Properties

Label 1170.2.cu.e.1151.1
Level $1170$
Weight $2$
Character 1170.1151
Analytic conductor $9.342$
Analytic rank $0$
Dimension $16$
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] = [1170,2,Mod(71,1170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1170, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1170.71");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.cu (of order \(12\), degree \(4\), 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: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 12x^{14} + 103x^{12} - 396x^{10} + 1089x^{8} - 1584x^{6} + 1648x^{4} - 768x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 1151.1
Root \(1.46923 - 0.848261i\) of defining polynomial
Character \(\chi\) \(=\) 1170.1151
Dual form 1170.2.cu.e.431.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.47231 - 0.394504i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.47231 - 0.394504i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{10} +(1.35157 - 0.362151i) q^{11} +(-3.30591 + 1.43909i) q^{13} +1.52425i q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.431501 - 0.747382i) q^{17} +(2.02848 - 7.57039i) q^{19} +(-0.258819 + 0.965926i) q^{20} +(-0.699622 - 1.21178i) q^{22} +(-1.90032 + 3.29146i) q^{23} -1.00000i q^{25} +(2.24569 + 2.82080i) q^{26} +(1.47231 - 0.394504i) q^{28} +(-6.11051 - 3.52790i) q^{29} +(-5.72126 - 5.72126i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-0.610235 + 0.610235i) q^{34} +(-1.32004 + 0.762124i) q^{35} +(-0.943831 - 3.52243i) q^{37} -7.83744 q^{38} +1.00000 q^{40} +(1.69652 + 6.33150i) q^{41} +(-1.97231 + 1.13871i) q^{43} +(-0.989414 + 0.989414i) q^{44} +(3.67114 + 0.983680i) q^{46} +(6.37736 + 6.37736i) q^{47} +(-4.05012 - 2.33834i) q^{49} +(-0.965926 + 0.258819i) q^{50} +(2.14345 - 2.89924i) q^{52} -4.69722i q^{53} +(0.699622 - 1.21178i) q^{55} +(-0.762124 - 1.32004i) q^{56} +(-1.82618 + 6.81538i) q^{58} +(1.25627 - 4.68848i) q^{59} +(-6.11102 - 10.5846i) q^{61} +(-4.04554 + 7.00708i) q^{62} +1.00000i q^{64} +(-1.32004 + 3.35522i) q^{65} +(4.17588 - 1.11892i) q^{67} +(0.747382 + 0.431501i) q^{68} +(1.07781 + 1.07781i) q^{70} +(-9.99904 - 2.67923i) q^{71} +(-4.27743 + 4.27743i) q^{73} +(-3.15812 + 1.82334i) q^{74} +(2.02848 + 7.57039i) q^{76} -2.13279 q^{77} -7.74153 q^{79} +(-0.258819 - 0.965926i) q^{80} +(5.67667 - 3.27743i) q^{82} +(-6.44154 + 6.44154i) q^{83} +(-0.833596 - 0.223361i) q^{85} +(1.61038 + 1.61038i) q^{86} +(1.21178 + 0.699622i) q^{88} +(-9.45809 + 2.53429i) q^{89} +(5.43505 - 0.814595i) q^{91} -3.80065i q^{92} +(4.50948 - 7.81064i) q^{94} +(-3.91872 - 6.78742i) q^{95} +(3.30059 - 12.3180i) q^{97} +(-1.21041 + 4.51732i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{7} - 12 q^{13} + 8 q^{16} + 36 q^{19} + 12 q^{22} - 8 q^{28} - 12 q^{31} + 16 q^{34} + 20 q^{37} + 16 q^{40} + 32 q^{46} - 12 q^{49} - 24 q^{52} - 12 q^{55} + 32 q^{58} - 44 q^{61} + 4 q^{67} - 4 q^{70} - 24 q^{73} + 36 q^{76} - 24 q^{79} - 4 q^{85} + 12 q^{88} + 36 q^{91} + 56 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 0.965926i −0.183013 0.683013i
\(3\) 0 0
\(4\) −0.866025 + 0.500000i −0.433013 + 0.250000i
\(5\) 0.707107 0.707107i 0.316228 0.316228i
\(6\) 0 0
\(7\) −1.47231 0.394504i −0.556481 0.149109i −0.0303917 0.999538i \(-0.509675\pi\)
−0.526089 + 0.850429i \(0.676342\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 0 0
\(10\) −0.866025 0.500000i −0.273861 0.158114i
\(11\) 1.35157 0.362151i 0.407512 0.109193i −0.0492390 0.998787i \(-0.515680\pi\)
0.456751 + 0.889594i \(0.349013\pi\)
\(12\) 0 0
\(13\) −3.30591 + 1.43909i −0.916893 + 0.399132i
\(14\) 1.52425i 0.407372i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −0.431501 0.747382i −0.104654 0.181267i 0.808943 0.587888i \(-0.200040\pi\)
−0.913597 + 0.406621i \(0.866707\pi\)
\(18\) 0 0
\(19\) 2.02848 7.57039i 0.465365 1.73677i −0.190312 0.981724i \(-0.560950\pi\)
0.655677 0.755042i \(-0.272384\pi\)
\(20\) −0.258819 + 0.965926i −0.0578737 + 0.215988i
\(21\) 0 0
\(22\) −0.699622 1.21178i −0.149160 0.258352i
\(23\) −1.90032 + 3.29146i −0.396245 + 0.686316i −0.993259 0.115914i \(-0.963020\pi\)
0.597014 + 0.802231i \(0.296354\pi\)
\(24\) 0 0
\(25\) 1.00000i 0.200000i
\(26\) 2.24569 + 2.82080i 0.440416 + 0.553204i
\(27\) 0 0
\(28\) 1.47231 0.394504i 0.278240 0.0745543i
\(29\) −6.11051 3.52790i −1.13469 0.655115i −0.189582 0.981865i \(-0.560713\pi\)
−0.945111 + 0.326750i \(0.894047\pi\)
\(30\) 0 0
\(31\) −5.72126 5.72126i −1.02757 1.02757i −0.999609 0.0279592i \(-0.991099\pi\)
−0.0279592 0.999609i \(-0.508901\pi\)
\(32\) −0.965926 0.258819i −0.170753 0.0457532i
\(33\) 0 0
\(34\) −0.610235 + 0.610235i −0.104654 + 0.104654i
\(35\) −1.32004 + 0.762124i −0.223127 + 0.128822i
\(36\) 0 0
\(37\) −0.943831 3.52243i −0.155165 0.579083i −0.999091 0.0426240i \(-0.986428\pi\)
0.843926 0.536459i \(-0.180238\pi\)
\(38\) −7.83744 −1.27140
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) 1.69652 + 6.33150i 0.264952 + 0.988815i 0.962280 + 0.272062i \(0.0877056\pi\)
−0.697328 + 0.716753i \(0.745628\pi\)
\(42\) 0 0
\(43\) −1.97231 + 1.13871i −0.300774 + 0.173652i −0.642791 0.766042i \(-0.722224\pi\)
0.342016 + 0.939694i \(0.388890\pi\)
\(44\) −0.989414 + 0.989414i −0.149160 + 0.149160i
\(45\) 0 0
\(46\) 3.67114 + 0.983680i 0.541280 + 0.145036i
\(47\) 6.37736 + 6.37736i 0.930234 + 0.930234i 0.997720 0.0674859i \(-0.0214978\pi\)
−0.0674859 + 0.997720i \(0.521498\pi\)
\(48\) 0 0
\(49\) −4.05012 2.33834i −0.578588 0.334048i
\(50\) −0.965926 + 0.258819i −0.136603 + 0.0366025i
\(51\) 0 0
\(52\) 2.14345 2.89924i 0.297243 0.402053i
\(53\) 4.69722i 0.645213i −0.946533 0.322607i \(-0.895441\pi\)
0.946533 0.322607i \(-0.104559\pi\)
\(54\) 0 0
\(55\) 0.699622 1.21178i 0.0943370 0.163396i
\(56\) −0.762124 1.32004i −0.101843 0.176397i
\(57\) 0 0
\(58\) −1.82618 + 6.81538i −0.239789 + 0.894904i
\(59\) 1.25627 4.68848i 0.163553 0.610387i −0.834668 0.550754i \(-0.814340\pi\)
0.998220 0.0596333i \(-0.0189931\pi\)
\(60\) 0 0
\(61\) −6.11102 10.5846i −0.782436 1.35522i −0.930519 0.366244i \(-0.880643\pi\)
0.148082 0.988975i \(-0.452690\pi\)
\(62\) −4.04554 + 7.00708i −0.513784 + 0.889900i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −1.32004 + 3.35522i −0.163730 + 0.416164i
\(66\) 0 0
\(67\) 4.17588 1.11892i 0.510165 0.136698i 0.00545147 0.999985i \(-0.498265\pi\)
0.504714 + 0.863287i \(0.331598\pi\)
\(68\) 0.747382 + 0.431501i 0.0906334 + 0.0523272i
\(69\) 0 0
\(70\) 1.07781 + 1.07781i 0.128822 + 0.128822i
\(71\) −9.99904 2.67923i −1.18667 0.317967i −0.389099 0.921196i \(-0.627214\pi\)
−0.797568 + 0.603229i \(0.793880\pi\)
\(72\) 0 0
\(73\) −4.27743 + 4.27743i −0.500635 + 0.500635i −0.911635 0.411000i \(-0.865180\pi\)
0.411000 + 0.911635i \(0.365180\pi\)
\(74\) −3.15812 + 1.82334i −0.367124 + 0.211959i
\(75\) 0 0
\(76\) 2.02848 + 7.57039i 0.232682 + 0.868383i
\(77\) −2.13279 −0.243054
\(78\) 0 0
\(79\) −7.74153 −0.870990 −0.435495 0.900191i \(-0.643427\pi\)
−0.435495 + 0.900191i \(0.643427\pi\)
\(80\) −0.258819 0.965926i −0.0289368 0.107994i
\(81\) 0 0
\(82\) 5.67667 3.27743i 0.626883 0.361931i
\(83\) −6.44154 + 6.44154i −0.707051 + 0.707051i −0.965914 0.258863i \(-0.916652\pi\)
0.258863 + 0.965914i \(0.416652\pi\)
\(84\) 0 0
\(85\) −0.833596 0.223361i −0.0904162 0.0242269i
\(86\) 1.61038 + 1.61038i 0.173652 + 0.173652i
\(87\) 0 0
\(88\) 1.21178 + 0.699622i 0.129176 + 0.0745799i
\(89\) −9.45809 + 2.53429i −1.00256 + 0.268634i −0.722516 0.691354i \(-0.757014\pi\)
−0.280040 + 0.959988i \(0.590348\pi\)
\(90\) 0 0
\(91\) 5.43505 0.814595i 0.569748 0.0853928i
\(92\) 3.80065i 0.396245i
\(93\) 0 0
\(94\) 4.50948 7.81064i 0.465117 0.805607i
\(95\) −3.91872 6.78742i −0.402052 0.696375i
\(96\) 0 0
\(97\) 3.30059 12.3180i 0.335124 1.25070i −0.568610 0.822607i \(-0.692519\pi\)
0.903735 0.428093i \(-0.140815\pi\)
\(98\) −1.21041 + 4.51732i −0.122270 + 0.456318i
\(99\) 0 0
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) 3.96815 6.87304i 0.394846 0.683893i −0.598236 0.801320i \(-0.704131\pi\)
0.993081 + 0.117427i \(0.0374647\pi\)
\(102\) 0 0
\(103\) 12.2088i 1.20297i 0.798885 + 0.601484i \(0.205424\pi\)
−0.798885 + 0.601484i \(0.794576\pi\)
\(104\) −3.35522 1.32004i −0.329006 0.129440i
\(105\) 0 0
\(106\) −4.53717 + 1.21573i −0.440689 + 0.118082i
\(107\) 6.02612 + 3.47918i 0.582567 + 0.336345i 0.762153 0.647397i \(-0.224143\pi\)
−0.179586 + 0.983742i \(0.557476\pi\)
\(108\) 0 0
\(109\) −4.14077 4.14077i −0.396614 0.396614i 0.480423 0.877037i \(-0.340483\pi\)
−0.877037 + 0.480423i \(0.840483\pi\)
\(110\) −1.35157 0.362151i −0.128867 0.0345297i
\(111\) 0 0
\(112\) −1.07781 + 1.07781i −0.101843 + 0.101843i
\(113\) 11.9157 6.87955i 1.12094 0.647174i 0.179298 0.983795i \(-0.442617\pi\)
0.941640 + 0.336621i \(0.109284\pi\)
\(114\) 0 0
\(115\) 0.983680 + 3.67114i 0.0917286 + 0.342336i
\(116\) 7.05580 0.655115
\(117\) 0 0
\(118\) −4.85387 −0.446835
\(119\) 0.340458 + 1.27061i 0.0312097 + 0.116476i
\(120\) 0 0
\(121\) −7.83070 + 4.52106i −0.711882 + 0.411005i
\(122\) −8.64229 + 8.64229i −0.782436 + 0.782436i
\(123\) 0 0
\(124\) 7.81538 + 2.09413i 0.701842 + 0.188058i
\(125\) −0.707107 0.707107i −0.0632456 0.0632456i
\(126\) 0 0
\(127\) −0.431191 0.248948i −0.0382620 0.0220906i 0.480747 0.876859i \(-0.340366\pi\)
−0.519009 + 0.854769i \(0.673699\pi\)
\(128\) 0.965926 0.258819i 0.0853766 0.0228766i
\(129\) 0 0
\(130\) 3.58254 + 0.406663i 0.314210 + 0.0356667i
\(131\) 15.7546i 1.37649i 0.725480 + 0.688244i \(0.241618\pi\)
−0.725480 + 0.688244i \(0.758382\pi\)
\(132\) 0 0
\(133\) −5.97310 + 10.3457i −0.517933 + 0.897087i
\(134\) −2.16160 3.74399i −0.186733 0.323432i
\(135\) 0 0
\(136\) 0.223361 0.833596i 0.0191531 0.0714803i
\(137\) 2.39109 8.92367i 0.204285 0.762401i −0.785382 0.619012i \(-0.787533\pi\)
0.989666 0.143389i \(-0.0458000\pi\)
\(138\) 0 0
\(139\) 8.70168 + 15.0718i 0.738067 + 1.27837i 0.953365 + 0.301821i \(0.0975945\pi\)
−0.215298 + 0.976548i \(0.569072\pi\)
\(140\) 0.762124 1.32004i 0.0644112 0.111563i
\(141\) 0 0
\(142\) 10.3518i 0.868701i
\(143\) −3.94698 + 3.14226i −0.330063 + 0.262769i
\(144\) 0 0
\(145\) −6.81538 + 1.82618i −0.565987 + 0.151656i
\(146\) 5.23876 + 3.02460i 0.433563 + 0.250317i
\(147\) 0 0
\(148\) 2.57859 + 2.57859i 0.211959 + 0.211959i
\(149\) 10.4871 + 2.81000i 0.859135 + 0.230204i 0.661384 0.750048i \(-0.269970\pi\)
0.197751 + 0.980252i \(0.436636\pi\)
\(150\) 0 0
\(151\) 7.36124 7.36124i 0.599049 0.599049i −0.341010 0.940060i \(-0.610769\pi\)
0.940060 + 0.341010i \(0.110769\pi\)
\(152\) 6.78742 3.91872i 0.550533 0.317850i
\(153\) 0 0
\(154\) 0.552007 + 2.06012i 0.0444820 + 0.166009i
\(155\) −8.09108 −0.649891
\(156\) 0 0
\(157\) −18.3502 −1.46450 −0.732252 0.681034i \(-0.761531\pi\)
−0.732252 + 0.681034i \(0.761531\pi\)
\(158\) 2.00366 + 7.47774i 0.159402 + 0.594897i
\(159\) 0 0
\(160\) −0.866025 + 0.500000i −0.0684653 + 0.0395285i
\(161\) 4.09636 4.09636i 0.322838 0.322838i
\(162\) 0 0
\(163\) 6.30538 + 1.68952i 0.493875 + 0.132334i 0.497156 0.867661i \(-0.334378\pi\)
−0.00328069 + 0.999995i \(0.501044\pi\)
\(164\) −4.63498 4.63498i −0.361931 0.361931i
\(165\) 0 0
\(166\) 7.88924 + 4.55485i 0.612324 + 0.353525i
\(167\) 15.2326 4.08157i 1.17874 0.315841i 0.384310 0.923204i \(-0.374439\pi\)
0.794425 + 0.607363i \(0.207773\pi\)
\(168\) 0 0
\(169\) 8.85803 9.51501i 0.681387 0.731924i
\(170\) 0.863002i 0.0661893i
\(171\) 0 0
\(172\) 1.13871 1.97231i 0.0868261 0.150387i
\(173\) −10.0015 17.3231i −0.760399 1.31705i −0.942645 0.333797i \(-0.891670\pi\)
0.182246 0.983253i \(-0.441663\pi\)
\(174\) 0 0
\(175\) −0.394504 + 1.47231i −0.0298217 + 0.111296i
\(176\) 0.362151 1.35157i 0.0272981 0.101878i
\(177\) 0 0
\(178\) 4.89587 + 8.47990i 0.366961 + 0.635595i
\(179\) −4.16414 + 7.21249i −0.311242 + 0.539087i −0.978632 0.205622i \(-0.934078\pi\)
0.667389 + 0.744709i \(0.267412\pi\)
\(180\) 0 0
\(181\) 24.3005i 1.80624i −0.429386 0.903121i \(-0.641270\pi\)
0.429386 0.903121i \(-0.358730\pi\)
\(182\) −2.19353 5.03902i −0.162595 0.373517i
\(183\) 0 0
\(184\) −3.67114 + 0.983680i −0.270640 + 0.0725178i
\(185\) −3.15812 1.82334i −0.232190 0.134055i
\(186\) 0 0
\(187\) −0.853867 0.853867i −0.0624409 0.0624409i
\(188\) −8.71164 2.33428i −0.635362 0.170245i
\(189\) 0 0
\(190\) −5.54191 + 5.54191i −0.402052 + 0.402052i
\(191\) 20.5835 11.8839i 1.48937 0.859890i 0.489446 0.872034i \(-0.337199\pi\)
0.999926 + 0.0121439i \(0.00386563\pi\)
\(192\) 0 0
\(193\) 6.40583 + 23.9069i 0.461102 + 1.72085i 0.669501 + 0.742811i \(0.266508\pi\)
−0.208399 + 0.978044i \(0.566825\pi\)
\(194\) −12.7525 −0.915576
\(195\) 0 0
\(196\) 4.67667 0.334048
\(197\) 0.859733 + 3.20857i 0.0612534 + 0.228601i 0.989766 0.142700i \(-0.0455785\pi\)
−0.928513 + 0.371301i \(0.878912\pi\)
\(198\) 0 0
\(199\) 6.71994 3.87976i 0.476364 0.275029i −0.242536 0.970142i \(-0.577979\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(200\) 0.707107 0.707107i 0.0500000 0.0500000i
\(201\) 0 0
\(202\) −7.66588 2.05407i −0.539369 0.144524i
\(203\) 7.60479 + 7.60479i 0.533751 + 0.533751i
\(204\) 0 0
\(205\) 5.67667 + 3.27743i 0.396476 + 0.228905i
\(206\) 11.7928 3.15987i 0.821642 0.220158i
\(207\) 0 0
\(208\) −0.406663 + 3.58254i −0.0281970 + 0.248405i
\(209\) 10.9665i 0.758568i
\(210\) 0 0
\(211\) 8.45747 14.6488i 0.582236 1.00846i −0.412978 0.910741i \(-0.635511\pi\)
0.995214 0.0977216i \(-0.0311555\pi\)
\(212\) 2.34861 + 4.06791i 0.161303 + 0.279385i
\(213\) 0 0
\(214\) 1.80096 6.72126i 0.123111 0.459456i
\(215\) −0.589442 + 2.19983i −0.0401996 + 0.150027i
\(216\) 0 0
\(217\) 6.16640 + 10.6805i 0.418603 + 0.725041i
\(218\) −2.92797 + 5.07139i −0.198307 + 0.343478i
\(219\) 0 0
\(220\) 1.39924i 0.0943370i
\(221\) 2.50205 + 1.84980i 0.168306 + 0.124431i
\(222\) 0 0
\(223\) −7.83487 + 2.09935i −0.524661 + 0.140583i −0.511422 0.859330i \(-0.670881\pi\)
−0.0132395 + 0.999912i \(0.504214\pi\)
\(224\) 1.32004 + 0.762124i 0.0881987 + 0.0509215i
\(225\) 0 0
\(226\) −9.72916 9.72916i −0.647174 0.647174i
\(227\) 6.48293 + 1.73710i 0.430287 + 0.115295i 0.467461 0.884014i \(-0.345169\pi\)
−0.0371739 + 0.999309i \(0.511836\pi\)
\(228\) 0 0
\(229\) −7.92188 + 7.92188i −0.523493 + 0.523493i −0.918624 0.395132i \(-0.870699\pi\)
0.395132 + 0.918624i \(0.370699\pi\)
\(230\) 3.29146 1.90032i 0.217032 0.125304i
\(231\) 0 0
\(232\) −1.82618 6.81538i −0.119894 0.447452i
\(233\) 9.48072 0.621102 0.310551 0.950557i \(-0.399486\pi\)
0.310551 + 0.950557i \(0.399486\pi\)
\(234\) 0 0
\(235\) 9.01896 0.588332
\(236\) 1.25627 + 4.68848i 0.0817764 + 0.305194i
\(237\) 0 0
\(238\) 1.13919 0.657714i 0.0738430 0.0426333i
\(239\) 3.11155 3.11155i 0.201270 0.201270i −0.599274 0.800544i \(-0.704544\pi\)
0.800544 + 0.599274i \(0.204544\pi\)
\(240\) 0 0
\(241\) 12.3375 + 3.30581i 0.794725 + 0.212946i 0.633267 0.773934i \(-0.281714\pi\)
0.161458 + 0.986880i \(0.448380\pi\)
\(242\) 6.39374 + 6.39374i 0.411005 + 0.411005i
\(243\) 0 0
\(244\) 10.5846 + 6.11102i 0.677610 + 0.391218i
\(245\) −4.51732 + 1.21041i −0.288601 + 0.0773303i
\(246\) 0 0
\(247\) 4.18852 + 27.9462i 0.266509 + 1.77817i
\(248\) 8.09108i 0.513784i
\(249\) 0 0
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) −0.756351 1.31004i −0.0477405 0.0826889i 0.841168 0.540774i \(-0.181869\pi\)
−0.888908 + 0.458085i \(0.848535\pi\)
\(252\) 0 0
\(253\) −1.37641 + 5.13682i −0.0865340 + 0.322949i
\(254\) −0.128865 + 0.480931i −0.00808572 + 0.0301763i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 5.11439 8.85838i 0.319027 0.552571i −0.661258 0.750158i \(-0.729977\pi\)
0.980285 + 0.197587i \(0.0633106\pi\)
\(258\) 0 0
\(259\) 5.55845i 0.345385i
\(260\) −0.534425 3.56572i −0.0331436 0.221137i
\(261\) 0 0
\(262\) 15.2178 4.07759i 0.940158 0.251915i
\(263\) −8.02732 4.63457i −0.494986 0.285780i 0.231655 0.972798i \(-0.425586\pi\)
−0.726640 + 0.687018i \(0.758919\pi\)
\(264\) 0 0
\(265\) −3.32144 3.32144i −0.204034 0.204034i
\(266\) 11.5391 + 3.09190i 0.707510 + 0.189577i
\(267\) 0 0
\(268\) −3.05696 + 3.05696i −0.186733 + 0.186733i
\(269\) 19.7102 11.3797i 1.20175 0.693831i 0.240806 0.970573i \(-0.422588\pi\)
0.960944 + 0.276742i \(0.0892548\pi\)
\(270\) 0 0
\(271\) 1.32539 + 4.94642i 0.0805116 + 0.300473i 0.994426 0.105433i \(-0.0336227\pi\)
−0.913915 + 0.405906i \(0.866956\pi\)
\(272\) −0.863002 −0.0523272
\(273\) 0 0
\(274\) −9.23846 −0.558116
\(275\) −0.362151 1.35157i −0.0218385 0.0815024i
\(276\) 0 0
\(277\) 1.83975 1.06218i 0.110540 0.0638201i −0.443711 0.896170i \(-0.646338\pi\)
0.554251 + 0.832350i \(0.313005\pi\)
\(278\) 12.3060 12.3060i 0.738067 0.738067i
\(279\) 0 0
\(280\) −1.47231 0.394504i −0.0879873 0.0235761i
\(281\) 7.20895 + 7.20895i 0.430050 + 0.430050i 0.888645 0.458595i \(-0.151647\pi\)
−0.458595 + 0.888645i \(0.651647\pi\)
\(282\) 0 0
\(283\) −12.0480 6.95589i −0.716177 0.413485i 0.0971670 0.995268i \(-0.469022\pi\)
−0.813344 + 0.581783i \(0.802355\pi\)
\(284\) 9.99904 2.67923i 0.593334 0.158983i
\(285\) 0 0
\(286\) 4.05675 + 2.99921i 0.239880 + 0.177347i
\(287\) 9.99122i 0.589763i
\(288\) 0 0
\(289\) 8.12761 14.0774i 0.478095 0.828085i
\(290\) 3.52790 + 6.11051i 0.207166 + 0.358821i
\(291\) 0 0
\(292\) 1.56565 5.84307i 0.0916226 0.341940i
\(293\) −0.629010 + 2.34750i −0.0367471 + 0.137142i −0.981862 0.189595i \(-0.939283\pi\)
0.945115 + 0.326737i \(0.105949\pi\)
\(294\) 0 0
\(295\) −2.42693 4.20357i −0.141302 0.244741i
\(296\) 1.82334 3.15812i 0.105980 0.183562i
\(297\) 0 0
\(298\) 10.8570i 0.628930i
\(299\) 1.54558 13.6160i 0.0893833 0.787433i
\(300\) 0 0
\(301\) 3.35308 0.898455i 0.193268 0.0517861i
\(302\) −9.01564 5.20518i −0.518792 0.299525i
\(303\) 0 0
\(304\) −5.54191 5.54191i −0.317850 0.317850i
\(305\) −11.8056 3.16330i −0.675986 0.181130i
\(306\) 0 0
\(307\) 17.8111 17.8111i 1.01653 1.01653i 0.0166732 0.999861i \(-0.494692\pi\)
0.999861 0.0166732i \(-0.00530750\pi\)
\(308\) 1.84705 1.06640i 0.105246 0.0607636i
\(309\) 0 0
\(310\) 2.09413 + 7.81538i 0.118938 + 0.443884i
\(311\) 7.46564 0.423338 0.211669 0.977341i \(-0.432110\pi\)
0.211669 + 0.977341i \(0.432110\pi\)
\(312\) 0 0
\(313\) −23.4344 −1.32459 −0.662296 0.749242i \(-0.730418\pi\)
−0.662296 + 0.749242i \(0.730418\pi\)
\(314\) 4.74938 + 17.7249i 0.268023 + 1.00028i
\(315\) 0 0
\(316\) 6.70436 3.87076i 0.377150 0.217748i
\(317\) 0.210690 0.210690i 0.0118335 0.0118335i −0.701165 0.712999i \(-0.747336\pi\)
0.712999 + 0.701165i \(0.247336\pi\)
\(318\) 0 0
\(319\) −9.53638 2.55527i −0.533935 0.143067i
\(320\) 0.707107 + 0.707107i 0.0395285 + 0.0395285i
\(321\) 0 0
\(322\) −5.01699 2.89656i −0.279586 0.161419i
\(323\) −6.53326 + 1.75058i −0.363520 + 0.0974050i
\(324\) 0 0
\(325\) 1.43909 + 3.30591i 0.0798265 + 0.183379i
\(326\) 6.52781i 0.361542i
\(327\) 0 0
\(328\) −3.27743 + 5.67667i −0.180966 + 0.313442i
\(329\) −6.87356 11.9054i −0.378952 0.656363i
\(330\) 0 0
\(331\) 6.36217 23.7439i 0.349697 1.30509i −0.537332 0.843371i \(-0.680568\pi\)
0.887029 0.461715i \(-0.152766\pi\)
\(332\) 2.35777 8.79930i 0.129399 0.482924i
\(333\) 0 0
\(334\) −7.88498 13.6572i −0.431447 0.747288i
\(335\) 2.16160 3.74399i 0.118101 0.204556i
\(336\) 0 0
\(337\) 1.32314i 0.0720759i −0.999350 0.0360379i \(-0.988526\pi\)
0.999350 0.0360379i \(-0.0114737\pi\)
\(338\) −11.4834 6.09353i −0.624615 0.331445i
\(339\) 0 0
\(340\) 0.833596 0.223361i 0.0452081 0.0121135i
\(341\) −9.80461 5.66069i −0.530949 0.306544i
\(342\) 0 0
\(343\) 12.5852 + 12.5852i 0.679536 + 0.679536i
\(344\) −2.19983 0.589442i −0.118607 0.0317806i
\(345\) 0 0
\(346\) −14.1442 + 14.1442i −0.760399 + 0.760399i
\(347\) 13.3649 7.71623i 0.717466 0.414229i −0.0963534 0.995347i \(-0.530718\pi\)
0.813819 + 0.581118i \(0.197385\pi\)
\(348\) 0 0
\(349\) 3.29516 + 12.2977i 0.176386 + 0.658281i 0.996311 + 0.0858107i \(0.0273480\pi\)
−0.819926 + 0.572470i \(0.805985\pi\)
\(350\) 1.52425 0.0814744
\(351\) 0 0
\(352\) −1.39924 −0.0745799
\(353\) 4.16209 + 15.5331i 0.221526 + 0.826745i 0.983767 + 0.179452i \(0.0574324\pi\)
−0.762241 + 0.647293i \(0.775901\pi\)
\(354\) 0 0
\(355\) −8.96489 + 5.17588i −0.475807 + 0.274707i
\(356\) 6.92381 6.92381i 0.366961 0.366961i
\(357\) 0 0
\(358\) 8.04449 + 2.15552i 0.425165 + 0.113923i
\(359\) 22.6408 + 22.6408i 1.19494 + 1.19494i 0.975663 + 0.219273i \(0.0703687\pi\)
0.219273 + 0.975663i \(0.429631\pi\)
\(360\) 0 0
\(361\) −36.7415 21.2127i −1.93377 1.11646i
\(362\) −23.4725 + 6.28943i −1.23369 + 0.330565i
\(363\) 0 0
\(364\) −4.29959 + 3.42298i −0.225360 + 0.179413i
\(365\) 6.04920i 0.316629i
\(366\) 0 0
\(367\) 2.86624 4.96447i 0.149616 0.259143i −0.781469 0.623944i \(-0.785529\pi\)
0.931086 + 0.364801i \(0.118863\pi\)
\(368\) 1.90032 + 3.29146i 0.0990612 + 0.171579i
\(369\) 0 0
\(370\) −0.943831 + 3.52243i −0.0490674 + 0.183122i
\(371\) −1.85307 + 6.91577i −0.0962068 + 0.359049i
\(372\) 0 0
\(373\) 9.39587 + 16.2741i 0.486500 + 0.842642i 0.999880 0.0155193i \(-0.00494013\pi\)
−0.513380 + 0.858161i \(0.671607\pi\)
\(374\) −0.603775 + 1.04577i −0.0312205 + 0.0540754i
\(375\) 0 0
\(376\) 9.01896i 0.465117i
\(377\) 25.2777 + 2.86933i 1.30187 + 0.147778i
\(378\) 0 0
\(379\) 11.4618 3.07117i 0.588752 0.157756i 0.0478693 0.998854i \(-0.484757\pi\)
0.540883 + 0.841098i \(0.318090\pi\)
\(380\) 6.78742 + 3.91872i 0.348187 + 0.201026i
\(381\) 0 0
\(382\) −16.8064 16.8064i −0.859890 0.859890i
\(383\) −30.5921 8.19714i −1.56319 0.418854i −0.629515 0.776988i \(-0.716746\pi\)
−0.933670 + 0.358134i \(0.883413\pi\)
\(384\) 0 0
\(385\) −1.50811 + 1.50811i −0.0768605 + 0.0768605i
\(386\) 21.4343 12.3751i 1.09098 0.629877i
\(387\) 0 0
\(388\) 3.30059 + 12.3180i 0.167562 + 0.625350i
\(389\) 4.71902 0.239264 0.119632 0.992818i \(-0.461829\pi\)
0.119632 + 0.992818i \(0.461829\pi\)
\(390\) 0 0
\(391\) 3.27997 0.165875
\(392\) −1.21041 4.51732i −0.0611350 0.228159i
\(393\) 0 0
\(394\) 2.87672 1.66088i 0.144927 0.0836737i
\(395\) −5.47409 + 5.47409i −0.275431 + 0.275431i
\(396\) 0 0
\(397\) −3.37761 0.905027i −0.169517 0.0454220i 0.173062 0.984911i \(-0.444634\pi\)
−0.342579 + 0.939489i \(0.611301\pi\)
\(398\) −5.48681 5.48681i −0.275029 0.275029i
\(399\) 0 0
\(400\) −0.866025 0.500000i −0.0433013 0.0250000i
\(401\) −4.05072 + 1.08539i −0.202283 + 0.0542016i −0.358538 0.933515i \(-0.616725\pi\)
0.156255 + 0.987717i \(0.450058\pi\)
\(402\) 0 0
\(403\) 27.1474 + 10.6805i 1.35231 + 0.532035i
\(404\) 7.93630i 0.394846i
\(405\) 0 0
\(406\) 5.37740 9.31392i 0.266876 0.462242i
\(407\) −2.55130 4.41898i −0.126463 0.219041i
\(408\) 0 0
\(409\) 4.06359 15.1655i 0.200932 0.749887i −0.789720 0.613468i \(-0.789774\pi\)
0.990651 0.136419i \(-0.0435593\pi\)
\(410\) 1.69652 6.33150i 0.0837852 0.312691i
\(411\) 0 0
\(412\) −6.10439 10.5731i −0.300742 0.520900i
\(413\) −3.69925 + 6.40728i −0.182028 + 0.315282i
\(414\) 0 0
\(415\) 9.10971i 0.447178i
\(416\) 3.56572 0.534425i 0.174824 0.0262023i
\(417\) 0 0
\(418\) −10.5928 + 2.83834i −0.518111 + 0.138828i
\(419\) 8.98610 + 5.18812i 0.439000 + 0.253456i 0.703173 0.711019i \(-0.251766\pi\)
−0.264174 + 0.964475i \(0.585099\pi\)
\(420\) 0 0
\(421\) 8.69941 + 8.69941i 0.423983 + 0.423983i 0.886573 0.462589i \(-0.153080\pi\)
−0.462589 + 0.886573i \(0.653080\pi\)
\(422\) −16.3386 4.37791i −0.795350 0.213113i
\(423\) 0 0
\(424\) 3.32144 3.32144i 0.161303 0.161303i
\(425\) −0.747382 + 0.431501i −0.0362533 + 0.0209309i
\(426\) 0 0
\(427\) 4.82165 + 17.9946i 0.233336 + 0.870822i
\(428\) −6.95836 −0.336345
\(429\) 0 0
\(430\) 2.27743 0.109827
\(431\) 3.55832 + 13.2798i 0.171398 + 0.639666i 0.997137 + 0.0756139i \(0.0240917\pi\)
−0.825739 + 0.564052i \(0.809242\pi\)
\(432\) 0 0
\(433\) 7.51405 4.33824i 0.361102 0.208482i −0.308462 0.951237i \(-0.599814\pi\)
0.669564 + 0.742754i \(0.266481\pi\)
\(434\) 8.72061 8.72061i 0.418603 0.418603i
\(435\) 0 0
\(436\) 5.65640 + 1.51563i 0.270892 + 0.0725854i
\(437\) 21.0628 + 21.0628i 1.00757 + 1.00757i
\(438\) 0 0
\(439\) 6.49527 + 3.75004i 0.310002 + 0.178980i 0.646927 0.762552i \(-0.276054\pi\)
−0.336925 + 0.941531i \(0.609387\pi\)
\(440\) 1.35157 0.362151i 0.0644333 0.0172649i
\(441\) 0 0
\(442\) 1.13919 2.89556i 0.0541860 0.137728i
\(443\) 8.57341i 0.407335i −0.979040 0.203668i \(-0.934714\pi\)
0.979040 0.203668i \(-0.0652862\pi\)
\(444\) 0 0
\(445\) −4.89587 + 8.47990i −0.232087 + 0.401986i
\(446\) 4.05563 + 7.02455i 0.192039 + 0.332622i
\(447\) 0 0
\(448\) 0.394504 1.47231i 0.0186386 0.0695601i
\(449\) −0.689391 + 2.57284i −0.0325344 + 0.121420i −0.980283 0.197597i \(-0.936686\pi\)
0.947749 + 0.319017i \(0.103353\pi\)
\(450\) 0 0
\(451\) 4.58592 + 7.94304i 0.215942 + 0.374023i
\(452\) −6.87955 + 11.9157i −0.323587 + 0.560469i
\(453\) 0 0
\(454\) 6.71162i 0.314992i
\(455\) 3.26715 4.41916i 0.153166 0.207174i
\(456\) 0 0
\(457\) −35.0828 + 9.40040i −1.64110 + 0.439732i −0.957102 0.289750i \(-0.906428\pi\)
−0.684000 + 0.729482i \(0.739761\pi\)
\(458\) 9.70228 + 5.60161i 0.453358 + 0.261746i
\(459\) 0 0
\(460\) −2.68746 2.68746i −0.125304 0.125304i
\(461\) −31.0267 8.31357i −1.44506 0.387202i −0.550755 0.834667i \(-0.685660\pi\)
−0.894301 + 0.447465i \(0.852327\pi\)
\(462\) 0 0
\(463\) −6.22741 + 6.22741i −0.289412 + 0.289412i −0.836848 0.547436i \(-0.815604\pi\)
0.547436 + 0.836848i \(0.315604\pi\)
\(464\) −6.11051 + 3.52790i −0.283673 + 0.163779i
\(465\) 0 0
\(466\) −2.45379 9.15767i −0.113670 0.424221i
\(467\) −39.9714 −1.84966 −0.924829 0.380384i \(-0.875792\pi\)
−0.924829 + 0.380384i \(0.875792\pi\)
\(468\) 0 0
\(469\) −6.58961 −0.304280
\(470\) −2.33428 8.71164i −0.107672 0.401838i
\(471\) 0 0
\(472\) 4.20357 2.42693i 0.193485 0.111709i
\(473\) −2.25332 + 2.25332i −0.103608 + 0.103608i
\(474\) 0 0
\(475\) −7.57039 2.02848i −0.347353 0.0930730i
\(476\) −0.930149 0.930149i −0.0426333 0.0426333i
\(477\) 0 0
\(478\) −3.81086 2.20020i −0.174305 0.100635i
\(479\) −8.95885 + 2.40052i −0.409340 + 0.109682i −0.457612 0.889152i \(-0.651295\pi\)
0.0482719 + 0.998834i \(0.484629\pi\)
\(480\) 0 0
\(481\) 8.18931 + 10.2865i 0.373400 + 0.469026i
\(482\) 12.7727i 0.581779i
\(483\) 0 0
\(484\) 4.52106 7.83070i 0.205503 0.355941i
\(485\) −6.37625 11.0440i −0.289531 0.501482i
\(486\) 0 0
\(487\) −0.998378 + 3.72600i −0.0452408 + 0.168841i −0.984850 0.173408i \(-0.944522\pi\)
0.939609 + 0.342249i \(0.111189\pi\)
\(488\) 3.16330 11.8056i 0.143196 0.534414i
\(489\) 0 0
\(490\) 2.33834 + 4.05012i 0.105635 + 0.182966i
\(491\) −14.5477 + 25.1973i −0.656527 + 1.13714i 0.324982 + 0.945720i \(0.394642\pi\)
−0.981509 + 0.191417i \(0.938692\pi\)
\(492\) 0 0
\(493\) 6.08918i 0.274243i
\(494\) 25.9098 11.2788i 1.16574 0.507457i
\(495\) 0 0
\(496\) −7.81538 + 2.09413i −0.350921 + 0.0940290i
\(497\) 13.6647 + 7.88932i 0.612946 + 0.353885i
\(498\) 0 0
\(499\) 21.9762 + 21.9762i 0.983790 + 0.983790i 0.999871 0.0160805i \(-0.00511881\pi\)
−0.0160805 + 0.999871i \(0.505119\pi\)
\(500\) 0.965926 + 0.258819i 0.0431975 + 0.0115747i
\(501\) 0 0
\(502\) −1.06964 + 1.06964i −0.0477405 + 0.0477405i
\(503\) −37.3168 + 21.5449i −1.66387 + 0.960639i −0.693037 + 0.720902i \(0.743728\pi\)
−0.970838 + 0.239736i \(0.922939\pi\)
\(504\) 0 0
\(505\) −2.05407 7.66588i −0.0914047 0.341127i
\(506\) 5.31803 0.236415
\(507\) 0 0
\(508\) 0.497897 0.0220906
\(509\) 8.52002 + 31.7971i 0.377643 + 1.40938i 0.849444 + 0.527679i \(0.176937\pi\)
−0.471801 + 0.881705i \(0.656396\pi\)
\(510\) 0 0
\(511\) 7.98516 4.61023i 0.353243 0.203945i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) −9.88024 2.64740i −0.435799 0.116772i
\(515\) 8.63291 + 8.63291i 0.380412 + 0.380412i
\(516\) 0 0
\(517\) 10.9290 + 6.30986i 0.480657 + 0.277507i
\(518\) 5.36905 1.43863i 0.235902 0.0632098i
\(519\) 0 0
\(520\) −3.30591 + 1.43909i −0.144974 + 0.0631084i
\(521\) 25.0972i 1.09953i −0.835320 0.549764i \(-0.814718\pi\)
0.835320 0.549764i \(-0.185282\pi\)
\(522\) 0 0
\(523\) 7.34971 12.7301i 0.321380 0.556647i −0.659393 0.751799i \(-0.729187\pi\)
0.980773 + 0.195152i \(0.0625199\pi\)
\(524\) −7.87731 13.6439i −0.344122 0.596036i
\(525\) 0 0
\(526\) −2.39903 + 8.95331i −0.104603 + 0.390383i
\(527\) −1.80724 + 6.74469i −0.0787244 + 0.293803i
\(528\) 0 0
\(529\) 4.27754 + 7.40892i 0.185980 + 0.322127i
\(530\) −2.34861 + 4.06791i −0.102017 + 0.176699i
\(531\) 0 0
\(532\) 11.9462i 0.517933i
\(533\) −14.7202 18.4899i −0.637601 0.800887i
\(534\) 0 0
\(535\) 6.72126 1.80096i 0.290585 0.0778621i
\(536\) 3.74399 + 2.16160i 0.161716 + 0.0933667i
\(537\) 0 0
\(538\) −16.0933 16.0933i −0.693831 0.693831i
\(539\) −6.32082 1.69366i −0.272257 0.0729511i
\(540\) 0 0
\(541\) −2.02274 + 2.02274i −0.0869644 + 0.0869644i −0.749251 0.662286i \(-0.769586\pi\)
0.662286 + 0.749251i \(0.269586\pi\)
\(542\) 4.43483 2.56045i 0.190492 0.109981i
\(543\) 0 0
\(544\) 0.223361 + 0.833596i 0.00957654 + 0.0357401i
\(545\) −5.85594 −0.250841
\(546\) 0 0
\(547\) 16.4927 0.705178 0.352589 0.935778i \(-0.385301\pi\)
0.352589 + 0.935778i \(0.385301\pi\)
\(548\) 2.39109 + 8.92367i 0.102142 + 0.381200i
\(549\) 0 0
\(550\) −1.21178 + 0.699622i −0.0516705 + 0.0298320i
\(551\) −39.1026 + 39.1026i −1.66583 + 1.66583i
\(552\) 0 0
\(553\) 11.3979 + 3.05407i 0.484689 + 0.129872i
\(554\) −1.50215 1.50215i −0.0638201 0.0638201i
\(555\) 0 0
\(556\) −15.0718 8.70168i −0.639185 0.369033i
\(557\) 11.6760 3.12859i 0.494730 0.132562i −0.00282317 0.999996i \(-0.500899\pi\)
0.497553 + 0.867434i \(0.334232\pi\)
\(558\) 0 0
\(559\) 4.88156 6.60282i 0.206468 0.279269i
\(560\) 1.52425i 0.0644112i
\(561\) 0 0
\(562\) 5.09750 8.82913i 0.215025 0.372434i
\(563\) −1.15276 1.99663i −0.0485829 0.0841480i 0.840711 0.541484i \(-0.182137\pi\)
−0.889294 + 0.457336i \(0.848804\pi\)
\(564\) 0 0
\(565\) 3.56112 13.2903i 0.149817 0.559126i
\(566\) −3.60064 + 13.4378i −0.151346 + 0.564831i
\(567\) 0 0
\(568\) −5.17588 8.96489i −0.217175 0.376158i
\(569\) −16.3433 + 28.3075i −0.685149 + 1.18671i 0.288241 + 0.957558i \(0.406930\pi\)
−0.973390 + 0.229155i \(0.926404\pi\)
\(570\) 0 0
\(571\) 15.0864i 0.631344i −0.948868 0.315672i \(-0.897770\pi\)
0.948868 0.315672i \(-0.102230\pi\)
\(572\) 1.84705 4.69477i 0.0772291 0.196298i
\(573\) 0 0
\(574\) −9.65078 + 2.58592i −0.402816 + 0.107934i
\(575\) 3.29146 + 1.90032i 0.137263 + 0.0792490i
\(576\) 0 0
\(577\) −10.7578 10.7578i −0.447851 0.447851i 0.446788 0.894640i \(-0.352568\pi\)
−0.894640 + 0.446788i \(0.852568\pi\)
\(578\) −15.7013 4.20716i −0.653090 0.174995i
\(579\) 0 0
\(580\) 4.98921 4.98921i 0.207166 0.207166i
\(581\) 12.0252 6.94272i 0.498887 0.288033i
\(582\) 0 0
\(583\) −1.70110 6.34860i −0.0704525 0.262932i
\(584\) −6.04920 −0.250317
\(585\) 0 0
\(586\) 2.43031 0.100395
\(587\) 9.06480 + 33.8303i 0.374144 + 1.39633i 0.854591 + 0.519301i \(0.173808\pi\)
−0.480447 + 0.877024i \(0.659526\pi\)
\(588\) 0 0
\(589\) −54.9176 + 31.7067i −2.26284 + 1.30645i
\(590\) −3.43220 + 3.43220i −0.141302 + 0.141302i
\(591\) 0 0
\(592\) −3.52243 0.943831i −0.144771 0.0387912i
\(593\) −17.3353 17.3353i −0.711875 0.711875i 0.255052 0.966927i \(-0.417907\pi\)
−0.966927 + 0.255052i \(0.917907\pi\)
\(594\) 0 0
\(595\) 1.13919 + 0.657714i 0.0467024 + 0.0269637i
\(596\) −10.4871 + 2.81000i −0.429567 + 0.115102i
\(597\) 0 0
\(598\) −13.5521 + 2.03116i −0.554185 + 0.0830603i
\(599\) 25.7906i 1.05377i 0.849935 + 0.526887i \(0.176641\pi\)
−0.849935 + 0.526887i \(0.823359\pi\)
\(600\) 0 0
\(601\) 14.9846 25.9541i 0.611236 1.05869i −0.379796 0.925070i \(-0.624006\pi\)
0.991032 0.133622i \(-0.0426607\pi\)
\(602\) −1.73568 3.00629i −0.0707411 0.122527i
\(603\) 0 0
\(604\) −2.69440 + 10.0556i −0.109634 + 0.409158i
\(605\) −2.34027 + 8.73402i −0.0951456 + 0.355088i
\(606\) 0 0
\(607\) 14.3192 + 24.8016i 0.581200 + 1.00667i 0.995337 + 0.0964535i \(0.0307499\pi\)
−0.414138 + 0.910214i \(0.635917\pi\)
\(608\) −3.91872 + 6.78742i −0.158925 + 0.275266i
\(609\) 0 0
\(610\) 12.2220i 0.494856i
\(611\) −30.2606 11.9054i −1.22421 0.481639i
\(612\) 0 0
\(613\) 9.67014 2.59110i 0.390573 0.104654i −0.0581877 0.998306i \(-0.518532\pi\)
0.448761 + 0.893652i \(0.351866\pi\)
\(614\) −21.8141 12.5944i −0.880344 0.508267i
\(615\) 0 0
\(616\) −1.50811 1.50811i −0.0607636 0.0607636i
\(617\) −44.4206 11.9025i −1.78831 0.479175i −0.796250 0.604967i \(-0.793186\pi\)
−0.992057 + 0.125792i \(0.959853\pi\)
\(618\) 0 0
\(619\) 4.18163 4.18163i 0.168074 0.168074i −0.618058 0.786132i \(-0.712080\pi\)
0.786132 + 0.618058i \(0.212080\pi\)
\(620\) 7.00708 4.04554i 0.281411 0.162473i
\(621\) 0 0
\(622\) −1.93225 7.21125i −0.0774762 0.289145i
\(623\) 14.9250 0.597959
\(624\) 0 0
\(625\) −1.00000 −0.0400000
\(626\) 6.06528 + 22.6359i 0.242417 + 0.904713i
\(627\) 0 0
\(628\) 15.8917 9.17509i 0.634149 0.366126i
\(629\) −2.22533 + 2.22533i −0.0887298 + 0.0887298i
\(630\) 0 0
\(631\) −26.5725 7.12008i −1.05783 0.283446i −0.312349 0.949968i \(-0.601116\pi\)
−0.745486 + 0.666522i \(0.767782\pi\)
\(632\) −5.47409 5.47409i −0.217748 0.217748i
\(633\) 0 0
\(634\) −0.258041 0.148980i −0.0102481 0.00591676i
\(635\) −0.480931 + 0.128865i −0.0190852 + 0.00511386i
\(636\) 0 0
\(637\) 16.7544 + 1.90183i 0.663833 + 0.0753532i
\(638\) 9.87279i 0.390867i
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −5.66029 9.80390i −0.223568 0.387231i 0.732321 0.680960i \(-0.238437\pi\)
−0.955889 + 0.293729i \(0.905104\pi\)
\(642\) 0 0
\(643\) 0.703879 2.62691i 0.0277583 0.103595i −0.950657 0.310244i \(-0.899589\pi\)
0.978415 + 0.206649i \(0.0662558\pi\)
\(644\) −1.49937 + 5.59573i −0.0590835 + 0.220503i
\(645\) 0 0
\(646\) 3.38186 + 5.85756i 0.133058 + 0.230463i
\(647\) 10.9801 19.0181i 0.431673 0.747679i −0.565345 0.824855i \(-0.691257\pi\)
0.997018 + 0.0771756i \(0.0245902\pi\)
\(648\) 0 0
\(649\) 6.79174i 0.266599i
\(650\) 2.82080 2.24569i 0.110641 0.0880831i
\(651\) 0 0
\(652\) −6.30538 + 1.68952i −0.246938 + 0.0661668i
\(653\) −36.4401 21.0387i −1.42601 0.823308i −0.429209 0.903205i \(-0.641208\pi\)
−0.996803 + 0.0798969i \(0.974541\pi\)
\(654\) 0 0
\(655\) 11.1402 + 11.1402i 0.435283 + 0.435283i
\(656\) 6.33150 + 1.69652i 0.247204 + 0.0662380i
\(657\) 0 0
\(658\) −9.72068 + 9.72068i −0.378952 + 0.378952i
\(659\) 20.6684 11.9329i 0.805128 0.464841i −0.0401329 0.999194i \(-0.512778\pi\)
0.845261 + 0.534353i \(0.179445\pi\)
\(660\) 0 0
\(661\) −4.77664 17.8267i −0.185790 0.693377i −0.994460 0.105115i \(-0.966479\pi\)
0.808670 0.588262i \(-0.200188\pi\)
\(662\) −24.5815 −0.955389
\(663\) 0 0
\(664\) −9.10971 −0.353525
\(665\) 3.09190 + 11.5391i 0.119899 + 0.447469i
\(666\) 0 0
\(667\) 23.2239 13.4083i 0.899232 0.519172i
\(668\) −11.1510 + 11.1510i −0.431447 + 0.431447i
\(669\) 0 0
\(670\) −4.17588 1.11892i −0.161328 0.0432278i
\(671\) −12.0927 12.0927i −0.466832 0.466832i
\(672\) 0 0
\(673\) −28.1091 16.2288i −1.08353 0.625574i −0.151681 0.988430i \(-0.548468\pi\)
−0.931845 + 0.362856i \(0.881802\pi\)
\(674\) −1.27805 + 0.342453i −0.0492288 + 0.0131908i
\(675\) 0 0
\(676\) −2.91377 + 12.6693i −0.112068 + 0.487279i
\(677\) 22.0711i 0.848262i 0.905601 + 0.424131i \(0.139420\pi\)
−0.905601 + 0.424131i \(0.860580\pi\)
\(678\) 0 0
\(679\) −9.71898 + 16.8338i −0.372980 + 0.646021i
\(680\) −0.431501 0.747382i −0.0165473 0.0286608i
\(681\) 0 0
\(682\) −2.93019 + 10.9356i −0.112203 + 0.418747i
\(683\) −7.14894 + 26.6802i −0.273547 + 1.02089i 0.683262 + 0.730173i \(0.260561\pi\)
−0.956809 + 0.290717i \(0.906106\pi\)
\(684\) 0 0
\(685\) −4.61923 8.00074i −0.176492 0.305693i
\(686\) 8.89907 15.4136i 0.339768 0.588495i
\(687\) 0 0
\(688\) 2.27743i 0.0868261i
\(689\) 6.75973 + 15.5286i 0.257525 + 0.591592i
\(690\) 0 0
\(691\) 22.7854 6.10532i 0.866796 0.232257i 0.202094 0.979366i \(-0.435225\pi\)
0.664702 + 0.747109i \(0.268559\pi\)
\(692\) 17.3231 + 10.0015i 0.658525 + 0.380200i
\(693\) 0 0
\(694\) −10.9124 10.9124i −0.414229 0.414229i
\(695\) 16.8104 + 4.50432i 0.637653 + 0.170859i
\(696\) 0 0
\(697\) 4.00000 4.00000i 0.151511 0.151511i
\(698\) 11.0258 6.36576i 0.417333 0.240947i
\(699\) 0 0
\(700\) −0.394504 1.47231i −0.0149109 0.0556481i
\(701\) −15.5374 −0.586838 −0.293419 0.955984i \(-0.594793\pi\)
−0.293419 + 0.955984i \(0.594793\pi\)
\(702\) 0 0
\(703\) −28.5807 −1.07794
\(704\) 0.362151 + 1.35157i 0.0136491 + 0.0509390i
\(705\) 0 0
\(706\) 13.9266 8.04054i 0.524135 0.302610i
\(707\) −8.55379 + 8.55379i −0.321698 + 0.321698i
\(708\) 0 0
\(709\) −13.4708 3.60950i −0.505908 0.135558i −0.00316760 0.999995i \(-0.501008\pi\)
−0.502741 + 0.864437i \(0.667675\pi\)
\(710\) 7.31980 + 7.31980i 0.274707 + 0.274707i
\(711\) 0 0
\(712\) −8.47990 4.89587i −0.317798 0.183480i
\(713\) 29.7035 7.95903i 1.11241 0.298068i
\(714\) 0 0
\(715\) −0.569020 + 5.01285i −0.0212801 + 0.187470i
\(716\) 8.32827i 0.311242i
\(717\) 0 0
\(718\) 16.0095 27.7292i 0.597468 1.03485i
\(719\) −21.2897 36.8748i −0.793970 1.37520i −0.923491 0.383620i \(-0.874677\pi\)
0.129520 0.991577i \(-0.458656\pi\)
\(720\) 0 0
\(721\) 4.81642 17.9751i 0.179373 0.669428i
\(722\) −10.9805 + 40.9799i −0.408653 + 1.52511i
\(723\) 0 0
\(724\) 12.1502 + 21.0449i 0.451560 + 0.782126i
\(725\) −3.52790 + 6.11051i −0.131023 + 0.226938i
\(726\) 0 0
\(727\) 29.5299i 1.09520i −0.836739 0.547602i \(-0.815541\pi\)
0.836739 0.547602i \(-0.184459\pi\)
\(728\) 4.41916 + 3.26715i 0.163785 + 0.121089i
\(729\) 0 0
\(730\) 5.84307 1.56565i 0.216262 0.0579472i
\(731\) 1.70211 + 0.982712i 0.0629547 + 0.0363469i
\(732\) 0 0
\(733\) −30.0045 30.0045i −1.10824 1.10824i −0.993382 0.114861i \(-0.963358\pi\)
−0.114861 0.993382i \(-0.536642\pi\)
\(734\) −5.53714 1.48367i −0.204380 0.0547634i
\(735\) 0 0
\(736\) 2.68746 2.68746i 0.0990612 0.0990612i
\(737\) 5.23876 3.02460i 0.192972 0.111412i
\(738\) 0 0
\(739\) 7.60296 + 28.3746i 0.279679 + 1.04378i 0.952640 + 0.304099i \(0.0983555\pi\)
−0.672961 + 0.739678i \(0.734978\pi\)
\(740\) 3.64668 0.134055
\(741\) 0 0
\(742\) 7.15973 0.262842
\(743\) 4.43565 + 16.5541i 0.162728 + 0.607310i 0.998319 + 0.0579577i \(0.0184589\pi\)
−0.835591 + 0.549352i \(0.814874\pi\)
\(744\) 0 0
\(745\) 9.40246 5.42851i 0.344479 0.198885i
\(746\) 13.2878 13.2878i 0.486500 0.486500i
\(747\) 0 0
\(748\) 1.16640 + 0.312537i 0.0426479 + 0.0114275i
\(749\) −7.49976 7.49976i −0.274035 0.274035i
\(750\) 0 0
\(751\) 0.0370080 + 0.0213666i 0.00135044 + 0.000779678i 0.500675 0.865635i \(-0.333085\pi\)
−0.499325 + 0.866415i \(0.666418\pi\)
\(752\) 8.71164 2.33428i 0.317681 0.0851223i
\(753\) 0 0
\(754\) −3.77080 25.1591i −0.137324 0.916239i
\(755\) 10.4104i 0.378872i
\(756\) 0 0
\(757\) −18.0155 + 31.2038i −0.654786 + 1.13412i 0.327162 + 0.944968i \(0.393908\pi\)
−0.981947 + 0.189154i \(0.939426\pi\)
\(758\) −5.93305 10.2764i −0.215498 0.373254i
\(759\) 0 0
\(760\) 2.02848 7.57039i 0.0735807 0.274607i
\(761\) 2.75831 10.2942i 0.0999887 0.373163i −0.897740 0.440526i \(-0.854792\pi\)
0.997729 + 0.0673632i \(0.0214586\pi\)
\(762\) 0 0
\(763\) 4.46295 + 7.73005i 0.161570 + 0.279847i
\(764\) −11.8839 + 20.5835i −0.429945 + 0.744686i
\(765\) 0 0
\(766\) 31.6713i 1.14433i
\(767\) 2.59403 + 17.3076i 0.0936649 + 0.624939i
\(768\) 0 0
\(769\) −49.0270 + 13.1368i −1.76796 + 0.473723i −0.988305 0.152487i \(-0.951272\pi\)
−0.779654 + 0.626210i \(0.784605\pi\)
\(770\) 1.84705 + 1.06640i 0.0665632 + 0.0384303i
\(771\) 0 0
\(772\) −17.5011 17.5011i −0.629877 0.629877i
\(773\) 13.4423 + 3.60186i 0.483487 + 0.129550i 0.492326 0.870411i \(-0.336147\pi\)
−0.00883893 + 0.999961i \(0.502814\pi\)
\(774\) 0 0
\(775\) −5.72126 + 5.72126i −0.205514 + 0.205514i
\(776\) 11.0440 6.37625i 0.396456 0.228894i
\(777\) 0 0
\(778\) −1.22137 4.55823i −0.0437884 0.163420i
\(779\) 51.3733 1.84064
\(780\) 0 0
\(781\) −14.4846 −0.518301
\(782\) −0.848918 3.16820i −0.0303572 0.113295i
\(783\) 0 0
\(784\) −4.05012 + 2.33834i −0.144647 + 0.0835120i
\(785\) −12.9755 + 12.9755i −0.463117 + 0.463117i
\(786\) 0 0
\(787\) −46.5856 12.4826i −1.66060 0.444956i −0.698046 0.716053i \(-0.745947\pi\)
−0.962552 + 0.271097i \(0.912613\pi\)
\(788\) −2.34883 2.34883i −0.0836737 0.0836737i
\(789\) 0 0
\(790\) 6.70436 + 3.87076i 0.238530 + 0.137716i
\(791\) −20.2577 + 5.42803i −0.720280 + 0.192998i
\(792\) 0 0
\(793\) 35.4347 + 26.1974i 1.25832 + 0.930296i
\(794\) 3.49676i 0.124095i
\(795\) 0 0
\(796\) −3.87976 + 6.71994i −0.137514 + 0.238182i
\(797\) −20.4594 35.4366i −0.724708 1.25523i −0.959094 0.283087i \(-0.908642\pi\)
0.234387 0.972143i \(-0.424692\pi\)
\(798\) 0 0
\(799\) 2.01449 7.51817i 0.0712674 0.265974i
\(800\) −0.258819 + 0.965926i −0.00915064 + 0.0341506i
\(801\) 0 0
\(802\) 2.09681 + 3.63178i 0.0740408 + 0.128242i
\(803\) −4.23215 + 7.33030i −0.149349 + 0.258680i
\(804\) 0 0
\(805\) 5.79313i 0.204181i
\(806\) 3.29034 28.9867i 0.115897 1.02101i
\(807\) 0 0
\(808\) 7.66588 2.05407i 0.269685 0.0722618i
\(809\) −26.0180 15.0215i −0.914745 0.528128i −0.0327903 0.999462i \(-0.510439\pi\)
−0.881955 + 0.471334i \(0.843773\pi\)
\(810\) 0 0
\(811\) −2.06570 2.06570i −0.0725365 0.0725365i 0.669908 0.742444i \(-0.266334\pi\)
−0.742444 + 0.669908i \(0.766334\pi\)
\(812\) −10.3883 2.78354i −0.364559 0.0976833i
\(813\) 0 0
\(814\) −3.60808 + 3.60808i −0.126463 + 0.126463i
\(815\) 5.65325 3.26390i 0.198025 0.114330i
\(816\) 0 0
\(817\) 4.61971 + 17.2410i 0.161623 + 0.603186i
\(818\) −15.7005 −0.548955
\(819\) 0 0
\(820\) −6.55485 −0.228905
\(821\) 2.81246 + 10.4962i 0.0981556 + 0.366322i 0.997479 0.0709626i \(-0.0226071\pi\)
−0.899323 + 0.437284i \(0.855940\pi\)
\(822\) 0 0
\(823\) 26.9741 15.5735i 0.940258 0.542858i 0.0502168 0.998738i \(-0.484009\pi\)
0.890041 + 0.455880i \(0.150675\pi\)
\(824\) −8.63291 + 8.63291i −0.300742 + 0.300742i
\(825\) 0 0
\(826\) 7.14640 + 1.91487i 0.248655 + 0.0666269i
\(827\) 10.4562 + 10.4562i 0.363596 + 0.363596i 0.865135 0.501539i \(-0.167233\pi\)
−0.501539 + 0.865135i \(0.667233\pi\)
\(828\) 0 0
\(829\) 9.25539 + 5.34360i 0.321453 + 0.185591i 0.652040 0.758185i \(-0.273913\pi\)
−0.330587 + 0.943775i \(0.607247\pi\)
\(830\) 8.79930 2.35777i 0.305428 0.0818393i
\(831\) 0 0
\(832\) −1.43909 3.30591i −0.0498915 0.114612i
\(833\) 4.03598i 0.139838i
\(834\) 0 0
\(835\) 7.88498 13.6572i 0.272871 0.472626i
\(836\) 5.48324 + 9.49725i 0.189642 + 0.328469i
\(837\) 0 0
\(838\) 2.68557 10.0227i 0.0927715 0.346228i
\(839\) 13.8616 51.7320i 0.478554 1.78599i −0.128926 0.991654i \(-0.541153\pi\)
0.607481 0.794334i \(-0.292180\pi\)
\(840\) 0 0
\(841\) 10.3922 + 17.9998i 0.358351 + 0.620683i
\(842\) 6.15141 10.6546i 0.211992 0.367180i
\(843\) 0 0
\(844\) 16.9149i 0.582236i
\(845\) −0.464553 12.9917i −0.0159811 0.446928i
\(846\) 0 0
\(847\) 13.3128 3.56715i 0.457433 0.122569i
\(848\) −4.06791 2.34861i −0.139693 0.0806516i
\(849\) 0 0
\(850\) 0.610235 + 0.610235i 0.0209309 + 0.0209309i
\(851\) 13.3875 + 3.58717i 0.458917 + 0.122967i
\(852\) 0 0
\(853\) 39.1661 39.1661i 1.34102 1.34102i 0.445979 0.895043i \(-0.352856\pi\)
0.895043 0.445979i \(-0.147144\pi\)
\(854\) 16.1336 9.31471i 0.552079 0.318743i
\(855\) 0 0
\(856\) 1.80096 + 6.72126i 0.0615554 + 0.229728i
\(857\) 47.7248 1.63025 0.815124 0.579287i \(-0.196669\pi\)
0.815124 + 0.579287i \(0.196669\pi\)
\(858\) 0 0
\(859\) 40.2327 1.37272 0.686361 0.727261i \(-0.259207\pi\)
0.686361 + 0.727261i \(0.259207\pi\)
\(860\) −0.589442 2.19983i −0.0200998 0.0750134i
\(861\) 0 0
\(862\) 11.9064 6.87414i 0.405532 0.234134i
\(863\) 3.57930 3.57930i 0.121841 0.121841i −0.643557 0.765398i \(-0.722542\pi\)
0.765398 + 0.643557i \(0.222542\pi\)
\(864\) 0 0
\(865\) −19.3214 5.17715i −0.656947 0.176028i
\(866\) −6.13520 6.13520i −0.208482 0.208482i
\(867\) 0 0
\(868\) −10.6805 6.16640i −0.362521 0.209301i
\(869\) −10.4632 + 2.80360i −0.354939 + 0.0951056i
\(870\) 0 0
\(871\) −12.1948 + 9.70854i −0.413206 + 0.328961i
\(872\) 5.85594i 0.198307i
\(873\) 0 0
\(874\) 14.8937 25.7966i 0.503786 0.872583i
\(875\) 0.762124 + 1.32004i 0.0257645 + 0.0446254i
\(876\) 0 0
\(877\) −2.16946 + 8.09654i −0.0732575 + 0.273401i −0.992833 0.119514i \(-0.961866\pi\)
0.919575 + 0.392914i \(0.128533\pi\)
\(878\) 1.94117 7.24453i 0.0655112 0.244491i
\(879\) 0 0
\(880\) −0.699622 1.21178i −0.0235842 0.0408491i
\(881\) 3.48542 6.03693i 0.117427 0.203389i −0.801320 0.598235i \(-0.795869\pi\)
0.918747 + 0.394846i \(0.129202\pi\)
\(882\) 0 0
\(883\) 48.1939i 1.62185i −0.585148 0.810926i \(-0.698964\pi\)
0.585148 0.810926i \(-0.301036\pi\)
\(884\) −3.09174 0.350951i −0.103987 0.0118038i
\(885\) 0 0
\(886\) −8.28128 + 2.21896i −0.278215 + 0.0745475i
\(887\) 10.3657 + 5.98462i 0.348045 + 0.200944i 0.663824 0.747889i \(-0.268932\pi\)
−0.315779 + 0.948833i \(0.602266\pi\)
\(888\) 0 0
\(889\) 0.536636 + 0.536636i 0.0179982 + 0.0179982i
\(890\) 9.45809 + 2.53429i 0.317036 + 0.0849496i
\(891\) 0 0
\(892\) 5.73552 5.73552i 0.192039 0.192039i
\(893\) 61.2155 35.3428i 2.04850 1.18270i
\(894\) 0 0
\(895\) 2.15552 + 8.04449i 0.0720509 + 0.268898i
\(896\) −1.52425 −0.0509215
\(897\) 0 0
\(898\) 2.66360 0.0888855
\(899\) 14.7757 + 55.1438i 0.492799 + 1.83915i
\(900\) 0 0
\(901\) −3.51062 + 2.02686i −0.116956 + 0.0675244i
\(902\) 6.48547 6.48547i 0.215942 0.215942i
\(903\) 0 0
\(904\) 13.2903 + 3.56112i 0.442028 + 0.118441i
\(905\) −17.1830 17.1830i −0.571184 0.571184i
\(906\) 0 0
\(907\) 0.305802 + 0.176555i 0.0101540 + 0.00586242i 0.505068 0.863079i \(-0.331467\pi\)
−0.494914 + 0.868942i \(0.664801\pi\)
\(908\) −6.48293 + 1.73710i −0.215143 + 0.0576475i
\(909\) 0 0
\(910\) −5.11419 2.01206i −0.169534 0.0666992i
\(911\) 0.0349872i 0.00115918i −1.00000 0.000579589i \(-0.999816\pi\)
1.00000 0.000579589i \(-0.000184489\pi\)
\(912\) 0 0
\(913\) −6.37335 + 11.0390i −0.210927 + 0.365336i
\(914\) 18.1602 + 31.4543i 0.600685 + 1.04042i
\(915\) 0 0
\(916\) 2.89961 10.8215i 0.0958058 0.357552i
\(917\) 6.21526 23.1957i 0.205246 0.765989i
\(918\) 0 0
\(919\) 16.6952 + 28.9169i 0.550724 + 0.953882i 0.998223 + 0.0595972i \(0.0189816\pi\)
−0.447499 + 0.894285i \(0.647685\pi\)
\(920\) −1.90032 + 3.29146i −0.0626518 + 0.108516i
\(921\) 0 0
\(922\) 32.1212i 1.05785i
\(923\) 36.9115 5.53224i 1.21496 0.182096i
\(924\) 0 0
\(925\) −3.52243 + 0.943831i −0.115817 + 0.0310330i
\(926\) 7.62699 + 4.40344i 0.250638 + 0.144706i
\(927\) 0 0
\(928\) 4.98921 + 4.98921i 0.163779 + 0.163779i
\(929\) 39.0790 + 10.4712i 1.28214 + 0.343549i 0.834670 0.550750i \(-0.185658\pi\)
0.447471 + 0.894299i \(0.352325\pi\)
\(930\) 0 0
\(931\) −25.9177 + 25.9177i −0.849417 + 0.849417i
\(932\) −8.21054 + 4.74036i −0.268945 + 0.155276i
\(933\) 0 0
\(934\) 10.3454 + 38.6094i 0.338511 + 1.26334i
\(935\) −1.20755 −0.0394911
\(936\) 0 0
\(937\) 38.3649 1.25333 0.626664 0.779290i \(-0.284420\pi\)
0.626664 + 0.779290i \(0.284420\pi\)
\(938\) 1.70552 + 6.36508i 0.0556871 + 0.207827i
\(939\) 0 0
\(940\) −7.81064 + 4.50948i −0.254755 + 0.147083i
\(941\) −15.8665 + 15.8665i −0.517233 + 0.517233i −0.916733 0.399500i \(-0.869184\pi\)
0.399500 + 0.916733i \(0.369184\pi\)
\(942\) 0 0
\(943\) −24.0638 6.44788i −0.783625 0.209972i
\(944\) −3.43220 3.43220i −0.111709 0.111709i
\(945\) 0 0
\(946\) 2.75974 + 1.59334i 0.0897269 + 0.0518039i
\(947\) 16.3183 4.37248i 0.530274 0.142087i 0.0162593 0.999868i \(-0.494824\pi\)
0.514015 + 0.857781i \(0.328158\pi\)
\(948\) 0 0
\(949\) 7.98516 20.2964i 0.259209 0.658848i
\(950\) 7.83744i 0.254280i
\(951\) 0 0
\(952\) −0.657714 + 1.13919i −0.0213166 + 0.0369215i
\(953\) 6.73104 + 11.6585i 0.218040 + 0.377656i 0.954209 0.299142i \(-0.0967004\pi\)
−0.736169 + 0.676798i \(0.763367\pi\)
\(954\) 0 0
\(955\) 6.15156 22.9580i 0.199060 0.742902i
\(956\) −1.13891 + 4.25046i −0.0368349 + 0.137470i
\(957\) 0 0
\(958\) 4.63744 + 8.03229i 0.149829 + 0.259511i
\(959\) −7.04085 + 12.1951i −0.227361 + 0.393801i
\(960\) 0 0
\(961\) 34.4656i 1.11179i
\(962\) 7.81649 10.5726i 0.252014 0.340875i
\(963\) 0 0
\(964\) −12.3375 + 3.30581i −0.397363 + 0.106473i
\(965\) 21.4343 + 12.3751i 0.689995 + 0.398369i
\(966\) 0 0
\(967\) −23.1158 23.1158i −0.743354 0.743354i 0.229868 0.973222i \(-0.426171\pi\)
−0.973222 + 0.229868i \(0.926171\pi\)
\(968\) −8.73402 2.34027i −0.280722 0.0752192i
\(969\) 0 0
\(970\) −9.01738 + 9.01738i −0.289531 + 0.289531i
\(971\) −31.4889 + 18.1801i −1.01053 + 0.583428i −0.911346 0.411642i \(-0.864956\pi\)
−0.0991808 + 0.995069i \(0.531622\pi\)
\(972\) 0 0
\(973\) −6.86570 25.6231i −0.220104 0.821440i
\(974\) 3.85744 0.123600
\(975\) 0 0
\(976\) −12.2220 −0.391218
\(977\) −11.2196 41.8720i −0.358945 1.33960i −0.875446 0.483316i \(-0.839432\pi\)
0.516501 0.856287i \(-0.327234\pi\)
\(978\) 0 0
\(979\) −11.8654 + 6.85051i −0.379221 + 0.218943i
\(980\) 3.30691 3.30691i 0.105635 0.105635i
\(981\) 0 0
\(982\) 28.1039 + 7.53042i 0.896832 + 0.240305i
\(983\) 26.2139 + 26.2139i 0.836093 + 0.836093i 0.988342 0.152249i \(-0.0486515\pi\)
−0.152249 + 0.988342i \(0.548652\pi\)
\(984\) 0 0
\(985\) 2.87672 + 1.66088i 0.0916600 + 0.0529199i
\(986\) 5.88169 1.57599i 0.187311 0.0501899i
\(987\) 0 0
\(988\) −17.6004 22.1078i −0.559945 0.703343i
\(989\) 8.65570i 0.275235i
\(990\) 0 0
\(991\) −15.8129 + 27.3888i −0.502314 + 0.870033i 0.497683 + 0.867359i \(0.334184\pi\)
−0.999996 + 0.00267380i \(0.999149\pi\)
\(992\) 4.04554 + 7.00708i 0.128446 + 0.222475i
\(993\) 0 0
\(994\) 4.08381 15.2410i 0.129531 0.483415i
\(995\) 2.00831 7.49512i 0.0636678 0.237611i
\(996\) 0 0
\(997\) −6.39203 11.0713i −0.202438 0.350633i 0.746876 0.664964i \(-0.231553\pi\)
−0.949313 + 0.314331i \(0.898220\pi\)
\(998\) 15.5395 26.9152i 0.491895 0.851987i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1170.2.cu.e.1151.1 yes 16
3.2 odd 2 inner 1170.2.cu.e.1151.3 yes 16
13.2 odd 12 inner 1170.2.cu.e.431.3 yes 16
39.2 even 12 inner 1170.2.cu.e.431.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1170.2.cu.e.431.1 16 39.2 even 12 inner
1170.2.cu.e.431.3 yes 16 13.2 odd 12 inner
1170.2.cu.e.1151.1 yes 16 1.1 even 1 trivial
1170.2.cu.e.1151.3 yes 16 3.2 odd 2 inner