Properties

Label 169.4.e.h.23.13
Level $169$
Weight $4$
Character 169.23
Analytic conductor $9.971$
Analytic rank $0$
Dimension $36$
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] = [169,4,Mod(23,169)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(169, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.23");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 169.e (of order \(6\), degree \(2\), not 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: \(9.97132279097\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 23.13
Character \(\chi\) \(=\) 169.23
Dual form 169.4.e.h.147.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.92949 - 1.11399i) q^{2} +(4.87434 + 8.44260i) q^{3} +(-1.51803 + 2.62931i) q^{4} -8.20685i q^{5} +(18.8100 + 10.8600i) q^{6} +(7.23560 + 4.17747i) q^{7} +24.5882i q^{8} +(-34.0183 + 58.9214i) q^{9} +O(q^{10})\) \(q+(1.92949 - 1.11399i) q^{2} +(4.87434 + 8.44260i) q^{3} +(-1.51803 + 2.62931i) q^{4} -8.20685i q^{5} +(18.8100 + 10.8600i) q^{6} +(7.23560 + 4.17747i) q^{7} +24.5882i q^{8} +(-34.0183 + 58.9214i) q^{9} +(-9.14239 - 15.8351i) q^{10} +(8.39957 - 4.84949i) q^{11} -29.5976 q^{12} +18.6147 q^{14} +(69.2872 - 40.0030i) q^{15} +(15.2469 + 26.4084i) q^{16} +(22.3109 - 38.6437i) q^{17} +151.585i q^{18} +(-75.9867 - 43.8709i) q^{19} +(21.5784 + 12.4583i) q^{20} +81.4497i q^{21} +(10.8046 - 18.7141i) q^{22} +(53.5263 + 92.7102i) q^{23} +(-207.589 + 119.851i) q^{24} +57.6475 q^{25} -400.052 q^{27} +(-21.9678 + 12.6831i) q^{28} +(7.02150 + 12.1616i) q^{29} +(89.1261 - 154.371i) q^{30} +171.090i q^{31} +(-111.515 - 64.3831i) q^{32} +(81.8846 + 47.2761i) q^{33} -99.4170i q^{34} +(34.2839 - 59.3815i) q^{35} +(-103.282 - 178.890i) q^{36} +(358.495 - 206.977i) q^{37} -195.488 q^{38} +201.792 q^{40} +(223.678 - 129.141i) q^{41} +(90.7344 + 157.157i) q^{42} +(30.5359 - 52.8897i) q^{43} +29.4468i q^{44} +(483.560 + 279.183i) q^{45} +(206.557 + 119.256i) q^{46} +68.7115i q^{47} +(-148.637 + 257.446i) q^{48} +(-136.597 - 236.594i) q^{49} +(111.231 - 64.2190i) q^{50} +435.004 q^{51} +328.701 q^{53} +(-771.899 + 445.656i) q^{54} +(-39.7991 - 68.9340i) q^{55} +(-102.717 + 177.911i) q^{56} -855.367i q^{57} +(27.0959 + 15.6438i) q^{58} +(127.431 + 73.5721i) q^{59} +242.904i q^{60} +(48.9041 - 84.7045i) q^{61} +(190.593 + 330.117i) q^{62} +(-492.286 + 284.221i) q^{63} -530.839 q^{64} +210.661 q^{66} +(586.817 - 338.799i) q^{67} +(67.7376 + 117.325i) q^{68} +(-521.810 + 903.802i) q^{69} -152.768i q^{70} +(-681.360 - 393.383i) q^{71} +(-1448.77 - 836.450i) q^{72} -997.675i q^{73} +(461.142 - 798.722i) q^{74} +(280.994 + 486.695i) q^{75} +(230.701 - 133.195i) q^{76} +81.0345 q^{77} +383.897 q^{79} +(216.729 - 125.129i) q^{80} +(-1031.50 - 1786.60i) q^{81} +(287.724 - 498.353i) q^{82} +519.718i q^{83} +(-214.157 - 123.643i) q^{84} +(-317.143 - 183.103i) q^{85} -136.067i q^{86} +(-68.4503 + 118.559i) q^{87} +(119.240 + 206.530i) q^{88} +(-591.687 + 341.611i) q^{89} +1244.03 q^{90} -325.019 q^{92} +(-1444.44 + 833.950i) q^{93} +(76.5442 + 132.578i) q^{94} +(-360.042 + 623.612i) q^{95} -1255.30i q^{96} +(300.765 + 173.647i) q^{97} +(-527.128 - 304.337i) q^{98} +659.886i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9} - 294 q^{10} - 156 q^{12} - 588 q^{14} - 538 q^{16} - 110 q^{17} - 680 q^{22} - 408 q^{23} - 1228 q^{25} - 2672 q^{27} - 560 q^{29} + 1042 q^{30} - 40 q^{35} - 1818 q^{36} + 2956 q^{38} + 52 q^{40} + 8 q^{42} - 1066 q^{43} + 264 q^{48} + 806 q^{49} - 1880 q^{51} - 1112 q^{53} + 500 q^{55} + 500 q^{56} + 272 q^{61} + 4070 q^{62} - 1136 q^{64} + 13116 q^{66} + 3072 q^{68} - 4100 q^{69} + 3980 q^{74} + 4786 q^{75} + 2872 q^{77} + 1648 q^{79} + 1670 q^{81} + 5514 q^{82} + 1572 q^{87} - 1272 q^{88} + 5120 q^{90} + 16040 q^{92} + 5062 q^{94} - 3228 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.92949 1.11399i 0.682179 0.393856i −0.118496 0.992954i \(-0.537807\pi\)
0.800676 + 0.599098i \(0.204474\pi\)
\(3\) 4.87434 + 8.44260i 0.938066 + 1.62478i 0.769072 + 0.639162i \(0.220719\pi\)
0.168994 + 0.985617i \(0.445948\pi\)
\(4\) −1.51803 + 2.62931i −0.189754 + 0.328664i
\(5\) 8.20685i 0.734043i −0.930212 0.367022i \(-0.880377\pi\)
0.930212 0.367022i \(-0.119623\pi\)
\(6\) 18.8100 + 10.8600i 1.27986 + 0.738927i
\(7\) 7.23560 + 4.17747i 0.390686 + 0.225562i 0.682457 0.730926i \(-0.260911\pi\)
−0.291772 + 0.956488i \(0.594245\pi\)
\(8\) 24.5882i 1.08666i
\(9\) −34.0183 + 58.9214i −1.25994 + 2.18228i
\(10\) −9.14239 15.8351i −0.289108 0.500749i
\(11\) 8.39957 4.84949i 0.230233 0.132925i −0.380446 0.924803i \(-0.624230\pi\)
0.610680 + 0.791878i \(0.290896\pi\)
\(12\) −29.5976 −0.712009
\(13\) 0 0
\(14\) 18.6147 0.355357
\(15\) 69.2872 40.0030i 1.19266 0.688581i
\(16\) 15.2469 + 26.4084i 0.238232 + 0.412630i
\(17\) 22.3109 38.6437i 0.318306 0.551322i −0.661829 0.749655i \(-0.730219\pi\)
0.980135 + 0.198333i \(0.0635528\pi\)
\(18\) 151.585i 1.98494i
\(19\) −75.9867 43.8709i −0.917502 0.529720i −0.0346647 0.999399i \(-0.511036\pi\)
−0.882837 + 0.469679i \(0.844370\pi\)
\(20\) 21.5784 + 12.4583i 0.241254 + 0.139288i
\(21\) 81.4497i 0.846370i
\(22\) 10.8046 18.7141i 0.104707 0.181358i
\(23\) 53.5263 + 92.7102i 0.485261 + 0.840496i 0.999857 0.0169365i \(-0.00539131\pi\)
−0.514596 + 0.857433i \(0.672058\pi\)
\(24\) −207.589 + 119.851i −1.76558 + 1.01936i
\(25\) 57.6475 0.461180
\(26\) 0 0
\(27\) −400.052 −2.85149
\(28\) −21.9678 + 12.6831i −0.148269 + 0.0856029i
\(29\) 7.02150 + 12.1616i 0.0449607 + 0.0778742i 0.887630 0.460557i \(-0.152350\pi\)
−0.842669 + 0.538431i \(0.819017\pi\)
\(30\) 89.1261 154.371i 0.542404 0.939472i
\(31\) 171.090i 0.991247i 0.868537 + 0.495624i \(0.165060\pi\)
−0.868537 + 0.495624i \(0.834940\pi\)
\(32\) −111.515 64.3831i −0.616038 0.355670i
\(33\) 81.8846 + 47.2761i 0.431948 + 0.249385i
\(34\) 99.4170i 0.501467i
\(35\) 34.2839 59.3815i 0.165573 0.286780i
\(36\) −103.282 178.890i −0.478157 0.828192i
\(37\) 358.495 206.977i 1.59287 0.919643i 0.600057 0.799957i \(-0.295144\pi\)
0.992812 0.119686i \(-0.0381889\pi\)
\(38\) −195.488 −0.834534
\(39\) 0 0
\(40\) 201.792 0.797653
\(41\) 223.678 129.141i 0.852017 0.491912i −0.00931374 0.999957i \(-0.502965\pi\)
0.861331 + 0.508044i \(0.169631\pi\)
\(42\) 90.7344 + 157.157i 0.333348 + 0.577376i
\(43\) 30.5359 52.8897i 0.108295 0.187572i −0.806785 0.590845i \(-0.798794\pi\)
0.915080 + 0.403273i \(0.132128\pi\)
\(44\) 29.4468i 0.100892i
\(45\) 483.560 + 279.183i 1.60188 + 0.924849i
\(46\) 206.557 + 119.256i 0.662070 + 0.382246i
\(47\) 68.7115i 0.213247i 0.994299 + 0.106623i \(0.0340039\pi\)
−0.994299 + 0.106623i \(0.965996\pi\)
\(48\) −148.637 + 257.446i −0.446955 + 0.774150i
\(49\) −136.597 236.594i −0.398243 0.689777i
\(50\) 111.231 64.2190i 0.314608 0.181639i
\(51\) 435.004 1.19437
\(52\) 0 0
\(53\) 328.701 0.851896 0.425948 0.904748i \(-0.359941\pi\)
0.425948 + 0.904748i \(0.359941\pi\)
\(54\) −771.899 + 445.656i −1.94522 + 1.12308i
\(55\) −39.7991 68.9340i −0.0975728 0.169001i
\(56\) −102.717 + 177.911i −0.245109 + 0.424541i
\(57\) 855.367i 1.98765i
\(58\) 27.0959 + 15.6438i 0.0613425 + 0.0354161i
\(59\) 127.431 + 73.5721i 0.281187 + 0.162344i 0.633961 0.773365i \(-0.281428\pi\)
−0.352773 + 0.935709i \(0.614761\pi\)
\(60\) 242.904i 0.522645i
\(61\) 48.9041 84.7045i 0.102648 0.177792i −0.810127 0.586255i \(-0.800602\pi\)
0.912775 + 0.408463i \(0.133935\pi\)
\(62\) 190.593 + 330.117i 0.390409 + 0.676208i
\(63\) −492.286 + 284.221i −0.984479 + 0.568389i
\(64\) −530.839 −1.03680
\(65\) 0 0
\(66\) 210.661 0.392888
\(67\) 586.817 338.799i 1.07002 0.617774i 0.141830 0.989891i \(-0.454701\pi\)
0.928186 + 0.372117i \(0.121368\pi\)
\(68\) 67.7376 + 117.325i 0.120800 + 0.209231i
\(69\) −521.810 + 903.802i −0.910414 + 1.57688i
\(70\) 152.768i 0.260847i
\(71\) −681.360 393.383i −1.13891 0.657549i −0.192749 0.981248i \(-0.561740\pi\)
−0.946160 + 0.323699i \(0.895074\pi\)
\(72\) −1448.77 836.450i −2.37138 1.36912i
\(73\) 997.675i 1.59958i −0.600282 0.799788i \(-0.704945\pi\)
0.600282 0.799788i \(-0.295055\pi\)
\(74\) 461.142 798.722i 0.724415 1.25472i
\(75\) 280.994 + 486.695i 0.432618 + 0.749316i
\(76\) 230.701 133.195i 0.348200 0.201033i
\(77\) 81.0345 0.119932
\(78\) 0 0
\(79\) 383.897 0.546731 0.273366 0.961910i \(-0.411863\pi\)
0.273366 + 0.961910i \(0.411863\pi\)
\(80\) 216.729 125.129i 0.302889 0.174873i
\(81\) −1031.50 1786.60i −1.41495 2.45076i
\(82\) 287.724 498.353i 0.387486 0.671145i
\(83\) 519.718i 0.687307i 0.939096 + 0.343654i \(0.111665\pi\)
−0.939096 + 0.343654i \(0.888335\pi\)
\(84\) −214.157 123.643i −0.278171 0.160602i
\(85\) −317.143 183.103i −0.404694 0.233650i
\(86\) 136.067i 0.170610i
\(87\) −68.4503 + 118.559i −0.0843522 + 0.146102i
\(88\) 119.240 + 206.530i 0.144444 + 0.250184i
\(89\) −591.687 + 341.611i −0.704705 + 0.406862i −0.809097 0.587675i \(-0.800044\pi\)
0.104393 + 0.994536i \(0.466710\pi\)
\(90\) 1244.03 1.45703
\(91\) 0 0
\(92\) −325.019 −0.368321
\(93\) −1444.44 + 833.950i −1.61056 + 0.929856i
\(94\) 76.5442 + 132.578i 0.0839887 + 0.145473i
\(95\) −360.042 + 623.612i −0.388837 + 0.673486i
\(96\) 1255.30i 1.33457i
\(97\) 300.765 + 173.647i 0.314826 + 0.181765i 0.649084 0.760717i \(-0.275152\pi\)
−0.334258 + 0.942482i \(0.608486\pi\)
\(98\) −527.128 304.337i −0.543346 0.313701i
\(99\) 659.886i 0.669909i
\(100\) −87.5110 + 151.573i −0.0875110 + 0.151573i
\(101\) 277.397 + 480.466i 0.273288 + 0.473348i 0.969702 0.244292i \(-0.0785556\pi\)
−0.696414 + 0.717640i \(0.745222\pi\)
\(102\) 839.338 484.592i 0.814773 0.470409i
\(103\) −1137.13 −1.08781 −0.543905 0.839147i \(-0.683055\pi\)
−0.543905 + 0.839147i \(0.683055\pi\)
\(104\) 0 0
\(105\) 668.445 0.621272
\(106\) 634.226 366.171i 0.581146 0.335525i
\(107\) 778.069 + 1347.66i 0.702980 + 1.21760i 0.967416 + 0.253193i \(0.0814808\pi\)
−0.264436 + 0.964403i \(0.585186\pi\)
\(108\) 607.293 1051.86i 0.541082 0.937181i
\(109\) 71.6448i 0.0629572i −0.999504 0.0314786i \(-0.989978\pi\)
0.999504 0.0314786i \(-0.0100216\pi\)
\(110\) −153.584 88.6719i −0.133124 0.0768594i
\(111\) 3494.85 + 2017.75i 2.98843 + 1.72537i
\(112\) 254.774i 0.214945i
\(113\) 490.436 849.460i 0.408286 0.707173i −0.586411 0.810013i \(-0.699460\pi\)
0.994698 + 0.102841i \(0.0327931\pi\)
\(114\) −952.873 1650.42i −0.782849 1.35593i
\(115\) 760.859 439.282i 0.616961 0.356203i
\(116\) −42.6355 −0.0341259
\(117\) 0 0
\(118\) 327.836 0.255760
\(119\) 322.866 186.407i 0.248715 0.143596i
\(120\) 983.602 + 1703.65i 0.748252 + 1.29601i
\(121\) −618.465 + 1071.21i −0.464662 + 0.804818i
\(122\) 217.916i 0.161714i
\(123\) 2180.57 + 1258.95i 1.59850 + 0.922893i
\(124\) −449.849 259.720i −0.325787 0.188093i
\(125\) 1498.96i 1.07257i
\(126\) −633.241 + 1096.81i −0.447727 + 0.775486i
\(127\) −1088.65 1885.60i −0.760649 1.31748i −0.942517 0.334159i \(-0.891548\pi\)
0.181868 0.983323i \(-0.441786\pi\)
\(128\) −132.133 + 76.2873i −0.0912426 + 0.0526790i
\(129\) 595.369 0.406351
\(130\) 0 0
\(131\) −1919.81 −1.28041 −0.640207 0.768202i \(-0.721152\pi\)
−0.640207 + 0.768202i \(0.721152\pi\)
\(132\) −248.607 + 143.534i −0.163928 + 0.0946438i
\(133\) −366.539 634.865i −0.238970 0.413908i
\(134\) 754.839 1307.42i 0.486628 0.842865i
\(135\) 3283.17i 2.09311i
\(136\) 950.180 + 548.587i 0.599098 + 0.345889i
\(137\) −644.334 372.006i −0.401819 0.231990i 0.285450 0.958394i \(-0.407857\pi\)
−0.687268 + 0.726404i \(0.741190\pi\)
\(138\) 2325.17i 1.43429i
\(139\) −1410.00 + 2442.19i −0.860392 + 1.49024i 0.0111596 + 0.999938i \(0.496448\pi\)
−0.871551 + 0.490304i \(0.836886\pi\)
\(140\) 104.088 + 180.286i 0.0628362 + 0.108836i
\(141\) −580.104 + 334.923i −0.346479 + 0.200040i
\(142\) −1752.91 −1.03592
\(143\) 0 0
\(144\) −2074.69 −1.20063
\(145\) 99.8084 57.6244i 0.0571630 0.0330031i
\(146\) −1111.40 1925.01i −0.630003 1.09120i
\(147\) 1331.64 2306.47i 0.747157 1.29411i
\(148\) 1256.79i 0.698025i
\(149\) −2506.80 1447.30i −1.37829 0.795755i −0.386335 0.922359i \(-0.626259\pi\)
−0.991953 + 0.126604i \(0.959592\pi\)
\(150\) 1084.35 + 626.050i 0.590246 + 0.340779i
\(151\) 494.004i 0.266235i −0.991100 0.133118i \(-0.957501\pi\)
0.991100 0.133118i \(-0.0424988\pi\)
\(152\) 1078.71 1868.38i 0.575624 0.997010i
\(153\) 1517.96 + 2629.19i 0.802091 + 1.38926i
\(154\) 156.356 90.2720i 0.0818149 0.0472359i
\(155\) 1404.11 0.727618
\(156\) 0 0
\(157\) 50.7450 0.0257955 0.0128977 0.999917i \(-0.495894\pi\)
0.0128977 + 0.999917i \(0.495894\pi\)
\(158\) 740.727 427.659i 0.372969 0.215334i
\(159\) 1602.20 + 2775.09i 0.799135 + 1.38414i
\(160\) −528.383 + 915.185i −0.261077 + 0.452199i
\(161\) 894.419i 0.437826i
\(162\) −3980.53 2298.16i −1.93049 1.11457i
\(163\) −651.079 375.900i −0.312861 0.180631i 0.335345 0.942095i \(-0.391147\pi\)
−0.648206 + 0.761465i \(0.724481\pi\)
\(164\) 784.161i 0.373370i
\(165\) 387.988 672.015i 0.183060 0.317069i
\(166\) 578.963 + 1002.79i 0.270700 + 0.468867i
\(167\) −2575.84 + 1487.16i −1.19356 + 0.689102i −0.959112 0.283027i \(-0.908662\pi\)
−0.234448 + 0.972129i \(0.575328\pi\)
\(168\) −2002.70 −0.919714
\(169\) 0 0
\(170\) −815.901 −0.368099
\(171\) 5169.88 2984.83i 2.31199 1.33483i
\(172\) 92.7090 + 160.577i 0.0410988 + 0.0711852i
\(173\) 816.869 1414.86i 0.358991 0.621790i −0.628802 0.777566i \(-0.716454\pi\)
0.987792 + 0.155775i \(0.0497876\pi\)
\(174\) 305.013i 0.132891i
\(175\) 417.114 + 240.821i 0.180177 + 0.104025i
\(176\) 256.134 + 147.879i 0.109698 + 0.0633341i
\(177\) 1434.46i 0.609156i
\(178\) −761.105 + 1318.27i −0.320490 + 0.555105i
\(179\) 1696.32 + 2938.12i 0.708320 + 1.22685i 0.965480 + 0.260477i \(0.0838798\pi\)
−0.257160 + 0.966369i \(0.582787\pi\)
\(180\) −1468.12 + 847.620i −0.607929 + 0.350988i
\(181\) 3801.07 1.56095 0.780473 0.625190i \(-0.214979\pi\)
0.780473 + 0.625190i \(0.214979\pi\)
\(182\) 0 0
\(183\) 953.501 0.385163
\(184\) −2279.58 + 1316.12i −0.913331 + 0.527312i
\(185\) −1698.63 2942.11i −0.675058 1.16924i
\(186\) −1858.03 + 3218.20i −0.732459 + 1.26866i
\(187\) 432.787i 0.169243i
\(188\) −180.664 104.306i −0.0700866 0.0404645i
\(189\) −2894.62 1671.21i −1.11403 0.643188i
\(190\) 1604.34i 0.612584i
\(191\) −632.755 + 1095.96i −0.239710 + 0.415189i −0.960631 0.277828i \(-0.910386\pi\)
0.720921 + 0.693017i \(0.243719\pi\)
\(192\) −2587.49 4481.66i −0.972583 1.68456i
\(193\) 1915.92 1106.16i 0.714565 0.412555i −0.0981838 0.995168i \(-0.531303\pi\)
0.812749 + 0.582614i \(0.197970\pi\)
\(194\) 773.767 0.286357
\(195\) 0 0
\(196\) 829.438 0.302273
\(197\) −3773.49 + 2178.63i −1.36472 + 0.787923i −0.990248 0.139315i \(-0.955510\pi\)
−0.374474 + 0.927238i \(0.622177\pi\)
\(198\) 735.109 + 1273.25i 0.263848 + 0.456998i
\(199\) 545.316 944.516i 0.194254 0.336457i −0.752402 0.658704i \(-0.771105\pi\)
0.946656 + 0.322247i \(0.104438\pi\)
\(200\) 1417.45i 0.501145i
\(201\) 5720.68 + 3302.84i 2.00749 + 1.15903i
\(202\) 1070.47 + 618.038i 0.372862 + 0.215272i
\(203\) 117.329i 0.0405658i
\(204\) −660.351 + 1143.76i −0.226636 + 0.392546i
\(205\) −1059.84 1835.70i −0.361085 0.625418i
\(206\) −2194.08 + 1266.75i −0.742081 + 0.428441i
\(207\) −7283.49 −2.44559
\(208\) 0 0
\(209\) −851.007 −0.281652
\(210\) 1289.76 744.644i 0.423819 0.244692i
\(211\) 363.724 + 629.989i 0.118672 + 0.205546i 0.919242 0.393694i \(-0.128803\pi\)
−0.800570 + 0.599240i \(0.795470\pi\)
\(212\) −498.979 + 864.257i −0.161651 + 0.279988i
\(213\) 7669.93i 2.46730i
\(214\) 3002.56 + 1733.53i 0.959116 + 0.553746i
\(215\) −434.058 250.603i −0.137686 0.0794931i
\(216\) 9836.58i 3.09859i
\(217\) −714.724 + 1237.94i −0.223588 + 0.387266i
\(218\) −79.8119 138.238i −0.0247961 0.0429481i
\(219\) 8422.97 4863.01i 2.59896 1.50051i
\(220\) 241.665 0.0740595
\(221\) 0 0
\(222\) 8991.05 2.71820
\(223\) −879.405 + 507.725i −0.264078 + 0.152465i −0.626193 0.779668i \(-0.715388\pi\)
0.362116 + 0.932133i \(0.382055\pi\)
\(224\) −537.917 931.700i −0.160451 0.277910i
\(225\) −1961.07 + 3396.68i −0.581058 + 1.00642i
\(226\) 2185.37i 0.643225i
\(227\) −4583.51 2646.29i −1.34017 0.773747i −0.353338 0.935496i \(-0.614953\pi\)
−0.986832 + 0.161748i \(0.948287\pi\)
\(228\) 2249.03 + 1298.48i 0.653269 + 0.377165i
\(229\) 3010.03i 0.868597i 0.900769 + 0.434298i \(0.143004\pi\)
−0.900769 + 0.434298i \(0.856996\pi\)
\(230\) 978.716 1695.19i 0.280585 0.485988i
\(231\) 394.989 + 684.142i 0.112504 + 0.194862i
\(232\) −299.032 + 172.646i −0.0846225 + 0.0488568i
\(233\) 2373.96 0.667482 0.333741 0.942665i \(-0.391689\pi\)
0.333741 + 0.942665i \(0.391689\pi\)
\(234\) 0 0
\(235\) 563.905 0.156532
\(236\) −386.888 + 223.370i −0.106713 + 0.0616108i
\(237\) 1871.24 + 3241.09i 0.512870 + 0.888318i
\(238\) 415.312 719.342i 0.113112 0.195916i
\(239\) 783.439i 0.212035i −0.994364 0.106018i \(-0.966190\pi\)
0.994364 0.106018i \(-0.0338100\pi\)
\(240\) 2112.82 + 1219.84i 0.568259 + 0.328085i
\(241\) 3046.16 + 1758.70i 0.814192 + 0.470074i 0.848410 0.529340i \(-0.177560\pi\)
−0.0342172 + 0.999414i \(0.510894\pi\)
\(242\) 2755.86i 0.732040i
\(243\) 4655.01 8062.71i 1.22888 2.12849i
\(244\) 148.476 + 257.169i 0.0389558 + 0.0674735i
\(245\) −1941.69 + 1121.04i −0.506327 + 0.292328i
\(246\) 5609.86 1.45395
\(247\) 0 0
\(248\) −4206.80 −1.07715
\(249\) −4387.77 + 2533.28i −1.11672 + 0.644740i
\(250\) −1669.83 2892.24i −0.422438 0.731685i
\(251\) 708.480 1227.12i 0.178163 0.308587i −0.763088 0.646294i \(-0.776318\pi\)
0.941251 + 0.337707i \(0.109651\pi\)
\(252\) 1725.83i 0.431417i
\(253\) 899.195 + 519.150i 0.223446 + 0.129007i
\(254\) −4201.10 2425.51i −1.03780 0.599173i
\(255\) 3570.02i 0.876718i
\(256\) 1953.39 3383.37i 0.476902 0.826018i
\(257\) −741.317 1284.00i −0.179930 0.311648i 0.761926 0.647664i \(-0.224254\pi\)
−0.941856 + 0.336015i \(0.890921\pi\)
\(258\) 1148.76 663.237i 0.277204 0.160044i
\(259\) 3458.56 0.829748
\(260\) 0 0
\(261\) −955.438 −0.226591
\(262\) −3704.26 + 2138.65i −0.873473 + 0.504300i
\(263\) −3614.82 6261.05i −0.847526 1.46796i −0.883409 0.468603i \(-0.844758\pi\)
0.0358825 0.999356i \(-0.488576\pi\)
\(264\) −1162.44 + 2013.40i −0.270996 + 0.469379i
\(265\) 2697.60i 0.625329i
\(266\) −1414.47 816.645i −0.326041 0.188240i
\(267\) −5768.17 3330.25i −1.32212 0.763326i
\(268\) 2057.23i 0.468901i
\(269\) 247.452 428.599i 0.0560870 0.0971456i −0.836619 0.547786i \(-0.815471\pi\)
0.892706 + 0.450640i \(0.148804\pi\)
\(270\) 3657.43 + 6334.86i 0.824387 + 1.42788i
\(271\) −3642.14 + 2102.79i −0.816399 + 0.471348i −0.849173 0.528115i \(-0.822899\pi\)
0.0327741 + 0.999463i \(0.489566\pi\)
\(272\) 1360.69 0.303323
\(273\) 0 0
\(274\) −1657.65 −0.365483
\(275\) 484.214 279.561i 0.106179 0.0613025i
\(276\) −1584.25 2744.00i −0.345510 0.598441i
\(277\) 2104.27 3644.71i 0.456439 0.790575i −0.542331 0.840165i \(-0.682458\pi\)
0.998770 + 0.0495898i \(0.0157914\pi\)
\(278\) 6282.92i 1.35548i
\(279\) −10080.9 5820.19i −2.16317 1.24891i
\(280\) 1460.09 + 842.981i 0.311632 + 0.179921i
\(281\) 4740.83i 1.00646i −0.864153 0.503228i \(-0.832145\pi\)
0.864153 0.503228i \(-0.167855\pi\)
\(282\) −746.205 + 1292.46i −0.157574 + 0.272926i
\(283\) −1871.41 3241.38i −0.393088 0.680848i 0.599767 0.800175i \(-0.295260\pi\)
−0.992855 + 0.119326i \(0.961927\pi\)
\(284\) 2068.66 1194.34i 0.432226 0.249546i
\(285\) −7019.87 −1.45902
\(286\) 0 0
\(287\) 2157.93 0.443828
\(288\) 7587.09 4380.41i 1.55234 0.896243i
\(289\) 1460.94 + 2530.43i 0.297363 + 0.515047i
\(290\) 128.387 222.372i 0.0259970 0.0450280i
\(291\) 3385.66i 0.682030i
\(292\) 2623.20 + 1514.51i 0.525723 + 0.303526i
\(293\) −4550.94 2627.49i −0.907402 0.523889i −0.0278075 0.999613i \(-0.508853\pi\)
−0.879594 + 0.475725i \(0.842186\pi\)
\(294\) 5933.77i 1.17709i
\(295\) 603.795 1045.80i 0.119167 0.206404i
\(296\) 5089.20 + 8814.75i 0.999337 + 1.73090i
\(297\) −3360.27 + 1940.05i −0.656507 + 0.379034i
\(298\) −6449.14 −1.25365
\(299\) 0 0
\(300\) −1706.23 −0.328364
\(301\) 441.891 255.126i 0.0846185 0.0488545i
\(302\) −550.318 953.179i −0.104858 0.181620i
\(303\) −2704.25 + 4683.91i −0.512724 + 0.888064i
\(304\) 2675.58i 0.504786i
\(305\) −695.157 401.349i −0.130507 0.0753482i
\(306\) 5857.79 + 3382.00i 1.09434 + 0.631817i
\(307\) 252.464i 0.0469344i −0.999725 0.0234672i \(-0.992529\pi\)
0.999725 0.0234672i \(-0.00747053\pi\)
\(308\) −123.013 + 213.065i −0.0227576 + 0.0394172i
\(309\) −5542.74 9600.30i −1.02044 1.76745i
\(310\) 2709.22 1564.17i 0.496366 0.286577i
\(311\) −2561.20 −0.466986 −0.233493 0.972359i \(-0.575016\pi\)
−0.233493 + 0.972359i \(0.575016\pi\)
\(312\) 0 0
\(313\) −695.893 −0.125668 −0.0628342 0.998024i \(-0.520014\pi\)
−0.0628342 + 0.998024i \(0.520014\pi\)
\(314\) 97.9122 56.5296i 0.0175971 0.0101597i
\(315\) 2332.56 + 4040.12i 0.417222 + 0.722650i
\(316\) −582.769 + 1009.39i −0.103745 + 0.179691i
\(317\) 5747.37i 1.01831i 0.860675 + 0.509155i \(0.170042\pi\)
−0.860675 + 0.509155i \(0.829958\pi\)
\(318\) 6182.86 + 3569.68i 1.09031 + 0.629489i
\(319\) 117.955 + 68.1014i 0.0207029 + 0.0119528i
\(320\) 4356.52i 0.761053i
\(321\) −7585.14 + 13137.9i −1.31888 + 2.28437i
\(322\) 996.377 + 1725.78i 0.172441 + 0.298676i
\(323\) −3390.67 + 1957.60i −0.584092 + 0.337226i
\(324\) 6263.39 1.07397
\(325\) 0 0
\(326\) −1675.00 −0.284570
\(327\) 604.869 349.221i 0.102291 0.0590580i
\(328\) 3175.34 + 5499.86i 0.534540 + 0.925850i
\(329\) −287.041 + 497.169i −0.0481005 + 0.0833125i
\(330\) 1728.87i 0.288397i
\(331\) 3676.07 + 2122.38i 0.610438 + 0.352437i 0.773137 0.634239i \(-0.218686\pi\)
−0.162699 + 0.986676i \(0.552020\pi\)
\(332\) −1366.50 788.950i −0.225893 0.130419i
\(333\) 28164.0i 4.63477i
\(334\) −3313.38 + 5738.94i −0.542815 + 0.940182i
\(335\) −2780.47 4815.92i −0.453473 0.785438i
\(336\) −2150.95 + 1241.85i −0.349238 + 0.201633i
\(337\) 7122.49 1.15130 0.575648 0.817698i \(-0.304750\pi\)
0.575648 + 0.817698i \(0.304750\pi\)
\(338\) 0 0
\(339\) 9562.20 1.53200
\(340\) 962.868 555.912i 0.153585 0.0886723i
\(341\) 829.699 + 1437.08i 0.131762 + 0.228218i
\(342\) 6650.16 11518.4i 1.05146 1.82118i
\(343\) 5148.28i 0.810440i
\(344\) 1300.46 + 750.823i 0.203827 + 0.117679i
\(345\) 7417.37 + 4282.42i 1.15750 + 0.668283i
\(346\) 3639.95i 0.565563i
\(347\) 1683.95 2916.69i 0.260517 0.451228i −0.705863 0.708349i \(-0.749440\pi\)
0.966379 + 0.257121i \(0.0827738\pi\)
\(348\) −207.820 359.954i −0.0320124 0.0554471i
\(349\) −5265.18 + 3039.86i −0.807561 + 0.466246i −0.846108 0.533011i \(-0.821060\pi\)
0.0385471 + 0.999257i \(0.487727\pi\)
\(350\) 1073.09 0.163884
\(351\) 0 0
\(352\) −1248.90 −0.189110
\(353\) 2798.12 1615.50i 0.421895 0.243581i −0.273993 0.961732i \(-0.588344\pi\)
0.695888 + 0.718151i \(0.255011\pi\)
\(354\) 1597.98 + 2767.78i 0.239920 + 0.415554i
\(355\) −3228.44 + 5591.82i −0.482670 + 0.836009i
\(356\) 2074.31i 0.308815i
\(357\) 3147.52 + 1817.22i 0.466622 + 0.269405i
\(358\) 6546.10 + 3779.39i 0.966402 + 0.557952i
\(359\) 5345.81i 0.785908i −0.919558 0.392954i \(-0.871453\pi\)
0.919558 0.392954i \(-0.128547\pi\)
\(360\) −6864.62 + 11889.9i −1.00499 + 1.74070i
\(361\) 419.816 + 727.143i 0.0612066 + 0.106013i
\(362\) 7334.14 4234.37i 1.06484 0.614788i
\(363\) −12058.4 −1.74353
\(364\) 0 0
\(365\) −8187.78 −1.17416
\(366\) 1839.77 1062.19i 0.262750 0.151699i
\(367\) 6085.66 + 10540.7i 0.865583 + 1.49923i 0.866467 + 0.499234i \(0.166385\pi\)
−0.000883749 1.00000i \(0.500281\pi\)
\(368\) −1632.22 + 2827.08i −0.231210 + 0.400467i
\(369\) 17572.6i 2.47911i
\(370\) −6554.99 3784.53i −0.921021 0.531752i
\(371\) 2378.35 + 1373.14i 0.332824 + 0.192156i
\(372\) 5063.86i 0.705776i
\(373\) 2231.98 3865.90i 0.309832 0.536645i −0.668493 0.743718i \(-0.733061\pi\)
0.978325 + 0.207073i \(0.0663938\pi\)
\(374\) −482.122 835.060i −0.0666576 0.115454i
\(375\) 12655.1 7306.44i 1.74269 1.00614i
\(376\) −1689.49 −0.231726
\(377\) 0 0
\(378\) −7446.87 −1.01330
\(379\) 4649.74 2684.53i 0.630188 0.363839i −0.150637 0.988589i \(-0.548132\pi\)
0.780825 + 0.624750i \(0.214799\pi\)
\(380\) −1093.11 1893.33i −0.147567 0.255594i
\(381\) 10612.9 18382.1i 1.42708 2.47177i
\(382\) 2819.54i 0.377645i
\(383\) −168.948 97.5419i −0.0225400 0.0130135i 0.488688 0.872459i \(-0.337476\pi\)
−0.511228 + 0.859445i \(0.670809\pi\)
\(384\) −1288.13 743.700i −0.171183 0.0988327i
\(385\) 665.038i 0.0880351i
\(386\) 2464.51 4268.65i 0.324974 0.562872i
\(387\) 2077.56 + 3598.44i 0.272889 + 0.472658i
\(388\) −913.145 + 527.204i −0.119479 + 0.0689813i
\(389\) −9120.52 −1.18876 −0.594381 0.804183i \(-0.702603\pi\)
−0.594381 + 0.804183i \(0.702603\pi\)
\(390\) 0 0
\(391\) 4776.89 0.617845
\(392\) 5817.42 3358.69i 0.749551 0.432754i
\(393\) −9357.79 16208.2i −1.20111 2.08039i
\(394\) −4853.95 + 8407.30i −0.620657 + 1.07501i
\(395\) 3150.59i 0.401325i
\(396\) −1735.05 1001.73i −0.220175 0.127118i
\(397\) −5727.43 3306.73i −0.724059 0.418036i 0.0921859 0.995742i \(-0.470615\pi\)
−0.816245 + 0.577706i \(0.803948\pi\)
\(398\) 2429.92i 0.306032i
\(399\) 3573.27 6189.09i 0.448339 0.776546i
\(400\) 878.945 + 1522.38i 0.109868 + 0.190297i
\(401\) −7438.51 + 4294.63i −0.926338 + 0.534822i −0.885652 0.464350i \(-0.846288\pi\)
−0.0406868 + 0.999172i \(0.512955\pi\)
\(402\) 14717.4 1.82596
\(403\) 0 0
\(404\) −1684.39 −0.207430
\(405\) −14662.4 + 8465.34i −1.79896 + 1.03863i
\(406\) 130.703 + 226.385i 0.0159771 + 0.0276731i
\(407\) 2007.47 3477.03i 0.244487 0.423465i
\(408\) 10696.0i 1.29787i
\(409\) −6508.70 3757.80i −0.786881 0.454306i 0.0519824 0.998648i \(-0.483446\pi\)
−0.838863 + 0.544342i \(0.816779\pi\)
\(410\) −4089.91 2361.31i −0.492649 0.284431i
\(411\) 7253.14i 0.870489i
\(412\) 1726.20 2989.86i 0.206417 0.357524i
\(413\) 614.691 + 1064.68i 0.0732372 + 0.126851i
\(414\) −14053.5 + 8113.77i −1.66833 + 0.963212i
\(415\) 4265.25 0.504513
\(416\) 0 0
\(417\) −27491.2 −3.22842
\(418\) −1642.01 + 948.016i −0.192137 + 0.110931i
\(419\) 2278.67 + 3946.76i 0.265680 + 0.460172i 0.967742 0.251945i \(-0.0810701\pi\)
−0.702061 + 0.712117i \(0.747737\pi\)
\(420\) −1014.72 + 1757.55i −0.117889 + 0.204190i
\(421\) 2225.19i 0.257599i 0.991671 + 0.128800i \(0.0411124\pi\)
−0.991671 + 0.128800i \(0.958888\pi\)
\(422\) 1403.61 + 810.373i 0.161911 + 0.0934795i
\(423\) −4048.58 2337.45i −0.465363 0.268678i
\(424\) 8082.17i 0.925719i
\(425\) 1286.17 2227.71i 0.146796 0.254259i
\(426\) −8544.26 14799.1i −0.971762 1.68314i
\(427\) 707.701 408.592i 0.0802063 0.0463071i
\(428\) −4724.54 −0.533574
\(429\) 0 0
\(430\) −1116.68 −0.125235
\(431\) 342.970 198.014i 0.0383302 0.0221299i −0.480712 0.876878i \(-0.659622\pi\)
0.519043 + 0.854748i \(0.326289\pi\)
\(432\) −6099.55 10564.7i −0.679316 1.17661i
\(433\) 2594.03 4492.99i 0.287901 0.498659i −0.685408 0.728159i \(-0.740376\pi\)
0.973308 + 0.229501i \(0.0737093\pi\)
\(434\) 3184.79i 0.352246i
\(435\) 973.000 + 561.762i 0.107245 + 0.0619182i
\(436\) 188.377 + 108.759i 0.0206918 + 0.0119464i
\(437\) 9392.99i 1.02821i
\(438\) 10834.7 18766.3i 1.18197 2.04723i
\(439\) 5664.93 + 9811.94i 0.615882 + 1.06674i 0.990229 + 0.139450i \(0.0445336\pi\)
−0.374347 + 0.927289i \(0.622133\pi\)
\(440\) 1694.97 978.589i 0.183646 0.106028i
\(441\) 18587.2 2.00705
\(442\) 0 0
\(443\) 15625.2 1.67579 0.837897 0.545828i \(-0.183785\pi\)
0.837897 + 0.545828i \(0.183785\pi\)
\(444\) −10610.6 + 6126.03i −1.13414 + 0.654794i
\(445\) 2803.55 + 4855.89i 0.298654 + 0.517284i
\(446\) −1131.20 + 1959.30i −0.120099 + 0.208017i
\(447\) 28218.5i 2.98588i
\(448\) −3840.94 2217.57i −0.405061 0.233862i
\(449\) 11852.9 + 6843.29i 1.24582 + 0.719276i 0.970273 0.242011i \(-0.0778071\pi\)
0.275549 + 0.961287i \(0.411140\pi\)
\(450\) 8738.49i 0.915414i
\(451\) 1252.53 2169.45i 0.130775 0.226509i
\(452\) 1489.00 + 2579.02i 0.154948 + 0.268378i
\(453\) 4170.68 2407.94i 0.432573 0.249746i
\(454\) −11791.8 −1.21898
\(455\) 0 0
\(456\) 21031.9 2.15989
\(457\) 10975.2 6336.55i 1.12341 0.648602i 0.181142 0.983457i \(-0.442020\pi\)
0.942270 + 0.334854i \(0.108687\pi\)
\(458\) 3353.16 + 5807.84i 0.342102 + 0.592539i
\(459\) −8925.55 + 15459.5i −0.907645 + 1.57209i
\(460\) 2667.38i 0.270364i
\(461\) −7928.34 4577.43i −0.800996 0.462456i 0.0428230 0.999083i \(-0.486365\pi\)
−0.843819 + 0.536627i \(0.819698\pi\)
\(462\) 1524.26 + 880.032i 0.153496 + 0.0886207i
\(463\) 6910.59i 0.693655i −0.937929 0.346827i \(-0.887259\pi\)
0.937929 0.346827i \(-0.112741\pi\)
\(464\) −214.112 + 370.852i −0.0214222 + 0.0371043i
\(465\) 6844.11 + 11854.3i 0.682554 + 1.18222i
\(466\) 4580.55 2644.58i 0.455343 0.262892i
\(467\) −2920.19 −0.289359 −0.144679 0.989479i \(-0.546215\pi\)
−0.144679 + 0.989479i \(0.546215\pi\)
\(468\) 0 0
\(469\) 5661.29 0.557386
\(470\) 1088.05 628.187i 0.106783 0.0616513i
\(471\) 247.348 + 428.420i 0.0241979 + 0.0419120i
\(472\) −1809.01 + 3133.29i −0.176412 + 0.305554i
\(473\) 592.334i 0.0575804i
\(474\) 7221.10 + 4169.11i 0.699739 + 0.403995i
\(475\) −4380.45 2529.05i −0.423134 0.244296i
\(476\) 1131.89i 0.108992i
\(477\) −11181.8 + 19367.5i −1.07334 + 1.85907i
\(478\) −872.746 1511.64i −0.0835115 0.144646i
\(479\) 14799.2 8544.31i 1.41167 0.815030i 0.416128 0.909306i \(-0.363387\pi\)
0.995546 + 0.0942761i \(0.0300536\pi\)
\(480\) −10302.1 −0.979630
\(481\) 0 0
\(482\) 7836.73 0.740567
\(483\) −7551.22 + 4359.70i −0.711371 + 0.410710i
\(484\) −1877.70 3252.28i −0.176343 0.305435i
\(485\) 1425.10 2468.34i 0.133423 0.231096i
\(486\) 20742.6i 1.93602i
\(487\) 11962.4 + 6906.48i 1.11307 + 0.642634i 0.939624 0.342209i \(-0.111175\pi\)
0.173450 + 0.984843i \(0.444508\pi\)
\(488\) 2082.73 + 1202.47i 0.193199 + 0.111543i
\(489\) 7329.06i 0.677774i
\(490\) −2497.65 + 4326.06i −0.230270 + 0.398840i
\(491\) −5924.21 10261.0i −0.544513 0.943125i −0.998637 0.0521862i \(-0.983381\pi\)
0.454124 0.890938i \(-0.349952\pi\)
\(492\) −6620.35 + 3822.26i −0.606644 + 0.350246i
\(493\) 626.625 0.0572450
\(494\) 0 0
\(495\) 5415.59 0.491743
\(496\) −4518.20 + 2608.59i −0.409019 + 0.236147i
\(497\) −3286.70 5692.73i −0.296637 0.513790i
\(498\) −5644.12 + 9775.90i −0.507870 + 0.879656i
\(499\) 5224.46i 0.468696i −0.972153 0.234348i \(-0.924705\pi\)
0.972153 0.234348i \(-0.0752955\pi\)
\(500\) 3941.24 + 2275.48i 0.352515 + 0.203525i
\(501\) −25111.0 14497.9i −2.23928 1.29285i
\(502\) 3156.97i 0.280682i
\(503\) −3942.20 + 6828.08i −0.349451 + 0.605267i −0.986152 0.165844i \(-0.946965\pi\)
0.636701 + 0.771111i \(0.280299\pi\)
\(504\) −6988.50 12104.4i −0.617644 1.06979i
\(505\) 3943.11 2276.56i 0.347458 0.200605i
\(506\) 2313.32 0.203241
\(507\) 0 0
\(508\) 6610.45 0.577345
\(509\) −3487.10 + 2013.28i −0.303660 + 0.175318i −0.644086 0.764953i \(-0.722762\pi\)
0.340426 + 0.940271i \(0.389429\pi\)
\(510\) −3976.98 6888.33i −0.345301 0.598079i
\(511\) 4167.76 7218.78i 0.360804 0.624931i
\(512\) 9924.86i 0.856681i
\(513\) 30398.7 + 17550.7i 2.61624 + 1.51049i
\(514\) −2860.73 1651.65i −0.245489 0.141733i
\(515\) 9332.23i 0.798499i
\(516\) −903.790 + 1565.41i −0.0771068 + 0.133553i
\(517\) 333.216 + 577.147i 0.0283459 + 0.0490965i
\(518\) 6673.28 3852.82i 0.566037 0.326802i
\(519\) 15926.8 1.34703
\(520\) 0 0
\(521\) 6196.12 0.521030 0.260515 0.965470i \(-0.416108\pi\)
0.260515 + 0.965470i \(0.416108\pi\)
\(522\) −1843.51 + 1064.35i −0.154575 + 0.0892441i
\(523\) −3949.69 6841.07i −0.330226 0.571968i 0.652330 0.757935i \(-0.273792\pi\)
−0.982556 + 0.185967i \(0.940458\pi\)
\(524\) 2914.33 5047.77i 0.242964 0.420826i
\(525\) 4695.37i 0.390329i
\(526\) −13949.6 8053.78i −1.15633 0.667607i
\(527\) 6611.55 + 3817.18i 0.546496 + 0.315520i
\(528\) 2883.25i 0.237646i
\(529\) 353.376 612.065i 0.0290438 0.0503053i
\(530\) −3005.11 5205.00i −0.246290 0.426586i
\(531\) −8669.95 + 5005.60i −0.708557 + 0.409085i
\(532\) 2225.68 0.181382
\(533\) 0 0
\(534\) −14839.5 −1.20256
\(535\) 11060.0 6385.50i 0.893768 0.516017i
\(536\) 8330.46 + 14428.8i 0.671308 + 1.16274i
\(537\) −16536.9 + 28642.8i −1.32890 + 2.30173i
\(538\) 1102.64i 0.0883609i
\(539\) −2294.72 1324.86i −0.183378 0.105873i
\(540\) −8632.49 4983.97i −0.687932 0.397178i
\(541\) 6146.22i 0.488441i 0.969720 + 0.244220i \(0.0785320\pi\)
−0.969720 + 0.244220i \(0.921468\pi\)
\(542\) −4684.99 + 8114.64i −0.371287 + 0.643088i
\(543\) 18527.7 + 32090.9i 1.46427 + 2.53619i
\(544\) −4976.00 + 2872.89i −0.392177 + 0.226423i
\(545\) −587.979 −0.0462133
\(546\) 0 0
\(547\) 5555.49 0.434252 0.217126 0.976144i \(-0.430332\pi\)
0.217126 + 0.976144i \(0.430332\pi\)
\(548\) 1956.24 1129.44i 0.152494 0.0880422i
\(549\) 3327.27 + 5763.00i 0.258660 + 0.448013i
\(550\) 622.859 1078.82i 0.0482887 0.0836385i
\(551\) 1232.16i 0.0952663i
\(552\) −22222.9 12830.4i −1.71353 0.989307i
\(553\) 2777.72 + 1603.72i 0.213600 + 0.123322i
\(554\) 9376.59i 0.719085i
\(555\) 16559.4 28681.7i 1.26650 2.19364i
\(556\) −4280.85 7414.65i −0.326526 0.565560i
\(557\) −6565.08 + 3790.35i −0.499410 + 0.288335i −0.728470 0.685078i \(-0.759768\pi\)
0.229060 + 0.973412i \(0.426435\pi\)
\(558\) −25934.6 −1.96756
\(559\) 0 0
\(560\) 2090.89 0.157779
\(561\) 3653.85 2109.55i 0.274983 0.158762i
\(562\) −5281.26 9147.41i −0.396399 0.686584i
\(563\) −6797.30 + 11773.3i −0.508831 + 0.881322i 0.491116 + 0.871094i \(0.336589\pi\)
−0.999948 + 0.0102278i \(0.996744\pi\)
\(564\) 2033.70i 0.151834i
\(565\) −6971.40 4024.94i −0.519095 0.299700i
\(566\) −7221.76 4169.48i −0.536313 0.309640i
\(567\) 17236.2i 1.27664i
\(568\) 9672.60 16753.4i 0.714530 1.23760i
\(569\) 2825.07 + 4893.16i 0.208143 + 0.360513i 0.951129 0.308793i \(-0.0999249\pi\)
−0.742987 + 0.669306i \(0.766592\pi\)
\(570\) −13544.8 + 7820.09i −0.995314 + 0.574645i
\(571\) −6297.53 −0.461547 −0.230773 0.973008i \(-0.574126\pi\)
−0.230773 + 0.973008i \(0.574126\pi\)
\(572\) 0 0
\(573\) −12337.0 −0.899454
\(574\) 4163.71 2403.92i 0.302770 0.174804i
\(575\) 3085.66 + 5344.52i 0.223793 + 0.387620i
\(576\) 18058.3 31277.8i 1.30630 2.26257i
\(577\) 17838.9i 1.28707i 0.765415 + 0.643537i \(0.222534\pi\)
−0.765415 + 0.643537i \(0.777466\pi\)
\(578\) 5637.76 + 3254.96i 0.405709 + 0.234236i
\(579\) 18677.7 + 10783.6i 1.34062 + 0.774007i
\(580\) 349.903i 0.0250499i
\(581\) −2171.11 + 3760.47i −0.155031 + 0.268521i
\(582\) 3771.60 + 6532.60i 0.268622 + 0.465266i
\(583\) 2760.94 1594.03i 0.196135 0.113238i
\(584\) 24531.1 1.73819
\(585\) 0 0
\(586\) −11708.0 −0.825348
\(587\) −394.120 + 227.545i −0.0277122 + 0.0159997i −0.513792 0.857915i \(-0.671760\pi\)
0.486080 + 0.873914i \(0.338426\pi\)
\(588\) 4042.96 + 7002.61i 0.283553 + 0.491127i
\(589\) 7505.87 13000.6i 0.525083 0.909471i
\(590\) 2690.50i 0.187739i
\(591\) −36786.5 21238.7i −2.56040 1.47825i
\(592\) 10931.8 + 6311.50i 0.758946 + 0.438178i
\(593\) 16240.6i 1.12466i 0.826913 + 0.562330i \(0.190095\pi\)
−0.826913 + 0.562330i \(0.809905\pi\)
\(594\) −4322.41 + 7486.63i −0.298570 + 0.517139i
\(595\) −1529.81 2649.71i −0.105405 0.182568i
\(596\) 7610.81 4394.10i 0.523072 0.301996i
\(597\) 10632.2 0.728891
\(598\) 0 0
\(599\) −6704.05 −0.457296 −0.228648 0.973509i \(-0.573430\pi\)
−0.228648 + 0.973509i \(0.573430\pi\)
\(600\) −11967.0 + 6909.13i −0.814249 + 0.470107i
\(601\) −13206.6 22874.5i −0.896354 1.55253i −0.832120 0.554596i \(-0.812873\pi\)
−0.0642341 0.997935i \(-0.520460\pi\)
\(602\) 568.417 984.527i 0.0384833 0.0666550i
\(603\) 46101.4i 3.11343i
\(604\) 1298.89 + 749.916i 0.0875019 + 0.0505193i
\(605\) 8791.29 + 5075.65i 0.590771 + 0.341082i
\(606\) 12050.1i 0.807758i
\(607\) 1663.19 2880.72i 0.111214 0.192628i −0.805046 0.593212i \(-0.797860\pi\)
0.916260 + 0.400584i \(0.131193\pi\)
\(608\) 5649.09 + 9784.51i 0.376811 + 0.652655i
\(609\) −990.558 + 571.899i −0.0659104 + 0.0380534i
\(610\) −1788.40 −0.118705
\(611\) 0 0
\(612\) −9217.27 −0.608801
\(613\) −22740.7 + 13129.3i −1.49835 + 0.865072i −0.999998 0.00190303i \(-0.999394\pi\)
−0.498351 + 0.866975i \(0.666061\pi\)
\(614\) −281.243 487.127i −0.0184854 0.0320177i
\(615\) 10332.0 17895.6i 0.677443 1.17337i
\(616\) 1992.50i 0.130325i
\(617\) 23688.3 + 13676.4i 1.54563 + 0.892370i 0.998467 + 0.0553441i \(0.0176256\pi\)
0.547163 + 0.837026i \(0.315708\pi\)
\(618\) −21389.4 12349.1i −1.39224 0.803812i
\(619\) 13056.5i 0.847795i −0.905710 0.423897i \(-0.860662\pi\)
0.905710 0.423897i \(-0.139338\pi\)
\(620\) −2131.49 + 3691.85i −0.138069 + 0.239142i
\(621\) −21413.3 37089.0i −1.38371 2.39666i
\(622\) −4941.83 + 2853.17i −0.318568 + 0.183925i
\(623\) −5708.28 −0.367091
\(624\) 0 0
\(625\) −5095.82 −0.326132
\(626\) −1342.72 + 775.220i −0.0857283 + 0.0494953i
\(627\) −4148.09 7184.71i −0.264209 0.457623i
\(628\) −77.0326 + 133.424i −0.00489480 + 0.00847805i
\(629\) 18471.4i 1.17091i
\(630\) 9001.33 + 5196.92i 0.569241 + 0.328651i
\(631\) −5674.99 3276.46i −0.358031 0.206709i 0.310186 0.950676i \(-0.399609\pi\)
−0.668217 + 0.743967i \(0.732942\pi\)
\(632\) 9439.35i 0.594109i
\(633\) −3545.83 + 6141.55i −0.222645 + 0.385632i
\(634\) 6402.54 + 11089.5i 0.401068 + 0.694671i
\(635\) −15474.9 + 8934.42i −0.967089 + 0.558349i
\(636\) −9728.76 −0.606557
\(637\) 0 0
\(638\) 303.458 0.0188308
\(639\) 46357.4 26764.5i 2.86991 1.65694i
\(640\) 626.079 + 1084.40i 0.0386686 + 0.0669760i
\(641\) −2882.38 + 4992.44i −0.177609 + 0.307628i −0.941061 0.338237i \(-0.890170\pi\)
0.763452 + 0.645864i \(0.223503\pi\)
\(642\) 33799.2i 2.07780i
\(643\) 10634.4 + 6139.75i 0.652221 + 0.376560i 0.789307 0.613999i \(-0.210440\pi\)
−0.137086 + 0.990559i \(0.543774\pi\)
\(644\) −2351.71 1357.76i −0.143898 0.0830795i
\(645\) 4886.10i 0.298279i
\(646\) −4361.52 + 7554.37i −0.265637 + 0.460097i
\(647\) −14512.1 25135.8i −0.881810 1.52734i −0.849327 0.527867i \(-0.822992\pi\)
−0.0324826 0.999472i \(-0.510341\pi\)
\(648\) 43929.4 25362.7i 2.66313 1.53756i
\(649\) 1427.15 0.0863182
\(650\) 0 0
\(651\) −13935.2 −0.838962
\(652\) 1976.72 1141.26i 0.118734 0.0685509i
\(653\) 8583.57 + 14867.2i 0.514396 + 0.890961i 0.999860 + 0.0167042i \(0.00531736\pi\)
−0.485464 + 0.874257i \(0.661349\pi\)
\(654\) 778.060 1347.64i 0.0465207 0.0805763i
\(655\) 15755.6i 0.939880i
\(656\) 6820.79 + 3937.99i 0.405956 + 0.234379i
\(657\) 58784.5 + 33939.2i 3.49072 + 2.01537i
\(658\) 1279.05i 0.0757787i
\(659\) −9156.49 + 15859.5i −0.541254 + 0.937479i 0.457579 + 0.889169i \(0.348717\pi\)
−0.998832 + 0.0483096i \(0.984617\pi\)
\(660\) 1177.96 + 2040.28i 0.0694727 + 0.120330i
\(661\) 5962.85 3442.65i 0.350874 0.202577i −0.314196 0.949358i \(-0.601735\pi\)
0.665070 + 0.746781i \(0.268402\pi\)
\(662\) 9457.28 0.555238
\(663\) 0 0
\(664\) −12779.0 −0.746867
\(665\) −5210.24 + 3008.13i −0.303826 + 0.175414i
\(666\) 31374.6 + 54342.3i 1.82543 + 3.16175i
\(667\) −751.669 + 1301.93i −0.0436353 + 0.0755786i
\(668\) 9030.25i 0.523040i
\(669\) −8573.03 4949.64i −0.495445 0.286045i
\(670\) −10729.8 6194.86i −0.618699 0.357206i
\(671\) 948.641i 0.0545781i
\(672\) 5243.98 9082.84i 0.301028 0.521396i
\(673\) 3119.13 + 5402.50i 0.178653 + 0.309437i 0.941420 0.337238i \(-0.109493\pi\)
−0.762766 + 0.646674i \(0.776159\pi\)
\(674\) 13742.8 7934.41i 0.785390 0.453445i
\(675\) −23062.0 −1.31505
\(676\) 0 0
\(677\) 25482.4 1.44663 0.723316 0.690517i \(-0.242617\pi\)
0.723316 + 0.690517i \(0.242617\pi\)
\(678\) 18450.2 10652.2i 1.04510 0.603388i
\(679\) 1450.81 + 2512.88i 0.0819986 + 0.142026i
\(680\) 4502.17 7797.99i 0.253898 0.439764i
\(681\) 51595.7i 2.90331i
\(682\) 3201.80 + 1848.56i 0.179770 + 0.103790i
\(683\) 23752.0 + 13713.2i 1.33067 + 0.768261i 0.985402 0.170243i \(-0.0544554\pi\)
0.345266 + 0.938505i \(0.387789\pi\)
\(684\) 18124.3i 1.01316i
\(685\) −3053.00 + 5287.95i −0.170291 + 0.294952i
\(686\) −5735.15 9933.57i −0.319197 0.552865i
\(687\) −25412.5 + 14671.9i −1.41128 + 0.814802i
\(688\) 1862.31 0.103197
\(689\) 0 0
\(690\) 19082.4 1.05283
\(691\) −12025.9 + 6943.15i −0.662064 + 0.382243i −0.793063 0.609140i \(-0.791515\pi\)
0.130999 + 0.991383i \(0.458182\pi\)
\(692\) 2480.07 + 4295.61i 0.136240 + 0.235975i
\(693\) −2756.66 + 4774.67i −0.151106 + 0.261724i
\(694\) 7503.65i 0.410425i
\(695\) 20042.7 + 11571.6i 1.09390 + 0.631565i
\(696\) −2915.17 1683.07i −0.158763 0.0916619i
\(697\) 11525.0i 0.626314i
\(698\) −6772.76 + 11730.8i −0.367268 + 0.636126i
\(699\) 11571.5 + 20042.4i 0.626143 + 1.08451i
\(700\) −1266.39 + 731.150i −0.0683785 + 0.0394784i
\(701\) −15744.4 −0.848301 −0.424151 0.905592i \(-0.639427\pi\)
−0.424151 + 0.905592i \(0.639427\pi\)
\(702\) 0 0
\(703\) −36321.1 −1.94861
\(704\) −4458.82 + 2574.30i −0.238705 + 0.137816i
\(705\) 2748.66 + 4760.83i 0.146838 + 0.254331i
\(706\) 3599.30 6234.18i 0.191872 0.332332i
\(707\) 4635.28i 0.246574i
\(708\) −3771.65 2177.56i −0.200208 0.115590i
\(709\) −24845.5 14344.6i −1.31607 0.759833i −0.332976 0.942935i \(-0.608053\pi\)
−0.983094 + 0.183102i \(0.941386\pi\)
\(710\) 14385.9i 0.760410i
\(711\) −13059.5 + 22619.8i −0.688847 + 1.19312i
\(712\) −8399.61 14548.5i −0.442119 0.765772i
\(713\) −15861.8 + 9157.81i −0.833140 + 0.481013i
\(714\) 8097.48 0.424427
\(715\) 0 0
\(716\) −10300.3 −0.537627
\(717\) 6614.26 3818.75i 0.344511 0.198903i
\(718\) −5955.20 10314.7i −0.309535 0.536130i
\(719\) −6309.54 + 10928.4i −0.327269 + 0.566846i −0.981969 0.189043i \(-0.939462\pi\)
0.654700 + 0.755889i \(0.272795\pi\)
\(720\) 17026.7i 0.881315i
\(721\) −8227.79 4750.32i −0.424991 0.245369i
\(722\) 1620.07 + 935.345i 0.0835078 + 0.0482132i
\(723\) 34290.0i 1.76384i
\(724\) −5770.15 + 9994.19i −0.296196 + 0.513027i
\(725\) 404.772 + 701.086i 0.0207350 + 0.0359140i
\(726\) −23266.7 + 13433.0i −1.18940 + 0.686702i
\(727\) 12644.5 0.645061 0.322531 0.946559i \(-0.395466\pi\)
0.322531 + 0.946559i \(0.395466\pi\)
\(728\) 0 0
\(729\) 35059.5 1.78121
\(730\) −15798.3 + 9121.13i −0.800986 + 0.462450i
\(731\) −1362.57 2360.04i −0.0689418 0.119411i
\(732\) −1447.45 + 2507.05i −0.0730863 + 0.126589i
\(733\) 19109.0i 0.962903i 0.876473 + 0.481451i \(0.159890\pi\)
−0.876473 + 0.481451i \(0.840110\pi\)
\(734\) 23484.5 + 13558.8i 1.18097 + 0.681831i
\(735\) −18928.9 10928.6i −0.949936 0.548446i
\(736\) 13784.7i 0.690370i
\(737\) 3286.00 5691.52i 0.164235 0.284464i
\(738\) 19575.8 + 33906.2i 0.976415 + 1.69120i
\(739\) 12205.4 7046.78i 0.607554 0.350771i −0.164454 0.986385i \(-0.552586\pi\)
0.772007 + 0.635614i \(0.219253\pi\)
\(740\) 10314.3 0.512381
\(741\) 0 0
\(742\) 6118.67 0.302727
\(743\) −15231.1 + 8793.70i −0.752054 + 0.434198i −0.826436 0.563031i \(-0.809635\pi\)
0.0743817 + 0.997230i \(0.476302\pi\)
\(744\) −20505.4 35516.3i −1.01043 1.75012i
\(745\) −11877.8 + 20572.9i −0.584119 + 1.01172i
\(746\) 9945.63i 0.488117i
\(747\) −30622.5 17679.9i −1.49989 0.865964i
\(748\) 1137.93 + 656.985i 0.0556242 + 0.0321147i
\(749\) 13001.5i 0.634263i
\(750\) 16278.7 28195.5i 0.792551 1.37274i
\(751\) −8293.48 14364.7i −0.402974 0.697971i 0.591109 0.806591i \(-0.298690\pi\)
−0.994083 + 0.108620i \(0.965357\pi\)
\(752\) −1814.56 + 1047.64i −0.0879922 + 0.0508023i
\(753\) 13813.5 0.668514
\(754\) 0 0
\(755\) −4054.22 −0.195428
\(756\) 8788.26 5073.91i 0.422786 0.244095i
\(757\) −16909.7 29288.5i −0.811882 1.40622i −0.911545 0.411199i \(-0.865110\pi\)
0.0996637 0.995021i \(-0.468223\pi\)
\(758\) 5981.10 10359.6i 0.286601 0.496407i
\(759\) 10122.1i 0.484068i
\(760\) −15333.5 8852.80i −0.731848 0.422533i
\(761\) −24362.4 14065.6i −1.16049 0.670011i −0.209071 0.977901i \(-0.567044\pi\)
−0.951422 + 0.307890i \(0.900377\pi\)
\(762\) 47290.9i 2.24825i
\(763\) 299.295 518.393i 0.0142008 0.0245965i
\(764\) −1921.09 3327.42i −0.0909719 0.157568i
\(765\) 21577.3 12457.7i 1.01978 0.588769i
\(766\) −434.645 −0.0205018
\(767\) 0 0
\(768\) 38085.9 1.78946
\(769\) 20555.1 11867.5i 0.963897 0.556506i 0.0665267 0.997785i \(-0.478808\pi\)
0.897370 + 0.441279i \(0.145475\pi\)
\(770\) −740.849 1283.19i −0.0346732 0.0600557i
\(771\) 7226.86 12517.3i 0.337573 0.584694i
\(772\) 6716.75i 0.313136i
\(773\) −8258.64 4768.13i −0.384272 0.221860i 0.295403 0.955373i \(-0.404546\pi\)
−0.679675 + 0.733513i \(0.737879\pi\)
\(774\) 8017.27 + 4628.77i 0.372319 + 0.214958i
\(775\) 9862.92i 0.457144i
\(776\) −4269.67 + 7395.29i −0.197516 + 0.342108i
\(777\) 16858.2 + 29199.3i 0.778359 + 1.34816i
\(778\) −17598.0 + 10160.2i −0.810949 + 0.468202i
\(779\) −22662.1 −1.04230
\(780\) 0 0
\(781\) −7630.84 −0.349619
\(782\) 9216.98 5321.42i 0.421481 0.243342i
\(783\) −2808.97 4865.28i −0.128205 0.222057i
\(784\) 4165.37 7214.62i 0.189749 0.328655i
\(785\) 416.457i 0.0189350i
\(786\) −36111.6 20849.0i −1.63875 0.946133i
\(787\) −15325.4 8848.10i −0.694143 0.400763i 0.111019 0.993818i \(-0.464588\pi\)
−0.805162 + 0.593055i \(0.797922\pi\)
\(788\) 13228.9i 0.598047i
\(789\) 35239.7 61037.0i 1.59007 2.75409i
\(790\) −3509.73 6079.04i −0.158064 0.273775i
\(791\) 7097.20 4097.57i 0.319023 0.184188i
\(792\) −16225.4 −0.727961
\(793\) 0 0
\(794\) −14734.7 −0.658584
\(795\) 22774.7 13149.0i 1.01602 0.586600i
\(796\) 1655.62 + 2867.61i 0.0737209 + 0.127688i
\(797\) −16283.4 + 28203.6i −0.723696 + 1.25348i 0.235812 + 0.971799i \(0.424225\pi\)
−0.959508 + 0.281680i \(0.909108\pi\)
\(798\) 15922.4i 0.706325i
\(799\) 2655.27 + 1533.02i 0.117568 + 0.0678777i
\(800\) −6428.55 3711.53i −0.284105 0.164028i
\(801\) 46484.1i 2.05048i
\(802\) −9568.38 + 16572.9i −0.421286 + 0.729689i
\(803\) −4838.22 8380.04i −0.212624 0.368275i
\(804\) −17368.4 + 10027.6i −0.761860 + 0.439860i
\(805\) 7340.36 0.321384
\(806\) 0 0
\(807\) 4824.66 0.210453
\(808\) −11813.8 + 6820.71i −0.514367 + 0.296970i
\(809\) −5811.13 10065.2i −0.252544 0.437420i 0.711681 0.702502i \(-0.247934\pi\)
−0.964226 + 0.265083i \(0.914601\pi\)
\(810\) −18860.7 + 32667.6i −0.818144 + 1.41707i
\(811\) 6494.39i 0.281195i −0.990067 0.140597i \(-0.955098\pi\)
0.990067 0.140597i \(-0.0449023\pi\)
\(812\) −308.493 178.109i −0.0133325 0.00769753i
\(813\) −35506.0 20499.4i −1.53167 0.884312i
\(814\) 8945.22i 0.385172i
\(815\) −3084.96 + 5343.31i −0.132591 + 0.229654i
\(816\) 6632.45 + 11487.7i 0.284537 + 0.492833i
\(817\) −4640.64 + 2679.27i −0.198721 + 0.114732i
\(818\) −16744.7 −0.715725
\(819\) 0 0
\(820\) 6435.49 0.274070
\(821\) −30222.4 + 17448.9i −1.28474 + 0.741743i −0.977710 0.209959i \(-0.932667\pi\)
−0.307026 + 0.951701i \(0.599334\pi\)
\(822\) −8079.95 13994.9i −0.342847 0.593829i
\(823\) 751.307 1301.30i 0.0318213 0.0551161i −0.849676 0.527305i \(-0.823203\pi\)
0.881497 + 0.472189i \(0.156536\pi\)
\(824\) 27959.9i 1.18208i
\(825\) 4720.45 + 2725.35i 0.199206 + 0.115012i
\(826\) 2372.09 + 1369.52i 0.0999218 + 0.0576899i
\(827\) 27887.8i 1.17262i 0.810088 + 0.586308i \(0.199419\pi\)
−0.810088 + 0.586308i \(0.800581\pi\)
\(828\) 11056.6 19150.6i 0.464062 0.803779i
\(829\) 15421.8 + 26711.4i 0.646107 + 1.11909i 0.984045 + 0.177922i \(0.0569373\pi\)
−0.337938 + 0.941168i \(0.609729\pi\)
\(830\) 8229.78 4751.47i 0.344168 0.198706i
\(831\) 41027.8 1.71268
\(832\) 0 0
\(833\) −12190.5 −0.507053
\(834\) −53044.1 + 30625.0i −2.20236 + 1.27153i
\(835\) 12204.9 + 21139.5i 0.505831 + 0.876125i
\(836\) 1291.86 2237.56i 0.0534448 0.0925690i
\(837\) 68445.0i 2.82653i
\(838\) 8793.35 + 5076.84i 0.362483 + 0.209280i
\(839\) 31695.5 + 18299.4i 1.30423 + 0.752997i 0.981127 0.193366i \(-0.0619405\pi\)
0.323103 + 0.946364i \(0.395274\pi\)
\(840\) 16435.9i 0.675110i
\(841\) 12095.9 20950.7i 0.495957 0.859023i
\(842\) 2478.85 + 4293.50i 0.101457 + 0.175729i
\(843\) 40024.9 23108.4i 1.63527 0.944123i
\(844\) −2208.58 −0.0900741
\(845\) 0 0
\(846\) −10415.6 −0.423282
\(847\) −8949.93 + 5167.24i −0.363073 + 0.209620i
\(848\) 5011.66 + 8680.44i 0.202949 + 0.351518i
\(849\) 18243.8 31599.2i 0.737485 1.27736i
\(850\) 5731.15i 0.231267i
\(851\) 38377.8 + 22157.4i 1.54591 + 0.892534i
\(852\) 20166.6 + 11643.2i 0.810913 + 0.468181i
\(853\) 21578.4i 0.866155i 0.901357 + 0.433077i \(0.142572\pi\)
−0.901357 + 0.433077i \(0.857428\pi\)
\(854\) 910.337 1576.75i 0.0364767 0.0631795i
\(855\) −24496.1 42428.4i −0.979822 1.69710i
\(856\) −33136.5 + 19131.4i −1.32311 + 0.763897i
\(857\) 31199.6 1.24359 0.621795 0.783180i \(-0.286404\pi\)
0.621795 + 0.783180i \(0.286404\pi\)
\(858\) 0 0
\(859\) 8035.71 0.319179 0.159590 0.987183i \(-0.448983\pi\)
0.159590 + 0.987183i \(0.448983\pi\)
\(860\) 1317.83 760.849i 0.0522531 0.0301683i
\(861\) 10518.5 + 18218.5i 0.416340 + 0.721122i
\(862\) 441.173 764.134i 0.0174320 0.0301932i
\(863\) 8741.47i 0.344801i 0.985027 + 0.172400i \(0.0551523\pi\)
−0.985027 + 0.172400i \(0.944848\pi\)
\(864\) 44611.8 + 25756.6i 1.75662 + 1.01419i
\(865\) −11611.5 6703.93i −0.456421 0.263515i
\(866\) 11558.9i 0.453566i
\(867\) −14242.3 + 24668.3i −0.557892 + 0.966297i
\(868\) −2169.95 3758.47i −0.0848536 0.146971i
\(869\) 3224.57 1861.71i 0.125876 0.0726744i
\(870\) 2503.20 0.0975475
\(871\) 0 0
\(872\) 1761.62 0.0684128
\(873\) −20463.1 + 11814.4i −0.793321 + 0.458024i
\(874\) −10463.7 18123.7i −0.404967 0.701423i
\(875\) 6261.87 10845.9i 0.241931 0.419038i
\(876\) 29528.8i 1.13891i
\(877\) −1510.46 872.066i −0.0581582 0.0335776i 0.470639 0.882326i \(-0.344023\pi\)
−0.528797 + 0.848748i \(0.677357\pi\)
\(878\) 21860.9 + 12621.4i 0.840284 + 0.485138i
\(879\) 51229.0i 1.96577i
\(880\) 1213.62 2102.06i 0.0464900 0.0805230i
\(881\) −2844.40 4926.65i −0.108775 0.188403i 0.806500 0.591235i \(-0.201359\pi\)
−0.915274 + 0.402832i \(0.868026\pi\)
\(882\) 35864.0 20706.1i 1.36916 0.790488i
\(883\) 3940.14 0.150165 0.0750827 0.997177i \(-0.476078\pi\)
0.0750827 + 0.997177i \(0.476078\pi\)
\(884\) 0 0
\(885\) 11772.4 0.447147
\(886\) 30148.8 17406.4i 1.14319 0.660022i
\(887\) 18440.2 + 31939.3i 0.698039 + 1.20904i 0.969145 + 0.246490i \(0.0792772\pi\)
−0.271106 + 0.962549i \(0.587389\pi\)
\(888\) −49612.9 + 85932.1i −1.87489 + 3.24740i
\(889\) 18191.3i 0.686295i
\(890\) 10818.9 + 6246.28i 0.407471 + 0.235254i
\(891\) −17328.2 10004.5i −0.651535 0.376164i
\(892\) 3082.97i 0.115724i
\(893\) 3014.44 5221.16i 0.112961 0.195654i
\(894\) −31435.3 54447.5i −1.17601 2.03691i
\(895\) 24112.7 13921.5i 0.900558 0.519937i
\(896\) −1274.75 −0.0475296
\(897\) 0 0
\(898\) 30493.5 1.13317
\(899\) −2080.73 + 1201.31i −0.0771926 + 0.0445671i
\(900\) −5953.95 10312.5i −0.220517 0.381946i
\(901\) 7333.62 12702.2i 0.271164 0.469669i
\(902\) 5581.26i 0.206026i
\(903\) 4307.85 + 2487.14i 0.158755 + 0.0916575i
\(904\) 20886.7 + 12059.0i 0.768454 + 0.443667i
\(905\) 31194.8i 1.14580i
\(906\) 5364.87 9292.23i 0.196728 0.340743i
\(907\) 8955.99 + 15512.2i 0.327871 + 0.567889i 0.982089 0.188417i \(-0.0603357\pi\)
−0.654219 + 0.756306i \(0.727002\pi\)
\(908\) 13915.9 8034.33i 0.508606 0.293644i
\(909\) −37746.3 −1.37730
\(910\) 0 0
\(911\) 51246.0 1.86373 0.931864 0.362807i \(-0.118181\pi\)
0.931864 + 0.362807i \(0.118181\pi\)
\(912\) 22588.8 13041.7i 0.820165 0.473523i
\(913\) 2520.37 + 4365.41i 0.0913604 + 0.158241i
\(914\) 14117.8 24452.7i 0.510912 0.884926i
\(915\) 7825.24i 0.282726i
\(916\) −7914.32 4569.34i −0.285477 0.164820i
\(917\) −13891.0 8019.95i −0.500240 0.288814i
\(918\) 39772.0i 1.42993i
\(919\) −12748.3 + 22080.6i −0.457591 + 0.792571i −0.998833 0.0482959i \(-0.984621\pi\)
0.541242 + 0.840867i \(0.317954\pi\)
\(920\) 10801.2 + 18708.2i 0.387070 + 0.670425i
\(921\) 2131.45 1230.59i 0.0762580 0.0440276i
\(922\) −20396.9 −0.728564
\(923\) 0 0
\(924\) −2398.43 −0.0853924
\(925\) 20666.3 11931.7i 0.734600 0.424121i
\(926\) −7698.35 13333.9i −0.273200 0.473197i
\(927\) 38683.1 67001.1i 1.37057 2.37390i
\(928\) 1808.26i 0.0639646i
\(929\) −39013.2 22524.3i −1.37781 0.795477i −0.385912 0.922536i \(-0.626113\pi\)
−0.991895 + 0.127058i \(0.959447\pi\)
\(930\) 26411.3 + 15248.6i 0.931249 + 0.537657i
\(931\) 23970.6i 0.843830i
\(932\) −3603.76 + 6241.89i −0.126658 + 0.219378i
\(933\) −12484.2 21623.2i −0.438064 0.758748i
\(934\) −5634.50 + 3253.08i −0.197394 + 0.113966i
\(935\) −3551.82 −0.124232
\(936\) 0 0
\(937\) −2280.50 −0.0795099 −0.0397550 0.999209i \(-0.512658\pi\)
−0.0397550 + 0.999209i \(0.512658\pi\)
\(938\) 10923.4 6306.65i 0.380237 0.219530i
\(939\) −3392.02 5875.14i −0.117885 0.204183i
\(940\) −856.028 + 1482.68i −0.0297027 + 0.0514466i
\(941\) 31174.8i 1.07999i 0.841669 + 0.539994i \(0.181573\pi\)
−0.841669 + 0.539994i \(0.818427\pi\)
\(942\) 954.514 + 551.089i 0.0330146 + 0.0190610i
\(943\) 23945.3 + 13824.9i 0.826901 + 0.477412i
\(944\) 4486.98i 0.154702i
\(945\) −13715.4 + 23755.7i −0.472128 + 0.817750i
\(946\) −659.856 1142.90i −0.0226784 0.0392802i
\(947\) 24589.9 14197.0i 0.843784 0.487159i −0.0147644 0.999891i \(-0.504700\pi\)
0.858549 + 0.512732i \(0.171366\pi\)
\(948\) −11362.4 −0.389277
\(949\) 0 0
\(950\) −11269.4 −0.384871
\(951\) −48522.8 + 28014.6i −1.65453 + 0.955243i
\(952\) 4583.41 + 7938.71i 0.156039 + 0.270268i
\(953\) −16958.4 + 29372.8i −0.576429 + 0.998404i 0.419456 + 0.907776i \(0.362221\pi\)
−0.995885 + 0.0906283i \(0.971112\pi\)
\(954\) 49826.0i 1.69096i
\(955\) 8994.42 + 5192.93i 0.304767 + 0.175957i
\(956\) 2059.91 + 1189.29i 0.0696884 + 0.0402346i
\(957\) 1327.80i 0.0448501i
\(958\) 19036.6 32972.4i 0.642010 1.11199i
\(959\) −3108.09 5383.38i −0.104657 0.181270i
\(960\) −36780.4 + 21235.1i −1.23654 + 0.713918i
\(961\) 519.228 0.0174290
\(962\) 0 0
\(963\) −105874. −3.54284
\(964\) −9248.35 + 5339.54i −0.308993 + 0.178397i
\(965\) −9078.08 15723.7i −0.302833 0.524522i
\(966\) −9713.35 + 16824.0i −0.323522 + 0.560356i
\(967\) 10792.9i 0.358920i −0.983765 0.179460i \(-0.942565\pi\)
0.983765 0.179460i \(-0.0574350\pi\)
\(968\) −26339.2 15207.0i −0.874561 0.504928i
\(969\) −33054.5 19084.0i −1.09584 0.632681i
\(970\) 6350.19i 0.210198i
\(971\) −3715.56 + 6435.55i −0.122799 + 0.212695i −0.920871 0.389868i \(-0.872520\pi\)
0.798071 + 0.602563i \(0.205854\pi\)
\(972\) 14132.9 + 24478.9i 0.466372 + 0.807780i
\(973\) −20404.4 + 11780.5i −0.672285 + 0.388144i
\(974\) 30775.1 1.01242
\(975\) 0 0
\(976\) 2982.54 0.0978164
\(977\) 10758.3 6211.30i 0.352291 0.203395i −0.313403 0.949620i \(-0.601469\pi\)
0.665694 + 0.746225i \(0.268136\pi\)
\(978\) −8164.53 14141.4i −0.266946 0.462364i
\(979\) −3313.28 + 5738.77i −0.108164 + 0.187346i
\(980\) 6807.08i 0.221882i
\(981\) 4221.42 + 2437.24i 0.137390 + 0.0793221i
\(982\) −22861.5 13199.1i −0.742911 0.428920i
\(983\) 38791.6i 1.25866i 0.777140 + 0.629328i \(0.216670\pi\)
−0.777140 + 0.629328i \(0.783330\pi\)
\(984\) −30955.4 + 53616.3i −1.00287 + 1.73702i
\(985\) 17879.7 + 30968.5i 0.578369 + 1.00177i
\(986\) 1209.07 698.057i 0.0390513 0.0225463i
\(987\) −5596.53 −0.180486
\(988\) 0 0
\(989\) 6537.89 0.210205
\(990\) 10449.3 6032.93i 0.335457 0.193676i
\(991\) 533.253 + 923.621i 0.0170932 + 0.0296062i 0.874445 0.485124i \(-0.161225\pi\)
−0.857352 + 0.514730i \(0.827892\pi\)
\(992\) 11015.3 19079.1i 0.352557 0.610646i
\(993\) 41380.8i 1.32244i
\(994\) −12683.3 7322.72i −0.404719 0.233665i
\(995\) −7751.50 4475.33i −0.246974 0.142590i
\(996\) 15382.4i 0.489369i
\(997\) 15325.8 26545.0i 0.486833 0.843219i −0.513053 0.858357i \(-0.671485\pi\)
0.999885 + 0.0151382i \(0.00481881\pi\)
\(998\) −5820.02 10080.6i −0.184599 0.319734i
\(999\) −143417. + 82801.7i −4.54204 + 2.62235i
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 169.4.e.h.23.13 36
13.2 odd 12 169.4.a.l.1.6 yes 9
13.3 even 3 169.4.b.g.168.13 18
13.4 even 6 inner 169.4.e.h.147.13 36
13.5 odd 4 169.4.c.k.146.4 18
13.6 odd 12 169.4.c.k.22.4 18
13.7 odd 12 169.4.c.l.22.6 18
13.8 odd 4 169.4.c.l.146.6 18
13.9 even 3 inner 169.4.e.h.147.6 36
13.10 even 6 169.4.b.g.168.6 18
13.11 odd 12 169.4.a.k.1.4 9
13.12 even 2 inner 169.4.e.h.23.6 36
39.2 even 12 1521.4.a.bg.1.4 9
39.11 even 12 1521.4.a.bh.1.6 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
169.4.a.k.1.4 9 13.11 odd 12
169.4.a.l.1.6 yes 9 13.2 odd 12
169.4.b.g.168.6 18 13.10 even 6
169.4.b.g.168.13 18 13.3 even 3
169.4.c.k.22.4 18 13.6 odd 12
169.4.c.k.146.4 18 13.5 odd 4
169.4.c.l.22.6 18 13.7 odd 12
169.4.c.l.146.6 18 13.8 odd 4
169.4.e.h.23.6 36 13.12 even 2 inner
169.4.e.h.23.13 36 1.1 even 1 trivial
169.4.e.h.147.6 36 13.9 even 3 inner
169.4.e.h.147.13 36 13.4 even 6 inner
1521.4.a.bg.1.4 9 39.2 even 12
1521.4.a.bh.1.6 9 39.11 even 12