Properties

Label 126.4.m.a.41.16
Level $126$
Weight $4$
Character 126.41
Analytic conductor $7.434$
Analytic rank $0$
Dimension $48$
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] = [126,4,Mod(41,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.41");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 126.m (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.43424066072\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.16
Character \(\chi\) \(=\) 126.41
Dual form 126.4.m.a.83.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.73205 - 1.00000i) q^{2} +(-2.86447 + 4.33530i) q^{3} +(2.00000 - 3.46410i) q^{4} +(4.49442 - 7.78456i) q^{5} +(-0.626101 + 10.3734i) q^{6} +(-13.8476 - 12.2981i) q^{7} -8.00000i q^{8} +(-10.5897 - 24.8366i) q^{9} +O(q^{10})\) \(q+(1.73205 - 1.00000i) q^{2} +(-2.86447 + 4.33530i) q^{3} +(2.00000 - 3.46410i) q^{4} +(4.49442 - 7.78456i) q^{5} +(-0.626101 + 10.3734i) q^{6} +(-13.8476 - 12.2981i) q^{7} -8.00000i q^{8} +(-10.5897 - 24.8366i) q^{9} -17.9777i q^{10} +(57.4672 - 33.1787i) q^{11} +(9.28899 + 18.5934i) q^{12} +(42.3739 + 24.4646i) q^{13} +(-36.2829 - 7.45331i) q^{14} +(20.8743 + 41.7833i) q^{15} +(-8.00000 - 13.8564i) q^{16} -18.7313 q^{17} +(-43.1785 - 32.4287i) q^{18} -109.755i q^{19} +(-17.9777 - 31.1383i) q^{20} +(92.9820 - 24.8061i) q^{21} +(66.3574 - 114.934i) q^{22} +(-30.4552 - 17.5833i) q^{23} +(34.6824 + 22.9157i) q^{24} +(22.1004 + 38.2790i) q^{25} +97.8583 q^{26} +(138.008 + 25.2344i) q^{27} +(-70.2971 + 23.3734i) q^{28} +(-53.0095 + 30.6051i) q^{29} +(77.9387 + 51.4965i) q^{30} +(-289.624 - 167.214i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-20.7732 + 344.177i) q^{33} +(-32.4436 + 18.7313i) q^{34} +(-157.972 + 52.5249i) q^{35} +(-107.216 - 12.9896i) q^{36} +251.926 q^{37} +(-109.755 - 190.101i) q^{38} +(-227.440 + 113.626i) q^{39} +(-62.2765 - 35.9554i) q^{40} +(-134.377 + 232.749i) q^{41} +(136.243 - 135.947i) q^{42} +(69.7048 + 120.732i) q^{43} -265.430i q^{44} +(-240.937 - 29.1904i) q^{45} -70.3332 q^{46} +(57.9089 + 100.301i) q^{47} +(82.9874 + 5.00881i) q^{48} +(40.5134 + 340.599i) q^{49} +(76.5579 + 44.2007i) q^{50} +(53.6553 - 81.2059i) q^{51} +(169.495 - 97.8583i) q^{52} +438.701i q^{53} +(264.271 - 94.3008i) q^{54} -596.476i q^{55} +(-98.3848 + 110.781i) q^{56} +(475.820 + 314.389i) q^{57} +(-61.2101 + 106.019i) q^{58} +(-113.087 + 195.872i) q^{59} +(186.490 + 11.2558i) q^{60} +(469.469 - 271.048i) q^{61} -668.858 q^{62} +(-158.802 + 474.161i) q^{63} -64.0000 q^{64} +(380.892 - 219.908i) q^{65} +(308.197 + 616.905i) q^{66} +(307.015 - 531.766i) q^{67} +(-37.4626 + 64.8872i) q^{68} +(163.467 - 81.6655i) q^{69} +(-221.091 + 248.948i) q^{70} +116.615i q^{71} +(-198.693 + 84.7173i) q^{72} -352.359i q^{73} +(436.348 - 251.926i) q^{74} +(-229.257 - 13.8371i) q^{75} +(-380.202 - 219.510i) q^{76} +(-1203.82 - 247.291i) q^{77} +(-280.312 + 424.245i) q^{78} +(390.954 + 677.153i) q^{79} -143.821 q^{80} +(-504.718 + 526.023i) q^{81} +537.510i q^{82} +(122.693 + 212.511i) q^{83} +(100.033 - 371.711i) q^{84} +(-84.1864 + 145.815i) q^{85} +(241.465 + 139.410i) q^{86} +(19.1619 - 317.479i) q^{87} +(-265.430 - 459.738i) q^{88} -1642.23 q^{89} +(-446.505 + 190.378i) q^{90} +(-285.910 - 859.894i) q^{91} +(-121.821 + 70.3332i) q^{92} +(1554.54 - 776.627i) q^{93} +(200.602 + 115.818i) q^{94} +(-854.394 - 493.284i) q^{95} +(148.747 - 74.3119i) q^{96} +(969.077 - 559.497i) q^{97} +(410.770 + 549.421i) q^{98} +(-1432.61 - 1075.94i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9} + 24 q^{11} - 132 q^{14} - 120 q^{15} - 384 q^{16} + 120 q^{18} + 180 q^{21} + 348 q^{23} - 600 q^{25} - 96 q^{28} - 84 q^{29} + 192 q^{30} + 96 q^{36} - 672 q^{37} + 1368 q^{39} + 1128 q^{42} + 84 q^{43} - 1008 q^{46} - 42 q^{49} + 456 q^{50} + 2016 q^{51} - 528 q^{56} + 732 q^{57} + 504 q^{58} - 1008 q^{60} - 774 q^{63} - 3072 q^{64} - 6972 q^{65} + 1176 q^{67} + 216 q^{70} - 384 q^{72} + 2520 q^{74} + 1500 q^{77} + 2832 q^{78} + 348 q^{79} + 2268 q^{81} - 1080 q^{84} + 720 q^{85} + 1200 q^{86} + 180 q^{91} + 1392 q^{92} + 5232 q^{93} - 5892 q^{95} + 972 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205 1.00000i 0.612372 0.353553i
\(3\) −2.86447 + 4.33530i −0.551267 + 0.834329i
\(4\) 2.00000 3.46410i 0.250000 0.433013i
\(5\) 4.49442 7.78456i 0.401993 0.696273i −0.591973 0.805958i \(-0.701651\pi\)
0.993966 + 0.109685i \(0.0349842\pi\)
\(6\) −0.626101 + 10.3734i −0.0426008 + 0.705822i
\(7\) −13.8476 12.2981i −0.747701 0.664035i
\(8\) 8.00000i 0.353553i
\(9\) −10.5897 24.8366i −0.392210 0.919876i
\(10\) 17.9777i 0.568504i
\(11\) 57.4672 33.1787i 1.57518 0.909432i 0.579665 0.814855i \(-0.303183\pi\)
0.995517 0.0945776i \(-0.0301501\pi\)
\(12\) 9.28899 + 18.5934i 0.223458 + 0.447288i
\(13\) 42.3739 + 24.4646i 0.904031 + 0.521942i 0.878506 0.477732i \(-0.158541\pi\)
0.0255249 + 0.999674i \(0.491874\pi\)
\(14\) −36.2829 7.45331i −0.692644 0.142284i
\(15\) 20.8743 + 41.7833i 0.359315 + 0.719227i
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −18.7313 −0.267236 −0.133618 0.991033i \(-0.542660\pi\)
−0.133618 + 0.991033i \(0.542660\pi\)
\(18\) −43.1785 32.4287i −0.565404 0.424640i
\(19\) 109.755i 1.32524i −0.748958 0.662618i \(-0.769445\pi\)
0.748958 0.662618i \(-0.230555\pi\)
\(20\) −17.9777 31.1383i −0.200997 0.348136i
\(21\) 92.9820 24.8061i 0.966207 0.257768i
\(22\) 66.3574 114.934i 0.643066 1.11382i
\(23\) −30.4552 17.5833i −0.276102 0.159407i 0.355556 0.934655i \(-0.384292\pi\)
−0.631657 + 0.775248i \(0.717625\pi\)
\(24\) 34.6824 + 22.9157i 0.294980 + 0.194902i
\(25\) 22.1004 + 38.2790i 0.176803 + 0.306232i
\(26\) 97.8583 0.738138
\(27\) 138.008 + 25.2344i 0.983691 + 0.179865i
\(28\) −70.2971 + 23.3734i −0.474461 + 0.157755i
\(29\) −53.0095 + 30.6051i −0.339435 + 0.195973i −0.660022 0.751246i \(-0.729453\pi\)
0.320587 + 0.947219i \(0.396120\pi\)
\(30\) 77.9387 + 51.4965i 0.474320 + 0.313398i
\(31\) −289.624 167.214i −1.67800 0.968794i −0.962934 0.269736i \(-0.913064\pi\)
−0.715065 0.699057i \(-0.753603\pi\)
\(32\) −27.7128 16.0000i −0.153093 0.0883883i
\(33\) −20.7732 + 344.177i −0.109580 + 1.81556i
\(34\) −32.4436 + 18.7313i −0.163648 + 0.0944822i
\(35\) −157.972 + 52.5249i −0.762920 + 0.253666i
\(36\) −107.216 12.9896i −0.496370 0.0601372i
\(37\) 251.926 1.11936 0.559680 0.828709i \(-0.310924\pi\)
0.559680 + 0.828709i \(0.310924\pi\)
\(38\) −109.755 190.101i −0.468542 0.811538i
\(39\) −227.440 + 113.626i −0.933834 + 0.466529i
\(40\) −62.2765 35.9554i −0.246170 0.142126i
\(41\) −134.377 + 232.749i −0.511859 + 0.886567i 0.488046 + 0.872818i \(0.337710\pi\)
−0.999905 + 0.0137487i \(0.995624\pi\)
\(42\) 136.243 135.947i 0.500543 0.499456i
\(43\) 69.7048 + 120.732i 0.247207 + 0.428174i 0.962750 0.270394i \(-0.0871540\pi\)
−0.715543 + 0.698569i \(0.753821\pi\)
\(44\) 265.430i 0.909432i
\(45\) −240.937 29.1904i −0.798150 0.0966989i
\(46\) −70.3332 −0.225436
\(47\) 57.9089 + 100.301i 0.179721 + 0.311286i 0.941785 0.336216i \(-0.109147\pi\)
−0.762064 + 0.647502i \(0.775814\pi\)
\(48\) 82.9874 + 5.00881i 0.249546 + 0.0150616i
\(49\) 40.5134 + 340.599i 0.118115 + 0.993000i
\(50\) 76.5579 + 44.2007i 0.216538 + 0.125019i
\(51\) 53.6553 81.2059i 0.147318 0.222963i
\(52\) 169.495 97.8583i 0.452015 0.260971i
\(53\) 438.701i 1.13698i 0.822689 + 0.568492i \(0.192473\pi\)
−0.822689 + 0.568492i \(0.807527\pi\)
\(54\) 264.271 94.3008i 0.665977 0.237643i
\(55\) 596.476i 1.46234i
\(56\) −98.3848 + 110.781i −0.234772 + 0.264352i
\(57\) 475.820 + 314.389i 1.10568 + 0.730559i
\(58\) −61.2101 + 106.019i −0.138574 + 0.240017i
\(59\) −113.087 + 195.872i −0.249536 + 0.432209i −0.963397 0.268078i \(-0.913611\pi\)
0.713861 + 0.700287i \(0.246945\pi\)
\(60\) 186.490 + 11.2558i 0.401263 + 0.0242187i
\(61\) 469.469 271.048i 0.985399 0.568920i 0.0815032 0.996673i \(-0.474028\pi\)
0.903896 + 0.427753i \(0.140695\pi\)
\(62\) −668.858 −1.37008
\(63\) −158.802 + 474.161i −0.317574 + 0.948233i
\(64\) −64.0000 −0.125000
\(65\) 380.892 219.908i 0.726828 0.419635i
\(66\) 308.197 + 616.905i 0.574794 + 1.15054i
\(67\) 307.015 531.766i 0.559819 0.969635i −0.437692 0.899125i \(-0.644204\pi\)
0.997511 0.0705100i \(-0.0224627\pi\)
\(68\) −37.4626 + 64.8872i −0.0668090 + 0.115717i
\(69\) 163.467 81.6655i 0.285204 0.142484i
\(70\) −221.091 + 248.948i −0.377507 + 0.425071i
\(71\) 116.615i 0.194925i 0.995239 + 0.0974625i \(0.0310726\pi\)
−0.995239 + 0.0974625i \(0.968927\pi\)
\(72\) −198.693 + 84.7173i −0.325225 + 0.138667i
\(73\) 352.359i 0.564938i −0.959276 0.282469i \(-0.908847\pi\)
0.959276 0.282469i \(-0.0911534\pi\)
\(74\) 436.348 251.926i 0.685465 0.395753i
\(75\) −229.257 13.8371i −0.352964 0.0213036i
\(76\) −380.202 219.510i −0.573844 0.331309i
\(77\) −1203.82 247.291i −1.78166 0.365993i
\(78\) −280.312 + 424.245i −0.406911 + 0.615850i
\(79\) 390.954 + 677.153i 0.556782 + 0.964375i 0.997762 + 0.0668582i \(0.0212975\pi\)
−0.440980 + 0.897517i \(0.645369\pi\)
\(80\) −143.821 −0.200997
\(81\) −504.718 + 526.023i −0.692343 + 0.721568i
\(82\) 537.510i 0.723879i
\(83\) 122.693 + 212.511i 0.162257 + 0.281038i 0.935678 0.352855i \(-0.114789\pi\)
−0.773421 + 0.633893i \(0.781456\pi\)
\(84\) 100.033 371.711i 0.129935 0.482822i
\(85\) −84.1864 + 145.815i −0.107427 + 0.186069i
\(86\) 241.465 + 139.410i 0.302765 + 0.174801i
\(87\) 19.1619 317.479i 0.0236134 0.391234i
\(88\) −265.430 459.738i −0.321533 0.556911i
\(89\) −1642.23 −1.95592 −0.977958 0.208803i \(-0.933043\pi\)
−0.977958 + 0.208803i \(0.933043\pi\)
\(90\) −446.505 + 190.378i −0.522953 + 0.222973i
\(91\) −285.910 859.894i −0.329357 0.990565i
\(92\) −121.821 + 70.3332i −0.138051 + 0.0797037i
\(93\) 1554.54 776.627i 1.73332 0.865940i
\(94\) 200.602 + 115.818i 0.220112 + 0.127082i
\(95\) −854.394 493.284i −0.922726 0.532736i
\(96\) 148.747 74.3119i 0.158140 0.0790045i
\(97\) 969.077 559.497i 1.01438 0.585652i 0.101909 0.994794i \(-0.467505\pi\)
0.912471 + 0.409141i \(0.134172\pi\)
\(98\) 410.770 + 549.421i 0.423409 + 0.566326i
\(99\) −1432.61 1075.94i −1.45437 1.09228i
\(100\) 176.803 0.176803
\(101\) 763.867 + 1323.06i 0.752551 + 1.30346i 0.946583 + 0.322461i \(0.104510\pi\)
−0.194032 + 0.980995i \(0.562157\pi\)
\(102\) 11.7277 194.308i 0.0113845 0.188621i
\(103\) 1493.11 + 862.049i 1.42836 + 0.824662i 0.996991 0.0775146i \(-0.0246984\pi\)
0.431366 + 0.902177i \(0.358032\pi\)
\(104\) 195.717 338.991i 0.184534 0.319623i
\(105\) 224.796 835.314i 0.208931 0.776364i
\(106\) 438.701 + 759.852i 0.401985 + 0.696258i
\(107\) 669.357i 0.604758i −0.953188 0.302379i \(-0.902219\pi\)
0.953188 0.302379i \(-0.0977809\pi\)
\(108\) 363.431 427.605i 0.323807 0.380985i
\(109\) −316.634 −0.278239 −0.139120 0.990276i \(-0.544427\pi\)
−0.139120 + 0.990276i \(0.544427\pi\)
\(110\) −596.476 1033.13i −0.517016 0.895498i
\(111\) −721.632 + 1092.17i −0.617066 + 0.933914i
\(112\) −59.6265 + 290.263i −0.0503051 + 0.244886i
\(113\) 580.400 + 335.094i 0.483181 + 0.278965i 0.721741 0.692163i \(-0.243342\pi\)
−0.238560 + 0.971128i \(0.576675\pi\)
\(114\) 1138.53 + 68.7176i 0.935381 + 0.0564561i
\(115\) −273.757 + 158.053i −0.221982 + 0.128161i
\(116\) 244.840i 0.195973i
\(117\) 158.893 1311.50i 0.125553 1.03631i
\(118\) 452.346i 0.352897i
\(119\) 259.384 + 230.360i 0.199813 + 0.177454i
\(120\) 334.266 166.994i 0.254285 0.127037i
\(121\) 1536.15 2660.69i 1.15413 1.99902i
\(122\) 542.096 938.938i 0.402287 0.696782i
\(123\) −624.115 1249.27i −0.457517 0.915794i
\(124\) −1158.50 + 668.858i −0.839000 + 0.484397i
\(125\) 1520.92 1.08828
\(126\) 199.108 + 980.073i 0.140778 + 0.692951i
\(127\) −2290.65 −1.60049 −0.800246 0.599671i \(-0.795298\pi\)
−0.800246 + 0.599671i \(0.795298\pi\)
\(128\) −110.851 + 64.0000i −0.0765466 + 0.0441942i
\(129\) −723.078 43.6423i −0.493515 0.0297867i
\(130\) 439.816 761.784i 0.296726 0.513945i
\(131\) 697.263 1207.69i 0.465039 0.805471i −0.534164 0.845381i \(-0.679374\pi\)
0.999203 + 0.0399094i \(0.0127069\pi\)
\(132\) 1150.72 + 760.314i 0.758766 + 0.501340i
\(133\) −1349.78 + 1519.84i −0.880003 + 0.990881i
\(134\) 1228.06i 0.791704i
\(135\) 816.705 960.919i 0.520672 0.612613i
\(136\) 149.851i 0.0944822i
\(137\) 1237.96 714.737i 0.772016 0.445724i −0.0615774 0.998102i \(-0.519613\pi\)
0.833593 + 0.552379i \(0.186280\pi\)
\(138\) 201.467 304.915i 0.124275 0.188088i
\(139\) −210.788 121.698i −0.128624 0.0742612i 0.434307 0.900765i \(-0.356993\pi\)
−0.562932 + 0.826504i \(0.690327\pi\)
\(140\) −133.993 + 652.282i −0.0808893 + 0.393771i
\(141\) −600.714 36.2568i −0.358789 0.0216551i
\(142\) 116.615 + 201.983i 0.0689164 + 0.119367i
\(143\) 3246.81 1.89868
\(144\) −259.429 + 345.428i −0.150133 + 0.199900i
\(145\) 550.208i 0.315119i
\(146\) −352.359 610.303i −0.199736 0.345953i
\(147\) −1592.65 799.997i −0.893601 0.448861i
\(148\) 503.851 872.696i 0.279840 0.484697i
\(149\) 1065.50 + 615.165i 0.585831 + 0.338230i 0.763447 0.645870i \(-0.223505\pi\)
−0.177616 + 0.984100i \(0.556839\pi\)
\(150\) −410.921 + 205.290i −0.223677 + 0.111746i
\(151\) 837.344 + 1450.32i 0.451272 + 0.781626i 0.998465 0.0553802i \(-0.0176371\pi\)
−0.547193 + 0.837006i \(0.684304\pi\)
\(152\) −878.039 −0.468542
\(153\) 198.358 + 465.223i 0.104813 + 0.245824i
\(154\) −2332.37 + 775.498i −1.22044 + 0.405788i
\(155\) −2603.38 + 1503.06i −1.34909 + 0.778897i
\(156\) −61.2692 + 1015.13i −0.0314452 + 0.520994i
\(157\) −518.343 299.266i −0.263492 0.152127i 0.362434 0.932009i \(-0.381946\pi\)
−0.625927 + 0.779882i \(0.715279\pi\)
\(158\) 1354.31 + 781.908i 0.681916 + 0.393704i
\(159\) −1901.90 1256.64i −0.948619 0.626782i
\(160\) −249.106 + 143.821i −0.123085 + 0.0710630i
\(161\) 205.490 + 618.028i 0.100590 + 0.302530i
\(162\) −348.174 + 1415.82i −0.168859 + 0.686649i
\(163\) −1800.96 −0.865414 −0.432707 0.901535i \(-0.642441\pi\)
−0.432707 + 0.901535i \(0.642441\pi\)
\(164\) 537.510 + 930.995i 0.255930 + 0.443283i
\(165\) 2585.90 + 1708.59i 1.22007 + 0.806141i
\(166\) 425.023 + 245.387i 0.198724 + 0.114733i
\(167\) −195.287 + 338.247i −0.0904895 + 0.156732i −0.907717 0.419583i \(-0.862176\pi\)
0.817228 + 0.576315i \(0.195510\pi\)
\(168\) −198.449 743.856i −0.0911349 0.341606i
\(169\) 98.5300 + 170.659i 0.0448475 + 0.0776782i
\(170\) 336.746i 0.151925i
\(171\) −2725.94 + 1162.27i −1.21905 + 0.519770i
\(172\) 557.639 0.247207
\(173\) 510.530 + 884.264i 0.224364 + 0.388609i 0.956128 0.292948i \(-0.0946364\pi\)
−0.731765 + 0.681557i \(0.761303\pi\)
\(174\) −284.290 569.052i −0.123862 0.247930i
\(175\) 164.721 801.865i 0.0711528 0.346373i
\(176\) −919.475 530.859i −0.393796 0.227358i
\(177\) −525.230 1051.33i −0.223043 0.446457i
\(178\) −2844.43 + 1642.23i −1.19775 + 0.691521i
\(179\) 2447.76i 1.02209i 0.859554 + 0.511045i \(0.170741\pi\)
−0.859554 + 0.511045i \(0.829259\pi\)
\(180\) −582.992 + 776.249i −0.241409 + 0.321434i
\(181\) 676.711i 0.277898i 0.990300 + 0.138949i \(0.0443724\pi\)
−0.990300 + 0.138949i \(0.955628\pi\)
\(182\) −1355.10 1203.47i −0.551907 0.490149i
\(183\) −169.703 + 2811.70i −0.0685510 + 1.13577i
\(184\) −140.666 + 243.641i −0.0563590 + 0.0976167i
\(185\) 1132.26 1961.13i 0.449975 0.779379i
\(186\) 1915.92 2899.70i 0.755280 1.14310i
\(187\) −1076.44 + 621.481i −0.420946 + 0.243033i
\(188\) 463.271 0.179721
\(189\) −1600.75 2046.67i −0.616071 0.787691i
\(190\) −1973.14 −0.753402
\(191\) 1970.38 1137.60i 0.746450 0.430963i −0.0779596 0.996957i \(-0.524841\pi\)
0.824410 + 0.565993i \(0.191507\pi\)
\(192\) 183.326 277.459i 0.0689084 0.104291i
\(193\) −1135.76 + 1967.19i −0.423593 + 0.733685i −0.996288 0.0860835i \(-0.972565\pi\)
0.572694 + 0.819769i \(0.305898\pi\)
\(194\) 1118.99 1938.15i 0.414119 0.717275i
\(195\) −137.685 + 2281.20i −0.0505631 + 0.837745i
\(196\) 1260.90 + 540.856i 0.459510 + 0.197105i
\(197\) 3485.27i 1.26048i 0.776400 + 0.630241i \(0.217044\pi\)
−0.776400 + 0.630241i \(0.782956\pi\)
\(198\) −3557.29 430.979i −1.27679 0.154689i
\(199\) 1681.87i 0.599119i −0.954078 0.299559i \(-0.903160\pi\)
0.954078 0.299559i \(-0.0968397\pi\)
\(200\) 306.232 176.803i 0.108269 0.0625093i
\(201\) 1425.93 + 2854.23i 0.500385 + 1.00160i
\(202\) 2646.11 + 1527.73i 0.921682 + 0.532134i
\(203\) 1110.44 + 228.109i 0.383929 + 0.0788676i
\(204\) −173.995 348.279i −0.0597161 0.119531i
\(205\) 1207.90 + 2092.14i 0.411528 + 0.712787i
\(206\) 3448.20 1.16625
\(207\) −114.200 + 942.605i −0.0383452 + 0.316500i
\(208\) 782.866i 0.260971i
\(209\) −3641.52 6307.30i −1.20521 2.08749i
\(210\) −445.956 1671.60i −0.146542 0.549293i
\(211\) −524.934 + 909.213i −0.171270 + 0.296648i −0.938864 0.344288i \(-0.888120\pi\)
0.767594 + 0.640936i \(0.221454\pi\)
\(212\) 1519.70 + 877.401i 0.492329 + 0.284246i
\(213\) −505.562 334.040i −0.162632 0.107456i
\(214\) −669.357 1159.36i −0.213814 0.370337i
\(215\) 1253.13 0.397502
\(216\) 201.875 1104.06i 0.0635919 0.347787i
\(217\) 1954.18 + 5877.35i 0.611330 + 1.83862i
\(218\) −548.427 + 316.634i −0.170386 + 0.0983724i
\(219\) 1527.58 + 1009.32i 0.471344 + 0.311432i
\(220\) −2066.25 1192.95i −0.633213 0.365586i
\(221\) −793.719 458.254i −0.241590 0.139482i
\(222\) −157.731 + 2613.33i −0.0476856 + 0.790069i
\(223\) 2044.58 1180.44i 0.613969 0.354475i −0.160548 0.987028i \(-0.551326\pi\)
0.774517 + 0.632553i \(0.217993\pi\)
\(224\) 186.987 + 562.377i 0.0557750 + 0.167747i
\(225\) 716.686 954.260i 0.212351 0.282744i
\(226\) 1340.38 0.394515
\(227\) 2115.70 + 3664.51i 0.618609 + 1.07146i 0.989740 + 0.142881i \(0.0456367\pi\)
−0.371131 + 0.928580i \(0.621030\pi\)
\(228\) 2040.72 1019.51i 0.592762 0.296135i
\(229\) 1566.76 + 904.568i 0.452115 + 0.261029i 0.708723 0.705487i \(-0.249272\pi\)
−0.256608 + 0.966516i \(0.582605\pi\)
\(230\) −316.107 + 547.513i −0.0906238 + 0.156965i
\(231\) 4520.38 4510.56i 1.28753 1.28473i
\(232\) 244.840 + 424.076i 0.0692869 + 0.120008i
\(233\) 3054.99i 0.858965i −0.903075 0.429483i \(-0.858696\pi\)
0.903075 0.429483i \(-0.141304\pi\)
\(234\) −1036.29 2430.47i −0.289505 0.678995i
\(235\) 1041.07 0.288986
\(236\) 452.346 + 783.486i 0.124768 + 0.216104i
\(237\) −4055.54 244.777i −1.11154 0.0670885i
\(238\) 679.627 + 139.610i 0.185099 + 0.0380235i
\(239\) −4054.15 2340.67i −1.09724 0.633494i −0.161748 0.986832i \(-0.551713\pi\)
−0.935496 + 0.353338i \(0.885047\pi\)
\(240\) 411.972 623.509i 0.110803 0.167697i
\(241\) −1242.85 + 717.561i −0.332196 + 0.191793i −0.656816 0.754051i \(-0.728097\pi\)
0.324620 + 0.945845i \(0.394764\pi\)
\(242\) 6144.61i 1.63219i
\(243\) −834.722 3694.88i −0.220360 0.975419i
\(244\) 2168.38i 0.568920i
\(245\) 2833.50 + 1215.42i 0.738880 + 0.316939i
\(246\) −2330.27 1539.68i −0.603953 0.399050i
\(247\) 2685.10 4650.74i 0.691697 1.19805i
\(248\) −1337.72 + 2316.99i −0.342520 + 0.593263i
\(249\) −1272.75 76.8185i −0.323925 0.0195509i
\(250\) 2634.31 1520.92i 0.666433 0.384765i
\(251\) −6180.07 −1.55411 −0.777057 0.629431i \(-0.783288\pi\)
−0.777057 + 0.629431i \(0.783288\pi\)
\(252\) 1324.94 + 1498.43i 0.331204 + 0.374572i
\(253\) −2333.56 −0.579881
\(254\) −3967.53 + 2290.65i −0.980098 + 0.565860i
\(255\) −391.003 782.656i −0.0960219 0.192203i
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −2736.86 + 4740.38i −0.664283 + 1.15057i 0.315196 + 0.949027i \(0.397930\pi\)
−0.979479 + 0.201546i \(0.935404\pi\)
\(258\) −1296.05 + 647.487i −0.312746 + 0.156243i
\(259\) −3488.57 3098.21i −0.836947 0.743294i
\(260\) 1759.26i 0.419635i
\(261\) 1321.48 + 992.482i 0.313401 + 0.235376i
\(262\) 2789.05i 0.657665i
\(263\) −3980.72 + 2298.27i −0.933316 + 0.538850i −0.887859 0.460116i \(-0.847808\pi\)
−0.0454569 + 0.998966i \(0.514474\pi\)
\(264\) 2753.41 + 166.186i 0.641898 + 0.0387425i
\(265\) 3415.09 + 1971.70i 0.791651 + 0.457060i
\(266\) −818.037 + 3982.22i −0.188560 + 0.917916i
\(267\) 4704.13 7119.58i 1.07823 1.63188i
\(268\) −1228.06 2127.06i −0.279910 0.484817i
\(269\) −1598.04 −0.362210 −0.181105 0.983464i \(-0.557967\pi\)
−0.181105 + 0.983464i \(0.557967\pi\)
\(270\) 453.656 2481.07i 0.102254 0.559233i
\(271\) 233.977i 0.0524469i 0.999656 + 0.0262235i \(0.00834814\pi\)
−0.999656 + 0.0262235i \(0.991652\pi\)
\(272\) 149.851 + 259.549i 0.0334045 + 0.0578583i
\(273\) 4546.88 + 1223.63i 1.00802 + 0.271274i
\(274\) 1429.47 2475.92i 0.315174 0.545898i
\(275\) 2540.09 + 1466.52i 0.556994 + 0.321581i
\(276\) 44.0357 729.596i 0.00960375 0.159118i
\(277\) 1072.11 + 1856.95i 0.232552 + 0.402791i 0.958558 0.284896i \(-0.0919592\pi\)
−0.726007 + 0.687688i \(0.758626\pi\)
\(278\) −486.793 −0.105021
\(279\) −1086.03 + 8964.03i −0.233042 + 1.92352i
\(280\) 420.199 + 1263.78i 0.0896846 + 0.269733i
\(281\) 7133.55 4118.56i 1.51442 0.874351i 0.514563 0.857453i \(-0.327954\pi\)
0.999857 0.0168983i \(-0.00537914\pi\)
\(282\) −1076.72 + 537.915i −0.227369 + 0.113590i
\(283\) −5110.18 2950.36i −1.07339 0.619721i −0.144283 0.989537i \(-0.546087\pi\)
−0.929105 + 0.369816i \(0.879421\pi\)
\(284\) 403.967 + 233.230i 0.0844050 + 0.0487312i
\(285\) 4585.92 2291.06i 0.953145 0.476177i
\(286\) 5623.64 3246.81i 1.16270 0.671286i
\(287\) 4723.18 1570.43i 0.971429 0.322994i
\(288\) −103.917 + 857.728i −0.0212617 + 0.175493i
\(289\) −4562.14 −0.928585
\(290\) 550.208 + 952.988i 0.111411 + 0.192970i
\(291\) −350.301 + 5803.90i −0.0705671 + 1.16918i
\(292\) −1220.61 704.718i −0.244625 0.141235i
\(293\) 938.848 1626.13i 0.187195 0.324231i −0.757119 0.653277i \(-0.773394\pi\)
0.944314 + 0.329046i \(0.106727\pi\)
\(294\) −3558.54 + 207.013i −0.705913 + 0.0410655i
\(295\) 1016.52 + 1760.66i 0.200623 + 0.347490i
\(296\) 2015.40i 0.395753i
\(297\) 8768.18 3128.78i 1.71307 0.611280i
\(298\) 2460.66 0.478329
\(299\) −860.335 1490.14i −0.166403 0.288218i
\(300\) −506.446 + 766.494i −0.0974656 + 0.147512i
\(301\) 519.532 2529.09i 0.0994861 0.484301i
\(302\) 2900.64 + 1674.69i 0.552693 + 0.319098i
\(303\) −7923.92 478.258i −1.50237 0.0906772i
\(304\) −1520.81 + 878.039i −0.286922 + 0.165654i
\(305\) 4872.82i 0.914808i
\(306\) 808.790 + 607.432i 0.151096 + 0.113479i
\(307\) 9599.67i 1.78463i −0.451412 0.892316i \(-0.649079\pi\)
0.451412 0.892316i \(-0.350921\pi\)
\(308\) −3264.28 + 3675.57i −0.603895 + 0.679984i
\(309\) −8014.21 + 4003.78i −1.47545 + 0.737111i
\(310\) −3006.13 + 5206.77i −0.550763 + 0.953950i
\(311\) 0.327604 0.567426i 5.97322e−5 0.000103459i −0.865996 0.500052i \(-0.833314\pi\)
0.866055 + 0.499948i \(0.166648\pi\)
\(312\) 909.004 + 1819.52i 0.164943 + 0.330160i
\(313\) 3460.31 1997.81i 0.624883 0.360776i −0.153885 0.988089i \(-0.549178\pi\)
0.778768 + 0.627313i \(0.215845\pi\)
\(314\) −1197.06 −0.215141
\(315\) 2977.42 + 3367.28i 0.532566 + 0.602302i
\(316\) 3127.63 0.556782
\(317\) −3027.91 + 1748.17i −0.536481 + 0.309738i −0.743652 0.668567i \(-0.766908\pi\)
0.207171 + 0.978305i \(0.433575\pi\)
\(318\) −4550.83 274.671i −0.802509 0.0484364i
\(319\) −2030.87 + 3517.57i −0.356448 + 0.617387i
\(320\) −287.643 + 498.212i −0.0502491 + 0.0870341i
\(321\) 2901.86 + 1917.35i 0.504567 + 0.333383i
\(322\) 973.947 + 864.965i 0.168559 + 0.149697i
\(323\) 2055.85i 0.354151i
\(324\) 812.762 + 2800.44i 0.139363 + 0.480185i
\(325\) 2162.70i 0.369124i
\(326\) −3119.36 + 1800.96i −0.529956 + 0.305970i
\(327\) 906.988 1372.70i 0.153384 0.232143i
\(328\) 1861.99 + 1075.02i 0.313449 + 0.180970i
\(329\) 431.613 2101.10i 0.0723271 0.352090i
\(330\) 6187.50 + 373.454i 1.03215 + 0.0622969i
\(331\) 1167.71 + 2022.54i 0.193907 + 0.335857i 0.946542 0.322581i \(-0.104551\pi\)
−0.752634 + 0.658439i \(0.771217\pi\)
\(332\) 981.548 0.162257
\(333\) −2667.81 6256.99i −0.439024 1.02967i
\(334\) 781.147i 0.127971i
\(335\) −2759.71 4779.96i −0.450087 0.779573i
\(336\) −1087.58 1089.95i −0.176584 0.176969i
\(337\) 955.521 1655.01i 0.154453 0.267520i −0.778407 0.627760i \(-0.783972\pi\)
0.932860 + 0.360240i \(0.117305\pi\)
\(338\) 341.318 + 197.060i 0.0549268 + 0.0317120i
\(339\) −3115.27 + 1556.34i −0.499110 + 0.249348i
\(340\) 336.746 + 583.261i 0.0537135 + 0.0930346i
\(341\) −22191.8 −3.52421
\(342\) −3559.20 + 4739.05i −0.562748 + 0.749293i
\(343\) 3627.71 5214.72i 0.571072 0.820900i
\(344\) 965.858 557.639i 0.151383 0.0874007i
\(345\) 98.9574 1639.56i 0.0154426 0.255857i
\(346\) 1768.53 + 1021.06i 0.274788 + 0.158649i
\(347\) 297.253 + 171.619i 0.0459866 + 0.0265504i 0.522817 0.852445i \(-0.324881\pi\)
−0.476830 + 0.878995i \(0.658214\pi\)
\(348\) −1061.46 701.337i −0.163506 0.108033i
\(349\) 3767.94 2175.42i 0.577918 0.333661i −0.182388 0.983227i \(-0.558383\pi\)
0.760306 + 0.649566i \(0.225049\pi\)
\(350\) −516.560 1553.59i −0.0788894 0.237266i
\(351\) 5230.59 + 4445.59i 0.795408 + 0.676034i
\(352\) −2123.44 −0.321533
\(353\) 1617.00 + 2800.73i 0.243808 + 0.422288i 0.961796 0.273768i \(-0.0882700\pi\)
−0.717988 + 0.696056i \(0.754937\pi\)
\(354\) −1961.06 1295.73i −0.294432 0.194540i
\(355\) 907.798 + 524.118i 0.135721 + 0.0783585i
\(356\) −3284.47 + 5688.87i −0.488979 + 0.846936i
\(357\) −1741.68 + 464.651i −0.258205 + 0.0688850i
\(358\) 2447.76 + 4239.64i 0.361363 + 0.625899i
\(359\) 6058.56i 0.890692i 0.895358 + 0.445346i \(0.146919\pi\)
−0.895358 + 0.445346i \(0.853081\pi\)
\(360\) −233.523 + 1927.50i −0.0341882 + 0.282189i
\(361\) −5187.12 −0.756250
\(362\) 676.711 + 1172.10i 0.0982518 + 0.170177i
\(363\) 7134.65 + 14281.2i 1.03160 + 2.06492i
\(364\) −3550.58 729.368i −0.511266 0.105026i
\(365\) −2742.96 1583.65i −0.393351 0.227101i
\(366\) 2517.76 + 5039.71i 0.359578 + 0.719753i
\(367\) −7201.91 + 4158.03i −1.02435 + 0.591409i −0.915361 0.402634i \(-0.868095\pi\)
−0.108990 + 0.994043i \(0.534762\pi\)
\(368\) 562.665i 0.0797037i
\(369\) 7203.71 + 872.757i 1.01629 + 0.123127i
\(370\) 4529.04i 0.636361i
\(371\) 5395.18 6074.96i 0.754997 0.850125i
\(372\) 418.773 6938.35i 0.0583665 0.967034i
\(373\) −431.018 + 746.545i −0.0598318 + 0.103632i −0.894390 0.447288i \(-0.852390\pi\)
0.834558 + 0.550920i \(0.185723\pi\)
\(374\) −1242.96 + 2152.87i −0.171850 + 0.297654i
\(375\) −4356.62 + 6593.64i −0.599933 + 0.907984i
\(376\) 802.409 463.271i 0.110056 0.0635409i
\(377\) −2994.96 −0.409146
\(378\) −4819.25 1944.19i −0.655755 0.264546i
\(379\) 9815.25 1.33028 0.665139 0.746719i \(-0.268372\pi\)
0.665139 + 0.746719i \(0.268372\pi\)
\(380\) −3417.57 + 1973.14i −0.461363 + 0.266368i
\(381\) 6561.50 9930.67i 0.882299 1.33534i
\(382\) 2275.20 3940.77i 0.304737 0.527820i
\(383\) 1352.71 2342.96i 0.180470 0.312584i −0.761570 0.648082i \(-0.775571\pi\)
0.942041 + 0.335498i \(0.108905\pi\)
\(384\) 40.0705 663.899i 0.00532510 0.0882278i
\(385\) −7335.52 + 8259.78i −0.971047 + 1.09340i
\(386\) 4543.03i 0.599052i
\(387\) 2260.43 3009.75i 0.296910 0.395334i
\(388\) 4475.97i 0.585652i
\(389\) −6056.01 + 3496.44i −0.789336 + 0.455723i −0.839729 0.543006i \(-0.817286\pi\)
0.0503926 + 0.998729i \(0.483953\pi\)
\(390\) 2042.72 + 4088.84i 0.265224 + 0.530888i
\(391\) 570.465 + 329.358i 0.0737843 + 0.0425994i
\(392\) 2724.79 324.107i 0.351079 0.0417599i
\(393\) 3238.43 + 6482.24i 0.415667 + 0.832025i
\(394\) 3485.27 + 6036.66i 0.445648 + 0.771884i
\(395\) 7028.45 0.895291
\(396\) −6592.38 + 2810.81i −0.836565 + 0.356688i
\(397\) 22.8921i 0.00289400i 0.999999 + 0.00144700i \(0.000460595\pi\)
−0.999999 + 0.00144700i \(0.999539\pi\)
\(398\) −1681.87 2913.09i −0.211821 0.366884i
\(399\) −2722.59 10205.2i −0.341604 1.28045i
\(400\) 353.606 612.463i 0.0442007 0.0765579i
\(401\) −10278.3 5934.17i −1.27998 0.738998i −0.303137 0.952947i \(-0.598034\pi\)
−0.976845 + 0.213949i \(0.931367\pi\)
\(402\) 5324.01 + 3517.74i 0.660541 + 0.436440i
\(403\) −8181.66 14171.0i −1.01131 1.75164i
\(404\) 6110.94 0.752551
\(405\) 1826.45 + 6293.18i 0.224091 + 0.772125i
\(406\) 2151.45 715.343i 0.262992 0.0874431i
\(407\) 14477.5 8358.56i 1.76320 1.01798i
\(408\) −649.647 429.242i −0.0788293 0.0520849i
\(409\) −3271.46 1888.78i −0.395510 0.228348i 0.289035 0.957319i \(-0.406666\pi\)
−0.684545 + 0.728971i \(0.739999\pi\)
\(410\) 4184.28 + 2415.80i 0.504017 + 0.290994i
\(411\) −447.498 + 7414.28i −0.0537067 + 0.889828i
\(412\) 5972.45 3448.20i 0.714179 0.412331i
\(413\) 3974.83 1321.61i 0.473580 0.157462i
\(414\) 744.805 + 1746.84i 0.0884182 + 0.207373i
\(415\) 2205.74 0.260905
\(416\) −782.866 1355.96i −0.0922672 0.159812i
\(417\) 1131.39 565.227i 0.132865 0.0663772i
\(418\) −12614.6 7283.04i −1.47608 0.852214i
\(419\) 5522.32 9564.93i 0.643873 1.11522i −0.340688 0.940177i \(-0.610660\pi\)
0.984561 0.175044i \(-0.0560068\pi\)
\(420\) −2444.02 2449.34i −0.283943 0.284561i
\(421\) −1394.24 2414.90i −0.161404 0.279561i 0.773968 0.633224i \(-0.218269\pi\)
−0.935373 + 0.353664i \(0.884936\pi\)
\(422\) 2099.74i 0.242212i
\(423\) 1877.91 2500.42i 0.215856 0.287410i
\(424\) 3509.60 0.401985
\(425\) −413.969 717.016i −0.0472481 0.0818362i
\(426\) −1209.70 73.0129i −0.137582 0.00830396i
\(427\) −9834.41 2020.21i −1.11457 0.228957i
\(428\) −2318.72 1338.71i −0.261868 0.151190i
\(429\) −9300.38 + 14075.9i −1.04668 + 1.58413i
\(430\) 2170.49 1253.13i 0.243419 0.140538i
\(431\) 10345.4i 1.15620i 0.815966 + 0.578100i \(0.196206\pi\)
−0.815966 + 0.578100i \(0.803794\pi\)
\(432\) −754.407 2114.17i −0.0840195 0.235459i
\(433\) 5236.75i 0.581206i 0.956844 + 0.290603i \(0.0938559\pi\)
−0.956844 + 0.290603i \(0.906144\pi\)
\(434\) 9262.09 + 8225.68i 1.02441 + 0.909782i
\(435\) −2385.32 1576.05i −0.262913 0.173715i
\(436\) −633.268 + 1096.85i −0.0695598 + 0.120481i
\(437\) −1929.85 + 3342.60i −0.211252 + 0.365900i
\(438\) 3655.17 + 220.612i 0.398746 + 0.0240668i
\(439\) 5187.63 2995.08i 0.563991 0.325621i −0.190755 0.981638i \(-0.561093\pi\)
0.754746 + 0.656017i \(0.227760\pi\)
\(440\) −4771.81 −0.517016
\(441\) 8030.31 4613.04i 0.867111 0.498115i
\(442\) −1833.01 −0.197257
\(443\) −3479.08 + 2008.65i −0.373129 + 0.215426i −0.674824 0.737978i \(-0.735781\pi\)
0.301696 + 0.953404i \(0.402447\pi\)
\(444\) 2340.13 + 4684.15i 0.250130 + 0.500676i
\(445\) −7380.89 + 12784.1i −0.786265 + 1.36185i
\(446\) 2360.88 4089.16i 0.250652 0.434142i
\(447\) −5719.00 + 2857.13i −0.605144 + 0.302321i
\(448\) 886.248 + 787.079i 0.0934627 + 0.0830044i
\(449\) 1948.54i 0.204805i 0.994743 + 0.102402i \(0.0326529\pi\)
−0.994743 + 0.102402i \(0.967347\pi\)
\(450\) 287.076 2369.51i 0.0300730 0.248222i
\(451\) 17833.9i 1.86201i
\(452\) 2321.60 1340.38i 0.241590 0.139482i
\(453\) −8686.13 524.262i −0.900905 0.0543752i
\(454\) 7329.01 + 4231.41i 0.757638 + 0.437422i
\(455\) −7978.90 1639.04i −0.822103 0.168878i
\(456\) 2515.11 3806.56i 0.258291 0.390918i
\(457\) −6701.72 11607.7i −0.685980 1.18815i −0.973128 0.230266i \(-0.926040\pi\)
0.287147 0.957886i \(-0.407293\pi\)
\(458\) 3618.27 0.369150
\(459\) −2585.07 472.673i −0.262878 0.0480664i
\(460\) 1264.43i 0.128161i
\(461\) −8561.65 14829.2i −0.864980 1.49819i −0.867067 0.498191i \(-0.833998\pi\)
0.00208770 0.999998i \(-0.499335\pi\)
\(462\) 3318.97 12332.9i 0.334226 1.24194i
\(463\) 6153.89 10658.9i 0.617701 1.06989i −0.372203 0.928151i \(-0.621397\pi\)
0.989904 0.141739i \(-0.0452693\pi\)
\(464\) 848.152 + 489.681i 0.0848588 + 0.0489933i
\(465\) 941.070 15591.9i 0.0938518 1.55496i
\(466\) −3054.99 5291.39i −0.303690 0.526007i
\(467\) 15514.3 1.53730 0.768648 0.639672i \(-0.220930\pi\)
0.768648 + 0.639672i \(0.220930\pi\)
\(468\) −4225.37 3173.41i −0.417346 0.313443i
\(469\) −10791.1 + 3587.99i −1.06245 + 0.353258i
\(470\) 1803.18 1041.07i 0.176967 0.102172i
\(471\) 2782.18 1389.94i 0.272179 0.135977i
\(472\) 1566.97 + 904.692i 0.152809 + 0.0882242i
\(473\) 8011.48 + 4625.43i 0.778791 + 0.449635i
\(474\) −7269.17 + 3631.57i −0.704397 + 0.351906i
\(475\) 4201.30 2425.62i 0.405829 0.234306i
\(476\) 1316.76 437.814i 0.126793 0.0421579i
\(477\) 10895.9 4645.69i 1.04588 0.445936i
\(478\) −9362.66 −0.895896
\(479\) 9726.27 + 16846.4i 0.927776 + 1.60695i 0.787035 + 0.616908i \(0.211615\pi\)
0.140741 + 0.990047i \(0.455052\pi\)
\(480\) 90.0468 1491.92i 0.00856261 0.141868i
\(481\) 10675.1 + 6163.25i 1.01194 + 0.584241i
\(482\) −1435.12 + 2485.71i −0.135618 + 0.234898i
\(483\) −3267.96 879.456i −0.307862 0.0828502i
\(484\) −6144.61 10642.8i −0.577067 0.999509i
\(485\) 10058.5i 0.941713i
\(486\) −5140.66 5565.00i −0.479805 0.519411i
\(487\) 20747.4 1.93050 0.965250 0.261329i \(-0.0841607\pi\)
0.965250 + 0.261329i \(0.0841607\pi\)
\(488\) −2168.38 3755.75i −0.201144 0.348391i
\(489\) 5158.80 7807.72i 0.477074 0.722040i
\(490\) 6123.18 728.336i 0.564525 0.0671487i
\(491\) 342.738 + 197.880i 0.0315022 + 0.0181878i 0.515668 0.856788i \(-0.327544\pi\)
−0.484166 + 0.874976i \(0.660877\pi\)
\(492\) −5575.82 336.536i −0.510930 0.0308378i
\(493\) 992.939 573.273i 0.0907093 0.0523711i
\(494\) 10740.4i 0.978207i
\(495\) −14814.5 + 6316.48i −1.34517 + 0.573545i
\(496\) 5350.86i 0.484397i
\(497\) 1434.15 1614.84i 0.129437 0.145746i
\(498\) −2281.29 + 1139.70i −0.205275 + 0.102552i
\(499\) −10146.7 + 17574.6i −0.910278 + 1.57665i −0.0966055 + 0.995323i \(0.530799\pi\)
−0.813672 + 0.581324i \(0.802535\pi\)
\(500\) 3041.84 5268.62i 0.272070 0.471239i
\(501\) −907.008 1815.52i −0.0808825 0.161899i
\(502\) −10704.2 + 6180.07i −0.951696 + 0.549462i
\(503\) −9434.59 −0.836318 −0.418159 0.908374i \(-0.637324\pi\)
−0.418159 + 0.908374i \(0.637324\pi\)
\(504\) 3793.29 + 1270.42i 0.335251 + 0.112279i
\(505\) 13732.6 1.21008
\(506\) −4041.85 + 2333.56i −0.355103 + 0.205019i
\(507\) −1022.09 61.6897i −0.0895321 0.00540382i
\(508\) −4581.31 + 7935.05i −0.400123 + 0.693034i
\(509\) 1055.39 1828.00i 0.0919048 0.159184i −0.816408 0.577476i \(-0.804038\pi\)
0.908313 + 0.418292i \(0.137371\pi\)
\(510\) −1459.89 964.597i −0.126755 0.0837511i
\(511\) −4333.34 + 4879.33i −0.375139 + 0.422405i
\(512\) 512.000i 0.0441942i
\(513\) 2769.59 15147.1i 0.238364 1.30362i
\(514\) 10947.4i 0.939438i
\(515\) 13421.4 7748.82i 1.14838 0.663017i
\(516\) −1597.34 + 2417.53i −0.136277 + 0.206252i
\(517\) 6655.72 + 3842.68i 0.566186 + 0.326888i
\(518\) −9140.59 1877.68i −0.775317 0.159267i
\(519\) −5295.95 319.643i −0.447912 0.0270343i
\(520\) −1759.26 3047.14i −0.148363 0.256973i
\(521\) 2781.94 0.233933 0.116967 0.993136i \(-0.462683\pi\)
0.116967 + 0.993136i \(0.462683\pi\)
\(522\) 3281.35 + 397.548i 0.275136 + 0.0333338i
\(523\) 16345.8i 1.36664i −0.730119 0.683320i \(-0.760536\pi\)
0.730119 0.683320i \(-0.239464\pi\)
\(524\) −2789.05 4830.78i −0.232520 0.402736i
\(525\) 3004.49 + 3011.03i 0.249765 + 0.250309i
\(526\) −4596.54 + 7961.45i −0.381024 + 0.659954i
\(527\) 5425.04 + 3132.15i 0.448422 + 0.258897i
\(528\) 4935.24 2465.57i 0.406778 0.203220i
\(529\) −5465.16 9465.93i −0.449179 0.778000i
\(530\) 7886.82 0.646380
\(531\) 6062.34 + 734.476i 0.495449 + 0.0600255i
\(532\) 2565.34 + 7715.45i 0.209063 + 0.628773i
\(533\) −11388.2 + 6574.97i −0.925473 + 0.534322i
\(534\) 1028.20 17035.6i 0.0833235 1.38053i
\(535\) −5210.65 3008.37i −0.421077 0.243109i
\(536\) −4254.13 2456.12i −0.342818 0.197926i
\(537\) −10611.8 7011.52i −0.852759 0.563444i
\(538\) −2767.89 + 1598.04i −0.221807 + 0.128060i
\(539\) 13628.8 + 18229.1i 1.08912 + 1.45674i
\(540\) −1695.31 4750.99i −0.135101 0.378611i
\(541\) −4367.39 −0.347077 −0.173539 0.984827i \(-0.555520\pi\)
−0.173539 + 0.984827i \(0.555520\pi\)
\(542\) 233.977 + 405.261i 0.0185428 + 0.0321170i
\(543\) −2933.75 1938.42i −0.231858 0.153196i
\(544\) 519.098 + 299.701i 0.0409120 + 0.0236206i
\(545\) −1423.09 + 2464.86i −0.111850 + 0.193730i
\(546\) 9099.06 2427.48i 0.713194 0.190269i
\(547\) −1279.61 2216.36i −0.100023 0.173244i 0.811671 0.584115i \(-0.198558\pi\)
−0.911694 + 0.410870i \(0.865225\pi\)
\(548\) 5717.90i 0.445724i
\(549\) −11703.4 8789.73i −0.909819 0.683309i
\(550\) 5866.09 0.454784
\(551\) 3359.05 + 5818.05i 0.259710 + 0.449832i
\(552\) −653.324 1307.73i −0.0503756 0.100835i
\(553\) 2913.90 14184.9i 0.224072 1.09079i
\(554\) 3713.90 + 2144.22i 0.284816 + 0.164439i
\(555\) 5258.77 + 10526.3i 0.402203 + 0.805073i
\(556\) −843.150 + 486.793i −0.0643121 + 0.0371306i
\(557\) 11605.3i 0.882823i 0.897305 + 0.441411i \(0.145522\pi\)
−0.897305 + 0.441411i \(0.854478\pi\)
\(558\) 7082.98 + 16612.2i 0.537359 + 1.26030i
\(559\) 6821.19i 0.516110i
\(560\) 1991.59 + 1768.73i 0.150285 + 0.133469i
\(561\) 389.110 6446.89i 0.0292838 0.485183i
\(562\) 8237.12 14267.1i 0.618259 1.07086i
\(563\) −147.052 + 254.701i −0.0110080 + 0.0190664i −0.871477 0.490437i \(-0.836837\pi\)
0.860469 + 0.509503i \(0.170171\pi\)
\(564\) −1327.02 + 2008.42i −0.0990741 + 0.149946i
\(565\) 5217.12 3012.11i 0.388471 0.224284i
\(566\) −11801.5 −0.876418
\(567\) 13458.2 1077.10i 0.996813 0.0797777i
\(568\) 932.921 0.0689164
\(569\) −6601.43 + 3811.34i −0.486373 + 0.280808i −0.723069 0.690776i \(-0.757269\pi\)
0.236695 + 0.971584i \(0.423936\pi\)
\(570\) 5651.99 8554.14i 0.415326 0.628585i
\(571\) −2212.29 + 3831.80i −0.162139 + 0.280834i −0.935636 0.352967i \(-0.885173\pi\)
0.773496 + 0.633801i \(0.218506\pi\)
\(572\) 6493.62 11247.3i 0.474671 0.822155i
\(573\) −712.254 + 11800.8i −0.0519281 + 0.860361i
\(574\) 6610.35 7443.24i 0.480681 0.541245i
\(575\) 1554.39i 0.112735i
\(576\) 677.738 + 1589.55i 0.0490262 + 0.114984i
\(577\) 21320.1i 1.53825i 0.639099 + 0.769124i \(0.279307\pi\)
−0.639099 + 0.769124i \(0.720693\pi\)
\(578\) −7901.85 + 4562.14i −0.568640 + 0.328304i
\(579\) −5275.01 10558.8i −0.378622 0.757873i
\(580\) 1905.98 + 1100.42i 0.136451 + 0.0787798i
\(581\) 914.473 4451.67i 0.0652990 0.317877i
\(582\) 5197.16 + 10402.9i 0.370153 + 0.740921i
\(583\) 14555.5 + 25210.9i 1.03401 + 1.79096i
\(584\) −2818.87 −0.199736
\(585\) −9495.30 7131.33i −0.671081 0.504007i
\(586\) 3755.39i 0.264734i
\(587\) 7958.62 + 13784.7i 0.559604 + 0.969262i 0.997529 + 0.0702508i \(0.0223800\pi\)
−0.437926 + 0.899011i \(0.644287\pi\)
\(588\) −5956.57 + 3917.10i −0.417763 + 0.274725i
\(589\) −18352.6 + 31787.6i −1.28388 + 2.22375i
\(590\) 3521.32 + 2033.03i 0.245712 + 0.141862i
\(591\) −15109.7 9983.43i −1.05166 0.694862i
\(592\) −2015.40 3490.78i −0.139920 0.242348i
\(593\) 10320.7 0.714702 0.357351 0.933970i \(-0.383680\pi\)
0.357351 + 0.933970i \(0.383680\pi\)
\(594\) 12058.2 14187.4i 0.832916 0.979992i
\(595\) 2959.03 983.861i 0.203880 0.0677888i
\(596\) 4261.99 2460.66i 0.292916 0.169115i
\(597\) 7291.42 + 4817.66i 0.499862 + 0.330274i
\(598\) −2980.29 1720.67i −0.203801 0.117665i
\(599\) −14115.3 8149.48i −0.962832 0.555891i −0.0657884 0.997834i \(-0.520956\pi\)
−0.897043 + 0.441942i \(0.854290\pi\)
\(600\) −110.696 + 1834.05i −0.00753194 + 0.124791i
\(601\) 10634.4 6139.76i 0.721772 0.416715i −0.0936324 0.995607i \(-0.529848\pi\)
0.815405 + 0.578891i \(0.196515\pi\)
\(602\) −1629.24 4900.05i −0.110304 0.331746i
\(603\) −16458.5 1994.01i −1.11151 0.134664i
\(604\) 6698.75 0.451272
\(605\) −13808.2 23916.6i −0.927908 1.60718i
\(606\) −14202.9 + 7095.55i −0.952067 + 0.475639i
\(607\) 16715.3 + 9650.56i 1.11771 + 0.645312i 0.940816 0.338918i \(-0.110061\pi\)
0.176896 + 0.984229i \(0.443394\pi\)
\(608\) −1756.08 + 3041.61i −0.117135 + 0.202884i
\(609\) −4169.74 + 4160.68i −0.277449 + 0.276846i
\(610\) −4872.82 8439.96i −0.323434 0.560203i
\(611\) 5666.86i 0.375216i
\(612\) 2008.30 + 243.313i 0.132648 + 0.0160708i
\(613\) 6168.41 0.406427 0.203214 0.979134i \(-0.434861\pi\)
0.203214 + 0.979134i \(0.434861\pi\)
\(614\) −9599.67 16627.1i −0.630963 1.09286i
\(615\) −12530.0 756.266i −0.821561 0.0495863i
\(616\) −1978.33 + 9630.55i −0.129398 + 0.629912i
\(617\) 1923.21 + 1110.37i 0.125487 + 0.0724500i 0.561430 0.827525i \(-0.310252\pi\)
−0.435942 + 0.899975i \(0.643585\pi\)
\(618\) −9877.24 + 14949.0i −0.642914 + 0.973035i
\(619\) 4974.55 2872.06i 0.323011 0.186491i −0.329723 0.944078i \(-0.606955\pi\)
0.652734 + 0.757587i \(0.273622\pi\)
\(620\) 12024.5i 0.778897i
\(621\) −3759.35 3195.15i −0.242927 0.206469i
\(622\) 1.31041i 8.44740e-5i
\(623\) 22741.0 + 20196.4i 1.46244 + 1.29880i
\(624\) 3393.96 + 2242.49i 0.217736 + 0.143865i
\(625\) 4073.10 7054.82i 0.260679 0.451508i
\(626\) 3995.62 6920.62i 0.255107 0.441859i
\(627\) 37775.1 + 2279.96i 2.40605 + 0.145220i
\(628\) −2073.37 + 1197.06i −0.131746 + 0.0760637i
\(629\) −4718.90 −0.299133
\(630\) 8524.32 + 2854.89i 0.539075 + 0.180542i
\(631\) −24057.5 −1.51777 −0.758885 0.651225i \(-0.774256\pi\)
−0.758885 + 0.651225i \(0.774256\pi\)
\(632\) 5417.22 3127.63i 0.340958 0.196852i
\(633\) −2438.05 4880.16i −0.153087 0.306428i
\(634\) −3496.33 + 6055.82i −0.219017 + 0.379349i
\(635\) −10295.2 + 17831.7i −0.643387 + 1.11438i
\(636\) −8156.94 + 4075.08i −0.508559 + 0.254069i
\(637\) −6615.90 + 15423.6i −0.411509 + 0.959351i
\(638\) 8123.49i 0.504094i
\(639\) 2896.33 1234.92i 0.179307 0.0764515i
\(640\) 1150.57i 0.0710630i
\(641\) 11837.8 6834.54i 0.729429 0.421136i −0.0887844 0.996051i \(-0.528298\pi\)
0.818213 + 0.574915i \(0.194965\pi\)
\(642\) 6943.52 + 419.085i 0.426852 + 0.0257632i
\(643\) −20421.6 11790.4i −1.25249 0.723124i −0.280885 0.959741i \(-0.590628\pi\)
−0.971603 + 0.236617i \(0.923961\pi\)
\(644\) 2551.89 + 524.215i 0.156147 + 0.0320761i
\(645\) −3589.55 + 5432.70i −0.219129 + 0.331647i
\(646\) 2055.85 + 3560.84i 0.125211 + 0.216872i
\(647\) −25891.5 −1.57326 −0.786629 0.617425i \(-0.788176\pi\)
−0.786629 + 0.617425i \(0.788176\pi\)
\(648\) 4208.19 + 4037.74i 0.255113 + 0.244780i
\(649\) 15008.3i 0.907744i
\(650\) 2162.70 + 3745.91i 0.130505 + 0.226041i
\(651\) −31077.8 8363.50i −1.87102 0.503520i
\(652\) −3601.93 + 6238.72i −0.216353 + 0.374735i
\(653\) 15330.2 + 8850.89i 0.918708 + 0.530416i 0.883223 0.468954i \(-0.155369\pi\)
0.0354854 + 0.999370i \(0.488702\pi\)
\(654\) 198.245 3284.58i 0.0118532 0.196387i
\(655\) −6267.58 10855.8i −0.373885 0.647588i
\(656\) 4300.08 0.255930
\(657\) −8751.41 + 3731.36i −0.519673 + 0.221574i
\(658\) −1353.53 4070.83i −0.0801914 0.241181i
\(659\) −16234.0 + 9372.72i −0.959618 + 0.554036i −0.896055 0.443942i \(-0.853580\pi\)
−0.0635624 + 0.997978i \(0.520246\pi\)
\(660\) 11090.5 5540.66i 0.654088 0.326773i
\(661\) 10069.2 + 5813.43i 0.592504 + 0.342082i 0.766087 0.642737i \(-0.222201\pi\)
−0.173583 + 0.984819i \(0.555535\pi\)
\(662\) 4045.08 + 2335.43i 0.237487 + 0.137113i
\(663\) 4260.25 2128.36i 0.249554 0.124673i
\(664\) 1700.09 981.548i 0.0993619 0.0573666i
\(665\) 5764.86 + 17338.2i 0.336168 + 1.01105i
\(666\) −10877.8 8169.61i −0.632890 0.475324i
\(667\) 2152.55 0.124958
\(668\) 781.147 + 1352.99i 0.0452447 + 0.0783662i
\(669\) −739.074 + 12245.2i −0.0427119 + 0.707663i
\(670\) −9559.92 5519.42i −0.551242 0.318259i
\(671\) 17986.0 31152.7i 1.03479 1.79231i
\(672\) −2973.69 800.265i −0.170703 0.0459388i
\(673\) −2240.43 3880.53i −0.128324 0.222264i 0.794703 0.606998i \(-0.207626\pi\)
−0.923027 + 0.384734i \(0.874293\pi\)
\(674\) 3822.08i 0.218429i
\(675\) 2084.08 + 5840.49i 0.118839 + 0.333038i
\(676\) 788.240 0.0448475
\(677\) 6548.02 + 11341.5i 0.371730 + 0.643855i 0.989832 0.142243i \(-0.0454315\pi\)
−0.618102 + 0.786098i \(0.712098\pi\)
\(678\) −3839.46 + 5810.93i −0.217483 + 0.329156i
\(679\) −20300.2 4170.10i −1.14735 0.235691i
\(680\) 1166.52 + 673.492i 0.0657854 + 0.0379812i
\(681\) −21947.1 1324.64i −1.23497 0.0745381i
\(682\) −38437.4 + 22191.8i −2.15813 + 1.24600i
\(683\) 12353.9i 0.692109i −0.938214 0.346054i \(-0.887521\pi\)
0.938214 0.346054i \(-0.112479\pi\)
\(684\) −1425.67 + 11767.5i −0.0796959 + 0.657808i
\(685\) 12849.3i 0.716711i
\(686\) 1068.65 12659.9i 0.0594770 0.704601i
\(687\) −8409.50 + 4201.26i −0.467019 + 0.233316i
\(688\) 1115.28 1931.72i 0.0618017 0.107044i
\(689\) −10732.6 + 18589.4i −0.593440 + 1.02787i
\(690\) −1468.16 2938.75i −0.0810026 0.162140i
\(691\) 10460.0 6039.10i 0.575858 0.332472i −0.183627 0.982996i \(-0.558784\pi\)
0.759486 + 0.650524i \(0.225451\pi\)
\(692\) 4084.24 0.224364
\(693\) 6606.15 + 32517.6i 0.362117 + 1.78245i
\(694\) 686.476 0.0375479
\(695\) −1894.74 + 1093.93i −0.103412 + 0.0597050i
\(696\) −2539.84 153.295i −0.138322 0.00834860i
\(697\) 2517.07 4359.69i 0.136787 0.236923i
\(698\) 4350.85 7535.89i 0.235934 0.408650i
\(699\) 13244.3 + 8750.91i 0.716659 + 0.473519i
\(700\) −2448.30 2174.34i −0.132196 0.117403i
\(701\) 14395.9i 0.775645i −0.921734 0.387822i \(-0.873227\pi\)
0.921734 0.387822i \(-0.126773\pi\)
\(702\) 13505.2 + 2469.39i 0.726100 + 0.132765i
\(703\) 27650.0i 1.48342i
\(704\) −3677.90 + 2123.44i −0.196898 + 0.113679i
\(705\) −2982.10 + 4513.34i −0.159309 + 0.241110i
\(706\) 5601.45 + 3234.00i 0.298603 + 0.172398i
\(707\) 5693.34 27715.3i 0.302857 1.47432i
\(708\) −4692.38 283.214i −0.249083 0.0150337i
\(709\) −14380.2 24907.2i −0.761719 1.31934i −0.941964 0.335715i \(-0.891022\pi\)
0.180244 0.983622i \(-0.442311\pi\)
\(710\) 2096.47 0.110816
\(711\) 12678.1 16880.8i 0.668730 0.890408i
\(712\) 13137.9i 0.691521i
\(713\) 5880.36 + 10185.1i 0.308866 + 0.534971i
\(714\) −2552.02 + 2546.48i −0.133763 + 0.133473i
\(715\) 14592.5 25275.0i 0.763258 1.32200i
\(716\) 8479.28 + 4895.51i 0.442578 + 0.255522i
\(717\) 21760.5 10871.2i 1.13342 0.566238i
\(718\) 6058.56 + 10493.7i 0.314907 + 0.545435i
\(719\) −12676.1 −0.657493 −0.328746 0.944418i \(-0.606626\pi\)
−0.328746 + 0.944418i \(0.606626\pi\)
\(720\) 1523.02 + 3572.04i 0.0788328 + 0.184892i
\(721\) −10074.5 30299.8i −0.520380 1.56508i
\(722\) −8984.36 + 5187.12i −0.463107 + 0.267375i
\(723\) 449.266 7443.57i 0.0231098 0.382890i
\(724\) 2344.20 + 1353.42i 0.120333 + 0.0694745i
\(725\) −2343.06 1352.77i −0.120026 0.0692972i
\(726\) 26638.7 + 17601.0i 1.36179 + 0.899773i
\(727\) 12063.6 6964.93i 0.615426 0.355316i −0.159660 0.987172i \(-0.551040\pi\)
0.775086 + 0.631856i \(0.217706\pi\)
\(728\) −6879.15 + 2287.28i −0.350218 + 0.116445i
\(729\) 18409.5 + 6965.09i 0.935297 + 0.353863i
\(730\) −6334.59 −0.321170
\(731\) −1305.66 2261.48i −0.0660625 0.114424i
\(732\) 9400.60 + 6211.26i 0.474667 + 0.313627i
\(733\) 868.392 + 501.367i 0.0437583 + 0.0252638i 0.521720 0.853117i \(-0.325291\pi\)
−0.477961 + 0.878381i \(0.658624\pi\)
\(734\) −8316.05 + 14403.8i −0.418190 + 0.724325i
\(735\) −13385.7 + 8802.55i −0.671752 + 0.441751i
\(736\) 562.665 + 974.565i 0.0281795 + 0.0488084i
\(737\) 40745.5i 2.03647i
\(738\) 13349.9 5692.05i 0.665878 0.283912i
\(739\) 25136.6 1.25124 0.625619 0.780129i \(-0.284847\pi\)
0.625619 + 0.780129i \(0.284847\pi\)
\(740\) −4529.04 7844.52i −0.224987 0.389690i
\(741\) 12471.0 + 24962.6i 0.618262 + 1.23755i
\(742\) 3269.77 15917.3i 0.161775 0.787525i
\(743\) −20262.2 11698.4i −1.00047 0.577620i −0.0920810 0.995752i \(-0.529352\pi\)
−0.908387 + 0.418131i \(0.862685\pi\)
\(744\) −6213.01 12436.3i −0.306156 0.612821i
\(745\) 9577.58 5529.62i 0.471000 0.271932i
\(746\) 1724.07i 0.0846150i
\(747\) 3978.79 5297.72i 0.194881 0.259482i
\(748\) 4971.85i 0.243033i
\(749\) −8231.82 + 9269.00i −0.401581 + 0.452179i
\(750\) −952.249 + 15777.1i −0.0463616 + 0.768133i
\(751\) 13579.4 23520.2i 0.659811 1.14283i −0.320853 0.947129i \(-0.603970\pi\)
0.980664 0.195697i \(-0.0626971\pi\)
\(752\) 926.542 1604.82i 0.0449302 0.0778214i
\(753\) 17702.6 26792.5i 0.856731 1.29664i
\(754\) −5187.42 + 2994.96i −0.250550 + 0.144655i
\(755\) 15053.5 0.725633
\(756\) −10291.4 + 1451.81i −0.495098 + 0.0698437i
\(757\) 20937.2 1.00525 0.502626 0.864504i \(-0.332367\pi\)
0.502626 + 0.864504i \(0.332367\pi\)
\(758\) 17000.5 9815.25i 0.814626 0.470325i
\(759\) 6684.41 10116.7i 0.319669 0.483811i
\(760\) −3946.27 + 6835.15i −0.188351 + 0.326233i
\(761\) −11543.8 + 19994.5i −0.549885 + 0.952429i 0.448397 + 0.893835i \(0.351995\pi\)
−0.998282 + 0.0585944i \(0.981338\pi\)
\(762\) 1434.18 23761.9i 0.0681822 1.12966i
\(763\) 4384.63 + 3894.00i 0.208040 + 0.184761i
\(764\) 9100.81i 0.430963i
\(765\) 4513.07 + 546.775i 0.213294 + 0.0258414i
\(766\) 5410.83i 0.255224i
\(767\) −9583.83 + 5533.23i −0.451176 + 0.260487i
\(768\) −594.495 1189.98i −0.0279323 0.0559110i
\(769\) −18738.6 10818.8i −0.878716 0.507327i −0.00848126 0.999964i \(-0.502700\pi\)
−0.870235 + 0.492637i \(0.836033\pi\)
\(770\) −4445.72 + 21641.9i −0.208069 + 1.01288i
\(771\) −12711.3 25443.8i −0.593759 1.18850i
\(772\) 4543.03 + 7868.75i 0.211797 + 0.366843i
\(773\) 13555.7 0.630742 0.315371 0.948968i \(-0.397871\pi\)
0.315371 + 0.948968i \(0.397871\pi\)
\(774\) 905.440 7473.47i 0.0420483 0.347065i
\(775\) 14782.0i 0.685142i
\(776\) −4475.97 7752.61i −0.207059 0.358637i
\(777\) 23424.5 6249.29i 1.08153 0.288536i
\(778\) −6992.88 + 12112.0i −0.322245 + 0.558145i
\(779\) 25545.3 + 14748.6i 1.17491 + 0.678335i
\(780\) 7626.94 + 5039.36i 0.350113 + 0.231331i
\(781\) 3869.14 + 6701.55i 0.177271 + 0.307042i
\(782\) 1317.43 0.0602447
\(783\) −8088.04 + 2886.08i −0.369148 + 0.131724i
\(784\) 4395.37 3286.16i 0.200226 0.149698i
\(785\) −4659.31 + 2690.05i −0.211844 + 0.122308i
\(786\) 12091.4 + 7989.14i 0.548709 + 0.362549i
\(787\) 19060.3 + 11004.5i 0.863311 + 0.498433i 0.865120 0.501566i \(-0.167242\pi\)
−0.00180871 + 0.999998i \(0.500576\pi\)
\(788\) 12073.3 + 6970.53i 0.545805 + 0.315120i
\(789\) 1438.95 23841.0i 0.0649278 1.07574i
\(790\) 12173.6 7028.45i 0.548251 0.316533i
\(791\) −3916.14 11778.1i −0.176033 0.529431i
\(792\) −8607.53 + 11460.8i −0.386181 + 0.514196i
\(793\) 26524.3 1.18777
\(794\) 22.8921 + 39.6502i 0.00102318 + 0.00177221i
\(795\) −18330.4 + 9157.57i −0.817749 + 0.408535i
\(796\) −5826.17 3363.74i −0.259426 0.149780i
\(797\) −14681.9 + 25429.8i −0.652520 + 1.13020i 0.329989 + 0.943985i \(0.392955\pi\)
−0.982509 + 0.186214i \(0.940378\pi\)
\(798\) −14920.9 14953.4i −0.661897 0.663338i
\(799\) −1084.71 1878.77i −0.0480279 0.0831867i
\(800\) 1414.42i 0.0625093i
\(801\) 17390.7 + 40787.6i 0.767129 + 1.79920i
\(802\) −23736.7 −1.04510
\(803\) −11690.8 20249.1i −0.513773 0.889881i
\(804\) 12739.2 + 768.890i 0.558802 + 0.0337272i
\(805\) 5734.64 + 1178.02i 0.251080 + 0.0515774i
\(806\) −28342.1 16363.3i −1.23860 0.715103i
\(807\) 4577.54 6928.00i 0.199674 0.302202i
\(808\) 10584.5 6110.94i 0.460841 0.266067i
\(809\) 41755.6i 1.81465i −0.420432 0.907324i \(-0.638122\pi\)
0.420432 0.907324i \(-0.361878\pi\)
\(810\) 9456.68 + 9073.66i 0.410215 + 0.393600i
\(811\) 505.959i 0.0219070i −0.999940 0.0109535i \(-0.996513\pi\)
0.999940 0.0109535i \(-0.00348668\pi\)
\(812\) 3011.07 3390.46i 0.130133 0.146529i
\(813\) −1014.36 670.220i −0.0437580 0.0289122i
\(814\) 16717.1 28954.9i 0.719822 1.24677i
\(815\) −8094.29 + 14019.7i −0.347890 + 0.602564i
\(816\) −1554.46 93.8216i −0.0666877 0.00402502i
\(817\) 13251.0 7650.44i 0.567432 0.327607i
\(818\) −7555.12 −0.322932
\(819\) −18329.2 + 16207.0i −0.782020 + 0.691477i
\(820\) 9663.18 0.411528
\(821\) −22334.9 + 12895.0i −0.949442 + 0.548161i −0.892908 0.450240i \(-0.851338\pi\)
−0.0565347 + 0.998401i \(0.518005\pi\)
\(822\) 6639.19 + 13289.4i 0.281713 + 0.563894i
\(823\) −7652.99 + 13255.4i −0.324139 + 0.561425i −0.981338 0.192292i \(-0.938408\pi\)
0.657199 + 0.753717i \(0.271741\pi\)
\(824\) 6896.39 11944.9i 0.291562 0.505001i
\(825\) −13633.8 + 6811.26i −0.575356 + 0.287439i
\(826\) 5563.00 6263.92i 0.234336 0.263861i
\(827\) 8921.04i 0.375109i 0.982254 + 0.187554i \(0.0600561\pi\)
−0.982254 + 0.187554i \(0.939944\pi\)
\(828\) 3036.88 + 2280.81i 0.127462 + 0.0957291i
\(829\) 1174.38i 0.0492011i −0.999697 0.0246006i \(-0.992169\pi\)
0.999697 0.0246006i \(-0.00783139\pi\)
\(830\) 3820.46 2205.74i 0.159771 0.0922440i
\(831\) −11121.4 671.249i −0.464258 0.0280209i
\(832\) −2711.93 1565.73i −0.113004 0.0652428i
\(833\) −758.869 6379.87i −0.0315645 0.265365i
\(834\) 1394.40 2110.39i 0.0578947 0.0876223i
\(835\) 1755.40 + 3040.45i 0.0727523 + 0.126011i
\(836\) −29132.2 −1.20521
\(837\) −35750.9 30385.4i −1.47638 1.25481i
\(838\) 22089.3i 0.910574i
\(839\) −13404.5 23217.3i −0.551579 0.955363i −0.998161 0.0606203i \(-0.980692\pi\)
0.446582 0.894743i \(-0.352641\pi\)
\(840\) −6682.51 1798.36i −0.274486 0.0738684i
\(841\) −10321.2 + 17876.8i −0.423189 + 0.732985i
\(842\) −4829.80 2788.49i −0.197679 0.114130i
\(843\) −2578.63 + 42723.6i −0.105353 + 1.74553i
\(844\) 2099.74 + 3636.85i 0.0856350 + 0.148324i
\(845\) 1771.34 0.0721136
\(846\) 752.215 6208.76i 0.0305694 0.252319i
\(847\) −53993.5 + 17952.5i −2.19037 + 0.728284i
\(848\) 6078.81 3509.60i 0.246164 0.142123i
\(849\) 27428.7 13703.0i 1.10877 0.553927i
\(850\) −1434.03 827.938i −0.0578669 0.0334095i
\(851\) −7672.43 4429.68i −0.309057 0.178434i
\(852\) −2168.27 + 1083.24i −0.0871876 + 0.0435576i
\(853\) −34918.2 + 20160.0i −1.40161 + 0.809222i −0.994558 0.104181i \(-0.966778\pi\)
−0.407056 + 0.913403i \(0.633445\pi\)
\(854\) −19053.9 + 6335.31i −0.763479 + 0.253852i
\(855\) −3203.79 + 26444.0i −0.128149 + 1.05774i
\(856\) −5354.85 −0.213814
\(857\) −3860.50 6686.58i −0.153876 0.266522i 0.778773 0.627306i \(-0.215842\pi\)
−0.932649 + 0.360784i \(0.882509\pi\)
\(858\) −2032.83 + 33680.5i −0.0808854 + 1.34013i
\(859\) −37480.7 21639.5i −1.48874 0.859523i −0.488820 0.872385i \(-0.662573\pi\)
−0.999917 + 0.0128616i \(0.995906\pi\)
\(860\) 2506.26 4340.97i 0.0993754 0.172123i
\(861\) −6721.10 + 24974.8i −0.266033 + 0.988548i
\(862\) 10345.4 + 17918.8i 0.408779 + 0.708025i
\(863\) 21165.5i 0.834856i 0.908710 + 0.417428i \(0.137068\pi\)
−0.908710 + 0.417428i \(0.862932\pi\)
\(864\) −3420.84 2907.44i −0.134698 0.114483i
\(865\) 9178.15 0.360770
\(866\) 5236.75 + 9070.32i 0.205487 + 0.355915i
\(867\) 13068.1 19778.2i 0.511898 0.774745i
\(868\) 24268.1 + 4985.21i 0.948978 + 0.194941i
\(869\) 44934.1 + 25942.7i 1.75407 + 1.01271i
\(870\) −5707.54 344.486i −0.222418 0.0134243i
\(871\) 26018.8 15022.0i 1.01219 0.584386i
\(872\) 2533.07i 0.0983724i
\(873\) −24158.2 18143.7i −0.936577 0.703405i
\(874\) 7719.41i 0.298756i
\(875\) −21061.1 18704.4i −0.813709 0.722657i
\(876\) 6551.55 3273.06i 0.252690 0.126240i
\(877\) 7087.12 12275.2i 0.272879 0.472640i −0.696719 0.717344i \(-0.745357\pi\)
0.969598 + 0.244704i \(0.0786908\pi\)
\(878\) 5990.16 10375.3i 0.230249 0.398802i
\(879\) 4360.48 + 8728.19i 0.167321 + 0.334920i
\(880\) −8265.02 + 4771.81i −0.316606 + 0.182793i
\(881\) −16308.0 −0.623645 −0.311823 0.950140i \(-0.600939\pi\)
−0.311823 + 0.950140i \(0.600939\pi\)
\(882\) 9295.87 16020.3i 0.354885 0.611602i
\(883\) −28226.0 −1.07574 −0.537871 0.843027i \(-0.680771\pi\)
−0.537871 + 0.843027i \(0.680771\pi\)
\(884\) −3174.87 + 1833.01i −0.120795 + 0.0697409i
\(885\) −10544.8 636.442i −0.400518 0.0241738i
\(886\) −4017.29 + 6958.16i −0.152329 + 0.263842i
\(887\) −25871.3 + 44810.5i −0.979340 + 1.69627i −0.314540 + 0.949244i \(0.601850\pi\)
−0.664800 + 0.747022i \(0.731483\pi\)
\(888\) 8737.38 + 5773.06i 0.330189 + 0.218166i
\(889\) 31720.1 + 28170.7i 1.19669 + 1.06278i
\(890\) 29523.6i 1.11195i
\(891\) −11552.0 + 46975.0i −0.434349 + 1.76624i
\(892\) 9443.51i 0.354475i
\(893\) 11008.5 6355.78i 0.412527 0.238172i
\(894\) −7048.47 + 10667.7i −0.263687 + 0.399084i
\(895\) 19054.7 + 11001.3i 0.711653 + 0.410873i
\(896\) 2322.10 + 477.012i 0.0865804 + 0.0177856i
\(897\) 8924.63 + 538.657i 0.332201 + 0.0200504i
\(898\) 1948.54 + 3374.97i 0.0724094 + 0.125417i
\(899\) 20470.4 0.759430
\(900\) −1872.28 4391.19i −0.0693438 0.162637i
\(901\) 8217.44i 0.303843i
\(902\) 17833.9 + 30889.2i 0.658319 + 1.14024i
\(903\) 9476.19 + 9496.83i 0.349223 + 0.349983i
\(904\) 2680.75 4643.20i 0.0986289 0.170830i
\(905\) 5267.90 + 3041.42i 0.193493 + 0.111713i
\(906\) −15569.1 + 7778.08i −0.570914 + 0.285220i
\(907\) 3027.85 + 5244.40i 0.110847 + 0.191993i 0.916112 0.400922i \(-0.131310\pi\)
−0.805265 + 0.592915i \(0.797977\pi\)
\(908\) 16925.6 0.618609
\(909\) 24771.2 32982.6i 0.903860 1.20348i
\(910\) −15458.9 + 5139.99i −0.563140 + 0.187241i
\(911\) 10003.4 5775.46i 0.363806 0.210043i −0.306943 0.951728i \(-0.599306\pi\)
0.670749 + 0.741685i \(0.265973\pi\)
\(912\) 549.741 9108.27i 0.0199602 0.330707i
\(913\) 14101.7 + 8141.62i 0.511170 + 0.295124i
\(914\) −23215.4 13403.4i −0.840151 0.485061i
\(915\) 21125.1 + 13958.0i 0.763251 + 0.504304i
\(916\) 6267.03 3618.27i 0.226057 0.130514i
\(917\) −24507.8 + 8148.69i −0.882572 + 0.293450i
\(918\) −4950.15 + 1766.38i −0.177973 + 0.0635068i
\(919\) −36885.9 −1.32400 −0.661999 0.749505i \(-0.730292\pi\)
−0.661999 + 0.749505i \(0.730292\pi\)
\(920\) 1264.43 + 2190.05i 0.0453119 + 0.0784825i
\(921\) 41617.4 + 27497.9i 1.48897 + 0.983808i
\(922\) −29658.4 17123.3i −1.05938 0.611633i
\(923\) −2852.94 + 4941.44i −0.101740 + 0.176218i
\(924\) −6584.28 24680.2i −0.234423 0.878700i
\(925\) 5567.65 + 9643.45i 0.197906 + 0.342783i
\(926\) 24615.6i 0.873562i
\(927\) 5598.85 46212.7i 0.198371 1.63735i
\(928\) 1958.72 0.0692869
\(929\) 11193.6 + 19388.0i 0.395319 + 0.684713i 0.993142 0.116915i \(-0.0373007\pi\)
−0.597823 + 0.801628i \(0.703967\pi\)
\(930\) −13961.9 27947.1i −0.492291 0.985399i
\(931\) 37382.4 4446.54i 1.31596 0.156530i
\(932\) −10582.8 6109.97i −0.371943 0.214741i
\(933\) 1.52155 + 3.04563i 5.33906e−5 + 0.000106870i
\(934\) 26871.6 15514.3i 0.941398 0.543516i
\(935\) 11172.8i 0.390791i
\(936\) −10492.0 1271.14i −0.366390 0.0443895i
\(937\) 18336.5i 0.639304i −0.947535 0.319652i \(-0.896434\pi\)
0.947535 0.319652i \(-0.103566\pi\)
\(938\) −15102.8 + 17005.7i −0.525719 + 0.591958i
\(939\) −1250.83 + 20724.2i −0.0434711 + 0.720242i
\(940\) 2082.13 3606.36i 0.0722465 0.125135i
\(941\) −5273.49 + 9133.95i −0.182689 + 0.316427i −0.942796 0.333372i \(-0.891814\pi\)
0.760106 + 0.649799i \(0.225147\pi\)
\(942\) 3428.95 5189.63i 0.118600 0.179498i
\(943\) 8184.98 4725.60i 0.282651 0.163188i
\(944\) 3618.77 0.124768
\(945\) −23126.9 + 3262.52i −0.796104 + 0.112307i
\(946\) 18501.7 0.635880
\(947\) 9941.78 5739.89i 0.341145 0.196960i −0.319633 0.947541i \(-0.603560\pi\)
0.660778 + 0.750581i \(0.270226\pi\)
\(948\) −8959.00 + 13559.2i −0.306936 + 0.464539i
\(949\) 8620.31 14930.8i 0.294865 0.510721i
\(950\) 4851.24 8402.60i 0.165679 0.286965i
\(951\) 1094.53 18134.5i 0.0373213 0.618350i
\(952\) 1842.88 2075.07i 0.0627395 0.0706445i
\(953\) 3274.36i 0.111298i −0.998450 0.0556489i \(-0.982277\pi\)
0.998450 0.0556489i \(-0.0177228\pi\)
\(954\) 14226.5 18942.4i 0.482808 0.642855i
\(955\) 20451.4i 0.692977i
\(956\) −16216.6 + 9362.66i −0.548622 + 0.316747i
\(957\) −9432.38 18880.4i −0.318605 0.637740i
\(958\) 33692.8 + 19452.5i 1.13629 + 0.656037i
\(959\) −25932.7 5327.16i −0.873213 0.179378i
\(960\) −1335.96 2674.13i −0.0449144 0.0899033i
\(961\) 41025.8 + 71058.8i 1.37712 + 2.38525i
\(962\) 24653.0 0.826242
\(963\) −16624.6 + 7088.26i −0.556303 + 0.237192i
\(964\) 5740.49i 0.191793i
\(965\) 10209.1 + 17682.7i 0.340563 + 0.589873i
\(966\) −6539.72 + 1744.69i −0.217818 + 0.0581103i
\(967\) −8316.55 + 14404.7i −0.276569 + 0.479031i −0.970530 0.240981i \(-0.922531\pi\)
0.693961 + 0.720013i \(0.255864\pi\)
\(968\) −21285.6 12289.2i −0.706760 0.408048i
\(969\) −8912.74 5888.92i −0.295478 0.195232i
\(970\) −10058.5 17421.8i −0.332946 0.576679i
\(971\) −23196.9 −0.766658 −0.383329 0.923612i \(-0.625223\pi\)
−0.383329 + 0.923612i \(0.625223\pi\)
\(972\) −14468.9 4498.20i −0.477459 0.148436i
\(973\) 1422.25 + 4277.52i 0.0468605 + 0.140936i
\(974\) 35935.5 20747.4i 1.18218 0.682535i
\(975\) −9375.97 6194.99i −0.307971 0.203486i
\(976\) −7511.50 4336.77i −0.246350 0.142230i
\(977\) 40553.6 + 23413.6i 1.32797 + 0.766703i 0.984985 0.172639i \(-0.0552294\pi\)
0.342983 + 0.939342i \(0.388563\pi\)
\(978\) 1127.59 18682.2i 0.0368673 0.610828i
\(979\) −94374.6 + 54487.2i −3.08092 + 1.77877i
\(980\) 9877.32 7384.70i 0.321959 0.240710i
\(981\) 3353.05 + 7864.13i 0.109128 + 0.255945i
\(982\) 791.521 0.0257214
\(983\) 7117.50 + 12327.9i 0.230939 + 0.399998i 0.958085 0.286485i \(-0.0924869\pi\)
−0.727146 + 0.686483i \(0.759154\pi\)
\(984\) −9994.14 + 4992.92i −0.323782 + 0.161757i
\(985\) 27131.3 + 15664.3i 0.877639 + 0.506705i
\(986\) 1146.55 1985.88i 0.0370319 0.0641412i
\(987\) 7872.57 + 7889.71i 0.253887 + 0.254440i
\(988\) −10740.4 18602.9i −0.345848 0.599027i
\(989\) 4902.56i 0.157626i
\(990\) −19342.9 + 25754.9i −0.620968 + 0.826814i
\(991\) 16183.4 0.518752 0.259376 0.965776i \(-0.416483\pi\)
0.259376 + 0.965776i \(0.416483\pi\)
\(992\) 5350.86 + 9267.97i 0.171260 + 0.296631i
\(993\) −12113.2 731.106i −0.387110 0.0233645i
\(994\) 869.169 4231.13i 0.0277348 0.135014i
\(995\) −13092.6 7559.04i −0.417150 0.240842i
\(996\) −2811.61 + 4255.30i −0.0894471 + 0.135376i
\(997\) −40829.3 + 23572.8i −1.29697 + 0.748805i −0.979879 0.199591i \(-0.936039\pi\)
−0.317089 + 0.948396i \(0.602705\pi\)
\(998\) 40586.8i 1.28733i
\(999\) 34767.8 + 6357.18i 1.10110 + 0.201334i
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 126.4.m.a.41.16 48
3.2 odd 2 378.4.m.a.125.5 48
7.6 odd 2 inner 126.4.m.a.41.21 yes 48
9.2 odd 6 inner 126.4.m.a.83.21 yes 48
9.4 even 3 1134.4.d.b.1133.4 48
9.5 odd 6 1134.4.d.b.1133.45 48
9.7 even 3 378.4.m.a.251.6 48
21.20 even 2 378.4.m.a.125.6 48
63.13 odd 6 1134.4.d.b.1133.46 48
63.20 even 6 inner 126.4.m.a.83.16 yes 48
63.34 odd 6 378.4.m.a.251.5 48
63.41 even 6 1134.4.d.b.1133.3 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.4.m.a.41.16 48 1.1 even 1 trivial
126.4.m.a.41.21 yes 48 7.6 odd 2 inner
126.4.m.a.83.16 yes 48 63.20 even 6 inner
126.4.m.a.83.21 yes 48 9.2 odd 6 inner
378.4.m.a.125.5 48 3.2 odd 2
378.4.m.a.125.6 48 21.20 even 2
378.4.m.a.251.5 48 63.34 odd 6
378.4.m.a.251.6 48 9.7 even 3
1134.4.d.b.1133.3 48 63.41 even 6
1134.4.d.b.1133.4 48 9.4 even 3
1134.4.d.b.1133.45 48 9.5 odd 6
1134.4.d.b.1133.46 48 63.13 odd 6