Properties

Label 637.2.h.k.471.3
Level $637$
Weight $2$
Character 637.471
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(165,637)]
 
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, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.h (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 471.3
Root \(-1.34203 + 2.32446i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.k.165.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(0.707107 - 1.22474i) q^{3} -1.00000 q^{4} +(-1.34203 + 2.32446i) q^{5} +(0.707107 - 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(0.707107 - 1.22474i) q^{3} -1.00000 q^{4} +(-1.34203 + 2.32446i) q^{5} +(0.707107 - 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.34203 + 2.32446i) q^{10} +(-2.89792 + 5.01934i) q^{11} +(-0.707107 + 1.22474i) q^{12} +(-2.75624 - 2.32446i) q^{13} +(1.89792 + 3.28729i) q^{15} -1.00000 q^{16} -5.51249 q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.41421 - 2.44949i) q^{19} +(1.34203 - 2.32446i) q^{20} +(-2.89792 + 5.01934i) q^{22} +1.79583 q^{23} +(-2.12132 + 3.67423i) q^{24} +(-1.10208 - 1.90887i) q^{25} +(-2.75624 - 2.32446i) q^{26} +5.65685 q^{27} +(4.39792 + 7.61741i) q^{29} +(1.89792 + 3.28729i) q^{30} +(-0.707107 - 1.22474i) q^{31} +5.00000 q^{32} +(4.09827 + 7.09841i) q^{33} -5.51249 q^{34} +(-0.500000 - 0.866025i) q^{36} -6.79583 q^{37} +(-1.41421 - 2.44949i) q^{38} +(-4.79583 + 1.73205i) q^{39} +(4.02609 - 6.97339i) q^{40} +(4.87756 + 8.44819i) q^{41} +(0.897916 - 1.55524i) q^{43} +(2.89792 - 5.01934i) q^{44} -2.68406 q^{45} +1.79583 q^{46} +(1.41421 - 2.44949i) q^{47} +(-0.707107 + 1.22474i) q^{48} +(-1.10208 - 1.90887i) q^{50} +(-3.89792 + 6.75139i) q^{51} +(2.75624 + 2.32446i) q^{52} +(-3.29583 - 5.70855i) q^{53} +5.65685 q^{54} +(-7.77817 - 13.4722i) q^{55} -4.00000 q^{57} +(4.39792 + 7.61741i) q^{58} -1.12548 q^{59} +(-1.89792 - 3.28729i) q^{60} +(0.779291 + 1.34977i) q^{61} +(-0.707107 - 1.22474i) q^{62} +7.00000 q^{64} +(9.10208 - 3.28729i) q^{65} +(4.09827 + 7.09841i) q^{66} +(-2.89792 + 5.01934i) q^{67} +5.51249 q^{68} +(1.26984 - 2.19944i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} +(-2.90061 - 5.02401i) q^{73} -6.79583 q^{74} -3.11716 q^{75} +(1.41421 + 2.44949i) q^{76} +(-4.79583 + 1.73205i) q^{78} +(5.89792 - 10.2155i) q^{79} +(1.34203 - 2.32446i) q^{80} +(2.50000 - 4.33013i) q^{81} +(4.87756 + 8.44819i) q^{82} +9.89949 q^{83} +(7.39792 - 12.8136i) q^{85} +(0.897916 - 1.55524i) q^{86} +12.4392 q^{87} +(8.69375 - 15.0580i) q^{88} -12.1504 q^{89} -2.68406 q^{90} -1.79583 q^{92} -2.00000 q^{93} +(1.41421 - 2.44949i) q^{94} +7.59166 q^{95} +(3.53553 - 6.12372i) q^{96} +(-2.12132 + 3.67423i) q^{97} -5.79583 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} - 8 q^{4} - 24 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{2} - 8 q^{4} - 24 q^{8} + 4 q^{9} - 4 q^{11} - 4 q^{15} - 8 q^{16} + 4 q^{18} - 4 q^{22} - 24 q^{23} - 28 q^{25} + 16 q^{29} - 4 q^{30} + 40 q^{32} - 4 q^{36} - 16 q^{37} - 12 q^{43} + 4 q^{44} - 24 q^{46} - 28 q^{50} - 12 q^{51} + 12 q^{53} - 32 q^{57} + 16 q^{58} + 4 q^{60} + 56 q^{64} + 92 q^{65} - 4 q^{67} - 24 q^{71} - 12 q^{72} - 16 q^{74} + 28 q^{79} + 20 q^{81} + 40 q^{85} - 12 q^{86} + 12 q^{88} + 24 q^{92} - 16 q^{93} - 16 q^{95} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107 0.353553 0.935414i \(-0.384973\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) 0.707107 1.22474i 0.408248 0.707107i −0.586445 0.809989i \(-0.699473\pi\)
0.994694 + 0.102882i \(0.0328064\pi\)
\(4\) −1.00000 −0.500000
\(5\) −1.34203 + 2.32446i −0.600174 + 1.03953i 0.392621 + 0.919700i \(0.371569\pi\)
−0.992794 + 0.119831i \(0.961765\pi\)
\(6\) 0.707107 1.22474i 0.288675 0.500000i
\(7\) 0 0
\(8\) −3.00000 −1.06066
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) −1.34203 + 2.32446i −0.424387 + 0.735060i
\(11\) −2.89792 + 5.01934i −0.873754 + 1.51339i −0.0156708 + 0.999877i \(0.504988\pi\)
−0.858084 + 0.513510i \(0.828345\pi\)
\(12\) −0.707107 + 1.22474i −0.204124 + 0.353553i
\(13\) −2.75624 2.32446i −0.764444 0.644690i
\(14\) 0 0
\(15\) 1.89792 + 3.28729i 0.490040 + 0.848774i
\(16\) −1.00000 −0.250000
\(17\) −5.51249 −1.33697 −0.668487 0.743724i \(-0.733058\pi\)
−0.668487 + 0.743724i \(0.733058\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −1.41421 2.44949i −0.324443 0.561951i 0.656957 0.753928i \(-0.271843\pi\)
−0.981399 + 0.191977i \(0.938510\pi\)
\(20\) 1.34203 2.32446i 0.300087 0.519766i
\(21\) 0 0
\(22\) −2.89792 + 5.01934i −0.617838 + 1.07013i
\(23\) 1.79583 0.374457 0.187228 0.982316i \(-0.440050\pi\)
0.187228 + 0.982316i \(0.440050\pi\)
\(24\) −2.12132 + 3.67423i −0.433013 + 0.750000i
\(25\) −1.10208 1.90887i −0.220417 0.381773i
\(26\) −2.75624 2.32446i −0.540544 0.455865i
\(27\) 5.65685 1.08866
\(28\) 0 0
\(29\) 4.39792 + 7.61741i 0.816672 + 1.41452i 0.908121 + 0.418708i \(0.137517\pi\)
−0.0914483 + 0.995810i \(0.529150\pi\)
\(30\) 1.89792 + 3.28729i 0.346510 + 0.600174i
\(31\) −0.707107 1.22474i −0.127000 0.219971i 0.795513 0.605937i \(-0.207202\pi\)
−0.922513 + 0.385966i \(0.873868\pi\)
\(32\) 5.00000 0.883883
\(33\) 4.09827 + 7.09841i 0.713418 + 1.23568i
\(34\) −5.51249 −0.945383
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −6.79583 −1.11723 −0.558614 0.829428i \(-0.688667\pi\)
−0.558614 + 0.829428i \(0.688667\pi\)
\(38\) −1.41421 2.44949i −0.229416 0.397360i
\(39\) −4.79583 + 1.73205i −0.767948 + 0.277350i
\(40\) 4.02609 6.97339i 0.636580 1.10259i
\(41\) 4.87756 + 8.44819i 0.761747 + 1.31939i 0.941949 + 0.335755i \(0.108992\pi\)
−0.180202 + 0.983630i \(0.557675\pi\)
\(42\) 0 0
\(43\) 0.897916 1.55524i 0.136931 0.237171i −0.789403 0.613876i \(-0.789610\pi\)
0.926333 + 0.376705i \(0.122943\pi\)
\(44\) 2.89792 5.01934i 0.436877 0.756694i
\(45\) −2.68406 −0.400116
\(46\) 1.79583 0.264781
\(47\) 1.41421 2.44949i 0.206284 0.357295i −0.744257 0.667893i \(-0.767196\pi\)
0.950541 + 0.310599i \(0.100530\pi\)
\(48\) −0.707107 + 1.22474i −0.102062 + 0.176777i
\(49\) 0 0
\(50\) −1.10208 1.90887i −0.155858 0.269954i
\(51\) −3.89792 + 6.75139i −0.545817 + 0.945383i
\(52\) 2.75624 + 2.32446i 0.382222 + 0.322345i
\(53\) −3.29583 5.70855i −0.452717 0.784129i 0.545836 0.837892i \(-0.316212\pi\)
−0.998554 + 0.0537624i \(0.982879\pi\)
\(54\) 5.65685 0.769800
\(55\) −7.77817 13.4722i −1.04881 1.81659i
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) 4.39792 + 7.61741i 0.577475 + 1.00022i
\(59\) −1.12548 −0.146524 −0.0732622 0.997313i \(-0.523341\pi\)
−0.0732622 + 0.997313i \(0.523341\pi\)
\(60\) −1.89792 3.28729i −0.245020 0.424387i
\(61\) 0.779291 + 1.34977i 0.0997780 + 0.172821i 0.911593 0.411095i \(-0.134853\pi\)
−0.811815 + 0.583915i \(0.801520\pi\)
\(62\) −0.707107 1.22474i −0.0898027 0.155543i
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 9.10208 3.28729i 1.12897 0.407738i
\(66\) 4.09827 + 7.09841i 0.504462 + 0.873754i
\(67\) −2.89792 + 5.01934i −0.354037 + 0.613210i −0.986953 0.161011i \(-0.948525\pi\)
0.632916 + 0.774221i \(0.281858\pi\)
\(68\) 5.51249 0.668487
\(69\) 1.26984 2.19944i 0.152871 0.264781i
\(70\) 0 0
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) −1.50000 2.59808i −0.176777 0.306186i
\(73\) −2.90061 5.02401i −0.339491 0.588015i 0.644846 0.764312i \(-0.276921\pi\)
−0.984337 + 0.176297i \(0.943588\pi\)
\(74\) −6.79583 −0.789999
\(75\) −3.11716 −0.359939
\(76\) 1.41421 + 2.44949i 0.162221 + 0.280976i
\(77\) 0 0
\(78\) −4.79583 + 1.73205i −0.543021 + 0.196116i
\(79\) 5.89792 10.2155i 0.663567 1.14933i −0.316104 0.948724i \(-0.602375\pi\)
0.979672 0.200608i \(-0.0642917\pi\)
\(80\) 1.34203 2.32446i 0.150043 0.259883i
\(81\) 2.50000 4.33013i 0.277778 0.481125i
\(82\) 4.87756 + 8.44819i 0.538637 + 0.932946i
\(83\) 9.89949 1.08661 0.543305 0.839535i \(-0.317173\pi\)
0.543305 + 0.839535i \(0.317173\pi\)
\(84\) 0 0
\(85\) 7.39792 12.8136i 0.802417 1.38983i
\(86\) 0.897916 1.55524i 0.0968247 0.167705i
\(87\) 12.4392 1.33362
\(88\) 8.69375 15.0580i 0.926757 1.60519i
\(89\) −12.1504 −1.28794 −0.643972 0.765049i \(-0.722715\pi\)
−0.643972 + 0.765049i \(0.722715\pi\)
\(90\) −2.68406 −0.282925
\(91\) 0 0
\(92\) −1.79583 −0.187228
\(93\) −2.00000 −0.207390
\(94\) 1.41421 2.44949i 0.145865 0.252646i
\(95\) 7.59166 0.778888
\(96\) 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
\(99\) −5.79583 −0.582503
\(100\) 1.10208 + 1.90887i 0.110208 + 0.190887i
\(101\) −1.48640 + 2.57452i −0.147902 + 0.256174i −0.930452 0.366414i \(-0.880585\pi\)
0.782550 + 0.622588i \(0.213919\pi\)
\(102\) −3.89792 + 6.75139i −0.385951 + 0.668487i
\(103\) −4.09827 + 7.09841i −0.403815 + 0.699428i −0.994183 0.107707i \(-0.965649\pi\)
0.590368 + 0.807134i \(0.298983\pi\)
\(104\) 8.26873 + 6.97339i 0.810815 + 0.683797i
\(105\) 0 0
\(106\) −3.29583 5.70855i −0.320119 0.554463i
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) −5.65685 −0.544331
\(109\) 8.79583 + 15.2348i 0.842488 + 1.45923i 0.887785 + 0.460258i \(0.152243\pi\)
−0.0452972 + 0.998974i \(0.514423\pi\)
\(110\) −7.77817 13.4722i −0.741620 1.28452i
\(111\) −4.80538 + 8.32316i −0.456106 + 0.789999i
\(112\) 0 0
\(113\) 8.29583 14.3688i 0.780406 1.35170i −0.151299 0.988488i \(-0.548346\pi\)
0.931705 0.363215i \(-0.118321\pi\)
\(114\) −4.00000 −0.374634
\(115\) −2.41006 + 4.17434i −0.224739 + 0.389260i
\(116\) −4.39792 7.61741i −0.408336 0.707259i
\(117\) 0.634922 3.54921i 0.0586986 0.328124i
\(118\) −1.12548 −0.103608
\(119\) 0 0
\(120\) −5.69375 9.86186i −0.519766 0.900260i
\(121\) −11.2958 19.5650i −1.02689 1.77863i
\(122\) 0.779291 + 1.34977i 0.0705537 + 0.122203i
\(123\) 13.7958 1.24393
\(124\) 0.707107 + 1.22474i 0.0635001 + 0.109985i
\(125\) −7.50417 −0.671194
\(126\) 0 0
\(127\) −3.79583 6.57457i −0.336826 0.583399i 0.647008 0.762483i \(-0.276020\pi\)
−0.983834 + 0.179084i \(0.942687\pi\)
\(128\) −3.00000 −0.265165
\(129\) −1.26984 2.19944i −0.111804 0.193649i
\(130\) 9.10208 3.28729i 0.798306 0.288314i
\(131\) −4.09827 + 7.09841i −0.358068 + 0.620191i −0.987638 0.156752i \(-0.949898\pi\)
0.629570 + 0.776944i \(0.283231\pi\)
\(132\) −4.09827 7.09841i −0.356709 0.617838i
\(133\) 0 0
\(134\) −2.89792 + 5.01934i −0.250342 + 0.433605i
\(135\) −7.59166 + 13.1491i −0.653386 + 1.13170i
\(136\) 16.5375 1.41808
\(137\) −9.20417 −0.786365 −0.393183 0.919460i \(-0.628626\pi\)
−0.393183 + 0.919460i \(0.628626\pi\)
\(138\) 1.26984 2.19944i 0.108096 0.187228i
\(139\) −7.63381 + 13.2221i −0.647491 + 1.12149i 0.336229 + 0.941780i \(0.390848\pi\)
−0.983720 + 0.179707i \(0.942485\pi\)
\(140\) 0 0
\(141\) −2.00000 3.46410i −0.168430 0.291730i
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) 19.6546 7.09841i 1.64360 0.593599i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −23.6085 −1.96058
\(146\) −2.90061 5.02401i −0.240056 0.415790i
\(147\) 0 0
\(148\) 6.79583 0.558614
\(149\) −2.29583 3.97650i −0.188082 0.325767i 0.756529 0.653960i \(-0.226894\pi\)
−0.944611 + 0.328193i \(0.893560\pi\)
\(150\) −3.11716 −0.254515
\(151\) 8.79583 + 15.2348i 0.715795 + 1.23979i 0.962652 + 0.270741i \(0.0872687\pi\)
−0.246858 + 0.969052i \(0.579398\pi\)
\(152\) 4.24264 + 7.34847i 0.344124 + 0.596040i
\(153\) −2.75624 4.77395i −0.222829 0.385951i
\(154\) 0 0
\(155\) 3.79583 0.304889
\(156\) 4.79583 1.73205i 0.383974 0.138675i
\(157\) −3.46335 5.99870i −0.276405 0.478748i 0.694083 0.719895i \(-0.255810\pi\)
−0.970489 + 0.241146i \(0.922477\pi\)
\(158\) 5.89792 10.2155i 0.469213 0.812701i
\(159\) −9.32202 −0.739284
\(160\) −6.71015 + 11.6223i −0.530484 + 0.918825i
\(161\) 0 0
\(162\) 2.50000 4.33013i 0.196419 0.340207i
\(163\) 6.69375 + 11.5939i 0.524295 + 0.908105i 0.999600 + 0.0282841i \(0.00900432\pi\)
−0.475305 + 0.879821i \(0.657662\pi\)
\(164\) −4.87756 8.44819i −0.380874 0.659693i
\(165\) −22.0000 −1.71270
\(166\) 9.89949 0.768350
\(167\) 7.63381 + 13.2221i 0.590722 + 1.02316i 0.994135 + 0.108142i \(0.0344902\pi\)
−0.403414 + 0.915018i \(0.632176\pi\)
\(168\) 0 0
\(169\) 2.19375 + 12.8136i 0.168750 + 0.985659i
\(170\) 7.39792 12.8136i 0.567394 0.982756i
\(171\) 1.41421 2.44949i 0.108148 0.187317i
\(172\) −0.897916 + 1.55524i −0.0684654 + 0.118586i
\(173\) 4.66101 + 8.07311i 0.354370 + 0.613787i 0.987010 0.160659i \(-0.0513620\pi\)
−0.632640 + 0.774446i \(0.718029\pi\)
\(174\) 12.4392 0.943012
\(175\) 0 0
\(176\) 2.89792 5.01934i 0.218439 0.378347i
\(177\) −0.795832 + 1.37842i −0.0598184 + 0.103608i
\(178\) −12.1504 −0.910714
\(179\) 0.204168 0.353630i 0.0152603 0.0264316i −0.858294 0.513158i \(-0.828476\pi\)
0.873555 + 0.486726i \(0.161809\pi\)
\(180\) 2.68406 0.200058
\(181\) 16.5375 1.22922 0.614610 0.788831i \(-0.289314\pi\)
0.614610 + 0.788831i \(0.289314\pi\)
\(182\) 0 0
\(183\) 2.20417 0.162937
\(184\) −5.38749 −0.397171
\(185\) 9.12020 15.7967i 0.670531 1.16139i
\(186\) −2.00000 −0.146647
\(187\) 15.9747 27.6690i 1.16819 2.02336i
\(188\) −1.41421 + 2.44949i −0.103142 + 0.178647i
\(189\) 0 0
\(190\) 7.59166 0.550757
\(191\) 12.8979 + 22.3398i 0.933260 + 1.61645i 0.777707 + 0.628627i \(0.216383\pi\)
0.155553 + 0.987827i \(0.450284\pi\)
\(192\) 4.94975 8.57321i 0.357217 0.618718i
\(193\) −1.70417 + 2.95171i −0.122669 + 0.212468i −0.920819 0.389990i \(-0.872479\pi\)
0.798151 + 0.602458i \(0.205812\pi\)
\(194\) −2.12132 + 3.67423i −0.152302 + 0.263795i
\(195\) 2.41006 13.4722i 0.172588 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 \(0.741344\pi\)
\(198\) −5.79583 −0.411892
\(199\) 22.0499 1.56308 0.781539 0.623856i \(-0.214435\pi\)
0.781539 + 0.623856i \(0.214435\pi\)
\(200\) 3.30625 + 5.72660i 0.233787 + 0.404932i
\(201\) 4.09827 + 7.09841i 0.289070 + 0.500684i
\(202\) −1.48640 + 2.57452i −0.104583 + 0.181142i
\(203\) 0 0
\(204\) 3.89792 6.75139i 0.272909 0.472692i
\(205\) −26.1833 −1.82872
\(206\) −4.09827 + 7.09841i −0.285540 + 0.494570i
\(207\) 0.897916 + 1.55524i 0.0624095 + 0.108096i
\(208\) 2.75624 + 2.32446i 0.191111 + 0.161172i
\(209\) 16.3931 1.13393
\(210\) 0 0
\(211\) 0.897916 + 1.55524i 0.0618151 + 0.107067i 0.895277 0.445510i \(-0.146978\pi\)
−0.833462 + 0.552577i \(0.813644\pi\)
\(212\) 3.29583 + 5.70855i 0.226359 + 0.392065i
\(213\) 4.24264 + 7.34847i 0.290701 + 0.503509i
\(214\) −6.00000 −0.410152
\(215\) 2.41006 + 4.17434i 0.164365 + 0.284688i
\(216\) −16.9706 −1.15470
\(217\) 0 0
\(218\) 8.79583 + 15.2348i 0.595729 + 1.03183i
\(219\) −8.20417 −0.554386
\(220\) 7.77817 + 13.4722i 0.524404 + 0.908295i
\(221\) 15.1937 + 12.8136i 1.02204 + 0.861934i
\(222\) −4.80538 + 8.32316i −0.322516 + 0.558614i
\(223\) −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
\(225\) 1.10208 1.90887i 0.0734723 0.127258i
\(226\) 8.29583 14.3688i 0.551831 0.955798i
\(227\) −20.9245 −1.38881 −0.694403 0.719587i \(-0.744331\pi\)
−0.694403 + 0.719587i \(0.744331\pi\)
\(228\) 4.00000 0.264906
\(229\) 6.36396 11.0227i 0.420542 0.728401i −0.575450 0.817837i \(-0.695173\pi\)
0.995993 + 0.0894361i \(0.0285065\pi\)
\(230\) −2.41006 + 4.17434i −0.158915 + 0.275248i
\(231\) 0 0
\(232\) −13.1937 22.8522i −0.866212 1.50032i
\(233\) 10.5917 18.3453i 0.693883 1.20184i −0.276673 0.960964i \(-0.589232\pi\)
0.970556 0.240876i \(-0.0774348\pi\)
\(234\) 0.634922 3.54921i 0.0415062 0.232019i
\(235\) 3.79583 + 6.57457i 0.247613 + 0.428878i
\(236\) 1.12548 0.0732622
\(237\) −8.34091 14.4469i −0.541800 0.938426i
\(238\) 0 0
\(239\) −19.7958 −1.28049 −0.640243 0.768172i \(-0.721166\pi\)
−0.640243 + 0.768172i \(0.721166\pi\)
\(240\) −1.89792 3.28729i −0.122510 0.212193i
\(241\) −4.38701 −0.282592 −0.141296 0.989967i \(-0.545127\pi\)
−0.141296 + 0.989967i \(0.545127\pi\)
\(242\) −11.2958 19.5650i −0.726124 1.25768i
\(243\) 4.94975 + 8.57321i 0.317526 + 0.549972i
\(244\) −0.779291 1.34977i −0.0498890 0.0864103i
\(245\) 0 0
\(246\) 13.7958 0.879590
\(247\) −1.79583 + 10.0387i −0.114266 + 0.638746i
\(248\) 2.12132 + 3.67423i 0.134704 + 0.233314i
\(249\) 7.00000 12.1244i 0.443607 0.768350i
\(250\) −7.50417 −0.474606
\(251\) −1.55858 + 2.69954i −0.0983769 + 0.170394i −0.911013 0.412378i \(-0.864698\pi\)
0.812636 + 0.582771i \(0.198032\pi\)
\(252\) 0 0
\(253\) −5.20417 + 9.01388i −0.327183 + 0.566698i
\(254\) −3.79583 6.57457i −0.238172 0.412525i
\(255\) −10.4622 18.1211i −0.655170 1.13479i
\(256\) −17.0000 −1.06250
\(257\) −15.4120 −0.961373 −0.480686 0.876893i \(-0.659612\pi\)
−0.480686 + 0.876893i \(0.659612\pi\)
\(258\) −1.26984 2.19944i −0.0790571 0.136931i
\(259\) 0 0
\(260\) −9.10208 + 3.28729i −0.564487 + 0.203869i
\(261\) −4.39792 + 7.61741i −0.272224 + 0.471506i
\(262\) −4.09827 + 7.09841i −0.253192 + 0.438542i
\(263\) 12.6937 21.9862i 0.782730 1.35573i −0.147616 0.989045i \(-0.547160\pi\)
0.930346 0.366683i \(-0.119507\pi\)
\(264\) −12.2948 21.2952i −0.756694 1.31063i
\(265\) 17.6924 1.08684
\(266\) 0 0
\(267\) −8.59166 + 14.8812i −0.525801 + 0.910714i
\(268\) 2.89792 5.01934i 0.177018 0.306605i
\(269\) 1.12548 0.0686215 0.0343107 0.999411i \(-0.489076\pi\)
0.0343107 + 0.999411i \(0.489076\pi\)
\(270\) −7.59166 + 13.1491i −0.462014 + 0.800232i
\(271\) 23.1754 1.40781 0.703903 0.710296i \(-0.251439\pi\)
0.703903 + 0.710296i \(0.251439\pi\)
\(272\) 5.51249 0.334244
\(273\) 0 0
\(274\) −9.20417 −0.556044
\(275\) 12.7750 0.770361
\(276\) −1.26984 + 2.19944i −0.0764357 + 0.132390i
\(277\) −6.18333 −0.371520 −0.185760 0.982595i \(-0.559475\pi\)
−0.185760 + 0.982595i \(0.559475\pi\)
\(278\) −7.63381 + 13.2221i −0.457845 + 0.793011i
\(279\) 0.707107 1.22474i 0.0423334 0.0733236i
\(280\) 0 0
\(281\) 15.2042 0.907005 0.453502 0.891255i \(-0.350174\pi\)
0.453502 + 0.891255i \(0.350174\pi\)
\(282\) −2.00000 3.46410i −0.119098 0.206284i
\(283\) −14.7049 + 25.4696i −0.874114 + 1.51401i −0.0164104 + 0.999865i \(0.505224\pi\)
−0.857704 + 0.514145i \(0.828109\pi\)
\(284\) 3.00000 5.19615i 0.178017 0.308335i
\(285\) 5.36812 9.29785i 0.317980 0.550757i
\(286\) 19.6546 7.09841i 1.16220 0.419738i
\(287\) 0 0
\(288\) 2.50000 + 4.33013i 0.147314 + 0.255155i
\(289\) 13.3875 0.787500
\(290\) −23.6085 −1.38634
\(291\) 3.00000 + 5.19615i 0.175863 + 0.304604i
\(292\) 2.90061 + 5.02401i 0.169745 + 0.294008i
\(293\) −4.87756 + 8.44819i −0.284950 + 0.493548i −0.972597 0.232497i \(-0.925310\pi\)
0.687647 + 0.726045i \(0.258644\pi\)
\(294\) 0 0
\(295\) 1.51042 2.61613i 0.0879401 0.152317i
\(296\) 20.3875 1.18500
\(297\) −16.3931 + 28.3937i −0.951223 + 1.64757i
\(298\) −2.29583 3.97650i −0.132994 0.230352i
\(299\) −4.94975 4.17434i −0.286251 0.241409i
\(300\) 3.11716 0.179970
\(301\) 0 0
\(302\) 8.79583 + 15.2348i 0.506143 + 0.876666i
\(303\) 2.10208 + 3.64092i 0.120762 + 0.209165i
\(304\) 1.41421 + 2.44949i 0.0811107 + 0.140488i
\(305\) −4.18333 −0.239537
\(306\) −2.75624 4.77395i −0.157564 0.272909i
\(307\) −34.2004 −1.95192 −0.975960 0.217951i \(-0.930063\pi\)
−0.975960 + 0.217951i \(0.930063\pi\)
\(308\) 0 0
\(309\) 5.79583 + 10.0387i 0.329713 + 0.571080i
\(310\) 3.79583 0.215589
\(311\) 5.93085 + 10.2725i 0.336308 + 0.582502i 0.983735 0.179625i \(-0.0574884\pi\)
−0.647427 + 0.762127i \(0.724155\pi\)
\(312\) 14.3875 5.19615i 0.814531 0.294174i
\(313\) 0.851476 1.47480i 0.0481283 0.0833606i −0.840958 0.541101i \(-0.818008\pi\)
0.889086 + 0.457740i \(0.151341\pi\)
\(314\) −3.46335 5.99870i −0.195448 0.338526i
\(315\) 0 0
\(316\) −5.89792 + 10.2155i −0.331784 + 0.574666i
\(317\) 6.29583 10.9047i 0.353609 0.612469i −0.633270 0.773931i \(-0.718288\pi\)
0.986879 + 0.161462i \(0.0516210\pi\)
\(318\) −9.32202 −0.522753
\(319\) −50.9792 −2.85428
\(320\) −9.39420 + 16.2712i −0.525152 + 0.909590i
\(321\) −4.24264 + 7.34847i −0.236801 + 0.410152i
\(322\) 0 0
\(323\) 7.79583 + 13.5028i 0.433772 + 0.751315i
\(324\) −2.50000 + 4.33013i −0.138889 + 0.240563i
\(325\) −1.39948 + 7.82305i −0.0776289 + 0.433945i
\(326\) 6.69375 + 11.5939i 0.370732 + 0.642127i
\(327\) 24.8784 1.37578
\(328\) −14.6327 25.3446i −0.807955 1.39942i
\(329\) 0 0
\(330\) −22.0000 −1.21106
\(331\) −0.306253 0.530445i −0.0168332 0.0291559i 0.857486 0.514507i \(-0.172025\pi\)
−0.874319 + 0.485351i \(0.838692\pi\)
\(332\) −9.89949 −0.543305
\(333\) −3.39792 5.88536i −0.186205 0.322516i
\(334\) 7.63381 + 13.2221i 0.417703 + 0.723483i
\(335\) −7.77817 13.4722i −0.424967 0.736065i
\(336\) 0 0
\(337\) −29.9792 −1.63307 −0.816534 0.577297i \(-0.804108\pi\)
−0.816534 + 0.577297i \(0.804108\pi\)
\(338\) 2.19375 + 12.8136i 0.119324 + 0.696966i
\(339\) −11.7321 20.3206i −0.637199 1.10366i
\(340\) −7.39792 + 12.8136i −0.401208 + 0.694913i
\(341\) 8.19654 0.443868
\(342\) 1.41421 2.44949i 0.0764719 0.132453i
\(343\) 0 0
\(344\) −2.69375 + 4.66571i −0.145237 + 0.251558i
\(345\) 3.40834 + 5.90341i 0.183499 + 0.317829i
\(346\) 4.66101 + 8.07311i 0.250577 + 0.434013i
\(347\) 14.9792 0.804123 0.402062 0.915613i \(-0.368294\pi\)
0.402062 + 0.915613i \(0.368294\pi\)
\(348\) −12.4392 −0.666810
\(349\) 6.50833 + 11.2728i 0.348383 + 0.603417i 0.985962 0.166968i \(-0.0533976\pi\)
−0.637579 + 0.770385i \(0.720064\pi\)
\(350\) 0 0
\(351\) −15.5917 13.1491i −0.832221 0.701849i
\(352\) −14.4896 + 25.0967i −0.772297 + 1.33766i
\(353\) −7.56162 + 13.0971i −0.402464 + 0.697089i −0.994023 0.109173i \(-0.965180\pi\)
0.591558 + 0.806262i \(0.298513\pi\)
\(354\) −0.795832 + 1.37842i −0.0422980 + 0.0732622i
\(355\) −8.05217 13.9468i −0.427365 0.740218i
\(356\) 12.1504 0.643972
\(357\) 0 0
\(358\) 0.204168 0.353630i 0.0107906 0.0186899i
\(359\) 2.00000 3.46410i 0.105556 0.182828i −0.808409 0.588621i \(-0.799671\pi\)
0.913965 + 0.405793i \(0.133004\pi\)
\(360\) 8.05217 0.424387
\(361\) 5.50000 9.52628i 0.289474 0.501383i
\(362\) 16.5375 0.869189
\(363\) −31.9494 −1.67691
\(364\) 0 0
\(365\) 15.5708 0.815014
\(366\) 2.20417 0.115214
\(367\) 10.6066 18.3712i 0.553660 0.958967i −0.444346 0.895855i \(-0.646564\pi\)
0.998006 0.0631123i \(-0.0201026\pi\)
\(368\) −1.79583 −0.0936142
\(369\) −4.87756 + 8.44819i −0.253916 + 0.439795i
\(370\) 9.12020 15.7967i 0.474137 0.821229i
\(371\) 0 0
\(372\) 2.00000 0.103695
\(373\) 6.29583 + 10.9047i 0.325986 + 0.564624i 0.981711 0.190375i \(-0.0609705\pi\)
−0.655726 + 0.754999i \(0.727637\pi\)
\(374\) 15.9747 27.6690i 0.826033 1.43073i
\(375\) −5.30625 + 9.19070i −0.274014 + 0.474606i
\(376\) −4.24264 + 7.34847i −0.218797 + 0.378968i
\(377\) 5.58467 31.2182i 0.287625 1.60782i
\(378\) 0 0
\(379\) 1.69375 + 2.93366i 0.0870020 + 0.150692i 0.906243 0.422758i \(-0.138938\pi\)
−0.819241 + 0.573450i \(0.805605\pi\)
\(380\) −7.59166 −0.389444
\(381\) −10.7362 −0.550034
\(382\) 12.8979 + 22.3398i 0.659915 + 1.14301i
\(383\) −7.48944 12.9721i −0.382692 0.662843i 0.608754 0.793359i \(-0.291670\pi\)
−0.991446 + 0.130517i \(0.958336\pi\)
\(384\) −2.12132 + 3.67423i −0.108253 + 0.187500i
\(385\) 0 0
\(386\) −1.70417 + 2.95171i −0.0867399 + 0.150238i
\(387\) 1.79583 0.0912872
\(388\) 2.12132 3.67423i 0.107694 0.186531i
\(389\) −14.1937 24.5843i −0.719652 1.24647i −0.961138 0.276069i \(-0.910968\pi\)
0.241486 0.970404i \(-0.422365\pi\)
\(390\) 2.41006 13.4722i 0.122038 0.682191i
\(391\) −9.89949 −0.500639
\(392\) 0 0
\(393\) 5.79583 + 10.0387i 0.292361 + 0.506384i
\(394\) 4.00000 + 6.92820i 0.201517 + 0.349038i
\(395\) 15.8303 + 27.4190i 0.796511 + 1.37960i
\(396\) 5.79583 0.291251
\(397\) 3.53553 + 6.12372i 0.177443 + 0.307341i 0.941004 0.338395i \(-0.109884\pi\)
−0.763561 + 0.645736i \(0.776551\pi\)
\(398\) 22.0499 1.10526
\(399\) 0 0
\(400\) 1.10208 + 1.90887i 0.0551042 + 0.0954433i
\(401\) 24.3875 1.21785 0.608927 0.793227i \(-0.291600\pi\)
0.608927 + 0.793227i \(0.291600\pi\)
\(402\) 4.09827 + 7.09841i 0.204403 + 0.354037i
\(403\) −0.897916 + 5.01934i −0.0447284 + 0.250031i
\(404\) 1.48640 2.57452i 0.0739511 0.128087i
\(405\) 6.71015 + 11.6223i 0.333430 + 0.577517i
\(406\) 0 0
\(407\) 19.6937 34.1106i 0.976183 1.69080i
\(408\) 11.6937 20.2542i 0.578927 1.00273i
\(409\) 28.6879 1.41853 0.709263 0.704944i \(-0.249028\pi\)
0.709263 + 0.704944i \(0.249028\pi\)
\(410\) −26.1833 −1.29310
\(411\) −6.50833 + 11.2728i −0.321032 + 0.556044i
\(412\) 4.09827 7.09841i 0.201907 0.349714i
\(413\) 0 0
\(414\) 0.897916 + 1.55524i 0.0441302 + 0.0764357i
\(415\) −13.2854 + 23.0110i −0.652155 + 1.12957i
\(416\) −13.7812 11.6223i −0.675680 0.569831i
\(417\) 10.7958 + 18.6989i 0.528674 + 0.915690i
\(418\) 16.3931 0.801812
\(419\) 14.2718 + 24.7194i 0.697221 + 1.20762i 0.969426 + 0.245384i \(0.0789139\pi\)
−0.272205 + 0.962239i \(0.587753\pi\)
\(420\) 0 0
\(421\) −6.59166 −0.321258 −0.160629 0.987015i \(-0.551352\pi\)
−0.160629 + 0.987015i \(0.551352\pi\)
\(422\) 0.897916 + 1.55524i 0.0437099 + 0.0757077i
\(423\) 2.82843 0.137523
\(424\) 9.88749 + 17.1256i 0.480179 + 0.831695i
\(425\) 6.07522 + 10.5226i 0.294692 + 0.510421i
\(426\) 4.24264 + 7.34847i 0.205557 + 0.356034i
\(427\) 0 0
\(428\) 6.00000 0.290021
\(429\) 5.20417 29.0912i 0.251260 1.40454i
\(430\) 2.41006 + 4.17434i 0.116223 + 0.201305i
\(431\) 2.59166 4.48889i 0.124836 0.216222i −0.796833 0.604200i \(-0.793493\pi\)
0.921669 + 0.387978i \(0.126826\pi\)
\(432\) −5.65685 −0.272166
\(433\) 6.71015 11.6223i 0.322469 0.558533i −0.658528 0.752556i \(-0.728821\pi\)
0.980997 + 0.194024i \(0.0621539\pi\)
\(434\) 0 0
\(435\) −16.6937 + 28.9144i −0.800404 + 1.38634i
\(436\) −8.79583 15.2348i −0.421244 0.729616i
\(437\) −2.53969 4.39887i −0.121490 0.210427i
\(438\) −8.20417 −0.392010
\(439\) −34.2004 −1.63230 −0.816148 0.577843i \(-0.803894\pi\)
−0.816148 + 0.577843i \(0.803894\pi\)
\(440\) 23.3345 + 40.4166i 1.11243 + 1.92678i
\(441\) 0 0
\(442\) 15.1937 + 12.8136i 0.722693 + 0.609479i
\(443\) −5.00000 + 8.66025i −0.237557 + 0.411461i −0.960013 0.279956i \(-0.909680\pi\)
0.722456 + 0.691417i \(0.243013\pi\)
\(444\) 4.80538 8.32316i 0.228053 0.395000i
\(445\) 16.3063 28.2433i 0.772991 1.33886i
\(446\) −2.82843 4.89898i −0.133930 0.231973i
\(447\) −6.49359 −0.307136
\(448\) 0 0
\(449\) −2.20417 + 3.81773i −0.104021 + 0.180170i −0.913338 0.407203i \(-0.866504\pi\)
0.809317 + 0.587372i \(0.199838\pi\)
\(450\) 1.10208 1.90887i 0.0519527 0.0899848i
\(451\) −56.5391 −2.66232
\(452\) −8.29583 + 14.3688i −0.390203 + 0.675852i
\(453\) 24.8784 1.16889
\(454\) −20.9245 −0.982034
\(455\) 0 0
\(456\) 12.0000 0.561951
\(457\) −14.5917 −0.682569 −0.341285 0.939960i \(-0.610862\pi\)
−0.341285 + 0.939960i \(0.610862\pi\)
\(458\) 6.36396 11.0227i 0.297368 0.515057i
\(459\) −31.1833 −1.45551
\(460\) 2.41006 4.17434i 0.112370 0.194630i
\(461\) 15.4842 26.8194i 0.721169 1.24910i −0.239362 0.970930i \(-0.576938\pi\)
0.960531 0.278172i \(-0.0897284\pi\)
\(462\) 0 0
\(463\) 11.3875 0.529222 0.264611 0.964355i \(-0.414756\pi\)
0.264611 + 0.964355i \(0.414756\pi\)
\(464\) −4.39792 7.61741i −0.204168 0.353630i
\(465\) 2.68406 4.64893i 0.124470 0.215589i
\(466\) 10.5917 18.3453i 0.490649 0.849830i
\(467\) −2.41006 + 4.17434i −0.111524 + 0.193166i −0.916385 0.400298i \(-0.868907\pi\)
0.804861 + 0.593464i \(0.202240\pi\)
\(468\) −0.634922 + 3.54921i −0.0293493 + 0.164062i
\(469\) 0 0
\(470\) 3.79583 + 6.57457i 0.175089 + 0.303262i
\(471\) −9.79583 −0.451368
\(472\) 3.37643 0.155413
\(473\) 5.20417 + 9.01388i 0.239288 + 0.414459i
\(474\) −8.34091 14.4469i −0.383111 0.663567i
\(475\) −3.11716 + 5.39909i −0.143025 + 0.247727i
\(476\) 0 0
\(477\) 3.29583 5.70855i 0.150906 0.261376i
\(478\) −19.7958 −0.905440
\(479\) −3.67990 + 6.37378i −0.168139 + 0.291225i −0.937766 0.347269i \(-0.887109\pi\)
0.769627 + 0.638494i \(0.220442\pi\)
\(480\) 9.48958 + 16.4364i 0.433138 + 0.750217i
\(481\) 18.7310 + 15.7967i 0.854058 + 0.720266i
\(482\) −4.38701 −0.199823
\(483\) 0 0
\(484\) 11.2958 + 19.5650i 0.513447 + 0.889316i
\(485\) −5.69375 9.86186i −0.258540 0.447804i
\(486\) 4.94975 + 8.57321i 0.224525 + 0.388889i
\(487\) 19.5917 0.887783 0.443891 0.896081i \(-0.353598\pi\)
0.443891 + 0.896081i \(0.353598\pi\)
\(488\) −2.33787 4.04932i −0.105831 0.183304i
\(489\) 18.9328 0.856170
\(490\) 0 0
\(491\) 4.79583 + 8.30662i 0.216433 + 0.374873i 0.953715 0.300712i \(-0.0972244\pi\)
−0.737282 + 0.675585i \(0.763891\pi\)
\(492\) −13.7958 −0.621964
\(493\) −24.2434 41.9909i −1.09187 1.89117i
\(494\) −1.79583 + 10.0387i −0.0807983 + 0.451661i
\(495\) 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
\(499\) −8.10208 + 14.0332i −0.362699 + 0.628213i −0.988404 0.151847i \(-0.951478\pi\)
0.625705 + 0.780060i \(0.284811\pi\)
\(500\) 7.50417 0.335597
\(501\) 21.5917 0.964644
\(502\) −1.55858 + 2.69954i −0.0695629 + 0.120487i
\(503\) −14.2718 + 24.7194i −0.636347 + 1.10218i 0.349881 + 0.936794i \(0.386222\pi\)
−0.986228 + 0.165391i \(0.947111\pi\)
\(504\) 0 0
\(505\) −3.98958 6.91015i −0.177534 0.307498i
\(506\) −5.20417 + 9.01388i −0.231354 + 0.400716i
\(507\) 17.2446 + 6.37378i 0.765858 + 0.283069i
\(508\) 3.79583 + 6.57457i 0.168413 + 0.291700i
\(509\) −26.4370 −1.17180 −0.585899 0.810384i \(-0.699258\pi\)
−0.585899 + 0.810384i \(0.699258\pi\)
\(510\) −10.4622 18.1211i −0.463275 0.802417i
\(511\) 0 0
\(512\) −11.0000 −0.486136
\(513\) −8.00000 13.8564i −0.353209 0.611775i
\(514\) −15.4120 −0.679793
\(515\) −11.0000 19.0526i −0.484718 0.839556i
\(516\) 1.26984 + 2.19944i 0.0559018 + 0.0968247i
\(517\) 8.19654 + 14.1968i 0.360484 + 0.624376i
\(518\) 0 0
\(519\) 13.1833 0.578684
\(520\) −27.3063 + 9.86186i −1.19746 + 0.432471i
\(521\) 12.5114 + 21.6703i 0.548133 + 0.949394i 0.998403 + 0.0565015i \(0.0179946\pi\)
−0.450269 + 0.892893i \(0.648672\pi\)
\(522\) −4.39792 + 7.61741i −0.192492 + 0.333405i
\(523\) −28.5730 −1.24941 −0.624705 0.780861i \(-0.714781\pi\)
−0.624705 + 0.780861i \(0.714781\pi\)
\(524\) 4.09827 7.09841i 0.179034 0.310096i
\(525\) 0 0
\(526\) 12.6937 21.9862i 0.553474 0.958645i
\(527\) 3.89792 + 6.75139i 0.169796 + 0.294095i
\(528\) −4.09827 7.09841i −0.178354 0.308919i
\(529\) −19.7750 −0.859782
\(530\) 17.6924 0.768509
\(531\) −0.562738 0.974691i −0.0244207 0.0422980i
\(532\) 0 0
\(533\) 6.19375 34.6230i 0.268281 1.49969i
\(534\) −8.59166 + 14.8812i −0.371798 + 0.643972i
\(535\) 8.05217 13.9468i 0.348126 0.602972i
\(536\) 8.69375 15.0580i 0.375513 0.650407i
\(537\) −0.288738 0.500109i −0.0124600 0.0215813i
\(538\) 1.12548 0.0485227
\(539\) 0 0
\(540\) 7.59166 13.1491i 0.326693 0.565849i
\(541\) 6.29583 10.9047i 0.270679 0.468830i −0.698357 0.715750i \(-0.746085\pi\)
0.969036 + 0.246920i \(0.0794185\pi\)
\(542\) 23.1754 0.995469
\(543\) 11.6937 20.2542i 0.501827 0.869189i
\(544\) −27.5624 −1.18173
\(545\) −47.2170 −2.02256
\(546\) 0 0
\(547\) −36.9792 −1.58111 −0.790557 0.612388i \(-0.790209\pi\)
−0.790557 + 0.612388i \(0.790209\pi\)
\(548\) 9.20417 0.393183
\(549\) −0.779291 + 1.34977i −0.0332593 + 0.0576069i
\(550\) 12.7750 0.544727
\(551\) 12.4392 21.5453i 0.529927 0.917861i
\(552\) −3.80953 + 6.59831i −0.162145 + 0.280843i
\(553\) 0 0
\(554\) −6.18333 −0.262704
\(555\) −12.8979 22.3398i −0.547486 0.948274i
\(556\) 7.63381 13.2221i 0.323745 0.560744i
\(557\) −10.2958 + 17.8329i −0.436248 + 0.755604i −0.997397 0.0721110i \(-0.977026\pi\)
0.561148 + 0.827715i \(0.310360\pi\)
\(558\) 0.707107 1.22474i 0.0299342 0.0518476i
\(559\) −6.08996 + 2.19944i −0.257578 + 0.0930262i
\(560\) 0 0
\(561\) −22.5917 39.1299i −0.953821 1.65207i
\(562\) 15.2042 0.641349
\(563\) 1.12548 0.0474331 0.0237166 0.999719i \(-0.492450\pi\)
0.0237166 + 0.999719i \(0.492450\pi\)
\(564\) 2.00000 + 3.46410i 0.0842152 + 0.145865i
\(565\) 22.2665 + 38.5667i 0.936758 + 1.62251i
\(566\) −14.7049 + 25.4696i −0.618092 + 1.07057i
\(567\) 0 0
\(568\) 9.00000 15.5885i 0.377632 0.654077i
\(569\) 6.40834 0.268651 0.134326 0.990937i \(-0.457113\pi\)
0.134326 + 0.990937i \(0.457113\pi\)
\(570\) 5.36812 9.29785i 0.224846 0.389444i
\(571\) −7.59166 13.1491i −0.317701 0.550275i 0.662307 0.749233i \(-0.269578\pi\)
−0.980008 + 0.198958i \(0.936244\pi\)
\(572\) −19.6546 + 7.09841i −0.821801 + 0.296800i
\(573\) 36.4808 1.52401
\(574\) 0 0
\(575\) −1.97916 3.42800i −0.0825366 0.142958i
\(576\) 3.50000 + 6.06218i 0.145833 + 0.252591i
\(577\) −4.58883 7.94808i −0.191035 0.330883i 0.754558 0.656233i \(-0.227851\pi\)
−0.945594 + 0.325350i \(0.894518\pi\)
\(578\) 13.3875 0.556846
\(579\) 2.41006 + 4.17434i 0.100159 + 0.173480i
\(580\) 23.6085 0.980291
\(581\) 0 0
\(582\) 3.00000 + 5.19615i 0.124354 + 0.215387i
\(583\) 38.2042 1.58225
\(584\) 8.70183 + 15.0720i 0.360084 + 0.623685i
\(585\) 7.39792 + 6.23899i 0.305866 + 0.257951i
\(586\) −4.87756 + 8.44819i −0.201490 + 0.348991i
\(587\) 1.55858 + 2.69954i 0.0643296 + 0.111422i 0.896396 0.443253i \(-0.146176\pi\)
−0.832067 + 0.554675i \(0.812842\pi\)
\(588\) 0 0
\(589\) −2.00000 + 3.46410i −0.0824086 + 0.142736i
\(590\) 1.51042 2.61613i 0.0621831 0.107704i
\(591\) 11.3137 0.465384
\(592\) 6.79583 0.279307
\(593\) −0.779291 + 1.34977i −0.0320017 + 0.0554285i −0.881583 0.472030i \(-0.843522\pi\)
0.849581 + 0.527458i \(0.176855\pi\)
\(594\) −16.3931 + 28.3937i −0.672617 + 1.16501i
\(595\) 0 0
\(596\) 2.29583 + 3.97650i 0.0940409 + 0.162884i
\(597\) 15.5917 27.0056i 0.638124 1.10526i
\(598\) −4.94975 4.17434i −0.202410 0.170702i
\(599\) 7.20417 + 12.4780i 0.294354 + 0.509837i 0.974834 0.222930i \(-0.0715621\pi\)
−0.680480 + 0.732767i \(0.738229\pi\)
\(600\) 9.35149 0.381773
\(601\) −15.4842 26.8194i −0.631612 1.09398i −0.987222 0.159350i \(-0.949060\pi\)
0.355610 0.934634i \(-0.384273\pi\)
\(602\) 0 0
\(603\) −5.79583 −0.236025
\(604\) −8.79583 15.2348i −0.357897 0.619896i
\(605\) 60.6373 2.46526
\(606\) 2.10208 + 3.64092i 0.0853913 + 0.147902i
\(607\) −17.9517 31.0932i −0.728636 1.26203i −0.957460 0.288566i \(-0.906821\pi\)
0.228824 0.973468i \(-0.426512\pi\)
\(608\) −7.07107 12.2474i −0.286770 0.496700i
\(609\) 0 0
\(610\) −4.18333 −0.169378
\(611\) −9.59166 + 3.46410i −0.388037 + 0.140143i
\(612\) 2.75624 + 4.77395i 0.111415 + 0.192976i
\(613\) 2.98958 5.17810i 0.120748 0.209142i −0.799315 0.600912i \(-0.794804\pi\)
0.920063 + 0.391771i \(0.128137\pi\)
\(614\) −34.2004 −1.38022
\(615\) −18.5144 + 32.0679i −0.746573 + 1.29310i
\(616\) 0 0
\(617\) 12.1937 21.1202i 0.490902 0.850267i −0.509043 0.860741i \(-0.670001\pi\)
0.999945 + 0.0104740i \(0.00333405\pi\)
\(618\) 5.79583 + 10.0387i 0.233143 + 0.403815i
\(619\) 16.9558 + 29.3684i 0.681512 + 1.18041i 0.974519 + 0.224303i \(0.0720107\pi\)
−0.293007 + 0.956110i \(0.594656\pi\)
\(620\) −3.79583 −0.152444
\(621\) 10.1588 0.407657
\(622\) 5.93085 + 10.2725i 0.237806 + 0.411891i
\(623\) 0 0
\(624\) 4.79583 1.73205i 0.191987 0.0693375i
\(625\) 15.5812 26.9875i 0.623250 1.07950i
\(626\) 0.851476 1.47480i 0.0340318 0.0589448i
\(627\) 11.5917 20.0773i 0.462926 0.801812i
\(628\) 3.46335 + 5.99870i 0.138203 + 0.239374i
\(629\) 37.4619 1.49370
\(630\) 0 0
\(631\) 10.2042 17.6741i 0.406222 0.703596i −0.588241 0.808685i \(-0.700179\pi\)
0.994463 + 0.105089i \(0.0335128\pi\)
\(632\) −17.6937 + 30.6465i −0.703819 + 1.21905i
\(633\) 2.53969 0.100944
\(634\) 6.29583 10.9047i 0.250039 0.433081i
\(635\) 20.3765 0.808615
\(636\) 9.32202 0.369642
\(637\) 0 0
\(638\) −50.9792 −2.01828
\(639\) −6.00000 −0.237356
\(640\) 4.02609 6.97339i 0.159145 0.275647i
\(641\) 4.79583 0.189424 0.0947120 0.995505i \(-0.469807\pi\)
0.0947120 + 0.995505i \(0.469807\pi\)
\(642\) −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
\(645\) 6.81667 0.268406
\(646\) 7.79583 + 13.5028i 0.306723 + 0.531260i
\(647\) −0.981107 + 1.69933i −0.0385713 + 0.0668074i −0.884667 0.466224i \(-0.845614\pi\)
0.846095 + 0.533032i \(0.178947\pi\)
\(648\) −7.50000 + 12.9904i −0.294628 + 0.510310i
\(649\) 3.26153 5.64914i 0.128026 0.221748i
\(650\) −1.39948 + 7.82305i −0.0548920 + 0.306845i
\(651\) 0 0
\(652\) −6.69375 11.5939i −0.262147 0.454053i
\(653\) 25.1833 0.985500 0.492750 0.870171i \(-0.335992\pi\)
0.492750 + 0.870171i \(0.335992\pi\)
\(654\) 24.8784 0.972821
\(655\) −11.0000 19.0526i −0.429806 0.744445i
\(656\) −4.87756 8.44819i −0.190437 0.329846i
\(657\) 2.90061 5.02401i 0.113164 0.196005i
\(658\) 0 0
\(659\) 18.7958 32.5553i 0.732182 1.26818i −0.223767 0.974643i \(-0.571836\pi\)
0.955949 0.293533i \(-0.0948311\pi\)
\(660\) 22.0000 0.856349
\(661\) 13.9256 24.1198i 0.541642 0.938152i −0.457168 0.889381i \(-0.651136\pi\)
0.998810 0.0487715i \(-0.0155306\pi\)
\(662\) −0.306253 0.530445i −0.0119028 0.0206163i
\(663\) 26.4370 9.54790i 1.02673 0.370810i
\(664\) −29.6985 −1.15252
\(665\) 0 0
\(666\) −3.39792 5.88536i −0.131667 0.228053i
\(667\) 7.89792 + 13.6796i 0.305809 + 0.529676i
\(668\) −7.63381 13.2221i −0.295361 0.511580i
\(669\) −8.00000 −0.309298
\(670\) −7.77817 13.4722i −0.300497 0.520476i
\(671\) −9.03328 −0.348726
\(672\) 0 0
\(673\) −11.9896 20.7666i −0.462164 0.800492i 0.536904 0.843643i \(-0.319594\pi\)
−0.999069 + 0.0431511i \(0.986260\pi\)
\(674\) −29.9792 −1.15475
\(675\) −6.23433 10.7982i −0.239959 0.415622i
\(676\) −2.19375 12.8136i −0.0843749 0.492829i
\(677\) 17.3889 30.1185i 0.668311 1.15755i −0.310065 0.950715i \(-0.600351\pi\)
0.978376 0.206833i \(-0.0663158\pi\)
\(678\) −11.7321 20.3206i −0.450568 0.780406i
\(679\) 0 0
\(680\) −22.1937 + 38.4407i −0.851091 + 1.47413i
\(681\) −14.7958 + 25.6271i −0.566977 + 0.982034i
\(682\) 8.19654 0.313862
\(683\) 50.7750 1.94285 0.971425 0.237345i \(-0.0762771\pi\)
0.971425 + 0.237345i \(0.0762771\pi\)
\(684\) −1.41421 + 2.44949i −0.0540738 + 0.0936586i
\(685\) 12.3523 21.3947i 0.471956 0.817451i
\(686\) 0 0
\(687\) −9.00000 15.5885i −0.343371 0.594737i
\(688\) −0.897916 + 1.55524i −0.0342327 + 0.0592928i
\(689\) −4.18519 + 23.3952i −0.159443 + 0.891285i
\(690\) 3.40834 + 5.90341i 0.129753 + 0.224739i
\(691\) −11.0250 −0.419410 −0.209705 0.977765i \(-0.567250\pi\)
−0.209705 + 0.977765i \(0.567250\pi\)
\(692\) −4.66101 8.07311i −0.177185 0.306893i
\(693\) 0 0
\(694\) 14.9792 0.568601
\(695\) −20.4896 35.4890i −0.777214 1.34617i
\(696\) −37.3176 −1.41452
\(697\) −26.8875 46.5705i −1.01844 1.76398i
\(698\) 6.50833 + 11.2728i 0.246344 + 0.426680i
\(699\) −14.9789 25.9442i −0.566553 0.981299i
\(700\) 0 0
\(701\) −10.4083 −0.393117 −0.196559 0.980492i \(-0.562977\pi\)
−0.196559 + 0.980492i \(0.562977\pi\)
\(702\) −15.5917 13.1491i −0.588469 0.496283i
\(703\) 9.61076 + 16.6463i 0.362477 + 0.627828i
\(704\) −20.2854 + 35.1354i −0.764535 + 1.32421i
\(705\) 10.7362 0.404350
\(706\) −7.56162 + 13.0971i −0.284585 + 0.492916i
\(707\) 0 0
\(708\) 0.795832 1.37842i 0.0299092 0.0518042i
\(709\) 9.39792 + 16.2777i 0.352946 + 0.611321i 0.986764 0.162162i \(-0.0518466\pi\)
−0.633818 + 0.773482i \(0.718513\pi\)
\(710\) −8.05217 13.9468i −0.302193 0.523413i
\(711\) 11.7958 0.442378
\(712\) 36.4513 1.36607
\(713\) −1.26984 2.19944i −0.0475561 0.0823695i
\(714\) 0 0
\(715\) −9.87707 + 55.2127i −0.369382 + 2.06484i
\(716\) −0.204168 + 0.353630i −0.00763013 + 0.0132158i
\(717\) −13.9978 + 24.2448i −0.522756 + 0.905440i
\(718\) 2.00000 3.46410i 0.0746393 0.129279i
\(719\) 14.5605 + 25.2195i 0.543015 + 0.940530i 0.998729 + 0.0504035i \(0.0160507\pi\)
−0.455714 + 0.890126i \(0.650616\pi\)
\(720\) 2.68406 0.100029
\(721\) 0 0
\(722\) 5.50000 9.52628i 0.204689 0.354531i
\(723\) −3.10208 + 5.37297i −0.115368 + 0.199823i
\(724\) −16.5375 −0.614610
\(725\) 9.69375 16.7901i 0.360017 0.623567i
\(726\) −31.9494 −1.18575
\(727\) 35.3259 1.31016 0.655082 0.755558i \(-0.272634\pi\)
0.655082 + 0.755558i \(0.272634\pi\)
\(728\) 0 0
\(729\) 29.0000 1.07407
\(730\) 15.5708 0.576302
\(731\) −4.94975 + 8.57321i −0.183073 + 0.317092i
\(732\) −2.20417 −0.0814684
\(733\) 0.346184 0.599609i 0.0127866 0.0221471i −0.859561 0.511033i \(-0.829263\pi\)
0.872348 + 0.488886i \(0.162596\pi\)
\(734\) 10.6066 18.3712i 0.391497 0.678092i
\(735\) 0 0
\(736\) 8.97916 0.330976
\(737\) −16.7958 29.0912i −0.618682 1.07159i
\(738\) −4.87756 + 8.44819i −0.179546 + 0.310982i
\(739\) −7.59166 + 13.1491i −0.279264 + 0.483699i −0.971202 0.238258i \(-0.923424\pi\)
0.691938 + 0.721957i \(0.256757\pi\)
\(740\) −9.12020 + 15.7967i −0.335265 + 0.580697i
\(741\) 11.0250 + 9.29785i 0.405012 + 0.341565i
\(742\) 0 0
\(743\) −4.59166 7.95299i −0.168452 0.291767i 0.769424 0.638738i \(-0.220543\pi\)
−0.937876 + 0.346971i \(0.887210\pi\)
\(744\) 6.00000 0.219971
\(745\) 12.3243 0.451527
\(746\) 6.29583 + 10.9047i 0.230507 + 0.399249i
\(747\) 4.94975 + 8.57321i 0.181102 + 0.313678i
\(748\) −15.9747 + 27.6690i −0.584094 + 1.01168i
\(749\) 0 0
\(750\) −5.30625 + 9.19070i −0.193757 + 0.335597i
\(751\) 1.79583 0.0655308 0.0327654 0.999463i \(-0.489569\pi\)
0.0327654 + 0.999463i \(0.489569\pi\)
\(752\) −1.41421 + 2.44949i −0.0515711 + 0.0893237i
\(753\) 2.20417 + 3.81773i 0.0803244 + 0.139126i
\(754\) 5.58467 31.2182i 0.203382 1.13690i
\(755\) −47.2170 −1.71840
\(756\) 0 0
\(757\) 12.5917 + 21.8094i 0.457652 + 0.792676i 0.998836 0.0482277i \(-0.0153573\pi\)
−0.541185 + 0.840904i \(0.682024\pi\)
\(758\) 1.69375 + 2.93366i 0.0615197 + 0.106555i
\(759\) 7.35981 + 12.7476i 0.267144 + 0.462707i
\(760\) −22.7750 −0.826136
\(761\) 4.66101 + 8.07311i 0.168961 + 0.292650i 0.938055 0.346486i \(-0.112625\pi\)
−0.769094 + 0.639136i \(0.779292\pi\)
\(762\) −10.7362 −0.388933
\(763\) 0 0
\(764\) −12.8979 22.3398i −0.466630 0.808227i
\(765\) 14.7958 0.534944
\(766\) −7.48944 12.9721i −0.270604 0.468700i
\(767\) 3.10208 + 2.61613i 0.112010 + 0.0944628i
\(768\) −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
\(771\) −10.8979 + 18.8757i −0.392479 + 0.679793i
\(772\) 1.70417 2.95171i 0.0613344 0.106234i
\(773\) −7.64854 −0.275099 −0.137549 0.990495i \(-0.543923\pi\)
−0.137549 + 0.990495i \(0.543923\pi\)
\(774\) 1.79583 0.0645498
\(775\) −1.55858 + 2.69954i −0.0559859 + 0.0969705i
\(776\) 6.36396 11.0227i 0.228453 0.395692i
\(777\) 0 0
\(778\) −14.1937 24.5843i −0.508870 0.881390i
\(779\) 13.7958 23.8951i 0.494287 0.856130i
\(780\) −2.41006 + 13.4722i −0.0862939 + 0.482382i
\(781\) −17.3875 30.1160i −0.622173 1.07764i
\(782\) −9.89949 −0.354005
\(783\) 24.8784 + 43.0906i 0.889080 + 1.53993i
\(784\) 0 0
\(785\) 18.5917 0.663565
\(786\) 5.79583 + 10.0387i 0.206730 + 0.358068i
\(787\) −25.4264 −0.906352 −0.453176 0.891421i \(-0.649709\pi\)
−0.453176 + 0.891421i \(0.649709\pi\)
\(788\) −4.00000 6.92820i −0.142494 0.246807i
\(789\) −17.9517 31.0932i −0.639096 1.10695i
\(790\) 15.8303 + 27.4190i 0.563219 + 0.975523i
\(791\) 0 0
\(792\) 17.3875 0.617838
\(793\) 0.989579 5.53173i 0.0351410 0.196438i
\(794\) 3.53553 + 6.12372i 0.125471 + 0.217323i
\(795\) 12.5104 21.6687i 0.443699 0.768509i
\(796\) −22.0499 −0.781539
\(797\) −13.1463 + 22.7700i −0.465666 + 0.806556i −0.999231 0.0392022i \(-0.987518\pi\)
0.533566 + 0.845759i \(0.320852\pi\)
\(798\) 0 0
\(799\) −7.79583 + 13.5028i −0.275797 + 0.477694i
\(800\) −5.51042 9.54433i −0.194823 0.337443i
\(801\) −6.07522 10.5226i −0.214657 0.371798i
\(802\) 24.3875 0.861152
\(803\) 33.6229 1.18653
\(804\) −4.09827 7.09841i −0.144535 0.250342i
\(805\) 0 0
\(806\) −0.897916 + 5.01934i −0.0316277 + 0.176799i
\(807\) 0.795832 1.37842i 0.0280146 0.0485227i
\(808\) 4.45919 7.72355i 0.156874 0.271714i
\(809\) −19.6833 + 34.0925i −0.692029 + 1.19863i 0.279143 + 0.960250i \(0.409950\pi\)
−0.971172 + 0.238380i \(0.923384\pi\)
\(810\) 6.71015 + 11.6223i 0.235770 + 0.408366i
\(811\) 38.4725 1.35095 0.675476 0.737382i \(-0.263938\pi\)
0.675476 + 0.737382i \(0.263938\pi\)
\(812\) 0 0
\(813\) 16.3875 28.3840i 0.574735 0.995469i
\(814\) 19.6937 34.1106i 0.690265 1.19557i
\(815\) −35.9328 −1.25867
\(816\) 3.89792 6.75139i 0.136454 0.236346i
\(817\) −5.07938 −0.177705
\(818\) 28.6879 1.00305
\(819\) 0 0
\(820\) 26.1833 0.914361
\(821\) −40.3667 −1.40881 −0.704403 0.709800i \(-0.748785\pi\)
−0.704403 + 0.709800i \(0.748785\pi\)
\(822\) −6.50833 + 11.2728i −0.227004 + 0.393183i
\(823\) 36.7750 1.28190 0.640948 0.767584i \(-0.278542\pi\)
0.640948 + 0.767584i \(0.278542\pi\)
\(824\) 12.2948 21.2952i 0.428310 0.741855i
\(825\) 9.03328 15.6461i 0.314498 0.544727i
\(826\) 0 0
\(827\) 26.9792 0.938157 0.469079 0.883156i \(-0.344586\pi\)
0.469079 + 0.883156i \(0.344586\pi\)
\(828\) −0.897916 1.55524i −0.0312047 0.0540482i
\(829\) 10.1013 17.4960i 0.350833 0.607661i −0.635563 0.772049i \(-0.719232\pi\)
0.986396 + 0.164389i \(0.0525651\pi\)
\(830\) −13.2854 + 23.0110i −0.461143 + 0.798724i
\(831\) −4.37227 + 7.57300i −0.151672 + 0.262704i
\(832\) −19.2937 16.2712i −0.668889 0.564104i
\(833\) 0 0
\(834\) 10.7958 + 18.6989i 0.373829 + 0.647491i
\(835\) −40.9792 −1.41814
\(836\) −16.3931 −0.566967
\(837\) −4.00000 6.92820i −0.138260 0.239474i
\(838\) 14.2718 + 24.7194i 0.493010 + 0.853918i
\(839\) 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
\(841\) −24.1833 + 41.8867i −0.833908 + 1.44437i
\(842\) −6.59166 −0.227164
\(843\) 10.7510 18.6212i 0.370283 0.641349i
\(844\) −0.897916 1.55524i −0.0309075 0.0535334i
\(845\) −32.7287 12.0969i −1.12590 0.416146i
\(846\) 2.82843 0.0972433
\(847\) 0 0
\(848\) 3.29583 + 5.70855i 0.113179 + 0.196032i
\(849\) 20.7958 + 36.0194i 0.713711 + 1.23618i
\(850\) 6.07522 + 10.5226i 0.208378 + 0.360922i
\(851\) −12.2042 −0.418354
\(852\) −4.24264 7.34847i −0.145350 0.251754i
\(853\) 13.1610 0.450625 0.225313 0.974287i \(-0.427660\pi\)
0.225313 + 0.974287i \(0.427660\pi\)
\(854\) 0 0
\(855\) 3.79583 + 6.57457i 0.129815 + 0.224846i
\(856\) 18.0000 0.615227
\(857\) −18.8753 32.6930i −0.644769 1.11677i −0.984355 0.176198i \(-0.943620\pi\)
0.339586 0.940575i \(-0.389713\pi\)
\(858\) 5.20417 29.0912i 0.177667 0.993158i
\(859\) 11.8764 20.5706i 0.405219 0.701860i −0.589128 0.808040i \(-0.700529\pi\)
0.994347 + 0.106180i \(0.0338619\pi\)
\(860\) −2.41006 4.17434i −0.0821823 0.142344i
\(861\) 0 0
\(862\) 2.59166 4.48889i 0.0882724 0.152892i
\(863\) −8.89792 + 15.4116i −0.302889 + 0.524618i −0.976789 0.214204i \(-0.931284\pi\)
0.673900 + 0.738822i \(0.264618\pi\)
\(864\) 28.2843 0.962250
\(865\) −25.0208 −0.850734
\(866\) 6.71015 11.6223i 0.228020 0.394942i
\(867\) 9.46639 16.3963i 0.321495 0.556846i
\(868\) 0 0
\(869\) 34.1833 + 59.2073i 1.15959 + 2.00847i
\(870\) −16.6937 + 28.9144i −0.565971 + 0.980291i
\(871\) 19.6546 7.09841i 0.665971 0.240521i
\(872\) −26.3875 45.7045i −0.893593 1.54775i
\(873\) −4.24264 −0.143592
\(874\) −2.53969 4.39887i −0.0859063 0.148794i
\(875\) 0 0
\(876\) 8.20417 0.277193
\(877\) 2.39792 + 4.15331i 0.0809719 + 0.140247i 0.903668 0.428235i \(-0.140864\pi\)
−0.822696 + 0.568482i \(0.807531\pi\)
\(878\) −34.2004 −1.15421
\(879\) 6.89792 + 11.9475i 0.232661 + 0.402981i
\(880\) 7.77817 + 13.4722i 0.262202 + 0.454148i
\(881\) −11.6599 20.1955i −0.392832 0.680405i 0.599990 0.800007i \(-0.295171\pi\)
−0.992822 + 0.119603i \(0.961838\pi\)
\(882\) 0 0
\(883\) −16.6125 −0.559055 −0.279528 0.960138i \(-0.590178\pi\)
−0.279528 + 0.960138i \(0.590178\pi\)
\(884\) −15.1937 12.8136i −0.511021 0.430967i
\(885\) −2.13606 3.69976i −0.0718028 0.124366i
\(886\) −5.00000 + 8.66025i −0.167978 + 0.290947i
\(887\) 28.5730 0.959388 0.479694 0.877436i \(-0.340748\pi\)
0.479694 + 0.877436i \(0.340748\pi\)
\(888\) 14.4161 24.9695i 0.483774 0.837921i
\(889\) 0 0
\(890\) 16.3063 28.2433i 0.546587 0.946716i
\(891\) 14.4896 + 25.0967i 0.485419 + 0.840771i
\(892\) 2.82843 + 4.89898i 0.0947027 + 0.164030i
\(893\) −8.00000 −0.267710
\(894\) −6.49359 −0.217178
\(895\) 0.548000 + 0.949164i 0.0183176 + 0.0317271i
\(896\) 0 0
\(897\) −8.61251 + 3.11047i −0.287563 + 0.103856i
\(898\) −2.20417 + 3.81773i −0.0735541 + 0.127399i
\(899\) 6.21959 10.7726i 0.207435 0.359288i
\(900\) −1.10208 + 1.90887i −0.0367361 + 0.0636289i
\(901\) 18.1682 + 31.4683i 0.605271 + 1.04836i
\(902\) −56.5391 −1.88255
\(903\) 0 0
\(904\) −24.8875 + 43.1064i −0.827746 + 1.43370i
\(905\) −22.1937 + 38.4407i −0.737745 + 1.27781i
\(906\) 24.8784 0.826528
\(907\) −24.6937 + 42.7708i −0.819942 + 1.42018i 0.0857816 + 0.996314i \(0.472661\pi\)
−0.905724 + 0.423868i \(0.860672\pi\)
\(908\) 20.9245 0.694403
\(909\) −2.97280 −0.0986014
\(910\) 0 0
\(911\) −43.1833 −1.43073 −0.715364 0.698752i \(-0.753739\pi\)
−0.715364 + 0.698752i \(0.753739\pi\)
\(912\) 4.00000 0.132453
\(913\) −28.6879 + 49.6889i −0.949431 + 1.64446i
\(914\) −14.5917 −0.482649
\(915\) −2.95806 + 5.12351i −0.0977904 + 0.169378i
\(916\) −6.36396 + 11.0227i −0.210271 + 0.364200i
\(917\) 0 0
\(918\) −31.1833 −1.02920
\(919\) −5.00000 8.66025i −0.164935 0.285675i 0.771697 0.635990i \(-0.219408\pi\)
−0.936632 + 0.350315i \(0.886075\pi\)
\(920\) 7.23017 12.5230i 0.238372 0.412872i
\(921\) −24.1833 + 41.8867i −0.796868 + 1.38022i
\(922\) 15.4842 26.8194i 0.509944 0.883249i
\(923\) 20.3470 7.34847i 0.669729 0.241878i
\(924\) 0 0
\(925\) 7.48958 + 12.9723i 0.246256 + 0.426528i
\(926\) 11.3875 0.374216
\(927\) −8.19654 −0.269210
\(928\) 21.9896 + 38.0871i 0.721843 + 1.25027i
\(929\) −14.0700 24.3699i −0.461620 0.799550i 0.537422 0.843314i \(-0.319398\pi\)
−0.999042 + 0.0437641i \(0.986065\pi\)
\(930\) 2.68406 4.64893i 0.0880137 0.152444i
\(931\) 0 0
\(932\) −10.5917 + 18.3453i −0.346941 + 0.600920i
\(933\) 16.7750 0.549188
\(934\) −2.41006 + 4.17434i −0.0788595 + 0.136589i
\(935\) 42.8771 + 74.2653i 1.40223 + 2.42873i
\(936\) −1.90477 + 10.6476i −0.0622593 + 0.348028i
\(937\) −6.63796 −0.216853 −0.108426 0.994104i \(-0.534581\pi\)
−0.108426 + 0.994104i \(0.534581\pi\)
\(938\) 0 0
\(939\) −1.20417 2.08568i −0.0392966 0.0680636i
\(940\) −3.79583 6.57457i −0.123806 0.214439i
\(941\) −11.7321 20.3206i −0.382455 0.662431i 0.608958 0.793203i \(-0.291588\pi\)
−0.991413 + 0.130772i \(0.958255\pi\)
\(942\) −9.79583 −0.319165
\(943\) 8.75928 + 15.1715i 0.285241 + 0.494053i
\(944\) 1.12548 0.0366311
\(945\) 0 0
\(946\) 5.20417 + 9.01388i 0.169202 + 0.293067i
\(947\) 28.2042 0.916512 0.458256 0.888820i \(-0.348474\pi\)
0.458256 + 0.888820i \(0.348474\pi\)
\(948\) 8.34091 + 14.4469i 0.270900 + 0.469213i
\(949\) −3.68333 + 20.5897i −0.119566 + 0.668371i
\(950\) −3.11716 + 5.39909i −0.101134 + 0.175170i
\(951\) −8.90365 15.4216i −0.288721 0.500079i
\(952\) 0 0
\(953\) 2.40834 4.17136i 0.0780137 0.135124i −0.824379 0.566038i \(-0.808476\pi\)
0.902393 + 0.430914i \(0.141809\pi\)
\(954\) 3.29583 5.70855i 0.106706 0.184821i
\(955\) −69.2375 −2.24047
\(956\) 19.7958 0.640243
\(957\) −36.0477 + 62.4365i −1.16526 + 2.01828i
\(958\) −3.67990 + 6.37378i −0.118892 + 0.205927i
\(959\) 0 0
\(960\) 13.2854 + 23.0110i 0.428785 + 0.742677i
\(961\) 14.5000 25.1147i 0.467742 0.810153i
\(962\) 18.7310 + 15.7967i 0.603910 + 0.509305i
\(963\) −3.00000 5.19615i −0.0966736 0.167444i
\(964\) 4.38701 0.141296
\(965\) −4.57409 7.92255i −0.147245 0.255036i
\(966\) 0 0
\(967\) 11.3875 0.366197 0.183099 0.983095i \(-0.441387\pi\)
0.183099 + 0.983095i \(0.441387\pi\)
\(968\) 33.8875 + 58.6949i 1.08919 + 1.88652i
\(969\) 22.0499 0.708346
\(970\) −5.69375 9.86186i −0.182815 0.316645i
\(971\) −11.3137 19.5959i −0.363074 0.628863i 0.625391 0.780312i \(-0.284940\pi\)
−0.988465 + 0.151449i \(0.951606\pi\)
\(972\) −4.94975 8.57321i −0.158763 0.274986i
\(973\) 0 0
\(974\) 19.5917 0.627757
\(975\) 8.59166 + 7.24573i 0.275153 + 0.232049i
\(976\) −0.779291 1.34977i −0.0249445 0.0432051i
\(977\) −0.193747 + 0.335580i −0.00619852 + 0.0107362i −0.869108 0.494622i \(-0.835306\pi\)
0.862910 + 0.505358i \(0.168640\pi\)
\(978\) 18.9328 0.605403
\(979\) 35.2110 60.9872i 1.12535 1.94916i
\(980\) 0 0
\(981\) −8.79583 + 15.2348i −0.280829 + 0.486411i
\(982\) 4.79583 + 8.30662i 0.153041 + 0.265075i
\(983\) 20.7801 + 35.9922i 0.662782 + 1.14797i 0.979882 + 0.199580i \(0.0639578\pi\)
−0.317099 + 0.948392i \(0.602709\pi\)
\(984\) −41.3875 −1.31939
\(985\) −21.4725 −0.684170
\(986\) −24.2434 41.9909i −0.772069 1.33726i
\(987\) 0 0
\(988\) 1.79583 10.0387i 0.0571330 0.319373i
\(989\) 1.61251 2.79294i 0.0512747 0.0888104i
\(990\) 7.77817 13.4722i 0.247207 0.428174i
\(991\) −9.10208 + 15.7653i −0.289137 + 0.500800i −0.973604 0.228244i \(-0.926702\pi\)
0.684467 + 0.729044i \(0.260035\pi\)
\(992\) −3.53553 6.12372i −0.112253 0.194428i
\(993\) −0.866213 −0.0274885
\(994\) 0 0
\(995\) −29.5917 + 51.2543i −0.938119 + 1.62487i
\(996\) −7.00000 + 12.1244i −0.221803 + 0.384175i
\(997\) 5.51249 0.174582 0.0872911 0.996183i \(-0.472179\pi\)
0.0872911 + 0.996183i \(0.472179\pi\)
\(998\) −8.10208 + 14.0332i −0.256467 + 0.444214i
\(999\) −38.4430 −1.21628
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.h.k.471.3 8
7.2 even 3 637.2.f.g.393.4 yes 8
7.3 odd 6 637.2.g.h.263.4 8
7.4 even 3 637.2.g.h.263.1 8
7.5 odd 6 637.2.f.g.393.1 yes 8
7.6 odd 2 inner 637.2.h.k.471.2 8
13.9 even 3 637.2.g.h.373.1 8
91.9 even 3 637.2.f.g.295.4 yes 8
91.16 even 3 8281.2.a.bv.1.2 4
91.23 even 6 8281.2.a.bn.1.1 4
91.48 odd 6 637.2.g.h.373.4 8
91.61 odd 6 637.2.f.g.295.1 8
91.68 odd 6 8281.2.a.bv.1.3 4
91.74 even 3 inner 637.2.h.k.165.3 8
91.75 odd 6 8281.2.a.bn.1.4 4
91.87 odd 6 inner 637.2.h.k.165.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.f.g.295.1 8 91.61 odd 6
637.2.f.g.295.4 yes 8 91.9 even 3
637.2.f.g.393.1 yes 8 7.5 odd 6
637.2.f.g.393.4 yes 8 7.2 even 3
637.2.g.h.263.1 8 7.4 even 3
637.2.g.h.263.4 8 7.3 odd 6
637.2.g.h.373.1 8 13.9 even 3
637.2.g.h.373.4 8 91.48 odd 6
637.2.h.k.165.2 8 91.87 odd 6 inner
637.2.h.k.165.3 8 91.74 even 3 inner
637.2.h.k.471.2 8 7.6 odd 2 inner
637.2.h.k.471.3 8 1.1 even 1 trivial
8281.2.a.bn.1.1 4 91.23 even 6
8281.2.a.bn.1.4 4 91.75 odd 6
8281.2.a.bv.1.2 4 91.16 even 3
8281.2.a.bv.1.3 4 91.68 odd 6