Properties

Label 729.2.g.d.55.4
Level $729$
Weight $2$
Character 729.55
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 55.4
Character \(\chi\) \(=\) 729.55
Dual form 729.2.g.d.676.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0742143 - 0.172048i) q^{2} +(1.34839 + 1.42921i) q^{4} +(-0.0921050 - 1.58138i) q^{5} +(-3.93765 - 0.933240i) q^{7} +(0.698107 - 0.254090i) q^{8} +O(q^{10})\) \(q+(0.0742143 - 0.172048i) q^{2} +(1.34839 + 1.42921i) q^{4} +(-0.0921050 - 1.58138i) q^{5} +(-3.93765 - 0.933240i) q^{7} +(0.698107 - 0.254090i) q^{8} +(-0.278909 - 0.101515i) q^{10} +(3.21202 + 2.11258i) q^{11} +(1.58861 + 0.185682i) q^{13} +(-0.452792 + 0.608205i) q^{14} +(-0.220403 + 3.78417i) q^{16} +(5.79317 - 4.86105i) q^{17} +(1.26984 + 1.06552i) q^{19} +(2.13593 - 2.26396i) q^{20} +(0.601842 - 0.395838i) q^{22} +(6.23886 - 1.47864i) q^{23} +(2.47391 - 0.289158i) q^{25} +(0.149844 - 0.259538i) q^{26} +(-3.97569 - 6.88610i) q^{28} +(-0.163549 - 0.219684i) q^{29} +(0.530826 - 1.77308i) q^{31} +(1.96248 + 0.985594i) q^{32} +(-0.406398 - 1.35746i) q^{34} +(-1.11313 + 6.31289i) q^{35} +(-0.295248 - 1.67443i) q^{37} +(0.277561 - 0.139396i) q^{38} +(-0.466113 - 1.08057i) q^{40} +(1.18553 + 2.74838i) q^{41} +(-4.35056 + 2.18493i) q^{43} +(1.31174 + 7.43922i) q^{44} +(0.208616 - 1.18312i) q^{46} +(-0.0382623 - 0.127805i) q^{47} +(8.37873 + 4.20796i) q^{49} +(0.133850 - 0.447090i) q^{50} +(1.87669 + 2.52084i) q^{52} +(-4.93888 - 8.55438i) q^{53} +(3.04495 - 5.27400i) q^{55} +(-2.98603 + 0.349017i) q^{56} +(-0.0499339 + 0.0118346i) q^{58} +(-6.47138 + 4.25629i) q^{59} +(-2.83624 + 3.00624i) q^{61} +(-0.265660 - 0.222915i) q^{62} +(-5.49230 + 4.60858i) q^{64} +(0.147315 - 2.52931i) q^{65} +(-8.03004 + 10.7862i) q^{67} +(14.7589 + 1.72507i) q^{68} +(1.00351 + 0.660018i) q^{70} +(2.39924 + 0.873251i) q^{71} +(5.29149 - 1.92595i) q^{73} +(-0.309995 - 0.0734701i) q^{74} +(0.189384 + 3.25160i) q^{76} +(-10.6763 - 11.3162i) q^{77} +(3.20983 - 7.44121i) q^{79} +6.00452 q^{80} +0.560836 q^{82} +(2.17210 - 5.03548i) q^{83} +(-8.22075 - 8.71349i) q^{85} +(0.0530398 + 0.910658i) q^{86} +(2.77911 + 0.658662i) q^{88} +(-6.33932 + 2.30732i) q^{89} +(-6.08212 - 2.21371i) q^{91} +(10.5257 + 6.92286i) q^{92} +(-0.0248282 - 0.00290200i) q^{94} +(1.56804 - 2.10624i) q^{95} +(-0.108820 + 1.86837i) q^{97} +(1.34579 - 1.12925i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{17}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0742143 0.172048i 0.0524774 0.121656i −0.889960 0.456038i \(-0.849268\pi\)
0.942438 + 0.334382i \(0.108527\pi\)
\(3\) 0 0
\(4\) 1.34839 + 1.42921i 0.674195 + 0.714605i
\(5\) −0.0921050 1.58138i −0.0411906 0.707215i −0.954180 0.299233i \(-0.903269\pi\)
0.912990 0.407983i \(-0.133768\pi\)
\(6\) 0 0
\(7\) −3.93765 0.933240i −1.48829 0.352732i −0.595557 0.803313i \(-0.703069\pi\)
−0.892735 + 0.450582i \(0.851217\pi\)
\(8\) 0.698107 0.254090i 0.246818 0.0898344i
\(9\) 0 0
\(10\) −0.278909 0.101515i −0.0881988 0.0321017i
\(11\) 3.21202 + 2.11258i 0.968459 + 0.636966i 0.932034 0.362371i \(-0.118033\pi\)
0.0364251 + 0.999336i \(0.488403\pi\)
\(12\) 0 0
\(13\) 1.58861 + 0.185682i 0.440602 + 0.0514990i 0.333502 0.942749i \(-0.391769\pi\)
0.107100 + 0.994248i \(0.465844\pi\)
\(14\) −0.452792 + 0.608205i −0.121014 + 0.162550i
\(15\) 0 0
\(16\) −0.220403 + 3.78417i −0.0551007 + 0.946042i
\(17\) 5.79317 4.86105i 1.40505 1.17898i 0.446246 0.894910i \(-0.352761\pi\)
0.958804 0.284067i \(-0.0916838\pi\)
\(18\) 0 0
\(19\) 1.26984 + 1.06552i 0.291321 + 0.244447i 0.776721 0.629845i \(-0.216882\pi\)
−0.485400 + 0.874292i \(0.661326\pi\)
\(20\) 2.13593 2.26396i 0.477609 0.506236i
\(21\) 0 0
\(22\) 0.601842 0.395838i 0.128313 0.0843929i
\(23\) 6.23886 1.47864i 1.30089 0.308317i 0.478926 0.877855i \(-0.341026\pi\)
0.821965 + 0.569538i \(0.192878\pi\)
\(24\) 0 0
\(25\) 2.47391 0.289158i 0.494781 0.0578316i
\(26\) 0.149844 0.259538i 0.0293868 0.0508995i
\(27\) 0 0
\(28\) −3.97569 6.88610i −0.751336 1.30135i
\(29\) −0.163549 0.219684i −0.0303703 0.0407944i 0.786679 0.617363i \(-0.211799\pi\)
−0.817049 + 0.576568i \(0.804391\pi\)
\(30\) 0 0
\(31\) 0.530826 1.77308i 0.0953391 0.318455i −0.896995 0.442041i \(-0.854254\pi\)
0.992334 + 0.123586i \(0.0394396\pi\)
\(32\) 1.96248 + 0.985594i 0.346920 + 0.174230i
\(33\) 0 0
\(34\) −0.406398 1.35746i −0.0696966 0.232803i
\(35\) −1.11313 + 6.31289i −0.188154 + 1.06707i
\(36\) 0 0
\(37\) −0.295248 1.67443i −0.0485385 0.275275i 0.950873 0.309582i \(-0.100189\pi\)
−0.999411 + 0.0343062i \(0.989078\pi\)
\(38\) 0.277561 0.139396i 0.0450263 0.0226131i
\(39\) 0 0
\(40\) −0.466113 1.08057i −0.0736989 0.170853i
\(41\) 1.18553 + 2.74838i 0.185149 + 0.429224i 0.985358 0.170497i \(-0.0545374\pi\)
−0.800209 + 0.599721i \(0.795278\pi\)
\(42\) 0 0
\(43\) −4.35056 + 2.18493i −0.663454 + 0.333199i −0.748459 0.663182i \(-0.769206\pi\)
0.0850049 + 0.996381i \(0.472909\pi\)
\(44\) 1.31174 + 7.43922i 0.197752 + 1.12151i
\(45\) 0 0
\(46\) 0.208616 1.18312i 0.0307587 0.174441i
\(47\) −0.0382623 0.127805i −0.00558113 0.0186423i 0.955154 0.296111i \(-0.0956898\pi\)
−0.960735 + 0.277469i \(0.910505\pi\)
\(48\) 0 0
\(49\) 8.37873 + 4.20796i 1.19696 + 0.601136i
\(50\) 0.133850 0.447090i 0.0189293 0.0632281i
\(51\) 0 0
\(52\) 1.87669 + 2.52084i 0.260250 + 0.349577i
\(53\) −4.93888 8.55438i −0.678407 1.17504i −0.975461 0.220174i \(-0.929337\pi\)
0.297054 0.954861i \(-0.403996\pi\)
\(54\) 0 0
\(55\) 3.04495 5.27400i 0.410580 0.711146i
\(56\) −2.98603 + 0.349017i −0.399025 + 0.0466393i
\(57\) 0 0
\(58\) −0.0499339 + 0.0118346i −0.00655665 + 0.00155395i
\(59\) −6.47138 + 4.25629i −0.842501 + 0.554122i −0.895800 0.444457i \(-0.853397\pi\)
0.0532989 + 0.998579i \(0.483026\pi\)
\(60\) 0 0
\(61\) −2.83624 + 3.00624i −0.363143 + 0.384909i −0.883023 0.469330i \(-0.844495\pi\)
0.519879 + 0.854240i \(0.325977\pi\)
\(62\) −0.265660 0.222915i −0.0337389 0.0283103i
\(63\) 0 0
\(64\) −5.49230 + 4.60858i −0.686537 + 0.576073i
\(65\) 0.147315 2.52931i 0.0182722 0.313722i
\(66\) 0 0
\(67\) −8.03004 + 10.7862i −0.981026 + 1.31775i −0.0330332 + 0.999454i \(0.510517\pi\)
−0.947993 + 0.318292i \(0.896891\pi\)
\(68\) 14.7589 + 1.72507i 1.78978 + 0.209195i
\(69\) 0 0
\(70\) 1.00351 + 0.660018i 0.119942 + 0.0788873i
\(71\) 2.39924 + 0.873251i 0.284737 + 0.103636i 0.480441 0.877027i \(-0.340477\pi\)
−0.195703 + 0.980663i \(0.562699\pi\)
\(72\) 0 0
\(73\) 5.29149 1.92595i 0.619322 0.225415i −0.0132549 0.999912i \(-0.504219\pi\)
0.632577 + 0.774497i \(0.281997\pi\)
\(74\) −0.309995 0.0734701i −0.0360362 0.00854073i
\(75\) 0 0
\(76\) 0.189384 + 3.25160i 0.0217239 + 0.372985i
\(77\) −10.6763 11.3162i −1.21667 1.28960i
\(78\) 0 0
\(79\) 3.20983 7.44121i 0.361134 0.837202i −0.636681 0.771127i \(-0.719693\pi\)
0.997815 0.0660746i \(-0.0210475\pi\)
\(80\) 6.00452 0.671325
\(81\) 0 0
\(82\) 0.560836 0.0619340
\(83\) 2.17210 5.03548i 0.238418 0.552716i −0.756432 0.654073i \(-0.773059\pi\)
0.994850 + 0.101357i \(0.0323183\pi\)
\(84\) 0 0
\(85\) −8.22075 8.71349i −0.891666 0.945111i
\(86\) 0.0530398 + 0.910658i 0.00571942 + 0.0981987i
\(87\) 0 0
\(88\) 2.77911 + 0.658662i 0.296255 + 0.0702136i
\(89\) −6.33932 + 2.30732i −0.671966 + 0.244576i −0.655394 0.755287i \(-0.727497\pi\)
−0.0165720 + 0.999863i \(0.505275\pi\)
\(90\) 0 0
\(91\) −6.08212 2.21371i −0.637580 0.232060i
\(92\) 10.5257 + 6.92286i 1.09738 + 0.721758i
\(93\) 0 0
\(94\) −0.0248282 0.00290200i −0.00256083 0.000299319i
\(95\) 1.56804 2.10624i 0.160877 0.216096i
\(96\) 0 0
\(97\) −0.108820 + 1.86837i −0.0110490 + 0.189704i 0.988267 + 0.152734i \(0.0488078\pi\)
−0.999316 + 0.0369704i \(0.988229\pi\)
\(98\) 1.34579 1.12925i 0.135945 0.114072i
\(99\) 0 0
\(100\) 3.74906 + 3.14584i 0.374906 + 0.314584i
\(101\) 11.4483 12.1345i 1.13915 1.20743i 0.163863 0.986483i \(-0.447605\pi\)
0.975286 0.220944i \(-0.0709139\pi\)
\(102\) 0 0
\(103\) 4.80896 3.16291i 0.473841 0.311650i −0.290032 0.957017i \(-0.593666\pi\)
0.763873 + 0.645367i \(0.223295\pi\)
\(104\) 1.15620 0.274025i 0.113375 0.0268704i
\(105\) 0 0
\(106\) −1.83830 + 0.214866i −0.178551 + 0.0208697i
\(107\) 0.810593 1.40399i 0.0783630 0.135729i −0.824181 0.566327i \(-0.808364\pi\)
0.902544 + 0.430598i \(0.141697\pi\)
\(108\) 0 0
\(109\) 5.75519 + 9.96829i 0.551248 + 0.954789i 0.998185 + 0.0602237i \(0.0191814\pi\)
−0.446937 + 0.894565i \(0.647485\pi\)
\(110\) −0.681403 0.915283i −0.0649692 0.0872688i
\(111\) 0 0
\(112\) 4.39941 14.6951i 0.415705 1.38855i
\(113\) −7.80192 3.91827i −0.733943 0.368600i 0.0422404 0.999107i \(-0.486550\pi\)
−0.776183 + 0.630508i \(0.782847\pi\)
\(114\) 0 0
\(115\) −2.91292 9.72982i −0.271631 0.907311i
\(116\) 0.0934474 0.529966i 0.00867637 0.0492061i
\(117\) 0 0
\(118\) 0.252018 + 1.42926i 0.0232001 + 0.131575i
\(119\) −27.3480 + 13.7347i −2.50699 + 1.25906i
\(120\) 0 0
\(121\) 1.49719 + 3.47088i 0.136108 + 0.315534i
\(122\) 0.306728 + 0.711075i 0.0277698 + 0.0643777i
\(123\) 0 0
\(124\) 3.24987 1.63214i 0.291847 0.146571i
\(125\) −2.06048 11.6855i −0.184295 1.04519i
\(126\) 0 0
\(127\) −3.29466 + 18.6850i −0.292354 + 1.65802i 0.385411 + 0.922745i \(0.374060\pi\)
−0.677766 + 0.735278i \(0.737052\pi\)
\(128\) 1.64497 + 5.49458i 0.145396 + 0.485657i
\(129\) 0 0
\(130\) −0.424229 0.213056i −0.0372074 0.0186863i
\(131\) −1.73595 + 5.79846i −0.151670 + 0.506614i −0.999729 0.0232885i \(-0.992586\pi\)
0.848058 + 0.529903i \(0.177772\pi\)
\(132\) 0 0
\(133\) −4.00579 5.38071i −0.347346 0.466567i
\(134\) 1.25980 + 2.18204i 0.108830 + 0.188500i
\(135\) 0 0
\(136\) 2.80911 4.86552i 0.240879 0.417215i
\(137\) −22.0876 + 2.58167i −1.88707 + 0.220567i −0.979800 0.199980i \(-0.935912\pi\)
−0.907271 + 0.420547i \(0.861838\pi\)
\(138\) 0 0
\(139\) −12.3791 + 2.93391i −1.04998 + 0.248851i −0.719162 0.694843i \(-0.755474\pi\)
−0.330822 + 0.943693i \(0.607326\pi\)
\(140\) −10.5234 + 6.92133i −0.889388 + 0.584960i
\(141\) 0 0
\(142\) 0.328299 0.347977i 0.0275502 0.0292015i
\(143\) 4.71039 + 3.95248i 0.393902 + 0.330523i
\(144\) 0 0
\(145\) −0.332341 + 0.278867i −0.0275994 + 0.0231587i
\(146\) 0.0613491 1.05332i 0.00507729 0.0871737i
\(147\) 0 0
\(148\) 1.99501 2.67976i 0.163989 0.220275i
\(149\) −9.73145 1.13744i −0.797231 0.0931830i −0.292282 0.956332i \(-0.594415\pi\)
−0.504949 + 0.863149i \(0.668489\pi\)
\(150\) 0 0
\(151\) 7.95586 + 5.23265i 0.647439 + 0.425827i 0.830304 0.557311i \(-0.188167\pi\)
−0.182865 + 0.983138i \(0.558537\pi\)
\(152\) 1.15722 + 0.421194i 0.0938630 + 0.0341633i
\(153\) 0 0
\(154\) −2.73925 + 0.997007i −0.220735 + 0.0803411i
\(155\) −2.85281 0.676128i −0.229143 0.0543079i
\(156\) 0 0
\(157\) −0.431930 7.41595i −0.0344718 0.591857i −0.970675 0.240397i \(-0.922722\pi\)
0.936203 0.351460i \(-0.114315\pi\)
\(158\) −1.04203 1.10449i −0.0828995 0.0878684i
\(159\) 0 0
\(160\) 1.37785 3.19421i 0.108928 0.252524i
\(161\) −25.9464 −2.04486
\(162\) 0 0
\(163\) 4.98806 0.390695 0.195347 0.980734i \(-0.437417\pi\)
0.195347 + 0.980734i \(0.437417\pi\)
\(164\) −2.32945 + 5.40026i −0.181899 + 0.421690i
\(165\) 0 0
\(166\) −0.705144 0.747409i −0.0547298 0.0580102i
\(167\) 0.253555 + 4.35337i 0.0196207 + 0.336874i 0.993806 + 0.111126i \(0.0354457\pi\)
−0.974186 + 0.225748i \(0.927517\pi\)
\(168\) 0 0
\(169\) −10.1604 2.40805i −0.781567 0.185235i
\(170\) −2.10924 + 0.767699i −0.161771 + 0.0588798i
\(171\) 0 0
\(172\) −8.98898 3.27172i −0.685403 0.249466i
\(173\) 13.4039 + 8.81588i 1.01908 + 0.670259i 0.945026 0.326996i \(-0.106036\pi\)
0.0740530 + 0.997254i \(0.476407\pi\)
\(174\) 0 0
\(175\) −10.0112 1.17015i −0.756778 0.0884547i
\(176\) −8.70228 + 11.6892i −0.655959 + 0.881106i
\(177\) 0 0
\(178\) −0.0734975 + 1.26190i −0.00550887 + 0.0945836i
\(179\) −14.7729 + 12.3960i −1.10418 + 0.926518i −0.997699 0.0677961i \(-0.978403\pi\)
−0.106483 + 0.994315i \(0.533959\pi\)
\(180\) 0 0
\(181\) 0.116035 + 0.0973645i 0.00862478 + 0.00723705i 0.647090 0.762414i \(-0.275986\pi\)
−0.638465 + 0.769651i \(0.720430\pi\)
\(182\) −0.832245 + 0.882128i −0.0616901 + 0.0653877i
\(183\) 0 0
\(184\) 3.97968 2.61748i 0.293386 0.192963i
\(185\) −2.62073 + 0.621124i −0.192680 + 0.0456659i
\(186\) 0 0
\(187\) 28.8771 3.37525i 2.11170 0.246823i
\(188\) 0.131068 0.227016i 0.00955910 0.0165568i
\(189\) 0 0
\(190\) −0.246003 0.426090i −0.0178470 0.0309119i
\(191\) −6.39393 8.58854i −0.462649 0.621445i 0.508171 0.861256i \(-0.330322\pi\)
−0.970820 + 0.239811i \(0.922914\pi\)
\(192\) 0 0
\(193\) −4.55179 + 15.2040i −0.327645 + 1.09441i 0.622505 + 0.782616i \(0.286115\pi\)
−0.950150 + 0.311794i \(0.899070\pi\)
\(194\) 0.313374 + 0.157382i 0.0224989 + 0.0112994i
\(195\) 0 0
\(196\) 5.28374 + 17.6489i 0.377410 + 1.26064i
\(197\) −0.213838 + 1.21273i −0.0152353 + 0.0864037i −0.991477 0.130279i \(-0.958413\pi\)
0.976242 + 0.216683i \(0.0695238\pi\)
\(198\) 0 0
\(199\) 0.406772 + 2.30692i 0.0288353 + 0.163533i 0.995825 0.0912821i \(-0.0290965\pi\)
−0.966990 + 0.254815i \(0.917985\pi\)
\(200\) 1.65358 0.830459i 0.116926 0.0587223i
\(201\) 0 0
\(202\) −1.23809 2.87021i −0.0871116 0.201947i
\(203\) 0.438980 + 1.01767i 0.0308104 + 0.0714265i
\(204\) 0 0
\(205\) 4.23704 2.12792i 0.295928 0.148620i
\(206\) −0.187278 1.06211i −0.0130483 0.0740004i
\(207\) 0 0
\(208\) −1.05279 + 5.97066i −0.0729978 + 0.413991i
\(209\) 1.82775 + 6.10510i 0.126428 + 0.422298i
\(210\) 0 0
\(211\) −10.1780 5.11157i −0.700681 0.351895i 0.0625316 0.998043i \(-0.480083\pi\)
−0.763212 + 0.646148i \(0.776379\pi\)
\(212\) 5.56648 18.5933i 0.382308 1.27700i
\(213\) 0 0
\(214\) −0.181396 0.243657i −0.0124000 0.0166560i
\(215\) 3.85592 + 6.67865i 0.262971 + 0.455480i
\(216\) 0 0
\(217\) −3.74492 + 6.48639i −0.254222 + 0.440325i
\(218\) 2.14214 0.250380i 0.145084 0.0169579i
\(219\) 0 0
\(220\) 11.6434 2.75954i 0.785000 0.186048i
\(221\) 10.1057 6.64664i 0.679785 0.447101i
\(222\) 0 0
\(223\) 10.3801 11.0023i 0.695106 0.736770i −0.279635 0.960106i \(-0.590213\pi\)
0.974741 + 0.223337i \(0.0716950\pi\)
\(224\) −6.80776 5.71239i −0.454863 0.381675i
\(225\) 0 0
\(226\) −1.25314 + 1.05151i −0.0833579 + 0.0699456i
\(227\) 1.23726 21.2429i 0.0821198 1.40994i −0.665789 0.746140i \(-0.731905\pi\)
0.747908 0.663802i \(-0.231058\pi\)
\(228\) 0 0
\(229\) 2.33003 3.12978i 0.153973 0.206822i −0.718443 0.695586i \(-0.755145\pi\)
0.872416 + 0.488764i \(0.162552\pi\)
\(230\) −1.89018 0.220930i −0.124635 0.0145677i
\(231\) 0 0
\(232\) −0.169994 0.111807i −0.0111607 0.00734049i
\(233\) 18.1958 + 6.62273i 1.19205 + 0.433869i 0.860441 0.509549i \(-0.170188\pi\)
0.331604 + 0.943419i \(0.392410\pi\)
\(234\) 0 0
\(235\) −0.198584 + 0.0722788i −0.0129542 + 0.00471495i
\(236\) −14.8091 3.50982i −0.963989 0.228470i
\(237\) 0 0
\(238\) 0.333413 + 5.72448i 0.0216120 + 0.371063i
\(239\) 9.74423 + 10.3283i 0.630302 + 0.668081i 0.961285 0.275556i \(-0.0888619\pi\)
−0.330983 + 0.943637i \(0.607380\pi\)
\(240\) 0 0
\(241\) −4.42332 + 10.2544i −0.284931 + 0.660544i −0.999227 0.0392991i \(-0.987487\pi\)
0.714297 + 0.699843i \(0.246747\pi\)
\(242\) 0.708270 0.0455293
\(243\) 0 0
\(244\) −8.12090 −0.519888
\(245\) 5.88266 13.6375i 0.375829 0.871271i
\(246\) 0 0
\(247\) 1.81943 + 1.92849i 0.115768 + 0.122707i
\(248\) −0.0799494 1.37268i −0.00507679 0.0871651i
\(249\) 0 0
\(250\) −2.16339 0.512733i −0.136825 0.0324281i
\(251\) −8.61554 + 3.13580i −0.543808 + 0.197930i −0.599293 0.800530i \(-0.704552\pi\)
0.0554853 + 0.998460i \(0.482329\pi\)
\(252\) 0 0
\(253\) 23.1630 + 8.43066i 1.45625 + 0.530031i
\(254\) 2.97020 + 1.95353i 0.186367 + 0.122575i
\(255\) 0 0
\(256\) −13.1750 1.53994i −0.823437 0.0962460i
\(257\) 10.3133 13.8532i 0.643328 0.864139i −0.354145 0.935191i \(-0.615228\pi\)
0.997473 + 0.0710513i \(0.0226354\pi\)
\(258\) 0 0
\(259\) −0.400066 + 6.86888i −0.0248589 + 0.426811i
\(260\) 3.81355 3.19995i 0.236506 0.198452i
\(261\) 0 0
\(262\) 0.868782 + 0.728995i 0.0536735 + 0.0450375i
\(263\) 3.22173 3.41483i 0.198660 0.210568i −0.620384 0.784299i \(-0.713023\pi\)
0.819044 + 0.573731i \(0.194505\pi\)
\(264\) 0 0
\(265\) −13.0729 + 8.59815i −0.803059 + 0.528180i
\(266\) −1.22303 + 0.289863i −0.0749886 + 0.0177726i
\(267\) 0 0
\(268\) −26.2434 + 3.06741i −1.60307 + 0.187372i
\(269\) 6.52546 11.3024i 0.397864 0.689121i −0.595598 0.803283i \(-0.703085\pi\)
0.993462 + 0.114162i \(0.0364182\pi\)
\(270\) 0 0
\(271\) −11.8170 20.4676i −0.717832 1.24332i −0.961857 0.273552i \(-0.911801\pi\)
0.244026 0.969769i \(-0.421532\pi\)
\(272\) 17.1182 + 22.9937i 1.03794 + 1.39420i
\(273\) 0 0
\(274\) −1.19504 + 3.99172i −0.0721952 + 0.241149i
\(275\) 8.55710 + 4.29753i 0.516012 + 0.259151i
\(276\) 0 0
\(277\) −6.82482 22.7965i −0.410064 1.36971i −0.874897 0.484310i \(-0.839071\pi\)
0.464833 0.885398i \(-0.346114\pi\)
\(278\) −0.413935 + 2.34754i −0.0248262 + 0.140796i
\(279\) 0 0
\(280\) 0.826957 + 4.68990i 0.0494201 + 0.280275i
\(281\) −12.3376 + 6.19616i −0.735997 + 0.369632i −0.776978 0.629528i \(-0.783248\pi\)
0.0409803 + 0.999160i \(0.486952\pi\)
\(282\) 0 0
\(283\) 5.81388 + 13.4781i 0.345599 + 0.801189i 0.999023 + 0.0441964i \(0.0140727\pi\)
−0.653424 + 0.756992i \(0.726668\pi\)
\(284\) 1.98705 + 4.60650i 0.117910 + 0.273346i
\(285\) 0 0
\(286\) 1.02959 0.517082i 0.0608812 0.0305757i
\(287\) −2.10332 11.9285i −0.124155 0.704119i
\(288\) 0 0
\(289\) 6.97903 39.5800i 0.410531 2.32824i
\(290\) 0.0233141 + 0.0778746i 0.00136905 + 0.00457295i
\(291\) 0 0
\(292\) 9.88758 + 4.96573i 0.578627 + 0.290597i
\(293\) −1.11671 + 3.73009i −0.0652392 + 0.217914i −0.984393 0.175985i \(-0.943689\pi\)
0.919154 + 0.393899i \(0.128874\pi\)
\(294\) 0 0
\(295\) 7.32687 + 9.84169i 0.426587 + 0.573005i
\(296\) −0.631572 1.09391i −0.0367094 0.0635825i
\(297\) 0 0
\(298\) −0.917907 + 1.58986i −0.0531729 + 0.0920982i
\(299\) 10.1857 1.19054i 0.589054 0.0688505i
\(300\) 0 0
\(301\) 19.1700 4.54338i 1.10494 0.261876i
\(302\) 1.49071 0.980453i 0.0857805 0.0564187i
\(303\) 0 0
\(304\) −4.31199 + 4.57044i −0.247309 + 0.262133i
\(305\) 5.01524 + 4.20829i 0.287172 + 0.240966i
\(306\) 0 0
\(307\) −0.636621 + 0.534188i −0.0363339 + 0.0304877i −0.660774 0.750585i \(-0.729772\pi\)
0.624440 + 0.781073i \(0.285327\pi\)
\(308\) 1.77743 30.5172i 0.101278 1.73888i
\(309\) 0 0
\(310\) −0.328046 + 0.440642i −0.0186317 + 0.0250268i
\(311\) −10.9127 1.27552i −0.618805 0.0723279i −0.199086 0.979982i \(-0.563797\pi\)
−0.419719 + 0.907654i \(0.637871\pi\)
\(312\) 0 0
\(313\) −14.4466 9.50167i −0.816570 0.537066i 0.0711419 0.997466i \(-0.477336\pi\)
−0.887712 + 0.460400i \(0.847706\pi\)
\(314\) −1.30795 0.476057i −0.0738121 0.0268654i
\(315\) 0 0
\(316\) 14.9632 5.44614i 0.841743 0.306370i
\(317\) −17.7179 4.19923i −0.995138 0.235852i −0.299384 0.954133i \(-0.596781\pi\)
−0.695754 + 0.718281i \(0.744929\pi\)
\(318\) 0 0
\(319\) −0.0612219 1.05114i −0.00342777 0.0588525i
\(320\) 7.79380 + 8.26094i 0.435687 + 0.461801i
\(321\) 0 0
\(322\) −1.92559 + 4.46402i −0.107309 + 0.248770i
\(323\) 12.5359 0.697518
\(324\) 0 0
\(325\) 3.98377 0.220980
\(326\) 0.370185 0.858185i 0.0205026 0.0475305i
\(327\) 0 0
\(328\) 1.52596 + 1.61743i 0.0842573 + 0.0893075i
\(329\) 0.0313908 + 0.538959i 0.00173063 + 0.0297138i
\(330\) 0 0
\(331\) 17.5916 + 4.16929i 0.966923 + 0.229165i 0.683598 0.729859i \(-0.260414\pi\)
0.283325 + 0.959024i \(0.408562\pi\)
\(332\) 10.1256 3.68542i 0.555714 0.202263i
\(333\) 0 0
\(334\) 0.767807 + 0.279459i 0.0420125 + 0.0152913i
\(335\) 17.7967 + 11.7051i 0.972340 + 0.639518i
\(336\) 0 0
\(337\) 20.8508 + 2.43711i 1.13582 + 0.132758i 0.663152 0.748485i \(-0.269218\pi\)
0.472664 + 0.881243i \(0.343292\pi\)
\(338\) −1.16834 + 1.56936i −0.0635496 + 0.0853619i
\(339\) 0 0
\(340\) 1.36862 23.4984i 0.0742241 1.27438i
\(341\) 5.45079 4.57376i 0.295177 0.247683i
\(342\) 0 0
\(343\) −7.36564 6.18050i −0.397707 0.333716i
\(344\) −2.48198 + 2.63075i −0.133820 + 0.141840i
\(345\) 0 0
\(346\) 2.51151 1.65185i 0.135020 0.0888039i
\(347\) −19.8413 + 4.70248i −1.06514 + 0.252443i −0.725577 0.688141i \(-0.758427\pi\)
−0.339562 + 0.940584i \(0.610279\pi\)
\(348\) 0 0
\(349\) −17.5899 + 2.05597i −0.941567 + 0.110053i −0.573007 0.819550i \(-0.694223\pi\)
−0.368560 + 0.929604i \(0.620149\pi\)
\(350\) −0.944298 + 1.63557i −0.0504748 + 0.0874250i
\(351\) 0 0
\(352\) 4.22137 + 7.31163i 0.225000 + 0.389711i
\(353\) 12.4103 + 16.6700i 0.660535 + 0.887252i 0.998547 0.0538897i \(-0.0171620\pi\)
−0.338012 + 0.941142i \(0.609755\pi\)
\(354\) 0 0
\(355\) 1.15996 3.87454i 0.0615644 0.205639i
\(356\) −11.8455 5.94905i −0.627811 0.315299i
\(357\) 0 0
\(358\) 1.03634 + 3.46161i 0.0547722 + 0.182952i
\(359\) 3.40920 19.3346i 0.179931 1.02044i −0.752366 0.658745i \(-0.771088\pi\)
0.932297 0.361693i \(-0.117801\pi\)
\(360\) 0 0
\(361\) −2.82216 16.0053i −0.148535 0.842383i
\(362\) 0.0253628 0.0127377i 0.00133304 0.000669477i
\(363\) 0 0
\(364\) −5.03722 11.6776i −0.264022 0.612071i
\(365\) −3.53303 8.19048i −0.184927 0.428709i
\(366\) 0 0
\(367\) −29.1383 + 14.6338i −1.52101 + 0.763878i −0.996179 0.0873300i \(-0.972167\pi\)
−0.524828 + 0.851209i \(0.675870\pi\)
\(368\) 4.22035 + 23.9348i 0.220001 + 1.24769i
\(369\) 0 0
\(370\) −0.0876322 + 0.496987i −0.00455578 + 0.0258371i
\(371\) 11.4643 + 38.2933i 0.595195 + 1.98809i
\(372\) 0 0
\(373\) −15.8648 7.96762i −0.821450 0.412548i −0.0121379 0.999926i \(-0.503864\pi\)
−0.809312 + 0.587379i \(0.800160\pi\)
\(374\) 1.56239 5.21874i 0.0807891 0.269854i
\(375\) 0 0
\(376\) −0.0591852 0.0794995i −0.00305224 0.00409987i
\(377\) −0.219025 0.379362i −0.0112803 0.0195381i
\(378\) 0 0
\(379\) −13.5735 + 23.5099i −0.697222 + 1.20762i 0.272204 + 0.962240i \(0.412247\pi\)
−0.969426 + 0.245384i \(0.921086\pi\)
\(380\) 5.12458 0.598978i 0.262886 0.0307269i
\(381\) 0 0
\(382\) −1.95216 + 0.462671i −0.0998814 + 0.0236723i
\(383\) 29.7103 19.5408i 1.51813 0.998488i 0.529465 0.848332i \(-0.322393\pi\)
0.988662 0.150156i \(-0.0479775\pi\)
\(384\) 0 0
\(385\) −16.9118 + 17.9255i −0.861908 + 0.913569i
\(386\) 2.27802 + 1.91148i 0.115948 + 0.0972919i
\(387\) 0 0
\(388\) −2.81703 + 2.36377i −0.143013 + 0.120002i
\(389\) 1.18310 20.3130i 0.0599855 1.02991i −0.825250 0.564768i \(-0.808966\pi\)
0.885236 0.465143i \(-0.153997\pi\)
\(390\) 0 0
\(391\) 28.9550 38.8934i 1.46432 1.96692i
\(392\) 6.91845 + 0.808650i 0.349434 + 0.0408430i
\(393\) 0 0
\(394\) 0.192779 + 0.126793i 0.00971205 + 0.00638771i
\(395\) −12.0630 4.39059i −0.606957 0.220914i
\(396\) 0 0
\(397\) −24.9491 + 9.08072i −1.25216 + 0.455748i −0.881130 0.472874i \(-0.843217\pi\)
−0.371028 + 0.928622i \(0.620995\pi\)
\(398\) 0.427089 + 0.101222i 0.0214080 + 0.00507380i
\(399\) 0 0
\(400\) 0.548968 + 9.42541i 0.0274484 + 0.471271i
\(401\) 17.6522 + 18.7102i 0.881508 + 0.934344i 0.998269 0.0588160i \(-0.0187325\pi\)
−0.116761 + 0.993160i \(0.537251\pi\)
\(402\) 0 0
\(403\) 1.17251 2.71818i 0.0584067 0.135402i
\(404\) 32.7795 1.63084
\(405\) 0 0
\(406\) 0.207667 0.0103063
\(407\) 2.58903 6.00204i 0.128333 0.297510i
\(408\) 0 0
\(409\) 19.1127 + 20.2582i 0.945060 + 1.00170i 0.999995 + 0.00321505i \(0.00102338\pi\)
−0.0549349 + 0.998490i \(0.517495\pi\)
\(410\) −0.0516558 0.886896i −0.00255110 0.0438007i
\(411\) 0 0
\(412\) 11.0048 + 2.60819i 0.542169 + 0.128496i
\(413\) 29.4542 10.7204i 1.44934 0.527518i
\(414\) 0 0
\(415\) −8.16308 2.97112i −0.400710 0.145846i
\(416\) 2.93461 + 1.93013i 0.143881 + 0.0946322i
\(417\) 0 0
\(418\) 1.18601 + 0.138625i 0.0580099 + 0.00678038i
\(419\) 0.643757 0.864716i 0.0314496 0.0422441i −0.786120 0.618074i \(-0.787913\pi\)
0.817570 + 0.575829i \(0.195321\pi\)
\(420\) 0 0
\(421\) −0.456887 + 7.84445i −0.0222673 + 0.382315i 0.968702 + 0.248226i \(0.0798477\pi\)
−0.990969 + 0.134089i \(0.957189\pi\)
\(422\) −1.63479 + 1.37175i −0.0795801 + 0.0667757i
\(423\) 0 0
\(424\) −5.62145 4.71695i −0.273002 0.229076i
\(425\) 12.9262 13.7009i 0.627011 0.664592i
\(426\) 0 0
\(427\) 13.9737 9.19062i 0.676233 0.444765i
\(428\) 3.09959 0.734617i 0.149824 0.0355090i
\(429\) 0 0
\(430\) 1.43521 0.167752i 0.0692121 0.00808973i
\(431\) −13.8447 + 23.9798i −0.666877 + 1.15507i 0.311895 + 0.950116i \(0.399036\pi\)
−0.978773 + 0.204949i \(0.934297\pi\)
\(432\) 0 0
\(433\) 9.89513 + 17.1389i 0.475530 + 0.823642i 0.999607 0.0280289i \(-0.00892305\pi\)
−0.524077 + 0.851671i \(0.675590\pi\)
\(434\) 0.838044 + 1.12569i 0.0402274 + 0.0540348i
\(435\) 0 0
\(436\) −6.48653 + 21.6665i −0.310649 + 1.03764i
\(437\) 9.49785 + 4.77000i 0.454344 + 0.228180i
\(438\) 0 0
\(439\) 9.64837 + 32.2278i 0.460492 + 1.53815i 0.801445 + 0.598069i \(0.204065\pi\)
−0.340953 + 0.940080i \(0.610750\pi\)
\(440\) 0.785626 4.45551i 0.0374533 0.212408i
\(441\) 0 0
\(442\) −0.393552 2.23195i −0.0187194 0.106163i
\(443\) −14.1788 + 7.12086i −0.673655 + 0.338322i −0.752526 0.658563i \(-0.771165\pi\)
0.0788709 + 0.996885i \(0.474868\pi\)
\(444\) 0 0
\(445\) 4.23264 + 9.81236i 0.200646 + 0.465151i
\(446\) −1.12257 2.60241i −0.0531553 0.123228i
\(447\) 0 0
\(448\) 25.9277 13.0214i 1.22497 0.615202i
\(449\) 0.153072 + 0.868114i 0.00722391 + 0.0409688i 0.988207 0.153126i \(-0.0489341\pi\)
−0.980983 + 0.194095i \(0.937823\pi\)
\(450\) 0 0
\(451\) −1.99820 + 11.3324i −0.0940916 + 0.533620i
\(452\) −4.92000 16.4339i −0.231417 0.772988i
\(453\) 0 0
\(454\) −3.56298 1.78940i −0.167219 0.0839805i
\(455\) −2.94053 + 9.82205i −0.137854 + 0.460465i
\(456\) 0 0
\(457\) −11.0899 14.8963i −0.518763 0.696820i 0.463122 0.886294i \(-0.346729\pi\)
−0.981886 + 0.189474i \(0.939322\pi\)
\(458\) −0.365551 0.633152i −0.0170811 0.0295853i
\(459\) 0 0
\(460\) 9.97822 17.2828i 0.465237 0.805814i
\(461\) 3.04933 0.356416i 0.142022 0.0165999i −0.0447850 0.998997i \(-0.514260\pi\)
0.186807 + 0.982397i \(0.440186\pi\)
\(462\) 0 0
\(463\) −27.8853 + 6.60895i −1.29594 + 0.307144i −0.820016 0.572341i \(-0.806035\pi\)
−0.475926 + 0.879485i \(0.657887\pi\)
\(464\) 0.867370 0.570478i 0.0402666 0.0264838i
\(465\) 0 0
\(466\) 2.48981 2.63905i 0.115338 0.122252i
\(467\) 10.6188 + 8.91027i 0.491382 + 0.412318i 0.854521 0.519417i \(-0.173851\pi\)
−0.363139 + 0.931735i \(0.618295\pi\)
\(468\) 0 0
\(469\) 41.6856 34.9784i 1.92486 1.61515i
\(470\) −0.00230237 + 0.0395302i −0.000106200 + 0.00182339i
\(471\) 0 0
\(472\) −3.43623 + 4.61566i −0.158165 + 0.212453i
\(473\) −18.5899 2.17285i −0.854764 0.0999076i
\(474\) 0 0
\(475\) 3.44956 + 2.26881i 0.158277 + 0.104100i
\(476\) −56.5056 20.5663i −2.58993 0.942657i
\(477\) 0 0
\(478\) 2.50012 0.909969i 0.114353 0.0416210i
\(479\) 24.7530 + 5.86656i 1.13099 + 0.268050i 0.753169 0.657827i \(-0.228524\pi\)
0.377824 + 0.925878i \(0.376673\pi\)
\(480\) 0 0
\(481\) −0.158122 2.71485i −0.00720975 0.123787i
\(482\) 1.43598 + 1.52205i 0.0654069 + 0.0693273i
\(483\) 0 0
\(484\) −2.94182 + 6.81990i −0.133719 + 0.309995i
\(485\) 2.96463 0.134617
\(486\) 0 0
\(487\) −1.98229 −0.0898263 −0.0449132 0.998991i \(-0.514301\pi\)
−0.0449132 + 0.998991i \(0.514301\pi\)
\(488\) −1.21614 + 2.81934i −0.0550522 + 0.127625i
\(489\) 0 0
\(490\) −1.90973 2.02420i −0.0862730 0.0914440i
\(491\) 0.0272326 + 0.467566i 0.00122899 + 0.0211010i 0.998867 0.0475911i \(-0.0151544\pi\)
−0.997638 + 0.0686921i \(0.978117\pi\)
\(492\) 0 0
\(493\) −2.01536 0.477650i −0.0907674 0.0215123i
\(494\) 0.466820 0.169909i 0.0210032 0.00764456i
\(495\) 0 0
\(496\) 6.59265 + 2.39953i 0.296019 + 0.107742i
\(497\) −8.63241 5.67763i −0.387217 0.254676i
\(498\) 0 0
\(499\) 23.5292 + 2.75017i 1.05331 + 0.123115i 0.625085 0.780557i \(-0.285064\pi\)
0.428227 + 0.903671i \(0.359138\pi\)
\(500\) 13.9228 18.7015i 0.622645 0.836358i
\(501\) 0 0
\(502\) −0.0998878 + 1.71501i −0.00445821 + 0.0765445i
\(503\) −0.513245 + 0.430663i −0.0228844 + 0.0192023i −0.654158 0.756358i \(-0.726977\pi\)
0.631274 + 0.775560i \(0.282532\pi\)
\(504\) 0 0
\(505\) −20.2437 16.9865i −0.900834 0.755889i
\(506\) 3.16951 3.35948i 0.140902 0.149347i
\(507\) 0 0
\(508\) −31.1472 + 20.4859i −1.38194 + 0.908913i
\(509\) −7.12235 + 1.68803i −0.315693 + 0.0748206i −0.385408 0.922746i \(-0.625939\pi\)
0.0697149 + 0.997567i \(0.477791\pi\)
\(510\) 0 0
\(511\) −22.6334 + 2.64547i −1.00124 + 0.117029i
\(512\) −6.97825 + 12.0867i −0.308398 + 0.534161i
\(513\) 0 0
\(514\) −1.61802 2.80249i −0.0713678 0.123613i
\(515\) −5.44469 7.31349i −0.239922 0.322271i
\(516\) 0 0
\(517\) 0.147099 0.491344i 0.00646939 0.0216093i
\(518\) 1.15209 + 0.578599i 0.0506197 + 0.0254222i
\(519\) 0 0
\(520\) −0.539830 1.80316i −0.0236731 0.0790737i
\(521\) 0.747254 4.23789i 0.0327378 0.185665i −0.964054 0.265708i \(-0.914394\pi\)
0.996791 + 0.0800423i \(0.0255056\pi\)
\(522\) 0 0
\(523\) −1.42678 8.09165i −0.0623885 0.353823i −0.999981 0.00608816i \(-0.998062\pi\)
0.937593 0.347735i \(-0.113049\pi\)
\(524\) −10.6280 + 5.33756i −0.464285 + 0.233172i
\(525\) 0 0
\(526\) −0.348417 0.807721i −0.0151917 0.0352183i
\(527\) −5.54387 12.8521i −0.241495 0.559848i
\(528\) 0 0
\(529\) 16.1834 8.12761i 0.703627 0.353375i
\(530\) 0.509102 + 2.88726i 0.0221140 + 0.125415i
\(531\) 0 0
\(532\) 2.28880 12.9804i 0.0992320 0.562773i
\(533\) 1.37303 + 4.58624i 0.0594726 + 0.198652i
\(534\) 0 0
\(535\) −2.29490 1.15254i −0.0992173 0.0498288i
\(536\) −2.86516 + 9.57029i −0.123756 + 0.413373i
\(537\) 0 0
\(538\) −1.46028 1.96149i −0.0629570 0.0845660i
\(539\) 18.0230 + 31.2167i 0.776305 + 1.34460i
\(540\) 0 0
\(541\) −1.90293 + 3.29597i −0.0818132 + 0.141705i −0.904029 0.427472i \(-0.859404\pi\)
0.822216 + 0.569176i \(0.192738\pi\)
\(542\) −4.39841 + 0.514100i −0.188928 + 0.0220825i
\(543\) 0 0
\(544\) 16.1600 3.82999i 0.692854 0.164209i
\(545\) 15.2336 10.0193i 0.652535 0.429179i
\(546\) 0 0
\(547\) 19.7705 20.9555i 0.845325 0.895992i −0.150375 0.988629i \(-0.548048\pi\)
0.995700 + 0.0926369i \(0.0295296\pi\)
\(548\) −33.4725 28.0867i −1.42987 1.19981i
\(549\) 0 0
\(550\) 1.37444 1.15329i 0.0586064 0.0491766i
\(551\) 0.0263976 0.453228i 0.00112457 0.0193082i
\(552\) 0 0
\(553\) −19.5836 + 26.3054i −0.832780 + 1.11862i
\(554\) −4.42859 0.517628i −0.188153 0.0219919i
\(555\) 0 0
\(556\) −20.8851 13.7363i −0.885724 0.582550i
\(557\) −0.617137 0.224620i −0.0261489 0.00951744i 0.328913 0.944360i \(-0.393318\pi\)
−0.355062 + 0.934843i \(0.615540\pi\)
\(558\) 0 0
\(559\) −7.31706 + 2.66319i −0.309479 + 0.112641i
\(560\) −23.6437 5.60366i −0.999128 0.236798i
\(561\) 0 0
\(562\) 0.150413 + 2.58250i 0.00634480 + 0.108936i
\(563\) 6.57618 + 6.97035i 0.277153 + 0.293765i 0.850965 0.525222i \(-0.176018\pi\)
−0.573812 + 0.818987i \(0.694536\pi\)
\(564\) 0 0
\(565\) −5.47769 + 12.6987i −0.230448 + 0.534238i
\(566\) 2.75035 0.115606
\(567\) 0 0
\(568\) 1.89681 0.0795884
\(569\) 10.0440 23.2846i 0.421066 0.976142i −0.567225 0.823563i \(-0.691983\pi\)
0.988291 0.152579i \(-0.0487578\pi\)
\(570\) 0 0
\(571\) −5.55709 5.89017i −0.232557 0.246496i 0.600577 0.799567i \(-0.294937\pi\)
−0.833134 + 0.553071i \(0.813456\pi\)
\(572\) 0.702509 + 12.0616i 0.0293734 + 0.504322i
\(573\) 0 0
\(574\) −2.20838 0.523395i −0.0921759 0.0218461i
\(575\) 15.0068 5.46202i 0.625826 0.227782i
\(576\) 0 0
\(577\) 2.58521 + 0.940940i 0.107624 + 0.0391718i 0.395271 0.918565i \(-0.370651\pi\)
−0.287647 + 0.957736i \(0.592873\pi\)
\(578\) −6.29172 4.13813i −0.261701 0.172124i
\(579\) 0 0
\(580\) −0.846686 0.0989634i −0.0351567 0.00410923i
\(581\) −13.2523 + 17.8009i −0.549797 + 0.738505i
\(582\) 0 0
\(583\) 2.20804 37.9106i 0.0914476 1.57010i
\(584\) 3.20466 2.68903i 0.132610 0.111273i
\(585\) 0 0
\(586\) 0.558878 + 0.468954i 0.0230870 + 0.0193723i
\(587\) −28.8821 + 30.6133i −1.19209 + 1.26354i −0.235580 + 0.971855i \(0.575699\pi\)
−0.956513 + 0.291689i \(0.905783\pi\)
\(588\) 0 0
\(589\) 2.56332 1.68592i 0.105620 0.0694671i
\(590\) 2.23700 0.530179i 0.0920959 0.0218271i
\(591\) 0 0
\(592\) 6.40142 0.748219i 0.263097 0.0307516i
\(593\) 3.28564 5.69090i 0.134925 0.233697i −0.790644 0.612277i \(-0.790254\pi\)
0.925569 + 0.378579i \(0.123587\pi\)
\(594\) 0 0
\(595\) 24.2387 + 41.9826i 0.993689 + 1.72112i
\(596\) −11.4961 15.4420i −0.470901 0.632529i
\(597\) 0 0
\(598\) 0.551094 1.84078i 0.0225359 0.0752752i
\(599\) 13.3200 + 6.68956i 0.544241 + 0.273328i 0.699606 0.714529i \(-0.253359\pi\)
−0.155365 + 0.987857i \(0.549655\pi\)
\(600\) 0 0
\(601\) 7.32196 + 24.4570i 0.298669 + 0.997624i 0.967216 + 0.253954i \(0.0817312\pi\)
−0.668547 + 0.743670i \(0.733084\pi\)
\(602\) 0.641010 3.63535i 0.0261256 0.148166i
\(603\) 0 0
\(604\) 3.24905 + 18.4263i 0.132202 + 0.749754i
\(605\) 5.35088 2.68731i 0.217544 0.109255i
\(606\) 0 0
\(607\) −11.8994 27.5859i −0.482982 1.11968i −0.969297 0.245894i \(-0.920918\pi\)
0.486315 0.873784i \(-0.338341\pi\)
\(608\) 1.44186 + 3.34261i 0.0584751 + 0.135561i
\(609\) 0 0
\(610\) 1.09623 0.550547i 0.0443851 0.0222910i
\(611\) −0.0370529 0.210137i −0.00149900 0.00850125i
\(612\) 0 0
\(613\) −2.50656 + 14.2154i −0.101239 + 0.574154i 0.891417 + 0.453183i \(0.149712\pi\)
−0.992656 + 0.120970i \(0.961399\pi\)
\(614\) 0.0446597 + 0.149174i 0.00180232 + 0.00602016i
\(615\) 0 0
\(616\) −10.3285 5.18716i −0.416147 0.208997i
\(617\) −3.90332 + 13.0380i −0.157142 + 0.524890i −0.999910 0.0133857i \(-0.995739\pi\)
0.842769 + 0.538276i \(0.180924\pi\)
\(618\) 0 0
\(619\) 13.0490 + 17.5278i 0.524482 + 0.704502i 0.982880 0.184245i \(-0.0589840\pi\)
−0.458398 + 0.888747i \(0.651577\pi\)
\(620\) −2.88037 4.98895i −0.115679 0.200361i
\(621\) 0 0
\(622\) −1.02933 + 1.78285i −0.0412724 + 0.0714859i
\(623\) 27.1153 3.16932i 1.08635 0.126976i
\(624\) 0 0
\(625\) −6.17147 + 1.46267i −0.246859 + 0.0585066i
\(626\) −2.70689 + 1.78035i −0.108189 + 0.0711570i
\(627\) 0 0
\(628\) 10.0165 10.6169i 0.399704 0.423661i
\(629\) −9.84993 8.26507i −0.392742 0.329550i
\(630\) 0 0
\(631\) −18.5327 + 15.5508i −0.737775 + 0.619066i −0.932239 0.361843i \(-0.882148\pi\)
0.194464 + 0.980910i \(0.437703\pi\)
\(632\) 0.350063 6.01035i 0.0139248 0.239079i
\(633\) 0 0
\(634\) −2.03739 + 2.73669i −0.0809151 + 0.108688i
\(635\) 29.8515 + 3.48914i 1.18462 + 0.138462i
\(636\) 0 0
\(637\) 12.5292 + 8.24060i 0.496426 + 0.326504i
\(638\) −0.185390 0.0674764i −0.00733966 0.00267142i
\(639\) 0 0
\(640\) 8.53752 3.10740i 0.337475 0.122831i
\(641\) −34.7871 8.24470i −1.37401 0.325646i −0.523688 0.851910i \(-0.675444\pi\)
−0.850321 + 0.526264i \(0.823592\pi\)
\(642\) 0 0
\(643\) −2.63836 45.2988i −0.104047 1.78641i −0.497896 0.867237i \(-0.665894\pi\)
0.393850 0.919175i \(-0.371143\pi\)
\(644\) −34.9858 37.0828i −1.37863 1.46127i
\(645\) 0 0
\(646\) 0.930345 2.15678i 0.0366039 0.0848575i
\(647\) −18.8974 −0.742935 −0.371468 0.928446i \(-0.621145\pi\)
−0.371468 + 0.928446i \(0.621145\pi\)
\(648\) 0 0
\(649\) −29.7779 −1.16888
\(650\) 0.295653 0.685400i 0.0115965 0.0268836i
\(651\) 0 0
\(652\) 6.72585 + 7.12898i 0.263405 + 0.279192i
\(653\) −1.26424 21.7062i −0.0494737 0.849430i −0.928195 0.372095i \(-0.878640\pi\)
0.878721 0.477336i \(-0.158397\pi\)
\(654\) 0 0
\(655\) 9.32948 + 2.21113i 0.364533 + 0.0863959i
\(656\) −10.6616 + 3.88051i −0.416266 + 0.151509i
\(657\) 0 0
\(658\) 0.0950565 + 0.0345978i 0.00370569 + 0.00134876i
\(659\) 13.6785 + 8.99649i 0.532839 + 0.350453i 0.787241 0.616645i \(-0.211509\pi\)
−0.254403 + 0.967098i \(0.581879\pi\)
\(660\) 0 0
\(661\) −20.5523 2.40222i −0.799392 0.0934355i −0.293418 0.955984i \(-0.594793\pi\)
−0.505974 + 0.862549i \(0.668867\pi\)
\(662\) 2.02287 2.71718i 0.0786210 0.105606i
\(663\) 0 0
\(664\) 0.236888 4.06721i 0.00919304 0.157838i
\(665\) −8.14001 + 6.83028i −0.315656 + 0.264867i
\(666\) 0 0
\(667\) −1.34519 1.12875i −0.0520860 0.0437054i
\(668\) −5.87999 + 6.23243i −0.227504 + 0.241140i
\(669\) 0 0
\(670\) 3.33461 2.19321i 0.128827 0.0847310i
\(671\) −15.4610 + 3.66431i −0.596863 + 0.141459i
\(672\) 0 0
\(673\) 23.8569 2.78847i 0.919615 0.107488i 0.356904 0.934141i \(-0.383832\pi\)
0.562711 + 0.826654i \(0.309758\pi\)
\(674\) 1.96673 3.40647i 0.0757555 0.131212i
\(675\) 0 0
\(676\) −10.2585 17.7683i −0.394559 0.683396i
\(677\) 27.0852 + 36.3818i 1.04097 + 1.39827i 0.913696 + 0.406399i \(0.133216\pi\)
0.127275 + 0.991867i \(0.459377\pi\)
\(678\) 0 0
\(679\) 2.17214 7.25544i 0.0833589 0.278438i
\(680\) −7.95298 3.99413i −0.304983 0.153168i
\(681\) 0 0
\(682\) −0.382379 1.27724i −0.0146421 0.0489079i
\(683\) −3.38555 + 19.2004i −0.129544 + 0.734683i 0.848960 + 0.528457i \(0.177229\pi\)
−0.978504 + 0.206226i \(0.933882\pi\)
\(684\) 0 0
\(685\) 6.11698 + 34.6911i 0.233718 + 1.32548i
\(686\) −1.60998 + 0.808562i −0.0614693 + 0.0308710i
\(687\) 0 0
\(688\) −7.30928 16.9448i −0.278664 0.646015i
\(689\) −6.25757 14.5067i −0.238394 0.552660i
\(690\) 0 0
\(691\) 18.3456 9.21350i 0.697899 0.350498i −0.0642194 0.997936i \(-0.520456\pi\)
0.762118 + 0.647438i \(0.224159\pi\)
\(692\) 5.47393 + 31.0442i 0.208088 + 1.18012i
\(693\) 0 0
\(694\) −0.663458 + 3.76266i −0.0251845 + 0.142828i
\(695\) 5.77980 + 19.3059i 0.219240 + 0.732314i
\(696\) 0 0
\(697\) 20.2280 + 10.1589i 0.766190 + 0.384795i
\(698\) −0.951699 + 3.17889i −0.0360223 + 0.120323i
\(699\) 0 0
\(700\) −11.8267 15.8860i −0.447006 0.600433i
\(701\) −3.27119 5.66587i −0.123551 0.213997i 0.797615 0.603168i \(-0.206095\pi\)
−0.921166 + 0.389171i \(0.872762\pi\)
\(702\) 0 0
\(703\) 1.40923 2.44085i 0.0531500 0.0920585i
\(704\) −27.3773 + 3.19995i −1.03182 + 0.120603i
\(705\) 0 0
\(706\) 3.78905 0.898022i 0.142603 0.0337975i
\(707\) −56.4038 + 37.0974i −2.12128 + 1.39519i
\(708\) 0 0
\(709\) −6.58581 + 6.98055i −0.247335 + 0.262160i −0.839133 0.543927i \(-0.816937\pi\)
0.591798 + 0.806087i \(0.298418\pi\)
\(710\) −0.580522 0.487116i −0.0217866 0.0182811i
\(711\) 0 0
\(712\) −3.83925 + 3.22152i −0.143882 + 0.120731i
\(713\) 0.690003 11.8469i 0.0258408 0.443670i
\(714\) 0 0
\(715\) 5.81653 7.81296i 0.217526 0.292188i
\(716\) −37.6362 4.39904i −1.40653 0.164400i
\(717\) 0 0
\(718\) −3.07346 2.02145i −0.114700 0.0754397i
\(719\) 24.3548 + 8.86441i 0.908280 + 0.330587i 0.753566 0.657372i \(-0.228332\pi\)
0.154714 + 0.987959i \(0.450554\pi\)
\(720\) 0 0
\(721\) −21.8878 + 7.96650i −0.815143 + 0.296688i
\(722\) −2.96312 0.702272i −0.110276 0.0261359i
\(723\) 0 0
\(724\) 0.0173055 + 0.297123i 0.000643152 + 0.0110425i
\(725\) −0.468129 0.496187i −0.0173859 0.0184279i
\(726\) 0 0
\(727\) −8.25148 + 19.1291i −0.306030 + 0.709458i −0.999944 0.0106003i \(-0.996626\pi\)
0.693913 + 0.720058i \(0.255885\pi\)
\(728\) −4.80845 −0.178213
\(729\) 0 0
\(730\) −1.67136 −0.0618597
\(731\) −14.5825 + 33.8059i −0.539352 + 1.25036i
\(732\) 0 0
\(733\) −5.85032 6.20098i −0.216086 0.229038i 0.610259 0.792202i \(-0.291065\pi\)
−0.826345 + 0.563164i \(0.809584\pi\)
\(734\) 0.355239 + 6.09922i 0.0131121 + 0.225126i
\(735\) 0 0
\(736\) 13.7010 + 3.24719i 0.505024 + 0.119693i
\(737\) −48.5793 + 17.6814i −1.78944 + 0.651304i
\(738\) 0 0
\(739\) 34.6163 + 12.5993i 1.27338 + 0.463473i 0.888238 0.459384i \(-0.151930\pi\)
0.385143 + 0.922857i \(0.374152\pi\)
\(740\) −4.42148 2.90805i −0.162537 0.106902i
\(741\) 0 0
\(742\) 7.43910 + 0.869507i 0.273098 + 0.0319206i
\(743\) −17.8874 + 24.0269i −0.656223 + 0.881461i −0.998304 0.0582096i \(-0.981461\pi\)
0.342081 + 0.939670i \(0.388868\pi\)
\(744\) 0 0
\(745\) −0.902417 + 15.4939i −0.0330620 + 0.567653i
\(746\) −2.54821 + 2.13820i −0.0932966 + 0.0782852i
\(747\) 0 0
\(748\) 43.7615 + 36.7203i 1.60008 + 1.34263i
\(749\) −4.50209 + 4.77194i −0.164503 + 0.174363i
\(750\) 0 0
\(751\) −5.85565 + 3.85132i −0.213676 + 0.140537i −0.651835 0.758360i \(-0.726001\pi\)
0.438160 + 0.898897i \(0.355630\pi\)
\(752\) 0.492069 0.116622i 0.0179439 0.00425278i
\(753\) 0 0
\(754\) −0.0815232 + 0.00952870i −0.00296890 + 0.000347015i
\(755\) 7.54205 13.0632i 0.274483 0.475419i
\(756\) 0 0
\(757\) −11.1739 19.3538i −0.406123 0.703426i 0.588328 0.808622i \(-0.299786\pi\)
−0.994452 + 0.105196i \(0.966453\pi\)
\(758\) 3.03749 + 4.08006i 0.110327 + 0.148194i
\(759\) 0 0
\(760\) 0.559483 1.86880i 0.0202946 0.0677886i
\(761\) 2.87464 + 1.44370i 0.104206 + 0.0523340i 0.500139 0.865945i \(-0.333282\pi\)
−0.395933 + 0.918279i \(0.629579\pi\)
\(762\) 0 0
\(763\) −13.3591 44.6226i −0.483633 1.61545i
\(764\) 3.65332 20.7190i 0.132172 0.749587i
\(765\) 0 0
\(766\) −1.15702 6.56181i −0.0418050 0.237088i
\(767\) −11.0708 + 5.55998i −0.399745 + 0.200759i
\(768\) 0 0
\(769\) −2.22533 5.15891i −0.0802476 0.186035i 0.873369 0.487060i \(-0.161931\pi\)
−0.953616 + 0.301025i \(0.902671\pi\)
\(770\) 1.82895 + 4.23998i 0.0659107 + 0.152798i
\(771\) 0 0
\(772\) −27.8673 + 13.9955i −1.00297 + 0.503709i
\(773\) −9.17966 52.0604i −0.330169 1.87248i −0.470531 0.882383i \(-0.655938\pi\)
0.140362 0.990100i \(-0.455173\pi\)
\(774\) 0 0
\(775\) 0.800512 4.53993i 0.0287552 0.163079i
\(776\) 0.398767 + 1.33197i 0.0143149 + 0.0478150i
\(777\) 0 0
\(778\) −3.40701 1.71106i −0.122147 0.0613447i
\(779\) −1.42302 + 4.75320i −0.0509848 + 0.170301i
\(780\) 0 0
\(781\) 5.86158 + 7.87347i 0.209744 + 0.281735i
\(782\) −4.54265 7.86810i −0.162445 0.281363i
\(783\)