Properties

Label 189.2.h.b.37.1
Level $189$
Weight $2$
Character 189.37
Analytic conductor $1.509$
Analytic rank $0$
Dimension $10$
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] = [189,2,Mod(37,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.50917259820\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.1
Root \(-1.02682 + 1.77851i\) of defining polynomial
Character \(\chi\) \(=\) 189.37
Dual form 189.2.h.b.46.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.05365 q^{2} +2.21746 q^{4} +(-0.0731228 - 0.126652i) q^{5} +(-2.33035 - 1.25278i) q^{7} -0.446582 q^{8} +O(q^{10})\) \(q-2.05365 q^{2} +2.21746 q^{4} +(-0.0731228 - 0.126652i) q^{5} +(-2.33035 - 1.25278i) q^{7} -0.446582 q^{8} +(0.150168 + 0.260099i) q^{10} +(0.832020 - 1.44110i) q^{11} +(0.0999454 - 0.173111i) q^{13} +(4.78572 + 2.57276i) q^{14} -3.51780 q^{16} +(-3.13555 - 5.43093i) q^{17} +(3.45879 - 5.99080i) q^{19} +(-0.162147 - 0.280847i) q^{20} +(-1.70867 + 2.95951i) q^{22} +(-3.09092 - 5.35363i) q^{23} +(2.48931 - 4.31160i) q^{25} +(-0.205252 + 0.355508i) q^{26} +(-5.16746 - 2.77798i) q^{28} +(2.46757 + 4.27396i) q^{29} -2.51780 q^{31} +8.11747 q^{32} +(6.43931 + 11.1532i) q^{34} +(0.0117348 + 0.386752i) q^{35} +(-3.50023 + 6.06257i) q^{37} +(-7.10312 + 12.3030i) q^{38} +(0.0326554 + 0.0565608i) q^{40} +(-1.15895 + 2.00736i) q^{41} +(-0.940993 - 1.62985i) q^{43} +(1.84497 - 3.19558i) q^{44} +(6.34765 + 10.9944i) q^{46} +1.81177 q^{47} +(3.86110 + 5.83883i) q^{49} +(-5.11215 + 8.85451i) q^{50} +(0.221625 - 0.383865i) q^{52} +(2.67307 + 4.62989i) q^{53} -0.243359 q^{55} +(1.04069 + 0.559468i) q^{56} +(-5.06752 - 8.77720i) q^{58} +4.57099 q^{59} -0.678276 q^{61} +5.17066 q^{62} -9.63481 q^{64} -0.0292332 q^{65} -6.18684 q^{67} +(-6.95296 - 12.0429i) q^{68} +(-0.0240991 - 0.794251i) q^{70} -1.27749 q^{71} +(-0.778603 - 1.34858i) q^{73} +(7.18823 - 12.4504i) q^{74} +(7.66972 - 13.2843i) q^{76} +(-3.74428 + 2.31594i) q^{77} +12.7957 q^{79} +(0.257231 + 0.445537i) q^{80} +(2.38008 - 4.12241i) q^{82} +(-3.75687 - 6.50709i) q^{83} +(-0.458561 + 0.794251i) q^{85} +(1.93247 + 3.34713i) q^{86} +(-0.371566 + 0.643571i) q^{88} +(-4.53394 + 7.85301i) q^{89} +(-0.449777 + 0.278199i) q^{91} +(-6.85398 - 11.8714i) q^{92} -3.72074 q^{94} -1.01167 q^{95} +(-3.98514 - 6.90246i) q^{97} +(-7.92933 - 11.9909i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} - 8 q^{13} + 20 q^{14} - 4 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{34} - 5 q^{35} - 20 q^{38} - 3 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} + 54 q^{47} - 8 q^{49} - 19 q^{50} - 10 q^{52} + 21 q^{53} + 4 q^{55} - 18 q^{56} - 10 q^{58} + 60 q^{59} + 28 q^{61} + 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} - 27 q^{68} + 40 q^{70} + 6 q^{71} + 15 q^{73} + 36 q^{74} + 5 q^{76} - 11 q^{77} + 8 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} + 6 q^{94} - 28 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.05365 −1.45215 −0.726073 0.687617i \(-0.758657\pi\)
−0.726073 + 0.687617i \(0.758657\pi\)
\(3\) 0 0
\(4\) 2.21746 1.10873
\(5\) −0.0731228 0.126652i −0.0327015 0.0566407i 0.849211 0.528053i \(-0.177078\pi\)
−0.881913 + 0.471412i \(0.843744\pi\)
\(6\) 0 0
\(7\) −2.33035 1.25278i −0.880791 0.473505i
\(8\) −0.446582 −0.157891
\(9\) 0 0
\(10\) 0.150168 + 0.260099i 0.0474874 + 0.0822506i
\(11\) 0.832020 1.44110i 0.250864 0.434508i −0.712900 0.701265i \(-0.752619\pi\)
0.963764 + 0.266757i \(0.0859521\pi\)
\(12\) 0 0
\(13\) 0.0999454 0.173111i 0.0277199 0.0480122i −0.851833 0.523814i \(-0.824509\pi\)
0.879553 + 0.475802i \(0.157842\pi\)
\(14\) 4.78572 + 2.57276i 1.27904 + 0.687599i
\(15\) 0 0
\(16\) −3.51780 −0.879449
\(17\) −3.13555 5.43093i −0.760483 1.31720i −0.942602 0.333919i \(-0.891629\pi\)
0.182119 0.983277i \(-0.441704\pi\)
\(18\) 0 0
\(19\) 3.45879 5.99080i 0.793500 1.37438i −0.130287 0.991476i \(-0.541590\pi\)
0.923787 0.382907i \(-0.125077\pi\)
\(20\) −0.162147 0.280847i −0.0362571 0.0627992i
\(21\) 0 0
\(22\) −1.70867 + 2.95951i −0.364291 + 0.630970i
\(23\) −3.09092 5.35363i −0.644501 1.11631i −0.984417 0.175852i \(-0.943732\pi\)
0.339916 0.940456i \(-0.389601\pi\)
\(24\) 0 0
\(25\) 2.48931 4.31160i 0.497861 0.862321i
\(26\) −0.205252 + 0.355508i −0.0402533 + 0.0697208i
\(27\) 0 0
\(28\) −5.16746 2.77798i −0.976559 0.524989i
\(29\) 2.46757 + 4.27396i 0.458217 + 0.793655i 0.998867 0.0475930i \(-0.0151551\pi\)
−0.540650 + 0.841248i \(0.681822\pi\)
\(30\) 0 0
\(31\) −2.51780 −0.452209 −0.226105 0.974103i \(-0.572599\pi\)
−0.226105 + 0.974103i \(0.572599\pi\)
\(32\) 8.11747 1.43498
\(33\) 0 0
\(34\) 6.43931 + 11.1532i 1.10433 + 1.91276i
\(35\) 0.0117348 + 0.386752i 0.00198354 + 0.0653730i
\(36\) 0 0
\(37\) −3.50023 + 6.06257i −0.575434 + 0.996681i 0.420560 + 0.907264i \(0.361833\pi\)
−0.995994 + 0.0894162i \(0.971500\pi\)
\(38\) −7.10312 + 12.3030i −1.15228 + 1.99581i
\(39\) 0 0
\(40\) 0.0326554 + 0.0565608i 0.00516327 + 0.00894304i
\(41\) −1.15895 + 2.00736i −0.180998 + 0.313498i −0.942221 0.334993i \(-0.891266\pi\)
0.761223 + 0.648491i \(0.224599\pi\)
\(42\) 0 0
\(43\) −0.940993 1.62985i −0.143500 0.248550i 0.785312 0.619100i \(-0.212502\pi\)
−0.928812 + 0.370550i \(0.879169\pi\)
\(44\) 1.84497 3.19558i 0.278140 0.481752i
\(45\) 0 0
\(46\) 6.34765 + 10.9944i 0.935910 + 1.62104i
\(47\) 1.81177 0.264275 0.132137 0.991231i \(-0.457816\pi\)
0.132137 + 0.991231i \(0.457816\pi\)
\(48\) 0 0
\(49\) 3.86110 + 5.83883i 0.551586 + 0.834118i
\(50\) −5.11215 + 8.85451i −0.722967 + 1.25222i
\(51\) 0 0
\(52\) 0.221625 0.383865i 0.0307338 0.0532325i
\(53\) 2.67307 + 4.62989i 0.367174 + 0.635964i 0.989123 0.147094i \(-0.0469920\pi\)
−0.621948 + 0.783058i \(0.713659\pi\)
\(54\) 0 0
\(55\) −0.243359 −0.0328145
\(56\) 1.04069 + 0.559468i 0.139069 + 0.0747621i
\(57\) 0 0
\(58\) −5.06752 8.77720i −0.665398 1.15250i
\(59\) 4.57099 0.595092 0.297546 0.954708i \(-0.403832\pi\)
0.297546 + 0.954708i \(0.403832\pi\)
\(60\) 0 0
\(61\) −0.678276 −0.0868443 −0.0434221 0.999057i \(-0.513826\pi\)
−0.0434221 + 0.999057i \(0.513826\pi\)
\(62\) 5.17066 0.656674
\(63\) 0 0
\(64\) −9.63481 −1.20435
\(65\) −0.0292332 −0.00362593
\(66\) 0 0
\(67\) −6.18684 −0.755842 −0.377921 0.925838i \(-0.623361\pi\)
−0.377921 + 0.925838i \(0.623361\pi\)
\(68\) −6.95296 12.0429i −0.843170 1.46041i
\(69\) 0 0
\(70\) −0.0240991 0.794251i −0.00288039 0.0949311i
\(71\) −1.27749 −0.151611 −0.0758053 0.997123i \(-0.524153\pi\)
−0.0758053 + 0.997123i \(0.524153\pi\)
\(72\) 0 0
\(73\) −0.778603 1.34858i −0.0911286 0.157839i 0.816858 0.576839i \(-0.195714\pi\)
−0.907986 + 0.419000i \(0.862381\pi\)
\(74\) 7.18823 12.4504i 0.835614 1.44733i
\(75\) 0 0
\(76\) 7.66972 13.2843i 0.879777 1.52382i
\(77\) −3.74428 + 2.31594i −0.426700 + 0.263926i
\(78\) 0 0
\(79\) 12.7957 1.43963 0.719817 0.694164i \(-0.244226\pi\)
0.719817 + 0.694164i \(0.244226\pi\)
\(80\) 0.257231 + 0.445537i 0.0287593 + 0.0498126i
\(81\) 0 0
\(82\) 2.38008 4.12241i 0.262835 0.455244i
\(83\) −3.75687 6.50709i −0.412370 0.714246i 0.582778 0.812631i \(-0.301966\pi\)
−0.995148 + 0.0983854i \(0.968632\pi\)
\(84\) 0 0
\(85\) −0.458561 + 0.794251i −0.0497379 + 0.0861486i
\(86\) 1.93247 + 3.34713i 0.208383 + 0.360930i
\(87\) 0 0
\(88\) −0.371566 + 0.643571i −0.0396090 + 0.0686048i
\(89\) −4.53394 + 7.85301i −0.480597 + 0.832418i −0.999752 0.0222619i \(-0.992913\pi\)
0.519155 + 0.854680i \(0.326247\pi\)
\(90\) 0 0
\(91\) −0.449777 + 0.278199i −0.0471494 + 0.0291632i
\(92\) −6.85398 11.8714i −0.714577 1.23768i
\(93\) 0 0
\(94\) −3.72074 −0.383765
\(95\) −1.01167 −0.103795
\(96\) 0 0
\(97\) −3.98514 6.90246i −0.404630 0.700839i 0.589649 0.807660i \(-0.299266\pi\)
−0.994278 + 0.106821i \(0.965933\pi\)
\(98\) −7.92933 11.9909i −0.800983 1.21126i
\(99\) 0 0
\(100\) 5.51993 9.56080i 0.551993 0.956080i
\(101\) 7.42150 12.8544i 0.738467 1.27906i −0.214719 0.976676i \(-0.568883\pi\)
0.953186 0.302386i \(-0.0977832\pi\)
\(102\) 0 0
\(103\) 0.101974 + 0.176624i 0.0100478 + 0.0174033i 0.871006 0.491273i \(-0.163468\pi\)
−0.860958 + 0.508676i \(0.830135\pi\)
\(104\) −0.0446339 + 0.0773081i −0.00437671 + 0.00758068i
\(105\) 0 0
\(106\) −5.48953 9.50815i −0.533191 0.923513i
\(107\) −3.48444 + 6.03524i −0.336854 + 0.583448i −0.983839 0.179054i \(-0.942696\pi\)
0.646985 + 0.762503i \(0.276030\pi\)
\(108\) 0 0
\(109\) 3.33058 + 5.76874i 0.319012 + 0.552545i 0.980282 0.197603i \(-0.0633157\pi\)
−0.661270 + 0.750148i \(0.729982\pi\)
\(110\) 0.499772 0.0476514
\(111\) 0 0
\(112\) 8.19771 + 4.40701i 0.774611 + 0.416424i
\(113\) 0.0193234 0.0334691i 0.00181779 0.00314851i −0.865115 0.501573i \(-0.832755\pi\)
0.866933 + 0.498425i \(0.166088\pi\)
\(114\) 0 0
\(115\) −0.452033 + 0.782945i −0.0421523 + 0.0730100i
\(116\) 5.47174 + 9.47733i 0.508038 + 0.879948i
\(117\) 0 0
\(118\) −9.38718 −0.864160
\(119\) 0.503195 + 16.5841i 0.0461278 + 1.52027i
\(120\) 0 0
\(121\) 4.11548 + 7.12823i 0.374135 + 0.648021i
\(122\) 1.39294 0.126111
\(123\) 0 0
\(124\) −5.58311 −0.501378
\(125\) −1.45933 −0.130526
\(126\) 0 0
\(127\) 13.4788 1.19605 0.598027 0.801476i \(-0.295952\pi\)
0.598027 + 0.801476i \(0.295952\pi\)
\(128\) 3.55154 0.313915
\(129\) 0 0
\(130\) 0.0600345 0.00526538
\(131\) −9.91665 17.1761i −0.866422 1.50069i −0.865628 0.500687i \(-0.833081\pi\)
−0.000793988 1.00000i \(-0.500253\pi\)
\(132\) 0 0
\(133\) −15.5653 + 9.62759i −1.34969 + 0.834818i
\(134\) 12.7056 1.09759
\(135\) 0 0
\(136\) 1.40028 + 2.42536i 0.120073 + 0.207973i
\(137\) −3.22255 + 5.58162i −0.275321 + 0.476870i −0.970216 0.242241i \(-0.922117\pi\)
0.694895 + 0.719111i \(0.255451\pi\)
\(138\) 0 0
\(139\) 6.26527 10.8518i 0.531413 0.920435i −0.467914 0.883774i \(-0.654994\pi\)
0.999328 0.0366611i \(-0.0116722\pi\)
\(140\) 0.0260214 + 0.857606i 0.00219921 + 0.0724809i
\(141\) 0 0
\(142\) 2.62352 0.220161
\(143\) −0.166313 0.288063i −0.0139078 0.0240890i
\(144\) 0 0
\(145\) 0.360872 0.625048i 0.0299688 0.0519074i
\(146\) 1.59897 + 2.76950i 0.132332 + 0.229206i
\(147\) 0 0
\(148\) −7.76161 + 13.4435i −0.638000 + 1.10505i
\(149\) 8.88364 + 15.3869i 0.727776 + 1.26054i 0.957821 + 0.287365i \(0.0927792\pi\)
−0.230045 + 0.973180i \(0.573887\pi\)
\(150\) 0 0
\(151\) −4.23300 + 7.33177i −0.344476 + 0.596651i −0.985259 0.171072i \(-0.945277\pi\)
0.640782 + 0.767723i \(0.278610\pi\)
\(152\) −1.54463 + 2.67538i −0.125286 + 0.217002i
\(153\) 0 0
\(154\) 7.68942 4.75612i 0.619631 0.383259i
\(155\) 0.184108 + 0.318885i 0.0147879 + 0.0256135i
\(156\) 0 0
\(157\) 5.69935 0.454858 0.227429 0.973795i \(-0.426968\pi\)
0.227429 + 0.973795i \(0.426968\pi\)
\(158\) −26.2779 −2.09056
\(159\) 0 0
\(160\) −0.593572 1.02810i −0.0469260 0.0812782i
\(161\) 0.496032 + 16.3481i 0.0390928 + 1.28841i
\(162\) 0 0
\(163\) −1.06267 + 1.84060i −0.0832349 + 0.144167i −0.904638 0.426181i \(-0.859859\pi\)
0.821403 + 0.570349i \(0.193192\pi\)
\(164\) −2.56993 + 4.45125i −0.200678 + 0.347584i
\(165\) 0 0
\(166\) 7.71528 + 13.3632i 0.598821 + 1.03719i
\(167\) 5.78723 10.0238i 0.447829 0.775663i −0.550415 0.834891i \(-0.685530\pi\)
0.998244 + 0.0592278i \(0.0188638\pi\)
\(168\) 0 0
\(169\) 6.48002 + 11.2237i 0.498463 + 0.863364i
\(170\) 0.941721 1.63111i 0.0722267 0.125100i
\(171\) 0 0
\(172\) −2.08661 3.61412i −0.159103 0.275574i
\(173\) 15.9109 1.20968 0.604842 0.796345i \(-0.293236\pi\)
0.604842 + 0.796345i \(0.293236\pi\)
\(174\) 0 0
\(175\) −11.2024 + 6.92902i −0.846825 + 0.523785i
\(176\) −2.92688 + 5.06950i −0.220622 + 0.382128i
\(177\) 0 0
\(178\) 9.31110 16.1273i 0.697897 1.20879i
\(179\) −3.87665 6.71456i −0.289755 0.501870i 0.683996 0.729485i \(-0.260240\pi\)
−0.973751 + 0.227615i \(0.926907\pi\)
\(180\) 0 0
\(181\) −12.1618 −0.903982 −0.451991 0.892022i \(-0.649286\pi\)
−0.451991 + 0.892022i \(0.649286\pi\)
\(182\) 0.923682 0.571323i 0.0684679 0.0423493i
\(183\) 0 0
\(184\) 1.38035 + 2.39084i 0.101761 + 0.176255i
\(185\) 1.02379 0.0752703
\(186\) 0 0
\(187\) −10.4354 −0.763110
\(188\) 4.01754 0.293009
\(189\) 0 0
\(190\) 2.07760 0.150725
\(191\) 4.96765 0.359447 0.179723 0.983717i \(-0.442480\pi\)
0.179723 + 0.983717i \(0.442480\pi\)
\(192\) 0 0
\(193\) −14.9044 −1.07284 −0.536422 0.843950i \(-0.680224\pi\)
−0.536422 + 0.843950i \(0.680224\pi\)
\(194\) 8.18406 + 14.1752i 0.587581 + 1.01772i
\(195\) 0 0
\(196\) 8.56183 + 12.9474i 0.611559 + 0.924811i
\(197\) 21.2608 1.51477 0.757386 0.652968i \(-0.226476\pi\)
0.757386 + 0.652968i \(0.226476\pi\)
\(198\) 0 0
\(199\) −9.97208 17.2722i −0.706902 1.22439i −0.966001 0.258540i \(-0.916759\pi\)
0.259098 0.965851i \(-0.416575\pi\)
\(200\) −1.11168 + 1.92549i −0.0786077 + 0.136152i
\(201\) 0 0
\(202\) −15.2411 + 26.3984i −1.07236 + 1.85739i
\(203\) −0.395997 13.0512i −0.0277935 0.916012i
\(204\) 0 0
\(205\) 0.338983 0.0236756
\(206\) −0.209419 0.362724i −0.0145909 0.0252722i
\(207\) 0 0
\(208\) −0.351587 + 0.608967i −0.0243782 + 0.0422243i
\(209\) −5.75556 9.96893i −0.398121 0.689565i
\(210\) 0 0
\(211\) 11.7569 20.3636i 0.809381 1.40189i −0.103912 0.994587i \(-0.533136\pi\)
0.913293 0.407303i \(-0.133531\pi\)
\(212\) 5.92742 + 10.2666i 0.407097 + 0.705112i
\(213\) 0 0
\(214\) 7.15581 12.3942i 0.489161 0.847252i
\(215\) −0.137616 + 0.238358i −0.00938535 + 0.0162559i
\(216\) 0 0
\(217\) 5.86735 + 3.15424i 0.398302 + 0.214123i
\(218\) −6.83983 11.8469i −0.463252 0.802376i
\(219\) 0 0
\(220\) −0.539638 −0.0363824
\(221\) −1.25354 −0.0843220
\(222\) 0 0
\(223\) 2.03052 + 3.51696i 0.135974 + 0.235513i 0.925969 0.377600i \(-0.123250\pi\)
−0.789995 + 0.613113i \(0.789917\pi\)
\(224\) −18.9166 10.1694i −1.26392 0.679470i
\(225\) 0 0
\(226\) −0.0396834 + 0.0687336i −0.00263970 + 0.00457209i
\(227\) −1.92643 + 3.33667i −0.127861 + 0.221462i −0.922848 0.385165i \(-0.874145\pi\)
0.794986 + 0.606627i \(0.207478\pi\)
\(228\) 0 0
\(229\) −6.55812 11.3590i −0.433373 0.750624i 0.563788 0.825919i \(-0.309343\pi\)
−0.997161 + 0.0752952i \(0.976010\pi\)
\(230\) 0.928316 1.60789i 0.0612113 0.106021i
\(231\) 0 0
\(232\) −1.10197 1.90868i −0.0723481 0.125311i
\(233\) 8.75115 15.1574i 0.573307 0.992997i −0.422916 0.906169i \(-0.638993\pi\)
0.996223 0.0868284i \(-0.0276732\pi\)
\(234\) 0 0
\(235\) −0.132482 0.229466i −0.00864218 0.0149687i
\(236\) 10.1360 0.659795
\(237\) 0 0
\(238\) −1.03338 34.0580i −0.0669843 2.20765i
\(239\) −3.65857 + 6.33683i −0.236653 + 0.409895i −0.959752 0.280849i \(-0.909384\pi\)
0.723099 + 0.690745i \(0.242717\pi\)
\(240\) 0 0
\(241\) −3.11553 + 5.39626i −0.200689 + 0.347604i −0.948751 0.316026i \(-0.897651\pi\)
0.748062 + 0.663629i \(0.230985\pi\)
\(242\) −8.45174 14.6389i −0.543299 0.941021i
\(243\) 0 0
\(244\) −1.50405 −0.0962868
\(245\) 0.457167 0.915969i 0.0292074 0.0585191i
\(246\) 0 0
\(247\) −0.691380 1.19751i −0.0439915 0.0761954i
\(248\) 1.12440 0.0713997
\(249\) 0 0
\(250\) 2.99694 0.189543
\(251\) −5.65283 −0.356803 −0.178402 0.983958i \(-0.557093\pi\)
−0.178402 + 0.983958i \(0.557093\pi\)
\(252\) 0 0
\(253\) −10.2868 −0.646727
\(254\) −27.6808 −1.73684
\(255\) 0 0
\(256\) 11.9760 0.748501
\(257\) 5.90082 + 10.2205i 0.368083 + 0.637539i 0.989266 0.146127i \(-0.0466808\pi\)
−0.621183 + 0.783666i \(0.713347\pi\)
\(258\) 0 0
\(259\) 15.7518 9.74293i 0.978770 0.605396i
\(260\) −0.0648233 −0.00402017
\(261\) 0 0
\(262\) 20.3653 + 35.2737i 1.25817 + 2.17922i
\(263\) −11.1200 + 19.2605i −0.685691 + 1.18765i 0.287528 + 0.957772i \(0.407166\pi\)
−0.973219 + 0.229879i \(0.926167\pi\)
\(264\) 0 0
\(265\) 0.390925 0.677101i 0.0240143 0.0415940i
\(266\) 31.9657 19.7716i 1.95994 1.21228i
\(267\) 0 0
\(268\) −13.7191 −0.838024
\(269\) 1.19442 + 2.06880i 0.0728251 + 0.126137i 0.900138 0.435604i \(-0.143465\pi\)
−0.827313 + 0.561741i \(0.810132\pi\)
\(270\) 0 0
\(271\) −11.6129 + 20.1142i −0.705435 + 1.22185i 0.261100 + 0.965312i \(0.415915\pi\)
−0.966534 + 0.256537i \(0.917419\pi\)
\(272\) 11.0302 + 19.1049i 0.668806 + 1.15841i
\(273\) 0 0
\(274\) 6.61797 11.4627i 0.399806 0.692484i
\(275\) −4.14231 7.17469i −0.249790 0.432650i
\(276\) 0 0
\(277\) 2.30900 3.99931i 0.138734 0.240295i −0.788283 0.615312i \(-0.789030\pi\)
0.927018 + 0.375017i \(0.122363\pi\)
\(278\) −12.8666 + 22.2857i −0.771690 + 1.33661i
\(279\) 0 0
\(280\) −0.00524055 0.172716i −0.000313183 0.0103218i
\(281\) −5.90841 10.2337i −0.352466 0.610489i 0.634215 0.773157i \(-0.281324\pi\)
−0.986681 + 0.162668i \(0.947990\pi\)
\(282\) 0 0
\(283\) 15.8497 0.942165 0.471082 0.882089i \(-0.343863\pi\)
0.471082 + 0.882089i \(0.343863\pi\)
\(284\) −2.83279 −0.168095
\(285\) 0 0
\(286\) 0.341548 + 0.591579i 0.0201962 + 0.0349808i
\(287\) 5.21555 3.22596i 0.307864 0.190422i
\(288\) 0 0
\(289\) −11.1634 + 19.3355i −0.656669 + 1.13738i
\(290\) −0.741102 + 1.28363i −0.0435190 + 0.0753772i
\(291\) 0 0
\(292\) −1.72652 2.99042i −0.101037 0.175001i
\(293\) −7.04804 + 12.2076i −0.411751 + 0.713173i −0.995081 0.0990615i \(-0.968416\pi\)
0.583330 + 0.812235i \(0.301749\pi\)
\(294\) 0 0
\(295\) −0.334243 0.578927i −0.0194604 0.0337064i
\(296\) 1.56314 2.70744i 0.0908557 0.157367i
\(297\) 0 0
\(298\) −18.2438 31.5993i −1.05684 1.83050i
\(299\) −1.23569 −0.0714619
\(300\) 0 0
\(301\) 0.151011 + 4.97698i 0.00870413 + 0.286868i
\(302\) 8.69307 15.0568i 0.500230 0.866424i
\(303\) 0 0
\(304\) −12.1673 + 21.0744i −0.697843 + 1.20870i
\(305\) 0.0495974 + 0.0859053i 0.00283994 + 0.00491892i
\(306\) 0 0
\(307\) 27.3916 1.56332 0.781660 0.623704i \(-0.214373\pi\)
0.781660 + 0.623704i \(0.214373\pi\)
\(308\) −8.30279 + 5.13550i −0.473095 + 0.292622i
\(309\) 0 0
\(310\) −0.378093 0.654877i −0.0214742 0.0371945i
\(311\) 14.0557 0.797026 0.398513 0.917163i \(-0.369526\pi\)
0.398513 + 0.917163i \(0.369526\pi\)
\(312\) 0 0
\(313\) 21.7446 1.22908 0.614540 0.788886i \(-0.289342\pi\)
0.614540 + 0.788886i \(0.289342\pi\)
\(314\) −11.7045 −0.660520
\(315\) 0 0
\(316\) 28.3740 1.59616
\(317\) −8.56297 −0.480944 −0.240472 0.970656i \(-0.577302\pi\)
−0.240472 + 0.970656i \(0.577302\pi\)
\(318\) 0 0
\(319\) 8.21228 0.459799
\(320\) 0.704524 + 1.22027i 0.0393841 + 0.0682153i
\(321\) 0 0
\(322\) −1.01867 33.5731i −0.0567684 1.87096i
\(323\) −43.3808 −2.41377
\(324\) 0 0
\(325\) −0.497589 0.861850i −0.0276013 0.0478068i
\(326\) 2.18235 3.77995i 0.120869 0.209352i
\(327\) 0 0
\(328\) 0.517568 0.896453i 0.0285779 0.0494984i
\(329\) −4.22208 2.26975i −0.232771 0.125135i
\(330\) 0 0
\(331\) 10.8472 0.596216 0.298108 0.954532i \(-0.403644\pi\)
0.298108 + 0.954532i \(0.403644\pi\)
\(332\) −8.33070 14.4292i −0.457207 0.791905i
\(333\) 0 0
\(334\) −11.8849 + 20.5853i −0.650314 + 1.12638i
\(335\) 0.452399 + 0.783578i 0.0247172 + 0.0428114i
\(336\) 0 0
\(337\) 1.67411 2.89964i 0.0911945 0.157954i −0.816819 0.576893i \(-0.804265\pi\)
0.908014 + 0.418940i \(0.137598\pi\)
\(338\) −13.3077 23.0496i −0.723842 1.25373i
\(339\) 0 0
\(340\) −1.01684 + 1.76122i −0.0551459 + 0.0955154i
\(341\) −2.09486 + 3.62840i −0.113443 + 0.196489i
\(342\) 0 0
\(343\) −1.68298 18.4436i −0.0908723 0.995863i
\(344\) 0.420231 + 0.727861i 0.0226573 + 0.0392437i
\(345\) 0 0
\(346\) −32.6754 −1.75664
\(347\) 11.5330 0.619126 0.309563 0.950879i \(-0.399817\pi\)
0.309563 + 0.950879i \(0.399817\pi\)
\(348\) 0 0
\(349\) −4.44917 7.70619i −0.238159 0.412503i 0.722027 0.691865i \(-0.243211\pi\)
−0.960186 + 0.279362i \(0.909877\pi\)
\(350\) 23.0058 14.2297i 1.22971 0.760612i
\(351\) 0 0
\(352\) 6.75390 11.6981i 0.359984 0.623511i
\(353\) −1.32349 + 2.29236i −0.0704424 + 0.122010i −0.899095 0.437753i \(-0.855774\pi\)
0.828653 + 0.559763i \(0.189108\pi\)
\(354\) 0 0
\(355\) 0.0934139 + 0.161798i 0.00495790 + 0.00858733i
\(356\) −10.0538 + 17.4137i −0.532852 + 0.922926i
\(357\) 0 0
\(358\) 7.96127 + 13.7893i 0.420766 + 0.728789i
\(359\) 12.9835 22.4882i 0.685245 1.18688i −0.288114 0.957596i \(-0.593028\pi\)
0.973360 0.229284i \(-0.0736384\pi\)
\(360\) 0 0
\(361\) −14.4264 24.9873i −0.759286 1.31512i
\(362\) 24.9761 1.31271
\(363\) 0 0
\(364\) −0.997362 + 0.616896i −0.0522760 + 0.0323341i
\(365\) −0.113867 + 0.197224i −0.00596009 + 0.0103232i
\(366\) 0 0
\(367\) −8.79371 + 15.2312i −0.459028 + 0.795060i −0.998910 0.0466808i \(-0.985136\pi\)
0.539882 + 0.841741i \(0.318469\pi\)
\(368\) 10.8732 + 18.8330i 0.566806 + 0.981736i
\(369\) 0 0
\(370\) −2.10249 −0.109303
\(371\) −0.428975 14.1380i −0.0222713 0.734011i
\(372\) 0 0
\(373\) −0.407538 0.705876i −0.0211015 0.0365489i 0.855282 0.518163i \(-0.173384\pi\)
−0.876383 + 0.481614i \(0.840051\pi\)
\(374\) 21.4306 1.10815
\(375\) 0 0
\(376\) −0.809107 −0.0417265
\(377\) 0.986490 0.0508068
\(378\) 0 0
\(379\) −20.4312 −1.04948 −0.524741 0.851262i \(-0.675838\pi\)
−0.524741 + 0.851262i \(0.675838\pi\)
\(380\) −2.24333 −0.115080
\(381\) 0 0
\(382\) −10.2018 −0.521969
\(383\) 8.94638 + 15.4956i 0.457139 + 0.791788i 0.998808 0.0488039i \(-0.0155409\pi\)
−0.541670 + 0.840591i \(0.682208\pi\)
\(384\) 0 0
\(385\) 0.567112 + 0.304874i 0.0289027 + 0.0155378i
\(386\) 30.6084 1.55793
\(387\) 0 0
\(388\) −8.83688 15.3059i −0.448625 0.777041i
\(389\) 7.81392 13.5341i 0.396181 0.686206i −0.597070 0.802189i \(-0.703669\pi\)
0.993251 + 0.115983i \(0.0370018\pi\)
\(390\) 0 0
\(391\) −19.3835 + 33.5731i −0.980264 + 1.69787i
\(392\) −1.72430 2.60752i −0.0870902 0.131700i
\(393\) 0 0
\(394\) −43.6622 −2.19967
\(395\) −0.935661 1.62061i −0.0470782 0.0815419i
\(396\) 0 0
\(397\) 9.63064 16.6808i 0.483348 0.837183i −0.516469 0.856306i \(-0.672754\pi\)
0.999817 + 0.0191225i \(0.00608724\pi\)
\(398\) 20.4791 + 35.4709i 1.02653 + 1.77799i
\(399\) 0 0
\(400\) −8.75687 + 15.1673i −0.437843 + 0.758367i
\(401\) 7.15064 + 12.3853i 0.357086 + 0.618491i 0.987473 0.157790i \(-0.0504370\pi\)
−0.630387 + 0.776281i \(0.717104\pi\)
\(402\) 0 0
\(403\) −0.251642 + 0.435857i −0.0125352 + 0.0217116i
\(404\) 16.4569 28.5041i 0.818760 1.41813i
\(405\) 0 0
\(406\) 0.813237 + 26.8024i 0.0403603 + 1.33018i
\(407\) 5.82452 + 10.0884i 0.288711 + 0.500062i
\(408\) 0 0
\(409\) 31.8610 1.57542 0.787712 0.616044i \(-0.211266\pi\)
0.787712 + 0.616044i \(0.211266\pi\)
\(410\) −0.696152 −0.0343805
\(411\) 0 0
\(412\) 0.226124 + 0.391657i 0.0111403 + 0.0192956i
\(413\) −10.6520 5.72643i −0.524151 0.281779i
\(414\) 0 0
\(415\) −0.549426 + 0.951633i −0.0269702 + 0.0467138i
\(416\) 0.811304 1.40522i 0.0397774 0.0688965i
\(417\) 0 0
\(418\) 11.8199 + 20.4726i 0.578130 + 1.00135i
\(419\) −11.9480 + 20.6945i −0.583697 + 1.01099i 0.411339 + 0.911482i \(0.365061\pi\)
−0.995036 + 0.0995110i \(0.968272\pi\)
\(420\) 0 0
\(421\) −1.22251 2.11744i −0.0595813 0.103198i 0.834696 0.550711i \(-0.185643\pi\)
−0.894278 + 0.447513i \(0.852310\pi\)
\(422\) −24.1446 + 41.8197i −1.17534 + 2.03575i
\(423\) 0 0
\(424\) −1.19375 2.06763i −0.0579734 0.100413i
\(425\) −31.2214 −1.51446
\(426\) 0 0
\(427\) 1.58062 + 0.849728i 0.0764917 + 0.0411212i
\(428\) −7.72661 + 13.3829i −0.373480 + 0.646886i
\(429\) 0 0
\(430\) 0.282615 0.489503i 0.0136289 0.0236059i
\(431\) −2.46382 4.26746i −0.118678 0.205556i 0.800566 0.599244i \(-0.204532\pi\)
−0.919244 + 0.393688i \(0.871199\pi\)
\(432\) 0 0
\(433\) 30.8539 1.48274 0.741371 0.671095i \(-0.234176\pi\)
0.741371 + 0.671095i \(0.234176\pi\)
\(434\) −12.0495 6.47768i −0.578393 0.310939i
\(435\) 0 0
\(436\) 7.38543 + 12.7919i 0.353698 + 0.612622i
\(437\) −42.7633 −2.04565
\(438\) 0 0
\(439\) 2.44822 0.116847 0.0584235 0.998292i \(-0.481393\pi\)
0.0584235 + 0.998292i \(0.481393\pi\)
\(440\) 0.108680 0.00518110
\(441\) 0 0
\(442\) 2.57432 0.122448
\(443\) 26.2950 1.24931 0.624657 0.780899i \(-0.285239\pi\)
0.624657 + 0.780899i \(0.285239\pi\)
\(444\) 0 0
\(445\) 1.32614 0.0628650
\(446\) −4.16996 7.22259i −0.197453 0.341999i
\(447\) 0 0
\(448\) 22.4525 + 12.0703i 1.06078 + 0.570266i
\(449\) 38.7077 1.82673 0.913365 0.407141i \(-0.133474\pi\)
0.913365 + 0.407141i \(0.133474\pi\)
\(450\) 0 0
\(451\) 1.92854 + 3.34034i 0.0908116 + 0.157290i
\(452\) 0.0428488 0.0742163i 0.00201544 0.00349084i
\(453\) 0 0
\(454\) 3.95620 6.85233i 0.185673 0.321596i
\(455\) 0.0681236 + 0.0366226i 0.00319368 + 0.00171690i
\(456\) 0 0
\(457\) −9.15511 −0.428258 −0.214129 0.976805i \(-0.568691\pi\)
−0.214129 + 0.976805i \(0.568691\pi\)
\(458\) 13.4681 + 23.3274i 0.629321 + 1.09002i
\(459\) 0 0
\(460\) −1.00237 + 1.73615i −0.0467355 + 0.0809483i
\(461\) −14.6152 25.3143i −0.680698 1.17900i −0.974768 0.223220i \(-0.928343\pi\)
0.294070 0.955784i \(-0.404990\pi\)
\(462\) 0 0
\(463\) −8.21031 + 14.2207i −0.381565 + 0.660891i −0.991286 0.131726i \(-0.957948\pi\)
0.609721 + 0.792616i \(0.291282\pi\)
\(464\) −8.68041 15.0349i −0.402978 0.697978i
\(465\) 0 0
\(466\) −17.9718 + 31.1280i −0.832526 + 1.44198i
\(467\) −7.68632 + 13.3131i −0.355680 + 0.616057i −0.987234 0.159276i \(-0.949084\pi\)
0.631554 + 0.775332i \(0.282418\pi\)
\(468\) 0 0
\(469\) 14.4175 + 7.75073i 0.665739 + 0.357895i
\(470\) 0.272071 + 0.471241i 0.0125497 + 0.0217367i
\(471\) 0 0
\(472\) −2.04132 −0.0939594
\(473\) −3.13170 −0.143996
\(474\) 0 0
\(475\) −17.2200 29.8259i −0.790106 1.36850i
\(476\) 1.11581 + 36.7747i 0.0511432 + 1.68556i
\(477\) 0 0
\(478\) 7.51341 13.0136i 0.343655 0.595228i
\(479\) −18.9646 + 32.8476i −0.866513 + 1.50084i −0.000975329 1.00000i \(0.500310\pi\)
−0.865537 + 0.500844i \(0.833023\pi\)
\(480\) 0 0
\(481\) 0.699663 + 1.21185i 0.0319019 + 0.0552557i
\(482\) 6.39820 11.0820i 0.291430 0.504772i
\(483\) 0 0
\(484\) 9.12591 + 15.8065i 0.414814 + 0.718479i
\(485\) −0.582809 + 1.00946i −0.0264640 + 0.0458370i
\(486\) 0 0
\(487\) 2.30247 + 3.98800i 0.104335 + 0.180714i 0.913466 0.406914i \(-0.133395\pi\)
−0.809131 + 0.587628i \(0.800062\pi\)
\(488\) 0.302906 0.0137119
\(489\) 0 0
\(490\) −0.938860 + 1.88108i −0.0424134 + 0.0849784i
\(491\) 15.1876 26.3056i 0.685405 1.18716i −0.287904 0.957659i \(-0.592958\pi\)
0.973309 0.229497i \(-0.0737082\pi\)
\(492\) 0 0
\(493\) 15.4744 26.8024i 0.696932 1.20712i
\(494\) 1.41985 + 2.45925i 0.0638820 + 0.110647i
\(495\) 0 0
\(496\) 8.85709 0.397695
\(497\) 2.97701 + 1.60041i 0.133537 + 0.0717884i
\(498\) 0 0
\(499\) −4.63436 8.02694i −0.207462 0.359335i 0.743452 0.668789i \(-0.233187\pi\)
−0.950914 + 0.309454i \(0.899854\pi\)
\(500\) −3.23600 −0.144718
\(501\) 0 0
\(502\) 11.6089 0.518131
\(503\) 22.4230 0.999791 0.499896 0.866086i \(-0.333372\pi\)
0.499896 + 0.866086i \(0.333372\pi\)
\(504\) 0 0
\(505\) −2.17072 −0.0965960
\(506\) 21.1255 0.939143
\(507\) 0 0
\(508\) 29.8888 1.32610
\(509\) −18.8207 32.5984i −0.834213 1.44490i −0.894670 0.446728i \(-0.852589\pi\)
0.0604572 0.998171i \(-0.480744\pi\)
\(510\) 0 0
\(511\) 0.124951 + 4.11808i 0.00552748 + 0.182173i
\(512\) −31.6976 −1.40085
\(513\) 0 0
\(514\) −12.1182 20.9893i −0.534511 0.925800i
\(515\) 0.0149133 0.0258306i 0.000657158 0.00113823i
\(516\) 0 0
\(517\) 1.50743 2.61095i 0.0662969 0.114830i
\(518\) −32.3486 + 20.0085i −1.42132 + 0.879124i
\(519\) 0 0
\(520\) 0.0130550 0.000572500
\(521\) −17.4641 30.2488i −0.765117 1.32522i −0.940185 0.340666i \(-0.889348\pi\)
0.175067 0.984556i \(-0.443986\pi\)
\(522\) 0 0
\(523\) −11.8735 + 20.5656i −0.519194 + 0.899270i 0.480557 + 0.876963i \(0.340434\pi\)
−0.999751 + 0.0223069i \(0.992899\pi\)
\(524\) −21.9898 38.0874i −0.960628 1.66386i
\(525\) 0 0
\(526\) 22.8366 39.5542i 0.995723 1.72464i
\(527\) 7.89468 + 13.6740i 0.343898 + 0.595648i
\(528\) 0 0
\(529\) −7.60755 + 13.1767i −0.330763 + 0.572898i
\(530\) −0.802820 + 1.39053i −0.0348723 + 0.0604006i
\(531\) 0 0
\(532\) −34.5155 + 21.3488i −1.49644 + 0.925587i
\(533\) 0.231664 + 0.401254i 0.0100345 + 0.0173802i
\(534\) 0 0
\(535\) 1.01917 0.0440626
\(536\) 2.76293 0.119340
\(537\) 0 0
\(538\) −2.45292 4.24857i −0.105753 0.183169i
\(539\) 11.6269 0.706212i 0.500804 0.0304187i
\(540\) 0 0
\(541\) 8.58542 14.8704i 0.369116 0.639328i −0.620311 0.784356i \(-0.712994\pi\)
0.989428 + 0.145028i \(0.0463271\pi\)
\(542\) 23.8488 41.3074i 1.02439 1.77430i
\(543\) 0 0
\(544\) −25.4527 44.0854i −1.09128 1.89015i
\(545\) 0.487083 0.843653i 0.0208643 0.0361381i
\(546\) 0 0
\(547\) −10.0046 17.3284i −0.427765 0.740910i 0.568910 0.822400i \(-0.307365\pi\)
−0.996674 + 0.0814901i \(0.974032\pi\)
\(548\) −7.14586 + 12.3770i −0.305256 + 0.528719i
\(549\) 0 0
\(550\) 8.50683 + 14.7343i 0.362732 + 0.628271i
\(551\) 34.1392 1.45438
\(552\) 0 0
\(553\) −29.8186 16.0302i −1.26802 0.681674i
\(554\) −4.74187 + 8.21316i −0.201463 + 0.348944i
\(555\) 0 0
\(556\) 13.8930 24.0633i 0.589193 1.02051i
\(557\) 0.122740 + 0.212593i 0.00520068 + 0.00900784i 0.868614 0.495489i \(-0.165011\pi\)
−0.863413 + 0.504497i \(0.831678\pi\)
\(558\) 0 0
\(559\) −0.376192 −0.0159112
\(560\) −0.0412806 1.36051i −0.00174442 0.0574922i
\(561\) 0 0
\(562\) 12.1338 + 21.0163i 0.511833 + 0.886520i
\(563\) 44.2509 1.86495 0.932477 0.361230i \(-0.117643\pi\)
0.932477 + 0.361230i \(0.117643\pi\)
\(564\) 0 0
\(565\) −0.00565192 −0.000237778
\(566\) −32.5496 −1.36816
\(567\) 0 0
\(568\) 0.570506 0.0239379
\(569\) 5.53533 0.232053 0.116027 0.993246i \(-0.462984\pi\)
0.116027 + 0.993246i \(0.462984\pi\)
\(570\) 0 0
\(571\) −4.10381 −0.171739 −0.0858696 0.996306i \(-0.527367\pi\)
−0.0858696 + 0.996306i \(0.527367\pi\)
\(572\) −0.368793 0.638768i −0.0154200 0.0267082i
\(573\) 0 0
\(574\) −10.7109 + 6.62498i −0.447064 + 0.276521i
\(575\) −30.7770 −1.28349
\(576\) 0 0
\(577\) −2.82275 4.88915i −0.117513 0.203538i 0.801269 0.598305i \(-0.204159\pi\)
−0.918781 + 0.394767i \(0.870825\pi\)
\(578\) 22.9256 39.7083i 0.953579 1.65165i
\(579\) 0 0
\(580\) 0.800218 1.38602i 0.0332272 0.0575513i
\(581\) 0.602904 + 19.8703i 0.0250127 + 0.824360i
\(582\) 0 0
\(583\) 8.89619 0.368442
\(584\) 0.347710 + 0.602252i 0.0143884 + 0.0249214i
\(585\) 0 0
\(586\) 14.4742 25.0700i 0.597923 1.03563i
\(587\) −9.36644 16.2232i −0.386595 0.669601i 0.605394 0.795926i \(-0.293015\pi\)
−0.991989 + 0.126324i \(0.959682\pi\)
\(588\) 0 0
\(589\) −8.70852 + 15.0836i −0.358828 + 0.621509i
\(590\) 0.686417 + 1.18891i 0.0282594 + 0.0489466i
\(591\) 0 0
\(592\) 12.3131 21.3269i 0.506065 0.876530i
\(593\) 9.43516 16.3422i 0.387456 0.671093i −0.604651 0.796491i \(-0.706687\pi\)
0.992107 + 0.125398i \(0.0400207\pi\)
\(594\) 0 0
\(595\) 2.06363 1.27641i 0.0846005 0.0523277i
\(596\) 19.6991 + 34.1198i 0.806906 + 1.39760i
\(597\) 0 0
\(598\) 2.53767 0.103773
\(599\) −2.67451 −0.109278 −0.0546388 0.998506i \(-0.517401\pi\)
−0.0546388 + 0.998506i \(0.517401\pi\)
\(600\) 0 0
\(601\) −6.60716 11.4439i −0.269511 0.466808i 0.699224 0.714902i \(-0.253529\pi\)
−0.968736 + 0.248095i \(0.920196\pi\)
\(602\) −0.310123 10.2209i −0.0126397 0.416575i
\(603\) 0 0
\(604\) −9.38650 + 16.2579i −0.381931 + 0.661524i
\(605\) 0.601872 1.04247i 0.0244696 0.0423825i
\(606\) 0 0
\(607\) −12.9026 22.3480i −0.523701 0.907076i −0.999619 0.0275869i \(-0.991218\pi\)
0.475919 0.879489i \(-0.342116\pi\)
\(608\) 28.0766 48.6301i 1.13866 1.97221i
\(609\) 0 0
\(610\) −0.101856 0.176419i −0.00412401 0.00714299i
\(611\) 0.181079 0.313637i 0.00732565 0.0126884i
\(612\) 0 0
\(613\) 13.4766 + 23.3422i 0.544316 + 0.942784i 0.998650 + 0.0519519i \(0.0165443\pi\)
−0.454333 + 0.890832i \(0.650122\pi\)
\(614\) −56.2526 −2.27017
\(615\) 0 0
\(616\) 1.67213 1.03426i 0.0673720 0.0416715i
\(617\) 4.76588 8.25474i 0.191867 0.332323i −0.754002 0.656872i \(-0.771879\pi\)
0.945869 + 0.324549i \(0.105212\pi\)
\(618\) 0 0
\(619\) −17.3536 + 30.0573i −0.697499 + 1.20810i 0.271832 + 0.962345i \(0.412370\pi\)
−0.969331 + 0.245759i \(0.920963\pi\)
\(620\) 0.408253 + 0.707114i 0.0163958 + 0.0283984i
\(621\) 0 0
\(622\) −28.8654 −1.15740
\(623\) 20.4038 12.6203i 0.817459 0.505621i
\(624\) 0 0
\(625\) −12.3398 21.3732i −0.493593 0.854928i
\(626\) −44.6558 −1.78480
\(627\) 0 0
\(628\) 12.6381 0.504314
\(629\) 43.9006 1.75043
\(630\) 0 0
\(631\) −36.7963 −1.46484 −0.732419 0.680854i \(-0.761609\pi\)
−0.732419 + 0.680854i \(0.761609\pi\)
\(632\) −5.71435 −0.227305
\(633\) 0 0
\(634\) 17.5853 0.698401
\(635\) −0.985611 1.70713i −0.0391128 0.0677453i
\(636\) 0 0
\(637\) 1.39666 0.0848329i 0.0553378 0.00336120i
\(638\) −16.8651 −0.667696
\(639\) 0 0
\(640\) −0.259699 0.449811i −0.0102655 0.0177804i
\(641\) −22.0922 + 38.2648i −0.872590 + 1.51137i −0.0132813 + 0.999912i \(0.504228\pi\)
−0.859308 + 0.511458i \(0.829106\pi\)
\(642\) 0 0
\(643\) 7.24065 12.5412i 0.285543 0.494575i −0.687197 0.726471i \(-0.741159\pi\)
0.972741 + 0.231895i \(0.0744926\pi\)
\(644\) 1.09993 + 36.2512i 0.0433433 + 1.42850i
\(645\) 0 0
\(646\) 89.0889 3.50515
\(647\) 16.6536 + 28.8448i 0.654719 + 1.13401i 0.981964 + 0.189068i \(0.0605465\pi\)
−0.327245 + 0.944940i \(0.606120\pi\)
\(648\) 0 0
\(649\) 3.80315 6.58725i 0.149287 0.258572i
\(650\) 1.02187 + 1.76993i 0.0400811 + 0.0694225i
\(651\) 0 0
\(652\) −2.35643 + 4.08146i −0.0922850 + 0.159842i
\(653\) −4.53322 7.85176i −0.177398 0.307263i 0.763590 0.645701i \(-0.223435\pi\)
−0.940989 + 0.338438i \(0.890101\pi\)
\(654\) 0 0
\(655\) −1.45027 + 2.51194i −0.0566666 + 0.0981495i
\(656\) 4.07696 7.06150i 0.159178 0.275705i
\(657\) 0 0
\(658\) 8.67065 + 4.66126i 0.338017 + 0.181715i
\(659\) −16.1806 28.0256i −0.630305 1.09172i −0.987489 0.157686i \(-0.949596\pi\)
0.357184 0.934034i \(-0.383737\pi\)
\(660\) 0 0
\(661\) −8.65915 −0.336802 −0.168401 0.985719i \(-0.553860\pi\)
−0.168401 + 0.985719i \(0.553860\pi\)
\(662\) −22.2763 −0.865794
\(663\) 0 0
\(664\) 1.67775 + 2.90595i 0.0651094 + 0.112773i
\(665\) 2.35754 + 1.26739i 0.0914214 + 0.0491473i
\(666\) 0 0
\(667\) 15.2541 26.4209i 0.590642 1.02302i
\(668\) 12.8329 22.2273i 0.496522 0.860001i
\(669\) 0 0
\(670\) −0.929067 1.60919i −0.0358930 0.0621685i
\(671\) −0.564339 + 0.977464i −0.0217861 + 0.0377346i
\(672\) 0 0
\(673\) 7.24842 + 12.5546i 0.279406 + 0.483946i 0.971237 0.238114i \(-0.0765291\pi\)
−0.691831 + 0.722059i \(0.743196\pi\)
\(674\) −3.43803 + 5.95484i −0.132428 + 0.229372i
\(675\) 0 0
\(676\) 14.3692 + 24.8881i 0.552661 + 0.957236i
\(677\) −38.3315 −1.47320 −0.736600 0.676329i \(-0.763570\pi\)
−0.736600 + 0.676329i \(0.763570\pi\)
\(678\) 0 0
\(679\) 0.639537 + 21.0777i 0.0245432 + 0.808887i
\(680\) 0.204785 0.354698i 0.00785315 0.0136021i
\(681\) 0 0
\(682\) 4.30209 7.45144i 0.164736 0.285330i
\(683\) 3.31659 + 5.74450i 0.126906 + 0.219807i 0.922476 0.386054i \(-0.126162\pi\)
−0.795570 + 0.605861i \(0.792829\pi\)
\(684\) 0 0
\(685\) 0.942567 0.0360136
\(686\) 3.45624 + 37.8767i 0.131960 + 1.44614i
\(687\) 0 0
\(688\) 3.31022 + 5.73347i 0.126201 + 0.218587i
\(689\) 1.06864 0.0407121
\(690\) 0 0
\(691\) −23.3875 −0.889704 −0.444852 0.895604i \(-0.646744\pi\)
−0.444852 + 0.895604i \(0.646744\pi\)
\(692\) 35.2818 1.34121
\(693\) 0 0
\(694\) −23.6848 −0.899061
\(695\) −1.83254 −0.0695121
\(696\) 0 0
\(697\) 14.5358 0.550583
\(698\) 9.13702 + 15.8258i 0.345841 + 0.599015i
\(699\) 0 0
\(700\) −24.8410 + 15.3648i −0.938900 + 0.580735i
\(701\) −9.26736 −0.350023 −0.175012 0.984566i \(-0.555996\pi\)
−0.175012 + 0.984566i \(0.555996\pi\)
\(702\) 0 0
\(703\) 24.2131 + 41.9383i 0.913214 + 1.58173i
\(704\) −8.01636 + 13.8847i −0.302128 + 0.523301i
\(705\) 0 0
\(706\) 2.71799 4.70769i 0.102293 0.177176i
\(707\) −33.3984 + 20.6579i −1.25608 + 0.776918i
\(708\) 0 0
\(709\) 14.2355 0.534626 0.267313 0.963610i \(-0.413864\pi\)
0.267313 + 0.963610i \(0.413864\pi\)
\(710\) −0.191839 0.332275i −0.00719959 0.0124701i
\(711\) 0 0
\(712\) 2.02478 3.50702i 0.0758817 0.131431i
\(713\) 7.78230 + 13.4793i 0.291449 + 0.504805i
\(714\) 0 0
\(715\) −0.0243226 + 0.0421280i −0.000909613 + 0.00157550i
\(716\) −8.59632 14.8893i −0.321260 0.556438i
\(717\) 0 0
\(718\) −26.6636 + 46.1827i −0.995077 + 1.72352i
\(719\) −6.92848 + 12.0005i −0.258389 + 0.447542i −0.965810 0.259249i \(-0.916525\pi\)
0.707422 + 0.706792i \(0.249858\pi\)
\(720\) 0 0
\(721\) −0.0163649 0.539348i −0.000609459 0.0200864i
\(722\) 29.6268 + 51.3151i 1.10259 + 1.90975i
\(723\) 0 0
\(724\) −26.9684 −1.00227
\(725\) 24.5702 0.912513
\(726\) 0 0
\(727\) 15.7000 + 27.1932i 0.582280 + 1.00854i 0.995208 + 0.0977755i \(0.0311727\pi\)
−0.412928 + 0.910764i \(0.635494\pi\)
\(728\) 0.200862 0.124239i 0.00744446 0.00460460i
\(729\) 0 0
\(730\) 0.233843 0.405028i 0.00865492 0.0149908i
\(731\) −5.90107 + 10.2209i −0.218259 + 0.378035i
\(732\) 0 0
\(733\) 13.3003 + 23.0368i 0.491257 + 0.850883i 0.999949 0.0100658i \(-0.00320409\pi\)
−0.508692 + 0.860949i \(0.669871\pi\)
\(734\) 18.0592 31.2794i 0.666576 1.15454i
\(735\) 0 0
\(736\) −25.0904 43.4579i −0.924845 1.60188i
\(737\) −5.14757 + 8.91586i −0.189613 + 0.328420i
\(738\) 0 0
\(739\) 16.5019 + 28.5822i 0.607034 + 1.05141i 0.991727 + 0.128368i \(0.0409740\pi\)
−0.384693 + 0.923045i \(0.625693\pi\)
\(740\) 2.27020 0.0834543
\(741\) 0 0
\(742\) 0.880963 + 29.0345i 0.0323412 + 1.06589i
\(743\) −19.3008 + 33.4299i −0.708076 + 1.22642i 0.257493 + 0.966280i \(0.417103\pi\)
−0.965570 + 0.260144i \(0.916230\pi\)
\(744\) 0 0
\(745\) 1.29919 2.25027i 0.0475988 0.0824435i
\(746\) 0.836938 + 1.44962i 0.0306425 + 0.0530743i
\(747\) 0 0
\(748\) −23.1400 −0.846082
\(749\) 15.6808 9.69900i 0.572964 0.354394i
\(750\) 0 0
\(751\) 18.9498 + 32.8220i 0.691487 + 1.19769i 0.971351 + 0.237651i \(0.0763776\pi\)
−0.279863 + 0.960040i \(0.590289\pi\)
\(752\) −6.37345 −0.232416
\(753\) 0 0
\(754\) −2.02590 −0.0737789
\(755\) 1.23811 0.0450596
\(756\) 0 0
\(757\) 22.5927 0.821147 0.410573 0.911828i \(-0.365329\pi\)
0.410573 + 0.911828i \(0.365329\pi\)
\(758\) 41.9585 1.52400
\(759\) 0 0
\(760\) 0.451792 0.0163882
\(761\) 13.8735 + 24.0296i 0.502913 + 0.871072i 0.999994 + 0.00336738i \(0.00107187\pi\)
−0.497081 + 0.867704i \(0.665595\pi\)
\(762\) 0 0
\(763\) −0.534493 17.6157i −0.0193500 0.637730i
\(764\) 11.0156 0.398529
\(765\) 0 0
\(766\) −18.3727 31.8224i −0.663832 1.14979i
\(767\) 0.456849 0.791286i 0.0164959 0.0285717i
\(768\) 0 0
\(769\) −6.07668 + 10.5251i −0.219131 + 0.379546i −0.954542 0.298075i \(-0.903655\pi\)
0.735412 + 0.677621i \(0.236989\pi\)
\(770\) −1.16465 0.626104i −0.0419710 0.0225632i
\(771\) 0 0
\(772\) −33.0499 −1.18949
\(773\) 20.7795 + 35.9912i 0.747388 + 1.29451i 0.949071 + 0.315063i \(0.102026\pi\)
−0.201682 + 0.979451i \(0.564641\pi\)
\(774\) 0 0
\(775\) −6.26756 + 10.8557i −0.225137 + 0.389950i
\(776\) 1.77969 + 3.08252i 0.0638873 + 0.110656i
\(777\) 0 0
\(778\) −16.0470 + 27.7942i −0.575313 + 0.996472i
\(779\) 8.01714 + 13.8861i 0.287244 + 0.497521i
\(780\) 0 0
\(781\) −1.06290 + 1.84100i −0.0380336 + 0.0658761i
\(782\) 39.8068 68.9473i 1.42349 2.46555i
\(783\) 0 0
\(784\) −13.5826 20.5398i −0.485091 0.733564i
\(785\) −0.416753 0.721837i −0.0148746 0.0257635i
\(786\) 0 0
\(787\) −20.8969 −0.744893 −0.372446 0.928054i \(-0.621481\pi\)
−0.372446 + 0.928054i \(0.621481\pi\)
\(788\) 47.1450 1.67947
\(789\) 0 0
\(790\) 1.92152 + 3.32816i 0.0683645 + 0.118411i
\(791\) −0.0869596 + 0.0537869i −0.00309193 + 0.00191244i
\(792\) 0 0
\(793\) −0.0677905 + 0.117417i −0.00240731 + 0.00416959i
\(794\) −19.7779 + 34.2564i −0.701892 + 1.21571i
\(795\) 0 0
\(796\) −22.1127 38.3003i −0.783763 1.35752i
\(797\) 0.319383 0.553188i 0.0113131 0.0195949i −0.860313 0.509765i \(-0.829732\pi\)
0.871627 + 0.490171i \(0.163066\pi\)
\(798\) 0 0
\(799\) −5.68091 9.83963i −0.200976 0.348101i
\(800\) 20.2069 34.9993i 0.714420 1.23741i
\(801\) 0 0
\(802\) −14.6849 25.4350i −0.518541 0.898139i
\(803\) −2.59125 −0.0914433
\(804\) 0 0
\(805\) 2.03425 1.25824i 0.0716980 0.0443472i
\(806\) 0.516783 0.895095i 0.0182029 0.0315284i
\(807\) 0 0
\(808\) −3.31431 + 5.74055i −0.116597 + 0.201952i
\(809\) −25.2796 43.7856i −0.888783 1.53942i −0.841315 0.540545i \(-0.818218\pi\)
−0.0474686 0.998873i \(-0.515115\pi\)
\(810\) 0 0
\(811\) −0.784071 −0.0275325 −0.0137662 0.999905i \(-0.504382\pi\)
−0.0137662 + 0.999905i \(0.504382\pi\)
\(812\) −0.878107 28.9404i −0.0308155 1.01561i
\(813\) 0 0
\(814\) −11.9615 20.7179i −0.419250 0.726163i
\(815\) 0.310823 0.0108876
\(816\) 0 0
\(817\) −13.0188 −0.455470
\(818\) −65.4311 −2.28775
\(819\) 0 0
\(820\) 0.751682 0.0262499
\(821\) −43.4413 −1.51611 −0.758056 0.652189i \(-0.773851\pi\)
−0.758056 + 0.652189i \(0.773851\pi\)
\(822\) 0 0
\(823\) 3.96546 0.138227 0.0691136 0.997609i \(-0.477983\pi\)
0.0691136 + 0.997609i \(0.477983\pi\)
\(824\) −0.0455399 0.0788774i −0.00158646 0.00274782i
\(825\) 0 0
\(826\) 21.8755 + 11.7600i 0.761144 + 0.409184i
\(827\) −29.3159 −1.01941 −0.509707 0.860348i \(-0.670246\pi\)
−0.509707 + 0.860348i \(0.670246\pi\)
\(828\) 0 0
\(829\) −17.5213 30.3478i −0.608541 1.05402i −0.991481 0.130251i \(-0.958422\pi\)
0.382940 0.923773i \(-0.374912\pi\)
\(830\) 1.12833 1.95432i 0.0391648 0.0678353i
\(831\) 0 0
\(832\) −0.962955 + 1.66789i −0.0333844 + 0.0578236i
\(833\) 19.6036 39.2773i 0.679225 1.36088i
\(834\) 0 0
\(835\) −1.69272 −0.0585788
\(836\) −12.7627 22.1057i −0.441408 0.764541i
\(837\) 0 0
\(838\) 24.5369 42.4992i 0.847614 1.46811i
\(839\) 18.7921 + 32.5489i 0.648777 + 1.12371i 0.983415 + 0.181368i \(0.0580524\pi\)
−0.334639 + 0.942347i \(0.608614\pi\)
\(840\) 0 0
\(841\) 2.32218 4.02213i 0.0800750 0.138694i
\(842\) 2.51060 + 4.34848i 0.0865208 + 0.149858i
\(843\) 0 0
\(844\) 26.0705 45.1555i 0.897385 1.55432i
\(845\) 0.947675 1.64142i 0.0326010 0.0564666i
\(846\) 0 0
\(847\) −0.660455 21.7671i −0.0226935 0.747926i
\(848\) −9.40331 16.2870i −0.322911 0.559298i
\(849\) 0 0
\(850\) 64.1177 2.19922
\(851\) 43.2757 1.48347
\(852\) 0 0
\(853\) 16.3849 + 28.3795i 0.561009 + 0.971696i 0.997409 + 0.0719434i \(0.0229201\pi\)
−0.436400 + 0.899753i \(0.643747\pi\)
\(854\) −3.24604 1.74504i −0.111077 0.0597140i
\(855\) 0 0
\(856\) 1.55609 2.69523i 0.0531861 0.0921211i
\(857\) 13.7673 23.8457i 0.470283 0.814554i −0.529139 0.848535i \(-0.677485\pi\)
0.999422 + 0.0339808i \(0.0108185\pi\)
\(858\) 0 0
\(859\) 23.2550 + 40.2789i 0.793451 + 1.37430i 0.923818 + 0.382832i \(0.125051\pi\)
−0.130366 + 0.991466i \(0.541615\pi\)
\(860\) −0.305158 + 0.528549i −0.0104058 + 0.0180234i
\(861\) 0 0
\(862\) 5.05981 + 8.76384i 0.172338 + 0.298498i
\(863\) −2.44007 + 4.22633i −0.0830610 + 0.143866i −0.904563 0.426339i \(-0.859803\pi\)
0.821502 + 0.570205i \(0.193136\pi\)
\(864\) 0 0
\(865\) −1.16345 2.01516i −0.0395585 0.0685174i
\(866\) −63.3629 −2.15316
\(867\) 0 0
\(868\) 13.0106 + 6.99439i 0.441609 + 0.237405i
\(869\) 10.6463 18.4400i 0.361152 0.625533i
\(870\) 0 0
\(871\) −0.618346 + 1.07101i −0.0209518 + 0.0362897i
\(872\) −1.48738 2.57622i −0.0503690 0.0872417i
\(873\) 0 0
\(874\) 87.8207 2.97058
\(875\) 3.40075 + 1.82821i 0.114966 + 0.0618049i
\(876\) 0 0
\(877\) −19.6446 34.0255i −0.663352 1.14896i −0.979729 0.200326i \(-0.935800\pi\)
0.316378 0.948633i \(-0.397533\pi\)
\(878\) −5.02777 −0.169679
\(879\) 0 0
\(880\) 0.856086 0.0288587
\(881\) −47.3713 −1.59598 −0.797990 0.602670i \(-0.794103\pi\)
−0.797990 + 0.602670i \(0.794103\pi\)
\(882\) 0 0
\(883\) −2.67206 −0.0899221 −0.0449610 0.998989i \(-0.514316\pi\)
−0.0449610 + 0.998989i \(0.514316\pi\)
\(884\) −2.77966 −0.0934902
\(885\) 0 0
\(886\) −54.0007 −1.81419
\(887\) −11.4800 19.8840i −0.385461 0.667638i 0.606372 0.795181i \(-0.292624\pi\)
−0.991833 + 0.127543i \(0.959291\pi\)
\(888\) 0 0
\(889\) −31.4105 16.8860i −1.05347 0.566338i
\(890\) −2.72342 −0.0912891
\(891\) 0 0
\(892\) 4.50259 + 7.79871i 0.150758 + 0.261120i
\(893\) 6.26655 10.8540i 0.209702 0.363214i
\(894\) 0 0
\(895\) −0.566944 + 0.981976i −0.0189508 + 0.0328238i
\(896\) −8.27635 4.44929i −0.276493 0.148640i
\(897\) 0 0
\(898\) −79.4920 −2.65268
\(899\) −6.21284 10.7610i −0.207210 0.358898i
\(900\) 0 0
\(901\) 16.7631 29.0345i 0.558459 0.967280i
\(902\) −3.96054 6.85986i −0.131872 0.228408i
\(903\) 0 0
\(904\) −0.00862948 + 0.0149467i −0.000287012 + 0.000497120i
\(905\) 0.889308 + 1.54033i 0.0295616 + 0.0512022i
\(906\) 0 0
\(907\) 13.9491 24.1606i 0.463173 0.802238i −0.535944 0.844253i \(-0.680044\pi\)
0.999117 + 0.0420148i \(0.0133777\pi\)
\(908\) −4.27177 + 7.39892i −0.141764 + 0.245542i
\(909\) 0 0
\(910\) −0.139902 0.0752099i −0.00463770 0.00249318i
\(911\) 18.7381 + 32.4553i 0.620820 + 1.07529i 0.989333 + 0.145670i \(0.0465337\pi\)
−0.368513 + 0.929623i \(0.620133\pi\)
\(912\) 0 0
\(913\) −12.5032 −0.413794
\(914\) 18.8014 0.621894
\(915\) 0 0
\(916\) −14.5424 25.1881i −0.480493 0.832239i
\(917\) 1.59143 + 52.4499i 0.0525536 + 1.73205i
\(918\) 0 0
\(919\) −15.1073 + 26.1667i −0.498345 + 0.863160i −0.999998 0.00190951i \(-0.999392\pi\)
0.501653 + 0.865069i \(0.332726\pi\)
\(920\) 0.201870 0.349649i 0.00665546 0.0115276i
\(921\) 0 0
\(922\) 30.0145 + 51.9866i 0.988474 + 1.71209i
\(923\) −0.127680 + 0.221147i −0.00420262 + 0.00727916i
\(924\) 0 0
\(925\) 17.4263 + 30.1832i 0.572972 + 0.992417i
\(926\) 16.8611 29.2042i 0.554089 0.959710i
\(927\) 0 0
\(928\) 20.0304 + 34.6937i 0.657531 + 1.13888i
\(929\) 45.9351 1.50708 0.753540 0.657402i \(-0.228344\pi\)
0.753540 + 0.657402i \(0.228344\pi\)
\(930\) 0 0
\(931\) 48.3340 2.93579i 1.58408 0.0962167i
\(932\) 19.4053 33.6110i 0.635642 1.10096i
\(933\) 0 0
\(934\) 15.7850 27.3404i 0.516500 0.894604i
\(935\) 0.763064 + 1.32167i 0.0249549 + 0.0432231i
\(936\) 0 0
\(937\) −45.3797 −1.48249 −0.741245 0.671235i \(-0.765764\pi\)
−0.741245 + 0.671235i \(0.765764\pi\)
\(938\) −29.6085 15.9172i −0.966751 0.519716i
\(939\) 0 0
\(940\) −0.293774 0.508831i −0.00958184 0.0165962i
\(941\) −49.4003 −1.61040 −0.805202 0.593000i \(-0.797943\pi\)
−0.805202 + 0.593000i \(0.797943\pi\)
\(942\) 0 0
\(943\) 14.3289 0.466613
\(944\) −16.0798 −0.523353
\(945\) 0 0
\(946\) 6.43141 0.209103
\(947\) −31.6505 −1.02850 −0.514252 0.857639i \(-0.671930\pi\)
−0.514252 + 0.857639i \(0.671930\pi\)
\(948\) 0 0
\(949\) −0.311271 −0.0101043
\(950\) 35.3637 + 61.2517i 1.14735 + 1.98727i
\(951\) 0 0
\(952\) −0.224718 7.40619i −0.00728315 0.240036i
\(953\) 19.1237 0.619477 0.309739 0.950822i \(-0.399758\pi\)
0.309739 + 0.950822i \(0.399758\pi\)
\(954\) 0 0
\(955\) −0.363249 0.629165i −0.0117545 0.0203593i
\(956\) −8.11273 + 14.0517i −0.262384 + 0.454463i
\(957\) 0 0
\(958\) 38.9465 67.4573i 1.25830 2.17945i
\(959\) 14.5022 8.97001i 0.468300 0.289657i
\(960\) 0 0
\(961\) −24.6607 −0.795507
\(962\) −1.43686 2.48871i −0.0463262 0.0802394i
\(963\) 0 0
\(964\) −6.90857 + 11.9660i −0.222510 + 0.385399i
\(965\) 1.08985 + 1.88768i 0.0350836 + 0.0607666i
\(966\) 0 0
\(967\) 4.98525 8.63470i 0.160315 0.277673i −0.774667 0.632370i \(-0.782082\pi\)
0.934982 + 0.354696i \(0.115416\pi\)
\(968\) −1.83790 3.18334i −0.0590724 0.102316i
\(969\) 0 0
\(970\) 1.19688 2.07306i 0.0384296 0.0665621i
\(971\) −0.522554 + 0.905090i −0.0167695 + 0.0290457i −0.874288 0.485407i \(-0.838671\pi\)
0.857519 + 0.514453i \(0.172005\pi\)
\(972\) 0 0
\(973\) −28.1951 + 17.4395i −0.903895 + 0.559084i
\(974\) −4.72847 8.18994i −0.151510 0.262423i
\(975\) 0 0
\(976\) 2.38603 0.0763751
\(977\) 18.8862 0.604222 0.302111 0.953273i \(-0.402309\pi\)
0.302111 + 0.953273i \(0.402309\pi\)
\(978\) 0 0
\(979\) 7.54466 + 13.0677i 0.241128 + 0.417647i
\(980\) 1.01375 2.03112i 0.0323830 0.0648819i
\(981\) 0 0
\(982\) −31.1899 + 54.0224i −0.995309 + 1.72393i
\(983\) 1.14446 1.98226i 0.0365025 0.0632242i −0.847197 0.531279i \(-0.821712\pi\)
0.883700 + 0.468055i \(0.155045\pi\)
\(984\) 0 0
\(985\) −1.55465 2.69274i −0.0495353 0.0857977i
\(986\) −31.7789 + 55.0427i −1.01205 + 1.75292i
\(987\) 0 0
\(988\) −1.53311 2.65542i −0.0487746 0.0844801i
\(989\) −5.81707 + 10.0755i −0.184972 + 0.320381i
\(990\) 0 0
\(991\) −9.53491 16.5150i −0.302886 0.524615i 0.673902 0.738821i \(-0.264617\pi\)
−0.976789 + 0.214206i \(0.931284\pi\)
\(992\) −20.4381 −0.648911
\(993\) 0 0
\(994\) −6.11372 3.28668i −0.193916 0.104247i
\(995\) −1.45837 + 2.52598i −0.0462336 + 0.0800789i
\(996\) 0 0
\(997\) −18.5075 + 32.0560i −0.586139 + 1.01522i 0.408593 + 0.912717i \(0.366020\pi\)
−0.994732 + 0.102507i \(0.967314\pi\)
\(998\) 9.51732 + 16.4845i 0.301266 + 0.521807i
\(999\) 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 189.2.h.b.37.1 10
3.2 odd 2 63.2.h.b.58.5 yes 10
4.3 odd 2 3024.2.q.i.2305.3 10
7.2 even 3 1323.2.f.e.442.5 10
7.3 odd 6 1323.2.g.f.361.5 10
7.4 even 3 189.2.g.b.172.5 10
7.5 odd 6 1323.2.f.f.442.5 10
7.6 odd 2 1323.2.h.f.226.1 10
9.2 odd 6 63.2.g.b.16.1 yes 10
9.4 even 3 567.2.e.e.163.5 10
9.5 odd 6 567.2.e.f.163.1 10
9.7 even 3 189.2.g.b.100.5 10
12.11 even 2 1008.2.q.i.625.5 10
21.2 odd 6 441.2.f.e.148.1 10
21.5 even 6 441.2.f.f.148.1 10
21.11 odd 6 63.2.g.b.4.1 10
21.17 even 6 441.2.g.f.67.1 10
21.20 even 2 441.2.h.f.373.5 10
28.11 odd 6 3024.2.t.i.1873.3 10
36.7 odd 6 3024.2.t.i.289.3 10
36.11 even 6 1008.2.t.i.961.2 10
63.2 odd 6 441.2.f.e.295.1 10
63.4 even 3 567.2.e.e.487.5 10
63.5 even 6 3969.2.a.ba.1.5 5
63.11 odd 6 63.2.h.b.25.5 yes 10
63.16 even 3 1323.2.f.e.883.5 10
63.20 even 6 441.2.g.f.79.1 10
63.23 odd 6 3969.2.a.z.1.5 5
63.25 even 3 inner 189.2.h.b.46.1 10
63.32 odd 6 567.2.e.f.487.1 10
63.34 odd 6 1323.2.g.f.667.5 10
63.38 even 6 441.2.h.f.214.5 10
63.40 odd 6 3969.2.a.bb.1.1 5
63.47 even 6 441.2.f.f.295.1 10
63.52 odd 6 1323.2.h.f.802.1 10
63.58 even 3 3969.2.a.bc.1.1 5
63.61 odd 6 1323.2.f.f.883.5 10
84.11 even 6 1008.2.t.i.193.2 10
252.11 even 6 1008.2.q.i.529.5 10
252.151 odd 6 3024.2.q.i.2881.3 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.g.b.4.1 10 21.11 odd 6
63.2.g.b.16.1 yes 10 9.2 odd 6
63.2.h.b.25.5 yes 10 63.11 odd 6
63.2.h.b.58.5 yes 10 3.2 odd 2
189.2.g.b.100.5 10 9.7 even 3
189.2.g.b.172.5 10 7.4 even 3
189.2.h.b.37.1 10 1.1 even 1 trivial
189.2.h.b.46.1 10 63.25 even 3 inner
441.2.f.e.148.1 10 21.2 odd 6
441.2.f.e.295.1 10 63.2 odd 6
441.2.f.f.148.1 10 21.5 even 6
441.2.f.f.295.1 10 63.47 even 6
441.2.g.f.67.1 10 21.17 even 6
441.2.g.f.79.1 10 63.20 even 6
441.2.h.f.214.5 10 63.38 even 6
441.2.h.f.373.5 10 21.20 even 2
567.2.e.e.163.5 10 9.4 even 3
567.2.e.e.487.5 10 63.4 even 3
567.2.e.f.163.1 10 9.5 odd 6
567.2.e.f.487.1 10 63.32 odd 6
1008.2.q.i.529.5 10 252.11 even 6
1008.2.q.i.625.5 10 12.11 even 2
1008.2.t.i.193.2 10 84.11 even 6
1008.2.t.i.961.2 10 36.11 even 6
1323.2.f.e.442.5 10 7.2 even 3
1323.2.f.e.883.5 10 63.16 even 3
1323.2.f.f.442.5 10 7.5 odd 6
1323.2.f.f.883.5 10 63.61 odd 6
1323.2.g.f.361.5 10 7.3 odd 6
1323.2.g.f.667.5 10 63.34 odd 6
1323.2.h.f.226.1 10 7.6 odd 2
1323.2.h.f.802.1 10 63.52 odd 6
3024.2.q.i.2305.3 10 4.3 odd 2
3024.2.q.i.2881.3 10 252.151 odd 6
3024.2.t.i.289.3 10 36.7 odd 6
3024.2.t.i.1873.3 10 28.11 odd 6
3969.2.a.z.1.5 5 63.23 odd 6
3969.2.a.ba.1.5 5 63.5 even 6
3969.2.a.bb.1.1 5 63.40 odd 6
3969.2.a.bc.1.1 5 63.58 even 3