Properties

Label 525.2.b.e.251.4
Level $525$
Weight $2$
Character 525.251
Analytic conductor $4.192$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(251,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.251");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.b (of order \(2\), degree \(1\), 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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.4
Root \(-1.18614 - 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 525.251
Dual form 525.2.b.e.251.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.52434i q^{2} +(-1.68614 + 0.396143i) q^{3} -4.37228 q^{4} +(-1.00000 - 4.25639i) q^{6} +(2.00000 - 1.73205i) q^{7} -5.98844i q^{8} +(2.68614 - 1.33591i) q^{9} +O(q^{10})\) \(q+2.52434i q^{2} +(-1.68614 + 0.396143i) q^{3} -4.37228 q^{4} +(-1.00000 - 4.25639i) q^{6} +(2.00000 - 1.73205i) q^{7} -5.98844i q^{8} +(2.68614 - 1.33591i) q^{9} -0.792287i q^{11} +(7.37228 - 1.73205i) q^{12} -5.84096i q^{13} +(4.37228 + 5.04868i) q^{14} +6.37228 q^{16} +1.37228 q^{17} +(3.37228 + 6.78073i) q^{18} -3.46410i q^{19} +(-2.68614 + 3.71277i) q^{21} +2.00000 q^{22} +1.87953i q^{23} +(2.37228 + 10.0974i) q^{24} +14.7446 q^{26} +(-4.00000 + 3.31662i) q^{27} +(-8.74456 + 7.57301i) q^{28} -4.25639i q^{29} +3.46410i q^{31} +4.10891i q^{32} +(0.313859 + 1.33591i) q^{33} +3.46410i q^{34} +(-11.7446 + 5.84096i) q^{36} -4.74456 q^{37} +8.74456 q^{38} +(2.31386 + 9.84868i) q^{39} -6.00000 q^{41} +(-9.37228 - 6.78073i) q^{42} +6.74456 q^{43} +3.46410i q^{44} -4.74456 q^{46} +7.37228 q^{47} +(-10.7446 + 2.52434i) q^{48} +(1.00000 - 6.92820i) q^{49} +(-2.31386 + 0.543620i) q^{51} +25.5383i q^{52} -8.51278i q^{53} +(-8.37228 - 10.0974i) q^{54} +(-10.3723 - 11.9769i) q^{56} +(1.37228 + 5.84096i) q^{57} +10.7446 q^{58} +2.74456 q^{59} +6.92820i q^{61} -8.74456 q^{62} +(3.05842 - 7.32435i) q^{63} +2.37228 q^{64} +(-3.37228 + 0.792287i) q^{66} +6.74456 q^{67} -6.00000 q^{68} +(-0.744563 - 3.16915i) q^{69} -13.5615i q^{71} +(-8.00000 - 16.0858i) q^{72} -6.92820i q^{73} -11.9769i q^{74} +15.1460i q^{76} +(-1.37228 - 1.58457i) q^{77} +(-24.8614 + 5.84096i) q^{78} +3.37228 q^{79} +(5.43070 - 7.17687i) q^{81} -15.1460i q^{82} -5.48913 q^{83} +(11.7446 - 16.2333i) q^{84} +17.0256i q^{86} +(1.68614 + 7.17687i) q^{87} -4.74456 q^{88} +3.25544 q^{89} +(-10.1168 - 11.6819i) q^{91} -8.21782i q^{92} +(-1.37228 - 5.84096i) q^{93} +18.6101i q^{94} +(-1.62772 - 6.92820i) q^{96} +1.08724i q^{97} +(17.4891 + 2.52434i) q^{98} +(-1.05842 - 2.12819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{3} - 6 q^{4} - 4 q^{6} + 8 q^{7} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{3} - 6 q^{4} - 4 q^{6} + 8 q^{7} + 5 q^{9} + 18 q^{12} + 6 q^{14} + 14 q^{16} - 6 q^{17} + 2 q^{18} - 5 q^{21} + 8 q^{22} - 2 q^{24} + 36 q^{26} - 16 q^{27} - 12 q^{28} + 7 q^{33} - 24 q^{36} + 4 q^{37} + 12 q^{38} + 15 q^{39} - 24 q^{41} - 26 q^{42} + 4 q^{43} + 4 q^{46} + 18 q^{47} - 20 q^{48} + 4 q^{49} - 15 q^{51} - 22 q^{54} - 30 q^{56} - 6 q^{57} + 20 q^{58} - 12 q^{59} - 12 q^{62} - 5 q^{63} - 2 q^{64} - 2 q^{66} + 4 q^{67} - 24 q^{68} + 20 q^{69} - 32 q^{72} + 6 q^{77} - 42 q^{78} + 2 q^{79} - 7 q^{81} + 24 q^{83} + 24 q^{84} + q^{87} + 4 q^{88} + 36 q^{89} - 6 q^{91} + 6 q^{93} - 18 q^{96} + 24 q^{98} + 13 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.52434i 1.78498i 0.451071 + 0.892488i \(0.351042\pi\)
−0.451071 + 0.892488i \(0.648958\pi\)
\(3\) −1.68614 + 0.396143i −0.973494 + 0.228714i
\(4\) −4.37228 −2.18614
\(5\) 0 0
\(6\) −1.00000 4.25639i −0.408248 1.73766i
\(7\) 2.00000 1.73205i 0.755929 0.654654i
\(8\) 5.98844i 2.11723i
\(9\) 2.68614 1.33591i 0.895380 0.445302i
\(10\) 0 0
\(11\) 0.792287i 0.238884i −0.992841 0.119442i \(-0.961890\pi\)
0.992841 0.119442i \(-0.0381105\pi\)
\(12\) 7.37228 1.73205i 2.12819 0.500000i
\(13\) 5.84096i 1.61999i −0.586436 0.809996i \(-0.699469\pi\)
0.586436 0.809996i \(-0.300531\pi\)
\(14\) 4.37228 + 5.04868i 1.16854 + 1.34932i
\(15\) 0 0
\(16\) 6.37228 1.59307
\(17\) 1.37228 0.332827 0.166414 0.986056i \(-0.446781\pi\)
0.166414 + 0.986056i \(0.446781\pi\)
\(18\) 3.37228 + 6.78073i 0.794854 + 1.59823i
\(19\) 3.46410i 0.794719i −0.917663 0.397360i \(-0.869927\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) 0 0
\(21\) −2.68614 + 3.71277i −0.586164 + 0.810192i
\(22\) 2.00000 0.426401
\(23\) 1.87953i 0.391909i 0.980613 + 0.195954i \(0.0627804\pi\)
−0.980613 + 0.195954i \(0.937220\pi\)
\(24\) 2.37228 + 10.0974i 0.484240 + 2.06111i
\(25\) 0 0
\(26\) 14.7446 2.89165
\(27\) −4.00000 + 3.31662i −0.769800 + 0.638285i
\(28\) −8.74456 + 7.57301i −1.65257 + 1.43117i
\(29\) 4.25639i 0.790392i −0.918597 0.395196i \(-0.870677\pi\)
0.918597 0.395196i \(-0.129323\pi\)
\(30\) 0 0
\(31\) 3.46410i 0.622171i 0.950382 + 0.311086i \(0.100693\pi\)
−0.950382 + 0.311086i \(0.899307\pi\)
\(32\) 4.10891i 0.726360i
\(33\) 0.313859 + 1.33591i 0.0546359 + 0.232552i
\(34\) 3.46410i 0.594089i
\(35\) 0 0
\(36\) −11.7446 + 5.84096i −1.95743 + 0.973494i
\(37\) −4.74456 −0.780001 −0.390001 0.920815i \(-0.627525\pi\)
−0.390001 + 0.920815i \(0.627525\pi\)
\(38\) 8.74456 1.41856
\(39\) 2.31386 + 9.84868i 0.370514 + 1.57705i
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) −9.37228 6.78073i −1.44617 1.04629i
\(43\) 6.74456 1.02854 0.514268 0.857629i \(-0.328064\pi\)
0.514268 + 0.857629i \(0.328064\pi\)
\(44\) 3.46410i 0.522233i
\(45\) 0 0
\(46\) −4.74456 −0.699548
\(47\) 7.37228 1.07536 0.537679 0.843150i \(-0.319301\pi\)
0.537679 + 0.843150i \(0.319301\pi\)
\(48\) −10.7446 + 2.52434i −1.55084 + 0.364357i
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) −2.31386 + 0.543620i −0.324005 + 0.0761221i
\(52\) 25.5383i 3.54153i
\(53\) 8.51278i 1.16932i −0.811278 0.584660i \(-0.801228\pi\)
0.811278 0.584660i \(-0.198772\pi\)
\(54\) −8.37228 10.0974i −1.13932 1.37408i
\(55\) 0 0
\(56\) −10.3723 11.9769i −1.38605 1.60048i
\(57\) 1.37228 + 5.84096i 0.181763 + 0.773654i
\(58\) 10.7446 1.41083
\(59\) 2.74456 0.357312 0.178656 0.983912i \(-0.442825\pi\)
0.178656 + 0.983912i \(0.442825\pi\)
\(60\) 0 0
\(61\) 6.92820i 0.887066i 0.896258 + 0.443533i \(0.146275\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) −8.74456 −1.11056
\(63\) 3.05842 7.32435i 0.385325 0.922781i
\(64\) 2.37228 0.296535
\(65\) 0 0
\(66\) −3.37228 + 0.792287i −0.415099 + 0.0975238i
\(67\) 6.74456 0.823979 0.411990 0.911188i \(-0.364834\pi\)
0.411990 + 0.911188i \(0.364834\pi\)
\(68\) −6.00000 −0.727607
\(69\) −0.744563 3.16915i −0.0896348 0.381521i
\(70\) 0 0
\(71\) 13.5615i 1.60945i −0.593649 0.804724i \(-0.702313\pi\)
0.593649 0.804724i \(-0.297687\pi\)
\(72\) −8.00000 16.0858i −0.942809 1.89573i
\(73\) 6.92820i 0.810885i −0.914121 0.405442i \(-0.867117\pi\)
0.914121 0.405442i \(-0.132883\pi\)
\(74\) 11.9769i 1.39228i
\(75\) 0 0
\(76\) 15.1460i 1.73737i
\(77\) −1.37228 1.58457i −0.156386 0.180579i
\(78\) −24.8614 + 5.84096i −2.81500 + 0.661359i
\(79\) 3.37228 0.379411 0.189706 0.981841i \(-0.439247\pi\)
0.189706 + 0.981841i \(0.439247\pi\)
\(80\) 0 0
\(81\) 5.43070 7.17687i 0.603411 0.797430i
\(82\) 15.1460i 1.67260i
\(83\) −5.48913 −0.602510 −0.301255 0.953544i \(-0.597406\pi\)
−0.301255 + 0.953544i \(0.597406\pi\)
\(84\) 11.7446 16.2333i 1.28144 1.77119i
\(85\) 0 0
\(86\) 17.0256i 1.83591i
\(87\) 1.68614 + 7.17687i 0.180773 + 0.769441i
\(88\) −4.74456 −0.505772
\(89\) 3.25544 0.345076 0.172538 0.985003i \(-0.444803\pi\)
0.172538 + 0.985003i \(0.444803\pi\)
\(90\) 0 0
\(91\) −10.1168 11.6819i −1.06053 1.22460i
\(92\) 8.21782i 0.856767i
\(93\) −1.37228 5.84096i −0.142299 0.605680i
\(94\) 18.6101i 1.91949i
\(95\) 0 0
\(96\) −1.62772 6.92820i −0.166128 0.707107i
\(97\) 1.08724i 0.110393i 0.998476 + 0.0551963i \(0.0175785\pi\)
−0.998476 + 0.0551963i \(0.982422\pi\)
\(98\) 17.4891 + 2.52434i 1.76667 + 0.254997i
\(99\) −1.05842 2.12819i −0.106375 0.213892i
\(100\) 0 0
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) −1.37228 5.84096i −0.135876 0.578341i
\(103\) 16.2333i 1.59951i 0.600326 + 0.799756i \(0.295038\pi\)
−0.600326 + 0.799756i \(0.704962\pi\)
\(104\) −34.9783 −3.42990
\(105\) 0 0
\(106\) 21.4891 2.08721
\(107\) 6.63325i 0.641260i 0.947204 + 0.320630i \(0.103895\pi\)
−0.947204 + 0.320630i \(0.896105\pi\)
\(108\) 17.4891 14.5012i 1.68289 1.39538i
\(109\) 0.116844 0.0111916 0.00559581 0.999984i \(-0.498219\pi\)
0.00559581 + 0.999984i \(0.498219\pi\)
\(110\) 0 0
\(111\) 8.00000 1.87953i 0.759326 0.178397i
\(112\) 12.7446 11.0371i 1.20425 1.04291i
\(113\) 10.0974i 0.949879i 0.880018 + 0.474939i \(0.157530\pi\)
−0.880018 + 0.474939i \(0.842470\pi\)
\(114\) −14.7446 + 3.46410i −1.38095 + 0.324443i
\(115\) 0 0
\(116\) 18.6101i 1.72791i
\(117\) −7.80298 15.6896i −0.721386 1.45051i
\(118\) 6.92820i 0.637793i
\(119\) 2.74456 2.37686i 0.251594 0.217886i
\(120\) 0 0
\(121\) 10.3723 0.942935
\(122\) −17.4891 −1.58339
\(123\) 10.1168 2.37686i 0.912205 0.214314i
\(124\) 15.1460i 1.36015i
\(125\) 0 0
\(126\) 18.4891 + 7.72049i 1.64714 + 0.687796i
\(127\) −10.7446 −0.953426 −0.476713 0.879059i \(-0.658172\pi\)
−0.476713 + 0.879059i \(0.658172\pi\)
\(128\) 14.2063i 1.25567i
\(129\) −11.3723 + 2.67181i −1.00127 + 0.235240i
\(130\) 0 0
\(131\) −17.4891 −1.52803 −0.764016 0.645197i \(-0.776775\pi\)
−0.764016 + 0.645197i \(0.776775\pi\)
\(132\) −1.37228 5.84096i −0.119442 0.508391i
\(133\) −6.00000 6.92820i −0.520266 0.600751i
\(134\) 17.0256i 1.47078i
\(135\) 0 0
\(136\) 8.21782i 0.704673i
\(137\) 13.2665i 1.13343i −0.823913 0.566717i \(-0.808213\pi\)
0.823913 0.566717i \(-0.191787\pi\)
\(138\) 8.00000 1.87953i 0.681005 0.159996i
\(139\) 1.28962i 0.109384i −0.998503 0.0546921i \(-0.982582\pi\)
0.998503 0.0546921i \(-0.0174177\pi\)
\(140\) 0 0
\(141\) −12.4307 + 2.92048i −1.04685 + 0.245949i
\(142\) 34.2337 2.87283
\(143\) −4.62772 −0.386989
\(144\) 17.1168 8.51278i 1.42640 0.709398i
\(145\) 0 0
\(146\) 17.4891 1.44741
\(147\) 1.05842 + 12.0781i 0.0872972 + 0.996182i
\(148\) 20.7446 1.70519
\(149\) 10.0974i 0.827207i −0.910457 0.413604i \(-0.864270\pi\)
0.910457 0.413604i \(-0.135730\pi\)
\(150\) 0 0
\(151\) 3.37228 0.274432 0.137216 0.990541i \(-0.456184\pi\)
0.137216 + 0.990541i \(0.456184\pi\)
\(152\) −20.7446 −1.68261
\(153\) 3.68614 1.83324i 0.298007 0.148209i
\(154\) 4.00000 3.46410i 0.322329 0.279145i
\(155\) 0 0
\(156\) −10.1168 43.0612i −0.809996 3.44766i
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 8.51278i 0.677240i
\(159\) 3.37228 + 14.3537i 0.267439 + 1.13833i
\(160\) 0 0
\(161\) 3.25544 + 3.75906i 0.256564 + 0.296255i
\(162\) 18.1168 + 13.7089i 1.42339 + 1.07708i
\(163\) −8.00000 −0.626608 −0.313304 0.949653i \(-0.601436\pi\)
−0.313304 + 0.949653i \(0.601436\pi\)
\(164\) 26.2337 2.04851
\(165\) 0 0
\(166\) 13.8564i 1.07547i
\(167\) 22.1168 1.71145 0.855726 0.517429i \(-0.173111\pi\)
0.855726 + 0.517429i \(0.173111\pi\)
\(168\) 22.2337 + 16.0858i 1.71537 + 1.24105i
\(169\) −21.1168 −1.62437
\(170\) 0 0
\(171\) −4.62772 9.30506i −0.353890 0.711576i
\(172\) −29.4891 −2.24852
\(173\) −16.1168 −1.22534 −0.612670 0.790338i \(-0.709905\pi\)
−0.612670 + 0.790338i \(0.709905\pi\)
\(174\) −18.1168 + 4.25639i −1.37343 + 0.322676i
\(175\) 0 0
\(176\) 5.04868i 0.380558i
\(177\) −4.62772 + 1.08724i −0.347841 + 0.0817220i
\(178\) 8.21782i 0.615952i
\(179\) 6.63325i 0.495792i −0.968787 0.247896i \(-0.920261\pi\)
0.968787 0.247896i \(-0.0797392\pi\)
\(180\) 0 0
\(181\) 18.6101i 1.38328i −0.722242 0.691640i \(-0.756889\pi\)
0.722242 0.691640i \(-0.243111\pi\)
\(182\) 29.4891 25.5383i 2.18588 1.89303i
\(183\) −2.74456 11.6819i −0.202884 0.863553i
\(184\) 11.2554 0.829762
\(185\) 0 0
\(186\) 14.7446 3.46410i 1.08112 0.254000i
\(187\) 1.08724i 0.0795069i
\(188\) −32.2337 −2.35088
\(189\) −2.25544 + 13.5615i −0.164059 + 0.986451i
\(190\) 0 0
\(191\) 15.6434i 1.13191i 0.824435 + 0.565957i \(0.191493\pi\)
−0.824435 + 0.565957i \(0.808507\pi\)
\(192\) −4.00000 + 0.939764i −0.288675 + 0.0678216i
\(193\) −22.2337 −1.60042 −0.800208 0.599723i \(-0.795278\pi\)
−0.800208 + 0.599723i \(0.795278\pi\)
\(194\) −2.74456 −0.197048
\(195\) 0 0
\(196\) −4.37228 + 30.2921i −0.312306 + 2.16372i
\(197\) 22.3692i 1.59374i −0.604152 0.796869i \(-0.706488\pi\)
0.604152 0.796869i \(-0.293512\pi\)
\(198\) 5.37228 2.67181i 0.381791 0.189878i
\(199\) 12.9715i 0.919528i 0.888041 + 0.459764i \(0.152066\pi\)
−0.888041 + 0.459764i \(0.847934\pi\)
\(200\) 0 0
\(201\) −11.3723 + 2.67181i −0.802139 + 0.188455i
\(202\) 15.1460i 1.06567i
\(203\) −7.37228 8.51278i −0.517433 0.597480i
\(204\) 10.1168 2.37686i 0.708321 0.166414i
\(205\) 0 0
\(206\) −40.9783 −2.85509
\(207\) 2.51087 + 5.04868i 0.174518 + 0.350907i
\(208\) 37.2203i 2.58076i
\(209\) −2.74456 −0.189845
\(210\) 0 0
\(211\) 6.11684 0.421101 0.210550 0.977583i \(-0.432474\pi\)
0.210550 + 0.977583i \(0.432474\pi\)
\(212\) 37.2203i 2.55630i
\(213\) 5.37228 + 22.8665i 0.368103 + 1.56679i
\(214\) −16.7446 −1.14463
\(215\) 0 0
\(216\) 19.8614 + 23.9538i 1.35140 + 1.62985i
\(217\) 6.00000 + 6.92820i 0.407307 + 0.470317i
\(218\) 0.294954i 0.0199768i
\(219\) 2.74456 + 11.6819i 0.185460 + 0.789391i
\(220\) 0 0
\(221\) 8.01544i 0.539177i
\(222\) 4.74456 + 20.1947i 0.318434 + 1.35538i
\(223\) 20.9870i 1.40539i −0.711490 0.702696i \(-0.751979\pi\)
0.711490 0.702696i \(-0.248021\pi\)
\(224\) 7.11684 + 8.21782i 0.475514 + 0.549076i
\(225\) 0 0
\(226\) −25.4891 −1.69551
\(227\) 15.6060 1.03580 0.517902 0.855440i \(-0.326713\pi\)
0.517902 + 0.855440i \(0.326713\pi\)
\(228\) −6.00000 25.5383i −0.397360 1.69132i
\(229\) 4.75372i 0.314135i −0.987588 0.157067i \(-0.949796\pi\)
0.987588 0.157067i \(-0.0502040\pi\)
\(230\) 0 0
\(231\) 2.94158 + 2.12819i 0.193542 + 0.140025i
\(232\) −25.4891 −1.67344
\(233\) 3.75906i 0.246264i −0.992390 0.123132i \(-0.960706\pi\)
0.992390 0.123132i \(-0.0392938\pi\)
\(234\) 39.6060 19.6974i 2.58912 1.28766i
\(235\) 0 0
\(236\) −12.0000 −0.781133
\(237\) −5.68614 + 1.33591i −0.369355 + 0.0867765i
\(238\) 6.00000 + 6.92820i 0.388922 + 0.449089i
\(239\) 15.6434i 1.01188i 0.862567 + 0.505942i \(0.168855\pi\)
−0.862567 + 0.505942i \(0.831145\pi\)
\(240\) 0 0
\(241\) 23.3639i 1.50500i 0.658593 + 0.752499i \(0.271152\pi\)
−0.658593 + 0.752499i \(0.728848\pi\)
\(242\) 26.1831i 1.68312i
\(243\) −6.31386 + 14.2525i −0.405034 + 0.914302i
\(244\) 30.2921i 1.93925i
\(245\) 0 0
\(246\) 6.00000 + 25.5383i 0.382546 + 1.62826i
\(247\) −20.2337 −1.28744
\(248\) 20.7446 1.31728
\(249\) 9.25544 2.17448i 0.586540 0.137802i
\(250\) 0 0
\(251\) 17.4891 1.10390 0.551952 0.833876i \(-0.313883\pi\)
0.551952 + 0.833876i \(0.313883\pi\)
\(252\) −13.3723 + 32.0241i −0.842375 + 2.01733i
\(253\) 1.48913 0.0936205
\(254\) 27.1229i 1.70184i
\(255\) 0 0
\(256\) −31.1168 −1.94480
\(257\) −23.4891 −1.46521 −0.732606 0.680653i \(-0.761696\pi\)
−0.732606 + 0.680653i \(0.761696\pi\)
\(258\) −6.74456 28.7075i −0.419898 1.78725i
\(259\) −9.48913 + 8.21782i −0.589626 + 0.510631i
\(260\) 0 0
\(261\) −5.68614 11.4333i −0.351963 0.707701i
\(262\) 44.1485i 2.72750i
\(263\) 13.5615i 0.836235i 0.908393 + 0.418118i \(0.137310\pi\)
−0.908393 + 0.418118i \(0.862690\pi\)
\(264\) 8.00000 1.87953i 0.492366 0.115677i
\(265\) 0 0
\(266\) 17.4891 15.1460i 1.07233 0.928662i
\(267\) −5.48913 + 1.28962i −0.335929 + 0.0789235i
\(268\) −29.4891 −1.80134
\(269\) −8.74456 −0.533165 −0.266583 0.963812i \(-0.585895\pi\)
−0.266583 + 0.963812i \(0.585895\pi\)
\(270\) 0 0
\(271\) 15.1460i 0.920056i 0.887905 + 0.460028i \(0.152161\pi\)
−0.887905 + 0.460028i \(0.847839\pi\)
\(272\) 8.74456 0.530217
\(273\) 21.6861 + 15.6896i 1.31250 + 0.949581i
\(274\) 33.4891 2.02315
\(275\) 0 0
\(276\) 3.25544 + 13.8564i 0.195954 + 0.834058i
\(277\) 6.23369 0.374546 0.187273 0.982308i \(-0.440035\pi\)
0.187273 + 0.982308i \(0.440035\pi\)
\(278\) 3.25544 0.195248
\(279\) 4.62772 + 9.30506i 0.277054 + 0.557080i
\(280\) 0 0
\(281\) 4.84630i 0.289106i 0.989497 + 0.144553i \(0.0461744\pi\)
−0.989497 + 0.144553i \(0.953826\pi\)
\(282\) −7.37228 31.3793i −0.439013 1.86861i
\(283\) 9.30506i 0.553129i 0.960995 + 0.276564i \(0.0891959\pi\)
−0.960995 + 0.276564i \(0.910804\pi\)
\(284\) 59.2945i 3.51848i
\(285\) 0 0
\(286\) 11.6819i 0.690767i
\(287\) −12.0000 + 10.3923i −0.708338 + 0.613438i
\(288\) 5.48913 + 11.0371i 0.323450 + 0.650368i
\(289\) −15.1168 −0.889226
\(290\) 0 0
\(291\) −0.430703 1.83324i −0.0252483 0.107466i
\(292\) 30.2921i 1.77271i
\(293\) 28.1168 1.64260 0.821302 0.570494i \(-0.193248\pi\)
0.821302 + 0.570494i \(0.193248\pi\)
\(294\) −30.4891 + 2.67181i −1.77816 + 0.155823i
\(295\) 0 0
\(296\) 28.4125i 1.65144i
\(297\) 2.62772 + 3.16915i 0.152476 + 0.183893i
\(298\) 25.4891 1.47655
\(299\) 10.9783 0.634889
\(300\) 0 0
\(301\) 13.4891 11.6819i 0.777500 0.673335i
\(302\) 8.51278i 0.489855i
\(303\) −10.1168 + 2.37686i −0.581198 + 0.136547i
\(304\) 22.0742i 1.26604i
\(305\) 0 0
\(306\) 4.62772 + 9.30506i 0.264549 + 0.531935i
\(307\) 7.13058i 0.406964i 0.979079 + 0.203482i \(0.0652258\pi\)
−0.979079 + 0.203482i \(0.934774\pi\)
\(308\) 6.00000 + 6.92820i 0.341882 + 0.394771i
\(309\) −6.43070 27.3716i −0.365830 1.55711i
\(310\) 0 0
\(311\) 20.2337 1.14735 0.573674 0.819084i \(-0.305518\pi\)
0.573674 + 0.819084i \(0.305518\pi\)
\(312\) 58.9783 13.8564i 3.33899 0.784465i
\(313\) 24.4511i 1.38206i 0.722827 + 0.691029i \(0.242842\pi\)
−0.722827 + 0.691029i \(0.757158\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −14.7446 −0.829446
\(317\) 8.51278i 0.478125i −0.971004 0.239063i \(-0.923160\pi\)
0.971004 0.239063i \(-0.0768401\pi\)
\(318\) −36.2337 + 8.51278i −2.03188 + 0.477373i
\(319\) −3.37228 −0.188812
\(320\) 0 0
\(321\) −2.62772 11.1846i −0.146665 0.624263i
\(322\) −9.48913 + 8.21782i −0.528808 + 0.457961i
\(323\) 4.75372i 0.264504i
\(324\) −23.7446 + 31.3793i −1.31914 + 1.74329i
\(325\) 0 0
\(326\) 20.1947i 1.11848i
\(327\) −0.197015 + 0.0462870i −0.0108950 + 0.00255968i
\(328\) 35.9306i 1.98394i
\(329\) 14.7446 12.7692i 0.812894 0.703987i
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 24.0000 1.31717
\(333\) −12.7446 + 6.33830i −0.698398 + 0.347336i
\(334\) 55.8304i 3.05490i
\(335\) 0 0
\(336\) −17.1168 + 23.6588i −0.933800 + 1.29069i
\(337\) 18.2337 0.993252 0.496626 0.867965i \(-0.334572\pi\)
0.496626 + 0.867965i \(0.334572\pi\)
\(338\) 53.3060i 2.89947i
\(339\) −4.00000 17.0256i −0.217250 0.924701i
\(340\) 0 0
\(341\) 2.74456 0.148626
\(342\) 23.4891 11.6819i 1.27015 0.631686i
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 40.3894i 2.17765i
\(345\) 0 0
\(346\) 40.6844i 2.18720i
\(347\) 18.3152i 0.983210i 0.870818 + 0.491605i \(0.163590\pi\)
−0.870818 + 0.491605i \(0.836410\pi\)
\(348\) −7.37228 31.3793i −0.395196 1.68211i
\(349\) 4.75372i 0.254461i 0.991873 + 0.127230i \(0.0406088\pi\)
−0.991873 + 0.127230i \(0.959391\pi\)
\(350\) 0 0
\(351\) 19.3723 + 23.3639i 1.03402 + 1.24707i
\(352\) 3.25544 0.173515
\(353\) −7.88316 −0.419578 −0.209789 0.977747i \(-0.567278\pi\)
−0.209789 + 0.977747i \(0.567278\pi\)
\(354\) −2.74456 11.6819i −0.145872 0.620887i
\(355\) 0 0
\(356\) −14.2337 −0.754384
\(357\) −3.68614 + 5.09496i −0.195091 + 0.269654i
\(358\) 16.7446 0.884978
\(359\) 9.80240i 0.517351i 0.965964 + 0.258675i \(0.0832860\pi\)
−0.965964 + 0.258675i \(0.916714\pi\)
\(360\) 0 0
\(361\) 7.00000 0.368421
\(362\) 46.9783 2.46912
\(363\) −17.4891 + 4.10891i −0.917941 + 0.215662i
\(364\) 44.2337 + 51.0767i 2.31848 + 2.67714i
\(365\) 0 0
\(366\) 29.4891 6.92820i 1.54142 0.362143i
\(367\) 25.3360i 1.32253i −0.750154 0.661263i \(-0.770021\pi\)
0.750154 0.661263i \(-0.229979\pi\)
\(368\) 11.9769i 0.624338i
\(369\) −16.1168 + 8.01544i −0.839009 + 0.417267i
\(370\) 0 0
\(371\) −14.7446 17.0256i −0.765500 0.883923i
\(372\) 6.00000 + 25.5383i 0.311086 + 1.32410i
\(373\) 24.7446 1.28122 0.640612 0.767864i \(-0.278681\pi\)
0.640612 + 0.767864i \(0.278681\pi\)
\(374\) 2.74456 0.141918
\(375\) 0 0
\(376\) 44.1485i 2.27678i
\(377\) −24.8614 −1.28043
\(378\) −34.2337 5.69349i −1.76079 0.292841i
\(379\) 1.48913 0.0764912 0.0382456 0.999268i \(-0.487823\pi\)
0.0382456 + 0.999268i \(0.487823\pi\)
\(380\) 0 0
\(381\) 18.1168 4.25639i 0.928154 0.218061i
\(382\) −39.4891 −2.02044
\(383\) 17.4891 0.893653 0.446826 0.894621i \(-0.352554\pi\)
0.446826 + 0.894621i \(0.352554\pi\)
\(384\) −5.62772 23.9538i −0.287188 1.22239i
\(385\) 0 0
\(386\) 56.1253i 2.85670i
\(387\) 18.1168 9.01011i 0.920931 0.458010i
\(388\) 4.75372i 0.241334i
\(389\) 13.7638i 0.697854i −0.937150 0.348927i \(-0.886546\pi\)
0.937150 0.348927i \(-0.113454\pi\)
\(390\) 0 0
\(391\) 2.57924i 0.130438i
\(392\) −41.4891 5.98844i −2.09552 0.302462i
\(393\) 29.4891 6.92820i 1.48753 0.349482i
\(394\) 56.4674 2.84479
\(395\) 0 0
\(396\) 4.62772 + 9.30506i 0.232552 + 0.467597i
\(397\) 3.66648i 0.184015i −0.995758 0.0920077i \(-0.970672\pi\)
0.995758 0.0920077i \(-0.0293284\pi\)
\(398\) −32.7446 −1.64134
\(399\) 12.8614 + 9.30506i 0.643876 + 0.465836i
\(400\) 0 0
\(401\) 2.67181i 0.133424i 0.997772 + 0.0667120i \(0.0212509\pi\)
−0.997772 + 0.0667120i \(0.978749\pi\)
\(402\) −6.74456 28.7075i −0.336388 1.43180i
\(403\) 20.2337 1.00791
\(404\) −26.2337 −1.30517
\(405\) 0 0
\(406\) 21.4891 18.6101i 1.06649 0.923605i
\(407\) 3.75906i 0.186329i
\(408\) 3.25544 + 13.8564i 0.161168 + 0.685994i
\(409\) 35.0458i 1.73290i −0.499262 0.866451i \(-0.666396\pi\)
0.499262 0.866451i \(-0.333604\pi\)
\(410\) 0 0
\(411\) 5.25544 + 22.3692i 0.259232 + 1.10339i
\(412\) 70.9764i 3.49676i
\(413\) 5.48913 4.75372i 0.270102 0.233915i
\(414\) −12.7446 + 6.33830i −0.626361 + 0.311510i
\(415\) 0 0
\(416\) 24.0000 1.17670
\(417\) 0.510875 + 2.17448i 0.0250176 + 0.106485i
\(418\) 6.92820i 0.338869i
\(419\) −2.74456 −0.134081 −0.0670403 0.997750i \(-0.521356\pi\)
−0.0670403 + 0.997750i \(0.521356\pi\)
\(420\) 0 0
\(421\) −25.6060 −1.24796 −0.623979 0.781441i \(-0.714485\pi\)
−0.623979 + 0.781441i \(0.714485\pi\)
\(422\) 15.4410i 0.751655i
\(423\) 19.8030 9.84868i 0.962854 0.478859i
\(424\) −50.9783 −2.47572
\(425\) 0 0
\(426\) −57.7228 + 13.5615i −2.79668 + 0.657055i
\(427\) 12.0000 + 13.8564i 0.580721 + 0.670559i
\(428\) 29.0024i 1.40189i
\(429\) 7.80298 1.83324i 0.376732 0.0885097i
\(430\) 0 0
\(431\) 31.6742i 1.52569i 0.646579 + 0.762847i \(0.276199\pi\)
−0.646579 + 0.762847i \(0.723801\pi\)
\(432\) −25.4891 + 21.1345i −1.22635 + 1.01683i
\(433\) 2.57924i 0.123950i 0.998078 + 0.0619752i \(0.0197400\pi\)
−0.998078 + 0.0619752i \(0.980260\pi\)
\(434\) −17.4891 + 15.1460i −0.839505 + 0.727033i
\(435\) 0 0
\(436\) −0.510875 −0.0244665
\(437\) 6.51087 0.311457
\(438\) −29.4891 + 6.92820i −1.40904 + 0.331042i
\(439\) 1.28962i 0.0615502i 0.999526 + 0.0307751i \(0.00979757\pi\)
−0.999526 + 0.0307751i \(0.990202\pi\)
\(440\) 0 0
\(441\) −6.56930 19.9460i −0.312824 0.949811i
\(442\) 20.2337 0.962418
\(443\) 6.63325i 0.315155i 0.987507 + 0.157578i \(0.0503684\pi\)
−0.987507 + 0.157578i \(0.949632\pi\)
\(444\) −34.9783 + 8.21782i −1.65999 + 0.390001i
\(445\) 0 0
\(446\) 52.9783 2.50859
\(447\) 4.00000 + 17.0256i 0.189194 + 0.805281i
\(448\) 4.74456 4.10891i 0.224160 0.194128i
\(449\) 28.2101i 1.33132i 0.746256 + 0.665660i \(0.231850\pi\)
−0.746256 + 0.665660i \(0.768150\pi\)
\(450\) 0 0
\(451\) 4.75372i 0.223844i
\(452\) 44.1485i 2.07657i
\(453\) −5.68614 + 1.33591i −0.267158 + 0.0627664i
\(454\) 39.3947i 1.84889i
\(455\) 0 0
\(456\) 34.9783 8.21782i 1.63801 0.384835i
\(457\) 32.9783 1.54266 0.771329 0.636437i \(-0.219592\pi\)
0.771329 + 0.636437i \(0.219592\pi\)
\(458\) 12.0000 0.560723
\(459\) −5.48913 + 4.55134i −0.256210 + 0.212438i
\(460\) 0 0
\(461\) −8.74456 −0.407275 −0.203637 0.979046i \(-0.565276\pi\)
−0.203637 + 0.979046i \(0.565276\pi\)
\(462\) −5.37228 + 7.42554i −0.249941 + 0.345467i
\(463\) −36.4674 −1.69478 −0.847391 0.530969i \(-0.821828\pi\)
−0.847391 + 0.530969i \(0.821828\pi\)
\(464\) 27.1229i 1.25915i
\(465\) 0 0
\(466\) 9.48913 0.439575
\(467\) 13.8832 0.642436 0.321218 0.947005i \(-0.395908\pi\)
0.321218 + 0.947005i \(0.395908\pi\)
\(468\) 34.1168 + 68.5996i 1.57705 + 3.17102i
\(469\) 13.4891 11.6819i 0.622870 0.539421i
\(470\) 0 0
\(471\) 0 0
\(472\) 16.4356i 0.756512i
\(473\) 5.34363i 0.245700i
\(474\) −3.37228 14.3537i −0.154894 0.659289i
\(475\) 0 0
\(476\) −12.0000 + 10.3923i −0.550019 + 0.476331i
\(477\) −11.3723 22.8665i −0.520701 1.04699i
\(478\) −39.4891 −1.80619
\(479\) 18.5109 0.845783 0.422892 0.906180i \(-0.361015\pi\)
0.422892 + 0.906180i \(0.361015\pi\)
\(480\) 0 0
\(481\) 27.7128i 1.26360i
\(482\) −58.9783 −2.68639
\(483\) −6.97825 5.04868i −0.317521 0.229723i
\(484\) −45.3505 −2.06139
\(485\) 0 0
\(486\) −35.9783 15.9383i −1.63201 0.722977i
\(487\) −14.5109 −0.657550 −0.328775 0.944408i \(-0.606636\pi\)
−0.328775 + 0.944408i \(0.606636\pi\)
\(488\) 41.4891 1.87812
\(489\) 13.4891 3.16915i 0.609999 0.143314i
\(490\) 0 0
\(491\) 10.8896i 0.491442i 0.969341 + 0.245721i \(0.0790248\pi\)
−0.969341 + 0.245721i \(0.920975\pi\)
\(492\) −44.2337 + 10.3923i −1.99421 + 0.468521i
\(493\) 5.84096i 0.263064i
\(494\) 51.0767i 2.29805i
\(495\) 0 0
\(496\) 22.0742i 0.991162i
\(497\) −23.4891 27.1229i −1.05363 1.21663i
\(498\) 5.48913 + 23.3639i 0.245974 + 1.04696i
\(499\) −10.3505 −0.463353 −0.231677 0.972793i \(-0.574421\pi\)
−0.231677 + 0.972793i \(0.574421\pi\)
\(500\) 0 0
\(501\) −37.2921 + 8.76144i −1.66609 + 0.391432i
\(502\) 44.1485i 1.97044i
\(503\) 27.6060 1.23089 0.615445 0.788180i \(-0.288976\pi\)
0.615445 + 0.788180i \(0.288976\pi\)
\(504\) −43.8614 18.3152i −1.95374 0.815823i
\(505\) 0 0
\(506\) 3.75906i 0.167110i
\(507\) 35.6060 8.36530i 1.58132 0.371516i
\(508\) 46.9783 2.08432
\(509\) −38.2337 −1.69468 −0.847339 0.531052i \(-0.821797\pi\)
−0.847339 + 0.531052i \(0.821797\pi\)
\(510\) 0 0
\(511\) −12.0000 13.8564i −0.530849 0.612971i
\(512\) 50.1369i 2.21576i
\(513\) 11.4891 + 13.8564i 0.507257 + 0.611775i
\(514\) 59.2945i 2.61537i
\(515\) 0 0
\(516\) 49.7228 11.6819i 2.18892 0.514268i
\(517\) 5.84096i 0.256885i
\(518\) −20.7446 23.9538i −0.911464 1.05247i
\(519\) 27.1753 6.38458i 1.19286 0.280252i
\(520\) 0 0
\(521\) 34.4674 1.51004 0.755022 0.655700i \(-0.227626\pi\)
0.755022 + 0.655700i \(0.227626\pi\)
\(522\) 28.8614 14.3537i 1.26323 0.628246i
\(523\) 10.3923i 0.454424i −0.973845 0.227212i \(-0.927039\pi\)
0.973845 0.227212i \(-0.0729610\pi\)
\(524\) 76.4674 3.34049
\(525\) 0 0
\(526\) −34.2337 −1.49266
\(527\) 4.75372i 0.207075i
\(528\) 2.00000 + 8.51278i 0.0870388 + 0.370471i
\(529\) 19.4674 0.846408
\(530\) 0 0
\(531\) 7.37228 3.66648i 0.319930 0.159112i
\(532\) 26.2337 + 30.2921i 1.13737 + 1.31333i
\(533\) 35.0458i 1.51800i
\(534\) −3.25544 13.8564i −0.140877 0.599625i
\(535\) 0 0
\(536\) 40.3894i 1.74456i
\(537\) 2.62772 + 11.1846i 0.113394 + 0.482651i
\(538\) 22.0742i 0.951688i
\(539\) −5.48913 0.792287i −0.236433 0.0341262i
\(540\) 0 0
\(541\) 18.6277 0.800868 0.400434 0.916326i \(-0.368859\pi\)
0.400434 + 0.916326i \(0.368859\pi\)
\(542\) −38.2337 −1.64228
\(543\) 7.37228 + 31.3793i 0.316375 + 1.34661i
\(544\) 5.63858i 0.241752i
\(545\) 0 0
\(546\) −39.6060 + 54.7431i −1.69498 + 2.34279i
\(547\) −42.9783 −1.83762 −0.918809 0.394703i \(-0.870847\pi\)
−0.918809 + 0.394703i \(0.870847\pi\)
\(548\) 58.0049i 2.47785i
\(549\) 9.25544 + 18.6101i 0.395012 + 0.794261i
\(550\) 0 0
\(551\) −14.7446 −0.628139
\(552\) −18.9783 + 4.45877i −0.807768 + 0.189778i
\(553\) 6.74456 5.84096i 0.286808 0.248383i
\(554\) 15.7359i 0.668556i
\(555\) 0 0
\(556\) 5.63858i 0.239129i
\(557\) 30.8820i 1.30851i 0.756274 + 0.654255i \(0.227018\pi\)
−0.756274 + 0.654255i \(0.772982\pi\)
\(558\) −23.4891 + 11.6819i −0.994374 + 0.494535i
\(559\) 39.3947i 1.66622i
\(560\) 0 0
\(561\) 0.430703 + 1.83324i 0.0181843 + 0.0773995i
\(562\) −12.2337 −0.516047
\(563\) −5.48913 −0.231339 −0.115670 0.993288i \(-0.536901\pi\)
−0.115670 + 0.993288i \(0.536901\pi\)
\(564\) 54.3505 12.7692i 2.28857 0.537679i
\(565\) 0 0
\(566\) −23.4891 −0.987322
\(567\) −1.56930 23.7600i −0.0659043 0.997826i
\(568\) −81.2119 −3.40758
\(569\) 10.6873i 0.448033i 0.974585 + 0.224017i \(0.0719170\pi\)
−0.974585 + 0.224017i \(0.928083\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 20.2337 0.846013
\(573\) −6.19702 26.3769i −0.258884 1.10191i
\(574\) −26.2337 30.2921i −1.09497 1.26437i
\(575\) 0 0
\(576\) 6.37228 3.16915i 0.265512 0.132048i
\(577\) 12.7692i 0.531587i 0.964030 + 0.265794i \(0.0856340\pi\)
−0.964030 + 0.265794i \(0.914366\pi\)
\(578\) 38.1600i 1.58725i
\(579\) 37.4891 8.80773i 1.55799 0.366037i
\(580\) 0 0
\(581\) −10.9783 + 9.50744i −0.455455 + 0.394435i
\(582\) 4.62772 1.08724i 0.191825 0.0450676i
\(583\) −6.74456 −0.279331
\(584\) −41.4891 −1.71683
\(585\) 0 0
\(586\) 70.9764i 2.93201i
\(587\) 5.48913 0.226560 0.113280 0.993563i \(-0.463864\pi\)
0.113280 + 0.993563i \(0.463864\pi\)
\(588\) −4.62772 52.8087i −0.190844 2.17779i
\(589\) 12.0000 0.494451
\(590\) 0 0
\(591\) 8.86141 + 37.7176i 0.364510 + 1.55149i
\(592\) −30.2337 −1.24260
\(593\) 1.37228 0.0563528 0.0281764 0.999603i \(-0.491030\pi\)
0.0281764 + 0.999603i \(0.491030\pi\)
\(594\) −8.00000 + 6.63325i −0.328244 + 0.272166i
\(595\) 0 0
\(596\) 44.1485i 1.80839i
\(597\) −5.13859 21.8719i −0.210309 0.895155i
\(598\) 27.7128i 1.13326i
\(599\) 1.78695i 0.0730129i 0.999333 + 0.0365065i \(0.0116230\pi\)
−0.999333 + 0.0365065i \(0.988377\pi\)
\(600\) 0 0
\(601\) 2.17448i 0.0886989i 0.999016 + 0.0443495i \(0.0141215\pi\)
−0.999016 + 0.0443495i \(0.985878\pi\)
\(602\) 29.4891 + 34.0511i 1.20189 + 1.38782i
\(603\) 18.1168 9.01011i 0.737775 0.366920i
\(604\) −14.7446 −0.599948
\(605\) 0 0
\(606\) −6.00000 25.5383i −0.243733 1.03742i
\(607\) 20.9870i 0.851836i −0.904762 0.425918i \(-0.859951\pi\)
0.904762 0.425918i \(-0.140049\pi\)
\(608\) 14.2337 0.577252
\(609\) 15.8030 + 11.4333i 0.640369 + 0.463299i
\(610\) 0 0
\(611\) 43.0612i 1.74207i
\(612\) −16.1168 + 8.01544i −0.651485 + 0.324005i
\(613\) 4.51087 0.182193 0.0910963 0.995842i \(-0.470963\pi\)
0.0910963 + 0.995842i \(0.470963\pi\)
\(614\) −18.0000 −0.726421
\(615\) 0 0
\(616\) −9.48913 + 8.21782i −0.382328 + 0.331106i
\(617\) 37.8102i 1.52218i 0.648646 + 0.761090i \(0.275335\pi\)
−0.648646 + 0.761090i \(0.724665\pi\)
\(618\) 69.0951 16.2333i 2.77941 0.652998i
\(619\) 1.28962i 0.0518342i −0.999664 0.0259171i \(-0.991749\pi\)
0.999664 0.0259171i \(-0.00825060\pi\)
\(620\) 0 0
\(621\) −6.23369 7.51811i −0.250149 0.301691i
\(622\) 51.0767i 2.04799i
\(623\) 6.51087 5.63858i 0.260853 0.225905i
\(624\) 14.7446 + 62.7586i 0.590255 + 2.51235i
\(625\) 0 0
\(626\) −61.7228 −2.46694
\(627\) 4.62772 1.08724i 0.184813 0.0434202i
\(628\) 0 0
\(629\) −6.51087 −0.259606
\(630\) 0 0
\(631\) −5.88316 −0.234205 −0.117102 0.993120i \(-0.537361\pi\)
−0.117102 + 0.993120i \(0.537361\pi\)
\(632\) 20.1947i 0.803302i
\(633\) −10.3139 + 2.42315i −0.409939 + 0.0963115i
\(634\) 21.4891 0.853442
\(635\) 0 0
\(636\) −14.7446 62.7586i −0.584660 2.48854i
\(637\) −40.4674 5.84096i −1.60338 0.231427i
\(638\) 8.51278i 0.337024i
\(639\) −18.1168 36.4280i −0.716691 1.44107i
\(640\) 0 0
\(641\) 29.7021i 1.17316i 0.809890 + 0.586582i \(0.199527\pi\)
−0.809890 + 0.586582i \(0.800473\pi\)
\(642\) 28.2337 6.63325i 1.11429 0.261793i
\(643\) 39.5971i 1.56156i −0.624807 0.780779i \(-0.714822\pi\)
0.624807 0.780779i \(-0.285178\pi\)
\(644\) −14.2337 16.4356i −0.560886 0.647655i
\(645\) 0 0
\(646\) 12.0000 0.472134
\(647\) −12.0000 −0.471769 −0.235884 0.971781i \(-0.575799\pi\)
−0.235884 + 0.971781i \(0.575799\pi\)
\(648\) −42.9783 32.5214i −1.68835 1.27756i
\(649\) 2.17448i 0.0853559i
\(650\) 0 0
\(651\) −12.8614 9.30506i −0.504078 0.364694i
\(652\) 34.9783 1.36985
\(653\) 33.0564i 1.29360i 0.762660 + 0.646799i \(0.223893\pi\)
−0.762660 + 0.646799i \(0.776107\pi\)
\(654\) −0.116844 0.497333i −0.00456896 0.0194473i
\(655\) 0 0
\(656\) −38.2337 −1.49277
\(657\) −9.25544 18.6101i −0.361089 0.726050i
\(658\) 32.2337 + 37.2203i 1.25660 + 1.45100i
\(659\) 20.3971i 0.794558i 0.917698 + 0.397279i \(0.130045\pi\)
−0.917698 + 0.397279i \(0.869955\pi\)
\(660\) 0 0
\(661\) 6.92820i 0.269476i −0.990881 0.134738i \(-0.956981\pi\)
0.990881 0.134738i \(-0.0430193\pi\)
\(662\) 10.0974i 0.392445i
\(663\) 3.17527 + 13.5152i 0.123317 + 0.524886i
\(664\) 32.8713i 1.27565i
\(665\) 0 0
\(666\) −16.0000 32.1716i −0.619987 1.24662i
\(667\) 8.00000 0.309761
\(668\) −96.7011 −3.74148
\(669\) 8.31386 + 35.3870i 0.321432 + 1.36814i
\(670\) 0 0
\(671\) 5.48913 0.211905
\(672\) −15.2554 11.0371i −0.588491 0.425766i
\(673\) −22.2337 −0.857046 −0.428523 0.903531i \(-0.640966\pi\)
−0.428523 + 0.903531i \(0.640966\pi\)
\(674\) 46.0280i 1.77293i
\(675\) 0 0
\(676\) 92.3288 3.55111
\(677\) −21.6060 −0.830385 −0.415192 0.909734i \(-0.636286\pi\)
−0.415192 + 0.909734i \(0.636286\pi\)
\(678\) 42.9783 10.0974i 1.65057 0.387786i
\(679\) 1.88316 + 2.17448i 0.0722689 + 0.0834489i
\(680\) 0 0
\(681\) −26.3139 + 6.18220i −1.00835 + 0.236903i
\(682\) 6.92820i 0.265295i
\(683\) 51.7764i 1.98117i −0.136906 0.990584i \(-0.543716\pi\)
0.136906 0.990584i \(-0.456284\pi\)
\(684\) 20.2337 + 40.6844i 0.773654 + 1.55561i
\(685\) 0 0
\(686\) 39.3505 25.2434i 1.50241 0.963797i
\(687\) 1.88316 + 8.01544i 0.0718469 + 0.305808i
\(688\) 42.9783 1.63853
\(689\) −49.7228 −1.89429
\(690\) 0 0
\(691\) 38.5099i 1.46498i −0.680775 0.732492i \(-0.738357\pi\)
0.680775 0.732492i \(-0.261643\pi\)
\(692\) 70.4674 2.67877
\(693\) −5.80298 2.42315i −0.220437 0.0920478i
\(694\) −46.2337 −1.75501
\(695\) 0 0
\(696\) 42.9783 10.0974i 1.62909 0.382739i
\(697\) −8.23369 −0.311873
\(698\) −12.0000 −0.454207
\(699\) 1.48913 + 6.33830i 0.0563239 + 0.239736i
\(700\) 0 0
\(701\) 45.8256i 1.73081i −0.501074 0.865405i \(-0.667061\pi\)
0.501074 0.865405i \(-0.332939\pi\)
\(702\) −58.9783 + 48.9022i −2.22599 + 1.84569i
\(703\) 16.4356i 0.619882i
\(704\) 1.87953i 0.0708374i
\(705\) 0 0
\(706\) 19.8997i 0.748937i
\(707\) 12.0000 10.3923i 0.451306 0.390843i
\(708\) 20.2337 4.75372i 0.760429 0.178656i
\(709\) 24.1168 0.905727 0.452864 0.891580i \(-0.350402\pi\)
0.452864 + 0.891580i \(0.350402\pi\)
\(710\) 0 0
\(711\) 9.05842 4.50506i 0.339717 0.168953i
\(712\) 19.4950i 0.730606i
\(713\) −6.51087 −0.243834
\(714\) −12.8614 9.30506i −0.481326 0.348233i
\(715\) 0 0
\(716\) 29.0024i 1.08387i
\(717\) −6.19702 26.3769i −0.231432 0.985064i
\(718\) −24.7446 −0.923459
\(719\) 40.4674 1.50918 0.754589 0.656197i \(-0.227836\pi\)
0.754589 + 0.656197i \(0.227836\pi\)
\(720\) 0 0
\(721\) 28.1168 + 32.4665i 1.04713 + 1.20912i
\(722\) 17.6704i 0.657623i
\(723\) −9.25544 39.3947i −0.344213 1.46511i
\(724\) 81.3687i 3.02404i
\(725\) 0 0
\(726\) −10.3723 44.1485i −0.384951 1.63850i
\(727\) 3.46410i 0.128476i −0.997935 0.0642382i \(-0.979538\pi\)
0.997935 0.0642382i \(-0.0204617\pi\)
\(728\) −69.9565 + 60.5841i −2.59276 + 2.24540i
\(729\) 5.00000 26.5330i 0.185185 0.982704i
\(730\) 0 0
\(731\) 9.25544 0.342325
\(732\) 12.0000 + 51.0767i 0.443533 + 1.88785i
\(733\) 10.1899i 0.376373i 0.982133 + 0.188187i \(0.0602610\pi\)
−0.982133 + 0.188187i \(0.939739\pi\)
\(734\) 63.9565 2.36068
\(735\) 0 0
\(736\) −7.72281 −0.284667
\(737\) 5.34363i 0.196835i
\(738\) −20.2337 40.6844i −0.744812 1.49761i
\(739\) −8.62772 −0.317376 −0.158688 0.987329i \(-0.550726\pi\)
−0.158688 + 0.987329i \(0.550726\pi\)
\(740\) 0 0
\(741\) 34.1168 8.01544i 1.25331 0.294455i
\(742\) 42.9783 37.2203i 1.57778 1.36640i
\(743\) 36.9253i 1.35466i 0.735680 + 0.677329i \(0.236863\pi\)
−0.735680 + 0.677329i \(0.763137\pi\)
\(744\) −34.9783 + 8.21782i −1.28236 + 0.301280i
\(745\) 0 0
\(746\) 62.4636i 2.28696i
\(747\) −14.7446 + 7.33296i −0.539475 + 0.268299i
\(748\) 4.75372i 0.173813i
\(749\) 11.4891 + 13.2665i 0.419804 + 0.484747i
\(750\) 0 0
\(751\) −22.3505 −0.815582 −0.407791 0.913075i \(-0.633701\pi\)
−0.407791 + 0.913075i \(0.633701\pi\)
\(752\) 46.9783 1.71312
\(753\) −29.4891 + 6.92820i −1.07464 + 0.252478i
\(754\) 62.7586i 2.28553i
\(755\) 0 0
\(756\) 9.86141 59.2945i 0.358656 2.15652i
\(757\) 54.2337 1.97116 0.985578 0.169219i \(-0.0541245\pi\)
0.985578 + 0.169219i \(0.0541245\pi\)
\(758\) 3.75906i 0.136535i
\(759\) −2.51087 + 0.589907i −0.0911390 + 0.0214123i
\(760\) 0 0
\(761\) −26.2337 −0.950970 −0.475485 0.879724i \(-0.657727\pi\)
−0.475485 + 0.879724i \(0.657727\pi\)
\(762\) 10.7446 + 45.7330i 0.389234 + 1.65673i
\(763\) 0.233688 0.202380i 0.00846007 0.00732664i
\(764\) 68.3972i 2.47452i
\(765\) 0 0
\(766\) 44.1485i 1.59515i
\(767\) 16.0309i 0.578842i
\(768\) 52.4674 12.3267i 1.89325 0.444803i
\(769\) 21.1894i 0.764108i 0.924140 + 0.382054i \(0.124783\pi\)
−0.924140 + 0.382054i \(0.875217\pi\)
\(770\) 0 0
\(771\) 39.6060 9.30506i 1.42637 0.335114i
\(772\) 97.2119 3.49873
\(773\) 46.6277 1.67708 0.838541 0.544838i \(-0.183409\pi\)
0.838541 + 0.544838i \(0.183409\pi\)
\(774\) 22.7446 + 45.7330i 0.817536 + 1.64384i
\(775\) 0 0
\(776\) 6.51087 0.233727
\(777\) 12.7446 17.6155i 0.457209 0.631951i
\(778\) 34.7446 1.24565
\(779\) 20.7846i 0.744686i
\(780\) 0 0
\(781\) −10.7446 −0.384471
\(782\) −6.51087 −0.232828
\(783\) 14.1168 + 17.0256i 0.504495 + 0.608444i
\(784\) 6.37228 44.1485i 0.227581 1.57673i
\(785\) 0 0
\(786\) 17.4891 + 74.4405i 0.623816 + 2.65521i
\(787\) 46.5253i 1.65845i 0.558916 + 0.829224i \(0.311217\pi\)
−0.558916 + 0.829224i \(0.688783\pi\)
\(788\) 97.8044i 3.48414i
\(789\) −5.37228 22.8665i −0.191258 0.814070i
\(790\) 0 0
\(791\) 17.4891 + 20.1947i 0.621842 + 0.718041i
\(792\) −12.7446 + 6.33830i −0.452858 + 0.225222i
\(793\) 40.4674 1.43704
\(794\) 9.25544 0.328463
\(795\) 0 0
\(796\) 56.7152i 2.01022i
\(797\) 42.8614 1.51823 0.759114 0.650957i \(-0.225632\pi\)
0.759114 + 0.650957i \(0.225632\pi\)
\(798\) −23.4891 + 32.4665i −0.831506 + 1.14930i
\(799\) 10.1168 0.357908
\(800\) 0 0
\(801\) 8.74456 4.34896i 0.308974 0.153663i
\(802\) −6.74456 −0.238159
\(803\) −5.48913 −0.193707
\(804\) 49.7228 11.6819i 1.75359 0.411990i
\(805\) 0 0
\(806\) 51.0767i 1.79910i
\(807\) 14.7446 3.46410i 0.519033 0.121942i
\(808\) 35.9306i 1.26404i
\(809\) 36.7229i 1.29111i −0.763714 0.645555i \(-0.776626\pi\)
0.763714 0.645555i \(-0.223374\pi\)
\(810\) 0 0
\(811\) 1.28962i 0.0452847i −0.999744 0.0226423i \(-0.992792\pi\)
0.999744 0.0226423i \(-0.00720790\pi\)
\(812\) 32.2337 + 37.2203i 1.13118 + 1.30617i
\(813\) −6.00000 25.5383i −0.210429 0.895668i
\(814\) −9.48913 −0.332594
\(815\) 0 0
\(816\) −14.7446 + 3.46410i −0.516163 + 0.121268i
\(817\) 23.3639i 0.817398i
\(818\) 88.4674 3.09319
\(819\) −42.7812 17.8641i −1.49490 0.624223i
\(820\) 0 0
\(821\) 11.7745i 0.410933i 0.978664 + 0.205466i \(0.0658711\pi\)
−0.978664 + 0.205466i \(0.934129\pi\)
\(822\) −56.4674 + 13.2665i −1.96953 + 0.462722i
\(823\) 48.2337 1.68132 0.840660 0.541563i \(-0.182167\pi\)
0.840660 + 0.541563i \(0.182167\pi\)
\(824\) 97.2119 3.38654
\(825\) 0 0
\(826\) 12.0000 + 13.8564i 0.417533 + 0.482126i
\(827\) 18.3152i 0.636881i 0.947943 + 0.318441i \(0.103159\pi\)
−0.947943 + 0.318441i \(0.896841\pi\)
\(828\) −10.9783 22.0742i −0.381521 0.767133i
\(829\) 32.4665i 1.12761i 0.825908 + 0.563805i \(0.190663\pi\)
−0.825908 + 0.563805i \(0.809337\pi\)
\(830\) 0 0
\(831\) −10.5109 + 2.46943i −0.364618 + 0.0856637i
\(832\) 13.8564i 0.480384i
\(833\) 1.37228 9.50744i 0.0475467 0.329413i
\(834\) −5.48913 + 1.28962i −0.190073 + 0.0446559i
\(835\) 0 0
\(836\) 12.0000 0.415029
\(837\) −11.4891 13.8564i −0.397122 0.478947i
\(838\) 6.92820i 0.239331i
\(839\) −53.4891 −1.84665 −0.923325 0.384020i \(-0.874539\pi\)
−0.923325 + 0.384020i \(0.874539\pi\)
\(840\) 0 0
\(841\) 10.8832 0.375281
\(842\) 64.6381i 2.22758i
\(843\) −1.91983 8.17154i −0.0661224 0.281443i
\(844\) −26.7446 −0.920586
\(845\) 0 0
\(846\) 24.8614 + 49.9894i 0.854753 + 1.71867i
\(847\) 20.7446 17.9653i 0.712792 0.617296i
\(848\) 54.2458i 1.86281i
\(849\) −3.68614 15.6896i −0.126508 0.538467i
\(850\) 0 0
\(851\) 8.91754i 0.305689i
\(852\) −23.4891 99.9788i −0.804724 3.42522i
\(853\) 46.7277i 1.59993i 0.600049 + 0.799963i \(0.295148\pi\)
−0.600049 + 0.799963i \(0.704852\pi\)
\(854\) −34.9783 + 30.2921i −1.19693 + 1.03657i
\(855\) 0 0
\(856\) 39.7228 1.35770
\(857\) 22.4674 0.767471 0.383735 0.923443i \(-0.374637\pi\)
0.383735 + 0.923443i \(0.374637\pi\)
\(858\) 4.62772 + 19.6974i 0.157988 + 0.672457i
\(859\) 45.4381i 1.55033i 0.631760 + 0.775164i \(0.282333\pi\)
−0.631760 + 0.775164i \(0.717667\pi\)
\(860\) 0 0
\(861\) 16.1168 22.2766i 0.549261 0.759185i
\(862\) −79.9565 −2.72333
\(863\) 28.0078i 0.953395i −0.879067 0.476698i \(-0.841834\pi\)
0.879067 0.476698i \(-0.158166\pi\)
\(864\) −13.6277 16.4356i −0.463624 0.559152i
\(865\) 0 0
\(866\) −6.51087 −0.221249
\(867\) 25.4891 5.98844i 0.865656 0.203378i
\(868\) −26.2337 30.2921i −0.890429 1.02818i
\(869\) 2.67181i 0.0906351i
\(870\) 0 0
\(871\) 39.3947i 1.33484i
\(872\) 0.699713i 0.0236953i
\(873\) 1.45245 + 2.92048i 0.0491581 + 0.0988433i
\(874\) 16.4356i 0.555944i
\(875\) 0 0
\(876\) −12.0000 51.0767i −0.405442 1.72572i
\(877\) −30.4674 −1.02881 −0.514405 0.857547i \(-0.671987\pi\)
−0.514405 + 0.857547i \(0.671987\pi\)
\(878\) −3.25544 −0.109866
\(879\) −47.4090 + 11.1383i −1.59906 + 0.375686i
\(880\) 0 0
\(881\) −2.23369 −0.0752549 −0.0376274 0.999292i \(-0.511980\pi\)
−0.0376274 + 0.999292i \(0.511980\pi\)
\(882\) 50.3505 16.5831i 1.69539 0.558383i
\(883\) −26.5109 −0.892162 −0.446081 0.894993i \(-0.647181\pi\)
−0.446081 + 0.894993i \(0.647181\pi\)
\(884\) 35.0458i 1.17872i
\(885\) 0 0
\(886\) −16.7446 −0.562545
\(887\) −41.4891 −1.39307 −0.696534 0.717524i \(-0.745276\pi\)
−0.696534 + 0.717524i \(0.745276\pi\)
\(888\) −11.2554 47.9075i −0.377708 1.60767i
\(889\) −21.4891 + 18.6101i −0.720722 + 0.624164i
\(890\) 0 0
\(891\) −5.68614 4.30268i −0.190493 0.144145i
\(892\) 91.7610i 3.07239i
\(893\) 25.5383i 0.854608i
\(894\) −42.9783 + 10.0974i −1.43741 + 0.337706i
\(895\) 0 0
\(896\) 24.6060 + 28.4125i 0.822028 + 0.949196i
\(897\) −18.5109 + 4.34896i −0.618060 + 0.145208i
\(898\) −71.2119 −2.37637
\(899\) 14.7446 0.491759
\(900\) 0 0
\(901\) 11.6819i 0.389181i
\(902\) −12.0000 −0.399556
\(903\) −18.1168 + 25.0410i −0.602891 + 0.833312i
\(904\) 60.4674 2.01112
\(905\) 0 0
\(906\) −3.37228 14.3537i −0.112037 0.476871i
\(907\) −8.00000 −0.265636 −0.132818 0.991140i \(-0.542403\pi\)
−0.132818 + 0.991140i \(0.542403\pi\)
\(908\) −68.2337 −2.26441
\(909\) 16.1168 8.01544i 0.534562 0.265855i
\(910\) 0 0
\(911\) 23.6588i 0.783851i 0.919997 + 0.391926i \(0.128191\pi\)
−0.919997 + 0.391926i \(0.871809\pi\)
\(912\) 8.74456 + 37.2203i 0.289561 + 1.23249i
\(913\) 4.34896i 0.143930i
\(914\) 83.2482i 2.75361i
\(915\) 0 0
\(916\) 20.7846i 0.686743i
\(917\) −34.9783 + 30.2921i −1.15508 + 1.00033i
\(918\) −11.4891 13.8564i −0.379198 0.457330i
\(919\) −11.3723 −0.375137 −0.187568 0.982252i \(-0.560061\pi\)
−0.187568 + 0.982252i \(0.560061\pi\)
\(920\) 0 0
\(921\) −2.82473 12.0232i −0.0930782 0.396177i
\(922\) 22.0742i 0.726976i
\(923\) −79.2119 −2.60729
\(924\) −12.8614 9.30506i −0.423109 0.306114i
\(925\) 0 0
\(926\) 92.0560i 3.02515i
\(927\) 21.6861 + 43.6048i 0.712266 + 1.43217i
\(928\) 17.4891 0.574109
\(929\) 7.02175 0.230376 0.115188 0.993344i \(-0.463253\pi\)
0.115188 + 0.993344i \(0.463253\pi\)
\(930\) 0 0
\(931\) −24.0000 3.46410i −0.786568 0.113531i
\(932\) 16.4356i 0.538368i
\(933\) −34.1168 + 8.01544i −1.11694 + 0.262414i
\(934\) 35.0458i 1.14673i
\(935\) 0 0
\(936\) −93.9565 + 46.7277i −3.07106 + 1.52734i
\(937\) 49.9894i 1.63308i 0.577287 + 0.816542i \(0.304112\pi\)
−0.577287 + 0.816542i \(0.695888\pi\)
\(938\) 29.4891 + 34.0511i 0.962854 + 1.11181i
\(939\) −9.68614 41.2280i −0.316095 1.34542i
\(940\) 0 0
\(941\) −27.2554 −0.888502 −0.444251 0.895902i \(-0.646530\pi\)
−0.444251 + 0.895902i \(0.646530\pi\)
\(942\) 0 0
\(943\) 11.2772i 0.367235i
\(944\) 17.4891 0.569223
\(945\) 0 0
\(946\) 13.4891 0.438569
\(947\) 48.2025i 1.56637i 0.621789 + 0.783185i \(0.286406\pi\)
−0.621789 + 0.783185i \(0.713594\pi\)
\(948\) 24.8614 5.84096i 0.807461 0.189706i
\(949\) −40.4674 −1.31363
\(950\) 0 0
\(951\) 3.37228 + 14.3537i 0.109354 + 0.465452i
\(952\) −14.2337 16.4356i −0.461316 0.532682i
\(953\) 38.8048i 1.25701i −0.777805 0.628506i \(-0.783667\pi\)
0.777805 0.628506i \(-0.216333\pi\)
\(954\) 57.7228 28.7075i 1.86885 0.929439i
\(955\) 0 0
\(956\) 68.3972i 2.21212i
\(957\) 5.68614 1.33591i 0.183807 0.0431838i
\(958\) 46.7277i 1.50970i
\(959\) −22.9783 26.5330i −0.742006 0.856795i
\(960\) 0 0
\(961\) 19.0000 0.612903
\(962\) −69.9565 −2.25549
\(963\) 8.86141 + 17.8178i 0.285555 + 0.574172i
\(964\) 102.153i 3.29014i
\(965\) 0 0
\(966\) 12.7446 17.6155i 0.410050 0.566768i
\(967\) 24.2337 0.779303 0.389651 0.920962i \(-0.372595\pi\)
0.389651 + 0.920962i \(0.372595\pi\)
\(968\) 62.1138i 1.99641i
\(969\) 1.88316 + 8.01544i 0.0604957 + 0.257493i
\(970\) 0 0
\(971\) −43.2119 −1.38674 −0.693369 0.720583i \(-0.743874\pi\)
−0.693369 + 0.720583i \(0.743874\pi\)
\(972\) 27.6060 62.3162i 0.885462 1.99879i
\(973\) −2.23369 2.57924i −0.0716087 0.0826867i
\(974\) 36.6303i 1.17371i
\(975\) 0 0
\(976\) 44.1485i 1.41316i
\(977\) 38.8048i 1.24148i −0.784018 0.620738i \(-0.786833\pi\)
0.784018 0.620738i \(-0.213167\pi\)
\(978\) 8.00000 + 34.0511i 0.255812 + 1.08883i
\(979\) 2.57924i 0.0824329i
\(980\) 0 0
\(981\) 0.313859 0.156093i 0.0100208 0.00498366i
\(982\) −27.4891 −0.877213
\(983\) −11.1386 −0.355266 −0.177633 0.984097i \(-0.556844\pi\)
−0.177633 + 0.984097i \(0.556844\pi\)
\(984\) −14.2337 60.5841i −0.453753 1.93135i
\(985\) 0 0
\(986\) 14.7446 0.469563
\(987\) −19.8030 + 27.3716i −0.630336 + 0.871247i
\(988\) 88.4674 2.81452
\(989\) 12.6766i 0.403092i
\(990\) 0 0
\(991\) 2.51087 0.0797606 0.0398803 0.999204i \(-0.487302\pi\)
0.0398803 + 0.999204i \(0.487302\pi\)
\(992\) −14.2337 −0.451920
\(993\) 6.74456 1.58457i 0.214032 0.0502849i
\(994\) 68.4674 59.2945i 2.17165 1.88071i
\(995\) 0 0
\(996\) −40.4674 + 9.50744i −1.28226 + 0.301255i
\(997\) 21.8719i 0.692688i 0.938107 + 0.346344i \(0.112577\pi\)
−0.938107 + 0.346344i \(0.887423\pi\)
\(998\) 26.1282i 0.827075i
\(999\) 18.9783 15.7359i 0.600445 0.497863i
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 525.2.b.e.251.4 4
3.2 odd 2 525.2.b.g.251.1 4
5.2 odd 4 525.2.g.d.524.2 8
5.3 odd 4 525.2.g.d.524.7 8
5.4 even 2 105.2.b.d.41.1 yes 4
7.6 odd 2 525.2.b.g.251.4 4
15.2 even 4 525.2.g.e.524.7 8
15.8 even 4 525.2.g.e.524.2 8
15.14 odd 2 105.2.b.c.41.4 yes 4
20.19 odd 2 1680.2.f.g.881.2 4
21.20 even 2 inner 525.2.b.e.251.1 4
35.4 even 6 735.2.s.j.656.2 4
35.9 even 6 735.2.s.g.521.1 4
35.13 even 4 525.2.g.e.524.8 8
35.19 odd 6 735.2.s.h.521.1 4
35.24 odd 6 735.2.s.i.656.2 4
35.27 even 4 525.2.g.e.524.1 8
35.34 odd 2 105.2.b.c.41.1 4
60.59 even 2 1680.2.f.h.881.4 4
105.44 odd 6 735.2.s.i.521.2 4
105.59 even 6 735.2.s.g.656.1 4
105.62 odd 4 525.2.g.d.524.8 8
105.74 odd 6 735.2.s.h.656.1 4
105.83 odd 4 525.2.g.d.524.1 8
105.89 even 6 735.2.s.j.521.2 4
105.104 even 2 105.2.b.d.41.4 yes 4
140.139 even 2 1680.2.f.h.881.3 4
420.419 odd 2 1680.2.f.g.881.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.b.c.41.1 4 35.34 odd 2
105.2.b.c.41.4 yes 4 15.14 odd 2
105.2.b.d.41.1 yes 4 5.4 even 2
105.2.b.d.41.4 yes 4 105.104 even 2
525.2.b.e.251.1 4 21.20 even 2 inner
525.2.b.e.251.4 4 1.1 even 1 trivial
525.2.b.g.251.1 4 3.2 odd 2
525.2.b.g.251.4 4 7.6 odd 2
525.2.g.d.524.1 8 105.83 odd 4
525.2.g.d.524.2 8 5.2 odd 4
525.2.g.d.524.7 8 5.3 odd 4
525.2.g.d.524.8 8 105.62 odd 4
525.2.g.e.524.1 8 35.27 even 4
525.2.g.e.524.2 8 15.8 even 4
525.2.g.e.524.7 8 15.2 even 4
525.2.g.e.524.8 8 35.13 even 4
735.2.s.g.521.1 4 35.9 even 6
735.2.s.g.656.1 4 105.59 even 6
735.2.s.h.521.1 4 35.19 odd 6
735.2.s.h.656.1 4 105.74 odd 6
735.2.s.i.521.2 4 105.44 odd 6
735.2.s.i.656.2 4 35.24 odd 6
735.2.s.j.521.2 4 105.89 even 6
735.2.s.j.656.2 4 35.4 even 6
1680.2.f.g.881.1 4 420.419 odd 2
1680.2.f.g.881.2 4 20.19 odd 2
1680.2.f.h.881.3 4 140.139 even 2
1680.2.f.h.881.4 4 60.59 even 2