Properties

Label 819.2.et.b.145.5
Level $819$
Weight $2$
Character 819.145
Analytic conductor $6.540$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [819,2,Mod(136,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 2, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.136");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.et (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 145.5
Character \(\chi\) \(=\) 819.145
Dual form 819.2.et.b.514.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.876516 - 0.876516i) q^{2} +0.463441i q^{4} +(2.51660 - 0.674321i) q^{5} +(2.20101 - 1.46818i) q^{7} +(2.15924 + 2.15924i) q^{8} +O(q^{10})\) \(q+(0.876516 - 0.876516i) q^{2} +0.463441i q^{4} +(2.51660 - 0.674321i) q^{5} +(2.20101 - 1.46818i) q^{7} +(2.15924 + 2.15924i) q^{8} +(1.61479 - 2.79689i) q^{10} +(-1.36505 + 0.365763i) q^{11} +(0.445209 + 3.57796i) q^{13} +(0.642345 - 3.21610i) q^{14} +2.85834 q^{16} -2.82813 q^{17} +(1.61939 - 6.04364i) q^{19} +(0.312508 + 1.16630i) q^{20} +(-0.875887 + 1.51708i) q^{22} +1.01874i q^{23} +(1.54845 - 0.893996i) q^{25} +(3.52637 + 2.74590i) q^{26} +(0.680412 + 1.02004i) q^{28} +(2.66549 + 4.61676i) q^{29} +(-1.73101 + 6.46023i) q^{31} +(-1.81311 + 1.81311i) q^{32} +(-2.47890 + 2.47890i) q^{34} +(4.54905 - 5.17900i) q^{35} +(-6.50927 - 6.50927i) q^{37} +(-3.87792 - 6.71676i) q^{38} +(6.88998 + 3.97793i) q^{40} +(2.51937 - 9.40242i) q^{41} +(0.850246 + 0.490890i) q^{43} +(-0.169509 - 0.632618i) q^{44} +(0.892940 + 0.892940i) q^{46} +(-0.594605 - 2.21910i) q^{47} +(2.68892 - 6.46295i) q^{49} +(0.573636 - 2.14084i) q^{50} +(-1.65817 + 0.206328i) q^{52} +(2.52978 + 4.38171i) q^{53} +(-3.18863 + 1.84096i) q^{55} +(7.92268 + 1.58238i) q^{56} +(6.38300 + 1.71032i) q^{58} +(5.39402 - 5.39402i) q^{59} +(-6.75223 + 3.89840i) q^{61} +(4.14523 + 7.17976i) q^{62} +8.89512i q^{64} +(3.53311 + 8.70408i) q^{65} +(-3.38240 - 12.6233i) q^{67} -1.31067i q^{68} +(-0.552160 - 8.52679i) q^{70} +(-2.97420 - 11.0999i) q^{71} +(8.43566 + 2.26033i) q^{73} -11.4110 q^{74} +(2.80087 + 0.750490i) q^{76} +(-2.46748 + 2.80917i) q^{77} +(-2.78395 + 4.82194i) q^{79} +(7.19330 - 1.92744i) q^{80} +(-6.03310 - 10.4496i) q^{82} +(0.445401 + 0.445401i) q^{83} +(-7.11727 + 1.90707i) q^{85} +(1.17553 - 0.314981i) q^{86} +(-3.73724 - 2.15770i) q^{88} +(-0.108264 + 0.108264i) q^{89} +(6.23298 + 7.22149i) q^{91} -0.472125 q^{92} +(-2.46625 - 1.42389i) q^{94} -16.3014i q^{95} +(-2.87974 + 0.771623i) q^{97} +(-3.30799 - 8.02176i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.876516 0.876516i 0.619790 0.619790i −0.325687 0.945478i \(-0.605596\pi\)
0.945478 + 0.325687i \(0.105596\pi\)
\(3\) 0 0
\(4\) 0.463441i 0.231720i
\(5\) 2.51660 0.674321i 1.12546 0.301566i 0.352368 0.935862i \(-0.385377\pi\)
0.773090 + 0.634296i \(0.218710\pi\)
\(6\) 0 0
\(7\) 2.20101 1.46818i 0.831905 0.554918i
\(8\) 2.15924 + 2.15924i 0.763408 + 0.763408i
\(9\) 0 0
\(10\) 1.61479 2.79689i 0.510641 0.884455i
\(11\) −1.36505 + 0.365763i −0.411577 + 0.110282i −0.458665 0.888609i \(-0.651672\pi\)
0.0470887 + 0.998891i \(0.485006\pi\)
\(12\) 0 0
\(13\) 0.445209 + 3.57796i 0.123479 + 0.992347i
\(14\) 0.642345 3.21610i 0.171674 0.859539i
\(15\) 0 0
\(16\) 2.85834 0.714585
\(17\) −2.82813 −0.685922 −0.342961 0.939350i \(-0.611430\pi\)
−0.342961 + 0.939350i \(0.611430\pi\)
\(18\) 0 0
\(19\) 1.61939 6.04364i 0.371513 1.38651i −0.486861 0.873480i \(-0.661858\pi\)
0.858373 0.513025i \(-0.171475\pi\)
\(20\) 0.312508 + 1.16630i 0.0698789 + 0.260792i
\(21\) 0 0
\(22\) −0.875887 + 1.51708i −0.186740 + 0.323443i
\(23\) 1.01874i 0.212422i 0.994344 + 0.106211i \(0.0338718\pi\)
−0.994344 + 0.106211i \(0.966128\pi\)
\(24\) 0 0
\(25\) 1.54845 0.893996i 0.309689 0.178799i
\(26\) 3.52637 + 2.74590i 0.691578 + 0.538516i
\(27\) 0 0
\(28\) 0.680412 + 1.02004i 0.128586 + 0.192769i
\(29\) 2.66549 + 4.61676i 0.494968 + 0.857310i 0.999983 0.00580039i \(-0.00184633\pi\)
−0.505015 + 0.863111i \(0.668513\pi\)
\(30\) 0 0
\(31\) −1.73101 + 6.46023i −0.310899 + 1.16029i 0.616848 + 0.787083i \(0.288409\pi\)
−0.927747 + 0.373210i \(0.878257\pi\)
\(32\) −1.81311 + 1.81311i −0.320515 + 0.320515i
\(33\) 0 0
\(34\) −2.47890 + 2.47890i −0.425128 + 0.425128i
\(35\) 4.54905 5.17900i 0.768930 0.875411i
\(36\) 0 0
\(37\) −6.50927 6.50927i −1.07012 1.07012i −0.997349 0.0727687i \(-0.976817\pi\)
−0.0727687 0.997349i \(-0.523183\pi\)
\(38\) −3.87792 6.71676i −0.629082 1.08960i
\(39\) 0 0
\(40\) 6.88998 + 3.97793i 1.08940 + 0.628966i
\(41\) 2.51937 9.40242i 0.393459 1.46841i −0.430929 0.902386i \(-0.641814\pi\)
0.824388 0.566025i \(-0.191519\pi\)
\(42\) 0 0
\(43\) 0.850246 + 0.490890i 0.129661 + 0.0748600i 0.563428 0.826165i \(-0.309482\pi\)
−0.433766 + 0.901025i \(0.642816\pi\)
\(44\) −0.169509 0.632618i −0.0255545 0.0953707i
\(45\) 0 0
\(46\) 0.892940 + 0.892940i 0.131657 + 0.131657i
\(47\) −0.594605 2.21910i −0.0867321 0.323688i 0.908904 0.417004i \(-0.136920\pi\)
−0.995637 + 0.0933159i \(0.970253\pi\)
\(48\) 0 0
\(49\) 2.68892 6.46295i 0.384132 0.923278i
\(50\) 0.573636 2.14084i 0.0811244 0.302760i
\(51\) 0 0
\(52\) −1.65817 + 0.206328i −0.229947 + 0.0286126i
\(53\) 2.52978 + 4.38171i 0.347492 + 0.601875i 0.985803 0.167904i \(-0.0536999\pi\)
−0.638311 + 0.769779i \(0.720367\pi\)
\(54\) 0 0
\(55\) −3.18863 + 1.84096i −0.429955 + 0.248235i
\(56\) 7.92268 + 1.58238i 1.05871 + 0.211454i
\(57\) 0 0
\(58\) 6.38300 + 1.71032i 0.838129 + 0.224576i
\(59\) 5.39402 5.39402i 0.702242 0.702242i −0.262650 0.964891i \(-0.584596\pi\)
0.964891 + 0.262650i \(0.0845963\pi\)
\(60\) 0 0
\(61\) −6.75223 + 3.89840i −0.864534 + 0.499139i −0.865528 0.500861i \(-0.833017\pi\)
0.000994018 1.00000i \(0.499684\pi\)
\(62\) 4.14523 + 7.17976i 0.526445 + 0.911830i
\(63\) 0 0
\(64\) 8.89512i 1.11189i
\(65\) 3.53311 + 8.70408i 0.438228 + 1.07961i
\(66\) 0 0
\(67\) −3.38240 12.6233i −0.413226 1.54218i −0.788363 0.615211i \(-0.789071\pi\)
0.375137 0.926970i \(-0.377596\pi\)
\(68\) 1.31067i 0.158942i
\(69\) 0 0
\(70\) −0.552160 8.52679i −0.0659958 1.01915i
\(71\) −2.97420 11.0999i −0.352973 1.31731i −0.883017 0.469341i \(-0.844491\pi\)
0.530044 0.847970i \(-0.322175\pi\)
\(72\) 0 0
\(73\) 8.43566 + 2.26033i 0.987320 + 0.264552i 0.716124 0.697973i \(-0.245914\pi\)
0.271196 + 0.962524i \(0.412581\pi\)
\(74\) −11.4110 −1.32650
\(75\) 0 0
\(76\) 2.80087 + 0.750490i 0.321282 + 0.0860871i
\(77\) −2.46748 + 2.80917i −0.281195 + 0.320135i
\(78\) 0 0
\(79\) −2.78395 + 4.82194i −0.313219 + 0.542511i −0.979057 0.203585i \(-0.934741\pi\)
0.665838 + 0.746096i \(0.268074\pi\)
\(80\) 7.19330 1.92744i 0.804236 0.215494i
\(81\) 0 0
\(82\) −6.03310 10.4496i −0.666244 1.15397i
\(83\) 0.445401 + 0.445401i 0.0488891 + 0.0488891i 0.731129 0.682240i \(-0.238994\pi\)
−0.682240 + 0.731129i \(0.738994\pi\)
\(84\) 0 0
\(85\) −7.11727 + 1.90707i −0.771977 + 0.206851i
\(86\) 1.17553 0.314981i 0.126760 0.0339653i
\(87\) 0 0
\(88\) −3.73724 2.15770i −0.398391 0.230011i
\(89\) −0.108264 + 0.108264i −0.0114760 + 0.0114760i −0.712821 0.701346i \(-0.752583\pi\)
0.701346 + 0.712821i \(0.252583\pi\)
\(90\) 0 0
\(91\) 6.23298 + 7.22149i 0.653394 + 0.757018i
\(92\) −0.472125 −0.0492224
\(93\) 0 0
\(94\) −2.46625 1.42389i −0.254375 0.146863i
\(95\) 16.3014i 1.67249i
\(96\) 0 0
\(97\) −2.87974 + 0.771623i −0.292393 + 0.0783465i −0.402034 0.915625i \(-0.631697\pi\)
0.109641 + 0.993971i \(0.465030\pi\)
\(98\) −3.30799 8.02176i −0.334157 0.810320i
\(99\) 0 0
\(100\) 0.414314 + 0.717613i 0.0414314 + 0.0717613i
\(101\) −2.65050 + 4.59080i −0.263735 + 0.456802i −0.967231 0.253897i \(-0.918288\pi\)
0.703497 + 0.710699i \(0.251621\pi\)
\(102\) 0 0
\(103\) −2.40977 + 4.17384i −0.237442 + 0.411261i −0.959979 0.280071i \(-0.909642\pi\)
0.722538 + 0.691331i \(0.242975\pi\)
\(104\) −6.76437 + 8.68700i −0.663301 + 0.851831i
\(105\) 0 0
\(106\) 6.05803 + 1.62325i 0.588408 + 0.157664i
\(107\) −1.77743 −0.171830 −0.0859151 0.996302i \(-0.527381\pi\)
−0.0859151 + 0.996302i \(0.527381\pi\)
\(108\) 0 0
\(109\) −9.63303 2.58116i −0.922677 0.247231i −0.233948 0.972249i \(-0.575165\pi\)
−0.688729 + 0.725019i \(0.741831\pi\)
\(110\) −1.18126 + 4.40852i −0.112629 + 0.420336i
\(111\) 0 0
\(112\) 6.29125 4.19654i 0.594467 0.396536i
\(113\) −8.26089 + 14.3083i −0.777119 + 1.34601i 0.156477 + 0.987682i \(0.449986\pi\)
−0.933596 + 0.358328i \(0.883347\pi\)
\(114\) 0 0
\(115\) 0.686957 + 2.56376i 0.0640591 + 0.239072i
\(116\) −2.13959 + 1.23530i −0.198656 + 0.114694i
\(117\) 0 0
\(118\) 9.45589i 0.870485i
\(119\) −6.22475 + 4.15219i −0.570622 + 0.380631i
\(120\) 0 0
\(121\) −7.79671 + 4.50143i −0.708792 + 0.409221i
\(122\) −2.50142 + 9.33544i −0.226468 + 0.845191i
\(123\) 0 0
\(124\) −2.99394 0.802223i −0.268863 0.0720417i
\(125\) −5.91742 + 5.91742i −0.529270 + 0.529270i
\(126\) 0 0
\(127\) −5.35860 + 3.09379i −0.475499 + 0.274529i −0.718539 0.695487i \(-0.755189\pi\)
0.243040 + 0.970016i \(0.421855\pi\)
\(128\) 4.17049 + 4.17049i 0.368623 + 0.368623i
\(129\) 0 0
\(130\) 10.7261 + 4.53244i 0.940740 + 0.397521i
\(131\) 2.15037 + 1.24152i 0.187879 + 0.108472i 0.590989 0.806680i \(-0.298738\pi\)
−0.403110 + 0.915151i \(0.632071\pi\)
\(132\) 0 0
\(133\) −5.30882 15.6797i −0.460333 1.35960i
\(134\) −14.0292 8.09978i −1.21194 0.699715i
\(135\) 0 0
\(136\) −6.10662 6.10662i −0.523639 0.523639i
\(137\) −9.30838 9.30838i −0.795268 0.795268i 0.187077 0.982345i \(-0.440099\pi\)
−0.982345 + 0.187077i \(0.940099\pi\)
\(138\) 0 0
\(139\) 15.3254 + 8.84813i 1.29988 + 0.750488i 0.980384 0.197098i \(-0.0631516\pi\)
0.319500 + 0.947586i \(0.396485\pi\)
\(140\) 2.40016 + 2.10822i 0.202851 + 0.178177i
\(141\) 0 0
\(142\) −12.3361 7.12227i −1.03523 0.597688i
\(143\) −1.91642 4.72124i −0.160259 0.394810i
\(144\) 0 0
\(145\) 9.82114 + 9.82114i 0.815602 + 0.815602i
\(146\) 9.37521 5.41278i 0.775898 0.447965i
\(147\) 0 0
\(148\) 3.01666 3.01666i 0.247968 0.247968i
\(149\) −16.1655 4.33154i −1.32433 0.354854i −0.473733 0.880669i \(-0.657094\pi\)
−0.850599 + 0.525815i \(0.823760\pi\)
\(150\) 0 0
\(151\) −2.27755 + 8.49993i −0.185344 + 0.691715i 0.809212 + 0.587516i \(0.199894\pi\)
−0.994557 + 0.104198i \(0.966772\pi\)
\(152\) 16.5463 9.55303i 1.34209 0.774853i
\(153\) 0 0
\(154\) 0.299501 + 4.62507i 0.0241345 + 0.372699i
\(155\) 17.4251i 1.39962i
\(156\) 0 0
\(157\) 4.38854 2.53373i 0.350244 0.202213i −0.314549 0.949241i \(-0.601853\pi\)
0.664793 + 0.747028i \(0.268520\pi\)
\(158\) 1.78633 + 6.66668i 0.142113 + 0.530373i
\(159\) 0 0
\(160\) −3.34025 + 5.78549i −0.264070 + 0.457383i
\(161\) 1.49569 + 2.24226i 0.117877 + 0.176715i
\(162\) 0 0
\(163\) −0.650182 + 2.42651i −0.0509262 + 0.190059i −0.986703 0.162534i \(-0.948033\pi\)
0.935777 + 0.352593i \(0.114700\pi\)
\(164\) 4.35746 + 1.16758i 0.340261 + 0.0911726i
\(165\) 0 0
\(166\) 0.780801 0.0606019
\(167\) 2.57849 + 0.690905i 0.199530 + 0.0534639i 0.357200 0.934028i \(-0.383732\pi\)
−0.157670 + 0.987492i \(0.550398\pi\)
\(168\) 0 0
\(169\) −12.6036 + 3.18588i −0.969506 + 0.245068i
\(170\) −4.56683 + 7.90998i −0.350260 + 0.606668i
\(171\) 0 0
\(172\) −0.227498 + 0.394039i −0.0173466 + 0.0300452i
\(173\) −0.770968 1.33536i −0.0586156 0.101525i 0.835229 0.549903i \(-0.185335\pi\)
−0.893844 + 0.448378i \(0.852002\pi\)
\(174\) 0 0
\(175\) 2.09561 4.24109i 0.158413 0.320596i
\(176\) −3.90177 + 1.04547i −0.294107 + 0.0788056i
\(177\) 0 0
\(178\) 0.189790i 0.0142254i
\(179\) −15.3074 8.83772i −1.14413 0.660562i −0.196678 0.980468i \(-0.563015\pi\)
−0.947449 + 0.319906i \(0.896349\pi\)
\(180\) 0 0
\(181\) 0.905550 0.0673090 0.0336545 0.999434i \(-0.489285\pi\)
0.0336545 + 0.999434i \(0.489285\pi\)
\(182\) 11.7931 + 0.866445i 0.874159 + 0.0642252i
\(183\) 0 0
\(184\) −2.19970 + 2.19970i −0.162164 + 0.162164i
\(185\) −20.7706 11.9919i −1.52708 0.881662i
\(186\) 0 0
\(187\) 3.86053 1.03442i 0.282310 0.0756446i
\(188\) 1.02842 0.275564i 0.0750052 0.0200976i
\(189\) 0 0
\(190\) −14.2884 14.2884i −1.03659 1.03659i
\(191\) 11.7133 + 20.2881i 0.847546 + 1.46799i 0.883392 + 0.468635i \(0.155254\pi\)
−0.0358466 + 0.999357i \(0.511413\pi\)
\(192\) 0 0
\(193\) 11.5170 3.08597i 0.829011 0.222133i 0.180729 0.983533i \(-0.442154\pi\)
0.648282 + 0.761400i \(0.275488\pi\)
\(194\) −1.84780 + 3.20048i −0.132664 + 0.229781i
\(195\) 0 0
\(196\) 2.99519 + 1.24616i 0.213942 + 0.0890112i
\(197\) −10.0281 2.68702i −0.714472 0.191442i −0.116768 0.993159i \(-0.537253\pi\)
−0.597704 + 0.801717i \(0.703920\pi\)
\(198\) 0 0
\(199\) −3.97515 −0.281791 −0.140896 0.990024i \(-0.544998\pi\)
−0.140896 + 0.990024i \(0.544998\pi\)
\(200\) 5.27383 + 1.41312i 0.372916 + 0.0999225i
\(201\) 0 0
\(202\) 1.70071 + 6.34712i 0.119661 + 0.446582i
\(203\) 12.6450 + 6.24815i 0.887504 + 0.438534i
\(204\) 0 0
\(205\) 25.3610i 1.77129i
\(206\) 1.54624 + 5.77064i 0.107731 + 0.402059i
\(207\) 0 0
\(208\) 1.27256 + 10.2270i 0.0882361 + 0.709117i
\(209\) 8.84215i 0.611624i
\(210\) 0 0
\(211\) 2.47669 + 4.28976i 0.170503 + 0.295319i 0.938596 0.345019i \(-0.112128\pi\)
−0.768093 + 0.640338i \(0.778794\pi\)
\(212\) −2.03066 + 1.17240i −0.139467 + 0.0805211i
\(213\) 0 0
\(214\) −1.55794 + 1.55794i −0.106499 + 0.106499i
\(215\) 2.47075 + 0.662035i 0.168504 + 0.0451504i
\(216\) 0 0
\(217\) 5.67477 + 16.7605i 0.385228 + 1.13778i
\(218\) −10.7059 + 6.18107i −0.725097 + 0.418635i
\(219\) 0 0
\(220\) −0.853175 1.47774i −0.0575211 0.0996294i
\(221\) −1.25911 10.1189i −0.0846968 0.680673i
\(222\) 0 0
\(223\) 4.57716 17.0822i 0.306509 1.14391i −0.625129 0.780521i \(-0.714954\pi\)
0.931638 0.363387i \(-0.118380\pi\)
\(224\) −1.32872 + 6.65264i −0.0887786 + 0.444498i
\(225\) 0 0
\(226\) 5.30063 + 19.7822i 0.352593 + 1.31589i
\(227\) 10.7232 + 10.7232i 0.711725 + 0.711725i 0.966896 0.255171i \(-0.0821317\pi\)
−0.255171 + 0.966896i \(0.582132\pi\)
\(228\) 0 0
\(229\) 3.87857 + 14.4750i 0.256303 + 0.956536i 0.967361 + 0.253403i \(0.0815498\pi\)
−0.711058 + 0.703134i \(0.751784\pi\)
\(230\) 2.84930 + 1.64505i 0.187877 + 0.108471i
\(231\) 0 0
\(232\) −4.21327 + 15.7241i −0.276615 + 1.03234i
\(233\) −5.38039 3.10637i −0.352481 0.203505i 0.313297 0.949655i \(-0.398567\pi\)
−0.665777 + 0.746150i \(0.731900\pi\)
\(234\) 0 0
\(235\) −2.99277 5.18363i −0.195227 0.338142i
\(236\) 2.49981 + 2.49981i 0.162724 + 0.162724i
\(237\) 0 0
\(238\) −1.81663 + 9.09555i −0.117755 + 0.589577i
\(239\) 14.1820 14.1820i 0.917358 0.917358i −0.0794785 0.996837i \(-0.525326\pi\)
0.996837 + 0.0794785i \(0.0253255\pi\)
\(240\) 0 0
\(241\) 0.812288 0.812288i 0.0523241 0.0523241i −0.680461 0.732785i \(-0.738220\pi\)
0.732785 + 0.680461i \(0.238220\pi\)
\(242\) −2.88836 + 10.7795i −0.185671 + 0.692934i
\(243\) 0 0
\(244\) −1.80668 3.12926i −0.115661 0.200330i
\(245\) 2.40885 18.0779i 0.153896 1.15495i
\(246\) 0 0
\(247\) 22.3448 + 3.10342i 1.42177 + 0.197466i
\(248\) −17.6869 + 10.2115i −1.12312 + 0.648433i
\(249\) 0 0
\(250\) 10.3734i 0.656073i
\(251\) 14.3378 24.8339i 0.904997 1.56750i 0.0840758 0.996459i \(-0.473206\pi\)
0.820921 0.571041i \(-0.193460\pi\)
\(252\) 0 0
\(253\) −0.372617 1.39062i −0.0234262 0.0874278i
\(254\) −1.98514 + 7.40865i −0.124559 + 0.464860i
\(255\) 0 0
\(256\) −10.4792 −0.654952
\(257\) 19.6195 1.22383 0.611916 0.790922i \(-0.290399\pi\)
0.611916 + 0.790922i \(0.290399\pi\)
\(258\) 0 0
\(259\) −23.8837 4.77025i −1.48406 0.296409i
\(260\) −4.03383 + 1.63739i −0.250167 + 0.101546i
\(261\) 0 0
\(262\) 2.97304 0.796624i 0.183675 0.0492156i
\(263\) 4.04343 7.00342i 0.249328 0.431850i −0.714011 0.700134i \(-0.753123\pi\)
0.963340 + 0.268285i \(0.0864568\pi\)
\(264\) 0 0
\(265\) 9.32114 + 9.32114i 0.572593 + 0.572593i
\(266\) −18.3967 9.09021i −1.12798 0.557357i
\(267\) 0 0
\(268\) 5.85015 1.56754i 0.357355 0.0957529i
\(269\) 14.3415i 0.874415i 0.899361 + 0.437207i \(0.144032\pi\)
−0.899361 + 0.437207i \(0.855968\pi\)
\(270\) 0 0
\(271\) 18.4862 18.4862i 1.12295 1.12295i 0.131660 0.991295i \(-0.457969\pi\)
0.991295 0.131660i \(-0.0420306\pi\)
\(272\) −8.08376 −0.490150
\(273\) 0 0
\(274\) −16.3179 −0.985799
\(275\) −1.78671 + 1.78671i −0.107743 + 0.107743i
\(276\) 0 0
\(277\) 5.86837i 0.352596i −0.984337 0.176298i \(-0.943588\pi\)
0.984337 0.176298i \(-0.0564123\pi\)
\(278\) 21.1885 5.67744i 1.27080 0.340510i
\(279\) 0 0
\(280\) 21.0052 1.36021i 1.25530 0.0812883i
\(281\) −16.4096 16.4096i −0.978913 0.978913i 0.0208690 0.999782i \(-0.493357\pi\)
−0.999782 + 0.0208690i \(0.993357\pi\)
\(282\) 0 0
\(283\) −11.1979 + 19.3953i −0.665645 + 1.15293i 0.313465 + 0.949600i \(0.398510\pi\)
−0.979110 + 0.203331i \(0.934823\pi\)
\(284\) 5.14413 1.37837i 0.305248 0.0817909i
\(285\) 0 0
\(286\) −5.81800 2.45847i −0.344026 0.145372i
\(287\) −8.25922 24.3937i −0.487527 1.43992i
\(288\) 0 0
\(289\) −9.00168 −0.529511
\(290\) 17.2168 1.01100
\(291\) 0 0
\(292\) −1.04753 + 3.90943i −0.0613020 + 0.228782i
\(293\) −1.22119 4.55756i −0.0713429 0.266255i 0.921036 0.389477i \(-0.127344\pi\)
−0.992379 + 0.123221i \(0.960677\pi\)
\(294\) 0 0
\(295\) 9.93730 17.2119i 0.578572 1.00212i
\(296\) 28.1102i 1.63387i
\(297\) 0 0
\(298\) −17.9660 + 10.3727i −1.04074 + 0.600873i
\(299\) −3.64500 + 0.453552i −0.210796 + 0.0262296i
\(300\) 0 0
\(301\) 2.59212 0.167855i 0.149407 0.00967499i
\(302\) 5.45401 + 9.44663i 0.313843 + 0.543592i
\(303\) 0 0
\(304\) 4.62876 17.2748i 0.265478 0.990776i
\(305\) −14.3639 + 14.3639i −0.822474 + 0.822474i
\(306\) 0 0
\(307\) 3.77977 3.77977i 0.215723 0.215723i −0.590970 0.806693i \(-0.701255\pi\)
0.806693 + 0.590970i \(0.201255\pi\)
\(308\) −1.30189 1.14353i −0.0741819 0.0651587i
\(309\) 0 0
\(310\) 15.2734 + 15.2734i 0.867469 + 0.867469i
\(311\) −1.26681 2.19418i −0.0718343 0.124421i 0.827871 0.560919i \(-0.189552\pi\)
−0.899705 + 0.436498i \(0.856219\pi\)
\(312\) 0 0
\(313\) 4.62033 + 2.66755i 0.261157 + 0.150779i 0.624862 0.780735i \(-0.285155\pi\)
−0.363705 + 0.931514i \(0.618489\pi\)
\(314\) 1.62578 6.06748i 0.0917478 0.342408i
\(315\) 0 0
\(316\) −2.23469 1.29020i −0.125711 0.0725792i
\(317\) 3.28216 + 12.2492i 0.184344 + 0.687982i 0.994770 + 0.102141i \(0.0325692\pi\)
−0.810426 + 0.585841i \(0.800764\pi\)
\(318\) 0 0
\(319\) −5.32715 5.32715i −0.298263 0.298263i
\(320\) 5.99817 + 22.3855i 0.335308 + 1.25139i
\(321\) 0 0
\(322\) 3.27637 + 0.654381i 0.182585 + 0.0364672i
\(323\) −4.57984 + 17.0922i −0.254829 + 0.951035i
\(324\) 0 0
\(325\) 3.88806 + 5.14226i 0.215671 + 0.285241i
\(326\) 1.55698 + 2.69677i 0.0862333 + 0.149360i
\(327\) 0 0
\(328\) 25.7420 14.8622i 1.42137 0.820626i
\(329\) −4.56676 4.01128i −0.251773 0.221149i
\(330\) 0 0
\(331\) −8.64629 2.31677i −0.475243 0.127341i 0.0132438 0.999912i \(-0.495784\pi\)
−0.488487 + 0.872571i \(0.662451\pi\)
\(332\) −0.206417 + 0.206417i −0.0113286 + 0.0113286i
\(333\) 0 0
\(334\) 2.86568 1.65450i 0.156803 0.0905303i
\(335\) −17.0243 29.4870i −0.930137 1.61105i
\(336\) 0 0
\(337\) 8.38324i 0.456664i −0.973583 0.228332i \(-0.926673\pi\)
0.973583 0.228332i \(-0.0733272\pi\)
\(338\) −8.25476 + 13.8397i −0.449000 + 0.752781i
\(339\) 0 0
\(340\) −0.883813 3.29844i −0.0479315 0.178883i
\(341\) 9.45165i 0.511836i
\(342\) 0 0
\(343\) −3.57038 18.1728i −0.192782 0.981242i
\(344\) 0.775938 + 2.89584i 0.0418358 + 0.156133i
\(345\) 0 0
\(346\) −1.84623 0.494695i −0.0992537 0.0265949i
\(347\) 27.5764 1.48038 0.740190 0.672398i \(-0.234735\pi\)
0.740190 + 0.672398i \(0.234735\pi\)
\(348\) 0 0
\(349\) −34.2817 9.18577i −1.83506 0.491703i −0.836633 0.547765i \(-0.815479\pi\)
−0.998427 + 0.0560618i \(0.982146\pi\)
\(350\) −1.88054 5.55421i −0.100519 0.296885i
\(351\) 0 0
\(352\) 1.81181 3.13814i 0.0965697 0.167264i
\(353\) 7.01577 1.87987i 0.373412 0.100055i −0.0672321 0.997737i \(-0.521417\pi\)
0.440644 + 0.897682i \(0.354750\pi\)
\(354\) 0 0
\(355\) −14.9697 25.9284i −0.794512 1.37613i
\(356\) −0.0501740 0.0501740i −0.00265922 0.00265922i
\(357\) 0 0
\(358\) −21.1635 + 5.67075i −1.11853 + 0.299709i
\(359\) −15.2059 + 4.07442i −0.802539 + 0.215040i −0.636698 0.771113i \(-0.719700\pi\)
−0.165841 + 0.986153i \(0.553034\pi\)
\(360\) 0 0
\(361\) −17.4486 10.0740i −0.918349 0.530209i
\(362\) 0.793728 0.793728i 0.0417174 0.0417174i
\(363\) 0 0
\(364\) −3.34673 + 2.88862i −0.175417 + 0.151405i
\(365\) 22.7534 1.19097
\(366\) 0 0
\(367\) 0.280231 + 0.161792i 0.0146280 + 0.00844546i 0.507296 0.861772i \(-0.330645\pi\)
−0.492668 + 0.870217i \(0.663978\pi\)
\(368\) 2.91190i 0.151793i
\(369\) 0 0
\(370\) −28.7168 + 7.69465i −1.49292 + 0.400026i
\(371\) 12.0012 + 5.93005i 0.623072 + 0.307873i
\(372\) 0 0
\(373\) 16.1440 + 27.9622i 0.835905 + 1.44783i 0.893292 + 0.449478i \(0.148390\pi\)
−0.0573868 + 0.998352i \(0.518277\pi\)
\(374\) 2.47712 4.29050i 0.128089 0.221856i
\(375\) 0 0
\(376\) 3.50767 6.07547i 0.180894 0.313318i
\(377\) −15.3319 + 11.5924i −0.789631 + 0.597040i
\(378\) 0 0
\(379\) 13.3271 + 3.57099i 0.684568 + 0.183430i 0.584308 0.811532i \(-0.301366\pi\)
0.100260 + 0.994961i \(0.468033\pi\)
\(380\) 7.55474 0.387550
\(381\) 0 0
\(382\) 28.0497 + 7.51589i 1.43515 + 0.384547i
\(383\) −4.35337 + 16.2470i −0.222447 + 0.830183i 0.760965 + 0.648793i \(0.224726\pi\)
−0.983411 + 0.181389i \(0.941941\pi\)
\(384\) 0 0
\(385\) −4.31538 + 8.73345i −0.219932 + 0.445098i
\(386\) 7.38992 12.7997i 0.376137 0.651489i
\(387\) 0 0
\(388\) −0.357602 1.33459i −0.0181545 0.0677534i
\(389\) −15.4854 + 8.94050i −0.785141 + 0.453302i −0.838249 0.545287i \(-0.816421\pi\)
0.0531079 + 0.998589i \(0.483087\pi\)
\(390\) 0 0
\(391\) 2.88112i 0.145705i
\(392\) 19.7611 8.14904i 0.998088 0.411589i
\(393\) 0 0
\(394\) −11.1450 + 6.43456i −0.561477 + 0.324169i
\(395\) −3.75455 + 14.0122i −0.188912 + 0.705030i
\(396\) 0 0
\(397\) 6.40627 + 1.71656i 0.321522 + 0.0861515i 0.415970 0.909378i \(-0.363442\pi\)
−0.0944484 + 0.995530i \(0.530109\pi\)
\(398\) −3.48428 + 3.48428i −0.174651 + 0.174651i
\(399\) 0 0
\(400\) 4.42599 2.55534i 0.221299 0.127767i
\(401\) 15.5895 + 15.5895i 0.778503 + 0.778503i 0.979576 0.201073i \(-0.0644430\pi\)
−0.201073 + 0.979576i \(0.564443\pi\)
\(402\) 0 0
\(403\) −23.8851 3.31734i −1.18980 0.165249i
\(404\) −2.12757 1.22835i −0.105850 0.0611127i
\(405\) 0 0
\(406\) 16.5601 5.60692i 0.821865 0.278267i
\(407\) 11.2663 + 6.50460i 0.558450 + 0.322421i
\(408\) 0 0
\(409\) −11.7049 11.7049i −0.578770 0.578770i 0.355794 0.934564i \(-0.384210\pi\)
−0.934564 + 0.355794i \(0.884210\pi\)
\(410\) −22.2293 22.2293i −1.09783 1.09783i
\(411\) 0 0
\(412\) −1.93433 1.11679i −0.0952975 0.0550201i
\(413\) 3.95295 19.7917i 0.194512 0.973885i
\(414\) 0 0
\(415\) 1.42124 + 0.820553i 0.0697659 + 0.0402793i
\(416\) −7.29444 5.68001i −0.357639 0.278486i
\(417\) 0 0
\(418\) 7.75028 + 7.75028i 0.379079 + 0.379079i
\(419\) 23.3376 13.4740i 1.14012 0.658247i 0.193658 0.981069i \(-0.437965\pi\)
0.946460 + 0.322822i \(0.104631\pi\)
\(420\) 0 0
\(421\) 11.8511 11.8511i 0.577587 0.577587i −0.356651 0.934238i \(-0.616081\pi\)
0.934238 + 0.356651i \(0.116081\pi\)
\(422\) 5.93090 + 1.58918i 0.288712 + 0.0773601i
\(423\) 0 0
\(424\) −3.99877 + 14.9236i −0.194197 + 0.724755i
\(425\) −4.37921 + 2.52834i −0.212423 + 0.122642i
\(426\) 0 0
\(427\) −9.13821 + 18.4939i −0.442229 + 0.894982i
\(428\) 0.823732i 0.0398166i
\(429\) 0 0
\(430\) 2.74593 1.58537i 0.132421 0.0764531i
\(431\) −1.60974 6.00762i −0.0775383 0.289377i 0.916259 0.400587i \(-0.131194\pi\)
−0.993797 + 0.111211i \(0.964527\pi\)
\(432\) 0 0
\(433\) 5.55807 9.62686i 0.267104 0.462637i −0.701009 0.713153i \(-0.747267\pi\)
0.968113 + 0.250515i \(0.0806000\pi\)
\(434\) 19.6649 + 9.71681i 0.943943 + 0.466422i
\(435\) 0 0
\(436\) 1.19622 4.46434i 0.0572884 0.213803i
\(437\) 6.15688 + 1.64973i 0.294524 + 0.0789174i
\(438\) 0 0
\(439\) 21.2653 1.01494 0.507470 0.861670i \(-0.330581\pi\)
0.507470 + 0.861670i \(0.330581\pi\)
\(440\) −10.8601 2.90996i −0.517736 0.138727i
\(441\) 0 0
\(442\) −9.97303 7.76577i −0.474369 0.369380i
\(443\) 3.28510 5.68996i 0.156080 0.270338i −0.777372 0.629041i \(-0.783448\pi\)
0.933452 + 0.358703i \(0.116781\pi\)
\(444\) 0 0
\(445\) −0.199453 + 0.345463i −0.00945497 + 0.0163765i
\(446\) −10.9609 18.9848i −0.519012 0.898955i
\(447\) 0 0
\(448\) 13.0596 + 19.5783i 0.617008 + 0.924987i
\(449\) 19.7570 5.29388i 0.932392 0.249834i 0.239518 0.970892i \(-0.423011\pi\)
0.692874 + 0.721058i \(0.256344\pi\)
\(450\) 0 0
\(451\) 13.7562i 0.647755i
\(452\) −6.63104 3.82843i −0.311898 0.180074i
\(453\) 0 0
\(454\) 18.7981 0.882241
\(455\) 20.5555 + 13.9706i 0.963658 + 0.654951i
\(456\) 0 0
\(457\) 0.506232 0.506232i 0.0236805 0.0236805i −0.695167 0.718848i \(-0.744670\pi\)
0.718848 + 0.695167i \(0.244670\pi\)
\(458\) 16.0872 + 9.28795i 0.751706 + 0.433998i
\(459\) 0 0
\(460\) −1.18815 + 0.318364i −0.0553978 + 0.0148438i
\(461\) −18.7893 + 5.03457i −0.875104 + 0.234484i −0.668294 0.743897i \(-0.732975\pi\)
−0.206811 + 0.978381i \(0.566308\pi\)
\(462\) 0 0
\(463\) 23.8616 + 23.8616i 1.10894 + 1.10894i 0.993290 + 0.115653i \(0.0368962\pi\)
0.115653 + 0.993290i \(0.463104\pi\)
\(464\) 7.61887 + 13.1963i 0.353697 + 0.612621i
\(465\) 0 0
\(466\) −7.43877 + 1.99321i −0.344594 + 0.0923338i
\(467\) 2.96432 5.13436i 0.137173 0.237590i −0.789253 0.614068i \(-0.789532\pi\)
0.926425 + 0.376479i \(0.122865\pi\)
\(468\) 0 0
\(469\) −25.9779 22.8181i −1.19955 1.05364i
\(470\) −7.16674 1.92032i −0.330577 0.0885778i
\(471\) 0 0
\(472\) 23.2940 1.07219
\(473\) −1.34017 0.359099i −0.0616213 0.0165114i
\(474\) 0 0
\(475\) −2.89545 10.8060i −0.132852 0.495812i
\(476\) −1.92429 2.88480i −0.0881999 0.132225i
\(477\) 0 0
\(478\) 24.8615i 1.13714i
\(479\) −5.78255 21.5808i −0.264211 0.986050i −0.962731 0.270459i \(-0.912824\pi\)
0.698520 0.715590i \(-0.253842\pi\)
\(480\) 0 0
\(481\) 20.3919 26.1879i 0.929791 1.19406i
\(482\) 1.42397i 0.0648599i
\(483\) 0 0
\(484\) −2.08615 3.61332i −0.0948249 0.164242i
\(485\) −6.72683 + 3.88374i −0.305450 + 0.176351i
\(486\) 0 0
\(487\) −3.79944 + 3.79944i −0.172169 + 0.172169i −0.787932 0.615763i \(-0.788848\pi\)
0.615763 + 0.787932i \(0.288848\pi\)
\(488\) −22.9973 6.16211i −1.04104 0.278946i
\(489\) 0 0
\(490\) −13.7341 17.9569i −0.620445 0.811211i
\(491\) −8.53958 + 4.93033i −0.385386 + 0.222503i −0.680159 0.733065i \(-0.738089\pi\)
0.294773 + 0.955567i \(0.404756\pi\)
\(492\) 0 0
\(493\) −7.53834 13.0568i −0.339510 0.588048i
\(494\) 22.3058 16.8654i 1.00359 0.758811i
\(495\) 0 0
\(496\) −4.94783 + 18.4655i −0.222164 + 0.829128i
\(497\) −22.8428 20.0643i −1.02464 0.900007i
\(498\) 0 0
\(499\) −0.0722859 0.269775i −0.00323596 0.0120768i 0.964289 0.264852i \(-0.0853232\pi\)
−0.967525 + 0.252776i \(0.918657\pi\)
\(500\) −2.74237 2.74237i −0.122643 0.122643i
\(501\) 0 0
\(502\) −9.19994 34.3346i −0.410613 1.53243i
\(503\) −14.3969 8.31203i −0.641924 0.370615i 0.143431 0.989660i \(-0.454186\pi\)
−0.785355 + 0.619045i \(0.787520\pi\)
\(504\) 0 0
\(505\) −3.57458 + 13.3405i −0.159067 + 0.593645i
\(506\) −1.54551 0.892300i −0.0687062 0.0396676i
\(507\) 0 0
\(508\) −1.43379 2.48339i −0.0636140 0.110183i
\(509\) 28.5307 + 28.5307i 1.26460 + 1.26460i 0.948839 + 0.315761i \(0.102260\pi\)
0.315761 + 0.948839i \(0.397740\pi\)
\(510\) 0 0
\(511\) 21.8856 7.41002i 0.968161 0.327800i
\(512\) −17.5262 + 17.5262i −0.774556 + 0.774556i
\(513\) 0 0
\(514\) 17.1968 17.1968i 0.758519 0.758519i
\(515\) −3.24992 + 12.1289i −0.143208 + 0.534461i
\(516\) 0 0
\(517\) 1.62333 + 2.81168i 0.0713938 + 0.123658i
\(518\) −25.1157 + 16.7533i −1.10352 + 0.736097i
\(519\) 0 0
\(520\) −11.1654 + 26.4231i −0.489635 + 1.15873i
\(521\) 15.9440 9.20528i 0.698520 0.403291i −0.108276 0.994121i \(-0.534533\pi\)
0.806796 + 0.590830i \(0.201200\pi\)
\(522\) 0 0
\(523\) 12.5007i 0.546617i 0.961926 + 0.273308i \(0.0881180\pi\)
−0.961926 + 0.273308i \(0.911882\pi\)
\(524\) −0.575369 + 0.996569i −0.0251351 + 0.0435353i
\(525\) 0 0
\(526\) −2.59448 9.68274i −0.113125 0.422187i
\(527\) 4.89553 18.2704i 0.213253 0.795870i
\(528\) 0 0
\(529\) 21.9622 0.954877
\(530\) 16.3402 0.709775
\(531\) 0 0
\(532\) 7.26660 2.46032i 0.315047 0.106669i
\(533\) 34.7631 + 4.82816i 1.50576 + 0.209131i
\(534\) 0 0
\(535\) −4.47307 + 1.19856i −0.193388 + 0.0518181i
\(536\) 19.9533 34.5602i 0.861853 1.49277i
\(537\) 0 0
\(538\) 12.5705 + 12.5705i 0.541954 + 0.541954i
\(539\) −1.30660 + 9.80573i −0.0562791 + 0.422363i
\(540\) 0 0
\(541\) 2.83805 0.760452i 0.122017 0.0326944i −0.197294 0.980344i \(-0.563215\pi\)
0.319311 + 0.947650i \(0.396549\pi\)
\(542\) 32.4068i 1.39199i
\(543\) 0 0
\(544\) 5.12771 5.12771i 0.219849 0.219849i
\(545\) −25.9830 −1.11299
\(546\) 0 0
\(547\) 30.4775 1.30312 0.651561 0.758596i \(-0.274114\pi\)
0.651561 + 0.758596i \(0.274114\pi\)
\(548\) 4.31388 4.31388i 0.184280 0.184280i
\(549\) 0 0
\(550\) 3.13216i 0.133556i
\(551\) 32.2185 8.63291i 1.37255 0.367774i
\(552\) 0 0
\(553\) 0.951944 + 14.7005i 0.0404808 + 0.625128i
\(554\) −5.14372 5.14372i −0.218536 0.218536i
\(555\) 0 0
\(556\) −4.10058 + 7.10242i −0.173904 + 0.301210i
\(557\) 2.05024 0.549361i 0.0868716 0.0232772i −0.215121 0.976587i \(-0.569015\pi\)
0.301993 + 0.953310i \(0.402348\pi\)
\(558\) 0 0
\(559\) −1.37785 + 3.26069i −0.0582767 + 0.137913i
\(560\) 13.0027 14.8034i 0.549466 0.625556i
\(561\) 0 0
\(562\) −28.7665 −1.21344
\(563\) 2.53466 0.106823 0.0534115 0.998573i \(-0.482990\pi\)
0.0534115 + 0.998573i \(0.482990\pi\)
\(564\) 0 0
\(565\) −11.1410 + 41.5787i −0.468705 + 1.74923i
\(566\) 7.18516 + 26.8154i 0.302015 + 1.12714i
\(567\) 0 0
\(568\) 17.5453 30.3893i 0.736184 1.27511i
\(569\) 35.0697i 1.47020i 0.677960 + 0.735099i \(0.262864\pi\)
−0.677960 + 0.735099i \(0.737136\pi\)
\(570\) 0 0
\(571\) 25.0216 14.4462i 1.04712 0.604556i 0.125279 0.992122i \(-0.460017\pi\)
0.921842 + 0.387566i \(0.126684\pi\)
\(572\) 2.18801 0.888145i 0.0914854 0.0371352i
\(573\) 0 0
\(574\) −28.6208 14.1421i −1.19461 0.590281i
\(575\) 0.910748 + 1.57746i 0.0379808 + 0.0657847i
\(576\) 0 0
\(577\) −4.00778 + 14.9572i −0.166846 + 0.622678i 0.830952 + 0.556345i \(0.187797\pi\)
−0.997798 + 0.0663329i \(0.978870\pi\)
\(578\) −7.89012 + 7.89012i −0.328186 + 0.328186i
\(579\) 0 0
\(580\) −4.55152 + 4.55152i −0.188992 + 0.188992i
\(581\) 1.63426 + 0.326407i 0.0678005 + 0.0135416i
\(582\) 0 0
\(583\) −5.05594 5.05594i −0.209396 0.209396i
\(584\) 13.3341 + 23.0953i 0.551767 + 0.955689i
\(585\) 0 0
\(586\) −5.06517 2.92438i −0.209240 0.120805i
\(587\) −3.18544 + 11.8882i −0.131477 + 0.490679i −0.999988 0.00499189i \(-0.998411\pi\)
0.868511 + 0.495671i \(0.165078\pi\)
\(588\) 0 0
\(589\) 36.2401 + 20.9232i 1.49325 + 0.862127i
\(590\) −6.37631 23.7967i −0.262508 0.979694i
\(591\) 0 0
\(592\) −18.6057 18.6057i −0.764690 0.764690i
\(593\) 8.83310 + 32.9656i 0.362732 + 1.35373i 0.870470 + 0.492222i \(0.163815\pi\)
−0.507738 + 0.861512i \(0.669518\pi\)
\(594\) 0 0
\(595\) −12.8653 + 14.6469i −0.527426 + 0.600464i
\(596\) 2.00741 7.49177i 0.0822268 0.306875i
\(597\) 0 0
\(598\) −2.79736 + 3.59245i −0.114392 + 0.146906i
\(599\) 5.99292 + 10.3800i 0.244864 + 0.424117i 0.962093 0.272720i \(-0.0879234\pi\)
−0.717229 + 0.696837i \(0.754590\pi\)
\(600\) 0 0
\(601\) 17.2242 9.94437i 0.702588 0.405639i −0.105723 0.994396i \(-0.533716\pi\)
0.808311 + 0.588756i \(0.200382\pi\)
\(602\) 2.12490 2.41916i 0.0866046 0.0985975i
\(603\) 0 0
\(604\) −3.93922 1.05551i −0.160284 0.0429481i
\(605\) −16.5858 + 16.5858i −0.674309 + 0.674309i
\(606\) 0 0
\(607\) −7.94179 + 4.58519i −0.322347 + 0.186107i −0.652438 0.757842i \(-0.726254\pi\)
0.330091 + 0.943949i \(0.392921\pi\)
\(608\) 8.02164 + 13.8939i 0.325321 + 0.563472i
\(609\) 0 0
\(610\) 25.1803i 1.01952i
\(611\) 7.67511 3.11543i 0.310502 0.126037i
\(612\) 0 0
\(613\) 4.92157 + 18.3676i 0.198780 + 0.741859i 0.991256 + 0.131955i \(0.0421254\pi\)
−0.792475 + 0.609904i \(0.791208\pi\)
\(614\) 6.62606i 0.267406i
\(615\) 0 0
\(616\) −11.3936 + 0.737802i −0.459061 + 0.0297269i
\(617\) −6.74741 25.1817i −0.271641 1.01378i −0.958059 0.286570i \(-0.907485\pi\)
0.686419 0.727207i \(-0.259182\pi\)
\(618\) 0 0
\(619\) −1.48444 0.397756i −0.0596649 0.0159872i 0.228863 0.973459i \(-0.426499\pi\)
−0.288528 + 0.957471i \(0.593166\pi\)
\(620\) −8.07550 −0.324320
\(621\) 0 0
\(622\) −3.03362 0.812855i −0.121637 0.0325925i
\(623\) −0.0793402 + 0.397242i −0.00317870 + 0.0159152i
\(624\) 0 0
\(625\) −15.3715 + 26.6243i −0.614861 + 1.06497i
\(626\) 6.38794 1.71164i 0.255314 0.0684111i
\(627\) 0 0
\(628\) 1.17423 + 2.03383i 0.0468570 + 0.0811587i
\(629\) 18.4091 + 18.4091i 0.734017 + 0.734017i
\(630\) 0 0
\(631\) 5.46012 1.46304i 0.217364 0.0582425i −0.148493 0.988913i \(-0.547442\pi\)
0.365858 + 0.930671i \(0.380776\pi\)
\(632\) −16.4230 + 4.40053i −0.653271 + 0.175043i
\(633\) 0 0
\(634\) 13.6135 + 7.85973i 0.540659 + 0.312150i
\(635\) −11.3992 + 11.3992i −0.452365 + 0.452365i
\(636\) 0 0
\(637\) 24.3213 + 6.74350i 0.963645 + 0.267187i
\(638\) −9.33866 −0.369721
\(639\) 0 0
\(640\) 13.3077 + 7.68321i 0.526034 + 0.303706i
\(641\) 2.17816i 0.0860321i −0.999074 0.0430160i \(-0.986303\pi\)
0.999074 0.0430160i \(-0.0136967\pi\)
\(642\) 0 0
\(643\) −23.5550 + 6.31154i −0.928918 + 0.248903i −0.691393 0.722479i \(-0.743003\pi\)
−0.237525 + 0.971381i \(0.576336\pi\)
\(644\) −1.03915 + 0.693162i −0.0409484 + 0.0273144i
\(645\) 0 0
\(646\) 10.9673 + 18.9959i 0.431501 + 0.747382i
\(647\) −12.8514 + 22.2592i −0.505239 + 0.875100i 0.494742 + 0.869040i \(0.335262\pi\)
−0.999982 + 0.00606025i \(0.998071\pi\)
\(648\) 0 0
\(649\) −5.39015 + 9.33602i −0.211582 + 0.366471i
\(650\) 7.91522 + 1.09932i 0.310460 + 0.0431191i
\(651\) 0 0
\(652\) −1.12455 0.301321i −0.0440406 0.0118006i
\(653\) −12.2898 −0.480938 −0.240469 0.970657i \(-0.577301\pi\)
−0.240469 + 0.970657i \(0.577301\pi\)
\(654\) 0 0
\(655\) 6.24880 + 1.67436i 0.244161 + 0.0654227i
\(656\) 7.20122 26.8753i 0.281160 1.04930i
\(657\) 0 0
\(658\) −7.51878 + 0.486886i −0.293113 + 0.0189808i
\(659\) 22.5477 39.0538i 0.878336 1.52132i 0.0251690 0.999683i \(-0.491988\pi\)
0.853167 0.521639i \(-0.174679\pi\)
\(660\) 0 0
\(661\) −3.90501 14.5737i −0.151887 0.566851i −0.999352 0.0359990i \(-0.988539\pi\)
0.847465 0.530852i \(-0.178128\pi\)
\(662\) −9.60929 + 5.54792i −0.373475 + 0.215626i
\(663\) 0 0
\(664\) 1.92346i 0.0746446i
\(665\) −23.9333 35.8796i −0.928094 1.39135i
\(666\) 0 0
\(667\) −4.70327 + 2.71543i −0.182111 + 0.105142i
\(668\) −0.320194 + 1.19498i −0.0123887 + 0.0462351i
\(669\) 0 0
\(670\) −40.7679 10.9237i −1.57500 0.422020i
\(671\) 7.79121 7.79121i 0.300776 0.300776i
\(672\) 0 0
\(673\) 10.7821 6.22503i 0.415618 0.239957i −0.277582 0.960702i \(-0.589533\pi\)
0.693201 + 0.720744i \(0.256200\pi\)
\(674\) −7.34804 7.34804i −0.283036 0.283036i
\(675\) 0 0
\(676\) −1.47647 5.84101i −0.0567872 0.224654i
\(677\) −32.6889 18.8729i −1.25634 0.725346i −0.283976 0.958831i \(-0.591654\pi\)
−0.972360 + 0.233485i \(0.924987\pi\)
\(678\) 0 0
\(679\) −5.20546 + 5.92631i −0.199767 + 0.227431i
\(680\) −19.4858 11.2501i −0.747245 0.431422i
\(681\) 0 0
\(682\) −8.28452 8.28452i −0.317231 0.317231i
\(683\) 12.7501 + 12.7501i 0.487870 + 0.487870i 0.907634 0.419763i \(-0.137887\pi\)
−0.419763 + 0.907634i \(0.637887\pi\)
\(684\) 0 0
\(685\) −29.7023 17.1486i −1.13487 0.655216i
\(686\) −19.0583 12.7993i −0.727648 0.488679i
\(687\) 0 0
\(688\) 2.43029 + 1.40313i 0.0926541 + 0.0534938i
\(689\) −14.5513 + 11.0022i −0.554361 + 0.419152i
\(690\) 0 0
\(691\) −13.2542 13.2542i −0.504212 0.504212i 0.408532 0.912744i \(-0.366041\pi\)
−0.912744 + 0.408532i \(0.866041\pi\)
\(692\) 0.618858 0.357298i 0.0235255 0.0135824i
\(693\) 0 0
\(694\) 24.1712 24.1712i 0.917525 0.917525i
\(695\) 44.5344 + 11.9330i 1.68929 + 0.452643i
\(696\) 0 0
\(697\) −7.12510 + 26.5912i −0.269883 + 1.00722i
\(698\) −38.1000 + 21.9970i −1.44210 + 0.832599i
\(699\) 0 0
\(700\) 1.96549 + 0.971191i 0.0742887 + 0.0367076i
\(701\) 12.1851i 0.460223i 0.973164 + 0.230112i \(0.0739092\pi\)
−0.973164 + 0.230112i \(0.926091\pi\)
\(702\) 0 0
\(703\) −49.8807 + 28.7986i −1.88129 + 1.08616i
\(704\) −3.25350 12.1422i −0.122621 0.457628i
\(705\) 0 0
\(706\) 4.50170 7.79717i 0.169424 0.293450i
\(707\) 0.906313 + 13.9958i 0.0340854 + 0.526367i
\(708\) 0 0
\(709\) −0.401518 + 1.49849i −0.0150793 + 0.0562768i −0.973056 0.230571i \(-0.925941\pi\)
0.957976 + 0.286848i \(0.0926073\pi\)
\(710\) −35.8478 9.60540i −1.34535 0.360484i
\(711\) 0 0
\(712\) −0.467538 −0.0175217
\(713\) −6.58129 1.76345i −0.246471 0.0660417i
\(714\) 0 0
\(715\) −8.00648 10.5892i −0.299425 0.396013i
\(716\) 4.09576 7.09406i 0.153066 0.265118i
\(717\) 0 0
\(718\) −9.75695 + 16.8995i −0.364126 + 0.630685i
\(719\) −11.1032 19.2313i −0.414080 0.717207i 0.581252 0.813724i \(-0.302563\pi\)
−0.995331 + 0.0965166i \(0.969230\pi\)
\(720\) 0 0
\(721\) 0.823996 + 12.7246i 0.0306872 + 0.473891i
\(722\) −24.1240 + 6.46400i −0.897802 + 0.240565i
\(723\) 0 0
\(724\) 0.419669i 0.0155969i
\(725\) 8.25472 + 4.76587i 0.306573 + 0.177000i
\(726\) 0 0
\(727\) 20.1830 0.748547 0.374274 0.927318i \(-0.377892\pi\)
0.374274 + 0.927318i \(0.377892\pi\)
\(728\) −2.13444 + 29.0515i −0.0791075 + 1.07672i
\(729\) 0 0
\(730\) 19.9437 19.9437i 0.738150 0.738150i
\(731\) −2.40461 1.38830i −0.0889376 0.0513481i
\(732\) 0 0
\(733\) 3.63806 0.974815i 0.134375 0.0360056i −0.191005 0.981589i \(-0.561175\pi\)
0.325380 + 0.945583i \(0.394508\pi\)
\(734\) 0.387440 0.103814i 0.0143007 0.00383185i
\(735\) 0 0
\(736\) −1.84708 1.84708i −0.0680844 0.0680844i
\(737\) 9.23426 + 15.9942i 0.340148 + 0.589154i
\(738\) 0 0
\(739\) 16.7825 4.49685i 0.617353 0.165419i 0.0634288 0.997986i \(-0.479796\pi\)
0.553924 + 0.832567i \(0.313130\pi\)
\(740\) 5.55754 9.62594i 0.204299 0.353856i
\(741\) 0 0
\(742\) 15.7170 5.32147i 0.576990 0.195357i
\(743\) −3.38542 0.907121i −0.124199 0.0332790i 0.196184 0.980567i \(-0.437145\pi\)
−0.320383 + 0.947288i \(0.603812\pi\)
\(744\) 0 0
\(745\) −43.6030 −1.59749
\(746\) 38.6598 + 10.3589i 1.41544 + 0.379265i
\(747\) 0 0
\(748\) 0.479395 + 1.78913i 0.0175284 + 0.0654169i
\(749\) −3.91214 + 2.60957i −0.142946 + 0.0953517i
\(750\) 0 0
\(751\) 1.77791i 0.0648770i −0.999474 0.0324385i \(-0.989673\pi\)
0.999474 0.0324385i \(-0.0103273\pi\)
\(752\) −1.69958 6.34293i −0.0619774 0.231303i
\(753\) 0 0
\(754\) −3.27768 + 23.5996i −0.119366 + 0.859445i
\(755\) 22.9267i 0.834389i
\(756\) 0 0
\(757\) −24.7027 42.7863i −0.897834 1.55509i −0.830258 0.557380i \(-0.811807\pi\)
−0.0675762 0.997714i \(-0.521527\pi\)
\(758\) 14.8115 8.55140i 0.537977 0.310601i
\(759\) 0 0
\(760\) 35.1987 35.1987i 1.27679 1.27679i
\(761\) −14.3625 3.84841i −0.520639 0.139505i −0.0110771 0.999939i \(-0.503526\pi\)
−0.509562 + 0.860434i \(0.670193\pi\)
\(762\) 0 0
\(763\) −24.9920 + 8.46180i −0.904773 + 0.306338i
\(764\) −9.40231 + 5.42843i −0.340164 + 0.196394i
\(765\) 0 0
\(766\) 10.4249 + 18.0565i 0.376669 + 0.652409i
\(767\) 21.7011 + 16.8981i 0.783580 + 0.610156i
\(768\) 0 0
\(769\) 7.72722 28.8384i 0.278651 1.03994i −0.674705 0.738088i \(-0.735729\pi\)
0.953355 0.301850i \(-0.0976043\pi\)
\(770\) 3.87251 + 11.4375i 0.139555 + 0.412179i
\(771\) 0 0
\(772\) 1.43016 + 5.33745i 0.0514727 + 0.192099i
\(773\) 26.2162 + 26.2162i 0.942932 + 0.942932i 0.998457 0.0555251i \(-0.0176833\pi\)
−0.0555251 + 0.998457i \(0.517683\pi\)
\(774\) 0 0
\(775\) 3.09504 + 11.5508i 0.111177 + 0.414919i
\(776\) −7.88418 4.55193i −0.283026 0.163405i
\(777\) 0 0
\(778\) −5.73671 + 21.4097i −0.205671 + 0.767575i
\(779\) −52.7449 30.4523i −1.88978 1.09107i
\(780\) 0 0
\(781\) 8.11984 + 14.0640i 0.290551 + 0.503248i
\(782\) −2.52535 2.52535i −0.0903063 0.0903063i
\(783\) 0 0
\(784\) 7.68586 18.4733i 0.274495 0.659761i
\(785\) 9.33567 9.33567i 0.333204 0.333204i
\(786\) 0 0
\(787\) 32.1979 32.1979i 1.14773 1.14773i 0.160734 0.986998i \(-0.448614\pi\)
0.986998 0.160734i \(-0.0513861\pi\)
\(788\) 1.24527 4.64743i 0.0443611 0.165558i
\(789\) 0 0
\(790\) 8.99097 + 15.5728i 0.319885 + 0.554056i
\(791\) 2.82473 + 43.6211i 0.100436 + 1.55099i
\(792\) 0 0
\(793\) −16.9545 22.4236i −0.602071 0.796285i
\(794\) 7.11979 4.11061i 0.252672 0.145880i
\(795\) 0 0
\(796\) 1.84225i 0.0652967i
\(797\) 5.85462 10.1405i 0.207381 0.359195i −0.743507 0.668728i \(-0.766839\pi\)
0.950889 + 0.309533i \(0.100173\pi\)
\(798\) 0 0
\(799\) 1.68162 + 6.27589i 0.0594914 + 0.222025i
\(800\) −1.18659 + 4.42841i −0.0419523 + 0.156568i
\(801\) 0 0
\(802\) 27.3289 0.965017
\(803\) −12.3418 −0.435533
\(804\) 0 0
\(805\) 5.27605 + 4.63429i 0.185956 + 0.163337i
\(806\) −23.8434 + 18.0280i −0.839847 + 0.635008i
\(807\) 0 0
\(808\) −15.6358 + 4.18959i −0.550064 + 0.147389i
\(809\) −19.8661 + 34.4091i −0.698456 + 1.20976i 0.270546 + 0.962707i \(0.412796\pi\)
−0.969002 + 0.247054i \(0.920538\pi\)
\(810\) 0 0
\(811\) 3.48546 + 3.48546i 0.122391 + 0.122391i 0.765649 0.643258i \(-0.222418\pi\)
−0.643258 + 0.765649i \(0.722418\pi\)
\(812\) −2.89565 + 5.86020i −0.101617 + 0.205653i
\(813\) 0 0
\(814\) 15.5765 4.17370i 0.545955 0.146288i
\(815\) 6.54500i 0.229261i
\(816\) 0 0
\(817\) 4.34364 4.34364i 0.151965 0.151965i
\(818\) −20.5190 −0.717432
\(819\) 0 0
\(820\) 11.7533 0.410444
\(821\) −20.1996 + 20.1996i −0.704971 + 0.704971i −0.965473 0.260502i \(-0.916112\pi\)
0.260502 + 0.965473i \(0.416112\pi\)
\(822\) 0 0
\(823\) 39.5422i 1.37835i −0.724593 0.689177i \(-0.757972\pi\)
0.724593 0.689177i \(-0.242028\pi\)
\(824\) −14.2156 + 3.80906i −0.495225 + 0.132695i
\(825\) 0 0
\(826\) −13.8829 20.8125i −0.483048 0.724161i
\(827\) 30.8511 + 30.8511i 1.07280 + 1.07280i 0.997133 + 0.0756634i \(0.0241074\pi\)
0.0756634 + 0.997133i \(0.475893\pi\)
\(828\) 0 0
\(829\) −21.4990 + 37.2373i −0.746690 + 1.29330i 0.202711 + 0.979239i \(0.435025\pi\)
−0.949401 + 0.314066i \(0.898309\pi\)
\(830\) 1.96497 0.526511i 0.0682049 0.0182755i
\(831\) 0 0
\(832\) −31.8264 + 3.96019i −1.10338 + 0.137295i
\(833\) −7.60463 + 18.2781i −0.263485 + 0.633297i
\(834\) 0 0
\(835\) 6.95493 0.240685
\(836\) −4.09781 −0.141726
\(837\) 0 0
\(838\) 8.64564 32.2660i 0.298659 1.11461i
\(839\) −12.0010 44.7884i −0.414321 1.54627i −0.786193 0.617982i \(-0.787951\pi\)
0.371872 0.928284i \(-0.378716\pi\)
\(840\) 0 0
\(841\) 0.290370 0.502936i 0.0100128 0.0173426i
\(842\) 20.7753i 0.715965i
\(843\) 0 0
\(844\) −1.98805 + 1.14780i −0.0684315 + 0.0395089i
\(845\) −29.5699 + 16.5165i −1.01723 + 0.568183i
\(846\) 0 0
\(847\) −10.5518 + 21.3547i −0.362563 + 0.733755i
\(848\) 7.23098 + 12.5244i 0.248313 + 0.430091i
\(849\) 0 0
\(850\) −1.62232 + 6.05457i −0.0556450 + 0.207670i
\(851\) 6.63124 6.63124i 0.227316 0.227316i
\(852\) 0 0
\(853\) −3.22439 + 3.22439i −0.110401 + 0.110401i −0.760149 0.649748i \(-0.774874\pi\)
0.649748 + 0.760149i \(0.274874\pi\)
\(854\) 8.20039 + 24.2200i 0.280612 + 0.828790i
\(855\) 0 0
\(856\) −3.83790 3.83790i −0.131177 0.131177i
\(857\) −12.4518 21.5671i −0.425345 0.736719i 0.571108 0.820875i \(-0.306514\pi\)
−0.996453 + 0.0841565i \(0.973180\pi\)
\(858\) 0 0
\(859\) 25.4805 + 14.7112i 0.869383 + 0.501939i 0.867143 0.498059i \(-0.165954\pi\)
0.00224010 + 0.999997i \(0.499287\pi\)
\(860\) −0.306814 + 1.14505i −0.0104623 + 0.0390457i
\(861\) 0 0
\(862\) −6.67673 3.85481i −0.227410 0.131295i
\(863\) 4.22635 + 15.7730i 0.143867 + 0.536918i 0.999803 + 0.0198370i \(0.00631473\pi\)
−0.855936 + 0.517081i \(0.827019\pi\)
\(864\) 0 0
\(865\) −2.84068 2.84068i −0.0965859 0.0965859i
\(866\) −3.56636 13.3098i −0.121190 0.452286i
\(867\) 0 0
\(868\) −7.76750 + 2.62992i −0.263646 + 0.0892653i
\(869\) 2.03653 7.60044i 0.0690846 0.257827i
\(870\) 0 0
\(871\) 43.6597 17.7221i 1.47935 0.600490i
\(872\) −15.2267 26.3734i −0.515641 0.893117i
\(873\) 0 0
\(874\) 6.84262 3.95059i 0.231455 0.133631i
\(875\) −4.33651 + 21.7121i −0.146601 + 0.734004i
\(876\) 0 0
\(877\) 32.8267 + 8.79590i 1.10848 + 0.297016i 0.766213 0.642587i \(-0.222139\pi\)
0.342267 + 0.939603i \(0.388805\pi\)
\(878\) 18.6394 18.6394i 0.629050 0.629050i
\(879\) 0 0
\(880\) −9.11420 + 5.26209i −0.307240 + 0.177385i
\(881\) −3.17840 5.50515i −0.107083 0.185473i 0.807504 0.589862i \(-0.200818\pi\)
−0.914587 + 0.404388i \(0.867484\pi\)
\(882\) 0 0
\(883\) 19.8386i 0.667623i 0.942640 + 0.333811i \(0.108335\pi\)
−0.942640 + 0.333811i \(0.891665\pi\)
\(884\) 4.68953 0.583523i 0.157726 0.0196260i
\(885\) 0 0
\(886\) −2.10790 7.86677i −0.0708161 0.264289i
\(887\) 1.06844i 0.0358749i −0.999839 0.0179374i \(-0.994290\pi\)
0.999839 0.0179374i \(-0.00570997\pi\)
\(888\) 0 0
\(889\) −7.25212 + 14.6768i −0.243228 + 0.492245i
\(890\) 0.127980 + 0.477627i 0.00428989 + 0.0160101i
\(891\) 0 0
\(892\) 7.91659 + 2.12124i 0.265067 + 0.0710245i
\(893\) −14.3743 −0.481018
\(894\) 0 0
\(895\) −44.4820 11.9189i −1.48687 0.398406i
\(896\) 15.3023 + 3.05630i 0.511215 + 0.102104i
\(897\) 0 0
\(898\) 12.6772 21.9575i 0.423043 0.732732i
\(899\) −34.4393 + 9.22799i −1.14862 + 0.307771i
\(900\) 0 0
\(901\) −7.15456 12.3921i −0.238353 0.412839i
\(902\) 12.0575 + 12.0575i 0.401472 + 0.401472i
\(903\) 0 0
\(904\) −48.7323 + 13.0578i −1.62081 + 0.434296i
\(905\) 2.27891 0.610631i 0.0757534 0.0202981i
\(906\) 0 0
\(907\) 2.07736 + 1.19936i 0.0689775 + 0.0398242i 0.534092 0.845426i \(-0.320654\pi\)
−0.465115 + 0.885250i \(0.653987\pi\)
\(908\) −4.96958 + 4.96958i −0.164921 + 0.164921i
\(909\) 0 0
\(910\) 30.2627 5.77181i 1.00320 0.191334i
\(911\) 6.07001 0.201108 0.100554 0.994932i \(-0.467938\pi\)
0.100554 + 0.994932i \(0.467938\pi\)
\(912\) 0 0
\(913\) −0.770903 0.445081i −0.0255132 0.0147300i
\(914\) 0.887440i 0.0293539i
\(915\) 0 0
\(916\) −6.70832 + 1.79749i −0.221649 + 0.0593907i
\(917\) 6.55575 0.424524i 0.216490 0.0140190i
\(918\) 0 0
\(919\) 0.559898 + 0.969772i 0.0184693 + 0.0319898i 0.875112 0.483920i \(-0.160787\pi\)
−0.856643 + 0.515910i \(0.827454\pi\)
\(920\) −4.05247 + 7.01909i −0.133606 + 0.231412i
\(921\) 0 0
\(922\) −12.0562 + 20.8820i −0.397050 + 0.687712i
\(923\) 38.3907 15.5833i 1.26365 0.512931i
\(924\) 0 0
\(925\) −15.8985 4.25999i −0.522740 0.140068i
\(926\) 41.8301 1.37462
\(927\) 0 0
\(928\) −13.2035 3.53787i −0.433426 0.116136i
\(929\) 8.03463 29.9857i 0.263608 0.983798i −0.699489 0.714643i \(-0.746589\pi\)
0.963097 0.269155i \(-0.0867442\pi\)
\(930\) 0 0
\(931\) −34.7053 26.7169i −1.13742 0.875611i
\(932\) 1.43962 2.49349i 0.0471562 0.0816770i
\(933\) 0 0
\(934\) −1.90207 7.09862i −0.0622376 0.232274i
\(935\) 9.01787 5.20647i 0.294916 0.170270i
\(936\) 0 0
\(937\) 7.31506i 0.238973i 0.992836 + 0.119486i \(0.0381248\pi\)
−0.992836 + 0.119486i \(0.961875\pi\)
\(938\) −42.7704 + 2.76964i −1.39650 + 0.0904319i
\(939\) 0 0
\(940\) 2.40230 1.38697i 0.0783545 0.0452380i
\(941\) −0.629247 + 2.34838i −0.0205129 + 0.0765550i −0.975424 0.220338i \(-0.929284\pi\)
0.954911 + 0.296893i \(0.0959506\pi\)
\(942\) 0 0
\(943\) 9.57860 + 2.56658i 0.311922 + 0.0835793i
\(944\) 15.4179 15.4179i 0.501812 0.501812i
\(945\) 0 0
\(946\) −1.48944 + 0.859928i −0.0484258 + 0.0279587i
\(947\) −16.4252 16.4252i −0.533748 0.533748i 0.387938 0.921685i \(-0.373187\pi\)
−0.921685 + 0.387938i \(0.873187\pi\)
\(948\) 0 0
\(949\) −4.33173 + 31.1888i −0.140614 + 1.01243i
\(950\) −12.0095 6.93369i −0.389640 0.224959i
\(951\) 0 0
\(952\) −22.4064 4.47517i −0.726194 0.145041i
\(953\) 33.8286 + 19.5310i 1.09582 + 0.632670i 0.935119 0.354334i \(-0.115292\pi\)
0.160697 + 0.987004i \(0.448626\pi\)
\(954\) 0 0
\(955\) 43.1584 + 43.1584i 1.39657 + 1.39657i
\(956\) 6.57252 + 6.57252i 0.212571 + 0.212571i
\(957\) 0 0
\(958\) −23.9844 13.8474i −0.774900 0.447388i
\(959\) −34.1542 6.82154i −1.10290 0.220279i
\(960\) 0 0
\(961\) −11.8914 6.86551i −0.383594 0.221468i
\(962\) −5.08026 40.8279i −0.163794 1.31635i
\(963\) 0 0
\(964\) 0.376448 + 0.376448i 0.0121246 + 0.0121246i
\(965\) 26.9027 15.5323i 0.866030 0.500003i
\(966\) 0 0
\(967\) −37.5795 + 37.5795i −1.20848 + 1.20848i −0.236956 + 0.971520i \(0.576150\pi\)
−0.971520 + 0.236956i \(0.923850\pi\)
\(968\) −26.5547 7.11531i −0.853500 0.228695i
\(969\) 0 0
\(970\) −2.49202 + 9.30033i −0.0800138 + 0.298616i
\(971\) 25.4016 14.6656i 0.815177 0.470642i −0.0335738 0.999436i \(-0.510689\pi\)
0.848750 + 0.528794i \(0.177356\pi\)
\(972\) 0 0
\(973\) 46.7220 3.02553i 1.49784 0.0969940i
\(974\) 6.66054i 0.213417i
\(975\) 0 0
\(976\) −19.3002 + 11.1430i −0.617783 + 0.356677i
\(977\) 14.2072 + 53.0221i 0.454530 + 1.69633i 0.689467 + 0.724318i \(0.257845\pi\)
−0.234937 + 0.972011i \(0.575488\pi\)
\(978\) 0 0
\(979\) 0.108187 0.187385i 0.00345766 0.00598884i
\(980\) 8.37802 + 1.11636i 0.267626 + 0.0356607i
\(981\) 0 0
\(982\) −3.16357 + 11.8066i −0.100953 + 0.376763i
\(983\) −41.7323 11.1821i −1.33105 0.356654i −0.477945 0.878390i \(-0.658618\pi\)
−0.853107 + 0.521735i \(0.825285\pi\)
\(984\) 0 0
\(985\) −27.0486 −0.861841
\(986\) −18.0519 4.83701i −0.574891 0.154042i
\(987\) 0 0
\(988\) −1.43825 + 10.3555i −0.0457569 + 0.329453i
\(989\) −0.500088 + 0.866178i −0.0159019 + 0.0275429i
\(990\) 0 0
\(991\) −15.3304 + 26.5530i −0.486986 + 0.843484i −0.999888 0.0149629i \(-0.995237\pi\)
0.512902 + 0.858447i \(0.328570\pi\)
\(992\) −8.57459 14.8516i −0.272243 0.471539i
\(993\) 0 0
\(994\) −37.6087 + 2.43539i −1.19288 + 0.0772459i
\(995\) −10.0039 + 2.68053i −0.317144 + 0.0849785i
\(996\) 0 0
\(997\) 32.7982i 1.03873i −0.854552 0.519365i \(-0.826168\pi\)
0.854552 0.519365i \(-0.173832\pi\)
\(998\) −0.299821 0.173102i −0.00949068 0.00547944i
\(999\) 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 819.2.et.b.145.5 28
3.2 odd 2 91.2.ba.a.54.3 yes 28
7.3 odd 6 819.2.gh.b.262.5 28
13.7 odd 12 819.2.gh.b.397.5 28
21.2 odd 6 637.2.bd.b.587.5 28
21.5 even 6 637.2.bd.a.587.5 28
21.11 odd 6 637.2.x.a.80.3 28
21.17 even 6 91.2.w.a.80.3 yes 28
21.20 even 2 637.2.bb.a.509.3 28
39.20 even 12 91.2.w.a.33.3 28
91.59 even 12 inner 819.2.et.b.514.5 28
273.20 odd 12 637.2.x.a.215.3 28
273.59 odd 12 91.2.ba.a.59.3 yes 28
273.137 even 12 637.2.bb.a.423.3 28
273.215 odd 12 637.2.bd.b.293.5 28
273.254 even 12 637.2.bd.a.293.5 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.w.a.33.3 28 39.20 even 12
91.2.w.a.80.3 yes 28 21.17 even 6
91.2.ba.a.54.3 yes 28 3.2 odd 2
91.2.ba.a.59.3 yes 28 273.59 odd 12
637.2.x.a.80.3 28 21.11 odd 6
637.2.x.a.215.3 28 273.20 odd 12
637.2.bb.a.423.3 28 273.137 even 12
637.2.bb.a.509.3 28 21.20 even 2
637.2.bd.a.293.5 28 273.254 even 12
637.2.bd.a.587.5 28 21.5 even 6
637.2.bd.b.293.5 28 273.215 odd 12
637.2.bd.b.587.5 28 21.2 odd 6
819.2.et.b.145.5 28 1.1 even 1 trivial
819.2.et.b.514.5 28 91.59 even 12 inner
819.2.gh.b.262.5 28 7.3 odd 6
819.2.gh.b.397.5 28 13.7 odd 12