Properties

Label 1080.2.d.i.109.13
Level $1080$
Weight $2$
Character 1080.109
Analytic conductor $8.624$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1080,2,Mod(109,1080)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1080.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1080.d (of order \(2\), degree \(1\), 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: \(8.62384341830\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 3x^{18} + 8x^{16} - 24x^{14} + 56x^{12} - 92x^{10} + 224x^{8} - 384x^{6} + 512x^{4} - 768x^{2} + 1024 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 109.13
Root \(-0.847166 - 1.13239i\) of defining polynomial
Character \(\chi\) \(=\) 1080.109
Dual form 1080.2.d.i.109.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.847166 - 1.13239i) q^{2} +(-0.564618 - 1.91865i) q^{4} +(-1.82935 + 1.28588i) q^{5} +1.09701i q^{7} +(-2.65098 - 0.986045i) q^{8} +O(q^{10})\) \(q+(0.847166 - 1.13239i) q^{2} +(-0.564618 - 1.91865i) q^{4} +(-1.82935 + 1.28588i) q^{5} +1.09701i q^{7} +(-2.65098 - 0.986045i) q^{8} +(-0.0936411 + 3.16089i) q^{10} +1.89459i q^{11} +4.10133 q^{13} +(1.24224 + 0.929350i) q^{14} +(-3.36241 + 2.16661i) q^{16} +1.70100i q^{17} +5.95035i q^{19} +(3.50003 + 2.78384i) q^{20} +(2.14542 + 1.60503i) q^{22} -0.424153i q^{23} +(1.69302 - 4.70465i) q^{25} +(3.47451 - 4.64430i) q^{26} +(2.10477 - 0.619392i) q^{28} +7.44798i q^{29} +2.46635 q^{31} +(-0.395078 + 5.64304i) q^{32} +(1.92620 + 1.44103i) q^{34} +(-1.41062 - 2.00681i) q^{35} -4.00954 q^{37} +(6.73812 + 5.04094i) q^{38} +(6.11751 - 1.60503i) q^{40} +8.17051 q^{41} +11.0436 q^{43} +(3.63505 - 1.06972i) q^{44} +(-0.480307 - 0.359328i) q^{46} -2.28638i q^{47} +5.79657 q^{49} +(-3.89323 - 5.90278i) q^{50} +(-2.31568 - 7.86900i) q^{52} -12.3020 q^{53} +(-2.43622 - 3.46586i) q^{55} +(1.08170 - 2.90816i) q^{56} +(8.43402 + 6.30968i) q^{58} +12.4017i q^{59} +2.83171i q^{61} +(2.08941 - 2.79287i) q^{62} +(6.05543 + 5.22798i) q^{64} +(-7.50275 + 5.27382i) q^{65} +4.91266 q^{67} +(3.26362 - 0.960415i) q^{68} +(-3.46753 - 0.102725i) q^{70} -1.69810 q^{71} -6.69321i q^{73} +(-3.39675 + 4.54036i) q^{74} +(11.4166 - 3.35968i) q^{76} -2.07838 q^{77} -12.7388 q^{79} +(3.36502 - 8.28714i) q^{80} +(6.92178 - 9.25221i) q^{82} +2.43343 q^{83} +(-2.18728 - 3.11172i) q^{85} +(9.35574 - 12.5056i) q^{86} +(1.86815 - 5.02253i) q^{88} -12.0320 q^{89} +4.49919i q^{91} +(-0.813800 + 0.239485i) q^{92} +(-2.58908 - 1.93695i) q^{94} +(-7.65144 - 10.8853i) q^{95} -2.20448i q^{97} +(4.91066 - 6.56398i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 6 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 6 q^{4} - 2 q^{10} - 4 q^{13} - 14 q^{16} - 34 q^{22} + 20 q^{25} + 20 q^{28} + 12 q^{31} + 6 q^{34} - 32 q^{37} - 6 q^{40} + 12 q^{43} + 2 q^{46} - 52 q^{49} - 50 q^{52} - 28 q^{55} + 6 q^{58} + 54 q^{64} + 12 q^{70} - 24 q^{76} + 36 q^{79} + 32 q^{82} - 44 q^{85} - 30 q^{88} - 22 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times\).

\(n\) \(217\) \(271\) \(541\) \(1001\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.847166 1.13239i 0.599037 0.800721i
\(3\) 0 0
\(4\) −0.564618 1.91865i −0.282309 0.959323i
\(5\) −1.82935 + 1.28588i −0.818109 + 0.575064i
\(6\) 0 0
\(7\) 1.09701i 0.414631i 0.978274 + 0.207315i \(0.0664726\pi\)
−0.978274 + 0.207315i \(0.933527\pi\)
\(8\) −2.65098 0.986045i −0.937264 0.348619i
\(9\) 0 0
\(10\) −0.0936411 + 3.16089i −0.0296119 + 0.999561i
\(11\) 1.89459i 0.571240i 0.958343 + 0.285620i \(0.0921996\pi\)
−0.958343 + 0.285620i \(0.907800\pi\)
\(12\) 0 0
\(13\) 4.10133 1.13750 0.568752 0.822509i \(-0.307427\pi\)
0.568752 + 0.822509i \(0.307427\pi\)
\(14\) 1.24224 + 0.929350i 0.332004 + 0.248379i
\(15\) 0 0
\(16\) −3.36241 + 2.16661i −0.840603 + 0.541652i
\(17\) 1.70100i 0.412553i 0.978494 + 0.206276i \(0.0661346\pi\)
−0.978494 + 0.206276i \(0.933865\pi\)
\(18\) 0 0
\(19\) 5.95035i 1.36510i 0.730837 + 0.682552i \(0.239130\pi\)
−0.730837 + 0.682552i \(0.760870\pi\)
\(20\) 3.50003 + 2.78384i 0.782632 + 0.622485i
\(21\) 0 0
\(22\) 2.14542 + 1.60503i 0.457404 + 0.342194i
\(23\) 0.424153i 0.0884420i −0.999022 0.0442210i \(-0.985919\pi\)
0.999022 0.0442210i \(-0.0140806\pi\)
\(24\) 0 0
\(25\) 1.69302 4.70465i 0.338604 0.940929i
\(26\) 3.47451 4.64430i 0.681407 0.910823i
\(27\) 0 0
\(28\) 2.10477 0.619392i 0.397765 0.117054i
\(29\) 7.44798i 1.38306i 0.722350 + 0.691528i \(0.243062\pi\)
−0.722350 + 0.691528i \(0.756938\pi\)
\(30\) 0 0
\(31\) 2.46635 0.442970 0.221485 0.975164i \(-0.428910\pi\)
0.221485 + 0.975164i \(0.428910\pi\)
\(32\) −0.395078 + 5.64304i −0.0698405 + 0.997558i
\(33\) 0 0
\(34\) 1.92620 + 1.44103i 0.330340 + 0.247134i
\(35\) −1.41062 2.00681i −0.238439 0.339213i
\(36\) 0 0
\(37\) −4.00954 −0.659164 −0.329582 0.944127i \(-0.606908\pi\)
−0.329582 + 0.944127i \(0.606908\pi\)
\(38\) 6.73812 + 5.04094i 1.09307 + 0.817748i
\(39\) 0 0
\(40\) 6.11751 1.60503i 0.967263 0.253778i
\(41\) 8.17051 1.27602 0.638009 0.770029i \(-0.279758\pi\)
0.638009 + 0.770029i \(0.279758\pi\)
\(42\) 0 0
\(43\) 11.0436 1.68413 0.842064 0.539377i \(-0.181340\pi\)
0.842064 + 0.539377i \(0.181340\pi\)
\(44\) 3.63505 1.06972i 0.548004 0.161266i
\(45\) 0 0
\(46\) −0.480307 0.359328i −0.0708174 0.0529801i
\(47\) 2.28638i 0.333503i −0.985999 0.166752i \(-0.946672\pi\)
0.985999 0.166752i \(-0.0533278\pi\)
\(48\) 0 0
\(49\) 5.79657 0.828081
\(50\) −3.89323 5.90278i −0.550586 0.834779i
\(51\) 0 0
\(52\) −2.31568 7.86900i −0.321128 1.09123i
\(53\) −12.3020 −1.68981 −0.844907 0.534913i \(-0.820345\pi\)
−0.844907 + 0.534913i \(0.820345\pi\)
\(54\) 0 0
\(55\) −2.43622 3.46586i −0.328499 0.467337i
\(56\) 1.08170 2.90816i 0.144548 0.388619i
\(57\) 0 0
\(58\) 8.43402 + 6.30968i 1.10744 + 0.828501i
\(59\) 12.4017i 1.61456i 0.590166 + 0.807282i \(0.299062\pi\)
−0.590166 + 0.807282i \(0.700938\pi\)
\(60\) 0 0
\(61\) 2.83171i 0.362564i 0.983431 + 0.181282i \(0.0580246\pi\)
−0.983431 + 0.181282i \(0.941975\pi\)
\(62\) 2.08941 2.79287i 0.265355 0.354695i
\(63\) 0 0
\(64\) 6.05543 + 5.22798i 0.756929 + 0.653497i
\(65\) −7.50275 + 5.27382i −0.930601 + 0.654137i
\(66\) 0 0
\(67\) 4.91266 0.600177 0.300089 0.953911i \(-0.402984\pi\)
0.300089 + 0.953911i \(0.402984\pi\)
\(68\) 3.26362 0.960415i 0.395772 0.116467i
\(69\) 0 0
\(70\) −3.46753 0.102725i −0.414449 0.0122780i
\(71\) −1.69810 −0.201528 −0.100764 0.994910i \(-0.532129\pi\)
−0.100764 + 0.994910i \(0.532129\pi\)
\(72\) 0 0
\(73\) 6.69321i 0.783381i −0.920097 0.391691i \(-0.871890\pi\)
0.920097 0.391691i \(-0.128110\pi\)
\(74\) −3.39675 + 4.54036i −0.394864 + 0.527807i
\(75\) 0 0
\(76\) 11.4166 3.35968i 1.30958 0.385381i
\(77\) −2.07838 −0.236854
\(78\) 0 0
\(79\) −12.7388 −1.43323 −0.716614 0.697470i \(-0.754309\pi\)
−0.716614 + 0.697470i \(0.754309\pi\)
\(80\) 3.36502 8.28714i 0.376221 0.926530i
\(81\) 0 0
\(82\) 6.92178 9.25221i 0.764383 1.02174i
\(83\) 2.43343 0.267104 0.133552 0.991042i \(-0.457362\pi\)
0.133552 + 0.991042i \(0.457362\pi\)
\(84\) 0 0
\(85\) −2.18728 3.11172i −0.237244 0.337513i
\(86\) 9.35574 12.5056i 1.00886 1.34852i
\(87\) 0 0
\(88\) 1.86815 5.02253i 0.199145 0.535403i
\(89\) −12.0320 −1.27539 −0.637695 0.770289i \(-0.720112\pi\)
−0.637695 + 0.770289i \(0.720112\pi\)
\(90\) 0 0
\(91\) 4.49919i 0.471644i
\(92\) −0.813800 + 0.239485i −0.0848445 + 0.0249680i
\(93\) 0 0
\(94\) −2.58908 1.93695i −0.267043 0.199781i
\(95\) −7.65144 10.8853i −0.785021 1.11680i
\(96\) 0 0
\(97\) 2.20448i 0.223831i −0.993718 0.111916i \(-0.964301\pi\)
0.993718 0.111916i \(-0.0356987\pi\)
\(98\) 4.91066 6.56398i 0.496051 0.663062i
\(99\) 0 0
\(100\) −9.98246 0.591978i −0.998246 0.0591978i
\(101\) 2.45373i 0.244156i 0.992521 + 0.122078i \(0.0389558\pi\)
−0.992521 + 0.122078i \(0.961044\pi\)
\(102\) 0 0
\(103\) 14.7324i 1.45163i 0.687891 + 0.725814i \(0.258537\pi\)
−0.687891 + 0.725814i \(0.741463\pi\)
\(104\) −10.8725 4.04409i −1.06614 0.396556i
\(105\) 0 0
\(106\) −10.4219 + 13.9307i −1.01226 + 1.35307i
\(107\) −11.1789 −1.08070 −0.540352 0.841439i \(-0.681709\pi\)
−0.540352 + 0.841439i \(0.681709\pi\)
\(108\) 0 0
\(109\) 3.23427i 0.309787i −0.987931 0.154894i \(-0.950497\pi\)
0.987931 0.154894i \(-0.0495035\pi\)
\(110\) −5.98859 0.177411i −0.570990 0.0169155i
\(111\) 0 0
\(112\) −2.37679 3.68860i −0.224585 0.348540i
\(113\) 14.2007i 1.33589i −0.744210 0.667945i \(-0.767174\pi\)
0.744210 0.667945i \(-0.232826\pi\)
\(114\) 0 0
\(115\) 0.545411 + 0.775923i 0.0508598 + 0.0723552i
\(116\) 14.2900 4.20527i 1.32680 0.390449i
\(117\) 0 0
\(118\) 14.0436 + 10.5063i 1.29282 + 0.967183i
\(119\) −1.86601 −0.171057
\(120\) 0 0
\(121\) 7.41053 0.673685
\(122\) 3.20660 + 2.39893i 0.290312 + 0.217189i
\(123\) 0 0
\(124\) −1.39255 4.73206i −0.125054 0.424951i
\(125\) 2.95249 + 10.7834i 0.264079 + 0.964501i
\(126\) 0 0
\(127\) 20.3182i 1.80294i 0.432837 + 0.901472i \(0.357513\pi\)
−0.432837 + 0.901472i \(0.642487\pi\)
\(128\) 11.0501 2.42815i 0.976698 0.214620i
\(129\) 0 0
\(130\) −0.384053 + 12.9638i −0.0336836 + 1.13700i
\(131\) 1.49044i 0.130221i −0.997878 0.0651104i \(-0.979260\pi\)
0.997878 0.0651104i \(-0.0207399\pi\)
\(132\) 0 0
\(133\) −6.52759 −0.566014
\(134\) 4.16184 5.56305i 0.359528 0.480575i
\(135\) 0 0
\(136\) 1.67726 4.50932i 0.143824 0.386671i
\(137\) 7.45176i 0.636647i −0.947982 0.318324i \(-0.896880\pi\)
0.947982 0.318324i \(-0.103120\pi\)
\(138\) 0 0
\(139\) 2.71608i 0.230375i −0.993344 0.115187i \(-0.963253\pi\)
0.993344 0.115187i \(-0.0367468\pi\)
\(140\) −3.05390 + 3.83957i −0.258102 + 0.324503i
\(141\) 0 0
\(142\) −1.43857 + 1.92291i −0.120722 + 0.161367i
\(143\) 7.77033i 0.649788i
\(144\) 0 0
\(145\) −9.57722 13.6249i −0.795344 1.13149i
\(146\) −7.57933 5.67027i −0.627270 0.469275i
\(147\) 0 0
\(148\) 2.26386 + 7.69289i 0.186088 + 0.632352i
\(149\) 6.06321i 0.496718i −0.968668 0.248359i \(-0.920109\pi\)
0.968668 0.248359i \(-0.0798912\pi\)
\(150\) 0 0
\(151\) −13.8664 −1.12843 −0.564215 0.825628i \(-0.690821\pi\)
−0.564215 + 0.825628i \(0.690821\pi\)
\(152\) 5.86731 15.7743i 0.475902 1.27946i
\(153\) 0 0
\(154\) −1.76074 + 2.35354i −0.141884 + 0.189654i
\(155\) −4.51181 + 3.17144i −0.362398 + 0.254736i
\(156\) 0 0
\(157\) −11.6208 −0.927439 −0.463720 0.885982i \(-0.653486\pi\)
−0.463720 + 0.885982i \(0.653486\pi\)
\(158\) −10.7919 + 14.4253i −0.858557 + 1.14762i
\(159\) 0 0
\(160\) −6.53355 10.8311i −0.516522 0.856274i
\(161\) 0.465300 0.0366708
\(162\) 0 0
\(163\) 5.01908 0.393124 0.196562 0.980491i \(-0.437022\pi\)
0.196562 + 0.980491i \(0.437022\pi\)
\(164\) −4.61322 15.6763i −0.360232 1.22411i
\(165\) 0 0
\(166\) 2.06152 2.75559i 0.160005 0.213876i
\(167\) 3.74825i 0.290048i 0.989428 + 0.145024i \(0.0463260\pi\)
−0.989428 + 0.145024i \(0.953674\pi\)
\(168\) 0 0
\(169\) 3.82087 0.293913
\(170\) −5.37667 0.159283i −0.412372 0.0122165i
\(171\) 0 0
\(172\) −6.23540 21.1887i −0.475445 1.61562i
\(173\) 10.6039 0.806202 0.403101 0.915155i \(-0.367932\pi\)
0.403101 + 0.915155i \(0.367932\pi\)
\(174\) 0 0
\(175\) 5.16104 + 1.85726i 0.390138 + 0.140396i
\(176\) −4.10483 6.37039i −0.309413 0.480186i
\(177\) 0 0
\(178\) −10.1931 + 13.6249i −0.764006 + 1.02123i
\(179\) 15.7506i 1.17725i 0.808405 + 0.588627i \(0.200331\pi\)
−0.808405 + 0.588627i \(0.799669\pi\)
\(180\) 0 0
\(181\) 20.9558i 1.55764i −0.627250 0.778818i \(-0.715820\pi\)
0.627250 0.778818i \(-0.284180\pi\)
\(182\) 5.09485 + 3.81157i 0.377655 + 0.282532i
\(183\) 0 0
\(184\) −0.418234 + 1.12442i −0.0308326 + 0.0828936i
\(185\) 7.33484 5.15579i 0.539268 0.379061i
\(186\) 0 0
\(187\) −3.22269 −0.235667
\(188\) −4.38676 + 1.29093i −0.319938 + 0.0941510i
\(189\) 0 0
\(190\) −18.8084 0.557197i −1.36451 0.0404233i
\(191\) 18.2070 1.31741 0.658707 0.752400i \(-0.271104\pi\)
0.658707 + 0.752400i \(0.271104\pi\)
\(192\) 0 0
\(193\) 8.88723i 0.639717i −0.947465 0.319859i \(-0.896365\pi\)
0.947465 0.319859i \(-0.103635\pi\)
\(194\) −2.49634 1.86756i −0.179227 0.134083i
\(195\) 0 0
\(196\) −3.27285 11.1216i −0.233775 0.794398i
\(197\) 8.73792 0.622551 0.311276 0.950320i \(-0.399244\pi\)
0.311276 + 0.950320i \(0.399244\pi\)
\(198\) 0 0
\(199\) 9.72289 0.689237 0.344619 0.938743i \(-0.388008\pi\)
0.344619 + 0.938743i \(0.388008\pi\)
\(200\) −9.12716 + 10.8025i −0.645388 + 0.763855i
\(201\) 0 0
\(202\) 2.77859 + 2.07872i 0.195501 + 0.146258i
\(203\) −8.17051 −0.573457
\(204\) 0 0
\(205\) −14.9467 + 10.5063i −1.04392 + 0.733792i
\(206\) 16.6828 + 12.4808i 1.16235 + 0.869579i
\(207\) 0 0
\(208\) −13.7903 + 8.88596i −0.956189 + 0.616130i
\(209\) −11.2735 −0.779802
\(210\) 0 0
\(211\) 14.0843i 0.969600i 0.874625 + 0.484800i \(0.161108\pi\)
−0.874625 + 0.484800i \(0.838892\pi\)
\(212\) 6.94595 + 23.6033i 0.477050 + 1.62108i
\(213\) 0 0
\(214\) −9.47038 + 12.6589i −0.647382 + 0.865343i
\(215\) −20.2025 + 14.2007i −1.37780 + 0.968481i
\(216\) 0 0
\(217\) 2.70561i 0.183669i
\(218\) −3.66246 2.73997i −0.248053 0.185574i
\(219\) 0 0
\(220\) −5.27423 + 6.63113i −0.355589 + 0.447071i
\(221\) 6.97635i 0.469280i
\(222\) 0 0
\(223\) 6.23727i 0.417679i −0.977950 0.208839i \(-0.933031\pi\)
0.977950 0.208839i \(-0.0669686\pi\)
\(224\) −6.19047 0.433404i −0.413618 0.0289580i
\(225\) 0 0
\(226\) −16.0808 12.0304i −1.06968 0.800248i
\(227\) −9.75082 −0.647184 −0.323592 0.946197i \(-0.604891\pi\)
−0.323592 + 0.946197i \(0.604891\pi\)
\(228\) 0 0
\(229\) 26.7906i 1.77037i −0.465239 0.885185i \(-0.654032\pi\)
0.465239 0.885185i \(-0.345968\pi\)
\(230\) 1.34070 + 0.0397182i 0.0884033 + 0.00261894i
\(231\) 0 0
\(232\) 7.34404 19.7445i 0.482160 1.29629i
\(233\) 27.7728i 1.81946i 0.415201 + 0.909730i \(0.363711\pi\)
−0.415201 + 0.909730i \(0.636289\pi\)
\(234\) 0 0
\(235\) 2.94002 + 4.18259i 0.191786 + 0.272842i
\(236\) 23.7945 7.00222i 1.54889 0.455806i
\(237\) 0 0
\(238\) −1.58082 + 2.11306i −0.102470 + 0.136969i
\(239\) 6.89512 0.446008 0.223004 0.974817i \(-0.428414\pi\)
0.223004 + 0.974817i \(0.428414\pi\)
\(240\) 0 0
\(241\) 10.7239 0.690784 0.345392 0.938458i \(-0.387746\pi\)
0.345392 + 0.938458i \(0.387746\pi\)
\(242\) 6.27795 8.39162i 0.403562 0.539434i
\(243\) 0 0
\(244\) 5.43306 1.59884i 0.347816 0.102355i
\(245\) −10.6039 + 7.45370i −0.677461 + 0.476199i
\(246\) 0 0
\(247\) 24.4043i 1.55281i
\(248\) −6.53826 2.43193i −0.415180 0.154428i
\(249\) 0 0
\(250\) 14.7123 + 5.79200i 0.930490 + 0.366318i
\(251\) 15.6506i 0.987859i −0.869502 0.493930i \(-0.835560\pi\)
0.869502 0.493930i \(-0.164440\pi\)
\(252\) 0 0
\(253\) 0.803596 0.0505217
\(254\) 23.0081 + 17.2129i 1.44366 + 1.08003i
\(255\) 0 0
\(256\) 6.61163 14.5700i 0.413227 0.910628i
\(257\) 12.0836i 0.753755i −0.926263 0.376878i \(-0.876998\pi\)
0.926263 0.376878i \(-0.123002\pi\)
\(258\) 0 0
\(259\) 4.39850i 0.273310i
\(260\) 14.3548 + 11.4174i 0.890246 + 0.708079i
\(261\) 0 0
\(262\) −1.68777 1.26265i −0.104270 0.0780070i
\(263\) 7.88836i 0.486417i −0.969974 0.243208i \(-0.921800\pi\)
0.969974 0.243208i \(-0.0781999\pi\)
\(264\) 0 0
\(265\) 22.5047 15.8190i 1.38245 0.971751i
\(266\) −5.52996 + 7.39179i −0.339063 + 0.453219i
\(267\) 0 0
\(268\) −2.77378 9.42566i −0.169435 0.575764i
\(269\) 27.9544i 1.70441i −0.523207 0.852206i \(-0.675265\pi\)
0.523207 0.852206i \(-0.324735\pi\)
\(270\) 0 0
\(271\) −8.19311 −0.497696 −0.248848 0.968543i \(-0.580052\pi\)
−0.248848 + 0.968543i \(0.580052\pi\)
\(272\) −3.68539 5.71946i −0.223460 0.346793i
\(273\) 0 0
\(274\) −8.43831 6.31288i −0.509777 0.381375i
\(275\) 8.91337 + 3.20758i 0.537497 + 0.193424i
\(276\) 0 0
\(277\) −28.7989 −1.73036 −0.865180 0.501461i \(-0.832796\pi\)
−0.865180 + 0.501461i \(0.832796\pi\)
\(278\) −3.07566 2.30097i −0.184466 0.138003i
\(279\) 0 0
\(280\) 1.76074 + 6.71096i 0.105224 + 0.401057i
\(281\) 26.2790 1.56767 0.783836 0.620968i \(-0.213260\pi\)
0.783836 + 0.620968i \(0.213260\pi\)
\(282\) 0 0
\(283\) 8.01908 0.476685 0.238342 0.971181i \(-0.423396\pi\)
0.238342 + 0.971181i \(0.423396\pi\)
\(284\) 0.958779 + 3.25806i 0.0568931 + 0.193330i
\(285\) 0 0
\(286\) 8.79905 + 6.58276i 0.520299 + 0.389247i
\(287\) 8.96313i 0.529077i
\(288\) 0 0
\(289\) 14.1066 0.829800
\(290\) −23.5423 0.697437i −1.38245 0.0409549i
\(291\) 0 0
\(292\) −12.8419 + 3.77911i −0.751516 + 0.221156i
\(293\) 10.3414 0.604154 0.302077 0.953284i \(-0.402320\pi\)
0.302077 + 0.953284i \(0.402320\pi\)
\(294\) 0 0
\(295\) −15.9471 22.6870i −0.928476 1.32089i
\(296\) 10.6292 + 3.95358i 0.617811 + 0.229797i
\(297\) 0 0
\(298\) −6.86593 5.13655i −0.397732 0.297552i
\(299\) 1.73959i 0.100603i
\(300\) 0 0
\(301\) 12.1149i 0.698291i
\(302\) −11.7471 + 15.7022i −0.675971 + 0.903558i
\(303\) 0 0
\(304\) −12.8921 20.0075i −0.739411 1.14751i
\(305\) −3.64124 5.18018i −0.208497 0.296616i
\(306\) 0 0
\(307\) −15.5835 −0.889395 −0.444698 0.895681i \(-0.646689\pi\)
−0.444698 + 0.895681i \(0.646689\pi\)
\(308\) 1.17349 + 3.98768i 0.0668660 + 0.227219i
\(309\) 0 0
\(310\) −0.230952 + 7.79587i −0.0131172 + 0.442776i
\(311\) 28.1450 1.59596 0.797978 0.602687i \(-0.205903\pi\)
0.797978 + 0.602687i \(0.205903\pi\)
\(312\) 0 0
\(313\) 7.10412i 0.401548i −0.979638 0.200774i \(-0.935654\pi\)
0.979638 0.200774i \(-0.0643457\pi\)
\(314\) −9.84474 + 13.1593i −0.555571 + 0.742621i
\(315\) 0 0
\(316\) 7.19257 + 24.4413i 0.404613 + 1.37493i
\(317\) −10.6039 −0.595576 −0.297788 0.954632i \(-0.596249\pi\)
−0.297788 + 0.954632i \(0.596249\pi\)
\(318\) 0 0
\(319\) −14.1109 −0.790057
\(320\) −17.8000 1.77722i −0.995053 0.0993495i
\(321\) 0 0
\(322\) 0.394187 0.526902i 0.0219672 0.0293631i
\(323\) −10.1215 −0.563177
\(324\) 0 0
\(325\) 6.94362 19.2953i 0.385163 1.07031i
\(326\) 4.25199 5.68356i 0.235496 0.314783i
\(327\) 0 0
\(328\) −21.6599 8.05648i −1.19597 0.444845i
\(329\) 2.50819 0.138281
\(330\) 0 0
\(331\) 32.0939i 1.76404i −0.471214 0.882019i \(-0.656184\pi\)
0.471214 0.882019i \(-0.343816\pi\)
\(332\) −1.37396 4.66889i −0.0754058 0.256239i
\(333\) 0 0
\(334\) 4.24449 + 3.17539i 0.232248 + 0.173750i
\(335\) −8.98696 + 6.31710i −0.491010 + 0.345140i
\(336\) 0 0
\(337\) 22.7507i 1.23931i 0.784875 + 0.619654i \(0.212727\pi\)
−0.784875 + 0.619654i \(0.787273\pi\)
\(338\) 3.23692 4.32672i 0.176065 0.235343i
\(339\) 0 0
\(340\) −4.73531 + 5.95355i −0.256808 + 0.322877i
\(341\) 4.67272i 0.253042i
\(342\) 0 0
\(343\) 14.0380i 0.757979i
\(344\) −29.2763 10.8895i −1.57847 0.587120i
\(345\) 0 0
\(346\) 8.98330 12.0078i 0.482945 0.645543i
\(347\) 23.2109 1.24603 0.623013 0.782211i \(-0.285908\pi\)
0.623013 + 0.782211i \(0.285908\pi\)
\(348\) 0 0
\(349\) 27.0786i 1.44948i 0.689021 + 0.724742i \(0.258041\pi\)
−0.689021 + 0.724742i \(0.741959\pi\)
\(350\) 6.47540 4.27091i 0.346125 0.228290i
\(351\) 0 0
\(352\) −10.6912 0.748510i −0.569845 0.0398957i
\(353\) 10.9128i 0.580832i −0.956900 0.290416i \(-0.906206\pi\)
0.956900 0.290416i \(-0.0937937\pi\)
\(354\) 0 0
\(355\) 3.10642 2.18356i 0.164871 0.115891i
\(356\) 6.79349 + 23.0852i 0.360054 + 1.22351i
\(357\) 0 0
\(358\) 17.8358 + 13.3434i 0.942652 + 0.705219i
\(359\) 4.15889 0.219498 0.109749 0.993959i \(-0.464995\pi\)
0.109749 + 0.993959i \(0.464995\pi\)
\(360\) 0 0
\(361\) −16.4067 −0.863508
\(362\) −23.7302 17.7531i −1.24723 0.933081i
\(363\) 0 0
\(364\) 8.63237 2.54033i 0.452459 0.133149i
\(365\) 8.60668 + 12.2442i 0.450494 + 0.640891i
\(366\) 0 0
\(367\) 29.0413i 1.51595i 0.652286 + 0.757973i \(0.273810\pi\)
−0.652286 + 0.757973i \(0.726190\pi\)
\(368\) 0.918973 + 1.42618i 0.0479048 + 0.0743447i
\(369\) 0 0
\(370\) 0.375457 12.6737i 0.0195191 0.658875i
\(371\) 13.4955i 0.700649i
\(372\) 0 0
\(373\) −8.47589 −0.438865 −0.219432 0.975628i \(-0.570421\pi\)
−0.219432 + 0.975628i \(0.570421\pi\)
\(374\) −2.73016 + 3.64935i −0.141173 + 0.188703i
\(375\) 0 0
\(376\) −2.25448 + 6.06117i −0.116266 + 0.312581i
\(377\) 30.5466i 1.57323i
\(378\) 0 0
\(379\) 26.9629i 1.38499i 0.721421 + 0.692497i \(0.243489\pi\)
−0.721421 + 0.692497i \(0.756511\pi\)
\(380\) −16.5648 + 20.8264i −0.849757 + 1.06837i
\(381\) 0 0
\(382\) 15.4244 20.6175i 0.789180 1.05488i
\(383\) 28.1503i 1.43842i −0.694795 0.719208i \(-0.744505\pi\)
0.694795 0.719208i \(-0.255495\pi\)
\(384\) 0 0
\(385\) 3.80208 2.67255i 0.193772 0.136206i
\(386\) −10.0638 7.52897i −0.512235 0.383214i
\(387\) 0 0
\(388\) −4.22963 + 1.24469i −0.214727 + 0.0631896i
\(389\) 28.4441i 1.44217i −0.692844 0.721087i \(-0.743643\pi\)
0.692844 0.721087i \(-0.256357\pi\)
\(390\) 0 0
\(391\) 0.721484 0.0364870
\(392\) −15.3666 5.71568i −0.776131 0.288685i
\(393\) 0 0
\(394\) 7.40248 9.89475i 0.372931 0.498490i
\(395\) 23.3037 16.3806i 1.17254 0.824197i
\(396\) 0 0
\(397\) 18.9844 0.952800 0.476400 0.879229i \(-0.341941\pi\)
0.476400 + 0.879229i \(0.341941\pi\)
\(398\) 8.23690 11.0101i 0.412879 0.551887i
\(399\) 0 0
\(400\) 4.50048 + 19.4871i 0.225024 + 0.974353i
\(401\) 5.95556 0.297406 0.148703 0.988882i \(-0.452490\pi\)
0.148703 + 0.988882i \(0.452490\pi\)
\(402\) 0 0
\(403\) 10.1153 0.503880
\(404\) 4.70785 1.38542i 0.234224 0.0689274i
\(405\) 0 0
\(406\) −6.92178 + 9.25221i −0.343522 + 0.459179i
\(407\) 7.59643i 0.376541i
\(408\) 0 0
\(409\) −30.3615 −1.50128 −0.750641 0.660711i \(-0.770255\pi\)
−0.750641 + 0.660711i \(0.770255\pi\)
\(410\) −0.765095 + 25.8261i −0.0377853 + 1.27546i
\(411\) 0 0
\(412\) 28.2663 8.31819i 1.39258 0.409808i
\(413\) −13.6048 −0.669448
\(414\) 0 0
\(415\) −4.45159 + 3.12910i −0.218520 + 0.153602i
\(416\) −1.62034 + 23.1440i −0.0794438 + 1.13473i
\(417\) 0 0
\(418\) −9.55050 + 12.7660i −0.467130 + 0.624404i
\(419\) 2.72901i 0.133321i −0.997776 0.0666604i \(-0.978766\pi\)
0.997776 0.0666604i \(-0.0212344\pi\)
\(420\) 0 0
\(421\) 9.28319i 0.452435i −0.974077 0.226218i \(-0.927364\pi\)
0.974077 0.226218i \(-0.0726360\pi\)
\(422\) 15.9489 + 11.9317i 0.776379 + 0.580826i
\(423\) 0 0
\(424\) 32.6125 + 12.1304i 1.58380 + 0.589102i
\(425\) 8.00260 + 2.87982i 0.388183 + 0.139692i
\(426\) 0 0
\(427\) −3.10642 −0.150330
\(428\) 6.31181 + 21.4483i 0.305093 + 1.03674i
\(429\) 0 0
\(430\) −1.03413 + 34.9075i −0.0498702 + 1.68339i
\(431\) −16.1731 −0.779031 −0.389515 0.921020i \(-0.627358\pi\)
−0.389515 + 0.921020i \(0.627358\pi\)
\(432\) 0 0
\(433\) 25.0559i 1.20411i −0.798456 0.602054i \(-0.794349\pi\)
0.798456 0.602054i \(-0.205651\pi\)
\(434\) 3.06381 + 2.29210i 0.147068 + 0.110024i
\(435\) 0 0
\(436\) −6.20543 + 1.82613i −0.297186 + 0.0874558i
\(437\) 2.52386 0.120733
\(438\) 0 0
\(439\) −9.83550 −0.469423 −0.234711 0.972065i \(-0.575415\pi\)
−0.234711 + 0.972065i \(0.575415\pi\)
\(440\) 3.04088 + 11.5902i 0.144968 + 0.552539i
\(441\) 0 0
\(442\) 7.89996 + 5.91013i 0.375763 + 0.281116i
\(443\) 34.2623 1.62785 0.813926 0.580968i \(-0.197326\pi\)
0.813926 + 0.580968i \(0.197326\pi\)
\(444\) 0 0
\(445\) 22.0107 15.4717i 1.04341 0.733430i
\(446\) −7.06303 5.28401i −0.334444 0.250205i
\(447\) 0 0
\(448\) −5.73514 + 6.64287i −0.270960 + 0.313846i
\(449\) −39.1812 −1.84907 −0.924537 0.381091i \(-0.875548\pi\)
−0.924537 + 0.381091i \(0.875548\pi\)
\(450\) 0 0
\(451\) 15.4798i 0.728913i
\(452\) −27.2462 + 8.01798i −1.28155 + 0.377134i
\(453\) 0 0
\(454\) −8.26056 + 11.0417i −0.387687 + 0.518214i
\(455\) −5.78543 8.23059i −0.271225 0.385856i
\(456\) 0 0
\(457\) 31.7386i 1.48467i 0.670029 + 0.742335i \(0.266282\pi\)
−0.670029 + 0.742335i \(0.733718\pi\)
\(458\) −30.3374 22.6961i −1.41757 1.06052i
\(459\) 0 0
\(460\) 1.18077 1.48455i 0.0550539 0.0692175i
\(461\) 25.3865i 1.18237i −0.806537 0.591184i \(-0.798661\pi\)
0.806537 0.591184i \(-0.201339\pi\)
\(462\) 0 0
\(463\) 40.4827i 1.88139i −0.339252 0.940696i \(-0.610174\pi\)
0.339252 0.940696i \(-0.389826\pi\)
\(464\) −16.1368 25.0432i −0.749134 1.16260i
\(465\) 0 0
\(466\) 31.4497 + 23.5282i 1.45688 + 1.08992i
\(467\) 23.7161 1.09745 0.548724 0.836003i \(-0.315114\pi\)
0.548724 + 0.836003i \(0.315114\pi\)
\(468\) 0 0
\(469\) 5.38924i 0.248852i
\(470\) 7.22701 + 0.214099i 0.333357 + 0.00987567i
\(471\) 0 0
\(472\) 12.2286 32.8767i 0.562868 1.51327i
\(473\) 20.9230i 0.962042i
\(474\) 0 0
\(475\) 27.9943 + 10.0741i 1.28447 + 0.462229i
\(476\) 1.05358 + 3.58022i 0.0482910 + 0.164099i
\(477\) 0 0
\(478\) 5.84132 7.80797i 0.267176 0.357128i
\(479\) 16.8331 0.769123 0.384561 0.923099i \(-0.374353\pi\)
0.384561 + 0.923099i \(0.374353\pi\)
\(480\) 0 0
\(481\) −16.4444 −0.749801
\(482\) 9.08489 12.1436i 0.413806 0.553126i
\(483\) 0 0
\(484\) −4.18412 14.2182i −0.190187 0.646281i
\(485\) 2.83470 + 4.03276i 0.128717 + 0.183118i
\(486\) 0 0
\(487\) 12.5175i 0.567220i 0.958940 + 0.283610i \(0.0915322\pi\)
−0.958940 + 0.283610i \(0.908468\pi\)
\(488\) 2.79219 7.50682i 0.126397 0.339818i
\(489\) 0 0
\(490\) −0.542797 + 18.3223i −0.0245211 + 0.827718i
\(491\) 28.1884i 1.27213i −0.771637 0.636063i \(-0.780562\pi\)
0.771637 0.636063i \(-0.219438\pi\)
\(492\) 0 0
\(493\) −12.6690 −0.570583
\(494\) 27.6352 + 20.6745i 1.24337 + 0.930191i
\(495\) 0 0
\(496\) −8.29289 + 5.34361i −0.372362 + 0.239935i
\(497\) 1.86283i 0.0835595i
\(498\) 0 0
\(499\) 16.8003i 0.752086i −0.926602 0.376043i \(-0.877284\pi\)
0.926602 0.376043i \(-0.122716\pi\)
\(500\) 19.0226 11.7533i 0.850717 0.525625i
\(501\) 0 0
\(502\) −17.7226 13.2587i −0.791000 0.591764i
\(503\) 30.4521i 1.35779i 0.734234 + 0.678897i \(0.237542\pi\)
−0.734234 + 0.678897i \(0.762458\pi\)
\(504\) 0 0
\(505\) −3.15521 4.48873i −0.140405 0.199746i
\(506\) 0.680780 0.909985i 0.0302643 0.0404538i
\(507\) 0 0
\(508\) 38.9834 11.4720i 1.72961 0.508988i
\(509\) 21.7030i 0.961968i −0.876729 0.480984i \(-0.840279\pi\)
0.876729 0.480984i \(-0.159721\pi\)
\(510\) 0 0
\(511\) 7.34252 0.324814
\(512\) −10.8978 19.8302i −0.481621 0.876380i
\(513\) 0 0
\(514\) −13.6834 10.2368i −0.603548 0.451527i
\(515\) −18.9441 26.9507i −0.834778 1.18759i
\(516\) 0 0
\(517\) 4.33176 0.190511
\(518\) −4.98082 3.72626i −0.218845 0.163723i
\(519\) 0 0
\(520\) 25.0899 6.58276i 1.10026 0.288673i
\(521\) 25.8137 1.13092 0.565459 0.824777i \(-0.308699\pi\)
0.565459 + 0.824777i \(0.308699\pi\)
\(522\) 0 0
\(523\) −35.2453 −1.54117 −0.770584 0.637339i \(-0.780035\pi\)
−0.770584 + 0.637339i \(0.780035\pi\)
\(524\) −2.85964 + 0.841532i −0.124924 + 0.0367625i
\(525\) 0 0
\(526\) −8.93270 6.68275i −0.389484 0.291382i
\(527\) 4.19526i 0.182748i
\(528\) 0 0
\(529\) 22.8201 0.992178
\(530\) 1.15198 38.8854i 0.0500386 1.68907i
\(531\) 0 0
\(532\) 3.68560 + 12.5241i 0.159791 + 0.542991i
\(533\) 33.5099 1.45148
\(534\) 0 0
\(535\) 20.4501 14.3747i 0.884133 0.621473i
\(536\) −13.0234 4.84410i −0.562525 0.209233i
\(537\) 0 0
\(538\) −31.6553 23.6820i −1.36476 1.02101i
\(539\) 10.9821i 0.473033i
\(540\) 0 0
\(541\) 3.29103i 0.141492i −0.997494 0.0707462i \(-0.977462\pi\)
0.997494 0.0707462i \(-0.0225380\pi\)
\(542\) −6.94093 + 9.27781i −0.298138 + 0.398516i
\(543\) 0 0
\(544\) −9.59881 0.672026i −0.411545 0.0288129i
\(545\) 4.15889 + 5.91661i 0.178147 + 0.253440i
\(546\) 0 0
\(547\) 32.4815 1.38881 0.694404 0.719585i \(-0.255668\pi\)
0.694404 + 0.719585i \(0.255668\pi\)
\(548\) −14.2973 + 4.20740i −0.610750 + 0.179731i
\(549\) 0 0
\(550\) 11.1833 7.37607i 0.476859 0.314517i
\(551\) −44.3181 −1.88801
\(552\) 0 0
\(553\) 13.9746i 0.594260i
\(554\) −24.3975 + 32.6117i −1.03655 + 1.38554i
\(555\) 0 0
\(556\) −5.21119 + 1.53355i −0.221004 + 0.0650368i
\(557\) 19.5774 0.829523 0.414761 0.909930i \(-0.363865\pi\)
0.414761 + 0.909930i \(0.363865\pi\)
\(558\) 0 0
\(559\) 45.2933 1.91570
\(560\) 9.09107 + 3.69146i 0.384168 + 0.155993i
\(561\) 0 0
\(562\) 22.2627 29.7581i 0.939093 1.25527i
\(563\) 7.22281 0.304405 0.152203 0.988349i \(-0.451363\pi\)
0.152203 + 0.988349i \(0.451363\pi\)
\(564\) 0 0
\(565\) 18.2604 + 25.9780i 0.768222 + 1.09290i
\(566\) 6.79349 9.08073i 0.285552 0.381692i
\(567\) 0 0
\(568\) 4.50164 + 1.67440i 0.188885 + 0.0702564i
\(569\) 13.6522 0.572329 0.286165 0.958180i \(-0.407620\pi\)
0.286165 + 0.958180i \(0.407620\pi\)
\(570\) 0 0
\(571\) 42.9453i 1.79721i 0.438762 + 0.898603i \(0.355417\pi\)
−0.438762 + 0.898603i \(0.644583\pi\)
\(572\) 14.9085 4.38727i 0.623356 0.183441i
\(573\) 0 0
\(574\) 10.1498 + 7.59326i 0.423643 + 0.316937i
\(575\) −1.99549 0.718100i −0.0832177 0.0299468i
\(576\) 0 0
\(577\) 3.16155i 0.131617i 0.997832 + 0.0658086i \(0.0209627\pi\)
−0.997832 + 0.0658086i \(0.979037\pi\)
\(578\) 11.9506 15.9742i 0.497081 0.664439i
\(579\) 0 0
\(580\) −20.7340 + 26.0682i −0.860931 + 1.08242i
\(581\) 2.66950i 0.110749i
\(582\) 0 0
\(583\) 23.3073i 0.965290i
\(584\) −6.59981 + 17.7436i −0.273102 + 0.734236i
\(585\) 0 0
\(586\) 8.76092 11.7106i 0.361910 0.483759i
\(587\) 15.2097 0.627773 0.313886 0.949461i \(-0.398369\pi\)
0.313886 + 0.949461i \(0.398369\pi\)
\(588\) 0 0
\(589\) 14.6757i 0.604700i
\(590\) −39.2004 1.16131i −1.61386 0.0478103i
\(591\) 0 0
\(592\) 13.4817 8.68709i 0.554095 0.357037i
\(593\) 20.6555i 0.848219i −0.905611 0.424110i \(-0.860587\pi\)
0.905611 0.424110i \(-0.139413\pi\)
\(594\) 0 0
\(595\) 3.41358 2.39947i 0.139943 0.0983687i
\(596\) −11.6332 + 3.42340i −0.476513 + 0.140228i
\(597\) 0 0
\(598\) −1.96990 1.47372i −0.0805550 0.0602650i
\(599\) 33.1741 1.35546 0.677728 0.735313i \(-0.262965\pi\)
0.677728 + 0.735313i \(0.262965\pi\)
\(600\) 0 0
\(601\) 48.2851 1.96959 0.984796 0.173716i \(-0.0555774\pi\)
0.984796 + 0.173716i \(0.0555774\pi\)
\(602\) 13.7188 + 10.2633i 0.559137 + 0.418302i
\(603\) 0 0
\(604\) 7.82921 + 26.6047i 0.318566 + 1.08253i
\(605\) −13.5564 + 9.52906i −0.551147 + 0.387411i
\(606\) 0 0
\(607\) 0.630607i 0.0255955i 0.999918 + 0.0127978i \(0.00407377\pi\)
−0.999918 + 0.0127978i \(0.995926\pi\)
\(608\) −33.5781 2.35085i −1.36177 0.0953395i
\(609\) 0 0
\(610\) −8.95073 0.265165i −0.362405 0.0107362i
\(611\) 9.37720i 0.379361i
\(612\) 0 0
\(613\) 22.1293 0.893794 0.446897 0.894585i \(-0.352529\pi\)
0.446897 + 0.894585i \(0.352529\pi\)
\(614\) −13.2018 + 17.6466i −0.532781 + 0.712158i
\(615\) 0 0
\(616\) 5.50976 + 2.04938i 0.221995 + 0.0825718i
\(617\) 20.2904i 0.816860i −0.912790 0.408430i \(-0.866076\pi\)
0.912790 0.408430i \(-0.133924\pi\)
\(618\) 0 0
\(619\) 20.6122i 0.828473i −0.910169 0.414236i \(-0.864049\pi\)
0.910169 0.414236i \(-0.135951\pi\)
\(620\) 8.63232 + 6.86593i 0.346682 + 0.275742i
\(621\) 0 0
\(622\) 23.8435 31.8711i 0.956036 1.27792i
\(623\) 13.1992i 0.528816i
\(624\) 0 0
\(625\) −19.2674 15.9301i −0.770695 0.637204i
\(626\) −8.04464 6.01837i −0.321528 0.240542i
\(627\) 0 0
\(628\) 6.56131 + 22.2962i 0.261825 + 0.889714i
\(629\) 6.82022i 0.271940i
\(630\) 0 0
\(631\) 24.4121 0.971829 0.485915 0.874006i \(-0.338487\pi\)
0.485915 + 0.874006i \(0.338487\pi\)
\(632\) 33.7704 + 12.5610i 1.34331 + 0.499651i
\(633\) 0 0
\(634\) −8.98330 + 12.0078i −0.356772 + 0.476891i
\(635\) −26.1267 37.1689i −1.03681 1.47500i
\(636\) 0 0
\(637\) 23.7736 0.941945
\(638\) −11.9542 + 15.9790i −0.473273 + 0.632615i
\(639\) 0 0
\(640\) −17.0921 + 18.6510i −0.675625 + 0.737246i
\(641\) −6.81719 −0.269263 −0.134631 0.990896i \(-0.542985\pi\)
−0.134631 + 0.990896i \(0.542985\pi\)
\(642\) 0 0
\(643\) −15.9317 −0.628286 −0.314143 0.949376i \(-0.601717\pi\)
−0.314143 + 0.949376i \(0.601717\pi\)
\(644\) −0.262717 0.892747i −0.0103525 0.0351792i
\(645\) 0 0
\(646\) −8.57463 + 11.4615i −0.337364 + 0.450948i
\(647\) 32.9746i 1.29636i −0.761485 0.648182i \(-0.775530\pi\)
0.761485 0.648182i \(-0.224470\pi\)
\(648\) 0 0
\(649\) −23.4961 −0.922304
\(650\) −15.9674 24.2092i −0.626293 0.949563i
\(651\) 0 0
\(652\) −2.83386 9.62984i −0.110983 0.377133i
\(653\) −9.46910 −0.370555 −0.185277 0.982686i \(-0.559318\pi\)
−0.185277 + 0.982686i \(0.559318\pi\)
\(654\) 0 0
\(655\) 1.91653 + 2.72654i 0.0748852 + 0.106535i
\(656\) −27.4726 + 17.7023i −1.07263 + 0.691158i
\(657\) 0 0
\(658\) 2.12485 2.84025i 0.0828353 0.110724i
\(659\) 41.5026i 1.61671i 0.588695 + 0.808356i \(0.299642\pi\)
−0.588695 + 0.808356i \(0.700358\pi\)
\(660\) 0 0
\(661\) 39.7673i 1.54677i 0.633937 + 0.773385i \(0.281438\pi\)
−0.633937 + 0.773385i \(0.718562\pi\)
\(662\) −36.3428 27.1888i −1.41250 1.05672i
\(663\) 0 0
\(664\) −6.45098 2.39947i −0.250347 0.0931175i
\(665\) 11.9412 8.39371i 0.463061 0.325494i
\(666\) 0 0
\(667\) 3.15908 0.122320
\(668\) 7.19157 2.11633i 0.278250 0.0818833i
\(669\) 0 0
\(670\) −0.460027 + 15.5284i −0.0177724 + 0.599914i
\(671\) −5.36493 −0.207111
\(672\) 0 0
\(673\) 16.8069i 0.647860i 0.946081 + 0.323930i \(0.105004\pi\)
−0.946081 + 0.323930i \(0.894996\pi\)
\(674\) 25.7627 + 19.2736i 0.992341 + 0.742392i
\(675\) 0 0
\(676\) −2.15733 7.33091i −0.0829744 0.281958i
\(677\) −8.73792 −0.335826 −0.167913 0.985802i \(-0.553703\pi\)
−0.167913 + 0.985802i \(0.553703\pi\)
\(678\) 0 0
\(679\) 2.41834 0.0928074
\(680\) 2.73016 + 10.4059i 0.104697 + 0.399047i
\(681\) 0 0
\(682\) 5.29135 + 3.95858i 0.202616 + 0.151582i
\(683\) −37.2358 −1.42479 −0.712395 0.701779i \(-0.752389\pi\)
−0.712395 + 0.701779i \(0.752389\pi\)
\(684\) 0 0
\(685\) 9.58208 + 13.6319i 0.366112 + 0.520847i
\(686\) 15.8965 + 11.8925i 0.606930 + 0.454057i
\(687\) 0 0
\(688\) −37.1330 + 23.9271i −1.41568 + 0.912211i
\(689\) −50.4547 −1.92217
\(690\) 0 0
\(691\) 46.4665i 1.76767i −0.467798 0.883835i \(-0.654953\pi\)
0.467798 0.883835i \(-0.345047\pi\)
\(692\) −5.98718 20.3452i −0.227598 0.773409i
\(693\) 0 0
\(694\) 19.6635 26.2838i 0.746416 0.997720i
\(695\) 3.49255 + 4.96864i 0.132480 + 0.188471i
\(696\) 0 0
\(697\) 13.8980i 0.526425i
\(698\) 30.6635 + 22.9401i 1.16063 + 0.868294i
\(699\) 0 0
\(700\) 0.649406 10.9509i 0.0245452 0.413904i
\(701\) 12.8977i 0.487141i −0.969883 0.243571i \(-0.921681\pi\)
0.969883 0.243571i \(-0.0783187\pi\)
\(702\) 0 0
\(703\) 23.8582i 0.899827i
\(704\) −9.90487 + 11.4726i −0.373304 + 0.432388i
\(705\) 0 0
\(706\) −12.3576 9.24500i −0.465085 0.347940i
\(707\) −2.69177 −0.101234
\(708\) 0 0
\(709\) 18.8715i 0.708733i 0.935107 + 0.354367i \(0.115304\pi\)
−0.935107 + 0.354367i \(0.884696\pi\)
\(710\) 0.159012 5.36751i 0.00596761 0.201439i
\(711\) 0 0
\(712\) 31.8967 + 11.8641i 1.19538 + 0.444626i
\(713\) 1.04611i 0.0391772i
\(714\) 0 0
\(715\) −9.99172 14.2146i −0.373669 0.531597i
\(716\) 30.2198 8.89307i 1.12937 0.332350i
\(717\) 0 0
\(718\) 3.52327 4.70949i 0.131487 0.175757i
\(719\) 18.6339 0.694927 0.347463 0.937694i \(-0.387043\pi\)
0.347463 + 0.937694i \(0.387043\pi\)
\(720\) 0 0
\(721\) −16.1616 −0.601889
\(722\) −13.8992 + 18.5787i −0.517273 + 0.691429i
\(723\) 0 0
\(724\) −40.2069 + 11.8321i −1.49428 + 0.439735i
\(725\) 35.0401 + 12.6096i 1.30136 + 0.468308i
\(726\) 0 0
\(727\) 24.8278i 0.920812i −0.887708 0.460406i \(-0.847704\pi\)
0.887708 0.460406i \(-0.152296\pi\)
\(728\) 4.43641 11.9273i 0.164424 0.442055i
\(729\) 0 0
\(730\) 21.1565 + 0.626760i 0.783038 + 0.0231974i
\(731\) 18.7851i 0.694792i
\(732\) 0 0
\(733\) 0.393641 0.0145395 0.00726973 0.999974i \(-0.497686\pi\)
0.00726973 + 0.999974i \(0.497686\pi\)
\(734\) 32.8861 + 24.6028i 1.21385 + 0.908107i
\(735\) 0 0
\(736\) 2.39351 + 0.167573i 0.0882261 + 0.00617684i
\(737\) 9.30748i 0.342845i
\(738\) 0 0
\(739\) 12.8787i 0.473750i 0.971540 + 0.236875i \(0.0761233\pi\)
−0.971540 + 0.236875i \(0.923877\pi\)
\(740\) −14.0335 11.1619i −0.515883 0.410320i
\(741\) 0 0
\(742\) −15.2821 11.4329i −0.561025 0.419715i
\(743\) 17.7082i 0.649650i 0.945774 + 0.324825i \(0.105305\pi\)
−0.945774 + 0.324825i \(0.894695\pi\)
\(744\) 0 0
\(745\) 7.79657 + 11.0917i 0.285644 + 0.406369i
\(746\) −7.18049 + 9.59802i −0.262896 + 0.351409i
\(747\) 0 0
\(748\) 1.81959 + 6.18321i 0.0665309 + 0.226081i
\(749\) 12.2634i 0.448093i
\(750\) 0 0
\(751\) −25.8147 −0.941993 −0.470996 0.882135i \(-0.656106\pi\)
−0.470996 + 0.882135i \(0.656106\pi\)
\(752\) 4.95369 + 7.68777i 0.180643 + 0.280344i
\(753\) 0 0
\(754\) 34.5907 + 25.8780i 1.25972 + 0.942423i
\(755\) 25.3664 17.8305i 0.923178 0.648919i
\(756\) 0 0
\(757\) −9.20871 −0.334696 −0.167348 0.985898i \(-0.553520\pi\)
−0.167348 + 0.985898i \(0.553520\pi\)
\(758\) 30.5326 + 22.8421i 1.10899 + 0.829663i
\(759\) 0 0
\(760\) 9.55050 + 36.4013i 0.346433 + 1.32041i
\(761\) 6.94667 0.251816 0.125908 0.992042i \(-0.459816\pi\)
0.125908 + 0.992042i \(0.459816\pi\)
\(762\) 0 0
\(763\) 3.54803 0.128447
\(764\) −10.2800 34.9329i −0.371918 1.26383i
\(765\) 0 0
\(766\) −31.8772 23.8480i −1.15177 0.861664i
\(767\) 50.8634i 1.83657i
\(768\) 0 0
\(769\) 0.468151 0.0168820 0.00844098 0.999964i \(-0.497313\pi\)
0.00844098 + 0.999964i \(0.497313\pi\)
\(770\) 0.194622 6.56954i 0.00701369 0.236750i
\(771\) 0 0
\(772\) −17.0515 + 5.01789i −0.613696 + 0.180598i
\(773\) −14.0083 −0.503843 −0.251921 0.967748i \(-0.581062\pi\)
−0.251921 + 0.967748i \(0.581062\pi\)
\(774\) 0 0
\(775\) 4.17558 11.6033i 0.149991 0.416803i
\(776\) −2.17372 + 5.84405i −0.0780320 + 0.209789i
\(777\) 0 0
\(778\) −32.2099 24.0969i −1.15478 0.863916i
\(779\) 48.6174i 1.74190i
\(780\) 0 0
\(781\) 3.21720i 0.115121i
\(782\) 0.611217 0.817002i 0.0218571 0.0292159i
\(783\) 0 0
\(784\) −19.4905 + 12.5589i −0.696088 + 0.448532i
\(785\) 21.2584 14.9429i 0.758746 0.533337i
\(786\) 0 0
\(787\) −30.3214 −1.08084 −0.540421 0.841395i \(-0.681735\pi\)
−0.540421 + 0.841395i \(0.681735\pi\)
\(788\) −4.93359 16.7650i −0.175752 0.597228i
\(789\) 0 0
\(790\) 1.19288 40.2660i 0.0424406 1.43260i
\(791\) 15.5783 0.553901
\(792\) 0 0
\(793\) 11.6138i 0.412417i
\(794\) 16.0829 21.4978i 0.570763 0.762927i
\(795\) 0 0
\(796\) −5.48972 18.6548i −0.194578 0.661202i
\(797\) −12.7941 −0.453190 −0.226595 0.973989i \(-0.572759\pi\)
−0.226595 + 0.973989i \(0.572759\pi\)
\(798\) 0 0
\(799\) 3.88914 0.137588
\(800\) 25.8796 + 11.4125i 0.914983 + 0.403492i
\(801\) 0 0
\(802\) 5.04535 6.74402i 0.178157 0.238140i
\(803\) 12.6809 0.447499
\(804\) 0 0
\(805\) −0.851195 + 0.598321i −0.0300007 + 0.0210880i
\(806\) 8.56935 11.4545i 0.301843 0.403467i
\(807\) 0 0
\(808\) 2.41949 6.50481i 0.0851174 0.228838i
\(809\) 36.8282 1.29481 0.647405 0.762146i \(-0.275854\pi\)
0.647405 + 0.762146i \(0.275854\pi\)
\(810\) 0 0
\(811\) 20.4801i 0.719153i −0.933116 0.359576i \(-0.882921\pi\)
0.933116 0.359576i \(-0.117079\pi\)
\(812\) 4.61322 + 15.6763i 0.161892 + 0.550131i
\(813\) 0 0
\(814\) −8.60213 6.43544i −0.301504 0.225562i
\(815\) −9.18163 + 6.45394i −0.321619 + 0.226072i
\(816\) 0 0
\(817\) 65.7131i 2.29901i
\(818\) −25.7213 + 34.3811i −0.899323 + 1.20211i
\(819\) 0 0
\(820\) 28.5971 + 22.7454i 0.998652 + 0.794303i
\(821\) 37.8925i 1.32246i 0.750184 + 0.661229i \(0.229965\pi\)
−0.750184 + 0.661229i \(0.770035\pi\)
\(822\) 0 0
\(823\) 1.89215i 0.0659562i 0.999456 + 0.0329781i \(0.0104992\pi\)
−0.999456 + 0.0329781i \(0.989501\pi\)
\(824\) 14.5268 39.0554i 0.506066 1.36056i
\(825\) 0 0
\(826\) −11.5255 + 15.4059i −0.401024 + 0.536041i
\(827\) −45.9585 −1.59813 −0.799067 0.601242i \(-0.794673\pi\)
−0.799067 + 0.601242i \(0.794673\pi\)
\(828\) 0 0
\(829\) 44.1972i 1.53503i −0.641029 0.767517i \(-0.721492\pi\)
0.641029 0.767517i \(-0.278508\pi\)
\(830\) −0.227869 + 7.69180i −0.00790945 + 0.266986i
\(831\) 0 0
\(832\) 24.8353 + 21.4416i 0.861009 + 0.743355i
\(833\) 9.85996i 0.341627i
\(834\) 0 0
\(835\) −4.81981 6.85685i −0.166796 0.237291i
\(836\) 6.36521 + 21.6298i 0.220145 + 0.748083i
\(837\) 0 0
\(838\) −3.09030 2.31192i −0.106753 0.0798640i
\(839\) 29.2610 1.01020 0.505102 0.863060i \(-0.331455\pi\)
0.505102 + 0.863060i \(0.331455\pi\)
\(840\) 0 0
\(841\) −26.4724 −0.912841
\(842\) −10.5122 7.86441i −0.362274 0.271025i
\(843\) 0 0
\(844\) 27.0227 7.95223i 0.930160 0.273727i
\(845\) −6.98970 + 4.91319i −0.240453 + 0.169019i
\(846\) 0 0
\(847\) 8.12942i 0.279330i
\(848\) 41.3645 26.6537i 1.42046 0.915291i
\(849\) 0 0
\(850\) 10.0406 6.62238i 0.344390 0.227146i
\(851\) 1.70066i 0.0582978i
\(852\) 0 0
\(853\) 10.0803 0.345143 0.172572 0.984997i \(-0.444792\pi\)
0.172572 + 0.984997i \(0.444792\pi\)
\(854\) −2.63165 + 3.51768i −0.0900532 + 0.120372i
\(855\) 0 0
\(856\) 29.6351 + 11.0229i 1.01291 + 0.376754i
\(857\) 43.9269i 1.50052i 0.661145 + 0.750258i \(0.270071\pi\)
−0.661145 + 0.750258i \(0.729929\pi\)
\(858\) 0 0
\(859\) 9.28531i 0.316811i −0.987374 0.158405i \(-0.949365\pi\)
0.987374 0.158405i \(-0.0506353\pi\)
\(860\) 38.6529 + 30.7435i 1.31805 + 1.04835i
\(861\) 0 0
\(862\) −13.7013 + 18.3143i −0.466668 + 0.623787i
\(863\) 33.4004i 1.13696i 0.822696 + 0.568481i \(0.192469\pi\)
−0.822696 + 0.568481i \(0.807531\pi\)
\(864\) 0 0
\(865\) −19.3983 + 13.6354i −0.659561 + 0.463618i
\(866\) −28.3730 21.2265i −0.964155 0.721305i
\(867\) 0 0
\(868\) 5.19111 1.52764i 0.176198 0.0518514i
\(869\) 24.1348i 0.818718i
\(870\) 0 0
\(871\) 20.1484 0.682703
\(872\) −3.18914 + 8.57401i −0.107998 + 0.290353i
\(873\) 0 0
\(874\) 2.13813 2.85800i 0.0723233 0.0966731i
\(875\) −11.8295 + 3.23892i −0.399912 + 0.109495i
\(876\) 0 0
\(877\) 5.85859 0.197830 0.0989152 0.995096i \(-0.468463\pi\)
0.0989152 + 0.995096i \(0.468463\pi\)
\(878\) −8.33231 + 11.1376i −0.281202 + 0.375877i
\(879\) 0 0
\(880\) 15.7007 + 6.37533i 0.529271 + 0.214912i
\(881\) −33.5615 −1.13071 −0.565357 0.824846i \(-0.691262\pi\)
−0.565357 + 0.824846i \(0.691262\pi\)
\(882\) 0 0
\(883\) 0.194722 0.00655291 0.00327645 0.999995i \(-0.498957\pi\)
0.00327645 + 0.999995i \(0.498957\pi\)
\(884\) 13.3852 3.93897i 0.450191 0.132482i
\(885\) 0 0
\(886\) 29.0259 38.7984i 0.975144 1.30346i
\(887\) 7.68201i 0.257937i −0.991649 0.128968i \(-0.958833\pi\)
0.991649 0.128968i \(-0.0411665\pi\)
\(888\) 0 0
\(889\) −22.2892 −0.747556
\(890\) 1.12669 38.0319i 0.0377667 1.27483i
\(891\) 0 0
\(892\) −11.9671 + 3.52168i −0.400689 + 0.117915i
\(893\) 13.6048 0.455267
\(894\) 0 0
\(895\) −20.2534 28.8133i −0.676996 0.963122i
\(896\) 2.66370 + 12.1220i 0.0889881 + 0.404969i
\(897\) 0 0
\(898\) −33.1930 + 44.3684i −1.10766 + 1.48059i
\(899\) 18.3693i 0.612652i
\(900\) 0 0
\(901\) 20.9257i 0.697138i
\(902\) 17.5291 + 13.1139i 0.583656 + 0.436646i
\(903\) 0 0
\(904\) −14.0025 + 37.6459i −0.465718 + 1.25208i
\(905\) 26.9467 + 38.3355i 0.895739 + 1.27432i
\(906\) 0 0
\(907\) −34.7134 −1.15264 −0.576320 0.817224i \(-0.695512\pi\)
−0.576320 + 0.817224i \(0.695512\pi\)
\(908\) 5.50549 + 18.7084i 0.182706 + 0.620859i
\(909\) 0 0
\(910\) −14.2215 0.421309i −0.471437 0.0139663i
\(911\) −18.8670 −0.625091 −0.312546 0.949903i \(-0.601182\pi\)
−0.312546 + 0.949903i \(0.601182\pi\)
\(912\) 0 0
\(913\) 4.61035i 0.152580i
\(914\) 35.9405 + 26.8879i 1.18881 + 0.889372i
\(915\) 0 0
\(916\) −51.4016 + 15.1264i −1.69836 + 0.499792i
\(917\) 1.63503 0.0539935
\(918\) 0 0
\(919\) −26.4932 −0.873931 −0.436965 0.899478i \(-0.643947\pi\)
−0.436965 + 0.899478i \(0.643947\pi\)
\(920\) −0.680780 2.59476i −0.0224446 0.0855467i
\(921\) 0 0
\(922\) −28.7474 21.5066i −0.946747 0.708282i
\(923\) −6.96447 −0.229238
\(924\) 0 0
\(925\) −6.78823 + 18.8635i −0.223196 + 0.620227i
\(926\) −45.8423 34.2956i −1.50647 1.12702i
\(927\) 0 0
\(928\) −42.0293 2.94253i −1.37968 0.0965933i
\(929\) −57.5829 −1.88923 −0.944617 0.328176i \(-0.893566\pi\)
−0.944617 + 0.328176i \(0.893566\pi\)
\(930\) 0 0
\(931\) 34.4916i 1.13042i
\(932\) 53.2863 15.6811i 1.74545 0.513650i
\(933\) 0 0
\(934\) 20.0914 26.8558i 0.657412 0.878750i
\(935\) 5.89543 4.14400i 0.192801 0.135523i
\(936\) 0 0
\(937\) 27.1596i 0.887267i 0.896208 + 0.443633i \(0.146311\pi\)
−0.896208 + 0.443633i \(0.853689\pi\)
\(938\) 6.10272 + 4.56558i 0.199261 + 0.149071i
\(939\) 0 0
\(940\) 6.36492 8.00242i 0.207601 0.261010i
\(941\) 47.4407i 1.54652i 0.634088 + 0.773261i \(0.281375\pi\)
−0.634088 + 0.773261i \(0.718625\pi\)
\(942\) 0 0
\(943\) 3.46555i 0.112854i
\(944\) −26.8696 41.6996i −0.874531 1.35721i
\(945\) 0 0
\(946\) 23.6930 + 17.7253i 0.770327 + 0.576299i
\(947\) −24.5863 −0.798947 −0.399473 0.916745i \(-0.630807\pi\)
−0.399473 + 0.916745i \(0.630807\pi\)
\(948\) 0 0
\(949\) 27.4511i 0.891099i
\(950\) 35.1236 23.1661i 1.13956 0.751606i
\(951\) 0 0
\(952\) 4.94677 + 1.83997i 0.160326 + 0.0596338i
\(953\) 50.0020i 1.61973i −0.586620 0.809863i \(-0.699542\pi\)
0.586620 0.809863i \(-0.300458\pi\)
\(954\) 0 0
\(955\) −33.3070 + 23.4121i −1.07779 + 0.757597i
\(956\) −3.89311 13.2293i −0.125912 0.427866i
\(957\) 0 0
\(958\) 14.2604 19.0616i 0.460733 0.615853i
\(959\) 8.17466 0.263973
\(960\) 0 0
\(961\) −24.9171 −0.803778
\(962\) −13.9312 + 18.6215i −0.449159 + 0.600382i
\(963\) 0 0
\(964\) −6.05489 20.5753i −0.195015 0.662686i
\(965\) 11.4279 + 16.2578i 0.367878 + 0.523358i
\(966\) 0 0
\(967\) 6.52916i 0.209964i 0.994474 + 0.104982i \(0.0334784\pi\)
−0.994474 + 0.104982i \(0.966522\pi\)
\(968\) −19.6452 7.30711i −0.631421 0.234860i
\(969\) 0 0
\(970\) 6.96813 + 0.206430i 0.223733 + 0.00662807i
\(971\) 22.2092i 0.712726i 0.934348 + 0.356363i \(0.115983\pi\)
−0.934348 + 0.356363i \(0.884017\pi\)
\(972\) 0 0
\(973\) 2.97956 0.0955204
\(974\) 14.1747 + 10.6044i 0.454185 + 0.339786i
\(975\) 0 0
\(976\) −6.13520 9.52138i −0.196383 0.304772i
\(977\) 48.6812i 1.55745i −0.627366 0.778725i \(-0.715867\pi\)
0.627366 0.778725i \(-0.284133\pi\)
\(978\) 0 0
\(979\) 22.7957i 0.728554i
\(980\) 20.2882 + 16.1367i 0.648083 + 0.515468i
\(981\) 0 0
\(982\) −31.9203 23.8803i −1.01862 0.762051i
\(983\) 1.13847i 0.0363115i 0.999835 + 0.0181558i \(0.00577948\pi\)
−0.999835 + 0.0181558i \(0.994221\pi\)
\(984\) 0 0
\(985\) −15.9847 + 11.2359i −0.509315 + 0.358007i
\(986\) −10.7328 + 14.3463i −0.341801 + 0.456878i
\(987\) 0 0
\(988\) 46.8233 13.7791i 1.48965 0.438372i
\(989\) 4.68416i 0.148948i
\(990\) 0 0
\(991\) 43.1309 1.37010 0.685049 0.728497i \(-0.259781\pi\)
0.685049 + 0.728497i \(0.259781\pi\)
\(992\) −0.974400 + 13.9177i −0.0309372 + 0.441888i
\(993\) 0 0
\(994\) −2.10946 1.57813i −0.0669079 0.0500552i
\(995\) −17.7865 + 12.5025i −0.563871 + 0.396355i
\(996\) 0 0
\(997\) −27.7853 −0.879969 −0.439984 0.898005i \(-0.645016\pi\)
−0.439984 + 0.898005i \(0.645016\pi\)
\(998\) −19.0245 14.2327i −0.602211 0.450527i
\(999\) 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 1080.2.d.i.109.13 yes 20
3.2 odd 2 inner 1080.2.d.i.109.8 yes 20
4.3 odd 2 4320.2.d.i.3889.6 20
5.4 even 2 1080.2.d.j.109.8 yes 20
8.3 odd 2 4320.2.d.j.3889.15 20
8.5 even 2 1080.2.d.j.109.7 yes 20
12.11 even 2 4320.2.d.i.3889.15 20
15.14 odd 2 1080.2.d.j.109.13 yes 20
20.19 odd 2 4320.2.d.j.3889.16 20
24.5 odd 2 1080.2.d.j.109.14 yes 20
24.11 even 2 4320.2.d.j.3889.6 20
40.19 odd 2 4320.2.d.i.3889.5 20
40.29 even 2 inner 1080.2.d.i.109.14 yes 20
60.59 even 2 4320.2.d.j.3889.5 20
120.29 odd 2 inner 1080.2.d.i.109.7 20
120.59 even 2 4320.2.d.i.3889.16 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1080.2.d.i.109.7 20 120.29 odd 2 inner
1080.2.d.i.109.8 yes 20 3.2 odd 2 inner
1080.2.d.i.109.13 yes 20 1.1 even 1 trivial
1080.2.d.i.109.14 yes 20 40.29 even 2 inner
1080.2.d.j.109.7 yes 20 8.5 even 2
1080.2.d.j.109.8 yes 20 5.4 even 2
1080.2.d.j.109.13 yes 20 15.14 odd 2
1080.2.d.j.109.14 yes 20 24.5 odd 2
4320.2.d.i.3889.5 20 40.19 odd 2
4320.2.d.i.3889.6 20 4.3 odd 2
4320.2.d.i.3889.15 20 12.11 even 2
4320.2.d.i.3889.16 20 120.59 even 2
4320.2.d.j.3889.5 20 60.59 even 2
4320.2.d.j.3889.6 20 24.11 even 2
4320.2.d.j.3889.15 20 8.3 odd 2
4320.2.d.j.3889.16 20 20.19 odd 2