Properties

Label 153.4.l.a.100.2
Level $153$
Weight $4$
Character 153.100
Analytic conductor $9.027$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [153,4,Mod(19,153)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(153, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("153.19");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 153 = 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 153.l (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.02729223088\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{8})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 17)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 100.2
Root \(-1.22788i\) of defining polynomial
Character \(\chi\) \(=\) 153.100
Dual form 153.4.l.a.127.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.161134 + 0.161134i) q^{2} -7.94807i q^{4} +(-2.54200 + 1.05293i) q^{5} +(-19.8837 - 8.23610i) q^{7} +(2.56978 - 2.56978i) q^{8} +O(q^{10})\) \(q+(0.161134 + 0.161134i) q^{2} -7.94807i q^{4} +(-2.54200 + 1.05293i) q^{5} +(-19.8837 - 8.23610i) q^{7} +(2.56978 - 2.56978i) q^{8} +(-0.579266 - 0.239940i) q^{10} +(-20.8709 + 50.3869i) q^{11} +52.4827i q^{13} +(-1.87682 - 4.53105i) q^{14} -62.7564 q^{16} +(-33.5380 - 61.5484i) q^{17} +(13.8808 + 13.8808i) q^{19} +(8.36878 + 20.2040i) q^{20} +(-11.4821 + 4.75602i) q^{22} +(5.33276 - 12.8744i) q^{23} +(-83.0352 + 83.0352i) q^{25} +(-8.45675 + 8.45675i) q^{26} +(-65.4611 + 158.037i) q^{28} +(-64.6920 + 26.7963i) q^{29} +(-63.9131 - 154.300i) q^{31} +(-30.6704 - 30.6704i) q^{32} +(4.51343 - 15.3216i) q^{34} +59.2165 q^{35} +(-76.0152 - 183.517i) q^{37} +4.47334i q^{38} +(-3.82658 + 9.23817i) q^{40} +(-401.250 - 166.203i) q^{41} +(89.9025 - 89.9025i) q^{43} +(400.479 + 165.884i) q^{44} +(2.93379 - 1.21522i) q^{46} +207.303i q^{47} +(84.9906 + 84.9906i) q^{49} -26.7596 q^{50} +417.136 q^{52} +(220.673 + 220.673i) q^{53} -150.059i q^{55} +(-72.2616 + 29.9317i) q^{56} +(-14.7419 - 6.10628i) q^{58} +(407.819 - 407.819i) q^{59} +(72.4205 + 29.9976i) q^{61} +(14.5644 - 35.1615i) q^{62} +492.167i q^{64} +(-55.2607 - 133.411i) q^{65} +359.997 q^{67} +(-489.191 + 266.562i) q^{68} +(9.54178 + 9.54178i) q^{70} +(-81.5842 - 196.962i) q^{71} +(26.8357 - 11.1157i) q^{73} +(17.3222 - 41.8194i) q^{74} +(110.326 - 110.326i) q^{76} +(829.983 - 829.983i) q^{77} +(327.389 - 790.386i) q^{79} +(159.527 - 66.0782i) q^{80} +(-37.8740 - 91.4360i) q^{82} +(-9.67821 - 9.67821i) q^{83} +(150.060 + 121.143i) q^{85} +28.9727 q^{86} +(75.8494 + 183.117i) q^{88} +651.126i q^{89} +(432.253 - 1043.55i) q^{91} +(-102.327 - 42.3851i) q^{92} +(-33.4035 + 33.4035i) q^{94} +(-49.9006 - 20.6695i) q^{95} +(-1107.41 + 458.705i) q^{97} +27.3897i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{2} + 20 q^{5} - 4 q^{7} - 28 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{2} + 20 q^{5} - 4 q^{7} - 28 q^{8} - 116 q^{10} - 40 q^{11} + 132 q^{14} + 184 q^{16} - 52 q^{17} - 12 q^{19} - 572 q^{20} - 620 q^{22} + 276 q^{23} - 464 q^{25} + 708 q^{26} + 452 q^{28} - 632 q^{29} + 188 q^{31} - 700 q^{32} + 764 q^{34} + 632 q^{35} + 940 q^{37} - 1864 q^{40} - 176 q^{41} - 1360 q^{43} + 1364 q^{44} + 452 q^{46} + 1044 q^{49} - 2856 q^{50} + 792 q^{52} + 360 q^{53} + 1788 q^{56} - 360 q^{58} + 584 q^{59} - 1052 q^{61} + 380 q^{62} - 404 q^{65} + 1080 q^{67} - 2532 q^{68} + 2072 q^{70} - 28 q^{71} + 824 q^{73} + 2292 q^{74} + 1328 q^{76} + 1252 q^{77} - 196 q^{79} + 904 q^{80} - 1528 q^{82} + 1008 q^{83} - 2824 q^{85} + 1200 q^{86} - 56 q^{88} + 2456 q^{91} - 396 q^{92} + 6360 q^{94} - 2172 q^{95} - 904 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/153\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(137\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.161134 + 0.161134i 0.0569694 + 0.0569694i 0.735018 0.678048i \(-0.237174\pi\)
−0.678048 + 0.735018i \(0.737174\pi\)
\(3\) 0 0
\(4\) 7.94807i 0.993509i
\(5\) −2.54200 + 1.05293i −0.227364 + 0.0941771i −0.493457 0.869770i \(-0.664267\pi\)
0.266094 + 0.963947i \(0.414267\pi\)
\(6\) 0 0
\(7\) −19.8837 8.23610i −1.07362 0.444707i −0.225352 0.974277i \(-0.572353\pi\)
−0.848266 + 0.529570i \(0.822353\pi\)
\(8\) 2.56978 2.56978i 0.113569 0.113569i
\(9\) 0 0
\(10\) −0.579266 0.239940i −0.0183180 0.00758756i
\(11\) −20.8709 + 50.3869i −0.572075 + 1.38111i 0.327711 + 0.944778i \(0.393723\pi\)
−0.899785 + 0.436333i \(0.856277\pi\)
\(12\) 0 0
\(13\) 52.4827i 1.11970i 0.828594 + 0.559850i \(0.189141\pi\)
−0.828594 + 0.559850i \(0.810859\pi\)
\(14\) −1.87682 4.53105i −0.0358287 0.0864982i
\(15\) 0 0
\(16\) −62.7564 −0.980569
\(17\) −33.5380 61.5484i −0.478479 0.878099i
\(18\) 0 0
\(19\) 13.8808 + 13.8808i 0.167604 + 0.167604i 0.785925 0.618321i \(-0.212187\pi\)
−0.618321 + 0.785925i \(0.712187\pi\)
\(20\) 8.36878 + 20.2040i 0.0935658 + 0.225888i
\(21\) 0 0
\(22\) −11.4821 + 4.75602i −0.111272 + 0.0460903i
\(23\) 5.33276 12.8744i 0.0483460 0.116717i −0.897862 0.440278i \(-0.854880\pi\)
0.946207 + 0.323560i \(0.104880\pi\)
\(24\) 0 0
\(25\) −83.0352 + 83.0352i −0.664282 + 0.664282i
\(26\) −8.45675 + 8.45675i −0.0637886 + 0.0637886i
\(27\) 0 0
\(28\) −65.4611 + 158.037i −0.441821 + 1.06665i
\(29\) −64.6920 + 26.7963i −0.414241 + 0.171584i −0.580063 0.814571i \(-0.696972\pi\)
0.165822 + 0.986156i \(0.446972\pi\)
\(30\) 0 0
\(31\) −63.9131 154.300i −0.370295 0.893971i −0.993700 0.112072i \(-0.964251\pi\)
0.623405 0.781899i \(-0.285749\pi\)
\(32\) −30.6704 30.6704i −0.169432 0.169432i
\(33\) 0 0
\(34\) 4.51343 15.3216i 0.0227661 0.0772835i
\(35\) 59.2165 0.285983
\(36\) 0 0
\(37\) −76.0152 183.517i −0.337752 0.815405i −0.997931 0.0642968i \(-0.979520\pi\)
0.660179 0.751108i \(-0.270480\pi\)
\(38\) 4.47334i 0.0190966i
\(39\) 0 0
\(40\) −3.82658 + 9.23817i −0.0151259 + 0.0365171i
\(41\) −401.250 166.203i −1.52841 0.633087i −0.549153 0.835722i \(-0.685050\pi\)
−0.979254 + 0.202634i \(0.935050\pi\)
\(42\) 0 0
\(43\) 89.9025 89.9025i 0.318837 0.318837i −0.529483 0.848320i \(-0.677614\pi\)
0.848320 + 0.529483i \(0.177614\pi\)
\(44\) 400.479 + 165.884i 1.37215 + 0.568361i
\(45\) 0 0
\(46\) 2.93379 1.21522i 0.00940357 0.00389509i
\(47\) 207.303i 0.643366i 0.946847 + 0.321683i \(0.104249\pi\)
−0.946847 + 0.321683i \(0.895751\pi\)
\(48\) 0 0
\(49\) 84.9906 + 84.9906i 0.247786 + 0.247786i
\(50\) −26.7596 −0.0756875
\(51\) 0 0
\(52\) 417.136 1.11243
\(53\) 220.673 + 220.673i 0.571920 + 0.571920i 0.932665 0.360745i \(-0.117477\pi\)
−0.360745 + 0.932665i \(0.617477\pi\)
\(54\) 0 0
\(55\) 150.059i 0.367891i
\(56\) −72.2616 + 29.9317i −0.172435 + 0.0714249i
\(57\) 0 0
\(58\) −14.7419 6.10628i −0.0333742 0.0138240i
\(59\) 407.819 407.819i 0.899890 0.899890i −0.0955362 0.995426i \(-0.530457\pi\)
0.995426 + 0.0955362i \(0.0304566\pi\)
\(60\) 0 0
\(61\) 72.4205 + 29.9976i 0.152008 + 0.0629639i 0.457390 0.889266i \(-0.348784\pi\)
−0.305382 + 0.952230i \(0.598784\pi\)
\(62\) 14.5644 35.1615i 0.0298335 0.0720245i
\(63\) 0 0
\(64\) 492.167i 0.961264i
\(65\) −55.2607 133.411i −0.105450 0.254579i
\(66\) 0 0
\(67\) 359.997 0.656428 0.328214 0.944603i \(-0.393553\pi\)
0.328214 + 0.944603i \(0.393553\pi\)
\(68\) −489.191 + 266.562i −0.872399 + 0.475373i
\(69\) 0 0
\(70\) 9.54178 + 9.54178i 0.0162923 + 0.0162923i
\(71\) −81.5842 196.962i −0.136370 0.329226i 0.840911 0.541173i \(-0.182020\pi\)
−0.977281 + 0.211947i \(0.932020\pi\)
\(72\) 0 0
\(73\) 26.8357 11.1157i 0.0430258 0.0178219i −0.361067 0.932540i \(-0.617587\pi\)
0.404093 + 0.914718i \(0.367587\pi\)
\(74\) 17.3222 41.8194i 0.0272116 0.0656947i
\(75\) 0 0
\(76\) 110.326 110.326i 0.166516 0.166516i
\(77\) 829.983 829.983i 1.22838 1.22838i
\(78\) 0 0
\(79\) 327.389 790.386i 0.466254 1.12564i −0.499531 0.866296i \(-0.666494\pi\)
0.965786 0.259342i \(-0.0835056\pi\)
\(80\) 159.527 66.0782i 0.222946 0.0923471i
\(81\) 0 0
\(82\) −37.8740 91.4360i −0.0510059 0.123139i
\(83\) −9.67821 9.67821i −0.0127991 0.0127991i 0.700678 0.713477i \(-0.252881\pi\)
−0.713477 + 0.700678i \(0.752881\pi\)
\(84\) 0 0
\(85\) 150.060 + 121.143i 0.191486 + 0.154586i
\(86\) 28.9727 0.0363280
\(87\) 0 0
\(88\) 75.8494 + 183.117i 0.0918815 + 0.221822i
\(89\) 651.126i 0.775497i 0.921765 + 0.387748i \(0.126747\pi\)
−0.921765 + 0.387748i \(0.873253\pi\)
\(90\) 0 0
\(91\) 432.253 1043.55i 0.497939 1.20213i
\(92\) −102.327 42.3851i −0.115960 0.0480321i
\(93\) 0 0
\(94\) −33.4035 + 33.4035i −0.0366522 + 0.0366522i
\(95\) −49.9006 20.6695i −0.0538915 0.0223226i
\(96\) 0 0
\(97\) −1107.41 + 458.705i −1.15918 + 0.480149i −0.877602 0.479389i \(-0.840858\pi\)
−0.281579 + 0.959538i \(0.590858\pi\)
\(98\) 27.3897i 0.0282325i
\(99\) 0 0
\(100\) 659.970 + 659.970i 0.659970 + 0.659970i
\(101\) −89.2435 −0.0879214 −0.0439607 0.999033i \(-0.513998\pi\)
−0.0439607 + 0.999033i \(0.513998\pi\)
\(102\) 0 0
\(103\) −1242.17 −1.18830 −0.594150 0.804354i \(-0.702511\pi\)
−0.594150 + 0.804354i \(0.702511\pi\)
\(104\) 134.869 + 134.869i 0.127163 + 0.127163i
\(105\) 0 0
\(106\) 71.1158i 0.0651639i
\(107\) −1420.54 + 588.407i −1.28345 + 0.531621i −0.917025 0.398829i \(-0.869417\pi\)
−0.366420 + 0.930449i \(0.619417\pi\)
\(108\) 0 0
\(109\) 95.9730 + 39.7533i 0.0843353 + 0.0349328i 0.424452 0.905450i \(-0.360467\pi\)
−0.340117 + 0.940383i \(0.610467\pi\)
\(110\) 24.1796 24.1796i 0.0209585 0.0209585i
\(111\) 0 0
\(112\) 1247.83 + 516.868i 1.05276 + 0.436066i
\(113\) 140.908 340.183i 0.117306 0.283201i −0.854311 0.519762i \(-0.826020\pi\)
0.971617 + 0.236562i \(0.0760205\pi\)
\(114\) 0 0
\(115\) 38.3418i 0.0310904i
\(116\) 212.979 + 514.176i 0.170471 + 0.411552i
\(117\) 0 0
\(118\) 131.427 0.102532
\(119\) 159.940 + 1500.03i 0.123207 + 1.15553i
\(120\) 0 0
\(121\) −1162.08 1162.08i −0.873091 0.873091i
\(122\) 6.83578 + 16.5030i 0.00507281 + 0.0122468i
\(123\) 0 0
\(124\) −1226.39 + 507.986i −0.888168 + 0.367891i
\(125\) 255.262 616.256i 0.182650 0.440957i
\(126\) 0 0
\(127\) −886.309 + 886.309i −0.619269 + 0.619269i −0.945344 0.326075i \(-0.894274\pi\)
0.326075 + 0.945344i \(0.394274\pi\)
\(128\) −324.668 + 324.668i −0.224194 + 0.224194i
\(129\) 0 0
\(130\) 12.5927 30.4014i 0.00849578 0.0205106i
\(131\) 1806.01 748.072i 1.20452 0.498927i 0.312060 0.950062i \(-0.398981\pi\)
0.892455 + 0.451136i \(0.148981\pi\)
\(132\) 0 0
\(133\) −161.678 390.326i −0.105408 0.254478i
\(134\) 58.0078 + 58.0078i 0.0373963 + 0.0373963i
\(135\) 0 0
\(136\) −244.351 71.9806i −0.154065 0.0453844i
\(137\) −1749.91 −1.09127 −0.545637 0.838022i \(-0.683712\pi\)
−0.545637 + 0.838022i \(0.683712\pi\)
\(138\) 0 0
\(139\) 78.9509 + 190.604i 0.0481765 + 0.116308i 0.946136 0.323770i \(-0.104951\pi\)
−0.897959 + 0.440079i \(0.854951\pi\)
\(140\) 470.657i 0.284127i
\(141\) 0 0
\(142\) 18.5912 44.8832i 0.0109869 0.0265248i
\(143\) −2644.44 1095.36i −1.54643 0.640552i
\(144\) 0 0
\(145\) 136.232 136.232i 0.0780241 0.0780241i
\(146\) 6.11526 + 2.53303i 0.00346646 + 0.00143585i
\(147\) 0 0
\(148\) −1458.61 + 604.174i −0.810112 + 0.335559i
\(149\) 2013.39i 1.10700i −0.832849 0.553501i \(-0.813292\pi\)
0.832849 0.553501i \(-0.186708\pi\)
\(150\) 0 0
\(151\) 53.4946 + 53.4946i 0.0288300 + 0.0288300i 0.721375 0.692545i \(-0.243511\pi\)
−0.692545 + 0.721375i \(0.743511\pi\)
\(152\) 71.3412 0.0380693
\(153\) 0 0
\(154\) 267.477 0.139960
\(155\) 324.935 + 324.935i 0.168383 + 0.168383i
\(156\) 0 0
\(157\) 2301.81i 1.17009i 0.811000 + 0.585046i \(0.198924\pi\)
−0.811000 + 0.585046i \(0.801076\pi\)
\(158\) 180.111 74.6046i 0.0906892 0.0375647i
\(159\) 0 0
\(160\) 110.258 + 45.6704i 0.0544791 + 0.0225660i
\(161\) −212.070 + 212.070i −0.103810 + 0.103810i
\(162\) 0 0
\(163\) −1748.91 724.420i −0.840398 0.348104i −0.0793874 0.996844i \(-0.525296\pi\)
−0.761010 + 0.648740i \(0.775296\pi\)
\(164\) −1320.99 + 3189.16i −0.628978 + 1.51849i
\(165\) 0 0
\(166\) 3.11898i 0.00145831i
\(167\) −41.5126 100.220i −0.0192356 0.0464388i 0.913970 0.405782i \(-0.133001\pi\)
−0.933205 + 0.359343i \(0.883001\pi\)
\(168\) 0 0
\(169\) −557.436 −0.253726
\(170\) 4.65948 + 43.7000i 0.00210215 + 0.0197155i
\(171\) 0 0
\(172\) −714.551 714.551i −0.316768 0.316768i
\(173\) 1054.59 + 2546.01i 0.463463 + 1.11890i 0.966966 + 0.254905i \(0.0820441\pi\)
−0.503504 + 0.863993i \(0.667956\pi\)
\(174\) 0 0
\(175\) 2334.93 967.161i 1.00860 0.417774i
\(176\) 1309.78 3162.10i 0.560959 1.35427i
\(177\) 0 0
\(178\) −104.918 + 104.918i −0.0441796 + 0.0441796i
\(179\) 1418.56 1418.56i 0.592337 0.592337i −0.345925 0.938262i \(-0.612435\pi\)
0.938262 + 0.345925i \(0.112435\pi\)
\(180\) 0 0
\(181\) −927.705 + 2239.68i −0.380971 + 0.919745i 0.610808 + 0.791779i \(0.290845\pi\)
−0.991779 + 0.127966i \(0.959155\pi\)
\(182\) 237.802 98.5008i 0.0968520 0.0401174i
\(183\) 0 0
\(184\) −19.3804 46.7883i −0.00776489 0.0187461i
\(185\) 386.461 + 386.461i 0.153585 + 0.153585i
\(186\) 0 0
\(187\) 3801.20 405.300i 1.48648 0.158495i
\(188\) 1647.66 0.639190
\(189\) 0 0
\(190\) −4.71012 11.3712i −0.00179846 0.00434188i
\(191\) 4153.64i 1.57354i 0.617243 + 0.786772i \(0.288249\pi\)
−0.617243 + 0.786772i \(0.711751\pi\)
\(192\) 0 0
\(193\) 794.611 1918.36i 0.296360 0.715475i −0.703628 0.710568i \(-0.748438\pi\)
0.999988 0.00490706i \(-0.00156197\pi\)
\(194\) −252.355 104.529i −0.0933917 0.0386841i
\(195\) 0 0
\(196\) 675.511 675.511i 0.246178 0.246178i
\(197\) −3513.98 1455.54i −1.27087 0.526410i −0.357638 0.933860i \(-0.616418\pi\)
−0.913227 + 0.407450i \(0.866418\pi\)
\(198\) 0 0
\(199\) 3346.19 1386.04i 1.19199 0.493736i 0.303584 0.952805i \(-0.401817\pi\)
0.888401 + 0.459068i \(0.151817\pi\)
\(200\) 426.764i 0.150884i
\(201\) 0 0
\(202\) −14.3802 14.3802i −0.00500883 0.00500883i
\(203\) 1507.01 0.521042
\(204\) 0 0
\(205\) 1194.98 0.407127
\(206\) −200.156 200.156i −0.0676968 0.0676968i
\(207\) 0 0
\(208\) 3293.63i 1.09794i
\(209\) −989.117 + 409.706i −0.327362 + 0.135598i
\(210\) 0 0
\(211\) −584.358 242.049i −0.190658 0.0789732i 0.285312 0.958435i \(-0.407903\pi\)
−0.475970 + 0.879462i \(0.657903\pi\)
\(212\) 1753.92 1753.92i 0.568207 0.568207i
\(213\) 0 0
\(214\) −323.709 134.085i −0.103403 0.0428311i
\(215\) −133.871 + 323.193i −0.0424648 + 0.102519i
\(216\) 0 0
\(217\) 3594.45i 1.12446i
\(218\) 9.05890 + 21.8701i 0.00281443 + 0.00679464i
\(219\) 0 0
\(220\) −1192.68 −0.365503
\(221\) 3230.23 1760.16i 0.983206 0.535753i
\(222\) 0 0
\(223\) 377.462 + 377.462i 0.113348 + 0.113348i 0.761506 0.648158i \(-0.224460\pi\)
−0.648158 + 0.761506i \(0.724460\pi\)
\(224\) 357.237 + 862.445i 0.106557 + 0.257252i
\(225\) 0 0
\(226\) 77.5201 32.1099i 0.0228166 0.00945096i
\(227\) −225.340 + 544.019i −0.0658870 + 0.159065i −0.953393 0.301730i \(-0.902436\pi\)
0.887506 + 0.460795i \(0.152436\pi\)
\(228\) 0 0
\(229\) 1867.57 1867.57i 0.538920 0.538920i −0.384292 0.923212i \(-0.625554\pi\)
0.923212 + 0.384292i \(0.125554\pi\)
\(230\) −6.17817 + 6.17817i −0.00177120 + 0.00177120i
\(231\) 0 0
\(232\) −97.3834 + 235.104i −0.0275583 + 0.0665317i
\(233\) −354.195 + 146.712i −0.0995882 + 0.0412508i −0.431921 0.901911i \(-0.642164\pi\)
0.332333 + 0.943162i \(0.392164\pi\)
\(234\) 0 0
\(235\) −218.276 526.964i −0.0605904 0.146278i
\(236\) −3241.37 3241.37i −0.894049 0.894049i
\(237\) 0 0
\(238\) −215.934 + 267.478i −0.0588107 + 0.0728488i
\(239\) 4344.62 1.17586 0.587929 0.808913i \(-0.299944\pi\)
0.587929 + 0.808913i \(0.299944\pi\)
\(240\) 0 0
\(241\) −785.906 1897.34i −0.210061 0.507131i 0.783371 0.621554i \(-0.213498\pi\)
−0.993432 + 0.114422i \(0.963498\pi\)
\(242\) 374.502i 0.0994790i
\(243\) 0 0
\(244\) 238.423 575.604i 0.0625552 0.151022i
\(245\) −305.535 126.557i −0.0796732 0.0330017i
\(246\) 0 0
\(247\) −728.503 + 728.503i −0.187666 + 0.187666i
\(248\) −560.759 232.274i −0.143581 0.0594734i
\(249\) 0 0
\(250\) 140.431 58.1685i 0.0355266 0.0147156i
\(251\) 907.953i 0.228325i 0.993462 + 0.114162i \(0.0364184\pi\)
−0.993462 + 0.114162i \(0.963582\pi\)
\(252\) 0 0
\(253\) 537.402 + 537.402i 0.133542 + 0.133542i
\(254\) −285.629 −0.0705589
\(255\) 0 0
\(256\) 3832.71 0.935720
\(257\) −5296.81 5296.81i −1.28563 1.28563i −0.937417 0.348209i \(-0.886790\pi\)
−0.348209 0.937417i \(-0.613210\pi\)
\(258\) 0 0
\(259\) 4275.06i 1.02564i
\(260\) −1060.36 + 439.216i −0.252926 + 0.104765i
\(261\) 0 0
\(262\) 411.549 + 170.469i 0.0970441 + 0.0401970i
\(263\) 5558.34 5558.34i 1.30320 1.30320i 0.376982 0.926221i \(-0.376962\pi\)
0.926221 0.376982i \(-0.123038\pi\)
\(264\) 0 0
\(265\) −793.304 328.597i −0.183895 0.0761720i
\(266\) 36.8429 88.9466i 0.00849241 0.0205025i
\(267\) 0 0
\(268\) 2861.29i 0.652167i
\(269\) 2890.74 + 6978.86i 0.655210 + 1.58182i 0.805117 + 0.593116i \(0.202102\pi\)
−0.149908 + 0.988700i \(0.547898\pi\)
\(270\) 0 0
\(271\) 6394.46 1.43334 0.716672 0.697411i \(-0.245665\pi\)
0.716672 + 0.697411i \(0.245665\pi\)
\(272\) 2104.72 + 3862.56i 0.469182 + 0.861037i
\(273\) 0 0
\(274\) −281.969 281.969i −0.0621693 0.0621693i
\(275\) −2450.86 5916.91i −0.537428 1.29747i
\(276\) 0 0
\(277\) −6247.84 + 2587.94i −1.35522 + 0.561351i −0.937741 0.347335i \(-0.887087\pi\)
−0.417480 + 0.908686i \(0.637087\pi\)
\(278\) −17.9912 + 43.4345i −0.00388143 + 0.00937061i
\(279\) 0 0
\(280\) 152.173 152.173i 0.0324788 0.0324788i
\(281\) −4453.39 + 4453.39i −0.945433 + 0.945433i −0.998586 0.0531529i \(-0.983073\pi\)
0.0531529 + 0.998586i \(0.483073\pi\)
\(282\) 0 0
\(283\) −1022.77 + 2469.18i −0.214831 + 0.518648i −0.994154 0.107975i \(-0.965563\pi\)
0.779323 + 0.626623i \(0.215563\pi\)
\(284\) −1565.47 + 648.437i −0.327089 + 0.135485i
\(285\) 0 0
\(286\) −249.609 602.609i −0.0516073 0.124591i
\(287\) 6609.47 + 6609.47i 1.35939 + 1.35939i
\(288\) 0 0
\(289\) −2663.41 + 4128.41i −0.542115 + 0.840304i
\(290\) 43.9033 0.00888998
\(291\) 0 0
\(292\) −88.3485 213.292i −0.0177062 0.0427465i
\(293\) 2183.30i 0.435323i 0.976024 + 0.217661i \(0.0698428\pi\)
−0.976024 + 0.217661i \(0.930157\pi\)
\(294\) 0 0
\(295\) −607.271 + 1466.08i −0.119853 + 0.289351i
\(296\) −666.939 276.255i −0.130963 0.0542467i
\(297\) 0 0
\(298\) 324.425 324.425i 0.0630653 0.0630653i
\(299\) 675.684 + 279.878i 0.130688 + 0.0541329i
\(300\) 0 0
\(301\) −2528.04 + 1047.15i −0.484099 + 0.200520i
\(302\) 17.2396i 0.00328485i
\(303\) 0 0
\(304\) −871.110 871.110i −0.164347 0.164347i
\(305\) −215.679 −0.0404909
\(306\) 0 0
\(307\) −3905.30 −0.726018 −0.363009 0.931786i \(-0.618250\pi\)
−0.363009 + 0.931786i \(0.618250\pi\)
\(308\) −6596.76 6596.76i −1.22041 1.22041i
\(309\) 0 0
\(310\) 104.716i 0.0191854i
\(311\) −6806.60 + 2819.39i −1.24105 + 0.514060i −0.904043 0.427441i \(-0.859415\pi\)
−0.337008 + 0.941502i \(0.609415\pi\)
\(312\) 0 0
\(313\) −2149.71 890.438i −0.388207 0.160800i 0.180039 0.983659i \(-0.442378\pi\)
−0.568246 + 0.822859i \(0.692378\pi\)
\(314\) −370.900 + 370.900i −0.0666595 + 0.0666595i
\(315\) 0 0
\(316\) −6282.05 2602.11i −1.11833 0.463228i
\(317\) −2858.75 + 6901.62i −0.506508 + 1.22282i 0.439372 + 0.898305i \(0.355201\pi\)
−0.945881 + 0.324514i \(0.894799\pi\)
\(318\) 0 0
\(319\) 3818.89i 0.670272i
\(320\) −518.218 1251.09i −0.0905290 0.218556i
\(321\) 0 0
\(322\) −68.3433 −0.0118280
\(323\) 388.808 1319.88i 0.0669779 0.227368i
\(324\) 0 0
\(325\) −4357.92 4357.92i −0.743796 0.743796i
\(326\) −165.079 398.537i −0.0280457 0.0677083i
\(327\) 0 0
\(328\) −1458.23 + 604.017i −0.245479 + 0.101681i
\(329\) 1707.37 4121.95i 0.286110 0.690730i
\(330\) 0 0
\(331\) 6613.70 6613.70i 1.09825 1.09825i 0.103637 0.994615i \(-0.466952\pi\)
0.994615 0.103637i \(-0.0330482\pi\)
\(332\) −76.9231 + 76.9231i −0.0127160 + 0.0127160i
\(333\) 0 0
\(334\) 9.45981 22.8380i 0.00154975 0.00374143i
\(335\) −915.114 + 379.053i −0.149248 + 0.0618205i
\(336\) 0 0
\(337\) 2657.39 + 6415.50i 0.429546 + 1.03702i 0.979432 + 0.201776i \(0.0646714\pi\)
−0.549885 + 0.835240i \(0.685329\pi\)
\(338\) −89.8218 89.8218i −0.0144546 0.0144546i
\(339\) 0 0
\(340\) 962.853 1192.69i 0.153582 0.190243i
\(341\) 9108.62 1.44651
\(342\) 0 0
\(343\) 1835.05 + 4430.19i 0.288872 + 0.697399i
\(344\) 462.058i 0.0724201i
\(345\) 0 0
\(346\) −240.318 + 580.178i −0.0373398 + 0.0901462i
\(347\) −2226.53 922.261i −0.344457 0.142679i 0.203747 0.979024i \(-0.434688\pi\)
−0.548204 + 0.836345i \(0.684688\pi\)
\(348\) 0 0
\(349\) −7781.94 + 7781.94i −1.19357 + 1.19357i −0.217518 + 0.976056i \(0.569796\pi\)
−0.976056 + 0.217518i \(0.930204\pi\)
\(350\) 532.080 + 220.395i 0.0812596 + 0.0336588i
\(351\) 0 0
\(352\) 2185.51 905.266i 0.330931 0.137076i
\(353\) 7713.23i 1.16299i 0.813552 + 0.581493i \(0.197531\pi\)
−0.813552 + 0.581493i \(0.802469\pi\)
\(354\) 0 0
\(355\) 414.775 + 414.775i 0.0620111 + 0.0620111i
\(356\) 5175.20 0.770463
\(357\) 0 0
\(358\) 457.157 0.0674902
\(359\) −7226.67 7226.67i −1.06242 1.06242i −0.997917 0.0645037i \(-0.979454\pi\)
−0.0645037 0.997917i \(-0.520546\pi\)
\(360\) 0 0
\(361\) 6473.65i 0.943818i
\(362\) −510.373 + 211.403i −0.0741011 + 0.0306937i
\(363\) 0 0
\(364\) −8294.22 3435.58i −1.19433 0.494706i
\(365\) −56.5124 + 56.5124i −0.00810409 + 0.00810409i
\(366\) 0 0
\(367\) 9536.68 + 3950.22i 1.35643 + 0.561853i 0.938076 0.346430i \(-0.112606\pi\)
0.418356 + 0.908283i \(0.362606\pi\)
\(368\) −334.665 + 807.952i −0.0474065 + 0.114450i
\(369\) 0 0
\(370\) 124.544i 0.0174993i
\(371\) −2570.31 6205.27i −0.359687 0.868361i
\(372\) 0 0
\(373\) −2744.09 −0.380921 −0.190461 0.981695i \(-0.560998\pi\)
−0.190461 + 0.981695i \(0.560998\pi\)
\(374\) 677.810 + 547.195i 0.0937132 + 0.0756545i
\(375\) 0 0
\(376\) 532.722 + 532.722i 0.0730666 + 0.0730666i
\(377\) −1406.34 3395.21i −0.192123 0.463826i
\(378\) 0 0
\(379\) −5917.45 + 2451.09i −0.802003 + 0.332200i −0.745758 0.666217i \(-0.767913\pi\)
−0.0562446 + 0.998417i \(0.517913\pi\)
\(380\) −164.283 + 396.614i −0.0221777 + 0.0535417i
\(381\) 0 0
\(382\) −669.293 + 669.293i −0.0896440 + 0.0896440i
\(383\) 2611.23 2611.23i 0.348375 0.348375i −0.511129 0.859504i \(-0.670773\pi\)
0.859504 + 0.511129i \(0.170773\pi\)
\(384\) 0 0
\(385\) −1235.90 + 2983.73i −0.163604 + 0.394974i
\(386\) 437.152 181.074i 0.0576437 0.0238768i
\(387\) 0 0
\(388\) 3645.82 + 8801.79i 0.477032 + 1.15166i
\(389\) 1508.22 + 1508.22i 0.196581 + 0.196581i 0.798532 0.601952i \(-0.205610\pi\)
−0.601952 + 0.798532i \(0.705610\pi\)
\(390\) 0 0
\(391\) −971.250 + 103.559i −0.125622 + 0.0133944i
\(392\) 436.813 0.0562816
\(393\) 0 0
\(394\) −331.685 800.758i −0.0424112 0.102390i
\(395\) 2353.88i 0.299840i
\(396\) 0 0
\(397\) −904.995 + 2184.85i −0.114409 + 0.276208i −0.970704 0.240280i \(-0.922761\pi\)
0.856295 + 0.516488i \(0.172761\pi\)
\(398\) 762.522 + 315.847i 0.0960346 + 0.0397788i
\(399\) 0 0
\(400\) 5210.99 5210.99i 0.651374 0.651374i
\(401\) −1906.65 789.759i −0.237440 0.0983509i 0.260791 0.965395i \(-0.416017\pi\)
−0.498231 + 0.867044i \(0.666017\pi\)
\(402\) 0 0
\(403\) 8098.08 3354.33i 1.00098 0.414619i
\(404\) 709.314i 0.0873507i
\(405\) 0 0
\(406\) 242.831 + 242.831i 0.0296835 + 0.0296835i
\(407\) 10833.4 1.31938
\(408\) 0 0
\(409\) 9245.03 1.11769 0.558847 0.829271i \(-0.311244\pi\)
0.558847 + 0.829271i \(0.311244\pi\)
\(410\) 192.552 + 192.552i 0.0231938 + 0.0231938i
\(411\) 0 0
\(412\) 9872.87i 1.18059i
\(413\) −11467.8 + 4750.11i −1.36633 + 0.565951i
\(414\) 0 0
\(415\) 34.7925 + 14.4115i 0.00411542 + 0.00170466i
\(416\) 1609.67 1609.67i 0.189712 0.189712i
\(417\) 0 0
\(418\) −225.398 93.3628i −0.0263746 0.0109247i
\(419\) −1590.19 + 3839.06i −0.185408 + 0.447614i −0.989065 0.147478i \(-0.952884\pi\)
0.803657 + 0.595092i \(0.202884\pi\)
\(420\) 0 0
\(421\) 4609.26i 0.533591i −0.963753 0.266795i \(-0.914035\pi\)
0.963753 0.266795i \(-0.0859648\pi\)
\(422\) −55.1576 133.162i −0.00636263 0.0153608i
\(423\) 0 0
\(424\) 1134.16 0.129905
\(425\) 7895.52 + 2325.85i 0.901150 + 0.265460i
\(426\) 0 0
\(427\) −1192.93 1192.93i −0.135198 0.135198i
\(428\) 4676.70 + 11290.5i 0.528170 + 1.27511i
\(429\) 0 0
\(430\) −73.6486 + 30.5063i −0.00825965 + 0.00342126i
\(431\) 6632.04 16011.2i 0.741193 1.78940i 0.140235 0.990118i \(-0.455214\pi\)
0.600958 0.799281i \(-0.294786\pi\)
\(432\) 0 0
\(433\) 8028.41 8028.41i 0.891041 0.891041i −0.103580 0.994621i \(-0.533030\pi\)
0.994621 + 0.103580i \(0.0330297\pi\)
\(434\) −579.188 + 579.188i −0.0640597 + 0.0640597i
\(435\) 0 0
\(436\) 315.962 762.801i 0.0347061 0.0837879i
\(437\) 252.730 104.684i 0.0276653 0.0114593i
\(438\) 0 0
\(439\) −1962.43 4737.72i −0.213352 0.515078i 0.780582 0.625053i \(-0.214923\pi\)
−0.993934 + 0.109975i \(0.964923\pi\)
\(440\) −385.619 385.619i −0.0417810 0.0417810i
\(441\) 0 0
\(442\) 804.121 + 236.877i 0.0865343 + 0.0254912i
\(443\) 3133.00 0.336012 0.168006 0.985786i \(-0.446267\pi\)
0.168006 + 0.985786i \(0.446267\pi\)
\(444\) 0 0
\(445\) −685.591 1655.16i −0.0730340 0.176320i
\(446\) 121.644i 0.0129148i
\(447\) 0 0
\(448\) 4053.54 9786.11i 0.427481 1.03203i
\(449\) −10855.2 4496.37i −1.14095 0.472599i −0.269464 0.963010i \(-0.586846\pi\)
−0.871491 + 0.490411i \(0.836846\pi\)
\(450\) 0 0
\(451\) 16748.9 16748.9i 1.74873 1.74873i
\(452\) −2703.80 1119.95i −0.281363 0.116544i
\(453\) 0 0
\(454\) −123.970 + 51.3500i −0.0128154 + 0.00530831i
\(455\) 3107.84i 0.320215i
\(456\) 0 0
\(457\) −8774.30 8774.30i −0.898128 0.898128i 0.0971425 0.995270i \(-0.469030\pi\)
−0.995270 + 0.0971425i \(0.969030\pi\)
\(458\) 601.859 0.0614039
\(459\) 0 0
\(460\) 304.744 0.0308886
\(461\) −5211.73 5211.73i −0.526539 0.526539i 0.393000 0.919539i \(-0.371437\pi\)
−0.919539 + 0.393000i \(0.871437\pi\)
\(462\) 0 0
\(463\) 11446.9i 1.14899i 0.818508 + 0.574495i \(0.194802\pi\)
−0.818508 + 0.574495i \(0.805198\pi\)
\(464\) 4059.84 1681.64i 0.406192 0.168250i
\(465\) 0 0
\(466\) −80.7131 33.4325i −0.00802352 0.00332345i
\(467\) −3124.20 + 3124.20i −0.309573 + 0.309573i −0.844744 0.535171i \(-0.820247\pi\)
0.535171 + 0.844744i \(0.320247\pi\)
\(468\) 0 0
\(469\) −7158.08 2964.97i −0.704754 0.291919i
\(470\) 49.7402 120.083i 0.00488158 0.0117852i
\(471\) 0 0
\(472\) 2096.01i 0.204399i
\(473\) 2653.56 + 6406.25i 0.257951 + 0.622748i
\(474\) 0 0
\(475\) −2305.19 −0.222673
\(476\) 11922.4 1271.21i 1.14803 0.122407i
\(477\) 0 0
\(478\) 700.065 + 700.065i 0.0669879 + 0.0669879i
\(479\) 108.152 + 261.102i 0.0103165 + 0.0249062i 0.928954 0.370196i \(-0.120709\pi\)
−0.918637 + 0.395102i \(0.870709\pi\)
\(480\) 0 0
\(481\) 9631.46 3989.48i 0.913008 0.378180i
\(482\) 179.090 432.363i 0.0169240 0.0408580i
\(483\) 0 0
\(484\) −9236.32 + 9236.32i −0.867423 + 0.867423i
\(485\) 2332.06 2332.06i 0.218337 0.218337i
\(486\) 0 0
\(487\) −2909.21 + 7023.45i −0.270696 + 0.653518i −0.999513 0.0311903i \(-0.990070\pi\)
0.728818 + 0.684708i \(0.240070\pi\)
\(488\) 263.192 109.018i 0.0244142 0.0101127i
\(489\) 0 0
\(490\) −28.8395 69.6247i −0.00265885 0.00641903i
\(491\) 9075.67 + 9075.67i 0.834174 + 0.834174i 0.988085 0.153911i \(-0.0491870\pi\)
−0.153911 + 0.988085i \(0.549187\pi\)
\(492\) 0 0
\(493\) 3818.91 + 3082.99i 0.348874 + 0.281645i
\(494\) −234.773 −0.0213825
\(495\) 0 0
\(496\) 4010.96 + 9683.31i 0.363100 + 0.876600i
\(497\) 4588.27i 0.414108i
\(498\) 0 0
\(499\) 1039.84 2510.39i 0.0932855 0.225211i −0.870349 0.492436i \(-0.836107\pi\)
0.963634 + 0.267225i \(0.0861066\pi\)
\(500\) −4898.05 2028.84i −0.438095 0.181465i
\(501\) 0 0
\(502\) −146.302 + 146.302i −0.0130075 + 0.0130075i
\(503\) −7589.15 3143.53i −0.672731 0.278654i 0.0200537 0.999799i \(-0.493616\pi\)
−0.692784 + 0.721145i \(0.743616\pi\)
\(504\) 0 0
\(505\) 226.857 93.9673i 0.0199901 0.00828018i
\(506\) 173.187i 0.0152157i
\(507\) 0 0
\(508\) 7044.45 + 7044.45i 0.615250 + 0.615250i
\(509\) −8243.18 −0.717824 −0.358912 0.933371i \(-0.616852\pi\)
−0.358912 + 0.933371i \(0.616852\pi\)
\(510\) 0 0
\(511\) −625.144 −0.0541188
\(512\) 3214.92 + 3214.92i 0.277502 + 0.277502i
\(513\) 0 0
\(514\) 1706.99i 0.146483i
\(515\) 3157.60 1307.92i 0.270176 0.111911i
\(516\) 0 0
\(517\) −10445.3 4326.60i −0.888560 0.368054i
\(518\) −688.858 + 688.858i −0.0584299 + 0.0584299i
\(519\) 0 0
\(520\) −484.844 200.829i −0.0408881 0.0169364i
\(521\) 3426.22 8271.63i 0.288110 0.695559i −0.711867 0.702314i \(-0.752150\pi\)
0.999977 + 0.00675482i \(0.00215014\pi\)
\(522\) 0 0
\(523\) 15665.1i 1.30973i 0.755747 + 0.654864i \(0.227274\pi\)
−0.755747 + 0.654864i \(0.772726\pi\)
\(524\) −5945.73 14354.3i −0.495688 1.19670i
\(525\) 0 0
\(526\) 1791.28 0.148485
\(527\) −7353.40 + 9108.65i −0.607816 + 0.752902i
\(528\) 0 0
\(529\) 8466.06 + 8466.06i 0.695821 + 0.695821i
\(530\) −74.8800 180.776i −0.00613694 0.0148159i
\(531\) 0 0
\(532\) −3102.34 + 1285.03i −0.252826 + 0.104724i
\(533\) 8722.79 21058.7i 0.708867 1.71136i
\(534\) 0 0
\(535\) 2991.46 2991.46i 0.241742 0.241742i
\(536\) 925.113 925.113i 0.0745500 0.0745500i
\(537\) 0 0
\(538\) −658.735 + 1590.33i −0.0527882 + 0.127442i
\(539\) −6056.24 + 2508.58i −0.483972 + 0.200468i
\(540\) 0 0
\(541\) −3547.46 8564.31i −0.281917 0.680607i 0.717963 0.696081i \(-0.245074\pi\)
−0.999880 + 0.0154734i \(0.995074\pi\)
\(542\) 1030.37 + 1030.37i 0.0816568 + 0.0816568i
\(543\) 0 0
\(544\) −859.092 + 2916.34i −0.0677082 + 0.229847i
\(545\) −285.821 −0.0224647
\(546\) 0 0
\(547\) −6005.27 14498.0i −0.469409 1.13325i −0.964422 0.264368i \(-0.914837\pi\)
0.495013 0.868886i \(-0.335163\pi\)
\(548\) 13908.4i 1.08419i
\(549\) 0 0
\(550\) 558.498 1348.33i 0.0432989 0.104533i
\(551\) −1269.93 526.023i −0.0981868 0.0406703i
\(552\) 0 0
\(553\) −13019.4 + 13019.4i −1.00116 + 1.00116i
\(554\) −1423.74 589.734i −0.109186 0.0452263i
\(555\) 0 0
\(556\) 1514.94 627.508i 0.115553 0.0478638i
\(557\) 3540.22i 0.269307i 0.990893 + 0.134654i \(0.0429922\pi\)
−0.990893 + 0.134654i \(0.957008\pi\)
\(558\) 0 0
\(559\) 4718.33 + 4718.33i 0.357002 + 0.357002i
\(560\) −3716.21 −0.280426
\(561\) 0 0
\(562\) −1435.18 −0.107722
\(563\) 222.747 + 222.747i 0.0166744 + 0.0166744i 0.715395 0.698720i \(-0.246247\pi\)
−0.698720 + 0.715395i \(0.746247\pi\)
\(564\) 0 0
\(565\) 1013.11i 0.0754371i
\(566\) −562.671 + 233.066i −0.0417859 + 0.0173083i
\(567\) 0 0
\(568\) −715.801 296.494i −0.0528773 0.0219025i
\(569\) 6032.76 6032.76i 0.444475 0.444475i −0.449038 0.893513i \(-0.648233\pi\)
0.893513 + 0.449038i \(0.148233\pi\)
\(570\) 0 0
\(571\) −8156.50 3378.53i −0.597791 0.247613i 0.0632073 0.998000i \(-0.479867\pi\)
−0.660999 + 0.750387i \(0.729867\pi\)
\(572\) −8706.03 + 21018.2i −0.636394 + 1.53639i
\(573\) 0 0
\(574\) 2130.02i 0.154887i
\(575\) 626.223 + 1511.84i 0.0454180 + 0.109649i
\(576\) 0 0
\(577\) −21726.1 −1.56754 −0.783769 0.621052i \(-0.786705\pi\)
−0.783769 + 0.621052i \(0.786705\pi\)
\(578\) −1094.39 + 236.062i −0.0787557 + 0.0169877i
\(579\) 0 0
\(580\) −1082.79 1082.79i −0.0775176 0.0775176i
\(581\) 112.728 + 272.149i 0.00804947 + 0.0194331i
\(582\) 0 0
\(583\) −15724.7 + 6513.37i −1.11707 + 0.462704i
\(584\) 40.3969 97.5267i 0.00286239 0.00691042i
\(585\) 0 0
\(586\) −351.803 + 351.803i −0.0248001 + 0.0248001i
\(587\) 17447.6 17447.6i 1.22682 1.22682i 0.261653 0.965162i \(-0.415732\pi\)
0.965162 0.261653i \(-0.0842678\pi\)
\(588\) 0 0
\(589\) 1254.64 3028.98i 0.0877702 0.211896i
\(590\) −334.087 + 138.384i −0.0233121 + 0.00965621i
\(591\) 0 0
\(592\) 4770.44 + 11516.9i 0.331189 + 0.799561i
\(593\) −6673.49 6673.49i −0.462137 0.462137i 0.437218 0.899356i \(-0.355964\pi\)
−0.899356 + 0.437218i \(0.855964\pi\)
\(594\) 0 0
\(595\) −1986.00 3644.68i −0.136837 0.251121i
\(596\) −16002.6 −1.09982
\(597\) 0 0
\(598\) 63.7779 + 153.973i 0.00436132 + 0.0105292i
\(599\) 28257.9i 1.92753i 0.266759 + 0.963763i \(0.414047\pi\)
−0.266759 + 0.963763i \(0.585953\pi\)
\(600\) 0 0
\(601\) 6674.25 16113.1i 0.452993 1.09362i −0.518186 0.855268i \(-0.673393\pi\)
0.971179 0.238353i \(-0.0766075\pi\)
\(602\) −576.084 238.622i −0.0390024 0.0161553i
\(603\) 0 0
\(604\) 425.179 425.179i 0.0286428 0.0286428i
\(605\) 4177.61 + 1730.42i 0.280734 + 0.116284i
\(606\) 0 0
\(607\) 418.146 173.202i 0.0279605 0.0115816i −0.368659 0.929565i \(-0.620183\pi\)
0.396620 + 0.917983i \(0.370183\pi\)
\(608\) 851.460i 0.0567948i
\(609\) 0 0
\(610\) −34.7531 34.7531i −0.00230674 0.00230674i
\(611\) −10879.8 −0.720377
\(612\) 0 0
\(613\) −10731.9 −0.707106 −0.353553 0.935415i \(-0.615027\pi\)
−0.353553 + 0.935415i \(0.615027\pi\)
\(614\) −629.277 629.277i −0.0413608 0.0413608i
\(615\) 0 0
\(616\) 4265.74i 0.279012i
\(617\) −18626.4 + 7715.29i −1.21535 + 0.503413i −0.895928 0.444200i \(-0.853488\pi\)
−0.319420 + 0.947613i \(0.603488\pi\)
\(618\) 0 0
\(619\) 2395.44 + 992.223i 0.155543 + 0.0644278i 0.459096 0.888386i \(-0.348173\pi\)
−0.303554 + 0.952814i \(0.598173\pi\)
\(620\) 2582.60 2582.60i 0.167290 0.167290i
\(621\) 0 0
\(622\) −1551.07 642.476i −0.0999877 0.0414163i
\(623\) 5362.74 12946.8i 0.344869 0.832588i
\(624\) 0 0
\(625\) 12843.4i 0.821977i
\(626\) −202.911 489.871i −0.0129552 0.0312766i
\(627\) 0 0
\(628\) 18295.0 1.16250
\(629\) −8745.78 + 10833.4i −0.554399 + 0.686734i
\(630\) 0 0
\(631\) −14799.4 14799.4i −0.933685 0.933685i 0.0642487 0.997934i \(-0.479535\pi\)
−0.997934 + 0.0642487i \(0.979535\pi\)
\(632\) −1189.80 2872.43i −0.0748856 0.180790i
\(633\) 0 0
\(634\) −1572.73 + 651.445i −0.0985188 + 0.0408078i
\(635\) 1319.78 3186.22i 0.0824783 0.199120i
\(636\) 0 0
\(637\) −4460.54 + 4460.54i −0.277446 + 0.277446i
\(638\) 615.353 615.353i 0.0381850 0.0381850i
\(639\) 0 0
\(640\) 483.453 1167.16i 0.0298596 0.0720876i
\(641\) 8975.50 3717.77i 0.553059 0.229085i −0.0886097 0.996066i \(-0.528242\pi\)
0.641669 + 0.766982i \(0.278242\pi\)
\(642\) 0 0
\(643\) −9268.20 22375.4i −0.568433 1.37232i −0.902876 0.429902i \(-0.858548\pi\)
0.334443 0.942416i \(-0.391452\pi\)
\(644\) 1685.55 + 1685.55i 0.103136 + 0.103136i
\(645\) 0 0
\(646\) 275.327 150.027i 0.0167687 0.00913734i
\(647\) −5143.07 −0.312511 −0.156256 0.987717i \(-0.549942\pi\)
−0.156256 + 0.987717i \(0.549942\pi\)
\(648\) 0 0
\(649\) 12037.2 + 29060.3i 0.728043 + 1.75765i
\(650\) 1404.42i 0.0847473i
\(651\) 0 0
\(652\) −5757.74 + 13900.4i −0.345845 + 0.834943i
\(653\) 2700.35 + 1118.52i 0.161827 + 0.0670308i 0.462126 0.886814i \(-0.347087\pi\)
−0.300300 + 0.953845i \(0.597087\pi\)
\(654\) 0 0
\(655\) −3803.20 + 3803.20i −0.226875 + 0.226875i
\(656\) 25181.0 + 10430.3i 1.49871 + 0.620786i
\(657\) 0 0
\(658\) 939.300 389.071i 0.0556500 0.0230510i
\(659\) 17368.4i 1.02667i −0.858188 0.513336i \(-0.828409\pi\)
0.858188 0.513336i \(-0.171591\pi\)
\(660\) 0 0
\(661\) 5685.94 + 5685.94i 0.334580 + 0.334580i 0.854323 0.519743i \(-0.173972\pi\)
−0.519743 + 0.854323i \(0.673972\pi\)
\(662\) 2131.38 0.125134
\(663\) 0 0
\(664\) −49.7417 −0.00290715
\(665\) 821.973 + 821.973i 0.0479319 + 0.0479319i
\(666\) 0 0
\(667\) 975.769i 0.0566446i
\(668\) −796.558 + 329.945i −0.0461374 + 0.0191107i
\(669\) 0 0
\(670\) −208.534 86.3777i −0.0120244 0.00498069i
\(671\) −3022.97 + 3022.97i −0.173920 + 0.173920i
\(672\) 0 0
\(673\) 8385.45 + 3473.37i 0.480290 + 0.198943i 0.609675 0.792652i \(-0.291300\pi\)
−0.129384 + 0.991595i \(0.541300\pi\)
\(674\) −605.559 + 1461.95i −0.0346072 + 0.0835493i
\(675\) 0 0
\(676\) 4430.54i 0.252079i
\(677\) 9550.85 + 23057.8i 0.542199 + 1.30899i 0.923168 + 0.384397i \(0.125591\pi\)
−0.380969 + 0.924588i \(0.624409\pi\)
\(678\) 0 0
\(679\) 25797.4 1.45805
\(680\) 696.930 74.3097i 0.0393030 0.00419066i
\(681\) 0 0
\(682\) 1467.71 + 1467.71i 0.0824068 + 0.0824068i
\(683\) 2322.36 + 5606.67i 0.130106 + 0.314105i 0.975486 0.220061i \(-0.0706258\pi\)
−0.845380 + 0.534166i \(0.820626\pi\)
\(684\) 0 0
\(685\) 4448.26 1842.53i 0.248116 0.102773i
\(686\) −418.166 + 1009.54i −0.0232735 + 0.0561873i
\(687\) 0 0
\(688\) −5641.96 + 5641.96i −0.312642 + 0.312642i
\(689\) −11581.5 + 11581.5i −0.640378 + 0.640378i
\(690\) 0 0
\(691\) 6641.71 16034.5i 0.365648 0.882752i −0.628804 0.777564i \(-0.716455\pi\)
0.994452 0.105189i \(-0.0335446\pi\)
\(692\) 20235.8 8381.96i 1.11163 0.460454i
\(693\) 0 0
\(694\) −210.163 507.378i −0.0114952 0.0277519i
\(695\) −401.387 401.387i −0.0219072 0.0219072i
\(696\) 0 0
\(697\) 3227.56 + 30270.4i 0.175398 + 1.64501i
\(698\) −2507.87 −0.135995
\(699\) 0 0
\(700\) −7687.07 18558.2i −0.415063 1.00205i
\(701\) 34827.5i 1.87649i −0.345976 0.938243i \(-0.612452\pi\)
0.345976 0.938243i \(-0.387548\pi\)
\(702\) 0 0
\(703\) 1492.21 3602.52i 0.0800566 0.193274i
\(704\) −24798.8 10272.0i −1.32761 0.549915i
\(705\) 0 0
\(706\) −1242.86 + 1242.86i −0.0662546 + 0.0662546i
\(707\) 1774.49 + 735.018i 0.0943941 + 0.0390993i
\(708\) 0 0
\(709\) −23731.7 + 9830.00i −1.25707 + 0.520696i −0.909009 0.416775i \(-0.863160\pi\)
−0.348062 + 0.937472i \(0.613160\pi\)
\(710\) 133.669i 0.00706548i
\(711\) 0 0
\(712\) 1673.25 + 1673.25i 0.0880725 + 0.0880725i
\(713\) −2327.35 −0.122244
\(714\) 0 0
\(715\) 7875.52 0.411927
\(716\) −11274.8 11274.8i −0.588492 0.588492i
\(717\) 0 0
\(718\) 2328.92i 0.121051i
\(719\) 16792.7 6955.77i 0.871018 0.360788i 0.0980115 0.995185i \(-0.468752\pi\)
0.773007 + 0.634398i \(0.218752\pi\)
\(720\) 0 0
\(721\) 24699.0 + 10230.7i 1.27578 + 0.528446i
\(722\) 1043.12 1043.12i 0.0537688 0.0537688i
\(723\) 0 0
\(724\) 17801.1 + 7373.46i 0.913775 + 0.378498i
\(725\) 3146.68 7596.75i 0.161193 0.389153i
\(726\) 0 0
\(727\) 8657.73i 0.441674i 0.975311 + 0.220837i \(0.0708789\pi\)
−0.975311 + 0.220837i \(0.929121\pi\)
\(728\) −1570.90 3792.48i −0.0799744 0.193075i
\(729\) 0 0
\(730\) −18.2121 −0.000923371
\(731\) −8548.50 2518.21i −0.432528 0.127414i
\(732\) 0 0
\(733\) −7989.74 7989.74i −0.402603 0.402603i 0.476546 0.879149i \(-0.341888\pi\)
−0.879149 + 0.476546i \(0.841888\pi\)
\(734\) 900.168 + 2173.20i 0.0452668 + 0.109284i
\(735\) 0 0
\(736\) −558.421 + 231.306i −0.0279670 + 0.0115843i
\(737\) −7513.48 + 18139.1i −0.375526 + 0.906600i
\(738\) 0 0
\(739\) 8885.48 8885.48i 0.442297 0.442297i −0.450486 0.892783i \(-0.648749\pi\)
0.892783 + 0.450486i \(0.148749\pi\)
\(740\) 3071.62 3071.62i 0.152588 0.152588i
\(741\) 0 0
\(742\) 585.716 1414.04i 0.0289789 0.0699612i
\(743\) −12980.0 + 5376.49i −0.640902 + 0.265470i −0.679377 0.733789i \(-0.737750\pi\)
0.0384753 + 0.999260i \(0.487750\pi\)
\(744\) 0 0
\(745\) 2119.96 + 5118.04i 0.104254 + 0.251692i
\(746\) −442.166 442.166i −0.0217009 0.0217009i
\(747\) 0 0
\(748\) −3221.36 30212.2i −0.157466 1.47683i
\(749\) 33091.7 1.61435
\(750\) 0 0
\(751\) −3111.79 7512.52i −0.151199 0.365027i 0.830073 0.557655i \(-0.188299\pi\)
−0.981272 + 0.192628i \(0.938299\pi\)
\(752\) 13009.6i 0.630865i
\(753\) 0 0
\(754\) 320.474 773.693i 0.0154788 0.0373690i
\(755\) −192.309 79.6572i −0.00927001 0.00383976i
\(756\) 0 0
\(757\) 16245.0 16245.0i 0.779964 0.779964i −0.199860 0.979824i \(-0.564049\pi\)
0.979824 + 0.199860i \(0.0640488\pi\)
\(758\) −1348.46 558.549i −0.0646149 0.0267644i
\(759\) 0 0
\(760\) −181.349 + 75.1174i −0.00865557 + 0.00358525i
\(761\) 15071.9i 0.717946i 0.933348 + 0.358973i \(0.116873\pi\)
−0.933348 + 0.358973i \(0.883127\pi\)
\(762\) 0 0
\(763\) −1580.89 1580.89i −0.0750091 0.0750091i
\(764\) 33013.4 1.56333
\(765\) 0 0
\(766\) 841.515 0.0396934
\(767\) 21403.4 + 21403.4i 1.00761 + 1.00761i
\(768\) 0 0
\(769\) 10392.1i 0.487321i −0.969861 0.243660i \(-0.921652\pi\)
0.969861 0.243660i \(-0.0783482\pi\)
\(770\) −679.926 + 281.635i −0.0318219 + 0.0131811i
\(771\) 0 0
\(772\) −15247.3 6315.63i −0.710831 0.294436i
\(773\) 24316.4 24316.4i 1.13144 1.13144i 0.141499 0.989938i \(-0.454808\pi\)
0.989938 0.141499i \(-0.0451921\pi\)
\(774\) 0 0
\(775\) 18119.4 + 7505.29i 0.839829 + 0.347868i
\(776\) −1667.03 + 4024.57i −0.0771172 + 0.186177i
\(777\) 0 0
\(778\) 486.052i 0.0223982i
\(779\) −3262.64 7876.71i −0.150059 0.362275i
\(780\) 0 0
\(781\) 11627.0 0.532712
\(782\) −173.188 139.814i −0.00791968 0.00639355i
\(783\) 0 0
\(784\) −5333.70 5333.70i −0.242971 0.242971i
\(785\) −2423.65 5851.21i −0.110196 0.266036i
\(786\) 0 0
\(787\) 23671.4 9805.02i 1.07217 0.444106i 0.224411 0.974494i \(-0.427954\pi\)
0.847754 + 0.530389i \(0.177954\pi\)
\(788\) −11568.7 + 27929.3i −0.522993 + 1.26262i
\(789\) 0 0
\(790\) −379.290 + 379.290i −0.0170817 + 0.0170817i
\(791\) −5603.56 + 5603.56i −0.251883 + 0.251883i
\(792\) 0 0
\(793\) −1574.35 + 3800.83i −0.0705006 + 0.170203i
\(794\) −497.879 + 206.228i −0.0222532 + 0.00921759i
\(795\) 0 0
\(796\) −11016.3 26595.7i −0.490532 1.18425i
\(797\) −20108.4 20108.4i −0.893698 0.893698i 0.101171 0.994869i \(-0.467741\pi\)
−0.994869 + 0.101171i \(0.967741\pi\)
\(798\) 0 0
\(799\) 12759.2 6952.51i 0.564939 0.307838i
\(800\) 5093.45 0.225101
\(801\) 0 0
\(802\) −179.969 434.483i −0.00792383 0.0191298i
\(803\) 1584.16i 0.0696188i
\(804\) 0 0
\(805\) 315.787 762.377i 0.0138261 0.0333792i
\(806\) 1845.37 + 764.378i 0.0806458 + 0.0334046i
\(807\) 0 0
\(808\) −229.336 + 229.336i −0.00998515 + 0.00998515i
\(809\) −20652.5 8554.55i −0.897532 0.371770i −0.114261 0.993451i \(-0.536450\pi\)
−0.783271 + 0.621681i \(0.786450\pi\)
\(810\) 0 0
\(811\) −5572.70 + 2308.29i −0.241287 + 0.0999444i −0.500050 0.865996i \(-0.666685\pi\)
0.258763 + 0.965941i \(0.416685\pi\)
\(812\) 11977.8i 0.517660i
\(813\) 0 0
\(814\) 1745.62 + 1745.62i 0.0751646 + 0.0751646i
\(815\) 5208.49 0.223859
\(816\) 0 0
\(817\) 2495.84 0.106877
\(818\) 1489.69 + 1489.69i 0.0636744 + 0.0636744i
\(819\) 0 0
\(820\) 9497.78i 0.404484i
\(821\) −11698.6 + 4845.73i −0.497302 + 0.205989i −0.617214 0.786795i \(-0.711739\pi\)
0.119912 + 0.992785i \(0.461739\pi\)
\(822\) 0 0
\(823\) 10190.3 + 4220.95i 0.431605 + 0.178777i 0.587900 0.808934i \(-0.299955\pi\)
−0.156295 + 0.987710i \(0.549955\pi\)
\(824\) −3192.10 + 3192.10i −0.134954 + 0.134954i
\(825\) 0 0
\(826\) −2613.25 1082.44i −0.110081 0.0455969i
\(827\) −10962.5 + 26465.9i −0.460948 + 1.11283i 0.507060 + 0.861911i \(0.330732\pi\)
−0.968009 + 0.250917i \(0.919268\pi\)
\(828\) 0 0
\(829\) 15663.7i 0.656239i 0.944636 + 0.328120i \(0.106415\pi\)
−0.944636 + 0.328120i \(0.893585\pi\)
\(830\) 3.28407 + 7.92844i 0.000137339 + 0.000331567i
\(831\) 0 0
\(832\) −25830.3 −1.07633
\(833\) 2380.62 8081.44i 0.0990201 0.336141i
\(834\) 0 0
\(835\) 211.050 + 211.050i 0.00874694 + 0.00874694i
\(836\) 3256.37 + 7861.57i 0.134718 + 0.325237i
\(837\) 0 0
\(838\) −874.837 + 362.369i −0.0360629 + 0.0149378i
\(839\) −8669.06 + 20929.0i −0.356721 + 0.861201i 0.639036 + 0.769177i \(0.279334\pi\)
−0.995757 + 0.0920240i \(0.970666\pi\)
\(840\) 0 0
\(841\) −13778.6 + 13778.6i −0.564952 + 0.564952i
\(842\) 742.709 742.709i 0.0303984 0.0303984i
\(843\) 0 0
\(844\) −1923.82 + 4644.52i −0.0784606 + 0.189421i
\(845\) 1417.00 586.942i 0.0576880 0.0238952i
\(846\) 0 0
\(847\) 13535.5 + 32677.6i 0.549097 + 1.32564i
\(848\) −13848.6 13848.6i −0.560807 0.560807i
\(849\) 0 0
\(850\) 897.462 + 1647.01i 0.0362149 + 0.0664611i
\(851\) −2768.04 −0.111501
\(852\) 0 0
\(853\) −1702.92 4111.21i −0.0683551 0.165024i 0.886010 0.463666i \(-0.153466\pi\)
−0.954365 + 0.298642i \(0.903466\pi\)
\(854\) 384.442i 0.0154044i
\(855\) 0 0
\(856\) −2138.39 + 5162.54i −0.0853841 + 0.206135i
\(857\) 20994.3 + 8696.11i 0.836815 + 0.346620i 0.759597 0.650394i \(-0.225396\pi\)
0.0772178 + 0.997014i \(0.475396\pi\)
\(858\) 0 0
\(859\) −29733.4 + 29733.4i −1.18102 + 1.18102i −0.201533 + 0.979482i \(0.564592\pi\)
−0.979482 + 0.201533i \(0.935408\pi\)
\(860\) 2568.76 + 1064.02i 0.101854 + 0.0421892i
\(861\) 0 0
\(862\) 3648.59 1511.30i 0.144166 0.0597157i
\(863\) 7875.51i 0.310644i −0.987864 0.155322i \(-0.950359\pi\)
0.987864 0.155322i \(-0.0496414\pi\)
\(864\) 0 0
\(865\) −5361.54 5361.54i −0.210749 0.210749i
\(866\) 2587.30 0.101524
\(867\) 0 0
\(868\) 28568.9 1.11716
\(869\) 32992.2 + 32992.2i 1.28790 + 1.28790i
\(870\) 0 0
\(871\) 18893.6i 0.735002i
\(872\) 348.786 144.472i 0.0135452 0.00561060i
\(873\) 0 0
\(874\) 57.5917 + 23.8552i 0.00222891 + 0.000923244i
\(875\) −10151.1 + 10151.1i −0.392194 + 0.392194i
\(876\) 0 0
\(877\) −24138.0 9998.27i −0.929397 0.384969i −0.133947 0.990988i \(-0.542765\pi\)
−0.795450 + 0.606020i \(0.792765\pi\)
\(878\) 447.194 1079.62i 0.0171891 0.0414983i
\(879\) 0 0
\(880\) 9417.18i 0.360742i
\(881\) −2449.18 5912.84i −0.0936604 0.226116i 0.870106 0.492865i \(-0.164051\pi\)
−0.963766 + 0.266749i \(0.914051\pi\)
\(882\) 0 0
\(883\) −43393.3 −1.65379 −0.826897 0.562354i \(-0.809896\pi\)
−0.826897 + 0.562354i \(0.809896\pi\)
\(884\) −13989.9 25674.1i −0.532275 0.976824i
\(885\) 0 0
\(886\) 504.832 + 504.832i 0.0191424 + 0.0191424i
\(887\) −7831.78 18907.6i −0.296466 0.715733i −0.999987 0.00505836i \(-0.998390\pi\)
0.703521 0.710675i \(-0.251610\pi\)
\(888\) 0 0
\(889\) 24922.8 10323.4i 0.940253 0.389466i
\(890\) 156.231 377.175i 0.00588413 0.0142055i
\(891\) 0 0
\(892\) 3000.09 3000.09i 0.112613 0.112613i
\(893\) −2877.53 + 2877.53i −0.107831 + 0.107831i
\(894\) 0 0
\(895\) −2112.34 + 5099.64i −0.0788913 + 0.190460i
\(896\) 9129.60 3781.60i 0.340400 0.140998i
\(897\) 0 0
\(898\) −1024.62 2473.66i −0.0380759 0.0919233i
\(899\) 8269.33 + 8269.33i 0.306783 + 0.306783i
\(900\) 0 0
\(901\) 6181.15 20983.0i 0.228550 0.775854i
\(902\) 5397.64 0.199248
\(903\) 0 0
\(904\) −512.091 1236.30i −0.0188406 0.0454852i
\(905\) 6670.07i 0.244995i
\(906\) 0 0
\(907\) −11555.0 + 27896.3i −0.423019 + 1.02126i 0.558433 + 0.829550i \(0.311403\pi\)
−0.981452 + 0.191709i \(0.938597\pi\)
\(908\) 4323.90 + 1791.02i 0.158033 + 0.0654593i
\(909\) 0 0
\(910\) −500.779 + 500.779i −0.0182425 + 0.0182425i
\(911\) −21246.6 8800.64i −0.772703 0.320064i −0.0387363 0.999249i \(-0.512333\pi\)
−0.733967 + 0.679185i \(0.762333\pi\)
\(912\) 0 0
\(913\) 689.648 285.662i 0.0249989 0.0103549i
\(914\) 2827.68i 0.102332i
\(915\) 0 0
\(916\) −14843.6 14843.6i −0.535422 0.535422i
\(917\) −42071.3 −1.51507
\(918\) 0 0
\(919\) −40432.8 −1.45131 −0.725656 0.688057i \(-0.758464\pi\)
−0.725656 + 0.688057i \(0.758464\pi\)
\(920\) 98.5299 + 98.5299i 0.00353091 + 0.00353091i
\(921\) 0 0
\(922\) 1679.57i 0.0599932i
\(923\) 10337.1 4281.76i 0.368634 0.152693i
\(924\) 0 0
\(925\) 21550.3 + 8926.43i 0.766021 + 0.317296i
\(926\) −1844.48 + 1844.48i −0.0654574 + 0.0654574i
\(927\) 0 0
\(928\) 2805.98 + 1162.28i 0.0992574 + 0.0411137i
\(929\) 13044.2 31491.4i 0.460673 1.11216i −0.507448 0.861682i \(-0.669411\pi\)
0.968121 0.250482i \(-0.0805890\pi\)
\(930\) 0 0
\(931\) 2359.48i 0.0830599i
\(932\) 1166.08 + 2815.16i 0.0409830 + 0.0989418i
\(933\) 0 0
\(934\) −1006.83 −0.0352724
\(935\) −9235.91 + 5032.68i −0.323044 + 0.176028i
\(936\) 0 0
\(937\) −539.977 539.977i −0.0188263 0.0188263i 0.697631 0.716457i \(-0.254238\pi\)
−0.716457 + 0.697631i \(0.754238\pi\)
\(938\) −675.652 1631.17i −0.0235190 0.0567799i
\(939\) 0 0
\(940\) −4188.35 + 1734.87i −0.145329 + 0.0601971i
\(941\) 170.281 411.094i 0.00589904 0.0142415i −0.920903 0.389793i \(-0.872547\pi\)
0.926802 + 0.375551i \(0.122547\pi\)
\(942\) 0 0
\(943\) −4279.54 + 4279.54i −0.147785 + 0.147785i
\(944\) −25593.3 + 25593.3i −0.882404 + 0.882404i
\(945\) 0 0
\(946\) −604.687 + 1459.84i −0.0207823 + 0.0501729i
\(947\) 10304.9 4268.42i 0.353604 0.146468i −0.198808 0.980038i \(-0.563707\pi\)
0.552413 + 0.833571i \(0.313707\pi\)
\(948\) 0 0
\(949\) 583.383 + 1408.41i 0.0199551 + 0.0481759i
\(950\) −371.445 371.445i −0.0126855 0.0126855i
\(951\) 0 0
\(952\) 4265.75 + 3443.74i 0.145225 + 0.117240i
\(953\) −48344.2 −1.64325 −0.821627 0.570026i \(-0.806933\pi\)
−0.821627 + 0.570026i \(0.806933\pi\)
\(954\) 0 0
\(955\) −4373.50 10558.6i −0.148192 0.357767i
\(956\) 34531.3i 1.16822i
\(957\) 0 0
\(958\) −24.6455 + 59.4994i −0.000831168 + 0.00200662i
\(959\) 34794.6 + 14412.4i 1.17161 + 0.485298i
\(960\) 0 0
\(961\) 1341.84 1341.84i 0.0450417 0.0450417i
\(962\) 2194.80 + 909.115i 0.0735583 + 0.0304688i
\(963\) 0 0
\(964\) −15080.2 + 6246.43i −0.503840 + 0.208697i
\(965\) 5713.15i 0.190583i
\(966\) 0 0
\(967\) −618.214 618.214i −0.0205589 0.0205589i 0.696753 0.717311i \(-0.254628\pi\)
−0.717311 + 0.696753i \(0.754628\pi\)
\(968\) −5972.59 −0.198312
\(969\) 0 0
\(970\) 751.547 0.0248770
\(971\) −20420.3 20420.3i −0.674892 0.674892i 0.283948 0.958840i \(-0.408356\pi\)
−0.958840 + 0.283948i \(0.908356\pi\)
\(972\) 0 0
\(973\) 4440.17i 0.146295i
\(974\) −1600.49 + 662.944i −0.0526519 + 0.0218091i
\(975\) 0 0
\(976\) −4544.85 1882.54i −0.149055 0.0617404i
\(977\) 3143.83 3143.83i 0.102948 0.102948i −0.653757 0.756705i \(-0.726808\pi\)
0.756705 + 0.653757i \(0.226808\pi\)
\(978\) 0 0
\(979\) −32808.2 13589.6i −1.07105 0.443642i
\(980\) −1005.88 + 2428.42i −0.0327875 + 0.0791561i
\(981\) 0 0
\(982\) 2924.80i 0.0950448i
\(983\) 15780.7 + 38098.1i 0.512032 + 1.23615i 0.942699 + 0.333644i \(0.108278\pi\)
−0.430667 + 0.902511i \(0.641722\pi\)
\(984\) 0 0
\(985\) 10465.1 0.338524
\(986\) 118.580 + 1112.13i 0.00382998 + 0.0359203i
\(987\) 0 0
\(988\) 5790.19 + 5790.19i 0.186448 + 0.186448i
\(989\) −678.014 1636.87i −0.0217994 0.0526284i
\(990\) 0 0
\(991\) −30566.7 + 12661.1i −0.979801 + 0.405847i −0.814352 0.580372i \(-0.802907\pi\)
−0.165449 + 0.986218i \(0.552907\pi\)
\(992\) −2772.20 + 6692.68i −0.0887272 + 0.214206i
\(993\) 0 0
\(994\) −739.325 + 739.325i −0.0235915 + 0.0235915i
\(995\) −7046.62 + 7046.62i −0.224515 + 0.224515i
\(996\) 0 0
\(997\) −4318.18 + 10425.0i −0.137170 + 0.331157i −0.977506 0.210909i \(-0.932358\pi\)
0.840336 + 0.542066i \(0.182358\pi\)
\(998\) 572.061 236.956i 0.0181446 0.00751573i
\(999\) 0 0
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 153.4.l.a.100.2 12
3.2 odd 2 17.4.d.a.15.2 yes 12
17.8 even 8 inner 153.4.l.a.127.2 12
51.5 even 16 289.4.a.g.1.7 12
51.8 odd 8 17.4.d.a.8.2 12
51.14 even 16 289.4.b.e.288.5 12
51.20 even 16 289.4.b.e.288.6 12
51.29 even 16 289.4.a.g.1.8 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.d.a.8.2 12 51.8 odd 8
17.4.d.a.15.2 yes 12 3.2 odd 2
153.4.l.a.100.2 12 1.1 even 1 trivial
153.4.l.a.127.2 12 17.8 even 8 inner
289.4.a.g.1.7 12 51.5 even 16
289.4.a.g.1.8 12 51.29 even 16
289.4.b.e.288.5 12 51.14 even 16
289.4.b.e.288.6 12 51.20 even 16