Properties

Label 693.2.m.i.190.2
Level $693$
Weight $2$
Character 693.190
Analytic conductor $5.534$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [693,2,Mod(64,693)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(693, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("693.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 693.m (of order \(5\), 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: \(5.53363286007\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} - 1175 x^{7} + 2135 x^{6} - 2300 x^{5} + 1850 x^{4} - 925 x^{3} + 700 x^{2} + \cdots + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 190.2
Root \(0.183009 - 0.132964i\) of defining polynomial
Character \(\chi\) \(=\) 693.190
Dual form 693.2.m.i.631.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.183009 - 0.132964i) q^{2} +(-0.602221 + 1.85345i) q^{4} +(-2.01892 - 1.46683i) q^{5} +(0.309017 - 0.951057i) q^{7} +(0.276036 + 0.849550i) q^{8} +O(q^{10})\) \(q+(0.183009 - 0.132964i) q^{2} +(-0.602221 + 1.85345i) q^{4} +(-2.01892 - 1.46683i) q^{5} +(0.309017 - 0.951057i) q^{7} +(0.276036 + 0.849550i) q^{8} -0.564516 q^{10} +(2.66598 + 1.97296i) q^{11} +(-4.15429 + 3.01827i) q^{13} +(-0.0699031 - 0.215140i) q^{14} +(-2.98979 - 2.17221i) q^{16} +(-1.16298 - 0.844956i) q^{17} +(-1.87526 - 5.77147i) q^{19} +(3.93453 - 2.85860i) q^{20} +(0.750229 + 0.00659095i) q^{22} -7.08292 q^{23} +(0.379361 + 1.16755i) q^{25} +(-0.358952 + 1.10474i) q^{26} +(1.57664 + 1.14549i) q^{28} +(-2.01408 + 6.19869i) q^{29} +(-6.22049 + 4.51945i) q^{31} -2.62252 q^{32} -0.325184 q^{34} +(-2.01892 + 1.46683i) q^{35} +(-1.23122 + 3.78932i) q^{37} +(-1.11058 - 0.806887i) q^{38} +(0.688853 - 2.12007i) q^{40} +(-2.08556 - 6.41868i) q^{41} -0.802299 q^{43} +(-5.26228 + 3.75309i) q^{44} +(-1.29624 + 0.941771i) q^{46} +(-2.08655 - 6.42174i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(0.224669 + 0.163231i) q^{50} +(-3.09240 - 9.51742i) q^{52} +(5.32469 - 3.86861i) q^{53} +(-2.48840 - 7.89379i) q^{55} +0.893270 q^{56} +(0.455607 + 1.40221i) q^{58} +(-0.888810 + 2.73548i) q^{59} +(0.691986 + 0.502757i) q^{61} +(-0.537482 + 1.65420i) q^{62} +(5.49964 - 3.99573i) q^{64} +12.8145 q^{65} -1.64668 q^{67} +(2.26645 - 1.64667i) q^{68} +(-0.174445 + 0.536886i) q^{70} +(3.65738 + 2.65724i) q^{71} +(-4.58827 + 14.1212i) q^{73} +(0.278517 + 0.857187i) q^{74} +11.8264 q^{76} +(2.70023 - 1.92582i) q^{77} +(-1.98444 + 1.44178i) q^{79} +(2.84989 + 8.77105i) q^{80} +(-1.23513 - 0.897372i) q^{82} +(1.81851 + 1.32122i) q^{83} +(1.10856 + 3.41180i) q^{85} +(-0.146828 + 0.106677i) q^{86} +(-0.940224 + 2.80949i) q^{88} -1.73566 q^{89} +(1.58680 + 4.88366i) q^{91} +(4.26549 - 13.1278i) q^{92} +(-1.23572 - 0.897800i) q^{94} +(-4.67976 + 14.4028i) q^{95} +(9.77095 - 7.09901i) q^{97} -0.226211 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8} + 12 q^{10} + 3 q^{11} - 7 q^{13} - 2 q^{14} + 17 q^{16} + 5 q^{17} + 19 q^{19} - q^{20} - 33 q^{22} - 32 q^{23} + 7 q^{25} + 27 q^{26} + 4 q^{28} - 3 q^{29} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 4 q^{37} + 5 q^{38} - 10 q^{40} + 10 q^{41} - 8 q^{43} + 38 q^{44} - 42 q^{46} + 23 q^{47} - 4 q^{49} - 52 q^{50} + 33 q^{52} - 4 q^{53} - 12 q^{55} + 20 q^{58} - 17 q^{59} - 7 q^{61} - 79 q^{62} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} - 18 q^{70} + 14 q^{71} - 35 q^{73} + 29 q^{74} + 52 q^{76} + 3 q^{77} + 15 q^{79} + 87 q^{80} + 19 q^{82} - 5 q^{83} + 6 q^{85} + 52 q^{86} + 55 q^{88} - 74 q^{89} + 13 q^{91} + 55 q^{92} - 24 q^{94} - 32 q^{95} + 20 q^{97} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(442\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.183009 0.132964i 0.129407 0.0940195i −0.521199 0.853435i \(-0.674515\pi\)
0.650606 + 0.759416i \(0.274515\pi\)
\(3\) 0 0
\(4\) −0.602221 + 1.85345i −0.301111 + 0.926723i
\(5\) −2.01892 1.46683i −0.902889 0.655987i 0.0363174 0.999340i \(-0.488437\pi\)
−0.939206 + 0.343353i \(0.888437\pi\)
\(6\) 0 0
\(7\) 0.309017 0.951057i 0.116797 0.359466i
\(8\) 0.276036 + 0.849550i 0.0975933 + 0.300361i
\(9\) 0 0
\(10\) −0.564516 −0.178516
\(11\) 2.66598 + 1.97296i 0.803822 + 0.594870i
\(12\) 0 0
\(13\) −4.15429 + 3.01827i −1.15219 + 0.837117i −0.988771 0.149439i \(-0.952253\pi\)
−0.163422 + 0.986556i \(0.552253\pi\)
\(14\) −0.0699031 0.215140i −0.0186824 0.0574985i
\(15\) 0 0
\(16\) −2.98979 2.17221i −0.747449 0.543053i
\(17\) −1.16298 0.844956i −0.282065 0.204932i 0.437753 0.899095i \(-0.355774\pi\)
−0.719817 + 0.694163i \(0.755774\pi\)
\(18\) 0 0
\(19\) −1.87526 5.77147i −0.430215 1.32406i −0.897912 0.440176i \(-0.854916\pi\)
0.467697 0.883889i \(-0.345084\pi\)
\(20\) 3.93453 2.85860i 0.879788 0.639203i
\(21\) 0 0
\(22\) 0.750229 + 0.00659095i 0.159949 + 0.00140520i
\(23\) −7.08292 −1.47689 −0.738446 0.674313i \(-0.764440\pi\)
−0.738446 + 0.674313i \(0.764440\pi\)
\(24\) 0 0
\(25\) 0.379361 + 1.16755i 0.0758722 + 0.233511i
\(26\) −0.358952 + 1.10474i −0.0703962 + 0.216657i
\(27\) 0 0
\(28\) 1.57664 + 1.14549i 0.297956 + 0.216478i
\(29\) −2.01408 + 6.19869i −0.374004 + 1.15107i 0.570143 + 0.821545i \(0.306888\pi\)
−0.944148 + 0.329522i \(0.893112\pi\)
\(30\) 0 0
\(31\) −6.22049 + 4.51945i −1.11723 + 0.811718i −0.983787 0.179338i \(-0.942604\pi\)
−0.133446 + 0.991056i \(0.542604\pi\)
\(32\) −2.62252 −0.463601
\(33\) 0 0
\(34\) −0.325184 −0.0557687
\(35\) −2.01892 + 1.46683i −0.341260 + 0.247940i
\(36\) 0 0
\(37\) −1.23122 + 3.78932i −0.202412 + 0.622960i 0.797398 + 0.603454i \(0.206209\pi\)
−0.999810 + 0.0195059i \(0.993791\pi\)
\(38\) −1.11058 0.806887i −0.180161 0.130894i
\(39\) 0 0
\(40\) 0.688853 2.12007i 0.108917 0.335213i
\(41\) −2.08556 6.41868i −0.325709 1.00243i −0.971120 0.238594i \(-0.923314\pi\)
0.645410 0.763836i \(-0.276686\pi\)
\(42\) 0 0
\(43\) −0.802299 −0.122349 −0.0611747 0.998127i \(-0.519485\pi\)
−0.0611747 + 0.998127i \(0.519485\pi\)
\(44\) −5.26228 + 3.75309i −0.793319 + 0.565799i
\(45\) 0 0
\(46\) −1.29624 + 0.941771i −0.191120 + 0.138857i
\(47\) −2.08655 6.42174i −0.304355 0.936707i −0.979917 0.199405i \(-0.936099\pi\)
0.675563 0.737303i \(-0.263901\pi\)
\(48\) 0 0
\(49\) −0.809017 0.587785i −0.115574 0.0839693i
\(50\) 0.224669 + 0.163231i 0.0317729 + 0.0230844i
\(51\) 0 0
\(52\) −3.09240 9.51742i −0.428838 1.31983i
\(53\) 5.32469 3.86861i 0.731402 0.531394i −0.158605 0.987342i \(-0.550700\pi\)
0.890007 + 0.455948i \(0.150700\pi\)
\(54\) 0 0
\(55\) −2.48840 7.89379i −0.335535 1.06440i
\(56\) 0.893270 0.119368
\(57\) 0 0
\(58\) 0.455607 + 1.40221i 0.0598241 + 0.184120i
\(59\) −0.888810 + 2.73548i −0.115713 + 0.356129i −0.992095 0.125488i \(-0.959950\pi\)
0.876382 + 0.481617i \(0.159950\pi\)
\(60\) 0 0
\(61\) 0.691986 + 0.502757i 0.0885997 + 0.0643715i 0.631203 0.775617i \(-0.282561\pi\)
−0.542604 + 0.839989i \(0.682561\pi\)
\(62\) −0.537482 + 1.65420i −0.0682603 + 0.210084i
\(63\) 0 0
\(64\) 5.49964 3.99573i 0.687455 0.499466i
\(65\) 12.8145 1.58944
\(66\) 0 0
\(67\) −1.64668 −0.201174 −0.100587 0.994928i \(-0.532072\pi\)
−0.100587 + 0.994928i \(0.532072\pi\)
\(68\) 2.26645 1.64667i 0.274848 0.199689i
\(69\) 0 0
\(70\) −0.174445 + 0.536886i −0.0208502 + 0.0641702i
\(71\) 3.65738 + 2.65724i 0.434051 + 0.315357i 0.783267 0.621686i \(-0.213552\pi\)
−0.349216 + 0.937042i \(0.613552\pi\)
\(72\) 0 0
\(73\) −4.58827 + 14.1212i −0.537016 + 1.65277i 0.202236 + 0.979337i \(0.435179\pi\)
−0.739252 + 0.673429i \(0.764821\pi\)
\(74\) 0.278517 + 0.857187i 0.0323769 + 0.0996459i
\(75\) 0 0
\(76\) 11.8264 1.35658
\(77\) 2.70023 1.92582i 0.307720 0.219467i
\(78\) 0 0
\(79\) −1.98444 + 1.44178i −0.223267 + 0.162213i −0.693796 0.720171i \(-0.744063\pi\)
0.470529 + 0.882385i \(0.344063\pi\)
\(80\) 2.84989 + 8.77105i 0.318627 + 0.980633i
\(81\) 0 0
\(82\) −1.23513 0.897372i −0.136397 0.0990982i
\(83\) 1.81851 + 1.32122i 0.199607 + 0.145023i 0.683099 0.730326i \(-0.260632\pi\)
−0.483492 + 0.875349i \(0.660632\pi\)
\(84\) 0 0
\(85\) 1.10856 + 3.41180i 0.120240 + 0.370061i
\(86\) −0.146828 + 0.106677i −0.0158328 + 0.0115032i
\(87\) 0 0
\(88\) −0.940224 + 2.80949i −0.100228 + 0.299492i
\(89\) −1.73566 −0.183980 −0.0919898 0.995760i \(-0.529323\pi\)
−0.0919898 + 0.995760i \(0.529323\pi\)
\(90\) 0 0
\(91\) 1.58680 + 4.88366i 0.166342 + 0.511947i
\(92\) 4.26549 13.1278i 0.444708 1.36867i
\(93\) 0 0
\(94\) −1.23572 0.897800i −0.127454 0.0926010i
\(95\) −4.67976 + 14.4028i −0.480134 + 1.47770i
\(96\) 0 0
\(97\) 9.77095 7.09901i 0.992089 0.720795i 0.0317117 0.999497i \(-0.489904\pi\)
0.960378 + 0.278702i \(0.0899042\pi\)
\(98\) −0.226211 −0.0228508
\(99\) 0 0
\(100\) −2.39246 −0.239246
\(101\) −2.98801 + 2.17091i −0.297318 + 0.216014i −0.726436 0.687234i \(-0.758825\pi\)
0.429118 + 0.903249i \(0.358825\pi\)
\(102\) 0 0
\(103\) −0.355853 + 1.09520i −0.0350632 + 0.107913i −0.967056 0.254563i \(-0.918069\pi\)
0.931993 + 0.362476i \(0.118069\pi\)
\(104\) −3.71090 2.69613i −0.363884 0.264377i
\(105\) 0 0
\(106\) 0.460080 1.41598i 0.0446869 0.137532i
\(107\) −0.360665 1.11001i −0.0348668 0.107309i 0.932108 0.362179i \(-0.117967\pi\)
−0.966975 + 0.254870i \(0.917967\pi\)
\(108\) 0 0
\(109\) 9.30234 0.891003 0.445501 0.895281i \(-0.353025\pi\)
0.445501 + 0.895281i \(0.353025\pi\)
\(110\) −1.50499 1.11377i −0.143495 0.106194i
\(111\) 0 0
\(112\) −2.98979 + 2.17221i −0.282509 + 0.205255i
\(113\) −1.01893 3.13595i −0.0958529 0.295005i 0.891622 0.452780i \(-0.149568\pi\)
−0.987475 + 0.157775i \(0.949568\pi\)
\(114\) 0 0
\(115\) 14.2999 + 10.3895i 1.33347 + 0.968822i
\(116\) −10.2760 7.46596i −0.954104 0.693197i
\(117\) 0 0
\(118\) 0.201059 + 0.618796i 0.0185090 + 0.0569648i
\(119\) −1.16298 + 0.844956i −0.106610 + 0.0774570i
\(120\) 0 0
\(121\) 3.21486 + 10.5197i 0.292260 + 0.956339i
\(122\) 0.193488 0.0175176
\(123\) 0 0
\(124\) −4.63045 14.2511i −0.415827 1.27978i
\(125\) −2.90909 + 8.95326i −0.260197 + 0.800804i
\(126\) 0 0
\(127\) 0.233972 + 0.169990i 0.0207616 + 0.0150842i 0.598118 0.801408i \(-0.295916\pi\)
−0.577356 + 0.816492i \(0.695916\pi\)
\(128\) 2.09601 6.45084i 0.185262 0.570179i
\(129\) 0 0
\(130\) 2.34516 1.70386i 0.205684 0.149438i
\(131\) 16.5059 1.44212 0.721062 0.692871i \(-0.243654\pi\)
0.721062 + 0.692871i \(0.243654\pi\)
\(132\) 0 0
\(133\) −6.06848 −0.526204
\(134\) −0.301357 + 0.218949i −0.0260333 + 0.0189143i
\(135\) 0 0
\(136\) 0.396808 1.22125i 0.0340260 0.104721i
\(137\) 7.54479 + 5.48161i 0.644595 + 0.468326i 0.861426 0.507883i \(-0.169572\pi\)
−0.216831 + 0.976209i \(0.569572\pi\)
\(138\) 0 0
\(139\) 1.49147 4.59026i 0.126505 0.389341i −0.867668 0.497145i \(-0.834382\pi\)
0.994172 + 0.107804i \(0.0343818\pi\)
\(140\) −1.50286 4.62532i −0.127015 0.390911i
\(141\) 0 0
\(142\) 1.02265 0.0858189
\(143\) −17.0302 0.149614i −1.42413 0.0125114i
\(144\) 0 0
\(145\) 13.1587 9.56035i 1.09277 0.793944i
\(146\) 1.03792 + 3.19438i 0.0858987 + 0.264369i
\(147\) 0 0
\(148\) −6.28183 4.56401i −0.516363 0.375160i
\(149\) 0.745845 + 0.541888i 0.0611020 + 0.0443932i 0.617917 0.786243i \(-0.287977\pi\)
−0.556815 + 0.830637i \(0.687977\pi\)
\(150\) 0 0
\(151\) 5.59210 + 17.2107i 0.455079 + 1.40059i 0.871043 + 0.491207i \(0.163444\pi\)
−0.415964 + 0.909381i \(0.636556\pi\)
\(152\) 4.38551 3.18626i 0.355712 0.258440i
\(153\) 0 0
\(154\) 0.238102 0.711474i 0.0191868 0.0573322i
\(155\) 19.1880 1.54121
\(156\) 0 0
\(157\) −3.79267 11.6726i −0.302688 0.931577i −0.980530 0.196369i \(-0.937085\pi\)
0.677842 0.735207i \(-0.262915\pi\)
\(158\) −0.171466 + 0.527718i −0.0136411 + 0.0419830i
\(159\) 0 0
\(160\) 5.29467 + 3.84680i 0.418580 + 0.304116i
\(161\) −2.18874 + 6.73626i −0.172497 + 0.530892i
\(162\) 0 0
\(163\) −6.55233 + 4.76055i −0.513218 + 0.372875i −0.814043 0.580804i \(-0.802738\pi\)
0.300825 + 0.953679i \(0.402738\pi\)
\(164\) 13.1526 1.02705
\(165\) 0 0
\(166\) 0.508478 0.0394655
\(167\) −10.5590 + 7.67154i −0.817077 + 0.593641i −0.915874 0.401466i \(-0.868501\pi\)
0.0987965 + 0.995108i \(0.468501\pi\)
\(168\) 0 0
\(169\) 4.13096 12.7138i 0.317766 0.977985i
\(170\) 0.656522 + 0.476991i 0.0503529 + 0.0365835i
\(171\) 0 0
\(172\) 0.483161 1.48702i 0.0368407 0.113384i
\(173\) −1.82697 5.62283i −0.138902 0.427496i 0.857275 0.514859i \(-0.172156\pi\)
−0.996176 + 0.0873636i \(0.972156\pi\)
\(174\) 0 0
\(175\) 1.22764 0.0928007
\(176\) −3.68503 11.6898i −0.277770 0.881153i
\(177\) 0 0
\(178\) −0.317641 + 0.230780i −0.0238082 + 0.0172977i
\(179\) −1.33961 4.12290i −0.100127 0.308160i 0.888429 0.459015i \(-0.151798\pi\)
−0.988556 + 0.150854i \(0.951798\pi\)
\(180\) 0 0
\(181\) −8.76223 6.36613i −0.651291 0.473191i 0.212420 0.977179i \(-0.431866\pi\)
−0.863711 + 0.503988i \(0.831866\pi\)
\(182\) 0.939748 + 0.682767i 0.0696587 + 0.0506100i
\(183\) 0 0
\(184\) −1.95514 6.01730i −0.144135 0.443601i
\(185\) 8.04404 5.84433i 0.591409 0.429684i
\(186\) 0 0
\(187\) −1.43342 4.54715i −0.104822 0.332520i
\(188\) 13.1589 0.959713
\(189\) 0 0
\(190\) 1.05862 + 3.25808i 0.0768000 + 0.236366i
\(191\) −3.60178 + 11.0851i −0.260616 + 0.802093i 0.732055 + 0.681245i \(0.238561\pi\)
−0.992671 + 0.120848i \(0.961439\pi\)
\(192\) 0 0
\(193\) −18.1587 13.1931i −1.30709 0.949659i −0.307096 0.951679i \(-0.599357\pi\)
−0.999998 + 0.00201912i \(0.999357\pi\)
\(194\) 0.844259 2.59836i 0.0606143 0.186552i
\(195\) 0 0
\(196\) 1.57664 1.14549i 0.112617 0.0818209i
\(197\) −24.1022 −1.71721 −0.858604 0.512639i \(-0.828668\pi\)
−0.858604 + 0.512639i \(0.828668\pi\)
\(198\) 0 0
\(199\) 18.7205 1.32706 0.663531 0.748148i \(-0.269057\pi\)
0.663531 + 0.748148i \(0.269057\pi\)
\(200\) −0.887178 + 0.644573i −0.0627330 + 0.0455782i
\(201\) 0 0
\(202\) −0.258179 + 0.794593i −0.0181654 + 0.0559074i
\(203\) 5.27292 + 3.83100i 0.370086 + 0.268883i
\(204\) 0 0
\(205\) −5.20455 + 16.0180i −0.363502 + 1.11874i
\(206\) 0.0804979 + 0.247747i 0.00560855 + 0.0172614i
\(207\) 0 0
\(208\) 18.9768 1.31580
\(209\) 6.38746 19.0864i 0.441830 1.32023i
\(210\) 0 0
\(211\) 6.12131 4.44739i 0.421408 0.306171i −0.356796 0.934182i \(-0.616131\pi\)
0.778204 + 0.628011i \(0.216131\pi\)
\(212\) 3.96362 + 12.1988i 0.272223 + 0.837815i
\(213\) 0 0
\(214\) −0.213596 0.155187i −0.0146011 0.0106083i
\(215\) 1.61978 + 1.17684i 0.110468 + 0.0802596i
\(216\) 0 0
\(217\) 2.37602 + 7.31263i 0.161295 + 0.496414i
\(218\) 1.70241 1.23687i 0.115302 0.0837717i
\(219\) 0 0
\(220\) 16.1293 + 0.141700i 1.08744 + 0.00955340i
\(221\) 7.38167 0.496545
\(222\) 0 0
\(223\) 5.41533 + 16.6667i 0.362637 + 1.11608i 0.951447 + 0.307811i \(0.0995966\pi\)
−0.588810 + 0.808271i \(0.700403\pi\)
\(224\) −0.810404 + 2.49417i −0.0541474 + 0.166649i
\(225\) 0 0
\(226\) −0.603440 0.438425i −0.0401403 0.0291636i
\(227\) 7.93471 24.4205i 0.526645 1.62085i −0.234394 0.972142i \(-0.575311\pi\)
0.761039 0.648706i \(-0.224689\pi\)
\(228\) 0 0
\(229\) 16.0484 11.6598i 1.06051 0.770503i 0.0863246 0.996267i \(-0.472488\pi\)
0.974182 + 0.225764i \(0.0724878\pi\)
\(230\) 3.99842 0.263648
\(231\) 0 0
\(232\) −5.82205 −0.382236
\(233\) −16.3539 + 11.8818i −1.07138 + 0.778405i −0.976160 0.217051i \(-0.930356\pi\)
−0.0952219 + 0.995456i \(0.530356\pi\)
\(234\) 0 0
\(235\) −5.20704 + 16.0256i −0.339670 + 1.04540i
\(236\) −4.53480 3.29472i −0.295190 0.214468i
\(237\) 0 0
\(238\) −0.100488 + 0.309269i −0.00651364 + 0.0200469i
\(239\) −5.28431 16.2634i −0.341814 1.05199i −0.963267 0.268544i \(-0.913458\pi\)
0.621454 0.783451i \(-0.286542\pi\)
\(240\) 0 0
\(241\) −24.1529 −1.55582 −0.777912 0.628373i \(-0.783721\pi\)
−0.777912 + 0.628373i \(0.783721\pi\)
\(242\) 1.98709 + 1.49774i 0.127735 + 0.0962786i
\(243\) 0 0
\(244\) −1.34856 + 0.979787i −0.0863328 + 0.0627245i
\(245\) 0.771159 + 2.37338i 0.0492676 + 0.151630i
\(246\) 0 0
\(247\) 25.2102 + 18.3163i 1.60409 + 1.16544i
\(248\) −5.55658 4.03709i −0.352843 0.256356i
\(249\) 0 0
\(250\) 0.658069 + 2.02533i 0.0416200 + 0.128093i
\(251\) 9.62305 6.99156i 0.607402 0.441303i −0.241097 0.970501i \(-0.577507\pi\)
0.848498 + 0.529198i \(0.177507\pi\)
\(252\) 0 0
\(253\) −18.8829 13.9743i −1.18716 0.878558i
\(254\) 0.0654215 0.00410491
\(255\) 0 0
\(256\) 3.72721 + 11.4712i 0.232951 + 0.716949i
\(257\) −7.09531 + 21.8371i −0.442593 + 1.36216i 0.442509 + 0.896764i \(0.354089\pi\)
−0.885102 + 0.465397i \(0.845911\pi\)
\(258\) 0 0
\(259\) 3.22339 + 2.34193i 0.200291 + 0.145520i
\(260\) −7.71715 + 23.7509i −0.478597 + 1.47297i
\(261\) 0 0
\(262\) 3.02072 2.19468i 0.186621 0.135588i
\(263\) −1.93774 −0.119486 −0.0597432 0.998214i \(-0.519028\pi\)
−0.0597432 + 0.998214i \(0.519028\pi\)
\(264\) 0 0
\(265\) −16.4247 −1.00896
\(266\) −1.11058 + 0.806887i −0.0680943 + 0.0494734i
\(267\) 0 0
\(268\) 0.991666 3.05203i 0.0605756 0.186433i
\(269\) 5.81421 + 4.22427i 0.354499 + 0.257558i 0.750754 0.660582i \(-0.229690\pi\)
−0.396255 + 0.918140i \(0.629690\pi\)
\(270\) 0 0
\(271\) 0.368071 1.13281i 0.0223587 0.0688130i −0.939255 0.343221i \(-0.888482\pi\)
0.961613 + 0.274408i \(0.0884819\pi\)
\(272\) 1.64165 + 5.05249i 0.0995398 + 0.306352i
\(273\) 0 0
\(274\) 2.10962 0.127447
\(275\) −1.29217 + 3.86113i −0.0779207 + 0.232835i
\(276\) 0 0
\(277\) −8.36543 + 6.07784i −0.502630 + 0.365182i −0.810021 0.586401i \(-0.800544\pi\)
0.307391 + 0.951583i \(0.400544\pi\)
\(278\) −0.337387 1.03837i −0.0202351 0.0622773i
\(279\) 0 0
\(280\) −1.80344 1.31028i −0.107776 0.0783040i
\(281\) −10.6396 7.73015i −0.634707 0.461142i 0.223321 0.974745i \(-0.428310\pi\)
−0.858028 + 0.513603i \(0.828310\pi\)
\(282\) 0 0
\(283\) 0.0927146 + 0.285346i 0.00551131 + 0.0169621i 0.953774 0.300524i \(-0.0971614\pi\)
−0.948263 + 0.317486i \(0.897161\pi\)
\(284\) −7.12761 + 5.17851i −0.422946 + 0.307288i
\(285\) 0 0
\(286\) −3.13656 + 2.23701i −0.185469 + 0.132277i
\(287\) −6.74900 −0.398381
\(288\) 0 0
\(289\) −4.61471 14.2026i −0.271454 0.835448i
\(290\) 1.13698 3.49926i 0.0667656 0.205483i
\(291\) 0 0
\(292\) −23.4098 17.0082i −1.36995 0.995330i
\(293\) −4.98880 + 15.3539i −0.291449 + 0.896987i 0.692942 + 0.720993i \(0.256314\pi\)
−0.984391 + 0.175994i \(0.943686\pi\)
\(294\) 0 0
\(295\) 5.80692 4.21898i 0.338092 0.245638i
\(296\) −3.55908 −0.206867
\(297\) 0 0
\(298\) 0.208548 0.0120808
\(299\) 29.4245 21.3782i 1.70166 1.23633i
\(300\) 0 0
\(301\) −0.247924 + 0.763031i −0.0142901 + 0.0439804i
\(302\) 3.31180 + 2.40617i 0.190573 + 0.138459i
\(303\) 0 0
\(304\) −6.93020 + 21.3290i −0.397474 + 1.22330i
\(305\) −0.659605 2.03005i −0.0377688 0.116241i
\(306\) 0 0
\(307\) −28.6376 −1.63443 −0.817217 0.576330i \(-0.804484\pi\)
−0.817217 + 0.576330i \(0.804484\pi\)
\(308\) 1.94326 + 6.16449i 0.110728 + 0.351255i
\(309\) 0 0
\(310\) 3.51157 2.55130i 0.199444 0.144904i
\(311\) 9.83377 + 30.2652i 0.557622 + 1.71618i 0.688916 + 0.724841i \(0.258087\pi\)
−0.131294 + 0.991343i \(0.541913\pi\)
\(312\) 0 0
\(313\) −0.0276872 0.0201159i −0.00156497 0.00113702i 0.587002 0.809585i \(-0.300308\pi\)
−0.588567 + 0.808448i \(0.700308\pi\)
\(314\) −2.24613 1.63191i −0.126756 0.0920938i
\(315\) 0 0
\(316\) −1.47719 4.54633i −0.0830985 0.255751i
\(317\) 18.1134 13.1602i 1.01735 0.739149i 0.0516132 0.998667i \(-0.483564\pi\)
0.965738 + 0.259518i \(0.0835637\pi\)
\(318\) 0 0
\(319\) −17.5992 + 12.5519i −0.985368 + 0.702770i
\(320\) −16.9644 −0.948339
\(321\) 0 0
\(322\) 0.495119 + 1.52382i 0.0275919 + 0.0849191i
\(323\) −2.69574 + 8.29662i −0.149995 + 0.461636i
\(324\) 0 0
\(325\) −5.09997 3.70534i −0.282895 0.205535i
\(326\) −0.566155 + 1.74244i −0.0313564 + 0.0965051i
\(327\) 0 0
\(328\) 4.87730 3.54357i 0.269304 0.195661i
\(329\) −6.75222 −0.372262
\(330\) 0 0
\(331\) 10.7577 0.591297 0.295648 0.955297i \(-0.404464\pi\)
0.295648 + 0.955297i \(0.404464\pi\)
\(332\) −3.54396 + 2.57484i −0.194500 + 0.141313i
\(333\) 0 0
\(334\) −0.912348 + 2.80792i −0.0499215 + 0.153642i
\(335\) 3.32452 + 2.41540i 0.181638 + 0.131968i
\(336\) 0 0
\(337\) 2.31915 7.13761i 0.126332 0.388810i −0.867809 0.496897i \(-0.834473\pi\)
0.994141 + 0.108087i \(0.0344726\pi\)
\(338\) −0.934471 2.87601i −0.0508285 0.156434i
\(339\) 0 0
\(340\) −6.99118 −0.379150
\(341\) −25.5004 0.224027i −1.38092 0.0121318i
\(342\) 0 0
\(343\) −0.809017 + 0.587785i −0.0436828 + 0.0317374i
\(344\) −0.221463 0.681593i −0.0119405 0.0367490i
\(345\) 0 0
\(346\) −1.08198 0.786107i −0.0581678 0.0422614i
\(347\) −22.3950 16.2710i −1.20223 0.873471i −0.207727 0.978187i \(-0.566607\pi\)
−0.994502 + 0.104716i \(0.966607\pi\)
\(348\) 0 0
\(349\) −3.41788 10.5192i −0.182955 0.563078i 0.816952 0.576706i \(-0.195662\pi\)
−0.999907 + 0.0136278i \(0.995662\pi\)
\(350\) 0.224669 0.163231i 0.0120090 0.00872508i
\(351\) 0 0
\(352\) −6.99159 5.17413i −0.372653 0.275782i
\(353\) −31.9202 −1.69894 −0.849469 0.527638i \(-0.823078\pi\)
−0.849469 + 0.527638i \(0.823078\pi\)
\(354\) 0 0
\(355\) −3.48623 10.7295i −0.185030 0.569464i
\(356\) 1.04525 3.21695i 0.0553982 0.170498i
\(357\) 0 0
\(358\) −0.793358 0.576408i −0.0419303 0.0304641i
\(359\) −1.10574 + 3.40313i −0.0583590 + 0.179610i −0.975986 0.217831i \(-0.930102\pi\)
0.917628 + 0.397441i \(0.130102\pi\)
\(360\) 0 0
\(361\) −14.4219 + 10.4781i −0.759046 + 0.551479i
\(362\) −2.45003 −0.128771
\(363\) 0 0
\(364\) −10.0072 −0.524520
\(365\) 29.9768 21.7794i 1.56906 1.13999i
\(366\) 0 0
\(367\) 0.708875 2.18169i 0.0370030 0.113883i −0.930849 0.365404i \(-0.880931\pi\)
0.967852 + 0.251521i \(0.0809307\pi\)
\(368\) 21.1765 + 15.3856i 1.10390 + 0.802031i
\(369\) 0 0
\(370\) 0.695045 2.13913i 0.0361337 0.111208i
\(371\) −2.03385 6.25954i −0.105592 0.324979i
\(372\) 0 0
\(373\) 7.96856 0.412596 0.206298 0.978489i \(-0.433858\pi\)
0.206298 + 0.978489i \(0.433858\pi\)
\(374\) −0.866934 0.641576i −0.0448281 0.0331751i
\(375\) 0 0
\(376\) 4.87963 3.54526i 0.251648 0.182833i
\(377\) −10.3423 31.8302i −0.532653 1.63934i
\(378\) 0 0
\(379\) 9.40174 + 6.83077i 0.482935 + 0.350873i 0.802461 0.596705i \(-0.203524\pi\)
−0.319526 + 0.947578i \(0.603524\pi\)
\(380\) −23.8766 17.3474i −1.22484 0.889902i
\(381\) 0 0
\(382\) 0.814764 + 2.50759i 0.0416869 + 0.128299i
\(383\) 10.1762 7.39343i 0.519979 0.377787i −0.296617 0.954996i \(-0.595859\pi\)
0.816596 + 0.577210i \(0.195859\pi\)
\(384\) 0 0
\(385\) −8.27640 0.0727103i −0.421804 0.00370566i
\(386\) −5.07741 −0.258433
\(387\) 0 0
\(388\) 7.27336 + 22.3851i 0.369249 + 1.13643i
\(389\) 0.135440 0.416842i 0.00686709 0.0211347i −0.947564 0.319565i \(-0.896463\pi\)
0.954431 + 0.298431i \(0.0964631\pi\)
\(390\) 0 0
\(391\) 8.23731 + 5.98476i 0.416579 + 0.302662i
\(392\) 0.276036 0.849550i 0.0139419 0.0429088i
\(393\) 0 0
\(394\) −4.41091 + 3.20471i −0.222218 + 0.161451i
\(395\) 6.12128 0.307995
\(396\) 0 0
\(397\) 16.8147 0.843905 0.421952 0.906618i \(-0.361345\pi\)
0.421952 + 0.906618i \(0.361345\pi\)
\(398\) 3.42602 2.48915i 0.171731 0.124770i
\(399\) 0 0
\(400\) 1.40196 4.31480i 0.0700981 0.215740i
\(401\) 29.8211 + 21.6663i 1.48919 + 1.08196i 0.974446 + 0.224621i \(0.0721143\pi\)
0.514747 + 0.857342i \(0.327886\pi\)
\(402\) 0 0
\(403\) 12.2008 37.5502i 0.607766 1.87051i
\(404\) −2.22423 6.84548i −0.110660 0.340575i
\(405\) 0 0
\(406\) 1.47437 0.0731720
\(407\) −10.7586 + 7.67308i −0.533283 + 0.380340i
\(408\) 0 0
\(409\) −13.1659 + 9.56556i −0.651010 + 0.472986i −0.863615 0.504152i \(-0.831805\pi\)
0.212605 + 0.977138i \(0.431805\pi\)
\(410\) 1.17733 + 3.62345i 0.0581441 + 0.178949i
\(411\) 0 0
\(412\) −1.81559 1.31911i −0.0894479 0.0649877i
\(413\) 2.32694 + 1.69062i 0.114501 + 0.0831898i
\(414\) 0 0
\(415\) −1.73341 5.33489i −0.0850898 0.261879i
\(416\) 10.8947 7.91548i 0.534158 0.388088i
\(417\) 0 0
\(418\) −1.36884 4.34228i −0.0669520 0.212388i
\(419\) −5.56352 −0.271796 −0.135898 0.990723i \(-0.543392\pi\)
−0.135898 + 0.990723i \(0.543392\pi\)
\(420\) 0 0
\(421\) 6.64120 + 20.4395i 0.323672 + 0.996161i 0.972036 + 0.234831i \(0.0754536\pi\)
−0.648364 + 0.761331i \(0.724546\pi\)
\(422\) 0.528912 1.62782i 0.0257470 0.0792412i
\(423\) 0 0
\(424\) 4.75638 + 3.45571i 0.230990 + 0.167824i
\(425\) 0.545341 1.67839i 0.0264529 0.0814137i
\(426\) 0 0
\(427\) 0.691986 0.502757i 0.0334875 0.0243301i
\(428\) 2.27455 0.109944
\(429\) 0 0
\(430\) 0.452910 0.0218413
\(431\) −22.4249 + 16.2927i −1.08017 + 0.784791i −0.977713 0.209947i \(-0.932671\pi\)
−0.102459 + 0.994737i \(0.532671\pi\)
\(432\) 0 0
\(433\) 2.87019 8.83352i 0.137932 0.424512i −0.858102 0.513479i \(-0.828356\pi\)
0.996035 + 0.0889667i \(0.0283565\pi\)
\(434\) 1.40715 + 1.02235i 0.0675452 + 0.0490744i
\(435\) 0 0
\(436\) −5.60207 + 17.2414i −0.268290 + 0.825713i
\(437\) 13.2823 + 40.8788i 0.635380 + 1.95550i
\(438\) 0 0
\(439\) −14.7118 −0.702156 −0.351078 0.936346i \(-0.614185\pi\)
−0.351078 + 0.936346i \(0.614185\pi\)
\(440\) 6.01928 4.29298i 0.286958 0.204660i
\(441\) 0 0
\(442\) 1.35091 0.981494i 0.0642563 0.0466849i
\(443\) −0.755067 2.32386i −0.0358743 0.110410i 0.931516 0.363701i \(-0.118487\pi\)
−0.967390 + 0.253291i \(0.918487\pi\)
\(444\) 0 0
\(445\) 3.50416 + 2.54592i 0.166113 + 0.120688i
\(446\) 3.20712 + 2.33011i 0.151861 + 0.110334i
\(447\) 0 0
\(448\) −2.10068 6.46522i −0.0992477 0.305453i
\(449\) 3.85849 2.80335i 0.182093 0.132298i −0.493005 0.870027i \(-0.664101\pi\)
0.675098 + 0.737728i \(0.264101\pi\)
\(450\) 0 0
\(451\) 7.10376 21.2268i 0.334503 0.999530i
\(452\) 6.42593 0.302250
\(453\) 0 0
\(454\) −1.79492 5.52420i −0.0842398 0.259264i
\(455\) 3.95989 12.1873i 0.185643 0.571349i
\(456\) 0 0
\(457\) −25.1503 18.2728i −1.17648 0.854764i −0.184712 0.982793i \(-0.559135\pi\)
−0.991770 + 0.128028i \(0.959135\pi\)
\(458\) 1.38666 4.26770i 0.0647944 0.199417i
\(459\) 0 0
\(460\) −27.8680 + 20.2473i −1.29935 + 0.944034i
\(461\) −29.7215 −1.38427 −0.692134 0.721769i \(-0.743329\pi\)
−0.692134 + 0.721769i \(0.743329\pi\)
\(462\) 0 0
\(463\) −25.4553 −1.18301 −0.591505 0.806302i \(-0.701466\pi\)
−0.591505 + 0.806302i \(0.701466\pi\)
\(464\) 19.4865 14.1578i 0.904640 0.657259i
\(465\) 0 0
\(466\) −1.41306 + 4.34896i −0.0654589 + 0.201462i
\(467\) −2.57665 1.87204i −0.119233 0.0866279i 0.526571 0.850131i \(-0.323478\pi\)
−0.645804 + 0.763503i \(0.723478\pi\)
\(468\) 0 0
\(469\) −0.508852 + 1.56609i −0.0234966 + 0.0723151i
\(470\) 1.17789 + 3.62517i 0.0543320 + 0.167217i
\(471\) 0 0
\(472\) −2.56927 −0.118260
\(473\) −2.13891 1.58290i −0.0983472 0.0727820i
\(474\) 0 0
\(475\) 6.02709 4.37894i 0.276542 0.200920i
\(476\) −0.865708 2.66437i −0.0396796 0.122121i
\(477\) 0 0
\(478\) −3.12952 2.27373i −0.143141 0.103998i
\(479\) 2.61599 + 1.90062i 0.119527 + 0.0868418i 0.645943 0.763386i \(-0.276464\pi\)
−0.526416 + 0.850227i \(0.676464\pi\)
\(480\) 0 0
\(481\) −6.32232 19.4581i −0.288273 0.887213i
\(482\) −4.42019 + 3.21146i −0.201334 + 0.146278i
\(483\) 0 0
\(484\) −21.4338 0.376632i −0.974264 0.0171196i
\(485\) −30.1398 −1.36858
\(486\) 0 0
\(487\) 3.05029 + 9.38784i 0.138222 + 0.425404i 0.996077 0.0884878i \(-0.0282034\pi\)
−0.857855 + 0.513891i \(0.828203\pi\)
\(488\) −0.236105 + 0.726655i −0.0106880 + 0.0328941i
\(489\) 0 0
\(490\) 0.456703 + 0.331814i 0.0206317 + 0.0149898i
\(491\) −1.30591 + 4.01917i −0.0589348 + 0.181383i −0.976190 0.216918i \(-0.930400\pi\)
0.917255 + 0.398300i \(0.130400\pi\)
\(492\) 0 0
\(493\) 7.57995 5.50716i 0.341384 0.248030i
\(494\) 7.04910 0.317154
\(495\) 0 0
\(496\) 28.4152 1.27588
\(497\) 3.65738 2.65724i 0.164056 0.119194i
\(498\) 0 0
\(499\) −6.30249 + 19.3971i −0.282138 + 0.868332i 0.705104 + 0.709104i \(0.250900\pi\)
−0.987242 + 0.159228i \(0.949100\pi\)
\(500\) −14.8425 10.7837i −0.663776 0.482261i
\(501\) 0 0
\(502\) 0.831480 2.55903i 0.0371108 0.114215i
\(503\) 7.40382 + 22.7866i 0.330120 + 1.01600i 0.969076 + 0.246762i \(0.0793665\pi\)
−0.638956 + 0.769243i \(0.720634\pi\)
\(504\) 0 0
\(505\) 9.21692 0.410147
\(506\) −5.31381 0.0466832i −0.236228 0.00207532i
\(507\) 0 0
\(508\) −0.455971 + 0.331282i −0.0202304 + 0.0146983i
\(509\) −1.14133 3.51264i −0.0505884 0.155695i 0.922571 0.385828i \(-0.126084\pi\)
−0.973159 + 0.230132i \(0.926084\pi\)
\(510\) 0 0
\(511\) 12.0122 + 8.72740i 0.531390 + 0.386078i
\(512\) 13.1822 + 9.57742i 0.582576 + 0.423266i
\(513\) 0 0
\(514\) 1.60504 + 4.93980i 0.0707952 + 0.217885i
\(515\) 2.32491 1.68915i 0.102448 0.0744328i
\(516\) 0 0
\(517\) 7.10714 21.2369i 0.312572 0.933997i
\(518\) 0.901299 0.0396008
\(519\) 0 0
\(520\) 3.53725 + 10.8865i 0.155119 + 0.477406i
\(521\) 0.0736294 0.226608i 0.00322576 0.00992787i −0.949431 0.313977i \(-0.898339\pi\)
0.952656 + 0.304049i \(0.0983386\pi\)
\(522\) 0 0
\(523\) 17.7914 + 12.9262i 0.777966 + 0.565225i 0.904368 0.426754i \(-0.140343\pi\)
−0.126402 + 0.991979i \(0.540343\pi\)
\(524\) −9.94018 + 30.5927i −0.434239 + 1.33645i
\(525\) 0 0
\(526\) −0.354624 + 0.257649i −0.0154623 + 0.0112340i
\(527\) 11.0531 0.481479
\(528\) 0 0
\(529\) 27.1678 1.18121
\(530\) −3.00587 + 2.18389i −0.130567 + 0.0948622i
\(531\) 0 0
\(532\) 3.65457 11.2476i 0.158446 0.487645i
\(533\) 28.0373 + 20.3703i 1.21443 + 0.882336i
\(534\) 0 0
\(535\) −0.900048 + 2.77006i −0.0389125 + 0.119760i
\(536\) −0.454542 1.39894i −0.0196332 0.0604249i
\(537\) 0 0
\(538\) 1.62573 0.0700900
\(539\) −0.997144 3.16318i −0.0429500 0.136248i
\(540\) 0 0
\(541\) −23.1629 + 16.8288i −0.995851 + 0.723528i −0.961195 0.275871i \(-0.911034\pi\)
−0.0346561 + 0.999399i \(0.511034\pi\)
\(542\) −0.0832618 0.256253i −0.00357640 0.0110070i
\(543\) 0 0
\(544\) 3.04995 + 2.21592i 0.130765 + 0.0950066i
\(545\) −18.7807 13.6450i −0.804477 0.584486i
\(546\) 0 0
\(547\) 1.98033 + 6.09482i 0.0846727 + 0.260596i 0.984425 0.175805i \(-0.0562529\pi\)
−0.899752 + 0.436401i \(0.856253\pi\)
\(548\) −14.7035 + 10.6827i −0.628103 + 0.456343i
\(549\) 0 0
\(550\) 0.276913 + 0.878433i 0.0118076 + 0.0374565i
\(551\) 39.5524 1.68499
\(552\) 0 0
\(553\) 0.757990 + 2.33285i 0.0322330 + 0.0992030i
\(554\) −0.722815 + 2.22460i −0.0307095 + 0.0945141i
\(555\) 0 0
\(556\) 7.60961 + 5.52871i 0.322719 + 0.234469i
\(557\) 6.95884 21.4171i 0.294855 0.907471i −0.688415 0.725317i \(-0.741693\pi\)
0.983270 0.182154i \(-0.0583070\pi\)
\(558\) 0 0
\(559\) 3.33298 2.42155i 0.140970 0.102421i
\(560\) 9.22243 0.389719
\(561\) 0 0
\(562\) −2.97498 −0.125492
\(563\) −24.1303 + 17.5317i −1.01697 + 0.738873i −0.965660 0.259810i \(-0.916340\pi\)
−0.0513116 + 0.998683i \(0.516340\pi\)
\(564\) 0 0
\(565\) −2.54277 + 7.82583i −0.106975 + 0.329235i
\(566\) 0.0549082 + 0.0398932i 0.00230797 + 0.00167684i
\(567\) 0 0
\(568\) −1.24789 + 3.84062i −0.0523604 + 0.161149i
\(569\) −9.04690 27.8435i −0.379266 1.16726i −0.940555 0.339640i \(-0.889695\pi\)
0.561290 0.827619i \(-0.310305\pi\)
\(570\) 0 0
\(571\) 37.9252 1.58712 0.793559 0.608493i \(-0.208226\pi\)
0.793559 + 0.608493i \(0.208226\pi\)
\(572\) 10.5332 31.4744i 0.440416 1.31601i
\(573\) 0 0
\(574\) −1.23513 + 0.897372i −0.0515532 + 0.0374556i
\(575\) −2.68699 8.26969i −0.112055 0.344870i
\(576\) 0 0
\(577\) −7.09721 5.15642i −0.295461 0.214665i 0.430172 0.902747i \(-0.358453\pi\)
−0.725633 + 0.688082i \(0.758453\pi\)
\(578\) −2.73297 1.98562i −0.113676 0.0825908i
\(579\) 0 0
\(580\) 9.79515 + 30.1464i 0.406721 + 1.25176i
\(581\) 1.81851 1.32122i 0.0754444 0.0548136i
\(582\) 0 0
\(583\) 21.8281 + 0.191765i 0.904027 + 0.00794211i
\(584\) −13.2632 −0.548836
\(585\) 0 0
\(586\) 1.12852 + 3.47324i 0.0466189 + 0.143478i
\(587\) −2.83372 + 8.72130i −0.116960 + 0.359966i −0.992351 0.123450i \(-0.960604\pi\)
0.875391 + 0.483416i \(0.160604\pi\)
\(588\) 0 0
\(589\) 37.7489 + 27.4262i 1.55542 + 1.13008i
\(590\) 0.501747 1.54422i 0.0206566 0.0635745i
\(591\) 0 0
\(592\) 11.9123 8.65480i 0.489593 0.355710i
\(593\) −7.25596 −0.297967 −0.148983 0.988840i \(-0.547600\pi\)
−0.148983 + 0.988840i \(0.547600\pi\)
\(594\) 0 0
\(595\) 3.58738 0.147068
\(596\) −1.45352 + 1.05605i −0.0595386 + 0.0432573i
\(597\) 0 0
\(598\) 2.54243 7.82479i 0.103968 0.319979i
\(599\) −16.1949 11.7663i −0.661708 0.480759i 0.205532 0.978650i \(-0.434108\pi\)
−0.867239 + 0.497892i \(0.834108\pi\)
\(600\) 0 0
\(601\) −3.48280 + 10.7189i −0.142066 + 0.437235i −0.996622 0.0821246i \(-0.973829\pi\)
0.854556 + 0.519360i \(0.173829\pi\)
\(602\) 0.0560832 + 0.172606i 0.00228578 + 0.00703491i
\(603\) 0 0
\(604\) −35.2668 −1.43499
\(605\) 8.94012 25.9542i 0.363468 1.05519i
\(606\) 0 0
\(607\) 10.9428 7.95040i 0.444154 0.322697i −0.343129 0.939288i \(-0.611487\pi\)
0.787283 + 0.616591i \(0.211487\pi\)
\(608\) 4.91792 + 15.1358i 0.199448 + 0.613838i
\(609\) 0 0
\(610\) −0.390637 0.283814i −0.0158164 0.0114913i
\(611\) 28.0507 + 20.3800i 1.13481 + 0.824487i
\(612\) 0 0
\(613\) −9.51673 29.2895i −0.384377 1.18299i −0.936931 0.349514i \(-0.886347\pi\)
0.552554 0.833477i \(-0.313653\pi\)
\(614\) −5.24093 + 3.80776i −0.211507 + 0.153669i
\(615\) 0 0
\(616\) 2.38144 + 1.76239i 0.0959508 + 0.0710085i
\(617\) −23.6896 −0.953707 −0.476853 0.878983i \(-0.658223\pi\)
−0.476853 + 0.878983i \(0.658223\pi\)
\(618\) 0 0
\(619\) −10.0393 30.8977i −0.403513 1.24188i −0.922131 0.386878i \(-0.873553\pi\)
0.518618 0.855006i \(-0.326447\pi\)
\(620\) −11.5554 + 35.5639i −0.464076 + 1.42828i
\(621\) 0 0
\(622\) 5.82385 + 4.23127i 0.233515 + 0.169659i
\(623\) −0.536349 + 1.65071i −0.0214884 + 0.0661344i
\(624\) 0 0
\(625\) 23.9721 17.4167i 0.958882 0.696669i
\(626\) −0.00774169 −0.000309420
\(627\) 0 0
\(628\) 23.9186 0.954456
\(629\) 4.63370 3.36658i 0.184758 0.134234i
\(630\) 0 0
\(631\) −4.67646 + 14.3927i −0.186167 + 0.572962i −0.999967 0.00818299i \(-0.997395\pi\)
0.813800 + 0.581145i \(0.197395\pi\)
\(632\) −1.77264 1.28790i −0.0705119 0.0512299i
\(633\) 0 0
\(634\) 1.56509 4.81686i 0.0621577 0.191302i
\(635\) −0.223023 0.686395i −0.00885041 0.0272387i
\(636\) 0 0
\(637\) 5.13499 0.203456
\(638\) −1.55187 + 4.63716i −0.0614393 + 0.183587i
\(639\) 0 0
\(640\) −13.6940 + 9.94925i −0.541302 + 0.393279i
\(641\) 5.11431 + 15.7402i 0.202003 + 0.621701i 0.999823 + 0.0188056i \(0.00598637\pi\)
−0.797820 + 0.602895i \(0.794014\pi\)
\(642\) 0 0
\(643\) −1.61403 1.17266i −0.0636513 0.0462454i 0.555505 0.831513i \(-0.312525\pi\)
−0.619156 + 0.785268i \(0.712525\pi\)
\(644\) −11.1672 8.11343i −0.440049 0.319714i
\(645\) 0 0
\(646\) 0.609806 + 1.87679i 0.0239925 + 0.0738413i
\(647\) 32.7261 23.7769i 1.28660 0.934767i 0.286866 0.957971i \(-0.407387\pi\)
0.999731 + 0.0232039i \(0.00738670\pi\)
\(648\) 0 0
\(649\) −7.76653 + 5.53913i −0.304863 + 0.217430i
\(650\) −1.42602 −0.0559329
\(651\) 0 0
\(652\) −4.87747 15.0113i −0.191016 0.587888i
\(653\) 12.8198 39.4552i 0.501676 1.54400i −0.304611 0.952477i \(-0.598527\pi\)
0.806288 0.591524i \(-0.201473\pi\)
\(654\) 0 0
\(655\) −33.3240 24.2113i −1.30208 0.946015i
\(656\) −7.70736 + 23.7208i −0.300922 + 0.926142i
\(657\) 0 0
\(658\) −1.23572 + 0.897800i −0.0481732 + 0.0349999i
\(659\) 51.1359 1.99197 0.995985 0.0895158i \(-0.0285320\pi\)
0.995985 + 0.0895158i \(0.0285320\pi\)
\(660\) 0 0
\(661\) −42.8840 −1.66800 −0.833998 0.551768i \(-0.813954\pi\)
−0.833998 + 0.551768i \(0.813954\pi\)
\(662\) 1.96875 1.43038i 0.0765178 0.0555934i
\(663\) 0 0
\(664\) −0.620472 + 1.90962i −0.0240790 + 0.0741075i
\(665\) 12.2518 + 8.90144i 0.475104 + 0.345183i
\(666\) 0 0
\(667\) 14.2655 43.9048i 0.552364 1.70000i
\(668\) −7.85995 24.1904i −0.304111 0.935956i
\(669\) 0 0
\(670\) 0.929577 0.0359127
\(671\) 0.852898 + 2.70560i 0.0329258 + 0.104448i
\(672\) 0 0
\(673\) 20.2313 14.6989i 0.779858 0.566600i −0.125078 0.992147i \(-0.539918\pi\)
0.904936 + 0.425547i \(0.139918\pi\)
\(674\) −0.524618 1.61461i −0.0202075 0.0621923i
\(675\) 0 0
\(676\) 21.0766 + 15.3130i 0.810638 + 0.588963i
\(677\) −8.02456 5.83018i −0.308409 0.224072i 0.422805 0.906221i \(-0.361046\pi\)
−0.731213 + 0.682149i \(0.761046\pi\)
\(678\) 0 0
\(679\) −3.73217 11.4864i −0.143228 0.440809i
\(680\) −2.59249 + 1.88356i −0.0994175 + 0.0722310i
\(681\) 0 0
\(682\) −4.69658 + 3.34963i −0.179841 + 0.128264i
\(683\) 39.8980 1.52666 0.763328 0.646011i \(-0.223564\pi\)
0.763328 + 0.646011i \(0.223564\pi\)
\(684\) 0 0
\(685\) −7.19174 22.1339i −0.274782 0.845692i
\(686\) −0.0699031 + 0.215140i −0.00266891 + 0.00821407i
\(687\) 0 0
\(688\) 2.39871 + 1.74276i 0.0914499 + 0.0664422i
\(689\) −10.4438 + 32.1427i −0.397877 + 1.22454i
\(690\) 0 0
\(691\) 5.35084 3.88762i 0.203556 0.147892i −0.481338 0.876535i \(-0.659849\pi\)
0.684893 + 0.728643i \(0.259849\pi\)
\(692\) 11.5218 0.437995
\(693\) 0 0
\(694\) −6.26194 −0.237700
\(695\) −9.74430 + 7.07965i −0.369622 + 0.268546i
\(696\) 0 0
\(697\) −2.99804 + 9.22701i −0.113559 + 0.349498i
\(698\) −2.02417 1.47065i −0.0766159 0.0556647i
\(699\) 0 0
\(700\) −0.739310 + 2.27536i −0.0279433 + 0.0860006i
\(701\) −4.51215 13.8870i −0.170421 0.524503i 0.828973 0.559288i \(-0.188925\pi\)
−0.999395 + 0.0347848i \(0.988925\pi\)
\(702\) 0 0
\(703\) 24.1788 0.911920
\(704\) 22.5453 + 0.198066i 0.849709 + 0.00746491i
\(705\) 0 0
\(706\) −5.84167 + 4.24422i −0.219854 + 0.159733i
\(707\) 1.14132 + 3.51261i 0.0429237 + 0.132105i
\(708\) 0 0
\(709\) 3.35261 + 2.43582i 0.125910 + 0.0914790i 0.648958 0.760824i \(-0.275205\pi\)
−0.523048 + 0.852303i \(0.675205\pi\)
\(710\) −2.06465 1.50006i −0.0774849 0.0562961i
\(711\) 0 0
\(712\) −0.479104 1.47453i −0.0179552 0.0552604i
\(713\) 44.0593 32.0109i 1.65003 1.19882i
\(714\) 0 0
\(715\) 34.1631 + 25.2824i 1.27763 + 0.945510i
\(716\) 8.44832 0.315729
\(717\) 0 0
\(718\) 0.250132 + 0.769827i 0.00933484 + 0.0287297i
\(719\) −5.26017 + 16.1891i −0.196171 + 0.603753i 0.803790 + 0.594914i \(0.202814\pi\)
−0.999961 + 0.00883941i \(0.997186\pi\)
\(720\) 0 0
\(721\) 0.931634 + 0.676872i 0.0346959 + 0.0252080i
\(722\) −1.24612 + 3.83517i −0.0463759 + 0.142730i
\(723\) 0 0
\(724\) 17.0761 12.4065i 0.634627 0.461084i
\(725\) −8.00136 −0.297163
\(726\) 0 0
\(727\) −21.6199 −0.801837 −0.400918 0.916114i \(-0.631309\pi\)
−0.400918 + 0.916114i \(0.631309\pi\)
\(728\) −3.71090 + 2.69613i −0.137535 + 0.0999252i
\(729\) 0 0
\(730\) 2.59015 7.97166i 0.0958657 0.295044i
\(731\) 0.933059 + 0.677907i 0.0345104 + 0.0250733i
\(732\) 0 0
\(733\) −14.9047 + 45.8719i −0.550517 + 1.69432i 0.156981 + 0.987602i \(0.449824\pi\)
−0.707498 + 0.706715i \(0.750176\pi\)
\(734\) −0.160355 0.493523i −0.00591883 0.0182163i
\(735\) 0 0
\(736\) 18.5751 0.684688
\(737\) −4.39001 3.24883i −0.161708 0.119672i
\(738\) 0 0
\(739\) 6.60439 4.79837i 0.242946 0.176511i −0.459649 0.888101i \(-0.652025\pi\)
0.702595 + 0.711590i \(0.252025\pi\)
\(740\) 5.98787 + 18.4288i 0.220118 + 0.677455i
\(741\) 0 0
\(742\) −1.20450 0.875124i −0.0442187 0.0321268i
\(743\) 15.8254 + 11.4978i 0.580577 + 0.421814i 0.838932 0.544236i \(-0.183180\pi\)
−0.258355 + 0.966050i \(0.583180\pi\)
\(744\) 0 0
\(745\) −0.710943 2.18806i −0.0260469 0.0801642i
\(746\) 1.45832 1.05953i 0.0533927 0.0387921i
\(747\) 0 0
\(748\) 9.29113 + 0.0816249i 0.339717 + 0.00298450i
\(749\) −1.16714 −0.0426462
\(750\) 0 0
\(751\) 0.344955 + 1.06166i 0.0125876 + 0.0387406i 0.957153 0.289583i \(-0.0935165\pi\)
−0.944565 + 0.328323i \(0.893516\pi\)
\(752\) −7.71103 + 23.7321i −0.281192 + 0.865421i
\(753\) 0 0
\(754\) −6.12498 4.45006i −0.223059 0.162062i
\(755\) 13.9552 42.9497i 0.507882 1.56310i
\(756\) 0 0
\(757\) 21.5015 15.6218i 0.781485 0.567782i −0.123939 0.992290i \(-0.539553\pi\)
0.905424 + 0.424508i \(0.139553\pi\)
\(758\) 2.62885 0.0954840
\(759\) 0 0
\(760\) −13.5277 −0.490701
\(761\) 5.09683 3.70306i 0.184760 0.134236i −0.491561 0.870843i \(-0.663573\pi\)
0.676321 + 0.736607i \(0.263573\pi\)
\(762\) 0 0
\(763\) 2.87458 8.84705i 0.104067 0.320285i
\(764\) −18.3766 13.3514i −0.664844 0.483037i
\(765\) 0 0
\(766\) 0.879273 2.70613i 0.0317694 0.0977763i
\(767\) −4.56403 14.0466i −0.164797 0.507195i
\(768\) 0 0
\(769\) 13.1916 0.475700 0.237850 0.971302i \(-0.423557\pi\)
0.237850 + 0.971302i \(0.423557\pi\)
\(770\) −1.52432 + 1.08715i −0.0549327 + 0.0391783i
\(771\) 0 0
\(772\) 35.3883 25.7111i 1.27365 0.925362i
\(773\) −14.1585 43.5753i −0.509245 1.56729i −0.793515 0.608550i \(-0.791751\pi\)
0.284270 0.958744i \(-0.408249\pi\)
\(774\) 0 0
\(775\) −7.63652 5.54825i −0.274312 0.199299i
\(776\) 8.72809 + 6.34133i 0.313320 + 0.227640i
\(777\) 0 0
\(778\) −0.0306381 0.0942944i −0.00109843 0.00338062i
\(779\) −33.1342 + 24.0734i −1.18716 + 0.862520i
\(780\) 0 0
\(781\) 4.50786 + 14.3000i 0.161304 + 0.511695i
\(782\) 2.30326 0.0823643
\(783\) 0 0
\(784\) 1.14200 + 3.51471i 0.0407857 + 0.125526i
\(785\) −9.46469 + 29.1293i −0.337809 + 1.03967i
\(786\) 0 0
\(787\) 15.2483 + 11.0785i 0.543543 + 0.394907i 0.825399 0.564549i \(-0.190950\pi\)
−0.281856 + 0.959457i \(0.590950\pi\)
\(788\) 14.5148 44.6721i 0.517070 1.59138i
\(789\) 0 0
\(790\) 1.12025 0.813909i 0.0398567 0.0289576i
\(791\) −3.29733 −0.117240
\(792\) 0 0
\(793\) −4.39217 −0.155970
\(794\) 3.07724 2.23574i 0.109207 0.0793435i
\(795\) 0 0
\(796\) −11.2739 + 34.6975i −0.399593 + 1.22982i
\(797\) −22.7830 16.5528i −0.807016 0.586331i 0.105948 0.994372i \(-0.466212\pi\)
−0.912964 + 0.408040i \(0.866212\pi\)
\(798\) 0 0
\(799\) −2.99947 + 9.23141i −0.106114 + 0.326584i
\(800\) −0.994884 3.06194i −0.0351744 0.108256i
\(801\) 0 0
\(802\) 8.33835 0.294437
\(803\) −40.0928 + 28.5944i −1.41485 + 1.00907i
\(804\) 0 0
\(805\) 14.2999 10.3895i 0.504004 0.366180i
\(806\) −2.75996 8.49429i −0.0972155 0.299199i
\(807\) 0 0
\(808\) −2.66910 1.93921i −0.0938985 0.0682213i
\(809\) −5.29544 3.84736i −0.186178 0.135266i 0.490792 0.871277i \(-0.336707\pi\)
−0.676970 + 0.736011i \(0.736707\pi\)
\(810\) 0 0
\(811\) 5.81096 + 17.8843i 0.204050 + 0.628002i 0.999751 + 0.0223122i \(0.00710279\pi\)
−0.795701 + 0.605690i \(0.792897\pi\)
\(812\) −10.2760 + 7.46596i −0.360617 + 0.262004i
\(813\) 0 0
\(814\) −0.948675 + 2.83474i −0.0332511 + 0.0993576i
\(815\) 20.2116 0.707980
\(816\) 0 0
\(817\) 1.50452 + 4.63044i 0.0526365 + 0.161999i
\(818\) −1.13760 + 3.50116i −0.0397751 + 0.122415i
\(819\) 0 0
\(820\) −26.5542 19.2927i −0.927311 0.673731i
\(821\) 3.58089 11.0208i 0.124974 0.384630i −0.868922 0.494948i \(-0.835187\pi\)
0.993896 + 0.110318i \(0.0351870\pi\)
\(822\) 0 0
\(823\) −9.98844 + 7.25702i −0.348175 + 0.252964i −0.748103 0.663583i \(-0.769035\pi\)
0.399928 + 0.916547i \(0.369035\pi\)
\(824\) −1.02866 −0.0358349
\(825\) 0 0
\(826\) 0.650640 0.0226387
\(827\) −3.63717 + 2.64256i −0.126477 + 0.0918907i −0.649225 0.760596i \(-0.724907\pi\)
0.522748 + 0.852487i \(0.324907\pi\)
\(828\) 0 0
\(829\) −6.13796 + 18.8907i −0.213180 + 0.656101i 0.786098 + 0.618102i \(0.212098\pi\)
−0.999278 + 0.0379987i \(0.987902\pi\)
\(830\) −1.02658 0.745851i −0.0356330 0.0258889i
\(831\) 0 0
\(832\) −10.7869 + 33.1988i −0.373970 + 1.15096i
\(833\) 0.444220 + 1.36717i 0.0153913 + 0.0473695i
\(834\) 0 0
\(835\) 32.5706 1.12715
\(836\) 31.5290 + 23.3331i 1.09045 + 0.806991i
\(837\) 0 0
\(838\) −1.01817 + 0.739747i −0.0351722 + 0.0255541i
\(839\) 13.5513 + 41.7065i 0.467842 + 1.43987i 0.855373 + 0.518012i \(0.173328\pi\)
−0.387532 + 0.921856i \(0.626672\pi\)
\(840\) 0 0
\(841\) −10.9057 7.92348i −0.376060 0.273224i
\(842\) 3.93311 + 2.85757i 0.135544 + 0.0984785i
\(843\) 0 0
\(844\) 4.55662 + 14.0238i 0.156845 + 0.482720i
\(845\) −26.9891 + 19.6087i −0.928453 + 0.674561i
\(846\) 0 0
\(847\) 10.9983 + 0.193261i 0.377906 + 0.00664052i
\(848\) −24.3232 −0.835261
\(849\) 0 0
\(850\) −0.123362 0.379670i −0.00423129 0.0130226i
\(851\) 8.72066 26.8394i 0.298940 0.920044i
\(852\) 0 0
\(853\) −31.6655 23.0063i −1.08421 0.787721i −0.105794 0.994388i \(-0.533738\pi\)
−0.978411 + 0.206667i \(0.933738\pi\)
\(854\) 0.0597911 0.184018i 0.00204601 0.00629697i
\(855\) 0 0
\(856\) 0.843455 0.612806i 0.0288287 0.0209453i
\(857\) −35.0524 −1.19737 −0.598684 0.800986i \(-0.704309\pi\)
−0.598684 + 0.800986i \(0.704309\pi\)
\(858\) 0 0
\(859\) −32.5206 −1.10959 −0.554794 0.831988i \(-0.687203\pi\)
−0.554794 + 0.831988i \(0.687203\pi\)
\(860\) −3.15667 + 2.29345i −0.107642 + 0.0782061i
\(861\) 0 0
\(862\) −1.93763 + 5.96341i −0.0659959 + 0.203114i
\(863\) 10.2696 + 7.46132i 0.349582 + 0.253986i 0.748694 0.662916i \(-0.230681\pi\)
−0.399111 + 0.916902i \(0.630681\pi\)
\(864\) 0 0
\(865\) −4.55924 + 14.0319i −0.155019 + 0.477099i
\(866\) −0.649269 1.99824i −0.0220630 0.0679031i
\(867\) 0 0
\(868\) −14.9844 −0.508605
\(869\) −8.13505 0.0714685i −0.275963 0.00242440i
\(870\) 0 0
\(871\) 6.84079 4.97012i 0.231791 0.168406i
\(872\) 2.56778 + 7.90281i 0.0869559 + 0.267623i
\(873\) 0 0
\(874\) 7.86619 + 5.71512i 0.266078 + 0.193317i
\(875\) 7.61610 + 5.53342i 0.257471 + 0.187064i
\(876\) 0 0
\(877\) −8.69388 26.7570i −0.293571 0.903520i −0.983698 0.179831i \(-0.942445\pi\)
0.690126 0.723689i \(-0.257555\pi\)
\(878\) −2.69239 + 1.95614i −0.0908638 + 0.0660164i
\(879\) 0 0
\(880\) −9.70720 + 29.0061i −0.327230 + 0.977797i
\(881\) 36.7964 1.23970 0.619850 0.784720i \(-0.287193\pi\)
0.619850 + 0.784720i \(0.287193\pi\)
\(882\) 0 0
\(883\) −0.705855 2.17240i −0.0237539 0.0731070i 0.938477 0.345342i \(-0.112237\pi\)
−0.962231 + 0.272235i \(0.912237\pi\)
\(884\) −4.44540 + 13.6815i −0.149515 + 0.460159i
\(885\) 0 0
\(886\) −0.447173 0.324890i −0.0150231 0.0109149i
\(887\) −13.0614 + 40.1989i −0.438560 + 1.34975i 0.450835 + 0.892607i \(0.351126\pi\)
−0.889395 + 0.457140i \(0.848874\pi\)
\(888\) 0 0
\(889\) 0.233972 0.169990i 0.00784716 0.00570130i
\(890\) 0.979808 0.0328432
\(891\) 0 0
\(892\) −34.1520 −1.14349
\(893\) −33.1500 + 24.0849i −1.10932 + 0.805971i
\(894\) 0 0
\(895\) −3.34304 + 10.2888i −0.111745 + 0.343917i
\(896\) −5.48741 3.98684i −0.183322 0.133191i
\(897\) 0 0
\(898\) 0.333393 1.02608i 0.0111255 0.0342406i
\(899\) −15.4861 47.6614i −0.516491 1.58960i
\(900\) 0 0
\(901\) −9.46132 −0.315202
\(902\) −1.52234 4.82923i −0.0506884 0.160796i
\(903\) 0 0
\(904\) 2.38288 1.73127i 0.0792535 0.0575810i
\(905\) 8.35220 + 25.7054i 0.277636 + 0.854477i
\(906\) 0 0
\(907\) −31.9793 23.2343i −1.06185 0.771483i −0.0874240 0.996171i \(-0.527864\pi\)
−0.974431 + 0.224689i \(0.927864\pi\)
\(908\) 40.4837 + 29.4131i 1.34350 + 0.976108i
\(909\) 0 0
\(910\) −0.895772 2.75690i −0.0296946 0.0913905i
\(911\) −28.5013 + 20.7074i −0.944291 + 0.686067i −0.949450 0.313919i \(-0.898358\pi\)
0.00515893 + 0.999987i \(0.498358\pi\)
\(912\) 0 0
\(913\) 2.24138 + 7.11019i 0.0741788 + 0.235313i
\(914\) −7.03234 −0.232609
\(915\) 0 0
\(916\) 11.9462 + 36.7666i 0.394713 + 1.21480i
\(917\) 5.10059 15.6980i 0.168436 0.518394i
\(918\) 0 0
\(919\) 32.0455 + 23.2824i 1.05708 + 0.768017i 0.973547 0.228488i \(-0.0733780\pi\)
0.0835379 + 0.996505i \(0.473378\pi\)
\(920\) −4.87909 + 15.0163i −0.160859 + 0.495073i
\(921\) 0 0
\(922\) −5.43930 + 3.95188i −0.179134 + 0.130148i
\(923\) −23.2141 −0.764101
\(924\) 0 0
\(925\) −4.89131 −0.160825
\(926\) −4.65855 + 3.38463i −0.153089 + 0.111226i
\(927\) 0 0
\(928\) 5.28196 16.2562i 0.173389 0.533636i
\(929\) 2.11685 + 1.53798i 0.0694516 + 0.0504595i 0.621969 0.783042i \(-0.286333\pi\)
−0.552518 + 0.833501i \(0.686333\pi\)
\(930\) 0 0
\(931\) −1.87526 + 5.77147i −0.0614593 + 0.189152i
\(932\) −12.1736 37.4666i −0.398761 1.22726i
\(933\) 0 0
\(934\) −0.720463 −0.0235743
\(935\) −3.77594 + 11.2829i −0.123487 + 0.368991i
\(936\) 0 0
\(937\) −43.5575 + 31.6464i −1.42296 + 1.03384i −0.431689 + 0.902022i \(0.642082\pi\)
−0.991274 + 0.131820i \(0.957918\pi\)
\(938\) 0.115108 + 0.354266i 0.00375841 + 0.0115672i
\(939\) 0 0
\(940\) −26.5668 19.3019i −0.866514 0.629559i
\(941\) 23.9854 + 17.4264i 0.781902 + 0.568085i 0.905549 0.424241i \(-0.139459\pi\)
−0.123647 + 0.992326i \(0.539459\pi\)
\(942\) 0 0
\(943\) 14.7718 + 45.4630i 0.481037 + 1.48048i
\(944\) 8.59940 6.24783i 0.279887 0.203349i
\(945\) 0 0
\(946\) −0.601908 0.00528791i −0.0195697 0.000171925i
\(947\) 15.7861 0.512980 0.256490 0.966547i \(-0.417434\pi\)
0.256490 + 0.966547i \(0.417434\pi\)
\(948\) 0 0
\(949\) −23.5607 72.5123i −0.764812 2.35385i
\(950\) 0.520771 1.60277i 0.0168961 0.0520007i
\(951\) 0 0
\(952\) −1.03886 0.754773i −0.0336695 0.0244623i
\(953\) 10.8502 33.3934i 0.351472 1.08172i −0.606555 0.795041i \(-0.707449\pi\)
0.958027 0.286678i \(-0.0925509\pi\)
\(954\) 0 0
\(955\) 23.5318 17.0968i 0.761470 0.553240i
\(956\) 33.3257 1.07783
\(957\) 0 0
\(958\) 0.731463 0.0236325
\(959\) 7.54479 5.48161i 0.243634 0.177011i
\(960\) 0 0
\(961\) 8.68955 26.7437i 0.280308 0.862700i
\(962\) −3.74426 2.72036i −0.120720 0.0877080i
\(963\) 0 0
\(964\) 14.5454 44.7661i 0.468475 1.44182i
\(965\) 17.3090 + 53.2716i 0.557196 + 1.71487i
\(966\) 0 0
\(967\) −49.2820 −1.58480 −0.792401 0.610001i \(-0.791169\pi\)
−0.792401 + 0.610001i \(0.791169\pi\)
\(968\) −8.04962 + 5.63500i −0.258725 + 0.181116i
\(969\) 0 0
\(970\) −5.51585 + 4.00750i −0.177103 + 0.128673i
\(971\) −11.5394 35.5148i −0.370318 1.13972i −0.946583 0.322460i \(-0.895490\pi\)
0.576265 0.817263i \(-0.304510\pi\)
\(972\) 0 0
\(973\) −3.90471 2.83694i −0.125179 0.0909481i
\(974\) 1.80647 + 1.31248i 0.0578831 + 0.0420545i
\(975\) 0 0
\(976\) −0.976800 3.00628i −0.0312666 0.0962287i
\(977\) 32.3999 23.5399i 1.03656 0.753108i 0.0669524 0.997756i \(-0.478672\pi\)
0.969612 + 0.244648i \(0.0786724\pi\)
\(978\) 0 0
\(979\) −4.62723 3.42439i −0.147887 0.109444i
\(980\) −4.86335 −0.155354
\(981\) 0 0
\(982\) 0.295411 + 0.909181i 0.00942694 + 0.0290131i
\(983\) 16.0817 49.4944i 0.512926 1.57862i −0.274098 0.961702i \(-0.588379\pi\)
0.787024 0.616923i \(-0.211621\pi\)
\(984\) 0 0
\(985\) 48.6604 + 35.3538i 1.55045 + 1.12647i
\(986\) 0.654946 2.01572i 0.0208577 0.0641935i
\(987\) 0 0
\(988\) −49.1304 + 35.6953i −1.56305 + 1.13562i
\(989\) 5.68262 0.180697
\(990\) 0 0
\(991\) 45.4828 1.44481 0.722404 0.691471i \(-0.243037\pi\)
0.722404 + 0.691471i \(0.243037\pi\)
\(992\) 16.3134 11.8524i 0.517951 0.376313i
\(993\) 0 0
\(994\) 0.316016 0.972598i 0.0100234 0.0308489i
\(995\) −37.7953 27.4599i −1.19819 0.870536i
\(996\) 0 0
\(997\) 8.63992 26.5909i 0.273629 0.842143i −0.715950 0.698152i \(-0.754006\pi\)
0.989579 0.143992i \(-0.0459939\pi\)
\(998\) 1.42569 + 4.38783i 0.0451296 + 0.138894i
\(999\) 0 0
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 693.2.m.i.190.2 16
3.2 odd 2 77.2.f.b.36.3 yes 16
11.2 odd 10 7623.2.a.cw.1.4 8
11.4 even 5 inner 693.2.m.i.631.2 16
11.9 even 5 7623.2.a.ct.1.5 8
21.2 odd 6 539.2.q.g.410.2 32
21.5 even 6 539.2.q.f.410.2 32
21.11 odd 6 539.2.q.g.520.3 32
21.17 even 6 539.2.q.f.520.3 32
21.20 even 2 539.2.f.e.344.3 16
33.2 even 10 847.2.a.o.1.5 8
33.5 odd 10 847.2.f.w.372.2 16
33.8 even 10 847.2.f.v.148.3 16
33.14 odd 10 847.2.f.w.148.2 16
33.17 even 10 847.2.f.v.372.3 16
33.20 odd 10 847.2.a.p.1.4 8
33.26 odd 10 77.2.f.b.15.3 16
33.29 even 10 847.2.f.x.323.2 16
33.32 even 2 847.2.f.x.729.2 16
231.20 even 10 5929.2.a.bt.1.4 8
231.26 even 30 539.2.q.f.312.3 32
231.59 even 30 539.2.q.f.422.2 32
231.125 even 10 539.2.f.e.246.3 16
231.158 odd 30 539.2.q.g.422.2 32
231.167 odd 10 5929.2.a.bs.1.5 8
231.191 odd 30 539.2.q.g.312.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.b.15.3 16 33.26 odd 10
77.2.f.b.36.3 yes 16 3.2 odd 2
539.2.f.e.246.3 16 231.125 even 10
539.2.f.e.344.3 16 21.20 even 2
539.2.q.f.312.3 32 231.26 even 30
539.2.q.f.410.2 32 21.5 even 6
539.2.q.f.422.2 32 231.59 even 30
539.2.q.f.520.3 32 21.17 even 6
539.2.q.g.312.3 32 231.191 odd 30
539.2.q.g.410.2 32 21.2 odd 6
539.2.q.g.422.2 32 231.158 odd 30
539.2.q.g.520.3 32 21.11 odd 6
693.2.m.i.190.2 16 1.1 even 1 trivial
693.2.m.i.631.2 16 11.4 even 5 inner
847.2.a.o.1.5 8 33.2 even 10
847.2.a.p.1.4 8 33.20 odd 10
847.2.f.v.148.3 16 33.8 even 10
847.2.f.v.372.3 16 33.17 even 10
847.2.f.w.148.2 16 33.14 odd 10
847.2.f.w.372.2 16 33.5 odd 10
847.2.f.x.323.2 16 33.29 even 10
847.2.f.x.729.2 16 33.32 even 2
5929.2.a.bs.1.5 8 231.167 odd 10
5929.2.a.bt.1.4 8 231.20 even 10
7623.2.a.ct.1.5 8 11.9 even 5
7623.2.a.cw.1.4 8 11.2 odd 10