Properties

Label 855.2.be.d.64.5
Level $855$
Weight $2$
Character 855.64
Analytic conductor $6.827$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [855,2,Mod(64,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.be (of order \(6\), 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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6x^{10} + 29x^{8} - 40x^{6} + 43x^{4} - 7x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 64.5
Root \(1.00376 - 0.579521i\) of defining polynomial
Character \(\chi\) \(=\) 855.64
Dual form 855.2.be.d.334.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.747190 - 0.431391i) q^{2} +(-0.627804 + 1.08739i) q^{4} +(0.0476457 - 2.23556i) q^{5} -0.566520i q^{7} +2.80888i q^{8} +O(q^{10})\) \(q+(0.747190 - 0.431391i) q^{2} +(-0.627804 + 1.08739i) q^{4} +(0.0476457 - 2.23556i) q^{5} -0.566520i q^{7} +2.80888i q^{8} +(-0.928799 - 1.69094i) q^{10} +1.91223 q^{11} +(-0.168469 - 0.0972656i) q^{13} +(-0.244391 - 0.423298i) q^{14} +(-0.0438854 - 0.0760118i) q^{16} +(4.58603 - 2.64775i) q^{17} +(2.36834 - 3.65936i) q^{19} +(2.40101 + 1.45530i) q^{20} +(1.42880 - 0.824918i) q^{22} +(2.92318 + 1.68770i) q^{23} +(-4.99546 - 0.213030i) q^{25} -0.167838 q^{26} +(0.616027 + 0.355664i) q^{28} +(4.36834 - 7.56619i) q^{29} +5.65662 q^{31} +(-4.93070 - 2.84674i) q^{32} +(2.28442 - 3.95674i) q^{34} +(-1.26649 - 0.0269922i) q^{35} -0.955582i q^{37} +(0.190988 - 3.75592i) q^{38} +(6.27942 + 0.133831i) q^{40} +(5.02496 + 8.70349i) q^{41} +(-4.27161 + 2.46622i) q^{43} +(-1.20051 + 2.07934i) q^{44} +2.91223 q^{46} +(-7.65516 - 4.41971i) q^{47} +6.67906 q^{49} +(-3.82446 + 1.99582i) q^{50} +(0.211531 - 0.122128i) q^{52} +(-7.10669 - 4.10305i) q^{53} +(0.0911095 - 4.27490i) q^{55} +1.59128 q^{56} -7.53785i q^{58} +(-1.85713 - 3.21664i) q^{59} +(1.75561 - 3.04080i) q^{61} +(4.22657 - 2.44021i) q^{62} -4.73669 q^{64} +(-0.225470 + 0.371988i) q^{65} +(3.50190 + 2.02182i) q^{67} +6.64906i q^{68} +(-0.957953 + 0.526183i) q^{70} +(2.59767 + 4.49929i) q^{71} +(7.45136 - 4.30205i) q^{73} +(-0.412229 - 0.714002i) q^{74} +(2.49230 + 4.87268i) q^{76} -1.08332i q^{77} +(3.31324 + 5.73870i) q^{79} +(-0.172020 + 0.0944869i) q^{80} +(7.50921 + 4.33544i) q^{82} +4.51737i q^{83} +(-5.70069 - 10.3785i) q^{85} +(-2.12780 + 3.68547i) q^{86} +5.37122i q^{88} +(-1.68676 + 2.92155i) q^{89} +(-0.0551029 + 0.0954410i) q^{91} +(-3.67037 + 2.11909i) q^{92} -7.62648 q^{94} +(-8.06789 - 5.46893i) q^{95} +(-13.1568 + 7.59611i) q^{97} +(4.99053 - 2.88128i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{4} + 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{4} + 2 q^{5} + 6 q^{10} - 4 q^{11} - 22 q^{14} - 14 q^{16} - 12 q^{19} + 40 q^{20} - 6 q^{25} + 44 q^{26} + 12 q^{29} + 60 q^{31} + 10 q^{34} + 10 q^{40} + 12 q^{41} - 20 q^{44} + 8 q^{46} - 4 q^{49} + 8 q^{50} - 18 q^{55} - 92 q^{56} - 20 q^{59} + 2 q^{61} + 24 q^{64} + 40 q^{65} + 46 q^{70} - 2 q^{71} + 22 q^{74} - 70 q^{76} + 24 q^{79} + 22 q^{80} + 2 q^{85} - 16 q^{86} - 36 q^{89} + 24 q^{91} - 60 q^{94} - 46 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.747190 0.431391i 0.528343 0.305039i −0.211998 0.977270i \(-0.567997\pi\)
0.740342 + 0.672231i \(0.234664\pi\)
\(3\) 0 0
\(4\) −0.627804 + 1.08739i −0.313902 + 0.543695i
\(5\) 0.0476457 2.23556i 0.0213078 0.999773i
\(6\) 0 0
\(7\) 0.566520i 0.214124i −0.994252 0.107062i \(-0.965856\pi\)
0.994252 0.107062i \(-0.0341444\pi\)
\(8\) 2.80888i 0.993088i
\(9\) 0 0
\(10\) −0.928799 1.69094i −0.293712 0.534723i
\(11\) 1.91223 0.576559 0.288279 0.957546i \(-0.406917\pi\)
0.288279 + 0.957546i \(0.406917\pi\)
\(12\) 0 0
\(13\) −0.168469 0.0972656i −0.0467249 0.0269766i 0.476456 0.879199i \(-0.341921\pi\)
−0.523180 + 0.852222i \(0.675255\pi\)
\(14\) −0.244391 0.423298i −0.0653163 0.113131i
\(15\) 0 0
\(16\) −0.0438854 0.0760118i −0.0109714 0.0190029i
\(17\) 4.58603 2.64775i 1.11228 0.642173i 0.172858 0.984947i \(-0.444700\pi\)
0.939418 + 0.342774i \(0.111367\pi\)
\(18\) 0 0
\(19\) 2.36834 3.65936i 0.543335 0.839516i
\(20\) 2.40101 + 1.45530i 0.536883 + 0.325416i
\(21\) 0 0
\(22\) 1.42880 0.824918i 0.304621 0.175873i
\(23\) 2.92318 + 1.68770i 0.609525 + 0.351910i 0.772780 0.634674i \(-0.218866\pi\)
−0.163254 + 0.986584i \(0.552199\pi\)
\(24\) 0 0
\(25\) −4.99546 0.213030i −0.999092 0.0426059i
\(26\) −0.167838 −0.0329157
\(27\) 0 0
\(28\) 0.616027 + 0.355664i 0.116418 + 0.0672141i
\(29\) 4.36834 7.56619i 0.811181 1.40501i −0.100857 0.994901i \(-0.532158\pi\)
0.912038 0.410106i \(-0.134508\pi\)
\(30\) 0 0
\(31\) 5.65662 1.01596 0.507980 0.861369i \(-0.330393\pi\)
0.507980 + 0.861369i \(0.330393\pi\)
\(32\) −4.93070 2.84674i −0.871633 0.503238i
\(33\) 0 0
\(34\) 2.28442 3.95674i 0.391776 0.678575i
\(35\) −1.26649 0.0269922i −0.214076 0.00456252i
\(36\) 0 0
\(37\) 0.955582i 0.157097i −0.996910 0.0785484i \(-0.974971\pi\)
0.996910 0.0785484i \(-0.0250285\pi\)
\(38\) 0.190988 3.75592i 0.0309824 0.609291i
\(39\) 0 0
\(40\) 6.27942 + 0.133831i 0.992863 + 0.0211605i
\(41\) 5.02496 + 8.70349i 0.784768 + 1.35926i 0.929138 + 0.369734i \(0.120551\pi\)
−0.144370 + 0.989524i \(0.546116\pi\)
\(42\) 0 0
\(43\) −4.27161 + 2.46622i −0.651415 + 0.376094i −0.788998 0.614396i \(-0.789400\pi\)
0.137583 + 0.990490i \(0.456066\pi\)
\(44\) −1.20051 + 2.07934i −0.180983 + 0.313472i
\(45\) 0 0
\(46\) 2.91223 0.429385
\(47\) −7.65516 4.41971i −1.11662 0.644681i −0.176084 0.984375i \(-0.556343\pi\)
−0.940536 + 0.339694i \(0.889676\pi\)
\(48\) 0 0
\(49\) 6.67906 0.954151
\(50\) −3.82446 + 1.99582i −0.540860 + 0.282252i
\(51\) 0 0
\(52\) 0.211531 0.122128i 0.0293341 0.0169361i
\(53\) −7.10669 4.10305i −0.976179 0.563597i −0.0750646 0.997179i \(-0.523916\pi\)
−0.901114 + 0.433581i \(0.857250\pi\)
\(54\) 0 0
\(55\) 0.0911095 4.27490i 0.0122852 0.576428i
\(56\) 1.59128 0.212644
\(57\) 0 0
\(58\) 7.53785i 0.989768i
\(59\) −1.85713 3.21664i −0.241777 0.418770i 0.719443 0.694551i \(-0.244397\pi\)
−0.961221 + 0.275781i \(0.911064\pi\)
\(60\) 0 0
\(61\) 1.75561 3.04080i 0.224783 0.389335i −0.731472 0.681872i \(-0.761166\pi\)
0.956254 + 0.292537i \(0.0944995\pi\)
\(62\) 4.22657 2.44021i 0.536775 0.309907i
\(63\) 0 0
\(64\) −4.73669 −0.592086
\(65\) −0.225470 + 0.371988i −0.0279661 + 0.0461395i
\(66\) 0 0
\(67\) 3.50190 + 2.02182i 0.427825 + 0.247005i 0.698420 0.715688i \(-0.253887\pi\)
−0.270594 + 0.962693i \(0.587220\pi\)
\(68\) 6.64906i 0.806318i
\(69\) 0 0
\(70\) −0.957953 + 0.526183i −0.114497 + 0.0628909i
\(71\) 2.59767 + 4.49929i 0.308286 + 0.533967i 0.977988 0.208663i \(-0.0669112\pi\)
−0.669701 + 0.742631i \(0.733578\pi\)
\(72\) 0 0
\(73\) 7.45136 4.30205i 0.872116 0.503516i 0.00406505 0.999992i \(-0.498706\pi\)
0.868051 + 0.496475i \(0.165373\pi\)
\(74\) −0.412229 0.714002i −0.0479207 0.0830010i
\(75\) 0 0
\(76\) 2.49230 + 4.87268i 0.285886 + 0.558934i
\(77\) 1.08332i 0.123455i
\(78\) 0 0
\(79\) 3.31324 + 5.73870i 0.372769 + 0.645654i 0.989990 0.141135i \(-0.0450751\pi\)
−0.617222 + 0.786789i \(0.711742\pi\)
\(80\) −0.172020 + 0.0944869i −0.0192324 + 0.0105640i
\(81\) 0 0
\(82\) 7.50921 + 4.33544i 0.829253 + 0.478770i
\(83\) 4.51737i 0.495845i 0.968780 + 0.247923i \(0.0797479\pi\)
−0.968780 + 0.247923i \(0.920252\pi\)
\(84\) 0 0
\(85\) −5.70069 10.3785i −0.618327 1.12571i
\(86\) −2.12780 + 3.68547i −0.229447 + 0.397414i
\(87\) 0 0
\(88\) 5.37122i 0.572574i
\(89\) −1.68676 + 2.92155i −0.178796 + 0.309684i −0.941468 0.337101i \(-0.890554\pi\)
0.762672 + 0.646785i \(0.223887\pi\)
\(90\) 0 0
\(91\) −0.0551029 + 0.0954410i −0.00577635 + 0.0100049i
\(92\) −3.67037 + 2.11909i −0.382663 + 0.220930i
\(93\) 0 0
\(94\) −7.62648 −0.786612
\(95\) −8.06789 5.46893i −0.827748 0.561100i
\(96\) 0 0
\(97\) −13.1568 + 7.59611i −1.33588 + 0.771268i −0.986193 0.165600i \(-0.947044\pi\)
−0.349683 + 0.936868i \(0.613711\pi\)
\(98\) 4.99053 2.88128i 0.504119 0.291053i
\(99\) 0 0
\(100\) 3.36782 5.29827i 0.336782 0.529827i
\(101\) 1.77068 3.06690i 0.176189 0.305168i −0.764383 0.644762i \(-0.776956\pi\)
0.940572 + 0.339594i \(0.110290\pi\)
\(102\) 0 0
\(103\) 15.6919i 1.54617i 0.634301 + 0.773086i \(0.281288\pi\)
−0.634301 + 0.773086i \(0.718712\pi\)
\(104\) 0.273207 0.473209i 0.0267902 0.0464020i
\(105\) 0 0
\(106\) −7.08007 −0.687677
\(107\) 1.05731i 0.102214i 0.998693 + 0.0511071i \(0.0162750\pi\)
−0.998693 + 0.0511071i \(0.983725\pi\)
\(108\) 0 0
\(109\) −3.37220 5.84081i −0.322998 0.559449i 0.658107 0.752924i \(-0.271357\pi\)
−0.981105 + 0.193476i \(0.938024\pi\)
\(110\) −1.77608 3.23347i −0.169342 0.308299i
\(111\) 0 0
\(112\) −0.0430622 + 0.0248620i −0.00406899 + 0.00234923i
\(113\) 7.90091i 0.743255i 0.928382 + 0.371627i \(0.121200\pi\)
−0.928382 + 0.371627i \(0.878800\pi\)
\(114\) 0 0
\(115\) 3.91223 6.45453i 0.364817 0.601888i
\(116\) 5.48493 + 9.50018i 0.509263 + 0.882069i
\(117\) 0 0
\(118\) −2.77525 1.60229i −0.255483 0.147503i
\(119\) −1.50000 2.59808i −0.137505 0.238165i
\(120\) 0 0
\(121\) −7.34338 −0.667580
\(122\) 3.02941i 0.274270i
\(123\) 0 0
\(124\) −3.55125 + 6.15095i −0.318912 + 0.552371i
\(125\) −0.714253 + 11.1575i −0.0638847 + 0.997957i
\(126\) 0 0
\(127\) −7.34074 4.23818i −0.651385 0.376078i 0.137601 0.990488i \(-0.456061\pi\)
−0.788987 + 0.614410i \(0.789394\pi\)
\(128\) 6.32219 3.65012i 0.558808 0.322628i
\(129\) 0 0
\(130\) −0.00799675 + 0.375212i −0.000701362 + 0.0329083i
\(131\) 0.937193 + 1.62327i 0.0818830 + 0.141825i 0.904059 0.427408i \(-0.140573\pi\)
−0.822176 + 0.569234i \(0.807240\pi\)
\(132\) 0 0
\(133\) −2.07310 1.34171i −0.179761 0.116341i
\(134\) 3.48878 0.301385
\(135\) 0 0
\(136\) 7.43719 + 12.8816i 0.637734 + 1.10459i
\(137\) −10.7918 6.23068i −0.922010 0.532323i −0.0377341 0.999288i \(-0.512014\pi\)
−0.884276 + 0.466965i \(0.845347\pi\)
\(138\) 0 0
\(139\) −0.156620 + 0.271275i −0.0132844 + 0.0230092i −0.872591 0.488451i \(-0.837562\pi\)
0.859307 + 0.511460i \(0.170895\pi\)
\(140\) 0.824458 1.36022i 0.0696794 0.114960i
\(141\) 0 0
\(142\) 3.88190 + 2.24122i 0.325762 + 0.188079i
\(143\) −0.322151 0.185994i −0.0269397 0.0155536i
\(144\) 0 0
\(145\) −16.7065 10.1262i −1.38740 0.840935i
\(146\) 3.71172 6.42889i 0.307184 0.532059i
\(147\) 0 0
\(148\) 1.03909 + 0.599919i 0.0854127 + 0.0493130i
\(149\) −2.18291 3.78091i −0.178831 0.309744i 0.762650 0.646812i \(-0.223898\pi\)
−0.941480 + 0.337068i \(0.890565\pi\)
\(150\) 0 0
\(151\) 0.197977 0.0161111 0.00805555 0.999968i \(-0.497436\pi\)
0.00805555 + 0.999968i \(0.497436\pi\)
\(152\) 10.2787 + 6.65239i 0.833713 + 0.539580i
\(153\) 0 0
\(154\) −0.467332 0.809443i −0.0376587 0.0652268i
\(155\) 0.269514 12.6457i 0.0216478 1.01573i
\(156\) 0 0
\(157\) −13.6572 + 7.88498i −1.08996 + 0.629290i −0.933566 0.358405i \(-0.883321\pi\)
−0.156395 + 0.987695i \(0.549987\pi\)
\(158\) 4.95124 + 2.85860i 0.393900 + 0.227418i
\(159\) 0 0
\(160\) −6.59899 + 10.8872i −0.521696 + 0.860712i
\(161\) 0.956115 1.65604i 0.0753524 0.130514i
\(162\) 0 0
\(163\) 9.18768i 0.719635i 0.933023 + 0.359817i \(0.117161\pi\)
−0.933023 + 0.359817i \(0.882839\pi\)
\(164\) −12.6188 −0.985361
\(165\) 0 0
\(166\) 1.94875 + 3.37533i 0.151252 + 0.261977i
\(167\) 2.65888 + 1.53510i 0.205750 + 0.118790i 0.599335 0.800498i \(-0.295432\pi\)
−0.393585 + 0.919288i \(0.628765\pi\)
\(168\) 0 0
\(169\) −6.48108 11.2256i −0.498545 0.863504i
\(170\) −8.73669 5.29549i −0.670073 0.406146i
\(171\) 0 0
\(172\) 6.19320i 0.472227i
\(173\) −9.01838 + 5.20676i −0.685655 + 0.395863i −0.801982 0.597348i \(-0.796221\pi\)
0.116328 + 0.993211i \(0.462888\pi\)
\(174\) 0 0
\(175\) −0.120685 + 2.83003i −0.00912296 + 0.213930i
\(176\) −0.0839190 0.145352i −0.00632563 0.0109563i
\(177\) 0 0
\(178\) 2.91061i 0.218159i
\(179\) −13.4432 −1.00479 −0.502397 0.864637i \(-0.667549\pi\)
−0.502397 + 0.864637i \(0.667549\pi\)
\(180\) 0 0
\(181\) −3.98108 + 6.89543i −0.295911 + 0.512533i −0.975196 0.221341i \(-0.928957\pi\)
0.679285 + 0.733874i \(0.262290\pi\)
\(182\) 0.0950835i 0.00704806i
\(183\) 0 0
\(184\) −4.74054 + 8.21086i −0.349477 + 0.605312i
\(185\) −2.13626 0.0455294i −0.157061 0.00334739i
\(186\) 0 0
\(187\) 8.76954 5.06310i 0.641292 0.370250i
\(188\) 9.61189 5.54942i 0.701019 0.404733i
\(189\) 0 0
\(190\) −8.38749 0.605920i −0.608493 0.0439580i
\(191\) 14.0999 1.02023 0.510115 0.860106i \(-0.329603\pi\)
0.510115 + 0.860106i \(0.329603\pi\)
\(192\) 0 0
\(193\) 3.44405 1.98842i 0.247908 0.143130i −0.370898 0.928674i \(-0.620950\pi\)
0.618806 + 0.785544i \(0.287617\pi\)
\(194\) −6.55378 + 11.3515i −0.470534 + 0.814989i
\(195\) 0 0
\(196\) −4.19314 + 7.26273i −0.299510 + 0.518767i
\(197\) 18.3494i 1.30734i 0.756781 + 0.653669i \(0.226771\pi\)
−0.756781 + 0.653669i \(0.773229\pi\)
\(198\) 0 0
\(199\) −0.803346 + 1.39144i −0.0569477 + 0.0986363i −0.893094 0.449870i \(-0.851470\pi\)
0.836146 + 0.548507i \(0.184803\pi\)
\(200\) 0.598374 14.0316i 0.0423114 0.992186i
\(201\) 0 0
\(202\) 3.05542i 0.214978i
\(203\) −4.28640 2.47475i −0.300846 0.173694i
\(204\) 0 0
\(205\) 19.6966 10.8189i 1.37567 0.755627i
\(206\) 6.76936 + 11.7249i 0.471643 + 0.816910i
\(207\) 0 0
\(208\) 0.0170742i 0.00118388i
\(209\) 4.52882 6.99754i 0.313265 0.484030i
\(210\) 0 0
\(211\) 3.04993 + 5.28263i 0.209966 + 0.363671i 0.951703 0.307019i \(-0.0993314\pi\)
−0.741738 + 0.670690i \(0.765998\pi\)
\(212\) 8.92322 5.15182i 0.612849 0.353829i
\(213\) 0 0
\(214\) 0.456115 + 0.790014i 0.0311794 + 0.0540042i
\(215\) 5.30985 + 9.66695i 0.362129 + 0.659280i
\(216\) 0 0
\(217\) 3.20459i 0.217542i
\(218\) −5.03934 2.90947i −0.341307 0.197054i
\(219\) 0 0
\(220\) 4.59128 + 2.78287i 0.309544 + 0.187621i
\(221\) −1.03014 −0.0692946
\(222\) 0 0
\(223\) 14.9175 8.61263i 0.998950 0.576744i 0.0910127 0.995850i \(-0.470990\pi\)
0.907938 + 0.419106i \(0.137656\pi\)
\(224\) −1.61274 + 2.79334i −0.107755 + 0.186638i
\(225\) 0 0
\(226\) 3.40838 + 5.90348i 0.226722 + 0.392694i
\(227\) 1.18505i 0.0786542i 0.999226 + 0.0393271i \(0.0125214\pi\)
−0.999226 + 0.0393271i \(0.987479\pi\)
\(228\) 0 0
\(229\) −6.24791 −0.412873 −0.206437 0.978460i \(-0.566187\pi\)
−0.206437 + 0.978460i \(0.566187\pi\)
\(230\) 0.138755 6.51046i 0.00914924 0.429287i
\(231\) 0 0
\(232\) 21.2525 + 12.2701i 1.39530 + 0.805574i
\(233\) 2.38752 1.37844i 0.156412 0.0903043i −0.419751 0.907639i \(-0.637883\pi\)
0.576163 + 0.817335i \(0.304549\pi\)
\(234\) 0 0
\(235\) −10.2453 + 16.9030i −0.668327 + 1.10263i
\(236\) 4.66365 0.303578
\(237\) 0 0
\(238\) −2.24157 1.29417i −0.145299 0.0838887i
\(239\) 17.3055 1.11940 0.559701 0.828695i \(-0.310916\pi\)
0.559701 + 0.828695i \(0.310916\pi\)
\(240\) 0 0
\(241\) 2.39331 4.14533i 0.154167 0.267024i −0.778589 0.627535i \(-0.784064\pi\)
0.932755 + 0.360510i \(0.117397\pi\)
\(242\) −5.48690 + 3.16786i −0.352711 + 0.203638i
\(243\) 0 0
\(244\) 2.20436 + 3.81806i 0.141120 + 0.244426i
\(245\) 0.318228 14.9314i 0.0203308 0.953934i
\(246\) 0 0
\(247\) −0.754923 + 0.386131i −0.0480346 + 0.0245689i
\(248\) 15.8888i 1.00894i
\(249\) 0 0
\(250\) 4.27956 + 8.64490i 0.270663 + 0.546751i
\(251\) −13.1240 + 22.7314i −0.828377 + 1.43479i 0.0709346 + 0.997481i \(0.477402\pi\)
−0.899311 + 0.437309i \(0.855932\pi\)
\(252\) 0 0
\(253\) 5.58979 + 3.22727i 0.351427 + 0.202897i
\(254\) −7.31324 −0.458874
\(255\) 0 0
\(256\) 7.88594 13.6589i 0.492871 0.853678i
\(257\) 19.2695 + 11.1252i 1.20200 + 0.693974i 0.960999 0.276552i \(-0.0891917\pi\)
0.240999 + 0.970525i \(0.422525\pi\)
\(258\) 0 0
\(259\) −0.541356 −0.0336382
\(260\) −0.262945 0.478710i −0.0163072 0.0296883i
\(261\) 0 0
\(262\) 1.40052 + 0.808593i 0.0865246 + 0.0499550i
\(263\) −7.63264 + 4.40671i −0.470649 + 0.271729i −0.716511 0.697576i \(-0.754262\pi\)
0.245863 + 0.969305i \(0.420929\pi\)
\(264\) 0 0
\(265\) −9.51122 + 15.6919i −0.584269 + 0.963948i
\(266\) −2.12780 0.108199i −0.130464 0.00663409i
\(267\) 0 0
\(268\) −4.39702 + 2.53862i −0.268591 + 0.155071i
\(269\) 2.38209 + 4.12590i 0.145239 + 0.251561i 0.929462 0.368918i \(-0.120272\pi\)
−0.784223 + 0.620479i \(0.786938\pi\)
\(270\) 0 0
\(271\) −1.75946 3.04748i −0.106880 0.185121i 0.807625 0.589696i \(-0.200753\pi\)
−0.914505 + 0.404576i \(0.867419\pi\)
\(272\) −0.402520 0.232395i −0.0244063 0.0140910i
\(273\) 0 0
\(274\) −10.7514 −0.649517
\(275\) −9.55246 0.407361i −0.576035 0.0245648i
\(276\) 0 0
\(277\) 32.7724i 1.96910i −0.175098 0.984551i \(-0.556024\pi\)
0.175098 0.984551i \(-0.443976\pi\)
\(278\) 0.270258i 0.0162090i
\(279\) 0 0
\(280\) 0.0758178 3.55741i 0.00453098 0.212596i
\(281\) 4.95997 8.59091i 0.295887 0.512491i −0.679304 0.733857i \(-0.737718\pi\)
0.975191 + 0.221366i \(0.0710516\pi\)
\(282\) 0 0
\(283\) −2.14066 + 1.23591i −0.127249 + 0.0734673i −0.562273 0.826951i \(-0.690073\pi\)
0.435024 + 0.900419i \(0.356740\pi\)
\(284\) −6.52330 −0.387087
\(285\) 0 0
\(286\) −0.320945 −0.0189779
\(287\) 4.93070 2.84674i 0.291050 0.168038i
\(288\) 0 0
\(289\) 5.52111 9.56285i 0.324771 0.562520i
\(290\) −16.8513 0.359146i −0.989543 0.0210898i
\(291\) 0 0
\(292\) 10.8034i 0.632219i
\(293\) 17.0284i 0.994812i −0.867518 0.497406i \(-0.834286\pi\)
0.867518 0.497406i \(-0.165714\pi\)
\(294\) 0 0
\(295\) −7.27947 + 3.99846i −0.423827 + 0.232799i
\(296\) 2.68411 0.156011
\(297\) 0 0
\(298\) −3.26209 1.88337i −0.188968 0.109101i
\(299\) −0.328310 0.568650i −0.0189867 0.0328859i
\(300\) 0 0
\(301\) 1.39716 + 2.41995i 0.0805310 + 0.139484i
\(302\) 0.147926 0.0854052i 0.00851220 0.00491452i
\(303\) 0 0
\(304\) −0.382090 0.0194293i −0.0219144 0.00111435i
\(305\) −6.71425 4.06965i −0.384457 0.233028i
\(306\) 0 0
\(307\) 18.1686 10.4896i 1.03694 0.598676i 0.117972 0.993017i \(-0.462361\pi\)
0.918964 + 0.394341i \(0.129027\pi\)
\(308\) 1.17799 + 0.680110i 0.0671220 + 0.0387529i
\(309\) 0 0
\(310\) −5.25386 9.56502i −0.298399 0.543257i
\(311\) 3.14805 0.178509 0.0892547 0.996009i \(-0.471551\pi\)
0.0892547 + 0.996009i \(0.471551\pi\)
\(312\) 0 0
\(313\) 10.6459 + 6.14641i 0.601742 + 0.347416i 0.769726 0.638374i \(-0.220393\pi\)
−0.167985 + 0.985790i \(0.553726\pi\)
\(314\) −6.80301 + 11.7832i −0.383916 + 0.664962i
\(315\) 0 0
\(316\) −8.32027 −0.468052
\(317\) −9.92630 5.73095i −0.557517 0.321882i 0.194631 0.980876i \(-0.437649\pi\)
−0.752148 + 0.658994i \(0.770982\pi\)
\(318\) 0 0
\(319\) 8.35327 14.4683i 0.467694 0.810069i
\(320\) −0.225683 + 10.5892i −0.0126160 + 0.591952i
\(321\) 0 0
\(322\) 1.64984i 0.0919417i
\(323\) 1.17223 23.0527i 0.0652246 1.28269i
\(324\) 0 0
\(325\) 0.820860 + 0.521776i 0.0455331 + 0.0289429i
\(326\) 3.96348 + 6.86495i 0.219517 + 0.380214i
\(327\) 0 0
\(328\) −24.4470 + 14.1145i −1.34986 + 0.779343i
\(329\) −2.50385 + 4.33680i −0.138042 + 0.239095i
\(330\) 0 0
\(331\) 5.85724 0.321943 0.160972 0.986959i \(-0.448537\pi\)
0.160972 + 0.986959i \(0.448537\pi\)
\(332\) −4.91213 2.83602i −0.269588 0.155647i
\(333\) 0 0
\(334\) 2.64892 0.144942
\(335\) 4.68676 7.73238i 0.256065 0.422465i
\(336\) 0 0
\(337\) −7.45644 + 4.30498i −0.406178 + 0.234507i −0.689146 0.724622i \(-0.742014\pi\)
0.282968 + 0.959129i \(0.408681\pi\)
\(338\) −9.68520 5.59175i −0.526805 0.304151i
\(339\) 0 0
\(340\) 14.8644 + 0.316799i 0.806134 + 0.0171808i
\(341\) 10.8168 0.585760
\(342\) 0 0
\(343\) 7.74945i 0.418431i
\(344\) −6.92730 11.9984i −0.373495 0.646912i
\(345\) 0 0
\(346\) −4.49230 + 7.78089i −0.241507 + 0.418303i
\(347\) −10.4704 + 6.04507i −0.562079 + 0.324517i −0.753980 0.656898i \(-0.771868\pi\)
0.191900 + 0.981414i \(0.438535\pi\)
\(348\) 0 0
\(349\) −18.9819 −1.01608 −0.508040 0.861333i \(-0.669630\pi\)
−0.508040 + 0.861333i \(0.669630\pi\)
\(350\) 1.13067 + 2.16663i 0.0604369 + 0.115811i
\(351\) 0 0
\(352\) −9.42863 5.44362i −0.502548 0.290146i
\(353\) 7.71759i 0.410766i 0.978682 + 0.205383i \(0.0658440\pi\)
−0.978682 + 0.205383i \(0.934156\pi\)
\(354\) 0 0
\(355\) 10.1822 5.59287i 0.540415 0.296839i
\(356\) −2.11791 3.66833i −0.112249 0.194421i
\(357\) 0 0
\(358\) −10.0447 + 5.79929i −0.530877 + 0.306502i
\(359\) 3.51507 + 6.08828i 0.185518 + 0.321327i 0.943751 0.330657i \(-0.107270\pi\)
−0.758233 + 0.651984i \(0.773937\pi\)
\(360\) 0 0
\(361\) −7.78190 17.3333i −0.409573 0.912277i
\(362\) 6.86960i 0.361058i
\(363\) 0 0
\(364\) −0.0691877 0.119837i −0.00362642 0.00628114i
\(365\) −9.26246 16.8629i −0.484819 0.882647i
\(366\) 0 0
\(367\) −29.1945 16.8554i −1.52394 0.879847i −0.999598 0.0283394i \(-0.990978\pi\)
−0.524342 0.851508i \(-0.675689\pi\)
\(368\) 0.296261i 0.0154437i
\(369\) 0 0
\(370\) −1.61584 + 0.887544i −0.0840033 + 0.0461412i
\(371\) −2.32446 + 4.02608i −0.120680 + 0.209024i
\(372\) 0 0
\(373\) 10.0097i 0.518281i 0.965840 + 0.259141i \(0.0834393\pi\)
−0.965840 + 0.259141i \(0.916561\pi\)
\(374\) 4.36834 7.56619i 0.225882 0.391239i
\(375\) 0 0
\(376\) 12.4144 21.5024i 0.640225 1.10890i
\(377\) −1.47186 + 0.849780i −0.0758047 + 0.0437659i
\(378\) 0 0
\(379\) 35.8064 1.83925 0.919626 0.392796i \(-0.128492\pi\)
0.919626 + 0.392796i \(0.128492\pi\)
\(380\) 11.0119 5.33952i 0.564899 0.273911i
\(381\) 0 0
\(382\) 10.5353 6.08255i 0.539032 0.311210i
\(383\) 14.0725 8.12477i 0.719072 0.415156i −0.0953393 0.995445i \(-0.530394\pi\)
0.814411 + 0.580289i \(0.197060\pi\)
\(384\) 0 0
\(385\) −2.42182 0.0516153i −0.123427 0.00263056i
\(386\) 1.71558 2.97146i 0.0873205 0.151244i
\(387\) 0 0
\(388\) 19.0755i 0.968411i
\(389\) 9.69280 16.7884i 0.491445 0.851207i −0.508507 0.861058i \(-0.669802\pi\)
0.999951 + 0.00985094i \(0.00313570\pi\)
\(390\) 0 0
\(391\) 17.8744 0.903947
\(392\) 18.7607i 0.947556i
\(393\) 0 0
\(394\) 7.91574 + 13.7105i 0.398789 + 0.690723i
\(395\) 12.9871 7.13353i 0.653451 0.358927i
\(396\) 0 0
\(397\) −4.63682 + 2.67707i −0.232716 + 0.134358i −0.611824 0.790994i \(-0.709564\pi\)
0.379109 + 0.925352i \(0.376231\pi\)
\(398\) 1.38622i 0.0694851i
\(399\) 0 0
\(400\) 0.203035 + 0.389063i 0.0101518 + 0.0194531i
\(401\) 4.16916 + 7.22120i 0.208198 + 0.360609i 0.951147 0.308739i \(-0.0999068\pi\)
−0.742949 + 0.669348i \(0.766574\pi\)
\(402\) 0 0
\(403\) −0.952965 0.550195i −0.0474706 0.0274072i
\(404\) 2.22328 + 3.85083i 0.110612 + 0.191586i
\(405\) 0 0
\(406\) −4.27034 −0.211933
\(407\) 1.82729i 0.0905755i
\(408\) 0 0
\(409\) −17.6613 + 30.5903i −0.873297 + 1.51259i −0.0147313 + 0.999891i \(0.504689\pi\)
−0.858566 + 0.512703i \(0.828644\pi\)
\(410\) 10.0499 16.5807i 0.496331 0.818864i
\(411\) 0 0
\(412\) −17.0632 9.85147i −0.840646 0.485347i
\(413\) −1.82229 + 1.05210i −0.0896689 + 0.0517704i
\(414\) 0 0
\(415\) 10.0988 + 0.215233i 0.495733 + 0.0105654i
\(416\) 0.553780 + 0.959176i 0.0271513 + 0.0470274i
\(417\) 0 0
\(418\) 0.365214 7.18219i 0.0178632 0.351292i
\(419\) 21.2453 1.03790 0.518949 0.854805i \(-0.326323\pi\)
0.518949 + 0.854805i \(0.326323\pi\)
\(420\) 0 0
\(421\) 7.43719 + 12.8816i 0.362467 + 0.627811i 0.988366 0.152093i \(-0.0486013\pi\)
−0.625900 + 0.779904i \(0.715268\pi\)
\(422\) 4.55775 + 2.63142i 0.221868 + 0.128096i
\(423\) 0 0
\(424\) 11.5250 19.9618i 0.559702 0.969432i
\(425\) −23.4734 + 12.2497i −1.13863 + 0.594200i
\(426\) 0 0
\(427\) −1.72268 0.994587i −0.0833661 0.0481314i
\(428\) −1.14971 0.663785i −0.0555733 0.0320853i
\(429\) 0 0
\(430\) 8.13770 + 4.93243i 0.392435 + 0.237863i
\(431\) −8.47590 + 14.6807i −0.408270 + 0.707144i −0.994696 0.102858i \(-0.967201\pi\)
0.586426 + 0.810003i \(0.300534\pi\)
\(432\) 0 0
\(433\) −20.0450 11.5730i −0.963299 0.556161i −0.0661122 0.997812i \(-0.521060\pi\)
−0.897187 + 0.441651i \(0.854393\pi\)
\(434\) −1.38243 2.39444i −0.0663587 0.114937i
\(435\) 0 0
\(436\) 8.46832 0.405559
\(437\) 13.0990 6.69993i 0.626610 0.320501i
\(438\) 0 0
\(439\) 16.7729 + 29.0515i 0.800525 + 1.38655i 0.919271 + 0.393626i \(0.128779\pi\)
−0.118745 + 0.992925i \(0.537887\pi\)
\(440\) 12.0077 + 0.255915i 0.572444 + 0.0122003i
\(441\) 0 0
\(442\) −0.769710 + 0.444392i −0.0366114 + 0.0211376i
\(443\) −27.1567 15.6789i −1.29025 0.744929i −0.311555 0.950228i \(-0.600850\pi\)
−0.978699 + 0.205299i \(0.934183\pi\)
\(444\) 0 0
\(445\) 6.45094 + 3.91005i 0.305804 + 0.185354i
\(446\) 7.43081 12.8705i 0.351859 0.609438i
\(447\) 0 0
\(448\) 2.68343i 0.126780i
\(449\) −16.0301 −0.756509 −0.378255 0.925702i \(-0.623476\pi\)
−0.378255 + 0.925702i \(0.623476\pi\)
\(450\) 0 0
\(451\) 9.60888 + 16.6431i 0.452465 + 0.783692i
\(452\) −8.59136 4.96022i −0.404104 0.233309i
\(453\) 0 0
\(454\) 0.511217 + 0.885455i 0.0239926 + 0.0415564i
\(455\) 0.210739 + 0.127733i 0.00987959 + 0.00598823i
\(456\) 0 0
\(457\) 15.3980i 0.720286i 0.932897 + 0.360143i \(0.117272\pi\)
−0.932897 + 0.360143i \(0.882728\pi\)
\(458\) −4.66837 + 2.69529i −0.218139 + 0.125943i
\(459\) 0 0
\(460\) 4.56247 + 8.30630i 0.212726 + 0.387283i
\(461\) −2.90705 5.03517i −0.135395 0.234511i 0.790353 0.612651i \(-0.209897\pi\)
−0.925748 + 0.378140i \(0.876564\pi\)
\(462\) 0 0
\(463\) 32.6788i 1.51871i −0.650675 0.759356i \(-0.725514\pi\)
0.650675 0.759356i \(-0.274486\pi\)
\(464\) −0.766826 −0.0355990
\(465\) 0 0
\(466\) 1.18929 2.05991i 0.0550927 0.0954234i
\(467\) 6.59041i 0.304968i 0.988306 + 0.152484i \(0.0487272\pi\)
−0.988306 + 0.152484i \(0.951273\pi\)
\(468\) 0 0
\(469\) 1.14540 1.98390i 0.0528898 0.0916078i
\(470\) −0.363369 + 17.0495i −0.0167610 + 0.786433i
\(471\) 0 0
\(472\) 9.03514 5.21644i 0.415876 0.240106i
\(473\) −8.16830 + 4.71597i −0.375579 + 0.216841i
\(474\) 0 0
\(475\) −12.6105 + 17.7757i −0.578610 + 0.815604i
\(476\) 3.76683 0.172652
\(477\) 0 0
\(478\) 12.9305 7.46545i 0.591429 0.341462i
\(479\) 18.4032 31.8753i 0.840864 1.45642i −0.0483016 0.998833i \(-0.515381\pi\)
0.889165 0.457586i \(-0.151286\pi\)
\(480\) 0 0
\(481\) −0.0929453 + 0.160986i −0.00423794 + 0.00734033i
\(482\) 4.12980i 0.188107i
\(483\) 0 0
\(484\) 4.61021 7.98511i 0.209555 0.362960i
\(485\) 16.3547 + 29.7749i 0.742628 + 1.35201i
\(486\) 0 0
\(487\) 2.45475i 0.111235i 0.998452 + 0.0556176i \(0.0177128\pi\)
−0.998452 + 0.0556176i \(0.982287\pi\)
\(488\) 8.54125 + 4.93129i 0.386644 + 0.223229i
\(489\) 0 0
\(490\) −6.20350 11.2939i −0.280246 0.510206i
\(491\) 8.89716 + 15.4103i 0.401523 + 0.695459i 0.993910 0.110195i \(-0.0351476\pi\)
−0.592387 + 0.805654i \(0.701814\pi\)
\(492\) 0 0
\(493\) 46.2651i 2.08367i
\(494\) −0.397498 + 0.614180i −0.0178843 + 0.0276333i
\(495\) 0 0
\(496\) −0.248243 0.429970i −0.0111464 0.0193062i
\(497\) 2.54894 1.47163i 0.114335 0.0660116i
\(498\) 0 0
\(499\) −14.6399 25.3570i −0.655371 1.13514i −0.981801 0.189915i \(-0.939179\pi\)
0.326429 0.945222i \(-0.394155\pi\)
\(500\) −11.6841 7.78140i −0.522530 0.347995i
\(501\) 0 0
\(502\) 22.6462i 1.01075i
\(503\) 25.4939 + 14.7189i 1.13672 + 0.656283i 0.945615 0.325287i \(-0.105461\pi\)
0.191100 + 0.981571i \(0.438794\pi\)
\(504\) 0 0
\(505\) −6.77188 4.10458i −0.301345 0.182652i
\(506\) 5.56885 0.247566
\(507\) 0 0
\(508\) 9.21710 5.32149i 0.408943 0.236103i
\(509\) −3.34723 + 5.79757i −0.148363 + 0.256973i −0.930623 0.365980i \(-0.880734\pi\)
0.782259 + 0.622953i \(0.214067\pi\)
\(510\) 0 0
\(511\) −2.43719 4.22134i −0.107815 0.186741i
\(512\) 0.992797i 0.0438758i
\(513\) 0 0
\(514\) 19.1973 0.846757
\(515\) 35.0803 + 0.747653i 1.54582 + 0.0329455i
\(516\) 0 0
\(517\) −14.6384 8.45150i −0.643797 0.371696i
\(518\) −0.404496 + 0.233536i −0.0177725 + 0.0102610i
\(519\) 0 0
\(520\) −1.04487 0.633318i −0.0458206 0.0277728i
\(521\) −20.0801 −0.879724 −0.439862 0.898065i \(-0.644973\pi\)
−0.439862 + 0.898065i \(0.644973\pi\)
\(522\) 0 0
\(523\) 31.5615 + 18.2220i 1.38009 + 0.796793i 0.992169 0.124901i \(-0.0398612\pi\)
0.387918 + 0.921694i \(0.373195\pi\)
\(524\) −2.35350 −0.102813
\(525\) 0 0
\(526\) −3.80202 + 6.58530i −0.165776 + 0.287133i
\(527\) 25.9414 14.9773i 1.13003 0.652421i
\(528\) 0 0
\(529\) −5.80335 10.0517i −0.252319 0.437030i
\(530\) −0.337335 + 15.8279i −0.0146529 + 0.687521i
\(531\) 0 0
\(532\) 2.76047 1.41193i 0.119681 0.0612151i
\(533\) 1.95503i 0.0846816i
\(534\) 0 0
\(535\) 2.36369 + 0.0503764i 0.102191 + 0.00217796i
\(536\) −5.67906 + 9.83641i −0.245298 + 0.424868i
\(537\) 0 0
\(538\) 3.55975 + 2.05522i 0.153472 + 0.0886069i
\(539\) 12.7719 0.550124
\(540\) 0 0
\(541\) 7.31456 12.6692i 0.314478 0.544691i −0.664849 0.746978i \(-0.731504\pi\)
0.979326 + 0.202287i \(0.0648373\pi\)
\(542\) −2.62930 1.51803i −0.112938 0.0652049i
\(543\) 0 0
\(544\) −30.1498 −1.29266
\(545\) −13.2182 + 7.26046i −0.566204 + 0.311004i
\(546\) 0 0
\(547\) 17.6831 + 10.2093i 0.756073 + 0.436519i 0.827884 0.560899i \(-0.189545\pi\)
−0.0718112 + 0.997418i \(0.522878\pi\)
\(548\) 13.5503 7.82329i 0.578842 0.334194i
\(549\) 0 0
\(550\) −7.31324 + 3.81647i −0.311838 + 0.162735i
\(551\) −17.3417 33.9047i −0.738782 1.44439i
\(552\) 0 0
\(553\) 3.25109 1.87702i 0.138250 0.0798188i
\(554\) −14.1377 24.4872i −0.600653 1.04036i
\(555\) 0 0
\(556\) −0.196654 0.340615i −0.00833999 0.0144453i
\(557\) −31.0728 17.9399i −1.31660 0.760138i −0.333418 0.942779i \(-0.608202\pi\)
−0.983180 + 0.182641i \(0.941535\pi\)
\(558\) 0 0
\(559\) 0.959512 0.0405830
\(560\) 0.0535287 + 0.0974526i 0.00226200 + 0.00411812i
\(561\) 0 0
\(562\) 8.55873i 0.361028i
\(563\) 37.7708i 1.59185i −0.605395 0.795925i \(-0.706985\pi\)
0.605395 0.795925i \(-0.293015\pi\)
\(564\) 0 0
\(565\) 17.6630 + 0.376444i 0.743086 + 0.0158371i
\(566\) −1.06632 + 1.84692i −0.0448208 + 0.0776319i
\(567\) 0 0
\(568\) −12.6380 + 7.29653i −0.530277 + 0.306155i
\(569\) 28.0844 1.17736 0.588681 0.808366i \(-0.299648\pi\)
0.588681 + 0.808366i \(0.299648\pi\)
\(570\) 0 0
\(571\) 20.6040 0.862253 0.431126 0.902292i \(-0.358116\pi\)
0.431126 + 0.902292i \(0.358116\pi\)
\(572\) 0.404496 0.233536i 0.0169128 0.00976463i
\(573\) 0 0
\(574\) 2.45611 4.25412i 0.102516 0.177563i
\(575\) −14.2431 9.05355i −0.593978 0.377559i
\(576\) 0 0
\(577\) 43.8371i 1.82496i 0.409119 + 0.912481i \(0.365836\pi\)
−0.409119 + 0.912481i \(0.634164\pi\)
\(578\) 9.52702i 0.396272i
\(579\) 0 0
\(580\) 21.4996 11.8093i 0.892720 0.490352i
\(581\) 2.55918 0.106173
\(582\) 0 0
\(583\) −13.5896 7.84597i −0.562825 0.324947i
\(584\) 12.0839 + 20.9300i 0.500036 + 0.866088i
\(585\) 0 0
\(586\) −7.34591 12.7235i −0.303457 0.525602i
\(587\) −32.8925 + 18.9905i −1.35762 + 0.783821i −0.989302 0.145880i \(-0.953399\pi\)
−0.368315 + 0.929701i \(0.620065\pi\)
\(588\) 0 0
\(589\) 13.3968 20.6996i 0.552006 0.852914i
\(590\) −3.71425 + 6.12790i −0.152913 + 0.252282i
\(591\) 0 0
\(592\) −0.0726355 + 0.0419361i −0.00298530 + 0.00172356i
\(593\) 4.65934 + 2.69007i 0.191336 + 0.110468i 0.592608 0.805491i \(-0.298098\pi\)
−0.401272 + 0.915959i \(0.631432\pi\)
\(594\) 0 0
\(595\) −5.87962 + 3.22955i −0.241041 + 0.132399i
\(596\) 5.48175 0.224541
\(597\) 0 0
\(598\) −0.490620 0.283260i −0.0200630 0.0115834i
\(599\) −11.2143 + 19.4237i −0.458202 + 0.793629i −0.998866 0.0476095i \(-0.984840\pi\)
0.540664 + 0.841239i \(0.318173\pi\)
\(600\) 0 0
\(601\) −29.5732 −1.20632 −0.603159 0.797621i \(-0.706091\pi\)
−0.603159 + 0.797621i \(0.706091\pi\)
\(602\) 2.08789 + 1.20544i 0.0850960 + 0.0491302i
\(603\) 0 0
\(604\) −0.124291 + 0.215278i −0.00505731 + 0.00875952i
\(605\) −0.349880 + 16.4166i −0.0142247 + 0.667428i
\(606\) 0 0
\(607\) 24.5915i 0.998139i 0.866562 + 0.499069i \(0.166325\pi\)
−0.866562 + 0.499069i \(0.833675\pi\)
\(608\) −22.0949 + 11.3012i −0.896065 + 0.458323i
\(609\) 0 0
\(610\) −6.77243 0.144338i −0.274208 0.00584409i
\(611\) 0.859772 + 1.48917i 0.0347826 + 0.0602453i
\(612\) 0 0
\(613\) −25.8856 + 14.9450i −1.04551 + 0.603624i −0.921388 0.388643i \(-0.872944\pi\)
−0.124119 + 0.992267i \(0.539611\pi\)
\(614\) 9.05027 15.6755i 0.365239 0.632613i
\(615\) 0 0
\(616\) 3.04290 0.122602
\(617\) 35.2594 + 20.3570i 1.41949 + 0.819544i 0.996254 0.0864749i \(-0.0275603\pi\)
0.423238 + 0.906019i \(0.360894\pi\)
\(618\) 0 0
\(619\) 28.4784 1.14464 0.572322 0.820029i \(-0.306043\pi\)
0.572322 + 0.820029i \(0.306043\pi\)
\(620\) 13.5816 + 8.23210i 0.545451 + 0.330609i
\(621\) 0 0
\(622\) 2.35219 1.35804i 0.0943143 0.0544524i
\(623\) 1.65512 + 0.955582i 0.0663109 + 0.0382846i
\(624\) 0 0
\(625\) 24.9092 + 2.12836i 0.996369 + 0.0851345i
\(626\) 10.6060 0.423902
\(627\) 0 0
\(628\) 19.8009i 0.790141i
\(629\) −2.53014 4.38233i −0.100883 0.174735i
\(630\) 0 0
\(631\) −21.2101 + 36.7369i −0.844359 + 1.46247i 0.0418172 + 0.999125i \(0.486685\pi\)
−0.886176 + 0.463348i \(0.846648\pi\)
\(632\) −16.1193 + 9.30649i −0.641192 + 0.370192i
\(633\) 0 0
\(634\) −9.88912 −0.392747
\(635\) −9.82446 + 16.2087i −0.389872 + 0.643224i
\(636\) 0 0
\(637\) −1.12521 0.649643i −0.0445826 0.0257398i
\(638\) 14.4141i 0.570659i
\(639\) 0 0
\(640\) −7.85884 14.3076i −0.310648 0.565556i
\(641\) −14.7630 25.5702i −0.583102 1.00996i −0.995109 0.0987822i \(-0.968505\pi\)
0.412007 0.911181i \(-0.364828\pi\)
\(642\) 0 0
\(643\) 18.7036 10.7985i 0.737597 0.425852i −0.0835979 0.996500i \(-0.526641\pi\)
0.821195 + 0.570648i \(0.193308\pi\)
\(644\) 1.20051 + 2.07934i 0.0473066 + 0.0819374i
\(645\) 0 0
\(646\) −9.06885 17.7305i −0.356809 0.697596i
\(647\) 12.6128i 0.495861i −0.968778 0.247930i \(-0.920250\pi\)
0.968778 0.247930i \(-0.0797504\pi\)
\(648\) 0 0
\(649\) −3.55125 6.15095i −0.139399 0.241446i
\(650\) 0.838428 + 0.0357544i 0.0328858 + 0.00140240i
\(651\) 0 0
\(652\) −9.99059 5.76807i −0.391262 0.225895i
\(653\) 26.6312i 1.04216i 0.853508 + 0.521080i \(0.174471\pi\)
−0.853508 + 0.521080i \(0.825529\pi\)
\(654\) 0 0
\(655\) 3.67356 2.01781i 0.143538 0.0788424i
\(656\) 0.441045 0.763913i 0.0172199 0.0298258i
\(657\) 0 0
\(658\) 4.32055i 0.168433i
\(659\) −19.9772 + 34.6016i −0.778202 + 1.34789i 0.154775 + 0.987950i \(0.450535\pi\)
−0.932977 + 0.359936i \(0.882798\pi\)
\(660\) 0 0
\(661\) 6.76165 11.7115i 0.262998 0.455526i −0.704039 0.710161i \(-0.748622\pi\)
0.967037 + 0.254635i \(0.0819555\pi\)
\(662\) 4.37648 2.52676i 0.170097 0.0982053i
\(663\) 0 0
\(664\) −12.6887 −0.492418
\(665\) −3.09826 + 4.57062i −0.120145 + 0.177241i
\(666\) 0 0
\(667\) 25.5389 14.7449i 0.988871 0.570925i
\(668\) −3.33851 + 1.92749i −0.129171 + 0.0745768i
\(669\) 0 0
\(670\) 0.166225 7.79938i 0.00642185 0.301316i
\(671\) 3.35713 5.81471i 0.129600 0.224475i
\(672\) 0 0
\(673\) 34.4110i 1.32645i 0.748421 + 0.663224i \(0.230812\pi\)
−0.748421 + 0.663224i \(0.769188\pi\)
\(674\) −3.71425 + 6.43327i −0.143068 + 0.247800i
\(675\) 0 0
\(676\) 16.2754 0.625977
\(677\) 29.6650i 1.14012i −0.821604 0.570059i \(-0.806920\pi\)
0.821604 0.570059i \(-0.193080\pi\)
\(678\) 0 0
\(679\) 4.30335 + 7.45361i 0.165147 + 0.286043i
\(680\) 29.1519 16.0125i 1.11793 0.614053i
\(681\) 0 0
\(682\) 8.08217 4.66625i 0.309482 0.178680i
\(683\) 27.8978i 1.06748i 0.845648 + 0.533740i \(0.179214\pi\)
−0.845648 + 0.533740i \(0.820786\pi\)
\(684\) 0 0
\(685\) −14.4432 + 23.8290i −0.551848 + 0.910458i
\(686\) −3.34304 5.79032i −0.127638 0.221075i
\(687\) 0 0
\(688\) 0.374923 + 0.216462i 0.0142938 + 0.00825253i
\(689\) 0.798172 + 1.38247i 0.0304079 + 0.0526680i
\(690\) 0 0
\(691\) −49.6386 −1.88834 −0.944170 0.329459i \(-0.893134\pi\)
−0.944170 + 0.329459i \(0.893134\pi\)
\(692\) 13.0753i 0.497049i
\(693\) 0 0
\(694\) −5.21558 + 9.03364i −0.197981 + 0.342912i
\(695\) 0.598988 + 0.363059i 0.0227209 + 0.0137716i
\(696\) 0 0
\(697\) 46.0893 + 26.6097i 1.74576 + 1.00791i
\(698\) −14.1831 + 8.18863i −0.536839 + 0.309944i
\(699\) 0 0
\(700\) −3.00157 1.90794i −0.113449 0.0721132i
\(701\) −24.9906 43.2851i −0.943883 1.63485i −0.757972 0.652287i \(-0.773810\pi\)
−0.185911 0.982567i \(-0.559524\pi\)
\(702\) 0 0
\(703\) −3.49682 2.26315i −0.131885 0.0853562i
\(704\) −9.05763 −0.341372
\(705\) 0 0
\(706\) 3.32929 + 5.76651i 0.125300 + 0.217025i
\(707\) −1.73746 1.00312i −0.0653440 0.0377264i
\(708\) 0 0
\(709\) 12.5938 21.8131i 0.472971 0.819209i −0.526551 0.850144i \(-0.676515\pi\)
0.999521 + 0.0309345i \(0.00984834\pi\)
\(710\) 5.19533 8.57144i 0.194977 0.321680i
\(711\) 0 0
\(712\) −8.20628 4.73790i −0.307543 0.177560i
\(713\) 16.5353 + 9.54667i 0.619253 + 0.357526i
\(714\) 0 0
\(715\) −0.431150 + 0.711327i −0.0161241 + 0.0266021i
\(716\) 8.43972 14.6180i 0.315407 0.546301i
\(717\) 0 0
\(718\) 5.25285 + 3.03274i 0.196035 + 0.113181i
\(719\) −8.58777 14.8745i −0.320270 0.554724i 0.660274 0.751025i \(-0.270440\pi\)
−0.980544 + 0.196301i \(0.937107\pi\)
\(720\) 0 0
\(721\) 8.88979 0.331073
\(722\) −13.2920 9.59421i −0.494676 0.357060i
\(723\) 0 0
\(724\) −4.99868 8.65796i −0.185774 0.321771i
\(725\) −23.4337 + 36.8660i −0.870306 + 1.36917i
\(726\) 0 0
\(727\) 0.914981 0.528264i 0.0339348 0.0195922i −0.482937 0.875655i \(-0.660430\pi\)
0.516871 + 0.856063i \(0.327097\pi\)
\(728\) −0.268082 0.154777i −0.00993579 0.00573643i
\(729\) 0 0
\(730\) −14.1953 8.60409i −0.525393 0.318452i
\(731\) −13.0598 + 22.6203i −0.483035 + 0.836641i
\(732\) 0 0
\(733\) 20.5025i 0.757277i 0.925545 + 0.378639i \(0.123608\pi\)
−0.925545 + 0.378639i \(0.876392\pi\)
\(734\) −29.0851 −1.07355
\(735\) 0 0
\(736\) −9.60888 16.6431i −0.354188 0.613472i
\(737\) 6.69644 + 3.86619i 0.246666 + 0.142413i
\(738\) 0 0
\(739\) 12.4548 + 21.5723i 0.458157 + 0.793551i 0.998864 0.0476601i \(-0.0151764\pi\)
−0.540707 + 0.841211i \(0.681843\pi\)
\(740\) 1.39066 2.29436i 0.0511218 0.0843425i
\(741\) 0 0
\(742\) 4.01100i 0.147248i
\(743\) −11.4812 + 6.62867i −0.421204 + 0.243182i −0.695592 0.718437i \(-0.744858\pi\)
0.274388 + 0.961619i \(0.411525\pi\)
\(744\) 0 0
\(745\) −8.55645 + 4.69988i −0.313484 + 0.172190i
\(746\) 4.31808 + 7.47913i 0.158096 + 0.273830i
\(747\) 0 0
\(748\) 12.7145i 0.464889i
\(749\) 0.598988 0.0218866
\(750\) 0 0
\(751\) −12.4183 + 21.5091i −0.453149 + 0.784877i −0.998580 0.0532786i \(-0.983033\pi\)
0.545430 + 0.838156i \(0.316366\pi\)
\(752\) 0.775843i 0.0282921i
\(753\) 0 0
\(754\) −0.733174 + 1.26989i −0.0267006 + 0.0462468i
\(755\) 0.00943273 0.442589i 0.000343292 0.0161075i
\(756\) 0 0
\(757\) −41.9726 + 24.2329i −1.52552 + 0.880760i −0.525980 + 0.850497i \(0.676301\pi\)
−0.999542 + 0.0302631i \(0.990365\pi\)
\(758\) 26.7542 15.4465i 0.971756 0.561044i
\(759\) 0 0
\(760\) 15.3616 22.6617i 0.557222 0.822027i
\(761\) −40.3726 −1.46351 −0.731753 0.681570i \(-0.761298\pi\)
−0.731753 + 0.681570i \(0.761298\pi\)
\(762\) 0 0
\(763\) −3.30894 + 1.91042i −0.119792 + 0.0691617i
\(764\) −8.85195 + 15.3320i −0.320252 + 0.554693i
\(765\) 0 0
\(766\) 7.00989 12.1415i 0.253278 0.438690i
\(767\) 0.722538i 0.0260893i
\(768\) 0 0
\(769\) −22.4772 + 38.9317i −0.810550 + 1.40391i 0.101930 + 0.994792i \(0.467498\pi\)
−0.912480 + 0.409121i \(0.865835\pi\)
\(770\) −1.83182 + 1.00618i −0.0660144 + 0.0362603i
\(771\) 0 0
\(772\) 4.99337i 0.179715i
\(773\) 3.19256 + 1.84323i 0.114828 + 0.0662962i 0.556314 0.830972i \(-0.312215\pi\)
−0.441486 + 0.897268i \(0.645548\pi\)
\(774\) 0 0
\(775\) −28.2574 1.20503i −1.01504 0.0432859i
\(776\) −21.3365 36.9560i −0.765937 1.32664i
\(777\) 0 0
\(778\) 16.7255i 0.599639i
\(779\) 43.7501 + 2.22469i 1.56751 + 0.0797078i
\(780\) 0 0
\(781\) 4.96733 + 8.60367i 0.177745 + 0.307864i
\(782\) 13.3556 7.71084i 0.477594 0.275739i
\(783\) 0 0
\(784\) −0.293113 0.507687i −0.0104683 0.0181317i
\(785\) 16.9766 + 30.9071i 0.605922 + 1.10312i
\(786\) 0 0
\(787\) 45.7141i 1.62953i −0.579790 0.814766i \(-0.696865\pi\)
0.579790 0.814766i \(-0.303135\pi\)
\(788\) −19.9529 11.5198i −0.710793 0.410376i
\(789\) 0 0
\(790\) 6.62648 10.9326i 0.235760 0.388965i
\(791\) 4.47602 0.159149
\(792\) 0 0
\(793\) −0.591531 + 0.341521i −0.0210059 + 0.0121278i
\(794\) −2.30973 + 4.00056i −0.0819691 + 0.141975i
\(795\) 0 0
\(796\) −1.00869 1.74710i −0.0357520 0.0619243i
\(797\) 30.3378i 1.07462i −0.843385 0.537310i \(-0.819441\pi\)
0.843385 0.537310i \(-0.180559\pi\)
\(798\) 0 0
\(799\) −46.8091 −1.65599
\(800\) 24.0247 + 15.2712i 0.849401 + 0.539917i
\(801\) 0 0
\(802\) 6.23031 + 3.59707i 0.220000 + 0.127017i
\(803\) 14.2487 8.22650i 0.502826 0.290307i
\(804\) 0 0
\(805\) −3.65662 2.21635i −0.128879 0.0781162i
\(806\) −0.949395 −0.0334410
\(807\) 0 0
\(808\) 8.61456 + 4.97362i 0.303059 + 0.174971i
\(809\) 34.5585 1.21501 0.607506 0.794315i \(-0.292170\pi\)
0.607506 + 0.794315i \(0.292170\pi\)
\(810\) 0 0
\(811\) −16.6377 + 28.8173i −0.584229 + 1.01191i 0.410742 + 0.911751i \(0.365270\pi\)
−0.994971 + 0.100162i \(0.968064\pi\)
\(812\) 5.38204 3.10732i 0.188873 0.109046i
\(813\) 0 0
\(814\) −0.788277 1.36534i −0.0276291 0.0478550i
\(815\) 20.5396 + 0.437753i 0.719472 + 0.0153338i
\(816\) 0 0
\(817\) −1.09186 + 21.4722i −0.0381994 + 0.751218i
\(818\) 30.4757i 1.06556i
\(819\) 0 0
\(820\) −0.601230 + 28.2100i −0.0209959 + 0.985137i
\(821\) 6.35063 10.9996i 0.221638 0.383889i −0.733667 0.679509i \(-0.762193\pi\)
0.955306 + 0.295620i \(0.0955262\pi\)
\(822\) 0 0
\(823\) 10.4002 + 6.00454i 0.362527 + 0.209305i 0.670189 0.742191i \(-0.266213\pi\)
−0.307662 + 0.951496i \(0.599547\pi\)
\(824\) −44.0767 −1.53549
\(825\) 0 0
\(826\) −0.907731 + 1.57224i −0.0315840 + 0.0547051i
\(827\) −7.40057 4.27272i −0.257343 0.148577i 0.365779 0.930702i \(-0.380803\pi\)
−0.623122 + 0.782125i \(0.714136\pi\)
\(828\) 0 0
\(829\) 27.1042 0.941369 0.470685 0.882302i \(-0.344007\pi\)
0.470685 + 0.882302i \(0.344007\pi\)
\(830\) 7.63861 4.19573i 0.265140 0.145636i
\(831\) 0 0
\(832\) 0.797985 + 0.460717i 0.0276652 + 0.0159725i
\(833\) 30.6303 17.6844i 1.06128 0.612729i
\(834\) 0 0
\(835\) 3.55850 5.87094i 0.123147 0.203172i
\(836\) 4.76584 + 9.31767i 0.164830 + 0.322258i
\(837\) 0 0
\(838\) 15.8743 9.16500i 0.548367 0.316600i
\(839\) 18.2190 + 31.5562i 0.628989 + 1.08944i 0.987755 + 0.156013i \(0.0498642\pi\)
−0.358766 + 0.933427i \(0.616802\pi\)
\(840\) 0 0
\(841\) −23.6649 40.9887i −0.816029 1.41340i
\(842\) 11.1140 + 6.41667i 0.383014 + 0.221133i
\(843\) 0 0
\(844\) −7.65903 −0.263635
\(845\) −25.4042 + 13.9540i −0.873931 + 0.480032i
\(846\) 0 0
\(847\) 4.16017i 0.142945i
\(848\) 0.720256i 0.0247337i
\(849\) 0 0
\(850\) −12.2547 + 19.2791i −0.420331 + 0.661267i
\(851\) 1.61274 2.79334i 0.0552838 0.0957544i
\(852\) 0 0
\(853\) −15.8890 + 9.17354i −0.544030 + 0.314096i −0.746711 0.665149i \(-0.768368\pi\)
0.202680 + 0.979245i \(0.435035\pi\)
\(854\) −1.71622 −0.0587279
\(855\) 0 0
\(856\) −2.96986 −0.101508
\(857\) −6.80508 + 3.92892i −0.232457 + 0.134209i −0.611705 0.791086i \(-0.709516\pi\)
0.379248 + 0.925295i \(0.376183\pi\)
\(858\) 0 0
\(859\) −17.1511 + 29.7066i −0.585188 + 1.01358i 0.409664 + 0.912237i \(0.365646\pi\)
−0.994852 + 0.101339i \(0.967687\pi\)
\(860\) −13.8453 0.295079i −0.472120 0.0100621i
\(861\) 0 0
\(862\) 14.6257i 0.498153i
\(863\) 35.9451i 1.22359i 0.791018 + 0.611793i \(0.209551\pi\)
−0.791018 + 0.611793i \(0.790449\pi\)
\(864\) 0 0
\(865\) 11.2103 + 20.4092i 0.381163 + 0.693934i
\(866\) −19.9699 −0.678604
\(867\) 0 0
\(868\) 3.48463 + 2.01185i 0.118276 + 0.0682868i
\(869\) 6.33568 + 10.9737i 0.214923 + 0.372258i
\(870\) 0 0
\(871\) −0.393308 0.681229i −0.0133267 0.0230826i
\(872\) 16.4061 9.47209i 0.555582 0.320765i
\(873\) 0 0
\(874\) 6.89716 10.6569i 0.233300 0.360475i
\(875\) 6.32094 + 0.404638i 0.213687 + 0.0136793i
\(876\) 0 0
\(877\) 21.8685 12.6258i 0.738448 0.426343i −0.0830567 0.996545i \(-0.526468\pi\)
0.821505 + 0.570202i \(0.193135\pi\)
\(878\) 25.0651 + 14.4713i 0.845905 + 0.488383i
\(879\) 0 0
\(880\) −0.328941 + 0.180681i −0.0110886 + 0.00609074i
\(881\) −17.7796 −0.599010 −0.299505 0.954095i \(-0.596821\pi\)
−0.299505 + 0.954095i \(0.596821\pi\)
\(882\) 0 0
\(883\) −6.54146 3.77671i −0.220138 0.127096i 0.385876 0.922550i \(-0.373899\pi\)
−0.606014 + 0.795454i \(0.707232\pi\)
\(884\) 0.646726 1.12016i 0.0217517 0.0376751i
\(885\) 0 0
\(886\) −27.0550 −0.908930
\(887\) 14.0648 + 8.12030i 0.472249 + 0.272653i 0.717181 0.696887i \(-0.245432\pi\)
−0.244932 + 0.969540i \(0.578766\pi\)
\(888\) 0 0
\(889\) −2.40101 + 4.15867i −0.0805273 + 0.139477i
\(890\) 6.50684 + 0.138678i 0.218110 + 0.00464849i
\(891\) 0 0
\(892\) 21.6282i 0.724165i
\(893\) −34.3034 + 17.5456i −1.14792 + 0.587142i
\(894\) 0 0
\(895\) −0.640512 + 30.0532i −0.0214100 + 1.00457i
\(896\) −2.06787 3.58165i −0.0690825 0.119654i
\(897\) 0 0
\(898\) −11.9776 + 6.91525i −0.399697 + 0.230765i
\(899\) 24.7101 42.7991i 0.824127 1.42743i
\(900\) 0 0
\(901\) −43.4553 −1.44771
\(902\) 14.3593 + 8.29036i 0.478113 + 0.276039i
\(903\) 0 0
\(904\) −22.1927 −0.738118
\(905\) 15.2255 + 9.22848i 0.506112 + 0.306765i
\(906\) 0 0
\(907\) 15.8080 9.12675i 0.524896 0.303049i −0.214040 0.976825i \(-0.568662\pi\)
0.738935 + 0.673776i \(0.235329\pi\)
\(908\) −1.28861 0.743977i −0.0427639 0.0246897i
\(909\) 0 0
\(910\) 0.212565 + 0.00453032i 0.00704646 + 0.000150179i
\(911\) −15.9019 −0.526853 −0.263426 0.964679i \(-0.584853\pi\)
−0.263426 + 0.964679i \(0.584853\pi\)
\(912\) 0 0
\(913\) 8.63824i 0.285884i
\(914\) 6.64254 + 11.5052i 0.219716 + 0.380558i
\(915\) 0 0
\(916\) 3.92246 6.79390i 0.129602 0.224477i
\(917\) 0.919612 0.530939i 0.0303683 0.0175331i
\(918\) 0 0
\(919\) 30.0748 0.992075 0.496038 0.868301i \(-0.334788\pi\)
0.496038 + 0.868301i \(0.334788\pi\)
\(920\) 18.1300 + 10.9890i 0.597728 + 0.362296i
\(921\) 0 0
\(922\) −4.34425 2.50815i −0.143070 0.0826016i
\(923\) 1.01065i 0.0332661i
\(924\) 0 0
\(925\) −0.203567 + 4.77357i −0.00669325 + 0.156954i
\(926\) −14.0973 24.4173i −0.463267 0.802402i
\(927\) 0 0
\(928\) −43.0780 + 24.8711i −1.41410 + 0.816433i
\(929\) 18.4221 + 31.9081i 0.604410 + 1.04687i 0.992144 + 0.125098i \(0.0399245\pi\)
−0.387734 + 0.921771i \(0.626742\pi\)
\(930\) 0 0
\(931\) 15.8183 24.4411i 0.518424 0.801025i
\(932\) 3.46155i 0.113387i
\(933\) 0 0
\(934\) 2.84304 + 4.92429i 0.0930272 + 0.161128i
\(935\) −10.9010 19.8461i −0.356502 0.649036i
\(936\) 0 0
\(937\) −37.4401 21.6160i −1.22311 0.706165i −0.257533 0.966270i \(-0.582910\pi\)
−0.965580 + 0.260105i \(0.916243\pi\)
\(938\) 1.97646i 0.0645338i
\(939\) 0 0
\(940\) −11.9481 21.7524i −0.389704 0.709484i
\(941\) −10.1601 + 17.5979i −0.331211 + 0.573674i −0.982750 0.184941i \(-0.940790\pi\)
0.651539 + 0.758615i \(0.274124\pi\)
\(942\) 0 0
\(943\) 33.9225i 1.10467i
\(944\) −0.163001 + 0.282327i −0.00530525 + 0.00918896i
\(945\) 0 0
\(946\) −4.06885 + 7.04745i −0.132290 + 0.229133i
\(947\) −18.6239 + 10.7525i −0.605195 + 0.349409i −0.771083 0.636735i \(-0.780284\pi\)
0.165888 + 0.986145i \(0.446951\pi\)
\(948\) 0 0
\(949\) −1.67376 −0.0543327
\(950\) −1.75420 + 18.7219i −0.0569137 + 0.607418i
\(951\) 0 0
\(952\) 7.29768 4.21332i 0.236519 0.136554i
\(953\) −15.3547 + 8.86503i −0.497387 + 0.287166i −0.727634 0.685966i \(-0.759380\pi\)
0.230247 + 0.973132i \(0.426047\pi\)
\(954\) 0 0
\(955\) 0.671797 31.5211i 0.0217388 1.02000i
\(956\) −10.8645 + 18.8179i −0.351383 + 0.608613i
\(957\) 0 0
\(958\) 31.7559i 1.02599i
\(959\) −3.52980 + 6.11379i −0.113983 + 0.197425i
\(960\) 0 0
\(961\) 0.997355 0.0321727
\(962\) 0.160383i 0.00517095i
\(963\) 0 0
\(964\) 3.00506 + 5.20491i 0.0967864 + 0.167639i
\(965\) −4.28115 7.79413i −0.137815 0.250902i
\(966\) 0 0
\(967\) 11.8239 6.82652i 0.380230 0.219526i −0.297688 0.954663i \(-0.596216\pi\)
0.677919 + 0.735137i \(0.262882\pi\)
\(968\) 20.6267i 0.662966i
\(969\) 0 0
\(970\) 25.0647 + 15.1922i 0.804778 + 0.487793i
\(971\) 13.9798 + 24.2136i 0.448632 + 0.777053i 0.998297 0.0583319i \(-0.0185782\pi\)
−0.549666 + 0.835385i \(0.685245\pi\)
\(972\) 0 0
\(973\) 0.153682 + 0.0887286i 0.00492683 + 0.00284451i
\(974\) 1.05895 + 1.83416i 0.0339311 + 0.0587704i
\(975\) 0 0
\(976\) −0.308182 −0.00986468
\(977\) 17.8540i 0.571200i 0.958349 + 0.285600i \(0.0921929\pi\)
−0.958349 + 0.285600i \(0.907807\pi\)
\(978\) 0 0
\(979\) −3.22547 + 5.58668i −0.103086 + 0.178551i
\(980\) 16.0365 + 9.72006i 0.512267 + 0.310496i
\(981\) 0 0
\(982\) 13.2957 + 7.67630i 0.424284 + 0.244961i
\(983\) 42.4736 24.5222i 1.35470 0.782136i 0.365795 0.930695i \(-0.380797\pi\)
0.988903 + 0.148559i \(0.0474636\pi\)
\(984\) 0 0
\(985\) 41.0211 + 0.874268i 1.30704 + 0.0278565i
\(986\) −19.9583 34.5688i −0.635602 1.10089i
\(987\) 0 0
\(988\) 0.0540692 1.06331i 0.00172017 0.0338284i
\(989\) −16.6489 −0.529405
\(990\) 0 0
\(991\) 12.5337 + 21.7089i 0.398145 + 0.689607i 0.993497 0.113858i \(-0.0363209\pi\)
−0.595352 + 0.803465i \(0.702988\pi\)
\(992\) −27.8911 16.1029i −0.885543 0.511269i
\(993\) 0 0
\(994\) 1.26969 2.19917i 0.0402722 0.0697536i
\(995\) 3.07236 + 1.86222i 0.0974005 + 0.0590365i
\(996\) 0 0
\(997\) 26.0000 + 15.0111i 0.823427 + 0.475406i 0.851597 0.524197i \(-0.175635\pi\)
−0.0281699 + 0.999603i \(0.508968\pi\)
\(998\) −21.8776 12.6310i −0.692522 0.399828i
\(999\) 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 855.2.be.d.64.5 12
3.2 odd 2 95.2.i.b.64.2 yes 12
5.4 even 2 inner 855.2.be.d.64.2 12
15.2 even 4 475.2.e.g.26.2 12
15.8 even 4 475.2.e.g.26.5 12
15.14 odd 2 95.2.i.b.64.5 yes 12
19.11 even 3 inner 855.2.be.d.334.2 12
57.11 odd 6 95.2.i.b.49.5 yes 12
57.26 odd 6 1805.2.b.f.1084.2 6
57.50 even 6 1805.2.b.g.1084.5 6
95.49 even 6 inner 855.2.be.d.334.5 12
285.68 even 12 475.2.e.g.201.5 12
285.83 even 12 9025.2.a.bu.1.2 6
285.107 odd 12 9025.2.a.bt.1.2 6
285.164 even 6 1805.2.b.g.1084.2 6
285.182 even 12 475.2.e.g.201.2 12
285.197 even 12 9025.2.a.bu.1.5 6
285.239 odd 6 95.2.i.b.49.2 12
285.254 odd 6 1805.2.b.f.1084.5 6
285.278 odd 12 9025.2.a.bt.1.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.i.b.49.2 12 285.239 odd 6
95.2.i.b.49.5 yes 12 57.11 odd 6
95.2.i.b.64.2 yes 12 3.2 odd 2
95.2.i.b.64.5 yes 12 15.14 odd 2
475.2.e.g.26.2 12 15.2 even 4
475.2.e.g.26.5 12 15.8 even 4
475.2.e.g.201.2 12 285.182 even 12
475.2.e.g.201.5 12 285.68 even 12
855.2.be.d.64.2 12 5.4 even 2 inner
855.2.be.d.64.5 12 1.1 even 1 trivial
855.2.be.d.334.2 12 19.11 even 3 inner
855.2.be.d.334.5 12 95.49 even 6 inner
1805.2.b.f.1084.2 6 57.26 odd 6
1805.2.b.f.1084.5 6 285.254 odd 6
1805.2.b.g.1084.2 6 285.164 even 6
1805.2.b.g.1084.5 6 57.50 even 6
9025.2.a.bt.1.2 6 285.107 odd 12
9025.2.a.bt.1.5 6 285.278 odd 12
9025.2.a.bu.1.2 6 285.83 even 12
9025.2.a.bu.1.5 6 285.197 even 12