Properties

Label 1470.2.d.f.1469.8
Level $1470$
Weight $2$
Character 1470.1469
Analytic conductor $11.738$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1470,2,Mod(1469,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.1469");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.d (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: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.3317760000.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1469.8
Root \(1.72286 + 0.178197i\) of defining polynomial
Character \(\chi\) \(=\) 1470.1469
Dual form 1470.2.d.f.1469.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(0.707107 + 1.58114i) q^{3} +1.00000 q^{4} +(-1.41421 + 1.73205i) q^{5} +(0.707107 + 1.58114i) q^{6} +1.00000 q^{8} +(-2.00000 + 2.23607i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(0.707107 + 1.58114i) q^{3} +1.00000 q^{4} +(-1.41421 + 1.73205i) q^{5} +(0.707107 + 1.58114i) q^{6} +1.00000 q^{8} +(-2.00000 + 2.23607i) q^{9} +(-1.41421 + 1.73205i) q^{10} -0.213422i q^{11} +(0.707107 + 1.58114i) q^{12} +6.70141 q^{13} +(-3.73861 - 1.01132i) q^{15} +1.00000 q^{16} +3.16228i q^{17} +(-2.00000 + 2.23607i) q^{18} +4.89433i q^{19} +(-1.41421 + 1.73205i) q^{20} -0.213422i q^{22} -6.47723 q^{23} +(0.707107 + 1.58114i) q^{24} +(-1.00000 - 4.89898i) q^{25} +6.70141 q^{26} +(-4.94975 - 1.58114i) q^{27} +2.02265i q^{29} +(-3.73861 - 1.01132i) q^{30} +0.301824i q^{31} +1.00000 q^{32} +(0.337449 - 0.150912i) q^{33} +3.16228i q^{34} +(-2.00000 + 2.23607i) q^{36} -7.13505i q^{37} +4.89433i q^{38} +(4.73861 + 10.5959i) q^{39} +(-1.41421 + 1.73205i) q^{40} -6.70141 q^{41} +2.02265i q^{43} -0.213422i q^{44} +(-1.04456 - 6.62638i) q^{45} -6.47723 q^{46} +7.75478i q^{47} +(0.707107 + 1.58114i) q^{48} +(-1.00000 - 4.89898i) q^{50} +(-5.00000 + 2.23607i) q^{51} +6.70141 q^{52} +5.00000 q^{53} +(-4.94975 - 1.58114i) q^{54} +(0.369657 + 0.301824i) q^{55} +(-7.73861 + 3.46081i) q^{57} +2.02265i q^{58} +4.91754 q^{59} +(-3.73861 - 1.01132i) q^{60} +3.46410i q^{61} +0.301824i q^{62} +1.00000 q^{64} +(-9.47723 + 11.6072i) q^{65} +(0.337449 - 0.150912i) q^{66} +5.32582i q^{67} +3.16228i q^{68} +(-4.58009 - 10.2414i) q^{69} -2.02265i q^{71} +(-2.00000 + 2.23607i) q^{72} -11.9886 q^{73} -7.13505i q^{74} +(7.03886 - 5.04524i) q^{75} +4.89433i q^{76} +(4.73861 + 10.5959i) q^{78} +0.522774 q^{79} +(-1.41421 + 1.73205i) q^{80} +(-1.00000 - 8.94427i) q^{81} -6.70141 q^{82} -16.7169i q^{83} +(-5.47723 - 4.47214i) q^{85} +2.02265i q^{86} +(-3.19808 + 1.43023i) q^{87} -0.213422i q^{88} +10.5744 q^{89} +(-1.04456 - 6.62638i) q^{90} -6.47723 q^{92} +(-0.477226 + 0.213422i) q^{93} +7.75478i q^{94} +(-8.47723 - 6.92163i) q^{95} +(0.707107 + 1.58114i) q^{96} -3.50333 q^{97} +(0.477226 + 0.426844i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 16 q^{9} - 8 q^{15} + 8 q^{16} - 16 q^{18} - 8 q^{23} - 8 q^{25} - 8 q^{30} + 8 q^{32} - 16 q^{36} + 16 q^{39} - 8 q^{46} - 8 q^{50} - 40 q^{51} + 40 q^{53} - 40 q^{57} - 8 q^{60} + 8 q^{64} - 32 q^{65} - 16 q^{72} + 16 q^{78} + 48 q^{79} - 8 q^{81} - 8 q^{92} + 40 q^{93} - 24 q^{95} - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.707107 + 1.58114i 0.408248 + 0.912871i
\(4\) 1.00000 0.500000
\(5\) −1.41421 + 1.73205i −0.632456 + 0.774597i
\(6\) 0.707107 + 1.58114i 0.288675 + 0.645497i
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −2.00000 + 2.23607i −0.666667 + 0.745356i
\(10\) −1.41421 + 1.73205i −0.447214 + 0.547723i
\(11\) 0.213422i 0.0643491i −0.999482 0.0321745i \(-0.989757\pi\)
0.999482 0.0321745i \(-0.0102432\pi\)
\(12\) 0.707107 + 1.58114i 0.204124 + 0.456435i
\(13\) 6.70141 1.85864 0.929318 0.369279i \(-0.120395\pi\)
0.929318 + 0.369279i \(0.120395\pi\)
\(14\) 0 0
\(15\) −3.73861 1.01132i −0.965306 0.261123i
\(16\) 1.00000 0.250000
\(17\) 3.16228i 0.766965i 0.923548 + 0.383482i \(0.125275\pi\)
−0.923548 + 0.383482i \(0.874725\pi\)
\(18\) −2.00000 + 2.23607i −0.471405 + 0.527046i
\(19\) 4.89433i 1.12284i 0.827532 + 0.561418i \(0.189744\pi\)
−0.827532 + 0.561418i \(0.810256\pi\)
\(20\) −1.41421 + 1.73205i −0.316228 + 0.387298i
\(21\) 0 0
\(22\) 0.213422i 0.0455017i
\(23\) −6.47723 −1.35059 −0.675297 0.737545i \(-0.735985\pi\)
−0.675297 + 0.737545i \(0.735985\pi\)
\(24\) 0.707107 + 1.58114i 0.144338 + 0.322749i
\(25\) −1.00000 4.89898i −0.200000 0.979796i
\(26\) 6.70141 1.31425
\(27\) −4.94975 1.58114i −0.952579 0.304290i
\(28\) 0 0
\(29\) 2.02265i 0.375596i 0.982208 + 0.187798i \(0.0601350\pi\)
−0.982208 + 0.187798i \(0.939865\pi\)
\(30\) −3.73861 1.01132i −0.682574 0.184641i
\(31\) 0.301824i 0.0542092i 0.999633 + 0.0271046i \(0.00862872\pi\)
−0.999633 + 0.0271046i \(0.991371\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.337449 0.150912i 0.0587424 0.0262704i
\(34\) 3.16228i 0.542326i
\(35\) 0 0
\(36\) −2.00000 + 2.23607i −0.333333 + 0.372678i
\(37\) 7.13505i 1.17299i −0.809951 0.586497i \(-0.800506\pi\)
0.809951 0.586497i \(-0.199494\pi\)
\(38\) 4.89433i 0.793965i
\(39\) 4.73861 + 10.5959i 0.758785 + 1.69670i
\(40\) −1.41421 + 1.73205i −0.223607 + 0.273861i
\(41\) −6.70141 −1.04658 −0.523292 0.852153i \(-0.675296\pi\)
−0.523292 + 0.852153i \(0.675296\pi\)
\(42\) 0 0
\(43\) 2.02265i 0.308451i 0.988036 + 0.154225i \(0.0492882\pi\)
−0.988036 + 0.154225i \(0.950712\pi\)
\(44\) 0.213422i 0.0321745i
\(45\) −1.04456 6.62638i −0.155713 0.987802i
\(46\) −6.47723 −0.955015
\(47\) 7.75478i 1.13115i 0.824696 + 0.565576i \(0.191346\pi\)
−0.824696 + 0.565576i \(0.808654\pi\)
\(48\) 0.707107 + 1.58114i 0.102062 + 0.228218i
\(49\) 0 0
\(50\) −1.00000 4.89898i −0.141421 0.692820i
\(51\) −5.00000 + 2.23607i −0.700140 + 0.313112i
\(52\) 6.70141 0.929318
\(53\) 5.00000 0.686803 0.343401 0.939189i \(-0.388421\pi\)
0.343401 + 0.939189i \(0.388421\pi\)
\(54\) −4.94975 1.58114i −0.673575 0.215166i
\(55\) 0.369657 + 0.301824i 0.0498446 + 0.0406979i
\(56\) 0 0
\(57\) −7.73861 + 3.46081i −1.02500 + 0.458396i
\(58\) 2.02265i 0.265586i
\(59\) 4.91754 0.640209 0.320105 0.947382i \(-0.396282\pi\)
0.320105 + 0.947382i \(0.396282\pi\)
\(60\) −3.73861 1.01132i −0.482653 0.130561i
\(61\) 3.46410i 0.443533i 0.975100 + 0.221766i \(0.0711822\pi\)
−0.975100 + 0.221766i \(0.928818\pi\)
\(62\) 0.301824i 0.0383317i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −9.47723 + 11.6072i −1.17551 + 1.43969i
\(66\) 0.337449 0.150912i 0.0415372 0.0185760i
\(67\) 5.32582i 0.650653i 0.945602 + 0.325326i \(0.105474\pi\)
−0.945602 + 0.325326i \(0.894526\pi\)
\(68\) 3.16228i 0.383482i
\(69\) −4.58009 10.2414i −0.551378 1.23292i
\(70\) 0 0
\(71\) 2.02265i 0.240044i −0.992771 0.120022i \(-0.961703\pi\)
0.992771 0.120022i \(-0.0382965\pi\)
\(72\) −2.00000 + 2.23607i −0.235702 + 0.263523i
\(73\) −11.9886 −1.40316 −0.701580 0.712591i \(-0.747522\pi\)
−0.701580 + 0.712591i \(0.747522\pi\)
\(74\) 7.13505i 0.829432i
\(75\) 7.03886 5.04524i 0.812778 0.582574i
\(76\) 4.89433i 0.561418i
\(77\) 0 0
\(78\) 4.73861 + 10.5959i 0.536542 + 1.19974i
\(79\) 0.522774 0.0588167 0.0294084 0.999567i \(-0.490638\pi\)
0.0294084 + 0.999567i \(0.490638\pi\)
\(80\) −1.41421 + 1.73205i −0.158114 + 0.193649i
\(81\) −1.00000 8.94427i −0.111111 0.993808i
\(82\) −6.70141 −0.740047
\(83\) 16.7169i 1.83491i −0.397835 0.917457i \(-0.630238\pi\)
0.397835 0.917457i \(-0.369762\pi\)
\(84\) 0 0
\(85\) −5.47723 4.47214i −0.594089 0.485071i
\(86\) 2.02265i 0.218108i
\(87\) −3.19808 + 1.43023i −0.342871 + 0.153336i
\(88\) 0.213422i 0.0227508i
\(89\) 10.5744 1.12088 0.560442 0.828194i \(-0.310631\pi\)
0.560442 + 0.828194i \(0.310631\pi\)
\(90\) −1.04456 6.62638i −0.110106 0.698482i
\(91\) 0 0
\(92\) −6.47723 −0.675297
\(93\) −0.477226 + 0.213422i −0.0494860 + 0.0221308i
\(94\) 7.75478i 0.799845i
\(95\) −8.47723 6.92163i −0.869745 0.710144i
\(96\) 0.707107 + 1.58114i 0.0721688 + 0.161374i
\(97\) −3.50333 −0.355709 −0.177854 0.984057i \(-0.556916\pi\)
−0.177854 + 0.984057i \(0.556916\pi\)
\(98\) 0 0
\(99\) 0.477226 + 0.426844i 0.0479630 + 0.0428994i
\(100\) −1.00000 4.89898i −0.100000 0.489898i
\(101\) 11.3137 1.12576 0.562878 0.826540i \(-0.309694\pi\)
0.562878 + 0.826540i \(0.309694\pi\)
\(102\) −5.00000 + 2.23607i −0.495074 + 0.221404i
\(103\) 10.5744 1.04193 0.520963 0.853579i \(-0.325573\pi\)
0.520963 + 0.853579i \(0.325573\pi\)
\(104\) 6.70141 0.657127
\(105\) 0 0
\(106\) 5.00000 0.485643
\(107\) 5.47723 0.529503 0.264752 0.964317i \(-0.414710\pi\)
0.264752 + 0.964317i \(0.414710\pi\)
\(108\) −4.94975 1.58114i −0.476290 0.152145i
\(109\) 12.4317 1.19074 0.595369 0.803452i \(-0.297006\pi\)
0.595369 + 0.803452i \(0.297006\pi\)
\(110\) 0.369657 + 0.301824i 0.0352454 + 0.0287778i
\(111\) 11.2815 5.04524i 1.07079 0.478873i
\(112\) 0 0
\(113\) 6.52277 0.613611 0.306806 0.951772i \(-0.400740\pi\)
0.306806 + 0.951772i \(0.400740\pi\)
\(114\) −7.73861 + 3.46081i −0.724787 + 0.324135i
\(115\) 9.16018 11.2189i 0.854191 1.04617i
\(116\) 2.02265i 0.187798i
\(117\) −13.4028 + 14.9848i −1.23909 + 1.38535i
\(118\) 4.91754 0.452696
\(119\) 0 0
\(120\) −3.73861 1.01132i −0.341287 0.0923207i
\(121\) 10.9545 0.995859
\(122\) 3.46410i 0.313625i
\(123\) −4.73861 10.5959i −0.427266 0.955397i
\(124\) 0.301824i 0.0271046i
\(125\) 9.89949 + 5.19615i 0.885438 + 0.464758i
\(126\) 0 0
\(127\) 13.6298i 1.20945i −0.796434 0.604726i \(-0.793283\pi\)
0.796434 0.604726i \(-0.206717\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.19808 + 1.43023i −0.281576 + 0.125924i
\(130\) −9.47723 + 11.6072i −0.831208 + 1.01802i
\(131\) −6.02651 −0.526539 −0.263269 0.964722i \(-0.584801\pi\)
−0.263269 + 0.964722i \(0.584801\pi\)
\(132\) 0.337449 0.150912i 0.0293712 0.0131352i
\(133\) 0 0
\(134\) 5.32582i 0.460081i
\(135\) 9.73861 6.33715i 0.838166 0.545415i
\(136\) 3.16228i 0.271163i
\(137\) 7.47723 0.638822 0.319411 0.947616i \(-0.396515\pi\)
0.319411 + 0.947616i \(0.396515\pi\)
\(138\) −4.58009 10.2414i −0.389883 0.871805i
\(139\) 7.53185i 0.638843i 0.947613 + 0.319422i \(0.103489\pi\)
−0.947613 + 0.319422i \(0.896511\pi\)
\(140\) 0 0
\(141\) −12.2614 + 5.48346i −1.03260 + 0.461791i
\(142\) 2.02265i 0.169737i
\(143\) 1.43023i 0.119602i
\(144\) −2.00000 + 2.23607i −0.166667 + 0.186339i
\(145\) −3.50333 2.86045i −0.290935 0.237548i
\(146\) −11.9886 −0.992184
\(147\) 0 0
\(148\) 7.13505i 0.586497i
\(149\) 2.44949i 0.200670i 0.994954 + 0.100335i \(0.0319915\pi\)
−0.994954 + 0.100335i \(0.968009\pi\)
\(150\) 7.03886 5.04524i 0.574721 0.411942i
\(151\) −2.00000 −0.162758 −0.0813788 0.996683i \(-0.525932\pi\)
−0.0813788 + 0.996683i \(0.525932\pi\)
\(152\) 4.89433i 0.396982i
\(153\) −7.07107 6.32456i −0.571662 0.511310i
\(154\) 0 0
\(155\) −0.522774 0.426844i −0.0419903 0.0342849i
\(156\) 4.73861 + 10.5959i 0.379393 + 0.848348i
\(157\) −8.79052 −0.701560 −0.350780 0.936458i \(-0.614084\pi\)
−0.350780 + 0.936458i \(0.614084\pi\)
\(158\) 0.522774 0.0415897
\(159\) 3.53553 + 7.90569i 0.280386 + 0.626962i
\(160\) −1.41421 + 1.73205i −0.111803 + 0.136931i
\(161\) 0 0
\(162\) −1.00000 8.94427i −0.0785674 0.702728i
\(163\) 14.6969i 1.15115i −0.817748 0.575577i \(-0.804778\pi\)
0.817748 0.575577i \(-0.195222\pi\)
\(164\) −6.70141 −0.523292
\(165\) −0.215838 + 0.797901i −0.0168030 + 0.0621165i
\(166\) 16.7169i 1.29748i
\(167\) 14.6830i 1.13620i 0.822958 + 0.568102i \(0.192322\pi\)
−0.822958 + 0.568102i \(0.807678\pi\)
\(168\) 0 0
\(169\) 31.9089 2.45453
\(170\) −5.47723 4.47214i −0.420084 0.342997i
\(171\) −10.9441 9.78866i −0.836913 0.748557i
\(172\) 2.02265i 0.154225i
\(173\) 11.5207i 0.875903i −0.898999 0.437952i \(-0.855704\pi\)
0.898999 0.437952i \(-0.144296\pi\)
\(174\) −3.19808 + 1.43023i −0.242446 + 0.108425i
\(175\) 0 0
\(176\) 0.213422i 0.0160873i
\(177\) 3.47723 + 7.77531i 0.261364 + 0.584428i
\(178\) 10.5744 0.792584
\(179\) 14.9104i 1.11445i 0.830361 + 0.557226i \(0.188134\pi\)
−0.830361 + 0.557226i \(0.811866\pi\)
\(180\) −1.04456 6.62638i −0.0778566 0.493901i
\(181\) 3.16228i 0.235050i −0.993070 0.117525i \(-0.962504\pi\)
0.993070 0.117525i \(-0.0374961\pi\)
\(182\) 0 0
\(183\) −5.47723 + 2.44949i −0.404888 + 0.181071i
\(184\) −6.47723 −0.477507
\(185\) 12.3583 + 10.0905i 0.908598 + 0.741867i
\(186\) −0.477226 + 0.213422i −0.0349919 + 0.0156488i
\(187\) 0.674899 0.0493535
\(188\) 7.75478i 0.565576i
\(189\) 0 0
\(190\) −8.47723 6.92163i −0.615003 0.502148i
\(191\) 1.59580i 0.115468i −0.998332 0.0577341i \(-0.981612\pi\)
0.998332 0.0577341i \(-0.0183876\pi\)
\(192\) 0.707107 + 1.58114i 0.0510310 + 0.114109i
\(193\) 7.34847i 0.528954i 0.964392 + 0.264477i \(0.0851994\pi\)
−0.964392 + 0.264477i \(0.914801\pi\)
\(194\) −3.50333 −0.251524
\(195\) −25.0540 6.77729i −1.79415 0.485332i
\(196\) 0 0
\(197\) 9.00000 0.641223 0.320612 0.947211i \(-0.396112\pi\)
0.320612 + 0.947211i \(0.396112\pi\)
\(198\) 0.477226 + 0.426844i 0.0339149 + 0.0303344i
\(199\) 22.4378i 1.59057i 0.606235 + 0.795286i \(0.292679\pi\)
−0.606235 + 0.795286i \(0.707321\pi\)
\(200\) −1.00000 4.89898i −0.0707107 0.346410i
\(201\) −8.42087 + 3.76593i −0.593962 + 0.265628i
\(202\) 11.3137 0.796030
\(203\) 0 0
\(204\) −5.00000 + 2.23607i −0.350070 + 0.156556i
\(205\) 9.47723 11.6072i 0.661918 0.810681i
\(206\) 10.5744 0.736753
\(207\) 12.9545 14.4835i 0.900397 1.00667i
\(208\) 6.70141 0.464659
\(209\) 1.04456 0.0722535
\(210\) 0 0
\(211\) 13.5228 0.930946 0.465473 0.885062i \(-0.345884\pi\)
0.465473 + 0.885062i \(0.345884\pi\)
\(212\) 5.00000 0.343401
\(213\) 3.19808 1.43023i 0.219129 0.0979975i
\(214\) 5.47723 0.374415
\(215\) −3.50333 2.86045i −0.238925 0.195081i
\(216\) −4.94975 1.58114i −0.336788 0.107583i
\(217\) 0 0
\(218\) 12.4317 0.841979
\(219\) −8.47723 18.9557i −0.572838 1.28090i
\(220\) 0.369657 + 0.301824i 0.0249223 + 0.0203490i
\(221\) 21.1917i 1.42551i
\(222\) 11.2815 5.04524i 0.757165 0.338614i
\(223\) 6.39617 0.428319 0.214160 0.976799i \(-0.431299\pi\)
0.214160 + 0.976799i \(0.431299\pi\)
\(224\) 0 0
\(225\) 12.9545 + 7.56189i 0.863630 + 0.504126i
\(226\) 6.52277 0.433889
\(227\) 10.3923i 0.689761i −0.938647 0.344881i \(-0.887919\pi\)
0.938647 0.344881i \(-0.112081\pi\)
\(228\) −7.73861 + 3.46081i −0.512502 + 0.229198i
\(229\) 7.23003i 0.477774i −0.971047 0.238887i \(-0.923218\pi\)
0.971047 0.238887i \(-0.0767825\pi\)
\(230\) 9.16018 11.2189i 0.604004 0.739751i
\(231\) 0 0
\(232\) 2.02265i 0.132793i
\(233\) −4.00000 −0.262049 −0.131024 0.991379i \(-0.541827\pi\)
−0.131024 + 0.991379i \(0.541827\pi\)
\(234\) −13.4028 + 14.9848i −0.876170 + 0.979588i
\(235\) −13.4317 10.9669i −0.876186 0.715403i
\(236\) 4.91754 0.320105
\(237\) 0.369657 + 0.826579i 0.0240118 + 0.0536921i
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) −3.73861 1.01132i −0.241326 0.0652806i
\(241\) 3.98886i 0.256945i −0.991713 0.128472i \(-0.958993\pi\)
0.991713 0.128472i \(-0.0410074\pi\)
\(242\) 10.9545 0.704179
\(243\) 13.4350 7.90569i 0.861858 0.507151i
\(244\) 3.46410i 0.221766i
\(245\) 0 0
\(246\) −4.73861 10.5959i −0.302123 0.675567i
\(247\) 32.7989i 2.08694i
\(248\) 0.301824i 0.0191658i
\(249\) 26.4317 11.8206i 1.67504 0.749100i
\(250\) 9.89949 + 5.19615i 0.626099 + 0.328634i
\(251\) 16.6009 1.04784 0.523920 0.851768i \(-0.324469\pi\)
0.523920 + 0.851768i \(0.324469\pi\)
\(252\) 0 0
\(253\) 1.38238i 0.0869095i
\(254\) 13.6298i 0.855212i
\(255\) 3.19808 11.8225i 0.200272 0.740356i
\(256\) 1.00000 0.0625000
\(257\) 23.6451i 1.47494i −0.675381 0.737469i \(-0.736021\pi\)
0.675381 0.737469i \(-0.263979\pi\)
\(258\) −3.19808 + 1.43023i −0.199104 + 0.0890420i
\(259\) 0 0
\(260\) −9.47723 + 11.6072i −0.587753 + 0.719847i
\(261\) −4.52277 4.04529i −0.279953 0.250397i
\(262\) −6.02651 −0.372319
\(263\) −2.00000 −0.123325 −0.0616626 0.998097i \(-0.519640\pi\)
−0.0616626 + 0.998097i \(0.519640\pi\)
\(264\) 0.337449 0.150912i 0.0207686 0.00928799i
\(265\) −7.07107 + 8.66025i −0.434372 + 0.531995i
\(266\) 0 0
\(267\) 7.47723 + 16.7196i 0.457599 + 1.02322i
\(268\) 5.32582i 0.325326i
\(269\) −28.8948 −1.76174 −0.880872 0.473354i \(-0.843043\pi\)
−0.880872 + 0.473354i \(0.843043\pi\)
\(270\) 9.73861 6.33715i 0.592673 0.385666i
\(271\) 6.32456i 0.384189i 0.981376 + 0.192095i \(0.0615281\pi\)
−0.981376 + 0.192095i \(0.938472\pi\)
\(272\) 3.16228i 0.191741i
\(273\) 0 0
\(274\) 7.47723 0.451716
\(275\) −1.04555 + 0.213422i −0.0630490 + 0.0128698i
\(276\) −4.58009 10.2414i −0.275689 0.616459i
\(277\) 9.79796i 0.588702i −0.955697 0.294351i \(-0.904896\pi\)
0.955697 0.294351i \(-0.0951035\pi\)
\(278\) 7.53185i 0.451730i
\(279\) −0.674899 0.603648i −0.0404051 0.0361395i
\(280\) 0 0
\(281\) 11.6072i 0.692427i −0.938156 0.346213i \(-0.887467\pi\)
0.938156 0.346213i \(-0.112533\pi\)
\(282\) −12.2614 + 5.48346i −0.730155 + 0.326535i
\(283\) 24.7165 1.46925 0.734623 0.678476i \(-0.237359\pi\)
0.734623 + 0.678476i \(0.237359\pi\)
\(284\) 2.02265i 0.120022i
\(285\) 4.94975 18.2980i 0.293198 1.08388i
\(286\) 1.43023i 0.0845711i
\(287\) 0 0
\(288\) −2.00000 + 2.23607i −0.117851 + 0.131762i
\(289\) 7.00000 0.411765
\(290\) −3.50333 2.86045i −0.205722 0.167972i
\(291\) −2.47723 5.53924i −0.145218 0.324716i
\(292\) −11.9886 −0.701580
\(293\) 4.59250i 0.268297i −0.990961 0.134148i \(-0.957170\pi\)
0.990961 0.134148i \(-0.0428299\pi\)
\(294\) 0 0
\(295\) −6.95445 + 8.51743i −0.404904 + 0.495904i
\(296\) 7.13505i 0.414716i
\(297\) −0.337449 + 1.05638i −0.0195808 + 0.0612976i
\(298\) 2.44949i 0.141895i
\(299\) −43.4065 −2.51027
\(300\) 7.03886 5.04524i 0.406389 0.291287i
\(301\) 0 0
\(302\) −2.00000 −0.115087
\(303\) 8.00000 + 17.8885i 0.459588 + 1.02767i
\(304\) 4.89433i 0.280709i
\(305\) −6.00000 4.89898i −0.343559 0.280515i
\(306\) −7.07107 6.32456i −0.404226 0.361551i
\(307\) 3.50333 0.199945 0.0999727 0.994990i \(-0.468124\pi\)
0.0999727 + 0.994990i \(0.468124\pi\)
\(308\) 0 0
\(309\) 7.47723 + 16.7196i 0.425365 + 0.951144i
\(310\) −0.522774 0.426844i −0.0296916 0.0242431i
\(311\) −28.8948 −1.63847 −0.819236 0.573457i \(-0.805602\pi\)
−0.819236 + 0.573457i \(0.805602\pi\)
\(312\) 4.73861 + 10.5959i 0.268271 + 0.599872i
\(313\) −23.2379 −1.31348 −0.656742 0.754115i \(-0.728066\pi\)
−0.656742 + 0.754115i \(0.728066\pi\)
\(314\) −8.79052 −0.496078
\(315\) 0 0
\(316\) 0.522774 0.0294084
\(317\) 33.9089 1.90451 0.952257 0.305298i \(-0.0987561\pi\)
0.952257 + 0.305298i \(0.0987561\pi\)
\(318\) 3.53553 + 7.90569i 0.198263 + 0.443329i
\(319\) 0.431677 0.0241693
\(320\) −1.41421 + 1.73205i −0.0790569 + 0.0968246i
\(321\) 3.87298 + 8.66025i 0.216169 + 0.483368i
\(322\) 0 0
\(323\) −15.4772 −0.861176
\(324\) −1.00000 8.94427i −0.0555556 0.496904i
\(325\) −6.70141 32.8301i −0.371727 1.82108i
\(326\) 14.6969i 0.813988i
\(327\) 8.79052 + 19.6562i 0.486117 + 1.08699i
\(328\) −6.70141 −0.370023
\(329\) 0 0
\(330\) −0.215838 + 0.797901i −0.0118815 + 0.0439230i
\(331\) −11.4317 −0.628342 −0.314171 0.949366i \(-0.601726\pi\)
−0.314171 + 0.949366i \(0.601726\pi\)
\(332\) 16.7169i 0.917457i
\(333\) 15.9545 + 14.2701i 0.874299 + 0.781996i
\(334\) 14.6830i 0.803417i
\(335\) −9.22460 7.53185i −0.503994 0.411509i
\(336\) 0 0
\(337\) 17.1464i 0.934025i −0.884251 0.467013i \(-0.845330\pi\)
0.884251 0.467013i \(-0.154670\pi\)
\(338\) 31.9089 1.73562
\(339\) 4.61230 + 10.3134i 0.250506 + 0.560148i
\(340\) −5.47723 4.47214i −0.297044 0.242536i
\(341\) 0.0644158 0.00348831
\(342\) −10.9441 9.78866i −0.591787 0.529310i
\(343\) 0 0
\(344\) 2.02265i 0.109054i
\(345\) 24.2158 + 6.55057i 1.30374 + 0.352671i
\(346\) 11.5207i 0.619357i
\(347\) −6.52277 −0.350161 −0.175080 0.984554i \(-0.556019\pi\)
−0.175080 + 0.984554i \(0.556019\pi\)
\(348\) −3.19808 + 1.43023i −0.171435 + 0.0766682i
\(349\) 32.5282i 1.74120i 0.491994 + 0.870599i \(0.336268\pi\)
−0.491994 + 0.870599i \(0.663732\pi\)
\(350\) 0 0
\(351\) −33.1703 10.5959i −1.77050 0.565565i
\(352\) 0.213422i 0.0113754i
\(353\) 13.2528i 0.705373i −0.935742 0.352687i \(-0.885268\pi\)
0.935742 0.352687i \(-0.114732\pi\)
\(354\) 3.47723 + 7.77531i 0.184812 + 0.413253i
\(355\) 3.50333 + 2.86045i 0.185937 + 0.151817i
\(356\) 10.5744 0.560442
\(357\) 0 0
\(358\) 14.9104i 0.788037i
\(359\) 6.49478i 0.342781i 0.985203 + 0.171391i \(0.0548261\pi\)
−0.985203 + 0.171391i \(0.945174\pi\)
\(360\) −1.04456 6.62638i −0.0550529 0.349241i
\(361\) −4.95445 −0.260761
\(362\) 3.16228i 0.166206i
\(363\) 7.74597 + 17.3205i 0.406558 + 0.909091i
\(364\) 0 0
\(365\) 16.9545 20.7649i 0.887437 1.08688i
\(366\) −5.47723 + 2.44949i −0.286299 + 0.128037i
\(367\) 8.11562 0.423632 0.211816 0.977310i \(-0.432062\pi\)
0.211816 + 0.977310i \(0.432062\pi\)
\(368\) −6.47723 −0.337649
\(369\) 13.4028 14.9848i 0.697723 0.780078i
\(370\) 12.3583 + 10.0905i 0.642476 + 0.524579i
\(371\) 0 0
\(372\) −0.477226 + 0.213422i −0.0247430 + 0.0110654i
\(373\) 3.61845i 0.187356i −0.995603 0.0936781i \(-0.970138\pi\)
0.995603 0.0936781i \(-0.0298624\pi\)
\(374\) 0.674899 0.0348982
\(375\) −1.21584 + 19.3267i −0.0627856 + 0.998027i
\(376\) 7.75478i 0.399922i
\(377\) 13.5546i 0.698097i
\(378\) 0 0
\(379\) −9.52277 −0.489152 −0.244576 0.969630i \(-0.578649\pi\)
−0.244576 + 0.969630i \(0.578649\pi\)
\(380\) −8.47723 6.92163i −0.434872 0.355072i
\(381\) 21.5507 9.63774i 1.10407 0.493757i
\(382\) 1.59580i 0.0816484i
\(383\) 0.826579i 0.0422362i −0.999777 0.0211181i \(-0.993277\pi\)
0.999777 0.0211181i \(-0.00672260\pi\)
\(384\) 0.707107 + 1.58114i 0.0360844 + 0.0806872i
\(385\) 0 0
\(386\) 7.34847i 0.374027i
\(387\) −4.52277 4.04529i −0.229906 0.205634i
\(388\) −3.50333 −0.177854
\(389\) 7.34847i 0.372582i 0.982495 + 0.186291i \(0.0596468\pi\)
−0.982495 + 0.186291i \(0.940353\pi\)
\(390\) −25.0540 6.77729i −1.26866 0.343181i
\(391\) 20.4828i 1.03586i
\(392\) 0 0
\(393\) −4.26139 9.52875i −0.214959 0.480662i
\(394\) 9.00000 0.453413
\(395\) −0.739315 + 0.905472i −0.0371990 + 0.0455592i
\(396\) 0.477226 + 0.426844i 0.0239815 + 0.0214497i
\(397\) 30.3734 1.52440 0.762198 0.647344i \(-0.224120\pi\)
0.762198 + 0.647344i \(0.224120\pi\)
\(398\) 22.4378i 1.12470i
\(399\) 0 0
\(400\) −1.00000 4.89898i −0.0500000 0.244949i
\(401\) 30.3494i 1.51558i −0.652500 0.757789i \(-0.726280\pi\)
0.652500 0.757789i \(-0.273720\pi\)
\(402\) −8.42087 + 3.76593i −0.419995 + 0.187827i
\(403\) 2.02265i 0.100755i
\(404\) 11.3137 0.562878
\(405\) 16.9061 + 10.9171i 0.840073 + 0.542473i
\(406\) 0 0
\(407\) −1.52277 −0.0754811
\(408\) −5.00000 + 2.23607i −0.247537 + 0.110702i
\(409\) 22.4378i 1.10948i 0.832025 + 0.554738i \(0.187182\pi\)
−0.832025 + 0.554738i \(0.812818\pi\)
\(410\) 9.47723 11.6072i 0.468047 0.573238i
\(411\) 5.28720 + 11.8225i 0.260798 + 0.583162i
\(412\) 10.5744 0.520963
\(413\) 0 0
\(414\) 12.9545 14.4835i 0.636677 0.711826i
\(415\) 28.9545 + 23.6412i 1.42132 + 1.16050i
\(416\) 6.70141 0.328564
\(417\) −11.9089 + 5.32582i −0.583181 + 0.260807i
\(418\) 1.04456 0.0510909
\(419\) −16.6009 −0.811007 −0.405504 0.914093i \(-0.632904\pi\)
−0.405504 + 0.914093i \(0.632904\pi\)
\(420\) 0 0
\(421\) −2.95445 −0.143991 −0.0719956 0.997405i \(-0.522937\pi\)
−0.0719956 + 0.997405i \(0.522937\pi\)
\(422\) 13.5228 0.658278
\(423\) −17.3402 15.5096i −0.843110 0.754101i
\(424\) 5.00000 0.242821
\(425\) 15.4919 3.16228i 0.751469 0.153393i
\(426\) 3.19808 1.43023i 0.154948 0.0692947i
\(427\) 0 0
\(428\) 5.47723 0.264752
\(429\) 2.26139 1.01132i 0.109181 0.0488271i
\(430\) −3.50333 2.86045i −0.168945 0.137943i
\(431\) 37.0576i 1.78500i −0.451045 0.892501i \(-0.648949\pi\)
0.451045 0.892501i \(-0.351051\pi\)
\(432\) −4.94975 1.58114i −0.238145 0.0760726i
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 2.04555 7.56189i 0.0980766 0.362565i
\(436\) 12.4317 0.595369
\(437\) 31.7017i 1.51650i
\(438\) −8.47723 18.9557i −0.405058 0.905736i
\(439\) 22.7396i 1.08530i 0.839958 + 0.542651i \(0.182579\pi\)
−0.839958 + 0.542651i \(0.817421\pi\)
\(440\) 0.369657 + 0.301824i 0.0176227 + 0.0143889i
\(441\) 0 0
\(442\) 21.1917i 1.00799i
\(443\) −36.9545 −1.75576 −0.877879 0.478882i \(-0.841042\pi\)
−0.877879 + 0.478882i \(0.841042\pi\)
\(444\) 11.2815 5.04524i 0.535396 0.239437i
\(445\) −14.9545 + 18.3154i −0.708909 + 0.868233i
\(446\) 6.39617 0.302867
\(447\) −3.87298 + 1.73205i −0.183186 + 0.0819232i
\(448\) 0 0
\(449\) 3.51660i 0.165959i 0.996551 + 0.0829793i \(0.0264435\pi\)
−0.996551 + 0.0829793i \(0.973556\pi\)
\(450\) 12.9545 + 7.56189i 0.610679 + 0.356471i
\(451\) 1.43023i 0.0673468i
\(452\) 6.52277 0.306806
\(453\) −1.41421 3.16228i −0.0664455 0.148577i
\(454\) 10.3923i 0.487735i
\(455\) 0 0
\(456\) −7.73861 + 3.46081i −0.362394 + 0.162067i
\(457\) 37.9113i 1.77342i −0.462330 0.886708i \(-0.652986\pi\)
0.462330 0.886708i \(-0.347014\pi\)
\(458\) 7.23003i 0.337837i
\(459\) 5.00000 15.6525i 0.233380 0.730595i
\(460\) 9.16018 11.2189i 0.427096 0.523083i
\(461\) −16.2957 −0.758965 −0.379482 0.925199i \(-0.623898\pi\)
−0.379482 + 0.925199i \(0.623898\pi\)
\(462\) 0 0
\(463\) 17.6751i 0.821433i −0.911763 0.410716i \(-0.865279\pi\)
0.911763 0.410716i \(-0.134721\pi\)
\(464\) 2.02265i 0.0938990i
\(465\) 0.305242 1.12840i 0.0141552 0.0523284i
\(466\) −4.00000 −0.185296
\(467\) 34.3392i 1.58903i −0.607246 0.794514i \(-0.707726\pi\)
0.607246 0.794514i \(-0.292274\pi\)
\(468\) −13.4028 + 14.9848i −0.619546 + 0.692673i
\(469\) 0 0
\(470\) −13.4317 10.9669i −0.619557 0.505866i
\(471\) −6.21584 13.8990i −0.286411 0.640434i
\(472\) 4.91754 0.226348
\(473\) 0.431677 0.0198485
\(474\) 0.369657 + 0.826579i 0.0169789 + 0.0379660i
\(475\) 23.9772 4.89433i 1.10015 0.224567i
\(476\) 0 0
\(477\) −10.0000 + 11.1803i −0.457869 + 0.511913i
\(478\) 0 0
\(479\) −11.3781 −0.519880 −0.259940 0.965625i \(-0.583703\pi\)
−0.259940 + 0.965625i \(0.583703\pi\)
\(480\) −3.73861 1.01132i −0.170644 0.0461604i
\(481\) 47.8149i 2.18017i
\(482\) 3.98886i 0.181687i
\(483\) 0 0
\(484\) 10.9545 0.497930
\(485\) 4.95445 6.06794i 0.224970 0.275531i
\(486\) 13.4350 7.90569i 0.609425 0.358610i
\(487\) 36.6308i 1.65990i 0.557839 + 0.829949i \(0.311631\pi\)
−0.557839 + 0.829949i \(0.688369\pi\)
\(488\) 3.46410i 0.156813i
\(489\) 23.2379 10.3923i 1.05085 0.469956i
\(490\) 0 0
\(491\) 4.04529i 0.182561i 0.995825 + 0.0912807i \(0.0290961\pi\)
−0.995825 + 0.0912807i \(0.970904\pi\)
\(492\) −4.73861 10.5959i −0.213633 0.477698i
\(493\) −6.39617 −0.288069
\(494\) 32.7989i 1.47569i
\(495\) −1.41421 + 0.222931i −0.0635642 + 0.0100200i
\(496\) 0.301824i 0.0135523i
\(497\) 0 0
\(498\) 26.4317 11.8206i 1.18443 0.529694i
\(499\) −41.9089 −1.87610 −0.938050 0.346500i \(-0.887370\pi\)
−0.938050 + 0.346500i \(0.887370\pi\)
\(500\) 9.89949 + 5.19615i 0.442719 + 0.232379i
\(501\) −23.2158 + 10.3824i −1.03721 + 0.463853i
\(502\) 16.6009 0.740935
\(503\) 22.4378i 1.00045i −0.865895 0.500225i \(-0.833251\pi\)
0.865895 0.500225i \(-0.166749\pi\)
\(504\) 0 0
\(505\) −16.0000 + 19.5959i −0.711991 + 0.872007i
\(506\) 1.38238i 0.0614543i
\(507\) 22.5630 + 50.4524i 1.00206 + 2.24067i
\(508\) 13.6298i 0.604726i
\(509\) −9.22460 −0.408873 −0.204437 0.978880i \(-0.565536\pi\)
−0.204437 + 0.978880i \(0.565536\pi\)
\(510\) 3.19808 11.8225i 0.141614 0.523511i
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 7.73861 24.2257i 0.341668 1.06959i
\(514\) 23.6451i 1.04294i
\(515\) −14.9545 + 18.3154i −0.658972 + 0.807072i
\(516\) −3.19808 + 1.43023i −0.140788 + 0.0629622i
\(517\) 1.65504 0.0727885
\(518\) 0 0
\(519\) 18.2158 8.14637i 0.799587 0.357586i
\(520\) −9.47723 + 11.6072i −0.415604 + 0.509009i
\(521\) 18.6256 0.816002 0.408001 0.912981i \(-0.366226\pi\)
0.408001 + 0.912981i \(0.366226\pi\)
\(522\) −4.52277 4.04529i −0.197956 0.177058i
\(523\) 14.0777 0.615576 0.307788 0.951455i \(-0.400411\pi\)
0.307788 + 0.951455i \(0.400411\pi\)
\(524\) −6.02651 −0.263269
\(525\) 0 0
\(526\) −2.00000 −0.0872041
\(527\) −0.954451 −0.0415765
\(528\) 0.337449 0.150912i 0.0146856 0.00656760i
\(529\) 18.9545 0.824107
\(530\) −7.07107 + 8.66025i −0.307148 + 0.376177i
\(531\) −9.83508 + 10.9960i −0.426806 + 0.477184i
\(532\) 0 0
\(533\) −44.9089 −1.94522
\(534\) 7.47723 + 16.7196i 0.323571 + 0.723527i
\(535\) −7.74597 + 9.48683i −0.334887 + 0.410152i
\(536\) 5.32582i 0.230041i
\(537\) −23.5753 + 10.5432i −1.01735 + 0.454973i
\(538\) −28.8948 −1.24574
\(539\) 0 0
\(540\) 9.73861 6.33715i 0.419083 0.272707i
\(541\) 19.4772 0.837391 0.418696 0.908127i \(-0.362487\pi\)
0.418696 + 0.908127i \(0.362487\pi\)
\(542\) 6.32456i 0.271663i
\(543\) 5.00000 2.23607i 0.214571 0.0959589i
\(544\) 3.16228i 0.135582i
\(545\) −17.5810 + 21.5323i −0.753089 + 0.922342i
\(546\) 0 0
\(547\) 23.2144i 0.992575i 0.868158 + 0.496287i \(0.165304\pi\)
−0.868158 + 0.496287i \(0.834696\pi\)
\(548\) 7.47723 0.319411
\(549\) −7.74597 6.92820i −0.330590 0.295689i
\(550\) −1.04555 + 0.213422i −0.0445824 + 0.00910033i
\(551\) −9.89949 −0.421733
\(552\) −4.58009 10.2414i −0.194942 0.435903i
\(553\) 0 0
\(554\) 9.79796i 0.416275i
\(555\) −7.21584 + 26.6752i −0.306295 + 1.13230i
\(556\) 7.53185i 0.319422i
\(557\) −37.8634 −1.60432 −0.802161 0.597108i \(-0.796316\pi\)
−0.802161 + 0.597108i \(0.796316\pi\)
\(558\) −0.674899 0.603648i −0.0285707 0.0255545i
\(559\) 13.5546i 0.573298i
\(560\) 0 0
\(561\) 0.477226 + 1.06711i 0.0201485 + 0.0450534i
\(562\) 11.6072i 0.489619i
\(563\) 10.3923i 0.437983i −0.975727 0.218992i \(-0.929723\pi\)
0.975727 0.218992i \(-0.0702768\pi\)
\(564\) −12.2614 + 5.48346i −0.516298 + 0.230895i
\(565\) −9.22460 + 11.2978i −0.388082 + 0.475301i
\(566\) 24.7165 1.03891
\(567\) 0 0
\(568\) 2.02265i 0.0848683i
\(569\) 12.0340i 0.504493i 0.967663 + 0.252246i \(0.0811693\pi\)
−0.967663 + 0.252246i \(0.918831\pi\)
\(570\) 4.94975 18.2980i 0.207322 0.766419i
\(571\) −6.95445 −0.291035 −0.145517 0.989356i \(-0.546485\pi\)
−0.145517 + 0.989356i \(0.546485\pi\)
\(572\) 1.43023i 0.0598008i
\(573\) 2.52319 1.12840i 0.105408 0.0471397i
\(574\) 0 0
\(575\) 6.47723 + 31.7318i 0.270119 + 1.32331i
\(576\) −2.00000 + 2.23607i −0.0833333 + 0.0931695i
\(577\) 14.8170 0.616841 0.308421 0.951250i \(-0.400200\pi\)
0.308421 + 0.951250i \(0.400200\pi\)
\(578\) 7.00000 0.291162
\(579\) −11.6190 + 5.19615i −0.482867 + 0.215945i
\(580\) −3.50333 2.86045i −0.145468 0.118774i
\(581\) 0 0
\(582\) −2.47723 5.53924i −0.102684 0.229609i
\(583\) 1.06711i 0.0441951i
\(584\) −11.9886 −0.496092
\(585\) −7.00000 44.4061i −0.289414 1.83597i
\(586\) 4.59250i 0.189715i
\(587\) 27.4110i 1.13137i −0.824621 0.565686i \(-0.808611\pi\)
0.824621 0.565686i \(-0.191389\pi\)
\(588\) 0 0
\(589\) −1.47723 −0.0608680
\(590\) −6.95445 + 8.51743i −0.286310 + 0.350657i
\(591\) 6.36396 + 14.2302i 0.261778 + 0.585354i
\(592\) 7.13505i 0.293249i
\(593\) 36.2942i 1.49042i 0.666828 + 0.745212i \(0.267652\pi\)
−0.666828 + 0.745212i \(0.732348\pi\)
\(594\) −0.337449 + 1.05638i −0.0138457 + 0.0433440i
\(595\) 0 0
\(596\) 2.44949i 0.100335i
\(597\) −35.4772 + 15.8659i −1.45199 + 0.649348i
\(598\) −43.4065 −1.77503
\(599\) 5.75267i 0.235048i −0.993070 0.117524i \(-0.962504\pi\)
0.993070 0.117524i \(-0.0374956\pi\)
\(600\) 7.03886 5.04524i 0.287360 0.205971i
\(601\) 16.7169i 0.681895i −0.940082 0.340947i \(-0.889252\pi\)
0.940082 0.340947i \(-0.110748\pi\)
\(602\) 0 0
\(603\) −11.9089 10.6516i −0.484968 0.433769i
\(604\) −2.00000 −0.0813788
\(605\) −15.4919 + 18.9737i −0.629837 + 0.771389i
\(606\) 8.00000 + 17.8885i 0.324978 + 0.726672i
\(607\) −26.4360 −1.07300 −0.536502 0.843899i \(-0.680255\pi\)
−0.536502 + 0.843899i \(0.680255\pi\)
\(608\) 4.89433i 0.198491i
\(609\) 0 0
\(610\) −6.00000 4.89898i −0.242933 0.198354i
\(611\) 51.9680i 2.10240i
\(612\) −7.07107 6.32456i −0.285831 0.255655i
\(613\) 25.4504i 1.02793i −0.857810 0.513967i \(-0.828175\pi\)
0.857810 0.513967i \(-0.171825\pi\)
\(614\) 3.50333 0.141383
\(615\) 25.0540 + 6.77729i 1.01027 + 0.273287i
\(616\) 0 0
\(617\) 25.4772 1.02567 0.512837 0.858486i \(-0.328594\pi\)
0.512837 + 0.858486i \(0.328594\pi\)
\(618\) 7.47723 + 16.7196i 0.300778 + 0.672560i
\(619\) 26.7284i 1.07431i 0.843484 + 0.537154i \(0.180500\pi\)
−0.843484 + 0.537154i \(0.819500\pi\)
\(620\) −0.522774 0.426844i −0.0209951 0.0171424i
\(621\) 32.0606 + 10.2414i 1.28655 + 0.410973i
\(622\) −28.8948 −1.15857
\(623\) 0 0
\(624\) 4.73861 + 10.5959i 0.189696 + 0.424174i
\(625\) −23.0000 + 9.79796i −0.920000 + 0.391918i
\(626\) −23.2379 −0.928773
\(627\) 0.738613 + 1.65159i 0.0294974 + 0.0659581i
\(628\) −8.79052 −0.350780
\(629\) 22.5630 0.899646
\(630\) 0 0
\(631\) −7.47723 −0.297664 −0.148832 0.988863i \(-0.547551\pi\)
−0.148832 + 0.988863i \(0.547551\pi\)
\(632\) 0.522774 0.0207949
\(633\) 9.56205 + 21.3814i 0.380057 + 0.849834i
\(634\) 33.9089 1.34669
\(635\) 23.6076 + 19.2755i 0.936837 + 0.764924i
\(636\) 3.53553 + 7.90569i 0.140193 + 0.313481i
\(637\) 0 0
\(638\) 0.431677 0.0170902
\(639\) 4.52277 + 4.04529i 0.178918 + 0.160029i
\(640\) −1.41421 + 1.73205i −0.0559017 + 0.0684653i
\(641\) 6.28136i 0.248099i −0.992276 0.124049i \(-0.960412\pi\)
0.992276 0.124049i \(-0.0395881\pi\)
\(642\) 3.87298 + 8.66025i 0.152854 + 0.341793i
\(643\) −20.4095 −0.804871 −0.402436 0.915448i \(-0.631836\pi\)
−0.402436 + 0.915448i \(0.631836\pi\)
\(644\) 0 0
\(645\) 2.04555 7.56189i 0.0805434 0.297749i
\(646\) −15.4772 −0.608943
\(647\) 23.8680i 0.938348i 0.883106 + 0.469174i \(0.155448\pi\)
−0.883106 + 0.469174i \(0.844552\pi\)
\(648\) −1.00000 8.94427i −0.0392837 0.351364i
\(649\) 1.04951i 0.0411969i
\(650\) −6.70141 32.8301i −0.262851 1.28770i
\(651\) 0 0
\(652\) 14.6969i 0.575577i
\(653\) −25.8634 −1.01211 −0.506056 0.862501i \(-0.668897\pi\)
−0.506056 + 0.862501i \(0.668897\pi\)
\(654\) 8.79052 + 19.6562i 0.343737 + 0.768619i
\(655\) 8.52277 10.4382i 0.333012 0.407855i
\(656\) −6.70141 −0.261646
\(657\) 23.9772 26.8073i 0.935440 1.04585i
\(658\) 0 0
\(659\) 34.2929i 1.33586i 0.744224 + 0.667930i \(0.232819\pi\)
−0.744224 + 0.667930i \(0.767181\pi\)
\(660\) −0.215838 + 0.797901i −0.00840150 + 0.0310583i
\(661\) 13.2528i 0.515473i −0.966215 0.257736i \(-0.917023\pi\)
0.966215 0.257736i \(-0.0829766\pi\)
\(662\) −11.4317 −0.444305
\(663\) −33.5071 + 14.9848i −1.30131 + 0.581962i
\(664\) 16.7169i 0.648740i
\(665\) 0 0
\(666\) 15.9545 + 14.2701i 0.618222 + 0.552955i
\(667\) 13.1011i 0.507278i
\(668\) 14.6830i 0.568102i
\(669\) 4.52277 + 10.1132i 0.174861 + 0.391000i
\(670\) −9.22460 7.53185i −0.356377 0.290981i
\(671\) 0.739315 0.0285409
\(672\) 0 0
\(673\) 48.4514i 1.86766i −0.357713 0.933832i \(-0.616443\pi\)
0.357713 0.933832i \(-0.383557\pi\)
\(674\) 17.1464i 0.660456i
\(675\) −2.79622 + 25.8299i −0.107627 + 0.994191i
\(676\) 31.9089 1.22727
\(677\) 32.9090i 1.26479i −0.774644 0.632397i \(-0.782071\pi\)
0.774644 0.632397i \(-0.217929\pi\)
\(678\) 4.61230 + 10.3134i 0.177134 + 0.396084i
\(679\) 0 0
\(680\) −5.47723 4.47214i −0.210042 0.171499i
\(681\) 16.4317 7.34847i 0.629663 0.281594i
\(682\) 0.0644158 0.00246661
\(683\) 2.95445 0.113049 0.0565245 0.998401i \(-0.481998\pi\)
0.0565245 + 0.998401i \(0.481998\pi\)
\(684\) −10.9441 9.78866i −0.418456 0.374279i
\(685\) −10.5744 + 12.9509i −0.404027 + 0.494830i
\(686\) 0 0
\(687\) 11.4317 5.11240i 0.436146 0.195050i
\(688\) 2.02265i 0.0771127i
\(689\) 33.5071 1.27652
\(690\) 24.2158 + 6.55057i 0.921881 + 0.249376i
\(691\) 3.46410i 0.131781i 0.997827 + 0.0658903i \(0.0209887\pi\)
−0.997827 + 0.0658903i \(0.979011\pi\)
\(692\) 11.5207i 0.437952i
\(693\) 0 0
\(694\) −6.52277 −0.247601
\(695\) −13.0455 10.6516i −0.494846 0.404040i
\(696\) −3.19808 + 1.43023i −0.121223 + 0.0542126i
\(697\) 21.1917i 0.802694i
\(698\) 32.5282i 1.23121i
\(699\) −2.82843 6.32456i −0.106981 0.239217i
\(700\) 0 0
\(701\) 7.03320i 0.265640i −0.991140 0.132820i \(-0.957597\pi\)
0.991140 0.132820i \(-0.0424033\pi\)
\(702\) −33.1703 10.5959i −1.25193 0.399915i
\(703\) 34.9213 1.31708
\(704\) 0.213422i 0.00804364i
\(705\) 7.84259 28.9921i 0.295369 1.09191i
\(706\) 13.2528i 0.498774i
\(707\) 0 0
\(708\) 3.47723 + 7.77531i 0.130682 + 0.292214i
\(709\) 10.4317 0.391770 0.195885 0.980627i \(-0.437242\pi\)
0.195885 + 0.980627i \(0.437242\pi\)
\(710\) 3.50333 + 2.86045i 0.131477 + 0.107351i
\(711\) −1.04555 + 1.16896i −0.0392111 + 0.0438394i
\(712\) 10.5744 0.396292
\(713\) 1.95498i 0.0732146i
\(714\) 0 0
\(715\) 2.47723 + 2.02265i 0.0926430 + 0.0756427i
\(716\) 14.9104i 0.557226i
\(717\) 0 0
\(718\) 6.49478i 0.242383i
\(719\) 47.2795 1.76323 0.881614 0.471970i \(-0.156457\pi\)
0.881614 + 0.471970i \(0.156457\pi\)
\(720\) −1.04456 6.62638i −0.0389283 0.246951i
\(721\) 0 0
\(722\) −4.95445 −0.184386
\(723\) 6.30694 2.82055i 0.234557 0.104897i
\(724\) 3.16228i 0.117525i
\(725\) 9.90890 2.02265i 0.368007 0.0751192i
\(726\) 7.74597 + 17.3205i 0.287480 + 0.642824i
\(727\) −23.6076 −0.875556 −0.437778 0.899083i \(-0.644234\pi\)
−0.437778 + 0.899083i \(0.644234\pi\)
\(728\) 0 0
\(729\) 22.0000 + 15.6525i 0.814815 + 0.579721i
\(730\) 16.9545 20.7649i 0.627512 0.768543i
\(731\) −6.39617 −0.236571
\(732\) −5.47723 + 2.44949i −0.202444 + 0.0905357i
\(733\) −36.3355 −1.34208 −0.671041 0.741420i \(-0.734152\pi\)
−0.671041 + 0.741420i \(0.734152\pi\)
\(734\) 8.11562 0.299553
\(735\) 0 0
\(736\) −6.47723 −0.238754
\(737\) 1.13665 0.0418689
\(738\) 13.4028 14.9848i 0.493365 0.551598i
\(739\) −4.47723 −0.164697 −0.0823487 0.996604i \(-0.526242\pi\)
−0.0823487 + 0.996604i \(0.526242\pi\)
\(740\) 12.3583 + 10.0905i 0.454299 + 0.370933i
\(741\) −51.8596 + 23.1923i −1.90511 + 0.851991i
\(742\) 0 0
\(743\) −19.4317 −0.712879 −0.356440 0.934318i \(-0.616009\pi\)
−0.356440 + 0.934318i \(0.616009\pi\)
\(744\) −0.477226 + 0.213422i −0.0174959 + 0.00782442i
\(745\) −4.24264 3.46410i −0.155438 0.126915i
\(746\) 3.61845i 0.132481i
\(747\) 37.3800 + 33.4337i 1.36766 + 1.22328i
\(748\) 0.674899 0.0246767
\(749\) 0 0
\(750\) −1.21584 + 19.3267i −0.0443961 + 0.705712i
\(751\) −32.0000 −1.16770 −0.583848 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) 7.75478i 0.282788i
\(753\) 11.7386 + 26.2483i 0.427779 + 0.956543i
\(754\) 13.5546i 0.493629i
\(755\) 2.82843 3.46410i 0.102937 0.126072i
\(756\) 0 0
\(757\) 30.2476i 1.09937i 0.835373 + 0.549683i \(0.185252\pi\)
−0.835373 + 0.549683i \(0.814748\pi\)
\(758\) −9.52277 −0.345883
\(759\) −2.18574 + 0.977491i −0.0793372 + 0.0354807i
\(760\) −8.47723 6.92163i −0.307501 0.251074i
\(761\) −9.52984 −0.345456 −0.172728 0.984970i \(-0.555258\pi\)
−0.172728 + 0.984970i \(0.555258\pi\)
\(762\) 21.5507 9.63774i 0.780698 0.349139i
\(763\) 0 0
\(764\) 1.59580i 0.0577341i
\(765\) 20.9545 3.30318i 0.757610 0.119427i
\(766\) 0.826579i 0.0298655i
\(767\) 32.9545 1.18992
\(768\) 0.707107 + 1.58114i 0.0255155 + 0.0570544i
\(769\) 28.8412i 1.04004i −0.854154 0.520020i \(-0.825924\pi\)
0.854154 0.520020i \(-0.174076\pi\)
\(770\) 0 0
\(771\) 37.3861 16.7196i 1.34643 0.602141i
\(772\) 7.34847i 0.264477i
\(773\) 28.8412i 1.03735i 0.854973 + 0.518673i \(0.173574\pi\)
−0.854973 + 0.518673i \(0.826426\pi\)
\(774\) −4.52277 4.04529i −0.162568 0.145405i
\(775\) 1.47863 0.301824i 0.0531139 0.0108418i
\(776\) −3.50333 −0.125762
\(777\) 0 0
\(778\) 7.34847i 0.263455i
\(779\) 32.7989i 1.17514i
\(780\) −25.0540 6.77729i −0.897076 0.242666i
\(781\) −0.431677 −0.0154466
\(782\) 20.4828i 0.732463i
\(783\) 3.19808 10.0116i 0.114290 0.357785i
\(784\) 0 0
\(785\) 12.4317 15.2256i 0.443706 0.543426i
\(786\) −4.26139 9.52875i −0.151999 0.339879i
\(787\) −34.6804 −1.23622 −0.618112 0.786090i \(-0.712102\pi\)
−0.618112 + 0.786090i \(0.712102\pi\)
\(788\) 9.00000 0.320612
\(789\) −1.41421 3.16228i −0.0503473 0.112580i
\(790\) −0.739315 + 0.905472i −0.0263036 + 0.0322152i
\(791\) 0 0
\(792\) 0.477226 + 0.426844i 0.0169575 + 0.0151672i
\(793\) 23.2144i 0.824366i
\(794\) 30.3734 1.07791
\(795\) −18.6931 5.05662i −0.662975 0.179340i
\(796\) 22.4378i 0.795286i
\(797\) 28.9201i 1.02440i 0.858865 + 0.512201i \(0.171170\pi\)
−0.858865 + 0.512201i \(0.828830\pi\)
\(798\) 0 0
\(799\) −24.5228 −0.867553
\(800\) −1.00000 4.89898i −0.0353553 0.173205i
\(801\) −21.1488 + 23.6451i −0.747256 + 0.835457i
\(802\) 30.3494i 1.07168i
\(803\) 2.55863i 0.0902921i
\(804\) −8.42087 + 3.76593i −0.296981 + 0.132814i
\(805\) 0 0
\(806\) 2.02265i 0.0712447i
\(807\) −20.4317 45.6866i −0.719229 1.60825i
\(808\) 11.3137 0.398015
\(809\) 40.1474i 1.41151i 0.708458 + 0.705753i \(0.249391\pi\)
−0.708458 + 0.705753i \(0.750609\pi\)
\(810\) 16.9061 + 10.9171i 0.594021 + 0.383586i
\(811\) 6.70527i 0.235454i −0.993046 0.117727i \(-0.962439\pi\)
0.993046 0.117727i \(-0.0375608\pi\)
\(812\) 0 0
\(813\) −10.0000 + 4.47214i −0.350715 + 0.156845i
\(814\) −1.52277 −0.0533732
\(815\) 25.4558 + 20.7846i 0.891679 + 0.728053i
\(816\) −5.00000 + 2.23607i −0.175035 + 0.0782780i
\(817\) −9.89949 −0.346339
\(818\) 22.4378i 0.784518i
\(819\) 0 0
\(820\) 9.47723 11.6072i 0.330959 0.405340i
\(821\) 50.9009i 1.77645i 0.459406 + 0.888226i \(0.348062\pi\)
−0.459406 + 0.888226i \(0.651938\pi\)
\(822\) 5.28720 + 11.8225i 0.184412 + 0.412358i
\(823\) 32.5855i 1.13586i 0.823077 + 0.567929i \(0.192255\pi\)
−0.823077 + 0.567929i \(0.807745\pi\)
\(824\) 10.5744 0.368376
\(825\) −1.07676 1.50225i −0.0374881 0.0523015i
\(826\) 0 0
\(827\) 39.9089 1.38777 0.693884 0.720087i \(-0.255898\pi\)
0.693884 + 0.720087i \(0.255898\pi\)
\(828\) 12.9545 14.4835i 0.450198 0.503337i
\(829\) 18.8296i 0.653980i 0.945028 + 0.326990i \(0.106034\pi\)
−0.945028 + 0.326990i \(0.893966\pi\)
\(830\) 28.9545 + 23.6412i 1.00502 + 0.820598i
\(831\) 15.4919 6.92820i 0.537409 0.240337i
\(832\) 6.70141 0.232330
\(833\) 0 0
\(834\) −11.9089 + 5.32582i −0.412372 + 0.184418i
\(835\) −25.4317 20.7649i −0.880099 0.718598i
\(836\) 1.04456 0.0361267
\(837\) 0.477226 1.49395i 0.0164953 0.0516385i
\(838\) −16.6009 −0.573469
\(839\) −37.3156 −1.28828 −0.644139 0.764908i \(-0.722784\pi\)
−0.644139 + 0.764908i \(0.722784\pi\)
\(840\) 0 0
\(841\) 24.9089 0.858928
\(842\) −2.95445 −0.101817
\(843\) 18.3526 8.20752i 0.632096 0.282682i
\(844\) 13.5228 0.465473
\(845\) −45.1260 + 55.2678i −1.55238 + 1.90127i
\(846\) −17.3402 15.5096i −0.596169 0.533230i
\(847\) 0 0
\(848\) 5.00000 0.171701
\(849\) 17.4772 + 39.0803i 0.599817 + 1.34123i
\(850\) 15.4919 3.16228i 0.531369 0.108465i
\(851\) 46.2153i 1.58424i
\(852\) 3.19808 1.43023i 0.109565 0.0489988i
\(853\) 53.9165 1.84607 0.923033 0.384720i \(-0.125702\pi\)
0.923033 + 0.384720i \(0.125702\pi\)
\(854\) 0 0
\(855\) 32.4317 5.11240i 1.10914 0.174840i
\(856\) 5.47723 0.187208
\(857\) 40.3619i 1.37874i −0.724411 0.689369i \(-0.757888\pi\)
0.724411 0.689369i \(-0.242112\pi\)
\(858\) 2.26139 1.01132i 0.0772025 0.0345260i
\(859\) 17.9242i 0.611564i −0.952102 0.305782i \(-0.901082\pi\)
0.952102 0.305782i \(-0.0989179\pi\)
\(860\) −3.50333 2.86045i −0.119462 0.0975407i
\(861\) 0 0
\(862\) 37.0576i 1.26219i
\(863\) −15.5228 −0.528401 −0.264201 0.964468i \(-0.585108\pi\)
−0.264201 + 0.964468i \(0.585108\pi\)
\(864\) −4.94975 1.58114i −0.168394 0.0537914i
\(865\) 19.9545 + 16.2927i 0.678472 + 0.553970i
\(866\) 0 0
\(867\) 4.94975 + 11.0680i 0.168102 + 0.375888i
\(868\) 0 0
\(869\) 0.111571i 0.00378480i
\(870\) 2.04555 7.56189i 0.0693506 0.256372i
\(871\) 35.6905i 1.20933i
\(872\) 12.4317 0.420990
\(873\) 7.00665 7.83368i 0.237139 0.265130i
\(874\) 31.7017i 1.07232i
\(875\) 0 0
\(876\) −8.47723 18.9557i −0.286419 0.640452i
\(877\) 42.2816i 1.42775i 0.700274 + 0.713874i \(0.253061\pi\)
−0.700274 + 0.713874i \(0.746939\pi\)
\(878\) 22.7396i 0.767424i
\(879\) 7.26139 3.24739i 0.244921 0.109532i
\(880\) 0.369657 + 0.301824i 0.0124611 + 0.0101745i
\(881\) 26.5004 0.892821 0.446411 0.894828i \(-0.352702\pi\)
0.446411 + 0.894828i \(0.352702\pi\)
\(882\) 0 0
\(883\) 29.2823i 0.985428i 0.870191 + 0.492714i \(0.163995\pi\)
−0.870191 + 0.492714i \(0.836005\pi\)
\(884\) 21.1917i 0.712755i
\(885\) −18.3848 4.97322i −0.617997 0.167173i
\(886\) −36.9545 −1.24151
\(887\) 3.46410i 0.116313i 0.998307 + 0.0581566i \(0.0185223\pi\)
−0.998307 + 0.0581566i \(0.981478\pi\)
\(888\) 11.2815 5.04524i 0.378582 0.169307i
\(889\) 0 0
\(890\) −14.9545 + 18.3154i −0.501274 + 0.613933i
\(891\) −1.90890 + 0.213422i −0.0639506 + 0.00714990i
\(892\) 6.39617 0.214160
\(893\) −37.9545 −1.27010
\(894\) −3.87298 + 1.73205i −0.129532 + 0.0579284i
\(895\) −25.8255 21.0864i −0.863251 0.704842i
\(896\) 0 0
\(897\) −30.6931 68.6318i −1.02481 2.29155i
\(898\) 3.51660i 0.117350i
\(899\) −0.610483 −0.0203608
\(900\) 12.9545 + 7.56189i 0.431815 + 0.252063i
\(901\) 15.8114i 0.526754i
\(902\) 1.43023i 0.0476213i
\(903\) 0 0
\(904\) 6.52277 0.216944
\(905\) 5.47723 + 4.47214i 0.182069 + 0.148659i
\(906\) −1.41421 3.16228i −0.0469841 0.105060i
\(907\) 9.79796i 0.325336i −0.986681 0.162668i \(-0.947990\pi\)
0.986681 0.162668i \(-0.0520099\pi\)
\(908\) 10.3923i 0.344881i
\(909\) −22.6274 + 25.2982i −0.750504 + 0.839089i
\(910\) 0 0
\(911\) 15.1238i 0.501073i 0.968107 + 0.250537i \(0.0806071\pi\)
−0.968107 + 0.250537i \(0.919393\pi\)
\(912\) −7.73861 + 3.46081i −0.256251 + 0.114599i
\(913\) −3.56774 −0.118075
\(914\) 37.9113i 1.25399i
\(915\) 3.50333 12.9509i 0.115816 0.428145i
\(916\) 7.23003i 0.238887i
\(917\) 0 0
\(918\) 5.00000 15.6525i 0.165025 0.516609i
\(919\) −32.4317 −1.06982 −0.534911 0.844908i \(-0.679655\pi\)
−0.534911 + 0.844908i \(0.679655\pi\)
\(920\) 9.16018 11.2189i 0.302002 0.369876i
\(921\) 2.47723 + 5.53924i 0.0816274 + 0.182524i
\(922\) −16.2957 −0.536669
\(923\) 13.5546i 0.446155i
\(924\) 0 0
\(925\) −34.9545 + 7.13505i −1.14930 + 0.234599i
\(926\) 17.6751i 0.580841i
\(927\) −21.1488 + 23.6451i −0.694617 + 0.776606i
\(928\) 2.02265i 0.0663966i
\(929\) 23.6720 0.776652 0.388326 0.921522i \(-0.373053\pi\)
0.388326 + 0.921522i \(0.373053\pi\)
\(930\) 0.305242 1.12840i 0.0100093 0.0370018i
\(931\) 0 0
\(932\) −4.00000 −0.131024
\(933\) −20.4317 45.6866i −0.668903 1.49571i
\(934\) 34.3392i 1.12361i
\(935\) −0.954451 + 1.16896i −0.0312139 + 0.0382291i
\(936\) −13.4028 + 14.9848i −0.438085 + 0.489794i
\(937\) 22.6918 0.741310 0.370655 0.928771i \(-0.379133\pi\)
0.370655 + 0.928771i \(0.379133\pi\)
\(938\) 0 0
\(939\) −16.4317 36.7423i −0.536228 1.19904i
\(940\) −13.4317 10.9669i −0.438093 0.357701i
\(941\) −4.98196 −0.162407 −0.0812036 0.996698i \(-0.525876\pi\)
−0.0812036 + 0.996698i \(0.525876\pi\)
\(942\) −6.21584 13.8990i −0.202523 0.452855i
\(943\) 43.4065 1.41351
\(944\) 4.91754 0.160052
\(945\) 0 0
\(946\) 0.431677 0.0140350
\(947\) −32.8634 −1.06792 −0.533958 0.845511i \(-0.679296\pi\)
−0.533958 + 0.845511i \(0.679296\pi\)
\(948\) 0.369657 + 0.826579i 0.0120059 + 0.0268460i
\(949\) −80.3406 −2.60797
\(950\) 23.9772 4.89433i 0.777924 0.158793i
\(951\) 23.9772 + 53.6147i 0.777514 + 1.73858i
\(952\) 0 0
\(953\) 25.0455 0.811305 0.405652 0.914027i \(-0.367044\pi\)
0.405652 + 0.914027i \(0.367044\pi\)
\(954\) −10.0000 + 11.1803i −0.323762 + 0.361977i
\(955\) 2.76401 + 2.25681i 0.0894413 + 0.0730285i
\(956\) 0 0
\(957\) 0.305242 + 0.682541i 0.00986706 + 0.0220634i
\(958\) −11.3781 −0.367611
\(959\) 0 0
\(960\) −3.73861 1.01132i −0.120663 0.0326403i
\(961\) 30.9089 0.997061
\(962\) 47.8149i 1.54161i
\(963\) −10.9545 + 12.2474i −0.353002 + 0.394669i
\(964\) 3.98886i 0.128472i
\(965\) −12.7279 10.3923i −0.409726 0.334540i
\(966\) 0 0
\(967\) 46.4287i 1.49305i 0.665359 + 0.746524i \(0.268279\pi\)
−0.665359 + 0.746524i \(0.731721\pi\)
\(968\) 10.9545 0.352089
\(969\) −10.9441 24.4716i −0.351574 0.786142i
\(970\) 4.95445 6.06794i 0.159078 0.194830i
\(971\) 0.980140 0.0314542 0.0157271 0.999876i \(-0.494994\pi\)
0.0157271 + 0.999876i \(0.494994\pi\)
\(972\) 13.4350 7.90569i 0.430929 0.253575i
\(973\) 0 0
\(974\) 36.6308i 1.17373i
\(975\) 47.1703 33.8102i 1.51066 1.08279i
\(976\) 3.46410i 0.110883i
\(977\) −39.9089 −1.27680 −0.638399 0.769705i \(-0.720403\pi\)
−0.638399 + 0.769705i \(0.720403\pi\)
\(978\) 23.2379 10.3923i 0.743066 0.332309i
\(979\) 2.25681i 0.0721278i
\(980\) 0 0
\(981\) −24.8634 + 27.7981i −0.793826 + 0.887524i
\(982\) 4.04529i 0.129090i
\(983\) 33.8144i 1.07851i 0.842142 + 0.539257i \(0.181295\pi\)
−0.842142 + 0.539257i \(0.818705\pi\)
\(984\) −4.73861 10.5959i −0.151061 0.337784i
\(985\) −12.7279 + 15.5885i −0.405545 + 0.496690i
\(986\) −6.39617 −0.203696
\(987\) 0 0
\(988\) 32.7989i 1.04347i
\(989\) 13.1011i 0.416592i
\(990\) −1.41421 + 0.222931i −0.0449467 + 0.00708521i
\(991\) 21.4772 0.682247 0.341123 0.940019i \(-0.389193\pi\)
0.341123 + 0.940019i \(0.389193\pi\)
\(992\) 0.301824i 0.00958292i
\(993\) −8.08342 18.0751i −0.256519 0.573595i
\(994\) 0 0
\(995\) −38.8634 31.7318i −1.23205 1.00597i
\(996\) 26.4317 11.8206i 0.837520 0.374550i
\(997\) −15.4919 −0.490634 −0.245317 0.969443i \(-0.578892\pi\)
−0.245317 + 0.969443i \(0.578892\pi\)
\(998\) −41.9089 −1.32660
\(999\) −11.2815 + 35.3167i −0.356931 + 1.11737i
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 1470.2.d.f.1469.8 8
3.2 odd 2 1470.2.d.e.1469.5 8
5.4 even 2 1470.2.d.e.1469.1 8
7.2 even 3 210.2.t.e.59.1 8
7.3 odd 6 210.2.t.e.89.2 yes 8
7.6 odd 2 inner 1470.2.d.f.1469.1 8
15.14 odd 2 inner 1470.2.d.f.1469.4 8
21.2 odd 6 210.2.t.f.59.3 yes 8
21.17 even 6 210.2.t.f.89.4 yes 8
21.20 even 2 1470.2.d.e.1469.4 8
35.2 odd 12 1050.2.s.i.101.6 16
35.3 even 12 1050.2.s.i.551.5 16
35.9 even 6 210.2.t.f.59.4 yes 8
35.17 even 12 1050.2.s.i.551.4 16
35.23 odd 12 1050.2.s.i.101.3 16
35.24 odd 6 210.2.t.f.89.3 yes 8
35.34 odd 2 1470.2.d.e.1469.8 8
105.2 even 12 1050.2.s.i.101.4 16
105.17 odd 12 1050.2.s.i.551.6 16
105.23 even 12 1050.2.s.i.101.5 16
105.38 odd 12 1050.2.s.i.551.3 16
105.44 odd 6 210.2.t.e.59.2 yes 8
105.59 even 6 210.2.t.e.89.1 yes 8
105.104 even 2 inner 1470.2.d.f.1469.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.t.e.59.1 8 7.2 even 3
210.2.t.e.59.2 yes 8 105.44 odd 6
210.2.t.e.89.1 yes 8 105.59 even 6
210.2.t.e.89.2 yes 8 7.3 odd 6
210.2.t.f.59.3 yes 8 21.2 odd 6
210.2.t.f.59.4 yes 8 35.9 even 6
210.2.t.f.89.3 yes 8 35.24 odd 6
210.2.t.f.89.4 yes 8 21.17 even 6
1050.2.s.i.101.3 16 35.23 odd 12
1050.2.s.i.101.4 16 105.2 even 12
1050.2.s.i.101.5 16 105.23 even 12
1050.2.s.i.101.6 16 35.2 odd 12
1050.2.s.i.551.3 16 105.38 odd 12
1050.2.s.i.551.4 16 35.17 even 12
1050.2.s.i.551.5 16 35.3 even 12
1050.2.s.i.551.6 16 105.17 odd 12
1470.2.d.e.1469.1 8 5.4 even 2
1470.2.d.e.1469.4 8 21.20 even 2
1470.2.d.e.1469.5 8 3.2 odd 2
1470.2.d.e.1469.8 8 35.34 odd 2
1470.2.d.f.1469.1 8 7.6 odd 2 inner
1470.2.d.f.1469.4 8 15.14 odd 2 inner
1470.2.d.f.1469.5 8 105.104 even 2 inner
1470.2.d.f.1469.8 8 1.1 even 1 trivial