Properties

Label 49.4.g.a.11.13
Level $49$
Weight $4$
Character 49.11
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 11.13
Character \(\chi\) \(=\) 49.11
Dual form 49.4.g.a.9.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.89764 - 3.61648i) q^{2} +(-0.609740 + 0.0919036i) q^{3} +(1.51482 - 20.2138i) q^{4} +(-3.10515 + 7.91179i) q^{5} +(-2.04418 + 2.56332i) q^{6} +(18.4911 - 1.03883i) q^{7} +(-40.6778 - 51.0084i) q^{8} +(-25.4371 + 7.84632i) q^{9} +O(q^{10})\) \(q+(3.89764 - 3.61648i) q^{2} +(-0.609740 + 0.0919036i) q^{3} +(1.51482 - 20.2138i) q^{4} +(-3.10515 + 7.91179i) q^{5} +(-2.04418 + 2.56332i) q^{6} +(18.4911 - 1.03883i) q^{7} +(-40.6778 - 51.0084i) q^{8} +(-25.4371 + 7.84632i) q^{9} +(16.5101 + 42.0670i) q^{10} +(28.9466 + 8.92886i) q^{11} +(0.934077 + 12.4644i) q^{12} +(14.6416 + 64.1490i) q^{13} +(68.3147 - 70.9216i) q^{14} +(1.16621 - 5.10951i) q^{15} +(-182.666 - 27.5324i) q^{16} +(9.72318 - 6.62915i) q^{17} +(-70.7687 + 122.575i) q^{18} +(-48.6730 - 84.3041i) q^{19} +(155.224 + 74.7517i) q^{20} +(-11.1793 + 2.33281i) q^{21} +(145.115 - 69.8835i) q^{22} +(-7.98047 - 5.44099i) q^{23} +(29.4908 + 27.3635i) q^{24} +(38.6771 + 35.8871i) q^{25} +(289.061 + 197.079i) q^{26} +(29.7891 - 14.3457i) q^{27} +(7.01193 - 375.349i) q^{28} +(-194.397 - 93.6164i) q^{29} +(-13.9330 - 24.1326i) q^{30} +(-126.916 + 219.824i) q^{31} +(-380.290 + 259.277i) q^{32} +(-18.4705 - 2.78399i) q^{33} +(13.9232 - 61.0017i) q^{34} +(-49.1986 + 149.523i) q^{35} +(120.071 + 526.067i) q^{36} +(-7.99614 - 106.701i) q^{37} +(-494.593 - 152.562i) q^{38} +(-14.8231 - 37.7686i) q^{39} +(529.878 - 163.446i) q^{40} +(-266.513 - 334.197i) q^{41} +(-35.1363 + 49.5222i) q^{42} +(100.325 - 125.803i) q^{43} +(224.335 - 571.597i) q^{44} +(16.9077 - 225.617i) q^{45} +(-50.7822 + 7.65418i) q^{46} +(-196.194 + 182.042i) q^{47} +113.909 q^{48} +(340.842 - 38.4182i) q^{49} +280.534 q^{50} +(-5.31937 + 4.93566i) q^{51} +(1318.88 - 198.788i) q^{52} +(-15.8842 + 211.960i) q^{53} +(64.2263 - 163.646i) q^{54} +(-160.527 + 201.294i) q^{55} +(-805.167 - 900.944i) q^{56} +(37.4257 + 46.9304i) q^{57} +(-1096.25 + 338.148i) q^{58} +(62.1204 + 158.280i) q^{59} +(-101.516 - 31.3136i) q^{60} +(-54.3988 - 725.902i) q^{61} +(300.319 + 1315.78i) q^{62} +(-462.210 + 171.512i) q^{63} +(-215.712 + 945.098i) q^{64} +(-552.998 - 83.3510i) q^{65} +(-82.0597 + 55.9473i) q^{66} +(261.524 - 452.972i) q^{67} +(-119.272 - 206.584i) q^{68} +(5.36606 + 2.58416i) q^{69} +(348.990 + 760.713i) q^{70} +(449.307 - 216.375i) q^{71} +(1434.96 + 978.336i) q^{72} +(838.099 + 777.643i) q^{73} +(-417.048 - 386.964i) q^{74} +(-26.8811 - 18.3272i) q^{75} +(-1777.84 + 856.161i) q^{76} +(544.531 + 135.034i) q^{77} +(-194.365 - 93.6010i) q^{78} +(412.211 + 713.971i) q^{79} +(785.034 - 1359.72i) q^{80} +(577.001 - 393.392i) q^{81} +(-2247.39 - 338.739i) q^{82} +(-90.0787 + 394.660i) q^{83} +(30.2205 + 229.510i) q^{84} +(22.2565 + 97.5122i) q^{85} +(-63.9352 - 853.156i) q^{86} +(127.135 + 39.2160i) q^{87} +(-722.041 - 1839.73i) q^{88} +(734.529 - 226.572i) q^{89} +(-750.039 - 940.520i) q^{90} +(337.379 + 1170.98i) q^{91} +(-122.072 + 153.074i) q^{92} +(57.1829 - 145.700i) q^{93} +(-106.344 + 1419.06i) q^{94} +(818.132 - 123.314i) q^{95} +(208.049 - 193.042i) q^{96} -424.107 q^{97} +(1189.54 - 1382.39i) q^{98} -806.378 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 \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{20}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.89764 3.61648i 1.37802 1.27862i 0.456807 0.889566i \(-0.348993\pi\)
0.921216 0.389053i \(-0.127198\pi\)
\(3\) −0.609740 + 0.0919036i −0.117345 + 0.0176869i −0.207452 0.978245i \(-0.566517\pi\)
0.0901074 + 0.995932i \(0.471279\pi\)
\(4\) 1.51482 20.2138i 0.189352 2.52673i
\(5\) −3.10515 + 7.91179i −0.277733 + 0.707652i 0.722141 + 0.691746i \(0.243158\pi\)
−0.999874 + 0.0159054i \(0.994937\pi\)
\(6\) −2.04418 + 2.56332i −0.139089 + 0.174412i
\(7\) 18.4911 1.03883i 0.998426 0.0560915i
\(8\) −40.6778 51.0084i −1.79772 2.25427i
\(9\) −25.4371 + 7.84632i −0.942116 + 0.290604i
\(10\) 16.5101 + 42.0670i 0.522094 + 1.33027i
\(11\) 28.9466 + 8.92886i 0.793431 + 0.244741i 0.664869 0.746960i \(-0.268488\pi\)
0.128563 + 0.991701i \(0.458964\pi\)
\(12\) 0.934077 + 12.4644i 0.0224704 + 0.299847i
\(13\) 14.6416 + 64.1490i 0.312373 + 1.36860i 0.850608 + 0.525800i \(0.176234\pi\)
−0.538235 + 0.842795i \(0.680909\pi\)
\(14\) 68.3147 70.9216i 1.30413 1.35390i
\(15\) 1.16621 5.10951i 0.0200743 0.0879513i
\(16\) −182.666 27.5324i −2.85415 0.430194i
\(17\) 9.72318 6.62915i 0.138719 0.0945768i −0.491972 0.870611i \(-0.663724\pi\)
0.630691 + 0.776034i \(0.282772\pi\)
\(18\) −70.7687 + 122.575i −0.926685 + 1.60507i
\(19\) −48.6730 84.3041i −0.587702 1.01793i −0.994533 0.104427i \(-0.966699\pi\)
0.406830 0.913504i \(-0.366634\pi\)
\(20\) 155.224 + 74.7517i 1.73545 + 0.835750i
\(21\) −11.1793 + 2.33281i −0.116168 + 0.0242410i
\(22\) 145.115 69.8835i 1.40630 0.677237i
\(23\) −7.98047 5.44099i −0.0723497 0.0493272i 0.526605 0.850110i \(-0.323465\pi\)
−0.598955 + 0.800783i \(0.704417\pi\)
\(24\) 29.4908 + 27.3635i 0.250824 + 0.232731i
\(25\) 38.6771 + 35.8871i 0.309417 + 0.287097i
\(26\) 289.061 + 197.079i 2.18037 + 1.48655i
\(27\) 29.7891 14.3457i 0.212330 0.102253i
\(28\) 7.01193 375.349i 0.0473261 2.53337i
\(29\) −194.397 93.6164i −1.24478 0.599453i −0.308670 0.951169i \(-0.599884\pi\)
−0.936107 + 0.351716i \(0.885598\pi\)
\(30\) −13.9330 24.1326i −0.0847933 0.146866i
\(31\) −126.916 + 219.824i −0.735313 + 1.27360i 0.219273 + 0.975664i \(0.429631\pi\)
−0.954586 + 0.297936i \(0.903702\pi\)
\(32\) −380.290 + 259.277i −2.10082 + 1.43232i
\(33\) −18.4705 2.78399i −0.0974336 0.0146857i
\(34\) 13.9232 61.0017i 0.0702299 0.307697i
\(35\) −49.1986 + 149.523i −0.237602 + 0.722116i
\(36\) 120.071 + 526.067i 0.555886 + 2.43550i
\(37\) −7.99614 106.701i −0.0355286 0.474096i −0.986384 0.164460i \(-0.947412\pi\)
0.950855 0.309636i \(-0.100207\pi\)
\(38\) −494.593 152.562i −2.11141 0.651284i
\(39\) −14.8231 37.7686i −0.0608614 0.155072i
\(40\) 529.878 163.446i 2.09453 0.646076i
\(41\) −266.513 334.197i −1.01518 1.27300i −0.961607 0.274432i \(-0.911510\pi\)
−0.0535737 0.998564i \(-0.517061\pi\)
\(42\) −35.1363 + 49.5222i −0.129087 + 0.181939i
\(43\) 100.325 125.803i 0.355799 0.446158i −0.571431 0.820650i \(-0.693612\pi\)
0.927230 + 0.374492i \(0.122183\pi\)
\(44\) 224.335 571.597i 0.768632 1.95844i
\(45\) 16.9077 225.617i 0.0560099 0.747400i
\(46\) −50.7822 + 7.65418i −0.162770 + 0.0245336i
\(47\) −196.194 + 182.042i −0.608891 + 0.564968i −0.923184 0.384358i \(-0.874423\pi\)
0.314293 + 0.949326i \(0.398232\pi\)
\(48\) 113.909 0.342528
\(49\) 340.842 38.4182i 0.993707 0.112006i
\(50\) 280.534 0.793470
\(51\) −5.31937 + 4.93566i −0.0146051 + 0.0135516i
\(52\) 1318.88 198.788i 3.51721 0.530135i
\(53\) −15.8842 + 211.960i −0.0411672 + 0.549338i 0.938047 + 0.346509i \(0.112633\pi\)
−0.979214 + 0.202830i \(0.934986\pi\)
\(54\) 64.2263 163.646i 0.161854 0.412396i
\(55\) −160.527 + 201.294i −0.393553 + 0.493500i
\(56\) −805.167 900.944i −1.92134 2.14989i
\(57\) 37.4257 + 46.9304i 0.0869677 + 0.109054i
\(58\) −1096.25 + 338.148i −2.48180 + 0.765535i
\(59\) 62.1204 + 158.280i 0.137074 + 0.349260i 0.982884 0.184225i \(-0.0589775\pi\)
−0.845810 + 0.533485i \(0.820882\pi\)
\(60\) −101.516 31.3136i −0.218428 0.0673760i
\(61\) −54.3988 725.902i −0.114181 1.52364i −0.700553 0.713601i \(-0.747063\pi\)
0.586371 0.810042i \(-0.300556\pi\)
\(62\) 300.319 + 1315.78i 0.615169 + 2.69523i
\(63\) −462.210 + 171.512i −0.924332 + 0.342991i
\(64\) −215.712 + 945.098i −0.421313 + 1.84589i
\(65\) −552.998 83.3510i −1.05524 0.159053i
\(66\) −82.0597 + 55.9473i −0.153043 + 0.104343i
\(67\) 261.524 452.972i 0.476869 0.825961i −0.522780 0.852468i \(-0.675105\pi\)
0.999649 + 0.0265071i \(0.00843845\pi\)
\(68\) −119.272 206.584i −0.212703 0.368412i
\(69\) 5.36606 + 2.58416i 0.00936229 + 0.00450864i
\(70\) 348.990 + 760.713i 0.595889 + 1.29889i
\(71\) 449.307 216.375i 0.751027 0.361676i −0.0188881 0.999822i \(-0.506013\pi\)
0.769915 + 0.638146i \(0.220298\pi\)
\(72\) 1434.96 + 978.336i 2.34877 + 1.60136i
\(73\) 838.099 + 777.643i 1.34373 + 1.24680i 0.943910 + 0.330202i \(0.107117\pi\)
0.399817 + 0.916595i \(0.369074\pi\)
\(74\) −417.048 386.964i −0.655147 0.607888i
\(75\) −26.8811 18.3272i −0.0413862 0.0282166i
\(76\) −1777.84 + 856.161i −2.68331 + 1.29222i
\(77\) 544.531 + 135.034i 0.805910 + 0.199851i
\(78\) −194.365 93.6010i −0.282147 0.135875i
\(79\) 412.211 + 713.971i 0.587056 + 1.01681i 0.994616 + 0.103632i \(0.0330463\pi\)
−0.407560 + 0.913178i \(0.633620\pi\)
\(80\) 785.034 1359.72i 1.09712 1.90026i
\(81\) 577.001 393.392i 0.791496 0.539633i
\(82\) −2247.39 338.739i −3.02662 0.456189i
\(83\) −90.0787 + 394.660i −0.119126 + 0.521923i 0.879790 + 0.475363i \(0.157683\pi\)
−0.998915 + 0.0465604i \(0.985174\pi\)
\(84\) 30.2205 + 229.510i 0.0392539 + 0.298114i
\(85\) 22.2565 + 97.5122i 0.0284007 + 0.124432i
\(86\) −63.9352 853.156i −0.0801664 1.06975i
\(87\) 127.135 + 39.2160i 0.156670 + 0.0483264i
\(88\) −722.041 1839.73i −0.874657 2.22859i
\(89\) 734.529 226.572i 0.874831 0.269850i 0.175354 0.984505i \(-0.443893\pi\)
0.699476 + 0.714656i \(0.253417\pi\)
\(90\) −750.039 940.520i −0.878457 1.10155i
\(91\) 337.379 + 1170.98i 0.388648 + 1.34892i
\(92\) −122.072 + 153.074i −0.138336 + 0.173468i
\(93\) 57.1829 145.700i 0.0637590 0.162455i
\(94\) −106.344 + 1419.06i −0.116687 + 1.55708i
\(95\) 818.132 123.314i 0.883564 0.133176i
\(96\) 208.049 193.042i 0.221187 0.205232i
\(97\) −424.107 −0.443934 −0.221967 0.975054i \(-0.571248\pi\)
−0.221967 + 0.975054i \(0.571248\pi\)
\(98\) 1189.54 1382.39i 1.22614 1.42492i
\(99\) −806.378 −0.818627
\(100\) 784.003 727.449i 0.784003 0.727449i
\(101\) −763.696 + 115.109i −0.752382 + 0.113403i −0.514026 0.857774i \(-0.671847\pi\)
−0.238356 + 0.971178i \(0.576608\pi\)
\(102\) −2.88329 + 38.4748i −0.00279890 + 0.0373487i
\(103\) 100.263 255.466i 0.0959145 0.244386i −0.874862 0.484373i \(-0.839048\pi\)
0.970776 + 0.239987i \(0.0771431\pi\)
\(104\) 2676.55 3356.29i 2.52363 3.16453i
\(105\) 16.2566 95.6920i 0.0151094 0.0889388i
\(106\) 704.638 + 883.588i 0.645665 + 0.809638i
\(107\) −677.364 + 208.939i −0.611993 + 0.188775i −0.585230 0.810867i \(-0.698996\pi\)
−0.0267623 + 0.999642i \(0.508520\pi\)
\(108\) −244.856 623.883i −0.218160 0.555863i
\(109\) 1457.40 + 449.550i 1.28068 + 0.395037i 0.859125 0.511766i \(-0.171009\pi\)
0.421554 + 0.906803i \(0.361485\pi\)
\(110\) 102.301 + 1365.11i 0.0886730 + 1.18326i
\(111\) 14.6818 + 64.3251i 0.0125544 + 0.0550042i
\(112\) −3406.29 319.346i −2.87379 0.269423i
\(113\) 180.997 793.001i 0.150680 0.660170i −0.842009 0.539464i \(-0.818627\pi\)
0.992688 0.120706i \(-0.0385160\pi\)
\(114\) 315.595 + 47.5682i 0.259282 + 0.0390805i
\(115\) 67.8285 46.2447i 0.0550003 0.0374986i
\(116\) −2186.82 + 3787.68i −1.75035 + 3.03170i
\(117\) −875.774 1516.88i −0.692011 1.19860i
\(118\) 814.539 + 392.261i 0.635461 + 0.306022i
\(119\) 172.906 132.681i 0.133195 0.102209i
\(120\) −308.067 + 148.357i −0.234354 + 0.112859i
\(121\) −341.540 232.858i −0.256604 0.174950i
\(122\) −2837.24 2632.57i −2.10550 1.95362i
\(123\) 193.218 + 179.280i 0.141641 + 0.131424i
\(124\) 4251.23 + 2898.44i 3.07880 + 2.09909i
\(125\) −1361.23 + 655.534i −0.974017 + 0.469062i
\(126\) −1181.26 + 2340.06i −0.835196 + 1.65452i
\(127\) 1836.73 + 884.525i 1.28334 + 0.618023i 0.946246 0.323449i \(-0.104842\pi\)
0.337092 + 0.941472i \(0.390557\pi\)
\(128\) 736.094 + 1274.95i 0.508298 + 0.880398i
\(129\) −49.6102 + 85.9274i −0.0338600 + 0.0586472i
\(130\) −2456.82 + 1675.03i −1.65752 + 1.13008i
\(131\) −1211.98 182.677i −0.808330 0.121836i −0.268141 0.963380i \(-0.586409\pi\)
−0.540189 + 0.841544i \(0.681647\pi\)
\(132\) −84.2544 + 369.143i −0.0555561 + 0.243407i
\(133\) −987.594 1508.31i −0.643874 0.983363i
\(134\) −618.840 2711.32i −0.398953 1.74793i
\(135\) 21.0004 + 280.231i 0.0133883 + 0.178655i
\(136\) −733.660 226.304i −0.462580 0.142687i
\(137\) −571.252 1455.53i −0.356243 0.907693i −0.990863 0.134869i \(-0.956939\pi\)
0.634620 0.772824i \(-0.281157\pi\)
\(138\) 30.2605 9.33413i 0.0186663 0.00575778i
\(139\) −241.954 303.401i −0.147642 0.185138i 0.702511 0.711673i \(-0.252062\pi\)
−0.850153 + 0.526535i \(0.823491\pi\)
\(140\) 2947.91 + 1220.99i 1.77960 + 0.737090i
\(141\) 102.897 129.029i 0.0614575 0.0770653i
\(142\) 968.721 2468.26i 0.572488 1.45867i
\(143\) −148.952 + 1987.63i −0.0871051 + 1.16234i
\(144\) 4862.52 732.906i 2.81396 0.424136i
\(145\) 1344.30 1247.33i 0.769919 0.714381i
\(146\) 6078.93 3.44586
\(147\) −204.294 + 54.7497i −0.114625 + 0.0307189i
\(148\) −2168.95 −1.20464
\(149\) −480.592 + 445.924i −0.264239 + 0.245178i −0.801154 0.598458i \(-0.795780\pi\)
0.536915 + 0.843637i \(0.319590\pi\)
\(150\) −171.053 + 25.7821i −0.0931094 + 0.0140340i
\(151\) −22.6940 + 302.831i −0.0122306 + 0.163205i 0.987744 + 0.156082i \(0.0498865\pi\)
−0.999975 + 0.00712324i \(0.997733\pi\)
\(152\) −2320.30 + 5912.04i −1.23817 + 3.15480i
\(153\) −195.315 + 244.918i −0.103205 + 0.129415i
\(154\) 2610.73 1442.97i 1.36610 0.755052i
\(155\) −1345.11 1686.71i −0.697044 0.874066i
\(156\) −785.902 + 242.419i −0.403350 + 0.124417i
\(157\) −159.130 405.457i −0.0808915 0.206108i 0.884706 0.466149i \(-0.154359\pi\)
−0.965598 + 0.260041i \(0.916264\pi\)
\(158\) 4188.71 + 1292.05i 2.10909 + 0.650567i
\(159\) −9.79464 130.700i −0.00488532 0.0651900i
\(160\) −870.489 3813.86i −0.430114 1.88445i
\(161\) −153.220 92.3196i −0.0750026 0.0451913i
\(162\) 826.244 3620.01i 0.400715 1.75565i
\(163\) −1846.02 278.243i −0.887065 0.133704i −0.310325 0.950631i \(-0.600438\pi\)
−0.576741 + 0.816927i \(0.695676\pi\)
\(164\) −7159.12 + 4881.00i −3.40874 + 2.32404i
\(165\) 79.3800 137.490i 0.0374529 0.0648703i
\(166\) 1076.19 + 1864.01i 0.503183 + 0.871538i
\(167\) −2383.15 1147.67i −1.10428 0.531791i −0.209275 0.977857i \(-0.567110\pi\)
−0.895000 + 0.446066i \(0.852825\pi\)
\(168\) 573.743 + 475.344i 0.263484 + 0.218295i
\(169\) −1921.29 + 925.245i −0.874507 + 0.421140i
\(170\) 439.399 + 299.577i 0.198237 + 0.135156i
\(171\) 1899.58 + 1762.55i 0.849499 + 0.788220i
\(172\) −2390.99 2218.51i −1.05995 0.983487i
\(173\) −534.524 364.432i −0.234908 0.160158i 0.440145 0.897927i \(-0.354927\pi\)
−0.675053 + 0.737769i \(0.735879\pi\)
\(174\) 637.350 306.932i 0.277686 0.133727i
\(175\) 752.462 + 623.413i 0.325033 + 0.269289i
\(176\) −5041.72 2427.97i −2.15929 1.03986i
\(177\) −52.4238 90.8007i −0.0222622 0.0385593i
\(178\) 2043.53 3539.50i 0.860502 1.49043i
\(179\) 558.065 380.482i 0.233027 0.158875i −0.441178 0.897420i \(-0.645439\pi\)
0.674204 + 0.738545i \(0.264487\pi\)
\(180\) −4534.97 683.537i −1.87787 0.283043i
\(181\) −279.592 + 1224.97i −0.114817 + 0.503047i 0.884515 + 0.466512i \(0.154489\pi\)
−0.999332 + 0.0365357i \(0.988368\pi\)
\(182\) 5549.79 + 3343.91i 2.26032 + 1.36191i
\(183\) 99.8822 + 437.612i 0.0403470 + 0.176772i
\(184\) 47.0920 + 628.399i 0.0188678 + 0.251773i
\(185\) 869.026 + 268.059i 0.345362 + 0.106530i
\(186\) −304.041 774.685i −0.119857 0.305391i
\(187\) 340.644 105.075i 0.133211 0.0410900i
\(188\) 3382.56 + 4241.59i 1.31223 + 1.64548i
\(189\) 535.931 296.213i 0.206261 0.114002i
\(190\) 2742.82 3439.39i 1.04729 1.31326i
\(191\) −1202.17 + 3063.09i −0.455425 + 1.16041i 0.500223 + 0.865896i \(0.333251\pi\)
−0.955649 + 0.294509i \(0.904844\pi\)
\(192\) 44.6707 596.089i 0.0167908 0.224057i
\(193\) 111.790 16.8496i 0.0416933 0.00628426i −0.128162 0.991753i \(-0.540908\pi\)
0.169856 + 0.985469i \(0.445670\pi\)
\(194\) −1653.02 + 1533.77i −0.611751 + 0.567622i
\(195\) 344.845 0.126640
\(196\) −260.265 6947.91i −0.0948489 2.53204i
\(197\) 2012.16 0.727718 0.363859 0.931454i \(-0.381459\pi\)
0.363859 + 0.931454i \(0.381459\pi\)
\(198\) −3142.97 + 2916.25i −1.12809 + 1.04671i
\(199\) 2121.11 319.706i 0.755587 0.113886i 0.240058 0.970759i \(-0.422834\pi\)
0.515529 + 0.856872i \(0.327596\pi\)
\(200\) 257.243 3432.67i 0.0909490 1.21363i
\(201\) −117.832 + 300.230i −0.0413493 + 0.105356i
\(202\) −2560.32 + 3210.54i −0.891800 + 1.11828i
\(203\) −3691.86 1529.13i −1.27644 0.528688i
\(204\) 91.7105 + 115.001i 0.0314756 + 0.0394692i
\(205\) 3471.66 1070.87i 1.18279 0.364841i
\(206\) −533.098 1358.31i −0.180304 0.459408i
\(207\) 245.692 + 75.7859i 0.0824965 + 0.0254468i
\(208\) −908.339 12120.9i −0.302798 4.04056i
\(209\) −656.180 2874.91i −0.217172 0.951493i
\(210\) −282.705 431.764i −0.0928977 0.141879i
\(211\) −962.506 + 4217.02i −0.314036 + 1.37588i 0.533793 + 0.845615i \(0.320766\pi\)
−0.847830 + 0.530268i \(0.822091\pi\)
\(212\) 4260.46 + 642.160i 1.38023 + 0.208037i
\(213\) −254.075 + 173.225i −0.0817321 + 0.0557240i
\(214\) −1884.49 + 3264.04i −0.601969 + 1.04264i
\(215\) 683.804 + 1184.38i 0.216907 + 0.375694i
\(216\) −1943.51 935.944i −0.612218 0.294828i
\(217\) −2118.45 + 4196.63i −0.662717 + 1.31284i
\(218\) 7306.22 3518.49i 2.26991 1.09313i
\(219\) −582.491 397.136i −0.179731 0.122539i
\(220\) 3825.76 + 3549.78i 1.17242 + 1.08785i
\(221\) 567.616 + 526.671i 0.172769 + 0.160306i
\(222\) 289.855 + 197.620i 0.0876296 + 0.0597449i
\(223\) 5560.74 2677.91i 1.66984 0.804153i 0.671858 0.740680i \(-0.265497\pi\)
0.997984 0.0634731i \(-0.0202177\pi\)
\(224\) −6762.63 + 5189.37i −2.01717 + 1.54790i
\(225\) −1265.42 609.392i −0.374938 0.180561i
\(226\) −2162.41 3745.40i −0.636466 1.10239i
\(227\) 1285.51 2226.56i 0.375868 0.651023i −0.614588 0.788848i \(-0.710678\pi\)
0.990457 + 0.137825i \(0.0440112\pi\)
\(228\) 1005.33 685.426i 0.292017 0.199094i
\(229\) 2464.24 + 371.424i 0.711097 + 0.107181i 0.494623 0.869108i \(-0.335306\pi\)
0.216474 + 0.976288i \(0.430544\pi\)
\(230\) 97.1279 425.545i 0.0278453 0.121998i
\(231\) −344.433 32.2912i −0.0981039 0.00919743i
\(232\) 3132.41 + 13724.0i 0.886434 + 3.88372i
\(233\) 256.130 + 3417.82i 0.0720157 + 0.960982i 0.909818 + 0.415008i \(0.136221\pi\)
−0.837802 + 0.545974i \(0.816160\pi\)
\(234\) −8899.23 2745.05i −2.48616 0.766878i
\(235\) −831.062 2117.51i −0.230692 0.587793i
\(236\) 3293.55 1015.92i 0.908439 0.280216i
\(237\) −316.958 397.453i −0.0868720 0.108934i
\(238\) 194.086 1142.45i 0.0528601 0.311152i
\(239\) −2584.40 + 3240.74i −0.699461 + 0.877097i −0.996983 0.0776184i \(-0.975268\pi\)
0.297522 + 0.954715i \(0.403840\pi\)
\(240\) −353.704 + 901.223i −0.0951312 + 0.242390i
\(241\) 172.576 2302.87i 0.0461270 0.615522i −0.925461 0.378843i \(-0.876322\pi\)
0.971588 0.236679i \(-0.0760589\pi\)
\(242\) −2173.32 + 327.576i −0.577300 + 0.0870139i
\(243\) −970.071 + 900.094i −0.256091 + 0.237618i
\(244\) −14755.7 −3.87145
\(245\) −754.407 + 2815.96i −0.196724 + 0.734306i
\(246\) 1401.46 0.363226
\(247\) 4695.37 4356.67i 1.20955 1.12230i
\(248\) 16375.5 2468.21i 4.19293 0.631983i
\(249\) 18.6539 248.919i 0.00474756 0.0633518i
\(250\) −2934.86 + 7477.90i −0.742467 + 1.89177i
\(251\) −1224.11 + 1534.98i −0.307828 + 0.386004i −0.911549 0.411192i \(-0.865113\pi\)
0.603721 + 0.797196i \(0.293684\pi\)
\(252\) 2766.75 + 9602.83i 0.691621 + 2.40048i
\(253\) −182.426 228.755i −0.0453321 0.0568447i
\(254\) 10357.8 3194.96i 2.55868 0.789249i
\(255\) −22.5324 57.4117i −0.00553347 0.0140991i
\(256\) 69.1828 + 21.3401i 0.0168903 + 0.00520998i
\(257\) −257.824 3440.42i −0.0625783 0.835050i −0.936877 0.349660i \(-0.886297\pi\)
0.874298 0.485389i \(-0.161322\pi\)
\(258\) 117.392 + 514.328i 0.0283275 + 0.124111i
\(259\) −258.702 1964.71i −0.0620654 0.471357i
\(260\) −2522.53 + 11051.9i −0.601695 + 2.63620i
\(261\) 5679.43 + 856.037i 1.34693 + 0.203017i
\(262\) −5384.51 + 3671.10i −1.26968 + 0.865653i
\(263\) −1202.20 + 2082.27i −0.281866 + 0.488207i −0.971844 0.235623i \(-0.924287\pi\)
0.689978 + 0.723830i \(0.257620\pi\)
\(264\) 609.335 + 1055.40i 0.142053 + 0.246043i
\(265\) −1627.66 783.839i −0.377307 0.181701i
\(266\) −9304.06 2307.24i −2.14462 0.531827i
\(267\) −427.049 + 205.656i −0.0978839 + 0.0471384i
\(268\) −8760.13 5972.56i −1.99668 1.36131i
\(269\) −2463.06 2285.38i −0.558273 0.518001i 0.349794 0.936827i \(-0.386252\pi\)
−0.908067 + 0.418825i \(0.862442\pi\)
\(270\) 1095.30 + 1016.29i 0.246881 + 0.229072i
\(271\) 593.502 + 404.643i 0.133036 + 0.0907022i 0.628009 0.778206i \(-0.283870\pi\)
−0.494974 + 0.868908i \(0.664822\pi\)
\(272\) −1958.61 + 943.215i −0.436610 + 0.210260i
\(273\) −313.331 682.985i −0.0694638 0.151414i
\(274\) −7490.41 3607.19i −1.65150 0.795323i
\(275\) 799.141 + 1384.15i 0.175236 + 0.303518i
\(276\) 60.3643 104.554i 0.0131649 0.0228022i
\(277\) −1599.67 + 1090.64i −0.346986 + 0.236571i −0.724254 0.689533i \(-0.757816\pi\)
0.377269 + 0.926104i \(0.376863\pi\)
\(278\) −2040.29 307.525i −0.440175 0.0663457i
\(279\) 1503.56 6587.51i 0.322637 1.41356i
\(280\) 9628.24 3572.75i 2.05499 0.762544i
\(281\) 880.246 + 3856.61i 0.186872 + 0.818740i 0.978253 + 0.207417i \(0.0665056\pi\)
−0.791381 + 0.611324i \(0.790637\pi\)
\(282\) −65.5748 875.034i −0.0138472 0.184778i
\(283\) 444.140 + 136.999i 0.0932910 + 0.0287765i 0.341049 0.940045i \(-0.389218\pi\)
−0.247758 + 0.968822i \(0.579694\pi\)
\(284\) −3693.14 9409.98i −0.771647 1.96612i
\(285\) −487.515 + 150.379i −0.101326 + 0.0312549i
\(286\) 6607.67 + 8285.75i 1.36615 + 1.71310i
\(287\) −5275.30 5902.81i −1.08499 1.21405i
\(288\) 7639.10 9579.13i 1.56298 1.95992i
\(289\) −1744.33 + 4444.47i −0.355043 + 0.904635i
\(290\) 728.659 9723.28i 0.147546 1.96887i
\(291\) 258.595 38.9770i 0.0520932 0.00785179i
\(292\) 16988.7 15763.2i 3.40475 3.15915i
\(293\) 2528.38 0.504127 0.252064 0.967711i \(-0.418891\pi\)
0.252064 + 0.967711i \(0.418891\pi\)
\(294\) −598.263 + 952.220i −0.118678 + 0.188893i
\(295\) −1445.17 −0.285224
\(296\) −5117.39 + 4748.24i −1.00487 + 0.932385i
\(297\) 990.386 149.277i 0.193495 0.0291647i
\(298\) −260.498 + 3476.10i −0.0506384 + 0.675722i
\(299\) 232.187 591.604i 0.0449088 0.114426i
\(300\) −411.183 + 515.608i −0.0791323 + 0.0992287i
\(301\) 1724.42 2430.46i 0.330213 0.465413i
\(302\) 1006.73 + 1262.40i 0.191823 + 0.240539i
\(303\) 455.077 140.373i 0.0862822 0.0266145i
\(304\) 6569.78 + 16739.5i 1.23948 + 3.15815i
\(305\) 5912.10 + 1823.64i 1.10992 + 0.342365i
\(306\) 124.471 + 1660.95i 0.0232534 + 0.310295i
\(307\) 237.179 + 1039.15i 0.0440928 + 0.193183i 0.992178 0.124834i \(-0.0398400\pi\)
−0.948085 + 0.318018i \(0.896983\pi\)
\(308\) 3554.41 10802.5i 0.657570 1.99847i
\(309\) −37.6561 + 164.982i −0.00693263 + 0.0303738i
\(310\) −11342.7 1709.64i −2.07814 0.313229i
\(311\) 5399.02 3680.99i 0.984406 0.671157i 0.0397468 0.999210i \(-0.487345\pi\)
0.944659 + 0.328053i \(0.106392\pi\)
\(312\) −1323.55 + 2292.45i −0.240164 + 0.415976i
\(313\) −778.589 1348.56i −0.140602 0.243530i 0.787121 0.616798i \(-0.211570\pi\)
−0.927724 + 0.373268i \(0.878237\pi\)
\(314\) −2086.56 1004.83i −0.375004 0.180593i
\(315\) 78.2638 4189.47i 0.0139989 0.749365i
\(316\) 15056.5 7250.83i 2.68036 1.29079i
\(317\) −3406.00 2322.17i −0.603470 0.411439i 0.222678 0.974892i \(-0.428520\pi\)
−0.826148 + 0.563453i \(0.809473\pi\)
\(318\) −510.851 474.000i −0.0900852 0.0835869i
\(319\) −4791.24 4445.62i −0.840934 0.780273i
\(320\) −6807.59 4641.34i −1.18924 0.810808i
\(321\) 393.814 189.651i 0.0684752 0.0329759i
\(322\) −931.067 + 194.288i −0.161138 + 0.0336250i
\(323\) −1032.12 497.043i −0.177798 0.0856229i
\(324\) −7077.91 12259.3i −1.21363 2.10207i
\(325\) −1735.83 + 3006.54i −0.296266 + 0.513147i
\(326\) −8201.39 + 5591.61i −1.39335 + 0.949972i
\(327\) −929.953 140.168i −0.157268 0.0237043i
\(328\) −6205.68 + 27188.8i −1.04467 + 4.57699i
\(329\) −3438.74 + 3569.96i −0.576242 + 0.598232i
\(330\) −187.836 822.963i −0.0313334 0.137281i
\(331\) 389.665 + 5199.71i 0.0647067 + 0.863451i 0.931257 + 0.364362i \(0.118713\pi\)
−0.866551 + 0.499089i \(0.833668\pi\)
\(332\) 7841.14 + 2418.67i 1.29620 + 0.399825i
\(333\) 1040.61 + 2651.43i 0.171246 + 0.436329i
\(334\) −13439.2 + 4145.44i −2.20167 + 0.679126i
\(335\) 2771.75 + 3475.66i 0.452050 + 0.566853i
\(336\) 2106.30 118.332i 0.341989 0.0192129i
\(337\) 337.953 423.779i 0.0546275 0.0685007i −0.753767 0.657142i \(-0.771765\pi\)
0.808395 + 0.588641i \(0.200337\pi\)
\(338\) −4142.37 + 10554.6i −0.666613 + 1.69850i
\(339\) −37.4817 + 500.159i −0.00600510 + 0.0801325i
\(340\) 2004.81 302.176i 0.319782 0.0481994i
\(341\) −5636.56 + 5229.96i −0.895122 + 0.830552i
\(342\) 13778.1 2.17846
\(343\) 6262.63 1064.47i 0.985860 0.167569i
\(344\) −10498.0 −1.64539
\(345\) −37.1077 + 34.4309i −0.00579076 + 0.00537304i
\(346\) −3401.34 + 512.670i −0.528489 + 0.0796569i
\(347\) 342.718 4573.25i 0.0530203 0.707507i −0.905838 0.423623i \(-0.860758\pi\)
0.958859 0.283884i \(-0.0916230\pi\)
\(348\) 985.291 2510.48i 0.151773 0.386712i
\(349\) −1824.44 + 2287.77i −0.279828 + 0.350893i −0.901806 0.432142i \(-0.857758\pi\)
0.621978 + 0.783035i \(0.286329\pi\)
\(350\) 5187.38 291.427i 0.792221 0.0445069i
\(351\) 1356.42 + 1700.90i 0.206269 + 0.258653i
\(352\) −13323.2 + 4109.65i −2.01741 + 0.622287i
\(353\) 840.751 + 2142.20i 0.126767 + 0.322996i 0.980141 0.198303i \(-0.0635429\pi\)
−0.853374 + 0.521299i \(0.825448\pi\)
\(354\) −532.708 164.319i −0.0799805 0.0246707i
\(355\) 316.747 + 4226.70i 0.0473555 + 0.631915i
\(356\) −3467.21 15190.8i −0.516185 2.26155i
\(357\) −93.2337 + 96.7916i −0.0138220 + 0.0143495i
\(358\) 799.129 3501.21i 0.117976 0.516885i
\(359\) 12056.2 + 1817.17i 1.77242 + 0.267150i 0.952328 0.305077i \(-0.0986824\pi\)
0.820095 + 0.572227i \(0.193920\pi\)
\(360\) −12196.1 + 8315.18i −1.78554 + 1.21736i
\(361\) −1308.62 + 2266.59i −0.190788 + 0.330455i
\(362\) 3340.34 + 5785.64i 0.484985 + 0.840018i
\(363\) 229.651 + 110.594i 0.0332054 + 0.0159909i
\(364\) 24181.0 5045.90i 3.48194 0.726586i
\(365\) −8754.96 + 4216.17i −1.25549 + 0.604615i
\(366\) 1971.92 + 1344.43i 0.281623 + 0.192007i
\(367\) −3804.56 3530.12i −0.541135 0.502100i 0.361579 0.932341i \(-0.382238\pi\)
−0.902714 + 0.430242i \(0.858428\pi\)
\(368\) 1307.95 + 1213.60i 0.185277 + 0.171912i
\(369\) 9401.55 + 6409.87i 1.32636 + 0.904294i
\(370\) 4356.58 2098.02i 0.612129 0.294786i
\(371\) −73.5263 + 3935.87i −0.0102892 + 0.550783i
\(372\) −2858.52 1376.59i −0.398407 0.191863i
\(373\) −3056.20 5293.49i −0.424246 0.734816i 0.572104 0.820181i \(-0.306128\pi\)
−0.996350 + 0.0853656i \(0.972794\pi\)
\(374\) 947.706 1641.48i 0.131029 0.226948i
\(375\) 769.751 524.808i 0.105999 0.0722692i
\(376\) 17266.4 + 2602.49i 2.36821 + 0.356950i
\(377\) 3159.13 13841.0i 0.431574 1.89085i
\(378\) 1017.62 3092.72i 0.138467 0.420826i
\(379\) −1583.14 6936.19i −0.214566 0.940074i −0.961420 0.275086i \(-0.911294\pi\)
0.746854 0.664988i \(-0.231563\pi\)
\(380\) −1253.32 16724.4i −0.169194 2.25774i
\(381\) −1201.22 370.528i −0.161524 0.0498234i
\(382\) 6391.96 + 16286.4i 0.856129 + 2.18138i
\(383\) 11575.9 3570.69i 1.54439 0.476380i 0.598567 0.801073i \(-0.295737\pi\)
0.945820 + 0.324692i \(0.105261\pi\)
\(384\) −565.999 709.740i −0.0752175 0.0943197i
\(385\) −2759.21 + 3888.91i −0.365253 + 0.514798i
\(386\) 374.780 469.960i 0.0494192 0.0619697i
\(387\) −1564.88 + 3987.25i −0.205548 + 0.523729i
\(388\) −642.444 + 8572.82i −0.0840597 + 1.12170i
\(389\) −1331.72 + 200.725i −0.173576 + 0.0261623i −0.235255 0.971934i \(-0.575592\pi\)
0.0616793 + 0.998096i \(0.480354\pi\)
\(390\) 1344.08 1247.13i 0.174513 0.161925i
\(391\) −113.665 −0.0147015
\(392\) −15824.4 15823.0i −2.03890 2.03873i
\(393\) 755.782 0.0970081
\(394\) 7842.67 7276.94i 1.00281 0.930474i
\(395\) −6928.76 + 1044.34i −0.882592 + 0.133029i
\(396\) −1221.51 + 16300.0i −0.155009 + 2.06845i
\(397\) −1178.71 + 3003.30i −0.149012 + 0.379676i −0.985817 0.167825i \(-0.946326\pi\)
0.836805 + 0.547501i \(0.184421\pi\)
\(398\) 7111.12 8917.06i 0.895598 1.12304i
\(399\) 740.795 + 828.915i 0.0929478 + 0.104004i
\(400\) −6076.91 7620.21i −0.759614 0.952526i
\(401\) 3160.55 974.900i 0.393592 0.121407i −0.0916408 0.995792i \(-0.529211\pi\)
0.485233 + 0.874385i \(0.338735\pi\)
\(402\) 626.511 + 1596.33i 0.0777302 + 0.198053i
\(403\) −15959.7 4922.93i −1.97273 0.608508i
\(404\) 1169.93 + 15611.6i 0.144074 + 1.92254i
\(405\) 1320.76 + 5786.64i 0.162048 + 0.709977i
\(406\) −19919.6 + 7391.54i −2.43495 + 0.903537i
\(407\) 721.258 3160.04i 0.0878413 0.384858i
\(408\) 468.141 + 70.5608i 0.0568049 + 0.00856197i
\(409\) −548.521 + 373.976i −0.0663145 + 0.0452125i −0.596024 0.802967i \(-0.703254\pi\)
0.529709 + 0.848179i \(0.322301\pi\)
\(410\) 9658.51 16729.0i 1.16341 2.01509i
\(411\) 482.083 + 834.993i 0.0578575 + 0.100212i
\(412\) −5012.06 2413.68i −0.599336 0.288625i
\(413\) 1313.10 + 2862.24i 0.156449 + 0.341021i
\(414\) 1231.70 593.153i 0.146219 0.0704152i
\(415\) −2842.76 1938.16i −0.336255 0.229254i
\(416\) −22200.4 20599.0i −2.61650 2.42776i
\(417\) 175.413 + 162.759i 0.0205995 + 0.0191136i
\(418\) −12954.6 8832.31i −1.51586 1.03350i
\(419\) −5117.54 + 2464.48i −0.596679 + 0.287345i −0.707745 0.706468i \(-0.750288\pi\)
0.111067 + 0.993813i \(0.464573\pi\)
\(420\) −1909.67 473.564i −0.221863 0.0550180i
\(421\) 10831.5 + 5216.19i 1.25391 + 0.603852i 0.938558 0.345122i \(-0.112163\pi\)
0.315354 + 0.948974i \(0.397877\pi\)
\(422\) 11499.2 + 19917.3i 1.32648 + 2.29753i
\(423\) 3562.26 6170.02i 0.409464 0.709212i
\(424\) 11457.9 7811.85i 1.31237 0.894757i
\(425\) 613.965 + 92.5403i 0.0700745 + 0.0105620i
\(426\) −363.826 + 1594.03i −0.0413790 + 0.181293i
\(427\) −1759.98 13366.2i −0.199465 1.51484i
\(428\) 3197.37 + 14008.6i 0.361100 + 1.58208i
\(429\) −91.8482 1225.63i −0.0103368 0.137935i
\(430\) 6948.52 + 2143.33i 0.779273 + 0.240374i
\(431\) 2950.14 + 7516.85i 0.329706 + 0.840078i 0.995572 + 0.0940061i \(0.0299673\pi\)
−0.665865 + 0.746072i \(0.731937\pi\)
\(432\) −5836.42 + 1800.30i −0.650011 + 0.200502i
\(433\) 3610.99 + 4528.04i 0.400769 + 0.502549i 0.940737 0.339137i \(-0.110135\pi\)
−0.539968 + 0.841686i \(0.681564\pi\)
\(434\) 6920.09 + 24018.3i 0.765381 + 2.65648i
\(435\) −705.042 + 884.094i −0.0777107 + 0.0974461i
\(436\) 11294.8 28778.7i 1.24065 3.16112i
\(437\) −70.2645 + 937.615i −0.00769155 + 0.102637i
\(438\) −3706.57 + 558.676i −0.404354 + 0.0609465i
\(439\) −6590.69 + 6115.27i −0.716530 + 0.664842i −0.951671 0.307119i \(-0.900635\pi\)
0.235142 + 0.971961i \(0.424445\pi\)
\(440\) 16797.6 1.81999
\(441\) −8368.59 + 3651.60i −0.903638 + 0.394299i
\(442\) 4117.06 0.443051
\(443\) −3415.28 + 3168.91i −0.366286 + 0.339864i −0.841746 0.539874i \(-0.818472\pi\)
0.475460 + 0.879737i \(0.342282\pi\)
\(444\) 1322.50 199.334i 0.141358 0.0213063i
\(445\) −488.230 + 6514.98i −0.0520097 + 0.694021i
\(446\) 11989.1 30547.8i 1.27287 3.24323i
\(447\) 252.054 316.066i 0.0266706 0.0334439i
\(448\) −3006.97 + 17700.0i −0.317111 + 1.86662i
\(449\) 6766.70 + 8485.17i 0.711225 + 0.891848i 0.997806 0.0662079i \(-0.0210901\pi\)
−0.286581 + 0.958056i \(0.592519\pi\)
\(450\) −7135.98 + 2201.16i −0.747541 + 0.230586i
\(451\) −4730.67 12053.5i −0.493921 1.25849i
\(452\) −15755.4 4859.90i −1.63954 0.505731i
\(453\) −13.9938 186.734i −0.00145140 0.0193676i
\(454\) −3041.88 13327.3i −0.314455 1.37772i
\(455\) −10312.1 966.782i −1.06250 0.0996119i
\(456\) 871.446 3818.05i 0.0894938 0.392098i
\(457\) −18198.4 2742.96i −1.86276 0.280767i −0.881321 0.472519i \(-0.843345\pi\)
−0.981443 + 0.191752i \(0.938583\pi\)
\(458\) 10947.9 7464.18i 1.11695 0.761524i
\(459\) 194.545 336.962i 0.0197834 0.0342659i
\(460\) −832.033 1441.12i −0.0843342 0.146071i
\(461\) −10438.8 5027.05i −1.05462 0.507881i −0.175504 0.984479i \(-0.556155\pi\)
−0.879121 + 0.476598i \(0.841870\pi\)
\(462\) −1459.25 + 1119.77i −0.146949 + 0.112763i
\(463\) −118.716 + 57.1705i −0.0119162 + 0.00573853i −0.439832 0.898080i \(-0.644962\pi\)
0.427916 + 0.903818i \(0.359248\pi\)
\(464\) 32932.1 + 22452.7i 3.29490 + 2.24642i
\(465\) 975.183 + 904.838i 0.0972538 + 0.0902384i
\(466\) 13358.8 + 12395.1i 1.32797 + 1.23217i
\(467\) −7685.77 5240.07i −0.761574 0.519232i 0.119142 0.992877i \(-0.461986\pi\)
−0.880716 + 0.473645i \(0.842938\pi\)
\(468\) −31988.6 + 15404.9i −3.15956 + 1.52157i
\(469\) 4365.30 8647.63i 0.429788 0.851408i
\(470\) −10897.1 5247.78i −1.06946 0.515025i
\(471\) 134.291 + 232.599i 0.0131376 + 0.0227550i
\(472\) 5546.69 9607.16i 0.540905 0.936875i
\(473\) 4027.34 2745.79i 0.391495 0.266917i
\(474\) −2672.77 402.855i −0.258997 0.0390374i
\(475\) 1142.90 5007.37i 0.110400 0.483692i
\(476\) −2420.07 3696.07i −0.233033 0.355902i
\(477\) −1259.06 5516.28i −0.120856 0.529504i
\(478\) 1647.00 + 21977.7i 0.157598 + 2.10300i
\(479\) 8134.70 + 2509.22i 0.775958 + 0.239351i 0.657345 0.753589i \(-0.271679\pi\)
0.118612 + 0.992941i \(0.462155\pi\)
\(480\) 881.280 + 2245.46i 0.0838016 + 0.213523i
\(481\) 6727.70 2075.22i 0.637748 0.196719i
\(482\) −7655.63 9599.86i −0.723453 0.907182i
\(483\) 101.909 + 42.2095i 0.00960044 + 0.00397640i
\(484\) −5224.32 + 6551.08i −0.490638 + 0.615241i
\(485\) 1316.92 3355.45i 0.123295 0.314150i
\(486\) −525.813 + 7016.48i −0.0490768 + 0.654885i
\(487\) 3373.93 508.538i 0.313937 0.0473184i 0.00981601 0.999952i \(-0.496875\pi\)
0.304121 + 0.952633i \(0.401637\pi\)
\(488\) −34814.3 + 32302.9i −3.22944 + 2.99649i
\(489\) 1151.17 0.106457
\(490\) 7243.45 + 13703.9i 0.667808 + 1.26343i
\(491\) −10192.8 −0.936855 −0.468427 0.883502i \(-0.655179\pi\)
−0.468427 + 0.883502i \(0.655179\pi\)
\(492\) 3916.62 3634.09i 0.358892 0.333003i
\(493\) −2510.75 + 378.435i −0.229368 + 0.0345717i
\(494\) 2545.06 33961.4i 0.231797 3.09311i
\(495\) 2503.92 6379.89i 0.227360 0.579303i
\(496\) 29235.4 36660.0i 2.64659 3.31872i
\(497\) 8083.41 4467.76i 0.729558 0.403233i
\(498\) −827.504 1037.66i −0.0744605 0.0933705i
\(499\) 12632.4 3896.59i 1.13328 0.349570i 0.329298 0.944226i \(-0.393188\pi\)
0.803980 + 0.594656i \(0.202712\pi\)
\(500\) 11188.8 + 28508.7i 1.00076 + 2.54989i
\(501\) 1558.58 + 480.758i 0.138986 + 0.0428716i
\(502\) 780.102 + 10409.7i 0.0693579 + 0.925517i
\(503\) 4732.19 + 20733.1i 0.419479 + 1.83786i 0.535401 + 0.844598i \(0.320161\pi\)
−0.115922 + 0.993258i \(0.536982\pi\)
\(504\) 27550.2 + 16599.8i 2.43489 + 1.46709i
\(505\) 1460.67 6399.63i 0.128711 0.563920i
\(506\) −1538.32 231.864i −0.135151 0.0203708i
\(507\) 1086.46 740.733i 0.0951700 0.0648858i
\(508\) 20661.9 35787.5i 1.80458 3.12562i
\(509\) −9576.31 16586.7i −0.833915 1.44438i −0.894911 0.446244i \(-0.852761\pi\)
0.0609965 0.998138i \(-0.480572\pi\)
\(510\) −295.451 142.282i −0.0256525 0.0123536i
\(511\) 16305.2 + 13508.8i 1.41155 + 1.16946i
\(512\) −10264.3 + 4943.04i −0.885984 + 0.426667i
\(513\) −2659.32 1813.10i −0.228873 0.156043i
\(514\) −13447.1 12477.1i −1.15394 1.07070i
\(515\) 1709.86 + 1586.52i 0.146302 + 0.135748i
\(516\) 1661.77 + 1132.98i 0.141774 + 0.0966598i
\(517\) −7304.59 + 3517.70i −0.621384 + 0.299243i
\(518\) −8113.67 6722.16i −0.688213 0.570183i
\(519\) 359.413 + 173.084i 0.0303979 + 0.0146388i
\(520\) 18243.2 + 31598.1i 1.53849 + 2.66474i
\(521\) −10517.8 + 18217.4i −0.884440 + 1.53190i −0.0380863 + 0.999274i \(0.512126\pi\)
−0.846354 + 0.532621i \(0.821207\pi\)
\(522\) 25232.2 17203.0i 2.11568 1.44244i
\(523\) −20599.2 3104.83i −1.72226 0.259588i −0.787867 0.615845i \(-0.788815\pi\)
−0.934388 + 0.356257i \(0.884053\pi\)
\(524\) −5528.52 + 24222.0i −0.460906 + 2.01936i
\(525\) −516.101 310.966i −0.0429038 0.0258508i
\(526\) 2844.75 + 12463.7i 0.235812 + 1.03316i
\(527\) 223.225 + 2978.73i 0.0184513 + 0.246215i
\(528\) 3297.28 + 1017.08i 0.271772 + 0.0838307i
\(529\) −4411.02 11239.1i −0.362540 0.923736i
\(530\) −9178.76 + 2831.27i −0.752264 + 0.232043i
\(531\) −2822.08 3538.78i −0.230636 0.289209i
\(532\) −31984.8 + 17678.2i −2.60661 + 1.44069i
\(533\) 17536.2 21989.7i 1.42510 1.78702i
\(534\) −920.732 + 2345.99i −0.0746142 + 0.190114i
\(535\) 450.233 6007.94i 0.0363837 0.485506i
\(536\) −33743.6 + 5086.03i −2.71922 + 0.409856i
\(537\) −305.307 + 283.284i −0.0245344 + 0.0227646i
\(538\) −17865.2 −1.43164
\(539\) 10209.3 + 1931.25i 0.815851 + 0.154332i
\(540\) 5696.34 0.453947
\(541\) 7176.50 6658.82i 0.570318 0.529177i −0.341441 0.939903i \(-0.610915\pi\)
0.911759 + 0.410726i \(0.134725\pi\)
\(542\) 3776.64 569.236i 0.299300 0.0451122i
\(543\) 57.8992 772.612i 0.00457586 0.0610607i
\(544\) −1978.84 + 5041.99i −0.155959 + 0.397378i
\(545\) −8082.19 + 10134.8i −0.635235 + 0.796560i
\(546\) −3691.25 1528.87i −0.289324 0.119835i
\(547\) −8626.98 10817.9i −0.674338 0.845594i 0.320481 0.947255i \(-0.396156\pi\)
−0.994819 + 0.101661i \(0.967584\pi\)
\(548\) −30287.1 + 9342.32i −2.36095 + 0.728256i
\(549\) 7079.41 + 18038.0i 0.550349 + 1.40227i
\(550\) 8120.52 + 2504.85i 0.629564 + 0.194195i
\(551\) 1569.61 + 20945.0i 0.121357 + 1.61940i
\(552\) −86.4660 378.832i −0.00666709 0.0292104i
\(553\) 8363.93 + 12773.9i 0.643166 + 0.982280i
\(554\) −2290.67 + 10036.1i −0.175670 + 0.769662i
\(555\) −554.516 83.5798i −0.0424106 0.00639237i
\(556\) −6499.41 + 4431.22i −0.495749 + 0.337996i
\(557\) −5708.03 + 9886.60i −0.434214 + 0.752080i −0.997231 0.0743648i \(-0.976307\pi\)
0.563017 + 0.826445i \(0.309640\pi\)
\(558\) −17963.3 31113.3i −1.36281 2.36045i
\(559\) 9539.05 + 4593.77i 0.721751 + 0.347577i
\(560\) 13103.6 25958.2i 0.988803 1.95881i
\(561\) −198.048 + 95.3748i −0.0149048 + 0.00717777i
\(562\) 17378.2 + 11848.3i 1.30437 + 0.889305i
\(563\) 7685.99 + 7131.56i 0.575357 + 0.533853i 0.913286 0.407318i \(-0.133536\pi\)
−0.337929 + 0.941171i \(0.609727\pi\)
\(564\) −2452.30 2275.40i −0.183086 0.169879i
\(565\) 5712.03 + 3894.40i 0.425322 + 0.289980i
\(566\) 2226.55 1072.25i 0.165351 0.0796290i
\(567\) 10260.7 7873.66i 0.759981 0.583179i
\(568\) −29313.8 14116.8i −2.16546 1.04283i
\(569\) −11234.9 19459.4i −0.827752 1.43371i −0.899798 0.436307i \(-0.856286\pi\)
0.0720465 0.997401i \(-0.477047\pi\)
\(570\) −1356.32 + 2349.21i −0.0996664 + 0.172627i
\(571\) −5485.53 + 3739.97i −0.402036 + 0.274103i −0.747412 0.664361i \(-0.768704\pi\)
0.345376 + 0.938464i \(0.387751\pi\)
\(572\) 39952.0 + 6021.79i 2.92041 + 0.440181i
\(573\) 451.505 1978.17i 0.0329178 0.144222i
\(574\) −41908.6 3929.01i −3.04744 0.285704i
\(575\) −113.400 496.837i −0.00822452 0.0360340i
\(576\) −1928.43 25733.1i −0.139499 1.86148i
\(577\) −10404.7 3209.42i −0.750697 0.231559i −0.104285 0.994548i \(-0.533255\pi\)
−0.646413 + 0.762988i \(0.723731\pi\)
\(578\) 9274.58 + 23631.2i 0.667425 + 1.70057i
\(579\) −66.6143 + 20.5478i −0.00478134 + 0.00147485i
\(580\) −23176.9 29063.0i −1.65926 2.08064i
\(581\) −1255.67 + 7391.28i −0.0896625 + 0.527783i
\(582\) 866.951 1087.12i 0.0617462 0.0774273i
\(583\) −2352.35 + 5993.70i −0.167109 + 0.425787i
\(584\) 5574.23 74382.9i 0.394971 5.27053i
\(585\) 14720.7 2218.78i 1.04038 0.156813i
\(586\) 9854.69 9143.81i 0.694699 0.644586i
\(587\) 22194.7 1.56060 0.780302 0.625402i \(-0.215065\pi\)
0.780302 + 0.625402i \(0.215065\pi\)
\(588\) 797.232 + 4212.50i 0.0559137 + 0.295443i
\(589\) 24709.4 1.72858
\(590\) −5632.75 + 5226.43i −0.393045 + 0.364693i
\(591\) −1226.90 + 184.925i −0.0853938 + 0.0128710i
\(592\) −1477.12 + 19710.8i −0.102549 + 1.36843i
\(593\) 10315.1 26282.4i 0.714316 1.82005i 0.161242 0.986915i \(-0.448450\pi\)
0.553074 0.833132i \(-0.313455\pi\)
\(594\) 3320.31 4163.54i 0.229350 0.287596i
\(595\) 512.846 + 1779.99i 0.0353355 + 0.122643i
\(596\) 8285.82 + 10390.1i 0.569464 + 0.714085i
\(597\) −1263.95 + 389.876i −0.0866497 + 0.0267279i
\(598\) −1234.54 3145.56i −0.0844216 0.215103i
\(599\) 15139.4 + 4669.88i 1.03269 + 0.318541i 0.764362 0.644787i \(-0.223054\pi\)
0.268324 + 0.963329i \(0.413530\pi\)
\(600\) 158.623 + 2116.68i 0.0107929 + 0.144022i
\(601\) 2720.15 + 11917.8i 0.184621 + 0.808878i 0.979392 + 0.201968i \(0.0647338\pi\)
−0.794771 + 0.606909i \(0.792409\pi\)
\(602\) −2068.52 15709.4i −0.140044 1.06357i
\(603\) −3098.25 + 13574.3i −0.209238 + 0.916731i
\(604\) 6086.99 + 917.465i 0.410060 + 0.0618065i
\(605\) 2902.85 1979.13i 0.195071 0.132997i
\(606\) 1266.07 2192.90i 0.0848690 0.146997i
\(607\) 5070.82 + 8782.91i 0.339074 + 0.587294i 0.984259 0.176733i \(-0.0565529\pi\)
−0.645185 + 0.764027i \(0.723220\pi\)
\(608\) 40367.9 + 19440.2i 2.69266 + 1.29672i
\(609\) 2391.61 + 593.075i 0.159134 + 0.0394624i
\(610\) 29638.4 14273.1i 1.96725 0.947378i
\(611\) −14550.4 9920.29i −0.963414 0.656844i
\(612\) 4654.85 + 4319.07i 0.307453 + 0.285275i
\(613\) 5930.61 + 5502.80i 0.390759 + 0.362571i 0.850948 0.525250i \(-0.176028\pi\)
−0.460189 + 0.887821i \(0.652218\pi\)
\(614\) 4682.49 + 3192.47i 0.307769 + 0.209833i
\(615\) −2018.39 + 972.008i −0.132341 + 0.0637319i
\(616\) −15262.5 33268.5i −0.998284 2.17602i
\(617\) −7608.13 3663.88i −0.496421 0.239064i 0.168883 0.985636i \(-0.445984\pi\)
−0.665304 + 0.746572i \(0.731698\pi\)
\(618\) 449.885 + 779.224i 0.0292832 + 0.0507200i
\(619\) −3018.73 + 5228.60i −0.196015 + 0.339508i −0.947233 0.320547i \(-0.896133\pi\)
0.751218 + 0.660054i \(0.229467\pi\)
\(620\) −36132.5 + 24634.7i −2.34051 + 1.59573i
\(621\) −315.786 47.5971i −0.0204059 0.00307569i
\(622\) 7731.20 33872.6i 0.498381 2.18355i
\(623\) 13346.9 4952.62i 0.858317 0.318495i
\(624\) 1667.81 + 7307.15i 0.106996 + 0.468782i
\(625\) −466.763 6228.52i −0.0298728 0.398625i
\(626\) −7911.68 2440.43i −0.505135 0.155813i
\(627\) 664.315 + 1692.65i 0.0423129 + 0.107811i
\(628\) −8436.89 + 2602.43i −0.536096 + 0.165364i
\(629\) −785.086 984.466i −0.0497670 0.0624058i
\(630\) −14846.1 16612.1i −0.938861 1.05054i
\(631\) −1766.26 + 2214.82i −0.111432 + 0.139732i −0.834420 0.551130i \(-0.814197\pi\)
0.722987 + 0.690861i \(0.242768\pi\)
\(632\) 19650.6 50069.0i 1.23681 3.15133i
\(633\) 199.320 2659.74i 0.0125154 0.167007i
\(634\) −21673.4 + 3266.75i −1.35767 + 0.204636i
\(635\) −12701.5 + 11785.3i −0.793770 + 0.736511i
\(636\) −2656.79 −0.165642
\(637\) 7454.95 + 21302.2i 0.463699 + 1.32500i
\(638\) −34752.0 −2.15650
\(639\) −9731.34 + 9029.36i −0.602450 + 0.558992i
\(640\) −12372.8 + 1864.90i −0.764186 + 0.115182i
\(641\) 38.2056 509.818i 0.00235418 0.0314144i −0.995903 0.0904280i \(-0.971176\pi\)
0.998257 + 0.0590136i \(0.0187955\pi\)
\(642\) 849.075 2163.41i 0.0521968 0.132995i
\(643\) −12044.7 + 15103.6i −0.738721 + 0.926326i −0.999234 0.0391441i \(-0.987537\pi\)
0.260513 + 0.965470i \(0.416108\pi\)
\(644\) −2098.23 + 2957.31i −0.128388 + 0.180954i
\(645\) −525.792 659.322i −0.0320977 0.0402493i
\(646\) −5820.37 + 1795.35i −0.354489 + 0.109345i
\(647\) 936.936 + 2387.27i 0.0569316 + 0.145059i 0.956510 0.291701i \(-0.0942211\pi\)
−0.899578 + 0.436760i \(0.856126\pi\)
\(648\) −43537.5 13429.5i −2.63937 0.814138i
\(649\) 384.916 + 5136.34i 0.0232808 + 0.310661i
\(650\) 4107.47 + 17996.0i 0.247859 + 1.08594i
\(651\) 906.018 2753.55i 0.0545463 0.165776i
\(652\) −8420.74 + 36893.7i −0.505800 + 2.21605i
\(653\) −6083.78 916.982i −0.364589 0.0549530i −0.0358069 0.999359i \(-0.511400\pi\)
−0.328782 + 0.944406i \(0.606638\pi\)
\(654\) −4131.54 + 2816.83i −0.247027 + 0.168420i
\(655\) 5208.68 9021.69i 0.310717 0.538178i
\(656\) 39481.6 + 68384.1i 2.34984 + 4.07005i
\(657\) −27420.5 13205.0i −1.62827 0.784134i
\(658\) −492.256 + 26350.5i −0.0291644 + 1.56117i
\(659\) 19632.7 9454.62i 1.16052 0.558877i 0.248342 0.968672i \(-0.420114\pi\)
0.912177 + 0.409796i \(0.134400\pi\)
\(660\) −2658.96 1812.85i −0.156818 0.106917i
\(661\) −8415.84 7808.76i −0.495217 0.459494i 0.392588 0.919715i \(-0.371580\pi\)
−0.887805 + 0.460220i \(0.847770\pi\)
\(662\) 20323.4 + 18857.4i 1.19319 + 1.10712i
\(663\) −394.502 268.967i −0.0231089 0.0157554i
\(664\) 23795.2 11459.2i 1.39071 0.669732i
\(665\) 15000.1 3130.10i 0.874703 0.182527i
\(666\) 13644.8 + 6570.97i 0.793879 + 0.382312i
\(667\) 1042.01 + 1804.81i 0.0604899 + 0.104772i
\(668\) −26808.7 + 46434.1i −1.55279 + 2.68951i
\(669\) −3144.50 + 2143.88i −0.181724 + 0.123897i
\(670\) 23372.9 + 3522.90i 1.34772 + 0.203137i
\(671\) 4906.81 21498.2i 0.282303 1.23685i
\(672\) 3646.53 3785.68i 0.209327 0.217315i
\(673\) −1764.85 7732.32i −0.101085 0.442881i −0.999989 0.00473550i \(-0.998493\pi\)
0.898904 0.438145i \(-0.144365\pi\)
\(674\) −215.372 2873.94i −0.0123083 0.164243i
\(675\) 1666.98 + 514.196i 0.0950550 + 0.0293206i
\(676\) 15792.3 + 40238.2i 0.898517 + 2.28938i
\(677\) 16130.4 4975.57i 0.915718 0.282462i 0.199142 0.979971i \(-0.436184\pi\)
0.716576 + 0.697509i \(0.245708\pi\)
\(678\) 1662.72 + 2084.99i 0.0941837 + 0.118103i
\(679\) −7842.21 + 440.575i −0.443235 + 0.0249009i
\(680\) 4068.59 5101.86i 0.229446 0.287716i
\(681\) −579.197 + 1475.77i −0.0325916 + 0.0830420i
\(682\) −3055.21 + 40769.0i −0.171540 + 2.28904i
\(683\) −14772.0 + 2226.53i −0.827579 + 0.124737i −0.549154 0.835721i \(-0.685050\pi\)
−0.278424 + 0.960458i \(0.589812\pi\)
\(684\) 38505.4 35727.7i 2.15247 1.99720i
\(685\) 13289.6 0.741271
\(686\) 20559.8 26797.6i 1.14428 1.49145i
\(687\) −1536.68 −0.0853391
\(688\) −21789.5 + 20217.7i −1.20744 + 1.12034i
\(689\) −13829.6 + 2084.48i −0.764681 + 0.115257i
\(690\) −20.1137 + 268.398i −0.00110973 + 0.0148083i
\(691\) −62.7871 + 159.979i −0.00345663 + 0.00880736i −0.932592 0.360933i \(-0.882458\pi\)
0.929135 + 0.369741i \(0.120553\pi\)
\(692\) −8176.27 + 10252.7i −0.449155 + 0.563222i
\(693\) −14910.8 + 837.689i −0.817338 + 0.0459180i
\(694\) −15203.3 19064.3i −0.831568 1.04275i
\(695\) 3151.75 972.186i 0.172018 0.0530606i
\(696\) −3171.24 8080.18i −0.172709 0.440055i
\(697\) −4806.80 1482.70i −0.261220 0.0805758i
\(698\) 1162.68 + 15514.9i 0.0630490 + 0.841331i
\(699\) −470.283 2060.44i −0.0254474 0.111492i
\(700\) 13741.4 14265.8i 0.741965 0.770279i
\(701\) 6678.18 29259.0i 0.359816 1.57646i −0.393833 0.919182i \(-0.628851\pi\)
0.753649 0.657277i \(-0.228292\pi\)
\(702\) 11438.1 + 1724.02i 0.614962 + 0.0926907i
\(703\) −8606.14 + 5867.57i −0.461717 + 0.314793i
\(704\) −14682.8 + 25431.3i −0.786049 + 1.36148i
\(705\) 701.339 + 1214.76i 0.0374666 + 0.0648941i
\(706\) 11024.2 + 5308.95i 0.587676 + 0.283010i
\(707\) −14002.0 + 2921.84i −0.744837 + 0.155427i
\(708\) −1914.84 + 922.139i −0.101644 + 0.0489493i
\(709\) −30792.0 20993.6i −1.63106 1.11204i −0.905938 0.423410i \(-0.860833\pi\)
−0.725118 0.688625i \(-0.758215\pi\)
\(710\) 16520.3 + 15328.6i 0.873235 + 0.810244i
\(711\) −16087.5 14927.0i −0.848564 0.787352i
\(712\) −41436.2 28250.7i −2.18102 1.48699i
\(713\) 2208.91 1063.75i 0.116023 0.0558736i
\(714\) −13.3464 + 714.436i −0.000699549 + 0.0374469i
\(715\) −15263.2 7350.37i −0.798337 0.384459i
\(716\) −6845.63 11857.0i −0.357309 0.618878i
\(717\) 1277.98 2213.53i 0.0665649 0.115294i
\(718\) 53562.3 36518.2i 2.78402 1.89811i
\(719\) −8277.42 1247.62i −0.429340 0.0647126i −0.0691824 0.997604i \(-0.522039\pi\)
−0.360158 + 0.932891i \(0.617277\pi\)
\(720\) −9300.23 + 40747.0i −0.481388 + 2.10910i
\(721\) 1588.59 4828.00i 0.0820555 0.249381i
\(722\) 3096.56 + 13566.9i 0.159615 + 0.699319i
\(723\) 106.415 + 1420.01i 0.00547389 + 0.0730440i
\(724\) 24337.9 + 7507.23i 1.24932 + 0.385365i
\(725\) −4159.07 10597.1i −0.213054 0.542852i
\(726\) 1295.06 399.473i 0.0662040 0.0204212i
\(727\) 21813.1 + 27352.8i 1.11280 + 1.39541i 0.909205 + 0.416350i \(0.136691\pi\)
0.203594 + 0.979055i \(0.434738\pi\)
\(728\) 46005.8 64842.0i 2.34215 3.30110i
\(729\) −11247.3 + 14103.7i −0.571424 + 0.716543i
\(730\) −18876.0 + 48095.2i −0.957029 + 2.43847i
\(731\) 141.506 1888.27i 0.00715978 0.0955407i
\(732\) 8997.12 1356.10i 0.454294 0.0684738i
\(733\) −18640.1 + 17295.5i −0.939274 + 0.871519i −0.991890 0.127096i \(-0.959434\pi\)
0.0526162 + 0.998615i \(0.483244\pi\)
\(734\) −27595.4 −1.38769
\(735\) 201.196 1786.34i 0.0100969 0.0896463i
\(736\) 4445.61 0.222646
\(737\) 11614.8 10776.9i 0.580509 0.538634i
\(738\) 59825.0 9017.17i 2.98399 0.449765i
\(739\) −1400.01 + 18681.8i −0.0696890 + 0.929936i 0.847323 + 0.531077i \(0.178213\pi\)
−0.917012 + 0.398859i \(0.869406\pi\)
\(740\) 6734.91 17160.3i 0.334568 0.852464i
\(741\) −2462.57 + 3087.96i −0.122084 + 0.153089i
\(742\) 13947.4 + 15606.5i 0.690062 + 0.772147i
\(743\) −8026.75 10065.2i −0.396329 0.496981i 0.543127 0.839651i \(-0.317240\pi\)
−0.939456 + 0.342669i \(0.888669\pi\)
\(744\) −9757.98 + 3009.94i −0.480840 + 0.148320i
\(745\) −2035.75 5187.00i −0.100113 0.255083i
\(746\) −31055.7 9579.42i −1.52417 0.470144i
\(747\) −805.287 10745.8i −0.0394430 0.526330i
\(748\) −1607.95 7044.89i −0.0785995 0.344367i
\(749\) −12308.1 + 4567.18i −0.600440 + 0.222805i
\(750\) 1102.26 4829.30i 0.0536649 0.235121i
\(751\) 4673.14 + 704.363i 0.227064 + 0.0342245i 0.261589 0.965179i \(-0.415754\pi\)
−0.0345244 + 0.999404i \(0.510992\pi\)
\(752\) 40850.0 27851.0i 1.98091 1.35056i
\(753\) 605.316 1048.44i 0.0292948 0.0507400i
\(754\) −37742.7 65372.3i −1.82295 3.15745i
\(755\) −2325.46 1119.88i −0.112096 0.0539825i
\(756\) −5175.76 11281.9i −0.248996 0.542750i
\(757\) 28086.0 13525.5i 1.34848 0.649395i 0.386445 0.922312i \(-0.373703\pi\)
0.962037 + 0.272917i \(0.0879886\pi\)
\(758\) −31255.1 21309.4i −1.49767 1.02110i
\(759\) 132.256 + 122.716i 0.00632488 + 0.00586863i
\(760\) −39569.9 36715.5i −1.88862 1.75238i
\(761\) −14603.6 9956.55i −0.695636 0.474277i 0.163156 0.986600i \(-0.447833\pi\)
−0.858793 + 0.512323i \(0.828785\pi\)
\(762\) −6021.94 + 2900.01i −0.286288 + 0.137869i
\(763\) 27416.0 + 6798.68i 1.30082 + 0.322580i
\(764\) 60095.6 + 28940.5i 2.84579 + 1.37046i
\(765\) −1331.25 2305.80i −0.0629171 0.108976i
\(766\) 32205.3 55781.2i 1.51909 2.63114i
\(767\) −9243.97 + 6302.43i −0.435177 + 0.296698i
\(768\) −44.1448 6.65376i −0.00207414 0.000312626i
\(769\) −4847.60 + 21238.7i −0.227320 + 0.995954i 0.724495 + 0.689280i \(0.242073\pi\)
−0.951815 + 0.306673i \(0.900784\pi\)
\(770\) 3309.78 + 25136.2i 0.154904 + 1.17642i
\(771\) 473.393 + 2074.07i 0.0221126 + 0.0968817i
\(772\) −171.254 2285.22i −0.00798389 0.106538i
\(773\) −501.004 154.539i −0.0233116 0.00719067i 0.283077 0.959097i \(-0.408645\pi\)
−0.306389 + 0.951906i \(0.599121\pi\)
\(774\) 8320.46 + 21200.2i 0.386399 + 0.984528i
\(775\) −12797.6 + 3947.53i −0.593164 + 0.182967i
\(776\) 17251.8 + 21633.0i 0.798070 + 1.00075i
\(777\) 338.305 + 1174.19i 0.0156199 + 0.0542134i
\(778\) −4464.65 + 5598.49i −0.205739 + 0.257989i
\(779\) −15202.2 + 38734.5i −0.699197 + 1.78153i
\(780\) 522.377 6970.64i 0.0239796 0.319986i
\(781\) 14937.9 2251.53i 0.684406 0.103158i
\(782\) −443.023 + 411.066i −0.0202589 + 0.0187975i
\(783\) −7133.89 −0.325600
\(784\) −63317.8 2366.51i −2.88437 0.107804i
\(785\) 3702.01 0.168319
\(786\) 2945.77 2733.27i 0.133679 0.124036i
\(787\) −14956.9 + 2254.38i −0.677451 + 0.102109i −0.478751 0.877951i \(-0.658910\pi\)
−0.198701 + 0.980060i \(0.563672\pi\)
\(788\) 3048.05 40673.4i 0.137795 1.83875i
\(789\) 541.662 1380.13i 0.0244406 0.0622737i
\(790\) −23228.9 + 29128.2i −1.04614 + 1.31182i
\(791\) 2523.05 14851.5i 0.113412 0.667583i
\(792\) 32801.7 + 41132.1i 1.47167 + 1.84541i
\(793\) 45769.4 14118.0i 2.04958 0.632213i
\(794\) 6267.20 + 15968.6i 0.280119 + 0.713732i
\(795\) 1064.49 + 328.351i 0.0474886 + 0.0146483i
\(796\) −3249.39 43360.1i −0.144688 1.93073i
\(797\) −5695.25 24952.5i −0.253119 1.10899i −0.928445 0.371469i \(-0.878854\pi\)
0.675326 0.737519i \(-0.264003\pi\)
\(798\) 5885.11 + 551.740i 0.261066 + 0.0244754i
\(799\) −700.850 + 3070.62i −0.0310316 + 0.135959i
\(800\) −24013.2 3619.40i −1.06124 0.159957i
\(801\) −16906.6 + 11526.7i −0.745772 + 0.508459i
\(802\) 8792.97 15229.9i 0.387145 0.670555i
\(803\) 17316.7 + 29993.4i 0.761013 + 1.31811i
\(804\) 5890.31 + 2836.62i 0.258377 + 0.124428i
\(805\) 1206.18 925.577i 0.0528104 0.0405246i
\(806\) −80009.0 + 38530.3i −3.49652 + 1.68384i
\(807\) 1711.86 + 1167.13i 0.0746721 + 0.0509106i
\(808\) 36937.0 + 34272.5i 1.60822 + 1.49221i
\(809\) 18132.9 + 16824.9i 0.788032 + 0.731187i 0.967581 0.252562i \(-0.0812732\pi\)
−0.179549 + 0.983749i \(0.557464\pi\)
\(810\) 26075.1 + 17777.7i 1.13109 + 0.771167i
\(811\) 10723.1 5163.97i 0.464290 0.223590i −0.187089 0.982343i \(-0.559905\pi\)
0.651379 + 0.758753i \(0.274191\pi\)
\(812\) −36502.0 + 72310.2i −1.57755 + 3.12511i
\(813\) −399.070 192.182i −0.0172153 0.00829043i
\(814\) −8617.00 14925.1i −0.371039 0.642659i
\(815\) 7933.57 13741.4i 0.340983 0.590599i
\(816\) 1107.56 755.119i 0.0475150 0.0323952i
\(817\) −15488.8 2334.56i −0.663261 0.0999706i
\(818\) −785.463 + 3441.34i −0.0335734 + 0.147095i
\(819\) −17769.8 27139.1i −0.758153 1.15790i
\(820\) −16387.3 71797.6i −0.697891 3.05766i
\(821\) 2643.95 + 35281.0i 0.112393 + 1.49978i 0.713527 + 0.700627i \(0.247096\pi\)
−0.601135 + 0.799148i \(0.705285\pi\)
\(822\) 4898.72 + 1511.06i 0.207862 + 0.0641169i
\(823\) −7230.68 18423.5i −0.306252 0.780318i −0.998290 0.0584569i \(-0.981382\pi\)
0.692038 0.721862i \(-0.256713\pi\)
\(824\) −17109.4 + 5277.54i −0.723342 + 0.223121i
\(825\) −614.477 770.530i −0.0259313 0.0325169i
\(826\) 15469.2 + 6407.18i 0.651626 + 0.269896i
\(827\) −20978.5 + 26306.2i −0.882097 + 1.10611i 0.111571 + 0.993756i \(0.464412\pi\)
−0.993668 + 0.112358i \(0.964160\pi\)
\(828\) 1904.10 4851.57i 0.0799179 0.203628i
\(829\) 472.629 6306.79i 0.0198011 0.264227i −0.978513 0.206185i \(-0.933895\pi\)
0.998314 0.0580420i \(-0.0184857\pi\)
\(830\) −18089.4 + 2726.53i −0.756495 + 0.114023i
\(831\) 875.151 812.022i 0.0365327 0.0338974i
\(832\) −63785.5 −2.65789
\(833\) 3059.38 2633.04i 0.127253 0.109519i
\(834\) 1272.31 0.0528256
\(835\) 16480.1 15291.3i 0.683016 0.633746i
\(836\) −59107.0 + 8908.94i −2.44528 + 0.368567i
\(837\) −627.174 + 8369.06i −0.0259000 + 0.345612i
\(838\) −11033.6 + 28113.1i −0.454832 + 1.15889i
\(839\) −3048.57 + 3822.78i −0.125445 + 0.157303i −0.840588 0.541675i \(-0.817790\pi\)
0.715143 + 0.698978i \(0.246362\pi\)
\(840\) −5542.38 + 3063.32i −0.227655 + 0.125827i
\(841\) 13819.7 + 17329.3i 0.566636 + 0.710539i
\(842\) 61081.6 18841.2i 2.50001 0.771152i
\(843\) −891.158 2270.63i −0.0364094 0.0927696i
\(844\) 83783.9 + 25843.9i 3.41702 + 1.05401i
\(845\) −1354.45 18073.9i −0.0551414 0.735811i
\(846\) −8429.34 36931.3i −0.342561 1.50086i
\(847\) −6557.35 3951.00i −0.266013 0.160281i
\(848\) 8737.27 38280.5i 0.353819 1.55018i
\(849\) −283.401 42.7158i −0.0114562 0.00172674i
\(850\) 2727.68 1859.70i 0.110069 0.0750438i
\(851\) −516.747 + 895.032i −0.0208153 + 0.0360532i
\(852\) 3116.67 + 5398.23i 0.125323 + 0.217066i
\(853\) −40547.9 19526.9i −1.62759 0.783806i −0.999986 0.00527357i \(-0.998321\pi\)
−0.627604 0.778533i \(-0.715964\pi\)
\(854\) −55198.4 45731.7i −2.21177 1.83244i
\(855\) −19843.4 + 9556.07i −0.793718 + 0.382235i
\(856\) 38211.3 + 26052.1i 1.52574 + 1.04023i
\(857\) −24719.2 22936.0i −0.985286 0.914212i 0.0110324 0.999939i \(-0.496488\pi\)
−0.996319 + 0.0857271i \(0.972679\pi\)
\(858\) −4790.45 4444.89i −0.190610 0.176860i
\(859\) 40169.3 + 27386.9i 1.59553 + 1.08781i 0.944378 + 0.328863i \(0.106665\pi\)
0.651150 + 0.758949i \(0.274287\pi\)
\(860\) 24976.7 12028.2i 0.990348 0.476927i
\(861\) 3759.05 + 3114.36i 0.148790 + 0.123272i
\(862\) 38683.1 + 18628.8i 1.52848 + 0.736078i
\(863\) 798.798 + 1383.56i 0.0315080 + 0.0545735i 0.881349 0.472465i \(-0.156636\pi\)
−0.849841 + 0.527038i \(0.823302\pi\)
\(864\) −7608.99 + 13179.1i −0.299610 + 0.518940i
\(865\) 4543.08 3097.42i 0.178577 0.121752i
\(866\) 30449.9 + 4589.58i 1.19484 + 0.180093i
\(867\) 655.123 2870.28i 0.0256622 0.112434i
\(868\) 81620.9 + 49179.0i 3.19170 + 1.92309i
\(869\) 5557.19 + 24347.6i 0.216933 + 0.950445i
\(870\) 449.312 + 5995.65i 0.0175093 + 0.233645i
\(871\) 32886.8 + 10144.2i 1.27937 + 0.394632i
\(872\) −36353.3 92626.6i −1.41179 3.59717i
\(873\) 10788.1 3327.68i 0.418237 0.129009i
\(874\) 3117.00 + 3908.59i 0.120634 + 0.151270i
\(875\) −24489.7 + 13535.6i −0.946174 + 0.522958i
\(876\) −8909.99 + 11172.8i −0.343654 + 0.430928i
\(877\) 2554.33 6508.32i 0.0983506 0.250593i −0.873227 0.487313i \(-0.837977\pi\)
0.971578 + 0.236720i \(0.0760723\pi\)
\(878\) −3572.39 + 47670.2i −0.137315 + 1.83234i
\(879\) −1541.65 + 232.367i −0.0591566 + 0.00891642i
\(880\) 34864.8 32349.8i 1.33556 1.23922i
\(881\) 30494.0 1.16614 0.583070 0.812422i \(-0.301851\pi\)
0.583070 + 0.812422i \(0.301851\pi\)
\(882\) −19411.8 + 44497.4i −0.741076 + 1.69876i
\(883\) 8614.02 0.328295 0.164148 0.986436i \(-0.447513\pi\)
0.164148 + 0.986436i \(0.447513\pi\)
\(884\) 11505.9 10675.9i 0.437765 0.406186i
\(885\) 881.179 132.816i 0.0334695 0.00504472i
\(886\) −1851.20 + 24702.5i −0.0701945 + 0.936680i
\(887\) −5488.37 + 13984.1i −0.207758 + 0.529359i −0.996331 0.0855823i \(-0.972725\pi\)
0.788573 + 0.614941i \(0.210820\pi\)
\(888\) 2683.90 3365.50i 0.101425 0.127183i
\(889\) 34882.1 + 14447.8i 1.31598 + 0.545065i
\(890\) 21658.3 + 27158.7i 0.815718 + 1.02288i
\(891\) 20214.8 6235.43i 0.760068 0.234450i
\(892\) −45707.3 116460.i −1.71569 4.37150i
\(893\) 24896.2 + 7679.46i 0.932945 + 0.287775i
\(894\) −160.630 2143.46i −0.00600926 0.0801879i
\(895\) 1277.42 + 5596.75i 0.0477089 + 0.209026i
\(896\) 14935.6 + 22810.6i 0.556880 + 0.850500i
\(897\) −87.2035 + 382.064i −0.00324598 + 0.0142216i
\(898\) 57060.6 + 8600.49i 2.12042 + 0.319602i
\(899\) 45251.1 30851.7i 1.67876 1.14456i
\(900\) −14235.0 + 24655.7i −0.527222 + 0.913176i
\(901\) 1250.67 + 2166.22i 0.0462440 + 0.0800969i
\(902\) −62029.8 29872.0i −2.28976 1.10269i
\(903\) −828.083 + 1640.43i −0.0305170 + 0.0604541i
\(904\) −47812.3 + 23025.2i −1.75909 + 0.847131i
\(905\) −8823.55 6015.80i −0.324094 0.220963i
\(906\) −729.861 677.212i −0.0267638 0.0248332i
\(907\) −38537.9 35757.9i −1.41084 1.30907i −0.890410 0.455160i \(-0.849582\pi\)
−0.520427 0.853906i \(-0.674227\pi\)
\(908\) −43060.0 29357.8i −1.57379 1.07299i
\(909\) 18523.1 8920.23i 0.675876 0.325485i
\(910\) −43689.3 + 33525.4i −1.59152 + 1.22127i
\(911\) 9478.57 + 4564.64i 0.344719 + 0.166008i 0.598230 0.801325i \(-0.295871\pi\)
−0.253511 + 0.967333i \(0.581585\pi\)
\(912\) −5544.29 9602.99i −0.201304 0.348670i
\(913\) −6131.34 + 10619.8i −0.222254 + 0.384955i
\(914\) −80850.4 + 55122.9i −2.92592 + 1.99486i
\(915\) −3772.44 568.604i −0.136299 0.0205437i
\(916\) 11240.8 49248.9i 0.405464 1.77645i
\(917\) −22600.6 2118.85i −0.813892 0.0763039i
\(918\) −460.350 2016.93i −0.0165510 0.0725146i
\(919\) 1582.51 + 21117.1i 0.0568031 + 0.757985i 0.950779 + 0.309870i \(0.100285\pi\)
−0.893976 + 0.448115i \(0.852095\pi\)
\(920\) −5117.98 1578.69i −0.183407 0.0565737i
\(921\) −240.119 611.813i −0.00859086 0.0218892i
\(922\) −58866.7 + 18158.0i −2.10268 + 0.648592i
\(923\) 20458.8 + 25654.5i 0.729588 + 0.914875i
\(924\) −1174.48 + 6913.38i −0.0418156 + 0.246140i
\(925\) 3519.93 4413.85i 0.125118 0.156893i
\(926\) −255.955 + 652.163i −0.00908337 + 0.0231441i
\(927\) −545.936 + 7285.01i −0.0193429 + 0.258113i
\(928\) 98199.5 14801.2i 3.47366 0.523570i
\(929\) 28141.1 26111.1i 0.993843 0.922151i −0.00312295 0.999995i \(-0.500994\pi\)
0.996966 + 0.0778439i \(0.0248036\pi\)
\(930\) 7073.24 0.249398
\(931\) −19828.6 26864.4i −0.698019 0.945699i
\(932\) 69475.2 2.44178
\(933\) −2953.70 + 2740.64i −0.103644 + 0.0961677i
\(934\) −48906.9 + 7371.54i −1.71337 + 0.258248i
\(935\) −226.421 + 3021.38i −0.00791952 + 0.105679i
\(936\) −41749.3 + 106375.i −1.45792 + 3.71473i
\(937\) −4879.06 + 6118.15i −0.170109 + 0.213310i −0.859577 0.511006i \(-0.829273\pi\)
0.689468 + 0.724316i \(0.257844\pi\)
\(938\) −14259.6 49492.3i −0.496368 1.72280i
\(939\) 598.674 + 750.714i 0.0208062 + 0.0260901i
\(940\) −44061.9 + 13591.3i −1.52887 + 0.471595i
\(941\) 4327.92 + 11027.4i 0.149932 + 0.382021i 0.986032 0.166557i \(-0.0532649\pi\)
−0.836100 + 0.548577i \(0.815170\pi\)
\(942\) 1364.61 + 420.926i 0.0471988 + 0.0145589i
\(943\) 308.537 + 4117.15i 0.0106547 + 0.142177i
\(944\) −6989.42 30622.7i −0.240981 1.05581i
\(945\) 679.432 + 5159.96i 0.0233883 + 0.177623i
\(946\) 5767.00 25266.9i 0.198204 0.868390i
\(947\) 13433.1 + 2024.72i 0.460948 + 0.0694768i 0.375412 0.926858i \(-0.377501\pi\)
0.0855368 + 0.996335i \(0.472739\pi\)
\(948\) −8514.18 + 5804.87i −0.291696 + 0.198875i
\(949\) −37613.9 + 65149.2i −1.28662 + 2.22848i
\(950\) −13654.4 23650.2i −0.466324 0.807697i
\(951\) 2290.19 + 1102.90i 0.0780911 + 0.0376067i
\(952\) −13801.3 3422.47i −0.469855 0.116516i
\(953\) −7813.17 + 3762.62i −0.265575 + 0.127894i −0.561933 0.827183i \(-0.689942\pi\)
0.296358 + 0.955077i \(0.404228\pi\)
\(954\) −24856.9 16947.1i −0.843575 0.575140i
\(955\) −20501.6 19022.7i −0.694676 0.644565i
\(956\) 61592.8 + 57149.8i 2.08374 + 1.93343i
\(957\) 3329.98 + 2270.34i 0.112480 + 0.0766873i
\(958\) 40780.6 19638.9i 1.37533 0.662322i
\(959\) −12075.1 26320.8i −0.406596 0.886282i
\(960\) 4577.42 + 2204.37i 0.153891 + 0.0741101i
\(961\) −17319.6 29998.4i −0.581370 1.00696i
\(962\) 18717.1 32419.0i 0.627302 1.08652i
\(963\) 15590.8 10629.6i 0.521709 0.355695i
\(964\) −46288.3 6976.84i −1.54652 0.233100i
\(965\) −213.814 + 936.778i −0.00713254 + 0.0312497i
\(966\) 549.854 204.034i 0.0183139 0.00679574i
\(967\) −1010.99 4429.44i −0.0336207 0.147302i 0.955332 0.295536i \(-0.0954983\pi\)
−0.988952 + 0.148234i \(0.952641\pi\)
\(968\) 2015.39 + 26893.6i 0.0669186 + 0.892967i
\(969\) 675.005 + 208.212i 0.0223780 + 0.00690270i
\(970\) −7002.04 17840.9i −0.231775 0.590554i
\(971\) 42778.2 13195.3i 1.41382 0.436105i 0.508583 0.861013i \(-0.330170\pi\)
0.905237 + 0.424908i \(0.139693\pi\)
\(972\) 16724.9 + 20972.3i 0.551903 + 0.692065i
\(973\) −4789.18 5358.87i −0.157795 0.176565i
\(974\) 11311.2 14183.8i 0.372110 0.466611i
\(975\) 782.092 1992.74i 0.0256892 0.0654551i
\(976\) −10049.0 + 134095.i −0.329572 + 4.39783i
\(977\) 4207.17 634.129i 0.137768 0.0207652i −0.0797962 0.996811i \(-0.525427\pi\)
0.217564 + 0.976046i \(0.430189\pi\)
\(978\) 4486.83 4163.17i 0.146700 0.136118i
\(979\) 23285.2 0.760161
\(980\) 55778.5 + 19515.1i 1.81814 + 0.636109i
\(981\) −40599.5 −1.32135
\(982\) −39727.9 + 36862.1i −1.29101 + 1.19788i
\(983\) 33640.0 5070.41i 1.09150 0.164518i 0.421466 0.906844i \(-0.361516\pi\)
0.670039 + 0.742326i \(0.266278\pi\)
\(984\) 1285.10 17148.5i 0.0416336 0.555562i
\(985\) −6248.06 + 15919.8i −0.202111 + 0.514971i
\(986\) −8417.39 + 10555.1i −0.271870 + 0.340915i
\(987\) 1768.64 2492.78i 0.0570381 0.0803912i
\(988\) −80952.3 101511.i −2.60672 3.26872i
\(989\) −1485.13 + 458.102i −0.0477496 + 0.0147288i
\(990\) −13313.4 33921.9i −0.427400 1.08900i
\(991\) −33439.0 10314.6i −1.07187 0.330629i −0.291903 0.956448i \(-0.594289\pi\)
−0.779968 + 0.625819i \(0.784765\pi\)
\(992\) −8730.70 116503.i −0.279435 3.72881i
\(993\) −715.467 3134.66i −0.0228647 0.100177i
\(994\) 15348.6 46647.2i 0.489767 1.48849i
\(995\) −4056.92 + 17774.5i −0.129259 + 0.566322i
\(996\) −5003.34 754.133i −0.159174 0.0239916i
\(997\) 5125.48 3494.49i 0.162814 0.111005i −0.479172 0.877721i \(-0.659063\pi\)
0.641986 + 0.766716i \(0.278111\pi\)
\(998\) 35144.7 60872.5i 1.11472 1.93075i
\(999\) −1768.90 3063.82i −0.0560215 0.0970321i
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.11.13 yes 156
49.3 odd 42 2401.4.a.f.1.2 78
49.9 even 21 inner 49.4.g.a.9.13 156
49.46 even 21 2401.4.a.g.1.2 78
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
49.4.g.a.9.13 156 49.9 even 21 inner
49.4.g.a.11.13 yes 156 1.1 even 1 trivial
2401.4.a.f.1.2 78 49.3 odd 42
2401.4.a.g.1.2 78 49.46 even 21