Properties

Label 891.2.n.a.379.1
Level $891$
Weight $2$
Character 891.379
Analytic conductor $7.115$
Analytic rank $0$
Dimension $8$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(136,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.136");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.n (of order \(15\), degree \(8\), 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: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{15})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 379.1
Root \(0.669131 - 0.743145i\) of defining polynomial
Character \(\chi\) \(=\) 891.379
Dual form 891.2.n.a.757.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.604528 - 0.128496i) q^{2} +(-1.47815 - 0.658114i) q^{4} +(-2.56082 + 0.544320i) q^{5} +(-0.313585 - 2.98357i) q^{7} +(1.80902 + 1.31433i) q^{8} +1.61803 q^{10} +(-1.62543 - 2.89102i) q^{11} +(1.18030 - 1.31086i) q^{13} +(-0.193806 + 1.84395i) q^{14} +(1.24064 + 1.37787i) q^{16} +(-0.500000 + 1.53884i) q^{17} +(-4.73607 - 3.44095i) q^{19} +(4.14350 + 0.880728i) q^{20} +(0.611130 + 1.95656i) q^{22} +(1.73607 + 3.00696i) q^{23} +(1.69381 - 0.754131i) q^{25} +(-0.881966 + 0.640786i) q^{26} +(-1.50000 + 4.61653i) q^{28} +(0.467465 + 4.44764i) q^{29} +(1.90977 - 2.12101i) q^{31} +(-2.80902 - 4.86536i) q^{32} +(0.500000 - 0.866025i) q^{34} +(2.42705 + 7.46969i) q^{35} +(-0.190983 + 0.138757i) q^{37} +(2.42094 + 2.68872i) q^{38} +(-5.34799 - 2.38108i) q^{40} +(-1.24852 + 11.8788i) q^{41} +(-3.11803 + 5.40059i) q^{43} +(0.500000 + 5.34307i) q^{44} +(-0.663119 - 2.04087i) q^{46} +(-1.47815 + 0.658114i) q^{47} +(-1.95630 + 0.415823i) q^{49} +(-1.12086 + 0.238246i) q^{50} +(-2.60735 + 1.16087i) q^{52} +(2.97214 + 9.14729i) q^{53} +(5.73607 + 6.51864i) q^{55} +(3.35410 - 5.80948i) q^{56} +(0.288910 - 2.74879i) q^{58} +(-9.43349 - 4.20006i) q^{59} +(5.25542 + 5.83674i) q^{61} +(-1.42705 + 1.03681i) q^{62} +(-0.0729490 - 0.224514i) q^{64} +(-2.30902 + 3.99933i) q^{65} +(4.78115 + 8.28120i) q^{67} +(1.75181 - 1.94558i) q^{68} +(-0.507392 - 4.82751i) q^{70} +(1.71885 - 5.29007i) q^{71} +(2.61803 - 1.90211i) q^{73} +(0.133284 - 0.0593421i) q^{74} +(4.73607 + 8.20311i) q^{76} +(-8.11584 + 5.75615i) q^{77} +(-9.26515 - 1.96937i) q^{79} +(-3.92705 - 2.85317i) q^{80} +(2.28115 - 7.02067i) q^{82} +(-0.473881 - 0.526298i) q^{83} +(0.442790 - 4.21286i) q^{85} +(2.57890 - 2.86416i) q^{86} +(0.859324 - 7.36624i) q^{88} -0.527864 q^{89} +(-4.28115 - 3.11044i) q^{91} +(-0.587244 - 5.58726i) q^{92} +(0.978148 - 0.207912i) q^{94} +(14.0012 + 6.23374i) q^{95} +(13.7278 + 2.91792i) q^{97} +1.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 3 q^{2} - 3 q^{4} - q^{5} + 3 q^{7} + 10 q^{8} + 4 q^{10} + 9 q^{11} + 9 q^{13} + 6 q^{14} - 9 q^{16} - 4 q^{17} - 20 q^{19} + 3 q^{20} + 8 q^{22} - 4 q^{23} + 6 q^{25} - 16 q^{26} - 12 q^{28} - 10 q^{29}+ \cdots - 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.604528 0.128496i −0.427466 0.0908607i −0.0108456 0.999941i \(-0.503452\pi\)
−0.416621 + 0.909080i \(0.636786\pi\)
\(3\) 0 0
\(4\) −1.47815 0.658114i −0.739074 0.329057i
\(5\) −2.56082 + 0.544320i −1.14524 + 0.243427i −0.741179 0.671307i \(-0.765733\pi\)
−0.404056 + 0.914734i \(0.632400\pi\)
\(6\) 0 0
\(7\) −0.313585 2.98357i −0.118524 1.12768i −0.878504 0.477735i \(-0.841458\pi\)
0.759980 0.649947i \(-0.225209\pi\)
\(8\) 1.80902 + 1.31433i 0.639584 + 0.464685i
\(9\) 0 0
\(10\) 1.61803 0.511667
\(11\) −1.62543 2.89102i −0.490084 0.871675i
\(12\) 0 0
\(13\) 1.18030 1.31086i 0.327357 0.363566i −0.556890 0.830586i \(-0.688006\pi\)
0.884247 + 0.467020i \(0.154672\pi\)
\(14\) −0.193806 + 1.84395i −0.0517969 + 0.492815i
\(15\) 0 0
\(16\) 1.24064 + 1.37787i 0.310159 + 0.344467i
\(17\) −0.500000 + 1.53884i −0.121268 + 0.373224i −0.993203 0.116398i \(-0.962865\pi\)
0.871935 + 0.489622i \(0.162865\pi\)
\(18\) 0 0
\(19\) −4.73607 3.44095i −1.08653 0.789409i −0.107719 0.994181i \(-0.534355\pi\)
−0.978810 + 0.204772i \(0.934355\pi\)
\(20\) 4.14350 + 0.880728i 0.926515 + 0.196937i
\(21\) 0 0
\(22\) 0.611130 + 1.95656i 0.130293 + 0.417141i
\(23\) 1.73607 + 3.00696i 0.361995 + 0.626994i 0.988289 0.152593i \(-0.0487623\pi\)
−0.626294 + 0.779587i \(0.715429\pi\)
\(24\) 0 0
\(25\) 1.69381 0.754131i 0.338761 0.150826i
\(26\) −0.881966 + 0.640786i −0.172968 + 0.125668i
\(27\) 0 0
\(28\) −1.50000 + 4.61653i −0.283473 + 0.872441i
\(29\) 0.467465 + 4.44764i 0.0868062 + 0.825905i 0.948137 + 0.317861i \(0.102965\pi\)
−0.861331 + 0.508044i \(0.830369\pi\)
\(30\) 0 0
\(31\) 1.90977 2.12101i 0.343004 0.380945i −0.546818 0.837251i \(-0.684161\pi\)
0.889823 + 0.456306i \(0.150828\pi\)
\(32\) −2.80902 4.86536i −0.496569 0.860082i
\(33\) 0 0
\(34\) 0.500000 0.866025i 0.0857493 0.148522i
\(35\) 2.42705 + 7.46969i 0.410246 + 1.26261i
\(36\) 0 0
\(37\) −0.190983 + 0.138757i −0.0313974 + 0.0228116i −0.603373 0.797459i \(-0.706177\pi\)
0.571976 + 0.820270i \(0.306177\pi\)
\(38\) 2.42094 + 2.68872i 0.392728 + 0.436169i
\(39\) 0 0
\(40\) −5.34799 2.38108i −0.845591 0.376481i
\(41\) −1.24852 + 11.8788i −0.194986 + 1.85516i 0.261208 + 0.965283i \(0.415879\pi\)
−0.456194 + 0.889881i \(0.650788\pi\)
\(42\) 0 0
\(43\) −3.11803 + 5.40059i −0.475496 + 0.823583i −0.999606 0.0280676i \(-0.991065\pi\)
0.524110 + 0.851650i \(0.324398\pi\)
\(44\) 0.500000 + 5.34307i 0.0753778 + 0.805498i
\(45\) 0 0
\(46\) −0.663119 2.04087i −0.0977716 0.300910i
\(47\) −1.47815 + 0.658114i −0.215610 + 0.0959958i −0.511700 0.859164i \(-0.670984\pi\)
0.296090 + 0.955160i \(0.404317\pi\)
\(48\) 0 0
\(49\) −1.95630 + 0.415823i −0.279471 + 0.0594033i
\(50\) −1.12086 + 0.238246i −0.158513 + 0.0336930i
\(51\) 0 0
\(52\) −2.60735 + 1.16087i −0.361575 + 0.160983i
\(53\) 2.97214 + 9.14729i 0.408254 + 1.25648i 0.918147 + 0.396240i \(0.129685\pi\)
−0.509893 + 0.860238i \(0.670315\pi\)
\(54\) 0 0
\(55\) 5.73607 + 6.51864i 0.773451 + 0.878973i
\(56\) 3.35410 5.80948i 0.448211 0.776324i
\(57\) 0 0
\(58\) 0.288910 2.74879i 0.0379357 0.360934i
\(59\) −9.43349 4.20006i −1.22814 0.546801i −0.312925 0.949778i \(-0.601309\pi\)
−0.915210 + 0.402977i \(0.867976\pi\)
\(60\) 0 0
\(61\) 5.25542 + 5.83674i 0.672888 + 0.747317i 0.978817 0.204737i \(-0.0656338\pi\)
−0.305929 + 0.952054i \(0.598967\pi\)
\(62\) −1.42705 + 1.03681i −0.181236 + 0.131675i
\(63\) 0 0
\(64\) −0.0729490 0.224514i −0.00911863 0.0280642i
\(65\) −2.30902 + 3.99933i −0.286398 + 0.496056i
\(66\) 0 0
\(67\) 4.78115 + 8.28120i 0.584111 + 1.01171i 0.994986 + 0.100018i \(0.0318900\pi\)
−0.410875 + 0.911692i \(0.634777\pi\)
\(68\) 1.75181 1.94558i 0.212438 0.235936i
\(69\) 0 0
\(70\) −0.507392 4.82751i −0.0606449 0.576998i
\(71\) 1.71885 5.29007i 0.203990 0.627815i −0.795764 0.605607i \(-0.792930\pi\)
0.999753 0.0222083i \(-0.00706970\pi\)
\(72\) 0 0
\(73\) 2.61803 1.90211i 0.306418 0.222625i −0.423940 0.905690i \(-0.639353\pi\)
0.730358 + 0.683065i \(0.239353\pi\)
\(74\) 0.133284 0.0593421i 0.0154940 0.00689838i
\(75\) 0 0
\(76\) 4.73607 + 8.20311i 0.543264 + 0.940961i
\(77\) −8.11584 + 5.75615i −0.924885 + 0.655974i
\(78\) 0 0
\(79\) −9.26515 1.96937i −1.04241 0.221571i −0.345268 0.938504i \(-0.612212\pi\)
−0.697142 + 0.716933i \(0.745545\pi\)
\(80\) −3.92705 2.85317i −0.439058 0.318994i
\(81\) 0 0
\(82\) 2.28115 7.02067i 0.251911 0.775303i
\(83\) −0.473881 0.526298i −0.0520152 0.0577687i 0.716576 0.697509i \(-0.245708\pi\)
−0.768591 + 0.639741i \(0.779042\pi\)
\(84\) 0 0
\(85\) 0.442790 4.21286i 0.0480273 0.456949i
\(86\) 2.57890 2.86416i 0.278090 0.308850i
\(87\) 0 0
\(88\) 0.859324 7.36624i 0.0916042 0.785244i
\(89\) −0.527864 −0.0559535 −0.0279767 0.999609i \(-0.508906\pi\)
−0.0279767 + 0.999609i \(0.508906\pi\)
\(90\) 0 0
\(91\) −4.28115 3.11044i −0.448787 0.326063i
\(92\) −0.587244 5.58726i −0.0612245 0.582512i
\(93\) 0 0
\(94\) 0.978148 0.207912i 0.100888 0.0214445i
\(95\) 14.0012 + 6.23374i 1.43649 + 0.639568i
\(96\) 0 0
\(97\) 13.7278 + 2.91792i 1.39384 + 0.296270i 0.842809 0.538213i \(-0.180900\pi\)
0.551033 + 0.834483i \(0.314234\pi\)
\(98\) 1.23607 0.124862
\(99\) 0 0
\(100\) −3.00000 −0.300000
\(101\) −2.93444 0.623735i −0.291988 0.0620640i 0.0595888 0.998223i \(-0.481021\pi\)
−0.351577 + 0.936159i \(0.614354\pi\)
\(102\) 0 0
\(103\) −5.48127 2.44042i −0.540086 0.240462i 0.118518 0.992952i \(-0.462186\pi\)
−0.658603 + 0.752490i \(0.728852\pi\)
\(104\) 3.85808 0.820060i 0.378316 0.0804135i
\(105\) 0 0
\(106\) −0.621346 5.91171i −0.0603504 0.574196i
\(107\) −3.42705 2.48990i −0.331306 0.240708i 0.409679 0.912230i \(-0.365641\pi\)
−0.740984 + 0.671522i \(0.765641\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) −2.62999 4.67777i −0.250760 0.446008i
\(111\) 0 0
\(112\) 3.72191 4.13360i 0.351687 0.390588i
\(113\) 0.0740275 0.704324i 0.00696392 0.0662573i −0.990488 0.137599i \(-0.956061\pi\)
0.997452 + 0.0713418i \(0.0227281\pi\)
\(114\) 0 0
\(115\) −6.08251 6.75531i −0.567197 0.629936i
\(116\) 2.23607 6.88191i 0.207614 0.638969i
\(117\) 0 0
\(118\) 5.16312 + 3.75123i 0.475304 + 0.345328i
\(119\) 4.74803 + 1.00922i 0.435251 + 0.0925155i
\(120\) 0 0
\(121\) −5.71598 + 9.39827i −0.519635 + 0.854389i
\(122\) −2.42705 4.20378i −0.219735 0.380592i
\(123\) 0 0
\(124\) −4.21878 + 1.87832i −0.378858 + 0.168678i
\(125\) 6.66312 4.84104i 0.595967 0.432996i
\(126\) 0 0
\(127\) −1.14590 + 3.52671i −0.101682 + 0.312945i −0.988937 0.148333i \(-0.952609\pi\)
0.887255 + 0.461279i \(0.152609\pi\)
\(128\) 1.18974 + 11.3196i 0.105159 + 1.00052i
\(129\) 0 0
\(130\) 1.90977 2.12101i 0.167498 0.186025i
\(131\) −3.57295 6.18853i −0.312170 0.540694i 0.666662 0.745360i \(-0.267723\pi\)
−0.978832 + 0.204666i \(0.934389\pi\)
\(132\) 0 0
\(133\) −8.78115 + 15.2094i −0.761423 + 1.31882i
\(134\) −1.82624 5.62058i −0.157763 0.485544i
\(135\) 0 0
\(136\) −2.92705 + 2.12663i −0.250993 + 0.182357i
\(137\) −4.99983 5.55288i −0.427165 0.474414i 0.490688 0.871335i \(-0.336745\pi\)
−0.917853 + 0.396921i \(0.870079\pi\)
\(138\) 0 0
\(139\) −0.780261 0.347395i −0.0661809 0.0294656i 0.373379 0.927679i \(-0.378199\pi\)
−0.439560 + 0.898213i \(0.644866\pi\)
\(140\) 1.32837 12.6386i 0.112268 1.06816i
\(141\) 0 0
\(142\) −1.71885 + 2.97713i −0.144242 + 0.249835i
\(143\) −5.70820 1.28157i −0.477344 0.107170i
\(144\) 0 0
\(145\) −3.61803 11.1352i −0.300461 0.924725i
\(146\) −1.82709 + 0.813473i −0.151211 + 0.0673235i
\(147\) 0 0
\(148\) 0.373619 0.0794152i 0.0307113 0.00652789i
\(149\) 14.6722 3.11868i 1.20199 0.255492i 0.436960 0.899481i \(-0.356055\pi\)
0.765035 + 0.643989i \(0.222722\pi\)
\(150\) 0 0
\(151\) 1.82709 0.813473i 0.148687 0.0661995i −0.331044 0.943615i \(-0.607401\pi\)
0.479731 + 0.877416i \(0.340734\pi\)
\(152\) −4.04508 12.4495i −0.328100 1.00979i
\(153\) 0 0
\(154\) 5.64590 2.43690i 0.454959 0.196371i
\(155\) −3.73607 + 6.47106i −0.300088 + 0.519768i
\(156\) 0 0
\(157\) 0.387613 3.68789i 0.0309349 0.294326i −0.968106 0.250541i \(-0.919392\pi\)
0.999041 0.0437851i \(-0.0139417\pi\)
\(158\) 5.34799 + 2.38108i 0.425463 + 0.189428i
\(159\) 0 0
\(160\) 9.84171 + 10.9303i 0.778055 + 0.864118i
\(161\) 8.42705 6.12261i 0.664145 0.482529i
\(162\) 0 0
\(163\) 5.64590 + 17.3763i 0.442221 + 1.36102i 0.885503 + 0.464634i \(0.153814\pi\)
−0.443282 + 0.896382i \(0.646186\pi\)
\(164\) 9.66312 16.7370i 0.754563 1.30694i
\(165\) 0 0
\(166\) 0.218847 + 0.379054i 0.0169858 + 0.0294203i
\(167\) −6.71435 + 7.45704i −0.519572 + 0.577043i −0.944636 0.328120i \(-0.893585\pi\)
0.425064 + 0.905163i \(0.360252\pi\)
\(168\) 0 0
\(169\) 1.03363 + 9.83437i 0.0795103 + 0.756490i
\(170\) −0.809017 + 2.48990i −0.0620488 + 0.190966i
\(171\) 0 0
\(172\) 8.16312 5.93085i 0.622432 0.452223i
\(173\) −14.0521 + 6.25641i −1.06836 + 0.475666i −0.864136 0.503258i \(-0.832135\pi\)
−0.204227 + 0.978924i \(0.565468\pi\)
\(174\) 0 0
\(175\) −2.78115 4.81710i −0.210235 0.364138i
\(176\) 1.96688 5.82632i 0.148259 0.439176i
\(177\) 0 0
\(178\) 0.319109 + 0.0678287i 0.0239182 + 0.00508397i
\(179\) −1.80902 1.31433i −0.135212 0.0982375i 0.518123 0.855306i \(-0.326631\pi\)
−0.653335 + 0.757069i \(0.726631\pi\)
\(180\) 0 0
\(181\) −5.39919 + 16.6170i −0.401318 + 1.23513i 0.522612 + 0.852571i \(0.324958\pi\)
−0.923930 + 0.382560i \(0.875042\pi\)
\(182\) 2.18840 + 2.43046i 0.162215 + 0.180158i
\(183\) 0 0
\(184\) −0.811552 + 7.72140i −0.0598284 + 0.569229i
\(185\) 0.413545 0.459289i 0.0304045 0.0337676i
\(186\) 0 0
\(187\) 5.26153 1.05576i 0.384761 0.0772051i
\(188\) 2.61803 0.190940
\(189\) 0 0
\(190\) −7.66312 5.56758i −0.555941 0.403915i
\(191\) −0.781051 7.43120i −0.0565149 0.537703i −0.985750 0.168215i \(-0.946200\pi\)
0.929235 0.369488i \(-0.120467\pi\)
\(192\) 0 0
\(193\) 18.1567 3.85932i 1.30695 0.277800i 0.498767 0.866736i \(-0.333786\pi\)
0.808179 + 0.588936i \(0.200453\pi\)
\(194\) −7.92388 3.52794i −0.568901 0.253291i
\(195\) 0 0
\(196\) 3.16535 + 0.672816i 0.226097 + 0.0480583i
\(197\) −24.3820 −1.73714 −0.868572 0.495564i \(-0.834961\pi\)
−0.868572 + 0.495564i \(0.834961\pi\)
\(198\) 0 0
\(199\) −16.7082 −1.18441 −0.592207 0.805786i \(-0.701743\pi\)
−0.592207 + 0.805786i \(0.701743\pi\)
\(200\) 4.05530 + 0.861981i 0.286753 + 0.0609512i
\(201\) 0 0
\(202\) 1.69381 + 0.754131i 0.119176 + 0.0530605i
\(203\) 13.1232 2.78943i 0.921070 0.195779i
\(204\) 0 0
\(205\) −3.26866 31.0992i −0.228293 2.17206i
\(206\) 3.00000 + 2.17963i 0.209020 + 0.151862i
\(207\) 0 0
\(208\) 3.27051 0.226769
\(209\) −2.24974 + 19.2851i −0.155618 + 1.33398i
\(210\) 0 0
\(211\) −14.9019 + 16.5502i −1.02589 + 1.13936i −0.0357366 + 0.999361i \(0.511378\pi\)
−0.990151 + 0.140002i \(0.955289\pi\)
\(212\) 1.62670 15.4771i 0.111722 1.06297i
\(213\) 0 0
\(214\) 1.75181 + 1.94558i 0.119751 + 0.132997i
\(215\) 5.04508 15.5272i 0.344072 1.05894i
\(216\) 0 0
\(217\) −6.92705 5.03280i −0.470239 0.341649i
\(218\) 0 0
\(219\) 0 0
\(220\) −4.18875 13.4105i −0.282405 0.904135i
\(221\) 1.42705 + 2.47172i 0.0959938 + 0.166266i
\(222\) 0 0
\(223\) 0.646976 0.288052i 0.0433247 0.0192894i −0.384960 0.922933i \(-0.625785\pi\)
0.428285 + 0.903644i \(0.359118\pi\)
\(224\) −13.6353 + 9.90659i −0.911044 + 0.661912i
\(225\) 0 0
\(226\) −0.135255 + 0.416272i −0.00899702 + 0.0276900i
\(227\) −2.60156 24.7522i −0.172672 1.64286i −0.646983 0.762504i \(-0.723970\pi\)
0.474312 0.880357i \(-0.342697\pi\)
\(228\) 0 0
\(229\) 6.69131 7.43145i 0.442174 0.491084i −0.480321 0.877093i \(-0.659480\pi\)
0.922495 + 0.386009i \(0.126147\pi\)
\(230\) 2.80902 + 4.86536i 0.185221 + 0.320812i
\(231\) 0 0
\(232\) −5.00000 + 8.66025i −0.328266 + 0.568574i
\(233\) −7.51722 23.1356i −0.492470 1.51567i −0.820863 0.571124i \(-0.806507\pi\)
0.328394 0.944541i \(-0.393493\pi\)
\(234\) 0 0
\(235\) 3.42705 2.48990i 0.223556 0.162423i
\(236\) 11.1800 + 12.4166i 0.727754 + 0.808253i
\(237\) 0 0
\(238\) −2.74064 1.22021i −0.177649 0.0790945i
\(239\) 0.267834 2.54827i 0.0173247 0.164834i −0.982439 0.186586i \(-0.940258\pi\)
0.999763 + 0.0217520i \(0.00692442\pi\)
\(240\) 0 0
\(241\) 11.5623 20.0265i 0.744794 1.29002i −0.205498 0.978658i \(-0.565881\pi\)
0.950291 0.311363i \(-0.100785\pi\)
\(242\) 4.66312 4.94704i 0.299757 0.318008i
\(243\) 0 0
\(244\) −3.92705 12.0862i −0.251404 0.773741i
\(245\) 4.78339 2.12970i 0.305599 0.136062i
\(246\) 0 0
\(247\) −10.1006 + 2.14695i −0.642685 + 0.136607i
\(248\) 6.24250 1.32689i 0.396399 0.0842573i
\(249\) 0 0
\(250\) −4.65010 + 2.07036i −0.294098 + 0.130941i
\(251\) 2.40983 + 7.41669i 0.152107 + 0.468138i 0.997856 0.0654431i \(-0.0208461\pi\)
−0.845749 + 0.533581i \(0.820846\pi\)
\(252\) 0 0
\(253\) 5.87132 9.90659i 0.369127 0.622822i
\(254\) 1.14590 1.98475i 0.0719000 0.124535i
\(255\) 0 0
\(256\) 0.685948 6.52636i 0.0428717 0.407897i
\(257\) 10.6645 + 4.74815i 0.665234 + 0.296181i 0.711436 0.702751i \(-0.248045\pi\)
−0.0462020 + 0.998932i \(0.514712\pi\)
\(258\) 0 0
\(259\) 0.473881 + 0.526298i 0.0294455 + 0.0327026i
\(260\) 6.04508 4.39201i 0.374900 0.272381i
\(261\) 0 0
\(262\) 1.36475 + 4.20025i 0.0843142 + 0.259493i
\(263\) −8.16312 + 14.1389i −0.503359 + 0.871844i 0.496633 + 0.867961i \(0.334570\pi\)
−0.999992 + 0.00388355i \(0.998764\pi\)
\(264\) 0 0
\(265\) −12.5902 21.8068i −0.773408 1.33958i
\(266\) 7.26281 8.06617i 0.445312 0.494569i
\(267\) 0 0
\(268\) −1.61728 15.3874i −0.0987910 0.939934i
\(269\) −4.79837 + 14.7679i −0.292562 + 0.900413i 0.691467 + 0.722408i \(0.256965\pi\)
−0.984029 + 0.178006i \(0.943035\pi\)
\(270\) 0 0
\(271\) 22.0623 16.0292i 1.34019 0.973705i 0.340753 0.940153i \(-0.389318\pi\)
0.999437 0.0335518i \(-0.0106819\pi\)
\(272\) −2.74064 + 1.22021i −0.166175 + 0.0739861i
\(273\) 0 0
\(274\) 2.30902 + 3.99933i 0.139493 + 0.241609i
\(275\) −4.93336 3.67104i −0.297493 0.221372i
\(276\) 0 0
\(277\) −29.8944 6.35426i −1.79618 0.381791i −0.815713 0.578457i \(-0.803655\pi\)
−0.980470 + 0.196667i \(0.936988\pi\)
\(278\) 0.427051 + 0.310271i 0.0256128 + 0.0186088i
\(279\) 0 0
\(280\) −5.42705 + 16.7027i −0.324328 + 0.998180i
\(281\) 0.511170 + 0.567712i 0.0304939 + 0.0338669i 0.758199 0.652023i \(-0.226080\pi\)
−0.727705 + 0.685890i \(0.759413\pi\)
\(282\) 0 0
\(283\) −0.0188507 + 0.179352i −0.00112055 + 0.0106614i −0.995068 0.0991963i \(-0.968373\pi\)
0.993947 + 0.109858i \(0.0350395\pi\)
\(284\) −6.02218 + 6.68830i −0.357350 + 0.396878i
\(285\) 0 0
\(286\) 3.28609 + 1.50823i 0.194311 + 0.0891836i
\(287\) 35.8328 2.11514
\(288\) 0 0
\(289\) 11.6353 + 8.45351i 0.684427 + 0.497265i
\(290\) 0.756375 + 7.19643i 0.0444159 + 0.422589i
\(291\) 0 0
\(292\) −5.12165 + 1.08864i −0.299722 + 0.0637078i
\(293\) −0.0509101 0.0226667i −0.00297420 0.00132420i 0.405249 0.914206i \(-0.367185\pi\)
−0.408223 + 0.912882i \(0.633851\pi\)
\(294\) 0 0
\(295\) 26.4437 + 5.62078i 1.53961 + 0.327254i
\(296\) −0.527864 −0.0306815
\(297\) 0 0
\(298\) −9.27051 −0.537026
\(299\) 5.99077 + 1.27338i 0.346455 + 0.0736414i
\(300\) 0 0
\(301\) 17.0908 + 7.60931i 0.985097 + 0.438593i
\(302\) −1.20906 + 0.256993i −0.0695734 + 0.0147883i
\(303\) 0 0
\(304\) −1.13456 10.7946i −0.0650716 0.619115i
\(305\) −16.6353 12.0862i −0.952532 0.692055i
\(306\) 0 0
\(307\) 0.562306 0.0320925 0.0160462 0.999871i \(-0.494892\pi\)
0.0160462 + 0.999871i \(0.494892\pi\)
\(308\) 15.7846 3.16729i 0.899411 0.180473i
\(309\) 0 0
\(310\) 3.09007 3.43187i 0.175504 0.194917i
\(311\) 0.264234 2.51402i 0.0149833 0.142557i −0.984473 0.175538i \(-0.943833\pi\)
0.999456 + 0.0329813i \(0.0105002\pi\)
\(312\) 0 0
\(313\) 17.2855 + 19.1975i 0.977036 + 1.08511i 0.996356 + 0.0852948i \(0.0271832\pi\)
−0.0193200 + 0.999813i \(0.506150\pi\)
\(314\) −0.708204 + 2.17963i −0.0399663 + 0.123004i
\(315\) 0 0
\(316\) 12.3992 + 9.00854i 0.697509 + 0.506770i
\(317\) −18.9376 4.02531i −1.06364 0.226084i −0.357325 0.933980i \(-0.616311\pi\)
−0.706317 + 0.707896i \(0.749645\pi\)
\(318\) 0 0
\(319\) 12.0984 8.58076i 0.677379 0.480430i
\(320\) 0.309017 + 0.535233i 0.0172746 + 0.0299204i
\(321\) 0 0
\(322\) −5.88113 + 2.61845i −0.327742 + 0.145920i
\(323\) 7.66312 5.56758i 0.426387 0.309789i
\(324\) 0 0
\(325\) 1.01064 3.11044i 0.0560604 0.172536i
\(326\) −1.18031 11.2299i −0.0653716 0.621969i
\(327\) 0 0
\(328\) −17.8713 + 19.8481i −0.986776 + 1.09593i
\(329\) 2.42705 + 4.20378i 0.133808 + 0.231762i
\(330\) 0 0
\(331\) −13.2984 + 23.0335i −0.730945 + 1.26603i 0.225535 + 0.974235i \(0.427587\pi\)
−0.956480 + 0.291798i \(0.905746\pi\)
\(332\) 0.354102 + 1.08981i 0.0194339 + 0.0598113i
\(333\) 0 0
\(334\) 5.01722 3.64522i 0.274530 0.199458i
\(335\) −16.7513 18.6042i −0.915222 1.01646i
\(336\) 0 0
\(337\) −0.266569 0.118684i −0.0145209 0.00646514i 0.399463 0.916749i \(-0.369196\pi\)
−0.413984 + 0.910284i \(0.635863\pi\)
\(338\) 0.638821 6.07798i 0.0347473 0.330598i
\(339\) 0 0
\(340\) −3.42705 + 5.93583i −0.185858 + 0.321915i
\(341\) −9.23607 2.07363i −0.500161 0.112293i
\(342\) 0 0
\(343\) −4.63525 14.2658i −0.250280 0.770283i
\(344\) −12.7387 + 5.67165i −0.686826 + 0.305795i
\(345\) 0 0
\(346\) 9.29884 1.97653i 0.499909 0.106259i
\(347\) −20.4866 + 4.35456i −1.09978 + 0.233765i −0.721836 0.692064i \(-0.756701\pi\)
−0.377942 + 0.925829i \(0.623368\pi\)
\(348\) 0 0
\(349\) −9.24929 + 4.11805i −0.495103 + 0.220434i −0.639070 0.769148i \(-0.720681\pi\)
0.143967 + 0.989582i \(0.454014\pi\)
\(350\) 1.06231 + 3.26944i 0.0567826 + 0.174759i
\(351\) 0 0
\(352\) −9.50000 + 16.0292i −0.506352 + 0.854359i
\(353\) −5.23607 + 9.06914i −0.278688 + 0.482701i −0.971059 0.238840i \(-0.923233\pi\)
0.692371 + 0.721542i \(0.256566\pi\)
\(354\) 0 0
\(355\) −1.52218 + 14.4825i −0.0807887 + 0.768653i
\(356\) 0.780261 + 0.347395i 0.0413537 + 0.0184119i
\(357\) 0 0
\(358\) 0.924716 + 1.02700i 0.0488727 + 0.0542787i
\(359\) −10.3262 + 7.50245i −0.544998 + 0.395964i −0.825938 0.563761i \(-0.809354\pi\)
0.280940 + 0.959725i \(0.409354\pi\)
\(360\) 0 0
\(361\) 4.71885 + 14.5231i 0.248360 + 0.764375i
\(362\) 5.39919 9.35167i 0.283775 0.491513i
\(363\) 0 0
\(364\) 4.28115 + 7.41517i 0.224393 + 0.388661i
\(365\) −5.66897 + 6.29602i −0.296727 + 0.329549i
\(366\) 0 0
\(367\) −0.581419 5.53184i −0.0303498 0.288759i −0.999161 0.0409586i \(-0.986959\pi\)
0.968811 0.247801i \(-0.0797079\pi\)
\(368\) −1.98936 + 6.12261i −0.103702 + 0.319163i
\(369\) 0 0
\(370\) −0.309017 + 0.224514i −0.0160650 + 0.0116719i
\(371\) 26.3595 11.7360i 1.36852 0.609304i
\(372\) 0 0
\(373\) 2.20820 + 3.82472i 0.114336 + 0.198037i 0.917514 0.397703i \(-0.130192\pi\)
−0.803178 + 0.595739i \(0.796859\pi\)
\(374\) −3.31641 0.0378495i −0.171487 0.00195715i
\(375\) 0 0
\(376\) −3.53897 0.752232i −0.182509 0.0387934i
\(377\) 6.38197 + 4.63677i 0.328688 + 0.238806i
\(378\) 0 0
\(379\) 0.489357 1.50609i 0.0251366 0.0773624i −0.937701 0.347443i \(-0.887050\pi\)
0.962838 + 0.270080i \(0.0870502\pi\)
\(380\) −16.5934 18.4288i −0.851221 0.945377i
\(381\) 0 0
\(382\) −0.482716 + 4.59274i −0.0246979 + 0.234985i
\(383\) −17.9919 + 19.9821i −0.919346 + 1.02104i 0.0803598 + 0.996766i \(0.474393\pi\)
−0.999705 + 0.0242708i \(0.992274\pi\)
\(384\) 0 0
\(385\) 17.6500 19.1581i 0.899529 0.976386i
\(386\) −11.4721 −0.583916
\(387\) 0 0
\(388\) −18.3713 13.3475i −0.932663 0.677619i
\(389\) 2.53696 + 24.1376i 0.128629 + 1.22382i 0.848303 + 0.529511i \(0.177624\pi\)
−0.719674 + 0.694312i \(0.755709\pi\)
\(390\) 0 0
\(391\) −5.49527 + 1.16805i −0.277908 + 0.0590711i
\(392\) −4.08550 1.81898i −0.206349 0.0918724i
\(393\) 0 0
\(394\) 14.7396 + 3.13300i 0.742570 + 0.157838i
\(395\) 24.7984 1.24774
\(396\) 0 0
\(397\) −38.7082 −1.94271 −0.971355 0.237635i \(-0.923628\pi\)
−0.971355 + 0.237635i \(0.923628\pi\)
\(398\) 10.1006 + 2.14695i 0.506297 + 0.107617i
\(399\) 0 0
\(400\) 3.14049 + 1.39824i 0.157024 + 0.0699118i
\(401\) −25.5200 + 5.42445i −1.27441 + 0.270884i −0.794947 0.606678i \(-0.792502\pi\)
−0.479462 + 0.877562i \(0.659168\pi\)
\(402\) 0 0
\(403\) −0.526242 5.00686i −0.0262140 0.249410i
\(404\) 3.92705 + 2.85317i 0.195378 + 0.141950i
\(405\) 0 0
\(406\) −8.29180 −0.411515
\(407\) 0.711579 + 0.326596i 0.0352716 + 0.0161888i
\(408\) 0 0
\(409\) −7.39773 + 8.21601i −0.365794 + 0.406255i −0.897742 0.440522i \(-0.854794\pi\)
0.531948 + 0.846777i \(0.321460\pi\)
\(410\) −2.02014 + 19.2204i −0.0997677 + 0.949226i
\(411\) 0 0
\(412\) 6.49606 + 7.21460i 0.320038 + 0.355438i
\(413\) −9.57295 + 29.4625i −0.471054 + 1.44976i
\(414\) 0 0
\(415\) 1.50000 + 1.08981i 0.0736321 + 0.0534969i
\(416\) −9.69328 2.06037i −0.475252 0.101018i
\(417\) 0 0
\(418\) 3.83810 11.3693i 0.187727 0.556090i
\(419\) 8.25329 + 14.2951i 0.403200 + 0.698362i 0.994110 0.108375i \(-0.0345647\pi\)
−0.590911 + 0.806737i \(0.701231\pi\)
\(420\) 0 0
\(421\) −34.0483 + 15.1593i −1.65941 + 0.738818i −0.999917 0.0128899i \(-0.995897\pi\)
−0.659496 + 0.751708i \(0.729230\pi\)
\(422\) 11.1353 8.09024i 0.542056 0.393827i
\(423\) 0 0
\(424\) −6.64590 + 20.4540i −0.322753 + 0.993333i
\(425\) 0.313585 + 2.98357i 0.0152111 + 0.144724i
\(426\) 0 0
\(427\) 15.7663 17.5102i 0.762983 0.847378i
\(428\) 3.42705 + 5.93583i 0.165653 + 0.286919i
\(429\) 0 0
\(430\) −5.04508 + 8.73834i −0.243296 + 0.421400i
\(431\) 12.2082 + 37.5730i 0.588048 + 1.80983i 0.586667 + 0.809828i \(0.300440\pi\)
0.00138127 + 0.999999i \(0.499560\pi\)
\(432\) 0 0
\(433\) 4.85410 3.52671i 0.233273 0.169483i −0.465008 0.885307i \(-0.653949\pi\)
0.698281 + 0.715824i \(0.253949\pi\)
\(434\) 3.54090 + 3.93257i 0.169969 + 0.188769i
\(435\) 0 0
\(436\) 0 0
\(437\) 2.12467 20.2149i 0.101637 0.967009i
\(438\) 0 0
\(439\) −1.64590 + 2.85078i −0.0785544 + 0.136060i −0.902626 0.430425i \(-0.858364\pi\)
0.824072 + 0.566485i \(0.191697\pi\)
\(440\) 1.80902 + 19.3314i 0.0862415 + 0.921588i
\(441\) 0 0
\(442\) −0.545085 1.67760i −0.0259270 0.0797952i
\(443\) 37.5692 16.7269i 1.78497 0.794718i 0.805648 0.592395i \(-0.201817\pi\)
0.979319 0.202324i \(-0.0648493\pi\)
\(444\) 0 0
\(445\) 1.35177 0.287327i 0.0640799 0.0136206i
\(446\) −0.428129 + 0.0910017i −0.0202725 + 0.00430906i
\(447\) 0 0
\(448\) −0.646976 + 0.288052i −0.0305668 + 0.0136092i
\(449\) 7.56231 + 23.2744i 0.356887 + 1.09839i 0.954907 + 0.296905i \(0.0959544\pi\)
−0.598020 + 0.801481i \(0.704046\pi\)
\(450\) 0 0
\(451\) 36.3713 15.6987i 1.71266 0.739222i
\(452\) −0.572949 + 0.992377i −0.0269493 + 0.0466775i
\(453\) 0 0
\(454\) −1.60785 + 15.2977i −0.0754603 + 0.717957i
\(455\) 12.6564 + 5.63497i 0.593339 + 0.264172i
\(456\) 0 0
\(457\) 5.48796 + 6.09500i 0.256716 + 0.285112i 0.857702 0.514148i \(-0.171892\pi\)
−0.600986 + 0.799260i \(0.705225\pi\)
\(458\) −5.00000 + 3.63271i −0.233635 + 0.169746i
\(459\) 0 0
\(460\) 4.54508 + 13.9883i 0.211916 + 0.652209i
\(461\) −10.5451 + 18.2646i −0.491134 + 0.850668i −0.999948 0.0102080i \(-0.996751\pi\)
0.508814 + 0.860876i \(0.330084\pi\)
\(462\) 0 0
\(463\) 7.89919 + 13.6818i 0.367106 + 0.635847i 0.989112 0.147166i \(-0.0470152\pi\)
−0.622005 + 0.783013i \(0.713682\pi\)
\(464\) −5.54829 + 6.16201i −0.257573 + 0.286064i
\(465\) 0 0
\(466\) 1.57153 + 14.9521i 0.0727996 + 0.692642i
\(467\) 3.01722 9.28605i 0.139620 0.429707i −0.856660 0.515882i \(-0.827464\pi\)
0.996280 + 0.0861747i \(0.0274643\pi\)
\(468\) 0 0
\(469\) 23.2082 16.8617i 1.07166 0.778603i
\(470\) −2.39169 + 1.06485i −0.110321 + 0.0491179i
\(471\) 0 0
\(472\) −11.5451 19.9967i −0.531406 0.920422i
\(473\) 20.6814 + 0.236032i 0.950930 + 0.0108528i
\(474\) 0 0
\(475\) −10.6169 2.25669i −0.487137 0.103544i
\(476\) −6.35410 4.61653i −0.291240 0.211598i
\(477\) 0 0
\(478\) −0.489357 + 1.50609i −0.0223827 + 0.0688868i
\(479\) 18.7960 + 20.8751i 0.858811 + 0.953806i 0.999342 0.0362702i \(-0.0115477\pi\)
−0.140531 + 0.990076i \(0.544881\pi\)
\(480\) 0 0
\(481\) −0.0435265 + 0.414127i −0.00198464 + 0.0188826i
\(482\) −9.56308 + 10.6209i −0.435586 + 0.483768i
\(483\) 0 0
\(484\) 14.6342 10.1303i 0.665191 0.460467i
\(485\) −36.7426 −1.66840
\(486\) 0 0
\(487\) −13.6074 9.88635i −0.616610 0.447993i 0.235126 0.971965i \(-0.424450\pi\)
−0.851736 + 0.523972i \(0.824450\pi\)
\(488\) 1.83576 + 17.4661i 0.0831010 + 0.790653i
\(489\) 0 0
\(490\) −3.16535 + 0.672816i −0.142996 + 0.0303947i
\(491\) −23.0348 10.2558i −1.03955 0.462837i −0.185289 0.982684i \(-0.559322\pi\)
−0.854259 + 0.519847i \(0.825989\pi\)
\(492\) 0 0
\(493\) −7.07794 1.50446i −0.318774 0.0677576i
\(494\) 6.38197 0.287138
\(495\) 0 0
\(496\) 5.29180 0.237609
\(497\) −16.3223 3.46941i −0.732154 0.155624i
\(498\) 0 0
\(499\) −16.0440 7.14323i −0.718227 0.319775i 0.0148796 0.999889i \(-0.495263\pi\)
−0.733106 + 0.680114i \(0.761930\pi\)
\(500\) −13.0350 + 2.77068i −0.582944 + 0.123909i
\(501\) 0 0
\(502\) −0.503792 4.79326i −0.0224853 0.213934i
\(503\) 22.7082 + 16.4985i 1.01251 + 0.735631i 0.964734 0.263227i \(-0.0847870\pi\)
0.0477750 + 0.998858i \(0.484787\pi\)
\(504\) 0 0
\(505\) 7.85410 0.349503
\(506\) −4.82234 + 5.23437i −0.214379 + 0.232696i
\(507\) 0 0
\(508\) 4.01478 4.45887i 0.178127 0.197830i
\(509\) 2.46876 23.4887i 0.109426 1.04112i −0.792691 0.609624i \(-0.791321\pi\)
0.902117 0.431492i \(-0.142013\pi\)
\(510\) 0 0
\(511\) −6.49606 7.21460i −0.287369 0.319155i
\(512\) 5.78115 17.7926i 0.255493 0.786327i
\(513\) 0 0
\(514\) −5.83688 4.24074i −0.257454 0.187051i
\(515\) 15.3649 + 3.26592i 0.677060 + 0.143914i
\(516\) 0 0
\(517\) 4.30524 + 3.20364i 0.189344 + 0.140896i
\(518\) −0.218847 0.379054i −0.00961559 0.0166547i
\(519\) 0 0
\(520\) −9.43349 + 4.20006i −0.413686 + 0.184185i
\(521\) −12.0000 + 8.71851i −0.525730 + 0.381965i −0.818758 0.574139i \(-0.805337\pi\)
0.293028 + 0.956104i \(0.405337\pi\)
\(522\) 0 0
\(523\) −3.70163 + 11.3924i −0.161861 + 0.498156i −0.998791 0.0491529i \(-0.984348\pi\)
0.836930 + 0.547309i \(0.184348\pi\)
\(524\) 1.20859 + 11.4990i 0.0527975 + 0.502335i
\(525\) 0 0
\(526\) 6.75164 7.49846i 0.294386 0.326948i
\(527\) 2.30902 + 3.99933i 0.100582 + 0.174214i
\(528\) 0 0
\(529\) 5.47214 9.47802i 0.237919 0.412088i
\(530\) 4.80902 + 14.8006i 0.208890 + 0.642898i
\(531\) 0 0
\(532\) 22.9894 16.7027i 0.996715 0.724156i
\(533\) 14.0978 + 15.6572i 0.610645 + 0.678190i
\(534\) 0 0
\(535\) 10.1314 + 4.51078i 0.438018 + 0.195018i
\(536\) −2.23502 + 21.2648i −0.0965383 + 0.918501i
\(537\) 0 0
\(538\) 4.79837 8.31103i 0.206873 0.358314i
\(539\) 4.38197 + 4.97980i 0.188745 + 0.214495i
\(540\) 0 0
\(541\) 6.04508 + 18.6049i 0.259899 + 0.799885i 0.992825 + 0.119577i \(0.0381540\pi\)
−0.732926 + 0.680308i \(0.761846\pi\)
\(542\) −15.3970 + 6.85518i −0.661357 + 0.294455i
\(543\) 0 0
\(544\) 8.89153 1.88995i 0.381221 0.0810310i
\(545\) 0 0
\(546\) 0 0
\(547\) 19.7491 8.79285i 0.844409 0.375955i 0.0615117 0.998106i \(-0.480408\pi\)
0.782897 + 0.622151i \(0.213741\pi\)
\(548\) 3.73607 + 11.4984i 0.159597 + 0.491189i
\(549\) 0 0
\(550\) 2.51064 + 2.85317i 0.107054 + 0.121660i
\(551\) 13.0902 22.6728i 0.557660 0.965895i
\(552\) 0 0
\(553\) −2.97032 + 28.2607i −0.126311 + 1.20177i
\(554\) 17.2555 + 7.68266i 0.733118 + 0.326405i
\(555\) 0 0
\(556\) 0.924716 + 1.02700i 0.0392167 + 0.0435545i
\(557\) 12.0623 8.76378i 0.511096 0.371333i −0.302143 0.953263i \(-0.597702\pi\)
0.813239 + 0.581929i \(0.197702\pi\)
\(558\) 0 0
\(559\) 3.39919 + 10.4616i 0.143770 + 0.442479i
\(560\) −7.28115 + 12.6113i −0.307685 + 0.532926i
\(561\) 0 0
\(562\) −0.236068 0.408882i −0.00995793 0.0172476i
\(563\) 5.94760 6.60548i 0.250661 0.278388i −0.604662 0.796482i \(-0.706692\pi\)
0.855323 + 0.518095i \(0.173358\pi\)
\(564\) 0 0
\(565\) 0.193806 + 1.84395i 0.00815350 + 0.0775753i
\(566\) 0.0344419 0.106001i 0.00144770 0.00445556i
\(567\) 0 0
\(568\) 10.0623 7.31069i 0.422205 0.306750i
\(569\) 21.9880 9.78970i 0.921786 0.410405i 0.109714 0.993963i \(-0.465006\pi\)
0.812072 + 0.583558i \(0.198340\pi\)
\(570\) 0 0
\(571\) −17.3435 30.0398i −0.725801 1.25712i −0.958643 0.284610i \(-0.908136\pi\)
0.232842 0.972515i \(-0.425197\pi\)
\(572\) 7.59415 + 5.65100i 0.317527 + 0.236280i
\(573\) 0 0
\(574\) −21.6620 4.60439i −0.904153 0.192184i
\(575\) 5.20820 + 3.78398i 0.217197 + 0.157803i
\(576\) 0 0
\(577\) 3.32624 10.2371i 0.138473 0.426176i −0.857641 0.514249i \(-0.828071\pi\)
0.996114 + 0.0880726i \(0.0280707\pi\)
\(578\) −5.94760 6.60548i −0.247387 0.274752i
\(579\) 0 0
\(580\) −1.98022 + 18.8405i −0.0822240 + 0.782309i
\(581\) −1.42164 + 1.57889i −0.0589797 + 0.0655036i
\(582\) 0 0
\(583\) 21.6140 23.4607i 0.895161 0.971645i
\(584\) 7.23607 0.299431
\(585\) 0 0
\(586\) 0.0278640 + 0.0202444i 0.00115105 + 0.000836289i
\(587\) −4.00396 38.0951i −0.165261 1.57235i −0.691728 0.722158i \(-0.743150\pi\)
0.526467 0.850196i \(-0.323516\pi\)
\(588\) 0 0
\(589\) −16.3431 + 3.47383i −0.673405 + 0.143137i
\(590\) −15.2637 6.79584i −0.628397 0.279780i
\(591\) 0 0
\(592\) −0.428129 0.0910017i −0.0175960 0.00374015i
\(593\) −22.2148 −0.912252 −0.456126 0.889915i \(-0.650763\pi\)
−0.456126 + 0.889915i \(0.650763\pi\)
\(594\) 0 0
\(595\) −12.7082 −0.520986
\(596\) −23.7401 5.04612i −0.972434 0.206697i
\(597\) 0 0
\(598\) −3.45797 1.53959i −0.141407 0.0629584i
\(599\) −8.11060 + 1.72396i −0.331390 + 0.0704392i −0.370602 0.928792i \(-0.620849\pi\)
0.0392119 + 0.999231i \(0.487515\pi\)
\(600\) 0 0
\(601\) −3.53649 33.6475i −0.144257 1.37251i −0.791940 0.610599i \(-0.790929\pi\)
0.647683 0.761910i \(-0.275738\pi\)
\(602\) −9.35410 6.79615i −0.381245 0.276991i
\(603\) 0 0
\(604\) −3.23607 −0.131674
\(605\) 9.52195 27.1786i 0.387122 1.10497i
\(606\) 0 0
\(607\) 8.91699 9.90332i 0.361930 0.401964i −0.534486 0.845177i \(-0.679495\pi\)
0.896416 + 0.443213i \(0.146162\pi\)
\(608\) −3.43779 + 32.7084i −0.139421 + 1.32650i
\(609\) 0 0
\(610\) 8.50345 + 9.44404i 0.344295 + 0.382378i
\(611\) −0.881966 + 2.71441i −0.0356805 + 0.109813i
\(612\) 0 0
\(613\) −28.0344 20.3682i −1.13230 0.822664i −0.146272 0.989244i \(-0.546728\pi\)
−0.986028 + 0.166580i \(0.946728\pi\)
\(614\) −0.339930 0.0722543i −0.0137185 0.00291595i
\(615\) 0 0
\(616\) −22.2471 0.253902i −0.896363 0.0102300i
\(617\) 9.79180 + 16.9599i 0.394203 + 0.682779i 0.992999 0.118122i \(-0.0376874\pi\)
−0.598796 + 0.800901i \(0.704354\pi\)
\(618\) 0 0
\(619\) −8.05716 + 3.58728i −0.323845 + 0.144185i −0.562219 0.826988i \(-0.690052\pi\)
0.238374 + 0.971173i \(0.423386\pi\)
\(620\) 9.78115 7.10642i 0.392821 0.285401i
\(621\) 0 0
\(622\) −0.482779 + 1.48584i −0.0193577 + 0.0595768i
\(623\) 0.165530 + 1.57492i 0.00663184 + 0.0630977i
\(624\) 0 0
\(625\) −20.6312 + 22.9132i −0.825247 + 0.916530i
\(626\) −7.98278 13.8266i −0.319056 0.552621i
\(627\) 0 0
\(628\) −3.00000 + 5.19615i −0.119713 + 0.207349i
\(629\) −0.118034 0.363271i −0.00470632 0.0144846i
\(630\) 0 0
\(631\) −37.4336 + 27.1971i −1.49021 + 1.08270i −0.516125 + 0.856513i \(0.672626\pi\)
−0.974084 + 0.226187i \(0.927374\pi\)
\(632\) −14.1724 15.7401i −0.563748 0.626106i
\(633\) 0 0
\(634\) 10.9311 + 4.86683i 0.434129 + 0.193287i
\(635\) 1.01478 9.65502i 0.0402705 0.383148i
\(636\) 0 0
\(637\) −1.76393 + 3.05522i −0.0698895 + 0.121052i
\(638\) −8.41641 + 3.63271i −0.333209 + 0.143820i
\(639\) 0 0
\(640\) −9.20820 28.3399i −0.363986 1.12023i
\(641\) −32.6525 + 14.5378i −1.28970 + 0.574210i −0.932955 0.359993i \(-0.882779\pi\)
−0.356742 + 0.934203i \(0.616113\pi\)
\(642\) 0 0
\(643\) 37.7196 8.01755i 1.48752 0.316181i 0.608723 0.793383i \(-0.291682\pi\)
0.878794 + 0.477201i \(0.158349\pi\)
\(644\) −16.4858 + 3.50416i −0.649632 + 0.138083i
\(645\) 0 0
\(646\) −5.34799 + 2.38108i −0.210414 + 0.0936823i
\(647\) −8.59017 26.4378i −0.337714 1.03938i −0.965369 0.260887i \(-0.915985\pi\)
0.627655 0.778492i \(-0.284015\pi\)
\(648\) 0 0
\(649\) 3.19098 + 34.0993i 0.125257 + 1.33851i
\(650\) −1.01064 + 1.75049i −0.0396407 + 0.0686597i
\(651\) 0 0
\(652\) 3.09010 29.4004i 0.121018 1.15141i
\(653\) −46.6223 20.7576i −1.82447 0.812307i −0.934010 0.357248i \(-0.883715\pi\)
−0.890461 0.455059i \(-0.849618\pi\)
\(654\) 0 0
\(655\) 12.5182 + 13.9029i 0.489128 + 0.543231i
\(656\) −17.9164 + 13.0170i −0.699518 + 0.508230i
\(657\) 0 0
\(658\) −0.927051 2.85317i −0.0361402 0.111228i
\(659\) −5.32624 + 9.22531i −0.207481 + 0.359367i −0.950920 0.309436i \(-0.899860\pi\)
0.743440 + 0.668803i \(0.233193\pi\)
\(660\) 0 0
\(661\) 4.95492 + 8.58216i 0.192724 + 0.333808i 0.946152 0.323723i \(-0.104935\pi\)
−0.753428 + 0.657530i \(0.771601\pi\)
\(662\) 10.9990 12.2156i 0.427487 0.474772i
\(663\) 0 0
\(664\) −0.165530 1.57492i −0.00642383 0.0611186i
\(665\) 14.2082 43.7284i 0.550971 1.69571i
\(666\) 0 0
\(667\) −12.5623 + 9.12705i −0.486414 + 0.353401i
\(668\) 14.8324 6.60380i 0.573882 0.255509i
\(669\) 0 0
\(670\) 7.73607 + 13.3993i 0.298870 + 0.517659i
\(671\) 8.33182 24.6807i 0.321646 0.952788i
\(672\) 0 0
\(673\) −12.1451 2.58152i −0.468158 0.0995101i −0.0322087 0.999481i \(-0.510254\pi\)
−0.435950 + 0.899971i \(0.643587\pi\)
\(674\) 0.145898 + 0.106001i 0.00561978 + 0.00408301i
\(675\) 0 0
\(676\) 4.94427 15.2169i 0.190164 0.585266i
\(677\) −9.05191 10.0532i −0.347893 0.386374i 0.543649 0.839313i \(-0.317042\pi\)
−0.891542 + 0.452938i \(0.850376\pi\)
\(678\) 0 0
\(679\) 4.40100 41.8727i 0.168895 1.60693i
\(680\) 6.33810 7.03917i 0.243055 0.269940i
\(681\) 0 0
\(682\) 5.31701 + 2.44037i 0.203599 + 0.0934465i
\(683\) 3.11146 0.119057 0.0595283 0.998227i \(-0.481040\pi\)
0.0595283 + 0.998227i \(0.481040\pi\)
\(684\) 0 0
\(685\) 15.8262 + 11.4984i 0.604689 + 0.439333i
\(686\) 0.969032 + 9.21973i 0.0369978 + 0.352011i
\(687\) 0 0
\(688\) −11.3096 + 2.40394i −0.431176 + 0.0916493i
\(689\) 15.4988 + 6.90051i 0.590458 + 0.262889i
\(690\) 0 0
\(691\) 25.7173 + 5.46637i 0.978331 + 0.207951i 0.669211 0.743073i \(-0.266632\pi\)
0.309120 + 0.951023i \(0.399966\pi\)
\(692\) 24.8885 0.946120
\(693\) 0 0
\(694\) 12.9443 0.491358
\(695\) 2.18720 + 0.464905i 0.0829654 + 0.0176348i
\(696\) 0 0
\(697\) −17.6554 7.86069i −0.668746 0.297745i
\(698\) 6.12062 1.30098i 0.231669 0.0492427i
\(699\) 0 0
\(700\) 0.940756 + 8.95070i 0.0355572 + 0.338305i
\(701\) −8.64590 6.28161i −0.326551 0.237253i 0.412415 0.910996i \(-0.364685\pi\)
−0.738966 + 0.673743i \(0.764685\pi\)
\(702\) 0 0
\(703\) 1.38197 0.0521218
\(704\) −0.530501 + 0.575828i −0.0199940 + 0.0217023i
\(705\) 0 0
\(706\) 4.33070 4.80973i 0.162988 0.181017i
\(707\) −0.940756 + 8.95070i −0.0353808 + 0.336626i
\(708\) 0 0
\(709\) 32.6152 + 36.2228i 1.22489 + 1.36038i 0.911790 + 0.410657i \(0.134701\pi\)
0.313100 + 0.949720i \(0.398633\pi\)
\(710\) 2.78115 8.55951i 0.104375 0.321233i
\(711\) 0 0
\(712\) −0.954915 0.693786i −0.0357870 0.0260007i
\(713\) 9.69328 + 2.06037i 0.363016 + 0.0771614i
\(714\) 0 0
\(715\) 15.3153 + 0.174790i 0.572759 + 0.00653678i
\(716\) 1.80902 + 3.13331i 0.0676061 + 0.117097i
\(717\) 0 0
\(718\) 7.20654 3.20856i 0.268946 0.119742i
\(719\) −1.28115 + 0.930812i −0.0477789 + 0.0347134i −0.611418 0.791307i \(-0.709401\pi\)
0.563639 + 0.826021i \(0.309401\pi\)
\(720\) 0 0
\(721\) −5.56231 + 17.1190i −0.207151 + 0.637546i
\(722\) −0.986508 9.38599i −0.0367140 0.349311i
\(723\) 0 0
\(724\) 18.9167 21.0091i 0.703032 0.780796i
\(725\) 4.14590 + 7.18091i 0.153975 + 0.266692i
\(726\) 0 0
\(727\) −19.4271 + 33.6486i −0.720509 + 1.24796i 0.240286 + 0.970702i \(0.422759\pi\)
−0.960796 + 0.277257i \(0.910575\pi\)
\(728\) −3.65654 11.2537i −0.135520 0.417089i
\(729\) 0 0
\(730\) 4.23607 3.07768i 0.156784 0.113910i
\(731\) −6.75164 7.49846i −0.249718 0.277340i
\(732\) 0 0
\(733\) −34.4482 15.3373i −1.27237 0.566496i −0.344287 0.938865i \(-0.611879\pi\)
−0.928085 + 0.372368i \(0.878546\pi\)
\(734\) −0.359337 + 3.41886i −0.0132634 + 0.126193i
\(735\) 0 0
\(736\) 9.75329 16.8932i 0.359511 0.622691i
\(737\) 16.1697 27.2829i 0.595618 1.00498i
\(738\) 0 0
\(739\) −7.72542 23.7764i −0.284184 0.874629i −0.986642 0.162904i \(-0.947914\pi\)
0.702458 0.711726i \(-0.252086\pi\)
\(740\) −0.913545 + 0.406737i −0.0335826 + 0.0149519i
\(741\) 0 0
\(742\) −17.4431 + 3.70765i −0.640357 + 0.136112i
\(743\) 34.4116 7.31440i 1.26244 0.268339i 0.472393 0.881388i \(-0.343390\pi\)
0.790045 + 0.613049i \(0.210057\pi\)
\(744\) 0 0
\(745\) −35.8754 + 15.9728i −1.31437 + 0.585196i
\(746\) −0.843459 2.59590i −0.0308812 0.0950426i
\(747\) 0 0
\(748\) −8.47214 1.90211i −0.309772 0.0695481i
\(749\) −6.35410 + 11.0056i −0.232174 + 0.402137i
\(750\) 0 0
\(751\) −1.24629 + 11.8577i −0.0454778 + 0.432693i 0.947966 + 0.318371i \(0.103136\pi\)
−0.993444 + 0.114321i \(0.963531\pi\)
\(752\) −2.74064 1.22021i −0.0999407 0.0444965i
\(753\) 0 0
\(754\) −3.26227 3.62312i −0.118805 0.131946i
\(755\) −4.23607 + 3.07768i −0.154166 + 0.112008i
\(756\) 0 0
\(757\) 0.600813 + 1.84911i 0.0218369 + 0.0672071i 0.961381 0.275220i \(-0.0887509\pi\)
−0.939544 + 0.342428i \(0.888751\pi\)
\(758\) −0.489357 + 0.847591i −0.0177742 + 0.0307859i
\(759\) 0 0
\(760\) 17.1353 + 29.6791i 0.621561 + 1.07658i
\(761\) 20.6685 22.9547i 0.749231 0.832106i −0.241147 0.970489i \(-0.577524\pi\)
0.990379 + 0.138383i \(0.0441904\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −3.73607 + 11.4984i −0.135166 + 0.415999i
\(765\) 0 0
\(766\) 13.4443 9.76784i 0.485761 0.352926i
\(767\) −16.6400 + 7.40862i −0.600837 + 0.267510i
\(768\) 0 0
\(769\) −6.34346 10.9872i −0.228751 0.396208i 0.728687 0.684847i \(-0.240131\pi\)
−0.957438 + 0.288638i \(0.906797\pi\)
\(770\) −13.1317 + 9.31364i −0.473234 + 0.335640i
\(771\) 0 0
\(772\) −29.3781 6.24451i −1.05734 0.224745i
\(773\) −25.2812 18.3678i −0.909300 0.660645i 0.0315378 0.999503i \(-0.489960\pi\)
−0.940838 + 0.338858i \(0.889960\pi\)
\(774\) 0 0
\(775\) 1.63525 5.03280i 0.0587401 0.180783i
\(776\) 20.9986 + 23.3213i 0.753807 + 0.837188i
\(777\) 0 0
\(778\) 1.56793 14.9178i 0.0562129 0.534830i
\(779\) 46.7876 51.9629i 1.67634 1.86176i
\(780\) 0 0
\(781\) −18.0875 + 3.62939i −0.647223 + 0.129870i
\(782\) 3.47214 0.124163
\(783\) 0 0
\(784\) −3.00000 2.17963i −0.107143 0.0778438i
\(785\) 1.01478 + 9.65502i 0.0362192 + 0.344602i
\(786\) 0 0
\(787\) 10.0669 2.13978i 0.358846 0.0762751i −0.0249609 0.999688i \(-0.507946\pi\)
0.383807 + 0.923413i \(0.374613\pi\)
\(788\) 36.0401 + 16.0461i 1.28388 + 0.571619i
\(789\) 0 0
\(790\) −14.9913 3.18650i −0.533367 0.113371i
\(791\) −2.12461 −0.0755425
\(792\) 0 0
\(793\) 13.8541 0.491974
\(794\) 23.4002 + 4.97387i 0.830442 + 0.176516i
\(795\) 0 0
\(796\) 24.6972 + 10.9959i 0.875369 + 0.389739i
\(797\) 10.5287 2.23795i 0.372946 0.0792722i −0.0176255 0.999845i \(-0.505611\pi\)
0.390572 + 0.920572i \(0.372277\pi\)
\(798\) 0 0
\(799\) −0.273659 2.60369i −0.00968136 0.0921120i
\(800\) −8.42705 6.12261i −0.297941 0.216467i
\(801\) 0 0
\(802\) 16.1246 0.569380
\(803\) −9.75446 4.47704i −0.344228 0.157991i
\(804\) 0 0
\(805\) −18.2475 + 20.2659i −0.643141 + 0.714280i
\(806\) −0.325236 + 3.09441i −0.0114559 + 0.108996i
\(807\) 0 0
\(808\) −4.48866 4.98517i −0.157911 0.175378i
\(809\) −2.98936 + 9.20029i −0.105100 + 0.323465i −0.989754 0.142783i \(-0.954395\pi\)
0.884654 + 0.466249i \(0.154395\pi\)
\(810\) 0 0
\(811\) −2.63525 1.91462i −0.0925363 0.0672316i 0.540555 0.841309i \(-0.318214\pi\)
−0.633091 + 0.774077i \(0.718214\pi\)
\(812\) −21.2338 4.51339i −0.745161 0.158389i
\(813\) 0 0
\(814\) −0.388203 0.288872i −0.0136065 0.0101250i
\(815\) −23.9164 41.4244i −0.837755 1.45103i
\(816\) 0 0
\(817\) 33.3504 14.8486i 1.16678 0.519485i
\(818\) 5.52786 4.01623i 0.193277 0.140424i
\(819\) 0 0
\(820\) −15.6353 + 48.1204i −0.546007 + 1.68044i
\(821\) 4.22467 + 40.1950i 0.147442 + 1.40282i 0.778775 + 0.627303i \(0.215841\pi\)
−0.631333 + 0.775512i \(0.717492\pi\)
\(822\) 0 0
\(823\) −23.7355 + 26.3609i −0.827367 + 0.918884i −0.997787 0.0664871i \(-0.978821\pi\)
0.170420 + 0.985372i \(0.445488\pi\)
\(824\) −6.70820 11.6190i −0.233691 0.404765i
\(825\) 0 0
\(826\) 9.57295 16.5808i 0.333085 0.576921i
\(827\) −16.4164 50.5245i −0.570854 1.75691i −0.649880 0.760037i \(-0.725181\pi\)
0.0790257 0.996873i \(-0.474819\pi\)
\(828\) 0 0
\(829\) −14.3090 + 10.3961i −0.496973 + 0.361072i −0.807859 0.589375i \(-0.799374\pi\)
0.310887 + 0.950447i \(0.399374\pi\)
\(830\) −0.766755 0.851568i −0.0266145 0.0295584i
\(831\) 0 0
\(832\) −0.380408 0.169368i −0.0131883 0.00587179i
\(833\) 0.338261 3.21834i 0.0117201 0.111509i
\(834\) 0 0
\(835\) 13.1353 22.7509i 0.454564 0.787328i
\(836\) 16.0172 27.0256i 0.553967 0.934700i
\(837\) 0 0
\(838\) −3.15248 9.70232i −0.108900 0.335161i
\(839\) 33.5346 14.9306i 1.15774 0.515461i 0.264213 0.964464i \(-0.414888\pi\)
0.893530 + 0.449004i \(0.148221\pi\)
\(840\) 0 0
\(841\) 8.80333 1.87121i 0.303563 0.0645243i
\(842\) 22.5311 4.78913i 0.776472 0.165044i
\(843\) 0 0
\(844\) 32.9191 14.6565i 1.13312 0.504498i
\(845\) −8.00000 24.6215i −0.275208 0.847004i
\(846\) 0 0
\(847\) 29.8328 + 14.1068i 1.02507 + 0.484717i
\(848\) −8.91641 + 15.4437i −0.306191 + 0.530338i
\(849\) 0 0
\(850\) 0.193806 1.84395i 0.00664751 0.0632468i
\(851\) −0.748797 0.333386i −0.0256684 0.0114283i
\(852\) 0 0
\(853\) −6.65402 7.39003i −0.227829 0.253030i 0.618382 0.785878i \(-0.287789\pi\)
−0.846211 + 0.532848i \(0.821122\pi\)
\(854\) −11.7812 + 8.55951i −0.403143 + 0.292900i
\(855\) 0 0
\(856\) −2.92705 9.00854i −0.100045 0.307905i
\(857\) 23.8607 41.3279i 0.815065 1.41173i −0.0942157 0.995552i \(-0.530034\pi\)
0.909281 0.416183i \(-0.136632\pi\)
\(858\) 0 0
\(859\) −3.55573 6.15870i −0.121320 0.210132i 0.798969 0.601373i \(-0.205379\pi\)
−0.920288 + 0.391241i \(0.872046\pi\)
\(860\) −17.6760 + 19.6312i −0.602748 + 0.669419i
\(861\) 0 0
\(862\) −2.55221 24.2827i −0.0869286 0.827070i
\(863\) −3.67376 + 11.3067i −0.125056 + 0.384884i −0.993911 0.110183i \(-0.964856\pi\)
0.868855 + 0.495067i \(0.164856\pi\)
\(864\) 0 0
\(865\) 32.5795 23.6704i 1.10774 0.804818i
\(866\) −3.38761 + 1.50826i −0.115116 + 0.0512528i
\(867\) 0 0
\(868\) 6.92705 + 11.9980i 0.235119 + 0.407239i
\(869\) 9.36633 + 29.9868i 0.317731 + 1.01723i
\(870\) 0 0
\(871\) 16.4987 + 3.50690i 0.559036 + 0.118827i
\(872\) 0 0
\(873\) 0 0
\(874\) −3.88197 + 11.9475i −0.131309 + 0.404129i
\(875\) −16.5330 18.3618i −0.558918 0.620741i
\(876\) 0 0
\(877\) −0.670697 + 6.38126i −0.0226478 + 0.215480i 0.977345 + 0.211653i \(0.0678847\pi\)
−0.999993 + 0.00382661i \(0.998782\pi\)
\(878\) 1.36131 1.51188i 0.0459419 0.0510236i
\(879\) 0 0
\(880\) −1.86544 + 15.9908i −0.0628839 + 0.539050i
\(881\) −13.9098 −0.468634 −0.234317 0.972160i \(-0.575285\pi\)
−0.234317 + 0.972160i \(0.575285\pi\)
\(882\) 0 0
\(883\) −8.56231 6.22088i −0.288145 0.209349i 0.434318 0.900760i \(-0.356990\pi\)
−0.722462 + 0.691411i \(0.756990\pi\)
\(884\) −0.482716 4.59274i −0.0162355 0.154470i
\(885\) 0 0
\(886\) −24.8610 + 5.28437i −0.835222 + 0.177532i
\(887\) −2.74064 1.22021i −0.0920216 0.0409706i 0.360210 0.932871i \(-0.382705\pi\)
−0.452231 + 0.891901i \(0.649372\pi\)
\(888\) 0 0
\(889\) 10.8815 + 2.31294i 0.364954 + 0.0775734i
\(890\) −0.854102 −0.0286296
\(891\) 0 0
\(892\) −1.14590 −0.0383675
\(893\) 9.26515 + 1.96937i 0.310046 + 0.0659024i
\(894\) 0 0
\(895\) 5.34799 + 2.38108i 0.178764 + 0.0795907i
\(896\) 33.3997 7.09933i 1.11581 0.237172i
\(897\) 0 0
\(898\) −1.58095 15.0418i −0.0527571 0.501950i
\(899\) 10.3262 + 7.50245i 0.344399 + 0.250221i
\(900\) 0 0
\(901\) −15.5623 −0.518456
\(902\) −24.0047 + 4.81672i −0.799270 + 0.160379i
\(903\) 0 0
\(904\) 1.05963 1.17684i 0.0352428 0.0391411i
\(905\) 4.78141 45.4921i 0.158939 1.51221i
\(906\) 0 0
\(907\) −28.7584 31.9394i −0.954906 1.06053i −0.998109 0.0614644i \(-0.980423\pi\)
0.0432032 0.999066i \(-0.486244\pi\)
\(908\) −12.4443 + 38.2995i −0.412978 + 1.27101i
\(909\) 0 0
\(910\) −6.92705 5.03280i −0.229630 0.166836i
\(911\) 17.6612 + 3.75400i 0.585141 + 0.124375i 0.490964 0.871180i \(-0.336645\pi\)
0.0941768 + 0.995555i \(0.469978\pi\)
\(912\) 0 0
\(913\) −0.751279 + 2.22546i −0.0248637 + 0.0736519i
\(914\) −2.53444 4.38978i −0.0838319 0.145201i
\(915\) 0 0
\(916\) −14.7815 + 6.58114i −0.488394 + 0.217447i
\(917\) −17.3435 + 12.6008i −0.572731 + 0.416114i
\(918\) 0 0
\(919\) 14.5106 44.6592i 0.478662 1.47317i −0.362293 0.932064i \(-0.618006\pi\)
0.840955 0.541106i \(-0.181994\pi\)
\(920\) −2.12467 20.2149i −0.0700483 0.666465i
\(921\) 0 0
\(922\) 8.72174 9.68648i 0.287235 0.319007i
\(923\) −4.90576 8.49703i −0.161475 0.279683i
\(924\) 0 0
\(925\) −0.218847 + 0.379054i −0.00719565 + 0.0124632i
\(926\) −3.01722 9.28605i −0.0991520 0.305159i
\(927\) 0 0
\(928\) 20.3262 14.7679i 0.667241 0.484779i
\(929\) 22.0067 + 24.4410i 0.722017 + 0.801882i 0.986717 0.162449i \(-0.0519394\pi\)
−0.264699 + 0.964331i \(0.585273\pi\)
\(930\) 0 0
\(931\) 10.6960 + 4.76216i 0.350546 + 0.156073i
\(932\) −4.11431 + 39.1451i −0.134769 + 1.28224i
\(933\) 0 0
\(934\) −3.01722 + 5.22598i −0.0987265 + 0.170999i
\(935\) −12.8992 + 5.56758i −0.421849 + 0.182079i
\(936\) 0 0
\(937\) −5.12868 15.7844i −0.167547 0.515655i 0.831668 0.555273i \(-0.187386\pi\)
−0.999215 + 0.0396173i \(0.987386\pi\)
\(938\) −16.1967 + 7.21123i −0.528841 + 0.235455i
\(939\) 0 0
\(940\) −6.70432 + 1.42505i −0.218671 + 0.0464799i
\(941\) −43.6559 + 9.27935i −1.42314 + 0.302498i −0.854228 0.519899i \(-0.825970\pi\)
−0.568914 + 0.822397i \(0.692636\pi\)
\(942\) 0 0
\(943\) −37.8867 + 16.8682i −1.23376 + 0.549305i
\(944\) −5.91641 18.2088i −0.192563 0.592647i
\(945\) 0 0
\(946\) −12.4721 2.80017i −0.405504 0.0910413i
\(947\) 9.16312 15.8710i 0.297761 0.515738i −0.677862 0.735189i \(-0.737093\pi\)
0.975623 + 0.219451i \(0.0704267\pi\)
\(948\) 0 0
\(949\) 0.596670 5.67693i 0.0193687 0.184281i
\(950\) 6.12825 + 2.72847i 0.198827 + 0.0885233i
\(951\) 0 0
\(952\) 7.26281 + 8.06617i 0.235389 + 0.261426i
\(953\) 30.5967 22.2298i 0.991126 0.720095i 0.0309585 0.999521i \(-0.490144\pi\)
0.960167 + 0.279426i \(0.0901440\pi\)
\(954\) 0 0
\(955\) 6.04508 + 18.6049i 0.195614 + 0.602039i
\(956\) −2.07295 + 3.59045i −0.0670440 + 0.116124i
\(957\) 0 0
\(958\) −8.68034 15.0348i −0.280449 0.485752i
\(959\) −14.9995 + 16.6586i −0.484359 + 0.537935i
\(960\) 0 0
\(961\) 2.38890 + 22.7289i 0.0770614 + 0.733190i
\(962\) 0.0795268 0.244758i 0.00256405 0.00789133i
\(963\) 0 0
\(964\) −30.2705 + 21.9928i −0.974947 + 0.708341i
\(965\) −44.3953 + 19.7661i −1.42914 + 0.636293i
\(966\) 0 0
\(967\) 17.3435 + 30.0398i 0.557728 + 0.966013i 0.997686 + 0.0679948i \(0.0216601\pi\)
−0.439958 + 0.898019i \(0.645007\pi\)
\(968\) −22.6927 + 9.48896i −0.729372 + 0.304987i
\(969\) 0 0
\(970\) 22.2120 + 4.72130i 0.713184 + 0.151592i
\(971\) 30.5623 + 22.2048i 0.980791 + 0.712586i 0.957885 0.287151i \(-0.0927082\pi\)
0.0229058 + 0.999738i \(0.492708\pi\)
\(972\) 0 0
\(973\) −0.791796 + 2.43690i −0.0253838 + 0.0781234i
\(974\) 6.95569 + 7.72508i 0.222875 + 0.247528i
\(975\) 0 0
\(976\) −1.52218 + 14.4825i −0.0487236 + 0.463575i
\(977\) 3.10431 3.44769i 0.0993157 0.110301i −0.691438 0.722436i \(-0.743022\pi\)
0.790753 + 0.612135i \(0.209689\pi\)
\(978\) 0 0
\(979\) 0.858004 + 1.52606i 0.0274219 + 0.0487732i
\(980\) −8.47214 −0.270632
\(981\) 0 0
\(982\) 12.6074 + 9.15981i 0.402318 + 0.292301i
\(983\) −2.85414 27.1554i −0.0910331 0.866122i −0.940800 0.338963i \(-0.889924\pi\)
0.849767 0.527159i \(-0.176743\pi\)
\(984\) 0 0
\(985\) 62.4379 13.2716i 1.98944 0.422868i
\(986\) 4.08550 + 1.81898i 0.130109 + 0.0579282i
\(987\) 0 0
\(988\) 16.3431 + 3.47383i 0.519943 + 0.110517i
\(989\) −21.6525 −0.688509
\(990\) 0 0
\(991\) 21.2705 0.675680 0.337840 0.941204i \(-0.390304\pi\)
0.337840 + 0.941204i \(0.390304\pi\)
\(992\) −15.6841 3.33375i −0.497969 0.105847i
\(993\) 0 0
\(994\) 9.42147 + 4.19471i 0.298831 + 0.133048i
\(995\) 42.7868 9.09461i 1.35643 0.288318i
\(996\) 0 0
\(997\) 1.35665 + 12.9076i 0.0429654 + 0.408788i 0.994774 + 0.102097i \(0.0325552\pi\)
−0.951809 + 0.306691i \(0.900778\pi\)
\(998\) 8.78115 + 6.37988i 0.277963 + 0.201952i
\(999\) 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 891.2.n.a.379.1 8
3.2 odd 2 891.2.n.d.379.1 8
9.2 odd 6 33.2.e.a.16.1 4
9.4 even 3 inner 891.2.n.a.676.1 8
9.5 odd 6 891.2.n.d.676.1 8
9.7 even 3 99.2.f.b.82.1 4
11.9 even 5 inner 891.2.n.a.460.1 8
33.20 odd 10 891.2.n.d.460.1 8
36.11 even 6 528.2.y.f.49.1 4
45.2 even 12 825.2.bx.b.49.2 8
45.29 odd 6 825.2.n.f.676.1 4
45.38 even 12 825.2.bx.b.49.1 8
99.2 even 30 363.2.e.j.130.1 4
99.20 odd 30 33.2.e.a.31.1 yes 4
99.25 even 15 1089.2.a.m.1.2 2
99.29 even 30 363.2.e.c.124.1 4
99.31 even 15 inner 891.2.n.a.757.1 8
99.38 odd 30 363.2.e.h.202.1 4
99.47 odd 30 363.2.a.h.1.1 2
99.52 odd 30 1089.2.a.s.1.1 2
99.65 even 6 363.2.e.j.148.1 4
99.74 even 30 363.2.a.e.1.2 2
99.83 even 30 363.2.e.c.202.1 4
99.86 odd 30 891.2.n.d.757.1 8
99.92 odd 30 363.2.e.h.124.1 4
99.97 even 15 99.2.f.b.64.1 4
396.47 even 30 5808.2.a.bl.1.1 2
396.119 even 30 528.2.y.f.97.1 4
396.371 odd 30 5808.2.a.bm.1.1 2
495.74 even 30 9075.2.a.bv.1.1 2
495.119 odd 30 825.2.n.f.526.1 4
495.218 even 60 825.2.bx.b.724.2 8
495.317 even 60 825.2.bx.b.724.1 8
495.344 odd 30 9075.2.a.x.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.2.e.a.16.1 4 9.2 odd 6
33.2.e.a.31.1 yes 4 99.20 odd 30
99.2.f.b.64.1 4 99.97 even 15
99.2.f.b.82.1 4 9.7 even 3
363.2.a.e.1.2 2 99.74 even 30
363.2.a.h.1.1 2 99.47 odd 30
363.2.e.c.124.1 4 99.29 even 30
363.2.e.c.202.1 4 99.83 even 30
363.2.e.h.124.1 4 99.92 odd 30
363.2.e.h.202.1 4 99.38 odd 30
363.2.e.j.130.1 4 99.2 even 30
363.2.e.j.148.1 4 99.65 even 6
528.2.y.f.49.1 4 36.11 even 6
528.2.y.f.97.1 4 396.119 even 30
825.2.n.f.526.1 4 495.119 odd 30
825.2.n.f.676.1 4 45.29 odd 6
825.2.bx.b.49.1 8 45.38 even 12
825.2.bx.b.49.2 8 45.2 even 12
825.2.bx.b.724.1 8 495.317 even 60
825.2.bx.b.724.2 8 495.218 even 60
891.2.n.a.379.1 8 1.1 even 1 trivial
891.2.n.a.460.1 8 11.9 even 5 inner
891.2.n.a.676.1 8 9.4 even 3 inner
891.2.n.a.757.1 8 99.31 even 15 inner
891.2.n.d.379.1 8 3.2 odd 2
891.2.n.d.460.1 8 33.20 odd 10
891.2.n.d.676.1 8 9.5 odd 6
891.2.n.d.757.1 8 99.86 odd 30
1089.2.a.m.1.2 2 99.25 even 15
1089.2.a.s.1.1 2 99.52 odd 30
5808.2.a.bl.1.1 2 396.47 even 30
5808.2.a.bm.1.1 2 396.371 odd 30
9075.2.a.x.1.2 2 495.344 odd 30
9075.2.a.bv.1.1 2 495.74 even 30