Properties

Label 30.3.b.a.29.4
Level $30$
Weight $3$
Character 30.29
Analytic conductor $0.817$
Analytic rank $0$
Dimension $4$
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] = [30,3,Mod(29,30)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(30, 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("30.29");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 30.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.817440793081\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-17})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 16x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 29.4
Root \(-0.707107 - 2.91548i\) of defining polynomial
Character \(\chi\) \(=\) 30.29
Dual form 30.3.b.a.29.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.41421 q^{2} +(-0.707107 + 2.91548i) q^{3} +2.00000 q^{4} +(-2.82843 - 4.12311i) q^{5} +(-1.00000 + 4.12311i) q^{6} -5.83095i q^{7} +2.82843 q^{8} +(-8.00000 - 4.12311i) q^{9} +O(q^{10})\) \(q+1.41421 q^{2} +(-0.707107 + 2.91548i) q^{3} +2.00000 q^{4} +(-2.82843 - 4.12311i) q^{5} +(-1.00000 + 4.12311i) q^{6} -5.83095i q^{7} +2.82843 q^{8} +(-8.00000 - 4.12311i) q^{9} +(-4.00000 - 5.83095i) q^{10} +16.4924i q^{11} +(-1.41421 + 5.83095i) q^{12} -8.24621i q^{14} +(14.0208 - 5.33074i) q^{15} +4.00000 q^{16} -11.3137 q^{17} +(-11.3137 - 5.83095i) q^{18} +12.0000 q^{19} +(-5.65685 - 8.24621i) q^{20} +(17.0000 + 4.12311i) q^{21} +23.3238i q^{22} +24.0416 q^{23} +(-2.00000 + 8.24621i) q^{24} +(-9.00000 + 23.3238i) q^{25} +(17.6777 - 20.4083i) q^{27} -11.6619i q^{28} +(19.8284 - 7.53880i) q^{30} -32.0000 q^{31} +5.65685 q^{32} +(-48.0833 - 11.6619i) q^{33} -16.0000 q^{34} +(-24.0416 + 16.4924i) q^{35} +(-16.0000 - 8.24621i) q^{36} -23.3238i q^{37} +16.9706 q^{38} +(-8.00000 - 11.6619i) q^{40} -57.7235i q^{41} +(24.0416 + 5.83095i) q^{42} +40.8167i q^{43} +32.9848i q^{44} +(5.62742 + 44.6467i) q^{45} +34.0000 q^{46} -35.3553 q^{47} +(-2.82843 + 11.6619i) q^{48} +15.0000 q^{49} +(-12.7279 + 32.9848i) q^{50} +(8.00000 - 32.9848i) q^{51} +67.8823 q^{53} +(25.0000 - 28.8617i) q^{54} +(68.0000 - 46.6476i) q^{55} -16.4924i q^{56} +(-8.48528 + 34.9857i) q^{57} +16.4924i q^{59} +(28.0416 - 10.6615i) q^{60} -16.0000 q^{61} -45.2548 q^{62} +(-24.0416 + 46.6476i) q^{63} +8.00000 q^{64} +(-68.0000 - 16.4924i) q^{66} +5.83095i q^{67} -22.6274 q^{68} +(-17.0000 + 70.0928i) q^{69} +(-34.0000 + 23.3238i) q^{70} +(-22.6274 - 11.6619i) q^{72} -116.619i q^{73} -32.9848i q^{74} +(-61.6360 - 42.7317i) q^{75} +24.0000 q^{76} +96.1665 q^{77} -72.0000 q^{79} +(-11.3137 - 16.4924i) q^{80} +(47.0000 + 65.9697i) q^{81} -81.6333i q^{82} -43.8406 q^{83} +(34.0000 + 8.24621i) q^{84} +(32.0000 + 46.6476i) q^{85} +57.7235i q^{86} +46.6476i q^{88} -65.9697i q^{89} +(7.95837 + 63.1400i) q^{90} +48.0833 q^{92} +(22.6274 - 93.2952i) q^{93} -50.0000 q^{94} +(-33.9411 - 49.4773i) q^{95} +(-4.00000 + 16.4924i) q^{96} +163.267i q^{97} +21.2132 q^{98} +(68.0000 - 131.939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{4} - 4 q^{6} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 8 q^{4} - 4 q^{6} - 32 q^{9} - 16 q^{10} + 8 q^{15} + 16 q^{16} + 48 q^{19} + 68 q^{21} - 8 q^{24} - 36 q^{25} + 68 q^{30} - 128 q^{31} - 64 q^{34} - 64 q^{36} - 32 q^{40} - 68 q^{45} + 136 q^{46} + 60 q^{49} + 32 q^{51} + 100 q^{54} + 272 q^{55} + 16 q^{60} - 64 q^{61} + 32 q^{64} - 272 q^{66} - 68 q^{69} - 136 q^{70} - 272 q^{75} + 96 q^{76} - 288 q^{79} + 188 q^{81} + 136 q^{84} + 128 q^{85} + 128 q^{90} - 200 q^{94} - 16 q^{96} + 272 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/30\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 0.707107
\(3\) −0.707107 + 2.91548i −0.235702 + 0.971825i
\(4\) 2.00000 0.500000
\(5\) −2.82843 4.12311i −0.565685 0.824621i
\(6\) −1.00000 + 4.12311i −0.166667 + 0.687184i
\(7\) 5.83095i 0.832993i −0.909137 0.416497i \(-0.863258\pi\)
0.909137 0.416497i \(-0.136742\pi\)
\(8\) 2.82843 0.353553
\(9\) −8.00000 4.12311i −0.888889 0.458123i
\(10\) −4.00000 5.83095i −0.400000 0.583095i
\(11\) 16.4924i 1.49931i 0.661828 + 0.749656i \(0.269781\pi\)
−0.661828 + 0.749656i \(0.730219\pi\)
\(12\) −1.41421 + 5.83095i −0.117851 + 0.485913i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 8.24621i 0.589015i
\(15\) 14.0208 5.33074i 0.934721 0.355382i
\(16\) 4.00000 0.250000
\(17\) −11.3137 −0.665512 −0.332756 0.943013i \(-0.607979\pi\)
−0.332756 + 0.943013i \(0.607979\pi\)
\(18\) −11.3137 5.83095i −0.628539 0.323942i
\(19\) 12.0000 0.631579 0.315789 0.948829i \(-0.397731\pi\)
0.315789 + 0.948829i \(0.397731\pi\)
\(20\) −5.65685 8.24621i −0.282843 0.412311i
\(21\) 17.0000 + 4.12311i 0.809524 + 0.196338i
\(22\) 23.3238i 1.06017i
\(23\) 24.0416 1.04529 0.522644 0.852551i \(-0.324946\pi\)
0.522644 + 0.852551i \(0.324946\pi\)
\(24\) −2.00000 + 8.24621i −0.0833333 + 0.343592i
\(25\) −9.00000 + 23.3238i −0.360000 + 0.932952i
\(26\) 0 0
\(27\) 17.6777 20.4083i 0.654729 0.755864i
\(28\) 11.6619i 0.416497i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 19.8284 7.53880i 0.660948 0.251293i
\(31\) −32.0000 −1.03226 −0.516129 0.856511i \(-0.672628\pi\)
−0.516129 + 0.856511i \(0.672628\pi\)
\(32\) 5.65685 0.176777
\(33\) −48.0833 11.6619i −1.45707 0.353391i
\(34\) −16.0000 −0.470588
\(35\) −24.0416 + 16.4924i −0.686904 + 0.471212i
\(36\) −16.0000 8.24621i −0.444444 0.229061i
\(37\) 23.3238i 0.630373i −0.949030 0.315187i \(-0.897933\pi\)
0.949030 0.315187i \(-0.102067\pi\)
\(38\) 16.9706 0.446594
\(39\) 0 0
\(40\) −8.00000 11.6619i −0.200000 0.291548i
\(41\) 57.7235i 1.40789i −0.710255 0.703945i \(-0.751420\pi\)
0.710255 0.703945i \(-0.248580\pi\)
\(42\) 24.0416 + 5.83095i 0.572420 + 0.138832i
\(43\) 40.8167i 0.949225i 0.880195 + 0.474612i \(0.157412\pi\)
−0.880195 + 0.474612i \(0.842588\pi\)
\(44\) 32.9848i 0.749656i
\(45\) 5.62742 + 44.6467i 0.125054 + 0.992150i
\(46\) 34.0000 0.739130
\(47\) −35.3553 −0.752241 −0.376121 0.926571i \(-0.622742\pi\)
−0.376121 + 0.926571i \(0.622742\pi\)
\(48\) −2.82843 + 11.6619i −0.0589256 + 0.242956i
\(49\) 15.0000 0.306122
\(50\) −12.7279 + 32.9848i −0.254558 + 0.659697i
\(51\) 8.00000 32.9848i 0.156863 0.646762i
\(52\) 0 0
\(53\) 67.8823 1.28080 0.640399 0.768043i \(-0.278769\pi\)
0.640399 + 0.768043i \(0.278769\pi\)
\(54\) 25.0000 28.8617i 0.462963 0.534477i
\(55\) 68.0000 46.6476i 1.23636 0.848138i
\(56\) 16.4924i 0.294508i
\(57\) −8.48528 + 34.9857i −0.148865 + 0.613784i
\(58\) 0 0
\(59\) 16.4924i 0.279533i 0.990185 + 0.139766i \(0.0446351\pi\)
−0.990185 + 0.139766i \(0.955365\pi\)
\(60\) 28.0416 10.6615i 0.467361 0.177691i
\(61\) −16.0000 −0.262295 −0.131148 0.991363i \(-0.541866\pi\)
−0.131148 + 0.991363i \(0.541866\pi\)
\(62\) −45.2548 −0.729917
\(63\) −24.0416 + 46.6476i −0.381613 + 0.740438i
\(64\) 8.00000 0.125000
\(65\) 0 0
\(66\) −68.0000 16.4924i −1.03030 0.249885i
\(67\) 5.83095i 0.0870291i 0.999053 + 0.0435146i \(0.0138555\pi\)
−0.999053 + 0.0435146i \(0.986145\pi\)
\(68\) −22.6274 −0.332756
\(69\) −17.0000 + 70.0928i −0.246377 + 1.01584i
\(70\) −34.0000 + 23.3238i −0.485714 + 0.333197i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −22.6274 11.6619i −0.314270 0.161971i
\(73\) 116.619i 1.59752i −0.601649 0.798761i \(-0.705489\pi\)
0.601649 0.798761i \(-0.294511\pi\)
\(74\) 32.9848i 0.445741i
\(75\) −61.6360 42.7317i −0.821814 0.569756i
\(76\) 24.0000 0.315789
\(77\) 96.1665 1.24892
\(78\) 0 0
\(79\) −72.0000 −0.911392 −0.455696 0.890135i \(-0.650610\pi\)
−0.455696 + 0.890135i \(0.650610\pi\)
\(80\) −11.3137 16.4924i −0.141421 0.206155i
\(81\) 47.0000 + 65.9697i 0.580247 + 0.814441i
\(82\) 81.6333i 0.995528i
\(83\) −43.8406 −0.528200 −0.264100 0.964495i \(-0.585075\pi\)
−0.264100 + 0.964495i \(0.585075\pi\)
\(84\) 34.0000 + 8.24621i 0.404762 + 0.0981692i
\(85\) 32.0000 + 46.6476i 0.376471 + 0.548795i
\(86\) 57.7235i 0.671203i
\(87\) 0 0
\(88\) 46.6476i 0.530087i
\(89\) 65.9697i 0.741232i −0.928786 0.370616i \(-0.879147\pi\)
0.928786 0.370616i \(-0.120853\pi\)
\(90\) 7.95837 + 63.1400i 0.0884263 + 0.701556i
\(91\) 0 0
\(92\) 48.0833 0.522644
\(93\) 22.6274 93.2952i 0.243306 1.00317i
\(94\) −50.0000 −0.531915
\(95\) −33.9411 49.4773i −0.357275 0.520813i
\(96\) −4.00000 + 16.4924i −0.0416667 + 0.171796i
\(97\) 163.267i 1.68316i 0.540131 + 0.841581i \(0.318375\pi\)
−0.540131 + 0.841581i \(0.681625\pi\)
\(98\) 21.2132 0.216461
\(99\) 68.0000 131.939i 0.686869 1.33272i
\(100\) −18.0000 + 46.6476i −0.180000 + 0.466476i
\(101\) 131.939i 1.30633i 0.757215 + 0.653165i \(0.226559\pi\)
−0.757215 + 0.653165i \(0.773441\pi\)
\(102\) 11.3137 46.6476i 0.110919 0.457330i
\(103\) 99.1262i 0.962390i 0.876614 + 0.481195i \(0.159797\pi\)
−0.876614 + 0.481195i \(0.840203\pi\)
\(104\) 0 0
\(105\) −31.0833 81.7547i −0.296031 0.778616i
\(106\) 96.0000 0.905660
\(107\) −55.1543 −0.515461 −0.257731 0.966217i \(-0.582975\pi\)
−0.257731 + 0.966217i \(0.582975\pi\)
\(108\) 35.3553 40.8167i 0.327364 0.377932i
\(109\) 80.0000 0.733945 0.366972 0.930232i \(-0.380394\pi\)
0.366972 + 0.930232i \(0.380394\pi\)
\(110\) 96.1665 65.9697i 0.874241 0.599724i
\(111\) 68.0000 + 16.4924i 0.612613 + 0.148580i
\(112\) 23.3238i 0.208248i
\(113\) −152.735 −1.35164 −0.675819 0.737068i \(-0.736210\pi\)
−0.675819 + 0.737068i \(0.736210\pi\)
\(114\) −12.0000 + 49.4773i −0.105263 + 0.434011i
\(115\) −68.0000 99.1262i −0.591304 0.861967i
\(116\) 0 0
\(117\) 0 0
\(118\) 23.3238i 0.197659i
\(119\) 65.9697i 0.554367i
\(120\) 39.6569 15.0776i 0.330474 0.125647i
\(121\) −151.000 −1.24793
\(122\) −22.6274 −0.185471
\(123\) 168.291 + 40.8167i 1.36822 + 0.331843i
\(124\) −64.0000 −0.516129
\(125\) 121.622 28.8617i 0.972979 0.230894i
\(126\) −34.0000 + 65.9697i −0.269841 + 0.523569i
\(127\) 40.8167i 0.321391i −0.987004 0.160696i \(-0.948626\pi\)
0.987004 0.160696i \(-0.0513737\pi\)
\(128\) 11.3137 0.0883883
\(129\) −119.000 28.8617i −0.922481 0.223734i
\(130\) 0 0
\(131\) 49.4773i 0.377689i 0.982007 + 0.188845i \(0.0604742\pi\)
−0.982007 + 0.188845i \(0.939526\pi\)
\(132\) −96.1665 23.3238i −0.728534 0.176696i
\(133\) 69.9714i 0.526101i
\(134\) 8.24621i 0.0615389i
\(135\) −134.146 15.1634i −0.993672 0.112322i
\(136\) −32.0000 −0.235294
\(137\) −50.9117 −0.371618 −0.185809 0.982586i \(-0.559491\pi\)
−0.185809 + 0.982586i \(0.559491\pi\)
\(138\) −24.0416 + 99.1262i −0.174215 + 0.718306i
\(139\) 44.0000 0.316547 0.158273 0.987395i \(-0.449407\pi\)
0.158273 + 0.987395i \(0.449407\pi\)
\(140\) −48.0833 + 32.9848i −0.343452 + 0.235606i
\(141\) 25.0000 103.078i 0.177305 0.731047i
\(142\) 0 0
\(143\) 0 0
\(144\) −32.0000 16.4924i −0.222222 0.114531i
\(145\) 0 0
\(146\) 164.924i 1.12962i
\(147\) −10.6066 + 43.7321i −0.0721538 + 0.297498i
\(148\) 46.6476i 0.315187i
\(149\) 8.24621i 0.0553437i −0.999617 0.0276718i \(-0.991191\pi\)
0.999617 0.0276718i \(-0.00880935\pi\)
\(150\) −87.1665 60.4318i −0.581110 0.402878i
\(151\) 136.000 0.900662 0.450331 0.892862i \(-0.351306\pi\)
0.450331 + 0.892862i \(0.351306\pi\)
\(152\) 33.9411 0.223297
\(153\) 90.5097 + 46.6476i 0.591566 + 0.304886i
\(154\) 136.000 0.883117
\(155\) 90.5097 + 131.939i 0.583933 + 0.851222i
\(156\) 0 0
\(157\) 116.619i 0.742796i −0.928474 0.371398i \(-0.878878\pi\)
0.928474 0.371398i \(-0.121122\pi\)
\(158\) −101.823 −0.644452
\(159\) −48.0000 + 197.909i −0.301887 + 1.24471i
\(160\) −16.0000 23.3238i −0.100000 0.145774i
\(161\) 140.186i 0.870718i
\(162\) 66.4680 + 93.2952i 0.410297 + 0.575896i
\(163\) 99.1262i 0.608136i 0.952650 + 0.304068i \(0.0983450\pi\)
−0.952650 + 0.304068i \(0.901655\pi\)
\(164\) 115.447i 0.703945i
\(165\) 87.9167 + 231.237i 0.532829 + 1.40144i
\(166\) −62.0000 −0.373494
\(167\) 292.742 1.75295 0.876474 0.481450i \(-0.159890\pi\)
0.876474 + 0.481450i \(0.159890\pi\)
\(168\) 48.0833 + 11.6619i 0.286210 + 0.0694161i
\(169\) 169.000 1.00000
\(170\) 45.2548 + 65.9697i 0.266205 + 0.388057i
\(171\) −96.0000 49.4773i −0.561404 0.289341i
\(172\) 81.6333i 0.474612i
\(173\) −164.049 −0.948259 −0.474129 0.880455i \(-0.657237\pi\)
−0.474129 + 0.880455i \(0.657237\pi\)
\(174\) 0 0
\(175\) 136.000 + 52.4786i 0.777143 + 0.299878i
\(176\) 65.9697i 0.374828i
\(177\) −48.0833 11.6619i −0.271657 0.0658865i
\(178\) 93.2952i 0.524131i
\(179\) 16.4924i 0.0921364i 0.998938 + 0.0460682i \(0.0146692\pi\)
−0.998938 + 0.0460682i \(0.985331\pi\)
\(180\) 11.2548 + 89.2935i 0.0625269 + 0.496075i
\(181\) −82.0000 −0.453039 −0.226519 0.974007i \(-0.572735\pi\)
−0.226519 + 0.974007i \(0.572735\pi\)
\(182\) 0 0
\(183\) 11.3137 46.6476i 0.0618235 0.254905i
\(184\) 68.0000 0.369565
\(185\) −96.1665 + 65.9697i −0.519819 + 0.356593i
\(186\) 32.0000 131.939i 0.172043 0.709352i
\(187\) 186.590i 0.997810i
\(188\) −70.7107 −0.376121
\(189\) −119.000 103.078i −0.629630 0.545384i
\(190\) −48.0000 69.9714i −0.252632 0.368271i
\(191\) 296.864i 1.55426i −0.629340 0.777130i \(-0.716675\pi\)
0.629340 0.777130i \(-0.283325\pi\)
\(192\) −5.65685 + 23.3238i −0.0294628 + 0.121478i
\(193\) 116.619i 0.604244i −0.953269 0.302122i \(-0.902305\pi\)
0.953269 0.302122i \(-0.0976950\pi\)
\(194\) 230.894i 1.19017i
\(195\) 0 0
\(196\) 30.0000 0.153061
\(197\) −192.333 −0.976310 −0.488155 0.872757i \(-0.662330\pi\)
−0.488155 + 0.872757i \(0.662330\pi\)
\(198\) 96.1665 186.590i 0.485690 0.942376i
\(199\) −312.000 −1.56784 −0.783920 0.620862i \(-0.786783\pi\)
−0.783920 + 0.620862i \(0.786783\pi\)
\(200\) −25.4558 + 65.9697i −0.127279 + 0.329848i
\(201\) −17.0000 4.12311i −0.0845771 0.0205130i
\(202\) 186.590i 0.923715i
\(203\) 0 0
\(204\) 16.0000 65.9697i 0.0784314 0.323381i
\(205\) −238.000 + 163.267i −1.16098 + 0.796423i
\(206\) 140.186i 0.680513i
\(207\) −192.333 99.1262i −0.929145 0.478870i
\(208\) 0 0
\(209\) 197.909i 0.946933i
\(210\) −43.9584 115.619i −0.209326 0.550565i
\(211\) −12.0000 −0.0568720 −0.0284360 0.999596i \(-0.509053\pi\)
−0.0284360 + 0.999596i \(0.509053\pi\)
\(212\) 135.765 0.640399
\(213\) 0 0
\(214\) −78.0000 −0.364486
\(215\) 168.291 115.447i 0.782751 0.536963i
\(216\) 50.0000 57.7235i 0.231481 0.267238i
\(217\) 186.590i 0.859864i
\(218\) 113.137 0.518977
\(219\) 340.000 + 82.4621i 1.55251 + 0.376539i
\(220\) 136.000 93.2952i 0.618182 0.424069i
\(221\) 0 0
\(222\) 96.1665 + 23.3238i 0.433183 + 0.105062i
\(223\) 40.8167i 0.183034i 0.995803 + 0.0915172i \(0.0291716\pi\)
−0.995803 + 0.0915172i \(0.970828\pi\)
\(224\) 32.9848i 0.147254i
\(225\) 168.167 149.483i 0.747407 0.664367i
\(226\) −216.000 −0.955752
\(227\) −159.806 −0.703992 −0.351996 0.936002i \(-0.614497\pi\)
−0.351996 + 0.936002i \(0.614497\pi\)
\(228\) −16.9706 + 69.9714i −0.0744323 + 0.306892i
\(229\) 82.0000 0.358079 0.179039 0.983842i \(-0.442701\pi\)
0.179039 + 0.983842i \(0.442701\pi\)
\(230\) −96.1665 140.186i −0.418115 0.609503i
\(231\) −68.0000 + 280.371i −0.294372 + 1.21373i
\(232\) 0 0
\(233\) 192.333 0.825464 0.412732 0.910853i \(-0.364575\pi\)
0.412732 + 0.910853i \(0.364575\pi\)
\(234\) 0 0
\(235\) 100.000 + 145.774i 0.425532 + 0.620314i
\(236\) 32.9848i 0.139766i
\(237\) 50.9117 209.914i 0.214817 0.885714i
\(238\) 93.2952i 0.391997i
\(239\) 461.788i 1.93217i −0.258231 0.966083i \(-0.583139\pi\)
0.258231 0.966083i \(-0.416861\pi\)
\(240\) 56.0833 21.3229i 0.233680 0.0888456i
\(241\) 304.000 1.26141 0.630705 0.776022i \(-0.282766\pi\)
0.630705 + 0.776022i \(0.282766\pi\)
\(242\) −213.546 −0.882423
\(243\) −225.567 + 90.3798i −0.928260 + 0.371933i
\(244\) −32.0000 −0.131148
\(245\) −42.4264 61.8466i −0.173169 0.252435i
\(246\) 238.000 + 57.7235i 0.967480 + 0.234648i
\(247\) 0 0
\(248\) −90.5097 −0.364958
\(249\) 31.0000 127.816i 0.124498 0.513318i
\(250\) 172.000 40.8167i 0.688000 0.163267i
\(251\) 346.341i 1.37984i 0.723884 + 0.689922i \(0.242355\pi\)
−0.723884 + 0.689922i \(0.757645\pi\)
\(252\) −48.0833 + 93.2952i −0.190807 + 0.370219i
\(253\) 396.505i 1.56721i
\(254\) 57.7235i 0.227258i
\(255\) −158.627 + 60.3104i −0.622068 + 0.236511i
\(256\) 16.0000 0.0625000
\(257\) 390.323 1.51877 0.759383 0.650644i \(-0.225501\pi\)
0.759383 + 0.650644i \(0.225501\pi\)
\(258\) −168.291 40.8167i −0.652292 0.158204i
\(259\) −136.000 −0.525097
\(260\) 0 0
\(261\) 0 0
\(262\) 69.9714i 0.267066i
\(263\) 295.571 1.12384 0.561921 0.827191i \(-0.310062\pi\)
0.561921 + 0.827191i \(0.310062\pi\)
\(264\) −136.000 32.9848i −0.515152 0.124943i
\(265\) −192.000 279.886i −0.724528 1.05617i
\(266\) 98.9545i 0.372010i
\(267\) 192.333 + 46.6476i 0.720348 + 0.174710i
\(268\) 11.6619i 0.0435146i
\(269\) 74.2159i 0.275896i 0.990440 + 0.137948i \(0.0440506\pi\)
−0.990440 + 0.137948i \(0.955949\pi\)
\(270\) −189.711 21.4443i −0.702632 0.0794234i
\(271\) 40.0000 0.147601 0.0738007 0.997273i \(-0.476487\pi\)
0.0738007 + 0.997273i \(0.476487\pi\)
\(272\) −45.2548 −0.166378
\(273\) 0 0
\(274\) −72.0000 −0.262774
\(275\) −384.666 148.432i −1.39879 0.539752i
\(276\) −34.0000 + 140.186i −0.123188 + 0.507919i
\(277\) 443.152i 1.59983i −0.600115 0.799914i \(-0.704878\pi\)
0.600115 0.799914i \(-0.295122\pi\)
\(278\) 62.2254 0.223832
\(279\) 256.000 + 131.939i 0.917563 + 0.472901i
\(280\) −68.0000 + 46.6476i −0.242857 + 0.166599i
\(281\) 519.511i 1.84879i 0.381431 + 0.924397i \(0.375431\pi\)
−0.381431 + 0.924397i \(0.624569\pi\)
\(282\) 35.3553 145.774i 0.125374 0.516928i
\(283\) 320.702i 1.13322i −0.823985 0.566612i \(-0.808254\pi\)
0.823985 0.566612i \(-0.191746\pi\)
\(284\) 0 0
\(285\) 168.250 63.9688i 0.590350 0.224452i
\(286\) 0 0
\(287\) −336.583 −1.17276
\(288\) −45.2548 23.3238i −0.157135 0.0809854i
\(289\) −161.000 −0.557093
\(290\) 0 0
\(291\) −476.000 115.447i −1.63574 0.396725i
\(292\) 233.238i 0.798761i
\(293\) 84.8528 0.289600 0.144800 0.989461i \(-0.453746\pi\)
0.144800 + 0.989461i \(0.453746\pi\)
\(294\) −15.0000 + 61.8466i −0.0510204 + 0.210363i
\(295\) 68.0000 46.6476i 0.230508 0.158128i
\(296\) 65.9697i 0.222871i
\(297\) 336.583 + 291.548i 1.13328 + 0.981642i
\(298\) 11.6619i 0.0391339i
\(299\) 0 0
\(300\) −123.272 85.4634i −0.410907 0.284878i
\(301\) 238.000 0.790698
\(302\) 192.333 0.636864
\(303\) −384.666 93.2952i −1.26953 0.307905i
\(304\) 48.0000 0.157895
\(305\) 45.2548 + 65.9697i 0.148377 + 0.216294i
\(306\) 128.000 + 65.9697i 0.418301 + 0.215587i
\(307\) 367.350i 1.19658i 0.801280 + 0.598290i \(0.204153\pi\)
−0.801280 + 0.598290i \(0.795847\pi\)
\(308\) 192.333 0.624458
\(309\) −289.000 70.0928i −0.935275 0.226838i
\(310\) 128.000 + 186.590i 0.412903 + 0.601905i
\(311\) 98.9545i 0.318182i −0.987264 0.159091i \(-0.949144\pi\)
0.987264 0.159091i \(-0.0508563\pi\)
\(312\) 0 0
\(313\) 186.590i 0.596136i −0.954545 0.298068i \(-0.903658\pi\)
0.954545 0.298068i \(-0.0963422\pi\)
\(314\) 164.924i 0.525236i
\(315\) 260.333 32.8132i 0.826454 0.104169i
\(316\) −144.000 −0.455696
\(317\) −520.431 −1.64174 −0.820868 0.571117i \(-0.806510\pi\)
−0.820868 + 0.571117i \(0.806510\pi\)
\(318\) −67.8823 + 279.886i −0.213466 + 0.880144i
\(319\) 0 0
\(320\) −22.6274 32.9848i −0.0707107 0.103078i
\(321\) 39.0000 160.801i 0.121495 0.500938i
\(322\) 198.252i 0.615691i
\(323\) −135.765 −0.420324
\(324\) 94.0000 + 131.939i 0.290123 + 0.407220i
\(325\) 0 0
\(326\) 140.186i 0.430017i
\(327\) −56.5685 + 233.238i −0.172992 + 0.713266i
\(328\) 163.267i 0.497764i
\(329\) 206.155i 0.626612i
\(330\) 124.333 + 327.019i 0.376767 + 0.990966i
\(331\) 292.000 0.882175 0.441088 0.897464i \(-0.354593\pi\)
0.441088 + 0.897464i \(0.354593\pi\)
\(332\) −87.6812 −0.264100
\(333\) −96.1665 + 186.590i −0.288788 + 0.560332i
\(334\) 414.000 1.23952
\(335\) 24.0416 16.4924i 0.0717661 0.0492311i
\(336\) 68.0000 + 16.4924i 0.202381 + 0.0490846i
\(337\) 326.533i 0.968942i 0.874807 + 0.484471i \(0.160988\pi\)
−0.874807 + 0.484471i \(0.839012\pi\)
\(338\) 239.002 0.707107
\(339\) 108.000 445.295i 0.318584 1.31356i
\(340\) 64.0000 + 93.2952i 0.188235 + 0.274398i
\(341\) 527.758i 1.54768i
\(342\) −135.765 69.9714i −0.396972 0.204595i
\(343\) 373.181i 1.08799i
\(344\) 115.447i 0.335602i
\(345\) 337.083 128.160i 0.977053 0.371477i
\(346\) −232.000 −0.670520
\(347\) 394.566 1.13708 0.568538 0.822657i \(-0.307509\pi\)
0.568538 + 0.822657i \(0.307509\pi\)
\(348\) 0 0
\(349\) 254.000 0.727794 0.363897 0.931439i \(-0.381446\pi\)
0.363897 + 0.931439i \(0.381446\pi\)
\(350\) 192.333 + 74.2159i 0.549523 + 0.212045i
\(351\) 0 0
\(352\) 93.2952i 0.265043i
\(353\) 345.068 0.977530 0.488765 0.872415i \(-0.337448\pi\)
0.488765 + 0.872415i \(0.337448\pi\)
\(354\) −68.0000 16.4924i −0.192090 0.0465888i
\(355\) 0 0
\(356\) 131.939i 0.370616i
\(357\) −192.333 46.6476i −0.538748 0.130666i
\(358\) 23.3238i 0.0651503i
\(359\) 395.818i 1.10256i 0.834321 + 0.551279i \(0.185860\pi\)
−0.834321 + 0.551279i \(0.814140\pi\)
\(360\) 15.9167 + 126.280i 0.0442132 + 0.350778i
\(361\) −217.000 −0.601108
\(362\) −115.966 −0.320347
\(363\) 106.773 440.237i 0.294141 1.21277i
\(364\) 0 0
\(365\) −480.833 + 329.848i −1.31735 + 0.903694i
\(366\) 16.0000 65.9697i 0.0437158 0.180245i
\(367\) 413.998i 1.12806i 0.825755 + 0.564029i \(0.190750\pi\)
−0.825755 + 0.564029i \(0.809250\pi\)
\(368\) 96.1665 0.261322
\(369\) −238.000 + 461.788i −0.644986 + 1.25146i
\(370\) −136.000 + 93.2952i −0.367568 + 0.252149i
\(371\) 395.818i 1.06690i
\(372\) 45.2548 186.590i 0.121653 0.501587i
\(373\) 629.743i 1.68832i 0.536092 + 0.844159i \(0.319900\pi\)
−0.536092 + 0.844159i \(0.680100\pi\)
\(374\) 263.879i 0.705558i
\(375\) −1.85429 + 374.995i −0.00494478 + 0.999988i
\(376\) −100.000 −0.265957
\(377\) 0 0
\(378\) −168.291 145.774i −0.445215 0.385645i
\(379\) −572.000 −1.50923 −0.754617 0.656165i \(-0.772178\pi\)
−0.754617 + 0.656165i \(0.772178\pi\)
\(380\) −67.8823 98.9545i −0.178638 0.260407i
\(381\) 119.000 + 28.8617i 0.312336 + 0.0757526i
\(382\) 419.829i 1.09903i
\(383\) −193.747 −0.505868 −0.252934 0.967484i \(-0.581395\pi\)
−0.252934 + 0.967484i \(0.581395\pi\)
\(384\) −8.00000 + 32.9848i −0.0208333 + 0.0858980i
\(385\) −272.000 396.505i −0.706494 1.02988i
\(386\) 164.924i 0.427265i
\(387\) 168.291 326.533i 0.434862 0.843755i
\(388\) 326.533i 0.841581i
\(389\) 387.572i 0.996329i −0.867083 0.498164i \(-0.834008\pi\)
0.867083 0.498164i \(-0.165992\pi\)
\(390\) 0 0
\(391\) −272.000 −0.695652
\(392\) 42.4264 0.108231
\(393\) −144.250 34.9857i −0.367048 0.0890222i
\(394\) −272.000 −0.690355
\(395\) 203.647 + 296.864i 0.515561 + 0.751553i
\(396\) 136.000 263.879i 0.343434 0.666361i
\(397\) 513.124i 1.29250i −0.763124 0.646252i \(-0.776336\pi\)
0.763124 0.646252i \(-0.223664\pi\)
\(398\) −441.235 −1.10863
\(399\) 204.000 + 49.4773i 0.511278 + 0.124003i
\(400\) −36.0000 + 93.2952i −0.0900000 + 0.233238i
\(401\) 65.9697i 0.164513i −0.996611 0.0822565i \(-0.973787\pi\)
0.996611 0.0822565i \(-0.0262127\pi\)
\(402\) −24.0416 5.83095i −0.0598051 0.0145049i
\(403\) 0 0
\(404\) 263.879i 0.653165i
\(405\) 139.064 380.376i 0.343368 0.939201i
\(406\) 0 0
\(407\) 384.666 0.945126
\(408\) 22.6274 93.2952i 0.0554594 0.228665i
\(409\) 640.000 1.56479 0.782396 0.622781i \(-0.213997\pi\)
0.782396 + 0.622781i \(0.213997\pi\)
\(410\) −336.583 + 230.894i −0.820934 + 0.563156i
\(411\) 36.0000 148.432i 0.0875912 0.361148i
\(412\) 198.252i 0.481195i
\(413\) 96.1665 0.232849
\(414\) −272.000 140.186i −0.657005 0.338613i
\(415\) 124.000 + 180.760i 0.298795 + 0.435565i
\(416\) 0 0
\(417\) −31.1127 + 128.281i −0.0746108 + 0.307628i
\(418\) 279.886i 0.669583i
\(419\) 577.235i 1.37765i 0.724928 + 0.688824i \(0.241873\pi\)
−0.724928 + 0.688824i \(0.758127\pi\)
\(420\) −62.1665 163.509i −0.148016 0.389308i
\(421\) −656.000 −1.55819 −0.779097 0.626903i \(-0.784322\pi\)
−0.779097 + 0.626903i \(0.784322\pi\)
\(422\) −16.9706 −0.0402146
\(423\) 282.843 + 145.774i 0.668659 + 0.344619i
\(424\) 192.000 0.452830
\(425\) 101.823 263.879i 0.239584 0.620891i
\(426\) 0 0
\(427\) 93.2952i 0.218490i
\(428\) −110.309 −0.257731
\(429\) 0 0
\(430\) 238.000 163.267i 0.553488 0.379690i
\(431\) 362.833i 0.841841i 0.907098 + 0.420920i \(0.138293\pi\)
−0.907098 + 0.420920i \(0.861707\pi\)
\(432\) 70.7107 81.6333i 0.163682 0.188966i
\(433\) 163.267i 0.377059i 0.982068 + 0.188530i \(0.0603722\pi\)
−0.982068 + 0.188530i \(0.939628\pi\)
\(434\) 263.879i 0.608016i
\(435\) 0 0
\(436\) 160.000 0.366972
\(437\) 288.500 0.660182
\(438\) 480.833 + 116.619i 1.09779 + 0.266254i
\(439\) 432.000 0.984055 0.492027 0.870580i \(-0.336256\pi\)
0.492027 + 0.870580i \(0.336256\pi\)
\(440\) 192.333 131.939i 0.437121 0.299862i
\(441\) −120.000 61.8466i −0.272109 0.140242i
\(442\) 0 0
\(443\) 123.037 0.277735 0.138867 0.990311i \(-0.455654\pi\)
0.138867 + 0.990311i \(0.455654\pi\)
\(444\) 136.000 + 32.9848i 0.306306 + 0.0742902i
\(445\) −272.000 + 186.590i −0.611236 + 0.419304i
\(446\) 57.7235i 0.129425i
\(447\) 24.0416 + 5.83095i 0.0537844 + 0.0130446i
\(448\) 46.6476i 0.104124i
\(449\) 865.852i 1.92840i −0.265174 0.964201i \(-0.585429\pi\)
0.265174 0.964201i \(-0.414571\pi\)
\(450\) 237.823 211.400i 0.528496 0.469778i
\(451\) 952.000 2.11086
\(452\) −305.470 −0.675819
\(453\) −96.1665 + 396.505i −0.212288 + 0.875286i
\(454\) −226.000 −0.497797
\(455\) 0 0
\(456\) −24.0000 + 98.9545i −0.0526316 + 0.217006i
\(457\) 466.476i 1.02074i 0.859956 + 0.510368i \(0.170491\pi\)
−0.859956 + 0.510368i \(0.829509\pi\)
\(458\) 115.966 0.253200
\(459\) −200.000 + 230.894i −0.435730 + 0.503037i
\(460\) −136.000 198.252i −0.295652 0.430983i
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) −96.1665 + 396.505i −0.208153 + 0.858235i
\(463\) 612.250i 1.32235i −0.750230 0.661177i \(-0.770057\pi\)
0.750230 0.661177i \(-0.229943\pi\)
\(464\) 0 0
\(465\) −448.666 + 170.584i −0.964873 + 0.366846i
\(466\) 272.000 0.583691
\(467\) −767.918 −1.64436 −0.822182 0.569225i \(-0.807243\pi\)
−0.822182 + 0.569225i \(0.807243\pi\)
\(468\) 0 0
\(469\) 34.0000 0.0724947
\(470\) 141.421 + 206.155i 0.300897 + 0.438628i
\(471\) 340.000 + 82.4621i 0.721868 + 0.175079i
\(472\) 46.6476i 0.0988297i
\(473\) −673.166 −1.42318
\(474\) 72.0000 296.864i 0.151899 0.626295i
\(475\) −108.000 + 279.886i −0.227368 + 0.589233i
\(476\) 131.939i 0.277184i
\(477\) −543.058 279.886i −1.13849 0.586762i
\(478\) 653.067i 1.36625i
\(479\) 560.742i 1.17065i −0.810798 0.585326i \(-0.800967\pi\)
0.810798 0.585326i \(-0.199033\pi\)
\(480\) 79.3137 30.1552i 0.165237 0.0628233i
\(481\) 0 0
\(482\) 429.921 0.891952
\(483\) 408.708 + 99.1262i 0.846186 + 0.205230i
\(484\) −302.000 −0.623967
\(485\) 673.166 461.788i 1.38797 0.952140i
\(486\) −319.000 + 127.816i −0.656379 + 0.262996i
\(487\) 647.236i 1.32903i −0.747277 0.664513i \(-0.768639\pi\)
0.747277 0.664513i \(-0.231361\pi\)
\(488\) −45.2548 −0.0927353
\(489\) −289.000 70.0928i −0.591002 0.143339i
\(490\) −60.0000 87.4643i −0.122449 0.178499i
\(491\) 346.341i 0.705379i 0.935740 + 0.352689i \(0.114733\pi\)
−0.935740 + 0.352689i \(0.885267\pi\)
\(492\) 336.583 + 81.6333i 0.684111 + 0.165921i
\(493\) 0 0
\(494\) 0 0
\(495\) −736.333 + 92.8097i −1.48754 + 0.187494i
\(496\) −128.000 −0.258065
\(497\) 0 0
\(498\) 43.8406 180.760i 0.0880334 0.362971i
\(499\) −660.000 −1.32265 −0.661323 0.750102i \(-0.730005\pi\)
−0.661323 + 0.750102i \(0.730005\pi\)
\(500\) 243.245 57.7235i 0.486489 0.115447i
\(501\) −207.000 + 853.483i −0.413174 + 1.70356i
\(502\) 489.800i 0.975697i
\(503\) −182.434 −0.362691 −0.181345 0.983419i \(-0.558045\pi\)
−0.181345 + 0.983419i \(0.558045\pi\)
\(504\) −68.0000 + 131.939i −0.134921 + 0.261784i
\(505\) 544.000 373.181i 1.07723 0.738972i
\(506\) 560.742i 1.10819i
\(507\) −119.501 + 492.715i −0.235702 + 0.971825i
\(508\) 81.6333i 0.160696i
\(509\) 395.818i 0.777639i 0.921314 + 0.388819i \(0.127117\pi\)
−0.921314 + 0.388819i \(0.872883\pi\)
\(510\) −224.333 + 85.2918i −0.439869 + 0.167239i
\(511\) −680.000 −1.33072
\(512\) 22.6274 0.0441942
\(513\) 212.132 244.900i 0.413513 0.477388i
\(514\) 552.000 1.07393
\(515\) 408.708 280.371i 0.793607 0.544410i
\(516\) −238.000 57.7235i −0.461240 0.111867i
\(517\) 583.095i 1.12784i
\(518\) −192.333 −0.371299
\(519\) 116.000 478.280i 0.223507 0.921542i
\(520\) 0 0
\(521\) 131.939i 0.253243i 0.991951 + 0.126621i \(0.0404133\pi\)
−0.991951 + 0.126621i \(0.959587\pi\)
\(522\) 0 0
\(523\) 145.774i 0.278726i −0.990241 0.139363i \(-0.955494\pi\)
0.990241 0.139363i \(-0.0445055\pi\)
\(524\) 98.9545i 0.188845i
\(525\) −249.167 + 359.397i −0.474603 + 0.684565i
\(526\) 418.000 0.794677
\(527\) 362.039 0.686980
\(528\) −192.333 46.6476i −0.364267 0.0883478i
\(529\) 49.0000 0.0926276
\(530\) −271.529 395.818i −0.512319 0.746827i
\(531\) 68.0000 131.939i 0.128060 0.248473i
\(532\) 139.943i 0.263050i
\(533\) 0 0
\(534\) 272.000 + 65.9697i 0.509363 + 0.123539i
\(535\) 156.000 + 227.407i 0.291589 + 0.425060i
\(536\) 16.4924i 0.0307694i
\(537\) −48.0833 11.6619i −0.0895405 0.0217168i
\(538\) 104.957i 0.195088i
\(539\) 247.386i 0.458973i
\(540\) −268.291 30.3268i −0.496836 0.0561608i
\(541\) 418.000 0.772643 0.386322 0.922364i \(-0.373745\pi\)
0.386322 + 0.922364i \(0.373745\pi\)
\(542\) 56.5685 0.104370
\(543\) 57.9828 239.069i 0.106782 0.440274i
\(544\) −64.0000 −0.117647
\(545\) −226.274 329.848i −0.415182 0.605227i
\(546\) 0 0
\(547\) 285.717i 0.522334i −0.965294 0.261167i \(-0.915893\pi\)
0.965294 0.261167i \(-0.0841073\pi\)
\(548\) −101.823 −0.185809
\(549\) 128.000 + 65.9697i 0.233151 + 0.120163i
\(550\) −544.000 209.914i −0.989091 0.381662i
\(551\) 0 0
\(552\) −48.0833 + 198.252i −0.0871074 + 0.359153i
\(553\) 419.829i 0.759184i
\(554\) 626.712i 1.13125i
\(555\) −124.333 327.019i −0.224024 0.589223i
\(556\) 88.0000 0.158273
\(557\) 424.264 0.761695 0.380847 0.924638i \(-0.375632\pi\)
0.380847 + 0.924638i \(0.375632\pi\)
\(558\) 362.039 + 186.590i 0.648815 + 0.334392i
\(559\) 0 0
\(560\) −96.1665 + 65.9697i −0.171726 + 0.117803i
\(561\) 544.000 + 131.939i 0.969697 + 0.235186i
\(562\) 734.700i 1.30730i
\(563\) −813.173 −1.44436 −0.722178 0.691707i \(-0.756859\pi\)
−0.722178 + 0.691707i \(0.756859\pi\)
\(564\) 50.0000 206.155i 0.0886525 0.365524i
\(565\) 432.000 + 629.743i 0.764602 + 1.11459i
\(566\) 453.542i 0.801310i
\(567\) 384.666 274.055i 0.678423 0.483342i
\(568\) 0 0
\(569\) 453.542i 0.797085i 0.917150 + 0.398543i \(0.130484\pi\)
−0.917150 + 0.398543i \(0.869516\pi\)
\(570\) 237.941 90.4656i 0.417441 0.158712i
\(571\) 220.000 0.385289 0.192644 0.981269i \(-0.438294\pi\)
0.192644 + 0.981269i \(0.438294\pi\)
\(572\) 0 0
\(573\) 865.499 + 209.914i 1.51047 + 0.366343i
\(574\) −476.000 −0.829268
\(575\) −216.375 + 560.742i −0.376304 + 0.975204i
\(576\) −64.0000 32.9848i −0.111111 0.0572654i
\(577\) 46.6476i 0.0808451i 0.999183 + 0.0404225i \(0.0128704\pi\)
−0.999183 + 0.0404225i \(0.987130\pi\)
\(578\) −227.688 −0.393925
\(579\) 340.000 + 82.4621i 0.587219 + 0.142422i
\(580\) 0 0
\(581\) 255.633i 0.439987i
\(582\) −673.166 163.267i −1.15664 0.280527i
\(583\) 1119.54i 1.92031i
\(584\) 329.848i 0.564809i
\(585\) 0 0
\(586\) 120.000 0.204778
\(587\) 55.1543 0.0939597 0.0469798 0.998896i \(-0.485040\pi\)
0.0469798 + 0.998896i \(0.485040\pi\)
\(588\) −21.2132 + 87.4643i −0.0360769 + 0.148749i
\(589\) −384.000 −0.651952
\(590\) 96.1665 65.9697i 0.162994 0.111813i
\(591\) 136.000 560.742i 0.230118 0.948803i
\(592\) 93.2952i 0.157593i
\(593\) 390.323 0.658217 0.329109 0.944292i \(-0.393252\pi\)
0.329109 + 0.944292i \(0.393252\pi\)
\(594\) 476.000 + 412.311i 0.801347 + 0.694126i
\(595\) 272.000 186.590i 0.457143 0.313597i
\(596\) 16.4924i 0.0276718i
\(597\) 220.617 909.628i 0.369543 1.52367i
\(598\) 0 0
\(599\) 98.9545i 0.165200i −0.996583 0.0825998i \(-0.973678\pi\)
0.996583 0.0825998i \(-0.0263223\pi\)
\(600\) −174.333 120.864i −0.290555 0.201439i
\(601\) −880.000 −1.46423 −0.732113 0.681183i \(-0.761466\pi\)
−0.732113 + 0.681183i \(0.761466\pi\)
\(602\) 336.583 0.559108
\(603\) 24.0416 46.6476i 0.0398700 0.0773592i
\(604\) 272.000 0.450331
\(605\) 427.092 + 622.589i 0.705938 + 1.02907i
\(606\) −544.000 131.939i −0.897690 0.217722i
\(607\) 425.659i 0.701251i 0.936516 + 0.350626i \(0.114031\pi\)
−0.936516 + 0.350626i \(0.885969\pi\)
\(608\) 67.8823 0.111648
\(609\) 0 0
\(610\) 64.0000 + 93.2952i 0.104918 + 0.152943i
\(611\) 0 0
\(612\) 181.019 + 93.2952i 0.295783 + 0.152443i
\(613\) 606.419i 0.989264i −0.869102 0.494632i \(-0.835303\pi\)
0.869102 0.494632i \(-0.164697\pi\)
\(614\) 519.511i 0.846110i
\(615\) −307.709 809.330i −0.500339 1.31598i
\(616\) 272.000 0.441558
\(617\) −113.137 −0.183366 −0.0916832 0.995788i \(-0.529225\pi\)
−0.0916832 + 0.995788i \(0.529225\pi\)
\(618\) −408.708 99.1262i −0.661339 0.160398i
\(619\) 52.0000 0.0840065 0.0420032 0.999117i \(-0.486626\pi\)
0.0420032 + 0.999117i \(0.486626\pi\)
\(620\) 181.019 + 263.879i 0.291967 + 0.425611i
\(621\) 425.000 490.650i 0.684380 0.790096i
\(622\) 139.943i 0.224988i
\(623\) −384.666 −0.617442
\(624\) 0 0
\(625\) −463.000 419.829i −0.740800 0.671726i
\(626\) 263.879i 0.421532i
\(627\) −576.999 139.943i −0.920254 0.223194i
\(628\) 233.238i 0.371398i
\(629\) 263.879i 0.419521i
\(630\) 368.167 46.4049i 0.584391 0.0736585i
\(631\) −544.000 −0.862124 −0.431062 0.902322i \(-0.641861\pi\)
−0.431062 + 0.902322i \(0.641861\pi\)
\(632\) −203.647 −0.322226
\(633\) 8.48528 34.9857i 0.0134049 0.0552697i
\(634\) −736.000 −1.16088
\(635\) −168.291 + 115.447i −0.265026 + 0.181806i
\(636\) −96.0000 + 395.818i −0.150943 + 0.622356i
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −32.0000 46.6476i −0.0500000 0.0728869i
\(641\) 849.360i 1.32505i −0.749038 0.662527i \(-0.769484\pi\)
0.749038 0.662527i \(-0.230516\pi\)
\(642\) 55.1543 227.407i 0.0859102 0.354217i
\(643\) 367.350i 0.571306i 0.958333 + 0.285653i \(0.0922105\pi\)
−0.958333 + 0.285653i \(0.907789\pi\)
\(644\) 280.371i 0.435359i
\(645\) 217.583 + 572.283i 0.337338 + 0.887260i
\(646\) −192.000 −0.297214
\(647\) −971.565 −1.50165 −0.750823 0.660504i \(-0.770343\pi\)
−0.750823 + 0.660504i \(0.770343\pi\)
\(648\) 132.936 + 186.590i 0.205148 + 0.287948i
\(649\) −272.000 −0.419106
\(650\) 0 0
\(651\) −544.000 131.939i −0.835637 0.202672i
\(652\) 198.252i 0.304068i
\(653\) 350.725 0.537098 0.268549 0.963266i \(-0.413456\pi\)
0.268549 + 0.963266i \(0.413456\pi\)
\(654\) −80.0000 + 329.848i −0.122324 + 0.504355i
\(655\) 204.000 139.943i 0.311450 0.213653i
\(656\) 230.894i 0.351972i
\(657\) −480.833 + 932.952i −0.731861 + 1.42002i
\(658\) 291.548i 0.443081i
\(659\) 577.235i 0.875925i −0.898993 0.437963i \(-0.855700\pi\)
0.898993 0.437963i \(-0.144300\pi\)
\(660\) 175.833 + 462.474i 0.266414 + 0.700719i
\(661\) 80.0000 0.121029 0.0605144 0.998167i \(-0.480726\pi\)
0.0605144 + 0.998167i \(0.480726\pi\)
\(662\) 412.950 0.623792
\(663\) 0 0
\(664\) −124.000 −0.186747
\(665\) −288.500 + 197.909i −0.433834 + 0.297608i
\(666\) −136.000 + 263.879i −0.204204 + 0.396214i
\(667\) 0 0
\(668\) 585.484 0.876474
\(669\) −119.000 28.8617i −0.177877 0.0431416i
\(670\) 34.0000 23.3238i 0.0507463 0.0348117i
\(671\) 263.879i 0.393262i
\(672\) 96.1665 + 23.3238i 0.143105 + 0.0347080i
\(673\) 489.800i 0.727786i −0.931441 0.363893i \(-0.881447\pi\)
0.931441 0.363893i \(-0.118553\pi\)
\(674\) 461.788i 0.685145i
\(675\) 316.901 + 595.986i 0.469483 + 0.882942i
\(676\) 338.000 0.500000
\(677\) 192.333 0.284096 0.142048 0.989860i \(-0.454631\pi\)
0.142048 + 0.989860i \(0.454631\pi\)
\(678\) 152.735 629.743i 0.225273 0.928824i
\(679\) 952.000 1.40206
\(680\) 90.5097 + 131.939i 0.133102 + 0.194029i
\(681\) 113.000 465.911i 0.165932 0.684157i
\(682\) 746.362i 1.09437i
\(683\) 236.174 0.345789 0.172894 0.984940i \(-0.444688\pi\)
0.172894 + 0.984940i \(0.444688\pi\)
\(684\) −192.000 98.9545i −0.280702 0.144670i
\(685\) 144.000 + 209.914i 0.210219 + 0.306444i
\(686\) 527.758i 0.769326i
\(687\) −57.9828 + 239.069i −0.0843999 + 0.347990i
\(688\) 163.267i 0.237306i
\(689\) 0 0
\(690\) 476.708 181.245i 0.690881 0.262674i
\(691\) −548.000 −0.793054 −0.396527 0.918023i \(-0.629785\pi\)
−0.396527 + 0.918023i \(0.629785\pi\)
\(692\) −328.098 −0.474129
\(693\) −769.332 396.505i −1.11015 0.572157i
\(694\) 558.000 0.804035
\(695\) −124.451 181.417i −0.179066 0.261031i
\(696\) 0 0
\(697\) 653.067i 0.936968i
\(698\) 359.210 0.514628
\(699\) −136.000 + 560.742i −0.194564 + 0.802207i
\(700\) 272.000 + 104.957i 0.388571 + 0.149939i
\(701\) 57.7235i 0.0823445i −0.999152 0.0411722i \(-0.986891\pi\)
0.999152 0.0411722i \(-0.0131092\pi\)
\(702\) 0 0
\(703\) 279.886i 0.398130i
\(704\) 131.939i 0.187414i
\(705\) −495.711 + 188.470i −0.703136 + 0.267333i
\(706\) 488.000 0.691218
\(707\) 769.332 1.08816
\(708\) −96.1665 23.3238i −0.135828 0.0329432i
\(709\) 1230.00 1.73484 0.867419 0.497579i \(-0.165777\pi\)
0.867419 + 0.497579i \(0.165777\pi\)
\(710\) 0 0
\(711\) 576.000 + 296.864i 0.810127 + 0.417530i
\(712\) 186.590i 0.262065i
\(713\) −769.332 −1.07901
\(714\) −272.000 65.9697i −0.380952 0.0923945i
\(715\) 0 0
\(716\) 32.9848i 0.0460682i
\(717\) 1346.33 + 326.533i 1.87773 + 0.455416i
\(718\) 559.771i 0.779626i
\(719\) 626.712i 0.871644i 0.900033 + 0.435822i \(0.143542\pi\)
−0.900033 + 0.435822i \(0.856458\pi\)
\(720\) 22.5097 + 178.587i 0.0312634 + 0.248037i
\(721\) 578.000 0.801664
\(722\) −306.884 −0.425048
\(723\) −214.960 + 886.305i −0.297317 + 1.22587i
\(724\) −164.000 −0.226519
\(725\) 0 0
\(726\) 151.000 622.589i 0.207989 0.857561i
\(727\) 367.350i 0.505296i −0.967558 0.252648i \(-0.918699\pi\)
0.967558 0.252648i \(-0.0813014\pi\)
\(728\) 0 0
\(729\) −104.000 721.543i −0.142661 0.989772i
\(730\) −680.000 + 466.476i −0.931507 + 0.639008i
\(731\) 461.788i 0.631721i
\(732\) 22.6274 93.2952i 0.0309118 0.127453i
\(733\) 1002.92i 1.36825i −0.729367 0.684123i \(-0.760185\pi\)
0.729367 0.684123i \(-0.239815\pi\)
\(734\) 585.481i 0.797658i
\(735\) 210.312 79.9610i 0.286139 0.108791i
\(736\) 136.000 0.184783
\(737\) −96.1665 −0.130484
\(738\) −336.583 + 653.067i −0.456074 + 0.884914i
\(739\) −340.000 −0.460081 −0.230041 0.973181i \(-0.573886\pi\)
−0.230041 + 0.973181i \(0.573886\pi\)
\(740\) −192.333 + 131.939i −0.259910 + 0.178296i
\(741\) 0 0
\(742\) 559.771i 0.754409i
\(743\) 1243.09 1.67307 0.836537 0.547911i \(-0.184577\pi\)
0.836537 + 0.547911i \(0.184577\pi\)
\(744\) 64.0000 263.879i 0.0860215 0.354676i
\(745\) −34.0000 + 23.3238i −0.0456376 + 0.0313071i
\(746\) 890.591i 1.19382i
\(747\) 350.725 + 180.760i 0.469511 + 0.241981i
\(748\) 373.181i 0.498905i
\(749\) 321.602i 0.429375i
\(750\) −2.62237 + 530.324i −0.00349649 + 0.707098i
\(751\) −520.000 −0.692410 −0.346205 0.938159i \(-0.612530\pi\)
−0.346205 + 0.938159i \(0.612530\pi\)
\(752\) −141.421 −0.188060
\(753\) −1009.75 244.900i −1.34097 0.325232i
\(754\) 0 0
\(755\) −384.666 560.742i −0.509492 0.742705i
\(756\) −238.000 206.155i −0.314815 0.272692i
\(757\) 816.333i 1.07838i 0.842184 + 0.539190i \(0.181269\pi\)
−0.842184 + 0.539190i \(0.818731\pi\)
\(758\) −808.930 −1.06719
\(759\) −1156.00 280.371i −1.52306 0.369395i
\(760\) −96.0000 139.943i −0.126316 0.184135i
\(761\) 395.818i 0.520129i 0.965591 + 0.260064i \(0.0837438\pi\)
−0.965591 + 0.260064i \(0.916256\pi\)
\(762\) 168.291 + 40.8167i 0.220855 + 0.0535652i
\(763\) 466.476i 0.611371i
\(764\) 593.727i 0.777130i
\(765\) −63.6670 505.120i −0.0832248 0.660288i
\(766\) −274.000 −0.357702
\(767\) 0 0
\(768\) −11.3137 + 46.6476i −0.0147314 + 0.0607391i
\(769\) −306.000 −0.397919 −0.198960 0.980008i \(-0.563756\pi\)
−0.198960 + 0.980008i \(0.563756\pi\)
\(770\) −384.666 560.742i −0.499566 0.728237i
\(771\) −276.000 + 1137.98i −0.357977 + 1.47598i
\(772\) 233.238i 0.302122i
\(773\) 305.470 0.395175 0.197587 0.980285i \(-0.436689\pi\)
0.197587 + 0.980285i \(0.436689\pi\)
\(774\) 238.000 461.788i 0.307494 0.596625i
\(775\) 288.000 746.362i 0.371613 0.963048i
\(776\) 461.788i 0.595087i
\(777\) 96.1665 396.505i 0.123766 0.510302i
\(778\) 548.109i 0.704511i
\(779\) 692.682i 0.889194i
\(780\) 0 0
\(781\) 0 0
\(782\) −384.666 −0.491900
\(783\) 0 0
\(784\) 60.0000 0.0765306
\(785\) −480.833 + 329.848i −0.612526 + 0.420189i
\(786\) −204.000 49.4773i −0.259542 0.0629482i
\(787\) 565.602i 0.718681i −0.933206 0.359341i \(-0.883002\pi\)
0.933206 0.359341i \(-0.116998\pi\)
\(788\) −384.666 −0.488155
\(789\) −209.000 + 861.729i −0.264892 + 1.09218i
\(790\) 288.000 + 419.829i 0.364557 + 0.531429i
\(791\) 890.591i 1.12590i
\(792\) 192.333 373.181i 0.242845 0.471188i
\(793\) 0 0
\(794\) 725.667i 0.913938i
\(795\) 951.765 361.862i 1.19719 0.455173i
\(796\) −624.000 −0.783920
\(797\) −1063.49 −1.33436 −0.667182 0.744894i \(-0.732500\pi\)
−0.667182 + 0.744894i \(0.732500\pi\)
\(798\) 288.500 + 69.9714i 0.361528 + 0.0876835i
\(799\) 400.000 0.500626
\(800\) −50.9117 + 131.939i −0.0636396 + 0.164924i
\(801\) −272.000 + 527.758i −0.339576 + 0.658873i
\(802\) 93.2952i 0.116328i
\(803\) 1923.33 2.39518
\(804\) −34.0000 8.24621i −0.0422886 0.0102565i
\(805\) −578.000 + 396.505i −0.718012 + 0.492552i
\(806\) 0 0
\(807\) −216.375 52.4786i −0.268122 0.0650292i
\(808\) 373.181i 0.461858i
\(809\) 791.636i 0.978537i −0.872133 0.489268i \(-0.837264\pi\)
0.872133 0.489268i \(-0.162736\pi\)
\(810\) 196.666 537.933i 0.242798 0.664115i
\(811\) 436.000 0.537608 0.268804 0.963195i \(-0.413372\pi\)
0.268804 + 0.963195i \(0.413372\pi\)
\(812\) 0 0
\(813\) −28.2843 + 116.619i −0.0347900 + 0.143443i
\(814\) 544.000 0.668305
\(815\) 408.708 280.371i 0.501482 0.344014i
\(816\) 32.0000 131.939i 0.0392157 0.161690i
\(817\) 489.800i 0.599510i
\(818\) 905.097 1.10648
\(819\) 0 0
\(820\) −476.000 + 326.533i −0.580488 + 0.398211i
\(821\) 799.882i 0.974278i 0.873324 + 0.487139i \(0.161960\pi\)
−0.873324 + 0.487139i \(0.838040\pi\)
\(822\) 50.9117 209.914i 0.0619364 0.255370i
\(823\) 1311.96i 1.59412i 0.603897 + 0.797062i \(0.293614\pi\)
−0.603897 + 0.797062i \(0.706386\pi\)
\(824\) 280.371i 0.340256i
\(825\) 704.749 1016.53i 0.854242 1.23215i
\(826\) 136.000 0.164649
\(827\) 985.707 1.19191 0.595953 0.803019i \(-0.296774\pi\)
0.595953 + 0.803019i \(0.296774\pi\)
\(828\) −384.666 198.252i −0.464573 0.239435i
\(829\) −1488.00 −1.79493 −0.897467 0.441082i \(-0.854595\pi\)
−0.897467 + 0.441082i \(0.854595\pi\)
\(830\) 175.362 + 255.633i 0.211280 + 0.307991i
\(831\) 1292.00 + 313.356i 1.55475 + 0.377083i
\(832\) 0 0
\(833\) −169.706 −0.203728
\(834\) −44.0000 + 181.417i −0.0527578 + 0.217526i
\(835\) −828.000 1207.01i −0.991617 1.44552i
\(836\) 395.818i 0.473467i
\(837\) −565.685 + 653.067i −0.675849 + 0.780247i
\(838\) 816.333i 0.974145i
\(839\) 461.788i 0.550403i 0.961387 + 0.275201i \(0.0887445\pi\)
−0.961387 + 0.275201i \(0.911255\pi\)
\(840\) −87.9167 231.237i −0.104663 0.275282i
\(841\) 841.000 1.00000
\(842\) −927.724 −1.10181
\(843\) −1514.62 367.350i −1.79671 0.435765i
\(844\) −24.0000 −0.0284360
\(845\) −478.004 696.805i −0.565685 0.824621i
\(846\) 400.000 + 206.155i 0.472813 + 0.243682i
\(847\) 880.474i 1.03952i
\(848\) 271.529 0.320199
\(849\) 935.000 + 226.771i 1.10130 + 0.267103i
\(850\) 144.000 373.181i 0.169412 0.439036i
\(851\) 560.742i 0.658922i
\(852\) 0 0
\(853\) 326.533i 0.382806i 0.981512 + 0.191403i \(0.0613037\pi\)
−0.981512 + 0.191403i \(0.938696\pi\)
\(854\) 131.939i 0.154496i
\(855\) 67.5290 + 535.761i 0.0789813 + 0.626621i
\(856\) −156.000 −0.182243
\(857\) −288.500 −0.336639 −0.168319 0.985732i \(-0.553834\pi\)
−0.168319 + 0.985732i \(0.553834\pi\)
\(858\) 0 0
\(859\) 796.000 0.926659 0.463329 0.886186i \(-0.346655\pi\)
0.463329 + 0.886186i \(0.346655\pi\)
\(860\) 336.583 230.894i 0.391375 0.268481i
\(861\) 238.000 981.299i 0.276423 1.13972i
\(862\) 513.124i 0.595271i
\(863\) −352.139 −0.408041 −0.204020 0.978967i \(-0.565401\pi\)
−0.204020 + 0.978967i \(0.565401\pi\)
\(864\) 100.000 115.447i 0.115741 0.133619i
\(865\) 464.000 + 676.390i 0.536416 + 0.781954i
\(866\) 230.894i 0.266621i
\(867\) 113.844 469.392i 0.131308 0.541397i
\(868\) 373.181i 0.429932i
\(869\) 1187.45i 1.36646i
\(870\) 0 0
\(871\) 0 0
\(872\) 226.274 0.259489
\(873\) 673.166 1306.13i 0.771095 1.49614i
\(874\) 408.000 0.466819
\(875\) −168.291 709.174i −0.192333 0.810485i
\(876\) 680.000 + 164.924i 0.776256 + 0.188270i
\(877\) 676.390i 0.771255i −0.922655 0.385627i \(-0.873985\pi\)
0.922655 0.385627i \(-0.126015\pi\)
\(878\) 610.940 0.695832
\(879\) −60.0000 + 247.386i −0.0682594 + 0.281441i
\(880\) 272.000 186.590i 0.309091 0.212035i
\(881\) 519.511i 0.589684i −0.955546 0.294842i \(-0.904733\pi\)
0.955546 0.294842i \(-0.0952670\pi\)
\(882\) −169.706 87.4643i −0.192410 0.0991658i
\(883\) 1591.85i 1.80277i 0.433014 + 0.901387i \(0.357450\pi\)
−0.433014 + 0.901387i \(0.642550\pi\)
\(884\) 0 0
\(885\) 87.9167 + 231.237i 0.0993409 + 0.261285i
\(886\) 174.000 0.196388
\(887\) −767.918 −0.865747 −0.432874 0.901455i \(-0.642500\pi\)
−0.432874 + 0.901455i \(0.642500\pi\)
\(888\) 192.333 + 46.6476i 0.216591 + 0.0525311i
\(889\) −238.000 −0.267717
\(890\) −384.666 + 263.879i −0.432209 + 0.296493i
\(891\) −1088.00 + 775.144i −1.22110 + 0.869971i
\(892\) 81.6333i 0.0915172i
\(893\) −424.264 −0.475100
\(894\) 34.0000 + 8.24621i 0.0380313 + 0.00922395i
\(895\) 68.0000 46.6476i 0.0759777 0.0521202i
\(896\) 65.9697i 0.0736269i
\(897\) 0 0
\(898\) 1224.50i 1.36359i
\(899\) 0 0
\(900\) 336.333 298.965i 0.373703 0.332183i
\(901\) −768.000 −0.852386
\(902\) 1346.33 1.49261
\(903\) −168.291 + 693.883i −0.186369 + 0.768420i
\(904\) −432.000 −0.477876
\(905\) 231.931 + 338.095i 0.256277 + 0.373585i
\(906\) −136.000 + 560.742i −0.150110 + 0.618921i
\(907\) 332.364i 0.366444i 0.983072 + 0.183222i \(0.0586526\pi\)
−0.983072 + 0.183222i \(0.941347\pi\)
\(908\) −319.612 −0.351996
\(909\) 544.000 1055.52i 0.598460 1.16118i
\(910\) 0 0
\(911\) 692.682i 0.760353i 0.924914 + 0.380177i \(0.124137\pi\)
−0.924914 + 0.380177i \(0.875863\pi\)
\(912\) −33.9411 + 139.943i −0.0372161 + 0.153446i
\(913\) 723.038i 0.791937i
\(914\) 659.697i 0.721769i
\(915\) −224.333 + 85.2918i −0.245173 + 0.0932150i
\(916\) 164.000 0.179039
\(917\) 288.500 0.314612
\(918\) −282.843 + 326.533i −0.308108 + 0.355701i
\(919\) −912.000 −0.992383 −0.496192 0.868213i \(-0.665269\pi\)
−0.496192 + 0.868213i \(0.665269\pi\)
\(920\) −192.333 280.371i −0.209058 0.304751i
\(921\) −1071.00 259.756i −1.16287 0.282037i
\(922\) 0 0
\(923\) 0 0
\(924\) −136.000 + 560.742i −0.147186 + 0.606864i
\(925\) 544.000 + 209.914i 0.588108 + 0.226934i
\(926\) 865.852i 0.935046i
\(927\) 408.708 793.009i 0.440893 0.855458i
\(928\) 0 0
\(929\) 1261.67i 1.35810i 0.734094 + 0.679048i \(0.237607\pi\)
−0.734094 + 0.679048i \(0.762393\pi\)
\(930\) −634.510 + 241.242i −0.682268 + 0.259400i
\(931\) 180.000 0.193340
\(932\) 384.666 0.412732
\(933\) 288.500 + 69.9714i 0.309217 + 0.0749962i
\(934\) −1086.00 −1.16274
\(935\) −769.332 + 527.758i −0.822815 + 0.564447i
\(936\) 0 0
\(937\) 816.333i 0.871220i −0.900135 0.435610i \(-0.856533\pi\)
0.900135 0.435610i \(-0.143467\pi\)
\(938\) 48.0833 0.0512615
\(939\) 544.000 + 131.939i 0.579340 + 0.140511i
\(940\) 200.000 + 291.548i 0.212766 + 0.310157i
\(941\) 1055.52i 1.12170i 0.827919 + 0.560848i \(0.189525\pi\)
−0.827919 + 0.560848i \(0.810475\pi\)
\(942\) 480.833 + 116.619i 0.510438 + 0.123799i
\(943\) 1387.77i 1.47165i
\(944\) 65.9697i 0.0698831i
\(945\) −88.4172 + 782.197i −0.0935631 + 0.827722i
\(946\) −952.000 −1.00634
\(947\) −114.551 −0.120962 −0.0604812 0.998169i \(-0.519264\pi\)
−0.0604812 + 0.998169i \(0.519264\pi\)
\(948\) 101.823 419.829i 0.107409 0.442857i
\(949\) 0 0
\(950\) −152.735 + 395.818i −0.160774 + 0.416651i
\(951\) 368.000 1517.30i 0.386961 1.59548i
\(952\) 186.590i 0.195998i
\(953\) 243.245 0.255241 0.127621 0.991823i \(-0.459266\pi\)
0.127621 + 0.991823i \(0.459266\pi\)
\(954\) −768.000 395.818i −0.805031 0.414904i
\(955\) −1224.00 + 839.657i −1.28168 + 0.879222i
\(956\) 923.576i 0.966083i
\(957\) 0 0
\(958\) 793.009i 0.827776i
\(959\) 296.864i 0.309555i
\(960\) 112.167 42.6459i 0.116840 0.0444228i
\(961\) 63.0000 0.0655567
\(962\) 0 0
\(963\) 441.235 + 227.407i 0.458188 + 0.236144i
\(964\) 608.000 0.630705
\(965\) −480.833 + 329.848i −0.498272 + 0.341812i
\(966\) 578.000 + 140.186i 0.598344 + 0.145120i
\(967\) 938.783i 0.970820i −0.874287 0.485410i \(-0.838670\pi\)
0.874287 0.485410i \(-0.161330\pi\)
\(968\) −427.092 −0.441211
\(969\) 96.0000 395.818i 0.0990712 0.408481i
\(970\) 952.000 653.067i 0.981443 0.673265i
\(971\) 1335.89i 1.37578i −0.725813 0.687892i \(-0.758536\pi\)
0.725813 0.687892i \(-0.241464\pi\)
\(972\) −451.134 + 180.760i −0.464130 + 0.185967i
\(973\) 256.562i 0.263681i
\(974\) 915.329i 0.939763i
\(975\) 0 0
\(976\) −64.0000 −0.0655738
\(977\) 305.470 0.312661 0.156331 0.987705i \(-0.450033\pi\)
0.156331 + 0.987705i \(0.450033\pi\)
\(978\) −408.708 99.1262i −0.417902 0.101356i
\(979\) 1088.00 1.11134
\(980\) −84.8528 123.693i −0.0865845 0.126218i
\(981\) −640.000 329.848i −0.652396 0.336237i
\(982\) 489.800i 0.498778i
\(983\) −1110.16 −1.12936 −0.564678 0.825311i \(-0.691000\pi\)
−0.564678 + 0.825311i \(0.691000\pi\)
\(984\) 476.000 + 115.447i 0.483740 + 0.117324i
\(985\) 544.000 + 793.009i 0.552284 + 0.805086i
\(986\) 0 0
\(987\) −601.041 145.774i −0.608957 0.147694i
\(988\) 0 0
\(989\) 981.299i 0.992213i
\(990\) −1041.33 + 131.253i −1.05185 + 0.132579i
\(991\) 640.000 0.645812 0.322906 0.946431i \(-0.395340\pi\)
0.322906 + 0.946431i \(0.395340\pi\)
\(992\) −181.019 −0.182479
\(993\) −206.475 + 851.319i −0.207931 + 0.857320i
\(994\) 0 0
\(995\) 882.469 + 1286.41i 0.886904 + 1.29287i
\(996\) 62.0000 255.633i 0.0622490 0.256659i
\(997\) 279.886i 0.280728i −0.990100 0.140364i \(-0.955173\pi\)
0.990100 0.140364i \(-0.0448273\pi\)
\(998\) −933.381 −0.935251
\(999\) −476.000 412.311i −0.476476 0.412723i
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 30.3.b.a.29.4 yes 4
3.2 odd 2 inner 30.3.b.a.29.2 yes 4
4.3 odd 2 240.3.c.c.209.3 4
5.2 odd 4 150.3.d.d.101.4 4
5.3 odd 4 150.3.d.d.101.1 4
5.4 even 2 inner 30.3.b.a.29.1 4
8.3 odd 2 960.3.c.e.449.2 4
8.5 even 2 960.3.c.f.449.3 4
9.2 odd 6 810.3.j.c.539.3 8
9.4 even 3 810.3.j.c.269.1 8
9.5 odd 6 810.3.j.c.269.4 8
9.7 even 3 810.3.j.c.539.2 8
12.11 even 2 240.3.c.c.209.1 4
15.2 even 4 150.3.d.d.101.2 4
15.8 even 4 150.3.d.d.101.3 4
15.14 odd 2 inner 30.3.b.a.29.3 yes 4
20.3 even 4 1200.3.l.t.401.4 4
20.7 even 4 1200.3.l.t.401.1 4
20.19 odd 2 240.3.c.c.209.2 4
24.5 odd 2 960.3.c.f.449.1 4
24.11 even 2 960.3.c.e.449.4 4
40.19 odd 2 960.3.c.e.449.3 4
40.29 even 2 960.3.c.f.449.2 4
45.4 even 6 810.3.j.c.269.3 8
45.14 odd 6 810.3.j.c.269.2 8
45.29 odd 6 810.3.j.c.539.1 8
45.34 even 6 810.3.j.c.539.4 8
60.23 odd 4 1200.3.l.t.401.3 4
60.47 odd 4 1200.3.l.t.401.2 4
60.59 even 2 240.3.c.c.209.4 4
120.29 odd 2 960.3.c.f.449.4 4
120.59 even 2 960.3.c.e.449.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
30.3.b.a.29.1 4 5.4 even 2 inner
30.3.b.a.29.2 yes 4 3.2 odd 2 inner
30.3.b.a.29.3 yes 4 15.14 odd 2 inner
30.3.b.a.29.4 yes 4 1.1 even 1 trivial
150.3.d.d.101.1 4 5.3 odd 4
150.3.d.d.101.2 4 15.2 even 4
150.3.d.d.101.3 4 15.8 even 4
150.3.d.d.101.4 4 5.2 odd 4
240.3.c.c.209.1 4 12.11 even 2
240.3.c.c.209.2 4 20.19 odd 2
240.3.c.c.209.3 4 4.3 odd 2
240.3.c.c.209.4 4 60.59 even 2
810.3.j.c.269.1 8 9.4 even 3
810.3.j.c.269.2 8 45.14 odd 6
810.3.j.c.269.3 8 45.4 even 6
810.3.j.c.269.4 8 9.5 odd 6
810.3.j.c.539.1 8 45.29 odd 6
810.3.j.c.539.2 8 9.7 even 3
810.3.j.c.539.3 8 9.2 odd 6
810.3.j.c.539.4 8 45.34 even 6
960.3.c.e.449.1 4 120.59 even 2
960.3.c.e.449.2 4 8.3 odd 2
960.3.c.e.449.3 4 40.19 odd 2
960.3.c.e.449.4 4 24.11 even 2
960.3.c.f.449.1 4 24.5 odd 2
960.3.c.f.449.2 4 40.29 even 2
960.3.c.f.449.3 4 8.5 even 2
960.3.c.f.449.4 4 120.29 odd 2
1200.3.l.t.401.1 4 20.7 even 4
1200.3.l.t.401.2 4 60.47 odd 4
1200.3.l.t.401.3 4 60.23 odd 4
1200.3.l.t.401.4 4 20.3 even 4