Properties

Label 637.2.g.h.263.2
Level $637$
Weight $2$
Character 637.263
Analytic conductor $5.086$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(263,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.263");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.1485512441856.7
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 24x^{6} + 455x^{4} + 2904x^{2} + 14641 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 263.2
Root \(-1.34203 - 2.32446i\) of defining polynomial
Character \(\chi\) \(=\) 637.263
Dual form 637.2.g.h.373.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} -1.41421 q^{3} +(0.500000 + 0.866025i) q^{4} +(2.04914 + 3.54921i) q^{5} +(0.707107 - 1.22474i) q^{6} -3.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} -1.41421 q^{3} +(0.500000 + 0.866025i) q^{4} +(2.04914 + 3.54921i) q^{5} +(0.707107 - 1.22474i) q^{6} -3.00000 q^{8} -1.00000 q^{9} -4.09827 q^{10} -3.79583 q^{11} +(-0.707107 - 1.22474i) q^{12} +(0.634922 + 3.54921i) q^{13} +(-2.89792 - 5.01934i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.634922 - 1.09972i) q^{17} +(0.500000 - 0.866025i) q^{18} +2.82843 q^{19} +(-2.04914 + 3.54921i) q^{20} +(1.89792 - 3.28729i) q^{22} +(3.89792 - 6.75139i) q^{23} +4.24264 q^{24} +(-5.89792 + 10.2155i) q^{25} +(-3.39116 - 1.22474i) q^{26} +5.65685 q^{27} +(-0.397916 - 0.689210i) q^{29} +5.79583 q^{30} +(-0.707107 + 1.22474i) q^{31} +(-2.50000 - 4.33013i) q^{32} +5.36812 q^{33} +1.26984 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-1.39792 + 2.42126i) q^{37} +(-1.41421 + 2.44949i) q^{38} +(-0.897916 - 5.01934i) q^{39} +(-6.14741 - 10.6476i) q^{40} +(1.48640 + 2.57452i) q^{41} +(-3.89792 + 6.75139i) q^{43} +(-1.89792 - 3.28729i) q^{44} +(-2.04914 - 3.54921i) q^{45} +(3.89792 + 6.75139i) q^{46} +(1.41421 + 2.44949i) q^{47} +(-0.707107 + 1.22474i) q^{48} +(-5.89792 - 10.2155i) q^{50} +(0.897916 + 1.55524i) q^{51} +(-2.75624 + 2.32446i) q^{52} +(6.29583 - 10.9047i) q^{53} +(-2.82843 + 4.89898i) q^{54} +(-7.77817 - 13.4722i) q^{55} -4.00000 q^{57} +0.795832 q^{58} +(-6.21959 - 10.7726i) q^{59} +(2.89792 - 5.01934i) q^{60} -8.34091 q^{61} +(-0.707107 - 1.22474i) q^{62} +7.00000 q^{64} +(-11.2958 + 9.52628i) q^{65} +(-2.68406 + 4.64893i) q^{66} -3.79583 q^{67} +(0.634922 - 1.09972i) q^{68} +(-5.51249 + 9.54790i) q^{69} +(-3.00000 + 5.19615i) q^{71} +3.00000 q^{72} +(-6.29178 + 10.8977i) q^{73} +(-1.39792 - 2.42126i) q^{74} +(8.34091 - 14.4469i) q^{75} +(1.41421 + 2.44949i) q^{76} +(4.79583 + 1.73205i) q^{78} +(1.10208 + 1.90887i) q^{79} +4.09827 q^{80} -5.00000 q^{81} -2.97280 q^{82} +9.89949 q^{83} +(2.60208 - 4.50694i) q^{85} +(-3.89792 - 6.75139i) q^{86} +(0.562738 + 0.974691i) q^{87} +11.3875 q^{88} +(-7.48944 + 12.9721i) q^{89} +4.09827 q^{90} +7.79583 q^{92} +(1.00000 - 1.73205i) q^{93} -2.82843 q^{94} +(5.79583 + 10.0387i) q^{95} +(3.53553 + 6.12372i) q^{96} +(-2.12132 + 3.67423i) q^{97} +3.79583 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} + 4 q^{4} - 24 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} + 4 q^{4} - 24 q^{8} - 8 q^{9} + 8 q^{11} - 4 q^{15} + 4 q^{16} + 4 q^{18} - 4 q^{22} + 12 q^{23} - 28 q^{25} + 16 q^{29} + 8 q^{30} - 20 q^{32} - 4 q^{36} + 8 q^{37} + 12 q^{39} - 12 q^{43} + 4 q^{44} + 12 q^{46} - 28 q^{50} - 12 q^{51} + 12 q^{53} - 32 q^{57} - 32 q^{58} + 4 q^{60} + 56 q^{64} - 52 q^{65} + 8 q^{67} - 24 q^{71} + 24 q^{72} + 8 q^{74} + 28 q^{79} - 40 q^{81} + 40 q^{85} - 12 q^{86} - 24 q^{88} + 24 q^{92} + 8 q^{93} + 8 q^{95} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i −0.986869 0.161521i \(-0.948360\pi\)
0.633316 + 0.773893i \(0.281693\pi\)
\(3\) −1.41421 −0.816497 −0.408248 0.912871i \(-0.633860\pi\)
−0.408248 + 0.912871i \(0.633860\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 2.04914 + 3.54921i 0.916401 + 1.58725i 0.804836 + 0.593497i \(0.202253\pi\)
0.111565 + 0.993757i \(0.464414\pi\)
\(6\) 0.707107 1.22474i 0.288675 0.500000i
\(7\) 0 0
\(8\) −3.00000 −1.06066
\(9\) −1.00000 −0.333333
\(10\) −4.09827 −1.29599
\(11\) −3.79583 −1.14449 −0.572243 0.820084i \(-0.693927\pi\)
−0.572243 + 0.820084i \(0.693927\pi\)
\(12\) −0.707107 1.22474i −0.204124 0.353553i
\(13\) 0.634922 + 3.54921i 0.176096 + 0.984373i
\(14\) 0 0
\(15\) −2.89792 5.01934i −0.748239 1.29599i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −0.634922 1.09972i −0.153991 0.266721i 0.778700 0.627396i \(-0.215879\pi\)
−0.932691 + 0.360676i \(0.882546\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) 2.82843 0.648886 0.324443 0.945905i \(-0.394823\pi\)
0.324443 + 0.945905i \(0.394823\pi\)
\(20\) −2.04914 + 3.54921i −0.458201 + 0.793627i
\(21\) 0 0
\(22\) 1.89792 3.28729i 0.404637 0.700852i
\(23\) 3.89792 6.75139i 0.812772 1.40776i −0.0981454 0.995172i \(-0.531291\pi\)
0.910917 0.412590i \(-0.135376\pi\)
\(24\) 4.24264 0.866025
\(25\) −5.89792 + 10.2155i −1.17958 + 2.04310i
\(26\) −3.39116 1.22474i −0.665062 0.240192i
\(27\) 5.65685 1.08866
\(28\) 0 0
\(29\) −0.397916 0.689210i −0.0738911 0.127983i 0.826712 0.562625i \(-0.190208\pi\)
−0.900604 + 0.434642i \(0.856875\pi\)
\(30\) 5.79583 1.05817
\(31\) −0.707107 + 1.22474i −0.127000 + 0.219971i −0.922513 0.385966i \(-0.873868\pi\)
0.795513 + 0.605937i \(0.207202\pi\)
\(32\) −2.50000 4.33013i −0.441942 0.765466i
\(33\) 5.36812 0.934469
\(34\) 1.26984 0.217777
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −1.39792 + 2.42126i −0.229816 + 0.398053i −0.957753 0.287591i \(-0.907146\pi\)
0.727937 + 0.685643i \(0.240479\pi\)
\(38\) −1.41421 + 2.44949i −0.229416 + 0.397360i
\(39\) −0.897916 5.01934i −0.143782 0.803737i
\(40\) −6.14741 10.6476i −0.971990 1.68354i
\(41\) 1.48640 + 2.57452i 0.232136 + 0.402072i 0.958437 0.285306i \(-0.0920951\pi\)
−0.726300 + 0.687378i \(0.758762\pi\)
\(42\) 0 0
\(43\) −3.89792 + 6.75139i −0.594427 + 1.02958i 0.399201 + 0.916863i \(0.369288\pi\)
−0.993628 + 0.112714i \(0.964046\pi\)
\(44\) −1.89792 3.28729i −0.286122 0.495577i
\(45\) −2.04914 3.54921i −0.305467 0.529085i
\(46\) 3.89792 + 6.75139i 0.574716 + 0.995438i
\(47\) 1.41421 + 2.44949i 0.206284 + 0.357295i 0.950541 0.310599i \(-0.100530\pi\)
−0.744257 + 0.667893i \(0.767196\pi\)
\(48\) −0.707107 + 1.22474i −0.102062 + 0.176777i
\(49\) 0 0
\(50\) −5.89792 10.2155i −0.834091 1.44469i
\(51\) 0.897916 + 1.55524i 0.125733 + 0.217777i
\(52\) −2.75624 + 2.32446i −0.382222 + 0.322345i
\(53\) 6.29583 10.9047i 0.864799 1.49788i −0.00244768 0.999997i \(-0.500779\pi\)
0.867247 0.497879i \(-0.165888\pi\)
\(54\) −2.82843 + 4.89898i −0.384900 + 0.666667i
\(55\) −7.77817 13.4722i −1.04881 1.81659i
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) 0.795832 0.104498
\(59\) −6.21959 10.7726i −0.809722 1.40248i −0.913057 0.407833i \(-0.866285\pi\)
0.103335 0.994647i \(-0.467049\pi\)
\(60\) 2.89792 5.01934i 0.374119 0.647994i
\(61\) −8.34091 −1.06794 −0.533972 0.845502i \(-0.679301\pi\)
−0.533972 + 0.845502i \(0.679301\pi\)
\(62\) −0.707107 1.22474i −0.0898027 0.155543i
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) −11.2958 + 9.52628i −1.40108 + 1.18159i
\(66\) −2.68406 + 4.64893i −0.330385 + 0.572243i
\(67\) −3.79583 −0.463735 −0.231867 0.972747i \(-0.574484\pi\)
−0.231867 + 0.972747i \(0.574484\pi\)
\(68\) 0.634922 1.09972i 0.0769956 0.133360i
\(69\) −5.51249 + 9.54790i −0.663625 + 1.14943i
\(70\) 0 0
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) 3.00000 0.353553
\(73\) −6.29178 + 10.8977i −0.736397 + 1.27548i 0.217711 + 0.976013i \(0.430141\pi\)
−0.954108 + 0.299463i \(0.903192\pi\)
\(74\) −1.39792 2.42126i −0.162504 0.281466i
\(75\) 8.34091 14.4469i 0.963126 1.66818i
\(76\) 1.41421 + 2.44949i 0.162221 + 0.280976i
\(77\) 0 0
\(78\) 4.79583 + 1.73205i 0.543021 + 0.196116i
\(79\) 1.10208 + 1.90887i 0.123994 + 0.214764i 0.921339 0.388759i \(-0.127096\pi\)
−0.797345 + 0.603524i \(0.793763\pi\)
\(80\) 4.09827 0.458201
\(81\) −5.00000 −0.555556
\(82\) −2.97280 −0.328290
\(83\) 9.89949 1.08661 0.543305 0.839535i \(-0.317173\pi\)
0.543305 + 0.839535i \(0.317173\pi\)
\(84\) 0 0
\(85\) 2.60208 4.50694i 0.282236 0.488847i
\(86\) −3.89792 6.75139i −0.420323 0.728021i
\(87\) 0.562738 + 0.974691i 0.0603318 + 0.104498i
\(88\) 11.3875 1.21391
\(89\) −7.48944 + 12.9721i −0.793879 + 1.37504i 0.129670 + 0.991557i \(0.458608\pi\)
−0.923549 + 0.383481i \(0.874725\pi\)
\(90\) 4.09827 0.431996
\(91\) 0 0
\(92\) 7.79583 0.812772
\(93\) 1.00000 1.73205i 0.103695 0.179605i
\(94\) −2.82843 −0.291730
\(95\) 5.79583 + 10.0387i 0.594640 + 1.02995i
\(96\) 3.53553 + 6.12372i 0.360844 + 0.625000i
\(97\) −2.12132 + 3.67423i −0.215387 + 0.373062i −0.953392 0.301733i \(-0.902435\pi\)
0.738005 + 0.674795i \(0.235768\pi\)
\(98\) 0 0
\(99\) 3.79583 0.381495
\(100\) −11.7958 −1.17958
\(101\) 9.75513 0.970671 0.485336 0.874328i \(-0.338697\pi\)
0.485336 + 0.874328i \(0.338697\pi\)
\(102\) −1.79583 −0.177814
\(103\) 2.68406 + 4.64893i 0.264468 + 0.458072i 0.967424 0.253161i \(-0.0814703\pi\)
−0.702956 + 0.711233i \(0.748137\pi\)
\(104\) −1.90477 10.6476i −0.186778 1.04409i
\(105\) 0 0
\(106\) 6.29583 + 10.9047i 0.611505 + 1.05916i
\(107\) 3.00000 5.19615i 0.290021 0.502331i −0.683793 0.729676i \(-0.739671\pi\)
0.973814 + 0.227345i \(0.0730044\pi\)
\(108\) 2.82843 + 4.89898i 0.272166 + 0.471405i
\(109\) −0.795832 + 1.37842i −0.0762268 + 0.132029i −0.901619 0.432531i \(-0.857621\pi\)
0.825392 + 0.564560i \(0.190954\pi\)
\(110\) 15.5563 1.48324
\(111\) 1.97695 3.42418i 0.187644 0.325009i
\(112\) 0 0
\(113\) −1.29583 + 2.24445i −0.121902 + 0.211140i −0.920518 0.390701i \(-0.872233\pi\)
0.798616 + 0.601841i \(0.205566\pi\)
\(114\) 2.00000 3.46410i 0.187317 0.324443i
\(115\) 31.9494 2.97930
\(116\) 0.397916 0.689210i 0.0369456 0.0639916i
\(117\) −0.634922 3.54921i −0.0586986 0.328124i
\(118\) 12.4392 1.14512
\(119\) 0 0
\(120\) 8.69375 + 15.0580i 0.793627 + 1.37460i
\(121\) 3.40834 0.309849
\(122\) 4.17046 7.22344i 0.377575 0.653980i
\(123\) −2.10208 3.64092i −0.189539 0.328290i
\(124\) −1.41421 −0.127000
\(125\) −27.8512 −2.49108
\(126\) 0 0
\(127\) 5.79583 + 10.0387i 0.514297 + 0.890788i 0.999862 + 0.0165881i \(0.00528038\pi\)
−0.485566 + 0.874200i \(0.661386\pi\)
\(128\) 1.50000 2.59808i 0.132583 0.229640i
\(129\) 5.51249 9.54790i 0.485347 0.840646i
\(130\) −2.60208 14.5456i −0.228218 1.27573i
\(131\) 2.68406 + 4.64893i 0.234507 + 0.406178i 0.959129 0.282968i \(-0.0913190\pi\)
−0.724622 + 0.689146i \(0.757986\pi\)
\(132\) 2.68406 + 4.64893i 0.233617 + 0.404637i
\(133\) 0 0
\(134\) 1.89792 3.28729i 0.163955 0.283978i
\(135\) 11.5917 + 20.0773i 0.997652 + 1.72798i
\(136\) 1.90477 + 3.29915i 0.163332 + 0.282900i
\(137\) 9.39792 + 16.2777i 0.802918 + 1.39069i 0.917688 + 0.397303i \(0.130054\pi\)
−0.114769 + 0.993392i \(0.536613\pi\)
\(138\) −5.51249 9.54790i −0.469254 0.812772i
\(139\) −0.851476 + 1.47480i −0.0722212 + 0.125091i −0.899875 0.436149i \(-0.856342\pi\)
0.827653 + 0.561240i \(0.189675\pi\)
\(140\) 0 0
\(141\) −2.00000 3.46410i −0.168430 0.291730i
\(142\) −3.00000 5.19615i −0.251754 0.436051i
\(143\) −2.41006 13.4722i −0.201539 1.12660i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 1.63077 2.82457i 0.135428 0.234568i
\(146\) −6.29178 10.8977i −0.520711 0.901898i
\(147\) 0 0
\(148\) −2.79583 −0.229816
\(149\) −14.5917 −1.19540 −0.597698 0.801721i \(-0.703918\pi\)
−0.597698 + 0.801721i \(0.703918\pi\)
\(150\) 8.34091 + 14.4469i 0.681033 + 1.17958i
\(151\) −0.795832 + 1.37842i −0.0647639 + 0.112174i −0.896589 0.442863i \(-0.853963\pi\)
0.831825 + 0.555037i \(0.187296\pi\)
\(152\) −8.48528 −0.688247
\(153\) 0.634922 + 1.09972i 0.0513304 + 0.0889069i
\(154\) 0 0
\(155\) −5.79583 −0.465532
\(156\) 3.89792 3.28729i 0.312083 0.263194i
\(157\) −0.0721845 + 0.125027i −0.00576095 + 0.00997825i −0.868892 0.495003i \(-0.835167\pi\)
0.863131 + 0.504981i \(0.168500\pi\)
\(158\) −2.20417 −0.175354
\(159\) −8.90365 + 15.4216i −0.706105 + 1.22301i
\(160\) 10.2457 17.7460i 0.809992 1.40295i
\(161\) 0 0
\(162\) 2.50000 4.33013i 0.196419 0.340207i
\(163\) 15.3875 1.20524 0.602621 0.798028i \(-0.294123\pi\)
0.602621 + 0.798028i \(0.294123\pi\)
\(164\) −1.48640 + 2.57452i −0.116068 + 0.201036i
\(165\) 11.0000 + 19.0526i 0.856349 + 1.48324i
\(166\) −4.94975 + 8.57321i −0.384175 + 0.665410i
\(167\) 0.851476 + 1.47480i 0.0658892 + 0.114123i 0.897088 0.441852i \(-0.145678\pi\)
−0.831199 + 0.555975i \(0.812345\pi\)
\(168\) 0 0
\(169\) −12.1937 + 4.50694i −0.937981 + 0.346688i
\(170\) 2.60208 + 4.50694i 0.199571 + 0.345667i
\(171\) −2.82843 −0.216295
\(172\) −7.79583 −0.594427
\(173\) 17.8073 1.35386 0.676932 0.736046i \(-0.263309\pi\)
0.676932 + 0.736046i \(0.263309\pi\)
\(174\) −1.12548 −0.0853221
\(175\) 0 0
\(176\) −1.89792 + 3.28729i −0.143061 + 0.247789i
\(177\) 8.79583 + 15.2348i 0.661135 + 1.14512i
\(178\) −7.48944 12.9721i −0.561357 0.972299i
\(179\) −19.5917 −1.46435 −0.732175 0.681117i \(-0.761495\pi\)
−0.732175 + 0.681117i \(0.761495\pi\)
\(180\) 2.04914 3.54921i 0.152734 0.264542i
\(181\) −3.80953 −0.283160 −0.141580 0.989927i \(-0.545218\pi\)
−0.141580 + 0.989927i \(0.545218\pi\)
\(182\) 0 0
\(183\) 11.7958 0.871973
\(184\) −11.6937 + 20.2542i −0.862074 + 1.49316i
\(185\) −11.4581 −0.842415
\(186\) 1.00000 + 1.73205i 0.0733236 + 0.127000i
\(187\) 2.41006 + 4.17434i 0.176241 + 0.305258i
\(188\) −1.41421 + 2.44949i −0.103142 + 0.178647i
\(189\) 0 0
\(190\) −11.5917 −0.840948
\(191\) −16.2042 −1.17249 −0.586246 0.810133i \(-0.699395\pi\)
−0.586246 + 0.810133i \(0.699395\pi\)
\(192\) −9.89949 −0.714435
\(193\) 22.5917 1.62618 0.813092 0.582136i \(-0.197783\pi\)
0.813092 + 0.582136i \(0.197783\pi\)
\(194\) −2.12132 3.67423i −0.152302 0.263795i
\(195\) 15.9747 13.4722i 1.14397 0.964764i
\(196\) 0 0
\(197\) 4.00000 + 6.92820i 0.284988 + 0.493614i 0.972606 0.232458i \(-0.0746770\pi\)
−0.687618 + 0.726073i \(0.741344\pi\)
\(198\) −1.89792 + 3.28729i −0.134879 + 0.233617i
\(199\) 2.53969 + 4.39887i 0.180034 + 0.311828i 0.941892 0.335916i \(-0.109046\pi\)
−0.761858 + 0.647744i \(0.775713\pi\)
\(200\) 17.6937 30.6465i 1.25114 2.16703i
\(201\) 5.36812 0.378638
\(202\) −4.87756 + 8.44819i −0.343184 + 0.594412i
\(203\) 0 0
\(204\) −0.897916 + 1.55524i −0.0628667 + 0.108888i
\(205\) −6.09166 + 10.5511i −0.425460 + 0.736919i
\(206\) −5.36812 −0.374014
\(207\) −3.89792 + 6.75139i −0.270924 + 0.469254i
\(208\) 3.39116 + 1.22474i 0.235135 + 0.0849208i
\(209\) −10.7362 −0.742641
\(210\) 0 0
\(211\) −3.89792 6.75139i −0.268344 0.464785i 0.700091 0.714054i \(-0.253143\pi\)
−0.968434 + 0.249269i \(0.919810\pi\)
\(212\) 12.5917 0.864799
\(213\) 4.24264 7.34847i 0.290701 0.503509i
\(214\) 3.00000 + 5.19615i 0.205076 + 0.355202i
\(215\) −31.9494 −2.17893
\(216\) −16.9706 −1.15470
\(217\) 0 0
\(218\) −0.795832 1.37842i −0.0539005 0.0933584i
\(219\) 8.89792 15.4116i 0.601265 1.04142i
\(220\) 7.77817 13.4722i 0.524404 0.908295i
\(221\) 3.50000 2.95171i 0.235435 0.198553i
\(222\) 1.97695 + 3.42418i 0.132684 + 0.229816i
\(223\) −2.82843 4.89898i −0.189405 0.328060i 0.755647 0.654979i \(-0.227323\pi\)
−0.945052 + 0.326920i \(0.893989\pi\)
\(224\) 0 0
\(225\) 5.89792 10.2155i 0.393194 0.681033i
\(226\) −1.29583 2.24445i −0.0861974 0.149298i
\(227\) 3.67990 + 6.37378i 0.244244 + 0.423043i 0.961919 0.273336i \(-0.0881270\pi\)
−0.717675 + 0.696378i \(0.754794\pi\)
\(228\) −2.00000 3.46410i −0.132453 0.229416i
\(229\) 6.36396 + 11.0227i 0.420542 + 0.728401i 0.995993 0.0894361i \(-0.0285065\pi\)
−0.575450 + 0.817837i \(0.695173\pi\)
\(230\) −15.9747 + 27.6690i −1.05334 + 1.82444i
\(231\) 0 0
\(232\) 1.19375 + 2.06763i 0.0783733 + 0.135747i
\(233\) −8.59166 14.8812i −0.562859 0.974900i −0.997245 0.0741732i \(-0.976368\pi\)
0.434387 0.900726i \(-0.356965\pi\)
\(234\) 3.39116 + 1.22474i 0.221687 + 0.0800641i
\(235\) −5.79583 + 10.0387i −0.378078 + 0.654851i
\(236\) 6.21959 10.7726i 0.404861 0.701240i
\(237\) −1.55858 2.69954i −0.101241 0.175354i
\(238\) 0 0
\(239\) −10.2042 −0.660053 −0.330026 0.943972i \(-0.607058\pi\)
−0.330026 + 0.943972i \(0.607058\pi\)
\(240\) −5.79583 −0.374119
\(241\) 5.58467 + 9.67293i 0.359740 + 0.623088i 0.987917 0.154982i \(-0.0495320\pi\)
−0.628177 + 0.778070i \(0.716199\pi\)
\(242\) −1.70417 + 2.95171i −0.109548 + 0.189743i
\(243\) −9.89949 −0.635053
\(244\) −4.17046 7.22344i −0.266986 0.462433i
\(245\) 0 0
\(246\) 4.20417 0.268048
\(247\) 1.79583 + 10.0387i 0.114266 + 0.638746i
\(248\) 2.12132 3.67423i 0.134704 0.233314i
\(249\) −14.0000 −0.887214
\(250\) 13.9256 24.1198i 0.880731 1.52547i
\(251\) −8.34091 + 14.4469i −0.526474 + 0.911879i 0.473050 + 0.881035i \(0.343153\pi\)
−0.999524 + 0.0308439i \(0.990181\pi\)
\(252\) 0 0
\(253\) −14.7958 + 25.6271i −0.930206 + 1.61116i
\(254\) −11.5917 −0.727326
\(255\) −3.67990 + 6.37378i −0.230444 + 0.399142i
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) 4.31483 7.47350i 0.269151 0.466184i −0.699492 0.714641i \(-0.746590\pi\)
0.968643 + 0.248457i \(0.0799235\pi\)
\(258\) 5.51249 + 9.54790i 0.343192 + 0.594427i
\(259\) 0 0
\(260\) −13.8979 5.01934i −0.861912 0.311286i
\(261\) 0.397916 + 0.689210i 0.0246304 + 0.0426610i
\(262\) −5.36812 −0.331643
\(263\) 3.38749 0.208882 0.104441 0.994531i \(-0.466695\pi\)
0.104441 + 0.994531i \(0.466695\pi\)
\(264\) −16.1043 −0.991154
\(265\) 51.6041 3.17001
\(266\) 0 0
\(267\) 10.5917 18.3453i 0.648199 1.12271i
\(268\) −1.89792 3.28729i −0.115934 0.200803i
\(269\) 6.21959 + 10.7726i 0.379215 + 0.656820i 0.990948 0.134244i \(-0.0428607\pi\)
−0.611733 + 0.791064i \(0.709527\pi\)
\(270\) −23.1833 −1.41089
\(271\) 8.75928 15.1715i 0.532088 0.921604i −0.467210 0.884147i \(-0.654741\pi\)
0.999298 0.0374577i \(-0.0119260\pi\)
\(272\) −1.26984 −0.0769956
\(273\) 0 0
\(274\) −18.7958 −1.13550
\(275\) 22.3875 38.7763i 1.35002 2.33830i
\(276\) −11.0250 −0.663625
\(277\) −16.0917 27.8716i −0.966854 1.67464i −0.704548 0.709656i \(-0.748850\pi\)
−0.262306 0.964985i \(-0.584483\pi\)
\(278\) −0.851476 1.47480i −0.0510681 0.0884526i
\(279\) 0.707107 1.22474i 0.0423334 0.0733236i
\(280\) 0 0
\(281\) 24.7958 1.47920 0.739598 0.673049i \(-0.235016\pi\)
0.739598 + 0.673049i \(0.235016\pi\)
\(282\) 4.00000 0.238197
\(283\) 15.8451 0.941893 0.470946 0.882162i \(-0.343913\pi\)
0.470946 + 0.882162i \(0.343913\pi\)
\(284\) −6.00000 −0.356034
\(285\) −8.19654 14.1968i −0.485521 0.840948i
\(286\) 12.8723 + 4.64893i 0.761155 + 0.274897i
\(287\) 0 0
\(288\) 2.50000 + 4.33013i 0.147314 + 0.255155i
\(289\) 7.69375 13.3260i 0.452573 0.783880i
\(290\) 1.63077 + 2.82457i 0.0957619 + 0.165865i
\(291\) 3.00000 5.19615i 0.175863 0.304604i
\(292\) −12.5836 −0.736397
\(293\) −1.48640 + 2.57452i −0.0868363 + 0.150405i −0.906172 0.422909i \(-0.861009\pi\)
0.819336 + 0.573314i \(0.194342\pi\)
\(294\) 0 0
\(295\) 25.4896 44.1492i 1.48406 2.57047i
\(296\) 4.19375 7.26378i 0.243757 0.422199i
\(297\) −21.4725 −1.24596
\(298\) 7.29583 12.6368i 0.422636 0.732027i
\(299\) 26.4370 + 9.54790i 1.52889 + 0.552170i
\(300\) 16.6818 0.963126
\(301\) 0 0
\(302\) −0.795832 1.37842i −0.0457950 0.0793192i
\(303\) −13.7958 −0.792550
\(304\) 1.41421 2.44949i 0.0811107 0.140488i
\(305\) −17.0917 29.6036i −0.978666 1.69510i
\(306\) −1.26984 −0.0725922
\(307\) 20.0583 1.14478 0.572392 0.819980i \(-0.306015\pi\)
0.572392 + 0.819980i \(0.306015\pi\)
\(308\) 0 0
\(309\) −3.79583 6.57457i −0.215937 0.374014i
\(310\) 2.89792 5.01934i 0.164591 0.285079i
\(311\) −14.4161 + 24.9695i −0.817464 + 1.41589i 0.0900809 + 0.995934i \(0.471287\pi\)
−0.907545 + 0.419955i \(0.862046\pi\)
\(312\) 2.69375 + 15.0580i 0.152503 + 0.852492i
\(313\) 7.63381 + 13.2221i 0.431488 + 0.747359i 0.997002 0.0773795i \(-0.0246553\pi\)
−0.565514 + 0.824739i \(0.691322\pi\)
\(314\) −0.0721845 0.125027i −0.00407360 0.00705569i
\(315\) 0 0
\(316\) −1.10208 + 1.90887i −0.0619971 + 0.107382i
\(317\) −3.29583 5.70855i −0.185112 0.320624i 0.758502 0.651671i \(-0.225932\pi\)
−0.943614 + 0.331047i \(0.892598\pi\)
\(318\) −8.90365 15.4216i −0.499292 0.864799i
\(319\) 1.51042 + 2.61613i 0.0845674 + 0.146475i
\(320\) 14.3440 + 24.8445i 0.801851 + 1.38885i
\(321\) −4.24264 + 7.34847i −0.236801 + 0.410152i
\(322\) 0 0
\(323\) −1.79583 3.11047i −0.0999227 0.173071i
\(324\) −2.50000 4.33013i −0.138889 0.240563i
\(325\) −40.0016 14.4469i −2.21889 0.801369i
\(326\) −7.69375 + 13.3260i −0.426117 + 0.738057i
\(327\) 1.12548 1.94938i 0.0622390 0.107801i
\(328\) −4.45919 7.72355i −0.246218 0.426462i
\(329\) 0 0
\(330\) −22.0000 −1.21106
\(331\) 29.3875 1.61528 0.807641 0.589674i \(-0.200744\pi\)
0.807641 + 0.589674i \(0.200744\pi\)
\(332\) 4.94975 + 8.57321i 0.271653 + 0.470516i
\(333\) 1.39792 2.42126i 0.0766053 0.132684i
\(334\) −1.70295 −0.0931814
\(335\) −7.77817 13.4722i −0.424967 0.736065i
\(336\) 0 0
\(337\) 17.9792 0.979387 0.489694 0.871895i \(-0.337109\pi\)
0.489694 + 0.871895i \(0.337109\pi\)
\(338\) 2.19375 12.8136i 0.119324 0.696966i
\(339\) 1.83258 3.17413i 0.0995322 0.172395i
\(340\) 5.20417 0.282236
\(341\) 2.68406 4.64893i 0.145350 0.251753i
\(342\) 1.41421 2.44949i 0.0764719 0.132453i
\(343\) 0 0
\(344\) 11.6937 20.2542i 0.630485 1.09203i
\(345\) −45.1833 −2.43259
\(346\) −8.90365 + 15.4216i −0.478663 + 0.829069i
\(347\) 16.4896 + 28.5608i 0.885207 + 1.53322i 0.845476 + 0.534013i \(0.179317\pi\)
0.0397307 + 0.999210i \(0.487350\pi\)
\(348\) −0.562738 + 0.974691i −0.0301659 + 0.0522489i
\(349\) 13.2907 + 23.0201i 0.711433 + 1.23224i 0.964319 + 0.264742i \(0.0852867\pi\)
−0.252887 + 0.967496i \(0.581380\pi\)
\(350\) 0 0
\(351\) 3.59166 + 20.0773i 0.191709 + 1.07165i
\(352\) 9.48958 + 16.4364i 0.505796 + 0.876065i
\(353\) −5.22375 −0.278032 −0.139016 0.990290i \(-0.544394\pi\)
−0.139016 + 0.990290i \(0.544394\pi\)
\(354\) −17.5917 −0.934986
\(355\) −24.5896 −1.30508
\(356\) −14.9789 −0.793879
\(357\) 0 0
\(358\) 9.79583 16.9669i 0.517726 0.896727i
\(359\) 2.00000 + 3.46410i 0.105556 + 0.182828i 0.913965 0.405793i \(-0.133004\pi\)
−0.808409 + 0.588621i \(0.799671\pi\)
\(360\) 6.14741 + 10.6476i 0.323997 + 0.561179i
\(361\) −11.0000 −0.578947
\(362\) 1.90477 3.29915i 0.100112 0.173400i
\(363\) −4.82012 −0.252990
\(364\) 0 0
\(365\) −51.5708 −2.69934
\(366\) −5.89792 + 10.2155i −0.308289 + 0.533972i
\(367\) −21.2132 −1.10732 −0.553660 0.832743i \(-0.686769\pi\)
−0.553660 + 0.832743i \(0.686769\pi\)
\(368\) −3.89792 6.75139i −0.203193 0.351940i
\(369\) −1.48640 2.57452i −0.0773788 0.134024i
\(370\) 5.72904 9.92299i 0.297839 0.515871i
\(371\) 0 0
\(372\) 2.00000 0.103695
\(373\) 6.59166 0.341303 0.170652 0.985331i \(-0.445413\pi\)
0.170652 + 0.985331i \(0.445413\pi\)
\(374\) −4.82012 −0.249242
\(375\) 39.3875 2.03396
\(376\) −4.24264 7.34847i −0.218797 0.378968i
\(377\) 2.19350 1.84988i 0.112971 0.0952737i
\(378\) 0 0
\(379\) −12.6937 21.9862i −0.652034 1.12936i −0.982629 0.185583i \(-0.940583\pi\)
0.330595 0.943773i \(-0.392751\pi\)
\(380\) −5.79583 + 10.0387i −0.297320 + 0.514973i
\(381\) −8.19654 14.1968i −0.419922 0.727326i
\(382\) 8.10208 14.0332i 0.414539 0.718002i
\(383\) −12.1504 −0.620859 −0.310429 0.950596i \(-0.600473\pi\)
−0.310429 + 0.950596i \(0.600473\pi\)
\(384\) −2.12132 + 3.67423i −0.108253 + 0.187500i
\(385\) 0 0
\(386\) −11.2958 + 19.5650i −0.574943 + 0.995830i
\(387\) 3.89792 6.75139i 0.198142 0.343192i
\(388\) −4.24264 −0.215387
\(389\) 0.193747 0.335580i 0.00982338 0.0170146i −0.861072 0.508483i \(-0.830206\pi\)
0.870895 + 0.491469i \(0.163540\pi\)
\(390\) 3.67990 + 20.5706i 0.186339 + 1.04163i
\(391\) −9.89949 −0.500639
\(392\) 0 0
\(393\) −3.79583 6.57457i −0.191474 0.331643i
\(394\) −8.00000 −0.403034
\(395\) −4.51664 + 7.82305i −0.227257 + 0.393620i
\(396\) 1.89792 + 3.28729i 0.0953739 + 0.165192i
\(397\) −7.07107 −0.354887 −0.177443 0.984131i \(-0.556783\pi\)
−0.177443 + 0.984131i \(0.556783\pi\)
\(398\) −5.07938 −0.254606
\(399\) 0 0
\(400\) 5.89792 + 10.2155i 0.294896 + 0.510774i
\(401\) 2.19375 3.79968i 0.109551 0.189747i −0.806038 0.591864i \(-0.798392\pi\)
0.915588 + 0.402117i \(0.131726\pi\)
\(402\) −2.68406 + 4.64893i −0.133869 + 0.231867i
\(403\) −4.79583 1.73205i −0.238897 0.0862796i
\(404\) 4.87756 + 8.44819i 0.242668 + 0.420313i
\(405\) −10.2457 17.7460i −0.509112 0.881808i
\(406\) 0 0
\(407\) 5.30625 9.19070i 0.263021 0.455566i
\(408\) −2.69375 4.66571i −0.133360 0.230987i
\(409\) 9.39420 + 16.2712i 0.464513 + 0.804561i 0.999179 0.0405026i \(-0.0128959\pi\)
−0.534666 + 0.845063i \(0.679563\pi\)
\(410\) −6.09166 10.5511i −0.300846 0.521080i
\(411\) −13.2907 23.0201i −0.655580 1.13550i
\(412\) −2.68406 + 4.64893i −0.132234 + 0.229036i
\(413\) 0 0
\(414\) −3.89792 6.75139i −0.191572 0.331813i
\(415\) 20.2854 + 35.1354i 0.995772 + 1.72473i
\(416\) 13.7812 11.6223i 0.675680 0.569831i
\(417\) 1.20417 2.08568i 0.0589684 0.102136i
\(418\) 5.36812 9.29785i 0.262563 0.454773i
\(419\) −12.8576 22.2699i −0.628133 1.08796i −0.987926 0.154926i \(-0.950486\pi\)
0.359794 0.933032i \(-0.382847\pi\)
\(420\) 0 0
\(421\) 12.5917 0.613680 0.306840 0.951761i \(-0.400728\pi\)
0.306840 + 0.951761i \(0.400728\pi\)
\(422\) 7.79583 0.379495
\(423\) −1.41421 2.44949i −0.0687614 0.119098i
\(424\) −18.8875 + 32.7141i −0.917258 + 1.58874i
\(425\) 14.9789 0.726582
\(426\) 4.24264 + 7.34847i 0.205557 + 0.356034i
\(427\) 0 0
\(428\) 6.00000 0.290021
\(429\) 3.40834 + 19.0526i 0.164556 + 0.919866i
\(430\) 15.9747 27.6690i 0.770369 1.33432i
\(431\) 33.1833 1.59838 0.799192 0.601075i \(-0.205261\pi\)
0.799192 + 0.601075i \(0.205261\pi\)
\(432\) 2.82843 4.89898i 0.136083 0.235702i
\(433\) −10.2457 + 17.7460i −0.492376 + 0.852820i −0.999961 0.00878126i \(-0.997205\pi\)
0.507586 + 0.861601i \(0.330538\pi\)
\(434\) 0 0
\(435\) −2.30625 + 3.99455i −0.110576 + 0.191524i
\(436\) −1.59166 −0.0762268
\(437\) 11.0250 19.0958i 0.527396 0.913476i
\(438\) 8.89792 + 15.4116i 0.425159 + 0.736397i
\(439\) −10.0291 + 17.3710i −0.478664 + 0.829070i −0.999701 0.0244638i \(-0.992212\pi\)
0.521037 + 0.853534i \(0.325545\pi\)
\(440\) 23.3345 + 40.4166i 1.11243 + 1.92678i
\(441\) 0 0
\(442\) 0.806253 + 4.50694i 0.0383495 + 0.214373i
\(443\) −5.00000 8.66025i −0.237557 0.411461i 0.722456 0.691417i \(-0.243013\pi\)
−0.960013 + 0.279956i \(0.909680\pi\)
\(444\) 3.95390 0.187644
\(445\) −61.3875 −2.91005
\(446\) 5.65685 0.267860
\(447\) 20.6357 0.976036
\(448\) 0 0
\(449\) −11.7958 + 20.4310i −0.556680 + 0.964198i 0.441091 + 0.897462i \(0.354592\pi\)
−0.997771 + 0.0667352i \(0.978742\pi\)
\(450\) 5.89792 + 10.2155i 0.278030 + 0.481563i
\(451\) −5.64212 9.77243i −0.265677 0.460166i
\(452\) −2.59166 −0.121902
\(453\) 1.12548 1.94938i 0.0528795 0.0915899i
\(454\) −7.35981 −0.345413
\(455\) 0 0
\(456\) 12.0000 0.561951
\(457\) −2.29583 + 3.97650i −0.107394 + 0.186013i −0.914714 0.404102i \(-0.867584\pi\)
0.807320 + 0.590115i \(0.200917\pi\)
\(458\) −12.7279 −0.594737
\(459\) −3.59166 6.22094i −0.167644 0.290369i
\(460\) 15.9747 + 27.6690i 0.744825 + 1.29007i
\(461\) 12.0930 20.9457i 0.563227 0.975538i −0.433985 0.900920i \(-0.642893\pi\)
0.997212 0.0746180i \(-0.0237737\pi\)
\(462\) 0 0
\(463\) −17.3875 −0.808065 −0.404033 0.914745i \(-0.632392\pi\)
−0.404033 + 0.914745i \(0.632392\pi\)
\(464\) −0.795832 −0.0369456
\(465\) 8.19654 0.380106
\(466\) 17.1833 0.796002
\(467\) −15.9747 27.6690i −0.739222 1.28037i −0.952846 0.303454i \(-0.901860\pi\)
0.213624 0.976916i \(-0.431473\pi\)
\(468\) 2.75624 2.32446i 0.127407 0.107448i
\(469\) 0 0
\(470\) −5.79583 10.0387i −0.267342 0.463050i
\(471\) 0.102084 0.176815i 0.00470379 0.00814721i
\(472\) 18.6588 + 32.3179i 0.858840 + 1.48755i
\(473\) 14.7958 25.6271i 0.680313 1.17834i
\(474\) 3.11716 0.143176
\(475\) −16.6818 + 28.8938i −0.765415 + 1.32574i
\(476\) 0 0
\(477\) −6.29583 + 10.9047i −0.288266 + 0.499292i
\(478\) 5.10208 8.83707i 0.233364 0.404198i
\(479\) 20.9245 0.956063 0.478032 0.878343i \(-0.341350\pi\)
0.478032 + 0.878343i \(0.341350\pi\)
\(480\) −14.4896 + 25.0967i −0.661356 + 1.14550i
\(481\) −9.48113 3.42418i −0.432302 0.156129i
\(482\) −11.1693 −0.508749
\(483\) 0 0
\(484\) 1.70417 + 2.95171i 0.0774622 + 0.134168i
\(485\) −17.3875 −0.789525
\(486\) 4.94975 8.57321i 0.224525 0.388889i
\(487\) −0.204168 0.353630i −0.00925176 0.0160245i 0.861362 0.507991i \(-0.169612\pi\)
−0.870614 + 0.491966i \(0.836278\pi\)
\(488\) 25.0227 1.13273
\(489\) −21.7612 −0.984076
\(490\) 0 0
\(491\) −4.79583 8.30662i −0.216433 0.374873i 0.737282 0.675585i \(-0.236109\pi\)
−0.953715 + 0.300712i \(0.902776\pi\)
\(492\) 2.10208 3.64092i 0.0947693 0.164145i
\(493\) −0.505291 + 0.875190i −0.0227572 + 0.0394166i
\(494\) −9.59166 3.46410i −0.431549 0.155857i
\(495\) 7.77817 + 13.4722i 0.349603 + 0.605530i
\(496\) 0.707107 + 1.22474i 0.0317500 + 0.0549927i
\(497\) 0 0
\(498\) 7.00000 12.1244i 0.313678 0.543305i
\(499\) −12.8979 22.3398i −0.577390 1.00007i −0.995777 0.0918002i \(-0.970738\pi\)
0.418387 0.908269i \(-0.362595\pi\)
\(500\) −13.9256 24.1198i −0.622771 1.07867i
\(501\) −1.20417 2.08568i −0.0537983 0.0931814i
\(502\) −8.34091 14.4469i −0.372273 0.644796i
\(503\) 12.8576 22.2699i 0.573290 0.992967i −0.422935 0.906160i \(-0.639000\pi\)
0.996225 0.0868074i \(-0.0276665\pi\)
\(504\) 0 0
\(505\) 19.9896 + 34.6230i 0.889525 + 1.54070i
\(506\) −14.7958 25.6271i −0.657755 1.13926i
\(507\) 17.2446 6.37378i 0.765858 0.283069i
\(508\) −5.79583 + 10.0387i −0.257148 + 0.445394i
\(509\) 3.04498 5.27406i 0.134966 0.233769i −0.790618 0.612309i \(-0.790241\pi\)
0.925585 + 0.378541i \(0.123574\pi\)
\(510\) −3.67990 6.37378i −0.162949 0.282236i
\(511\) 0 0
\(512\) −11.0000 −0.486136
\(513\) 16.0000 0.706417
\(514\) 4.31483 + 7.47350i 0.190319 + 0.329642i
\(515\) −11.0000 + 19.0526i −0.484718 + 0.839556i
\(516\) 11.0250 0.485347
\(517\) −5.36812 9.29785i −0.236089 0.408919i
\(518\) 0 0
\(519\) −25.1833 −1.10543
\(520\) 33.8875 28.5788i 1.48606 1.25326i
\(521\) 2.33787 4.04932i 0.102424 0.177404i −0.810259 0.586072i \(-0.800673\pi\)
0.912683 + 0.408669i \(0.134007\pi\)
\(522\) −0.795832 −0.0348326
\(523\) 21.0688 36.4923i 0.921276 1.59570i 0.123832 0.992303i \(-0.460482\pi\)
0.797444 0.603393i \(-0.206185\pi\)
\(524\) −2.68406 + 4.64893i −0.117254 + 0.203089i
\(525\) 0 0
\(526\) −1.69375 + 2.93366i −0.0738509 + 0.127913i
\(527\) 1.79583 0.0782276
\(528\) 2.68406 4.64893i 0.116809 0.202318i
\(529\) −18.8875 32.7141i −0.821195 1.42235i
\(530\) −25.8020 + 44.6904i −1.12077 + 1.94123i
\(531\) 6.21959 + 10.7726i 0.269907 + 0.467493i
\(532\) 0 0
\(533\) −8.19375 + 6.91015i −0.354911 + 0.299312i
\(534\) 10.5917 + 18.3453i 0.458346 + 0.793879i
\(535\) 24.5896 1.06310
\(536\) 11.3875 0.491865
\(537\) 27.7068 1.19564
\(538\) −12.4392 −0.536291
\(539\) 0 0
\(540\) −11.5917 + 20.0773i −0.498826 + 0.863992i
\(541\) −3.29583 5.70855i −0.141699 0.245430i 0.786438 0.617670i \(-0.211923\pi\)
−0.928136 + 0.372240i \(0.878590\pi\)
\(542\) 8.75928 + 15.1715i 0.376243 + 0.651673i
\(543\) 5.38749 0.231200
\(544\) −3.17461 + 5.49859i −0.136110 + 0.235750i
\(545\) −6.52307 −0.279418
\(546\) 0 0
\(547\) 10.9792 0.469435 0.234717 0.972064i \(-0.424584\pi\)
0.234717 + 0.972064i \(0.424584\pi\)
\(548\) −9.39792 + 16.2777i −0.401459 + 0.695347i
\(549\) 8.34091 0.355981
\(550\) 22.3875 + 38.7763i 0.954606 + 1.65343i
\(551\) −1.12548 1.94938i −0.0479469 0.0830464i
\(552\) 16.5375 28.6437i 0.703881 1.21916i
\(553\) 0 0
\(554\) 32.1833 1.36734
\(555\) 16.2042 0.687829
\(556\) −1.70295 −0.0722212
\(557\) 1.40834 0.0596732 0.0298366 0.999555i \(-0.490501\pi\)
0.0298366 + 0.999555i \(0.490501\pi\)
\(558\) 0.707107 + 1.22474i 0.0299342 + 0.0518476i
\(559\) −26.4370 9.54790i −1.11816 0.403833i
\(560\) 0 0
\(561\) −3.40834 5.90341i −0.143900 0.249242i
\(562\) −12.3979 + 21.4738i −0.522975 + 0.905818i
\(563\) 6.21959 + 10.7726i 0.262125 + 0.454013i 0.966806 0.255511i \(-0.0822435\pi\)
−0.704682 + 0.709524i \(0.748910\pi\)
\(564\) 2.00000 3.46410i 0.0842152 0.145865i
\(565\) −10.6213 −0.446843
\(566\) −7.92254 + 13.7222i −0.333009 + 0.576789i
\(567\) 0 0
\(568\) 9.00000 15.5885i 0.377632 0.654077i
\(569\) −12.7958 + 22.1630i −0.536429 + 0.929123i 0.462664 + 0.886534i \(0.346894\pi\)
−0.999093 + 0.0425886i \(0.986440\pi\)
\(570\) 16.3931 0.686631
\(571\) 11.5917 20.0773i 0.485096 0.840211i −0.514757 0.857336i \(-0.672118\pi\)
0.999853 + 0.0171250i \(0.00545132\pi\)
\(572\) 10.4622 8.82327i 0.437448 0.368919i
\(573\) 22.9162 0.957336
\(574\) 0 0
\(575\) 45.9792 + 79.6382i 1.91746 + 3.32114i
\(576\) −7.00000 −0.291667
\(577\) 12.3670 21.4203i 0.514845 0.891738i −0.485007 0.874510i \(-0.661183\pi\)
0.999852 0.0172271i \(-0.00548384\pi\)
\(578\) 7.69375 + 13.3260i 0.320018 + 0.554287i
\(579\) −31.9494 −1.32777
\(580\) 3.26153 0.135428
\(581\) 0 0
\(582\) 3.00000 + 5.19615i 0.124354 + 0.215387i
\(583\) −23.8979 + 41.3924i −0.989751 + 1.71430i
\(584\) 18.8753 32.6930i 0.781067 1.35285i
\(585\) 11.2958 9.52628i 0.467025 0.393863i
\(586\) −1.48640 2.57452i −0.0614025 0.106352i
\(587\) 8.34091 + 14.4469i 0.344266 + 0.596287i 0.985220 0.171293i \(-0.0547944\pi\)
−0.640954 + 0.767579i \(0.721461\pi\)
\(588\) 0 0
\(589\) −2.00000 + 3.46410i −0.0824086 + 0.142736i
\(590\) 25.4896 + 44.1492i 1.04939 + 1.81760i
\(591\) −5.65685 9.79796i −0.232692 0.403034i
\(592\) 1.39792 + 2.42126i 0.0574540 + 0.0995132i
\(593\) −4.17046 7.22344i −0.171260 0.296631i 0.767601 0.640929i \(-0.221451\pi\)
−0.938861 + 0.344297i \(0.888117\pi\)
\(594\) 10.7362 18.5957i 0.440513 0.762991i
\(595\) 0 0
\(596\) −7.29583 12.6368i −0.298849 0.517621i
\(597\) −3.59166 6.22094i −0.146997 0.254606i
\(598\) −21.4872 + 18.1211i −0.878677 + 0.741028i
\(599\) 16.7958 29.0912i 0.686259 1.18864i −0.286780 0.957996i \(-0.592585\pi\)
0.973039 0.230639i \(-0.0740817\pi\)
\(600\) −25.0227 + 43.3407i −1.02155 + 1.76937i
\(601\) −12.0930 20.9457i −0.493284 0.854393i 0.506686 0.862130i \(-0.330870\pi\)
−0.999970 + 0.00773797i \(0.997537\pi\)
\(602\) 0 0
\(603\) 3.79583 0.154578
\(604\) −1.59166 −0.0647639
\(605\) 6.98415 + 12.0969i 0.283946 + 0.491809i
\(606\) 6.89792 11.9475i 0.280209 0.485336i
\(607\) −4.79064 −0.194446 −0.0972231 0.995263i \(-0.530996\pi\)
−0.0972231 + 0.995263i \(0.530996\pi\)
\(608\) −7.07107 12.2474i −0.286770 0.496700i
\(609\) 0 0
\(610\) 34.1833 1.38404
\(611\) −7.79583 + 6.57457i −0.315386 + 0.265979i
\(612\) −0.634922 + 1.09972i −0.0256652 + 0.0444535i
\(613\) 41.9792 1.69552 0.847761 0.530378i \(-0.177950\pi\)
0.847761 + 0.530378i \(0.177950\pi\)
\(614\) −10.0291 + 17.3710i −0.404743 + 0.701035i
\(615\) 8.61491 14.9215i 0.347387 0.601692i
\(616\) 0 0
\(617\) −2.19375 + 3.79968i −0.0883169 + 0.152969i −0.906800 0.421561i \(-0.861482\pi\)
0.818483 + 0.574531i \(0.194815\pi\)
\(618\) 7.59166 0.305381
\(619\) −16.9558 + 29.3684i −0.681512 + 1.18041i 0.293007 + 0.956110i \(0.405344\pi\)
−0.974519 + 0.224303i \(0.927989\pi\)
\(620\) −2.89792 5.01934i −0.116383 0.201581i
\(621\) 22.0499 38.1916i 0.884834 1.53258i
\(622\) −14.4161 24.9695i −0.578034 1.00118i
\(623\) 0 0
\(624\) −4.79583 1.73205i −0.191987 0.0693375i
\(625\) −27.5812 47.7721i −1.10325 1.91088i
\(626\) −15.2676 −0.610216
\(627\) 15.1833 0.606364
\(628\) −0.144369 −0.00576095
\(629\) 3.55027 0.141559
\(630\) 0 0
\(631\) 19.7958 34.2874i 0.788060 1.36496i −0.139095 0.990279i \(-0.544419\pi\)
0.927154 0.374680i \(-0.122247\pi\)
\(632\) −3.30625 5.72660i −0.131516 0.227792i
\(633\) 5.51249 + 9.54790i 0.219102 + 0.379495i
\(634\) 6.59166 0.261788
\(635\) −23.7529 + 41.1412i −0.942605 + 1.63264i
\(636\) −17.8073 −0.706105
\(637\) 0 0
\(638\) −3.02084 −0.119596
\(639\) 3.00000 5.19615i 0.118678 0.205557i
\(640\) 12.2948 0.485995
\(641\) 2.39792 + 4.15331i 0.0947120 + 0.164046i 0.909488 0.415729i \(-0.136474\pi\)
−0.814776 + 0.579775i \(0.803140\pi\)
\(642\) −4.24264 7.34847i −0.167444 0.290021i
\(643\) 2.82843 4.89898i 0.111542 0.193197i −0.804850 0.593478i \(-0.797754\pi\)
0.916392 + 0.400281i \(0.131088\pi\)
\(644\) 0 0
\(645\) 45.1833 1.77909
\(646\) 3.59166 0.141312
\(647\) −38.7318 −1.52270 −0.761351 0.648339i \(-0.775464\pi\)
−0.761351 + 0.648339i \(0.775464\pi\)
\(648\) 15.0000 0.589256
\(649\) 23.6085 + 40.8912i 0.926716 + 1.60512i
\(650\) 32.5122 27.4190i 1.27523 1.07546i
\(651\) 0 0
\(652\) 7.69375 + 13.3260i 0.301310 + 0.521885i
\(653\) 6.59166 11.4171i 0.257952 0.446785i −0.707741 0.706472i \(-0.750286\pi\)
0.965693 + 0.259686i \(0.0836191\pi\)
\(654\) 1.12548 + 1.94938i 0.0440096 + 0.0762268i
\(655\) −11.0000 + 19.0526i −0.429806 + 0.744445i
\(656\) 2.97280 0.116068
\(657\) 6.29178 10.8977i 0.245466 0.425159i
\(658\) 0 0
\(659\) 9.20417 15.9421i 0.358543 0.621016i −0.629174 0.777264i \(-0.716607\pi\)
0.987718 + 0.156249i \(0.0499401\pi\)
\(660\) −11.0000 + 19.0526i −0.428174 + 0.741620i
\(661\) −7.50417 −0.291879 −0.145939 0.989294i \(-0.546620\pi\)
−0.145939 + 0.989294i \(0.546620\pi\)
\(662\) −14.6937 + 25.4503i −0.571089 + 0.989155i
\(663\) −4.94975 + 4.17434i −0.192232 + 0.162118i
\(664\) −29.6985 −1.15252
\(665\) 0 0
\(666\) 1.39792 + 2.42126i 0.0541681 + 0.0938220i
\(667\) −6.20417 −0.240226
\(668\) −0.851476 + 1.47480i −0.0329446 + 0.0570617i
\(669\) 4.00000 + 6.92820i 0.154649 + 0.267860i
\(670\) 15.5563 0.600994
\(671\) 31.6607 1.22225
\(672\) 0 0
\(673\) 11.9896 + 20.7666i 0.462164 + 0.800492i 0.999069 0.0431511i \(-0.0137397\pi\)
−0.536904 + 0.843643i \(0.680406\pi\)
\(674\) −8.98958 + 15.5704i −0.346266 + 0.599750i
\(675\) −33.3636 + 57.7875i −1.28417 + 2.22424i
\(676\) −10.0000 8.30662i −0.384615 0.319486i
\(677\) 3.82427 + 6.62383i 0.146979 + 0.254575i 0.930109 0.367283i \(-0.119712\pi\)
−0.783131 + 0.621857i \(0.786378\pi\)
\(678\) 1.83258 + 3.17413i 0.0703799 + 0.121902i
\(679\) 0 0
\(680\) −7.80625 + 13.5208i −0.299356 + 0.518500i
\(681\) −5.20417 9.01388i −0.199424 0.345413i
\(682\) 2.68406 + 4.64893i 0.102778 + 0.178017i
\(683\) 3.38749 + 5.86731i 0.129619 + 0.224506i 0.923529 0.383529i \(-0.125291\pi\)
−0.793910 + 0.608035i \(0.791958\pi\)
\(684\) −1.41421 2.44949i −0.0540738 0.0936586i
\(685\) −38.5152 + 66.7103i −1.47159 + 2.54887i
\(686\) 0 0
\(687\) −9.00000 15.5885i −0.343371 0.594737i
\(688\) 3.89792 + 6.75139i 0.148607 + 0.257394i
\(689\) 42.7004 + 15.4216i 1.62676 + 0.587515i
\(690\) 22.5917 39.1299i 0.860050 1.48965i
\(691\) −1.26984 + 2.19944i −0.0483072 + 0.0836705i −0.889168 0.457581i \(-0.848716\pi\)
0.840861 + 0.541251i \(0.182049\pi\)
\(692\) 8.90365 + 15.4216i 0.338466 + 0.586240i
\(693\) 0 0
\(694\) −32.9792 −1.25187
\(695\) −6.97916 −0.264735
\(696\) −1.68821 2.92407i −0.0639916 0.110837i
\(697\) 1.88749 3.26924i 0.0714940 0.123831i
\(698\) −26.5813 −1.00612
\(699\) 12.1504 + 21.0452i 0.459572 + 0.796002i
\(700\) 0 0
\(701\) −29.5917 −1.11766 −0.558831 0.829282i \(-0.688750\pi\)
−0.558831 + 0.829282i \(0.688750\pi\)
\(702\) −19.1833 6.92820i −0.724028 0.261488i
\(703\) −3.95390 + 6.84836i −0.149124 + 0.258291i
\(704\) −26.5708 −1.00143
\(705\) 8.19654 14.1968i 0.308700 0.534684i
\(706\) 2.61187 4.52390i 0.0982992 0.170259i
\(707\) 0 0
\(708\) −8.79583 + 15.2348i −0.330568 + 0.572560i
\(709\) −9.20417 −0.345670 −0.172835 0.984951i \(-0.555293\pi\)
−0.172835 + 0.984951i \(0.555293\pi\)
\(710\) 12.2948 21.2952i 0.461416 0.799196i
\(711\) −1.10208 1.90887i −0.0413314 0.0715881i
\(712\) 22.4683 38.9163i 0.842036 1.45845i
\(713\) 5.51249 + 9.54790i 0.206444 + 0.357572i
\(714\) 0 0
\(715\) 42.8771 36.1602i 1.60351 1.35231i
\(716\) −9.79583 16.9669i −0.366087 0.634082i
\(717\) 14.4309 0.538931
\(718\) −4.00000 −0.149279
\(719\) −1.99169 −0.0742775 −0.0371387 0.999310i \(-0.511824\pi\)
−0.0371387 + 0.999310i \(0.511824\pi\)
\(720\) −4.09827 −0.152734
\(721\) 0 0
\(722\) 5.50000 9.52628i 0.204689 0.354531i
\(723\) −7.89792 13.6796i −0.293727 0.508749i
\(724\) −1.90477 3.29915i −0.0707901 0.122612i
\(725\) 9.38749 0.348643
\(726\) 2.41006 4.17434i 0.0894456 0.154924i
\(727\) −32.4974 −1.20526 −0.602632 0.798020i \(-0.705881\pi\)
−0.602632 + 0.798020i \(0.705881\pi\)
\(728\) 0 0
\(729\) 29.0000 1.07407
\(730\) 25.7854 44.6616i 0.954361 1.65300i
\(731\) 9.89949 0.366146
\(732\) 5.89792 + 10.2155i 0.217993 + 0.377575i
\(733\) −16.6096 28.7687i −0.613491 1.06260i −0.990647 0.136448i \(-0.956431\pi\)
0.377156 0.926150i \(-0.376902\pi\)
\(734\) 10.6066 18.3712i 0.391497 0.678092i
\(735\) 0 0
\(736\) −38.9792 −1.43679
\(737\) 14.4083 0.530738
\(738\) 2.97280 0.109430
\(739\) −23.1833 −0.852812 −0.426406 0.904532i \(-0.640221\pi\)
−0.426406 + 0.904532i \(0.640221\pi\)
\(740\) −5.72904 9.92299i −0.210604 0.364776i
\(741\) −2.53969 14.1968i −0.0932978 0.521534i
\(742\) 0 0
\(743\) 14.5917 + 25.2735i 0.535316 + 0.927195i 0.999148 + 0.0412716i \(0.0131409\pi\)
−0.463832 + 0.885923i \(0.653526\pi\)
\(744\) −3.00000 + 5.19615i −0.109985 + 0.190500i
\(745\) −29.9003 51.7888i −1.09546 1.89740i
\(746\) −3.29583 + 5.70855i −0.120669 + 0.209005i
\(747\) −9.89949 −0.362204
\(748\) −2.41006 + 4.17434i −0.0881205 + 0.152629i
\(749\) 0 0
\(750\) −19.6937 + 34.1106i −0.719114 + 1.24554i
\(751\) 3.89792 6.75139i 0.142237 0.246362i −0.786102 0.618097i \(-0.787904\pi\)
0.928339 + 0.371735i \(0.121237\pi\)
\(752\) 2.82843 0.103142
\(753\) 11.7958 20.4310i 0.429864 0.744546i
\(754\) 0.505291 + 2.82457i 0.0184016 + 0.102865i
\(755\) −6.52307 −0.237399
\(756\) 0 0
\(757\) −6.59166 11.4171i −0.239578 0.414961i 0.721015 0.692919i \(-0.243676\pi\)
−0.960593 + 0.277958i \(0.910342\pi\)
\(758\) 25.3875 0.922115
\(759\) 20.9245 36.2422i 0.759510 1.31551i
\(760\) −17.3875 30.1160i −0.630711 1.09242i
\(761\) 17.8073 0.645514 0.322757 0.946482i \(-0.395390\pi\)
0.322757 + 0.946482i \(0.395390\pi\)
\(762\) 16.3931 0.593859
\(763\) 0 0
\(764\) −8.10208 14.0332i −0.293123 0.507704i
\(765\) −2.60208 + 4.50694i −0.0940786 + 0.162949i
\(766\) 6.07522 10.5226i 0.219507 0.380197i
\(767\) 34.2854 28.9144i 1.23797 1.04404i
\(768\) −12.0208 20.8207i −0.433764 0.751301i
\(769\) 2.12132 + 3.67423i 0.0764968 + 0.132496i 0.901736 0.432287i \(-0.142293\pi\)
−0.825239 + 0.564783i \(0.808960\pi\)
\(770\) 0 0
\(771\) −6.10208 + 10.5691i −0.219761 + 0.380638i
\(772\) 11.2958 + 19.5650i 0.406546 + 0.704158i
\(773\) 17.3889 + 30.1185i 0.625436 + 1.08329i 0.988456 + 0.151506i \(0.0484124\pi\)
−0.363020 + 0.931781i \(0.618254\pi\)
\(774\) 3.89792 + 6.75139i 0.140108 + 0.242674i
\(775\) −8.34091 14.4469i −0.299614 0.518947i
\(776\) 6.36396 11.0227i 0.228453 0.395692i
\(777\) 0 0
\(778\) 0.193747 + 0.335580i 0.00694618 + 0.0120311i
\(779\) 4.20417 + 7.28183i 0.150630 + 0.260899i
\(780\) 19.6546 + 7.09841i 0.703748 + 0.254164i
\(781\) 11.3875 19.7237i 0.407477 0.705770i
\(782\) 4.94975 8.57321i 0.177003 0.306578i
\(783\) −2.25095 3.89876i −0.0804424 0.139330i
\(784\) 0 0
\(785\) −0.591663 −0.0211174
\(786\) 7.59166 0.270786
\(787\) −21.1985 36.7168i −0.755644 1.30881i −0.945054 0.326915i \(-0.893991\pi\)
0.189410 0.981898i \(-0.439342\pi\)
\(788\) −4.00000 + 6.92820i −0.142494 + 0.246807i
\(789\) −4.79064 −0.170551
\(790\) −4.51664 7.82305i −0.160695 0.278332i
\(791\) 0 0
\(792\) −11.3875 −0.404637
\(793\) −5.29583 29.6036i −0.188060 1.05126i
\(794\) 3.53553 6.12372i 0.125471 0.217323i
\(795\) −72.9792 −2.58830
\(796\) −2.53969 + 4.39887i −0.0900169 + 0.155914i
\(797\) 0.418369 0.724636i 0.0148194 0.0256679i −0.858521 0.512779i \(-0.828616\pi\)
0.873340 + 0.487111i \(0.161949\pi\)
\(798\) 0 0
\(799\) 1.79583 3.11047i 0.0635320 0.110041i
\(800\) 58.9792 2.08523
\(801\) 7.48944 12.9721i 0.264626 0.458346i
\(802\) 2.19375 + 3.79968i 0.0774639 + 0.134171i
\(803\) 23.8825 41.3657i 0.842796 1.45977i
\(804\) 2.68406 + 4.64893i 0.0946594 + 0.163955i
\(805\) 0 0
\(806\) 3.89792 3.28729i 0.137298 0.115790i
\(807\) −8.79583 15.2348i −0.309628 0.536291i
\(808\) −29.2654 −1.02955
\(809\) −37.3667 −1.31374 −0.656871 0.754003i \(-0.728120\pi\)
−0.656871 + 0.754003i \(0.728120\pi\)
\(810\) 20.4914 0.719993
\(811\) 52.0372 1.82727 0.913636 0.406533i \(-0.133262\pi\)
0.913636 + 0.406533i \(0.133262\pi\)
\(812\) 0 0
\(813\) −12.3875 + 21.4558i −0.434448 + 0.752487i
\(814\) 5.30625 + 9.19070i 0.185984 + 0.322134i
\(815\) 31.5311 + 54.6134i 1.10449 + 1.91302i
\(816\) 1.79583 0.0628667
\(817\) −11.0250 + 19.0958i −0.385715 + 0.668078i
\(818\) −18.7884 −0.656921
\(819\) 0 0
\(820\) −12.1833 −0.425460
\(821\) −18.1833 + 31.4944i −0.634602 + 1.09916i 0.351997 + 0.936001i \(0.385503\pi\)
−0.986599 + 0.163162i \(0.947831\pi\)
\(822\) 26.5813 0.927130
\(823\) 10.3875 + 17.9917i 0.362085 + 0.627150i 0.988304 0.152497i \(-0.0487316\pi\)
−0.626219 + 0.779648i \(0.715398\pi\)
\(824\) −8.05217 13.9468i −0.280511 0.485859i
\(825\) −31.6607 + 54.8379i −1.10228 + 1.90921i
\(826\) 0 0
\(827\) −20.9792 −0.729517 −0.364758 0.931102i \(-0.618848\pi\)
−0.364758 + 0.931102i \(0.618848\pi\)
\(828\) −7.79583 −0.270924
\(829\) 27.2737 0.947254 0.473627 0.880725i \(-0.342944\pi\)
0.473627 + 0.880725i \(0.342944\pi\)
\(830\) −40.5708 −1.40823
\(831\) 22.7570 + 39.4164i 0.789433 + 1.36734i
\(832\) 4.44446 + 24.8445i 0.154084 + 0.861326i
\(833\) 0 0
\(834\) 1.20417 + 2.08568i 0.0416969 + 0.0722212i
\(835\) −3.48958 + 6.04413i −0.120762 + 0.209166i
\(836\) −5.36812 9.29785i −0.185660 0.321573i
\(837\) −4.00000 + 6.92820i −0.138260 + 0.239474i
\(838\) 25.7151 0.888314
\(839\) 2.82843 4.89898i 0.0976481 0.169132i −0.813063 0.582176i \(-0.802201\pi\)
0.910711 + 0.413045i \(0.135535\pi\)
\(840\) 0 0
\(841\) 14.1833 24.5662i 0.489080 0.847112i
\(842\) −6.29583 + 10.9047i −0.216969 + 0.375801i
\(843\) −35.0666 −1.20776
\(844\) 3.89792 6.75139i 0.134172 0.232392i
\(845\) −40.9827 34.0428i −1.40985 1.17111i
\(846\) 2.82843 0.0972433
\(847\) 0 0
\(848\) −6.29583 10.9047i −0.216200 0.374469i
\(849\) −22.4083 −0.769052
\(850\) −7.48944 + 12.9721i −0.256886 + 0.444939i
\(851\) 10.8979 + 18.8757i 0.373576 + 0.647052i
\(852\) 8.48528 0.290701
\(853\) 33.5080 1.14729 0.573646 0.819103i \(-0.305528\pi\)
0.573646 + 0.819103i \(0.305528\pi\)
\(854\) 0 0
\(855\) −5.79583 10.0387i −0.198213 0.343315i
\(856\) −9.00000 + 15.5885i −0.307614 + 0.532803i
\(857\) −8.70183 + 15.0720i −0.297249 + 0.514850i −0.975506 0.219975i \(-0.929402\pi\)
0.678257 + 0.734825i \(0.262736\pi\)
\(858\) −18.2042 6.57457i −0.621480 0.224452i
\(859\) 5.09412 + 8.82327i 0.173809 + 0.301046i 0.939748 0.341867i \(-0.111059\pi\)
−0.765939 + 0.642913i \(0.777726\pi\)
\(860\) −15.9747 27.6690i −0.544733 0.943506i
\(861\) 0 0
\(862\) −16.5917 + 28.7376i −0.565114 + 0.978807i
\(863\) −4.10208 7.10502i −0.139637 0.241858i 0.787723 0.616030i \(-0.211260\pi\)
−0.927359 + 0.374173i \(0.877927\pi\)
\(864\) −14.1421 24.4949i −0.481125 0.833333i
\(865\) 36.4896 + 63.2018i 1.24068 + 2.14893i
\(866\) −10.2457 17.7460i −0.348162 0.603035i
\(867\) −10.8806 + 18.8458i −0.369525 + 0.640035i
\(868\) 0 0
\(869\) −4.18333 7.24573i −0.141910 0.245795i
\(870\) −2.30625 3.99455i −0.0781893 0.135428i
\(871\) −2.41006 13.4722i −0.0816617 0.456488i
\(872\) 2.38749 4.13526i 0.0808508 0.140038i
\(873\) 2.12132 3.67423i 0.0717958 0.124354i
\(874\) 11.0250 + 19.0958i 0.372925 + 0.645925i
\(875\) 0 0
\(876\) 17.7958 0.601265
\(877\) 4.79583 0.161944 0.0809719 0.996716i \(-0.474198\pi\)
0.0809719 + 0.996716i \(0.474198\pi\)
\(878\) −10.0291 17.3710i −0.338467 0.586241i
\(879\) 2.10208 3.64092i 0.0709015 0.122805i
\(880\) −15.5563 −0.524404
\(881\) 5.29593 + 9.17282i 0.178424 + 0.309040i 0.941341 0.337457i \(-0.109567\pi\)
−0.762917 + 0.646497i \(0.776233\pi\)
\(882\) 0 0
\(883\) −45.3875 −1.52741 −0.763705 0.645565i \(-0.776622\pi\)
−0.763705 + 0.645565i \(0.776622\pi\)
\(884\) 4.30625 + 1.55524i 0.144835 + 0.0523082i
\(885\) −36.0477 + 62.4365i −1.21173 + 2.09878i
\(886\) 10.0000 0.335957
\(887\) −21.0688 + 36.4923i −0.707422 + 1.22529i 0.258388 + 0.966041i \(0.416809\pi\)
−0.965810 + 0.259250i \(0.916525\pi\)
\(888\) −5.93085 + 10.2725i −0.199026 + 0.344724i
\(889\) 0 0
\(890\) 30.6937 53.1631i 1.02886 1.78203i
\(891\) 18.9792 0.635826
\(892\) 2.82843 4.89898i 0.0947027 0.164030i
\(893\) 4.00000 + 6.92820i 0.133855 + 0.231843i
\(894\) −10.3179 + 17.8711i −0.345081 + 0.597698i
\(895\) −40.1460 69.5349i −1.34193 2.32429i
\(896\) 0 0
\(897\) −37.3875 13.5028i −1.24833 0.450845i
\(898\) −11.7958 20.4310i −0.393632 0.681791i
\(899\) 1.12548 0.0375367
\(900\) 11.7958 0.393194
\(901\) −15.9895 −0.532686
\(902\) 11.2842 0.375724
\(903\) 0 0
\(904\) 3.88749 6.73334i 0.129296 0.223947i
\(905\) −7.80625 13.5208i −0.259489 0.449447i
\(906\) 1.12548 + 1.94938i 0.0373914 + 0.0647639i
\(907\) 20.6125 0.684427 0.342214 0.939622i \(-0.388823\pi\)
0.342214 + 0.939622i \(0.388823\pi\)
\(908\) −3.67990 + 6.37378i −0.122122 + 0.211521i
\(909\) −9.75513 −0.323557
\(910\) 0 0
\(911\) −4.81667 −0.159584 −0.0797918 0.996812i \(-0.525426\pi\)
−0.0797918 + 0.996812i \(0.525426\pi\)
\(912\) −2.00000 + 3.46410i −0.0662266 + 0.114708i
\(913\) −37.5768 −1.24361
\(914\) −2.29583 3.97650i −0.0759394 0.131531i
\(915\) 24.1713 + 41.8659i 0.799077 + 1.38404i
\(916\) −6.36396 + 11.0227i −0.210271 + 0.364200i
\(917\) 0 0
\(918\) 7.18333 0.237085
\(919\) 10.0000 0.329870 0.164935 0.986304i \(-0.447259\pi\)
0.164935 + 0.986304i \(0.447259\pi\)
\(920\) −95.8483 −3.16003
\(921\) −28.3667 −0.934713
\(922\) 12.0930 + 20.9457i 0.398262 + 0.689810i
\(923\) −20.3470 7.34847i −0.669729 0.241878i
\(924\) 0 0
\(925\) −16.4896 28.5608i −0.542174 0.939073i
\(926\) 8.69375 15.0580i 0.285694 0.494837i
\(927\) −2.68406 4.64893i −0.0881560 0.152691i
\(928\) −1.98958 + 3.44605i −0.0653111 + 0.113122i
\(929\) 21.3576 0.700719 0.350360 0.936615i \(-0.386059\pi\)
0.350360 + 0.936615i \(0.386059\pi\)
\(930\) −4.09827 + 7.09841i −0.134388 + 0.232766i
\(931\) 0 0
\(932\) 8.59166 14.8812i 0.281429 0.487450i
\(933\) 20.3875 35.3122i 0.667457 1.15607i
\(934\) 31.9494 1.04542
\(935\) −9.87707 + 17.1076i −0.323015 + 0.559478i
\(936\) 1.90477 + 10.6476i 0.0622593 + 0.348028i
\(937\) 13.7090 0.447854 0.223927 0.974606i \(-0.428112\pi\)
0.223927 + 0.974606i \(0.428112\pi\)
\(938\) 0 0
\(939\) −10.7958 18.6989i −0.352309 0.610216i
\(940\) −11.5917 −0.378078
\(941\) 1.83258 3.17413i 0.0597405 0.103474i −0.834608 0.550844i \(-0.814306\pi\)
0.894349 + 0.447370i \(0.147639\pi\)
\(942\) 0.102084 + 0.176815i 0.00332608 + 0.00576095i
\(943\) 23.1754 0.754695
\(944\) −12.4392 −0.404861
\(945\) 0 0
\(946\) 14.7958 + 25.6271i 0.481054 + 0.833210i
\(947\) −18.8979 + 32.7322i −0.614100 + 1.06365i 0.376442 + 0.926440i \(0.377147\pi\)
−0.990542 + 0.137212i \(0.956186\pi\)
\(948\) 1.55858 2.69954i 0.0506204 0.0876771i
\(949\) −42.6729 15.4116i −1.38522 0.500283i
\(950\) −16.6818 28.8938i −0.541230 0.937438i
\(951\) 4.66101 + 8.07311i 0.151144 + 0.261788i
\(952\) 0 0
\(953\) 21.5917 37.3979i 0.699423 1.21144i −0.269244 0.963072i \(-0.586774\pi\)
0.968667 0.248364i \(-0.0798928\pi\)
\(954\) −6.29583 10.9047i −0.203835 0.353053i
\(955\) −33.2045 57.5120i −1.07447 1.86104i
\(956\) −5.10208 8.83707i −0.165013 0.285811i
\(957\) −2.13606 3.69976i −0.0690490 0.119596i
\(958\) −10.4622 + 18.1211i −0.338019 + 0.585467i
\(959\) 0 0
\(960\) −20.2854 35.1354i −0.654709 1.13399i
\(961\) 14.5000 + 25.1147i 0.467742 + 0.810153i
\(962\) 7.70599 6.49881i 0.248451 0.209530i
\(963\) −3.00000 + 5.19615i −0.0966736 + 0.167444i
\(964\) −5.58467 + 9.67293i −0.179870 + 0.311544i
\(965\) 46.2934 + 80.1825i 1.49024 + 2.58117i
\(966\) 0 0
\(967\) −17.3875 −0.559144 −0.279572 0.960125i \(-0.590193\pi\)
−0.279572 + 0.960125i \(0.590193\pi\)
\(968\) −10.2250 −0.328644
\(969\) 2.53969 + 4.39887i 0.0815866 + 0.141312i
\(970\) 8.69375 15.0580i 0.279139 0.483484i
\(971\) 22.6274 0.726148 0.363074 0.931760i \(-0.381727\pi\)
0.363074 + 0.931760i \(0.381727\pi\)
\(972\) −4.94975 8.57321i −0.158763 0.274986i
\(973\) 0 0
\(974\) 0.408337 0.0130840
\(975\) 56.5708 + 20.4310i 1.81172 + 0.654315i
\(976\) −4.17046 + 7.22344i −0.133493 + 0.231217i
\(977\) −28.3875 −0.908196 −0.454098 0.890952i \(-0.650038\pi\)
−0.454098 + 0.890952i \(0.650038\pi\)
\(978\) 10.8806 18.8458i 0.347923 0.602621i
\(979\) 28.4286 49.2398i 0.908583 1.57371i
\(980\) 0 0
\(981\) 0.795832 1.37842i 0.0254089 0.0440096i
\(982\) 9.59166 0.306082
\(983\) 0.433107 0.750163i 0.0138140 0.0239265i −0.859036 0.511916i \(-0.828936\pi\)
0.872850 + 0.487989i \(0.162269\pi\)
\(984\) 6.30625 + 10.9228i 0.201036 + 0.348205i
\(985\) −16.3931 + 28.3937i −0.522327 + 0.904697i
\(986\) −0.505291 0.875190i −0.0160918 0.0278717i
\(987\) 0 0
\(988\) −7.79583 + 6.57457i −0.248018 + 0.209165i
\(989\) 30.3875 + 52.6327i 0.966266 + 1.67362i
\(990\) −15.5563 −0.494413
\(991\) 27.7958 0.882964 0.441482 0.897270i \(-0.354453\pi\)
0.441482 + 0.897270i \(0.354453\pi\)
\(992\) 7.07107 0.224507
\(993\) −41.5602 −1.31887
\(994\) 0 0
\(995\) −10.4083 + 18.0278i −0.329966 + 0.571519i
\(996\) −7.00000 12.1244i −0.221803 0.384175i
\(997\) 0.634922 + 1.09972i 0.0201082 + 0.0348284i 0.875904 0.482485i \(-0.160266\pi\)
−0.855796 + 0.517313i \(0.826932\pi\)
\(998\) 25.7958 0.816553
\(999\) −7.90781 + 13.6967i −0.250192 + 0.433345i
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 637.2.g.h.263.2 8
7.2 even 3 637.2.h.k.471.4 8
7.3 odd 6 637.2.f.g.393.2 yes 8
7.4 even 3 637.2.f.g.393.3 yes 8
7.5 odd 6 637.2.h.k.471.1 8
7.6 odd 2 inner 637.2.g.h.263.3 8
13.9 even 3 637.2.h.k.165.4 8
91.3 odd 6 8281.2.a.bv.1.4 4
91.9 even 3 inner 637.2.g.h.373.2 8
91.10 odd 6 8281.2.a.bn.1.3 4
91.48 odd 6 637.2.h.k.165.1 8
91.61 odd 6 inner 637.2.g.h.373.3 8
91.74 even 3 637.2.f.g.295.3 yes 8
91.81 even 3 8281.2.a.bv.1.1 4
91.87 odd 6 637.2.f.g.295.2 8
91.88 even 6 8281.2.a.bn.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.f.g.295.2 8 91.87 odd 6
637.2.f.g.295.3 yes 8 91.74 even 3
637.2.f.g.393.2 yes 8 7.3 odd 6
637.2.f.g.393.3 yes 8 7.4 even 3
637.2.g.h.263.2 8 1.1 even 1 trivial
637.2.g.h.263.3 8 7.6 odd 2 inner
637.2.g.h.373.2 8 91.9 even 3 inner
637.2.g.h.373.3 8 91.61 odd 6 inner
637.2.h.k.165.1 8 91.48 odd 6
637.2.h.k.165.4 8 13.9 even 3
637.2.h.k.471.1 8 7.5 odd 6
637.2.h.k.471.4 8 7.2 even 3
8281.2.a.bn.1.2 4 91.88 even 6
8281.2.a.bn.1.3 4 91.10 odd 6
8281.2.a.bv.1.1 4 91.81 even 3
8281.2.a.bv.1.4 4 91.3 odd 6