Properties

Label 810.3.j.f.269.4
Level $810$
Weight $3$
Character 810.269
Analytic conductor $22.071$
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] = [810,3,Mod(269,810)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(810, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("810.269");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 810.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(22.0709014132\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.81622204416.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 14x^{6} + 165x^{4} - 434x^{2} + 961 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 270)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.4
Root \(1.43806 - 0.830265i\) of defining polynomial
Character \(\chi\) \(=\) 810.269
Dual form 810.3.j.f.539.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(4.24083 + 2.64865i) q^{5} +(-11.8534 - 6.84358i) q^{7} -2.82843 q^{8} +O(q^{10})\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(4.24083 + 2.64865i) q^{5} +(-11.8534 - 6.84358i) q^{7} -2.82843 q^{8} +(6.24264 - 3.32106i) q^{10} +(10.6621 + 6.15576i) q^{11} +(-14.7295 + 8.50411i) q^{13} +(-16.7633 + 9.67828i) q^{14} +(-2.00000 + 3.46410i) q^{16} -6.89949 q^{17} -7.24264 q^{19} +(0.346763 - 9.99399i) q^{20} +(15.0785 - 8.70556i) q^{22} +(17.3995 + 30.1368i) q^{23} +(10.9693 + 22.4650i) q^{25} +24.0532i q^{26} +27.3743i q^{28} +(-18.3035 - 10.5675i) q^{29} +(19.1066 + 33.0936i) q^{31} +(2.82843 + 4.89898i) q^{32} +(-4.87868 + 8.45012i) q^{34} +(-32.1421 - 60.4180i) q^{35} -21.5380i q^{37} +(-5.12132 + 8.87039i) q^{38} +(-11.9949 - 7.49151i) q^{40} +(-31.4928 + 18.1824i) q^{41} +(-5.40331 - 3.11960i) q^{43} -24.6230i q^{44} +49.2132 q^{46} +(-20.1005 + 34.8151i) q^{47} +(69.1690 + 119.804i) q^{49} +(35.2703 + 2.45051i) q^{50} +(29.4591 + 17.0082i) q^{52} -38.2721 q^{53} +(28.9117 + 54.3457i) q^{55} +(33.5265 + 19.3566i) q^{56} +(-25.8851 + 14.9448i) q^{58} +(36.0537 - 20.8156i) q^{59} +(7.52944 - 13.0414i) q^{61} +54.0416 q^{62} +8.00000 q^{64} +(-84.9899 - 2.94891i) q^{65} +(-111.386 + 64.3089i) q^{67} +(6.89949 + 11.9503i) q^{68} +(-96.7246 - 3.35607i) q^{70} +104.967i q^{71} +2.11232i q^{73} +(-26.3786 - 15.2297i) q^{74} +(7.24264 + 12.5446i) q^{76} +(-84.2548 - 145.934i) q^{77} +(22.0477 - 38.1878i) q^{79} +(-17.6569 + 9.39338i) q^{80} +51.4275i q^{82} +(-27.5122 + 47.6525i) q^{83} +(-29.2596 - 18.2743i) q^{85} +(-7.64144 + 4.41179i) q^{86} +(-30.1569 - 17.4111i) q^{88} -68.1020i q^{89} +232.794 q^{91} +(34.7990 - 60.2736i) q^{92} +(28.4264 + 49.2360i) q^{94} +(-30.7148 - 19.1832i) q^{95} +(-87.6794 - 50.6217i) q^{97} +195.640 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4} + 12 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{4} + 12 q^{5} + 16 q^{10} - 16 q^{16} + 24 q^{17} - 24 q^{19} + 24 q^{20} + 60 q^{23} + 12 q^{25} + 68 q^{31} - 56 q^{34} - 144 q^{35} - 24 q^{38} - 16 q^{40} + 224 q^{46} - 240 q^{47} + 180 q^{49} + 96 q^{50} - 408 q^{53} - 176 q^{55} + 196 q^{61} + 240 q^{62} + 64 q^{64} - 24 q^{65} - 24 q^{68} - 80 q^{70} + 24 q^{76} - 312 q^{77} - 180 q^{79} - 96 q^{80} + 108 q^{83} - 20 q^{85} + 912 q^{91} + 120 q^{92} - 112 q^{94} - 60 q^{95} + 1056 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 1.22474i 0.353553 0.612372i
\(3\) 0 0
\(4\) −1.00000 1.73205i −0.250000 0.433013i
\(5\) 4.24083 + 2.64865i 0.848166 + 0.529730i
\(6\) 0 0
\(7\) −11.8534 6.84358i −1.69335 0.977654i −0.951784 0.306769i \(-0.900752\pi\)
−0.741562 0.670885i \(-0.765915\pi\)
\(8\) −2.82843 −0.353553
\(9\) 0 0
\(10\) 6.24264 3.32106i 0.624264 0.332106i
\(11\) 10.6621 + 6.15576i 0.969281 + 0.559615i 0.899017 0.437914i \(-0.144282\pi\)
0.0702641 + 0.997528i \(0.477616\pi\)
\(12\) 0 0
\(13\) −14.7295 + 8.50411i −1.13304 + 0.654162i −0.944698 0.327941i \(-0.893645\pi\)
−0.188344 + 0.982103i \(0.560312\pi\)
\(14\) −16.7633 + 9.67828i −1.19738 + 0.691306i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −6.89949 −0.405853 −0.202926 0.979194i \(-0.565045\pi\)
−0.202926 + 0.979194i \(0.565045\pi\)
\(18\) 0 0
\(19\) −7.24264 −0.381192 −0.190596 0.981669i \(-0.561042\pi\)
−0.190596 + 0.981669i \(0.561042\pi\)
\(20\) 0.346763 9.99399i 0.0173381 0.499699i
\(21\) 0 0
\(22\) 15.0785 8.70556i 0.685385 0.395707i
\(23\) 17.3995 + 30.1368i 0.756500 + 1.31030i 0.944625 + 0.328151i \(0.106426\pi\)
−0.188125 + 0.982145i \(0.560241\pi\)
\(24\) 0 0
\(25\) 10.9693 + 22.4650i 0.438773 + 0.898598i
\(26\) 24.0532i 0.925125i
\(27\) 0 0
\(28\) 27.3743i 0.977654i
\(29\) −18.3035 10.5675i −0.631156 0.364398i 0.150044 0.988679i \(-0.452059\pi\)
−0.781200 + 0.624281i \(0.785392\pi\)
\(30\) 0 0
\(31\) 19.1066 + 33.0936i 0.616342 + 1.06754i 0.990147 + 0.140029i \(0.0447194\pi\)
−0.373805 + 0.927507i \(0.621947\pi\)
\(32\) 2.82843 + 4.89898i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −4.87868 + 8.45012i −0.143491 + 0.248533i
\(35\) −32.1421 60.4180i −0.918347 1.72623i
\(36\) 0 0
\(37\) 21.5380i 0.582108i −0.956707 0.291054i \(-0.905994\pi\)
0.956707 0.291054i \(-0.0940060\pi\)
\(38\) −5.12132 + 8.87039i −0.134772 + 0.233431i
\(39\) 0 0
\(40\) −11.9949 7.49151i −0.299872 0.187288i
\(41\) −31.4928 + 18.1824i −0.768117 + 0.443473i −0.832203 0.554472i \(-0.812920\pi\)
0.0640853 + 0.997944i \(0.479587\pi\)
\(42\) 0 0
\(43\) −5.40331 3.11960i −0.125658 0.0725489i 0.435853 0.900018i \(-0.356447\pi\)
−0.561512 + 0.827469i \(0.689780\pi\)
\(44\) 24.6230i 0.559615i
\(45\) 0 0
\(46\) 49.2132 1.06985
\(47\) −20.1005 + 34.8151i −0.427670 + 0.740747i −0.996666 0.0815940i \(-0.973999\pi\)
0.568995 + 0.822341i \(0.307332\pi\)
\(48\) 0 0
\(49\) 69.1690 + 119.804i 1.41161 + 2.44499i
\(50\) 35.2703 + 2.45051i 0.705406 + 0.0490102i
\(51\) 0 0
\(52\) 29.4591 + 17.0082i 0.566521 + 0.327081i
\(53\) −38.2721 −0.722115 −0.361057 0.932544i \(-0.617584\pi\)
−0.361057 + 0.932544i \(0.617584\pi\)
\(54\) 0 0
\(55\) 28.9117 + 54.3457i 0.525667 + 0.988103i
\(56\) 33.5265 + 19.3566i 0.598688 + 0.345653i
\(57\) 0 0
\(58\) −25.8851 + 14.9448i −0.446295 + 0.257668i
\(59\) 36.0537 20.8156i 0.611080 0.352807i −0.162308 0.986740i \(-0.551894\pi\)
0.773388 + 0.633933i \(0.218560\pi\)
\(60\) 0 0
\(61\) 7.52944 13.0414i 0.123433 0.213793i −0.797686 0.603073i \(-0.793943\pi\)
0.921119 + 0.389280i \(0.127276\pi\)
\(62\) 54.0416 0.871639
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) −84.9899 2.94891i −1.30754 0.0453678i
\(66\) 0 0
\(67\) −111.386 + 64.3089i −1.66248 + 0.959834i −0.690956 + 0.722897i \(0.742810\pi\)
−0.971525 + 0.236937i \(0.923856\pi\)
\(68\) 6.89949 + 11.9503i 0.101463 + 0.175739i
\(69\) 0 0
\(70\) −96.7246 3.35607i −1.38178 0.0479438i
\(71\) 104.967i 1.47841i 0.673478 + 0.739207i \(0.264800\pi\)
−0.673478 + 0.739207i \(0.735200\pi\)
\(72\) 0 0
\(73\) 2.11232i 0.0289359i 0.999895 + 0.0144680i \(0.00460546\pi\)
−0.999895 + 0.0144680i \(0.995395\pi\)
\(74\) −26.3786 15.2297i −0.356467 0.205806i
\(75\) 0 0
\(76\) 7.24264 + 12.5446i 0.0952979 + 0.165061i
\(77\) −84.2548 145.934i −1.09422 1.89524i
\(78\) 0 0
\(79\) 22.0477 38.1878i 0.279085 0.483390i −0.692072 0.721828i \(-0.743302\pi\)
0.971158 + 0.238438i \(0.0766355\pi\)
\(80\) −17.6569 + 9.39338i −0.220711 + 0.117417i
\(81\) 0 0
\(82\) 51.4275i 0.627165i
\(83\) −27.5122 + 47.6525i −0.331472 + 0.574127i −0.982801 0.184669i \(-0.940879\pi\)
0.651329 + 0.758796i \(0.274212\pi\)
\(84\) 0 0
\(85\) −29.2596 18.2743i −0.344231 0.214992i
\(86\) −7.64144 + 4.41179i −0.0888539 + 0.0512998i
\(87\) 0 0
\(88\) −30.1569 17.4111i −0.342693 0.197854i
\(89\) 68.1020i 0.765191i −0.923916 0.382595i \(-0.875030\pi\)
0.923916 0.382595i \(-0.124970\pi\)
\(90\) 0 0
\(91\) 232.794 2.55818
\(92\) 34.7990 60.2736i 0.378250 0.655148i
\(93\) 0 0
\(94\) 28.4264 + 49.2360i 0.302409 + 0.523787i
\(95\) −30.7148 19.1832i −0.323314 0.201929i
\(96\) 0 0
\(97\) −87.6794 50.6217i −0.903911 0.521873i −0.0254441 0.999676i \(-0.508100\pi\)
−0.878467 + 0.477803i \(0.841433\pi\)
\(98\) 195.640 1.99632
\(99\) 0 0
\(100\) 27.9411 41.4644i 0.279411 0.414644i
\(101\) −13.1893 7.61484i −0.130587 0.0753944i 0.433283 0.901258i \(-0.357355\pi\)
−0.563870 + 0.825863i \(0.690688\pi\)
\(102\) 0 0
\(103\) 66.7640 38.5462i 0.648194 0.374235i −0.139570 0.990212i \(-0.544572\pi\)
0.787764 + 0.615977i \(0.211239\pi\)
\(104\) 41.6614 24.0532i 0.400591 0.231281i
\(105\) 0 0
\(106\) −27.0624 + 46.8735i −0.255306 + 0.442203i
\(107\) 78.4264 0.732957 0.366479 0.930427i \(-0.380563\pi\)
0.366479 + 0.930427i \(0.380563\pi\)
\(108\) 0 0
\(109\) −146.279 −1.34201 −0.671006 0.741452i \(-0.734137\pi\)
−0.671006 + 0.741452i \(0.734137\pi\)
\(110\) 87.0033 + 3.01876i 0.790939 + 0.0274433i
\(111\) 0 0
\(112\) 47.4137 27.3743i 0.423336 0.244413i
\(113\) 27.2132 + 47.1347i 0.240825 + 0.417121i 0.960949 0.276724i \(-0.0892487\pi\)
−0.720125 + 0.693845i \(0.755915\pi\)
\(114\) 0 0
\(115\) −6.03350 + 173.890i −0.0524652 + 1.51209i
\(116\) 42.2702i 0.364398i
\(117\) 0 0
\(118\) 58.8755i 0.498945i
\(119\) 81.7826 + 47.2172i 0.687249 + 0.396783i
\(120\) 0 0
\(121\) 15.2868 + 26.4775i 0.126337 + 0.218822i
\(122\) −10.6482 18.4433i −0.0872806 0.151174i
\(123\) 0 0
\(124\) 38.2132 66.1872i 0.308171 0.533768i
\(125\) −12.9828 + 124.324i −0.103862 + 0.994592i
\(126\) 0 0
\(127\) 159.215i 1.25366i 0.779154 + 0.626832i \(0.215649\pi\)
−0.779154 + 0.626832i \(0.784351\pi\)
\(128\) 5.65685 9.79796i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −63.7086 + 102.006i −0.490066 + 0.784660i
\(131\) 95.5252 55.1515i 0.729200 0.421004i −0.0889293 0.996038i \(-0.528345\pi\)
0.818130 + 0.575034i \(0.195011\pi\)
\(132\) 0 0
\(133\) 85.8501 + 49.5656i 0.645489 + 0.372673i
\(134\) 181.893i 1.35741i
\(135\) 0 0
\(136\) 19.5147 0.143491
\(137\) 108.959 188.723i 0.795324 1.37754i −0.127309 0.991863i \(-0.540634\pi\)
0.922633 0.385679i \(-0.126033\pi\)
\(138\) 0 0
\(139\) 53.1249 + 92.0150i 0.382193 + 0.661979i 0.991376 0.131052i \(-0.0418355\pi\)
−0.609182 + 0.793030i \(0.708502\pi\)
\(140\) −72.5049 + 116.090i −0.517892 + 0.829213i
\(141\) 0 0
\(142\) 128.558 + 74.2232i 0.905340 + 0.522698i
\(143\) −209.397 −1.46431
\(144\) 0 0
\(145\) −49.6325 93.2948i −0.342293 0.643413i
\(146\) 2.58706 + 1.49364i 0.0177196 + 0.0102304i
\(147\) 0 0
\(148\) −37.3049 + 21.5380i −0.252060 + 0.145527i
\(149\) 12.2622 7.07960i 0.0822968 0.0475141i −0.458287 0.888804i \(-0.651537\pi\)
0.540584 + 0.841290i \(0.318203\pi\)
\(150\) 0 0
\(151\) −36.6690 + 63.5127i −0.242841 + 0.420614i −0.961522 0.274726i \(-0.911413\pi\)
0.718681 + 0.695340i \(0.244746\pi\)
\(152\) 20.4853 0.134772
\(153\) 0 0
\(154\) −238.309 −1.54746
\(155\) −6.62546 + 190.951i −0.0427449 + 1.23194i
\(156\) 0 0
\(157\) 60.7475 35.0726i 0.386927 0.223392i −0.293901 0.955836i \(-0.594954\pi\)
0.680828 + 0.732444i \(0.261620\pi\)
\(158\) −31.1802 54.0057i −0.197343 0.341808i
\(159\) 0 0
\(160\) −0.980793 + 28.2673i −0.00612996 + 0.176670i
\(161\) 476.299i 2.95838i
\(162\) 0 0
\(163\) 9.05959i 0.0555803i 0.999614 + 0.0277902i \(0.00884702\pi\)
−0.999614 + 0.0277902i \(0.991153\pi\)
\(164\) 62.9856 + 36.3648i 0.384059 + 0.221736i
\(165\) 0 0
\(166\) 38.9081 + 67.3908i 0.234386 + 0.405969i
\(167\) −31.9264 55.2982i −0.191176 0.331127i 0.754464 0.656341i \(-0.227897\pi\)
−0.945640 + 0.325215i \(0.894563\pi\)
\(168\) 0 0
\(169\) 60.1396 104.165i 0.355856 0.616360i
\(170\) −43.0711 + 22.9136i −0.253359 + 0.134786i
\(171\) 0 0
\(172\) 12.4784i 0.0725489i
\(173\) 13.9939 24.2382i 0.0808896 0.140105i −0.822743 0.568414i \(-0.807557\pi\)
0.903632 + 0.428309i \(0.140891\pi\)
\(174\) 0 0
\(175\) 23.7167 341.356i 0.135524 1.95060i
\(176\) −42.6484 + 24.6230i −0.242320 + 0.139904i
\(177\) 0 0
\(178\) −83.4075 48.1554i −0.468582 0.270536i
\(179\) 21.0660i 0.117687i −0.998267 0.0588435i \(-0.981259\pi\)
0.998267 0.0588435i \(-0.0187413\pi\)
\(180\) 0 0
\(181\) 53.6030 0.296149 0.148075 0.988976i \(-0.452692\pi\)
0.148075 + 0.988976i \(0.452692\pi\)
\(182\) 164.610 285.113i 0.904452 1.56656i
\(183\) 0 0
\(184\) −49.2132 85.2398i −0.267463 0.463260i
\(185\) 57.0466 91.3391i 0.308360 0.493725i
\(186\) 0 0
\(187\) −73.5630 42.4716i −0.393385 0.227121i
\(188\) 80.4020 0.427670
\(189\) 0 0
\(190\) −45.2132 + 24.0532i −0.237964 + 0.126596i
\(191\) −193.144 111.512i −1.01123 0.583831i −0.0996752 0.995020i \(-0.531780\pi\)
−0.911550 + 0.411189i \(0.865114\pi\)
\(192\) 0 0
\(193\) −152.614 + 88.1118i −0.790746 + 0.456538i −0.840225 0.542237i \(-0.817577\pi\)
0.0494788 + 0.998775i \(0.484244\pi\)
\(194\) −123.997 + 71.5899i −0.639162 + 0.369020i
\(195\) 0 0
\(196\) 138.338 239.609i 0.705807 1.22249i
\(197\) −277.586 −1.40906 −0.704532 0.709672i \(-0.748843\pi\)
−0.704532 + 0.709672i \(0.748843\pi\)
\(198\) 0 0
\(199\) 71.5736 0.359666 0.179833 0.983697i \(-0.442444\pi\)
0.179833 + 0.983697i \(0.442444\pi\)
\(200\) −31.0259 63.5405i −0.155130 0.317702i
\(201\) 0 0
\(202\) −18.6525 + 10.7690i −0.0923389 + 0.0533119i
\(203\) 144.640 + 250.523i 0.712510 + 1.23410i
\(204\) 0 0
\(205\) −181.714 6.30497i −0.886412 0.0307560i
\(206\) 109.025i 0.529248i
\(207\) 0 0
\(208\) 68.0328i 0.327081i
\(209\) −77.2217 44.5840i −0.369482 0.213320i
\(210\) 0 0
\(211\) −159.746 276.689i −0.757091 1.31132i −0.944328 0.329005i \(-0.893287\pi\)
0.187237 0.982315i \(-0.440047\pi\)
\(212\) 38.2721 + 66.2892i 0.180529 + 0.312685i
\(213\) 0 0
\(214\) 55.4558 96.0523i 0.259139 0.448843i
\(215\) −14.6518 27.5412i −0.0681479 0.128099i
\(216\) 0 0
\(217\) 523.030i 2.41028i
\(218\) −103.435 + 179.155i −0.474473 + 0.821811i
\(219\) 0 0
\(220\) 65.2178 104.422i 0.296445 0.474646i
\(221\) 101.626 58.6740i 0.459848 0.265493i
\(222\) 0 0
\(223\) −140.676 81.2193i −0.630834 0.364212i 0.150241 0.988649i \(-0.451995\pi\)
−0.781075 + 0.624437i \(0.785328\pi\)
\(224\) 77.4262i 0.345653i
\(225\) 0 0
\(226\) 76.9706 0.340578
\(227\) 120.549 208.797i 0.531052 0.919809i −0.468291 0.883574i \(-0.655130\pi\)
0.999343 0.0362347i \(-0.0115364\pi\)
\(228\) 0 0
\(229\) −51.1102 88.5254i −0.223189 0.386574i 0.732586 0.680675i \(-0.238313\pi\)
−0.955774 + 0.294101i \(0.904980\pi\)
\(230\) 208.705 + 130.349i 0.907413 + 0.566733i
\(231\) 0 0
\(232\) 51.7702 + 29.8895i 0.223147 + 0.128834i
\(233\) −241.966 −1.03848 −0.519239 0.854629i \(-0.673785\pi\)
−0.519239 + 0.854629i \(0.673785\pi\)
\(234\) 0 0
\(235\) −177.456 + 94.4058i −0.755131 + 0.401727i
\(236\) −72.1075 41.6313i −0.305540 0.176404i
\(237\) 0 0
\(238\) 115.658 66.7752i 0.485958 0.280568i
\(239\) −325.157 + 187.729i −1.36049 + 0.785478i −0.989689 0.143235i \(-0.954250\pi\)
−0.370799 + 0.928713i \(0.620916\pi\)
\(240\) 0 0
\(241\) 159.140 275.638i 0.660330 1.14373i −0.320198 0.947350i \(-0.603750\pi\)
0.980529 0.196375i \(-0.0629171\pi\)
\(242\) 43.2376 0.178668
\(243\) 0 0
\(244\) −30.1177 −0.123433
\(245\) −23.9853 + 691.274i −0.0978990 + 2.82153i
\(246\) 0 0
\(247\) 106.681 61.5922i 0.431906 0.249361i
\(248\) −54.0416 93.6028i −0.217910 0.377431i
\(249\) 0 0
\(250\) 143.085 + 103.811i 0.572340 + 0.415244i
\(251\) 85.5417i 0.340804i 0.985375 + 0.170402i \(0.0545066\pi\)
−0.985375 + 0.170402i \(0.945493\pi\)
\(252\) 0 0
\(253\) 428.429i 1.69339i
\(254\) 194.998 + 112.582i 0.767709 + 0.443237i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −107.114 185.526i −0.416785 0.721893i 0.578829 0.815449i \(-0.303510\pi\)
−0.995614 + 0.0935562i \(0.970177\pi\)
\(258\) 0 0
\(259\) −147.397 + 255.299i −0.569100 + 0.985711i
\(260\) 79.8823 + 150.156i 0.307239 + 0.577522i
\(261\) 0 0
\(262\) 155.992i 0.595389i
\(263\) −53.4386 + 92.5584i −0.203189 + 0.351933i −0.949554 0.313603i \(-0.898464\pi\)
0.746365 + 0.665536i \(0.231797\pi\)
\(264\) 0 0
\(265\) −162.305 101.369i −0.612473 0.382526i
\(266\) 121.410 70.0963i 0.456430 0.263520i
\(267\) 0 0
\(268\) 222.772 + 128.618i 0.831241 + 0.479917i
\(269\) 365.927i 1.36032i 0.733062 + 0.680161i \(0.238090\pi\)
−0.733062 + 0.680161i \(0.761910\pi\)
\(270\) 0 0
\(271\) −92.8894 −0.342765 −0.171383 0.985205i \(-0.554823\pi\)
−0.171383 + 0.985205i \(0.554823\pi\)
\(272\) 13.7990 23.9006i 0.0507316 0.0878697i
\(273\) 0 0
\(274\) −154.092 266.895i −0.562379 0.974069i
\(275\) −21.3331 + 307.048i −0.0775747 + 1.11654i
\(276\) 0 0
\(277\) 195.841 + 113.069i 0.707006 + 0.408190i 0.809951 0.586497i \(-0.199493\pi\)
−0.102946 + 0.994687i \(0.532827\pi\)
\(278\) 150.260 0.540503
\(279\) 0 0
\(280\) 90.9117 + 170.888i 0.324685 + 0.610314i
\(281\) 54.9106 + 31.7026i 0.195411 + 0.112821i 0.594513 0.804086i \(-0.297345\pi\)
−0.399102 + 0.916907i \(0.630678\pi\)
\(282\) 0 0
\(283\) 314.459 181.553i 1.11116 0.641531i 0.172033 0.985091i \(-0.444966\pi\)
0.939131 + 0.343560i \(0.111633\pi\)
\(284\) 181.809 104.967i 0.640172 0.369604i
\(285\) 0 0
\(286\) −148.066 + 256.458i −0.517713 + 0.896706i
\(287\) 497.730 1.73425
\(288\) 0 0
\(289\) −241.397 −0.835284
\(290\) −149.358 5.18229i −0.515027 0.0178700i
\(291\) 0 0
\(292\) 3.65865 2.11232i 0.0125296 0.00723398i
\(293\) −113.717 196.963i −0.388112 0.672229i 0.604084 0.796921i \(-0.293539\pi\)
−0.992196 + 0.124691i \(0.960206\pi\)
\(294\) 0 0
\(295\) 208.031 + 7.21808i 0.705190 + 0.0244681i
\(296\) 60.9187i 0.205806i
\(297\) 0 0
\(298\) 20.0241i 0.0671950i
\(299\) −512.573 295.934i −1.71429 0.989747i
\(300\) 0 0
\(301\) 42.6985 + 73.9559i 0.141855 + 0.245701i
\(302\) 51.8579 + 89.8205i 0.171715 + 0.297419i
\(303\) 0 0
\(304\) 14.4853 25.0892i 0.0476490 0.0825304i
\(305\) 66.4731 35.3634i 0.217945 0.115946i
\(306\) 0 0
\(307\) 340.164i 1.10803i 0.832508 + 0.554013i \(0.186904\pi\)
−0.832508 + 0.554013i \(0.813096\pi\)
\(308\) −168.510 + 291.867i −0.547109 + 0.947621i
\(309\) 0 0
\(310\) 229.181 + 143.137i 0.739295 + 0.461733i
\(311\) −334.951 + 193.384i −1.07701 + 0.621815i −0.930089 0.367333i \(-0.880271\pi\)
−0.146925 + 0.989148i \(0.546938\pi\)
\(312\) 0 0
\(313\) 325.974 + 188.201i 1.04145 + 0.601282i 0.920244 0.391345i \(-0.127990\pi\)
0.121207 + 0.992627i \(0.461323\pi\)
\(314\) 99.2002i 0.315924i
\(315\) 0 0
\(316\) −88.1909 −0.279085
\(317\) 177.700 307.785i 0.560566 0.970929i −0.436881 0.899519i \(-0.643917\pi\)
0.997447 0.0714099i \(-0.0227499\pi\)
\(318\) 0 0
\(319\) −130.103 225.344i −0.407845 0.706408i
\(320\) 33.9267 + 21.1892i 0.106021 + 0.0662162i
\(321\) 0 0
\(322\) −583.345 336.794i −1.81163 1.04594i
\(323\) 49.9706 0.154708
\(324\) 0 0
\(325\) −352.617 237.614i −1.08498 0.731121i
\(326\) 11.0957 + 6.40610i 0.0340359 + 0.0196506i
\(327\) 0 0
\(328\) 89.0751 51.4275i 0.271570 0.156791i
\(329\) 476.519 275.119i 1.44839 0.836227i
\(330\) 0 0
\(331\) 222.095 384.681i 0.670983 1.16218i −0.306642 0.951825i \(-0.599206\pi\)
0.977626 0.210352i \(-0.0674611\pi\)
\(332\) 110.049 0.331472
\(333\) 0 0
\(334\) −90.3015 −0.270364
\(335\) −642.702 22.2999i −1.91851 0.0665669i
\(336\) 0 0
\(337\) 352.547 203.543i 1.04613 0.603985i 0.124569 0.992211i \(-0.460245\pi\)
0.921564 + 0.388226i \(0.126912\pi\)
\(338\) −85.0503 147.311i −0.251628 0.435832i
\(339\) 0 0
\(340\) −2.39249 + 68.9535i −0.00703673 + 0.202804i
\(341\) 470.463i 1.37966i
\(342\) 0 0
\(343\) 1222.78i 3.56497i
\(344\) 15.2829 + 8.82357i 0.0444270 + 0.0256499i
\(345\) 0 0
\(346\) −19.7904 34.2779i −0.0571976 0.0990691i
\(347\) −244.706 423.843i −0.705204 1.22145i −0.966618 0.256222i \(-0.917522\pi\)
0.261414 0.965227i \(-0.415811\pi\)
\(348\) 0 0
\(349\) −40.8970 + 70.8356i −0.117183 + 0.202967i −0.918650 0.395071i \(-0.870720\pi\)
0.801467 + 0.598039i \(0.204053\pi\)
\(350\) −401.304 270.422i −1.14658 0.772634i
\(351\) 0 0
\(352\) 69.6445i 0.197854i
\(353\) −125.693 + 217.707i −0.356072 + 0.616735i −0.987301 0.158862i \(-0.949218\pi\)
0.631229 + 0.775597i \(0.282551\pi\)
\(354\) 0 0
\(355\) −278.022 + 445.149i −0.783160 + 1.25394i
\(356\) −117.956 + 68.1020i −0.331337 + 0.191298i
\(357\) 0 0
\(358\) −25.8004 14.8959i −0.0720682 0.0416086i
\(359\) 518.500i 1.44429i −0.691742 0.722145i \(-0.743156\pi\)
0.691742 0.722145i \(-0.256844\pi\)
\(360\) 0 0
\(361\) −308.544 −0.854693
\(362\) 37.9031 65.6500i 0.104705 0.181354i
\(363\) 0 0
\(364\) −232.794 403.211i −0.639544 1.10772i
\(365\) −5.59480 + 8.95801i −0.0153282 + 0.0245425i
\(366\) 0 0
\(367\) 296.166 + 170.992i 0.806992 + 0.465917i 0.845910 0.533325i \(-0.179058\pi\)
−0.0389180 + 0.999242i \(0.512391\pi\)
\(368\) −139.196 −0.378250
\(369\) 0 0
\(370\) −71.5290 134.454i −0.193322 0.363389i
\(371\) 453.655 + 261.918i 1.22279 + 0.705978i
\(372\) 0 0
\(373\) −95.5252 + 55.1515i −0.256100 + 0.147859i −0.622554 0.782577i \(-0.713905\pi\)
0.366454 + 0.930436i \(0.380572\pi\)
\(374\) −104.034 + 60.0640i −0.278165 + 0.160599i
\(375\) 0 0
\(376\) 56.8528 98.4720i 0.151204 0.261894i
\(377\) 359.470 0.953502
\(378\) 0 0
\(379\) 324.345 0.855792 0.427896 0.903828i \(-0.359255\pi\)
0.427896 + 0.903828i \(0.359255\pi\)
\(380\) −2.51148 + 72.3828i −0.00660915 + 0.190481i
\(381\) 0 0
\(382\) −273.147 + 157.701i −0.715044 + 0.412831i
\(383\) 286.240 + 495.782i 0.747363 + 1.29447i 0.949082 + 0.315028i \(0.102014\pi\)
−0.201719 + 0.979443i \(0.564653\pi\)
\(384\) 0 0
\(385\) 29.2164 842.042i 0.0758869 2.18712i
\(386\) 249.218i 0.645642i
\(387\) 0 0
\(388\) 202.487i 0.521873i
\(389\) 624.981 + 360.833i 1.60664 + 0.927592i 0.990116 + 0.140253i \(0.0447915\pi\)
0.616520 + 0.787339i \(0.288542\pi\)
\(390\) 0 0
\(391\) −120.048 207.929i −0.307027 0.531787i
\(392\) −195.640 338.858i −0.499081 0.864433i
\(393\) 0 0
\(394\) −196.283 + 339.972i −0.498180 + 0.862873i
\(395\) 194.647 103.551i 0.492777 0.262155i
\(396\) 0 0
\(397\) 379.321i 0.955468i 0.878505 + 0.477734i \(0.158542\pi\)
−0.878505 + 0.477734i \(0.841458\pi\)
\(398\) 50.6102 87.6594i 0.127161 0.220250i
\(399\) 0 0
\(400\) −99.7595 6.93108i −0.249399 0.0173277i
\(401\) 303.952 175.487i 0.757985 0.437623i −0.0705866 0.997506i \(-0.522487\pi\)
0.828572 + 0.559883i \(0.189154\pi\)
\(402\) 0 0
\(403\) −562.863 324.969i −1.39668 0.806375i
\(404\) 30.4593i 0.0753944i
\(405\) 0 0
\(406\) 409.103 1.00764
\(407\) 132.583 229.640i 0.325756 0.564227i
\(408\) 0 0
\(409\) 266.713 + 461.961i 0.652111 + 1.12949i 0.982610 + 0.185682i \(0.0594495\pi\)
−0.330499 + 0.943806i \(0.607217\pi\)
\(410\) −136.214 + 218.096i −0.332228 + 0.531940i
\(411\) 0 0
\(412\) −133.528 77.0924i −0.324097 0.187118i
\(413\) −569.813 −1.37969
\(414\) 0 0
\(415\) −242.889 + 129.216i −0.585276 + 0.311364i
\(416\) −83.3229 48.1065i −0.200295 0.115641i
\(417\) 0 0
\(418\) −109.208 + 63.0513i −0.261263 + 0.150840i
\(419\) 207.634 119.878i 0.495547 0.286104i −0.231326 0.972876i \(-0.574306\pi\)
0.726873 + 0.686772i \(0.240973\pi\)
\(420\) 0 0
\(421\) −212.471 + 368.010i −0.504681 + 0.874133i 0.495305 + 0.868719i \(0.335056\pi\)
−0.999985 + 0.00541323i \(0.998277\pi\)
\(422\) −451.831 −1.07069
\(423\) 0 0
\(424\) 108.250 0.255306
\(425\) −75.6827 154.997i −0.178077 0.364698i
\(426\) 0 0
\(427\) −178.499 + 103.057i −0.418031 + 0.241350i
\(428\) −78.4264 135.839i −0.183239 0.317380i
\(429\) 0 0
\(430\) −44.0913 1.52984i −0.102538 0.00355777i
\(431\) 544.039i 1.26227i 0.775673 + 0.631135i \(0.217411\pi\)
−0.775673 + 0.631135i \(0.782589\pi\)
\(432\) 0 0
\(433\) 602.735i 1.39200i 0.718043 + 0.695999i \(0.245038\pi\)
−0.718043 + 0.695999i \(0.754962\pi\)
\(434\) −640.578 369.838i −1.47599 0.852161i
\(435\) 0 0
\(436\) 146.279 + 253.363i 0.335503 + 0.581108i
\(437\) −126.018 218.270i −0.288371 0.499474i
\(438\) 0 0
\(439\) −201.143 + 348.390i −0.458185 + 0.793600i −0.998865 0.0476287i \(-0.984834\pi\)
0.540680 + 0.841228i \(0.318167\pi\)
\(440\) −81.7746 153.713i −0.185851 0.349347i
\(441\) 0 0
\(442\) 165.955i 0.375464i
\(443\) 219.257 379.765i 0.494938 0.857257i −0.505045 0.863093i \(-0.668524\pi\)
0.999983 + 0.00583572i \(0.00185758\pi\)
\(444\) 0 0
\(445\) 180.378 288.809i 0.405344 0.649009i
\(446\) −198.946 + 114.861i −0.446067 + 0.257537i
\(447\) 0 0
\(448\) −94.8274 54.7486i −0.211668 0.122207i
\(449\) 670.866i 1.49413i −0.664749 0.747067i \(-0.731462\pi\)
0.664749 0.747067i \(-0.268538\pi\)
\(450\) 0 0
\(451\) −447.706 −0.992695
\(452\) 54.4264 94.2693i 0.120412 0.208560i
\(453\) 0 0
\(454\) −170.482 295.283i −0.375510 0.650403i
\(455\) 987.240 + 616.589i 2.16976 + 1.35514i
\(456\) 0 0
\(457\) 601.913 + 347.514i 1.31710 + 0.760425i 0.983260 0.182206i \(-0.0583238\pi\)
0.333835 + 0.942632i \(0.391657\pi\)
\(458\) −144.561 −0.315636
\(459\) 0 0
\(460\) 307.220 163.440i 0.667870 0.355304i
\(461\) 11.3352 + 6.54436i 0.0245882 + 0.0141960i 0.512244 0.858840i \(-0.328814\pi\)
−0.487656 + 0.873036i \(0.662148\pi\)
\(462\) 0 0
\(463\) −202.894 + 117.141i −0.438215 + 0.253004i −0.702840 0.711348i \(-0.748085\pi\)
0.264625 + 0.964351i \(0.414752\pi\)
\(464\) 73.2141 42.2702i 0.157789 0.0910995i
\(465\) 0 0
\(466\) −171.095 + 296.346i −0.367158 + 0.635936i
\(467\) 742.882 1.59075 0.795377 0.606115i \(-0.207273\pi\)
0.795377 + 0.606115i \(0.207273\pi\)
\(468\) 0 0
\(469\) 1760.41 3.75354
\(470\) −9.85722 + 284.093i −0.0209728 + 0.604453i
\(471\) 0 0
\(472\) −101.975 + 58.8755i −0.216049 + 0.124736i
\(473\) −38.4071 66.5230i −0.0811989 0.140641i
\(474\) 0 0
\(475\) −79.4468 162.706i −0.167256 0.342538i
\(476\) 188.869i 0.396783i
\(477\) 0 0
\(478\) 530.978i 1.11083i
\(479\) 387.469 + 223.705i 0.808913 + 0.467026i 0.846578 0.532264i \(-0.178659\pi\)
−0.0376655 + 0.999290i \(0.511992\pi\)
\(480\) 0 0
\(481\) 183.161 + 317.245i 0.380793 + 0.659553i
\(482\) −225.057 389.811i −0.466924 0.808736i
\(483\) 0 0
\(484\) 30.5736 52.9550i 0.0631686 0.109411i
\(485\) −237.754 446.910i −0.490215 0.921464i
\(486\) 0 0
\(487\) 50.3166i 0.103319i 0.998665 + 0.0516597i \(0.0164511\pi\)
−0.998665 + 0.0516597i \(0.983549\pi\)
\(488\) −21.2965 + 36.8866i −0.0436403 + 0.0755872i
\(489\) 0 0
\(490\) 829.675 + 518.181i 1.69321 + 1.05751i
\(491\) −684.707 + 395.316i −1.39452 + 0.805124i −0.993811 0.111084i \(-0.964568\pi\)
−0.400704 + 0.916208i \(0.631234\pi\)
\(492\) 0 0
\(493\) 126.285 + 72.9107i 0.256156 + 0.147892i
\(494\) 174.209i 0.352650i
\(495\) 0 0
\(496\) −152.853 −0.308171
\(497\) 718.352 1244.22i 1.44538 2.50347i
\(498\) 0 0
\(499\) 300.195 + 519.953i 0.601593 + 1.04199i 0.992580 + 0.121593i \(0.0388004\pi\)
−0.390987 + 0.920396i \(0.627866\pi\)
\(500\) 228.318 101.837i 0.456636 0.203674i
\(501\) 0 0
\(502\) 104.767 + 60.4871i 0.208699 + 0.120492i
\(503\) 433.368 0.861566 0.430783 0.902456i \(-0.358237\pi\)
0.430783 + 0.902456i \(0.358237\pi\)
\(504\) 0 0
\(505\) −35.7645 67.2270i −0.0708208 0.133123i
\(506\) 524.716 + 302.945i 1.03699 + 0.598705i
\(507\) 0 0
\(508\) 275.769 159.215i 0.542852 0.313416i
\(509\) −832.870 + 480.857i −1.63629 + 0.944710i −0.654190 + 0.756331i \(0.726990\pi\)
−0.982096 + 0.188380i \(0.939676\pi\)
\(510\) 0 0
\(511\) 14.4558 25.0383i 0.0282893 0.0489985i
\(512\) −22.6274 −0.0441942
\(513\) 0 0
\(514\) −302.963 −0.589423
\(515\) 385.230 + 13.3664i 0.748020 + 0.0259542i
\(516\) 0 0
\(517\) −428.627 + 247.468i −0.829065 + 0.478661i
\(518\) 208.451 + 361.047i 0.402415 + 0.697003i
\(519\) 0 0
\(520\) 240.388 + 8.34077i 0.462284 + 0.0160399i
\(521\) 5.90542i 0.0113348i −0.999984 0.00566739i \(-0.998196\pi\)
0.999984 0.00566739i \(-0.00180400\pi\)
\(522\) 0 0
\(523\) 165.846i 0.317104i 0.987351 + 0.158552i \(0.0506826\pi\)
−0.987351 + 0.158552i \(0.949317\pi\)
\(524\) −191.050 110.303i −0.364600 0.210502i
\(525\) 0 0
\(526\) 75.5736 + 130.897i 0.143676 + 0.248854i
\(527\) −131.826 228.329i −0.250144 0.433262i
\(528\) 0 0
\(529\) −340.985 + 590.603i −0.644584 + 1.11645i
\(530\) −238.919 + 127.104i −0.450790 + 0.239819i
\(531\) 0 0
\(532\) 198.262i 0.372673i
\(533\) 309.250 535.636i 0.580206 1.00495i
\(534\) 0 0
\(535\) 332.593 + 207.724i 0.621670 + 0.388269i
\(536\) 315.048 181.893i 0.587776 0.339353i
\(537\) 0 0
\(538\) 448.167 + 258.749i 0.833024 + 0.480947i
\(539\) 1703.15i 3.15984i
\(540\) 0 0
\(541\) 216.985 0.401081 0.200541 0.979685i \(-0.435730\pi\)
0.200541 + 0.979685i \(0.435730\pi\)
\(542\) −65.6827 + 113.766i −0.121186 + 0.209900i
\(543\) 0 0
\(544\) −19.5147 33.8005i −0.0358726 0.0621332i
\(545\) −620.346 387.442i −1.13825 0.710903i
\(546\) 0 0
\(547\) −87.1611 50.3225i −0.159344 0.0919973i 0.418208 0.908351i \(-0.362658\pi\)
−0.577552 + 0.816354i \(0.695992\pi\)
\(548\) −435.838 −0.795324
\(549\) 0 0
\(550\) 360.971 + 243.243i 0.656310 + 0.442260i
\(551\) 132.566 + 76.5369i 0.240591 + 0.138906i
\(552\) 0 0
\(553\) −522.682 + 301.771i −0.945175 + 0.545697i
\(554\) 276.960 159.903i 0.499928 0.288634i
\(555\) 0 0
\(556\) 106.250 184.030i 0.191097 0.330989i
\(557\) −116.662 −0.209447 −0.104723 0.994501i \(-0.533396\pi\)
−0.104723 + 0.994501i \(0.533396\pi\)
\(558\) 0 0
\(559\) 106.118 0.189835
\(560\) 273.578 + 9.49239i 0.488533 + 0.0169507i
\(561\) 0 0
\(562\) 77.6553 44.8343i 0.138177 0.0797763i
\(563\) 266.953 + 462.377i 0.474162 + 0.821273i 0.999562 0.0295822i \(-0.00941769\pi\)
−0.525400 + 0.850855i \(0.676084\pi\)
\(564\) 0 0
\(565\) −9.43653 + 271.968i −0.0167018 + 0.481360i
\(566\) 513.510i 0.907262i
\(567\) 0 0
\(568\) 296.893i 0.522698i
\(569\) −97.5590 56.3257i −0.171457 0.0989907i 0.411816 0.911267i \(-0.364895\pi\)
−0.583273 + 0.812276i \(0.698228\pi\)
\(570\) 0 0
\(571\) 430.768 + 746.111i 0.754409 + 1.30668i 0.945668 + 0.325135i \(0.105410\pi\)
−0.191258 + 0.981540i \(0.561257\pi\)
\(572\) 209.397 + 362.686i 0.366079 + 0.634067i
\(573\) 0 0
\(574\) 351.948 609.592i 0.613150 1.06201i
\(575\) −486.161 + 721.459i −0.845498 + 1.25471i
\(576\) 0 0
\(577\) 37.3256i 0.0646891i 0.999477 + 0.0323446i \(0.0102974\pi\)
−0.999477 + 0.0323446i \(0.989703\pi\)
\(578\) −170.693 + 295.650i −0.295317 + 0.511505i
\(579\) 0 0
\(580\) −111.959 + 179.261i −0.193033 + 0.309070i
\(581\) 652.227 376.564i 1.12259 0.648130i
\(582\) 0 0
\(583\) −408.060 235.594i −0.699932 0.404106i
\(584\) 5.97455i 0.0102304i
\(585\) 0 0
\(586\) −321.640 −0.548873
\(587\) −269.051 + 466.011i −0.458350 + 0.793885i −0.998874 0.0474434i \(-0.984893\pi\)
0.540524 + 0.841328i \(0.318226\pi\)
\(588\) 0 0
\(589\) −138.382 239.685i −0.234944 0.406936i
\(590\) 155.941 249.681i 0.264306 0.423188i
\(591\) 0 0
\(592\) 74.6098 + 43.0760i 0.126030 + 0.0727635i
\(593\) 884.169 1.49101 0.745505 0.666500i \(-0.232208\pi\)
0.745505 + 0.666500i \(0.232208\pi\)
\(594\) 0 0
\(595\) 221.765 + 416.854i 0.372713 + 0.700595i
\(596\) −24.5244 14.1592i −0.0411484 0.0237570i
\(597\) 0 0
\(598\) −724.888 + 418.514i −1.21219 + 0.699857i
\(599\) 38.7750 22.3868i 0.0647330 0.0373736i −0.467284 0.884107i \(-0.654768\pi\)
0.532017 + 0.846734i \(0.321434\pi\)
\(600\) 0 0
\(601\) −197.287 + 341.711i −0.328264 + 0.568570i −0.982168 0.188008i \(-0.939797\pi\)
0.653903 + 0.756578i \(0.273130\pi\)
\(602\) 120.770 0.200614
\(603\) 0 0
\(604\) 146.676 0.242841
\(605\) −5.30089 + 152.776i −0.00876181 + 0.252522i
\(606\) 0 0
\(607\) 186.345 107.586i 0.306993 0.177243i −0.338587 0.940935i \(-0.609949\pi\)
0.645580 + 0.763692i \(0.276616\pi\)
\(608\) −20.4853 35.4815i −0.0336929 0.0583578i
\(609\) 0 0
\(610\) 3.69241 106.418i 0.00605313 0.174456i
\(611\) 683.747i 1.11906i
\(612\) 0 0
\(613\) 333.937i 0.544758i 0.962190 + 0.272379i \(0.0878105\pi\)
−0.962190 + 0.272379i \(0.912189\pi\)
\(614\) 416.614 + 240.532i 0.678525 + 0.391747i
\(615\) 0 0
\(616\) 238.309 + 412.763i 0.386865 + 0.670069i
\(617\) −32.7117 56.6584i −0.0530174 0.0918288i 0.838299 0.545211i \(-0.183551\pi\)
−0.891316 + 0.453382i \(0.850217\pi\)
\(618\) 0 0
\(619\) 9.96342 17.2571i 0.0160960 0.0278791i −0.857865 0.513875i \(-0.828210\pi\)
0.873961 + 0.485996i \(0.161543\pi\)
\(620\) 337.362 179.475i 0.544133 0.289477i
\(621\) 0 0
\(622\) 546.973i 0.879379i
\(623\) −466.061 + 807.241i −0.748091 + 1.29573i
\(624\) 0 0
\(625\) −384.348 + 492.850i −0.614957 + 0.788560i
\(626\) 460.997 266.157i 0.736417 0.425171i
\(627\) 0 0
\(628\) −121.495 70.1452i −0.193463 0.111696i
\(629\) 148.601i 0.236250i
\(630\) 0 0
\(631\) −210.625 −0.333796 −0.166898 0.985974i \(-0.553375\pi\)
−0.166898 + 0.985974i \(0.553375\pi\)
\(632\) −62.3604 + 108.011i −0.0986715 + 0.170904i
\(633\) 0 0
\(634\) −251.305 435.273i −0.396380 0.686551i
\(635\) −421.706 + 675.206i −0.664103 + 1.06332i
\(636\) 0 0
\(637\) −2037.66 1176.44i −3.19883 1.84685i
\(638\) −367.986 −0.576780
\(639\) 0 0
\(640\) 49.9411 26.5685i 0.0780330 0.0415132i
\(641\) −1019.97 588.881i −1.59122 0.918692i −0.993098 0.117287i \(-0.962580\pi\)
−0.598122 0.801405i \(-0.704086\pi\)
\(642\) 0 0
\(643\) −32.5995 + 18.8213i −0.0506990 + 0.0292711i −0.525135 0.851019i \(-0.675985\pi\)
0.474436 + 0.880290i \(0.342652\pi\)
\(644\) −824.974 + 476.299i −1.28102 + 0.739595i
\(645\) 0 0
\(646\) 35.3345 61.2012i 0.0546974 0.0947387i
\(647\) 695.382 1.07478 0.537389 0.843334i \(-0.319411\pi\)
0.537389 + 0.843334i \(0.319411\pi\)
\(648\) 0 0
\(649\) 512.544 0.789744
\(650\) −540.355 + 263.848i −0.831315 + 0.405919i
\(651\) 0 0
\(652\) 15.6917 9.05959i 0.0240670 0.0138951i
\(653\) −462.148 800.464i −0.707731 1.22583i −0.965697 0.259672i \(-0.916386\pi\)
0.257966 0.966154i \(-0.416948\pi\)
\(654\) 0 0
\(655\) 551.183 + 19.1245i 0.841501 + 0.0291977i
\(656\) 145.459i 0.221736i
\(657\) 0 0
\(658\) 778.153i 1.18260i
\(659\) 58.6043 + 33.8352i 0.0889291 + 0.0513433i 0.543805 0.839212i \(-0.316983\pi\)
−0.454876 + 0.890555i \(0.650316\pi\)
\(660\) 0 0
\(661\) −516.434 894.489i −0.781291 1.35324i −0.931190 0.364535i \(-0.881228\pi\)
0.149898 0.988701i \(-0.452105\pi\)
\(662\) −314.090 544.021i −0.474457 0.821783i
\(663\) 0 0
\(664\) 77.8162 134.782i 0.117193 0.202984i
\(665\) 232.794 + 437.586i 0.350066 + 0.658024i
\(666\) 0 0
\(667\) 735.480i 1.10267i
\(668\) −63.8528 + 110.596i −0.0955880 + 0.165563i
\(669\) 0 0
\(670\) −481.771 + 771.377i −0.719061 + 1.15131i
\(671\) 160.559 92.6988i 0.239283 0.138150i
\(672\) 0 0
\(673\) −8.80797 5.08528i −0.0130876 0.00755614i 0.493442 0.869779i \(-0.335739\pi\)
−0.506530 + 0.862223i \(0.669072\pi\)
\(674\) 575.707i 0.854164i
\(675\) 0 0
\(676\) −240.558 −0.355856
\(677\) 288.468 499.641i 0.426098 0.738023i −0.570425 0.821350i \(-0.693221\pi\)
0.996522 + 0.0833273i \(0.0265547\pi\)
\(678\) 0 0
\(679\) 692.867 + 1200.08i 1.02042 + 1.76742i
\(680\) 82.7586 + 51.6876i 0.121704 + 0.0760112i
\(681\) 0 0
\(682\) 576.197 + 332.667i 0.844863 + 0.487782i
\(683\) 526.009 0.770145 0.385073 0.922886i \(-0.374176\pi\)
0.385073 + 0.922886i \(0.374176\pi\)
\(684\) 0 0
\(685\) 961.940 511.748i 1.40429 0.747078i
\(686\) −1497.60 864.639i −2.18309 1.26041i
\(687\) 0 0
\(688\) 21.6132 12.4784i 0.0314146 0.0181372i
\(689\) 563.730 325.470i 0.818186 0.472380i
\(690\) 0 0
\(691\) −211.452 + 366.245i −0.306008 + 0.530022i −0.977485 0.211003i \(-0.932327\pi\)
0.671477 + 0.741025i \(0.265660\pi\)
\(692\) −55.9756 −0.0808896
\(693\) 0 0
\(694\) −692.132 −0.997308
\(695\) −18.4217 + 530.929i −0.0265061 + 0.763927i
\(696\) 0 0
\(697\) 217.284 125.449i 0.311742 0.179985i
\(698\) 57.8370 + 100.177i 0.0828611 + 0.143520i
\(699\) 0 0
\(700\) −614.962 + 300.277i −0.878518 + 0.428968i
\(701\) 881.146i 1.25698i −0.777816 0.628492i \(-0.783672\pi\)
0.777816 0.628492i \(-0.216328\pi\)
\(702\) 0 0
\(703\) 155.992i 0.221895i
\(704\) 85.2967 + 49.2461i 0.121160 + 0.0699518i
\(705\) 0 0
\(706\) 177.757 + 307.885i 0.251781 + 0.436097i
\(707\) 104.225 + 180.524i 0.147419 + 0.255338i
\(708\) 0 0
\(709\) −50.7136 + 87.8386i −0.0715284 + 0.123891i −0.899571 0.436774i \(-0.856121\pi\)
0.828043 + 0.560665i \(0.189454\pi\)
\(710\) 348.603 + 655.274i 0.490990 + 0.922921i
\(711\) 0 0
\(712\) 192.621i 0.270536i
\(713\) −664.890 + 1151.62i −0.932525 + 1.61518i
\(714\) 0 0
\(715\) −888.017 554.619i −1.24198 0.775691i
\(716\) −36.4873 + 21.0660i −0.0509599 + 0.0294217i
\(717\) 0 0
\(718\) −635.030 366.635i −0.884443 0.510634i
\(719\) 36.2956i 0.0504807i −0.999681 0.0252404i \(-0.991965\pi\)
0.999681 0.0252404i \(-0.00803511\pi\)
\(720\) 0 0
\(721\) −1055.18 −1.46349
\(722\) −218.174 + 377.888i −0.302180 + 0.523390i
\(723\) 0 0
\(724\) −53.6030 92.8432i −0.0740373 0.128236i
\(725\) 36.6223 527.107i 0.0505135 0.727044i
\(726\) 0 0
\(727\) 457.049 + 263.878i 0.628679 + 0.362968i 0.780240 0.625480i \(-0.215097\pi\)
−0.151561 + 0.988448i \(0.548430\pi\)
\(728\) −658.441 −0.904452
\(729\) 0 0
\(730\) 7.01515 + 13.1865i 0.00960980 + 0.0180637i
\(731\) 37.2801 + 21.5237i 0.0509988 + 0.0294442i
\(732\) 0 0
\(733\) 1130.97 652.966i 1.54293 0.890813i 0.544282 0.838902i \(-0.316802\pi\)
0.998652 0.0519106i \(-0.0165311\pi\)
\(734\) 418.842 241.819i 0.570630 0.329453i
\(735\) 0 0
\(736\) −98.4264 + 170.480i −0.133732 + 0.231630i
\(737\) −1583.48 −2.14855
\(738\) 0 0
\(739\) 754.875 1.02148 0.510741 0.859735i \(-0.329371\pi\)
0.510741 + 0.859735i \(0.329371\pi\)
\(740\) −215.251 7.46858i −0.290879 0.0100927i
\(741\) 0 0
\(742\) 641.565 370.408i 0.864643 0.499202i
\(743\) 656.294 + 1136.73i 0.883302 + 1.52992i 0.847647 + 0.530560i \(0.178018\pi\)
0.0356548 + 0.999364i \(0.488648\pi\)
\(744\) 0 0
\(745\) 70.7534 + 2.45494i 0.0949710 + 0.00329522i
\(746\) 155.992i 0.209105i
\(747\) 0 0
\(748\) 169.887i 0.227121i
\(749\) −929.621 536.717i −1.24115 0.716578i
\(750\) 0 0
\(751\) −616.216 1067.32i −0.820528 1.42120i −0.905290 0.424795i \(-0.860346\pi\)
0.0847620 0.996401i \(-0.472987\pi\)
\(752\) −80.4020 139.260i −0.106918 0.185187i
\(753\) 0 0
\(754\) 254.184 440.259i 0.337114 0.583898i
\(755\) −323.730 + 172.223i −0.428781 + 0.228110i
\(756\) 0 0
\(757\) 401.164i 0.529939i 0.964257 + 0.264970i \(0.0853619\pi\)
−0.964257 + 0.264970i \(0.914638\pi\)
\(758\) 229.347 397.240i 0.302568 0.524064i
\(759\) 0 0
\(760\) 86.8746 + 54.2583i 0.114309 + 0.0713925i
\(761\) −454.776 + 262.565i −0.597603 + 0.345027i −0.768098 0.640332i \(-0.778797\pi\)
0.170495 + 0.985359i \(0.445463\pi\)
\(762\) 0 0
\(763\) 1733.91 + 1001.07i 2.27249 + 1.31202i
\(764\) 446.047i 0.583831i
\(765\) 0 0
\(766\) 809.609 1.05693
\(767\) −354.037 + 613.209i −0.461586 + 0.799491i
\(768\) 0 0
\(769\) 271.375 + 470.035i 0.352894 + 0.611229i 0.986755 0.162217i \(-0.0518645\pi\)
−0.633862 + 0.773446i \(0.718531\pi\)
\(770\) −1010.63 631.196i −1.31250 0.819735i
\(771\) 0 0
\(772\) 305.228 + 176.224i 0.395373 + 0.228269i
\(773\) 522.640 0.676119 0.338059 0.941125i \(-0.390230\pi\)
0.338059 + 0.941125i \(0.390230\pi\)
\(774\) 0 0
\(775\) −533.860 + 792.243i −0.688852 + 1.02225i
\(776\) 247.995 + 143.180i 0.319581 + 0.184510i
\(777\) 0 0
\(778\) 883.857 510.295i 1.13606 0.655906i
\(779\) 228.091 131.688i 0.292800 0.169048i
\(780\) 0 0
\(781\) −646.154 + 1119.17i −0.827342 + 1.43300i
\(782\) −339.546 −0.434202
\(783\) 0 0
\(784\) −553.352 −0.705807
\(785\) 350.515 + 12.1619i 0.446516 + 0.0154928i
\(786\) 0 0
\(787\) −717.835 + 414.442i −0.912116 + 0.526610i −0.881111 0.472909i \(-0.843204\pi\)
−0.0310043 + 0.999519i \(0.509871\pi\)
\(788\) 277.586 + 480.793i 0.352266 + 0.610143i
\(789\) 0 0
\(790\) 10.8121 311.614i 0.0136862 0.394449i
\(791\) 744.942i 0.941773i
\(792\) 0 0
\(793\) 256.125i 0.322982i
\(794\) 464.571 + 268.220i 0.585102 + 0.337809i
\(795\) 0 0
\(796\) −71.5736 123.969i −0.0899166 0.155740i
\(797\) 306.803 + 531.398i 0.384947 + 0.666748i 0.991762 0.128095i \(-0.0408863\pi\)
−0.606815 + 0.794843i \(0.707553\pi\)
\(798\) 0 0
\(799\) 138.683 240.207i 0.173571 0.300634i
\(800\) −79.0294 + 117.279i −0.0987868 + 0.146599i
\(801\) 0 0
\(802\) 496.352i 0.618892i
\(803\) −13.0030 + 22.5218i −0.0161930 + 0.0280471i
\(804\) 0 0
\(805\) 1261.55 2019.90i 1.56714 2.50920i
\(806\) −796.008 + 459.576i −0.987604 + 0.570193i
\(807\) 0 0
\(808\) 37.3049 + 21.5380i 0.0461695 + 0.0266559i
\(809\) 545.471i 0.674254i −0.941459 0.337127i \(-0.890545\pi\)
0.941459 0.337127i \(-0.109455\pi\)
\(810\) 0 0
\(811\) −293.192 −0.361519 −0.180759 0.983527i \(-0.557856\pi\)
−0.180759 + 0.983527i \(0.557856\pi\)
\(812\) 289.279 501.046i 0.356255 0.617052i
\(813\) 0 0
\(814\) −187.500 324.760i −0.230345 0.398968i
\(815\) −23.9957 + 38.4202i −0.0294426 + 0.0471414i
\(816\) 0 0
\(817\) 39.1342 + 22.5942i 0.0478999 + 0.0276550i
\(818\) 754.379 0.922224
\(819\) 0 0
\(820\) 170.794 + 321.044i 0.208285 + 0.391517i
\(821\) 739.318 + 426.846i 0.900509 + 0.519909i 0.877365 0.479823i \(-0.159299\pi\)
0.0231439 + 0.999732i \(0.492632\pi\)
\(822\) 0 0
\(823\) 175.349 101.238i 0.213060 0.123010i −0.389673 0.920953i \(-0.627412\pi\)
0.602733 + 0.797943i \(0.294079\pi\)
\(824\) −188.837 + 109.025i −0.229171 + 0.132312i
\(825\) 0 0
\(826\) −402.919 + 697.876i −0.487795 + 0.844886i
\(827\) 15.3734 0.0185894 0.00929471 0.999957i \(-0.497041\pi\)
0.00929471 + 0.999957i \(0.497041\pi\)
\(828\) 0 0
\(829\) −1135.22 −1.36938 −0.684692 0.728833i \(-0.740063\pi\)
−0.684692 + 0.728833i \(0.740063\pi\)
\(830\) −13.4919 + 388.847i −0.0162553 + 0.468491i
\(831\) 0 0
\(832\) −117.836 + 68.0328i −0.141630 + 0.0817702i
\(833\) −477.231 826.589i −0.572907 0.992304i
\(834\) 0 0
\(835\) 11.0709 319.072i 0.0132586 0.382122i
\(836\) 178.336i 0.213320i
\(837\) 0 0
\(838\) 339.065i 0.404612i
\(839\) 215.216 + 124.255i 0.256515 + 0.148099i 0.622744 0.782426i \(-0.286018\pi\)
−0.366229 + 0.930525i \(0.619351\pi\)
\(840\) 0 0
\(841\) −197.154 341.481i −0.234428 0.406041i
\(842\) 300.479 + 520.444i 0.356863 + 0.618105i
\(843\) 0 0
\(844\) −319.492 + 553.377i −0.378546 + 0.655660i
\(845\) 530.938 282.457i 0.628329 0.334269i
\(846\) 0 0
\(847\) 418.465i 0.494056i
\(848\) 76.5442 132.578i 0.0902643 0.156342i
\(849\) 0 0
\(850\) −243.347 16.9073i −0.286291 0.0198909i
\(851\) 649.087 374.750i 0.762734 0.440365i
\(852\) 0 0
\(853\) 17.4261 + 10.0609i 0.0204291 + 0.0117948i 0.510180 0.860068i \(-0.329579\pi\)
−0.489751 + 0.871863i \(0.662912\pi\)
\(854\) 291.488i 0.341321i
\(855\) 0 0
\(856\) −221.823 −0.259139
\(857\) 92.7837 160.706i 0.108266 0.187522i −0.806802 0.590822i \(-0.798804\pi\)
0.915068 + 0.403300i \(0.132137\pi\)
\(858\) 0 0
\(859\) 549.239 + 951.309i 0.639393 + 1.10746i 0.985566 + 0.169291i \(0.0541476\pi\)
−0.346173 + 0.938171i \(0.612519\pi\)
\(860\) −33.0509 + 52.9189i −0.0384313 + 0.0615336i
\(861\) 0 0
\(862\) 666.308 + 384.693i 0.772980 + 0.446280i
\(863\) −32.5736 −0.0377446 −0.0188723 0.999822i \(-0.506008\pi\)
−0.0188723 + 0.999822i \(0.506008\pi\)
\(864\) 0 0
\(865\) 123.544 65.7250i 0.142826 0.0759827i
\(866\) 738.197 + 426.198i 0.852421 + 0.492146i
\(867\) 0 0
\(868\) −905.914 + 523.030i −1.04368 + 0.602569i
\(869\) 470.150 271.441i 0.541024 0.312360i
\(870\) 0 0
\(871\) 1093.78 1894.48i 1.25577 2.17506i
\(872\) 413.740 0.474473
\(873\) 0 0
\(874\) −356.434 −0.407819
\(875\) 1004.71 1384.82i 1.14824 1.58265i
\(876\) 0 0
\(877\) −867.139 + 500.643i −0.988756 + 0.570859i −0.904902 0.425619i \(-0.860056\pi\)
−0.0838540 + 0.996478i \(0.526723\pi\)
\(878\) 284.459 + 492.698i 0.323986 + 0.561160i
\(879\) 0 0
\(880\) −246.082 8.53836i −0.279639 0.00970268i
\(881\) 1664.18i 1.88897i 0.328559 + 0.944483i \(0.393437\pi\)
−0.328559 + 0.944483i \(0.606563\pi\)
\(882\) 0 0
\(883\) 221.400i 0.250736i −0.992110 0.125368i \(-0.959989\pi\)
0.992110 0.125368i \(-0.0400112\pi\)
\(884\) −203.253 117.348i −0.229924 0.132747i
\(885\) 0 0
\(886\) −310.077 537.069i −0.349974 0.606172i
\(887\) 829.771 + 1437.21i 0.935481 + 1.62030i 0.773775 + 0.633461i \(0.218366\pi\)
0.161706 + 0.986839i \(0.448300\pi\)
\(888\) 0 0
\(889\) 1089.60 1887.25i 1.22565 2.12289i
\(890\) −226.171 425.136i −0.254124 0.477681i
\(891\) 0 0
\(892\) 324.877i 0.364212i
\(893\) 145.581 252.153i 0.163024 0.282366i
\(894\) 0 0
\(895\) 55.7964 89.3372i 0.0623423 0.0998181i
\(896\) −134.106 + 77.4262i −0.149672 + 0.0864132i
\(897\) 0 0
\(898\) −821.640 474.374i −0.914966 0.528256i
\(899\) 807.640i 0.898376i
\(900\) 0 0
\(901\) 264.058 0.293072
\(902\) −316.576 + 548.325i −0.350971 + 0.607899i
\(903\) 0 0
\(904\) −76.9706 133.317i −0.0851444 0.147474i
\(905\) 227.321 + 141.976i 0.251184 + 0.156879i
\(906\) 0 0
\(907\) 145.920 + 84.2471i 0.160882 + 0.0928854i 0.578280 0.815839i \(-0.303724\pi\)
−0.417397 + 0.908724i \(0.637058\pi\)
\(908\) −482.195 −0.531052
\(909\) 0 0
\(910\) 1453.25 773.123i 1.59698 0.849585i
\(911\) −1252.73 723.264i −1.37511 0.793923i −0.383548 0.923521i \(-0.625298\pi\)
−0.991567 + 0.129598i \(0.958631\pi\)
\(912\) 0 0
\(913\) −586.675 + 338.717i −0.642579 + 0.370993i
\(914\) 851.233 491.460i 0.931327 0.537702i
\(915\) 0 0
\(916\) −102.220 + 177.051i −0.111594 + 0.193287i
\(917\) −1509.73 −1.64638
\(918\) 0 0
\(919\) −1279.60 −1.39239 −0.696193 0.717855i \(-0.745124\pi\)
−0.696193 + 0.717855i \(0.745124\pi\)
\(920\) 17.0653 491.836i 0.0185492 0.534604i
\(921\) 0 0
\(922\) 16.0303 9.25512i 0.0173865 0.0100381i
\(923\) −892.654 1546.12i −0.967122 1.67510i
\(924\) 0 0
\(925\) 483.850 236.257i 0.523081 0.255413i
\(926\) 331.324i 0.357801i
\(927\) 0 0
\(928\) 119.558i 0.128834i
\(929\) 851.532 + 491.632i 0.916612 + 0.529206i 0.882553 0.470214i \(-0.155823\pi\)
0.0340592 + 0.999420i \(0.489157\pi\)
\(930\) 0 0
\(931\) −500.967 867.700i −0.538095 0.932008i
\(932\) 241.966 + 419.097i 0.259620 + 0.449674i
\(933\) 0 0
\(934\) 525.297 909.841i 0.562417 0.974134i
\(935\) −199.476 374.958i −0.213343 0.401024i
\(936\) 0 0
\(937\) 964.938i 1.02982i −0.857245 0.514908i \(-0.827826\pi\)
0.857245 0.514908i \(-0.172174\pi\)
\(938\) 1244.80 2156.05i 1.32708 2.29856i
\(939\) 0 0
\(940\) 340.971 + 212.957i 0.362736 + 0.226550i
\(941\) −891.907 + 514.943i −0.947829 + 0.547230i −0.892406 0.451233i \(-0.850984\pi\)
−0.0554234 + 0.998463i \(0.517651\pi\)
\(942\) 0 0
\(943\) −1095.92 632.729i −1.16216 0.670974i
\(944\) 166.525i 0.176404i
\(945\) 0 0
\(946\) −108.632 −0.114833
\(947\) 93.4340 161.832i 0.0986631 0.170890i −0.812468 0.583005i \(-0.801877\pi\)
0.911132 + 0.412116i \(0.135210\pi\)
\(948\) 0 0
\(949\) −17.9634 31.1136i −0.0189288 0.0327856i
\(950\) −255.450 17.7482i −0.268895 0.0186823i
\(951\) 0 0
\(952\) −231.316 133.550i −0.242979 0.140284i
\(953\) −857.170 −0.899444 −0.449722 0.893169i \(-0.648477\pi\)
−0.449722 + 0.893169i \(0.648477\pi\)
\(954\) 0 0
\(955\) −523.736 984.474i −0.548415 1.03086i
\(956\) 650.313 + 375.458i 0.680244 + 0.392739i
\(957\) 0 0
\(958\) 547.964 316.367i 0.571988 0.330237i
\(959\) −2583.08 + 1491.34i −2.69352 + 1.55510i
\(960\) 0 0
\(961\) −249.624 + 432.362i −0.259755 + 0.449909i
\(962\) 518.059 0.538523
\(963\) 0 0
\(964\) −636.558 −0.660330
\(965\) −880.588 30.5539i −0.912526 0.0316621i
\(966\) 0 0
\(967\) 1068.71 617.021i 1.10518 0.638077i 0.167605 0.985854i \(-0.446397\pi\)
0.937577 + 0.347777i \(0.113063\pi\)
\(968\) −43.2376 74.8897i −0.0446669 0.0773654i
\(969\) 0 0
\(970\) −715.469 24.8247i −0.737597 0.0255925i
\(971\) 1313.38i 1.35261i 0.736624 + 0.676303i \(0.236419\pi\)
−0.736624 + 0.676303i \(0.763581\pi\)
\(972\) 0 0
\(973\) 1454.26i 1.49461i
\(974\) 61.6250 + 35.5792i 0.0632700 + 0.0365289i
\(975\) 0 0
\(976\) 30.1177 + 52.1655i 0.0308583 + 0.0534482i
\(977\) −54.7431 94.8178i −0.0560318 0.0970499i 0.836649 0.547739i \(-0.184511\pi\)
−0.892681 + 0.450690i \(0.851178\pi\)
\(978\) 0 0
\(979\) 419.219 726.109i 0.428212 0.741685i
\(980\) 1221.31 649.731i 1.24623 0.662991i
\(981\) 0 0
\(982\) 1118.12i 1.13862i
\(983\) 170.997 296.176i 0.173955 0.301298i −0.765844 0.643026i \(-0.777679\pi\)
0.939799 + 0.341728i \(0.111012\pi\)
\(984\) 0 0
\(985\) −1177.19 735.227i −1.19512 0.746424i
\(986\) 178.594 103.111i 0.181130 0.104575i
\(987\) 0 0
\(988\) −213.362 123.184i −0.215953 0.124681i
\(989\) 217.118i 0.219533i
\(990\) 0 0
\(991\) 140.258 0.141532 0.0707658 0.997493i \(-0.477456\pi\)
0.0707658 + 0.997493i \(0.477456\pi\)
\(992\) −108.083 + 187.206i −0.108955 + 0.188715i
\(993\) 0 0
\(994\) −1015.90 1759.60i −1.02204 1.77022i
\(995\) 303.532 + 189.573i 0.305057 + 0.190526i
\(996\) 0 0
\(997\) 536.619 + 309.817i 0.538233 + 0.310749i 0.744363 0.667776i \(-0.232753\pi\)
−0.206129 + 0.978525i \(0.566087\pi\)
\(998\) 849.079 0.850781
\(999\) 0 0
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 810.3.j.f.269.4 8
3.2 odd 2 810.3.j.a.269.1 8
5.4 even 2 810.3.j.a.269.2 8
9.2 odd 6 270.3.b.d.269.3 yes 4
9.4 even 3 inner 810.3.j.f.539.3 8
9.5 odd 6 810.3.j.a.539.2 8
9.7 even 3 270.3.b.a.269.2 yes 4
15.14 odd 2 inner 810.3.j.f.269.3 8
36.7 odd 6 2160.3.c.g.1889.2 4
36.11 even 6 2160.3.c.m.1889.3 4
45.2 even 12 1350.3.d.o.701.5 8
45.4 even 6 810.3.j.a.539.1 8
45.7 odd 12 1350.3.d.o.701.1 8
45.14 odd 6 inner 810.3.j.f.539.4 8
45.29 odd 6 270.3.b.a.269.1 4
45.34 even 6 270.3.b.d.269.4 yes 4
45.38 even 12 1350.3.d.o.701.4 8
45.43 odd 12 1350.3.d.o.701.8 8
180.79 odd 6 2160.3.c.m.1889.4 4
180.119 even 6 2160.3.c.g.1889.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
270.3.b.a.269.1 4 45.29 odd 6
270.3.b.a.269.2 yes 4 9.7 even 3
270.3.b.d.269.3 yes 4 9.2 odd 6
270.3.b.d.269.4 yes 4 45.34 even 6
810.3.j.a.269.1 8 3.2 odd 2
810.3.j.a.269.2 8 5.4 even 2
810.3.j.a.539.1 8 45.4 even 6
810.3.j.a.539.2 8 9.5 odd 6
810.3.j.f.269.3 8 15.14 odd 2 inner
810.3.j.f.269.4 8 1.1 even 1 trivial
810.3.j.f.539.3 8 9.4 even 3 inner
810.3.j.f.539.4 8 45.14 odd 6 inner
1350.3.d.o.701.1 8 45.7 odd 12
1350.3.d.o.701.4 8 45.38 even 12
1350.3.d.o.701.5 8 45.2 even 12
1350.3.d.o.701.8 8 45.43 odd 12
2160.3.c.g.1889.1 4 180.119 even 6
2160.3.c.g.1889.2 4 36.7 odd 6
2160.3.c.m.1889.3 4 36.11 even 6
2160.3.c.m.1889.4 4 180.79 odd 6