Properties

Label 100.3.d.b.99.7
Level $100$
Weight $3$
Character 100.99
Analytic conductor $2.725$
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] = [100,3,Mod(99,100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(100, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("100.99");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 100.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.72480264360\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 20)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 99.7
Root \(0.951057 - 0.309017i\) of defining polynomial
Character \(\chi\) \(=\) 100.99
Dual form 100.3.d.b.99.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.90211 - 0.618034i) q^{2} +2.35114 q^{3} +(3.23607 - 2.35114i) q^{4} +(4.47214 - 1.45309i) q^{6} -5.25731 q^{7} +(4.70228 - 6.47214i) q^{8} -3.47214 q^{9} +O(q^{10})\) \(q+(1.90211 - 0.618034i) q^{2} +2.35114 q^{3} +(3.23607 - 2.35114i) q^{4} +(4.47214 - 1.45309i) q^{6} -5.25731 q^{7} +(4.70228 - 6.47214i) q^{8} -3.47214 q^{9} +19.9192i q^{11} +(7.60845 - 5.52786i) q^{12} -8.47214i q^{13} +(-10.0000 + 3.24920i) q^{14} +(4.94427 - 15.2169i) q^{16} -11.8885i q^{17} +(-6.60440 + 2.14590i) q^{18} +15.2169i q^{19} -12.3607 q^{21} +(12.3107 + 37.8885i) q^{22} +0.555029 q^{23} +(11.0557 - 15.2169i) q^{24} +(-5.23607 - 16.1150i) q^{26} -29.3238 q^{27} +(-17.0130 + 12.3607i) q^{28} +10.9443 q^{29} -8.29451i q^{31} -32.0000i q^{32} +46.8328i q^{33} +(-7.34752 - 22.6134i) q^{34} +(-11.2361 + 8.16348i) q^{36} +18.3607i q^{37} +(9.40456 + 28.9443i) q^{38} -19.9192i q^{39} -14.5836 q^{41} +(-23.5114 + 7.63932i) q^{42} -22.2703 q^{43} +(46.8328 + 64.4598i) q^{44} +(1.05573 - 0.343027i) q^{46} +53.3902 q^{47} +(11.6247 - 35.7771i) q^{48} -21.3607 q^{49} -27.9516i q^{51} +(-19.9192 - 27.4164i) q^{52} -66.3607i q^{53} +(-55.7771 + 18.1231i) q^{54} +(-24.7214 + 34.0260i) q^{56} +35.7771i q^{57} +(20.8172 - 6.76393i) q^{58} -17.4370i q^{59} +90.1378 q^{61} +(-5.12629 - 15.7771i) q^{62} +18.2541 q^{63} +(-19.7771 - 60.8676i) q^{64} +(28.9443 + 89.0813i) q^{66} +50.2220 q^{67} +(-27.9516 - 38.4721i) q^{68} +1.30495 q^{69} -80.7868i q^{71} +(-16.3270 + 22.4721i) q^{72} -5.55418i q^{73} +(11.3475 + 34.9241i) q^{74} +(35.7771 + 49.2429i) q^{76} -104.721i q^{77} +(-12.3107 - 37.8885i) q^{78} +13.8448i q^{79} -37.6950 q^{81} +(-27.7396 + 9.01316i) q^{82} +76.2155 q^{83} +(-40.0000 + 29.0617i) q^{84} +(-42.3607 + 13.7638i) q^{86} +25.7315 q^{87} +(128.920 + 93.6656i) q^{88} +111.443 q^{89} +44.5407i q^{91} +(1.79611 - 1.30495i) q^{92} -19.5016i q^{93} +(101.554 - 32.9970i) q^{94} -75.2365i q^{96} +92.8328i q^{97} +(-40.6304 + 13.2016i) q^{98} -69.1621i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} + 8 q^{9} - 80 q^{14} - 32 q^{16} + 80 q^{21} + 160 q^{24} - 24 q^{26} + 16 q^{29} - 184 q^{34} - 72 q^{36} - 224 q^{41} + 160 q^{44} + 80 q^{46} + 8 q^{49} - 160 q^{54} + 160 q^{56} + 256 q^{61} + 128 q^{64} + 160 q^{66} - 240 q^{69} + 216 q^{74} - 552 q^{81} - 320 q^{84} - 160 q^{86} + 176 q^{89} + 240 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).

\(n\) \(51\) \(77\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.90211 0.618034i 0.951057 0.309017i
\(3\) 2.35114 0.783714 0.391857 0.920026i \(-0.371833\pi\)
0.391857 + 0.920026i \(0.371833\pi\)
\(4\) 3.23607 2.35114i 0.809017 0.587785i
\(5\) 0 0
\(6\) 4.47214 1.45309i 0.745356 0.242181i
\(7\) −5.25731 −0.751044 −0.375522 0.926813i \(-0.622537\pi\)
−0.375522 + 0.926813i \(0.622537\pi\)
\(8\) 4.70228 6.47214i 0.587785 0.809017i
\(9\) −3.47214 −0.385793
\(10\) 0 0
\(11\) 19.9192i 1.81084i 0.424522 + 0.905418i \(0.360442\pi\)
−0.424522 + 0.905418i \(0.639558\pi\)
\(12\) 7.60845 5.52786i 0.634038 0.460655i
\(13\) 8.47214i 0.651703i −0.945421 0.325851i \(-0.894349\pi\)
0.945421 0.325851i \(-0.105651\pi\)
\(14\) −10.0000 + 3.24920i −0.714286 + 0.232085i
\(15\) 0 0
\(16\) 4.94427 15.2169i 0.309017 0.951057i
\(17\) 11.8885i 0.699326i −0.936876 0.349663i \(-0.886296\pi\)
0.936876 0.349663i \(-0.113704\pi\)
\(18\) −6.60440 + 2.14590i −0.366911 + 0.119217i
\(19\) 15.2169i 0.800890i 0.916321 + 0.400445i \(0.131144\pi\)
−0.916321 + 0.400445i \(0.868856\pi\)
\(20\) 0 0
\(21\) −12.3607 −0.588604
\(22\) 12.3107 + 37.8885i 0.559579 + 1.72221i
\(23\) 0.555029 0.0241317 0.0120659 0.999927i \(-0.496159\pi\)
0.0120659 + 0.999927i \(0.496159\pi\)
\(24\) 11.0557 15.2169i 0.460655 0.634038i
\(25\) 0 0
\(26\) −5.23607 16.1150i −0.201387 0.619806i
\(27\) −29.3238 −1.08606
\(28\) −17.0130 + 12.3607i −0.607608 + 0.441453i
\(29\) 10.9443 0.377389 0.188694 0.982036i \(-0.439574\pi\)
0.188694 + 0.982036i \(0.439574\pi\)
\(30\) 0 0
\(31\) 8.29451i 0.267565i −0.991011 0.133782i \(-0.957288\pi\)
0.991011 0.133782i \(-0.0427123\pi\)
\(32\) 32.0000i 1.00000i
\(33\) 46.8328i 1.41918i
\(34\) −7.34752 22.6134i −0.216104 0.665099i
\(35\) 0 0
\(36\) −11.2361 + 8.16348i −0.312113 + 0.226763i
\(37\) 18.3607i 0.496235i 0.968730 + 0.248117i \(0.0798118\pi\)
−0.968730 + 0.248117i \(0.920188\pi\)
\(38\) 9.40456 + 28.9443i 0.247489 + 0.761691i
\(39\) 19.9192i 0.510748i
\(40\) 0 0
\(41\) −14.5836 −0.355697 −0.177849 0.984058i \(-0.556914\pi\)
−0.177849 + 0.984058i \(0.556914\pi\)
\(42\) −23.5114 + 7.63932i −0.559795 + 0.181889i
\(43\) −22.2703 −0.517915 −0.258957 0.965889i \(-0.583379\pi\)
−0.258957 + 0.965889i \(0.583379\pi\)
\(44\) 46.8328 + 64.4598i 1.06438 + 1.46500i
\(45\) 0 0
\(46\) 1.05573 0.343027i 0.0229506 0.00745711i
\(47\) 53.3902 1.13596 0.567981 0.823042i \(-0.307725\pi\)
0.567981 + 0.823042i \(0.307725\pi\)
\(48\) 11.6247 35.7771i 0.242181 0.745356i
\(49\) −21.3607 −0.435932
\(50\) 0 0
\(51\) 27.9516i 0.548071i
\(52\) −19.9192 27.4164i −0.383061 0.527239i
\(53\) 66.3607i 1.25209i −0.779788 0.626044i \(-0.784673\pi\)
0.779788 0.626044i \(-0.215327\pi\)
\(54\) −55.7771 + 18.1231i −1.03291 + 0.335612i
\(55\) 0 0
\(56\) −24.7214 + 34.0260i −0.441453 + 0.607608i
\(57\) 35.7771i 0.627668i
\(58\) 20.8172 6.76393i 0.358918 0.116620i
\(59\) 17.4370i 0.295543i −0.989022 0.147771i \(-0.952790\pi\)
0.989022 0.147771i \(-0.0472100\pi\)
\(60\) 0 0
\(61\) 90.1378 1.47767 0.738834 0.673887i \(-0.235377\pi\)
0.738834 + 0.673887i \(0.235377\pi\)
\(62\) −5.12629 15.7771i −0.0826820 0.254469i
\(63\) 18.2541 0.289748
\(64\) −19.7771 60.8676i −0.309017 0.951057i
\(65\) 0 0
\(66\) 28.9443 + 89.0813i 0.438550 + 1.34972i
\(67\) 50.2220 0.749582 0.374791 0.927109i \(-0.377715\pi\)
0.374791 + 0.927109i \(0.377715\pi\)
\(68\) −27.9516 38.4721i −0.411054 0.565767i
\(69\) 1.30495 0.0189123
\(70\) 0 0
\(71\) 80.7868i 1.13784i −0.822392 0.568921i \(-0.807361\pi\)
0.822392 0.568921i \(-0.192639\pi\)
\(72\) −16.3270 + 22.4721i −0.226763 + 0.312113i
\(73\) 5.55418i 0.0760846i −0.999276 0.0380423i \(-0.987888\pi\)
0.999276 0.0380423i \(-0.0121122\pi\)
\(74\) 11.3475 + 34.9241i 0.153345 + 0.471947i
\(75\) 0 0
\(76\) 35.7771 + 49.2429i 0.470751 + 0.647933i
\(77\) 104.721i 1.36002i
\(78\) −12.3107 37.8885i −0.157830 0.485751i
\(79\) 13.8448i 0.175251i 0.996154 + 0.0876253i \(0.0279278\pi\)
−0.996154 + 0.0876253i \(0.972072\pi\)
\(80\) 0 0
\(81\) −37.6950 −0.465371
\(82\) −27.7396 + 9.01316i −0.338288 + 0.109917i
\(83\) 76.2155 0.918260 0.459130 0.888369i \(-0.348161\pi\)
0.459130 + 0.888369i \(0.348161\pi\)
\(84\) −40.0000 + 29.0617i −0.476190 + 0.345973i
\(85\) 0 0
\(86\) −42.3607 + 13.7638i −0.492566 + 0.160044i
\(87\) 25.7315 0.295765
\(88\) 128.920 + 93.6656i 1.46500 + 1.06438i
\(89\) 111.443 1.25217 0.626083 0.779757i \(-0.284657\pi\)
0.626083 + 0.779757i \(0.284657\pi\)
\(90\) 0 0
\(91\) 44.5407i 0.489458i
\(92\) 1.79611 1.30495i 0.0195230 0.0141843i
\(93\) 19.5016i 0.209694i
\(94\) 101.554 32.9970i 1.08036 0.351031i
\(95\) 0 0
\(96\) 75.2365i 0.783714i
\(97\) 92.8328i 0.957039i 0.878077 + 0.478520i \(0.158826\pi\)
−0.878077 + 0.478520i \(0.841174\pi\)
\(98\) −40.6304 + 13.2016i −0.414596 + 0.134710i
\(99\) 69.1621i 0.698607i
\(100\) 0 0
\(101\) 64.1115 0.634767 0.317383 0.948297i \(-0.397196\pi\)
0.317383 + 0.948297i \(0.397196\pi\)
\(102\) −17.2751 53.1672i −0.169363 0.521247i
\(103\) −137.769 −1.33757 −0.668783 0.743458i \(-0.733184\pi\)
−0.668783 + 0.743458i \(0.733184\pi\)
\(104\) −54.8328 39.8384i −0.527239 0.383061i
\(105\) 0 0
\(106\) −41.0132 126.226i −0.386917 1.19081i
\(107\) −51.3320 −0.479739 −0.239869 0.970805i \(-0.577105\pi\)
−0.239869 + 0.970805i \(0.577105\pi\)
\(108\) −94.8936 + 68.9443i −0.878645 + 0.638373i
\(109\) −133.469 −1.22449 −0.612243 0.790669i \(-0.709733\pi\)
−0.612243 + 0.790669i \(0.709733\pi\)
\(110\) 0 0
\(111\) 43.1685i 0.388906i
\(112\) −25.9936 + 80.0000i −0.232085 + 0.714286i
\(113\) 170.721i 1.51081i 0.655259 + 0.755404i \(0.272559\pi\)
−0.655259 + 0.755404i \(0.727441\pi\)
\(114\) 22.1115 + 68.0521i 0.193960 + 0.596948i
\(115\) 0 0
\(116\) 35.4164 25.7315i 0.305314 0.221824i
\(117\) 29.4164i 0.251422i
\(118\) −10.7767 33.1672i −0.0913277 0.281078i
\(119\) 62.5018i 0.525225i
\(120\) 0 0
\(121\) −275.774 −2.27912
\(122\) 171.452 55.7082i 1.40535 0.456625i
\(123\) −34.2881 −0.278765
\(124\) −19.5016 26.8416i −0.157271 0.216464i
\(125\) 0 0
\(126\) 34.7214 11.2817i 0.275566 0.0895369i
\(127\) −198.637 −1.56407 −0.782035 0.623235i \(-0.785818\pi\)
−0.782035 + 0.623235i \(0.785818\pi\)
\(128\) −75.2365 103.554i −0.587785 0.809017i
\(129\) −52.3607 −0.405897
\(130\) 0 0
\(131\) 7.77041i 0.0593161i 0.999560 + 0.0296580i \(0.00944183\pi\)
−0.999560 + 0.0296580i \(0.990558\pi\)
\(132\) 110.111 + 151.554i 0.834171 + 1.14814i
\(133\) 80.0000i 0.601504i
\(134\) 95.5279 31.0389i 0.712895 0.231633i
\(135\) 0 0
\(136\) −76.9443 55.9033i −0.565767 0.411054i
\(137\) 0.832816i 0.00607895i −0.999995 0.00303947i \(-0.999033\pi\)
0.999995 0.00303947i \(-0.000967496\pi\)
\(138\) 2.48217 0.806504i 0.0179867 0.00584424i
\(139\) 237.658i 1.70977i 0.518817 + 0.854885i \(0.326373\pi\)
−0.518817 + 0.854885i \(0.673627\pi\)
\(140\) 0 0
\(141\) 125.528 0.890269
\(142\) −49.9290 153.666i −0.351613 1.08215i
\(143\) 168.758 1.18013
\(144\) −17.1672 + 52.8352i −0.119217 + 0.366911i
\(145\) 0 0
\(146\) −3.43267 10.5647i −0.0235114 0.0723607i
\(147\) −50.2220 −0.341646
\(148\) 43.1685 + 59.4164i 0.291679 + 0.401462i
\(149\) 36.9706 0.248125 0.124062 0.992274i \(-0.460408\pi\)
0.124062 + 0.992274i \(0.460408\pi\)
\(150\) 0 0
\(151\) 282.723i 1.87234i 0.351552 + 0.936168i \(0.385654\pi\)
−0.351552 + 0.936168i \(0.614346\pi\)
\(152\) 98.4859 + 71.5542i 0.647933 + 0.470751i
\(153\) 41.2786i 0.269795i
\(154\) −64.7214 199.192i −0.420269 1.29345i
\(155\) 0 0
\(156\) −46.8328 64.4598i −0.300210 0.413204i
\(157\) 204.748i 1.30413i −0.758165 0.652063i \(-0.773904\pi\)
0.758165 0.652063i \(-0.226096\pi\)
\(158\) 8.55656 + 26.3344i 0.0541554 + 0.166673i
\(159\) 156.023i 0.981279i
\(160\) 0 0
\(161\) −2.91796 −0.0181240
\(162\) −71.7002 + 23.2968i −0.442594 + 0.143808i
\(163\) −107.235 −0.657885 −0.328943 0.944350i \(-0.606692\pi\)
−0.328943 + 0.944350i \(0.606692\pi\)
\(164\) −47.1935 + 34.2881i −0.287765 + 0.209074i
\(165\) 0 0
\(166\) 144.971 47.1038i 0.873317 0.283758i
\(167\) 33.2090 0.198856 0.0994280 0.995045i \(-0.468299\pi\)
0.0994280 + 0.995045i \(0.468299\pi\)
\(168\) −58.1234 + 80.0000i −0.345973 + 0.476190i
\(169\) 97.2229 0.575284
\(170\) 0 0
\(171\) 52.8352i 0.308978i
\(172\) −72.0683 + 52.3607i −0.419002 + 0.304423i
\(173\) 226.361i 1.30844i −0.756303 0.654222i \(-0.772996\pi\)
0.756303 0.654222i \(-0.227004\pi\)
\(174\) 48.9443 15.9030i 0.281289 0.0913963i
\(175\) 0 0
\(176\) 303.108 + 98.4859i 1.72221 + 0.559579i
\(177\) 40.9969i 0.231621i
\(178\) 211.977 68.8754i 1.19088 0.386940i
\(179\) 224.337i 1.25328i −0.779308 0.626641i \(-0.784429\pi\)
0.779308 0.626641i \(-0.215571\pi\)
\(180\) 0 0
\(181\) 86.2229 0.476370 0.238185 0.971220i \(-0.423448\pi\)
0.238185 + 0.971220i \(0.423448\pi\)
\(182\) 27.5276 + 84.7214i 0.151251 + 0.465502i
\(183\) 211.927 1.15807
\(184\) 2.60990 3.59222i 0.0141843 0.0195230i
\(185\) 0 0
\(186\) −12.0526 37.0942i −0.0647990 0.199431i
\(187\) 236.810 1.26636
\(188\) 172.774 125.528i 0.919012 0.667701i
\(189\) 154.164 0.815683
\(190\) 0 0
\(191\) 31.0198i 0.162407i −0.996698 0.0812036i \(-0.974124\pi\)
0.996698 0.0812036i \(-0.0258764\pi\)
\(192\) −46.4987 143.108i −0.242181 0.745356i
\(193\) 110.223i 0.571103i 0.958363 + 0.285552i \(0.0921768\pi\)
−0.958363 + 0.285552i \(0.907823\pi\)
\(194\) 57.3738 + 176.579i 0.295741 + 0.910198i
\(195\) 0 0
\(196\) −69.1246 + 50.2220i −0.352677 + 0.256235i
\(197\) 172.525i 0.875760i 0.899033 + 0.437880i \(0.144271\pi\)
−0.899033 + 0.437880i \(0.855729\pi\)
\(198\) −42.7445 131.554i −0.215882 0.664415i
\(199\) 272.208i 1.36788i 0.729538 + 0.683940i \(0.239735\pi\)
−0.729538 + 0.683940i \(0.760265\pi\)
\(200\) 0 0
\(201\) 118.079 0.587457
\(202\) 121.947 39.6231i 0.603699 0.196154i
\(203\) −57.5374 −0.283436
\(204\) −65.7183 90.4534i −0.322148 0.443399i
\(205\) 0 0
\(206\) −262.053 + 85.1461i −1.27210 + 0.413330i
\(207\) −1.92714 −0.00930984
\(208\) −128.920 41.8885i −0.619806 0.201387i
\(209\) −303.108 −1.45028
\(210\) 0 0
\(211\) 205.266i 0.972826i −0.873729 0.486413i \(-0.838305\pi\)
0.873729 0.486413i \(-0.161695\pi\)
\(212\) −156.023 214.748i −0.735959 1.01296i
\(213\) 189.941i 0.891743i
\(214\) −97.6393 + 31.7249i −0.456259 + 0.148247i
\(215\) 0 0
\(216\) −137.889 + 189.787i −0.638373 + 0.878645i
\(217\) 43.6068i 0.200953i
\(218\) −253.873 + 82.4884i −1.16456 + 0.378387i
\(219\) 13.0586i 0.0596285i
\(220\) 0 0
\(221\) −100.721 −0.455753
\(222\) 26.6796 + 82.1115i 0.120179 + 0.369871i
\(223\) −235.731 −1.05709 −0.528545 0.848905i \(-0.677262\pi\)
−0.528545 + 0.848905i \(0.677262\pi\)
\(224\) 168.234i 0.751044i
\(225\) 0 0
\(226\) 105.512 + 324.731i 0.466865 + 1.43686i
\(227\) −58.5165 −0.257782 −0.128891 0.991659i \(-0.541142\pi\)
−0.128891 + 0.991659i \(0.541142\pi\)
\(228\) 84.1170 + 115.777i 0.368934 + 0.507794i
\(229\) −162.721 −0.710574 −0.355287 0.934757i \(-0.615617\pi\)
−0.355287 + 0.934757i \(0.615617\pi\)
\(230\) 0 0
\(231\) 246.215i 1.06586i
\(232\) 51.4631 70.8328i 0.221824 0.305314i
\(233\) 319.050i 1.36931i 0.728867 + 0.684656i \(0.240047\pi\)
−0.728867 + 0.684656i \(0.759953\pi\)
\(234\) 18.1803 + 55.9533i 0.0776938 + 0.239117i
\(235\) 0 0
\(236\) −40.9969 56.4274i −0.173716 0.239099i
\(237\) 32.5511i 0.137346i
\(238\) 38.6282 + 118.885i 0.162303 + 0.499519i
\(239\) 236.810i 0.990837i −0.868654 0.495419i \(-0.835015\pi\)
0.868654 0.495419i \(-0.164985\pi\)
\(240\) 0 0
\(241\) −0.917961 −0.00380897 −0.00190448 0.999998i \(-0.500606\pi\)
−0.00190448 + 0.999998i \(0.500606\pi\)
\(242\) −524.553 + 170.438i −2.16758 + 0.704288i
\(243\) 175.287 0.721347
\(244\) 291.692 211.927i 1.19546 0.868552i
\(245\) 0 0
\(246\) −65.2198 + 21.1912i −0.265121 + 0.0861431i
\(247\) 128.920 0.521942
\(248\) −53.6832 39.0031i −0.216464 0.157271i
\(249\) 179.193 0.719653
\(250\) 0 0
\(251\) 136.690i 0.544582i −0.962215 0.272291i \(-0.912219\pi\)
0.962215 0.272291i \(-0.0877813\pi\)
\(252\) 59.0715 42.9180i 0.234411 0.170309i
\(253\) 11.0557i 0.0436985i
\(254\) −377.830 + 122.764i −1.48752 + 0.483324i
\(255\) 0 0
\(256\) −207.108 150.473i −0.809017 0.587785i
\(257\) 274.944i 1.06982i 0.844908 + 0.534911i \(0.179655\pi\)
−0.844908 + 0.534911i \(0.820345\pi\)
\(258\) −99.5959 + 32.3607i −0.386031 + 0.125429i
\(259\) 96.5278i 0.372694i
\(260\) 0 0
\(261\) −38.0000 −0.145594
\(262\) 4.80238 + 14.7802i 0.0183297 + 0.0564130i
\(263\) −406.385 −1.54519 −0.772596 0.634899i \(-0.781042\pi\)
−0.772596 + 0.634899i \(0.781042\pi\)
\(264\) 303.108 + 220.221i 1.14814 + 0.834171i
\(265\) 0 0
\(266\) −49.4427 152.169i −0.185875 0.572064i
\(267\) 262.018 0.981339
\(268\) 162.522 118.079i 0.606424 0.440593i
\(269\) 348.525 1.29563 0.647816 0.761797i \(-0.275683\pi\)
0.647816 + 0.761797i \(0.275683\pi\)
\(270\) 0 0
\(271\) 247.849i 0.914571i −0.889320 0.457286i \(-0.848822\pi\)
0.889320 0.457286i \(-0.151178\pi\)
\(272\) −180.907 58.7802i −0.665099 0.216104i
\(273\) 104.721i 0.383595i
\(274\) −0.514708 1.58411i −0.00187850 0.00578142i
\(275\) 0 0
\(276\) 4.22291 3.06813i 0.0153004 0.0111164i
\(277\) 54.7539i 0.197667i 0.995104 + 0.0988337i \(0.0315112\pi\)
−0.995104 + 0.0988337i \(0.968489\pi\)
\(278\) 146.881 + 452.053i 0.528348 + 1.62609i
\(279\) 28.7997i 0.103225i
\(280\) 0 0
\(281\) −50.3607 −0.179220 −0.0896098 0.995977i \(-0.528562\pi\)
−0.0896098 + 0.995977i \(0.528562\pi\)
\(282\) 238.768 77.5805i 0.846696 0.275108i
\(283\) 147.336 0.520621 0.260310 0.965525i \(-0.416175\pi\)
0.260310 + 0.965525i \(0.416175\pi\)
\(284\) −189.941 261.432i −0.668807 0.920534i
\(285\) 0 0
\(286\) 320.997 104.298i 1.12237 0.364679i
\(287\) 76.6705 0.267145
\(288\) 111.108i 0.385793i
\(289\) 147.663 0.510943
\(290\) 0 0
\(291\) 218.263i 0.750045i
\(292\) −13.0586 17.9737i −0.0447214 0.0615537i
\(293\) 178.859i 0.610441i 0.952282 + 0.305220i \(0.0987301\pi\)
−0.952282 + 0.305220i \(0.901270\pi\)
\(294\) −95.5279 + 31.0389i −0.324925 + 0.105574i
\(295\) 0 0
\(296\) 118.833 + 86.3371i 0.401462 + 0.291679i
\(297\) 584.105i 1.96668i
\(298\) 70.3222 22.8491i 0.235981 0.0766748i
\(299\) 4.70228i 0.0157267i
\(300\) 0 0
\(301\) 117.082 0.388977
\(302\) 174.732 + 537.771i 0.578584 + 1.78070i
\(303\) 150.735 0.497475
\(304\) 231.554 + 75.2365i 0.761691 + 0.247489i
\(305\) 0 0
\(306\) 25.5116 + 78.5166i 0.0833713 + 0.256590i
\(307\) −284.550 −0.926873 −0.463436 0.886130i \(-0.653384\pi\)
−0.463436 + 0.886130i \(0.653384\pi\)
\(308\) −246.215 338.885i −0.799398 1.10028i
\(309\) −323.915 −1.04827
\(310\) 0 0
\(311\) 282.199i 0.907392i 0.891157 + 0.453696i \(0.149895\pi\)
−0.891157 + 0.453696i \(0.850105\pi\)
\(312\) −128.920 93.6656i −0.413204 0.300210i
\(313\) 567.548i 1.81325i −0.421935 0.906626i \(-0.638649\pi\)
0.421935 0.906626i \(-0.361351\pi\)
\(314\) −126.541 389.453i −0.402997 1.24030i
\(315\) 0 0
\(316\) 32.5511 + 44.8027i 0.103010 + 0.141781i
\(317\) 161.141i 0.508331i −0.967161 0.254165i \(-0.918199\pi\)
0.967161 0.254165i \(-0.0818008\pi\)
\(318\) −96.4277 296.774i −0.303232 0.933252i
\(319\) 218.001i 0.683389i
\(320\) 0 0
\(321\) −120.689 −0.375978
\(322\) −5.55029 + 1.80340i −0.0172369 + 0.00560062i
\(323\) 180.907 0.560083
\(324\) −121.984 + 88.6264i −0.376493 + 0.273538i
\(325\) 0 0
\(326\) −203.974 + 66.2751i −0.625686 + 0.203298i
\(327\) −313.805 −0.959647
\(328\) −68.5762 + 94.3870i −0.209074 + 0.287765i
\(329\) −280.689 −0.853158
\(330\) 0 0
\(331\) 331.966i 1.00292i 0.865181 + 0.501459i \(0.167203\pi\)
−0.865181 + 0.501459i \(0.832797\pi\)
\(332\) 246.639 179.193i 0.742888 0.539739i
\(333\) 63.7508i 0.191444i
\(334\) 63.1672 20.5243i 0.189123 0.0614499i
\(335\) 0 0
\(336\) −61.1146 + 188.091i −0.181889 + 0.559795i
\(337\) 269.108i 0.798541i 0.916833 + 0.399271i \(0.130737\pi\)
−0.916833 + 0.399271i \(0.869263\pi\)
\(338\) 184.929 60.0871i 0.547127 0.177772i
\(339\) 401.390i 1.18404i
\(340\) 0 0
\(341\) 165.220 0.484516
\(342\) −32.6539 100.498i −0.0954793 0.293855i
\(343\) 369.908 1.07845
\(344\) −104.721 + 144.137i −0.304423 + 0.419002i
\(345\) 0 0
\(346\) −139.899 430.564i −0.404331 1.24440i
\(347\) −503.075 −1.44978 −0.724892 0.688863i \(-0.758110\pi\)
−0.724892 + 0.688863i \(0.758110\pi\)
\(348\) 83.2690 60.4984i 0.239279 0.173846i
\(349\) 0.504658 0.00144601 0.000723006 1.00000i \(-0.499770\pi\)
0.000723006 1.00000i \(0.499770\pi\)
\(350\) 0 0
\(351\) 248.435i 0.707791i
\(352\) 637.414 1.81084
\(353\) 335.994i 0.951824i −0.879493 0.475912i \(-0.842118\pi\)
0.879493 0.475912i \(-0.157882\pi\)
\(354\) −25.3375 77.9807i −0.0715748 0.220285i
\(355\) 0 0
\(356\) 360.636 262.018i 1.01302 0.736004i
\(357\) 146.950i 0.411626i
\(358\) −138.648 426.715i −0.387285 1.19194i
\(359\) 98.4859i 0.274334i −0.990548 0.137167i \(-0.956200\pi\)
0.990548 0.137167i \(-0.0437997\pi\)
\(360\) 0 0
\(361\) 129.446 0.358576
\(362\) 164.006 53.2887i 0.453054 0.147206i
\(363\) −648.384 −1.78618
\(364\) 104.721 + 144.137i 0.287696 + 0.395980i
\(365\) 0 0
\(366\) 403.108 130.978i 1.10139 0.357863i
\(367\) 498.473 1.35824 0.679118 0.734029i \(-0.262362\pi\)
0.679118 + 0.734029i \(0.262362\pi\)
\(368\) 2.74421 8.44582i 0.00745711 0.0229506i
\(369\) 50.6362 0.137226
\(370\) 0 0
\(371\) 348.879i 0.940374i
\(372\) −45.8509 63.1084i −0.123255 0.169646i
\(373\) 600.354i 1.60953i 0.593594 + 0.804765i \(0.297709\pi\)
−0.593594 + 0.804765i \(0.702291\pi\)
\(374\) 450.440 146.357i 1.20438 0.391328i
\(375\) 0 0
\(376\) 251.056 345.549i 0.667701 0.919012i
\(377\) 92.7214i 0.245945i
\(378\) 293.238 95.2786i 0.775761 0.252060i
\(379\) 303.490i 0.800765i −0.916348 0.400383i \(-0.868877\pi\)
0.916348 0.400383i \(-0.131123\pi\)
\(380\) 0 0
\(381\) −467.023 −1.22578
\(382\) −19.1713 59.0031i −0.0501866 0.154458i
\(383\) 332.583 0.868362 0.434181 0.900826i \(-0.357038\pi\)
0.434181 + 0.900826i \(0.357038\pi\)
\(384\) −176.892 243.470i −0.460655 0.634038i
\(385\) 0 0
\(386\) 68.1215 + 209.656i 0.176481 + 0.543151i
\(387\) 77.3256 0.199808
\(388\) 218.263 + 300.413i 0.562534 + 0.774261i
\(389\) −392.354 −1.00862 −0.504312 0.863522i \(-0.668254\pi\)
−0.504312 + 0.863522i \(0.668254\pi\)
\(390\) 0 0
\(391\) 6.59849i 0.0168759i
\(392\) −100.444 + 138.249i −0.256235 + 0.352677i
\(393\) 18.2693i 0.0464868i
\(394\) 106.626 + 328.162i 0.270625 + 0.832897i
\(395\) 0 0
\(396\) −162.610 223.813i −0.410631 0.565185i
\(397\) 334.190i 0.841789i −0.907110 0.420895i \(-0.861716\pi\)
0.907110 0.420895i \(-0.138284\pi\)
\(398\) 168.234 + 517.771i 0.422698 + 1.30093i
\(399\) 188.091i 0.471407i
\(400\) 0 0
\(401\) 121.003 0.301753 0.150877 0.988553i \(-0.451790\pi\)
0.150877 + 0.988553i \(0.451790\pi\)
\(402\) 224.599 72.9768i 0.558705 0.181534i
\(403\) −70.2722 −0.174373
\(404\) 207.469 150.735i 0.513537 0.373107i
\(405\) 0 0
\(406\) −109.443 + 35.5601i −0.269563 + 0.0875864i
\(407\) −365.730 −0.898599
\(408\) −180.907 131.437i −0.443399 0.322148i
\(409\) 607.410 1.48511 0.742555 0.669785i \(-0.233614\pi\)
0.742555 + 0.669785i \(0.233614\pi\)
\(410\) 0 0
\(411\) 1.95807i 0.00476415i
\(412\) −445.831 + 323.915i −1.08211 + 0.786201i
\(413\) 91.6718i 0.221966i
\(414\) −3.66563 + 1.19104i −0.00885418 + 0.00287690i
\(415\) 0 0
\(416\) −271.108 −0.651703
\(417\) 558.768i 1.33997i
\(418\) −576.546 + 187.331i −1.37930 + 0.448161i
\(419\) 466.760i 1.11398i 0.830518 + 0.556992i \(0.188045\pi\)
−0.830518 + 0.556992i \(0.811955\pi\)
\(420\) 0 0
\(421\) −73.0883 −0.173606 −0.0868031 0.996225i \(-0.527665\pi\)
−0.0868031 + 0.996225i \(0.527665\pi\)
\(422\) −126.862 390.440i −0.300620 0.925212i
\(423\) −185.378 −0.438246
\(424\) −429.495 312.047i −1.01296 0.735959i
\(425\) 0 0
\(426\) −117.390 361.290i −0.275564 0.848098i
\(427\) −473.882 −1.10979
\(428\) −166.114 + 120.689i −0.388117 + 0.281983i
\(429\) 396.774 0.924881
\(430\) 0 0
\(431\) 463.630i 1.07571i −0.843038 0.537853i \(-0.819235\pi\)
0.843038 0.537853i \(-0.180765\pi\)
\(432\) −144.985 + 446.217i −0.335612 + 1.03291i
\(433\) 99.8359i 0.230568i −0.993333 0.115284i \(-0.963222\pi\)
0.993333 0.115284i \(-0.0367778\pi\)
\(434\) 26.9505 + 82.9451i 0.0620979 + 0.191118i
\(435\) 0 0
\(436\) −431.915 + 313.805i −0.990630 + 0.719735i
\(437\) 8.44582i 0.0193268i
\(438\) −8.07069 24.8390i −0.0184262 0.0567101i
\(439\) 374.086i 0.852133i −0.904692 0.426066i \(-0.859899\pi\)
0.904692 0.426066i \(-0.140101\pi\)
\(440\) 0 0
\(441\) 74.1672 0.168180
\(442\) −191.583 + 62.2492i −0.433447 + 0.140835i
\(443\) 290.100 0.654854 0.327427 0.944877i \(-0.393818\pi\)
0.327427 + 0.944877i \(0.393818\pi\)
\(444\) 101.495 + 139.696i 0.228593 + 0.314631i
\(445\) 0 0
\(446\) −448.387 + 145.690i −1.00535 + 0.326659i
\(447\) 86.9231 0.194459
\(448\) 103.974 + 320.000i 0.232085 + 0.714286i
\(449\) −299.921 −0.667976 −0.333988 0.942577i \(-0.608394\pi\)
−0.333988 + 0.942577i \(0.608394\pi\)
\(450\) 0 0
\(451\) 290.493i 0.644109i
\(452\) 401.390 + 552.466i 0.888031 + 1.22227i
\(453\) 664.721i 1.46738i
\(454\) −111.305 + 36.1652i −0.245165 + 0.0796590i
\(455\) 0 0
\(456\) 231.554 + 168.234i 0.507794 + 0.368934i
\(457\) 822.328i 1.79941i −0.436503 0.899703i \(-0.643783\pi\)
0.436503 0.899703i \(-0.356217\pi\)
\(458\) −309.514 + 100.567i −0.675796 + 0.219579i
\(459\) 348.617i 0.759513i
\(460\) 0 0
\(461\) −456.885 −0.991075 −0.495537 0.868587i \(-0.665029\pi\)
−0.495537 + 0.868587i \(0.665029\pi\)
\(462\) −152.169 468.328i −0.329370 1.01370i
\(463\) −400.249 −0.864469 −0.432234 0.901761i \(-0.642275\pi\)
−0.432234 + 0.901761i \(0.642275\pi\)
\(464\) 54.1115 166.538i 0.116620 0.358918i
\(465\) 0 0
\(466\) 197.183 + 606.868i 0.423140 + 1.30229i
\(467\) 913.145 1.95534 0.977672 0.210139i \(-0.0673915\pi\)
0.977672 + 0.210139i \(0.0673915\pi\)
\(468\) 69.1621 + 95.1935i 0.147782 + 0.203405i
\(469\) −264.033 −0.562969
\(470\) 0 0
\(471\) 481.391i 1.02206i
\(472\) −112.855 81.9938i −0.239099 0.173716i
\(473\) 443.607i 0.937858i
\(474\) 20.1177 + 61.9158i 0.0424423 + 0.130624i
\(475\) 0 0
\(476\) 146.950 + 202.260i 0.308720 + 0.424916i
\(477\) 230.413i 0.483047i
\(478\) −146.357 450.440i −0.306186 0.942342i
\(479\) 526.131i 1.09840i 0.835692 + 0.549198i \(0.185067\pi\)
−0.835692 + 0.549198i \(0.814933\pi\)
\(480\) 0 0
\(481\) 155.554 0.323397
\(482\) −1.74606 + 0.567331i −0.00362254 + 0.00117704i
\(483\) −6.86054 −0.0142040
\(484\) −892.423 + 648.384i −1.84385 + 1.33964i
\(485\) 0 0
\(486\) 333.416 108.334i 0.686042 0.222909i
\(487\) 443.541 0.910762 0.455381 0.890297i \(-0.349503\pi\)
0.455381 + 0.890297i \(0.349503\pi\)
\(488\) 423.853 583.384i 0.868552 1.19546i
\(489\) −252.125 −0.515594
\(490\) 0 0
\(491\) 287.163i 0.584854i −0.956288 0.292427i \(-0.905537\pi\)
0.956288 0.292427i \(-0.0944628\pi\)
\(492\) −110.959 + 80.6161i −0.225526 + 0.163854i
\(493\) 130.111i 0.263918i
\(494\) 245.220 79.6767i 0.496396 0.161289i
\(495\) 0 0
\(496\) −126.217 41.0103i −0.254469 0.0826820i
\(497\) 424.721i 0.854570i
\(498\) 340.846 110.748i 0.684430 0.222385i
\(499\) 810.936i 1.62512i −0.582876 0.812561i \(-0.698073\pi\)
0.582876 0.812561i \(-0.301927\pi\)
\(500\) 0 0
\(501\) 78.0789 0.155846
\(502\) −84.4791 260.000i −0.168285 0.517928i
\(503\) −642.471 −1.27728 −0.638639 0.769506i \(-0.720502\pi\)
−0.638639 + 0.769506i \(0.720502\pi\)
\(504\) 85.8359 118.143i 0.170309 0.234411i
\(505\) 0 0
\(506\) 6.83282 + 21.0292i 0.0135036 + 0.0415598i
\(507\) 228.585 0.450858
\(508\) −642.802 + 467.023i −1.26536 + 0.919337i
\(509\) 915.050 1.79774 0.898870 0.438216i \(-0.144389\pi\)
0.898870 + 0.438216i \(0.144389\pi\)
\(510\) 0 0
\(511\) 29.2000i 0.0571429i
\(512\) −486.941 158.217i −0.951057 0.309017i
\(513\) 446.217i 0.869818i
\(514\) 169.925 + 522.975i 0.330593 + 1.01746i
\(515\) 0 0
\(516\) −169.443 + 123.107i −0.328377 + 0.238580i
\(517\) 1063.49i 2.05704i
\(518\) −59.6575 183.607i −0.115169 0.354453i
\(519\) 532.206i 1.02544i
\(520\) 0 0
\(521\) 1006.98 1.93279 0.966396 0.257058i \(-0.0827533\pi\)
0.966396 + 0.257058i \(0.0827533\pi\)
\(522\) −72.2803 + 23.4853i −0.138468 + 0.0449910i
\(523\) 774.173 1.48025 0.740127 0.672467i \(-0.234765\pi\)
0.740127 + 0.672467i \(0.234765\pi\)
\(524\) 18.2693 + 25.1456i 0.0348651 + 0.0479877i
\(525\) 0 0
\(526\) −772.991 + 251.160i −1.46956 + 0.477490i
\(527\) −98.6096 −0.187115
\(528\) 712.650 + 231.554i 1.34972 + 0.438550i
\(529\) −528.692 −0.999418
\(530\) 0 0
\(531\) 60.5437i 0.114018i
\(532\) −188.091 258.885i −0.353555 0.486627i
\(533\) 123.554i 0.231809i
\(534\) 498.387 161.936i 0.933309 0.303250i
\(535\) 0 0
\(536\) 236.158 325.043i 0.440593 0.606424i
\(537\) 527.449i 0.982214i
\(538\) 662.933 215.400i 1.23222 0.400372i
\(539\) 425.487i 0.789401i
\(540\) 0 0
\(541\) −259.115 −0.478955 −0.239477 0.970902i \(-0.576976\pi\)
−0.239477 + 0.970902i \(0.576976\pi\)
\(542\) −153.179 471.437i −0.282618 0.869809i
\(543\) 202.722 0.373337
\(544\) −380.433 −0.699326
\(545\) 0 0
\(546\) 64.7214 + 199.192i 0.118537 + 0.364820i
\(547\) −149.818 −0.273890 −0.136945 0.990579i \(-0.543728\pi\)
−0.136945 + 0.990579i \(0.543728\pi\)
\(548\) −1.95807 2.69505i −0.00357312 0.00491797i
\(549\) −312.971 −0.570074
\(550\) 0 0
\(551\) 166.538i 0.302247i
\(552\) 6.13625 8.44582i 0.0111164 0.0153004i
\(553\) 72.7864i 0.131621i
\(554\) 33.8398 + 104.148i 0.0610826 + 0.187993i
\(555\) 0 0
\(556\) 558.768 + 769.078i 1.00498 + 1.38323i
\(557\) 511.698i 0.918668i −0.888264 0.459334i \(-0.848088\pi\)
0.888264 0.459334i \(-0.151912\pi\)
\(558\) 17.7992 + 54.7802i 0.0318981 + 0.0981724i
\(559\) 188.677i 0.337526i
\(560\) 0 0
\(561\) 556.774 0.992467
\(562\) −95.7917 + 31.1246i −0.170448 + 0.0553819i
\(563\) −490.726 −0.871627 −0.435814 0.900037i \(-0.643539\pi\)
−0.435814 + 0.900037i \(0.643539\pi\)
\(564\) 406.217 295.134i 0.720242 0.523287i
\(565\) 0 0
\(566\) 280.249 91.0585i 0.495140 0.160881i
\(567\) 198.175 0.349514
\(568\) −522.863 379.882i −0.920534 0.668807i
\(569\) 232.748 0.409047 0.204523 0.978862i \(-0.434436\pi\)
0.204523 + 0.978862i \(0.434436\pi\)
\(570\) 0 0
\(571\) 210.755i 0.369098i −0.982823 0.184549i \(-0.940918\pi\)
0.982823 0.184549i \(-0.0590824\pi\)
\(572\) 546.113 396.774i 0.954742 0.693661i
\(573\) 72.9318i 0.127281i
\(574\) 145.836 47.3850i 0.254070 0.0825522i
\(575\) 0 0
\(576\) 68.6687 + 211.341i 0.119217 + 0.366911i
\(577\) 341.712i 0.592222i −0.955154 0.296111i \(-0.904310\pi\)
0.955154 0.296111i \(-0.0956898\pi\)
\(578\) 280.871 91.2605i 0.485936 0.157890i
\(579\) 259.150i 0.447581i
\(580\) 0 0
\(581\) −400.689 −0.689654
\(582\) 134.894 + 415.161i 0.231777 + 0.713335i
\(583\) 1321.85 2.26733
\(584\) −35.9474 26.1173i −0.0615537 0.0447214i
\(585\) 0 0
\(586\) 110.541 + 340.210i 0.188637 + 0.580564i
\(587\) 618.412 1.05351 0.526756 0.850016i \(-0.323408\pi\)
0.526756 + 0.850016i \(0.323408\pi\)
\(588\) −162.522 + 118.079i −0.276397 + 0.200815i
\(589\) 126.217 0.214290
\(590\) 0 0
\(591\) 405.630i 0.686345i
\(592\) 279.393 + 90.7802i 0.471947 + 0.153345i
\(593\) 120.663i 0.203478i 0.994811 + 0.101739i \(0.0324407\pi\)
−0.994811 + 0.101739i \(0.967559\pi\)
\(594\) −360.997 1111.03i −0.607739 1.87043i
\(595\) 0 0
\(596\) 119.639 86.9231i 0.200737 0.145844i
\(597\) 640.000i 1.07203i
\(598\) −2.90617 8.94427i −0.00485982 0.0149570i
\(599\) 849.927i 1.41891i 0.704751 + 0.709455i \(0.251059\pi\)
−0.704751 + 0.709455i \(0.748941\pi\)
\(600\) 0 0
\(601\) −11.3576 −0.0188978 −0.00944890 0.999955i \(-0.503008\pi\)
−0.00944890 + 0.999955i \(0.503008\pi\)
\(602\) 222.703 72.3607i 0.369939 0.120200i
\(603\) −174.378 −0.289183
\(604\) 664.721 + 914.910i 1.10053 + 1.51475i
\(605\) 0 0
\(606\) 286.715 93.1594i 0.473127 0.153728i
\(607\) −1115.12 −1.83710 −0.918550 0.395305i \(-0.870639\pi\)
−0.918550 + 0.395305i \(0.870639\pi\)
\(608\) 486.941 0.800890
\(609\) −135.279 −0.222132
\(610\) 0 0
\(611\) 452.329i 0.740309i
\(612\) 97.0519 + 133.580i 0.158582 + 0.218269i
\(613\) 499.475i 0.814805i 0.913249 + 0.407402i \(0.133565\pi\)
−0.913249 + 0.407402i \(0.866435\pi\)
\(614\) −541.246 + 175.862i −0.881508 + 0.286419i
\(615\) 0 0
\(616\) −677.771 492.429i −1.10028 0.799398i
\(617\) 545.935i 0.884822i −0.896813 0.442411i \(-0.854123\pi\)
0.896813 0.442411i \(-0.145877\pi\)
\(618\) −616.123 + 200.190i −0.996962 + 0.323933i
\(619\) 455.011i 0.735075i −0.930009 0.367537i \(-0.880201\pi\)
0.930009 0.367537i \(-0.119799\pi\)
\(620\) 0 0
\(621\) −16.2755 −0.0262086
\(622\) 174.408 + 536.774i 0.280399 + 0.862981i
\(623\) −585.889 −0.940432
\(624\) −303.108 98.4859i −0.485751 0.157830i
\(625\) 0 0
\(626\) −350.764 1079.54i −0.560326 1.72451i
\(627\) −712.650 −1.13660
\(628\) −481.391 662.577i −0.766546 1.05506i
\(629\) 218.282 0.347030
\(630\) 0 0
\(631\) 267.706i 0.424257i 0.977242 + 0.212128i \(0.0680395\pi\)
−0.977242 + 0.212128i \(0.931960\pi\)
\(632\) 89.6054 + 65.1021i 0.141781 + 0.103010i
\(633\) 482.610i 0.762417i
\(634\) −99.5905 306.508i −0.157083 0.483451i
\(635\) 0 0
\(636\) −366.833 504.902i −0.576781 0.793871i
\(637\) 180.971i 0.284098i
\(638\) 134.732 + 414.663i 0.211179 + 0.649941i
\(639\) 280.503i 0.438971i
\(640\) 0 0
\(641\) −418.571 −0.652997 −0.326499 0.945198i \(-0.605869\pi\)
−0.326499 + 0.945198i \(0.605869\pi\)
\(642\) −229.564 + 74.5898i −0.357576 + 0.116183i
\(643\) −439.339 −0.683265 −0.341633 0.939834i \(-0.610980\pi\)
−0.341633 + 0.939834i \(0.610980\pi\)
\(644\) −9.44272 + 6.86054i −0.0146626 + 0.0106530i
\(645\) 0 0
\(646\) 344.105 111.807i 0.532671 0.173075i
\(647\) 419.644 0.648600 0.324300 0.945954i \(-0.394871\pi\)
0.324300 + 0.945954i \(0.394871\pi\)
\(648\) −177.253 + 243.967i −0.273538 + 0.376493i
\(649\) 347.331 0.535179
\(650\) 0 0
\(651\) 102.526i 0.157490i
\(652\) −347.021 + 252.125i −0.532240 + 0.386695i
\(653\) 370.085i 0.566746i −0.959010 0.283373i \(-0.908547\pi\)
0.959010 0.283373i \(-0.0914534\pi\)
\(654\) −596.892 + 193.942i −0.912678 + 0.296547i
\(655\) 0 0
\(656\) −72.1052 + 221.917i −0.109917 + 0.338288i
\(657\) 19.2849i 0.0293529i
\(658\) −533.902 + 173.475i −0.811401 + 0.263640i
\(659\) 322.823i 0.489868i 0.969540 + 0.244934i \(0.0787664\pi\)
−0.969540 + 0.244934i \(0.921234\pi\)
\(660\) 0 0
\(661\) −812.735 −1.22955 −0.614777 0.788701i \(-0.710754\pi\)
−0.614777 + 0.788701i \(0.710754\pi\)
\(662\) 205.166 + 631.437i 0.309919 + 0.953832i
\(663\) −236.810 −0.357180
\(664\) 358.387 493.277i 0.539739 0.742888i
\(665\) 0 0
\(666\) −39.4001 121.261i −0.0591594 0.182074i
\(667\) 6.07439 0.00910703
\(668\) 107.466 78.0789i 0.160878 0.116885i
\(669\) −554.237 −0.828456
\(670\) 0 0
\(671\) 1795.47i 2.67581i
\(672\) 395.542i 0.588604i
\(673\) 467.378i 0.694469i 0.937778 + 0.347235i \(0.112879\pi\)
−0.937778 + 0.347235i \(0.887121\pi\)
\(674\) 166.318 + 511.875i 0.246763 + 0.759458i
\(675\) 0 0
\(676\) 314.620 228.585i 0.465414 0.338143i
\(677\) 548.237i 0.809803i −0.914360 0.404902i \(-0.867306\pi\)
0.914360 0.404902i \(-0.132694\pi\)
\(678\) 248.073 + 763.489i 0.365889 + 1.12609i
\(679\) 488.051i 0.718779i
\(680\) 0 0
\(681\) −137.580 −0.202027
\(682\) 314.267 102.111i 0.460802 0.149724i
\(683\) −23.9663 −0.0350898 −0.0175449 0.999846i \(-0.505585\pi\)
−0.0175449 + 0.999846i \(0.505585\pi\)
\(684\) −124.223 170.978i −0.181612 0.249968i
\(685\) 0 0
\(686\) 703.607 228.616i 1.02567 0.333259i
\(687\) −382.581 −0.556886
\(688\) −110.111 + 338.885i −0.160044 + 0.492566i
\(689\) −562.217 −0.815989
\(690\) 0 0
\(691\) 186.981i 0.270595i −0.990805 0.135298i \(-0.956801\pi\)
0.990805 0.135298i \(-0.0431990\pi\)
\(692\) −532.206 732.519i −0.769084 1.05855i
\(693\) 363.607i 0.524685i
\(694\) −956.906 + 310.917i −1.37883 + 0.448008i
\(695\) 0 0
\(696\) 120.997 166.538i 0.173846 0.239279i
\(697\) 173.378i 0.248748i
\(698\) 0.959917 0.311896i 0.00137524 0.000446842i
\(699\) 750.130i 1.07315i
\(700\) 0 0
\(701\) −706.636 −1.00804 −0.504020 0.863692i \(-0.668146\pi\)
−0.504020 + 0.863692i \(0.668146\pi\)
\(702\) 153.541 + 472.551i 0.218720 + 0.673150i
\(703\) −279.393 −0.397429
\(704\) 1212.43 393.943i 1.72221 0.559579i
\(705\) 0 0
\(706\) −207.656 639.098i −0.294130 0.905238i
\(707\) −337.054 −0.476738
\(708\) −96.3895 132.669i −0.136143 0.187385i
\(709\) 188.597 0.266005 0.133002 0.991116i \(-0.457538\pi\)
0.133002 + 0.991116i \(0.457538\pi\)
\(710\) 0 0
\(711\) 48.0710i 0.0676104i
\(712\) 524.035 721.272i 0.736004 1.01302i
\(713\) 4.60369i 0.00645679i
\(714\) 90.8204 + 279.516i 0.127199 + 0.391480i
\(715\) 0 0
\(716\) −527.449 725.971i −0.736661 1.01393i
\(717\) 556.774i 0.776533i
\(718\) −60.8676 187.331i −0.0847738 0.260907i
\(719\) 156.085i 0.217086i −0.994092 0.108543i \(-0.965381\pi\)
0.994092 0.108543i \(-0.0346186\pi\)
\(720\) 0 0
\(721\) 724.296 1.00457
\(722\) 246.221 80.0019i 0.341026 0.110806i
\(723\) −2.15825 −0.00298514
\(724\) 279.023 202.722i 0.385391 0.280003i
\(725\) 0 0
\(726\) −1233.30 + 400.723i −1.69876 + 0.551960i
\(727\) −715.164 −0.983719 −0.491859 0.870675i \(-0.663683\pi\)
−0.491859 + 0.870675i \(0.663683\pi\)
\(728\) 288.273 + 209.443i 0.395980 + 0.287696i
\(729\) 751.381 1.03070
\(730\) 0 0
\(731\) 264.762i 0.362191i
\(732\) 685.809 498.269i 0.936897 0.680696i
\(733\) 1233.29i 1.68252i 0.540632 + 0.841259i \(0.318185\pi\)
−0.540632 + 0.841259i \(0.681815\pi\)
\(734\) 948.152 308.073i 1.29176 0.419718i
\(735\) 0 0
\(736\) 17.7609i 0.0241317i
\(737\) 1000.38i 1.35737i
\(738\) 96.3158 31.2949i 0.130509 0.0424050i
\(739\) 8.55656i 0.0115786i −0.999983 0.00578928i \(-0.998157\pi\)
0.999983 0.00578928i \(-0.00184280\pi\)
\(740\) 0 0
\(741\) 303.108 0.409053
\(742\) 215.619 + 663.607i 0.290592 + 0.894349i
\(743\) 1010.56 1.36011 0.680053 0.733163i \(-0.261957\pi\)
0.680053 + 0.733163i \(0.261957\pi\)
\(744\) −126.217 91.7018i −0.169646 0.123255i
\(745\) 0 0
\(746\) 371.039 + 1141.94i 0.497372 + 1.53075i
\(747\) −264.631 −0.354258
\(748\) 766.334 556.774i 1.02451 0.744350i
\(749\) 269.868 0.360305
\(750\) 0 0
\(751\) 1104.31i 1.47046i −0.677820 0.735228i \(-0.737075\pi\)
0.677820 0.735228i \(-0.262925\pi\)
\(752\) 263.976 812.433i 0.351031 1.08036i
\(753\) 321.378i 0.426796i
\(754\) −57.3050 176.367i −0.0760013 0.233908i
\(755\) 0 0
\(756\) 498.885 362.461i 0.659901 0.479446i
\(757\) 875.633i 1.15671i 0.815783 + 0.578357i \(0.196306\pi\)
−0.815783 + 0.578357i \(0.803694\pi\)
\(758\) −187.567 577.272i −0.247450 0.761573i
\(759\) 25.9936i 0.0342471i
\(760\) 0 0
\(761\) −647.207 −0.850470 −0.425235 0.905083i \(-0.639808\pi\)
−0.425235 + 0.905083i \(0.639808\pi\)
\(762\) −888.331 + 288.636i −1.16579 + 0.378788i
\(763\) 701.688 0.919644
\(764\) −72.9318 100.382i −0.0954605 0.131390i
\(765\) 0 0
\(766\) 632.610 205.547i 0.825861 0.268339i
\(767\) −147.729 −0.192606
\(768\) −486.941 353.783i −0.634038 0.460655i
\(769\) −631.430 −0.821106 −0.410553 0.911837i \(-0.634664\pi\)
−0.410553 + 0.911837i \(0.634664\pi\)
\(770\) 0 0
\(771\) 646.433i 0.838434i
\(772\) 259.150 + 356.689i 0.335686 + 0.462032i
\(773\) 421.522i 0.545306i −0.962112 0.272653i \(-0.912099\pi\)
0.962112 0.272653i \(-0.0879011\pi\)
\(774\) 147.082 47.7899i 0.190028 0.0617440i
\(775\) 0 0
\(776\) 600.827 + 436.526i 0.774261 + 0.562534i
\(777\) 226.950i 0.292086i
\(778\) −746.303 + 242.488i −0.959258 + 0.311682i
\(779\) 221.917i 0.284874i
\(780\) 0 0
\(781\) 1609.21 2.06044
\(782\) −4.07809 12.5511i −0.00521495 0.0160500i
\(783\) −320.927 −0.409869
\(784\) −105.613 + 325.043i −0.134710 + 0.414596i
\(785\) 0 0
\(786\) 11.2911 + 34.7503i 0.0143652 + 0.0442116i
\(787\) 838.633 1.06561 0.532804 0.846239i \(-0.321138\pi\)
0.532804 + 0.846239i \(0.321138\pi\)
\(788\) 405.630 + 558.302i 0.514759 + 0.708505i
\(789\) −955.469 −1.21099
\(790\) 0 0
\(791\) 897.535i 1.13468i
\(792\) −447.627 325.220i −0.565185 0.410631i
\(793\) 763.659i 0.963001i
\(794\) −206.541 635.668i −0.260127 0.800589i
\(795\) 0 0
\(796\) 640.000 + 880.884i 0.804020 + 1.10664i
\(797\) 1213.57i 1.52268i −0.648354 0.761339i \(-0.724542\pi\)
0.648354 0.761339i \(-0.275458\pi\)
\(798\) −116.247 357.771i −0.145673 0.448334i
\(799\) 634.732i 0.794408i
\(800\) 0 0
\(801\) −386.944 −0.483076
\(802\) 230.162 74.7840i 0.286985 0.0932469i
\(803\) 110.635 0.137777
\(804\) 382.111 277.620i 0.475263 0.345299i
\(805\) 0 0
\(806\) −133.666 + 43.4306i −0.165838 + 0.0538841i
\(807\) 819.431 1.01540
\(808\) 301.470 414.938i 0.373107 0.513537i
\(809\) 229.214 0.283330 0.141665 0.989915i \(-0.454754\pi\)
0.141665 + 0.989915i \(0.454754\pi\)
\(810\) 0 0
\(811\) 454.225i 0.560080i 0.959988 + 0.280040i \(0.0903478\pi\)
−0.959988 + 0.280040i \(0.909652\pi\)
\(812\) −186.195 + 135.279i −0.229304 + 0.166599i
\(813\) 582.728i 0.716762i
\(814\) −695.659 + 226.033i −0.854618 + 0.277682i
\(815\) 0 0
\(816\) −425.337 138.201i −0.521247 0.169363i
\(817\) 338.885i 0.414792i
\(818\) 1155.36 375.400i 1.41242 0.458924i
\(819\) 154.651i 0.188829i
\(820\) 0 0
\(821\) 1130.90 1.37747 0.688733 0.725015i \(-0.258167\pi\)
0.688733 + 0.725015i \(0.258167\pi\)
\(822\) −1.21015 3.72447i −0.00147220 0.00453098i
\(823\) −780.148 −0.947931 −0.473966 0.880543i \(-0.657178\pi\)
−0.473966 + 0.880543i \(0.657178\pi\)
\(824\) −647.830 + 891.661i −0.786201 + 1.08211i
\(825\) 0 0
\(826\) 56.6563 + 174.370i 0.0685912 + 0.211102i
\(827\) 209.175 0.252932 0.126466 0.991971i \(-0.459636\pi\)
0.126466 + 0.991971i \(0.459636\pi\)
\(828\) −6.23634 + 4.53097i −0.00753182 + 0.00547219i
\(829\) 508.525 0.613419 0.306710 0.951803i \(-0.400772\pi\)
0.306710 + 0.951803i \(0.400772\pi\)
\(830\) 0 0
\(831\) 128.734i 0.154915i
\(832\) −515.679 + 167.554i −0.619806 + 0.201387i
\(833\) 253.947i 0.304859i
\(834\) 345.337 + 1062.84i 0.414074 + 1.27439i
\(835\) 0 0
\(836\) −980.879 + 712.650i −1.17330 + 0.852453i
\(837\) 243.226i 0.290593i
\(838\) 288.473 + 887.830i 0.344240 + 1.05946i
\(839\) 274.028i 0.326613i 0.986575 + 0.163306i \(0.0522159\pi\)
−0.986575 + 0.163306i \(0.947784\pi\)
\(840\) 0 0
\(841\) −721.223 −0.857578
\(842\) −139.022 + 45.1710i −0.165109 + 0.0536473i
\(843\) −118.405 −0.140457
\(844\) −482.610 664.256i −0.571813 0.787033i
\(845\) 0 0
\(846\) −352.610 + 114.570i −0.416797 + 0.135425i
\(847\) 1449.83 1.71172
\(848\) −1009.80 328.105i −1.19081 0.386917i
\(849\) 346.407 0.408018
\(850\) 0 0
\(851\) 10.1907i 0.0119750i
\(852\) −446.578 614.663i −0.524153 0.721435i
\(853\) 1583.28i 1.85613i −0.372416 0.928066i \(-0.621471\pi\)
0.372416 0.928066i \(-0.378529\pi\)
\(854\) −901.378 + 292.875i −1.05548 + 0.342945i
\(855\) 0 0
\(856\) −241.378 + 332.228i −0.281983 + 0.388117i
\(857\) 1007.38i 1.17547i 0.809054 + 0.587735i \(0.199980\pi\)
−0.809054 + 0.587735i \(0.800020\pi\)
\(858\) 754.709 245.220i 0.879614 0.285804i
\(859\) 76.6086i 0.0891835i 0.999005 + 0.0445917i \(0.0141987\pi\)
−0.999005 + 0.0445917i \(0.985801\pi\)
\(860\) 0 0
\(861\) 180.263 0.209365
\(862\) −286.539 881.876i −0.332412 1.02306i
\(863\) 255.450 0.296002 0.148001 0.988987i \(-0.452716\pi\)
0.148001 + 0.988987i \(0.452716\pi\)
\(864\) 938.360i 1.08606i
\(865\) 0 0
\(866\) −61.7020 189.899i −0.0712494 0.219283i
\(867\) 347.175 0.400433
\(868\) 102.526 + 141.115i 0.118117 + 0.162574i
\(869\) −275.777 −0.317350
\(870\) 0 0
\(871\) 425.487i 0.488504i
\(872\) −627.609 + 863.830i −0.719735 + 0.990630i
\(873\) 322.328i 0.369219i
\(874\) 5.21981 + 16.0649i 0.00597232 + 0.0183809i
\(875\) 0 0
\(876\) −30.7027 42.2587i −0.0350488 0.0482405i
\(877\) 601.522i 0.685886i −0.939356 0.342943i \(-0.888576\pi\)
0.939356 0.342943i \(-0.111424\pi\)
\(878\) −231.198 711.554i −0.263323 0.810426i
\(879\) 420.523i 0.478411i
\(880\) 0 0
\(881\) 237.850 0.269977 0.134989 0.990847i \(-0.456900\pi\)
0.134989 + 0.990847i \(0.456900\pi\)
\(882\) 141.074 45.8378i 0.159948 0.0519703i
\(883\) 1.30294 0.00147559 0.000737794 1.00000i \(-0.499765\pi\)
0.000737794 1.00000i \(0.499765\pi\)
\(884\) −325.941 + 236.810i −0.368712 + 0.267885i
\(885\) 0 0
\(886\) 551.803 179.292i 0.622803 0.202361i
\(887\) −536.353 −0.604682 −0.302341 0.953200i \(-0.597768\pi\)
−0.302341 + 0.953200i \(0.597768\pi\)
\(888\) 279.393 + 202.991i 0.314631 + 0.228593i
\(889\) 1044.30 1.17469
\(890\) 0 0
\(891\) 750.855i 0.842710i
\(892\) −762.842 + 554.237i −0.855203 + 0.621342i
\(893\) 812.433i 0.909780i
\(894\) 165.337 53.7214i 0.184941 0.0600911i
\(895\) 0 0
\(896\) 395.542 + 544.417i 0.441453 + 0.607608i
\(897\) 11.0557i 0.0123252i
\(898\) −570.484 + 185.361i −0.635283 + 0.206416i
\(899\) 90.7773i 0.100976i
\(900\) 0 0
\(901\) −788.932 −0.875618
\(902\) −179.535 552.551i −0.199041 0.612584i
\(903\) 275.276 0.304846
\(904\) 1104.93 + 802.780i 1.22227 + 0.888031i
\(905\) 0 0
\(906\) 410.820 + 1264.38i 0.453444 + 1.39556i
\(907\) 332.159 0.366217 0.183108 0.983093i \(-0.441384\pi\)
0.183108 + 0.983093i \(0.441384\pi\)
\(908\) −189.363 + 137.580i −0.208550 + 0.151520i
\(909\) −222.604 −0.244889
\(910\) 0 0
\(911\) 1450.06i 1.59172i −0.605478 0.795862i \(-0.707018\pi\)
0.605478 0.795862i \(-0.292982\pi\)
\(912\) 544.417 + 176.892i 0.596948 + 0.193960i
\(913\) 1518.15i 1.66282i
\(914\) −508.227 1564.16i −0.556047 1.71134i
\(915\) 0 0
\(916\) −526.577 + 382.581i −0.574866 + 0.417665i
\(917\) 40.8514i 0.0445490i
\(918\) 215.457 + 663.108i 0.234703 + 0.722340i
\(919\) 814.405i 0.886186i −0.896476 0.443093i \(-0.853881\pi\)
0.896476 0.443093i \(-0.146119\pi\)
\(920\) 0 0
\(921\) −669.017 −0.726403
\(922\) −869.048 + 282.371i −0.942568 + 0.306259i
\(923\) −684.437 −0.741535
\(924\) −578.885 796.767i −0.626499 0.862302i
\(925\) 0 0
\(926\) −761.319 + 247.367i −0.822159 + 0.267136i
\(927\) 478.353 0.516023
\(928\) 350.217i 0.377389i
\(929\) −400.039 −0.430612 −0.215306 0.976547i \(-0.569075\pi\)
−0.215306 + 0.976547i \(0.569075\pi\)
\(930\) 0 0
\(931\) 325.043i 0.349134i
\(932\) 750.130 + 1032.47i 0.804861 + 1.10780i
\(933\) 663.489i 0.711135i
\(934\) 1736.91 564.355i 1.85964 0.604234i
\(935\) 0 0
\(936\) 190.387 + 138.324i 0.203405 + 0.147782i
\(937\) 249.279i 0.266039i −0.991113 0.133020i \(-0.957533\pi\)
0.991113 0.133020i \(-0.0424673\pi\)
\(938\) −502.220 + 163.181i −0.535415 + 0.173967i
\(939\) 1334.39i 1.42107i
\(940\) 0 0
\(941\) 724.229 0.769638 0.384819 0.922992i \(-0.374264\pi\)
0.384819 + 0.922992i \(0.374264\pi\)
\(942\) −297.516 915.659i −0.315834 0.972038i
\(943\) −8.09432 −0.00858358
\(944\) −265.337 86.2134i −0.281078 0.0913277i
\(945\) 0 0
\(946\) −274.164 843.790i −0.289814 0.891956i
\(947\) −1141.54 −1.20542 −0.602712 0.797959i \(-0.705913\pi\)
−0.602712 + 0.797959i \(0.705913\pi\)
\(948\) 76.5322 + 105.337i 0.0807301 + 0.111115i
\(949\) −47.0557 −0.0495845
\(950\) 0 0
\(951\) 378.865i 0.398386i
\(952\) 404.520 + 293.901i 0.424916 + 0.308720i
\(953\) 1295.33i 1.35921i 0.733579 + 0.679604i \(0.237848\pi\)
−0.733579 + 0.679604i \(0.762152\pi\)
\(954\) 142.403 + 438.272i 0.149270 + 0.459405i
\(955\) 0 0
\(956\) −556.774 766.334i −0.582400 0.801604i
\(957\) 512.551i 0.535581i
\(958\) 325.167 + 1000.76i 0.339423 + 1.04464i
\(959\) 4.37837i 0.00456556i
\(960\) 0 0
\(961\) 892.201 0.928409
\(962\) 295.882 96.1378i 0.307569 0.0999353i
\(963\) 178.232 0.185080
\(964\) −2.97058 + 2.15825i −0.00308152 + 0.00223885i
\(965\) 0 0
\(966\) −13.0495 + 4.24005i −0.0135088 + 0.00438928i
\(967\) −398.477 −0.412075 −0.206037 0.978544i \(-0.566057\pi\)
−0.206037 + 0.978544i \(0.566057\pi\)
\(968\) −1296.77 + 1784.85i −1.33964 + 1.84385i
\(969\) 425.337 0.438945
\(970\) 0 0
\(971\) 928.093i 0.955811i −0.878411 0.477906i \(-0.841396\pi\)
0.878411 0.477906i \(-0.158604\pi\)
\(972\) 567.242 412.125i 0.583582 0.423997i
\(973\) 1249.44i 1.28411i
\(974\) 843.666 274.124i 0.866186 0.281441i
\(975\) 0 0
\(976\) 445.666 1371.62i 0.456625 1.40535i
\(977\) 1378.05i 1.41049i 0.708962 + 0.705247i \(0.249164\pi\)
−0.708962 + 0.705247i \(0.750836\pi\)
\(978\) −479.571 + 155.822i −0.490359 + 0.159327i
\(979\) 2219.85i 2.26747i
\(980\) 0 0
\(981\) 463.423 0.472398
\(982\) −177.477 546.217i −0.180730 0.556229i
\(983\) −311.291 −0.316675 −0.158337 0.987385i \(-0.550613\pi\)
−0.158337 + 0.987385i \(0.550613\pi\)
\(984\) −161.232 + 221.917i −0.163854 + 0.225526i
\(985\) 0 0
\(986\) −80.4133 247.487i −0.0815551 0.251001i
\(987\) −659.939 −0.668631
\(988\) 417.193 303.108i 0.422260 0.306790i
\(989\) −12.3607 −0.0124982
\(990\) 0 0
\(991\) 961.147i 0.969876i 0.874549 + 0.484938i \(0.161158\pi\)
−0.874549 + 0.484938i \(0.838842\pi\)
\(992\) −265.424 −0.267565
\(993\) 780.498i 0.786000i
\(994\) 262.492 + 807.868i 0.264077 + 0.812745i
\(995\) 0 0
\(996\) 579.882 421.309i 0.582211 0.423001i
\(997\) 1089.68i 1.09296i 0.837473 + 0.546479i \(0.184032\pi\)
−0.837473 + 0.546479i \(0.815968\pi\)
\(998\) −501.186 1542.49i −0.502190 1.54558i
\(999\) 538.404i 0.538943i
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 100.3.d.b.99.7 8
3.2 odd 2 900.3.f.e.199.2 8
4.3 odd 2 inner 100.3.d.b.99.1 8
5.2 odd 4 20.3.b.a.11.4 yes 4
5.3 odd 4 100.3.b.f.51.1 4
5.4 even 2 inner 100.3.d.b.99.2 8
8.3 odd 2 1600.3.h.n.1599.6 8
8.5 even 2 1600.3.h.n.1599.3 8
12.11 even 2 900.3.f.e.199.8 8
15.2 even 4 180.3.c.a.91.1 4
15.8 even 4 900.3.c.k.451.4 4
15.14 odd 2 900.3.f.e.199.7 8
20.3 even 4 100.3.b.f.51.2 4
20.7 even 4 20.3.b.a.11.3 4
20.19 odd 2 inner 100.3.d.b.99.8 8
40.3 even 4 1600.3.b.s.1151.3 4
40.13 odd 4 1600.3.b.s.1151.2 4
40.19 odd 2 1600.3.h.n.1599.4 8
40.27 even 4 320.3.b.c.191.2 4
40.29 even 2 1600.3.h.n.1599.5 8
40.37 odd 4 320.3.b.c.191.3 4
60.23 odd 4 900.3.c.k.451.3 4
60.47 odd 4 180.3.c.a.91.2 4
60.59 even 2 900.3.f.e.199.1 8
80.27 even 4 1280.3.g.e.1151.5 8
80.37 odd 4 1280.3.g.e.1151.3 8
80.67 even 4 1280.3.g.e.1151.4 8
80.77 odd 4 1280.3.g.e.1151.6 8
120.77 even 4 2880.3.e.e.2431.1 4
120.107 odd 4 2880.3.e.e.2431.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.3.b.a.11.3 4 20.7 even 4
20.3.b.a.11.4 yes 4 5.2 odd 4
100.3.b.f.51.1 4 5.3 odd 4
100.3.b.f.51.2 4 20.3 even 4
100.3.d.b.99.1 8 4.3 odd 2 inner
100.3.d.b.99.2 8 5.4 even 2 inner
100.3.d.b.99.7 8 1.1 even 1 trivial
100.3.d.b.99.8 8 20.19 odd 2 inner
180.3.c.a.91.1 4 15.2 even 4
180.3.c.a.91.2 4 60.47 odd 4
320.3.b.c.191.2 4 40.27 even 4
320.3.b.c.191.3 4 40.37 odd 4
900.3.c.k.451.3 4 60.23 odd 4
900.3.c.k.451.4 4 15.8 even 4
900.3.f.e.199.1 8 60.59 even 2
900.3.f.e.199.2 8 3.2 odd 2
900.3.f.e.199.7 8 15.14 odd 2
900.3.f.e.199.8 8 12.11 even 2
1280.3.g.e.1151.3 8 80.37 odd 4
1280.3.g.e.1151.4 8 80.67 even 4
1280.3.g.e.1151.5 8 80.27 even 4
1280.3.g.e.1151.6 8 80.77 odd 4
1600.3.b.s.1151.2 4 40.13 odd 4
1600.3.b.s.1151.3 4 40.3 even 4
1600.3.h.n.1599.3 8 8.5 even 2
1600.3.h.n.1599.4 8 40.19 odd 2
1600.3.h.n.1599.5 8 40.29 even 2
1600.3.h.n.1599.6 8 8.3 odd 2
2880.3.e.e.2431.1 4 120.77 even 4
2880.3.e.e.2431.2 4 120.107 odd 4