Properties

Label 287.2.l.a.27.19
Level $287$
Weight $2$
Character 287.27
Analytic conductor $2.292$
Analytic rank $0$
Dimension $104$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [287,2,Mod(27,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.27");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 287.l (of order \(8\), degree \(4\), 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: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(104\)
Relative dimension: \(26\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 27.19
Character \(\chi\) \(=\) 287.27
Dual form 287.2.l.a.202.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.814711 + 0.814711i) q^{2} +(-0.0360204 - 0.0869609i) q^{3} -0.672492i q^{4} +(0.788699 + 0.788699i) q^{5} +(0.0415018 - 0.100194i) q^{6} +(-0.714546 - 2.54743i) q^{7} +(2.17731 - 2.17731i) q^{8} +(2.11506 - 2.11506i) q^{9} +O(q^{10})\) \(q+(0.814711 + 0.814711i) q^{2} +(-0.0360204 - 0.0869609i) q^{3} -0.672492i q^{4} +(0.788699 + 0.788699i) q^{5} +(0.0415018 - 0.100194i) q^{6} +(-0.714546 - 2.54743i) q^{7} +(2.17731 - 2.17731i) q^{8} +(2.11506 - 2.11506i) q^{9} +1.28512i q^{10} +(1.30604 + 3.15306i) q^{11} +(-0.0584805 + 0.0242234i) q^{12} +(-0.275147 - 0.664263i) q^{13} +(1.49327 - 2.65757i) q^{14} +(0.0401767 - 0.0969952i) q^{15} +2.20277 q^{16} +(-2.89431 + 6.98749i) q^{17} +3.44632 q^{18} +(1.24941 - 3.01635i) q^{19} +(0.530394 - 0.530394i) q^{20} +(-0.195789 + 0.153897i) q^{21} +(-1.50479 + 3.63288i) q^{22} +4.78693i q^{23} +(-0.267768 - 0.110913i) q^{24} -3.75591i q^{25} +(0.317017 - 0.765348i) q^{26} +(-0.520995 - 0.215803i) q^{27} +(-1.71313 + 0.480527i) q^{28} +(-6.54356 + 2.71043i) q^{29} +(0.111755 - 0.0462906i) q^{30} +9.53707 q^{31} +(-2.56000 - 2.56000i) q^{32} +(0.227149 - 0.227149i) q^{33} +(-8.05082 + 3.33476i) q^{34} +(1.44560 - 2.57272i) q^{35} +(-1.42236 - 1.42236i) q^{36} -7.77797 q^{37} +(3.47537 - 1.43954i) q^{38} +(-0.0478540 + 0.0478540i) q^{39} +3.43448 q^{40} +(-5.21477 - 3.71566i) q^{41} +(-0.284893 - 0.0341297i) q^{42} +(1.02762 + 1.02762i) q^{43} +(2.12041 - 0.878302i) q^{44} +3.33628 q^{45} +(-3.89996 + 3.89996i) q^{46} +(0.458390 - 1.10665i) q^{47} +(-0.0793446 - 0.191555i) q^{48} +(-5.97885 + 3.64052i) q^{49} +(3.05998 - 3.05998i) q^{50} +0.711893 q^{51} +(-0.446712 + 0.185034i) q^{52} +(3.60556 + 8.70460i) q^{53} +(-0.248643 - 0.600277i) q^{54} +(-1.45674 + 3.51689i) q^{55} +(-7.10234 - 3.99076i) q^{56} -0.307309 q^{57} +(-7.53933 - 3.12289i) q^{58} +10.3717i q^{59} +(-0.0652285 - 0.0270185i) q^{60} +(-1.09617 + 1.09617i) q^{61} +(7.76995 + 7.76995i) q^{62} +(-6.89927 - 3.87666i) q^{63} -8.57685i q^{64} +(0.306896 - 0.740912i) q^{65} +0.370121 q^{66} +(-9.99517 - 4.14014i) q^{67} +(4.69904 + 1.94640i) q^{68} +(0.416276 - 0.172427i) q^{69} +(3.27377 - 0.918280i) q^{70} +(2.66198 - 1.10263i) q^{71} -9.21026i q^{72} +(-5.00377 + 5.00377i) q^{73} +(-6.33680 - 6.33680i) q^{74} +(-0.326617 + 0.135289i) q^{75} +(-2.02848 - 0.840222i) q^{76} +(7.09899 - 5.58006i) q^{77} -0.0779744 q^{78} +(2.77239 + 6.69315i) q^{79} +(1.73732 + 1.73732i) q^{80} -8.92034i q^{81} +(-1.22134 - 7.27572i) q^{82} -15.6167i q^{83} +(0.103495 + 0.131667i) q^{84} +(-7.79377 + 3.22828i) q^{85} +1.67443i q^{86} +(0.471403 + 0.471403i) q^{87} +(9.70884 + 4.02153i) q^{88} +(-4.66542 - 11.2633i) q^{89} +(2.71811 + 2.71811i) q^{90} +(-1.49556 + 1.17557i) q^{91} +3.21917 q^{92} +(-0.343529 - 0.829352i) q^{93} +(1.27506 - 0.528145i) q^{94} +(3.36441 - 1.39358i) q^{95} +(-0.130408 + 0.314832i) q^{96} +(14.8144 + 6.13631i) q^{97} +(-7.83700 - 1.90506i) q^{98} +(9.43125 + 3.90655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 104 q - 8 q^{2} - 4 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 104 q - 8 q^{2} - 4 q^{7} + 8 q^{8} + 8 q^{9} - 8 q^{11} - 8 q^{14} - 32 q^{15} - 96 q^{16} - 16 q^{18} - 24 q^{21} + 24 q^{22} + 12 q^{28} - 16 q^{29} + 48 q^{30} - 72 q^{32} - 44 q^{35} + 56 q^{36} + 32 q^{37} - 8 q^{39} - 8 q^{42} - 32 q^{43} + 72 q^{44} - 88 q^{46} - 12 q^{49} + 80 q^{50} + 32 q^{51} - 8 q^{53} + 104 q^{56} - 32 q^{57} - 96 q^{58} + 112 q^{60} - 132 q^{63} + 80 q^{65} + 56 q^{67} + 148 q^{70} - 104 q^{71} + 32 q^{74} - 16 q^{77} - 168 q^{78} - 124 q^{84} + 8 q^{85} - 64 q^{88} + 8 q^{91} + 104 q^{92} - 64 q^{93} - 8 q^{95} - 8 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{8}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.814711 + 0.814711i 0.576088 + 0.576088i 0.933823 0.357735i \(-0.116451\pi\)
−0.357735 + 0.933823i \(0.616451\pi\)
\(3\) −0.0360204 0.0869609i −0.0207964 0.0502069i 0.913140 0.407646i \(-0.133650\pi\)
−0.933937 + 0.357439i \(0.883650\pi\)
\(4\) 0.672492i 0.336246i
\(5\) 0.788699 + 0.788699i 0.352717 + 0.352717i 0.861119 0.508403i \(-0.169764\pi\)
−0.508403 + 0.861119i \(0.669764\pi\)
\(6\) 0.0415018 0.100194i 0.0169430 0.0409041i
\(7\) −0.714546 2.54743i −0.270073 0.962840i
\(8\) 2.17731 2.17731i 0.769795 0.769795i
\(9\) 2.11506 2.11506i 0.705019 0.705019i
\(10\) 1.28512i 0.406392i
\(11\) 1.30604 + 3.15306i 0.393786 + 0.950684i 0.989107 + 0.147196i \(0.0470248\pi\)
−0.595321 + 0.803488i \(0.702975\pi\)
\(12\) −0.0584805 + 0.0242234i −0.0168819 + 0.00699270i
\(13\) −0.275147 0.664263i −0.0763120 0.184234i 0.881120 0.472893i \(-0.156790\pi\)
−0.957432 + 0.288660i \(0.906790\pi\)
\(14\) 1.49327 2.65757i 0.399094 0.710266i
\(15\) 0.0401767 0.0969952i 0.0103736 0.0250441i
\(16\) 2.20277 0.550692
\(17\) −2.89431 + 6.98749i −0.701974 + 1.69472i 0.0171676 + 0.999853i \(0.494535\pi\)
−0.719142 + 0.694863i \(0.755465\pi\)
\(18\) 3.44632 0.812305
\(19\) 1.24941 3.01635i 0.286635 0.691999i −0.713326 0.700833i \(-0.752812\pi\)
0.999961 + 0.00883369i \(0.00281189\pi\)
\(20\) 0.530394 0.530394i 0.118600 0.118600i
\(21\) −0.195789 + 0.153897i −0.0427247 + 0.0335831i
\(22\) −1.50479 + 3.63288i −0.320822 + 0.774532i
\(23\) 4.78693i 0.998144i 0.866561 + 0.499072i \(0.166326\pi\)
−0.866561 + 0.499072i \(0.833674\pi\)
\(24\) −0.267768 0.110913i −0.0546580 0.0226401i
\(25\) 3.75591i 0.751182i
\(26\) 0.317017 0.765348i 0.0621722 0.150097i
\(27\) −0.520995 0.215803i −0.100266 0.0415313i
\(28\) −1.71313 + 0.480527i −0.323751 + 0.0908110i
\(29\) −6.54356 + 2.71043i −1.21511 + 0.503315i −0.895851 0.444354i \(-0.853433\pi\)
−0.319257 + 0.947668i \(0.603433\pi\)
\(30\) 0.111755 0.0462906i 0.0204037 0.00845147i
\(31\) 9.53707 1.71291 0.856454 0.516224i \(-0.172663\pi\)
0.856454 + 0.516224i \(0.172663\pi\)
\(32\) −2.56000 2.56000i −0.452548 0.452548i
\(33\) 0.227149 0.227149i 0.0395416 0.0395416i
\(34\) −8.05082 + 3.33476i −1.38070 + 0.571906i
\(35\) 1.44560 2.57272i 0.244350 0.434869i
\(36\) −1.42236 1.42236i −0.237060 0.237060i
\(37\) −7.77797 −1.27869 −0.639346 0.768920i \(-0.720795\pi\)
−0.639346 + 0.768920i \(0.720795\pi\)
\(38\) 3.47537 1.43954i 0.563779 0.233525i
\(39\) −0.0478540 + 0.0478540i −0.00766278 + 0.00766278i
\(40\) 3.43448 0.543039
\(41\) −5.21477 3.71566i −0.814410 0.580289i
\(42\) −0.284893 0.0341297i −0.0439600 0.00526633i
\(43\) 1.02762 + 1.02762i 0.156711 + 0.156711i 0.781107 0.624397i \(-0.214655\pi\)
−0.624397 + 0.781107i \(0.714655\pi\)
\(44\) 2.12041 0.878302i 0.319664 0.132409i
\(45\) 3.33628 0.497344
\(46\) −3.89996 + 3.89996i −0.575018 + 0.575018i
\(47\) 0.458390 1.10665i 0.0668630 0.161422i −0.886916 0.461931i \(-0.847157\pi\)
0.953779 + 0.300510i \(0.0971567\pi\)
\(48\) −0.0793446 0.191555i −0.0114524 0.0276486i
\(49\) −5.97885 + 3.64052i −0.854121 + 0.520074i
\(50\) 3.05998 3.05998i 0.432746 0.432746i
\(51\) 0.711893 0.0996850
\(52\) −0.446712 + 0.185034i −0.0619478 + 0.0256596i
\(53\) 3.60556 + 8.70460i 0.495262 + 1.19567i 0.952009 + 0.306071i \(0.0990146\pi\)
−0.456747 + 0.889597i \(0.650985\pi\)
\(54\) −0.248643 0.600277i −0.0338360 0.0816874i
\(55\) −1.45674 + 3.51689i −0.196427 + 0.474217i
\(56\) −7.10234 3.99076i −0.949090 0.533288i
\(57\) −0.307309 −0.0407041
\(58\) −7.53933 3.12289i −0.989962 0.410056i
\(59\) 10.3717i 1.35028i 0.737688 + 0.675142i \(0.235918\pi\)
−0.737688 + 0.675142i \(0.764082\pi\)
\(60\) −0.0652285 0.0270185i −0.00842097 0.00348808i
\(61\) −1.09617 + 1.09617i −0.140350 + 0.140350i −0.773791 0.633441i \(-0.781642\pi\)
0.633441 + 0.773791i \(0.281642\pi\)
\(62\) 7.76995 + 7.76995i 0.986785 + 0.986785i
\(63\) −6.89927 3.87666i −0.869226 0.488413i
\(64\) 8.57685i 1.07211i
\(65\) 0.306896 0.740912i 0.0380657 0.0918988i
\(66\) 0.370121 0.0455588
\(67\) −9.99517 4.14014i −1.22110 0.505798i −0.323344 0.946281i \(-0.604807\pi\)
−0.897761 + 0.440483i \(0.854807\pi\)
\(68\) 4.69904 + 1.94640i 0.569842 + 0.236036i
\(69\) 0.416276 0.172427i 0.0501137 0.0207578i
\(70\) 3.27377 0.918280i 0.391290 0.109755i
\(71\) 2.66198 1.10263i 0.315918 0.130858i −0.219089 0.975705i \(-0.570309\pi\)
0.535008 + 0.844847i \(0.320309\pi\)
\(72\) 9.21026i 1.08544i
\(73\) −5.00377 + 5.00377i −0.585647 + 0.585647i −0.936450 0.350802i \(-0.885909\pi\)
0.350802 + 0.936450i \(0.385909\pi\)
\(74\) −6.33680 6.33680i −0.736638 0.736638i
\(75\) −0.326617 + 0.135289i −0.0377145 + 0.0156219i
\(76\) −2.02848 0.840222i −0.232682 0.0963801i
\(77\) 7.09899 5.58006i 0.809005 0.635907i
\(78\) −0.0779744 −0.00882887
\(79\) 2.77239 + 6.69315i 0.311919 + 0.753038i 0.999634 + 0.0270575i \(0.00861373\pi\)
−0.687715 + 0.725980i \(0.741386\pi\)
\(80\) 1.73732 + 1.73732i 0.194238 + 0.194238i
\(81\) 8.92034i 0.991149i
\(82\) −1.22134 7.27572i −0.134874 0.803469i
\(83\) 15.6167i 1.71416i −0.515183 0.857080i \(-0.672276\pi\)
0.515183 0.857080i \(-0.327724\pi\)
\(84\) 0.103495 + 0.131667i 0.0112922 + 0.0143660i
\(85\) −7.79377 + 3.22828i −0.845353 + 0.350157i
\(86\) 1.67443i 0.180558i
\(87\) 0.471403 + 0.471403i 0.0505397 + 0.0505397i
\(88\) 9.70884 + 4.02153i 1.03497 + 0.428697i
\(89\) −4.66542 11.2633i −0.494534 1.19391i −0.952390 0.304883i \(-0.901382\pi\)
0.457856 0.889026i \(-0.348618\pi\)
\(90\) 2.71811 + 2.71811i 0.286514 + 0.286514i
\(91\) −1.49556 + 1.17557i −0.156778 + 0.123233i
\(92\) 3.21917 0.335622
\(93\) −0.343529 0.829352i −0.0356223 0.0859998i
\(94\) 1.27506 0.528145i 0.131512 0.0544740i
\(95\) 3.36441 1.39358i 0.345181 0.142979i
\(96\) −0.130408 + 0.314832i −0.0133097 + 0.0321324i
\(97\) 14.8144 + 6.13631i 1.50417 + 0.623048i 0.974345 0.225058i \(-0.0722572\pi\)
0.529826 + 0.848106i \(0.322257\pi\)
\(98\) −7.83700 1.90506i −0.791657 0.192440i
\(99\) 9.43125 + 3.90655i 0.947876 + 0.392623i
\(100\) −2.52582 −0.252582
\(101\) −5.89823 + 14.2396i −0.586896 + 1.41689i 0.299560 + 0.954078i \(0.403160\pi\)
−0.886455 + 0.462814i \(0.846840\pi\)
\(102\) 0.579987 + 0.579987i 0.0574273 + 0.0574273i
\(103\) 6.84936 + 6.84936i 0.674887 + 0.674887i 0.958839 0.283951i \(-0.0916454\pi\)
−0.283951 + 0.958839i \(0.591645\pi\)
\(104\) −2.04539 0.847227i −0.200567 0.0830774i
\(105\) −0.275797 0.0330400i −0.0269150 0.00322438i
\(106\) −4.15424 + 10.0292i −0.403495 + 0.974124i
\(107\) 0.603441i 0.0583369i 0.999575 + 0.0291684i \(0.00928592\pi\)
−0.999575 + 0.0291684i \(0.990714\pi\)
\(108\) −0.145126 + 0.350365i −0.0139648 + 0.0337139i
\(109\) −1.04012 + 2.51107i −0.0996253 + 0.240517i −0.965832 0.259169i \(-0.916551\pi\)
0.866207 + 0.499686i \(0.166551\pi\)
\(110\) −4.05207 + 1.67842i −0.386350 + 0.160031i
\(111\) 0.280166 + 0.676380i 0.0265921 + 0.0641991i
\(112\) −1.57398 5.61141i −0.148727 0.530228i
\(113\) 11.0973i 1.04395i 0.852962 + 0.521973i \(0.174804\pi\)
−0.852962 + 0.521973i \(0.825196\pi\)
\(114\) −0.250368 0.250368i −0.0234491 0.0234491i
\(115\) −3.77545 + 3.77545i −0.352062 + 0.352062i
\(116\) 1.82274 + 4.40049i 0.169238 + 0.408576i
\(117\) −1.98691 0.823003i −0.183689 0.0760867i
\(118\) −8.44996 + 8.44996i −0.777882 + 0.777882i
\(119\) 19.8683 + 2.38019i 1.82132 + 0.218192i
\(120\) −0.123711 0.298666i −0.0112932 0.0272643i
\(121\) −0.457876 + 0.457876i −0.0416251 + 0.0416251i
\(122\) −1.78612 −0.161708
\(123\) −0.135279 + 0.587321i −0.0121977 + 0.0529569i
\(124\) 6.41360i 0.575959i
\(125\) 6.90577 6.90577i 0.617671 0.617671i
\(126\) −2.46255 8.77927i −0.219382 0.782119i
\(127\) 10.6252i 0.942836i −0.881910 0.471418i \(-0.843742\pi\)
0.881910 0.471418i \(-0.156258\pi\)
\(128\) 1.86766 1.86766i 0.165079 0.165079i
\(129\) 0.0523475 0.126378i 0.00460894 0.0111270i
\(130\) 0.853660 0.353598i 0.0748709 0.0310126i
\(131\) −3.26490 3.26490i −0.285256 0.285256i 0.549945 0.835201i \(-0.314649\pi\)
−0.835201 + 0.549945i \(0.814649\pi\)
\(132\) −0.152756 0.152756i −0.0132957 0.0132957i
\(133\) −8.57673 1.02748i −0.743697 0.0890937i
\(134\) −4.77016 11.5162i −0.412079 0.994847i
\(135\) −0.240704 0.581112i −0.0207165 0.0500141i
\(136\) 8.91211 + 21.5157i 0.764207 + 1.84496i
\(137\) −4.72775 1.95830i −0.403919 0.167309i 0.171469 0.985190i \(-0.445149\pi\)
−0.575388 + 0.817881i \(0.695149\pi\)
\(138\) 0.479623 + 0.198666i 0.0408282 + 0.0169116i
\(139\) 7.87249i 0.667736i −0.942620 0.333868i \(-0.891646\pi\)
0.942620 0.333868i \(-0.108354\pi\)
\(140\) −1.73013 0.972153i −0.146223 0.0821619i
\(141\) −0.112747 −0.00949499
\(142\) 3.06706 + 1.27042i 0.257382 + 0.106611i
\(143\) 1.73511 1.73511i 0.145097 0.145097i
\(144\) 4.65898 4.65898i 0.388248 0.388248i
\(145\) −7.29861 3.02318i −0.606117 0.251062i
\(146\) −8.15326 −0.674768
\(147\) 0.531943 + 0.388793i 0.0438739 + 0.0320671i
\(148\) 5.23063i 0.429955i
\(149\) 8.92224 + 3.69571i 0.730939 + 0.302765i 0.716938 0.697137i \(-0.245543\pi\)
0.0140010 + 0.999902i \(0.495543\pi\)
\(150\) −0.376320 0.155877i −0.0307264 0.0127273i
\(151\) 6.73448 + 16.2585i 0.548044 + 1.32310i 0.918931 + 0.394418i \(0.129054\pi\)
−0.370887 + 0.928678i \(0.620946\pi\)
\(152\) −3.84717 9.28790i −0.312047 0.753348i
\(153\) 8.65730 + 20.9006i 0.699901 + 1.68971i
\(154\) 10.3298 + 1.23749i 0.832396 + 0.0997197i
\(155\) 7.52187 + 7.52187i 0.604171 + 0.604171i
\(156\) 0.0321815 + 0.0321815i 0.00257658 + 0.00257658i
\(157\) −1.67323 + 0.693074i −0.133538 + 0.0553133i −0.448452 0.893807i \(-0.648024\pi\)
0.314914 + 0.949120i \(0.398024\pi\)
\(158\) −3.19428 + 7.71168i −0.254123 + 0.613508i
\(159\) 0.627086 0.627086i 0.0497311 0.0497311i
\(160\) 4.03813i 0.319242i
\(161\) 12.1944 3.42048i 0.961053 0.269572i
\(162\) 7.26750 7.26750i 0.570989 0.570989i
\(163\) 9.12699i 0.714881i 0.933936 + 0.357441i \(0.116351\pi\)
−0.933936 + 0.357441i \(0.883649\pi\)
\(164\) −2.49876 + 3.50689i −0.195120 + 0.273842i
\(165\) 0.358304 0.0278939
\(166\) 12.7231 12.7231i 0.987506 0.987506i
\(167\) 4.15767 + 10.0375i 0.321731 + 0.776726i 0.999154 + 0.0411327i \(0.0130966\pi\)
−0.677423 + 0.735594i \(0.736903\pi\)
\(168\) −0.0912115 + 0.761375i −0.00703712 + 0.0587413i
\(169\) 8.82685 8.82685i 0.678988 0.678988i
\(170\) −8.97979 3.71955i −0.688718 0.285276i
\(171\) −3.73718 9.02234i −0.285789 0.689956i
\(172\) 0.691066 0.691066i 0.0526933 0.0526933i
\(173\) −4.27015 4.27015i −0.324653 0.324653i 0.525896 0.850549i \(-0.323730\pi\)
−0.850549 + 0.525896i \(0.823730\pi\)
\(174\) 0.768115i 0.0582306i
\(175\) −9.56793 + 2.68377i −0.723268 + 0.202874i
\(176\) 2.87691 + 6.94547i 0.216855 + 0.523534i
\(177\) 0.901935 0.373594i 0.0677936 0.0280810i
\(178\) 5.37538 12.9773i 0.402902 0.972691i
\(179\) 8.07217 19.4879i 0.603342 1.45660i −0.266778 0.963758i \(-0.585959\pi\)
0.870121 0.492839i \(-0.164041\pi\)
\(180\) 2.24363i 0.167230i
\(181\) 3.67297 8.86734i 0.273010 0.659104i −0.726599 0.687061i \(-0.758900\pi\)
0.999609 + 0.0279575i \(0.00890032\pi\)
\(182\) −2.17620 0.260705i −0.161310 0.0193247i
\(183\) 0.134808 + 0.0558394i 0.00996532 + 0.00412777i
\(184\) 10.4226 + 10.4226i 0.768366 + 0.768366i
\(185\) −6.13448 6.13448i −0.451016 0.451016i
\(186\) 0.395805 0.955559i 0.0290219 0.0700650i
\(187\) −25.8121 −1.88757
\(188\) −0.744214 0.308264i −0.0542774 0.0224824i
\(189\) −0.177470 + 1.48140i −0.0129090 + 0.107756i
\(190\) 3.87639 + 1.60565i 0.281223 + 0.116486i
\(191\) 7.68454 18.5521i 0.556034 1.34238i −0.356849 0.934162i \(-0.616149\pi\)
0.912882 0.408222i \(-0.133851\pi\)
\(192\) −0.745851 + 0.308942i −0.0538272 + 0.0222959i
\(193\) −7.49519 + 3.10461i −0.539515 + 0.223475i −0.635765 0.771883i \(-0.719315\pi\)
0.0962496 + 0.995357i \(0.469315\pi\)
\(194\) 7.07011 + 17.0687i 0.507604 + 1.22546i
\(195\) −0.0754849 −0.00540558
\(196\) 2.44822 + 4.02073i 0.174873 + 0.287195i
\(197\) −6.53173 6.53173i −0.465366 0.465366i 0.435043 0.900410i \(-0.356733\pi\)
−0.900410 + 0.435043i \(0.856733\pi\)
\(198\) 4.50103 + 10.8664i 0.319874 + 0.772245i
\(199\) 15.0868 + 6.24917i 1.06948 + 0.442992i 0.846806 0.531902i \(-0.178523\pi\)
0.222670 + 0.974894i \(0.428523\pi\)
\(200\) −8.17777 8.17777i −0.578256 0.578256i
\(201\) 1.01832i 0.0718267i
\(202\) −16.4065 + 6.79579i −1.15436 + 0.478150i
\(203\) 11.5803 + 14.7326i 0.812779 + 1.03402i
\(204\) 0.478743i 0.0335187i
\(205\) −1.18234 7.04342i −0.0825785 0.491934i
\(206\) 11.1605i 0.777589i
\(207\) 10.1246 + 10.1246i 0.703710 + 0.703710i
\(208\) −0.606085 1.46322i −0.0420244 0.101456i
\(209\) 11.1425 0.770745
\(210\) −0.197777 0.251613i −0.0136479 0.0173629i
\(211\) −3.43627 1.42335i −0.236563 0.0979874i 0.261253 0.965270i \(-0.415864\pi\)
−0.497815 + 0.867283i \(0.665864\pi\)
\(212\) 5.85377 2.42471i 0.402039 0.166530i
\(213\) −0.191771 0.191771i −0.0131399 0.0131399i
\(214\) −0.491630 + 0.491630i −0.0336072 + 0.0336072i
\(215\) 1.62096i 0.110549i
\(216\) −1.60424 + 0.664497i −0.109155 + 0.0452133i
\(217\) −6.81467 24.2951i −0.462610 1.64926i
\(218\) −2.89319 + 1.19840i −0.195952 + 0.0811658i
\(219\) 0.615370 + 0.254895i 0.0415829 + 0.0172242i
\(220\) 2.36508 + 0.979648i 0.159454 + 0.0660479i
\(221\) 5.43790 0.365793
\(222\) −0.322800 + 0.779308i −0.0216649 + 0.0523037i
\(223\) 11.9534i 0.800459i −0.916415 0.400229i \(-0.868930\pi\)
0.916415 0.400229i \(-0.131070\pi\)
\(224\) −4.69219 + 8.35066i −0.313510 + 0.557952i
\(225\) −7.94396 7.94396i −0.529597 0.529597i
\(226\) −9.04110 + 9.04110i −0.601405 + 0.601405i
\(227\) −24.2716 10.0536i −1.61097 0.667284i −0.618054 0.786136i \(-0.712079\pi\)
−0.992912 + 0.118852i \(0.962079\pi\)
\(228\) 0.206663i 0.0136866i
\(229\) −19.7510 8.18114i −1.30518 0.540625i −0.381708 0.924283i \(-0.624664\pi\)
−0.923475 + 0.383658i \(0.874664\pi\)
\(230\) −6.15179 −0.405637
\(231\) −0.740955 0.416339i −0.0487513 0.0273931i
\(232\) −8.34590 + 20.1488i −0.547936 + 1.32283i
\(233\) −5.23653 12.6421i −0.343057 0.828212i −0.997403 0.0720172i \(-0.977056\pi\)
0.654347 0.756195i \(-0.272944\pi\)
\(234\) −0.948244 2.28926i −0.0619886 0.149654i
\(235\) 1.23435 0.511283i 0.0805198 0.0333524i
\(236\) 6.97491 0.454028
\(237\) 0.482180 0.482180i 0.0313209 0.0313209i
\(238\) 14.2478 + 18.1261i 0.923545 + 1.17494i
\(239\) −3.83686 9.26300i −0.248186 0.599174i 0.749864 0.661592i \(-0.230119\pi\)
−0.998050 + 0.0624179i \(0.980119\pi\)
\(240\) 0.0885000 0.213658i 0.00571265 0.0137916i
\(241\) 16.0398 16.0398i 1.03321 1.03321i 0.0337849 0.999429i \(-0.489244\pi\)
0.999429 0.0337849i \(-0.0107561\pi\)
\(242\) −0.746074 −0.0479594
\(243\) −2.33871 + 0.968724i −0.150028 + 0.0621437i
\(244\) 0.737166 + 0.737166i 0.0471922 + 0.0471922i
\(245\) −7.58678 1.84424i −0.484702 0.117824i
\(246\) −0.588710 + 0.368283i −0.0375348 + 0.0234809i
\(247\) −2.34743 −0.149363
\(248\) 20.7651 20.7651i 1.31859 1.31859i
\(249\) −1.35805 + 0.562521i −0.0860627 + 0.0356483i
\(250\) 11.2524 0.711665
\(251\) 13.3598 + 13.3598i 0.843264 + 0.843264i 0.989282 0.146018i \(-0.0466457\pi\)
−0.146018 + 0.989282i \(0.546646\pi\)
\(252\) −2.60703 + 4.63971i −0.164227 + 0.292274i
\(253\) −15.0935 + 6.25192i −0.948919 + 0.393055i
\(254\) 8.65649 8.65649i 0.543156 0.543156i
\(255\) 0.561469 + 0.561469i 0.0351606 + 0.0351606i
\(256\) −14.1105 −0.881906
\(257\) 1.80914 0.749372i 0.112851 0.0467445i −0.325543 0.945527i \(-0.605547\pi\)
0.438395 + 0.898783i \(0.355547\pi\)
\(258\) 0.145610 0.0603135i 0.00906526 0.00375495i
\(259\) 5.55772 + 19.8139i 0.345340 + 1.23117i
\(260\) −0.498258 0.206385i −0.0309006 0.0127995i
\(261\) −8.10728 + 19.5727i −0.501828 + 1.21152i
\(262\) 5.31990i 0.328665i
\(263\) −3.08178 1.27651i −0.190030 0.0787132i 0.285639 0.958337i \(-0.407794\pi\)
−0.475669 + 0.879624i \(0.657794\pi\)
\(264\) 0.989147i 0.0608778i
\(265\) −4.02160 + 9.70901i −0.247045 + 0.596420i
\(266\) −6.15046 7.82465i −0.377109 0.479760i
\(267\) −0.811418 + 0.811418i −0.0496580 + 0.0496580i
\(268\) −2.78421 + 6.72168i −0.170073 + 0.410592i
\(269\) −19.5764 −1.19360 −0.596798 0.802391i \(-0.703561\pi\)
−0.596798 + 0.802391i \(0.703561\pi\)
\(270\) 0.277334 0.669543i 0.0168780 0.0407471i
\(271\) −19.6352 −1.19275 −0.596377 0.802704i \(-0.703394\pi\)
−0.596377 + 0.802704i \(0.703394\pi\)
\(272\) −6.37551 + 15.3918i −0.386572 + 0.933267i
\(273\) 0.156099 + 0.0877111i 0.00944754 + 0.00530852i
\(274\) −2.25630 5.44720i −0.136308 0.329077i
\(275\) 11.8426 4.90537i 0.714136 0.295805i
\(276\) −0.115956 0.279942i −0.00697972 0.0168505i
\(277\) 11.8237i 0.710417i −0.934787 0.355208i \(-0.884410\pi\)
0.934787 0.355208i \(-0.115590\pi\)
\(278\) 6.41380 6.41380i 0.384674 0.384674i
\(279\) 20.1714 20.1714i 1.20763 1.20763i
\(280\) −2.45410 8.74912i −0.146660 0.522860i
\(281\) 9.63206 23.2539i 0.574601 1.38721i −0.323000 0.946399i \(-0.604691\pi\)
0.897601 0.440810i \(-0.145309\pi\)
\(282\) −0.0918560 0.0918560i −0.00546994 0.00546994i
\(283\) 16.6814i 0.991604i 0.868436 + 0.495802i \(0.165126\pi\)
−0.868436 + 0.495802i \(0.834874\pi\)
\(284\) −0.741508 1.79016i −0.0440004 0.106226i
\(285\) −0.242374 0.242374i −0.0143570 0.0143570i
\(286\) 2.82723 0.167177
\(287\) −5.73922 + 15.9393i −0.338775 + 0.940867i
\(288\) −10.8291 −0.638109
\(289\) −28.4272 28.4272i −1.67219 1.67219i
\(290\) −3.48324 8.40928i −0.204543 0.493810i
\(291\) 1.50930i 0.0884769i
\(292\) 3.36500 + 3.36500i 0.196922 + 0.196922i
\(293\) −2.78796 + 6.73072i −0.162874 + 0.393213i −0.984155 0.177311i \(-0.943260\pi\)
0.821281 + 0.570524i \(0.193260\pi\)
\(294\) 0.116626 + 0.750134i 0.00680177 + 0.0437487i
\(295\) −8.18017 + 8.18017i −0.476268 + 0.476268i
\(296\) −16.9351 + 16.9351i −0.984330 + 0.984330i
\(297\) 1.92458i 0.111675i
\(298\) 4.25811 + 10.2800i 0.246666 + 0.595504i
\(299\) 3.17978 1.31711i 0.183892 0.0761704i
\(300\) 0.0909810 + 0.219648i 0.00525279 + 0.0126814i
\(301\) 1.88351 3.35208i 0.108564 0.193210i
\(302\) −7.75930 + 18.7326i −0.446498 + 1.07794i
\(303\) 1.45074 0.0833430
\(304\) 2.75217 6.64433i 0.157848 0.381079i
\(305\) −1.72909 −0.0990077
\(306\) −9.97473 + 24.0811i −0.570217 + 1.37663i
\(307\) 17.9278 17.9278i 1.02319 1.02319i 0.0234670 0.999725i \(-0.492530\pi\)
0.999725 0.0234670i \(-0.00747046\pi\)
\(308\) −3.75255 4.77402i −0.213821 0.272025i
\(309\) 0.348910 0.842343i 0.0198488 0.0479192i
\(310\) 12.2563i 0.696111i
\(311\) −16.3648 6.77851i −0.927961 0.384374i −0.133057 0.991108i \(-0.542479\pi\)
−0.794905 + 0.606734i \(0.792479\pi\)
\(312\) 0.208386i 0.0117975i
\(313\) −7.06116 + 17.0471i −0.399120 + 0.963562i 0.588755 + 0.808312i \(0.299618\pi\)
−0.987875 + 0.155250i \(0.950382\pi\)
\(314\) −1.92785 0.798543i −0.108795 0.0450644i
\(315\) −2.38393 8.49896i −0.134319 0.478862i
\(316\) 4.50109 1.86441i 0.253206 0.104881i
\(317\) −16.4339 + 6.80716i −0.923022 + 0.382328i −0.793027 0.609187i \(-0.791496\pi\)
−0.129995 + 0.991515i \(0.541496\pi\)
\(318\) 1.02179 0.0572990
\(319\) −17.0923 17.0923i −0.956986 0.956986i
\(320\) 6.76455 6.76455i 0.378150 0.378150i
\(321\) 0.0524758 0.0217362i 0.00292891 0.00121320i
\(322\) 12.7216 + 7.14820i 0.708947 + 0.398354i
\(323\) 17.4606 + 17.4606i 0.971531 + 0.971531i
\(324\) −5.99886 −0.333270
\(325\) −2.49491 + 1.03343i −0.138393 + 0.0573242i
\(326\) −7.43586 + 7.43586i −0.411834 + 0.411834i
\(327\) 0.255830 0.0141474
\(328\) −19.4443 + 3.26402i −1.07363 + 0.180225i
\(329\) −3.14666 0.376965i −0.173481 0.0207827i
\(330\) 0.291914 + 0.291914i 0.0160694 + 0.0160694i
\(331\) 10.8784 4.50597i 0.597929 0.247670i −0.0631284 0.998005i \(-0.520108\pi\)
0.661058 + 0.750335i \(0.270108\pi\)
\(332\) −10.5021 −0.576380
\(333\) −16.4508 + 16.4508i −0.901501 + 0.901501i
\(334\) −4.79037 + 11.5650i −0.262117 + 0.632807i
\(335\) −4.61786 11.1485i −0.252301 0.609108i
\(336\) −0.431278 + 0.339000i −0.0235281 + 0.0184940i
\(337\) 11.5294 11.5294i 0.628047 0.628047i −0.319529 0.947576i \(-0.603525\pi\)
0.947576 + 0.319529i \(0.103525\pi\)
\(338\) 14.3827 0.782313
\(339\) 0.965032 0.399729i 0.0524133 0.0217103i
\(340\) 2.17100 + 5.24125i 0.117739 + 0.284247i
\(341\) 12.4558 + 30.0710i 0.674519 + 1.62843i
\(342\) 4.30588 10.3953i 0.232835 0.562114i
\(343\) 13.5461 + 12.6294i 0.731423 + 0.681924i
\(344\) 4.47489 0.241270
\(345\) 0.464309 + 0.192323i 0.0249976 + 0.0103543i
\(346\) 6.95787i 0.374057i
\(347\) 2.27614 + 0.942806i 0.122189 + 0.0506125i 0.442940 0.896551i \(-0.353935\pi\)
−0.320751 + 0.947164i \(0.603935\pi\)
\(348\) 0.317015 0.317015i 0.0169938 0.0169938i
\(349\) 7.59106 + 7.59106i 0.406340 + 0.406340i 0.880460 0.474120i \(-0.157234\pi\)
−0.474120 + 0.880460i \(0.657234\pi\)
\(350\) −9.98159 5.60860i −0.533539 0.299792i
\(351\) 0.405455i 0.0216416i
\(352\) 4.72837 11.4153i 0.252023 0.608437i
\(353\) 1.19922 0.0638280 0.0319140 0.999491i \(-0.489840\pi\)
0.0319140 + 0.999491i \(0.489840\pi\)
\(354\) 1.03919 + 0.430445i 0.0552321 + 0.0228779i
\(355\) 2.96914 + 1.22986i 0.157585 + 0.0652740i
\(356\) −7.57450 + 3.13746i −0.401448 + 0.166285i
\(357\) −0.508680 1.81350i −0.0269222 0.0959806i
\(358\) 22.4535 9.30055i 1.18671 0.491549i
\(359\) 12.1748i 0.642562i −0.946984 0.321281i \(-0.895887\pi\)
0.946984 0.321281i \(-0.104113\pi\)
\(360\) 7.26412 7.26412i 0.382853 0.382853i
\(361\) 5.89767 + 5.89767i 0.310404 + 0.310404i
\(362\) 10.2167 4.23191i 0.536979 0.222424i
\(363\) 0.0563102 + 0.0233245i 0.00295552 + 0.00122422i
\(364\) 0.790559 + 1.00575i 0.0414366 + 0.0527159i
\(365\) −7.89294 −0.413135
\(366\) 0.0643368 + 0.155323i 0.00336294 + 0.00811885i
\(367\) 9.85692 + 9.85692i 0.514527 + 0.514527i 0.915910 0.401383i \(-0.131470\pi\)
−0.401383 + 0.915910i \(0.631470\pi\)
\(368\) 10.5445i 0.549670i
\(369\) −18.8884 + 3.17069i −0.983289 + 0.165060i
\(370\) 9.99565i 0.519649i
\(371\) 19.5980 15.4048i 1.01748 0.799776i
\(372\) −0.557733 + 0.231021i −0.0289171 + 0.0119779i
\(373\) 17.1821i 0.889657i 0.895616 + 0.444829i \(0.146735\pi\)
−0.895616 + 0.444829i \(0.853265\pi\)
\(374\) −21.0294 21.0294i −1.08740 1.08740i
\(375\) −0.849281 0.351784i −0.0438567 0.0181660i
\(376\) −1.41146 3.40758i −0.0727907 0.175732i
\(377\) 3.60088 + 3.60088i 0.185455 + 0.185455i
\(378\) −1.35150 + 1.06233i −0.0695137 + 0.0546403i
\(379\) 17.3832 0.892917 0.446458 0.894804i \(-0.352685\pi\)
0.446458 + 0.894804i \(0.352685\pi\)
\(380\) −0.937174 2.26254i −0.0480760 0.116066i
\(381\) −0.923979 + 0.382725i −0.0473369 + 0.0196076i
\(382\) 21.3753 8.85394i 1.09366 0.453007i
\(383\) 3.39273 8.19076i 0.173360 0.418529i −0.813188 0.582002i \(-0.802270\pi\)
0.986548 + 0.163473i \(0.0522697\pi\)
\(384\) −0.229687 0.0951396i −0.0117212 0.00485507i
\(385\) 9.99995 + 1.19798i 0.509645 + 0.0610546i
\(386\) −8.63577 3.57705i −0.439549 0.182067i
\(387\) 4.34695 0.220968
\(388\) 4.12662 9.96255i 0.209498 0.505772i
\(389\) 3.40678 + 3.40678i 0.172731 + 0.172731i 0.788178 0.615447i \(-0.211025\pi\)
−0.615447 + 0.788178i \(0.711025\pi\)
\(390\) −0.0614983 0.0614983i −0.00311409 0.00311409i
\(391\) −33.4486 13.8549i −1.69157 0.700671i
\(392\) −5.09126 + 20.9443i −0.257148 + 1.05785i
\(393\) −0.166316 + 0.401522i −0.00838952 + 0.0202541i
\(394\) 10.6429i 0.536183i
\(395\) −3.09229 + 7.46546i −0.155590 + 0.375628i
\(396\) 2.62713 6.34244i 0.132018 0.318720i
\(397\) 13.3755 5.54030i 0.671296 0.278060i −0.0208873 0.999782i \(-0.506649\pi\)
0.692183 + 0.721722i \(0.256649\pi\)
\(398\) 7.20013 + 17.3827i 0.360910 + 0.871314i
\(399\) 0.219587 + 0.782850i 0.0109931 + 0.0391915i
\(400\) 8.27340i 0.413670i
\(401\) 9.41445 + 9.41445i 0.470135 + 0.470135i 0.901958 0.431823i \(-0.142130\pi\)
−0.431823 + 0.901958i \(0.642130\pi\)
\(402\) −0.829635 + 0.829635i −0.0413784 + 0.0413784i
\(403\) −2.62409 6.33512i −0.130715 0.315575i
\(404\) 9.57601 + 3.96651i 0.476424 + 0.197341i
\(405\) 7.03546 7.03546i 0.349595 0.349595i
\(406\) −2.56817 + 21.4374i −0.127456 + 1.06392i
\(407\) −10.1584 24.5244i −0.503531 1.21563i
\(408\) 1.55001 1.55001i 0.0767370 0.0767370i
\(409\) −4.65594 −0.230221 −0.115111 0.993353i \(-0.536722\pi\)
−0.115111 + 0.993353i \(0.536722\pi\)
\(410\) 4.77509 6.70162i 0.235825 0.330970i
\(411\) 0.481668i 0.0237589i
\(412\) 4.60614 4.60614i 0.226928 0.226928i
\(413\) 26.4213 7.41108i 1.30011 0.364675i
\(414\) 16.4973i 0.810797i
\(415\) 12.3169 12.3169i 0.604613 0.604613i
\(416\) −0.996137 + 2.40489i −0.0488396 + 0.117909i
\(417\) −0.684599 + 0.283570i −0.0335250 + 0.0138865i
\(418\) 9.07794 + 9.07794i 0.444017 + 0.444017i
\(419\) −10.4578 10.4578i −0.510897 0.510897i 0.403904 0.914801i \(-0.367653\pi\)
−0.914801 + 0.403904i \(0.867653\pi\)
\(420\) −0.0222192 + 0.185471i −0.00108418 + 0.00905008i
\(421\) 7.75555 + 18.7236i 0.377983 + 0.912531i 0.992344 + 0.123506i \(0.0394138\pi\)
−0.614361 + 0.789025i \(0.710586\pi\)
\(422\) −1.63995 3.95918i −0.0798314 0.192730i
\(423\) −1.37111 3.31015i −0.0666655 0.160945i
\(424\) 26.8030 + 11.1022i 1.30167 + 0.539169i
\(425\) 26.2444 + 10.8708i 1.27304 + 0.527310i
\(426\) 0.312476i 0.0151395i
\(427\) 3.57568 + 2.00916i 0.173039 + 0.0972299i
\(428\) 0.405810 0.0196156
\(429\) −0.213386 0.0883874i −0.0103024 0.00426738i
\(430\) −1.32062 + 1.32062i −0.0636858 + 0.0636858i
\(431\) 11.6613 11.6613i 0.561704 0.561704i −0.368087 0.929791i \(-0.619987\pi\)
0.929791 + 0.368087i \(0.119987\pi\)
\(432\) −1.14763 0.475365i −0.0552155 0.0228710i
\(433\) −38.7864 −1.86396 −0.931978 0.362514i \(-0.881919\pi\)
−0.931978 + 0.362514i \(0.881919\pi\)
\(434\) 14.2415 25.3454i 0.683612 1.21662i
\(435\) 0.743590i 0.0356524i
\(436\) 1.68867 + 0.699472i 0.0808728 + 0.0334986i
\(437\) 14.4391 + 5.98086i 0.690715 + 0.286103i
\(438\) 0.293683 + 0.709014i 0.0140327 + 0.0338780i
\(439\) 0.171342 + 0.413657i 0.00817773 + 0.0197428i 0.927916 0.372790i \(-0.121599\pi\)
−0.919738 + 0.392533i \(0.871599\pi\)
\(440\) 4.48557 + 10.8291i 0.213841 + 0.516258i
\(441\) −4.94569 + 20.3455i −0.235509 + 0.968833i
\(442\) 4.43031 + 4.43031i 0.210729 + 0.210729i
\(443\) 5.65387 + 5.65387i 0.268624 + 0.268624i 0.828545 0.559922i \(-0.189169\pi\)
−0.559922 + 0.828545i \(0.689169\pi\)
\(444\) 0.454860 0.188409i 0.0215867 0.00894151i
\(445\) 5.20376 12.5630i 0.246682 0.595542i
\(446\) 9.73856 9.73856i 0.461134 0.461134i
\(447\) 0.909007i 0.0429946i
\(448\) −21.8490 + 6.12856i −1.03227 + 0.289547i
\(449\) −6.19326 + 6.19326i −0.292278 + 0.292278i −0.837980 0.545701i \(-0.816263\pi\)
0.545701 + 0.837980i \(0.316263\pi\)
\(450\) 12.9441i 0.610189i
\(451\) 4.90501 21.2953i 0.230968 1.00276i
\(452\) 7.46286 0.351023
\(453\) 1.17127 1.17127i 0.0550312 0.0550312i
\(454\) −11.5836 27.9652i −0.543643 1.31247i
\(455\) −2.10672 0.252381i −0.0987643 0.0118318i
\(456\) −0.669107 + 0.669107i −0.0313338 + 0.0313338i
\(457\) 13.9488 + 5.77779i 0.652498 + 0.270274i 0.684278 0.729221i \(-0.260117\pi\)
−0.0317797 + 0.999495i \(0.510117\pi\)
\(458\) −9.42610 22.7566i −0.440453 1.06335i
\(459\) 3.01585 3.01585i 0.140768 0.140768i
\(460\) 2.53896 + 2.53896i 0.118380 + 0.118380i
\(461\) 2.09161i 0.0974160i −0.998813 0.0487080i \(-0.984490\pi\)
0.998813 0.0487080i \(-0.0155104\pi\)
\(462\) −0.264469 0.942860i −0.0123042 0.0438658i
\(463\) −2.17025 5.23944i −0.100860 0.243497i 0.865392 0.501095i \(-0.167069\pi\)
−0.966252 + 0.257597i \(0.917069\pi\)
\(464\) −14.4140 + 5.97045i −0.669151 + 0.277171i
\(465\) 0.383168 0.925050i 0.0177690 0.0428981i
\(466\) 6.03340 14.5659i 0.279492 0.674753i
\(467\) 1.84528i 0.0853892i 0.999088 + 0.0426946i \(0.0135942\pi\)
−0.999088 + 0.0426946i \(0.986406\pi\)
\(468\) −0.553463 + 1.33618i −0.0255838 + 0.0617649i
\(469\) −3.40472 + 28.4204i −0.157215 + 1.31233i
\(470\) 1.42218 + 0.589087i 0.0656004 + 0.0271726i
\(471\) 0.120541 + 0.120541i 0.00555422 + 0.00555422i
\(472\) 22.5824 + 22.5824i 1.03944 + 1.03944i
\(473\) −1.89803 + 4.58226i −0.0872717 + 0.210693i
\(474\) 0.785674 0.0360872
\(475\) −11.3292 4.69269i −0.519817 0.215315i
\(476\) 1.60066 13.3613i 0.0733661 0.612413i
\(477\) 26.0367 + 10.7847i 1.19214 + 0.493799i
\(478\) 4.42074 10.6726i 0.202200 0.488153i
\(479\) −7.69775 + 3.18851i −0.351719 + 0.145687i −0.551546 0.834144i \(-0.685962\pi\)
0.199827 + 0.979831i \(0.435962\pi\)
\(480\) −0.351160 + 0.145455i −0.0160282 + 0.00663909i
\(481\) 2.14009 + 5.16662i 0.0975795 + 0.235578i
\(482\) 26.1356 1.19044
\(483\) −0.736695 0.937228i −0.0335208 0.0426454i
\(484\) 0.307918 + 0.307918i 0.0139963 + 0.0139963i
\(485\) 6.84437 + 16.5238i 0.310787 + 0.750306i
\(486\) −2.69460 1.11614i −0.122229 0.0506291i
\(487\) −1.42667 1.42667i −0.0646486 0.0646486i 0.674043 0.738692i \(-0.264556\pi\)
−0.738692 + 0.674043i \(0.764556\pi\)
\(488\) 4.77340i 0.216082i
\(489\) 0.793692 0.328758i 0.0358920 0.0148669i
\(490\) −4.67851 7.68355i −0.211354 0.347108i
\(491\) 18.0123i 0.812885i 0.913676 + 0.406442i \(0.133231\pi\)
−0.913676 + 0.406442i \(0.866769\pi\)
\(492\) 0.394969 + 0.0909744i 0.0178066 + 0.00410144i
\(493\) 53.5679i 2.41258i
\(494\) −1.91247 1.91247i −0.0860463 0.0860463i
\(495\) 4.35732 + 10.5195i 0.195847 + 0.472817i
\(496\) 21.0080 0.943285
\(497\) −4.71097 5.99333i −0.211316 0.268838i
\(498\) −1.56471 0.648123i −0.0701162 0.0290431i
\(499\) 14.0600 5.82386i 0.629414 0.260712i −0.0450900 0.998983i \(-0.514357\pi\)
0.674504 + 0.738271i \(0.264357\pi\)
\(500\) −4.64408 4.64408i −0.207690 0.207690i
\(501\) 0.723110 0.723110i 0.0323062 0.0323062i
\(502\) 21.7688i 0.971588i
\(503\) 7.70444 3.19128i 0.343524 0.142292i −0.204250 0.978919i \(-0.565475\pi\)
0.547774 + 0.836627i \(0.315475\pi\)
\(504\) −23.4625 + 6.58115i −1.04510 + 0.293148i
\(505\) −15.8827 + 6.57882i −0.706769 + 0.292753i
\(506\) −17.3903 7.20331i −0.773095 0.320226i
\(507\) −1.08554 0.449644i −0.0482104 0.0199694i
\(508\) −7.14538 −0.317025
\(509\) −4.94035 + 11.9271i −0.218977 + 0.528658i −0.994748 0.102357i \(-0.967361\pi\)
0.775770 + 0.631015i \(0.217361\pi\)
\(510\) 0.914870i 0.0405111i
\(511\) 16.3222 + 9.17136i 0.722052 + 0.405717i
\(512\) −15.2313 15.2313i −0.673135 0.673135i
\(513\) −1.30188 + 1.30188i −0.0574793 + 0.0574793i
\(514\) 2.08445 + 0.863408i 0.0919412 + 0.0380833i
\(515\) 10.8042i 0.476088i
\(516\) −0.0849882 0.0352033i −0.00374140 0.00154974i
\(517\) 4.08801 0.179791
\(518\) −11.6146 + 20.6705i −0.510318 + 0.908211i
\(519\) −0.217524 + 0.525148i −0.00954822 + 0.0230514i
\(520\) −0.944987 2.28140i −0.0414404 0.100046i
\(521\) −14.7147 35.5245i −0.644664 1.55636i −0.820320 0.571904i \(-0.806205\pi\)
0.175657 0.984451i \(-0.443795\pi\)
\(522\) −22.5512 + 9.34101i −0.987039 + 0.408845i
\(523\) 10.5400 0.460882 0.230441 0.973086i \(-0.425983\pi\)
0.230441 + 0.973086i \(0.425983\pi\)
\(524\) −2.19562 + 2.19562i −0.0959161 + 0.0959161i
\(525\) 0.578024 + 0.735366i 0.0252270 + 0.0320940i
\(526\) −1.47077 3.55075i −0.0641285 0.154820i
\(527\) −27.6033 + 66.6402i −1.20242 + 2.90289i
\(528\) 0.500357 0.500357i 0.0217752 0.0217752i
\(529\) 0.0853008 0.00370873
\(530\) −11.1865 + 4.63359i −0.485909 + 0.201270i
\(531\) 21.9368 + 21.9368i 0.951975 + 0.951975i
\(532\) −0.690972 + 5.76779i −0.0299574 + 0.250065i
\(533\) −1.03335 + 4.48634i −0.0447594 + 0.194325i
\(534\) −1.32214 −0.0572147
\(535\) −0.475933 + 0.475933i −0.0205764 + 0.0205764i
\(536\) −30.7769 + 12.7482i −1.32936 + 0.550639i
\(537\) −1.98545 −0.0856785
\(538\) −15.9491 15.9491i −0.687616 0.687616i
\(539\) −19.2874 14.0970i −0.830767 0.607201i
\(540\) −0.390793 + 0.161872i −0.0168171 + 0.00696586i
\(541\) 21.8873 21.8873i 0.941010 0.941010i −0.0573442 0.998354i \(-0.518263\pi\)
0.998354 + 0.0573442i \(0.0182632\pi\)
\(542\) −15.9970 15.9970i −0.687131 0.687131i
\(543\) −0.903413 −0.0387692
\(544\) 25.2974 10.4785i 1.08462 0.449263i
\(545\) −2.80082 + 1.16014i −0.119974 + 0.0496948i
\(546\) 0.0557163 + 0.198635i 0.00238444 + 0.00850078i
\(547\) −28.5549 11.8278i −1.22092 0.505721i −0.323216 0.946325i \(-0.604764\pi\)
−0.897701 + 0.440604i \(0.854764\pi\)
\(548\) −1.31694 + 3.17938i −0.0562569 + 0.135816i
\(549\) 4.63692i 0.197899i
\(550\) 13.6448 + 5.65184i 0.581814 + 0.240995i
\(551\) 23.1242i 0.985122i
\(552\) 0.530934 1.28179i 0.0225980 0.0545565i
\(553\) 15.0694 11.8451i 0.640814 0.503703i
\(554\) 9.63289 9.63289i 0.409262 0.409262i
\(555\) −0.312494 + 0.754426i −0.0132646 + 0.0320236i
\(556\) −5.29419 −0.224524
\(557\) −15.4545 + 37.3104i −0.654827 + 1.58089i 0.150863 + 0.988555i \(0.451795\pi\)
−0.805690 + 0.592337i \(0.798205\pi\)
\(558\) 32.8678 1.39140
\(559\) 0.399864 0.965356i 0.0169124 0.0408302i
\(560\) 3.18432 5.66711i 0.134562 0.239479i
\(561\) 0.929761 + 2.24464i 0.0392545 + 0.0947689i
\(562\) 26.7925 11.0978i 1.13017 0.468133i
\(563\) 7.01654 + 16.9394i 0.295712 + 0.713912i 0.999992 + 0.00398961i \(0.00126994\pi\)
−0.704280 + 0.709922i \(0.748730\pi\)
\(564\) 0.0758213i 0.00319265i
\(565\) −8.75243 + 8.75243i −0.368218 + 0.368218i
\(566\) −13.5905 + 13.5905i −0.571251 + 0.571251i
\(567\) −22.7240 + 6.37400i −0.954318 + 0.267683i
\(568\) 3.39519 8.19670i 0.142459 0.343926i
\(569\) −19.3314 19.3314i −0.810413 0.810413i 0.174283 0.984696i \(-0.444239\pi\)
−0.984696 + 0.174283i \(0.944239\pi\)
\(570\) 0.394930i 0.0165418i
\(571\) 4.45125 + 10.7463i 0.186279 + 0.449717i 0.989238 0.146318i \(-0.0467421\pi\)
−0.802959 + 0.596035i \(0.796742\pi\)
\(572\) −1.16685 1.16685i −0.0487884 0.0487884i
\(573\) −1.89011 −0.0789605
\(574\) −17.6617 + 8.31012i −0.737186 + 0.346858i
\(575\) 17.9793 0.749787
\(576\) −18.1405 18.1405i −0.755855 0.755855i
\(577\) −8.01182 19.3422i −0.333536 0.805228i −0.998306 0.0581796i \(-0.981470\pi\)
0.664770 0.747048i \(-0.268530\pi\)
\(578\) 46.3199i 1.92665i
\(579\) 0.539959 + 0.539959i 0.0224399 + 0.0224399i
\(580\) −2.03307 + 4.90826i −0.0844186 + 0.203804i
\(581\) −39.7826 + 11.1589i −1.65046 + 0.462948i
\(582\) 1.22965 1.22965i 0.0509705 0.0509705i
\(583\) −22.7371 + 22.7371i −0.941675 + 0.941675i
\(584\) 21.7895i 0.901657i
\(585\) −0.917968 2.21617i −0.0379533 0.0916274i
\(586\) −7.75497 + 3.21222i −0.320355 + 0.132695i
\(587\) 1.07044 + 2.58427i 0.0441817 + 0.106664i 0.944430 0.328713i \(-0.106615\pi\)
−0.900248 + 0.435377i \(0.856615\pi\)
\(588\) 0.261460 0.357728i 0.0107824 0.0147524i
\(589\) 11.9158 28.7672i 0.490980 1.18533i
\(590\) −13.3289 −0.548744
\(591\) −0.332730 + 0.803280i −0.0136867 + 0.0330425i
\(592\) −17.1331 −0.704165
\(593\) −0.638917 + 1.54248i −0.0262372 + 0.0633421i −0.936455 0.350787i \(-0.885914\pi\)
0.910218 + 0.414130i \(0.135914\pi\)
\(594\) 1.56797 1.56797i 0.0643347 0.0643347i
\(595\) 13.7929 + 17.5474i 0.565452 + 0.719372i
\(596\) 2.48534 6.00014i 0.101803 0.245775i
\(597\) 1.53706i 0.0629077i
\(598\) 3.66367 + 1.51754i 0.149818 + 0.0620568i
\(599\) 28.6870i 1.17212i 0.810268 + 0.586059i \(0.199321\pi\)
−0.810268 + 0.586059i \(0.800679\pi\)
\(600\) −0.416580 + 1.00571i −0.0170068 + 0.0410581i
\(601\) 8.61645 + 3.56905i 0.351472 + 0.145585i 0.551433 0.834219i \(-0.314081\pi\)
−0.199960 + 0.979804i \(0.564081\pi\)
\(602\) 4.26549 1.19645i 0.173848 0.0487638i
\(603\) −29.8970 + 12.3837i −1.21750 + 0.504304i
\(604\) 10.9337 4.52889i 0.444886 0.184278i
\(605\) −0.722253 −0.0293638
\(606\) 1.18194 + 1.18194i 0.0480129 + 0.0480129i
\(607\) −23.5991 + 23.5991i −0.957857 + 0.957857i −0.999147 0.0412906i \(-0.986853\pi\)
0.0412906 + 0.999147i \(0.486853\pi\)
\(608\) −10.9204 + 4.52336i −0.442879 + 0.183446i
\(609\) 0.864029 1.53771i 0.0350122 0.0623111i
\(610\) −1.40871 1.40871i −0.0570371 0.0570371i
\(611\) −0.861232 −0.0348417
\(612\) 14.0555 5.82197i 0.568159 0.235339i
\(613\) 6.43061 6.43061i 0.259730 0.259730i −0.565214 0.824944i \(-0.691206\pi\)
0.824944 + 0.565214i \(0.191206\pi\)
\(614\) 29.2119 1.17890
\(615\) −0.569914 + 0.356525i −0.0229812 + 0.0143765i
\(616\) 3.30718 27.6062i 0.133250 1.11229i
\(617\) 13.5261 + 13.5261i 0.544540 + 0.544540i 0.924856 0.380317i \(-0.124185\pi\)
−0.380317 + 0.924856i \(0.624185\pi\)
\(618\) 0.970527 0.402005i 0.0390403 0.0161710i
\(619\) 21.1898 0.851690 0.425845 0.904796i \(-0.359977\pi\)
0.425845 + 0.904796i \(0.359977\pi\)
\(620\) 5.05840 5.05840i 0.203150 0.203150i
\(621\) 1.03303 2.49397i 0.0414543 0.100079i
\(622\) −7.81003 18.8551i −0.313154 0.756020i
\(623\) −25.3589 + 19.9330i −1.01598 + 0.798600i
\(624\) −0.105411 + 0.105411i −0.00421983 + 0.00421983i
\(625\) −7.88639 −0.315456
\(626\) −19.6413 + 8.13569i −0.785024 + 0.325168i
\(627\) −0.401358 0.968965i −0.0160287 0.0386967i
\(628\) 0.466087 + 1.12523i 0.0185989 + 0.0449017i
\(629\) 22.5119 54.3485i 0.897608 2.16702i
\(630\) 4.98199 8.86641i 0.198487 0.353246i
\(631\) −11.5992 −0.461756 −0.230878 0.972983i \(-0.574160\pi\)
−0.230878 + 0.972983i \(0.574160\pi\)
\(632\) 20.6094 + 8.53669i 0.819798 + 0.339571i
\(633\) 0.350091i 0.0139149i
\(634\) −18.9348 7.84304i −0.751996 0.311487i
\(635\) 8.38010 8.38010i 0.332554 0.332554i
\(636\) −0.421710 0.421710i −0.0167219 0.0167219i
\(637\) 4.06333 + 2.96985i 0.160995 + 0.117670i
\(638\) 27.8506i 1.10262i
\(639\) 3.29811 7.96235i 0.130471 0.314986i
\(640\) 2.94604 0.116453
\(641\) −20.8936 8.65442i −0.825248 0.341829i −0.0702284 0.997531i \(-0.522373\pi\)
−0.755020 + 0.655702i \(0.772373\pi\)
\(642\) 0.0604613 + 0.0250439i 0.00238622 + 0.000988404i
\(643\) −14.8045 + 6.13222i −0.583832 + 0.241831i −0.654995 0.755634i \(-0.727329\pi\)
0.0711625 + 0.997465i \(0.477329\pi\)
\(644\) −2.30025 8.20064i −0.0906425 0.323150i
\(645\) 0.140961 0.0583878i 0.00555032 0.00229902i
\(646\) 28.4506i 1.11937i
\(647\) 17.4107 17.4107i 0.684487 0.684487i −0.276521 0.961008i \(-0.589181\pi\)
0.961008 + 0.276521i \(0.0891815\pi\)
\(648\) −19.4223 19.4223i −0.762981 0.762981i
\(649\) −32.7027 + 13.5459i −1.28369 + 0.531723i
\(650\) −2.87458 1.19069i −0.112750 0.0467026i
\(651\) −1.86725 + 1.46773i −0.0731834 + 0.0575248i
\(652\) 6.13783 0.240376
\(653\) 2.11401 + 5.10366i 0.0827275 + 0.199722i 0.959831 0.280580i \(-0.0905270\pi\)
−0.877103 + 0.480302i \(0.840527\pi\)
\(654\) 0.208428 + 0.208428i 0.00815017 + 0.00815017i
\(655\) 5.15005i 0.201229i
\(656\) −11.4869 8.18475i −0.448490 0.319561i
\(657\) 21.1665i 0.825784i
\(658\) −2.25650 2.87074i −0.0879676 0.111913i
\(659\) −9.90272 + 4.10184i −0.385755 + 0.159785i −0.567129 0.823629i \(-0.691946\pi\)
0.181373 + 0.983414i \(0.441946\pi\)
\(660\) 0.240957i 0.00937923i
\(661\) 21.6477 + 21.6477i 0.841997 + 0.841997i 0.989118 0.147122i \(-0.0470009\pi\)
−0.147122 + 0.989118i \(0.547001\pi\)
\(662\) 12.5338 + 5.19167i 0.487140 + 0.201780i
\(663\) −0.195875 0.472884i −0.00760716 0.0183653i
\(664\) −34.0025 34.0025i −1.31955 1.31955i
\(665\) −5.95409 7.57483i −0.230890 0.293739i
\(666\) −26.8054 −1.03869
\(667\) −12.9746 31.3236i −0.502380 1.21285i
\(668\) 6.75015 2.79600i 0.261171 0.108181i
\(669\) −1.03948 + 0.430566i −0.0401886 + 0.0166466i
\(670\) 5.32058 12.8450i 0.205552 0.496247i
\(671\) −4.88793 2.02465i −0.188696 0.0781606i
\(672\) 0.895196 + 0.107243i 0.0345329 + 0.00413699i
\(673\) 2.63992 + 1.09349i 0.101761 + 0.0421510i 0.432983 0.901402i \(-0.357461\pi\)
−0.331222 + 0.943553i \(0.607461\pi\)
\(674\) 18.7863 0.723620
\(675\) −0.810537 + 1.95681i −0.0311976 + 0.0753176i
\(676\) −5.93599 5.93599i −0.228307 0.228307i
\(677\) 27.9038 + 27.9038i 1.07243 + 1.07243i 0.997164 + 0.0752651i \(0.0239803\pi\)
0.0752651 + 0.997164i \(0.476020\pi\)
\(678\) 1.11189 + 0.460558i 0.0427017 + 0.0176876i
\(679\) 5.04631 42.1233i 0.193659 1.61654i
\(680\) −9.94047 + 23.9984i −0.381200 + 0.920297i
\(681\) 2.47282i 0.0947587i
\(682\) −14.3513 + 34.6470i −0.549538 + 1.32670i
\(683\) −5.14302 + 12.4164i −0.196792 + 0.475099i −0.991214 0.132268i \(-0.957774\pi\)
0.794422 + 0.607367i \(0.207774\pi\)
\(684\) −6.06745 + 2.51322i −0.231995 + 0.0960954i
\(685\) −2.18426 5.27328i −0.0834565 0.201482i
\(686\) 0.746880 + 21.3255i 0.0285160 + 0.814212i
\(687\) 2.01225i 0.0767722i
\(688\) 2.26361 + 2.26361i 0.0862993 + 0.0862993i
\(689\) 4.79009 4.79009i 0.182488 0.182488i
\(690\) 0.221590 + 0.534966i 0.00843579 + 0.0203658i
\(691\) 17.9457 + 7.43335i 0.682686 + 0.282778i 0.696949 0.717121i \(-0.254540\pi\)
−0.0142633 + 0.999898i \(0.504540\pi\)
\(692\) −2.87164 + 2.87164i −0.109163 + 0.109163i
\(693\) 3.21262 26.8169i 0.122037 1.01869i
\(694\) 1.08628 + 2.62251i 0.0412345 + 0.0995490i
\(695\) 6.20902 6.20902i 0.235522 0.235522i
\(696\) 2.05278 0.0778104
\(697\) 41.0564 25.6839i 1.55512 0.972846i
\(698\) 12.3690i 0.468175i
\(699\) −0.910747 + 0.910747i −0.0344476 + 0.0344476i
\(700\) 1.80481 + 6.43436i 0.0682156 + 0.243196i
\(701\) 30.3417i 1.14599i 0.819558 + 0.572996i \(0.194219\pi\)
−0.819558 + 0.572996i \(0.805781\pi\)
\(702\) −0.330329 + 0.330329i −0.0124675 + 0.0124675i
\(703\) −9.71792 + 23.4611i −0.366518 + 0.884853i
\(704\) 27.0433 11.2017i 1.01923 0.422181i
\(705\) −0.0889232 0.0889232i −0.00334904 0.00334904i
\(706\) 0.977017 + 0.977017i 0.0367705 + 0.0367705i
\(707\) 40.4890 + 4.85051i 1.52274 + 0.182422i
\(708\) −0.251239 0.606544i −0.00944213 0.0227953i
\(709\) 5.92714 + 14.3094i 0.222598 + 0.537400i 0.995241 0.0974408i \(-0.0310657\pi\)
−0.772643 + 0.634841i \(0.781066\pi\)
\(710\) 1.41701 + 3.42097i 0.0531795 + 0.128387i
\(711\) 20.0201 + 8.29262i 0.750814 + 0.310997i
\(712\) −34.6818 14.3657i −1.29976 0.538376i
\(713\) 45.6533i 1.70973i
\(714\) 1.06305 1.89191i 0.0397837 0.0708028i
\(715\) 2.73696 0.102356
\(716\) −13.1055 5.42847i −0.489775 0.202872i
\(717\) −0.667314 + 0.667314i −0.0249213 + 0.0249213i
\(718\) 9.91895 9.91895i 0.370172 0.370172i
\(719\) −15.9099 6.59010i −0.593340 0.245769i 0.0657469 0.997836i \(-0.479057\pi\)
−0.659087 + 0.752067i \(0.729057\pi\)
\(720\) 7.34906 0.273883
\(721\) 12.5541 22.3425i 0.467540 0.832077i
\(722\) 9.60980i 0.357640i
\(723\) −1.97259 0.817075i −0.0733616 0.0303874i
\(724\) −5.96322 2.47005i −0.221621 0.0917985i
\(725\) 10.1801 + 24.5770i 0.378081 + 0.912767i
\(726\) 0.0268739 + 0.0648793i 0.000997383 + 0.00240789i
\(727\) −14.9121 36.0010i −0.553060 1.33521i −0.915169 0.403069i \(-0.867943\pi\)
0.362109 0.932136i \(-0.382057\pi\)
\(728\) −0.696732 + 5.81587i −0.0258226 + 0.215550i
\(729\) −18.7544 18.7544i −0.694608 0.694608i
\(730\) −6.43046 6.43046i −0.238002 0.238002i
\(731\) −10.1547 + 4.20623i −0.375587 + 0.155573i
\(732\) 0.0375516 0.0906576i 0.00138795 0.00335080i
\(733\) 20.7970 20.7970i 0.768156 0.768156i −0.209625 0.977782i \(-0.567224\pi\)
0.977782 + 0.209625i \(0.0672245\pi\)
\(734\) 16.0611i 0.592825i
\(735\) 0.112902 + 0.726184i 0.00416447 + 0.0267857i
\(736\) 12.2545 12.2545i 0.451708 0.451708i
\(737\) 36.9226i 1.36006i
\(738\) −17.9718 12.8054i −0.661550 0.471372i
\(739\) −35.8479 −1.31868 −0.659342 0.751843i \(-0.729165\pi\)
−0.659342 + 0.751843i \(0.729165\pi\)
\(740\) −4.12539 + 4.12539i −0.151652 + 0.151652i
\(741\) 0.0845552 + 0.204134i 0.00310621 + 0.00749906i
\(742\) 28.5172 + 3.41631i 1.04690 + 0.125417i
\(743\) 3.72292 3.72292i 0.136581 0.136581i −0.635511 0.772092i \(-0.719211\pi\)
0.772092 + 0.635511i \(0.219211\pi\)
\(744\) −2.55372 1.05779i −0.0936240 0.0387803i
\(745\) 4.12216 + 9.95177i 0.151024 + 0.364605i
\(746\) −13.9985 + 13.9985i −0.512520 + 0.512520i
\(747\) −33.0303 33.0303i −1.20851 1.20851i
\(748\) 17.3584i 0.634687i
\(749\) 1.53723 0.431187i 0.0561691 0.0157552i
\(750\) −0.405316 0.978520i −0.0148001 0.0357305i
\(751\) 11.9648 4.95600i 0.436603 0.180847i −0.153545 0.988142i \(-0.549069\pi\)
0.590149 + 0.807295i \(0.299069\pi\)
\(752\) 1.00973 2.43770i 0.0368209 0.0888936i
\(753\) 0.680556 1.64301i 0.0248008 0.0598745i
\(754\) 5.86735i 0.213676i
\(755\) −7.51156 + 18.1345i −0.273374 + 0.659982i
\(756\) 0.996232 + 0.119347i 0.0362326 + 0.00434061i
\(757\) 22.2028 + 9.19672i 0.806976 + 0.334260i 0.747747 0.663984i \(-0.231136\pi\)
0.0592292 + 0.998244i \(0.481136\pi\)
\(758\) 14.1623 + 14.1623i 0.514398 + 0.514398i
\(759\) 1.08735 + 1.08735i 0.0394682 + 0.0394682i
\(760\) 4.29109 10.3596i 0.155654 0.375783i
\(761\) −5.63436 −0.204245 −0.102123 0.994772i \(-0.532563\pi\)
−0.102123 + 0.994772i \(0.532563\pi\)
\(762\) −1.06459 0.440966i −0.0385659 0.0159745i
\(763\) 7.13999 + 0.855360i 0.258485 + 0.0309661i
\(764\) −12.4762 5.16780i −0.451372 0.186964i
\(765\) −9.65625 + 23.3123i −0.349123 + 0.842856i
\(766\) 9.43720 3.90901i 0.340980 0.141238i
\(767\) 6.88956 2.85375i 0.248768 0.103043i
\(768\) 0.508266 + 1.22706i 0.0183405 + 0.0442778i
\(769\) 9.50986 0.342934 0.171467 0.985190i \(-0.445149\pi\)
0.171467 + 0.985190i \(0.445149\pi\)
\(770\) 7.17106 + 9.12308i 0.258427 + 0.328773i
\(771\) −0.130332 0.130332i −0.00469380 0.00469380i
\(772\) 2.08783 + 5.04046i 0.0751425 + 0.181410i
\(773\) −0.959510 0.397442i −0.0345112 0.0142950i 0.365361 0.930866i \(-0.380946\pi\)
−0.399872 + 0.916571i \(0.630946\pi\)
\(774\) 3.54150 + 3.54150i 0.127297 + 0.127297i
\(775\) 35.8203i 1.28670i
\(776\) 45.6161 18.8948i 1.63752 0.678284i
\(777\) 1.52284 1.19701i 0.0546316 0.0429424i
\(778\) 5.55108i 0.199016i
\(779\) −17.7232 + 11.0872i −0.634999 + 0.397240i
\(780\) 0.0507630i 0.00181761i
\(781\) 6.95330 + 6.95330i 0.248809 + 0.248809i
\(782\) −15.9632 38.5387i −0.570845 1.37814i
\(783\) 3.99408 0.142737
\(784\) −13.1700 + 8.01922i −0.470358 + 0.286401i
\(785\) −1.86630 0.773047i −0.0666111 0.0275912i
\(786\) −0.462623 + 0.191625i −0.0165012 + 0.00683503i
\(787\) 10.6012 + 10.6012i 0.377893 + 0.377893i 0.870342 0.492448i \(-0.163898\pi\)
−0.492448 + 0.870342i \(0.663898\pi\)
\(788\) −4.39254 + 4.39254i −0.156478 + 0.156478i
\(789\) 0.313974i 0.0111778i
\(790\) −8.60152 + 3.56287i −0.306028 + 0.126761i
\(791\) 28.2697 7.92954i 1.00515 0.281942i
\(792\) 29.0405 12.0290i 1.03191 0.427431i
\(793\) 1.02975 + 0.426538i 0.0365676 + 0.0151468i
\(794\) 15.4109 + 6.38340i 0.546912 + 0.226538i
\(795\) 0.989164 0.0350820
\(796\) 4.20252 10.1458i 0.148954 0.359607i
\(797\) 50.7236i 1.79672i 0.439259 + 0.898360i \(0.355241\pi\)
−0.439259 + 0.898360i \(0.644759\pi\)
\(798\) −0.458897 + 0.816696i −0.0162448 + 0.0289107i
\(799\) 6.40599 + 6.40599i 0.226628 + 0.226628i
\(800\) −9.61512 + 9.61512i −0.339946 + 0.339946i
\(801\) −33.6902 13.9549i −1.19038 0.493073i
\(802\) 15.3401i 0.541678i
\(803\) −22.3123 9.24207i −0.787385 0.326146i
\(804\) 0.684812 0.0241514
\(805\) 12.3154 + 6.91997i 0.434062 + 0.243897i
\(806\) 3.02342 7.29917i 0.106495 0.257102i
\(807\) 0.705151 + 1.70239i 0.0248225 + 0.0599268i
\(808\) 18.1617 + 43.8462i 0.638927 + 1.54251i
\(809\) 31.5055 13.0500i 1.10768 0.458814i 0.247539 0.968878i \(-0.420378\pi\)
0.860136 + 0.510064i \(0.170378\pi\)
\(810\) 11.4637 0.402795
\(811\) 7.72248 7.72248i 0.271173 0.271173i −0.558399 0.829572i \(-0.688584\pi\)
0.829572 + 0.558399i \(0.188584\pi\)
\(812\) 9.90754 7.78768i 0.347686 0.273294i
\(813\) 0.707268 + 1.70750i 0.0248050 + 0.0598845i
\(814\) 11.7042 28.2564i 0.410232 0.990388i
\(815\) −7.19845 + 7.19845i −0.252151 + 0.252151i
\(816\) 1.56814 0.0548957
\(817\) 4.38359 1.81574i 0.153362 0.0635248i
\(818\) −3.79324 3.79324i −0.132628 0.132628i
\(819\) −0.676811 + 5.64958i −0.0236497 + 0.197412i
\(820\) −4.73665 + 0.795117i −0.165411 + 0.0277667i
\(821\) 8.66366 0.302364 0.151182 0.988506i \(-0.451692\pi\)
0.151182 + 0.988506i \(0.451692\pi\)
\(822\) −0.392420 + 0.392420i −0.0136872 + 0.0136872i
\(823\) −25.6579 + 10.6279i −0.894380 + 0.370464i −0.782056 0.623208i \(-0.785829\pi\)
−0.112323 + 0.993672i \(0.535829\pi\)
\(824\) 29.8263 1.03905
\(825\) −0.853151 0.853151i −0.0297029 0.0297029i
\(826\) 27.5636 + 15.4878i 0.959060 + 0.538891i
\(827\) −4.71501 + 1.95302i −0.163957 + 0.0679132i −0.463152 0.886279i \(-0.653282\pi\)
0.299195 + 0.954192i \(0.403282\pi\)
\(828\) 6.80873 6.80873i 0.236620 0.236620i
\(829\) 5.45004 + 5.45004i 0.189288 + 0.189288i 0.795388 0.606100i \(-0.207267\pi\)
−0.606100 + 0.795388i \(0.707267\pi\)
\(830\) 20.0694 0.696620
\(831\) −1.02820 + 0.425894i −0.0356678 + 0.0147741i
\(832\) −5.69729 + 2.35989i −0.197518 + 0.0818146i
\(833\) −8.13344 52.3140i −0.281807 1.81257i
\(834\) −0.788778 0.326723i −0.0273131 0.0113135i
\(835\) −4.63742 + 11.1957i −0.160485 + 0.387444i
\(836\) 7.49327i 0.259160i
\(837\) −4.96876 2.05813i −0.171746 0.0711394i
\(838\) 17.0402i 0.588643i
\(839\) −1.18730 + 2.86640i −0.0409902 + 0.0989592i −0.943049 0.332655i \(-0.892056\pi\)
0.902058 + 0.431614i \(0.142056\pi\)
\(840\) −0.672434 + 0.528557i −0.0232012 + 0.0182369i
\(841\) 14.9656 14.9656i 0.516057 0.516057i
\(842\) −8.93576 + 21.5728i −0.307947 + 0.743449i
\(843\) −2.36913 −0.0815971
\(844\) −0.957192 + 2.31086i −0.0329479 + 0.0795433i
\(845\) 13.9234 0.478981
\(846\) 1.57976 3.81387i 0.0543131 0.131124i
\(847\) 1.49358 + 0.839237i 0.0513202 + 0.0288365i
\(848\) 7.94222 + 19.1742i 0.272737 + 0.658445i
\(849\) 1.45063 0.600869i 0.0497854 0.0206218i
\(850\) 12.5250 + 30.2381i 0.429605 + 1.03716i
\(851\) 37.2326i 1.27632i
\(852\) −0.128964 + 0.128964i −0.00441825 + 0.00441825i
\(853\) −24.5598 + 24.5598i −0.840910 + 0.840910i −0.988977 0.148067i \(-0.952695\pi\)
0.148067 + 0.988977i \(0.452695\pi\)
\(854\) 1.27627 + 4.55003i 0.0436729 + 0.155699i
\(855\) 4.16840 10.0634i 0.142556 0.344161i
\(856\) 1.31388 + 1.31388i 0.0449074 + 0.0449074i
\(857\) 24.7647i 0.845945i −0.906143 0.422972i \(-0.860987\pi\)
0.906143 0.422972i \(-0.139013\pi\)
\(858\) −0.101838 0.245858i −0.00347668 0.00839346i
\(859\) −3.83759 3.83759i −0.130937 0.130937i 0.638601 0.769538i \(-0.279513\pi\)
−0.769538 + 0.638601i \(0.779513\pi\)
\(860\) 1.09009 0.0371716
\(861\) 1.59283 0.0750523i 0.0542833 0.00255778i
\(862\) 19.0011 0.647182
\(863\) 3.33573 + 3.33573i 0.113549 + 0.113549i 0.761599 0.648049i \(-0.224415\pi\)
−0.648049 + 0.761599i \(0.724415\pi\)
\(864\) 0.781290 + 1.88620i 0.0265800 + 0.0641699i
\(865\) 6.73572i 0.229021i
\(866\) −31.5997 31.5997i −1.07380 1.07380i
\(867\) −1.44810 + 3.49601i −0.0491799 + 0.118731i
\(868\) −16.3382 + 4.58282i −0.554556 + 0.155551i
\(869\) −17.4830 + 17.4830i −0.593072 + 0.593072i
\(870\) −0.605811 + 0.605811i −0.0205389 + 0.0205389i
\(871\) 7.77857i 0.263567i
\(872\) 3.20271 + 7.73203i 0.108457 + 0.261840i
\(873\) 44.3119 18.3546i 1.49973 0.621208i
\(874\) 6.89100 + 16.6363i 0.233092 + 0.562733i
\(875\) −22.5265 12.6575i −0.761535 0.427902i
\(876\) 0.171415 0.413832i 0.00579157 0.0139821i
\(877\) −2.77338 −0.0936505 −0.0468252 0.998903i \(-0.514910\pi\)
−0.0468252 + 0.998903i \(0.514910\pi\)
\(878\) −0.197416 + 0.476605i −0.00666248 + 0.0160847i
\(879\) 0.685733 0.0231292
\(880\) −3.20887 + 7.74689i −0.108171 + 0.261148i
\(881\) 4.90597 4.90597i 0.165286 0.165286i −0.619618 0.784904i \(-0.712712\pi\)
0.784904 + 0.619618i \(0.212712\pi\)
\(882\) −20.6050 + 12.5464i −0.693807 + 0.422459i
\(883\) 8.40132 20.2826i 0.282727 0.682563i −0.717170 0.696898i \(-0.754563\pi\)
0.999897 + 0.0143347i \(0.00456304\pi\)
\(884\) 3.65694i 0.122996i
\(885\) 1.00601 + 0.416702i 0.0338166 + 0.0140073i
\(886\) 9.21254i 0.309501i
\(887\) −0.543373 + 1.31182i −0.0182447 + 0.0440465i −0.932739 0.360551i \(-0.882589\pi\)
0.914495 + 0.404598i \(0.132589\pi\)
\(888\) 2.08269 + 0.862680i 0.0698906 + 0.0289497i
\(889\) −27.0671 + 7.59221i −0.907800 + 0.254635i
\(890\) 14.4748 5.99564i 0.485195 0.200974i
\(891\) 28.1264 11.6503i 0.942269 0.390301i
\(892\) −8.03857 −0.269151
\(893\) −2.76533 2.76533i −0.0925383 0.0925383i
\(894\) 0.740578 0.740578i 0.0247686 0.0247686i
\(895\) 21.7366 9.00360i 0.726575 0.300957i
\(896\) −6.09227 3.42321i −0.203529 0.114362i
\(897\) −0.229074 0.229074i −0.00764856 0.00764856i
\(898\) −10.0914 −0.336756
\(899\) −62.4064 + 25.8496i −2.08137 + 0.862131i
\(900\) −5.34225 + 5.34225i −0.178075 + 0.178075i
\(901\) −71.2589 −2.37398
\(902\) 21.3457 13.3533i 0.710733 0.444618i
\(903\) −0.359344 0.0430489i −0.0119582 0.00143258i
\(904\) 24.1623 + 24.1623i 0.803625 + 0.803625i
\(905\) 9.89052 4.09679i 0.328772 0.136182i
\(906\) 1.90850 0.0634056
\(907\) −36.9034 + 36.9034i −1.22536 + 1.22536i −0.259658 + 0.965701i \(0.583610\pi\)
−0.965701 + 0.259658i \(0.916390\pi\)
\(908\) −6.76100 + 16.3225i −0.224372 + 0.541681i
\(909\) 17.6424 + 42.5926i 0.585162 + 1.41271i
\(910\) −1.51075 1.92198i −0.0500808 0.0637131i
\(911\) 19.5729 19.5729i 0.648480 0.648480i −0.304146 0.952626i \(-0.598371\pi\)
0.952626 + 0.304146i \(0.0983710\pi\)
\(912\) −0.676931 −0.0224154
\(913\) 49.2405 20.3961i 1.62962 0.675012i
\(914\) 6.65703 + 16.0715i 0.220195 + 0.531597i
\(915\) 0.0622827 + 0.150364i 0.00205900 + 0.00497087i
\(916\) −5.50175 + 13.2824i −0.181783 + 0.438863i
\(917\) −5.98420 + 10.6500i −0.197616 + 0.351695i
\(918\) 4.91409 0.162189
\(919\) −30.8250 12.7681i −1.01682 0.421182i −0.188884 0.981999i \(-0.560487\pi\)
−0.827940 + 0.560817i \(0.810487\pi\)
\(920\) 16.4406i 0.542031i
\(921\) −2.20478 0.913250i −0.0726500 0.0300926i
\(922\) 1.70406 1.70406i 0.0561202 0.0561202i
\(923\) −1.46487 1.46487i −0.0482168 0.0482168i
\(924\) −0.279985 + 0.498287i −0.00921082 + 0.0163924i
\(925\) 29.2134i 0.960529i
\(926\) 2.50050 6.03675i 0.0821717 0.198380i
\(927\) 28.9736 0.951616
\(928\) 23.6902 + 9.81280i 0.777669 + 0.322121i
\(929\) 1.63427 + 0.676937i 0.0536187 + 0.0222096i 0.409332 0.912386i \(-0.365762\pi\)
−0.355713 + 0.934595i \(0.615762\pi\)
\(930\) 1.06582 0.441477i 0.0349496 0.0144766i
\(931\) 3.51104 + 22.5828i 0.115070 + 0.740123i
\(932\) −8.50172 + 3.52153i −0.278483 + 0.115351i
\(933\) 1.66726i 0.0545837i
\(934\) −1.50337 + 1.50337i −0.0491917 + 0.0491917i
\(935\) −20.3580 20.3580i −0.665776 0.665776i
\(936\) −6.11804 + 2.53417i −0.199974 + 0.0828321i
\(937\) −2.30269 0.953807i −0.0752257 0.0311595i 0.344753 0.938693i \(-0.387963\pi\)
−0.419979 + 0.907534i \(0.637963\pi\)
\(938\) −25.9282 + 20.3805i −0.846587 + 0.665448i
\(939\) 1.73678 0.0566777
\(940\) −0.343834 0.830088i −0.0112146 0.0270745i
\(941\) −2.41892 2.41892i −0.0788546 0.0788546i 0.666579 0.745434i \(-0.267758\pi\)
−0.745434 + 0.666579i \(0.767758\pi\)
\(942\) 0.196412i 0.00639943i
\(943\) 17.7866 24.9627i 0.579212 0.812899i
\(944\) 22.8465i 0.743591i
\(945\) −1.30835 + 1.02841i −0.0425606 + 0.0334542i
\(946\) −5.27957 + 2.18687i −0.171654 + 0.0711012i
\(947\) 36.7952i 1.19568i −0.801615 0.597841i \(-0.796025\pi\)
0.801615 0.597841i \(-0.203975\pi\)
\(948\) −0.324262 0.324262i −0.0105315 0.0105315i
\(949\) 4.70060 + 1.94705i 0.152588 + 0.0632039i
\(950\) −5.40680 13.0532i −0.175420 0.423501i
\(951\) 1.18391 + 1.18391i 0.0383910 + 0.0383910i
\(952\) 48.4418 38.0770i 1.57001 1.23408i
\(953\) −24.8078 −0.803603 −0.401802 0.915727i \(-0.631616\pi\)
−0.401802 + 0.915727i \(0.631616\pi\)
\(954\) 12.4259 + 29.9988i 0.402304 + 0.971247i
\(955\) 20.6928 8.57125i 0.669604 0.277359i
\(956\) −6.22930 + 2.58026i −0.201470 + 0.0834516i
\(957\) −0.870691 + 2.10203i −0.0281454 + 0.0679491i
\(958\) −8.86916 3.67373i −0.286550 0.118693i
\(959\) −1.61044 + 13.4429i −0.0520039 + 0.434095i
\(960\) −0.831914 0.344590i −0.0268499 0.0111216i
\(961\) 59.9556 1.93405
\(962\) −2.46575 + 5.95286i −0.0794991 + 0.191928i
\(963\) 1.27631 + 1.27631i 0.0411286 + 0.0411286i
\(964\) −10.7866 10.7866i −0.347414 0.347414i
\(965\) −8.36005 3.46284i −0.269119 0.111473i
\(966\) 0.163377 1.36376i 0.00525656 0.0438784i
\(967\) −14.5951 + 35.2357i −0.469347 + 1.13310i 0.495102 + 0.868835i \(0.335131\pi\)
−0.964449 + 0.264269i \(0.914869\pi\)
\(968\) 1.99388i 0.0640856i
\(969\) 0.889450 2.14732i 0.0285732 0.0689819i
\(970\) −7.88592 + 19.0383i −0.253202 + 0.611283i
\(971\) −32.1610 + 13.3215i −1.03209 + 0.427508i −0.833468 0.552568i \(-0.813648\pi\)
−0.198627 + 0.980075i \(0.563648\pi\)
\(972\) 0.651459 + 1.57276i 0.0208956 + 0.0504464i
\(973\) −20.0547 + 5.62526i −0.642923 + 0.180338i
\(974\) 2.32465i 0.0744865i
\(975\) 0.179735 + 0.179735i 0.00575614 + 0.00575614i
\(976\) −2.41461 + 2.41461i −0.0772897 + 0.0772897i
\(977\) −8.93852 21.5795i −0.285969 0.690389i 0.713984 0.700162i \(-0.246889\pi\)
−0.999952 + 0.00977310i \(0.996889\pi\)
\(978\) 0.914472 + 0.378787i 0.0292416 + 0.0121123i
\(979\) 29.4207 29.4207i 0.940290 0.940290i
\(980\) −1.24024 + 5.10205i −0.0396179 + 0.162979i
\(981\) 3.11114 + 7.51096i 0.0993311 + 0.239806i
\(982\) −14.6748 + 14.6748i −0.468293 + 0.468293i
\(983\) 8.93198 0.284886 0.142443 0.989803i \(-0.454504\pi\)
0.142443 + 0.989803i \(0.454504\pi\)
\(984\) 0.984234 + 1.57332i 0.0313762 + 0.0501557i
\(985\) 10.3031i 0.328285i
\(986\) 43.6424 43.6424i 1.38986 1.38986i
\(987\) 0.0805627 + 0.287215i 0.00256434 + 0.00914215i
\(988\) 1.57863i 0.0502228i
\(989\) −4.91914 + 4.91914i −0.156420 + 0.156420i
\(990\) −5.02040 + 12.1203i −0.159559 + 0.385209i
\(991\) 30.3927 12.5891i 0.965457 0.399905i 0.156438 0.987688i \(-0.449999\pi\)
0.809019 + 0.587782i \(0.199999\pi\)
\(992\) −24.4149 24.4149i −0.775173 0.775173i
\(993\) −0.783686 0.783686i −0.0248695 0.0248695i
\(994\) 1.04475 8.72092i 0.0331375 0.276611i
\(995\) 6.97025 + 16.8277i 0.220972 + 0.533473i
\(996\) 0.378291 + 0.913276i 0.0119866 + 0.0289382i
\(997\) −9.04506 21.8367i −0.286460 0.691575i 0.713499 0.700656i \(-0.247109\pi\)
−0.999959 + 0.00908096i \(0.997109\pi\)
\(998\) 16.1996 + 6.71011i 0.512791 + 0.212405i
\(999\) 4.05229 + 1.67851i 0.128209 + 0.0531058i
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 287.2.l.a.27.19 104
7.6 odd 2 inner 287.2.l.a.27.20 yes 104
41.38 odd 8 inner 287.2.l.a.202.20 yes 104
287.202 even 8 inner 287.2.l.a.202.19 yes 104
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.2.l.a.27.19 104 1.1 even 1 trivial
287.2.l.a.27.20 yes 104 7.6 odd 2 inner
287.2.l.a.202.19 yes 104 287.202 even 8 inner
287.2.l.a.202.20 yes 104 41.38 odd 8 inner