Properties

Label 637.2.i.a.538.1
Level $637$
Weight $2$
Character 637.538
Analytic conductor $5.086$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(489,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.489");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.i (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 538.1
Character \(\chi\) \(=\) 637.538
Dual form 637.2.i.a.489.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.74842 + 1.74842i) q^{2} -2.04432i q^{3} -4.11394i q^{4} +(1.15810 + 1.15810i) q^{5} +(3.57432 + 3.57432i) q^{6} +(3.69606 + 3.69606i) q^{8} -1.17922 q^{9} +O(q^{10})\) \(q+(-1.74842 + 1.74842i) q^{2} -2.04432i q^{3} -4.11394i q^{4} +(1.15810 + 1.15810i) q^{5} +(3.57432 + 3.57432i) q^{6} +(3.69606 + 3.69606i) q^{8} -1.17922 q^{9} -4.04969 q^{10} +(4.06767 + 4.06767i) q^{11} -8.41020 q^{12} +(-3.57432 + 0.473526i) q^{13} +(2.36752 - 2.36752i) q^{15} -4.69665 q^{16} -1.98394 q^{17} +(2.06178 - 2.06178i) q^{18} +(0.672509 + 0.672509i) q^{19} +(4.76435 - 4.76435i) q^{20} -14.2240 q^{22} +3.54086i q^{23} +(7.55591 - 7.55591i) q^{24} -2.31761i q^{25} +(5.42149 - 7.07734i) q^{26} -3.72224i q^{27} +2.83949 q^{29} +8.27883i q^{30} +(3.17048 + 3.17048i) q^{31} +(0.819587 - 0.819587i) q^{32} +(8.31559 - 8.31559i) q^{33} +(3.46875 - 3.46875i) q^{34} +4.85126i q^{36} +(2.73645 + 2.73645i) q^{37} -2.35166 q^{38} +(0.968037 + 7.30704i) q^{39} +8.56081i q^{40} +(4.02565 + 4.02565i) q^{41} +5.30948i q^{43} +(16.7341 - 16.7341i) q^{44} +(-1.36566 - 1.36566i) q^{45} +(-6.19091 - 6.19091i) q^{46} +(0.328312 - 0.328312i) q^{47} +9.60143i q^{48} +(4.05216 + 4.05216i) q^{50} +4.05579i q^{51} +(1.94806 + 14.7046i) q^{52} +12.6367 q^{53} +(6.50804 + 6.50804i) q^{54} +9.42152i q^{55} +(1.37482 - 1.37482i) q^{57} +(-4.96463 + 4.96463i) q^{58} +(8.48852 - 8.48852i) q^{59} +(-9.73984 - 9.73984i) q^{60} +5.05917i q^{61} -11.0867 q^{62} -6.52733i q^{64} +(-4.68781 - 3.59103i) q^{65} +29.0783i q^{66} +(-4.29762 + 4.29762i) q^{67} +8.16180i q^{68} +7.23863 q^{69} +(-4.84596 + 4.84596i) q^{71} +(-4.35849 - 4.35849i) q^{72} +(3.10617 - 3.10617i) q^{73} -9.56894 q^{74} -4.73794 q^{75} +(2.76666 - 2.76666i) q^{76} +(-14.4683 - 11.0832i) q^{78} +6.16515 q^{79} +(-5.43918 - 5.43918i) q^{80} -11.1471 q^{81} -14.0771 q^{82} +(-11.5176 - 11.5176i) q^{83} +(-2.29759 - 2.29759i) q^{85} +(-9.28320 - 9.28320i) q^{86} -5.80482i q^{87} +30.0687i q^{88} +(-2.57087 + 2.57087i) q^{89} +4.77549 q^{90} +14.5669 q^{92} +(6.48146 - 6.48146i) q^{93} +1.14805i q^{94} +1.55766i q^{95} +(-1.67549 - 1.67549i) q^{96} +(7.09855 + 7.09855i) q^{97} +(-4.79669 - 4.79669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 44 q^{15} - 24 q^{16} + 8 q^{18} - 8 q^{22} + 16 q^{29} - 8 q^{32} + 16 q^{37} + 12 q^{39} + 84 q^{44} - 24 q^{46} + 88 q^{50} + 24 q^{53} + 40 q^{57} - 52 q^{58} - 32 q^{60} + 16 q^{65} - 32 q^{67} - 36 q^{71} - 44 q^{72} - 24 q^{74} - 176 q^{78} + 64 q^{79} - 32 q^{81} - 84 q^{85} - 84 q^{86} + 48 q^{92} - 12 q^{93} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.74842 + 1.74842i −1.23632 + 1.23632i −0.274825 + 0.961494i \(0.588620\pi\)
−0.961494 + 0.274825i \(0.911380\pi\)
\(3\) 2.04432i 1.18029i −0.807299 0.590143i \(-0.799071\pi\)
0.807299 0.590143i \(-0.200929\pi\)
\(4\) 4.11394i 2.05697i
\(5\) 1.15810 + 1.15810i 0.517917 + 0.517917i 0.916941 0.399023i \(-0.130651\pi\)
−0.399023 + 0.916941i \(0.630651\pi\)
\(6\) 3.57432 + 3.57432i 1.45921 + 1.45921i
\(7\) 0 0
\(8\) 3.69606 + 3.69606i 1.30676 + 1.30676i
\(9\) −1.17922 −0.393075
\(10\) −4.04969 −1.28062
\(11\) 4.06767 + 4.06767i 1.22645 + 1.22645i 0.965299 + 0.261149i \(0.0841013\pi\)
0.261149 + 0.965299i \(0.415899\pi\)
\(12\) −8.41020 −2.42782
\(13\) −3.57432 + 0.473526i −0.991338 + 0.131333i
\(14\) 0 0
\(15\) 2.36752 2.36752i 0.611291 0.611291i
\(16\) −4.69665 −1.17416
\(17\) −1.98394 −0.481175 −0.240588 0.970627i \(-0.577340\pi\)
−0.240588 + 0.970627i \(0.577340\pi\)
\(18\) 2.06178 2.06178i 0.485966 0.485966i
\(19\) 0.672509 + 0.672509i 0.154284 + 0.154284i 0.780028 0.625744i \(-0.215205\pi\)
−0.625744 + 0.780028i \(0.715205\pi\)
\(20\) 4.76435 4.76435i 1.06534 1.06534i
\(21\) 0 0
\(22\) −14.2240 −3.03256
\(23\) 3.54086i 0.738320i 0.929366 + 0.369160i \(0.120355\pi\)
−0.929366 + 0.369160i \(0.879645\pi\)
\(24\) 7.55591 7.55591i 1.54234 1.54234i
\(25\) 2.31761i 0.463523i
\(26\) 5.42149 7.07734i 1.06324 1.38798i
\(27\) 3.72224i 0.716345i
\(28\) 0 0
\(29\) 2.83949 0.527281 0.263640 0.964621i \(-0.415077\pi\)
0.263640 + 0.964621i \(0.415077\pi\)
\(30\) 8.27883i 1.51150i
\(31\) 3.17048 + 3.17048i 0.569435 + 0.569435i 0.931970 0.362535i \(-0.118089\pi\)
−0.362535 + 0.931970i \(0.618089\pi\)
\(32\) 0.819587 0.819587i 0.144884 0.144884i
\(33\) 8.31559 8.31559i 1.44756 1.44756i
\(34\) 3.46875 3.46875i 0.594886 0.594886i
\(35\) 0 0
\(36\) 4.85126i 0.808544i
\(37\) 2.73645 + 2.73645i 0.449870 + 0.449870i 0.895311 0.445441i \(-0.146953\pi\)
−0.445441 + 0.895311i \(0.646953\pi\)
\(38\) −2.35166 −0.381489
\(39\) 0.968037 + 7.30704i 0.155010 + 1.17006i
\(40\) 8.56081i 1.35358i
\(41\) 4.02565 + 4.02565i 0.628701 + 0.628701i 0.947741 0.319040i \(-0.103360\pi\)
−0.319040 + 0.947741i \(0.603360\pi\)
\(42\) 0 0
\(43\) 5.30948i 0.809688i 0.914386 + 0.404844i \(0.132674\pi\)
−0.914386 + 0.404844i \(0.867326\pi\)
\(44\) 16.7341 16.7341i 2.52277 2.52277i
\(45\) −1.36566 1.36566i −0.203580 0.203580i
\(46\) −6.19091 6.19091i −0.912799 0.912799i
\(47\) 0.328312 0.328312i 0.0478892 0.0478892i −0.682757 0.730646i \(-0.739219\pi\)
0.730646 + 0.682757i \(0.239219\pi\)
\(48\) 9.60143i 1.38585i
\(49\) 0 0
\(50\) 4.05216 + 4.05216i 0.573062 + 0.573062i
\(51\) 4.05579i 0.567924i
\(52\) 1.94806 + 14.7046i 0.270147 + 2.03916i
\(53\) 12.6367 1.73578 0.867891 0.496754i \(-0.165475\pi\)
0.867891 + 0.496754i \(0.165475\pi\)
\(54\) 6.50804 + 6.50804i 0.885631 + 0.885631i
\(55\) 9.42152i 1.27040i
\(56\) 0 0
\(57\) 1.37482 1.37482i 0.182099 0.182099i
\(58\) −4.96463 + 4.96463i −0.651887 + 0.651887i
\(59\) 8.48852 8.48852i 1.10511 1.10511i 0.111327 0.993784i \(-0.464490\pi\)
0.993784 0.111327i \(-0.0355100\pi\)
\(60\) −9.73984 9.73984i −1.25741 1.25741i
\(61\) 5.05917i 0.647760i 0.946098 + 0.323880i \(0.104987\pi\)
−0.946098 + 0.323880i \(0.895013\pi\)
\(62\) −11.0867 −1.40801
\(63\) 0 0
\(64\) 6.52733i 0.815916i
\(65\) −4.68781 3.59103i −0.581451 0.445412i
\(66\) 29.0783i 3.57929i
\(67\) −4.29762 + 4.29762i −0.525038 + 0.525038i −0.919089 0.394051i \(-0.871073\pi\)
0.394051 + 0.919089i \(0.371073\pi\)
\(68\) 8.16180i 0.989764i
\(69\) 7.23863 0.871429
\(70\) 0 0
\(71\) −4.84596 + 4.84596i −0.575110 + 0.575110i −0.933552 0.358442i \(-0.883308\pi\)
0.358442 + 0.933552i \(0.383308\pi\)
\(72\) −4.35849 4.35849i −0.513653 0.513653i
\(73\) 3.10617 3.10617i 0.363550 0.363550i −0.501568 0.865118i \(-0.667243\pi\)
0.865118 + 0.501568i \(0.167243\pi\)
\(74\) −9.56894 −1.11237
\(75\) −4.73794 −0.547090
\(76\) 2.76666 2.76666i 0.317358 0.317358i
\(77\) 0 0
\(78\) −14.4683 11.0832i −1.63821 1.25493i
\(79\) 6.16515 0.693634 0.346817 0.937933i \(-0.387263\pi\)
0.346817 + 0.937933i \(0.387263\pi\)
\(80\) −5.43918 5.43918i −0.608119 0.608119i
\(81\) −11.1471 −1.23857
\(82\) −14.0771 −1.55455
\(83\) −11.5176 11.5176i −1.26422 1.26422i −0.949027 0.315194i \(-0.897930\pi\)
−0.315194 0.949027i \(-0.602070\pi\)
\(84\) 0 0
\(85\) −2.29759 2.29759i −0.249209 0.249209i
\(86\) −9.28320 9.28320i −1.00103 1.00103i
\(87\) 5.80482i 0.622342i
\(88\) 30.0687i 3.20533i
\(89\) −2.57087 + 2.57087i −0.272512 + 0.272512i −0.830111 0.557599i \(-0.811723\pi\)
0.557599 + 0.830111i \(0.311723\pi\)
\(90\) 4.77549 0.503381
\(91\) 0 0
\(92\) 14.5669 1.51870
\(93\) 6.48146 6.48146i 0.672096 0.672096i
\(94\) 1.14805i 0.118413i
\(95\) 1.55766i 0.159813i
\(96\) −1.67549 1.67549i −0.171004 0.171004i
\(97\) 7.09855 + 7.09855i 0.720749 + 0.720749i 0.968758 0.248009i \(-0.0797763\pi\)
−0.248009 + 0.968758i \(0.579776\pi\)
\(98\) 0 0
\(99\) −4.79669 4.79669i −0.482086 0.482086i
\(100\) −9.53454 −0.953454
\(101\) 4.25958 0.423844 0.211922 0.977287i \(-0.432028\pi\)
0.211922 + 0.977287i \(0.432028\pi\)
\(102\) −7.09122 7.09122i −0.702136 0.702136i
\(103\) 4.17124 0.411004 0.205502 0.978657i \(-0.434117\pi\)
0.205502 + 0.978657i \(0.434117\pi\)
\(104\) −14.9611 11.4607i −1.46706 1.12382i
\(105\) 0 0
\(106\) −22.0942 + 22.0942i −2.14598 + 2.14598i
\(107\) −3.82964 −0.370225 −0.185113 0.982717i \(-0.559265\pi\)
−0.185113 + 0.982717i \(0.559265\pi\)
\(108\) −15.3131 −1.47350
\(109\) −1.01114 + 1.01114i −0.0968495 + 0.0968495i −0.753871 0.657022i \(-0.771816\pi\)
0.657022 + 0.753871i \(0.271816\pi\)
\(110\) −16.4728 16.4728i −1.57062 1.57062i
\(111\) 5.59417 5.59417i 0.530975 0.530975i
\(112\) 0 0
\(113\) 15.2149 1.43129 0.715647 0.698462i \(-0.246132\pi\)
0.715647 + 0.698462i \(0.246132\pi\)
\(114\) 4.80753i 0.450266i
\(115\) −4.10066 + 4.10066i −0.382389 + 0.382389i
\(116\) 11.6815i 1.08460i
\(117\) 4.21493 0.558394i 0.389670 0.0516235i
\(118\) 29.6830i 2.73254i
\(119\) 0 0
\(120\) 17.5010 1.59761
\(121\) 22.0918i 2.00835i
\(122\) −8.84555 8.84555i −0.800838 0.800838i
\(123\) 8.22970 8.22970i 0.742047 0.742047i
\(124\) 13.0432 13.0432i 1.17131 1.17131i
\(125\) 8.47452 8.47452i 0.757984 0.757984i
\(126\) 0 0
\(127\) 6.12999i 0.543949i −0.962304 0.271974i \(-0.912323\pi\)
0.962304 0.271974i \(-0.0876766\pi\)
\(128\) 13.0517 + 13.0517i 1.15362 + 1.15362i
\(129\) 10.8542 0.955663
\(130\) 14.4749 1.91763i 1.26953 0.168187i
\(131\) 1.50908i 0.131849i −0.997825 0.0659247i \(-0.979000\pi\)
0.997825 0.0659247i \(-0.0209997\pi\)
\(132\) −34.2099 34.2099i −2.97759 2.97759i
\(133\) 0 0
\(134\) 15.0281i 1.29823i
\(135\) 4.31072 4.31072i 0.371008 0.371008i
\(136\) −7.33275 7.33275i −0.628778 0.628778i
\(137\) 4.82093 + 4.82093i 0.411880 + 0.411880i 0.882393 0.470513i \(-0.155931\pi\)
−0.470513 + 0.882393i \(0.655931\pi\)
\(138\) −12.6562 + 12.6562i −1.07736 + 1.07736i
\(139\) 6.26924i 0.531750i −0.964007 0.265875i \(-0.914339\pi\)
0.964007 0.265875i \(-0.0856609\pi\)
\(140\) 0 0
\(141\) −0.671172 0.671172i −0.0565229 0.0565229i
\(142\) 16.9456i 1.42204i
\(143\) −16.4653 12.6130i −1.37690 1.05475i
\(144\) 5.53840 0.461533
\(145\) 3.28841 + 3.28841i 0.273088 + 0.273088i
\(146\) 10.8618i 0.898929i
\(147\) 0 0
\(148\) 11.2576 11.2576i 0.925370 0.925370i
\(149\) −1.91470 + 1.91470i −0.156858 + 0.156858i −0.781173 0.624315i \(-0.785378\pi\)
0.624315 + 0.781173i \(0.285378\pi\)
\(150\) 8.28390 8.28390i 0.676378 0.676378i
\(151\) −0.199984 0.199984i −0.0162745 0.0162745i 0.698923 0.715197i \(-0.253663\pi\)
−0.715197 + 0.698923i \(0.753663\pi\)
\(152\) 4.97127i 0.403223i
\(153\) 2.33951 0.189138
\(154\) 0 0
\(155\) 7.34346i 0.589841i
\(156\) 30.0608 3.98245i 2.40679 0.318851i
\(157\) 1.02239i 0.0815953i −0.999167 0.0407976i \(-0.987010\pi\)
0.999167 0.0407976i \(-0.0129899\pi\)
\(158\) −10.7793 + 10.7793i −0.857553 + 0.857553i
\(159\) 25.8334i 2.04872i
\(160\) 1.89832 0.150076
\(161\) 0 0
\(162\) 19.4898 19.4898i 1.53126 1.53126i
\(163\) −11.9892 11.9892i −0.939069 0.939069i 0.0591785 0.998247i \(-0.481152\pi\)
−0.998247 + 0.0591785i \(0.981152\pi\)
\(164\) 16.5613 16.5613i 1.29322 1.29322i
\(165\) 19.2606 1.49943
\(166\) 40.2752 3.12596
\(167\) 0.350041 0.350041i 0.0270870 0.0270870i −0.693434 0.720521i \(-0.743903\pi\)
0.720521 + 0.693434i \(0.243903\pi\)
\(168\) 0 0
\(169\) 12.5515 3.38507i 0.965504 0.260390i
\(170\) 8.03432 0.616204
\(171\) −0.793039 0.793039i −0.0606452 0.0606452i
\(172\) 21.8429 1.66551
\(173\) −3.97561 −0.302260 −0.151130 0.988514i \(-0.548291\pi\)
−0.151130 + 0.988514i \(0.548291\pi\)
\(174\) 10.1493 + 10.1493i 0.769413 + 0.769413i
\(175\) 0 0
\(176\) −19.1044 19.1044i −1.44005 1.44005i
\(177\) −17.3532 17.3532i −1.30435 1.30435i
\(178\) 8.98993i 0.673824i
\(179\) 6.43482i 0.480961i −0.970654 0.240481i \(-0.922695\pi\)
0.970654 0.240481i \(-0.0773050\pi\)
\(180\) −5.61824 + 5.61824i −0.418759 + 0.418759i
\(181\) −10.7701 −0.800535 −0.400268 0.916398i \(-0.631083\pi\)
−0.400268 + 0.916398i \(0.631083\pi\)
\(182\) 0 0
\(183\) 10.3425 0.764542
\(184\) −13.0872 + 13.0872i −0.964803 + 0.964803i
\(185\) 6.33817i 0.465991i
\(186\) 22.6646i 1.66185i
\(187\) −8.06999 8.06999i −0.590136 0.590136i
\(188\) −1.35066 1.35066i −0.0985067 0.0985067i
\(189\) 0 0
\(190\) −2.72345 2.72345i −0.197580 0.197580i
\(191\) 2.04668 0.148092 0.0740461 0.997255i \(-0.476409\pi\)
0.0740461 + 0.997255i \(0.476409\pi\)
\(192\) −13.3439 −0.963014
\(193\) −2.03484 2.03484i −0.146471 0.146471i 0.630069 0.776539i \(-0.283027\pi\)
−0.776539 + 0.630069i \(0.783027\pi\)
\(194\) −24.8225 −1.78215
\(195\) −7.34119 + 9.58336i −0.525714 + 0.686278i
\(196\) 0 0
\(197\) −4.42190 + 4.42190i −0.315047 + 0.315047i −0.846861 0.531814i \(-0.821511\pi\)
0.531814 + 0.846861i \(0.321511\pi\)
\(198\) 16.7733 1.19202
\(199\) −20.8127 −1.47537 −0.737687 0.675143i \(-0.764082\pi\)
−0.737687 + 0.675143i \(0.764082\pi\)
\(200\) 8.56605 8.56605i 0.605711 0.605711i
\(201\) 8.78569 + 8.78569i 0.619695 + 0.619695i
\(202\) −7.44753 + 7.44753i −0.524006 + 0.524006i
\(203\) 0 0
\(204\) 16.6853 1.16820
\(205\) 9.32421i 0.651231i
\(206\) −7.29307 + 7.29307i −0.508133 + 0.508133i
\(207\) 4.17547i 0.290215i
\(208\) 16.7873 2.22399i 1.16399 0.154206i
\(209\) 5.47108i 0.378443i
\(210\) 0 0
\(211\) −15.4637 −1.06456 −0.532281 0.846568i \(-0.678665\pi\)
−0.532281 + 0.846568i \(0.678665\pi\)
\(212\) 51.9866i 3.57046i
\(213\) 9.90668 + 9.90668i 0.678794 + 0.678794i
\(214\) 6.69582 6.69582i 0.457717 0.457717i
\(215\) −6.14890 + 6.14890i −0.419351 + 0.419351i
\(216\) 13.7576 13.7576i 0.936088 0.936088i
\(217\) 0 0
\(218\) 3.53579i 0.239474i
\(219\) −6.35000 6.35000i −0.429093 0.429093i
\(220\) 38.7596 2.61317
\(221\) 7.09122 0.939445i 0.477007 0.0631939i
\(222\) 19.5619i 1.31291i
\(223\) −16.7037 16.7037i −1.11856 1.11856i −0.991953 0.126611i \(-0.959590\pi\)
−0.126611 0.991953i \(-0.540410\pi\)
\(224\) 0 0
\(225\) 2.73299i 0.182199i
\(226\) −26.6020 + 26.6020i −1.76954 + 1.76954i
\(227\) 15.1706 + 15.1706i 1.00691 + 1.00691i 0.999976 + 0.00693052i \(0.00220607\pi\)
0.00693052 + 0.999976i \(0.497794\pi\)
\(228\) −5.65593 5.65593i −0.374573 0.374573i
\(229\) −0.715649 + 0.715649i −0.0472914 + 0.0472914i −0.730357 0.683066i \(-0.760646\pi\)
0.683066 + 0.730357i \(0.260646\pi\)
\(230\) 14.3394i 0.945509i
\(231\) 0 0
\(232\) 10.4949 + 10.4949i 0.689027 + 0.689027i
\(233\) 2.17601i 0.142555i 0.997457 + 0.0712775i \(0.0227076\pi\)
−0.997457 + 0.0712775i \(0.977292\pi\)
\(234\) −6.39316 + 8.34577i −0.417934 + 0.545580i
\(235\) 0.760435 0.0496053
\(236\) −34.9213 34.9213i −2.27318 2.27318i
\(237\) 12.6035i 0.818686i
\(238\) 0 0
\(239\) −8.20062 + 8.20062i −0.530454 + 0.530454i −0.920708 0.390253i \(-0.872387\pi\)
0.390253 + 0.920708i \(0.372387\pi\)
\(240\) −11.1194 + 11.1194i −0.717754 + 0.717754i
\(241\) 4.54828 4.54828i 0.292981 0.292981i −0.545276 0.838257i \(-0.683575\pi\)
0.838257 + 0.545276i \(0.183575\pi\)
\(242\) −38.6258 38.6258i −2.48296 2.48296i
\(243\) 11.6215i 0.745518i
\(244\) 20.8131 1.33242
\(245\) 0 0
\(246\) 28.7780i 1.83482i
\(247\) −2.72221 2.08531i −0.173210 0.132685i
\(248\) 23.4366i 1.48822i
\(249\) −23.5456 + 23.5456i −1.49214 + 1.49214i
\(250\) 29.6340i 1.87422i
\(251\) 1.99071 0.125652 0.0628261 0.998024i \(-0.479989\pi\)
0.0628261 + 0.998024i \(0.479989\pi\)
\(252\) 0 0
\(253\) −14.4030 + 14.4030i −0.905511 + 0.905511i
\(254\) 10.7178 + 10.7178i 0.672495 + 0.672495i
\(255\) −4.69700 + 4.69700i −0.294138 + 0.294138i
\(256\) −32.5850 −2.03656
\(257\) −2.10565 −0.131347 −0.0656735 0.997841i \(-0.520920\pi\)
−0.0656735 + 0.997841i \(0.520920\pi\)
\(258\) −18.9778 + 18.9778i −1.18151 + 1.18151i
\(259\) 0 0
\(260\) −14.7733 + 19.2854i −0.916200 + 1.19603i
\(261\) −3.34840 −0.207261
\(262\) 2.63851 + 2.63851i 0.163008 + 0.163008i
\(263\) −20.2729 −1.25008 −0.625040 0.780593i \(-0.714917\pi\)
−0.625040 + 0.780593i \(0.714917\pi\)
\(264\) 61.4699 3.78321
\(265\) 14.6345 + 14.6345i 0.898992 + 0.898992i
\(266\) 0 0
\(267\) 5.25567 + 5.25567i 0.321642 + 0.321642i
\(268\) 17.6802 + 17.6802i 1.07999 + 1.07999i
\(269\) 1.31985i 0.0804729i 0.999190 + 0.0402365i \(0.0128111\pi\)
−0.999190 + 0.0402365i \(0.987189\pi\)
\(270\) 15.0739i 0.917368i
\(271\) −19.4649 + 19.4649i −1.18241 + 1.18241i −0.203287 + 0.979119i \(0.565163\pi\)
−0.979119 + 0.203287i \(0.934837\pi\)
\(272\) 9.31784 0.564977
\(273\) 0 0
\(274\) −16.8580 −1.01843
\(275\) 9.42728 9.42728i 0.568487 0.568487i
\(276\) 29.7793i 1.79250i
\(277\) 16.8151i 1.01032i −0.863025 0.505162i \(-0.831433\pi\)
0.863025 0.505162i \(-0.168567\pi\)
\(278\) 10.9613 + 10.9613i 0.657413 + 0.657413i
\(279\) −3.73871 3.73871i −0.223831 0.223831i
\(280\) 0 0
\(281\) −14.9251 14.9251i −0.890356 0.890356i 0.104200 0.994556i \(-0.466772\pi\)
−0.994556 + 0.104200i \(0.966772\pi\)
\(282\) 2.34698 0.139761
\(283\) −31.0846 −1.84779 −0.923895 0.382646i \(-0.875013\pi\)
−0.923895 + 0.382646i \(0.875013\pi\)
\(284\) 19.9360 + 19.9360i 1.18299 + 1.18299i
\(285\) 3.18436 0.188625
\(286\) 50.8411 6.73543i 3.00629 0.398274i
\(287\) 0 0
\(288\) −0.966477 + 0.966477i −0.0569502 + 0.0569502i
\(289\) −13.0640 −0.768471
\(290\) −11.4991 −0.675248
\(291\) 14.5117 14.5117i 0.850689 0.850689i
\(292\) −12.7786 12.7786i −0.747813 0.747813i
\(293\) −10.7578 + 10.7578i −0.628478 + 0.628478i −0.947685 0.319207i \(-0.896583\pi\)
0.319207 + 0.947685i \(0.396583\pi\)
\(294\) 0 0
\(295\) 19.6611 1.14471
\(296\) 20.2282i 1.17574i
\(297\) 15.1408 15.1408i 0.878560 0.878560i
\(298\) 6.69539i 0.387854i
\(299\) −1.67669 12.6562i −0.0969654 0.731925i
\(300\) 19.4916i 1.12535i
\(301\) 0 0
\(302\) 0.699311 0.0402408
\(303\) 8.70792i 0.500257i
\(304\) −3.15854 3.15854i −0.181155 0.181155i
\(305\) −5.85901 + 5.85901i −0.335486 + 0.335486i
\(306\) −4.09044 + 4.09044i −0.233835 + 0.233835i
\(307\) −18.9532 + 18.9532i −1.08172 + 1.08172i −0.0853681 + 0.996349i \(0.527207\pi\)
−0.996349 + 0.0853681i \(0.972793\pi\)
\(308\) 0 0
\(309\) 8.52732i 0.485102i
\(310\) −12.8395 12.8395i −0.729232 0.729232i
\(311\) 11.2472 0.637773 0.318886 0.947793i \(-0.396691\pi\)
0.318886 + 0.947793i \(0.396691\pi\)
\(312\) −23.4293 + 30.5852i −1.32643 + 1.73155i
\(313\) 29.3033i 1.65632i −0.560493 0.828159i \(-0.689388\pi\)
0.560493 0.828159i \(-0.310612\pi\)
\(314\) 1.78756 + 1.78756i 0.100878 + 0.100878i
\(315\) 0 0
\(316\) 25.3631i 1.42679i
\(317\) 10.7595 10.7595i 0.604313 0.604313i −0.337141 0.941454i \(-0.609460\pi\)
0.941454 + 0.337141i \(0.109460\pi\)
\(318\) 45.1676 + 45.1676i 2.53287 + 2.53287i
\(319\) 11.5501 + 11.5501i 0.646682 + 0.646682i
\(320\) 7.55929 7.55929i 0.422577 0.422577i
\(321\) 7.82900i 0.436972i
\(322\) 0 0
\(323\) −1.33421 1.33421i −0.0742377 0.0742377i
\(324\) 45.8586i 2.54770i
\(325\) 1.09745 + 8.28390i 0.0608756 + 0.459508i
\(326\) 41.9244 2.32198
\(327\) 2.06709 + 2.06709i 0.114310 + 0.114310i
\(328\) 29.7581i 1.64312i
\(329\) 0 0
\(330\) −33.6755 + 33.6755i −1.85378 + 1.85378i
\(331\) 18.1860 18.1860i 0.999591 0.999591i −0.000408961 1.00000i \(-0.500130\pi\)
1.00000 0.000408961i \(0.000130176\pi\)
\(332\) −47.3828 + 47.3828i −2.60047 + 2.60047i
\(333\) −3.22689 3.22689i −0.176833 0.176833i
\(334\) 1.22404i 0.0669763i
\(335\) −9.95413 −0.543852
\(336\) 0 0
\(337\) 3.72672i 0.203008i −0.994835 0.101504i \(-0.967635\pi\)
0.994835 0.101504i \(-0.0323654\pi\)
\(338\) −16.0268 + 27.8639i −0.871746 + 1.51560i
\(339\) 31.1040i 1.68934i
\(340\) −9.45217 + 9.45217i −0.512616 + 0.512616i
\(341\) 25.7929i 1.39676i
\(342\) 2.77313 0.149954
\(343\) 0 0
\(344\) −19.6242 + 19.6242i −1.05806 + 1.05806i
\(345\) 8.38305 + 8.38305i 0.451328 + 0.451328i
\(346\) 6.95104 6.95104i 0.373690 0.373690i
\(347\) −13.5429 −0.727021 −0.363511 0.931590i \(-0.618422\pi\)
−0.363511 + 0.931590i \(0.618422\pi\)
\(348\) −23.8807 −1.28014
\(349\) 21.5796 21.5796i 1.15513 1.15513i 0.169620 0.985509i \(-0.445746\pi\)
0.985509 0.169620i \(-0.0542541\pi\)
\(350\) 0 0
\(351\) 1.76258 + 13.3045i 0.0940794 + 0.710140i
\(352\) 6.66761 0.355385
\(353\) −1.95991 1.95991i −0.104315 0.104315i 0.653023 0.757338i \(-0.273501\pi\)
−0.757338 + 0.653023i \(0.773501\pi\)
\(354\) 60.6814 3.22518
\(355\) −11.2242 −0.595719
\(356\) 10.5764 + 10.5764i 0.560550 + 0.560550i
\(357\) 0 0
\(358\) 11.2508 + 11.2508i 0.594621 + 0.594621i
\(359\) 6.44914 + 6.44914i 0.340373 + 0.340373i 0.856507 0.516135i \(-0.172630\pi\)
−0.516135 + 0.856507i \(0.672630\pi\)
\(360\) 10.0951i 0.532059i
\(361\) 18.0955i 0.952393i
\(362\) 18.8307 18.8307i 0.989718 0.989718i
\(363\) 45.1626 2.37042
\(364\) 0 0
\(365\) 7.19451 0.376578
\(366\) −18.0831 + 18.0831i −0.945218 + 0.945218i
\(367\) 12.1238i 0.632857i 0.948616 + 0.316429i \(0.102484\pi\)
−0.948616 + 0.316429i \(0.897516\pi\)
\(368\) 16.6302i 0.866907i
\(369\) −4.74715 4.74715i −0.247127 0.247127i
\(370\) −11.0818 11.0818i −0.576114 0.576114i
\(371\) 0 0
\(372\) −26.6644 26.6644i −1.38248 1.38248i
\(373\) 27.7054 1.43453 0.717266 0.696800i \(-0.245393\pi\)
0.717266 + 0.696800i \(0.245393\pi\)
\(374\) 28.2195 1.45919
\(375\) −17.3246 17.3246i −0.894638 0.894638i
\(376\) 2.42692 0.125159
\(377\) −10.1493 + 1.34457i −0.522714 + 0.0692491i
\(378\) 0 0
\(379\) 1.97532 1.97532i 0.101466 0.101466i −0.654552 0.756017i \(-0.727143\pi\)
0.756017 + 0.654552i \(0.227143\pi\)
\(380\) 6.40814 0.328731
\(381\) −12.5316 −0.642015
\(382\) −3.57845 + 3.57845i −0.183089 + 0.183089i
\(383\) 12.8554 + 12.8554i 0.656881 + 0.656881i 0.954641 0.297759i \(-0.0962393\pi\)
−0.297759 + 0.954641i \(0.596239\pi\)
\(384\) 26.6818 26.6818i 1.36160 1.36160i
\(385\) 0 0
\(386\) 7.11550 0.362169
\(387\) 6.26107i 0.318268i
\(388\) 29.2030 29.2030i 1.48256 1.48256i
\(389\) 5.50490i 0.279109i 0.990214 + 0.139555i \(0.0445671\pi\)
−0.990214 + 0.139555i \(0.955433\pi\)
\(390\) −3.92024 29.5912i −0.198509 1.49841i
\(391\) 7.02483i 0.355261i
\(392\) 0 0
\(393\) −3.08505 −0.155620
\(394\) 15.4627i 0.778998i
\(395\) 7.13985 + 7.13985i 0.359245 + 0.359245i
\(396\) −19.7333 + 19.7333i −0.991637 + 0.991637i
\(397\) −17.6301 + 17.6301i −0.884830 + 0.884830i −0.994021 0.109190i \(-0.965174\pi\)
0.109190 + 0.994021i \(0.465174\pi\)
\(398\) 36.3893 36.3893i 1.82403 1.82403i
\(399\) 0 0
\(400\) 10.8850i 0.544251i
\(401\) −5.78568 5.78568i −0.288923 0.288923i 0.547731 0.836654i \(-0.315492\pi\)
−0.836654 + 0.547731i \(0.815492\pi\)
\(402\) −30.7221 −1.53228
\(403\) −12.8336 9.83101i −0.639288 0.489718i
\(404\) 17.5237i 0.871834i
\(405\) −12.9094 12.9094i −0.641476 0.641476i
\(406\) 0 0
\(407\) 22.2620i 1.10348i
\(408\) −14.9904 + 14.9904i −0.742138 + 0.742138i
\(409\) 3.17378 + 3.17378i 0.156933 + 0.156933i 0.781206 0.624273i \(-0.214605\pi\)
−0.624273 + 0.781206i \(0.714605\pi\)
\(410\) −16.3026 16.3026i −0.805129 0.805129i
\(411\) 9.85551 9.85551i 0.486136 0.486136i
\(412\) 17.1602i 0.845424i
\(413\) 0 0
\(414\) 7.30047 + 7.30047i 0.358799 + 0.358799i
\(415\) 26.6770i 1.30952i
\(416\) −2.54137 + 3.31756i −0.124601 + 0.162657i
\(417\) −12.8163 −0.627617
\(418\) −9.56575 9.56575i −0.467876 0.467876i
\(419\) 35.1474i 1.71706i 0.512760 + 0.858532i \(0.328623\pi\)
−0.512760 + 0.858532i \(0.671377\pi\)
\(420\) 0 0
\(421\) 24.7123 24.7123i 1.20440 1.20440i 0.231589 0.972814i \(-0.425607\pi\)
0.972814 0.231589i \(-0.0743926\pi\)
\(422\) 27.0370 27.0370i 1.31614 1.31614i
\(423\) −0.387153 + 0.387153i −0.0188240 + 0.0188240i
\(424\) 46.7060 + 46.7060i 2.26824 + 2.26824i
\(425\) 4.59800i 0.223036i
\(426\) −34.6421 −1.67841
\(427\) 0 0
\(428\) 15.7549i 0.761543i
\(429\) −25.7849 + 33.6602i −1.24491 + 1.62513i
\(430\) 21.5017i 1.03690i
\(431\) 25.2942 25.2942i 1.21838 1.21838i 0.250181 0.968199i \(-0.419510\pi\)
0.968199 0.250181i \(-0.0804901\pi\)
\(432\) 17.4820i 0.841105i
\(433\) 3.82925 0.184022 0.0920110 0.995758i \(-0.470670\pi\)
0.0920110 + 0.995758i \(0.470670\pi\)
\(434\) 0 0
\(435\) 6.72255 6.72255i 0.322322 0.322322i
\(436\) 4.15977 + 4.15977i 0.199217 + 0.199217i
\(437\) −2.38126 + 2.38126i −0.113911 + 0.113911i
\(438\) 22.2049 1.06099
\(439\) 4.29882 0.205171 0.102586 0.994724i \(-0.467288\pi\)
0.102586 + 0.994724i \(0.467288\pi\)
\(440\) −34.8225 + 34.8225i −1.66010 + 1.66010i
\(441\) 0 0
\(442\) −10.7559 + 14.0410i −0.511606 + 0.667861i
\(443\) −14.7499 −0.700789 −0.350395 0.936602i \(-0.613952\pi\)
−0.350395 + 0.936602i \(0.613952\pi\)
\(444\) −23.0141 23.0141i −1.09220 1.09220i
\(445\) −5.95465 −0.282277
\(446\) 58.4102 2.76580
\(447\) 3.91425 + 3.91425i 0.185137 + 0.185137i
\(448\) 0 0
\(449\) −13.9834 13.9834i −0.659915 0.659915i 0.295445 0.955360i \(-0.404532\pi\)
−0.955360 + 0.295445i \(0.904532\pi\)
\(450\) −4.77841 4.77841i −0.225257 0.225257i
\(451\) 32.7500i 1.54214i
\(452\) 62.5931i 2.94413i
\(453\) −0.408830 + 0.408830i −0.0192085 + 0.0192085i
\(454\) −53.0491 −2.48972
\(455\) 0 0
\(456\) 10.1628 0.475919
\(457\) −21.6338 + 21.6338i −1.01199 + 1.01199i −0.0120601 + 0.999927i \(0.503839\pi\)
−0.999927 + 0.0120601i \(0.996161\pi\)
\(458\) 2.50251i 0.116935i
\(459\) 7.38468i 0.344687i
\(460\) 16.8699 + 16.8699i 0.786563 + 0.786563i
\(461\) 4.39870 + 4.39870i 0.204868 + 0.204868i 0.802082 0.597214i \(-0.203726\pi\)
−0.597214 + 0.802082i \(0.703726\pi\)
\(462\) 0 0
\(463\) 6.67812 + 6.67812i 0.310358 + 0.310358i 0.845048 0.534690i \(-0.179572\pi\)
−0.534690 + 0.845048i \(0.679572\pi\)
\(464\) −13.3361 −0.619113
\(465\) 15.0123 0.696181
\(466\) −3.80457 3.80457i −0.176243 0.176243i
\(467\) −38.1046 −1.76327 −0.881636 0.471930i \(-0.843558\pi\)
−0.881636 + 0.471930i \(0.843558\pi\)
\(468\) −2.29720 17.3400i −0.106188 0.801541i
\(469\) 0 0
\(470\) −1.32956 + 1.32956i −0.0613280 + 0.0613280i
\(471\) −2.09008 −0.0963058
\(472\) 62.7482 2.88822
\(473\) −21.5972 + 21.5972i −0.993040 + 0.993040i
\(474\) 22.0362 + 22.0362i 1.01216 + 1.01216i
\(475\) 1.55862 1.55862i 0.0715142 0.0715142i
\(476\) 0 0
\(477\) −14.9015 −0.682293
\(478\) 28.6763i 1.31162i
\(479\) −8.20919 + 8.20919i −0.375087 + 0.375087i −0.869326 0.494239i \(-0.835447\pi\)
0.494239 + 0.869326i \(0.335447\pi\)
\(480\) 3.88077i 0.177132i
\(481\) −11.0767 8.48518i −0.505056 0.386891i
\(482\) 15.9046i 0.724436i
\(483\) 0 0
\(484\) 90.8845 4.13111
\(485\) 16.4416i 0.746577i
\(486\) −20.3192 20.3192i −0.921699 0.921699i
\(487\) 23.5164 23.5164i 1.06563 1.06563i 0.0679387 0.997689i \(-0.478358\pi\)
0.997689 0.0679387i \(-0.0216422\pi\)
\(488\) −18.6990 + 18.6990i −0.846463 + 0.846463i
\(489\) −24.5098 + 24.5098i −1.10837 + 1.10837i
\(490\) 0 0
\(491\) 2.41523i 0.108998i 0.998514 + 0.0544989i \(0.0173561\pi\)
−0.998514 + 0.0544989i \(0.982644\pi\)
\(492\) −33.8565 33.8565i −1.52637 1.52637i
\(493\) −5.63337 −0.253714
\(494\) 8.40557 1.11357i 0.378185 0.0501019i
\(495\) 11.1101i 0.499361i
\(496\) −14.8906 14.8906i −0.668609 0.668609i
\(497\) 0 0
\(498\) 82.3352i 3.68953i
\(499\) −0.347869 + 0.347869i −0.0155727 + 0.0155727i −0.714850 0.699278i \(-0.753505\pi\)
0.699278 + 0.714850i \(0.253505\pi\)
\(500\) −34.8637 34.8637i −1.55915 1.55915i
\(501\) −0.715594 0.715594i −0.0319704 0.0319704i
\(502\) −3.48059 + 3.48059i −0.155346 + 0.155346i
\(503\) 15.5328i 0.692575i −0.938128 0.346288i \(-0.887442\pi\)
0.938128 0.346288i \(-0.112558\pi\)
\(504\) 0 0
\(505\) 4.93301 + 4.93301i 0.219516 + 0.219516i
\(506\) 50.3651i 2.23900i
\(507\) −6.92015 25.6593i −0.307335 1.13957i
\(508\) −25.2184 −1.11889
\(509\) 24.6288 + 24.6288i 1.09165 + 1.09165i 0.995352 + 0.0963018i \(0.0307014\pi\)
0.0963018 + 0.995352i \(0.469299\pi\)
\(510\) 16.4247i 0.727297i
\(511\) 0 0
\(512\) 30.8689 30.8689i 1.36422 1.36422i
\(513\) 2.50324 2.50324i 0.110521 0.110521i
\(514\) 3.68156 3.68156i 0.162387 0.162387i
\(515\) 4.83070 + 4.83070i 0.212866 + 0.212866i
\(516\) 44.6538i 1.96577i
\(517\) 2.67092 0.117467
\(518\) 0 0
\(519\) 8.12741i 0.356754i
\(520\) −4.05377 30.5991i −0.177769 1.34186i
\(521\) 5.71857i 0.250535i 0.992123 + 0.125268i \(0.0399789\pi\)
−0.992123 + 0.125268i \(0.960021\pi\)
\(522\) 5.85441 5.85441i 0.256241 0.256241i
\(523\) 26.8158i 1.17257i 0.810104 + 0.586286i \(0.199411\pi\)
−0.810104 + 0.586286i \(0.800589\pi\)
\(524\) −6.20829 −0.271210
\(525\) 0 0
\(526\) 35.4455 35.4455i 1.54550 1.54550i
\(527\) −6.29003 6.29003i −0.273998 0.273998i
\(528\) −39.0554 + 39.0554i −1.69967 + 1.69967i
\(529\) 10.4623 0.454884
\(530\) −51.1746 −2.22288
\(531\) −10.0099 + 10.0099i −0.434391 + 0.434391i
\(532\) 0 0
\(533\) −16.2952 12.4827i −0.705825 0.540687i
\(534\) −18.3783 −0.795305
\(535\) −4.43510 4.43510i −0.191746 0.191746i
\(536\) −31.7685 −1.37219
\(537\) −13.1548 −0.567672
\(538\) −2.30766 2.30766i −0.0994903 0.0994903i
\(539\) 0 0
\(540\) −17.7341 17.7341i −0.763152 0.763152i
\(541\) 14.1144 + 14.1144i 0.606825 + 0.606825i 0.942115 0.335290i \(-0.108834\pi\)
−0.335290 + 0.942115i \(0.608834\pi\)
\(542\) 68.0655i 2.92366i
\(543\) 22.0175i 0.944861i
\(544\) −1.62601 + 1.62601i −0.0697145 + 0.0697145i
\(545\) −2.34200 −0.100320
\(546\) 0 0
\(547\) −11.1973 −0.478763 −0.239382 0.970926i \(-0.576945\pi\)
−0.239382 + 0.970926i \(0.576945\pi\)
\(548\) 19.8330 19.8330i 0.847226 0.847226i
\(549\) 5.96589i 0.254618i
\(550\) 32.9657i 1.40566i
\(551\) 1.90958 + 1.90958i 0.0813510 + 0.0813510i
\(552\) 26.7544 + 26.7544i 1.13874 + 1.13874i
\(553\) 0 0
\(554\) 29.3999 + 29.3999i 1.24908 + 1.24908i
\(555\) 12.9572 0.550003
\(556\) −25.7913 −1.09380
\(557\) 21.9072 + 21.9072i 0.928236 + 0.928236i 0.997592 0.0693555i \(-0.0220943\pi\)
−0.0693555 + 0.997592i \(0.522094\pi\)
\(558\) 13.0737 0.553453
\(559\) −2.51418 18.9778i −0.106338 0.802675i
\(560\) 0 0
\(561\) −16.4976 + 16.4976i −0.696529 + 0.696529i
\(562\) 52.1907 2.20153
\(563\) 35.6713 1.50336 0.751682 0.659526i \(-0.229243\pi\)
0.751682 + 0.659526i \(0.229243\pi\)
\(564\) −2.76117 + 2.76117i −0.116266 + 0.116266i
\(565\) 17.6203 + 17.6203i 0.741293 + 0.741293i
\(566\) 54.3490 54.3490i 2.28446 2.28446i
\(567\) 0 0
\(568\) −35.8220 −1.50306
\(569\) 15.7402i 0.659864i −0.944005 0.329932i \(-0.892974\pi\)
0.944005 0.329932i \(-0.107026\pi\)
\(570\) −5.56759 + 5.56759i −0.233201 + 0.233201i
\(571\) 5.63180i 0.235683i −0.993032 0.117842i \(-0.962402\pi\)
0.993032 0.117842i \(-0.0375975\pi\)
\(572\) −51.8892 + 67.7373i −2.16960 + 2.83224i
\(573\) 4.18405i 0.174791i
\(574\) 0 0
\(575\) 8.20634 0.342228
\(576\) 7.69719i 0.320716i
\(577\) −27.0981 27.0981i −1.12811 1.12811i −0.990484 0.137626i \(-0.956053\pi\)
−0.137626 0.990484i \(-0.543947\pi\)
\(578\) 22.8414 22.8414i 0.950075 0.950075i
\(579\) −4.15985 + 4.15985i −0.172877 + 0.172877i
\(580\) 13.5283 13.5283i 0.561734 0.561734i
\(581\) 0 0
\(582\) 50.7450i 2.10345i
\(583\) 51.4018 + 51.4018i 2.12885 + 2.12885i
\(584\) 22.9612 0.950142
\(585\) 5.52798 + 4.23463i 0.228554 + 0.175080i
\(586\) 37.6183i 1.55400i
\(587\) 18.6594 + 18.6594i 0.770156 + 0.770156i 0.978134 0.207977i \(-0.0666880\pi\)
−0.207977 + 0.978134i \(0.566688\pi\)
\(588\) 0 0
\(589\) 4.26435i 0.175710i
\(590\) −34.3758 + 34.3758i −1.41523 + 1.41523i
\(591\) 9.03975 + 9.03975i 0.371846 + 0.371846i
\(592\) −12.8522 12.8522i −0.528220 0.528220i
\(593\) 32.2761 32.2761i 1.32542 1.32542i 0.416104 0.909317i \(-0.363395\pi\)
0.909317 0.416104i \(-0.136605\pi\)
\(594\) 52.9450i 2.17236i
\(595\) 0 0
\(596\) 7.87696 + 7.87696i 0.322653 + 0.322653i
\(597\) 42.5477i 1.74136i
\(598\) 25.0598 + 19.1967i 1.02477 + 0.785013i
\(599\) 4.68759 0.191530 0.0957650 0.995404i \(-0.469470\pi\)
0.0957650 + 0.995404i \(0.469470\pi\)
\(600\) −17.5117 17.5117i −0.714912 0.714912i
\(601\) 34.8781i 1.42271i −0.702835 0.711353i \(-0.748083\pi\)
0.702835 0.711353i \(-0.251917\pi\)
\(602\) 0 0
\(603\) 5.06786 5.06786i 0.206379 0.206379i
\(604\) −0.822722 + 0.822722i −0.0334761 + 0.0334761i
\(605\) −25.5845 + 25.5845i −1.04016 + 1.04016i
\(606\) 15.2251 + 15.2251i 0.618477 + 0.618477i
\(607\) 29.8381i 1.21109i −0.795811 0.605545i \(-0.792955\pi\)
0.795811 0.605545i \(-0.207045\pi\)
\(608\) 1.10236 0.0447066
\(609\) 0 0
\(610\) 20.4880i 0.829536i
\(611\) −1.01803 + 1.32896i −0.0411850 + 0.0537638i
\(612\) 9.62460i 0.389051i
\(613\) −30.1015 + 30.1015i −1.21579 + 1.21579i −0.246694 + 0.969093i \(0.579344\pi\)
−0.969093 + 0.246694i \(0.920656\pi\)
\(614\) 66.2764i 2.67470i
\(615\) 19.0616 0.768639
\(616\) 0 0
\(617\) 13.3408 13.3408i 0.537079 0.537079i −0.385591 0.922670i \(-0.626002\pi\)
0.922670 + 0.385591i \(0.126002\pi\)
\(618\) 14.9093 + 14.9093i 0.599742 + 0.599742i
\(619\) −2.03692 + 2.03692i −0.0818708 + 0.0818708i −0.746856 0.664985i \(-0.768438\pi\)
0.664985 + 0.746856i \(0.268438\pi\)
\(620\) 30.2106 1.21329
\(621\) 13.1799 0.528892
\(622\) −19.6649 + 19.6649i −0.788491 + 0.788491i
\(623\) 0 0
\(624\) −4.54653 34.3186i −0.182007 1.37384i
\(625\) 8.04059 0.321623
\(626\) 51.2344 + 51.2344i 2.04774 + 2.04774i
\(627\) 11.1846 0.446671
\(628\) −4.20604 −0.167839
\(629\) −5.42895 5.42895i −0.216466 0.216466i
\(630\) 0 0
\(631\) −25.3632 25.3632i −1.00969 1.00969i −0.999953 0.00973923i \(-0.996900\pi\)
−0.00973923 0.999953i \(-0.503100\pi\)
\(632\) 22.7868 + 22.7868i 0.906409 + 0.906409i
\(633\) 31.6126i 1.25649i
\(634\) 37.6242i 1.49425i
\(635\) 7.09914 7.09914i 0.281721 0.281721i
\(636\) −106.277 −4.21416
\(637\) 0 0
\(638\) −40.3889 −1.59901
\(639\) 5.71448 5.71448i 0.226061 0.226061i
\(640\) 30.2303i 1.19496i
\(641\) 3.27503i 0.129356i 0.997906 + 0.0646779i \(0.0206020\pi\)
−0.997906 + 0.0646779i \(0.979398\pi\)
\(642\) −13.6884 13.6884i −0.540237 0.540237i
\(643\) −30.3555 30.3555i −1.19710 1.19710i −0.975030 0.222072i \(-0.928718\pi\)
−0.222072 0.975030i \(-0.571282\pi\)
\(644\) 0 0
\(645\) 12.5703 + 12.5703i 0.494955 + 0.494955i
\(646\) 4.66553 0.183563
\(647\) 33.2683 1.30791 0.653956 0.756532i \(-0.273108\pi\)
0.653956 + 0.756532i \(0.273108\pi\)
\(648\) −41.2004 41.2004i −1.61850 1.61850i
\(649\) 69.0569 2.71072
\(650\) −16.4025 12.5649i −0.643361 0.492837i
\(651\) 0 0
\(652\) −49.3230 + 49.3230i −1.93164 + 1.93164i
\(653\) −30.9543 −1.21134 −0.605668 0.795718i \(-0.707094\pi\)
−0.605668 + 0.795718i \(0.707094\pi\)
\(654\) −7.22827 −0.282648
\(655\) 1.74767 1.74767i 0.0682871 0.0682871i
\(656\) −18.9071 18.9071i −0.738197 0.738197i
\(657\) −3.66288 + 3.66288i −0.142902 + 0.142902i
\(658\) 0 0
\(659\) −43.2836 −1.68609 −0.843045 0.537843i \(-0.819239\pi\)
−0.843045 + 0.537843i \(0.819239\pi\)
\(660\) 79.2368i 3.08429i
\(661\) −29.3071 + 29.3071i −1.13992 + 1.13992i −0.151451 + 0.988465i \(0.548395\pi\)
−0.988465 + 0.151451i \(0.951605\pi\)
\(662\) 63.5934i 2.47163i
\(663\) −1.92052 14.4967i −0.0745869 0.563005i
\(664\) 85.1395i 3.30406i
\(665\) 0 0
\(666\) 11.2839 0.437243
\(667\) 10.0542i 0.389302i
\(668\) −1.44005 1.44005i −0.0557172 0.0557172i
\(669\) −34.1476 + 34.1476i −1.32022 + 1.32022i
\(670\) 17.4040 17.4040i 0.672375 0.672375i
\(671\) −20.5790 + 20.5790i −0.794443 + 0.794443i
\(672\) 0 0
\(673\) 12.5591i 0.484116i −0.970262 0.242058i \(-0.922178\pi\)
0.970262 0.242058i \(-0.0778224\pi\)
\(674\) 6.51588 + 6.51588i 0.250982 + 0.250982i
\(675\) −8.62671 −0.332042
\(676\) −13.9260 51.6364i −0.535615 1.98601i
\(677\) 8.39322i 0.322578i −0.986907 0.161289i \(-0.948435\pi\)
0.986907 0.161289i \(-0.0515651\pi\)
\(678\) 54.3828 + 54.3828i 2.08856 + 2.08856i
\(679\) 0 0
\(680\) 16.9841i 0.651310i
\(681\) 31.0134 31.0134i 1.18844 1.18844i
\(682\) −45.0968 45.0968i −1.72685 1.72685i
\(683\) 7.43844 + 7.43844i 0.284624 + 0.284624i 0.834950 0.550326i \(-0.185497\pi\)
−0.550326 + 0.834950i \(0.685497\pi\)
\(684\) −3.26252 + 3.26252i −0.124746 + 0.124746i
\(685\) 11.1662i 0.426640i
\(686\) 0 0
\(687\) 1.46301 + 1.46301i 0.0558174 + 0.0558174i
\(688\) 24.9367i 0.950704i
\(689\) −45.1676 + 5.98380i −1.72075 + 0.227965i
\(690\) −29.3142 −1.11597
\(691\) −24.8760 24.8760i −0.946329 0.946329i 0.0523022 0.998631i \(-0.483344\pi\)
−0.998631 + 0.0523022i \(0.983344\pi\)
\(692\) 16.3555i 0.621741i
\(693\) 0 0
\(694\) 23.6787 23.6787i 0.898830 0.898830i
\(695\) 7.26040 7.26040i 0.275403 0.275403i
\(696\) 21.4550 21.4550i 0.813248 0.813248i
\(697\) −7.98664 7.98664i −0.302515 0.302515i
\(698\) 75.4604i 2.85622i
\(699\) 4.44844 0.168256
\(700\) 0 0
\(701\) 0.321018i 0.0121247i −0.999982 0.00606234i \(-0.998070\pi\)
0.999982 0.00606234i \(-0.00192972\pi\)
\(702\) −26.3435 20.1801i −0.994273 0.761648i
\(703\) 3.68058i 0.138816i
\(704\) 26.5510 26.5510i 1.00068 1.00068i
\(705\) 1.55457i 0.0585484i
\(706\) 6.85348 0.257934
\(707\) 0 0
\(708\) −71.3901 + 71.3901i −2.68300 + 2.68300i
\(709\) 17.7156 + 17.7156i 0.665324 + 0.665324i 0.956630 0.291306i \(-0.0940898\pi\)
−0.291306 + 0.956630i \(0.594090\pi\)
\(710\) 19.6246 19.6246i 0.736499 0.736499i
\(711\) −7.27010 −0.272650
\(712\) −19.0042 −0.712213
\(713\) −11.2262 + 11.2262i −0.420425 + 0.420425i
\(714\) 0 0
\(715\) −4.46134 33.6755i −0.166844 1.25939i
\(716\) −26.4725 −0.989323
\(717\) 16.7647 + 16.7647i 0.626088 + 0.626088i
\(718\) −22.5516 −0.841619
\(719\) −31.0503 −1.15798 −0.578990 0.815335i \(-0.696553\pi\)
−0.578990 + 0.815335i \(0.696553\pi\)
\(720\) 6.41402 + 6.41402i 0.239036 + 0.239036i
\(721\) 0 0
\(722\) 31.6385 + 31.6385i 1.17746 + 1.17746i
\(723\) −9.29813 9.29813i −0.345801 0.345801i
\(724\) 44.3076i 1.64668i
\(725\) 6.58085i 0.244407i
\(726\) −78.9632 + 78.9632i −2.93060 + 2.93060i
\(727\) 40.0423 1.48509 0.742543 0.669798i \(-0.233619\pi\)
0.742543 + 0.669798i \(0.233619\pi\)
\(728\) 0 0
\(729\) −9.68335 −0.358642
\(730\) −12.5790 + 12.5790i −0.465571 + 0.465571i
\(731\) 10.5337i 0.389602i
\(732\) 42.5486i 1.57264i
\(733\) 9.71594 + 9.71594i 0.358866 + 0.358866i 0.863395 0.504529i \(-0.168334\pi\)
−0.504529 + 0.863395i \(0.668334\pi\)
\(734\) −21.1975 21.1975i −0.782414 0.782414i
\(735\) 0 0
\(736\) 2.90204 + 2.90204i 0.106971 + 0.106971i
\(737\) −34.9625 −1.28786
\(738\) 16.6000 0.611055
\(739\) −23.6966 23.6966i −0.871693 0.871693i 0.120964 0.992657i \(-0.461401\pi\)
−0.992657 + 0.120964i \(0.961401\pi\)
\(740\) 26.0749 0.958531
\(741\) −4.26304 + 5.56506i −0.156607 + 0.204438i
\(742\) 0 0
\(743\) 16.7361 16.7361i 0.613988 0.613988i −0.329994 0.943983i \(-0.607047\pi\)
0.943983 + 0.329994i \(0.107047\pi\)
\(744\) 47.9118 1.75653
\(745\) −4.43482 −0.162479
\(746\) −48.4407 + 48.4407i −1.77354 + 1.77354i
\(747\) 13.5818 + 13.5818i 0.496934 + 0.496934i
\(748\) −33.1995 + 33.1995i −1.21389 + 1.21389i
\(749\) 0 0
\(750\) 60.5813 2.21212
\(751\) 11.4871i 0.419170i −0.977790 0.209585i \(-0.932789\pi\)
0.977790 0.209585i \(-0.0672114\pi\)
\(752\) −1.54196 + 1.54196i −0.0562296 + 0.0562296i
\(753\) 4.06963i 0.148306i
\(754\) 15.3943 20.0960i 0.560627 0.731855i
\(755\) 0.463202i 0.0168576i
\(756\) 0 0
\(757\) −17.1190 −0.622200 −0.311100 0.950377i \(-0.600697\pi\)
−0.311100 + 0.950377i \(0.600697\pi\)
\(758\) 6.90739i 0.250888i
\(759\) 29.4443 + 29.4443i 1.06876 + 1.06876i
\(760\) −5.75722 + 5.75722i −0.208836 + 0.208836i
\(761\) 24.1664 24.1664i 0.876030 0.876030i −0.117091 0.993121i \(-0.537357\pi\)
0.993121 + 0.117091i \(0.0373571\pi\)
\(762\) 21.9106 21.9106i 0.793736 0.793736i
\(763\) 0 0
\(764\) 8.41991i 0.304622i
\(765\) 2.70938 + 2.70938i 0.0979578 + 0.0979578i
\(766\) −44.9534 −1.62423
\(767\) −26.3211 + 34.3602i −0.950402 + 1.24068i
\(768\) 66.6140i 2.40373i
\(769\) −5.13005 5.13005i −0.184994 0.184994i 0.608534 0.793528i \(-0.291758\pi\)
−0.793528 + 0.608534i \(0.791758\pi\)
\(770\) 0 0
\(771\) 4.30462i 0.155027i
\(772\) −8.37120 + 8.37120i −0.301286 + 0.301286i
\(773\) −15.3264 15.3264i −0.551253 0.551253i 0.375549 0.926802i \(-0.377454\pi\)
−0.926802 + 0.375549i \(0.877454\pi\)
\(774\) 10.9470 + 10.9470i 0.393481 + 0.393481i
\(775\) 7.34795 7.34795i 0.263946 0.263946i
\(776\) 52.4734i 1.88368i
\(777\) 0 0
\(778\) −9.62487 9.62487i −0.345068 0.345068i
\(779\) 5.41458i 0.193997i
\(780\) 39.4254 + 30.2012i 1.41166 + 1.08138i
\(781\) −39.4235 −1.41068
\(782\) 12.2824 + 12.2824i 0.439216 + 0.439216i
\(783\) 10.5693i 0.377715i
\(784\) 0 0
\(785\) 1.18402 1.18402i 0.0422596 0.0422596i
\(786\) 5.39395 5.39395i 0.192396 0.192396i
\(787\) 9.46268 9.46268i 0.337308 0.337308i −0.518045 0.855353i \(-0.673340\pi\)
0.855353 + 0.518045i \(0.173340\pi\)
\(788\) 18.1914 + 18.1914i 0.648043 + 0.648043i
\(789\) 41.4442i 1.47545i
\(790\) −24.9669 −0.888283
\(791\) 0 0
\(792\) 35.4577i 1.25994i
\(793\) −2.39565 18.0831i −0.0850720 0.642149i
\(794\) 61.6497i 2.18787i
\(795\) 29.9176 29.9176i 1.06107 1.06107i
\(796\) 85.6223i 3.03480i
\(797\) 53.9645 1.91152 0.955760 0.294149i \(-0.0950363\pi\)
0.955760 + 0.294149i \(0.0950363\pi\)
\(798\) 0 0
\(799\) −0.651349 + 0.651349i −0.0230431 + 0.0230431i
\(800\) −1.89949 1.89949i −0.0671570 0.0671570i
\(801\) 3.03164 3.03164i 0.107118 0.107118i
\(802\) 20.2316 0.714402
\(803\) 25.2698 0.891751
\(804\) 36.1438 36.1438i 1.27469 1.27469i
\(805\) 0 0
\(806\) 39.6273 5.24983i 1.39581 0.184917i
\(807\) 2.69820 0.0949811
\(808\) 15.7437 + 15.7437i 0.553860 + 0.553860i
\(809\) 25.4183 0.893659 0.446829 0.894619i \(-0.352553\pi\)
0.446829 + 0.894619i \(0.352553\pi\)
\(810\) 45.1423 1.58614
\(811\) 15.9565 + 15.9565i 0.560310 + 0.560310i 0.929395 0.369085i \(-0.120329\pi\)
−0.369085 + 0.929395i \(0.620329\pi\)
\(812\) 0 0
\(813\) 39.7923 + 39.7923i 1.39558 + 1.39558i
\(814\) −38.9232 38.9232i −1.36426 1.36426i
\(815\) 27.7694i 0.972720i
\(816\) 19.0486i 0.666835i
\(817\) −3.57067 + 3.57067i −0.124922 + 0.124922i
\(818\) −11.0982 −0.388040
\(819\) 0 0
\(820\) 38.3593 1.33956
\(821\) 27.7719 27.7719i 0.969244 0.969244i −0.0302966 0.999541i \(-0.509645\pi\)
0.999541 + 0.0302966i \(0.00964518\pi\)
\(822\) 34.4631i 1.20204i
\(823\) 30.3011i 1.05623i −0.849173 0.528115i \(-0.822899\pi\)
0.849173 0.528115i \(-0.177101\pi\)
\(824\) 15.4171 + 15.4171i 0.537082 + 0.537082i
\(825\) −19.2723 19.2723i −0.670977 0.670977i
\(826\) 0 0
\(827\) −7.62275 7.62275i −0.265069 0.265069i 0.562041 0.827110i \(-0.310016\pi\)
−0.827110 + 0.562041i \(0.810016\pi\)
\(828\) −17.1776 −0.596964
\(829\) 34.6984 1.20513 0.602563 0.798071i \(-0.294146\pi\)
0.602563 + 0.798071i \(0.294146\pi\)
\(830\) 46.6427 + 46.6427i 1.61899 + 1.61899i
\(831\) −34.3754 −1.19247
\(832\) 3.09086 + 23.3308i 0.107156 + 0.808849i
\(833\) 0 0
\(834\) 22.4083 22.4083i 0.775936 0.775936i
\(835\) 0.810764 0.0280576
\(836\) 22.5077 0.778446
\(837\) 11.8013 11.8013i 0.407912 0.407912i
\(838\) −61.4524 61.4524i −2.12284 2.12284i
\(839\) −5.64491 + 5.64491i −0.194884 + 0.194884i −0.797803 0.602919i \(-0.794004\pi\)
0.602919 + 0.797803i \(0.294004\pi\)
\(840\) 0 0
\(841\) −20.9373 −0.721975
\(842\) 86.4149i 2.97805i
\(843\) −30.5116 + 30.5116i −1.05088 + 1.05088i
\(844\) 63.6166i 2.18977i
\(845\) 18.4562 + 10.6157i 0.634912 + 0.365191i
\(846\) 1.35381i 0.0465450i
\(847\) 0 0
\(848\) −59.3501 −2.03809
\(849\) 63.5468i 2.18092i
\(850\) −8.03923 8.03923i −0.275743 0.275743i
\(851\) −9.68939 + 9.68939i −0.332148 + 0.332148i
\(852\) 40.7555 40.7555i 1.39626 1.39626i
\(853\) 5.56139 5.56139i 0.190418 0.190418i −0.605458 0.795877i \(-0.707010\pi\)
0.795877 + 0.605458i \(0.207010\pi\)
\(854\) 0 0
\(855\) 1.83684i 0.0628185i
\(856\) −14.1546 14.1546i −0.483794 0.483794i
\(857\) 30.7159 1.04923 0.524617 0.851338i \(-0.324209\pi\)
0.524617 + 0.851338i \(0.324209\pi\)
\(858\) −13.7693 103.935i −0.470077 3.54829i
\(859\) 9.70111i 0.330998i 0.986210 + 0.165499i \(0.0529234\pi\)
−0.986210 + 0.165499i \(0.947077\pi\)
\(860\) 25.2962 + 25.2962i 0.862594 + 0.862594i
\(861\) 0 0
\(862\) 88.4499i 3.01261i
\(863\) −3.00951 + 3.00951i −0.102445 + 0.102445i −0.756471 0.654027i \(-0.773078\pi\)
0.654027 + 0.756471i \(0.273078\pi\)
\(864\) −3.05070 3.05070i −0.103787 0.103787i
\(865\) −4.60415 4.60415i −0.156546 0.156546i
\(866\) −6.69514 + 6.69514i −0.227510 + 0.227510i
\(867\) 26.7069i 0.907015i
\(868\) 0 0
\(869\) 25.0778 + 25.0778i 0.850705 + 0.850705i
\(870\) 23.5077i 0.796985i
\(871\) 13.3260 17.3961i 0.451535 0.589444i
\(872\) −7.47446 −0.253117
\(873\) −8.37079 8.37079i −0.283308 0.283308i
\(874\) 8.32688i 0.281661i
\(875\) 0 0
\(876\) −26.1235 + 26.1235i −0.882633 + 0.882633i
\(877\) −12.6009 + 12.6009i −0.425502 + 0.425502i −0.887093 0.461591i \(-0.847279\pi\)
0.461591 + 0.887093i \(0.347279\pi\)
\(878\) −7.51613 + 7.51613i −0.253657 + 0.253657i
\(879\) 21.9923 + 21.9923i 0.741783 + 0.741783i
\(880\) 44.2495i 1.49165i
\(881\) 38.7999 1.30720 0.653600 0.756840i \(-0.273258\pi\)
0.653600 + 0.756840i \(0.273258\pi\)
\(882\) 0 0
\(883\) 42.2858i 1.42303i −0.702671 0.711514i \(-0.748010\pi\)
0.702671 0.711514i \(-0.251990\pi\)
\(884\) −3.86483 29.1729i −0.129988 0.981191i
\(885\) 40.1934i 1.35109i
\(886\) 25.7890 25.7890i 0.866399 0.866399i
\(887\) 24.8047i 0.832860i −0.909168 0.416430i \(-0.863281\pi\)
0.909168 0.416430i \(-0.136719\pi\)
\(888\) 41.3528 1.38771
\(889\) 0 0
\(890\) 10.4112 10.4112i 0.348985 0.348985i
\(891\) −45.3427 45.3427i −1.51904 1.51904i
\(892\) −68.7181 + 68.7181i −2.30085 + 2.30085i
\(893\) 0.441585 0.0147771
\(894\) −13.6875 −0.457778
\(895\) 7.45216 7.45216i 0.249098 0.249098i
\(896\) 0 0
\(897\) −25.8732 + 3.42768i −0.863881 + 0.114447i
\(898\) 48.8975 1.63173
\(899\) 9.00256 + 9.00256i 0.300252 + 0.300252i
\(900\) 11.2434 0.374779
\(901\) −25.0704 −0.835215
\(902\) −57.2608 57.2608i −1.90658 1.90658i
\(903\) 0 0
\(904\) 56.2351 + 56.2351i 1.87035 + 1.87035i
\(905\) −12.4728 12.4728i −0.414611 0.414611i
\(906\) 1.42961i 0.0474957i
\(907\) 36.6433i 1.21672i −0.793660 0.608361i \(-0.791827\pi\)
0.793660 0.608361i \(-0.208173\pi\)
\(908\) 62.4109 62.4109i 2.07118 2.07118i
\(909\) −5.02300 −0.166602
\(910\) 0 0
\(911\) −22.0142 −0.729363 −0.364682 0.931132i \(-0.618822\pi\)
−0.364682 + 0.931132i \(0.618822\pi\)
\(912\) −6.45705 + 6.45705i −0.213814 + 0.213814i
\(913\) 93.6995i 3.10100i
\(914\) 75.6500i 2.50228i
\(915\) 11.9777 + 11.9777i 0.395970 + 0.395970i
\(916\) 2.94414 + 2.94414i 0.0972772 + 0.0972772i
\(917\) 0 0
\(918\) −12.9115 12.9115i −0.426144 0.426144i
\(919\) 33.7663 1.11385 0.556924 0.830563i \(-0.311981\pi\)
0.556924 + 0.830563i \(0.311981\pi\)
\(920\) −30.3126 −0.999377
\(921\) 38.7464 + 38.7464i 1.27674 + 1.27674i
\(922\) −15.3815 −0.506564
\(923\) 15.0263 19.6157i 0.494598 0.645659i
\(924\) 0 0
\(925\) 6.34205 6.34205i 0.208525 0.208525i
\(926\) −23.3523 −0.767404
\(927\) −4.91883 −0.161555
\(928\) 2.32721 2.32721i 0.0763944 0.0763944i
\(929\) −16.4202 16.4202i −0.538730 0.538730i 0.384426 0.923156i \(-0.374399\pi\)
−0.923156 + 0.384426i \(0.874399\pi\)
\(930\) −26.2479 + 26.2479i −0.860702 + 0.860702i
\(931\) 0 0
\(932\) 8.95197 0.293231
\(933\) 22.9929i 0.752754i
\(934\) 66.6229 66.6229i 2.17997 2.17997i
\(935\) 18.6917i 0.611283i
\(936\) 17.6425 + 13.5148i 0.576663 + 0.441744i
\(937\) 7.15492i 0.233741i 0.993147 + 0.116870i \(0.0372862\pi\)
−0.993147 + 0.116870i \(0.962714\pi\)
\(938\) 0 0
\(939\) −59.9051 −1.95493
\(940\) 3.12838i 0.102037i
\(941\) −3.40215 3.40215i −0.110907 0.110907i 0.649476 0.760382i \(-0.274988\pi\)
−0.760382 + 0.649476i \(0.774988\pi\)
\(942\) 3.65434 3.65434i 0.119065 0.119065i
\(943\) −14.2543 + 14.2543i −0.464183 + 0.464183i
\(944\) −39.8676 + 39.8676i −1.29758 + 1.29758i
\(945\) 0 0
\(946\) 75.5219i 2.45543i
\(947\) 13.3142 + 13.3142i 0.432653 + 0.432653i 0.889530 0.456877i \(-0.151032\pi\)
−0.456877 + 0.889530i \(0.651032\pi\)
\(948\) −51.8501 −1.68401
\(949\) −9.63161 + 12.5733i −0.312655 + 0.408147i
\(950\) 5.45023i 0.176829i
\(951\) −21.9958 21.9958i −0.713262 0.713262i
\(952\) 0 0
\(953\) 4.93813i 0.159962i −0.996796 0.0799809i \(-0.974514\pi\)
0.996796 0.0799809i \(-0.0254859\pi\)
\(954\) 26.0541 26.0541i 0.843532 0.843532i
\(955\) 2.37025 + 2.37025i 0.0766996 + 0.0766996i
\(956\) 33.7369 + 33.7369i 1.09113 + 1.09113i
\(957\) 23.6121 23.6121i 0.763270 0.763270i
\(958\) 28.7062i 0.927456i
\(959\) 0 0
\(960\) −15.4536 15.4536i −0.498762 0.498762i
\(961\) 10.8961i 0.351487i
\(962\) 34.2025 4.53114i 1.10273 0.146090i
\(963\) 4.51601 0.145526
\(964\) −18.7114 18.7114i −0.602653 0.602653i
\(965\) 4.71308i 0.151720i
\(966\) 0 0
\(967\) −10.3931 + 10.3931i −0.334219 + 0.334219i −0.854186 0.519967i \(-0.825944\pi\)
0.519967 + 0.854186i \(0.325944\pi\)
\(968\) −81.6527 + 81.6527i −2.62442 + 2.62442i
\(969\) −2.72756 + 2.72756i −0.0876217 + 0.0876217i
\(970\) −28.7469 28.7469i −0.923007 0.923007i
\(971\) 5.88769i 0.188945i 0.995527 + 0.0944724i \(0.0301164\pi\)
−0.995527 + 0.0944724i \(0.969884\pi\)
\(972\) 47.8101 1.53351
\(973\) 0 0
\(974\) 82.2330i 2.63491i
\(975\) 16.9349 2.24354i 0.542351 0.0718507i
\(976\) 23.7611i 0.760575i
\(977\) 8.72187 8.72187i 0.279037 0.279037i −0.553687 0.832725i \(-0.686780\pi\)
0.832725 + 0.553687i \(0.186780\pi\)
\(978\) 85.7067i 2.74060i
\(979\) −20.9149 −0.668443
\(980\) 0 0
\(981\) 1.19236 1.19236i 0.0380691 0.0380691i
\(982\) −4.22284 4.22284i −0.134756 0.134756i
\(983\) 3.51722 3.51722i 0.112182 0.112182i −0.648788 0.760970i \(-0.724724\pi\)
0.760970 + 0.648788i \(0.224724\pi\)
\(984\) 60.8350 1.93935
\(985\) −10.2420 −0.326337
\(986\) 9.84950 9.84950i 0.313672 0.313672i
\(987\) 0 0
\(988\) −8.57886 + 11.1990i −0.272930 + 0.356289i
\(989\) −18.8001 −0.597809
\(990\) 19.4251 + 19.4251i 0.617370 + 0.617370i
\(991\) −15.1947 −0.482677 −0.241338 0.970441i \(-0.577586\pi\)
−0.241338 + 0.970441i \(0.577586\pi\)
\(992\) 5.19697 0.165004
\(993\) −37.1778 37.1778i −1.17980 1.17980i
\(994\) 0 0
\(995\) −24.1032 24.1032i −0.764122 0.764122i
\(996\) 96.8653 + 96.8653i 3.06930 + 3.06930i
\(997\) 59.7990i 1.89385i 0.321450 + 0.946926i \(0.395830\pi\)
−0.321450 + 0.946926i \(0.604170\pi\)
\(998\) 1.21644i 0.0385057i
\(999\) 10.1857 10.1857i 0.322262 0.322262i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 637.2.i.a.538.1 32
7.2 even 3 637.2.bc.b.31.8 32
7.3 odd 6 637.2.bc.b.460.1 32
7.4 even 3 91.2.bb.a.5.1 32
7.5 odd 6 91.2.bb.a.31.8 yes 32
7.6 odd 2 inner 637.2.i.a.538.2 32
13.8 odd 4 inner 637.2.i.a.489.1 32
21.5 even 6 819.2.fn.e.577.1 32
21.11 odd 6 819.2.fn.e.460.8 32
91.34 even 4 inner 637.2.i.a.489.2 32
91.47 even 12 91.2.bb.a.73.1 yes 32
91.60 odd 12 91.2.bb.a.47.8 yes 32
91.73 even 12 637.2.bc.b.411.8 32
91.86 odd 12 637.2.bc.b.619.1 32
273.47 odd 12 819.2.fn.e.73.8 32
273.242 even 12 819.2.fn.e.775.1 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.bb.a.5.1 32 7.4 even 3
91.2.bb.a.31.8 yes 32 7.5 odd 6
91.2.bb.a.47.8 yes 32 91.60 odd 12
91.2.bb.a.73.1 yes 32 91.47 even 12
637.2.i.a.489.1 32 13.8 odd 4 inner
637.2.i.a.489.2 32 91.34 even 4 inner
637.2.i.a.538.1 32 1.1 even 1 trivial
637.2.i.a.538.2 32 7.6 odd 2 inner
637.2.bc.b.31.8 32 7.2 even 3
637.2.bc.b.411.8 32 91.73 even 12
637.2.bc.b.460.1 32 7.3 odd 6
637.2.bc.b.619.1 32 91.86 odd 12
819.2.fn.e.73.8 32 273.47 odd 12
819.2.fn.e.460.8 32 21.11 odd 6
819.2.fn.e.577.1 32 21.5 even 6
819.2.fn.e.775.1 32 273.242 even 12