Properties

Label 507.2.f.e.239.3
Level $507$
Weight $2$
Character 507.239
Analytic conductor $4.048$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [507,2,Mod(239,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.239");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.f (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: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.56070144.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 239.3
Root \(0.500000 + 0.564882i\) of defining polynomial
Character \(\chi\) \(=\) 507.239
Dual form 507.2.f.e.437.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.06488 + 1.06488i) q^{2} +(1.36603 + 1.06488i) q^{3} +0.267949i q^{4} +(1.06488 + 1.06488i) q^{5} +(0.320682 + 2.58863i) q^{6} +(-1.00000 - 1.00000i) q^{7} +(1.84443 - 1.84443i) q^{8} +(0.732051 + 2.90931i) q^{9} +O(q^{10})\) \(q+(1.06488 + 1.06488i) q^{2} +(1.36603 + 1.06488i) q^{3} +0.267949i q^{4} +(1.06488 + 1.06488i) q^{5} +(0.320682 + 2.58863i) q^{6} +(-1.00000 - 1.00000i) q^{7} +(1.84443 - 1.84443i) q^{8} +(0.732051 + 2.90931i) q^{9} +2.26795i q^{10} +(-2.90931 + 2.90931i) q^{11} +(-0.285334 + 0.366025i) q^{12} -2.12976i q^{14} +(0.320682 + 2.58863i) q^{15} +4.46410 q^{16} +5.03908 q^{17} +(-2.31853 + 3.87762i) q^{18} +(-2.73205 + 2.73205i) q^{19} +(-0.285334 + 0.285334i) q^{20} +(-0.301143 - 2.43091i) q^{21} -6.19615 q^{22} +(4.48364 - 0.555437i) q^{24} -2.73205i q^{25} +(-2.09808 + 4.75374i) q^{27} +(0.267949 - 0.267949i) q^{28} -7.16884i q^{29} +(-2.41510 + 3.09808i) q^{30} +(2.46410 - 2.46410i) q^{31} +(1.06488 + 1.06488i) q^{32} +(-7.07227 + 0.876119i) q^{33} +(5.36603 + 5.36603i) q^{34} -2.12976i q^{35} +(-0.779548 + 0.196152i) q^{36} +(-3.83013 - 3.83013i) q^{37} -5.81863 q^{38} +3.92820 q^{40} +(-3.97420 - 3.97420i) q^{41} +(2.26795 - 2.90931i) q^{42} +2.19615i q^{43} +(-0.779548 - 0.779548i) q^{44} +(-2.31853 + 3.87762i) q^{45} +(-4.25953 + 4.25953i) q^{47} +(6.09808 + 4.75374i) q^{48} -5.00000i q^{49} +(2.90931 - 2.90931i) q^{50} +(6.88351 + 5.36603i) q^{51} -0.779548i q^{53} +(-7.29638 + 2.82797i) q^{54} -6.19615 q^{55} -3.68886 q^{56} +(-6.64136 + 0.822738i) q^{57} +(7.63397 - 7.63397i) q^{58} +(2.12976 - 2.12976i) q^{59} +(-0.693622 + 0.0859264i) q^{60} -7.00000 q^{61} +5.24796 q^{62} +(2.17726 - 3.64136i) q^{63} -6.66025i q^{64} +(-8.46410 - 6.59817i) q^{66} +(4.19615 - 4.19615i) q^{67} +1.35022i q^{68} +(2.26795 - 2.26795i) q^{70} +(-2.12976 - 2.12976i) q^{71} +(6.71624 + 4.01581i) q^{72} +(0.901924 + 0.901924i) q^{73} -8.15727i q^{74} +(2.90931 - 3.73205i) q^{75} +(-0.732051 - 0.732051i) q^{76} +5.81863 q^{77} +2.00000 q^{79} +(4.75374 + 4.75374i) q^{80} +(-7.92820 + 4.25953i) q^{81} -8.46410i q^{82} +(2.90931 + 2.90931i) q^{83} +(0.651360 - 0.0806910i) q^{84} +(5.36603 + 5.36603i) q^{85} +(-2.33864 + 2.33864i) q^{86} +(7.63397 - 9.79282i) q^{87} +10.7321i q^{88} +(-6.59817 + 6.59817i) q^{89} +(-6.59817 + 1.66025i) q^{90} +(5.99000 - 0.742047i) q^{93} -9.07180 q^{94} -5.81863 q^{95} +(0.320682 + 2.58863i) q^{96} +(1.19615 - 1.19615i) q^{97} +(5.32441 - 5.32441i) q^{98} +(-10.5939 - 6.33434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{3} - 16 q^{6} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{3} - 16 q^{6} - 8 q^{7} - 8 q^{9} - 16 q^{15} + 8 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} - 8 q^{22} - 12 q^{24} + 4 q^{27} + 16 q^{28} - 8 q^{31} - 4 q^{33} + 36 q^{34} + 4 q^{37} - 24 q^{40} + 32 q^{42} - 4 q^{45} + 28 q^{48} + 8 q^{54} - 8 q^{55} - 16 q^{57} + 68 q^{58} - 44 q^{60} - 56 q^{61} + 8 q^{63} - 40 q^{66} - 8 q^{67} + 32 q^{70} + 36 q^{72} + 28 q^{73} + 8 q^{76} + 16 q^{79} - 8 q^{81} - 4 q^{84} + 36 q^{85} + 68 q^{87} + 20 q^{93} - 128 q^{94} - 16 q^{96} - 32 q^{97} - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.06488 + 1.06488i 0.752986 + 0.752986i 0.975035 0.222050i \(-0.0712747\pi\)
−0.222050 + 0.975035i \(0.571275\pi\)
\(3\) 1.36603 + 1.06488i 0.788675 + 0.614810i
\(4\) 0.267949i 0.133975i
\(5\) 1.06488 + 1.06488i 0.476230 + 0.476230i 0.903924 0.427694i \(-0.140674\pi\)
−0.427694 + 0.903924i \(0.640674\pi\)
\(6\) 0.320682 + 2.58863i 0.130918 + 1.05680i
\(7\) −1.00000 1.00000i −0.377964 0.377964i 0.492403 0.870367i \(-0.336119\pi\)
−0.870367 + 0.492403i \(0.836119\pi\)
\(8\) 1.84443 1.84443i 0.652105 0.652105i
\(9\) 0.732051 + 2.90931i 0.244017 + 0.969771i
\(10\) 2.26795i 0.717189i
\(11\) −2.90931 + 2.90931i −0.877191 + 0.877191i −0.993243 0.116052i \(-0.962976\pi\)
0.116052 + 0.993243i \(0.462976\pi\)
\(12\) −0.285334 + 0.366025i −0.0823689 + 0.105662i
\(13\) 0 0
\(14\) 2.12976i 0.569204i
\(15\) 0.320682 + 2.58863i 0.0827997 + 0.668382i
\(16\) 4.46410 1.11603
\(17\) 5.03908 1.22216 0.611078 0.791570i \(-0.290736\pi\)
0.611078 + 0.791570i \(0.290736\pi\)
\(18\) −2.31853 + 3.87762i −0.546482 + 0.913965i
\(19\) −2.73205 + 2.73205i −0.626775 + 0.626775i −0.947255 0.320480i \(-0.896156\pi\)
0.320480 + 0.947255i \(0.396156\pi\)
\(20\) −0.285334 + 0.285334i −0.0638027 + 0.0638027i
\(21\) −0.301143 2.43091i −0.0657148 0.530468i
\(22\) −6.19615 −1.32102
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 4.48364 0.555437i 0.915219 0.113378i
\(25\) 2.73205i 0.546410i
\(26\) 0 0
\(27\) −2.09808 + 4.75374i −0.403775 + 0.914858i
\(28\) 0.267949 0.267949i 0.0506376 0.0506376i
\(29\) 7.16884i 1.33122i −0.746299 0.665610i \(-0.768171\pi\)
0.746299 0.665610i \(-0.231829\pi\)
\(30\) −2.41510 + 3.09808i −0.440935 + 0.565629i
\(31\) 2.46410 2.46410i 0.442566 0.442566i −0.450308 0.892873i \(-0.648686\pi\)
0.892873 + 0.450308i \(0.148686\pi\)
\(32\) 1.06488 + 1.06488i 0.188246 + 0.188246i
\(33\) −7.07227 + 0.876119i −1.23112 + 0.152513i
\(34\) 5.36603 + 5.36603i 0.920266 + 0.920266i
\(35\) 2.12976i 0.359996i
\(36\) −0.779548 + 0.196152i −0.129925 + 0.0326921i
\(37\) −3.83013 3.83013i −0.629669 0.629669i 0.318316 0.947985i \(-0.396883\pi\)
−0.947985 + 0.318316i \(0.896883\pi\)
\(38\) −5.81863 −0.943906
\(39\) 0 0
\(40\) 3.92820 0.621103
\(41\) −3.97420 3.97420i −0.620665 0.620665i 0.325036 0.945701i \(-0.394623\pi\)
−0.945701 + 0.325036i \(0.894623\pi\)
\(42\) 2.26795 2.90931i 0.349952 0.448917i
\(43\) 2.19615i 0.334910i 0.985880 + 0.167455i \(0.0535549\pi\)
−0.985880 + 0.167455i \(0.946445\pi\)
\(44\) −0.779548 0.779548i −0.117521 0.117521i
\(45\) −2.31853 + 3.87762i −0.345626 + 0.578042i
\(46\) 0 0
\(47\) −4.25953 + 4.25953i −0.621316 + 0.621316i −0.945868 0.324552i \(-0.894787\pi\)
0.324552 + 0.945868i \(0.394787\pi\)
\(48\) 6.09808 + 4.75374i 0.880181 + 0.686144i
\(49\) 5.00000i 0.714286i
\(50\) 2.90931 2.90931i 0.411439 0.411439i
\(51\) 6.88351 + 5.36603i 0.963884 + 0.751394i
\(52\) 0 0
\(53\) 0.779548i 0.107079i −0.998566 0.0535396i \(-0.982950\pi\)
0.998566 0.0535396i \(-0.0170503\pi\)
\(54\) −7.29638 + 2.82797i −0.992912 + 0.384838i
\(55\) −6.19615 −0.835489
\(56\) −3.68886 −0.492945
\(57\) −6.64136 + 0.822738i −0.879670 + 0.108974i
\(58\) 7.63397 7.63397i 1.00239 1.00239i
\(59\) 2.12976 2.12976i 0.277272 0.277272i −0.554747 0.832019i \(-0.687185\pi\)
0.832019 + 0.554747i \(0.187185\pi\)
\(60\) −0.693622 + 0.0859264i −0.0895462 + 0.0110931i
\(61\) −7.00000 −0.896258 −0.448129 0.893969i \(-0.647910\pi\)
−0.448129 + 0.893969i \(0.647910\pi\)
\(62\) 5.24796 0.666491
\(63\) 2.17726 3.64136i 0.274309 0.458769i
\(64\) 6.66025i 0.832532i
\(65\) 0 0
\(66\) −8.46410 6.59817i −1.04186 0.812179i
\(67\) 4.19615 4.19615i 0.512642 0.512642i −0.402693 0.915335i \(-0.631926\pi\)
0.915335 + 0.402693i \(0.131926\pi\)
\(68\) 1.35022i 0.163738i
\(69\) 0 0
\(70\) 2.26795 2.26795i 0.271072 0.271072i
\(71\) −2.12976 2.12976i −0.252757 0.252757i 0.569343 0.822100i \(-0.307198\pi\)
−0.822100 + 0.569343i \(0.807198\pi\)
\(72\) 6.71624 + 4.01581i 0.791517 + 0.473268i
\(73\) 0.901924 + 0.901924i 0.105562 + 0.105562i 0.757915 0.652353i \(-0.226218\pi\)
−0.652353 + 0.757915i \(0.726218\pi\)
\(74\) 8.15727i 0.948263i
\(75\) 2.90931 3.73205i 0.335939 0.430940i
\(76\) −0.732051 0.732051i −0.0839720 0.0839720i
\(77\) 5.81863 0.663094
\(78\) 0 0
\(79\) 2.00000 0.225018 0.112509 0.993651i \(-0.464111\pi\)
0.112509 + 0.993651i \(0.464111\pi\)
\(80\) 4.75374 + 4.75374i 0.531485 + 0.531485i
\(81\) −7.92820 + 4.25953i −0.880911 + 0.473281i
\(82\) 8.46410i 0.934704i
\(83\) 2.90931 + 2.90931i 0.319339 + 0.319339i 0.848513 0.529174i \(-0.177498\pi\)
−0.529174 + 0.848513i \(0.677498\pi\)
\(84\) 0.651360 0.0806910i 0.0710692 0.00880411i
\(85\) 5.36603 + 5.36603i 0.582027 + 0.582027i
\(86\) −2.33864 + 2.33864i −0.252182 + 0.252182i
\(87\) 7.63397 9.79282i 0.818448 1.04990i
\(88\) 10.7321i 1.14404i
\(89\) −6.59817 + 6.59817i −0.699405 + 0.699405i −0.964282 0.264877i \(-0.914669\pi\)
0.264877 + 0.964282i \(0.414669\pi\)
\(90\) −6.59817 + 1.66025i −0.695509 + 0.175006i
\(91\) 0 0
\(92\) 0 0
\(93\) 5.99000 0.742047i 0.621134 0.0769467i
\(94\) −9.07180 −0.935684
\(95\) −5.81863 −0.596978
\(96\) 0.320682 + 2.58863i 0.0327295 + 0.264201i
\(97\) 1.19615 1.19615i 0.121451 0.121451i −0.643769 0.765220i \(-0.722630\pi\)
0.765220 + 0.643769i \(0.222630\pi\)
\(98\) 5.32441 5.32441i 0.537847 0.537847i
\(99\) −10.5939 6.33434i −1.06472 0.636625i
\(100\) 0.732051 0.0732051
\(101\) −6.02751 −0.599759 −0.299880 0.953977i \(-0.596947\pi\)
−0.299880 + 0.953977i \(0.596947\pi\)
\(102\) 1.61594 + 13.0443i 0.160002 + 1.29158i
\(103\) 6.92820i 0.682656i 0.939944 + 0.341328i \(0.110877\pi\)
−0.939944 + 0.341328i \(0.889123\pi\)
\(104\) 0 0
\(105\) 2.26795 2.90931i 0.221329 0.283920i
\(106\) 0.830127 0.830127i 0.0806291 0.0806291i
\(107\) 19.0150i 1.83825i 0.393970 + 0.919123i \(0.371101\pi\)
−0.393970 + 0.919123i \(0.628899\pi\)
\(108\) −1.27376 0.562178i −0.122568 0.0540956i
\(109\) 13.1962 13.1962i 1.26396 1.26396i 0.314806 0.949156i \(-0.398060\pi\)
0.949156 0.314806i \(-0.101940\pi\)
\(110\) −6.59817 6.59817i −0.629111 0.629111i
\(111\) −1.15342 9.31069i −0.109477 0.883731i
\(112\) −4.46410 4.46410i −0.421818 0.421818i
\(113\) 10.2870i 0.967723i 0.875145 + 0.483861i \(0.160766\pi\)
−0.875145 + 0.483861i \(0.839234\pi\)
\(114\) −7.94839 6.19615i −0.744435 0.580323i
\(115\) 0 0
\(116\) 1.92089 0.178350
\(117\) 0 0
\(118\) 4.53590 0.417563
\(119\) −5.03908 5.03908i −0.461932 0.461932i
\(120\) 5.36603 + 4.18307i 0.489849 + 0.381861i
\(121\) 5.92820i 0.538928i
\(122\) −7.45418 7.45418i −0.674869 0.674869i
\(123\) −1.19680 9.66090i −0.107912 0.871094i
\(124\) 0.660254 + 0.660254i 0.0592926 + 0.0592926i
\(125\) 8.23373 8.23373i 0.736447 0.736447i
\(126\) 6.19615 1.55910i 0.551997 0.138895i
\(127\) 9.12436i 0.809656i −0.914393 0.404828i \(-0.867331\pi\)
0.914393 0.404828i \(-0.132669\pi\)
\(128\) 9.22215 9.22215i 0.815131 0.815131i
\(129\) −2.33864 + 3.00000i −0.205906 + 0.264135i
\(130\) 0 0
\(131\) 7.94839i 0.694454i 0.937781 + 0.347227i \(0.112877\pi\)
−0.937781 + 0.347227i \(0.887123\pi\)
\(132\) −0.234755 1.89501i −0.0204328 0.164939i
\(133\) 5.46410 0.473798
\(134\) 8.93682 0.772023
\(135\) −7.29638 + 2.82797i −0.627973 + 0.243393i
\(136\) 9.29423 9.29423i 0.796974 0.796974i
\(137\) −4.75374 + 4.75374i −0.406140 + 0.406140i −0.880390 0.474250i \(-0.842719\pi\)
0.474250 + 0.880390i \(0.342719\pi\)
\(138\) 0 0
\(139\) 18.3923 1.56001 0.780007 0.625770i \(-0.215215\pi\)
0.780007 + 0.625770i \(0.215215\pi\)
\(140\) 0.570669 0.0482303
\(141\) −10.3545 + 1.28273i −0.872008 + 0.108025i
\(142\) 4.53590i 0.380644i
\(143\) 0 0
\(144\) 3.26795 + 12.9875i 0.272329 + 1.08229i
\(145\) 7.63397 7.63397i 0.633967 0.633967i
\(146\) 1.92089i 0.158974i
\(147\) 5.32441 6.83013i 0.439150 0.563339i
\(148\) 1.02628 1.02628i 0.0843597 0.0843597i
\(149\) 6.10396 + 6.10396i 0.500056 + 0.500056i 0.911455 0.411399i \(-0.134960\pi\)
−0.411399 + 0.911455i \(0.634960\pi\)
\(150\) 7.07227 0.876119i 0.577449 0.0715348i
\(151\) −0.535898 0.535898i −0.0436108 0.0436108i 0.684965 0.728576i \(-0.259817\pi\)
−0.728576 + 0.684965i \(0.759817\pi\)
\(152\) 10.0782i 0.817446i
\(153\) 3.68886 + 14.6603i 0.298227 + 1.18521i
\(154\) 6.19615 + 6.19615i 0.499300 + 0.499300i
\(155\) 5.24796 0.421526
\(156\) 0 0
\(157\) −4.80385 −0.383389 −0.191694 0.981455i \(-0.561398\pi\)
−0.191694 + 0.981455i \(0.561398\pi\)
\(158\) 2.12976 + 2.12976i 0.169435 + 0.169435i
\(159\) 0.830127 1.06488i 0.0658334 0.0844507i
\(160\) 2.26795i 0.179297i
\(161\) 0 0
\(162\) −12.9785 3.90671i −1.01969 0.306940i
\(163\) 2.92820 + 2.92820i 0.229355 + 0.229355i 0.812423 0.583068i \(-0.198148\pi\)
−0.583068 + 0.812423i \(0.698148\pi\)
\(164\) 1.06488 1.06488i 0.0831533 0.0831533i
\(165\) −8.46410 6.59817i −0.658929 0.513667i
\(166\) 6.19615i 0.480915i
\(167\) 9.50749 9.50749i 0.735711 0.735711i −0.236034 0.971745i \(-0.575848\pi\)
0.971745 + 0.236034i \(0.0758475\pi\)
\(168\) −5.03908 3.92820i −0.388773 0.303067i
\(169\) 0 0
\(170\) 11.4284i 0.876516i
\(171\) −9.94839 5.94839i −0.760772 0.454885i
\(172\) −0.588457 −0.0448694
\(173\) −17.4559 −1.32715 −0.663573 0.748112i \(-0.730961\pi\)
−0.663573 + 0.748112i \(0.730961\pi\)
\(174\) 18.5575 2.29892i 1.40684 0.174281i
\(175\) −2.73205 + 2.73205i −0.206524 + 0.206524i
\(176\) −12.9875 + 12.9875i −0.978967 + 0.978967i
\(177\) 5.17726 0.641364i 0.389147 0.0482078i
\(178\) −14.0526 −1.05328
\(179\) −26.5456 −1.98411 −0.992056 0.125798i \(-0.959851\pi\)
−0.992056 + 0.125798i \(0.959851\pi\)
\(180\) −1.03901 0.621248i −0.0774430 0.0463051i
\(181\) 3.00000i 0.222988i 0.993765 + 0.111494i \(0.0355636\pi\)
−0.993765 + 0.111494i \(0.964436\pi\)
\(182\) 0 0
\(183\) −9.56218 7.45418i −0.706857 0.551029i
\(184\) 0 0
\(185\) 8.15727i 0.599734i
\(186\) 7.16884 + 5.58846i 0.525645 + 0.409766i
\(187\) −14.6603 + 14.6603i −1.07206 + 1.07206i
\(188\) −1.14134 1.14134i −0.0832406 0.0832406i
\(189\) 6.85182 2.65567i 0.498397 0.193171i
\(190\) −6.19615 6.19615i −0.449516 0.449516i
\(191\) 4.83020i 0.349501i −0.984613 0.174750i \(-0.944088\pi\)
0.984613 0.174750i \(-0.0559119\pi\)
\(192\) 7.09239 9.09808i 0.511849 0.656597i
\(193\) 0.0980762 + 0.0980762i 0.00705968 + 0.00705968i 0.710628 0.703568i \(-0.248411\pi\)
−0.703568 + 0.710628i \(0.748411\pi\)
\(194\) 2.54752 0.182902
\(195\) 0 0
\(196\) 1.33975 0.0956961
\(197\) 2.90931 + 2.90931i 0.207280 + 0.207280i 0.803110 0.595830i \(-0.203177\pi\)
−0.595830 + 0.803110i \(0.703177\pi\)
\(198\) −4.53590 18.0265i −0.322352 1.28109i
\(199\) 12.9282i 0.916456i 0.888835 + 0.458228i \(0.151516\pi\)
−0.888835 + 0.458228i \(0.848484\pi\)
\(200\) −5.03908 5.03908i −0.356317 0.356317i
\(201\) 10.2005 1.26364i 0.719485 0.0891304i
\(202\) −6.41858 6.41858i −0.451610 0.451610i
\(203\) −7.16884 + 7.16884i −0.503154 + 0.503154i
\(204\) −1.43782 + 1.84443i −0.100668 + 0.129136i
\(205\) 8.46410i 0.591158i
\(206\) −7.37772 + 7.37772i −0.514030 + 0.514030i
\(207\) 0 0
\(208\) 0 0
\(209\) 15.8968i 1.09960i
\(210\) 5.51318 0.682977i 0.380445 0.0471299i
\(211\) −1.80385 −0.124182 −0.0620910 0.998070i \(-0.519777\pi\)
−0.0620910 + 0.998070i \(0.519777\pi\)
\(212\) 0.208879 0.0143459
\(213\) −0.641364 5.17726i −0.0439455 0.354740i
\(214\) −20.2487 + 20.2487i −1.38417 + 1.38417i
\(215\) −2.33864 + 2.33864i −0.159494 + 0.159494i
\(216\) 4.89819 + 12.6377i 0.333280 + 0.859887i
\(217\) −4.92820 −0.334548
\(218\) 28.1047 1.90349
\(219\) 0.271608 + 2.19249i 0.0183536 + 0.148155i
\(220\) 1.66025i 0.111934i
\(221\) 0 0
\(222\) 8.68653 11.1430i 0.583002 0.747872i
\(223\) −18.3205 + 18.3205i −1.22683 + 1.22683i −0.261676 + 0.965156i \(0.584275\pi\)
−0.965156 + 0.261676i \(0.915725\pi\)
\(224\) 2.12976i 0.142301i
\(225\) 7.94839 2.00000i 0.529893 0.133333i
\(226\) −10.9545 + 10.9545i −0.728681 + 0.728681i
\(227\) 14.3377 + 14.3377i 0.951626 + 0.951626i 0.998883 0.0472572i \(-0.0150480\pi\)
−0.0472572 + 0.998883i \(0.515048\pi\)
\(228\) −0.220452 1.77955i −0.0145998 0.117853i
\(229\) 14.1244 + 14.1244i 0.933364 + 0.933364i 0.997914 0.0645507i \(-0.0205614\pi\)
−0.0645507 + 0.997914i \(0.520561\pi\)
\(230\) 0 0
\(231\) 7.94839 + 6.19615i 0.522966 + 0.407677i
\(232\) −13.2224 13.2224i −0.868095 0.868095i
\(233\) −17.4559 −1.14357 −0.571786 0.820403i \(-0.693749\pi\)
−0.571786 + 0.820403i \(0.693749\pi\)
\(234\) 0 0
\(235\) −9.07180 −0.591779
\(236\) 0.570669 + 0.570669i 0.0371474 + 0.0371474i
\(237\) 2.73205 + 2.12976i 0.177466 + 0.138343i
\(238\) 10.7321i 0.695656i
\(239\) 6.59817 + 6.59817i 0.426800 + 0.426800i 0.887537 0.460737i \(-0.152415\pi\)
−0.460737 + 0.887537i \(0.652415\pi\)
\(240\) 1.43156 + 11.5559i 0.0924066 + 0.745931i
\(241\) −10.2942 10.2942i −0.663110 0.663110i 0.293002 0.956112i \(-0.405346\pi\)
−0.956112 + 0.293002i \(0.905346\pi\)
\(242\) 6.31284 6.31284i 0.405805 0.405805i
\(243\) −15.3660 2.62398i −0.985731 0.168328i
\(244\) 1.87564i 0.120076i
\(245\) 5.32441 5.32441i 0.340164 0.340164i
\(246\) 9.01327 11.5622i 0.574665 0.737178i
\(247\) 0 0
\(248\) 9.08973i 0.577198i
\(249\) 0.876119 + 7.07227i 0.0555218 + 0.448187i
\(250\) 17.5359 1.10907
\(251\) 0.988427 0.0623890 0.0311945 0.999513i \(-0.490069\pi\)
0.0311945 + 0.999513i \(0.490069\pi\)
\(252\) 0.975700 + 0.583396i 0.0614634 + 0.0367505i
\(253\) 0 0
\(254\) 9.71637 9.71637i 0.609659 0.609659i
\(255\) 1.61594 + 13.0443i 0.101194 + 0.816867i
\(256\) 6.32051 0.395032
\(257\) 21.5065 1.34154 0.670770 0.741665i \(-0.265964\pi\)
0.670770 + 0.741665i \(0.265964\pi\)
\(258\) −5.68503 + 0.704266i −0.353934 + 0.0438457i
\(259\) 7.66025i 0.475985i
\(260\) 0 0
\(261\) 20.8564 5.24796i 1.29098 0.324840i
\(262\) −8.46410 + 8.46410i −0.522914 + 0.522914i
\(263\) 22.2861i 1.37422i −0.726554 0.687109i \(-0.758879\pi\)
0.726554 0.687109i \(-0.241121\pi\)
\(264\) −11.4284 + 14.6603i −0.703368 + 0.902276i
\(265\) 0.830127 0.830127i 0.0509943 0.0509943i
\(266\) 5.81863 + 5.81863i 0.356763 + 0.356763i
\(267\) −16.0396 + 1.98699i −0.981605 + 0.121602i
\(268\) 1.12436 + 1.12436i 0.0686810 + 0.0686810i
\(269\) 14.3377i 0.874184i 0.899417 + 0.437092i \(0.143992\pi\)
−0.899417 + 0.437092i \(0.856008\pi\)
\(270\) −10.7812 4.75833i −0.656126 0.289583i
\(271\) 5.46410 + 5.46410i 0.331921 + 0.331921i 0.853315 0.521395i \(-0.174588\pi\)
−0.521395 + 0.853315i \(0.674588\pi\)
\(272\) 22.4950 1.36396
\(273\) 0 0
\(274\) −10.1244 −0.611635
\(275\) 7.94839 + 7.94839i 0.479306 + 0.479306i
\(276\) 0 0
\(277\) 27.5885i 1.65763i 0.559523 + 0.828815i \(0.310984\pi\)
−0.559523 + 0.828815i \(0.689016\pi\)
\(278\) 19.5856 + 19.5856i 1.17467 + 1.17467i
\(279\) 8.97269 + 5.36500i 0.537181 + 0.321194i
\(280\) −3.92820 3.92820i −0.234755 0.234755i
\(281\) −12.1315 + 12.1315i −0.723703 + 0.723703i −0.969357 0.245655i \(-0.920997\pi\)
0.245655 + 0.969357i \(0.420997\pi\)
\(282\) −12.3923 9.66040i −0.737951 0.575268i
\(283\) 6.58846i 0.391643i 0.980640 + 0.195822i \(0.0627373\pi\)
−0.980640 + 0.195822i \(0.937263\pi\)
\(284\) 0.570669 0.570669i 0.0338630 0.0338630i
\(285\) −7.94839 6.19615i −0.470822 0.367028i
\(286\) 0 0
\(287\) 7.94839i 0.469179i
\(288\) −2.31853 + 3.87762i −0.136621 + 0.228491i
\(289\) 8.39230 0.493665
\(290\) 16.2586 0.954736
\(291\) 2.90774 0.360213i 0.170455 0.0211161i
\(292\) −0.241670 + 0.241670i −0.0141427 + 0.0141427i
\(293\) 1.27376 1.27376i 0.0744140 0.0744140i −0.668920 0.743334i \(-0.733243\pi\)
0.743334 + 0.668920i \(0.233243\pi\)
\(294\) 12.9432 1.60341i 0.754860 0.0935127i
\(295\) 4.53590 0.264090
\(296\) −14.1288 −0.821220
\(297\) −7.72617 19.9341i −0.448318 1.15669i
\(298\) 13.0000i 0.753070i
\(299\) 0 0
\(300\) 1.00000 + 0.779548i 0.0577350 + 0.0450072i
\(301\) 2.19615 2.19615i 0.126584 0.126584i
\(302\) 1.14134i 0.0656766i
\(303\) −8.23373 6.41858i −0.473015 0.368738i
\(304\) −12.1962 + 12.1962i −0.699497 + 0.699497i
\(305\) −7.45418 7.45418i −0.426825 0.426825i
\(306\) −11.6832 + 19.5397i −0.667887 + 1.11701i
\(307\) −8.39230 8.39230i −0.478974 0.478974i 0.425829 0.904803i \(-0.359982\pi\)
−0.904803 + 0.425829i \(0.859982\pi\)
\(308\) 1.55910i 0.0888377i
\(309\) −7.37772 + 9.46410i −0.419704 + 0.538394i
\(310\) 5.58846 + 5.58846i 0.317403 + 0.317403i
\(311\) −10.0782 −0.571480 −0.285740 0.958307i \(-0.592239\pi\)
−0.285740 + 0.958307i \(0.592239\pi\)
\(312\) 0 0
\(313\) 2.00000 0.113047 0.0565233 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) −5.11553 5.11553i −0.288686 0.288686i
\(315\) 6.19615 1.55910i 0.349114 0.0878451i
\(316\) 0.535898i 0.0301466i
\(317\) −11.3519 11.3519i −0.637587 0.637587i 0.312373 0.949960i \(-0.398876\pi\)
−0.949960 + 0.312373i \(0.898876\pi\)
\(318\) 2.01796 0.249987i 0.113162 0.0140186i
\(319\) 20.8564 + 20.8564i 1.16773 + 1.16773i
\(320\) 7.09239 7.09239i 0.396477 0.396477i
\(321\) −20.2487 + 25.9749i −1.13017 + 1.44978i
\(322\) 0 0
\(323\) −13.7670 + 13.7670i −0.766017 + 0.766017i
\(324\) −1.14134 2.12436i −0.0634076 0.118020i
\(325\) 0 0
\(326\) 6.23638i 0.345401i
\(327\) 32.0786 3.97393i 1.77395 0.219759i
\(328\) −14.6603 −0.809477
\(329\) 8.51906 0.469671
\(330\) −1.98699 16.0396i −0.109380 0.882948i
\(331\) −24.1962 + 24.1962i −1.32994 + 1.32994i −0.424524 + 0.905417i \(0.639559\pi\)
−0.905417 + 0.424524i \(0.860441\pi\)
\(332\) −0.779548 + 0.779548i −0.0427833 + 0.0427833i
\(333\) 8.33919 13.9469i 0.456985 0.764285i
\(334\) 20.2487 1.10796
\(335\) 8.93682 0.488271
\(336\) −1.34433 10.8518i −0.0733394 0.592015i
\(337\) 18.4641i 1.00580i −0.864344 0.502902i \(-0.832266\pi\)
0.864344 0.502902i \(-0.167734\pi\)
\(338\) 0 0
\(339\) −10.9545 + 14.0524i −0.594966 + 0.763219i
\(340\) −1.43782 + 1.43782i −0.0779769 + 0.0779769i
\(341\) 14.3377i 0.776429i
\(342\) −4.25953 16.9282i −0.230329 0.915372i
\(343\) −12.0000 + 12.0000i −0.647939 + 0.647939i
\(344\) 4.05065 + 4.05065i 0.218396 + 0.218396i
\(345\) 0 0
\(346\) −18.5885 18.5885i −0.999322 0.999322i
\(347\) 20.5741i 1.10447i −0.833687 0.552237i \(-0.813774\pi\)
0.833687 0.552237i \(-0.186226\pi\)
\(348\) 2.62398 + 2.04552i 0.140660 + 0.109651i
\(349\) 20.1244 + 20.1244i 1.07723 + 1.07723i 0.996757 + 0.0804755i \(0.0256439\pi\)
0.0804755 + 0.996757i \(0.474356\pi\)
\(350\) −5.81863 −0.311019
\(351\) 0 0
\(352\) −6.19615 −0.330256
\(353\) −10.0017 10.0017i −0.532337 0.532337i 0.388930 0.921267i \(-0.372845\pi\)
−0.921267 + 0.388930i \(0.872845\pi\)
\(354\) 6.19615 + 4.83020i 0.329322 + 0.256722i
\(355\) 4.53590i 0.240740i
\(356\) −1.76798 1.76798i −0.0937025 0.0937025i
\(357\) −1.51748 12.2495i −0.0803137 0.648314i
\(358\) −28.2679 28.2679i −1.49401 1.49401i
\(359\) 18.2354 18.2354i 0.962429 0.962429i −0.0368904 0.999319i \(-0.511745\pi\)
0.999319 + 0.0368904i \(0.0117452\pi\)
\(360\) 2.87564 + 11.4284i 0.151560 + 0.602328i
\(361\) 4.07180i 0.214305i
\(362\) −3.19465 + 3.19465i −0.167907 + 0.167907i
\(363\) 6.31284 8.09808i 0.331338 0.425039i
\(364\) 0 0
\(365\) 1.92089i 0.100544i
\(366\) −2.24477 18.1204i −0.117336 0.947169i
\(367\) 30.3923 1.58647 0.793233 0.608919i \(-0.208396\pi\)
0.793233 + 0.608919i \(0.208396\pi\)
\(368\) 0 0
\(369\) 8.65286 14.4715i 0.450450 0.753356i
\(370\) 8.68653 8.68653i 0.451591 0.451591i
\(371\) −0.779548 + 0.779548i −0.0404721 + 0.0404721i
\(372\) 0.198831 + 1.60502i 0.0103089 + 0.0832162i
\(373\) 11.5885 0.600028 0.300014 0.953935i \(-0.403009\pi\)
0.300014 + 0.953935i \(0.403009\pi\)
\(374\) −31.2229 −1.61450
\(375\) 20.0154 2.47953i 1.03359 0.128042i
\(376\) 15.7128i 0.810326i
\(377\) 0 0
\(378\) 10.1244 + 4.46841i 0.520741 + 0.229830i
\(379\) −10.4641 + 10.4641i −0.537505 + 0.537505i −0.922795 0.385291i \(-0.874101\pi\)
0.385291 + 0.922795i \(0.374101\pi\)
\(380\) 1.55910i 0.0799799i
\(381\) 9.71637 12.4641i 0.497785 0.638555i
\(382\) 5.14359 5.14359i 0.263169 0.263169i
\(383\) −23.2745 23.2745i −1.18927 1.18927i −0.977269 0.212002i \(-0.932002\pi\)
−0.212002 0.977269i \(-0.567998\pi\)
\(384\) 22.4182 2.77719i 1.14402 0.141723i
\(385\) 6.19615 + 6.19615i 0.315785 + 0.315785i
\(386\) 0.208879i 0.0106317i
\(387\) −6.38929 + 1.60770i −0.324786 + 0.0817237i
\(388\) 0.320508 + 0.320508i 0.0162713 + 0.0162713i
\(389\) −22.4950 −1.14054 −0.570270 0.821457i \(-0.693161\pi\)
−0.570270 + 0.821457i \(0.693161\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −9.22215 9.22215i −0.465789 0.465789i
\(393\) −8.46410 + 10.8577i −0.426957 + 0.547699i
\(394\) 6.19615i 0.312158i
\(395\) 2.12976 + 2.12976i 0.107160 + 0.107160i
\(396\) 1.69728 2.83862i 0.0852916 0.142646i
\(397\) 9.73205 + 9.73205i 0.488438 + 0.488438i 0.907813 0.419375i \(-0.137751\pi\)
−0.419375 + 0.907813i \(0.637751\pi\)
\(398\) −13.7670 + 13.7670i −0.690078 + 0.690078i
\(399\) 7.46410 + 5.81863i 0.373672 + 0.291296i
\(400\) 12.1962i 0.609808i
\(401\) −8.80439 + 8.80439i −0.439670 + 0.439670i −0.891901 0.452231i \(-0.850628\pi\)
0.452231 + 0.891901i \(0.350628\pi\)
\(402\) 12.2079 + 9.51666i 0.608876 + 0.474648i
\(403\) 0 0
\(404\) 1.61507i 0.0803525i
\(405\) −12.9785 3.90671i −0.644907 0.194126i
\(406\) −15.2679 −0.757736
\(407\) 22.2861 1.10468
\(408\) 22.5934 2.79889i 1.11854 0.138566i
\(409\) 21.2224 21.2224i 1.04938 1.04938i 0.0506661 0.998716i \(-0.483866\pi\)
0.998716 0.0506661i \(-0.0161344\pi\)
\(410\) 9.01327 9.01327i 0.445134 0.445134i
\(411\) −11.5559 + 1.43156i −0.570011 + 0.0706135i
\(412\) −1.85641 −0.0914586
\(413\) −4.25953 −0.209598
\(414\) 0 0
\(415\) 6.19615i 0.304157i
\(416\) 0 0
\(417\) 25.1244 + 19.5856i 1.23034 + 0.959113i
\(418\) 16.9282 16.9282i 0.827985 0.827985i
\(419\) 9.50749i 0.464471i −0.972660 0.232236i \(-0.925396\pi\)
0.972660 0.232236i \(-0.0746040\pi\)
\(420\) 0.779548 + 0.607695i 0.0380380 + 0.0296525i
\(421\) 7.83013 7.83013i 0.381617 0.381617i −0.490067 0.871685i \(-0.663028\pi\)
0.871685 + 0.490067i \(0.163028\pi\)
\(422\) −1.92089 1.92089i −0.0935072 0.0935072i
\(423\) −15.5105 9.27411i −0.754146 0.450923i
\(424\) −1.43782 1.43782i −0.0698268 0.0698268i
\(425\) 13.7670i 0.667798i
\(426\) 4.83020 6.19615i 0.234024 0.300205i
\(427\) 7.00000 + 7.00000i 0.338754 + 0.338754i
\(428\) −5.09505 −0.246278
\(429\) 0 0
\(430\) −4.98076 −0.240194
\(431\) 26.7545 + 26.7545i 1.28872 + 1.28872i 0.935566 + 0.353152i \(0.114890\pi\)
0.353152 + 0.935566i \(0.385110\pi\)
\(432\) −9.36603 + 21.2212i −0.450623 + 1.02101i
\(433\) 31.0526i 1.49229i −0.665783 0.746145i \(-0.731902\pi\)
0.665783 0.746145i \(-0.268098\pi\)
\(434\) −5.24796 5.24796i −0.251910 0.251910i
\(435\) 18.5575 2.29892i 0.889763 0.110225i
\(436\) 3.53590 + 3.53590i 0.169339 + 0.169339i
\(437\) 0 0
\(438\) −2.04552 + 2.62398i −0.0977386 + 0.125379i
\(439\) 1.26795i 0.0605159i −0.999542 0.0302580i \(-0.990367\pi\)
0.999542 0.0302580i \(-0.00963288\pi\)
\(440\) −11.4284 + 11.4284i −0.544826 + 0.544826i
\(441\) 14.5466 3.66025i 0.692694 0.174298i
\(442\) 0 0
\(443\) 11.2195i 0.533054i −0.963827 0.266527i \(-0.914124\pi\)
0.963827 0.266527i \(-0.0858762\pi\)
\(444\) 2.49479 0.309057i 0.118398 0.0146672i
\(445\) −14.0526 −0.666155
\(446\) −39.0184 −1.84757
\(447\) 1.83816 + 14.8382i 0.0869422 + 0.701821i
\(448\) −6.66025 + 6.66025i −0.314667 + 0.314667i
\(449\) 14.5466 14.5466i 0.686495 0.686495i −0.274961 0.961455i \(-0.588665\pi\)
0.961455 + 0.274961i \(0.0886648\pi\)
\(450\) 10.5939 + 6.33434i 0.499400 + 0.298603i
\(451\) 23.1244 1.08888
\(452\) −2.75640 −0.129650
\(453\) −0.161382 1.30272i −0.00758239 0.0612071i
\(454\) 30.5359i 1.43312i
\(455\) 0 0
\(456\) −10.7321 + 13.7670i −0.502574 + 0.644700i
\(457\) 2.75833 2.75833i 0.129029 0.129029i −0.639643 0.768672i \(-0.720918\pi\)
0.768672 + 0.639643i \(0.220918\pi\)
\(458\) 30.0816i 1.40562i
\(459\) −10.5724 + 23.9545i −0.493476 + 1.11810i
\(460\) 0 0
\(461\) −15.0408 15.0408i −0.700519 0.700519i 0.264003 0.964522i \(-0.414957\pi\)
−0.964522 + 0.264003i \(0.914957\pi\)
\(462\) 1.86593 + 15.0623i 0.0868108 + 0.700760i
\(463\) −23.0526 23.0526i −1.07134 1.07134i −0.997251 0.0740918i \(-0.976394\pi\)
−0.0740918 0.997251i \(-0.523606\pi\)
\(464\) 32.0024i 1.48568i
\(465\) 7.16884 + 5.58846i 0.332447 + 0.259159i
\(466\) −18.5885 18.5885i −0.861094 0.861094i
\(467\) 19.1679 0.886984 0.443492 0.896278i \(-0.353739\pi\)
0.443492 + 0.896278i \(0.353739\pi\)
\(468\) 0 0
\(469\) −8.39230 −0.387521
\(470\) −9.66040 9.66040i −0.445601 0.445601i
\(471\) −6.56218 5.11553i −0.302369 0.235711i
\(472\) 7.85641i 0.361620i
\(473\) −6.38929 6.38929i −0.293780 0.293780i
\(474\) 0.641364 + 5.17726i 0.0294588 + 0.237800i
\(475\) 7.46410 + 7.46410i 0.342476 + 0.342476i
\(476\) 1.35022 1.35022i 0.0618871 0.0618871i
\(477\) 2.26795 0.570669i 0.103842 0.0261291i
\(478\) 14.0526i 0.642749i
\(479\) 14.5466 14.5466i 0.664649 0.664649i −0.291823 0.956472i \(-0.594262\pi\)
0.956472 + 0.291823i \(0.0942618\pi\)
\(480\) −2.41510 + 3.09808i −0.110234 + 0.141407i
\(481\) 0 0
\(482\) 21.9243i 0.998624i
\(483\) 0 0
\(484\) 1.58846 0.0722026
\(485\) 2.54752 0.115677
\(486\) −13.5688 19.1572i −0.615492 0.868990i
\(487\) 4.07180 4.07180i 0.184511 0.184511i −0.608807 0.793318i \(-0.708352\pi\)
0.793318 + 0.608807i \(0.208352\pi\)
\(488\) −12.9110 + 12.9110i −0.584454 + 0.584454i
\(489\) 0.881808 + 7.11819i 0.0398767 + 0.321896i
\(490\) 11.3397 0.512278
\(491\) 28.5225 1.28720 0.643600 0.765362i \(-0.277440\pi\)
0.643600 + 0.765362i \(0.277440\pi\)
\(492\) 2.58863 0.320682i 0.116705 0.0144575i
\(493\) 36.1244i 1.62696i
\(494\) 0 0
\(495\) −4.53590 18.0265i −0.203873 0.810233i
\(496\) 11.0000 11.0000i 0.493915 0.493915i
\(497\) 4.25953i 0.191066i
\(498\) −6.59817 + 8.46410i −0.295671 + 0.379285i
\(499\) 2.46410 2.46410i 0.110308 0.110308i −0.649798 0.760107i \(-0.725147\pi\)
0.760107 + 0.649798i \(0.225147\pi\)
\(500\) 2.20622 + 2.20622i 0.0986652 + 0.0986652i
\(501\) 23.1118 2.86311i 1.03256 0.127914i
\(502\) 1.05256 + 1.05256i 0.0469780 + 0.0469780i
\(503\) 3.27110i 0.145851i 0.997337 + 0.0729256i \(0.0232336\pi\)
−0.997337 + 0.0729256i \(0.976766\pi\)
\(504\) −2.70043 10.7321i −0.120287 0.478044i
\(505\) −6.41858 6.41858i −0.285623 0.285623i
\(506\) 0 0
\(507\) 0 0
\(508\) 2.44486 0.108473
\(509\) −10.3635 10.3635i −0.459354 0.459354i 0.439090 0.898443i \(-0.355301\pi\)
−0.898443 + 0.439090i \(0.855301\pi\)
\(510\) −12.1699 + 15.6114i −0.538891 + 0.691286i
\(511\) 1.80385i 0.0797975i
\(512\) −11.7137 11.7137i −0.517678 0.517678i
\(513\) −7.25542 18.7195i −0.320335 0.826487i
\(514\) 22.9019 + 22.9019i 1.01016 + 1.01016i
\(515\) −7.37772 + 7.37772i −0.325101 + 0.325101i
\(516\) −0.803848 0.626638i −0.0353874 0.0275862i
\(517\) 24.7846i 1.09003i
\(518\) −8.15727 + 8.15727i −0.358410 + 0.358410i
\(519\) −23.8452 18.5885i −1.04669 0.815943i
\(520\) 0 0
\(521\) 2.49155i 0.109157i −0.998509 0.0545785i \(-0.982618\pi\)
0.998509 0.0545785i \(-0.0173815\pi\)
\(522\) 27.7981 + 16.6212i 1.21669 + 0.727489i
\(523\) −38.9808 −1.70451 −0.852255 0.523127i \(-0.824765\pi\)
−0.852255 + 0.523127i \(0.824765\pi\)
\(524\) −2.12976 −0.0930392
\(525\) −6.64136 + 0.822738i −0.289853 + 0.0359072i
\(526\) 23.7321 23.7321i 1.03477 1.03477i
\(527\) 12.4168 12.4168i 0.540884 0.540884i
\(528\) −31.5713 + 3.91108i −1.37397 + 0.170208i
\(529\) −23.0000 −1.00000
\(530\) 1.76798 0.0767959
\(531\) 7.75525 + 4.63706i 0.336549 + 0.201231i
\(532\) 1.46410i 0.0634769i
\(533\) 0 0
\(534\) −19.1962 14.9643i −0.830699 0.647570i
\(535\) −20.2487 + 20.2487i −0.875428 + 0.875428i
\(536\) 15.4790i 0.668592i
\(537\) −36.2620 28.2679i −1.56482 1.21985i
\(538\) −15.2679 + 15.2679i −0.658248 + 0.658248i
\(539\) 14.5466 + 14.5466i 0.626565 + 0.626565i
\(540\) −0.757753 1.95506i −0.0326085 0.0841324i
\(541\) 12.6865 + 12.6865i 0.545437 + 0.545437i 0.925118 0.379681i \(-0.123966\pi\)
−0.379681 + 0.925118i \(0.623966\pi\)
\(542\) 11.6373i 0.499863i
\(543\) −3.19465 + 4.09808i −0.137095 + 0.175865i
\(544\) 5.36603 + 5.36603i 0.230066 + 0.230066i
\(545\) 28.1047 1.20387
\(546\) 0 0
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) −1.27376 1.27376i −0.0544124 0.0544124i
\(549\) −5.12436 20.3652i −0.218702 0.869165i
\(550\) 16.9282i 0.721821i
\(551\) 19.5856 + 19.5856i 0.834376 + 0.834376i
\(552\) 0 0
\(553\) −2.00000 2.00000i −0.0850487 0.0850487i
\(554\) −29.3785 + 29.3785i −1.24817 + 1.24817i
\(555\) 8.68653 11.1430i 0.368723 0.472996i
\(556\) 4.92820i 0.209002i
\(557\) 18.1030 18.1030i 0.767049 0.767049i −0.210537 0.977586i \(-0.567521\pi\)
0.977586 + 0.210537i \(0.0675213\pi\)
\(558\) 3.84177 + 15.2679i 0.162635 + 0.646344i
\(559\) 0 0
\(560\) 9.50749i 0.401765i
\(561\) −35.6377 + 4.41483i −1.50463 + 0.186394i
\(562\) −25.8372 −1.08988
\(563\) 10.0782 0.424744 0.212372 0.977189i \(-0.431881\pi\)
0.212372 + 0.977189i \(0.431881\pi\)
\(564\) −0.343706 2.77449i −0.0144726 0.116827i
\(565\) −10.9545 + 10.9545i −0.460859 + 0.460859i
\(566\) −7.01593 + 7.01593i −0.294902 + 0.294902i
\(567\) 12.1877 + 3.66867i 0.511837 + 0.154070i
\(568\) −7.85641 −0.329647
\(569\) 2.70043 0.113208 0.0566040 0.998397i \(-0.481973\pi\)
0.0566040 + 0.998397i \(0.481973\pi\)
\(570\) −1.86593 15.0623i −0.0781551 0.630889i
\(571\) 1.94744i 0.0814979i 0.999169 + 0.0407489i \(0.0129744\pi\)
−0.999169 + 0.0407489i \(0.987026\pi\)
\(572\) 0 0
\(573\) 5.14359 6.59817i 0.214877 0.275643i
\(574\) −8.46410 + 8.46410i −0.353285 + 0.353285i
\(575\) 0 0
\(576\) 19.3768 4.87564i 0.807365 0.203152i
\(577\) 22.4904 22.4904i 0.936287 0.936287i −0.0618016 0.998088i \(-0.519685\pi\)
0.998088 + 0.0618016i \(0.0196846\pi\)
\(578\) 8.93682 + 8.93682i 0.371723 + 0.371723i
\(579\) 0.0295350 + 0.238414i 0.00122743 + 0.00990816i
\(580\) 2.04552 + 2.04552i 0.0849355 + 0.0849355i
\(581\) 5.81863i 0.241397i
\(582\) 3.47998 + 2.71281i 0.144250 + 0.112450i
\(583\) 2.26795 + 2.26795i 0.0939289 + 0.0939289i
\(584\) 3.32707 0.137675
\(585\) 0 0
\(586\) 2.71281 0.112065
\(587\) −13.1963 13.1963i −0.544672 0.544672i 0.380223 0.924895i \(-0.375847\pi\)
−0.924895 + 0.380223i \(0.875847\pi\)
\(588\) 1.83013 + 1.42667i 0.0754732 + 0.0588350i
\(589\) 13.4641i 0.554779i
\(590\) 4.83020 + 4.83020i 0.198856 + 0.198856i
\(591\) 0.876119 + 7.07227i 0.0360387 + 0.290914i
\(592\) −17.0981 17.0981i −0.702727 0.702727i
\(593\) 10.3635 10.3635i 0.425578 0.425578i −0.461541 0.887119i \(-0.652703\pi\)
0.887119 + 0.461541i \(0.152703\pi\)
\(594\) 13.0000 29.4549i 0.533396 1.20855i
\(595\) 10.7321i 0.439971i
\(596\) −1.63555 + 1.63555i −0.0669948 + 0.0669948i
\(597\) −13.7670 + 17.6603i −0.563446 + 0.722786i
\(598\) 0 0
\(599\) 20.7270i 0.846881i 0.905924 + 0.423441i \(0.139178\pi\)
−0.905924 + 0.423441i \(0.860822\pi\)
\(600\) −1.51748 12.2495i −0.0619510 0.500085i
\(601\) 23.5885 0.962193 0.481097 0.876668i \(-0.340239\pi\)
0.481097 + 0.876668i \(0.340239\pi\)
\(602\) 4.67729 0.190632
\(603\) 15.2797 + 9.13612i 0.622238 + 0.372052i
\(604\) 0.143594 0.143594i 0.00584274 0.00584274i
\(605\) 6.31284 6.31284i 0.256653 0.256653i
\(606\) −1.93291 15.6030i −0.0785192 0.633828i
\(607\) −0.196152 −0.00796158 −0.00398079 0.999992i \(-0.501267\pi\)
−0.00398079 + 0.999992i \(0.501267\pi\)
\(608\) −5.81863 −0.235976
\(609\) −17.4268 + 2.15885i −0.706169 + 0.0874809i
\(610\) 15.8756i 0.642786i
\(611\) 0 0
\(612\) −3.92820 + 0.988427i −0.158788 + 0.0399548i
\(613\) 31.0263 31.0263i 1.25314 1.25314i 0.298835 0.954305i \(-0.403402\pi\)
0.954305 0.298835i \(-0.0965979\pi\)
\(614\) 17.8736i 0.721321i
\(615\) 9.01327 11.5622i 0.363450 0.466232i
\(616\) 10.7321 10.7321i 0.432407 0.432407i
\(617\) −13.0639 13.0639i −0.525934 0.525934i 0.393424 0.919357i \(-0.371291\pi\)
−0.919357 + 0.393424i \(0.871291\pi\)
\(618\) −17.9346 + 2.22175i −0.721434 + 0.0893719i
\(619\) 31.6603 + 31.6603i 1.27253 + 1.27253i 0.944755 + 0.327778i \(0.106300\pi\)
0.327778 + 0.944755i \(0.393700\pi\)
\(620\) 1.40619i 0.0564738i
\(621\) 0 0
\(622\) −10.7321 10.7321i −0.430316 0.430316i
\(623\) 13.1963 0.528701
\(624\) 0 0
\(625\) 3.87564 0.155026
\(626\) 2.12976 + 2.12976i 0.0851225 + 0.0851225i
\(627\) 16.9282 21.7154i 0.676047 0.867230i
\(628\) 1.28719i 0.0513644i
\(629\) −19.3003 19.3003i −0.769554 0.769554i
\(630\) 8.25843 + 4.93792i 0.329024 + 0.196731i
\(631\) −15.6603 15.6603i −0.623425 0.623425i 0.322981 0.946406i \(-0.395315\pi\)
−0.946406 + 0.322981i \(0.895315\pi\)
\(632\) 3.68886 3.68886i 0.146735 0.146735i
\(633\) −2.46410 1.92089i −0.0979392 0.0763483i
\(634\) 24.1769i 0.960188i
\(635\) 9.71637 9.71637i 0.385582 0.385582i
\(636\) 0.285334 + 0.222432i 0.0113142 + 0.00882000i
\(637\) 0 0
\(638\) 44.4192i 1.75857i
\(639\) 4.63706 7.75525i 0.183439 0.306793i
\(640\) 19.6410 0.776379
\(641\) −45.3517 −1.79128 −0.895642 0.444775i \(-0.853284\pi\)
−0.895642 + 0.444775i \(0.853284\pi\)
\(642\) −49.2228 + 6.09776i −1.94267 + 0.240659i
\(643\) 5.12436 5.12436i 0.202085 0.202085i −0.598808 0.800893i \(-0.704359\pi\)
0.800893 + 0.598808i \(0.204359\pi\)
\(644\) 0 0
\(645\) −5.68503 + 0.704266i −0.223848 + 0.0277305i
\(646\) −29.3205 −1.15360
\(647\) 16.4675 0.647402 0.323701 0.946159i \(-0.395073\pi\)
0.323701 + 0.946159i \(0.395073\pi\)
\(648\) −6.76661 + 22.4794i −0.265818 + 0.883075i
\(649\) 12.3923i 0.486441i
\(650\) 0 0
\(651\) −6.73205 5.24796i −0.263850 0.205684i
\(652\) −0.784610 + 0.784610i −0.0307277 + 0.0307277i
\(653\) 9.66040i 0.378041i 0.981973 + 0.189020i \(0.0605312\pi\)
−0.981973 + 0.189020i \(0.939469\pi\)
\(654\) 38.3917 + 29.9282i 1.50124 + 1.17029i
\(655\) −8.46410 + 8.46410i −0.330720 + 0.330720i
\(656\) −17.7412 17.7412i −0.692678 0.692678i
\(657\) −1.96372 + 3.28423i −0.0766122 + 0.128130i
\(658\) 9.07180 + 9.07180i 0.353655 + 0.353655i
\(659\) 27.1163i 1.05630i 0.849151 + 0.528150i \(0.177114\pi\)
−0.849151 + 0.528150i \(0.822886\pi\)
\(660\) 1.76798 2.26795i 0.0688183 0.0882798i
\(661\) 6.90192 + 6.90192i 0.268454 + 0.268454i 0.828477 0.560023i \(-0.189208\pi\)
−0.560023 + 0.828477i \(0.689208\pi\)
\(662\) −51.5321 −2.00285
\(663\) 0 0
\(664\) 10.7321 0.416484
\(665\) 5.81863 + 5.81863i 0.225637 + 0.225637i
\(666\) 23.7321 5.97154i 0.919598 0.231392i
\(667\) 0 0
\(668\) 2.54752 + 2.54752i 0.0985666 + 0.0985666i
\(669\) −44.5355 + 5.51709i −1.72184 + 0.213303i
\(670\) 9.51666 + 9.51666i 0.367661 + 0.367661i
\(671\) 20.3652 20.3652i 0.786189 0.786189i
\(672\) 2.26795 2.90931i 0.0874880 0.112229i
\(673\) 42.7128i 1.64646i 0.567709 + 0.823229i \(0.307830\pi\)
−0.567709 + 0.823229i \(0.692170\pi\)
\(674\) 19.6621 19.6621i 0.757356 0.757356i
\(675\) 12.9875 + 5.73205i 0.499888 + 0.220627i
\(676\) 0 0
\(677\) 9.66040i 0.371279i 0.982618 + 0.185640i \(0.0594357\pi\)
−0.982618 + 0.185640i \(0.940564\pi\)
\(678\) −26.6293 + 3.29887i −1.02269 + 0.126692i
\(679\) −2.39230 −0.0918082
\(680\) 19.7945 0.759085
\(681\) 4.31769 + 34.8536i 0.165454 + 1.33559i
\(682\) −15.2679 + 15.2679i −0.584640 + 0.584640i
\(683\) −33.1438 + 33.1438i −1.26821 + 1.26821i −0.321200 + 0.947011i \(0.604086\pi\)
−0.947011 + 0.321200i \(0.895914\pi\)
\(684\) 1.59387 2.66566i 0.0609430 0.101924i
\(685\) −10.1244 −0.386832
\(686\) −25.5572 −0.975778
\(687\) 4.25345 + 34.3350i 0.162279 + 1.30996i
\(688\) 9.80385i 0.373768i
\(689\) 0 0
\(690\) 0 0
\(691\) −13.3397 + 13.3397i −0.507468 + 0.507468i −0.913748 0.406281i \(-0.866826\pi\)
0.406281 + 0.913748i \(0.366826\pi\)
\(692\) 4.67729i 0.177804i
\(693\) 4.25953 + 16.9282i 0.161806 + 0.643049i
\(694\) 21.9090 21.9090i 0.831653 0.831653i
\(695\) 19.5856 + 19.5856i 0.742926 + 0.742926i
\(696\) −3.98184 32.1425i −0.150931 1.21836i
\(697\) −20.0263 20.0263i −0.758549 0.758549i
\(698\) 42.8601i 1.62228i
\(699\) −23.8452 18.5885i −0.901907 0.703080i
\(700\) −0.732051 0.732051i −0.0276689 0.0276689i
\(701\) −12.7786 −0.482641 −0.241320 0.970446i \(-0.577580\pi\)
−0.241320 + 0.970446i \(0.577580\pi\)
\(702\) 0 0
\(703\) 20.9282 0.789322
\(704\) 19.3768 + 19.3768i 0.730289 + 0.730289i
\(705\) −12.3923 9.66040i −0.466721 0.363832i
\(706\) 21.3013i 0.801684i
\(707\) 6.02751 + 6.02751i 0.226688 + 0.226688i
\(708\) 0.171853 + 1.38724i 0.00645863 + 0.0521358i
\(709\) 8.29423 + 8.29423i 0.311496 + 0.311496i 0.845489 0.533993i \(-0.179309\pi\)
−0.533993 + 0.845489i \(0.679309\pi\)
\(710\) 4.83020 4.83020i 0.181274 0.181274i
\(711\) 1.46410 + 5.81863i 0.0549081 + 0.218216i
\(712\) 24.3397i 0.912171i
\(713\) 0 0
\(714\) 11.4284 14.6603i 0.427696 0.548646i
\(715\) 0 0
\(716\) 7.11287i 0.265821i
\(717\) 1.98699 + 16.0396i 0.0742056 + 0.599008i
\(718\) 38.8372 1.44939
\(719\) 7.37772 0.275143 0.137571 0.990492i \(-0.456070\pi\)
0.137571 + 0.990492i \(0.456070\pi\)
\(720\) −10.3501 + 17.3101i −0.385727 + 0.645110i
\(721\) 6.92820 6.92820i 0.258020 0.258020i
\(722\) −4.33598 + 4.33598i −0.161369 + 0.161369i
\(723\) −3.10003 25.0243i −0.115292 0.930665i
\(724\) −0.803848 −0.0298748
\(725\) −19.5856 −0.727392
\(726\) 15.3459 1.90107i 0.569541 0.0705552i
\(727\) 19.5167i 0.723833i −0.932211 0.361916i \(-0.882123\pi\)
0.932211 0.361916i \(-0.117877\pi\)
\(728\) 0 0
\(729\) −18.1962 19.9474i −0.673932 0.738794i
\(730\) −2.04552 + 2.04552i −0.0757080 + 0.0757080i
\(731\) 11.0666i 0.409312i
\(732\) 1.99734 2.56218i 0.0738238 0.0947008i
\(733\) 6.77757 6.77757i 0.250335 0.250335i −0.570773 0.821108i \(-0.693356\pi\)
0.821108 + 0.570773i \(0.193356\pi\)
\(734\) 32.3642 + 32.3642i 1.19459 + 1.19459i
\(735\) 12.9432 1.60341i 0.477415 0.0591426i
\(736\) 0 0
\(737\) 24.4158i 0.899369i
\(738\) 24.6247 6.19615i 0.906448 0.228084i
\(739\) −8.14359 8.14359i −0.299567 0.299567i 0.541277 0.840844i \(-0.317941\pi\)
−0.840844 + 0.541277i \(0.817941\pi\)
\(740\) 2.18573 0.0803492
\(741\) 0 0
\(742\) −1.66025 −0.0609498
\(743\) 6.23638 + 6.23638i 0.228791 + 0.228791i 0.812187 0.583397i \(-0.198277\pi\)
−0.583397 + 0.812187i \(0.698277\pi\)
\(744\) 9.67949 12.4168i 0.354867 0.455222i
\(745\) 13.0000i 0.476283i
\(746\) 12.3403 + 12.3403i 0.451812 + 0.451812i
\(747\) −6.33434 + 10.5939i −0.231761 + 0.387609i
\(748\) −3.92820 3.92820i −0.143629 0.143629i
\(749\) 19.0150 19.0150i 0.694792 0.694792i
\(750\) 23.9545 + 18.6737i 0.874694 + 0.681866i
\(751\) 33.8038i 1.23352i 0.787151 + 0.616760i \(0.211555\pi\)
−0.787151 + 0.616760i \(0.788445\pi\)
\(752\) −19.0150 + 19.0150i −0.693405 + 0.693405i
\(753\) 1.35022 + 1.05256i 0.0492046 + 0.0383574i
\(754\) 0 0
\(755\) 1.14134i 0.0415375i
\(756\) 0.711584 + 1.83594i 0.0258801 + 0.0667725i
\(757\) 16.7846 0.610047 0.305024 0.952345i \(-0.401336\pi\)
0.305024 + 0.952345i \(0.401336\pi\)
\(758\) −22.2861 −0.809467
\(759\) 0 0
\(760\) −10.7321 + 10.7321i −0.389292 + 0.389292i
\(761\) −12.9875 + 12.9875i −0.470795 + 0.470795i −0.902172 0.431377i \(-0.858028\pi\)
0.431377 + 0.902172i \(0.358028\pi\)
\(762\) 23.6196 2.92602i 0.855647 0.105998i
\(763\) −26.3923 −0.955466
\(764\) 1.29425 0.0468242
\(765\) −11.6832 + 19.5397i −0.422409 + 0.706458i
\(766\) 49.5692i 1.79101i
\(767\) 0 0
\(768\) 8.63397 + 6.73060i 0.311552 + 0.242870i
\(769\) 29.5885 29.5885i 1.06699 1.06699i 0.0693980 0.997589i \(-0.477892\pi\)
0.997589 0.0693980i \(-0.0221078\pi\)
\(770\) 13.1963i 0.475563i
\(771\) 29.3785 + 22.9019i 1.05804 + 0.824793i
\(772\) −0.0262794 + 0.0262794i −0.000945818 + 0.000945818i
\(773\) 30.4433 + 30.4433i 1.09497 + 1.09497i 0.994989 + 0.0999818i \(0.0318785\pi\)
0.0999818 + 0.994989i \(0.468122\pi\)
\(774\) −8.51585 5.09184i −0.306096 0.183022i
\(775\) −6.73205 6.73205i −0.241822 0.241822i
\(776\) 4.41244i 0.158397i
\(777\) −8.15727 + 10.4641i −0.292640 + 0.375398i
\(778\) −23.9545 23.9545i −0.858810 0.858810i
\(779\) 21.7154 0.778035
\(780\) 0 0
\(781\) 12.3923 0.443432
\(782\) 0 0
\(783\) 34.0788 + 15.0408i 1.21788 + 0.537514i
\(784\) 22.3205i 0.797161i
\(785\) −5.11553 5.11553i −0.182581 0.182581i
\(786\) −20.5755 + 2.54890i −0.733902 + 0.0909164i
\(787\) −11.7321 11.7321i −0.418202 0.418202i 0.466381 0.884584i \(-0.345557\pi\)
−0.884584 + 0.466381i \(0.845557\pi\)
\(788\) −0.779548 + 0.779548i −0.0277702 + 0.0277702i
\(789\) 23.7321 30.4433i 0.844883 1.08381i
\(790\) 4.53590i 0.161380i
\(791\) 10.2870 10.2870i 0.365765 0.365765i
\(792\) −31.2229 + 7.85641i −1.10946 + 0.279165i
\(793\) 0 0
\(794\) 20.7270i 0.735573i
\(795\) 2.01796 0.249987i 0.0715697 0.00886612i
\(796\) −3.46410 −0.122782
\(797\) 40.3126 1.42795 0.713973 0.700173i \(-0.246894\pi\)
0.713973 + 0.700173i \(0.246894\pi\)
\(798\) 1.75224 + 14.1445i 0.0620286 + 0.500711i
\(799\) −21.4641 + 21.4641i −0.759345 + 0.759345i
\(800\) 2.90931 2.90931i 0.102860 0.102860i
\(801\) −24.0264 14.3660i −0.848929 0.507596i
\(802\) −18.7513 −0.662131
\(803\) −5.24796 −0.185196
\(804\) 0.338592 + 2.73320i 0.0119412 + 0.0963927i
\(805\) 0 0
\(806\) 0 0
\(807\) −15.2679 + 19.5856i −0.537457 + 0.689447i
\(808\) −11.1173 + 11.1173i −0.391106 + 0.391106i
\(809\) 27.7429i 0.975389i 0.873014 + 0.487694i \(0.162162\pi\)
−0.873014 + 0.487694i \(0.837838\pi\)
\(810\) −9.66040 17.9808i −0.339432 0.631780i
\(811\) −19.0000 + 19.0000i −0.667180 + 0.667180i −0.957062 0.289882i \(-0.906384\pi\)
0.289882 + 0.957062i \(0.406384\pi\)
\(812\) −1.92089 1.92089i −0.0674099 0.0674099i
\(813\) 1.64548 + 13.2827i 0.0577094 + 0.465846i
\(814\) 23.7321 + 23.7321i 0.831808 + 0.831808i
\(815\) 6.23638i 0.218451i
\(816\) 30.7287 + 23.9545i 1.07572 + 0.838575i
\(817\) −6.00000 6.00000i −0.209913 0.209913i
\(818\) 45.1988 1.58034
\(819\) 0 0
\(820\) 2.26795 0.0792002
\(821\) 30.4433 + 30.4433i 1.06248 + 1.06248i 0.997913 + 0.0645667i \(0.0205665\pi\)
0.0645667 + 0.997913i \(0.479433\pi\)
\(822\) −13.8301 10.7812i −0.482381 0.376039i
\(823\) 8.53590i 0.297543i −0.988872 0.148771i \(-0.952468\pi\)
0.988872 0.148771i \(-0.0475318\pi\)
\(824\) 12.7786 + 12.7786i 0.445163 + 0.445163i
\(825\) 2.39360 + 19.3218i 0.0833345 + 0.672699i
\(826\) −4.53590 4.53590i −0.157824 0.157824i
\(827\) −31.7936 + 31.7936i −1.10557 + 1.10557i −0.111845 + 0.993726i \(0.535676\pi\)
−0.993726 + 0.111845i \(0.964324\pi\)
\(828\) 0 0
\(829\) 48.1244i 1.67143i −0.549165 0.835714i \(-0.685054\pi\)
0.549165 0.835714i \(-0.314946\pi\)
\(830\) −6.59817 + 6.59817i −0.229026 + 0.229026i
\(831\) −29.3785 + 37.6865i −1.01913 + 1.30733i
\(832\) 0 0
\(833\) 25.1954i 0.872968i
\(834\) 5.89808 + 47.6109i 0.204234 + 1.64863i
\(835\) 20.2487 0.700736
\(836\) 4.25953 0.147319
\(837\) 6.54383 + 16.8836i 0.226188 + 0.583582i
\(838\) 10.1244 10.1244i 0.349740 0.349740i
\(839\) 7.16884 7.16884i 0.247496 0.247496i −0.572446 0.819942i \(-0.694005\pi\)
0.819942 + 0.572446i \(0.194005\pi\)
\(840\) −1.18295 9.54910i −0.0408157 0.329475i
\(841\) −22.3923 −0.772148
\(842\) 16.6763 0.574704
\(843\) −29.4905 + 3.65331i −1.01571 + 0.125827i
\(844\) 0.483340i 0.0166372i
\(845\) 0 0
\(846\) −6.64102 26.3927i −0.228323 0.907400i
\(847\) −5.92820 + 5.92820i −0.203695 + 0.203695i
\(848\) 3.47998i 0.119503i
\(849\) −7.01593 + 9.00000i −0.240786 + 0.308879i
\(850\) 14.6603 14.6603i 0.502843 0.502843i
\(851\) 0 0
\(852\) 1.38724 0.171853i 0.0475262 0.00588758i
\(853\) 22.3660 + 22.3660i 0.765798 + 0.765798i 0.977364 0.211566i \(-0.0678562\pi\)
−0.211566 + 0.977364i \(0.567856\pi\)
\(854\) 14.9084i 0.510153i
\(855\) −4.25953 16.9282i −0.145673 0.578932i
\(856\) 35.0718 + 35.0718i 1.19873 + 1.19873i
\(857\) −3.32707 −0.113651 −0.0568253 0.998384i \(-0.518098\pi\)
−0.0568253 + 0.998384i \(0.518098\pi\)
\(858\) 0 0
\(859\) 39.1769 1.33670 0.668350 0.743847i \(-0.267001\pi\)
0.668350 + 0.743847i \(0.267001\pi\)
\(860\) −0.626638 0.626638i −0.0213682 0.0213682i
\(861\) −8.46410 + 10.8577i −0.288456 + 0.370030i
\(862\) 56.9808i 1.94077i
\(863\) −18.2354 18.2354i −0.620741 0.620741i 0.324980 0.945721i \(-0.394642\pi\)
−0.945721 + 0.324980i \(0.894642\pi\)
\(864\) −7.29638 + 2.82797i −0.248228 + 0.0962096i
\(865\) −18.5885 18.5885i −0.632027 0.632027i
\(866\) 33.0673 33.0673i 1.12367 1.12367i
\(867\) 11.4641 + 8.93682i 0.389341 + 0.303510i
\(868\) 1.32051i 0.0448210i
\(869\) −5.81863 + 5.81863i −0.197383 + 0.197383i
\(870\) 22.2096 + 17.3135i 0.752977 + 0.586981i
\(871\) 0 0
\(872\) 48.6788i 1.64847i
\(873\) 4.35563 + 2.60434i 0.147416 + 0.0881435i
\(874\) 0 0
\(875\) −16.4675 −0.556701
\(876\) −0.587477 + 0.0727771i −0.0198490 + 0.00245891i
\(877\) 21.2224 21.2224i 0.716631 0.716631i −0.251283 0.967914i \(-0.580852\pi\)
0.967914 + 0.251283i \(0.0808525\pi\)
\(878\) 1.35022 1.35022i 0.0455676 0.0455676i
\(879\) 3.09640 0.383584i 0.104439 0.0129380i
\(880\) −27.6603 −0.932427
\(881\) 23.4834 0.791175 0.395588 0.918428i \(-0.370541\pi\)
0.395588 + 0.918428i \(0.370541\pi\)
\(882\) 19.3881 + 11.5926i 0.652832 + 0.390345i
\(883\) 33.3731i 1.12309i 0.827445 + 0.561547i \(0.189793\pi\)
−0.827445 + 0.561547i \(0.810207\pi\)
\(884\) 0 0
\(885\) 6.19615 + 4.83020i 0.208281 + 0.162365i
\(886\) 11.9474 11.9474i 0.401382 0.401382i
\(887\) 25.2514i 0.847858i −0.905696 0.423929i \(-0.860651\pi\)
0.905696 0.423929i \(-0.139349\pi\)
\(888\) −19.3003 15.0455i −0.647676 0.504895i
\(889\) −9.12436 + 9.12436i −0.306021 + 0.306021i
\(890\) −14.9643 14.9643i −0.501605 0.501605i
\(891\) 10.6733 35.4579i 0.357570 1.18789i
\(892\) −4.90897 4.90897i −0.164364 0.164364i
\(893\) 23.2745i 0.778852i
\(894\) −13.8435 + 17.7583i −0.462995 + 0.593927i
\(895\) −28.2679 28.2679i −0.944893 0.944893i
\(896\) −18.4443 −0.616181
\(897\) 0 0
\(898\) 30.9808 1.03384
\(899\) −17.6648 17.6648i −0.589153 0.589153i
\(900\) 0.535898 + 2.12976i 0.0178633 + 0.0709922i
\(901\) 3.92820i 0.130867i
\(902\) 24.6247 + 24.6247i 0.819913 + 0.819913i
\(903\) 5.33864 0.661356i 0.177659 0.0220085i
\(904\) 18.9737 + 18.9737i 0.631057 + 0.631057i
\(905\) −3.19465 + 3.19465i −0.106194 + 0.106194i
\(906\) 1.21539 1.55910i 0.0403786 0.0517975i
\(907\) 17.3205i 0.575118i 0.957763 + 0.287559i \(0.0928437\pi\)
−0.957763 + 0.287559i \(0.907156\pi\)
\(908\) −3.84177 + 3.84177i −0.127494 + 0.127494i
\(909\) −4.41244 17.5359i −0.146351 0.581629i
\(910\) 0 0
\(911\) 1.55910i 0.0516552i 0.999666 + 0.0258276i \(0.00822209\pi\)
−0.999666 + 0.0258276i \(0.991778\pi\)
\(912\) −29.6477 + 3.67279i −0.981734 + 0.121618i
\(913\) −16.9282 −0.560242
\(914\) 5.87459 0.194314
\(915\) −2.24477 18.1204i −0.0742099 0.599043i
\(916\) −3.78461 + 3.78461i −0.125047 + 0.125047i
\(917\) 7.94839 7.94839i 0.262479 0.262479i
\(918\) −36.7670 + 14.2504i −1.21349 + 0.470333i
\(919\) 13.4115 0.442406 0.221203 0.975228i \(-0.429002\pi\)
0.221203 + 0.975228i \(0.429002\pi\)
\(920\) 0 0
\(921\) −2.52728 20.4009i −0.0832768 0.672233i
\(922\) 32.0333i 1.05496i
\(923\) 0 0
\(924\) −1.66025 + 2.12976i −0.0546183 + 0.0700641i
\(925\) −10.4641 + 10.4641i −0.344058 + 0.344058i
\(926\) 49.0965i 1.61341i
\(927\) −20.1563 + 5.07180i −0.662020 + 0.166580i
\(928\) 7.63397 7.63397i 0.250597 0.250597i
\(929\) −14.4141 14.4141i −0.472913 0.472913i 0.429943 0.902856i \(-0.358534\pi\)
−0.902856 + 0.429943i \(0.858534\pi\)
\(930\) 1.68292 + 13.5850i 0.0551853 + 0.445471i
\(931\) 13.6603 + 13.6603i 0.447697 + 0.447697i
\(932\) 4.67729i 0.153210i
\(933\) −13.7670 10.7321i −0.450712 0.351352i
\(934\) 20.4115 + 20.4115i 0.667886 + 0.667886i
\(935\) −31.2229 −1.02110
\(936\) 0 0
\(937\) −37.0000 −1.20874 −0.604369 0.796705i \(-0.706575\pi\)
−0.604369 + 0.796705i \(0.706575\pi\)
\(938\) −8.93682 8.93682i −0.291797 0.291797i
\(939\) 2.73205 + 2.12976i 0.0891571 + 0.0695022i
\(940\) 2.43078i 0.0792833i
\(941\) −9.14570 9.14570i −0.298141 0.298141i 0.542144 0.840285i \(-0.317613\pi\)
−0.840285 + 0.542144i \(0.817613\pi\)
\(942\) −1.54051 12.4354i −0.0501924 0.405167i
\(943\) 0 0
\(944\) 9.50749 9.50749i 0.309442 0.309442i
\(945\) 10.1244 + 4.46841i 0.329345 + 0.145357i
\(946\) 13.6077i 0.442424i
\(947\) −7.58660 + 7.58660i −0.246531 + 0.246531i −0.819546 0.573014i \(-0.805774\pi\)
0.573014 + 0.819546i \(0.305774\pi\)
\(948\) −0.570669 + 0.732051i −0.0185345 + 0.0237759i
\(949\) 0 0
\(950\) 15.8968i 0.515760i
\(951\) −3.41855 27.5955i −0.110854 0.894844i
\(952\) −18.5885 −0.602455
\(953\) −1.97685 −0.0640366 −0.0320183 0.999487i \(-0.510193\pi\)
−0.0320183 + 0.999487i \(0.510193\pi\)
\(954\) 3.02279 + 1.80740i 0.0978666 + 0.0585169i
\(955\) 5.14359 5.14359i 0.166443 0.166443i
\(956\) −1.76798 + 1.76798i −0.0571804 + 0.0571804i
\(957\) 6.28076 + 50.7000i 0.203028 + 1.63890i
\(958\) 30.9808 1.00094
\(959\) 9.50749 0.307013
\(960\) 17.2409 2.13582i 0.556449 0.0689334i
\(961\) 18.8564i 0.608271i
\(962\) 0 0
\(963\) −55.3205 + 13.9199i −1.78268 + 0.448563i
\(964\) 2.75833 2.75833i 0.0888398 0.0888398i
\(965\) 0.208879i 0.00672406i
\(966\) 0 0
\(967\) 27.8564 27.8564i 0.895802 0.895802i −0.0992599 0.995062i \(-0.531648\pi\)
0.995062 + 0.0992599i \(0.0316475\pi\)
\(968\) −10.9342 10.9342i −0.351437 0.351437i
\(969\) −33.4663 + 4.14584i −1.07509 + 0.133184i
\(970\) 2.71281 + 2.71281i 0.0871032 + 0.0871032i
\(971\) 47.8433i 1.53536i −0.640832 0.767682i \(-0.721410\pi\)
0.640832 0.767682i \(-0.278590\pi\)
\(972\) 0.703093 4.11731i 0.0225517 0.132063i
\(973\) −18.3923 18.3923i −0.589630 0.589630i
\(974\) 8.67197 0.277868
\(975\) 0 0
\(976\) −31.2487 −1.00025
\(977\) −16.7528 16.7528i −0.535969 0.535969i 0.386373 0.922342i \(-0.373728\pi\)
−0.922342 + 0.386373i \(0.873728\pi\)
\(978\) −6.64102 + 8.51906i −0.212356 + 0.272409i
\(979\) 38.3923i 1.22702i
\(980\) 1.42667 + 1.42667i 0.0455734 + 0.0455734i
\(981\) 48.0520 + 28.7315i 1.53418 + 0.917326i
\(982\) 30.3731 + 30.3731i 0.969244 + 0.969244i
\(983\) −30.4433 + 30.4433i −0.970992 + 0.970992i −0.999591 0.0285990i \(-0.990895\pi\)
0.0285990 + 0.999591i \(0.490895\pi\)
\(984\) −20.0263 15.6114i −0.638414 0.497675i
\(985\) 6.19615i 0.197426i
\(986\) 38.4682 38.4682i 1.22508 1.22508i
\(987\) 11.6373 + 9.07180i 0.370418 + 0.288758i
\(988\) 0 0
\(989\) 0 0
\(990\) 14.3660 24.0264i 0.456580 0.763608i
\(991\) −57.5692 −1.82875 −0.914373 0.404872i \(-0.867316\pi\)
−0.914373 + 0.404872i \(0.867316\pi\)
\(992\) 5.24796 0.166623
\(993\) −58.8186 + 7.28650i −1.86655 + 0.231230i
\(994\) −4.53590 + 4.53590i −0.143870 + 0.143870i
\(995\) −13.7670 + 13.7670i −0.436444 + 0.436444i
\(996\) −1.89501 + 0.234755i −0.0600457 + 0.00743851i
\(997\) −7.00000 −0.221692 −0.110846 0.993838i \(-0.535356\pi\)
−0.110846 + 0.993838i \(0.535356\pi\)
\(998\) 5.24796 0.166121
\(999\) 26.2433 10.1715i 0.830303 0.321813i
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 507.2.f.e.239.3 8
3.2 odd 2 inner 507.2.f.e.239.2 8
13.2 odd 12 507.2.k.e.488.2 8
13.3 even 3 507.2.k.d.188.1 8
13.4 even 6 507.2.k.e.80.1 8
13.5 odd 4 507.2.f.f.437.3 8
13.6 odd 12 39.2.k.b.11.1 8
13.7 odd 12 507.2.k.d.89.2 8
13.8 odd 4 inner 507.2.f.e.437.2 8
13.9 even 3 507.2.k.f.80.2 8
13.10 even 6 39.2.k.b.32.2 yes 8
13.11 odd 12 507.2.k.f.488.1 8
13.12 even 2 507.2.f.f.239.2 8
39.2 even 12 507.2.k.e.488.1 8
39.5 even 4 507.2.f.f.437.2 8
39.8 even 4 inner 507.2.f.e.437.3 8
39.11 even 12 507.2.k.f.488.2 8
39.17 odd 6 507.2.k.e.80.2 8
39.20 even 12 507.2.k.d.89.1 8
39.23 odd 6 39.2.k.b.32.1 yes 8
39.29 odd 6 507.2.k.d.188.2 8
39.32 even 12 39.2.k.b.11.2 yes 8
39.35 odd 6 507.2.k.f.80.1 8
39.38 odd 2 507.2.f.f.239.3 8
52.19 even 12 624.2.cn.c.401.1 8
52.23 odd 6 624.2.cn.c.305.2 8
65.19 odd 12 975.2.bo.d.401.2 8
65.23 odd 12 975.2.bp.e.149.1 8
65.32 even 12 975.2.bp.e.674.2 8
65.49 even 6 975.2.bo.d.851.1 8
65.58 even 12 975.2.bp.f.674.1 8
65.62 odd 12 975.2.bp.f.149.2 8
156.23 even 6 624.2.cn.c.305.1 8
156.71 odd 12 624.2.cn.c.401.2 8
195.23 even 12 975.2.bp.e.149.2 8
195.32 odd 12 975.2.bp.e.674.1 8
195.62 even 12 975.2.bp.f.149.1 8
195.149 even 12 975.2.bo.d.401.1 8
195.179 odd 6 975.2.bo.d.851.2 8
195.188 odd 12 975.2.bp.f.674.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.k.b.11.1 8 13.6 odd 12
39.2.k.b.11.2 yes 8 39.32 even 12
39.2.k.b.32.1 yes 8 39.23 odd 6
39.2.k.b.32.2 yes 8 13.10 even 6
507.2.f.e.239.2 8 3.2 odd 2 inner
507.2.f.e.239.3 8 1.1 even 1 trivial
507.2.f.e.437.2 8 13.8 odd 4 inner
507.2.f.e.437.3 8 39.8 even 4 inner
507.2.f.f.239.2 8 13.12 even 2
507.2.f.f.239.3 8 39.38 odd 2
507.2.f.f.437.2 8 39.5 even 4
507.2.f.f.437.3 8 13.5 odd 4
507.2.k.d.89.1 8 39.20 even 12
507.2.k.d.89.2 8 13.7 odd 12
507.2.k.d.188.1 8 13.3 even 3
507.2.k.d.188.2 8 39.29 odd 6
507.2.k.e.80.1 8 13.4 even 6
507.2.k.e.80.2 8 39.17 odd 6
507.2.k.e.488.1 8 39.2 even 12
507.2.k.e.488.2 8 13.2 odd 12
507.2.k.f.80.1 8 39.35 odd 6
507.2.k.f.80.2 8 13.9 even 3
507.2.k.f.488.1 8 13.11 odd 12
507.2.k.f.488.2 8 39.11 even 12
624.2.cn.c.305.1 8 156.23 even 6
624.2.cn.c.305.2 8 52.23 odd 6
624.2.cn.c.401.1 8 52.19 even 12
624.2.cn.c.401.2 8 156.71 odd 12
975.2.bo.d.401.1 8 195.149 even 12
975.2.bo.d.401.2 8 65.19 odd 12
975.2.bo.d.851.1 8 65.49 even 6
975.2.bo.d.851.2 8 195.179 odd 6
975.2.bp.e.149.1 8 65.23 odd 12
975.2.bp.e.149.2 8 195.23 even 12
975.2.bp.e.674.1 8 195.32 odd 12
975.2.bp.e.674.2 8 65.32 even 12
975.2.bp.f.149.1 8 195.62 even 12
975.2.bp.f.149.2 8 65.62 odd 12
975.2.bp.f.674.1 8 65.58 even 12
975.2.bp.f.674.2 8 195.188 odd 12