Properties

Label 882.2.t.b.815.3
Level $882$
Weight $2$
Character 882.815
Analytic conductor $7.043$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,2,Mod(803,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.803");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.t (of order \(6\), 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: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 815.3
Root \(-1.69547 + 0.354107i\) of defining polynomial
Character \(\chi\) \(=\) 882.815
Dual form 882.2.t.b.803.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(1.15440 - 1.29126i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.79035 q^{5} +(-1.64537 + 0.541068i) q^{6} -1.00000i q^{8} +(-0.334727 - 2.98127i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(1.15440 - 1.29126i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.79035 q^{5} +(-1.64537 + 0.541068i) q^{6} -1.00000i q^{8} +(-0.334727 - 2.98127i) q^{9} +(1.55049 + 0.895175i) q^{10} -2.40150i q^{11} +(1.69547 + 0.354107i) q^{12} +(4.23601 + 2.44566i) q^{13} +(-2.06678 + 2.31181i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.83233 - 3.17369i) q^{17} +(-1.20075 + 2.74922i) q^{18} +(2.61281 - 1.50851i) q^{19} +(-0.895175 - 1.55049i) q^{20} +(-1.20075 + 2.07976i) q^{22} -3.76638i q^{23} +(-1.29126 - 1.15440i) q^{24} -1.79465 q^{25} +(-2.44566 - 4.23601i) q^{26} +(-4.23601 - 3.00935i) q^{27} +(-5.68202 + 3.28052i) q^{29} +(2.94579 - 0.968701i) q^{30} +(-4.02408 + 2.32330i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-3.10098 - 2.77229i) q^{33} +(-3.17369 + 1.83233i) q^{34} +(2.41449 - 1.78052i) q^{36} +(-4.68202 - 8.10950i) q^{37} -3.01701 q^{38} +(8.04805 - 2.64654i) q^{39} +1.79035i q^{40} +(4.04094 - 6.99911i) q^{41} +(-3.48127 - 6.02973i) q^{43} +(2.07976 - 1.20075i) q^{44} +(0.599278 + 5.33751i) q^{45} +(-1.88319 + 3.26178i) q^{46} +(-2.56802 + 4.44794i) q^{47} +(0.541068 + 1.64537i) q^{48} +(1.55421 + 0.897324i) q^{50} +(-1.98283 - 6.02973i) q^{51} +4.89133i q^{52} +(2.16382 + 4.72418i) q^{54} +4.29953i q^{55} +(1.06834 - 5.11524i) q^{57} +6.56103 q^{58} +(-7.29501 - 12.6353i) q^{59} +(-3.03548 - 0.633975i) q^{60} +(9.81058 + 5.66414i) q^{61} +4.64661 q^{62} -1.00000 q^{64} +(-7.58394 - 4.37859i) q^{65} +(1.29938 + 3.95136i) q^{66} +(-0.285115 - 0.493834i) q^{67} +3.66466 q^{68} +(-4.86340 - 4.34791i) q^{69} -5.96254i q^{71} +(-2.98127 + 0.334727i) q^{72} +(10.7226 + 6.19070i) q^{73} +9.36404i q^{74} +(-2.07174 + 2.31737i) q^{75} +(2.61281 + 1.50851i) q^{76} +(-8.29308 - 1.73205i) q^{78} +(-1.51831 + 2.62979i) q^{79} +(0.895175 - 1.55049i) q^{80} +(-8.77592 + 1.99582i) q^{81} +(-6.99911 + 4.04094i) q^{82} +(7.00270 + 12.1290i) q^{83} +(-3.28052 + 5.68202i) q^{85} +6.96254i q^{86} +(-2.32330 + 11.1240i) q^{87} -2.40150 q^{88} +(-1.87432 - 3.24641i) q^{89} +(2.14977 - 4.92206i) q^{90} +(3.26178 - 1.88319i) q^{92} +(-1.64539 + 7.87817i) q^{93} +(4.44794 - 2.56802i) q^{94} +(-4.67784 + 2.70075i) q^{95} +(0.354107 - 1.69547i) q^{96} +(-4.77256 + 2.75544i) q^{97} +(-7.15953 + 0.803848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 36 q^{39} + 4 q^{43} + 12 q^{44} - 12 q^{46} + 60 q^{50} - 36 q^{51} + 48 q^{57} + 24 q^{58} - 24 q^{60} - 16 q^{64} - 84 q^{65} - 28 q^{67} + 12 q^{72} - 24 q^{78} - 4 q^{79} - 36 q^{81} - 12 q^{85} - 48 q^{92} + 12 q^{93} - 12 q^{95} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 1.15440 1.29126i 0.666492 0.745512i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −1.79035 −0.800669 −0.400334 0.916369i \(-0.631106\pi\)
−0.400334 + 0.916369i \(0.631106\pi\)
\(6\) −1.64537 + 0.541068i −0.671720 + 0.220890i
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −0.334727 2.98127i −0.111576 0.993756i
\(10\) 1.55049 + 0.895175i 0.490307 + 0.283079i
\(11\) 2.40150i 0.724081i −0.932162 0.362040i \(-0.882080\pi\)
0.932162 0.362040i \(-0.117920\pi\)
\(12\) 1.69547 + 0.354107i 0.489439 + 0.102222i
\(13\) 4.23601 + 2.44566i 1.17486 + 0.678305i 0.954820 0.297186i \(-0.0960482\pi\)
0.220039 + 0.975491i \(0.429382\pi\)
\(14\) 0 0
\(15\) −2.06678 + 2.31181i −0.533640 + 0.596908i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.83233 3.17369i 0.444406 0.769734i −0.553605 0.832780i \(-0.686748\pi\)
0.998011 + 0.0630460i \(0.0200815\pi\)
\(18\) −1.20075 + 2.74922i −0.283020 + 0.647997i
\(19\) 2.61281 1.50851i 0.599419 0.346075i −0.169394 0.985548i \(-0.554181\pi\)
0.768813 + 0.639474i \(0.220848\pi\)
\(20\) −0.895175 1.55049i −0.200167 0.346700i
\(21\) 0 0
\(22\) −1.20075 + 2.07976i −0.256001 + 0.443407i
\(23\) 3.76638i 0.785345i −0.919678 0.392673i \(-0.871551\pi\)
0.919678 0.392673i \(-0.128449\pi\)
\(24\) −1.29126 1.15440i −0.263578 0.235641i
\(25\) −1.79465 −0.358930
\(26\) −2.44566 4.23601i −0.479634 0.830750i
\(27\) −4.23601 3.00935i −0.815221 0.579150i
\(28\) 0 0
\(29\) −5.68202 + 3.28052i −1.05512 + 0.609176i −0.924080 0.382200i \(-0.875167\pi\)
−0.131045 + 0.991376i \(0.541833\pi\)
\(30\) 2.94579 0.968701i 0.537825 0.176860i
\(31\) −4.02408 + 2.32330i −0.722746 + 0.417278i −0.815763 0.578387i \(-0.803682\pi\)
0.0930163 + 0.995665i \(0.470349\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) −3.10098 2.77229i −0.539811 0.482594i
\(34\) −3.17369 + 1.83233i −0.544284 + 0.314242i
\(35\) 0 0
\(36\) 2.41449 1.78052i 0.402415 0.296753i
\(37\) −4.68202 8.10950i −0.769719 1.33319i −0.937715 0.347405i \(-0.887063\pi\)
0.167996 0.985788i \(-0.446271\pi\)
\(38\) −3.01701 −0.489424
\(39\) 8.04805 2.64654i 1.28872 0.423786i
\(40\) 1.79035i 0.283079i
\(41\) 4.04094 6.99911i 0.631088 1.09308i −0.356241 0.934394i \(-0.615942\pi\)
0.987330 0.158683i \(-0.0507248\pi\)
\(42\) 0 0
\(43\) −3.48127 6.02973i −0.530888 0.919526i −0.999350 0.0360419i \(-0.988525\pi\)
0.468462 0.883484i \(-0.344808\pi\)
\(44\) 2.07976 1.20075i 0.313536 0.181020i
\(45\) 0.599278 + 5.33751i 0.0893351 + 0.795669i
\(46\) −1.88319 + 3.26178i −0.277661 + 0.480924i
\(47\) −2.56802 + 4.44794i −0.374584 + 0.648799i −0.990265 0.139197i \(-0.955548\pi\)
0.615680 + 0.787996i \(0.288881\pi\)
\(48\) 0.541068 + 1.64537i 0.0780965 + 0.237489i
\(49\) 0 0
\(50\) 1.55421 + 0.897324i 0.219799 + 0.126901i
\(51\) −1.98283 6.02973i −0.277652 0.844331i
\(52\) 4.89133i 0.678305i
\(53\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 2.16382 + 4.72418i 0.294458 + 0.642880i
\(55\) 4.29953i 0.579749i
\(56\) 0 0
\(57\) 1.06834 5.11524i 0.141506 0.677530i
\(58\) 6.56103 0.861506
\(59\) −7.29501 12.6353i −0.949729 1.64498i −0.745994 0.665953i \(-0.768025\pi\)
−0.203735 0.979026i \(-0.565308\pi\)
\(60\) −3.03548 0.633975i −0.391879 0.0818458i
\(61\) 9.81058 + 5.66414i 1.25612 + 0.725219i 0.972317 0.233665i \(-0.0750718\pi\)
0.283799 + 0.958884i \(0.408405\pi\)
\(62\) 4.64661 0.590120
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −7.58394 4.37859i −0.940672 0.543097i
\(66\) 1.29938 + 3.95136i 0.159942 + 0.486379i
\(67\) −0.285115 0.493834i −0.0348324 0.0603315i 0.848084 0.529862i \(-0.177756\pi\)
−0.882916 + 0.469531i \(0.844423\pi\)
\(68\) 3.66466 0.444406
\(69\) −4.86340 4.34791i −0.585484 0.523427i
\(70\) 0 0
\(71\) 5.96254i 0.707623i −0.935317 0.353811i \(-0.884885\pi\)
0.935317 0.353811i \(-0.115115\pi\)
\(72\) −2.98127 + 0.334727i −0.351346 + 0.0394479i
\(73\) 10.7226 + 6.19070i 1.25499 + 0.724567i 0.972096 0.234585i \(-0.0753731\pi\)
0.282891 + 0.959152i \(0.408706\pi\)
\(74\) 9.36404i 1.08855i
\(75\) −2.07174 + 2.31737i −0.239224 + 0.267586i
\(76\) 2.61281 + 1.50851i 0.299710 + 0.173037i
\(77\) 0 0
\(78\) −8.29308 1.73205i −0.939007 0.196116i
\(79\) −1.51831 + 2.62979i −0.170824 + 0.295875i −0.938708 0.344713i \(-0.887976\pi\)
0.767884 + 0.640588i \(0.221309\pi\)
\(80\) 0.895175 1.55049i 0.100084 0.173350i
\(81\) −8.77592 + 1.99582i −0.975102 + 0.221758i
\(82\) −6.99911 + 4.04094i −0.772922 + 0.446247i
\(83\) 7.00270 + 12.1290i 0.768646 + 1.33133i 0.938297 + 0.345830i \(0.112403\pi\)
−0.169651 + 0.985504i \(0.554264\pi\)
\(84\) 0 0
\(85\) −3.28052 + 5.68202i −0.355822 + 0.616302i
\(86\) 6.96254i 0.750790i
\(87\) −2.32330 + 11.1240i −0.249084 + 1.19262i
\(88\) −2.40150 −0.256001
\(89\) −1.87432 3.24641i −0.198677 0.344119i 0.749423 0.662092i \(-0.230331\pi\)
−0.948100 + 0.317973i \(0.896998\pi\)
\(90\) 2.14977 4.92206i 0.226605 0.518831i
\(91\) 0 0
\(92\) 3.26178 1.88319i 0.340064 0.196336i
\(93\) −1.64539 + 7.87817i −0.170619 + 0.816928i
\(94\) 4.44794 2.56802i 0.458770 0.264871i
\(95\) −4.67784 + 2.70075i −0.479936 + 0.277091i
\(96\) 0.354107 1.69547i 0.0361409 0.173043i
\(97\) −4.77256 + 2.75544i −0.484580 + 0.279772i −0.722323 0.691556i \(-0.756926\pi\)
0.237743 + 0.971328i \(0.423592\pi\)
\(98\) 0 0
\(99\) −7.15953 + 0.803848i −0.719560 + 0.0807897i
\(100\) −0.897324 1.55421i −0.0897324 0.155421i
\(101\) −0.250324 −0.0249082 −0.0124541 0.999922i \(-0.503964\pi\)
−0.0124541 + 0.999922i \(0.503964\pi\)
\(102\) −1.29768 + 6.21332i −0.128490 + 0.615210i
\(103\) 0.167931i 0.0165468i 0.999966 + 0.00827339i \(0.00263353\pi\)
−0.999966 + 0.00827339i \(0.997366\pi\)
\(104\) 2.44566 4.23601i 0.239817 0.415375i
\(105\) 0 0
\(106\) 0 0
\(107\) 6.92024 3.99540i 0.669004 0.386250i −0.126695 0.991942i \(-0.540437\pi\)
0.795699 + 0.605692i \(0.207104\pi\)
\(108\) 0.488168 5.17317i 0.0469740 0.497789i
\(109\) 9.47667 16.4141i 0.907700 1.57218i 0.0904491 0.995901i \(-0.471170\pi\)
0.817251 0.576282i \(-0.195497\pi\)
\(110\) 2.14977 3.72350i 0.204972 0.355022i
\(111\) −15.8764 3.31587i −1.50692 0.314728i
\(112\) 0 0
\(113\) −1.00418 0.579764i −0.0944653 0.0545396i 0.452023 0.892006i \(-0.350702\pi\)
−0.546488 + 0.837467i \(0.684036\pi\)
\(114\) −3.48283 + 3.89576i −0.326197 + 0.364871i
\(115\) 6.74314i 0.628801i
\(116\) −5.68202 3.28052i −0.527562 0.304588i
\(117\) 5.87327 13.4473i 0.542984 1.24320i
\(118\) 14.5900i 1.34312i
\(119\) 0 0
\(120\) 2.31181 + 2.06678i 0.211039 + 0.188670i
\(121\) 5.23278 0.475707
\(122\) −5.66414 9.81058i −0.512807 0.888208i
\(123\) −4.37285 13.2977i −0.394286 1.19901i
\(124\) −4.02408 2.32330i −0.361373 0.208639i
\(125\) 12.1648 1.08805
\(126\) 0 0
\(127\) 1.40150 0.124363 0.0621817 0.998065i \(-0.480194\pi\)
0.0621817 + 0.998065i \(0.480194\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −11.8047 2.46548i −1.03935 0.217073i
\(130\) 4.37859 + 7.58394i 0.384028 + 0.665156i
\(131\) −10.4918 −0.916671 −0.458335 0.888779i \(-0.651554\pi\)
−0.458335 + 0.888779i \(0.651554\pi\)
\(132\) 0.850388 4.07167i 0.0740168 0.354393i
\(133\) 0 0
\(134\) 0.570231i 0.0492604i
\(135\) 7.58394 + 5.38779i 0.652722 + 0.463707i
\(136\) −3.17369 1.83233i −0.272142 0.157121i
\(137\) 4.72056i 0.403305i −0.979457 0.201652i \(-0.935369\pi\)
0.979457 0.201652i \(-0.0646311\pi\)
\(138\) 2.03787 + 6.19710i 0.173475 + 0.527532i
\(139\) 2.04707 + 1.18187i 0.173630 + 0.100245i 0.584296 0.811540i \(-0.301371\pi\)
−0.410666 + 0.911786i \(0.634704\pi\)
\(140\) 0 0
\(141\) 2.77895 + 8.45070i 0.234030 + 0.711677i
\(142\) −2.98127 + 5.16371i −0.250182 + 0.433329i
\(143\) 5.87327 10.1728i 0.491148 0.850692i
\(144\) 2.74922 + 1.20075i 0.229101 + 0.100063i
\(145\) 10.1728 5.87327i 0.844805 0.487749i
\(146\) −6.19070 10.7226i −0.512346 0.887410i
\(147\) 0 0
\(148\) 4.68202 8.10950i 0.384860 0.666597i
\(149\) 17.3640i 1.42252i 0.702930 + 0.711259i \(0.251875\pi\)
−0.702930 + 0.711259i \(0.748125\pi\)
\(150\) 2.95286 0.971027i 0.241100 0.0792840i
\(151\) −11.2328 −0.914110 −0.457055 0.889438i \(-0.651096\pi\)
−0.457055 + 0.889438i \(0.651096\pi\)
\(152\) −1.50851 2.61281i −0.122356 0.211927i
\(153\) −10.0750 4.40035i −0.814512 0.355748i
\(154\) 0 0
\(155\) 7.20451 4.15953i 0.578680 0.334101i
\(156\) 6.31599 + 5.64654i 0.505684 + 0.452085i
\(157\) 11.9885 6.92154i 0.956783 0.552399i 0.0616014 0.998101i \(-0.480379\pi\)
0.895181 + 0.445702i \(0.147046\pi\)
\(158\) 2.62979 1.51831i 0.209215 0.120790i
\(159\) 0 0
\(160\) −1.55049 + 0.895175i −0.122577 + 0.0707698i
\(161\) 0 0
\(162\) 8.59808 + 2.65953i 0.675529 + 0.208952i
\(163\) 2.16789 + 3.75489i 0.169802 + 0.294106i 0.938350 0.345686i \(-0.112354\pi\)
−0.768548 + 0.639792i \(0.779020\pi\)
\(164\) 8.08188 0.631088
\(165\) 5.55183 + 4.96337i 0.432210 + 0.386398i
\(166\) 14.0054i 1.08703i
\(167\) 6.20756 10.7518i 0.480355 0.832000i −0.519391 0.854537i \(-0.673841\pi\)
0.999746 + 0.0225370i \(0.00717435\pi\)
\(168\) 0 0
\(169\) 5.46254 + 9.46139i 0.420195 + 0.727799i
\(170\) 5.68202 3.28052i 0.435791 0.251604i
\(171\) −5.37184 7.28454i −0.410795 0.557063i
\(172\) 3.48127 6.02973i 0.265444 0.459763i
\(173\) −8.70908 + 15.0846i −0.662139 + 1.14686i 0.317913 + 0.948120i \(0.397018\pi\)
−0.980052 + 0.198739i \(0.936315\pi\)
\(174\) 7.57405 8.47203i 0.574187 0.642263i
\(175\) 0 0
\(176\) 2.07976 + 1.20075i 0.156768 + 0.0905101i
\(177\) −24.7369 5.16642i −1.85934 0.388332i
\(178\) 3.74863i 0.280972i
\(179\) 11.3640 + 6.56103i 0.849388 + 0.490395i 0.860444 0.509544i \(-0.170186\pi\)
−0.0110562 + 0.999939i \(0.503519\pi\)
\(180\) −4.32278 + 3.18775i −0.322201 + 0.237601i
\(181\) 13.3577i 0.992873i 0.868073 + 0.496437i \(0.165359\pi\)
−0.868073 + 0.496437i \(0.834641\pi\)
\(182\) 0 0
\(183\) 18.6392 6.12937i 1.37785 0.453096i
\(184\) −3.76638 −0.277661
\(185\) 8.38245 + 14.5188i 0.616290 + 1.06745i
\(186\) 5.36404 6.00000i 0.393310 0.439941i
\(187\) −7.62164 4.40035i −0.557349 0.321786i
\(188\) −5.13604 −0.374584
\(189\) 0 0
\(190\) 5.40150 0.391866
\(191\) 8.01361 + 4.62666i 0.579845 + 0.334774i 0.761072 0.648668i \(-0.224674\pi\)
−0.181227 + 0.983441i \(0.558007\pi\)
\(192\) −1.15440 + 1.29126i −0.0833116 + 0.0931890i
\(193\) 12.2801 + 21.2698i 0.883941 + 1.53103i 0.846923 + 0.531716i \(0.178452\pi\)
0.0370176 + 0.999315i \(0.488214\pi\)
\(194\) 5.51087 0.395658
\(195\) −14.4088 + 4.73823i −1.03184 + 0.339312i
\(196\) 0 0
\(197\) 12.4861i 0.889598i 0.895630 + 0.444799i \(0.146725\pi\)
−0.895630 + 0.444799i \(0.853275\pi\)
\(198\) 6.60226 + 2.88361i 0.469202 + 0.204929i
\(199\) −0.155144 0.0895727i −0.0109979 0.00634964i 0.494491 0.869183i \(-0.335355\pi\)
−0.505489 + 0.862833i \(0.668688\pi\)
\(200\) 1.79465i 0.126901i
\(201\) −0.966808 0.201923i −0.0681934 0.0142425i
\(202\) 0.216787 + 0.125162i 0.0152531 + 0.00880637i
\(203\) 0 0
\(204\) 4.23048 4.73205i 0.296193 0.331310i
\(205\) −7.23469 + 12.5309i −0.505293 + 0.875193i
\(206\) 0.0839657 0.145433i 0.00585017 0.0101328i
\(207\) −11.2286 + 1.26071i −0.780441 + 0.0876253i
\(208\) −4.23601 + 2.44566i −0.293715 + 0.169576i
\(209\) −3.62268 6.27467i −0.250586 0.434028i
\(210\) 0 0
\(211\) 7.56103 13.0961i 0.520523 0.901572i −0.479192 0.877710i \(-0.659070\pi\)
0.999715 0.0238622i \(-0.00759629\pi\)
\(212\) 0 0
\(213\) −7.69921 6.88314i −0.527541 0.471625i
\(214\) −7.99080 −0.546240
\(215\) 6.23269 + 10.7953i 0.425066 + 0.736235i
\(216\) −3.00935 + 4.23601i −0.204760 + 0.288224i
\(217\) 0 0
\(218\) −16.4141 + 9.47667i −1.11170 + 0.641841i
\(219\) 20.3720 6.69919i 1.37661 0.452689i
\(220\) −3.72350 + 2.14977i −0.251039 + 0.144937i
\(221\) 15.5236 8.96254i 1.04423 0.602885i
\(222\) 12.0914 + 10.8098i 0.811525 + 0.725509i
\(223\) 7.27049 4.19762i 0.486868 0.281093i −0.236406 0.971654i \(-0.575970\pi\)
0.723274 + 0.690561i \(0.242636\pi\)
\(224\) 0 0
\(225\) 0.600717 + 5.35033i 0.0400478 + 0.356688i
\(226\) 0.579764 + 1.00418i 0.0385653 + 0.0667971i
\(227\) 2.42522 0.160967 0.0804836 0.996756i \(-0.474354\pi\)
0.0804836 + 0.996756i \(0.474354\pi\)
\(228\) 4.96410 1.63241i 0.328756 0.108109i
\(229\) 2.01975i 0.133469i 0.997771 + 0.0667344i \(0.0212580\pi\)
−0.997771 + 0.0667344i \(0.978742\pi\)
\(230\) 3.37157 5.83973i 0.222315 0.385061i
\(231\) 0 0
\(232\) 3.28052 + 5.68202i 0.215376 + 0.373043i
\(233\) −11.0236 + 6.36446i −0.722178 + 0.416950i −0.815554 0.578681i \(-0.803568\pi\)
0.0933759 + 0.995631i \(0.470234\pi\)
\(234\) −11.8101 + 8.70908i −0.772048 + 0.569331i
\(235\) 4.59766 7.96337i 0.299918 0.519473i
\(236\) 7.29501 12.6353i 0.474864 0.822489i
\(237\) 1.64302 + 4.99637i 0.106726 + 0.324549i
\(238\) 0 0
\(239\) 15.1117 + 8.72474i 0.977494 + 0.564356i 0.901513 0.432753i \(-0.142458\pi\)
0.0759814 + 0.997109i \(0.475791\pi\)
\(240\) −0.968701 2.94579i −0.0625294 0.190150i
\(241\) 11.4332i 0.736476i −0.929732 0.368238i \(-0.879961\pi\)
0.929732 0.368238i \(-0.120039\pi\)
\(242\) −4.53172 2.61639i −0.291310 0.168188i
\(243\) −7.55378 + 13.6360i −0.484575 + 0.874750i
\(244\) 11.3283i 0.725219i
\(245\) 0 0
\(246\) −2.86185 + 13.7026i −0.182465 + 0.873643i
\(247\) 14.7572 0.938977
\(248\) 2.32330 + 4.02408i 0.147530 + 0.255529i
\(249\) 23.7457 + 4.95940i 1.50482 + 0.314289i
\(250\) −10.5350 6.08240i −0.666293 0.384685i
\(251\) 27.3560 1.72669 0.863347 0.504611i \(-0.168364\pi\)
0.863347 + 0.504611i \(0.168364\pi\)
\(252\) 0 0
\(253\) −9.04499 −0.568653
\(254\) −1.21374 0.700752i −0.0761567 0.0439691i
\(255\) 3.54997 + 10.7953i 0.222307 + 0.676030i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 3.49673 0.218120 0.109060 0.994035i \(-0.465216\pi\)
0.109060 + 0.994035i \(0.465216\pi\)
\(258\) 8.99047 + 8.03754i 0.559722 + 0.500396i
\(259\) 0 0
\(260\) 8.75718i 0.543097i
\(261\) 11.6820 + 15.8415i 0.723099 + 0.980567i
\(262\) 9.08614 + 5.24589i 0.561344 + 0.324092i
\(263\) 9.64348i 0.594643i −0.954777 0.297321i \(-0.903907\pi\)
0.954777 0.297321i \(-0.0960932\pi\)
\(264\) −2.77229 + 3.10098i −0.170623 + 0.190852i
\(265\) 0 0
\(266\) 0 0
\(267\) −6.35568 1.32741i −0.388961 0.0812365i
\(268\) 0.285115 0.493834i 0.0174162 0.0301657i
\(269\) −3.45554 + 5.98517i −0.210688 + 0.364922i −0.951930 0.306316i \(-0.900904\pi\)
0.741242 + 0.671238i \(0.234237\pi\)
\(270\) −3.87399 8.45794i −0.235764 0.514734i
\(271\) 17.8672 10.3156i 1.08535 0.626629i 0.153017 0.988224i \(-0.451101\pi\)
0.932335 + 0.361595i \(0.117768\pi\)
\(272\) 1.83233 + 3.17369i 0.111101 + 0.192433i
\(273\) 0 0
\(274\) −2.36028 + 4.08812i −0.142590 + 0.246973i
\(275\) 4.30986i 0.259894i
\(276\) 1.33370 6.38578i 0.0802794 0.384379i
\(277\) −15.5144 −0.932168 −0.466084 0.884740i \(-0.654336\pi\)
−0.466084 + 0.884740i \(0.654336\pi\)
\(278\) −1.18187 2.04707i −0.0708841 0.122775i
\(279\) 8.27336 + 11.2192i 0.495313 + 0.671675i
\(280\) 0 0
\(281\) 11.7759 6.79883i 0.702492 0.405584i −0.105783 0.994389i \(-0.533735\pi\)
0.808275 + 0.588805i \(0.200401\pi\)
\(282\) 1.81871 8.70799i 0.108302 0.518553i
\(283\) −4.71796 + 2.72392i −0.280454 + 0.161920i −0.633629 0.773637i \(-0.718435\pi\)
0.353175 + 0.935557i \(0.385102\pi\)
\(284\) 5.16371 2.98127i 0.306410 0.176906i
\(285\) −1.91271 + 9.15807i −0.113299 + 0.542477i
\(286\) −10.1728 + 5.87327i −0.601530 + 0.347294i
\(287\) 0 0
\(288\) −1.78052 2.41449i −0.104918 0.142275i
\(289\) 1.78512 + 3.09191i 0.105007 + 0.181877i
\(290\) −11.7465 −0.689781
\(291\) −1.95144 + 9.34351i −0.114395 + 0.547726i
\(292\) 12.3814i 0.724567i
\(293\) −12.2311 + 21.1849i −0.714550 + 1.23764i 0.248583 + 0.968610i \(0.420035\pi\)
−0.963133 + 0.269026i \(0.913298\pi\)
\(294\) 0 0
\(295\) 13.0606 + 22.6216i 0.760418 + 1.31708i
\(296\) −8.10950 + 4.68202i −0.471355 + 0.272137i
\(297\) −7.22697 + 10.1728i −0.419351 + 0.590286i
\(298\) 8.68202 15.0377i 0.502936 0.871111i
\(299\) 9.21130 15.9544i 0.532703 0.922670i
\(300\) −3.04277 0.635497i −0.175674 0.0366904i
\(301\) 0 0
\(302\) 9.72787 + 5.61639i 0.559776 + 0.323187i
\(303\) −0.288974 + 0.323235i −0.0166011 + 0.0185693i
\(304\) 3.01701i 0.173037i
\(305\) −17.5644 10.1408i −1.00573 0.580660i
\(306\) 6.52499 + 8.84830i 0.373009 + 0.505824i
\(307\) 31.2223i 1.78195i −0.454053 0.890975i \(-0.650022\pi\)
0.454053 0.890975i \(-0.349978\pi\)
\(308\) 0 0
\(309\) 0.216844 + 0.193860i 0.0123358 + 0.0110283i
\(310\) −8.31905 −0.472491
\(311\) 5.45501 + 9.44836i 0.309325 + 0.535767i 0.978215 0.207594i \(-0.0665634\pi\)
−0.668889 + 0.743362i \(0.733230\pi\)
\(312\) −2.64654 8.04805i −0.149831 0.455631i
\(313\) 2.96532 + 1.71203i 0.167610 + 0.0967694i 0.581458 0.813576i \(-0.302482\pi\)
−0.413849 + 0.910346i \(0.635816\pi\)
\(314\) −13.8431 −0.781210
\(315\) 0 0
\(316\) −3.03663 −0.170824
\(317\) −16.4953 9.52357i −0.926468 0.534897i −0.0407755 0.999168i \(-0.512983\pi\)
−0.885693 + 0.464272i \(0.846316\pi\)
\(318\) 0 0
\(319\) 7.87817 + 13.6454i 0.441093 + 0.763995i
\(320\) 1.79035 0.100084
\(321\) 2.82960 13.5481i 0.157933 0.756183i
\(322\) 0 0
\(323\) 11.0563i 0.615191i
\(324\) −6.11639 6.60226i −0.339799 0.366792i
\(325\) −7.60215 4.38910i −0.421692 0.243464i
\(326\) 4.33577i 0.240136i
\(327\) −10.2550 31.1853i −0.567105 1.72455i
\(328\) −6.99911 4.04094i −0.386461 0.223123i
\(329\) 0 0
\(330\) −2.32634 7.07432i −0.128061 0.389429i
\(331\) −0.0366251 + 0.0634366i −0.00201310 + 0.00348679i −0.867030 0.498256i \(-0.833974\pi\)
0.865017 + 0.501742i \(0.167307\pi\)
\(332\) −7.00270 + 12.1290i −0.384323 + 0.665667i
\(333\) −22.6094 + 16.6728i −1.23899 + 0.913665i
\(334\) −10.7518 + 6.20756i −0.588313 + 0.339663i
\(335\) 0.510456 + 0.884136i 0.0278892 + 0.0483055i
\(336\) 0 0
\(337\) 1.11639 1.93364i 0.0608136 0.105332i −0.834016 0.551741i \(-0.813964\pi\)
0.894829 + 0.446408i \(0.147297\pi\)
\(338\) 10.9251i 0.594246i
\(339\) −1.90785 + 0.627383i −0.103620 + 0.0340748i
\(340\) −6.56103 −0.355822
\(341\) 5.57943 + 9.66385i 0.302143 + 0.523327i
\(342\) 1.00987 + 8.99452i 0.0546077 + 0.486368i
\(343\) 0 0
\(344\) −6.02973 + 3.48127i −0.325101 + 0.187697i
\(345\) 8.70718 + 7.78428i 0.468779 + 0.419091i
\(346\) 15.0846 8.70908i 0.810952 0.468203i
\(347\) −27.5751 + 15.9205i −1.48031 + 0.854656i −0.999751 0.0223084i \(-0.992898\pi\)
−0.480556 + 0.876964i \(0.659565\pi\)
\(348\) −10.7953 + 3.54997i −0.578690 + 0.190298i
\(349\) 12.7613 7.36772i 0.683095 0.394385i −0.117925 0.993022i \(-0.537624\pi\)
0.801020 + 0.598637i \(0.204291\pi\)
\(350\) 0 0
\(351\) −10.5839 23.1075i −0.564929 1.23339i
\(352\) −1.20075 2.07976i −0.0640003 0.110852i
\(353\) −2.15957 −0.114943 −0.0574713 0.998347i \(-0.518304\pi\)
−0.0574713 + 0.998347i \(0.518304\pi\)
\(354\) 18.8396 + 16.8427i 1.00131 + 0.895179i
\(355\) 10.6750i 0.566571i
\(356\) 1.87432 3.24641i 0.0993385 0.172059i
\(357\) 0 0
\(358\) −6.56103 11.3640i −0.346761 0.600608i
\(359\) 28.2712 16.3224i 1.49210 0.861463i 0.492139 0.870517i \(-0.336215\pi\)
0.999959 + 0.00905364i \(0.00288190\pi\)
\(360\) 5.33751 0.599278i 0.281312 0.0315847i
\(361\) −4.94882 + 8.57161i −0.260464 + 0.451138i
\(362\) 6.67887 11.5681i 0.351034 0.608008i
\(363\) 6.04071 6.75690i 0.317055 0.354645i
\(364\) 0 0
\(365\) −19.1972 11.0835i −1.00483 0.580138i
\(366\) −19.2067 4.01142i −1.00395 0.209680i
\(367\) 29.7003i 1.55034i −0.631751 0.775171i \(-0.717664\pi\)
0.631751 0.775171i \(-0.282336\pi\)
\(368\) 3.26178 + 1.88319i 0.170032 + 0.0981682i
\(369\) −22.2188 9.70433i −1.15667 0.505187i
\(370\) 16.7649i 0.871566i
\(371\) 0 0
\(372\) −7.64539 + 2.51413i −0.396395 + 0.130352i
\(373\) −2.01672 −0.104422 −0.0522109 0.998636i \(-0.516627\pi\)
−0.0522109 + 0.998636i \(0.516627\pi\)
\(374\) 4.40035 + 7.62164i 0.227537 + 0.394105i
\(375\) 14.0430 15.7080i 0.725179 0.811156i
\(376\) 4.44794 + 2.56802i 0.229385 + 0.132436i
\(377\) −32.0921 −1.65283
\(378\) 0 0
\(379\) −18.8709 −0.969332 −0.484666 0.874699i \(-0.661059\pi\)
−0.484666 + 0.874699i \(0.661059\pi\)
\(380\) −4.67784 2.70075i −0.239968 0.138546i
\(381\) 1.61789 1.80971i 0.0828873 0.0927144i
\(382\) −4.62666 8.01361i −0.236721 0.410012i
\(383\) −0.836511 −0.0427437 −0.0213719 0.999772i \(-0.506803\pi\)
−0.0213719 + 0.999772i \(0.506803\pi\)
\(384\) 1.64537 0.541068i 0.0839650 0.0276113i
\(385\) 0 0
\(386\) 24.5602i 1.25008i
\(387\) −16.8110 + 12.3969i −0.854550 + 0.630170i
\(388\) −4.77256 2.75544i −0.242290 0.139886i
\(389\) 24.8219i 1.25852i 0.777195 + 0.629260i \(0.216642\pi\)
−0.777195 + 0.629260i \(0.783358\pi\)
\(390\) 14.8475 + 3.10098i 0.751833 + 0.157024i
\(391\) −11.9533 6.90127i −0.604507 0.349012i
\(392\) 0 0
\(393\) −12.1117 + 13.5477i −0.610954 + 0.683389i
\(394\) 6.24305 10.8133i 0.314520 0.544765i
\(395\) 2.71831 4.70825i 0.136773 0.236898i
\(396\) −4.27592 5.79841i −0.214873 0.291381i
\(397\) −2.62744 + 1.51695i −0.131867 + 0.0761336i −0.564482 0.825445i \(-0.690924\pi\)
0.432615 + 0.901579i \(0.357591\pi\)
\(398\) 0.0895727 + 0.155144i 0.00448987 + 0.00777669i
\(399\) 0 0
\(400\) 0.897324 1.55421i 0.0448662 0.0777105i
\(401\) 13.0771i 0.653038i −0.945191 0.326519i \(-0.894124\pi\)
0.945191 0.326519i \(-0.105876\pi\)
\(402\) 0.736319 + 0.658274i 0.0367242 + 0.0328317i
\(403\) −22.7281 −1.13217
\(404\) −0.125162 0.216787i −0.00622705 0.0107856i
\(405\) 15.7120 3.57322i 0.780733 0.177555i
\(406\) 0 0
\(407\) −19.4750 + 11.2439i −0.965339 + 0.557339i
\(408\) −6.02973 + 1.98283i −0.298516 + 0.0981649i
\(409\) 4.82124 2.78354i 0.238395 0.137637i −0.376044 0.926602i \(-0.622716\pi\)
0.614439 + 0.788965i \(0.289382\pi\)
\(410\) 12.5309 7.23469i 0.618855 0.357296i
\(411\) −6.09549 5.44941i −0.300668 0.268799i
\(412\) −0.145433 + 0.0839657i −0.00716496 + 0.00413669i
\(413\) 0 0
\(414\) 10.3546 + 4.52249i 0.508901 + 0.222268i
\(415\) −12.5373 21.7152i −0.615431 1.06596i
\(416\) 4.89133 0.239817
\(417\) 3.88924 1.27895i 0.190457 0.0626304i
\(418\) 7.24536i 0.354382i
\(419\) −8.19938 + 14.2017i −0.400566 + 0.693800i −0.993794 0.111234i \(-0.964520\pi\)
0.593228 + 0.805034i \(0.297853\pi\)
\(420\) 0 0
\(421\) −7.72892 13.3869i −0.376684 0.652437i 0.613893 0.789389i \(-0.289603\pi\)
−0.990578 + 0.136952i \(0.956269\pi\)
\(422\) −13.0961 + 7.56103i −0.637508 + 0.368065i
\(423\) 14.1201 + 6.16711i 0.686543 + 0.299855i
\(424\) 0 0
\(425\) −3.28839 + 5.69566i −0.159510 + 0.276280i
\(426\) 3.22614 + 9.81058i 0.156307 + 0.475324i
\(427\) 0 0
\(428\) 6.92024 + 3.99540i 0.334502 + 0.193125i
\(429\) −6.35568 19.3274i −0.306855 0.933136i
\(430\) 12.4654i 0.601134i
\(431\) 21.6737 + 12.5133i 1.04398 + 0.602744i 0.920959 0.389660i \(-0.127407\pi\)
0.123024 + 0.992404i \(0.460741\pi\)
\(432\) 4.72418 2.16382i 0.227292 0.104107i
\(433\) 2.25168i 0.108209i −0.998535 0.0541044i \(-0.982770\pi\)
0.998535 0.0541044i \(-0.0172304\pi\)
\(434\) 0 0
\(435\) 4.15953 19.9159i 0.199434 0.954893i
\(436\) 18.9533 0.907700
\(437\) −5.68161 9.84084i −0.271788 0.470751i
\(438\) −20.9923 4.38434i −1.00305 0.209492i
\(439\) 16.2293 + 9.37000i 0.774583 + 0.447206i 0.834507 0.550997i \(-0.185752\pi\)
−0.0599239 + 0.998203i \(0.519086\pi\)
\(440\) 4.29953 0.204972
\(441\) 0 0
\(442\) −17.9251 −0.852609
\(443\) 1.04314 + 0.602256i 0.0495610 + 0.0286141i 0.524576 0.851364i \(-0.324224\pi\)
−0.475015 + 0.879978i \(0.657557\pi\)
\(444\) −5.06658 15.4073i −0.240449 0.731199i
\(445\) 3.35568 + 5.81221i 0.159074 + 0.275525i
\(446\) −8.39524 −0.397526
\(447\) 22.4216 + 20.0450i 1.06050 + 0.948097i
\(448\) 0 0
\(449\) 26.8022i 1.26487i 0.774612 + 0.632436i \(0.217945\pi\)
−0.774612 + 0.632436i \(0.782055\pi\)
\(450\) 2.15493 4.93388i 0.101584 0.232585i
\(451\) −16.8084 9.70433i −0.791476 0.456959i
\(452\) 1.15953i 0.0545396i
\(453\) −12.9671 + 14.5045i −0.609248 + 0.681480i
\(454\) −2.10030 1.21261i −0.0985719 0.0569105i
\(455\) 0 0
\(456\) −5.11524 1.06834i −0.239543 0.0500298i
\(457\) −6.92442 + 11.9934i −0.323911 + 0.561030i −0.981291 0.192529i \(-0.938331\pi\)
0.657381 + 0.753559i \(0.271664\pi\)
\(458\) 1.00987 1.74915i 0.0471883 0.0817326i
\(459\) −17.3125 + 7.92967i −0.808080 + 0.370125i
\(460\) −5.83973 + 3.37157i −0.272279 + 0.157200i
\(461\) −2.40241 4.16110i −0.111892 0.193802i 0.804641 0.593761i \(-0.202358\pi\)
−0.916533 + 0.399959i \(0.869024\pi\)
\(462\) 0 0
\(463\) 10.5194 18.2201i 0.488877 0.846760i −0.511041 0.859556i \(-0.670740\pi\)
0.999918 + 0.0127960i \(0.00407321\pi\)
\(464\) 6.56103i 0.304588i
\(465\) 2.94583 14.1047i 0.136610 0.654089i
\(466\) 12.7289 0.589656
\(467\) 2.91151 + 5.04288i 0.134729 + 0.233357i 0.925494 0.378763i \(-0.123650\pi\)
−0.790765 + 0.612120i \(0.790317\pi\)
\(468\) 14.5824 1.63726i 0.674070 0.0756823i
\(469\) 0 0
\(470\) −7.96337 + 4.59766i −0.367323 + 0.212074i
\(471\) 4.90192 23.4705i 0.225869 1.08146i
\(472\) −12.6353 + 7.29501i −0.581588 + 0.335780i
\(473\) −14.4804 + 8.36028i −0.665811 + 0.384406i
\(474\) 1.07529 5.14850i 0.0493897 0.236478i
\(475\) −4.68907 + 2.70724i −0.215149 + 0.124217i
\(476\) 0 0
\(477\) 0 0
\(478\) −8.72474 15.1117i −0.399060 0.691193i
\(479\) 26.9561 1.23166 0.615828 0.787881i \(-0.288822\pi\)
0.615828 + 0.787881i \(0.288822\pi\)
\(480\) −0.633975 + 3.03548i −0.0289368 + 0.138550i
\(481\) 45.8026i 2.08842i
\(482\) −5.71659 + 9.90142i −0.260383 + 0.450997i
\(483\) 0 0
\(484\) 2.61639 + 4.53172i 0.118927 + 0.205987i
\(485\) 8.54455 4.93320i 0.387988 0.224005i
\(486\) 13.3598 8.03223i 0.606011 0.364349i
\(487\) 6.81338 11.8011i 0.308744 0.534760i −0.669344 0.742953i \(-0.733425\pi\)
0.978088 + 0.208193i \(0.0667581\pi\)
\(488\) 5.66414 9.81058i 0.256404 0.444104i
\(489\) 7.35116 + 1.53533i 0.332431 + 0.0694299i
\(490\) 0 0
\(491\) −33.7430 19.4815i −1.52280 0.879188i −0.999637 0.0269544i \(-0.991419\pi\)
−0.523162 0.852234i \(-0.675248\pi\)
\(492\) 9.32971 10.4358i 0.420616 0.470484i
\(493\) 24.0440i 1.08289i
\(494\) −12.7801 7.37859i −0.575004 0.331979i
\(495\) 12.8181 1.43917i 0.576129 0.0646858i
\(496\) 4.64661i 0.208639i
\(497\) 0 0
\(498\) −18.0847 16.1678i −0.810393 0.724497i
\(499\) 26.0097 1.16435 0.582176 0.813063i \(-0.302201\pi\)
0.582176 + 0.813063i \(0.302201\pi\)
\(500\) 6.08240 + 10.5350i 0.272013 + 0.471141i
\(501\) −6.71743 20.4275i −0.300113 0.912632i
\(502\) −23.6910 13.6780i −1.05738 0.610478i
\(503\) −10.5271 −0.469378 −0.234689 0.972070i \(-0.575407\pi\)
−0.234689 + 0.972070i \(0.575407\pi\)
\(504\) 0 0
\(505\) 0.448168 0.0199432
\(506\) 7.83319 + 4.52249i 0.348228 + 0.201049i
\(507\) 18.5231 + 3.86864i 0.822640 + 0.171812i
\(508\) 0.700752 + 1.21374i 0.0310908 + 0.0538509i
\(509\) 0.938871 0.0416147 0.0208074 0.999784i \(-0.493376\pi\)
0.0208074 + 0.999784i \(0.493376\pi\)
\(510\) 2.32330 11.1240i 0.102878 0.492580i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) −15.6075 1.47281i −0.689088 0.0650261i
\(514\) −3.02826 1.74837i −0.133571 0.0771172i
\(515\) 0.300656i 0.0132485i
\(516\) −3.76721 11.4560i −0.165842 0.504320i
\(517\) 10.6818 + 6.16711i 0.469783 + 0.271229i
\(518\) 0 0
\(519\) 9.42442 + 28.6593i 0.413686 + 1.25801i
\(520\) −4.37859 + 7.58394i −0.192014 + 0.332578i
\(521\) −19.7527 + 34.2127i −0.865382 + 1.49889i 0.00128461 + 0.999999i \(0.499591\pi\)
−0.866667 + 0.498887i \(0.833742\pi\)
\(522\) −2.19615 19.5602i −0.0961230 0.856126i
\(523\) −21.0697 + 12.1646i −0.921315 + 0.531922i −0.884054 0.467384i \(-0.845197\pi\)
−0.0372609 + 0.999306i \(0.511863\pi\)
\(524\) −5.24589 9.08614i −0.229168 0.396930i
\(525\) 0 0
\(526\) −4.82174 + 8.35150i −0.210238 + 0.364143i
\(527\) 17.0283i 0.741763i
\(528\) 3.95136 1.29938i 0.171961 0.0565482i
\(529\) 8.81436 0.383233
\(530\) 0 0
\(531\) −35.2274 + 25.9777i −1.52874 + 1.12734i
\(532\) 0 0
\(533\) 34.2349 19.7655i 1.48288 0.856141i
\(534\) 4.84047 + 4.32741i 0.209468 + 0.187266i
\(535\) −12.3896 + 7.15316i −0.535651 + 0.309258i
\(536\) −0.493834 + 0.285115i −0.0213304 + 0.0123151i
\(537\) 21.5907 7.09993i 0.931706 0.306385i
\(538\) 5.98517 3.45554i 0.258039 0.148979i
\(539\) 0 0
\(540\) −0.873992 + 9.26178i −0.0376106 + 0.398564i
\(541\) −21.3640 37.0036i −0.918512 1.59091i −0.801677 0.597758i \(-0.796058\pi\)
−0.116835 0.993151i \(-0.537275\pi\)
\(542\) −20.6312 −0.886187
\(543\) 17.2484 + 15.4202i 0.740199 + 0.661743i
\(544\) 3.66466i 0.157121i
\(545\) −16.9665 + 29.3869i −0.726767 + 1.25880i
\(546\) 0 0
\(547\) −12.2477 21.2136i −0.523672 0.907026i −0.999620 0.0275530i \(-0.991229\pi\)
0.475949 0.879473i \(-0.342105\pi\)
\(548\) 4.08812 2.36028i 0.174636 0.100826i
\(549\) 13.6025 31.1439i 0.580539 1.32919i
\(550\) 2.15493 3.73244i 0.0918864 0.159152i
\(551\) −9.89735 + 17.1427i −0.421641 + 0.730304i
\(552\) −4.34791 + 4.86340i −0.185059 + 0.207000i
\(553\) 0 0
\(554\) 13.4358 + 7.75718i 0.570834 + 0.329571i
\(555\) 28.4243 + 5.93656i 1.20655 + 0.251993i
\(556\) 2.36375i 0.100245i
\(557\) 2.20344 + 1.27216i 0.0933627 + 0.0539030i 0.545954 0.837815i \(-0.316167\pi\)
−0.452592 + 0.891718i \(0.649501\pi\)
\(558\) −1.55534 13.8528i −0.0658430 0.586435i
\(559\) 34.0560i 1.44042i
\(560\) 0 0
\(561\) −14.4804 + 4.76178i −0.611364 + 0.201043i
\(562\) −13.5977 −0.573583
\(563\) 7.90707 + 13.6954i 0.333243 + 0.577194i 0.983146 0.182823i \(-0.0585236\pi\)
−0.649902 + 0.760018i \(0.725190\pi\)
\(564\) −5.92904 + 6.63199i −0.249658 + 0.279257i
\(565\) 1.79783 + 1.03798i 0.0756354 + 0.0436681i
\(566\) 5.44783 0.228990
\(567\) 0 0
\(568\) −5.96254 −0.250182
\(569\) 5.52793 + 3.19155i 0.231743 + 0.133797i 0.611376 0.791340i \(-0.290616\pi\)
−0.379633 + 0.925137i \(0.623950\pi\)
\(570\) 6.23549 6.97477i 0.261176 0.292141i
\(571\) 3.91188 + 6.77557i 0.163707 + 0.283549i 0.936195 0.351480i \(-0.114322\pi\)
−0.772488 + 0.635029i \(0.780988\pi\)
\(572\) 11.7465 0.491148
\(573\) 15.2252 5.00668i 0.636040 0.209157i
\(574\) 0 0
\(575\) 6.75933i 0.281884i
\(576\) 0.334727 + 2.98127i 0.0139469 + 0.124219i
\(577\) −12.4012 7.15986i −0.516270 0.298069i 0.219137 0.975694i \(-0.429676\pi\)
−0.735407 + 0.677625i \(0.763009\pi\)
\(578\) 3.57023i 0.148502i
\(579\) 41.6410 + 8.69693i 1.73054 + 0.361432i
\(580\) 10.1728 + 5.87327i 0.422403 + 0.243874i
\(581\) 0 0
\(582\) 6.36175 7.11600i 0.263703 0.294968i
\(583\) 0 0
\(584\) 6.19070 10.7226i 0.256173 0.443705i
\(585\) −10.5152 + 24.0754i −0.434750 + 0.995395i
\(586\) 21.1849 12.2311i 0.875141 0.505263i
\(587\) 2.37575 + 4.11492i 0.0980577 + 0.169841i 0.910881 0.412670i \(-0.135404\pi\)
−0.812823 + 0.582511i \(0.802070\pi\)
\(588\) 0 0
\(589\) −7.00943 + 12.1407i −0.288819 + 0.500249i
\(590\) 26.1212i 1.07539i
\(591\) 16.1229 + 14.4139i 0.663206 + 0.592910i
\(592\) 9.36404 0.384860
\(593\) 1.79035 + 3.10098i 0.0735208 + 0.127342i 0.900442 0.434976i \(-0.143243\pi\)
−0.826921 + 0.562318i \(0.809910\pi\)
\(594\) 11.3451 5.19642i 0.465497 0.213212i
\(595\) 0 0
\(596\) −15.0377 + 8.68202i −0.615968 + 0.355629i
\(597\) −0.294761 + 0.0969299i −0.0120638 + 0.00396708i
\(598\) −15.9544 + 9.21130i −0.652426 + 0.376678i
\(599\) 13.0471 7.53277i 0.533091 0.307780i −0.209183 0.977877i \(-0.567080\pi\)
0.742274 + 0.670096i \(0.233747\pi\)
\(600\) 2.31737 + 2.07174i 0.0946060 + 0.0845784i
\(601\) 19.8704 11.4722i 0.810530 0.467960i −0.0366096 0.999330i \(-0.511656\pi\)
0.847140 + 0.531370i \(0.178322\pi\)
\(602\) 0 0
\(603\) −1.37682 + 1.01531i −0.0560683 + 0.0413464i
\(604\) −5.61639 9.72787i −0.228528 0.395821i
\(605\) −9.36850 −0.380884
\(606\) 0.411876 0.135442i 0.0167313 0.00550197i
\(607\) 24.4832i 0.993741i 0.867825 + 0.496870i \(0.165518\pi\)
−0.867825 + 0.496870i \(0.834482\pi\)
\(608\) 1.50851 2.61281i 0.0611780 0.105963i
\(609\) 0 0
\(610\) 10.1408 + 17.5644i 0.410589 + 0.711161i
\(611\) −21.7563 + 12.5610i −0.880167 + 0.508165i
\(612\) −1.22666 10.9253i −0.0495848 0.441631i
\(613\) 0.440043 0.762177i 0.0177732 0.0307840i −0.857002 0.515313i \(-0.827676\pi\)
0.874775 + 0.484529i \(0.161009\pi\)
\(614\) −15.6111 + 27.0393i −0.630014 + 1.09122i
\(615\) 7.82892 + 23.8075i 0.315693 + 0.960011i
\(616\) 0 0
\(617\) −11.7607 6.79005i −0.473468 0.273357i 0.244222 0.969719i \(-0.421467\pi\)
−0.717690 + 0.696362i \(0.754801\pi\)
\(618\) −0.0908623 0.276309i −0.00365502 0.0111148i
\(619\) 35.4869i 1.42634i 0.700992 + 0.713169i \(0.252741\pi\)
−0.700992 + 0.713169i \(0.747259\pi\)
\(620\) 7.20451 + 4.15953i 0.289340 + 0.167051i
\(621\) −11.3344 + 15.9544i −0.454833 + 0.640230i
\(622\) 10.9100i 0.437452i
\(623\) 0 0
\(624\) −1.73205 + 8.29308i −0.0693375 + 0.331989i
\(625\) −12.8060 −0.512240
\(626\) −1.71203 2.96532i −0.0684263 0.118518i
\(627\) −12.2843 2.56563i −0.490587 0.102461i
\(628\) 11.9885 + 6.92154i 0.478391 + 0.276199i
\(629\) −34.3161 −1.36827
\(630\) 0 0
\(631\) 26.9822 1.07415 0.537073 0.843536i \(-0.319530\pi\)
0.537073 + 0.843536i \(0.319530\pi\)
\(632\) 2.62979 + 1.51831i 0.104608 + 0.0603952i
\(633\) −8.18207 24.8814i −0.325208 0.988947i
\(634\) 9.52357 + 16.4953i 0.378229 + 0.655112i
\(635\) −2.50918 −0.0995739
\(636\) 0 0
\(637\) 0 0
\(638\) 15.7563i 0.623800i
\(639\) −17.7759 + 1.99582i −0.703204 + 0.0789534i
\(640\) −1.55049 0.895175i −0.0612884 0.0353849i
\(641\) 1.07708i 0.0425420i 0.999774 + 0.0212710i \(0.00677128\pi\)
−0.999774 + 0.0212710i \(0.993229\pi\)
\(642\) −9.22457 + 10.3182i −0.364065 + 0.407228i
\(643\) −33.3126 19.2330i −1.31372 0.758477i −0.331010 0.943627i \(-0.607389\pi\)
−0.982710 + 0.185150i \(0.940723\pi\)
\(644\) 0 0
\(645\) 21.1346 + 4.41407i 0.832175 + 0.173804i
\(646\) −5.52817 + 9.57507i −0.217503 + 0.376726i
\(647\) −4.47605 + 7.75275i −0.175972 + 0.304792i −0.940497 0.339802i \(-0.889640\pi\)
0.764525 + 0.644594i \(0.222973\pi\)
\(648\) 1.99582 + 8.77592i 0.0784032 + 0.344751i
\(649\) −30.3438 + 17.5190i −1.19110 + 0.687680i
\(650\) 4.38910 + 7.60215i 0.172155 + 0.298181i
\(651\) 0 0
\(652\) −2.16789 + 3.75489i −0.0849010 + 0.147053i
\(653\) 11.3846i 0.445513i 0.974874 + 0.222757i \(0.0715055\pi\)
−0.974874 + 0.222757i \(0.928494\pi\)
\(654\) −6.71150 + 32.1348i −0.262440 + 1.25657i
\(655\) 18.7839 0.733949
\(656\) 4.04094 + 6.99911i 0.157772 + 0.273269i
\(657\) 14.8670 34.0392i 0.580017 1.32799i
\(658\) 0 0
\(659\) 31.4373 18.1503i 1.22462 0.707036i 0.258723 0.965952i \(-0.416698\pi\)
0.965900 + 0.258915i \(0.0833650\pi\)
\(660\) −1.52249 + 7.28972i −0.0592629 + 0.283752i
\(661\) −31.2425 + 18.0379i −1.21519 + 0.701593i −0.963886 0.266315i \(-0.914194\pi\)
−0.251308 + 0.967907i \(0.580861\pi\)
\(662\) 0.0634366 0.0366251i 0.00246553 0.00142348i
\(663\) 6.34739 30.3914i 0.246512 1.18030i
\(664\) 12.1290 7.00270i 0.470698 0.271757i
\(665\) 0 0
\(666\) 27.9167 3.13439i 1.08175 0.121455i
\(667\) 12.3557 + 21.4007i 0.478414 + 0.828637i
\(668\) 12.4151 0.480355
\(669\) 2.97281 14.2339i 0.114935 0.550313i
\(670\) 1.02091i 0.0394413i
\(671\) 13.6025 23.5602i 0.525117 0.909530i
\(672\) 0 0
\(673\) 4.78512 + 8.28806i 0.184453 + 0.319481i 0.943392 0.331680i \(-0.107615\pi\)
−0.758939 + 0.651161i \(0.774282\pi\)
\(674\) −1.93364 + 1.11639i −0.0744811 + 0.0430017i
\(675\) 7.60215 + 5.40073i 0.292607 + 0.207874i
\(676\) −5.46254 + 9.46139i −0.210098 + 0.363900i
\(677\) −7.81408 + 13.5344i −0.300320 + 0.520169i −0.976208 0.216835i \(-0.930427\pi\)
0.675889 + 0.737004i \(0.263760\pi\)
\(678\) 1.96594 + 0.410596i 0.0755015 + 0.0157689i
\(679\) 0 0
\(680\) 5.68202 + 3.28052i 0.217896 + 0.125802i
\(681\) 2.79967 3.13160i 0.107283 0.120003i
\(682\) 11.1589i 0.427294i
\(683\) −9.63996 5.56563i −0.368863 0.212963i 0.304099 0.952640i \(-0.401645\pi\)
−0.672961 + 0.739678i \(0.734978\pi\)
\(684\) 3.62268 8.29442i 0.138517 0.317145i
\(685\) 8.45145i 0.322913i
\(686\) 0 0
\(687\) 2.60803 + 2.33159i 0.0995025 + 0.0889559i
\(688\) 6.96254 0.265444
\(689\) 0 0
\(690\) −3.64850 11.0950i −0.138896 0.422378i
\(691\) 2.61903 + 1.51210i 0.0996324 + 0.0575228i 0.548988 0.835830i \(-0.315013\pi\)
−0.449356 + 0.893353i \(0.648346\pi\)
\(692\) −17.4182 −0.662139
\(693\) 0 0
\(694\) 31.8409 1.20867
\(695\) −3.66497 2.11597i −0.139020 0.0802633i
\(696\) 11.1240 + 2.32330i 0.421655 + 0.0880646i
\(697\) −14.8087 25.6494i −0.560919 0.971540i
\(698\) −14.7354 −0.557745
\(699\) −4.50739 + 21.5815i −0.170485 + 0.816286i
\(700\) 0 0
\(701\) 50.1486i 1.89409i 0.321103 + 0.947044i \(0.395946\pi\)
−0.321103 + 0.947044i \(0.604054\pi\)
\(702\) −2.38779 + 25.3037i −0.0901214 + 0.955025i
\(703\) −24.4664 14.1257i −0.922769 0.532761i
\(704\) 2.40150i 0.0905101i
\(705\) −4.97529 15.1297i −0.187380 0.569817i
\(706\) 1.87025 + 1.07979i 0.0703876 + 0.0406383i
\(707\) 0 0
\(708\) −7.89419 24.0060i −0.296682 0.902200i
\(709\) 1.80385 3.12436i 0.0677449 0.117338i −0.830163 0.557520i \(-0.811753\pi\)
0.897908 + 0.440183i \(0.145086\pi\)
\(710\) 5.33751 9.24484i 0.200313 0.346953i
\(711\) 8.34834 + 3.64623i 0.313087 + 0.136744i
\(712\) −3.24641 + 1.87432i −0.121664 + 0.0702429i
\(713\) 8.75046 + 15.1562i 0.327707 + 0.567605i
\(714\) 0 0
\(715\) −10.5152 + 18.2129i −0.393246 + 0.681123i
\(716\) 13.1221i 0.490395i
\(717\) 28.7109 9.44136i 1.07223 0.352594i
\(718\) −32.6448 −1.21829
\(719\) −17.1580 29.7186i −0.639887 1.10832i −0.985457 0.169924i \(-0.945648\pi\)
0.345571 0.938393i \(-0.387685\pi\)
\(720\) −4.92206 2.14977i −0.183434 0.0801171i
\(721\) 0 0
\(722\) 8.57161 4.94882i 0.319002 0.184176i
\(723\) −14.7633 13.1984i −0.549051 0.490855i
\(724\) −11.5681 + 6.67887i −0.429927 + 0.248218i
\(725\) 10.1972 5.88737i 0.378716 0.218651i
\(726\) −8.60986 + 2.83129i −0.319542 + 0.105079i
\(727\) −19.4757 + 11.2443i −0.722315 + 0.417029i −0.815604 0.578610i \(-0.803595\pi\)
0.0932892 + 0.995639i \(0.470262\pi\)
\(728\) 0 0
\(729\) 8.88761 + 25.4953i 0.329171 + 0.944270i
\(730\) 11.0835 + 19.1972i 0.410220 + 0.710521i
\(731\) −25.5154 −0.943720
\(732\) 14.6278 + 13.0774i 0.540659 + 0.483353i
\(733\) 31.1845i 1.15182i 0.817512 + 0.575912i \(0.195353\pi\)
−0.817512 + 0.575912i \(0.804647\pi\)
\(734\) −14.8501 + 25.7212i −0.548129 + 0.949387i
\(735\) 0 0
\(736\) −1.88319 3.26178i −0.0694154 0.120231i
\(737\) −1.18595 + 0.684706i −0.0436849 + 0.0252215i
\(738\) 14.3899 + 19.5136i 0.529700 + 0.718306i
\(739\) −2.04314 + 3.53882i −0.0751581 + 0.130178i −0.901155 0.433497i \(-0.857279\pi\)
0.825997 + 0.563675i \(0.190613\pi\)
\(740\) −8.38245 + 14.5188i −0.308145 + 0.533723i
\(741\) 17.0357 19.0554i 0.625821 0.700018i
\(742\) 0 0
\(743\) −1.78246 1.02910i −0.0653921 0.0377542i 0.466947 0.884285i \(-0.345354\pi\)
−0.532340 + 0.846531i \(0.678687\pi\)
\(744\) 7.87817 + 1.64539i 0.288828 + 0.0603231i
\(745\) 31.0877i 1.13897i
\(746\) 1.74653 + 1.00836i 0.0639450 + 0.0369187i
\(747\) 33.8159 24.9368i 1.23726 0.912391i
\(748\) 8.80071i 0.321786i
\(749\) 0 0
\(750\) −20.0156 + 6.58198i −0.730866 + 0.240340i
\(751\) 23.8105 0.868859 0.434429 0.900706i \(-0.356950\pi\)
0.434429 + 0.900706i \(0.356950\pi\)
\(752\) −2.56802 4.44794i −0.0936461 0.162200i
\(753\) 31.5797 35.3238i 1.15083 1.28727i
\(754\) 27.7926 + 16.0461i 1.01215 + 0.584363i
\(755\) 20.1106 0.731900
\(756\) 0 0
\(757\) 10.0754 0.366197 0.183098 0.983095i \(-0.441387\pi\)
0.183098 + 0.983095i \(0.441387\pi\)
\(758\) 16.3427 + 9.43544i 0.593592 + 0.342711i
\(759\) −10.4415 + 11.6795i −0.379003 + 0.423938i
\(760\) 2.70075 + 4.67784i 0.0979666 + 0.169683i
\(761\) 27.8735 1.01041 0.505207 0.862998i \(-0.331416\pi\)
0.505207 + 0.862998i \(0.331416\pi\)
\(762\) −2.30599 + 0.758309i −0.0835374 + 0.0274707i
\(763\) 0 0
\(764\) 9.25333i 0.334774i
\(765\) 18.0377 + 7.87817i 0.652154 + 0.284836i
\(766\) 0.724440 + 0.418256i 0.0261751 + 0.0151122i
\(767\) 71.3645i 2.57682i
\(768\) −1.69547 0.354107i −0.0611799 0.0127777i
\(769\) 6.21166 + 3.58631i 0.223998 + 0.129326i 0.607800 0.794090i \(-0.292052\pi\)
−0.383802 + 0.923415i \(0.625385\pi\)
\(770\) 0 0
\(771\) 4.03663 4.51521i 0.145376 0.162611i
\(772\) −12.2801 + 21.2698i −0.441970 + 0.765515i
\(773\) −1.07077 + 1.85462i −0.0385128 + 0.0667061i −0.884639 0.466276i \(-0.845595\pi\)
0.846127 + 0.532982i \(0.178929\pi\)
\(774\) 20.7572 2.33055i 0.746102 0.0837698i
\(775\) 7.22181 4.16951i 0.259415 0.149773i
\(776\) 2.75544 + 4.77256i 0.0989144 + 0.171325i
\(777\) 0 0
\(778\) 12.4109 21.4964i 0.444954 0.770682i
\(779\) 24.3831i 0.873615i
\(780\) −11.3078 10.1093i −0.404886 0.361970i
\(781\) −14.3191 −0.512376
\(782\) 6.90127 + 11.9533i 0.246789 + 0.427451i
\(783\) 33.9413 + 3.20289i 1.21296 + 0.114462i
\(784\) 0 0
\(785\) −21.4635 + 12.3920i −0.766066 + 0.442288i
\(786\) 17.2629 5.67677i 0.615746 0.202484i
\(787\) 15.8961 9.17759i 0.566633 0.327146i −0.189170 0.981944i \(-0.560580\pi\)
0.755804 + 0.654798i \(0.227247\pi\)
\(788\) −10.8133 + 6.24305i −0.385207 + 0.222400i
\(789\) −12.4523 11.1324i −0.443313 0.396325i
\(790\) −4.70825 + 2.71831i −0.167512 + 0.0967131i
\(791\) 0 0
\(792\) 0.803848 + 7.15953i 0.0285635 + 0.254403i
\(793\) 27.7052 + 47.9868i 0.983839 + 1.70406i
\(794\) 3.03390 0.107669
\(795\) 0 0
\(796\) 0.179145i 0.00634964i
\(797\) −12.4226 + 21.5166i −0.440031 + 0.762156i −0.997691 0.0679130i \(-0.978366\pi\)
0.557660 + 0.830069i \(0.311699\pi\)
\(798\) 0 0
\(799\) 9.41094 + 16.3002i 0.332935 + 0.576660i
\(800\) −1.55421 + 0.897324i −0.0549497 + 0.0317252i
\(801\) −9.05103 + 6.67450i −0.319803 + 0.235832i
\(802\) −6.53854 + 11.3251i −0.230884 + 0.399903i
\(803\) 14.8670 25.7504i 0.524645 0.908712i
\(804\) −0.308534 0.938241i −0.0108811 0.0330892i
\(805\) 0 0
\(806\) 19.6831 + 11.3640i 0.693307 + 0.400281i
\(807\) 3.73936 + 11.3713i 0.131632 + 0.400288i
\(808\) 0.250324i 0.00880637i
\(809\) 32.7237 + 18.8930i 1.15050 + 0.664244i 0.949010 0.315246i \(-0.102087\pi\)
0.201494 + 0.979490i \(0.435420\pi\)
\(810\) −15.3936 4.76148i −0.540875 0.167301i
\(811\) 36.5165i 1.28227i −0.767429 0.641134i \(-0.778464\pi\)
0.767429 0.641134i \(-0.221536\pi\)
\(812\) 0 0
\(813\) 7.30565 34.9795i 0.256220 1.22679i
\(814\) 22.4878 0.788196
\(815\) −3.88128 6.72257i −0.135955 0.235481i
\(816\) 6.21332 + 1.29768i 0.217510 + 0.0454280i
\(817\) −18.1918 10.5030i −0.636449 0.367454i
\(818\) −5.56709 −0.194649
\(819\) 0 0
\(820\) −14.4694 −0.505293
\(821\) 5.52142 + 3.18779i 0.192699 + 0.111255i 0.593245 0.805022i \(-0.297846\pi\)
−0.400547 + 0.916276i \(0.631180\pi\)
\(822\) 2.55414 + 7.76707i 0.0890860 + 0.270908i
\(823\) −14.0293 24.2995i −0.489032 0.847028i 0.510888 0.859647i \(-0.329317\pi\)
−0.999920 + 0.0126187i \(0.995983\pi\)
\(824\) 0.167931 0.00585017
\(825\) 5.56516 + 4.97529i 0.193754 + 0.173217i
\(826\) 0 0
\(827\) 0.581579i 0.0202235i −0.999949 0.0101117i \(-0.996781\pi\)
0.999949 0.0101117i \(-0.00321872\pi\)
\(828\) −6.70610 9.09390i −0.233053 0.316035i
\(829\) 44.9680 + 25.9623i 1.56180 + 0.901708i 0.997075 + 0.0764314i \(0.0243526\pi\)
0.564729 + 0.825276i \(0.308981\pi\)
\(830\) 25.0746i 0.870351i
\(831\) −17.9098 + 20.0331i −0.621283 + 0.694942i
\(832\) −4.23601 2.44566i −0.146857 0.0847881i
\(833\) 0 0
\(834\) −4.00766 0.837019i −0.138774 0.0289836i
\(835\) −11.1137 + 19.2495i −0.384606 + 0.666156i
\(836\) 3.62268 6.27467i 0.125293 0.217014i
\(837\) 24.0377 + 2.26833i 0.830864 + 0.0784049i
\(838\) 14.2017 8.19938i 0.490591 0.283243i
\(839\) 3.33038 + 5.76838i 0.114977 + 0.199147i 0.917771 0.397111i \(-0.129987\pi\)
−0.802793 + 0.596257i \(0.796654\pi\)
\(840\) 0 0
\(841\) 7.02357 12.1652i 0.242192 0.419489i
\(842\) 15.4578i 0.532712i
\(843\) 4.81502 23.0544i 0.165838 0.794035i
\(844\) 15.1221 0.520523
\(845\) −9.77985 16.9392i −0.336437 0.582726i
\(846\) −9.14481 12.4009i −0.314405 0.426353i
\(847\) 0 0
\(848\) 0 0
\(849\) −1.92911 + 9.23662i −0.0662070 + 0.317000i
\(850\) 5.69566 3.28839i 0.195360 0.112791i
\(851\) −30.5435 + 17.6343i −1.04702 + 0.604495i
\(852\) 2.11137 10.1093i 0.0723345 0.346338i
\(853\) 19.2287 11.1017i 0.658378 0.380115i −0.133281 0.991078i \(-0.542551\pi\)
0.791659 + 0.610964i \(0.209218\pi\)
\(854\) 0 0
\(855\) 9.61746 + 13.0419i 0.328910 + 0.446023i
\(856\) −3.99540 6.92024i −0.136560 0.236529i
\(857\) −15.2966 −0.522522 −0.261261 0.965268i \(-0.584138\pi\)
−0.261261 + 0.965268i \(0.584138\pi\)
\(858\) −4.15953 + 19.9159i −0.142004 + 0.679917i
\(859\) 4.25646i 0.145229i 0.997360 + 0.0726143i \(0.0231342\pi\)
−0.997360 + 0.0726143i \(0.976866\pi\)
\(860\) −6.23269 + 10.7953i −0.212533 + 0.368118i
\(861\) 0 0
\(862\) −12.5133 21.6737i −0.426204 0.738208i
\(863\) −20.4922 + 11.8312i −0.697562 + 0.402738i −0.806439 0.591317i \(-0.798608\pi\)
0.108876 + 0.994055i \(0.465275\pi\)
\(864\) −5.17317 0.488168i −0.175995 0.0166078i
\(865\) 15.5923 27.0067i 0.530154 0.918254i
\(866\) −1.12584 + 1.95001i −0.0382576 + 0.0662641i
\(867\) 6.05321 + 1.26424i 0.205578 + 0.0429359i
\(868\) 0 0
\(869\) 6.31546 + 3.64623i 0.214237 + 0.123690i
\(870\) −13.5602 + 15.1679i −0.459734 + 0.514240i
\(871\) 2.78919i 0.0945079i
\(872\) −16.4141 9.47667i −0.555851 0.320920i
\(873\) 9.81220 + 13.3060i 0.332093 + 0.450338i
\(874\) 11.3632i 0.384367i
\(875\) 0 0
\(876\) 15.9877 + 14.2931i 0.540173 + 0.482918i
\(877\) −20.3923 −0.688599 −0.344300 0.938860i \(-0.611884\pi\)
−0.344300 + 0.938860i \(0.611884\pi\)
\(878\) −9.37000 16.2293i −0.316222 0.547713i
\(879\) 13.2357 + 40.2495i 0.446430 + 1.35758i
\(880\) −3.72350 2.14977i −0.125519 0.0724686i
\(881\) −32.4586 −1.09356 −0.546780 0.837276i \(-0.684147\pi\)
−0.546780 + 0.837276i \(0.684147\pi\)
\(882\) 0 0
\(883\) −24.8311 −0.835632 −0.417816 0.908532i \(-0.637204\pi\)
−0.417816 + 0.908532i \(0.637204\pi\)
\(884\) 15.5236 + 8.96254i 0.522114 + 0.301443i
\(885\) 44.2877 + 9.24970i 1.48871 + 0.310925i
\(886\) −0.602256 1.04314i −0.0202332 0.0350449i
\(887\) −9.72119 −0.326405 −0.163203 0.986593i \(-0.552182\pi\)
−0.163203 + 0.986593i \(0.552182\pi\)
\(888\) −3.31587 + 15.8764i −0.111273 + 0.532778i
\(889\) 0 0
\(890\) 6.71136i 0.224965i
\(891\) 4.79297 + 21.0754i 0.160571 + 0.706052i
\(892\) 7.27049 + 4.19762i 0.243434 + 0.140547i
\(893\) 15.4955i 0.518537i
\(894\) −9.39513 28.5703i −0.314220 0.955533i
\(895\) −20.3456 11.7465i −0.680079 0.392644i
\(896\) 0 0
\(897\) −9.96789 30.3120i −0.332818 1.01209i
\(898\) 13.4011 23.2114i 0.447200 0.774573i
\(899\) 15.2433 26.4021i 0.508392 0.880560i
\(900\) −4.33316 + 3.19540i −0.144439 + 0.106513i
\(901\) 0 0
\(902\) 9.70433 + 16.8084i 0.323119 + 0.559658i
\(903\) 0 0
\(904\) −0.579764 + 1.00418i −0.0192827 + 0.0333985i
\(905\) 23.9150i 0.794963i
\(906\) 18.4821 6.07770i 0.614026 0.201918i
\(907\) −16.0863 −0.534136 −0.267068 0.963678i \(-0.586055\pi\)
−0.267068 + 0.963678i \(0.586055\pi\)
\(908\) 1.21261 + 2.10030i 0.0402418 + 0.0697009i
\(909\) 0.0837902 + 0.746284i 0.00277915 + 0.0247527i
\(910\) 0 0
\(911\) 27.0087 15.5935i 0.894838 0.516635i 0.0193161 0.999813i \(-0.493851\pi\)
0.875522 + 0.483179i \(0.160518\pi\)
\(912\) 3.89576 + 3.48283i 0.129001 + 0.115328i
\(913\) 29.1279 16.8170i 0.963993 0.556562i
\(914\) 11.9934 6.92442i 0.396708 0.229039i
\(915\) −33.3707 + 10.9737i −1.10320 + 0.362780i
\(916\) −1.74915 + 1.00987i −0.0577936 + 0.0333672i
\(917\) 0 0
\(918\) 18.9579 + 1.78897i 0.625705 + 0.0590449i
\(919\) −12.8832 22.3143i −0.424977 0.736082i 0.571441 0.820643i \(-0.306385\pi\)
−0.996418 + 0.0845609i \(0.973051\pi\)
\(920\) 6.74314 0.222315
\(921\) −40.3162 36.0430i −1.32846 1.18766i
\(922\) 4.80483i 0.158239i
\(923\) 14.5824 25.2574i 0.479984 0.831357i
\(924\) 0 0
\(925\) 8.40258 + 14.5537i 0.276275 + 0.478522i
\(926\) −18.2201 + 10.5194i −0.598750 + 0.345689i
\(927\) 0.500648 0.0562111i 0.0164435 0.00184622i
\(928\) −3.28052 + 5.68202i −0.107688 + 0.186521i
\(929\) 27.3744 47.4138i 0.898124 1.55560i 0.0682329 0.997669i \(-0.478264\pi\)
0.829891 0.557926i \(-0.188403\pi\)
\(930\) −9.60351 + 10.7421i −0.314911 + 0.352247i
\(931\) 0 0
\(932\) −11.0236 6.36446i −0.361089 0.208475i
\(933\) 18.4976 + 3.86331i 0.605584 + 0.126479i
\(934\) 5.82302i 0.190535i
\(935\) 13.6454 + 7.87817i 0.446252 + 0.257644i
\(936\) −13.4473 5.87327i −0.439539 0.191974i
\(937\) 58.2065i 1.90152i 0.309924 + 0.950761i \(0.399696\pi\)
−0.309924 + 0.950761i \(0.600304\pi\)
\(938\) 0 0
\(939\) 5.63384 1.85265i 0.183853 0.0604588i
\(940\) 9.19531 0.299918
\(941\) −16.6658 28.8660i −0.543289 0.941005i −0.998712 0.0507297i \(-0.983845\pi\)
0.455423 0.890275i \(-0.349488\pi\)
\(942\) −15.9804 + 17.8751i −0.520671 + 0.582401i
\(943\) −26.3613 15.2197i −0.858443 0.495622i
\(944\) 14.5900 0.474864
\(945\) 0 0
\(946\) 16.7206 0.543632
\(947\) 6.59497 + 3.80761i 0.214308 + 0.123731i 0.603312 0.797505i \(-0.293847\pi\)
−0.389004 + 0.921236i \(0.627181\pi\)
\(948\) −3.50548 + 3.92109i −0.113853 + 0.127351i
\(949\) 30.2808 + 52.4478i 0.982955 + 1.70253i
\(950\) 5.41447 0.175669
\(951\) −31.3396 + 10.3058i −1.01626 + 0.334188i
\(952\) 0 0
\(953\) 55.7861i 1.80709i −0.428495 0.903544i \(-0.640956\pi\)
0.428495 0.903544i \(-0.359044\pi\)
\(954\) 0 0
\(955\) −14.3472 8.28334i −0.464264 0.268043i
\(956\) 17.4495i 0.564356i
\(957\) 26.7144 + 5.57943i 0.863553 + 0.180357i
\(958\) −23.3447 13.4781i −0.754232 0.435456i
\(959\) 0 0
\(960\) 2.06678 2.31181i 0.0667050 0.0746135i
\(961\) −4.70451 + 8.14845i −0.151758 + 0.262853i
\(962\) −22.9013 + 39.6662i −0.738367 + 1.27889i
\(963\) −14.2277 19.2937i −0.458483 0.621731i
\(964\) 9.90142 5.71659i 0.318903 0.184119i
\(965\) −21.9857 38.0803i −0.707744 1.22585i
\(966\) 0 0
\(967\) −13.3369 + 23.1003i −0.428887 + 0.742855i −0.996775 0.0802517i \(-0.974428\pi\)
0.567887 + 0.823106i \(0.307761\pi\)
\(968\) 5.23278i 0.168188i
\(969\) −14.2766 12.7634i −0.458632 0.410020i
\(970\) −9.86639 −0.316791
\(971\) −4.29971 7.44731i −0.137984 0.238996i 0.788749 0.614715i \(-0.210729\pi\)
−0.926733 + 0.375719i \(0.877396\pi\)
\(972\) −15.5860 + 0.276237i −0.499921 + 0.00886031i
\(973\) 0 0
\(974\) −11.8011 + 6.81338i −0.378132 + 0.218315i
\(975\) −14.4434 + 4.74961i −0.462559 + 0.152109i
\(976\) −9.81058 + 5.66414i −0.314029 + 0.181305i
\(977\) 12.7973 7.38854i 0.409423 0.236380i −0.281119 0.959673i \(-0.590705\pi\)
0.690542 + 0.723293i \(0.257372\pi\)
\(978\) −5.59863 5.00521i −0.179024 0.160049i
\(979\) −7.79627 + 4.50118i −0.249170 + 0.143858i
\(980\) 0 0
\(981\) −52.1068 22.7583i −1.66364 0.726615i
\(982\) 19.4815 + 33.7430i 0.621680 + 1.07678i
\(983\) 20.5135 0.654280 0.327140 0.944976i \(-0.393915\pi\)
0.327140 + 0.944976i \(0.393915\pi\)
\(984\) −13.2977 + 4.37285i −0.423915 + 0.139401i
\(985\) 22.3545i 0.712273i
\(986\) 12.0220 20.8227i 0.382858 0.663130i
\(987\) 0 0
\(988\) 7.37859 + 12.7801i 0.234744 + 0.406589i
\(989\) −22.7103 + 13.1118i −0.722145 + 0.416931i
\(990\) −11.8203 5.16267i −0.375675 0.164080i
\(991\) 4.64647 8.04792i 0.147600 0.255651i −0.782740 0.622349i \(-0.786179\pi\)
0.930340 + 0.366698i \(0.119512\pi\)
\(992\) −2.32330 + 4.02408i −0.0737650 + 0.127765i
\(993\) 0.0396334 + 0.120524i 0.00125773 + 0.00382471i
\(994\) 0 0
\(995\) 0.277763 + 0.160366i 0.00880567 + 0.00508396i
\(996\) 7.57788 + 23.0441i 0.240114 + 0.730179i
\(997\) 0.0199668i 0.000632354i 1.00000 0.000316177i \(0.000100642\pi\)
−1.00000 0.000316177i \(0.999899\pi\)
\(998\) −22.5250 13.0048i −0.713018 0.411661i
\(999\) −4.57123 + 48.4418i −0.144627 + 1.53263i
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 882.2.t.b.815.3 16
3.2 odd 2 2646.2.t.a.2285.8 16
7.2 even 3 882.2.l.a.509.7 16
7.3 odd 6 126.2.m.a.41.8 yes 16
7.4 even 3 126.2.m.a.41.5 16
7.5 odd 6 882.2.l.a.509.6 16
7.6 odd 2 inner 882.2.t.b.815.2 16
9.2 odd 6 882.2.l.a.227.2 16
9.7 even 3 2646.2.l.b.521.8 16
21.2 odd 6 2646.2.l.b.1097.1 16
21.5 even 6 2646.2.l.b.1097.4 16
21.11 odd 6 378.2.m.a.125.1 16
21.17 even 6 378.2.m.a.125.4 16
21.20 even 2 2646.2.t.a.2285.5 16
28.3 even 6 1008.2.cc.b.545.1 16
28.11 odd 6 1008.2.cc.b.545.8 16
63.2 odd 6 inner 882.2.t.b.803.2 16
63.4 even 3 1134.2.d.a.1133.11 16
63.11 odd 6 126.2.m.a.83.8 yes 16
63.16 even 3 2646.2.t.a.1979.5 16
63.20 even 6 882.2.l.a.227.3 16
63.25 even 3 378.2.m.a.251.4 16
63.31 odd 6 1134.2.d.a.1133.14 16
63.32 odd 6 1134.2.d.a.1133.6 16
63.34 odd 6 2646.2.l.b.521.5 16
63.38 even 6 126.2.m.a.83.5 yes 16
63.47 even 6 inner 882.2.t.b.803.3 16
63.52 odd 6 378.2.m.a.251.1 16
63.59 even 6 1134.2.d.a.1133.3 16
63.61 odd 6 2646.2.t.a.1979.8 16
84.11 even 6 3024.2.cc.b.881.3 16
84.59 odd 6 3024.2.cc.b.881.6 16
252.11 even 6 1008.2.cc.b.209.1 16
252.115 even 6 3024.2.cc.b.2897.3 16
252.151 odd 6 3024.2.cc.b.2897.6 16
252.227 odd 6 1008.2.cc.b.209.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.m.a.41.5 16 7.4 even 3
126.2.m.a.41.8 yes 16 7.3 odd 6
126.2.m.a.83.5 yes 16 63.38 even 6
126.2.m.a.83.8 yes 16 63.11 odd 6
378.2.m.a.125.1 16 21.11 odd 6
378.2.m.a.125.4 16 21.17 even 6
378.2.m.a.251.1 16 63.52 odd 6
378.2.m.a.251.4 16 63.25 even 3
882.2.l.a.227.2 16 9.2 odd 6
882.2.l.a.227.3 16 63.20 even 6
882.2.l.a.509.6 16 7.5 odd 6
882.2.l.a.509.7 16 7.2 even 3
882.2.t.b.803.2 16 63.2 odd 6 inner
882.2.t.b.803.3 16 63.47 even 6 inner
882.2.t.b.815.2 16 7.6 odd 2 inner
882.2.t.b.815.3 16 1.1 even 1 trivial
1008.2.cc.b.209.1 16 252.11 even 6
1008.2.cc.b.209.8 16 252.227 odd 6
1008.2.cc.b.545.1 16 28.3 even 6
1008.2.cc.b.545.8 16 28.11 odd 6
1134.2.d.a.1133.3 16 63.59 even 6
1134.2.d.a.1133.6 16 63.32 odd 6
1134.2.d.a.1133.11 16 63.4 even 3
1134.2.d.a.1133.14 16 63.31 odd 6
2646.2.l.b.521.5 16 63.34 odd 6
2646.2.l.b.521.8 16 9.7 even 3
2646.2.l.b.1097.1 16 21.2 odd 6
2646.2.l.b.1097.4 16 21.5 even 6
2646.2.t.a.1979.5 16 63.16 even 3
2646.2.t.a.1979.8 16 63.61 odd 6
2646.2.t.a.2285.5 16 21.20 even 2
2646.2.t.a.2285.8 16 3.2 odd 2
3024.2.cc.b.881.3 16 84.11 even 6
3024.2.cc.b.881.6 16 84.59 odd 6
3024.2.cc.b.2897.3 16 252.115 even 6
3024.2.cc.b.2897.6 16 252.151 odd 6