Properties

Label 567.2.w.a.37.2
Level $567$
Weight $2$
Character 567.37
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(37,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.w (of order \(9\), degree \(6\), 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: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 37.2
Character \(\chi\) \(=\) 567.37
Dual form 567.2.w.a.46.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.442261 - 2.50819i) q^{2} +(-4.21603 + 1.53451i) q^{4} +(0.331479 - 1.87991i) q^{5} +(0.0136229 - 2.64572i) q^{7} +(3.16655 + 5.48462i) q^{8} +O(q^{10})\) \(q+(-0.442261 - 2.50819i) q^{2} +(-4.21603 + 1.53451i) q^{4} +(0.331479 - 1.87991i) q^{5} +(0.0136229 - 2.64572i) q^{7} +(3.16655 + 5.48462i) q^{8} -4.86178 q^{10} +(-0.887121 - 5.03112i) q^{11} +(1.83772 + 1.54203i) q^{13} +(-6.64198 + 1.13593i) q^{14} +(5.48215 - 4.60007i) q^{16} +2.53610 q^{17} -7.48553 q^{19} +(1.48722 + 8.43443i) q^{20} +(-12.2266 + 4.45014i) q^{22} +(-0.538569 - 0.451913i) q^{23} +(1.27427 + 0.463795i) q^{25} +(3.05495 - 5.29132i) q^{26} +(4.00244 + 11.1753i) q^{28} +(-2.92117 + 2.45115i) q^{29} +(-1.15880 + 0.421768i) q^{31} +(-4.25952 - 3.57416i) q^{32} +(-1.12162 - 6.36101i) q^{34} +(-4.96920 - 0.902610i) q^{35} +(4.19267 + 7.26192i) q^{37} +(3.31056 + 18.7751i) q^{38} +(11.3603 - 4.13480i) q^{40} +(-1.73284 - 1.45403i) q^{41} +(5.28345 + 1.92302i) q^{43} +(11.4604 + 19.8500i) q^{44} +(-0.895295 + 1.55070i) q^{46} +(-7.11320 - 2.58899i) q^{47} +(-6.99963 - 0.0720845i) q^{49} +(0.599727 - 3.40122i) q^{50} +(-10.1141 - 3.68124i) q^{52} +(-4.42304 - 7.66093i) q^{53} -9.75212 q^{55} +(14.5539 - 8.30307i) q^{56} +(7.43987 + 6.24279i) q^{58} +(3.83685 + 3.21950i) q^{59} +(5.36583 + 1.95300i) q^{61} +(1.57037 + 2.71996i) q^{62} +(0.0755905 - 0.130927i) q^{64} +(3.50804 - 2.94360i) q^{65} +(0.871145 - 4.94051i) q^{67} +(-10.6923 + 3.89167i) q^{68} +(-0.0662313 + 12.8629i) q^{70} +(4.19743 - 7.27016i) q^{71} +(4.59111 - 7.95204i) q^{73} +(16.3600 - 13.7277i) q^{74} +(31.5593 - 11.4866i) q^{76} +(-13.3230 + 2.27853i) q^{77} +(-1.42181 - 8.06351i) q^{79} +(-6.83051 - 11.8308i) q^{80} +(-2.88061 + 4.98936i) q^{82} +(1.74493 - 1.46417i) q^{83} +(0.840664 - 4.76764i) q^{85} +(2.48663 - 14.1024i) q^{86} +(24.7847 - 20.7968i) q^{88} -7.14912 q^{89} +(4.10480 - 4.84107i) q^{91} +(2.96409 + 1.07884i) q^{92} +(-3.34779 + 18.9863i) q^{94} +(-2.48130 + 14.0722i) q^{95} +(11.6472 + 4.23925i) q^{97} +(2.91486 + 17.5883i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} - 51 q^{32} - 18 q^{34} + 12 q^{35} + 3 q^{37} + 57 q^{38} - 66 q^{40} - 12 q^{43} - 3 q^{44} + 3 q^{46} + 21 q^{47} + 12 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 57 q^{56} - 3 q^{58} + 18 q^{59} + 33 q^{61} - 75 q^{62} - 30 q^{64} - 81 q^{65} - 3 q^{67} - 6 q^{68} - 42 q^{70} + 18 q^{71} + 21 q^{73} + 93 q^{74} - 24 q^{76} - 87 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} - 159 q^{86} + 57 q^{88} + 150 q^{89} + 6 q^{91} + 66 q^{92} + 33 q^{94} + 147 q^{95} - 12 q^{97} - 99 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.442261 2.50819i −0.312726 1.77356i −0.584697 0.811252i \(-0.698786\pi\)
0.271971 0.962306i \(-0.412325\pi\)
\(3\) 0 0
\(4\) −4.21603 + 1.53451i −2.10802 + 0.767255i
\(5\) 0.331479 1.87991i 0.148242 0.840723i −0.816464 0.577396i \(-0.804069\pi\)
0.964707 0.263327i \(-0.0848199\pi\)
\(6\) 0 0
\(7\) 0.0136229 2.64572i 0.00514896 0.999987i
\(8\) 3.16655 + 5.48462i 1.11954 + 1.93911i
\(9\) 0 0
\(10\) −4.86178 −1.53743
\(11\) −0.887121 5.03112i −0.267477 1.51694i −0.761887 0.647710i \(-0.775727\pi\)
0.494410 0.869229i \(-0.335384\pi\)
\(12\) 0 0
\(13\) 1.83772 + 1.54203i 0.509691 + 0.427681i 0.861020 0.508570i \(-0.169826\pi\)
−0.351330 + 0.936252i \(0.614270\pi\)
\(14\) −6.64198 + 1.13593i −1.77514 + 0.303590i
\(15\) 0 0
\(16\) 5.48215 4.60007i 1.37054 1.15002i
\(17\) 2.53610 0.615094 0.307547 0.951533i \(-0.400492\pi\)
0.307547 + 0.951533i \(0.400492\pi\)
\(18\) 0 0
\(19\) −7.48553 −1.71730 −0.858650 0.512563i \(-0.828696\pi\)
−0.858650 + 0.512563i \(0.828696\pi\)
\(20\) 1.48722 + 8.43443i 0.332552 + 1.88600i
\(21\) 0 0
\(22\) −12.2266 + 4.45014i −2.60673 + 0.948772i
\(23\) −0.538569 0.451913i −0.112299 0.0942303i 0.584909 0.811099i \(-0.301130\pi\)
−0.697208 + 0.716869i \(0.745575\pi\)
\(24\) 0 0
\(25\) 1.27427 + 0.463795i 0.254854 + 0.0927591i
\(26\) 3.05495 5.29132i 0.599124 1.03771i
\(27\) 0 0
\(28\) 4.00244 + 11.1753i 0.756391 + 2.11194i
\(29\) −2.92117 + 2.45115i −0.542447 + 0.455167i −0.872374 0.488839i \(-0.837420\pi\)
0.329927 + 0.944007i \(0.392976\pi\)
\(30\) 0 0
\(31\) −1.15880 + 0.421768i −0.208126 + 0.0757518i −0.443980 0.896037i \(-0.646434\pi\)
0.235853 + 0.971789i \(0.424212\pi\)
\(32\) −4.25952 3.57416i −0.752983 0.631828i
\(33\) 0 0
\(34\) −1.12162 6.36101i −0.192356 1.09090i
\(35\) −4.96920 0.902610i −0.839948 0.152569i
\(36\) 0 0
\(37\) 4.19267 + 7.26192i 0.689271 + 1.19385i 0.972074 + 0.234674i \(0.0754024\pi\)
−0.282803 + 0.959178i \(0.591264\pi\)
\(38\) 3.31056 + 18.7751i 0.537044 + 3.04573i
\(39\) 0 0
\(40\) 11.3603 4.13480i 1.79622 0.653769i
\(41\) −1.73284 1.45403i −0.270624 0.227081i 0.497368 0.867540i \(-0.334300\pi\)
−0.767993 + 0.640459i \(0.778744\pi\)
\(42\) 0 0
\(43\) 5.28345 + 1.92302i 0.805719 + 0.293258i 0.711854 0.702327i \(-0.247856\pi\)
0.0938645 + 0.995585i \(0.470078\pi\)
\(44\) 11.4604 + 19.8500i 1.72772 + 2.99251i
\(45\) 0 0
\(46\) −0.895295 + 1.55070i −0.132004 + 0.228638i
\(47\) −7.11320 2.58899i −1.03757 0.377644i −0.233610 0.972330i \(-0.575054\pi\)
−0.803957 + 0.594687i \(0.797276\pi\)
\(48\) 0 0
\(49\) −6.99963 0.0720845i −0.999947 0.0102978i
\(50\) 0.599727 3.40122i 0.0848143 0.481006i
\(51\) 0 0
\(52\) −10.1141 3.68124i −1.40258 0.510496i
\(53\) −4.42304 7.66093i −0.607551 1.05231i −0.991643 0.129015i \(-0.958819\pi\)
0.384091 0.923295i \(-0.374515\pi\)
\(54\) 0 0
\(55\) −9.75212 −1.31498
\(56\) 14.5539 8.30307i 1.94485 1.10954i
\(57\) 0 0
\(58\) 7.43987 + 6.24279i 0.976903 + 0.819719i
\(59\) 3.83685 + 3.21950i 0.499516 + 0.419144i 0.857422 0.514614i \(-0.172065\pi\)
−0.357906 + 0.933758i \(0.616509\pi\)
\(60\) 0 0
\(61\) 5.36583 + 1.95300i 0.687024 + 0.250056i 0.661861 0.749627i \(-0.269767\pi\)
0.0251637 + 0.999683i \(0.491989\pi\)
\(62\) 1.57037 + 2.71996i 0.199437 + 0.345435i
\(63\) 0 0
\(64\) 0.0755905 0.130927i 0.00944881 0.0163658i
\(65\) 3.50804 2.94360i 0.435119 0.365108i
\(66\) 0 0
\(67\) 0.871145 4.94051i 0.106427 0.603579i −0.884213 0.467083i \(-0.845305\pi\)
0.990641 0.136496i \(-0.0435841\pi\)
\(68\) −10.6923 + 3.89167i −1.29663 + 0.471934i
\(69\) 0 0
\(70\) −0.0662313 + 12.8629i −0.00791616 + 1.53741i
\(71\) 4.19743 7.27016i 0.498143 0.862809i −0.501855 0.864952i \(-0.667349\pi\)
0.999998 + 0.00214287i \(0.000682096\pi\)
\(72\) 0 0
\(73\) 4.59111 7.95204i 0.537349 0.930716i −0.461697 0.887038i \(-0.652759\pi\)
0.999046 0.0436778i \(-0.0139075\pi\)
\(74\) 16.3600 13.7277i 1.90181 1.59581i
\(75\) 0 0
\(76\) 31.5593 11.4866i 3.62009 1.31761i
\(77\) −13.3230 + 2.27853i −1.51830 + 0.259663i
\(78\) 0 0
\(79\) −1.42181 8.06351i −0.159967 0.907216i −0.954104 0.299477i \(-0.903188\pi\)
0.794137 0.607739i \(-0.207923\pi\)
\(80\) −6.83051 11.8308i −0.763674 1.32272i
\(81\) 0 0
\(82\) −2.88061 + 4.98936i −0.318110 + 0.550982i
\(83\) 1.74493 1.46417i 0.191531 0.160714i −0.541980 0.840392i \(-0.682325\pi\)
0.733510 + 0.679678i \(0.237881\pi\)
\(84\) 0 0
\(85\) 0.840664 4.76764i 0.0911828 0.517123i
\(86\) 2.48663 14.1024i 0.268140 1.52070i
\(87\) 0 0
\(88\) 24.7847 20.7968i 2.64205 2.21695i
\(89\) −7.14912 −0.757805 −0.378903 0.925437i \(-0.623698\pi\)
−0.378903 + 0.925437i \(0.623698\pi\)
\(90\) 0 0
\(91\) 4.10480 4.84107i 0.430300 0.507482i
\(92\) 2.96409 + 1.07884i 0.309028 + 0.112477i
\(93\) 0 0
\(94\) −3.34779 + 18.9863i −0.345298 + 1.95828i
\(95\) −2.48130 + 14.0722i −0.254576 + 1.44377i
\(96\) 0 0
\(97\) 11.6472 + 4.23925i 1.18260 + 0.430431i 0.857119 0.515118i \(-0.172252\pi\)
0.325480 + 0.945549i \(0.394474\pi\)
\(98\) 2.91486 + 17.5883i 0.294446 + 1.77668i
\(99\) 0 0
\(100\) −6.08405 −0.608405
\(101\) −1.41526 + 1.18754i −0.140823 + 0.118165i −0.710478 0.703719i \(-0.751521\pi\)
0.569655 + 0.821884i \(0.307077\pi\)
\(102\) 0 0
\(103\) 0.457161 2.59269i 0.0450454 0.255465i −0.953966 0.299914i \(-0.903042\pi\)
0.999012 + 0.0444488i \(0.0141532\pi\)
\(104\) −2.63822 + 14.9621i −0.258699 + 1.46715i
\(105\) 0 0
\(106\) −17.2589 + 14.4820i −1.67634 + 1.40661i
\(107\) −0.780834 + 1.35244i −0.0754861 + 0.130746i −0.901298 0.433201i \(-0.857384\pi\)
0.825811 + 0.563946i \(0.190718\pi\)
\(108\) 0 0
\(109\) −6.02903 10.4426i −0.577476 1.00022i −0.995768 0.0919055i \(-0.970704\pi\)
0.418291 0.908313i \(-0.362629\pi\)
\(110\) 4.31299 + 24.4602i 0.411227 + 2.33219i
\(111\) 0 0
\(112\) −12.0958 14.5669i −1.14294 1.37644i
\(113\) −4.34324 + 1.58081i −0.408578 + 0.148710i −0.538129 0.842863i \(-0.680869\pi\)
0.129551 + 0.991573i \(0.458646\pi\)
\(114\) 0 0
\(115\) −1.02808 + 0.862663i −0.0958691 + 0.0804437i
\(116\) 8.55442 14.8167i 0.794258 1.37570i
\(117\) 0 0
\(118\) 6.37823 11.0474i 0.587164 1.01700i
\(119\) 0.0345489 6.70979i 0.00316709 0.615085i
\(120\) 0 0
\(121\) −14.1885 + 5.16420i −1.28987 + 0.469472i
\(122\) 2.52540 14.3223i 0.228639 1.29668i
\(123\) 0 0
\(124\) 4.23833 3.55638i 0.380613 0.319372i
\(125\) 6.06657 10.5076i 0.542611 0.939830i
\(126\) 0 0
\(127\) −7.70504 13.3455i −0.683711 1.18422i −0.973840 0.227235i \(-0.927031\pi\)
0.290129 0.956988i \(-0.406302\pi\)
\(128\) −10.8120 3.93523i −0.955651 0.347829i
\(129\) 0 0
\(130\) −8.93457 7.49700i −0.783614 0.657530i
\(131\) 10.9636 + 9.19952i 0.957891 + 0.803766i 0.980609 0.195976i \(-0.0627876\pi\)
−0.0227181 + 0.999742i \(0.507232\pi\)
\(132\) 0 0
\(133\) −0.101974 + 19.8046i −0.00884230 + 1.71728i
\(134\) −12.7770 −1.10377
\(135\) 0 0
\(136\) 8.03067 + 13.9095i 0.688624 + 1.19273i
\(137\) −14.0474 5.11283i −1.20015 0.436818i −0.336873 0.941550i \(-0.609369\pi\)
−0.863276 + 0.504732i \(0.831591\pi\)
\(138\) 0 0
\(139\) −2.41128 + 13.6750i −0.204522 + 1.15990i 0.693669 + 0.720294i \(0.255993\pi\)
−0.898191 + 0.439606i \(0.855118\pi\)
\(140\) 22.3354 3.81986i 1.88768 0.322837i
\(141\) 0 0
\(142\) −20.0913 7.31263i −1.68602 0.613663i
\(143\) 6.12784 10.6137i 0.512436 0.887565i
\(144\) 0 0
\(145\) 3.63964 + 6.30405i 0.302256 + 0.523523i
\(146\) −21.9757 7.99850i −1.81872 0.661960i
\(147\) 0 0
\(148\) −28.8199 24.1828i −2.36898 1.98781i
\(149\) 19.1201 6.95914i 1.56638 0.570115i 0.594191 0.804324i \(-0.297472\pi\)
0.972186 + 0.234209i \(0.0752501\pi\)
\(150\) 0 0
\(151\) 0.314253 + 1.78222i 0.0255736 + 0.145035i 0.994921 0.100659i \(-0.0320952\pi\)
−0.969347 + 0.245694i \(0.920984\pi\)
\(152\) −23.7033 41.0553i −1.92259 3.33003i
\(153\) 0 0
\(154\) 11.6072 + 32.4089i 0.935338 + 2.61158i
\(155\) 0.408770 + 2.31825i 0.0328332 + 0.186206i
\(156\) 0 0
\(157\) −3.12303 2.62054i −0.249245 0.209142i 0.509602 0.860410i \(-0.329793\pi\)
−0.758847 + 0.651269i \(0.774237\pi\)
\(158\) −19.5960 + 7.13236i −1.55897 + 0.567420i
\(159\) 0 0
\(160\) −8.13105 + 6.82276i −0.642816 + 0.539387i
\(161\) −1.20297 + 1.41874i −0.0948073 + 0.111813i
\(162\) 0 0
\(163\) 9.85163 17.0635i 0.771640 1.33652i −0.165024 0.986289i \(-0.552770\pi\)
0.936664 0.350229i \(-0.113896\pi\)
\(164\) 9.53694 + 3.47116i 0.744710 + 0.271052i
\(165\) 0 0
\(166\) −4.44413 3.72907i −0.344931 0.289432i
\(167\) −7.13093 + 2.59545i −0.551808 + 0.200842i −0.602850 0.797855i \(-0.705968\pi\)
0.0510416 + 0.998697i \(0.483746\pi\)
\(168\) 0 0
\(169\) −1.25807 7.13488i −0.0967748 0.548837i
\(170\) −12.3299 −0.945663
\(171\) 0 0
\(172\) −25.2261 −1.92347
\(173\) −2.38045 + 1.99744i −0.180983 + 0.151862i −0.728778 0.684750i \(-0.759912\pi\)
0.547796 + 0.836612i \(0.315467\pi\)
\(174\) 0 0
\(175\) 1.24443 3.36503i 0.0940701 0.254373i
\(176\) −28.0068 23.5005i −2.11109 1.77142i
\(177\) 0 0
\(178\) 3.16178 + 17.9313i 0.236985 + 1.34401i
\(179\) 4.63958 0.346778 0.173389 0.984853i \(-0.444528\pi\)
0.173389 + 0.984853i \(0.444528\pi\)
\(180\) 0 0
\(181\) 3.64910 + 6.32043i 0.271235 + 0.469794i 0.969178 0.246360i \(-0.0792344\pi\)
−0.697943 + 0.716153i \(0.745901\pi\)
\(182\) −13.9577 8.15460i −1.03461 0.604459i
\(183\) 0 0
\(184\) 0.773167 4.38485i 0.0569987 0.323255i
\(185\) 15.0416 5.47468i 1.10588 0.402507i
\(186\) 0 0
\(187\) −2.24982 12.7594i −0.164523 0.933059i
\(188\) 33.9623 2.47696
\(189\) 0 0
\(190\) 36.3930 2.64023
\(191\) −0.203565 1.15448i −0.0147295 0.0835350i 0.976557 0.215259i \(-0.0690597\pi\)
−0.991286 + 0.131724i \(0.957949\pi\)
\(192\) 0 0
\(193\) −12.9902 + 4.72806i −0.935057 + 0.340333i −0.764212 0.644965i \(-0.776872\pi\)
−0.170845 + 0.985298i \(0.554650\pi\)
\(194\) 5.48172 31.0884i 0.393564 2.23201i
\(195\) 0 0
\(196\) 29.6213 10.4371i 2.11581 0.745507i
\(197\) 5.52414 + 9.56810i 0.393579 + 0.681699i 0.992919 0.118796i \(-0.0379035\pi\)
−0.599340 + 0.800495i \(0.704570\pi\)
\(198\) 0 0
\(199\) 17.1606 1.21648 0.608242 0.793752i \(-0.291875\pi\)
0.608242 + 0.793752i \(0.291875\pi\)
\(200\) 1.49129 + 8.45751i 0.105450 + 0.598036i
\(201\) 0 0
\(202\) 3.60449 + 3.02453i 0.253611 + 0.212805i
\(203\) 6.44525 + 7.76197i 0.452368 + 0.544784i
\(204\) 0 0
\(205\) −3.30785 + 2.77561i −0.231030 + 0.193857i
\(206\) −6.70513 −0.467169
\(207\) 0 0
\(208\) 17.1681 1.19039
\(209\) 6.64058 + 37.6606i 0.459338 + 2.60504i
\(210\) 0 0
\(211\) 13.4382 4.89112i 0.925126 0.336718i 0.164850 0.986319i \(-0.447286\pi\)
0.760276 + 0.649600i \(0.225064\pi\)
\(212\) 30.4035 + 25.5115i 2.08812 + 1.75214i
\(213\) 0 0
\(214\) 3.73752 + 1.36035i 0.255491 + 0.0929913i
\(215\) 5.36646 9.29499i 0.365990 0.633913i
\(216\) 0 0
\(217\) 1.10009 + 3.07160i 0.0746792 + 0.208514i
\(218\) −23.5256 + 19.7403i −1.59335 + 1.33698i
\(219\) 0 0
\(220\) 41.1153 14.9647i 2.77199 1.00892i
\(221\) 4.66063 + 3.91073i 0.313508 + 0.263064i
\(222\) 0 0
\(223\) 3.86958 + 21.9455i 0.259126 + 1.46958i 0.785255 + 0.619173i \(0.212532\pi\)
−0.526129 + 0.850405i \(0.676357\pi\)
\(224\) −9.51424 + 11.2208i −0.635697 + 0.749720i
\(225\) 0 0
\(226\) 5.88582 + 10.1945i 0.391519 + 0.678130i
\(227\) −1.65669 9.39555i −0.109958 0.623604i −0.989124 0.147087i \(-0.953010\pi\)
0.879165 0.476517i \(-0.158101\pi\)
\(228\) 0 0
\(229\) 20.8461 7.58736i 1.37755 0.501387i 0.456115 0.889921i \(-0.349241\pi\)
0.921434 + 0.388534i \(0.127019\pi\)
\(230\) 2.61840 + 2.19710i 0.172652 + 0.144872i
\(231\) 0 0
\(232\) −22.6937 8.25982i −1.48991 0.542283i
\(233\) −12.1286 21.0074i −0.794572 1.37624i −0.923111 0.384534i \(-0.874362\pi\)
0.128539 0.991704i \(-0.458971\pi\)
\(234\) 0 0
\(235\) −7.22497 + 12.5140i −0.471305 + 0.816324i
\(236\) −21.1167 7.68584i −1.37458 0.500305i
\(237\) 0 0
\(238\) −16.8447 + 2.88083i −1.09188 + 0.186736i
\(239\) 2.26897 12.8680i 0.146768 0.832361i −0.819163 0.573560i \(-0.805562\pi\)
0.965931 0.258800i \(-0.0833271\pi\)
\(240\) 0 0
\(241\) 3.33094 + 1.21236i 0.214565 + 0.0780952i 0.447066 0.894501i \(-0.352469\pi\)
−0.232502 + 0.972596i \(0.574691\pi\)
\(242\) 19.2278 + 33.3036i 1.23601 + 2.14083i
\(243\) 0 0
\(244\) −25.6194 −1.64012
\(245\) −2.45575 + 13.1348i −0.156892 + 0.839152i
\(246\) 0 0
\(247\) −13.7563 11.5429i −0.875292 0.734457i
\(248\) −5.98263 5.02003i −0.379898 0.318772i
\(249\) 0 0
\(250\) −29.0381 10.5690i −1.83653 0.668442i
\(251\) −5.68335 9.84385i −0.358730 0.621338i 0.629019 0.777390i \(-0.283457\pi\)
−0.987749 + 0.156052i \(0.950123\pi\)
\(252\) 0 0
\(253\) −1.79585 + 3.11050i −0.112904 + 0.195556i
\(254\) −30.0654 + 25.2279i −1.88647 + 1.58294i
\(255\) 0 0
\(256\) −5.03609 + 28.5611i −0.314755 + 1.78507i
\(257\) −6.42672 + 2.33913i −0.400888 + 0.145911i −0.534592 0.845110i \(-0.679535\pi\)
0.133705 + 0.991021i \(0.457313\pi\)
\(258\) 0 0
\(259\) 19.2701 10.9937i 1.19739 0.683115i
\(260\) −10.2730 + 17.7934i −0.637107 + 1.10350i
\(261\) 0 0
\(262\) 18.2254 31.5673i 1.12597 1.95023i
\(263\) 17.5328 14.7118i 1.08112 0.907168i 0.0851078 0.996372i \(-0.472877\pi\)
0.996013 + 0.0892033i \(0.0284321\pi\)
\(264\) 0 0
\(265\) −15.8680 + 5.77549i −0.974766 + 0.354786i
\(266\) 49.7188 8.50304i 3.04845 0.521355i
\(267\) 0 0
\(268\) 3.90849 + 22.1661i 0.238749 + 1.35401i
\(269\) 13.4922 + 23.3691i 0.822631 + 1.42484i 0.903716 + 0.428132i \(0.140828\pi\)
−0.0810850 + 0.996707i \(0.525839\pi\)
\(270\) 0 0
\(271\) 1.48284 2.56836i 0.0900764 0.156017i −0.817467 0.575976i \(-0.804622\pi\)
0.907543 + 0.419959i \(0.137956\pi\)
\(272\) 13.9033 11.6662i 0.843009 0.707368i
\(273\) 0 0
\(274\) −6.61133 + 37.4947i −0.399405 + 2.26514i
\(275\) 1.20298 6.82243i 0.0725423 0.411408i
\(276\) 0 0
\(277\) 9.56519 8.02615i 0.574717 0.482244i −0.308491 0.951227i \(-0.599824\pi\)
0.883207 + 0.468983i \(0.155379\pi\)
\(278\) 35.3660 2.12111
\(279\) 0 0
\(280\) −10.7847 30.1124i −0.644512 1.79956i
\(281\) 14.5771 + 5.30564i 0.869598 + 0.316508i 0.738004 0.674796i \(-0.235768\pi\)
0.131594 + 0.991304i \(0.457991\pi\)
\(282\) 0 0
\(283\) 3.61208 20.4851i 0.214716 1.21771i −0.666684 0.745341i \(-0.732287\pi\)
0.881399 0.472372i \(-0.156602\pi\)
\(284\) −6.54036 + 37.0922i −0.388099 + 2.20102i
\(285\) 0 0
\(286\) −29.3313 10.6757i −1.73440 0.631270i
\(287\) −3.87055 + 4.56480i −0.228471 + 0.269452i
\(288\) 0 0
\(289\) −10.5682 −0.621660
\(290\) 14.2021 11.9170i 0.833974 0.699788i
\(291\) 0 0
\(292\) −7.15379 + 40.5712i −0.418644 + 2.37425i
\(293\) −3.44178 + 19.5193i −0.201071 + 1.14033i 0.702433 + 0.711750i \(0.252097\pi\)
−0.903504 + 0.428580i \(0.859014\pi\)
\(294\) 0 0
\(295\) 7.32423 6.14576i 0.426433 0.357820i
\(296\) −26.5526 + 45.9904i −1.54334 + 2.67314i
\(297\) 0 0
\(298\) −25.9109 44.8790i −1.50098 2.59977i
\(299\) −0.292875 1.66098i −0.0169374 0.0960567i
\(300\) 0 0
\(301\) 5.15974 13.9523i 0.297402 0.804198i
\(302\) 4.33116 1.57641i 0.249230 0.0907124i
\(303\) 0 0
\(304\) −41.0368 + 34.4340i −2.35362 + 1.97492i
\(305\) 5.45014 9.43992i 0.312074 0.540528i
\(306\) 0 0
\(307\) −3.62970 + 6.28682i −0.207158 + 0.358808i −0.950818 0.309750i \(-0.899755\pi\)
0.743660 + 0.668558i \(0.233088\pi\)
\(308\) 52.6737 30.0506i 3.00136 1.71229i
\(309\) 0 0
\(310\) 5.63382 2.05054i 0.319980 0.116463i
\(311\) −2.92785 + 16.6047i −0.166023 + 0.941564i 0.781980 + 0.623303i \(0.214210\pi\)
−0.948003 + 0.318260i \(0.896901\pi\)
\(312\) 0 0
\(313\) 0.661842 0.555351i 0.0374095 0.0313903i −0.623891 0.781511i \(-0.714449\pi\)
0.661301 + 0.750121i \(0.270005\pi\)
\(314\) −5.19160 + 8.99212i −0.292979 + 0.507455i
\(315\) 0 0
\(316\) 18.3680 + 31.8142i 1.03328 + 1.78969i
\(317\) 17.5152 + 6.37501i 0.983751 + 0.358056i 0.783298 0.621647i \(-0.213536\pi\)
0.200454 + 0.979703i \(0.435758\pi\)
\(318\) 0 0
\(319\) 14.9235 + 12.5223i 0.835553 + 0.701112i
\(320\) −0.221074 0.185503i −0.0123584 0.0103699i
\(321\) 0 0
\(322\) 4.09050 + 2.38982i 0.227955 + 0.133179i
\(323\) −18.9840 −1.05630
\(324\) 0 0
\(325\) 1.62656 + 2.81728i 0.0902252 + 0.156275i
\(326\) −47.1556 17.1632i −2.61170 0.950583i
\(327\) 0 0
\(328\) 2.48766 14.1082i 0.137358 0.778997i
\(329\) −6.94665 + 18.7842i −0.382981 + 1.03561i
\(330\) 0 0
\(331\) 7.33190 + 2.66859i 0.402998 + 0.146679i 0.535563 0.844495i \(-0.320099\pi\)
−0.132566 + 0.991174i \(0.542322\pi\)
\(332\) −5.10990 + 8.85060i −0.280442 + 0.485740i
\(333\) 0 0
\(334\) 9.66361 + 16.7379i 0.528769 + 0.915855i
\(335\) −8.99896 3.27535i −0.491666 0.178952i
\(336\) 0 0
\(337\) 5.28418 + 4.43395i 0.287847 + 0.241533i 0.775265 0.631636i \(-0.217616\pi\)
−0.487417 + 0.873169i \(0.662061\pi\)
\(338\) −17.3392 + 6.31097i −0.943130 + 0.343271i
\(339\) 0 0
\(340\) 3.77173 + 21.3905i 0.204551 + 1.16006i
\(341\) 3.14996 + 5.45589i 0.170580 + 0.295453i
\(342\) 0 0
\(343\) −0.286070 + 18.5180i −0.0154463 + 0.999881i
\(344\) 6.18327 + 35.0671i 0.333380 + 1.89069i
\(345\) 0 0
\(346\) 6.06274 + 5.08724i 0.325935 + 0.273492i
\(347\) −25.1323 + 9.14741i −1.34917 + 0.491059i −0.912690 0.408653i \(-0.865999\pi\)
−0.436484 + 0.899712i \(0.643776\pi\)
\(348\) 0 0
\(349\) 3.39785 2.85113i 0.181883 0.152618i −0.547301 0.836936i \(-0.684345\pi\)
0.729183 + 0.684318i \(0.239900\pi\)
\(350\) −8.99050 1.63304i −0.480562 0.0872898i
\(351\) 0 0
\(352\) −14.2033 + 24.6008i −0.757038 + 1.31123i
\(353\) 16.6914 + 6.07519i 0.888396 + 0.323350i 0.745593 0.666401i \(-0.232166\pi\)
0.142803 + 0.989751i \(0.454388\pi\)
\(354\) 0 0
\(355\) −12.2759 10.3007i −0.651538 0.546705i
\(356\) 30.1409 10.9704i 1.59747 0.581430i
\(357\) 0 0
\(358\) −2.05191 11.6369i −0.108447 0.615031i
\(359\) −1.63662 −0.0863773 −0.0431887 0.999067i \(-0.513752\pi\)
−0.0431887 + 0.999067i \(0.513752\pi\)
\(360\) 0 0
\(361\) 37.0332 1.94912
\(362\) 14.2390 11.9479i 0.748384 0.627968i
\(363\) 0 0
\(364\) −9.87731 + 26.7090i −0.517711 + 1.39993i
\(365\) −13.4273 11.2668i −0.702816 0.589733i
\(366\) 0 0
\(367\) 1.85953 + 10.5459i 0.0970665 + 0.550492i 0.994094 + 0.108518i \(0.0346105\pi\)
−0.897028 + 0.441974i \(0.854278\pi\)
\(368\) −5.03134 −0.262277
\(369\) 0 0
\(370\) −20.3838 35.3059i −1.05971 1.83546i
\(371\) −20.3289 + 11.5977i −1.05542 + 0.602125i
\(372\) 0 0
\(373\) 1.23468 7.00219i 0.0639291 0.362560i −0.936015 0.351961i \(-0.885515\pi\)
0.999944 0.0105990i \(-0.00337383\pi\)
\(374\) −31.0080 + 11.2860i −1.60338 + 0.583584i
\(375\) 0 0
\(376\) −8.32465 47.2114i −0.429311 2.43474i
\(377\) −9.14802 −0.471147
\(378\) 0 0
\(379\) −24.5784 −1.26251 −0.631253 0.775577i \(-0.717459\pi\)
−0.631253 + 0.775577i \(0.717459\pi\)
\(380\) −11.1326 63.1362i −0.571091 3.23882i
\(381\) 0 0
\(382\) −2.80562 + 1.02116i −0.143548 + 0.0522471i
\(383\) −1.55708 + 8.83062i −0.0795629 + 0.451223i 0.918835 + 0.394642i \(0.129131\pi\)
−0.998398 + 0.0565818i \(0.981980\pi\)
\(384\) 0 0
\(385\) −0.132852 + 25.8013i −0.00677076 + 1.31496i
\(386\) 17.6039 + 30.4909i 0.896017 + 1.55195i
\(387\) 0 0
\(388\) −55.6103 −2.82319
\(389\) −0.581400 3.29728i −0.0294781 0.167179i 0.966515 0.256611i \(-0.0826059\pi\)
−0.995993 + 0.0894321i \(0.971495\pi\)
\(390\) 0 0
\(391\) −1.36586 1.14609i −0.0690746 0.0579605i
\(392\) −21.7693 38.6186i −1.09952 1.95053i
\(393\) 0 0
\(394\) 21.5555 18.0872i 1.08595 0.911220i
\(395\) −15.6300 −0.786431
\(396\) 0 0
\(397\) −25.4202 −1.27580 −0.637902 0.770118i \(-0.720197\pi\)
−0.637902 + 0.770118i \(0.720197\pi\)
\(398\) −7.58948 43.0421i −0.380426 2.15750i
\(399\) 0 0
\(400\) 9.11921 3.31912i 0.455961 0.165956i
\(401\) 10.6771 + 8.95915i 0.533189 + 0.447399i 0.869201 0.494459i \(-0.164634\pi\)
−0.336012 + 0.941858i \(0.609078\pi\)
\(402\) 0 0
\(403\) −2.77992 1.01181i −0.138478 0.0504018i
\(404\) 4.14447 7.17844i 0.206195 0.357141i
\(405\) 0 0
\(406\) 16.6180 19.5987i 0.824738 0.972669i
\(407\) 32.8161 27.5360i 1.62664 1.36491i
\(408\) 0 0
\(409\) 5.47500 1.99274i 0.270721 0.0985345i −0.203092 0.979160i \(-0.565099\pi\)
0.473814 + 0.880625i \(0.342877\pi\)
\(410\) 8.42470 + 7.06916i 0.416066 + 0.349121i
\(411\) 0 0
\(412\) 2.05110 + 11.6324i 0.101050 + 0.573086i
\(413\) 8.57016 10.1074i 0.421710 0.497351i
\(414\) 0 0
\(415\) −2.17410 3.76566i −0.106723 0.184849i
\(416\) −2.31633 13.1366i −0.113568 0.644074i
\(417\) 0 0
\(418\) 91.5230 33.3116i 4.47654 1.62933i
\(419\) −16.8842 14.1676i −0.824849 0.692130i 0.129253 0.991612i \(-0.458742\pi\)
−0.954102 + 0.299481i \(0.903186\pi\)
\(420\) 0 0
\(421\) 5.29354 + 1.92669i 0.257991 + 0.0939011i 0.467778 0.883846i \(-0.345055\pi\)
−0.209787 + 0.977747i \(0.567277\pi\)
\(422\) −18.2111 31.5425i −0.886500 1.53546i
\(423\) 0 0
\(424\) 28.0116 48.5174i 1.36036 2.35621i
\(425\) 3.23166 + 1.17623i 0.156759 + 0.0570555i
\(426\) 0 0
\(427\) 5.24019 14.1699i 0.253591 0.685728i
\(428\) 1.21668 6.90015i 0.0588105 0.333531i
\(429\) 0 0
\(430\) −25.6870 9.34929i −1.23874 0.450863i
\(431\) 0.373189 + 0.646383i 0.0179759 + 0.0311352i 0.874873 0.484352i \(-0.160944\pi\)
−0.856898 + 0.515487i \(0.827611\pi\)
\(432\) 0 0
\(433\) −24.3464 −1.17001 −0.585007 0.811028i \(-0.698908\pi\)
−0.585007 + 0.811028i \(0.698908\pi\)
\(434\) 7.21762 4.11769i 0.346457 0.197656i
\(435\) 0 0
\(436\) 41.4428 + 34.7747i 1.98475 + 1.66540i
\(437\) 4.03147 + 3.38281i 0.192852 + 0.161822i
\(438\) 0 0
\(439\) −12.2779 4.46877i −0.585990 0.213283i 0.0319749 0.999489i \(-0.489820\pi\)
−0.617965 + 0.786206i \(0.712043\pi\)
\(440\) −30.8806 53.4867i −1.47217 2.54988i
\(441\) 0 0
\(442\) 7.74763 13.4193i 0.368517 0.638291i
\(443\) −12.5398 + 10.5221i −0.595782 + 0.499921i −0.890087 0.455791i \(-0.849356\pi\)
0.294305 + 0.955712i \(0.404912\pi\)
\(444\) 0 0
\(445\) −2.36979 + 13.4397i −0.112339 + 0.637104i
\(446\) 53.3320 19.4113i 2.52534 0.919150i
\(447\) 0 0
\(448\) −0.345365 0.201775i −0.0163170 0.00953296i
\(449\) −4.59743 + 7.96298i −0.216966 + 0.375796i −0.953879 0.300191i \(-0.902949\pi\)
0.736913 + 0.675988i \(0.236283\pi\)
\(450\) 0 0
\(451\) −5.77814 + 10.0080i −0.272082 + 0.471260i
\(452\) 15.8855 13.3295i 0.747190 0.626967i
\(453\) 0 0
\(454\) −22.8331 + 8.31058i −1.07161 + 0.390035i
\(455\) −7.74013 9.32139i −0.362863 0.436993i
\(456\) 0 0
\(457\) 0.969719 + 5.49955i 0.0453616 + 0.257258i 0.999052 0.0435315i \(-0.0138609\pi\)
−0.953690 + 0.300790i \(0.902750\pi\)
\(458\) −28.2500 48.9304i −1.32003 2.28637i
\(459\) 0 0
\(460\) 3.01066 5.21462i 0.140373 0.243133i
\(461\) 30.7540 25.8057i 1.43236 1.20189i 0.488057 0.872812i \(-0.337706\pi\)
0.944302 0.329080i \(-0.106738\pi\)
\(462\) 0 0
\(463\) 2.21658 12.5708i 0.103013 0.584216i −0.888982 0.457942i \(-0.848587\pi\)
0.991995 0.126275i \(-0.0403021\pi\)
\(464\) −4.73881 + 26.8751i −0.219994 + 1.24765i
\(465\) 0 0
\(466\) −47.3264 + 39.7116i −2.19236 + 1.83960i
\(467\) −26.3120 −1.21757 −0.608786 0.793334i \(-0.708343\pi\)
−0.608786 + 0.793334i \(0.708343\pi\)
\(468\) 0 0
\(469\) −13.0593 2.37211i −0.603023 0.109534i
\(470\) 34.5828 + 12.5871i 1.59519 + 0.580600i
\(471\) 0 0
\(472\) −5.50818 + 31.2384i −0.253534 + 1.43786i
\(473\) 4.98787 28.2876i 0.229342 1.30066i
\(474\) 0 0
\(475\) −9.53857 3.47176i −0.437660 0.159295i
\(476\) 10.1506 + 28.3417i 0.465251 + 1.29904i
\(477\) 0 0
\(478\) −33.2788 −1.52214
\(479\) −4.90009 + 4.11167i −0.223891 + 0.187867i −0.747833 0.663887i \(-0.768905\pi\)
0.523942 + 0.851754i \(0.324461\pi\)
\(480\) 0 0
\(481\) −3.49314 + 19.8106i −0.159273 + 0.903284i
\(482\) 1.56769 8.89081i 0.0714063 0.404965i
\(483\) 0 0
\(484\) 51.8947 43.5448i 2.35885 1.97931i
\(485\) 11.8302 20.4906i 0.537184 0.930430i
\(486\) 0 0
\(487\) 12.4068 + 21.4891i 0.562204 + 0.973766i 0.997304 + 0.0733840i \(0.0233799\pi\)
−0.435100 + 0.900382i \(0.643287\pi\)
\(488\) 6.27968 + 35.6138i 0.284268 + 1.61216i
\(489\) 0 0
\(490\) 34.0306 + 0.350459i 1.53735 + 0.0158321i
\(491\) 22.7505 8.28052i 1.02672 0.373695i 0.226887 0.973921i \(-0.427145\pi\)
0.799830 + 0.600227i \(0.204923\pi\)
\(492\) 0 0
\(493\) −7.40836 + 6.21635i −0.333656 + 0.279970i
\(494\) −22.8679 + 39.6084i −1.02888 + 1.78206i
\(495\) 0 0
\(496\) −4.41254 + 7.64275i −0.198129 + 0.343170i
\(497\) −19.1776 11.2042i −0.860233 0.502579i
\(498\) 0 0
\(499\) −10.5810 + 3.85117i −0.473670 + 0.172402i −0.567814 0.823157i \(-0.692211\pi\)
0.0941440 + 0.995559i \(0.469989\pi\)
\(500\) −9.45283 + 53.6097i −0.422743 + 2.39750i
\(501\) 0 0
\(502\) −22.1767 + 18.6085i −0.989795 + 0.830537i
\(503\) −17.1285 + 29.6675i −0.763724 + 1.32281i 0.177195 + 0.984176i \(0.443298\pi\)
−0.940919 + 0.338632i \(0.890036\pi\)
\(504\) 0 0
\(505\) 1.76335 + 3.05421i 0.0784679 + 0.135910i
\(506\) 8.59596 + 3.12868i 0.382137 + 0.139087i
\(507\) 0 0
\(508\) 52.9635 + 44.4417i 2.34988 + 1.97178i
\(509\) 3.58928 + 3.01177i 0.159092 + 0.133494i 0.718859 0.695156i \(-0.244665\pi\)
−0.559767 + 0.828650i \(0.689109\pi\)
\(510\) 0 0
\(511\) −20.9763 12.2551i −0.927937 0.542134i
\(512\) 50.8521 2.24737
\(513\) 0 0
\(514\) 8.70928 + 15.0849i 0.384150 + 0.665367i
\(515\) −4.72249 1.71884i −0.208098 0.0757414i
\(516\) 0 0
\(517\) −6.71525 + 38.0841i −0.295336 + 1.67494i
\(518\) −36.0967 43.4710i −1.58600 1.91000i
\(519\) 0 0
\(520\) 27.2529 + 9.91925i 1.19512 + 0.434988i
\(521\) −11.9426 + 20.6852i −0.523215 + 0.906234i 0.476420 + 0.879218i \(0.341934\pi\)
−0.999635 + 0.0270167i \(0.991399\pi\)
\(522\) 0 0
\(523\) 1.37400 + 2.37984i 0.0600809 + 0.104063i 0.894501 0.447065i \(-0.147531\pi\)
−0.834420 + 0.551128i \(0.814197\pi\)
\(524\) −60.3395 21.9618i −2.63594 0.959405i
\(525\) 0 0
\(526\) −44.6541 37.4692i −1.94701 1.63374i
\(527\) −2.93883 + 1.06964i −0.128017 + 0.0465945i
\(528\) 0 0
\(529\) −3.90808 22.1638i −0.169916 0.963644i
\(530\) 21.5038 + 37.2458i 0.934068 + 1.61785i
\(531\) 0 0
\(532\) −29.9604 83.6533i −1.29895 3.62683i
\(533\) −0.942323 5.34418i −0.0408165 0.231482i
\(534\) 0 0
\(535\) 2.28365 + 1.91621i 0.0987307 + 0.0828449i
\(536\) 29.8554 10.8665i 1.28956 0.469360i
\(537\) 0 0
\(538\) 52.6471 44.1761i 2.26978 1.90457i
\(539\) 5.84685 + 35.2799i 0.251842 + 1.51961i
\(540\) 0 0
\(541\) −5.74161 + 9.94476i −0.246851 + 0.427559i −0.962650 0.270747i \(-0.912729\pi\)
0.715799 + 0.698306i \(0.246063\pi\)
\(542\) −7.09774 2.58337i −0.304874 0.110965i
\(543\) 0 0
\(544\) −10.8025 9.06441i −0.463155 0.388633i
\(545\) −21.6297 + 7.87255i −0.926513 + 0.337223i
\(546\) 0 0
\(547\) 3.11707 + 17.6778i 0.133276 + 0.755848i 0.976044 + 0.217571i \(0.0698135\pi\)
−0.842768 + 0.538277i \(0.819075\pi\)
\(548\) 67.0699 2.86508
\(549\) 0 0
\(550\) −17.6440 −0.752342
\(551\) 21.8665 18.3482i 0.931544 0.781658i
\(552\) 0 0
\(553\) −21.3531 + 3.65187i −0.908028 + 0.155293i
\(554\) −24.3614 20.4416i −1.03502 0.868482i
\(555\) 0 0
\(556\) −10.8184 61.3545i −0.458804 2.60201i
\(557\) 45.9853 1.94846 0.974230 0.225557i \(-0.0724203\pi\)
0.974230 + 0.225557i \(0.0724203\pi\)
\(558\) 0 0
\(559\) 6.74414 + 11.6812i 0.285247 + 0.494062i
\(560\) −31.3940 + 17.9104i −1.32664 + 0.756854i
\(561\) 0 0
\(562\) 6.86064 38.9086i 0.289399 1.64126i
\(563\) 18.0454 6.56797i 0.760521 0.276807i 0.0674952 0.997720i \(-0.478499\pi\)
0.693026 + 0.720913i \(0.256277\pi\)
\(564\) 0 0
\(565\) 1.53209 + 8.68892i 0.0644556 + 0.365546i
\(566\) −52.9780 −2.22683
\(567\) 0 0
\(568\) 53.1654 2.23077
\(569\) −0.239150 1.35629i −0.0100257 0.0568584i 0.979384 0.202005i \(-0.0647457\pi\)
−0.989410 + 0.145147i \(0.953635\pi\)
\(570\) 0 0
\(571\) 14.2757 5.19591i 0.597418 0.217442i −0.0255711 0.999673i \(-0.508140\pi\)
0.622989 + 0.782231i \(0.285918\pi\)
\(572\) −9.54829 + 54.1511i −0.399234 + 2.26417i
\(573\) 0 0
\(574\) 13.1612 + 7.68924i 0.549337 + 0.320943i
\(575\) −0.476686 0.825644i −0.0198792 0.0344317i
\(576\) 0 0
\(577\) 31.4052 1.30742 0.653708 0.756747i \(-0.273213\pi\)
0.653708 + 0.756747i \(0.273213\pi\)
\(578\) 4.67392 + 26.5071i 0.194409 + 1.10255i
\(579\) 0 0
\(580\) −25.0185 20.9930i −1.03884 0.871687i
\(581\) −3.85001 4.63654i −0.159725 0.192356i
\(582\) 0 0
\(583\) −34.6193 + 29.0490i −1.43378 + 1.20309i
\(584\) 58.1519 2.40634
\(585\) 0 0
\(586\) 50.4803 2.08532
\(587\) −1.22265 6.93397i −0.0504640 0.286196i 0.949124 0.314903i \(-0.101972\pi\)
−0.999588 + 0.0287074i \(0.990861\pi\)
\(588\) 0 0
\(589\) 8.67423 3.15716i 0.357415 0.130089i
\(590\) −18.6539 15.6525i −0.767971 0.644404i
\(591\) 0 0
\(592\) 56.3902 + 20.5243i 2.31762 + 0.843545i
\(593\) 5.45147 9.44223i 0.223865 0.387746i −0.732113 0.681183i \(-0.761466\pi\)
0.955978 + 0.293437i \(0.0947991\pi\)
\(594\) 0 0
\(595\) −12.6024 2.28911i −0.516647 0.0938442i
\(596\) −69.9320 + 58.6799i −2.86453 + 2.40362i
\(597\) 0 0
\(598\) −4.03651 + 1.46917i −0.165065 + 0.0600789i
\(599\) −1.15123 0.965994i −0.0470378 0.0394694i 0.618966 0.785418i \(-0.287552\pi\)
−0.666004 + 0.745949i \(0.731996\pi\)
\(600\) 0 0
\(601\) −7.12875 40.4292i −0.290788 1.64914i −0.683846 0.729626i \(-0.739694\pi\)
0.393058 0.919514i \(-0.371417\pi\)
\(602\) −37.2770 6.77103i −1.51930 0.275966i
\(603\) 0 0
\(604\) −4.05973 7.03167i −0.165188 0.286114i
\(605\) 5.00504 + 28.3850i 0.203484 + 1.15401i
\(606\) 0 0
\(607\) −34.2294 + 12.4585i −1.38933 + 0.505674i −0.924993 0.379984i \(-0.875929\pi\)
−0.464336 + 0.885659i \(0.653707\pi\)
\(608\) 31.8847 + 26.7545i 1.29310 + 1.08504i
\(609\) 0 0
\(610\) −26.0875 9.49507i −1.05625 0.384444i
\(611\) −9.07975 15.7266i −0.367327 0.636230i
\(612\) 0 0
\(613\) −12.8717 + 22.2945i −0.519884 + 0.900465i 0.479849 + 0.877351i \(0.340691\pi\)
−0.999733 + 0.0231137i \(0.992642\pi\)
\(614\) 17.3738 + 6.32355i 0.701149 + 0.255198i
\(615\) 0 0
\(616\) −54.6848 65.8565i −2.20331 2.65343i
\(617\) 0.999808 5.67019i 0.0402508 0.228273i −0.958046 0.286615i \(-0.907470\pi\)
0.998297 + 0.0583413i \(0.0185812\pi\)
\(618\) 0 0
\(619\) 45.2759 + 16.4791i 1.81979 + 0.662351i 0.995341 + 0.0964202i \(0.0307392\pi\)
0.824453 + 0.565931i \(0.191483\pi\)
\(620\) −5.28076 9.14655i −0.212081 0.367334i
\(621\) 0 0
\(622\) 42.9425 1.72184
\(623\) −0.0973915 + 18.9145i −0.00390191 + 0.757795i
\(624\) 0 0
\(625\) −12.5485 10.5294i −0.501940 0.421178i
\(626\) −1.68563 1.41441i −0.0673714 0.0565313i
\(627\) 0 0
\(628\) 17.1880 + 6.25594i 0.685878 + 0.249639i
\(629\) 10.6330 + 18.4169i 0.423966 + 0.734331i
\(630\) 0 0
\(631\) −12.8364 + 22.2334i −0.511011 + 0.885096i 0.488908 + 0.872335i \(0.337395\pi\)
−0.999919 + 0.0127609i \(0.995938\pi\)
\(632\) 39.7231 33.3316i 1.58010 1.32586i
\(633\) 0 0
\(634\) 8.24344 46.7508i 0.327389 1.85671i
\(635\) −27.6425 + 10.0610i −1.09696 + 0.399260i
\(636\) 0 0
\(637\) −12.7522 10.9261i −0.505260 0.432907i
\(638\) 24.8081 42.9690i 0.982163 1.70116i
\(639\) 0 0
\(640\) −10.9818 + 19.0211i −0.434095 + 0.751875i
\(641\) −37.6441 + 31.5872i −1.48685 + 1.24762i −0.588384 + 0.808581i \(0.700236\pi\)
−0.898469 + 0.439037i \(0.855320\pi\)
\(642\) 0 0
\(643\) 13.3947 4.87526i 0.528234 0.192261i −0.0641158 0.997942i \(-0.520423\pi\)
0.592350 + 0.805681i \(0.298200\pi\)
\(644\) 2.89468 7.82744i 0.114067 0.308444i
\(645\) 0 0
\(646\) 8.39590 + 47.6155i 0.330332 + 1.87341i
\(647\) −6.07459 10.5215i −0.238817 0.413643i 0.721558 0.692354i \(-0.243426\pi\)
−0.960375 + 0.278711i \(0.910093\pi\)
\(648\) 0 0
\(649\) 12.7939 22.1597i 0.502206 0.869846i
\(650\) 6.34691 5.32569i 0.248946 0.208891i
\(651\) 0 0
\(652\) −15.3506 + 87.0578i −0.601178 + 3.40945i
\(653\) −2.05909 + 11.6777i −0.0805786 + 0.456984i 0.917645 + 0.397402i \(0.130088\pi\)
−0.998223 + 0.0595823i \(0.981023\pi\)
\(654\) 0 0
\(655\) 20.9285 17.5611i 0.817744 0.686169i
\(656\) −16.1883 −0.632048
\(657\) 0 0
\(658\) 50.1867 + 9.11595i 1.95648 + 0.355377i
\(659\) −29.6236 10.7821i −1.15397 0.420012i −0.307032 0.951699i \(-0.599336\pi\)
−0.846940 + 0.531688i \(0.821558\pi\)
\(660\) 0 0
\(661\) −7.34033 + 41.6291i −0.285506 + 1.61918i 0.417968 + 0.908462i \(0.362742\pi\)
−0.703474 + 0.710721i \(0.748369\pi\)
\(662\) 3.45072 19.5700i 0.134116 0.760610i
\(663\) 0 0
\(664\) 13.5558 + 4.93392i 0.526068 + 0.191473i
\(665\) 37.1971 + 6.75652i 1.44244 + 0.262007i
\(666\) 0 0
\(667\) 2.68096 0.103807
\(668\) 26.0815 21.8850i 1.00912 0.846755i
\(669\) 0 0
\(670\) −4.23532 + 24.0197i −0.163624 + 0.927961i
\(671\) 5.06564 28.7287i 0.195557 1.10906i
\(672\) 0 0
\(673\) −16.3534 + 13.7221i −0.630377 + 0.528949i −0.901046 0.433724i \(-0.857199\pi\)
0.270669 + 0.962672i \(0.412755\pi\)
\(674\) 8.78420 15.2147i 0.338355 0.586048i
\(675\) 0 0
\(676\) 16.2526 + 28.1504i 0.625101 + 1.08271i
\(677\) −0.772285 4.37985i −0.0296813 0.168331i 0.966364 0.257178i \(-0.0827928\pi\)
−0.996045 + 0.0888472i \(0.971682\pi\)
\(678\) 0 0
\(679\) 11.3745 30.7576i 0.436514 1.18037i
\(680\) 28.8107 10.4862i 1.10484 0.402129i
\(681\) 0 0
\(682\) 12.2913 10.3136i 0.470658 0.394929i
\(683\) −0.356609 + 0.617664i −0.0136452 + 0.0236343i −0.872767 0.488136i \(-0.837677\pi\)
0.859122 + 0.511771i \(0.171010\pi\)
\(684\) 0 0
\(685\) −14.2681 + 24.7131i −0.545156 + 0.944238i
\(686\) 46.5733 7.47230i 1.77818 0.285294i
\(687\) 0 0
\(688\) 37.8107 13.7620i 1.44152 0.524670i
\(689\) 3.68507 20.8991i 0.140390 0.796191i
\(690\) 0 0
\(691\) 22.0972 18.5418i 0.840618 0.705362i −0.117084 0.993122i \(-0.537355\pi\)
0.957703 + 0.287760i \(0.0929104\pi\)
\(692\) 6.97098 12.0741i 0.264997 0.458988i
\(693\) 0 0
\(694\) 34.0585 + 58.9911i 1.29284 + 2.23927i
\(695\) 24.9086 + 9.06598i 0.944836 + 0.343892i
\(696\) 0 0
\(697\) −4.39465 3.68755i −0.166459 0.139676i
\(698\) −8.65392 7.26150i −0.327556 0.274852i
\(699\) 0 0
\(700\) −0.0828822 + 16.0967i −0.00313265 + 0.608397i
\(701\) 22.9917 0.868384 0.434192 0.900820i \(-0.357034\pi\)
0.434192 + 0.900820i \(0.357034\pi\)
\(702\) 0 0
\(703\) −31.3844 54.3593i −1.18368 2.05020i
\(704\) −0.725765 0.264157i −0.0273533 0.00995578i
\(705\) 0 0
\(706\) 7.85574 44.5521i 0.295655 1.67674i
\(707\) 3.12262 + 3.76055i 0.117438 + 0.141430i
\(708\) 0 0
\(709\) 9.30398 + 3.38637i 0.349418 + 0.127178i 0.510766 0.859720i \(-0.329362\pi\)
−0.161348 + 0.986898i \(0.551584\pi\)
\(710\) −20.4070 + 35.3459i −0.765860 + 1.32651i
\(711\) 0 0
\(712\) −22.6380 39.2102i −0.848396 1.46947i
\(713\) 0.814695 + 0.296525i 0.0305106 + 0.0111049i
\(714\) 0 0
\(715\) −17.9216 15.0380i −0.670231 0.562391i
\(716\) −19.5606 + 7.11948i −0.731014 + 0.266067i
\(717\) 0 0
\(718\) 0.723812 + 4.10494i 0.0270124 + 0.153195i
\(719\) −18.9108 32.7545i −0.705254 1.22154i −0.966600 0.256290i \(-0.917500\pi\)
0.261346 0.965245i \(-0.415834\pi\)
\(720\) 0 0
\(721\) −6.85329 1.24484i −0.255230 0.0463602i
\(722\) −16.3784 92.8863i −0.609539 3.45687i
\(723\) 0 0
\(724\) −25.0835 21.0475i −0.932220 0.782226i
\(725\) −4.85918 + 1.76860i −0.180465 + 0.0656841i
\(726\) 0 0
\(727\) 17.8869 15.0089i 0.663390 0.556651i −0.247711 0.968834i \(-0.579678\pi\)
0.911101 + 0.412184i \(0.135234\pi\)
\(728\) 39.5495 + 7.18381i 1.46580 + 0.266250i
\(729\) 0 0
\(730\) −22.3210 + 38.6611i −0.826136 + 1.43091i
\(731\) 13.3993 + 4.87696i 0.495592 + 0.180381i
\(732\) 0 0
\(733\) 9.51189 + 7.98142i 0.351330 + 0.294801i 0.801324 0.598231i \(-0.204129\pi\)
−0.449994 + 0.893032i \(0.648574\pi\)
\(734\) 25.6287 9.32809i 0.945973 0.344306i
\(735\) 0 0
\(736\) 0.678834 + 3.84986i 0.0250222 + 0.141908i
\(737\) −25.6291 −0.944059
\(738\) 0 0
\(739\) −20.7136 −0.761962 −0.380981 0.924583i \(-0.624414\pi\)
−0.380981 + 0.924583i \(0.624414\pi\)
\(740\) −55.0148 + 46.1629i −2.02238 + 1.69698i
\(741\) 0 0
\(742\) 38.0800 + 45.8595i 1.39796 + 1.68356i
\(743\) 23.6815 + 19.8712i 0.868791 + 0.729002i 0.963843 0.266470i \(-0.0858573\pi\)
−0.0950521 + 0.995472i \(0.530302\pi\)
\(744\) 0 0
\(745\) −6.74466 38.2509i −0.247105 1.40140i
\(746\) −18.1089 −0.663013
\(747\) 0 0
\(748\) 29.0647 + 50.3416i 1.06271 + 1.84067i
\(749\) 3.56755 + 2.08429i 0.130355 + 0.0761583i
\(750\) 0 0
\(751\) 7.05756 40.0254i 0.257534 1.46055i −0.531949 0.846776i \(-0.678540\pi\)
0.789483 0.613772i \(-0.210349\pi\)
\(752\) −50.9052 + 18.5280i −1.85632 + 0.675646i
\(753\) 0 0
\(754\) 4.04582 + 22.9450i 0.147340 + 0.835606i
\(755\) 3.45459 0.125725
\(756\) 0 0
\(757\) 38.0821 1.38412 0.692058 0.721842i \(-0.256704\pi\)
0.692058 + 0.721842i \(0.256704\pi\)
\(758\) 10.8701 + 61.6472i 0.394819 + 2.23913i
\(759\) 0 0
\(760\) −85.0376 + 30.9512i −3.08464 + 1.12272i
\(761\) 4.05379 22.9902i 0.146950 0.833394i −0.818831 0.574035i \(-0.805377\pi\)
0.965781 0.259359i \(-0.0835114\pi\)
\(762\) 0 0
\(763\) −27.7103 + 15.8088i −1.00318 + 0.572319i
\(764\) 2.62979 + 4.55494i 0.0951426 + 0.164792i
\(765\) 0 0
\(766\) 22.8375 0.825152
\(767\) 2.08649 + 11.8331i 0.0753388 + 0.427267i
\(768\) 0 0
\(769\) 22.2044 + 18.6317i 0.800711 + 0.671876i 0.948371 0.317162i \(-0.102730\pi\)
−0.147660 + 0.989038i \(0.547174\pi\)
\(770\) 64.7734 11.0777i 2.33427 0.399213i
\(771\) 0 0
\(772\) 47.5120 39.8673i 1.70999 1.43486i
\(773\) −2.04887 −0.0736929 −0.0368464 0.999321i \(-0.511731\pi\)
−0.0368464 + 0.999321i \(0.511731\pi\)
\(774\) 0 0
\(775\) −1.67223 −0.0600684
\(776\) 13.6309 + 77.3046i 0.489320 + 2.77507i
\(777\) 0 0
\(778\) −8.01308 + 2.91652i −0.287283 + 0.104562i
\(779\) 12.9712 + 10.8842i 0.464743 + 0.389966i
\(780\) 0 0
\(781\) −40.3006 14.6682i −1.44207 0.524871i
\(782\) −2.27055 + 3.93271i −0.0811948 + 0.140634i
\(783\) 0 0