Properties

Label 1089.2.e.k.364.2
Level $1089$
Weight $2$
Character 1089.364
Analytic conductor $8.696$
Analytic rank $0$
Dimension $16$
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] = [1089,2,Mod(364,1089)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1089, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1089.364");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1089.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.69570878012\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 3x^{14} + 5x^{12} + 15x^{10} + 45x^{8} + 60x^{6} + 80x^{4} + 192x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 364.2
Root \(-1.27069 + 0.620769i\) of defining polynomial
Character \(\chi\) \(=\) 1089.364
Dual form 1089.2.e.k.727.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.17295 - 2.03160i) q^{2} +(0.949292 - 1.44874i) q^{3} +(-1.75160 + 3.03386i) q^{4} +(0.779999 - 1.35100i) q^{5} +(-4.05673 - 0.229291i) q^{6} +(-1.95114 - 3.37948i) q^{7} +3.52635 q^{8} +(-1.19769 - 2.75055i) q^{9} +O(q^{10})\) \(q+(-1.17295 - 2.03160i) q^{2} +(0.949292 - 1.44874i) q^{3} +(-1.75160 + 3.03386i) q^{4} +(0.779999 - 1.35100i) q^{5} +(-4.05673 - 0.229291i) q^{6} +(-1.95114 - 3.37948i) q^{7} +3.52635 q^{8} +(-1.19769 - 2.75055i) q^{9} -3.65958 q^{10} +(2.73250 + 5.41764i) q^{12} +(2.71943 - 4.71018i) q^{13} +(-4.57717 + 7.92789i) q^{14} +(-1.21680 - 2.41251i) q^{15} +(-0.633017 - 1.09642i) q^{16} -4.32064 q^{17} +(-4.18320 + 5.65948i) q^{18} +1.61865 q^{19} +(2.73250 + 4.73282i) q^{20} +(-6.74818 - 0.381415i) q^{21} +(3.94929 - 6.84037i) q^{23} +(3.34754 - 5.10877i) q^{24} +(1.28320 + 2.22257i) q^{25} -12.7590 q^{26} +(-5.12179 - 0.875938i) q^{27} +13.6705 q^{28} +(0.742708 + 1.28641i) q^{29} +(-3.47401 + 5.30178i) q^{30} +(-0.729291 + 1.26317i) q^{31} +(2.04137 - 3.53575i) q^{32} +(5.06788 + 8.77782i) q^{34} -6.08755 q^{35} +(10.4427 + 1.18425i) q^{36} +9.31895 q^{37} +(-1.89858 - 3.28844i) q^{38} +(-4.24230 - 8.41108i) q^{39} +(2.75055 - 4.76410i) q^{40} +(-1.76318 + 3.05391i) q^{41} +(7.14037 + 14.1570i) q^{42} +(0.412180 + 0.713916i) q^{43} +(-4.65019 - 0.527352i) q^{45} -18.5292 q^{46} +(2.92698 + 5.06968i) q^{47} +(-2.18934 - 0.123744i) q^{48} +(-4.11391 + 7.12550i) q^{49} +(3.01026 - 5.21392i) q^{50} +(-4.10155 + 6.25948i) q^{51} +(9.52671 + 16.5007i) q^{52} -10.7404 q^{53} +(4.22802 + 11.4329i) q^{54} +(-6.88042 - 11.9172i) q^{56} +(1.53657 - 2.34500i) q^{57} +(1.74231 - 3.01777i) q^{58} +(2.69160 - 4.66200i) q^{59} +(9.45056 + 0.534156i) q^{60} +(6.65480 + 11.5265i) q^{61} +3.42167 q^{62} +(-6.95857 + 9.41428i) q^{63} -12.1097 q^{64} +(-4.24230 - 7.34788i) q^{65} +(-1.69769 + 2.94048i) q^{67} +(7.56805 - 13.1082i) q^{68} +(-6.16089 - 12.2150i) q^{69} +(7.14037 + 12.3675i) q^{70} -6.26216 q^{71} +(-4.22348 - 9.69942i) q^{72} -1.06706 q^{73} +(-10.9306 - 18.9324i) q^{74} +(4.43806 + 0.250844i) q^{75} +(-2.83522 + 4.91075i) q^{76} +(-12.1120 + 18.4844i) q^{78} +(4.95388 + 8.58037i) q^{79} -1.97501 q^{80} +(-6.13108 + 6.58862i) q^{81} +8.27244 q^{82} +(-2.37941 - 4.12126i) q^{83} +(12.9773 - 19.8050i) q^{84} +(-3.37010 + 5.83718i) q^{85} +(0.966929 - 1.67477i) q^{86} +(2.56872 + 0.145187i) q^{87} +3.47075 q^{89} +(4.38305 + 10.0659i) q^{90} -21.2239 q^{91} +(13.8352 + 23.9632i) q^{92} +(1.13769 + 2.25567i) q^{93} +(6.86638 - 11.8929i) q^{94} +(1.26254 - 2.18679i) q^{95} +(-3.18452 - 6.31386i) q^{96} +(-4.63396 - 8.02625i) q^{97} +19.3016 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{3} - 16 q^{4} + 4 q^{5} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{3} - 16 q^{4} + 4 q^{5} - 14 q^{9} - 6 q^{12} + 4 q^{14} - 52 q^{15} - 24 q^{16} - 6 q^{20} + 46 q^{23} - 12 q^{25} - 60 q^{26} - 32 q^{27} + 14 q^{31} + 38 q^{34} + 54 q^{36} - 12 q^{37} + 4 q^{38} - 4 q^{42} - 28 q^{45} + 16 q^{47} + 20 q^{48} - 42 q^{49} - 96 q^{53} + 46 q^{56} + 50 q^{58} + 48 q^{59} + 12 q^{60} - 12 q^{64} - 22 q^{67} - 10 q^{69} - 4 q^{70} + 68 q^{71} - 10 q^{75} - 72 q^{78} - 148 q^{80} - 14 q^{81} + 112 q^{82} + 14 q^{86} - 16 q^{89} - 96 q^{91} + 84 q^{92} + 30 q^{93} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(848\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.17295 2.03160i −0.829398 1.43656i −0.898511 0.438950i \(-0.855350\pi\)
0.0691136 0.997609i \(-0.477983\pi\)
\(3\) 0.949292 1.44874i 0.548074 0.836430i
\(4\) −1.75160 + 3.03386i −0.875801 + 1.51693i
\(5\) 0.779999 1.35100i 0.348826 0.604184i −0.637215 0.770686i \(-0.719914\pi\)
0.986041 + 0.166501i \(0.0532471\pi\)
\(6\) −4.05673 0.229291i −1.65615 0.0936076i
\(7\) −1.95114 3.37948i −0.737462 1.27732i −0.953635 0.300967i \(-0.902691\pi\)
0.216172 0.976355i \(-0.430643\pi\)
\(8\) 3.52635 1.24675
\(9\) −1.19769 2.75055i −0.399230 0.916851i
\(10\) −3.65958 −1.15726
\(11\) 0 0
\(12\) 2.73250 + 5.41764i 0.788804 + 1.56394i
\(13\) 2.71943 4.71018i 0.754233 1.30637i −0.191522 0.981488i \(-0.561342\pi\)
0.945755 0.324882i \(-0.105324\pi\)
\(14\) −4.57717 + 7.92789i −1.22330 + 2.11882i
\(15\) −1.21680 2.41251i −0.314175 0.622906i
\(16\) −0.633017 1.09642i −0.158254 0.274105i
\(17\) −4.32064 −1.04791 −0.523955 0.851746i \(-0.675544\pi\)
−0.523955 + 0.851746i \(0.675544\pi\)
\(18\) −4.18320 + 5.65948i −0.985990 + 1.33395i
\(19\) 1.61865 0.371343 0.185671 0.982612i \(-0.440554\pi\)
0.185671 + 0.982612i \(0.440554\pi\)
\(20\) 2.73250 + 4.73282i 0.611005 + 1.05829i
\(21\) −6.74818 0.381415i −1.47257 0.0832316i
\(22\) 0 0
\(23\) 3.94929 6.84037i 0.823484 1.42632i −0.0795879 0.996828i \(-0.525360\pi\)
0.903072 0.429489i \(-0.141306\pi\)
\(24\) 3.34754 5.10877i 0.683314 1.04282i
\(25\) 1.28320 + 2.22257i 0.256641 + 0.444515i
\(26\) −12.7590 −2.50224
\(27\) −5.12179 0.875938i −0.985689 0.168574i
\(28\) 13.6705 2.58348
\(29\) 0.742708 + 1.28641i 0.137917 + 0.238880i 0.926708 0.375782i \(-0.122626\pi\)
−0.788791 + 0.614662i \(0.789292\pi\)
\(30\) −3.47401 + 5.30178i −0.634265 + 0.967969i
\(31\) −0.729291 + 1.26317i −0.130984 + 0.226872i −0.924056 0.382256i \(-0.875147\pi\)
0.793072 + 0.609128i \(0.208480\pi\)
\(32\) 2.04137 3.53575i 0.360866 0.625038i
\(33\) 0 0
\(34\) 5.06788 + 8.77782i 0.869134 + 1.50538i
\(35\) −6.08755 −1.02898
\(36\) 10.4427 + 1.18425i 1.74045 + 0.197375i
\(37\) 9.31895 1.53203 0.766013 0.642825i \(-0.222238\pi\)
0.766013 + 0.642825i \(0.222238\pi\)
\(38\) −1.89858 3.28844i −0.307991 0.533456i
\(39\) −4.24230 8.41108i −0.679311 1.34685i
\(40\) 2.75055 4.76410i 0.434901 0.753270i
\(41\) −1.76318 + 3.05391i −0.275362 + 0.476941i −0.970226 0.242200i \(-0.922131\pi\)
0.694864 + 0.719141i \(0.255464\pi\)
\(42\) 7.14037 + 14.1570i 1.10178 + 2.18447i
\(43\) 0.412180 + 0.713916i 0.0628568 + 0.108871i 0.895741 0.444576i \(-0.146646\pi\)
−0.832884 + 0.553447i \(0.813312\pi\)
\(44\) 0 0
\(45\) −4.65019 0.527352i −0.693209 0.0786130i
\(46\) −18.5292 −2.73198
\(47\) 2.92698 + 5.06968i 0.426944 + 0.739489i 0.996600 0.0823947i \(-0.0262568\pi\)
−0.569656 + 0.821883i \(0.692923\pi\)
\(48\) −2.18934 0.123744i −0.316004 0.0178609i
\(49\) −4.11391 + 7.12550i −0.587702 + 1.01793i
\(50\) 3.01026 5.21392i 0.425714 0.737359i
\(51\) −4.10155 + 6.25948i −0.574332 + 0.876503i
\(52\) 9.52671 + 16.5007i 1.32112 + 2.28824i
\(53\) −10.7404 −1.47530 −0.737652 0.675181i \(-0.764065\pi\)
−0.737652 + 0.675181i \(0.764065\pi\)
\(54\) 4.22802 + 11.4329i 0.575361 + 1.55582i
\(55\) 0 0
\(56\) −6.88042 11.9172i −0.919435 1.59251i
\(57\) 1.53657 2.34500i 0.203523 0.310602i
\(58\) 1.74231 3.01777i 0.228777 0.396253i
\(59\) 2.69160 4.66200i 0.350417 0.606940i −0.635905 0.771767i \(-0.719373\pi\)
0.986323 + 0.164827i \(0.0527065\pi\)
\(60\) 9.45056 + 0.534156i 1.22006 + 0.0689593i
\(61\) 6.65480 + 11.5265i 0.852060 + 1.47581i 0.879346 + 0.476184i \(0.157980\pi\)
−0.0272853 + 0.999628i \(0.508686\pi\)
\(62\) 3.42167 0.434553
\(63\) −6.95857 + 9.41428i −0.876697 + 1.18609i
\(64\) −12.1097 −1.51371
\(65\) −4.24230 7.34788i −0.526192 0.911392i
\(66\) 0 0
\(67\) −1.69769 + 2.94048i −0.207406 + 0.359237i −0.950897 0.309509i \(-0.899835\pi\)
0.743491 + 0.668746i \(0.233169\pi\)
\(68\) 7.56805 13.1082i 0.917760 1.58961i
\(69\) −6.16089 12.2150i −0.741684 1.47051i
\(70\) 7.14037 + 12.3675i 0.853437 + 1.47820i
\(71\) −6.26216 −0.743182 −0.371591 0.928397i \(-0.621188\pi\)
−0.371591 + 0.928397i \(0.621188\pi\)
\(72\) −4.22348 9.69942i −0.497742 1.14309i
\(73\) −1.06706 −0.124890 −0.0624449 0.998048i \(-0.519890\pi\)
−0.0624449 + 0.998048i \(0.519890\pi\)
\(74\) −10.9306 18.9324i −1.27066 2.20085i
\(75\) 4.43806 + 0.250844i 0.512464 + 0.0289650i
\(76\) −2.83522 + 4.91075i −0.325223 + 0.563302i
\(77\) 0 0
\(78\) −12.1120 + 18.4844i −1.37141 + 2.09295i
\(79\) 4.95388 + 8.58037i 0.557355 + 0.965367i 0.997716 + 0.0675465i \(0.0215171\pi\)
−0.440361 + 0.897821i \(0.645150\pi\)
\(80\) −1.97501 −0.220813
\(81\) −6.13108 + 6.58862i −0.681231 + 0.732068i
\(82\) 8.27244 0.913539
\(83\) −2.37941 4.12126i −0.261174 0.452367i 0.705380 0.708829i \(-0.250776\pi\)
−0.966554 + 0.256462i \(0.917443\pi\)
\(84\) 12.9773 19.8050i 1.41594 2.16090i
\(85\) −3.37010 + 5.83718i −0.365538 + 0.633131i
\(86\) 0.966929 1.67477i 0.104267 0.180595i
\(87\) 2.56872 + 0.145187i 0.275395 + 0.0155657i
\(88\) 0 0
\(89\) 3.47075 0.367899 0.183949 0.982936i \(-0.441112\pi\)
0.183949 + 0.982936i \(0.441112\pi\)
\(90\) 4.38305 + 10.0659i 0.462014 + 1.06104i
\(91\) −21.2239 −2.22487
\(92\) 13.8352 + 23.9632i 1.44242 + 2.49834i
\(93\) 1.13769 + 2.25567i 0.117973 + 0.233902i
\(94\) 6.86638 11.8929i 0.708213 1.22666i
\(95\) 1.26254 2.18679i 0.129534 0.224360i
\(96\) −3.18452 6.31386i −0.325019 0.644406i
\(97\) −4.63396 8.02625i −0.470507 0.814943i 0.528924 0.848669i \(-0.322596\pi\)
−0.999431 + 0.0337268i \(0.989262\pi\)
\(98\) 19.3016 1.94975
\(99\) 0 0
\(100\) −8.99065 −0.899065
\(101\) 1.76318 + 3.05391i 0.175443 + 0.303876i 0.940314 0.340307i \(-0.110531\pi\)
−0.764872 + 0.644183i \(0.777198\pi\)
\(102\) 17.5277 + 0.990683i 1.73550 + 0.0980923i
\(103\) 4.18179 7.24307i 0.412044 0.713681i −0.583069 0.812422i \(-0.698148\pi\)
0.995113 + 0.0987416i \(0.0314817\pi\)
\(104\) 9.58966 16.6098i 0.940344 1.62872i
\(105\) −5.77887 + 8.81928i −0.563960 + 0.860673i
\(106\) 12.5979 + 21.8202i 1.22361 + 2.11936i
\(107\) 6.81480 0.658811 0.329406 0.944188i \(-0.393152\pi\)
0.329406 + 0.944188i \(0.393152\pi\)
\(108\) 11.6288 14.0045i 1.11898 1.34759i
\(109\) 16.3403 1.56512 0.782559 0.622576i \(-0.213914\pi\)
0.782559 + 0.622576i \(0.213914\pi\)
\(110\) 0 0
\(111\) 8.84641 13.5007i 0.839664 1.28143i
\(112\) −2.47021 + 4.27854i −0.233413 + 0.404284i
\(113\) −1.07622 + 1.86408i −0.101243 + 0.175357i −0.912197 0.409752i \(-0.865615\pi\)
0.810954 + 0.585110i \(0.198949\pi\)
\(114\) −6.56641 0.371141i −0.615000 0.0347605i
\(115\) −6.16089 10.6710i −0.574506 0.995073i
\(116\) −5.20372 −0.483153
\(117\) −16.2126 1.83859i −1.49886 0.169977i
\(118\) −12.6284 −1.16254
\(119\) 8.43019 + 14.6015i 0.772794 + 1.33852i
\(120\) −4.29086 8.50735i −0.391700 0.776611i
\(121\) 0 0
\(122\) 15.6114 27.0398i 1.41339 2.44807i
\(123\) 2.75055 + 5.45344i 0.248009 + 0.491720i
\(124\) −2.55486 4.42514i −0.229433 0.397389i
\(125\) 11.8036 1.05574
\(126\) 27.2881 + 3.09459i 2.43102 + 0.275688i
\(127\) 0.250266 0.0222075 0.0111038 0.999938i \(-0.496465\pi\)
0.0111038 + 0.999938i \(0.496465\pi\)
\(128\) 10.1213 + 17.5306i 0.894605 + 1.54950i
\(129\) 1.42556 + 0.0805741i 0.125513 + 0.00709415i
\(130\) −9.95197 + 17.2373i −0.872845 + 1.51181i
\(131\) −5.24892 + 9.09140i −0.458600 + 0.794319i −0.998887 0.0471618i \(-0.984982\pi\)
0.540287 + 0.841481i \(0.318316\pi\)
\(132\) 0 0
\(133\) −3.15821 5.47018i −0.273851 0.474325i
\(134\) 7.96519 0.688088
\(135\) −5.17838 + 6.23630i −0.445684 + 0.536735i
\(136\) −15.2361 −1.30649
\(137\) −5.49018 9.50928i −0.469058 0.812432i 0.530316 0.847800i \(-0.322073\pi\)
−0.999374 + 0.0353676i \(0.988740\pi\)
\(138\) −17.5896 + 26.8440i −1.49733 + 2.28511i
\(139\) 3.92786 6.80325i 0.333157 0.577044i −0.649972 0.759958i \(-0.725220\pi\)
0.983129 + 0.182914i \(0.0585528\pi\)
\(140\) 10.6630 18.4688i 0.901186 1.56090i
\(141\) 10.1232 + 0.572175i 0.852527 + 0.0481858i
\(142\) 7.34517 + 12.7222i 0.616393 + 1.06762i
\(143\) 0 0
\(144\) −2.25760 + 3.05432i −0.188133 + 0.254526i
\(145\) 2.31725 0.192437
\(146\) 1.25160 + 2.16784i 0.103583 + 0.179412i
\(147\) 6.41769 + 12.7242i 0.529322 + 1.04947i
\(148\) −16.3231 + 28.2724i −1.34175 + 2.32398i
\(149\) 3.83385 6.64043i 0.314082 0.544005i −0.665160 0.746701i \(-0.731637\pi\)
0.979242 + 0.202695i \(0.0649701\pi\)
\(150\) −4.69599 9.31060i −0.383426 0.760208i
\(151\) 0.175658 + 0.304248i 0.0142948 + 0.0247594i 0.873084 0.487569i \(-0.162116\pi\)
−0.858790 + 0.512329i \(0.828783\pi\)
\(152\) 5.70792 0.462974
\(153\) 5.17479 + 11.8842i 0.418357 + 0.960777i
\(154\) 0 0
\(155\) 1.13769 + 1.97054i 0.0913816 + 0.158278i
\(156\) 32.9489 + 1.86231i 2.63802 + 0.149104i
\(157\) 5.17711 8.96702i 0.413179 0.715646i −0.582057 0.813148i \(-0.697752\pi\)
0.995235 + 0.0975018i \(0.0310852\pi\)
\(158\) 11.6213 20.1286i 0.924538 1.60135i
\(159\) −10.1958 + 15.5600i −0.808576 + 1.23399i
\(160\) −3.18452 5.51576i −0.251759 0.436059i
\(161\) −30.8225 −2.42915
\(162\) 20.5769 + 4.72782i 1.61667 + 0.371453i
\(163\) 21.4071 1.67674 0.838368 0.545104i \(-0.183510\pi\)
0.838368 + 0.545104i \(0.183510\pi\)
\(164\) −6.17677 10.6985i −0.482325 0.835411i
\(165\) 0 0
\(166\) −5.58184 + 9.66803i −0.433235 + 0.750385i
\(167\) 7.24882 12.5553i 0.560930 0.971560i −0.436485 0.899711i \(-0.643777\pi\)
0.997416 0.0718486i \(-0.0228898\pi\)
\(168\) −23.7965 1.34500i −1.83594 0.103769i
\(169\) −8.29056 14.3597i −0.637735 1.10459i
\(170\) 15.8118 1.21271
\(171\) −1.93864 4.45217i −0.148251 0.340466i
\(172\) −2.88790 −0.220200
\(173\) 5.06968 + 8.78094i 0.385441 + 0.667603i 0.991830 0.127565i \(-0.0407162\pi\)
−0.606390 + 0.795168i \(0.707383\pi\)
\(174\) −2.71800 5.38891i −0.206051 0.408532i
\(175\) 5.00743 8.67312i 0.378526 0.655626i
\(176\) 0 0
\(177\) −4.19890 8.32503i −0.315608 0.625747i
\(178\) −4.07100 7.05118i −0.305134 0.528508i
\(179\) −2.31066 −0.172707 −0.0863533 0.996265i \(-0.527521\pi\)
−0.0863533 + 0.996265i \(0.527521\pi\)
\(180\) 9.74519 13.1843i 0.726364 0.982701i
\(181\) −7.72462 −0.574166 −0.287083 0.957906i \(-0.592686\pi\)
−0.287083 + 0.957906i \(0.592686\pi\)
\(182\) 24.8945 + 43.1186i 1.84531 + 3.19616i
\(183\) 23.0162 + 1.30090i 1.70141 + 0.0961653i
\(184\) 13.9266 24.1216i 1.02668 1.77827i
\(185\) 7.26877 12.5899i 0.534411 0.925626i
\(186\) 3.24817 4.95711i 0.238167 0.363473i
\(187\) 0 0
\(188\) −20.5076 −1.49567
\(189\) 7.03313 + 19.0181i 0.511585 + 1.38336i
\(190\) −5.92357 −0.429741
\(191\) −9.67377 16.7555i −0.699969 1.21238i −0.968477 0.249104i \(-0.919864\pi\)
0.268508 0.963278i \(-0.413470\pi\)
\(192\) −11.4957 + 17.5438i −0.829627 + 1.26612i
\(193\) −5.48564 + 9.50141i −0.394865 + 0.683926i −0.993084 0.117406i \(-0.962542\pi\)
0.598219 + 0.801333i \(0.295875\pi\)
\(194\) −10.8708 + 18.8287i −0.780475 + 1.35182i
\(195\) −14.6723 0.829297i −1.05071 0.0593872i
\(196\) −14.4119 24.9621i −1.02942 1.78301i
\(197\) −20.7343 −1.47726 −0.738629 0.674112i \(-0.764527\pi\)
−0.738629 + 0.674112i \(0.764527\pi\)
\(198\) 0 0
\(199\) −4.85396 −0.344088 −0.172044 0.985089i \(-0.555037\pi\)
−0.172044 + 0.985089i \(0.555037\pi\)
\(200\) 4.52503 + 7.83758i 0.319968 + 0.554201i
\(201\) 2.64839 + 5.25089i 0.186803 + 0.370369i
\(202\) 4.13622 7.16415i 0.291024 0.504068i
\(203\) 2.89826 5.01993i 0.203418 0.352330i
\(204\) −11.8061 23.4077i −0.826595 1.63886i
\(205\) 2.75055 + 4.76410i 0.192107 + 0.332739i
\(206\) −19.6200 −1.36699
\(207\) −23.5448 2.67009i −1.63648 0.185584i
\(208\) −6.88578 −0.477443
\(209\) 0 0
\(210\) 24.6955 + 1.39582i 1.70415 + 0.0963207i
\(211\) −2.15989 + 3.74105i −0.148693 + 0.257544i −0.930745 0.365670i \(-0.880840\pi\)
0.782052 + 0.623214i \(0.214173\pi\)
\(212\) 18.8129 32.5848i 1.29207 2.23794i
\(213\) −5.94462 + 9.07223i −0.407318 + 0.621619i
\(214\) −7.99339 13.8450i −0.546417 0.946422i
\(215\) 1.28600 0.0877044
\(216\) −18.0612 3.08887i −1.22891 0.210171i
\(217\) 5.69180 0.386385
\(218\) −19.1663 33.1970i −1.29811 2.24838i
\(219\) −1.01295 + 1.54589i −0.0684489 + 0.104462i
\(220\) 0 0
\(221\) −11.7497 + 20.3510i −0.790368 + 1.36896i
\(222\) −37.8045 2.13675i −2.53727 0.143409i
\(223\) −3.70877 6.42378i −0.248358 0.430168i 0.714712 0.699418i \(-0.246558\pi\)
−0.963070 + 0.269250i \(0.913224\pi\)
\(224\) −15.9320 −1.06450
\(225\) 4.57643 6.19147i 0.305095 0.412765i
\(226\) 5.04941 0.335882
\(227\) −1.30996 2.26891i −0.0869450 0.150593i 0.819273 0.573403i \(-0.194377\pi\)
−0.906218 + 0.422810i \(0.861044\pi\)
\(228\) 4.42294 + 8.76924i 0.292917 + 0.580757i
\(229\) −5.75481 + 9.96762i −0.380288 + 0.658679i −0.991103 0.133095i \(-0.957509\pi\)
0.610815 + 0.791773i \(0.290842\pi\)
\(230\) −14.4528 + 25.0329i −0.952987 + 1.65062i
\(231\) 0 0
\(232\) 2.61905 + 4.53633i 0.171949 + 0.297825i
\(233\) −16.5445 −1.08387 −0.541934 0.840421i \(-0.682308\pi\)
−0.541934 + 0.840421i \(0.682308\pi\)
\(234\) 15.2813 + 35.0942i 0.998968 + 2.29418i
\(235\) 9.13216 0.595717
\(236\) 9.42924 + 16.3319i 0.613791 + 1.06312i
\(237\) 17.1334 + 0.968399i 1.11293 + 0.0629043i
\(238\) 19.7763 34.2535i 1.28191 2.22033i
\(239\) 2.57250 4.45570i 0.166401 0.288215i −0.770751 0.637137i \(-0.780119\pi\)
0.937152 + 0.348921i \(0.113452\pi\)
\(240\) −1.87486 + 2.86128i −0.121022 + 0.184695i
\(241\) −11.5165 19.9472i −0.741843 1.28491i −0.951655 0.307167i \(-0.900619\pi\)
0.209813 0.977742i \(-0.432715\pi\)
\(242\) 0 0
\(243\) 3.72500 + 15.1369i 0.238959 + 0.971030i
\(244\) −46.6263 −2.98494
\(245\) 6.41769 + 11.1158i 0.410011 + 0.710160i
\(246\) 7.85297 11.9846i 0.500687 0.764111i
\(247\) 4.40179 7.62412i 0.280079 0.485111i
\(248\) −2.57174 + 4.45438i −0.163306 + 0.282853i
\(249\) −8.22939 0.465134i −0.521516 0.0294767i
\(250\) −13.8450 23.9802i −0.875632 1.51664i
\(251\) 7.91075 0.499322 0.249661 0.968333i \(-0.419681\pi\)
0.249661 + 0.968333i \(0.419681\pi\)
\(252\) −16.3730 37.6014i −1.03140 2.36867i
\(253\) 0 0
\(254\) −0.293548 0.508441i −0.0184189 0.0319024i
\(255\) 5.25734 + 10.4236i 0.329227 + 0.652749i
\(256\) 11.6338 20.1503i 0.727110 1.25939i
\(257\) −5.21659 + 9.03541i −0.325402 + 0.563613i −0.981594 0.190981i \(-0.938833\pi\)
0.656191 + 0.754594i \(0.272166\pi\)
\(258\) −1.50841 2.99067i −0.0939093 0.186191i
\(259\) −18.1826 31.4932i −1.12981 1.95689i
\(260\) 29.7233 1.84336
\(261\) 2.64880 3.58358i 0.163957 0.221818i
\(262\) 24.6268 1.52145
\(263\) −12.9795 22.4812i −0.800351 1.38625i −0.919385 0.393358i \(-0.871313\pi\)
0.119035 0.992890i \(-0.462020\pi\)
\(264\) 0 0
\(265\) −8.37748 + 14.5102i −0.514624 + 0.891356i
\(266\) −7.40881 + 12.8324i −0.454264 + 0.786808i
\(267\) 3.29476 5.02821i 0.201636 0.307722i
\(268\) −5.94735 10.3011i −0.363292 0.629241i
\(269\) −19.9804 −1.21822 −0.609112 0.793084i \(-0.708474\pi\)
−0.609112 + 0.793084i \(0.708474\pi\)
\(270\) 18.7436 + 3.20557i 1.14070 + 0.195085i
\(271\) −0.296230 −0.0179947 −0.00899734 0.999960i \(-0.502864\pi\)
−0.00899734 + 0.999960i \(0.502864\pi\)
\(272\) 2.73504 + 4.73723i 0.165836 + 0.287237i
\(273\) −20.1477 + 30.7480i −1.21940 + 1.86095i
\(274\) −12.8794 + 22.3077i −0.778071 + 1.34766i
\(275\) 0 0
\(276\) 47.8501 + 2.70454i 2.88024 + 0.162794i
\(277\) 13.2896 + 23.0182i 0.798494 + 1.38303i 0.920597 + 0.390514i \(0.127703\pi\)
−0.122103 + 0.992517i \(0.538964\pi\)
\(278\) −18.4287 −1.10528
\(279\) 4.34788 + 0.493069i 0.260301 + 0.0295193i
\(280\) −21.4669 −1.28289
\(281\) 3.40362 + 5.89524i 0.203043 + 0.351680i 0.949507 0.313745i \(-0.101584\pi\)
−0.746465 + 0.665425i \(0.768250\pi\)
\(282\) −10.7115 21.2374i −0.637862 1.26467i
\(283\) 1.03790 1.79770i 0.0616967 0.106862i −0.833527 0.552478i \(-0.813682\pi\)
0.895224 + 0.445617i \(0.147016\pi\)
\(284\) 10.9688 18.9985i 0.650879 1.12736i
\(285\) −1.96956 3.90499i −0.116667 0.231312i
\(286\) 0 0
\(287\) 13.7608 0.812277
\(288\) −12.1702 1.38015i −0.717135 0.0813263i
\(289\) 1.66794 0.0981143
\(290\) −2.71800 4.70772i −0.159607 0.276447i
\(291\) −16.0269 0.905860i −0.939515 0.0531024i
\(292\) 1.86906 3.23731i 0.109379 0.189449i
\(293\) −1.51851 + 2.63014i −0.0887123 + 0.153654i −0.906967 0.421202i \(-0.861609\pi\)
0.818255 + 0.574856i \(0.194942\pi\)
\(294\) 18.3228 27.9629i 1.06861 1.63083i
\(295\) −4.19890 7.27270i −0.244469 0.423433i
\(296\) 32.8619 1.91006
\(297\) 0 0
\(298\) −17.9876 −1.04199
\(299\) −21.4796 37.2038i −1.24220 2.15155i
\(300\) −8.53475 + 13.0251i −0.492754 + 0.752005i
\(301\) 1.60844 2.78590i 0.0927091 0.160577i
\(302\) 0.412074 0.713733i 0.0237122 0.0410707i
\(303\) 6.09809 + 0.344671i 0.350326 + 0.0198008i
\(304\) −1.02463 1.77471i −0.0587666 0.101787i
\(305\) 20.7630 1.18888
\(306\) 18.0741 24.4526i 1.03323 1.39786i
\(307\) −17.9515 −1.02455 −0.512273 0.858823i \(-0.671196\pi\)
−0.512273 + 0.858823i \(0.671196\pi\)
\(308\) 0 0
\(309\) −6.52358 12.9341i −0.371113 0.735796i
\(310\) 2.66890 4.62267i 0.151583 0.262550i
\(311\) 13.1958 22.8557i 0.748262 1.29603i −0.200392 0.979716i \(-0.564222\pi\)
0.948655 0.316313i \(-0.102445\pi\)
\(312\) −14.9598 29.6604i −0.846935 1.67919i
\(313\) 4.32409 + 7.48955i 0.244412 + 0.423334i 0.961966 0.273168i \(-0.0880716\pi\)
−0.717554 + 0.696503i \(0.754738\pi\)
\(314\) −24.2899 −1.37076
\(315\) 7.29100 + 16.7441i 0.410801 + 0.943425i
\(316\) −34.7089 −1.95253
\(317\) 3.89806 + 6.75163i 0.218937 + 0.379209i 0.954483 0.298265i \(-0.0964079\pi\)
−0.735546 + 0.677474i \(0.763075\pi\)
\(318\) 43.5708 + 2.46267i 2.44333 + 0.138100i
\(319\) 0 0
\(320\) −9.44556 + 16.3602i −0.528023 + 0.914562i
\(321\) 6.46923 9.87286i 0.361077 0.551050i
\(322\) 36.1531 + 62.6191i 2.01474 + 3.48962i
\(323\) −6.99359 −0.389134
\(324\) −9.24975 30.1415i −0.513875 1.67453i
\(325\) 13.9583 0.774268
\(326\) −25.1094 43.4908i −1.39068 2.40873i
\(327\) 15.5117 23.6729i 0.857801 1.30911i
\(328\) −6.21759 + 10.7692i −0.343309 + 0.594629i
\(329\) 11.4219 19.7833i 0.629710 1.09069i
\(330\) 0 0
\(331\) −3.90032 6.75555i −0.214381 0.371319i 0.738700 0.674034i \(-0.235440\pi\)
−0.953081 + 0.302716i \(0.902107\pi\)
\(332\) 16.6711 0.914947
\(333\) −11.1612 25.6323i −0.611631 1.40464i
\(334\) −34.0099 −1.86094
\(335\) 2.64839 + 4.58715i 0.144697 + 0.250623i
\(336\) 3.85353 + 7.64027i 0.210227 + 0.416811i
\(337\) 3.55988 6.16589i 0.193919 0.335877i −0.752627 0.658447i \(-0.771214\pi\)
0.946546 + 0.322570i \(0.104547\pi\)
\(338\) −19.4487 + 33.6862i −1.05787 + 1.83229i
\(339\) 1.67891 + 3.32872i 0.0911858 + 0.180791i
\(340\) −11.8061 20.4488i −0.640278 1.10899i
\(341\) 0 0
\(342\) −6.77112 + 9.16069i −0.366140 + 0.495353i
\(343\) 4.79131 0.258706
\(344\) 1.45349 + 2.51752i 0.0783671 + 0.135736i
\(345\) −21.3079 1.20435i −1.14718 0.0648399i
\(346\) 11.8929 20.5991i 0.639367 1.10742i
\(347\) −10.5041 + 18.1937i −0.563891 + 0.976687i 0.433261 + 0.901268i \(0.357363\pi\)
−0.997152 + 0.0754190i \(0.975971\pi\)
\(348\) −4.93985 + 7.53883i −0.264804 + 0.404124i
\(349\) −10.4589 18.1154i −0.559853 0.969694i −0.997508 0.0705511i \(-0.977524\pi\)
0.437655 0.899143i \(-0.355809\pi\)
\(350\) −23.4937 −1.25579
\(351\) −18.0542 + 21.7425i −0.963660 + 1.16053i
\(352\) 0 0
\(353\) 12.7877 + 22.1489i 0.680619 + 1.17887i 0.974792 + 0.223115i \(0.0716225\pi\)
−0.294173 + 0.955752i \(0.595044\pi\)
\(354\) −11.9881 + 18.2953i −0.637158 + 0.972384i
\(355\) −4.88448 + 8.46016i −0.259241 + 0.449019i
\(356\) −6.07938 + 10.5298i −0.322206 + 0.558078i
\(357\) 29.1565 + 1.64796i 1.54312 + 0.0872191i
\(358\) 2.71028 + 4.69434i 0.143243 + 0.248103i
\(359\) 35.7137 1.88490 0.942449 0.334350i \(-0.108517\pi\)
0.942449 + 0.334350i \(0.108517\pi\)
\(360\) −16.3982 1.85963i −0.864261 0.0980111i
\(361\) −16.3800 −0.862104
\(362\) 9.06055 + 15.6933i 0.476212 + 0.824824i
\(363\) 0 0
\(364\) 37.1759 64.3906i 1.94855 3.37498i
\(365\) −0.832305 + 1.44159i −0.0435648 + 0.0754565i
\(366\) −24.3538 48.2856i −1.27299 2.52393i
\(367\) 2.93712 + 5.08725i 0.153317 + 0.265552i 0.932445 0.361313i \(-0.117671\pi\)
−0.779128 + 0.626865i \(0.784338\pi\)
\(368\) −9.99988 −0.521280
\(369\) 10.5117 + 1.19207i 0.547217 + 0.0620568i
\(370\) −34.1035 −1.77296
\(371\) 20.9560 + 36.2969i 1.08798 + 1.88444i
\(372\) −8.83617 0.499430i −0.458134 0.0258943i
\(373\) 9.99046 17.3040i 0.517287 0.895967i −0.482512 0.875889i \(-0.660275\pi\)
0.999798 0.0200773i \(-0.00639122\pi\)
\(374\) 0 0
\(375\) 11.2050 17.1003i 0.578626 0.883056i
\(376\) 10.3216 + 17.8775i 0.532294 + 0.921961i
\(377\) 8.07896 0.416088
\(378\) 30.3876 36.5956i 1.56297 1.88228i
\(379\) 26.3439 1.35320 0.676599 0.736352i \(-0.263453\pi\)
0.676599 + 0.736352i \(0.263453\pi\)
\(380\) 4.42294 + 7.66076i 0.226892 + 0.392989i
\(381\) 0.237576 0.362570i 0.0121714 0.0185750i
\(382\) −22.6936 + 39.3065i −1.16111 + 2.01109i
\(383\) 0.812128 1.40665i 0.0414978 0.0718763i −0.844531 0.535507i \(-0.820120\pi\)
0.886028 + 0.463631i \(0.153454\pi\)
\(384\) 35.0053 + 1.97854i 1.78636 + 0.100967i
\(385\) 0 0
\(386\) 25.7374 1.31000
\(387\) 1.47000 1.98877i 0.0747244 0.101095i
\(388\) 32.4674 1.64828
\(389\) 3.57443 + 6.19109i 0.181231 + 0.313901i 0.942300 0.334770i \(-0.108659\pi\)
−0.761069 + 0.648671i \(0.775325\pi\)
\(390\) 15.5250 + 30.7811i 0.786141 + 1.55866i
\(391\) −17.0635 + 29.5548i −0.862937 + 1.49465i
\(392\) −14.5071 + 25.1270i −0.732720 + 1.26911i
\(393\) 8.18830 + 16.2347i 0.413045 + 0.818933i
\(394\) 24.3202 + 42.1239i 1.22523 + 2.12217i
\(395\) 15.4561 0.777680
\(396\) 0 0
\(397\) −28.2612 −1.41839 −0.709195 0.705012i \(-0.750941\pi\)
−0.709195 + 0.705012i \(0.750941\pi\)
\(398\) 5.69343 + 9.86131i 0.285386 + 0.494303i
\(399\) −10.9229 0.617376i −0.546830 0.0309074i
\(400\) 1.62458 2.81386i 0.0812290 0.140693i
\(401\) −2.08005 + 3.60275i −0.103873 + 0.179913i −0.913277 0.407339i \(-0.866457\pi\)
0.809404 + 0.587252i \(0.199790\pi\)
\(402\) 7.56129 11.5395i 0.377123 0.575537i
\(403\) 3.96650 + 6.87019i 0.197586 + 0.342228i
\(404\) −12.3535 −0.614612
\(405\) 4.11897 + 13.4222i 0.204673 + 0.666954i
\(406\) −13.5980 −0.674857
\(407\) 0 0
\(408\) −14.4635 + 22.0732i −0.716051 + 1.09278i
\(409\) 13.4436 23.2850i 0.664743 1.15137i −0.314612 0.949220i \(-0.601874\pi\)
0.979355 0.202149i \(-0.0647924\pi\)
\(410\) 6.45250 11.1761i 0.318666 0.551946i
\(411\) −18.9882 1.07324i −0.936621 0.0529389i
\(412\) 14.6497 + 25.3740i 0.721737 + 1.25008i
\(413\) −21.0068 −1.03368
\(414\) 22.1922 + 50.9656i 1.09069 + 2.50482i
\(415\) −7.42375 −0.364418
\(416\) −11.1027 19.2304i −0.544354 0.942848i
\(417\) −6.12745 12.1487i −0.300063 0.594925i
\(418\) 0 0
\(419\) 8.44088 14.6200i 0.412364 0.714236i −0.582784 0.812627i \(-0.698036\pi\)
0.995148 + 0.0983917i \(0.0313698\pi\)
\(420\) −16.6342 32.9802i −0.811667 1.60927i
\(421\) 16.5021 + 28.5826i 0.804266 + 1.39303i 0.916786 + 0.399379i \(0.130774\pi\)
−0.112520 + 0.993649i \(0.535892\pi\)
\(422\) 10.1338 0.493303
\(423\) 10.4388 14.1227i 0.507552 0.686670i
\(424\) −37.8744 −1.83934
\(425\) −5.54426 9.60295i −0.268936 0.465811i
\(426\) 25.4039 + 1.43586i 1.23082 + 0.0695674i
\(427\) 25.9689 44.9795i 1.25672 2.17671i
\(428\) −11.9368 + 20.6752i −0.576988 + 0.999372i
\(429\) 0 0
\(430\) −1.50841 2.61264i −0.0727418 0.125993i
\(431\) −11.0594 −0.532713 −0.266356 0.963875i \(-0.585820\pi\)
−0.266356 + 0.963875i \(0.585820\pi\)
\(432\) 2.28179 + 6.17011i 0.109783 + 0.296859i
\(433\) 28.1486 1.35273 0.676367 0.736565i \(-0.263553\pi\)
0.676367 + 0.736565i \(0.263553\pi\)
\(434\) −6.67617 11.5635i −0.320466 0.555064i
\(435\) 2.19974 3.35709i 0.105470 0.160960i
\(436\) −28.6217 + 49.5743i −1.37073 + 2.37418i
\(437\) 6.39251 11.0721i 0.305795 0.529653i
\(438\) 4.32877 + 0.244667i 0.206837 + 0.0116906i
\(439\) −0.934408 1.61844i −0.0445969 0.0772440i 0.842865 0.538125i \(-0.180867\pi\)
−0.887462 + 0.460881i \(0.847534\pi\)
\(440\) 0 0
\(441\) 24.5263 + 2.78139i 1.16792 + 0.132447i
\(442\) 55.1269 2.62212
\(443\) −9.71051 16.8191i −0.461360 0.799099i 0.537669 0.843156i \(-0.319305\pi\)
−0.999029 + 0.0440568i \(0.985972\pi\)
\(444\) 25.4640 + 50.4867i 1.20847 + 2.39599i
\(445\) 2.70718 4.68898i 0.128333 0.222279i
\(446\) −8.70038 + 15.0695i −0.411975 + 0.713561i
\(447\) −5.98080 11.8580i −0.282882 0.560862i
\(448\) 23.6278 + 40.9245i 1.11631 + 1.93350i
\(449\) 15.6490 0.738520 0.369260 0.929326i \(-0.379611\pi\)
0.369260 + 0.929326i \(0.379611\pi\)
\(450\) −17.9465 2.03521i −0.846006 0.0959409i
\(451\) 0 0
\(452\) −3.77024 6.53024i −0.177337 0.307157i
\(453\) 0.607527 + 0.0343381i 0.0285441 + 0.00161334i
\(454\) −3.07302 + 5.32263i −0.144224 + 0.249803i
\(455\) −16.5547 + 28.6735i −0.776094 + 1.34423i
\(456\) 5.41848 8.26929i 0.253744 0.387245i
\(457\) −5.42276 9.39250i −0.253666 0.439363i 0.710866 0.703327i \(-0.248303\pi\)
−0.964532 + 0.263965i \(0.914970\pi\)
\(458\) 27.0003 1.26164
\(459\) 22.1294 + 3.78461i 1.03291 + 0.176651i
\(460\) 43.1657 2.01261
\(461\) 19.7612 + 34.2274i 0.920371 + 1.59413i 0.798841 + 0.601542i \(0.205447\pi\)
0.121530 + 0.992588i \(0.461220\pi\)
\(462\) 0 0
\(463\) −11.8195 + 20.4719i −0.549298 + 0.951412i 0.449025 + 0.893519i \(0.351771\pi\)
−0.998323 + 0.0578925i \(0.981562\pi\)
\(464\) 0.940294 1.62864i 0.0436521 0.0756076i
\(465\) 3.93480 + 0.222399i 0.182472 + 0.0103135i
\(466\) 19.4058 + 33.6119i 0.898957 + 1.55704i
\(467\) −2.49010 −0.115228 −0.0576140 0.998339i \(-0.518349\pi\)
−0.0576140 + 0.998339i \(0.518349\pi\)
\(468\) 33.9761 45.9665i 1.57055 2.12480i
\(469\) 13.2497 0.611816
\(470\) −10.7115 18.5529i −0.494086 0.855782i
\(471\) −8.07628 16.0126i −0.372136 0.737822i
\(472\) 9.49155 16.4399i 0.436884 0.756706i
\(473\) 0 0
\(474\) −18.1291 35.9441i −0.832699 1.65097i
\(475\) 2.07705 + 3.59756i 0.0953017 + 0.165067i
\(476\) −59.0653 −2.70726
\(477\) 12.8636 + 29.5420i 0.588985 + 1.35263i
\(478\) −12.0696 −0.552051
\(479\) −5.75027 9.95976i −0.262737 0.455073i 0.704232 0.709970i \(-0.251292\pi\)
−0.966968 + 0.254897i \(0.917958\pi\)
\(480\) −11.0139 0.622520i −0.502715 0.0284140i
\(481\) 25.3422 43.8940i 1.15550 2.00139i
\(482\) −27.0164 + 46.7938i −1.23057 + 2.13140i
\(483\) −29.2596 + 44.6538i −1.33136 + 2.03182i
\(484\) 0 0
\(485\) −14.4579 −0.656501
\(486\) 26.3828 25.3224i 1.19675 1.14865i
\(487\) −26.7429 −1.21184 −0.605918 0.795527i \(-0.707194\pi\)
−0.605918 + 0.795527i \(0.707194\pi\)
\(488\) 23.4672 + 40.6464i 1.06231 + 1.83998i
\(489\) 20.3216 31.0134i 0.918976 1.40247i
\(490\) 15.0552 26.0764i 0.680125 1.17801i
\(491\) 5.85088 10.1340i 0.264047 0.457342i −0.703267 0.710926i \(-0.748276\pi\)
0.967313 + 0.253584i \(0.0816094\pi\)
\(492\) −21.3629 1.20745i −0.963113 0.0544362i
\(493\) −3.20898 5.55811i −0.144525 0.250325i
\(494\) −20.6522 −0.929188
\(495\) 0 0
\(496\) 1.84661 0.0829155
\(497\) 12.2184 + 21.1628i 0.548068 + 0.949282i
\(498\) 8.70766 + 17.2644i 0.390200 + 0.773637i
\(499\) 12.3613 21.4104i 0.553368 0.958462i −0.444660 0.895699i \(-0.646676\pi\)
0.998028 0.0627627i \(-0.0199911\pi\)
\(500\) −20.6752 + 35.8105i −0.924622 + 1.60149i
\(501\) −11.3081 22.4203i −0.505210 1.00167i
\(502\) −9.27888 16.0715i −0.414137 0.717306i
\(503\) −44.8075 −1.99787 −0.998933 0.0461829i \(-0.985294\pi\)
−0.998933 + 0.0461829i \(0.985294\pi\)
\(504\) −24.5384 + 33.1981i −1.09303 + 1.47876i
\(505\) 5.50111 0.244796
\(506\) 0 0
\(507\) −28.6736 1.62066i −1.27344 0.0719761i
\(508\) −0.438367 + 0.759273i −0.0194494 + 0.0336873i
\(509\) −16.8263 + 29.1440i −0.745813 + 1.29179i 0.204001 + 0.978971i \(0.434605\pi\)
−0.949814 + 0.312815i \(0.898728\pi\)
\(510\) 15.0100 22.9071i 0.664653 1.01434i
\(511\) 2.08198 + 3.60610i 0.0921016 + 0.159525i
\(512\) −14.0979 −0.623043
\(513\) −8.29037 1.41783i −0.366029 0.0625989i
\(514\) 24.4751 1.07955
\(515\) −6.52358 11.2992i −0.287463 0.497901i
\(516\) −2.74146 + 4.18381i −0.120686 + 0.184182i
\(517\) 0 0
\(518\) −42.6544 + 73.8796i −1.87413 + 3.24608i
\(519\) 17.5339 + 0.991035i 0.769653 + 0.0435016i
\(520\) −14.9598 25.9112i −0.656033 1.13628i
\(521\) −35.7515 −1.56630 −0.783151 0.621832i \(-0.786389\pi\)
−0.783151 + 0.621832i \(0.786389\pi\)
\(522\) −10.3873 1.17797i −0.454640 0.0515582i
\(523\) 30.0048 1.31202 0.656009 0.754753i \(-0.272243\pi\)
0.656009 + 0.754753i \(0.272243\pi\)
\(524\) −18.3880 31.8490i −0.803285 1.39133i
\(525\) −7.81157 15.4878i −0.340925 0.675942i
\(526\) −30.4485 + 52.7384i −1.32762 + 2.29950i
\(527\) 3.15100 5.45770i 0.137260 0.237741i
\(528\) 0 0
\(529\) −19.6938 34.1107i −0.856253 1.48307i
\(530\) 39.3053 1.70731
\(531\) −16.0468 1.81978i −0.696371 0.0789716i
\(532\) 22.1277 0.959358
\(533\) 9.58966 + 16.6098i 0.415374 + 0.719449i
\(534\) −14.0799 0.795811i −0.609297 0.0344381i
\(535\) 5.31553 9.20678i 0.229811 0.398044i
\(536\) −5.98666 + 10.3692i −0.258584 + 0.447881i
\(537\) −2.19349 + 3.34754i −0.0946560 + 0.144457i
\(538\) 23.4359 + 40.5921i 1.01039 + 1.75005i
\(539\) 0 0
\(540\) −9.84961 26.6340i −0.423860 1.14615i
\(541\) −4.66677 −0.200640 −0.100320 0.994955i \(-0.531987\pi\)
−0.100320 + 0.994955i \(0.531987\pi\)
\(542\) 0.347461 + 0.601821i 0.0149247 + 0.0258504i
\(543\) −7.33292 + 11.1910i −0.314686 + 0.480250i
\(544\) −8.82001 + 15.2767i −0.378155 + 0.654983i
\(545\) 12.7454 22.0757i 0.545954 0.945620i
\(546\) 86.0998 + 4.86646i 3.68473 + 0.208265i
\(547\) −10.4912 18.1714i −0.448573 0.776951i 0.549721 0.835349i \(-0.314734\pi\)
−0.998293 + 0.0583977i \(0.981401\pi\)
\(548\) 38.4665 1.64321
\(549\) 23.7337 32.1095i 1.01293 1.37040i
\(550\) 0 0
\(551\) 1.20218 + 2.08224i 0.0512147 + 0.0887064i
\(552\) −21.7255 43.0744i −0.924697 1.83337i
\(553\) 19.3314 33.4830i 0.822057 1.42384i
\(554\) 31.1759 53.9983i 1.32454 2.29417i
\(555\) −11.3393 22.4820i −0.481325 0.954309i
\(556\) 13.7601 + 23.8332i 0.583558 + 1.01075i
\(557\) 28.2882 1.19861 0.599304 0.800522i \(-0.295444\pi\)
0.599304 + 0.800522i \(0.295444\pi\)
\(558\) −4.09810 9.41149i −0.173487 0.398420i
\(559\) 4.48357 0.189635
\(560\) 3.85353 + 6.67450i 0.162841 + 0.282049i
\(561\) 0 0
\(562\) 7.98451 13.8296i 0.336806 0.583366i
\(563\) −5.64908 + 9.78450i −0.238081 + 0.412368i −0.960163 0.279439i \(-0.909852\pi\)
0.722083 + 0.691806i \(0.243185\pi\)
\(564\) −19.4677 + 29.7102i −0.819739 + 1.25102i
\(565\) 1.67891 + 2.90795i 0.0706322 + 0.122339i
\(566\) −4.86960 −0.204685
\(567\) 34.2287 + 7.86452i 1.43747 + 0.330279i
\(568\) −22.0826 −0.926565
\(569\) 9.00491 + 15.5970i 0.377505 + 0.653858i 0.990699 0.136075i \(-0.0434487\pi\)
−0.613193 + 0.789933i \(0.710115\pi\)
\(570\) −5.62320 + 8.58171i −0.235530 + 0.359448i
\(571\) −1.83865 + 3.18464i −0.0769452 + 0.133273i −0.901931 0.431881i \(-0.857850\pi\)
0.824985 + 0.565154i \(0.191183\pi\)
\(572\) 0 0
\(573\) −33.4575 1.89106i −1.39771 0.0790000i
\(574\) −16.1407 27.9565i −0.673700 1.16688i
\(575\) 20.2710 0.845358
\(576\) 14.5037 + 33.3084i 0.604320 + 1.38785i
\(577\) 20.7404 0.863433 0.431717 0.902009i \(-0.357908\pi\)
0.431717 + 0.902009i \(0.357908\pi\)
\(578\) −1.95641 3.38859i −0.0813758 0.140947i
\(579\) 8.55759 + 16.9669i 0.355641 + 0.705119i
\(580\) −4.05889 + 7.03021i −0.168536 + 0.291914i
\(581\) −9.28514 + 16.0823i −0.385213 + 0.667208i
\(582\) 16.9584 + 33.6228i 0.702947 + 1.39371i
\(583\) 0 0
\(584\) −3.76283 −0.155707
\(585\) −15.1298 + 20.4691i −0.625539 + 0.846295i
\(586\) 7.12452 0.294311
\(587\) 10.0497 + 17.4066i 0.414796 + 0.718448i 0.995407 0.0957333i \(-0.0305196\pi\)
−0.580611 + 0.814181i \(0.697186\pi\)
\(588\) −49.8446 2.81727i −2.05556 0.116182i
\(589\) −1.18046 + 2.04462i −0.0486402 + 0.0842472i
\(590\) −9.85016 + 17.0610i −0.405524 + 0.702389i
\(591\) −19.6829 + 30.0386i −0.809647 + 1.23562i
\(592\) −5.89906 10.2175i −0.242450 0.419935i
\(593\) −12.9393 −0.531354 −0.265677 0.964062i \(-0.585596\pi\)
−0.265677 + 0.964062i \(0.585596\pi\)
\(594\) 0 0
\(595\) 26.3021 1.07828
\(596\) 13.4308 + 23.2628i 0.550146 + 0.952881i
\(597\) −4.60783 + 7.03212i −0.188586 + 0.287806i
\(598\) −50.3888 + 87.2760i −2.06055 + 3.56898i
\(599\) 23.1779 40.1453i 0.947024 1.64029i 0.195376 0.980728i \(-0.437407\pi\)
0.751648 0.659565i \(-0.229259\pi\)
\(600\) 15.6502 + 0.884566i 0.638916 + 0.0361123i
\(601\) −3.96474 6.86713i −0.161725 0.280116i 0.773762 0.633476i \(-0.218372\pi\)
−0.935487 + 0.353360i \(0.885039\pi\)
\(602\) −7.54646 −0.307571
\(603\) 10.1213 + 1.14780i 0.412170 + 0.0467419i
\(604\) −1.23073 −0.0500777
\(605\) 0 0
\(606\) −6.45250 12.7932i −0.262115 0.519687i
\(607\) −5.50806 + 9.54024i −0.223565 + 0.387226i −0.955888 0.293731i \(-0.905103\pi\)
0.732323 + 0.680958i \(0.238436\pi\)
\(608\) 3.30425 5.72313i 0.134005 0.232103i
\(609\) −4.52128 8.96420i −0.183211 0.363248i
\(610\) −24.3538 42.1820i −0.986057 1.70790i
\(611\) 31.8388 1.28806
\(612\) −45.1191 5.11671i −1.82383 0.206831i
\(613\) 16.8348 0.679951 0.339976 0.940434i \(-0.389581\pi\)
0.339976 + 0.940434i \(0.389581\pi\)
\(614\) 21.0561 + 36.4703i 0.849756 + 1.47182i
\(615\) 9.51301 + 0.537686i 0.383602 + 0.0216816i
\(616\) 0 0
\(617\) −5.92051 + 10.2546i −0.238351 + 0.412836i −0.960241 0.279172i \(-0.909940\pi\)
0.721890 + 0.692007i \(0.243273\pi\)
\(618\) −18.6251 + 28.4243i −0.749213 + 1.14339i
\(619\) −6.10792 10.5792i −0.245498 0.425215i 0.716774 0.697306i \(-0.245618\pi\)
−0.962271 + 0.272091i \(0.912285\pi\)
\(620\) −7.97114 −0.320129
\(621\) −26.2192 + 31.5756i −1.05214 + 1.26709i
\(622\) −61.9116 −2.48243
\(623\) −6.77193 11.7293i −0.271312 0.469925i
\(624\) −6.53661 + 9.97569i −0.261674 + 0.399347i
\(625\) 2.79076 4.83373i 0.111630 0.193349i
\(626\) 10.1439 17.5697i 0.405430 0.702225i
\(627\) 0 0
\(628\) 18.1365 + 31.4133i 0.723725 + 1.25353i
\(629\) −40.2639 −1.60542
\(630\) 25.4655 34.4524i 1.01457 1.37262i
\(631\) −25.7140 −1.02366 −0.511830 0.859087i \(-0.671032\pi\)
−0.511830 + 0.859087i \(0.671032\pi\)
\(632\) 17.4691 + 30.2574i 0.694885 + 1.20358i
\(633\) 3.36943 + 6.68047i 0.133923 + 0.265525i
\(634\) 9.14442 15.8386i 0.363171 0.629031i
\(635\) 0.195207 0.338109i 0.00774656 0.0134174i
\(636\) −29.3480 58.1875i −1.16373 2.30728i
\(637\) 22.3750 + 38.7546i 0.886528 + 1.53551i
\(638\) 0 0
\(639\) 7.50012 + 17.2244i 0.296700 + 0.681387i
\(640\) 31.5784 1.24825
\(641\) 18.0588 + 31.2788i 0.713280 + 1.23544i 0.963619 + 0.267279i \(0.0861244\pi\)
−0.250340 + 0.968158i \(0.580542\pi\)
\(642\) −27.6458 1.56257i −1.09109 0.0616697i
\(643\) −13.1004 + 22.6906i −0.516630 + 0.894830i 0.483183 + 0.875519i \(0.339480\pi\)
−0.999814 + 0.0193105i \(0.993853\pi\)
\(644\) 53.9888 93.5113i 2.12746 3.68486i
\(645\) 1.22079 1.86308i 0.0480685 0.0733586i
\(646\) 8.20310 + 14.2082i 0.322747 + 0.559014i
\(647\) 38.2700 1.50455 0.752275 0.658849i \(-0.228956\pi\)
0.752275 + 0.658849i \(0.228956\pi\)
\(648\) −21.6204 + 23.2338i −0.849328 + 0.912710i
\(649\) 0 0
\(650\) −16.3723 28.3577i −0.642176 1.11228i
\(651\) 5.40318 8.24593i 0.211767 0.323184i
\(652\) −37.4968 + 64.9464i −1.46849 + 2.54350i
\(653\) 0.0125540 0.0217442i 0.000491277 0.000850916i −0.865780 0.500425i \(-0.833177\pi\)
0.866271 + 0.499574i \(0.166510\pi\)
\(654\) −66.2882 3.74668i −2.59207 0.146507i
\(655\) 8.18830 + 14.1826i 0.319943 + 0.554158i
\(656\) 4.46449 0.174309
\(657\) 1.27801 + 2.93500i 0.0498598 + 0.114505i
\(658\) −53.5891 −2.08912
\(659\) 3.66456 + 6.34720i 0.142751 + 0.247252i 0.928532 0.371253i \(-0.121072\pi\)
−0.785781 + 0.618505i \(0.787739\pi\)
\(660\) 0 0
\(661\) −19.9071 + 34.4802i −0.774298 + 1.34112i 0.160890 + 0.986972i \(0.448564\pi\)
−0.935188 + 0.354151i \(0.884770\pi\)
\(662\) −9.14972 + 15.8478i −0.355614 + 0.615942i
\(663\) 18.3294 + 36.3413i 0.711857 + 1.41138i
\(664\) −8.39065 14.5330i −0.325620 0.563991i
\(665\) −9.85360 −0.382106
\(666\) −38.9831 + 52.7404i −1.51056 + 2.04365i
\(667\) 11.7327 0.454292
\(668\) 25.3941 + 43.9839i 0.982527 + 1.70179i
\(669\) −12.8271 0.725002i −0.495924 0.0280302i
\(670\) 6.21284 10.7610i 0.240023 0.415732i
\(671\) 0 0
\(672\) −15.1241 + 23.0813i −0.583425 + 0.890379i
\(673\) −16.8191 29.1316i −0.648329 1.12294i −0.983522 0.180789i \(-0.942135\pi\)
0.335193 0.942150i \(-0.391199\pi\)
\(674\) −16.7022 −0.643343
\(675\) −4.62546 12.5076i −0.178034 0.481416i
\(676\) 58.0870 2.23412
\(677\) −12.8857 22.3187i −0.495238 0.857777i 0.504747 0.863267i \(-0.331586\pi\)
−0.999985 + 0.00549037i \(0.998252\pi\)
\(678\) 4.79337 7.31528i 0.184088 0.280942i
\(679\) −18.0830 + 31.3207i −0.693963 + 1.20198i
\(680\) −11.8842 + 20.5840i −0.455736 + 0.789359i
\(681\) −4.53060 0.256074i −0.173613 0.00981279i
\(682\) 0 0
\(683\) 17.5636 0.672052 0.336026 0.941853i \(-0.390917\pi\)
0.336026 + 0.941853i \(0.390917\pi\)
\(684\) 16.9030 + 1.91688i 0.646303 + 0.0732936i
\(685\) −17.1293 −0.654479
\(686\) −5.61994 9.73402i −0.214570 0.371647i
\(687\) 8.97749 + 17.7994i 0.342512 + 0.679089i
\(688\) 0.521834 0.903843i 0.0198947 0.0344587i
\(689\) −29.2077 + 50.5891i −1.11272 + 1.92729i
\(690\) 22.5463 + 44.7018i 0.858322 + 1.70177i
\(691\) 21.6147 + 37.4377i 0.822260 + 1.42420i 0.903995 + 0.427542i \(0.140620\pi\)
−0.0817354 + 0.996654i \(0.526046\pi\)
\(692\) −35.5202 −1.35028
\(693\) 0 0
\(694\) 49.2830 1.87076
\(695\) −6.12745 10.6131i −0.232427 0.402576i
\(696\) 9.05821 + 0.511980i 0.343351 + 0.0194066i
\(697\) 7.61806 13.1949i 0.288555 0.499791i
\(698\) −24.5355 + 42.4967i −0.928682 + 1.60852i
\(699\) −15.7056 + 23.9687i −0.594040 + 0.906579i
\(700\) 17.5420 + 30.3837i 0.663027 + 1.14840i
\(701\) 46.3884 1.75206 0.876032 0.482252i \(-0.160181\pi\)
0.876032 + 0.482252i \(0.160181\pi\)
\(702\) 65.3487 + 11.1761i 2.46643 + 0.421813i
\(703\) 15.0841 0.568907
\(704\) 0 0
\(705\) 8.66909 13.2301i 0.326497 0.498275i
\(706\) 29.9985 51.9589i 1.12901 1.95550i
\(707\) 6.88042 11.9172i 0.258765 0.448194i
\(708\) 32.6118 + 1.84326i 1.22563 + 0.0692738i
\(709\) 2.49915 + 4.32865i 0.0938575 + 0.162566i 0.909131 0.416510i \(-0.136747\pi\)
−0.815274 + 0.579076i \(0.803414\pi\)
\(710\) 22.9169 0.860056
\(711\) 17.6676 23.9025i 0.662585 0.896415i
\(712\) 12.2391 0.458680
\(713\) 5.76036 + 9.97724i 0.215727 + 0.373651i
\(714\) −30.8510 61.1673i −1.15457 2.28913i
\(715\) 0 0
\(716\) 4.04735 7.01022i 0.151257 0.261984i
\(717\) −4.01309 7.95664i −0.149872 0.297146i
\(718\) −41.8902 72.5560i −1.56333 2.70777i
\(719\) 45.0421 1.67979 0.839894 0.542751i \(-0.182617\pi\)
0.839894 + 0.542751i \(0.182617\pi\)
\(720\) 2.36545 + 5.43237i 0.0881551 + 0.202453i
\(721\) −32.6370 −1.21547
\(722\) 19.2128 + 33.2776i 0.715027 + 1.23846i
\(723\) −39.8307 2.25128i −1.48132 0.0837259i
\(724\) 13.5305 23.4354i 0.502855 0.870971i
\(725\) −1.90609 + 3.30145i −0.0707905 + 0.122613i
\(726\) 0 0
\(727\) 5.14525 + 8.91183i 0.190827 + 0.330521i 0.945524 0.325551i \(-0.105550\pi\)
−0.754698 + 0.656073i \(0.772217\pi\)
\(728\) −74.8432 −2.77387
\(729\) 25.4655 + 8.97274i 0.943165 + 0.332324i
\(730\) 3.90499 0.144530
\(731\) −1.78088 3.08458i −0.0658683 0.114087i
\(732\) −44.2620 + 67.5493i −1.63597 + 2.49669i
\(733\) −7.91739 + 13.7133i −0.292436 + 0.506513i −0.974385 0.224886i \(-0.927799\pi\)
0.681949 + 0.731399i \(0.261132\pi\)
\(734\) 6.89017 11.9341i 0.254321 0.440497i
\(735\) 22.1961 + 1.25455i 0.818716 + 0.0462747i
\(736\) −16.1239 27.9274i −0.594335 1.02942i
\(737\) 0 0
\(738\) −9.90782 22.7538i −0.364712 0.837579i
\(739\) 37.8681 1.39300 0.696500 0.717557i \(-0.254740\pi\)
0.696500 + 0.717557i \(0.254740\pi\)
\(740\) 25.4640 + 44.1049i 0.936075 + 1.62133i
\(741\) −6.86678 13.6146i −0.252257 0.500143i
\(742\) 49.1605 85.1485i 1.80474 3.12590i
\(743\) −8.94538 + 15.4939i −0.328174 + 0.568414i −0.982150 0.188101i \(-0.939767\pi\)
0.653975 + 0.756516i \(0.273100\pi\)
\(744\) 4.01191 + 7.95429i 0.147084 + 0.291618i
\(745\) −5.98080 10.3591i −0.219120 0.379526i
\(746\) −46.8731 −1.71615
\(747\) −8.48595 + 11.4807i −0.310485 + 0.420057i
\(748\) 0 0
\(749\) −13.2966 23.0305i −0.485849 0.841515i
\(750\) −47.8839 2.70645i −1.74847 0.0988256i
\(751\) 18.7341 32.4484i 0.683617 1.18406i −0.290253 0.956950i \(-0.593739\pi\)
0.973869 0.227109i \(-0.0729273\pi\)
\(752\) 3.70566 6.41839i 0.135131 0.234055i
\(753\) 7.50961 11.4606i 0.273666 0.417648i
\(754\) −9.47618 16.4132i −0.345102 0.597735i
\(755\) 0.548051 0.0199456
\(756\) −70.0174 11.9745i −2.54651 0.435509i
\(757\) −41.4462 −1.50639 −0.753194 0.657799i \(-0.771488\pi\)
−0.753194 + 0.657799i \(0.771488\pi\)
\(758\) −30.9000 53.5204i −1.12234 1.94395i
\(759\) 0 0
\(760\) 4.45217 7.71139i 0.161497 0.279721i
\(761\) 25.2996 43.8202i 0.917111 1.58848i 0.113329 0.993558i \(-0.463849\pi\)
0.803782 0.594925i \(-0.202818\pi\)
\(762\) −1.01526 0.0573837i −0.0367790 0.00207879i
\(763\) −31.8823 55.2217i −1.15422 1.99916i
\(764\) 67.7784 2.45214
\(765\) 20.0918 + 2.27850i 0.726420 + 0.0823793i
\(766\) −3.81033 −0.137673
\(767\) −14.6392 25.3559i −0.528592 0.915549i
\(768\) −18.1486 35.9828i −0.654882 1.29842i
\(769\) −2.68893 + 4.65736i −0.0969651 + 0.167949i −0.910427 0.413670i \(-0.864247\pi\)
0.813462 + 0.581618i \(0.197580\pi\)
\(770\) 0 0
\(771\) 8.13787 + 16.1347i 0.293078 + 0.581078i
\(772\) −19.2173 33.2854i −0.691647 1.19797i
\(773\) 9.31573 0.335063 0.167532 0.985867i \(-0.446420\pi\)
0.167532 + 0.985867i \(0.446420\pi\)
\(774\) −5.76462 0.653734i −0.207205 0.0234980i
\(775\) −3.74331 −0.134464
\(776\) −16.3410 28.3034i −0.586607 1.01603i
\(777\) −62.8860 3.55439i −2.25602 0.127513i
\(778\) 8.38522 14.5236i 0.300625 0.520697i
\(779\) −2.85396 + 4.94320i −0.102254 + 0.177109i
\(780\) 28.2161 43.0613i 1.01030 1.54184i
\(781\) 0 0
\(782\) 80.0581 2.86287
\(783\) −2.67718 7.23928i −0.0956747 0.258711i
\(784\) 10.4167 0.372025
\(785\) −8.07628 13.9885i −0.288255 0.499272i
\(786\) 23.3780 35.6778i 0.833866 1.27258i
\(787\) 10.0907 17.4777i 0.359696 0.623012i −0.628214 0.778041i \(-0.716214\pi\)
0.987910 + 0.155029i \(0.0495471\pi\)
\(788\) 36.3183 62.9051i 1.29378 2.24090i
\(789\) −44.8907 2.53727i −1.59815 0.0903293i
\(790\) −18.1291 31.4006i −0.645006 1.11718i
\(791\) 8.39947 0.298651
\(792\) 0 0
\(793\) 72.3890 2.57061
\(794\) 33.1489 + 57.4155i 1.17641 + 2.03760i
\(795\) 13.0688 + 25.9112i 0.463504 + 0.918976i
\(796\) 8.50221 14.7263i 0.301353 0.521958i
\(797\) −4.88362 + 8.45869i −0.172987 + 0.299622i −0.939463 0.342651i \(-0.888675\pi\)
0.766476 + 0.642273i \(0.222008\pi\)
\(798\) 11.5577 + 22.9152i 0.409139 + 0.811188i
\(799\) −12.6464 21.9043i −0.447399 0.774917i
\(800\) 10.4779 0.370451
\(801\) −4.15688 9.54648i −0.146876 0.337308i
\(802\) 9.75913 0.344607
\(803\) 0 0
\(804\) −20.5694 1.16261i −0.725427 0.0410020i
\(805\) −24.0415 + 41.6411i −0.847353 + 1.46766i
\(806\) 9.30499 16.1167i 0.327754 0.567687i
\(807\) −18.9672 + 28.9463i −0.667677 + 1.01896i
\(808\) 6.21759 + 10.7692i 0.218734 + 0.378858i
\(809\) 4.69697 0.165137 0.0825683 0.996585i \(-0.473688\pi\)
0.0825683 + 0.996585i \(0.473688\pi\)
\(810\) 22.4372 24.1116i 0.788363 0.847195i
\(811\) 36.1706 1.27012 0.635060 0.772463i \(-0.280975\pi\)
0.635060 + 0.772463i \(0.280975\pi\)
\(812\) 10.1532 + 17.5858i 0.356307 + 0.617142i
\(813\) −0.281209 + 0.429160i −0.00986241 + 0.0150513i
\(814\) 0 0
\(815\) 16.6975 28.9210i 0.584890 1.01306i
\(816\) 9.45936 + 0.534654i 0.331144 + 0.0187166i
\(817\) 0.667173 + 1.15558i 0.0233414 + 0.0404286i
\(818\) −63.0744 −2.20535
\(819\) 25.4197 + 58.3776i 0.888236 + 2.03988i
\(820\) −19.2715 −0.672990
\(821\) −6.91422 11.9758i −0.241308 0.417958i 0.719779 0.694203i \(-0.244243\pi\)
−0.961087 + 0.276245i \(0.910910\pi\)
\(822\) 20.0918 + 39.8354i 0.700782 + 1.38942i
\(823\) 22.1891 38.4326i 0.773463 1.33968i −0.162192 0.986759i \(-0.551856\pi\)
0.935654 0.352917i \(-0.114810\pi\)
\(824\) 14.7465 25.5416i 0.513718 0.889785i
\(825\) 0 0
\(826\) 24.6398 + 42.6775i 0.857330 + 1.48494i
\(827\) 22.5598 0.784483 0.392241 0.919862i \(-0.371700\pi\)
0.392241 + 0.919862i \(0.371700\pi\)
\(828\) 49.3419 66.7549i 1.71475 2.31989i
\(829\) −40.8016 −1.41710 −0.708549 0.705662i \(-0.750650\pi\)
−0.708549 + 0.705662i \(0.750650\pi\)
\(830\) 8.70766 + 15.0821i 0.302247 + 0.523508i
\(831\) 45.9631 + 2.59789i 1.59444 + 0.0901197i
\(832\) −32.9315 + 57.0390i −1.14169 + 1.97747i
\(833\) 17.7747 30.7867i 0.615858 1.06670i
\(834\) −17.4942 + 26.6983i −0.605774 + 0.924487i
\(835\) −11.3081 19.5863i −0.391334 0.677811i
\(836\) 0 0
\(837\) 4.84173 5.83087i 0.167355 0.201544i
\(838\) −39.6028 −1.36806
\(839\) 20.8365 + 36.0899i 0.719357 + 1.24596i 0.961255 + 0.275661i \(0.0888967\pi\)
−0.241898 + 0.970302i \(0.577770\pi\)
\(840\) −20.3783 + 31.0999i −0.703119 + 1.07305i
\(841\) 13.3968 23.2039i 0.461958 0.800134i
\(842\) 38.7122 67.0516i 1.33411 2.31075i
\(843\) 11.7717 + 0.665349i 0.405438 + 0.0229158i
\(844\) −7.56655 13.1056i −0.260451 0.451115i
\(845\) −25.8665 −0.889834
\(846\) −40.9359 4.64231i −1.40740 0.159606i
\(847\) 0 0
\(848\) 6.79884 + 11.7759i 0.233473 + 0.404388i
\(849\) −1.61912 3.21018i −0.0555681 0.110173i
\(850\) −13.0062 + 22.5275i −0.446110 + 0.772686i
\(851\) 36.8033 63.7451i 1.26160 2.18515i
\(852\) −17.1113 33.9261i −0.586224 1.16229i
\(853\) 5.52310 + 9.56628i 0.189107 + 0.327543i 0.944953 0.327207i \(-0.106107\pi\)
−0.755846 + 0.654750i \(0.772774\pi\)
\(854\) −121.841 −4.16930
\(855\) −7.52701 0.853597i −0.257418 0.0291924i
\(856\) 24.0314 0.821376
\(857\) 2.17038 + 3.75922i 0.0741389 + 0.128412i 0.900711 0.434418i \(-0.143046\pi\)
−0.826573 + 0.562830i \(0.809713\pi\)
\(858\) 0 0
\(859\) 21.7145 37.6105i 0.740888 1.28325i −0.211204 0.977442i \(-0.567738\pi\)
0.952092 0.305813i \(-0.0989282\pi\)
\(860\) −2.25256 + 3.90155i −0.0768116 + 0.133042i
\(861\) 13.0631 19.9359i 0.445188 0.679412i
\(862\) 12.9721 + 22.4683i 0.441831 + 0.765273i
\(863\) −8.21888 −0.279774 −0.139887 0.990167i \(-0.544674\pi\)
−0.139887 + 0.990167i \(0.544674\pi\)
\(864\) −13.5525 + 16.3213i −0.461067 + 0.555260i
\(865\) 15.8174 0.537807
\(866\) −33.0167 57.1867i −1.12195 1.94328i
\(867\) 1.58336 2.41641i 0.0537739 0.0820657i
\(868\) −9.96977 + 17.2681i −0.338396 + 0.586119i
\(869\) 0 0
\(870\) −9.40044 0.531323i −0.318705 0.0180135i
\(871\) 9.23348 + 15.9929i 0.312865 + 0.541897i
\(872\) 57.6218 1.95132
\(873\) −16.5266 + 22.3589i −0.559340 + 0.756734i
\(874\) −29.9922 −1.01450
\(875\) −23.0305 39.8899i −0.778572 1.34853i
\(876\) −2.91573 5.78094i −0.0985136 0.195320i
\(877\) −9.76218 + 16.9086i −0.329645 + 0.570962i −0.982441 0.186571i \(-0.940262\pi\)
0.652796 + 0.757534i \(0.273596\pi\)
\(878\) −2.19202 + 3.79669i −0.0739771 + 0.128132i
\(879\) 2.36887 + 4.69669i 0.0799001 + 0.158416i
\(880\) 0 0
\(881\) −31.7440 −1.06948 −0.534742 0.845016i \(-0.679591\pi\)
−0.534742 + 0.845016i \(0.679591\pi\)
\(882\) −23.1173 53.0900i −0.778400 1.78763i
\(883\) 10.5442 0.354842 0.177421 0.984135i \(-0.443225\pi\)
0.177421 + 0.984135i \(0.443225\pi\)
\(884\) −41.1615 71.2938i −1.38441 2.39787i
\(885\) −14.5222 0.820813i −0.488159 0.0275913i
\(886\) −22.7798 + 39.4558i −0.765302 + 1.32554i
\(887\) 22.6002 39.1447i 0.758841 1.31435i −0.184601 0.982814i \(-0.559099\pi\)
0.943442 0.331538i \(-0.107567\pi\)
\(888\) 31.1956 47.6084i 1.04685 1.59763i
\(889\) −0.488305 0.845768i −0.0163772 0.0283662i
\(890\) −12.7015 −0.425755
\(891\) 0 0
\(892\) 25.9852 0.870048
\(893\) 4.73775 + 8.20602i 0.158543 + 0.274604i
\(894\) −17.0755 + 26.0593i −0.571090 + 0.871555i
\(895\) −1.80231 + 3.12169i −0.0602446 + 0.104347i
\(896\) 39.4962 68.4094i 1.31948 2.28540i
\(897\) −74.2890 4.19890i −2.48044 0.140197i
\(898\) −18.3554 31.7924i −0.612527 1.06093i
\(899\) −2.16660 −0.0722602
\(900\) 10.7680 + 24.7293i 0.358934 + 0.824309i
\(901\) 46.4053 1.54599
\(902\) 0 0
\(903\) −2.50917 4.97485i −0.0834999 0.165553i
\(904\) −3.79515 + 6.57339i −0.126225 + 0.218628i
\(905\) −6.02519 + 10.4359i −0.200284 + 0.346902i
\(906\) −0.642835 1.27453i −0.0213567 0.0423434i
\(907\) −12.7111 22.0162i −0.422064 0.731036i 0.574077 0.818801i \(-0.305361\pi\)
−0.996141 + 0.0877648i \(0.972028\pi\)
\(908\) 9.17811 0.304586
\(909\) 6.28821 8.50735i 0.208567 0.282171i
\(910\) 77.6708 2.57476
\(911\) −9.48804 16.4338i −0.314353 0.544475i 0.664947 0.746891i \(-0.268454\pi\)
−0.979300 + 0.202416i \(0.935121\pi\)
\(912\) −3.54377 0.200298i −0.117346 0.00663252i
\(913\) 0 0
\(914\) −12.7212 + 22.0338i −0.420780 + 0.728813i
\(915\) 19.7101 30.0801i 0.651596 0.994418i
\(916\) −20.1603 34.9186i −0.666114 1.15374i
\(917\) 40.9656 1.35280
\(918\) −18.2678 49.3973i −0.602926 1.63035i
\(919\) 29.5351 0.974272 0.487136 0.873326i \(-0.338042\pi\)
0.487136 + 0.873326i \(0.338042\pi\)
\(920\) −21.7255 37.6296i −0.716268 1.24061i
\(921\) −17.0412 + 26.0070i −0.561527 + 0.856961i
\(922\) 46.3576 80.2938i 1.52671 2.64434i
\(923\) −17.0295 + 29.4959i −0.560532 + 0.970870i
\(924\) 0 0
\(925\) 11.9581 + 20.7121i 0.393180 + 0.681008i
\(926\) 55.4544 1.82235
\(927\) −24.9309 2.82728i −0.818839 0.0928600i
\(928\) 6.06456 0.199079
\(929\) 3.79837 + 6.57896i 0.124620 + 0.215849i 0.921584 0.388178i \(-0.126895\pi\)
−0.796964 + 0.604027i \(0.793562\pi\)
\(930\) −4.16348 8.25481i −0.136526 0.270686i
\(931\) −6.65897 + 11.5337i −0.218239 + 0.378001i
\(932\) 28.9794 50.1938i 0.949253 1.64415i
\(933\) −20.5853 40.8139i −0.673934 1.33619i
\(934\) 2.92075 + 5.05889i 0.0955699 + 0.165532i
\(935\) 0 0
\(936\) −57.1715 6.48351i −1.86871 0.211920i
\(937\) −56.6799 −1.85165 −0.925826 0.377949i \(-0.876629\pi\)
−0.925826 + 0.377949i \(0.876629\pi\)
\(938\) −15.5412 26.9182i −0.507439 0.878910i
\(939\) 14.9552 + 0.845286i 0.488046 + 0.0275849i
\(940\) −15.9959 + 27.7057i −0.521729 + 0.903662i
\(941\) −10.8614 + 18.8125i −0.354072 + 0.613271i −0.986959 0.160974i \(-0.948537\pi\)
0.632887 + 0.774244i \(0.281870\pi\)
\(942\) −23.0582 + 35.1897i −0.751277 + 1.14654i
\(943\) 13.9266 + 24.1216i 0.453513 + 0.785507i
\(944\) −6.81533 −0.221820
\(945\) 31.1792 + 5.33232i 1.01426 + 0.173460i
\(946\) 0 0
\(947\) 21.9773 + 38.0658i 0.714166 + 1.23697i 0.963280 + 0.268497i \(0.0865271\pi\)
−0.249115 + 0.968474i \(0.580140\pi\)
\(948\) −32.9489 + 50.2842i −1.07013 + 1.63315i
\(949\) −2.90179 + 5.02605i −0.0941961 + 0.163152i
\(950\) 4.87254 8.43949i 0.158086 0.273813i
\(951\) 13.4817 + 0.762003i 0.437176 + 0.0247097i
\(952\) 29.7278 + 51.4901i 0.963484 + 1.66880i
\(953\) 13.0139 0.421563 0.210781 0.977533i \(-0.432399\pi\)
0.210781 + 0.977533i \(0.432399\pi\)
\(954\) 44.9292 60.7849i 1.45464 1.96798i
\(955\) −30.1821 −0.976670
\(956\) 9.01200 + 15.6092i 0.291469 + 0.504839i
\(957\) 0 0
\(958\) −13.4895 + 23.3645i −0.435826 + 0.754873i
\(959\) −21.4243 + 37.1079i −0.691825 + 1.19828i
\(960\) 14.7351 + 29.2147i 0.475572 + 0.942902i
\(961\) 14.4363 + 25.0044i 0.465686 + 0.806592i
\(962\) −118.900 −3.83349
\(963\) −8.16201 18.7445i −0.263017 0.604032i
\(964\) 80.6893 2.59883
\(965\) 8.55759 + 14.8222i 0.275479 + 0.477143i
\(966\) 125.039 + 7.06732i 4.02305 + 0.227387i
\(967\) −17.3961 + 30.1309i −0.559420 + 0.968944i 0.438125 + 0.898914i \(0.355643\pi\)
−0.997545 + 0.0700298i \(0.977691\pi\)
\(968\) 0 0
\(969\) −6.63896 + 10.1319i −0.213274 + 0.325483i
\(970\) 16.9584 + 29.3728i 0.544500 + 0.943102i
\(971\) 1.24869 0.0400724 0.0200362 0.999799i \(-0.493622\pi\)
0.0200362 + 0.999799i \(0.493622\pi\)
\(972\) −52.4479 15.2126i −1.68227 0.487945i
\(973\) −30.6552 −0.982762
\(974\) 31.3680 + 54.3309i 1.00509 + 1.74088i
\(975\) 13.2505 20.2219i 0.424356 0.647621i
\(976\) 8.42521 14.5929i 0.269684 0.467107i
\(977\) −7.19890 + 12.4689i −0.230313 + 0.398914i −0.957900 0.287101i \(-0.907308\pi\)
0.727587 + 0.686015i \(0.240642\pi\)
\(978\) −86.8430 4.90846i −2.77693 0.156955i
\(979\) 0 0
\(980\) −44.9650 −1.43635
\(981\) −19.5706 44.9449i −0.624842 1.43498i
\(982\) −27.4511 −0.875998
\(983\) 23.5165 + 40.7318i 0.750060 + 1.29914i 0.947793 + 0.318886i \(0.103309\pi\)
−0.197733 + 0.980256i \(0.563358\pi\)
\(984\) 9.69942 + 19.2308i 0.309206 + 0.613054i
\(985\) −16.1727 + 28.0120i −0.515306 + 0.892537i
\(986\) −7.52791 + 13.0387i −0.239737 + 0.415237i
\(987\) −17.8182 35.3275i −0.567158 1.12449i
\(988\) 15.4204 + 26.7089i 0.490587 + 0.849722i
\(989\) 6.51127 0.207046
\(990\) 0 0
\(991\) 37.6903 1.19727 0.598636 0.801022i \(-0.295710\pi\)
0.598636 + 0.801022i \(0.295710\pi\)
\(992\) 2.97750 + 5.15718i 0.0945356 + 0.163741i
\(993\) −13.4896 0.762446i −0.428079 0.0241955i
\(994\) 28.6629 49.6457i 0.909133 1.57467i
\(995\) −3.78608 + 6.55769i −0.120027 + 0.207893i
\(996\) 15.8258 24.1521i 0.501459 0.765289i
\(997\) −1.81341 3.14093i −0.0574314 0.0994741i 0.835880 0.548912i \(-0.184958\pi\)
−0.893312 + 0.449438i \(0.851624\pi\)
\(998\) −57.9966 −1.83585
\(999\) −47.7297 8.16282i −1.51010 0.258260i
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 1089.2.e.k.364.2 16
9.4 even 3 9801.2.a.bz.1.7 8
9.5 odd 6 9801.2.a.ca.1.2 8
9.7 even 3 inner 1089.2.e.k.727.2 yes 16
11.10 odd 2 inner 1089.2.e.k.364.7 yes 16
99.32 even 6 9801.2.a.ca.1.7 8
99.43 odd 6 inner 1089.2.e.k.727.7 yes 16
99.76 odd 6 9801.2.a.bz.1.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1089.2.e.k.364.2 16 1.1 even 1 trivial
1089.2.e.k.364.7 yes 16 11.10 odd 2 inner
1089.2.e.k.727.2 yes 16 9.7 even 3 inner
1089.2.e.k.727.7 yes 16 99.43 odd 6 inner
9801.2.a.bz.1.2 8 99.76 odd 6
9801.2.a.bz.1.7 8 9.4 even 3
9801.2.a.ca.1.2 8 9.5 odd 6
9801.2.a.ca.1.7 8 99.32 even 6