Properties

Label 637.2.f.l.295.4
Level $637$
Weight $2$
Character 637.295
Analytic conductor $5.086$
Analytic rank $0$
Dimension $16$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(295,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.295");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.f (of order \(3\), degree \(2\), 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: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: 16.0.468066644398978174550016.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 8x^{14} + 45x^{12} + 124x^{10} + 248x^{8} + 250x^{6} + 177x^{4} + 14x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.4
Root \(1.04641 + 1.81243i\) of defining polynomial
Character \(\chi\) \(=\) 637.295
Dual form 637.2.f.l.393.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.289905 - 0.502131i) q^{2} +(0.946019 - 1.63855i) q^{3} +(0.831910 + 1.44091i) q^{4} +1.47362 q^{5} +(-0.548512 - 0.950050i) q^{6} +2.12432 q^{8} +(-0.289905 - 0.502131i) q^{9} +O(q^{10})\) \(q+(0.289905 - 0.502131i) q^{2} +(0.946019 - 1.63855i) q^{3} +(0.831910 + 1.44091i) q^{4} +1.47362 q^{5} +(-0.548512 - 0.950050i) q^{6} +2.12432 q^{8} +(-0.289905 - 0.502131i) q^{9} +(0.427209 - 0.739948i) q^{10} +(-0.289905 + 0.502131i) q^{11} +3.14801 q^{12} +(-0.128893 - 3.60325i) q^{13} +(1.39407 - 2.41460i) q^{15} +(-1.04797 + 1.81513i) q^{16} +(0.598285 + 1.03626i) q^{17} -0.336180 q^{18} +(0.230479 + 0.399201i) q^{19} +(1.22592 + 2.12335i) q^{20} +(0.168090 + 0.291141i) q^{22} +(-1.18398 + 2.05071i) q^{23} +(2.00965 - 3.48081i) q^{24} -2.82845 q^{25} +(-1.84667 - 0.979879i) q^{26} +4.57909 q^{27} +(3.44550 - 5.96777i) q^{29} +(-0.808297 - 1.40001i) q^{30} +4.44342 q^{31} +(2.73194 + 4.73187i) q^{32} +(0.548512 + 0.950050i) q^{33} +0.693783 q^{34} +(0.482350 - 0.835455i) q^{36} +(-4.58150 + 7.93540i) q^{37} +0.267268 q^{38} +(-6.02605 - 3.19754i) q^{39} +3.13044 q^{40} +(2.00845 - 3.47874i) q^{41} +(-4.02951 - 6.97931i) q^{43} -0.964700 q^{44} +(-0.427209 - 0.739948i) q^{45} +(0.686481 + 1.18902i) q^{46} -11.5193 q^{47} +(1.98280 + 3.43430i) q^{48} +(-0.819983 + 1.42025i) q^{50} +2.26396 q^{51} +(5.08473 - 3.18330i) q^{52} -9.39519 q^{53} +(1.32750 - 2.29930i) q^{54} +(-0.427209 + 0.739948i) q^{55} +0.872150 q^{57} +(-1.99773 - 3.46018i) q^{58} +(-0.120459 - 0.208642i) q^{59} +4.63896 q^{60} +(-3.86355 - 6.69187i) q^{61} +(1.28817 - 2.23118i) q^{62} -1.02385 q^{64} +(-0.189939 - 5.30981i) q^{65} +0.636066 q^{66} +(0.724287 - 1.25450i) q^{67} +(-0.995438 + 1.72415i) q^{68} +(2.24013 + 3.88001i) q^{69} +(6.25725 + 10.8379i) q^{71} +(-0.615852 - 1.06669i) q^{72} -3.69401 q^{73} +(2.65640 + 4.60103i) q^{74} +(-2.67577 + 4.63457i) q^{75} +(-0.383476 + 0.664199i) q^{76} +(-3.35257 + 2.09888i) q^{78} +16.0793 q^{79} +(-1.54430 + 2.67481i) q^{80} +(5.20163 - 9.00948i) q^{81} +(-1.16452 - 2.01701i) q^{82} -15.4005 q^{83} +(0.881643 + 1.52705i) q^{85} -4.67270 q^{86} +(-6.51901 - 11.2913i) q^{87} +(-0.615852 + 1.06669i) q^{88} +(-1.24553 + 2.15733i) q^{89} -0.495401 q^{90} -3.93984 q^{92} +(4.20356 - 7.28078i) q^{93} +(-3.33950 + 5.78418i) q^{94} +(0.339638 + 0.588270i) q^{95} +10.3379 q^{96} +(-7.82275 - 13.5494i) q^{97} +0.336180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} - 4 q^{16} - 56 q^{18} + 28 q^{22} + 12 q^{23} - 24 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} - 8 q^{37} - 4 q^{39} + 32 q^{43} - 8 q^{44} - 4 q^{46} + 36 q^{50} - 88 q^{51} - 8 q^{53} - 96 q^{57} - 48 q^{58} + 128 q^{60} - 64 q^{64} + 16 q^{65} + 20 q^{67} + 8 q^{71} + 28 q^{72} + 76 q^{74} + 28 q^{78} - 8 q^{79} + 56 q^{81} + 36 q^{85} + 8 q^{86} + 28 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.289905 0.502131i 0.204994 0.355060i −0.745137 0.666912i \(-0.767616\pi\)
0.950131 + 0.311852i \(0.100949\pi\)
\(3\) 0.946019 1.63855i 0.546185 0.946019i −0.452347 0.891842i \(-0.649413\pi\)
0.998531 0.0541772i \(-0.0172536\pi\)
\(4\) 0.831910 + 1.44091i 0.415955 + 0.720455i
\(5\) 1.47362 0.659022 0.329511 0.944152i \(-0.393116\pi\)
0.329511 + 0.944152i \(0.393116\pi\)
\(6\) −0.548512 0.950050i −0.223929 0.387856i
\(7\) 0 0
\(8\) 2.12432 0.751061
\(9\) −0.289905 0.502131i −0.0966351 0.167377i
\(10\) 0.427209 0.739948i 0.135095 0.233992i
\(11\) −0.289905 + 0.502131i −0.0874097 + 0.151398i −0.906415 0.422387i \(-0.861192\pi\)
0.819006 + 0.573785i \(0.194526\pi\)
\(12\) 3.14801 0.908753
\(13\) −0.128893 3.60325i −0.0357485 0.999361i
\(14\) 0 0
\(15\) 1.39407 2.41460i 0.359947 0.623447i
\(16\) −1.04797 + 1.81513i −0.261992 + 0.453784i
\(17\) 0.598285 + 1.03626i 0.145105 + 0.251330i 0.929412 0.369043i \(-0.120315\pi\)
−0.784307 + 0.620373i \(0.786981\pi\)
\(18\) −0.336180 −0.0792384
\(19\) 0.230479 + 0.399201i 0.0528755 + 0.0915831i 0.891252 0.453509i \(-0.149828\pi\)
−0.838376 + 0.545092i \(0.816495\pi\)
\(20\) 1.22592 + 2.12335i 0.274123 + 0.474796i
\(21\) 0 0
\(22\) 0.168090 + 0.291141i 0.0358369 + 0.0620714i
\(23\) −1.18398 + 2.05071i −0.246876 + 0.427602i −0.962657 0.270723i \(-0.912737\pi\)
0.715781 + 0.698324i \(0.246071\pi\)
\(24\) 2.00965 3.48081i 0.410218 0.710518i
\(25\) −2.82845 −0.565690
\(26\) −1.84667 0.979879i −0.362161 0.192170i
\(27\) 4.57909 0.881247
\(28\) 0 0
\(29\) 3.44550 5.96777i 0.639813 1.10819i −0.345661 0.938359i \(-0.612345\pi\)
0.985474 0.169828i \(-0.0543214\pi\)
\(30\) −0.808297 1.40001i −0.147574 0.255606i
\(31\) 4.44342 0.798061 0.399031 0.916938i \(-0.369347\pi\)
0.399031 + 0.916938i \(0.369347\pi\)
\(32\) 2.73194 + 4.73187i 0.482944 + 0.836484i
\(33\) 0.548512 + 0.950050i 0.0954837 + 0.165383i
\(34\) 0.693783 0.118983
\(35\) 0 0
\(36\) 0.482350 0.835455i 0.0803917 0.139242i
\(37\) −4.58150 + 7.93540i −0.753195 + 1.30457i 0.193072 + 0.981185i \(0.438155\pi\)
−0.946267 + 0.323387i \(0.895179\pi\)
\(38\) 0.267268 0.0433566
\(39\) −6.02605 3.19754i −0.964940 0.512017i
\(40\) 3.13044 0.494965
\(41\) 2.00845 3.47874i 0.313667 0.543288i −0.665486 0.746410i \(-0.731776\pi\)
0.979153 + 0.203123i \(0.0651090\pi\)
\(42\) 0 0
\(43\) −4.02951 6.97931i −0.614494 1.06433i −0.990473 0.137706i \(-0.956027\pi\)
0.375979 0.926628i \(-0.377306\pi\)
\(44\) −0.964700 −0.145434
\(45\) −0.427209 0.739948i −0.0636846 0.110305i
\(46\) 0.686481 + 1.18902i 0.101216 + 0.175312i
\(47\) −11.5193 −1.68026 −0.840129 0.542386i \(-0.817521\pi\)
−0.840129 + 0.542386i \(0.817521\pi\)
\(48\) 1.98280 + 3.43430i 0.286192 + 0.495699i
\(49\) 0 0
\(50\) −0.819983 + 1.42025i −0.115963 + 0.200854i
\(51\) 2.26396 0.317017
\(52\) 5.08473 3.18330i 0.705125 0.441444i
\(53\) −9.39519 −1.29053 −0.645264 0.763959i \(-0.723253\pi\)
−0.645264 + 0.763959i \(0.723253\pi\)
\(54\) 1.32750 2.29930i 0.180650 0.312895i
\(55\) −0.427209 + 0.739948i −0.0576049 + 0.0997746i
\(56\) 0 0
\(57\) 0.872150 0.115519
\(58\) −1.99773 3.46018i −0.262315 0.454344i
\(59\) −0.120459 0.208642i −0.0156825 0.0271629i 0.858078 0.513520i \(-0.171659\pi\)
−0.873760 + 0.486357i \(0.838325\pi\)
\(60\) 4.63896 0.598888
\(61\) −3.86355 6.69187i −0.494677 0.856806i 0.505304 0.862941i \(-0.331380\pi\)
−0.999981 + 0.00613544i \(0.998047\pi\)
\(62\) 1.28817 2.23118i 0.163598 0.283360i
\(63\) 0 0
\(64\) −1.02385 −0.127982
\(65\) −0.189939 5.30981i −0.0235590 0.658600i
\(66\) 0.636066 0.0782943
\(67\) 0.724287 1.25450i 0.0884857 0.153262i −0.818385 0.574670i \(-0.805131\pi\)
0.906871 + 0.421408i \(0.138464\pi\)
\(68\) −0.995438 + 1.72415i −0.120715 + 0.209084i
\(69\) 2.24013 + 3.88001i 0.269680 + 0.467099i
\(70\) 0 0
\(71\) 6.25725 + 10.8379i 0.742599 + 1.28622i 0.951308 + 0.308241i \(0.0997405\pi\)
−0.208709 + 0.977978i \(0.566926\pi\)
\(72\) −0.615852 1.06669i −0.0725788 0.125710i
\(73\) −3.69401 −0.432352 −0.216176 0.976354i \(-0.569358\pi\)
−0.216176 + 0.976354i \(0.569358\pi\)
\(74\) 2.65640 + 4.60103i 0.308801 + 0.534858i
\(75\) −2.67577 + 4.63457i −0.308971 + 0.535154i
\(76\) −0.383476 + 0.664199i −0.0439877 + 0.0761889i
\(77\) 0 0
\(78\) −3.35257 + 2.09888i −0.379603 + 0.237651i
\(79\) 16.0793 1.80907 0.904533 0.426403i \(-0.140219\pi\)
0.904533 + 0.426403i \(0.140219\pi\)
\(80\) −1.54430 + 2.67481i −0.172658 + 0.299053i
\(81\) 5.20163 9.00948i 0.577958 1.00105i
\(82\) −1.16452 2.01701i −0.128600 0.222741i
\(83\) −15.4005 −1.69042 −0.845212 0.534431i \(-0.820526\pi\)
−0.845212 + 0.534431i \(0.820526\pi\)
\(84\) 0 0
\(85\) 0.881643 + 1.52705i 0.0956276 + 0.165632i
\(86\) −4.67270 −0.503870
\(87\) −6.51901 11.2913i −0.698911 1.21055i
\(88\) −0.615852 + 1.06669i −0.0656500 + 0.113709i
\(89\) −1.24553 + 2.15733i −0.132026 + 0.228676i −0.924458 0.381285i \(-0.875482\pi\)
0.792431 + 0.609961i \(0.208815\pi\)
\(90\) −0.495401 −0.0522198
\(91\) 0 0
\(92\) −3.93984 −0.410757
\(93\) 4.20356 7.28078i 0.435889 0.754982i
\(94\) −3.33950 + 5.78418i −0.344443 + 0.596593i
\(95\) 0.339638 + 0.588270i 0.0348461 + 0.0603552i
\(96\) 10.3379 1.05511
\(97\) −7.82275 13.5494i −0.794280 1.37573i −0.923295 0.384091i \(-0.874515\pi\)
0.129015 0.991643i \(-0.458818\pi\)
\(98\) 0 0
\(99\) 0.336180 0.0337874
\(100\) −2.35302 4.07555i −0.235302 0.407555i
\(101\) −7.00682 + 12.1362i −0.697205 + 1.20759i 0.272227 + 0.962233i \(0.412240\pi\)
−0.969432 + 0.245361i \(0.921093\pi\)
\(102\) 0.656332 1.13680i 0.0649866 0.112560i
\(103\) 10.7492 1.05915 0.529576 0.848262i \(-0.322351\pi\)
0.529576 + 0.848262i \(0.322351\pi\)
\(104\) −0.273810 7.65445i −0.0268493 0.750581i
\(105\) 0 0
\(106\) −2.72371 + 4.71761i −0.264551 + 0.458215i
\(107\) −1.87761 + 3.25212i −0.181516 + 0.314394i −0.942397 0.334497i \(-0.891434\pi\)
0.760881 + 0.648891i \(0.224767\pi\)
\(108\) 3.80939 + 6.59806i 0.366559 + 0.634899i
\(109\) −8.20833 −0.786215 −0.393108 0.919492i \(-0.628600\pi\)
−0.393108 + 0.919492i \(0.628600\pi\)
\(110\) 0.247700 + 0.429030i 0.0236173 + 0.0409064i
\(111\) 8.66838 + 15.0141i 0.822766 + 1.42507i
\(112\) 0 0
\(113\) 3.90423 + 6.76233i 0.367279 + 0.636146i 0.989139 0.146982i \(-0.0469560\pi\)
−0.621860 + 0.783129i \(0.713623\pi\)
\(114\) 0.252841 0.437933i 0.0236807 0.0410162i
\(115\) −1.74473 + 3.02196i −0.162697 + 0.281799i
\(116\) 11.4654 1.06453
\(117\) −1.77193 + 1.10932i −0.163815 + 0.102557i
\(118\) −0.139687 −0.0128593
\(119\) 0 0
\(120\) 2.96145 5.12939i 0.270342 0.468247i
\(121\) 5.33191 + 9.23514i 0.484719 + 0.839558i
\(122\) −4.48026 −0.405623
\(123\) −3.80007 6.58191i −0.342641 0.593471i
\(124\) 3.69652 + 6.40257i 0.331958 + 0.574967i
\(125\) −11.5361 −1.03182
\(126\) 0 0
\(127\) 0.469682 0.813513i 0.0416775 0.0721876i −0.844434 0.535659i \(-0.820063\pi\)
0.886112 + 0.463472i \(0.153396\pi\)
\(128\) −5.76071 + 9.97784i −0.509179 + 0.881925i
\(129\) −15.2480 −1.34251
\(130\) −2.72128 1.44397i −0.238672 0.126644i
\(131\) −1.13717 −0.0993546 −0.0496773 0.998765i \(-0.515819\pi\)
−0.0496773 + 0.998765i \(0.515819\pi\)
\(132\) −0.912625 + 1.58071i −0.0794338 + 0.137583i
\(133\) 0 0
\(134\) −0.419949 0.727373i −0.0362781 0.0628355i
\(135\) 6.74783 0.580761
\(136\) 1.27095 + 2.20135i 0.108983 + 0.188764i
\(137\) 4.31998 + 7.48243i 0.369081 + 0.639267i 0.989422 0.145065i \(-0.0463391\pi\)
−0.620341 + 0.784332i \(0.713006\pi\)
\(138\) 2.59770 0.221131
\(139\) 7.27709 + 12.6043i 0.617235 + 1.06908i 0.989988 + 0.141151i \(0.0450804\pi\)
−0.372753 + 0.927930i \(0.621586\pi\)
\(140\) 0 0
\(141\) −10.8975 + 18.8749i −0.917731 + 1.58956i
\(142\) 7.25604 0.608913
\(143\) 1.84667 + 0.979879i 0.154426 + 0.0819416i
\(144\) 1.21525 0.101270
\(145\) 5.07734 8.79422i 0.421650 0.730320i
\(146\) −1.07091 + 1.85488i −0.0886295 + 0.153511i
\(147\) 0 0
\(148\) −15.2456 −1.25318
\(149\) −6.69011 11.5876i −0.548075 0.949294i −0.998406 0.0564323i \(-0.982027\pi\)
0.450331 0.892861i \(-0.351306\pi\)
\(150\) 1.55144 + 2.68717i 0.126675 + 0.219407i
\(151\) 16.1392 1.31339 0.656693 0.754158i \(-0.271955\pi\)
0.656693 + 0.754158i \(0.271955\pi\)
\(152\) 0.489611 + 0.848032i 0.0397127 + 0.0687845i
\(153\) 0.346892 0.600834i 0.0280445 0.0485745i
\(154\) 0 0
\(155\) 6.54790 0.525940
\(156\) −0.405757 11.3431i −0.0324866 0.908172i
\(157\) −0.628681 −0.0501742 −0.0250871 0.999685i \(-0.507986\pi\)
−0.0250871 + 0.999685i \(0.507986\pi\)
\(158\) 4.66148 8.07393i 0.370848 0.642327i
\(159\) −8.88803 + 15.3945i −0.704867 + 1.22087i
\(160\) 4.02584 + 6.97296i 0.318271 + 0.551261i
\(161\) 0 0
\(162\) −3.01596 5.22379i −0.236956 0.410420i
\(163\) 5.84207 + 10.1188i 0.457586 + 0.792563i 0.998833 0.0483011i \(-0.0153807\pi\)
−0.541246 + 0.840864i \(0.682047\pi\)
\(164\) 6.68340 0.521886
\(165\) 0.808297 + 1.40001i 0.0629258 + 0.108991i
\(166\) −4.46469 + 7.73306i −0.346527 + 0.600202i
\(167\) −11.0293 + 19.1033i −0.853474 + 1.47826i 0.0245803 + 0.999698i \(0.492175\pi\)
−0.878054 + 0.478562i \(0.841158\pi\)
\(168\) 0 0
\(169\) −12.9668 + 0.928867i −0.997444 + 0.0714513i
\(170\) 1.02237 0.0784123
\(171\) 0.133634 0.231461i 0.0102193 0.0177003i
\(172\) 6.70437 11.6123i 0.511204 0.885431i
\(173\) −5.69534 9.86463i −0.433009 0.749994i 0.564122 0.825692i \(-0.309215\pi\)
−0.997131 + 0.0756980i \(0.975881\pi\)
\(174\) −7.55958 −0.573090
\(175\) 0 0
\(176\) −0.607623 1.05243i −0.0458013 0.0793302i
\(177\) −0.455828 −0.0342621
\(178\) 0.722173 + 1.25084i 0.0541292 + 0.0937544i
\(179\) 1.73621 3.00721i 0.129771 0.224769i −0.793817 0.608157i \(-0.791909\pi\)
0.923588 + 0.383387i \(0.125243\pi\)
\(180\) 0.710799 1.23114i 0.0529799 0.0917638i
\(181\) 21.0992 1.56829 0.784145 0.620578i \(-0.213102\pi\)
0.784145 + 0.620578i \(0.213102\pi\)
\(182\) 0 0
\(183\) −14.6200 −1.08074
\(184\) −2.51514 + 4.35636i −0.185419 + 0.321155i
\(185\) −6.75138 + 11.6937i −0.496372 + 0.859741i
\(186\) −2.43727 4.22147i −0.178709 0.309533i
\(187\) −0.693783 −0.0507345
\(188\) −9.58300 16.5982i −0.698912 1.21055i
\(189\) 0 0
\(190\) 0.393851 0.0285730
\(191\) −5.95945 10.3221i −0.431211 0.746879i 0.565767 0.824565i \(-0.308580\pi\)
−0.996978 + 0.0776864i \(0.975247\pi\)
\(192\) −0.968585 + 1.67764i −0.0699016 + 0.121073i
\(193\) −7.18970 + 12.4529i −0.517526 + 0.896381i 0.482267 + 0.876024i \(0.339814\pi\)
−0.999793 + 0.0203567i \(0.993520\pi\)
\(194\) −9.07143 −0.651290
\(195\) −8.88009 4.71195i −0.635916 0.337430i
\(196\) 0 0
\(197\) −3.48462 + 6.03553i −0.248269 + 0.430014i −0.963046 0.269339i \(-0.913195\pi\)
0.714777 + 0.699353i \(0.246528\pi\)
\(198\) 0.0974604 0.168806i 0.00692621 0.0119965i
\(199\) −1.78676 3.09476i −0.126660 0.219382i 0.795721 0.605664i \(-0.207092\pi\)
−0.922381 + 0.386282i \(0.873759\pi\)
\(200\) −6.00854 −0.424868
\(201\) −1.37038 2.37357i −0.0966591 0.167418i
\(202\) 4.06263 + 7.03668i 0.285846 + 0.495099i
\(203\) 0 0
\(204\) 1.88341 + 3.26216i 0.131865 + 0.228397i
\(205\) 2.95969 5.12633i 0.206714 0.358038i
\(206\) 3.11626 5.39751i 0.217120 0.376062i
\(207\) 1.37296 0.0954275
\(208\) 6.67545 + 3.54213i 0.462859 + 0.245603i
\(209\) −0.267268 −0.0184873
\(210\) 0 0
\(211\) 7.05694 12.2230i 0.485820 0.841464i −0.514048 0.857762i \(-0.671855\pi\)
0.999867 + 0.0162974i \(0.00518784\pi\)
\(212\) −7.81595 13.5376i −0.536802 0.929768i
\(213\) 23.6779 1.62238
\(214\) 1.08866 + 1.88561i 0.0744192 + 0.128898i
\(215\) −5.93795 10.2848i −0.404965 0.701420i
\(216\) 9.72746 0.661870
\(217\) 0 0
\(218\) −2.37964 + 4.12165i −0.161169 + 0.279154i
\(219\) −3.49461 + 6.05284i −0.236144 + 0.409013i
\(220\) −1.42160 −0.0958442
\(221\) 3.65678 2.28933i 0.245982 0.153997i
\(222\) 10.0520 0.674649
\(223\) 0.454565 0.787329i 0.0304399 0.0527235i −0.850404 0.526130i \(-0.823643\pi\)
0.880844 + 0.473407i \(0.156976\pi\)
\(224\) 0 0
\(225\) 0.819983 + 1.42025i 0.0546655 + 0.0946835i
\(226\) 4.52743 0.301160
\(227\) 1.16756 + 2.02228i 0.0774938 + 0.134223i 0.902168 0.431385i \(-0.141975\pi\)
−0.824674 + 0.565608i \(0.808642\pi\)
\(228\) 0.725550 + 1.25669i 0.0480508 + 0.0832263i
\(229\) −16.6807 −1.10229 −0.551147 0.834408i \(-0.685810\pi\)
−0.551147 + 0.834408i \(0.685810\pi\)
\(230\) 1.01161 + 1.75216i 0.0667036 + 0.115534i
\(231\) 0 0
\(232\) 7.31934 12.6775i 0.480538 0.832317i
\(233\) −16.5264 −1.08268 −0.541341 0.840803i \(-0.682083\pi\)
−0.541341 + 0.840803i \(0.682083\pi\)
\(234\) 0.0433313 + 1.21134i 0.00283266 + 0.0791878i
\(235\) −16.9750 −1.10733
\(236\) 0.200423 0.347143i 0.0130464 0.0225971i
\(237\) 15.2114 26.3469i 0.988084 1.71141i
\(238\) 0 0
\(239\) 3.18043 0.205725 0.102862 0.994696i \(-0.467200\pi\)
0.102862 + 0.994696i \(0.467200\pi\)
\(240\) 2.92188 + 5.06085i 0.188607 + 0.326676i
\(241\) −7.92992 13.7350i −0.510811 0.884751i −0.999922 0.0125290i \(-0.996012\pi\)
0.489110 0.872222i \(-0.337322\pi\)
\(242\) 6.18299 0.397458
\(243\) −2.97304 5.14945i −0.190720 0.330338i
\(244\) 6.42825 11.1341i 0.411527 0.712785i
\(245\) 0 0
\(246\) −4.40664 −0.280957
\(247\) 1.40871 0.881927i 0.0896343 0.0561157i
\(248\) 9.43925 0.599393
\(249\) −14.5692 + 25.2345i −0.923284 + 1.59917i
\(250\) −3.34439 + 5.79265i −0.211518 + 0.366359i
\(251\) 1.24788 + 2.16139i 0.0787654 + 0.136426i 0.902718 0.430234i \(-0.141569\pi\)
−0.823952 + 0.566659i \(0.808236\pi\)
\(252\) 0 0
\(253\) −0.686481 1.18902i −0.0431587 0.0747531i
\(254\) −0.272326 0.471683i −0.0170873 0.0295960i
\(255\) 3.33620 0.208921
\(256\) 2.31626 + 4.01189i 0.144767 + 0.250743i
\(257\) 5.26020 9.11094i 0.328123 0.568325i −0.654017 0.756480i \(-0.726917\pi\)
0.982139 + 0.188155i \(0.0602508\pi\)
\(258\) −4.42046 + 7.65647i −0.275206 + 0.476671i
\(259\) 0 0
\(260\) 7.49294 4.69097i 0.464693 0.290921i
\(261\) −3.99547 −0.247313
\(262\) −0.329670 + 0.571006i −0.0203671 + 0.0352768i
\(263\) 15.6749 27.1498i 0.966558 1.67413i 0.261188 0.965288i \(-0.415886\pi\)
0.705370 0.708839i \(-0.250781\pi\)
\(264\) 1.16522 + 2.01821i 0.0717140 + 0.124212i
\(265\) −13.8449 −0.850486
\(266\) 0 0
\(267\) 2.35660 + 4.08174i 0.144221 + 0.249799i
\(268\) 2.41017 0.147224
\(269\) −10.5633 18.2961i −0.644054 1.11553i −0.984519 0.175277i \(-0.943918\pi\)
0.340465 0.940257i \(-0.389415\pi\)
\(270\) 1.95623 3.38829i 0.119052 0.206205i
\(271\) 3.26004 5.64655i 0.198033 0.343004i −0.749857 0.661599i \(-0.769878\pi\)
0.947891 + 0.318596i \(0.103211\pi\)
\(272\) −2.50793 −0.152066
\(273\) 0 0
\(274\) 5.00954 0.302638
\(275\) 0.819983 1.42025i 0.0494468 0.0856444i
\(276\) −3.72717 + 6.45565i −0.224349 + 0.388584i
\(277\) 7.26548 + 12.5842i 0.436540 + 0.756110i 0.997420 0.0717873i \(-0.0228703\pi\)
−0.560880 + 0.827897i \(0.689537\pi\)
\(278\) 8.43866 0.506117
\(279\) −1.28817 2.23118i −0.0771207 0.133577i
\(280\) 0 0
\(281\) 27.1832 1.62161 0.810807 0.585314i \(-0.199029\pi\)
0.810807 + 0.585314i \(0.199029\pi\)
\(282\) 6.31846 + 10.9439i 0.376259 + 0.651699i
\(283\) 4.28791 7.42688i 0.254890 0.441482i −0.709976 0.704226i \(-0.751294\pi\)
0.964866 + 0.262744i \(0.0846274\pi\)
\(284\) −10.4109 + 18.0323i −0.617775 + 1.07002i
\(285\) 1.28522 0.0761296
\(286\) 1.02739 0.643196i 0.0607506 0.0380330i
\(287\) 0 0
\(288\) 1.58401 2.74358i 0.0933387 0.161667i
\(289\) 7.78411 13.4825i 0.457889 0.793087i
\(290\) −2.94390 5.09898i −0.172872 0.299422i
\(291\) −29.6019 −1.73529
\(292\) −3.07309 5.32274i −0.179839 0.311490i
\(293\) −5.24356 9.08212i −0.306332 0.530583i 0.671225 0.741254i \(-0.265768\pi\)
−0.977557 + 0.210671i \(0.932435\pi\)
\(294\) 0 0
\(295\) −0.177511 0.307458i −0.0103351 0.0179009i
\(296\) −9.73258 + 16.8573i −0.565695 + 0.979812i
\(297\) −1.32750 + 2.29930i −0.0770295 + 0.133419i
\(298\) −7.75799 −0.449408
\(299\) 7.54181 + 4.00183i 0.436154 + 0.231432i
\(300\) −8.90400 −0.514073
\(301\) 0 0
\(302\) 4.67882 8.10396i 0.269236 0.466331i
\(303\) 13.2572 + 22.9621i 0.761605 + 1.31914i
\(304\) −0.966139 −0.0554118
\(305\) −5.69340 9.86125i −0.326003 0.564654i
\(306\) −0.201131 0.348370i −0.0114979 0.0199150i
\(307\) 19.1751 1.09438 0.547190 0.837008i \(-0.315697\pi\)
0.547190 + 0.837008i \(0.315697\pi\)
\(308\) 0 0
\(309\) 10.1690 17.6132i 0.578493 1.00198i
\(310\) 1.89827 3.28790i 0.107814 0.186740i
\(311\) 3.48854 0.197817 0.0989086 0.995097i \(-0.468465\pi\)
0.0989086 + 0.995097i \(0.468465\pi\)
\(312\) −12.8013 6.79261i −0.724729 0.384556i
\(313\) 20.3214 1.14864 0.574318 0.818632i \(-0.305267\pi\)
0.574318 + 0.818632i \(0.305267\pi\)
\(314\) −0.182258 + 0.315680i −0.0102854 + 0.0178148i
\(315\) 0 0
\(316\) 13.3766 + 23.1689i 0.752490 + 1.30335i
\(317\) −27.8220 −1.56264 −0.781320 0.624131i \(-0.785453\pi\)
−0.781320 + 0.624131i \(0.785453\pi\)
\(318\) 5.15337 + 8.92591i 0.288987 + 0.500540i
\(319\) 1.99773 + 3.46018i 0.111852 + 0.193733i
\(320\) −1.50877 −0.0843427
\(321\) 3.55252 + 6.15314i 0.198282 + 0.343435i
\(322\) 0 0
\(323\) −0.275784 + 0.477672i −0.0153450 + 0.0265784i
\(324\) 17.3091 0.961619
\(325\) 0.364568 + 10.1916i 0.0202226 + 0.565329i
\(326\) 6.77459 0.375210
\(327\) −7.76524 + 13.4498i −0.429419 + 0.743775i
\(328\) 4.26660 7.38996i 0.235583 0.408042i
\(329\) 0 0
\(330\) 0.937318 0.0515976
\(331\) 4.67148 + 8.09123i 0.256768 + 0.444734i 0.965374 0.260869i \(-0.0840092\pi\)
−0.708607 + 0.705604i \(0.750676\pi\)
\(332\) −12.8118 22.1907i −0.703141 1.21788i
\(333\) 5.31281 0.291140
\(334\) 6.39491 + 11.0763i 0.349914 + 0.606069i
\(335\) 1.06732 1.84866i 0.0583140 0.101003i
\(336\) 0 0
\(337\) 22.9182 1.24844 0.624218 0.781250i \(-0.285418\pi\)
0.624218 + 0.781250i \(0.285418\pi\)
\(338\) −3.29272 + 6.78030i −0.179100 + 0.368800i
\(339\) 14.7739 0.802409
\(340\) −1.46689 + 2.54074i −0.0795535 + 0.137791i
\(341\) −1.28817 + 2.23118i −0.0697583 + 0.120825i
\(342\) −0.0774824 0.134204i −0.00418977 0.00725690i
\(343\) 0 0
\(344\) −8.55996 14.8263i −0.461522 0.799380i
\(345\) 3.30109 + 5.71766i 0.177725 + 0.307828i
\(346\) −6.60444 −0.355057
\(347\) 13.3355 + 23.0978i 0.715889 + 1.23996i 0.962616 + 0.270871i \(0.0873117\pi\)
−0.246726 + 0.969085i \(0.579355\pi\)
\(348\) 10.8465 18.7866i 0.581431 1.00707i
\(349\) −7.61723 + 13.1934i −0.407741 + 0.706228i −0.994636 0.103435i \(-0.967017\pi\)
0.586895 + 0.809663i \(0.300350\pi\)
\(350\) 0 0
\(351\) −0.590213 16.4996i −0.0315033 0.880683i
\(352\) −3.16802 −0.168856
\(353\) 11.2044 19.4066i 0.596352 1.03291i −0.397003 0.917817i \(-0.629950\pi\)
0.993355 0.115094i \(-0.0367170\pi\)
\(354\) −0.132147 + 0.228885i −0.00702353 + 0.0121651i
\(355\) 9.22079 + 15.9709i 0.489389 + 0.847646i
\(356\) −4.14468 −0.219668
\(357\) 0 0
\(358\) −1.00667 1.74361i −0.0532044 0.0921528i
\(359\) 16.0385 0.846482 0.423241 0.906017i \(-0.360892\pi\)
0.423241 + 0.906017i \(0.360892\pi\)
\(360\) −0.907530 1.57189i −0.0478310 0.0828457i
\(361\) 9.39376 16.2705i 0.494408 0.856340i
\(362\) 6.11676 10.5945i 0.321490 0.556837i
\(363\) 20.1764 1.05898
\(364\) 0 0
\(365\) −5.44356 −0.284929
\(366\) −4.23841 + 7.34114i −0.221545 + 0.383727i
\(367\) 3.45002 5.97561i 0.180090 0.311924i −0.761821 0.647787i \(-0.775695\pi\)
0.941911 + 0.335863i \(0.109028\pi\)
\(368\) −2.48154 4.29815i −0.129359 0.224057i
\(369\) −2.32904 −0.121245
\(370\) 3.91452 + 6.78015i 0.203506 + 0.352483i
\(371\) 0 0
\(372\) 13.9879 0.725240
\(373\) −3.84264 6.65566i −0.198965 0.344617i 0.749228 0.662312i \(-0.230425\pi\)
−0.948193 + 0.317695i \(0.897091\pi\)
\(374\) −0.201131 + 0.348370i −0.0104003 + 0.0180138i
\(375\) −10.9134 + 18.9026i −0.563566 + 0.976125i
\(376\) −24.4706 −1.26198
\(377\) −21.9475 11.6458i −1.13035 0.599788i
\(378\) 0 0
\(379\) 12.5817 21.7922i 0.646281 1.11939i −0.337723 0.941245i \(-0.609657\pi\)
0.984004 0.178146i \(-0.0570098\pi\)
\(380\) −0.565096 + 0.978775i −0.0289888 + 0.0502101i
\(381\) −0.888656 1.53920i −0.0455272 0.0788555i
\(382\) −6.91070 −0.353582
\(383\) 11.0218 + 19.0904i 0.563189 + 0.975473i 0.997216 + 0.0745724i \(0.0237592\pi\)
−0.434026 + 0.900900i \(0.642907\pi\)
\(384\) 10.8995 + 18.8785i 0.556212 + 0.963387i
\(385\) 0 0
\(386\) 4.16866 + 7.22033i 0.212179 + 0.367505i
\(387\) −2.33635 + 4.04668i −0.118763 + 0.205704i
\(388\) 13.0156 22.5438i 0.660769 1.14449i
\(389\) −10.9812 −0.556767 −0.278383 0.960470i \(-0.589799\pi\)
−0.278383 + 0.960470i \(0.589799\pi\)
\(390\) −4.94040 + 3.09294i −0.250167 + 0.156617i
\(391\) −2.83342 −0.143292
\(392\) 0 0
\(393\) −1.07578 + 1.86331i −0.0542660 + 0.0939914i
\(394\) 2.02042 + 3.49946i 0.101787 + 0.176300i
\(395\) 23.6948 1.19221
\(396\) 0.279672 + 0.484405i 0.0140540 + 0.0243423i
\(397\) −12.5382 21.7168i −0.629275 1.08994i −0.987698 0.156377i \(-0.950019\pi\)
0.358423 0.933559i \(-0.383315\pi\)
\(398\) −2.07196 −0.103858
\(399\) 0 0
\(400\) 2.96413 5.13402i 0.148206 0.256701i
\(401\) 11.3301 19.6243i 0.565797 0.979989i −0.431178 0.902267i \(-0.641902\pi\)
0.996975 0.0777222i \(-0.0247647\pi\)
\(402\) −1.58912 −0.0792581
\(403\) −0.572726 16.0107i −0.0285295 0.797551i
\(404\) −23.3162 −1.16002
\(405\) 7.66521 13.2765i 0.380887 0.659716i
\(406\) 0 0
\(407\) −2.65640 4.60103i −0.131673 0.228064i
\(408\) 4.80937 0.238099
\(409\) 8.57324 + 14.8493i 0.423919 + 0.734250i 0.996319 0.0857251i \(-0.0273207\pi\)
−0.572400 + 0.819975i \(0.693987\pi\)
\(410\) −1.71606 2.97230i −0.0847501 0.146791i
\(411\) 16.3472 0.806345
\(412\) 8.94238 + 15.4887i 0.440560 + 0.763072i
\(413\) 0 0
\(414\) 0.398029 0.689407i 0.0195621 0.0338825i
\(415\) −22.6944 −1.11403
\(416\) 16.6979 10.4538i 0.818684 0.512538i
\(417\) 27.5371 1.34850
\(418\) −0.0774824 + 0.134204i −0.00378979 + 0.00656411i
\(419\) 16.9902 29.4279i 0.830027 1.43765i −0.0679891 0.997686i \(-0.521658\pi\)
0.898016 0.439963i \(-0.145008\pi\)
\(420\) 0 0
\(421\) −32.3623 −1.57724 −0.788621 0.614879i \(-0.789205\pi\)
−0.788621 + 0.614879i \(0.789205\pi\)
\(422\) −4.09169 7.08701i −0.199180 0.344990i
\(423\) 3.33950 + 5.78418i 0.162372 + 0.281236i
\(424\) −19.9584 −0.969266
\(425\) −1.69222 2.93101i −0.0820847 0.142175i
\(426\) 6.86435 11.8894i 0.332579 0.576044i
\(427\) 0 0
\(428\) −6.24802 −0.302009
\(429\) 3.35257 2.09888i 0.161863 0.101335i
\(430\) −6.88577 −0.332061
\(431\) 9.45640 16.3790i 0.455499 0.788947i −0.543218 0.839592i \(-0.682794\pi\)
0.998717 + 0.0506447i \(0.0161276\pi\)
\(432\) −4.79874 + 8.31167i −0.230880 + 0.399895i
\(433\) −9.57006 16.5758i −0.459908 0.796584i 0.539048 0.842275i \(-0.318784\pi\)
−0.998956 + 0.0456914i \(0.985451\pi\)
\(434\) 0 0
\(435\) −9.60653 16.6390i −0.460598 0.797779i
\(436\) −6.82859 11.8275i −0.327030 0.566433i
\(437\) −1.09153 −0.0522148
\(438\) 2.02621 + 3.50950i 0.0968161 + 0.167690i
\(439\) −4.80144 + 8.31634i −0.229160 + 0.396917i −0.957560 0.288236i \(-0.906931\pi\)
0.728399 + 0.685153i \(0.240265\pi\)
\(440\) −0.907530 + 1.57189i −0.0432648 + 0.0749368i
\(441\) 0 0
\(442\) −0.0894239 2.49987i −0.00425346 0.118907i
\(443\) −40.3996 −1.91944 −0.959721 0.280955i \(-0.909349\pi\)
−0.959721 + 0.280955i \(0.909349\pi\)
\(444\) −14.4226 + 24.9807i −0.684468 + 1.18553i
\(445\) −1.83544 + 3.17907i −0.0870081 + 0.150703i
\(446\) −0.263561 0.456502i −0.0124800 0.0216160i
\(447\) −25.3159 −1.19740
\(448\) 0 0
\(449\) 13.3112 + 23.0556i 0.628194 + 1.08806i 0.987914 + 0.155003i \(0.0495387\pi\)
−0.359720 + 0.933060i \(0.617128\pi\)
\(450\) 0.950869 0.0448244
\(451\) 1.16452 + 2.01701i 0.0548352 + 0.0949773i
\(452\) −6.49594 + 11.2513i −0.305543 + 0.529217i
\(453\) 15.2680 26.4449i 0.717351 1.24249i
\(454\) 1.35393 0.0635430
\(455\) 0 0
\(456\) 1.85273 0.0867619
\(457\) 0.806434 1.39678i 0.0377234 0.0653388i −0.846547 0.532314i \(-0.821323\pi\)
0.884271 + 0.466975i \(0.154656\pi\)
\(458\) −4.83583 + 8.37590i −0.225963 + 0.391380i
\(459\) 2.73960 + 4.74513i 0.127874 + 0.221484i
\(460\) −5.80582 −0.270698
\(461\) 7.96032 + 13.7877i 0.370749 + 0.642156i 0.989681 0.143289i \(-0.0457677\pi\)
−0.618932 + 0.785445i \(0.712434\pi\)
\(462\) 0 0
\(463\) −28.8475 −1.34066 −0.670328 0.742065i \(-0.733847\pi\)
−0.670328 + 0.742065i \(0.733847\pi\)
\(464\) 7.22154 + 12.5081i 0.335252 + 0.580673i
\(465\) 6.19444 10.7291i 0.287260 0.497549i
\(466\) −4.79110 + 8.29842i −0.221943 + 0.384417i
\(467\) −7.44536 −0.344530 −0.172265 0.985051i \(-0.555109\pi\)
−0.172265 + 0.985051i \(0.555109\pi\)
\(468\) −3.07252 1.63034i −0.142027 0.0753626i
\(469\) 0 0
\(470\) −4.92114 + 8.52367i −0.226995 + 0.393167i
\(471\) −0.594744 + 1.03013i −0.0274044 + 0.0474657i
\(472\) −0.255895 0.443222i −0.0117785 0.0204010i
\(473\) 4.67270 0.214851
\(474\) −8.81971 15.2762i −0.405103 0.701658i
\(475\) −0.651899 1.12912i −0.0299112 0.0518077i
\(476\) 0 0
\(477\) 2.72371 + 4.71761i 0.124710 + 0.216005i
\(478\) 0.922022 1.59699i 0.0421723 0.0730446i
\(479\) −18.6263 + 32.2617i −0.851058 + 1.47408i 0.0291956 + 0.999574i \(0.490705\pi\)
−0.880254 + 0.474503i \(0.842628\pi\)
\(480\) 15.2341 0.695338
\(481\) 29.1837 + 15.4855i 1.33066 + 0.706077i
\(482\) −9.19570 −0.418853
\(483\) 0 0
\(484\) −8.87134 + 15.3656i −0.403243 + 0.698437i
\(485\) −11.5277 19.9666i −0.523448 0.906638i
\(486\) −3.44760 −0.156386
\(487\) −12.0863 20.9341i −0.547684 0.948616i −0.998433 0.0559651i \(-0.982176\pi\)
0.450749 0.892651i \(-0.351157\pi\)
\(488\) −8.20742 14.2157i −0.371533 0.643513i
\(489\) 22.1069 0.999707
\(490\) 0 0
\(491\) −3.03571 + 5.25800i −0.137000 + 0.237290i −0.926360 0.376640i \(-0.877079\pi\)
0.789360 + 0.613931i \(0.210413\pi\)
\(492\) 6.32263 10.9511i 0.285046 0.493714i
\(493\) 8.24555 0.371361
\(494\) −0.0344490 0.963033i −0.00154993 0.0433289i
\(495\) 0.495401 0.0222666
\(496\) −4.65656 + 8.06540i −0.209086 + 0.362147i
\(497\) 0 0
\(498\) 8.44736 + 14.6313i 0.378535 + 0.655642i
\(499\) −2.51565 −0.112616 −0.0563079 0.998413i \(-0.517933\pi\)
−0.0563079 + 0.998413i \(0.517933\pi\)
\(500\) −9.59703 16.6225i −0.429192 0.743383i
\(501\) 20.8679 + 36.1442i 0.932308 + 1.61481i
\(502\) 1.44707 0.0645858
\(503\) 17.0026 + 29.4493i 0.758107 + 1.31308i 0.943815 + 0.330474i \(0.107209\pi\)
−0.185708 + 0.982605i \(0.559458\pi\)
\(504\) 0 0
\(505\) −10.3254 + 17.8841i −0.459473 + 0.795831i
\(506\) −0.796058 −0.0353891
\(507\) −10.7448 + 22.1255i −0.477194 + 0.982627i
\(508\) 1.56293 0.0693439
\(509\) −14.6524 + 25.3787i −0.649457 + 1.12489i 0.333796 + 0.942645i \(0.391670\pi\)
−0.983253 + 0.182247i \(0.941663\pi\)
\(510\) 0.967183 1.67521i 0.0428276 0.0741795i
\(511\) 0 0
\(512\) −20.3568 −0.899654
\(513\) 1.05538 + 1.82798i 0.0465964 + 0.0807073i
\(514\) −3.04992 5.28262i −0.134526 0.233006i
\(515\) 15.8402 0.698004
\(516\) −12.6849 21.9709i −0.558423 0.967217i
\(517\) 3.33950 5.78418i 0.146871 0.254388i
\(518\) 0 0
\(519\) −21.5516 −0.946011
\(520\) −0.403492 11.2797i −0.0176943 0.494649i
\(521\) −9.14772 −0.400769 −0.200385 0.979717i \(-0.564219\pi\)
−0.200385 + 0.979717i \(0.564219\pi\)
\(522\) −1.15831 + 2.00625i −0.0506977 + 0.0878111i
\(523\) 7.05373 12.2174i 0.308438 0.534231i −0.669583 0.742737i \(-0.733527\pi\)
0.978021 + 0.208507i \(0.0668604\pi\)
\(524\) −0.946019 1.63855i −0.0413270 0.0715805i
\(525\) 0 0
\(526\) −9.08849 15.7417i −0.396277 0.686372i
\(527\) 2.65843 + 4.60453i 0.115803 + 0.200577i
\(528\) −2.29929 −0.100064
\(529\) 8.69640 + 15.0626i 0.378104 + 0.654896i
\(530\) −4.01371 + 6.95196i −0.174345 + 0.301974i
\(531\) −0.0698437 + 0.120973i −0.00303096 + 0.00524977i
\(532\) 0 0
\(533\) −12.7936 6.78856i −0.554154 0.294045i
\(534\) 2.73276 0.118258
\(535\) −2.76688 + 4.79238i −0.119623 + 0.207193i
\(536\) 1.53862 2.66496i 0.0664582 0.115109i
\(537\) −3.28498 5.68976i −0.141758 0.245531i
\(538\) −12.2494 −0.528109
\(539\) 0 0
\(540\) 5.61359 + 9.72302i 0.241570 + 0.418412i
\(541\) 7.80293 0.335474 0.167737 0.985832i \(-0.446354\pi\)
0.167737 + 0.985832i \(0.446354\pi\)
\(542\) −1.89020 3.27393i −0.0811912 0.140627i
\(543\) 19.9602 34.5721i 0.856576 1.48363i
\(544\) −3.26896 + 5.66200i −0.140155 + 0.242756i
\(545\) −12.0959 −0.518133
\(546\) 0 0
\(547\) 6.99390 0.299038 0.149519 0.988759i \(-0.452228\pi\)
0.149519 + 0.988759i \(0.452228\pi\)
\(548\) −7.18767 + 12.4494i −0.307042 + 0.531813i
\(549\) −2.24013 + 3.88001i −0.0956063 + 0.165595i
\(550\) −0.475435 0.823477i −0.0202726 0.0351132i
\(551\) 3.17646 0.135322
\(552\) 4.75875 + 8.24240i 0.202546 + 0.350820i
\(553\) 0 0
\(554\) 8.42520 0.357952
\(555\) 12.7739 + 22.1250i 0.542221 + 0.939154i
\(556\) −12.1078 + 20.9713i −0.513484 + 0.889380i
\(557\) 3.62124 6.27218i 0.153437 0.265761i −0.779052 0.626960i \(-0.784299\pi\)
0.932489 + 0.361199i \(0.117632\pi\)
\(558\) −1.49379 −0.0632371
\(559\) −24.6288 + 15.4189i −1.04169 + 0.652149i
\(560\) 0 0
\(561\) −0.656332 + 1.13680i −0.0277104 + 0.0479958i
\(562\) 7.88055 13.6495i 0.332421 0.575770i
\(563\) −7.96606 13.7976i −0.335730 0.581501i 0.647895 0.761730i \(-0.275650\pi\)
−0.983625 + 0.180229i \(0.942316\pi\)
\(564\) −36.2628 −1.52694
\(565\) 5.75334 + 9.96509i 0.242045 + 0.419234i
\(566\) −2.48618 4.30618i −0.104502 0.181002i
\(567\) 0 0
\(568\) 13.2924 + 23.0231i 0.557737 + 0.966029i
\(569\) 21.1379 36.6120i 0.886149 1.53485i 0.0417571 0.999128i \(-0.486704\pi\)
0.844392 0.535727i \(-0.179962\pi\)
\(570\) 0.372591 0.645346i 0.0156061 0.0270306i
\(571\) 13.6249 0.570186 0.285093 0.958500i \(-0.407976\pi\)
0.285093 + 0.958500i \(0.407976\pi\)
\(572\) 0.124343 + 3.47605i 0.00519905 + 0.145341i
\(573\) −22.5510 −0.942082
\(574\) 0 0
\(575\) 3.34882 5.80032i 0.139655 0.241890i
\(576\) 0.296821 + 0.514108i 0.0123675 + 0.0214212i
\(577\) 26.3849 1.09842 0.549209 0.835685i \(-0.314929\pi\)
0.549209 + 0.835685i \(0.314929\pi\)
\(578\) −4.51331 7.81728i −0.187729 0.325156i
\(579\) 13.6032 + 23.5614i 0.565329 + 0.979179i
\(580\) 16.8956 0.701550
\(581\) 0 0
\(582\) −8.58174 + 14.8640i −0.355725 + 0.616133i
\(583\) 2.72371 4.71761i 0.112805 0.195384i
\(584\) −7.84727 −0.324722
\(585\) −2.61115 + 1.63471i −0.107958 + 0.0675871i
\(586\) −6.08054 −0.251185
\(587\) −11.0720 + 19.1773i −0.456990 + 0.791530i −0.998800 0.0489708i \(-0.984406\pi\)
0.541810 + 0.840501i \(0.317739\pi\)
\(588\) 0 0
\(589\) 1.02411 + 1.77382i 0.0421979 + 0.0730889i
\(590\) −0.205846 −0.00847453
\(591\) 6.59303 + 11.4195i 0.271201 + 0.469734i
\(592\) −9.60254 16.6321i −0.394662 0.683575i
\(593\) 26.0838 1.07114 0.535568 0.844492i \(-0.320098\pi\)
0.535568 + 0.844492i \(0.320098\pi\)
\(594\) 0.769700 + 1.33316i 0.0315812 + 0.0547002i
\(595\) 0 0
\(596\) 11.1311 19.2797i 0.455949 0.789727i
\(597\) −6.76124 −0.276719
\(598\) 4.19585 2.62682i 0.171581 0.107419i
\(599\) −16.8440 −0.688229 −0.344114 0.938928i \(-0.611821\pi\)
−0.344114 + 0.938928i \(0.611821\pi\)
\(600\) −5.68420 + 9.84532i −0.232056 + 0.401933i
\(601\) 4.31691 7.47710i 0.176090 0.304997i −0.764448 0.644686i \(-0.776988\pi\)
0.940538 + 0.339688i \(0.110322\pi\)
\(602\) 0 0
\(603\) −0.839898 −0.0342033
\(604\) 13.4263 + 23.2551i 0.546309 + 0.946235i
\(605\) 7.85719 + 13.6091i 0.319440 + 0.553287i
\(606\) 15.3733 0.624498
\(607\) 10.9181 + 18.9107i 0.443153 + 0.767564i 0.997922 0.0644411i \(-0.0205265\pi\)
−0.554768 + 0.832005i \(0.687193\pi\)
\(608\) −1.25931 + 2.18119i −0.0510718 + 0.0884590i
\(609\) 0 0
\(610\) −6.60218 −0.267315
\(611\) 1.48475 + 41.5068i 0.0600668 + 1.67918i
\(612\) 1.15433 0.0466610
\(613\) 24.0244 41.6114i 0.970334 1.68067i 0.275791 0.961218i \(-0.411060\pi\)
0.694543 0.719451i \(-0.255607\pi\)
\(614\) 5.55896 9.62840i 0.224341 0.388571i
\(615\) −5.59985 9.69922i −0.225808 0.391110i
\(616\) 0 0
\(617\) 8.23709 + 14.2671i 0.331613 + 0.574370i 0.982828 0.184523i \(-0.0590739\pi\)
−0.651215 + 0.758893i \(0.725741\pi\)
\(618\) −5.89608 10.2123i −0.237175 0.410799i
\(619\) −42.0533 −1.69027 −0.845133 0.534557i \(-0.820479\pi\)
−0.845133 + 0.534557i \(0.820479\pi\)
\(620\) 5.44726 + 9.43493i 0.218767 + 0.378916i
\(621\) −5.42153 + 9.39037i −0.217559 + 0.376823i
\(622\) 1.01135 1.75170i 0.0405513 0.0702370i
\(623\) 0 0
\(624\) 12.1191 7.58716i 0.485151 0.303730i
\(625\) −2.85760 −0.114304
\(626\) 5.89129 10.2040i 0.235463 0.407835i
\(627\) −0.252841 + 0.437933i −0.0100975 + 0.0174894i
\(628\) −0.523006 0.905872i −0.0208702 0.0361482i
\(629\) −10.9642 −0.437170
\(630\) 0 0
\(631\) 6.06667 + 10.5078i 0.241510 + 0.418308i 0.961145 0.276045i \(-0.0890239\pi\)
−0.719634 + 0.694353i \(0.755691\pi\)
\(632\) 34.1577 1.35872
\(633\) −13.3520 23.1263i −0.530694 0.919190i
\(634\) −8.06575 + 13.9703i −0.320332 + 0.554831i
\(635\) 0.692131 1.19881i 0.0274664 0.0475732i
\(636\) −29.5762 −1.17277
\(637\) 0 0
\(638\) 2.31661 0.0917157
\(639\) 3.62802 6.28391i 0.143522 0.248588i
\(640\) −8.48908 + 14.7035i −0.335560 + 0.581207i
\(641\) 0.202177 + 0.350182i 0.00798553 + 0.0138313i 0.869991 0.493068i \(-0.164125\pi\)
−0.862005 + 0.506900i \(0.830791\pi\)
\(642\) 4.11957 0.162587
\(643\) 14.1741 + 24.5503i 0.558973 + 0.968169i 0.997583 + 0.0694914i \(0.0221377\pi\)
−0.438610 + 0.898678i \(0.644529\pi\)
\(644\) 0 0
\(645\) −22.4697 −0.884742
\(646\) 0.159902 + 0.276959i 0.00629128 + 0.0108968i
\(647\) −17.4045 + 30.1455i −0.684242 + 1.18514i 0.289433 + 0.957198i \(0.406533\pi\)
−0.973675 + 0.227943i \(0.926800\pi\)
\(648\) 11.0499 19.1390i 0.434082 0.751852i
\(649\) 0.139687 0.00548321
\(650\) 5.22321 + 2.77154i 0.204871 + 0.108709i
\(651\) 0 0
\(652\) −9.72016 + 16.8358i −0.380671 + 0.659341i
\(653\) 12.5750 21.7805i 0.492098 0.852338i −0.507861 0.861439i \(-0.669564\pi\)
0.999959 + 0.00910088i \(0.00289694\pi\)
\(654\) 4.50237 + 7.79833i 0.176056 + 0.304939i
\(655\) −1.67575 −0.0654768
\(656\) 4.20959 + 7.29122i 0.164357 + 0.284674i
\(657\) 1.07091 + 1.85488i 0.0417803 + 0.0723657i
\(658\) 0 0
\(659\) −4.33723 7.51230i −0.168954 0.292638i 0.769098 0.639131i \(-0.220706\pi\)
−0.938053 + 0.346493i \(0.887372\pi\)
\(660\) −1.34486 + 2.32937i −0.0523486 + 0.0906704i
\(661\) 9.50000 16.4545i 0.369507 0.640005i −0.619982 0.784616i \(-0.712860\pi\)
0.989489 + 0.144612i \(0.0461932\pi\)
\(662\) 5.41714 0.210543
\(663\) −0.291808 8.15759i −0.0113329 0.316815i
\(664\) −32.7156 −1.26961
\(665\) 0 0
\(666\) 1.54021 2.66772i 0.0596819 0.103372i
\(667\) 8.15877 + 14.1314i 0.315909 + 0.547170i
\(668\) −36.7016 −1.42003
\(669\) −0.860054 1.48966i −0.0332516 0.0575935i
\(670\) −0.618844 1.07187i −0.0239080 0.0414099i
\(671\) 4.48026 0.172958
\(672\) 0 0
\(673\) 0.284273 0.492376i 0.0109579 0.0189797i −0.860494 0.509460i \(-0.829845\pi\)
0.871452 + 0.490480i \(0.163179\pi\)
\(674\) 6.64412 11.5079i 0.255922 0.443269i
\(675\) −12.9517 −0.498513
\(676\) −12.1256 17.9112i −0.466369 0.688893i
\(677\) −27.6797 −1.06382 −0.531908 0.846802i \(-0.678525\pi\)
−0.531908 + 0.846802i \(0.678525\pi\)
\(678\) 4.28304 7.41844i 0.164489 0.284903i
\(679\) 0 0
\(680\) 1.87289 + 3.24394i 0.0718221 + 0.124400i
\(681\) 4.41814 0.169304
\(682\) 0.746894 + 1.29366i 0.0286001 + 0.0495368i
\(683\) 11.8958 + 20.6042i 0.455181 + 0.788397i 0.998699 0.0510006i \(-0.0162411\pi\)
−0.543517 + 0.839398i \(0.682908\pi\)
\(684\) 0.444686 0.0170030
\(685\) 6.36600 + 11.0262i 0.243232 + 0.421291i
\(686\) 0 0
\(687\) −15.7803 + 27.3323i −0.602056 + 1.04279i
\(688\) 16.8912 0.643970
\(689\) 1.21098 + 33.8532i 0.0461345 + 1.28970i
\(690\) 3.82801 0.145730
\(691\) 18.4217 31.9073i 0.700793 1.21381i −0.267395 0.963587i \(-0.586163\pi\)
0.968188 0.250222i \(-0.0805037\pi\)
\(692\) 9.47603 16.4130i 0.360224 0.623927i
\(693\) 0 0
\(694\) 15.4642 0.587012
\(695\) 10.7236 + 18.5739i 0.406771 + 0.704548i
\(696\) −13.8485 23.9863i −0.524925 0.909197i
\(697\) 4.80650 0.182059
\(698\) 4.41655 + 7.64969i 0.167169 + 0.289545i
\(699\) −15.6343 + 27.0794i −0.591344 + 1.02424i
\(700\) 0 0
\(701\) 2.34987 0.0887533 0.0443767 0.999015i \(-0.485870\pi\)
0.0443767 + 0.999015i \(0.485870\pi\)
\(702\) −8.45606 4.48696i −0.319153 0.169349i
\(703\) −4.22376 −0.159302
\(704\) 0.296821 0.514108i 0.0111868 0.0193762i
\(705\) −16.0587 + 27.8145i −0.604805 + 1.04755i
\(706\) −6.49645 11.2522i −0.244497 0.423481i
\(707\) 0 0
\(708\) −0.379208 0.656807i −0.0142515 0.0246843i
\(709\) −5.04160 8.73231i −0.189341 0.327949i 0.755689 0.654930i \(-0.227302\pi\)
−0.945031 + 0.326981i \(0.893969\pi\)
\(710\) 10.6926 0.401287
\(711\) −4.66148 8.07393i −0.174819 0.302796i
\(712\) −2.64591 + 4.58285i −0.0991597 + 0.171750i
\(713\) −5.26090 + 9.11214i −0.197022 + 0.341252i
\(714\) 0 0
\(715\) 2.72128 + 1.44397i 0.101770 + 0.0540013i
\(716\) 5.77749 0.215915
\(717\) 3.00875 5.21130i 0.112364 0.194620i
\(718\) 4.64966 8.05344i 0.173524 0.300552i
\(719\) 3.25113 + 5.63113i 0.121247 + 0.210006i 0.920260 0.391308i \(-0.127977\pi\)
−0.799013 + 0.601314i \(0.794644\pi\)
\(720\) 1.79081 0.0667394
\(721\) 0 0
\(722\) −5.44660 9.43379i −0.202701 0.351089i
\(723\) −30.0074 −1.11599
\(724\) 17.5526 + 30.4020i 0.652338 + 1.12988i
\(725\) −9.74542 + 16.8796i −0.361936 + 0.626891i
\(726\) 5.84923 10.1312i 0.217085 0.376003i
\(727\) 3.12636 0.115950 0.0579750 0.998318i \(-0.481536\pi\)
0.0579750 + 0.998318i \(0.481536\pi\)
\(728\) 0 0
\(729\) 19.9595 0.739242
\(730\) −1.57812 + 2.73338i −0.0584087 + 0.101167i
\(731\) 4.82158 8.35123i 0.178333 0.308881i
\(732\) −12.1625 21.0661i −0.449539 0.778625i
\(733\) 7.66440 0.283091 0.141545 0.989932i \(-0.454793\pi\)
0.141545 + 0.989932i \(0.454793\pi\)
\(734\) −2.00036 3.46472i −0.0738346 0.127885i
\(735\) 0 0
\(736\) −12.9382 −0.476909
\(737\) 0.419949 + 0.727373i 0.0154690 + 0.0267931i
\(738\) −0.675201 + 1.16948i −0.0248545 + 0.0430493i
\(739\) −10.2162 + 17.6950i −0.375810 + 0.650922i −0.990448 0.137887i \(-0.955969\pi\)
0.614638 + 0.788809i \(0.289302\pi\)
\(740\) −22.4662 −0.825873
\(741\) −0.112414 3.14257i −0.00412964 0.115445i
\(742\) 0 0
\(743\) −5.07080 + 8.78288i −0.186030 + 0.322213i −0.943923 0.330166i \(-0.892895\pi\)
0.757893 + 0.652378i \(0.226229\pi\)
\(744\) 8.92971 15.4667i 0.327379 0.567037i
\(745\) −9.85866 17.0757i −0.361193 0.625605i
\(746\) −4.45601 −0.163146
\(747\) 4.46469 + 7.73306i 0.163354 + 0.282938i
\(748\) −0.577165 0.999680i −0.0211033 0.0365519i
\(749\) 0 0
\(750\) 6.32771 + 10.9599i 0.231055 + 0.400200i
\(751\) 11.1481 19.3090i 0.406799 0.704597i −0.587730 0.809057i \(-0.699978\pi\)
0.994529 + 0.104461i \(0.0333116\pi\)
\(752\) 12.0718 20.9090i 0.440214 0.762474i
\(753\) 4.72207 0.172082
\(754\) −12.2104 + 7.64432i −0.444676 + 0.278390i
\(755\) 23.7829 0.865550
\(756\) 0 0
\(757\) −12.2909 + 21.2884i −0.446720 + 0.773741i −0.998170 0.0604666i \(-0.980741\pi\)
0.551451 + 0.834207i \(0.314074\pi\)
\(758\) −7.29503 12.6354i −0.264967 0.458937i
\(759\) −2.59770 −0.0942905
\(760\) 0.721500 + 1.24967i 0.0261715 + 0.0453304i
\(761\) −17.6167 30.5130i −0.638603 1.10609i −0.985739 0.168279i \(-0.946179\pi\)
0.347136 0.937815i \(-0.387154\pi\)
\(762\) −1.03050 −0.0373312
\(763\) 0 0
\(764\) 9.91545 17.1741i 0.358728 0.621336i
\(765\) 0.511186 0.885399i 0.0184820 0.0320117i
\(766\) 12.7811 0.461802
\(767\) −0.736262 + 0.460938i −0.0265849 + 0.0166435i
\(768\) 8.76493 0.316277
\(769\) 4.62257 8.00653i 0.166694 0.288723i −0.770561 0.637366i \(-0.780024\pi\)
0.937256 + 0.348643i \(0.113357\pi\)
\(770\) 0 0
\(771\) −9.95251 17.2383i −0.358431 0.620821i
\(772\) −23.9247 −0.861070
\(773\) −3.16336 5.47909i −0.113778 0.197069i 0.803513 0.595288i \(-0.202962\pi\)
−0.917291 + 0.398218i \(0.869629\pi\)
\(774\) 1.35464 + 2.34630i 0.0486915 + 0.0843362i
\(775\) −12.5680 −0.451456
\(776\) −16.6180 28.7833i −0.596553 1.03326i