Properties

Label 49.4.g.a.2.3
Level $49$
Weight $4$
Character 49.2
Analytic conductor $2.891$
Analytic rank $0$
Dimension $156$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [49,4,Mod(2,49)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(49, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([26]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("49.2");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 49.g (of order \(21\), degree \(12\), 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: \(2.89109359028\)
Analytic rank: \(0\)
Dimension: \(156\)
Relative dimension: \(13\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 2.3
Character \(\chi\) \(=\) 49.2
Dual form 49.4.g.a.25.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.74530 - 1.15527i) q^{2} +(-3.45495 + 8.80308i) q^{3} +(6.08268 + 4.14710i) q^{4} +(-0.875096 + 0.131899i) q^{5} +(23.1098 - 28.9787i) q^{6} +(-6.85447 - 17.2051i) q^{7} +(1.55937 + 1.95538i) q^{8} +(-45.7650 - 42.4637i) q^{9} +O(q^{10})\) \(q+(-3.74530 - 1.15527i) q^{2} +(-3.45495 + 8.80308i) q^{3} +(6.08268 + 4.14710i) q^{4} +(-0.875096 + 0.131899i) q^{5} +(23.1098 - 28.9787i) q^{6} +(-6.85447 - 17.2051i) q^{7} +(1.55937 + 1.95538i) q^{8} +(-45.7650 - 42.4637i) q^{9} +(3.42987 + 0.516970i) q^{10} +(3.12966 - 2.90390i) q^{11} +(-57.5226 + 39.2182i) q^{12} +(-5.46270 - 23.9337i) q^{13} +(5.79542 + 72.3570i) q^{14} +(1.86229 - 8.15924i) q^{15} +(-25.0981 - 63.9489i) q^{16} +(-2.19811 - 29.3317i) q^{17} +(122.346 + 211.910i) q^{18} +(39.3280 - 68.1181i) q^{19} +(-5.86993 - 2.82681i) q^{20} +(175.140 - 0.897492i) q^{21} +(-15.0763 + 7.26037i) q^{22} +(-15.0914 + 201.380i) q^{23} +(-22.6009 + 6.97146i) q^{24} +(-118.698 + 36.6135i) q^{25} +(-7.19042 + 95.9495i) q^{26} +(301.880 - 145.378i) q^{27} +(29.6579 - 133.079i) q^{28} +(-221.653 - 106.743i) q^{29} +(-16.4010 + 28.4073i) q^{30} +(-125.508 - 217.386i) q^{31} +(18.6263 + 248.550i) q^{32} +(14.7504 + 37.5835i) q^{33} +(-25.6535 + 112.395i) q^{34} +(8.26766 + 14.1520i) q^{35} +(-102.273 - 448.085i) q^{36} +(-178.988 + 122.032i) q^{37} +(-225.990 + 209.688i) q^{38} +(229.563 + 34.6011i) q^{39} +(-1.62251 - 1.50547i) q^{40} +(-28.0156 - 35.1305i) q^{41} +(-656.987 - 198.973i) q^{42} +(164.681 - 206.504i) q^{43} +(31.0795 - 4.68448i) q^{44} +(45.6497 + 31.1235i) q^{45} +(289.171 - 736.794i) q^{46} +(275.681 + 85.0363i) q^{47} +649.660 q^{48} +(-249.033 + 235.864i) q^{49} +486.858 q^{50} +(265.804 + 81.9897i) q^{51} +(66.0274 - 168.235i) q^{52} +(-534.333 - 364.302i) q^{53} +(-1298.58 + 195.730i) q^{54} +(-2.35573 + 2.95399i) q^{55} +(22.9540 - 40.2322i) q^{56} +(463.773 + 581.552i) q^{57} +(706.841 + 655.852i) q^{58} +(-407.389 - 61.4040i) q^{59} +(45.1649 - 41.9069i) q^{60} +(354.524 - 241.710i) q^{61} +(218.925 + 959.171i) q^{62} +(-416.899 + 1078.46i) q^{63} +(95.0885 - 416.610i) q^{64} +(7.93723 + 20.2237i) q^{65} +(-11.8256 - 157.802i) q^{66} +(219.313 + 379.861i) q^{67} +(108.271 - 187.531i) q^{68} +(-1720.63 - 828.610i) q^{69} +(-14.6154 - 62.5549i) q^{70} +(249.424 - 120.116i) q^{71} +(11.6685 - 155.705i) q^{72} +(-168.226 + 51.8908i) q^{73} +(811.344 - 250.266i) q^{74} +(87.7848 - 1171.41i) q^{75} +(521.712 - 251.243i) q^{76} +(-71.4142 - 33.9415i) q^{77} +(-819.808 - 394.799i) q^{78} +(-94.0732 + 162.940i) q^{79} +(30.3981 + 52.6510i) q^{80} +(110.823 + 1478.83i) q^{81} +(64.3416 + 163.940i) q^{82} +(-50.6148 + 221.758i) q^{83} +(1069.04 + 720.863i) q^{84} +(5.79240 + 25.3782i) q^{85} +(-855.347 + 583.166i) q^{86} +(1705.47 - 1582.44i) q^{87} +(10.5585 + 1.59144i) q^{88} +(795.067 + 737.715i) q^{89} +(-135.016 - 169.304i) q^{90} +(-374.338 + 258.039i) q^{91} +(-926.941 + 1162.35i) q^{92} +(2347.29 - 353.797i) q^{93} +(-934.266 - 636.972i) q^{94} +(-25.4310 + 64.7972i) q^{95} +(-2252.36 - 694.761i) q^{96} -478.924 q^{97} +(1205.19 - 595.680i) q^{98} -266.540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 156 q - 13 q^{2} - 7 q^{3} + 35 q^{4} - 7 q^{5} - 70 q^{6} - 42 q^{7} + 16 q^{8} + 198 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 156 q - 13 q^{2} - 7 q^{3} + 35 q^{4} - 7 q^{5} - 70 q^{6} - 42 q^{7} + 16 q^{8} + 198 q^{9} + 85 q^{11} - 427 q^{12} + 14 q^{13} - 203 q^{14} + 230 q^{15} + 127 q^{16} + 189 q^{17} - 16 q^{18} - 490 q^{19} - 406 q^{20} + 231 q^{21} + 590 q^{22} - 377 q^{23} - 812 q^{24} + 142 q^{25} + 490 q^{26} + 14 q^{27} - 280 q^{28} + 172 q^{29} - 39 q^{30} - 1162 q^{31} - 1099 q^{32} - 49 q^{33} + 882 q^{34} + 847 q^{35} + 812 q^{36} - 377 q^{37} - 1596 q^{38} - 770 q^{39} - 1694 q^{40} - 938 q^{41} - 3290 q^{42} - 10 q^{43} + 4354 q^{44} + 1176 q^{45} + 3408 q^{46} + 1379 q^{47} + 9604 q^{48} + 2576 q^{49} - 6184 q^{50} + 2271 q^{51} + 6874 q^{52} + 1905 q^{53} + 1617 q^{54} - 1834 q^{55} + 1736 q^{56} + 2673 q^{57} - 4716 q^{58} + 63 q^{59} - 10850 q^{60} - 2625 q^{61} - 4298 q^{62} - 1806 q^{63} - 2756 q^{64} - 196 q^{65} + 2100 q^{66} - 202 q^{67} - 5635 q^{68} - 3248 q^{69} + 6650 q^{70} + 2608 q^{71} - 6424 q^{72} - 2471 q^{73} + 2582 q^{74} + 3612 q^{75} - 4529 q^{76} - 1281 q^{77} + 5040 q^{78} - 608 q^{79} - 12348 q^{80} - 17375 q^{81} - 3234 q^{82} - 9842 q^{83} - 11564 q^{84} - 512 q^{85} - 2301 q^{86} + 2254 q^{87} + 4033 q^{88} + 4977 q^{89} + 18312 q^{90} - 8932 q^{91} + 7714 q^{92} + 14164 q^{93} + 2506 q^{94} + 11504 q^{95} + 12642 q^{96} + 11116 q^{97} + 29771 q^{98} - 10804 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{13}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.74530 1.15527i −1.32416 0.408450i −0.449542 0.893259i \(-0.648413\pi\)
−0.874620 + 0.484809i \(0.838889\pi\)
\(3\) −3.45495 + 8.80308i −0.664906 + 1.69415i 0.0535362 + 0.998566i \(0.482951\pi\)
−0.718442 + 0.695587i \(0.755145\pi\)
\(4\) 6.08268 + 4.14710i 0.760335 + 0.518387i
\(5\) −0.875096 + 0.131899i −0.0782709 + 0.0117974i −0.188061 0.982157i \(-0.560220\pi\)
0.109790 + 0.993955i \(0.464982\pi\)
\(6\) 23.1098 28.9787i 1.57242 1.97175i
\(7\) −6.85447 17.2051i −0.370106 0.928989i
\(8\) 1.55937 + 1.95538i 0.0689149 + 0.0864166i
\(9\) −45.7650 42.4637i −1.69500 1.57273i
\(10\) 3.42987 + 0.516970i 0.108462 + 0.0163480i
\(11\) 3.12966 2.90390i 0.0857845 0.0795963i −0.636115 0.771594i \(-0.719460\pi\)
0.721900 + 0.691998i \(0.243269\pi\)
\(12\) −57.5226 + 39.2182i −1.38378 + 0.943444i
\(13\) −5.46270 23.9337i −0.116545 0.510616i −0.999177 0.0405524i \(-0.987088\pi\)
0.882633 0.470063i \(-0.155769\pi\)
\(14\) 5.79542 + 72.3570i 0.110635 + 1.38130i
\(15\) 1.86229 8.15924i 0.0320561 0.140447i
\(16\) −25.0981 63.9489i −0.392158 0.999201i
\(17\) −2.19811 29.3317i −0.0313600 0.418470i −0.990686 0.136169i \(-0.956521\pi\)
0.959326 0.282302i \(-0.0910979\pi\)
\(18\) 122.346 + 211.910i 1.60207 + 2.77487i
\(19\) 39.3280 68.1181i 0.474867 0.822493i −0.524719 0.851276i \(-0.675830\pi\)
0.999586 + 0.0287822i \(0.00916293\pi\)
\(20\) −5.86993 2.82681i −0.0656278 0.0316047i
\(21\) 175.140 0.897492i 1.81994 0.00932613i
\(22\) −15.0763 + 7.26037i −0.146104 + 0.0703598i
\(23\) −15.0914 + 201.380i −0.136816 + 1.82568i 0.333009 + 0.942924i \(0.391936\pi\)
−0.469825 + 0.882760i \(0.655683\pi\)
\(24\) −22.6009 + 6.97146i −0.192225 + 0.0592935i
\(25\) −118.698 + 36.6135i −0.949586 + 0.292908i
\(26\) −7.19042 + 95.9495i −0.0542369 + 0.723741i
\(27\) 301.880 145.378i 2.15174 1.03622i
\(28\) 29.6579 133.079i 0.200172 0.898201i
\(29\) −221.653 106.743i −1.41931 0.683504i −0.442334 0.896850i \(-0.645849\pi\)
−0.976977 + 0.213347i \(0.931564\pi\)
\(30\) −16.4010 + 28.4073i −0.0998131 + 0.172881i
\(31\) −125.508 217.386i −0.727158 1.25947i −0.958080 0.286502i \(-0.907507\pi\)
0.230921 0.972972i \(-0.425826\pi\)
\(32\) 18.6263 + 248.550i 0.102897 + 1.37306i
\(33\) 14.7504 + 37.5835i 0.0778098 + 0.198256i
\(34\) −25.6535 + 112.395i −0.129398 + 0.566931i
\(35\) 8.26766 + 14.1520i 0.0399283 + 0.0683466i
\(36\) −102.273 448.085i −0.473484 2.07447i
\(37\) −178.988 + 122.032i −0.795283 + 0.542215i −0.891433 0.453152i \(-0.850299\pi\)
0.0961501 + 0.995367i \(0.469347\pi\)
\(38\) −225.990 + 209.688i −0.964748 + 0.895155i
\(39\) 229.563 + 34.6011i 0.942552 + 0.142067i
\(40\) −1.62251 1.50547i −0.00641353 0.00595089i
\(41\) −28.0156 35.1305i −0.106715 0.133816i 0.725606 0.688110i \(-0.241560\pi\)
−0.832321 + 0.554294i \(0.812988\pi\)
\(42\) −656.987 198.973i −2.41370 0.731003i
\(43\) 164.681 206.504i 0.584038 0.732360i −0.398758 0.917056i \(-0.630559\pi\)
0.982796 + 0.184696i \(0.0591300\pi\)
\(44\) 31.0795 4.68448i 0.106487 0.0160503i
\(45\) 45.6497 + 31.1235i 0.151224 + 0.103102i
\(46\) 289.171 736.794i 0.926867 2.36162i
\(47\) 275.681 + 85.0363i 0.855579 + 0.263911i 0.691358 0.722513i \(-0.257013\pi\)
0.164221 + 0.986424i \(0.447489\pi\)
\(48\) 649.660 1.95355
\(49\) −249.033 + 235.864i −0.726043 + 0.687650i
\(50\) 486.858 1.37704
\(51\) 265.804 + 81.9897i 0.729804 + 0.225115i
\(52\) 66.0274 168.235i 0.176084 0.448654i
\(53\) −534.333 364.302i −1.38484 0.944166i −0.999774 0.0212755i \(-0.993227\pi\)
−0.385063 0.922890i \(-0.625820\pi\)
\(54\) −1298.58 + 195.730i −3.27249 + 0.493249i
\(55\) −2.35573 + 2.95399i −0.00577540 + 0.00724212i
\(56\) 22.9540 40.2322i 0.0547742 0.0960046i
\(57\) 463.773 + 581.552i 1.07769 + 1.35138i
\(58\) 706.841 + 655.852i 1.60022 + 1.48479i
\(59\) −407.389 61.4040i −0.898940 0.135493i −0.316715 0.948521i \(-0.602580\pi\)
−0.582226 + 0.813027i \(0.697818\pi\)
\(60\) 45.1649 41.9069i 0.0971794 0.0901693i
\(61\) 354.524 241.710i 0.744134 0.507342i −0.130905 0.991395i \(-0.541788\pi\)
0.875039 + 0.484053i \(0.160836\pi\)
\(62\) 218.925 + 959.171i 0.448443 + 1.96476i
\(63\) −416.899 + 1078.46i −0.833720 + 2.15672i
\(64\) 95.0885 416.610i 0.185720 0.813692i
\(65\) 7.93723 + 20.2237i 0.0151460 + 0.0385914i
\(66\) −11.8256 157.802i −0.0220551 0.294304i
\(67\) 219.313 + 379.861i 0.399900 + 0.692647i 0.993713 0.111956i \(-0.0357115\pi\)
−0.593813 + 0.804603i \(0.702378\pi\)
\(68\) 108.271 187.531i 0.193086 0.334434i
\(69\) −1720.63 828.610i −3.00202 1.44569i
\(70\) −14.6154 62.5549i −0.0249554 0.106811i
\(71\) 249.424 120.116i 0.416918 0.200777i −0.213652 0.976910i \(-0.568536\pi\)
0.630569 + 0.776133i \(0.282821\pi\)
\(72\) 11.6685 155.705i 0.0190992 0.254861i
\(73\) −168.226 + 51.8908i −0.269717 + 0.0831967i −0.426664 0.904410i \(-0.640311\pi\)
0.156946 + 0.987607i \(0.449835\pi\)
\(74\) 811.344 250.266i 1.27455 0.393147i
\(75\) 87.7848 1171.41i 0.135154 1.80350i
\(76\) 521.712 251.243i 0.787428 0.379205i
\(77\) −71.4142 33.9415i −0.105694 0.0502337i
\(78\) −819.808 394.799i −1.19006 0.573105i
\(79\) −94.0732 + 162.940i −0.133975 + 0.232052i −0.925206 0.379466i \(-0.876108\pi\)
0.791230 + 0.611518i \(0.209441\pi\)
\(80\) 30.3981 + 52.6510i 0.0424826 + 0.0735820i
\(81\) 110.823 + 1478.83i 0.152021 + 2.02857i
\(82\) 64.3416 + 163.940i 0.0866504 + 0.220782i
\(83\) −50.6148 + 221.758i −0.0669362 + 0.293266i −0.997306 0.0733564i \(-0.976629\pi\)
0.930370 + 0.366623i \(0.119486\pi\)
\(84\) 1069.04 + 720.863i 1.38859 + 0.936341i
\(85\) 5.79240 + 25.3782i 0.00739146 + 0.0323841i
\(86\) −855.347 + 583.166i −1.07249 + 0.731213i
\(87\) 1705.47 1582.44i 2.10167 1.95006i
\(88\) 10.5585 + 1.59144i 0.0127903 + 0.00192782i
\(89\) 795.067 + 737.715i 0.946932 + 0.878625i 0.992734 0.120326i \(-0.0383940\pi\)
−0.0458024 + 0.998951i \(0.514584\pi\)
\(90\) −135.016 169.304i −0.158132 0.198292i
\(91\) −374.338 + 258.039i −0.431223 + 0.297251i
\(92\) −926.941 + 1162.35i −1.05044 + 1.31721i
\(93\) 2347.29 353.797i 2.61723 0.394485i
\(94\) −934.266 636.972i −1.02513 0.698922i
\(95\) −25.4310 + 64.7972i −0.0274649 + 0.0699795i
\(96\) −2252.36 694.761i −2.39459 0.738633i
\(97\) −478.924 −0.501313 −0.250656 0.968076i \(-0.580646\pi\)
−0.250656 + 0.968076i \(0.580646\pi\)
\(98\) 1205.19 595.680i 1.24227 0.614008i
\(99\) −266.540 −0.270588
\(100\) −873.843 269.545i −0.873843 0.269545i
\(101\) −211.636 + 539.239i −0.208501 + 0.531251i −0.996421 0.0845259i \(-0.973062\pi\)
0.787921 + 0.615777i \(0.211158\pi\)
\(102\) −900.794 614.151i −0.874430 0.596177i
\(103\) −895.616 + 134.992i −0.856773 + 0.129138i −0.562716 0.826650i \(-0.690244\pi\)
−0.294057 + 0.955788i \(0.595006\pi\)
\(104\) 38.2811 48.0030i 0.0360940 0.0452604i
\(105\) −153.146 + 23.8862i −0.142338 + 0.0222006i
\(106\) 1580.37 + 1981.72i 1.44810 + 1.81586i
\(107\) −893.418 828.971i −0.807196 0.748969i 0.164201 0.986427i \(-0.447495\pi\)
−0.971398 + 0.237458i \(0.923686\pi\)
\(108\) 2439.14 + 367.641i 2.17320 + 0.327558i
\(109\) 326.426 302.879i 0.286843 0.266152i −0.523606 0.851961i \(-0.675414\pi\)
0.810449 + 0.585809i \(0.199223\pi\)
\(110\) 12.2356 8.34207i 0.0106056 0.00723078i
\(111\) −455.862 1997.26i −0.389806 1.70785i
\(112\) −928.215 + 870.151i −0.783107 + 0.734121i
\(113\) 58.7636 257.460i 0.0489205 0.214335i −0.944560 0.328340i \(-0.893511\pi\)
0.993480 + 0.114005i \(0.0363680\pi\)
\(114\) −1065.12 2713.87i −0.875063 2.22962i
\(115\) −13.3556 178.218i −0.0108297 0.144512i
\(116\) −905.574 1568.50i −0.724831 1.25544i
\(117\) −766.312 + 1327.29i −0.605518 + 1.04879i
\(118\) 1454.85 + 700.620i 1.13500 + 0.546587i
\(119\) −489.589 + 238.872i −0.377148 + 0.184012i
\(120\) 18.8584 9.08175i 0.0143461 0.00690872i
\(121\) −98.1036 + 1309.10i −0.0737067 + 0.983548i
\(122\) −1607.04 + 495.706i −1.19258 + 0.367861i
\(123\) 406.049 125.249i 0.297660 0.0918160i
\(124\) 138.098 1842.78i 0.100012 1.33457i
\(125\) 198.710 95.6939i 0.142186 0.0684730i
\(126\) 2807.32 3557.52i 1.98489 2.51531i
\(127\) −329.121 158.496i −0.229958 0.110742i 0.315357 0.948973i \(-0.397876\pi\)
−0.545315 + 0.838231i \(0.683590\pi\)
\(128\) 159.557 276.360i 0.110179 0.190836i
\(129\) 1248.90 + 2163.16i 0.852400 + 1.47640i
\(130\) −6.36338 84.9134i −0.00429312 0.0572877i
\(131\) 288.057 + 733.957i 0.192119 + 0.489512i 0.994180 0.107730i \(-0.0343582\pi\)
−0.802061 + 0.597242i \(0.796263\pi\)
\(132\) −66.1404 + 289.780i −0.0436120 + 0.191077i
\(133\) −1441.55 209.730i −0.939839 0.136736i
\(134\) −382.549 1676.06i −0.246621 1.08052i
\(135\) −244.999 + 167.037i −0.156194 + 0.106491i
\(136\) 53.9272 50.0371i 0.0340016 0.0315489i
\(137\) −357.674 53.9107i −0.223052 0.0336197i 0.0365652 0.999331i \(-0.488358\pi\)
−0.259617 + 0.965712i \(0.583596\pi\)
\(138\) 5486.99 + 5091.18i 3.38466 + 3.14051i
\(139\) 1479.97 + 1855.83i 0.903092 + 1.13244i 0.990670 + 0.136284i \(0.0435159\pi\)
−0.0875778 + 0.996158i \(0.527913\pi\)
\(140\) −8.40036 + 120.369i −0.00507115 + 0.0726646i
\(141\) −1701.05 + 2133.04i −1.01598 + 1.27400i
\(142\) −1072.93 + 161.719i −0.634074 + 0.0955713i
\(143\) −86.5975 59.0411i −0.0506409 0.0345264i
\(144\) −1566.89 + 3992.38i −0.906768 + 2.31041i
\(145\) 208.047 + 64.1741i 0.119154 + 0.0367543i
\(146\) 690.004 0.391131
\(147\) −1215.93 3007.15i −0.682234 1.68725i
\(148\) −1594.81 −0.885759
\(149\) −884.224 272.747i −0.486164 0.149962i 0.0419765 0.999119i \(-0.486635\pi\)
−0.528141 + 0.849157i \(0.677111\pi\)
\(150\) −1682.07 + 4285.85i −0.915604 + 2.33292i
\(151\) −556.169 379.189i −0.299738 0.204358i 0.404107 0.914712i \(-0.367582\pi\)
−0.703844 + 0.710354i \(0.748535\pi\)
\(152\) 194.524 29.3198i 0.103802 0.0156457i
\(153\) −1144.94 + 1435.71i −0.604986 + 0.758628i
\(154\) 228.256 + 209.624i 0.119437 + 0.109688i
\(155\) 138.505 + 173.679i 0.0717739 + 0.0900017i
\(156\) 1252.86 + 1162.49i 0.643009 + 0.596626i
\(157\) 300.058 + 45.2265i 0.152530 + 0.0229902i 0.224863 0.974390i \(-0.427806\pi\)
−0.0723332 + 0.997381i \(0.523044\pi\)
\(158\) 540.571 501.577i 0.272187 0.252553i
\(159\) 5053.08 3445.13i 2.52035 1.71834i
\(160\) −49.0834 215.049i −0.0242524 0.106257i
\(161\) 3568.22 1120.71i 1.74668 0.548596i
\(162\) 1293.38 5666.68i 0.627270 2.74825i
\(163\) 331.975 + 845.859i 0.159523 + 0.406459i 0.988180 0.153299i \(-0.0489896\pi\)
−0.828657 + 0.559757i \(0.810894\pi\)
\(164\) −24.7204 329.871i −0.0117704 0.157065i
\(165\) −17.8653 30.9436i −0.00842916 0.0145997i
\(166\) 445.758 772.076i 0.208419 0.360992i
\(167\) −155.343 74.8094i −0.0719810 0.0346642i 0.397547 0.917582i \(-0.369862\pi\)
−0.469528 + 0.882918i \(0.655576\pi\)
\(168\) 274.862 + 341.066i 0.126227 + 0.156630i
\(169\) 1436.45 691.758i 0.653823 0.314865i
\(170\) 7.62439 101.740i 0.00343979 0.0459008i
\(171\) −4692.40 + 1447.41i −2.09846 + 0.647289i
\(172\) 1858.09 573.146i 0.823711 0.254081i
\(173\) 210.545 2809.53i 0.0925288 1.23471i −0.736863 0.676043i \(-0.763694\pi\)
0.829391 0.558668i \(-0.188687\pi\)
\(174\) −8215.62 + 3956.43i −3.57945 + 1.72377i
\(175\) 1443.55 + 1791.25i 0.623556 + 0.773748i
\(176\) −264.250 127.256i −0.113174 0.0545016i
\(177\) 1948.05 3374.12i 0.827257 1.43285i
\(178\) −2125.50 3681.48i −0.895017 1.55022i
\(179\) −84.6440 1129.50i −0.0353441 0.471634i −0.986592 0.163206i \(-0.947816\pi\)
0.951248 0.308427i \(-0.0998027\pi\)
\(180\) 148.601 + 378.628i 0.0615335 + 0.156785i
\(181\) 830.706 3639.56i 0.341138 1.49462i −0.455539 0.890216i \(-0.650554\pi\)
0.796677 0.604406i \(-0.206589\pi\)
\(182\) 1700.11 533.971i 0.692421 0.217476i
\(183\) 902.931 + 3956.00i 0.364735 + 1.59801i
\(184\) −417.309 + 284.516i −0.167198 + 0.113994i
\(185\) 140.536 130.398i 0.0558508 0.0518220i
\(186\) −9200.03 1386.68i −3.62677 0.546648i
\(187\) −92.0559 85.4154i −0.0359989 0.0334021i
\(188\) 1324.22 + 1660.52i 0.513718 + 0.644182i
\(189\) −4570.47 4197.40i −1.75901 1.61543i
\(190\) 170.105 213.305i 0.0649512 0.0814462i
\(191\) −1330.17 + 200.491i −0.503916 + 0.0759532i −0.396081 0.918216i \(-0.629630\pi\)
−0.107835 + 0.994169i \(0.534392\pi\)
\(192\) 3338.92 + 2276.44i 1.25503 + 0.855666i
\(193\) −816.032 + 2079.22i −0.304349 + 0.775468i 0.694105 + 0.719874i \(0.255800\pi\)
−0.998453 + 0.0555938i \(0.982295\pi\)
\(194\) 1793.71 + 553.286i 0.663819 + 0.204761i
\(195\) −205.454 −0.0754505
\(196\) −2492.94 + 401.921i −0.908504 + 0.146473i
\(197\) −2481.89 −0.897600 −0.448800 0.893632i \(-0.648149\pi\)
−0.448800 + 0.893632i \(0.648149\pi\)
\(198\) 998.270 + 307.926i 0.358303 + 0.110522i
\(199\) 1073.57 2735.41i 0.382428 0.974411i −0.601980 0.798511i \(-0.705621\pi\)
0.984408 0.175900i \(-0.0562835\pi\)
\(200\) −256.688 175.007i −0.0907528 0.0618742i
\(201\) −4101.66 + 618.225i −1.43935 + 0.216946i
\(202\) 1415.61 1775.11i 0.493078 0.618300i
\(203\) −317.205 + 4545.24i −0.109672 + 1.57149i
\(204\) 1276.78 + 1601.03i 0.438199 + 0.549484i
\(205\) 29.1500 + 27.0473i 0.00993135 + 0.00921495i
\(206\) 3510.30 + 529.092i 1.18725 + 0.178950i
\(207\) 9242.02 8575.35i 3.10321 2.87936i
\(208\) −1393.43 + 950.023i −0.464504 + 0.316693i
\(209\) −74.7250 327.392i −0.0247313 0.108355i
\(210\) 601.171 + 87.4638i 0.197546 + 0.0287408i
\(211\) −64.3874 + 282.100i −0.0210076 + 0.0920405i −0.984345 0.176253i \(-0.943602\pi\)
0.963337 + 0.268293i \(0.0864596\pi\)
\(212\) −1739.38 4431.87i −0.563496 1.43576i
\(213\) 195.644 + 2610.69i 0.0629358 + 0.839820i
\(214\) 2388.43 + 4136.88i 0.762942 + 1.32146i
\(215\) −116.874 + 202.432i −0.0370732 + 0.0642127i
\(216\) 755.012 + 363.594i 0.237833 + 0.114535i
\(217\) −2879.87 + 3649.45i −0.900913 + 1.14166i
\(218\) −1572.47 + 757.261i −0.488537 + 0.235267i
\(219\) 124.414 1660.19i 0.0383886 0.512260i
\(220\) −26.5797 + 8.19874i −0.00814546 + 0.00251254i
\(221\) −690.008 + 212.839i −0.210023 + 0.0647834i
\(222\) −600.040 + 8006.98i −0.181406 + 2.42069i
\(223\) 1918.26 923.785i 0.576037 0.277405i −0.123098 0.992394i \(-0.539283\pi\)
0.699135 + 0.714990i \(0.253569\pi\)
\(224\) 4148.67 2024.15i 1.23747 0.603768i
\(225\) 6986.98 + 3364.75i 2.07022 + 0.996963i
\(226\) −517.523 + 896.377i −0.152324 + 0.263832i
\(227\) 1736.79 + 3008.21i 0.507819 + 0.879568i 0.999959 + 0.00905200i \(0.00288138\pi\)
−0.492140 + 0.870516i \(0.663785\pi\)
\(228\) 409.223 + 5460.71i 0.118866 + 1.58616i
\(229\) −2124.01 5411.88i −0.612919 1.56169i −0.813220 0.581957i \(-0.802287\pi\)
0.200301 0.979734i \(-0.435808\pi\)
\(230\) −155.869 + 682.907i −0.0446857 + 0.195781i
\(231\) 545.523 511.398i 0.155380 0.145660i
\(232\) −136.916 599.868i −0.0387456 0.169756i
\(233\) −106.068 + 72.3158i −0.0298229 + 0.0203329i −0.578140 0.815938i \(-0.696221\pi\)
0.548317 + 0.836271i \(0.315269\pi\)
\(234\) 4403.45 4085.80i 1.23018 1.14144i
\(235\) −252.463 38.0527i −0.0700804 0.0105629i
\(236\) −2223.37 2062.98i −0.613257 0.569020i
\(237\) −1109.35 1391.08i −0.304051 0.381268i
\(238\) 2109.62 329.039i 0.574564 0.0896152i
\(239\) −2741.78 + 3438.08i −0.742054 + 0.930507i −0.999358 0.0358237i \(-0.988595\pi\)
0.257304 + 0.966331i \(0.417166\pi\)
\(240\) −568.514 + 85.6898i −0.152906 + 0.0230469i
\(241\) −1859.22 1267.59i −0.496941 0.338809i 0.288774 0.957397i \(-0.406752\pi\)
−0.785715 + 0.618589i \(0.787705\pi\)
\(242\) 1879.79 4789.64i 0.499329 1.27227i
\(243\) −4756.38 1467.15i −1.25565 0.387316i
\(244\) 3158.85 0.828790
\(245\) 186.817 239.251i 0.0487155 0.0623884i
\(246\) −1665.47 −0.431652
\(247\) −1845.15 569.155i −0.475321 0.146617i
\(248\) 229.361 584.401i 0.0587275 0.149635i
\(249\) −1777.28 1211.73i −0.452332 0.308395i
\(250\) −854.782 + 128.838i −0.216245 + 0.0325936i
\(251\) 1881.04 2358.74i 0.473027 0.593158i −0.486882 0.873468i \(-0.661866\pi\)
0.959910 + 0.280310i \(0.0904373\pi\)
\(252\) −7008.34 + 4831.00i −1.75192 + 1.20764i
\(253\) 537.558 + 674.077i 0.133581 + 0.167505i
\(254\) 1049.55 + 973.838i 0.259270 + 0.240567i
\(255\) −243.418 36.6894i −0.0597782 0.00901012i
\(256\) −3422.86 + 3175.95i −0.835660 + 0.775379i
\(257\) −4349.98 + 2965.77i −1.05581 + 0.719842i −0.961250 0.275677i \(-0.911098\pi\)
−0.0945638 + 0.995519i \(0.530146\pi\)
\(258\) −2178.47 9544.49i −0.525680 2.30316i
\(259\) 3326.45 + 2243.05i 0.798051 + 0.538132i
\(260\) −35.5902 + 155.931i −0.00848927 + 0.0371939i
\(261\) 5611.28 + 14297.3i 1.33077 + 3.39073i
\(262\) −230.939 3081.67i −0.0544560 0.726665i
\(263\) −384.808 666.507i −0.0902216 0.156268i 0.817383 0.576095i \(-0.195424\pi\)
−0.907604 + 0.419827i \(0.862091\pi\)
\(264\) −50.4888 + 87.4492i −0.0117704 + 0.0203869i
\(265\) 515.644 + 248.321i 0.119531 + 0.0575632i
\(266\) 5156.75 + 2450.89i 1.18865 + 0.564938i
\(267\) −9241.08 + 4450.27i −2.11814 + 1.02004i
\(268\) −241.312 + 3220.08i −0.0550017 + 0.733947i
\(269\) 6346.55 1957.65i 1.43850 0.443718i 0.525189 0.850986i \(-0.323995\pi\)
0.913309 + 0.407268i \(0.133518\pi\)
\(270\) 1110.57 342.564i 0.250322 0.0772141i
\(271\) −42.3155 + 564.662i −0.00948519 + 0.126571i −0.999936 0.0112939i \(-0.996405\pi\)
0.990451 + 0.137865i \(0.0440240\pi\)
\(272\) −1820.56 + 876.737i −0.405838 + 0.195441i
\(273\) −978.217 4186.84i −0.216866 0.928201i
\(274\) 1277.31 + 615.122i 0.281625 + 0.135624i
\(275\) −265.163 + 459.276i −0.0581452 + 0.100711i
\(276\) −7029.69 12175.8i −1.53311 2.65542i
\(277\) 388.599 + 5185.49i 0.0842912 + 1.12479i 0.865631 + 0.500682i \(0.166917\pi\)
−0.781340 + 0.624105i \(0.785464\pi\)
\(278\) −3398.96 8660.40i −0.733294 1.86840i
\(279\) −3487.16 + 15278.2i −0.748282 + 3.27844i
\(280\) −14.7803 + 38.2347i −0.00315462 + 0.00816056i
\(281\) −1097.44 4808.21i −0.232982 1.02076i −0.947151 0.320787i \(-0.896053\pi\)
0.714170 0.699973i \(-0.246805\pi\)
\(282\) 8835.16 6023.71i 1.86570 1.27201i
\(283\) 5809.72 5390.63i 1.22033 1.13230i 0.233186 0.972432i \(-0.425085\pi\)
0.987139 0.159865i \(-0.0511057\pi\)
\(284\) 2015.30 + 303.757i 0.421077 + 0.0634672i
\(285\) −482.552 447.743i −0.100294 0.0930596i
\(286\) 256.125 + 321.170i 0.0529544 + 0.0664027i
\(287\) −412.392 + 722.813i −0.0848179 + 0.148663i
\(288\) 9701.95 12165.9i 1.98504 2.48917i
\(289\) 4002.61 603.296i 0.814697 0.122796i
\(290\) −705.060 480.702i −0.142767 0.0973372i
\(291\) 1654.66 4216.00i 0.333326 0.849300i
\(292\) −1238.46 382.014i −0.248203 0.0765606i
\(293\) −9139.85 −1.82237 −0.911187 0.411993i \(-0.864833\pi\)
−0.911187 + 0.411993i \(0.864833\pi\)
\(294\) 1079.95 + 12667.4i 0.214231 + 2.51285i
\(295\) 364.603 0.0719594
\(296\) −517.728 159.698i −0.101663 0.0313590i
\(297\) 522.620 1331.61i 0.102106 0.260162i
\(298\) 2996.59 + 2043.04i 0.582508 + 0.397148i
\(299\) 4902.21 738.889i 0.948168 0.142913i
\(300\) 5391.91 6761.24i 1.03767 1.30120i
\(301\) −4681.72 1417.89i −0.896511 0.271514i
\(302\) 1644.95 + 2062.70i 0.313431 + 0.393030i
\(303\) −4015.77 3726.09i −0.761387 0.706464i
\(304\) −5343.14 805.348i −1.00806 0.151940i
\(305\) −278.361 + 258.281i −0.0522587 + 0.0484890i
\(306\) 5946.77 4054.44i 1.11096 0.757440i
\(307\) 1210.99 + 5305.68i 0.225129 + 0.986355i 0.953552 + 0.301227i \(0.0973963\pi\)
−0.728423 + 0.685127i \(0.759747\pi\)
\(308\) −293.631 502.617i −0.0543219 0.0929846i
\(309\) 1905.96 8350.57i 0.350895 1.53737i
\(310\) −318.094 810.491i −0.0582791 0.148493i
\(311\) 766.124 + 10223.2i 0.139688 + 1.86401i 0.424508 + 0.905424i \(0.360447\pi\)
−0.284820 + 0.958581i \(0.591934\pi\)
\(312\) 290.315 + 502.840i 0.0526790 + 0.0912427i
\(313\) −3341.73 + 5788.04i −0.603468 + 1.04524i 0.388824 + 0.921312i \(0.372882\pi\)
−0.992292 + 0.123925i \(0.960452\pi\)
\(314\) −1071.56 516.035i −0.192584 0.0927438i
\(315\) 222.578 998.744i 0.0398123 0.178644i
\(316\) −1247.94 + 600.978i −0.222159 + 0.106986i
\(317\) −143.862 + 1919.71i −0.0254893 + 0.340131i 0.969850 + 0.243701i \(0.0783615\pi\)
−0.995340 + 0.0964302i \(0.969258\pi\)
\(318\) −22905.3 + 7065.36i −4.03920 + 1.24593i
\(319\) −1003.67 + 309.591i −0.176159 + 0.0543379i
\(320\) −28.2609 + 377.116i −0.00493698 + 0.0658794i
\(321\) 10384.2 5000.77i 1.80558 0.869520i
\(322\) −14658.8 + 75.1177i −2.53696 + 0.0130005i
\(323\) −2084.47 1003.83i −0.359081 0.172924i
\(324\) −5458.75 + 9454.84i −0.936000 + 1.62120i
\(325\) 1524.71 + 2640.87i 0.260233 + 0.450736i
\(326\) −266.149 3551.51i −0.0452167 0.603374i
\(327\) 1538.48 + 3919.98i 0.260178 + 0.662922i
\(328\) 25.0069 109.563i 0.00420969 0.0184438i
\(329\) −426.585 5326.00i −0.0714845 0.892499i
\(330\) 31.1626 + 136.532i 0.00519831 + 0.0227753i
\(331\) −4892.38 + 3335.57i −0.812416 + 0.553896i −0.896748 0.442542i \(-0.854077\pi\)
0.0843320 + 0.996438i \(0.473124\pi\)
\(332\) −1227.53 + 1138.98i −0.202920 + 0.188282i
\(333\) 13373.3 + 2015.71i 2.20076 + 0.331712i
\(334\) 495.381 + 459.647i 0.0811559 + 0.0753017i
\(335\) −242.023 303.487i −0.0394720 0.0494963i
\(336\) −4453.07 11177.5i −0.723020 1.81483i
\(337\) 6779.97 8501.81i 1.09593 1.37425i 0.174979 0.984572i \(-0.444014\pi\)
0.920950 0.389680i \(-0.127414\pi\)
\(338\) −6179.09 + 931.349i −0.994374 + 0.149878i
\(339\) 2063.42 + 1406.81i 0.330588 + 0.225391i
\(340\) −70.0124 + 178.389i −0.0111675 + 0.0284544i
\(341\) −1024.07 315.883i −0.162628 0.0501642i
\(342\) 19246.6 3.04309
\(343\) 5765.05 + 2667.92i 0.907532 + 0.419982i
\(344\) 660.592 0.103537
\(345\) 1615.01 + 498.164i 0.252026 + 0.0777398i
\(346\) −4034.33 + 10279.3i −0.626840 + 1.59716i
\(347\) −7026.22 4790.40i −1.08700 0.741101i −0.119208 0.992869i \(-0.538036\pi\)
−0.967788 + 0.251768i \(0.918988\pi\)
\(348\) 16936.3 2552.74i 2.60886 0.393222i
\(349\) 5668.06 7107.53i 0.869354 1.09014i −0.125825 0.992053i \(-0.540158\pi\)
0.995178 0.0980825i \(-0.0312709\pi\)
\(350\) −3337.15 8376.46i −0.509653 1.27926i
\(351\) −5128.51 6430.95i −0.779885 0.977944i
\(352\) 780.060 + 723.790i 0.118117 + 0.109597i
\(353\) −20.2809 3.05685i −0.00305791 0.000460906i 0.147513 0.989060i \(-0.452873\pi\)
−0.150571 + 0.988599i \(0.548111\pi\)
\(354\) −11194.1 + 10386.6i −1.68067 + 1.55943i
\(355\) −202.426 + 138.012i −0.0302639 + 0.0206336i
\(356\) 1776.76 + 7784.50i 0.264517 + 1.15893i
\(357\) −411.302 5135.18i −0.0609759 0.761296i
\(358\) −987.856 + 4328.08i −0.145838 + 0.638956i
\(359\) 1530.81 + 3900.45i 0.225051 + 0.573420i 0.998146 0.0608704i \(-0.0193876\pi\)
−0.773095 + 0.634290i \(0.781292\pi\)
\(360\) 10.3264 + 137.796i 0.00151180 + 0.0201735i
\(361\) 336.113 + 582.164i 0.0490032 + 0.0848760i
\(362\) −7315.92 + 12671.5i −1.06220 + 1.83978i
\(363\) −11185.2 5386.50i −1.61727 0.778837i
\(364\) −3347.09 + 17.1519i −0.481965 + 0.00246979i
\(365\) 140.369 67.5983i 0.0201295 0.00969386i
\(366\) 1188.51 15859.5i 0.169738 2.26500i
\(367\) −3379.27 + 1042.37i −0.480645 + 0.148259i −0.525604 0.850730i \(-0.676160\pi\)
0.0449590 + 0.998989i \(0.485684\pi\)
\(368\) 13256.8 4089.19i 1.87788 0.579249i
\(369\) −209.636 + 2797.40i −0.0295751 + 0.394652i
\(370\) −676.993 + 326.023i −0.0951222 + 0.0458084i
\(371\) −2605.30 + 11690.4i −0.364583 + 1.63594i
\(372\) 15745.1 + 7582.42i 2.19447 + 1.05680i
\(373\) 2671.82 4627.73i 0.370889 0.642398i −0.618814 0.785538i \(-0.712386\pi\)
0.989703 + 0.143139i \(0.0457197\pi\)
\(374\) 246.099 + 426.255i 0.0340253 + 0.0589335i
\(375\) 155.866 + 2079.88i 0.0214636 + 0.286412i
\(376\) 263.609 + 671.665i 0.0361558 + 0.0921236i
\(377\) −1343.92 + 5888.08i −0.183595 + 0.804381i
\(378\) 12268.6 + 21000.6i 1.66939 + 2.85756i
\(379\) −2026.53 8878.82i −0.274660 1.20336i −0.904444 0.426593i \(-0.859714\pi\)
0.629784 0.776770i \(-0.283143\pi\)
\(380\) −423.409 + 288.676i −0.0571591 + 0.0389704i
\(381\) 2532.35 2349.68i 0.340515 0.315952i
\(382\) 5213.52 + 785.811i 0.698290 + 0.105250i
\(383\) −5014.77 4653.03i −0.669041 0.620779i 0.270701 0.962663i \(-0.412745\pi\)
−0.939742 + 0.341884i \(0.888935\pi\)
\(384\) 1881.56 + 2359.40i 0.250047 + 0.313549i
\(385\) 66.9711 + 20.2826i 0.00886536 + 0.00268493i
\(386\) 5458.34 6844.54i 0.719747 0.902534i
\(387\) −16305.5 + 2457.67i −2.14175 + 0.322817i
\(388\) −2913.14 1986.14i −0.381165 0.259874i
\(389\) −147.590 + 376.052i −0.0192367 + 0.0490144i −0.940169 0.340707i \(-0.889334\pi\)
0.920933 + 0.389722i \(0.127429\pi\)
\(390\) 769.485 + 237.355i 0.0999086 + 0.0308177i
\(391\) 5940.01 0.768285
\(392\) −849.538 119.156i −0.109460 0.0153528i
\(393\) −7456.30 −0.957050
\(394\) 9295.41 + 2867.25i 1.18857 + 0.366625i
\(395\) 60.8314 154.996i 0.00774876 0.0197435i
\(396\) −1621.28 1105.37i −0.205738 0.140270i
\(397\) 6417.87 967.338i 0.811344 0.122290i 0.269750 0.962930i \(-0.413059\pi\)
0.541594 + 0.840640i \(0.317821\pi\)
\(398\) −7180.96 + 9004.64i −0.904395 + 1.13408i
\(399\) 6826.77 11965.5i 0.856556 1.50131i
\(400\) 5320.49 + 6671.69i 0.665062 + 0.833961i
\(401\) 6338.14 + 5880.94i 0.789306 + 0.732369i 0.967840 0.251565i \(-0.0809451\pi\)
−0.178534 + 0.983934i \(0.557136\pi\)
\(402\) 16076.1 + 2423.09i 1.99454 + 0.300628i
\(403\) −4517.24 + 4191.38i −0.558361 + 0.518083i
\(404\) −3523.59 + 2402.34i −0.433924 + 0.295844i
\(405\) −292.038 1279.50i −0.0358308 0.156985i
\(406\) 6439.01 16656.8i 0.787100 2.03612i
\(407\) −205.803 + 901.684i −0.0250646 + 0.109815i
\(408\) 254.165 + 647.601i 0.0308407 + 0.0785809i
\(409\) −942.040 12570.7i −0.113890 1.51975i −0.702703 0.711484i \(-0.748024\pi\)
0.588813 0.808269i \(-0.299595\pi\)
\(410\) −77.9286 134.976i −0.00938687 0.0162585i
\(411\) 1710.33 2962.37i 0.205266 0.355531i
\(412\) −6007.57 2893.09i −0.718378 0.345953i
\(413\) 1735.97 + 7430.06i 0.206832 + 0.885253i
\(414\) −44521.0 + 21440.2i −5.28523 + 2.54523i
\(415\) 15.0431 200.736i 0.00177936 0.0237439i
\(416\) 5846.97 1803.55i 0.689114 0.212563i
\(417\) −21450.2 + 6616.52i −2.51900 + 0.777009i
\(418\) −98.3587 + 1312.51i −0.0115093 + 0.153581i
\(419\) −4475.14 + 2155.11i −0.521778 + 0.251275i −0.676184 0.736733i \(-0.736368\pi\)
0.154407 + 0.988007i \(0.450653\pi\)
\(420\) −1030.59 489.818i −0.119733 0.0569064i
\(421\) −3404.88 1639.71i −0.394166 0.189820i 0.226293 0.974059i \(-0.427339\pi\)
−0.620459 + 0.784239i \(0.713054\pi\)
\(422\) 567.051 982.162i 0.0654114 0.113296i
\(423\) −9005.59 15598.1i −1.03515 1.79292i
\(424\) −120.871 1612.91i −0.0138443 0.184740i
\(425\) 1334.85 + 3401.14i 0.152352 + 0.388188i
\(426\) 2283.31 10003.8i 0.259687 1.13776i
\(427\) −6588.73 4442.83i −0.746724 0.503522i
\(428\) −1996.55 8747.46i −0.225483 0.987907i
\(429\) 818.934 558.340i 0.0921643 0.0628366i
\(430\) 671.591 623.145i 0.0753186 0.0698854i
\(431\) 6916.28 + 1042.46i 0.772959 + 0.116505i 0.523667 0.851923i \(-0.324564\pi\)
0.249293 + 0.968428i \(0.419802\pi\)
\(432\) −16873.4 15656.2i −1.87921 1.74366i
\(433\) −4489.41 5629.54i −0.498261 0.624800i 0.467575 0.883954i \(-0.345128\pi\)
−0.965836 + 0.259153i \(0.916556\pi\)
\(434\) 15002.1 10341.2i 1.65927 1.14377i
\(435\) −1283.72 + 1609.74i −0.141494 + 0.177428i
\(436\) 3241.61 488.594i 0.356067 0.0536684i
\(437\) 13124.1 + 8947.89i 1.43664 + 0.979487i
\(438\) −2383.93 + 6074.15i −0.260065 + 0.662635i
\(439\) 10330.5 + 3186.55i 1.12312 + 0.346436i 0.800047 0.599938i \(-0.204808\pi\)
0.323073 + 0.946374i \(0.395284\pi\)
\(440\) −9.44964 −0.00102385
\(441\) 21412.7 219.461i 2.31213 0.0236973i
\(442\) 2830.17 0.304565
\(443\) 1255.32 + 387.215i 0.134632 + 0.0415285i 0.361339 0.932435i \(-0.382320\pi\)
−0.226707 + 0.973963i \(0.572796\pi\)
\(444\) 5509.98 14039.2i 0.588946 1.50061i
\(445\) −793.064 540.702i −0.0844828 0.0575994i
\(446\) −8251.67 + 1243.74i −0.876072 + 0.132047i
\(447\) 5455.97 6841.57i 0.577312 0.723926i
\(448\) −7819.61 + 1219.63i −0.824647 + 0.128621i
\(449\) 2167.53 + 2718.00i 0.227822 + 0.285680i 0.882583 0.470156i \(-0.155802\pi\)
−0.654761 + 0.755836i \(0.727231\pi\)
\(450\) −22281.1 20673.8i −2.33409 2.16572i
\(451\) −189.695 28.5919i −0.0198057 0.00298523i
\(452\) 1425.15 1322.35i 0.148304 0.137606i
\(453\) 5259.57 3585.91i 0.545510 0.371923i
\(454\) −3029.50 13273.1i −0.313175 1.37211i
\(455\) 293.546 275.184i 0.0302454 0.0283534i
\(456\) −413.967 + 1813.71i −0.0425127 + 0.186260i
\(457\) −5059.02 12890.2i −0.517836 1.31942i −0.915657 0.401961i \(-0.868329\pi\)
0.397821 0.917463i \(-0.369766\pi\)
\(458\) 1702.85 + 22722.9i 0.173731 + 2.31828i
\(459\) −4927.75 8535.12i −0.501106 0.867942i
\(460\) 657.849 1139.43i 0.0666790 0.115491i
\(461\) −2286.60 1101.17i −0.231014 0.111250i 0.314796 0.949159i \(-0.398064\pi\)
−0.545810 + 0.837909i \(0.683778\pi\)
\(462\) −2633.95 + 1285.11i −0.265243 + 0.129413i
\(463\) 16569.3 7979.34i 1.66315 0.800932i 0.664596 0.747203i \(-0.268604\pi\)
0.998556 0.0537286i \(-0.0171106\pi\)
\(464\) −1263.00 + 16853.5i −0.126365 + 1.68622i
\(465\) −2007.44 + 619.213i −0.200199 + 0.0617534i
\(466\) 480.800 148.307i 0.0477953 0.0147429i
\(467\) 617.300 8237.30i 0.0611676 0.816224i −0.879284 0.476297i \(-0.841979\pi\)
0.940452 0.339927i \(-0.110402\pi\)
\(468\) −10165.6 + 4895.52i −1.00407 + 0.483537i
\(469\) 5032.28 6377.04i 0.495456 0.627856i
\(470\) 901.589 + 434.182i 0.0884834 + 0.0426114i
\(471\) −1434.82 + 2485.18i −0.140367 + 0.243123i
\(472\) −515.200 892.352i −0.0502415 0.0870209i
\(473\) −84.2700 1124.50i −0.00819183 0.109312i
\(474\) 2547.77 + 6491.61i 0.246884 + 0.629050i
\(475\) −2174.12 + 9525.44i −0.210011 + 0.920120i
\(476\) −3968.64 577.393i −0.382148 0.0555983i
\(477\) 8984.15 + 39362.1i 0.862381 + 3.77834i
\(478\) 14240.7 9709.14i 1.36267 0.929050i
\(479\) −681.111 + 631.979i −0.0649703 + 0.0602836i −0.711990 0.702190i \(-0.752206\pi\)
0.647019 + 0.762474i \(0.276015\pi\)
\(480\) 2062.67 + 310.897i 0.196141 + 0.0295635i
\(481\) 3898.43 + 3617.22i 0.369549 + 0.342892i
\(482\) 5498.91 + 6895.42i 0.519644 + 0.651613i
\(483\) −2462.36 + 35283.3i −0.231970 + 3.32390i
\(484\) −6025.71 + 7556.00i −0.565900 + 0.709617i
\(485\) 419.104 63.1698i 0.0392382 0.00591421i
\(486\) 16119.1 + 10989.8i 1.50448 + 1.02574i
\(487\) 2827.84 7205.21i 0.263124 0.670430i −0.736860 0.676045i \(-0.763692\pi\)
0.999984 + 0.00561572i \(0.00178755\pi\)
\(488\) 1025.47 + 316.315i 0.0951246 + 0.0293421i
\(489\) −8593.11 −0.794671
\(490\) −976.084 + 680.240i −0.0899898 + 0.0627146i
\(491\) −11514.1 −1.05830 −0.529148 0.848530i \(-0.677488\pi\)
−0.529148 + 0.848530i \(0.677488\pi\)
\(492\) 2989.29 + 922.073i 0.273917 + 0.0844924i
\(493\) −2643.73 + 6736.11i −0.241516 + 0.615374i
\(494\) 6253.12 + 4263.30i 0.569516 + 0.388290i
\(495\) 233.248 35.1565i 0.0211792 0.00319225i
\(496\) −10751.6 + 13482.1i −0.973308 + 1.22049i
\(497\) −3776.28 3468.03i −0.340824 0.313003i
\(498\) 5256.57 + 6591.53i 0.472997 + 0.593119i
\(499\) 4503.47 + 4178.61i 0.404014 + 0.374870i 0.855844 0.517234i \(-0.173038\pi\)
−0.451830 + 0.892104i \(0.649229\pi\)
\(500\) 1605.54 + 241.997i 0.143604 + 0.0216448i
\(501\) 1195.26 1109.04i 0.106587 0.0988983i
\(502\) −9770.02 + 6661.09i −0.868640 + 0.592229i
\(503\) −1542.34 6757.42i −0.136718 0.599003i −0.996143 0.0877408i \(-0.972035\pi\)
0.859425 0.511262i \(-0.170822\pi\)
\(504\) −2758.90 + 866.516i −0.243832 + 0.0765827i
\(505\) 114.076 499.801i 0.0100521 0.0440413i
\(506\) −1234.57 3145.64i −0.108465 0.276365i
\(507\) 1126.73 + 15035.2i 0.0986979 + 1.31703i
\(508\) −1344.63 2328.98i −0.117438 0.203409i
\(509\) 3026.04 5241.26i 0.263511 0.456414i −0.703662 0.710535i \(-0.748453\pi\)
0.967172 + 0.254121i \(0.0817862\pi\)
\(510\) 869.287 + 418.627i 0.0754758 + 0.0363473i
\(511\) 2045.89 + 2538.66i 0.177113 + 0.219773i
\(512\) 14188.6 6832.88i 1.22472 0.589792i
\(513\) 1969.48 26280.9i 0.169503 2.26186i
\(514\) 19718.2 6082.26i 1.69209 0.521940i
\(515\) 765.944 236.263i 0.0655370 0.0202155i
\(516\) −1374.18 + 18337.1i −0.117238 + 1.56443i
\(517\) 1109.73 534.416i 0.0944017 0.0454615i
\(518\) −9867.19 12243.8i −0.836949 1.03854i
\(519\) 24005.1 + 11560.3i 2.03027 + 0.977724i
\(520\) −27.1681 + 47.0565i −0.00229115 + 0.00396839i
\(521\) −8269.89 14323.9i −0.695414 1.20449i −0.970041 0.242941i \(-0.921888\pi\)
0.274627 0.961551i \(-0.411446\pi\)
\(522\) −4498.64 60030.2i −0.377204 5.03343i
\(523\) −2686.24 6844.43i −0.224591 0.572248i 0.773514 0.633779i \(-0.218497\pi\)
−0.998105 + 0.0615305i \(0.980402\pi\)
\(524\) −1291.64 + 5659.02i −0.107682 + 0.471786i
\(525\) −20755.9 + 6519.02i −1.72545 + 0.541930i
\(526\) 671.224 + 2940.82i 0.0556402 + 0.243776i
\(527\) −6100.44 + 4159.21i −0.504249 + 0.343791i
\(528\) 2033.22 1886.55i 0.167584 0.155495i
\(529\) −28295.2 4264.82i −2.32557 0.350523i
\(530\) −1644.36 1525.74i −0.134767 0.125046i
\(531\) 16036.7 + 20109.4i 1.31061 + 1.64345i
\(532\) −7898.73 7253.99i −0.643710 0.591166i
\(533\) −687.760 + 862.424i −0.0558915 + 0.0700858i
\(534\) 39751.8 5991.62i 3.22140 0.485548i
\(535\) 891.167 + 607.588i 0.0720159 + 0.0490996i
\(536\) −400.784 + 1021.18i −0.0322971 + 0.0822917i
\(537\) 10235.5 + 3157.23i 0.822520 + 0.253714i
\(538\) −26031.3 −2.08604
\(539\) −94.4623 + 1461.34i −0.00754876 + 0.116780i
\(540\) −2182.97 −0.173963
\(541\) −73.9669 22.8158i −0.00587816 0.00181317i 0.291815 0.956475i \(-0.405741\pi\)
−0.297693 + 0.954662i \(0.596217\pi\)
\(542\) 810.821 2065.94i 0.0642578 0.163726i
\(543\) 29169.3 + 19887.3i 2.30529 + 1.57172i
\(544\) 7249.47 1092.68i 0.571358 0.0861183i
\(545\) −245.704 + 308.103i −0.0193116 + 0.0242160i
\(546\) −1173.22 + 16811.0i −0.0919579 + 1.31767i
\(547\) 426.490 + 534.801i 0.0333371 + 0.0418034i 0.798221 0.602365i \(-0.205775\pi\)
−0.764883 + 0.644169i \(0.777203\pi\)
\(548\) −1952.04 1811.23i −0.152166 0.141190i
\(549\) −26488.7 3992.53i −2.05922 0.310377i
\(550\) 1523.70 1413.79i 0.118129 0.109608i
\(551\) −15988.3 + 10900.6i −1.23616 + 0.842800i
\(552\) −1062.84 4656.59i −0.0819517 0.359054i
\(553\) 3448.22 + 501.677i 0.265159 + 0.0385777i
\(554\) 4535.23 19870.1i 0.347804 1.52383i
\(555\) 662.361 + 1687.67i 0.0506588 + 0.129077i
\(556\) 1305.90 + 17426.0i 0.0996087 + 1.32919i
\(557\) −7388.63 12797.5i −0.562058 0.973513i −0.997317 0.0732078i \(-0.976676\pi\)
0.435259 0.900306i \(-0.356657\pi\)
\(558\) 30710.9 53192.9i 2.32992 4.03554i
\(559\) −5841.99 2813.35i −0.442021 0.212866i
\(560\) 697.504 883.897i 0.0526338 0.0666990i
\(561\) 1069.97 515.269i 0.0805241 0.0387784i
\(562\) −1444.54 + 19276.0i −0.108424 + 1.44681i
\(563\) −5685.68 + 1753.80i −0.425618 + 0.131286i −0.500162 0.865932i \(-0.666726\pi\)
0.0745438 + 0.997218i \(0.476250\pi\)
\(564\) −19192.9 + 5920.21i −1.43292 + 0.441996i
\(565\) −17.4649 + 233.053i −0.00130045 + 0.0173533i
\(566\) −27986.8 + 13477.7i −2.07839 + 1.00090i
\(567\) 24683.8 12043.3i 1.82826 0.892013i
\(568\) 623.816 + 300.414i 0.0460823 + 0.0221921i
\(569\) −559.605 + 969.265i −0.0412300 + 0.0714125i −0.885904 0.463869i \(-0.846461\pi\)
0.844674 + 0.535281i \(0.179794\pi\)
\(570\) 1290.04 + 2234.41i 0.0947959 + 0.164191i
\(571\) 1029.47 + 13737.4i 0.0754502 + 1.00681i 0.898537 + 0.438898i \(0.144631\pi\)
−0.823087 + 0.567916i \(0.807750\pi\)
\(572\) −281.895 718.257i −0.0206060 0.0525032i
\(573\) 2830.75 12402.3i 0.206381 0.904213i
\(574\) 2379.57 2230.72i 0.173034 0.162210i
\(575\) −5581.93 24456.0i −0.404839 1.77372i
\(576\) −22042.6 + 15028.4i −1.59451 + 1.08712i
\(577\) −13175.9 + 12225.4i −0.950639 + 0.882064i −0.993128 0.117033i \(-0.962662\pi\)
0.0424890 + 0.999097i \(0.486471\pi\)
\(578\) −15687.9 2364.57i −1.12895 0.170161i
\(579\) −15484.1 14367.2i −1.11140 1.03123i
\(580\) 999.348 + 1253.14i 0.0715443 + 0.0897137i
\(581\) 4162.31 649.199i 0.297215 0.0463568i
\(582\) −11067.8 + 13878.6i −0.788274 + 0.988464i
\(583\) −2730.18 + 411.509i −0.193950 + 0.0292332i
\(584\) −363.792 248.029i −0.0257771 0.0175745i
\(585\) 495.528 1262.58i 0.0350214 0.0892332i
\(586\) 34231.4 + 10559.0i 2.41312 + 0.744348i
\(587\) 13078.6 0.919614 0.459807 0.888019i \(-0.347919\pi\)
0.459807 + 0.888019i \(0.347919\pi\)
\(588\) 5074.83 23334.1i 0.355923 1.63654i
\(589\) −19743.9 −1.38121
\(590\) −1365.55 421.215i −0.0952859 0.0293918i
\(591\) 8574.81 21848.3i 0.596820 1.52067i
\(592\) 12296.1 + 8383.32i 0.853658 + 0.582014i
\(593\) 5760.23 868.215i 0.398894 0.0601236i 0.0534680 0.998570i \(-0.482972\pi\)
0.345426 + 0.938446i \(0.387734\pi\)
\(594\) −3495.74 + 4383.52i −0.241468 + 0.302791i
\(595\) 396.931 273.613i 0.0273488 0.0188521i
\(596\) −4247.34 5326.00i −0.291909 0.366043i
\(597\) 20370.9 + 18901.4i 1.39652 + 1.29578i
\(598\) −19213.8 2896.02i −1.31390 0.198039i
\(599\) −1904.77 + 1767.37i −0.129928 + 0.120556i −0.742461 0.669890i \(-0.766341\pi\)
0.612532 + 0.790445i \(0.290151\pi\)
\(600\) 2427.44 1655.00i 0.165166 0.112609i
\(601\) 2569.22 + 11256.5i 0.174377 + 0.763997i 0.984162 + 0.177270i \(0.0567266\pi\)
−0.809785 + 0.586727i \(0.800416\pi\)
\(602\) 15896.4 + 10719.1i 1.07623 + 0.725708i
\(603\) 6093.45 26697.2i 0.411517 1.80297i
\(604\) −1810.46 4612.97i −0.121964 0.310760i
\(605\) −86.8198 1158.53i −0.00583426 0.0778527i
\(606\) 10735.6 + 18594.6i 0.719644 + 1.24646i
\(607\) −7194.85 + 12461.8i −0.481104 + 0.833296i −0.999765 0.0216838i \(-0.993097\pi\)
0.518661 + 0.854980i \(0.326431\pi\)
\(608\) 17663.3 + 8506.21i 1.17819 + 0.567388i
\(609\) −38916.1 18496.0i −2.58943 1.23070i
\(610\) 1340.93 645.757i 0.0890043 0.0428622i
\(611\) 529.267 7062.58i 0.0350440 0.467629i
\(612\) −12918.3 + 3984.77i −0.853255 + 0.263194i
\(613\) −16421.4 + 5065.32i −1.08198 + 0.333746i −0.783959 0.620813i \(-0.786803\pi\)
−0.298020 + 0.954559i \(0.596326\pi\)
\(614\) 1593.99 21270.3i 0.104769 1.39805i
\(615\) −338.811 + 163.163i −0.0222149 + 0.0106982i
\(616\) −44.9922 192.569i −0.00294283 0.0125955i
\(617\) −7748.41 3731.44i −0.505574 0.243472i 0.163669 0.986515i \(-0.447667\pi\)
−0.669243 + 0.743044i \(0.733381\pi\)
\(618\) −16785.6 + 29073.4i −1.09258 + 1.89240i
\(619\) 4505.40 + 7803.58i 0.292548 + 0.506708i 0.974412 0.224771i \(-0.0721635\pi\)
−0.681863 + 0.731480i \(0.738830\pi\)
\(620\) 122.214 + 1630.83i 0.00791648 + 0.105638i
\(621\) 24720.5 + 62986.7i 1.59742 + 4.07016i
\(622\) 8941.22 39174.1i 0.576383 2.52530i
\(623\) 7242.71 18735.9i 0.465767 1.20487i
\(624\) −3548.90 15548.7i −0.227676 0.997512i
\(625\) 12667.8 8636.78i 0.810741 0.552754i
\(626\) 19202.5 17817.3i 1.22602 1.13758i
\(627\) 3140.22 + 473.313i 0.200014 + 0.0301472i
\(628\) 1637.60 + 1519.47i 0.104056 + 0.0965501i
\(629\) 3972.85 + 4981.80i 0.251841 + 0.315798i
\(630\) −1987.44 + 3483.45i −0.125685 + 0.220292i
\(631\) −14002.2 + 17558.2i −0.883389 + 1.10774i 0.110112 + 0.993919i \(0.464879\pi\)
−0.993502 + 0.113816i \(0.963692\pi\)
\(632\) −465.304 + 70.1333i −0.0292861 + 0.00441416i
\(633\) −2260.89 1541.45i −0.141963 0.0967884i
\(634\) 2756.59 7023.68i 0.172678 0.439978i
\(635\) 308.917 + 95.2884i 0.0193055 + 0.00595497i
\(636\) 45023.5 2.80707
\(637\) 7005.48 + 4671.81i 0.435741 + 0.290587i
\(638\) 4116.71 0.255458
\(639\) −16515.5 5094.35i −1.02244 0.315382i
\(640\) −103.176 + 262.887i −0.00637246 + 0.0162368i
\(641\) 17758.1 + 12107.3i 1.09423 + 0.746034i 0.969238 0.246124i \(-0.0791570\pi\)
0.124992 + 0.992158i \(0.460109\pi\)
\(642\) −44669.2 + 6732.80i −2.74603 + 0.413898i
\(643\) −3315.75 + 4157.82i −0.203360 + 0.255005i −0.873045 0.487640i \(-0.837858\pi\)
0.669685 + 0.742645i \(0.266429\pi\)
\(644\) 26352.0 + 7980.86i 1.61244 + 0.488339i
\(645\) −1378.23 1728.24i −0.0841359 0.105503i
\(646\) 6647.27 + 6167.76i 0.404850 + 0.375646i
\(647\) 14122.6 + 2128.65i 0.858143 + 0.129344i 0.563351 0.826217i \(-0.309512\pi\)
0.294791 + 0.955562i \(0.404750\pi\)
\(648\) −2718.87 + 2522.74i −0.164826 + 0.152936i
\(649\) −1453.30 + 990.843i −0.0878999 + 0.0599291i
\(650\) −2659.56 11652.3i −0.160487 0.703140i
\(651\) −22176.6 37960.4i −1.33513 2.28538i
\(652\) −1488.56 + 6521.82i −0.0894120 + 0.391739i
\(653\) −9368.61 23870.8i −0.561443 1.43053i −0.876473 0.481451i \(-0.840110\pi\)
0.315030 0.949082i \(-0.397985\pi\)
\(654\) −1233.42 16458.9i −0.0737470 0.984086i
\(655\) −348.886 604.288i −0.0208124 0.0360481i
\(656\) −1543.42 + 2673.28i −0.0918602 + 0.159106i
\(657\) 9902.34 + 4768.72i 0.588017 + 0.283174i
\(658\) −4555.29 + 20440.3i −0.269884 + 1.21101i
\(659\) 11261.6 5423.29i 0.665689 0.320579i −0.0703460 0.997523i \(-0.522410\pi\)
0.736035 + 0.676944i \(0.236696\pi\)
\(660\) 19.6573 262.309i 0.00115934 0.0154703i
\(661\) 14793.5 4563.19i 0.870499 0.268513i 0.172846 0.984949i \(-0.444704\pi\)
0.697653 + 0.716435i \(0.254228\pi\)
\(662\) 22176.9 6840.67i 1.30201 0.401616i
\(663\) 510.305 6809.55i 0.0298923 0.398885i
\(664\) −512.549 + 246.831i −0.0299560 + 0.0144260i
\(665\) 1289.16 6.60621i 0.0751752 0.000385230i
\(666\) −47758.4 22999.2i −2.77868 1.33814i
\(667\) 24840.9 43025.8i 1.44205 2.49770i
\(668\) −634.661 1099.27i −0.0367602 0.0636704i
\(669\) 1504.65 + 20078.2i 0.0869556 + 1.16034i
\(670\) 555.837 + 1416.25i 0.0320506 + 0.0816635i
\(671\) 407.637 1785.98i 0.0234526 0.102752i
\(672\) 3485.27 + 43514.3i 0.200070 + 2.49792i
\(673\) 5542.03 + 24281.2i 0.317429 + 1.39075i 0.842045 + 0.539407i \(0.181351\pi\)
−0.524617 + 0.851339i \(0.675791\pi\)
\(674\) −35214.9 + 24009.1i −2.01250 + 1.37210i
\(675\) −30509.8 + 28309.0i −1.73974 + 1.61424i
\(676\) 11606.2 + 1749.36i 0.660346 + 0.0995312i
\(677\) −7111.16 6598.19i −0.403699 0.374578i 0.452030 0.892003i \(-0.350700\pi\)
−0.855729 + 0.517425i \(0.826891\pi\)
\(678\) −6102.85 7652.73i −0.345691 0.433483i
\(679\) 3282.77 + 8239.94i 0.185539 + 0.465714i
\(680\) −40.5916 + 50.9002i −0.00228914 + 0.00287049i
\(681\) −32482.0 + 4895.88i −1.82777 + 0.275493i
\(682\) 3470.50 + 2366.15i 0.194857 + 0.132851i
\(683\) −5977.12 + 15229.5i −0.334858 + 0.853205i 0.659938 + 0.751320i \(0.270583\pi\)
−0.994796 + 0.101885i \(0.967513\pi\)
\(684\) −34544.9 10655.7i −1.93108 0.595659i
\(685\) 320.110 0.0178551
\(686\) −18509.7 16652.3i −1.03018 0.926806i
\(687\) 54979.6 3.05328
\(688\) −17338.9 5348.33i −0.960810 0.296371i
\(689\) −5800.19 + 14778.6i −0.320710 + 0.817157i
\(690\) −5473.16 3731.54i −0.301971 0.205880i
\(691\) −26303.5 + 3964.62i −1.44810 + 0.218265i −0.825555 0.564322i \(-0.809138\pi\)
−0.622541 + 0.782588i \(0.713899\pi\)
\(692\) 12932.1 16216.3i 0.710411 0.890828i
\(693\) 1826.99 + 4585.85i 0.100147 + 0.251374i
\(694\) 20781.1 + 26058.6i 1.13666 + 1.42532i
\(695\) −1539.90 1428.82i −0.0840458 0.0779831i
\(696\) 5753.73 + 867.235i 0.313354 + 0.0472305i
\(697\) −968.856 + 898.967i −0.0526514 + 0.0488534i
\(698\) −29439.7 + 20071.6i −1.59643 + 1.08843i
\(699\) −270.142 1183.57i −0.0146176 0.0640440i
\(700\) 1352.17 + 16882.2i 0.0730105 + 0.911551i
\(701\) −665.675 + 2916.51i −0.0358662 + 0.157140i −0.989690 0.143227i \(-0.954252\pi\)
0.953824 + 0.300367i \(0.0971092\pi\)
\(702\) 11778.3 + 30010.6i 0.633252 + 1.61350i
\(703\) 1273.35 + 16991.6i 0.0683146 + 0.911595i
\(704\) −912.200 1579.98i −0.0488350 0.0845847i
\(705\) 1207.23 2090.98i 0.0644921 0.111704i
\(706\) 72.4264 + 34.8787i 0.00386091 + 0.00185932i
\(707\) 10728.3 54.9766i 0.570694 0.00292448i
\(708\) 25842.2 12444.9i 1.37176 0.660607i
\(709\) 161.805 2159.14i 0.00857084 0.114370i −0.991277 0.131792i \(-0.957927\pi\)
0.999848 + 0.0174222i \(0.00554594\pi\)
\(710\) 917.588 283.038i 0.0485021 0.0149609i
\(711\) 11224.3 3462.23i 0.592044 0.182622i
\(712\) −202.714 + 2705.03i −0.0106700 + 0.142381i
\(713\) 45671.4 21994.2i 2.39889 1.15524i
\(714\) −4392.08 + 19707.9i −0.230209 + 1.03299i
\(715\) 83.5686 + 40.2445i 0.00437103 + 0.00210498i
\(716\) 4169.27 7221.39i 0.217616 0.376922i
\(717\) −20793.0 36014.5i −1.08302 1.87585i
\(718\) −1227.27 16376.8i −0.0637903 0.851223i
\(719\) −90.9415 231.715i −0.00471703 0.0120188i 0.928496 0.371343i \(-0.121103\pi\)
−0.933213 + 0.359324i \(0.883007\pi\)
\(720\) 844.590 3700.39i 0.0437167 0.191535i
\(721\) 8461.53 + 14483.9i 0.437065 + 0.748139i
\(722\) −586.284 2568.68i −0.0302206 0.132405i
\(723\) 17582.2 11987.4i 0.904413 0.616618i
\(724\) 20146.5 18693.3i 1.03417 0.959571i
\(725\) 30218.1 + 4554.64i 1.54796 + 0.233318i
\(726\) 35668.9 + 33095.9i 1.82341 + 1.69188i
\(727\) −9358.31 11734.9i −0.477415 0.598659i 0.483555 0.875314i \(-0.339345\pi\)
−0.960969 + 0.276655i \(0.910774\pi\)
\(728\) −1088.30 329.597i −0.0554051 0.0167798i
\(729\) 4383.76 5497.06i 0.222718 0.279280i
\(730\) −603.819 + 91.0111i −0.0306142 + 0.00461434i
\(731\) −6419.10 4376.47i −0.324786 0.221436i
\(732\) −10913.7 + 27807.6i −0.551067 + 1.40410i
\(733\) −8211.36 2532.87i −0.413770 0.127631i 0.0808790 0.996724i \(-0.474227\pi\)
−0.494649 + 0.869093i \(0.664703\pi\)
\(734\) 13860.6 0.697008
\(735\) 1460.70 + 2471.16i 0.0733043 + 0.124014i
\(736\) −50334.3 −2.52085
\(737\) 1789.45 + 551.973i 0.0894374 + 0.0275878i
\(738\) 4016.90 10234.9i 0.200358 0.510503i
\(739\) −6438.31 4389.57i −0.320483 0.218502i 0.392383 0.919802i \(-0.371651\pi\)
−0.712866 + 0.701300i \(0.752603\pi\)
\(740\) 1395.61 210.354i 0.0693292 0.0104497i
\(741\) 11385.2 14276.6i 0.564436 0.707780i
\(742\) 23263.2 40774.1i 1.15097 2.01734i
\(743\) −3615.48 4533.67i −0.178518 0.223855i 0.684519 0.728995i \(-0.260012\pi\)
−0.863037 + 0.505140i \(0.831441\pi\)
\(744\) 4352.10 + 4038.16i 0.214457 + 0.198987i
\(745\) 809.756 + 122.051i 0.0398217 + 0.00600216i
\(746\) −15353.0 + 14245.5i −0.753505 + 0.699150i
\(747\) 11733.1 7999.47i 0.574686 0.391814i
\(748\) −205.720 901.319i −0.0100560 0.0440581i
\(749\) −8138.64 + 21053.5i −0.397036 + 1.02707i
\(750\) 1819.06 7969.84i 0.0885637 0.388023i
\(751\) −5780.81 14729.3i −0.280885 0.715684i −0.999788 0.0205736i \(-0.993451\pi\)
0.718903 0.695110i \(-0.244644\pi\)
\(752\) −1481.09 19763.7i −0.0718214 0.958390i
\(753\) 14265.3 + 24708.2i 0.690381 + 1.19577i
\(754\) 11835.7 20500.0i 0.571658 0.990141i
\(755\) 536.716 + 258.469i 0.0258716 + 0.0124591i
\(756\) −10393.7 44485.6i −0.500019 2.14012i
\(757\) −11045.4 + 5319.17i −0.530318 + 0.255388i −0.679827 0.733373i \(-0.737945\pi\)
0.149509 + 0.988760i \(0.452231\pi\)
\(758\) −2667.48 + 35595.0i −0.127819 + 1.70563i
\(759\) −7791.19 + 2403.26i −0.372598 + 0.114931i
\(760\) −166.360 + 51.3152i −0.00794014 + 0.00244921i
\(761\) 1762.98 23525.3i 0.0839788 1.12062i −0.782916 0.622128i \(-0.786269\pi\)
0.866895 0.498491i \(-0.166112\pi\)
\(762\) −12198.9 + 5874.68i −0.579947 + 0.279288i
\(763\) −7448.54 3540.12i −0.353415 0.167970i
\(764\) −8922.48 4296.84i −0.422518 0.203474i
\(765\) 812.562 1407.40i 0.0384029 0.0665158i
\(766\) 13406.3 + 23220.4i 0.632361 + 1.09528i
\(767\) 755.821 + 10085.7i 0.0355816 + 0.474804i
\(768\) −16132.3 41104.5i −0.757975 1.93129i
\(769\) −7987.33 + 34994.8i −0.374552 + 1.64102i 0.339267 + 0.940690i \(0.389821\pi\)
−0.713819 + 0.700330i \(0.753036\pi\)
\(770\) −227.395 153.334i −0.0106425 0.00717634i
\(771\) −11078.9 48539.8i −0.517505 2.26734i
\(772\) −13586.4 + 9263.04i −0.633400 + 0.431845i
\(773\) −12974.1 + 12038.2i −0.603684 + 0.560137i −0.921678 0.387956i \(-0.873181\pi\)
0.317994 + 0.948093i \(0.396991\pi\)
\(774\) 63908.4 + 9632.64i 2.96788 + 0.447336i
\(775\) 22856.9 + 21208.1i 1.05941 + 0.982989i
\(776\) −746.817 936.479i −0.0345479 0.0433217i
\(777\) −31238.4 + 21533.3i −1.44231 + 0.994213i
\(778\) 987.209 1237.92i 0.0454925 0.0570458i
\(779\) −3494.82 + 526.759i −0.160738 + 0.0242274i
\(780\) −1249.71 852.037i −0.0573676 0.0391126i
\(781\) 431.807 1100.23i 0.0197839 0.0504087i
\(782\) −22247.1 6862.32i −1.01733 0.313806i
\(783\) −82430.8 −3.76224
\(784\) 21333.5 + 10005.6i 0.971824 + 0.455796i
\(785\) −268.545 −0.0122099
\(786\) 27926.1 + 8614.05i 1.26729 + 0.390907i
\(787\) −3596.67 + 9164.16i −0.162906 + 0.415079i −0.988896 0.148606i \(-0.952521\pi\)
0.825990 + 0.563685i \(0.190617\pi\)
\(788\) −15096.5 10292.6i −0.682477 0.465305i
\(789\) 7196.81 1084.74i 0.324731 0.0489454i
\(790\) −406.894 + 510.229i −0.0183248 + 0.0229786i
\(791\) −4832.43 + 753.717i −0.217220 + 0.0338800i
\(792\) −415.633 521.188i −0.0186476 0.0233833i
\(793\) −7721.67 7164.67i −0.345781 0.320838i
\(794\) −25154.3 3791.41i −1.12430 0.169461i
\(795\) −3967.52 + 3681.32i −0.176998 + 0.164230i
\(796\) 17874.2 12186.4i 0.795896 0.542633i
\(797\) −1149.41 5035.91i −0.0510845 0.223816i 0.942942 0.332958i \(-0.108047\pi\)
−0.994026 + 0.109142i \(0.965190\pi\)
\(798\) −39391.7 + 36927.6i −1.74743 + 1.63812i
\(799\) 1888.29 8273.12i 0.0836079 0.366310i
\(800\) −11311.2 28820.5i −0.499890 1.27370i
\(801\) −5060.15 67523.1i −0.223211 2.97854i
\(802\) −16944.1 29348.1i −0.746033 1.29217i
\(803\) −375.804 + 650.912i −0.0165154 + 0.0286055i
\(804\) −27512.9 13249.5i −1.20685 0.581187i
\(805\) −2974.71 + 1451.37i −0.130242 + 0.0635455i
\(806\) 21760.6 10479.3i 0.950972 0.457964i
\(807\) −4693.68 + 62632.7i −0.204740 + 2.73207i
\(808\) −1384.44 + 427.043i −0.0602777 + 0.0185932i
\(809\) 19608.5 6048.41i 0.852160 0.262856i 0.162248 0.986750i \(-0.448126\pi\)
0.689912 + 0.723894i \(0.257649\pi\)
\(810\) −384.402 + 5129.49i −0.0166747 + 0.222508i
\(811\) 28813.9 13876.0i 1.24759 0.600806i 0.310723 0.950501i \(-0.399429\pi\)
0.936864 + 0.349694i \(0.113715\pi\)
\(812\) −20779.0 + 26331.7i −0.898030 + 1.13801i
\(813\) −4824.56 2323.39i −0.208124 0.100227i
\(814\) 1812.48 3139.31i 0.0780436 0.135176i
\(815\) −402.078 696.420i −0.0172812 0.0299319i
\(816\) −1428.02 19055.6i −0.0612633 0.817501i
\(817\) −7590.05 19339.1i −0.325021 0.828141i
\(818\) −10994.3 + 48169.1i −0.469934 + 2.05892i
\(819\) 28088.9 + 4086.62i 1.19842 + 0.174357i
\(820\) 65.1425 + 285.408i 0.00277424 + 0.0121547i
\(821\) 26189.2 17855.5i 1.11329 0.759027i 0.140352 0.990102i \(-0.455176\pi\)
0.972936 + 0.231074i \(0.0742241\pi\)
\(822\) −9828.02 + 9119.07i −0.417021 + 0.386939i
\(823\) −15215.3 2293.34i −0.644437 0.0971332i −0.181311 0.983426i \(-0.558034\pi\)
−0.463126 + 0.886293i \(0.653272\pi\)
\(824\) −1660.56 1540.77i −0.0702041 0.0651399i
\(825\) −3126.92 3921.03i −0.131958 0.165470i
\(826\) 2082.02 29833.3i 0.0877030 1.25670i
\(827\) −12778.1 + 16023.2i −0.537290 + 0.673740i −0.974179 0.225775i \(-0.927509\pi\)
0.436890 + 0.899515i \(0.356080\pi\)
\(828\) 91779.1 13833.5i 3.85211 0.580611i
\(829\) −30062.0 20495.9i −1.25946 0.858688i −0.265049 0.964235i \(-0.585388\pi\)
−0.994414 + 0.105547i \(0.966341\pi\)
\(830\) −288.245 + 734.436i −0.0120544 + 0.0307140i
\(831\) −46990.9 14494.8i −1.96161 0.605076i
\(832\) −10490.4 −0.437128
\(833\) 7465.70 + 6786.11i 0.310530 + 0.282262i
\(834\) 87981.4 3.65293
\(835\) 145.808 + 44.9757i 0.00604297 + 0.00186401i
\(836\) 903.197 2301.31i 0.0373657 0.0952063i
\(837\) −69491.5 47378.5i −2.86975 1.95656i
\(838\) 19250.5 2901.54i 0.793551 0.119609i
\(839\) −2216.59 + 2779.51i −0.0912099 + 0.114374i −0.825342 0.564633i \(-0.809018\pi\)
0.734132 + 0.679006i \(0.237589\pi\)
\(840\) −285.517 262.211i −0.0117277 0.0107704i
\(841\) 22529.9 + 28251.7i 0.923775 + 1.15838i
\(842\) 10858.0 + 10074.7i 0.444407 + 0.412350i
\(843\) 46118.6 + 6951.26i 1.88423 + 0.284003i
\(844\) −1561.54 + 1448.90i −0.0636855 + 0.0590915i
\(845\) −1165.79 + 794.821i −0.0474608 + 0.0323582i
\(846\) 15708.5 + 68823.5i 0.638381 + 2.79693i
\(847\) 23195.7 7285.31i 0.940985 0.295544i
\(848\) −9885.98 + 43313.3i −0.400337 + 1.75399i
\(849\) 27381.8 + 69767.8i 1.10688 + 2.82029i
\(850\) −1070.17 14280.4i −0.0431841 0.576252i
\(851\) −21873.7 37886.3i −0.881105 1.52612i
\(852\) −9636.76 + 16691.4i −0.387500 + 0.671169i
\(853\) 28971.7 + 13952.0i 1.16292 + 0.560033i 0.912890 0.408205i \(-0.133845\pi\)
0.250030 + 0.968238i \(0.419560\pi\)
\(854\) 19544.1 + 24251.5i 0.783120 + 0.971744i
\(855\) 3915.39 1885.55i 0.156612 0.0754204i
\(856\) 227.790 3039.65i 0.00909544 0.121370i
\(857\) 36412.3 11231.7i 1.45137 0.447688i 0.533917 0.845537i \(-0.320720\pi\)
0.917451 + 0.397850i \(0.130243\pi\)
\(858\) −3712.18 + 1145.06i −0.147706 + 0.0455613i
\(859\) 1626.18 21699.9i 0.0645920 0.861920i −0.866975 0.498351i \(-0.833939\pi\)
0.931567 0.363569i \(-0.118442\pi\)
\(860\) −1550.41 + 746.639i −0.0614751 + 0.0296048i
\(861\) −4938.18 6127.60i −0.195462 0.242541i
\(862\) −24699.2 11894.5i −0.975937 0.469986i
\(863\) −5531.43 + 9580.72i −0.218183 + 0.377904i −0.954253 0.299002i \(-0.903346\pi\)
0.736069 + 0.676906i \(0.236680\pi\)
\(864\) 41756.6 + 72324.6i 1.64420 + 2.84784i
\(865\) 186.329 + 2486.38i 0.00732412 + 0.0977336i
\(866\) 10310.5 + 26270.8i 0.404579 + 1.03085i
\(867\) −8517.96 + 37319.6i −0.333662 + 1.46187i
\(868\) −32651.9 + 10255.3i −1.27682 + 0.401023i
\(869\) 178.743 + 783.125i 0.00697750 + 0.0305704i
\(870\) 6667.60 4545.89i 0.259831 0.177150i
\(871\) 7893.41 7324.02i 0.307070 0.284920i
\(872\) 1101.26 + 165.989i 0.0427677 + 0.00644619i
\(873\) 21918.0 + 20336.9i 0.849726 + 0.788430i
\(874\) −38816.6 48674.4i −1.50228 1.88380i
\(875\) −3008.48 2762.91i −0.116234 0.106747i
\(876\) 7641.72 9582.42i 0.294737 0.369589i
\(877\) −11896.4 + 1793.09i −0.458052 + 0.0690402i −0.374015 0.927422i \(-0.622019\pi\)
−0.0840364 + 0.996463i \(0.526781\pi\)
\(878\) −35009.6 23869.1i −1.34569 0.917476i
\(879\) 31577.7 80458.8i 1.21171 3.08738i
\(880\) 248.029 + 76.5068i 0.00950120 + 0.00293073i
\(881\) 25428.5 0.972428 0.486214 0.873840i \(-0.338378\pi\)
0.486214 + 0.873840i \(0.338378\pi\)
\(882\) −80450.2 23915.5i −3.07132 0.913011i
\(883\) −738.549 −0.0281474 −0.0140737 0.999901i \(-0.504480\pi\)
−0.0140737 + 0.999901i \(0.504480\pi\)
\(884\) −5079.77 1566.90i −0.193270 0.0596160i
\(885\) −1259.69 + 3209.63i −0.0478462 + 0.121910i
\(886\) −4254.20 2900.47i −0.161312 0.109981i
\(887\) 7177.61 1081.85i 0.271703 0.0409526i −0.0117775 0.999931i \(-0.503749\pi\)
0.283481 + 0.958978i \(0.408511\pi\)
\(888\) 3194.56 4005.85i 0.120723 0.151382i
\(889\) −471.000 + 6748.97i −0.0177692 + 0.254615i
\(890\) 2345.60 + 2941.29i 0.0883424 + 0.110778i
\(891\) 4641.22 + 4306.42i 0.174508 + 0.161920i
\(892\) 15499.2 + 2336.13i 0.581784 + 0.0876898i
\(893\) 16634.5 15434.6i 0.623351 0.578385i
\(894\) −28338.1 + 19320.6i −1.06014 + 0.722792i
\(895\) 223.051 + 977.252i 0.00833049 + 0.0364983i
\(896\) −5848.49 850.891i −0.218063 0.0317257i
\(897\) −10432.4 + 45707.4i −0.388325 + 1.70136i
\(898\) −4978.02 12683.8i −0.184987 0.471340i
\(899\) 4614.89 + 61581.5i 0.171207 + 2.28460i
\(900\) 28545.6 + 49442.4i 1.05724 + 1.83120i
\(901\) −9511.10 + 16473.7i −0.351677 + 0.609122i
\(902\) 677.432 + 326.234i 0.0250067 + 0.0120426i
\(903\) 28656.9 36314.8i 1.05608 1.33830i
\(904\) 595.068 286.569i 0.0218934 0.0105433i
\(905\) −246.891 + 3294.53i −0.00906844 + 0.121010i
\(906\) −23841.3 + 7354.08i −0.874256 + 0.269672i
\(907\) −5719.91 + 1764.36i −0.209401 + 0.0645916i −0.397681 0.917524i \(-0.630185\pi\)
0.188280 + 0.982115i \(0.439709\pi\)
\(908\) −1911.01 + 25500.6i −0.0698447 + 0.932013i
\(909\) 32583.7 15691.5i 1.18892 0.572555i
\(910\) −1417.33 + 691.519i −0.0516308 + 0.0251908i
\(911\) 793.011 + 381.894i 0.0288404 + 0.0138888i 0.448248 0.893909i \(-0.352048\pi\)
−0.419408 + 0.907798i \(0.637762\pi\)
\(912\) 25549.8 44253.6i 0.927675 1.60678i
\(913\) 485.557 + 841.009i 0.0176009 + 0.0304856i
\(914\) 4055.89 + 54122.0i 0.146780 + 1.95864i
\(915\) −1311.95 3342.78i −0.0474006 0.120775i
\(916\) 9523.96 41727.2i 0.343538 1.50514i
\(917\) 10653.3 9986.94i 0.383647 0.359649i
\(918\) 8595.52 + 37659.4i 0.309035 + 1.35397i
\(919\) 7814.07 5327.54i 0.280481 0.191229i −0.414906 0.909865i \(-0.636185\pi\)
0.695387 + 0.718635i \(0.255233\pi\)
\(920\) 327.658 304.022i 0.0117419 0.0108949i
\(921\) −50890.2 7670.46i −1.82072 0.274430i
\(922\) 7291.84 + 6765.84i 0.260460 + 0.241671i
\(923\) −4237.35 5313.47i −0.151109 0.189485i
\(924\) 5439.06 848.333i 0.193649 0.0302036i
\(925\) 16777.5 21038.4i 0.596370 0.747825i
\(926\) −71275.1 + 10743.0i −2.52942 + 0.381249i
\(927\) 46720.2 + 31853.3i 1.65533 + 1.12859i
\(928\) 22402.3 57080.2i 0.792449 2.01913i
\(929\) 33320.9 + 10278.1i 1.17677 + 0.362986i 0.820638 0.571448i \(-0.193618\pi\)
0.356135 + 0.934435i \(0.384094\pi\)
\(930\) 8233.81 0.290320
\(931\) 6272.65 + 26239.7i 0.220814 + 0.923707i
\(932\) −945.077 −0.0332157
\(933\) −92642.7 28576.5i −3.25079 1.00274i
\(934\) −11828.3 + 30138.0i −0.414383 + 1.05583i
\(935\) 91.8240 + 62.6045i 0.00321173 + 0.00218972i
\(936\) −3790.33 + 571.300i −0.132362 + 0.0199503i
\(937\) −33170.4 + 41594.4i −1.15649 + 1.45019i −0.285844 + 0.958276i \(0.592274\pi\)
−0.870644 + 0.491914i \(0.836297\pi\)
\(938\) −26214.6 + 18070.3i −0.912512 + 0.629014i
\(939\) −39407.0 49414.9i −1.36954 1.71735i
\(940\) −1377.85 1278.45i −0.0478089 0.0443602i
\(941\) −13097.8 1974.17i −0.453747 0.0683913i −0.0818069 0.996648i \(-0.526069\pi\)
−0.371940 + 0.928257i \(0.621307\pi\)
\(942\) 8244.88 7650.13i 0.285173 0.264602i
\(943\) 7497.38 5111.63i 0.258906 0.176519i
\(944\) 6297.96 + 27593.2i 0.217141 + 0.951357i
\(945\) 4553.24 + 3070.28i 0.156737 + 0.105689i
\(946\) −983.491 + 4308.96i −0.0338013 + 0.148093i
\(947\) 2069.19 + 5272.22i 0.0710030 + 0.180913i 0.961970 0.273156i \(-0.0880674\pi\)
−0.890967 + 0.454068i \(0.849972\pi\)
\(948\) −978.868 13062.1i −0.0335360 0.447507i
\(949\) 2160.91 + 3742.80i 0.0739156 + 0.128026i
\(950\) 19147.2 33163.9i 0.653912 1.13261i
\(951\) −16402.3 7898.93i −0.559286 0.269338i
\(952\) −1230.54 584.846i −0.0418928 0.0199107i
\(953\) −23297.4 + 11219.5i −0.791897 + 0.381357i −0.785688 0.618623i \(-0.787691\pi\)
−0.00620921 + 0.999981i \(0.501976\pi\)
\(954\) 11825.6 157802.i 0.401330 5.35537i
\(955\) 1137.59 350.899i 0.0385460 0.0118899i
\(956\) −30935.4 + 9542.32i −1.04657 + 0.322825i
\(957\) 742.278 9905.01i 0.0250726 0.334570i
\(958\) 3281.07 1580.08i 0.110654 0.0532881i
\(959\) 1524.12 + 6523.35i 0.0513207 + 0.219656i
\(960\) −3222.14 1551.70i −0.108327 0.0521676i
\(961\) −16609.0 + 28767.7i −0.557518 + 0.965649i
\(962\) −10421.9 18051.3i −0.349289 0.604987i
\(963\) 5686.10 + 75875.8i 0.190272 + 2.53901i
\(964\) −6052.19 15420.7i −0.202207 0.515216i
\(965\) 439.859 1927.15i 0.0146731 0.0642871i
\(966\) 49984.0 129302.i 1.66481 4.30664i
\(967\) 3432.74 + 15039.8i 0.114157 + 0.500153i 0.999387 + 0.0350009i \(0.0111434\pi\)
−0.885231 + 0.465153i \(0.845999\pi\)
\(968\) −2712.78 + 1849.54i −0.0900743 + 0.0614116i
\(969\) 16038.5 14881.6i 0.531715 0.493359i
\(970\) −1642.65 247.589i −0.0543734 0.00819547i
\(971\) −28131.8 26102.5i −0.929757 0.862688i 0.0610275 0.998136i \(-0.480562\pi\)
−0.990784 + 0.135448i \(0.956753\pi\)
\(972\) −22847.1 28649.4i −0.753932 0.945401i
\(973\) 21785.3 38183.9i 0.717786 1.25809i
\(974\) −18915.1 + 23718.7i −0.622256 + 0.780284i
\(975\) −28515.6 + 4298.04i −0.936647 + 0.141177i
\(976\) −24355.0 16604.9i −0.798754 0.544581i
\(977\) −6654.09 + 16954.3i −0.217895 + 0.555187i −0.997467 0.0711251i \(-0.977341\pi\)
0.779573 + 0.626312i \(0.215436\pi\)
\(978\) 32183.8 + 9927.37i 1.05227 + 0.324583i
\(979\) 4630.54 0.151167
\(980\) 2128.54 680.536i 0.0693815 0.0221826i
\(981\) −27800.3 −0.904785
\(982\) 43123.6 + 13301.9i 1.40135 + 0.432261i
\(983\) 15085.9 38438.2i 0.489486 1.24719i −0.446382 0.894842i \(-0.647288\pi\)
0.935869 0.352349i \(-0.114617\pi\)
\(984\) 878.090 + 598.671i 0.0284476 + 0.0193953i
\(985\) 2171.89 327.360i 0.0702560 0.0105894i
\(986\) 17683.6 22174.5i 0.571156 0.716207i
\(987\) 48359.0 + 14645.8i 1.55956 + 0.472322i
\(988\) −8863.14 11114.0i −0.285399 0.357879i
\(989\) 39100.5 + 36280.0i 1.25715 + 1.16647i
\(990\) −914.197 137.793i −0.0293486 0.00442359i
\(991\) 526.247 488.286i 0.0168686 0.0156518i −0.671693 0.740829i \(-0.734433\pi\)
0.688562 + 0.725177i \(0.258242\pi\)
\(992\) 51693.7 35244.1i 1.65451 1.12803i
\(993\) −12460.3 54592.2i −0.398204 1.74464i
\(994\) 10136.8 + 17351.4i 0.323459 + 0.553676i
\(995\) −578.676 + 2535.35i −0.0184375 + 0.0807798i
\(996\) −5785.47 14741.1i −0.184056 0.468966i
\(997\) −4199.49 56038.3i −0.133399 1.78009i −0.516406 0.856344i \(-0.672730\pi\)
0.383006 0.923746i \(-0.374889\pi\)
\(998\) −12039.4 20852.9i −0.381864 0.661408i
\(999\) −36292.2 + 62860.0i −1.14939 + 1.99079i
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 49.4.g.a.2.3 156
49.5 odd 42 2401.4.a.f.1.14 78
49.25 even 21 inner 49.4.g.a.25.3 yes 156
49.44 even 21 2401.4.a.g.1.14 78
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
49.4.g.a.2.3 156 1.1 even 1 trivial
49.4.g.a.25.3 yes 156 49.25 even 21 inner
2401.4.a.f.1.14 78 49.5 odd 42
2401.4.a.g.1.14 78 49.44 even 21