Properties

Label 729.2.g.d.109.2
Level $729$
Weight $2$
Character 729.109
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
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] = [729,2,Mod(28,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([44]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.g (of order \(27\), degree \(18\), 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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 109.2
Character \(\chi\) \(=\) 729.109
Dual form 729.2.g.d.622.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.936951 - 0.993110i) q^{2} +(0.00789919 - 0.135624i) q^{4} +(3.78436 - 0.442328i) q^{5} +(1.56116 + 0.784043i) q^{7} +(-2.23391 + 1.87447i) q^{8} +O(q^{10})\) \(q+(-0.936951 - 0.993110i) q^{2} +(0.00789919 - 0.135624i) q^{4} +(3.78436 - 0.442328i) q^{5} +(1.56116 + 0.784043i) q^{7} +(-2.23391 + 1.87447i) q^{8} +(-3.98504 - 3.34385i) q^{10} +(-1.21227 - 2.81037i) q^{11} +(1.81780 + 0.430827i) q^{13} +(-0.684088 - 2.28501i) q^{14} +(3.68475 + 0.430686i) q^{16} +(1.21594 - 6.89593i) q^{17} +(0.858206 + 4.86713i) q^{19} +(-0.0300968 - 0.516743i) q^{20} +(-1.65516 + 3.83710i) q^{22} +(-1.70229 + 0.854924i) q^{23} +(9.26048 - 2.19477i) q^{25} +(-1.27533 - 2.20894i) q^{26} +(0.118667 - 0.205537i) q^{28} +(-0.0649657 + 0.217001i) q^{29} +(3.29127 + 2.16470i) q^{31} +(0.458106 + 0.615343i) q^{32} +(-7.98769 + 5.25359i) q^{34} +(6.25478 + 2.27656i) q^{35} +(0.346276 - 0.126034i) q^{37} +(4.02950 - 5.41256i) q^{38} +(-7.62478 + 8.08179i) q^{40} +(2.97164 - 3.14975i) q^{41} +(-1.93907 + 2.60463i) q^{43} +(-0.390729 + 0.142214i) q^{44} +(2.44400 + 0.889543i) q^{46} +(1.46028 - 0.960441i) q^{47} +(-2.35762 - 3.16683i) q^{49} +(-10.8563 - 7.14028i) q^{50} +(0.0727895 - 0.243134i) q^{52} +(-3.03142 + 5.25057i) q^{53} +(-5.83078 - 10.0992i) q^{55} +(-4.95715 + 1.17487i) q^{56} +(0.276375 - 0.138801i) q^{58} +(0.791355 - 1.83457i) q^{59} +(-0.743636 - 12.7677i) q^{61} +(-0.933972 - 5.29682i) q^{62} +(1.47029 - 8.33845i) q^{64} +(7.06978 + 0.826338i) q^{65} +(1.81970 + 6.07822i) q^{67} +(-0.925647 - 0.219382i) q^{68} +(-3.59956 - 8.34471i) q^{70} +(-10.6917 - 8.97137i) q^{71} +(2.42680 - 2.03633i) q^{73} +(-0.449609 - 0.225802i) q^{74} +(0.666878 - 0.0779468i) q^{76} +(0.310898 - 5.33790i) q^{77} +(1.79892 + 1.90674i) q^{79} +14.1349 q^{80} -5.91234 q^{82} +(-0.154287 - 0.163535i) q^{83} +(1.55128 - 26.6345i) q^{85} +(4.40350 - 0.514695i) q^{86} +(7.97607 + 4.00573i) q^{88} +(-5.45275 + 4.57540i) q^{89} +(2.50009 + 2.09782i) q^{91} +(0.102501 + 0.237625i) q^{92} +(-2.32203 - 0.550332i) q^{94} +(5.40063 + 18.0393i) q^{95} +(-15.4740 - 1.80865i) q^{97} +(-0.936040 + 5.30854i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.936951 0.993110i −0.662525 0.702235i 0.305753 0.952111i \(-0.401092\pi\)
−0.968278 + 0.249876i \(0.919610\pi\)
\(3\) 0 0
\(4\) 0.00789919 0.135624i 0.00394959 0.0678119i
\(5\) 3.78436 0.442328i 1.69242 0.197815i 0.785423 0.618960i \(-0.212446\pi\)
0.906993 + 0.421145i \(0.138372\pi\)
\(6\) 0 0
\(7\) 1.56116 + 0.784043i 0.590062 + 0.296340i 0.718666 0.695356i \(-0.244753\pi\)
−0.128604 + 0.991696i \(0.541049\pi\)
\(8\) −2.23391 + 1.87447i −0.789806 + 0.662726i
\(9\) 0 0
\(10\) −3.98504 3.34385i −1.26018 1.05742i
\(11\) −1.21227 2.81037i −0.365515 0.847358i −0.997384 0.0722832i \(-0.976971\pi\)
0.631870 0.775075i \(-0.282288\pi\)
\(12\) 0 0
\(13\) 1.81780 + 0.430827i 0.504167 + 0.119490i 0.474826 0.880080i \(-0.342511\pi\)
0.0293412 + 0.999569i \(0.490659\pi\)
\(14\) −0.684088 2.28501i −0.182830 0.610695i
\(15\) 0 0
\(16\) 3.68475 + 0.430686i 0.921188 + 0.107671i
\(17\) 1.21594 6.89593i 0.294908 1.67251i −0.372667 0.927965i \(-0.621557\pi\)
0.667575 0.744542i \(-0.267332\pi\)
\(18\) 0 0
\(19\) 0.858206 + 4.86713i 0.196886 + 1.11660i 0.909707 + 0.415250i \(0.136306\pi\)
−0.712821 + 0.701346i \(0.752583\pi\)
\(20\) −0.0300968 0.516743i −0.00672986 0.115547i
\(21\) 0 0
\(22\) −1.65516 + 3.83710i −0.352882 + 0.818073i
\(23\) −1.70229 + 0.854924i −0.354953 + 0.178264i −0.617336 0.786700i \(-0.711788\pi\)
0.262383 + 0.964964i \(0.415492\pi\)
\(24\) 0 0
\(25\) 9.26048 2.19477i 1.85210 0.438955i
\(26\) −1.27533 2.20894i −0.250113 0.433209i
\(27\) 0 0
\(28\) 0.118667 0.205537i 0.0224259 0.0388428i
\(29\) −0.0649657 + 0.217001i −0.0120638 + 0.0402960i −0.963810 0.266592i \(-0.914102\pi\)
0.951746 + 0.306888i \(0.0992876\pi\)
\(30\) 0 0
\(31\) 3.29127 + 2.16470i 0.591130 + 0.388792i 0.809540 0.587065i \(-0.199717\pi\)
−0.218410 + 0.975857i \(0.570087\pi\)
\(32\) 0.458106 + 0.615343i 0.0809825 + 0.108778i
\(33\) 0 0
\(34\) −7.98769 + 5.25359i −1.36988 + 0.900983i
\(35\) 6.25478 + 2.27656i 1.05725 + 0.384808i
\(36\) 0 0
\(37\) 0.346276 0.126034i 0.0569274 0.0207199i −0.313400 0.949621i \(-0.601468\pi\)
0.370327 + 0.928902i \(0.379246\pi\)
\(38\) 4.02950 5.41256i 0.653671 0.878033i
\(39\) 0 0
\(40\) −7.62478 + 8.08179i −1.20558 + 1.27784i
\(41\) 2.97164 3.14975i 0.464092 0.491909i −0.452482 0.891773i \(-0.649461\pi\)
0.916574 + 0.399865i \(0.130943\pi\)
\(42\) 0 0
\(43\) −1.93907 + 2.60463i −0.295706 + 0.397202i −0.925001 0.379964i \(-0.875936\pi\)
0.629295 + 0.777166i \(0.283344\pi\)
\(44\) −0.390729 + 0.142214i −0.0589046 + 0.0214395i
\(45\) 0 0
\(46\) 2.44400 + 0.889543i 0.360348 + 0.131156i
\(47\) 1.46028 0.960441i 0.213004 0.140095i −0.438524 0.898719i \(-0.644499\pi\)
0.651528 + 0.758625i \(0.274128\pi\)
\(48\) 0 0
\(49\) −2.35762 3.16683i −0.336803 0.452405i
\(50\) −10.8563 7.14028i −1.53531 1.00979i
\(51\) 0 0
\(52\) 0.0727895 0.243134i 0.0100941 0.0337166i
\(53\) −3.03142 + 5.25057i −0.416398 + 0.721222i −0.995574 0.0939804i \(-0.970041\pi\)
0.579176 + 0.815202i \(0.303374\pi\)
\(54\) 0 0
\(55\) −5.83078 10.0992i −0.786223 1.36178i
\(56\) −4.95715 + 1.17487i −0.662427 + 0.156998i
\(57\) 0 0
\(58\) 0.276375 0.138801i 0.0362899 0.0182255i
\(59\) 0.791355 1.83457i 0.103026 0.238840i −0.858904 0.512136i \(-0.828854\pi\)
0.961930 + 0.273296i \(0.0881137\pi\)
\(60\) 0 0
\(61\) −0.743636 12.7677i −0.0952129 1.63474i −0.620777 0.783987i \(-0.713183\pi\)
0.525564 0.850754i \(-0.323854\pi\)
\(62\) −0.933972 5.29682i −0.118615 0.672696i
\(63\) 0 0
\(64\) 1.47029 8.33845i 0.183787 1.04231i
\(65\) 7.06978 + 0.826338i 0.876898 + 0.102495i
\(66\) 0 0
\(67\) 1.81970 + 6.07822i 0.222312 + 0.742573i 0.994270 + 0.106899i \(0.0340922\pi\)
−0.771958 + 0.635673i \(0.780723\pi\)
\(68\) −0.925647 0.219382i −0.112251 0.0266040i
\(69\) 0 0
\(70\) −3.59956 8.34471i −0.430229 0.997384i
\(71\) −10.6917 8.97137i −1.26887 1.06471i −0.994678 0.103030i \(-0.967146\pi\)
−0.274189 0.961676i \(-0.588409\pi\)
\(72\) 0 0
\(73\) 2.42680 2.03633i 0.284036 0.238334i −0.489627 0.871932i \(-0.662867\pi\)
0.773663 + 0.633598i \(0.218423\pi\)
\(74\) −0.449609 0.225802i −0.0522660 0.0262490i
\(75\) 0 0
\(76\) 0.666878 0.0779468i 0.0764961 0.00894111i
\(77\) 0.310898 5.33790i 0.0354301 0.608311i
\(78\) 0 0
\(79\) 1.79892 + 1.90674i 0.202394 + 0.214525i 0.820619 0.571476i \(-0.193629\pi\)
−0.618224 + 0.786002i \(0.712148\pi\)
\(80\) 14.1349 1.58033
\(81\) 0 0
\(82\) −5.91234 −0.652908
\(83\) −0.154287 0.163535i −0.0169352 0.0179503i 0.718851 0.695165i \(-0.244669\pi\)
−0.735786 + 0.677214i \(0.763187\pi\)
\(84\) 0 0
\(85\) 1.55128 26.6345i 0.168260 2.88892i
\(86\) 4.40350 0.514695i 0.474841 0.0555010i
\(87\) 0 0
\(88\) 7.97607 + 4.00573i 0.850252 + 0.427012i
\(89\) −5.45275 + 4.57540i −0.577990 + 0.484991i −0.884286 0.466945i \(-0.845355\pi\)
0.306296 + 0.951936i \(0.400910\pi\)
\(90\) 0 0
\(91\) 2.50009 + 2.09782i 0.262080 + 0.219912i
\(92\) 0.102501 + 0.237625i 0.0106865 + 0.0247741i
\(93\) 0 0
\(94\) −2.32203 0.550332i −0.239500 0.0567624i
\(95\) 5.40063 + 18.0393i 0.554093 + 1.85080i
\(96\) 0 0
\(97\) −15.4740 1.80865i −1.57115 0.183641i −0.714535 0.699600i \(-0.753362\pi\)
−0.856613 + 0.515959i \(0.827436\pi\)
\(98\) −0.936040 + 5.30854i −0.0945543 + 0.536244i
\(99\) 0 0
\(100\) −0.224513 1.27328i −0.0224513 0.127328i
\(101\) 0.499658 + 8.57880i 0.0497179 + 0.853623i 0.927328 + 0.374249i \(0.122099\pi\)
−0.877611 + 0.479374i \(0.840864\pi\)
\(102\) 0 0
\(103\) −0.457458 + 1.06051i −0.0450747 + 0.104495i −0.939266 0.343191i \(-0.888492\pi\)
0.894191 + 0.447686i \(0.147752\pi\)
\(104\) −4.86838 + 2.44499i −0.477384 + 0.239751i
\(105\) 0 0
\(106\) 8.05469 1.90900i 0.782341 0.185418i
\(107\) 5.53177 + 9.58130i 0.534776 + 0.926259i 0.999174 + 0.0406326i \(0.0129373\pi\)
−0.464398 + 0.885626i \(0.653729\pi\)
\(108\) 0 0
\(109\) −7.60162 + 13.1664i −0.728103 + 1.26111i 0.229581 + 0.973290i \(0.426264\pi\)
−0.957684 + 0.287822i \(0.907069\pi\)
\(110\) −4.56647 + 15.2531i −0.435396 + 1.45432i
\(111\) 0 0
\(112\) 5.41480 + 3.56137i 0.511651 + 0.336518i
\(113\) −1.26634 1.70099i −0.119128 0.160016i 0.738559 0.674189i \(-0.235507\pi\)
−0.857687 + 0.514173i \(0.828099\pi\)
\(114\) 0 0
\(115\) −6.06393 + 3.98831i −0.565464 + 0.371912i
\(116\) 0.0289173 + 0.0105250i 0.00268490 + 0.000977224i
\(117\) 0 0
\(118\) −2.56339 + 0.932997i −0.235979 + 0.0858894i
\(119\) 7.30497 9.81228i 0.669646 0.899490i
\(120\) 0 0
\(121\) 1.12010 1.18723i 0.101827 0.107930i
\(122\) −11.9830 + 12.7013i −1.08489 + 1.14992i
\(123\) 0 0
\(124\) 0.319584 0.429275i 0.0286995 0.0385501i
\(125\) 16.1725 5.88629i 1.44651 0.526486i
\(126\) 0 0
\(127\) 10.6417 + 3.87328i 0.944302 + 0.343698i 0.767863 0.640614i \(-0.221320\pi\)
0.176439 + 0.984312i \(0.443542\pi\)
\(128\) −8.37672 + 5.50945i −0.740404 + 0.486971i
\(129\) 0 0
\(130\) −5.80339 7.79531i −0.508991 0.683694i
\(131\) 9.05051 + 5.95261i 0.790747 + 0.520082i 0.879459 0.475975i \(-0.157905\pi\)
−0.0887122 + 0.996057i \(0.528275\pi\)
\(132\) 0 0
\(133\) −2.47624 + 8.27123i −0.214718 + 0.717207i
\(134\) 4.33137 7.50216i 0.374174 0.648088i
\(135\) 0 0
\(136\) 10.2099 + 17.6841i 0.875494 + 1.51640i
\(137\) −12.3269 + 2.92153i −1.05316 + 0.249603i −0.720507 0.693447i \(-0.756091\pi\)
−0.332650 + 0.943050i \(0.607943\pi\)
\(138\) 0 0
\(139\) −8.67894 + 4.35873i −0.736138 + 0.369703i −0.777032 0.629461i \(-0.783276\pi\)
0.0408939 + 0.999163i \(0.486979\pi\)
\(140\) 0.358163 0.830314i 0.0302703 0.0701744i
\(141\) 0 0
\(142\) 1.10801 + 19.0237i 0.0929819 + 1.59644i
\(143\) −0.992892 5.63097i −0.0830298 0.470886i
\(144\) 0 0
\(145\) −0.149868 + 0.849944i −0.0124459 + 0.0705840i
\(146\) −4.29610 0.502142i −0.355547 0.0415575i
\(147\) 0 0
\(148\) −0.0143579 0.0479588i −0.00118021 0.00394219i
\(149\) 4.03952 + 0.957383i 0.330930 + 0.0784319i 0.392722 0.919657i \(-0.371533\pi\)
−0.0617920 + 0.998089i \(0.519682\pi\)
\(150\) 0 0
\(151\) −1.28290 2.97410i −0.104401 0.242029i 0.858006 0.513639i \(-0.171703\pi\)
−0.962407 + 0.271611i \(0.912444\pi\)
\(152\) −11.0405 9.26404i −0.895499 0.751413i
\(153\) 0 0
\(154\) −5.59242 + 4.69260i −0.450650 + 0.378141i
\(155\) 13.4129 + 6.73619i 1.07735 + 0.541064i
\(156\) 0 0
\(157\) 7.42674 0.868061i 0.592718 0.0692788i 0.185554 0.982634i \(-0.440592\pi\)
0.407164 + 0.913355i \(0.366518\pi\)
\(158\) 0.208107 3.57305i 0.0165561 0.284257i
\(159\) 0 0
\(160\) 2.00582 + 2.12605i 0.158574 + 0.168079i
\(161\) −3.32785 −0.262271
\(162\) 0 0
\(163\) −9.71856 −0.761216 −0.380608 0.924736i \(-0.624285\pi\)
−0.380608 + 0.924736i \(0.624285\pi\)
\(164\) −0.403708 0.427906i −0.0315243 0.0334138i
\(165\) 0 0
\(166\) −0.0178486 + 0.306448i −0.00138532 + 0.0237850i
\(167\) 0.715618 0.0836438i 0.0553762 0.00647255i −0.0883597 0.996089i \(-0.528162\pi\)
0.143736 + 0.989616i \(0.454088\pi\)
\(168\) 0 0
\(169\) −8.49843 4.26807i −0.653726 0.328313i
\(170\) −27.9045 + 23.4146i −2.14017 + 1.79582i
\(171\) 0 0
\(172\) 0.337932 + 0.283559i 0.0257671 + 0.0216212i
\(173\) 0.868881 + 2.01429i 0.0660598 + 0.153144i 0.948048 0.318128i \(-0.103054\pi\)
−0.881988 + 0.471272i \(0.843795\pi\)
\(174\) 0 0
\(175\) 16.1779 + 3.83423i 1.22293 + 0.289840i
\(176\) −3.25655 10.8776i −0.245471 0.819931i
\(177\) 0 0
\(178\) 9.65284 + 1.12825i 0.723511 + 0.0845663i
\(179\) −4.40985 + 25.0095i −0.329608 + 1.86930i 0.145482 + 0.989361i \(0.453527\pi\)
−0.475090 + 0.879937i \(0.657584\pi\)
\(180\) 0 0
\(181\) 2.09357 + 11.8732i 0.155614 + 0.882531i 0.958222 + 0.286024i \(0.0923338\pi\)
−0.802608 + 0.596506i \(0.796555\pi\)
\(182\) −0.259091 4.44842i −0.0192051 0.329739i
\(183\) 0 0
\(184\) 2.20024 5.10072i 0.162204 0.376030i
\(185\) 1.25468 0.630125i 0.0922461 0.0463277i
\(186\) 0 0
\(187\) −20.8541 + 4.94252i −1.52501 + 0.361433i
\(188\) −0.118724 0.205635i −0.00865881 0.0149975i
\(189\) 0 0
\(190\) 12.8549 22.2654i 0.932596 1.61530i
\(191\) 4.19556 14.0141i 0.303580 1.01403i −0.661033 0.750357i \(-0.729882\pi\)
0.964613 0.263671i \(-0.0849332\pi\)
\(192\) 0 0
\(193\) 17.7456 + 11.6714i 1.27735 + 0.840128i 0.992945 0.118575i \(-0.0378326\pi\)
0.284408 + 0.958703i \(0.408203\pi\)
\(194\) 12.7022 + 17.0620i 0.911965 + 1.22498i
\(195\) 0 0
\(196\) −0.448121 + 0.294734i −0.0320086 + 0.0210524i
\(197\) 16.9847 + 6.18193i 1.21011 + 0.440444i 0.866742 0.498756i \(-0.166210\pi\)
0.343369 + 0.939201i \(0.388432\pi\)
\(198\) 0 0
\(199\) 22.9288 8.34541i 1.62538 0.591590i 0.640985 0.767554i \(-0.278526\pi\)
0.984397 + 0.175963i \(0.0563040\pi\)
\(200\) −16.5730 + 22.2614i −1.17189 + 1.57412i
\(201\) 0 0
\(202\) 8.05155 8.53414i 0.566505 0.600460i
\(203\) −0.271560 + 0.287836i −0.0190597 + 0.0202021i
\(204\) 0 0
\(205\) 9.85252 13.2342i 0.688130 0.924319i
\(206\) 1.48182 0.539338i 0.103243 0.0375774i
\(207\) 0 0
\(208\) 6.51260 + 2.37039i 0.451567 + 0.164357i
\(209\) 12.6380 8.31217i 0.874192 0.574965i
\(210\) 0 0
\(211\) −9.16549 12.3114i −0.630979 0.847551i 0.365551 0.930791i \(-0.380881\pi\)
−0.996530 + 0.0832399i \(0.973473\pi\)
\(212\) 0.688157 + 0.452608i 0.0472628 + 0.0310852i
\(213\) 0 0
\(214\) 4.33229 14.4709i 0.296149 0.989208i
\(215\) −6.18604 + 10.7145i −0.421885 + 0.730726i
\(216\) 0 0
\(217\) 3.44097 + 5.95994i 0.233589 + 0.404587i
\(218\) 20.1980 4.78702i 1.36798 0.324218i
\(219\) 0 0
\(220\) −1.41575 + 0.711017i −0.0954500 + 0.0479368i
\(221\) 5.18128 12.0116i 0.348531 0.807985i
\(222\) 0 0
\(223\) 0.835212 + 14.3400i 0.0559299 + 0.960280i 0.903228 + 0.429162i \(0.141191\pi\)
−0.847298 + 0.531118i \(0.821772\pi\)
\(224\) 0.232720 + 1.31982i 0.0155493 + 0.0881844i
\(225\) 0 0
\(226\) −0.502773 + 2.85137i −0.0334440 + 0.189670i
\(227\) −11.1437 1.30251i −0.739633 0.0864507i −0.262071 0.965049i \(-0.584405\pi\)
−0.477562 + 0.878598i \(0.658479\pi\)
\(228\) 0 0
\(229\) −2.75304 9.19578i −0.181926 0.607674i −0.999493 0.0318410i \(-0.989863\pi\)
0.817567 0.575833i \(-0.195322\pi\)
\(230\) 9.64244 + 2.28530i 0.635804 + 0.150688i
\(231\) 0 0
\(232\) −0.261634 0.606536i −0.0171771 0.0398210i
\(233\) 13.4395 + 11.2771i 0.880451 + 0.738786i 0.966272 0.257524i \(-0.0829067\pi\)
−0.0858206 + 0.996311i \(0.527351\pi\)
\(234\) 0 0
\(235\) 5.10139 4.28057i 0.332778 0.279234i
\(236\) −0.242560 0.121818i −0.0157893 0.00792969i
\(237\) 0 0
\(238\) −16.5891 + 1.93899i −1.07531 + 0.125686i
\(239\) −1.58767 + 27.2592i −0.102698 + 1.76325i 0.417002 + 0.908905i \(0.363081\pi\)
−0.519700 + 0.854349i \(0.673956\pi\)
\(240\) 0 0
\(241\) −3.56923 3.78316i −0.229914 0.243695i 0.602138 0.798392i \(-0.294316\pi\)
−0.832052 + 0.554697i \(0.812834\pi\)
\(242\) −2.22853 −0.143255
\(243\) 0 0
\(244\) −1.73748 −0.111231
\(245\) −10.3229 10.9416i −0.659503 0.699032i
\(246\) 0 0
\(247\) −0.536842 + 9.21721i −0.0341584 + 0.586477i
\(248\) −11.4101 + 1.33365i −0.724541 + 0.0846866i
\(249\) 0 0
\(250\) −20.9985 10.5459i −1.32806 0.666979i
\(251\) −3.65188 + 3.06429i −0.230505 + 0.193416i −0.750723 0.660617i \(-0.770295\pi\)
0.520219 + 0.854033i \(0.325850\pi\)
\(252\) 0 0
\(253\) 4.46630 + 3.74767i 0.280794 + 0.235614i
\(254\) −6.12421 14.1975i −0.384267 0.890831i
\(255\) 0 0
\(256\) −3.15763 0.748372i −0.197352 0.0467733i
\(257\) −0.871576 2.91127i −0.0543674 0.181600i 0.926493 0.376312i \(-0.122808\pi\)
−0.980860 + 0.194712i \(0.937623\pi\)
\(258\) 0 0
\(259\) 0.639407 + 0.0747360i 0.0397308 + 0.00464387i
\(260\) 0.167917 0.952303i 0.0104137 0.0590593i
\(261\) 0 0
\(262\) −2.56828 14.5655i −0.158669 0.899857i
\(263\) 1.45254 + 24.9392i 0.0895675 + 1.53781i 0.681495 + 0.731823i \(0.261330\pi\)
−0.591927 + 0.805991i \(0.701633\pi\)
\(264\) 0 0
\(265\) −9.14950 + 21.2109i −0.562049 + 1.30298i
\(266\) 10.5344 5.29056i 0.645903 0.324385i
\(267\) 0 0
\(268\) 0.838725 0.198781i 0.0512333 0.0121425i
\(269\) −12.6465 21.9043i −0.771069 1.33553i −0.936977 0.349390i \(-0.886389\pi\)
0.165908 0.986141i \(-0.446944\pi\)
\(270\) 0 0
\(271\) −11.3545 + 19.6666i −0.689737 + 1.19466i 0.282186 + 0.959360i \(0.408941\pi\)
−0.971923 + 0.235300i \(0.924393\pi\)
\(272\) 7.45041 24.8861i 0.451747 1.50894i
\(273\) 0 0
\(274\) 14.4511 + 9.50464i 0.873023 + 0.574196i
\(275\) −17.3944 23.3647i −1.04892 1.40894i
\(276\) 0 0
\(277\) 24.0470 15.8160i 1.44485 0.950291i 0.446386 0.894841i \(-0.352711\pi\)
0.998461 0.0554503i \(-0.0176594\pi\)
\(278\) 12.4604 + 4.53523i 0.747328 + 0.272005i
\(279\) 0 0
\(280\) −18.2400 + 6.63880i −1.09005 + 0.396744i
\(281\) −1.10177 + 1.47993i −0.0657261 + 0.0882855i −0.833771 0.552111i \(-0.813822\pi\)
0.768045 + 0.640396i \(0.221230\pi\)
\(282\) 0 0
\(283\) −4.12133 + 4.36835i −0.244988 + 0.259672i −0.838186 0.545385i \(-0.816384\pi\)
0.593198 + 0.805056i \(0.297865\pi\)
\(284\) −1.30119 + 1.37918i −0.0772112 + 0.0818391i
\(285\) 0 0
\(286\) −4.66189 + 6.26200i −0.275663 + 0.370280i
\(287\) 7.10874 2.58737i 0.419616 0.152728i
\(288\) 0 0
\(289\) −30.1005 10.9557i −1.77062 0.644452i
\(290\) 0.984507 0.647521i 0.0578123 0.0380237i
\(291\) 0 0
\(292\) −0.257005 0.345218i −0.0150401 0.0202023i
\(293\) −8.87378 5.83638i −0.518412 0.340965i 0.263189 0.964744i \(-0.415226\pi\)
−0.781600 + 0.623780i \(0.785596\pi\)
\(294\) 0 0
\(295\) 2.18329 7.29270i 0.127116 0.424597i
\(296\) −0.537301 + 0.930632i −0.0312300 + 0.0540919i
\(297\) 0 0
\(298\) −2.83404 4.90871i −0.164172 0.284354i
\(299\) −3.46276 + 0.820688i −0.200256 + 0.0474616i
\(300\) 0 0
\(301\) −5.06934 + 2.54592i −0.292192 + 0.146744i
\(302\) −1.75159 + 4.06065i −0.100793 + 0.233664i
\(303\) 0 0
\(304\) 1.06607 + 18.3038i 0.0611435 + 1.04979i
\(305\) −8.46171 47.9888i −0.484516 2.74783i
\(306\) 0 0
\(307\) 0.293712 1.66572i 0.0167630 0.0950677i −0.975278 0.220980i \(-0.929075\pi\)
0.992041 + 0.125912i \(0.0401857\pi\)
\(308\) −0.721491 0.0843302i −0.0411108 0.00480516i
\(309\) 0 0
\(310\) −5.87741 19.6319i −0.333815 1.11502i
\(311\) −26.4251 6.26288i −1.49843 0.355135i −0.602065 0.798447i \(-0.705655\pi\)
−0.896367 + 0.443312i \(0.853803\pi\)
\(312\) 0 0
\(313\) 10.6694 + 24.7345i 0.603071 + 1.39808i 0.896906 + 0.442220i \(0.145809\pi\)
−0.293835 + 0.955856i \(0.594932\pi\)
\(314\) −7.82057 6.56224i −0.441340 0.370329i
\(315\) 0 0
\(316\) 0.272810 0.228915i 0.0153467 0.0128774i
\(317\) 4.75988 + 2.39050i 0.267342 + 0.134264i 0.577421 0.816447i \(-0.304059\pi\)
−0.310079 + 0.950711i \(0.600356\pi\)
\(318\) 0 0
\(319\) 0.688608 0.0804867i 0.0385546 0.00450639i
\(320\) 1.87579 32.2060i 0.104860 1.80037i
\(321\) 0 0
\(322\) 3.11803 + 3.30492i 0.173761 + 0.184176i
\(323\) 34.6069 1.92558
\(324\) 0 0
\(325\) 17.7793 0.986217
\(326\) 9.10582 + 9.65161i 0.504325 + 0.534553i
\(327\) 0 0
\(328\) −0.734246 + 12.6065i −0.0405420 + 0.696079i
\(329\) 3.03275 0.354478i 0.167201 0.0195430i
\(330\) 0 0
\(331\) 12.9227 + 6.49005i 0.710298 + 0.356725i 0.766983 0.641667i \(-0.221757\pi\)
−0.0566852 + 0.998392i \(0.518053\pi\)
\(332\) −0.0233980 + 0.0196332i −0.00128413 + 0.00107751i
\(333\) 0 0
\(334\) −0.753567 0.632318i −0.0412334 0.0345989i
\(335\) 9.57496 + 22.1972i 0.523136 + 1.21277i
\(336\) 0 0
\(337\) 14.0973 + 3.34111i 0.767927 + 0.182002i 0.595866 0.803084i \(-0.296809\pi\)
0.172061 + 0.985086i \(0.444957\pi\)
\(338\) 3.72395 + 12.4389i 0.202556 + 0.676585i
\(339\) 0 0
\(340\) −3.60002 0.420782i −0.195238 0.0228201i
\(341\) 2.09369 11.8739i 0.113380 0.643008i
\(342\) 0 0
\(343\) −3.32120 18.8355i −0.179328 1.01702i
\(344\) −0.550588 9.45324i −0.0296857 0.509684i
\(345\) 0 0
\(346\) 1.18632 2.75019i 0.0637767 0.147851i
\(347\) −3.16541 + 1.58973i −0.169928 + 0.0853411i −0.531730 0.846914i \(-0.678458\pi\)
0.361802 + 0.932255i \(0.382162\pi\)
\(348\) 0 0
\(349\) −28.8257 + 6.83182i −1.54301 + 0.365699i −0.912037 0.410109i \(-0.865491\pi\)
−0.630969 + 0.775808i \(0.717343\pi\)
\(350\) −11.3501 19.6589i −0.606687 1.05081i
\(351\) 0 0
\(352\) 1.17399 2.03341i 0.0625739 0.108381i
\(353\) −7.82072 + 26.1230i −0.416255 + 1.39039i 0.451000 + 0.892524i \(0.351068\pi\)
−0.867255 + 0.497865i \(0.834118\pi\)
\(354\) 0 0
\(355\) −44.4294 29.2217i −2.35807 1.55092i
\(356\) 0.577461 + 0.775664i 0.0306054 + 0.0411101i
\(357\) 0 0
\(358\) 28.9690 19.0532i 1.53106 1.00699i
\(359\) 1.58829 + 0.578092i 0.0838270 + 0.0305105i 0.383593 0.923502i \(-0.374686\pi\)
−0.299766 + 0.954013i \(0.596909\pi\)
\(360\) 0 0
\(361\) −5.09828 + 1.85562i −0.268330 + 0.0976642i
\(362\) 9.82986 13.2038i 0.516646 0.693976i
\(363\) 0 0
\(364\) 0.304263 0.322500i 0.0159477 0.0169036i
\(365\) 8.28316 8.77964i 0.433561 0.459547i
\(366\) 0 0
\(367\) 3.25794 4.37617i 0.170063 0.228434i −0.708918 0.705291i \(-0.750816\pi\)
0.878981 + 0.476856i \(0.158224\pi\)
\(368\) −6.64073 + 2.41703i −0.346172 + 0.125996i
\(369\) 0 0
\(370\) −1.80136 0.655641i −0.0936482 0.0340852i
\(371\) −8.84920 + 5.82021i −0.459428 + 0.302170i
\(372\) 0 0
\(373\) 12.5081 + 16.8013i 0.647643 + 0.869936i 0.997769 0.0667668i \(-0.0212683\pi\)
−0.350125 + 0.936703i \(0.613861\pi\)
\(374\) 24.4478 + 16.0796i 1.26416 + 0.831454i
\(375\) 0 0
\(376\) −1.46181 + 4.88279i −0.0753872 + 0.251811i
\(377\) −0.211584 + 0.366475i −0.0108972 + 0.0188744i
\(378\) 0 0
\(379\) −17.0149 29.4707i −0.873998 1.51381i −0.857826 0.513940i \(-0.828185\pi\)
−0.0161719 0.999869i \(-0.505148\pi\)
\(380\) 2.48923 0.589957i 0.127695 0.0302642i
\(381\) 0 0
\(382\) −17.8486 + 8.96391i −0.913215 + 0.458634i
\(383\) −3.94156 + 9.13755i −0.201404 + 0.466907i −0.988745 0.149611i \(-0.952198\pi\)
0.787341 + 0.616518i \(0.211457\pi\)
\(384\) 0 0
\(385\) −1.18456 20.3381i −0.0603706 1.03652i
\(386\) −5.03570 28.5589i −0.256310 1.45361i
\(387\) 0 0
\(388\) −0.367528 + 2.08436i −0.0186584 + 0.105817i
\(389\) 17.4378 + 2.03818i 0.884130 + 0.103340i 0.546026 0.837768i \(-0.316140\pi\)
0.338105 + 0.941108i \(0.390214\pi\)
\(390\) 0 0
\(391\) 3.82561 + 12.7784i 0.193469 + 0.646233i
\(392\) 11.2028 + 2.65512i 0.565829 + 0.134104i
\(393\) 0 0
\(394\) −9.77451 22.6599i −0.492433 1.14159i
\(395\) 7.65116 + 6.42008i 0.384972 + 0.323030i
\(396\) 0 0
\(397\) −12.8659 + 10.7958i −0.645721 + 0.541824i −0.905769 0.423771i \(-0.860706\pi\)
0.260048 + 0.965596i \(0.416262\pi\)
\(398\) −29.7711 14.9516i −1.49229 0.749457i
\(399\) 0 0
\(400\) 35.0678 4.09884i 1.75339 0.204942i
\(401\) 0.152825 2.62391i 0.00763173 0.131032i −0.992340 0.123535i \(-0.960577\pi\)
0.999972 0.00749640i \(-0.00238620\pi\)
\(402\) 0 0
\(403\) 5.05027 + 5.35297i 0.251572 + 0.266650i
\(404\) 1.16744 0.0580822
\(405\) 0 0
\(406\) 0.540291 0.0268142
\(407\) −0.773983 0.820374i −0.0383649 0.0406644i
\(408\) 0 0
\(409\) 0.456729 7.84174i 0.0225838 0.387749i −0.968010 0.250912i \(-0.919269\pi\)
0.990594 0.136837i \(-0.0436936\pi\)
\(410\) −22.3744 + 2.61519i −1.10499 + 0.129155i
\(411\) 0 0
\(412\) 0.140217 + 0.0704194i 0.00690797 + 0.00346931i
\(413\) 2.67381 2.24359i 0.131570 0.110400i
\(414\) 0 0
\(415\) −0.656214 0.550629i −0.0322123 0.0270293i
\(416\) 0.567640 + 1.31594i 0.0278308 + 0.0645191i
\(417\) 0 0
\(418\) −20.0961 4.76287i −0.982934 0.232960i
\(419\) −9.07933 30.3271i −0.443554 1.48158i −0.829213 0.558933i \(-0.811211\pi\)
0.385658 0.922642i \(-0.373974\pi\)
\(420\) 0 0
\(421\) 0.514644 + 0.0601533i 0.0250822 + 0.00293169i 0.128625 0.991693i \(-0.458944\pi\)
−0.103543 + 0.994625i \(0.533018\pi\)
\(422\) −3.63895 + 20.6375i −0.177141 + 1.00462i
\(423\) 0 0
\(424\) −3.07014 17.4116i −0.149099 0.845583i
\(425\) −3.87483 66.5283i −0.187957 3.22710i
\(426\) 0 0
\(427\) 8.84952 20.5155i 0.428258 0.992815i
\(428\) 1.34315 0.674554i 0.0649235 0.0326058i
\(429\) 0 0
\(430\) 16.4367 3.89558i 0.792650 0.187862i
\(431\) −5.66734 9.81613i −0.272986 0.472826i 0.696639 0.717422i \(-0.254678\pi\)
−0.969625 + 0.244596i \(0.921345\pi\)
\(432\) 0 0
\(433\) 3.59806 6.23203i 0.172912 0.299492i −0.766525 0.642215i \(-0.778016\pi\)
0.939437 + 0.342723i \(0.111349\pi\)
\(434\) 2.69486 9.00144i 0.129357 0.432083i
\(435\) 0 0
\(436\) 1.72563 + 1.13496i 0.0826426 + 0.0543549i
\(437\) −5.62194 7.55158i −0.268934 0.361241i
\(438\) 0 0
\(439\) 1.52694 1.00428i 0.0728767 0.0479317i −0.512548 0.858659i \(-0.671298\pi\)
0.585424 + 0.810727i \(0.300928\pi\)
\(440\) 31.9561 + 11.6311i 1.52345 + 0.554490i
\(441\) 0 0
\(442\) −16.7834 + 6.10867i −0.798306 + 0.290560i
\(443\) −9.44074 + 12.6811i −0.448543 + 0.602498i −0.967676 0.252196i \(-0.918847\pi\)
0.519133 + 0.854693i \(0.326255\pi\)
\(444\) 0 0
\(445\) −18.6113 + 19.7268i −0.882261 + 0.935142i
\(446\) 13.4587 14.2654i 0.637287 0.675485i
\(447\) 0 0
\(448\) 8.83306 11.8649i 0.417323 0.560562i
\(449\) −9.12091 + 3.31974i −0.430442 + 0.156668i −0.548150 0.836380i \(-0.684668\pi\)
0.117708 + 0.993048i \(0.462445\pi\)
\(450\) 0 0
\(451\) −12.4544 4.53304i −0.586455 0.213452i
\(452\) −0.240698 + 0.158310i −0.0113215 + 0.00744627i
\(453\) 0 0
\(454\) 9.14756 + 12.2873i 0.429316 + 0.576672i
\(455\) 10.3892 + 6.83305i 0.487051 + 0.320339i
\(456\) 0 0
\(457\) −0.736953 + 2.46159i −0.0344732 + 0.115149i −0.973494 0.228711i \(-0.926549\pi\)
0.939021 + 0.343859i \(0.111734\pi\)
\(458\) −6.55296 + 11.3501i −0.306200 + 0.530354i
\(459\) 0 0
\(460\) 0.493010 + 0.853918i 0.0229867 + 0.0398141i
\(461\) 3.15508 0.747767i 0.146947 0.0348270i −0.156484 0.987680i \(-0.550016\pi\)
0.303431 + 0.952853i \(0.401868\pi\)
\(462\) 0 0
\(463\) 8.67454 4.35652i 0.403140 0.202465i −0.235663 0.971835i \(-0.575726\pi\)
0.638803 + 0.769370i \(0.279430\pi\)
\(464\) −0.332842 + 0.771614i −0.0154518 + 0.0358213i
\(465\) 0 0
\(466\) −1.39277 23.9130i −0.0645190 1.10775i
\(467\) 0.550626 + 3.12276i 0.0254799 + 0.144504i 0.994894 0.100928i \(-0.0321812\pi\)
−0.969414 + 0.245432i \(0.921070\pi\)
\(468\) 0 0
\(469\) −1.92475 + 10.9158i −0.0888765 + 0.504044i
\(470\) −9.03084 1.05555i −0.416561 0.0486890i
\(471\) 0 0
\(472\) 1.67103 + 5.58163i 0.0769154 + 0.256915i
\(473\) 9.67065 + 2.29199i 0.444657 + 0.105386i
\(474\) 0 0
\(475\) 18.6297 + 43.1884i 0.854787 + 1.98162i
\(476\) −1.27308 1.06824i −0.0583513 0.0489626i
\(477\) 0 0
\(478\) 28.5590 23.9639i 1.30626 1.09608i
\(479\) −24.7479 12.4289i −1.13076 0.567890i −0.217824 0.975988i \(-0.569896\pi\)
−0.912938 + 0.408098i \(0.866192\pi\)
\(480\) 0 0
\(481\) 0.683759 0.0799200i 0.0311767 0.00364404i
\(482\) −0.412903 + 7.08927i −0.0188072 + 0.322908i
\(483\) 0 0
\(484\) −0.152169 0.161290i −0.00691679 0.00733137i
\(485\) −59.3592 −2.69536
\(486\) 0 0
\(487\) 10.4889 0.475298 0.237649 0.971351i \(-0.423623\pi\)
0.237649 + 0.971351i \(0.423623\pi\)
\(488\) 25.5940 + 27.1280i 1.15859 + 1.22803i
\(489\) 0 0
\(490\) −1.19419 + 20.5035i −0.0539480 + 0.926252i
\(491\) 5.88746 0.688145i 0.265697 0.0310556i 0.0177989 0.999842i \(-0.494334\pi\)
0.247898 + 0.968786i \(0.420260\pi\)
\(492\) 0 0
\(493\) 1.41743 + 0.711858i 0.0638376 + 0.0320605i
\(494\) 9.65671 8.10294i 0.434476 0.364568i
\(495\) 0 0
\(496\) 11.1952 + 9.39390i 0.502680 + 0.421798i
\(497\) −9.65744 22.3885i −0.433195 1.00426i
\(498\) 0 0
\(499\) −37.0899 8.79048i −1.66037 0.393516i −0.709895 0.704307i \(-0.751258\pi\)
−0.950478 + 0.310791i \(0.899406\pi\)
\(500\) −0.670572 2.23987i −0.0299889 0.100170i
\(501\) 0 0
\(502\) 6.46481 + 0.755628i 0.288539 + 0.0337253i
\(503\) −2.25782 + 12.8047i −0.100671 + 0.570935i 0.892190 + 0.451660i \(0.149168\pi\)
−0.992861 + 0.119275i \(0.961943\pi\)
\(504\) 0 0
\(505\) 5.68553 + 32.2442i 0.253003 + 1.43485i
\(506\) −0.462855 7.94691i −0.0205764 0.353283i
\(507\) 0 0
\(508\) 0.609370 1.41268i 0.0270364 0.0626775i
\(509\) 24.3118 12.2098i 1.07760 0.541192i 0.180752 0.983529i \(-0.442147\pi\)
0.896849 + 0.442337i \(0.145850\pi\)
\(510\) 0 0
\(511\) 5.38519 1.27631i 0.238227 0.0564608i
\(512\) 12.2415 + 21.2028i 0.541002 + 0.937042i
\(513\) 0 0
\(514\) −2.07458 + 3.59329i −0.0915060 + 0.158493i
\(515\) −1.26209 + 4.21569i −0.0556145 + 0.185765i
\(516\) 0 0
\(517\) −4.46945 2.93960i −0.196566 0.129284i
\(518\) −0.524872 0.705026i −0.0230616 0.0309771i
\(519\) 0 0
\(520\) −17.3422 + 11.4061i −0.760505 + 0.500192i
\(521\) 8.60146 + 3.13068i 0.376837 + 0.137157i 0.523493 0.852030i \(-0.324629\pi\)
−0.146656 + 0.989188i \(0.546851\pi\)
\(522\) 0 0
\(523\) 24.5766 8.94516i 1.07466 0.391144i 0.256743 0.966480i \(-0.417351\pi\)
0.817918 + 0.575335i \(0.195128\pi\)
\(524\) 0.878807 1.18044i 0.0383909 0.0515679i
\(525\) 0 0
\(526\) 23.4064 24.8093i 1.02057 1.08174i
\(527\) 18.9296 20.0642i 0.824587 0.874011i
\(528\) 0 0
\(529\) −11.5677 + 15.5382i −0.502945 + 0.675573i
\(530\) 29.6374 10.7871i 1.28737 0.468564i
\(531\) 0 0
\(532\) 1.10222 + 0.401173i 0.0477871 + 0.0173931i
\(533\) 6.75885 4.44537i 0.292758 0.192550i
\(534\) 0 0
\(535\) 25.1723 + 33.8122i 1.08829 + 1.46183i
\(536\) −15.4585 10.1672i −0.667705 0.439157i
\(537\) 0 0
\(538\) −9.90429 + 33.0826i −0.427004 + 1.42629i
\(539\) −6.04188 + 10.4648i −0.260242 + 0.450753i
\(540\) 0 0
\(541\) 4.36966 + 7.56848i 0.187867 + 0.325394i 0.944539 0.328400i \(-0.106509\pi\)
−0.756672 + 0.653794i \(0.773176\pi\)
\(542\) 30.1697 7.15035i 1.29590 0.307134i
\(543\) 0 0
\(544\) 4.80039 2.41085i 0.205815 0.103364i
\(545\) −22.9434 + 53.1887i −0.982786 + 2.27835i
\(546\) 0 0
\(547\) −1.76688 30.3361i −0.0755461 1.29708i −0.796731 0.604334i \(-0.793439\pi\)
0.721185 0.692743i \(-0.243598\pi\)
\(548\) 0.298856 + 1.69490i 0.0127665 + 0.0724024i
\(549\) 0 0
\(550\) −6.90604 + 39.1661i −0.294475 + 1.67005i
\(551\) −1.11192 0.129965i −0.0473696 0.00553671i
\(552\) 0 0
\(553\) 1.31343 + 4.38716i 0.0558527 + 0.186561i
\(554\) −38.2379 9.06256i −1.62457 0.385031i
\(555\) 0 0
\(556\) 0.522591 + 1.21150i 0.0221628 + 0.0513791i
\(557\) −19.9818 16.7668i −0.846658 0.710430i 0.112393 0.993664i \(-0.464148\pi\)
−0.959051 + 0.283234i \(0.908593\pi\)
\(558\) 0 0
\(559\) −4.64699 + 3.89929i −0.196547 + 0.164922i
\(560\) 22.0668 + 11.0824i 0.932494 + 0.468316i
\(561\) 0 0
\(562\) 2.50204 0.292447i 0.105542 0.0123361i
\(563\) −2.52063 + 43.2776i −0.106232 + 1.82393i 0.353006 + 0.935621i \(0.385159\pi\)
−0.459238 + 0.888313i \(0.651878\pi\)
\(564\) 0 0
\(565\) −5.54469 5.87703i −0.233267 0.247249i
\(566\) 8.19974 0.344661
\(567\) 0 0
\(568\) 40.7008 1.70777
\(569\) −4.50377 4.77371i −0.188808 0.200124i 0.626054 0.779779i \(-0.284669\pi\)
−0.814862 + 0.579655i \(0.803187\pi\)
\(570\) 0 0
\(571\) −1.39116 + 23.8854i −0.0582184 + 0.999571i 0.835086 + 0.550119i \(0.185418\pi\)
−0.893304 + 0.449452i \(0.851619\pi\)
\(572\) −0.771537 + 0.0901797i −0.0322596 + 0.00377060i
\(573\) 0 0
\(574\) −9.23009 4.63553i −0.385257 0.193483i
\(575\) −13.8877 + 11.6532i −0.579157 + 0.485970i
\(576\) 0 0
\(577\) −24.0397 20.1717i −1.00078 0.839758i −0.0136918 0.999906i \(-0.504358\pi\)
−0.987093 + 0.160148i \(0.948803\pi\)
\(578\) 17.3225 + 40.1581i 0.720521 + 1.67036i
\(579\) 0 0
\(580\) 0.114089 + 0.0270395i 0.00473728 + 0.00112276i
\(581\) −0.112648 0.376272i −0.00467344 0.0156104i
\(582\) 0 0
\(583\) 18.4310 + 2.15427i 0.763332 + 0.0892208i
\(584\) −1.60421 + 9.09795i −0.0663828 + 0.376476i
\(585\) 0 0
\(586\) 2.51813 + 14.2810i 0.104023 + 0.589944i
\(587\) 2.58150 + 44.3226i 0.106550 + 1.82939i 0.453217 + 0.891400i \(0.350276\pi\)
−0.346667 + 0.937988i \(0.612687\pi\)
\(588\) 0 0
\(589\) −7.71130 + 17.8768i −0.317739 + 0.736601i
\(590\) −9.28809 + 4.66465i −0.382385 + 0.192041i
\(591\) 0 0
\(592\) 1.33022 0.315268i 0.0546717 0.0129574i
\(593\) 9.54772 + 16.5371i 0.392078 + 0.679099i 0.992723 0.120417i \(-0.0384230\pi\)
−0.600646 + 0.799515i \(0.705090\pi\)
\(594\) 0 0
\(595\) 23.3044 40.3644i 0.955387 1.65478i
\(596\) 0.161753 0.540292i 0.00662565 0.0221312i
\(597\) 0 0
\(598\) 4.05947 + 2.66995i 0.166004 + 0.109183i
\(599\) 0.526426 + 0.707113i 0.0215092 + 0.0288918i 0.812748 0.582616i \(-0.197971\pi\)
−0.791239 + 0.611508i \(0.790563\pi\)
\(600\) 0 0
\(601\) −23.6223 + 15.5366i −0.963575 + 0.633753i −0.930730 0.365707i \(-0.880827\pi\)
−0.0328449 + 0.999460i \(0.510457\pi\)
\(602\) 7.27810 + 2.64901i 0.296633 + 0.107966i
\(603\) 0 0
\(604\) −0.413492 + 0.150499i −0.0168248 + 0.00612371i
\(605\) 3.71370 4.98837i 0.150983 0.202806i
\(606\) 0 0
\(607\) 25.6511 27.1886i 1.04115 1.10355i 0.0466354 0.998912i \(-0.485150\pi\)
0.994510 0.104638i \(-0.0333684\pi\)
\(608\) −2.60181 + 2.75775i −0.105517 + 0.111842i
\(609\) 0 0
\(610\) −39.7299 + 53.3666i −1.60862 + 2.16075i
\(611\) 3.06828 1.11676i 0.124129 0.0451794i
\(612\) 0 0
\(613\) 7.96120 + 2.89764i 0.321550 + 0.117035i 0.497752 0.867319i \(-0.334159\pi\)
−0.176202 + 0.984354i \(0.556381\pi\)
\(614\) −1.92944 + 1.26901i −0.0778658 + 0.0512131i
\(615\) 0 0
\(616\) 9.31124 + 12.5072i 0.375160 + 0.503928i
\(617\) −31.0820 20.4430i −1.25132 0.823003i −0.261479 0.965209i \(-0.584210\pi\)
−0.989837 + 0.142206i \(0.954580\pi\)
\(618\) 0 0
\(619\) 11.0925 37.0515i 0.445845 1.48923i −0.379817 0.925062i \(-0.624013\pi\)
0.825662 0.564165i \(-0.190802\pi\)
\(620\) 1.01954 1.76589i 0.0409456 0.0709199i
\(621\) 0 0
\(622\) 18.5394 + 32.1111i 0.743360 + 1.28754i
\(623\) −12.0999 + 2.86773i −0.484773 + 0.114893i
\(624\) 0 0
\(625\) 16.0751 8.07322i 0.643004 0.322929i
\(626\) 14.5674 33.7709i 0.582229 1.34976i
\(627\) 0 0
\(628\) −0.0590645 1.01410i −0.00235693 0.0404670i
\(629\) −0.448072 2.54114i −0.0178658 0.101322i
\(630\) 0 0
\(631\) −0.0118315 + 0.0670997i −0.000471004 + 0.00267120i −0.985042 0.172312i \(-0.944876\pi\)
0.984571 + 0.174984i \(0.0559872\pi\)
\(632\) −7.59276 0.887466i −0.302024 0.0353015i
\(633\) 0 0
\(634\) −2.08575 6.96688i −0.0828355 0.276690i
\(635\) 41.9854 + 9.95073i 1.66614 + 0.394883i
\(636\) 0 0
\(637\) −2.92133 6.77240i −0.115747 0.268332i
\(638\) −0.725124 0.608452i −0.0287079 0.0240888i
\(639\) 0 0
\(640\) −29.2635 + 24.5550i −1.15674 + 0.970621i
\(641\) −9.70187 4.87246i −0.383201 0.192451i 0.246762 0.969076i \(-0.420633\pi\)
−0.629963 + 0.776625i \(0.716930\pi\)
\(642\) 0 0
\(643\) −31.0638 + 3.63084i −1.22504 + 0.143186i −0.703908 0.710291i \(-0.748563\pi\)
−0.521130 + 0.853477i \(0.674489\pi\)
\(644\) −0.0262873 + 0.451335i −0.00103586 + 0.0177851i
\(645\) 0 0
\(646\) −32.4250 34.3685i −1.27574 1.35221i
\(647\) −22.3771 −0.879735 −0.439868 0.898063i \(-0.644975\pi\)
−0.439868 + 0.898063i \(0.644975\pi\)
\(648\) 0 0
\(649\) −6.11515 −0.240041
\(650\) −16.6583 17.6568i −0.653393 0.692556i
\(651\) 0 0
\(652\) −0.0767687 + 1.31807i −0.00300650 + 0.0516195i
\(653\) 37.2153 4.34984i 1.45635 0.170223i 0.649220 0.760601i \(-0.275095\pi\)
0.807127 + 0.590378i \(0.201021\pi\)
\(654\) 0 0
\(655\) 36.8834 + 18.5235i 1.44115 + 0.723774i
\(656\) 12.3063 10.3262i 0.480481 0.403171i
\(657\) 0 0
\(658\) −3.19358 2.67973i −0.124499 0.104467i
\(659\) −1.83219 4.24750i −0.0713722 0.165459i 0.878796 0.477199i \(-0.158348\pi\)
−0.950168 + 0.311739i \(0.899088\pi\)
\(660\) 0 0
\(661\) 7.13756 + 1.69163i 0.277619 + 0.0657969i 0.367067 0.930195i \(-0.380362\pi\)
−0.0894479 + 0.995992i \(0.528510\pi\)
\(662\) −5.66265 18.9146i −0.220085 0.735136i
\(663\) 0 0
\(664\) 0.651205 + 0.0761150i 0.0252717 + 0.00295383i
\(665\) −5.71239 + 32.3966i −0.221517 + 1.25629i
\(666\) 0 0
\(667\) −0.0749283 0.424939i −0.00290124 0.0164537i
\(668\) −0.00569128 0.0977156i −0.000220202 0.00378073i
\(669\) 0 0
\(670\) 13.0730 30.3067i 0.505056 1.17085i
\(671\) −34.9806 + 17.5679i −1.35041 + 0.678201i
\(672\) 0 0
\(673\) 12.0828 2.86368i 0.465759 0.110387i 0.00896566 0.999960i \(-0.497146\pi\)
0.456793 + 0.889573i \(0.348998\pi\)
\(674\) −9.89036 17.1306i −0.380962 0.659846i
\(675\) 0 0
\(676\) −0.645983 + 1.11888i −0.0248455 + 0.0430337i
\(677\) 7.09365 23.6945i 0.272631 0.910652i −0.706550 0.707663i \(-0.749749\pi\)
0.979181 0.202989i \(-0.0650654\pi\)
\(678\) 0 0
\(679\) −22.7393 14.9559i −0.872655 0.573954i
\(680\) 46.4602 + 62.4069i 1.78167 + 2.39319i
\(681\) 0 0
\(682\) −13.7538 + 9.04600i −0.526659 + 0.346389i
\(683\) −3.75317 1.36604i −0.143611 0.0522702i 0.269215 0.963080i \(-0.413236\pi\)
−0.412826 + 0.910810i \(0.635458\pi\)
\(684\) 0 0
\(685\) −45.3571 + 16.5086i −1.73301 + 0.630762i
\(686\) −15.5939 + 20.9462i −0.595378 + 0.799731i
\(687\) 0 0
\(688\) −8.26678 + 8.76227i −0.315168 + 0.334058i
\(689\) −7.77261 + 8.23848i −0.296113 + 0.313861i
\(690\) 0 0
\(691\) 3.18637 4.28004i 0.121215 0.162820i −0.737374 0.675485i \(-0.763934\pi\)
0.858589 + 0.512665i \(0.171342\pi\)
\(692\) 0.280049 0.101930i 0.0106459 0.00387478i
\(693\) 0 0
\(694\) 4.54461 + 1.65410i 0.172511 + 0.0627889i
\(695\) −30.9162 + 20.3339i −1.17272 + 0.771310i
\(696\) 0 0
\(697\) −18.1071 24.3221i −0.685857 0.921266i
\(698\) 33.7931 + 22.2260i 1.27909 + 0.841268i
\(699\) 0 0
\(700\) 0.647804 2.16382i 0.0244847 0.0817846i
\(701\) −9.39904 + 16.2796i −0.354997 + 0.614873i −0.987117 0.159997i \(-0.948851\pi\)
0.632120 + 0.774870i \(0.282185\pi\)
\(702\) 0 0
\(703\) 0.910600 + 1.57721i 0.0343439 + 0.0594854i
\(704\) −25.2165 + 5.97642i −0.950383 + 0.225245i
\(705\) 0 0
\(706\) 33.2707 16.7092i 1.25216 0.628858i
\(707\) −5.94611 + 13.7846i −0.223626 + 0.518424i
\(708\) 0 0
\(709\) −1.06948 18.3623i −0.0401653 0.689612i −0.956954 0.290240i \(-0.906265\pi\)
0.916789 0.399373i \(-0.130772\pi\)
\(710\) 12.6078 + 71.5025i 0.473163 + 2.68344i
\(711\) 0 0
\(712\) 3.60448 20.4420i 0.135084 0.766098i
\(713\) −7.45337 0.871174i −0.279131 0.0326257i
\(714\) 0 0
\(715\) −6.24820 20.8704i −0.233669 0.780510i
\(716\) 3.35705 + 0.795635i 0.125459 + 0.0297343i
\(717\) 0 0
\(718\) −0.914046 2.11900i −0.0341119 0.0790802i
\(719\) −2.04229 1.71368i −0.0761644 0.0639095i 0.603911 0.797052i \(-0.293608\pi\)
−0.680075 + 0.733143i \(0.738053\pi\)
\(720\) 0 0
\(721\) −1.54565 + 1.29695i −0.0575630 + 0.0483011i
\(722\) 6.61967 + 3.32452i 0.246359 + 0.123726i
\(723\) 0 0
\(724\) 1.62683 0.190149i 0.0604607 0.00706684i
\(725\) −0.125346 + 2.15212i −0.00465525 + 0.0799276i
\(726\) 0 0
\(727\) 0.291613 + 0.309092i 0.0108153 + 0.0114636i 0.732759 0.680489i \(-0.238232\pi\)
−0.721943 + 0.691952i \(0.756751\pi\)
\(728\) −9.51728 −0.352734
\(729\) 0 0
\(730\) −16.4801 −0.609955
\(731\) 15.6035 + 16.5388i 0.577117 + 0.611708i
\(732\) 0 0
\(733\) 1.38421 23.7660i 0.0511269 0.877816i −0.871085 0.491132i \(-0.836583\pi\)
0.922212 0.386684i \(-0.126380\pi\)
\(734\) −7.39855 + 0.864767i −0.273086 + 0.0319191i
\(735\) 0 0
\(736\) −1.30590 0.655849i −0.0481362 0.0241749i
\(737\) 14.8761 12.4825i 0.547967 0.459799i
\(738\) 0 0
\(739\) 19.6618 + 16.4982i 0.723271 + 0.606896i 0.928288 0.371862i \(-0.121281\pi\)
−0.205017 + 0.978758i \(0.565725\pi\)
\(740\) −0.0755490 0.175142i −0.00277724 0.00643836i
\(741\) 0 0
\(742\) 14.0714 + 3.33498i 0.516577 + 0.122431i
\(743\) 2.35323 + 7.86035i 0.0863318 + 0.288368i 0.990243 0.139352i \(-0.0445020\pi\)
−0.903911 + 0.427720i \(0.859317\pi\)
\(744\) 0 0
\(745\) 15.7105 + 1.83629i 0.575587 + 0.0672764i
\(746\) 4.96605 28.1639i 0.181820 1.03115i
\(747\) 0 0
\(748\) 0.505593 + 2.86736i 0.0184863 + 0.104841i
\(749\) 1.12381 + 19.2951i 0.0410631 + 0.705026i
\(750\) 0 0
\(751\) 8.47798 19.6542i 0.309366 0.717190i −0.690616 0.723222i \(-0.742661\pi\)
0.999982 + 0.00603122i \(0.00191981\pi\)
\(752\) 5.79441 2.91006i 0.211301 0.106119i
\(753\) 0 0
\(754\) 0.562195 0.133243i 0.0204739 0.00485241i
\(755\) −6.17048 10.6876i −0.224567 0.388961i
\(756\) 0 0
\(757\) 12.5431 21.7253i 0.455886 0.789618i −0.542852 0.839828i \(-0.682656\pi\)
0.998739 + 0.0502098i \(0.0159890\pi\)
\(758\) −13.3255 + 44.5103i −0.484005 + 1.61669i
\(759\) 0 0
\(760\) −45.8788 30.1749i −1.66420 1.09456i
\(761\) −28.0836 37.7228i −1.01803 1.36745i −0.928444 0.371472i \(-0.878853\pi\)
−0.0895859 0.995979i \(-0.528554\pi\)
\(762\) 0 0
\(763\) −22.1903 + 14.5948i −0.803344 + 0.528368i
\(764\) −1.86751 0.679718i −0.0675641 0.0245913i
\(765\) 0 0
\(766\) 12.7676 4.64704i 0.461314 0.167905i
\(767\) 2.22891 2.99394i 0.0804812 0.108105i
\(768\) 0 0
\(769\) 31.9385 33.8528i 1.15173 1.22076i 0.180258 0.983619i \(-0.442307\pi\)
0.971474 0.237145i \(-0.0762118\pi\)
\(770\) −19.0881 + 20.2322i −0.687886 + 0.729117i
\(771\) 0 0
\(772\) 1.72310 2.31452i 0.0620157 0.0833016i
\(773\) 37.5202 13.6562i 1.34951 0.491180i 0.436713 0.899601i \(-0.356142\pi\)
0.912794 + 0.408420i \(0.133920\pi\)
\(774\) 0 0
\(775\) 35.2298 + 12.8226i 1.26549 + 0.460601i
\(776\) 37.9578 24.9652i 1.36261 0.896200i
\(777\) 0 0
\(778\) −14.3142 19.2273i −0.513189 0.689333i
\(779\) 17.8805 + 11.7602i 0.640637 + 0.421354i
\(780\) 0 0
\(781\) −12.2516 + 40.9233i −0.438398 + 1.46435i
\(782\) 9.10598 15.7720i 0.325629 0.564006i
\(783\) 0