Properties

Label 630.2.be.b.341.1
Level $630$
Weight $2$
Character 630.341
Analytic conductor $5.031$
Analytic rank $0$
Dimension $8$
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] = [630,2,Mod(341,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.341");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.be (of order \(6\), degree \(2\), 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: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 341.1
Root \(-0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 630.341
Dual form 630.2.be.b.521.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.63896 - 0.189469i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.63896 - 0.189469i) q^{7} -1.00000i q^{8} +(-0.866025 + 0.500000i) q^{10} +(4.67303 - 2.69798i) q^{11} +2.51764i q^{13} +(2.19067 + 1.48356i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.24969 - 3.89658i) q^{17} +(-2.48004 - 1.43185i) q^{19} +1.00000 q^{20} -5.39595 q^{22} +(-0.232051 - 0.133975i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(1.25882 - 2.18034i) q^{26} +(-1.15539 - 2.38014i) q^{28} -8.89898i q^{29} +(4.18154 - 2.41421i) q^{31} +(0.866025 - 0.500000i) q^{32} +4.49938i q^{34} +(-1.48356 + 2.19067i) q^{35} +(3.25882 - 5.64444i) q^{37} +(1.43185 + 2.48004i) q^{38} +(-0.866025 - 0.500000i) q^{40} -0.760279 q^{41} -5.86370 q^{43} +(4.67303 + 2.69798i) q^{44} +(0.133975 + 0.232051i) q^{46} +(-3.99768 + 6.92418i) q^{47} +(6.92820 + 1.00000i) q^{49} +1.00000i q^{50} +(-2.18034 + 1.25882i) q^{52} +(7.27319 - 4.19918i) q^{53} -5.39595i q^{55} +(-0.189469 + 2.63896i) q^{56} +(-4.44949 + 7.70674i) q^{58} +(-6.33573 - 10.9738i) q^{59} +(-2.27035 - 1.31079i) q^{61} -4.82843 q^{62} -1.00000 q^{64} +(2.18034 + 1.25882i) q^{65} +(-4.91119 - 8.50643i) q^{67} +(2.24969 - 3.89658i) q^{68} +(2.38014 - 1.15539i) q^{70} -4.76268i q^{71} +(10.0951 - 5.82843i) q^{73} +(-5.64444 + 3.25882i) q^{74} -2.86370i q^{76} +(-12.8431 + 6.23445i) q^{77} +(-4.29618 + 7.44120i) q^{79} +(0.500000 + 0.866025i) q^{80} +(0.658421 + 0.380139i) q^{82} -9.45001 q^{83} -4.49938 q^{85} +(5.07812 + 2.93185i) q^{86} +(-2.69798 - 4.67303i) q^{88} +(3.98502 - 6.90226i) q^{89} +(0.477014 - 6.64394i) q^{91} -0.267949i q^{92} +(6.92418 - 3.99768i) q^{94} +(-2.48004 + 1.43185i) q^{95} +6.16353i q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} + 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} + 4 q^{5} + 24 q^{11} - 4 q^{16} + 8 q^{20} + 12 q^{23} - 4 q^{25} + 8 q^{26} + 24 q^{37} - 4 q^{38} + 32 q^{41} - 16 q^{43} + 24 q^{44} + 8 q^{46} - 8 q^{47} + 24 q^{53} - 16 q^{58} - 24 q^{59} - 16 q^{62} - 8 q^{64} - 24 q^{67} - 16 q^{77} - 24 q^{79} + 4 q^{80} - 16 q^{83} - 16 q^{89} - 20 q^{91} - 12 q^{94} - 44 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) −2.63896 0.189469i −0.997433 0.0716124i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.866025 + 0.500000i −0.273861 + 0.158114i
\(11\) 4.67303 2.69798i 1.40897 0.813471i 0.413683 0.910421i \(-0.364242\pi\)
0.995289 + 0.0969504i \(0.0309088\pi\)
\(12\) 0 0
\(13\) 2.51764i 0.698267i 0.937073 + 0.349134i \(0.113524\pi\)
−0.937073 + 0.349134i \(0.886476\pi\)
\(14\) 2.19067 + 1.48356i 0.585481 + 0.396499i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.24969 3.89658i −0.545630 0.945058i −0.998567 0.0535160i \(-0.982957\pi\)
0.452937 0.891542i \(-0.350376\pi\)
\(18\) 0 0
\(19\) −2.48004 1.43185i −0.568960 0.328489i 0.187774 0.982212i \(-0.439873\pi\)
−0.756734 + 0.653723i \(0.773206\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) −5.39595 −1.15042
\(23\) −0.232051 0.133975i −0.0483859 0.0279356i 0.475612 0.879655i \(-0.342227\pi\)
−0.523998 + 0.851720i \(0.675560\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 1.25882 2.18034i 0.246875 0.427600i
\(27\) 0 0
\(28\) −1.15539 2.38014i −0.218349 0.449804i
\(29\) 8.89898i 1.65250i −0.563304 0.826250i \(-0.690470\pi\)
0.563304 0.826250i \(-0.309530\pi\)
\(30\) 0 0
\(31\) 4.18154 2.41421i 0.751027 0.433606i −0.0750380 0.997181i \(-0.523908\pi\)
0.826065 + 0.563575i \(0.190574\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 4.49938i 0.771637i
\(35\) −1.48356 + 2.19067i −0.250768 + 0.370291i
\(36\) 0 0
\(37\) 3.25882 5.64444i 0.535747 0.927940i −0.463380 0.886160i \(-0.653364\pi\)
0.999127 0.0417807i \(-0.0133031\pi\)
\(38\) 1.43185 + 2.48004i 0.232277 + 0.402316i
\(39\) 0 0
\(40\) −0.866025 0.500000i −0.136931 0.0790569i
\(41\) −0.760279 −0.118736 −0.0593678 0.998236i \(-0.518908\pi\)
−0.0593678 + 0.998236i \(0.518908\pi\)
\(42\) 0 0
\(43\) −5.86370 −0.894206 −0.447103 0.894482i \(-0.647544\pi\)
−0.447103 + 0.894482i \(0.647544\pi\)
\(44\) 4.67303 + 2.69798i 0.704486 + 0.406735i
\(45\) 0 0
\(46\) 0.133975 + 0.232051i 0.0197535 + 0.0342140i
\(47\) −3.99768 + 6.92418i −0.583121 + 1.01000i 0.411986 + 0.911190i \(0.364835\pi\)
−0.995107 + 0.0988053i \(0.968498\pi\)
\(48\) 0 0
\(49\) 6.92820 + 1.00000i 0.989743 + 0.142857i
\(50\) 1.00000i 0.141421i
\(51\) 0 0
\(52\) −2.18034 + 1.25882i −0.302359 + 0.174567i
\(53\) 7.27319 4.19918i 0.999050 0.576802i 0.0910826 0.995843i \(-0.470967\pi\)
0.907967 + 0.419042i \(0.137634\pi\)
\(54\) 0 0
\(55\) 5.39595i 0.727590i
\(56\) −0.189469 + 2.63896i −0.0253188 + 0.352646i
\(57\) 0 0
\(58\) −4.44949 + 7.70674i −0.584247 + 1.01194i
\(59\) −6.33573 10.9738i −0.824842 1.42867i −0.902040 0.431653i \(-0.857931\pi\)
0.0771977 0.997016i \(-0.475403\pi\)
\(60\) 0 0
\(61\) −2.27035 1.31079i −0.290689 0.167829i 0.347564 0.937656i \(-0.387009\pi\)
−0.638253 + 0.769827i \(0.720342\pi\)
\(62\) −4.82843 −0.613211
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 2.18034 + 1.25882i 0.270438 + 0.156137i
\(66\) 0 0
\(67\) −4.91119 8.50643i −0.599997 1.03923i −0.992821 0.119612i \(-0.961835\pi\)
0.392824 0.919614i \(-0.371498\pi\)
\(68\) 2.24969 3.89658i 0.272815 0.472529i
\(69\) 0 0
\(70\) 2.38014 1.15539i 0.284481 0.138096i
\(71\) 4.76268i 0.565226i −0.959234 0.282613i \(-0.908799\pi\)
0.959234 0.282613i \(-0.0912013\pi\)
\(72\) 0 0
\(73\) 10.0951 5.82843i 1.18155 0.682166i 0.225174 0.974319i \(-0.427705\pi\)
0.956372 + 0.292153i \(0.0943716\pi\)
\(74\) −5.64444 + 3.25882i −0.656153 + 0.378830i
\(75\) 0 0
\(76\) 2.86370i 0.328489i
\(77\) −12.8431 + 6.23445i −1.46361 + 0.710482i
\(78\) 0 0
\(79\) −4.29618 + 7.44120i −0.483358 + 0.837200i −0.999817 0.0191114i \(-0.993916\pi\)
0.516460 + 0.856312i \(0.327250\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) 0 0
\(82\) 0.658421 + 0.380139i 0.0727104 + 0.0419794i
\(83\) −9.45001 −1.03727 −0.518636 0.854995i \(-0.673560\pi\)
−0.518636 + 0.854995i \(0.673560\pi\)
\(84\) 0 0
\(85\) −4.49938 −0.488026
\(86\) 5.07812 + 2.93185i 0.547587 + 0.316150i
\(87\) 0 0
\(88\) −2.69798 4.67303i −0.287605 0.498147i
\(89\) 3.98502 6.90226i 0.422412 0.731638i −0.573763 0.819021i \(-0.694517\pi\)
0.996175 + 0.0873828i \(0.0278503\pi\)
\(90\) 0 0
\(91\) 0.477014 6.64394i 0.0500046 0.696474i
\(92\) 0.267949i 0.0279356i
\(93\) 0 0
\(94\) 6.92418 3.99768i 0.714175 0.412329i
\(95\) −2.48004 + 1.43185i −0.254447 + 0.146905i
\(96\) 0 0
\(97\) 6.16353i 0.625812i 0.949784 + 0.312906i \(0.101302\pi\)
−0.949784 + 0.312906i \(0.898698\pi\)
\(98\) −5.50000 4.33013i −0.555584 0.437409i
\(99\) 0 0
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 7.02458 + 12.1669i 0.698972 + 1.21065i 0.968823 + 0.247753i \(0.0796920\pi\)
−0.269852 + 0.962902i \(0.586975\pi\)
\(102\) 0 0
\(103\) 12.2776 + 7.08845i 1.20974 + 0.698446i 0.962703 0.270560i \(-0.0872088\pi\)
0.247040 + 0.969005i \(0.420542\pi\)
\(104\) 2.51764 0.246875
\(105\) 0 0
\(106\) −8.39836 −0.815721
\(107\) 1.42178 + 0.820863i 0.137448 + 0.0793559i 0.567147 0.823616i \(-0.308047\pi\)
−0.429699 + 0.902972i \(0.641380\pi\)
\(108\) 0 0
\(109\) 9.94887 + 17.2319i 0.952929 + 1.65052i 0.739039 + 0.673663i \(0.235280\pi\)
0.213890 + 0.976858i \(0.431387\pi\)
\(110\) −2.69798 + 4.67303i −0.257242 + 0.445556i
\(111\) 0 0
\(112\) 1.48356 2.19067i 0.140184 0.206999i
\(113\) 5.95867i 0.560545i 0.959921 + 0.280272i \(0.0904248\pi\)
−0.959921 + 0.280272i \(0.909575\pi\)
\(114\) 0 0
\(115\) −0.232051 + 0.133975i −0.0216388 + 0.0124932i
\(116\) 7.70674 4.44949i 0.715553 0.413125i
\(117\) 0 0
\(118\) 12.6715i 1.16650i
\(119\) 5.19856 + 10.7091i 0.476551 + 0.981706i
\(120\) 0 0
\(121\) 9.05816 15.6892i 0.823469 1.42629i
\(122\) 1.31079 + 2.27035i 0.118673 + 0.205548i
\(123\) 0 0
\(124\) 4.18154 + 2.41421i 0.375513 + 0.216803i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −14.5103 −1.28758 −0.643792 0.765200i \(-0.722640\pi\)
−0.643792 + 0.765200i \(0.722640\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −1.25882 2.18034i −0.110406 0.191228i
\(131\) −7.73325 + 13.3944i −0.675657 + 1.17027i 0.300619 + 0.953744i \(0.402807\pi\)
−0.976276 + 0.216529i \(0.930527\pi\)
\(132\) 0 0
\(133\) 6.27343 + 4.24849i 0.543975 + 0.368391i
\(134\) 9.82237i 0.848524i
\(135\) 0 0
\(136\) −3.89658 + 2.24969i −0.334129 + 0.192909i
\(137\) −7.46651 + 4.31079i −0.637907 + 0.368296i −0.783808 0.621004i \(-0.786725\pi\)
0.145901 + 0.989299i \(0.453392\pi\)
\(138\) 0 0
\(139\) 10.2512i 0.869495i 0.900552 + 0.434748i \(0.143162\pi\)
−0.900552 + 0.434748i \(0.856838\pi\)
\(140\) −2.63896 0.189469i −0.223033 0.0160130i
\(141\) 0 0
\(142\) −2.38134 + 4.12460i −0.199838 + 0.346129i
\(143\) 6.79253 + 11.7650i 0.568020 + 0.983839i
\(144\) 0 0
\(145\) −7.70674 4.44949i −0.640010 0.369510i
\(146\) −11.6569 −0.964728
\(147\) 0 0
\(148\) 6.51764 0.535747
\(149\) 7.96640 + 4.59940i 0.652633 + 0.376798i 0.789464 0.613797i \(-0.210359\pi\)
−0.136831 + 0.990594i \(0.543692\pi\)
\(150\) 0 0
\(151\) 6.37429 + 11.0406i 0.518733 + 0.898471i 0.999763 + 0.0217674i \(0.00692931\pi\)
−0.481030 + 0.876704i \(0.659737\pi\)
\(152\) −1.43185 + 2.48004i −0.116139 + 0.201158i
\(153\) 0 0
\(154\) 14.2397 + 1.02236i 1.14747 + 0.0823845i
\(155\) 4.82843i 0.387829i
\(156\) 0 0
\(157\) 11.9899 6.92236i 0.956896 0.552464i 0.0616798 0.998096i \(-0.480354\pi\)
0.895216 + 0.445632i \(0.147021\pi\)
\(158\) 7.44120 4.29618i 0.591990 0.341786i
\(159\) 0 0
\(160\) 1.00000i 0.0790569i
\(161\) 0.586988 + 0.397520i 0.0462612 + 0.0313289i
\(162\) 0 0
\(163\) 10.3025 17.8444i 0.806954 1.39768i −0.108010 0.994150i \(-0.534448\pi\)
0.914964 0.403535i \(-0.132219\pi\)
\(164\) −0.380139 0.658421i −0.0296839 0.0514140i
\(165\) 0 0
\(166\) 8.18394 + 4.72500i 0.635197 + 0.366731i
\(167\) −6.84961 −0.530038 −0.265019 0.964243i \(-0.585378\pi\)
−0.265019 + 0.964243i \(0.585378\pi\)
\(168\) 0 0
\(169\) 6.66150 0.512423
\(170\) 3.89658 + 2.24969i 0.298854 + 0.172543i
\(171\) 0 0
\(172\) −2.93185 5.07812i −0.223552 0.387203i
\(173\) 6.37902 11.0488i 0.484988 0.840024i −0.514863 0.857272i \(-0.672157\pi\)
0.999851 + 0.0172486i \(0.00549068\pi\)
\(174\) 0 0
\(175\) 1.15539 + 2.38014i 0.0873396 + 0.179922i
\(176\) 5.39595i 0.406735i
\(177\) 0 0
\(178\) −6.90226 + 3.98502i −0.517347 + 0.298690i
\(179\) 16.3390 9.43331i 1.22123 0.705079i 0.256052 0.966663i \(-0.417578\pi\)
0.965181 + 0.261584i \(0.0842449\pi\)
\(180\) 0 0
\(181\) 25.5498i 1.89910i 0.313615 + 0.949550i \(0.398460\pi\)
−0.313615 + 0.949550i \(0.601540\pi\)
\(182\) −3.73508 + 5.51532i −0.276862 + 0.408822i
\(183\) 0 0
\(184\) −0.133975 + 0.232051i −0.00987674 + 0.0171070i
\(185\) −3.25882 5.64444i −0.239593 0.414987i
\(186\) 0 0
\(187\) −21.0257 12.1392i −1.53755 0.887707i
\(188\) −7.99536 −0.583121
\(189\) 0 0
\(190\) 2.86370 0.207755
\(191\) 7.00657 + 4.04524i 0.506977 + 0.292704i 0.731590 0.681745i \(-0.238778\pi\)
−0.224613 + 0.974448i \(0.572112\pi\)
\(192\) 0 0
\(193\) 7.06350 + 12.2343i 0.508442 + 0.880648i 0.999952 + 0.00977575i \(0.00311177\pi\)
−0.491510 + 0.870872i \(0.663555\pi\)
\(194\) 3.08176 5.33777i 0.221258 0.383230i
\(195\) 0 0
\(196\) 2.59808 + 6.50000i 0.185577 + 0.464286i
\(197\) 14.2738i 1.01697i −0.861072 0.508483i \(-0.830207\pi\)
0.861072 0.508483i \(-0.169793\pi\)
\(198\) 0 0
\(199\) 3.06742 1.77098i 0.217444 0.125541i −0.387322 0.921944i \(-0.626600\pi\)
0.604766 + 0.796403i \(0.293267\pi\)
\(200\) −0.866025 + 0.500000i −0.0612372 + 0.0353553i
\(201\) 0 0
\(202\) 14.0492i 0.988495i
\(203\) −1.68608 + 23.4840i −0.118339 + 1.64826i
\(204\) 0 0
\(205\) −0.380139 + 0.658421i −0.0265501 + 0.0459861i
\(206\) −7.08845 12.2776i −0.493876 0.855418i
\(207\) 0 0
\(208\) −2.18034 1.25882i −0.151179 0.0872834i
\(209\) −15.4524 −1.06887
\(210\) 0 0
\(211\) −3.92340 −0.270098 −0.135049 0.990839i \(-0.543119\pi\)
−0.135049 + 0.990839i \(0.543119\pi\)
\(212\) 7.27319 + 4.19918i 0.499525 + 0.288401i
\(213\) 0 0
\(214\) −0.820863 1.42178i −0.0561131 0.0971907i
\(215\) −2.93185 + 5.07812i −0.199951 + 0.346325i
\(216\) 0 0
\(217\) −11.4923 + 5.57874i −0.780150 + 0.378709i
\(218\) 19.8977i 1.34764i
\(219\) 0 0
\(220\) 4.67303 2.69798i 0.315056 0.181898i
\(221\) 9.81017 5.66390i 0.659903 0.380995i
\(222\) 0 0
\(223\) 14.6904i 0.983740i 0.870669 + 0.491870i \(0.163686\pi\)
−0.870669 + 0.491870i \(0.836314\pi\)
\(224\) −2.38014 + 1.15539i −0.159030 + 0.0771980i
\(225\) 0 0
\(226\) 2.97934 5.16036i 0.198182 0.343262i
\(227\) 11.3913 + 19.7303i 0.756068 + 1.30955i 0.944842 + 0.327527i \(0.106215\pi\)
−0.188774 + 0.982021i \(0.560451\pi\)
\(228\) 0 0
\(229\) −17.5089 10.1087i −1.15702 0.668005i −0.206431 0.978461i \(-0.566185\pi\)
−0.950588 + 0.310456i \(0.899518\pi\)
\(230\) 0.267949 0.0176680
\(231\) 0 0
\(232\) −8.89898 −0.584247
\(233\) −2.27840 1.31543i −0.149263 0.0861769i 0.423509 0.905892i \(-0.360798\pi\)
−0.572771 + 0.819715i \(0.694132\pi\)
\(234\) 0 0
\(235\) 3.99768 + 6.92418i 0.260780 + 0.451684i
\(236\) 6.33573 10.9738i 0.412421 0.714334i
\(237\) 0 0
\(238\) 0.852491 11.8737i 0.0552588 0.769656i
\(239\) 16.8766i 1.09165i −0.837898 0.545827i \(-0.816216\pi\)
0.837898 0.545827i \(-0.183784\pi\)
\(240\) 0 0
\(241\) −12.5793 + 7.26268i −0.810306 + 0.467831i −0.847062 0.531494i \(-0.821631\pi\)
0.0367560 + 0.999324i \(0.488298\pi\)
\(242\) −15.6892 + 9.05816i −1.00854 + 0.582280i
\(243\) 0 0
\(244\) 2.62158i 0.167829i
\(245\) 4.33013 5.50000i 0.276642 0.351382i
\(246\) 0 0
\(247\) 3.60488 6.24384i 0.229373 0.397286i
\(248\) −2.41421 4.18154i −0.153303 0.265528i
\(249\) 0 0
\(250\) 0.866025 + 0.500000i 0.0547723 + 0.0316228i
\(251\) −15.7243 −0.992507 −0.496254 0.868178i \(-0.665291\pi\)
−0.496254 + 0.868178i \(0.665291\pi\)
\(252\) 0 0
\(253\) −1.44584 −0.0908993
\(254\) 12.5663 + 7.25517i 0.788481 + 0.455230i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −9.83083 + 17.0275i −0.613230 + 1.06215i 0.377462 + 0.926025i \(0.376797\pi\)
−0.990692 + 0.136121i \(0.956536\pi\)
\(258\) 0 0
\(259\) −9.66933 + 14.2780i −0.600823 + 0.887192i
\(260\) 2.51764i 0.156137i
\(261\) 0 0
\(262\) 13.3944 7.73325i 0.827508 0.477762i
\(263\) 3.74275 2.16088i 0.230788 0.133245i −0.380148 0.924926i \(-0.624127\pi\)
0.610935 + 0.791680i \(0.290794\pi\)
\(264\) 0 0
\(265\) 8.39836i 0.515907i
\(266\) −3.30871 6.81601i −0.202870 0.417917i
\(267\) 0 0
\(268\) 4.91119 8.50643i 0.299999 0.519613i
\(269\) −8.79895 15.2402i −0.536482 0.929214i −0.999090 0.0426509i \(-0.986420\pi\)
0.462608 0.886563i \(-0.346914\pi\)
\(270\) 0 0
\(271\) −9.12436 5.26795i −0.554265 0.320005i 0.196575 0.980489i \(-0.437018\pi\)
−0.750840 + 0.660484i \(0.770351\pi\)
\(272\) 4.49938 0.272815
\(273\) 0 0
\(274\) 8.62158 0.520849
\(275\) −4.67303 2.69798i −0.281794 0.162694i
\(276\) 0 0
\(277\) −1.50971 2.61489i −0.0907097 0.157114i 0.817100 0.576496i \(-0.195580\pi\)
−0.907810 + 0.419382i \(0.862247\pi\)
\(278\) 5.12560 8.87780i 0.307413 0.532455i
\(279\) 0 0
\(280\) 2.19067 + 1.48356i 0.130918 + 0.0886599i
\(281\) 10.6880i 0.637591i −0.947824 0.318795i \(-0.896722\pi\)
0.947824 0.318795i \(-0.103278\pi\)
\(282\) 0 0
\(283\) −15.2149 + 8.78434i −0.904434 + 0.522175i −0.878636 0.477492i \(-0.841546\pi\)
−0.0257976 + 0.999667i \(0.508213\pi\)
\(284\) 4.12460 2.38134i 0.244750 0.141307i
\(285\) 0 0
\(286\) 13.5851i 0.803301i
\(287\) 2.00634 + 0.144049i 0.118431 + 0.00850295i
\(288\) 0 0
\(289\) −1.62220 + 2.80973i −0.0954235 + 0.165278i
\(290\) 4.44949 + 7.70674i 0.261283 + 0.452555i
\(291\) 0 0
\(292\) 10.0951 + 5.82843i 0.590773 + 0.341083i
\(293\) 14.6710 0.857086 0.428543 0.903521i \(-0.359027\pi\)
0.428543 + 0.903521i \(0.359027\pi\)
\(294\) 0 0
\(295\) −12.6715 −0.737761
\(296\) −5.64444 3.25882i −0.328076 0.189415i
\(297\) 0 0
\(298\) −4.59940 7.96640i −0.266436 0.461481i
\(299\) 0.337300 0.584220i 0.0195065 0.0337863i
\(300\) 0 0
\(301\) 15.4741 + 1.11099i 0.891911 + 0.0640363i
\(302\) 12.7486i 0.733599i
\(303\) 0 0
\(304\) 2.48004 1.43185i 0.142240 0.0821223i
\(305\) −2.27035 + 1.31079i −0.130000 + 0.0750556i
\(306\) 0 0
\(307\) 21.2772i 1.21435i −0.794567 0.607177i \(-0.792302\pi\)
0.794567 0.607177i \(-0.207698\pi\)
\(308\) −11.8208 8.00524i −0.673550 0.456141i
\(309\) 0 0
\(310\) −2.41421 + 4.18154i −0.137118 + 0.237496i
\(311\) 5.91724 + 10.2490i 0.335536 + 0.581165i 0.983588 0.180431i \(-0.0577493\pi\)
−0.648052 + 0.761596i \(0.724416\pi\)
\(312\) 0 0
\(313\) −3.90551 2.25485i −0.220753 0.127452i 0.385546 0.922689i \(-0.374013\pi\)
−0.606299 + 0.795237i \(0.707346\pi\)
\(314\) −13.8447 −0.781302
\(315\) 0 0
\(316\) −8.59235 −0.483358
\(317\) 15.9202 + 9.19151i 0.894165 + 0.516247i 0.875303 0.483576i \(-0.160662\pi\)
0.0188626 + 0.999822i \(0.493995\pi\)
\(318\) 0 0
\(319\) −24.0092 41.5852i −1.34426 2.32833i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) 0 0
\(322\) −0.309587 0.637756i −0.0172526 0.0355408i
\(323\) 12.8849i 0.716934i
\(324\) 0 0
\(325\) 2.18034 1.25882i 0.120943 0.0698267i
\(326\) −17.8444 + 10.3025i −0.988313 + 0.570603i
\(327\) 0 0
\(328\) 0.760279i 0.0419794i
\(329\) 11.8616 17.5152i 0.653952 0.965644i
\(330\) 0 0
\(331\) −3.98066 + 6.89471i −0.218797 + 0.378967i −0.954440 0.298401i \(-0.903547\pi\)
0.735643 + 0.677369i \(0.236880\pi\)
\(332\) −4.72500 8.18394i −0.259318 0.449152i
\(333\) 0 0
\(334\) 5.93193 + 3.42480i 0.324581 + 0.187397i
\(335\) −9.82237 −0.536654
\(336\) 0 0
\(337\) −6.89417 −0.375549 −0.187775 0.982212i \(-0.560127\pi\)
−0.187775 + 0.982212i \(0.560127\pi\)
\(338\) −5.76903 3.33075i −0.313794 0.181169i
\(339\) 0 0
\(340\) −2.24969 3.89658i −0.122007 0.211321i
\(341\) 13.0270 22.5634i 0.705451 1.22188i
\(342\) 0 0
\(343\) −18.0938 3.95164i −0.976972 0.213368i
\(344\) 5.86370i 0.316150i
\(345\) 0 0
\(346\) −11.0488 + 6.37902i −0.593986 + 0.342938i
\(347\) 14.1645 8.17789i 0.760392 0.439012i −0.0690448 0.997614i \(-0.521995\pi\)
0.829436 + 0.558601i \(0.188662\pi\)
\(348\) 0 0
\(349\) 24.5851i 1.31601i 0.753014 + 0.658004i \(0.228599\pi\)
−0.753014 + 0.658004i \(0.771401\pi\)
\(350\) 0.189469 2.63896i 0.0101275 0.141058i
\(351\) 0 0
\(352\) 2.69798 4.67303i 0.143803 0.249073i
\(353\) −6.85906 11.8802i −0.365071 0.632321i 0.623717 0.781651i \(-0.285622\pi\)
−0.988788 + 0.149329i \(0.952289\pi\)
\(354\) 0 0
\(355\) −4.12460 2.38134i −0.218911 0.126388i
\(356\) 7.97005 0.422412
\(357\) 0 0
\(358\) −18.8666 −0.997132
\(359\) 10.3059 + 5.95011i 0.543924 + 0.314035i 0.746668 0.665197i \(-0.231652\pi\)
−0.202744 + 0.979232i \(0.564986\pi\)
\(360\) 0 0
\(361\) −5.39960 9.35238i −0.284190 0.492231i
\(362\) 12.7749 22.1268i 0.671433 1.16296i
\(363\) 0 0
\(364\) 5.99233 2.90887i 0.314083 0.152466i
\(365\) 11.6569i 0.610148i
\(366\) 0 0
\(367\) −10.9026 + 6.29461i −0.569110 + 0.328576i −0.756794 0.653654i \(-0.773235\pi\)
0.187684 + 0.982230i \(0.439902\pi\)
\(368\) 0.232051 0.133975i 0.0120965 0.00698391i
\(369\) 0 0
\(370\) 6.51764i 0.338836i
\(371\) −19.9893 + 9.70342i −1.03779 + 0.503776i
\(372\) 0 0
\(373\) 13.5868 23.5331i 0.703499 1.21850i −0.263731 0.964596i \(-0.584953\pi\)
0.967230 0.253900i \(-0.0817136\pi\)
\(374\) 12.1392 + 21.0257i 0.627704 + 1.08722i
\(375\) 0 0
\(376\) 6.92418 + 3.99768i 0.357087 + 0.206164i
\(377\) 22.4044 1.15389
\(378\) 0 0
\(379\) 15.7335 0.808174 0.404087 0.914721i \(-0.367589\pi\)
0.404087 + 0.914721i \(0.367589\pi\)
\(380\) −2.48004 1.43185i −0.127223 0.0734524i
\(381\) 0 0
\(382\) −4.04524 7.00657i −0.206973 0.358487i
\(383\) 7.89060 13.6669i 0.403191 0.698347i −0.590918 0.806732i \(-0.701234\pi\)
0.994109 + 0.108384i \(0.0345677\pi\)
\(384\) 0 0
\(385\) −1.02236 + 14.2397i −0.0521045 + 0.725722i
\(386\) 14.1270i 0.719046i
\(387\) 0 0
\(388\) −5.33777 + 3.08176i −0.270984 + 0.156453i
\(389\) 13.7556 7.94182i 0.697438 0.402666i −0.108954 0.994047i \(-0.534750\pi\)
0.806393 + 0.591381i \(0.201417\pi\)
\(390\) 0 0
\(391\) 1.20560i 0.0609700i
\(392\) 1.00000 6.92820i 0.0505076 0.349927i
\(393\) 0 0
\(394\) −7.13689 + 12.3615i −0.359552 + 0.622762i
\(395\) 4.29618 + 7.44120i 0.216164 + 0.374407i
\(396\) 0 0
\(397\) 32.3557 + 18.6806i 1.62388 + 0.937550i 0.985867 + 0.167528i \(0.0535784\pi\)
0.638017 + 0.770022i \(0.279755\pi\)
\(398\) −3.54195 −0.177542
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −24.4856 14.1368i −1.22275 0.705957i −0.257249 0.966345i \(-0.582816\pi\)
−0.965504 + 0.260389i \(0.916149\pi\)
\(402\) 0 0
\(403\) 6.07812 + 10.5276i 0.302773 + 0.524417i
\(404\) −7.02458 + 12.1669i −0.349486 + 0.605327i
\(405\) 0 0
\(406\) 13.2022 19.4947i 0.655214 0.967507i
\(407\) 35.1689i 1.74326i
\(408\) 0 0
\(409\) 13.8647 8.00481i 0.685567 0.395812i −0.116382 0.993204i \(-0.537130\pi\)
0.801949 + 0.597392i \(0.203796\pi\)
\(410\) 0.658421 0.380139i 0.0325171 0.0187737i
\(411\) 0 0
\(412\) 14.1769i 0.698446i
\(413\) 14.6405 + 30.1599i 0.720414 + 1.48407i
\(414\) 0 0
\(415\) −4.72500 + 8.18394i −0.231941 + 0.401734i
\(416\) 1.25882 + 2.18034i 0.0617187 + 0.106900i
\(417\) 0 0
\(418\) 13.3822 + 7.72620i 0.654544 + 0.377901i
\(419\) −29.5137 −1.44184 −0.720919 0.693020i \(-0.756280\pi\)
−0.720919 + 0.693020i \(0.756280\pi\)
\(420\) 0 0
\(421\) 0.309114 0.0150653 0.00753265 0.999972i \(-0.497602\pi\)
0.00753265 + 0.999972i \(0.497602\pi\)
\(422\) 3.39776 + 1.96170i 0.165400 + 0.0954939i
\(423\) 0 0
\(424\) −4.19918 7.27319i −0.203930 0.353217i
\(425\) −2.24969 + 3.89658i −0.109126 + 0.189012i
\(426\) 0 0
\(427\) 5.74301 + 3.88928i 0.277924 + 0.188215i
\(428\) 1.64173i 0.0793559i
\(429\) 0 0
\(430\) 5.07812 2.93185i 0.244889 0.141386i
\(431\) −7.63843 + 4.41005i −0.367930 + 0.212425i −0.672554 0.740048i \(-0.734803\pi\)
0.304624 + 0.952473i \(0.401469\pi\)
\(432\) 0 0
\(433\) 9.56388i 0.459611i −0.973237 0.229805i \(-0.926191\pi\)
0.973237 0.229805i \(-0.0738089\pi\)
\(434\) 12.7420 + 0.914836i 0.611636 + 0.0439135i
\(435\) 0 0
\(436\) −9.94887 + 17.2319i −0.476464 + 0.825260i
\(437\) 0.383663 + 0.664525i 0.0183531 + 0.0317885i
\(438\) 0 0
\(439\) −31.3336 18.0905i −1.49547 0.863412i −0.495487 0.868615i \(-0.665010\pi\)
−0.999986 + 0.00520362i \(0.998344\pi\)
\(440\) −5.39595 −0.257242
\(441\) 0 0
\(442\) −11.3278 −0.538809
\(443\) 3.53830 + 2.04284i 0.168110 + 0.0970582i 0.581694 0.813408i \(-0.302390\pi\)
−0.413584 + 0.910466i \(0.635723\pi\)
\(444\) 0 0
\(445\) −3.98502 6.90226i −0.188908 0.327199i
\(446\) 7.34519 12.7222i 0.347805 0.602415i
\(447\) 0 0
\(448\) 2.63896 + 0.189469i 0.124679 + 0.00895155i
\(449\) 19.9377i 0.940918i 0.882422 + 0.470459i \(0.155912\pi\)
−0.882422 + 0.470459i \(0.844088\pi\)
\(450\) 0 0
\(451\) −3.55281 + 2.05121i −0.167295 + 0.0965879i
\(452\) −5.16036 + 2.97934i −0.242723 + 0.140136i
\(453\) 0 0
\(454\) 22.7826i 1.06924i
\(455\) −5.51532 3.73508i −0.258562 0.175103i
\(456\) 0 0
\(457\) 10.0623 17.4283i 0.470693 0.815264i −0.528745 0.848780i \(-0.677337\pi\)
0.999438 + 0.0335168i \(0.0106707\pi\)
\(458\) 10.1087 + 17.5089i 0.472351 + 0.818136i
\(459\) 0 0
\(460\) −0.232051 0.133975i −0.0108194 0.00624660i
\(461\) 0.909299 0.0423503 0.0211751 0.999776i \(-0.493259\pi\)
0.0211751 + 0.999776i \(0.493259\pi\)
\(462\) 0 0
\(463\) 21.4280 0.995843 0.497922 0.867222i \(-0.334097\pi\)
0.497922 + 0.867222i \(0.334097\pi\)
\(464\) 7.70674 + 4.44949i 0.357777 + 0.206562i
\(465\) 0 0
\(466\) 1.31543 + 2.27840i 0.0609363 + 0.105545i
\(467\) 6.34607 10.9917i 0.293661 0.508636i −0.681012 0.732273i \(-0.738460\pi\)
0.974672 + 0.223637i \(0.0717930\pi\)
\(468\) 0 0
\(469\) 11.3487 + 23.3786i 0.524035 + 1.07952i
\(470\) 7.99536i 0.368798i
\(471\) 0 0
\(472\) −10.9738 + 6.33573i −0.505111 + 0.291626i
\(473\) −27.4013 + 15.8201i −1.25991 + 0.727411i
\(474\) 0 0
\(475\) 2.86370i 0.131396i
\(476\) −6.67511 + 9.85666i −0.305953 + 0.451779i
\(477\) 0 0
\(478\) −8.43828 + 14.6155i −0.385958 + 0.668499i
\(479\) −6.43828 11.1514i −0.294172 0.509522i 0.680620 0.732637i \(-0.261711\pi\)
−0.974792 + 0.223115i \(0.928377\pi\)
\(480\) 0 0
\(481\) 14.2107 + 8.20453i 0.647950 + 0.374094i
\(482\) 14.5254 0.661612
\(483\) 0 0
\(484\) 18.1163 0.823469
\(485\) 5.33777 + 3.08176i 0.242376 + 0.139936i
\(486\) 0 0
\(487\) 10.4097 + 18.0301i 0.471708 + 0.817022i 0.999476 0.0323665i \(-0.0103044\pi\)
−0.527768 + 0.849388i \(0.676971\pi\)
\(488\) −1.31079 + 2.27035i −0.0593366 + 0.102774i
\(489\) 0 0
\(490\) −6.50000 + 2.59808i −0.293640 + 0.117369i
\(491\) 27.3271i 1.23325i 0.787256 + 0.616627i \(0.211501\pi\)
−0.787256 + 0.616627i \(0.788499\pi\)
\(492\) 0 0
\(493\) −34.6755 + 20.0199i −1.56171 + 0.901653i
\(494\) −6.24384 + 3.60488i −0.280924 + 0.162191i
\(495\) 0 0
\(496\) 4.82843i 0.216803i
\(497\) −0.902379 + 12.5685i −0.0404772 + 0.563775i
\(498\) 0 0
\(499\) −16.6802 + 28.8909i −0.746708 + 1.29334i 0.202685 + 0.979244i \(0.435033\pi\)
−0.949393 + 0.314092i \(0.898300\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 0 0
\(502\) 13.6176 + 7.86214i 0.607784 + 0.350904i
\(503\) 16.2936 0.726494 0.363247 0.931693i \(-0.381668\pi\)
0.363247 + 0.931693i \(0.381668\pi\)
\(504\) 0 0
\(505\) 14.0492 0.625179
\(506\) 1.25214 + 0.722921i 0.0556642 + 0.0321377i
\(507\) 0 0
\(508\) −7.25517 12.5663i −0.321896 0.557540i
\(509\) −12.3400 + 21.3735i −0.546961 + 0.947365i 0.451519 + 0.892261i \(0.350882\pi\)
−0.998481 + 0.0551036i \(0.982451\pi\)
\(510\) 0 0
\(511\) −27.7449 + 13.4683i −1.22736 + 0.595801i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 17.0275 9.83083i 0.751051 0.433619i
\(515\) 12.2776 7.08845i 0.541014 0.312354i
\(516\) 0 0
\(517\) 43.1426i 1.89741i
\(518\) 15.5129 7.53044i 0.681597 0.330869i
\(519\) 0 0
\(520\) 1.25882 2.18034i 0.0552029 0.0956142i
\(521\) −0.141663 0.245367i −0.00620635 0.0107497i 0.862906 0.505365i \(-0.168642\pi\)
−0.869112 + 0.494616i \(0.835309\pi\)
\(522\) 0 0
\(523\) −9.77021 5.64083i −0.427222 0.246656i 0.270941 0.962596i \(-0.412665\pi\)
−0.698162 + 0.715940i \(0.745999\pi\)
\(524\) −15.4665 −0.675657
\(525\) 0 0
\(526\) −4.32175 −0.188437
\(527\) −18.8143 10.8625i −0.819565 0.473176i
\(528\) 0 0
\(529\) −11.4641 19.8564i −0.498439 0.863322i
\(530\) −4.19918 + 7.27319i −0.182401 + 0.315927i
\(531\) 0 0
\(532\) −0.542582 + 7.55719i −0.0235239 + 0.327646i
\(533\) 1.91411i 0.0829092i
\(534\) 0 0
\(535\) 1.42178 0.820863i 0.0614688 0.0354890i
\(536\) −8.50643 + 4.91119i −0.367422 + 0.212131i
\(537\) 0 0
\(538\) 17.5979i 0.758700i
\(539\) 35.0737 14.0191i 1.51073 0.603845i
\(540\) 0 0
\(541\) 17.4125 30.1593i 0.748621 1.29665i −0.199862 0.979824i \(-0.564049\pi\)
0.948484 0.316826i \(-0.102617\pi\)
\(542\) 5.26795 + 9.12436i 0.226278 + 0.391925i
\(543\) 0 0
\(544\) −3.89658 2.24969i −0.167064 0.0964546i
\(545\) 19.8977 0.852325
\(546\) 0 0
\(547\) 35.4261 1.51471 0.757356 0.653002i \(-0.226491\pi\)
0.757356 + 0.653002i \(0.226491\pi\)
\(548\) −7.46651 4.31079i −0.318953 0.184148i
\(549\) 0 0
\(550\) 2.69798 + 4.67303i 0.115042 + 0.199259i
\(551\) −12.7420 + 22.0698i −0.542828 + 0.940206i
\(552\) 0 0
\(553\) 12.7473 18.8230i 0.542071 0.800436i
\(554\) 3.01942i 0.128283i
\(555\) 0 0
\(556\) −8.87780 + 5.12560i −0.376503 + 0.217374i
\(557\) −7.05105 + 4.07093i −0.298763 + 0.172491i −0.641887 0.766799i \(-0.721848\pi\)
0.343124 + 0.939290i \(0.388515\pi\)
\(558\) 0 0
\(559\) 14.7627i 0.624395i
\(560\) −1.15539 2.38014i −0.0488243 0.100579i
\(561\) 0 0
\(562\) −5.34398 + 9.25605i −0.225422 + 0.390443i
\(563\) −10.2088 17.6821i −0.430248 0.745212i 0.566646 0.823961i \(-0.308241\pi\)
−0.996894 + 0.0787491i \(0.974907\pi\)
\(564\) 0 0
\(565\) 5.16036 + 2.97934i 0.217098 + 0.125342i
\(566\) 17.5687 0.738467
\(567\) 0 0
\(568\) −4.76268 −0.199838
\(569\) −22.5542 13.0217i −0.945520 0.545896i −0.0538334 0.998550i \(-0.517144\pi\)
−0.891686 + 0.452654i \(0.850477\pi\)
\(570\) 0 0
\(571\) 6.18811 + 10.7181i 0.258964 + 0.448539i 0.965965 0.258674i \(-0.0832855\pi\)
−0.707000 + 0.707213i \(0.749952\pi\)
\(572\) −6.79253 + 11.7650i −0.284010 + 0.491920i
\(573\) 0 0
\(574\) −1.66552 1.12792i −0.0695175 0.0470786i
\(575\) 0.267949i 0.0111743i
\(576\) 0 0
\(577\) 23.3399 13.4753i 0.971654 0.560985i 0.0719139 0.997411i \(-0.477089\pi\)
0.899740 + 0.436426i \(0.143756\pi\)
\(578\) 2.80973 1.62220i 0.116869 0.0674746i
\(579\) 0 0
\(580\) 8.89898i 0.369510i
\(581\) 24.9382 + 1.79048i 1.03461 + 0.0742816i
\(582\) 0 0
\(583\) 22.6586 39.2458i 0.938422 1.62539i
\(584\) −5.82843 10.0951i −0.241182 0.417740i
\(585\) 0 0
\(586\) −12.7054 7.33548i −0.524856 0.303026i
\(587\) 35.3511 1.45910 0.729548 0.683930i \(-0.239731\pi\)
0.729548 + 0.683930i \(0.239731\pi\)
\(588\) 0 0
\(589\) −13.8272 −0.569739
\(590\) 10.9738 + 6.33573i 0.451785 + 0.260838i
\(591\) 0 0
\(592\) 3.25882 + 5.64444i 0.133937 + 0.231985i
\(593\) −14.7057 + 25.4711i −0.603893 + 1.04597i 0.388333 + 0.921519i \(0.373051\pi\)
−0.992225 + 0.124454i \(0.960282\pi\)
\(594\) 0 0
\(595\) 11.8737 + 0.852491i 0.486773 + 0.0349487i
\(596\) 9.19881i 0.376798i
\(597\) 0 0
\(598\) −0.584220 + 0.337300i −0.0238905 + 0.0137932i
\(599\) −26.5494 + 15.3283i −1.08478 + 0.626298i −0.932182 0.361990i \(-0.882097\pi\)
−0.152598 + 0.988288i \(0.548764\pi\)
\(600\) 0 0
\(601\) 34.3407i 1.40078i −0.713758 0.700392i \(-0.753008\pi\)
0.713758 0.700392i \(-0.246992\pi\)
\(602\) −12.8454 8.69918i −0.523541 0.354552i
\(603\) 0 0
\(604\) −6.37429 + 11.0406i −0.259366 + 0.449236i
\(605\) −9.05816 15.6892i −0.368266 0.637856i
\(606\) 0 0
\(607\) 28.2475 + 16.3087i 1.14653 + 0.661950i 0.948040 0.318153i \(-0.103062\pi\)
0.198492 + 0.980103i \(0.436396\pi\)
\(608\) −2.86370 −0.116139
\(609\) 0 0
\(610\) 2.62158 0.106145
\(611\) −17.4326 10.0647i −0.705247 0.407174i
\(612\) 0 0
\(613\) 7.99843 + 13.8537i 0.323054 + 0.559545i 0.981117 0.193418i \(-0.0619572\pi\)
−0.658063 + 0.752963i \(0.728624\pi\)
\(614\) −10.6386 + 18.4266i −0.429339 + 0.743636i
\(615\) 0 0
\(616\) 6.23445 + 12.8431i 0.251193 + 0.517464i
\(617\) 25.1429i 1.01221i 0.862471 + 0.506107i \(0.168916\pi\)
−0.862471 + 0.506107i \(0.831084\pi\)
\(618\) 0 0
\(619\) 32.3379 18.6703i 1.29977 0.750423i 0.319406 0.947618i \(-0.396517\pi\)
0.980364 + 0.197195i \(0.0631832\pi\)
\(620\) 4.18154 2.41421i 0.167935 0.0969571i
\(621\) 0 0
\(622\) 11.8345i 0.474519i
\(623\) −11.8241 + 17.4597i −0.473722 + 0.699510i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 2.25485 + 3.90551i 0.0901219 + 0.156096i
\(627\) 0 0
\(628\) 11.9899 + 6.92236i 0.478448 + 0.276232i
\(629\) −29.3253 −1.16928
\(630\) 0 0
\(631\) 49.5015 1.97062 0.985311 0.170767i \(-0.0546245\pi\)
0.985311 + 0.170767i \(0.0546245\pi\)
\(632\) 7.44120 + 4.29618i 0.295995 + 0.170893i
\(633\) 0 0
\(634\) −9.19151 15.9202i −0.365041 0.632270i
\(635\) −7.25517 + 12.5663i −0.287913 + 0.498679i
\(636\) 0 0
\(637\) −2.51764 + 17.4427i −0.0997525 + 0.691105i
\(638\) 48.0185i 1.90107i
\(639\) 0 0
\(640\) 0.866025 0.500000i 0.0342327 0.0197642i
\(641\) 31.4439 18.1542i 1.24196 0.717046i 0.272467 0.962165i \(-0.412160\pi\)
0.969493 + 0.245119i \(0.0788271\pi\)
\(642\) 0 0
\(643\) 10.2653i 0.404824i −0.979300 0.202412i \(-0.935122\pi\)
0.979300 0.202412i \(-0.0648780\pi\)
\(644\) −0.0507680 + 0.707107i −0.00200054 + 0.0278639i
\(645\) 0 0
\(646\) 6.44244 11.1586i 0.253474 0.439031i
\(647\) 10.9108 + 18.8980i 0.428946 + 0.742956i 0.996780 0.0801869i \(-0.0255517\pi\)
−0.567834 + 0.823143i \(0.692218\pi\)
\(648\) 0 0
\(649\) −59.2142 34.1873i −2.32436 1.34197i
\(650\) −2.51764 −0.0987499
\(651\) 0 0
\(652\) 20.6050 0.806954
\(653\) −40.9556 23.6457i −1.60272 0.925329i −0.990941 0.134297i \(-0.957122\pi\)
−0.611775 0.791032i \(-0.709544\pi\)
\(654\) 0 0
\(655\) 7.73325 + 13.3944i 0.302163 + 0.523362i
\(656\) 0.380139 0.658421i 0.0148419 0.0257070i
\(657\) 0 0
\(658\) −19.0301 + 9.23779i −0.741869 + 0.360127i
\(659\) 3.58255i 0.139556i 0.997563 + 0.0697782i \(0.0222291\pi\)
−0.997563 + 0.0697782i \(0.977771\pi\)
\(660\) 0 0
\(661\) −1.41761 + 0.818459i −0.0551388 + 0.0318344i −0.527316 0.849669i \(-0.676802\pi\)
0.472177 + 0.881504i \(0.343468\pi\)
\(662\) 6.89471 3.98066i 0.267970 0.154713i
\(663\) 0 0
\(664\) 9.45001i 0.366731i
\(665\) 6.81601 3.30871i 0.264314 0.128306i
\(666\) 0 0
\(667\) −1.19224 + 2.06502i −0.0461636 + 0.0799577i
\(668\) −3.42480 5.93193i −0.132510 0.229513i
\(669\) 0 0
\(670\) 8.50643 + 4.91119i 0.328632 + 0.189736i
\(671\) −14.1459 −0.546097
\(672\) 0 0
\(673\) −2.02242 −0.0779587 −0.0389794 0.999240i \(-0.512411\pi\)
−0.0389794 + 0.999240i \(0.512411\pi\)
\(674\) 5.97053 + 3.44709i 0.229976 + 0.132777i
\(675\) 0 0
\(676\) 3.33075 + 5.76903i 0.128106 + 0.221886i
\(677\) −11.4413 + 19.8169i −0.439725 + 0.761626i −0.997668 0.0682532i \(-0.978257\pi\)
0.557943 + 0.829879i \(0.311591\pi\)
\(678\) 0 0
\(679\) 1.16780 16.2653i 0.0448159 0.624205i
\(680\) 4.49938i 0.172543i
\(681\) 0 0
\(682\) −22.5634 + 13.0270i −0.863997 + 0.498829i
\(683\) −27.1977 + 15.7026i −1.04069 + 0.600844i −0.920029 0.391850i \(-0.871835\pi\)
−0.120663 + 0.992694i \(0.538502\pi\)
\(684\) 0 0
\(685\) 8.62158i 0.329414i
\(686\) 13.6938 + 12.4691i 0.522834 + 0.476073i
\(687\) 0 0
\(688\) 2.93185 5.07812i 0.111776 0.193601i
\(689\) 10.5720 + 18.3113i 0.402762 + 0.697604i
\(690\) 0 0
\(691\) 29.3677 + 16.9554i 1.11720 + 0.645015i 0.940684 0.339283i \(-0.110184\pi\)
0.176515 + 0.984298i \(0.443518\pi\)
\(692\) 12.7580 0.484988
\(693\) 0 0
\(694\) −16.3558 −0.620857
\(695\) 8.87780 + 5.12560i 0.336754 + 0.194425i
\(696\) 0 0
\(697\) 1.71039 + 2.96248i 0.0647857 + 0.112212i
\(698\) 12.2925 21.2913i 0.465279 0.805887i
\(699\) 0 0
\(700\) −1.48356 + 2.19067i −0.0560734 + 0.0827996i
\(701\) 10.5296i 0.397699i −0.980030 0.198849i \(-0.936280\pi\)
0.980030 0.198849i \(-0.0637205\pi\)
\(702\) 0 0
\(703\) −16.1640 + 9.33229i −0.609637 + 0.351974i
\(704\) −4.67303 + 2.69798i −0.176122 + 0.101684i
\(705\) 0 0
\(706\) 13.7181i 0.516288i
\(707\) −16.2323 33.4390i −0.610479 1.25760i
\(708\) 0 0
\(709\) −7.52572 + 13.0349i −0.282634 + 0.489537i −0.972033 0.234845i \(-0.924542\pi\)
0.689398 + 0.724382i \(0.257875\pi\)
\(710\) 2.38134 + 4.12460i 0.0893702 + 0.154794i
\(711\) 0 0
\(712\) −6.90226 3.98502i −0.258673 0.149345i
\(713\) −1.29377 −0.0484522
\(714\) 0 0
\(715\) 13.5851 0.508052
\(716\) 16.3390 + 9.43331i 0.610616 + 0.352539i
\(717\) 0 0
\(718\) −5.95011 10.3059i −0.222056 0.384613i
\(719\) −12.2137 + 21.1547i −0.455494 + 0.788938i −0.998716 0.0506506i \(-0.983871\pi\)
0.543223 + 0.839589i \(0.317204\pi\)
\(720\) 0 0
\(721\) −31.0569 21.0323i −1.15662 0.783285i
\(722\) 10.7992i 0.401905i
\(723\) 0 0
\(724\) −22.1268 + 12.7749i −0.822335 + 0.474775i
\(725\) −7.70674 + 4.44949i −0.286221 + 0.165250i
\(726\) 0 0
\(727\) 43.7349i 1.62204i −0.585020 0.811019i \(-0.698913\pi\)
0.585020 0.811019i \(-0.301087\pi\)
\(728\) −6.64394 0.477014i −0.246241 0.0176793i
\(729\) 0 0
\(730\) −5.82843 + 10.0951i −0.215720 + 0.373638i
\(731\) 13.1915 + 22.8484i 0.487906 + 0.845077i
\(732\) 0 0
\(733\) 38.7280 + 22.3596i 1.43045 + 0.825872i 0.997155 0.0753789i \(-0.0240166\pi\)
0.433297 + 0.901251i \(0.357350\pi\)
\(734\) 12.5892 0.464677
\(735\) 0 0
\(736\) −0.267949 −0.00987674
\(737\) −45.9003 26.5005i −1.69076 0.976160i
\(738\) 0 0
\(739\) 10.7360 + 18.5954i 0.394932 + 0.684042i 0.993092 0.117334i \(-0.0374348\pi\)
−0.598161 + 0.801376i \(0.704102\pi\)
\(740\) 3.25882 5.64444i 0.119797 0.207494i
\(741\) 0 0
\(742\) 22.1629 + 1.59123i 0.813626 + 0.0584157i
\(743\) 29.5637i 1.08459i −0.840190 0.542293i \(-0.817556\pi\)
0.840190 0.542293i \(-0.182444\pi\)
\(744\) 0 0
\(745\) 7.96640 4.59940i 0.291866 0.168509i
\(746\) −23.5331 + 13.5868i −0.861607 + 0.497449i
\(747\) 0 0
\(748\) 24.2784i 0.887707i
\(749\) −3.59648 2.43561i −0.131413 0.0889951i
\(750\) 0 0
\(751\) −0.596750 + 1.03360i −0.0217757 + 0.0377166i −0.876708 0.481023i \(-0.840265\pi\)
0.854932 + 0.518740i \(0.173599\pi\)
\(752\) −3.99768 6.92418i −0.145780 0.252499i
\(753\) 0 0
\(754\) −19.4028 11.2022i −0.706608 0.407960i
\(755\) 12.7486 0.463969
\(756\) 0 0
\(757\) −26.8915 −0.977386 −0.488693 0.872456i \(-0.662526\pi\)
−0.488693 + 0.872456i \(0.662526\pi\)
\(758\) −13.6256 7.86673i −0.494903 0.285732i
\(759\) 0 0
\(760\) 1.43185 + 2.48004i 0.0519387 + 0.0899605i
\(761\) 0.939574 1.62739i 0.0340595 0.0589928i −0.848493 0.529206i \(-0.822490\pi\)
0.882553 + 0.470213i \(0.155823\pi\)
\(762\) 0 0
\(763\) −22.9897 47.3594i −0.832284 1.71452i
\(764\) 8.09049i 0.292704i
\(765\) 0 0
\(766\) −13.6669 + 7.89060i −0.493806 + 0.285099i
\(767\) 27.6281 15.9511i 0.997592 0.575960i
\(768\) 0 0
\(769\) 50.6544i 1.82664i −0.407239 0.913322i \(-0.633508\pi\)
0.407239 0.913322i \(-0.366492\pi\)
\(770\) 8.00524 11.8208i 0.288489 0.425991i
\(771\) 0 0
\(772\) −7.06350 + 12.2343i −0.254221 + 0.440324i
\(773\) 24.3353 + 42.1499i 0.875279 + 1.51603i 0.856466 + 0.516204i \(0.172655\pi\)
0.0188128 + 0.999823i \(0.494011\pi\)
\(774\) 0 0
\(775\) −4.18154 2.41421i −0.150205 0.0867211i
\(776\) 6.16353 0.221258
\(777\) 0 0
\(778\) −15.8836 −0.569456
\(779\) 1.88552 + 1.08861i 0.0675558 + 0.0390034i
\(780\) 0 0
\(781\) −12.8496 22.2562i −0.459795 0.796388i
\(782\) 0.602802 1.04408i 0.0215562 0.0373364i
\(783\) 0 0
\(784\) −4.33013 + 5.50000i −0.154647 + 0.196429i
\(785\) 13.8447i 0.494139i
\(786\) 0 0
\(787\) −12.9437 + 7.47307i −0.461395 + 0.266386i −0.712630 0.701540i \(-0.752496\pi\)
0.251236 + 0.967926i \(0.419163\pi\)
\(788\) 12.3615 7.13689i 0.440359 0.254241i
\(789\) 0 0
\(790\) 8.59235i 0.305702i
\(791\) 1.12898 15.7247i 0.0401420 0.559105i
\(792\) 0 0
\(793\) 3.30009 5.71593i 0.117190 0.202979i
\(794\) −18.6806 32.3557i −0.662948 1.14826i
\(795\) 0 0
\(796\) 3.06742 + 1.77098i 0.108722 + 0.0627706i
\(797\) 15.0557 0.533301 0.266650 0.963793i \(-0.414083\pi\)
0.266650 + 0.963793i \(0.414083\pi\)
\(798\) 0 0
\(799\) 35.9741 1.27267
\(800\) −0.866025 0.500000i −0.0306186 0.0176777i
\(801\) 0 0
\(802\) 14.1368 + 24.4856i 0.499187 + 0.864617i
\(803\) 31.4499 54.4729i 1.10984 1.92231i
\(804\) 0 0
\(805\) 0.637756 0.309587i 0.0224780 0.0109115i
\(806\) 12.1562i 0.428185i
\(807\) 0 0
\(808\) 12.1669 7.02458i 0.428031 0.247124i
\(809\) −30.7426 + 17.7493i −1.08085 + 0.624031i −0.931127 0.364696i \(-0.881173\pi\)
−0.149727 + 0.988727i \(0.547840\pi\)
\(810\) 0 0
\(811\) 24.5935i 0.863594i 0.901971 + 0.431797i \(0.142120\pi\)
−0.901971 + 0.431797i \(0.857880\pi\)
\(812\) −21.1808 + 10.2818i −0.743301 + 0.360822i
\(813\) 0 0
\(814\) −17.5844 + 30.4571i −0.616334 + 1.06752i
\(815\) −10.3025 17.8444i −0.360881 0.625064i
\(816\) 0 0
\(817\) 14.5422 + 8.39595i 0.508768 + 0.293737i
\(818\) −16.0096 −0.559763
\(819\) 0 0
\(820\) −0.760279 −0.0265501
\(821\) 12.3035 + 7.10342i 0.429395 + 0.247911i 0.699089 0.715035i \(-0.253589\pi\)
−0.269694 + 0.962946i \(0.586923\pi\)
\(822\) 0 0
\(823\) −0.945584 1.63780i −0.0329610 0.0570901i 0.849074 0.528273i \(-0.177160\pi\)
−0.882035 + 0.471183i \(0.843827\pi\)
\(824\) 7.08845 12.2776i 0.246938 0.427709i
\(825\) 0 0
\(826\) 2.40085 33.4395i 0.0835361 1.16351i
\(827\) 31.9280i 1.11024i −0.831769 0.555122i \(-0.812671\pi\)
0.831769 0.555122i \(-0.187329\pi\)
\(828\) 0 0
\(829\) 3.38864 1.95643i 0.117692 0.0679497i −0.439998 0.897999i \(-0.645021\pi\)
0.557691 + 0.830049i \(0.311688\pi\)
\(830\) 8.18394 4.72500i 0.284069 0.164007i
\(831\) 0 0
\(832\) 2.51764i 0.0872834i
\(833\) −11.6897 29.2460i −0.405025 1.01331i
\(834\) 0 0
\(835\) −3.42480 + 5.93193i −0.118520 + 0.205283i
\(836\) −7.72620 13.3822i −0.267216 0.462832i
\(837\) 0 0
\(838\) 25.5596 + 14.7568i 0.882941 + 0.509766i
\(839\) 15.3513 0.529984 0.264992 0.964251i \(-0.414631\pi\)
0.264992 + 0.964251i \(0.414631\pi\)
\(840\) 0 0
\(841\) −50.1918 −1.73075
\(842\) −0.267701 0.154557i −0.00922557 0.00532639i
\(843\) 0 0
\(844\) −1.96170 3.39776i −0.0675244 0.116956i
\(845\) 3.33075 5.76903i 0.114581 0.198461i
\(846\) 0 0
\(847\) −26.8767 + 39.6869i −0.923495 + 1.36366i
\(848\) 8.39836i 0.288401i
\(849\) 0 0
\(850\) 3.89658 2.24969i 0.133651 0.0771637i
\(851\) −1.51242 + 0.873198i −0.0518452 + 0.0299328i
\(852\) 0 0
\(853\) 22.2302i 0.761148i 0.924750 + 0.380574i \(0.124274\pi\)
−0.924750 + 0.380574i \(0.875726\pi\)
\(854\) −3.02896 6.23972i −0.103649 0.213519i
\(855\) 0 0
\(856\) 0.820863 1.42178i 0.0280565 0.0485953i
\(857\) −26.4098 45.7432i −0.902143 1.56256i −0.824707 0.565560i \(-0.808660\pi\)
−0.0774356 0.996997i \(-0.524673\pi\)
\(858\) 0 0
\(859\) −15.2916 8.82859i −0.521742 0.301228i 0.215905 0.976414i \(-0.430730\pi\)
−0.737647 + 0.675187i \(0.764063\pi\)
\(860\) −5.86370 −0.199951
\(861\) 0 0
\(862\) 8.82010 0.300414
\(863\) 14.2452 + 8.22446i 0.484912 + 0.279964i 0.722461 0.691412i \(-0.243011\pi\)
−0.237549 + 0.971375i \(0.576344\pi\)
\(864\) 0 0
\(865\) −6.37902 11.0488i −0.216893 0.375670i
\(866\) −4.78194 + 8.28256i −0.162497 + 0.281453i
\(867\) 0 0
\(868\) −10.5775 7.16328i −0.359024 0.243138i
\(869\) 46.3639i 1.57279i
\(870\) 0 0
\(871\) 21.4161 12.3646i 0.725657 0.418958i
\(872\) 17.2319 9.94887i 0.583547 0.336911i
\(873\) 0 0
\(874\) 0.767327i 0.0259552i
\(875\) 2.63896 + 0.189469i 0.0892131 + 0.00640521i
\(876\) 0 0
\(877\) −27.1078 + 46.9521i −0.915366 + 1.58546i −0.109001 + 0.994042i \(0.534765\pi\)
−0.806365 + 0.591418i \(0.798568\pi\)
\(878\) 18.0905 + 31.3336i 0.610524 + 1.05746i
\(879\) 0 0
\(880\) 4.67303 + 2.69798i 0.157528 + 0.0909488i
\(881\) 50.1647 1.69009 0.845046 0.534694i \(-0.179573\pi\)
0.845046 + 0.534694i \(0.179573\pi\)
\(882\) 0 0
\(883\) −0.841563 −0.0283208 −0.0141604 0.999900i \(-0.504508\pi\)
−0.0141604 + 0.999900i \(0.504508\pi\)
\(884\) 9.81017 + 5.66390i 0.329952 + 0.190498i
\(885\) 0 0
\(886\) −2.04284 3.53830i −0.0686305 0.118872i
\(887\) 20.0492 34.7262i 0.673185 1.16599i −0.303811 0.952732i \(-0.598259\pi\)
0.976996 0.213258i \(-0.0684075\pi\)
\(888\) 0 0
\(889\) 38.2922 + 2.74926i 1.28428 + 0.0922071i
\(890\) 7.97005i 0.267157i
\(891\) 0 0
\(892\) −12.7222 + 7.34519i −0.425972 + 0.245935i
\(893\) 19.8288 11.4482i 0.663546 0.383098i
\(894\) 0 0
\(895\) 18.8666i 0.630642i
\(896\) −2.19067 1.48356i −0.0731852 0.0495624i
\(897\) 0 0
\(898\) 9.96885 17.2665i 0.332665 0.576192i
\(899\) −21.4840 37.2114i −0.716533 1.24107i
\(900\) 0 0
\(901\) −32.7248 18.8937i −1.09022 0.629440i
\(902\) 4.10243 0.136596
\(903\) 0 0
\(904\) 5.95867 0.198182
\(905\) 22.1268 + 12.7749i 0.735518 + 0.424652i
\(906\) 0 0
\(907\) 22.5945 + 39.1348i 0.750238 + 1.29945i 0.947707 + 0.319142i \(0.103395\pi\)
−0.197469 + 0.980309i \(0.563272\pi\)
\(908\) −11.3913 + 19.7303i −0.378034 + 0.654774i
\(909\) 0 0
\(910\) 2.90887 + 5.99233i 0.0964279 + 0.198644i
\(911\) 58.2281i 1.92918i 0.263746 + 0.964592i \(0.415042\pi\)
−0.263746 + 0.964592i \(0.584958\pi\)
\(912\) 0 0
\(913\) −44.1602 + 25.4959i −1.46149 + 0.843791i
\(914\) −17.4283 + 10.0623i −0.576478 + 0.332830i
\(915\) 0 0
\(916\) 20.2175i 0.668005i
\(917\) 22.9455 33.8820i 0.757729 1.11888i
\(918\) 0 0
\(919\) −6.61745 + 11.4618i −0.218290 + 0.378089i −0.954285 0.298898i \(-0.903381\pi\)
0.735996 + 0.676986i \(0.236714\pi\)
\(920\) 0.133975 + 0.232051i 0.00441701 + 0.00765049i
\(921\) 0 0
\(922\) −0.787476 0.454649i −0.0259341 0.0149731i
\(923\) 11.9907 0.394679
\(924\) 0 0
\(925\) −6.51764 −0.214299
\(926\) −18.5572 10.7140i −0.609827 0.352084i
\(927\) 0 0
\(928\) −4.44949 7.70674i −0.146062 0.252986i
\(929\) −10.4434 + 18.0885i −0.342637 + 0.593464i −0.984921 0.173002i \(-0.944653\pi\)
0.642285 + 0.766466i \(0.277987\pi\)
\(930\) 0 0
\(931\) −15.7504 12.4002i −0.516197 0.406400i
\(932\) 2.63087i 0.0861769i
\(933\) 0 0
\(934\) −10.9917 + 6.34607i −0.359660 + 0.207650i
\(935\) −21.0257 + 12.1392i −0.687615 + 0.396995i
\(936\) 0 0
\(937\) 23.2465i 0.759430i 0.925103 + 0.379715i \(0.123978\pi\)
−0.925103 + 0.379715i \(0.876022\pi\)
\(938\) 1.86103 25.9208i 0.0607649 0.846345i
\(939\) 0 0
\(940\) −3.99768 + 6.92418i −0.130390 + 0.225842i
\(941\) −0.752551 1.30346i −0.0245325 0.0424915i 0.853499 0.521095i \(-0.174476\pi\)
−0.878031 + 0.478604i \(0.841143\pi\)
\(942\) 0 0
\(943\) 0.176423 + 0.101858i 0.00574513 + 0.00331695i
\(944\) 12.6715 0.412421
\(945\) 0 0
\(946\) 31.6403 1.02871
\(947\) 21.0122 + 12.1314i 0.682805 + 0.394218i 0.800911 0.598783i \(-0.204349\pi\)
−0.118106 + 0.993001i \(0.537682\pi\)
\(948\) 0 0
\(949\) 14.6739 + 25.4159i 0.476334 + 0.825035i
\(950\) 1.43185 2.48004i 0.0464554 0.0804631i
\(951\) 0 0
\(952\) 10.7091 5.19856i 0.347085 0.168486i
\(953\) 56.7061i 1.83689i 0.395547 + 0.918446i \(0.370555\pi\)
−0.395547 + 0.918446i \(0.629445\pi\)
\(954\) 0 0
\(955\) 7.00657 4.04524i 0.226727 0.130901i
\(956\) 14.6155 8.43828i 0.472700 0.272913i
\(957\) 0 0
\(958\) 12.8766i 0.416023i
\(959\) 20.5206 9.96132i 0.662643 0.321668i
\(960\) 0 0
\(961\) −3.84315 + 6.65652i −0.123972 + 0.214727i
\(962\) −8.20453 14.2107i −0.264525 0.458170i
\(963\) 0 0
\(964\) −12.5793 7.26268i −0.405153 0.233915i
\(965\) 14.1270 0.454764
\(966\) 0 0
\(967\) 7.23556 0.232680 0.116340 0.993209i \(-0.462884\pi\)
0.116340 + 0.993209i \(0.462884\pi\)
\(968\) −15.6892 9.05816i −0.504270 0.291140i
\(969\) 0 0
\(970\) −3.08176 5.33777i −0.0989495 0.171386i
\(971\) 19.3560 33.5256i 0.621163 1.07589i −0.368106 0.929784i \(-0.619994\pi\)
0.989269 0.146103i \(-0.0466730\pi\)
\(972\) 0 0
\(973\) 1.94228 27.0525i 0.0622667 0.867263i
\(974\) 20.8194i 0.667096i
\(975\) 0 0
\(976\) 2.27035 1.31079i 0.0726722 0.0419573i
\(977\) −15.7279 + 9.08052i −0.503181 + 0.290512i −0.730026 0.683419i \(-0.760492\pi\)
0.226845 + 0.973931i \(0.427159\pi\)
\(978\) 0 0
\(979\) 43.0060i 1.37448i
\(980\) 6.92820 + 1.00000i 0.221313 + 0.0319438i
\(981\) 0 0
\(982\) 13.6635 23.6659i 0.436021 0.755211i
\(983\) −8.19988 14.2026i −0.261536 0.452993i 0.705115 0.709093i \(-0.250896\pi\)
−0.966650 + 0.256100i \(0.917562\pi\)
\(984\) 0 0
\(985\) −12.3615 7.13689i −0.393869 0.227400i
\(986\) 40.0399 1.27513
\(987\) 0 0
\(988\) 7.20977 0.229373
\(989\) 1.36068 + 0.785587i 0.0432670 + 0.0249802i
\(990\) 0 0
\(991\) 5.44584 + 9.43247i 0.172993 + 0.299632i 0.939465 0.342645i \(-0.111323\pi\)
−0.766472 + 0.642278i \(0.777990\pi\)
\(992\) 2.41421 4.18154i 0.0766514 0.132764i
\(993\) 0 0
\(994\) 7.06574 10.4335i 0.224112 0.330930i
\(995\) 3.54195i 0.112287i
\(996\) 0 0
\(997\) 30.7856 17.7740i 0.974988 0.562910i 0.0742349 0.997241i \(-0.476349\pi\)
0.900753 + 0.434331i \(0.143015\pi\)
\(998\) 28.8909 16.6802i 0.914527 0.528002i
\(999\) 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 630.2.be.b.341.1 yes 8
3.2 odd 2 630.2.be.a.341.3 8
5.2 odd 4 3150.2.bp.f.1349.3 8
5.3 odd 4 3150.2.bp.c.1349.2 8
5.4 even 2 3150.2.bf.c.1601.4 8
7.2 even 3 4410.2.b.b.881.8 8
7.3 odd 6 630.2.be.a.521.3 yes 8
7.5 odd 6 4410.2.b.e.881.8 8
15.2 even 4 3150.2.bp.a.1349.3 8
15.8 even 4 3150.2.bp.d.1349.2 8
15.14 odd 2 3150.2.bf.b.1601.2 8
21.2 odd 6 4410.2.b.e.881.1 8
21.5 even 6 4410.2.b.b.881.1 8
21.17 even 6 inner 630.2.be.b.521.1 yes 8
35.3 even 12 3150.2.bp.a.899.3 8
35.17 even 12 3150.2.bp.d.899.2 8
35.24 odd 6 3150.2.bf.b.1151.2 8
105.17 odd 12 3150.2.bp.c.899.2 8
105.38 odd 12 3150.2.bp.f.899.3 8
105.59 even 6 3150.2.bf.c.1151.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.be.a.341.3 8 3.2 odd 2
630.2.be.a.521.3 yes 8 7.3 odd 6
630.2.be.b.341.1 yes 8 1.1 even 1 trivial
630.2.be.b.521.1 yes 8 21.17 even 6 inner
3150.2.bf.b.1151.2 8 35.24 odd 6
3150.2.bf.b.1601.2 8 15.14 odd 2
3150.2.bf.c.1151.4 8 105.59 even 6
3150.2.bf.c.1601.4 8 5.4 even 2
3150.2.bp.a.899.3 8 35.3 even 12
3150.2.bp.a.1349.3 8 15.2 even 4
3150.2.bp.c.899.2 8 105.17 odd 12
3150.2.bp.c.1349.2 8 5.3 odd 4
3150.2.bp.d.899.2 8 35.17 even 12
3150.2.bp.d.1349.2 8 15.8 even 4
3150.2.bp.f.899.3 8 105.38 odd 12
3150.2.bp.f.1349.3 8 5.2 odd 4
4410.2.b.b.881.1 8 21.5 even 6
4410.2.b.b.881.8 8 7.2 even 3
4410.2.b.e.881.1 8 21.2 odd 6
4410.2.b.e.881.8 8 7.5 odd 6