Properties

Label 441.2.bg.a.278.2
Level $441$
Weight $2$
Character 441.278
Analytic conductor $3.521$
Analytic rank $0$
Dimension $216$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(17,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([21, 25]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bg (of order \(42\), degree \(12\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(18\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 278.2
Character \(\chi\) \(=\) 441.278
Dual form 441.2.bg.a.395.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.21867 + 0.870763i) q^{2} +(2.69816 - 2.50352i) q^{4} +(-1.55712 + 1.06163i) q^{5} +(0.00333353 + 2.64575i) q^{7} +(-1.73808 + 3.60916i) q^{8} +O(q^{10})\) \(q+(-2.21867 + 0.870763i) q^{2} +(2.69816 - 2.50352i) q^{4} +(-1.55712 + 1.06163i) q^{5} +(0.00333353 + 2.64575i) q^{7} +(-1.73808 + 3.60916i) q^{8} +(2.53032 - 3.71129i) q^{10} +(-0.0972657 + 0.645316i) q^{11} +(0.531850 + 0.424136i) q^{13} +(-2.31122 - 5.86714i) q^{14} +(0.163378 - 2.18013i) q^{16} +(5.58077 - 1.72144i) q^{17} +(-5.58665 - 3.22545i) q^{19} +(-1.54355 + 6.76274i) q^{20} +(-0.346117 - 1.51644i) q^{22} +(-2.20835 + 7.15930i) q^{23} +(-0.529125 + 1.34819i) q^{25} +(-1.54932 - 0.477902i) q^{26} +(6.63269 + 7.13030i) q^{28} +(-4.23402 - 0.966388i) q^{29} +(-2.43240 + 1.40435i) q^{31} +(-0.825605 - 2.67654i) q^{32} +(-10.8829 + 8.67884i) q^{34} +(-2.81400 - 4.11622i) q^{35} +(-2.42947 - 2.25422i) q^{37} +(15.2035 + 2.29156i) q^{38} +(-1.12518 - 7.46510i) q^{40} +(-3.48592 - 1.67873i) q^{41} +(-2.03931 + 0.982079i) q^{43} +(1.35313 + 1.98467i) q^{44} +(-1.33445 - 17.8071i) q^{46} +(-1.26639 - 3.22670i) q^{47} +(-6.99998 + 0.0176394i) q^{49} -3.45192i q^{50} +(2.49685 - 0.187113i) q^{52} +(-6.96046 - 7.50159i) q^{53} +(-0.533632 - 1.10810i) q^{55} +(-9.55472 - 4.58649i) q^{56} +(10.2354 - 1.54274i) q^{58} +(1.50981 + 1.02937i) q^{59} +(-6.85694 + 7.39003i) q^{61} +(4.17384 - 5.23382i) q^{62} +(6.88858 + 8.63800i) q^{64} +(-1.27843 - 0.0958053i) q^{65} +(-5.80262 - 10.0504i) q^{67} +(10.7481 - 18.6163i) q^{68} +(9.82758 + 6.68221i) q^{70} +(-15.2200 + 3.47387i) q^{71} +(8.21602 + 3.22455i) q^{73} +(7.35308 + 2.88587i) q^{74} +(-23.1486 + 5.28353i) q^{76} +(-1.70767 - 0.255190i) q^{77} +(4.60480 - 7.97575i) q^{79} +(2.06009 + 3.56818i) q^{80} +(9.19589 + 0.689136i) q^{82} +(5.98518 + 7.50517i) q^{83} +(-6.86243 + 8.60521i) q^{85} +(3.66939 - 3.95466i) q^{86} +(-2.15999 - 1.47266i) q^{88} +(4.81648 - 0.725967i) q^{89} +(-1.12039 + 1.40856i) q^{91} +(11.9650 + 24.8456i) q^{92} +(5.61939 + 6.05626i) q^{94} +(12.1233 - 0.908519i) q^{95} +8.08055i q^{97} +(15.5153 - 6.13446i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{41}{42}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.21867 + 0.870763i −1.56884 + 0.615722i −0.981129 0.193352i \(-0.938064\pi\)
−0.587706 + 0.809075i \(0.699969\pi\)
\(3\) 0 0
\(4\) 2.69816 2.50352i 1.34908 1.25176i
\(5\) −1.55712 + 1.06163i −0.696367 + 0.474775i −0.859042 0.511904i \(-0.828940\pi\)
0.162675 + 0.986680i \(0.447988\pi\)
\(6\) 0 0
\(7\) 0.00333353 + 2.64575i 0.00125996 + 0.999999i
\(8\) −1.73808 + 3.60916i −0.614503 + 1.27603i
\(9\) 0 0
\(10\) 2.53032 3.71129i 0.800156 1.17361i
\(11\) −0.0972657 + 0.645316i −0.0293267 + 0.194570i −0.998697 0.0510342i \(-0.983748\pi\)
0.969370 + 0.245604i \(0.0789864\pi\)
\(12\) 0 0
\(13\) 0.531850 + 0.424136i 0.147509 + 0.117634i 0.694464 0.719528i \(-0.255642\pi\)
−0.546955 + 0.837162i \(0.684213\pi\)
\(14\) −2.31122 5.86714i −0.617699 1.56806i
\(15\) 0 0
\(16\) 0.163378 2.18013i 0.0408445 0.545032i
\(17\) 5.58077 1.72144i 1.35354 0.417511i 0.468677 0.883369i \(-0.344731\pi\)
0.884859 + 0.465859i \(0.154254\pi\)
\(18\) 0 0
\(19\) −5.58665 3.22545i −1.28167 0.739970i −0.304513 0.952508i \(-0.598494\pi\)
−0.977153 + 0.212539i \(0.931827\pi\)
\(20\) −1.54355 + 6.76274i −0.345149 + 1.51219i
\(21\) 0 0
\(22\) −0.346117 1.51644i −0.0737924 0.323305i
\(23\) −2.20835 + 7.15930i −0.460473 + 1.49282i 0.366415 + 0.930451i \(0.380585\pi\)
−0.826889 + 0.562366i \(0.809891\pi\)
\(24\) 0 0
\(25\) −0.529125 + 1.34819i −0.105825 + 0.269638i
\(26\) −1.54932 0.477902i −0.303847 0.0937244i
\(27\) 0 0
\(28\) 6.63269 + 7.13030i 1.25346 + 1.34750i
\(29\) −4.23402 0.966388i −0.786239 0.179454i −0.189491 0.981883i \(-0.560684\pi\)
−0.596748 + 0.802429i \(0.703541\pi\)
\(30\) 0 0
\(31\) −2.43240 + 1.40435i −0.436872 + 0.252228i −0.702270 0.711911i \(-0.747830\pi\)
0.265398 + 0.964139i \(0.414497\pi\)
\(32\) −0.825605 2.67654i −0.145948 0.473151i
\(33\) 0 0
\(34\) −10.8829 + 8.67884i −1.86641 + 1.48841i
\(35\) −2.81400 4.11622i −0.475652 0.695769i
\(36\) 0 0
\(37\) −2.42947 2.25422i −0.399403 0.370592i 0.454745 0.890622i \(-0.349730\pi\)
−0.854148 + 0.520030i \(0.825921\pi\)
\(38\) 15.2035 + 2.29156i 2.46634 + 0.371741i
\(39\) 0 0
\(40\) −1.12518 7.46510i −0.177907 1.18034i
\(41\) −3.48592 1.67873i −0.544410 0.262174i 0.141403 0.989952i \(-0.454839\pi\)
−0.685813 + 0.727778i \(0.740553\pi\)
\(42\) 0 0
\(43\) −2.03931 + 0.982079i −0.310991 + 0.149766i −0.582869 0.812566i \(-0.698070\pi\)
0.271877 + 0.962332i \(0.412356\pi\)
\(44\) 1.35313 + 1.98467i 0.203991 + 0.299200i
\(45\) 0 0
\(46\) −1.33445 17.8071i −0.196755 2.62551i
\(47\) −1.26639 3.22670i −0.184722 0.470663i 0.808275 0.588805i \(-0.200401\pi\)
−0.992997 + 0.118142i \(0.962306\pi\)
\(48\) 0 0
\(49\) −6.99998 + 0.0176394i −0.999997 + 0.00251991i
\(50\) 3.45192i 0.488176i
\(51\) 0 0
\(52\) 2.49685 0.187113i 0.346251 0.0259479i
\(53\) −6.96046 7.50159i −0.956093 1.03042i −0.999508 0.0313660i \(-0.990014\pi\)
0.0434150 0.999057i \(-0.486176\pi\)
\(54\) 0 0
\(55\) −0.533632 1.10810i −0.0719549 0.149416i
\(56\) −9.55472 4.58649i −1.27680 0.612895i
\(57\) 0 0
\(58\) 10.2354 1.54274i 1.34397 0.202571i
\(59\) 1.50981 + 1.02937i 0.196561 + 0.134013i 0.657601 0.753366i \(-0.271571\pi\)
−0.461040 + 0.887379i \(0.652524\pi\)
\(60\) 0 0
\(61\) −6.85694 + 7.39003i −0.877942 + 0.946196i −0.998920 0.0464590i \(-0.985206\pi\)
0.120978 + 0.992655i \(0.461397\pi\)
\(62\) 4.17384 5.23382i 0.530078 0.664696i
\(63\) 0 0
\(64\) 6.88858 + 8.63800i 0.861072 + 1.07975i
\(65\) −1.27843 0.0958053i −0.158570 0.0118832i
\(66\) 0 0
\(67\) −5.80262 10.0504i −0.708903 1.22786i −0.965264 0.261275i \(-0.915857\pi\)
0.256361 0.966581i \(-0.417476\pi\)
\(68\) 10.7481 18.6163i 1.30340 2.25756i
\(69\) 0 0
\(70\) 9.82758 + 6.68221i 1.17462 + 0.798677i
\(71\) −15.2200 + 3.47387i −1.80628 + 0.412272i −0.986948 0.161042i \(-0.948514\pi\)
−0.819335 + 0.573314i \(0.805657\pi\)
\(72\) 0 0
\(73\) 8.21602 + 3.22455i 0.961612 + 0.377405i 0.793641 0.608387i \(-0.208183\pi\)
0.167971 + 0.985792i \(0.446278\pi\)
\(74\) 7.35308 + 2.88587i 0.854779 + 0.335476i
\(75\) 0 0
\(76\) −23.1486 + 5.28353i −2.65533 + 0.606062i
\(77\) −1.70767 0.255190i −0.194607 0.0290815i
\(78\) 0 0
\(79\) 4.60480 7.97575i 0.518080 0.897342i −0.481699 0.876337i \(-0.659980\pi\)
0.999779 0.0210049i \(-0.00668657\pi\)
\(80\) 2.06009 + 3.56818i 0.230325 + 0.398934i
\(81\) 0 0
\(82\) 9.19589 + 0.689136i 1.01552 + 0.0761024i
\(83\) 5.98518 + 7.50517i 0.656959 + 0.823800i 0.993008 0.118044i \(-0.0376625\pi\)
−0.336050 + 0.941844i \(0.609091\pi\)
\(84\) 0 0
\(85\) −6.86243 + 8.60521i −0.744335 + 0.933367i
\(86\) 3.66939 3.95466i 0.395680 0.426442i
\(87\) 0 0
\(88\) −2.15999 1.47266i −0.230256 0.156986i
\(89\) 4.81648 0.725967i 0.510545 0.0769524i 0.111283 0.993789i \(-0.464504\pi\)
0.399263 + 0.916836i \(0.369266\pi\)
\(90\) 0 0
\(91\) −1.12039 + 1.40856i −0.117448 + 0.147657i
\(92\) 11.9650 + 24.8456i 1.24744 + 2.59033i
\(93\) 0 0
\(94\) 5.61939 + 6.05626i 0.579596 + 0.624656i
\(95\) 12.1233 0.908519i 1.24383 0.0932121i
\(96\) 0 0
\(97\) 8.08055i 0.820455i 0.911983 + 0.410228i \(0.134551\pi\)
−0.911983 + 0.410228i \(0.865449\pi\)
\(98\) 15.5153 6.13446i 1.56728 0.619674i
\(99\) 0 0
\(100\) 1.94756 + 4.96230i 0.194756 + 0.496230i
\(101\) 1.39058 + 18.5561i 0.138368 + 1.84640i 0.446172 + 0.894947i \(0.352787\pi\)
−0.307803 + 0.951450i \(0.599594\pi\)
\(102\) 0 0
\(103\) 5.51061 + 8.08258i 0.542977 + 0.796400i 0.995441 0.0953822i \(-0.0304073\pi\)
−0.452464 + 0.891783i \(0.649455\pi\)
\(104\) −2.45517 + 1.18235i −0.240749 + 0.115939i
\(105\) 0 0
\(106\) 21.9751 + 10.5826i 2.13441 + 1.02788i
\(107\) 1.47113 + 9.76031i 0.142220 + 0.943565i 0.940137 + 0.340798i \(0.110697\pi\)
−0.797917 + 0.602767i \(0.794065\pi\)
\(108\) 0 0
\(109\) −6.35767 0.958265i −0.608955 0.0917852i −0.162677 0.986679i \(-0.552013\pi\)
−0.446278 + 0.894894i \(0.647251\pi\)
\(110\) 2.14884 + 1.99383i 0.204884 + 0.190105i
\(111\) 0 0
\(112\) 5.76861 + 0.424989i 0.545083 + 0.0401577i
\(113\) 10.0205 7.99108i 0.942649 0.751737i −0.0261316 0.999659i \(-0.508319\pi\)
0.968780 + 0.247921i \(0.0797475\pi\)
\(114\) 0 0
\(115\) −4.16185 13.4924i −0.388094 1.25817i
\(116\) −13.8434 + 7.99251i −1.28533 + 0.742086i
\(117\) 0 0
\(118\) −4.24611 0.969146i −0.390886 0.0892171i
\(119\) 4.57310 + 14.7596i 0.419216 + 1.35301i
\(120\) 0 0
\(121\) 10.1043 + 3.11677i 0.918575 + 0.283343i
\(122\) 8.77832 22.3668i 0.794752 2.02499i
\(123\) 0 0
\(124\) −3.04718 + 9.87872i −0.273645 + 0.887135i
\(125\) −2.70417 11.8478i −0.241868 1.05970i
\(126\) 0 0
\(127\) −1.96619 + 8.61442i −0.174471 + 0.764406i 0.809651 + 0.586912i \(0.199656\pi\)
−0.984122 + 0.177495i \(0.943201\pi\)
\(128\) −17.9537 10.3656i −1.58689 0.916194i
\(129\) 0 0
\(130\) 2.91984 0.900652i 0.256087 0.0789924i
\(131\) 0.225403 3.00779i 0.0196935 0.262792i −0.978663 0.205474i \(-0.934126\pi\)
0.998356 0.0573173i \(-0.0182547\pi\)
\(132\) 0 0
\(133\) 8.51512 14.7916i 0.738354 1.28260i
\(134\) 21.6256 + 17.2459i 1.86817 + 1.48982i
\(135\) 0 0
\(136\) −3.48687 + 23.1339i −0.298997 + 1.98371i
\(137\) −1.34187 + 1.96816i −0.114644 + 0.168151i −0.879272 0.476320i \(-0.841970\pi\)
0.764628 + 0.644472i \(0.222923\pi\)
\(138\) 0 0
\(139\) 9.71304 20.1693i 0.823849 1.71074i 0.128928 0.991654i \(-0.458846\pi\)
0.694921 0.719086i \(-0.255439\pi\)
\(140\) −17.8977 4.06131i −1.51263 0.343243i
\(141\) 0 0
\(142\) 30.7432 20.9604i 2.57992 1.75896i
\(143\) −0.325433 + 0.301957i −0.0272141 + 0.0252510i
\(144\) 0 0
\(145\) 7.61885 2.99018i 0.632711 0.248321i
\(146\) −21.0364 −1.74099
\(147\) 0 0
\(148\) −12.1986 −1.00272
\(149\) −11.0236 + 4.32645i −0.903089 + 0.354436i −0.771025 0.636805i \(-0.780256\pi\)
−0.132064 + 0.991241i \(0.542161\pi\)
\(150\) 0 0
\(151\) −15.9225 + 14.7740i −1.29576 + 1.20229i −0.329664 + 0.944098i \(0.606936\pi\)
−0.966094 + 0.258190i \(0.916874\pi\)
\(152\) 21.3512 14.5570i 1.73181 1.18073i
\(153\) 0 0
\(154\) 4.01096 0.920794i 0.323212 0.0741997i
\(155\) 2.29665 4.76905i 0.184472 0.383060i
\(156\) 0 0
\(157\) 13.5566 19.8839i 1.08194 1.58691i 0.310537 0.950561i \(-0.399491\pi\)
0.771401 0.636350i \(-0.219556\pi\)
\(158\) −3.27154 + 21.7052i −0.260269 + 1.72678i
\(159\) 0 0
\(160\) 4.12707 + 3.29123i 0.326273 + 0.260194i
\(161\) −18.9491 5.81888i −1.49340 0.458592i
\(162\) 0 0
\(163\) −1.41529 + 18.8857i −0.110854 + 1.47924i 0.613435 + 0.789745i \(0.289787\pi\)
−0.724289 + 0.689497i \(0.757832\pi\)
\(164\) −13.6083 + 4.19761i −1.06263 + 0.327778i
\(165\) 0 0
\(166\) −19.8144 11.4398i −1.53789 0.887902i
\(167\) −3.44716 + 15.1030i −0.266749 + 1.16870i 0.647021 + 0.762472i \(0.276014\pi\)
−0.913770 + 0.406231i \(0.866843\pi\)
\(168\) 0 0
\(169\) −2.78980 12.2229i −0.214600 0.940224i
\(170\) 7.73235 25.0677i 0.593044 1.92260i
\(171\) 0 0
\(172\) −3.04371 + 7.75525i −0.232081 + 0.591332i
\(173\) 2.35855 + 0.727517i 0.179318 + 0.0553121i 0.383114 0.923701i \(-0.374852\pi\)
−0.203796 + 0.979013i \(0.565328\pi\)
\(174\) 0 0
\(175\) −3.56873 1.39544i −0.269771 0.105485i
\(176\) 1.39098 + 0.317482i 0.104849 + 0.0239311i
\(177\) 0 0
\(178\) −10.0540 + 5.80469i −0.753580 + 0.435080i
\(179\) 0.843671 + 2.73511i 0.0630589 + 0.204432i 0.981620 0.190848i \(-0.0611238\pi\)
−0.918561 + 0.395280i \(0.870648\pi\)
\(180\) 0 0
\(181\) 11.8568 9.45547i 0.881308 0.702819i −0.0743711 0.997231i \(-0.523695\pi\)
0.955679 + 0.294411i \(0.0951235\pi\)
\(182\) 1.25925 4.10071i 0.0933415 0.303965i
\(183\) 0 0
\(184\) −22.0007 20.4137i −1.62192 1.50492i
\(185\) 6.17614 + 0.930903i 0.454079 + 0.0684414i
\(186\) 0 0
\(187\) 0.568055 + 3.76880i 0.0415403 + 0.275602i
\(188\) −11.4950 5.53572i −0.838362 0.403734i
\(189\) 0 0
\(190\) −26.1066 + 12.5723i −1.89397 + 0.912088i
\(191\) 3.80774 + 5.58493i 0.275518 + 0.404111i 0.938911 0.344160i \(-0.111836\pi\)
−0.663393 + 0.748272i \(0.730884\pi\)
\(192\) 0 0
\(193\) 0.511397 + 6.82411i 0.0368111 + 0.491210i 0.984891 + 0.173177i \(0.0554033\pi\)
−0.948080 + 0.318033i \(0.896978\pi\)
\(194\) −7.03624 17.9281i −0.505173 1.28716i
\(195\) 0 0
\(196\) −18.8429 + 17.5722i −1.34592 + 1.25516i
\(197\) 4.55093i 0.324240i 0.986771 + 0.162120i \(0.0518332\pi\)
−0.986771 + 0.162120i \(0.948167\pi\)
\(198\) 0 0
\(199\) −5.37432 + 0.402750i −0.380975 + 0.0285502i −0.263842 0.964566i \(-0.584990\pi\)
−0.117134 + 0.993116i \(0.537371\pi\)
\(200\) −3.94616 4.25295i −0.279036 0.300729i
\(201\) 0 0
\(202\) −19.2432 39.9589i −1.35395 2.81150i
\(203\) 2.54271 11.2054i 0.178463 0.786464i
\(204\) 0 0
\(205\) 7.21021 1.08676i 0.503583 0.0759029i
\(206\) −19.2642 13.1341i −1.34220 0.915098i
\(207\) 0 0
\(208\) 1.01156 1.09021i 0.0701393 0.0755922i
\(209\) 2.62483 3.29143i 0.181563 0.227673i
\(210\) 0 0
\(211\) −3.02491 3.79311i −0.208243 0.261129i 0.666731 0.745299i \(-0.267693\pi\)
−0.874974 + 0.484170i \(0.839122\pi\)
\(212\) −37.5608 2.81479i −2.57969 0.193321i
\(213\) 0 0
\(214\) −11.7629 20.3739i −0.804093 1.39273i
\(215\) 2.13285 3.69421i 0.145459 0.251943i
\(216\) 0 0
\(217\) −3.72366 6.43084i −0.252778 0.436554i
\(218\) 14.9400 3.40996i 1.01186 0.230951i
\(219\) 0 0
\(220\) −4.21397 1.65386i −0.284106 0.111503i
\(221\) 3.69826 + 1.45146i 0.248772 + 0.0976358i
\(222\) 0 0
\(223\) 8.69380 1.98430i 0.582180 0.132879i 0.0787193 0.996897i \(-0.474917\pi\)
0.503461 + 0.864018i \(0.332060\pi\)
\(224\) 7.07871 2.19327i 0.472966 0.146544i
\(225\) 0 0
\(226\) −15.2738 + 26.4550i −1.01600 + 1.75976i
\(227\) 7.04102 + 12.1954i 0.467329 + 0.809437i 0.999303 0.0373231i \(-0.0118831\pi\)
−0.531974 + 0.846760i \(0.678550\pi\)
\(228\) 0 0
\(229\) 18.1348 + 1.35902i 1.19838 + 0.0898063i 0.658926 0.752208i \(-0.271011\pi\)
0.539456 + 0.842014i \(0.318630\pi\)
\(230\) 20.9824 + 26.3111i 1.38354 + 1.73490i
\(231\) 0 0
\(232\) 10.8469 13.6016i 0.712135 0.892989i
\(233\) 7.25919 7.82354i 0.475565 0.512537i −0.449015 0.893524i \(-0.648225\pi\)
0.924581 + 0.380987i \(0.124416\pi\)
\(234\) 0 0
\(235\) 5.39749 + 3.67995i 0.352093 + 0.240053i
\(236\) 6.65076 1.00244i 0.432928 0.0652533i
\(237\) 0 0
\(238\) −22.9983 28.7645i −1.49076 1.86453i
\(239\) 9.07961 + 18.8540i 0.587311 + 1.21956i 0.956913 + 0.290374i \(0.0937799\pi\)
−0.369602 + 0.929190i \(0.620506\pi\)
\(240\) 0 0
\(241\) −14.5707 15.7035i −0.938582 1.01155i −0.999910 0.0134331i \(-0.995724\pi\)
0.0613279 0.998118i \(-0.480466\pi\)
\(242\) −25.1321 + 1.88339i −1.61555 + 0.121069i
\(243\) 0 0
\(244\) 37.1060i 2.37547i
\(245\) 10.8811 7.45885i 0.695169 0.476529i
\(246\) 0 0
\(247\) −1.60323 4.08496i −0.102011 0.259920i
\(248\) −0.840806 11.2198i −0.0533913 0.712457i
\(249\) 0 0
\(250\) 16.3162 + 23.9315i 1.03193 + 1.51356i
\(251\) −3.25960 + 1.56974i −0.205744 + 0.0990812i −0.533918 0.845536i \(-0.679281\pi\)
0.328174 + 0.944617i \(0.393567\pi\)
\(252\) 0 0
\(253\) −4.40521 2.12144i −0.276953 0.133374i
\(254\) −3.13881 20.8246i −0.196946 1.30665i
\(255\) 0 0
\(256\) 27.0091 + 4.07097i 1.68807 + 0.254436i
\(257\) −7.50781 6.96623i −0.468324 0.434542i 0.410375 0.911917i \(-0.365398\pi\)
−0.878700 + 0.477375i \(0.841588\pi\)
\(258\) 0 0
\(259\) 5.95600 6.43529i 0.370088 0.399869i
\(260\) −3.68926 + 2.94209i −0.228798 + 0.182461i
\(261\) 0 0
\(262\) 2.11898 + 6.86956i 0.130911 + 0.424403i
\(263\) 3.46319 1.99947i 0.213549 0.123293i −0.389411 0.921064i \(-0.627321\pi\)
0.602960 + 0.797772i \(0.293988\pi\)
\(264\) 0 0
\(265\) 18.8022 + 4.29148i 1.15501 + 0.263624i
\(266\) −6.01222 + 40.2324i −0.368633 + 2.46680i
\(267\) 0 0
\(268\) −40.8179 12.5906i −2.49335 0.769096i
\(269\) 2.48226 6.32470i 0.151346 0.385624i −0.835013 0.550230i \(-0.814540\pi\)
0.986359 + 0.164606i \(0.0526353\pi\)
\(270\) 0 0
\(271\) −6.74647 + 21.8715i −0.409819 + 1.32860i 0.481986 + 0.876179i \(0.339916\pi\)
−0.891805 + 0.452421i \(0.850561\pi\)
\(272\) −2.84118 12.4480i −0.172272 0.754773i
\(273\) 0 0
\(274\) 1.26336 5.53515i 0.0763225 0.334391i
\(275\) −0.818542 0.472585i −0.0493599 0.0284980i
\(276\) 0 0
\(277\) −8.19644 + 2.52827i −0.492476 + 0.151909i −0.531039 0.847347i \(-0.678198\pi\)
0.0385627 + 0.999256i \(0.487722\pi\)
\(278\) −3.98730 + 53.2068i −0.239142 + 3.19113i
\(279\) 0 0
\(280\) 19.7470 3.00184i 1.18011 0.179394i
\(281\) −13.5840 10.8329i −0.810356 0.646238i 0.128051 0.991768i \(-0.459128\pi\)
−0.938408 + 0.345530i \(0.887699\pi\)
\(282\) 0 0
\(283\) −4.82901 + 32.0384i −0.287055 + 1.90449i 0.122969 + 0.992411i \(0.460758\pi\)
−0.410024 + 0.912075i \(0.634480\pi\)
\(284\) −32.3691 + 47.4767i −1.92075 + 2.81722i
\(285\) 0 0
\(286\) 0.459094 0.953318i 0.0271468 0.0563709i
\(287\) 4.42988 9.22848i 0.261488 0.544740i
\(288\) 0 0
\(289\) 14.1356 9.63750i 0.831507 0.566912i
\(290\) −14.3000 + 13.2684i −0.839723 + 0.779149i
\(291\) 0 0
\(292\) 30.2408 11.8686i 1.76971 0.694560i
\(293\) 14.5324 0.848993 0.424496 0.905430i \(-0.360451\pi\)
0.424496 + 0.905430i \(0.360451\pi\)
\(294\) 0 0
\(295\) −3.44377 −0.200504
\(296\) 12.3584 4.85033i 0.718320 0.281920i
\(297\) 0 0
\(298\) 20.6904 19.1979i 1.19856 1.11210i
\(299\) −4.21103 + 2.87103i −0.243530 + 0.166036i
\(300\) 0 0
\(301\) −2.60513 5.39222i −0.150157 0.310802i
\(302\) 22.4622 46.6433i 1.29256 2.68402i
\(303\) 0 0
\(304\) −7.94463 + 11.6526i −0.455656 + 0.668324i
\(305\) 2.83164 18.7867i 0.162139 1.07573i
\(306\) 0 0
\(307\) 4.07997 + 3.25367i 0.232856 + 0.185697i 0.732966 0.680265i \(-0.238135\pi\)
−0.500109 + 0.865962i \(0.666707\pi\)
\(308\) −5.24643 + 3.58665i −0.298943 + 0.204368i
\(309\) 0 0
\(310\) −0.942800 + 12.5808i −0.0535474 + 0.714541i
\(311\) 2.72915 0.841833i 0.154756 0.0477359i −0.216409 0.976303i \(-0.569435\pi\)
0.371165 + 0.928567i \(0.378958\pi\)
\(312\) 0 0
\(313\) 15.4116 + 8.89791i 0.871117 + 0.502940i 0.867719 0.497055i \(-0.165585\pi\)
0.00339768 + 0.999994i \(0.498918\pi\)
\(314\) −12.7635 + 55.9205i −0.720285 + 3.15578i
\(315\) 0 0
\(316\) −7.54300 33.0480i −0.424327 1.85910i
\(317\) 0.955904 3.09897i 0.0536889 0.174055i −0.924757 0.380558i \(-0.875732\pi\)
0.978446 + 0.206503i \(0.0662082\pi\)
\(318\) 0 0
\(319\) 1.03545 2.63829i 0.0579741 0.147716i
\(320\) −19.8967 6.13733i −1.11226 0.343087i
\(321\) 0 0
\(322\) 47.1086 3.58999i 2.62526 0.200062i
\(323\) −36.7303 8.38344i −2.04373 0.466467i
\(324\) 0 0
\(325\) −0.853231 + 0.492613i −0.0473287 + 0.0273253i
\(326\) −13.3049 43.1335i −0.736891 2.38894i
\(327\) 0 0
\(328\) 12.1176 9.66348i 0.669083 0.533576i
\(329\) 8.53283 3.36130i 0.470430 0.185315i
\(330\) 0 0
\(331\) −13.3975 12.4310i −0.736392 0.683272i 0.219953 0.975510i \(-0.429409\pi\)
−0.956346 + 0.292238i \(0.905600\pi\)
\(332\) 34.9383 + 5.26610i 1.91749 + 0.289015i
\(333\) 0 0
\(334\) −5.50302 36.5101i −0.301112 1.99775i
\(335\) 19.7053 + 9.48955i 1.07661 + 0.518470i
\(336\) 0 0
\(337\) −12.9190 + 6.22147i −0.703743 + 0.338905i −0.751297 0.659964i \(-0.770572\pi\)
0.0475542 + 0.998869i \(0.484857\pi\)
\(338\) 16.8329 + 24.6893i 0.915589 + 1.34292i
\(339\) 0 0
\(340\) 3.02745 + 40.3985i 0.164186 + 2.19091i
\(341\) −0.669658 1.70626i −0.0362640 0.0923992i
\(342\) 0 0
\(343\) −0.0700040 18.5201i −0.00377986 0.999993i
\(344\) 9.06711i 0.488866i
\(345\) 0 0
\(346\) −5.86634 + 0.439622i −0.315377 + 0.0236342i
\(347\) 8.48613 + 9.14588i 0.455560 + 0.490976i 0.918504 0.395411i \(-0.129398\pi\)
−0.462945 + 0.886387i \(0.653207\pi\)
\(348\) 0 0
\(349\) −5.62020 11.6705i −0.300843 0.624706i 0.694671 0.719328i \(-0.255550\pi\)
−0.995513 + 0.0946218i \(0.969836\pi\)
\(350\) 9.13293 0.0115071i 0.488176 0.000615081i
\(351\) 0 0
\(352\) 1.80752 0.272440i 0.0963411 0.0145211i
\(353\) −21.8743 14.9136i −1.16425 0.793773i −0.182363 0.983231i \(-0.558374\pi\)
−0.981889 + 0.189458i \(0.939327\pi\)
\(354\) 0 0
\(355\) 20.0115 21.5673i 1.06210 1.14467i
\(356\) 11.1781 14.0169i 0.592440 0.742896i
\(357\) 0 0
\(358\) −4.25346 5.33367i −0.224802 0.281893i
\(359\) −8.44775 0.633071i −0.445855 0.0334122i −0.150089 0.988673i \(-0.547956\pi\)
−0.295766 + 0.955260i \(0.595575\pi\)
\(360\) 0 0
\(361\) 11.3071 + 19.5845i 0.595111 + 1.03076i
\(362\) −18.0728 + 31.3030i −0.949885 + 1.64525i
\(363\) 0 0
\(364\) 0.503378 + 6.60542i 0.0263842 + 0.346218i
\(365\) −16.2166 + 3.70134i −0.848818 + 0.193737i
\(366\) 0 0
\(367\) 4.17842 + 1.63991i 0.218112 + 0.0856025i 0.471881 0.881662i \(-0.343575\pi\)
−0.253769 + 0.967265i \(0.581670\pi\)
\(368\) 15.2474 + 5.98416i 0.794825 + 0.311946i
\(369\) 0 0
\(370\) −14.5134 + 3.31259i −0.754516 + 0.172213i
\(371\) 19.8241 18.4406i 1.02922 0.957390i
\(372\) 0 0
\(373\) −13.0224 + 22.5554i −0.674274 + 1.16788i 0.302407 + 0.953179i \(0.402210\pi\)
−0.976681 + 0.214697i \(0.931123\pi\)
\(374\) −4.54206 7.86707i −0.234864 0.406797i
\(375\) 0 0
\(376\) 13.8468 + 1.03767i 0.714092 + 0.0535138i
\(377\) −1.84199 2.30978i −0.0948671 0.118960i
\(378\) 0 0
\(379\) −10.1826 + 12.7685i −0.523044 + 0.655876i −0.971252 0.238053i \(-0.923491\pi\)
0.448209 + 0.893929i \(0.352062\pi\)
\(380\) 30.4362 32.8024i 1.56134 1.68273i
\(381\) 0 0
\(382\) −13.3113 9.07546i −0.681063 0.464341i
\(383\) −19.4310 + 2.92875i −0.992878 + 0.149652i −0.625337 0.780355i \(-0.715038\pi\)
−0.367541 + 0.930007i \(0.619800\pi\)
\(384\) 0 0
\(385\) 2.92997 1.41555i 0.149325 0.0721431i
\(386\) −7.07680 14.6951i −0.360200 0.747963i
\(387\) 0 0
\(388\) 20.2298 + 21.8026i 1.02701 + 1.10686i
\(389\) 7.09818 0.531935i 0.359892 0.0269702i 0.106443 0.994319i \(-0.466054\pi\)
0.253449 + 0.967349i \(0.418435\pi\)
\(390\) 0 0
\(391\) 43.7560i 2.21283i
\(392\) 12.1028 25.2947i 0.611286 1.27757i
\(393\) 0 0
\(394\) −3.96278 10.0970i −0.199642 0.508679i
\(395\) 1.29704 + 17.3078i 0.0652613 + 0.870851i
\(396\) 0 0
\(397\) 14.4992 + 21.2664i 0.727693 + 1.06733i 0.994618 + 0.103612i \(0.0330399\pi\)
−0.266925 + 0.963717i \(0.586008\pi\)
\(398\) 11.5731 5.57333i 0.580109 0.279366i
\(399\) 0 0
\(400\) 2.85277 + 1.37382i 0.142639 + 0.0686912i
\(401\) 5.73624 + 38.0575i 0.286454 + 1.90050i 0.416745 + 0.909023i \(0.363171\pi\)
−0.130291 + 0.991476i \(0.541591\pi\)
\(402\) 0 0
\(403\) −1.88931 0.284767i −0.0941131 0.0141853i
\(404\) 50.2075 + 46.5858i 2.49792 + 2.31773i
\(405\) 0 0
\(406\) 4.11581 + 27.0751i 0.204264 + 1.34372i
\(407\) 1.69099 1.34852i 0.0838192 0.0668436i
\(408\) 0 0
\(409\) 7.66146 + 24.8378i 0.378835 + 1.22815i 0.921558 + 0.388240i \(0.126917\pi\)
−0.542724 + 0.839911i \(0.682607\pi\)
\(410\) −15.0508 + 8.68956i −0.743304 + 0.429147i
\(411\) 0 0
\(412\) 35.1034 + 8.01213i 1.72942 + 0.394729i
\(413\) −2.71843 + 3.99801i −0.133765 + 0.196729i
\(414\) 0 0
\(415\) −17.2874 5.33245i −0.848604 0.261760i
\(416\) 0.696122 1.77369i 0.0341302 0.0869623i
\(417\) 0 0
\(418\) −2.95756 + 9.58819i −0.144659 + 0.468974i
\(419\) −2.78683 12.2099i −0.136146 0.596493i −0.996261 0.0863937i \(-0.972466\pi\)
0.860115 0.510099i \(-0.170391\pi\)
\(420\) 0 0
\(421\) 0.571227 2.50271i 0.0278399 0.121975i −0.959099 0.283072i \(-0.908646\pi\)
0.986938 + 0.161098i \(0.0515035\pi\)
\(422\) 10.0142 + 5.78168i 0.487482 + 0.281448i
\(423\) 0 0
\(424\) 39.1723 12.0830i 1.90237 0.586804i
\(425\) −0.632100 + 8.43479i −0.0306614 + 0.409147i
\(426\) 0 0
\(427\) −19.5750 18.1171i −0.947302 0.876749i
\(428\) 28.4045 + 22.6518i 1.37298 + 1.09492i
\(429\) 0 0
\(430\) −1.51531 + 10.0534i −0.0730748 + 0.484819i
\(431\) 22.5961 33.1424i 1.08842 1.59641i 0.330816 0.943695i \(-0.392676\pi\)
0.757601 0.652718i \(-0.226371\pi\)
\(432\) 0 0
\(433\) 11.9382 24.7899i 0.573713 1.19133i −0.389110 0.921191i \(-0.627217\pi\)
0.962822 0.270135i \(-0.0870684\pi\)
\(434\) 13.8613 + 11.0255i 0.665364 + 0.529240i
\(435\) 0 0
\(436\) −19.5530 + 13.3310i −0.936421 + 0.638441i
\(437\) 35.4293 32.8736i 1.69481 1.57256i
\(438\) 0 0
\(439\) −37.4380 + 14.6933i −1.78682 + 0.701274i −0.790805 + 0.612069i \(0.790338\pi\)
−0.996013 + 0.0892056i \(0.971567\pi\)
\(440\) 4.92679 0.234876
\(441\) 0 0
\(442\) −9.46909 −0.450399
\(443\) −13.1010 + 5.14177i −0.622448 + 0.244293i −0.655541 0.755159i \(-0.727559\pi\)
0.0330932 + 0.999452i \(0.489464\pi\)
\(444\) 0 0
\(445\) −6.72915 + 6.24374i −0.318992 + 0.295981i
\(446\) −17.5608 + 11.9728i −0.831528 + 0.566926i
\(447\) 0 0
\(448\) −22.8310 + 18.2542i −1.07866 + 0.862432i
\(449\) 4.22605 8.77548i 0.199439 0.414140i −0.777131 0.629339i \(-0.783326\pi\)
0.976570 + 0.215199i \(0.0690400\pi\)
\(450\) 0 0
\(451\) 1.42237 2.08624i 0.0669770 0.0982372i
\(452\) 7.03101 46.6477i 0.330711 2.19412i
\(453\) 0 0
\(454\) −26.2410 20.9265i −1.23155 0.982129i
\(455\) 0.249215 3.38273i 0.0116834 0.158585i
\(456\) 0 0
\(457\) −1.07114 + 14.2933i −0.0501057 + 0.668614i 0.914444 + 0.404712i \(0.132628\pi\)
−0.964550 + 0.263901i \(0.914991\pi\)
\(458\) −41.4185 + 12.7759i −1.93536 + 0.596979i
\(459\) 0 0
\(460\) −45.0078 25.9853i −2.09850 1.21157i
\(461\) 5.71927 25.0577i 0.266373 1.16706i −0.647826 0.761789i \(-0.724321\pi\)
0.914198 0.405267i \(-0.132821\pi\)
\(462\) 0 0
\(463\) −1.45321 6.36694i −0.0675365 0.295897i 0.929868 0.367892i \(-0.119920\pi\)
−0.997405 + 0.0719954i \(0.977063\pi\)
\(464\) −2.79860 + 9.07282i −0.129922 + 0.421195i
\(465\) 0 0
\(466\) −9.29327 + 23.6789i −0.430503 + 1.09690i
\(467\) −15.0319 4.63672i −0.695592 0.214562i −0.0732575 0.997313i \(-0.523340\pi\)
−0.622335 + 0.782751i \(0.713816\pi\)
\(468\) 0 0
\(469\) 26.5716 15.3858i 1.22696 0.710450i
\(470\) −15.1796 3.46464i −0.700183 0.159812i
\(471\) 0 0
\(472\) −6.33933 + 3.66001i −0.291791 + 0.168466i
\(473\) −0.435396 1.41152i −0.0200195 0.0649018i
\(474\) 0 0
\(475\) 7.30455 5.82519i 0.335156 0.267278i
\(476\) 49.2899 + 28.3748i 2.25920 + 1.30056i
\(477\) 0 0
\(478\) −36.5620 33.9246i −1.67231 1.55168i
\(479\) 28.4563 + 4.28910i 1.30020 + 0.195974i 0.762406 0.647100i \(-0.224018\pi\)
0.537798 + 0.843074i \(0.319256\pi\)
\(480\) 0 0
\(481\) −0.336018 2.22934i −0.0153211 0.101649i
\(482\) 46.0016 + 22.1532i 2.09531 + 1.00905i
\(483\) 0 0
\(484\) 35.0660 16.8869i 1.59391 0.767585i
\(485\) −8.57855 12.5824i −0.389532 0.571338i
\(486\) 0 0
\(487\) 0.958609 + 12.7918i 0.0434387 + 0.579650i 0.975877 + 0.218321i \(0.0700579\pi\)
−0.932438 + 0.361329i \(0.882323\pi\)
\(488\) −14.7539 37.5922i −0.667876 1.70172i
\(489\) 0 0
\(490\) −17.6467 + 26.0236i −0.797196 + 1.17563i
\(491\) 13.5607i 0.611987i −0.952034 0.305994i \(-0.901011\pi\)
0.952034 0.305994i \(-0.0989886\pi\)
\(492\) 0 0
\(493\) −25.2927 + 1.89543i −1.13913 + 0.0853657i
\(494\) 7.11406 + 7.66714i 0.320077 + 0.344961i
\(495\) 0 0
\(496\) 2.66425 + 5.53238i 0.119629 + 0.248411i
\(497\) −9.24172 40.2568i −0.414548 1.80576i
\(498\) 0 0
\(499\) −6.55494 + 0.987999i −0.293440 + 0.0442289i −0.294112 0.955771i \(-0.595024\pi\)
0.000672682 1.00000i \(0.499786\pi\)
\(500\) −36.9574 25.1971i −1.65278 1.12685i
\(501\) 0 0
\(502\) 5.86510 6.32108i 0.261772 0.282123i
\(503\) −14.0917 + 17.6704i −0.628316 + 0.787883i −0.989488 0.144616i \(-0.953805\pi\)
0.361172 + 0.932499i \(0.382377\pi\)
\(504\) 0 0
\(505\) −21.8650 27.4178i −0.972979 1.22008i
\(506\) 11.6210 + 0.870872i 0.516615 + 0.0387150i
\(507\) 0 0
\(508\) 16.2613 + 28.1654i 0.721480 + 1.24964i
\(509\) 8.18340 14.1741i 0.362723 0.628254i −0.625685 0.780076i \(-0.715181\pi\)
0.988408 + 0.151821i \(0.0485139\pi\)
\(510\) 0 0
\(511\) −8.50396 + 21.7483i −0.376193 + 0.962087i
\(512\) −23.0465 + 5.26021i −1.01852 + 0.232471i
\(513\) 0 0
\(514\) 22.7233 + 8.91823i 1.00228 + 0.393366i
\(515\) −17.1614 6.73536i −0.756222 0.296795i
\(516\) 0 0
\(517\) 2.20542 0.503373i 0.0969943 0.0221383i
\(518\) −7.61078 + 19.4640i −0.334399 + 0.855201i
\(519\) 0 0
\(520\) 2.56779 4.44755i 0.112605 0.195038i
\(521\) 4.55691 + 7.89280i 0.199642 + 0.345790i 0.948412 0.317040i \(-0.102689\pi\)
−0.748770 + 0.662829i \(0.769355\pi\)
\(522\) 0 0
\(523\) −1.57530 0.118053i −0.0688831 0.00516208i 0.0402439 0.999190i \(-0.487186\pi\)
−0.109127 + 0.994028i \(0.534806\pi\)
\(524\) −6.92189 8.67978i −0.302384 0.379178i
\(525\) 0 0
\(526\) −5.94259 + 7.45178i −0.259109 + 0.324913i
\(527\) −11.1572 + 12.0246i −0.486014 + 0.523799i
\(528\) 0 0
\(529\) −27.3753 18.6641i −1.19023 0.811484i
\(530\) −45.4528 + 6.85090i −1.97434 + 0.297584i
\(531\) 0 0
\(532\) −14.0561 61.2279i −0.609407 2.65457i
\(533\) −1.14198 2.37134i −0.0494646 0.102714i
\(534\) 0 0
\(535\) −12.6526 13.6362i −0.547019 0.589546i
\(536\) 46.3590 3.47413i 2.00240 0.150059i
\(537\) 0 0
\(538\) 16.1939i 0.698167i
\(539\) 0.669475 4.51891i 0.0288363 0.194643i
\(540\) 0 0
\(541\) 13.8278 + 35.2327i 0.594505 + 1.51477i 0.838446 + 0.544984i \(0.183464\pi\)
−0.243942 + 0.969790i \(0.578441\pi\)
\(542\) −4.07673 54.4002i −0.175111 2.33669i
\(543\) 0 0
\(544\) −9.21503 13.5160i −0.395091 0.579492i
\(545\) 10.9170 5.25736i 0.467634 0.225200i
\(546\) 0 0
\(547\) 24.3589 + 11.7306i 1.04151 + 0.501566i 0.874823 0.484443i \(-0.160978\pi\)
0.166690 + 0.986009i \(0.446692\pi\)
\(548\) 1.30676 + 8.66981i 0.0558222 + 0.370356i
\(549\) 0 0
\(550\) 2.22758 + 0.335754i 0.0949844 + 0.0143166i
\(551\) 20.5370 + 19.0555i 0.874904 + 0.811793i
\(552\) 0 0
\(553\) 21.1172 + 12.1566i 0.897994 + 0.516949i
\(554\) 15.9837 12.7465i 0.679080 0.541549i
\(555\) 0 0
\(556\) −24.2871 78.7368i −1.03000 3.33918i
\(557\) −17.8120 + 10.2837i −0.754717 + 0.435736i −0.827396 0.561620i \(-0.810178\pi\)
0.0726790 + 0.997355i \(0.476845\pi\)
\(558\) 0 0
\(559\) −1.50114 0.342626i −0.0634915 0.0144915i
\(560\) −9.43363 + 5.46237i −0.398644 + 0.230827i
\(561\) 0 0
\(562\) 39.5714 + 12.2062i 1.66922 + 0.514886i
\(563\) −8.44139 + 21.5083i −0.355762 + 0.906468i 0.635203 + 0.772346i \(0.280917\pi\)
−0.990965 + 0.134122i \(0.957179\pi\)
\(564\) 0 0
\(565\) −7.11959 + 23.0812i −0.299524 + 0.971032i
\(566\) −17.1839 75.2875i −0.722292 3.16457i
\(567\) 0 0
\(568\) 13.9158 60.9693i 0.583895 2.55821i
\(569\) −12.6638 7.31147i −0.530895 0.306513i 0.210486 0.977597i \(-0.432495\pi\)
−0.741381 + 0.671084i \(0.765829\pi\)
\(570\) 0 0
\(571\) 24.5887 7.58460i 1.02900 0.317406i 0.266119 0.963940i \(-0.414259\pi\)
0.762885 + 0.646535i \(0.223782\pi\)
\(572\) −0.122111 + 1.62946i −0.00510571 + 0.0681310i
\(573\) 0 0
\(574\) −1.79263 + 24.3323i −0.0748228 + 1.01561i
\(575\) −8.48359 6.76544i −0.353790 0.282138i
\(576\) 0 0
\(577\) 5.85704 38.8589i 0.243832 1.61772i −0.446885 0.894591i \(-0.647467\pi\)
0.690717 0.723126i \(-0.257295\pi\)
\(578\) −22.9703 + 33.6912i −0.955437 + 1.40137i
\(579\) 0 0
\(580\) 13.0709 27.1419i 0.542738 1.12701i
\(581\) −19.8369 + 15.8603i −0.822972 + 0.657996i
\(582\) 0 0
\(583\) 5.51791 3.76205i 0.228529 0.155808i
\(584\) −25.9180 + 24.0484i −1.07249 + 0.995129i
\(585\) 0 0
\(586\) −32.2426 + 12.6543i −1.33193 + 0.522744i
\(587\) −28.0801 −1.15899 −0.579495 0.814976i \(-0.696750\pi\)
−0.579495 + 0.814976i \(0.696750\pi\)
\(588\) 0 0
\(589\) 18.1186 0.746565
\(590\) 7.64059 2.99871i 0.314558 0.123455i
\(591\) 0 0
\(592\) −5.31141 + 4.92827i −0.218297 + 0.202550i
\(593\) 21.7849 14.8527i 0.894598 0.609927i −0.0263324 0.999653i \(-0.508383\pi\)
0.920931 + 0.389727i \(0.127430\pi\)
\(594\) 0 0
\(595\) −22.7901 18.1276i −0.934304 0.743158i
\(596\) −18.9121 + 39.2713i −0.774668 + 1.60861i
\(597\) 0 0
\(598\) 6.84289 10.0367i 0.279827 0.410430i
\(599\) −2.15673 + 14.3089i −0.0881215 + 0.584648i 0.900573 + 0.434704i \(0.143147\pi\)
−0.988695 + 0.149943i \(0.952091\pi\)
\(600\) 0 0
\(601\) 17.2316 + 13.7417i 0.702890 + 0.560536i 0.908391 0.418121i \(-0.137311\pi\)
−0.205502 + 0.978657i \(0.565883\pi\)
\(602\) 10.4753 + 9.69510i 0.426940 + 0.395143i
\(603\) 0 0
\(604\) −5.97456 + 79.7249i −0.243101 + 3.24396i
\(605\) −19.0426 + 5.87385i −0.774190 + 0.238806i
\(606\) 0 0
\(607\) 20.0654 + 11.5848i 0.814429 + 0.470211i 0.848491 0.529209i \(-0.177511\pi\)
−0.0340628 + 0.999420i \(0.510845\pi\)
\(608\) −4.02071 + 17.6159i −0.163061 + 0.714418i
\(609\) 0 0
\(610\) 10.0763 + 44.1472i 0.407978 + 1.78747i
\(611\) 0.695034 2.25324i 0.0281181 0.0911565i
\(612\) 0 0
\(613\) 1.46128 3.72327i 0.0590204 0.150381i −0.898322 0.439338i \(-0.855213\pi\)
0.957342 + 0.288957i \(0.0933083\pi\)
\(614\) −11.8853 3.66612i −0.479651 0.147953i
\(615\) 0 0
\(616\) 3.88908 5.71970i 0.156696 0.230453i
\(617\) 15.7453 + 3.59377i 0.633884 + 0.144680i 0.527376 0.849632i \(-0.323176\pi\)
0.106508 + 0.994312i \(0.466033\pi\)
\(618\) 0 0
\(619\) −18.0870 + 10.4425i −0.726977 + 0.419720i −0.817315 0.576191i \(-0.804538\pi\)
0.0903385 + 0.995911i \(0.471205\pi\)
\(620\) −5.74270 18.6174i −0.230632 0.747692i
\(621\) 0 0
\(622\) −5.32205 + 4.24419i −0.213395 + 0.170177i
\(623\) 1.93678 + 12.7408i 0.0775956 + 0.510448i
\(624\) 0 0
\(625\) 11.4802 + 10.6521i 0.459210 + 0.426085i
\(626\) −41.9413 6.32163i −1.67631 0.252663i
\(627\) 0 0
\(628\) −13.2020 87.5893i −0.526816 3.49519i
\(629\) −17.4388 8.39810i −0.695332 0.334854i
\(630\) 0 0
\(631\) 31.5757 15.2061i 1.25701 0.605343i 0.317627 0.948216i \(-0.397114\pi\)
0.939382 + 0.342872i \(0.111400\pi\)
\(632\) 20.7822 + 30.4819i 0.826672 + 1.21251i
\(633\) 0 0
\(634\) 0.577630 + 7.70794i 0.0229406 + 0.306122i
\(635\) −6.08373 15.5011i −0.241426 0.615142i
\(636\) 0 0
\(637\) −3.73042 2.95956i −0.147805 0.117262i
\(638\) 6.75512i 0.267438i
\(639\) 0 0
\(640\) 38.9605 2.91968i 1.54005 0.115411i
\(641\) 18.0974 + 19.5044i 0.714806 + 0.770377i 0.981097 0.193515i \(-0.0619889\pi\)
−0.266292 + 0.963892i \(0.585798\pi\)
\(642\) 0 0
\(643\) −5.79296 12.0292i −0.228452 0.474386i 0.754960 0.655771i \(-0.227656\pi\)
−0.983412 + 0.181385i \(0.941942\pi\)
\(644\) −65.6952 + 31.7392i −2.58876 + 1.25070i
\(645\) 0 0
\(646\) 88.7922 13.3833i 3.49348 0.526558i
\(647\) 39.3133 + 26.8034i 1.54557 + 1.05375i 0.972113 + 0.234512i \(0.0753492\pi\)
0.573454 + 0.819238i \(0.305603\pi\)
\(648\) 0 0
\(649\) −0.811122 + 0.874182i −0.0318393 + 0.0343147i
\(650\) 1.46409 1.83591i 0.0574262 0.0720102i
\(651\) 0 0
\(652\) 43.4621 + 54.4998i 1.70211 + 2.13438i
\(653\) −3.16428 0.237130i −0.123828 0.00927961i 0.0126721 0.999920i \(-0.495966\pi\)
−0.136500 + 0.990640i \(0.543585\pi\)
\(654\) 0 0
\(655\) 2.84218 + 4.92280i 0.111053 + 0.192350i
\(656\) −4.22937 + 7.32549i −0.165129 + 0.286012i
\(657\) 0 0
\(658\) −16.0046 + 14.8877i −0.623925 + 0.580382i
\(659\) 22.7243 5.18667i 0.885213 0.202044i 0.244338 0.969690i \(-0.421429\pi\)
0.640874 + 0.767646i \(0.278572\pi\)
\(660\) 0 0
\(661\) −2.60493 1.02236i −0.101320 0.0397652i 0.314140 0.949377i \(-0.398284\pi\)
−0.415460 + 0.909612i \(0.636379\pi\)
\(662\) 40.5491 + 15.9143i 1.57598 + 0.618528i
\(663\) 0 0
\(664\) −37.4901 + 8.55686i −1.45490 + 0.332071i
\(665\) 2.44413 + 32.0723i 0.0947792 + 1.24371i
\(666\) 0 0
\(667\) 16.2689 28.1785i 0.629933 1.09108i
\(668\) 28.5097 + 49.3802i 1.10307 + 1.91058i
\(669\) 0 0
\(670\) −51.9826 3.89555i −2.00826 0.150498i
\(671\) −4.10196 5.14369i −0.158354 0.198570i
\(672\) 0 0
\(673\) −2.74477 + 3.44183i −0.105803 + 0.132673i −0.831914 0.554905i \(-0.812755\pi\)
0.726111 + 0.687578i \(0.241326\pi\)
\(674\) 23.2456 25.0528i 0.895386 0.964996i
\(675\) 0 0
\(676\) −38.1276 25.9950i −1.46645 0.999807i
\(677\) 36.6933 5.53062i 1.41024 0.212559i 0.600628 0.799529i \(-0.294917\pi\)
0.809609 + 0.586970i \(0.199679\pi\)
\(678\) 0 0
\(679\) −21.3791 + 0.0269368i −0.820455 + 0.00103374i
\(680\) −19.1301 39.7241i −0.733607 1.52335i
\(681\) 0 0
\(682\) 2.97150 + 3.20251i 0.113785 + 0.122631i
\(683\) 18.0839 1.35520i 0.691961 0.0518553i 0.275892 0.961189i \(-0.411027\pi\)
0.416069 + 0.909333i \(0.363408\pi\)
\(684\) 0 0
\(685\) 4.48924i 0.171525i
\(686\) 16.2820 + 41.0291i 0.621648 + 1.56650i
\(687\) 0 0
\(688\) 1.80788 + 4.60640i 0.0689247 + 0.175617i
\(689\) −0.520224 6.94191i −0.0198190 0.264466i
\(690\) 0 0
\(691\) 3.01327 + 4.41965i 0.114630 + 0.168131i 0.879266 0.476331i \(-0.158034\pi\)
−0.764636 + 0.644462i \(0.777081\pi\)
\(692\) 8.18510 3.94174i 0.311151 0.149842i
\(693\) 0 0
\(694\) −26.7918 12.9023i −1.01700 0.489763i
\(695\) 6.28795 + 41.7178i 0.238515 + 1.58245i
\(696\) 0 0
\(697\) −22.3440 3.36782i −0.846339 0.127565i
\(698\) 22.6316 + 20.9990i 0.856618 + 0.794825i
\(699\) 0 0
\(700\) −13.1225 + 5.16929i −0.495984 + 0.195381i
\(701\) −21.0842 + 16.8141i −0.796338 + 0.635059i −0.934746 0.355317i \(-0.884373\pi\)
0.138408 + 0.990375i \(0.455802\pi\)
\(702\) 0 0
\(703\) 6.30172 + 20.4297i 0.237674 + 0.770520i
\(704\) −6.24426 + 3.60513i −0.235339 + 0.135873i
\(705\) 0 0
\(706\) 61.5181 + 14.0411i 2.31526 + 0.528444i
\(707\) −49.0901 + 3.74100i −1.84622 + 0.140695i
\(708\) 0 0
\(709\) −31.3445 9.66851i −1.17717 0.363108i −0.356380 0.934341i \(-0.615989\pi\)
−0.820788 + 0.571233i \(0.806465\pi\)
\(710\) −25.6189 + 65.2759i −0.961460 + 2.44976i
\(711\) 0 0
\(712\) −5.75128 + 18.6452i −0.215538 + 0.698759i
\(713\) −4.68255 20.5156i −0.175363 0.768314i
\(714\) 0 0
\(715\) 0.186172 0.815675i 0.00696245 0.0305045i
\(716\) 9.12377 + 5.26761i 0.340971 + 0.196860i
\(717\) 0 0
\(718\) 19.2940 5.95141i 0.720046 0.222105i
\(719\) 0.716547 9.56166i 0.0267227 0.356590i −0.967774 0.251821i \(-0.918971\pi\)
0.994497 0.104769i \(-0.0334103\pi\)
\(720\) 0 0
\(721\) −21.3661 + 14.6066i −0.795716 + 0.543980i
\(722\) −42.1401 33.6056i −1.56829 1.25067i
\(723\) 0 0
\(724\) 8.31947 55.1961i 0.309191 2.05135i
\(725\) 3.54320 5.19692i 0.131591 0.193009i
\(726\) 0 0
\(727\) 6.28579 13.0526i 0.233127 0.484093i −0.751284 0.659980i \(-0.770565\pi\)
0.984410 + 0.175887i \(0.0562792\pi\)
\(728\) −3.13638 6.49183i −0.116242 0.240603i
\(729\) 0 0
\(730\) 32.7563 22.3329i 1.21237 0.826578i
\(731\) −9.69032 + 8.99130i −0.358410 + 0.332555i
\(732\) 0 0
\(733\) 8.26480 3.24370i 0.305267 0.119809i −0.207763 0.978179i \(-0.566618\pi\)
0.513030 + 0.858371i \(0.328523\pi\)
\(734\) −10.6985 −0.394889
\(735\) 0 0
\(736\) 20.9854 0.773532
\(737\) 7.05010 2.76696i 0.259694 0.101922i
\(738\) 0 0
\(739\) 12.6949 11.7791i 0.466988 0.433302i −0.411252 0.911522i \(-0.634908\pi\)
0.878240 + 0.478220i \(0.158718\pi\)
\(740\) 18.9947 12.9504i 0.698260 0.476066i
\(741\) 0 0
\(742\) −27.9257 + 58.1758i −1.02519 + 2.13570i
\(743\) −8.23846 + 17.1073i −0.302240 + 0.627608i −0.995674 0.0929122i \(-0.970382\pi\)
0.693434 + 0.720520i \(0.256097\pi\)
\(744\) 0 0
\(745\) 12.5721 18.4398i 0.460604 0.675583i
\(746\) 9.25192 61.3824i 0.338737 2.24737i
\(747\) 0 0
\(748\) 10.9680 + 8.74667i 0.401029 + 0.319810i
\(749\) −25.8184 + 3.92478i −0.943385 + 0.143408i
\(750\) 0 0
\(751\) 0.437249 5.83469i 0.0159555 0.212911i −0.983528 0.180758i \(-0.942145\pi\)
0.999483 0.0321523i \(-0.0102362\pi\)
\(752\) −7.24152 + 2.23371i −0.264071 + 0.0814552i
\(753\) 0 0
\(754\) 6.09803 + 3.52070i 0.222077 + 0.128216i
\(755\) 9.10891 39.9088i 0.331507 1.45243i
\(756\) 0 0
\(757\) 7.60558 + 33.3222i 0.276429 + 1.21112i 0.902272 + 0.431167i \(0.141898\pi\)
−0.625843 + 0.779949i \(0.715245\pi\)
\(758\) 11.4734 37.1958i 0.416732 1.35101i
\(759\) 0 0
\(760\) −17.7923 + 45.3341i −0.645396 + 1.64444i
\(761\) −7.35231 2.26789i −0.266521 0.0822108i 0.158614 0.987341i \(-0.449297\pi\)
−0.425135 + 0.905130i \(0.639774\pi\)
\(762\) 0 0
\(763\) 2.51414 16.8240i 0.0910178 0.609070i
\(764\) 24.2559 + 5.53624i 0.877546 + 0.200294i
\(765\) 0 0
\(766\) 40.5607 23.4177i 1.46552 0.846117i
\(767\) 0.366399 + 1.18784i 0.0132299 + 0.0428903i
\(768\) 0 0
\(769\) −19.9737 + 15.9285i −0.720272 + 0.574397i −0.913540 0.406749i \(-0.866663\pi\)
0.193269 + 0.981146i \(0.438091\pi\)
\(770\) −5.26802 + 5.69194i −0.189846 + 0.205123i
\(771\) 0 0
\(772\) 18.4642 + 17.1322i 0.664539 + 0.616602i
\(773\) −37.6301 5.67182i −1.35346 0.204001i −0.568058 0.822988i \(-0.692305\pi\)
−0.785401 + 0.618987i \(0.787543\pi\)
\(774\) 0 0
\(775\) −0.606281 4.02241i −0.0217782 0.144489i
\(776\) −29.1640 14.0446i −1.04693 0.504173i
\(777\) 0 0
\(778\) −15.2853 + 7.36102i −0.548005 + 0.263905i
\(779\) 14.0600 + 20.6222i 0.503750 + 0.738866i
\(780\) 0 0
\(781\) −0.761357 10.1596i −0.0272435 0.363539i
\(782\) −38.1011 97.0800i −1.36249 3.47157i