Properties

Label 588.2.n.d.275.1
Level $588$
Weight $2$
Character 588.275
Analytic conductor $4.695$
Analytic rank $0$
Dimension $24$
Inner twists $8$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [588,2,Mod(263,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.263"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 588.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,0,0,-12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.69520363885\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 275.1
Character \(\chi\) \(=\) 588.275
Dual form 588.2.n.d.263.1

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.13414 + 0.844822i) q^{2} +(-1.36816 - 1.06214i) q^{3} +(0.572551 - 1.91629i) q^{4} +(3.44057 + 1.98641i) q^{5} +(2.44900 + 0.0487576i) q^{6} +(0.969574 + 2.65705i) q^{8} +(0.743736 + 2.90635i) q^{9} +(-5.58025 + 0.653796i) q^{10} +(1.65172 + 2.86086i) q^{11} +(-2.81871 + 2.01367i) q^{12} -0.850601 q^{13} +(-2.59742 - 6.37208i) q^{15} +(-3.34437 - 2.19435i) q^{16} +(0.499236 - 0.288234i) q^{17} +(-3.29885 - 2.66788i) q^{18} +(-3.11023 - 1.79569i) q^{19} +(5.77645 - 5.45582i) q^{20} +(-4.29021 - 1.84921i) q^{22} +(-1.98085 + 3.43094i) q^{23} +(1.49561 - 4.66510i) q^{24} +(5.39167 + 9.33865i) q^{25} +(0.964701 - 0.718606i) q^{26} +(2.06938 - 4.76630i) q^{27} +3.37929i q^{29} +(8.32911 + 5.03249i) q^{30} +(4.24264 - 2.44949i) q^{31} +(5.64683 - 0.336691i) q^{32} +(0.778803 - 5.66848i) q^{33} +(-0.322697 + 0.748663i) q^{34} +(5.99525 + 0.238815i) q^{36} +(-2.14510 + 3.71543i) q^{37} +(5.04449 - 0.591024i) q^{38} +(1.16376 + 0.903453i) q^{39} +(-1.94212 + 11.0677i) q^{40} -5.35550i q^{41} +7.66518i q^{43} +(6.42795 - 1.52719i) q^{44} +(-3.21433 + 11.4769i) q^{45} +(-0.651966 - 5.56464i) q^{46} +(-4.54525 + 7.87260i) q^{47} +(2.24494 + 6.55441i) q^{48} +(-14.0044 - 6.03634i) q^{50} +(-0.989179 - 0.135905i) q^{51} +(-0.487013 + 1.63000i) q^{52} +(-0.527096 + 0.304319i) q^{53} +(1.67971 + 7.15392i) q^{54} +13.1240i q^{55} +(2.34803 + 5.76029i) q^{57} +(-2.85490 - 3.83259i) q^{58} +(3.93980 + 6.82394i) q^{59} +(-13.6979 + 1.32907i) q^{60} +(4.87315 - 8.44054i) q^{61} +(-2.74237 + 6.36234i) q^{62} +(-6.11985 + 5.15242i) q^{64} +(-2.92655 - 1.68964i) q^{65} +(3.90558 + 7.08680i) q^{66} +(7.83384 - 4.52287i) q^{67} +(-0.266503 - 1.12171i) q^{68} +(6.35425 - 2.59015i) q^{69} +9.15654 q^{71} +(-7.00121 + 4.79407i) q^{72} +(0.707107 + 1.22474i) q^{73} +(-0.706026 - 6.02605i) q^{74} +(2.54223 - 18.5035i) q^{75} +(-5.22185 + 4.93200i) q^{76} +(-2.08312 - 0.0414733i) q^{78} +(6.00000 + 3.46410i) q^{79} +(-7.14764 - 14.1931i) q^{80} +(-7.89371 + 4.32311i) q^{81} +(4.52445 + 6.07390i) q^{82} -4.13877 q^{83} +2.29021 q^{85} +(-6.47571 - 8.69339i) q^{86} +(3.58926 - 4.62341i) q^{87} +(-6.00000 + 7.16253i) q^{88} +(4.98550 + 2.87838i) q^{89} +(-6.05039 - 15.7319i) q^{90} +(5.44055 + 5.76029i) q^{92} +(-8.40631 - 1.15496i) q^{93} +(-1.49600 - 12.7686i) q^{94} +(-7.13398 - 12.3564i) q^{95} +(-8.08339 - 5.53705i) q^{96} -13.5487 q^{97} +(-7.08622 + 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 12 q^{4} - 36 q^{16} - 12 q^{18} + 12 q^{25} + 12 q^{30} + 12 q^{36} + 96 q^{39} - 96 q^{46} - 12 q^{51} - 24 q^{57} - 120 q^{58} - 84 q^{60} - 48 q^{64} + 48 q^{67} - 72 q^{72} - 24 q^{78} + 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.13414 + 0.844822i −0.801959 + 0.597379i
\(3\) −1.36816 1.06214i −0.789909 0.613224i
\(4\) 0.572551 1.91629i 0.286276 0.958147i
\(5\) 3.44057 + 1.98641i 1.53867 + 0.888351i 0.998917 + 0.0465264i \(0.0148152\pi\)
0.539752 + 0.841824i \(0.318518\pi\)
\(6\) 2.44900 + 0.0487576i 0.999802 + 0.0199052i
\(7\) 0 0
\(8\) 0.969574 + 2.65705i 0.342796 + 0.939410i
\(9\) 0.743736 + 2.90635i 0.247912 + 0.968783i
\(10\) −5.58025 + 0.653796i −1.76463 + 0.206748i
\(11\) 1.65172 + 2.86086i 0.498013 + 0.862583i 0.999997 0.00229340i \(-0.000730012\pi\)
−0.501985 + 0.864876i \(0.667397\pi\)
\(12\) −2.81871 + 2.01367i −0.813691 + 0.581298i
\(13\) −0.850601 −0.235914 −0.117957 0.993019i \(-0.537635\pi\)
−0.117957 + 0.993019i \(0.537635\pi\)
\(14\) 0 0
\(15\) −2.59742 6.37208i −0.670650 1.64527i
\(16\) −3.34437 2.19435i −0.836092 0.548589i
\(17\) 0.499236 0.288234i 0.121082 0.0699070i −0.438236 0.898860i \(-0.644396\pi\)
0.559318 + 0.828953i \(0.311063\pi\)
\(18\) −3.29885 2.66788i −0.777546 0.628826i
\(19\) −3.11023 1.79569i −0.713537 0.411960i 0.0988326 0.995104i \(-0.468489\pi\)
−0.812369 + 0.583144i \(0.801822\pi\)
\(20\) 5.77645 5.45582i 1.29165 1.21996i
\(21\) 0 0
\(22\) −4.29021 1.84921i −0.914675 0.394254i
\(23\) −1.98085 + 3.43094i −0.413037 + 0.715401i −0.995220 0.0976569i \(-0.968865\pi\)
0.582183 + 0.813057i \(0.302199\pi\)
\(24\) 1.49561 4.66510i 0.305291 0.952259i
\(25\) 5.39167 + 9.33865i 1.07833 + 1.86773i
\(26\) 0.964701 0.718606i 0.189193 0.140930i
\(27\) 2.06938 4.76630i 0.398253 0.917276i
\(28\) 0 0
\(29\) 3.37929i 0.627518i 0.949503 + 0.313759i \(0.101588\pi\)
−0.949503 + 0.313759i \(0.898412\pi\)
\(30\) 8.32911 + 5.03249i 1.52068 + 0.918802i
\(31\) 4.24264 2.44949i 0.762001 0.439941i −0.0680129 0.997684i \(-0.521666\pi\)
0.830014 + 0.557743i \(0.188333\pi\)
\(32\) 5.64683 0.336691i 0.998227 0.0595191i
\(33\) 0.778803 5.66848i 0.135572 0.986755i
\(34\) −0.322697 + 0.748663i −0.0553421 + 0.128395i
\(35\) 0 0
\(36\) 5.99525 + 0.238815i 0.999208 + 0.0398026i
\(37\) −2.14510 + 3.71543i −0.352653 + 0.610812i −0.986713 0.162471i \(-0.948054\pi\)
0.634061 + 0.773283i \(0.281387\pi\)
\(38\) 5.04449 0.591024i 0.818324 0.0958767i
\(39\) 1.16376 + 0.903453i 0.186351 + 0.144668i
\(40\) −1.94212 + 11.0677i −0.307076 + 1.74996i
\(41\) 5.35550i 0.836389i −0.908357 0.418195i \(-0.862663\pi\)
0.908357 0.418195i \(-0.137337\pi\)
\(42\) 0 0
\(43\) 7.66518i 1.16893i 0.811419 + 0.584464i \(0.198695\pi\)
−0.811419 + 0.584464i \(0.801305\pi\)
\(44\) 6.42795 1.52719i 0.969050 0.230233i
\(45\) −3.21433 + 11.4769i −0.479164 + 1.71087i
\(46\) −0.651966 5.56464i −0.0961272 0.820461i
\(47\) −4.54525 + 7.87260i −0.662993 + 1.14834i 0.316833 + 0.948481i \(0.397381\pi\)
−0.979825 + 0.199856i \(0.935953\pi\)
\(48\) 2.24494 + 6.55441i 0.324029 + 0.946047i
\(49\) 0 0
\(50\) −14.0044 6.03634i −1.98052 0.853667i
\(51\) −0.989179 0.135905i −0.138513 0.0190305i
\(52\) −0.487013 + 1.63000i −0.0675365 + 0.226041i
\(53\) −0.527096 + 0.304319i −0.0724023 + 0.0418015i −0.535764 0.844368i \(-0.679976\pi\)
0.463362 + 0.886169i \(0.346643\pi\)
\(54\) 1.67971 + 7.15392i 0.228579 + 0.973525i
\(55\) 13.1240i 1.76964i
\(56\) 0 0
\(57\) 2.34803 + 5.76029i 0.311005 + 0.762969i
\(58\) −2.85490 3.83259i −0.374866 0.503244i
\(59\) 3.93980 + 6.82394i 0.512919 + 0.888401i 0.999888 + 0.0149820i \(0.00476911\pi\)
−0.486969 + 0.873419i \(0.661898\pi\)
\(60\) −13.6979 + 1.32907i −1.76840 + 0.171582i
\(61\) 4.87315 8.44054i 0.623943 1.08070i −0.364802 0.931085i \(-0.618863\pi\)
0.988744 0.149615i \(-0.0478034\pi\)
\(62\) −2.74237 + 6.36234i −0.348281 + 0.808018i
\(63\) 0 0
\(64\) −6.11985 + 5.15242i −0.764982 + 0.644052i
\(65\) −2.92655 1.68964i −0.362994 0.209575i
\(66\) 3.90558 + 7.08680i 0.480744 + 0.872325i
\(67\) 7.83384 4.52287i 0.957056 0.552557i 0.0617904 0.998089i \(-0.480319\pi\)
0.895266 + 0.445532i \(0.146986\pi\)
\(68\) −0.266503 1.12171i −0.0323182 0.136027i
\(69\) 6.35425 2.59015i 0.764962 0.311817i
\(70\) 0 0
\(71\) 9.15654 1.08668 0.543341 0.839512i \(-0.317159\pi\)
0.543341 + 0.839512i \(0.317159\pi\)
\(72\) −7.00121 + 4.79407i −0.825100 + 0.564986i
\(73\) 0.707107 + 1.22474i 0.0827606 + 0.143346i 0.904435 0.426612i \(-0.140293\pi\)
−0.821674 + 0.569958i \(0.806960\pi\)
\(74\) −0.706026 6.02605i −0.0820738 0.700514i
\(75\) 2.54223 18.5035i 0.293551 2.13660i
\(76\) −5.22185 + 4.93200i −0.598987 + 0.565739i
\(77\) 0 0
\(78\) −2.08312 0.0414733i −0.235867 0.00469593i
\(79\) 6.00000 + 3.46410i 0.675053 + 0.389742i 0.797988 0.602673i \(-0.205898\pi\)
−0.122936 + 0.992415i \(0.539231\pi\)
\(80\) −7.14764 14.1931i −0.799130 1.58684i
\(81\) −7.89371 + 4.32311i −0.877079 + 0.480346i
\(82\) 4.52445 + 6.07390i 0.499642 + 0.670750i
\(83\) −4.13877 −0.454289 −0.227144 0.973861i \(-0.572939\pi\)
−0.227144 + 0.973861i \(0.572939\pi\)
\(84\) 0 0
\(85\) 2.29021 0.248408
\(86\) −6.47571 8.69339i −0.698294 0.937433i
\(87\) 3.58926 4.62341i 0.384809 0.495682i
\(88\) −6.00000 + 7.16253i −0.639602 + 0.763528i
\(89\) 4.98550 + 2.87838i 0.528462 + 0.305108i 0.740390 0.672177i \(-0.234641\pi\)
−0.211928 + 0.977285i \(0.567974\pi\)
\(90\) −6.05039 15.7319i −0.637768 1.65829i
\(91\) 0 0
\(92\) 5.44055 + 5.76029i 0.567217 + 0.600552i
\(93\) −8.40631 1.15496i −0.871694 0.119764i
\(94\) −1.49600 12.7686i −0.154300 1.31698i
\(95\) −7.13398 12.3564i −0.731931 1.26774i
\(96\) −8.08339 5.53705i −0.825007 0.565122i
\(97\) −13.5487 −1.37567 −0.687833 0.725869i \(-0.741438\pi\)
−0.687833 + 0.725869i \(0.741438\pi\)
\(98\) 0 0
\(99\) −7.08622 + 6.92820i −0.712192 + 0.696311i
\(100\) 20.9826 4.98517i 2.09826 0.498517i
\(101\) 6.18294 3.56972i 0.615225 0.355200i −0.159782 0.987152i \(-0.551079\pi\)
0.775008 + 0.631952i \(0.217746\pi\)
\(102\) 1.23668 0.681544i 0.122450 0.0674829i
\(103\) 9.10090 + 5.25441i 0.896738 + 0.517732i 0.876141 0.482056i \(-0.160110\pi\)
0.0205978 + 0.999788i \(0.493443\pi\)
\(104\) −0.824720 2.26009i −0.0808705 0.221620i
\(105\) 0 0
\(106\) 0.340706 0.790444i 0.0330923 0.0767747i
\(107\) −0.616561 + 1.06792i −0.0596052 + 0.103239i −0.894288 0.447491i \(-0.852318\pi\)
0.834683 + 0.550731i \(0.185651\pi\)
\(108\) −7.94881 6.69450i −0.764875 0.644179i
\(109\) 1.60147 + 2.77382i 0.153393 + 0.265684i 0.932473 0.361241i \(-0.117647\pi\)
−0.779080 + 0.626925i \(0.784313\pi\)
\(110\) −11.0874 14.8845i −1.05715 1.41918i
\(111\) 6.88114 2.80492i 0.653128 0.266231i
\(112\) 0 0
\(113\) 19.9097i 1.87294i −0.350744 0.936471i \(-0.614071\pi\)
0.350744 0.936471i \(-0.385929\pi\)
\(114\) −7.52942 4.54931i −0.705195 0.426082i
\(115\) −13.6305 + 7.86959i −1.27105 + 0.733843i
\(116\) 6.47571 + 1.93482i 0.601255 + 0.179643i
\(117\) −0.632623 2.47214i −0.0584860 0.228550i
\(118\) −10.2333 4.41088i −0.942052 0.406054i
\(119\) 0 0
\(120\) 14.4126 13.0797i 1.31568 1.19401i
\(121\) 0.0436371 0.0755817i 0.00396701 0.00687107i
\(122\) 1.60392 + 13.6897i 0.145212 + 1.23941i
\(123\) −5.68827 + 7.32720i −0.512894 + 0.660671i
\(124\) −2.26481 9.53261i −0.203386 0.856053i
\(125\) 22.9762i 2.05505i
\(126\) 0 0
\(127\) 16.4426i 1.45904i −0.683957 0.729522i \(-0.739742\pi\)
0.683957 0.729522i \(-0.260258\pi\)
\(128\) 2.58790 11.0138i 0.228740 0.973488i
\(129\) 8.14146 10.4872i 0.716815 0.923347i
\(130\) 4.74657 0.556119i 0.416302 0.0487749i
\(131\) 1.13845 1.97186i 0.0994670 0.172282i −0.811997 0.583661i \(-0.801620\pi\)
0.911464 + 0.411379i \(0.134953\pi\)
\(132\) −10.4166 4.73791i −0.906646 0.412382i
\(133\) 0 0
\(134\) −5.06366 + 11.7478i −0.437434 + 1.01485i
\(135\) 16.5877 12.2881i 1.42764 1.05759i
\(136\) 1.24990 + 1.04703i 0.107178 + 0.0897822i
\(137\) −7.97118 + 4.60216i −0.681024 + 0.393189i −0.800241 0.599679i \(-0.795295\pi\)
0.119217 + 0.992868i \(0.461962\pi\)
\(138\) −5.01841 + 8.30581i −0.427195 + 0.707037i
\(139\) 11.1056i 0.941960i −0.882144 0.470980i \(-0.843900\pi\)
0.882144 0.470980i \(-0.156100\pi\)
\(140\) 0 0
\(141\) 14.5804 5.94333i 1.22789 0.500519i
\(142\) −10.3848 + 7.73565i −0.871474 + 0.649161i
\(143\) −1.40495 2.43345i −0.117488 0.203496i
\(144\) 3.89023 11.3519i 0.324186 0.945994i
\(145\) −6.71266 + 11.6267i −0.557456 + 0.965542i
\(146\) −1.83665 0.791654i −0.152002 0.0655177i
\(147\) 0 0
\(148\) 5.89167 + 6.23792i 0.484292 + 0.512754i
\(149\) 5.81744 + 3.35870i 0.476584 + 0.275156i 0.718992 0.695019i \(-0.244604\pi\)
−0.242408 + 0.970174i \(0.577937\pi\)
\(150\) 12.7489 + 23.1333i 1.04094 + 1.88882i
\(151\) 11.4426 6.60641i 0.931188 0.537622i 0.0440012 0.999031i \(-0.485989\pi\)
0.887187 + 0.461410i \(0.152656\pi\)
\(152\) 1.75565 10.0051i 0.142402 0.811522i
\(153\) 1.20901 + 1.23658i 0.0977425 + 0.0999718i
\(154\) 0 0
\(155\) 19.4628 1.56329
\(156\) 2.39759 1.71283i 0.191961 0.137136i
\(157\) 1.19412 + 2.06828i 0.0953011 + 0.165066i 0.909734 0.415191i \(-0.136285\pi\)
−0.814433 + 0.580257i \(0.802952\pi\)
\(158\) −9.73140 + 1.14015i −0.774188 + 0.0907057i
\(159\) 1.04438 + 0.143490i 0.0828249 + 0.0113795i
\(160\) 20.0971 + 10.0585i 1.58881 + 0.795196i
\(161\) 0 0
\(162\) 5.30032 11.5718i 0.416433 0.909167i
\(163\) −15.8412 9.14590i −1.24078 0.716362i −0.271524 0.962432i \(-0.587528\pi\)
−0.969252 + 0.246069i \(0.920861\pi\)
\(164\) −10.2627 3.06630i −0.801384 0.239438i
\(165\) 13.9395 17.9558i 1.08519 1.39785i
\(166\) 4.69394 3.49652i 0.364321 0.271383i
\(167\) −19.3650 −1.49851 −0.749253 0.662284i \(-0.769587\pi\)
−0.749253 + 0.662284i \(0.769587\pi\)
\(168\) 0 0
\(169\) −12.2765 −0.944344
\(170\) −2.59742 + 1.93482i −0.199213 + 0.148394i
\(171\) 2.90572 10.3749i 0.222206 0.793392i
\(172\) 14.6887 + 4.38871i 1.12001 + 0.334636i
\(173\) −4.83696 2.79262i −0.367748 0.212319i 0.304726 0.952440i \(-0.401435\pi\)
−0.672474 + 0.740121i \(0.734768\pi\)
\(174\) −0.164766 + 8.27589i −0.0124909 + 0.627394i
\(175\) 0 0
\(176\) 0.753784 13.1922i 0.0568186 0.994403i
\(177\) 1.85766 13.5209i 0.139630 1.01629i
\(178\) −8.08598 + 0.947373i −0.606070 + 0.0710086i
\(179\) 9.68969 + 16.7830i 0.724241 + 1.25442i 0.959286 + 0.282438i \(0.0911432\pi\)
−0.235044 + 0.971985i \(0.575523\pi\)
\(180\) 20.1527 + 12.7307i 1.50209 + 0.948890i
\(181\) 10.8735 0.808222 0.404111 0.914710i \(-0.367581\pi\)
0.404111 + 0.914710i \(0.367581\pi\)
\(182\) 0 0
\(183\) −15.6323 + 6.37208i −1.15557 + 0.471038i
\(184\) −11.0368 1.93668i −0.813642 0.142774i
\(185\) −14.7607 + 8.52212i −1.08523 + 0.626559i
\(186\) 10.5097 5.79195i 0.770607 0.424686i
\(187\) 1.64920 + 0.952164i 0.120601 + 0.0696291i
\(188\) 12.4838 + 13.2175i 0.910477 + 0.963986i
\(189\) 0 0
\(190\) 18.5299 + 7.98697i 1.34430 + 0.579436i
\(191\) −0.616561 + 1.06792i −0.0446128 + 0.0772716i −0.887470 0.460866i \(-0.847539\pi\)
0.842857 + 0.538138i \(0.180872\pi\)
\(192\) 13.8455 0.549231i 0.999214 0.0396373i
\(193\) −7.89167 13.6688i −0.568055 0.983900i −0.996758 0.0804546i \(-0.974363\pi\)
0.428703 0.903445i \(-0.358971\pi\)
\(194\) 15.3662 11.4463i 1.10323 0.821795i
\(195\) 2.20936 + 5.42010i 0.158216 + 0.388141i
\(196\) 0 0
\(197\) 17.3868i 1.23876i 0.785092 + 0.619379i \(0.212615\pi\)
−0.785092 + 0.619379i \(0.787385\pi\)
\(198\) 2.18367 13.8442i 0.155187 0.983861i
\(199\) −3.95565 + 2.28380i −0.280409 + 0.161894i −0.633608 0.773654i \(-0.718427\pi\)
0.353200 + 0.935548i \(0.385094\pi\)
\(200\) −19.5857 + 23.3805i −1.38491 + 1.65325i
\(201\) −15.5219 2.13258i −1.09483 0.150421i
\(202\) −3.99654 + 9.27205i −0.281196 + 0.652379i
\(203\) 0 0
\(204\) −0.826790 + 1.81775i −0.0578869 + 0.127268i
\(205\) 10.6382 18.4260i 0.743007 1.28693i
\(206\) −14.7607 + 1.72940i −1.02843 + 0.120493i
\(207\) −11.4447 3.20534i −0.795464 0.222786i
\(208\) 2.84472 + 1.86652i 0.197246 + 0.129420i
\(209\) 11.8639i 0.820646i
\(210\) 0 0
\(211\) 1.11224i 0.0765696i 0.999267 + 0.0382848i \(0.0121894\pi\)
−0.999267 + 0.0382848i \(0.987811\pi\)
\(212\) 0.281376 + 1.18431i 0.0193250 + 0.0813388i
\(213\) −12.5276 9.72549i −0.858379 0.666379i
\(214\) −0.202931 1.73205i −0.0138721 0.118401i
\(215\) −15.2262 + 26.3726i −1.03842 + 1.79859i
\(216\) 14.6707 + 0.877174i 0.998217 + 0.0596841i
\(217\) 0 0
\(218\) −4.15967 1.79295i −0.281729 0.121434i
\(219\) 0.333408 2.42669i 0.0225296 0.163981i
\(220\) 25.1494 + 7.51416i 1.69558 + 0.506605i
\(221\) −0.424650 + 0.245172i −0.0285651 + 0.0164920i
\(222\) −5.43452 + 8.99451i −0.364741 + 0.603672i
\(223\) 23.6328i 1.58257i −0.611447 0.791285i \(-0.709412\pi\)
0.611447 0.791285i \(-0.290588\pi\)
\(224\) 0 0
\(225\) −23.1314 + 22.6156i −1.54209 + 1.50770i
\(226\) 16.8201 + 22.5804i 1.11886 + 1.50202i
\(227\) 6.14917 + 10.6507i 0.408135 + 0.706910i 0.994681 0.103006i \(-0.0328461\pi\)
−0.586546 + 0.809916i \(0.699513\pi\)
\(228\) 12.3828 1.20146i 0.820070 0.0795688i
\(229\) −4.51474 + 7.81976i −0.298342 + 0.516744i −0.975757 0.218857i \(-0.929767\pi\)
0.677414 + 0.735602i \(0.263100\pi\)
\(230\) 8.81054 20.4406i 0.580950 1.34781i
\(231\) 0 0
\(232\) −8.97895 + 3.27647i −0.589497 + 0.215111i
\(233\) 6.55912 + 3.78691i 0.429703 + 0.248089i 0.699220 0.714907i \(-0.253531\pi\)
−0.269517 + 0.962996i \(0.586864\pi\)
\(234\) 2.80600 + 2.26930i 0.183434 + 0.148349i
\(235\) −31.2765 + 18.0575i −2.04025 + 1.17794i
\(236\) 15.3324 3.64277i 0.998055 0.237124i
\(237\) −4.52963 11.1123i −0.294231 0.721819i
\(238\) 0 0
\(239\) −9.25206 −0.598466 −0.299233 0.954180i \(-0.596731\pi\)
−0.299233 + 0.954180i \(0.596731\pi\)
\(240\) −5.29589 + 27.0103i −0.341848 + 1.74350i
\(241\) −7.83018 13.5623i −0.504386 0.873623i −0.999987 0.00507224i \(-0.998385\pi\)
0.495601 0.868550i \(-0.334948\pi\)
\(242\) 0.0143625 + 0.122586i 0.000923254 + 0.00788012i
\(243\) 15.3916 + 2.46947i 0.987372 + 0.158417i
\(244\) −13.3844 14.1710i −0.856850 0.907207i
\(245\) 0 0
\(246\) 0.261122 13.1157i 0.0166485 0.836223i
\(247\) 2.64557 + 1.52742i 0.168333 + 0.0971873i
\(248\) 10.6220 + 8.89796i 0.674496 + 0.565021i
\(249\) 5.66250 + 4.39593i 0.358847 + 0.278581i
\(250\) −19.4108 26.0583i −1.22765 1.64807i
\(251\) −3.08987 −0.195031 −0.0975155 0.995234i \(-0.531090\pi\)
−0.0975155 + 0.995234i \(0.531090\pi\)
\(252\) 0 0
\(253\) −13.0873 −0.822790
\(254\) 13.8911 + 18.6482i 0.871603 + 1.17009i
\(255\) −3.13337 2.43251i −0.196219 0.152330i
\(256\) 6.36962 + 14.6775i 0.398101 + 0.917341i
\(257\) −6.38190 3.68459i −0.398092 0.229839i 0.287568 0.957760i \(-0.407153\pi\)
−0.685660 + 0.727922i \(0.740486\pi\)
\(258\) −0.373736 + 18.7721i −0.0232678 + 1.16870i
\(259\) 0 0
\(260\) −4.91346 + 4.64072i −0.304720 + 0.287805i
\(261\) −9.82139 + 2.51330i −0.607929 + 0.155569i
\(262\) 0.374703 + 3.19815i 0.0231492 + 0.197583i
\(263\) −11.1017 19.2288i −0.684563 1.18570i −0.973574 0.228372i \(-0.926660\pi\)
0.289011 0.957326i \(-0.406673\pi\)
\(264\) 15.8165 3.42669i 0.973441 0.210898i
\(265\) −2.41801 −0.148537
\(266\) 0 0
\(267\) −3.76375 9.23337i −0.230338 0.565073i
\(268\) −4.18188 17.6015i −0.255449 1.07518i
\(269\) 8.67226 5.00693i 0.528757 0.305278i −0.211753 0.977323i \(-0.567917\pi\)
0.740510 + 0.672045i \(0.234584\pi\)
\(270\) −8.43149 + 27.9501i −0.513124 + 1.70099i
\(271\) −20.4250 11.7924i −1.24073 0.716335i −0.271486 0.962442i \(-0.587515\pi\)
−0.969243 + 0.246107i \(0.920848\pi\)
\(272\) −2.30212 0.131539i −0.139586 0.00797574i
\(273\) 0 0
\(274\) 5.15243 11.9537i 0.311270 0.722151i
\(275\) −17.8111 + 30.8497i −1.07405 + 1.86031i
\(276\) −1.32535 13.6596i −0.0797767 0.822212i
\(277\) −14.5299 25.1665i −0.873018 1.51211i −0.858860 0.512211i \(-0.828826\pi\)
−0.0141582 0.999900i \(-0.504507\pi\)
\(278\) 9.38221 + 12.5953i 0.562708 + 0.755413i
\(279\) 10.2745 + 10.5088i 0.615117 + 0.629146i
\(280\) 0 0
\(281\) 23.2889i 1.38930i −0.719347 0.694651i \(-0.755559\pi\)
0.719347 0.694651i \(-0.244441\pi\)
\(282\) −11.5152 + 19.0584i −0.685719 + 1.13491i
\(283\) 15.0916 8.71312i 0.897101 0.517941i 0.0208421 0.999783i \(-0.493365\pi\)
0.876258 + 0.481842i \(0.160032\pi\)
\(284\) 5.24259 17.5466i 0.311090 1.04120i
\(285\) −3.36375 + 24.4828i −0.199251 + 1.45024i
\(286\) 3.64925 + 1.57294i 0.215785 + 0.0930100i
\(287\) 0 0
\(288\) 5.17829 + 16.1612i 0.305134 + 0.952310i
\(289\) −8.33384 + 14.4346i −0.490226 + 0.849096i
\(290\) −2.20936 18.8573i −0.129738 1.10734i
\(291\) 18.5369 + 14.3906i 1.08665 + 0.843592i
\(292\) 2.75183 0.653796i 0.161038 0.0382605i
\(293\) 1.20747i 0.0705412i 0.999378 + 0.0352706i \(0.0112293\pi\)
−0.999378 + 0.0352706i \(0.988771\pi\)
\(294\) 0 0
\(295\) 31.3043i 1.82261i
\(296\) −11.9519 2.09727i −0.694691 0.121901i
\(297\) 17.0538 1.95238i 0.989561 0.113289i
\(298\) −9.43531 + 1.10546i −0.546573 + 0.0640377i
\(299\) 1.68492 2.91836i 0.0974412 0.168773i
\(300\) −34.0025 15.4658i −1.96314 0.892921i
\(301\) 0 0
\(302\) −7.39632 + 17.1596i −0.425610 + 0.987423i
\(303\) −12.2508 1.68316i −0.703789 0.0966950i
\(304\) 6.46138 + 12.8304i 0.370586 + 0.735875i
\(305\) 33.5328 19.3602i 1.92008 1.10856i
\(306\) −2.41588 0.381063i −0.138106 0.0217839i
\(307\) 34.0275i 1.94205i 0.238973 + 0.971026i \(0.423189\pi\)
−0.238973 + 0.971026i \(0.576811\pi\)
\(308\) 0 0
\(309\) −6.87062 16.8553i −0.390856 0.958863i
\(310\) −22.0735 + 16.4426i −1.25369 + 0.933877i
\(311\) −13.3558 23.1329i −0.757337 1.31175i −0.944204 0.329361i \(-0.893167\pi\)
0.186867 0.982385i \(-0.440167\pi\)
\(312\) −1.27217 + 3.96814i −0.0720225 + 0.224651i
\(313\) −4.66276 + 8.07614i −0.263555 + 0.456490i −0.967184 0.254077i \(-0.918228\pi\)
0.703629 + 0.710567i \(0.251562\pi\)
\(314\) −3.10162 1.33690i −0.175035 0.0754455i
\(315\) 0 0
\(316\) 10.0735 9.51439i 0.566681 0.535226i
\(317\) 23.3767 + 13.4966i 1.31297 + 0.758043i 0.982587 0.185805i \(-0.0594891\pi\)
0.330382 + 0.943847i \(0.392822\pi\)
\(318\) −1.30570 + 0.719579i −0.0732200 + 0.0403520i
\(319\) −9.66769 + 5.58164i −0.541286 + 0.312512i
\(320\) −31.2906 + 5.57069i −1.74920 + 0.311411i
\(321\) 1.97783 0.806210i 0.110392 0.0449982i
\(322\) 0 0
\(323\) −2.07032 −0.115196
\(324\) 3.76480 + 17.6019i 0.209156 + 0.977882i
\(325\) −4.58616 7.94346i −0.254394 0.440624i
\(326\) 25.6928 3.01023i 1.42299 0.166721i
\(327\) 0.755108 5.49601i 0.0417575 0.303930i
\(328\) 14.2299 5.19256i 0.785712 0.286711i
\(329\) 0 0
\(330\) −0.639895 + 32.1407i −0.0352251 + 1.76929i
\(331\) 12.6382 + 7.29669i 0.694660 + 0.401062i 0.805356 0.592792i \(-0.201974\pi\)
−0.110695 + 0.993854i \(0.535308\pi\)
\(332\) −2.36966 + 7.93109i −0.130052 + 0.435275i
\(333\) −12.3937 3.47112i −0.679171 0.190216i
\(334\) 21.9626 16.3600i 1.20174 0.895177i
\(335\) 35.9372 1.96346
\(336\) 0 0
\(337\) 31.6823 1.72585 0.862924 0.505335i \(-0.168631\pi\)
0.862924 + 0.505335i \(0.168631\pi\)
\(338\) 13.9233 10.3714i 0.757325 0.564132i
\(339\) −21.1468 + 27.2396i −1.14853 + 1.47945i
\(340\) 1.31126 4.38871i 0.0711131 0.238011i
\(341\) 14.0153 + 8.09175i 0.758972 + 0.438193i
\(342\) 5.46949 + 14.2215i 0.295756 + 0.769009i
\(343\) 0 0
\(344\) −20.3668 + 7.43196i −1.09810 + 0.400704i
\(345\) 27.0073 + 3.71059i 1.45403 + 0.199772i
\(346\) 7.84507 0.919147i 0.421753 0.0494136i
\(347\) −1.07687 1.86519i −0.0578092 0.100128i 0.835673 0.549228i \(-0.185078\pi\)
−0.893482 + 0.449100i \(0.851745\pi\)
\(348\) −6.80479 9.52523i −0.364775 0.510606i
\(349\) 33.0517 1.76922 0.884608 0.466335i \(-0.154426\pi\)
0.884608 + 0.466335i \(0.154426\pi\)
\(350\) 0 0
\(351\) −1.76022 + 4.05422i −0.0939535 + 0.216398i
\(352\) 10.2902 + 15.5987i 0.548470 + 0.831413i
\(353\) 13.5161 7.80351i 0.719388 0.415339i −0.0951392 0.995464i \(-0.530330\pi\)
0.814528 + 0.580125i \(0.196996\pi\)
\(354\) 9.31588 + 16.9040i 0.495133 + 0.898435i
\(355\) 31.5037 + 18.1887i 1.67204 + 0.965354i
\(356\) 8.37028 7.90567i 0.443624 0.419000i
\(357\) 0 0
\(358\) −25.1681 10.8483i −1.33018 0.573348i
\(359\) 16.8237 29.1394i 0.887919 1.53792i 0.0455885 0.998960i \(-0.485484\pi\)
0.842331 0.538961i \(-0.181183\pi\)
\(360\) −33.6111 + 2.58701i −1.77146 + 0.136348i
\(361\) −3.05096 5.28443i −0.160577 0.278128i
\(362\) −12.3321 + 9.18619i −0.648161 + 0.482815i
\(363\) −0.139981 + 0.0570595i −0.00734708 + 0.00299485i
\(364\) 0 0
\(365\) 5.61842i 0.294082i
\(366\) 12.3459 20.4333i 0.645331 1.06807i
\(367\) 6.79444 3.92277i 0.354667 0.204767i −0.312072 0.950059i \(-0.601023\pi\)
0.666739 + 0.745291i \(0.267690\pi\)
\(368\) 14.1534 7.12764i 0.737797 0.371554i
\(369\) 15.5650 3.98308i 0.810279 0.207351i
\(370\) 9.54109 22.1355i 0.496018 1.15077i
\(371\) 0 0
\(372\) −7.02629 + 15.4477i −0.364296 + 0.800926i
\(373\) −0.493136 + 0.854137i −0.0255336 + 0.0442256i −0.878510 0.477724i \(-0.841462\pi\)
0.852976 + 0.521950i \(0.174795\pi\)
\(374\) −2.67483 + 0.313389i −0.138312 + 0.0162050i
\(375\) 24.4038 31.4352i 1.26021 1.62331i
\(376\) −25.3249 4.44389i −1.30603 0.229176i
\(377\) 2.87443i 0.148040i
\(378\) 0 0
\(379\) 18.8285i 0.967153i −0.875302 0.483576i \(-0.839337\pi\)
0.875302 0.483576i \(-0.160663\pi\)
\(380\) −27.7631 + 6.59612i −1.42422 + 0.338374i
\(381\) −17.4643 + 22.4961i −0.894721 + 1.15251i
\(382\) −0.202931 1.73205i −0.0103829 0.0886194i
\(383\) −1.81144 + 3.13750i −0.0925602 + 0.160319i −0.908588 0.417694i \(-0.862838\pi\)
0.816028 + 0.578013i \(0.196172\pi\)
\(384\) −15.2388 + 12.3199i −0.777650 + 0.628697i
\(385\) 0 0
\(386\) 20.4979 + 8.83526i 1.04332 + 0.449703i
\(387\) −22.2777 + 5.70087i −1.13244 + 0.289792i
\(388\) −7.75735 + 25.9634i −0.393820 + 1.31809i
\(389\) −12.6579 + 7.30807i −0.641783 + 0.370534i −0.785301 0.619114i \(-0.787492\pi\)
0.143518 + 0.989648i \(0.454159\pi\)
\(390\) −7.08475 4.28064i −0.358750 0.216759i
\(391\) 2.28380i 0.115497i
\(392\) 0 0
\(393\) −3.65197 + 1.48863i −0.184217 + 0.0750914i
\(394\) −14.6887 19.7191i −0.740008 0.993432i
\(395\) 13.7623 + 23.8370i 0.692455 + 1.19937i
\(396\) 9.21925 + 17.5460i 0.463285 + 0.881722i
\(397\) 3.04852 5.28019i 0.153001 0.265005i −0.779328 0.626616i \(-0.784440\pi\)
0.932329 + 0.361610i \(0.117773\pi\)
\(398\) 2.55687 5.93197i 0.128164 0.297343i
\(399\) 0 0
\(400\) 2.46056 43.0631i 0.123028 2.15316i
\(401\) −6.31340 3.64505i −0.315276 0.182025i 0.334009 0.942570i \(-0.391598\pi\)
−0.649285 + 0.760545i \(0.724932\pi\)
\(402\) 19.4056 10.6946i 0.967865 0.533397i
\(403\) −3.60879 + 2.08354i −0.179767 + 0.103788i
\(404\) −3.30059 13.8922i −0.164210 0.691162i
\(405\) −35.7463 0.806210i −1.77625 0.0400609i
\(406\) 0 0
\(407\) −14.1724 −0.702502
\(408\) −0.597975 2.76007i −0.0296042 0.136644i
\(409\) 10.0950 + 17.4850i 0.499165 + 0.864580i 1.00000 0.000963491i \(-0.000306689\pi\)
−0.500834 + 0.865543i \(0.666973\pi\)
\(410\) 3.50140 + 29.8851i 0.172922 + 1.47592i
\(411\) 15.7940 + 2.16997i 0.779060 + 0.107037i
\(412\) 15.2797 14.4316i 0.752778 0.710993i
\(413\) 0 0
\(414\) 15.6879 6.03347i 0.771018 0.296529i
\(415\) −14.2397 8.22130i −0.699000 0.403568i
\(416\) −4.80319 + 0.286389i −0.235496 + 0.0140414i
\(417\) −11.7956 + 15.1942i −0.577633 + 0.744063i
\(418\) 10.0229 + 13.4554i 0.490237 + 0.658124i
\(419\) −1.32886 −0.0649189 −0.0324594 0.999473i \(-0.510334\pi\)
−0.0324594 + 0.999473i \(0.510334\pi\)
\(420\) 0 0
\(421\) −7.31859 −0.356686 −0.178343 0.983968i \(-0.557074\pi\)
−0.178343 + 0.983968i \(0.557074\pi\)
\(422\) −0.939643 1.26143i −0.0457411 0.0614057i
\(423\) −26.2610 7.35493i −1.27685 0.357609i
\(424\) −1.31965 1.10546i −0.0640879 0.0536860i
\(425\) 5.38343 + 3.10812i 0.261135 + 0.150766i
\(426\) 22.4244 + 0.446451i 1.08647 + 0.0216306i
\(427\) 0 0
\(428\) 1.69343 + 1.79295i 0.0818549 + 0.0866655i
\(429\) −0.662451 + 4.82161i −0.0319834 + 0.232790i
\(430\) −5.01146 42.7736i −0.241674 2.06273i
\(431\) 0.0894647 + 0.154957i 0.00430936 + 0.00746403i 0.868172 0.496263i \(-0.165295\pi\)
−0.863863 + 0.503727i \(0.831962\pi\)
\(432\) −17.3797 + 11.3993i −0.836183 + 0.548450i
\(433\) 15.2499 0.732866 0.366433 0.930444i \(-0.380579\pi\)
0.366433 + 0.930444i \(0.380579\pi\)
\(434\) 0 0
\(435\) 21.5331 8.77742i 1.03243 0.420845i
\(436\) 6.23238 1.48073i 0.298477 0.0709139i
\(437\) 12.3218 7.11402i 0.589434 0.340310i
\(438\) 1.67199 + 3.03388i 0.0798909 + 0.144965i
\(439\) −25.8988 14.9527i −1.23608 0.713654i −0.267793 0.963476i \(-0.586294\pi\)
−0.968292 + 0.249823i \(0.919628\pi\)
\(440\) −34.8711 + 12.7247i −1.66242 + 0.606626i
\(441\) 0 0
\(442\) 0.274487 0.636813i 0.0130560 0.0302901i
\(443\) 2.50795 4.34390i 0.119156 0.206385i −0.800277 0.599630i \(-0.795314\pi\)
0.919434 + 0.393245i \(0.128648\pi\)
\(444\) −1.43524 14.7922i −0.0681137 0.702009i
\(445\) 11.4353 + 19.8065i 0.542086 + 0.938920i
\(446\) 19.9655 + 26.8029i 0.945395 + 1.26916i
\(447\) −4.39181 10.7742i −0.207725 0.509601i
\(448\) 0 0
\(449\) 14.4978i 0.684195i 0.939664 + 0.342098i \(0.111137\pi\)
−0.939664 + 0.342098i \(0.888863\pi\)
\(450\) 7.12811 45.1911i 0.336023 2.13033i
\(451\) 15.3214 8.84580i 0.721455 0.416532i
\(452\) −38.1528 11.3993i −1.79456 0.536178i
\(453\) −22.6723 3.11499i −1.06524 0.146355i
\(454\) −15.9719 6.88441i −0.749600 0.323101i
\(455\) 0 0
\(456\) −13.0288 + 11.8239i −0.610129 + 0.553704i
\(457\) 9.92844 17.1966i 0.464433 0.804422i −0.534743 0.845015i \(-0.679591\pi\)
0.999176 + 0.0405933i \(0.0129248\pi\)
\(458\) −1.48595 12.6829i −0.0694341 0.592631i
\(459\) −0.340700 2.97598i −0.0159025 0.138907i
\(460\) 7.27627 + 30.6259i 0.339258 + 1.42794i
\(461\) 17.3910i 0.809978i −0.914322 0.404989i \(-0.867275\pi\)
0.914322 0.404989i \(-0.132725\pi\)
\(462\) 0 0
\(463\) 15.3304i 0.712462i −0.934398 0.356231i \(-0.884062\pi\)
0.934398 0.356231i \(-0.115938\pi\)
\(464\) 7.41536 11.3016i 0.344249 0.524663i
\(465\) −26.6283 20.6721i −1.23486 0.958647i
\(466\) −10.6382 + 1.24640i −0.492807 + 0.0577384i
\(467\) 10.5410 18.2575i 0.487778 0.844857i −0.512123 0.858912i \(-0.671141\pi\)
0.999901 + 0.0140554i \(0.00447412\pi\)
\(468\) −5.09956 0.203137i −0.235727 0.00938999i
\(469\) 0 0
\(470\) 20.2166 46.9028i 0.932521 2.16346i
\(471\) 0.563040 4.09805i 0.0259435 0.188828i
\(472\) −14.3116 + 17.0846i −0.658746 + 0.786381i
\(473\) −21.9290 + 12.6607i −1.00830 + 0.582141i
\(474\) 14.5251 + 8.77615i 0.667161 + 0.403102i
\(475\) 38.7272i 1.77692i
\(476\) 0 0
\(477\) −1.27648 1.30559i −0.0584459 0.0597790i
\(478\) 10.4931 7.81634i 0.479945 0.357511i
\(479\) 3.79982 + 6.58149i 0.173618 + 0.300716i 0.939682 0.342049i \(-0.111121\pi\)
−0.766064 + 0.642764i \(0.777787\pi\)
\(480\) −16.8126 35.1075i −0.767386 1.60243i
\(481\) 1.82463 3.16034i 0.0831958 0.144099i
\(482\) 20.3382 + 8.76642i 0.926381 + 0.399299i
\(483\) 0 0
\(484\) −0.119852 0.126896i −0.00544784 0.00576800i
\(485\) −46.6154 26.9134i −2.11670 1.22207i
\(486\) −19.5425 + 10.2024i −0.886467 + 0.462792i
\(487\) 13.3691 7.71865i 0.605811 0.349765i −0.165513 0.986208i \(-0.552928\pi\)
0.771324 + 0.636442i \(0.219595\pi\)
\(488\) 27.1518 + 4.76448i 1.22911 + 0.215678i
\(489\) 11.9591 + 29.3386i 0.540809 + 1.32674i
\(490\) 0 0
\(491\) 40.5166 1.82849 0.914243 0.405165i \(-0.132786\pi\)
0.914243 + 0.405165i \(0.132786\pi\)
\(492\) 10.7842 + 15.0956i 0.486191 + 0.680562i
\(493\) 0.974025 + 1.68706i 0.0438679 + 0.0759814i
\(494\) −4.29084 + 0.502725i −0.193054 + 0.0226187i
\(495\) −38.1429 + 9.76079i −1.71440 + 0.438715i
\(496\) −19.5640 1.11786i −0.878450 0.0501932i
\(497\) 0 0
\(498\) −10.1359 0.201796i −0.454199 0.00904272i
\(499\) 26.2986 + 15.1835i 1.17729 + 0.679707i 0.955385 0.295362i \(-0.0954403\pi\)
0.221902 + 0.975069i \(0.428774\pi\)
\(500\) 44.0292 + 13.1551i 1.96904 + 0.588312i
\(501\) 26.4944 + 20.5682i 1.18368 + 0.918921i
\(502\) 3.50435 2.61039i 0.156407 0.116507i
\(503\) −13.8974 −0.619652 −0.309826 0.950793i \(-0.600271\pi\)
−0.309826 + 0.950793i \(0.600271\pi\)
\(504\) 0 0
\(505\) 28.3638 1.26217
\(506\) 14.8428 11.0564i 0.659844 0.491518i
\(507\) 16.7962 + 13.0393i 0.745946 + 0.579095i
\(508\) −31.5089 9.41423i −1.39798 0.417689i
\(509\) −25.6830 14.8281i −1.13838 0.657243i −0.192350 0.981326i \(-0.561611\pi\)
−0.946029 + 0.324083i \(0.894944\pi\)
\(510\) 5.60872 + 0.111665i 0.248358 + 0.00494461i
\(511\) 0 0
\(512\) −19.6239 11.2651i −0.867262 0.497853i
\(513\) −14.9951 + 11.1083i −0.662049 + 0.490445i
\(514\) 10.3508 1.21272i 0.456554 0.0534909i
\(515\) 20.8748 + 36.1563i 0.919855 + 1.59324i
\(516\) −15.4352 21.6059i −0.679496 0.951147i
\(517\) −30.0299 −1.32071
\(518\) 0 0
\(519\) 3.65161 + 8.95827i 0.160288 + 0.393225i
\(520\) 1.65197 9.41423i 0.0724435 0.412841i
\(521\) −29.0727 + 16.7851i −1.27370 + 0.735369i −0.975682 0.219192i \(-0.929658\pi\)
−0.298015 + 0.954561i \(0.596325\pi\)
\(522\) 9.01555 11.1478i 0.394600 0.487924i
\(523\) 8.82946 + 5.09769i 0.386085 + 0.222906i 0.680463 0.732783i \(-0.261779\pi\)
−0.294377 + 0.955689i \(0.595112\pi\)
\(524\) −3.12684 3.31060i −0.136596 0.144624i
\(525\) 0 0
\(526\) 28.8358 + 12.4291i 1.25730 + 0.541937i
\(527\) 1.41205 2.44575i 0.0615099 0.106538i
\(528\) −15.0433 + 17.2485i −0.654674 + 0.750645i
\(529\) 3.65243 + 6.32620i 0.158801 + 0.275052i
\(530\) 2.74237 2.04279i 0.119121 0.0887332i
\(531\) −16.9026 + 16.5256i −0.733509 + 0.717152i
\(532\) 0 0
\(533\) 4.55539i 0.197316i
\(534\) 12.0692 + 7.29225i 0.522284 + 0.315567i
\(535\) −4.24264 + 2.44949i −0.183425 + 0.105901i
\(536\) 19.6130 + 16.4297i 0.847152 + 0.709654i
\(537\) 4.56879 33.2537i 0.197158 1.43500i
\(538\) −5.60560 + 13.0051i −0.241675 + 0.560689i
\(539\) 0 0
\(540\) −14.0504 38.8225i −0.604633 1.67065i
\(541\) −5.15243 + 8.92427i −0.221520 + 0.383684i −0.955270 0.295736i \(-0.904435\pi\)
0.733750 + 0.679420i \(0.237769\pi\)
\(542\) 33.1272 3.88127i 1.42294 0.166715i
\(543\) −14.8767 11.5492i −0.638422 0.495622i
\(544\) 2.72205 1.79569i 0.116707 0.0769898i
\(545\) 12.7247i 0.545066i
\(546\) 0 0
\(547\) 5.44070i 0.232628i 0.993213 + 0.116314i \(0.0371078\pi\)
−0.993213 + 0.116314i \(0.962892\pi\)
\(548\) 4.25519 + 17.9101i 0.181773 + 0.765081i
\(549\) 28.1555 + 7.88552i 1.20165 + 0.336546i
\(550\) −5.86223 50.0351i −0.249966 2.13350i
\(551\) 6.06817 10.5104i 0.258513 0.447757i
\(552\) 13.0431 + 14.3722i 0.555150 + 0.611723i
\(553\) 0 0
\(554\) 37.7402 + 16.2672i 1.60343 + 0.691128i
\(555\) 29.2467 + 4.01827i 1.24145 + 0.170566i
\(556\) −21.2815 6.35850i −0.902537 0.269660i
\(557\) 3.84264 2.21855i 0.162818 0.0940030i −0.416377 0.909192i \(-0.636700\pi\)
0.579195 + 0.815189i \(0.303367\pi\)
\(558\) −20.5308 3.23837i −0.869137 0.137091i
\(559\) 6.52001i 0.275767i
\(560\) 0 0
\(561\) −1.24504 3.05438i −0.0525657 0.128956i
\(562\) 19.6750 + 26.4129i 0.829940 + 1.11416i
\(563\) −19.5639 33.8857i −0.824522 1.42811i −0.902284 0.431141i \(-0.858111\pi\)
0.0777627 0.996972i \(-0.475222\pi\)
\(564\) −3.04113 31.3432i −0.128055 1.31979i
\(565\) 39.5488 68.5005i 1.66383 2.88184i
\(566\) −9.75493 + 22.6316i −0.410030 + 0.951277i
\(567\) 0 0
\(568\) 8.87794 + 24.3294i 0.372510 + 1.02084i
\(569\) −38.4653 22.2079i −1.61255 0.931005i −0.988777 0.149398i \(-0.952266\pi\)
−0.623771 0.781607i \(-0.714400\pi\)
\(570\) −16.8687 30.6088i −0.706551 1.28206i
\(571\) 2.15883 1.24640i 0.0903442 0.0521603i −0.454147 0.890927i \(-0.650056\pi\)
0.544491 + 0.838766i \(0.316723\pi\)
\(572\) −5.46762 + 1.29903i −0.228613 + 0.0543152i
\(573\) 1.97783 0.806210i 0.0826249 0.0336799i
\(574\) 0 0
\(575\) −42.7205 −1.78157
\(576\) −19.5263 13.9544i −0.813595 0.581432i
\(577\) 18.2933 + 31.6849i 0.761560 + 1.31906i 0.942046 + 0.335482i \(0.108899\pi\)
−0.180487 + 0.983577i \(0.557767\pi\)
\(578\) −2.74295 23.4115i −0.114092 0.973791i
\(579\) −3.72100 + 27.0831i −0.154640 + 1.12554i
\(580\) 18.4368 + 19.5203i 0.765546 + 0.810536i
\(581\) 0 0
\(582\) −33.1809 0.660605i −1.37539 0.0273830i
\(583\) −1.74123 1.00530i −0.0721145 0.0416353i
\(584\) −2.56862 + 3.06630i −0.106290 + 0.126884i
\(585\) 2.73411 9.76222i 0.113042 0.403618i
\(586\) −1.02010 1.36944i −0.0421398 0.0565711i
\(587\) −36.8412 −1.52060 −0.760299 0.649573i \(-0.774948\pi\)
−0.760299 + 0.649573i \(0.774948\pi\)
\(588\) 0 0
\(589\) −17.5941 −0.724954
\(590\) −26.4466 35.5035i −1.08879 1.46166i
\(591\) 18.4671 23.7879i 0.759636 0.978505i
\(592\) 15.3270 7.71865i 0.629935 0.317234i
\(593\) 14.9125 + 8.60972i 0.612382 + 0.353559i 0.773897 0.633311i \(-0.218305\pi\)
−0.161515 + 0.986870i \(0.551638\pi\)
\(594\) −17.6920 + 16.6217i −0.725911 + 0.681996i
\(595\) 0 0
\(596\) 9.76705 9.22491i 0.400074 0.377867i
\(597\) 7.83768 + 1.07683i 0.320775 + 0.0440719i
\(598\) 0.554563 + 4.73329i 0.0226778 + 0.193558i
\(599\) −9.51076 16.4731i −0.388599 0.673073i 0.603662 0.797240i \(-0.293708\pi\)
−0.992261 + 0.124167i \(0.960374\pi\)
\(600\) 51.6296 11.1857i 2.10777 0.456652i
\(601\) −7.95144 −0.324346 −0.162173 0.986762i \(-0.551850\pi\)
−0.162173 + 0.986762i \(0.551850\pi\)
\(602\) 0 0
\(603\) 18.9713 + 19.4040i 0.772573 + 0.790194i
\(604\) −6.10833 25.7100i −0.248544 1.04612i
\(605\) 0.300273 0.173363i 0.0122078 0.00704820i
\(606\) 15.3161 8.44080i 0.622174 0.342884i
\(607\) −20.5976 11.8920i −0.836030 0.482682i 0.0198827 0.999802i \(-0.493671\pi\)
−0.855913 + 0.517120i \(0.827004\pi\)
\(608\) −18.1675 9.09279i −0.736791 0.368761i
\(609\) 0 0
\(610\) −21.6750 + 50.2864i −0.877596 + 2.03604i
\(611\) 3.86619 6.69644i 0.156409 0.270909i
\(612\) 3.06187 1.60881i 0.123769 0.0650322i
\(613\) 14.8779 + 25.7694i 0.600914 + 1.04081i 0.992683 + 0.120751i \(0.0385301\pi\)
−0.391768 + 0.920064i \(0.628137\pi\)
\(614\) −28.7472 38.5920i −1.16014 1.55745i
\(615\) −34.1257 + 13.9105i −1.37608 + 0.560924i
\(616\) 0 0
\(617\) 28.7008i 1.15545i 0.816232 + 0.577724i \(0.196059\pi\)
−0.816232 + 0.577724i \(0.803941\pi\)
\(618\) 22.0320 + 13.3118i 0.886255 + 0.535479i
\(619\) −19.9082 + 11.4940i −0.800177 + 0.461983i −0.843533 0.537077i \(-0.819528\pi\)
0.0433558 + 0.999060i \(0.486195\pi\)
\(620\) 11.1434 37.2964i 0.447532 1.49786i
\(621\) 12.2538 + 16.5413i 0.491726 + 0.663779i
\(622\) 34.6905 + 14.9527i 1.39096 + 0.599549i
\(623\) 0 0
\(624\) −1.90955 5.57518i −0.0764431 0.223186i
\(625\) −18.6819 + 32.3580i −0.747275 + 1.29432i
\(626\) −1.53467 13.0987i −0.0613378 0.523529i
\(627\) −12.6011 + 16.2318i −0.503240 + 0.648236i
\(628\) 4.64712 1.10409i 0.185440 0.0440580i
\(629\) 2.47316i 0.0986115i
\(630\) 0 0
\(631\) 15.3304i 0.610292i −0.952306 0.305146i \(-0.901295\pi\)
0.952306 0.305146i \(-0.0987052\pi\)
\(632\) −3.38685 + 19.3010i −0.134722 + 0.767753i
\(633\) 1.18135 1.52172i 0.0469543 0.0604830i
\(634\) −37.9147 + 4.44218i −1.50579 + 0.176421i
\(635\) 32.6618 56.5719i 1.29614 2.24499i
\(636\) 0.872931 1.91919i 0.0346140 0.0761008i
\(637\) 0 0
\(638\) 6.24902 14.4978i 0.247401 0.573975i
\(639\) 6.81005 + 26.6121i 0.269401 + 1.05276i
\(640\) 30.7817 32.7529i 1.21675 1.29467i
\(641\) 11.6038 6.69943i 0.458321 0.264612i −0.253017 0.967462i \(-0.581423\pi\)
0.711338 + 0.702850i \(0.248090\pi\)
\(642\) −1.56203 + 2.58527i −0.0616484 + 0.102032i
\(643\) 2.68122i 0.105737i 0.998601 + 0.0528684i \(0.0168364\pi\)
−0.998601 + 0.0528684i \(0.983164\pi\)
\(644\) 0 0
\(645\) 48.8432 19.9097i 1.92320 0.783942i
\(646\) 2.34803 1.74905i 0.0923822 0.0688155i
\(647\) 9.86799 + 17.0919i 0.387951 + 0.671950i 0.992174 0.124865i \(-0.0398497\pi\)
−0.604223 + 0.796815i \(0.706516\pi\)
\(648\) −19.1403 16.7824i −0.751901 0.659276i
\(649\) −13.0149 + 22.5425i −0.510880 + 0.884870i
\(650\) 11.9122 + 5.13452i 0.467233 + 0.201392i
\(651\) 0 0
\(652\) −26.5961 + 25.1198i −1.04158 + 0.983769i
\(653\) 30.5038 + 17.6114i 1.19371 + 0.689186i 0.959145 0.282915i \(-0.0913015\pi\)
0.234561 + 0.972101i \(0.424635\pi\)
\(654\) 3.78675 + 6.87118i 0.148074 + 0.268684i
\(655\) 7.83384 4.52287i 0.306094 0.176723i
\(656\) −11.7519 + 17.9108i −0.458833 + 0.699299i
\(657\) −3.03363 + 2.96599i −0.118353 + 0.115714i
\(658\) 0 0
\(659\) −39.7628 −1.54894 −0.774469 0.632612i \(-0.781983\pi\)
−0.774469 + 0.632612i \(0.781983\pi\)
\(660\) −26.4275 36.9927i −1.02869 1.43994i
\(661\) −7.46659 12.9325i −0.290417 0.503017i 0.683492 0.729958i \(-0.260461\pi\)
−0.973908 + 0.226942i \(0.927127\pi\)
\(662\) −20.4979 + 2.40159i −0.796675 + 0.0933404i
\(663\) 0.841396 + 0.115601i 0.0326771 + 0.00448957i
\(664\) −4.01284 10.9969i −0.155728 0.426763i
\(665\) 0 0
\(666\) 16.9887 6.53375i 0.658298 0.253178i
\(667\) −11.5941 6.69388i −0.448927 0.259188i
\(668\) −11.0874 + 37.1090i −0.428986 + 1.43579i
\(669\) −25.1012 + 32.3335i −0.970470 + 1.25009i
\(670\) −40.7578 + 30.3605i −1.57461 + 1.17293i
\(671\) 32.1963 1.24292
\(672\) 0 0
\(673\) 1.52059 0.0586145 0.0293072 0.999570i \(-0.490670\pi\)
0.0293072 + 0.999570i \(0.490670\pi\)
\(674\) −35.9322 + 26.7659i −1.38406 + 1.03099i
\(675\) 55.6683 6.37310i 2.14267 0.245301i
\(676\) −7.02891 + 23.5253i −0.270343 + 0.904821i
\(677\) 14.2074 + 8.20266i 0.546036 + 0.315254i 0.747522 0.664238i \(-0.231244\pi\)
−0.201486 + 0.979491i \(0.564577\pi\)
\(678\) 0.970748 48.7588i 0.0372813 1.87257i
\(679\) 0 0
\(680\) 2.22052 + 6.08520i 0.0851532 + 0.233357i
\(681\) 2.89940 21.1031i 0.111105 0.808672i
\(682\) −22.7314 + 2.66327i −0.870431 + 0.101982i
\(683\) 4.57827 + 7.92980i 0.175183 + 0.303425i 0.940224 0.340555i \(-0.110615\pi\)
−0.765042 + 0.643981i \(0.777282\pi\)
\(684\) −18.2178 11.5084i −0.696574 0.440035i
\(685\) −36.5672 −1.39716
\(686\) 0 0
\(687\) 14.4825 5.90343i 0.552543 0.225230i
\(688\) 16.8201 25.6352i 0.641261 0.977333i
\(689\) 0.448349 0.258854i 0.0170807 0.00986156i
\(690\) −33.7649 + 18.6081i −1.28541 + 0.708397i
\(691\) −28.7221 16.5827i −1.09264 0.630836i −0.158362 0.987381i \(-0.550621\pi\)
−0.934278 + 0.356545i \(0.883955\pi\)
\(692\) −8.12090 + 7.67013i −0.308710 + 0.291575i
\(693\) 0 0
\(694\) 2.79707 + 1.20562i 0.106175 + 0.0457649i
\(695\) 22.0602 38.2094i 0.836791 1.44937i
\(696\) 15.7647 + 5.05411i 0.597560 + 0.191576i
\(697\) −1.54364 2.67366i −0.0584694 0.101272i
\(698\) −37.4853 + 27.9228i −1.41884 + 1.05689i
\(699\) −4.95173 12.1478i −0.187292 0.459472i
\(700\) 0 0
\(701\) 38.1529i 1.44101i −0.693448 0.720507i \(-0.743909\pi\)
0.693448 0.720507i \(-0.256091\pi\)
\(702\) −1.42876 6.08513i −0.0539251 0.229668i
\(703\) 13.3435 7.70390i 0.503261 0.290558i
\(704\) −24.8487 8.99771i −0.936519 0.339114i
\(705\) 61.9708 + 8.51429i 2.33396 + 0.320667i
\(706\) −8.73656 + 20.2690i −0.328805 + 0.762833i
\(707\) 0 0
\(708\) −24.8464 11.3012i −0.933783 0.424725i
\(709\) −6.97895 + 12.0879i −0.262100 + 0.453970i −0.966800 0.255535i \(-0.917748\pi\)
0.704700 + 0.709505i \(0.251082\pi\)
\(710\) −51.0958 + 5.98651i −1.91759 + 0.224670i
\(711\) −5.60547 + 20.0145i −0.210221 + 0.750601i
\(712\) −2.81420 + 16.0375i −0.105466 + 0.601032i
\(713\) 19.4083i 0.726848i
\(714\) 0 0
\(715\) 11.1633i 0.417483i
\(716\) 37.7091 8.95915i 1.40925 0.334819i
\(717\) 12.6583 + 9.82694i 0.472733 + 0.366994i
\(718\) 5.53724 + 47.2612i 0.206648 + 1.76377i
\(719\) −10.0890 + 17.4746i −0.376255 + 0.651693i −0.990514 0.137412i \(-0.956122\pi\)
0.614259 + 0.789105i \(0.289455\pi\)
\(720\) 35.9342 31.3295i 1.33919 1.16758i
\(721\) 0 0
\(722\) 7.92462 + 3.41576i 0.294924 + 0.127121i
\(723\) −3.69201 + 26.8721i −0.137307 + 0.999384i
\(724\) 6.22565 20.8369i 0.231374 0.774396i
\(725\) −31.5580 + 18.2200i −1.17203 + 0.676674i
\(726\) 0.110553 0.182972i 0.00410300 0.00679074i
\(727\) 1.62103i 0.0601206i 0.999548 + 0.0300603i \(0.00956993\pi\)
−0.999548 + 0.0300603i \(0.990430\pi\)
\(728\) 0 0
\(729\) −18.4353 19.7266i −0.682789 0.730615i
\(730\) −4.74657 6.37208i −0.175678 0.235841i
\(731\) 2.20936 + 3.82673i 0.0817163 + 0.141537i
\(732\) 3.26052 + 33.6043i 0.120512 + 1.24205i
\(733\) −13.9026 + 24.0801i −0.513505 + 0.889417i 0.486372 + 0.873752i \(0.338320\pi\)
−0.999877 + 0.0156654i \(0.995013\pi\)
\(734\) −4.39181 + 10.1891i −0.162105 + 0.376086i
\(735\) 0 0
\(736\) −10.0304 + 20.0409i −0.369725 + 0.738716i
\(737\) 25.8786 + 14.9410i 0.953252 + 0.550360i
\(738\) −14.2879 + 17.6670i −0.525943 + 0.650331i
\(739\) 25.1030 14.4932i 0.923429 0.533142i 0.0387013 0.999251i \(-0.487678\pi\)
0.884727 + 0.466109i \(0.154345\pi\)
\(740\) 7.87961 + 33.1653i 0.289660 + 1.21918i
\(741\) −1.99724 4.89971i −0.0733704 0.179995i
\(742\) 0 0
\(743\) 10.4018 0.381604 0.190802 0.981629i \(-0.438891\pi\)
0.190802 + 0.981629i \(0.438891\pi\)
\(744\) −5.08175 23.4558i −0.186306 0.859932i
\(745\) 13.3435 + 23.1117i 0.488870 + 0.846747i
\(746\) −0.162308 1.38532i −0.00594251 0.0507203i
\(747\) −3.07815 12.0287i −0.112624 0.440107i
\(748\) 2.76888 2.61518i 0.101240 0.0956205i
\(749\) 0 0
\(750\) −1.12027 + 56.2688i −0.0409063 + 2.05465i
\(751\) 14.7045 + 8.48962i 0.536573 + 0.309791i 0.743689 0.668526i \(-0.233074\pi\)
−0.207116 + 0.978316i \(0.566408\pi\)
\(752\) 32.4763 16.3550i 1.18429 0.596406i
\(753\) 4.22745 + 3.28186i 0.154057 + 0.119598i
\(754\) 2.42838 + 3.26000i 0.0884363 + 0.118722i
\(755\) 52.4922 1.91039
\(756\) 0 0
\(757\) −10.9716 −0.398770 −0.199385 0.979921i \(-0.563894\pi\)
−0.199385 + 0.979921i \(0.563894\pi\)
\(758\) 15.9067 + 21.3541i 0.577757 + 0.775617i
\(759\) 17.9055 + 13.9005i 0.649929 + 0.504555i
\(760\) 25.9147 30.9358i 0.940026 1.12216i
\(761\) −10.0723 5.81526i −0.365121 0.210803i 0.306204 0.951966i \(-0.400941\pi\)
−0.671325 + 0.741163i \(0.734274\pi\)
\(762\) 0.801702 40.2680i 0.0290426 1.45876i
\(763\) 0 0
\(764\) 1.69343 + 1.79295i 0.0612660 + 0.0648666i
\(765\) 1.70331 + 6.65613i 0.0615833 + 0.240653i
\(766\) −0.596206 5.08871i −0.0215418 0.183863i
\(767\) −3.35120 5.80445i −0.121005 0.209586i
\(768\) 6.87478 26.8466i 0.248072 0.968742i
\(769\) 0.123424 0.00445080 0.00222540 0.999998i \(-0.499292\pi\)
0.00222540 + 0.999998i \(0.499292\pi\)
\(770\) 0 0
\(771\) 4.81794 + 11.8196i 0.173514 + 0.425671i
\(772\) −30.7118 + 7.29669i −1.10534 + 0.262614i
\(773\) −13.4620 + 7.77229i −0.484194 + 0.279550i −0.722163 0.691723i \(-0.756852\pi\)
0.237968 + 0.971273i \(0.423519\pi\)
\(774\) 20.4498 25.2863i 0.735053 0.908896i
\(775\) 45.7498 + 26.4137i 1.64338 + 0.948808i
\(776\) −13.1365 35.9997i −0.471573 1.29231i
\(777\) 0 0
\(778\) 8.18188 18.9821i 0.293334 0.680541i
\(779\) −9.61685 + 16.6569i −0.344559 + 0.596794i
\(780\) 11.6515 1.13051i 0.417190 0.0404786i
\(781\) 15.1240 + 26.1956i 0.541181 + 0.937353i
\(782\) −1.92940 2.59015i −0.0689953 0.0926235i
\(783\) 16.1067 + 6.99304i 0.575607 + 0.249911i
\(784\) 0 0
\(785\) 9.48806i 0.338643i
\(786\) 2.88422 4.77358i 0.102877 0.170268i
\(787\) −36.3048 + 20.9606i −1.29413 + 0.747164i −0.979383 0.202014i \(-0.935252\pi\)
−0.314743 + 0.949177i \(0.601918\pi\)
\(788\) 33.3182 + 9.95483i 1.18691 + 0.354626i
\(789\) −5.23459 + 38.0996i −0.186356 + 1.35638i
\(790\) −35.7463 15.4078i −1.27180 0.548185i
\(791\) 0 0
\(792\) −25.2792 12.1111i −0.898258 0.430348i
\(793\) −4.14510 + 7.17953i −0.147197 + 0.254953i
\(794\) 1.00337 + 8.56394i 0.0356083 + 0.303923i
\(795\) 3.30824 + 2.56826i 0.117331 + 0.0910868i
\(796\) 2.11161 + 8.88779i 0.0748442 + 0.315019i
\(797\) 20.7831i 0.736175i −0.929791 0.368088i \(-0.880013\pi\)
0.929791 0.368088i \(-0.119987\pi\)
\(798\) 0 0
\(799\) 5.24038i 0.185391i
\(800\) 33.5901 + 50.9184i 1.18759 + 1.80024i
\(801\) −4.65768 + 16.6304i −0.164571 + 0.587605i
\(802\) 10.2397 1.19971i 0.361577 0.0423632i
\(803\) −2.33589 + 4.04587i −0.0824316 + 0.142776i
\(804\) −12.9737 + 28.5235i −0.457548 + 1.00595i
\(805\) 0 0
\(806\) 2.33266 5.41181i 0.0821645 0.190623i
\(807\) −17.1831 2.36082i −0.604874 0.0831048i
\(808\) 15.4797 + 12.9673i 0.544576 + 0.456187i
\(809\) 1.65777 0.957115i 0.0582842 0.0336504i −0.470575 0.882360i \(-0.655953\pi\)
0.528859 + 0.848710i \(0.322620\pi\)
\(810\) 41.2225 29.2849i 1.44841 1.02897i
\(811\) 4.68171i 0.164397i 0.996616 + 0.0821986i \(0.0261942\pi\)
−0.996616 + 0.0821986i \(0.973806\pi\)
\(812\) 0 0
\(813\) 15.4196 + 37.8280i 0.540789 + 1.32668i
\(814\) 16.0735 11.9732i 0.563378 0.419660i
\(815\) −36.3351 62.9342i −1.27276 2.20449i
\(816\) 3.00996 + 2.62513i 0.105370 + 0.0918978i
\(817\) 13.7643 23.8405i 0.481552 0.834073i
\(818\) −26.2209 11.3020i −0.916792 0.395166i
\(819\) 0 0
\(820\) −29.2186 30.9358i −1.02036 1.08033i
\(821\) 1.44771 + 0.835834i 0.0505253 + 0.0291708i 0.525050 0.851071i \(-0.324047\pi\)
−0.474525 + 0.880242i \(0.657380\pi\)
\(822\) −19.7458 + 10.8821i −0.688715 + 0.379555i
\(823\) 23.7559 13.7155i 0.828078 0.478091i −0.0251160 0.999685i \(-0.507996\pi\)
0.853194 + 0.521593i \(0.174662\pi\)
\(824\) −5.13724 + 29.2761i −0.178964 + 1.01988i
\(825\) 57.1350 23.2896i 1.98918 0.810840i
\(826\) 0 0
\(827\) −25.9621 −0.902789 −0.451395 0.892324i \(-0.649073\pi\)
−0.451395 + 0.892324i \(0.649073\pi\)
\(828\) −12.6951 + 20.0963i −0.441184 + 0.698394i
\(829\) −14.5674 25.2315i −0.505948 0.876328i −0.999976 0.00688179i \(-0.997809\pi\)
0.494028 0.869446i \(-0.335524\pi\)
\(830\) 23.0954 2.70591i 0.801652 0.0939234i
\(831\) −6.85100 + 49.8646i −0.237659 + 1.72979i
\(832\) 5.20555 4.38265i 0.180470 0.151941i
\(833\) 0 0
\(834\) 0.541480 27.1975i 0.0187499 0.941774i
\(835\) −66.6265 38.4668i −2.30571 1.33120i
\(836\) −22.7348 6.79272i −0.786300 0.234931i
\(837\) −2.89536 25.2906i −0.100078 0.874173i
\(838\) 1.50711 1.12265i 0.0520623 0.0387812i
\(839\) 14.3863 0.496671 0.248336 0.968674i \(-0.420116\pi\)
0.248336 + 0.968674i \(0.420116\pi\)
\(840\) 0 0
\(841\) 17.5804 0.606221
\(842\) 8.30031 6.18290i 0.286048 0.213077i
\(843\) −24.7360 + 31.8631i −0.851954 + 1.09742i
\(844\) 2.13138 + 0.636813i 0.0733650 + 0.0219200i
\(845\) −42.2381 24.3862i −1.45303 0.838909i
\(846\) 35.9973 13.8443i 1.23761 0.475978i
\(847\) 0 0
\(848\) 2.43059 + 0.138880i 0.0834668 + 0.00476916i
\(849\) −29.9022 4.10833i −1.02624 0.140997i
\(850\) −8.73138 + 1.02299i −0.299484 + 0.0350882i
\(851\) −8.49827 14.7194i −0.291317 0.504576i
\(852\) −25.8096 + 18.4383i −0.884223 + 0.631686i
\(853\) 49.4483 1.69308 0.846539 0.532327i \(-0.178682\pi\)
0.846539 + 0.532327i \(0.178682\pi\)
\(854\) 0 0
\(855\) 30.6062 29.9237i 1.04671 1.02337i
\(856\) −3.43531 0.602812i −0.117416 0.0206037i
\(857\) −10.0283 + 5.78983i −0.342560 + 0.197777i −0.661403 0.750030i \(-0.730039\pi\)
0.318844 + 0.947807i \(0.396705\pi\)
\(858\) −3.32209 6.02804i −0.113414 0.205794i
\(859\) 6.27765 + 3.62441i 0.214191 + 0.123663i 0.603258 0.797546i \(-0.293869\pi\)
−0.389067 + 0.921210i \(0.627202\pi\)
\(860\) 41.8198 + 44.2775i 1.42604 + 1.50985i
\(861\) 0 0
\(862\) −0.232377 0.100162i −0.00791479 0.00341152i
\(863\) −10.4435 + 18.0886i −0.355500 + 0.615744i −0.987203 0.159466i \(-0.949023\pi\)
0.631703 + 0.775210i \(0.282356\pi\)
\(864\) 10.0807 27.6112i 0.342952 0.939353i
\(865\) −11.0946 19.2164i −0.377228 0.653378i
\(866\) −17.2956 + 12.8835i −0.587728 + 0.437799i
\(867\) 26.7336 10.8973i 0.907920 0.370090i
\(868\) 0 0
\(869\) 22.8869i 0.776385i
\(870\) −17.0062 + 28.1465i −0.576565 + 0.954255i
\(871\) −6.66347 + 3.84716i −0.225783 + 0.130356i
\(872\) −5.81744 + 6.94460i −0.197004 + 0.235174i
\(873\) −10.0767 39.3774i −0.341044 1.33272i
\(874\) −7.96462 + 18.4781i −0.269407 + 0.625030i
\(875\) 0 0
\(876\) −4.45937 2.02831i −0.150668 0.0685304i
\(877\) 28.5877 49.5154i 0.965339 1.67202i 0.256639 0.966507i \(-0.417385\pi\)
0.708701 0.705509i \(-0.249282\pi\)
\(878\) 42.0053 4.92144i 1.41761 0.166091i
\(879\) 1.28250 1.65202i 0.0432576 0.0557211i
\(880\) 28.7987 43.8915i 0.970804 1.47958i
\(881\) 26.8284i 0.903870i −0.892051 0.451935i \(-0.850734\pi\)
0.892051 0.451935i \(-0.149266\pi\)
\(882\) 0 0
\(883\) 27.6059i 0.929012i 0.885570 + 0.464506i \(0.153768\pi\)
−0.885570 + 0.464506i \(0.846232\pi\)
\(884\) 0.226688 + 0.954128i 0.00762433 + 0.0320908i
\(885\) 33.2494 42.8294i 1.11767 1.43969i
\(886\) 0.825451 + 7.04537i 0.0277316 + 0.236694i
\(887\) 13.1703 22.8116i 0.442215 0.765939i −0.555639 0.831424i \(-0.687526\pi\)
0.997854 + 0.0654853i \(0.0208595\pi\)
\(888\) 14.1246 + 15.5640i 0.473990 + 0.522292i
\(889\) 0 0
\(890\) −29.7022 12.8026i −0.995622 0.429144i
\(891\) −25.4060 15.4423i −0.851135 0.517335i
\(892\) −45.2874 13.5310i −1.51634 0.453051i
\(893\) 28.2736 16.3238i 0.946139 0.546254i
\(894\) 14.0832 + 8.50912i 0.471012 + 0.284588i
\(895\) 76.9909i 2.57352i
\(896\) 0 0
\(897\) −5.40493 + 2.20318i −0.180465 + 0.0735621i
\(898\) −12.2481 16.4426i −0.408724 0.548696i
\(899\) 8.27753 + 14.3371i 0.276071 + 0.478169i
\(900\) 30.0942 + 57.2751i 1.00314 + 1.90917i
\(901\) −0.175430 + 0.303854i −0.00584443 + 0.0101228i
\(902\) −9.90347 + 22.9762i −0.329749 + 0.765024i
\(903\) 0 0
\(904\) 52.9010 19.3039i 1.75946 0.642038i
\(905\) 37.4111 + 21.5993i 1.24359 + 0.717985i
\(906\) 28.3452 15.6212i 0.941705 0.518980i
\(907\) 9.51618 5.49417i 0.315980 0.182431i −0.333619 0.942708i \(-0.608270\pi\)
0.649599 + 0.760277i \(0.274937\pi\)
\(908\) 23.9305 5.68556i 0.794163 0.188682i
\(909\) 14.9733 + 15.3148i 0.496634 + 0.507961i
\(910\) 0 0
\(911\) 6.42795 0.212968 0.106484 0.994314i \(-0.466041\pi\)
0.106484 + 0.994314i \(0.466041\pi\)
\(912\) 4.78742 24.4170i 0.158527 0.808526i
\(913\) −6.83609 11.8404i −0.226241 0.391862i
\(914\) 3.26779 + 27.8911i 0.108089 + 0.922556i
\(915\) −66.4414 9.12852i −2.19649 0.301779i
\(916\) 12.4000 + 13.1288i 0.409709 + 0.433787i
\(917\) 0 0
\(918\) 2.90057 + 3.08734i 0.0957331 + 0.101898i
\(919\) 47.7559 + 27.5719i 1.57532 + 0.909512i 0.995499 + 0.0947691i \(0.0302113\pi\)
0.579822 + 0.814743i \(0.303122\pi\)
\(920\) −34.1257 28.5869i −1.12509 0.942481i
\(921\) 36.1418 46.5552i 1.19091 1.53404i
\(922\) 14.6923 + 19.7238i 0.483864 + 0.649569i
\(923\) −7.78856 −0.256364
\(924\) 0 0
\(925\) −46.2628 −1.52111
\(926\) 12.9514 + 17.3868i 0.425610 + 0.571365i
\(927\) −8.50246 + 30.3583i −0.279258 + 0.997096i
\(928\) 1.13777 + 19.0823i 0.0373493 + 0.626406i
\(929\) −41.5330 23.9791i −1.36265 0.786728i −0.372677 0.927961i \(-0.621560\pi\)
−0.989976 + 0.141233i \(0.954893\pi\)
\(930\) 47.6645 + 0.948960i 1.56298 + 0.0311176i
\(931\) 0 0
\(932\) 11.0123 10.4010i 0.360719 0.340697i
\(933\) −6.29739 + 45.8352i −0.206167 + 1.50058i
\(934\) 3.46939 + 29.6118i 0.113522 + 0.968929i
\(935\) 3.78278 + 6.55197i 0.123710 + 0.214272i
\(936\) 5.95523 4.07784i 0.194653 0.133288i
\(937\) −36.7501 −1.20057 −0.600287 0.799784i \(-0.704947\pi\)
−0.600287 + 0.799784i \(0.704947\pi\)
\(938\) 0 0
\(939\) 14.9574 6.09698i 0.488115 0.198968i
\(940\) 16.6961 + 70.2738i 0.544566 + 2.29208i
\(941\) −34.3080 + 19.8077i −1.11841 + 0.645714i −0.940994 0.338422i \(-0.890107\pi\)
−0.177415 + 0.984136i \(0.556774\pi\)
\(942\) 2.82356 + 5.12344i 0.0919965 + 0.166931i
\(943\) 18.3744 + 10.6085i 0.598353 + 0.345459i
\(944\) 1.79798 31.4671i 0.0585193 1.02417i
\(945\) 0 0
\(946\) 14.1745 32.8852i 0.460854 1.06919i
\(947\) −5.92594 + 10.2640i −0.192567 + 0.333536i −0.946100 0.323874i \(-0.895015\pi\)
0.753533 + 0.657410i \(0.228348\pi\)
\(948\) −23.8878 + 2.31776i −0.775840 + 0.0752773i
\(949\) −0.601466 1.04177i −0.0195244 0.0338172i
\(950\) 32.7176 + 43.9221i 1.06150 + 1.42502i
\(951\) −17.6480 43.2948i −0.572275 1.40393i
\(952\) 0 0
\(953\) 39.8193i 1.28987i 0.764236 + 0.644937i \(0.223116\pi\)
−0.764236 + 0.644937i \(0.776884\pi\)
\(954\) 2.55070 + 0.402328i 0.0825819 + 0.0130259i
\(955\) −4.24264 + 2.44949i −0.137289 + 0.0792636i
\(956\) −5.29728 + 17.7297i −0.171326 + 0.573418i
\(957\) 19.1554 + 2.63180i 0.619207 + 0.0850741i
\(958\) −9.86972 4.25416i −0.318876 0.137446i
\(959\) 0 0
\(960\) 48.7274 + 25.6132i 1.57267 + 0.826664i
\(961\) −3.50000 + 6.06218i −0.112903 + 0.195554i
\(962\) 0.600546 + 5.12576i 0.0193624 + 0.165261i
\(963\) −3.56229 0.997694i −0.114793 0.0321502i
\(964\) −30.4725 + 7.23984i −0.981453 + 0.233179i
\(965\) 62.7045i 2.01853i
\(966\) 0 0
\(967\) 23.4388i 0.753741i −0.926266 0.376871i \(-0.877000\pi\)
0.926266 0.376871i \(-0.123000\pi\)
\(968\) 0.243134 + 0.0426641i 0.00781462 + 0.00137127i
\(969\) 2.83253 + 2.19896i 0.0909941 + 0.0706408i
\(970\) 75.6054 8.85811i 2.42754 0.284417i
\(971\) 5.55718 9.62532i 0.178338 0.308891i −0.762973 0.646430i \(-0.776261\pi\)
0.941312 + 0.337539i \(0.109595\pi\)
\(972\) 13.5447 28.0810i 0.434447 0.900697i
\(973\) 0 0
\(974\) −8.64155 + 20.0485i −0.276893 + 0.642396i
\(975\) −2.16242 + 15.7391i −0.0692529 + 0.504054i
\(976\) −34.8191 + 17.5349i −1.11453 + 0.561278i
\(977\) 9.58812 5.53570i 0.306751 0.177103i −0.338721 0.940887i \(-0.609994\pi\)
0.645472 + 0.763784i \(0.276661\pi\)
\(978\) −38.3492 23.1707i −1.22627 0.740918i
\(979\) 19.0171i 0.607790i
\(980\) 0 0
\(981\) −6.87062 + 6.71741i −0.219362 + 0.214470i
\(982\) −45.9515 + 34.2293i −1.46637 + 1.09230i
\(983\) 15.9716 + 27.6637i 0.509416 + 0.882334i 0.999941 + 0.0109070i \(0.00347189\pi\)
−0.490524 + 0.871427i \(0.663195\pi\)
\(984\) −24.9839 8.00977i −0.796459 0.255342i
\(985\) −34.5373 + 59.8204i −1.10045 + 1.90604i
\(986\) −2.52995 1.09049i −0.0805700 0.0347282i
\(987\) 0 0
\(988\) 4.44171 4.19516i 0.141310 0.133466i
\(989\) −26.2988 15.1836i −0.836252 0.482811i
\(990\) 35.0133 43.2941i 1.11280 1.37598i
\(991\) −18.0000 + 10.3923i −0.571789 + 0.330122i −0.757863 0.652413i \(-0.773757\pi\)
0.186075 + 0.982536i \(0.440423\pi\)
\(992\) 23.1327 15.2603i 0.734465 0.484515i
\(993\) −9.54109 23.4066i −0.302777 0.742785i
\(994\) 0 0
\(995\) −18.1463 −0.575275
\(996\) 11.6660 8.33413i 0.369650 0.264077i
\(997\) −20.7685 35.9721i −0.657745 1.13925i −0.981198 0.193003i \(-0.938177\pi\)
0.323453 0.946244i \(-0.395156\pi\)
\(998\) −42.6537 + 4.99740i −1.35018 + 0.158190i
\(999\) 13.2698 + 17.9129i 0.419838 + 0.566738i
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 588.2.n.d.275.1 24
3.2 odd 2 inner 588.2.n.d.275.12 24
4.3 odd 2 588.2.n.h.275.8 24
7.2 even 3 588.2.e.f.491.24 yes 24
7.3 odd 6 588.2.n.h.263.6 24
7.4 even 3 588.2.n.h.263.5 24
7.5 odd 6 588.2.e.f.491.23 yes 24
7.6 odd 2 inner 588.2.n.d.275.2 24
12.11 even 2 588.2.n.h.275.5 24
21.2 odd 6 588.2.e.f.491.1 24
21.5 even 6 588.2.e.f.491.2 yes 24
21.11 odd 6 588.2.n.h.263.8 24
21.17 even 6 588.2.n.h.263.7 24
21.20 even 2 inner 588.2.n.d.275.11 24
28.3 even 6 inner 588.2.n.d.263.11 24
28.11 odd 6 inner 588.2.n.d.263.12 24
28.19 even 6 588.2.e.f.491.4 yes 24
28.23 odd 6 588.2.e.f.491.3 yes 24
28.27 even 2 588.2.n.h.275.7 24
84.11 even 6 inner 588.2.n.d.263.1 24
84.23 even 6 588.2.e.f.491.22 yes 24
84.47 odd 6 588.2.e.f.491.21 yes 24
84.59 odd 6 inner 588.2.n.d.263.2 24
84.83 odd 2 588.2.n.h.275.6 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
588.2.e.f.491.1 24 21.2 odd 6
588.2.e.f.491.2 yes 24 21.5 even 6
588.2.e.f.491.3 yes 24 28.23 odd 6
588.2.e.f.491.4 yes 24 28.19 even 6
588.2.e.f.491.21 yes 24 84.47 odd 6
588.2.e.f.491.22 yes 24 84.23 even 6
588.2.e.f.491.23 yes 24 7.5 odd 6
588.2.e.f.491.24 yes 24 7.2 even 3
588.2.n.d.263.1 24 84.11 even 6 inner
588.2.n.d.263.2 24 84.59 odd 6 inner
588.2.n.d.263.11 24 28.3 even 6 inner
588.2.n.d.263.12 24 28.11 odd 6 inner
588.2.n.d.275.1 24 1.1 even 1 trivial
588.2.n.d.275.2 24 7.6 odd 2 inner
588.2.n.d.275.11 24 21.20 even 2 inner
588.2.n.d.275.12 24 3.2 odd 2 inner
588.2.n.h.263.5 24 7.4 even 3
588.2.n.h.263.6 24 7.3 odd 6
588.2.n.h.263.7 24 21.17 even 6
588.2.n.h.263.8 24 21.11 odd 6
588.2.n.h.275.5 24 12.11 even 2
588.2.n.h.275.6 24 84.83 odd 2
588.2.n.h.275.7 24 28.27 even 2
588.2.n.h.275.8 24 4.3 odd 2