Properties

Label 588.2.x.a.559.6
Level $588$
Weight $2$
Character 588.559
Analytic conductor $4.695$
Analytic rank $0$
Dimension $168$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [588,2,Mod(55,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([7, 0, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("588.55");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 588.x (of order \(14\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.69520363885\)
Analytic rank: \(0\)
Dimension: \(168\)
Relative dimension: \(28\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 559.6
Character \(\chi\) \(=\) 588.559
Dual form 588.2.x.a.223.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.16344 + 0.803993i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(0.707190 - 1.87080i) q^{4} +(-3.84631 + 0.877896i) q^{5} +(1.04273 + 0.955366i) q^{6} +(-2.22982 + 1.42405i) q^{7} +(0.681335 + 2.74514i) q^{8} +(-0.900969 + 0.433884i) q^{9} +O(q^{10})\) \(q+(-1.16344 + 0.803993i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(0.707190 - 1.87080i) q^{4} +(-3.84631 + 0.877896i) q^{5} +(1.04273 + 0.955366i) q^{6} +(-2.22982 + 1.42405i) q^{7} +(0.681335 + 2.74514i) q^{8} +(-0.900969 + 0.433884i) q^{9} +(3.76914 - 4.11379i) q^{10} +(-0.211161 + 0.438481i) q^{11} +(-1.98126 - 0.273167i) q^{12} +(1.80566 - 3.74949i) q^{13} +(1.44933 - 3.44955i) q^{14} +(1.71177 + 3.55453i) q^{15} +(-2.99977 - 2.64602i) q^{16} +(3.87770 + 3.09236i) q^{17} +(0.699384 - 1.22917i) q^{18} -1.26247 q^{19} +(-1.07771 + 7.81651i) q^{20} +(1.88453 + 1.85703i) q^{21} +(-0.106862 - 0.679919i) q^{22} +(-1.01756 + 0.811475i) q^{23} +(2.52470 - 1.27510i) q^{24} +(9.51858 - 4.58391i) q^{25} +(0.913788 + 5.81405i) q^{26} +(0.623490 + 0.781831i) q^{27} +(1.08720 + 5.17861i) q^{28} +(3.84838 - 4.82572i) q^{29} +(-4.84936 - 2.75923i) q^{30} -1.46864 q^{31} +(5.61743 + 0.666694i) q^{32} +(0.474475 + 0.108296i) q^{33} +(-6.99771 - 0.480136i) q^{34} +(7.32641 - 7.43489i) q^{35} +(0.174553 + 1.99237i) q^{36} +(5.94597 - 7.45601i) q^{37} +(1.46881 - 1.01502i) q^{38} +(-4.05728 - 0.926049i) q^{39} +(-5.03057 - 9.96052i) q^{40} +(-0.785690 + 0.179329i) q^{41} +(-3.68557 - 0.645398i) q^{42} +(9.95871 + 2.27301i) q^{43} +(0.670978 + 0.705130i) q^{44} +(3.08450 - 2.45981i) q^{45} +(0.531448 - 1.76221i) q^{46} +(-7.29098 - 3.51115i) q^{47} +(-1.91217 + 3.51335i) q^{48} +(2.94417 - 6.35074i) q^{49} +(-7.38887 + 12.9860i) q^{50} +(2.15196 - 4.46859i) q^{51} +(-5.73760 - 6.02963i) q^{52} +(4.02092 + 5.04208i) q^{53} +(-1.35398 - 0.408333i) q^{54} +(0.427252 - 1.87191i) q^{55} +(-5.42846 - 5.15090i) q^{56} +(0.280926 + 1.23082i) q^{57} +(-0.597521 + 8.70852i) q^{58} +(0.246939 - 1.08191i) q^{59} +(7.86035 - 0.688650i) q^{60} +(4.52728 + 3.61038i) q^{61} +(1.70867 - 1.18077i) q^{62} +(1.39112 - 2.25051i) q^{63} +(-7.07157 + 3.74072i) q^{64} +(-3.65347 + 16.0069i) q^{65} +(-0.639093 + 0.255479i) q^{66} -5.76579i q^{67} +(8.52745 - 5.06750i) q^{68} +(1.01756 + 0.811475i) q^{69} +(-2.54624 + 14.5404i) q^{70} +(3.14148 - 2.50524i) q^{71} +(-1.80493 - 2.17766i) q^{72} +(6.35632 + 13.1990i) q^{73} +(-0.923202 + 13.4551i) q^{74} +(-6.58706 - 8.25991i) q^{75} +(-0.892806 + 2.36183i) q^{76} +(-0.153568 - 1.27844i) q^{77} +(5.46495 - 2.18463i) q^{78} +17.2973i q^{79} +(13.8610 + 7.54393i) q^{80} +(0.623490 - 0.781831i) q^{81} +(0.769925 - 0.840328i) q^{82} +(4.95499 - 2.38620i) q^{83} +(4.80684 - 2.21229i) q^{84} +(-17.6296 - 8.48997i) q^{85} +(-13.4139 + 5.36222i) q^{86} +(-5.56108 - 2.67807i) q^{87} +(-1.34756 - 0.280915i) q^{88} +(-6.19385 - 12.8617i) q^{89} +(-1.61097 + 5.34176i) q^{90} +(1.31317 + 10.9320i) q^{91} +(0.798499 + 2.47751i) q^{92} +(0.326802 + 1.43181i) q^{93} +(11.3056 - 1.77688i) q^{94} +(4.85586 - 1.10832i) q^{95} +(-0.600018 - 5.62494i) q^{96} +3.59515i q^{97} +(1.68059 + 9.75580i) q^{98} -0.486678i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9} + 20 q^{10} - 12 q^{14} + 36 q^{16} + 12 q^{19} - 25 q^{20} + 2 q^{21} - 6 q^{22} - 15 q^{24} + 32 q^{25} + 6 q^{26} - 28 q^{27} - 66 q^{28} - 8 q^{30} - 4 q^{31} + 25 q^{32} - 68 q^{34} - 12 q^{35} - 10 q^{37} + 35 q^{38} + 14 q^{39} + 16 q^{40} + 9 q^{42} + 20 q^{44} - 28 q^{46} - 8 q^{47} + 8 q^{48} - 8 q^{49} + 114 q^{50} + 20 q^{52} - 8 q^{53} - q^{56} + 12 q^{57} - 6 q^{58} + 20 q^{59} + 10 q^{60} - 14 q^{61} - 16 q^{62} - 12 q^{63} + 42 q^{64} - 8 q^{65} - 6 q^{66} - 16 q^{68} + 59 q^{70} + 28 q^{71} - 15 q^{72} + 22 q^{74} + 18 q^{75} + 7 q^{76} + 8 q^{77} + 6 q^{78} + 26 q^{80} - 28 q^{81} + 12 q^{82} + 10 q^{83} + 11 q^{84} - 24 q^{85} - 6 q^{86} - 242 q^{88} + 20 q^{90} - 16 q^{91} + 7 q^{92} - 4 q^{93} - 53 q^{94} - 10 q^{96} - 118 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{13}{14}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.16344 + 0.803993i −0.822677 + 0.568509i
\(3\) −0.222521 0.974928i −0.128473 0.562875i
\(4\) 0.707190 1.87080i 0.353595 0.935399i
\(5\) −3.84631 + 0.877896i −1.72012 + 0.392607i −0.964850 0.262802i \(-0.915353\pi\)
−0.755274 + 0.655409i \(0.772496\pi\)
\(6\) 1.04273 + 0.955366i 0.425691 + 0.390026i
\(7\) −2.22982 + 1.42405i −0.842792 + 0.538240i
\(8\) 0.681335 + 2.74514i 0.240888 + 0.970553i
\(9\) −0.900969 + 0.433884i −0.300323 + 0.144628i
\(10\) 3.76914 4.11379i 1.19191 1.30089i
\(11\) −0.211161 + 0.438481i −0.0636676 + 0.132207i −0.930374 0.366611i \(-0.880518\pi\)
0.866707 + 0.498818i \(0.166232\pi\)
\(12\) −1.98126 0.273167i −0.571940 0.0788566i
\(13\) 1.80566 3.74949i 0.500800 1.03992i −0.485389 0.874299i \(-0.661322\pi\)
0.986189 0.165624i \(-0.0529638\pi\)
\(14\) 1.44933 3.44955i 0.387351 0.921932i
\(15\) 1.71177 + 3.55453i 0.441977 + 0.917775i
\(16\) −2.99977 2.64602i −0.749941 0.661504i
\(17\) 3.87770 + 3.09236i 0.940480 + 0.750007i 0.968348 0.249604i \(-0.0803005\pi\)
−0.0278684 + 0.999612i \(0.508872\pi\)
\(18\) 0.699384 1.22917i 0.164847 0.289718i
\(19\) −1.26247 −0.289631 −0.144815 0.989459i \(-0.546259\pi\)
−0.144815 + 0.989459i \(0.546259\pi\)
\(20\) −1.07771 + 7.81651i −0.240983 + 1.74782i
\(21\) 1.88453 + 1.85703i 0.411237 + 0.405237i
\(22\) −0.106862 0.679919i −0.0227831 0.144959i
\(23\) −1.01756 + 0.811475i −0.212175 + 0.169204i −0.723811 0.689998i \(-0.757611\pi\)
0.511636 + 0.859203i \(0.329040\pi\)
\(24\) 2.52470 1.27510i 0.515352 0.260279i
\(25\) 9.51858 4.58391i 1.90372 0.916781i
\(26\) 0.913788 + 5.81405i 0.179209 + 1.14023i
\(27\) 0.623490 + 0.781831i 0.119991 + 0.150464i
\(28\) 1.08720 + 5.17861i 0.205462 + 0.978665i
\(29\) 3.84838 4.82572i 0.714627 0.896114i −0.283393 0.959004i \(-0.591460\pi\)
0.998020 + 0.0628897i \(0.0200316\pi\)
\(30\) −4.84936 2.75923i −0.885368 0.503764i
\(31\) −1.46864 −0.263775 −0.131887 0.991265i \(-0.542104\pi\)
−0.131887 + 0.991265i \(0.542104\pi\)
\(32\) 5.61743 + 0.666694i 0.993031 + 0.117856i
\(33\) 0.474475 + 0.108296i 0.0825956 + 0.0188519i
\(34\) −6.99771 0.480136i −1.20010 0.0823427i
\(35\) 7.32641 7.43489i 1.23839 1.25673i
\(36\) 0.174553 + 1.99237i 0.0290921 + 0.332061i
\(37\) 5.94597 7.45601i 0.977511 1.22576i 0.00332925 0.999994i \(-0.498940\pi\)
0.974182 0.225765i \(-0.0724883\pi\)
\(38\) 1.46881 1.01502i 0.238272 0.164658i
\(39\) −4.05728 0.926049i −0.649685 0.148286i
\(40\) −5.03057 9.96052i −0.795403 1.57490i
\(41\) −0.785690 + 0.179329i −0.122704 + 0.0280064i −0.283432 0.958992i \(-0.591473\pi\)
0.160728 + 0.986999i \(0.448616\pi\)
\(42\) −3.68557 0.645398i −0.568697 0.0995871i
\(43\) 9.95871 + 2.27301i 1.51869 + 0.346631i 0.898906 0.438142i \(-0.144363\pi\)
0.619783 + 0.784773i \(0.287221\pi\)
\(44\) 0.670978 + 0.705130i 0.101154 + 0.106302i
\(45\) 3.08450 2.45981i 0.459811 0.366687i
\(46\) 0.531448 1.76221i 0.0783577 0.259824i
\(47\) −7.29098 3.51115i −1.06350 0.512154i −0.181493 0.983392i \(-0.558093\pi\)
−0.882006 + 0.471238i \(0.843807\pi\)
\(48\) −1.91217 + 3.51335i −0.275997 + 0.507108i
\(49\) 2.94417 6.35074i 0.420595 0.907248i
\(50\) −7.38887 + 12.9860i −1.04494 + 1.83649i
\(51\) 2.15196 4.46859i 0.301335 0.625728i
\(52\) −5.73760 6.02963i −0.795662 0.836159i
\(53\) 4.02092 + 5.04208i 0.552316 + 0.692583i 0.977117 0.212704i \(-0.0682272\pi\)
−0.424800 + 0.905287i \(0.639656\pi\)
\(54\) −1.35398 0.408333i −0.184253 0.0555671i
\(55\) 0.427252 1.87191i 0.0576107 0.252409i
\(56\) −5.42846 5.15090i −0.725409 0.688318i
\(57\) 0.280926 + 1.23082i 0.0372096 + 0.163026i
\(58\) −0.597521 + 8.70852i −0.0784583 + 1.14348i
\(59\) 0.246939 1.08191i 0.0321487 0.140853i −0.956307 0.292366i \(-0.905557\pi\)
0.988455 + 0.151513i \(0.0484146\pi\)
\(60\) 7.86035 0.688650i 1.01477 0.0889043i
\(61\) 4.52728 + 3.61038i 0.579659 + 0.462262i 0.868896 0.494995i \(-0.164830\pi\)
−0.289237 + 0.957257i \(0.593402\pi\)
\(62\) 1.70867 1.18077i 0.217002 0.149958i
\(63\) 1.39112 2.25051i 0.175265 0.283537i
\(64\) −7.07157 + 3.74072i −0.883946 + 0.467590i
\(65\) −3.65347 + 16.0069i −0.453158 + 1.98541i
\(66\) −0.639093 + 0.255479i −0.0786670 + 0.0314473i
\(67\) 5.76579i 0.704404i −0.935924 0.352202i \(-0.885433\pi\)
0.935924 0.352202i \(-0.114567\pi\)
\(68\) 8.52745 5.06750i 1.03410 0.614525i
\(69\) 1.01756 + 0.811475i 0.122500 + 0.0976901i
\(70\) −2.54624 + 14.5404i −0.304334 + 1.73791i
\(71\) 3.14148 2.50524i 0.372825 0.297318i −0.419096 0.907942i \(-0.637653\pi\)
0.791920 + 0.610624i \(0.209081\pi\)
\(72\) −1.80493 2.17766i −0.212713 0.256640i
\(73\) 6.35632 + 13.1990i 0.743952 + 1.54483i 0.835785 + 0.549057i \(0.185013\pi\)
−0.0918335 + 0.995774i \(0.529273\pi\)
\(74\) −0.923202 + 13.4551i −0.107320 + 1.56413i
\(75\) −6.58706 8.25991i −0.760608 0.953772i
\(76\) −0.892806 + 2.36183i −0.102412 + 0.270920i
\(77\) −0.153568 1.27844i −0.0175006 0.145691i
\(78\) 5.46495 2.18463i 0.618783 0.247360i
\(79\) 17.2973i 1.94610i 0.230603 + 0.973048i \(0.425930\pi\)
−0.230603 + 0.973048i \(0.574070\pi\)
\(80\) 13.8610 + 7.54393i 1.54970 + 0.843437i
\(81\) 0.623490 0.781831i 0.0692766 0.0868702i
\(82\) 0.769925 0.840328i 0.0850240 0.0927987i
\(83\) 4.95499 2.38620i 0.543881 0.261919i −0.141708 0.989909i \(-0.545259\pi\)
0.685588 + 0.727989i \(0.259545\pi\)
\(84\) 4.80684 2.21229i 0.524470 0.241381i
\(85\) −17.6296 8.48997i −1.91220 0.920867i
\(86\) −13.4139 + 5.36222i −1.44645 + 0.578223i
\(87\) −5.56108 2.67807i −0.596210 0.287120i
\(88\) −1.34756 0.280915i −0.143651 0.0299456i
\(89\) −6.19385 12.8617i −0.656547 1.36333i −0.917404 0.397957i \(-0.869719\pi\)
0.260857 0.965377i \(-0.415995\pi\)
\(90\) −1.61097 + 5.34176i −0.169811 + 0.563071i
\(91\) 1.31317 + 10.9320i 0.137658 + 1.14599i
\(92\) 0.798499 + 2.47751i 0.0832493 + 0.258298i
\(93\) 0.326802 + 1.43181i 0.0338878 + 0.148472i
\(94\) 11.3056 1.77688i 1.16608 0.183271i
\(95\) 4.85586 1.10832i 0.498200 0.113711i
\(96\) −0.600018 5.62494i −0.0612390 0.574093i
\(97\) 3.59515i 0.365033i 0.983203 + 0.182516i \(0.0584242\pi\)
−0.983203 + 0.182516i \(0.941576\pi\)
\(98\) 1.68059 + 9.75580i 0.169765 + 0.985485i
\(99\) 0.486678i 0.0489129i
\(100\) −1.84412 21.0490i −0.184412 2.10490i
\(101\) −9.20206 + 2.10031i −0.915640 + 0.208989i −0.654280 0.756253i \(-0.727028\pi\)
−0.261360 + 0.965241i \(0.584171\pi\)
\(102\) 1.08904 + 6.92910i 0.107831 + 0.686083i
\(103\) −3.13189 13.7217i −0.308595 1.35204i −0.856779 0.515684i \(-0.827538\pi\)
0.548185 0.836357i \(-0.315319\pi\)
\(104\) 11.5231 + 2.40213i 1.12994 + 0.235548i
\(105\) −8.87876 5.48830i −0.866478 0.535603i
\(106\) −8.73190 2.63336i −0.848117 0.255775i
\(107\) 7.50112 + 15.5762i 0.725161 + 1.50581i 0.857431 + 0.514598i \(0.172059\pi\)
−0.132271 + 0.991214i \(0.542227\pi\)
\(108\) 1.90357 0.613520i 0.183171 0.0590360i
\(109\) −1.60357 0.772241i −0.153595 0.0739672i 0.355507 0.934673i \(-0.384308\pi\)
−0.509102 + 0.860706i \(0.670022\pi\)
\(110\) 1.00792 + 2.52137i 0.0961017 + 0.240403i
\(111\) −8.59217 4.13777i −0.815533 0.392740i
\(112\) 10.4570 + 1.62832i 0.988092 + 0.153862i
\(113\) 13.6982 6.59671i 1.28862 0.620566i 0.341028 0.940053i \(-0.389225\pi\)
0.947591 + 0.319487i \(0.103511\pi\)
\(114\) −1.31641 1.20612i −0.123293 0.112964i
\(115\) 3.20145 4.01450i 0.298537 0.374354i
\(116\) −6.30641 10.6122i −0.585535 0.985323i
\(117\) 4.16162i 0.384742i
\(118\) 0.582550 + 1.45728i 0.0536281 + 0.134153i
\(119\) −13.0502 1.37337i −1.19631 0.125896i
\(120\) −8.59138 + 7.12087i −0.784282 + 0.650044i
\(121\) 6.71071 + 8.41497i 0.610065 + 0.764997i
\(122\) −8.16995 0.560567i −0.739672 0.0507514i
\(123\) 0.349665 + 0.726087i 0.0315282 + 0.0654691i
\(124\) −1.03860 + 2.74752i −0.0932695 + 0.246735i
\(125\) −17.1647 + 13.6884i −1.53526 + 1.22433i
\(126\) 0.190901 + 3.73678i 0.0170068 + 0.332899i
\(127\) −2.69476 2.14900i −0.239121 0.190693i 0.496596 0.867982i \(-0.334583\pi\)
−0.735717 + 0.677289i \(0.763155\pi\)
\(128\) 5.21984 10.0376i 0.461373 0.887206i
\(129\) 10.2148i 0.899364i
\(130\) −8.61885 21.5605i −0.755923 1.89098i
\(131\) 0.220049 0.964099i 0.0192258 0.0842338i −0.964405 0.264430i \(-0.914816\pi\)
0.983631 + 0.180196i \(0.0576733\pi\)
\(132\) 0.538144 0.811062i 0.0468394 0.0705939i
\(133\) 2.81508 1.79782i 0.244098 0.155891i
\(134\) 4.63566 + 6.70816i 0.400460 + 0.579497i
\(135\) −3.08450 2.45981i −0.265472 0.211707i
\(136\) −5.84694 + 12.7517i −0.501371 + 1.09345i
\(137\) 4.05489 17.7656i 0.346432 1.51782i −0.438781 0.898594i \(-0.644590\pi\)
0.785213 0.619225i \(-0.212553\pi\)
\(138\) −1.83629 0.125994i −0.156315 0.0107253i
\(139\) −2.69583 11.8112i −0.228657 1.00181i −0.950736 0.310002i \(-0.899670\pi\)
0.722079 0.691811i \(-0.243187\pi\)
\(140\) −8.72801 18.9641i −0.737651 1.60276i
\(141\) −1.80072 + 7.88948i −0.151648 + 0.664414i
\(142\) −1.64072 + 5.44043i −0.137686 + 0.456551i
\(143\) 1.26280 + 1.58350i 0.105600 + 0.132419i
\(144\) 3.85076 + 1.08243i 0.320897 + 0.0902025i
\(145\) −10.5656 + 21.9397i −0.877426 + 1.82199i
\(146\) −18.0072 10.2459i −1.49028 0.847954i
\(147\) −6.84665 1.45718i −0.564702 0.120186i
\(148\) −9.74375 16.3965i −0.800931 1.34778i
\(149\) −6.45073 3.10651i −0.528464 0.254495i 0.150573 0.988599i \(-0.451888\pi\)
−0.679037 + 0.734104i \(0.737602\pi\)
\(150\) 14.3046 + 4.31397i 1.16796 + 0.352234i
\(151\) −14.3752 + 11.4638i −1.16984 + 0.932915i −0.998630 0.0523203i \(-0.983338\pi\)
−0.171208 + 0.985235i \(0.554767\pi\)
\(152\) −0.860165 3.46566i −0.0697686 0.281102i
\(153\) −4.83541 1.10365i −0.390920 0.0892249i
\(154\) 1.20652 + 1.36392i 0.0972243 + 0.109908i
\(155\) 5.64884 1.28931i 0.453725 0.103560i
\(156\) −4.60172 + 6.93546i −0.368432 + 0.555282i
\(157\) −2.24926 0.513379i −0.179511 0.0409721i 0.131821 0.991274i \(-0.457918\pi\)
−0.311331 + 0.950301i \(0.600775\pi\)
\(158\) −13.9069 20.1244i −1.10637 1.60101i
\(159\) 4.02092 5.04208i 0.318880 0.399863i
\(160\) −22.1917 + 2.36721i −1.75441 + 0.187144i
\(161\) 1.11339 3.25849i 0.0877472 0.256805i
\(162\) −0.0968063 + 1.41090i −0.00760582 + 0.110850i
\(163\) 20.1553 + 4.60033i 1.57869 + 0.360325i 0.919947 0.392044i \(-0.128232\pi\)
0.658742 + 0.752369i \(0.271089\pi\)
\(164\) −0.220144 + 1.59669i −0.0171904 + 0.124680i
\(165\) −1.92005 −0.149476
\(166\) −3.84635 + 6.75998i −0.298535 + 0.524676i
\(167\) −5.97855 + 7.49686i −0.462634 + 0.580124i −0.957350 0.288930i \(-0.906700\pi\)
0.494716 + 0.869054i \(0.335272\pi\)
\(168\) −3.81381 + 6.43854i −0.294242 + 0.496744i
\(169\) −2.69293 3.37682i −0.207148 0.259756i
\(170\) 27.3369 4.29650i 2.09664 0.329527i
\(171\) 1.13745 0.547765i 0.0869827 0.0418887i
\(172\) 11.2950 17.0233i 0.861238 1.29801i
\(173\) 14.8636 11.8533i 1.13006 0.901191i 0.134095 0.990968i \(-0.457187\pi\)
0.995962 + 0.0897778i \(0.0286157\pi\)
\(174\) 8.62314 1.35529i 0.653718 0.102744i
\(175\) −14.6970 + 23.7762i −1.11099 + 1.79731i
\(176\) 1.79366 0.756604i 0.135203 0.0570312i
\(177\) −1.10973 −0.0834127
\(178\) 17.5469 + 9.98398i 1.31519 + 0.748331i
\(179\) −2.37352 1.89282i −0.177405 0.141476i 0.530761 0.847521i \(-0.321906\pi\)
−0.708167 + 0.706045i \(0.750477\pi\)
\(180\) −2.42048 7.51003i −0.180412 0.559765i
\(181\) −6.09541 12.6573i −0.453069 0.940806i −0.994952 0.100353i \(-0.968003\pi\)
0.541883 0.840454i \(-0.317711\pi\)
\(182\) −10.3171 11.6630i −0.764753 0.864519i
\(183\) 2.51245 5.21716i 0.185726 0.385663i
\(184\) −2.92091 2.24045i −0.215332 0.165168i
\(185\) −16.3245 + 33.8981i −1.20020 + 2.49224i
\(186\) −1.53138 1.40309i −0.112287 0.102879i
\(187\) −2.17476 + 1.04731i −0.159034 + 0.0765869i
\(188\) −11.7248 + 11.1569i −0.855116 + 0.813700i
\(189\) −2.50363 0.855461i −0.182113 0.0622256i
\(190\) −4.75842 + 5.19354i −0.345212 + 0.376779i
\(191\) 12.8094 2.92366i 0.926856 0.211549i 0.267654 0.963515i \(-0.413752\pi\)
0.659202 + 0.751966i \(0.270894\pi\)
\(192\) 5.22050 + 6.06188i 0.376757 + 0.437478i
\(193\) 1.21712 + 5.33255i 0.0876101 + 0.383845i 0.999656 0.0262441i \(-0.00835473\pi\)
−0.912045 + 0.410089i \(0.865498\pi\)
\(194\) −2.89048 4.18275i −0.207524 0.300304i
\(195\) 16.4186 1.17576
\(196\) −9.79886 9.99912i −0.699919 0.714223i
\(197\) −5.42046 −0.386192 −0.193096 0.981180i \(-0.561853\pi\)
−0.193096 + 0.981180i \(0.561853\pi\)
\(198\) 0.391285 + 0.566221i 0.0278074 + 0.0402395i
\(199\) −4.19586 18.3833i −0.297437 1.30316i −0.873929 0.486054i \(-0.838436\pi\)
0.576492 0.817103i \(-0.304421\pi\)
\(200\) 19.0688 + 23.0066i 1.34837 + 1.62681i
\(201\) −5.62123 + 1.28301i −0.396491 + 0.0904966i
\(202\) 9.01742 9.84198i 0.634464 0.692480i
\(203\) −1.70913 + 16.2408i −0.119957 + 1.13988i
\(204\) −6.83798 7.18602i −0.478754 0.503122i
\(205\) 2.86458 1.37951i 0.200071 0.0963491i
\(206\) 14.6759 + 13.4464i 1.02252 + 0.936854i
\(207\) 0.564702 1.17262i 0.0392495 0.0815024i
\(208\) −15.3378 + 6.46979i −1.06348 + 0.448599i
\(209\) 0.266585 0.553570i 0.0184401 0.0382912i
\(210\) 14.7425 0.753146i 1.01733 0.0519720i
\(211\) −10.0671 20.9046i −0.693048 1.43913i −0.888715 0.458459i \(-0.848402\pi\)
0.195667 0.980670i \(-0.437313\pi\)
\(212\) 12.2763 3.95663i 0.843137 0.271742i
\(213\) −3.14148 2.50524i −0.215250 0.171657i
\(214\) −21.2503 12.0912i −1.45264 0.826536i
\(215\) −40.2998 −2.74842
\(216\) −1.72143 + 2.24425i −0.117128 + 0.152702i
\(217\) 3.27479 2.09141i 0.222307 0.141974i
\(218\) 2.48654 0.390807i 0.168410 0.0264688i
\(219\) 11.4537 9.13402i 0.773969 0.617220i
\(220\) −3.19982 2.12310i −0.215732 0.143139i
\(221\) 18.5966 8.95565i 1.25094 0.602422i
\(222\) 13.3232 2.09399i 0.894196 0.140540i
\(223\) 9.77737 + 12.2604i 0.654741 + 0.821019i 0.992759 0.120120i \(-0.0383280\pi\)
−0.338018 + 0.941140i \(0.609757\pi\)
\(224\) −13.4752 + 6.51289i −0.900353 + 0.435161i
\(225\) −6.58706 + 8.25991i −0.439137 + 0.550661i
\(226\) −10.6333 + 18.6881i −0.707319 + 1.24312i
\(227\) 5.31375 0.352686 0.176343 0.984329i \(-0.443573\pi\)
0.176343 + 0.984329i \(0.443573\pi\)
\(228\) 2.50128 + 0.344866i 0.165651 + 0.0228393i
\(229\) 21.3557 + 4.87430i 1.41122 + 0.322103i 0.859164 0.511701i \(-0.170984\pi\)
0.552061 + 0.833804i \(0.313842\pi\)
\(230\) −0.497075 + 7.24458i −0.0327761 + 0.477693i
\(231\) −1.21221 + 0.434196i −0.0797577 + 0.0285680i
\(232\) 15.8693 + 7.27641i 1.04187 + 0.477720i
\(233\) 2.34249 2.93739i 0.153462 0.192435i −0.699157 0.714968i \(-0.746441\pi\)
0.852619 + 0.522533i \(0.175013\pi\)
\(234\) −3.34592 4.84180i −0.218730 0.316519i
\(235\) 31.1258 + 7.10426i 2.03042 + 0.463431i
\(236\) −1.84940 1.22709i −0.120386 0.0798767i
\(237\) 16.8636 3.84901i 1.09541 0.250020i
\(238\) 16.2873 8.89446i 1.05575 0.576542i
\(239\) 6.92758 + 1.58118i 0.448108 + 0.102278i 0.440619 0.897694i \(-0.354759\pi\)
0.00748909 + 0.999972i \(0.497616\pi\)
\(240\) 4.27043 15.1921i 0.275655 0.980647i
\(241\) 6.35072 5.06453i 0.409086 0.326235i −0.397231 0.917718i \(-0.630029\pi\)
0.806317 + 0.591484i \(0.201458\pi\)
\(242\) −14.5731 4.39495i −0.936794 0.282518i
\(243\) −0.900969 0.433884i −0.0577972 0.0278337i
\(244\) 9.95594 5.91639i 0.637364 0.378758i
\(245\) −5.74890 + 27.0116i −0.367284 + 1.72571i
\(246\) −0.990584 0.563631i −0.0631573 0.0359358i
\(247\) −2.27959 + 4.73363i −0.145047 + 0.301193i
\(248\) −1.00063 4.03161i −0.0635403 0.256008i
\(249\) −3.42896 4.29978i −0.217301 0.272487i
\(250\) 8.96475 29.7260i 0.566981 1.88004i
\(251\) −0.449468 + 1.96925i −0.0283702 + 0.124298i −0.987130 0.159919i \(-0.948877\pi\)
0.958760 + 0.284217i \(0.0917337\pi\)
\(252\) −3.22645 4.19405i −0.203247 0.264200i
\(253\) −0.140948 0.617532i −0.00886131 0.0388239i
\(254\) 4.86298 + 0.333665i 0.305130 + 0.0209360i
\(255\) −4.35415 + 19.0768i −0.272668 + 1.19463i
\(256\) 1.99719 + 15.8749i 0.124824 + 0.992179i
\(257\) −5.51642 4.39920i −0.344105 0.274414i 0.436153 0.899873i \(-0.356341\pi\)
−0.780258 + 0.625458i \(0.784912\pi\)
\(258\) 8.21264 + 11.8843i 0.511297 + 0.739886i
\(259\) −2.64070 + 25.0929i −0.164085 + 1.55920i
\(260\) 27.3620 + 18.1548i 1.69692 + 1.12591i
\(261\) −1.37347 + 6.01758i −0.0850158 + 0.372479i
\(262\) 0.519115 + 1.29859i 0.0320710 + 0.0802272i
\(263\) 24.6901i 1.52246i −0.648483 0.761229i \(-0.724596\pi\)
0.648483 0.761229i \(-0.275404\pi\)
\(264\) 0.0259895 + 1.37629i 0.00159954 + 0.0847046i
\(265\) −19.8921 15.8635i −1.22196 0.974484i
\(266\) −1.82974 + 4.35496i −0.112189 + 0.267020i
\(267\) −11.1609 + 8.90055i −0.683038 + 0.544705i
\(268\) −10.7866 4.07751i −0.658899 0.249074i
\(269\) 3.38566 + 7.03040i 0.206428 + 0.428651i 0.978319 0.207103i \(-0.0664035\pi\)
−0.771892 + 0.635754i \(0.780689\pi\)
\(270\) 5.56631 + 0.381923i 0.338755 + 0.0232431i
\(271\) 16.4026 + 20.5683i 0.996389 + 1.24943i 0.968290 + 0.249828i \(0.0803739\pi\)
0.0280990 + 0.999605i \(0.491055\pi\)
\(272\) −3.44974 19.5368i −0.209171 1.18459i
\(273\) 10.3657 3.71285i 0.627363 0.224712i
\(274\) 9.56582 + 23.9293i 0.577892 + 1.44562i
\(275\) 5.14166i 0.310054i
\(276\) 2.23771 1.32978i 0.134694 0.0800432i
\(277\) 8.41073 10.5467i 0.505352 0.633691i −0.462075 0.886841i \(-0.652895\pi\)
0.967427 + 0.253149i \(0.0814664\pi\)
\(278\) 12.6326 + 11.5742i 0.757651 + 0.694175i
\(279\) 1.32320 0.637218i 0.0792177 0.0381492i
\(280\) 25.4015 + 15.0464i 1.51803 + 0.899191i
\(281\) 2.69279 + 1.29678i 0.160638 + 0.0773594i 0.512475 0.858702i \(-0.328729\pi\)
−0.351837 + 0.936061i \(0.614443\pi\)
\(282\) −4.24806 10.6267i −0.252968 0.632812i
\(283\) 11.1751 + 5.38163i 0.664289 + 0.319905i 0.735469 0.677559i \(-0.236962\pi\)
−0.0711795 + 0.997464i \(0.522676\pi\)
\(284\) −2.46518 7.64875i −0.146282 0.453870i
\(285\) −2.16106 4.48749i −0.128010 0.265816i
\(286\) −2.74231 0.827025i −0.162156 0.0489030i
\(287\) 1.49657 1.51873i 0.0883399 0.0896479i
\(288\) −5.35040 + 1.83664i −0.315275 + 0.108225i
\(289\) 1.69099 + 7.40869i 0.0994697 + 0.435805i
\(290\) −5.34692 34.0202i −0.313982 1.99774i
\(291\) 3.50502 0.799997i 0.205468 0.0468967i
\(292\) 29.1879 2.55717i 1.70809 0.149647i
\(293\) 6.94236i 0.405577i −0.979223 0.202788i \(-0.935000\pi\)
0.979223 0.202788i \(-0.0650003\pi\)
\(294\) 9.13724 3.80932i 0.532894 0.222164i
\(295\) 4.37815i 0.254906i
\(296\) 24.5190 + 11.2425i 1.42514 + 0.653455i
\(297\) −0.474475 + 0.108296i −0.0275319 + 0.00628397i
\(298\) 10.0026 1.57210i 0.579438 0.0910695i
\(299\) 1.20526 + 5.28058i 0.0697018 + 0.305384i
\(300\) −20.1109 + 6.48173i −1.16110 + 0.374223i
\(301\) −25.4430 + 9.11329i −1.46651 + 0.525281i
\(302\) 7.50785 24.8951i 0.432028 1.43255i
\(303\) 4.09530 + 8.50399i 0.235269 + 0.488541i
\(304\) 3.78712 + 3.34052i 0.217206 + 0.191592i
\(305\) −20.5829 9.91219i −1.17857 0.567570i
\(306\) 6.51304 2.60360i 0.372326 0.148838i
\(307\) 9.88187 + 4.75886i 0.563988 + 0.271602i 0.694078 0.719900i \(-0.255812\pi\)
−0.130090 + 0.991502i \(0.541527\pi\)
\(308\) −2.50030 0.616804i −0.142468 0.0351457i
\(309\) −12.6808 + 6.10674i −0.721384 + 0.347400i
\(310\) −5.53549 + 6.04166i −0.314395 + 0.343143i
\(311\) 4.50930 5.65449i 0.255699 0.320637i −0.637368 0.770559i \(-0.719977\pi\)
0.893068 + 0.449923i \(0.148548\pi\)
\(312\) −0.222239 11.7688i −0.0125818 0.666275i
\(313\) 7.77323i 0.439369i 0.975571 + 0.219684i \(0.0705028\pi\)
−0.975571 + 0.219684i \(0.929497\pi\)
\(314\) 3.02964 1.21110i 0.170972 0.0683466i
\(315\) −3.37499 + 9.87741i −0.190159 + 0.556529i
\(316\) 32.3597 + 12.2325i 1.82038 + 0.688129i
\(317\) 7.45847 + 9.35262i 0.418909 + 0.525296i 0.945849 0.324607i \(-0.105232\pi\)
−0.526940 + 0.849903i \(0.676661\pi\)
\(318\) −0.624310 + 9.09895i −0.0350095 + 0.510244i
\(319\) 1.30336 + 2.70645i 0.0729740 + 0.151532i
\(320\) 23.9155 20.5961i 1.33692 1.15136i
\(321\) 13.5166 10.7791i 0.754420 0.601630i
\(322\) 1.32445 + 4.68622i 0.0738085 + 0.261153i
\(323\) −4.89548 3.90401i −0.272392 0.217225i
\(324\) −1.02172 1.71933i −0.0567624 0.0955181i
\(325\) 43.9668i 2.43884i
\(326\) −27.1482 + 10.8526i −1.50360 + 0.601067i
\(327\) −0.396050 + 1.73521i −0.0219016 + 0.0959573i
\(328\) −1.02760 2.03465i −0.0567397 0.112345i
\(329\) 21.2576 2.55349i 1.17197 0.140778i
\(330\) 2.23387 1.54371i 0.122970 0.0849785i
\(331\) −14.2131 11.3346i −0.781222 0.623004i 0.149487 0.988764i \(-0.452238\pi\)
−0.930709 + 0.365760i \(0.880809\pi\)
\(332\) −0.959974 10.9573i −0.0526854 0.601359i
\(333\) −2.12209 + 9.29749i −0.116290 + 0.509499i
\(334\) 0.928261 13.5289i 0.0507922 0.740266i
\(335\) 5.06177 + 22.1771i 0.276554 + 1.21166i
\(336\) −0.739403 10.5571i −0.0403378 0.575939i
\(337\) −6.91159 + 30.2816i −0.376498 + 1.64955i 0.331591 + 0.943423i \(0.392415\pi\)
−0.708089 + 0.706123i \(0.750443\pi\)
\(338\) 5.84801 + 1.76364i 0.318090 + 0.0959294i
\(339\) −9.47945 11.8869i −0.514853 0.645605i
\(340\) −28.3505 + 26.9774i −1.53752 + 1.46305i
\(341\) 0.310119 0.643970i 0.0167939 0.0348729i
\(342\) −0.882952 + 1.55179i −0.0477446 + 0.0839113i
\(343\) 2.47881 + 18.3536i 0.133843 + 0.991003i
\(344\) 0.545490 + 28.8867i 0.0294109 + 1.55747i
\(345\) −4.62624 2.22788i −0.249068 0.119945i
\(346\) −7.76292 + 25.7408i −0.417337 + 1.38384i
\(347\) 22.8895 18.2538i 1.22877 0.979914i 0.228794 0.973475i \(-0.426522\pi\)
0.999979 0.00643910i \(-0.00204964\pi\)
\(348\) −8.94287 + 8.50974i −0.479388 + 0.456170i
\(349\) 1.49584 + 0.341417i 0.0800707 + 0.0182756i 0.262369 0.964968i \(-0.415496\pi\)
−0.182298 + 0.983243i \(0.558354\pi\)
\(350\) −2.01683 39.4785i −0.107804 2.11021i
\(351\) 4.05728 0.926049i 0.216562 0.0494288i
\(352\) −1.47852 + 2.32236i −0.0788052 + 0.123782i
\(353\) −32.2813 7.36800i −1.71816 0.392159i −0.753874 0.657020i \(-0.771817\pi\)
−0.964287 + 0.264861i \(0.914674\pi\)
\(354\) 1.29111 0.892219i 0.0686217 0.0474209i
\(355\) −9.88376 + 12.3938i −0.524576 + 0.657797i
\(356\) −28.4418 + 2.49180i −1.50741 + 0.132065i
\(357\) 1.56502 + 13.0286i 0.0828294 + 0.689548i
\(358\) 4.28326 + 0.293889i 0.226378 + 0.0155325i
\(359\) −13.4995 3.08118i −0.712477 0.162618i −0.149105 0.988821i \(-0.547639\pi\)
−0.563372 + 0.826203i \(0.690496\pi\)
\(360\) 8.85410 + 6.79143i 0.466652 + 0.357940i
\(361\) −17.4062 −0.916114
\(362\) 17.2680 + 9.82530i 0.907586 + 0.516406i
\(363\) 6.71071 8.41497i 0.352221 0.441671i
\(364\) 21.3803 + 5.27435i 1.12063 + 0.276451i
\(365\) −36.0358 45.1875i −1.88620 2.36522i
\(366\) 1.27147 + 8.08985i 0.0664609 + 0.422863i
\(367\) 24.4659 11.7821i 1.27711 0.615023i 0.332463 0.943116i \(-0.392120\pi\)
0.944645 + 0.328093i \(0.106406\pi\)
\(368\) 5.19961 + 0.258240i 0.271049 + 0.0134617i
\(369\) 0.630075 0.502468i 0.0328004 0.0261574i
\(370\) −8.26129 52.5632i −0.429484 2.73263i
\(371\) −16.1461 5.51692i −0.838263 0.286424i
\(372\) 2.90975 + 0.401184i 0.150863 + 0.0208004i
\(373\) 8.11851 0.420361 0.210180 0.977663i \(-0.432595\pi\)
0.210180 + 0.977663i \(0.432595\pi\)
\(374\) 1.68818 2.96698i 0.0872935 0.153419i
\(375\) 17.1647 + 13.6884i 0.886382 + 0.706866i
\(376\) 4.67099 22.4070i 0.240888 1.15555i
\(377\) −11.1451 23.1431i −0.574004 1.19193i
\(378\) 3.60062 1.01763i 0.185196 0.0523411i
\(379\) −1.47164 + 3.05588i −0.0755928 + 0.156970i −0.935340 0.353749i \(-0.884907\pi\)
0.859747 + 0.510719i \(0.170621\pi\)
\(380\) 1.36057 9.86811i 0.0697960 0.506224i
\(381\) −1.49548 + 3.10540i −0.0766157 + 0.159094i
\(382\) −12.5524 + 13.7002i −0.642235 + 0.700962i
\(383\) −2.98516 + 1.43758i −0.152534 + 0.0734567i −0.508594 0.861007i \(-0.669834\pi\)
0.356059 + 0.934463i \(0.384120\pi\)
\(384\) −10.9475 2.85539i −0.558660 0.145714i
\(385\) 1.71300 + 4.78245i 0.0873027 + 0.243736i
\(386\) −5.70338 5.22555i −0.290294 0.265973i
\(387\) −9.95871 + 2.27301i −0.506230 + 0.115544i
\(388\) 6.72581 + 2.54246i 0.341451 + 0.129074i
\(389\) −3.05499 13.3848i −0.154894 0.678636i −0.991421 0.130710i \(-0.958274\pi\)
0.836526 0.547927i \(-0.184583\pi\)
\(390\) −19.1020 + 13.2004i −0.967269 + 0.668429i
\(391\) −6.45515 −0.326451
\(392\) 19.4396 + 3.75517i 0.981849 + 0.189665i
\(393\) −0.988893 −0.0498831
\(394\) 6.30638 4.35801i 0.317711 0.219553i
\(395\) −15.1852 66.5307i −0.764051 3.34752i
\(396\) −0.910475 0.344173i −0.0457531 0.0172954i
\(397\) −13.8667 + 3.16498i −0.695949 + 0.158846i −0.555839 0.831290i \(-0.687603\pi\)
−0.140110 + 0.990136i \(0.544746\pi\)
\(398\) 19.6617 + 18.0144i 0.985551 + 0.902981i
\(399\) −2.37916 2.34445i −0.119107 0.117369i
\(400\) −40.6826 11.4357i −2.03413 0.571784i
\(401\) −1.13160 + 0.544952i −0.0565096 + 0.0272136i −0.461925 0.886919i \(-0.652841\pi\)
0.405416 + 0.914133i \(0.367127\pi\)
\(402\) 5.50844 6.01214i 0.274736 0.299858i
\(403\) −2.65186 + 5.50665i −0.132099 + 0.274306i
\(404\) −2.57835 + 18.7005i −0.128278 + 0.930385i
\(405\) −1.71177 + 3.55453i −0.0850585 + 0.176626i
\(406\) −11.0690 20.2693i −0.549345 1.00595i
\(407\) 2.01376 + 4.18162i 0.0998184 + 0.207275i
\(408\) 13.7331 + 2.86282i 0.679890 + 0.141731i
\(409\) 3.43363 + 2.73823i 0.169782 + 0.135397i 0.704695 0.709511i \(-0.251084\pi\)
−0.534912 + 0.844908i \(0.679655\pi\)
\(410\) −2.22365 + 3.90808i −0.109818 + 0.193006i
\(411\) −18.2225 −0.898849
\(412\) −27.8854 3.84472i −1.37381 0.189416i
\(413\) 0.990065 + 2.76412i 0.0487179 + 0.136013i
\(414\) 0.285778 + 1.81829i 0.0140452 + 0.0893639i
\(415\) −16.9636 + 13.5280i −0.832711 + 0.664065i
\(416\) 12.6429 19.8587i 0.619871 0.973653i
\(417\) −10.9152 + 5.25648i −0.534519 + 0.257411i
\(418\) 0.134910 + 0.858378i 0.00659868 + 0.0419847i
\(419\) −10.1665 12.7483i −0.496664 0.622797i 0.468809 0.883300i \(-0.344683\pi\)
−0.965473 + 0.260502i \(0.916112\pi\)
\(420\) −16.5465 + 12.7291i −0.807385 + 0.621116i
\(421\) −3.44855 + 4.32435i −0.168072 + 0.210756i −0.858733 0.512423i \(-0.828748\pi\)
0.690661 + 0.723178i \(0.257320\pi\)
\(422\) 28.5196 + 16.2273i 1.38831 + 0.789935i
\(423\) 8.09238 0.393465
\(424\) −11.1016 + 14.4733i −0.539141 + 0.702887i
\(425\) 51.0852 + 11.6599i 2.47800 + 0.565587i
\(426\) 5.66912 + 0.388978i 0.274670 + 0.0188460i
\(427\) −15.2364 1.60343i −0.737340 0.0775954i
\(428\) 34.4447 3.01772i 1.66495 0.145867i
\(429\) 1.26280 1.58350i 0.0609684 0.0764520i
\(430\) 46.8864 32.4007i 2.26106 1.56250i
\(431\) 26.8429 + 6.12673i 1.29298 + 0.295114i 0.813050 0.582193i \(-0.197805\pi\)
0.479929 + 0.877307i \(0.340662\pi\)
\(432\) 0.198416 3.99508i 0.00954631 0.192213i
\(433\) 9.19233 2.09809i 0.441755 0.100828i 0.00414277 0.999991i \(-0.498681\pi\)
0.437613 + 0.899164i \(0.355824\pi\)
\(434\) −2.12855 + 5.06614i −0.102173 + 0.243183i
\(435\) 23.7407 + 5.41866i 1.13828 + 0.259805i
\(436\) −2.57874 + 2.45384i −0.123499 + 0.117518i
\(437\) 1.28464 1.02446i 0.0614525 0.0490067i
\(438\) −5.98201 + 19.8356i −0.285832 + 0.947781i
\(439\) 21.0168 + 10.1212i 1.00308 + 0.483057i 0.861982 0.506939i \(-0.169223\pi\)
0.141096 + 0.989996i \(0.454937\pi\)
\(440\) 5.42976 0.102534i 0.258854 0.00488814i
\(441\) 0.102878 + 6.99924i 0.00489897 + 0.333297i
\(442\) −14.4358 + 25.3709i −0.686639 + 1.20677i
\(443\) −9.55931 + 19.8501i −0.454176 + 0.943107i 0.540624 + 0.841264i \(0.318188\pi\)
−0.994801 + 0.101843i \(0.967526\pi\)
\(444\) −13.8172 + 13.1480i −0.655737 + 0.623977i
\(445\) 35.1147 + 44.0324i 1.66460 + 2.08734i
\(446\) −21.2327 6.40335i −1.00540 0.303207i
\(447\) −1.59320 + 6.98026i −0.0753557 + 0.330155i
\(448\) 10.4413 18.4114i 0.493307 0.869856i
\(449\) 9.07246 + 39.7490i 0.428156 + 1.87587i 0.480085 + 0.877222i \(0.340606\pi\)
−0.0519288 + 0.998651i \(0.516537\pi\)
\(450\) 1.02274 14.9059i 0.0482125 0.702670i
\(451\) 0.0872752 0.382378i 0.00410963 0.0180055i
\(452\) −2.65387 30.2917i −0.124828 1.42480i
\(453\) 14.3752 + 11.4638i 0.675406 + 0.538619i
\(454\) −6.18224 + 4.27222i −0.290147 + 0.200505i
\(455\) −14.6481 40.8952i −0.686711 1.91720i
\(456\) −3.18736 + 1.60978i −0.149262 + 0.0753849i
\(457\) 5.51778 24.1750i 0.258111 1.13086i −0.665158 0.746703i \(-0.731636\pi\)
0.923269 0.384155i \(-0.125507\pi\)
\(458\) −28.7650 + 11.4989i −1.34410 + 0.537307i
\(459\) 4.95976i 0.231502i
\(460\) −5.24627 8.82828i −0.244609 0.411621i
\(461\) 22.7659 + 18.1552i 1.06031 + 0.845572i 0.988405 0.151840i \(-0.0485197\pi\)
0.0719082 + 0.997411i \(0.477091\pi\)
\(462\) 1.06125 1.47977i 0.0493737 0.0688452i
\(463\) 16.0344 12.7870i 0.745180 0.594262i −0.175546 0.984471i \(-0.556169\pi\)
0.920726 + 0.390210i \(0.127598\pi\)
\(464\) −24.3132 + 4.29314i −1.12871 + 0.199304i
\(465\) −2.51397 5.22031i −0.116583 0.242086i
\(466\) −0.363708 + 5.30083i −0.0168484 + 0.245556i
\(467\) −1.47883 1.85440i −0.0684323 0.0858113i 0.746437 0.665456i \(-0.231763\pi\)
−0.814869 + 0.579645i \(0.803191\pi\)
\(468\) 7.78556 + 2.94306i 0.359887 + 0.136043i
\(469\) 8.21078 + 12.8567i 0.379138 + 0.593666i
\(470\) −41.9248 + 16.7596i −1.93385 + 0.773061i
\(471\) 2.30711i 0.106306i
\(472\) 3.13824 0.0592619i 0.144449 0.00272775i
\(473\) −3.09957 + 3.88673i −0.142518 + 0.178712i
\(474\) −16.5252 + 18.0363i −0.759029 + 0.828435i
\(475\) −12.0169 + 5.78705i −0.551374 + 0.265528i
\(476\) −11.7983 + 23.4431i −0.540773 + 1.07451i
\(477\) −5.81040 2.79814i −0.266040 0.128118i
\(478\) −9.33109 + 3.73013i −0.426794 + 0.170612i
\(479\) −4.95680 2.38707i −0.226482 0.109068i 0.317202 0.948358i \(-0.397257\pi\)
−0.543684 + 0.839290i \(0.682971\pi\)
\(480\) 7.24597 + 21.1085i 0.330732 + 0.963468i
\(481\) −17.2199 35.7574i −0.785158 1.63040i
\(482\) −3.31684 + 10.9982i −0.151078 + 0.500955i
\(483\) −3.42455 0.360389i −0.155822 0.0163983i
\(484\) 20.4884 6.60340i 0.931293 0.300155i
\(485\) −3.15617 13.8281i −0.143314 0.627901i
\(486\) 1.39706 0.219575i 0.0633721 0.00996011i
\(487\) 9.95959 2.27321i 0.451312 0.103009i 0.00917788 0.999958i \(-0.497079\pi\)
0.442134 + 0.896949i \(0.354221\pi\)
\(488\) −6.82641 + 14.8879i −0.309017 + 0.673943i
\(489\) 20.6737i 0.934896i
\(490\) −15.0286 36.0485i −0.678924 1.62850i
\(491\) 27.1990i 1.22747i −0.789510 0.613737i \(-0.789665\pi\)
0.789510 0.613737i \(-0.210335\pi\)
\(492\) 1.60564 0.140671i 0.0723879 0.00634195i
\(493\) 29.8457 6.81209i 1.34418 0.306801i
\(494\) −1.15363 7.34007i −0.0519043 0.330245i
\(495\) 0.427252 + 1.87191i 0.0192036 + 0.0841363i
\(496\) 4.40557 + 3.88604i 0.197816 + 0.174488i
\(497\) −3.43733 + 10.0599i −0.154185 + 0.451246i
\(498\) 7.44638 + 2.24568i 0.333680 + 0.100631i
\(499\) −17.7260 36.8083i −0.793523 1.64777i −0.761399 0.648283i \(-0.775487\pi\)
−0.0321234 0.999484i \(-0.510227\pi\)
\(500\) 13.4695 + 41.7920i 0.602375 + 1.86900i
\(501\) 8.63925 + 4.16044i 0.385973 + 0.185875i
\(502\) −1.06033 2.65248i −0.0473250 0.118386i
\(503\) −16.8855 8.13161i −0.752885 0.362570i 0.0177537 0.999842i \(-0.494349\pi\)
−0.770639 + 0.637272i \(0.780063\pi\)
\(504\) 7.12577 + 2.28548i 0.317407 + 0.101803i
\(505\) 33.5502 16.1569i 1.49296 0.718973i
\(506\) 0.660476 + 0.605141i 0.0293617 + 0.0269018i
\(507\) −2.69293 + 3.37682i −0.119597 + 0.149970i
\(508\) −5.92605 + 3.52160i −0.262926 + 0.156246i
\(509\) 12.8302i 0.568688i −0.958722 0.284344i \(-0.908224\pi\)
0.958722 0.284344i \(-0.0917757\pi\)
\(510\) −10.2718 25.6954i −0.454843 1.13781i
\(511\) −32.9695 20.3797i −1.45849 0.901546i
\(512\) −15.0869 16.8637i −0.666753 0.745279i
\(513\) −0.787138 0.987039i −0.0347530 0.0435788i
\(514\) 9.95495 + 0.683043i 0.439094 + 0.0301277i
\(515\) 24.0925 + 50.0285i 1.06164 + 2.20452i
\(516\) −19.1098 7.22381i −0.841264 0.318011i
\(517\) 3.07915 2.45554i 0.135421 0.107994i
\(518\) −17.1022 31.3172i −0.751428 1.37600i
\(519\) −14.8636 11.8533i −0.652439 0.520303i
\(520\) −46.4304 + 0.876782i −2.03611 + 0.0384494i
\(521\) 21.6112i 0.946802i 0.880847 + 0.473401i \(0.156974\pi\)
−0.880847 + 0.473401i \(0.843026\pi\)
\(522\) −3.24014 8.10536i −0.141817 0.354762i
\(523\) 2.90380 12.7224i 0.126974 0.556310i −0.870919 0.491427i \(-0.836475\pi\)
0.997893 0.0648831i \(-0.0206674\pi\)
\(524\) −1.64802 1.09347i −0.0719940 0.0477684i
\(525\) 26.4505 + 9.03780i 1.15439 + 0.394442i
\(526\) 19.8507 + 28.7255i 0.865532 + 1.25249i
\(527\) −5.69493 4.54155i −0.248075 0.197833i
\(528\) −1.13676 1.58033i −0.0494712 0.0687752i
\(529\) −4.74105 + 20.7719i −0.206133 + 0.903126i
\(530\) 35.8974 + 2.46304i 1.55929 + 0.106988i
\(531\) 0.246939 + 1.08191i 0.0107162 + 0.0469509i
\(532\) −1.37256 6.53784i −0.0595081 0.283451i
\(533\) −0.746299 + 3.26975i −0.0323258 + 0.141629i
\(534\) 5.82911 19.3286i 0.252250 0.836430i
\(535\) −42.5260 53.3259i −1.83856 2.30548i
\(536\) 15.8279 3.92844i 0.683661 0.169683i
\(537\) −1.31720 + 2.73520i −0.0568416 + 0.118033i
\(538\) −9.59142 5.45741i −0.413515 0.235286i
\(539\) 2.16299 + 2.63199i 0.0931664 + 0.113368i
\(540\) −6.78313 + 4.03093i −0.291900 + 0.173464i
\(541\) −10.6254 5.11694i −0.456823 0.219994i 0.191298 0.981532i \(-0.438730\pi\)
−0.648121 + 0.761538i \(0.724445\pi\)
\(542\) −35.6202 10.7423i −1.53002 0.461423i
\(543\) −10.9836 + 8.75909i −0.471349 + 0.375889i
\(544\) 19.7210 + 19.9564i 0.845532 + 0.855621i
\(545\) 6.84580 + 1.56251i 0.293242 + 0.0669305i
\(546\) −9.07482 + 12.6537i −0.388366 + 0.541527i
\(547\) 4.06595 0.928027i 0.173848 0.0396796i −0.134711 0.990885i \(-0.543011\pi\)
0.308558 + 0.951205i \(0.400153\pi\)
\(548\) −30.3683 20.1495i −1.29727 0.860745i
\(549\) −5.64542 1.28853i −0.240941 0.0549932i
\(550\) −4.13386 5.98202i −0.176268 0.255074i
\(551\) −4.85847 + 6.09233i −0.206978 + 0.259542i
\(552\) −1.53431 + 3.34622i −0.0653047 + 0.142425i
\(553\) −24.6322 38.5698i −1.04747 1.64015i
\(554\) −1.30590 + 19.0327i −0.0554822 + 0.808621i
\(555\) 36.6807 + 8.37213i 1.55701 + 0.355377i
\(556\) −24.0028 3.30941i −1.01795 0.140350i
\(557\) −4.99764 −0.211757 −0.105878 0.994379i \(-0.533765\pi\)
−0.105878 + 0.994379i \(0.533765\pi\)
\(558\) −1.02714 + 1.80521i −0.0434824 + 0.0764205i
\(559\) 26.5047 33.2358i 1.12103 1.40573i
\(560\) −41.6503 + 2.91711i −1.76005 + 0.123271i
\(561\) 1.50498 + 1.88719i 0.0635404 + 0.0796771i
\(562\) −4.17551 + 0.656259i −0.176133 + 0.0276826i
\(563\) −23.1339 + 11.1407i −0.974980 + 0.469525i −0.852376 0.522930i \(-0.824839\pi\)
−0.122604 + 0.992456i \(0.539125\pi\)
\(564\) 13.4862 + 8.94815i 0.567870 + 0.376785i
\(565\) −46.8964 + 37.3986i −1.97294 + 1.57337i
\(566\) −17.3283 + 2.72347i −0.728364 + 0.114476i
\(567\) −0.276902 + 2.63122i −0.0116288 + 0.110501i
\(568\) 9.01764 + 6.91688i 0.378372 + 0.290226i
\(569\) 41.5754 1.74293 0.871465 0.490458i \(-0.163170\pi\)
0.871465 + 0.490458i \(0.163170\pi\)
\(570\) 6.12217 + 3.48345i 0.256430 + 0.145906i
\(571\) −21.8240 17.4040i −0.913305 0.728337i 0.0494312 0.998778i \(-0.484259\pi\)
−0.962737 + 0.270441i \(0.912831\pi\)
\(572\) 3.85544 1.24260i 0.161204 0.0519559i
\(573\) −5.70072 11.8377i −0.238151 0.494526i
\(574\) −0.520124 + 2.97019i −0.0217096 + 0.123973i
\(575\) −5.96598 + 12.3885i −0.248798 + 0.516635i
\(576\) 4.74822 6.43851i 0.197843 0.268271i
\(577\) −10.9482 + 22.7343i −0.455781 + 0.946439i 0.538796 + 0.842436i \(0.318879\pi\)
−0.994577 + 0.104003i \(0.966835\pi\)
\(578\) −7.92390 7.26003i −0.329591 0.301978i
\(579\) 4.92801 2.37321i 0.204801 0.0986271i
\(580\) 33.5729 + 35.2817i 1.39404 + 1.46499i
\(581\) −7.65066 + 12.3769i −0.317403 + 0.513482i
\(582\) −3.43469 + 3.74876i −0.142372 + 0.155391i
\(583\) −3.05992 + 0.698407i −0.126729 + 0.0289251i
\(584\) −31.9024 + 26.4420i −1.32013 + 1.09418i
\(585\) −3.65347 16.0069i −0.151053 0.661804i
\(586\) 5.58161 + 8.07702i 0.230574 + 0.333659i
\(587\) 39.8734 1.64575 0.822875 0.568223i \(-0.192369\pi\)
0.822875 + 0.568223i \(0.192369\pi\)
\(588\) −7.56797 + 11.7782i −0.312098 + 0.485725i
\(589\) 1.85411 0.0763973
\(590\) −3.52001 5.09372i −0.144916 0.209705i
\(591\) 1.20616 + 5.28455i 0.0496150 + 0.217378i
\(592\) −37.5652 + 6.63314i −1.54392 + 0.272620i
\(593\) 7.31927 1.67058i 0.300566 0.0686023i −0.0695781 0.997577i \(-0.522165\pi\)
0.370144 + 0.928974i \(0.379308\pi\)
\(594\) 0.464955 0.507471i 0.0190773 0.0208218i
\(595\) 51.4009 6.17434i 2.10723 0.253123i
\(596\) −10.3735 + 9.87111i −0.424916 + 0.404337i
\(597\) −16.9887 + 8.18133i −0.695301 + 0.334840i
\(598\) −5.64779 5.17462i −0.230955 0.211606i
\(599\) −6.77195 + 14.0621i −0.276694 + 0.574562i −0.992288 0.123955i \(-0.960442\pi\)
0.715593 + 0.698517i \(0.246156\pi\)
\(600\) 18.1866 23.7102i 0.742465 0.967963i
\(601\) 5.39703 11.2070i 0.220149 0.457145i −0.761418 0.648261i \(-0.775496\pi\)
0.981567 + 0.191116i \(0.0612107\pi\)
\(602\) 22.2744 31.0588i 0.907836 1.26586i
\(603\) 2.50168 + 5.19480i 0.101876 + 0.211549i
\(604\) 11.2805 + 35.0002i 0.458998 + 1.42414i
\(605\) −33.1990 26.4753i −1.34973 1.07637i
\(606\) −11.6018 6.60129i −0.471291 0.268159i
\(607\) −3.42482 −0.139009 −0.0695047 0.997582i \(-0.522142\pi\)
−0.0695047 + 0.997582i \(0.522142\pi\)
\(608\) −7.09184 0.841681i −0.287612 0.0341347i
\(609\) 16.2139 1.94763i 0.657020 0.0789221i
\(610\) 31.9163 5.01624i 1.29225 0.203102i
\(611\) −26.3301 + 20.9975i −1.06520 + 0.849470i
\(612\) −5.48426 + 8.26558i −0.221688 + 0.334116i
\(613\) −4.55139 + 2.19183i −0.183829 + 0.0885274i −0.523534 0.852004i \(-0.675387\pi\)
0.339706 + 0.940532i \(0.389673\pi\)
\(614\) −15.3231 + 2.40831i −0.618389 + 0.0971914i
\(615\) −1.98235 2.48579i −0.0799361 0.100237i
\(616\) 3.40486 1.29261i 0.137186 0.0520807i
\(617\) 1.35133 1.69452i 0.0544025 0.0682186i −0.753886 0.657005i \(-0.771823\pi\)
0.808288 + 0.588787i \(0.200394\pi\)
\(618\) 9.84355 17.3001i 0.395966 0.695912i
\(619\) 45.4088 1.82513 0.912566 0.408930i \(-0.134098\pi\)
0.912566 + 0.408930i \(0.134098\pi\)
\(620\) 1.58276 11.4796i 0.0635652 0.461032i
\(621\) −1.26887 0.289612i −0.0509181 0.0116217i
\(622\) −0.700138 + 10.2041i −0.0280730 + 0.409148i
\(623\) 32.1268 + 19.8588i 1.28713 + 0.795627i
\(624\) 9.72056 + 13.5136i 0.389134 + 0.540976i
\(625\) 21.0686 26.4192i 0.842743 1.05677i
\(626\) −6.24962 9.04369i −0.249785 0.361459i
\(627\) −0.599011 0.136720i −0.0239222 0.00546009i
\(628\) −2.55108 + 3.84486i −0.101799 + 0.153426i
\(629\) 46.1133 10.5251i 1.83866 0.419662i
\(630\) −4.01477 14.2053i −0.159952 0.565951i
\(631\) −22.9974 5.24901i −0.915512 0.208960i −0.261288 0.965261i \(-0.584147\pi\)
−0.654224 + 0.756301i \(0.727005\pi\)
\(632\) −47.4834 + 11.7852i −1.88879 + 0.468792i
\(633\) −18.1403 + 14.4664i −0.721012 + 0.574988i
\(634\) −16.1969 4.88467i −0.643262 0.193995i
\(635\) 12.2515 + 5.90001i 0.486186 + 0.234135i
\(636\) −6.58915 11.0880i −0.261277 0.439669i
\(637\) −18.4959 22.5064i −0.732834 0.891737i
\(638\) −3.69235 2.10090i −0.146181 0.0831756i
\(639\) −1.74339 + 3.62018i −0.0689674 + 0.143212i
\(640\) −11.2652 + 43.1902i −0.445295 + 1.70724i
\(641\) 9.17682 + 11.5074i 0.362463 + 0.454514i 0.929305 0.369312i \(-0.120407\pi\)
−0.566843 + 0.823826i \(0.691835\pi\)
\(642\) −7.05939 + 23.4081i −0.278612 + 0.923842i
\(643\) −4.95656 + 21.7161i −0.195468 + 0.856400i 0.778125 + 0.628109i \(0.216171\pi\)
−0.973593 + 0.228291i \(0.926686\pi\)
\(644\) −5.30861 4.38729i −0.209188 0.172884i
\(645\) 8.96754 + 39.2894i 0.353097 + 1.54702i
\(646\) 8.83440 + 0.606158i 0.347585 + 0.0238490i
\(647\) −9.27536 + 40.6380i −0.364652 + 1.59765i 0.376572 + 0.926387i \(0.377103\pi\)
−0.741224 + 0.671258i \(0.765754\pi\)
\(648\) 2.57104 + 1.17888i 0.101000 + 0.0463106i
\(649\) 0.422254 + 0.336736i 0.0165749 + 0.0132180i
\(650\) 35.3490 + 51.1528i 1.38650 + 2.00638i
\(651\) −2.76768 2.72730i −0.108474 0.106891i
\(652\) 22.8599 34.4533i 0.895264 1.34929i
\(653\) −0.444252 + 1.94640i −0.0173849 + 0.0761683i −0.982876 0.184267i \(-0.941009\pi\)
0.965491 + 0.260435i \(0.0838661\pi\)
\(654\) −0.934316 2.33724i −0.0365346 0.0913931i
\(655\) 3.90141i 0.152441i
\(656\) 2.83139 + 1.54101i 0.110547 + 0.0601662i
\(657\) −11.4537 9.13402i −0.446851 0.356352i
\(658\) −22.6790 + 20.0618i −0.884119 + 0.782091i
\(659\) −0.189703 + 0.151283i −0.00738980 + 0.00589317i −0.627178 0.778876i \(-0.715790\pi\)
0.619788 + 0.784769i \(0.287219\pi\)
\(660\) −1.35784 + 3.59203i −0.0528539 + 0.139820i
\(661\) 6.24063 + 12.9588i 0.242732 + 0.504039i 0.986370 0.164544i \(-0.0526154\pi\)
−0.743637 + 0.668583i \(0.766901\pi\)
\(662\) 25.6490 + 1.75986i 0.996877 + 0.0683991i
\(663\) −12.8692 16.1375i −0.499800 0.626729i
\(664\) 9.92645 + 11.9763i 0.385221 + 0.464772i
\(665\) −9.24937 + 9.38632i −0.358675 + 0.363986i
\(666\) −5.00619 12.5232i −0.193986 0.485265i
\(667\) 8.03332i 0.311051i
\(668\) 9.79714 + 16.4863i 0.379063 + 0.637876i
\(669\) 9.77737 12.2604i 0.378015 0.474016i
\(670\) −23.7193 21.7321i −0.916355 0.839583i
\(671\) −2.53907 + 1.22275i −0.0980198 + 0.0472039i
\(672\) 9.34812 + 11.6881i 0.360612 + 0.450880i
\(673\) −17.6721 8.51045i −0.681211 0.328054i 0.0610789 0.998133i \(-0.480546\pi\)
−0.742290 + 0.670079i \(0.766260\pi\)
\(674\) −16.3050 40.7878i −0.628046 1.57109i
\(675\) 9.51858 + 4.58391i 0.366370 + 0.176435i
\(676\) −8.22177 + 2.64987i −0.316222 + 0.101918i
\(677\) 12.5278 + 26.0143i 0.481484 + 0.999811i 0.990301 + 0.138937i \(0.0443685\pi\)
−0.508818 + 0.860874i \(0.669917\pi\)
\(678\) 20.5857 + 6.20824i 0.790590 + 0.238426i
\(679\) −5.11968 8.01654i −0.196475 0.307646i
\(680\) 11.2945 54.1802i 0.433123 2.07772i
\(681\) −1.18242 5.18052i −0.0453105 0.198518i
\(682\) 0.156942 + 0.998555i 0.00600961 + 0.0382366i
\(683\) −36.7231 + 8.38181i −1.40517 + 0.320721i −0.856858 0.515552i \(-0.827587\pi\)
−0.548313 + 0.836273i \(0.684730\pi\)
\(684\) −0.220368 2.51531i −0.00842597 0.0961751i
\(685\) 71.8919i 2.74685i
\(686\) −17.6401 19.3604i −0.673504 0.739184i
\(687\) 21.9049i 0.835724i
\(688\) −23.8594 33.1694i −0.909630 1.26457i
\(689\) 26.1657 5.97214i 0.996832 0.227520i
\(690\) 7.17355 1.12746i 0.273092 0.0429216i
\(691\) −10.6364 46.6012i −0.404629 1.77279i −0.608251 0.793745i \(-0.708129\pi\)
0.203622 0.979050i \(-0.434729\pi\)
\(692\) −11.6638 36.1893i −0.443390 1.37571i
\(693\) 0.693053 + 1.08520i 0.0263269 + 0.0412234i
\(694\) −11.9547 + 39.6402i −0.453793 + 1.50472i
\(695\) 20.7380 + 43.0629i 0.786637 + 1.63347i
\(696\) 3.56272 17.0906i 0.135045 0.647817i
\(697\) −3.60122 1.73426i −0.136406 0.0656896i
\(698\) −2.01482 + 0.805430i −0.0762622 + 0.0304860i
\(699\) −3.38500 1.63013i −0.128033 0.0616572i
\(700\) 34.0869 + 44.3093i 1.28836 + 1.67474i
\(701\) 15.9593 7.68557i 0.602773 0.290280i −0.107502 0.994205i \(-0.534285\pi\)
0.710275 + 0.703925i \(0.248571\pi\)
\(702\) −3.97587 + 4.33943i −0.150060 + 0.163781i
\(703\) −7.50661 + 9.41299i −0.283117 + 0.355018i
\(704\) −0.146993 3.89064i −0.00553999 0.146634i
\(705\) 31.9263i 1.20241i
\(706\) 43.4812 17.3817i 1.63644 0.654170i
\(707\) 17.5280 17.7875i 0.659207 0.668968i
\(708\) −0.784792 + 2.07609i −0.0294943 + 0.0780241i
\(709\) −4.07602 5.11117i −0.153078 0.191954i 0.699379 0.714751i \(-0.253460\pi\)
−0.852457 + 0.522797i \(0.824889\pi\)
\(710\) 1.53461 22.3660i 0.0575927 0.839380i
\(711\) −7.50501 15.5843i −0.281460 0.584457i
\(712\) 31.0870 25.7661i 1.16503 0.965625i
\(713\) 1.49442 1.19176i 0.0559666 0.0446318i
\(714\) −12.2957 13.8998i −0.460156 0.520186i
\(715\) −6.24726 4.98202i −0.233634 0.186317i
\(716\) −5.21961 + 3.10179i −0.195066 + 0.115919i
\(717\) 7.10574i 0.265369i
\(718\) 18.1831 7.26875i 0.678588 0.271267i
\(719\) 3.52189 15.4304i 0.131344 0.575458i −0.865830 0.500338i \(-0.833209\pi\)
0.997175 0.0751195i \(-0.0239338\pi\)
\(720\) −15.7615 0.782798i −0.587396 0.0291731i
\(721\) 26.5239 + 26.1370i 0.987803 + 0.973391i
\(722\) 20.2510 13.9944i 0.753666 0.520819i
\(723\) −6.35072 5.06453i −0.236186 0.188352i
\(724\) −27.9898 + 2.45220i −1.04023 + 0.0911354i
\(725\) 14.5105 63.5746i 0.538906 2.36110i
\(726\) −1.04194 + 15.1857i −0.0386700 + 0.563594i
\(727\) 4.18546 + 18.3377i 0.155230 + 0.680108i 0.991315 + 0.131508i \(0.0419818\pi\)
−0.836085 + 0.548600i \(0.815161\pi\)
\(728\) −29.1152 + 11.0532i −1.07908 + 0.409659i
\(729\) −0.222521 + 0.974928i −0.00824152 + 0.0361084i
\(730\) 78.2559 + 23.6004i 2.89638 + 0.873490i
\(731\) 31.5879 + 39.6100i 1.16832 + 1.46503i
\(732\) −7.98346 8.38980i −0.295077 0.310096i
\(733\) −3.82154 + 7.93551i −0.141152 + 0.293105i −0.959546 0.281553i \(-0.909150\pi\)
0.818394 + 0.574658i \(0.194865\pi\)
\(734\) −18.9918 + 33.3782i −0.701002 + 1.23201i
\(735\) 27.6136 0.405879i 1.01854 0.0149711i
\(736\) −6.25706 + 3.88001i −0.230638 + 0.143019i
\(737\) 2.52819 + 1.21751i 0.0931272 + 0.0448477i
\(738\) −0.329074 + 1.09117i −0.0121134 + 0.0401664i
\(739\) −8.42770 + 6.72086i −0.310018 + 0.247231i −0.766122 0.642696i \(-0.777816\pi\)
0.456104 + 0.889927i \(0.349245\pi\)
\(740\) 51.8719 + 54.5121i 1.90685 + 2.00391i
\(741\) 5.12220 + 1.16911i 0.188169 + 0.0429483i
\(742\) 23.2206 6.56274i 0.852454 0.240926i
\(743\) 36.8536 8.41160i 1.35203 0.308592i 0.515676 0.856784i \(-0.327541\pi\)
0.836352 + 0.548192i \(0.184684\pi\)
\(744\) −3.70787 + 1.87266i −0.135937 + 0.0686552i
\(745\) 27.5387 + 6.28553i 1.00894 + 0.230284i
\(746\) −9.44541 + 6.52723i −0.345821 + 0.238979i
\(747\) −3.42896 + 4.29978i −0.125459 + 0.157321i
\(748\) 0.421336 + 4.80919i 0.0154056 + 0.175841i
\(749\) −38.9075 24.0502i −1.42165 0.878775i
\(750\) −30.9755 2.12533i −1.13107 0.0776062i
\(751\) 5.22211 + 1.19191i 0.190558 + 0.0434935i 0.316735 0.948514i \(-0.397414\pi\)
−0.126177 + 0.992008i \(0.540271\pi\)
\(752\) 12.5807 + 29.8247i 0.458770 + 1.08759i
\(753\) 2.01989 0.0736090
\(754\) 31.5736 + 17.9650i 1.14984 + 0.654248i
\(755\) 45.2275 56.7135i 1.64600 2.06401i
\(756\) −3.37094 + 4.07882i −0.122600 + 0.148345i
\(757\) −11.6979 14.6687i −0.425167 0.533143i 0.522400 0.852701i \(-0.325037\pi\)
−0.947567 + 0.319558i \(0.896465\pi\)
\(758\) −0.744748 4.73852i −0.0270505 0.172111i
\(759\) −0.570686 + 0.274828i −0.0207146 + 0.00997561i
\(760\) 6.35095 + 12.5749i 0.230373 + 0.456138i
\(761\) −32.3377 + 25.7884i −1.17224 + 0.934830i −0.998749 0.0500060i \(-0.984076\pi\)
−0.173490 + 0.984836i \(0.555505\pi\)
\(762\) −0.756815 4.81530i −0.0274165 0.174440i
\(763\) 4.67539 0.561613i 0.169260 0.0203318i
\(764\) 3.58910 26.0314i 0.129849 0.941782i
\(765\) 19.5674 0.707460
\(766\) 2.31725 4.07258i 0.0837258 0.147148i
\(767\) −3.61073 2.87946i −0.130376 0.103971i
\(768\) 15.0324 5.47960i 0.542436 0.197728i
\(769\) −19.7651 41.0426i −0.712746 1.48003i −0.870300 0.492523i \(-0.836075\pi\)
0.157553 0.987511i \(-0.449639\pi\)
\(770\) −5.83804 4.18686i −0.210388 0.150884i
\(771\) −3.06138 + 6.35702i −0.110253 + 0.228943i
\(772\) 10.8368 + 1.49414i 0.390027 + 0.0537752i
\(773\) 14.5155 30.1418i 0.522087 1.08413i −0.458618 0.888633i \(-0.651655\pi\)
0.980705 0.195492i \(-0.0626303\pi\)
\(774\) 9.75888 10.6512i 0.350776 0.382851i
\(775\) −13.9793 + 6.73209i −0.502152 + 0.241824i
\(776\) −9.86920 + 2.44950i −0.354283 + 0.0879321i
\(777\) 25.0514 3.00920i 0.898713 0.107954i
\(778\) 14.3156 + 13.1162i 0.513239 + 0.470240i
\(779\) 0.991911 0.226397i 0.0355389 0.00811152i
\(780\) 11.6110 30.7158i 0.415742 1.09980i
\(781\) 0.435144 + 1.90649i 0.0155707 + 0.0682196i
\(782\) 7.51019 5.18990i 0.268564 0.185590i
\(783\) 6.17233 0.220581
\(784\) −25.6360 + 11.2604i −0.915571 + 0.402157i
\(785\) 9.10206 0.324866
\(786\) 1.15052 0.795063i 0.0410376 0.0283590i
\(787\) 5.97033 + 26.1577i 0.212819 + 0.932422i 0.962641 + 0.270782i \(0.0872821\pi\)
−0.749822 + 0.661640i \(0.769861\pi\)
\(788\) −3.83329 + 10.1406i −0.136555 + 0.361243i
\(789\) −24.0711 + 5.49407i −0.856954 + 0.195594i
\(790\) 71.1574 + 65.1958i 2.53167 + 2.31956i
\(791\) −21.1505 + 34.2164i −0.752023 + 1.21659i
\(792\) 1.33600 0.331590i 0.0474726 0.0117826i
\(793\) 21.7118 10.4559i 0.771010 0.371299i
\(794\) 13.5885 14.8310i 0.482236 0.526332i
\(795\) −11.0393 + 22.9234i −0.391524 + 0.813008i
\(796\) −37.3587 5.15086i −1.32414 0.182567i
\(797\) −15.1041 + 31.3640i −0.535015 + 1.11097i 0.441846 + 0.897091i \(0.354324\pi\)
−0.976860 + 0.213878i \(0.931390\pi\)
\(798\) 4.65293 + 0.814797i 0.164712 + 0.0288435i
\(799\) −17.4145 36.1615i −0.616080 1.27930i
\(800\) 56.5260 19.4038i 1.99850 0.686028i
\(801\) 11.1609 + 8.90055i 0.394352 + 0.314486i
\(802\) 0.878417 1.54382i 0.0310180 0.0545142i
\(803\) −7.12974 −0.251603
\(804\) −1.57503 + 11.4235i −0.0555469 + 0.402877i
\(805\) −1.42182 + 13.5106i −0.0501125 + 0.476187i
\(806\) −1.34202 8.53873i −0.0472707 0.300764i
\(807\) 6.10076 4.86519i 0.214757 0.171263i
\(808\) −12.0353 23.8299i −0.423401 0.838334i
\(809\) −23.0258 + 11.0886i −0.809543 + 0.389855i −0.792403 0.609998i \(-0.791170\pi\)
−0.0171397 + 0.999853i \(0.505456\pi\)
\(810\) −0.866273 5.51173i −0.0304377 0.193663i
\(811\) −3.11922 3.91138i −0.109531 0.137347i 0.724044 0.689754i \(-0.242281\pi\)
−0.833575 + 0.552406i \(0.813710\pi\)
\(812\) 29.1745 + 14.6827i 1.02382 + 0.515263i
\(813\) 16.4026 20.5683i 0.575266 0.721360i
\(814\) −5.70488 3.24601i −0.199956 0.113773i
\(815\) −81.5624 −2.85701
\(816\) −18.2793 + 7.71060i −0.639905 + 0.269925i
\(817\) −12.5726 2.86961i −0.439859 0.100395i
\(818\) −6.19635 0.425152i −0.216650 0.0148651i
\(819\) −5.92636 9.27966i −0.207084 0.324258i
\(820\) −0.554980 6.33462i −0.0193808 0.221215i
\(821\) 3.04246 3.81513i 0.106183 0.133149i −0.725901 0.687800i \(-0.758577\pi\)
0.832083 + 0.554651i \(0.187148\pi\)
\(822\) 21.2008 14.6508i 0.739463 0.511004i
\(823\) −8.59591 1.96196i −0.299635 0.0683896i 0.0700606 0.997543i \(-0.477681\pi\)
−0.369695 + 0.929153i \(0.620538\pi\)
\(824\) 35.5341 17.9466i 1.23789 0.625198i
\(825\) 5.01275 1.14413i 0.174522 0.0398334i
\(826\) −3.37421 2.41988i −0.117404 0.0841984i
\(827\) 9.77035 + 2.23002i 0.339748 + 0.0775453i 0.388991 0.921242i \(-0.372824\pi\)
−0.0492428 + 0.998787i \(0.515681\pi\)
\(828\) −1.79437 1.88570i −0.0623588 0.0655328i
\(829\) −12.3118 + 9.81837i −0.427608 + 0.341006i −0.813528 0.581526i \(-0.802456\pi\)
0.385919 + 0.922532i \(0.373884\pi\)
\(830\) 8.85971 29.3777i 0.307525 1.01971i
\(831\) −12.1539 5.85299i −0.421613 0.203038i
\(832\) 1.25695 + 33.2693i 0.0435768 + 1.15340i
\(833\) 31.0554 15.5218i 1.07600 0.537799i
\(834\) 8.47301 14.8913i 0.293396 0.515645i
\(835\) 16.4139 34.0838i 0.568026 1.17952i
\(836\) −0.847091 0.890206i −0.0292972 0.0307884i
\(837\) −0.915680 1.14823i −0.0316505 0.0396885i
\(838\) 22.0777 + 6.65817i 0.762660 + 0.230003i
\(839\) 0.313744 1.37460i 0.0108317 0.0474566i −0.969223 0.246183i \(-0.920823\pi\)
0.980055 + 0.198727i \(0.0636806\pi\)
\(840\) 9.01674 28.1128i 0.311107 0.969983i
\(841\) −2.02442 8.86956i −0.0698076 0.305847i
\(842\) 0.535441 7.80374i 0.0184525 0.268935i
\(843\) 0.665065 2.91384i 0.0229060 0.100358i
\(844\) −46.2276 + 4.05003i −1.59122 + 0.139408i
\(845\) 13.3223 + 10.6242i 0.458303 + 0.365484i
\(846\) −9.41500 + 6.50622i −0.323694 + 0.223688i
\(847\) −26.9470 9.20745i −0.925909 0.316372i
\(848\) 1.27960 25.7645i 0.0439416 0.884756i
\(849\) 2.76002 12.0924i 0.0947235 0.415011i
\(850\) −68.8091 + 27.5066i −2.36013 + 0.943469i
\(851\) 12.4119i 0.425475i
\(852\) −6.90843 + 4.10538i −0.236679 + 0.140648i
\(853\) −19.3758 15.4516i −0.663413 0.529054i 0.232886 0.972504i \(-0.425183\pi\)
−0.896299 + 0.443450i \(0.853755\pi\)
\(854\) 19.0158 10.3844i 0.650706 0.355348i
\(855\) −3.89409 + 3.10544i −0.133175 + 0.106204i
\(856\) −37.6481 + 31.2042i −1.28679 + 1.06654i
\(857\) 1.44565 + 3.00192i 0.0493824 + 0.102544i 0.924200 0.381909i \(-0.124733\pi\)
−0.874818 + 0.484452i \(0.839019\pi\)
\(858\) −0.196069 + 2.85759i −0.00669367 + 0.0975564i
\(859\) −18.1252 22.7283i −0.618424 0.775479i 0.369698 0.929152i \(-0.379461\pi\)
−0.988122 + 0.153673i \(0.950890\pi\)
\(860\) −28.4996 + 75.3927i −0.971828 + 2.57087i
\(861\) −1.81367 1.12110i −0.0618098 0.0382070i
\(862\) −36.1560 + 14.4535i −1.23148 + 0.492287i
\(863\) 27.6905i 0.942594i −0.881974 0.471297i \(-0.843786\pi\)
0.881974 0.471297i \(-0.156214\pi\)
\(864\) 2.98117 + 4.80756i 0.101421 + 0.163557i
\(865\) −46.7640 + 58.6402i −1.59002 + 1.99383i
\(866\) −9.00789 + 9.83158i −0.306100 + 0.334091i
\(867\) 6.84666 3.29718i 0.232525 0.111978i
\(868\) −1.59671 7.60550i −0.0541958 0.258147i
\(869\) −7.58453 3.65252i −0.257288 0.123903i
\(870\) −31.9775 + 12.7831i −1.08414 + 0.433387i
\(871\) −21.6188 10.4111i −0.732526 0.352766i
\(872\) 1.02734 4.92819i 0.0347900 0.166889i
\(873\) −1.55988 3.23912i −0.0527939 0.109628i
\(874\) −0.670937 + 2.22474i −0.0226948 + 0.0752530i
\(875\) 18.7812 54.9660i 0.634921 1.85819i
\(876\) −8.98796 27.8870i −0.303675 0.942216i
\(877\) 0.173924 + 0.762012i 0.00587301 + 0.0257313i 0.977780 0.209636i \(-0.0672279\pi\)
−0.971907 + 0.235367i \(0.924371\pi\)
\(878\) −32.5892 + 5.12200i −1.09983 + 0.172859i
\(879\) −6.76830 + 1.54482i −0.228289 + 0.0521055i
\(880\) −6.23477 + 4.48479i −0.210174 + 0.151182i
\(881\) 40.5201i 1.36516i 0.730813 + 0.682578i \(0.239141\pi\)
−0.730813 + 0.682578i \(0.760859\pi\)
\(882\) −5.74704 8.06049i −0.193513 0.271411i
\(883\) 37.3098i 1.25557i −0.778386 0.627787i \(-0.783961\pi\)
0.778386 0.627787i \(-0.216039\pi\)
\(884\) −3.60288 41.1238i −0.121178 1.38314i
\(885\) 4.26838 0.974231i 0.143480 0.0327484i
\(886\) −4.83766 30.7800i −0.162524 1.03408i
\(887\) 4.46507 + 19.5627i 0.149922 + 0.656852i 0.992905 + 0.118912i \(0.0379405\pi\)
−0.842983 + 0.537941i \(0.819202\pi\)
\(888\) 5.50461 26.4059i 0.184723 0.886124i
\(889\) 9.06911 + 0.954405i 0.304168 + 0.0320097i
\(890\) −76.2557 22.9972i −2.55610 0.770867i
\(891\) 0.211161 + 0.438481i 0.00707417 + 0.0146897i
\(892\) 29.8512 9.62102i 0.999493 0.322136i
\(893\) 9.20465 + 4.43272i 0.308022 + 0.148335i
\(894\) −3.75849 9.40204i −0.125703 0.314451i
\(895\) 10.7910 + 5.19667i 0.360703 + 0.173706i
\(896\) 2.65475 + 29.8153i 0.0886889 + 0.996059i
\(897\) 4.87999 2.35008i 0.162938 0.0784668i
\(898\) −42.5132 38.9515i −1.41868 1.29983i
\(899\) −5.65188 + 7.08723i −0.188501 + 0.236372i
\(900\) 10.7943 + 18.1644i 0.359811 + 0.605479i
\(901\) 31.9858i 1.06560i
\(902\) 0.205890 + 0.515043i 0.00685537 + 0.0171490i
\(903\) 14.5464 + 22.7772i 0.484074 + 0.757977i
\(904\) 27.4419 + 33.1089i 0.912705 + 1.10119i
\(905\) 34.5566 + 43.3326i 1.14870 + 1.44043i
\(906\) −25.9416 1.77994i −0.861851 0.0591345i
\(907\) 0.382040 + 0.793314i 0.0126854 + 0.0263416i 0.907215 0.420667i \(-0.138204\pi\)
−0.894530 + 0.447008i \(0.852489\pi\)
\(908\) 3.75783 9.94095i 0.124708 0.329902i
\(909\) 7.37948 5.88494i 0.244762 0.195191i
\(910\) 49.9216 + 35.8022i 1.65489 + 1.18683i
\(911\) 6.07476 + 4.84446i 0.201266 + 0.160504i 0.718936 0.695076i \(-0.244629\pi\)
−0.517670 + 0.855580i \(0.673201\pi\)
\(912\) 2.41405 4.43550i 0.0799373 0.146874i
\(913\) 2.67654i 0.0885806i
\(914\) 13.0169 + 32.5624i 0.430561 + 1.07707i
\(915\) −5.08355 + 22.2725i −0.168057 + 0.736306i
\(916\) 24.2214 36.5051i 0.800296 1.20616i
\(917\) 0.882255 + 2.46313i 0.0291346 + 0.0813396i
\(918\) −3.98761 5.77039i −0.131611 0.190451i
\(919\) −14.7939 11.7978i −0.488007 0.389173i 0.348344 0.937367i \(-0.386744\pi\)
−0.836351 + 0.548194i \(0.815315\pi\)
\(920\) 13.2016 + 6.05322i 0.435244 + 0.199569i
\(921\) 2.44062 10.6931i 0.0804212 0.352348i
\(922\) −41.0834 2.81887i −1.35301 0.0928346i
\(923\) −3.72096 16.3026i −0.122477 0.536606i
\(924\) −0.0449707 + 2.57486i −0.00147943 + 0.0847068i
\(925\) 22.4195 98.2263i 0.737149 3.22966i
\(926\) −8.37439 + 27.7684i −0.275200 + 0.912527i
\(927\) 8.77537 + 11.0040i 0.288221 + 0.361418i
\(928\) 24.8353 24.5425i 0.815259 0.805646i
\(929\) 16.9738 35.2465i 0.556893 1.15640i −0.412517 0.910950i \(-0.635350\pi\)
0.969409 0.245450i \(-0.0789356\pi\)
\(930\) 7.12195 + 4.05231i 0.233538 + 0.132880i
\(931\) −3.71693 + 8.01762i −0.121817 + 0.262767i
\(932\) −3.83868 6.45963i −0.125740 0.211592i
\(933\) −6.51613 3.13800i −0.213329 0.102734i
\(934\) 3.21146 + 0.968511i 0.105082 + 0.0316906i
\(935\) 7.44539 5.93750i 0.243490 0.194177i
\(936\) −11.4242 + 2.83546i −0.373413 + 0.0926799i
\(937\) −30.9970 7.07487i −1.01263 0.231126i −0.316155 0.948708i \(-0.602392\pi\)
−0.696474 + 0.717582i \(0.745249\pi\)
\(938\) −19.8894 8.35657i −0.649413 0.272852i
\(939\) 7.57834 1.72971i 0.247310 0.0564468i
\(940\) 35.3025 53.2060i 1.15144 1.73539i
\(941\) −49.6590 11.3343i −1.61884 0.369489i −0.685382 0.728184i \(-0.740365\pi\)
−0.933455 + 0.358695i \(0.883222\pi\)
\(942\) −1.85490 2.68418i −0.0604358 0.0874554i
\(943\) 0.653964 0.820046i 0.0212960 0.0267044i
\(944\) −3.60351 + 2.59207i −0.117284 + 0.0843648i
\(945\) 10.3808 + 1.09244i 0.337686 + 0.0355371i
\(946\) 0.481255 7.01402i 0.0156470 0.228045i
\(947\) 41.4233 + 9.45461i 1.34608 + 0.307233i 0.834028 0.551722i \(-0.186029\pi\)
0.512050 + 0.858956i \(0.328886\pi\)
\(948\) 4.72505 34.2704i 0.153463 1.11305i
\(949\) 60.9671 1.97908
\(950\) 9.32824 16.3944i 0.302648 0.531905i
\(951\) 7.45847 9.35262i 0.241857 0.303280i
\(952\) −5.12150 36.7604i −0.165989 1.19141i
\(953\) −6.79970 8.52656i −0.220264 0.276202i 0.659406 0.751787i \(-0.270808\pi\)
−0.879670 + 0.475585i \(0.842236\pi\)
\(954\) 9.00975 1.41605i 0.291701 0.0458463i
\(955\) −46.7023 + 22.4906i −1.51125 + 0.727780i
\(956\) 7.85717 11.8419i 0.254119 0.382995i
\(957\) 2.34857 1.87292i 0.0759185 0.0605430i
\(958\) 7.68613 1.20802i 0.248328 0.0390293i
\(959\) 16.2575 + 45.3884i 0.524981 + 1.46567i
\(960\) −25.4014 18.7328i −0.819826 0.604599i
\(961\) −28.8431 −0.930423
\(962\) 48.7830 + 27.7570i 1.57283 + 0.894921i
\(963\) −13.5166 10.7791i −0.435565 0.347351i
\(964\) −4.98354 15.4625i −0.160509 0.498013i
\(965\) −9.36284 19.4421i −0.301400 0.625864i
\(966\) 4.27401 2.33402i 0.137514 0.0750959i
\(967\) −25.0168 + 51.9480i −0.804487 + 1.67053i −0.0644956 + 0.997918i \(0.520544\pi\)
−0.739991 + 0.672616i \(0.765170\pi\)
\(968\) −18.5280 + 24.1552i −0.595512 + 0.776379i
\(969\) −2.71679 + 5.64146i −0.0872757 + 0.181230i
\(970\) 14.7897 + 13.5506i 0.474869 + 0.435084i
\(971\) 18.3674 8.84529i 0.589439 0.283859i −0.115294 0.993331i \(-0.536781\pi\)
0.704733 + 0.709472i \(0.251067\pi\)
\(972\) −1.44886 + 1.37869i −0.0464723 + 0.0442216i
\(973\) 22.8309 + 22.4978i 0.731926 + 0.721247i
\(974\) −9.75975 + 10.6522i −0.312723 + 0.341318i
\(975\) −42.8645 + 9.78354i −1.37276 + 0.313324i
\(976\) −4.02764 22.8096i −0.128921 0.730116i
\(977\) −9.04987 39.6501i −0.289531 1.26852i −0.885170 0.465267i \(-0.845958\pi\)
0.595639 0.803252i \(-0.296899\pi\)
\(978\) 16.6215 + 24.0526i 0.531497 + 0.769118i
\(979\) 6.94750 0.222043
\(980\) 46.4677 + 29.8574i 1.48436 + 0.953758i
\(981\) 1.77983 0.0568257
\(982\) 21.8678 + 31.6445i 0.697830 + 1.00982i
\(983\) −2.85683 12.5166i −0.0911189 0.399218i 0.908716 0.417416i \(-0.137064\pi\)
−0.999834 + 0.0181981i \(0.994207\pi\)
\(984\) −1.75497 + 1.45459i −0.0559464 + 0.0463706i
\(985\) 20.8488 4.75860i 0.664297 0.151621i
\(986\) −29.2469 + 31.9212i −0.931410 + 1.01658i
\(987\) −7.21973 20.1564i −0.229807 0.641586i
\(988\) 7.24355 + 7.61223i 0.230448 + 0.242177i
\(989\) −11.9781 + 5.76833i −0.380880 + 0.183422i
\(990\) −2.00209 1.83435i −0.0636306 0.0582996i
\(991\) 3.48812 7.24315i 0.110804 0.230086i −0.838192 0.545375i \(-0.816387\pi\)
0.948996 + 0.315289i \(0.102101\pi\)
\(992\) −8.24996 0.979131i −0.261937 0.0310874i
\(993\) −7.88767 + 16.3789i −0.250308 + 0.519769i
\(994\) −4.08893 14.4676i −0.129693 0.458886i
\(995\) 32.2772 + 67.0243i 1.02326 + 2.12481i
\(996\) −10.4689 + 3.37413i −0.331721 + 0.106913i
\(997\) 38.2141 + 30.4748i 1.21025 + 0.965145i 0.999922 0.0124847i \(-0.00397411\pi\)
0.210332 + 0.977630i \(0.432546\pi\)
\(998\) 50.2168 + 28.5728i 1.58958 + 0.904455i
\(999\) 9.53659 0.301724
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 588.2.x.a.559.6 yes 168
4.3 odd 2 588.2.x.b.559.14 yes 168
49.27 odd 14 588.2.x.b.223.14 yes 168
196.27 even 14 inner 588.2.x.a.223.6 168
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
588.2.x.a.223.6 168 196.27 even 14 inner
588.2.x.a.559.6 yes 168 1.1 even 1 trivial
588.2.x.b.223.14 yes 168 49.27 odd 14
588.2.x.b.559.14 yes 168 4.3 odd 2