Properties

Label 950.2.q.d.107.2
Level $950$
Weight $2$
Character 950.107
Analytic conductor $7.586$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(107,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.q (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 107.2
Root \(-0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 950.107
Dual form 950.2.q.d.293.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965926 + 0.258819i) q^{2} +(0.517638 - 1.93185i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.00000 - 1.73205i) q^{6} +(1.22474 + 1.22474i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(0.965926 + 0.258819i) q^{2} +(0.517638 - 1.93185i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.00000 - 1.73205i) q^{6} +(1.22474 + 1.22474i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +3.00000 q^{11} +(1.41421 - 1.41421i) q^{12} +(1.93185 - 0.517638i) q^{13} +(0.866025 + 1.50000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.707107 - 0.707107i) q^{18} +(-2.59808 + 3.50000i) q^{19} +(3.00000 - 1.73205i) q^{21} +(2.89778 + 0.776457i) q^{22} +(-1.34486 - 5.01910i) q^{23} +(1.73205 - 1.00000i) q^{24} +2.00000 q^{26} +(2.82843 - 2.82843i) q^{27} +(0.448288 + 1.67303i) q^{28} +3.46410i q^{31} +(0.258819 + 0.965926i) q^{32} +(1.55291 - 5.79555i) q^{33} +(-0.500000 - 0.866025i) q^{36} +(0.707107 - 0.707107i) q^{37} +(-3.41542 + 2.70831i) q^{38} -4.00000i q^{39} +(-4.50000 + 2.59808i) q^{41} +(3.34607 - 0.896575i) q^{42} +(-6.69213 - 1.79315i) q^{43} +(2.59808 + 1.50000i) q^{44} -5.19615i q^{46} +(10.0382 - 2.68973i) q^{47} +(1.93185 - 0.517638i) q^{48} -4.00000i q^{49} +(1.93185 + 0.517638i) q^{52} +(2.89778 - 0.776457i) q^{53} +(3.46410 - 2.00000i) q^{54} +1.73205i q^{56} +(5.41662 + 6.83083i) q^{57} +(-5.19615 - 9.00000i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(-0.896575 + 3.34607i) q^{62} +(-0.448288 - 1.67303i) q^{63} +1.00000i q^{64} +(3.00000 - 5.19615i) q^{66} +(0.517638 + 1.93185i) q^{67} -10.3923 q^{69} +(-9.00000 + 5.19615i) q^{71} +(-0.258819 - 0.965926i) q^{72} +(-3.34607 - 0.896575i) q^{73} +(0.866025 - 0.500000i) q^{74} +(-4.00000 + 1.73205i) q^{76} +(3.67423 + 3.67423i) q^{77} +(1.03528 - 3.86370i) q^{78} +(-1.73205 - 3.00000i) q^{79} +(-5.50000 - 9.52628i) q^{81} +(-5.01910 + 1.34486i) q^{82} +3.46410 q^{84} +(-6.00000 - 3.46410i) q^{86} +(2.12132 + 2.12132i) q^{88} +(-2.59808 + 4.50000i) q^{89} +(3.00000 + 1.73205i) q^{91} +(1.34486 - 5.01910i) q^{92} +(6.69213 + 1.79315i) q^{93} +10.3923 q^{94} +2.00000 q^{96} +(-7.72741 - 2.07055i) q^{97} +(1.03528 - 3.86370i) q^{98} +(-2.59808 - 1.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{6} + 24 q^{11} + 4 q^{16} + 24 q^{21} + 16 q^{26} - 4 q^{36} - 36 q^{41} - 16 q^{61} + 24 q^{66} - 72 q^{71} - 32 q^{76} - 44 q^{81} - 48 q^{86} + 24 q^{91} + 16 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 + 0.258819i 0.683013 + 0.183013i
\(3\) 0.517638 1.93185i 0.298858 1.11536i −0.639246 0.769002i \(-0.720753\pi\)
0.938104 0.346353i \(-0.112580\pi\)
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) 0 0
\(6\) 1.00000 1.73205i 0.408248 0.707107i
\(7\) 1.22474 + 1.22474i 0.462910 + 0.462910i 0.899608 0.436698i \(-0.143852\pi\)
−0.436698 + 0.899608i \(0.643852\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) 0 0
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 1.41421 1.41421i 0.408248 0.408248i
\(13\) 1.93185 0.517638i 0.535799 0.143567i 0.0192343 0.999815i \(-0.493877\pi\)
0.516565 + 0.856248i \(0.327210\pi\)
\(14\) 0.866025 + 1.50000i 0.231455 + 0.400892i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) −2.59808 + 3.50000i −0.596040 + 0.802955i
\(20\) 0 0
\(21\) 3.00000 1.73205i 0.654654 0.377964i
\(22\) 2.89778 + 0.776457i 0.617808 + 0.165541i
\(23\) −1.34486 5.01910i −0.280423 1.04655i −0.952119 0.305727i \(-0.901100\pi\)
0.671696 0.740827i \(-0.265566\pi\)
\(24\) 1.73205 1.00000i 0.353553 0.204124i
\(25\) 0 0
\(26\) 2.00000 0.392232
\(27\) 2.82843 2.82843i 0.544331 0.544331i
\(28\) 0.448288 + 1.67303i 0.0847184 + 0.316173i
\(29\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(30\) 0 0
\(31\) 3.46410i 0.622171i 0.950382 + 0.311086i \(0.100693\pi\)
−0.950382 + 0.311086i \(0.899307\pi\)
\(32\) 0.258819 + 0.965926i 0.0457532 + 0.170753i
\(33\) 1.55291 5.79555i 0.270328 1.00888i
\(34\) 0 0
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 0.707107 0.707107i 0.116248 0.116248i −0.646590 0.762838i \(-0.723806\pi\)
0.762838 + 0.646590i \(0.223806\pi\)
\(38\) −3.41542 + 2.70831i −0.554054 + 0.439346i
\(39\) 4.00000i 0.640513i
\(40\) 0 0
\(41\) −4.50000 + 2.59808i −0.702782 + 0.405751i −0.808383 0.588657i \(-0.799657\pi\)
0.105601 + 0.994409i \(0.466323\pi\)
\(42\) 3.34607 0.896575i 0.516309 0.138345i
\(43\) −6.69213 1.79315i −1.02054 0.273453i −0.290513 0.956871i \(-0.593826\pi\)
−0.730027 + 0.683418i \(0.760493\pi\)
\(44\) 2.59808 + 1.50000i 0.391675 + 0.226134i
\(45\) 0 0
\(46\) 5.19615i 0.766131i
\(47\) 10.0382 2.68973i 1.46422 0.392337i 0.563276 0.826269i \(-0.309541\pi\)
0.900946 + 0.433932i \(0.142874\pi\)
\(48\) 1.93185 0.517638i 0.278839 0.0747146i
\(49\) 4.00000i 0.571429i
\(50\) 0 0
\(51\) 0 0
\(52\) 1.93185 + 0.517638i 0.267900 + 0.0717835i
\(53\) 2.89778 0.776457i 0.398040 0.106655i −0.0542455 0.998528i \(-0.517275\pi\)
0.452286 + 0.891873i \(0.350609\pi\)
\(54\) 3.46410 2.00000i 0.471405 0.272166i
\(55\) 0 0
\(56\) 1.73205i 0.231455i
\(57\) 5.41662 + 6.83083i 0.717449 + 0.904766i
\(58\) 0 0
\(59\) −5.19615 9.00000i −0.676481 1.17170i −0.976034 0.217620i \(-0.930171\pi\)
0.299552 0.954080i \(-0.403163\pi\)
\(60\) 0 0
\(61\) −2.00000 + 3.46410i −0.256074 + 0.443533i −0.965187 0.261562i \(-0.915762\pi\)
0.709113 + 0.705095i \(0.249096\pi\)
\(62\) −0.896575 + 3.34607i −0.113865 + 0.424951i
\(63\) −0.448288 1.67303i −0.0564789 0.210782i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 3.00000 5.19615i 0.369274 0.639602i
\(67\) 0.517638 + 1.93185i 0.0632396 + 0.236013i 0.990310 0.138874i \(-0.0443482\pi\)
−0.927071 + 0.374887i \(0.877682\pi\)
\(68\) 0 0
\(69\) −10.3923 −1.25109
\(70\) 0 0
\(71\) −9.00000 + 5.19615i −1.06810 + 0.616670i −0.927663 0.373419i \(-0.878185\pi\)
−0.140441 + 0.990089i \(0.544852\pi\)
\(72\) −0.258819 0.965926i −0.0305021 0.113835i
\(73\) −3.34607 0.896575i −0.391627 0.104936i 0.0576314 0.998338i \(-0.481645\pi\)
−0.449259 + 0.893402i \(0.648312\pi\)
\(74\) 0.866025 0.500000i 0.100673 0.0581238i
\(75\) 0 0
\(76\) −4.00000 + 1.73205i −0.458831 + 0.198680i
\(77\) 3.67423 + 3.67423i 0.418718 + 0.418718i
\(78\) 1.03528 3.86370i 0.117222 0.437478i
\(79\) −1.73205 3.00000i −0.194871 0.337526i 0.751987 0.659178i \(-0.229095\pi\)
−0.946858 + 0.321651i \(0.895762\pi\)
\(80\) 0 0
\(81\) −5.50000 9.52628i −0.611111 1.05848i
\(82\) −5.01910 + 1.34486i −0.554267 + 0.148515i
\(83\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(84\) 3.46410 0.377964
\(85\) 0 0
\(86\) −6.00000 3.46410i −0.646997 0.373544i
\(87\) 0 0
\(88\) 2.12132 + 2.12132i 0.226134 + 0.226134i
\(89\) −2.59808 + 4.50000i −0.275396 + 0.476999i −0.970235 0.242166i \(-0.922142\pi\)
0.694839 + 0.719165i \(0.255475\pi\)
\(90\) 0 0
\(91\) 3.00000 + 1.73205i 0.314485 + 0.181568i
\(92\) 1.34486 5.01910i 0.140212 0.523277i
\(93\) 6.69213 + 1.79315i 0.693942 + 0.185941i
\(94\) 10.3923 1.07188
\(95\) 0 0
\(96\) 2.00000 0.204124
\(97\) −7.72741 2.07055i −0.784599 0.210233i −0.155788 0.987791i \(-0.549792\pi\)
−0.628811 + 0.777558i \(0.716458\pi\)
\(98\) 1.03528 3.86370i 0.104579 0.390293i
\(99\) −2.59808 1.50000i −0.261116 0.150756i
\(100\) 0 0
\(101\) −9.00000 + 15.5885i −0.895533 + 1.55111i −0.0623905 + 0.998052i \(0.519872\pi\)
−0.833143 + 0.553058i \(0.813461\pi\)
\(102\) 0 0
\(103\) −4.94975 4.94975i −0.487713 0.487713i 0.419871 0.907584i \(-0.362075\pi\)
−0.907584 + 0.419871i \(0.862075\pi\)
\(104\) 1.73205 + 1.00000i 0.169842 + 0.0980581i
\(105\) 0 0
\(106\) 3.00000 0.291386
\(107\) 4.24264 4.24264i 0.410152 0.410152i −0.471640 0.881791i \(-0.656338\pi\)
0.881791 + 0.471640i \(0.156338\pi\)
\(108\) 3.86370 1.03528i 0.371785 0.0996195i
\(109\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(110\) 0 0
\(111\) −1.00000 1.73205i −0.0949158 0.164399i
\(112\) −0.448288 + 1.67303i −0.0423592 + 0.158087i
\(113\) 12.7279 + 12.7279i 1.19734 + 1.19734i 0.974959 + 0.222383i \(0.0713835\pi\)
0.222383 + 0.974959i \(0.428617\pi\)
\(114\) 3.46410 + 8.00000i 0.324443 + 0.749269i
\(115\) 0 0
\(116\) 0 0
\(117\) −1.93185 0.517638i −0.178600 0.0478557i
\(118\) −2.68973 10.0382i −0.247609 0.924091i
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) −2.82843 + 2.82843i −0.256074 + 0.256074i
\(123\) 2.68973 + 10.0382i 0.242524 + 0.905114i
\(124\) −1.73205 + 3.00000i −0.155543 + 0.269408i
\(125\) 0 0
\(126\) 1.73205i 0.154303i
\(127\) −1.81173 6.76148i −0.160765 0.599984i −0.998542 0.0539720i \(-0.982812\pi\)
0.837777 0.546012i \(-0.183855\pi\)
\(128\) −0.258819 + 0.965926i −0.0228766 + 0.0853766i
\(129\) −6.92820 + 12.0000i −0.609994 + 1.05654i
\(130\) 0 0
\(131\) 7.50000 + 12.9904i 0.655278 + 1.13497i 0.981824 + 0.189794i \(0.0607819\pi\)
−0.326546 + 0.945181i \(0.605885\pi\)
\(132\) 4.24264 4.24264i 0.369274 0.369274i
\(133\) −7.46859 + 1.10463i −0.647609 + 0.0957833i
\(134\) 2.00000i 0.172774i
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(138\) −10.0382 2.68973i −0.854508 0.228965i
\(139\) 17.3205 + 10.0000i 1.46911 + 0.848189i 0.999400 0.0346338i \(-0.0110265\pi\)
0.469706 + 0.882823i \(0.344360\pi\)
\(140\) 0 0
\(141\) 20.7846i 1.75038i
\(142\) −10.0382 + 2.68973i −0.842387 + 0.225717i
\(143\) 5.79555 1.55291i 0.484649 0.129861i
\(144\) 1.00000i 0.0833333i
\(145\) 0 0
\(146\) −3.00000 1.73205i −0.248282 0.143346i
\(147\) −7.72741 2.07055i −0.637346 0.170776i
\(148\) 0.965926 0.258819i 0.0793986 0.0212748i
\(149\) −5.19615 + 3.00000i −0.425685 + 0.245770i −0.697507 0.716578i \(-0.745707\pi\)
0.271821 + 0.962348i \(0.412374\pi\)
\(150\) 0 0
\(151\) 20.7846i 1.69143i 0.533637 + 0.845714i \(0.320825\pi\)
−0.533637 + 0.845714i \(0.679175\pi\)
\(152\) −4.31199 + 0.637756i −0.349749 + 0.0517289i
\(153\) 0 0
\(154\) 2.59808 + 4.50000i 0.209359 + 0.362620i
\(155\) 0 0
\(156\) 2.00000 3.46410i 0.160128 0.277350i
\(157\) −4.93117 + 18.4034i −0.393550 + 1.46875i 0.430686 + 0.902502i \(0.358272\pi\)
−0.824236 + 0.566246i \(0.808395\pi\)
\(158\) −0.896575 3.34607i −0.0713277 0.266199i
\(159\) 6.00000i 0.475831i
\(160\) 0 0
\(161\) 4.50000 7.79423i 0.354650 0.614271i
\(162\) −2.84701 10.6252i −0.223682 0.834793i
\(163\) −17.1464 + 17.1464i −1.34301 + 1.34301i −0.449966 + 0.893045i \(0.648564\pi\)
−0.893045 + 0.449966i \(0.851436\pi\)
\(164\) −5.19615 −0.405751
\(165\) 0 0
\(166\) 0 0
\(167\) −5.43520 20.2844i −0.420588 1.56966i −0.773372 0.633952i \(-0.781432\pi\)
0.352784 0.935705i \(-0.385235\pi\)
\(168\) 3.34607 + 0.896575i 0.258155 + 0.0691723i
\(169\) −7.79423 + 4.50000i −0.599556 + 0.346154i
\(170\) 0 0
\(171\) 4.00000 1.73205i 0.305888 0.132453i
\(172\) −4.89898 4.89898i −0.373544 0.373544i
\(173\) −3.88229 + 14.4889i −0.295165 + 1.10157i 0.645922 + 0.763404i \(0.276473\pi\)
−0.941086 + 0.338166i \(0.890193\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) −20.0764 + 5.37945i −1.50903 + 0.404344i
\(178\) −3.67423 + 3.67423i −0.275396 + 0.275396i
\(179\) 5.19615 0.388379 0.194189 0.980964i \(-0.437792\pi\)
0.194189 + 0.980964i \(0.437792\pi\)
\(180\) 0 0
\(181\) −18.0000 10.3923i −1.33793 0.772454i −0.351429 0.936214i \(-0.614304\pi\)
−0.986500 + 0.163760i \(0.947638\pi\)
\(182\) 2.44949 + 2.44949i 0.181568 + 0.181568i
\(183\) 5.65685 + 5.65685i 0.418167 + 0.418167i
\(184\) 2.59808 4.50000i 0.191533 0.331744i
\(185\) 0 0
\(186\) 6.00000 + 3.46410i 0.439941 + 0.254000i
\(187\) 0 0
\(188\) 10.0382 + 2.68973i 0.732111 + 0.196168i
\(189\) 6.92820 0.503953
\(190\) 0 0
\(191\) 24.0000 1.73658 0.868290 0.496058i \(-0.165220\pi\)
0.868290 + 0.496058i \(0.165220\pi\)
\(192\) 1.93185 + 0.517638i 0.139419 + 0.0373573i
\(193\) −0.517638 + 1.93185i −0.0372604 + 0.139058i −0.982050 0.188619i \(-0.939599\pi\)
0.944790 + 0.327677i \(0.106266\pi\)
\(194\) −6.92820 4.00000i −0.497416 0.287183i
\(195\) 0 0
\(196\) 2.00000 3.46410i 0.142857 0.247436i
\(197\) −3.67423 3.67423i −0.261778 0.261778i 0.563998 0.825776i \(-0.309263\pi\)
−0.825776 + 0.563998i \(0.809263\pi\)
\(198\) −2.12132 2.12132i −0.150756 0.150756i
\(199\) 6.92820 + 4.00000i 0.491127 + 0.283552i 0.725042 0.688705i \(-0.241820\pi\)
−0.233915 + 0.972257i \(0.575154\pi\)
\(200\) 0 0
\(201\) 4.00000 0.282138
\(202\) −12.7279 + 12.7279i −0.895533 + 0.895533i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −3.50000 6.06218i −0.243857 0.422372i
\(207\) −1.34486 + 5.01910i −0.0934745 + 0.348851i
\(208\) 1.41421 + 1.41421i 0.0980581 + 0.0980581i
\(209\) −7.79423 + 10.5000i −0.539138 + 0.726300i
\(210\) 0 0
\(211\) 19.5000 11.2583i 1.34244 0.775055i 0.355271 0.934763i \(-0.384389\pi\)
0.987164 + 0.159708i \(0.0510552\pi\)
\(212\) 2.89778 + 0.776457i 0.199020 + 0.0533273i
\(213\) 5.37945 + 20.0764i 0.368594 + 1.37561i
\(214\) 5.19615 3.00000i 0.355202 0.205076i
\(215\) 0 0
\(216\) 4.00000 0.272166
\(217\) −4.24264 + 4.24264i −0.288009 + 0.288009i
\(218\) 0 0
\(219\) −3.46410 + 6.00000i −0.234082 + 0.405442i
\(220\) 0 0
\(221\) 0 0
\(222\) −0.517638 1.93185i −0.0347416 0.129657i
\(223\) 5.95284 22.2163i 0.398632 1.48771i −0.416874 0.908964i \(-0.636874\pi\)
0.815506 0.578749i \(-0.196459\pi\)
\(224\) −0.866025 + 1.50000i −0.0578638 + 0.100223i
\(225\) 0 0
\(226\) 9.00000 + 15.5885i 0.598671 + 1.03693i
\(227\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(228\) 1.27551 + 8.62398i 0.0844729 + 0.571137i
\(229\) 20.0000i 1.32164i −0.750546 0.660819i \(-0.770209\pi\)
0.750546 0.660819i \(-0.229791\pi\)
\(230\) 0 0
\(231\) 9.00000 5.19615i 0.592157 0.341882i
\(232\) 0 0
\(233\) −10.0382 2.68973i −0.657624 0.176210i −0.0854505 0.996342i \(-0.527233\pi\)
−0.572174 + 0.820133i \(0.693900\pi\)
\(234\) −1.73205 1.00000i −0.113228 0.0653720i
\(235\) 0 0
\(236\) 10.3923i 0.676481i
\(237\) −6.69213 + 1.79315i −0.434701 + 0.116478i
\(238\) 0 0
\(239\) 24.0000i 1.55243i −0.630468 0.776215i \(-0.717137\pi\)
0.630468 0.776215i \(-0.282863\pi\)
\(240\) 0 0
\(241\) −12.0000 6.92820i −0.772988 0.446285i 0.0609515 0.998141i \(-0.480586\pi\)
−0.833939 + 0.551856i \(0.813920\pi\)
\(242\) −1.93185 0.517638i −0.124184 0.0332750i
\(243\) −9.65926 + 2.58819i −0.619642 + 0.166032i
\(244\) −3.46410 + 2.00000i −0.221766 + 0.128037i
\(245\) 0 0
\(246\) 10.3923i 0.662589i
\(247\) −3.20736 + 8.10634i −0.204080 + 0.515794i
\(248\) −2.44949 + 2.44949i −0.155543 + 0.155543i
\(249\) 0 0
\(250\) 0 0
\(251\) −12.0000 + 20.7846i −0.757433 + 1.31191i 0.186722 + 0.982413i \(0.440214\pi\)
−0.944156 + 0.329500i \(0.893120\pi\)
\(252\) 0.448288 1.67303i 0.0282395 0.105391i
\(253\) −4.03459 15.0573i −0.253652 0.946644i
\(254\) 7.00000i 0.439219i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(258\) −9.79796 + 9.79796i −0.609994 + 0.609994i
\(259\) 1.73205 0.107624
\(260\) 0 0
\(261\) 0 0
\(262\) 3.88229 + 14.4889i 0.239848 + 0.895126i
\(263\) 25.0955 + 6.72432i 1.54745 + 0.414639i 0.928665 0.370918i \(-0.120957\pi\)
0.618789 + 0.785557i \(0.287624\pi\)
\(264\) 5.19615 3.00000i 0.319801 0.184637i
\(265\) 0 0
\(266\) −7.50000 0.866025i −0.459855 0.0530994i
\(267\) 7.34847 + 7.34847i 0.449719 + 0.449719i
\(268\) −0.517638 + 1.93185i −0.0316198 + 0.118007i
\(269\) −10.3923 18.0000i −0.633630 1.09748i −0.986804 0.161922i \(-0.948231\pi\)
0.353174 0.935558i \(-0.385102\pi\)
\(270\) 0 0
\(271\) −1.00000 1.73205i −0.0607457 0.105215i 0.834053 0.551684i \(-0.186015\pi\)
−0.894799 + 0.446469i \(0.852681\pi\)
\(272\) 0 0
\(273\) 4.89898 4.89898i 0.296500 0.296500i
\(274\) 0 0
\(275\) 0 0
\(276\) −9.00000 5.19615i −0.541736 0.312772i
\(277\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(278\) 14.1421 + 14.1421i 0.848189 + 0.848189i
\(279\) 1.73205 3.00000i 0.103695 0.179605i
\(280\) 0 0
\(281\) 13.5000 + 7.79423i 0.805342 + 0.464965i 0.845336 0.534235i \(-0.179400\pi\)
−0.0399934 + 0.999200i \(0.512734\pi\)
\(282\) 5.37945 20.0764i 0.320342 1.19553i
\(283\) −30.1146 8.06918i −1.79013 0.479663i −0.797759 0.602977i \(-0.793981\pi\)
−0.992368 + 0.123314i \(0.960648\pi\)
\(284\) −10.3923 −0.616670
\(285\) 0 0
\(286\) 6.00000 0.354787
\(287\) −8.69333 2.32937i −0.513151 0.137498i
\(288\) 0.258819 0.965926i 0.0152511 0.0569177i
\(289\) 14.7224 + 8.50000i 0.866025 + 0.500000i
\(290\) 0 0
\(291\) −8.00000 + 13.8564i −0.468968 + 0.812277i
\(292\) −2.44949 2.44949i −0.143346 0.143346i
\(293\) −6.36396 6.36396i −0.371787 0.371787i 0.496341 0.868128i \(-0.334677\pi\)
−0.868128 + 0.496341i \(0.834677\pi\)
\(294\) −6.92820 4.00000i −0.404061 0.233285i
\(295\) 0 0
\(296\) 1.00000 0.0581238
\(297\) 8.48528 8.48528i 0.492366 0.492366i
\(298\) −5.79555 + 1.55291i −0.335727 + 0.0899579i
\(299\) −5.19615 9.00000i −0.300501 0.520483i
\(300\) 0 0
\(301\) −6.00000 10.3923i −0.345834 0.599002i
\(302\) −5.37945 + 20.0764i −0.309553 + 1.15527i
\(303\) 25.4558 + 25.4558i 1.46240 + 1.46240i
\(304\) −4.33013 0.500000i −0.248350 0.0286770i
\(305\) 0 0
\(306\) 0 0
\(307\) −19.3185 5.17638i −1.10257 0.295432i −0.338757 0.940874i \(-0.610006\pi\)
−0.763809 + 0.645442i \(0.776673\pi\)
\(308\) 1.34486 + 5.01910i 0.0766307 + 0.285990i
\(309\) −12.1244 + 7.00000i −0.689730 + 0.398216i
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 2.82843 2.82843i 0.160128 0.160128i
\(313\) −2.68973 10.0382i −0.152032 0.567392i −0.999341 0.0362920i \(-0.988445\pi\)
0.847309 0.531100i \(-0.178221\pi\)
\(314\) −9.52628 + 16.5000i −0.537599 + 0.931149i
\(315\) 0 0
\(316\) 3.46410i 0.194871i
\(317\) −6.98811 26.0800i −0.392492 1.46480i −0.826011 0.563654i \(-0.809395\pi\)
0.433519 0.901144i \(-0.357272\pi\)
\(318\) 1.55291 5.79555i 0.0870831 0.324999i
\(319\) 0 0
\(320\) 0 0
\(321\) −6.00000 10.3923i −0.334887 0.580042i
\(322\) 6.36396 6.36396i 0.354650 0.354650i
\(323\) 0 0
\(324\) 11.0000i 0.611111i
\(325\) 0 0
\(326\) −21.0000 + 12.1244i −1.16308 + 0.671506i
\(327\) 0 0
\(328\) −5.01910 1.34486i −0.277133 0.0742576i
\(329\) 15.5885 + 9.00000i 0.859419 + 0.496186i
\(330\) 0 0
\(331\) 19.0526i 1.04722i −0.851957 0.523612i \(-0.824584\pi\)
0.851957 0.523612i \(-0.175416\pi\)
\(332\) 0 0
\(333\) −0.965926 + 0.258819i −0.0529324 + 0.0141832i
\(334\) 21.0000i 1.14907i
\(335\) 0 0
\(336\) 3.00000 + 1.73205i 0.163663 + 0.0944911i
\(337\) 1.93185 + 0.517638i 0.105235 + 0.0281975i 0.311052 0.950393i \(-0.399319\pi\)
−0.205817 + 0.978590i \(0.565985\pi\)
\(338\) −8.69333 + 2.32937i −0.472855 + 0.126701i
\(339\) 31.1769 18.0000i 1.69330 0.977626i
\(340\) 0 0
\(341\) 10.3923i 0.562775i
\(342\) 4.31199 0.637756i 0.233166 0.0344859i
\(343\) 13.4722 13.4722i 0.727430 0.727430i
\(344\) −3.46410 6.00000i −0.186772 0.323498i
\(345\) 0 0
\(346\) −7.50000 + 12.9904i −0.403202 + 0.698367i
\(347\) −2.68973 + 10.0382i −0.144392 + 0.538879i 0.855390 + 0.517985i \(0.173318\pi\)
−0.999782 + 0.0208935i \(0.993349\pi\)
\(348\) 0 0
\(349\) 4.00000i 0.214115i −0.994253 0.107058i \(-0.965857\pi\)
0.994253 0.107058i \(-0.0341429\pi\)
\(350\) 0 0
\(351\) 4.00000 6.92820i 0.213504 0.369800i
\(352\) 0.776457 + 2.89778i 0.0413853 + 0.154452i
\(353\) −7.34847 + 7.34847i −0.391120 + 0.391120i −0.875086 0.483967i \(-0.839196\pi\)
0.483967 + 0.875086i \(0.339196\pi\)
\(354\) −20.7846 −1.10469
\(355\) 0 0
\(356\) −4.50000 + 2.59808i −0.238500 + 0.137698i
\(357\) 0 0
\(358\) 5.01910 + 1.34486i 0.265268 + 0.0710782i
\(359\) 5.19615 3.00000i 0.274242 0.158334i −0.356572 0.934268i \(-0.616054\pi\)
0.630814 + 0.775934i \(0.282721\pi\)
\(360\) 0 0
\(361\) −5.50000 18.1865i −0.289474 0.957186i
\(362\) −14.6969 14.6969i −0.772454 0.772454i
\(363\) −1.03528 + 3.86370i −0.0543379 + 0.202792i
\(364\) 1.73205 + 3.00000i 0.0907841 + 0.157243i
\(365\) 0 0
\(366\) 4.00000 + 6.92820i 0.209083 + 0.362143i
\(367\) −3.34607 + 0.896575i −0.174663 + 0.0468009i −0.345091 0.938569i \(-0.612152\pi\)
0.170427 + 0.985370i \(0.445485\pi\)
\(368\) 3.67423 3.67423i 0.191533 0.191533i
\(369\) 5.19615 0.270501
\(370\) 0 0
\(371\) 4.50000 + 2.59808i 0.233628 + 0.134885i
\(372\) 4.89898 + 4.89898i 0.254000 + 0.254000i
\(373\) −21.9203 21.9203i −1.13499 1.13499i −0.989335 0.145655i \(-0.953471\pi\)
−0.145655 0.989335i \(-0.546529\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 9.00000 + 5.19615i 0.464140 + 0.267971i
\(377\) 0 0
\(378\) 6.69213 + 1.79315i 0.344206 + 0.0922297i
\(379\) 3.46410 0.177939 0.0889695 0.996034i \(-0.471643\pi\)
0.0889695 + 0.996034i \(0.471643\pi\)
\(380\) 0 0
\(381\) −14.0000 −0.717242
\(382\) 23.1822 + 6.21166i 1.18611 + 0.317816i
\(383\) 6.21166 23.1822i 0.317401 1.18456i −0.604333 0.796732i \(-0.706560\pi\)
0.921733 0.387824i \(-0.126773\pi\)
\(384\) 1.73205 + 1.00000i 0.0883883 + 0.0510310i
\(385\) 0 0
\(386\) −1.00000 + 1.73205i −0.0508987 + 0.0881591i
\(387\) 4.89898 + 4.89898i 0.249029 + 0.249029i
\(388\) −5.65685 5.65685i −0.287183 0.287183i
\(389\) 25.9808 + 15.0000i 1.31728 + 0.760530i 0.983290 0.182047i \(-0.0582724\pi\)
0.333987 + 0.942578i \(0.391606\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 2.82843 2.82843i 0.142857 0.142857i
\(393\) 28.9778 7.76457i 1.46174 0.391671i
\(394\) −2.59808 4.50000i −0.130889 0.226707i
\(395\) 0 0
\(396\) −1.50000 2.59808i −0.0753778 0.130558i
\(397\) −0.448288 + 1.67303i −0.0224989 + 0.0839671i −0.976262 0.216591i \(-0.930506\pi\)
0.953764 + 0.300558i \(0.0971729\pi\)
\(398\) 5.65685 + 5.65685i 0.283552 + 0.283552i
\(399\) −1.73205 + 15.0000i −0.0867110 + 0.750939i
\(400\) 0 0
\(401\) 18.0000 10.3923i 0.898877 0.518967i 0.0220414 0.999757i \(-0.492983\pi\)
0.876836 + 0.480790i \(0.159650\pi\)
\(402\) 3.86370 + 1.03528i 0.192704 + 0.0516349i
\(403\) 1.79315 + 6.69213i 0.0893232 + 0.333359i
\(404\) −15.5885 + 9.00000i −0.775555 + 0.447767i
\(405\) 0 0
\(406\) 0 0
\(407\) 2.12132 2.12132i 0.105150 0.105150i
\(408\) 0 0
\(409\) −18.1865 + 31.5000i −0.899266 + 1.55757i −0.0708321 + 0.997488i \(0.522565\pi\)
−0.828434 + 0.560087i \(0.810768\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −1.81173 6.76148i −0.0892577 0.333114i
\(413\) 4.65874 17.3867i 0.229242 0.855542i
\(414\) −2.59808 + 4.50000i −0.127688 + 0.221163i
\(415\) 0 0
\(416\) 1.00000 + 1.73205i 0.0490290 + 0.0849208i
\(417\) 28.2843 28.2843i 1.38509 1.38509i
\(418\) −10.2462 + 8.12493i −0.501160 + 0.397403i
\(419\) 9.00000i 0.439679i 0.975536 + 0.219839i \(0.0705533\pi\)
−0.975536 + 0.219839i \(0.929447\pi\)
\(420\) 0 0
\(421\) 9.00000 5.19615i 0.438633 0.253245i −0.264385 0.964417i \(-0.585169\pi\)
0.703018 + 0.711172i \(0.251835\pi\)
\(422\) 21.7494 5.82774i 1.05875 0.283690i
\(423\) −10.0382 2.68973i −0.488074 0.130779i
\(424\) 2.59808 + 1.50000i 0.126174 + 0.0728464i
\(425\) 0 0
\(426\) 20.7846i 1.00702i
\(427\) −6.69213 + 1.79315i −0.323855 + 0.0867767i
\(428\) 5.79555 1.55291i 0.280139 0.0750629i
\(429\) 12.0000i 0.579365i
\(430\) 0 0
\(431\) −9.00000 5.19615i −0.433515 0.250290i 0.267328 0.963606i \(-0.413859\pi\)
−0.700843 + 0.713316i \(0.747193\pi\)
\(432\) 3.86370 + 1.03528i 0.185893 + 0.0498097i
\(433\) −27.0459 + 7.24693i −1.29974 + 0.348265i −0.841353 0.540485i \(-0.818241\pi\)
−0.458391 + 0.888751i \(0.651574\pi\)
\(434\) −5.19615 + 3.00000i −0.249423 + 0.144005i
\(435\) 0 0
\(436\) 0 0
\(437\) 21.0609 + 8.33298i 1.00748 + 0.398620i
\(438\) −4.89898 + 4.89898i −0.234082 + 0.234082i
\(439\) 12.1244 + 21.0000i 0.578664 + 1.00228i 0.995633 + 0.0933546i \(0.0297590\pi\)
−0.416969 + 0.908921i \(0.636908\pi\)
\(440\) 0 0
\(441\) −2.00000 + 3.46410i −0.0952381 + 0.164957i
\(442\) 0 0
\(443\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(444\) 2.00000i 0.0949158i
\(445\) 0 0
\(446\) 11.5000 19.9186i 0.544541 0.943172i
\(447\) 3.10583 + 11.5911i 0.146901 + 0.548241i
\(448\) −1.22474 + 1.22474i −0.0578638 + 0.0578638i
\(449\) −5.19615 −0.245222 −0.122611 0.992455i \(-0.539127\pi\)
−0.122611 + 0.992455i \(0.539127\pi\)
\(450\) 0 0
\(451\) −13.5000 + 7.79423i −0.635690 + 0.367016i
\(452\) 4.65874 + 17.3867i 0.219129 + 0.817800i
\(453\) 40.1528 + 10.7589i 1.88654 + 0.505497i
\(454\) 0 0
\(455\) 0 0
\(456\) −1.00000 + 8.66025i −0.0468293 + 0.405554i
\(457\) 26.9444 + 26.9444i 1.26041 + 1.26041i 0.950897 + 0.309509i \(0.100165\pi\)
0.309509 + 0.950897i \(0.399835\pi\)
\(458\) 5.17638 19.3185i 0.241876 0.902695i
\(459\) 0 0
\(460\) 0 0
\(461\) −9.00000 15.5885i −0.419172 0.726027i 0.576685 0.816967i \(-0.304346\pi\)
−0.995856 + 0.0909401i \(0.971013\pi\)
\(462\) 10.0382 2.68973i 0.467019 0.125137i
\(463\) 23.2702 23.2702i 1.08146 1.08146i 0.0850817 0.996374i \(-0.472885\pi\)
0.996374 0.0850817i \(-0.0271151\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −9.00000 5.19615i −0.416917 0.240707i
\(467\) 29.3939 + 29.3939i 1.36019 + 1.36019i 0.873673 + 0.486513i \(0.161731\pi\)
0.486513 + 0.873673i \(0.338269\pi\)
\(468\) −1.41421 1.41421i −0.0653720 0.0653720i
\(469\) −1.73205 + 3.00000i −0.0799787 + 0.138527i
\(470\) 0 0
\(471\) 33.0000 + 19.0526i 1.52056 + 0.877896i
\(472\) 2.68973 10.0382i 0.123805 0.462045i
\(473\) −20.0764 5.37945i −0.923113 0.247348i
\(474\) −6.92820 −0.318223
\(475\) 0 0
\(476\) 0 0
\(477\) −2.89778 0.776457i −0.132680 0.0355515i
\(478\) 6.21166 23.1822i 0.284115 1.06033i
\(479\) 5.19615 + 3.00000i 0.237418 + 0.137073i 0.613990 0.789314i \(-0.289564\pi\)
−0.376571 + 0.926388i \(0.622897\pi\)
\(480\) 0 0
\(481\) 1.00000 1.73205i 0.0455961 0.0789747i
\(482\) −9.79796 9.79796i −0.446285 0.446285i
\(483\) −12.7279 12.7279i −0.579141 0.579141i
\(484\) −1.73205 1.00000i −0.0787296 0.0454545i
\(485\) 0 0
\(486\) −10.0000 −0.453609
\(487\) 17.6777 17.6777i 0.801052 0.801052i −0.182208 0.983260i \(-0.558325\pi\)
0.983260 + 0.182208i \(0.0583245\pi\)
\(488\) −3.86370 + 1.03528i −0.174902 + 0.0468648i
\(489\) 24.2487 + 42.0000i 1.09656 + 1.89931i
\(490\) 0 0
\(491\) 10.5000 + 18.1865i 0.473858 + 0.820747i 0.999552 0.0299272i \(-0.00952753\pi\)
−0.525694 + 0.850674i \(0.676194\pi\)
\(492\) −2.68973 + 10.0382i −0.121262 + 0.452557i
\(493\) 0 0
\(494\) −5.19615 + 7.00000i −0.233786 + 0.314945i
\(495\) 0 0
\(496\) −3.00000 + 1.73205i −0.134704 + 0.0777714i
\(497\) −17.3867 4.65874i −0.779899 0.208973i
\(498\) 0 0
\(499\) −6.06218 + 3.50000i −0.271380 + 0.156682i −0.629515 0.776989i \(-0.716746\pi\)
0.358134 + 0.933670i \(0.383413\pi\)
\(500\) 0 0
\(501\) −42.0000 −1.87642
\(502\) −16.9706 + 16.9706i −0.757433 + 0.757433i
\(503\) −1.34486 5.01910i −0.0599645 0.223791i 0.929441 0.368972i \(-0.120290\pi\)
−0.989405 + 0.145181i \(0.953623\pi\)
\(504\) 0.866025 1.50000i 0.0385758 0.0668153i
\(505\) 0 0
\(506\) 15.5885i 0.692991i
\(507\) 4.65874 + 17.3867i 0.206902 + 0.772169i
\(508\) 1.81173 6.76148i 0.0803827 0.299992i
\(509\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(510\) 0 0
\(511\) −3.00000 5.19615i −0.132712 0.229864i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 2.55103 + 17.2480i 0.112631 + 0.761516i
\(514\) 0 0
\(515\) 0 0
\(516\) −12.0000 + 6.92820i −0.528271 + 0.304997i
\(517\) 30.1146 8.06918i 1.32444 0.354882i
\(518\) 1.67303 + 0.448288i 0.0735088 + 0.0196966i
\(519\) 25.9808 + 15.0000i 1.14043 + 0.658427i
\(520\) 0 0
\(521\) 20.7846i 0.910590i −0.890341 0.455295i \(-0.849534\pi\)
0.890341 0.455295i \(-0.150466\pi\)
\(522\) 0 0
\(523\) −27.0459 + 7.24693i −1.18264 + 0.316886i −0.795971 0.605334i \(-0.793039\pi\)
−0.386664 + 0.922221i \(0.626373\pi\)
\(524\) 15.0000i 0.655278i
\(525\) 0 0
\(526\) 22.5000 + 12.9904i 0.981047 + 0.566408i
\(527\) 0 0
\(528\) 5.79555 1.55291i 0.252219 0.0675819i
\(529\) −3.46410 + 2.00000i −0.150613 + 0.0869565i
\(530\) 0 0
\(531\) 10.3923i 0.450988i
\(532\) −7.02030 2.77766i −0.304369 0.120427i
\(533\) −7.34847 + 7.34847i −0.318298 + 0.318298i
\(534\) 5.19615 + 9.00000i 0.224860 + 0.389468i
\(535\) 0 0
\(536\) −1.00000 + 1.73205i −0.0431934 + 0.0748132i
\(537\) 2.68973 10.0382i 0.116070 0.433180i
\(538\) −5.37945 20.0764i −0.231925 0.865555i
\(539\) 12.0000i 0.516877i
\(540\) 0 0
\(541\) 5.00000 8.66025i 0.214967 0.372333i −0.738296 0.674477i \(-0.764369\pi\)
0.953262 + 0.302144i \(0.0977023\pi\)
\(542\) −0.517638 1.93185i −0.0222345 0.0829801i
\(543\) −29.3939 + 29.3939i −1.26141 + 1.26141i
\(544\) 0 0
\(545\) 0 0
\(546\) 6.00000 3.46410i 0.256776 0.148250i
\(547\) 5.69402 + 21.2504i 0.243459 + 0.908600i 0.974152 + 0.225894i \(0.0725303\pi\)
−0.730693 + 0.682706i \(0.760803\pi\)
\(548\) 0 0
\(549\) 3.46410 2.00000i 0.147844 0.0853579i
\(550\) 0 0
\(551\) 0 0
\(552\) −7.34847 7.34847i −0.312772 0.312772i
\(553\) 1.55291 5.79555i 0.0660366 0.246452i
\(554\) 0 0
\(555\) 0 0
\(556\) 10.0000 + 17.3205i 0.424094 + 0.734553i
\(557\) 5.01910 1.34486i 0.212666 0.0569837i −0.150913 0.988547i \(-0.548221\pi\)
0.363579 + 0.931563i \(0.381555\pi\)
\(558\) 2.44949 2.44949i 0.103695 0.103695i
\(559\) −13.8564 −0.586064
\(560\) 0 0
\(561\) 0 0
\(562\) 11.0227 + 11.0227i 0.464965 + 0.464965i
\(563\) 16.9706 + 16.9706i 0.715224 + 0.715224i 0.967623 0.252399i \(-0.0812196\pi\)
−0.252399 + 0.967623i \(0.581220\pi\)
\(564\) 10.3923 18.0000i 0.437595 0.757937i
\(565\) 0 0
\(566\) −27.0000 15.5885i −1.13489 0.655232i
\(567\) 4.93117 18.4034i 0.207089 0.772868i
\(568\) −10.0382 2.68973i −0.421193 0.112858i
\(569\) 5.19615 0.217834 0.108917 0.994051i \(-0.465262\pi\)
0.108917 + 0.994051i \(0.465262\pi\)
\(570\) 0 0
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 5.79555 + 1.55291i 0.242324 + 0.0649306i
\(573\) 12.4233 46.3644i 0.518991 1.93690i
\(574\) −7.79423 4.50000i −0.325325 0.187826i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) −7.34847 7.34847i −0.305921 0.305921i 0.537404 0.843325i \(-0.319405\pi\)
−0.843325 + 0.537404i \(0.819405\pi\)
\(578\) 12.0208 + 12.0208i 0.500000 + 0.500000i
\(579\) 3.46410 + 2.00000i 0.143963 + 0.0831172i
\(580\) 0 0
\(581\) 0 0
\(582\) −11.3137 + 11.3137i −0.468968 + 0.468968i
\(583\) 8.69333 2.32937i 0.360041 0.0964727i
\(584\) −1.73205 3.00000i −0.0716728 0.124141i
\(585\) 0 0
\(586\) −4.50000 7.79423i −0.185893 0.321977i
\(587\) 5.37945 20.0764i 0.222034 0.828641i −0.761537 0.648121i \(-0.775555\pi\)
0.983571 0.180520i \(-0.0577782\pi\)
\(588\) −5.65685 5.65685i −0.233285 0.233285i
\(589\) −12.1244 9.00000i −0.499575 0.370839i
\(590\) 0 0
\(591\) −9.00000 + 5.19615i −0.370211 + 0.213741i
\(592\) 0.965926 + 0.258819i 0.0396993 + 0.0106374i
\(593\) 10.7589 + 40.1528i 0.441815 + 1.64888i 0.724210 + 0.689579i \(0.242204\pi\)
−0.282395 + 0.959298i \(0.591129\pi\)
\(594\) 10.3923 6.00000i 0.426401 0.246183i
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 11.3137 11.3137i 0.463039 0.463039i
\(598\) −2.68973 10.0382i −0.109991 0.410492i
\(599\) 10.3923 18.0000i 0.424618 0.735460i −0.571767 0.820416i \(-0.693742\pi\)
0.996385 + 0.0849563i \(0.0270751\pi\)
\(600\) 0 0
\(601\) 22.5167i 0.918474i 0.888314 + 0.459237i \(0.151877\pi\)
−0.888314 + 0.459237i \(0.848123\pi\)
\(602\) −3.10583 11.5911i −0.126584 0.472418i
\(603\) 0.517638 1.93185i 0.0210799 0.0786711i
\(604\) −10.3923 + 18.0000i −0.422857 + 0.732410i
\(605\) 0 0
\(606\) 18.0000 + 31.1769i 0.731200 + 1.26648i
\(607\) −7.77817 + 7.77817i −0.315706 + 0.315706i −0.847115 0.531409i \(-0.821663\pi\)
0.531409 + 0.847115i \(0.321663\pi\)
\(608\) −4.05317 1.60368i −0.164378 0.0650379i
\(609\) 0 0
\(610\) 0 0
\(611\) 18.0000 10.3923i 0.728202 0.420428i
\(612\) 0 0
\(613\) −5.01910 1.34486i −0.202719 0.0543185i 0.156030 0.987752i \(-0.450130\pi\)
−0.358750 + 0.933434i \(0.616797\pi\)
\(614\) −17.3205 10.0000i −0.698999 0.403567i
\(615\) 0 0
\(616\) 5.19615i 0.209359i
\(617\) 30.1146 8.06918i 1.21237 0.324853i 0.404677 0.914460i \(-0.367384\pi\)
0.807690 + 0.589607i \(0.200717\pi\)
\(618\) −13.5230 + 3.62347i −0.543973 + 0.145757i
\(619\) 31.0000i 1.24600i −0.782224 0.622998i \(-0.785915\pi\)
0.782224 0.622998i \(-0.214085\pi\)
\(620\) 0 0
\(621\) −18.0000 10.3923i −0.722315 0.417029i
\(622\) 0 0
\(623\) −8.69333 + 2.32937i −0.348291 + 0.0933243i
\(624\) 3.46410 2.00000i 0.138675 0.0800641i
\(625\) 0 0
\(626\) 10.3923i 0.415360i
\(627\) 16.2499 + 20.4925i 0.648957 + 0.818391i
\(628\) −13.4722 + 13.4722i −0.537599 + 0.537599i
\(629\) 0 0
\(630\) 0 0
\(631\) 13.0000 22.5167i 0.517522 0.896374i −0.482271 0.876022i \(-0.660188\pi\)
0.999793 0.0203520i \(-0.00647871\pi\)
\(632\) 0.896575 3.34607i 0.0356639 0.133099i
\(633\) −11.6555 43.4988i −0.463264 1.72892i
\(634\) 27.0000i 1.07231i
\(635\) 0 0
\(636\) 3.00000 5.19615i 0.118958 0.206041i
\(637\) −2.07055 7.72741i −0.0820383 0.306171i
\(638\) 0 0
\(639\) 10.3923 0.411113
\(640\) 0 0
\(641\) 18.0000 10.3923i 0.710957 0.410471i −0.100458 0.994941i \(-0.532031\pi\)
0.811415 + 0.584470i \(0.198698\pi\)
\(642\) −3.10583 11.5911i −0.122577 0.457465i
\(643\) 33.4607 + 8.96575i 1.31956 + 0.353575i 0.848813 0.528694i \(-0.177318\pi\)
0.470747 + 0.882268i \(0.343985\pi\)
\(644\) 7.79423 4.50000i 0.307136 0.177325i
\(645\) 0 0
\(646\) 0 0
\(647\) 3.67423 + 3.67423i 0.144449 + 0.144449i 0.775633 0.631184i \(-0.217431\pi\)
−0.631184 + 0.775633i \(0.717431\pi\)
\(648\) 2.84701 10.6252i 0.111841 0.417397i
\(649\) −15.5885 27.0000i −0.611900 1.05984i
\(650\) 0 0
\(651\) 6.00000 + 10.3923i 0.235159 + 0.407307i
\(652\) −23.4225 + 6.27603i −0.917294 + 0.245788i
\(653\) −11.0227 + 11.0227i −0.431352 + 0.431352i −0.889088 0.457736i \(-0.848660\pi\)
0.457736 + 0.889088i \(0.348660\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −4.50000 2.59808i −0.175695 0.101438i
\(657\) 2.44949 + 2.44949i 0.0955637 + 0.0955637i
\(658\) 12.7279 + 12.7279i 0.496186 + 0.496186i
\(659\) 7.79423 13.5000i 0.303620 0.525885i −0.673333 0.739339i \(-0.735138\pi\)
0.976953 + 0.213454i \(0.0684713\pi\)
\(660\) 0 0
\(661\) −9.00000 5.19615i −0.350059 0.202107i 0.314652 0.949207i \(-0.398112\pi\)
−0.664711 + 0.747100i \(0.731446\pi\)
\(662\) 4.93117 18.4034i 0.191655 0.715267i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −1.00000 −0.0387492
\(667\) 0 0
\(668\) 5.43520 20.2844i 0.210294 0.784829i
\(669\) −39.8372 23.0000i −1.54019 0.889231i
\(670\) 0 0
\(671\) −6.00000 + 10.3923i −0.231627 + 0.401190i
\(672\) 2.44949 + 2.44949i 0.0944911 + 0.0944911i
\(673\) −22.6274 22.6274i −0.872223 0.872223i 0.120492 0.992714i \(-0.461553\pi\)
−0.992714 + 0.120492i \(0.961553\pi\)
\(674\) 1.73205 + 1.00000i 0.0667161 + 0.0385186i
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) 23.3345 23.3345i 0.896819 0.896819i −0.0983348 0.995153i \(-0.531352\pi\)
0.995153 + 0.0983348i \(0.0313516\pi\)
\(678\) 34.7733 9.31749i 1.33546 0.357836i
\(679\) −6.92820 12.0000i −0.265880 0.460518i
\(680\) 0 0
\(681\) 0 0
\(682\) −2.68973 + 10.0382i −0.102995 + 0.384382i
\(683\) 25.4558 + 25.4558i 0.974041 + 0.974041i 0.999671 0.0256307i \(-0.00815939\pi\)
−0.0256307 + 0.999671i \(0.508159\pi\)
\(684\) 4.33013 + 0.500000i 0.165567 + 0.0191180i
\(685\) 0 0
\(686\) 16.5000 9.52628i 0.629973 0.363715i
\(687\) −38.6370 10.3528i −1.47409 0.394982i
\(688\) −1.79315 6.69213i −0.0683632 0.255135i
\(689\) 5.19615 3.00000i 0.197958 0.114291i
\(690\) 0 0
\(691\) −17.0000 −0.646710 −0.323355 0.946278i \(-0.604811\pi\)
−0.323355 + 0.946278i \(0.604811\pi\)
\(692\) −10.6066 + 10.6066i −0.403202 + 0.403202i
\(693\) −1.34486 5.01910i −0.0510871 0.190660i
\(694\) −5.19615 + 9.00000i −0.197243 + 0.341635i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 1.03528 3.86370i 0.0391858 0.146243i
\(699\) −10.3923 + 18.0000i −0.393073 + 0.680823i
\(700\) 0 0
\(701\) −6.00000 10.3923i −0.226617 0.392512i 0.730186 0.683248i \(-0.239433\pi\)
−0.956803 + 0.290736i \(0.906100\pi\)
\(702\) 5.65685 5.65685i 0.213504 0.213504i
\(703\) 0.637756 + 4.31199i 0.0240534 + 0.162630i
\(704\) 3.00000i 0.113067i
\(705\) 0 0
\(706\) −9.00000 + 5.19615i −0.338719 + 0.195560i
\(707\) −30.1146 + 8.06918i −1.13258 + 0.303473i
\(708\) −20.0764 5.37945i −0.754517 0.202172i
\(709\) −27.7128 16.0000i −1.04078 0.600893i −0.120723 0.992686i \(-0.538521\pi\)
−0.920053 + 0.391794i \(0.871855\pi\)
\(710\) 0 0
\(711\) 3.46410i 0.129914i
\(712\) −5.01910 + 1.34486i −0.188099 + 0.0504009i
\(713\) 17.3867 4.65874i 0.651136 0.174471i
\(714\) 0 0
\(715\) 0 0
\(716\) 4.50000 + 2.59808i 0.168173 + 0.0970947i
\(717\) −46.3644 12.4233i −1.73151 0.463957i
\(718\) 5.79555 1.55291i 0.216288 0.0579542i
\(719\) 15.5885 9.00000i 0.581351 0.335643i −0.180319 0.983608i \(-0.557713\pi\)
0.761670 + 0.647965i \(0.224380\pi\)
\(720\) 0 0
\(721\) 12.1244i 0.451535i
\(722\) −0.605571 18.9903i −0.0225370 0.706748i
\(723\) −19.5959 + 19.5959i −0.728780 + 0.728780i
\(724\) −10.3923 18.0000i −0.386227 0.668965i
\(725\) 0 0
\(726\) −2.00000 + 3.46410i −0.0742270 + 0.128565i
\(727\) −6.27603 + 23.4225i −0.232765 + 0.868691i 0.746379 + 0.665522i \(0.231791\pi\)
−0.979144 + 0.203169i \(0.934876\pi\)
\(728\) 0.896575 + 3.34607i 0.0332293 + 0.124013i
\(729\) 13.0000i 0.481481i
\(730\) 0 0
\(731\) 0 0
\(732\) 2.07055 + 7.72741i 0.0765298 + 0.285613i
\(733\) −33.0681 + 33.0681i −1.22140 + 1.22140i −0.254264 + 0.967135i \(0.581833\pi\)
−0.967135 + 0.254264i \(0.918167\pi\)
\(734\) −3.46410 −0.127862
\(735\) 0 0
\(736\) 4.50000 2.59808i 0.165872 0.0957664i
\(737\) 1.55291 + 5.79555i 0.0572023 + 0.213482i
\(738\) 5.01910 + 1.34486i 0.184756 + 0.0495051i
\(739\) −14.7224 + 8.50000i −0.541573 + 0.312678i −0.745716 0.666264i \(-0.767893\pi\)
0.204143 + 0.978941i \(0.434559\pi\)
\(740\) 0 0
\(741\) 14.0000 + 10.3923i 0.514303 + 0.381771i
\(742\) 3.67423 + 3.67423i 0.134885 + 0.134885i
\(743\) 5.43520 20.2844i 0.199398 0.744164i −0.791686 0.610928i \(-0.790796\pi\)
0.991084 0.133236i \(-0.0425368\pi\)
\(744\) 3.46410 + 6.00000i 0.127000 + 0.219971i
\(745\) 0 0
\(746\) −15.5000 26.8468i −0.567495 0.982931i
\(747\) 0 0
\(748\) 0 0
\(749\) 10.3923 0.379727
\(750\) 0 0
\(751\) 39.0000 + 22.5167i 1.42313 + 0.821645i 0.996565 0.0828123i \(-0.0263902\pi\)
0.426565 + 0.904457i \(0.359724\pi\)
\(752\) 7.34847 + 7.34847i 0.267971 + 0.267971i
\(753\) 33.9411 + 33.9411i 1.23688 + 1.23688i
\(754\) 0 0
\(755\) 0 0
\(756\) 6.00000 + 3.46410i 0.218218 + 0.125988i
\(757\) −5.82774 + 21.7494i −0.211813 + 0.790496i 0.775451 + 0.631407i \(0.217522\pi\)
−0.987264 + 0.159089i \(0.949144\pi\)
\(758\) 3.34607 + 0.896575i 0.121535 + 0.0325651i
\(759\) −31.1769 −1.13165
\(760\) 0 0
\(761\) 21.0000 0.761249 0.380625 0.924730i \(-0.375709\pi\)
0.380625 + 0.924730i \(0.375709\pi\)
\(762\) −13.5230 3.62347i −0.489885 0.131264i
\(763\) 0 0
\(764\) 20.7846 + 12.0000i 0.751961 + 0.434145i
\(765\) 0 0
\(766\) 12.0000 20.7846i 0.433578 0.750978i
\(767\) −14.6969 14.6969i −0.530676 0.530676i
\(768\) 1.41421 + 1.41421i 0.0510310 + 0.0510310i
\(769\) 29.4449 + 17.0000i 1.06181 + 0.613036i 0.925932 0.377690i \(-0.123282\pi\)
0.135877 + 0.990726i \(0.456615\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.41421 + 1.41421i −0.0508987 + 0.0508987i
\(773\) 20.2844 5.43520i 0.729581 0.195491i 0.125138 0.992139i \(-0.460063\pi\)
0.604443 + 0.796649i \(0.293396\pi\)
\(774\) 3.46410 + 6.00000i 0.124515 + 0.215666i
\(775\) 0 0
\(776\) −4.00000 6.92820i −0.143592 0.248708i
\(777\) 0.896575 3.34607i 0.0321645 0.120039i
\(778\) 21.2132 + 21.2132i 0.760530 + 0.760530i
\(779\) 2.59808 22.5000i 0.0930857 0.806146i
\(780\) 0 0
\(781\) −27.0000 + 15.5885i −0.966136 + 0.557799i
\(782\) 0 0
\(783\) 0 0
\(784\) 3.46410 2.00000i 0.123718 0.0714286i
\(785\) 0 0
\(786\) 30.0000 1.07006
\(787\) −11.3137 + 11.3137i −0.403290 + 0.403290i −0.879391 0.476101i \(-0.842050\pi\)
0.476101 + 0.879391i \(0.342050\pi\)
\(788\) −1.34486 5.01910i −0.0479088 0.178798i
\(789\) 25.9808 45.0000i 0.924940 1.60204i
\(790\) 0 0
\(791\) 31.1769i 1.10852i
\(792\) −0.776457 2.89778i −0.0275902 0.102968i
\(793\) −2.07055 + 7.72741i −0.0735275 + 0.274408i
\(794\) −0.866025 + 1.50000i −0.0307341 + 0.0532330i
\(795\) 0 0
\(796\) 4.00000 + 6.92820i 0.141776 + 0.245564i
\(797\) −10.6066 + 10.6066i −0.375705 + 0.375705i −0.869550 0.493845i \(-0.835591\pi\)
0.493845 + 0.869550i \(0.335591\pi\)
\(798\) −5.55532 + 14.0406i −0.196656 + 0.497032i
\(799\) 0 0
\(800\) 0 0
\(801\) 4.50000 2.59808i 0.159000 0.0917985i
\(802\) 20.0764 5.37945i 0.708922 0.189955i
\(803\) −10.0382 2.68973i −0.354240 0.0949184i
\(804\) 3.46410 + 2.00000i 0.122169 + 0.0705346i
\(805\) 0 0
\(806\) 6.92820i 0.244036i
\(807\) −40.1528 + 10.7589i −1.41344 + 0.378731i
\(808\) −17.3867 + 4.65874i −0.611661 + 0.163894i
\(809\) 42.0000i 1.47664i 0.674450 + 0.738321i \(0.264381\pi\)
−0.674450 + 0.738321i \(0.735619\pi\)
\(810\) 0 0
\(811\) −40.5000 23.3827i −1.42215 0.821077i −0.425665 0.904881i \(-0.639960\pi\)
−0.996482 + 0.0838036i \(0.973293\pi\)
\(812\) 0 0
\(813\) −3.86370 + 1.03528i −0.135506 + 0.0363087i
\(814\) 2.59808 1.50000i 0.0910625 0.0525750i
\(815\) 0 0
\(816\) 0 0
\(817\) 23.6627 18.7637i 0.827853 0.656459i
\(818\) −25.7196 + 25.7196i −0.899266 + 0.899266i
\(819\) −1.73205 3.00000i −0.0605228 0.104828i
\(820\) 0 0
\(821\) −3.00000 + 5.19615i −0.104701 + 0.181347i −0.913616 0.406578i \(-0.866722\pi\)
0.808915 + 0.587925i \(0.200055\pi\)
\(822\) 0 0
\(823\) 1.34486 + 5.01910i 0.0468790 + 0.174955i 0.985396 0.170278i \(-0.0544666\pi\)
−0.938517 + 0.345233i \(0.887800\pi\)
\(824\) 7.00000i 0.243857i
\(825\) 0 0
\(826\) 9.00000 15.5885i 0.313150 0.542392i
\(827\) 9.31749 + 34.7733i 0.324001 + 1.20919i 0.915313 + 0.402744i \(0.131944\pi\)
−0.591312 + 0.806443i \(0.701390\pi\)
\(828\) −3.67423 + 3.67423i −0.127688 + 0.127688i
\(829\) −27.7128 −0.962506 −0.481253 0.876582i \(-0.659818\pi\)
−0.481253 + 0.876582i \(0.659818\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0.517638 + 1.93185i 0.0179459 + 0.0669749i
\(833\) 0 0
\(834\) 34.6410 20.0000i 1.19952 0.692543i
\(835\) 0 0
\(836\) −12.0000 + 5.19615i −0.415029 + 0.179713i
\(837\) 9.79796 + 9.79796i 0.338667 + 0.338667i
\(838\) −2.32937 + 8.69333i −0.0804668 + 0.300306i
\(839\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(840\) 0 0
\(841\) 14.5000 + 25.1147i 0.500000 + 0.866025i
\(842\) 10.0382 2.68973i 0.345939 0.0926941i
\(843\) 22.0454 22.0454i 0.759284 0.759284i
\(844\) 22.5167 0.775055
\(845\) 0 0
\(846\) −9.00000 5.19615i −0.309426 0.178647i
\(847\) −2.44949 2.44949i −0.0841655 0.0841655i
\(848\) 2.12132 + 2.12132i 0.0728464 + 0.0728464i
\(849\) −31.1769 + 54.0000i −1.06999 + 1.85328i
\(850\) 0 0
\(851\) −4.50000 2.59808i −0.154258 0.0890609i
\(852\) −5.37945 + 20.0764i −0.184297 + 0.687806i
\(853\) −13.3843 3.58630i −0.458268 0.122793i 0.0222973 0.999751i \(-0.492902\pi\)
−0.480566 + 0.876959i \(0.659569\pi\)
\(854\) −6.92820 −0.237078
\(855\) 0 0
\(856\) 6.00000 0.205076
\(857\) −46.3644 12.4233i −1.58378 0.424372i −0.643686 0.765290i \(-0.722596\pi\)
−0.940093 + 0.340917i \(0.889262\pi\)
\(858\) 3.10583 11.5911i 0.106031 0.395714i
\(859\) −9.52628 5.50000i −0.325032 0.187658i 0.328601 0.944469i \(-0.393423\pi\)
−0.653633 + 0.756811i \(0.726756\pi\)
\(860\) 0 0
\(861\) −9.00000 + 15.5885i −0.306719 + 0.531253i
\(862\) −7.34847 7.34847i −0.250290 0.250290i
\(863\) 10.6066 + 10.6066i 0.361053 + 0.361053i 0.864201 0.503148i \(-0.167825\pi\)
−0.503148 + 0.864201i \(0.667825\pi\)
\(864\) 3.46410 + 2.00000i 0.117851 + 0.0680414i
\(865\) 0 0
\(866\) −28.0000 −0.951479
\(867\) 24.0416 24.0416i 0.816497 0.816497i
\(868\) −5.79555 + 1.55291i −0.196714 + 0.0527093i
\(869\) −5.19615 9.00000i −0.176267 0.305304i
\(870\) 0 0
\(871\) 2.00000 + 3.46410i 0.0677674 + 0.117377i
\(872\) 0 0
\(873\) 5.65685 + 5.65685i 0.191456 + 0.191456i
\(874\) 18.1865 + 13.5000i 0.615169 + 0.456644i
\(875\) 0 0
\(876\) −6.00000 + 3.46410i −0.202721 + 0.117041i
\(877\) −45.3985 12.1645i −1.53300 0.410766i −0.609003 0.793168i \(-0.708430\pi\)
−0.923996 + 0.382402i \(0.875097\pi\)
\(878\) 6.27603 + 23.4225i 0.211806 + 0.790470i
\(879\) −15.5885 + 9.00000i −0.525786 + 0.303562i
\(880\) 0 0
\(881\) 15.0000 0.505363 0.252681 0.967550i \(-0.418688\pi\)
0.252681 + 0.967550i \(0.418688\pi\)
\(882\) −2.82843 + 2.82843i −0.0952381 + 0.0952381i
\(883\) −9.86233 36.8067i −0.331894 1.23864i −0.907198 0.420705i \(-0.861783\pi\)
0.575304 0.817940i \(-0.304884\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(888\) 0.517638 1.93185i 0.0173708 0.0648287i
\(889\) 6.06218 10.5000i 0.203319 0.352159i
\(890\) 0 0
\(891\) −16.5000 28.5788i −0.552771 0.957427i
\(892\) 16.2635 16.2635i 0.544541 0.544541i
\(893\) −16.6660 + 42.1218i −0.557705 + 1.40955i
\(894\) 12.0000i 0.401340i
\(895\) 0 0
\(896\) −1.50000 + 0.866025i −0.0501115 + 0.0289319i
\(897\) −20.0764 + 5.37945i −0.670331 + 0.179615i
\(898\) −5.01910 1.34486i −0.167489 0.0448787i
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) −15.0573 + 4.03459i −0.501353 + 0.134337i
\(903\) −23.1822 + 6.21166i −0.771456 + 0.206711i
\(904\) 18.0000i 0.598671i
\(905\) 0 0
\(906\) 36.0000 + 20.7846i 1.19602 + 0.690522i
\(907\) −42.5007 11.3880i −1.41121 0.378134i −0.528856 0.848712i \(-0.677379\pi\)
−0.882358 + 0.470578i \(0.844045\pi\)
\(908\) 0 0
\(909\) 15.5885 9.00000i 0.517036 0.298511i
\(910\) 0 0
\(911\) 31.1769i 1.03294i −0.856306 0.516469i \(-0.827246\pi\)
0.856306 0.516469i \(-0.172754\pi\)
\(912\) −3.20736 + 8.10634i −0.106206 + 0.268428i
\(913\) 0 0
\(914\) 19.0526 + 33.0000i 0.630203 + 1.09154i
\(915\) 0 0
\(916\) 10.0000 17.3205i 0.330409 0.572286i
\(917\) −6.72432 + 25.0955i −0.222056 + 0.828726i
\(918\) 0 0
\(919\) 46.0000i 1.51740i 0.651440 + 0.758700i \(0.274165\pi\)
−0.651440 + 0.758700i \(0.725835\pi\)
\(920\) 0 0
\(921\) −20.0000 + 34.6410i −0.659022 + 1.14146i
\(922\) −4.65874 17.3867i −0.153428 0.572599i
\(923\) −14.6969 + 14.6969i −0.483756 + 0.483756i
\(924\) 10.3923 0.341882
\(925\) 0 0
\(926\) 28.5000 16.4545i 0.936568 0.540728i
\(927\) 1.81173 + 6.76148i 0.0595051 + 0.222076i
\(928\) 0 0
\(929\) −18.1865 + 10.5000i −0.596681 + 0.344494i −0.767735 0.640768i \(-0.778616\pi\)
0.171054 + 0.985262i \(0.445283\pi\)
\(930\) 0 0
\(931\) 14.0000 + 10.3923i 0.458831 + 0.340594i
\(932\) −7.34847 7.34847i −0.240707 0.240707i
\(933\) 0 0
\(934\) 20.7846 + 36.0000i 0.680093 + 1.17796i
\(935\) 0 0
\(936\) −1.00000 1.73205i −0.0326860 0.0566139i
\(937\) −36.8067 + 9.86233i −1.20242 + 0.322188i −0.803785 0.594920i \(-0.797184\pi\)
−0.398638 + 0.917108i \(0.630517\pi\)
\(938\) −2.44949 + 2.44949i −0.0799787 + 0.0799787i
\(939\) −20.7846 −0.678280
\(940\) 0 0
\(941\) 36.0000 + 20.7846i 1.17357 + 0.677559i 0.954517 0.298155i \(-0.0963712\pi\)
0.219049 + 0.975714i \(0.429705\pi\)
\(942\) 26.9444 + 26.9444i 0.877896 + 0.877896i
\(943\) 19.0919 + 19.0919i 0.621717 + 0.621717i
\(944\) 5.19615 9.00000i 0.169120 0.292925i
\(945\) 0 0
\(946\) −18.0000 10.3923i −0.585230 0.337883i
\(947\) 10.7589 40.1528i 0.349617 1.30479i −0.537507 0.843259i \(-0.680634\pi\)
0.887124 0.461531i \(-0.152700\pi\)
\(948\) −6.69213 1.79315i −0.217350 0.0582388i
\(949\) −6.92820 −0.224899
\(950\) 0 0
\(951\) −54.0000 −1.75107
\(952\) 0 0
\(953\) 9.31749 34.7733i 0.301823 1.12642i −0.633823 0.773478i \(-0.718515\pi\)
0.935646 0.352940i \(-0.114818\pi\)
\(954\) −2.59808 1.50000i −0.0841158 0.0485643i
\(955\) 0 0
\(956\) 12.0000 20.7846i 0.388108 0.672222i
\(957\) 0 0
\(958\) 4.24264 + 4.24264i 0.137073 + 0.137073i
\(959\) 0 0
\(960\) 0 0
\(961\) 19.0000 0.612903
\(962\) 1.41421 1.41421i 0.0455961 0.0455961i
\(963\) −5.79555 + 1.55291i −0.186759 + 0.0500420i
\(964\) −6.92820 12.0000i −0.223142 0.386494i
\(965\) 0 0
\(966\) −9.00000 15.5885i −0.289570 0.501550i
\(967\) 9.86233 36.8067i 0.317151 1.18362i −0.604819 0.796363i \(-0.706755\pi\)
0.921970 0.387261i \(-0.126579\pi\)
\(968\) −1.41421 1.41421i −0.0454545 0.0454545i
\(969\) 0 0
\(970\) 0 0
\(971\) 9.00000 5.19615i 0.288824 0.166752i −0.348588 0.937276i \(-0.613339\pi\)
0.637411 + 0.770524i \(0.280005\pi\)
\(972\) −9.65926 2.58819i −0.309821 0.0830162i
\(973\) 8.96575 + 33.4607i 0.287429 + 1.07270i
\(974\) 21.6506 12.5000i 0.693731 0.400526i
\(975\) 0 0
\(976\) −4.00000 −0.128037
\(977\) −33.9411 + 33.9411i −1.08587 + 1.08587i −0.0899242 + 0.995949i \(0.528662\pi\)
−0.995949 + 0.0899242i \(0.971338\pi\)
\(978\) 12.5521 + 46.8449i 0.401371 + 1.49794i
\(979\) −7.79423 + 13.5000i −0.249105 + 0.431462i
\(980\) 0 0
\(981\) 0 0
\(982\) 5.43520 + 20.2844i 0.173444 + 0.647303i
\(983\) 5.43520 20.2844i 0.173356 0.646973i −0.823470 0.567360i \(-0.807965\pi\)
0.996826 0.0796132i \(-0.0253685\pi\)
\(984\) −5.19615 + 9.00000i −0.165647 + 0.286910i
\(985\) 0 0
\(986\) 0 0
\(987\) 25.4558 25.4558i 0.810268 0.810268i
\(988\) −6.83083 + 5.41662i −0.217318 + 0.172326i
\(989\) 36.0000i 1.14473i
\(990\) 0 0
\(991\) −6.00000 + 3.46410i −0.190596 + 0.110041i −0.592262 0.805746i \(-0.701765\pi\)
0.401665 + 0.915786i \(0.368431\pi\)
\(992\) −3.34607 + 0.896575i −0.106238 + 0.0284663i
\(993\) −36.8067 9.86233i −1.16803 0.312972i
\(994\) −15.5885 9.00000i −0.494436 0.285463i
\(995\) 0 0
\(996\) 0 0
\(997\) 8.36516 2.24144i 0.264927 0.0709871i −0.123910 0.992293i \(-0.539543\pi\)
0.388837 + 0.921306i \(0.372877\pi\)
\(998\) −6.76148 + 1.81173i −0.214031 + 0.0573494i
\(999\) 4.00000i 0.126554i
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 950.2.q.d.107.2 yes 8
5.2 odd 4 inner 950.2.q.d.943.1 yes 8
5.3 odd 4 inner 950.2.q.d.943.2 yes 8
5.4 even 2 inner 950.2.q.d.107.1 8
19.8 odd 6 inner 950.2.q.d.407.2 yes 8
95.8 even 12 inner 950.2.q.d.293.2 yes 8
95.27 even 12 inner 950.2.q.d.293.1 yes 8
95.84 odd 6 inner 950.2.q.d.407.1 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.q.d.107.1 8 5.4 even 2 inner
950.2.q.d.107.2 yes 8 1.1 even 1 trivial
950.2.q.d.293.1 yes 8 95.27 even 12 inner
950.2.q.d.293.2 yes 8 95.8 even 12 inner
950.2.q.d.407.1 yes 8 95.84 odd 6 inner
950.2.q.d.407.2 yes 8 19.8 odd 6 inner
950.2.q.d.943.1 yes 8 5.2 odd 4 inner
950.2.q.d.943.2 yes 8 5.3 odd 4 inner