Properties

Label 729.2.g.d.109.1
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 109.1
Character \(\chi\) \(=\) 729.109
Dual form 729.2.g.d.622.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.31781 - 1.39680i) q^{2} +(-0.0981285 + 1.68480i) q^{4} +(-0.783127 + 0.0915344i) q^{5} +(1.06502 + 0.534872i) q^{7} +(-0.459476 + 0.385546i) q^{8} +O(q^{10})\) \(q+(-1.31781 - 1.39680i) q^{2} +(-0.0981285 + 1.68480i) q^{4} +(-0.783127 + 0.0915344i) q^{5} +(1.06502 + 0.534872i) q^{7} +(-0.459476 + 0.385546i) q^{8} +(1.15987 + 0.973243i) q^{10} +(-0.814497 - 1.88822i) q^{11} +(2.96806 + 0.703443i) q^{13} +(-0.656382 - 2.19247i) q^{14} +(4.49652 + 0.525568i) q^{16} +(-0.788777 + 4.47337i) q^{17} +(-0.838570 - 4.75577i) q^{19} +(-0.0773702 - 1.32839i) q^{20} +(-1.56410 + 3.62599i) q^{22} +(5.89280 - 2.95948i) q^{23} +(-4.26032 + 1.00971i) q^{25} +(-2.92877 - 5.07278i) q^{26} +(-1.00566 + 1.74186i) q^{28} +(2.88435 - 9.63442i) q^{29} +(7.44201 + 4.89468i) q^{31} +(-4.47508 - 6.01108i) q^{32} +(7.28784 - 4.79329i) q^{34} +(-0.883002 - 0.321387i) q^{35} +(-0.563666 + 0.205158i) q^{37} +(-5.53776 + 7.43850i) q^{38} +(0.324537 - 0.343989i) q^{40} +(0.763120 - 0.808860i) q^{41} +(4.47179 - 6.00665i) q^{43} +(3.26119 - 1.18698i) q^{44} +(-11.8994 - 4.33101i) q^{46} +(0.765373 - 0.503394i) q^{47} +(-3.33194 - 4.47557i) q^{49} +(7.02464 + 4.62018i) q^{50} +(-1.47641 + 4.93156i) q^{52} +(3.63216 - 6.29109i) q^{53} +(0.810691 + 1.40416i) q^{55} +(-0.695567 + 0.164852i) q^{56} +(-17.2583 + 8.66746i) q^{58} +(-2.06499 + 4.78719i) q^{59} +(0.00126297 + 0.0216843i) q^{61} +(-2.97027 - 16.8452i) q^{62} +(-0.926691 + 5.25553i) q^{64} +(-2.38876 - 0.279206i) q^{65} +(-4.31847 - 14.4247i) q^{67} +(-7.45934 - 1.76790i) q^{68} +(0.714717 + 1.65690i) q^{70} +(3.88852 + 3.26285i) q^{71} +(-0.586995 + 0.492548i) q^{73} +(1.02937 + 0.516967i) q^{74} +(8.09481 - 0.946147i) q^{76} +(0.142500 - 2.44663i) q^{77} +(-5.44517 - 5.77154i) q^{79} -3.56945 q^{80} -2.13546 q^{82} +(9.18487 + 9.73539i) q^{83} +(0.208244 - 3.57542i) q^{85} +(-14.2830 + 1.66945i) q^{86} +(1.10224 + 0.553563i) q^{88} +(-4.47086 + 3.75149i) q^{89} +(2.78478 + 2.33671i) q^{91} +(4.40788 + 10.2186i) q^{92} +(-1.71175 - 0.405693i) q^{94} +(1.09202 + 3.64761i) q^{95} +(-7.21661 - 0.843501i) q^{97} +(-1.86060 + 10.5520i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31781 1.39680i −0.931831 0.987683i 0.0681188 0.997677i \(-0.478300\pi\)
−0.999950 + 0.00999381i \(0.996819\pi\)
\(3\) 0 0
\(4\) −0.0981285 + 1.68480i −0.0490642 + 0.842400i
\(5\) −0.783127 + 0.0915344i −0.350225 + 0.0409354i −0.289387 0.957212i \(-0.593451\pi\)
−0.0608381 + 0.998148i \(0.519377\pi\)
\(6\) 0 0
\(7\) 1.06502 + 0.534872i 0.402539 + 0.202162i 0.638537 0.769591i \(-0.279540\pi\)
−0.235999 + 0.971753i \(0.575836\pi\)
\(8\) −0.459476 + 0.385546i −0.162449 + 0.136311i
\(9\) 0 0
\(10\) 1.15987 + 0.973243i 0.366782 + 0.307766i
\(11\) −0.814497 1.88822i −0.245580 0.569319i 0.750188 0.661225i \(-0.229963\pi\)
−0.995768 + 0.0919065i \(0.970704\pi\)
\(12\) 0 0
\(13\) 2.96806 + 0.703443i 0.823192 + 0.195100i 0.620564 0.784156i \(-0.286904\pi\)
0.202628 + 0.979256i \(0.435052\pi\)
\(14\) −0.656382 2.19247i −0.175425 0.585962i
\(15\) 0 0
\(16\) 4.49652 + 0.525568i 1.12413 + 0.131392i
\(17\) −0.788777 + 4.47337i −0.191306 + 1.08495i 0.726275 + 0.687404i \(0.241250\pi\)
−0.917581 + 0.397548i \(0.869861\pi\)
\(18\) 0 0
\(19\) −0.838570 4.75577i −0.192381 1.09105i −0.916099 0.400952i \(-0.868679\pi\)
0.723718 0.690096i \(-0.242432\pi\)
\(20\) −0.0773702 1.32839i −0.0173005 0.297038i
\(21\) 0 0
\(22\) −1.56410 + 3.62599i −0.333467 + 0.773064i
\(23\) 5.89280 2.95948i 1.22873 0.617093i 0.288453 0.957494i \(-0.406859\pi\)
0.940281 + 0.340401i \(0.110563\pi\)
\(24\) 0 0
\(25\) −4.26032 + 1.00971i −0.852063 + 0.201943i
\(26\) −2.92877 5.07278i −0.574379 0.994853i
\(27\) 0 0
\(28\) −1.00566 + 1.74186i −0.190052 + 0.329180i
\(29\) 2.88435 9.63442i 0.535611 1.78907i −0.0750566 0.997179i \(-0.523914\pi\)
0.610668 0.791887i \(-0.290901\pi\)
\(30\) 0 0
\(31\) 7.44201 + 4.89468i 1.33662 + 0.879111i 0.998086 0.0618416i \(-0.0196974\pi\)
0.338538 + 0.940953i \(0.390068\pi\)
\(32\) −4.47508 6.01108i −0.791091 1.06262i
\(33\) 0 0
\(34\) 7.28784 4.79329i 1.24985 0.822043i
\(35\) −0.883002 0.321387i −0.149255 0.0543242i
\(36\) 0 0
\(37\) −0.563666 + 0.205158i −0.0926661 + 0.0337277i −0.387937 0.921686i \(-0.626812\pi\)
0.295271 + 0.955414i \(0.404590\pi\)
\(38\) −5.53776 + 7.43850i −0.898343 + 1.20668i
\(39\) 0 0
\(40\) 0.324537 0.343989i 0.0513138 0.0543894i
\(41\) 0.763120 0.808860i 0.119179 0.126323i −0.665036 0.746811i \(-0.731584\pi\)
0.784216 + 0.620488i \(0.213066\pi\)
\(42\) 0 0
\(43\) 4.47179 6.00665i 0.681941 0.916006i −0.317539 0.948245i \(-0.602857\pi\)
0.999480 + 0.0322396i \(0.0102639\pi\)
\(44\) 3.26119 1.18698i 0.491643 0.178944i
\(45\) 0 0
\(46\) −11.8994 4.33101i −1.75447 0.638573i
\(47\) 0.765373 0.503394i 0.111641 0.0734275i −0.492461 0.870335i \(-0.663902\pi\)
0.604102 + 0.796907i \(0.293532\pi\)
\(48\) 0 0
\(49\) −3.33194 4.47557i −0.475991 0.639367i
\(50\) 7.02464 + 4.62018i 0.993434 + 0.653392i
\(51\) 0 0
\(52\) −1.47641 + 4.93156i −0.204742 + 0.683885i
\(53\) 3.63216 6.29109i 0.498916 0.864147i −0.501084 0.865399i \(-0.667065\pi\)
0.999999 + 0.00125165i \(0.000398413\pi\)
\(54\) 0 0
\(55\) 0.810691 + 1.40416i 0.109314 + 0.189337i
\(56\) −0.695567 + 0.164852i −0.0929490 + 0.0220293i
\(57\) 0 0
\(58\) −17.2583 + 8.66746i −2.26613 + 1.13809i
\(59\) −2.06499 + 4.78719i −0.268839 + 0.623239i −0.998141 0.0609534i \(-0.980586\pi\)
0.729302 + 0.684192i \(0.239845\pi\)
\(60\) 0 0
\(61\) 0.00126297 + 0.0216843i 0.000161707 + 0.00277640i 0.998388 0.0567566i \(-0.0180759\pi\)
−0.998226 + 0.0595330i \(0.981039\pi\)
\(62\) −2.97027 16.8452i −0.377224 2.13934i
\(63\) 0 0
\(64\) −0.926691 + 5.25553i −0.115836 + 0.656941i
\(65\) −2.38876 0.279206i −0.296289 0.0346312i
\(66\) 0 0
\(67\) −4.31847 14.4247i −0.527586 1.76226i −0.639765 0.768571i \(-0.720968\pi\)
0.112179 0.993688i \(-0.464217\pi\)
\(68\) −7.45934 1.76790i −0.904578 0.214389i
\(69\) 0 0
\(70\) 0.714717 + 1.65690i 0.0854250 + 0.198037i
\(71\) 3.88852 + 3.26285i 0.461482 + 0.387229i 0.843676 0.536853i \(-0.180387\pi\)
−0.382194 + 0.924082i \(0.624831\pi\)
\(72\) 0 0
\(73\) −0.586995 + 0.492548i −0.0687026 + 0.0576483i −0.676492 0.736450i \(-0.736501\pi\)
0.607790 + 0.794098i \(0.292056\pi\)
\(74\) 1.02937 + 0.516967i 0.119661 + 0.0600962i
\(75\) 0 0
\(76\) 8.09481 0.946147i 0.928538 0.108531i
\(77\) 0.142500 2.44663i 0.0162394 0.278820i
\(78\) 0 0
\(79\) −5.44517 5.77154i −0.612630 0.649349i 0.344576 0.938758i \(-0.388023\pi\)
−0.957206 + 0.289409i \(0.906541\pi\)
\(80\) −3.56945 −0.399077
\(81\) 0 0
\(82\) −2.13546 −0.235822
\(83\) 9.18487 + 9.73539i 1.00817 + 1.06860i 0.997641 + 0.0686535i \(0.0218703\pi\)
0.0105297 + 0.999945i \(0.496648\pi\)
\(84\) 0 0
\(85\) 0.208244 3.57542i 0.0225873 0.387809i
\(86\) −14.2830 + 1.66945i −1.54018 + 0.180021i
\(87\) 0 0
\(88\) 1.10224 + 0.553563i 0.117499 + 0.0590101i
\(89\) −4.47086 + 3.75149i −0.473910 + 0.397658i −0.848218 0.529647i \(-0.822325\pi\)
0.374309 + 0.927304i \(0.377880\pi\)
\(90\) 0 0
\(91\) 2.78478 + 2.33671i 0.291925 + 0.244954i
\(92\) 4.40788 + 10.2186i 0.459553 + 1.06536i
\(93\) 0 0
\(94\) −1.71175 0.405693i −0.176554 0.0418440i
\(95\) 1.09202 + 3.64761i 0.112039 + 0.374237i
\(96\) 0 0
\(97\) −7.21661 0.843501i −0.732736 0.0856445i −0.258461 0.966022i \(-0.583215\pi\)
−0.474274 + 0.880377i \(0.657290\pi\)
\(98\) −1.86060 + 10.5520i −0.187949 + 1.06591i
\(99\) 0 0
\(100\) −1.28311 7.27686i −0.128311 0.727686i
\(101\) −0.419625 7.20469i −0.0417543 0.716893i −0.952615 0.304179i \(-0.901618\pi\)
0.910861 0.412714i \(-0.135419\pi\)
\(102\) 0 0
\(103\) −0.596404 + 1.38262i −0.0587654 + 0.136234i −0.945069 0.326872i \(-0.894006\pi\)
0.886303 + 0.463105i \(0.153265\pi\)
\(104\) −1.63496 + 0.821108i −0.160321 + 0.0805163i
\(105\) 0 0
\(106\) −13.5739 + 3.21706i −1.31841 + 0.312469i
\(107\) −1.73493 3.00499i −0.167722 0.290503i 0.769897 0.638169i \(-0.220308\pi\)
−0.937619 + 0.347666i \(0.886974\pi\)
\(108\) 0 0
\(109\) 3.95947 6.85801i 0.379249 0.656878i −0.611705 0.791086i \(-0.709516\pi\)
0.990953 + 0.134209i \(0.0428492\pi\)
\(110\) 0.892986 2.98278i 0.0851429 0.284397i
\(111\) 0 0
\(112\) 4.50776 + 2.96480i 0.425943 + 0.280147i
\(113\) 3.20052 + 4.29904i 0.301080 + 0.404420i 0.926757 0.375662i \(-0.122585\pi\)
−0.625677 + 0.780082i \(0.715177\pi\)
\(114\) 0 0
\(115\) −4.34392 + 2.85704i −0.405072 + 0.266420i
\(116\) 15.9490 + 5.80497i 1.48083 + 0.538978i
\(117\) 0 0
\(118\) 9.40799 3.42423i 0.866076 0.315226i
\(119\) −3.23274 + 4.34232i −0.296345 + 0.398060i
\(120\) 0 0
\(121\) 4.64670 4.92522i 0.422428 0.447747i
\(122\) 0.0286242 0.0303399i 0.00259152 0.00274685i
\(123\) 0 0
\(124\) −8.97684 + 12.0580i −0.806144 + 1.08284i
\(125\) 6.94848 2.52904i 0.621491 0.226204i
\(126\) 0 0
\(127\) 5.22612 + 1.90215i 0.463743 + 0.168789i 0.563316 0.826242i \(-0.309525\pi\)
−0.0995729 + 0.995030i \(0.531748\pi\)
\(128\) −3.96013 + 2.60462i −0.350030 + 0.230218i
\(129\) 0 0
\(130\) 2.75793 + 3.70454i 0.241887 + 0.324910i
\(131\) −2.04212 1.34312i −0.178421 0.117349i 0.457157 0.889386i \(-0.348868\pi\)
−0.635578 + 0.772037i \(0.719238\pi\)
\(132\) 0 0
\(133\) 1.65063 5.51350i 0.143128 0.478081i
\(134\) −14.4574 + 25.0410i −1.24893 + 2.16322i
\(135\) 0 0
\(136\) −1.36227 2.35952i −0.116813 0.202327i
\(137\) 10.6941 2.53455i 0.913658 0.216541i 0.253209 0.967412i \(-0.418514\pi\)
0.660449 + 0.750871i \(0.270366\pi\)
\(138\) 0 0
\(139\) −12.7658 + 6.41125i −1.08278 + 0.543795i −0.898453 0.439069i \(-0.855308\pi\)
−0.184331 + 0.982864i \(0.559012\pi\)
\(140\) 0.628120 1.45615i 0.0530858 0.123067i
\(141\) 0 0
\(142\) −0.566782 9.73127i −0.0475633 0.816630i
\(143\) −1.08922 6.17729i −0.0910854 0.516571i
\(144\) 0 0
\(145\) −1.37694 + 7.80899i −0.114348 + 0.648501i
\(146\) 1.46154 + 0.170829i 0.120958 + 0.0141379i
\(147\) 0 0
\(148\) −0.290338 0.969796i −0.0238656 0.0797167i
\(149\) 10.0150 + 2.37361i 0.820464 + 0.194454i 0.619351 0.785114i \(-0.287396\pi\)
0.201113 + 0.979568i \(0.435544\pi\)
\(150\) 0 0
\(151\) 4.03089 + 9.34466i 0.328030 + 0.760458i 0.999806 + 0.0197039i \(0.00627235\pi\)
−0.671776 + 0.740754i \(0.734468\pi\)
\(152\) 2.21887 + 1.86185i 0.179974 + 0.151016i
\(153\) 0 0
\(154\) −3.60523 + 3.02515i −0.290518 + 0.243774i
\(155\) −6.27607 3.15196i −0.504106 0.253171i
\(156\) 0 0
\(157\) 20.4692 2.39250i 1.63362 0.190942i 0.750757 0.660579i \(-0.229689\pi\)
0.882860 + 0.469636i \(0.155615\pi\)
\(158\) −0.885974 + 15.2116i −0.0704843 + 1.21017i
\(159\) 0 0
\(160\) 4.05478 + 4.29781i 0.320558 + 0.339772i
\(161\) 7.85887 0.619366
\(162\) 0 0
\(163\) 18.6813 1.46324 0.731618 0.681715i \(-0.238766\pi\)
0.731618 + 0.681715i \(0.238766\pi\)
\(164\) 1.28788 + 1.36508i 0.100567 + 0.106595i
\(165\) 0 0
\(166\) 1.49445 25.6588i 0.115992 1.99151i
\(167\) 16.7625 1.95926i 1.29712 0.151612i 0.560634 0.828063i \(-0.310557\pi\)
0.736487 + 0.676452i \(0.236483\pi\)
\(168\) 0 0
\(169\) −3.30268 1.65867i −0.254052 0.127590i
\(170\) −5.26856 + 4.42084i −0.404080 + 0.339063i
\(171\) 0 0
\(172\) 9.68120 + 8.12349i 0.738184 + 0.619410i
\(173\) −0.496104 1.15010i −0.0377181 0.0874404i 0.898316 0.439351i \(-0.144791\pi\)
−0.936034 + 0.351910i \(0.885532\pi\)
\(174\) 0 0
\(175\) −5.07737 1.20336i −0.383813 0.0909655i
\(176\) −2.67002 8.91847i −0.201260 0.672255i
\(177\) 0 0
\(178\) 11.1318 + 1.30112i 0.834364 + 0.0975231i
\(179\) −1.77871 + 10.0875i −0.132947 + 0.753978i 0.843321 + 0.537410i \(0.180597\pi\)
−0.976268 + 0.216568i \(0.930514\pi\)
\(180\) 0 0
\(181\) 3.12183 + 17.7048i 0.232044 + 1.31599i 0.848751 + 0.528793i \(0.177355\pi\)
−0.616707 + 0.787193i \(0.711534\pi\)
\(182\) −0.405904 6.96911i −0.0300876 0.516585i
\(183\) 0 0
\(184\) −1.56658 + 3.63175i −0.115490 + 0.267736i
\(185\) 0.422643 0.212259i 0.0310733 0.0156056i
\(186\) 0 0
\(187\) 9.08915 2.15417i 0.664665 0.157528i
\(188\) 0.773013 + 1.33890i 0.0563778 + 0.0976492i
\(189\) 0 0
\(190\) 3.65589 6.33218i 0.265226 0.459385i
\(191\) −2.38919 + 7.98046i −0.172876 + 0.577446i 0.827008 + 0.562190i \(0.190041\pi\)
−0.999884 + 0.0152551i \(0.995144\pi\)
\(192\) 0 0
\(193\) 18.7290 + 12.3183i 1.34815 + 0.886689i 0.998735 0.0502808i \(-0.0160116\pi\)
0.349410 + 0.936970i \(0.386382\pi\)
\(194\) 8.33191 + 11.1917i 0.598196 + 0.803517i
\(195\) 0 0
\(196\) 7.86740 5.17447i 0.561957 0.369605i
\(197\) 19.3055 + 7.02662i 1.37546 + 0.500626i 0.920798 0.390039i \(-0.127538\pi\)
0.454661 + 0.890665i \(0.349761\pi\)
\(198\) 0 0
\(199\) −23.4867 + 8.54846i −1.66493 + 0.605984i −0.991126 0.132928i \(-0.957562\pi\)
−0.673802 + 0.738912i \(0.735340\pi\)
\(200\) 1.56822 2.10649i 0.110890 0.148951i
\(201\) 0 0
\(202\) −9.51049 + 10.0805i −0.669155 + 0.709263i
\(203\) 8.22506 8.71806i 0.577286 0.611888i
\(204\) 0 0
\(205\) −0.523581 + 0.703292i −0.0365685 + 0.0491200i
\(206\) 2.71718 0.988973i 0.189315 0.0689050i
\(207\) 0 0
\(208\) 12.9762 + 4.72296i 0.899740 + 0.327478i
\(209\) −8.29690 + 5.45696i −0.573909 + 0.377466i
\(210\) 0 0
\(211\) −5.35225 7.18932i −0.368464 0.494933i 0.578763 0.815496i \(-0.303536\pi\)
−0.947227 + 0.320562i \(0.896128\pi\)
\(212\) 10.2428 + 6.73680i 0.703479 + 0.462685i
\(213\) 0 0
\(214\) −1.91105 + 6.38334i −0.130636 + 0.436356i
\(215\) −2.95216 + 5.11329i −0.201336 + 0.348724i
\(216\) 0 0
\(217\) 5.30783 + 9.19344i 0.360319 + 0.624091i
\(218\) −14.7971 + 3.50697i −1.00218 + 0.237522i
\(219\) 0 0
\(220\) −2.44528 + 1.22806i −0.164861 + 0.0827961i
\(221\) −5.48790 + 12.7224i −0.369156 + 0.855800i
\(222\) 0 0
\(223\) 0.437201 + 7.50645i 0.0292772 + 0.502669i 0.980791 + 0.195063i \(0.0624910\pi\)
−0.951514 + 0.307607i \(0.900472\pi\)
\(224\) −1.55088 8.79550i −0.103623 0.587674i
\(225\) 0 0
\(226\) 1.78721 10.1358i 0.118884 0.674222i
\(227\) 9.60064 + 1.12215i 0.637217 + 0.0744800i 0.428566 0.903510i \(-0.359019\pi\)
0.208651 + 0.977990i \(0.433093\pi\)
\(228\) 0 0
\(229\) −2.29389 7.66212i −0.151584 0.506327i 0.848141 0.529771i \(-0.177722\pi\)
−0.999725 + 0.0234439i \(0.992537\pi\)
\(230\) 9.71515 + 2.30253i 0.640598 + 0.151824i
\(231\) 0 0
\(232\) 2.38922 + 5.53883i 0.156860 + 0.363642i
\(233\) −17.1136 14.3600i −1.12115 0.940754i −0.122485 0.992470i \(-0.539086\pi\)
−0.998662 + 0.0517161i \(0.983531\pi\)
\(234\) 0 0
\(235\) −0.553306 + 0.464279i −0.0360937 + 0.0302862i
\(236\) −7.86283 3.94886i −0.511826 0.257049i
\(237\) 0 0
\(238\) 10.3255 1.20687i 0.669301 0.0782301i
\(239\) 0.376574 6.46553i 0.0243586 0.418220i −0.963983 0.265965i \(-0.914309\pi\)
0.988341 0.152255i \(-0.0486536\pi\)
\(240\) 0 0
\(241\) 1.91577 + 2.03059i 0.123405 + 0.130802i 0.786130 0.618061i \(-0.212082\pi\)
−0.662725 + 0.748863i \(0.730600\pi\)
\(242\) −13.0030 −0.835864
\(243\) 0 0
\(244\) −0.0366577 −0.00234677
\(245\) 3.01900 + 3.19995i 0.192877 + 0.204437i
\(246\) 0 0
\(247\) 0.856485 14.7053i 0.0544969 0.935675i
\(248\) −5.30655 + 0.620246i −0.336966 + 0.0393857i
\(249\) 0 0
\(250\) −12.6893 6.37282i −0.802543 0.403052i
\(251\) −8.90582 + 7.47287i −0.562131 + 0.471684i −0.879024 0.476778i \(-0.841805\pi\)
0.316893 + 0.948461i \(0.397360\pi\)
\(252\) 0 0
\(253\) −10.3878 8.71640i −0.653075 0.547995i
\(254\) −4.23011 9.80649i −0.265420 0.615314i
\(255\) 0 0
\(256\) 19.2423 + 4.56051i 1.20265 + 0.285032i
\(257\) −5.98437 19.9892i −0.373295 1.24689i −0.914012 0.405687i \(-0.867032\pi\)
0.540718 0.841204i \(-0.318153\pi\)
\(258\) 0 0
\(259\) −0.710046 0.0829925i −0.0441201 0.00515690i
\(260\) 0.704811 3.99718i 0.0437105 0.247895i
\(261\) 0 0
\(262\) 0.815054 + 4.62240i 0.0503542 + 0.285573i
\(263\) 1.20185 + 20.6350i 0.0741095 + 1.27241i 0.806380 + 0.591398i \(0.201424\pi\)
−0.732271 + 0.681014i \(0.761539\pi\)
\(264\) 0 0
\(265\) −2.26859 + 5.25919i −0.139358 + 0.323069i
\(266\) −9.87645 + 4.96014i −0.605564 + 0.304126i
\(267\) 0 0
\(268\) 24.7265 5.86029i 1.51041 0.357974i
\(269\) −6.13247 10.6218i −0.373903 0.647620i 0.616259 0.787544i \(-0.288648\pi\)
−0.990162 + 0.139924i \(0.955314\pi\)
\(270\) 0 0
\(271\) 3.52249 6.10113i 0.213976 0.370617i −0.738979 0.673728i \(-0.764692\pi\)
0.952955 + 0.303111i \(0.0980253\pi\)
\(272\) −5.89781 + 19.7001i −0.357607 + 1.19449i
\(273\) 0 0
\(274\) −17.6330 11.5974i −1.06525 0.700625i
\(275\) 5.37657 + 7.22199i 0.324219 + 0.435502i
\(276\) 0 0
\(277\) −25.5545 + 16.8075i −1.53542 + 1.00986i −0.550908 + 0.834566i \(0.685719\pi\)
−0.984515 + 0.175298i \(0.943911\pi\)
\(278\) 25.7781 + 9.38247i 1.54607 + 0.562723i
\(279\) 0 0
\(280\) 0.529627 0.192769i 0.0316513 0.0115201i
\(281\) 10.0305 13.4733i 0.598371 0.803752i −0.395003 0.918680i \(-0.629256\pi\)
0.993374 + 0.114928i \(0.0366638\pi\)
\(282\) 0 0
\(283\) −14.0046 + 14.8441i −0.832490 + 0.882387i −0.994536 0.104396i \(-0.966709\pi\)
0.162046 + 0.986783i \(0.448191\pi\)
\(284\) −5.87883 + 6.23119i −0.348844 + 0.369753i
\(285\) 0 0
\(286\) −7.19302 + 9.66191i −0.425332 + 0.571321i
\(287\) 1.24537 0.453278i 0.0735120 0.0267562i
\(288\) 0 0
\(289\) −3.41413 1.24264i −0.200831 0.0730967i
\(290\) 12.7221 8.36745i 0.747067 0.491354i
\(291\) 0 0
\(292\) −0.772244 1.03730i −0.0451921 0.0607036i
\(293\) −17.9293 11.7923i −1.04744 0.688912i −0.0955731 0.995422i \(-0.530468\pi\)
−0.951867 + 0.306510i \(0.900839\pi\)
\(294\) 0 0
\(295\) 1.17896 3.93799i 0.0686416 0.229279i
\(296\) 0.179893 0.311584i 0.0104561 0.0181104i
\(297\) 0 0
\(298\) −9.88246 17.1169i −0.572476 0.991557i
\(299\) 19.5720 4.63865i 1.13188 0.268260i
\(300\) 0 0
\(301\) 7.97531 4.00535i 0.459689 0.230865i
\(302\) 7.74064 17.9448i 0.445424 1.03261i
\(303\) 0 0
\(304\) −1.27117 21.8251i −0.0729065 1.25176i
\(305\) −0.00297393 0.0168660i −0.000170287 0.000965744i
\(306\) 0 0
\(307\) −1.40936 + 7.99290i −0.0804366 + 0.456179i 0.917812 + 0.397016i \(0.129954\pi\)
−0.998248 + 0.0591628i \(0.981157\pi\)
\(308\) 4.10811 + 0.480169i 0.234081 + 0.0273602i
\(309\) 0 0
\(310\) 3.86801 + 12.9201i 0.219688 + 0.733810i
\(311\) −22.7672 5.39594i −1.29101 0.305976i −0.472942 0.881094i \(-0.656808\pi\)
−0.818070 + 0.575118i \(0.804956\pi\)
\(312\) 0 0
\(313\) −1.40659 3.26084i −0.0795052 0.184314i 0.873827 0.486237i \(-0.161631\pi\)
−0.953332 + 0.301923i \(0.902371\pi\)
\(314\) −30.3163 25.4384i −1.71085 1.43557i
\(315\) 0 0
\(316\) 10.2582 8.60767i 0.577070 0.484220i
\(317\) −16.7208 8.39751i −0.939135 0.471651i −0.0877207 0.996145i \(-0.527958\pi\)
−0.851414 + 0.524494i \(0.824255\pi\)
\(318\) 0 0
\(319\) −20.5412 + 2.40092i −1.15008 + 0.134426i
\(320\) 0.244655 4.20057i 0.0136766 0.234819i
\(321\) 0 0
\(322\) −10.3565 10.9772i −0.577144 0.611737i
\(323\) 21.9358 1.22054
\(324\) 0 0
\(325\) −13.3551 −0.740810
\(326\) −24.6184 26.0940i −1.36349 1.44521i
\(327\) 0 0
\(328\) −0.0387825 + 0.665869i −0.00214140 + 0.0367665i
\(329\) 1.08439 0.126747i 0.0597841 0.00698776i
\(330\) 0 0
\(331\) 6.45255 + 3.24059i 0.354664 + 0.178119i 0.617206 0.786801i \(-0.288264\pi\)
−0.262542 + 0.964921i \(0.584561\pi\)
\(332\) −17.3035 + 14.5194i −0.949652 + 0.796853i
\(333\) 0 0
\(334\) −24.8264 20.8319i −1.35844 1.13987i
\(335\) 4.70227 + 10.9011i 0.256912 + 0.595590i
\(336\) 0 0
\(337\) −19.9946 4.73881i −1.08918 0.258140i −0.353474 0.935444i \(-0.615000\pi\)
−0.735703 + 0.677305i \(0.763148\pi\)
\(338\) 2.03548 + 6.79896i 0.110715 + 0.369815i
\(339\) 0 0
\(340\) 6.00343 + 0.701701i 0.325582 + 0.0380551i
\(341\) 3.18073 18.0388i 0.172246 0.976857i
\(342\) 0 0
\(343\) −2.60337 14.7645i −0.140569 0.797206i
\(344\) 0.261163 + 4.48399i 0.0140809 + 0.241760i
\(345\) 0 0
\(346\) −0.952682 + 2.20856i −0.0512165 + 0.118733i
\(347\) −11.6485 + 5.85011i −0.625326 + 0.314050i −0.733096 0.680126i \(-0.761925\pi\)
0.107770 + 0.994176i \(0.465629\pi\)
\(348\) 0 0
\(349\) −7.68114 + 1.82046i −0.411162 + 0.0974472i −0.430991 0.902356i \(-0.641836\pi\)
0.0198291 + 0.999803i \(0.493688\pi\)
\(350\) 5.01016 + 8.67785i 0.267804 + 0.463851i
\(351\) 0 0
\(352\) −7.70528 + 13.3459i −0.410693 + 0.711341i
\(353\) −4.04363 + 13.5067i −0.215221 + 0.718888i 0.780390 + 0.625294i \(0.215021\pi\)
−0.995610 + 0.0935941i \(0.970164\pi\)
\(354\) 0 0
\(355\) −3.34386 2.19929i −0.177474 0.116726i
\(356\) −5.88180 7.90063i −0.311735 0.418732i
\(357\) 0 0
\(358\) 16.4342 10.8090i 0.868575 0.571271i
\(359\) −2.55305 0.929234i −0.134745 0.0490431i 0.273768 0.961796i \(-0.411730\pi\)
−0.408512 + 0.912753i \(0.633952\pi\)
\(360\) 0 0
\(361\) −4.05995 + 1.47770i −0.213682 + 0.0777738i
\(362\) 20.6160 27.6921i 1.08355 1.45546i
\(363\) 0 0
\(364\) −4.21016 + 4.46251i −0.220672 + 0.233899i
\(365\) 0.414607 0.439457i 0.0217015 0.0230023i
\(366\) 0 0
\(367\) 16.6172 22.3208i 0.867411 1.16514i −0.117672 0.993053i \(-0.537543\pi\)
0.985083 0.172083i \(-0.0550496\pi\)
\(368\) 28.0525 10.2103i 1.46234 0.532247i
\(369\) 0 0
\(370\) −0.853445 0.310628i −0.0443685 0.0161488i
\(371\) 7.23324 4.75737i 0.375531 0.246991i
\(372\) 0 0
\(373\) 6.47060 + 8.69152i 0.335035 + 0.450030i 0.937433 0.348166i \(-0.113195\pi\)
−0.602398 + 0.798196i \(0.705788\pi\)
\(374\) −14.9867 9.85690i −0.774944 0.509688i
\(375\) 0 0
\(376\) −0.157589 + 0.526383i −0.00812703 + 0.0271462i
\(377\) 15.3382 26.5665i 0.789958 1.36825i
\(378\) 0 0
\(379\) 2.86635 + 4.96467i 0.147235 + 0.255018i 0.930204 0.367042i \(-0.119629\pi\)
−0.782970 + 0.622060i \(0.786296\pi\)
\(380\) −6.25265 + 1.48191i −0.320754 + 0.0760202i
\(381\) 0 0
\(382\) 14.2956 7.17950i 0.731424 0.367335i
\(383\) −5.42592 + 12.5787i −0.277252 + 0.642741i −0.998766 0.0496578i \(-0.984187\pi\)
0.721515 + 0.692399i \(0.243446\pi\)
\(384\) 0 0
\(385\) 0.112355 + 1.92907i 0.00572616 + 0.0983144i
\(386\) −7.47516 42.3938i −0.380476 2.15779i
\(387\) 0 0
\(388\) 2.12928 12.0758i 0.108098 0.613055i
\(389\) −14.0779 1.64547i −0.713776 0.0834285i −0.248549 0.968619i \(-0.579954\pi\)
−0.465228 + 0.885191i \(0.654028\pi\)
\(390\) 0 0
\(391\) 8.59074 + 28.6951i 0.434452 + 1.45117i
\(392\) 3.25648 + 0.771800i 0.164477 + 0.0389818i
\(393\) 0 0
\(394\) −15.6262 36.2256i −0.787236 1.82502i
\(395\) 4.79255 + 4.02143i 0.241140 + 0.202340i
\(396\) 0 0
\(397\) −3.48565 + 2.92481i −0.174940 + 0.146792i −0.726053 0.687638i \(-0.758647\pi\)
0.551114 + 0.834430i \(0.314203\pi\)
\(398\) 42.8914 + 21.5409i 2.14995 + 1.07975i
\(399\) 0 0
\(400\) −19.6873 + 2.30111i −0.984363 + 0.115056i
\(401\) 0.618000 10.6106i 0.0308614 0.529870i −0.947081 0.320995i \(-0.895983\pi\)
0.977942 0.208875i \(-0.0669803\pi\)
\(402\) 0 0
\(403\) 18.6452 + 19.7627i 0.928783 + 0.984452i
\(404\) 12.1796 0.605960
\(405\) 0 0
\(406\) −23.0164 −1.14228
\(407\) 0.846486 + 0.897222i 0.0419587 + 0.0444737i
\(408\) 0 0
\(409\) −1.68065 + 28.8557i −0.0831030 + 1.42682i 0.656777 + 0.754085i \(0.271919\pi\)
−0.739880 + 0.672738i \(0.765118\pi\)
\(410\) 1.67233 0.195468i 0.0825907 0.00965347i
\(411\) 0 0
\(412\) −2.27091 1.14050i −0.111880 0.0561882i
\(413\) −4.75978 + 3.99393i −0.234214 + 0.196529i
\(414\) 0 0
\(415\) −8.08404 6.78331i −0.396830 0.332980i
\(416\) −9.05387 20.9892i −0.443902 1.02908i
\(417\) 0 0
\(418\) 18.5560 + 4.39785i 0.907603 + 0.215106i
\(419\) 11.3748 + 37.9943i 0.555693 + 1.85614i 0.515388 + 0.856957i \(0.327648\pi\)
0.0403048 + 0.999187i \(0.487167\pi\)
\(420\) 0 0
\(421\) −37.2678 4.35598i −1.81632 0.212297i −0.861149 0.508353i \(-0.830254\pi\)
−0.955171 + 0.296056i \(0.904328\pi\)
\(422\) −2.98877 + 16.9502i −0.145491 + 0.825121i
\(423\) 0 0
\(424\) 0.756613 + 4.29097i 0.0367444 + 0.208388i
\(425\) −1.15639 19.8544i −0.0560931 0.963081i
\(426\) 0 0
\(427\) −0.0102533 + 0.0237697i −0.000496190 + 0.00115030i
\(428\) 5.23305 2.62814i 0.252949 0.127036i
\(429\) 0 0
\(430\) 11.0326 2.61477i 0.532039 0.126096i
\(431\) 0.730348 + 1.26500i 0.0351796 + 0.0609329i 0.883079 0.469224i \(-0.155466\pi\)
−0.847900 + 0.530157i \(0.822133\pi\)
\(432\) 0 0
\(433\) −3.07185 + 5.32060i −0.147624 + 0.255692i −0.930349 0.366676i \(-0.880496\pi\)
0.782725 + 0.622368i \(0.213829\pi\)
\(434\) 5.84664 19.5291i 0.280648 0.937429i
\(435\) 0 0
\(436\) 11.1658 + 7.34389i 0.534747 + 0.351708i
\(437\) −19.0161 25.5431i −0.909663 1.22189i
\(438\) 0 0
\(439\) −13.1947 + 8.67829i −0.629749 + 0.414192i −0.823865 0.566786i \(-0.808187\pi\)
0.194116 + 0.980979i \(0.437816\pi\)
\(440\) −0.913860 0.332618i −0.0435666 0.0158569i
\(441\) 0 0
\(442\) 25.0026 9.10019i 1.18925 0.432852i
\(443\) −11.3597 + 15.2588i −0.539718 + 0.724967i −0.985406 0.170221i \(-0.945552\pi\)
0.445688 + 0.895188i \(0.352959\pi\)
\(444\) 0 0
\(445\) 3.15786 3.34713i 0.149697 0.158669i
\(446\) 9.90883 10.5027i 0.469197 0.497320i
\(447\) 0 0
\(448\) −3.79797 + 5.10156i −0.179437 + 0.241026i
\(449\) −17.8139 + 6.48373i −0.840690 + 0.305986i −0.726239 0.687443i \(-0.758733\pi\)
−0.114452 + 0.993429i \(0.536511\pi\)
\(450\) 0 0
\(451\) −2.14886 0.782122i −0.101186 0.0368287i
\(452\) −7.55709 + 4.97038i −0.355456 + 0.233787i
\(453\) 0 0
\(454\) −11.0844 14.8889i −0.520216 0.698771i
\(455\) −2.39473 1.57504i −0.112267 0.0738389i
\(456\) 0 0
\(457\) 10.9564 36.5970i 0.512520 1.71193i −0.173931 0.984758i \(-0.555647\pi\)
0.686450 0.727177i \(-0.259168\pi\)
\(458\) −7.67951 + 13.3013i −0.358840 + 0.621529i
\(459\) 0 0
\(460\) −4.38728 7.59899i −0.204558 0.354305i
\(461\) −7.03505 + 1.66734i −0.327655 + 0.0776556i −0.391151 0.920326i \(-0.627923\pi\)
0.0634963 + 0.997982i \(0.479775\pi\)
\(462\) 0 0
\(463\) 1.22851 0.616980i 0.0570936 0.0286735i −0.420023 0.907513i \(-0.637978\pi\)
0.477117 + 0.878840i \(0.341682\pi\)
\(464\) 18.0331 41.8054i 0.837165 1.94077i
\(465\) 0 0
\(466\) 2.49444 + 42.8279i 0.115553 + 1.98396i
\(467\) 1.50717 + 8.54757i 0.0697434 + 0.395534i 0.999617 + 0.0276564i \(0.00880442\pi\)
−0.929874 + 0.367878i \(0.880084\pi\)
\(468\) 0 0
\(469\) 3.11612 17.6724i 0.143889 0.816035i
\(470\) 1.37765 + 0.161025i 0.0635465 + 0.00742752i
\(471\) 0 0
\(472\) −0.896868 2.99575i −0.0412817 0.137890i
\(473\) −14.9841 3.55130i −0.688970 0.163289i
\(474\) 0 0
\(475\) 8.37453 + 19.4143i 0.384250 + 0.890791i
\(476\) −6.99873 5.87263i −0.320786 0.269172i
\(477\) 0 0
\(478\) −9.52727 + 7.99433i −0.435767 + 0.365652i
\(479\) −1.89904 0.953732i −0.0867692 0.0435771i 0.404885 0.914367i \(-0.367311\pi\)
−0.491655 + 0.870790i \(0.663608\pi\)
\(480\) 0 0
\(481\) −1.81731 + 0.212413i −0.0828622 + 0.00968520i
\(482\) 0.311711 5.35186i 0.0141980 0.243771i
\(483\) 0 0
\(484\) 7.84204 + 8.31207i 0.356456 + 0.377821i
\(485\) 5.72873 0.260128
\(486\) 0 0
\(487\) −7.22045 −0.327190 −0.163595 0.986528i \(-0.552309\pi\)
−0.163595 + 0.986528i \(0.552309\pi\)
\(488\) −0.00894061 0.00947650i −0.000404723 0.000428981i
\(489\) 0 0
\(490\) 0.491215 8.43384i 0.0221908 0.381002i
\(491\) 21.4296 2.50477i 0.967106 0.113039i 0.382147 0.924101i \(-0.375185\pi\)
0.584959 + 0.811063i \(0.301111\pi\)
\(492\) 0 0
\(493\) 40.8232 + 20.5022i 1.83859 + 0.923373i
\(494\) −21.6690 + 18.1824i −0.974933 + 0.818066i
\(495\) 0 0
\(496\) 30.8906 + 25.9203i 1.38703 + 1.16386i
\(497\) 2.39613 + 5.55485i 0.107481 + 0.249169i
\(498\) 0 0
\(499\) 7.51219 + 1.78042i 0.336292 + 0.0797026i 0.395292 0.918555i \(-0.370643\pi\)
−0.0590007 + 0.998258i \(0.518791\pi\)
\(500\) 3.57909 + 11.9550i 0.160062 + 0.534643i
\(501\) 0 0
\(502\) 22.1742 + 2.59180i 0.989685 + 0.115678i
\(503\) −1.71945 + 9.75150i −0.0766666 + 0.434798i 0.922179 + 0.386763i \(0.126407\pi\)
−0.998846 + 0.0480347i \(0.984704\pi\)
\(504\) 0 0
\(505\) 0.988096 + 5.60377i 0.0439697 + 0.249365i
\(506\) 1.51410 + 25.9962i 0.0673101 + 1.15567i
\(507\) 0 0
\(508\) −3.71758 + 8.61831i −0.164941 + 0.382376i
\(509\) 18.7721 9.42770i 0.832059 0.417876i 0.0188320 0.999823i \(-0.494005\pi\)
0.813227 + 0.581947i \(0.197709\pi\)
\(510\) 0 0
\(511\) −0.888610 + 0.210604i −0.0393098 + 0.00931659i
\(512\) −14.2477 24.6777i −0.629665 1.09061i
\(513\) 0 0
\(514\) −20.0345 + 34.7008i −0.883686 + 1.53059i
\(515\) 0.340503 1.13736i 0.0150043 0.0501180i
\(516\) 0 0
\(517\) −1.57391 1.03518i −0.0692205 0.0455270i
\(518\) 0.819781 + 1.10116i 0.0360191 + 0.0483821i
\(519\) 0 0
\(520\) 1.20522 0.792687i 0.0528525 0.0347616i
\(521\) −20.5557 7.48165i −0.900560 0.327777i −0.150083 0.988673i \(-0.547954\pi\)
−0.750477 + 0.660896i \(0.770176\pi\)
\(522\) 0 0
\(523\) 28.4317 10.3483i 1.24323 0.452499i 0.365121 0.930960i \(-0.381028\pi\)
0.878109 + 0.478461i \(0.158805\pi\)
\(524\) 2.46329 3.30877i 0.107609 0.144544i
\(525\) 0 0
\(526\) 27.2391 28.8718i 1.18768 1.25887i
\(527\) −27.7658 + 29.4301i −1.20950 + 1.28199i
\(528\) 0 0
\(529\) 12.2320 16.4304i 0.531824 0.714364i
\(530\) 10.3356 3.76184i 0.448949 0.163404i
\(531\) 0 0
\(532\) 9.12717 + 3.32202i 0.395713 + 0.144028i
\(533\) 2.83397 1.86393i 0.122753 0.0807359i
\(534\) 0 0
\(535\) 1.63373 + 2.19448i 0.0706323 + 0.0948756i
\(536\) 7.54562 + 4.96283i 0.325921 + 0.214362i
\(537\) 0 0
\(538\) −6.75499 + 22.5632i −0.291228 + 0.972770i
\(539\) −5.73699 + 9.93675i −0.247110 + 0.428006i
\(540\) 0 0
\(541\) −2.75454 4.77101i −0.118427 0.205122i 0.800717 0.599042i \(-0.204452\pi\)
−0.919144 + 0.393921i \(0.871119\pi\)
\(542\) −13.1640 + 3.11992i −0.565442 + 0.134012i
\(543\) 0 0
\(544\) 30.4197 15.2773i 1.30423 0.655010i
\(545\) −2.47302 + 5.73312i −0.105933 + 0.245580i
\(546\) 0 0
\(547\) 0.232144 + 3.98575i 0.00992575 + 0.170419i 0.999628 + 0.0272766i \(0.00868350\pi\)
−0.989702 + 0.143142i \(0.954279\pi\)
\(548\) 3.22081 + 18.2661i 0.137586 + 0.780290i
\(549\) 0 0
\(550\) 3.00235 17.0272i 0.128021 0.726041i
\(551\) −48.2378 5.63819i −2.05500 0.240195i
\(552\) 0 0
\(553\) −2.71216 9.05926i −0.115333 0.385239i
\(554\) 57.1526 + 13.5454i 2.42818 + 0.575490i
\(555\) 0 0
\(556\) −9.54898 22.1370i −0.404967 0.938819i
\(557\) 4.09443 + 3.43564i 0.173487 + 0.145573i 0.725397 0.688331i \(-0.241656\pi\)
−0.551910 + 0.833904i \(0.686101\pi\)
\(558\) 0 0
\(559\) 17.4979 14.6825i 0.740081 0.621002i
\(560\) −3.80153 1.90920i −0.160644 0.0806784i
\(561\) 0 0
\(562\) −32.0378 + 3.74468i −1.35143 + 0.157960i
\(563\) 0.673539 11.5642i 0.0283863 0.487374i −0.953916 0.300073i \(-0.902989\pi\)
0.982303 0.187301i \(-0.0599739\pi\)
\(564\) 0 0
\(565\) −2.89992 3.07374i −0.122001 0.129313i
\(566\) 39.1895 1.64726
\(567\) 0 0
\(568\) −3.04466 −0.127751
\(569\) −29.3906 31.1523i −1.23212 1.30597i −0.936501 0.350665i \(-0.885956\pi\)
−0.295619 0.955306i \(-0.595526\pi\)
\(570\) 0 0
\(571\) −1.84172 + 31.6212i −0.0770737 + 1.32330i 0.709016 + 0.705192i \(0.249139\pi\)
−0.786090 + 0.618112i \(0.787898\pi\)
\(572\) 10.5144 1.22896i 0.439629 0.0513852i
\(573\) 0 0
\(574\) −2.27430 1.14220i −0.0949274 0.0476743i
\(575\) −22.1170 + 18.5583i −0.922341 + 0.773936i
\(576\) 0 0
\(577\) 17.4676 + 14.6571i 0.727188 + 0.610183i 0.929363 0.369166i \(-0.120357\pi\)
−0.202176 + 0.979349i \(0.564801\pi\)
\(578\) 2.76346 + 6.40641i 0.114945 + 0.266472i
\(579\) 0 0
\(580\) −13.0215 3.08614i −0.540687 0.128145i
\(581\) 4.57486 + 15.2811i 0.189797 + 0.633966i
\(582\) 0 0
\(583\) −14.8373 1.73423i −0.614499 0.0718246i
\(584\) 0.0798104 0.452627i 0.00330258 0.0187298i
\(585\) 0 0
\(586\) 7.15597 + 40.5835i 0.295610 + 1.67649i
\(587\) −0.152598 2.62001i −0.00629841 0.108139i 0.993694 0.112129i \(-0.0357671\pi\)
−0.999992 + 0.00398975i \(0.998730\pi\)
\(588\) 0 0
\(589\) 17.0373 39.4970i 0.702011 1.62744i
\(590\) −7.05421 + 3.54276i −0.290417 + 0.145853i
\(591\) 0 0
\(592\) −2.64236 + 0.626250i −0.108600 + 0.0257387i
\(593\) 5.12692 + 8.88008i 0.210537 + 0.364661i 0.951883 0.306462i \(-0.0991454\pi\)
−0.741346 + 0.671124i \(0.765812\pi\)
\(594\) 0 0
\(595\) 2.13417 3.69650i 0.0874926 0.151542i
\(596\) −4.98182 + 16.6404i −0.204063 + 0.681619i
\(597\) 0 0
\(598\) −32.2714 21.2252i −1.31968 0.867965i
\(599\) 4.30284 + 5.77972i 0.175809 + 0.236153i 0.881290 0.472577i \(-0.156676\pi\)
−0.705480 + 0.708730i \(0.749269\pi\)
\(600\) 0 0
\(601\) 14.1176 9.28526i 0.575867 0.378754i −0.227912 0.973682i \(-0.573190\pi\)
0.803779 + 0.594928i \(0.202819\pi\)
\(602\) −16.1046 5.86159i −0.656374 0.238901i
\(603\) 0 0
\(604\) −16.1394 + 5.87428i −0.656705 + 0.239021i
\(605\) −3.18813 + 4.28240i −0.129616 + 0.174104i
\(606\) 0 0
\(607\) 7.49458 7.94379i 0.304196 0.322429i −0.557185 0.830388i \(-0.688119\pi\)
0.861381 + 0.507960i \(0.169600\pi\)
\(608\) −24.8346 + 26.3232i −1.00718 + 1.06755i
\(609\) 0 0
\(610\) −0.0196393 + 0.0263801i −0.000795171 + 0.00106810i
\(611\) 2.62578 0.955706i 0.106228 0.0386637i
\(612\) 0 0
\(613\) 7.35009 + 2.67521i 0.296867 + 0.108051i 0.486160 0.873870i \(-0.338397\pi\)
−0.189293 + 0.981921i \(0.560619\pi\)
\(614\) 13.0217 8.56451i 0.525513 0.345636i
\(615\) 0 0
\(616\) 0.877814 + 1.17911i 0.0353681 + 0.0475076i
\(617\) −2.01117 1.32277i −0.0809668 0.0532527i 0.508380 0.861133i \(-0.330244\pi\)
−0.589347 + 0.807880i \(0.700615\pi\)
\(618\) 0 0
\(619\) −9.09854 + 30.3912i −0.365701 + 1.22153i 0.555195 + 0.831720i \(0.312643\pi\)
−0.920897 + 0.389807i \(0.872542\pi\)
\(620\) 5.92628 10.2646i 0.238005 0.412237i
\(621\) 0 0
\(622\) 22.4659 + 38.9120i 0.900799 + 1.56023i
\(623\) −6.76810 + 1.60407i −0.271158 + 0.0642657i
\(624\) 0 0
\(625\) 14.3531 7.20838i 0.574122 0.288335i
\(626\) −2.70111 + 6.26188i −0.107958 + 0.250275i
\(627\) 0 0
\(628\) 2.02228 + 34.7212i 0.0806978 + 1.38553i
\(629\) −0.473140 2.68331i −0.0188653 0.106991i
\(630\) 0 0
\(631\) −1.13730 + 6.44997i −0.0452753 + 0.256769i −0.999041 0.0437817i \(-0.986059\pi\)
0.953766 + 0.300551i \(0.0971705\pi\)
\(632\) 4.72712 + 0.552521i 0.188035 + 0.0219781i
\(633\) 0 0
\(634\) 10.3052 + 34.4219i 0.409273 + 1.36707i
\(635\) −4.26682 1.01126i −0.169324 0.0401305i
\(636\) 0 0
\(637\) −6.74108 15.6276i −0.267091 0.619187i
\(638\) 30.4229 + 25.5278i 1.20445 + 1.01066i
\(639\) 0 0
\(640\) 2.86287 2.40224i 0.113165 0.0949568i
\(641\) 33.1107 + 16.6288i 1.30779 + 0.656798i 0.959796 0.280698i \(-0.0905659\pi\)
0.347996 + 0.937496i \(0.386862\pi\)
\(642\) 0 0
\(643\) −16.0317 + 1.87384i −0.632230 + 0.0738971i −0.426171 0.904642i \(-0.640138\pi\)
−0.206059 + 0.978540i \(0.566064\pi\)
\(644\) −0.771179 + 13.2406i −0.0303887 + 0.521754i
\(645\) 0 0
\(646\) −28.9071 30.6398i −1.13734 1.20551i
\(647\) −9.95741 −0.391466 −0.195733 0.980657i \(-0.562709\pi\)
−0.195733 + 0.980657i \(0.562709\pi\)
\(648\) 0 0
\(649\) 10.7212 0.420843
\(650\) 17.5995 + 18.6544i 0.690310 + 0.731686i
\(651\) 0 0
\(652\) −1.83317 + 31.4743i −0.0717925 + 1.23263i
\(653\) 19.9874 2.33619i 0.782168 0.0914223i 0.284369 0.958715i \(-0.408216\pi\)
0.497799 + 0.867292i \(0.334142\pi\)
\(654\) 0 0
\(655\) 1.72218 + 0.864912i 0.0672912 + 0.0337949i
\(656\) 3.85649 3.23598i 0.150571 0.126344i
\(657\) 0 0
\(658\) −1.60605 1.34764i −0.0626104 0.0525364i
\(659\) −3.56046 8.25406i −0.138696 0.321533i 0.834685 0.550728i \(-0.185650\pi\)
−0.973380 + 0.229195i \(0.926391\pi\)
\(660\) 0 0
\(661\) −0.602072 0.142694i −0.0234179 0.00555014i 0.218890 0.975749i \(-0.429756\pi\)
−0.242308 + 0.970199i \(0.577904\pi\)
\(662\) −3.97678 13.2834i −0.154562 0.516273i
\(663\) 0 0
\(664\) −7.97366 0.931988i −0.309438 0.0361681i
\(665\) −0.787980 + 4.46886i −0.0305566 + 0.173295i
\(666\) 0 0
\(667\) −11.5159 65.3099i −0.445897 2.52881i
\(668\) 1.65608 + 28.4337i 0.0640755 + 1.10013i
\(669\) 0 0
\(670\) 9.02990 20.9337i 0.348855 0.808737i
\(671\) 0.0399161 0.0200466i 0.00154094 0.000773890i
\(672\) 0 0
\(673\) 12.4696 2.95534i 0.480666 0.113920i 0.0168623 0.999858i \(-0.494632\pi\)
0.463804 + 0.885938i \(0.346484\pi\)
\(674\) 19.7299 + 34.1732i 0.759969 + 1.31630i
\(675\) 0 0
\(676\) 3.11861 5.40159i 0.119946 0.207753i
\(677\) 8.37100 27.9611i 0.321724 1.07463i −0.632255 0.774760i \(-0.717871\pi\)
0.953979 0.299872i \(-0.0969441\pi\)
\(678\) 0 0
\(679\) −7.23465 4.75830i −0.277640 0.182607i
\(680\) 1.28280 + 1.72311i 0.0491933 + 0.0660781i
\(681\) 0 0
\(682\) −29.3881 + 19.3289i −1.12533 + 0.740141i
\(683\) 39.5288 + 14.3873i 1.51253 + 0.550516i 0.959269 0.282493i \(-0.0911614\pi\)
0.553260 + 0.833009i \(0.313384\pi\)
\(684\) 0 0
\(685\) −8.14283 + 2.96375i −0.311122 + 0.113239i
\(686\) −17.1922 + 23.0931i −0.656401 + 0.881699i
\(687\) 0 0
\(688\) 23.2644 24.6588i 0.886946 0.940107i
\(689\) 15.2059 16.1173i 0.579298 0.614020i
\(690\) 0 0
\(691\) 7.51788 10.0983i 0.285994 0.384156i −0.635789 0.771863i \(-0.719325\pi\)
0.921783 + 0.387707i \(0.126733\pi\)
\(692\) 1.98637 0.722979i 0.0755104 0.0274835i
\(693\) 0 0
\(694\) 23.5219 + 8.56128i 0.892880 + 0.324982i
\(695\) 9.41042 6.18933i 0.356958 0.234775i
\(696\) 0 0
\(697\) 3.01640 + 4.05173i 0.114254 + 0.153470i
\(698\) 12.6651 + 8.32996i 0.479381 + 0.315294i
\(699\) 0 0
\(700\) 2.52566 8.43628i 0.0954608 0.318861i
\(701\) −2.24313 + 3.88521i −0.0847218 + 0.146742i −0.905273 0.424831i \(-0.860333\pi\)
0.820551 + 0.571574i \(0.193667\pi\)
\(702\) 0 0
\(703\) 1.44835 + 2.50862i 0.0546257 + 0.0946145i
\(704\) 10.6784 2.53082i 0.402456 0.0953838i
\(705\) 0 0
\(706\) 24.1948 12.1511i 0.910583 0.457312i
\(707\) 3.40667 7.89756i 0.128121 0.297018i
\(708\) 0 0
\(709\) −0.197090 3.38390i −0.00740186 0.127085i −0.999985 0.00551558i \(-0.998244\pi\)
0.992583 0.121569i \(-0.0387927\pi\)
\(710\) 1.33461 + 7.56894i 0.0500870 + 0.284057i
\(711\) 0 0
\(712\) 0.607877 3.44744i 0.0227811 0.129198i
\(713\) 58.3400 + 6.81896i 2.18485 + 0.255372i
\(714\) 0 0
\(715\) 1.41843 + 4.73790i 0.0530464 + 0.177187i
\(716\) −16.8209 3.98664i −0.628628 0.148988i
\(717\) 0 0
\(718\) 2.06648 + 4.79064i 0.0771203 + 0.178785i
\(719\) −14.7252 12.3559i −0.549159 0.460799i 0.325497 0.945543i \(-0.394468\pi\)
−0.874656 + 0.484744i \(0.838913\pi\)
\(720\) 0 0
\(721\) −1.37470 + 1.15351i −0.0511966 + 0.0429591i
\(722\) 7.41428 + 3.72359i 0.275931 + 0.138578i
\(723\) 0 0
\(724\) −30.1354 + 3.52232i −1.11997 + 0.130906i
\(725\) −2.56026 + 43.9580i −0.0950858 + 1.63256i
\(726\) 0 0
\(727\) 18.0748 + 19.1582i 0.670359 + 0.710539i 0.969889 0.243548i \(-0.0783113\pi\)
−0.299530 + 0.954087i \(0.596830\pi\)
\(728\) −2.18045 −0.0808128
\(729\) 0 0
\(730\) −1.16020 −0.0429411
\(731\) 23.3428 + 24.7419i 0.863363 + 0.915111i
\(732\) 0 0
\(733\) −0.896233 + 15.3877i −0.0331031 + 0.568359i 0.940455 + 0.339919i \(0.110400\pi\)
−0.973558 + 0.228440i \(0.926638\pi\)
\(734\) −53.0758 + 6.20368i −1.95907 + 0.228982i
\(735\) 0 0
\(736\) −44.1604 22.1782i −1.62778 0.817499i
\(737\) −23.7196 + 19.9031i −0.873722 + 0.733140i
\(738\) 0 0
\(739\) −29.4693 24.7277i −1.08405 0.909622i −0.0877951 0.996139i \(-0.527982\pi\)
−0.996250 + 0.0865164i \(0.972427\pi\)
\(740\) 0.316141 + 0.732897i 0.0116216 + 0.0269418i
\(741\) 0 0
\(742\) −16.1771 3.83404i −0.593880 0.140752i
\(743\) 2.84619 + 9.50692i 0.104416 + 0.348775i 0.994192 0.107624i \(-0.0343242\pi\)
−0.889775 + 0.456399i \(0.849139\pi\)
\(744\) 0 0
\(745\) −8.06031 0.942116i −0.295307 0.0345164i
\(746\) 3.61327 20.4919i 0.132291 0.750260i
\(747\) 0 0
\(748\) 2.73744 + 15.5248i 0.100091 + 0.567643i
\(749\) −0.240448 4.12832i −0.00878576 0.150846i
\(750\) 0 0
\(751\) −0.667802 + 1.54814i −0.0243684 + 0.0564924i −0.929966 0.367646i \(-0.880164\pi\)
0.905597 + 0.424139i \(0.139423\pi\)
\(752\) 3.70608 1.86126i 0.135147 0.0678733i
\(753\) 0 0
\(754\) −57.3208 + 13.5853i −2.08750 + 0.494747i
\(755\) −4.01206 6.94909i −0.146014 0.252903i
\(756\) 0 0
\(757\) −20.2972 + 35.1558i −0.737716 + 1.27776i 0.215806 + 0.976436i \(0.430762\pi\)
−0.953522 + 0.301325i \(0.902571\pi\)
\(758\) 3.15732 10.5462i 0.114679 0.383055i
\(759\) 0 0
\(760\) −1.90808 1.25496i −0.0692133 0.0455223i
\(761\) −21.2314 28.5187i −0.769638 1.03380i −0.998182 0.0602701i \(-0.980804\pi\)
0.228544 0.973534i \(-0.426604\pi\)
\(762\) 0 0
\(763\) 7.88506 5.18608i 0.285458 0.187749i
\(764\) −13.2110 4.80842i −0.477958 0.173963i
\(765\) 0 0
\(766\) 24.7202 8.99741i 0.893177 0.325090i
\(767\) −9.49654 + 12.7561i −0.342900 + 0.460595i
\(768\) 0 0
\(769\) −4.97291 + 5.27097i −0.179328 + 0.190076i −0.810802 0.585321i \(-0.800969\pi\)
0.631474 + 0.775397i \(0.282450\pi\)
\(770\) 2.54645 2.69908i 0.0917677 0.0972681i
\(771\) 0 0
\(772\) −22.5917 + 30.3459i −0.813093 + 1.09217i
\(773\) −27.7323 + 10.0937i −0.997463 + 0.363047i −0.788606 0.614899i \(-0.789197\pi\)
−0.208857 + 0.977946i \(0.566974\pi\)
\(774\) 0 0
\(775\) −36.6475 13.3386i −1.31642 0.479137i
\(776\) 3.64106 2.39477i 0.130707 0.0859671i
\(777\) 0 0
\(778\) 16.2536 + 21.8323i 0.582718 + 0.782726i
\(779\) −4.48668 2.95094i −0.160752 0.105728i
\(780\) 0 0
\(781\) 2.99379 9.99994i 0.107126 0.357826i
\(782\) 28.7602 49.8141i 1.02846 1.78135i
\(783\) 0