279i −0.589424 0.807824i \(-0.700645\pi\)
0.994308 + 0.106544i \(0.0339786\pi\)
\(710\) 15782.7i 0.834247i
\(711\) 2490.73 + 773.862i 0.131378 + 0.0408187i
\(712\) 22403.9i 1.17924i
\(713\) 28124.5 1.47724
\(714\) −14696.7 19955.9i −0.770321 1.04598i
\(715\) 7003.46i 0.366314i
\(716\) −1349.70 2337.75i −0.0704478 0.122019i
\(717\) −8458.76 + 944.327i −0.440583 + 0.0491862i
\(718\) 4308.71 + 2487.63i 0.223955 + 0.129300i
\(719\) −20833.7 12028.3i −1.08062 0.623895i −0.149555 0.988753i \(-0.547784\pi\)
−0.931063 + 0.364858i \(0.881118\pi\)
\(720\) −93384.4 + 21113.8i −4.83365 + 1.09287i
\(721\) −29077.8 16788.1i −1.50196 0.867158i
\(722\) 7411.12 0.382013
\(723\) 10080.0 23039.3i 0.518504 1.18512i
\(724\) −19451.6 + 33691.2i −0.998500 + 1.72945i
\(725\) −72651.1 + 41945.1i −3.72165 + 2.14869i
\(726\) 32971.4 3680.89i 1.68551 0.188169i
\(727\) −6331.42 3655.44i −0.322998 0.186483i 0.329730 0.944075i \(-0.393042\pi\)
−0.652728 + 0.757592i \(0.726375\pi\)
\(728\) 52870.4 2.69163
\(729\) 15463.7 12177.6i 0.785637 0.618688i
\(730\) 11224.0 + 19440.5i 0.569064 + 0.985648i
\(731\) 1000.37 1732.69i 0.0506157 0.0876690i
\(732\) −7017.10 3070.06i −0.354316 0.155017i
\(733\) 4340.63 2506.06i 0.218724 0.126280i −0.386635 0.922233i \(-0.626363\pi\)
0.605359 + 0.795952i \(0.293029\pi\)
\(734\) 54822.5i 2.75686i
\(735\) 21993.6 + 29864.0i 1.10373 + 1.49871i
\(736\) 68682.6i 3.43978i
\(737\) 6111.95 + 606.585i 0.305477 + 0.0303173i
\(738\) 4749.19 + 5139.42i 0.236884 + 0.256348i
\(739\) −4739.07 2736.11i −0.235899 0.136197i 0.377391 0.926054i \(-0.376821\pi\)
−0.613291 + 0.789857i \(0.710155\pi\)
\(740\) 13783.8 0.684735
\(741\) 1640.34 + 14693.3i 0.0813216 + 0.728435i
\(742\) 65777.2i 3.25439i
\(743\) 11797.0 + 6811.03i 0.582492 + 0.336302i 0.762123 0.647432i \(-0.224157\pi\)
−0.179631 + 0.983734i \(0.557490\pi\)
\(744\) −6474.24 57992.7i −0.319028 2.85768i
\(745\) 28828.6i 1.41772i
\(746\) 7705.35i 0.378167i
\(747\) −6758.80 29893.6i −0.331046 1.46419i
\(748\) 6617.09 3820.38i 0.323456 0.186747i
\(749\) 2266.25 + 3925.26i 0.110557 + 0.191490i
\(750\) −48534.7 65902.9i −2.36298 3.20858i
\(751\) −27849.6 −1.35319 −0.676595 0.736355i \(-0.736545\pi\)
−0.676595 + 0.736355i \(0.736545\pi\)
\(752\) 13382.4i 0.648942i
\(753\) 20120.6 + 27320.7i 0.973750 + 1.32221i
\(754\) −25392.3 + 43980.8i −1.22644 + 2.12425i
\(755\) −33659.8 + 58300.4i −1.62252 + 2.81029i
\(756\) −73095.6 14062.5i −3.51648 0.676520i
\(757\) 25383.1 14654.9i 1.21871 0.703623i 0.254069 0.967186i \(-0.418231\pi\)
0.964642 + 0.263563i \(0.0848978\pi\)
\(758\) −20533.7 + 11855.1i −0.983929 + 0.568072i
\(759\) 8519.60 + 3727.43i 0.407433 + 0.178257i
\(760\) −57906.2 + 100296.i −2.76379 + 4.78702i
\(761\) 21280.1i 1.01367i 0.862043 + 0.506835i \(0.169185\pi\)
−0.862043 + 0.506835i \(0.830815\pi\)
\(762\) −1878.36 + 4293.29i −0.0892992 + 0.204107i
\(763\) −24265.9 42029.9i −1.15136 1.99421i
\(764\) 43128.8 2.04234
\(765\) 4047.02 + 17899.6i 0.191268 + 0.845962i
\(766\) 544.363 + 942.865i 0.0256771 + 0.0444740i
\(767\) −5117.03 + 8862.95i −0.240893 + 0.417239i
\(768\) 5422.56 605.368i 0.254778 0.0284432i
\(769\) 3759.33 2170.45i 0.176287 0.101780i −0.409260 0.912418i \(-0.634213\pi\)
0.585547 + 0.810638i \(0.300880\pi\)
\(770\) −27150.7 + 15675.5i −1.27071 + 0.733643i
\(771\) −845.912 7577.22i −0.0395133 0.353939i
\(772\) −13779.1 23866.2i −0.642386 1.11265i
\(773\) 16846.0 9726.04i 0.783840 0.452550i −0.0539494 0.998544i \(-0.517181\pi\)
0.837789 + 0.545993i \(0.183848\pi\)
\(774\) −1853.98 8199.99i −0.0860982 0.380804i
\(775\) 41749.5 24104.1i 1.93508 1.11722i
\(776\) 66980.0 + 38670.9i 3.09851 + 1.78892i
\(777\) 4336.85 + 1897.42i 0.200236 + 0.0876056i
\(778\) −26401.7 + 15243.0i −1.21664 + 0.702428i
\(779\) 4447.24 0.204543
\(780\) −59681.5 26111.3i −2.73967 1.19864i
\(781\) 1447.17 + 835.524i 0.0663045 + 0.0382809i
\(782\) −28800.0 −1.31699
\(783\) 28127.3 32482.7i 1.28376 1.48255i
\(784\) 31724.2 + 54948.0i 1.44516 + 2.50310i
\(785\) 2752.86 4768.09i 0.125164 0.216791i
\(786\) −33311.1 + 24532.2i −1.51167 + 1.11328i
\(787\) 1525.41 + 880.695i 0.0690914 + 0.0398899i 0.534148 0.845391i \(-0.320633\pi\)
−0.465056 + 0.885281i \(0.653966\pi\)
\(788\) 34986.1 60597.7i 1.58163 2.73947i
\(789\) −5829.84 2550.62i −0.263052 0.115088i
\(790\) 10217.9i 0.460174i
\(791\) 15861.0 + 9157.34i 0.712960 + 0.411628i
\(792\) 5724.74 18425.5i 0.256843 0.826668i
\(793\) −1151.02 1993.63i −0.0515434 0.0892758i
\(794\) −2513.00 + 4352.64i −0.112321 + 0.194546i
\(795\) 19522.6 44621.8i 0.870936 1.99066i
\(796\) −50500.8 −2.24869
\(797\) 12690.7 7327.00i 0.564026 0.325641i −0.190734 0.981642i \(-0.561087\pi\)
0.754760 + 0.656001i \(0.227753\pi\)
\(798\) −53290.7 + 39246.3i −2.36400 + 1.74098i
\(799\) 2565.08 0.113575
\(800\) −58864.5 101956.i −2.60147 4.50587i
\(801\) −6962.64 + 6433.97i −0.307132 + 0.283812i
\(802\) 13810.0 23919.6i 0.608040 1.05316i
\(803\) −2376.74 −0.104450
\(804\) −27956.6 + 49822.7i −1.22631 + 2.18546i
\(805\) 84464.8 3.69813
\(806\) 14591.9 25273.9i 0.637689 1.10451i
\(807\) 31458.5 + 13763.5i 1.37223 + 0.600368i
\(808\) −28754.8 49804.8i −1.25197 2.16847i
\(809\) 35548.4 1.54489 0.772444 0.635083i \(-0.219034\pi\)
0.772444 + 0.635083i \(0.219034\pi\)
\(810\) 63534.3 + 43698.1i 2.75601 + 1.89555i
\(811\) 17941.0 10358.3i 0.776812 0.448493i −0.0584870 0.998288i \(-0.518628\pi\)
0.835299 + 0.549795i \(0.185294\pi\)
\(812\) −162495. −7.02272
\(813\) −8815.66 3856.95i −0.380294 0.166383i
\(814\) −1020.88 + 1768.22i −0.0439582 + 0.0761379i
\(815\) −8164.31 14141.0i −0.350900 0.607776i
\(816\) 3483.16 + 31200.3i 0.149430 + 1.33851i
\(817\) −4627.02 2671.41i −0.198138 0.114395i
\(818\) 48403.6i 2.06894i
\(819\) −15183.4 16431.0i −0.647802 0.701031i
\(820\) −9797.70 + 16970.1i −0.417257 + 0.722710i
\(821\) −8859.32 5114.93i −0.376605 0.217433i 0.299735 0.954022i \(-0.403102\pi\)
−0.676340 + 0.736590i \(0.736435\pi\)
\(822\) 26514.9 + 36003.3i 1.12508 + 1.52769i
\(823\) −11179.9 + 19364.2i −0.473522 + 0.820164i −0.999541 0.0303091i \(-0.990351\pi\)
0.526019 + 0.850473i \(0.323684\pi\)
\(824\) 40476.8 + 70107.8i 1.71126 + 2.96398i
\(825\) 15841.6 1768.54i 0.668524 0.0746333i
\(826\) −45812.7 −1.92981
\(827\) −24944.0 14401.4i −1.04884 0.605546i −0.126513 0.991965i \(-0.540379\pi\)
−0.922324 + 0.386419i \(0.873712\pi\)
\(828\) −63528.1 + 58704.4i −2.66637 + 2.46391i
\(829\) 20978.6 0.878909 0.439455 0.898265i \(-0.355172\pi\)
0.439455 + 0.898265i \(0.355172\pi\)
\(830\) 103982. 60034.3i 4.34853 2.51063i
\(831\) −2282.46 + 5216.92i −0.0952802 + 0.217777i
\(832\) −23209.1 13399.8i −0.967104 0.558357i
\(833\) 10532.2 6080.78i 0.438079 0.252925i
\(834\) −68309.2 + 50306.8i −2.83615 + 2.08871i
\(835\) −34916.6 + 20159.1i −1.44711 + 0.835490i
\(836\) −10202.0 17670.4i −0.422063 0.731034i
\(837\) −16163.6 + 18666.4i −0.667497 + 0.770856i
\(838\) 62993.9 36369.6i 2.59677 1.49924i
\(839\) −21014.1 + 12132.5i −0.864706 + 0.499238i −0.865586 0.500761i \(-0.833054\pi\)
0.000879119 1.00000i \(0.499720\pi\)
\(840\) −19443.8 174167.i −0.798659 7.15395i
\(841\) 34705.6 60111.9i 1.42300 2.46471i
\(842\) −24855.4 43050.8i −1.01731 1.76203i
\(843\) 12942.3 + 17573.7i 0.528772 + 0.717995i
\(844\) 19465.6 0.793881
\(845\) 12150.5 + 21045.2i 0.494661 + 0.856779i
\(846\) 7915.99 7314.94i 0.321699 0.297273i
\(847\) 31905.0i 1.29429i
\(848\) 41660.8 72158.6i 1.68707 2.92210i
\(849\) −15456.3 + 35327.8i −0.624805 + 1.42809i
\(850\) −42752.3 + 24683.0i −1.72517 + 0.996025i
\(851\) 4763.90 2750.44i 0.191897 0.110792i
\(852\) −12515.6 + 9217.24i −0.503262 + 0.370631i
\(853\) −16577.7 + 28713.4i −0.665426 + 1.15255i 0.313743 + 0.949508i \(0.398417\pi\)
−0.979170 + 0.203044i \(0.934916\pi\)
\(854\) 5152.53 8924.45i 0.206459 0.357598i
\(855\) 47799.5 10807.3i 1.91194 0.432281i
\(856\) 10928.1i 0.436347i
\(857\) 11924.8 0.475313 0.237656 0.971349i \(-0.423621\pi\)
0.237656 + 0.971349i \(0.423621\pi\)
\(858\) 7769.87 5722.18i 0.309160 0.227683i
\(859\) −3380.18 5854.65i −0.134261 0.232547i 0.791054 0.611747i \(-0.209533\pi\)
−0.925315 + 0.379199i \(0.876199\pi\)
\(860\) 20387.6 11770.8i 0.808384 0.466721i
\(861\) −5418.71 + 3990.65i −0.214482 + 0.157957i
\(862\) 41261.9i 1.63038i
\(863\) 38368.0i 1.51340i 0.653763 + 0.756700i \(0.273189\pi\)
−0.653763 + 0.756700i \(0.726811\pi\)
\(864\) 45585.2 + 39473.0i 1.79495 + 1.55428i
\(865\) 3621.28 + 2090.75i 0.142344 + 0.0821822i
\(866\) 79393.2i 3.11535i
\(867\) −19390.7 + 2164.76i −0.759566 + 0.0847971i
\(868\) 93379.0 3.65149
\(869\) −936.915 540.928i −0.0365738 0.0211159i
\(870\) 154220. + 67473.2i 6.00984 + 2.62937i
\(871\) −15645.6 + 7074.83i −0.608645 + 0.275226i
\(872\) 117012.i 4.54420i
\(873\) −7217.30 31921.5i −0.279804 1.23755i
\(874\) 76908.0i 2.97649i
\(875\) 68164.9 39355.0i 2.63359 1.52051i
\(876\) 8861.32 20253.9i 0.341777 0.781183i
\(877\) 22234.7 38511.6i 0.856115 1.48283i −0.0194918 0.999810i \(-0.506205\pi\)
0.875607 0.483025i \(-0.160462\pi\)
\(878\) −14320.6 24804.0i −0.550452 0.953410i
\(879\) 23050.1 + 10084.7i 0.884482 + 0.386971i
\(880\) 39713.0 1.52128
\(881\) −16640.6 9607.47i −0.636364 0.367405i 0.146849 0.989159i \(-0.453087\pi\)
−0.783213 + 0.621754i \(0.786420\pi\)
\(882\) 15162.3 48800.8i 0.578844 1.86305i
\(883\) −496.314 + 286.547i −0.0189154 + 0.0109208i −0.509428 0.860513i \(-0.670143\pi\)
0.490512 + 0.871434i \(0.336810\pi\)
\(884\) −10680.4 + 18499.0i −0.406359 + 0.703835i
\(885\) 31078.3 + 13597.1i 1.18044 + 0.516455i
\(886\) 52591.5 1.99418
\(887\) −22775.0 13149.1i −0.862129 0.497750i 0.00259578 0.999997i \(-0.499174\pi\)
−0.864725 + 0.502246i \(0.832507\pi\)
\(888\) −6768.05 9190.01i −0.255767 0.347294i
\(889\) −3902.87 2253.32i −0.147242 0.0850101i
\(890\) −32164.3 18570.1i −1.21141 0.699405i
\(891\) −7370.27 + 3512.32i −0.277119 + 0.132062i
\(892\) −28597.7 49532.6i −1.07345 1.85928i
\(893\) 6849.85i 0.256687i
\(894\) 31983.5 23554.5i 1.19652 0.881184i
\(895\) −2689.26 −0.100438
\(896\) 28970.6i 1.08018i
\(897\) −25837.1 + 2884.43i −0.961734 + 0.107367i
\(898\) 2158.04i 0.0801945i
\(899\) −26951.5 + 46681.4i −0.999871 + 1.73183i
\(900\) −43991.9 + 141591.i −1.62933 + 5.24411i
\(901\) −13831.1 7985.40i −0.511411 0.295263i
\(902\) −1451.31 2513.75i −0.0535736 0.0927923i
\(903\) 8034.91 897.009i 0.296108 0.0330571i
\(904\) −22078.7 38241.5i −0.812309 1.40696i
\(905\) 19378.6 + 33564.6i 0.711784 + 1.23285i
\(906\) 92182.2 10291.1i 3.38029 0.377372i
\(907\) 8477.02 + 14682.6i 0.310336 + 0.537518i 0.978435 0.206555i \(-0.0662251\pi\)
−0.668099 + 0.744072i \(0.732892\pi\)
\(908\) −55449.4 32013.7i −2.02660 1.17006i
\(909\) −7220.40 + 23239.3i −0.263460 + 0.847965i
\(910\) 43823.1 75903.8i 1.59640 2.76504i
\(911\) 23047.2i 0.838186i −0.907943 0.419093i \(-0.862348\pi\)
0.907943 0.419093i \(-0.137652\pi\)
\(912\) 83317.8 9301.51i 3.02514 0.337723i
\(913\) 12712.6i 0.460818i
\(914\) −31975.3 −1.15716
\(915\) −6144.13 + 4524.89i −0.221988 + 0.163484i
\(916\) 24236.8i 0.874243i
\(917\) −19892.3 34454.5i −0.716360 1.24077i
\(918\) 16551.8 19114.8i 0.595087 0.687235i
\(919\) 18797.9 + 10853.0i 0.674740 + 0.389561i 0.797870 0.602829i \(-0.205960\pi\)
−0.123130 + 0.992391i \(0.539293\pi\)
\(920\) −176365. 101824.i −6.32018 3.64896i
\(921\) 5136.91 + 6975.17i 0.183786 + 0.249554i
\(922\) −8628.76 4981.82i −0.308214 0.177947i
\(923\) −4671.66 −0.166598
\(924\) 28286.8 + 12375.8i 1.00711 + 0.440621i
\(925\) 4714.53 8165.81i 0.167581 0.290260i
\(926\) 84826.9 48974.8i 3.01035 1.73803i
\(927\) 10163.8 32712.9i 0.360112 1.15904i
\(928\) 114000. + 65818.2i 4.03259 + 2.32822i
\(929\) −32462.1 −1.14644 −0.573222 0.819400i \(-0.694307\pi\)
−0.573222 + 0.819400i \(0.694307\pi\)
\(930\) −88624.0 38774.0i −3.12483 1.36715i
\(931\) −16238.3 28125.5i −0.571630 0.990092i
\(932\) 5295.41 9171.91i 0.186112 0.322356i
\(933\) 15016.5 34322.6i 0.526923 1.20436i
\(934\) 6346.35 3664.07i 0.222333 0.128364i
\(935\) 7612.05i 0.266247i
\(936\) 11895.4 + 52612.1i 0.415398 + 1.83727i
\(937\) 3834.24i 0.133681i 0.997764 + 0.0668405i \(0.0212919\pi\)
−0.997764 + 0.0668405i \(0.978708\pi\)
\(938\) −62446.0 44818.8i −2.17370 1.56011i
\(939\) −8249.47 3609.24i −0.286700 0.125435i
\(940\) 26138.2 + 15090.9i 0.906951 + 0.523628i
\(941\) 29435.5 1.01973 0.509867 0.860253i \(-0.329694\pi\)
0.509867 + 0.860253i \(0.329694\pi\)
\(942\) −7539.11 + 841.658i −0.260762 + 0.0291111i
\(943\) 7820.17i 0.270053i
\(944\) 50257.2 + 29016.0i 1.73277 + 1.00041i
\(945\) −48543.2 + 56060.0i −1.67102 + 1.92977i
\(946\) 3487.16i 0.119849i
\(947\) 11154.2i 0.382748i −0.981517 0.191374i \(-0.938706\pi\)
0.981517 0.191374i \(-0.0612943\pi\)
\(948\) 8102.77 5967.35i 0.277601 0.204441i
\(949\) 5754.34 3322.27i 0.196832 0.113641i
\(950\) 65914.1 + 114167.i 2.25109 + 3.89900i
\(951\) −2355.55 + 1734.76i −0.0803195 + 0.0591518i
\(952\) −57464.8 −1.95635
\(953\) 19181.3i 0.651985i −0.945372 0.325993i \(-0.894302\pi\)
0.945372 0.325993i \(-0.105698\pi\)
\(954\) −65455.9 + 14799.3i −2.22140 + 0.502248i
\(955\) 21483.4 37210.3i 0.727943 1.26083i
\(956\) −16419.4 + 28439.2i −0.555483 + 0.962124i
\(957\) −14351.1 + 10569.0i −0.484750 + 0.356998i
\(958\) −82592.5 + 47684.8i −2.78543 + 1.60817i
\(959\) −37239.1 + 21500.0i −1.25392 + 0.723953i
\(960\) −35606.3 + 81383.6i −1.19707 + 2.73609i
\(961\) 592.411 1026.09i 0.0198856 0.0344428i
\(962\) 5708.07i 0.191305i
\(963\) −3396.20 + 3138.33i −0.113646 + 0.105017i
\(964\) −48513.5 84027.9i −1.62087 2.80742i
\(965\) −27454.7 −0.915854
\(966\) −69012.0 93708.1i −2.29858 3.12113i
\(967\) −685.852 1187.93i −0.0228082 0.0395049i 0.854396 0.519622i \(-0.173927\pi\)
−0.877204 + 0.480117i \(0.840594\pi\)
\(968\) 38462.1 66618.3i 1.27709 2.21198i
\(969\) −1782.88 15970.1i −0.0591067 0.529445i
\(970\) 111036. 64106.9i 3.67542 2.12201i
\(971\) −22768.2 + 13145.2i −0.752489 + 0.434450i −0.826593 0.562801i \(-0.809724\pi\)
0.0741033 + 0.997251i \(0.476391\pi\)
\(972\) −2452.04 75902.4i −0.0809149 2.50470i
\(973\) −40792.0 70653.7i −1.34402 2.32791i
\(974\) −24555.9 + 14177.3i −0.807824 + 0.466397i
\(975\) −35881.9 + 26425.5i −1.17861 + 0.867994i
\(976\) −11304.8 + 6526.84i −0.370757 + 0.214056i
\(977\) 32216.4 + 18600.2i 1.05496 + 0.609081i 0.924033 0.382312i \(-0.124872\pi\)
0.130925 + 0.991392i \(0.458205\pi\)
\(978\) −9017.84 + 20611.7i −0.294845 + 0.673914i
\(979\) 3405.50 1966.17i 0.111175 0.0641869i
\(980\) 143098. 4.66438
\(981\) 36364.9 33603.7i 1.18353 1.09366i
\(982\) 11351.5 + 6553.82i 0.368882 + 0.212974i
\(983\) 4723.70 0.153268 0.0766342 0.997059i \(-0.475583\pi\)
0.0766342 + 0.997059i \(0.475583\pi\)
\(984\) 16125.2 1800.20i 0.522411 0.0583214i
\(985\) −34854.6 60370.0i −1.12747 1.95284i
\(986\) 27598.8 47802.6i 0.891406 1.54396i
\(987\) 6146.59 + 8346.16i 0.198225 + 0.269160i
\(988\) 49400.2 + 28521.2i 1.59072 + 0.918403i
\(989\) 4697.50 8136.31i 0.151033 0.261597i
\(990\) −21707.6 23491.2i −0.696880 0.754142i
\(991\) 27165.4i 0.870774i −0.900243 0.435387i \(-0.856612\pi\)
0.900243 0.435387i \(-0.143388\pi\)
\(992\) −65511.2 37822.9i −2.09676 1.21056i
\(993\) 5330.46 + 47747.3i 0.170349 + 1.52590i
\(994\) −10456.3 18110.9i −0.333657 0.577910i
\(995\) −25155.5 + 43570.7i −0.801492 + 1.38822i
\(996\) −108333. 47397.2i −3.44646 1.50787i
\(997\) −2117.47 −0.0672627 −0.0336313 0.999434i \(-0.510707\pi\)
−0.0336313 + 0.999434i \(0.510707\pi\)
\(998\) −30042.4 + 17345.0i −0.952881 + 0.550146i
\(999\) −912.399 + 4742.56i −0.0288959 + 0.150198i
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.38.2 132
3.2 odd 2 inner 201.4.f.a.38.65 yes 132
67.30 odd 6 inner 201.4.f.a.164.65 yes 132
201.164 even 6 inner 201.4.f.a.164.2 yes 132
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.4.f.a.38.2 132 1.1 even 1 trivial
201.4.f.a.38.65 yes 132 3.2 odd 2 inner
201.4.f.a.164.2 yes 132 201.164 even 6 inner
201.4.f.a.164.65 yes 132 67.30 odd 6 inner