Properties

Label 243.2.g.a.19.5
Level $243$
Weight $2$
Character 243.19
Analytic conductor $1.940$
Analytic rank $0$
Dimension $144$
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] = [243,2,Mod(10,243)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(243, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("243.10");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 243 = 3^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 243.g (of order \(27\), degree \(18\), not 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: \(1.94036476912\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 19.5
Character \(\chi\) \(=\) 243.19
Dual form 243.2.g.a.64.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.702679 - 0.0821314i) q^{2} +(-1.45908 + 0.345808i) q^{4} +(-3.06981 - 1.54172i) q^{5} +(-0.775884 - 2.59163i) q^{7} +(-2.32646 + 0.846761i) q^{8} +O(q^{10})\) \(q+(0.702679 - 0.0821314i) q^{2} +(-1.45908 + 0.345808i) q^{4} +(-3.06981 - 1.54172i) q^{5} +(-0.775884 - 2.59163i) q^{7} +(-2.32646 + 0.846761i) q^{8} +(-2.28372 - 0.831205i) q^{10} +(0.0859074 - 1.47497i) q^{11} +(-3.31531 + 4.45324i) q^{13} +(-0.758052 - 1.75736i) q^{14} +(1.11479 - 0.559869i) q^{16} +(3.86594 - 3.24391i) q^{17} +(-3.94119 - 3.30705i) q^{19} +(5.01223 + 1.18792i) q^{20} +(-0.0607763 - 1.04349i) q^{22} +(0.497394 - 1.66141i) q^{23} +(4.06106 + 5.45495i) q^{25} +(-1.96385 + 3.40149i) q^{26} +(2.02828 + 3.51309i) q^{28} +(-0.851040 + 1.97293i) q^{29} +(2.61206 + 2.76862i) q^{31} +(4.87430 - 3.20588i) q^{32} +(2.45009 - 2.59694i) q^{34} +(-1.61375 + 9.15202i) q^{35} +(-0.891723 - 5.05721i) q^{37} +(-3.04100 - 2.00010i) q^{38} +(8.44725 + 0.987342i) q^{40} +(-4.48158 - 0.523822i) q^{41} +(-0.688837 - 0.453055i) q^{43} +(0.384712 + 2.18181i) q^{44} +(0.213054 - 1.20829i) q^{46} +(-4.60630 + 4.88239i) q^{47} +(-0.266150 + 0.175050i) q^{49} +(3.30164 + 3.49954i) q^{50} +(3.29733 - 7.64408i) q^{52} +(-2.58797 - 4.48249i) q^{53} +(-2.53771 + 4.39545i) q^{55} +(3.99955 + 5.37233i) q^{56} +(-0.435968 + 1.45623i) q^{58} +(-0.205501 - 3.52832i) q^{59} +(-5.27331 - 1.24980i) q^{61} +(2.06283 + 1.73092i) q^{62} +(1.25051 - 1.04930i) q^{64} +(17.0430 - 8.55933i) q^{65} +(-2.59382 - 6.01314i) q^{67} +(-4.51893 + 6.06998i) q^{68} +(-0.382279 + 6.56347i) q^{70} +(-3.30039 - 1.20125i) q^{71} +(0.668031 - 0.243143i) q^{73} +(-1.04195 - 3.48036i) q^{74} +(6.89410 + 3.46235i) q^{76} +(-3.88925 + 0.921768i) q^{77} +(15.5883 - 1.82202i) q^{79} -4.28536 q^{80} -3.19214 q^{82} +(5.89572 - 0.689111i) q^{83} +(-16.8689 + 3.99800i) q^{85} +(-0.521241 - 0.261777i) q^{86} +(1.04909 + 3.50421i) q^{88} +(3.78422 - 1.37734i) q^{89} +(14.1135 + 5.13688i) q^{91} +(-0.151207 + 2.59613i) q^{92} +(-2.83575 + 3.80908i) q^{94} +(7.00017 + 16.2282i) q^{95} +(-10.7605 + 5.40414i) q^{97} +(-0.172641 + 0.144863i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26} - 9 q^{28} - 9 q^{29} - 18 q^{31} - 36 q^{32} - 18 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} - 18 q^{40} - 18 q^{43} - 54 q^{44} - 18 q^{46} - 36 q^{47} - 18 q^{49} - 99 q^{50} - 45 q^{53} - 9 q^{55} - 126 q^{56} - 18 q^{58} - 45 q^{59} - 18 q^{61} - 81 q^{62} - 18 q^{64} + 9 q^{67} + 99 q^{68} + 36 q^{70} + 90 q^{71} - 18 q^{73} + 162 q^{74} + 63 q^{76} + 162 q^{77} + 36 q^{79} + 288 q^{80} - 36 q^{82} + 90 q^{83} + 36 q^{85} + 162 q^{86} + 63 q^{88} + 81 q^{89} - 18 q^{91} + 144 q^{92} + 36 q^{94} - 18 q^{95} + 9 q^{97} - 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{26}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.702679 0.0821314i 0.496869 0.0580757i 0.136032 0.990704i \(-0.456565\pi\)
0.360837 + 0.932629i \(0.382491\pi\)
\(3\) 0 0
\(4\) −1.45908 + 0.345808i −0.729539 + 0.172904i
\(5\) −3.06981 1.54172i −1.37286 0.689477i −0.399070 0.916920i \(-0.630667\pi\)
−0.973791 + 0.227443i \(0.926963\pi\)
\(6\) 0 0
\(7\) −0.775884 2.59163i −0.293257 0.979545i −0.969955 0.243285i \(-0.921775\pi\)
0.676698 0.736260i \(-0.263410\pi\)
\(8\) −2.32646 + 0.846761i −0.822527 + 0.299375i
\(9\) 0 0
\(10\) −2.28372 0.831205i −0.722174 0.262850i
\(11\) 0.0859074 1.47497i 0.0259021 0.444721i −0.960278 0.279045i \(-0.909982\pi\)
0.986180 0.165677i \(-0.0529808\pi\)
\(12\) 0 0
\(13\) −3.31531 + 4.45324i −0.919502 + 1.23511i 0.0521373 + 0.998640i \(0.483397\pi\)
−0.971640 + 0.236466i \(0.924011\pi\)
\(14\) −0.758052 1.75736i −0.202598 0.469675i
\(15\) 0 0
\(16\) 1.11479 0.559869i 0.278698 0.139967i
\(17\) 3.86594 3.24391i 0.937627 0.786763i −0.0395437 0.999218i \(-0.512590\pi\)
0.977171 + 0.212455i \(0.0681460\pi\)
\(18\) 0 0
\(19\) −3.94119 3.30705i −0.904171 0.758690i 0.0668301 0.997764i \(-0.478711\pi\)
−0.971001 + 0.239075i \(0.923156\pi\)
\(20\) 5.01223 + 1.18792i 1.12077 + 0.265627i
\(21\) 0 0
\(22\) −0.0607763 1.04349i −0.0129576 0.222473i
\(23\) 0.497394 1.66141i 0.103714 0.346428i −0.890343 0.455290i \(-0.849536\pi\)
0.994057 + 0.108862i \(0.0347207\pi\)
\(24\) 0 0
\(25\) 4.06106 + 5.45495i 0.812212 + 1.09099i
\(26\) −1.96385 + 3.40149i −0.385143 + 0.667087i
\(27\) 0 0
\(28\) 2.02828 + 3.51309i 0.383309 + 0.663911i
\(29\) −0.851040 + 1.97293i −0.158034 + 0.366364i −0.978775 0.204936i \(-0.934301\pi\)
0.820741 + 0.571300i \(0.193561\pi\)
\(30\) 0 0
\(31\) 2.61206 + 2.76862i 0.469139 + 0.497259i 0.918131 0.396277i \(-0.129698\pi\)
−0.448991 + 0.893536i \(0.648217\pi\)
\(32\) 4.87430 3.20588i 0.861662 0.566724i
\(33\) 0 0
\(34\) 2.45009 2.59694i 0.420186 0.445371i
\(35\) −1.61375 + 9.15202i −0.272773 + 1.54697i
\(36\) 0 0
\(37\) −0.891723 5.05721i −0.146598 0.831401i −0.966070 0.258281i \(-0.916844\pi\)
0.819472 0.573120i \(-0.194267\pi\)
\(38\) −3.04100 2.00010i −0.493316 0.324459i
\(39\) 0 0
\(40\) 8.44725 + 0.987342i 1.33563 + 0.156112i
\(41\) −4.48158 0.523822i −0.699906 0.0818072i −0.241304 0.970449i \(-0.577575\pi\)
−0.458601 + 0.888642i \(0.651649\pi\)
\(42\) 0 0
\(43\) −0.688837 0.453055i −0.105047 0.0690902i 0.495899 0.868380i \(-0.334839\pi\)
−0.600945 + 0.799290i \(0.705209\pi\)
\(44\) 0.384712 + 2.18181i 0.0579975 + 0.328920i
\(45\) 0 0
\(46\) 0.213054 1.20829i 0.0314131 0.178153i
\(47\) −4.60630 + 4.88239i −0.671898 + 0.712170i −0.970201 0.242301i \(-0.922098\pi\)
0.298303 + 0.954471i \(0.403579\pi\)
\(48\) 0 0
\(49\) −0.266150 + 0.175050i −0.0380215 + 0.0250071i
\(50\) 3.30164 + 3.49954i 0.466923 + 0.494909i
\(51\) 0 0
\(52\) 3.29733 7.64408i 0.457258 1.06004i
\(53\) −2.58797 4.48249i −0.355485 0.615717i 0.631716 0.775200i \(-0.282351\pi\)
−0.987201 + 0.159482i \(0.949017\pi\)
\(54\) 0 0
\(55\) −2.53771 + 4.39545i −0.342185 + 0.592682i
\(56\) 3.99955 + 5.37233i 0.534463 + 0.717908i
\(57\) 0 0
\(58\) −0.435968 + 1.45623i −0.0572454 + 0.191213i
\(59\) −0.205501 3.52832i −0.0267540 0.459348i −0.984906 0.173089i \(-0.944625\pi\)
0.958152 0.286259i \(-0.0924118\pi\)
\(60\) 0 0
\(61\) −5.27331 1.24980i −0.675178 0.160020i −0.121297 0.992616i \(-0.538705\pi\)
−0.553881 + 0.832596i \(0.686854\pi\)
\(62\) 2.06283 + 1.73092i 0.261980 + 0.219827i
\(63\) 0 0
\(64\) 1.25051 1.04930i 0.156314 0.131163i
\(65\) 17.0430 8.55933i 2.11393 1.06165i
\(66\) 0 0
\(67\) −2.59382 6.01314i −0.316885 0.734622i −0.999991 0.00430260i \(-0.998630\pi\)
0.683106 0.730320i \(-0.260629\pi\)
\(68\) −4.51893 + 6.06998i −0.548001 + 0.736093i
\(69\) 0 0
\(70\) −0.382279 + 6.56347i −0.0456910 + 0.784485i
\(71\) −3.30039 1.20125i −0.391685 0.142562i 0.138667 0.990339i \(-0.455718\pi\)
−0.530352 + 0.847777i \(0.677940\pi\)
\(72\) 0 0
\(73\) 0.668031 0.243143i 0.0781871 0.0284578i −0.302630 0.953108i \(-0.597865\pi\)
0.380818 + 0.924650i \(0.375643\pi\)
\(74\) −1.04195 3.48036i −0.121124 0.404584i
\(75\) 0 0
\(76\) 6.89410 + 3.46235i 0.790808 + 0.397159i
\(77\) −3.88925 + 0.921768i −0.443221 + 0.105045i
\(78\) 0 0
\(79\) 15.5883 1.82202i 1.75383 0.204993i 0.822396 0.568915i \(-0.192637\pi\)
0.931429 + 0.363922i \(0.118563\pi\)
\(80\) −4.28536 −0.479118
\(81\) 0 0
\(82\) −3.19214 −0.352513
\(83\) 5.89572 0.689111i 0.647140 0.0756398i 0.213810 0.976875i \(-0.431413\pi\)
0.433330 + 0.901235i \(0.357339\pi\)
\(84\) 0 0
\(85\) −16.8689 + 3.99800i −1.82969 + 0.433644i
\(86\) −0.521241 0.261777i −0.0562069 0.0282282i
\(87\) 0 0
\(88\) 1.04909 + 3.50421i 0.111833 + 0.373550i
\(89\) 3.78422 1.37734i 0.401127 0.145998i −0.133576 0.991039i \(-0.542646\pi\)
0.534702 + 0.845040i \(0.320424\pi\)
\(90\) 0 0
\(91\) 14.1135 + 5.13688i 1.47949 + 0.538491i
\(92\) −0.151207 + 2.59613i −0.0157645 + 0.270665i
\(93\) 0 0
\(94\) −2.83575 + 3.80908i −0.292486 + 0.392876i
\(95\) 7.00017 + 16.2282i 0.718203 + 1.66498i
\(96\) 0 0
\(97\) −10.7605 + 5.40414i −1.09257 + 0.548707i −0.901460 0.432862i \(-0.857504\pi\)
−0.191106 + 0.981569i \(0.561207\pi\)
\(98\) −0.172641 + 0.144863i −0.0174394 + 0.0146334i
\(99\) 0 0
\(100\) −7.81176 6.55484i −0.781176 0.655484i
\(101\) −16.3766 3.88132i −1.62953 0.386206i −0.688690 0.725056i \(-0.741814\pi\)
−0.940840 + 0.338850i \(0.889962\pi\)
\(102\) 0 0
\(103\) −1.01132 17.3637i −0.0996486 1.71090i −0.564434 0.825478i \(-0.690906\pi\)
0.464786 0.885423i \(-0.346131\pi\)
\(104\) 3.94210 13.1675i 0.386555 1.29118i
\(105\) 0 0
\(106\) −2.18666 2.93720i −0.212388 0.285286i
\(107\) 3.74462 6.48587i 0.362006 0.627013i −0.626285 0.779594i \(-0.715425\pi\)
0.988291 + 0.152581i \(0.0487586\pi\)
\(108\) 0 0
\(109\) −1.69921 2.94312i −0.162755 0.281899i 0.773101 0.634283i \(-0.218705\pi\)
−0.935856 + 0.352384i \(0.885371\pi\)
\(110\) −1.42219 + 3.29701i −0.135601 + 0.314358i
\(111\) 0 0
\(112\) −2.31592 2.45474i −0.218834 0.231951i
\(113\) −1.71662 + 1.12904i −0.161486 + 0.106211i −0.627680 0.778472i \(-0.715995\pi\)
0.466194 + 0.884683i \(0.345625\pi\)
\(114\) 0 0
\(115\) −4.08833 + 4.33338i −0.381239 + 0.404090i
\(116\) 0.559478 3.17296i 0.0519462 0.294602i
\(117\) 0 0
\(118\) −0.434187 2.46240i −0.0399701 0.226682i
\(119\) −11.4065 7.50219i −1.04563 0.687725i
\(120\) 0 0
\(121\) 8.75745 + 1.02360i 0.796132 + 0.0930545i
\(122\) −3.80809 0.445102i −0.344768 0.0402976i
\(123\) 0 0
\(124\) −4.76860 3.13636i −0.428233 0.281653i
\(125\) −1.07411 6.09158i −0.0960713 0.544847i
\(126\) 0 0
\(127\) −1.46076 + 8.28439i −0.129622 + 0.735121i 0.848833 + 0.528661i \(0.177306\pi\)
−0.978455 + 0.206460i \(0.933806\pi\)
\(128\) −7.21464 + 7.64707i −0.637690 + 0.675912i
\(129\) 0 0
\(130\) 11.2728 7.41423i 0.988689 0.650271i
\(131\) 7.36003 + 7.80118i 0.643049 + 0.681592i 0.964121 0.265463i \(-0.0855247\pi\)
−0.321072 + 0.947055i \(0.604043\pi\)
\(132\) 0 0
\(133\) −5.51276 + 12.7800i −0.478017 + 1.10817i
\(134\) −2.31649 4.01228i −0.200114 0.346608i
\(135\) 0 0
\(136\) −6.24712 + 10.8203i −0.535686 + 0.927835i
\(137\) −6.37060 8.55720i −0.544277 0.731091i 0.441849 0.897089i \(-0.354323\pi\)
−0.986126 + 0.165999i \(0.946915\pi\)
\(138\) 0 0
\(139\) −0.808205 + 2.69959i −0.0685510 + 0.228976i −0.985399 0.170260i \(-0.945539\pi\)
0.916848 + 0.399236i \(0.130725\pi\)
\(140\) −0.810255 13.9115i −0.0684791 1.17574i
\(141\) 0 0
\(142\) −2.41778 0.573024i −0.202895 0.0480871i
\(143\) 6.28360 + 5.27257i 0.525461 + 0.440914i
\(144\) 0 0
\(145\) 5.65423 4.74447i 0.469559 0.394006i
\(146\) 0.449442 0.225718i 0.0371961 0.0186806i
\(147\) 0 0
\(148\) 3.04992 + 7.07050i 0.250702 + 0.581191i
\(149\) 0.410135 0.550907i 0.0335996 0.0451321i −0.785006 0.619488i \(-0.787340\pi\)
0.818606 + 0.574356i \(0.194748\pi\)
\(150\) 0 0
\(151\) −0.0292138 + 0.501582i −0.00237739 + 0.0408182i −0.999288 0.0377236i \(-0.987989\pi\)
0.996911 + 0.0785418i \(0.0250264\pi\)
\(152\) 11.9693 + 4.35647i 0.970838 + 0.353356i
\(153\) 0 0
\(154\) −2.65719 + 0.967136i −0.214122 + 0.0779341i
\(155\) −3.75010 12.5262i −0.301215 1.00613i
\(156\) 0 0
\(157\) −11.3361 5.69318i −0.904716 0.454365i −0.0653065 0.997865i \(-0.520802\pi\)
−0.839409 + 0.543500i \(0.817099\pi\)
\(158\) 10.8040 2.56059i 0.859517 0.203709i
\(159\) 0 0
\(160\) −19.9057 + 2.32665i −1.57369 + 0.183938i
\(161\) −4.69169 −0.369757
\(162\) 0 0
\(163\) 13.8238 1.08276 0.541382 0.840777i \(-0.317901\pi\)
0.541382 + 0.840777i \(0.317901\pi\)
\(164\) 6.72012 0.785469i 0.524753 0.0613348i
\(165\) 0 0
\(166\) 4.08620 0.968448i 0.317151 0.0751662i
\(167\) −2.47720 1.24410i −0.191692 0.0962712i 0.350365 0.936613i \(-0.386058\pi\)
−0.542056 + 0.840342i \(0.682354\pi\)
\(168\) 0 0
\(169\) −5.11159 17.0739i −0.393199 1.31338i
\(170\) −11.5250 + 4.19477i −0.883931 + 0.321725i
\(171\) 0 0
\(172\) 1.16174 + 0.422837i 0.0885815 + 0.0322410i
\(173\) −1.20706 + 20.7244i −0.0917709 + 1.57565i 0.567266 + 0.823535i \(0.308001\pi\)
−0.659037 + 0.752111i \(0.729036\pi\)
\(174\) 0 0
\(175\) 10.9863 14.7572i 0.830487 1.11554i
\(176\) −0.730023 1.69238i −0.0550276 0.127568i
\(177\) 0 0
\(178\) 2.54597 1.27863i 0.190829 0.0958377i
\(179\) 10.8498 9.10407i 0.810953 0.680470i −0.139882 0.990168i \(-0.544672\pi\)
0.950835 + 0.309698i \(0.100228\pi\)
\(180\) 0 0
\(181\) −0.124097 0.104130i −0.00922404 0.00773989i 0.638164 0.769901i \(-0.279694\pi\)
−0.647388 + 0.762161i \(0.724139\pi\)
\(182\) 10.3391 + 2.45042i 0.766387 + 0.181637i
\(183\) 0 0
\(184\) 0.249653 + 4.28637i 0.0184047 + 0.315996i
\(185\) −5.05937 + 16.8995i −0.371972 + 1.24247i
\(186\) 0 0
\(187\) −4.45256 5.98083i −0.325604 0.437362i
\(188\) 5.03258 8.71668i 0.367038 0.635729i
\(189\) 0 0
\(190\) 6.25172 + 10.8283i 0.453548 + 0.785568i
\(191\) −9.22017 + 21.3748i −0.667148 + 1.54662i 0.161512 + 0.986871i \(0.448363\pi\)
−0.828660 + 0.559753i \(0.810896\pi\)
\(192\) 0 0
\(193\) −7.36724 7.80882i −0.530305 0.562091i 0.405732 0.913992i \(-0.367017\pi\)
−0.936037 + 0.351901i \(0.885535\pi\)
\(194\) −7.11735 + 4.68115i −0.510996 + 0.336087i
\(195\) 0 0
\(196\) 0.327800 0.347448i 0.0234143 0.0248177i
\(197\) 1.18741 6.73411i 0.0845992 0.479786i −0.912843 0.408310i \(-0.866118\pi\)
0.997442 0.0714755i \(-0.0227708\pi\)
\(198\) 0 0
\(199\) 1.86766 + 10.5920i 0.132395 + 0.750848i 0.976639 + 0.214889i \(0.0689389\pi\)
−0.844244 + 0.535959i \(0.819950\pi\)
\(200\) −14.0669 9.25195i −0.994681 0.654212i
\(201\) 0 0
\(202\) −11.8263 1.38229i −0.832092 0.0972577i
\(203\) 5.77342 + 0.674816i 0.405215 + 0.0473628i
\(204\) 0 0
\(205\) 12.9500 + 8.51737i 0.904469 + 0.594879i
\(206\) −2.13675 12.1181i −0.148874 0.844307i
\(207\) 0 0
\(208\) −1.20265 + 6.82057i −0.0833888 + 0.472922i
\(209\) −5.21639 + 5.52905i −0.360825 + 0.382453i
\(210\) 0 0
\(211\) −7.27097 + 4.78219i −0.500554 + 0.329220i −0.774552 0.632511i \(-0.782024\pi\)
0.273997 + 0.961730i \(0.411654\pi\)
\(212\) 5.32612 + 5.64536i 0.365800 + 0.387725i
\(213\) 0 0
\(214\) 2.09857 4.86504i 0.143455 0.332567i
\(215\) 1.41612 + 2.45278i 0.0965783 + 0.167279i
\(216\) 0 0
\(217\) 5.14859 8.91762i 0.349509 0.605368i
\(218\) −1.43572 1.92851i −0.0972393 0.130615i
\(219\) 0 0
\(220\) 2.18274 7.29086i 0.147160 0.491550i
\(221\) 1.62910 + 27.9705i 0.109585 + 1.88150i
\(222\) 0 0
\(223\) 7.66506 + 1.81665i 0.513290 + 0.121652i 0.479095 0.877763i \(-0.340965\pi\)
0.0341954 + 0.999415i \(0.489113\pi\)
\(224\) −12.0903 10.1450i −0.807820 0.677842i
\(225\) 0 0
\(226\) −1.11350 + 0.934340i −0.0740691 + 0.0621514i
\(227\) 17.0823 8.57908i 1.13380 0.569413i 0.219964 0.975508i \(-0.429406\pi\)
0.913831 + 0.406095i \(0.133110\pi\)
\(228\) 0 0
\(229\) 10.7024 + 24.8109i 0.707234 + 1.63955i 0.767244 + 0.641356i \(0.221628\pi\)
−0.0600094 + 0.998198i \(0.519113\pi\)
\(230\) −2.51688 + 3.38075i −0.165958 + 0.222920i
\(231\) 0 0
\(232\) 0.309305 5.31057i 0.0203069 0.348656i
\(233\) 17.0044 + 6.18909i 1.11400 + 0.405461i 0.832457 0.554089i \(-0.186933\pi\)
0.281538 + 0.959550i \(0.409156\pi\)
\(234\) 0 0
\(235\) 21.6677 7.88641i 1.41345 0.514453i
\(236\) 1.51996 + 5.07702i 0.0989410 + 0.330486i
\(237\) 0 0
\(238\) −8.63130 4.33480i −0.559484 0.280983i
\(239\) 10.3119 2.44398i 0.667025 0.158088i 0.116866 0.993148i \(-0.462715\pi\)
0.550159 + 0.835060i \(0.314567\pi\)
\(240\) 0 0
\(241\) 16.7613 1.95911i 1.07969 0.126198i 0.442396 0.896820i \(-0.354128\pi\)
0.637292 + 0.770622i \(0.280054\pi\)
\(242\) 6.23775 0.400978
\(243\) 0 0
\(244\) 8.12635 0.520236
\(245\) 1.08691 0.127041i 0.0694401 0.00811638i
\(246\) 0 0
\(247\) 27.7934 6.58715i 1.76845 0.419130i
\(248\) −8.42120 4.22928i −0.534747 0.268560i
\(249\) 0 0
\(250\) −1.25506 4.19221i −0.0793772 0.265138i
\(251\) 17.5886 6.40174i 1.11018 0.404074i 0.279123 0.960255i \(-0.409956\pi\)
0.831061 + 0.556181i \(0.187734\pi\)
\(252\) 0 0
\(253\) −2.40781 0.876370i −0.151378 0.0550969i
\(254\) −0.346038 + 5.94124i −0.0217124 + 0.372787i
\(255\) 0 0
\(256\) −6.39115 + 8.58480i −0.399447 + 0.536550i
\(257\) −11.4433 26.5285i −0.713812 1.65480i −0.755061 0.655654i \(-0.772393\pi\)
0.0412491 0.999149i \(-0.486866\pi\)
\(258\) 0 0
\(259\) −12.4146 + 6.23483i −0.771404 + 0.387413i
\(260\) −21.9072 + 18.3823i −1.35863 + 1.14002i
\(261\) 0 0
\(262\) 5.81246 + 4.87724i 0.359095 + 0.301317i
\(263\) 23.3642 + 5.53742i 1.44070 + 0.341452i 0.875386 0.483424i \(-0.160607\pi\)
0.565313 + 0.824876i \(0.308755\pi\)
\(264\) 0 0
\(265\) 1.03384 + 17.7503i 0.0635082 + 1.09039i
\(266\) −2.82406 + 9.43301i −0.173154 + 0.578375i
\(267\) 0 0
\(268\) 5.86397 + 7.87668i 0.358199 + 0.481145i
\(269\) −12.8618 + 22.2774i −0.784200 + 1.35827i 0.145276 + 0.989391i \(0.453593\pi\)
−0.929476 + 0.368883i \(0.879740\pi\)
\(270\) 0 0
\(271\) −5.12617 8.87880i −0.311393 0.539348i 0.667271 0.744815i \(-0.267462\pi\)
−0.978664 + 0.205466i \(0.934129\pi\)
\(272\) 2.49355 5.78069i 0.151194 0.350506i
\(273\) 0 0
\(274\) −5.17930 5.48974i −0.312893 0.331647i
\(275\) 8.39478 5.52133i 0.506224 0.332949i
\(276\) 0 0
\(277\) 4.07014 4.31409i 0.244551 0.259209i −0.593459 0.804865i \(-0.702238\pi\)
0.838009 + 0.545656i \(0.183719\pi\)
\(278\) −0.346187 + 1.96333i −0.0207629 + 0.117752i
\(279\) 0 0
\(280\) −3.99526 22.6582i −0.238762 1.35409i
\(281\) −17.3504 11.4115i −1.03504 0.680754i −0.0861213 0.996285i \(-0.527447\pi\)
−0.948916 + 0.315530i \(0.897818\pi\)
\(282\) 0 0
\(283\) −11.6779 1.36495i −0.694180 0.0811380i −0.238316 0.971188i \(-0.576596\pi\)
−0.455864 + 0.890050i \(0.650670\pi\)
\(284\) 5.23093 + 0.611408i 0.310399 + 0.0362804i
\(285\) 0 0
\(286\) 4.84840 + 3.18884i 0.286692 + 0.188560i
\(287\) 2.11963 + 12.0210i 0.125118 + 0.709580i
\(288\) 0 0
\(289\) 1.47052 8.33972i 0.0865011 0.490572i
\(290\) 3.58344 3.79823i 0.210427 0.223040i
\(291\) 0 0
\(292\) −0.890628 + 0.585775i −0.0521201 + 0.0342799i
\(293\) −18.5895 19.7037i −1.08601 1.15110i −0.987766 0.155942i \(-0.950159\pi\)
−0.0982448 0.995162i \(-0.531323\pi\)
\(294\) 0 0
\(295\) −4.80882 + 11.1481i −0.279980 + 0.649067i
\(296\) 6.35680 + 11.0103i 0.369482 + 0.639961i
\(297\) 0 0
\(298\) 0.242947 0.420796i 0.0140735 0.0243761i
\(299\) 5.74964 + 7.72311i 0.332510 + 0.446639i
\(300\) 0 0
\(301\) −0.639695 + 2.13673i −0.0368714 + 0.123159i
\(302\) 0.0206677 + 0.354851i 0.00118929 + 0.0204194i
\(303\) 0 0
\(304\) −6.24512 1.48012i −0.358182 0.0848907i
\(305\) 14.2612 + 11.9666i 0.816596 + 0.685205i
\(306\) 0 0
\(307\) −18.6794 + 15.6739i −1.06609 + 0.894557i −0.994693 0.102891i \(-0.967191\pi\)
−0.0713990 + 0.997448i \(0.522746\pi\)
\(308\) 5.35595 2.68986i 0.305184 0.153269i
\(309\) 0 0
\(310\) −3.66391 8.49390i −0.208096 0.482421i
\(311\) 10.1301 13.6072i 0.574428 0.771591i −0.416038 0.909347i \(-0.636582\pi\)
0.990466 + 0.137756i \(0.0439891\pi\)
\(312\) 0 0
\(313\) −0.678174 + 11.6438i −0.0383327 + 0.658146i 0.923346 + 0.383968i \(0.125443\pi\)
−0.961679 + 0.274178i \(0.911594\pi\)
\(314\) −8.43320 3.06943i −0.475913 0.173218i
\(315\) 0 0
\(316\) −22.1145 + 8.04903i −1.24404 + 0.452793i
\(317\) −7.94087 26.5244i −0.446004 1.48976i −0.825414 0.564528i \(-0.809058\pi\)
0.379410 0.925229i \(-0.376127\pi\)
\(318\) 0 0
\(319\) 2.83691 + 1.42475i 0.158837 + 0.0797707i
\(320\) −5.45656 + 1.29323i −0.305031 + 0.0722937i
\(321\) 0 0
\(322\) −3.29675 + 0.385335i −0.183721 + 0.0214739i
\(323\) −25.9641 −1.44468
\(324\) 0 0
\(325\) −37.7559 −2.09432
\(326\) 9.71370 1.13537i 0.537992 0.0628822i
\(327\) 0 0
\(328\) 10.8698 2.57618i 0.600182 0.142246i
\(329\) 16.2273 + 8.14967i 0.894641 + 0.449306i
\(330\) 0 0
\(331\) 5.34775 + 17.8627i 0.293939 + 0.981824i 0.969617 + 0.244628i \(0.0786657\pi\)
−0.675678 + 0.737197i \(0.736149\pi\)
\(332\) −8.36402 + 3.04425i −0.459035 + 0.167075i
\(333\) 0 0
\(334\) −1.84286 0.670745i −0.100837 0.0367016i
\(335\) −1.30804 + 22.4581i −0.0714657 + 1.22702i
\(336\) 0 0
\(337\) 18.0513 24.2471i 0.983319 1.32083i 0.0364052 0.999337i \(-0.488409\pi\)
0.946913 0.321489i \(-0.104183\pi\)
\(338\) −4.99411 11.5777i −0.271644 0.629741i
\(339\) 0 0
\(340\) 23.2305 11.6668i 1.25985 0.632720i
\(341\) 4.30804 3.61487i 0.233293 0.195756i
\(342\) 0 0
\(343\) −13.8464 11.6185i −0.747635 0.627341i
\(344\) 1.98618 + 0.470733i 0.107088 + 0.0253802i
\(345\) 0 0
\(346\) 0.853949 + 14.6617i 0.0459086 + 0.788219i
\(347\) 0.883973 2.95267i 0.0474541 0.158508i −0.930978 0.365074i \(-0.881044\pi\)
0.978433 + 0.206566i \(0.0662289\pi\)
\(348\) 0 0
\(349\) −5.36161 7.20189i −0.287001 0.385509i 0.635119 0.772415i \(-0.280951\pi\)
−0.922119 + 0.386906i \(0.873544\pi\)
\(350\) 6.50782 11.2719i 0.347858 0.602507i
\(351\) 0 0
\(352\) −4.30985 7.46487i −0.229716 0.397879i
\(353\) 13.2238 30.6562i 0.703832 1.63167i −0.0694350 0.997586i \(-0.522120\pi\)
0.773267 0.634080i \(-0.218621\pi\)
\(354\) 0 0
\(355\) 8.27961 + 8.77587i 0.439436 + 0.465775i
\(356\) −5.04518 + 3.31827i −0.267394 + 0.175868i
\(357\) 0 0
\(358\) 6.87620 7.28835i 0.363419 0.385201i
\(359\) −0.100805 + 0.571693i −0.00532028 + 0.0301728i −0.987352 0.158541i \(-0.949321\pi\)
0.982032 + 0.188714i \(0.0604320\pi\)
\(360\) 0 0
\(361\) 1.29708 + 7.35609i 0.0682672 + 0.387162i
\(362\) −0.0957525 0.0629774i −0.00503264 0.00331002i
\(363\) 0 0
\(364\) −22.3690 2.61456i −1.17245 0.137040i
\(365\) −2.42559 0.283510i −0.126961 0.0148396i
\(366\) 0 0
\(367\) −21.2493 13.9759i −1.10920 0.729534i −0.143620 0.989633i \(-0.545874\pi\)
−0.965582 + 0.260099i \(0.916245\pi\)
\(368\) −0.375682 2.13060i −0.0195838 0.111065i
\(369\) 0 0
\(370\) −2.16714 + 12.2904i −0.112664 + 0.638950i
\(371\) −9.60900 + 10.1850i −0.498875 + 0.528776i
\(372\) 0 0
\(373\) −9.67641 + 6.36427i −0.501025 + 0.329530i −0.774738 0.632282i \(-0.782118\pi\)
0.273713 + 0.961811i \(0.411748\pi\)
\(374\) −3.61994 3.83691i −0.187182 0.198402i
\(375\) 0 0
\(376\) 6.58214 15.2591i 0.339448 0.786928i
\(377\) −5.96447 10.3308i −0.307186 0.532062i
\(378\) 0 0
\(379\) 9.18651 15.9115i 0.471880 0.817319i −0.527603 0.849491i \(-0.676909\pi\)
0.999482 + 0.0321718i \(0.0102424\pi\)
\(380\) −15.8256 21.2575i −0.811838 1.09049i
\(381\) 0 0
\(382\) −4.72328 + 15.7769i −0.241664 + 0.807215i
\(383\) −1.55227 26.6514i −0.0793171 1.36182i −0.769713 0.638390i \(-0.779601\pi\)
0.690396 0.723432i \(-0.257436\pi\)
\(384\) 0 0
\(385\) 13.3604 + 3.16646i 0.680907 + 0.161378i
\(386\) −5.81815 4.88201i −0.296136 0.248488i
\(387\) 0 0
\(388\) 13.8316 11.6061i 0.702196 0.589212i
\(389\) 2.83188 1.42222i 0.143582 0.0721095i −0.375558 0.926799i \(-0.622549\pi\)
0.519140 + 0.854689i \(0.326252\pi\)
\(390\) 0 0
\(391\) −3.46657 8.03640i −0.175312 0.406418i
\(392\) 0.470962 0.632612i 0.0237872 0.0319517i
\(393\) 0 0
\(394\) 0.281283 4.82945i 0.0141708 0.243304i
\(395\) −50.6623 18.4396i −2.54910 0.927795i
\(396\) 0 0
\(397\) 3.81860 1.38986i 0.191650 0.0697550i −0.244412 0.969671i \(-0.578595\pi\)
0.436062 + 0.899916i \(0.356373\pi\)
\(398\) 2.18230 + 7.28940i 0.109389 + 0.365384i
\(399\) 0 0
\(400\) 7.58129 + 3.80747i 0.379064 + 0.190373i
\(401\) −20.7711 + 4.92283i −1.03726 + 0.245835i −0.713757 0.700393i \(-0.753008\pi\)
−0.323501 + 0.946228i \(0.604860\pi\)
\(402\) 0 0
\(403\) −20.9891 + 2.45328i −1.04554 + 0.122206i
\(404\) 25.2369 1.25558
\(405\) 0 0
\(406\) 4.11229 0.204089
\(407\) −7.53586 + 0.880816i −0.373539 + 0.0436604i
\(408\) 0 0
\(409\) −21.5944 + 5.11798i −1.06778 + 0.253068i −0.726691 0.686965i \(-0.758943\pi\)
−0.341085 + 0.940032i \(0.610795\pi\)
\(410\) 9.79926 + 4.92137i 0.483951 + 0.243049i
\(411\) 0 0
\(412\) 7.48012 + 24.9853i 0.368519 + 1.23094i
\(413\) −8.98466 + 3.27015i −0.442106 + 0.160913i
\(414\) 0 0
\(415\) −19.1612 6.97410i −0.940585 0.342345i
\(416\) −1.88329 + 32.3349i −0.0923360 + 1.58535i
\(417\) 0 0
\(418\) −3.21134 + 4.31358i −0.157072 + 0.210984i
\(419\) 10.1002 + 23.4148i 0.493425 + 1.14389i 0.965045 + 0.262086i \(0.0844103\pi\)
−0.471620 + 0.881802i \(0.656330\pi\)
\(420\) 0 0
\(421\) 16.6167 8.34520i 0.809847 0.406720i 0.00484167 0.999988i \(-0.498459\pi\)
0.805005 + 0.593268i \(0.202163\pi\)
\(422\) −4.71639 + 3.95752i −0.229590 + 0.192649i
\(423\) 0 0
\(424\) 9.81639 + 8.23693i 0.476726 + 0.400021i
\(425\) 33.3951 + 7.91479i 1.61990 + 0.383924i
\(426\) 0 0
\(427\) 0.852460 + 14.6362i 0.0412534 + 0.708294i
\(428\) −3.22083 + 10.7583i −0.155684 + 0.520022i
\(429\) 0 0
\(430\) 1.19653 + 1.60721i 0.0577016 + 0.0775067i
\(431\) −3.46440 + 6.00052i −0.166874 + 0.289035i −0.937319 0.348472i \(-0.886701\pi\)
0.770445 + 0.637507i \(0.220034\pi\)
\(432\) 0 0
\(433\) −12.4509 21.5656i −0.598352 1.03638i −0.993064 0.117571i \(-0.962489\pi\)
0.394713 0.918805i \(-0.370844\pi\)
\(434\) 2.88539 6.68909i 0.138503 0.321087i
\(435\) 0 0
\(436\) 3.49703 + 3.70663i 0.167477 + 0.177516i
\(437\) −7.45469 + 4.90303i −0.356606 + 0.234544i
\(438\) 0 0
\(439\) 5.58416 5.91886i 0.266517 0.282492i −0.580269 0.814425i \(-0.697053\pi\)
0.846786 + 0.531933i \(0.178534\pi\)
\(440\) 2.18199 12.3747i 0.104022 0.589938i
\(441\) 0 0
\(442\) 3.44199 + 19.5205i 0.163719 + 0.928495i
\(443\) 21.0995 + 13.8773i 1.00247 + 0.659332i 0.940870 0.338769i \(-0.110011\pi\)
0.0615961 + 0.998101i \(0.480381\pi\)
\(444\) 0 0
\(445\) −13.7403 1.60601i −0.651354 0.0761324i
\(446\) 5.53528 + 0.646982i 0.262103 + 0.0306355i
\(447\) 0 0
\(448\) −3.68966 2.42673i −0.174320 0.114652i
\(449\) 6.85970 + 38.9033i 0.323729 + 1.83596i 0.518458 + 0.855103i \(0.326506\pi\)
−0.194728 + 0.980857i \(0.562383\pi\)
\(450\) 0 0
\(451\) −1.15762 + 6.56522i −0.0545104 + 0.309144i
\(452\) 2.11425 2.24097i 0.0994459 0.105407i
\(453\) 0 0
\(454\) 11.2988 7.43134i 0.530279 0.348770i
\(455\) −35.4060 37.5282i −1.65986 1.75935i
\(456\) 0 0
\(457\) 8.26023 19.1494i 0.386397 0.895770i −0.608375 0.793650i \(-0.708178\pi\)
0.994772 0.102120i \(-0.0325625\pi\)
\(458\) 9.55811 + 16.5551i 0.446621 + 0.773570i
\(459\) 0 0
\(460\) 4.46668 7.73651i 0.208260 0.360717i
\(461\) −10.1557 13.6414i −0.472996 0.635344i 0.500039 0.866003i \(-0.333319\pi\)
−0.973035 + 0.230659i \(0.925912\pi\)
\(462\) 0 0
\(463\) −2.70861 + 9.04739i −0.125880 + 0.420468i −0.997577 0.0695778i \(-0.977835\pi\)
0.871697 + 0.490046i \(0.163020\pi\)
\(464\) 0.155852 + 2.67588i 0.00723525 + 0.124224i
\(465\) 0 0
\(466\) 12.4570 + 2.95235i 0.577057 + 0.136765i
\(467\) −23.3985 19.6337i −1.08275 0.908538i −0.0866068 0.996243i \(-0.527602\pi\)
−0.996147 + 0.0877046i \(0.972047\pi\)
\(468\) 0 0
\(469\) −13.5714 + 11.3877i −0.626667 + 0.525836i
\(470\) 14.5777 7.32122i 0.672421 0.337703i
\(471\) 0 0
\(472\) 3.46573 + 8.03446i 0.159523 + 0.369816i
\(473\) −0.727420 + 0.977095i −0.0334468 + 0.0449269i
\(474\) 0 0
\(475\) 2.03439 34.9291i 0.0933442 1.60266i
\(476\) 19.2373 + 7.00181i 0.881741 + 0.320928i
\(477\) 0 0
\(478\) 7.04526 2.56427i 0.322243 0.117287i
\(479\) −3.56899 11.9212i −0.163071 0.544696i 0.836925 0.547317i \(-0.184351\pi\)
−0.999997 + 0.00262129i \(0.999166\pi\)
\(480\) 0 0
\(481\) 25.4773 + 12.7952i 1.16167 + 0.583410i
\(482\) 11.6169 2.75326i 0.529135 0.125407i
\(483\) 0 0
\(484\) −13.1318 + 1.53488i −0.596899 + 0.0697674i
\(485\) 41.3645 1.87826
\(486\) 0 0
\(487\) 13.2205 0.599077 0.299538 0.954084i \(-0.403167\pi\)
0.299538 + 0.954084i \(0.403167\pi\)
\(488\) 13.3264 1.55763i 0.603258 0.0705107i
\(489\) 0 0
\(490\) 0.753314 0.178539i 0.0340313 0.00806556i
\(491\) 16.2050 + 8.13845i 0.731321 + 0.367283i 0.775168 0.631755i \(-0.217665\pi\)
−0.0438474 + 0.999038i \(0.513962\pi\)
\(492\) 0 0
\(493\) 3.10994 + 10.3879i 0.140065 + 0.467848i
\(494\) 18.9888 6.91136i 0.854347 0.310957i
\(495\) 0 0
\(496\) 4.46196 + 1.62402i 0.200348 + 0.0729207i
\(497\) −0.552464 + 9.48544i −0.0247814 + 0.425480i
\(498\) 0 0
\(499\) −5.68067 + 7.63047i −0.254302 + 0.341587i −0.910880 0.412671i \(-0.864596\pi\)
0.656578 + 0.754258i \(0.272003\pi\)
\(500\) 3.67372 + 8.51665i 0.164294 + 0.380876i
\(501\) 0 0
\(502\) 11.8334 5.94295i 0.528150 0.265247i
\(503\) −13.1149 + 11.0047i −0.584766 + 0.490677i −0.886508 0.462713i \(-0.846876\pi\)
0.301743 + 0.953389i \(0.402432\pi\)
\(504\) 0 0
\(505\) 44.2891 + 37.1630i 1.97084 + 1.65373i
\(506\) −1.76389 0.418051i −0.0784146 0.0185846i
\(507\) 0 0
\(508\) −0.733442 12.5927i −0.0325412 0.558711i
\(509\) 8.28987 27.6901i 0.367442 1.22734i −0.551909 0.833904i \(-0.686100\pi\)
0.919351 0.393438i \(-0.128714\pi\)
\(510\) 0 0
\(511\) −1.14845 1.54264i −0.0508046 0.0682424i
\(512\) 6.72742 11.6522i 0.297313 0.514961i
\(513\) 0 0
\(514\) −10.2198 17.7012i −0.450775 0.780765i
\(515\) −23.6654 + 54.8626i −1.04282 + 2.41754i
\(516\) 0 0
\(517\) 6.80568 + 7.21360i 0.299314 + 0.317254i
\(518\) −8.21138 + 5.40071i −0.360787 + 0.237294i
\(519\) 0 0
\(520\) −32.4021 + 34.3443i −1.42093 + 1.50610i
\(521\) −0.716780 + 4.06506i −0.0314027 + 0.178093i −0.996475 0.0838901i \(-0.973266\pi\)
0.965072 + 0.261984i \(0.0843766\pi\)
\(522\) 0 0
\(523\) 0.273945 + 1.55362i 0.0119788 + 0.0679351i 0.990211 0.139577i \(-0.0445744\pi\)
−0.978232 + 0.207512i \(0.933463\pi\)
\(524\) −13.4366 8.83737i −0.586979 0.386062i
\(525\) 0 0
\(526\) 16.8723 + 1.97209i 0.735669 + 0.0859874i
\(527\) 19.0792 + 2.23004i 0.831102 + 0.0971419i
\(528\) 0 0
\(529\) 16.7033 + 10.9860i 0.726232 + 0.477650i
\(530\) 2.18431 + 12.3879i 0.0948806 + 0.538094i
\(531\) 0 0
\(532\) 3.62411 20.5534i 0.157125 0.891102i
\(533\) 17.1906 18.2209i 0.744606 0.789236i
\(534\) 0 0
\(535\) −21.4947 + 14.1373i −0.929295 + 0.611207i
\(536\) 11.1261 + 11.7930i 0.480574 + 0.509379i
\(537\) 0 0
\(538\) −7.20807 + 16.7102i −0.310762 + 0.720428i
\(539\) 0.235330 + 0.407603i 0.0101364 + 0.0175567i
\(540\) 0 0
\(541\) −5.71173 + 9.89300i −0.245566 + 0.425333i −0.962291 0.272023i \(-0.912307\pi\)
0.716724 + 0.697357i \(0.245641\pi\)
\(542\) −4.33128 5.81792i −0.186045 0.249901i
\(543\) 0 0
\(544\) 8.44416 28.2055i 0.362041 1.20930i
\(545\) 0.678798 + 11.6545i 0.0290765 + 0.499224i
\(546\) 0 0
\(547\) −7.89641 1.87148i −0.337626 0.0800188i 0.0583057 0.998299i \(-0.481430\pi\)
−0.395932 + 0.918280i \(0.629578\pi\)
\(548\) 12.2543 + 10.2826i 0.523479 + 0.439251i
\(549\) 0 0
\(550\) 5.44536 4.56920i 0.232191 0.194831i
\(551\) 9.87869 4.96127i 0.420847 0.211357i
\(552\) 0 0
\(553\) −16.8167 38.9856i −0.715121 1.65784i
\(554\) 2.50568 3.36571i 0.106456 0.142995i
\(555\) 0 0
\(556\) 0.245694 4.21840i 0.0104197 0.178900i
\(557\) −11.2047 4.07820i −0.474760 0.172799i 0.0935472 0.995615i \(-0.470179\pi\)
−0.568308 + 0.822816i \(0.692402\pi\)
\(558\) 0 0
\(559\) 4.30127 1.56553i 0.181924 0.0662151i
\(560\) 3.32494 + 11.1061i 0.140504 + 0.469317i
\(561\) 0 0
\(562\) −13.1290 6.59363i −0.553813 0.278135i
\(563\) −19.7078 + 4.67084i −0.830586 + 0.196852i −0.623850 0.781544i \(-0.714432\pi\)
−0.206736 + 0.978397i \(0.566284\pi\)
\(564\) 0 0
\(565\) 7.01035 0.819393i 0.294928 0.0344721i
\(566\) −8.31793 −0.349629
\(567\) 0 0
\(568\) 8.69539 0.364851
\(569\) −14.5280 + 1.69808i −0.609045 + 0.0711871i −0.415024 0.909810i \(-0.636227\pi\)
−0.194020 + 0.980997i \(0.562153\pi\)
\(570\) 0 0
\(571\) 22.4579 5.32262i 0.939834 0.222745i 0.267977 0.963425i \(-0.413645\pi\)
0.671857 + 0.740681i \(0.265497\pi\)
\(572\) −10.9916 5.52017i −0.459580 0.230810i
\(573\) 0 0
\(574\) 2.47673 + 8.27285i 0.103377 + 0.345302i
\(575\) 11.0829 4.03383i 0.462187 0.168222i
\(576\) 0 0
\(577\) −28.1182 10.2342i −1.17057 0.426054i −0.317711 0.948188i \(-0.602914\pi\)
−0.852864 + 0.522133i \(0.825136\pi\)
\(578\) 0.348349 5.98093i 0.0144894 0.248774i
\(579\) 0 0
\(580\) −6.60929 + 8.87782i −0.274436 + 0.368631i
\(581\) −6.36032 14.7449i −0.263871 0.611721i
\(582\) 0 0
\(583\) −6.83388 + 3.43210i −0.283030 + 0.142143i
\(584\) −1.34826 + 1.13132i −0.0557914 + 0.0468146i
\(585\) 0 0
\(586\) −14.6808 12.3186i −0.606457 0.508877i
\(587\) −0.309986 0.0734680i −0.0127945 0.00303235i 0.224214 0.974540i \(-0.428019\pi\)
−0.237008 + 0.971508i \(0.576167\pi\)
\(588\) 0 0
\(589\) −1.13865 19.5499i −0.0469173 0.805538i
\(590\) −2.46345 + 8.22849i −0.101419 + 0.338761i
\(591\) 0 0
\(592\) −3.82546 5.13849i −0.157226 0.211191i
\(593\) −15.7701 + 27.3146i −0.647601 + 1.12168i 0.336093 + 0.941829i \(0.390894\pi\)
−0.983694 + 0.179849i \(0.942439\pi\)
\(594\) 0 0
\(595\) 23.4496 + 40.6160i 0.961341 + 1.66509i
\(596\) −0.407911 + 0.945644i −0.0167087 + 0.0387351i
\(597\) 0 0
\(598\) 4.67446 + 4.95464i 0.191153 + 0.202610i
\(599\) −17.9196 + 11.7859i −0.732173 + 0.481558i −0.860036 0.510234i \(-0.829559\pi\)
0.127862 + 0.991792i \(0.459188\pi\)
\(600\) 0 0
\(601\) −0.281882 + 0.298777i −0.0114982 + 0.0121874i −0.733097 0.680124i \(-0.761926\pi\)
0.721599 + 0.692311i \(0.243407\pi\)
\(602\) −0.274008 + 1.55397i −0.0111677 + 0.0633353i
\(603\) 0 0
\(604\) −0.130826 0.741950i −0.00532323 0.0301895i
\(605\) −25.3056 16.6438i −1.02882 0.676666i
\(606\) 0 0
\(607\) 38.2675 + 4.47283i 1.55323 + 0.181546i 0.848987 0.528414i \(-0.177213\pi\)
0.704242 + 0.709960i \(0.251287\pi\)
\(608\) −29.8125 3.48459i −1.20906 0.141319i
\(609\) 0 0
\(610\) 11.0039 + 7.23738i 0.445535 + 0.293033i
\(611\) −6.47113 36.6996i −0.261794 1.48471i
\(612\) 0 0
\(613\) 7.63138 43.2797i 0.308228 1.74805i −0.299677 0.954041i \(-0.596879\pi\)
0.607905 0.794010i \(-0.292010\pi\)
\(614\) −11.8383 + 12.5479i −0.477756 + 0.506392i
\(615\) 0 0
\(616\) 8.26764 5.43771i 0.333113 0.219092i
\(617\) 23.5508 + 24.9623i 0.948118 + 1.00495i 0.999980 + 0.00629197i \(0.00200281\pi\)
−0.0518624 + 0.998654i \(0.516516\pi\)
\(618\) 0 0
\(619\) −2.19382 + 5.08585i −0.0881772 + 0.204418i −0.956598 0.291409i \(-0.905876\pi\)
0.868421 + 0.495827i \(0.165135\pi\)
\(620\) 9.80334 + 16.9799i 0.393711 + 0.681928i
\(621\) 0 0
\(622\) 6.00067 10.3935i 0.240605 0.416740i
\(623\) −6.50569 8.73866i −0.260645 0.350107i
\(624\) 0 0
\(625\) 3.65804 12.2187i 0.146322 0.488749i
\(626\) 0.479783 + 8.23755i 0.0191760 + 0.329239i
\(627\) 0 0
\(628\) 18.5089 + 4.38670i 0.738587 + 0.175048i
\(629\) −19.8525 16.6582i −0.791569 0.664206i
\(630\) 0 0
\(631\) −19.4299 + 16.3036i −0.773492 + 0.649037i −0.941601 0.336732i \(-0.890678\pi\)
0.168109 + 0.985768i \(0.446234\pi\)
\(632\) −34.7228 + 17.4384i −1.38120 + 0.693664i
\(633\) 0 0
\(634\) −7.75837 17.9859i −0.308124 0.714312i
\(635\) 17.2565 23.1794i 0.684802 0.919848i
\(636\) 0 0
\(637\) 0.102833 1.76558i 0.00407440 0.0699547i
\(638\) 2.11046 + 0.768143i 0.0835537 + 0.0304111i
\(639\) 0 0
\(640\) 33.9372 12.3521i 1.34149 0.488261i
\(641\) 6.05781 + 20.2345i 0.239269 + 0.799215i 0.990300 + 0.138947i \(0.0443719\pi\)
−0.751031 + 0.660267i \(0.770443\pi\)
\(642\) 0 0
\(643\) −14.2822 7.17277i −0.563233 0.282866i 0.144314 0.989532i \(-0.453902\pi\)
−0.707548 + 0.706665i \(0.750199\pi\)
\(644\) 6.84553 1.62242i 0.269752 0.0639324i
\(645\) 0 0
\(646\) −18.2445 + 2.13247i −0.717819 + 0.0839010i
\(647\) 34.6617 1.36269 0.681346 0.731961i \(-0.261395\pi\)
0.681346 + 0.731961i \(0.261395\pi\)
\(648\) 0 0
\(649\) −5.22183 −0.204975
\(650\) −26.5303 + 3.10094i −1.04060 + 0.121629i
\(651\) 0 0
\(652\) −20.1700 + 4.78038i −0.789918 + 0.187214i
\(653\) 19.2963 + 9.69097i 0.755123 + 0.379237i 0.784336 0.620336i \(-0.213004\pi\)
−0.0292132 + 0.999573i \(0.509300\pi\)
\(654\) 0 0
\(655\) −10.5667 35.2952i −0.412875 1.37910i
\(656\) −5.28930 + 1.92515i −0.206512 + 0.0751644i
\(657\) 0 0
\(658\) 12.0719 + 4.39383i 0.470613 + 0.171289i
\(659\) 0.469329 8.05806i 0.0182824 0.313897i −0.976752 0.214370i \(-0.931230\pi\)
0.995035 0.0995270i \(-0.0317330\pi\)
\(660\) 0 0
\(661\) −20.5095 + 27.5490i −0.797727 + 1.07153i 0.198092 + 0.980184i \(0.436526\pi\)
−0.995819 + 0.0913501i \(0.970882\pi\)
\(662\) 5.22484 + 12.1125i 0.203069 + 0.470768i
\(663\) 0 0
\(664\) −13.1326 + 6.59546i −0.509645 + 0.255953i
\(665\) 36.6263 30.7331i 1.42031 1.19178i
\(666\) 0 0
\(667\) 2.85455 + 2.39525i 0.110529 + 0.0927445i
\(668\) 4.04465 + 0.958599i 0.156492 + 0.0370893i
\(669\) 0 0
\(670\) 0.925388 + 15.8883i 0.0357509 + 0.613819i
\(671\) −2.29643 + 7.67062i −0.0886529 + 0.296121i
\(672\) 0 0
\(673\) 1.11229 + 1.49406i 0.0428755 + 0.0575918i 0.823044 0.567978i \(-0.192274\pi\)
−0.780168 + 0.625570i \(0.784867\pi\)
\(674\) 10.6928 18.5205i 0.411873 0.713385i
\(675\) 0 0
\(676\) 13.3625 + 23.1445i 0.513942 + 0.890173i
\(677\) 5.68035 13.1685i 0.218314 0.506108i −0.773501 0.633795i \(-0.781496\pi\)
0.991814 + 0.127687i \(0.0407554\pi\)
\(678\) 0 0
\(679\) 22.3545 + 23.6944i 0.857886 + 0.909306i
\(680\) 35.8594 23.5851i 1.37514 0.904446i
\(681\) 0 0
\(682\) 2.73027 2.89392i 0.104548 0.110814i
\(683\) 4.45517 25.2665i 0.170472 0.966797i −0.772768 0.634688i \(-0.781129\pi\)
0.943241 0.332109i \(-0.107760\pi\)
\(684\) 0 0
\(685\) 6.36375 + 36.0906i 0.243147 + 1.37895i
\(686\) −10.6838 7.02686i −0.407910 0.268287i
\(687\) 0 0
\(688\) −1.02156 0.119403i −0.0389466 0.00455221i
\(689\) 28.5415 + 3.33602i 1.08735 + 0.127092i
\(690\) 0 0
\(691\) −37.0368 24.3595i −1.40895 0.926678i −0.999900 0.0141644i \(-0.995491\pi\)
−0.409046 0.912514i \(-0.634138\pi\)
\(692\) −5.40546 30.6559i −0.205485 1.16536i
\(693\) 0 0
\(694\) 0.378642 2.14738i 0.0143730 0.0815136i
\(695\) 6.64304 7.04121i 0.251985 0.267088i
\(696\) 0 0
\(697\) −19.0247 + 12.5128i −0.720613 + 0.473955i
\(698\) −4.35899 4.62026i −0.164990 0.174880i
\(699\) 0 0
\(700\) −10.9267 + 25.3310i −0.412992 + 0.957422i
\(701\) −5.89393 10.2086i −0.222611 0.385573i 0.732989 0.680240i \(-0.238125\pi\)
−0.955600 + 0.294667i \(0.904791\pi\)
\(702\) 0 0
\(703\) −13.2100 + 22.8804i −0.498225 + 0.862951i
\(704\) −1.44027 1.93461i −0.0542821 0.0729135i
\(705\) 0 0
\(706\) 6.77425 22.6276i 0.254952 0.851600i
\(707\) 2.64737 + 45.4535i 0.0995645 + 1.70946i
\(708\) 0 0
\(709\) −33.1090 7.84699i −1.24344 0.294700i −0.444315 0.895870i \(-0.646553\pi\)
−0.799121 + 0.601171i \(0.794701\pi\)
\(710\) 6.53868 + 5.48661i 0.245392 + 0.205909i
\(711\) 0 0
\(712\) −7.63755 + 6.40867i −0.286229 + 0.240175i
\(713\) 5.89904 2.96261i 0.220921 0.110950i
\(714\) 0 0
\(715\) −11.1607 25.8733i −0.417385 0.967607i
\(716\) −12.6825 + 17.0355i −0.473965 + 0.636646i
\(717\) 0 0
\(718\) −0.0238795 + 0.409996i −0.000891177 + 0.0153009i
\(719\) −22.1565 8.06429i −0.826297 0.300747i −0.105959 0.994371i \(-0.533791\pi\)
−0.720338 + 0.693623i \(0.756013\pi\)
\(720\) 0 0
\(721\) −44.2158 + 16.0932i −1.64668 + 0.599343i
\(722\) 1.51559 + 5.06244i 0.0564046 + 0.188404i
\(723\) 0 0
\(724\) 0.217075 + 0.109019i 0.00806755 + 0.00405167i
\(725\) −14.2184 + 3.36981i −0.528057 + 0.125152i
\(726\) 0 0
\(727\) −8.85231 + 1.03469i −0.328314 + 0.0383744i −0.278653 0.960392i \(-0.589888\pi\)
−0.0496606 + 0.998766i \(0.515814\pi\)
\(728\) −37.1841 −1.37813
\(729\) 0 0
\(730\) −1.72769 −0.0639448
\(731\) −4.13266 + 0.483039i −0.152852 + 0.0178659i
\(732\) 0 0
\(733\) 23.3268 5.52856i 0.861597 0.204202i 0.224016 0.974586i \(-0.428083\pi\)
0.637581 + 0.770383i \(0.279935\pi\)
\(734\) −16.0793 8.07531i −0.593497 0.298065i
\(735\) 0 0
\(736\) −2.90183 9.69279i −0.106963 0.357281i
\(737\) −9.09205 + 3.30924i −0.334910 + 0.121897i
\(738\) 0 0
\(739\) 26.2622 + 9.55867i 0.966071 + 0.351621i 0.776410 0.630228i \(-0.217039\pi\)
0.189662 + 0.981850i \(0.439261\pi\)
\(740\) 1.53804 26.4072i 0.0565396 0.970748i
\(741\) 0 0
\(742\) −5.91554 + 7.94595i −0.217166 + 0.291705i
\(743\) −15.5338 36.0115i −0.569882 1.32113i −0.922728 0.385453i \(-0.874045\pi\)
0.352846 0.935681i \(-0.385214\pi\)
\(744\) 0 0
\(745\) −2.10838 + 1.05887i −0.0772451 + 0.0387940i
\(746\) −6.27670 + 5.26678i −0.229806 + 0.192830i
\(747\) 0 0
\(748\) 8.56485 + 7.18676i 0.313162 + 0.262774i
\(749\) −19.7144 4.67240i −0.720348 0.170726i
\(750\) 0 0
\(751\) −1.57245 26.9978i −0.0573794 0.985165i −0.897011 0.442009i \(-0.854266\pi\)
0.839631 0.543157i \(-0.182771\pi\)
\(752\) −2.40156 + 8.02177i −0.0875759 + 0.292524i
\(753\) 0 0
\(754\) −5.03959 6.76935i −0.183531 0.246525i
\(755\) 0.862979 1.49472i 0.0314070 0.0543986i
\(756\) 0 0
\(757\) −10.2471 17.7485i −0.372437 0.645080i 0.617503 0.786569i \(-0.288144\pi\)
−0.989940 + 0.141489i \(0.954811\pi\)
\(758\) 5.14834 11.9352i 0.186996 0.433506i
\(759\) 0 0
\(760\) −30.0270 31.8268i −1.08919 1.15448i
\(761\) 12.5960 8.28454i 0.456606 0.300314i −0.300292 0.953847i \(-0.597084\pi\)
0.756898 + 0.653533i \(0.226714\pi\)
\(762\) 0 0
\(763\) −6.30909 + 6.68724i −0.228404 + 0.242094i
\(764\) 6.06139 34.3758i 0.219293 1.24367i
\(765\) 0 0
\(766\) −3.27966 18.5999i −0.118499 0.672041i
\(767\) 16.3937 + 10.7823i 0.591943 + 0.389327i
\(768\) 0 0
\(769\) −13.4640 1.57372i −0.485526 0.0567498i −0.130191 0.991489i \(-0.541559\pi\)
−0.355335 + 0.934739i \(0.615633\pi\)
\(770\) 9.64811 + 1.12770i 0.347694 + 0.0406396i
\(771\) 0 0
\(772\) 13.4497 + 8.84602i 0.484066 + 0.318375i
\(773\) −0.729570 4.13760i −0.0262408 0.148819i 0.968872 0.247561i \(-0.0796292\pi\)
−0.995113 + 0.0987422i \(0.968518\pi\)
\(774\) 0 0
\(775\) −4.49496 + 25.4922i −0.161464 + 0.915705i
\(776\) 20.4579 21.6841i 0.734395 0.778414i
\(777\) 0 0
\(778\) 1.87309 1.23195i 0.0671536 0.0441676i
\(779\) 15.9305 + 16.8853i 0.570768 + 0.604979i
\(780\) 0 0
\(781\) −2.05533 + 4.76480i −0.0735456 + 0.170498i
\(782\) −3.09593 5.36230i −0.110710 0.191755i
\(783\) 0 0
\(784\) −0.198697 + 0.344153i −0.00709632 + 0.0122912i
\(785\) 26.0223 + 34.9540i 0.928775 + 1.24756i
\(786\) 0 0
\(787\) 2.79703 9.34272i 0.0997032 0.333032i −0.893555 0.448953i \(-0.851797\pi\)
0.993258 + 0.115921i \(0.0369821\pi\)
\(788\) 0.596191 + 10.2362i 0.0212384 + 0.364650i
\(789\) 0 0
\(790\) −37.1138 8.79614i −1.32045 0.312952i
\(791\) 4.25795 + 3.57284i 0.151395 + 0.127036i
\(792\) 0 0
\(793\) 23.0483 19.3398i 0.818470 0.686778i
\(794\) 2.56910 1.29025i 0.0911740 0.0457893i
\(795\) 0 0
\(796\) −6.38786 14.8087i −0.226412 0.524881i
\(797\) −6.07994 + 8.16677i −0.215362 + 0.289282i −0.896656 0.442729i \(-0.854010\pi\)
0.681293 + 0.732011i \(0.261418\pi\)
\(798\) 0 0
\(799\) −1.96964 + 33.8174i −0.0696808 + 1.19637i
\(800\) 37.2827 + 13.5698i 1.31814 + 0.479765i
\(801\) 0 0
\(802\) −14.1911 + 5.16513i −0.501105 + 0.182387i
\(803\) −0.301241 1.00622i −0.0106306 0.0355086i
\(804\) 0 0
\(805\) 14.4026 + 7.23325i 0.507625 + 0.254939i
\(806\) −14.5471 + 3.44773i −0.512400 + 0.121441i
\(807\) 0 0
\(808\) 41.3859 4.83732i 1.45595 0.170176i
\(809\) −20.1073 −0.706936 −0.353468 0.935447i \(-0.614998\pi\)
−0.353468 + 0.935447i \(0.614998\pi\)
\(810\) 0 0
\(811\) −0.159394 −0.00559707 −0.00279854 0.999996i \(-0.500891\pi\)
−0.00279854 + 0.999996i \(0.500891\pi\)
\(812\) −8.65723 + 1.01188i −0.303809 + 0.0355102i
\(813\) 0 0
\(814\) −5.22295 + 1.23786i −0.183064 + 0.0433870i
\(815\) −42.4365 21.3124i −1.48648 0.746541i
\(816\) 0 0
\(817\) 1.21656 + 4.06359i 0.0425620 + 0.142167i
\(818\) −14.7536 + 5.36988i −0.515848 + 0.187753i
\(819\) 0 0
\(820\) −21.8405 7.94928i −0.762702 0.277601i
\(821\) −0.275861 + 4.73635i −0.00962762 + 0.165300i 0.990067 + 0.140595i \(0.0449016\pi\)
−0.999695 + 0.0247047i \(0.992135\pi\)
\(822\) 0 0
\(823\) 15.8519 21.2928i 0.552564 0.742222i −0.434829 0.900513i \(-0.643191\pi\)
0.987392 + 0.158291i \(0.0505985\pi\)
\(824\) 17.0557 + 39.5397i 0.594165 + 1.37743i
\(825\) 0 0
\(826\) −6.04475 + 3.03579i −0.210324 + 0.105629i
\(827\) −5.34609 + 4.48590i −0.185902 + 0.155990i −0.730989 0.682389i \(-0.760941\pi\)
0.545087 + 0.838379i \(0.316496\pi\)
\(828\) 0 0
\(829\) 28.3490 + 23.7877i 0.984603 + 0.826180i 0.984777 0.173820i \(-0.0556111\pi\)
−0.000174449 1.00000i \(0.500056\pi\)
\(830\) −14.0370 3.32682i −0.487230 0.115476i
\(831\) 0 0
\(832\) 0.526962 + 9.04759i 0.0182691 + 0.313669i
\(833\) −0.461075 + 1.54010i −0.0159753 + 0.0533612i
\(834\) 0 0
\(835\) 5.68650 + 7.63829i 0.196789 + 0.264334i
\(836\) 5.69913 9.87118i 0.197109 0.341402i
\(837\) 0 0
\(838\) 9.02026 + 15.6236i 0.311600 + 0.539707i
\(839\) 3.05189 7.07508i 0.105363 0.244259i −0.857376 0.514690i \(-0.827907\pi\)
0.962739 + 0.270431i \(0.0871662\pi\)
\(840\) 0 0
\(841\) 16.7328 + 17.7357i 0.576994 + 0.611578i
\(842\) 10.9908 7.22875i 0.378767 0.249119i
\(843\) 0 0
\(844\) 8.95519 9.49195i 0.308250 0.326726i
\(845\) −10.6315 + 60.2943i −0.365735 + 2.07419i
\(846\) 0 0
\(847\) −4.14197 23.4903i −0.142320 0.807136i
\(848\) −5.39465 3.54812i −0.185253 0.121843i
\(849\) 0 0
\(850\) 24.1161 + 2.81877i 0.827176 + 0.0966830i
\(851\) −8.84564 1.03391i −0.303225 0.0354419i
\(852\) 0 0
\(853\) 28.4706 + 18.7254i 0.974815 + 0.641146i 0.933718 0.358009i \(-0.116544\pi\)
0.0410969 + 0.999155i \(0.486915\pi\)
\(854\) 1.80110 + 10.2145i 0.0616322 + 0.349534i
\(855\) 0 0
\(856\) −3.21971 + 18.2599i −0.110048 + 0.624110i
\(857\) −27.1852 + 28.8146i −0.928629 + 0.984290i −0.999913 0.0131665i \(-0.995809\pi\)
0.0712840 + 0.997456i \(0.477290\pi\)
\(858\) 0 0
\(859\) 45.6548 30.0277i 1.55772 1.02453i 0.580003 0.814614i \(-0.303051\pi\)
0.977719 0.209916i \(-0.0673191\pi\)
\(860\) −2.91441 3.08910i −0.0993807 0.105337i
\(861\) 0 0
\(862\) −1.94153 + 4.50098i −0.0661289 + 0.153304i
\(863\) 0.634182 + 1.09844i 0.0215878 + 0.0373912i 0.876617 0.481188i \(-0.159795\pi\)
−0.855030 + 0.518579i \(0.826461\pi\)
\(864\) 0 0
\(865\) 35.6566 61.7590i 1.21236 2.09987i
\(866\) −10.5202 14.1311i −0.357491 0.480194i
\(867\) 0 0
\(868\) −4.42841 + 14.7919i −0.150310 + 0.502071i
\(869\) −1.34827 23.1489i −0.0457370 0.785273i
\(870\) 0 0
\(871\) 35.3773 + 8.38457i 1.19871 + 0.284100i
\(872\) 6.44525 + 5.40821i 0.218264 + 0.183145i
\(873\) 0 0
\(874\) −4.83556 + 4.05752i −0.163565 + 0.137248i
\(875\) −14.9538 + 7.51006i −0.505529 + 0.253886i
\(876\) 0 0
\(877\) 17.3720 + 40.2727i 0.586609 + 1.35991i 0.910378 + 0.413777i \(0.135791\pi\)
−0.323769 + 0.946136i \(0.604950\pi\)
\(878\) 3.43775 4.61769i 0.116018 0.155840i
\(879\) 0 0
\(880\) −0.368144 + 6.32079i −0.0124101 + 0.213074i
\(881\) 25.7921 + 9.38756i 0.868959 + 0.316275i 0.737745 0.675079i \(-0.235891\pi\)
0.131213 + 0.991354i \(0.458113\pi\)
\(882\) 0 0
\(883\) −19.1938 + 6.98597i −0.645923 + 0.235097i −0.644147 0.764902i \(-0.722787\pi\)
−0.00177579 + 0.999998i \(0.500565\pi\)
\(884\) −12.0494 40.2478i −0.405265 1.35368i
\(885\) 0 0
\(886\) 15.9659 + 8.01838i 0.536385 + 0.269383i
\(887\) 36.8182 8.72608i 1.23623 0.292993i 0.440009 0.897993i \(-0.354975\pi\)
0.796225 + 0.605000i \(0.206827\pi\)
\(888\) 0 0
\(889\) 22.6035 2.64197i 0.758097 0.0886088i
\(890\) −9.78695 −0.328059
\(891\) 0 0
\(892\) −11.8121 −0.395499
\(893\) 34.3006 4.00917i 1.14783 0.134162i
\(894\) 0 0
\(895\) −47.3428 + 11.2204i −1.58249 + 0.375058i
\(896\) 25.4161 + 12.7645i 0.849093 + 0.426431i
\(897\) 0 0
\(898\) 8.01535 + 26.7731i 0.267476 + 0.893431i
\(899\) −7.68526 + 2.79721i −0.256318 + 0.0932921i
\(900\) 0 0
\(901\) −24.5457 8.93390i −0.817735 0.297631i
\(902\) −0.274228 + 4.70832i −0.00913081 + 0.156770i
\(903\) 0 0
\(904\) 3.03761 4.08022i 0.101030 0.135706i
\(905\) 0.220415 + 0.510980i 0.00732685 + 0.0169856i
\(906\) 0 0
\(907\) −7.38063 + 3.70669i −0.245070 + 0.123079i −0.567095 0.823652i \(-0.691933\pi\)
0.322025 + 0.946731i \(0.395636\pi\)
\(908\) −21.9578 + 18.4247i −0.728694 + 0.611447i
\(909\) 0 0
\(910\) −27.9613 23.4623i −0.926909 0.777769i
\(911\) −32.7705 7.76674i −1.08573 0.257324i −0.351478 0.936196i \(-0.614321\pi\)
−0.734256 + 0.678872i \(0.762469\pi\)
\(912\) 0 0
\(913\) −0.509935 8.75524i −0.0168764 0.289756i
\(914\) 4.23153 14.1343i 0.139967 0.467521i
\(915\) 0 0
\(916\) −24.1954 32.5001i −0.799440 1.07383i
\(917\) 14.5073 25.1273i 0.479072 0.829777i
\(918\) 0 0
\(919\) −13.1853 22.8376i −0.434943 0.753343i 0.562348 0.826901i \(-0.309898\pi\)
−0.997291 + 0.0735573i \(0.976565\pi\)
\(920\) 5.84199 13.5433i 0.192605 0.446508i
\(921\) 0 0
\(922\) −8.25656 8.75144i −0.271915 0.288213i
\(923\) 16.2913 10.7149i 0.536234 0.352687i
\(924\) 0 0
\(925\) 23.9655 25.4019i 0.787980 0.835210i
\(926\) −1.16021 + 6.57988i −0.0381269 + 0.216228i
\(927\) 0 0
\(928\) 2.17675 + 12.3450i 0.0714554 + 0.405244i
\(929\) 43.9934 + 28.9349i 1.44338 + 0.949324i 0.998557 + 0.0537033i \(0.0171025\pi\)
0.444819 + 0.895620i \(0.353268\pi\)
\(930\) 0 0
\(931\) 1.62785 + 0.190268i 0.0533506 + 0.00623579i
\(932\) −26.9510 3.15012i −0.882808 0.103185i
\(933\) 0 0
\(934\) −18.0542 11.8744i −0.590751 0.388543i
\(935\) 4.44778 + 25.2246i 0.145458 + 0.824933i
\(936\) 0 0
\(937\) 1.27631 7.23831i 0.0416952 0.236465i −0.956837 0.290625i \(-0.906137\pi\)
0.998532 + 0.0541595i \(0.0172479\pi\)
\(938\) −8.60102 + 9.11655i −0.280833 + 0.297666i
\(939\) 0 0
\(940\) −28.8877 + 18.9998i −0.942214 + 0.619704i
\(941\) 17.9105 + 18.9841i 0.583867 + 0.618862i 0.950207 0.311618i \(-0.100871\pi\)
−0.366341 + 0.930481i \(0.619390\pi\)
\(942\) 0 0
\(943\) −3.09939 + 7.18520i −0.100930 + 0.233982i
\(944\) −2.20449 3.81828i −0.0717499 0.124274i
\(945\) 0 0
\(946\) −0.430893 + 0.746328i −0.0140095 + 0.0242652i
\(947\) −5.65952 7.60205i −0.183910 0.247033i 0.700601 0.713553i \(-0.252915\pi\)
−0.884511 + 0.466520i \(0.845508\pi\)
\(948\) 0 0
\(949\) −1.13196 + 3.78100i −0.0367449 + 0.122736i
\(950\) −1.43925 24.7110i −0.0466956 0.801732i
\(951\) 0 0
\(952\) 32.8894 + 7.79492i 1.06595 + 0.252635i
\(953\) 39.9630 + 33.5329i 1.29453 + 1.08624i 0.991063 + 0.133395i \(0.0425878\pi\)
0.303464 + 0.952843i \(0.401857\pi\)
\(954\) 0 0
\(955\) 61.2580 51.4016i 1.98226 1.66332i
\(956\) −14.2008 + 7.13190i −0.459286 + 0.230662i
\(957\) 0 0
\(958\) −3.48696 8.08369i −0.112659 0.261172i
\(959\) −17.2343 + 23.1496i −0.556523 + 0.747541i
\(960\) 0 0
\(961\) 0.960082 16.4840i 0.0309704 0.531741i
\(962\) 18.9533 + 6.89842i 0.611078 + 0.222414i
\(963\) 0 0
\(964\) −23.7785 + 8.65468i −0.765855 + 0.278748i
\(965\) 10.5770 + 35.3298i 0.340487 + 1.13731i
\(966\) 0 0
\(967\) 4.03800 + 2.02796i 0.129853 + 0.0652148i 0.512540 0.858664i \(-0.328705\pi\)
−0.382686 + 0.923878i \(0.625001\pi\)
\(968\) −21.2406 + 5.03411i −0.682698 + 0.161802i
\(969\) 0 0
\(970\) 29.0659 3.39732i 0.933251 0.109081i
\(971\) −12.4268 −0.398796 −0.199398 0.979919i \(-0.563899\pi\)
−0.199398 + 0.979919i \(0.563899\pi\)
\(972\) 0 0
\(973\) 7.62342 0.244396
\(974\) 9.28975 1.08582i 0.297663 0.0347918i
\(975\) 0 0
\(976\) −6.57836 + 1.55910i −0.210568 + 0.0499056i
\(977\) −16.8202 8.44744i −0.538127 0.270258i 0.158909 0.987293i \(-0.449202\pi\)
−0.697037 + 0.717035i \(0.745499\pi\)
\(978\) 0 0
\(979\) −1.70645 5.69995i −0.0545385 0.182171i
\(980\) −1.54195 + 0.561225i −0.0492559 + 0.0179277i
\(981\) 0 0
\(982\) 12.0553 + 4.38778i 0.384701 + 0.140020i
\(983\) 0.665467 11.4256i 0.0212251 0.364421i −0.970926 0.239379i \(-0.923056\pi\)
0.992151 0.125042i \(-0.0399067\pi\)
\(984\) 0 0
\(985\) −14.0272 + 18.8418i −0.446944 + 0.600350i
\(986\) 3.03846 + 7.04395i 0.0967644 + 0.224325i
\(987\) 0 0
\(988\) −38.2748 + 19.2223i −1.21768 + 0.611543i
\(989\) −1.09533 + 0.919094i −0.0348296 + 0.0292255i
\(990\) 0 0
\(991\) −22.6012 18.9647i −0.717951 0.602432i 0.208867 0.977944i \(-0.433022\pi\)
−0.926818 + 0.375512i \(0.877467\pi\)
\(992\) 21.6078 + 5.12114i 0.686048 + 0.162596i
\(993\) 0 0
\(994\) 0.390848 + 6.71060i 0.0123969 + 0.212847i
\(995\) 10.5965 35.3949i 0.335933 1.12209i
\(996\) 0 0
\(997\) 26.5603 + 35.6767i 0.841173 + 1.12989i 0.990006 + 0.141029i \(0.0450410\pi\)
−0.148833 + 0.988862i \(0.547552\pi\)
\(998\) −3.36499 + 5.82833i −0.106517 + 0.184493i
\(999\) 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 243.2.g.a.19.5 144
3.2 odd 2 81.2.g.a.61.4 yes 144
9.2 odd 6 729.2.g.c.541.5 144
9.4 even 3 729.2.g.a.55.4 144
9.5 odd 6 729.2.g.d.55.5 144
9.7 even 3 729.2.g.b.541.4 144
81.2 odd 54 6561.2.a.c.1.47 72
81.4 even 27 inner 243.2.g.a.64.5 144
81.23 odd 54 729.2.g.d.676.5 144
81.31 even 27 729.2.g.b.190.4 144
81.50 odd 54 729.2.g.c.190.5 144
81.58 even 27 729.2.g.a.676.4 144
81.77 odd 54 81.2.g.a.4.4 144
81.79 even 27 6561.2.a.d.1.26 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.4.4 144 81.77 odd 54
81.2.g.a.61.4 yes 144 3.2 odd 2
243.2.g.a.19.5 144 1.1 even 1 trivial
243.2.g.a.64.5 144 81.4 even 27 inner
729.2.g.a.55.4 144 9.4 even 3
729.2.g.a.676.4 144 81.58 even 27
729.2.g.b.190.4 144 81.31 even 27
729.2.g.b.541.4 144 9.7 even 3
729.2.g.c.190.5 144 81.50 odd 54
729.2.g.c.541.5 144 9.2 odd 6
729.2.g.d.55.5 144 9.5 odd 6
729.2.g.d.676.5 144 81.23 odd 54
6561.2.a.c.1.47 72 81.2 odd 54
6561.2.a.d.1.26 72 81.79 even 27