Properties

Label 891.2.n.d.757.1
Level $891$
Weight $2$
Character 891.757
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 757.1
Root \(0.669131 + 0.743145i\) of defining polynomial
Character \(\chi\) \(=\) 891.757
Dual form 891.2.n.d.379.1

$q$-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 \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.604528 0.128496i 0.427466 0.0908607i 0.0108456 0.999941i \(-0.496548\pi\)
0.416621 + 0.909080i \(0.363214\pi\)
\(3\) 0 0
\(4\) −1.47815 + 0.658114i −0.739074 + 0.329057i
\(5\) 2.56082 + 0.544320i 1.14524 + 0.243427i 0.741179 0.671307i \(-0.234267\pi\)
0.404056 + 0.914734i \(0.367600\pi\)
\(6\) 0 0
\(7\) −0.313585 + 2.98357i −0.118524 + 1.12768i 0.759980 + 0.649947i \(0.225209\pi\)
−0.878504 + 0.477735i \(0.841458\pi\)
\(8\) −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 0.884247 0.467020i \(-0.154672\pi\)
−0.556890 + 0.830586i \(0.688006\pi\)
\(14\) 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 \(-0.0371348\pi\)
−0.871935 + 0.489622i \(0.837135\pi\)
\(18\) 0 0
\(19\) −4.73607 + 3.44095i −1.08653 + 0.789409i −0.978810 0.204772i \(-0.934355\pi\)
−0.107719 + 0.994181i \(0.534355\pi\)
\(20\) −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 \(-0.951238\pi\)
0.626294 + 0.779587i \(0.284571\pi\)
\(24\) 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 0.861331 + 0.508044i \(0.169631\pi\)
−0.948137 + 0.317861i \(0.897035\pi\)
\(30\) 0 0
\(31\) 1.90977 + 2.12101i 0.343004 + 0.380945i 0.889823 0.456306i \(-0.150828\pi\)
−0.546818 + 0.837251i \(0.684161\pi\)
\(32\) 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 0.571976 0.820270i \(-0.306177\pi\)
−0.603373 + 0.797459i \(0.706177\pi\)
\(38\) −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 0.456194 + 0.889881i \(0.349212\pi\)
−0.261208 + 0.965283i \(0.584121\pi\)
\(42\) 0 0
\(43\) −3.11803 5.40059i −0.475496 0.823583i 0.524110 0.851650i \(-0.324398\pi\)
−0.999606 + 0.0280676i \(0.991065\pi\)
\(44\) −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 \(-0.329016\pi\)
−0.296090 + 0.955160i \(0.595683\pi\)
\(48\) 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 0.509893 + 0.860238i \(0.329685\pi\)
−0.918147 + 0.396240i \(0.870315\pi\)
\(54\) 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 \(-0.398691\pi\)
0.915210 + 0.402977i \(0.132024\pi\)
\(60\) 0 0
\(61\) 5.25542 5.83674i 0.672888 0.747317i −0.305929 0.952054i \(-0.598967\pi\)
0.978817 + 0.204737i \(0.0656338\pi\)
\(62\) 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 −0.410875 0.911692i \(-0.634777\pi\)
0.994986 0.100018i \(-0.0318900\pi\)
\(68\) −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 −0.999753 0.0222083i \(-0.992930\pi\)
0.795764 0.605607i \(-0.207070\pi\)
\(72\) 0 0
\(73\) 2.61803 + 1.90211i 0.306418 + 0.222625i 0.730358 0.683065i \(-0.239353\pi\)
−0.423940 + 0.905690i \(0.639353\pi\)
\(74\) −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 −0.697142 0.716933i \(-0.745545\pi\)
−0.345268 + 0.938504i \(0.612212\pi\)
\(80\) 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 \(-0.754292\pi\)
0.768591 + 0.639741i \(0.220958\pi\)
\(84\) 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 \(-0.491094\pi\)
0.0279767 + 0.999609i \(0.491094\pi\)
\(90\) 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 0.551033 0.834483i \(-0.314234\pi\)
0.842809 + 0.538213i \(0.180900\pi\)
\(98\) −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 \(-0.518979\pi\)
0.351577 + 0.936159i \(0.385646\pi\)
\(102\) 0 0
\(103\) −5.48127 + 2.44042i −0.540086 + 0.240462i −0.658603 0.752490i \(-0.728852\pi\)
0.118518 + 0.992952i \(0.462186\pi\)
\(104\) −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 \(-0.634359\pi\)
0.740984 + 0.671522i \(0.234359\pi\)
\(108\) 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 \(-0.0439386\pi\)
−0.997452 + 0.0713418i \(0.977272\pi\)
\(114\) 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 0.887255 0.461279i \(-0.152609\pi\)
−0.988937 + 0.148333i \(0.952609\pi\)
\(128\) −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 \(-0.732277\pi\)
0.978832 + 0.204666i \(0.0656108\pi\)
\(132\) 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 \(-0.663255\pi\)
0.917853 + 0.396921i \(0.129921\pi\)
\(138\) 0 0
\(139\) −0.780261 + 0.347395i −0.0661809 + 0.0294656i −0.439560 0.898213i \(-0.644866\pi\)
0.373379 + 0.927679i \(0.378199\pi\)
\(140\) −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 \(-0.643945\pi\)
−0.765035 + 0.643989i \(0.777278\pi\)
\(150\) 0 0
\(151\) 1.82709 + 0.813473i 0.148687 + 0.0661995i 0.479731 0.877416i \(-0.340734\pi\)
−0.331044 + 0.943615i \(0.607401\pi\)
\(152\) 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 0.999041 + 0.0437851i \(0.0139417\pi\)
−0.968106 + 0.250541i \(0.919392\pi\)
\(158\) −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 −0.443282 0.896382i \(-0.646186\pi\)
0.885503 0.464634i \(-0.153814\pi\)
\(164\) −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 \(-0.106415\pi\)
−0.425064 + 0.905163i \(0.639748\pi\)
\(168\) 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 \(-0.167865\pi\)
0.204227 + 0.978924i \(0.434532\pi\)
\(174\) 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 \(-0.673369\pi\)
0.653335 + 0.757069i \(0.273369\pi\)
\(180\) 0 0
\(181\) −5.39919 16.6170i −0.401318 1.23513i −0.923930 0.382560i \(-0.875042\pi\)
0.522612 0.852571i \(-0.324958\pi\)
\(182\) −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 −0.929235 0.369488i \(-0.879533\pi\)
0.985750 0.168215i \(-0.0538003\pi\)
\(192\) 0 0
\(193\) 18.1567 + 3.85932i 1.30695 + 0.277800i 0.808179 0.588936i \(-0.200453\pi\)
0.498767 + 0.866736i \(0.333786\pi\)
\(194\) 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 \(-0.165039\pi\)
0.868572 + 0.495564i \(0.165039\pi\)
\(198\) 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 −0.990151 0.140002i \(-0.955289\pi\)
−0.0357366 0.999361i \(-0.511378\pi\)
\(212\) −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 0.428285 0.903644i \(-0.359118\pi\)
−0.384960 + 0.922933i \(0.625785\pi\)
\(224\) 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 −0.474312 0.880357i \(-0.657303\pi\)
0.646983 0.762504i \(-0.276030\pi\)
\(228\) 0 0
\(229\) 6.69131 + 7.43145i 0.442174 + 0.491084i 0.922495 0.386009i \(-0.126147\pi\)
−0.480321 + 0.877093i \(0.659480\pi\)
\(230\) −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 −0.328394 0.944541i \(-0.606507\pi\)
0.820863 0.571124i \(-0.193493\pi\)
\(234\) 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 \(-0.0597422\pi\)
−0.999763 + 0.0217520i \(0.993076\pi\)
\(240\) 0 0
\(241\) 11.5623 + 20.0265i 0.744794 + 1.29002i 0.950291 + 0.311363i \(0.100785\pi\)
−0.205498 + 0.978658i \(0.565881\pi\)
\(242\) −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 \(-0.979154\pi\)
0.845749 + 0.533581i \(0.179154\pi\)
\(252\) 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 \(-0.751955\pi\)
0.0462020 + 0.998932i \(0.485288\pi\)
\(258\) 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 0.999992 + 0.00388355i \(0.00123617\pi\)
−0.496633 + 0.867961i \(0.665430\pi\)
\(264\) 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 0.984029 + 0.178006i \(0.0569645\pi\)
−0.691467 + 0.722408i \(0.743035\pi\)
\(270\) 0 0
\(271\) 22.0623 + 16.0292i 1.34019 + 0.973705i 0.999437 + 0.0335518i \(0.0106819\pi\)
0.340753 + 0.940153i \(0.389318\pi\)
\(272\) 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 −0.980470 0.196667i \(-0.936988\pi\)
−0.815713 + 0.578457i \(0.803655\pi\)
\(278\) −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 \(-0.773920\pi\)
0.727705 + 0.685890i \(0.240587\pi\)
\(282\) 0 0
\(283\) −0.0188507 0.179352i −0.00112055 0.0106614i 0.993947 0.109858i \(-0.0350395\pi\)
−0.995068 + 0.0991963i \(0.968373\pi\)
\(284\) 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 \(-0.632815\pi\)
0.408223 + 0.912882i \(0.366149\pi\)
\(294\) 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 \(-0.0561665\pi\)
−0.999456 + 0.0329813i \(0.989500\pi\)
\(312\) 0 0
\(313\) 17.2855 19.1975i 0.977036 1.08511i −0.0193200 0.999813i \(-0.506150\pi\)
0.996356 0.0852948i \(-0.0271832\pi\)
\(314\) 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 \(-0.383689\pi\)
0.706317 + 0.707896i \(0.250355\pi\)
\(318\) 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 −0.956480 0.291798i \(-0.905746\pi\)
0.225535 0.974235i \(-0.427587\pi\)
\(332\) −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 −0.413984 0.910284i \(-0.635863\pi\)
0.399463 + 0.916749i \(0.369196\pi\)
\(338\) −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 \(-0.243299\pi\)
0.377942 + 0.925829i \(0.376632\pi\)
\(348\) 0 0
\(349\) −9.24929 4.11805i −0.495103 0.220434i 0.143967 0.989582i \(-0.454014\pi\)
−0.639070 + 0.769148i \(0.720681\pi\)
\(350\) −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 \(-0.0767672\pi\)
−0.692371 + 0.721542i \(0.743434\pi\)
\(354\) 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 \(-0.190646\pi\)
−0.280940 + 0.959725i \(0.590646\pi\)
\(360\) 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 0.968811 + 0.247801i \(0.0797079\pi\)
−0.999161 + 0.0409586i \(0.986959\pi\)
\(368\) 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 −0.803178 0.595739i \(-0.796859\pi\)
0.917514 + 0.397703i \(0.130192\pi\)
\(374\) 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 0.962838 0.270080i \(-0.0870502\pi\)
−0.937701 + 0.347443i \(0.887050\pi\)
\(380\) 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 0.999705 + 0.0242708i \(0.00772639\pi\)
−0.0803598 + 0.996766i \(0.525607\pi\)
\(384\) 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 0.719674 + 0.694312i \(0.244291\pi\)
−0.848303 + 0.529511i \(0.822376\pi\)
\(390\) 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 \(-0.207498\pi\)
0.479462 + 0.877562i \(0.340832\pi\)
\(402\) 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 0.531948 0.846777i \(-0.321460\pi\)
−0.897742 + 0.440522i \(0.854794\pi\)
\(410\) 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 \(-0.965435\pi\)
0.590911 + 0.806737i \(0.298769\pi\)
\(420\) 0 0
\(421\) −34.0483 15.1593i −1.65941 0.738818i −0.659496 0.751708i \(-0.729230\pi\)
−0.999917 + 0.0128899i \(0.995897\pi\)
\(422\) −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 −0.00138127 + 0.999999i \(0.500440\pi\)
−0.586667 + 0.809828i \(0.699560\pi\)
\(432\) 0 0
\(433\) 4.85410 + 3.52671i 0.233273 + 0.169483i 0.698281 0.715824i \(-0.253949\pi\)
−0.465008 + 0.885307i \(0.653949\pi\)
\(434\) −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 0.824072 0.566485i \(-0.191697\pi\)
−0.902626 + 0.430425i \(0.858364\pi\)
\(440\) −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 −0.979319 0.202324i \(-0.935151\pi\)
−0.805648 0.592395i \(-0.798183\pi\)
\(444\) 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 0.598020 + 0.801481i \(0.295954\pi\)
−0.954907 + 0.296905i \(0.904046\pi\)
\(450\) 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 −0.600986 0.799260i \(-0.705225\pi\)
0.857702 + 0.514148i \(0.171892\pi\)
\(458\) 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 \(-0.00324936\pi\)
−0.508814 + 0.860876i \(0.669916\pi\)
\(462\) 0 0
\(463\) 7.89919 13.6818i 0.367106 0.635847i −0.622005 0.783013i \(-0.713682\pi\)
0.989112 + 0.147166i \(0.0470152\pi\)
\(464\) 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 \(-0.172536\pi\)
−0.996280 + 0.0861747i \(0.972536\pi\)
\(468\) 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 \(-0.988452\pi\)
0.140531 + 0.990076i \(0.455119\pi\)
\(480\) 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 −0.851736 0.523972i \(-0.824450\pi\)
0.235126 + 0.971965i \(0.424450\pi\)
\(488\) −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 \(-0.440678\pi\)
0.854259 + 0.519847i \(0.174011\pi\)
\(492\) 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 −0.733106 0.680114i \(-0.761930\pi\)
0.0148796 + 0.999889i \(0.495263\pi\)
\(500\) 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 \(-0.915213\pi\)
−0.0477750 + 0.998858i \(0.515213\pi\)
\(504\) 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 −0.902117 0.431492i \(-0.857987\pi\)
0.792691 0.609624i \(-0.208679\pi\)
\(510\) 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 \(-0.194663\pi\)
−0.293028 + 0.956104i \(0.594663\pi\)
\(522\) 0 0
\(523\) −3.70163 11.3924i −0.161861 0.498156i 0.836930 0.547309i \(-0.184348\pi\)
−0.998791 + 0.0491529i \(0.984348\pi\)
\(524\) −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 −0.732926 0.680308i \(-0.761846\pi\)
0.992825 0.119577i \(-0.0381540\pi\)
\(542\) 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 0.782897 0.622151i \(-0.213741\pi\)
0.0615117 + 0.998106i \(0.480408\pi\)
\(548\) −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 \(-0.402298\pi\)
−0.813239 + 0.581929i \(0.802298\pi\)
\(558\) 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 \(-0.293308\pi\)
−0.855323 + 0.518095i \(0.826642\pi\)
\(564\) 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 \(-0.534994\pi\)
−0.812072 + 0.583558i \(0.801660\pi\)
\(570\) 0 0
\(571\) −17.3435 + 30.0398i −0.725801 + 1.25712i 0.232842 + 0.972515i \(0.425197\pi\)
−0.958643 + 0.284610i \(0.908136\pi\)
\(572\) −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 0.996114 0.0880726i \(-0.0280707\pi\)
−0.857641 + 0.514249i \(0.828071\pi\)
\(578\) 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 −0.526467 0.850196i \(-0.676484\pi\)
0.691728 0.722158i \(-0.256850\pi\)
\(588\) 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 \(-0.349237\pi\)
0.456126 + 0.889915i \(0.349237\pi\)
\(594\) 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 \(-0.379151\pi\)
−0.0392119 + 0.999231i \(0.512485\pi\)
\(600\) 0 0
\(601\) −3.53649 + 33.6475i −0.144257 + 1.37251i 0.647683 + 0.761910i \(0.275738\pi\)
−0.791940 + 0.610599i \(0.790929\pi\)
\(602\) 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 0.896416 0.443213i \(-0.146162\pi\)
−0.534486 + 0.845177i \(0.679495\pi\)
\(608\) 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 −0.986028 0.166580i \(-0.946728\pi\)
−0.146272 + 0.989244i \(0.546728\pi\)
\(614\) 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 \(-0.962313\pi\)
0.598796 + 0.800901i \(0.295646\pi\)
\(618\) 0 0
\(619\) −8.05716 3.58728i −0.323845 0.144185i 0.238374 0.971173i \(-0.423386\pi\)
−0.562219 + 0.826988i \(0.690052\pi\)
\(620\) −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 −0.974084 0.226187i \(-0.927374\pi\)
−0.516125 0.856513i \(-0.672626\pi\)
\(632\) 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 \(-0.117221\pi\)
0.356742 + 0.934203i \(0.383887\pi\)
\(642\) 0 0
\(643\) 37.7196 + 8.01755i 1.48752 + 0.316181i 0.878794 0.477201i \(-0.158349\pi\)
0.608723 + 0.793383i \(0.291682\pi\)
\(644\) 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 −0.627655 0.778492i \(-0.715985\pi\)
0.965369 0.260887i \(-0.0840149\pi\)
\(648\) 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 0.890461 0.455059i \(-0.150382\pi\)
0.934010 0.357248i \(-0.116285\pi\)
\(654\) 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 \(-0.100140\pi\)
−0.743440 + 0.668803i \(0.766807\pi\)
\(660\) 0 0
\(661\) 4.95492 8.58216i 0.192724 0.333808i −0.753428 0.657530i \(-0.771601\pi\)
0.946152 + 0.323723i \(0.104935\pi\)
\(662\) −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 −0.435950 0.899971i \(-0.643587\pi\)
−0.0322087 + 0.999481i \(0.510254\pi\)
\(674\) −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 \(-0.682958\pi\)
0.891542 + 0.452938i \(0.149624\pi\)
\(678\) 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 \(-0.518960\pi\)
−0.0595283 + 0.998227i \(0.518960\pi\)
\(684\) 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 0.309120 0.951023i \(-0.399966\pi\)
0.669211 + 0.743073i \(0.266632\pi\)
\(692\) −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 \(-0.635315\pi\)
0.738966 + 0.673743i \(0.235315\pi\)
\(702\) 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 0.313100 0.949720i \(-0.398633\pi\)
0.911790 0.410657i \(-0.134701\pi\)
\(710\) −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 \(-0.290599\pi\)
−0.563639 + 0.826021i \(0.690599\pi\)
\(720\) 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 −0.960796 0.277257i \(-0.910575\pi\)
0.240286 0.970702i \(-0.422759\pi\)
\(728\) 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 −0.928085 0.372368i \(-0.878546\pi\)
−0.344287 + 0.938865i \(0.611879\pi\)
\(734\) 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 0.702458 + 0.711726i \(0.252086\pi\)
−0.986642 + 0.162904i \(0.947914\pi\)
\(740\) 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 \(-0.656610\pi\)
−0.790045 + 0.613049i \(0.789943\pi\)
\(744\) 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 −0.993444 0.114321i \(-0.963531\pi\)
0.947966 0.318371i \(-0.103136\pi\)
\(752\) 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 −0.939544 0.342428i \(-0.888751\pi\)
0.961381 + 0.275220i \(0.0887509\pi\)
\(758\) 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 \(-0.422476\pi\)
−0.990379 + 0.138383i \(0.955810\pi\)
\(762\) 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 −0.957438 0.288638i \(-0.906797\pi\)
0.728687 + 0.684847i \(0.240131\pi\)
\(770\) 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 \(-0.510040\pi\)
0.940838 + 0.338858i \(0.110040\pi\)
\(774\) 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 0.383807 0.923413i \(-0.374613\pi\)
−0.0249609 + 0.999688i \(0.507946\pi\)
\(788\) −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 \(-0.494389\pi\)
−0.390572 + 0.920572i \(0.627723\pi\)
\(798\) 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 \(-0.0456052\pi\)
−0.884654 + 0.466249i \(0.845605\pi\)
\(810\) 0 0
\(811\) −2.63525 + 1.91462i −0.0925363 + 0.0672316i −0.633091 0.774077i \(-0.718214\pi\)
0.540555 + 0.841309i \(0.318214\pi\)
\(812\) 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 0.631333 + 0.775512i \(0.282508\pi\)
−0.778775 + 0.627303i \(0.784159\pi\)
\(822\) 0 0
\(823\) −23.7355 26.3609i −0.827367 0.918884i 0.170420 0.985372i \(-0.445488\pi\)
−0.997787 + 0.0664871i \(0.978821\pi\)
\(824\) 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 −0.0790257 0.996873i \(-0.525181\pi\)
0.649880 0.760037i \(-0.274819\pi\)
\(828\) 0 0
\(829\) −14.3090 10.3961i −0.496973 0.361072i 0.310887 0.950447i \(-0.399374\pi\)
−0.807859 + 0.589375i \(0.799374\pi\)
\(830\) 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 \(-0.585112\pi\)
−0.893530 + 0.449004i \(0.851779\pi\)
\(840\) 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 −0.846211 0.532848i \(-0.821122\pi\)
0.618382 + 0.785878i \(0.287789\pi\)
\(854\) 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 −0.909281 0.416183i \(-0.863368\pi\)
0.0942157 0.995552i \(-0.469966\pi\)
\(858\) 0 0
\(859\) −3.55573 + 6.15870i −0.121320 + 0.210132i −0.920288 0.391241i \(-0.872046\pi\)
0.798969 + 0.601373i \(0.205379\pi\)
\(860\) 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 \(-0.0351436\pi\)
−0.868855 + 0.495067i \(0.835144\pi\)
\(864\) 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 −0.999993 0.00382661i \(-0.998782\pi\)
0.977345 0.211653i \(-0.0678847\pi\)
\(878\) −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 \(-0.424715\pi\)
0.234317 + 0.972160i \(0.424715\pi\)
\(882\) 0 0
\(883\) −8.56231 + 6.22088i −0.288145 + 0.209349i −0.722462 0.691411i \(-0.756990\pi\)
0.434318 + 0.900760i \(0.356990\pi\)
\(884\) 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 \(-0.617295\pi\)
0.452231 + 0.891901i \(0.350628\pi\)
\(888\) 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 0.0432032 + 0.999066i \(0.486244\pi\)
−0.998109 + 0.0614644i \(0.980423\pi\)
\(908\) 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 \(-0.663355\pi\)
−0.0941768 + 0.995555i \(0.530022\pi\)
\(912\) 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 0.840955 + 0.541106i \(0.181994\pi\)
−0.362293 + 0.932064i \(0.618006\pi\)
\(920\) 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 \(-0.948061\pi\)
0.264699 + 0.964331i \(0.414727\pi\)
\(930\) 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 −0.999215 0.0396173i \(-0.987386\pi\)
0.831668 + 0.555273i \(0.187386\pi\)
\(938\) 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 \(-0.174030\pi\)
0.568914 + 0.822397i \(0.307364\pi\)
\(942\) 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 \(-0.262907\pi\)
−0.975623 + 0.219451i \(0.929573\pi\)
\(948\) 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 \(-0.509856\pi\)
−0.960167 + 0.279426i \(0.909856\pi\)
\(954\) 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 −0.439958 0.898019i \(-0.645007\pi\)
0.997686 0.0679948i \(-0.0216601\pi\)
\(968\) 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 \(-0.907292\pi\)
−0.0229058 + 0.999738i \(0.507292\pi\)
\(972\) 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 \(-0.256978\pi\)
−0.790753 + 0.612135i \(0.790311\pi\)
\(978\) 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 −0.849767 0.527159i \(-0.823257\pi\)
0.940800 0.338963i \(-0.110076\pi\)
\(984\) 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 −0.951809 0.306691i \(-0.900778\pi\)
0.994774 0.102097i \(-0.0325552\pi\)
\(998\) −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.d.757.1 8
3.2 odd 2 891.2.n.a.757.1 8
9.2 odd 6 891.2.n.a.460.1 8
9.4 even 3 33.2.e.a.31.1 yes 4
9.5 odd 6 99.2.f.b.64.1 4
9.7 even 3 inner 891.2.n.d.460.1 8
11.5 even 5 inner 891.2.n.d.676.1 8
33.5 odd 10 891.2.n.a.676.1 8
36.31 odd 6 528.2.y.f.97.1 4
45.4 even 6 825.2.n.f.526.1 4
45.13 odd 12 825.2.bx.b.724.2 8
45.22 odd 12 825.2.bx.b.724.1 8
99.4 even 15 363.2.a.h.1.1 2
99.5 odd 30 99.2.f.b.82.1 4
99.13 odd 30 363.2.e.c.124.1 4
99.16 even 15 inner 891.2.n.d.379.1 8
99.31 even 15 363.2.e.h.124.1 4
99.38 odd 30 891.2.n.a.379.1 8
99.40 odd 30 363.2.a.e.1.2 2
99.49 even 15 33.2.e.a.16.1 4
99.58 even 15 363.2.e.h.202.1 4
99.59 odd 30 1089.2.a.m.1.2 2
99.76 odd 6 363.2.e.j.130.1 4
99.85 odd 30 363.2.e.c.202.1 4
99.94 odd 30 363.2.e.j.148.1 4
99.95 even 30 1089.2.a.s.1.1 2
396.103 odd 30 5808.2.a.bl.1.1 2
396.139 even 30 5808.2.a.bm.1.1 2
396.247 odd 30 528.2.y.f.49.1 4
495.4 even 30 9075.2.a.x.1.2 2
495.49 even 30 825.2.n.f.676.1 4
495.139 odd 30 9075.2.a.bv.1.1 2
495.148 odd 60 825.2.bx.b.49.1 8
495.247 odd 60 825.2.bx.b.49.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.2.e.a.16.1 4 99.49 even 15
33.2.e.a.31.1 yes 4 9.4 even 3
99.2.f.b.64.1 4 9.5 odd 6
99.2.f.b.82.1 4 99.5 odd 30
363.2.a.e.1.2 2 99.40 odd 30
363.2.a.h.1.1 2 99.4 even 15
363.2.e.c.124.1 4 99.13 odd 30
363.2.e.c.202.1 4 99.85 odd 30
363.2.e.h.124.1 4 99.31 even 15
363.2.e.h.202.1 4 99.58 even 15
363.2.e.j.130.1 4 99.76 odd 6
363.2.e.j.148.1 4 99.94 odd 30
528.2.y.f.49.1 4 396.247 odd 30
528.2.y.f.97.1 4 36.31 odd 6
825.2.n.f.526.1 4 45.4 even 6
825.2.n.f.676.1 4 495.49 even 30
825.2.bx.b.49.1 8 495.148 odd 60
825.2.bx.b.49.2 8 495.247 odd 60
825.2.bx.b.724.1 8 45.22 odd 12
825.2.bx.b.724.2 8 45.13 odd 12
891.2.n.a.379.1 8 99.38 odd 30
891.2.n.a.460.1 8 9.2 odd 6
891.2.n.a.676.1 8 33.5 odd 10
891.2.n.a.757.1 8 3.2 odd 2
891.2.n.d.379.1 8 99.16 even 15 inner
891.2.n.d.460.1 8 9.7 even 3 inner
891.2.n.d.676.1 8 11.5 even 5 inner
891.2.n.d.757.1 8 1.1 even 1 trivial
1089.2.a.m.1.2 2 99.59 odd 30
1089.2.a.s.1.1 2 99.95 even 30
5808.2.a.bl.1.1 2 396.103 odd 30
5808.2.a.bm.1.1 2 396.139 even 30
9075.2.a.x.1.2 2 495.4 even 30
9075.2.a.bv.1.1 2 495.139 odd 30