Properties

Label 567.2.g.j.109.4
Level $567$
Weight $2$
Character 567.109
Analytic conductor $4.528$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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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] = [567,2,Mod(109,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.109"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,-1,0,-5,4,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.1767277521.3
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.4
Root \(0.373419 - 0.0835272i\) of defining polynomial
Character \(\chi\) \(=\) 567.109
Dual form 567.2.g.j.541.4

$q$-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)
 
\(f(q)\) \(=\) \(q+(1.18584 - 2.05393i) q^{2} +(-1.81242 - 3.13920i) q^{4} +1.22875 q^{5} +(2.61263 + 0.417345i) q^{7} -3.85358 q^{8} +(1.45709 - 2.52376i) q^{10} +2.66102 q^{11} +(1.81242 - 3.13920i) q^{13} +(3.95535 - 4.87125i) q^{14} +(-0.944883 + 1.63659i) q^{16} +(-3.36579 + 5.82972i) q^{17} +(-1.25730 - 2.17771i) q^{19} +(-2.22700 - 3.85728i) q^{20} +(3.15554 - 5.46555i) q^{22} -7.99651 q^{23} -3.49018 q^{25} +(-4.29846 - 7.44516i) q^{26} +(-3.42505 - 8.95796i) q^{28} +(-1.12484 - 1.94827i) q^{29} +(5.11263 + 8.85533i) q^{31} +(-1.61263 - 2.79315i) q^{32} +(7.98256 + 13.8262i) q^{34} +(3.21025 + 0.512810i) q^{35} +(1.76951 + 3.06488i) q^{37} -5.96382 q^{38} -4.73507 q^{40} +(-0.932674 + 1.61544i) q^{41} +(-2.56972 - 4.45088i) q^{43} +(-4.82288 - 8.35348i) q^{44} +(-9.48256 + 16.4243i) q^{46} +(1.07321 - 1.85885i) q^{47} +(6.65165 + 2.18073i) q^{49} +(-4.13879 + 7.16859i) q^{50} -13.1394 q^{52} +(-1.48605 + 2.57391i) q^{53} +3.26972 q^{55} +(-10.0680 - 1.60827i) q^{56} -5.33549 q^{58} +(4.36405 + 7.55875i) q^{59} +(7.50239 - 12.9945i) q^{61} +24.2510 q^{62} -11.4288 q^{64} +(2.22700 - 3.85728i) q^{65} +(1.32463 + 2.29432i) q^{67} +24.4009 q^{68} +(4.86011 - 5.98553i) q^{70} -10.1150 q^{71} +(-3.64707 + 6.31691i) q^{73} +8.39340 q^{74} +(-4.55751 + 7.89384i) q^{76} +(6.95226 + 1.11056i) q^{77} +(0.156882 - 0.271728i) q^{79} +(-1.16102 + 2.01095i) q^{80} +(2.21200 + 3.83129i) q^{82} +(-3.84686 - 6.66295i) q^{83} +(-4.13570 + 7.16324i) q^{85} -12.1891 q^{86} -10.2545 q^{88} +(3.59628 + 6.22894i) q^{89} +(6.04530 - 7.44516i) q^{91} +(14.4930 + 25.1026i) q^{92} +(-2.54530 - 4.40859i) q^{94} +(-1.54490 - 2.67585i) q^{95} +(6.59195 + 11.4176i) q^{97} +(12.3668 - 11.0760i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{2} - 5 q^{4} + 4 q^{5} - 2 q^{7} - 6 q^{8} + 7 q^{10} + 10 q^{11} + 5 q^{13} + 7 q^{14} + q^{16} - 6 q^{17} + 8 q^{19} + 8 q^{20} + 7 q^{22} - 24 q^{23} + 16 q^{25} - q^{26} + 5 q^{28} + 10 q^{29}+ \cdots + 11 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.18584 2.05393i 0.838513 1.45235i −0.0526243 0.998614i \(-0.516759\pi\)
0.891138 0.453733i \(-0.149908\pi\)
\(3\) 0 0
\(4\) −1.81242 3.13920i −0.906209 1.56960i
\(5\) 1.22875 0.549512 0.274756 0.961514i \(-0.411403\pi\)
0.274756 + 0.961514i \(0.411403\pi\)
\(6\) 0 0
\(7\) 2.61263 + 0.417345i 0.987480 + 0.157741i
\(8\) −3.85358 −1.36245
\(9\) 0 0
\(10\) 1.45709 2.52376i 0.460773 0.798082i
\(11\) 2.66102 0.802328 0.401164 0.916006i \(-0.368606\pi\)
0.401164 + 0.916006i \(0.368606\pi\)
\(12\) 0 0
\(13\) 1.81242 3.13920i 0.502674 0.870658i −0.497321 0.867567i \(-0.665683\pi\)
0.999995 0.00309084i \(-0.000983846\pi\)
\(14\) 3.95535 4.87125i 1.05711 1.30190i
\(15\) 0 0
\(16\) −0.944883 + 1.63659i −0.236221 + 0.409146i
\(17\) −3.36579 + 5.82972i −0.816324 + 1.41391i 0.0920492 + 0.995754i \(0.470658\pi\)
−0.908373 + 0.418160i \(0.862675\pi\)
\(18\) 0 0
\(19\) −1.25730 2.17771i −0.288445 0.499601i 0.684994 0.728549i \(-0.259805\pi\)
−0.973439 + 0.228948i \(0.926471\pi\)
\(20\) −2.22700 3.85728i −0.497972 0.862514i
\(21\) 0 0
\(22\) 3.15554 5.46555i 0.672763 1.16526i
\(23\) −7.99651 −1.66739 −0.833694 0.552227i \(-0.813778\pi\)
−0.833694 + 0.552227i \(0.813778\pi\)
\(24\) 0 0
\(25\) −3.49018 −0.698037
\(26\) −4.29846 7.44516i −0.842998 1.46012i
\(27\) 0 0
\(28\) −3.42505 8.95796i −0.647273 1.69290i
\(29\) −1.12484 1.94827i −0.208877 0.361785i 0.742484 0.669864i \(-0.233647\pi\)
−0.951361 + 0.308078i \(0.900314\pi\)
\(30\) 0 0
\(31\) 5.11263 + 8.85533i 0.918255 + 1.59046i 0.802064 + 0.597237i \(0.203735\pi\)
0.116191 + 0.993227i \(0.462932\pi\)
\(32\) −1.61263 2.79315i −0.285075 0.493764i
\(33\) 0 0
\(34\) 7.98256 + 13.8262i 1.36900 + 2.37117i
\(35\) 3.21025 + 0.512810i 0.542632 + 0.0866807i
\(36\) 0 0
\(37\) 1.76951 + 3.06488i 0.290906 + 0.503863i 0.974024 0.226444i \(-0.0727101\pi\)
−0.683119 + 0.730308i \(0.739377\pi\)
\(38\) −5.96382 −0.967459
\(39\) 0 0
\(40\) −4.73507 −0.748680
\(41\) −0.932674 + 1.61544i −0.145659 + 0.252289i −0.929619 0.368523i \(-0.879864\pi\)
0.783959 + 0.620812i \(0.213197\pi\)
\(42\) 0 0
\(43\) −2.56972 4.45088i −0.391879 0.678753i 0.600819 0.799385i \(-0.294841\pi\)
−0.992697 + 0.120632i \(0.961508\pi\)
\(44\) −4.82288 8.35348i −0.727077 1.25933i
\(45\) 0 0
\(46\) −9.48256 + 16.4243i −1.39813 + 2.42163i
\(47\) 1.07321 1.85885i 0.156544 0.271142i −0.777076 0.629406i \(-0.783298\pi\)
0.933620 + 0.358265i \(0.116631\pi\)
\(48\) 0 0
\(49\) 6.65165 + 2.18073i 0.950235 + 0.311533i
\(50\) −4.13879 + 7.16859i −0.585313 + 1.01379i
\(51\) 0 0
\(52\) −13.1394 −1.82211
\(53\) −1.48605 + 2.57391i −0.204124 + 0.353553i −0.949853 0.312696i \(-0.898768\pi\)
0.745729 + 0.666249i \(0.232101\pi\)
\(54\) 0 0
\(55\) 3.26972 0.440888
\(56\) −10.0680 1.60827i −1.34539 0.214914i
\(57\) 0 0
\(58\) −5.33549 −0.700584
\(59\) 4.36405 + 7.55875i 0.568150 + 0.984065i 0.996749 + 0.0805702i \(0.0256741\pi\)
−0.428599 + 0.903495i \(0.640993\pi\)
\(60\) 0 0
\(61\) 7.50239 12.9945i 0.960583 1.66378i 0.239542 0.970886i \(-0.423003\pi\)
0.721041 0.692893i \(-0.243664\pi\)
\(62\) 24.2510 3.07988
\(63\) 0 0
\(64\) −11.4288 −1.42860
\(65\) 2.22700 3.85728i 0.276225 0.478436i
\(66\) 0 0
\(67\) 1.32463 + 2.29432i 0.161829 + 0.280296i 0.935525 0.353261i \(-0.114927\pi\)
−0.773696 + 0.633557i \(0.781594\pi\)
\(68\) 24.4009 2.95904
\(69\) 0 0
\(70\) 4.86011 5.98553i 0.580895 0.715407i
\(71\) −10.1150 −1.20043 −0.600216 0.799838i \(-0.704919\pi\)
−0.600216 + 0.799838i \(0.704919\pi\)
\(72\) 0 0
\(73\) −3.64707 + 6.31691i −0.426857 + 0.739338i −0.996592 0.0824907i \(-0.973713\pi\)
0.569735 + 0.821829i \(0.307046\pi\)
\(74\) 8.39340 0.975713
\(75\) 0 0
\(76\) −4.55751 + 7.89384i −0.522782 + 0.905486i
\(77\) 6.95226 + 1.11056i 0.792283 + 0.126560i
\(78\) 0 0
\(79\) 0.156882 0.271728i 0.0176506 0.0305717i −0.857065 0.515208i \(-0.827715\pi\)
0.874716 + 0.484636i \(0.161048\pi\)
\(80\) −1.16102 + 2.01095i −0.129806 + 0.224831i
\(81\) 0 0
\(82\) 2.21200 + 3.83129i 0.244274 + 0.423096i
\(83\) −3.84686 6.66295i −0.422247 0.731354i 0.573912 0.818917i \(-0.305425\pi\)
−0.996159 + 0.0875633i \(0.972092\pi\)
\(84\) 0 0
\(85\) −4.13570 + 7.16324i −0.448580 + 0.776963i
\(86\) −12.1891 −1.31438
\(87\) 0 0
\(88\) −10.2545 −1.09313
\(89\) 3.59628 + 6.22894i 0.381205 + 0.660266i 0.991235 0.132112i \(-0.0421759\pi\)
−0.610030 + 0.792378i \(0.708843\pi\)
\(90\) 0 0
\(91\) 6.04530 7.44516i 0.633720 0.780465i
\(92\) 14.4930 + 25.1026i 1.51100 + 2.61713i
\(93\) 0 0
\(94\) −2.54530 4.40859i −0.262528 0.454712i
\(95\) −1.54490 2.67585i −0.158504 0.274536i
\(96\) 0 0
\(97\) 6.59195 + 11.4176i 0.669311 + 1.15928i 0.978097 + 0.208149i \(0.0667440\pi\)
−0.308786 + 0.951132i \(0.599923\pi\)
\(98\) 12.3668 11.0760i 1.24924 1.11885i
\(99\) 0 0
\(100\) 6.32567 + 10.9564i 0.632567 + 1.09564i
\(101\) −2.78302 −0.276921 −0.138460 0.990368i \(-0.544215\pi\)
−0.138460 + 0.990368i \(0.544215\pi\)
\(102\) 0 0
\(103\) 6.00647 0.591835 0.295917 0.955214i \(-0.404375\pi\)
0.295917 + 0.955214i \(0.404375\pi\)
\(104\) −6.98430 + 12.0972i −0.684867 + 1.18622i
\(105\) 0 0
\(106\) 3.52442 + 6.10447i 0.342322 + 0.592919i
\(107\) 5.86818 + 10.1640i 0.567299 + 0.982590i 0.996832 + 0.0795391i \(0.0253448\pi\)
−0.429533 + 0.903051i \(0.641322\pi\)
\(108\) 0 0
\(109\) 3.99237 6.91499i 0.382400 0.662336i −0.609005 0.793166i \(-0.708431\pi\)
0.991405 + 0.130830i \(0.0417644\pi\)
\(110\) 3.87735 6.71577i 0.369691 0.640323i
\(111\) 0 0
\(112\) −3.15165 + 3.88145i −0.297803 + 0.366762i
\(113\) −2.32005 + 4.01844i −0.218252 + 0.378023i −0.954274 0.298935i \(-0.903369\pi\)
0.736022 + 0.676958i \(0.236702\pi\)
\(114\) 0 0
\(115\) −9.82567 −0.916249
\(116\) −4.07735 + 7.06217i −0.378572 + 0.655706i
\(117\) 0 0
\(118\) 20.7002 1.90561
\(119\) −11.2266 + 13.8262i −1.02914 + 1.26745i
\(120\) 0 0
\(121\) −3.91897 −0.356270
\(122\) −17.7932 30.8188i −1.61092 2.79020i
\(123\) 0 0
\(124\) 18.5324 32.0991i 1.66426 2.88259i
\(125\) −10.4323 −0.933091
\(126\) 0 0
\(127\) −3.32633 −0.295164 −0.147582 0.989050i \(-0.547149\pi\)
−0.147582 + 0.989050i \(0.547149\pi\)
\(128\) −10.3274 + 17.8876i −0.912824 + 1.58106i
\(129\) 0 0
\(130\) −5.28172 9.14820i −0.463237 0.802351i
\(131\) −8.44702 −0.738020 −0.369010 0.929425i \(-0.620303\pi\)
−0.369010 + 0.929425i \(0.620303\pi\)
\(132\) 0 0
\(133\) −2.37600 6.21427i −0.206026 0.538846i
\(134\) 6.28317 0.542783
\(135\) 0 0
\(136\) 12.9703 22.4653i 1.11220 1.92638i
\(137\) 13.9965 1.19580 0.597901 0.801570i \(-0.296001\pi\)
0.597901 + 0.801570i \(0.296001\pi\)
\(138\) 0 0
\(139\) 2.82005 4.88446i 0.239193 0.414295i −0.721290 0.692633i \(-0.756450\pi\)
0.960483 + 0.278339i \(0.0897837\pi\)
\(140\) −4.20851 11.0071i −0.355684 0.930266i
\(141\) 0 0
\(142\) −11.9948 + 20.7755i −1.00658 + 1.74344i
\(143\) 4.82288 8.35348i 0.403310 0.698553i
\(144\) 0 0
\(145\) −1.38214 2.39393i −0.114780 0.198805i
\(146\) 8.64965 + 14.9816i 0.715850 + 1.23989i
\(147\) 0 0
\(148\) 6.41418 11.1097i 0.527243 0.913211i
\(149\) 8.76945 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(150\) 0 0
\(151\) −9.56075 −0.778042 −0.389021 0.921229i \(-0.627187\pi\)
−0.389021 + 0.921229i \(0.627187\pi\)
\(152\) 4.84511 + 8.39198i 0.392991 + 0.680680i
\(153\) 0 0
\(154\) 10.5253 12.9625i 0.848149 1.04455i
\(155\) 6.28212 + 10.8809i 0.504592 + 0.873979i
\(156\) 0 0
\(157\) −1.07953 1.86981i −0.0861562 0.149227i 0.819727 0.572754i \(-0.194125\pi\)
−0.905883 + 0.423527i \(0.860792\pi\)
\(158\) −0.372073 0.644449i −0.0296005 0.0512696i
\(159\) 0 0
\(160\) −1.98151 3.43207i −0.156652 0.271329i
\(161\) −20.8919 3.33730i −1.64651 0.263016i
\(162\) 0 0
\(163\) −10.4871 18.1643i −0.821416 1.42273i −0.904628 0.426202i \(-0.859851\pi\)
0.0832119 0.996532i \(-0.473482\pi\)
\(164\) 6.76158 0.527991
\(165\) 0 0
\(166\) −18.2470 −1.41624
\(167\) −2.13704 + 3.70147i −0.165370 + 0.286428i −0.936786 0.349902i \(-0.886215\pi\)
0.771417 + 0.636330i \(0.219548\pi\)
\(168\) 0 0
\(169\) −0.0697192 0.120757i −0.00536302 0.00928902i
\(170\) 9.80853 + 16.9889i 0.752280 + 1.30299i
\(171\) 0 0
\(172\) −9.31481 + 16.1337i −0.710248 + 1.23019i
\(173\) −0.908300 + 1.57322i −0.0690567 + 0.119610i −0.898486 0.439001i \(-0.855332\pi\)
0.829430 + 0.558611i \(0.188666\pi\)
\(174\) 0 0
\(175\) −9.11855 1.45661i −0.689298 0.110109i
\(176\) −2.51435 + 4.35499i −0.189526 + 0.328269i
\(177\) 0 0
\(178\) 17.0584 1.27858
\(179\) −4.02507 + 6.97162i −0.300848 + 0.521083i −0.976328 0.216295i \(-0.930603\pi\)
0.675481 + 0.737378i \(0.263936\pi\)
\(180\) 0 0
\(181\) 25.3467 1.88401 0.942004 0.335601i \(-0.108939\pi\)
0.942004 + 0.335601i \(0.108939\pi\)
\(182\) −8.12309 21.2454i −0.602124 1.57481i
\(183\) 0 0
\(184\) 30.8152 2.27173
\(185\) 2.17428 + 3.76596i 0.159856 + 0.276879i
\(186\) 0 0
\(187\) −8.95644 + 15.5130i −0.654960 + 1.13442i
\(188\) −7.78042 −0.567445
\(189\) 0 0
\(190\) −7.32801 −0.531630
\(191\) 3.57560 6.19313i 0.258722 0.448119i −0.707178 0.707035i \(-0.750032\pi\)
0.965900 + 0.258917i \(0.0833655\pi\)
\(192\) 0 0
\(193\) −5.67777 9.83418i −0.408695 0.707880i 0.586049 0.810276i \(-0.300683\pi\)
−0.994744 + 0.102396i \(0.967349\pi\)
\(194\) 31.2679 2.24490
\(195\) 0 0
\(196\) −5.20981 24.8333i −0.372129 1.77380i
\(197\) 20.0998 1.43205 0.716024 0.698075i \(-0.245960\pi\)
0.716024 + 0.698075i \(0.245960\pi\)
\(198\) 0 0
\(199\) −5.16251 + 8.94173i −0.365961 + 0.633862i −0.988930 0.148384i \(-0.952593\pi\)
0.622969 + 0.782246i \(0.285926\pi\)
\(200\) 13.4497 0.951038
\(201\) 0 0
\(202\) −3.30021 + 5.71613i −0.232202 + 0.402186i
\(203\) −2.12568 5.55956i −0.149193 0.390204i
\(204\) 0 0
\(205\) −1.14602 + 1.98496i −0.0800415 + 0.138636i
\(206\) 7.12269 12.3369i 0.496261 0.859550i
\(207\) 0 0
\(208\) 3.42505 + 5.93235i 0.237484 + 0.411335i
\(209\) −3.34570 5.79493i −0.231427 0.400844i
\(210\) 0 0
\(211\) −0.299369 + 0.518522i −0.0206094 + 0.0356965i −0.876146 0.482046i \(-0.839894\pi\)
0.855537 + 0.517742i \(0.173227\pi\)
\(212\) 10.7734 0.739917
\(213\) 0 0
\(214\) 27.8348 1.90275
\(215\) −3.15753 5.46900i −0.215342 0.372983i
\(216\) 0 0
\(217\) 9.66167 + 25.2694i 0.655877 + 1.71540i
\(218\) −9.46860 16.4001i −0.641295 1.11076i
\(219\) 0 0
\(220\) −5.92609 10.2643i −0.399537 0.692019i
\(221\) 12.2004 + 21.1318i 0.820690 + 1.42148i
\(222\) 0 0
\(223\) −1.51002 2.61543i −0.101119 0.175142i 0.811027 0.585008i \(-0.198909\pi\)
−0.912146 + 0.409866i \(0.865575\pi\)
\(224\) −3.04749 7.97049i −0.203619 0.532551i
\(225\) 0 0
\(226\) 5.50239 + 9.53043i 0.366014 + 0.633954i
\(227\) −20.1080 −1.33462 −0.667309 0.744781i \(-0.732554\pi\)
−0.667309 + 0.744781i \(0.732554\pi\)
\(228\) 0 0
\(229\) −20.0065 −1.32206 −0.661032 0.750357i \(-0.729881\pi\)
−0.661032 + 0.750357i \(0.729881\pi\)
\(230\) −11.6516 + 20.1812i −0.768287 + 1.33071i
\(231\) 0 0
\(232\) 4.33465 + 7.50783i 0.284584 + 0.492913i
\(233\) 0.151398 + 0.262229i 0.00991839 + 0.0171792i 0.870942 0.491386i \(-0.163509\pi\)
−0.861024 + 0.508565i \(0.830176\pi\)
\(234\) 0 0
\(235\) 1.31870 2.28406i 0.0860226 0.148995i
\(236\) 15.8190 27.3992i 1.02973 1.78354i
\(237\) 0 0
\(238\) 15.0852 + 39.4542i 0.977826 + 2.55743i
\(239\) −1.77340 + 3.07162i −0.114712 + 0.198686i −0.917664 0.397356i \(-0.869928\pi\)
0.802953 + 0.596043i \(0.203261\pi\)
\(240\) 0 0
\(241\) 6.00647 0.386911 0.193455 0.981109i \(-0.438031\pi\)
0.193455 + 0.981109i \(0.438031\pi\)
\(242\) −4.64726 + 8.04929i −0.298737 + 0.517428i
\(243\) 0 0
\(244\) −54.3899 −3.48196
\(245\) 8.17318 + 2.67956i 0.522165 + 0.171191i
\(246\) 0 0
\(247\) −9.11502 −0.579975
\(248\) −19.7019 34.1247i −1.25107 2.16692i
\(249\) 0 0
\(250\) −12.3710 + 21.4272i −0.782409 + 1.35517i
\(251\) −21.0113 −1.32622 −0.663109 0.748523i \(-0.730764\pi\)
−0.663109 + 0.748523i \(0.730764\pi\)
\(252\) 0 0
\(253\) −21.2789 −1.33779
\(254\) −3.94448 + 6.83205i −0.247499 + 0.428681i
\(255\) 0 0
\(256\) 13.0645 + 22.6284i 0.816530 + 1.41427i
\(257\) 20.5690 1.28306 0.641530 0.767098i \(-0.278300\pi\)
0.641530 + 0.767098i \(0.278300\pi\)
\(258\) 0 0
\(259\) 3.34396 + 8.74589i 0.207783 + 0.543443i
\(260\) −16.1450 −1.00127
\(261\) 0 0
\(262\) −10.0168 + 17.3496i −0.618839 + 1.07186i
\(263\) −14.2030 −0.875796 −0.437898 0.899025i \(-0.644277\pi\)
−0.437898 + 0.899025i \(0.644277\pi\)
\(264\) 0 0
\(265\) −1.82597 + 3.16268i −0.112169 + 0.194282i
\(266\) −15.5812 2.48897i −0.955347 0.152608i
\(267\) 0 0
\(268\) 4.80156 8.31654i 0.293302 0.508013i
\(269\) 15.5662 26.9615i 0.949090 1.64387i 0.201742 0.979439i \(-0.435340\pi\)
0.747348 0.664433i \(-0.231327\pi\)
\(270\) 0 0
\(271\) 0.821392 + 1.42269i 0.0498960 + 0.0864225i 0.889895 0.456166i \(-0.150778\pi\)
−0.839999 + 0.542588i \(0.817444\pi\)
\(272\) −6.36056 11.0168i −0.385665 0.667992i
\(273\) 0 0
\(274\) 16.5976 28.7478i 1.00270 1.73672i
\(275\) −9.28745 −0.560055
\(276\) 0 0
\(277\) −22.0950 −1.32756 −0.663779 0.747929i \(-0.731049\pi\)
−0.663779 + 0.747929i \(0.731049\pi\)
\(278\) −6.68823 11.5844i −0.401133 0.694783i
\(279\) 0 0
\(280\) −12.3710 1.97616i −0.739307 0.118098i
\(281\) −7.74070 13.4073i −0.461771 0.799811i 0.537278 0.843405i \(-0.319453\pi\)
−0.999049 + 0.0435938i \(0.986119\pi\)
\(282\) 0 0
\(283\) 13.1174 + 22.7200i 0.779749 + 1.35057i 0.932086 + 0.362237i \(0.117987\pi\)
−0.152337 + 0.988329i \(0.548680\pi\)
\(284\) 18.3326 + 31.7531i 1.08784 + 1.88420i
\(285\) 0 0
\(286\) −11.4383 19.8117i −0.676361 1.17149i
\(287\) −3.11093 + 3.83129i −0.183632 + 0.226154i
\(288\) 0 0
\(289\) −14.1571 24.5208i −0.832770 1.44240i
\(290\) −6.55596 −0.384979
\(291\) 0 0
\(292\) 26.4400 1.54729
\(293\) 8.45425 14.6432i 0.493903 0.855464i −0.506073 0.862491i \(-0.668903\pi\)
0.999975 + 0.00702646i \(0.00223661\pi\)
\(294\) 0 0
\(295\) 5.36230 + 9.28778i 0.312205 + 0.540755i
\(296\) −6.81895 11.8108i −0.396343 0.686487i
\(297\) 0 0
\(298\) 10.3991 18.0118i 0.602406 1.04340i
\(299\) −14.4930 + 25.1026i −0.838153 + 1.45172i
\(300\) 0 0
\(301\) −4.85617 12.7010i −0.279905 0.732071i
\(302\) −11.3375 + 19.6371i −0.652399 + 1.12999i
\(303\) 0 0
\(304\) 4.75201 0.272546
\(305\) 9.21853 15.9670i 0.527852 0.914266i
\(306\) 0 0
\(307\) −14.6835 −0.838034 −0.419017 0.907978i \(-0.637625\pi\)
−0.419017 + 0.907978i \(0.637625\pi\)
\(308\) −9.11412 23.8373i −0.519325 1.35826i
\(309\) 0 0
\(310\) 29.7983 1.69243
\(311\) −5.91109 10.2383i −0.335187 0.580561i 0.648334 0.761356i \(-0.275466\pi\)
−0.983521 + 0.180795i \(0.942133\pi\)
\(312\) 0 0
\(313\) 0.177560 0.307543i 0.0100363 0.0173833i −0.860964 0.508666i \(-0.830139\pi\)
0.871000 + 0.491283i \(0.163472\pi\)
\(314\) −5.12061 −0.288973
\(315\) 0 0
\(316\) −1.13734 −0.0639805
\(317\) 5.22486 9.04972i 0.293457 0.508283i −0.681168 0.732127i \(-0.738528\pi\)
0.974625 + 0.223845i \(0.0718609\pi\)
\(318\) 0 0
\(319\) −2.99321 5.18440i −0.167588 0.290270i
\(320\) −14.0431 −0.785031
\(321\) 0 0
\(322\) −31.6290 + 38.9530i −1.76261 + 2.17077i
\(323\) 16.9272 0.941857
\(324\) 0 0
\(325\) −6.32567 + 10.9564i −0.350885 + 0.607751i
\(326\) −49.7441 −2.75507
\(327\) 0 0
\(328\) 3.59414 6.22523i 0.198453 0.343731i
\(329\) 3.57968 4.40859i 0.197354 0.243054i
\(330\) 0 0
\(331\) −7.43352 + 12.8752i −0.408583 + 0.707686i −0.994731 0.102517i \(-0.967310\pi\)
0.586148 + 0.810204i \(0.300644\pi\)
\(332\) −13.9442 + 24.1521i −0.765289 + 1.32552i
\(333\) 0 0
\(334\) 5.06837 + 8.77868i 0.277329 + 0.480348i
\(335\) 1.62763 + 2.81914i 0.0889269 + 0.154026i
\(336\) 0 0
\(337\) −4.70676 + 8.15235i −0.256394 + 0.444087i −0.965273 0.261243i \(-0.915868\pi\)
0.708879 + 0.705330i \(0.249201\pi\)
\(338\) −0.330703 −0.0179878
\(339\) 0 0
\(340\) 29.9825 1.62603
\(341\) 13.6048 + 23.5642i 0.736742 + 1.27607i
\(342\) 0 0
\(343\) 16.4682 + 8.47347i 0.889197 + 0.457524i
\(344\) 9.90262 + 17.1518i 0.533914 + 0.924766i
\(345\) 0 0
\(346\) 2.15419 + 3.73117i 0.115810 + 0.200589i
\(347\) −13.2932 23.0245i −0.713618 1.23602i −0.963490 0.267744i \(-0.913722\pi\)
0.249872 0.968279i \(-0.419611\pi\)
\(348\) 0 0
\(349\) −4.77648 8.27311i −0.255679 0.442850i 0.709401 0.704806i \(-0.248966\pi\)
−0.965080 + 0.261956i \(0.915632\pi\)
\(350\) −13.8049 + 17.0016i −0.737902 + 0.908772i
\(351\) 0 0
\(352\) −4.29124 7.43264i −0.228724 0.396161i
\(353\) 17.0729 0.908697 0.454349 0.890824i \(-0.349872\pi\)
0.454349 + 0.890824i \(0.349872\pi\)
\(354\) 0 0
\(355\) −12.4288 −0.659651
\(356\) 13.0359 22.5789i 0.690903 1.19668i
\(357\) 0 0
\(358\) 9.54614 + 16.5344i 0.504529 + 0.873870i
\(359\) −12.8333 22.2280i −0.677318 1.17315i −0.975786 0.218730i \(-0.929809\pi\)
0.298467 0.954420i \(-0.403525\pi\)
\(360\) 0 0
\(361\) 6.33839 10.9784i 0.333599 0.577811i
\(362\) 30.0571 52.0604i 1.57977 2.73624i
\(363\) 0 0
\(364\) −34.3285 5.48367i −1.79930 0.287423i
\(365\) −4.48132 + 7.76187i −0.234563 + 0.406275i
\(366\) 0 0
\(367\) −10.3752 −0.541579 −0.270790 0.962639i \(-0.587285\pi\)
−0.270790 + 0.962639i \(0.587285\pi\)
\(368\) 7.55577 13.0870i 0.393872 0.682205i
\(369\) 0 0
\(370\) 10.3134 0.536166
\(371\) −4.95669 + 6.10447i −0.257339 + 0.316928i
\(372\) 0 0
\(373\) −19.8152 −1.02599 −0.512996 0.858391i \(-0.671465\pi\)
−0.512996 + 0.858391i \(0.671465\pi\)
\(374\) 21.2417 + 36.7918i 1.09838 + 1.90246i
\(375\) 0 0
\(376\) −4.13570 + 7.16324i −0.213282 + 0.369416i
\(377\) −8.15470 −0.419988
\(378\) 0 0
\(379\) 14.1716 0.727948 0.363974 0.931409i \(-0.381420\pi\)
0.363974 + 0.931409i \(0.381420\pi\)
\(380\) −5.60002 + 9.69952i −0.287275 + 0.497575i
\(381\) 0 0
\(382\) −8.48016 14.6881i −0.433883 0.751507i
\(383\) −13.4487 −0.687197 −0.343598 0.939117i \(-0.611646\pi\)
−0.343598 + 0.939117i \(0.611646\pi\)
\(384\) 0 0
\(385\) 8.54255 + 1.36460i 0.435369 + 0.0695464i
\(386\) −26.9316 −1.37078
\(387\) 0 0
\(388\) 23.8947 41.3869i 1.21307 2.10110i
\(389\) 20.9297 1.06118 0.530590 0.847629i \(-0.321971\pi\)
0.530590 + 0.847629i \(0.321971\pi\)
\(390\) 0 0
\(391\) 26.9146 46.6174i 1.36113 2.35754i
\(392\) −25.6327 8.40363i −1.29465 0.424447i
\(393\) 0 0
\(394\) 23.8350 41.2835i 1.20079 2.07983i
\(395\) 0.192768 0.333884i 0.00969921 0.0167995i
\(396\) 0 0
\(397\) 12.5708 + 21.7732i 0.630909 + 1.09277i 0.987366 + 0.158454i \(0.0506511\pi\)
−0.356458 + 0.934312i \(0.616016\pi\)
\(398\) 12.2438 + 21.2069i 0.613726 + 1.06300i
\(399\) 0 0
\(400\) 3.29782 5.71198i 0.164891 0.285599i
\(401\) 21.1603 1.05669 0.528347 0.849029i \(-0.322812\pi\)
0.528347 + 0.849029i \(0.322812\pi\)
\(402\) 0 0
\(403\) 37.0649 1.84633
\(404\) 5.04400 + 8.73646i 0.250948 + 0.434655i
\(405\) 0 0
\(406\) −13.9396 2.22674i −0.691813 0.110511i
\(407\) 4.70870 + 8.15571i 0.233402 + 0.404264i
\(408\) 0 0
\(409\) −0.271903 0.470950i −0.0134447 0.0232870i 0.859225 0.511598i \(-0.170946\pi\)
−0.872670 + 0.488311i \(0.837613\pi\)
\(410\) 2.71798 + 4.70769i 0.134232 + 0.232496i
\(411\) 0 0
\(412\) −10.8862 18.8555i −0.536326 0.928944i
\(413\) 8.24702 + 21.5695i 0.405810 + 1.06137i
\(414\) 0 0
\(415\) −4.72681 8.18707i −0.232030 0.401888i
\(416\) −11.6910 −0.573200
\(417\) 0 0
\(418\) −15.8698 −0.776219
\(419\) 11.9044 20.6190i 0.581566 1.00730i −0.413728 0.910401i \(-0.635773\pi\)
0.995294 0.0969018i \(-0.0308933\pi\)
\(420\) 0 0
\(421\) 1.45490 + 2.51997i 0.0709077 + 0.122816i 0.899299 0.437334i \(-0.144077\pi\)
−0.828392 + 0.560149i \(0.810744\pi\)
\(422\) 0.710005 + 1.22976i 0.0345625 + 0.0598640i
\(423\) 0 0
\(424\) 5.72660 9.91876i 0.278108 0.481698i
\(425\) 11.7472 20.3468i 0.569824 0.986965i
\(426\) 0 0
\(427\) 25.0242 30.8188i 1.21100 1.49143i
\(428\) 21.2712 36.8428i 1.02818 1.78086i
\(429\) 0 0
\(430\) −14.9773 −0.722268
\(431\) 15.6897 27.1754i 0.755747 1.30899i −0.189255 0.981928i \(-0.560607\pi\)
0.945002 0.327065i \(-0.106059\pi\)
\(432\) 0 0
\(433\) −26.9281 −1.29408 −0.647042 0.762455i \(-0.723994\pi\)
−0.647042 + 0.762455i \(0.723994\pi\)
\(434\) 63.3588 + 10.1210i 3.04132 + 0.485824i
\(435\) 0 0
\(436\) −28.9434 −1.38614
\(437\) 10.0540 + 17.4141i 0.480949 + 0.833028i
\(438\) 0 0
\(439\) 12.6647 21.9359i 0.604453 1.04694i −0.387685 0.921792i \(-0.626725\pi\)
0.992138 0.125151i \(-0.0399416\pi\)
\(440\) −12.6001 −0.600687
\(441\) 0 0
\(442\) 57.8709 2.75264
\(443\) 6.51570 11.2855i 0.309570 0.536191i −0.668698 0.743534i \(-0.733148\pi\)
0.978268 + 0.207343i \(0.0664815\pi\)
\(444\) 0 0
\(445\) 4.41891 + 7.65378i 0.209477 + 0.362824i
\(446\) −7.16256 −0.339157
\(447\) 0 0
\(448\) −29.8592 4.76974i −1.41071 0.225349i
\(449\) −19.4353 −0.917206 −0.458603 0.888641i \(-0.651650\pi\)
−0.458603 + 0.888641i \(0.651650\pi\)
\(450\) 0 0
\(451\) −2.48187 + 4.29872i −0.116866 + 0.202419i
\(452\) 16.8196 0.791126
\(453\) 0 0
\(454\) −23.8449 + 41.3005i −1.11909 + 1.93833i
\(455\) 7.42814 9.14820i 0.348236 0.428874i
\(456\) 0 0
\(457\) 14.3487 24.8528i 0.671206 1.16256i −0.306356 0.951917i \(-0.599110\pi\)
0.977562 0.210646i \(-0.0675567\pi\)
\(458\) −23.7244 + 41.0919i −1.10857 + 1.92010i
\(459\) 0 0
\(460\) 17.8082 + 30.8448i 0.830313 + 1.43814i
\(461\) 11.5240 + 19.9601i 0.536725 + 0.929635i 0.999078 + 0.0429386i \(0.0136720\pi\)
−0.462353 + 0.886696i \(0.652995\pi\)
\(462\) 0 0
\(463\) −14.6074 + 25.3007i −0.678863 + 1.17583i 0.296460 + 0.955045i \(0.404194\pi\)
−0.975324 + 0.220780i \(0.929140\pi\)
\(464\) 4.25135 0.197364
\(465\) 0 0
\(466\) 0.718132 0.0332668
\(467\) −2.18254 3.78027i −0.100996 0.174930i 0.811099 0.584908i \(-0.198870\pi\)
−0.912095 + 0.409978i \(0.865536\pi\)
\(468\) 0 0
\(469\) 2.50323 + 6.54703i 0.115589 + 0.302314i
\(470\) −3.12753 5.41704i −0.144262 0.249869i
\(471\) 0 0
\(472\) −16.8172 29.1283i −0.774075 1.34074i
\(473\) −6.83808 11.8439i −0.314415 0.544583i
\(474\) 0 0
\(475\) 4.38821 + 7.60061i 0.201345 + 0.348740i
\(476\) 63.7504 + 10.1836i 2.92200 + 0.466763i
\(477\) 0 0
\(478\) 4.20592 + 7.28487i 0.192374 + 0.333202i
\(479\) −15.9229 −0.727535 −0.363767 0.931490i \(-0.618510\pi\)
−0.363767 + 0.931490i \(0.618510\pi\)
\(480\) 0 0
\(481\) 12.8284 0.584923
\(482\) 7.12269 12.3369i 0.324430 0.561929i
\(483\) 0 0
\(484\) 7.10281 + 12.3024i 0.322855 + 0.559201i
\(485\) 8.09983 + 14.0293i 0.367794 + 0.637038i
\(486\) 0 0
\(487\) 19.1329 33.1391i 0.866993 1.50168i 0.00193753 0.999998i \(-0.499383\pi\)
0.865055 0.501677i \(-0.167283\pi\)
\(488\) −28.9111 + 50.0755i −1.30874 + 2.26681i
\(489\) 0 0
\(490\) 15.1957 13.6096i 0.686472 0.614820i
\(491\) −6.69540 + 11.5968i −0.302159 + 0.523355i −0.976625 0.214951i \(-0.931041\pi\)
0.674466 + 0.738306i \(0.264374\pi\)
\(492\) 0 0
\(493\) 15.1439 0.682045
\(494\) −10.8089 + 18.7216i −0.486317 + 0.842325i
\(495\) 0 0
\(496\) −19.3233 −0.867643
\(497\) −26.4268 4.22145i −1.18540 0.189358i
\(498\) 0 0
\(499\) 5.40706 0.242053 0.121027 0.992649i \(-0.461381\pi\)
0.121027 + 0.992649i \(0.461381\pi\)
\(500\) 18.9076 + 32.7490i 0.845576 + 1.46458i
\(501\) 0 0
\(502\) −24.9159 + 43.1556i −1.11205 + 1.92613i
\(503\) 9.49157 0.423208 0.211604 0.977355i \(-0.432131\pi\)
0.211604 + 0.977355i \(0.432131\pi\)
\(504\) 0 0
\(505\) −3.41962 −0.152171
\(506\) −25.2333 + 43.7053i −1.12176 + 1.94294i
\(507\) 0 0
\(508\) 6.02870 + 10.4420i 0.267480 + 0.463289i
\(509\) −37.2297 −1.65018 −0.825088 0.565005i \(-0.808874\pi\)
−0.825088 + 0.565005i \(0.808874\pi\)
\(510\) 0 0
\(511\) −12.1648 + 14.9816i −0.538137 + 0.662749i
\(512\) 20.6597 0.913039
\(513\) 0 0
\(514\) 24.3915 42.2473i 1.07586 1.86345i
\(515\) 7.38042 0.325220
\(516\) 0 0
\(517\) 2.85583 4.94645i 0.125599 0.217544i
\(518\) 21.9288 + 3.50294i 0.963497 + 0.153910i
\(519\) 0 0
\(520\) −8.58193 + 14.8643i −0.376342 + 0.651844i
\(521\) 7.60082 13.1650i 0.332998 0.576769i −0.650100 0.759848i \(-0.725273\pi\)
0.983098 + 0.183079i \(0.0586065\pi\)
\(522\) 0 0
\(523\) −2.39824 4.15387i −0.104867 0.181636i 0.808817 0.588061i \(-0.200109\pi\)
−0.913684 + 0.406425i \(0.866775\pi\)
\(524\) 15.3095 + 26.5169i 0.668800 + 1.15840i
\(525\) 0 0
\(526\) −16.8425 + 29.1720i −0.734366 + 1.27196i
\(527\) −68.8321 −2.99837
\(528\) 0 0
\(529\) 40.9442 1.78018
\(530\) 4.33061 + 7.50084i 0.188110 + 0.325816i
\(531\) 0 0
\(532\) −15.2015 + 18.7216i −0.659070 + 0.811685i
\(533\) 3.38079 + 5.85570i 0.146438 + 0.253639i
\(534\) 0 0
\(535\) 7.21050 + 12.4890i 0.311737 + 0.539945i
\(536\) −5.10456 8.84135i −0.220483 0.381888i
\(537\) 0 0
\(538\) −36.9180 63.9439i −1.59165 2.75682i
\(539\) 17.7002 + 5.80297i 0.762400 + 0.249952i
\(540\) 0 0
\(541\) 3.22660 + 5.58864i 0.138722 + 0.240274i 0.927013 0.375029i \(-0.122367\pi\)
−0.788291 + 0.615303i \(0.789034\pi\)
\(542\) 3.89615 0.167354
\(543\) 0 0
\(544\) 21.7111 0.930854
\(545\) 4.90561 8.49676i 0.210133 0.363961i
\(546\) 0 0
\(547\) −13.1281 22.7385i −0.561316 0.972227i −0.997382 0.0723129i \(-0.976962\pi\)
0.436066 0.899915i \(-0.356371\pi\)
\(548\) −25.3675 43.9378i −1.08365 1.87693i
\(549\) 0 0
\(550\) −11.0134 + 19.0758i −0.469613 + 0.813394i
\(551\) −2.82852 + 4.89913i −0.120499 + 0.208710i
\(552\) 0 0
\(553\) 0.523278 0.644449i 0.0222521 0.0274048i
\(554\) −26.2010 + 45.3815i −1.11318 + 1.92808i
\(555\) 0 0
\(556\) −20.4444 −0.867036
\(557\) 0.00716610 0.0124121i 0.000303638 0.000525916i −0.865874 0.500263i \(-0.833237\pi\)
0.866177 + 0.499737i \(0.166570\pi\)
\(558\) 0 0
\(559\) −18.6296 −0.787949
\(560\) −3.87257 + 4.76931i −0.163646 + 0.201540i
\(561\) 0 0
\(562\) −36.7168 −1.54881
\(563\) 8.59130 + 14.8806i 0.362080 + 0.627141i 0.988303 0.152503i \(-0.0487333\pi\)
−0.626223 + 0.779644i \(0.715400\pi\)
\(564\) 0 0
\(565\) −2.85075 + 4.93764i −0.119932 + 0.207728i
\(566\) 62.2205 2.61532
\(567\) 0 0
\(568\) 38.9791 1.63553
\(569\) 14.7390 25.5286i 0.617889 1.07022i −0.371981 0.928240i \(-0.621321\pi\)
0.989870 0.141975i \(-0.0453453\pi\)
\(570\) 0 0
\(571\) 16.4161 + 28.4335i 0.686991 + 1.18990i 0.972807 + 0.231619i \(0.0744023\pi\)
−0.285815 + 0.958285i \(0.592264\pi\)
\(572\) −34.9643 −1.46193
\(573\) 0 0
\(574\) 4.18016 + 10.9329i 0.174477 + 0.456331i
\(575\) 27.9093 1.16390
\(576\) 0 0
\(577\) −15.9787 + 27.6759i −0.665201 + 1.15216i 0.314030 + 0.949413i \(0.398321\pi\)
−0.979231 + 0.202748i \(0.935013\pi\)
\(578\) −67.1520 −2.79315
\(579\) 0 0
\(580\) −5.01002 + 8.67761i −0.208030 + 0.360318i
\(581\) −7.26966 19.0133i −0.301596 0.788804i
\(582\) 0 0
\(583\) −3.95440 + 6.84922i −0.163775 + 0.283666i
\(584\) 14.0543 24.3427i 0.581570 1.00731i
\(585\) 0 0
\(586\) −20.0507 34.7289i −0.828288 1.43464i
\(587\) 2.37316 + 4.11044i 0.0979509 + 0.169656i 0.910836 0.412768i \(-0.135438\pi\)
−0.812885 + 0.582424i \(0.802105\pi\)
\(588\) 0 0
\(589\) 12.8562 22.2676i 0.529732 0.917522i
\(590\) 25.4353 1.04715
\(591\) 0 0
\(592\) −6.68792 −0.274872
\(593\) 0.970397 + 1.68078i 0.0398494 + 0.0690212i 0.885262 0.465092i \(-0.153979\pi\)
−0.845413 + 0.534113i \(0.820646\pi\)
\(594\) 0 0
\(595\) −13.7946 + 16.9889i −0.565523 + 0.696476i
\(596\) −15.8939 27.5290i −0.651040 1.12763i
\(597\) 0 0
\(598\) 34.3727 + 59.5353i 1.40560 + 2.43458i
\(599\) 4.40067 + 7.62219i 0.179807 + 0.311434i 0.941814 0.336134i \(-0.109119\pi\)
−0.762008 + 0.647568i \(0.775786\pi\)
\(600\) 0 0
\(601\) 7.48016 + 12.9560i 0.305122 + 0.528487i 0.977289 0.211913i \(-0.0679694\pi\)
−0.672166 + 0.740400i \(0.734636\pi\)
\(602\) −31.8455 5.08704i −1.29793 0.207332i
\(603\) 0 0
\(604\) 17.3281 + 30.0131i 0.705069 + 1.22122i
\(605\) −4.81542 −0.195775
\(606\) 0 0
\(607\) 2.79138 0.113299 0.0566494 0.998394i \(-0.481958\pi\)
0.0566494 + 0.998394i \(0.481958\pi\)
\(608\) −4.05512 + 7.02367i −0.164457 + 0.284847i
\(609\) 0 0
\(610\) −21.8633 37.8684i −0.885221 1.53325i
\(611\) −3.89021 6.73804i −0.157381 0.272592i
\(612\) 0 0
\(613\) −13.3218 + 23.0740i −0.538062 + 0.931950i 0.460947 + 0.887428i \(0.347510\pi\)
−0.999008 + 0.0445225i \(0.985823\pi\)
\(614\) −17.4123 + 30.1590i −0.702703 + 1.21712i
\(615\) 0 0
\(616\) −26.7911 4.27964i −1.07944 0.172432i
\(617\) 19.0560 33.0060i 0.767166 1.32877i −0.171927 0.985110i \(-0.554999\pi\)
0.939094 0.343661i \(-0.111667\pi\)
\(618\) 0 0
\(619\) −23.9315 −0.961890 −0.480945 0.876751i \(-0.659706\pi\)
−0.480945 + 0.876751i \(0.659706\pi\)
\(620\) 22.7716 39.4417i 0.914531 1.58401i
\(621\) 0 0
\(622\) −28.0384 −1.12424
\(623\) 6.79613 + 17.7748i 0.272281 + 0.712132i
\(624\) 0 0
\(625\) 4.63231 0.185293
\(626\) −0.421114 0.729391i −0.0168311 0.0291523i
\(627\) 0 0
\(628\) −3.91314 + 6.77775i −0.156151 + 0.270462i
\(629\) −23.8232 −0.949893
\(630\) 0 0
\(631\) −16.6748 −0.663812 −0.331906 0.943313i \(-0.607692\pi\)
−0.331906 + 0.943313i \(0.607692\pi\)
\(632\) −0.604558 + 1.04712i −0.0240480 + 0.0416524i
\(633\) 0 0
\(634\) −12.3917 21.4630i −0.492135 0.852404i
\(635\) −4.08721 −0.162196
\(636\) 0 0
\(637\) 18.9013 16.9285i 0.748898 0.670730i
\(638\) −14.1978 −0.562098
\(639\) 0 0
\(640\) −12.6898 + 21.9793i −0.501607 + 0.868809i
\(641\) 32.0213 1.26477 0.632383 0.774656i \(-0.282077\pi\)
0.632383 + 0.774656i \(0.282077\pi\)
\(642\) 0 0
\(643\) 1.75969 3.04788i 0.0693956 0.120197i −0.829240 0.558893i \(-0.811226\pi\)
0.898635 + 0.438696i \(0.144560\pi\)
\(644\) 27.3884 + 71.6325i 1.07925 + 2.82271i
\(645\) 0 0
\(646\) 20.0730 34.7674i 0.789760 1.36790i
\(647\) −20.7773 + 35.9873i −0.816839 + 1.41481i 0.0911605 + 0.995836i \(0.470942\pi\)
−0.908000 + 0.418971i \(0.862391\pi\)
\(648\) 0 0
\(649\) 11.6128 + 20.1140i 0.455843 + 0.789543i
\(650\) 15.0024 + 25.9850i 0.588444 + 1.01921i
\(651\) 0 0
\(652\) −38.0142 + 65.8424i −1.48875 + 2.57859i
\(653\) 10.2858 0.402513 0.201257 0.979539i \(-0.435497\pi\)
0.201257 + 0.979539i \(0.435497\pi\)
\(654\) 0 0
\(655\) −10.3792 −0.405550
\(656\) −1.76254 3.05280i −0.0688155 0.119192i
\(657\) 0 0
\(658\) −4.81002 12.5803i −0.187514 0.490430i
\(659\) −10.1776 17.6281i −0.396461 0.686691i 0.596825 0.802371i \(-0.296429\pi\)
−0.993287 + 0.115680i \(0.963095\pi\)
\(660\) 0 0
\(661\) 8.32637 + 14.4217i 0.323858 + 0.560939i 0.981281 0.192584i \(-0.0616866\pi\)
−0.657422 + 0.753522i \(0.728353\pi\)
\(662\) 17.6299 + 30.5358i 0.685204 + 1.18681i
\(663\) 0 0
\(664\) 14.8242 + 25.6762i 0.575290 + 0.996431i
\(665\) −2.91950 7.63576i −0.113214 0.296102i
\(666\) 0 0
\(667\) 8.99477 + 15.5794i 0.348279 + 0.603236i
\(668\) 15.4929 0.599437
\(669\) 0 0
\(670\) 7.72041 0.298265
\(671\) 19.9640 34.5787i 0.770703 1.33490i
\(672\) 0 0
\(673\) −5.10939 8.84973i −0.196953 0.341132i 0.750586 0.660772i \(-0.229771\pi\)
−0.947539 + 0.319641i \(0.896438\pi\)
\(674\) 11.1629 + 19.3347i 0.429979 + 0.744746i
\(675\) 0 0
\(676\) −0.252721 + 0.437725i −0.00972003 + 0.0168356i
\(677\) −3.19342 + 5.53117i −0.122733 + 0.212580i −0.920845 0.389930i \(-0.872499\pi\)
0.798111 + 0.602510i \(0.205833\pi\)
\(678\) 0 0
\(679\) 12.4572 + 32.5810i 0.478065 + 1.25035i
\(680\) 15.9373 27.6041i 0.611166 1.05857i
\(681\) 0 0
\(682\) 64.5323 2.47107
\(683\) 15.4061 26.6842i 0.589499 1.02104i −0.404800 0.914405i \(-0.632659\pi\)
0.994298 0.106636i \(-0.0340079\pi\)
\(684\) 0 0
\(685\) 17.1981 0.657107
\(686\) 36.9325 23.7763i 1.41009 0.907783i
\(687\) 0 0
\(688\) 9.71234 0.370279
\(689\) 5.38668 + 9.32999i 0.205216 + 0.355444i
\(690\) 0 0
\(691\) 2.43402 4.21585i 0.0925945 0.160378i −0.816008 0.578041i \(-0.803817\pi\)
0.908602 + 0.417663i \(0.137151\pi\)
\(692\) 6.58487 0.250319
\(693\) 0 0
\(694\) −63.0544 −2.39351
\(695\) 3.46512 6.00176i 0.131439 0.227660i
\(696\) 0 0
\(697\) −6.27837 10.8745i −0.237810 0.411900i
\(698\) −22.6565 −0.857562
\(699\) 0 0
\(700\) 11.9540 + 31.2650i 0.451820 + 1.18170i
\(701\) 44.4038 1.67711 0.838554 0.544819i \(-0.183402\pi\)
0.838554 + 0.544819i \(0.183402\pi\)
\(702\) 0 0
\(703\) 4.44961 7.70696i 0.167820 0.290673i
\(704\) −30.4122 −1.14620
\(705\) 0 0
\(706\) 20.2456 35.0665i 0.761955 1.31974i
\(707\) −7.27100 1.16148i −0.273454 0.0436819i
\(708\) 0 0
\(709\) 13.2884 23.0162i 0.499056 0.864391i −0.500943 0.865480i \(-0.667013\pi\)
0.999999 + 0.00108957i \(0.000346820\pi\)
\(710\) −14.7385 + 25.5279i −0.553126 + 0.958043i
\(711\) 0 0
\(712\) −13.8586 24.0037i −0.519372 0.899578i
\(713\) −40.8832 70.8117i −1.53109 2.65192i
\(714\) 0 0
\(715\) 5.92609 10.2643i 0.221623 0.383863i
\(716\) 29.1804 1.09052
\(717\) 0 0
\(718\) −60.8730 −2.27176
\(719\) 16.9462 + 29.3517i 0.631987 + 1.09463i 0.987145 + 0.159828i \(0.0510939\pi\)
−0.355157 + 0.934807i \(0.615573\pi\)
\(720\) 0 0
\(721\) 15.6927 + 2.50677i 0.584425 + 0.0933569i
\(722\) −15.0326 26.0372i −0.559455 0.969005i
\(723\) 0 0
\(724\) −45.9389 79.5685i −1.70731 2.95714i
\(725\) 3.92589 + 6.79984i 0.145804 + 0.252540i
\(726\) 0 0
\(727\) 11.9709 + 20.7341i 0.443974 + 0.768986i 0.997980 0.0635267i \(-0.0202348\pi\)
−0.554006 + 0.832513i \(0.686901\pi\)
\(728\) −23.2961 + 28.6905i −0.863410 + 1.06334i
\(729\) 0 0
\(730\) 10.6282 + 18.4086i 0.393368 + 0.681334i
\(731\) 34.5965 1.27960
\(732\) 0 0
\(733\) −37.5703 −1.38769 −0.693846 0.720124i \(-0.744085\pi\)
−0.693846 + 0.720124i \(0.744085\pi\)
\(734\) −12.3033 + 21.3099i −0.454121 + 0.786561i
\(735\) 0 0
\(736\) 12.8954 + 22.3355i 0.475331 + 0.823297i
\(737\) 3.52486 + 6.10523i 0.129840 + 0.224889i
\(738\) 0 0
\(739\) 2.82055 4.88534i 0.103756 0.179710i −0.809473 0.587156i \(-0.800247\pi\)
0.913229 + 0.407446i \(0.133581\pi\)
\(740\) 7.88140 13.6510i 0.289726 0.501820i
\(741\) 0 0
\(742\) 6.66032 + 17.4196i 0.244508 + 0.639494i
\(743\) −7.58516 + 13.1379i −0.278273 + 0.481982i −0.970956 0.239260i \(-0.923095\pi\)
0.692683 + 0.721242i \(0.256429\pi\)
\(744\) 0 0
\(745\) 10.7754 0.394781
\(746\) −23.4976 + 40.6990i −0.860308 + 1.49010i
\(747\) 0 0
\(748\) 64.9312 2.37412
\(749\) 11.0895 + 29.0038i 0.405201 + 1.05978i
\(750\) 0 0
\(751\) 25.8935 0.944869 0.472434 0.881366i \(-0.343375\pi\)
0.472434 + 0.881366i \(0.343375\pi\)
\(752\) 2.02811 + 3.51280i 0.0739577 + 0.128099i
\(753\) 0 0
\(754\) −9.67014 + 16.7492i −0.352166 + 0.609969i
\(755\) −11.7477 −0.427543
\(756\) 0 0
\(757\) 36.9054 1.34135 0.670675 0.741752i \(-0.266005\pi\)
0.670675 + 0.741752i \(0.266005\pi\)
\(758\) 16.8052 29.1075i 0.610394 1.05723i
\(759\) 0 0
\(760\) 5.95341 + 10.3116i 0.215953 + 0.374041i
\(761\) 28.4009 1.02953 0.514765 0.857331i \(-0.327879\pi\)
0.514765 + 0.857331i \(0.327879\pi\)
\(762\) 0 0
\(763\) 13.3165 16.4001i 0.482090 0.593724i
\(764\) −25.9219 −0.937823
\(765\) 0 0
\(766\) −15.9480 + 27.6227i −0.576223 + 0.998048i
\(767\) 31.6379 1.14238
\(768\) 0 0
\(769\) 2.63076 4.55661i 0.0948677 0.164316i −0.814686 0.579903i \(-0.803091\pi\)
0.909553 + 0.415587i \(0.136424\pi\)
\(770\) 12.9329 15.9276i 0.466068 0.573991i
\(771\) 0 0
\(772\) −20.5810 + 35.6473i −0.740726 + 1.28297i
\(773\) 20.6873 35.8315i 0.744071 1.28877i −0.206556 0.978435i \(-0.566226\pi\)
0.950627 0.310335i \(-0.100441\pi\)
\(774\) 0 0
\(775\) −17.8440 30.9067i −0.640976 1.11020i
\(776\) −25.4026 43.9986i −0.911901 1.57946i
\(777\) 0 0
\(778\) 24.8192 42.9882i 0.889813 1.54120i
\(779\) 4.69061 0.168059
\(780\) 0 0
\(781\) −26.9163 −0.963140
\(782\) −63.8326 110.561i −2.28265 3.95366i
\(783\) 0 0
\(784\) −9.85398 + 8.82545i −0.351928 + 0.315195i
\(785\) −1.32647 2.29752i −0.0473438 0.0820019i
\(786\) 0 0
\(787\) −2.68064 4.64301i −0.0955547 0.165506i 0.814285 0.580465i \(-0.197129\pi\)
−0.909840 + 0.414959i \(0.863796\pi\)
\(788\) −36.4292 63.0972i −1.29774 2.24774i
\(789\) 0 0
\(790\) −0.457183 0.791864i −0.0162658 0.0281733i
\(791\) −7.73849 + 9.53043i −0.275149 + 0.338863i
\(792\) 0 0
\(793\) −27.1949 47.1030i −0.965721 1.67268i
\(794\) 59.6275 2.11610
\(795\) 0 0
\(796\) 37.4265 1.32655
\(797\) −15.2102 + 26.3448i −0.538773 + 0.933182i 0.460197 + 0.887817i \(0.347779\pi\)
−0.998970 + 0.0453658i \(0.985555\pi\)
\(798\) 0 0
\(799\) 7.22439 + 12.5130i 0.255581 + 0.442679i
\(800\) 5.62837 + 9.74862i 0.198993 + 0.344666i
\(801\) 0 0
\(802\) 25.0926 43.4617i 0.886052 1.53469i
\(803\) −9.70492 + 16.8094i −0.342479 + 0.593191i
\(804\) 0 0
\(805\) −25.6708 4.10069i −0.904778 0.144530i
\(806\) 43.9529 76.1287i 1.54817 2.68152i
\(807\) 0 0
\(808\) 10.7246 0.377290
\(809\) −21.7729 + 37.7117i −0.765494 + 1.32587i 0.174491 + 0.984659i \(0.444172\pi\)
−0.939985 + 0.341216i \(0.889161\pi\)
\(810\) 0 0
\(811\) 17.4078 0.611272 0.305636 0.952148i \(-0.401131\pi\)
0.305636 + 0.952148i \(0.401131\pi\)
\(812\) −13.6000 + 16.7492i −0.477265 + 0.587781i
\(813\) 0 0
\(814\) 22.3350 0.782842
\(815\) −12.8860 22.3192i −0.451378 0.781809i
\(816\) 0 0
\(817\) −6.46182 + 11.1922i −0.226071 + 0.391566i
\(818\) −1.28973 −0.0450944
\(819\) 0 0
\(820\) 8.30826 0.290137
\(821\) −11.5318 + 19.9736i −0.402462 + 0.697085i −0.994022 0.109176i \(-0.965179\pi\)
0.591560 + 0.806261i \(0.298512\pi\)
\(822\) 0 0
\(823\) −5.03902 8.72784i −0.175649 0.304233i 0.764737 0.644343i \(-0.222869\pi\)
−0.940386 + 0.340110i \(0.889536\pi\)
\(824\) −23.1464 −0.806344
\(825\) 0 0
\(826\) 54.0819 + 8.63911i 1.88175 + 0.300593i
\(827\) −28.4954 −0.990882 −0.495441 0.868642i \(-0.664993\pi\)
−0.495441 + 0.868642i \(0.664993\pi\)
\(828\) 0 0
\(829\) 0.907602 1.57201i 0.0315223 0.0545983i −0.849834 0.527051i \(-0.823298\pi\)
0.881356 + 0.472452i \(0.156631\pi\)
\(830\) −22.4209 −0.778241
\(831\) 0 0
\(832\) −20.7137 + 35.8772i −0.718120 + 1.24382i
\(833\) −35.1011 + 31.4374i −1.21618 + 1.08924i
\(834\) 0 0
\(835\) −2.62588 + 4.54816i −0.0908725 + 0.157396i
\(836\) −12.1276 + 21.0057i −0.419443 + 0.726496i
\(837\) 0 0
\(838\) −28.2333 48.9015i −0.975302 1.68927i
\(839\) −3.43860 5.95583i −0.118714 0.205618i 0.800544 0.599273i \(-0.204544\pi\)
−0.919258 + 0.393655i \(0.871210\pi\)
\(840\) 0 0
\(841\) 11.9695 20.7318i 0.412741 0.714888i
\(842\) 6.90112 0.237828
\(843\) 0 0
\(844\) 2.17032 0.0747057
\(845\) −0.0856672 0.148380i −0.00294704 0.00510442i
\(846\) 0 0
\(847\) −10.2388 1.63556i −0.351810 0.0561985i
\(848\) −2.80828 4.86408i −0.0964367 0.167033i
\(849\) 0 0
\(850\) −27.8606 48.2560i −0.955611 1.65517i
\(851\) −14.1499 24.5083i −0.485052 0.840135i
\(852\) 0 0
\(853\) 1.34635 + 2.33195i 0.0460982 + 0.0798445i 0.888154 0.459546i \(-0.151988\pi\)
−0.842056 + 0.539391i \(0.818655\pi\)
\(854\) −33.6250 87.9439i −1.15063 3.00938i
\(855\) 0 0
\(856\) −22.6135 39.1678i −0.772914 1.33873i
\(857\) −23.6722 −0.808625 −0.404313 0.914621i \(-0.632489\pi\)
−0.404313 + 0.914621i \(0.632489\pi\)
\(858\) 0 0
\(859\) −13.0275 −0.444492 −0.222246 0.974991i \(-0.571339\pi\)
−0.222246 + 0.974991i \(0.571339\pi\)
\(860\) −11.4455 + 19.8242i −0.390289 + 0.676001i
\(861\) 0 0
\(862\) −37.2109 64.4512i −1.26741 2.19522i
\(863\) −9.87796 17.1091i −0.336250 0.582401i 0.647475 0.762087i \(-0.275825\pi\)
−0.983724 + 0.179686i \(0.942492\pi\)
\(864\) 0 0
\(865\) −1.11607 + 1.93309i −0.0379475 + 0.0657270i
\(866\) −31.9324 + 55.3085i −1.08511 + 1.87946i
\(867\) 0 0
\(868\) 61.8148 76.1287i 2.09813 2.58397i
\(869\) 0.417466 0.723073i 0.0141616 0.0245286i
\(870\) 0 0
\(871\) 9.60311 0.325389
\(872\) −15.3849 + 26.6475i −0.520999 + 0.902398i
\(873\) 0 0
\(874\) 47.6897 1.61313
\(875\) −27.2557 4.35385i −0.921409 0.147187i
\(876\) 0 0
\(877\) 12.6814 0.428222 0.214111 0.976809i \(-0.431315\pi\)
0.214111 + 0.976809i \(0.431315\pi\)
\(878\) −30.0365 52.0248i −1.01368 1.75575i
\(879\) 0 0
\(880\) −3.08950 + 5.35117i −0.104147 + 0.180388i
\(881\) −43.7202 −1.47297 −0.736485 0.676454i \(-0.763516\pi\)
−0.736485 + 0.676454i \(0.763516\pi\)
\(882\) 0 0
\(883\) −1.03795 −0.0349298 −0.0174649 0.999847i \(-0.505560\pi\)
−0.0174649 + 0.999847i \(0.505560\pi\)
\(884\) 44.2246 76.5992i 1.48743 2.57631i
\(885\) 0 0
\(886\) −15.4531 26.7656i −0.519157 0.899207i
\(887\) −6.38256 −0.214305 −0.107153 0.994243i \(-0.534173\pi\)
−0.107153 + 0.994243i \(0.534173\pi\)
\(888\) 0 0
\(889\) −8.69046 1.38823i −0.291469 0.0465596i
\(890\) 20.9604 0.702596
\(891\) 0 0
\(892\) −5.47358 + 9.48052i −0.183269 + 0.317431i
\(893\) −5.39739 −0.180617
\(894\) 0 0
\(895\) −4.94578 + 8.56634i −0.165319 + 0.286341i
\(896\) −34.4470 + 42.4236i −1.15079 + 1.41727i
\(897\) 0 0
\(898\) −23.0470 + 39.9186i −0.769090 + 1.33210i
\(899\) 11.5017 19.9216i 0.383604 0.664422i
\(900\) 0 0
\(901\) −10.0034 17.3265i −0.333263 0.577228i
\(902\) 5.88617 + 10.1952i 0.195988 + 0.339461i
\(903\) 0 0
\(904\) 8.94049 15.4854i 0.297356 0.515036i
\(905\) 31.1447 1.03528
\(906\) 0 0
\(907\) −45.4262 −1.50835 −0.754176 0.656672i \(-0.771964\pi\)
−0.754176 + 0.656672i \(0.771964\pi\)
\(908\) 36.4442 + 63.1232i 1.20944 + 2.09482i
\(909\) 0 0
\(910\) −9.98121 26.1051i −0.330874 0.865377i
\(911\) −2.24354 3.88592i −0.0743318 0.128746i 0.826464 0.562990i \(-0.190349\pi\)
−0.900795 + 0.434244i \(0.857016\pi\)
\(912\) 0 0
\(913\) −10.2366 17.7303i −0.338781 0.586786i
\(914\) −34.0305 58.9426i −1.12563 1.94965i
\(915\) 0 0
\(916\) 36.2601 + 62.8043i 1.19807 + 2.07511i
\(917\) −22.0689 3.52532i −0.728780 0.116416i
\(918\) 0 0
\(919\) 17.3189 + 29.9972i 0.571298 + 0.989517i 0.996433 + 0.0843873i \(0.0268933\pi\)
−0.425135 + 0.905130i \(0.639773\pi\)
\(920\) 37.8640 1.24834
\(921\) 0 0
\(922\) 54.6622 1.80020
\(923\) −18.3326 + 31.7531i −0.603426 + 1.04517i
\(924\) 0 0
\(925\) −6.17592 10.6970i −0.203063 0.351715i
\(926\) 34.6440 + 60.0051i 1.13847 + 1.97189i
\(927\) 0 0
\(928\) −3.62788 + 6.28368i −0.119091 + 0.206272i
\(929\) −7.63640 + 13.2266i −0.250542 + 0.433952i −0.963675 0.267077i \(-0.913942\pi\)
0.713133 + 0.701029i \(0.247275\pi\)
\(930\) 0 0
\(931\) −3.61412 17.2272i −0.118448 0.564598i
\(932\) 0.548792 0.950535i 0.0179763 0.0311358i
\(933\) 0 0
\(934\) −10.3525 −0.338746
\(935\) −11.0052 + 19.0615i −0.359908 + 0.623379i
\(936\) 0 0
\(937\) 16.6920 0.545305 0.272652 0.962113i \(-0.412099\pi\)
0.272652 + 0.962113i \(0.412099\pi\)
\(938\) 16.4156 + 2.62224i 0.535987 + 0.0856193i
\(939\) 0 0
\(940\) −9.56015 −0.311818
\(941\) −10.6239 18.4012i −0.346330 0.599862i 0.639264 0.768987i \(-0.279239\pi\)
−0.985595 + 0.169125i \(0.945906\pi\)
\(942\) 0 0
\(943\) 7.45814 12.9179i 0.242870 0.420664i
\(944\) −16.4940 −0.536836
\(945\) 0 0
\(946\) −32.4354 −1.05456
\(947\) −19.6573 + 34.0475i −0.638777 + 1.10639i 0.346924 + 0.937893i \(0.387226\pi\)
−0.985701 + 0.168501i \(0.946107\pi\)
\(948\) 0 0
\(949\) 13.2200 + 22.8977i 0.429140 + 0.743292i
\(950\) 20.8148 0.675322
\(951\) 0 0
\(952\) 43.2625 53.2804i 1.40214 1.72683i
\(953\) −15.1311 −0.490143 −0.245072 0.969505i \(-0.578811\pi\)
−0.245072 + 0.969505i \(0.578811\pi\)
\(954\) 0 0
\(955\) 4.39351 7.60977i 0.142170 0.246247i
\(956\) 12.8566 0.415811
\(957\) 0 0
\(958\) −18.8819 + 32.7045i −0.610047 + 1.05663i
\(959\) 36.5677 + 5.84137i 1.18083 + 0.188628i
\(960\) 0 0
\(961\) −36.7779 + 63.7012i −1.18638 + 2.05488i
\(962\) 15.2123 26.3486i 0.490466 0.849512i
\(963\) 0 0
\(964\) −10.8862 18.8555i −0.350622 0.607295i
\(965\) −6.97653 12.0837i −0.224582 0.388988i
\(966\) 0 0
\(967\) −15.6941 + 27.1829i −0.504687 + 0.874143i 0.495299 + 0.868723i \(0.335059\pi\)
−0.999985 + 0.00542015i \(0.998275\pi\)
\(968\) 15.1021 0.485399
\(969\) 0 0
\(970\) 38.4203 1.23360
\(971\) −17.4760 30.2694i −0.560833 0.971391i −0.997424 0.0717309i \(-0.977148\pi\)
0.436591 0.899660i \(-0.356186\pi\)
\(972\) 0 0
\(973\) 9.40624 11.5844i 0.301550 0.371377i
\(974\) −45.3769 78.5951i −1.45397 2.51835i
\(975\) 0 0
\(976\) 14.1778 + 24.5566i 0.453819 + 0.786038i
\(977\) 3.84316 + 6.65655i 0.122954 + 0.212962i 0.920931 0.389725i \(-0.127430\pi\)
−0.797978 + 0.602687i \(0.794097\pi\)
\(978\) 0 0
\(979\) 9.56978 + 16.5753i 0.305851 + 0.529750i
\(980\) −6.40153 30.5137i −0.204489 0.974726i
\(981\) 0 0
\(982\) 15.8793 + 27.5037i 0.506729 + 0.877680i
\(983\) 2.18071 0.0695538 0.0347769 0.999395i \(-0.488928\pi\)
0.0347769 + 0.999395i \(0.488928\pi\)
\(984\) 0 0
\(985\) 24.6975 0.786928
\(986\) 17.9581 31.1044i 0.571904 0.990566i
\(987\) 0 0
\(988\) 16.5202 + 28.6139i 0.525579 + 0.910329i
\(989\) 20.5488 + 35.5915i 0.653413 + 1.13175i
\(990\) 0 0
\(991\) 2.85159 4.93909i 0.0905837 0.156895i −0.817173 0.576392i \(-0.804460\pi\)
0.907757 + 0.419497i \(0.137793\pi\)
\(992\) 16.4895 28.5607i 0.523543 0.906803i
\(993\) 0 0
\(994\) −40.0084 + 49.2728i −1.26899 + 1.56284i
\(995\) −6.34341 + 10.9871i −0.201100 + 0.348315i
\(996\) 0 0
\(997\) 31.3797 0.993804 0.496902 0.867807i \(-0.334471\pi\)
0.496902 + 0.867807i \(0.334471\pi\)
\(998\) 6.41189 11.1057i 0.202965 0.351545i
\(999\) 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 567.2.g.j.109.4 8
3.2 odd 2 567.2.g.k.109.1 8
7.2 even 3 567.2.h.k.352.1 8
9.2 odd 6 567.2.h.j.298.4 8
9.4 even 3 567.2.e.c.487.4 yes 8
9.5 odd 6 567.2.e.d.487.1 yes 8
9.7 even 3 567.2.h.k.298.1 8
21.2 odd 6 567.2.h.j.352.4 8
63.2 odd 6 567.2.g.k.541.1 8
63.4 even 3 3969.2.a.x.1.1 4
63.16 even 3 inner 567.2.g.j.541.4 8
63.23 odd 6 567.2.e.d.163.1 yes 8
63.31 odd 6 3969.2.a.w.1.1 4
63.32 odd 6 3969.2.a.s.1.4 4
63.58 even 3 567.2.e.c.163.4 8
63.59 even 6 3969.2.a.t.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
567.2.e.c.163.4 8 63.58 even 3
567.2.e.c.487.4 yes 8 9.4 even 3
567.2.e.d.163.1 yes 8 63.23 odd 6
567.2.e.d.487.1 yes 8 9.5 odd 6
567.2.g.j.109.4 8 1.1 even 1 trivial
567.2.g.j.541.4 8 63.16 even 3 inner
567.2.g.k.109.1 8 3.2 odd 2
567.2.g.k.541.1 8 63.2 odd 6
567.2.h.j.298.4 8 9.2 odd 6
567.2.h.j.352.4 8 21.2 odd 6
567.2.h.k.298.1 8 9.7 even 3
567.2.h.k.352.1 8 7.2 even 3
3969.2.a.s.1.4 4 63.32 odd 6
3969.2.a.t.1.4 4 63.59 even 6
3969.2.a.w.1.1 4 63.31 odd 6
3969.2.a.x.1.1 4 63.4 even 3