Properties

Label 729.2.g.c.28.2
Level $729$
Weight $2$
Character 729.28
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
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 28.2
Character \(\chi\) \(=\) 729.28
Dual form 729.2.g.c.703.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.29056 + 0.848814i) q^{2} +(0.152898 - 0.354458i) q^{4} +(0.349244 - 0.370177i) q^{5} +(-3.96148 - 0.463031i) q^{7} +(-0.432916 - 2.45519i) q^{8} +O(q^{10})\) \(q+(-1.29056 + 0.848814i) q^{2} +(0.152898 - 0.354458i) q^{4} +(0.349244 - 0.370177i) q^{5} +(-3.96148 - 0.463031i) q^{7} +(-0.432916 - 2.45519i) q^{8} +(-0.136509 + 0.774179i) q^{10} +(1.09805 - 3.66773i) q^{11} +(-0.181020 + 3.10799i) q^{13} +(5.50556 - 2.76500i) q^{14} +(3.17252 + 3.36268i) q^{16} +(-1.41129 + 0.513668i) q^{17} +(6.30242 + 2.29389i) q^{19} +(-0.0778134 - 0.180392i) q^{20} +(1.69613 + 5.66546i) q^{22} +(1.17843 - 0.137739i) q^{23} +(0.275664 + 4.73298i) q^{25} +(-2.40449 - 4.16470i) q^{26} +(-0.769829 + 1.33338i) q^{28} +(6.17988 + 3.10365i) q^{29} +(-0.0276800 - 0.0371807i) q^{31} +(-2.09689 - 0.496972i) q^{32} +(1.38535 - 1.86084i) q^{34} +(-1.55493 + 1.30474i) q^{35} +(-2.33905 - 1.96269i) q^{37} +(-10.0807 + 2.38918i) q^{38} +(-1.06005 - 0.697205i) q^{40} +(4.96389 + 3.26480i) q^{41} +(0.231769 - 0.0549304i) q^{43} +(-1.13217 - 0.950001i) q^{44} +(-1.40392 + 1.17803i) q^{46} +(-2.82910 + 3.80014i) q^{47} +(8.66765 + 2.05427i) q^{49} +(-4.37318 - 5.87420i) q^{50} +(1.07397 + 0.539370i) q^{52} +(6.81173 - 11.7983i) q^{53} +(-0.974224 - 1.68741i) q^{55} +(0.578162 + 9.92665i) q^{56} +(-10.6099 + 1.24012i) q^{58} +(0.400604 + 1.33811i) q^{59} +(-0.124364 - 0.288308i) q^{61} +(0.0672822 + 0.0244887i) q^{62} +(-5.56048 + 2.02385i) q^{64} +(1.08729 + 1.15246i) q^{65} +(4.90826 - 2.46502i) q^{67} +(-0.0337102 + 0.578782i) q^{68} +(0.899246 - 3.00369i) q^{70} +(-2.03991 + 11.5689i) q^{71} +(2.70207 + 15.3242i) q^{73} +(4.68464 + 0.547556i) q^{74} +(1.77672 - 1.88321i) q^{76} +(-6.04817 + 14.0212i) q^{77} +(11.6941 - 7.69136i) q^{79} +2.35277 q^{80} -9.17740 q^{82} +(-0.587346 + 0.386304i) q^{83} +(-0.302737 + 0.701823i) q^{85} +(-0.252487 + 0.267620i) q^{86} +(-9.48034 - 1.10809i) q^{88} +(2.00921 + 11.3948i) q^{89} +(2.15620 - 12.2284i) q^{91} +(0.131358 - 0.438765i) q^{92} +(0.425507 - 7.30568i) q^{94} +(3.05023 - 1.53188i) q^{95} +(8.92799 + 9.46312i) q^{97} +(-12.9298 + 4.70606i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{22}{27}\right)\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.29056 + 0.848814i −0.912563 + 0.600202i −0.916607 0.399790i \(-0.869083\pi\)
0.00404373 + 0.999992i \(0.498713\pi\)
\(3\) 0 0
\(4\) 0.152898 0.354458i 0.0764491 0.177229i
\(5\) 0.349244 0.370177i 0.156187 0.165548i −0.644555 0.764558i \(-0.722957\pi\)
0.800742 + 0.599010i \(0.204439\pi\)
\(6\) 0 0
\(7\) −3.96148 0.463031i −1.49730 0.175009i −0.672358 0.740226i \(-0.734718\pi\)
−0.824942 + 0.565217i \(0.808793\pi\)
\(8\) −0.432916 2.45519i −0.153059 0.868041i
\(9\) 0 0
\(10\) −0.136509 + 0.774179i −0.0431678 + 0.244817i
\(11\) 1.09805 3.66773i 0.331074 1.10586i −0.616775 0.787140i \(-0.711561\pi\)
0.947848 0.318723i \(-0.103254\pi\)
\(12\) 0 0
\(13\) −0.181020 + 3.10799i −0.0502059 + 0.862002i 0.875373 + 0.483448i \(0.160616\pi\)
−0.925579 + 0.378554i \(0.876421\pi\)
\(14\) 5.50556 2.76500i 1.47142 0.738976i
\(15\) 0 0
\(16\) 3.17252 + 3.36268i 0.793131 + 0.840669i
\(17\) −1.41129 + 0.513668i −0.342288 + 0.124583i −0.507444 0.861685i \(-0.669410\pi\)
0.165156 + 0.986268i \(0.447187\pi\)
\(18\) 0 0
\(19\) 6.30242 + 2.29389i 1.44587 + 0.526255i 0.941436 0.337192i \(-0.109477\pi\)
0.504439 + 0.863447i \(0.331699\pi\)
\(20\) −0.0778134 0.180392i −0.0173996 0.0403368i
\(21\) 0 0
\(22\) 1.69613 + 5.66546i 0.361616 + 1.20788i
\(23\) 1.17843 0.137739i 0.245720 0.0287206i 0.00765887 0.999971i \(-0.497562\pi\)
0.238062 + 0.971250i \(0.423488\pi\)
\(24\) 0 0
\(25\) 0.275664 + 4.73298i 0.0551329 + 0.946595i
\(26\) −2.40449 4.16470i −0.471559 0.816765i
\(27\) 0 0
\(28\) −0.769829 + 1.33338i −0.145484 + 0.251986i
\(29\) 6.17988 + 3.10365i 1.14757 + 0.576333i 0.917852 0.396923i \(-0.129922\pi\)
0.229722 + 0.973256i \(0.426218\pi\)
\(30\) 0 0
\(31\) −0.0276800 0.0371807i −0.00497148 0.00667785i 0.799631 0.600492i \(-0.205029\pi\)
−0.804602 + 0.593814i \(0.797621\pi\)
\(32\) −2.09689 0.496972i −0.370681 0.0878530i
\(33\) 0 0
\(34\) 1.38535 1.86084i 0.237585 0.319132i
\(35\) −1.55493 + 1.30474i −0.262831 + 0.220541i
\(36\) 0 0
\(37\) −2.33905 1.96269i −0.384537 0.322665i 0.429943 0.902856i \(-0.358533\pi\)
−0.814481 + 0.580191i \(0.802978\pi\)
\(38\) −10.0807 + 2.38918i −1.63531 + 0.387576i
\(39\) 0 0
\(40\) −1.06005 0.697205i −0.167608 0.110238i
\(41\) 4.96389 + 3.26480i 0.775229 + 0.509876i 0.874407 0.485194i \(-0.161251\pi\)
−0.0991780 + 0.995070i \(0.531621\pi\)
\(42\) 0 0
\(43\) 0.231769 0.0549304i 0.0353445 0.00837680i −0.212906 0.977073i \(-0.568293\pi\)
0.248250 + 0.968696i \(0.420145\pi\)
\(44\) −1.13217 0.950001i −0.170681 0.143218i
\(45\) 0 0
\(46\) −1.40392 + 1.17803i −0.206997 + 0.173691i
\(47\) −2.82910 + 3.80014i −0.412666 + 0.554307i −0.959053 0.283226i \(-0.908595\pi\)
0.546387 + 0.837533i \(0.316003\pi\)
\(48\) 0 0
\(49\) 8.66765 + 2.05427i 1.23824 + 0.293467i
\(50\) −4.37318 5.87420i −0.618461 0.830737i
\(51\) 0 0
\(52\) 1.07397 + 0.539370i 0.148933 + 0.0747972i
\(53\) 6.81173 11.7983i 0.935663 1.62062i 0.162216 0.986755i \(-0.448136\pi\)
0.773447 0.633860i \(-0.218531\pi\)
\(54\) 0 0
\(55\) −0.974224 1.68741i −0.131364 0.227530i
\(56\) 0.578162 + 9.92665i 0.0772601 + 1.32650i
\(57\) 0 0
\(58\) −10.6099 + 1.24012i −1.39315 + 0.162836i
\(59\) 0.400604 + 1.33811i 0.0521543 + 0.174207i 0.980099 0.198512i \(-0.0636107\pi\)
−0.927944 + 0.372719i \(0.878426\pi\)
\(60\) 0 0
\(61\) −0.124364 0.288308i −0.0159232 0.0369141i 0.910069 0.414457i \(-0.136028\pi\)
−0.925992 + 0.377543i \(0.876769\pi\)
\(62\) 0.0672822 + 0.0244887i 0.00854485 + 0.00311007i
\(63\) 0 0
\(64\) −5.56048 + 2.02385i −0.695060 + 0.252981i
\(65\) 1.08729 + 1.15246i 0.134861 + 0.142945i
\(66\) 0 0
\(67\) 4.90826 2.46502i 0.599639 0.301150i −0.122966 0.992411i \(-0.539241\pi\)
0.722605 + 0.691261i \(0.242944\pi\)
\(68\) −0.0337102 + 0.578782i −0.00408797 + 0.0701877i
\(69\) 0 0
\(70\) 0.899246 3.00369i 0.107480 0.359010i
\(71\) −2.03991 + 11.5689i −0.242093 + 1.37298i 0.585054 + 0.810994i \(0.301073\pi\)
−0.827147 + 0.561985i \(0.810038\pi\)
\(72\) 0 0
\(73\) 2.70207 + 15.3242i 0.316253 + 1.79356i 0.565106 + 0.825019i \(0.308835\pi\)
−0.248853 + 0.968541i \(0.580053\pi\)
\(74\) 4.68464 + 0.547556i 0.544579 + 0.0636521i
\(75\) 0 0
\(76\) 1.77672 1.88321i 0.203804 0.216019i
\(77\) −6.04817 + 14.0212i −0.689253 + 1.59787i
\(78\) 0 0
\(79\) 11.6941 7.69136i 1.31569 0.865346i 0.319093 0.947723i \(-0.396622\pi\)
0.996601 + 0.0823774i \(0.0262513\pi\)
\(80\) 2.35277 0.263048
\(81\) 0 0
\(82\) −9.17740 −1.01347
\(83\) −0.587346 + 0.386304i −0.0644696 + 0.0424023i −0.581335 0.813665i \(-0.697469\pi\)
0.516865 + 0.856067i \(0.327099\pi\)
\(84\) 0 0
\(85\) −0.302737 + 0.701823i −0.0328364 + 0.0761234i
\(86\) −0.252487 + 0.267620i −0.0272263 + 0.0288582i
\(87\) 0 0
\(88\) −9.48034 1.10809i −1.01061 0.118123i
\(89\) 2.00921 + 11.3948i 0.212976 + 1.20785i 0.884384 + 0.466760i \(0.154579\pi\)
−0.671408 + 0.741088i \(0.734310\pi\)
\(90\) 0 0
\(91\) 2.15620 12.2284i 0.226032 1.28189i
\(92\) 0.131358 0.438765i 0.0136950 0.0457444i
\(93\) 0 0
\(94\) 0.425507 7.30568i 0.0438877 0.753523i
\(95\) 3.05023 1.53188i 0.312947 0.157168i
\(96\) 0 0
\(97\) 8.92799 + 9.46312i 0.906500 + 0.960834i 0.999393 0.0348418i \(-0.0110927\pi\)
−0.0928924 + 0.995676i \(0.529611\pi\)
\(98\) −12.9298 + 4.70606i −1.30611 + 0.475384i
\(99\) 0 0
\(100\) 1.71979 + 0.625952i 0.171979 + 0.0625952i
\(101\) −4.89713 11.3528i −0.487283 1.12965i −0.967585 0.252545i \(-0.918732\pi\)
0.480302 0.877103i \(-0.340527\pi\)
\(102\) 0 0
\(103\) 0.599460 + 2.00234i 0.0590666 + 0.197296i 0.982430 0.186631i \(-0.0597567\pi\)
−0.923364 + 0.383927i \(0.874572\pi\)
\(104\) 7.70907 0.901062i 0.755937 0.0883564i
\(105\) 0 0
\(106\) 1.22359 + 21.0082i 0.118846 + 2.04050i
\(107\) 0.831363 + 1.43996i 0.0803709 + 0.139207i 0.903409 0.428779i \(-0.141056\pi\)
−0.823038 + 0.567986i \(0.807723\pi\)
\(108\) 0 0
\(109\) −2.14981 + 3.72357i −0.205914 + 0.356654i −0.950424 0.310958i \(-0.899350\pi\)
0.744510 + 0.667612i \(0.232683\pi\)
\(110\) 2.68959 + 1.35076i 0.256442 + 0.128790i
\(111\) 0 0
\(112\) −11.0109 14.7902i −1.04043 1.39754i
\(113\) −13.8508 3.28270i −1.30297 0.308810i −0.480189 0.877165i \(-0.659432\pi\)
−0.822784 + 0.568354i \(0.807580\pi\)
\(114\) 0 0
\(115\) 0.360573 0.484334i 0.0336236 0.0451644i
\(116\) 2.04501 1.71596i 0.189874 0.159323i
\(117\) 0 0
\(118\) −1.65281 1.38687i −0.152154 0.127672i
\(119\) 5.82865 1.38142i 0.534312 0.126634i
\(120\) 0 0
\(121\) −3.05618 2.01008i −0.277834 0.182735i
\(122\) 0.405219 + 0.266517i 0.0366868 + 0.0241293i
\(123\) 0 0
\(124\) −0.0174112 + 0.00412654i −0.00156357 + 0.000370574i
\(125\) 3.79760 + 3.18657i 0.339668 + 0.285015i
\(126\) 0 0
\(127\) 14.1754 11.8946i 1.25787 1.05548i 0.261961 0.965078i \(-0.415631\pi\)
0.995906 0.0903976i \(-0.0288138\pi\)
\(128\) 8.03198 10.7888i 0.709933 0.953606i
\(129\) 0 0
\(130\) −2.38143 0.564410i −0.208865 0.0495020i
\(131\) −3.31614 4.45435i −0.289732 0.389178i 0.633296 0.773909i \(-0.281701\pi\)
−0.923029 + 0.384731i \(0.874294\pi\)
\(132\) 0 0
\(133\) −23.9048 12.0054i −2.07281 1.04100i
\(134\) −4.24205 + 7.34745i −0.366458 + 0.634723i
\(135\) 0 0
\(136\) 1.87212 + 3.24261i 0.160533 + 0.278052i
\(137\) −0.173481 2.97856i −0.0148215 0.254475i −0.997577 0.0695670i \(-0.977838\pi\)
0.982756 0.184908i \(-0.0591988\pi\)
\(138\) 0 0
\(139\) 5.85385 0.684217i 0.496517 0.0580345i 0.135851 0.990729i \(-0.456623\pi\)
0.360667 + 0.932695i \(0.382549\pi\)
\(140\) 0.224730 + 0.750649i 0.0189931 + 0.0634415i
\(141\) 0 0
\(142\) −7.18724 16.6619i −0.603140 1.39824i
\(143\) 11.2005 + 4.07665i 0.936633 + 0.340907i
\(144\) 0 0
\(145\) 3.30719 1.20372i 0.274647 0.0999633i
\(146\) −16.4946 17.4832i −1.36510 1.44692i
\(147\) 0 0
\(148\) −1.05333 + 0.529002i −0.0865831 + 0.0434837i
\(149\) −0.316650 + 5.43668i −0.0259410 + 0.445390i 0.960182 + 0.279375i \(0.0901271\pi\)
−0.986123 + 0.166015i \(0.946910\pi\)
\(150\) 0 0
\(151\) 4.27673 14.2853i 0.348035 1.16252i −0.587482 0.809237i \(-0.699881\pi\)
0.935517 0.353281i \(-0.114934\pi\)
\(152\) 2.90352 16.4667i 0.235507 1.33563i
\(153\) 0 0
\(154\) −4.09590 23.2290i −0.330057 1.87185i
\(155\) −0.0234305 0.00273864i −0.00188199 0.000219973i
\(156\) 0 0
\(157\) −5.75380 + 6.09867i −0.459203 + 0.486727i −0.915055 0.403329i \(-0.867853\pi\)
0.455852 + 0.890056i \(0.349335\pi\)
\(158\) −8.56345 + 19.8523i −0.681272 + 1.57937i
\(159\) 0 0
\(160\) −0.916293 + 0.602656i −0.0724394 + 0.0476441i
\(161\) −4.73212 −0.372944
\(162\) 0 0
\(163\) 3.04537 0.238531 0.119266 0.992862i \(-0.461946\pi\)
0.119266 + 0.992862i \(0.461946\pi\)
\(164\) 1.91620 1.26031i 0.149630 0.0984134i
\(165\) 0 0
\(166\) 0.430105 0.997096i 0.0333826 0.0773896i
\(167\) 14.4823 15.3503i 1.12067 1.18785i 0.140422 0.990092i \(-0.455154\pi\)
0.980252 0.197753i \(-0.0633645\pi\)
\(168\) 0 0
\(169\) 3.28526 + 0.383992i 0.252712 + 0.0295378i
\(170\) −0.205018 1.16271i −0.0157241 0.0891760i
\(171\) 0 0
\(172\) 0.0159666 0.0905513i 0.00121744 0.00690447i
\(173\) −0.486058 + 1.62355i −0.0369543 + 0.123436i −0.974477 0.224489i \(-0.927929\pi\)
0.937522 + 0.347925i \(0.113114\pi\)
\(174\) 0 0
\(175\) 1.09947 18.8773i 0.0831125 1.42699i
\(176\) 15.8170 7.94358i 1.19225 0.598770i
\(177\) 0 0
\(178\) −12.2651 13.0002i −0.919307 0.974409i
\(179\) 11.3362 4.12604i 0.847308 0.308395i 0.118366 0.992970i \(-0.462235\pi\)
0.728942 + 0.684575i \(0.240012\pi\)
\(180\) 0 0
\(181\) −7.09567 2.58261i −0.527417 0.191964i 0.0645678 0.997913i \(-0.479433\pi\)
−0.591985 + 0.805949i \(0.701655\pi\)
\(182\) 7.59697 + 17.6117i 0.563125 + 1.30547i
\(183\) 0 0
\(184\) −0.848339 2.83365i −0.0625404 0.208899i
\(185\) −1.54344 + 0.180403i −0.113476 + 0.0132635i
\(186\) 0 0
\(187\) 0.334333 + 5.74027i 0.0244488 + 0.419770i
\(188\) 0.914425 + 1.58383i 0.0666913 + 0.115513i
\(189\) 0 0
\(190\) −2.63622 + 4.56607i −0.191251 + 0.331257i
\(191\) −11.5732 5.81226i −0.837404 0.420560i −0.0222137 0.999753i \(-0.507071\pi\)
−0.815190 + 0.579193i \(0.803368\pi\)
\(192\) 0 0
\(193\) 10.7961 + 14.5016i 0.777118 + 1.04385i 0.997653 + 0.0684715i \(0.0218122\pi\)
−0.220535 + 0.975379i \(0.570780\pi\)
\(194\) −19.5545 4.63451i −1.40393 0.332738i
\(195\) 0 0
\(196\) 2.05342 2.75822i 0.146673 0.197016i
\(197\) 7.47510 6.27235i 0.532579 0.446886i −0.336412 0.941715i \(-0.609214\pi\)
0.868991 + 0.494828i \(0.164769\pi\)
\(198\) 0 0
\(199\) −6.35460 5.33214i −0.450465 0.377985i 0.389143 0.921177i \(-0.372771\pi\)
−0.839609 + 0.543192i \(0.817216\pi\)
\(200\) 11.5010 2.72579i 0.813245 0.192743i
\(201\) 0 0
\(202\) 15.9565 + 10.4947i 1.12269 + 0.738407i
\(203\) −23.0444 15.1565i −1.61740 1.06378i
\(204\) 0 0
\(205\) 2.94216 0.697305i 0.205490 0.0487019i
\(206\) −2.47325 2.07530i −0.172320 0.144593i
\(207\) 0 0
\(208\) −11.0255 + 9.25146i −0.764478 + 0.641473i
\(209\) 15.3337 20.5968i 1.06066 1.42471i
\(210\) 0 0
\(211\) −11.0335 2.61499i −0.759577 0.180023i −0.167464 0.985878i \(-0.553558\pi\)
−0.592113 + 0.805855i \(0.701706\pi\)
\(212\) −3.14049 4.21840i −0.215689 0.289721i
\(213\) 0 0
\(214\) −2.29519 1.15269i −0.156896 0.0787960i
\(215\) 0.0606102 0.104980i 0.00413358 0.00715957i
\(216\) 0 0
\(217\) 0.0924381 + 0.160108i 0.00627511 + 0.0108688i
\(218\) −0.386170 6.63028i −0.0261547 0.449059i
\(219\) 0 0
\(220\) −0.747071 + 0.0873201i −0.0503676 + 0.00588712i
\(221\) −1.34100 4.47926i −0.0902057 0.301308i
\(222\) 0 0
\(223\) 7.49598 + 17.3776i 0.501968 + 1.16369i 0.961319 + 0.275438i \(0.0888227\pi\)
−0.459351 + 0.888255i \(0.651918\pi\)
\(224\) 8.07667 + 2.93967i 0.539646 + 0.196415i
\(225\) 0 0
\(226\) 20.6617 7.52023i 1.37439 0.500239i
\(227\) 7.61638 + 8.07290i 0.505517 + 0.535817i 0.928996 0.370089i \(-0.120673\pi\)
−0.423479 + 0.905906i \(0.639191\pi\)
\(228\) 0 0
\(229\) 2.72124 1.36666i 0.179825 0.0903113i −0.356609 0.934254i \(-0.616067\pi\)
0.536434 + 0.843942i \(0.319771\pi\)
\(230\) −0.0542316 + 0.931121i −0.00357593 + 0.0613963i
\(231\) 0 0
\(232\) 4.94468 16.5164i 0.324634 1.08435i
\(233\) −2.47370 + 14.0290i −0.162057 + 0.919073i 0.789989 + 0.613121i \(0.210086\pi\)
−0.952047 + 0.305953i \(0.901025\pi\)
\(234\) 0 0
\(235\) 0.418679 + 2.37444i 0.0273116 + 0.154892i
\(236\) 0.535556 + 0.0625975i 0.0348617 + 0.00407475i
\(237\) 0 0
\(238\) −6.34966 + 6.73024i −0.411587 + 0.436257i
\(239\) −3.14737 + 7.29642i −0.203586 + 0.471966i −0.989167 0.146793i \(-0.953105\pi\)
0.785581 + 0.618759i \(0.212364\pi\)
\(240\) 0 0
\(241\) −3.02761 + 1.99129i −0.195026 + 0.128270i −0.643266 0.765643i \(-0.722421\pi\)
0.448241 + 0.893913i \(0.352051\pi\)
\(242\) 5.65036 0.363219
\(243\) 0 0
\(244\) −0.121208 −0.00775955
\(245\) 3.78757 2.49112i 0.241979 0.159152i
\(246\) 0 0
\(247\) −8.27026 + 19.1726i −0.526224 + 1.21993i
\(248\) −0.0793026 + 0.0840558i −0.00503572 + 0.00533755i
\(249\) 0 0
\(250\) −7.60584 0.888995i −0.481035 0.0562250i
\(251\) −0.441351 2.50303i −0.0278578 0.157990i 0.967706 0.252083i \(-0.0811157\pi\)
−0.995563 + 0.0940939i \(0.970005\pi\)
\(252\) 0 0
\(253\) 0.788785 4.47342i 0.0495905 0.281242i
\(254\) −8.19794 + 27.3830i −0.514384 + 1.71816i
\(255\) 0 0
\(256\) −0.519916 + 8.92662i −0.0324948 + 0.557914i
\(257\) −25.0214 + 12.5662i −1.56079 + 0.783860i −0.999055 0.0434541i \(-0.986164\pi\)
−0.561739 + 0.827314i \(0.689867\pi\)
\(258\) 0 0
\(259\) 8.35731 + 8.85823i 0.519298 + 0.550424i
\(260\) 0.574742 0.209189i 0.0356440 0.0129733i
\(261\) 0 0
\(262\) 8.06059 + 2.93381i 0.497985 + 0.181252i
\(263\) −0.974610 2.25940i −0.0600970 0.139321i 0.885521 0.464599i \(-0.153801\pi\)
−0.945618 + 0.325278i \(0.894542\pi\)
\(264\) 0 0
\(265\) −1.98849 6.64202i −0.122152 0.408016i
\(266\) 41.0410 4.79700i 2.51638 0.294123i
\(267\) 0 0
\(268\) −0.123282 2.11667i −0.00753064 0.129296i
\(269\) −5.65271 9.79078i −0.344652 0.596954i 0.640639 0.767842i \(-0.278670\pi\)
−0.985290 + 0.170888i \(0.945336\pi\)
\(270\) 0 0
\(271\) 2.14084 3.70804i 0.130047 0.225248i −0.793648 0.608378i \(-0.791821\pi\)
0.923694 + 0.383130i \(0.125154\pi\)
\(272\) −6.20465 3.11609i −0.376212 0.188941i
\(273\) 0 0
\(274\) 2.75213 + 3.69675i 0.166262 + 0.223329i
\(275\) 17.6620 + 4.18597i 1.06506 + 0.252423i
\(276\) 0 0
\(277\) 11.2400 15.0980i 0.675349 0.907151i −0.323893 0.946094i \(-0.604992\pi\)
0.999241 + 0.0389429i \(0.0123990\pi\)
\(278\) −6.97397 + 5.85185i −0.418271 + 0.350971i
\(279\) 0 0
\(280\) 3.87654 + 3.25280i 0.231668 + 0.194392i
\(281\) −13.2369 + 3.13720i −0.789647 + 0.187150i −0.605602 0.795768i \(-0.707068\pi\)
−0.184046 + 0.982918i \(0.558919\pi\)
\(282\) 0 0
\(283\) −13.9445 9.17147i −0.828917 0.545187i 0.0626713 0.998034i \(-0.480038\pi\)
−0.891588 + 0.452847i \(0.850408\pi\)
\(284\) 3.78880 + 2.49193i 0.224824 + 0.147869i
\(285\) 0 0
\(286\) −17.9152 + 4.24599i −1.05935 + 0.251071i
\(287\) −18.1527 15.2319i −1.07152 0.899110i
\(288\) 0 0
\(289\) −11.2949 + 9.47752i −0.664404 + 0.557501i
\(290\) −3.24639 + 4.36066i −0.190634 + 0.256067i
\(291\) 0 0
\(292\) 5.84492 + 1.38527i 0.342048 + 0.0810669i
\(293\) −15.1735 20.3815i −0.886444 1.19070i −0.980771 0.195160i \(-0.937478\pi\)
0.0943276 0.995541i \(-0.469930\pi\)
\(294\) 0 0
\(295\) 0.635248 + 0.319033i 0.0369855 + 0.0185748i
\(296\) −3.80617 + 6.59249i −0.221229 + 0.383181i
\(297\) 0 0
\(298\) −4.20607 7.28513i −0.243651 0.422016i
\(299\) 0.214772 + 3.68749i 0.0124206 + 0.213253i
\(300\) 0 0
\(301\) −0.943585 + 0.110289i −0.0543874 + 0.00635697i
\(302\) 6.60616 + 22.0661i 0.380142 + 1.26976i
\(303\) 0 0
\(304\) 12.2809 + 28.4704i 0.704361 + 1.63289i
\(305\) −0.150158 0.0546532i −0.00859805 0.00312943i
\(306\) 0 0
\(307\) −9.43080 + 3.43253i −0.538244 + 0.195905i −0.596816 0.802378i \(-0.703568\pi\)
0.0585714 + 0.998283i \(0.481345\pi\)
\(308\) 4.04518 + 4.28764i 0.230496 + 0.244311i
\(309\) 0 0
\(310\) 0.0325631 0.0163538i 0.00184946 0.000928834i
\(311\) −1.56707 + 26.9055i −0.0888602 + 1.52567i 0.599543 + 0.800342i \(0.295349\pi\)
−0.688403 + 0.725328i \(0.741688\pi\)
\(312\) 0 0
\(313\) −3.73743 + 12.4839i −0.211252 + 0.705631i 0.785028 + 0.619460i \(0.212648\pi\)
−0.996280 + 0.0861711i \(0.972537\pi\)
\(314\) 2.24898 12.7546i 0.126917 0.719784i
\(315\) 0 0
\(316\) −0.938250 5.32108i −0.0527807 0.299334i
\(317\) −9.42954 1.10216i −0.529616 0.0619032i −0.152917 0.988239i \(-0.548867\pi\)
−0.376699 + 0.926336i \(0.622941\pi\)
\(318\) 0 0
\(319\) 18.1691 19.2582i 1.01728 1.07825i
\(320\) −1.19278 + 2.76518i −0.0666785 + 0.154578i
\(321\) 0 0
\(322\) 6.10709 4.01669i 0.340335 0.223842i
\(323\) −10.0729 −0.560468
\(324\) 0 0
\(325\) −14.7599 −0.818735
\(326\) −3.93023 + 2.58495i −0.217675 + 0.143167i
\(327\) 0 0
\(328\) 5.86675 13.6007i 0.323937 0.750971i
\(329\) 12.9670 13.7442i 0.714894 0.757744i
\(330\) 0 0
\(331\) 23.3551 + 2.72982i 1.28371 + 0.150045i 0.730452 0.682964i \(-0.239309\pi\)
0.553261 + 0.833008i \(0.313383\pi\)
\(332\) 0.0471242 + 0.267255i 0.00258628 + 0.0146675i
\(333\) 0 0
\(334\) −5.66068 + 32.1033i −0.309739 + 1.75661i
\(335\) 0.801686 2.67782i 0.0438008 0.146305i
\(336\) 0 0
\(337\) 0.180721 3.10287i 0.00984453 0.169024i −0.989802 0.142448i \(-0.954503\pi\)
0.999647 0.0265759i \(-0.00846036\pi\)
\(338\) −4.56576 + 2.29301i −0.248344 + 0.124723i
\(339\) 0 0
\(340\) 0.202479 + 0.214615i 0.0109810 + 0.0116391i
\(341\) −0.166763 + 0.0606967i −0.00903071 + 0.00328691i
\(342\) 0 0
\(343\) −7.15012 2.60243i −0.386070 0.140518i
\(344\) −0.235201 0.545258i −0.0126812 0.0293983i
\(345\) 0 0
\(346\) −0.750803 2.50786i −0.0403634 0.134823i
\(347\) 22.1439 2.58826i 1.18875 0.138945i 0.501363 0.865237i \(-0.332832\pi\)
0.687386 + 0.726292i \(0.258758\pi\)
\(348\) 0 0
\(349\) −0.175177 3.00767i −0.00937701 0.160997i −0.999746 0.0225430i \(-0.992824\pi\)
0.990369 0.138454i \(-0.0442133\pi\)
\(350\) 14.6043 + 25.2955i 0.780635 + 1.35210i
\(351\) 0 0
\(352\) −4.12524 + 7.14512i −0.219876 + 0.380836i
\(353\) 1.93406 + 0.971320i 0.102939 + 0.0516981i 0.499524 0.866300i \(-0.333508\pi\)
−0.396584 + 0.917998i \(0.629805\pi\)
\(354\) 0 0
\(355\) 3.57013 + 4.79551i 0.189483 + 0.254519i
\(356\) 4.34619 + 1.03007i 0.230348 + 0.0545934i
\(357\) 0 0
\(358\) −11.1278 + 14.9472i −0.588123 + 0.789986i
\(359\) −0.496794 + 0.416860i −0.0262198 + 0.0220010i −0.655803 0.754932i \(-0.727670\pi\)
0.629584 + 0.776933i \(0.283226\pi\)
\(360\) 0 0
\(361\) 19.9037 + 16.7012i 1.04756 + 0.879011i
\(362\) 11.3495 2.68989i 0.596518 0.141377i
\(363\) 0 0
\(364\) −4.00479 2.63399i −0.209908 0.138059i
\(365\) 6.61635 + 4.35164i 0.346315 + 0.227775i
\(366\) 0 0
\(367\) −9.21403 + 2.18376i −0.480968 + 0.113992i −0.463946 0.885864i \(-0.653567\pi\)
−0.0170223 + 0.999855i \(0.505419\pi\)
\(368\) 4.20178 + 3.52571i 0.219033 + 0.183790i
\(369\) 0 0
\(370\) 1.83878 1.54292i 0.0955935 0.0802124i
\(371\) −32.4475 + 43.5846i −1.68459 + 2.26280i
\(372\) 0 0
\(373\) −4.75011 1.12580i −0.245951 0.0582915i 0.105791 0.994388i \(-0.466263\pi\)
−0.351742 + 0.936097i \(0.614411\pi\)
\(374\) −5.30390 7.12437i −0.274258 0.368392i
\(375\) 0 0
\(376\) 10.5548 + 5.30083i 0.544323 + 0.273369i
\(377\) −10.7648 + 18.6452i −0.554415 + 0.960275i
\(378\) 0 0
\(379\) 13.0190 + 22.5495i 0.668739 + 1.15829i 0.978257 + 0.207396i \(0.0664989\pi\)
−0.309518 + 0.950894i \(0.600168\pi\)
\(380\) −0.0766134 1.31540i −0.00393018 0.0674787i
\(381\) 0 0
\(382\) 19.8694 2.32240i 1.01661 0.118824i
\(383\) 2.30331 + 7.69359i 0.117694 + 0.393124i 0.996454 0.0841390i \(-0.0268140\pi\)
−0.878760 + 0.477263i \(0.841629\pi\)
\(384\) 0 0
\(385\) 3.07805 + 7.13573i 0.156872 + 0.363670i
\(386\) −26.2422 9.55136i −1.33569 0.486152i
\(387\) 0 0
\(388\) 4.71935 1.71770i 0.239589 0.0872032i
\(389\) 15.6093 + 16.5449i 0.791422 + 0.838858i 0.989977 0.141231i \(-0.0451062\pi\)
−0.198555 + 0.980090i \(0.563625\pi\)
\(390\) 0 0
\(391\) −1.59236 + 0.799714i −0.0805291 + 0.0404433i
\(392\) 1.29126 22.1700i 0.0652184 1.11976i
\(393\) 0 0
\(394\) −4.32300 + 14.4398i −0.217789 + 0.727467i
\(395\) 1.23695 7.01507i 0.0622375 0.352967i
\(396\) 0 0
\(397\) 4.29294 + 24.3465i 0.215456 + 1.22191i 0.880113 + 0.474765i \(0.157467\pi\)
−0.664656 + 0.747149i \(0.731422\pi\)
\(398\) 12.7270 + 1.48757i 0.637946 + 0.0745652i
\(399\) 0 0
\(400\) −15.0409 + 15.9424i −0.752046 + 0.797122i
\(401\) −6.72403 + 15.5880i −0.335782 + 0.778430i 0.663754 + 0.747951i \(0.268962\pi\)
−0.999535 + 0.0304785i \(0.990297\pi\)
\(402\) 0 0
\(403\) 0.120568 0.0792988i 0.00600592 0.00395015i
\(404\) −4.77286 −0.237459
\(405\) 0 0
\(406\) 42.6052 2.11446
\(407\) −9.76702 + 6.42387i −0.484133 + 0.318419i
\(408\) 0 0
\(409\) 4.47516 10.3746i 0.221282 0.512990i −0.771023 0.636808i \(-0.780255\pi\)
0.992305 + 0.123818i \(0.0395138\pi\)
\(410\) −3.20515 + 3.39726i −0.158291 + 0.167779i
\(411\) 0 0
\(412\) 0.801401 + 0.0936703i 0.0394822 + 0.00461481i
\(413\) −0.967401 5.48640i −0.0476027 0.269968i
\(414\) 0 0
\(415\) −0.0621265 + 0.352337i −0.00304967 + 0.0172955i
\(416\) 1.92416 6.42715i 0.0943398 0.315117i
\(417\) 0 0
\(418\) −2.30625 + 39.5969i −0.112803 + 1.93675i
\(419\) 28.9814 14.5550i 1.41584 0.711059i 0.434021 0.900903i \(-0.357094\pi\)
0.981814 + 0.189843i \(0.0607980\pi\)
\(420\) 0 0
\(421\) 0.455943 + 0.483271i 0.0222213 + 0.0235532i 0.738389 0.674375i \(-0.235587\pi\)
−0.716168 + 0.697928i \(0.754105\pi\)
\(422\) 16.4590 5.99059i 0.801212 0.291617i
\(423\) 0 0
\(424\) −31.9159 11.6164i −1.54997 0.564144i
\(425\) −2.82022 6.53801i −0.136801 0.317140i
\(426\) 0 0
\(427\) 0.359170 + 1.19971i 0.0173815 + 0.0580581i
\(428\) 0.637521 0.0745155i 0.0308157 0.00360184i
\(429\) 0 0
\(430\) 0.0108874 + 0.186930i 0.000525037 + 0.00901454i
\(431\) −15.1861 26.3031i −0.731488 1.26698i −0.956247 0.292561i \(-0.905493\pi\)
0.224759 0.974414i \(-0.427841\pi\)
\(432\) 0 0
\(433\) 5.68299 9.84323i 0.273107 0.473035i −0.696549 0.717510i \(-0.745282\pi\)
0.969656 + 0.244474i \(0.0786153\pi\)
\(434\) −0.255198 0.128165i −0.0122499 0.00615214i
\(435\) 0 0
\(436\) 0.991149 + 1.33134i 0.0474674 + 0.0637598i
\(437\) 7.74294 + 1.83511i 0.370395 + 0.0877853i
\(438\) 0 0
\(439\) −4.28247 + 5.75236i −0.204391 + 0.274545i −0.892485 0.451076i \(-0.851040\pi\)
0.688094 + 0.725621i \(0.258448\pi\)
\(440\) −3.72114 + 3.12241i −0.177399 + 0.148855i
\(441\) 0 0
\(442\) 5.53271 + 4.64249i 0.263164 + 0.220821i
\(443\) −1.69953 + 0.402796i −0.0807471 + 0.0191374i −0.270791 0.962638i \(-0.587285\pi\)
0.190044 + 0.981776i \(0.439137\pi\)
\(444\) 0 0
\(445\) 4.91981 + 3.23581i 0.233221 + 0.153392i
\(446\) −24.4244 16.0642i −1.15653 0.760661i
\(447\) 0 0
\(448\) 22.9649 5.44277i 1.08499 0.257147i
\(449\) 25.6694 + 21.5392i 1.21142 + 1.01650i 0.999229 + 0.0392691i \(0.0125030\pi\)
0.212187 + 0.977229i \(0.431941\pi\)
\(450\) 0 0
\(451\) 17.4250 14.6213i 0.820510 0.688490i
\(452\) −3.28134 + 4.40761i −0.154341 + 0.207316i
\(453\) 0 0
\(454\) −16.6818 3.95366i −0.782915 0.185554i
\(455\) −3.77365 5.06889i −0.176911 0.237633i
\(456\) 0 0
\(457\) 10.2116 + 5.12846i 0.477679 + 0.239899i 0.671312 0.741175i \(-0.265731\pi\)
−0.193634 + 0.981074i \(0.562027\pi\)
\(458\) −2.35188 + 4.07358i −0.109896 + 0.190346i
\(459\) 0 0
\(460\) −0.116545 0.201862i −0.00543394 0.00941186i
\(461\) −0.967981 16.6196i −0.0450834 0.774051i −0.942776 0.333428i \(-0.891795\pi\)
0.897692 0.440623i \(-0.145242\pi\)
\(462\) 0 0
\(463\) 4.54546 0.531288i 0.211245 0.0246910i −0.00981201 0.999952i \(-0.503123\pi\)
0.221057 + 0.975261i \(0.429049\pi\)
\(464\) 9.16922 + 30.6273i 0.425670 + 1.42184i
\(465\) 0 0
\(466\) −8.71560 20.2050i −0.403742 0.935980i
\(467\) −31.8531 11.5936i −1.47398 0.536486i −0.524805 0.851222i \(-0.675862\pi\)
−0.949179 + 0.314736i \(0.898084\pi\)
\(468\) 0 0
\(469\) −20.5854 + 7.49246i −0.950544 + 0.345970i
\(470\) −2.55579 2.70898i −0.117890 0.124956i
\(471\) 0 0
\(472\) 3.11189 1.56285i 0.143236 0.0719360i
\(473\) 0.0530238 0.910384i 0.00243804 0.0418595i
\(474\) 0 0
\(475\) −9.11959 + 30.4616i −0.418436 + 1.39767i
\(476\) 0.401537 2.27723i 0.0184044 0.104377i
\(477\) 0 0
\(478\) −2.13144 12.0880i −0.0974898 0.552892i
\(479\) −8.62453 1.00806i −0.394065 0.0460596i −0.0832467 0.996529i \(-0.526529\pi\)
−0.310818 + 0.950469i \(0.600603\pi\)
\(480\) 0 0
\(481\) 6.52345 6.91445i 0.297444 0.315272i
\(482\) 2.21708 5.13976i 0.100985 0.234110i
\(483\) 0 0
\(484\) −1.17977 + 0.775949i −0.0536261 + 0.0352704i
\(485\) 6.62108 0.300648
\(486\) 0 0
\(487\) −21.3432 −0.967154 −0.483577 0.875302i \(-0.660663\pi\)
−0.483577 + 0.875302i \(0.660663\pi\)
\(488\) −0.654012 + 0.430150i −0.0296057 + 0.0194720i
\(489\) 0 0
\(490\) −2.77358 + 6.42989i −0.125298 + 0.290473i
\(491\) −2.89262 + 3.06600i −0.130542 + 0.138366i −0.789347 0.613947i \(-0.789581\pi\)
0.658805 + 0.752314i \(0.271062\pi\)
\(492\) 0 0
\(493\) −10.3158 1.20575i −0.464602 0.0543042i
\(494\) −5.60073 31.7633i −0.251989 1.42910i
\(495\) 0 0
\(496\) 0.0372113 0.211036i 0.00167084 0.00947578i
\(497\) 13.4379 44.8856i 0.602770 2.01339i
\(498\) 0 0
\(499\) −1.76905 + 30.3734i −0.0791936 + 1.35970i 0.691445 + 0.722429i \(0.256975\pi\)
−0.770638 + 0.637273i \(0.780062\pi\)
\(500\) 1.71015 0.858870i 0.0764803 0.0384098i
\(501\) 0 0
\(502\) 2.69419 + 2.85568i 0.120248 + 0.127455i
\(503\) −11.9111 + 4.33528i −0.531089 + 0.193301i −0.593624 0.804742i \(-0.702304\pi\)
0.0625356 + 0.998043i \(0.480081\pi\)
\(504\) 0 0
\(505\) −5.91285 2.15210i −0.263118 0.0957673i
\(506\) 2.77913 + 6.44275i 0.123547 + 0.286415i
\(507\) 0 0
\(508\) −2.04874 6.84326i −0.0908981 0.303621i
\(509\) 3.48848 0.407744i 0.154624 0.0180730i −0.0384287 0.999261i \(-0.512235\pi\)
0.193053 + 0.981188i \(0.438161\pi\)
\(510\) 0 0
\(511\) −3.60862 61.9577i −0.159636 2.74085i
\(512\) 6.54427 + 11.3350i 0.289219 + 0.500941i
\(513\) 0 0
\(514\) 21.6252 37.4560i 0.953849 1.65211i
\(515\) 0.950578 + 0.477398i 0.0418875 + 0.0210367i
\(516\) 0 0
\(517\) 10.8314 + 14.5491i 0.476364 + 0.639869i
\(518\) −18.3046 4.33827i −0.804258 0.190613i
\(519\) 0 0
\(520\) 2.35880 3.16841i 0.103440 0.138944i
\(521\) 6.50992 5.46247i 0.285205 0.239315i −0.488950 0.872312i \(-0.662620\pi\)
0.774154 + 0.632997i \(0.218175\pi\)
\(522\) 0 0
\(523\) −9.72249 8.15814i −0.425135 0.356730i 0.404978 0.914327i \(-0.367279\pi\)
−0.830112 + 0.557596i \(0.811724\pi\)
\(524\) −2.08591 + 0.494370i −0.0911234 + 0.0215966i
\(525\) 0 0
\(526\) 3.17560 + 2.08863i 0.138463 + 0.0910685i
\(527\) 0.0581631 + 0.0382545i 0.00253362 + 0.00166639i
\(528\) 0 0
\(529\) −21.0103 + 4.97953i −0.913491 + 0.216501i
\(530\) 8.20411 + 6.88406i 0.356364 + 0.299025i
\(531\) 0 0
\(532\) −7.91043 + 6.63763i −0.342960 + 0.287778i
\(533\) −11.0455 + 14.8367i −0.478435 + 0.642650i
\(534\) 0 0
\(535\) 0.823391 + 0.195147i 0.0355983 + 0.00843695i
\(536\) −8.17695 10.9836i −0.353191 0.474417i
\(537\) 0 0
\(538\) 15.6057 + 7.83748i 0.672810 + 0.337898i
\(539\) 17.0520 29.5349i 0.734481 1.27216i
\(540\) 0 0
\(541\) −6.14520 10.6438i −0.264203 0.457612i 0.703152 0.711040i \(-0.251775\pi\)
−0.967354 + 0.253427i \(0.918442\pi\)
\(542\) 0.384559 + 6.60262i 0.0165182 + 0.283607i
\(543\) 0 0
\(544\) 3.21460 0.375733i 0.137825 0.0161094i
\(545\) 0.627575 + 2.09625i 0.0268824 + 0.0897933i
\(546\) 0 0
\(547\) −10.6521 24.6944i −0.455452 1.05586i −0.979000 0.203861i \(-0.934651\pi\)
0.523548 0.851996i \(-0.324608\pi\)
\(548\) −1.08230 0.393924i −0.0462335 0.0168276i
\(549\) 0 0
\(550\) −26.3469 + 9.58950i −1.12344 + 0.408898i
\(551\) 31.8287 + 33.7365i 1.35595 + 1.43722i
\(552\) 0 0
\(553\) −49.8875 + 25.0545i −2.12143 + 1.06542i
\(554\) −1.69055 + 29.0256i −0.0718245 + 1.23318i
\(555\) 0 0
\(556\) 0.652517 2.17956i 0.0276729 0.0924339i
\(557\) 3.81879 21.6574i 0.161807 0.917654i −0.790488 0.612477i \(-0.790173\pi\)
0.952296 0.305177i \(-0.0987157\pi\)
\(558\) 0 0
\(559\) 0.128768 + 0.730281i 0.00544631 + 0.0308876i
\(560\) −9.32047 1.08941i −0.393862 0.0460358i
\(561\) 0 0
\(562\) 14.4201 15.2844i 0.608275 0.644734i
\(563\) 18.7536 43.4757i 0.790370 1.83228i 0.333505 0.942748i \(-0.391768\pi\)
0.456865 0.889536i \(-0.348972\pi\)
\(564\) 0 0
\(565\) −6.05249 + 3.98079i −0.254630 + 0.167473i
\(566\) 25.7811 1.08366
\(567\) 0 0
\(568\) 29.2870 1.22886
\(569\) 14.4816 9.52469i 0.607099 0.399296i −0.208408 0.978042i \(-0.566828\pi\)
0.815508 + 0.578746i \(0.196458\pi\)
\(570\) 0 0
\(571\) 14.1217 32.7377i 0.590973 1.37003i −0.315967 0.948770i \(-0.602329\pi\)
0.906940 0.421260i \(-0.138412\pi\)
\(572\) 3.15754 3.34680i 0.132023 0.139937i
\(573\) 0 0
\(574\) 36.3561 + 4.24942i 1.51747 + 0.177367i
\(575\) 0.976768 + 5.53953i 0.0407341 + 0.231014i
\(576\) 0 0
\(577\) −0.228884 + 1.29807i −0.00952858 + 0.0540393i −0.989201 0.146563i \(-0.953179\pi\)
0.979673 + 0.200602i \(0.0642899\pi\)
\(578\) 6.53204 21.8185i 0.271697 0.907532i
\(579\) 0 0
\(580\) 0.0789958 1.35630i 0.00328012 0.0563175i
\(581\) 2.50563 1.25838i 0.103951 0.0522063i
\(582\) 0 0
\(583\) −35.7933 37.9386i −1.48241 1.57126i
\(584\) 36.4540 13.2682i 1.50848 0.549041i
\(585\) 0 0
\(586\) 36.8824 + 13.4241i 1.52360 + 0.554544i
\(587\) 1.99538 + 4.62581i 0.0823582 + 0.190928i 0.954419 0.298469i \(-0.0964761\pi\)
−0.872061 + 0.489397i \(0.837217\pi\)
\(588\) 0 0
\(589\) −0.0891625 0.297824i −0.00367388 0.0122716i
\(590\) −1.09062 + 0.127476i −0.0449003 + 0.00524809i
\(591\) 0 0
\(592\) −0.820774 14.0922i −0.0337336 0.579184i
\(593\) 13.0012 + 22.5187i 0.533895 + 0.924732i 0.999216 + 0.0395907i \(0.0126054\pi\)
−0.465321 + 0.885142i \(0.654061\pi\)
\(594\) 0 0
\(595\) 1.52425 2.64009i 0.0624883 0.108233i
\(596\) 1.87866 + 0.943497i 0.0769528 + 0.0386472i
\(597\) 0 0
\(598\) −3.40717 4.57663i −0.139330 0.187152i
\(599\) −17.4587 4.13779i −0.713344 0.169066i −0.142108 0.989851i \(-0.545388\pi\)
−0.571236 + 0.820786i \(0.693536\pi\)
\(600\) 0 0
\(601\) −20.4833 + 27.5138i −0.835531 + 1.12231i 0.155389 + 0.987853i \(0.450337\pi\)
−0.990919 + 0.134459i \(0.957070\pi\)
\(602\) 1.12414 0.943264i 0.0458164 0.0384446i
\(603\) 0 0
\(604\) −4.40962 3.70011i −0.179425 0.150555i
\(605\) −1.81144 + 0.429319i −0.0736455 + 0.0174543i
\(606\) 0 0
\(607\) 1.64151 + 1.07964i 0.0666267 + 0.0438211i 0.582385 0.812913i \(-0.302120\pi\)
−0.515759 + 0.856734i \(0.672490\pi\)
\(608\) −12.0755 7.94216i −0.489725 0.322097i
\(609\) 0 0
\(610\) 0.240179 0.0569234i 0.00972456 0.00230476i
\(611\) −11.2987 9.48071i −0.457095 0.383549i
\(612\) 0 0
\(613\) −1.60067 + 1.34312i −0.0646505 + 0.0542482i −0.674540 0.738238i \(-0.735658\pi\)
0.609890 + 0.792486i \(0.291214\pi\)
\(614\) 9.25743 12.4349i 0.373599 0.501831i
\(615\) 0 0
\(616\) 37.0431 + 8.77938i 1.49251 + 0.353731i
\(617\) −24.8220 33.3418i −0.999298 1.34229i −0.938928 0.344113i \(-0.888180\pi\)
−0.0603694 0.998176i \(-0.519228\pi\)
\(618\) 0 0
\(619\) −6.28378 3.15583i −0.252567 0.126844i 0.318012 0.948087i \(-0.396985\pi\)
−0.570579 + 0.821243i \(0.693281\pi\)
\(620\) −0.00455322 + 0.00788641i −0.000182862 + 0.000316726i
\(621\) 0 0
\(622\) −20.8154 36.0533i −0.834620 1.44561i
\(623\) −2.68331 46.0707i −0.107505 1.84578i
\(624\) 0 0
\(625\) −21.0388 + 2.45908i −0.841553 + 0.0983634i
\(626\) −5.77312 19.2836i −0.230740 0.770727i
\(627\) 0 0
\(628\) 1.28198 + 2.97195i 0.0511564 + 0.118594i
\(629\) 4.30925 + 1.56844i 0.171821 + 0.0625378i
\(630\) 0 0
\(631\) 6.32771 2.30310i 0.251902 0.0916848i −0.212983 0.977056i \(-0.568318\pi\)
0.464885 + 0.885371i \(0.346096\pi\)
\(632\) −23.9463 25.3816i −0.952534 1.00963i
\(633\) 0 0
\(634\) 13.1049 6.58153i 0.520463 0.261386i
\(635\) 0.547578 9.40155i 0.0217300 0.373089i
\(636\) 0 0
\(637\) −7.95367 + 26.5671i −0.315136 + 1.05263i
\(638\) −7.10175 + 40.2760i −0.281161 + 1.59454i
\(639\) 0 0
\(640\) −1.18865 6.74119i −0.0469857 0.266469i
\(641\) −12.9949 1.51889i −0.513270 0.0599926i −0.144484 0.989507i \(-0.546152\pi\)
−0.368786 + 0.929515i \(0.620226\pi\)
\(642\) 0 0
\(643\) 1.79987 1.90775i 0.0709800 0.0752344i −0.690910 0.722941i \(-0.742790\pi\)
0.761890 + 0.647706i \(0.224272\pi\)
\(644\) −0.723533 + 1.67734i −0.0285112 + 0.0660964i
\(645\) 0 0
\(646\) 12.9996 8.54998i 0.511463 0.336394i
\(647\) 2.94663 0.115844 0.0579219 0.998321i \(-0.481553\pi\)
0.0579219 + 0.998321i \(0.481553\pi\)
\(648\) 0 0
\(649\) 5.34772 0.209916
\(650\) 19.0486 12.5285i 0.747147 0.491406i
\(651\) 0 0
\(652\) 0.465631 1.07945i 0.0182355 0.0422747i
\(653\) −24.1758 + 25.6248i −0.946071 + 1.00278i 0.0539200 + 0.998545i \(0.482828\pi\)
−0.999991 + 0.00423147i \(0.998653\pi\)
\(654\) 0 0
\(655\) −2.80704 0.328096i −0.109680 0.0128198i
\(656\) 4.76957 + 27.0496i 0.186221 + 1.05611i
\(657\) 0 0
\(658\) −5.06840 + 28.7443i −0.197587 + 1.12057i
\(659\) −4.81941 + 16.0979i −0.187738 + 0.627087i 0.811357 + 0.584550i \(0.198729\pi\)
−0.999095 + 0.0425366i \(0.986456\pi\)
\(660\) 0 0
\(661\) 0.169220 2.90540i 0.00658190 0.113007i −0.993417 0.114555i \(-0.963456\pi\)
0.999999 + 0.00154821i \(0.000492812\pi\)
\(662\) −32.4583 + 16.3012i −1.26153 + 0.633562i
\(663\) 0 0
\(664\) 1.20272 + 1.27481i 0.0466746 + 0.0494722i
\(665\) −12.7928 + 4.65618i −0.496082 + 0.180559i
\(666\) 0 0
\(667\) 7.71007 + 2.80623i 0.298535 + 0.108658i
\(668\) −3.22673 7.48041i −0.124846 0.289426i
\(669\) 0 0
\(670\) 1.23835 + 4.13637i 0.0478415 + 0.159802i
\(671\) −1.19399 + 0.139558i −0.0460936 + 0.00538757i
\(672\) 0 0
\(673\) −0.176906 3.03736i −0.00681923 0.117082i −1.00000 0.000496017i \(-0.999842\pi\)
0.993181 0.116586i \(-0.0371949\pi\)
\(674\) 2.40053 + 4.15783i 0.0924648 + 0.160154i
\(675\) 0 0
\(676\) 0.638419 1.10577i 0.0245546 0.0425298i
\(677\) 33.4519 + 16.8002i 1.28566 + 0.645684i 0.954590 0.297921i \(-0.0962933\pi\)
0.331072 + 0.943605i \(0.392590\pi\)
\(678\) 0 0
\(679\) −30.9864 41.6219i −1.18915 1.59730i
\(680\) 1.85417 + 0.439446i 0.0711042 + 0.0168520i
\(681\) 0 0
\(682\) 0.163697 0.219883i 0.00626829 0.00841977i
\(683\) −23.8512 + 20.0135i −0.912641 + 0.765797i −0.972620 0.232403i \(-0.925341\pi\)
0.0599783 + 0.998200i \(0.480897\pi\)
\(684\) 0 0
\(685\) −1.16318 0.976025i −0.0444429 0.0372920i
\(686\) 11.4366 2.71053i 0.436653 0.103489i
\(687\) 0 0
\(688\) 0.920007 + 0.605098i 0.0350749 + 0.0230691i
\(689\) 35.4358 + 23.3065i 1.35000 + 0.887907i
\(690\) 0 0
\(691\) 10.4258 2.47095i 0.396615 0.0939995i −0.0274683 0.999623i \(-0.508745\pi\)
0.424083 + 0.905623i \(0.360596\pi\)
\(692\) 0.501162 + 0.420525i 0.0190513 + 0.0159859i
\(693\) 0 0
\(694\) −26.3811 + 22.1364i −1.00141 + 0.840286i
\(695\) 1.79114 2.40592i 0.0679419 0.0912618i
\(696\) 0 0
\(697\) −8.68251 2.05779i −0.328874 0.0779445i
\(698\) 2.77903 + 3.73289i 0.105188 + 0.141292i
\(699\) 0 0
\(700\) −6.52308 3.27602i −0.246549 0.123822i
\(701\) −10.3580 + 17.9406i −0.391216 + 0.677607i −0.992610 0.121346i \(-0.961279\pi\)
0.601394 + 0.798953i \(0.294612\pi\)
\(702\) 0 0
\(703\) −10.2395 17.7353i −0.386188 0.668898i
\(704\) 1.31727 + 22.6166i 0.0496464 + 0.852396i
\(705\) 0 0
\(706\) −3.32048 + 0.388109i −0.124968 + 0.0146067i
\(707\) 14.1432 + 47.2416i 0.531910 + 1.77670i
\(708\) 0 0
\(709\) −7.20452 16.7019i −0.270571 0.627255i 0.727708 0.685887i \(-0.240585\pi\)
−0.998280 + 0.0586319i \(0.981326\pi\)
\(710\) −8.67796 3.15852i −0.325678 0.118537i
\(711\) 0 0
\(712\) 27.1066 9.86600i 1.01586 0.369744i
\(713\) −0.0377403 0.0400024i −0.00141339 0.00149810i
\(714\) 0 0
\(715\) 5.42080 2.72243i 0.202726 0.101813i
\(716\) 0.270778 4.64907i 0.0101194 0.173744i
\(717\) 0 0
\(718\) 0.287306 0.959668i 0.0107222 0.0358145i
\(719\) −5.53156 + 31.3710i −0.206292 + 1.16994i 0.689101 + 0.724666i \(0.258006\pi\)
−0.895393 + 0.445277i \(0.853105\pi\)
\(720\) 0 0
\(721\) −1.44761 8.20980i −0.0539118 0.305749i
\(722\) −39.8631 4.65933i −1.48355 0.173402i
\(723\) 0 0
\(724\) −2.00034 + 2.12024i −0.0743421 + 0.0787981i
\(725\) −12.9859 + 30.1048i −0.482285 + 1.11806i
\(726\) 0 0
\(727\) −7.91945 + 5.20870i −0.293716 + 0.193180i −0.687811 0.725890i \(-0.741428\pi\)
0.394095 + 0.919070i \(0.371058\pi\)
\(728\) −30.9566 −1.14733
\(729\) 0 0
\(730\) −12.2325 −0.452746
\(731\) −0.298878 + 0.196575i −0.0110544 + 0.00727060i
\(732\) 0 0
\(733\) −16.6921 + 38.6967i −0.616538 + 1.42930i 0.268271 + 0.963343i \(0.413548\pi\)
−0.884809 + 0.465953i \(0.845712\pi\)
\(734\) 10.0376 10.6393i 0.370496 0.392703i
\(735\) 0 0
\(736\) −2.53950 0.296824i −0.0936070 0.0109411i
\(737\) −3.65153 20.7089i −0.134506 0.762821i
\(738\) 0 0
\(739\) 8.32565 47.2171i 0.306264 1.73691i −0.311232 0.950334i \(-0.600742\pi\)
0.617496 0.786574i \(-0.288147\pi\)
\(740\) −0.172045 + 0.574669i −0.00632449 + 0.0211253i
\(741\) 0 0
\(742\) 4.88024 83.7904i 0.179159 3.07604i
\(743\) −9.21372 + 4.62730i −0.338019 + 0.169759i −0.609709 0.792625i \(-0.708714\pi\)
0.271690 + 0.962385i \(0.412417\pi\)
\(744\) 0 0
\(745\) 1.90195 + 2.01594i 0.0696819 + 0.0738585i
\(746\) 7.08589 2.57905i 0.259433 0.0944258i
\(747\) 0 0
\(748\) 2.08580 + 0.759170i 0.0762645 + 0.0277580i
\(749\) −2.62669 6.08934i −0.0959770 0.222500i
\(750\) 0 0
\(751\) −7.18583 24.0023i −0.262215 0.875858i −0.983141 0.182847i \(-0.941469\pi\)
0.720927 0.693011i \(-0.243716\pi\)
\(752\) −21.7540 + 2.54268i −0.793287 + 0.0927220i
\(753\) 0 0
\(754\) −1.93368 33.2000i −0.0704205 1.20907i
\(755\) −3.79446 6.57219i −0.138094 0.239187i
\(756\) 0 0
\(757\) 3.05875 5.29791i 0.111172 0.192556i −0.805071 0.593178i \(-0.797873\pi\)
0.916243 + 0.400623i \(0.131206\pi\)
\(758\) −35.9421 18.0508i −1.30547 0.655634i
\(759\) 0 0
\(760\) −5.08156 6.82572i −0.184328 0.247595i
\(761\) 43.6455 + 10.3442i 1.58215 + 0.374976i 0.925357 0.379097i \(-0.123766\pi\)
0.656790 + 0.754073i \(0.271914\pi\)
\(762\) 0 0
\(763\) 10.2406 13.7555i 0.370733 0.497981i
\(764\) −3.82972 + 3.21351i −0.138554 + 0.116261i
\(765\) 0 0
\(766\) −9.50299 7.97396i −0.343357 0.288111i
\(767\) −4.23136 + 1.00285i −0.152785 + 0.0362108i
\(768\) 0 0
\(769\) −31.6906 20.8432i −1.14279 0.751626i −0.170490 0.985359i \(-0.554535\pi\)
−0.972301 + 0.233734i \(0.924906\pi\)
\(770\) −10.0293 6.59639i −0.361431 0.237717i
\(771\) 0 0
\(772\) 6.79092 1.60948i 0.244411 0.0579264i
\(773\) 11.7711 + 9.87712i 0.423377 + 0.355255i 0.829446 0.558587i \(-0.188656\pi\)
−0.406069 + 0.913842i \(0.633101\pi\)
\(774\) 0 0
\(775\) 0.168345 0.141258i 0.00604713 0.00507415i
\(776\) 19.3687 26.0167i 0.695295 0.933944i
\(777\) 0 0
\(778\) −34.1882 8.10276i −1.22571 0.290498i
\(779\) 23.7954 + 31.9628i 0.852559 + 1.14518i
\(780\) 0 0
\(781\) 40.1918 + 20.1851i 1.43818 + 0.722279i