Properties

Label 105.3.t.b.86.5
Level $105$
Weight $3$
Character 105.86
Analytic conductor $2.861$
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] = [105,3,Mod(11,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.11");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.t (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: \(2.86104277578\)
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 86.5
Character \(\chi\) \(=\) 105.86
Dual form 105.3.t.b.11.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.31825 - 1.33844i) q^{2} +(2.46021 + 1.71679i) q^{3} +(1.58287 + 2.74161i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-3.40557 - 7.27281i) q^{6} +(4.89419 - 5.00469i) q^{7} +2.23323i q^{8} +(3.10528 + 8.44732i) q^{9} +O(q^{10})\) \(q+(-2.31825 - 1.33844i) q^{2} +(2.46021 + 1.71679i) q^{3} +(1.58287 + 2.74161i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-3.40557 - 7.27281i) q^{6} +(4.89419 - 5.00469i) q^{7} +2.23323i q^{8} +(3.10528 + 8.44732i) q^{9} +(2.99285 + 5.18377i) q^{10} +(15.6726 - 9.04859i) q^{11} +(-0.812567 + 9.46238i) q^{12} +2.70603 q^{13} +(-18.0445 + 5.05154i) q^{14} +(-2.84475 - 6.07514i) q^{15} +(9.32053 - 16.1436i) q^{16} +(-3.39734 + 1.96145i) q^{17} +(4.10744 - 23.7393i) q^{18} +(14.7810 - 25.6015i) q^{19} -7.07880i q^{20} +(20.6327 - 3.91032i) q^{21} -48.4441 q^{22} +(-5.66814 - 3.27250i) q^{23} +(-3.83399 + 5.49423i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-6.27326 - 3.62187i) q^{26} +(-6.86260 + 26.1133i) q^{27} +(21.4677 + 5.49618i) q^{28} +18.8690i q^{29} +(-1.53638 + 17.8913i) q^{30} +(12.6486 + 21.9079i) q^{31} +(-35.4786 + 20.4836i) q^{32} +(54.0924 + 4.64510i) q^{33} +10.5012 q^{34} +(-15.0730 + 4.21967i) q^{35} +(-18.2440 + 21.8845i) q^{36} +(-33.5038 + 58.0303i) q^{37} +(-68.5323 + 39.5671i) q^{38} +(6.65740 + 4.64567i) q^{39} +(2.49683 - 4.32464i) q^{40} -38.7488i q^{41} +(-53.0656 - 18.5507i) q^{42} -63.9074 q^{43} +(49.6153 + 28.6454i) q^{44} +(3.43104 - 19.8300i) q^{45} +(8.76013 + 15.1730i) q^{46} +(33.6085 + 19.4039i) q^{47} +(50.6457 - 23.7154i) q^{48} +(-1.09384 - 48.9878i) q^{49} -13.3844i q^{50} +(-11.7256 - 1.00691i) q^{51} +(4.28328 + 7.41886i) q^{52} +(-0.787120 + 0.454444i) q^{53} +(50.8605 - 51.3521i) q^{54} -40.4665 q^{55} +(11.1766 + 10.9299i) q^{56} +(80.3167 - 37.6092i) q^{57} +(25.2551 - 43.7430i) q^{58} +(-20.6520 + 11.9234i) q^{59} +(12.1528 - 17.4153i) q^{60} +(-25.3438 + 43.8968i) q^{61} -67.7176i q^{62} +(57.4741 + 25.8018i) q^{63} +35.1002 q^{64} +(-5.24020 - 3.02543i) q^{65} +(-119.183 - 83.1683i) q^{66} +(-34.7257 - 60.1466i) q^{67} +(-10.7551 - 6.20944i) q^{68} +(-8.32663 - 17.7820i) q^{69} +(40.5908 + 10.3921i) q^{70} +55.2444i q^{71} +(-18.8648 + 6.93482i) q^{72} +(14.8601 + 25.7384i) q^{73} +(155.341 - 89.6861i) q^{74} +(-1.28338 + 14.9450i) q^{75} +93.5856 q^{76} +(31.4193 - 122.722i) q^{77} +(-9.21556 - 19.6804i) q^{78} +(-14.9827 + 25.9507i) q^{79} +(-36.0983 + 20.8413i) q^{80} +(-61.7144 + 52.4626i) q^{81} +(-51.8631 + 89.8295i) q^{82} -78.4979i q^{83} +(43.3794 + 50.3773i) q^{84} +8.77189 q^{85} +(148.153 + 85.5364i) q^{86} +(-32.3940 + 46.4216i) q^{87} +(20.2076 + 35.0006i) q^{88} +(-133.421 - 77.0307i) q^{89} +(-34.4953 + 41.3787i) q^{90} +(13.2438 - 13.5428i) q^{91} -20.7198i q^{92} +(-6.49315 + 75.6131i) q^{93} +(-51.9421 - 89.9663i) q^{94} +(-57.2466 + 33.0514i) q^{95} +(-122.451 - 10.5153i) q^{96} +32.8490 q^{97} +(-63.0316 + 115.030i) q^{98} +(125.104 + 104.293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 4 q^{3} + 36 q^{4} - 24 q^{6} - 58 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 4 q^{3} + 36 q^{4} - 24 q^{6} - 58 q^{7} - 2 q^{9} + 20 q^{10} - 42 q^{12} - 100 q^{13} + 20 q^{15} - 12 q^{16} - 14 q^{18} + 50 q^{19} - 12 q^{21} + 256 q^{22} - 140 q^{24} + 90 q^{25} + 4 q^{27} - 48 q^{28} + 60 q^{30} - 82 q^{31} - 76 q^{33} - 64 q^{34} + 296 q^{36} - 26 q^{37} - 130 q^{39} - 60 q^{40} - 98 q^{42} - 204 q^{43} + 40 q^{45} + 28 q^{46} + 532 q^{48} - 382 q^{49} + 208 q^{51} + 200 q^{52} - 44 q^{54} - 160 q^{55} + 252 q^{57} + 264 q^{58} - 130 q^{60} - 324 q^{61} - 258 q^{63} - 24 q^{64} - 164 q^{66} - 142 q^{67} - 112 q^{69} + 200 q^{70} - 322 q^{72} + 386 q^{73} - 20 q^{75} - 424 q^{76} - 440 q^{78} + 334 q^{79} + 186 q^{81} - 68 q^{82} + 80 q^{84} - 200 q^{85} + 342 q^{87} + 180 q^{88} + 100 q^{90} + 46 q^{91} - 2 q^{93} + 324 q^{94} + 732 q^{96} + 1616 q^{97} + 384 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31825 1.33844i −1.15913 0.669222i −0.208032 0.978122i \(-0.566706\pi\)
−0.951095 + 0.308900i \(0.900039\pi\)
\(3\) 2.46021 + 1.71679i 0.820071 + 0.572262i
\(4\) 1.58287 + 2.74161i 0.395717 + 0.685402i
\(5\) −1.93649 1.11803i −0.387298 0.223607i
\(6\) −3.40557 7.27281i −0.567595 1.21213i
\(7\) 4.89419 5.00469i 0.699170 0.714956i
\(8\) 2.23323i 0.279154i
\(9\) 3.10528 + 8.44732i 0.345031 + 0.938591i
\(10\) 2.99285 + 5.18377i 0.299285 + 0.518377i
\(11\) 15.6726 9.04859i 1.42478 0.822599i 0.428080 0.903741i \(-0.359190\pi\)
0.996703 + 0.0811419i \(0.0258567\pi\)
\(12\) −0.812567 + 9.46238i −0.0677139 + 0.788532i
\(13\) 2.70603 0.208156 0.104078 0.994569i \(-0.466811\pi\)
0.104078 + 0.994569i \(0.466811\pi\)
\(14\) −18.0445 + 5.05154i −1.28889 + 0.360824i
\(15\) −2.84475 6.07514i −0.189650 0.405010i
\(16\) 9.32053 16.1436i 0.582533 1.00898i
\(17\) −3.39734 + 1.96145i −0.199843 + 0.115380i −0.596582 0.802552i \(-0.703475\pi\)
0.396739 + 0.917931i \(0.370142\pi\)
\(18\) 4.10744 23.7393i 0.228191 1.31885i
\(19\) 14.7810 25.6015i 0.777948 1.34745i −0.155174 0.987887i \(-0.549594\pi\)
0.933122 0.359559i \(-0.117073\pi\)
\(20\) 7.07880i 0.353940i
\(21\) 20.6327 3.91032i 0.982511 0.186206i
\(22\) −48.4441 −2.20201
\(23\) −5.66814 3.27250i −0.246441 0.142283i 0.371693 0.928356i \(-0.378778\pi\)
−0.618133 + 0.786073i \(0.712111\pi\)
\(24\) −3.83399 + 5.49423i −0.159750 + 0.228926i
\(25\) 2.50000 + 4.33013i 0.100000 + 0.173205i
\(26\) −6.27326 3.62187i −0.241279 0.139303i
\(27\) −6.86260 + 26.1133i −0.254170 + 0.967159i
\(28\) 21.4677 + 5.49618i 0.766705 + 0.196292i
\(29\) 18.8690i 0.650654i 0.945602 + 0.325327i \(0.105474\pi\)
−0.945602 + 0.325327i \(0.894526\pi\)
\(30\) −1.53638 + 17.8913i −0.0512128 + 0.596376i
\(31\) 12.6486 + 21.9079i 0.408018 + 0.706708i 0.994668 0.103133i \(-0.0328867\pi\)
−0.586650 + 0.809841i \(0.699553\pi\)
\(32\) −35.4786 + 20.4836i −1.10871 + 0.640111i
\(33\) 54.0924 + 4.64510i 1.63916 + 0.140761i
\(34\) 10.5012 0.308859
\(35\) −15.0730 + 4.21967i −0.430656 + 0.120562i
\(36\) −18.2440 + 21.8845i −0.506777 + 0.607901i
\(37\) −33.5038 + 58.0303i −0.905509 + 1.56839i −0.0852768 + 0.996357i \(0.527177\pi\)
−0.820232 + 0.572031i \(0.806156\pi\)
\(38\) −68.5323 + 39.5671i −1.80348 + 1.04124i
\(39\) 6.65740 + 4.64567i 0.170702 + 0.119120i
\(40\) 2.49683 4.32464i 0.0624208 0.108116i
\(41\) 38.7488i 0.945092i −0.881306 0.472546i \(-0.843335\pi\)
0.881306 0.472546i \(-0.156665\pi\)
\(42\) −53.0656 18.5507i −1.26347 0.441682i
\(43\) −63.9074 −1.48622 −0.743109 0.669171i \(-0.766650\pi\)
−0.743109 + 0.669171i \(0.766650\pi\)
\(44\) 49.6153 + 28.6454i 1.12762 + 0.651032i
\(45\) 3.43104 19.8300i 0.0762453 0.440666i
\(46\) 8.76013 + 15.1730i 0.190438 + 0.329847i
\(47\) 33.6085 + 19.4039i 0.715075 + 0.412849i 0.812937 0.582351i \(-0.197867\pi\)
−0.0978620 + 0.995200i \(0.531200\pi\)
\(48\) 50.6457 23.7154i 1.05512 0.494071i
\(49\) −1.09384 48.9878i −0.0223233 0.999751i
\(50\) 13.3844i 0.267689i
\(51\) −11.7256 1.00691i −0.229913 0.0197434i
\(52\) 4.28328 + 7.41886i 0.0823708 + 0.142670i
\(53\) −0.787120 + 0.454444i −0.0148513 + 0.00857442i −0.507407 0.861706i \(-0.669396\pi\)
0.492556 + 0.870281i \(0.336063\pi\)
\(54\) 50.8605 51.3521i 0.941860 0.950964i
\(55\) −40.4665 −0.735755
\(56\) 11.1766 + 10.9299i 0.199583 + 0.195176i
\(57\) 80.3167 37.6092i 1.40907 0.659810i
\(58\) 25.2551 43.7430i 0.435432 0.754190i
\(59\) −20.6520 + 11.9234i −0.350033 + 0.202092i −0.664700 0.747110i \(-0.731441\pi\)
0.314667 + 0.949202i \(0.398107\pi\)
\(60\) 12.1528 17.4153i 0.202547 0.290256i
\(61\) −25.3438 + 43.8968i −0.415472 + 0.719619i −0.995478 0.0949935i \(-0.969717\pi\)
0.580006 + 0.814612i \(0.303050\pi\)
\(62\) 67.7176i 1.09222i
\(63\) 57.4741 + 25.8018i 0.912287 + 0.409552i
\(64\) 35.1002 0.548440
\(65\) −5.24020 3.02543i −0.0806184 0.0465451i
\(66\) −119.183 83.1683i −1.80580 1.26013i
\(67\) −34.7257 60.1466i −0.518294 0.897711i −0.999774 0.0212540i \(-0.993234\pi\)
0.481481 0.876457i \(-0.340099\pi\)
\(68\) −10.7551 6.20944i −0.158163 0.0913154i
\(69\) −8.32663 17.7820i −0.120676 0.257711i
\(70\) 40.5908 + 10.3921i 0.579868 + 0.148458i
\(71\) 55.2444i 0.778090i 0.921219 + 0.389045i \(0.127195\pi\)
−0.921219 + 0.389045i \(0.872805\pi\)
\(72\) −18.8648 + 6.93482i −0.262012 + 0.0963170i
\(73\) 14.8601 + 25.7384i 0.203563 + 0.352581i 0.949674 0.313241i \(-0.101415\pi\)
−0.746111 + 0.665821i \(0.768081\pi\)
\(74\) 155.341 89.6861i 2.09920 1.21197i
\(75\) −1.28338 + 14.9450i −0.0171117 + 0.199267i
\(76\) 93.5856 1.23139
\(77\) 31.4193 122.722i 0.408043 1.59379i
\(78\) −9.21556 19.6804i −0.118148 0.252313i
\(79\) −14.9827 + 25.9507i −0.189654 + 0.328490i −0.945135 0.326680i \(-0.894070\pi\)
0.755481 + 0.655171i \(0.227403\pi\)
\(80\) −36.0983 + 20.8413i −0.451228 + 0.260517i
\(81\) −61.7144 + 52.4626i −0.761907 + 0.647687i
\(82\) −51.8631 + 89.8295i −0.632476 + 1.09548i
\(83\) 78.4979i 0.945758i −0.881127 0.472879i \(-0.843215\pi\)
0.881127 0.472879i \(-0.156785\pi\)
\(84\) 43.3794 + 50.3773i 0.516422 + 0.599730i
\(85\) 8.77189 0.103199
\(86\) 148.153 + 85.5364i 1.72271 + 0.994610i
\(87\) −32.3940 + 46.4216i −0.372345 + 0.533582i
\(88\) 20.2076 + 35.0006i 0.229632 + 0.397734i
\(89\) −133.421 77.0307i −1.49911 0.865513i −0.499114 0.866537i \(-0.666341\pi\)
−0.999999 + 0.00102332i \(0.999674\pi\)
\(90\) −34.4953 + 41.3787i −0.383282 + 0.459763i
\(91\) 13.2438 13.5428i 0.145536 0.148822i
\(92\) 20.7198i 0.225215i
\(93\) −6.49315 + 75.6131i −0.0698188 + 0.813044i
\(94\) −51.9421 89.9663i −0.552575 0.957089i
\(95\) −57.2466 + 33.0514i −0.602596 + 0.347909i
\(96\) −122.451 10.5153i −1.27553 0.109534i
\(97\) 32.8490 0.338650 0.169325 0.985560i \(-0.445841\pi\)
0.169325 + 0.985560i \(0.445841\pi\)
\(98\) −63.0316 + 115.030i −0.643180 + 1.17378i
\(99\) 125.104 + 104.293i 1.26368 + 1.05347i
\(100\) −7.91434 + 13.7080i −0.0791434 + 0.137080i
\(101\) 52.7241 30.4403i 0.522021 0.301389i −0.215740 0.976451i \(-0.569216\pi\)
0.737761 + 0.675062i \(0.235883\pi\)
\(102\) 25.8352 + 18.0283i 0.253286 + 0.176748i
\(103\) 22.1261 38.3235i 0.214816 0.372073i −0.738399 0.674364i \(-0.764418\pi\)
0.953216 + 0.302291i \(0.0977513\pi\)
\(104\) 6.04319i 0.0581076i
\(105\) −44.3270 15.4958i −0.422162 0.147579i
\(106\) 2.43299 0.0229528
\(107\) 129.731 + 74.9005i 1.21244 + 0.700004i 0.963291 0.268460i \(-0.0865146\pi\)
0.249152 + 0.968464i \(0.419848\pi\)
\(108\) −82.4550 + 22.5194i −0.763472 + 0.208513i
\(109\) 41.1471 + 71.2689i 0.377496 + 0.653843i 0.990697 0.136084i \(-0.0434517\pi\)
−0.613201 + 0.789927i \(0.710118\pi\)
\(110\) 93.8116 + 54.1622i 0.852833 + 0.492383i
\(111\) −182.052 + 85.2480i −1.64011 + 0.768000i
\(112\) −35.1774 125.656i −0.314084 1.12193i
\(113\) 56.1617i 0.497006i −0.968631 0.248503i \(-0.920061\pi\)
0.968631 0.248503i \(-0.0799386\pi\)
\(114\) −236.532 20.3118i −2.07485 0.178174i
\(115\) 7.31754 + 12.6743i 0.0636308 + 0.110212i
\(116\) −51.7313 + 29.8671i −0.445959 + 0.257475i
\(117\) 8.40298 + 22.8587i 0.0718203 + 0.195373i
\(118\) 63.8353 0.540977
\(119\) −6.81074 + 26.6024i −0.0572331 + 0.223549i
\(120\) 13.5672 6.35300i 0.113060 0.0529417i
\(121\) 103.254 178.841i 0.853338 1.47802i
\(122\) 117.507 67.8426i 0.963170 0.556086i
\(123\) 66.5234 95.3302i 0.540840 0.775042i
\(124\) −40.0420 + 69.3547i −0.322919 + 0.559312i
\(125\) 11.1803i 0.0894427i
\(126\) −98.7052 136.741i −0.783374 1.08525i
\(127\) 31.3811 0.247095 0.123548 0.992339i \(-0.460573\pi\)
0.123548 + 0.992339i \(0.460573\pi\)
\(128\) 60.5431 + 34.9546i 0.472993 + 0.273083i
\(129\) −157.226 109.715i −1.21880 0.850506i
\(130\) 8.09874 + 14.0274i 0.0622980 + 0.107903i
\(131\) 0.204424 + 0.118024i 0.00156049 + 0.000900947i 0.500780 0.865575i \(-0.333047\pi\)
−0.499220 + 0.866476i \(0.666380\pi\)
\(132\) 72.8861 + 155.653i 0.552168 + 1.17919i
\(133\) −55.7864 199.273i −0.419446 1.49829i
\(134\) 185.914i 1.38741i
\(135\) 42.4849 42.8956i 0.314703 0.317745i
\(136\) −4.38039 7.58705i −0.0322087 0.0557872i
\(137\) −234.604 + 135.448i −1.71244 + 0.988675i −0.781182 + 0.624303i \(0.785383\pi\)
−0.931253 + 0.364372i \(0.881284\pi\)
\(138\) −4.49702 + 52.3680i −0.0325871 + 0.379478i
\(139\) −70.1988 −0.505027 −0.252514 0.967593i \(-0.581257\pi\)
−0.252514 + 0.967593i \(0.581257\pi\)
\(140\) −35.4272 34.6450i −0.253051 0.247464i
\(141\) 49.3718 + 105.436i 0.350154 + 0.747776i
\(142\) 73.9415 128.071i 0.520715 0.901905i
\(143\) 42.4105 24.4857i 0.296577 0.171229i
\(144\) 165.313 + 28.6030i 1.14801 + 0.198632i
\(145\) 21.0961 36.5396i 0.145491 0.251997i
\(146\) 79.5575i 0.544914i
\(147\) 81.4105 122.398i 0.553813 0.832641i
\(148\) −212.129 −1.43330
\(149\) −50.9648 29.4245i −0.342046 0.197480i 0.319131 0.947711i \(-0.396609\pi\)
−0.661176 + 0.750231i \(0.729942\pi\)
\(150\) 22.9782 32.9286i 0.153188 0.219524i
\(151\) 128.237 + 222.112i 0.849249 + 1.47094i 0.881879 + 0.471475i \(0.156278\pi\)
−0.0326304 + 0.999467i \(0.510388\pi\)
\(152\) 57.1741 + 33.0095i 0.376145 + 0.217168i
\(153\) −27.1187 22.6075i −0.177247 0.147762i
\(154\) −237.095 + 242.448i −1.53958 + 1.57434i
\(155\) 56.5661i 0.364942i
\(156\) −2.19883 + 25.6054i −0.0140950 + 0.164137i
\(157\) −36.6914 63.5513i −0.233703 0.404785i 0.725192 0.688547i \(-0.241751\pi\)
−0.958895 + 0.283761i \(0.908418\pi\)
\(158\) 69.4672 40.1069i 0.439666 0.253841i
\(159\) −2.71667 0.233289i −0.0170860 0.00146723i
\(160\) 91.6053 0.572533
\(161\) −44.1188 + 12.3510i −0.274030 + 0.0767145i
\(162\) 213.288 39.0204i 1.31659 0.240866i
\(163\) −32.3989 + 56.1166i −0.198766 + 0.344274i −0.948129 0.317887i \(-0.897027\pi\)
0.749362 + 0.662160i \(0.230360\pi\)
\(164\) 106.234 61.3342i 0.647768 0.373989i
\(165\) −99.5562 69.4724i −0.603371 0.421045i
\(166\) −105.065 + 181.978i −0.632922 + 1.09625i
\(167\) 208.422i 1.24803i 0.781411 + 0.624017i \(0.214500\pi\)
−0.781411 + 0.624017i \(0.785500\pi\)
\(168\) 8.73265 + 46.0777i 0.0519801 + 0.274272i
\(169\) −161.677 −0.956671
\(170\) −20.3355 11.7407i −0.119620 0.0690629i
\(171\) 262.163 + 45.3602i 1.53312 + 0.265264i
\(172\) −101.157 175.209i −0.588121 1.01866i
\(173\) −152.382 87.9780i −0.880823 0.508543i −0.00989305 0.999951i \(-0.503149\pi\)
−0.870930 + 0.491408i \(0.836482\pi\)
\(174\) 137.230 64.2596i 0.788680 0.369308i
\(175\) 33.9064 + 8.68073i 0.193751 + 0.0496042i
\(176\) 337.351i 1.91676i
\(177\) −71.2781 6.12090i −0.402701 0.0345813i
\(178\) 206.203 + 357.153i 1.15844 + 2.00648i
\(179\) −119.555 + 69.0248i −0.667902 + 0.385614i −0.795281 0.606240i \(-0.792677\pi\)
0.127379 + 0.991854i \(0.459344\pi\)
\(180\) 59.7969 21.9817i 0.332205 0.122120i
\(181\) 220.457 1.21800 0.608998 0.793172i \(-0.291572\pi\)
0.608998 + 0.793172i \(0.291572\pi\)
\(182\) −48.8288 + 13.6696i −0.268290 + 0.0751077i
\(183\) −137.713 + 64.4854i −0.752527 + 0.352379i
\(184\) 7.30826 12.6583i 0.0397188 0.0687950i
\(185\) 129.760 74.9169i 0.701404 0.404956i
\(186\) 116.257 166.600i 0.625036 0.895696i
\(187\) −35.4968 + 61.4822i −0.189822 + 0.328782i
\(188\) 122.855i 0.653485i
\(189\) 97.1021 + 162.149i 0.513768 + 0.857929i
\(190\) 176.950 0.931314
\(191\) −164.995 95.2597i −0.863846 0.498742i 0.00145232 0.999999i \(-0.499538\pi\)
−0.865298 + 0.501257i \(0.832871\pi\)
\(192\) 86.3539 + 60.2595i 0.449760 + 0.313852i
\(193\) 50.5882 + 87.6213i 0.262115 + 0.453996i 0.966804 0.255520i \(-0.0822467\pi\)
−0.704689 + 0.709517i \(0.748913\pi\)
\(194\) −76.1523 43.9666i −0.392538 0.226632i
\(195\) −7.69798 16.4395i −0.0394768 0.0843051i
\(196\) 132.574 80.5401i 0.676397 0.410919i
\(197\) 73.4072i 0.372625i 0.982491 + 0.186313i \(0.0596537\pi\)
−0.982491 + 0.186313i \(0.940346\pi\)
\(198\) −150.433 409.223i −0.759761 2.06678i
\(199\) 39.3463 + 68.1497i 0.197720 + 0.342461i 0.947789 0.318899i \(-0.103313\pi\)
−0.750069 + 0.661360i \(0.769980\pi\)
\(200\) −9.67019 + 5.58309i −0.0483509 + 0.0279154i
\(201\) 17.8265 207.590i 0.0886889 1.03279i
\(202\) −162.970 −0.806784
\(203\) 94.4333 + 92.3482i 0.465189 + 0.454917i
\(204\) −15.7995 33.7407i −0.0774483 0.165396i
\(205\) −43.3224 + 75.0367i −0.211329 + 0.366032i
\(206\) −102.588 + 59.2291i −0.497999 + 0.287520i
\(207\) 10.0427 58.0426i 0.0485154 0.280399i
\(208\) 25.2216 43.6851i 0.121258 0.210024i
\(209\) 534.989i 2.55976i
\(210\) 82.0209 + 95.2524i 0.390576 + 0.453583i
\(211\) −26.1357 −0.123866 −0.0619329 0.998080i \(-0.519726\pi\)
−0.0619329 + 0.998080i \(0.519726\pi\)
\(212\) −2.49181 1.43865i −0.0117538 0.00678608i
\(213\) −94.8429 + 135.913i −0.445272 + 0.638089i
\(214\) −200.500 347.277i −0.936917 1.62279i
\(215\) 123.756 + 71.4506i 0.575610 + 0.332328i
\(216\) −58.3171 15.3258i −0.269987 0.0709528i
\(217\) 171.547 + 43.9195i 0.790539 + 0.202394i
\(218\) 220.292i 1.01052i
\(219\) −7.62843 + 88.8334i −0.0348330 + 0.405632i
\(220\) −64.0531 110.943i −0.291151 0.504288i
\(221\) −9.19329 + 5.30775i −0.0415986 + 0.0240170i
\(222\) 536.143 + 46.0404i 2.41506 + 0.207389i
\(223\) −383.186 −1.71832 −0.859161 0.511705i \(-0.829014\pi\)
−0.859161 + 0.511705i \(0.829014\pi\)
\(224\) −71.1249 + 277.810i −0.317522 + 1.24022i
\(225\) −28.8148 + 34.5646i −0.128066 + 0.153620i
\(226\) −75.1693 + 130.197i −0.332608 + 0.576093i
\(227\) 207.499 119.799i 0.914091 0.527751i 0.0323460 0.999477i \(-0.489702\pi\)
0.881745 + 0.471726i \(0.156369\pi\)
\(228\) 230.240 + 160.667i 1.00983 + 0.704678i
\(229\) 178.359 308.927i 0.778861 1.34903i −0.153738 0.988112i \(-0.549131\pi\)
0.932599 0.360915i \(-0.117536\pi\)
\(230\) 39.1765i 0.170332i
\(231\) 287.986 247.982i 1.24669 1.07351i
\(232\) −42.1388 −0.181633
\(233\) 51.5126 + 29.7408i 0.221084 + 0.127643i 0.606452 0.795120i \(-0.292592\pi\)
−0.385368 + 0.922763i \(0.625925\pi\)
\(234\) 11.1148 64.2391i 0.0474993 0.274526i
\(235\) −43.3884 75.1510i −0.184632 0.319791i
\(236\) −65.3786 37.7464i −0.277028 0.159942i
\(237\) −81.4124 + 38.1222i −0.343512 + 0.160853i
\(238\) 51.3948 52.5552i 0.215945 0.220820i
\(239\) 279.616i 1.16994i 0.811054 + 0.584971i \(0.198894\pi\)
−0.811054 + 0.584971i \(0.801106\pi\)
\(240\) −124.590 10.6989i −0.519123 0.0445789i
\(241\) 110.381 + 191.186i 0.458014 + 0.793304i 0.998856 0.0478204i \(-0.0152275\pi\)
−0.540842 + 0.841124i \(0.681894\pi\)
\(242\) −478.737 + 276.399i −1.97825 + 1.14215i
\(243\) −241.898 + 23.1186i −0.995464 + 0.0951383i
\(244\) −160.464 −0.657637
\(245\) −52.6518 + 96.0874i −0.214905 + 0.392193i
\(246\) −281.812 + 131.962i −1.14558 + 0.536429i
\(247\) 39.9978 69.2783i 0.161934 0.280479i
\(248\) −48.9256 + 28.2472i −0.197281 + 0.113900i
\(249\) 134.764 193.122i 0.541222 0.775588i
\(250\) −14.9643 + 25.9189i −0.0598571 + 0.103675i
\(251\) 289.707i 1.15421i 0.816670 + 0.577106i \(0.195818\pi\)
−0.816670 + 0.577106i \(0.804182\pi\)
\(252\) 20.2354 + 198.412i 0.0802993 + 0.787350i
\(253\) −118.446 −0.468166
\(254\) −72.7494 42.0019i −0.286415 0.165362i
\(255\) 21.5807 + 15.0595i 0.0846302 + 0.0590567i
\(256\) −163.770 283.658i −0.639726 1.10804i
\(257\) −135.364 78.1525i −0.526709 0.304095i 0.212966 0.977060i \(-0.431688\pi\)
−0.739675 + 0.672964i \(0.765021\pi\)
\(258\) 217.641 + 464.786i 0.843570 + 1.80150i
\(259\) 126.450 + 451.688i 0.488223 + 1.74397i
\(260\) 19.1554i 0.0736747i
\(261\) −159.392 + 58.5934i −0.610698 + 0.224496i
\(262\) −0.315937 0.547219i −0.00120587 0.00208862i
\(263\) 25.0501 14.4627i 0.0952475 0.0549912i −0.451620 0.892211i \(-0.649154\pi\)
0.546867 + 0.837219i \(0.315820\pi\)
\(264\) −10.3736 + 120.801i −0.0392940 + 0.457580i
\(265\) 2.03234 0.00766919
\(266\) −137.389 + 536.632i −0.516499 + 2.01741i
\(267\) −195.999 418.567i −0.734078 1.56767i
\(268\) 109.932 190.408i 0.410195 0.710479i
\(269\) 175.613 101.390i 0.652838 0.376916i −0.136705 0.990612i \(-0.543651\pi\)
0.789543 + 0.613696i \(0.210318\pi\)
\(270\) −155.904 + 42.5791i −0.577423 + 0.157700i
\(271\) 189.529 328.273i 0.699367 1.21134i −0.269319 0.963051i \(-0.586799\pi\)
0.968686 0.248288i \(-0.0798681\pi\)
\(272\) 73.1272i 0.268850i
\(273\) 55.8327 10.5814i 0.204515 0.0387598i
\(274\) 725.161 2.64657
\(275\) 78.3631 + 45.2429i 0.284957 + 0.164520i
\(276\) 35.5714 50.9750i 0.128882 0.184692i
\(277\) 66.1143 + 114.513i 0.238680 + 0.413406i 0.960336 0.278846i \(-0.0899520\pi\)
−0.721656 + 0.692252i \(0.756619\pi\)
\(278\) 162.739 + 93.9572i 0.585391 + 0.337975i
\(279\) −145.786 + 174.877i −0.522531 + 0.626798i
\(280\) −9.42352 33.6615i −0.0336554 0.120220i
\(281\) 33.0779i 0.117715i −0.998266 0.0588574i \(-0.981254\pi\)
0.998266 0.0588574i \(-0.0187457\pi\)
\(282\) 26.6645 310.510i 0.0945551 1.10110i
\(283\) −39.7064 68.7735i −0.140305 0.243016i 0.787306 0.616562i \(-0.211475\pi\)
−0.927612 + 0.373546i \(0.878142\pi\)
\(284\) −151.458 + 87.4445i −0.533304 + 0.307903i
\(285\) −197.581 16.9670i −0.693267 0.0595332i
\(286\) −131.091 −0.458360
\(287\) −193.926 189.644i −0.675699 0.660780i
\(288\) −283.202 236.092i −0.983341 0.819762i
\(289\) −136.805 + 236.954i −0.473375 + 0.819910i
\(290\) −97.8124 + 56.4720i −0.337284 + 0.194731i
\(291\) 80.8155 + 56.3947i 0.277716 + 0.193796i
\(292\) −47.0430 + 81.4809i −0.161106 + 0.279044i
\(293\) 127.804i 0.436192i −0.975927 0.218096i \(-0.930015\pi\)
0.975927 0.218096i \(-0.0699846\pi\)
\(294\) −352.554 + 174.787i −1.19916 + 0.594513i
\(295\) 53.3231 0.180756
\(296\) −129.595 74.8219i −0.437822 0.252777i
\(297\) 128.734 + 471.361i 0.433447 + 1.58707i
\(298\) 78.7663 + 136.427i 0.264316 + 0.457809i
\(299\) −15.3381 8.85548i −0.0512981 0.0296170i
\(300\) −43.0047 + 20.1374i −0.143349 + 0.0671248i
\(301\) −312.775 + 319.836i −1.03912 + 1.06258i
\(302\) 686.550i 2.27335i
\(303\) 181.972 + 15.6265i 0.600567 + 0.0515728i
\(304\) −275.534 477.239i −0.906361 1.56986i
\(305\) 98.1561 56.6705i 0.321823 0.185805i
\(306\) 32.6092 + 88.7069i 0.106566 + 0.289892i
\(307\) 178.227 0.580545 0.290273 0.956944i \(-0.406254\pi\)
0.290273 + 0.956944i \(0.406254\pi\)
\(308\) 386.188 108.113i 1.25386 0.351017i
\(309\) 120.228 56.2982i 0.389088 0.182195i
\(310\) −75.7105 + 131.135i −0.244228 + 0.423015i
\(311\) −440.590 + 254.375i −1.41669 + 0.817926i −0.996006 0.0892815i \(-0.971543\pi\)
−0.420683 + 0.907208i \(0.638210\pi\)
\(312\) −10.3749 + 14.8675i −0.0332528 + 0.0476523i
\(313\) 149.067 258.191i 0.476251 0.824892i −0.523378 0.852100i \(-0.675329\pi\)
0.999630 + 0.0272088i \(0.00866190\pi\)
\(314\) 196.437i 0.625597i
\(315\) −82.4507 114.223i −0.261748 0.362612i
\(316\) −94.8623 −0.300197
\(317\) 272.046 + 157.066i 0.858190 + 0.495476i 0.863406 0.504510i \(-0.168327\pi\)
−0.00521565 + 0.999986i \(0.501660\pi\)
\(318\) 5.98568 + 4.17693i 0.0188229 + 0.0131350i
\(319\) 170.737 + 295.726i 0.535227 + 0.927040i
\(320\) −67.9712 39.2432i −0.212410 0.122635i
\(321\) 190.579 + 406.992i 0.593703 + 1.26789i
\(322\) 118.810 + 30.4177i 0.368974 + 0.0944650i
\(323\) 115.969i 0.359038i
\(324\) −241.518 86.1553i −0.745425 0.265912i
\(325\) 6.76507 + 11.7174i 0.0208156 + 0.0360537i
\(326\) 150.218 86.7284i 0.460791 0.266038i
\(327\) −21.1229 + 245.977i −0.0645961 + 0.752224i
\(328\) 86.5351 0.263826
\(329\) 261.597 73.2340i 0.795128 0.222596i
\(330\) 137.812 + 294.305i 0.417611 + 0.891834i
\(331\) 72.4842 125.546i 0.218985 0.379294i −0.735513 0.677511i \(-0.763059\pi\)
0.954498 + 0.298217i \(0.0963920\pi\)
\(332\) 215.210 124.252i 0.648224 0.374253i
\(333\) −594.240 102.817i −1.78450 0.308760i
\(334\) 278.961 483.174i 0.835212 1.44663i
\(335\) 155.298i 0.463576i
\(336\) 129.181 369.533i 0.384468 1.09980i
\(337\) −187.624 −0.556748 −0.278374 0.960473i \(-0.589796\pi\)
−0.278374 + 0.960473i \(0.589796\pi\)
\(338\) 374.809 + 216.396i 1.10890 + 0.640226i
\(339\) 96.4177 138.170i 0.284418 0.407580i
\(340\) 13.8847 + 24.0491i 0.0408375 + 0.0707326i
\(341\) 396.472 + 228.903i 1.16267 + 0.671270i
\(342\) −547.049 456.047i −1.59956 1.33347i
\(343\) −250.522 234.281i −0.730385 0.683035i
\(344\) 142.720i 0.414884i
\(345\) −3.75647 + 43.7442i −0.0108883 + 0.126795i
\(346\) 235.507 + 407.911i 0.680657 + 1.17893i
\(347\) 516.443 298.168i 1.48831 0.859274i 0.488396 0.872622i \(-0.337582\pi\)
0.999911 + 0.0133476i \(0.00424878\pi\)
\(348\) −178.545 15.3323i −0.513061 0.0440583i
\(349\) −44.7573 −0.128244 −0.0641221 0.997942i \(-0.520425\pi\)
−0.0641221 + 0.997942i \(0.520425\pi\)
\(350\) −66.9850 65.5060i −0.191386 0.187160i
\(351\) −18.5704 + 70.6633i −0.0529071 + 0.201320i
\(352\) −370.695 + 642.062i −1.05311 + 1.82404i
\(353\) 552.513 318.993i 1.56519 0.903664i 0.568475 0.822701i \(-0.307534\pi\)
0.996717 0.0809631i \(-0.0257996\pi\)
\(354\) 157.048 + 109.592i 0.443639 + 0.309581i
\(355\) 61.7651 106.980i 0.173986 0.301353i
\(356\) 487.717i 1.36999i
\(357\) −62.4265 + 53.7548i −0.174864 + 0.150574i
\(358\) 369.544 1.03224
\(359\) −95.5156 55.1460i −0.266060 0.153610i 0.361036 0.932552i \(-0.382423\pi\)
−0.627096 + 0.778942i \(0.715757\pi\)
\(360\) 44.2850 + 7.66231i 0.123014 + 0.0212842i
\(361\) −256.457 444.196i −0.710407 1.23046i
\(362\) −511.076 295.070i −1.41181 0.815110i
\(363\) 561.058 262.722i 1.54561 0.723751i
\(364\) 58.0923 + 14.8728i 0.159594 + 0.0408594i
\(365\) 66.4562i 0.182072i
\(366\) 405.563 + 34.8271i 1.10809 + 0.0951559i
\(367\) −296.749 513.984i −0.808581 1.40050i −0.913847 0.406059i \(-0.866903\pi\)
0.105266 0.994444i \(-0.466430\pi\)
\(368\) −105.660 + 61.0029i −0.287120 + 0.165769i
\(369\) 327.323 120.326i 0.887055 0.326086i
\(370\) −401.088 −1.08402
\(371\) −1.57796 + 6.16343i −0.00425327 + 0.0166130i
\(372\) −217.579 + 101.884i −0.584890 + 0.273881i
\(373\) 92.0852 159.496i 0.246877 0.427604i −0.715781 0.698325i \(-0.753929\pi\)
0.962658 + 0.270722i \(0.0872623\pi\)
\(374\) 164.581 95.0209i 0.440056 0.254067i
\(375\) 19.1943 27.5060i 0.0511847 0.0733493i
\(376\) −43.3335 + 75.0558i −0.115249 + 0.199616i
\(377\) 51.0599i 0.135437i
\(378\) −8.08048 505.868i −0.0213769 1.33827i
\(379\) 486.561 1.28380 0.641901 0.766787i \(-0.278146\pi\)
0.641901 + 0.766787i \(0.278146\pi\)
\(380\) −181.228 104.632i −0.476915 0.275347i
\(381\) 77.2042 + 53.8747i 0.202636 + 0.141403i
\(382\) 255.000 + 441.672i 0.667538 + 1.15621i
\(383\) −517.073 298.532i −1.35006 0.779458i −0.361803 0.932255i \(-0.617839\pi\)
−0.988258 + 0.152797i \(0.951172\pi\)
\(384\) 88.9393 + 189.935i 0.231613 + 0.494623i
\(385\) −198.051 + 202.522i −0.514417 + 0.526032i
\(386\) 270.838i 0.701653i
\(387\) −198.450 539.846i −0.512792 1.39495i
\(388\) 51.9956 + 90.0591i 0.134009 + 0.232111i
\(389\) 262.695 151.667i 0.675310 0.389890i −0.122776 0.992434i \(-0.539180\pi\)
0.798085 + 0.602544i \(0.205846\pi\)
\(390\) −4.15750 + 48.4142i −0.0106602 + 0.124139i
\(391\) 25.6755 0.0656661
\(392\) 109.401 2.44280i 0.279085 0.00623164i
\(393\) 0.300303 + 0.641316i 0.000764130 + 0.00163185i
\(394\) 98.2514 170.176i 0.249369 0.431920i
\(395\) 58.0276 33.5022i 0.146905 0.0848158i
\(396\) −87.9075 + 508.069i −0.221989 + 1.28300i
\(397\) −140.150 + 242.747i −0.353022 + 0.611452i −0.986777 0.162081i \(-0.948179\pi\)
0.633755 + 0.773534i \(0.281513\pi\)
\(398\) 210.651i 0.529274i
\(399\) 204.863 586.027i 0.513441 1.46874i
\(400\) 93.2053 0.233013
\(401\) −110.748 63.9406i −0.276180 0.159453i 0.355513 0.934671i \(-0.384306\pi\)
−0.631693 + 0.775219i \(0.717640\pi\)
\(402\) −319.174 + 457.387i −0.793965 + 1.13778i
\(403\) 34.2273 + 59.2835i 0.0849313 + 0.147105i
\(404\) 166.910 + 96.3658i 0.413145 + 0.238529i
\(405\) 178.165 32.5946i 0.439912 0.0804805i
\(406\) −95.3173 340.480i −0.234772 0.838622i
\(407\) 1212.65i 2.97948i
\(408\) 2.24868 26.1860i 0.00551146 0.0641813i
\(409\) −48.0455 83.2172i −0.117471 0.203465i 0.801294 0.598271i \(-0.204145\pi\)
−0.918765 + 0.394806i \(0.870812\pi\)
\(410\) 200.865 115.969i 0.489914 0.282852i
\(411\) −809.711 69.5327i −1.97010 0.169179i
\(412\) 140.091 0.340026
\(413\) −41.4016 + 161.712i −0.100246 + 0.391555i
\(414\) −100.968 + 121.116i −0.243885 + 0.292551i
\(415\) −87.7634 + 152.011i −0.211478 + 0.366291i
\(416\) −96.0059 + 55.4290i −0.230783 + 0.133243i
\(417\) −172.704 120.516i −0.414158 0.289008i
\(418\) −716.053 + 1240.24i −1.71305 + 2.96708i
\(419\) 339.702i 0.810745i 0.914152 + 0.405373i \(0.132858\pi\)
−0.914152 + 0.405373i \(0.867142\pi\)
\(420\) −27.6803 146.055i −0.0659056 0.347750i
\(421\) −323.174 −0.767634 −0.383817 0.923409i \(-0.625391\pi\)
−0.383817 + 0.923409i \(0.625391\pi\)
\(422\) 60.5891 + 34.9811i 0.143576 + 0.0828937i
\(423\) −59.5469 + 344.157i −0.140773 + 0.813609i
\(424\) −1.01488 1.75782i −0.00239359 0.00414581i
\(425\) −16.9867 9.80727i −0.0399687 0.0230759i
\(426\) 401.782 188.139i 0.943150 0.441640i
\(427\) 95.6523 + 341.677i 0.224010 + 0.800180i
\(428\) 474.230i 1.10801i
\(429\) 146.376 + 12.5698i 0.341202 + 0.0293002i
\(430\) −191.265 331.281i −0.444803 0.770421i
\(431\) 234.768 135.543i 0.544705 0.314485i −0.202279 0.979328i \(-0.564835\pi\)
0.746984 + 0.664843i \(0.231501\pi\)
\(432\) 357.601 + 354.177i 0.827779 + 0.819855i
\(433\) 642.220 1.48319 0.741594 0.670849i \(-0.234070\pi\)
0.741594 + 0.670849i \(0.234070\pi\)
\(434\) −338.905 331.423i −0.780888 0.763646i
\(435\) 114.632 53.6775i 0.263521 0.123397i
\(436\) −130.261 + 225.618i −0.298763 + 0.517473i
\(437\) −167.562 + 96.7418i −0.383437 + 0.221377i
\(438\) 136.583 195.728i 0.311834 0.446868i
\(439\) −267.354 + 463.071i −0.609007 + 1.05483i 0.382398 + 0.923998i \(0.375098\pi\)
−0.991404 + 0.130833i \(0.958235\pi\)
\(440\) 90.3712i 0.205389i
\(441\) 410.419 161.361i 0.930655 0.365898i
\(442\) 28.4165 0.0642907
\(443\) 174.920 + 100.990i 0.394854 + 0.227969i 0.684261 0.729237i \(-0.260125\pi\)
−0.289407 + 0.957206i \(0.593458\pi\)
\(444\) −521.881 364.180i −1.17541 0.820224i
\(445\) 172.246 + 298.339i 0.387069 + 0.670424i
\(446\) 888.322 + 512.873i 1.99175 + 1.14994i
\(447\) −74.8685 159.886i −0.167491 0.357688i
\(448\) 171.787 175.666i 0.383453 0.392111i
\(449\) 751.940i 1.67470i 0.546668 + 0.837350i \(0.315896\pi\)
−0.546668 + 0.837350i \(0.684104\pi\)
\(450\) 113.063 41.5625i 0.251250 0.0923611i
\(451\) −350.622 607.294i −0.777431 1.34655i
\(452\) 153.973 88.8966i 0.340649 0.196674i
\(453\) −65.8304 + 766.598i −0.145321 + 1.69227i
\(454\) −641.380 −1.41273
\(455\) −40.7878 + 11.4185i −0.0896436 + 0.0250957i
\(456\) 83.9901 + 179.366i 0.184189 + 0.393347i
\(457\) −7.76422 + 13.4480i −0.0169895 + 0.0294268i −0.874395 0.485214i \(-0.838742\pi\)
0.857406 + 0.514641i \(0.172075\pi\)
\(458\) −826.964 + 477.448i −1.80560 + 1.04246i
\(459\) −27.9055 102.176i −0.0607963 0.222607i
\(460\) −23.1654 + 40.1236i −0.0503595 + 0.0872253i
\(461\) 344.491i 0.747269i −0.927576 0.373634i \(-0.878112\pi\)
0.927576 0.373634i \(-0.121888\pi\)
\(462\) −999.534 + 189.432i −2.16349 + 0.410026i
\(463\) −172.651 −0.372896 −0.186448 0.982465i \(-0.559698\pi\)
−0.186448 + 0.982465i \(0.559698\pi\)
\(464\) 304.614 + 175.869i 0.656495 + 0.379027i
\(465\) 97.1119 139.164i 0.208843 0.299278i
\(466\) −79.6129 137.894i −0.170843 0.295909i
\(467\) −593.172 342.468i −1.27018 0.733336i −0.295155 0.955449i \(-0.595371\pi\)
−0.975021 + 0.222113i \(0.928705\pi\)
\(468\) −49.3687 + 59.2199i −0.105489 + 0.126538i
\(469\) −470.969 120.578i −1.00420 0.257095i
\(470\) 232.292i 0.494239i
\(471\) 18.8356 219.341i 0.0399906 0.465692i
\(472\) −26.6278 46.1207i −0.0564148 0.0977133i
\(473\) −1001.60 + 578.271i −2.11754 + 1.22256i
\(474\) 239.759 + 20.5889i 0.505821 + 0.0434366i
\(475\) 147.810 0.311179
\(476\) −83.7137 + 23.4356i −0.175869 + 0.0492345i
\(477\) −6.28307 5.23788i −0.0131720 0.0109809i
\(478\) 374.251 648.221i 0.782951 1.35611i
\(479\) 204.293 117.949i 0.426499 0.246239i −0.271355 0.962479i \(-0.587472\pi\)
0.697854 + 0.716240i \(0.254138\pi\)
\(480\) 225.368 + 157.267i 0.469517 + 0.327639i
\(481\) −90.6623 + 157.032i −0.188487 + 0.326469i
\(482\) 590.958i 1.22605i
\(483\) −129.746 45.3564i −0.268625 0.0939056i
\(484\) 653.749 1.35072
\(485\) −63.6118 36.7263i −0.131158 0.0757243i
\(486\) 591.723 + 270.172i 1.21754 + 0.555909i
\(487\) −261.107 452.251i −0.536155 0.928647i −0.999106 0.0422639i \(-0.986543\pi\)
0.462952 0.886384i \(-0.346790\pi\)
\(488\) −98.0317 56.5987i −0.200885 0.115981i
\(489\) −176.049 + 82.4366i −0.360017 + 0.168582i
\(490\) 250.668 152.283i 0.511567 0.310783i
\(491\) 907.148i 1.84755i −0.382933 0.923776i \(-0.625086\pi\)
0.382933 0.923776i \(-0.374914\pi\)
\(492\) 366.656 + 31.4860i 0.745235 + 0.0639959i
\(493\) −37.0106 64.1042i −0.0750722 0.130029i
\(494\) −185.450 + 107.070i −0.375405 + 0.216740i
\(495\) −125.660 341.834i −0.253858 0.690573i
\(496\) 471.565 0.950736
\(497\) 276.481 + 270.376i 0.556300 + 0.544017i
\(498\) −570.900 + 267.330i −1.14639 + 0.536808i
\(499\) −23.5236 + 40.7441i −0.0471415 + 0.0816515i −0.888633 0.458618i \(-0.848345\pi\)
0.841492 + 0.540270i \(0.181678\pi\)
\(500\) 30.6521 17.6970i 0.0613042 0.0353940i
\(501\) −357.816 + 512.762i −0.714203 + 1.02348i
\(502\) 387.757 671.614i 0.772424 1.33788i
\(503\) 55.4203i 0.110180i 0.998481 + 0.0550898i \(0.0175445\pi\)
−0.998481 + 0.0550898i \(0.982455\pi\)
\(504\) −57.6215 + 128.353i −0.114328 + 0.254669i
\(505\) −136.133 −0.269570
\(506\) 274.588 + 158.534i 0.542664 + 0.313307i
\(507\) −397.761 277.566i −0.784538 0.547467i
\(508\) 49.6722 + 86.0347i 0.0977798 + 0.169360i
\(509\) 220.030 + 127.035i 0.432280 + 0.249577i 0.700317 0.713832i \(-0.253042\pi\)
−0.268038 + 0.963408i \(0.586375\pi\)
\(510\) −29.8733 63.7963i −0.0585751 0.125091i
\(511\) 201.541 + 51.5985i 0.394404 + 0.100976i
\(512\) 597.151i 1.16631i
\(513\) 567.103 + 561.674i 1.10546 + 1.09488i
\(514\) 209.206 + 362.355i 0.407015 + 0.704970i
\(515\) −85.6940 + 49.4754i −0.166396 + 0.0960688i
\(516\) 51.9290 604.716i 0.100638 1.17193i
\(517\) 702.312 1.35844
\(518\) 311.416 1216.37i 0.601190 2.34821i
\(519\) −223.853 478.052i −0.431317 0.921103i
\(520\) 6.75649 11.7026i 0.0129933 0.0225050i
\(521\) −188.089 + 108.593i −0.361016 + 0.208433i −0.669526 0.742788i \(-0.733503\pi\)
0.308510 + 0.951221i \(0.400170\pi\)
\(522\) 447.935 + 77.5030i 0.858114 + 0.148473i
\(523\) 260.787 451.696i 0.498636 0.863664i −0.501362 0.865237i \(-0.667168\pi\)
0.999999 + 0.00157381i \(0.000500960\pi\)
\(524\) 0.747265i 0.00142608i
\(525\) 68.5140 + 79.5665i 0.130503 + 0.151555i
\(526\) −77.4300 −0.147205
\(527\) −85.9429 49.6191i −0.163079 0.0941540i
\(528\) 579.159 829.954i 1.09689 1.57188i
\(529\) −243.081 421.029i −0.459511 0.795897i
\(530\) −4.71147 2.72017i −0.00888957 0.00513239i
\(531\) −164.851 137.428i −0.310454 0.258810i
\(532\) 458.025 468.367i 0.860950 0.880389i
\(533\) 104.855i 0.196726i
\(534\) −105.854 + 1232.68i −0.198229 + 2.30839i
\(535\) −167.483 290.088i −0.313052 0.542221i
\(536\) 134.322 77.5506i 0.250600 0.144684i
\(537\) −412.630 35.4340i −0.768399 0.0659851i
\(538\) −542.822 −1.00896
\(539\) −460.414 757.869i −0.854200 1.40606i
\(540\) 184.851 + 48.5790i 0.342316 + 0.0899610i
\(541\) 39.6152 68.6156i 0.0732260 0.126831i −0.827087 0.562073i \(-0.810004\pi\)
0.900313 + 0.435242i \(0.143337\pi\)
\(542\) −878.750 + 507.347i −1.62131 + 0.936064i
\(543\) 542.372 + 378.478i 0.998843 + 0.697014i
\(544\) 80.3551 139.179i 0.147712 0.255844i
\(545\) 184.015i 0.337643i
\(546\) −143.597 50.1986i −0.262998 0.0919388i
\(547\) −280.601 −0.512982 −0.256491 0.966547i \(-0.582566\pi\)
−0.256491 + 0.966547i \(0.582566\pi\)
\(548\) −742.693 428.794i −1.35528 0.782471i
\(549\) −449.510 77.7754i −0.818779 0.141667i
\(550\) −121.110 209.769i −0.220201 0.381399i
\(551\) 483.073 + 278.902i 0.876721 + 0.506175i
\(552\) 39.7115 18.5953i 0.0719411 0.0336872i
\(553\) 56.5474 + 201.991i 0.102256 + 0.365265i
\(554\) 353.961i 0.638920i
\(555\) 447.853 + 38.4587i 0.806942 + 0.0692949i
\(556\) −111.115 192.457i −0.199848 0.346147i
\(557\) 798.395 460.954i 1.43338 0.827565i 0.436007 0.899943i \(-0.356392\pi\)
0.997377 + 0.0723785i \(0.0230590\pi\)
\(558\) 572.032 210.282i 1.02515 0.376850i
\(559\) −172.935 −0.309365
\(560\) −72.3672 + 282.662i −0.129227 + 0.504754i
\(561\) −192.881 + 90.3189i −0.343817 + 0.160996i
\(562\) −44.2729 + 76.6829i −0.0787774 + 0.136446i
\(563\) −210.180 + 121.347i −0.373321 + 0.215537i −0.674909 0.737901i \(-0.735817\pi\)
0.301587 + 0.953439i \(0.402484\pi\)
\(564\) −210.916 + 302.250i −0.373965 + 0.535904i
\(565\) −62.7907 + 108.757i −0.111134 + 0.192490i
\(566\) 212.579i 0.375581i
\(567\) −39.4829 + 565.624i −0.0696347 + 0.997573i
\(568\) −123.374 −0.217207
\(569\) −247.611 142.958i −0.435168 0.251245i 0.266378 0.963869i \(-0.414173\pi\)
−0.701546 + 0.712624i \(0.747507\pi\)
\(570\) 435.334 + 303.785i 0.763743 + 0.532956i
\(571\) 432.123 + 748.459i 0.756783 + 1.31079i 0.944483 + 0.328560i \(0.106563\pi\)
−0.187701 + 0.982226i \(0.560103\pi\)
\(572\) 134.260 + 77.5153i 0.234721 + 0.135516i
\(573\) −242.381 517.620i −0.423004 0.903350i
\(574\) 195.741 + 699.201i 0.341012 + 1.21812i
\(575\) 32.7250i 0.0569131i
\(576\) 108.996 + 296.502i 0.189229 + 0.514761i
\(577\) 348.257 + 603.199i 0.603566 + 1.04541i 0.992276 + 0.124046i \(0.0395872\pi\)
−0.388711 + 0.921360i \(0.627080\pi\)
\(578\) 634.299 366.213i 1.09740 0.633586i
\(579\) −25.9695 + 302.416i −0.0448523 + 0.522308i
\(580\) 133.570 0.230292
\(581\) −392.858 384.184i −0.676175 0.661246i
\(582\) −111.870 238.904i −0.192216 0.410489i
\(583\) −8.22416 + 14.2447i −0.0141066 + 0.0244334i
\(584\) −57.4799 + 33.1860i −0.0984244 + 0.0568254i
\(585\) 9.28448 53.6604i 0.0158709 0.0917272i
\(586\) −171.059 + 296.283i −0.291909 + 0.505602i
\(587\) 596.728i 1.01657i 0.861188 + 0.508287i \(0.169721\pi\)
−0.861188 + 0.508287i \(0.830279\pi\)
\(588\) 464.430 + 29.4555i 0.789847 + 0.0500944i
\(589\) 747.834 1.26967
\(590\) −123.617 71.3700i −0.209520 0.120966i
\(591\) −126.025 + 180.597i −0.213239 + 0.305579i
\(592\) 624.547 + 1081.75i 1.05498 + 1.82728i
\(593\) 394.499 + 227.764i 0.665260 + 0.384088i 0.794278 0.607554i \(-0.207849\pi\)
−0.129019 + 0.991642i \(0.541183\pi\)
\(594\) 332.453 1265.04i 0.559685 2.12969i
\(595\) 42.9313 43.9006i 0.0721534 0.0737825i
\(596\) 186.301i 0.312585i
\(597\) −20.1985 + 235.212i −0.0338333 + 0.393990i
\(598\) 23.7051 + 41.0585i 0.0396407 + 0.0686597i
\(599\) −974.123 + 562.410i −1.62625 + 0.938915i −0.641049 + 0.767500i \(0.721501\pi\)
−0.985199 + 0.171415i \(0.945166\pi\)
\(600\) −33.3757 2.86608i −0.0556261 0.00477681i
\(601\) −1026.03 −1.70721 −0.853603 0.520923i \(-0.825588\pi\)
−0.853603 + 0.520923i \(0.825588\pi\)
\(602\) 1153.17 322.831i 1.91557 0.536264i
\(603\) 400.245 480.111i 0.663756 0.796204i
\(604\) −405.963 + 703.149i −0.672124 + 1.16415i
\(605\) −399.900 + 230.883i −0.660992 + 0.381624i
\(606\) −400.942 279.785i −0.661620 0.461692i
\(607\) 302.447 523.854i 0.498266 0.863022i −0.501732 0.865023i \(-0.667304\pi\)
0.999998 + 0.00200136i \(0.000637054\pi\)
\(608\) 1211.07i 1.99189i
\(609\) 73.7836 + 389.318i 0.121155 + 0.639274i
\(610\) −303.401 −0.497379
\(611\) 90.9456 + 52.5075i 0.148847 + 0.0859369i
\(612\) 19.0556 110.134i 0.0311366 0.179957i
\(613\) −377.326 653.548i −0.615540 1.06615i −0.990289 0.139021i \(-0.955605\pi\)
0.374749 0.927126i \(-0.377729\pi\)
\(614\) −413.176 238.548i −0.672926 0.388514i
\(615\) −235.404 + 110.231i −0.382771 + 0.179237i
\(616\) 274.067 + 70.1668i 0.444914 + 0.113907i
\(617\) 145.504i 0.235825i −0.993024 0.117912i \(-0.962380\pi\)
0.993024 0.117912i \(-0.0376202\pi\)
\(618\) −354.071 30.4053i −0.572931 0.0491996i
\(619\) 425.339 + 736.709i 0.687139 + 1.19016i 0.972759 + 0.231817i \(0.0744671\pi\)
−0.285620 + 0.958343i \(0.592200\pi\)
\(620\) 155.082 89.5366i 0.250132 0.144414i
\(621\) 124.354 125.556i 0.200248 0.202184i
\(622\) 1361.87 2.18950
\(623\) −1038.50 + 290.728i −1.66694 + 0.466659i
\(624\) 137.048 64.1745i 0.219629 0.102844i
\(625\) −12.5000 + 21.6506i −0.0200000 + 0.0346410i
\(626\) −691.149 + 399.035i −1.10407 + 0.637436i
\(627\) 918.463 1316.19i 1.46485 2.09918i
\(628\) 116.155 201.187i 0.184960 0.320361i
\(629\) 262.865i 0.417909i
\(630\) 38.2607 + 375.153i 0.0607313 + 0.595482i
\(631\) −1034.07 −1.63878 −0.819390 0.573237i \(-0.805687\pi\)
−0.819390 + 0.573237i \(0.805687\pi\)
\(632\) −57.9541 33.4598i −0.0916995 0.0529427i
\(633\) −64.2993 44.8694i −0.101579 0.0708837i
\(634\) −420.448 728.238i −0.663168 1.14864i
\(635\) −60.7693 35.0852i −0.0956997 0.0552522i
\(636\) −3.66054 7.81730i −0.00575556 0.0122914i
\(637\) −2.95996 132.562i −0.00464672 0.208104i
\(638\) 914.090i 1.43274i
\(639\) −466.667 + 171.549i −0.730308 + 0.268465i
\(640\) −78.1608 135.379i −0.122126 0.211529i
\(641\) 619.639 357.749i 0.966675 0.558110i 0.0684543 0.997654i \(-0.478193\pi\)
0.898221 + 0.439544i \(0.144860\pi\)
\(642\) 102.927 1198.59i 0.160323 1.86696i
\(643\) 47.5168 0.0738986 0.0369493 0.999317i \(-0.488236\pi\)
0.0369493 + 0.999317i \(0.488236\pi\)
\(644\) −103.696 101.406i −0.161019 0.157463i
\(645\) 181.801 + 388.246i 0.281861 + 0.601932i
\(646\) 155.218 268.846i 0.240276 0.416170i
\(647\) 790.372 456.321i 1.22159 0.705288i 0.256337 0.966587i \(-0.417484\pi\)
0.965258 + 0.261299i \(0.0841510\pi\)
\(648\) −117.161 137.823i −0.180805 0.212690i
\(649\) −215.780 + 373.742i −0.332481 + 0.575874i
\(650\) 36.2187i 0.0557210i
\(651\) 346.641 + 402.561i 0.532475 + 0.618373i
\(652\) −205.133 −0.314621
\(653\) 474.633 + 274.029i 0.726850 + 0.419647i 0.817269 0.576257i \(-0.195487\pi\)
−0.0904189 + 0.995904i \(0.528821\pi\)
\(654\) 378.195 541.966i 0.578280 0.828694i
\(655\) −0.263910 0.457105i −0.000402916 0.000697870i
\(656\) −625.546 361.159i −0.953576 0.550547i
\(657\) −171.276 + 205.453i −0.260694 + 0.312713i
\(658\) −704.468 180.358i −1.07062 0.274101i
\(659\) 682.581i 1.03578i −0.855446 0.517891i \(-0.826717\pi\)
0.855446 0.517891i \(-0.173283\pi\)
\(660\) 32.8818 382.910i 0.0498208 0.580166i
\(661\) −300.416 520.336i −0.454487 0.787195i 0.544171 0.838974i \(-0.316844\pi\)
−0.998659 + 0.0517791i \(0.983511\pi\)
\(662\) −336.073 + 194.032i −0.507664 + 0.293100i
\(663\) −31.7297 2.72474i −0.0478578 0.00410971i
\(664\) 175.304 0.264012
\(665\) −114.764 + 448.261i −0.172577 + 0.674077i
\(666\) 1239.98 + 1033.71i 1.86184 + 1.55212i
\(667\) 61.7487 106.952i 0.0925768 0.160348i
\(668\) −571.410 + 329.904i −0.855405 + 0.493868i
\(669\) −942.719 657.849i −1.40915 0.983332i
\(670\) 207.858 360.020i 0.310235 0.537343i
\(671\) 917.302i 1.36707i
\(672\) −651.922 + 561.364i −0.970123 + 0.835363i
\(673\) −161.729 −0.240310 −0.120155 0.992755i \(-0.538339\pi\)
−0.120155 + 0.992755i \(0.538339\pi\)
\(674\) 434.961 + 251.125i 0.645342 + 0.372588i
\(675\) −130.230 + 35.5673i −0.192934 + 0.0526923i
\(676\) −255.914 443.256i −0.378571 0.655704i
\(677\) −104.116 60.1113i −0.153790 0.0887907i 0.421130 0.907000i \(-0.361634\pi\)
−0.574920 + 0.818210i \(0.694967\pi\)
\(678\) −408.453 + 191.263i −0.602438 + 0.282098i
\(679\) 160.769 164.399i 0.236773 0.242119i
\(680\) 19.5897i 0.0288084i
\(681\) 716.161 + 61.4992i 1.05163 + 0.0903072i
\(682\) −612.748 1061.31i −0.898458 1.55617i
\(683\) 292.871 169.089i 0.428801 0.247569i −0.270034 0.962851i \(-0.587035\pi\)
0.698836 + 0.715282i \(0.253702\pi\)
\(684\) 290.610 + 790.547i 0.424868 + 1.15577i
\(685\) 605.744 0.884298
\(686\) 267.202 + 878.433i 0.389507 + 1.28051i
\(687\) 969.163 453.821i 1.41072 0.660584i
\(688\) −595.650 + 1031.70i −0.865771 + 1.49956i
\(689\) −2.12997 + 1.22974i −0.00309139 + 0.00178482i
\(690\) 67.2577 96.3824i 0.0974749 0.139685i
\(691\) 165.191 286.119i 0.239061 0.414065i −0.721384 0.692535i \(-0.756494\pi\)
0.960445 + 0.278470i \(0.0898272\pi\)
\(692\) 557.030i 0.804956i
\(693\) 1134.24 115.677i 1.63671 0.166923i
\(694\) −1596.33 −2.30018
\(695\) 135.939 + 78.4846i 0.195596 + 0.112928i
\(696\) −103.670 72.3434i −0.148952 0.103942i
\(697\) 76.0039 + 131.643i 0.109044 + 0.188870i
\(698\) 103.759 + 59.9051i 0.148651 + 0.0858239i
\(699\) 75.6732 + 161.605i 0.108259 + 0.231194i
\(700\) 29.8702 + 106.699i 0.0426717 + 0.152426i
\(701\) 462.419i 0.659656i 0.944041 + 0.329828i \(0.106991\pi\)
−0.944041 + 0.329828i \(0.893009\pi\)
\(702\) 137.630 138.960i 0.196054 0.197949i
\(703\) 990.442 + 1715.50i 1.40888 + 2.44025i
\(704\) 550.111 317.607i 0.781408 0.451146i
\(705\) 22.2735 259.376i 0.0315936 0.367909i
\(706\) −1707.82 −2.41901
\(707\) 105.697 412.848i 0.149501 0.583943i
\(708\) −96.0428 205.105i −0.135654 0.289697i
\(709\) 277.738 481.056i 0.391732 0.678500i −0.600946 0.799290i \(-0.705209\pi\)
0.992678 + 0.120790i \(0.0385427\pi\)
\(710\) −286.374 + 165.338i −0.403344 + 0.232871i
\(711\) −265.739 45.9790i −0.373755 0.0646680i
\(712\) 172.028 297.961i 0.241612 0.418484i
\(713\) 165.570i 0.232216i
\(714\) 216.668 41.0630i 0.303457 0.0575112i
\(715\) −109.503 −0.153152
\(716\) −378.478 218.514i −0.528601 0.305188i
\(717\) −480.042 + 687.915i −0.669514 + 0.959435i
\(718\) 147.620 + 255.685i 0.205598 + 0.356107i
\(719\) 874.330 + 504.795i 1.21604 + 0.702079i 0.964068 0.265657i \(-0.0855888\pi\)
0.251968 + 0.967736i \(0.418922\pi\)
\(720\) −288.149 240.215i −0.400207 0.333632i
\(721\) −83.5081 298.297i −0.115823 0.413726i
\(722\) 1373.01i 1.90168i
\(723\) −56.6644 + 659.860i −0.0783741 + 0.912670i
\(724\) 348.955 + 604.407i 0.481982 + 0.834817i
\(725\) −81.7050 + 47.1724i −0.112697 + 0.0650654i
\(726\) −1652.31 141.890i −2.27591 0.195441i
\(727\) −448.687 −0.617177 −0.308588 0.951196i \(-0.599857\pi\)
−0.308588 + 0.951196i \(0.599857\pi\)
\(728\) 30.2443 + 29.5765i 0.0415444 + 0.0406271i
\(729\) −634.809 358.410i −0.870795 0.491647i
\(730\) −88.9480 + 154.062i −0.121847 + 0.211044i
\(731\) 217.115 125.351i 0.297011 0.171479i
\(732\) −394.774 275.482i −0.539309 0.376341i
\(733\) −50.8478 + 88.0709i −0.0693694 + 0.120151i −0.898624 0.438720i \(-0.855432\pi\)
0.829254 + 0.558871i \(0.188765\pi\)
\(734\) 1588.73i 2.16448i
\(735\) −294.496 + 146.003i −0.400675 + 0.198644i
\(736\) 268.130 0.364307
\(737\) −1088.48 628.436i −1.47691 0.852695i
\(738\) −919.868 159.158i −1.24643 0.215661i
\(739\) 94.0310 + 162.866i 0.127241 + 0.220388i 0.922607 0.385742i \(-0.126055\pi\)
−0.795366 + 0.606130i \(0.792721\pi\)
\(740\) 410.785 + 237.167i 0.555115 + 0.320496i
\(741\) 217.339 101.771i 0.293305 0.137343i
\(742\) 11.9075 12.1764i 0.0160479 0.0164102i
\(743\) 122.415i 0.164757i 0.996601 + 0.0823786i \(0.0262517\pi\)
−0.996601 + 0.0823786i \(0.973748\pi\)
\(744\) −168.862 14.5007i −0.226965 0.0194902i
\(745\) 65.7953 + 113.961i 0.0883158 + 0.152967i
\(746\) −426.954 + 246.502i −0.572324 + 0.330431i
\(747\) 663.097 243.758i 0.887680 0.326316i
\(748\) −224.747 −0.300464
\(749\) 1009.78 282.689i 1.34818 0.377421i
\(750\) −81.3124 + 38.0754i −0.108417 + 0.0507673i
\(751\) 330.331 572.150i 0.439855 0.761850i −0.557823 0.829960i \(-0.688363\pi\)
0.997678 + 0.0681093i \(0.0216967\pi\)
\(752\) 626.499 361.709i 0.833110 0.480996i
\(753\) −497.365 + 712.741i −0.660512 + 0.946535i
\(754\) 68.3408 118.370i 0.0906377 0.156989i
\(755\) 573.492i 0.759591i
\(756\) −290.848 + 522.876i −0.384720 + 0.691635i
\(757\) 225.258 0.297567 0.148783 0.988870i \(-0.452464\pi\)
0.148783 + 0.988870i \(0.452464\pi\)
\(758\) −1127.97 651.235i −1.48809 0.859149i
\(759\) −291.402 203.347i −0.383929 0.267914i
\(760\) −73.8114 127.845i −0.0971203 0.168217i
\(761\) 1106.40 + 638.781i 1.45388 + 0.839396i 0.998698 0.0510038i \(-0.0162421\pi\)
0.455179 + 0.890400i \(0.349575\pi\)
\(762\) −106.871 228.229i −0.140250 0.299513i
\(763\) 558.060 + 142.875i 0.731403 + 0.187254i
\(764\) 603.134i 0.789442i
\(765\) 27.2392 + 74.0990i 0.0356068 + 0.0968614i
\(766\) 799.138 + 1384.15i 1.04326 + 1.80698i
\(767\) −55.8847 + 32.2651i −0.0728614 + 0.0420666i
\(768\) 84.0715 979.016i 0.109468 1.27476i
\(769\) 282.171 0.366933 0.183466 0.983026i \(-0.441268\pi\)
0.183466 + 0.983026i \(0.441268\pi\)
\(770\) 730.197 204.418i 0.948308 0.265478i
\(771\) −198.853 424.663i −0.257916 0.550795i
\(772\) −160.149 + 277.386i −0.207447 + 0.359308i
\(773\) 1175.22 678.511i 1.52033 0.877763i 0.520618 0.853790i \(-0.325702\pi\)
0.999713 0.0239731i \(-0.00763161\pi\)
\(774\) −262.495 + 1517.11i −0.339141 + 1.96010i
\(775\) −63.2428 + 109.540i −0.0816036 + 0.141342i
\(776\) 73.3595i 0.0945355i
\(777\) −464.359 + 1328.33i −0.597630 + 1.70957i
\(778\) −811.993 −1.04369
\(779\) −992.025 572.746i −1.27346 0.735232i
\(780\) 32.8858 47.1264i 0.0421612 0.0604184i
\(781\) 499.884 + 865.824i 0.640056 + 1.10861i
\(782\) −59.5222 34.3652i −0.0761154 0.0439452i
\(783\) −492.731 129.490i −0.629286 0.165377i
\(784\) −801.036 438.934i −1.02173 0.559864i
\(785\) 164.089i 0.209030i
\(786\) 0.162187 1.88867i 0.000206344 0.00240289i
\(787\) 5.69060 + 9.85641i 0.00723075 + 0.0125240i 0.869618 0.493725i \(-0.164365\pi\)
−0.862387 + 0.506249i \(0.831032\pi\)
\(788\) −201.254 + 116.194i −0.255398 + 0.147454i
\(789\) 86.4579 + 7.42443i 0.109579 + 0.00940993i
\(790\) −179.364 −0.227042
\(791\) −281.072 274.866i −0.355338 0.347492i
\(792\) −232.911 + 279.387i −0.294080 + 0.352761i
\(793\) −68.5810 + 118.786i −0.0864830 + 0.149793i
\(794\) 649.805 375.165i 0.818395 0.472500i
\(795\) 4.99998 + 3.48909i 0.00628928 + 0.00438879i
\(796\) −124.560 + 215.744i −0.156482 + 0.271035i
\(797\) 592.055i 0.742855i −0.928462 0.371427i \(-0.878868\pi\)
0.928462 0.371427i \(-0.121132\pi\)
\(798\) −1259.29 + 1084.36i −1.57806 + 1.35885i
\(799\) −152.239 −0.190538
\(800\) −177.393 102.418i −0.221741 0.128022i
\(801\) 236.393 1366.25i 0.295122 1.70568i
\(802\) 171.162 + 296.461i 0.213419 + 0.369652i
\(803\) 465.792 + 268.925i 0.580065 + 0.334901i
\(804\) 597.347 279.714i 0.742969 0.347903i
\(805\) 99.2446 + 25.4086i 0.123285 + 0.0315635i
\(806\) 183.246i 0.227352i
\(807\) 606.112 + 52.0489i 0.751068 + 0.0644968i
\(808\) 67.9802 + 117.745i 0.0841340 + 0.145724i
\(809\) −382.368 + 220.760i −0.472643 + 0.272880i −0.717345 0.696718i \(-0.754643\pi\)
0.244703 + 0.969598i \(0.421310\pi\)
\(810\) −456.657 162.901i −0.563774 0.201112i
\(811\) 991.633 1.22273 0.611364 0.791349i \(-0.290621\pi\)
0.611364 + 0.791349i \(0.290621\pi\)
\(812\) −103.707 + 405.074i −0.127718 + 0.498860i
\(813\) 1029.86 482.241i 1.26673 0.593162i
\(814\) 1623.06 2811.23i 1.99394 3.45360i
\(815\) 125.481 72.4462i 0.153964 0.0888911i
\(816\) −125.544 + 179.908i −0.153853 + 0.220476i
\(817\) −944.616 + 1636.12i −1.15620 + 2.00260i
\(818\) 257.225i 0.314456i
\(819\) 155.526 + 69.8203i 0.189898 + 0.0852507i
\(820\) −274.295 −0.334506
\(821\) −1124.01 648.945i −1.36907 0.790432i −0.378260 0.925699i \(-0.623477\pi\)
−0.990809 + 0.135267i \(0.956811\pi\)
\(822\) 1784.05 + 1244.95i 2.17038 + 1.51453i
\(823\) −351.690 609.145i −0.427327 0.740152i 0.569308 0.822125i \(-0.307211\pi\)
−0.996635 + 0.0819727i \(0.973878\pi\)
\(824\) 85.5854 + 49.4128i 0.103866 + 0.0599669i
\(825\) 115.117 + 245.840i 0.139536 + 0.297988i
\(826\) 312.422 319.476i 0.378235 0.386775i
\(827\) 288.953i 0.349400i −0.984622 0.174700i \(-0.944105\pi\)
0.984622 0.174700i \(-0.0558955\pi\)
\(828\) 175.026 64.3407i 0.211385 0.0777061i
\(829\) 130.042 + 225.240i 0.156866 + 0.271701i 0.933737 0.357960i \(-0.116527\pi\)
−0.776871 + 0.629660i \(0.783194\pi\)
\(830\) 406.916 234.933i 0.490260 0.283052i
\(831\) −33.9399 + 395.231i −0.0408422 + 0.475609i
\(832\) 94.9820 0.114161
\(833\) 99.8035 + 164.283i 0.119812 + 0.197218i
\(834\) 239.067 + 510.542i 0.286651 + 0.612161i
\(835\) 233.023 403.607i 0.279069 0.483362i
\(836\) 1466.73 846.817i 1.75446 1.01294i
\(837\) −658.891 + 179.950i −0.787205 + 0.214994i
\(838\) 454.673 787.516i 0.542569 0.939756i
\(839\) 233.481i 0.278285i 0.990272 + 0.139142i \(0.0444346\pi\)
−0.990272 + 0.139142i \(0.955565\pi\)
\(840\) 34.6057 98.9925i 0.0411973 0.117848i
\(841\) 484.962 0.576650
\(842\) 749.199 + 432.550i 0.889785 + 0.513718i
\(843\) 56.7877 81.3786i 0.0673638 0.0965345i
\(844\) −41.3693 71.6537i −0.0490158 0.0848978i
\(845\) 313.087 + 180.761i 0.370517 + 0.213918i
\(846\) 598.680 718.142i 0.707659 0.848868i
\(847\) −389.700 1392.03i −0.460094 1.64349i
\(848\) 16.9426i 0.0199795i
\(849\) 20.3833 237.365i 0.0240086 0.279581i
\(850\) 26.2530 + 45.4715i 0.0308859 + 0.0534959i
\(851\) 379.809 219.283i 0.446309 0.257677i
\(852\) −522.743 44.8898i −0.613549 0.0526875i
\(853\) 394.198 0.462131 0.231065 0.972938i \(-0.425779\pi\)
0.231065 + 0.972938i \(0.425779\pi\)
\(854\) 235.569 920.119i 0.275842 1.07742i
\(855\) −456.962 380.947i −0.534459 0.445552i
\(856\) −167.270 + 289.721i −0.195409 + 0.338459i
\(857\) −887.436 + 512.361i −1.03551 + 0.597854i −0.918559 0.395283i \(-0.870647\pi\)
−0.116955 + 0.993137i \(0.537313\pi\)
\(858\) −322.512 225.055i −0.375888 0.262302i
\(859\) −17.8720 + 30.9551i −0.0208055 + 0.0360362i −0.876241 0.481874i \(-0.839956\pi\)
0.855435 + 0.517910i \(0.173290\pi\)
\(860\) 452.387i 0.526032i
\(861\) −151.520 799.493i −0.175981 0.928563i
\(862\) −725.668 −0.841843
\(863\) 644.308 + 371.991i 0.746591 + 0.431045i 0.824461 0.565919i \(-0.191479\pi\)
−0.0778698 + 0.996964i \(0.524812\pi\)
\(864\) −291.418 1067.03i −0.337290 1.23499i
\(865\) 196.725 + 340.737i 0.227427 + 0.393916i
\(866\) −1488.83 859.576i −1.71920 0.992582i
\(867\) −743.370 + 348.091i −0.857404 + 0.401489i
\(868\) 151.126 + 539.833i 0.174108 + 0.621927i
\(869\) 542.288i 0.624036i
\(870\) −337.590 28.9900i −0.388034 0.0333218i
\(871\) −93.9686 162.758i −0.107886 0.186864i
\(872\) −159.160 + 91.8911i −0.182523 + 0.105380i
\(873\) 102.005 + 277.486i 0.116845 + 0.317853i
\(874\) 517.934 0.592602
\(875\) −55.9541 54.7187i −0.0639476 0.0625356i
\(876\) −255.621 + 119.697i −0.291805 + 0.136641i
\(877\) −54.4422 + 94.2966i −0.0620777 + 0.107522i −0.895394 0.445275i \(-0.853106\pi\)
0.833316 + 0.552797i \(0.186439\pi\)
\(878\) 1239.59 715.677i 1.41183 0.815122i
\(879\) 219.413 314.425i 0.249616 0.357708i
\(880\) −377.169 + 653.276i −0.428602 + 0.742360i
\(881\) 798.705i 0.906589i −0.891361 0.453295i \(-0.850249\pi\)
0.891361 0.453295i \(-0.149751\pi\)
\(882\) −1167.43 175.247i −1.32361 0.198693i
\(883\) 1467.29 1.66171 0.830857 0.556487i \(-0.187851\pi\)
0.830857 + 0.556487i \(0.187851\pi\)
\(884\) −29.1035 16.8029i −0.0329225 0.0190078i
\(885\) 131.186 + 91.5445i 0.148233 + 0.103440i
\(886\) −270.340 468.242i −0.305124 0.528490i
\(887\) −738.838 426.568i −0.832963 0.480911i 0.0219031 0.999760i \(-0.493027\pi\)
−0.854866 + 0.518849i \(0.826361\pi\)
\(888\) −190.379 406.565i −0.214390 0.457844i
\(889\) 153.585 157.053i 0.172762 0.176662i
\(890\) 922.166i 1.03614i
\(891\) −492.514 + 1380.65i −0.552765 + 1.54956i
\(892\) −606.533 1050.55i −0.679969 1.17774i
\(893\) 993.537 573.619i 1.11258 0.642350i
\(894\) −40.4348 + 470.865i −0.0452290 + 0.526694i
\(895\) 308.688 0.344903
\(896\) 471.246 131.925i 0.525945 0.147238i
\(897\) −22.5321 48.1187i −0.0251194 0.0536440i
\(898\) 1006.43 1743.19i 1.12075 1.94119i
\(899\) −413.380 + 238.665i −0.459822 + 0.265478i
\(900\) −140.372 24.2876i −0.155969 0.0269862i
\(901\) 1.78274 3.08780i 0.00197863 0.00342708i
\(902\) 1877.15i 2.08110i
\(903\) −1318.58 + 249.898i −1.46022 + 0.276742i
\(904\) 125.422 0.138741
\(905\) −426.914 246.479i −0.471728 0.272352i
\(906\) 1178.66 1689.06i 1.30095 1.86430i
\(907\) 297.719 + 515.664i 0.328246 + 0.568538i 0.982164 0.188027i \(-0.0602093\pi\)
−0.653918 + 0.756565i \(0.726876\pi\)
\(908\) 656.886 + 379.253i 0.723443 + 0.417680i
\(909\) 420.862 + 350.852i 0.462994 + 0.385975i
\(910\) 109.840 + 28.1212i 0.120703 + 0.0309024i
\(911\) 303.048i 0.332654i 0.986071 + 0.166327i \(0.0531907\pi\)
−0.986071 + 0.166327i \(0.946809\pi\)
\(912\) 141.446 1647.14i 0.155094 1.80608i
\(913\) −710.295 1230.27i −0.777980 1.34750i
\(914\) 35.9989 20.7840i 0.0393861 0.0227396i
\(915\) 338.776 + 29.0919i 0.370247 + 0.0317944i
\(916\) 1129.28 1.23283
\(917\) 1.59116 0.445445i 0.00173518 0.000485763i
\(918\) −72.0655 + 274.221i −0.0785027 + 0.298715i
\(919\) −336.839 + 583.422i −0.366528 + 0.634845i −0.989020 0.147781i \(-0.952787\pi\)
0.622492 + 0.782626i \(0.286120\pi\)
\(920\) −28.3048 + 16.3418i −0.0307661 + 0.0177628i
\(921\) 438.477 + 305.979i 0.476088 + 0.332224i
\(922\) −461.082 + 798.617i −0.500089 + 0.866179i
\(923\) 149.493i 0.161964i
\(924\) 1135.71 + 397.022i 1.22913 + 0.429677i
\(925\) −335.038 −0.362204
\(926\) 400.248 + 231.083i 0.432234 + 0.249550i
\(927\) 392.439 + 67.9008i 0.423343 + 0.0732479i
\(928\) −386.503 669.443i −0.416491 0.721383i
\(929\) −507.044 292.742i −0.545795 0.315115i 0.201629 0.979462i \(-0.435376\pi\)
−0.747424 + 0.664347i \(0.768710\pi\)
\(930\) −411.394 + 192.640i −0.442359 + 0.207140i
\(931\) −1270.33 696.085i −1.36448 0.747675i
\(932\) 188.303i 0.202042i
\(933\) −1520.65 130.584i −1.62985 0.139961i
\(934\) 916.749 + 1587.86i 0.981530 + 1.70006i
\(935\) 137.478 79.3732i 0.147036 0.0848911i
\(936\) −51.0488 + 18.7658i −0.0545393 + 0.0200489i
\(937\) −829.644 −0.885426 −0.442713 0.896663i \(-0.645984\pi\)
−0.442713 + 0.896663i \(0.645984\pi\)
\(938\) 930.440 + 909.896i 0.991940 + 0.970038i
\(939\) 809.995 379.289i 0.862614 0.403929i
\(940\) 137.356 237.908i 0.146124 0.253094i
\(941\) −607.379 + 350.670i −0.645461 + 0.372657i −0.786715 0.617316i \(-0.788220\pi\)
0.141254 + 0.989973i \(0.454887\pi\)
\(942\) −337.241 + 483.277i −0.358005 + 0.513033i
\(943\) −126.805 + 219.633i −0.134470 + 0.232909i
\(944\) 444.530i 0.470901i
\(945\) −6.74982 422.563i −0.00714266 0.447157i
\(946\) 3095.94 3.27266
\(947\) −796.450 459.830i −0.841024 0.485565i 0.0165883 0.999862i \(-0.494720\pi\)
−0.857612 + 0.514297i \(0.828053\pi\)
\(948\) −233.381 162.858i −0.246183 0.171791i
\(949\) 40.2117 + 69.6487i 0.0423727 + 0.0733917i
\(950\) −342.662 197.836i −0.360696 0.208248i
\(951\) 399.643 + 853.461i 0.420234 + 0.897436i
\(952\) −59.4093 15.2100i −0.0624047 0.0159769i
\(953\) 664.086i 0.696837i −0.937339 0.348419i \(-0.886719\pi\)
0.937339 0.348419i \(-0.113281\pi\)
\(954\) 7.55513 + 20.5523i 0.00791943 + 0.0215433i
\(955\) 213.007 + 368.939i 0.223044 + 0.386324i
\(956\) −766.598 + 442.595i −0.801881 + 0.462966i
\(957\) −87.6482 + 1020.67i −0.0915865 + 1.06653i
\(958\) −631.470 −0.659155
\(959\) −470.317 + 1837.03i −0.490424 + 1.91557i
\(960\) −99.8513 213.239i −0.104012 0.222124i
\(961\) 160.528 278.043i 0.167043 0.289326i
\(962\) 420.356 242.693i 0.436961 0.252279i
\(963\) −229.856 + 1328.47i −0.238687 + 1.37951i
\(964\) −349.438 + 605.245i −0.362488 + 0.627848i
\(965\) 226.237i 0.234443i
\(966\) 240.076 + 278.805i 0.248526 + 0.288618i
\(967\) −614.911 −0.635895 −0.317948 0.948108i \(-0.602994\pi\)
−0.317948 + 0.948108i \(0.602994\pi\)
\(968\) 399.394 + 230.590i 0.412597 + 0.238213i
\(969\) −199.094 + 285.309i −0.205464 + 0.294436i
\(970\) 98.3122 + 170.282i 0.101353 + 0.175548i
\(971\) −261.561 151.012i −0.269372 0.155522i 0.359230 0.933249i \(-0.383039\pi\)
−0.628602 + 0.777727i \(0.716373\pi\)
\(972\) −446.274 626.595i −0.459130 0.644645i
\(973\) −343.566 + 351.323i −0.353100 + 0.361072i
\(974\) 1397.91i 1.43523i
\(975\) −3.47285 + 40.4416i −0.00356190 + 0.0414785i
\(976\) 472.435 + 818.282i 0.484053 + 0.838404i
\(977\) −383.518 + 221.424i −0.392546 + 0.226637i −0.683263 0.730172i \(-0.739440\pi\)
0.290716 + 0.956809i \(0.406106\pi\)
\(978\) 518.462 + 44.5221i 0.530125 + 0.0455236i
\(979\) −2788.08 −2.84788
\(980\) −346.775 + 7.74308i −0.353852 + 0.00790110i
\(981\) −474.258 + 568.893i −0.483443 + 0.579911i
\(982\) −1214.17 + 2103.00i −1.23642 + 2.14155i
\(983\) −717.229 + 414.092i −0.729632 + 0.421253i −0.818288 0.574809i \(-0.805076\pi\)
0.0886553 + 0.996062i \(0.471743\pi\)
\(984\) 212.895 + 148.562i 0.216356 + 0.150978i
\(985\) 82.0717 142.152i 0.0833215 0.144317i
\(986\) 198.147i 0.200960i
\(987\) 769.311 + 268.935i 0.779444 + 0.272478i
\(988\) 253.245 0.256321
\(989\) 362.236 + 209.137i 0.366265 + 0.211463i
\(990\) −166.214 + 960.646i −0.167893 + 0.970349i
\(991\) 484.472 + 839.130i 0.488872 + 0.846750i 0.999918 0.0128027i \(-0.00407532\pi\)
−0.511046 + 0.859553i \(0.670742\pi\)
\(992\) −897.505 518.175i −0.904743 0.522354i
\(993\) 393.863 184.430i 0.396639 0.185731i
\(994\) −279.069 996.856i −0.280754 1.00287i
\(995\) 175.962i 0.176846i
\(996\) 742.777 + 63.7848i 0.745760 + 0.0640410i
\(997\) −521.713 903.634i −0.523283 0.906353i −0.999633 0.0270969i \(-0.991374\pi\)
0.476350 0.879256i \(-0.341960\pi\)
\(998\) 109.067 62.9701i 0.109286 0.0630963i
\(999\) −1285.44 1273.14i −1.28673 1.27441i
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 105.3.t.b.86.5 yes 36
3.2 odd 2 inner 105.3.t.b.86.14 yes 36
7.4 even 3 inner 105.3.t.b.11.14 yes 36
21.11 odd 6 inner 105.3.t.b.11.5 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.3.t.b.11.5 36 21.11 odd 6 inner
105.3.t.b.11.14 yes 36 7.4 even 3 inner
105.3.t.b.86.5 yes 36 1.1 even 1 trivial
105.3.t.b.86.14 yes 36 3.2 odd 2 inner