Properties

Label 76.4.k.a.3.16
Level $76$
Weight $4$
Character 76.3
Analytic conductor $4.484$
Analytic rank $0$
Dimension $168$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [76,4,Mod(3,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 13]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 76.k (of order \(18\), degree \(6\), 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: \(4.48414516044\)
Analytic rank: \(0\)
Dimension: \(168\)
Relative dimension: \(28\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 3.16
Character \(\chi\) \(=\) 76.3
Dual form 76.4.k.a.51.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.311236 - 2.81125i) q^{2} +(8.99625 - 3.27437i) q^{3} +(-7.80626 - 1.74992i) q^{4} +(1.82627 - 10.3573i) q^{5} +(-6.40511 - 26.3098i) q^{6} +(-21.9414 + 12.6679i) q^{7} +(-7.34906 + 21.4007i) q^{8} +(49.5278 - 41.5588i) q^{9} +O(q^{10})\) \(q+(0.311236 - 2.81125i) q^{2} +(8.99625 - 3.27437i) q^{3} +(-7.80626 - 1.74992i) q^{4} +(1.82627 - 10.3573i) q^{5} +(-6.40511 - 26.3098i) q^{6} +(-21.9414 + 12.6679i) q^{7} +(-7.34906 + 21.4007i) q^{8} +(49.5278 - 41.5588i) q^{9} +(-28.5485 - 8.35765i) q^{10} +(49.1745 + 28.3909i) q^{11} +(-75.9570 + 9.81783i) q^{12} +(-5.39805 + 14.8310i) q^{13} +(28.7836 + 65.6254i) q^{14} +(-17.4840 - 99.1565i) q^{15} +(57.8755 + 27.3207i) q^{16} +(7.84449 + 6.58231i) q^{17} +(-101.417 - 152.170i) q^{18} +(-58.6882 - 58.4354i) q^{19} +(-32.3808 + 77.6558i) q^{20} +(-155.911 + 185.807i) q^{21} +(95.1189 - 129.406i) q^{22} +(14.7647 - 2.60342i) q^{23} +(3.95988 + 216.590i) q^{24} +(13.5236 + 4.92218i) q^{25} +(40.0137 + 19.7912i) q^{26} +(180.242 - 312.189i) q^{27} +(193.448 - 60.4930i) q^{28} +(-71.1539 - 84.7979i) q^{29} +(-284.196 + 18.2908i) q^{30} +(74.0030 + 128.177i) q^{31} +(94.8183 - 154.199i) q^{32} +(535.349 + 94.3964i) q^{33} +(20.9460 - 20.0042i) q^{34} +(91.1338 + 250.388i) q^{35} +(-459.352 + 237.749i) q^{36} +59.8146i q^{37} +(-182.542 + 146.800i) q^{38} +151.099i q^{39} +(208.232 + 115.200i) q^{40} +(148.039 + 406.735i) q^{41} +(473.826 + 496.135i) q^{42} +(-287.236 - 50.6474i) q^{43} +(-334.188 - 307.679i) q^{44} +(-339.985 - 588.871i) q^{45} +(-2.72355 - 42.3176i) q^{46} +(-26.3499 - 31.4026i) q^{47} +(610.121 + 56.2783i) q^{48} +(149.449 - 258.854i) q^{49} +(18.0465 - 36.4862i) q^{50} +(92.1239 + 33.5304i) q^{51} +(68.0918 - 106.329i) q^{52} +(-99.8184 + 17.6007i) q^{53} +(-821.543 - 603.870i) q^{54} +(383.859 - 457.465i) q^{55} +(-109.853 - 562.659i) q^{56} +(-719.313 - 333.532i) q^{57} +(-260.534 + 173.639i) q^{58} +(-351.567 - 295.000i) q^{59} +(-37.0318 + 804.638i) q^{60} +(80.0696 + 454.097i) q^{61} +(383.370 - 168.148i) q^{62} +(-560.248 + 1539.27i) q^{63} +(-403.983 - 314.551i) q^{64} +(143.751 + 82.9945i) q^{65} +(431.992 - 1475.62i) q^{66} +(-209.391 + 175.700i) q^{67} +(-49.7177 - 65.1105i) q^{68} +(124.302 - 71.7661i) q^{69} +(732.267 - 178.270i) q^{70} +(52.3347 - 296.805i) q^{71} +(525.405 + 1365.35i) q^{72} +(-33.8235 + 12.3107i) q^{73} +(168.154 + 18.6164i) q^{74} +137.779 q^{75} +(355.878 + 558.862i) q^{76} -1438.61 q^{77} +(424.777 + 47.0273i) q^{78} +(44.5451 - 16.2131i) q^{79} +(388.665 - 549.538i) q^{80} +(296.153 - 1679.57i) q^{81} +(1189.51 - 289.586i) q^{82} +(-922.988 + 532.887i) q^{83} +(1542.23 - 1177.63i) q^{84} +(82.5010 - 69.2266i) q^{85} +(-231.781 + 791.728i) q^{86} +(-917.777 - 529.879i) q^{87} +(-968.974 + 843.725i) q^{88} +(-229.920 + 631.699i) q^{89} +(-1761.28 + 772.505i) q^{90} +(-69.4367 - 393.795i) q^{91} +(-119.813 - 5.51414i) q^{92} +(1085.45 + 910.799i) q^{93} +(-96.4817 + 64.3026i) q^{94} +(-712.412 + 501.132i) q^{95} +(348.104 - 1697.69i) q^{96} +(448.147 - 534.081i) q^{97} +(-681.190 - 500.705i) q^{98} +(3615.40 - 637.493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 168 q - 6 q^{2} - 24 q^{4} - 12 q^{5} - 24 q^{6} - 9 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 168 q - 6 q^{2} - 24 q^{4} - 12 q^{5} - 24 q^{6} - 9 q^{8} + 18 q^{9} - 105 q^{10} - 9 q^{12} - 120 q^{13} + 69 q^{14} + 192 q^{16} - 12 q^{17} + 558 q^{20} + 6 q^{21} - 30 q^{22} + 96 q^{24} - 12 q^{25} - 411 q^{26} + 756 q^{28} - 12 q^{29} + 276 q^{30} - 471 q^{32} - 576 q^{33} + 36 q^{34} - 2673 q^{36} - 648 q^{38} - 2298 q^{40} - 606 q^{41} - 321 q^{42} - 1203 q^{44} - 6 q^{45} + 1566 q^{46} + 3237 q^{48} + 2346 q^{49} + 3204 q^{50} + 1077 q^{52} + 576 q^{53} - 627 q^{54} - 12 q^{57} - 4116 q^{58} + 90 q^{60} + 3528 q^{61} - 3300 q^{62} - 381 q^{64} + 1242 q^{65} + 276 q^{66} + 1170 q^{68} - 4770 q^{69} + 1449 q^{70} + 1146 q^{72} - 3468 q^{73} + 3105 q^{74} + 4386 q^{76} - 9396 q^{77} + 6939 q^{78} + 2133 q^{80} + 1980 q^{81} + 7299 q^{82} + 315 q^{84} - 516 q^{85} - 3804 q^{86} - 5841 q^{88} + 3576 q^{89} - 8898 q^{90} - 7668 q^{92} + 5694 q^{93} + 18942 q^{96} + 774 q^{97} + 8745 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.311236 2.81125i 0.110038 0.993927i
\(3\) 8.99625 3.27437i 1.73133 0.630152i 0.732605 0.680654i \(-0.238304\pi\)
0.998724 + 0.0505019i \(0.0160821\pi\)
\(4\) −7.80626 1.74992i −0.975783 0.218740i
\(5\) 1.82627 10.3573i 0.163346 0.926383i −0.787407 0.616434i \(-0.788577\pi\)
0.950753 0.309949i \(-0.100312\pi\)
\(6\) −6.40511 26.3098i −0.435813 1.79016i
\(7\) −21.9414 + 12.6679i −1.18472 + 0.684000i −0.957103 0.289750i \(-0.906428\pi\)
−0.227621 + 0.973750i \(0.573095\pi\)
\(8\) −7.34906 + 21.4007i −0.324786 + 0.945788i
\(9\) 49.5278 41.5588i 1.83436 1.53921i
\(10\) −28.5485 8.35765i −0.902783 0.264292i
\(11\) 49.1745 + 28.3909i 1.34788 + 0.778199i 0.987949 0.154780i \(-0.0494668\pi\)
0.359931 + 0.932979i \(0.382800\pi\)
\(12\) −75.9570 + 9.81783i −1.82724 + 0.236180i
\(13\) −5.39805 + 14.8310i −0.115165 + 0.316414i −0.983862 0.178931i \(-0.942736\pi\)
0.868696 + 0.495345i \(0.164958\pi\)
\(14\) 28.7836 + 65.6254i 0.549482 + 1.25280i
\(15\) −17.4840 99.1565i −0.300956 1.70681i
\(16\) 57.8755 + 27.3207i 0.904305 + 0.426886i
\(17\) 7.84449 + 6.58231i 0.111916 + 0.0939085i 0.697028 0.717044i \(-0.254505\pi\)
−0.585112 + 0.810952i \(0.698950\pi\)
\(18\) −101.417 152.170i −1.32802 1.99260i
\(19\) −58.6882 58.4354i −0.708632 0.705579i
\(20\) −32.3808 + 77.6558i −0.362028 + 0.868219i
\(21\) −155.911 + 185.807i −1.62012 + 1.93079i
\(22\) 95.1189 129.406i 0.921792 1.25406i
\(23\) 14.7647 2.60342i 0.133855 0.0236022i −0.106319 0.994332i \(-0.533907\pi\)
0.240174 + 0.970730i \(0.422796\pi\)
\(24\) 3.95988 + 216.590i 0.0336794 + 1.84213i
\(25\) 13.5236 + 4.92218i 0.108189 + 0.0393775i
\(26\) 40.0137 + 19.7912i 0.301820 + 0.149284i
\(27\) 180.242 312.189i 1.28473 2.22521i
\(28\) 193.448 60.4930i 1.30565 0.408289i
\(29\) −71.1539 84.7979i −0.455619 0.542985i 0.488512 0.872557i \(-0.337540\pi\)
−0.944130 + 0.329572i \(0.893095\pi\)
\(30\) −284.196 + 18.2908i −1.72956 + 0.111314i
\(31\) 74.0030 + 128.177i 0.428753 + 0.742621i 0.996763 0.0804002i \(-0.0256198\pi\)
−0.568010 + 0.823022i \(0.692287\pi\)
\(32\) 94.8183 154.199i 0.523802 0.851840i
\(33\) 535.349 + 94.3964i 2.82401 + 0.497949i
\(34\) 20.9460 20.0042i 0.105653 0.100903i
\(35\) 91.1338 + 250.388i 0.440126 + 1.20924i
\(36\) −459.352 + 237.749i −2.12663 + 1.10069i
\(37\) 59.8146i 0.265769i 0.991132 + 0.132885i \(0.0424240\pi\)
−0.991132 + 0.132885i \(0.957576\pi\)
\(38\) −182.542 + 146.800i −0.779271 + 0.626688i
\(39\) 151.099i 0.620389i
\(40\) 208.232 + 115.200i 0.823109 + 0.455367i
\(41\) 148.039 + 406.735i 0.563900 + 1.54930i 0.813869 + 0.581048i \(0.197357\pi\)
−0.249970 + 0.968254i \(0.580421\pi\)
\(42\) 473.826 + 496.135i 1.74078 + 1.82274i
\(43\) −287.236 50.6474i −1.01868 0.179620i −0.360718 0.932675i \(-0.617468\pi\)
−0.657957 + 0.753055i \(0.728579\pi\)
\(44\) −334.188 307.679i −1.14502 1.05419i
\(45\) −339.985 588.871i −1.12627 1.95075i
\(46\) −2.72355 42.3176i −0.00872970 0.135639i
\(47\) −26.3499 31.4026i −0.0817773 0.0974583i 0.723604 0.690215i \(-0.242484\pi\)
−0.805382 + 0.592757i \(0.798040\pi\)
\(48\) 610.121 + 56.2783i 1.83465 + 0.169231i
\(49\) 149.449 258.854i 0.435713 0.754677i
\(50\) 18.0465 36.4862i 0.0510432 0.103199i
\(51\) 92.1239 + 33.5304i 0.252940 + 0.0920626i
\(52\) 68.0918 106.329i 0.181589 0.283560i
\(53\) −99.8184 + 17.6007i −0.258700 + 0.0456158i −0.301494 0.953468i \(-0.597485\pi\)
0.0427937 + 0.999084i \(0.486374\pi\)
\(54\) −821.543 603.870i −2.07033 1.52178i
\(55\) 383.859 457.465i 0.941082 1.12154i
\(56\) −109.853 562.659i −0.262138 1.34265i
\(57\) −719.313 333.532i −1.67150 0.775043i
\(58\) −260.534 + 173.639i −0.589823 + 0.393103i
\(59\) −351.567 295.000i −0.775766 0.650945i 0.166413 0.986056i \(-0.446782\pi\)
−0.942179 + 0.335111i \(0.891226\pi\)
\(60\) −37.0318 + 804.638i −0.0796797 + 1.73130i
\(61\) 80.0696 + 454.097i 0.168063 + 0.953135i 0.945849 + 0.324606i \(0.105232\pi\)
−0.777786 + 0.628529i \(0.783657\pi\)
\(62\) 383.370 168.148i 0.785291 0.344432i
\(63\) −560.248 + 1539.27i −1.12039 + 3.07825i
\(64\) −403.983 314.551i −0.789029 0.614356i
\(65\) 143.751 + 82.9945i 0.274309 + 0.158372i
\(66\) 431.992 1475.62i 0.805674 2.75207i
\(67\) −209.391 + 175.700i −0.381808 + 0.320375i −0.813412 0.581688i \(-0.802392\pi\)
0.431604 + 0.902063i \(0.357948\pi\)
\(68\) −49.7177 65.1105i −0.0886640 0.116115i
\(69\) 124.302 71.7661i 0.216873 0.125212i
\(70\) 732.267 178.270i 1.25032 0.304391i
\(71\) 52.3347 296.805i 0.0874787 0.496116i −0.909315 0.416107i \(-0.863394\pi\)
0.996794 0.0800088i \(-0.0254949\pi\)
\(72\) 525.405 + 1365.35i 0.859995 + 2.23483i
\(73\) −33.8235 + 12.3107i −0.0542293 + 0.0197379i −0.368992 0.929432i \(-0.620297\pi\)
0.314763 + 0.949170i \(0.398075\pi\)
\(74\) 168.154 + 18.6164i 0.264155 + 0.0292448i
\(75\) 137.779 0.212124
\(76\) 355.878 + 558.862i 0.537132 + 0.843498i
\(77\) −1438.61 −2.12915
\(78\) 424.777 + 47.0273i 0.616621 + 0.0682666i
\(79\) 44.5451 16.2131i 0.0634394 0.0230901i −0.310106 0.950702i \(-0.600364\pi\)
0.373545 + 0.927612i \(0.378142\pi\)
\(80\) 388.665 549.538i 0.543175 0.768003i
\(81\) 296.153 1679.57i 0.406246 2.30394i
\(82\) 1189.51 289.586i 1.60194 0.389993i
\(83\) −922.988 + 532.887i −1.22062 + 0.704722i −0.965049 0.262069i \(-0.915595\pi\)
−0.255566 + 0.966792i \(0.582262\pi\)
\(84\) 1542.23 1177.63i 2.00323 1.52964i
\(85\) 82.5010 69.2266i 0.105276 0.0883373i
\(86\) −231.781 + 791.728i −0.290623 + 0.992724i
\(87\) −917.777 529.879i −1.13099 0.652977i
\(88\) −968.974 + 843.725i −1.17378 + 1.02206i
\(89\) −229.920 + 631.699i −0.273837 + 0.752360i 0.724192 + 0.689598i \(0.242213\pi\)
−0.998029 + 0.0627613i \(0.980009\pi\)
\(90\) −1761.28 + 772.505i −2.06283 + 0.904769i
\(91\) −69.4367 393.795i −0.0799884 0.453637i
\(92\) −119.813 5.51414i −0.135776 0.00624879i
\(93\) 1085.45 + 910.799i 1.21028 + 1.01554i
\(94\) −96.4817 + 64.3026i −0.105865 + 0.0705565i
\(95\) −712.412 + 501.132i −0.769389 + 0.541211i
\(96\) 348.104 1697.69i 0.370085 1.80489i
\(97\) 448.147 534.081i 0.469098 0.559049i −0.478676 0.877991i \(-0.658883\pi\)
0.947774 + 0.318943i \(0.103328\pi\)
\(98\) −681.190 500.705i −0.702149 0.516110i
\(99\) 3615.40 637.493i 3.67032 0.647176i
\(100\) −96.9552 62.0891i −0.0969552 0.0620891i
\(101\) −1403.35 510.776i −1.38255 0.503209i −0.459603 0.888124i \(-0.652008\pi\)
−0.922952 + 0.384916i \(0.874231\pi\)
\(102\) 122.935 248.548i 0.119337 0.241273i
\(103\) 358.623 621.153i 0.343070 0.594214i −0.641932 0.766762i \(-0.721867\pi\)
0.985001 + 0.172548i \(0.0552000\pi\)
\(104\) −277.724 224.516i −0.261857 0.211689i
\(105\) 1639.72 + 1954.15i 1.52401 + 1.81624i
\(106\) 18.4129 + 286.093i 0.0168719 + 0.262149i
\(107\) 224.123 + 388.193i 0.202494 + 0.350729i 0.949331 0.314277i \(-0.101762\pi\)
−0.746838 + 0.665006i \(0.768429\pi\)
\(108\) −1953.32 + 2121.62i −1.74036 + 1.89030i
\(109\) 284.365 + 50.1413i 0.249883 + 0.0440611i 0.297187 0.954819i \(-0.403952\pi\)
−0.0473035 + 0.998881i \(0.515063\pi\)
\(110\) −1166.58 1221.50i −1.01117 1.05878i
\(111\) 195.855 + 538.107i 0.167475 + 0.460134i
\(112\) −1615.96 + 133.705i −1.36334 + 0.112803i
\(113\) 698.398i 0.581414i −0.956812 0.290707i \(-0.906110\pi\)
0.956812 0.290707i \(-0.0938905\pi\)
\(114\) −1161.52 + 1918.36i −0.954265 + 1.57606i
\(115\) 157.677i 0.127856i
\(116\) 407.056 + 786.468i 0.325812 + 0.629498i
\(117\) 349.005 + 958.885i 0.275774 + 0.757683i
\(118\) −938.740 + 896.530i −0.732356 + 0.699426i
\(119\) −255.503 45.0520i −0.196823 0.0347052i
\(120\) 2250.51 + 354.538i 1.71202 + 0.269706i
\(121\) 946.591 + 1639.54i 0.711188 + 1.23181i
\(122\) 1301.50 83.7645i 0.965840 0.0621613i
\(123\) 2663.60 + 3174.36i 1.95259 + 2.32701i
\(124\) −353.387 1130.08i −0.255928 0.818423i
\(125\) 732.994 1269.58i 0.524488 0.908440i
\(126\) 4152.90 + 2054.07i 2.93627 + 1.45231i
\(127\) −2560.58 931.973i −1.78909 0.651175i −0.999285 0.0378168i \(-0.987960\pi\)
−0.789805 0.613358i \(-0.789818\pi\)
\(128\) −1010.01 + 1037.80i −0.697449 + 0.716634i
\(129\) −2749.88 + 484.878i −1.87685 + 0.330939i
\(130\) 278.059 378.289i 0.187595 0.255216i
\(131\) 487.724 581.247i 0.325287 0.387662i −0.578473 0.815702i \(-0.696351\pi\)
0.903760 + 0.428039i \(0.140796\pi\)
\(132\) −4013.89 1673.70i −2.64670 1.10361i
\(133\) 2027.95 + 538.699i 1.32215 + 0.351211i
\(134\) 428.766 + 643.334i 0.276416 + 0.414743i
\(135\) −2904.25 2436.96i −1.85154 1.55363i
\(136\) −198.516 + 119.504i −0.125166 + 0.0753485i
\(137\) −282.888 1604.33i −0.176414 1.00049i −0.936499 0.350670i \(-0.885954\pi\)
0.760085 0.649823i \(-0.225157\pi\)
\(138\) −163.065 371.782i −0.100587 0.229334i
\(139\) 1071.34 2943.49i 0.653741 1.79614i 0.0502951 0.998734i \(-0.483984\pi\)
0.603446 0.797404i \(-0.293794\pi\)
\(140\) −273.255 2114.07i −0.164959 1.27623i
\(141\) −339.874 196.226i −0.202997 0.117200i
\(142\) −818.104 239.502i −0.483477 0.141539i
\(143\) −686.513 + 576.053i −0.401462 + 0.336867i
\(144\) 4001.86 1052.10i 2.31589 0.608855i
\(145\) −1008.22 + 582.097i −0.577436 + 0.333383i
\(146\) 24.0815 + 98.9179i 0.0136507 + 0.0560719i
\(147\) 496.902 2818.07i 0.278801 1.58116i
\(148\) 104.671 466.929i 0.0581345 0.259333i
\(149\) −1077.66 + 392.235i −0.592517 + 0.215659i −0.620836 0.783940i \(-0.713207\pi\)
0.0283190 + 0.999599i \(0.490985\pi\)
\(150\) 42.8816 387.330i 0.0233418 0.210836i
\(151\) 2930.13 1.57914 0.789571 0.613660i \(-0.210303\pi\)
0.789571 + 0.613660i \(0.210303\pi\)
\(152\) 1681.86 826.526i 0.897481 0.441053i
\(153\) 662.073 0.349840
\(154\) −447.747 + 4044.29i −0.234289 + 2.11622i
\(155\) 1462.71 532.384i 0.757987 0.275885i
\(156\) 264.411 1179.52i 0.135704 0.605365i
\(157\) −317.240 + 1799.16i −0.161264 + 0.914576i 0.791568 + 0.611081i \(0.209265\pi\)
−0.952833 + 0.303496i \(0.901846\pi\)
\(158\) −31.7150 130.273i −0.0159691 0.0655949i
\(159\) −840.360 + 485.182i −0.419150 + 0.241997i
\(160\) −1423.92 1263.67i −0.703569 0.624387i
\(161\) −290.978 + 244.160i −0.142437 + 0.119519i
\(162\) −4629.52 1355.30i −2.24524 0.657300i
\(163\) −934.281 539.407i −0.448948 0.259200i 0.258438 0.966028i \(-0.416792\pi\)
−0.707386 + 0.706828i \(0.750126\pi\)
\(164\) −443.880 3434.14i −0.211349 1.63513i
\(165\) 1955.38 5372.36i 0.922583 2.53478i
\(166\) 1210.81 + 2760.60i 0.566128 + 1.29075i
\(167\) 614.841 + 3486.94i 0.284897 + 1.61573i 0.705652 + 0.708558i \(0.250654\pi\)
−0.420755 + 0.907174i \(0.638235\pi\)
\(168\) −2830.62 4702.12i −1.29992 2.15938i
\(169\) 1492.18 + 1252.09i 0.679190 + 0.569908i
\(170\) −168.936 253.477i −0.0762165 0.114358i
\(171\) −5335.20 455.166i −2.38592 0.203552i
\(172\) 2153.61 + 898.007i 0.954716 + 0.398095i
\(173\) 2130.06 2538.50i 0.936100 1.11560i −0.0570050 0.998374i \(-0.518155\pi\)
0.993105 0.117227i \(-0.0374005\pi\)
\(174\) −1775.27 + 2415.18i −0.773464 + 1.05227i
\(175\) −359.080 + 63.3154i −0.155108 + 0.0273497i
\(176\) 2070.34 + 2986.63i 0.886693 + 1.27912i
\(177\) −4128.73 1502.73i −1.75330 0.638149i
\(178\) 1704.31 + 842.970i 0.717658 + 0.354962i
\(179\) −851.585 + 1474.99i −0.355589 + 0.615898i −0.987219 0.159372i \(-0.949053\pi\)
0.631630 + 0.775270i \(0.282386\pi\)
\(180\) 1623.53 + 5191.83i 0.672283 + 2.14987i
\(181\) −1722.20 2052.43i −0.707237 0.842852i 0.286088 0.958203i \(-0.407645\pi\)
−0.993325 + 0.115351i \(0.963201\pi\)
\(182\) −1128.67 + 72.6409i −0.459684 + 0.0295852i
\(183\) 2207.21 + 3823.00i 0.891593 + 1.54428i
\(184\) −52.7917 + 335.108i −0.0211514 + 0.134264i
\(185\) 619.517 + 109.238i 0.246204 + 0.0434125i
\(186\) 2898.31 2767.99i 1.14255 1.09118i
\(187\) 198.871 + 546.395i 0.0777696 + 0.213670i
\(188\) 150.742 + 291.247i 0.0584788 + 0.112986i
\(189\) 9133.13i 3.51501i
\(190\) 1187.08 + 2158.74i 0.453262 + 0.824270i
\(191\) 1145.37i 0.433908i −0.976182 0.216954i \(-0.930388\pi\)
0.976182 0.216954i \(-0.0696121\pi\)
\(192\) −4664.28 1506.99i −1.75321 0.566445i
\(193\) −486.666 1337.10i −0.181508 0.498688i 0.815254 0.579104i \(-0.196597\pi\)
−0.996761 + 0.0804155i \(0.974375\pi\)
\(194\) −1361.96 1426.08i −0.504035 0.527766i
\(195\) 1564.97 + 275.947i 0.574718 + 0.101338i
\(196\) −1619.62 + 1759.16i −0.590239 + 0.641093i
\(197\) 1049.95 + 1818.56i 0.379724 + 0.657701i 0.991022 0.133700i \(-0.0426857\pi\)
−0.611298 + 0.791400i \(0.709352\pi\)
\(198\) −666.911 10362.2i −0.239370 3.71924i
\(199\) 442.773 + 527.676i 0.157725 + 0.187970i 0.839120 0.543947i \(-0.183071\pi\)
−0.681394 + 0.731916i \(0.738626\pi\)
\(200\) −204.724 + 253.241i −0.0723808 + 0.0895343i
\(201\) −1308.43 + 2266.26i −0.459150 + 0.795272i
\(202\) −1872.69 + 3786.18i −0.652287 + 1.31879i
\(203\) 2635.42 + 959.215i 0.911184 + 0.331644i
\(204\) −660.468 422.957i −0.226677 0.145161i
\(205\) 4483.03 790.479i 1.52736 0.269314i
\(206\) −1634.60 1201.50i −0.552855 0.406373i
\(207\) 623.069 742.545i 0.209209 0.249326i
\(208\) −717.609 + 710.875i −0.239218 + 0.236973i
\(209\) −1226.93 4539.75i −0.406070 1.50249i
\(210\) 6003.94 4001.48i 1.97291 1.31490i
\(211\) −1345.95 1129.39i −0.439143 0.368485i 0.396245 0.918145i \(-0.370313\pi\)
−0.835389 + 0.549660i \(0.814757\pi\)
\(212\) 810.009 + 37.2790i 0.262413 + 0.0120770i
\(213\) −501.032 2841.49i −0.161174 0.914065i
\(214\) 1161.06 509.247i 0.370881 0.162670i
\(215\) −1049.14 + 2882.49i −0.332794 + 0.914343i
\(216\) 5356.45 + 6151.61i 1.68732 + 1.93780i
\(217\) −3247.46 1874.92i −1.01591 0.586534i
\(218\) 229.464 783.816i 0.0712903 0.243517i
\(219\) −263.975 + 221.501i −0.0814510 + 0.0683455i
\(220\) −3797.03 + 2899.37i −1.16362 + 0.888525i
\(221\) −139.967 + 80.8102i −0.0426028 + 0.0245968i
\(222\) 1573.71 383.120i 0.475769 0.115826i
\(223\) 240.818 1365.75i 0.0723155 0.410122i −0.927064 0.374903i \(-0.877676\pi\)
0.999380 0.0352189i \(-0.0112128\pi\)
\(224\) −127.067 + 4584.50i −0.0379020 + 1.36748i
\(225\) 874.354 318.239i 0.259068 0.0942929i
\(226\) −1963.37 217.366i −0.577883 0.0639779i
\(227\) 4099.53 1.19866 0.599329 0.800503i \(-0.295434\pi\)
0.599329 + 0.800503i \(0.295434\pi\)
\(228\) 5031.49 + 3862.38i 1.46148 + 1.12190i
\(229\) 2168.29 0.625697 0.312849 0.949803i \(-0.398717\pi\)
0.312849 + 0.949803i \(0.398717\pi\)
\(230\) −443.269 49.0746i −0.127080 0.0140691i
\(231\) −12942.1 + 4710.54i −3.68627 + 1.34169i
\(232\) 2337.65 899.560i 0.661527 0.254565i
\(233\) −849.437 + 4817.40i −0.238835 + 1.35450i 0.595551 + 0.803318i \(0.296934\pi\)
−0.834385 + 0.551181i \(0.814177\pi\)
\(234\) 2804.29 682.703i 0.783428 0.190725i
\(235\) −373.368 + 215.564i −0.103642 + 0.0598376i
\(236\) 2228.20 + 2918.06i 0.614591 + 0.804872i
\(237\) 347.651 291.714i 0.0952842 0.0799530i
\(238\) −206.174 + 704.261i −0.0561525 + 0.191809i
\(239\) 795.869 + 459.495i 0.215399 + 0.124361i 0.603818 0.797122i \(-0.293645\pi\)
−0.388419 + 0.921483i \(0.626979\pi\)
\(240\) 1697.13 6216.41i 0.456456 1.67195i
\(241\) 1162.50 3193.94i 0.310718 0.853691i −0.681794 0.731544i \(-0.738800\pi\)
0.992512 0.122147i \(-0.0389779\pi\)
\(242\) 4903.78 2150.82i 1.30259 0.571322i
\(243\) −1145.12 6494.32i −0.302304 1.71445i
\(244\) 169.591 3684.92i 0.0444956 0.966815i
\(245\) −2408.09 2020.63i −0.627948 0.526911i
\(246\) 9752.92 6500.08i 2.52774 1.68467i
\(247\) 1183.46 554.969i 0.304865 0.142963i
\(248\) −3286.93 + 641.738i −0.841615 + 0.164316i
\(249\) −6558.56 + 7816.19i −1.66920 + 1.98928i
\(250\) −3340.98 2455.77i −0.845209 0.621266i
\(251\) 1941.63 342.362i 0.488265 0.0860944i 0.0759048 0.997115i \(-0.475815\pi\)
0.412361 + 0.911021i \(0.364704\pi\)
\(252\) 7067.04 11035.5i 1.76660 2.75863i
\(253\) 799.961 + 291.162i 0.198787 + 0.0723526i
\(254\) −3416.95 + 6908.36i −0.844089 + 1.70657i
\(255\) 515.526 892.918i 0.126602 0.219281i
\(256\) 2603.16 + 3162.40i 0.635536 + 0.772071i
\(257\) 2330.20 + 2777.03i 0.565580 + 0.674031i 0.970717 0.240224i \(-0.0772209\pi\)
−0.405138 + 0.914256i \(0.632776\pi\)
\(258\) 507.254 + 7881.52i 0.122404 + 1.90187i
\(259\) −757.724 1312.42i −0.181786 0.314863i
\(260\) −976.922 899.430i −0.233024 0.214540i
\(261\) −7048.19 1242.79i −1.67154 0.294738i
\(262\) −1482.23 1552.02i −0.349514 0.365970i
\(263\) −300.586 825.853i −0.0704750 0.193628i 0.899455 0.437014i \(-0.143964\pi\)
−0.969930 + 0.243386i \(0.921742\pi\)
\(264\) −5954.46 + 10763.1i −1.38815 + 2.50919i
\(265\) 1065.99i 0.247107i
\(266\) 2145.59 5533.42i 0.494566 1.27547i
\(267\) 6435.77i 1.47514i
\(268\) 1942.02 1005.14i 0.442641 0.229100i
\(269\) 2508.42 + 6891.82i 0.568554 + 1.56209i 0.806763 + 0.590875i \(0.201217\pi\)
−0.238209 + 0.971214i \(0.576560\pi\)
\(270\) −7754.81 + 7406.12i −1.74794 + 1.66934i
\(271\) 2959.32 + 521.808i 0.663343 + 0.116965i 0.495175 0.868793i \(-0.335104\pi\)
0.168168 + 0.985758i \(0.446215\pi\)
\(272\) 274.171 + 595.272i 0.0611178 + 0.132697i
\(273\) −1914.10 3315.32i −0.424346 0.734989i
\(274\) −4598.23 + 295.942i −1.01383 + 0.0652500i
\(275\) 525.271 + 625.993i 0.115182 + 0.137268i
\(276\) −1095.92 + 342.705i −0.239010 + 0.0747407i
\(277\) 4004.50 6935.99i 0.868617 1.50449i 0.00520709 0.999986i \(-0.498343\pi\)
0.863410 0.504503i \(-0.168324\pi\)
\(278\) −7941.44 3927.93i −1.71329 0.847415i
\(279\) 8992.09 + 3272.85i 1.92954 + 0.702296i
\(280\) −6028.23 + 110.213i −1.28663 + 0.0235232i
\(281\) −1891.80 + 333.575i −0.401620 + 0.0708164i −0.370810 0.928709i \(-0.620920\pi\)
−0.0308100 + 0.999525i \(0.509809\pi\)
\(282\) −657.423 + 894.399i −0.138826 + 0.188868i
\(283\) −839.187 + 1000.10i −0.176270 + 0.210071i −0.846945 0.531681i \(-0.821560\pi\)
0.670674 + 0.741752i \(0.266005\pi\)
\(284\) −927.924 + 2225.36i −0.193881 + 0.464967i
\(285\) −4768.15 + 6841.00i −0.991020 + 1.42185i
\(286\) 1405.76 + 2109.25i 0.290645 + 0.436093i
\(287\) −8400.66 7048.99i −1.72779 1.44979i
\(288\) −1712.20 11577.7i −0.350320 2.36883i
\(289\) −834.924 4735.09i −0.169942 0.963788i
\(290\) 1322.63 + 3015.53i 0.267818 + 0.610614i
\(291\) 2282.87 6272.13i 0.459876 1.26350i
\(292\) 285.578 36.9124i 0.0572335 0.00739773i
\(293\) −3577.18 2065.28i −0.713246 0.411793i 0.0990160 0.995086i \(-0.468430\pi\)
−0.812262 + 0.583293i \(0.801764\pi\)
\(294\) −7767.64 2274.00i −1.54088 0.451096i
\(295\) −3697.45 + 3102.53i −0.729743 + 0.612327i
\(296\) −1280.08 439.581i −0.251361 0.0863181i
\(297\) 17726.7 10234.5i 3.46332 1.99955i
\(298\) 767.266 + 3151.64i 0.149149 + 0.612650i
\(299\) −41.0893 + 233.029i −0.00794735 + 0.0450716i
\(300\) −1075.54 241.102i −0.206987 0.0464001i
\(301\) 6943.94 2527.39i 1.32971 0.483974i
\(302\) 911.960 8237.32i 0.173766 1.56955i
\(303\) −14297.3 −2.71076
\(304\) −1800.12 4985.38i −0.339617 0.940564i
\(305\) 4849.44 0.910421
\(306\) 206.061 1861.25i 0.0384958 0.347715i
\(307\) 2614.82 951.716i 0.486109 0.176929i −0.0873266 0.996180i \(-0.527832\pi\)
0.573436 + 0.819250i \(0.305610\pi\)
\(308\) 11230.2 + 2517.46i 2.07759 + 0.465732i
\(309\) 1192.38 6762.31i 0.219521 1.24497i
\(310\) −1041.42 4277.75i −0.190802 0.783742i
\(311\) 9081.98 5243.48i 1.65592 0.956047i 0.681354 0.731954i \(-0.261391\pi\)
0.974568 0.224093i \(-0.0719420\pi\)
\(312\) −3233.62 1110.43i −0.586756 0.201493i
\(313\) −1138.74 + 955.517i −0.205640 + 0.172553i −0.739791 0.672836i \(-0.765076\pi\)
0.534151 + 0.845389i \(0.320631\pi\)
\(314\) 4959.15 + 1451.80i 0.891277 + 0.260924i
\(315\) 14919.5 + 8613.76i 2.66863 + 1.54073i
\(316\) −376.102 + 48.6132i −0.0669538 + 0.00865413i
\(317\) −1725.00 + 4739.41i −0.305633 + 0.839721i 0.687861 + 0.725842i \(0.258550\pi\)
−0.993495 + 0.113879i \(0.963672\pi\)
\(318\) 1102.42 + 2513.47i 0.194404 + 0.443234i
\(319\) −1091.47 6190.02i −0.191569 1.08644i
\(320\) −3995.67 + 3609.71i −0.698015 + 0.630590i
\(321\) 3287.36 + 2758.42i 0.571596 + 0.479626i
\(322\) 595.832 + 894.005i 0.103119 + 0.154723i
\(323\) −75.7395 844.700i −0.0130472 0.145512i
\(324\) −5250.97 + 12592.9i −0.900372 + 2.15928i
\(325\) −146.002 + 173.998i −0.0249192 + 0.0296975i
\(326\) −1807.19 + 2458.62i −0.307028 + 0.417700i
\(327\) 2722.40 480.033i 0.460395 0.0811800i
\(328\) −9792.38 + 179.032i −1.64846 + 0.0301385i
\(329\) 975.958 + 355.220i 0.163545 + 0.0595255i
\(330\) −14494.5 7169.14i −2.41786 1.19590i
\(331\) 1397.55 2420.63i 0.232074 0.401964i −0.726344 0.687331i \(-0.758782\pi\)
0.958418 + 0.285367i \(0.0921156\pi\)
\(332\) 8137.60 2544.70i 1.34521 0.420659i
\(333\) 2485.82 + 2962.49i 0.409076 + 0.487518i
\(334\) 9994.02 643.214i 1.63727 0.105375i
\(335\) 1437.37 + 2489.59i 0.234423 + 0.406033i
\(336\) −14099.8 + 6494.10i −2.28931 + 1.05441i
\(337\) −6864.03 1210.31i −1.10952 0.195638i −0.411283 0.911508i \(-0.634919\pi\)
−0.698234 + 0.715870i \(0.746030\pi\)
\(338\) 3984.35 3805.20i 0.641184 0.612353i
\(339\) −2286.81 6282.97i −0.366379 1.00662i
\(340\) −765.166 + 396.030i −0.122050 + 0.0631699i
\(341\) 8404.06i 1.33462i
\(342\) −2940.09 + 14856.9i −0.464859 + 2.34904i
\(343\) 1117.33i 0.175890i
\(344\) 3194.80 5774.84i 0.500733 0.905113i
\(345\) −516.292 1418.50i −0.0805687 0.221361i
\(346\) −6473.42 6778.20i −1.00582 1.05317i
\(347\) −8465.60 1492.71i −1.30968 0.230931i −0.525140 0.851016i \(-0.675987\pi\)
−0.784535 + 0.620084i \(0.787098\pi\)
\(348\) 6237.16 + 5742.41i 0.960767 + 0.884557i
\(349\) −3651.73 6324.98i −0.560093 0.970109i −0.997488 0.0708398i \(-0.977432\pi\)
0.437395 0.899270i \(-0.355901\pi\)
\(350\) 66.2372 + 1029.17i 0.0101158 + 0.157175i
\(351\) 3657.12 + 4358.39i 0.556133 + 0.662773i
\(352\) 9040.52 4890.71i 1.36892 0.740556i
\(353\) −391.307 + 677.763i −0.0590004 + 0.102192i −0.894017 0.448033i \(-0.852125\pi\)
0.835017 + 0.550225i \(0.185458\pi\)
\(354\) −5509.57 + 11139.2i −0.827204 + 1.67243i
\(355\) −2978.51 1084.09i −0.445304 0.162078i
\(356\) 2900.24 4528.87i 0.431776 0.674241i
\(357\) −2446.08 + 431.311i −0.362634 + 0.0639422i
\(358\) 3881.52 + 2853.09i 0.573029 + 0.421202i
\(359\) −6139.12 + 7316.32i −0.902536 + 1.07560i 0.0942548 + 0.995548i \(0.469953\pi\)
−0.996791 + 0.0800522i \(0.974491\pi\)
\(360\) 15100.8 2948.28i 2.21079 0.431633i
\(361\) 29.6139 + 6858.94i 0.00431753 + 0.999991i
\(362\) −6305.92 + 4202.74i −0.915557 + 0.610196i
\(363\) 13884.2 + 11650.3i 2.00753 + 1.68452i
\(364\) −147.070 + 3195.58i −0.0211773 + 0.460148i
\(365\) 65.7351 + 372.802i 0.00942666 + 0.0534613i
\(366\) 11434.4 5015.16i 1.63302 0.716248i
\(367\) 3960.55 10881.5i 0.563322 1.54771i −0.251413 0.967880i \(-0.580895\pi\)
0.814735 0.579834i \(-0.196883\pi\)
\(368\) 925.643 + 252.708i 0.131121 + 0.0357971i
\(369\) 24235.5 + 13992.4i 3.41910 + 1.97402i
\(370\) 499.910 1707.62i 0.0702407 0.239932i
\(371\) 1967.19 1650.67i 0.275287 0.230993i
\(372\) −6879.47 9009.39i −0.958827 1.25569i
\(373\) −11007.9 + 6355.42i −1.52806 + 0.882229i −0.528622 + 0.848857i \(0.677291\pi\)
−0.999443 + 0.0333714i \(0.989376\pi\)
\(374\) 1597.95 389.020i 0.220930 0.0537854i
\(375\) 2437.12 13821.6i 0.335606 1.90332i
\(376\) 865.686 333.128i 0.118735 0.0456909i
\(377\) 1641.73 597.541i 0.224280 0.0816311i
\(378\) 25675.5 + 2842.56i 3.49367 + 0.386787i
\(379\) −8402.23 −1.13877 −0.569385 0.822071i \(-0.692819\pi\)
−0.569385 + 0.822071i \(0.692819\pi\)
\(380\) 6438.22 2665.30i 0.869141 0.359808i
\(381\) −26087.2 −3.50784
\(382\) −3219.94 356.481i −0.431273 0.0477465i
\(383\) −2213.69 + 805.719i −0.295338 + 0.107494i −0.485440 0.874270i \(-0.661340\pi\)
0.190102 + 0.981764i \(0.439118\pi\)
\(384\) −5688.21 + 12643.4i −0.755925 + 1.68023i
\(385\) −2627.29 + 14900.1i −0.347790 + 1.97241i
\(386\) −3910.40 + 951.986i −0.515633 + 0.125531i
\(387\) −16331.0 + 9428.71i −2.14509 + 1.23847i
\(388\) −4432.96 + 3384.96i −0.580024 + 0.442900i
\(389\) 6430.17 5395.55i 0.838104 0.703253i −0.119032 0.992890i \(-0.537979\pi\)
0.957136 + 0.289638i \(0.0935348\pi\)
\(390\) 1262.83 4313.65i 0.163964 0.560077i
\(391\) 132.958 + 76.7634i 0.0171969 + 0.00992863i
\(392\) 4441.35 + 5100.66i 0.572251 + 0.657200i
\(393\) 2484.47 6826.03i 0.318893 0.876151i
\(394\) 5439.21 2385.66i 0.695491 0.305045i
\(395\) −86.5722 490.975i −0.0110276 0.0625409i
\(396\) −29338.3 1350.24i −3.72300 0.171343i
\(397\) −5447.64 4571.11i −0.688688 0.577878i 0.229843 0.973228i \(-0.426179\pi\)
−0.918530 + 0.395350i \(0.870623\pi\)
\(398\) 1621.24 1080.51i 0.204184 0.136084i
\(399\) 20007.9 1793.99i 2.51039 0.225093i
\(400\) 648.207 + 654.348i 0.0810259 + 0.0817935i
\(401\) 20.0152 23.8532i 0.00249255 0.00297051i −0.764797 0.644272i \(-0.777161\pi\)
0.767289 + 0.641301i \(0.221605\pi\)
\(402\) 5963.80 + 4383.65i 0.739918 + 0.543873i
\(403\) −2300.47 + 405.635i −0.284353 + 0.0501392i
\(404\) 10061.1 + 6443.00i 1.23900 + 0.793443i
\(405\) −16854.9 6134.69i −2.06797 0.752679i
\(406\) 3516.83 7110.29i 0.429895 0.869157i
\(407\) −1698.19 + 2941.36i −0.206821 + 0.358225i
\(408\) −1394.60 + 1725.10i −0.169223 + 0.209327i
\(409\) 7190.49 + 8569.29i 0.869308 + 1.03600i 0.999012 + 0.0444477i \(0.0141528\pi\)
−0.129704 + 0.991553i \(0.541403\pi\)
\(410\) −826.957 12848.9i −0.0996109 1.54772i
\(411\) −7798.11 13506.7i −0.935894 1.62102i
\(412\) −3886.48 + 4221.32i −0.464740 + 0.504781i
\(413\) 11450.9 + 2019.10i 1.36431 + 0.240565i
\(414\) −1893.56 1982.71i −0.224791 0.235374i
\(415\) 3833.64 + 10532.8i 0.453460 + 1.24587i
\(416\) 1775.10 + 2238.63i 0.209210 + 0.263841i
\(417\) 29988.3i 3.52166i
\(418\) −13144.2 + 2036.28i −1.53805 + 0.238272i
\(419\) 1936.91i 0.225833i 0.993604 + 0.112916i \(0.0360193\pi\)
−0.993604 + 0.112916i \(0.963981\pi\)
\(420\) −9380.51 18124.0i −1.08981 2.10562i
\(421\) 2115.58 + 5812.52i 0.244910 + 0.672886i 0.999854 + 0.0170959i \(0.00544206\pi\)
−0.754943 + 0.655790i \(0.772336\pi\)
\(422\) −3593.90 + 3432.31i −0.414570 + 0.395929i
\(423\) −2610.11 460.233i −0.300018 0.0529013i
\(424\) 356.904 2265.54i 0.0408792 0.259491i
\(425\) 73.6863 + 127.628i 0.00841015 + 0.0145668i
\(426\) −8144.09 + 524.153i −0.926250 + 0.0596133i
\(427\) −7509.28 8949.21i −0.851053 1.01425i
\(428\) −1070.26 3422.54i −0.120871 0.386529i
\(429\) −4289.84 + 7430.21i −0.482786 + 0.836210i
\(430\) 7776.86 + 3846.52i 0.872171 + 0.431386i
\(431\) 8830.70 + 3214.11i 0.986914 + 0.359207i 0.784524 0.620098i \(-0.212907\pi\)
0.202389 + 0.979305i \(0.435129\pi\)
\(432\) 18960.8 13143.7i 2.11170 1.46384i
\(433\) −7576.89 + 1336.01i −0.840928 + 0.148278i −0.577490 0.816398i \(-0.695968\pi\)
−0.263438 + 0.964676i \(0.584857\pi\)
\(434\) −6281.59 + 8545.87i −0.694761 + 0.945196i
\(435\) −7164.21 + 8537.97i −0.789650 + 0.941068i
\(436\) −2132.09 889.033i −0.234194 0.0976536i
\(437\) −1018.65 709.991i −0.111507 0.0777197i
\(438\) 540.537 + 811.038i 0.0589677 + 0.0884770i
\(439\) 5595.51 + 4695.19i 0.608335 + 0.510454i 0.894113 0.447842i \(-0.147807\pi\)
−0.285777 + 0.958296i \(0.592252\pi\)
\(440\) 6969.09 + 11576.8i 0.755087 + 1.25432i
\(441\) −3355.75 19031.4i −0.362353 2.05501i
\(442\) 183.615 + 418.634i 0.0197594 + 0.0450507i
\(443\) −69.3384 + 190.506i −0.00743649 + 0.0204316i −0.943355 0.331784i \(-0.892349\pi\)
0.935919 + 0.352216i \(0.114572\pi\)
\(444\) −587.250 4543.34i −0.0627695 0.485625i
\(445\) 6122.79 + 3535.00i 0.652243 + 0.376573i
\(446\) −3764.51 1102.07i −0.399674 0.117006i
\(447\) −8410.54 + 7057.28i −0.889944 + 0.746752i
\(448\) 12848.6 + 1784.08i 1.35500 + 0.188147i
\(449\) −8094.34 + 4673.27i −0.850769 + 0.491192i −0.860910 0.508757i \(-0.830105\pi\)
0.0101409 + 0.999949i \(0.496772\pi\)
\(450\) −622.519 2557.07i −0.0652129 0.267870i
\(451\) −4267.82 + 24204.0i −0.445596 + 2.52710i
\(452\) −1222.14 + 5451.88i −0.127179 + 0.567334i
\(453\) 26360.1 9594.31i 2.73401 0.995099i
\(454\) 1275.92 11524.8i 0.131898 1.19138i
\(455\) −4205.45 −0.433307
\(456\) 12424.1 12942.7i 1.27590 1.32916i
\(457\) 8409.75 0.860813 0.430406 0.902635i \(-0.358370\pi\)
0.430406 + 0.902635i \(0.358370\pi\)
\(458\) 674.849 6095.61i 0.0688507 0.621898i
\(459\) 3468.83 1262.55i 0.352748 0.128390i
\(460\) −275.922 + 1230.87i −0.0279673 + 0.124760i
\(461\) 2152.48 12207.3i 0.217464 1.23330i −0.659116 0.752041i \(-0.729069\pi\)
0.876580 0.481257i \(-0.159820\pi\)
\(462\) 9214.46 + 37849.6i 0.927912 + 3.81152i
\(463\) −7855.39 + 4535.31i −0.788490 + 0.455235i −0.839431 0.543467i \(-0.817111\pi\)
0.0509406 + 0.998702i \(0.483778\pi\)
\(464\) −1801.33 6851.70i −0.180225 0.685522i
\(465\) 11415.7 9578.93i 1.13848 0.955295i
\(466\) 13278.5 + 3887.33i 1.31999 + 0.386431i
\(467\) −3366.21 1943.48i −0.333553 0.192577i 0.323864 0.946104i \(-0.395018\pi\)
−0.657418 + 0.753526i \(0.728351\pi\)
\(468\) −1046.45 8096.04i −0.103360 0.799657i
\(469\) 2368.58 6507.63i 0.233200 0.640713i
\(470\) 489.799 + 1116.72i 0.0480697 + 0.109597i
\(471\) 3037.13 + 17224.4i 0.297120 + 1.68505i
\(472\) 8896.91 5355.83i 0.867613 0.522292i
\(473\) −12686.8 10645.5i −1.23327 1.03484i
\(474\) −711.879 1068.13i −0.0689825 0.103503i
\(475\) −506.046 1079.13i −0.0488820 0.104240i
\(476\) 1915.69 + 798.798i 0.184465 + 0.0769178i
\(477\) −4212.33 + 5020.05i −0.404338 + 0.481871i
\(478\) 1539.46 2094.38i 0.147308 0.200407i
\(479\) 338.101 59.6164i 0.0322510 0.00568672i −0.157499 0.987519i \(-0.550343\pi\)
0.189750 + 0.981832i \(0.439232\pi\)
\(480\) −16947.7 6705.84i −1.61157 0.637663i
\(481\) −887.112 322.882i −0.0840932 0.0306074i
\(482\) −8617.15 4262.14i −0.814316 0.402770i
\(483\) −1818.25 + 3149.29i −0.171290 + 0.296683i
\(484\) −4520.26 14455.2i −0.424518 1.35755i
\(485\) −4713.19 5616.96i −0.441268 0.525883i
\(486\) −18613.6 + 1197.97i −1.73730 + 0.111813i
\(487\) 6026.52 + 10438.2i 0.560755 + 0.971255i 0.997431 + 0.0716367i \(0.0228222\pi\)
−0.436676 + 0.899619i \(0.643844\pi\)
\(488\) −10306.5 1623.64i −0.956048 0.150612i
\(489\) −10171.2 1793.46i −0.940612 0.165855i
\(490\) −6429.97 + 6140.85i −0.592809 + 0.566154i
\(491\) −3442.08 9457.05i −0.316373 0.869227i −0.991333 0.131373i \(-0.958061\pi\)
0.674960 0.737854i \(-0.264161\pi\)
\(492\) −15237.9 29441.0i −1.39630 2.69777i
\(493\) 1133.55i 0.103555i
\(494\) −1191.82 3499.72i −0.108548 0.318745i
\(495\) 38609.9i 3.50583i
\(496\) 781.077 + 9440.13i 0.0707084 + 0.854585i
\(497\) 2611.59 + 7175.28i 0.235706 + 0.647596i
\(498\) 19932.0 + 20870.4i 1.79352 + 1.87796i
\(499\) 16406.1 + 2892.84i 1.47182 + 0.259521i 0.851304 0.524673i \(-0.175812\pi\)
0.620515 + 0.784194i \(0.286924\pi\)
\(500\) −7943.62 + 8628.02i −0.710499 + 0.771714i
\(501\) 16948.8 + 29356.1i 1.51141 + 2.61784i
\(502\) −358.161 5564.97i −0.0318436 0.494774i
\(503\) −4401.94 5246.02i −0.390204 0.465027i 0.534803 0.844977i \(-0.320386\pi\)
−0.925007 + 0.379950i \(0.875941\pi\)
\(504\) −28824.2 23301.9i −2.54748 2.05942i
\(505\) −7853.13 + 13602.0i −0.692000 + 1.19858i
\(506\) 1067.51 2158.27i 0.0937874 0.189618i
\(507\) 17523.8 + 6378.15i 1.53503 + 0.558705i
\(508\) 18357.7 + 11756.0i 1.60332 + 1.02675i
\(509\) −7989.05 + 1408.69i −0.695695 + 0.122670i −0.510303 0.859995i \(-0.670467\pi\)
−0.185392 + 0.982665i \(0.559355\pi\)
\(510\) −2349.77 1727.18i −0.204018 0.149963i
\(511\) 586.183 698.586i 0.0507460 0.0604768i
\(512\) 9700.50 6333.87i 0.837316 0.546719i
\(513\) −28821.0 + 7789.27i −2.48046 + 0.670380i
\(514\) 8532.16 5686.47i 0.732174 0.487976i
\(515\) −5778.51 4848.75i −0.494431 0.414877i
\(516\) 22314.8 + 1026.99i 1.90379 + 0.0876178i
\(517\) −404.196 2292.31i −0.0343840 0.195001i
\(518\) −3925.36 + 1721.68i −0.332955 + 0.146035i
\(519\) 10850.5 29811.6i 0.917699 2.52136i
\(520\) −2832.58 + 2466.44i −0.238878 + 0.208001i
\(521\) −6925.69 3998.55i −0.582380 0.336237i 0.179699 0.983722i \(-0.442488\pi\)
−0.762079 + 0.647485i \(0.775821\pi\)
\(522\) −5687.43 + 19427.4i −0.476881 + 1.62896i
\(523\) −10742.1 + 9013.71i −0.898127 + 0.753618i −0.969823 0.243809i \(-0.921603\pi\)
0.0716966 + 0.997426i \(0.477159\pi\)
\(524\) −4824.44 + 3683.89i −0.402207 + 0.307121i
\(525\) −3023.05 + 1745.36i −0.251308 + 0.145093i
\(526\) −2415.23 + 587.987i −0.200207 + 0.0487404i
\(527\) −263.185 + 1492.59i −0.0217543 + 0.123375i
\(528\) 28404.6 + 20089.4i 2.34120 + 1.65583i
\(529\) −11222.0 + 4084.48i −0.922333 + 0.335702i
\(530\) 2996.77 + 331.774i 0.245606 + 0.0271912i
\(531\) −29672.2 −2.42498
\(532\) −14888.0 7753.98i −1.21331 0.631913i
\(533\) −6831.42 −0.555163
\(534\) 18092.6 + 2003.04i 1.46618 + 0.162322i
\(535\) 4429.93 1612.36i 0.357986 0.130296i
\(536\) −2221.28 5772.34i −0.179001 0.465163i
\(537\) −2831.42 + 16057.8i −0.227532 + 1.29040i
\(538\) 20155.4 4906.81i 1.61517 0.393211i
\(539\) 14698.2 8486.02i 1.17458 0.678143i
\(540\) 18406.9 + 24105.8i 1.46686 + 1.92101i
\(541\) 17044.0 14301.7i 1.35449 1.13655i 0.376853 0.926273i \(-0.377006\pi\)
0.977641 0.210282i \(-0.0674381\pi\)
\(542\) 2387.98 8156.98i 0.189248 0.646444i
\(543\) −22213.7 12825.1i −1.75558 1.01359i
\(544\) 1758.79 585.493i 0.138617 0.0461449i
\(545\) 1038.65 2853.68i 0.0816350 0.224290i
\(546\) −9915.92 + 4349.17i −0.777220 + 0.340892i
\(547\) −3214.64 18231.1i −0.251276 1.42506i −0.805454 0.592659i \(-0.798078\pi\)
0.554178 0.832398i \(-0.313033\pi\)
\(548\) −599.167 + 13018.9i −0.0467065 + 1.01485i
\(549\) 22837.4 + 19162.9i 1.77537 + 1.48971i
\(550\) 1923.31 1281.84i 0.149109 0.0993776i
\(551\) −779.302 + 9134.54i −0.0602530 + 0.706251i
\(552\) 622.340 + 3187.58i 0.0479865 + 0.245783i
\(553\) −771.995 + 920.028i −0.0593645 + 0.0707479i
\(554\) −18252.5 13416.4i −1.39977 1.02889i
\(555\) 5931.01 1045.80i 0.453617 0.0799849i
\(556\) −13514.0 + 21102.9i −1.03080 + 1.60964i
\(557\) 17447.0 + 6350.21i 1.32721 + 0.483064i 0.905761 0.423788i \(-0.139300\pi\)
0.421447 + 0.906853i \(0.361522\pi\)
\(558\) 11999.5 24260.4i 0.910355 1.84054i
\(559\) 2301.67 3986.60i 0.174150 0.301637i
\(560\) −1566.36 + 16981.2i −0.118198 + 1.28140i
\(561\) 3578.19 + 4264.33i 0.269290 + 0.320927i
\(562\) 348.968 + 5422.14i 0.0261928 + 0.406973i
\(563\) 6836.44 + 11841.1i 0.511761 + 0.886396i 0.999907 + 0.0136343i \(0.00434007\pi\)
−0.488146 + 0.872762i \(0.662327\pi\)
\(564\) 2309.77 + 2126.55i 0.172445 + 0.158766i
\(565\) −7233.51 1275.46i −0.538612 0.0949719i
\(566\) 2550.36 + 2670.43i 0.189399 + 0.198316i
\(567\) 14778.5 + 40603.7i 1.09460 + 3.00740i
\(568\) 5967.23 + 3301.24i 0.440809 + 0.243868i
\(569\) 22496.0i 1.65744i 0.559664 + 0.828720i \(0.310930\pi\)
−0.559664 + 0.828720i \(0.689070\pi\)
\(570\) 17747.8 + 15533.6i 1.30416 + 1.14146i
\(571\) 8286.53i 0.607322i 0.952780 + 0.303661i \(0.0982090\pi\)
−0.952780 + 0.303661i \(0.901791\pi\)
\(572\) 6367.15 3295.48i 0.465427 0.240893i
\(573\) −3750.38 10304.1i −0.273428 0.751237i
\(574\) −22431.1 + 21422.5i −1.63110 + 1.55776i
\(575\) 212.486 + 37.4671i 0.0154109 + 0.00271736i
\(576\) −33080.7 + 1210.02i −2.39299 + 0.0875306i
\(577\) −790.332 1368.90i −0.0570225 0.0987658i 0.836105 0.548569i \(-0.184827\pi\)
−0.893128 + 0.449804i \(0.851494\pi\)
\(578\) −13571.4 + 873.453i −0.976635 + 0.0628561i
\(579\) −8756.34 10435.4i −0.628499 0.749016i
\(580\) 8889.07 2779.69i 0.636376 0.199001i
\(581\) 13501.1 23384.6i 0.964061 1.66980i
\(582\) −16922.0 8369.82i −1.20522 0.596117i
\(583\) −5408.23 1968.43i −0.384195 0.139836i
\(584\) −14.8881 814.320i −0.00105492 0.0577000i
\(585\) 10568.8 1863.57i 0.746952 0.131708i
\(586\) −6919.38 + 9413.56i −0.487776 + 0.663601i
\(587\) 10516.7 12533.3i 0.739470 0.881266i −0.256896 0.966439i \(-0.582700\pi\)
0.996366 + 0.0851727i \(0.0271442\pi\)
\(588\) −8810.35 + 21129.1i −0.617913 + 1.48188i
\(589\) 3146.96 11846.9i 0.220150 0.828764i
\(590\) 7571.22 + 11360.1i 0.528309 + 0.792691i
\(591\) 15400.2 + 12922.3i 1.07188 + 0.899413i
\(592\) −1634.18 + 3461.80i −0.113453 + 0.240337i
\(593\) 1010.19 + 5729.05i 0.0699551 + 0.396735i 0.999600 + 0.0282785i \(0.00900253\pi\)
−0.929645 + 0.368456i \(0.879886\pi\)
\(594\) −23254.6 53019.4i −1.60631 3.66231i
\(595\) −933.233 + 2564.04i −0.0643006 + 0.176664i
\(596\) 9098.85 1176.07i 0.625341 0.0808286i
\(597\) 5711.10 + 3297.31i 0.391524 + 0.226047i
\(598\) 642.315 + 188.039i 0.0439234 + 0.0128587i
\(599\) 17767.3 14908.5i 1.21194 1.01694i 0.212734 0.977110i \(-0.431763\pi\)
0.999207 0.0398285i \(-0.0126812\pi\)
\(600\) −1012.54 + 2948.56i −0.0688948 + 0.200624i
\(601\) 8904.16 5140.82i 0.604340 0.348916i −0.166407 0.986057i \(-0.553217\pi\)
0.770747 + 0.637142i \(0.219883\pi\)
\(602\) −4943.92 20307.8i −0.334716 1.37489i
\(603\) −3068.80 + 17404.0i −0.207249 + 1.17537i
\(604\) −22873.3 5127.49i −1.54090 0.345422i
\(605\) 18709.9 6809.86i 1.25730 0.457620i
\(606\) −4449.83 + 40193.3i −0.298287 + 2.69429i
\(607\) 27479.8 1.83751 0.918757 0.394823i \(-0.129194\pi\)
0.918757 + 0.394823i \(0.129194\pi\)
\(608\) −14575.4 + 3508.95i −0.972223 + 0.234057i
\(609\) 26849.7 1.78655
\(610\) 1509.32 13633.0i 0.100181 0.904892i
\(611\) 607.971 221.283i 0.0402551 0.0146517i
\(612\) −5168.32 1158.58i −0.341368 0.0765240i
\(613\) −2525.22 + 14321.2i −0.166383 + 0.943603i 0.781245 + 0.624225i \(0.214585\pi\)
−0.947627 + 0.319378i \(0.896526\pi\)
\(614\) −1861.69 7647.12i −0.122364 0.502626i
\(615\) 37742.1 21790.4i 2.47465 1.42874i
\(616\) 10572.4 30787.3i 0.691518 2.01373i
\(617\) −12439.8 + 10438.2i −0.811679 + 0.681080i −0.951008 0.309166i \(-0.899950\pi\)
0.139329 + 0.990246i \(0.455506\pi\)
\(618\) −18639.4 5456.75i −1.21325 0.355182i
\(619\) 16993.1 + 9810.98i 1.10341 + 0.637054i 0.937115 0.349022i \(-0.113486\pi\)
0.166296 + 0.986076i \(0.446819\pi\)
\(620\) −12350.0 + 1596.30i −0.799978 + 0.103401i
\(621\) 1848.47 5078.62i 0.119447 0.328177i
\(622\) −11914.1 27163.7i −0.768026 1.75107i
\(623\) −2957.52 16773.0i −0.190194 1.07864i
\(624\) −4128.13 + 8744.92i −0.264836 + 0.561021i
\(625\) −10432.7 8754.09i −0.667694 0.560262i
\(626\) 2331.78 + 3498.68i 0.148877 + 0.223379i
\(627\) −25902.6 36823.3i −1.64984 2.34542i
\(628\) 5624.85 13489.6i 0.357414 0.857153i
\(629\) −393.719 + 469.216i −0.0249580 + 0.0297438i
\(630\) 28858.9 39261.5i 1.82503 2.48288i
\(631\) −6722.56 + 1185.37i −0.424122 + 0.0747841i −0.381635 0.924313i \(-0.624639\pi\)
−0.0424864 + 0.999097i \(0.513528\pi\)
\(632\) 19.6074 + 1072.45i 0.00123408 + 0.0674995i
\(633\) −15806.6 5753.12i −0.992503 0.361242i
\(634\) 12786.8 + 6324.49i 0.800990 + 0.396179i
\(635\) −14329.0 + 24818.6i −0.895479 + 1.55102i
\(636\) 7409.11 2316.90i 0.461934 0.144451i
\(637\) 3032.34 + 3613.80i 0.188611 + 0.224778i
\(638\) −17741.4 + 1141.83i −1.10092 + 0.0708553i
\(639\) −9742.82 16875.1i −0.603161 1.04471i
\(640\) 8904.20 + 12356.3i 0.549952 + 0.763165i
\(641\) −9567.76 1687.05i −0.589553 0.103954i −0.129090 0.991633i \(-0.541206\pi\)
−0.460463 + 0.887679i \(0.652317\pi\)
\(642\) 8777.75 8383.06i 0.539611 0.515348i
\(643\) 2841.20 + 7806.14i 0.174255 + 0.478762i 0.995818 0.0913553i \(-0.0291199\pi\)
−0.821563 + 0.570118i \(0.806898\pi\)
\(644\) 2698.72 1396.79i 0.165131 0.0854676i
\(645\) 29366.8i 1.79274i
\(646\) −2398.24 49.9780i −0.146064 0.00304390i
\(647\) 14378.2i 0.873674i 0.899541 + 0.436837i \(0.143901\pi\)
−0.899541 + 0.436837i \(0.856099\pi\)
\(648\) 33767.6 + 18681.1i 2.04709 + 1.13251i
\(649\) −8912.84 24487.8i −0.539075 1.48110i
\(650\) 443.712 + 464.603i 0.0267751 + 0.0280357i
\(651\) −35354.1 6233.88i −2.12847 0.375307i
\(652\) 6349.32 + 5845.68i 0.381378 + 0.351126i
\(653\) −13507.7 23396.1i −0.809491 1.40208i −0.913217 0.407474i \(-0.866410\pi\)
0.103725 0.994606i \(-0.466924\pi\)
\(654\) −502.184 7802.76i −0.0300259 0.466532i
\(655\) −5129.42 6113.00i −0.305989 0.364664i
\(656\) −2544.43 + 27584.6i −0.151438 + 1.64176i
\(657\) −1163.58 + 2015.39i −0.0690955 + 0.119677i
\(658\) 1302.36 2633.11i 0.0771602 0.156002i
\(659\) −18905.6 6881.07i −1.11754 0.406750i −0.283784 0.958888i \(-0.591590\pi\)
−0.833753 + 0.552138i \(0.813812\pi\)
\(660\) −24665.4 + 38516.3i −1.45470 + 2.27159i
\(661\) −10325.9 + 1820.73i −0.607610 + 0.107138i −0.468984 0.883207i \(-0.655380\pi\)
−0.138626 + 0.990345i \(0.544269\pi\)
\(662\) −6370.04 4682.26i −0.373986 0.274896i
\(663\) −994.579 + 1185.29i −0.0582598 + 0.0694313i
\(664\) −4621.08 23668.8i −0.270080 1.38333i
\(665\) 9283.04 20020.3i 0.541324 1.16745i
\(666\) 9101.97 6066.24i 0.529571 0.352946i
\(667\) −1271.33 1066.77i −0.0738022 0.0619274i
\(668\) 1302.26 28295.9i 0.0754280 1.63892i
\(669\) −2305.50 13075.1i −0.133237 0.755625i
\(670\) 7446.23 3265.95i 0.429363 0.188320i
\(671\) −8954.86 + 24603.3i −0.515199 + 1.41550i
\(672\) 13868.2 + 41659.3i 0.796097 + 2.39143i
\(673\) −21.9615 12.6795i −0.00125788 0.000726238i 0.499371 0.866388i \(-0.333565\pi\)
−0.500629 + 0.865662i \(0.666898\pi\)
\(674\) −5538.82 + 18919.8i −0.316539 + 1.08125i
\(675\) 3974.17 3334.72i 0.226616 0.190153i
\(676\) −9457.29 12385.3i −0.538080 0.704672i
\(677\) 9774.49 5643.31i 0.554896 0.320369i −0.196199 0.980564i \(-0.562860\pi\)
0.751094 + 0.660195i \(0.229526\pi\)
\(678\) −18374.7 + 4473.32i −1.04082 + 0.253388i
\(679\) −3067.30 + 17395.6i −0.173361 + 0.983181i
\(680\) 875.194 + 2274.33i 0.0493561 + 0.128260i
\(681\) 36880.4 13423.4i 2.07527 0.755337i
\(682\) 23625.9 + 2615.64i 1.32652 + 0.146859i
\(683\) −5344.84 −0.299436 −0.149718 0.988729i \(-0.547837\pi\)
−0.149718 + 0.988729i \(0.547837\pi\)
\(684\) 40851.5 + 12889.3i 2.28362 + 0.720521i
\(685\) −17133.2 −0.955657
\(686\) −3141.10 347.753i −0.174822 0.0193546i
\(687\) 19506.5 7099.78i 1.08329 0.394284i
\(688\) −15240.2 10778.7i −0.844516 0.597290i
\(689\) 277.789 1575.42i 0.0153598 0.0871098i
\(690\) −4148.45 + 1009.94i −0.228882 + 0.0557213i
\(691\) −18938.9 + 10934.4i −1.04265 + 0.601973i −0.920582 0.390549i \(-0.872285\pi\)
−0.122066 + 0.992522i \(0.538952\pi\)
\(692\) −21070.0 + 16088.8i −1.15746 + 0.883821i
\(693\) −71251.2 + 59786.9i −3.90564 + 3.27722i
\(694\) −6831.19 + 23334.4i −0.373643 + 1.27631i
\(695\) −28530.0 16471.8i −1.55713 0.899007i
\(696\) 18084.6 15747.0i 0.984906 0.857598i
\(697\) −1515.96 + 4165.07i −0.0823833 + 0.226346i
\(698\) −18917.6 + 8297.36i −1.02585 + 0.449942i
\(699\) 8132.18 + 46119.9i 0.440039 + 2.49559i
\(700\) 2913.87 + 134.105i 0.157334 + 0.00724097i
\(701\) 29.9588 + 25.1384i 0.00161416 + 0.00135444i 0.643594 0.765367i \(-0.277442\pi\)
−0.641980 + 0.766721i \(0.721887\pi\)
\(702\) 13390.7 8924.60i 0.719945 0.479825i
\(703\) 3495.29 3510.41i 0.187521 0.188333i
\(704\) −10935.3 26937.3i −0.585425 1.44210i
\(705\) −2653.07 + 3161.81i −0.141731 + 0.168909i
\(706\) 1783.57 + 1311.01i 0.0950788 + 0.0698871i
\(707\) 37261.8 6570.25i 1.98214 0.349505i
\(708\) 29600.3 + 18955.7i 1.57125 + 1.00621i
\(709\) 9850.75 + 3585.38i 0.521795 + 0.189918i 0.589471 0.807789i \(-0.299336\pi\)
−0.0676760 + 0.997707i \(0.521558\pi\)
\(710\) −3974.67 + 8035.94i −0.210094 + 0.424766i
\(711\) 1532.42 2654.24i 0.0808304 0.140002i
\(712\) −11829.1 9562.85i −0.622634 0.503347i
\(713\) 1426.33 + 1699.84i 0.0749180 + 0.0892838i
\(714\) 451.214 + 7010.80i 0.0236502 + 0.367468i
\(715\) 4712.59 + 8162.44i 0.246491 + 0.426934i
\(716\) 9228.81 10023.9i 0.481699 0.523201i
\(717\) 8664.39 + 1527.77i 0.451294 + 0.0795752i
\(718\) 18657.3 + 19535.7i 0.969755 + 1.01541i
\(719\) −11.3152 31.0882i −0.000586906 0.00161251i 0.939399 0.342826i \(-0.111384\pi\)
−0.939986 + 0.341214i \(0.889162\pi\)
\(720\) −3588.42 43369.9i −0.185740 2.24486i
\(721\) 18171.9i 0.938639i
\(722\) 19291.4 + 2051.49i 0.994393 + 0.105746i
\(723\) 32539.9i 1.67382i
\(724\) 9852.32 + 19035.6i 0.505744 + 0.977142i
\(725\) −544.865 1497.00i −0.0279114 0.0766859i
\(726\) 37073.1 35406.1i 1.89519 1.80998i
\(727\) −9166.96 1616.38i −0.467653 0.0824598i −0.0651440 0.997876i \(-0.520751\pi\)
−0.402509 + 0.915416i \(0.631862\pi\)
\(728\) 8937.79 + 1408.03i 0.455023 + 0.0716826i
\(729\) −8542.66 14796.3i −0.434012 0.751731i
\(730\) 1068.50 68.7685i 0.0541739 0.00348663i
\(731\) −1919.84 2287.98i −0.0971380 0.115765i
\(732\) −10540.1 33705.8i −0.532204 1.70191i
\(733\) 12113.5 20981.2i 0.610399 1.05724i −0.380774 0.924668i \(-0.624342\pi\)
0.991173 0.132575i \(-0.0423244\pi\)
\(734\) −29358.0 14520.8i −1.47633 0.730209i
\(735\) −28280.1 10293.1i −1.41922 0.516553i
\(736\) 998.520 2523.56i 0.0500080 0.126386i
\(737\) −15285.0 + 2695.15i −0.763947 + 0.134705i
\(738\) 46879.0 63777.1i 2.33827 3.18112i
\(739\) 7630.22 9093.35i 0.379814 0.452644i −0.541942 0.840416i \(-0.682311\pi\)
0.921755 + 0.387772i \(0.126755\pi\)
\(740\) −4644.96 1936.84i −0.230746 0.0962159i
\(741\) 8829.51 8867.72i 0.437733 0.439627i
\(742\) −4028.19 6044.01i −0.199298 0.299033i
\(743\) 5842.08 + 4902.09i 0.288459 + 0.242046i 0.775521 0.631321i \(-0.217487\pi\)
−0.487062 + 0.873367i \(0.661932\pi\)
\(744\) −27468.8 + 16535.9i −1.35357 + 0.814831i
\(745\) 2094.40 + 11877.9i 0.102997 + 0.584125i
\(746\) 14440.6 + 32924.0i 0.708725 + 1.61586i
\(747\) −23567.4 + 64751.0i −1.15433 + 3.17150i
\(748\) −596.294 4613.31i −0.0291480 0.225507i
\(749\) −9835.15 5678.33i −0.479798 0.277011i
\(750\) −38097.4 11153.1i −1.85483 0.543006i
\(751\) −1658.97 + 1392.04i −0.0806081 + 0.0676383i −0.682201 0.731164i \(-0.738977\pi\)
0.601593 + 0.798803i \(0.294533\pi\)
\(752\) −667.074 2537.34i −0.0323480 0.123042i
\(753\) 16346.4 9437.58i 0.791096 0.456739i
\(754\) −1168.87 4801.29i −0.0564560 0.231900i
\(755\) 5351.20 30348.1i 0.257947 1.46289i
\(756\) 15982.3 71295.7i 0.768875 3.42989i
\(757\) −33603.1 + 12230.5i −1.61338 + 0.587221i −0.982104 0.188339i \(-0.939690\pi\)
−0.631273 + 0.775560i \(0.717467\pi\)
\(758\) −2615.07 + 23620.8i −0.125308 + 1.13185i
\(759\) 8150.02 0.389759
\(760\) −5489.03 18929.0i −0.261984 0.903456i
\(761\) −14687.3 −0.699624 −0.349812 0.936820i \(-0.613754\pi\)
−0.349812 + 0.936820i \(0.613754\pi\)
\(762\) −8119.26 + 73337.7i −0.385997 + 3.48654i
\(763\) −6874.55 + 2502.13i −0.326180 + 0.118720i
\(764\) −2004.32 + 8941.10i −0.0949132 + 0.423400i
\(765\) 1209.12 6857.28i 0.0571450 0.324086i
\(766\) 1576.10 + 6474.02i 0.0743430 + 0.305373i
\(767\) 6272.93 3621.68i 0.295310 0.170497i
\(768\) 33773.5 + 19926.1i 1.58684 + 0.936224i
\(769\) 13850.6 11622.1i 0.649501 0.544996i −0.257418 0.966300i \(-0.582872\pi\)
0.906920 + 0.421304i \(0.138427\pi\)
\(770\) 41070.2 + 12023.4i 1.92216 + 0.562719i
\(771\) 30056.1 + 17352.9i 1.40395 + 0.810569i
\(772\) 1459.22 + 11289.4i 0.0680289 + 0.526315i
\(773\) 9485.73 26061.8i 0.441369 1.21265i −0.497224 0.867622i \(-0.665647\pi\)
0.938592 0.345028i \(-0.112131\pi\)
\(774\) 21423.7 + 48845.1i 0.994907 + 2.26835i
\(775\) 369.876 + 2097.67i 0.0171436 + 0.0972264i
\(776\) 8136.27 + 13515.7i 0.376385 + 0.625238i
\(777\) −11114.0 9325.75i −0.513144 0.430579i
\(778\) −13167.0 19756.1i −0.606758 0.910399i
\(779\) 15079.5 32521.3i 0.693557 1.49576i
\(780\) −11733.7 4892.69i −0.538633 0.224598i
\(781\) 11000.1 13109.4i 0.503988 0.600630i
\(782\) 257.183 349.887i 0.0117607 0.0159999i
\(783\) −39297.9 + 6929.27i −1.79360 + 0.316261i
\(784\) 15721.6 10898.3i 0.716179 0.496458i
\(785\) 18055.0 + 6571.49i 0.820906 + 0.298785i
\(786\) −18416.4 9108.97i −0.835740 0.413367i
\(787\) −11992.8 + 20772.1i −0.543198 + 0.940846i 0.455520 + 0.890225i \(0.349453\pi\)
−0.998718 + 0.0506207i \(0.983880\pi\)
\(788\) −5013.82 16033.5i −0.226662 0.724834i
\(789\) −5408.29 6445.35i −0.244031 0.290824i
\(790\) −1407.20 + 90.5672i −0.0633745 + 0.00407878i
\(791\) 8847.21 + 15323.8i 0.397687 + 0.688815i
\(792\) −12927.0 + 82057.2i −0.579975 + 3.68153i
\(793\) −7166.95 1263.73i −0.320940 0.0565905i
\(794\) −14546.0 + 13892.0i −0.650150 + 0.620917i
\(795\) 3490.45 + 9589.92i 0.155715 + 0.427823i
\(796\) −2533.01 4894.00i −0.112789 0.217919i
\(797\) 22555.6i 1.00246i 0.865314 + 0.501230i \(0.167119\pi\)
−0.865314 + 0.501230i \(0.832881\pi\)
\(798\) 1183.80 56805.5i 0.0525137 2.51991i
\(799\) 419.781i 0.0185867i
\(800\) 2041.28 1618.62i 0.0902128 0.0715334i
\(801\) 14865.2 + 40841.9i 0.655727 + 1.80159i
\(802\) −60.8279 63.6918i −0.00267819 0.00280428i
\(803\) −2012.77 354.905i −0.0884546 0.0155969i
\(804\) 14179.7 15401.4i 0.621989 0.675578i
\(805\) 1997.43 + 3459.65i 0.0874535 + 0.151474i
\(806\) 424.353 + 6593.44i 0.0185449 + 0.288144i
\(807\) 45132.7 + 53787.1i 1.96871 + 2.34621i
\(808\) 21244.2 26278.9i 0.924963 1.14417i
\(809\) −4393.17 + 7609.19i −0.190922 + 0.330686i −0.945556 0.325460i \(-0.894481\pi\)
0.754634 + 0.656146i \(0.227814\pi\)
\(810\) −22492.0 + 45474.1i −0.975664 + 1.97259i
\(811\) 33962.0 + 12361.2i 1.47049 + 0.535215i 0.948234 0.317573i \(-0.102868\pi\)
0.522257 + 0.852788i \(0.325090\pi\)
\(812\) −18894.2 12099.7i −0.816574 0.522925i
\(813\) 28331.4 4995.58i 1.22217 0.215502i
\(814\) 7740.36 + 5689.50i 0.333292 + 0.244984i
\(815\) −7293.04 + 8691.51i −0.313453 + 0.373559i
\(816\) 4415.65 + 4457.48i 0.189435 + 0.191229i
\(817\) 13897.8 + 19757.1i 0.595130 + 0.846040i
\(818\) 26328.4 17547.2i 1.12537 0.750029i
\(819\) −19804.7 16618.1i −0.844971 0.709015i
\(820\) −36379.0 1674.27i −1.54928 0.0713023i
\(821\) 633.179 + 3590.94i 0.0269161 + 0.152649i 0.995304 0.0968015i \(-0.0308612\pi\)
−0.968388 + 0.249450i \(0.919750\pi\)
\(822\) −40397.8 + 17718.7i −1.71416 + 0.751836i
\(823\) 4754.58 13063.1i 0.201378 0.553282i −0.797360 0.603504i \(-0.793771\pi\)
0.998738 + 0.0502219i \(0.0159929\pi\)
\(824\) 10657.6 + 12239.7i 0.450576 + 0.517463i
\(825\) 6775.20 + 3911.66i 0.285918 + 0.165075i
\(826\) 9240.13 31562.9i 0.389231 1.32956i
\(827\) −15069.1 + 12644.5i −0.633619 + 0.531670i −0.902051 0.431629i \(-0.857939\pi\)
0.268432 + 0.963299i \(0.413495\pi\)
\(828\) −6163.24 + 4706.18i −0.258680 + 0.197525i
\(829\) −12562.5 + 7252.94i −0.526312 + 0.303866i −0.739513 0.673142i \(-0.764944\pi\)
0.213202 + 0.977008i \(0.431611\pi\)
\(830\) 30803.6 7499.13i 1.28820 0.313613i
\(831\) 13314.5 75510.1i 0.555805 3.15213i
\(832\) 6845.82 4293.52i 0.285260 0.178907i
\(833\) 2876.21 1046.86i 0.119634 0.0435431i
\(834\) −84304.6 9333.43i −3.50028 0.387518i
\(835\) 37238.1 1.54332
\(836\) 1633.55 + 37585.5i 0.0675806 + 1.55493i
\(837\) 53353.9 2.20332
\(838\) 5445.13 + 602.834i 0.224462 + 0.0248503i
\(839\) −17838.0 + 6492.51i −0.734013 + 0.267159i −0.681863 0.731480i \(-0.738830\pi\)
−0.0521506 + 0.998639i \(0.516608\pi\)
\(840\) −53870.6 + 20730.2i −2.21275 + 0.851498i
\(841\) 2107.30 11951.1i 0.0864037 0.490020i
\(842\) 16998.9 4138.38i 0.695749 0.169380i
\(843\) −15926.8 + 9195.36i −0.650711 + 0.375688i
\(844\) 8530.52 + 11171.6i 0.347906 + 0.455620i
\(845\) 15693.3 13168.3i 0.638896 0.536097i
\(846\) −2106.19 + 7194.43i −0.0855936 + 0.292375i
\(847\) −41539.0 23982.6i −1.68512 0.972905i
\(848\) −6257.91 1708.46i −0.253417 0.0691849i
\(849\) −4274.83 + 11745.0i −0.172805 + 0.474779i
\(850\) 381.730 167.428i 0.0154038 0.00675617i
\(851\) 155.722 + 883.146i 0.00627273 + 0.0355744i
\(852\) −1061.21 + 23058.2i −0.0426717 + 0.927185i
\(853\) 2676.38 + 2245.75i 0.107430 + 0.0901443i 0.694920 0.719087i \(-0.255440\pi\)
−0.587491 + 0.809231i \(0.699884\pi\)
\(854\) −27495.6 + 18325.2i −1.10173 + 0.734279i
\(855\) −14457.8 + 54426.9i −0.578299 + 2.17703i
\(856\) −9954.71 + 1943.55i −0.397482 + 0.0776042i
\(857\) −8941.48 + 10656.0i −0.356400 + 0.424742i −0.914218 0.405222i \(-0.867194\pi\)
0.557818 + 0.829963i \(0.311639\pi\)
\(858\) 19553.0 + 14372.4i 0.778007 + 0.571869i
\(859\) 27407.6 4832.70i 1.08863 0.191955i 0.399603 0.916688i \(-0.369148\pi\)
0.689030 + 0.724733i \(0.258037\pi\)
\(860\) 13234.0 20665.5i 0.524738 0.819405i
\(861\) −98655.4 35907.6i −3.90495 1.42129i
\(862\) 11784.1 23825.0i 0.465624 0.941394i
\(863\) −6548.14 + 11341.7i −0.258286 + 0.447365i −0.965783 0.259352i \(-0.916491\pi\)
0.707497 + 0.706717i \(0.249825\pi\)
\(864\) −31049.1 57394.5i −1.22258 2.25995i
\(865\) −22401.9 26697.6i −0.880565 1.04942i
\(866\) 1397.66 + 21716.3i 0.0548435 + 0.852138i
\(867\) −23015.6 39864.2i −0.901558 1.56154i
\(868\) 22069.5 + 20318.9i 0.863006 + 0.794550i
\(869\) 2650.79 + 467.406i 0.103477 + 0.0182459i
\(870\) 21772.6 + 22797.7i 0.848461 + 0.888408i
\(871\) −1475.50 4053.91i −0.0574002 0.157706i
\(872\) −3162.88 + 5717.13i −0.122831 + 0.222026i
\(873\) 45076.3i 1.74754i
\(874\) −2313.00 + 2642.70i −0.0895177 + 0.102277i
\(875\) 37141.9i 1.43500i
\(876\) 2448.27 1267.16i 0.0944284 0.0488737i
\(877\) 3562.84 + 9788.83i 0.137182 + 0.376904i 0.989193 0.146620i \(-0.0468393\pi\)
−0.852011 + 0.523524i \(0.824617\pi\)
\(878\) 14940.9 14269.1i 0.574294 0.548471i
\(879\) −38943.7 6866.82i −1.49435 0.263495i
\(880\) 34714.3 15988.7i 1.32979 0.612478i
\(881\) 15697.0 + 27188.0i 0.600278 + 1.03971i 0.992779 + 0.119960i \(0.0382767\pi\)
−0.392501 + 0.919752i \(0.628390\pi\)
\(882\) −54546.5 + 3510.61i −2.08240 + 0.134023i
\(883\) −16099.8 19187.0i −0.613591 0.731250i 0.366363 0.930472i \(-0.380603\pi\)
−0.979954 + 0.199222i \(0.936158\pi\)
\(884\) 1234.03 385.894i 0.0469514 0.0146821i
\(885\) −23104.4 + 40018.0i −0.877566 + 1.51999i
\(886\) 513.979 + 254.220i 0.0194892 + 0.00963960i
\(887\) −18791.9 6839.69i −0.711353 0.258911i −0.0391024 0.999235i \(-0.512450\pi\)
−0.672250 + 0.740324i \(0.734672\pi\)
\(888\) −12955.2 + 236.859i −0.489583 + 0.00895096i
\(889\) 67988.7 11988.2i 2.56498 0.452275i
\(890\) 11843.4 16112.5i 0.446058 0.606845i
\(891\) 62247.7 74184.0i 2.34049 2.78929i
\(892\) −4269.84 + 10240.0i −0.160274 + 0.384372i
\(893\) −288.594 + 3382.73i −0.0108146 + 0.126762i
\(894\) 17222.1 + 25840.6i 0.644289 + 0.966711i
\(895\) 13721.6 + 11513.8i 0.512474 + 0.430016i
\(896\) 9014.43 35565.4i 0.336106 1.32607i
\(897\) 393.373 + 2230.93i 0.0146425 + 0.0830419i
\(898\) 10618.5 + 24209.7i 0.394592 + 0.899653i
\(899\) 5603.53 15395.6i 0.207885 0.571158i
\(900\) −7382.33 + 954.204i −0.273420 + 0.0353409i
\(901\) −898.878 518.968i −0.0332364 0.0191890i
\(902\) 66715.2 + 19531.1i 2.46272 + 0.720968i
\(903\) 54193.8 45474.0i 1.99719 1.67584i
\(904\) 14946.2 + 5132.57i 0.549894 + 0.188835i
\(905\) −24402.8 + 14089.0i −0.896328 + 0.517495i
\(906\) −18767.8 77091.1i −0.688210 2.82691i
\(907\) 704.499 3995.41i 0.0257911 0.146268i −0.969193 0.246303i \(-0.920784\pi\)
0.994984 + 0.100034i \(0.0318953\pi\)
\(908\) −32002.0 7173.86i −1.16963 0.262195i
\(909\) −90731.8 + 33023.7i −3.31065 + 1.20498i
\(910\) −1308.89 + 11822.6i −0.0476804 + 0.430676i
\(911\) −1757.66 −0.0639230 −0.0319615 0.999489i \(-0.510175\pi\)
−0.0319615 + 0.999489i \(0.510175\pi\)
\(912\) −32518.3 38955.5i −1.18069 1.41441i
\(913\) −60516.7 −2.19366
\(914\) 2617.41 23641.9i 0.0947225 0.855585i
\(915\) 43626.8 15878.9i 1.57624 0.573703i
\(916\) −16926.2 3794.34i −0.610545 0.136865i
\(917\) −3338.18 + 18931.8i −0.120214 + 0.681769i
\(918\) −2469.73 10144.7i −0.0887942 0.364733i
\(919\) −26388.8 + 15235.6i −0.947211 + 0.546873i −0.892214 0.451614i \(-0.850849\pi\)
−0.0549979 + 0.998486i \(0.517515\pi\)
\(920\) 3374.40 + 1158.78i 0.120925 + 0.0415258i
\(921\) 20407.3 17123.7i 0.730123 0.612646i
\(922\) −33647.8 9850.49i −1.20188 0.351853i
\(923\) 4119.41 + 2378.34i 0.146904 + 0.0848149i
\(924\) 109272. 14124.0i 3.89048 0.502864i
\(925\) −294.419 + 808.908i −0.0104653 + 0.0287532i
\(926\) 10305.0 + 23495.0i 0.365706 + 0.833795i
\(927\) −8052.55 45668.3i −0.285308 1.61806i
\(928\) −19822.5 + 2931.50i −0.701190 + 0.103697i
\(929\) 40986.5 + 34391.8i 1.44750 + 1.21459i 0.934382 + 0.356272i \(0.115952\pi\)
0.513113 + 0.858321i \(0.328492\pi\)
\(930\) −23375.8 35073.8i −0.824217 1.23668i
\(931\) −23897.2 + 6458.55i −0.841244 + 0.227358i
\(932\) 15061.0 36119.4i 0.529335 1.26945i
\(933\) 64534.7 76909.4i 2.26449 2.69871i
\(934\) −6511.29 + 8858.37i −0.228111 + 0.310337i
\(935\) 6022.36 1061.90i 0.210644 0.0371422i
\(936\) −23085.7 + 422.072i −0.806175 + 0.0147392i
\(937\) −19958.8 7264.39i −0.695864 0.253274i −0.0302199 0.999543i \(-0.509621\pi\)
−0.665644 + 0.746270i \(0.731843\pi\)
\(938\) −17557.4 8684.08i −0.611161 0.302287i
\(939\) −7115.68 + 12324.7i −0.247297 + 0.428330i
\(940\) 3291.83 1029.38i 0.114221 0.0357179i
\(941\) 31852.0 + 37959.8i 1.10345 + 1.31504i 0.944778 + 0.327710i \(0.106277\pi\)
0.158672 + 0.987331i \(0.449279\pi\)
\(942\) 49367.5 3177.28i 1.70752 0.109895i
\(943\) 3244.66 + 5619.92i 0.112047 + 0.194072i
\(944\) −12287.5 26678.4i −0.423650 0.919817i
\(945\) 94594.4 + 16679.5i 3.25625 + 0.574165i
\(946\) −33875.6 + 32352.4i −1.16426 + 1.11191i
\(947\) −15677.8 43074.4i −0.537972 1.47807i −0.849376 0.527788i \(-0.823021\pi\)
0.311404 0.950278i \(-0.399201\pi\)
\(948\) −3224.33 + 1668.83i −0.110466 + 0.0571742i
\(949\) 568.091i 0.0194321i
\(950\) −3191.20 + 1086.76i −0.108986 + 0.0371148i
\(951\) 48285.2i 1.64643i
\(952\) 2841.85 5136.86i 0.0967489 0.174881i
\(953\) −12824.2 35234.1i −0.435903 1.19763i −0.942134 0.335236i \(-0.891184\pi\)
0.506231 0.862398i \(-0.331038\pi\)
\(954\) 12801.6 + 13404.3i 0.434452 + 0.454907i
\(955\) −11863.0 2091.76i −0.401965 0.0708773i
\(956\) −5408.68 4979.65i −0.182980 0.168466i
\(957\) −30087.5 52113.1i −1.01629 1.76027i
\(958\) −62.3674 969.042i −0.00210334 0.0326809i
\(959\) 26530.4 + 31617.7i 0.893339 + 1.06464i
\(960\) −24126.5 + 45557.1i −0.811125 + 1.53161i
\(961\) 3942.61 6828.80i 0.132342 0.229224i
\(962\) −1183.80 + 2393.40i −0.0396750 + 0.0802145i
\(963\) 27233.2 + 9912.06i 0.911294 + 0.331684i
\(964\) −14663.9 + 22898.4i −0.489930 + 0.765051i
\(965\) −14737.5 + 2598.63i −0.491625 + 0.0866868i
\(966\) 8287.55 + 6091.72i 0.276033 + 0.202896i
\(967\) −12478.3 + 14871.1i −0.414971 + 0.494543i −0.932524 0.361108i \(-0.882399\pi\)
0.517553 + 0.855651i \(0.326843\pi\)
\(968\) −42044.0 + 8208.63i −1.39602 + 0.272557i
\(969\) −3447.23 7351.13i −0.114284 0.243707i
\(970\) −17257.6 + 11501.8i −0.571246 + 0.380721i
\(971\) −5913.08 4961.66i −0.195427 0.163983i 0.539823 0.841778i \(-0.318491\pi\)
−0.735250 + 0.677796i \(0.762935\pi\)
\(972\) −2425.42 + 52700.3i −0.0800364 + 1.73906i
\(973\) 13781.0 + 78155.8i 0.454057 + 2.57509i
\(974\) 31220.2 13693.3i 1.02706 0.450474i
\(975\) −743.736 + 2043.40i −0.0244293 + 0.0671191i
\(976\) −7772.20 + 28468.7i −0.254899 + 0.933669i
\(977\) −10821.1 6247.54i −0.354346 0.204582i 0.312252 0.949999i \(-0.398917\pi\)
−0.666598 + 0.745418i \(0.732250\pi\)
\(978\) −8207.53 + 28035.7i −0.268352 + 0.916650i
\(979\) −29240.7 + 24535.9i −0.954584 + 0.800991i
\(980\) 15262.2 + 19987.5i 0.497484 + 0.651508i
\(981\) 16167.8 9334.48i 0.526196 0.303799i
\(982\) −27657.4 + 6733.19i −0.898762 + 0.218803i
\(983\) −2241.14 + 12710.2i −0.0727176 + 0.412402i 0.926620 + 0.376000i \(0.122701\pi\)
−0.999337 + 0.0364018i \(0.988410\pi\)
\(984\) −87508.5 + 33674.5i −2.83503 + 1.09096i
\(985\) 20752.8 7553.41i 0.671310 0.244337i
\(986\) −3186.70 352.802i −0.102926 0.0113950i
\(987\) 9943.08 0.320660
\(988\) −10209.5 + 2261.28i −0.328754 + 0.0728145i
\(989\) −4372.81 −0.140594
\(990\) −108542. 12016.8i −3.48454 0.385776i
\(991\) 28052.9 10210.4i 0.899223 0.327290i 0.149281 0.988795i \(-0.452304\pi\)
0.749941 + 0.661504i \(0.230082\pi\)
\(992\) 26781.7 + 742.301i 0.857176 + 0.0237581i
\(993\) 4646.69 26352.7i 0.148498 0.842173i
\(994\) 20984.3 5108.63i 0.669600 0.163014i
\(995\) 6273.92 3622.25i 0.199896 0.115410i
\(996\) 64875.6 49538.2i 2.06392 1.57598i
\(997\) 18287.1 15344.7i 0.580901 0.487434i −0.304342 0.952563i \(-0.598436\pi\)
0.885243 + 0.465129i \(0.153992\pi\)
\(998\) 13238.7 45221.3i 0.419902 1.43432i
\(999\) 18673.4 + 10781.1i 0.591393 + 0.341441i
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 76.4.k.a.3.16 168
4.3 odd 2 inner 76.4.k.a.3.26 yes 168
19.13 odd 18 inner 76.4.k.a.51.26 yes 168
76.51 even 18 inner 76.4.k.a.51.16 yes 168
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.4.k.a.3.16 168 1.1 even 1 trivial
76.4.k.a.3.26 yes 168 4.3 odd 2 inner
76.4.k.a.51.16 yes 168 76.51 even 18 inner
76.4.k.a.51.26 yes 168 19.13 odd 18 inner