Properties

Label 567.2.e.g.487.7
Level $567$
Weight $2$
Character 567.487
Analytic conductor $4.528$
Analytic rank $0$
Dimension $16$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(163,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.163");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4x^{14} + 14x^{12} - 39x^{10} + 77x^{8} - 156x^{6} + 224x^{4} - 256x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 487.7
Root \(1.41264 + 0.0667052i\) of defining polynomial
Character \(\chi\) \(=\) 567.487
Dual form 567.2.e.g.163.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.764088 + 1.32344i) q^{2} +(-0.167661 + 0.290398i) q^{4} +(1.41264 + 2.44676i) q^{5} +(1.65876 + 2.06119i) q^{7} +2.54392 q^{8} +O(q^{10})\) \(q+(0.764088 + 1.32344i) q^{2} +(-0.167661 + 0.290398i) q^{4} +(1.41264 + 2.44676i) q^{5} +(1.65876 + 2.06119i) q^{7} +2.54392 q^{8} +(-2.15876 + 3.73909i) q^{10} +(1.81857 - 3.14986i) q^{11} -5.62908 q^{13} +(-1.46042 + 3.77020i) q^{14} +(2.27910 + 3.94752i) q^{16} +(1.60110 - 2.77319i) q^{17} +(-2.03544 - 3.52548i) q^{19} -0.947380 q^{20} +5.55820 q^{22} +(2.35159 + 4.07307i) q^{23} +(-1.49110 + 2.58266i) q^{25} +(-4.30111 - 7.44975i) q^{26} +(-0.876676 + 0.136119i) q^{28} -4.32626 q^{29} +(-1.79099 + 3.10208i) q^{31} +(-0.938949 + 1.62631i) q^{32} +4.89353 q^{34} +(-2.70001 + 6.97032i) q^{35} +(2.15578 + 3.73392i) q^{37} +(3.11051 - 5.38756i) q^{38} +(3.59364 + 6.22437i) q^{40} -3.15192 q^{41} -9.19325 q^{43} +(0.609809 + 1.05622i) q^{44} +(-3.59364 + 6.22437i) q^{46} +(2.42321 + 4.19713i) q^{47} +(-1.49702 + 6.83805i) q^{49} -4.55733 q^{50} +(0.943779 - 1.63467i) q^{52} +(7.06707 - 12.2405i) q^{53} +10.2760 q^{55} +(4.21976 + 5.24351i) q^{56} +(-3.30564 - 5.72554i) q^{58} +(0.750489 - 1.29988i) q^{59} +(-6.60254 - 11.4359i) q^{61} -5.47388 q^{62} +6.24665 q^{64} +(-7.95186 - 13.7730i) q^{65} +(6.34108 - 10.9831i) q^{67} +(0.536885 + 0.929913i) q^{68} +(-11.2878 + 1.75263i) q^{70} +2.91413 q^{71} +(-1.46456 + 2.53670i) q^{73} +(-3.29441 + 5.70608i) q^{74} +1.36506 q^{76} +(9.50905 - 1.47644i) q^{77} +(-0.446763 - 0.773817i) q^{79} +(-6.43910 + 11.1528i) q^{80} +(-2.40834 - 4.17137i) q^{82} -8.04863 q^{83} +9.04711 q^{85} +(-7.02446 - 12.1667i) q^{86} +(4.62631 - 8.01300i) q^{88} +(2.82863 + 4.89934i) q^{89} +(-9.33731 - 11.6026i) q^{91} -1.57708 q^{92} +(-3.70310 + 6.41396i) q^{94} +(5.75068 - 9.96047i) q^{95} +5.13578 q^{97} +(-10.1936 + 3.24366i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 6 q^{4} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 6 q^{4} + 6 q^{7} - 14 q^{10} + 12 q^{13} - 6 q^{16} - 24 q^{19} + 4 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} - 36 q^{40} + 20 q^{43} + 36 q^{46} - 14 q^{49} - 34 q^{52} + 8 q^{55} + 22 q^{58} - 36 q^{61} + 76 q^{64} + 18 q^{67} - 58 q^{70} - 32 q^{73} + 116 q^{76} + 32 q^{79} + 2 q^{82} + 60 q^{85} + 72 q^{88} - 22 q^{91} - 54 q^{94} + 28 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.764088 + 1.32344i 0.540292 + 0.935813i 0.998887 + 0.0471677i \(0.0150195\pi\)
−0.458595 + 0.888645i \(0.651647\pi\)
\(3\) 0 0
\(4\) −0.167661 + 0.290398i −0.0838307 + 0.145199i
\(5\) 1.41264 + 2.44676i 0.631752 + 1.09423i 0.987193 + 0.159527i \(0.0509971\pi\)
−0.355442 + 0.934698i \(0.615670\pi\)
\(6\) 0 0
\(7\) 1.65876 + 2.06119i 0.626953 + 0.779057i
\(8\) 2.54392 0.899412
\(9\) 0 0
\(10\) −2.15876 + 3.73909i −0.682661 + 1.18240i
\(11\) 1.81857 3.14986i 0.548321 0.949719i −0.450069 0.892994i \(-0.648601\pi\)
0.998390 0.0567257i \(-0.0180660\pi\)
\(12\) 0 0
\(13\) −5.62908 −1.56123 −0.780613 0.625015i \(-0.785093\pi\)
−0.780613 + 0.625015i \(0.785093\pi\)
\(14\) −1.46042 + 3.77020i −0.390314 + 1.00763i
\(15\) 0 0
\(16\) 2.27910 + 3.94752i 0.569776 + 0.986880i
\(17\) 1.60110 2.77319i 0.388324 0.672597i −0.603900 0.797060i \(-0.706388\pi\)
0.992224 + 0.124463i \(0.0397209\pi\)
\(18\) 0 0
\(19\) −2.03544 3.52548i −0.466962 0.808801i 0.532326 0.846539i \(-0.321318\pi\)
−0.999288 + 0.0377382i \(0.987985\pi\)
\(20\) −0.947380 −0.211841
\(21\) 0 0
\(22\) 5.55820 1.18501
\(23\) 2.35159 + 4.07307i 0.490340 + 0.849294i 0.999938 0.0111185i \(-0.00353920\pi\)
−0.509598 + 0.860413i \(0.670206\pi\)
\(24\) 0 0
\(25\) −1.49110 + 2.58266i −0.298220 + 0.516532i
\(26\) −4.30111 7.44975i −0.843518 1.46102i
\(27\) 0 0
\(28\) −0.876676 + 0.136119i −0.165676 + 0.0257241i
\(29\) −4.32626 −0.803366 −0.401683 0.915779i \(-0.631575\pi\)
−0.401683 + 0.915779i \(0.631575\pi\)
\(30\) 0 0
\(31\) −1.79099 + 3.10208i −0.321670 + 0.557150i −0.980833 0.194851i \(-0.937578\pi\)
0.659162 + 0.752001i \(0.270911\pi\)
\(32\) −0.938949 + 1.62631i −0.165984 + 0.287493i
\(33\) 0 0
\(34\) 4.89353 0.839233
\(35\) −2.70001 + 6.97032i −0.456386 + 1.17820i
\(36\) 0 0
\(37\) 2.15578 + 3.73392i 0.354408 + 0.613852i 0.987016 0.160619i \(-0.0513492\pi\)
−0.632609 + 0.774472i \(0.718016\pi\)
\(38\) 3.11051 5.38756i 0.504591 0.873977i
\(39\) 0 0
\(40\) 3.59364 + 6.22437i 0.568205 + 0.984159i
\(41\) −3.15192 −0.492246 −0.246123 0.969239i \(-0.579157\pi\)
−0.246123 + 0.969239i \(0.579157\pi\)
\(42\) 0 0
\(43\) −9.19325 −1.40196 −0.700979 0.713182i \(-0.747253\pi\)
−0.700979 + 0.713182i \(0.747253\pi\)
\(44\) 0.609809 + 1.05622i 0.0919322 + 0.159231i
\(45\) 0 0
\(46\) −3.59364 + 6.22437i −0.529854 + 0.917733i
\(47\) 2.42321 + 4.19713i 0.353462 + 0.612215i 0.986854 0.161617i \(-0.0516710\pi\)
−0.633391 + 0.773832i \(0.718338\pi\)
\(48\) 0 0
\(49\) −1.49702 + 6.83805i −0.213859 + 0.976864i
\(50\) −4.55733 −0.644504
\(51\) 0 0
\(52\) 0.943779 1.63467i 0.130879 0.226688i
\(53\) 7.06707 12.2405i 0.970736 1.68136i 0.277395 0.960756i \(-0.410529\pi\)
0.693342 0.720609i \(-0.256138\pi\)
\(54\) 0 0
\(55\) 10.2760 1.38561
\(56\) 4.21976 + 5.24351i 0.563889 + 0.700693i
\(57\) 0 0
\(58\) −3.30564 5.72554i −0.434052 0.751800i
\(59\) 0.750489 1.29988i 0.0977053 0.169231i −0.813029 0.582223i \(-0.802183\pi\)
0.910734 + 0.412992i \(0.135516\pi\)
\(60\) 0 0
\(61\) −6.60254 11.4359i −0.845369 1.46422i −0.885301 0.465019i \(-0.846047\pi\)
0.0399317 0.999202i \(-0.487286\pi\)
\(62\) −5.47388 −0.695184
\(63\) 0 0
\(64\) 6.24665 0.780831
\(65\) −7.95186 13.7730i −0.986307 1.70833i
\(66\) 0 0
\(67\) 6.34108 10.9831i 0.774686 1.34180i −0.160285 0.987071i \(-0.551241\pi\)
0.934971 0.354725i \(-0.115425\pi\)
\(68\) 0.536885 + 0.929913i 0.0651069 + 0.112768i
\(69\) 0 0
\(70\) −11.2878 + 1.75263i −1.34916 + 0.209480i
\(71\) 2.91413 0.345844 0.172922 0.984936i \(-0.444679\pi\)
0.172922 + 0.984936i \(0.444679\pi\)
\(72\) 0 0
\(73\) −1.46456 + 2.53670i −0.171414 + 0.296898i −0.938914 0.344151i \(-0.888167\pi\)
0.767500 + 0.641048i \(0.221500\pi\)
\(74\) −3.29441 + 5.70608i −0.382967 + 0.663319i
\(75\) 0 0
\(76\) 1.36506 0.156583
\(77\) 9.50905 1.47644i 1.08366 0.168257i
\(78\) 0 0
\(79\) −0.446763 0.773817i −0.0502648 0.0870612i 0.839798 0.542899i \(-0.182673\pi\)
−0.890063 + 0.455837i \(0.849340\pi\)
\(80\) −6.43910 + 11.1528i −0.719913 + 1.24693i
\(81\) 0 0
\(82\) −2.40834 4.17137i −0.265957 0.460651i
\(83\) −8.04863 −0.883452 −0.441726 0.897150i \(-0.645634\pi\)
−0.441726 + 0.897150i \(0.645634\pi\)
\(84\) 0 0
\(85\) 9.04711 0.981297
\(86\) −7.02446 12.1667i −0.757467 1.31197i
\(87\) 0 0
\(88\) 4.62631 8.01300i 0.493166 0.854189i
\(89\) 2.82863 + 4.89934i 0.299835 + 0.519329i 0.976098 0.217331i \(-0.0697352\pi\)
−0.676263 + 0.736660i \(0.736402\pi\)
\(90\) 0 0
\(91\) −9.33731 11.6026i −0.978816 1.21628i
\(92\) −1.57708 −0.164422
\(93\) 0 0
\(94\) −3.70310 + 6.41396i −0.381946 + 0.661549i
\(95\) 5.75068 9.96047i 0.590007 1.02192i
\(96\) 0 0
\(97\) 5.13578 0.521460 0.260730 0.965412i \(-0.416037\pi\)
0.260730 + 0.965412i \(0.416037\pi\)
\(98\) −10.1936 + 3.24366i −1.02971 + 0.327660i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 1.26223 2.18625i 0.125597 0.217540i −0.796369 0.604811i \(-0.793249\pi\)
0.921966 + 0.387271i \(0.126582\pi\)
\(102\) 0 0
\(103\) −4.92321 8.52725i −0.485098 0.840215i 0.514755 0.857337i \(-0.327883\pi\)
−0.999853 + 0.0171225i \(0.994549\pi\)
\(104\) −14.3199 −1.40418
\(105\) 0 0
\(106\) 21.5995 2.09792
\(107\) 1.35126 + 2.34045i 0.130631 + 0.226260i 0.923920 0.382586i \(-0.124966\pi\)
−0.793289 + 0.608845i \(0.791633\pi\)
\(108\) 0 0
\(109\) 4.52873 7.84400i 0.433774 0.751319i −0.563421 0.826170i \(-0.690515\pi\)
0.997195 + 0.0748515i \(0.0238483\pi\)
\(110\) 7.85174 + 13.5996i 0.748634 + 1.29667i
\(111\) 0 0
\(112\) −4.35611 + 11.2457i −0.411613 + 1.06262i
\(113\) −0.465776 −0.0438165 −0.0219082 0.999760i \(-0.506974\pi\)
−0.0219082 + 0.999760i \(0.506974\pi\)
\(114\) 0 0
\(115\) −6.64389 + 11.5076i −0.619546 + 1.07309i
\(116\) 0.725346 1.25634i 0.0673467 0.116648i
\(117\) 0 0
\(118\) 2.29376 0.211158
\(119\) 8.37191 1.29988i 0.767452 0.119160i
\(120\) 0 0
\(121\) −1.11442 1.93024i −0.101311 0.175476i
\(122\) 10.0898 17.4761i 0.913492 1.58221i
\(123\) 0 0
\(124\) −0.600558 1.04020i −0.0539317 0.0934125i
\(125\) 5.70084 0.509899
\(126\) 0 0
\(127\) −15.7574 −1.39825 −0.699123 0.715002i \(-0.746426\pi\)
−0.699123 + 0.715002i \(0.746426\pi\)
\(128\) 6.65089 + 11.5197i 0.587861 + 1.01821i
\(129\) 0 0
\(130\) 12.1518 21.0476i 1.06579 1.84600i
\(131\) 6.07396 + 10.5204i 0.530685 + 0.919173i 0.999359 + 0.0358017i \(0.0113985\pi\)
−0.468674 + 0.883371i \(0.655268\pi\)
\(132\) 0 0
\(133\) 3.89038 10.0434i 0.337339 0.870870i
\(134\) 19.3806 1.67423
\(135\) 0 0
\(136\) 4.07307 7.05477i 0.349263 0.604941i
\(137\) 1.08169 1.87353i 0.0924146 0.160067i −0.816112 0.577894i \(-0.803875\pi\)
0.908527 + 0.417827i \(0.137208\pi\)
\(138\) 0 0
\(139\) −21.4514 −1.81949 −0.909743 0.415173i \(-0.863721\pi\)
−0.909743 + 0.415173i \(0.863721\pi\)
\(140\) −1.57148 1.95273i −0.132814 0.165036i
\(141\) 0 0
\(142\) 2.22665 + 3.85668i 0.186857 + 0.323645i
\(143\) −10.2369 + 17.7308i −0.856053 + 1.48273i
\(144\) 0 0
\(145\) −6.11144 10.5853i −0.507528 0.879063i
\(146\) −4.47622 −0.370454
\(147\) 0 0
\(148\) −1.44576 −0.118841
\(149\) −5.54862 9.61049i −0.454561 0.787322i 0.544102 0.839019i \(-0.316870\pi\)
−0.998663 + 0.0516967i \(0.983537\pi\)
\(150\) 0 0
\(151\) −1.04355 + 1.80748i −0.0849228 + 0.147091i −0.905358 0.424649i \(-0.860398\pi\)
0.820436 + 0.571739i \(0.193731\pi\)
\(152\) −5.17799 8.96855i −0.419991 0.727445i
\(153\) 0 0
\(154\) 9.21974 + 11.4565i 0.742948 + 0.923193i
\(155\) −10.1201 −0.812863
\(156\) 0 0
\(157\) 10.8077 18.7194i 0.862547 1.49397i −0.00691621 0.999976i \(-0.502202\pi\)
0.869463 0.493998i \(-0.164465\pi\)
\(158\) 0.682733 1.18253i 0.0543153 0.0940769i
\(159\) 0 0
\(160\) −5.30559 −0.419444
\(161\) −4.49465 + 11.6033i −0.354228 + 0.914471i
\(162\) 0 0
\(163\) 4.69122 + 8.12543i 0.367444 + 0.636432i 0.989165 0.146807i \(-0.0468995\pi\)
−0.621721 + 0.783239i \(0.713566\pi\)
\(164\) 0.528454 0.915310i 0.0412654 0.0714737i
\(165\) 0 0
\(166\) −6.14986 10.6519i −0.477322 0.826746i
\(167\) 17.4047 1.34682 0.673408 0.739271i \(-0.264830\pi\)
0.673408 + 0.739271i \(0.264830\pi\)
\(168\) 0 0
\(169\) 18.6865 1.43743
\(170\) 6.91279 + 11.9733i 0.530187 + 0.918310i
\(171\) 0 0
\(172\) 1.54135 2.66970i 0.117527 0.203563i
\(173\) 10.7738 + 18.6607i 0.819116 + 1.41875i 0.906334 + 0.422561i \(0.138869\pi\)
−0.0872187 + 0.996189i \(0.527798\pi\)
\(174\) 0 0
\(175\) −7.79674 + 1.21058i −0.589378 + 0.0915112i
\(176\) 16.5789 1.24968
\(177\) 0 0
\(178\) −4.32265 + 7.48705i −0.323996 + 0.561178i
\(179\) −2.82863 + 4.89934i −0.211422 + 0.366194i −0.952160 0.305601i \(-0.901143\pi\)
0.740738 + 0.671794i \(0.234476\pi\)
\(180\) 0 0
\(181\) 1.12427 0.0835664 0.0417832 0.999127i \(-0.486696\pi\)
0.0417832 + 0.999127i \(0.486696\pi\)
\(182\) 8.22083 21.2228i 0.609368 1.57314i
\(183\) 0 0
\(184\) 5.98225 + 10.3616i 0.441018 + 0.763865i
\(185\) −6.09067 + 10.5494i −0.447795 + 0.775604i
\(186\) 0 0
\(187\) −5.82344 10.0865i −0.425852 0.737597i
\(188\) −1.62512 −0.118524
\(189\) 0 0
\(190\) 17.5761 1.27510
\(191\) −1.96950 3.41127i −0.142508 0.246831i 0.785932 0.618312i \(-0.212183\pi\)
−0.928440 + 0.371481i \(0.878850\pi\)
\(192\) 0 0
\(193\) −9.04339 + 15.6636i −0.650957 + 1.12749i 0.331933 + 0.943303i \(0.392299\pi\)
−0.982891 + 0.184189i \(0.941034\pi\)
\(194\) 3.92419 + 6.79690i 0.281741 + 0.487989i
\(195\) 0 0
\(196\) −1.73476 1.58121i −0.123912 0.112943i
\(197\) 25.4842 1.81567 0.907836 0.419326i \(-0.137734\pi\)
0.907836 + 0.419326i \(0.137734\pi\)
\(198\) 0 0
\(199\) −6.31454 + 10.9371i −0.447626 + 0.775311i −0.998231 0.0594551i \(-0.981064\pi\)
0.550605 + 0.834766i \(0.314397\pi\)
\(200\) −3.79324 + 6.57009i −0.268223 + 0.464575i
\(201\) 0 0
\(202\) 3.85782 0.271436
\(203\) −7.17623 8.91724i −0.503673 0.625868i
\(204\) 0 0
\(205\) −4.45252 7.71199i −0.310977 0.538629i
\(206\) 7.52353 13.0311i 0.524189 0.907922i
\(207\) 0 0
\(208\) −12.8292 22.2209i −0.889548 1.54074i
\(209\) −14.8064 −1.02418
\(210\) 0 0
\(211\) 2.31156 0.159134 0.0795670 0.996830i \(-0.474646\pi\)
0.0795670 + 0.996830i \(0.474646\pi\)
\(212\) 2.36975 + 4.10452i 0.162755 + 0.281900i
\(213\) 0 0
\(214\) −2.06496 + 3.57662i −0.141158 + 0.244493i
\(215\) −12.9868 22.4937i −0.885689 1.53406i
\(216\) 0 0
\(217\) −9.36479 + 1.45405i −0.635724 + 0.0987071i
\(218\) 13.8414 0.937458
\(219\) 0 0
\(220\) −1.72288 + 2.98412i −0.116157 + 0.201189i
\(221\) −9.01272 + 15.6105i −0.606261 + 1.05008i
\(222\) 0 0
\(223\) 9.29962 0.622749 0.311374 0.950287i \(-0.399211\pi\)
0.311374 + 0.950287i \(0.399211\pi\)
\(224\) −4.90963 + 0.762304i −0.328038 + 0.0509336i
\(225\) 0 0
\(226\) −0.355894 0.616426i −0.0236737 0.0410040i
\(227\) 0.964092 1.66986i 0.0639890 0.110832i −0.832256 0.554391i \(-0.812951\pi\)
0.896245 + 0.443559i \(0.146284\pi\)
\(228\) 0 0
\(229\) −1.67059 2.89355i −0.110396 0.191211i 0.805534 0.592549i \(-0.201879\pi\)
−0.915930 + 0.401338i \(0.868545\pi\)
\(230\) −20.3061 −1.33894
\(231\) 0 0
\(232\) −11.0057 −0.722556
\(233\) −10.5758 18.3178i −0.692842 1.20004i −0.970903 0.239474i \(-0.923025\pi\)
0.278061 0.960563i \(-0.410308\pi\)
\(234\) 0 0
\(235\) −6.84626 + 11.8581i −0.446601 + 0.773535i
\(236\) 0.251656 + 0.435881i 0.0163814 + 0.0283734i
\(237\) 0 0
\(238\) 8.11720 + 10.0865i 0.526160 + 0.653810i
\(239\) −24.1151 −1.55987 −0.779937 0.625858i \(-0.784749\pi\)
−0.779937 + 0.625858i \(0.784749\pi\)
\(240\) 0 0
\(241\) −4.61720 + 7.99722i −0.297420 + 0.515146i −0.975545 0.219800i \(-0.929459\pi\)
0.678125 + 0.734947i \(0.262793\pi\)
\(242\) 1.70304 2.94975i 0.109475 0.189617i
\(243\) 0 0
\(244\) 4.42796 0.283471
\(245\) −18.8458 + 5.99686i −1.20402 + 0.383125i
\(246\) 0 0
\(247\) 11.4576 + 19.8452i 0.729033 + 1.26272i
\(248\) −4.55612 + 7.89144i −0.289314 + 0.501107i
\(249\) 0 0
\(250\) 4.35595 + 7.54472i 0.275494 + 0.477170i
\(251\) −18.5790 −1.17270 −0.586349 0.810058i \(-0.699435\pi\)
−0.586349 + 0.810058i \(0.699435\pi\)
\(252\) 0 0
\(253\) 17.1062 1.07545
\(254\) −12.0401 20.8540i −0.755461 1.30850i
\(255\) 0 0
\(256\) −3.91708 + 6.78458i −0.244818 + 0.424037i
\(257\) −5.10987 8.85056i −0.318745 0.552083i 0.661481 0.749962i \(-0.269928\pi\)
−0.980226 + 0.197879i \(0.936595\pi\)
\(258\) 0 0
\(259\) −4.12039 + 10.6372i −0.256029 + 0.660960i
\(260\) 5.33288 0.330731
\(261\) 0 0
\(262\) −9.28209 + 16.0770i −0.573449 + 0.993243i
\(263\) 4.56887 7.91352i 0.281729 0.487969i −0.690082 0.723731i \(-0.742425\pi\)
0.971811 + 0.235763i \(0.0757588\pi\)
\(264\) 0 0
\(265\) 39.9329 2.45306
\(266\) 16.2644 2.52533i 0.997233 0.154838i
\(267\) 0 0
\(268\) 2.12631 + 3.68287i 0.129885 + 0.224967i
\(269\) −11.4606 + 19.8504i −0.698767 + 1.21030i 0.270127 + 0.962825i \(0.412934\pi\)
−0.968894 + 0.247475i \(0.920399\pi\)
\(270\) 0 0
\(271\) 4.65781 + 8.06757i 0.282942 + 0.490070i 0.972108 0.234533i \(-0.0753562\pi\)
−0.689166 + 0.724604i \(0.742023\pi\)
\(272\) 14.5963 0.885030
\(273\) 0 0
\(274\) 3.30601 0.199723
\(275\) 5.42336 + 9.39353i 0.327041 + 0.566451i
\(276\) 0 0
\(277\) −0.0916589 + 0.158758i −0.00550725 + 0.00953884i −0.868766 0.495223i \(-0.835086\pi\)
0.863259 + 0.504762i \(0.168420\pi\)
\(278\) −16.3908 28.3896i −0.983053 1.70270i
\(279\) 0 0
\(280\) −6.86862 + 17.7319i −0.410479 + 1.05969i
\(281\) −16.2019 −0.966527 −0.483263 0.875475i \(-0.660549\pi\)
−0.483263 + 0.875475i \(0.660549\pi\)
\(282\) 0 0
\(283\) −10.3492 + 17.9253i −0.615195 + 1.06555i 0.375155 + 0.926962i \(0.377590\pi\)
−0.990350 + 0.138588i \(0.955744\pi\)
\(284\) −0.488588 + 0.846258i −0.0289923 + 0.0502162i
\(285\) 0 0
\(286\) −31.2876 −1.85007
\(287\) −5.22828 6.49670i −0.308615 0.383488i
\(288\) 0 0
\(289\) 3.37296 + 5.84213i 0.198409 + 0.343655i
\(290\) 9.33936 16.1762i 0.548426 0.949902i
\(291\) 0 0
\(292\) −0.491101 0.850612i −0.0287395 0.0497783i
\(293\) 16.0234 0.936097 0.468049 0.883703i \(-0.344957\pi\)
0.468049 + 0.883703i \(0.344957\pi\)
\(294\) 0 0
\(295\) 4.24068 0.246902
\(296\) 5.48413 + 9.49879i 0.318758 + 0.552106i
\(297\) 0 0
\(298\) 8.47927 14.6865i 0.491191 0.850768i
\(299\) −13.2373 22.9276i −0.765532 1.32594i
\(300\) 0 0
\(301\) −15.2494 18.9490i −0.878962 1.09221i
\(302\) −3.18945 −0.183532
\(303\) 0 0
\(304\) 9.27794 16.0699i 0.532127 0.921670i
\(305\) 18.6540 32.3097i 1.06813 1.85005i
\(306\) 0 0
\(307\) −5.32307 −0.303804 −0.151902 0.988396i \(-0.548540\pi\)
−0.151902 + 0.988396i \(0.548540\pi\)
\(308\) −1.16554 + 3.00895i −0.0664130 + 0.171451i
\(309\) 0 0
\(310\) −7.73262 13.3933i −0.439183 0.760688i
\(311\) −9.21297 + 15.9573i −0.522420 + 0.904857i 0.477240 + 0.878773i \(0.341637\pi\)
−0.999660 + 0.0260843i \(0.991696\pi\)
\(312\) 0 0
\(313\) −2.32344 4.02432i −0.131329 0.227468i 0.792860 0.609403i \(-0.208591\pi\)
−0.924189 + 0.381936i \(0.875258\pi\)
\(314\) 33.0321 1.86411
\(315\) 0 0
\(316\) 0.299620 0.0168549
\(317\) 5.24006 + 9.07606i 0.294311 + 0.509762i 0.974824 0.222974i \(-0.0715764\pi\)
−0.680513 + 0.732736i \(0.738243\pi\)
\(318\) 0 0
\(319\) −7.86762 + 13.6271i −0.440502 + 0.762972i
\(320\) 8.82426 + 15.2841i 0.493291 + 0.854405i
\(321\) 0 0
\(322\) −18.7906 + 2.91757i −1.04716 + 0.162590i
\(323\) −13.0358 −0.725329
\(324\) 0 0
\(325\) 8.39353 14.5380i 0.465589 0.806424i
\(326\) −7.16901 + 12.4171i −0.397054 + 0.687719i
\(327\) 0 0
\(328\) −8.01822 −0.442732
\(329\) −4.63155 + 11.9568i −0.255346 + 0.659197i
\(330\) 0 0
\(331\) −6.42677 11.1315i −0.353247 0.611842i 0.633569 0.773686i \(-0.281589\pi\)
−0.986816 + 0.161844i \(0.948256\pi\)
\(332\) 1.34944 2.33731i 0.0740604 0.128276i
\(333\) 0 0
\(334\) 13.2987 + 23.0341i 0.727674 + 1.26037i
\(335\) 35.8306 1.95764
\(336\) 0 0
\(337\) 7.29218 0.397230 0.198615 0.980078i \(-0.436356\pi\)
0.198615 + 0.980078i \(0.436356\pi\)
\(338\) 14.2782 + 24.7305i 0.776630 + 1.34516i
\(339\) 0 0
\(340\) −1.51685 + 2.62726i −0.0822628 + 0.142483i
\(341\) 6.51408 + 11.2827i 0.352757 + 0.610993i
\(342\) 0 0
\(343\) −16.5777 + 8.25707i −0.895113 + 0.445840i
\(344\) −23.3869 −1.26094
\(345\) 0 0
\(346\) −16.4642 + 28.5169i −0.885123 + 1.53308i
\(347\) −8.76942 + 15.1891i −0.470767 + 0.815392i −0.999441 0.0334327i \(-0.989356\pi\)
0.528674 + 0.848825i \(0.322689\pi\)
\(348\) 0 0
\(349\) 21.0160 1.12496 0.562481 0.826810i \(-0.309847\pi\)
0.562481 + 0.826810i \(0.309847\pi\)
\(350\) −7.55953 9.39353i −0.404074 0.502105i
\(351\) 0 0
\(352\) 3.41510 + 5.91512i 0.182025 + 0.315277i
\(353\) −2.52669 + 4.37636i −0.134482 + 0.232930i −0.925400 0.378993i \(-0.876270\pi\)
0.790917 + 0.611923i \(0.209604\pi\)
\(354\) 0 0
\(355\) 4.11662 + 7.13019i 0.218487 + 0.378431i
\(356\) −1.89701 −0.100541
\(357\) 0 0
\(358\) −8.64530 −0.456918
\(359\) 7.23806 + 12.5367i 0.382010 + 0.661661i 0.991349 0.131249i \(-0.0418986\pi\)
−0.609339 + 0.792910i \(0.708565\pi\)
\(360\) 0 0
\(361\) 1.21398 2.10268i 0.0638938 0.110667i
\(362\) 0.859042 + 1.48791i 0.0451503 + 0.0782026i
\(363\) 0 0
\(364\) 4.93488 0.766226i 0.258658 0.0401611i
\(365\) −8.27559 −0.433164
\(366\) 0 0
\(367\) −7.46142 + 12.9236i −0.389483 + 0.674604i −0.992380 0.123215i \(-0.960680\pi\)
0.602897 + 0.797819i \(0.294013\pi\)
\(368\) −10.7190 + 18.5659i −0.558768 + 0.967814i
\(369\) 0 0
\(370\) −18.6152 −0.967761
\(371\) 36.9526 5.73754i 1.91849 0.297878i
\(372\) 0 0
\(373\) −3.91054 6.77325i −0.202480 0.350705i 0.746847 0.664996i \(-0.231567\pi\)
−0.949327 + 0.314290i \(0.898233\pi\)
\(374\) 8.89924 15.4139i 0.460169 0.797036i
\(375\) 0 0
\(376\) 6.16447 + 10.6772i 0.317908 + 0.550633i
\(377\) 24.3528 1.25424
\(378\) 0 0
\(379\) 11.6097 0.596350 0.298175 0.954511i \(-0.403622\pi\)
0.298175 + 0.954511i \(0.403622\pi\)
\(380\) 1.92833 + 3.33997i 0.0989214 + 0.171337i
\(381\) 0 0
\(382\) 3.00974 5.21303i 0.153992 0.266722i
\(383\) −12.5382 21.7168i −0.640672 1.10968i −0.985283 0.170931i \(-0.945322\pi\)
0.344611 0.938746i \(-0.388011\pi\)
\(384\) 0 0
\(385\) 17.0454 + 21.1807i 0.868713 + 1.07947i
\(386\) −27.6398 −1.40683
\(387\) 0 0
\(388\) −0.861073 + 1.49142i −0.0437143 + 0.0757155i
\(389\) −11.7497 + 20.3510i −0.595732 + 1.03184i 0.397712 + 0.917510i \(0.369804\pi\)
−0.993443 + 0.114327i \(0.963529\pi\)
\(390\) 0 0
\(391\) 15.0605 0.761643
\(392\) −3.80829 + 17.3955i −0.192348 + 0.878603i
\(393\) 0 0
\(394\) 19.4721 + 33.7267i 0.980992 + 1.69913i
\(395\) 1.26223 2.18625i 0.0635098 0.110002i
\(396\) 0 0
\(397\) 9.86170 + 17.0810i 0.494945 + 0.857269i 0.999983 0.00582755i \(-0.00185498\pi\)
−0.505038 + 0.863097i \(0.668522\pi\)
\(398\) −19.2995 −0.967395
\(399\) 0 0
\(400\) −13.5935 −0.679674
\(401\) −7.18983 12.4532i −0.359043 0.621881i 0.628758 0.777601i \(-0.283564\pi\)
−0.987801 + 0.155720i \(0.950230\pi\)
\(402\) 0 0
\(403\) 10.0816 17.4618i 0.502200 0.869836i
\(404\) 0.423255 + 0.733099i 0.0210577 + 0.0364730i
\(405\) 0 0
\(406\) 6.31816 16.3109i 0.313565 0.809495i
\(407\) 15.6818 0.777317
\(408\) 0 0
\(409\) 5.78795 10.0250i 0.286196 0.495705i −0.686703 0.726938i \(-0.740943\pi\)
0.972898 + 0.231233i \(0.0742759\pi\)
\(410\) 6.80424 11.7853i 0.336037 0.582034i
\(411\) 0 0
\(412\) 3.30173 0.162664
\(413\) 3.92419 0.609299i 0.193097 0.0299816i
\(414\) 0 0
\(415\) −11.3698 19.6931i −0.558122 0.966696i
\(416\) 5.28542 9.15462i 0.259139 0.448842i
\(417\) 0 0
\(418\) −11.3134 19.5954i −0.553356 0.958440i
\(419\) 34.1721 1.66942 0.834708 0.550693i \(-0.185636\pi\)
0.834708 + 0.550693i \(0.185636\pi\)
\(420\) 0 0
\(421\) −10.2213 −0.498156 −0.249078 0.968483i \(-0.580128\pi\)
−0.249078 + 0.968483i \(0.580128\pi\)
\(422\) 1.76623 + 3.05920i 0.0859789 + 0.148920i
\(423\) 0 0
\(424\) 17.9781 31.1389i 0.873092 1.51224i
\(425\) 4.77480 + 8.27020i 0.231612 + 0.401164i
\(426\) 0 0
\(427\) 12.6196 32.5786i 0.610705 1.57659i
\(428\) −0.906215 −0.0438036
\(429\) 0 0
\(430\) 19.8460 34.3744i 0.957061 1.65768i
\(431\) 0.0380526 0.0659090i 0.00183293 0.00317472i −0.865107 0.501587i \(-0.832750\pi\)
0.866940 + 0.498412i \(0.166083\pi\)
\(432\) 0 0
\(433\) −29.2697 −1.40661 −0.703305 0.710888i \(-0.748293\pi\)
−0.703305 + 0.710888i \(0.748293\pi\)
\(434\) −9.07987 11.2827i −0.435848 0.541588i
\(435\) 0 0
\(436\) 1.51859 + 2.63027i 0.0727271 + 0.125967i
\(437\) 9.57303 16.5810i 0.457940 0.793175i
\(438\) 0 0
\(439\) 2.17263 + 3.76310i 0.103694 + 0.179603i 0.913204 0.407503i \(-0.133600\pi\)
−0.809510 + 0.587106i \(0.800267\pi\)
\(440\) 26.1412 1.24623
\(441\) 0 0
\(442\) −27.5461 −1.31023
\(443\) 10.2772 + 17.8006i 0.488284 + 0.845732i 0.999909 0.0134764i \(-0.00428979\pi\)
−0.511625 + 0.859209i \(0.670956\pi\)
\(444\) 0 0
\(445\) −7.99168 + 13.8420i −0.378842 + 0.656173i
\(446\) 7.10573 + 12.3075i 0.336466 + 0.582776i
\(447\) 0 0
\(448\) 10.3617 + 12.8755i 0.489544 + 0.608312i
\(449\) −12.4720 −0.588588 −0.294294 0.955715i \(-0.595085\pi\)
−0.294294 + 0.955715i \(0.595085\pi\)
\(450\) 0 0
\(451\) −5.73199 + 9.92810i −0.269909 + 0.467496i
\(452\) 0.0780926 0.135260i 0.00367317 0.00636211i
\(453\) 0 0
\(454\) 2.94661 0.138291
\(455\) 15.1986 39.2365i 0.712521 1.83943i
\(456\) 0 0
\(457\) 15.4674 + 26.7903i 0.723534 + 1.25320i 0.959575 + 0.281454i \(0.0908168\pi\)
−0.236041 + 0.971743i \(0.575850\pi\)
\(458\) 2.55296 4.42186i 0.119292 0.206620i
\(459\) 0 0
\(460\) −2.22785 3.85875i −0.103874 0.179915i
\(461\) 8.02281 0.373660 0.186830 0.982392i \(-0.440179\pi\)
0.186830 + 0.982392i \(0.440179\pi\)
\(462\) 0 0
\(463\) −16.8223 −0.781800 −0.390900 0.920433i \(-0.627836\pi\)
−0.390900 + 0.920433i \(0.627836\pi\)
\(464\) −9.85998 17.0780i −0.457738 0.792826i
\(465\) 0 0
\(466\) 16.1616 27.9928i 0.748674 1.29674i
\(467\) −0.480399 0.832075i −0.0222302 0.0385038i 0.854696 0.519128i \(-0.173743\pi\)
−0.876926 + 0.480625i \(0.840410\pi\)
\(468\) 0 0
\(469\) 33.1566 5.14813i 1.53103 0.237719i
\(470\) −20.9246 −0.965179
\(471\) 0 0
\(472\) 1.90918 3.30680i 0.0878773 0.152208i
\(473\) −16.7186 + 28.9575i −0.768723 + 1.33147i
\(474\) 0 0
\(475\) 12.1402 0.557029
\(476\) −1.02616 + 2.64913i −0.0470341 + 0.121423i
\(477\) 0 0
\(478\) −18.4260 31.9148i −0.842787 1.45975i
\(479\) −12.0645 + 20.8964i −0.551242 + 0.954779i 0.446944 + 0.894562i \(0.352512\pi\)
−0.998185 + 0.0602166i \(0.980821\pi\)
\(480\) 0 0
\(481\) −12.1350 21.0185i −0.553311 0.958362i
\(482\) −14.1118 −0.642774
\(483\) 0 0
\(484\) 0.747384 0.0339720
\(485\) 7.25501 + 12.5661i 0.329433 + 0.570595i
\(486\) 0 0
\(487\) −7.39944 + 12.8162i −0.335301 + 0.580758i −0.983543 0.180677i \(-0.942171\pi\)
0.648242 + 0.761435i \(0.275505\pi\)
\(488\) −16.7963 29.0921i −0.760335 1.31694i
\(489\) 0 0
\(490\) −22.3364 20.3592i −1.00905 0.919735i
\(491\) 6.30383 0.284488 0.142244 0.989832i \(-0.454568\pi\)
0.142244 + 0.989832i \(0.454568\pi\)
\(492\) 0 0
\(493\) −6.92677 + 11.9975i −0.311966 + 0.540341i
\(494\) −17.5093 + 30.3270i −0.787781 + 1.36448i
\(495\) 0 0
\(496\) −16.3274 −0.733120
\(497\) 4.83385 + 6.00658i 0.216828 + 0.269432i
\(498\) 0 0
\(499\) 14.2986 + 24.7658i 0.640092 + 1.10867i 0.985412 + 0.170187i \(0.0544370\pi\)
−0.345320 + 0.938485i \(0.612230\pi\)
\(500\) −0.955811 + 1.65551i −0.0427452 + 0.0740368i
\(501\) 0 0
\(502\) −14.1960 24.5882i −0.633600 1.09743i
\(503\) −35.4133 −1.57900 −0.789500 0.613750i \(-0.789660\pi\)
−0.789500 + 0.613750i \(0.789660\pi\)
\(504\) 0 0
\(505\) 7.13231 0.317384
\(506\) 13.0706 + 22.6390i 0.581060 + 1.00642i
\(507\) 0 0
\(508\) 2.64191 4.57592i 0.117216 0.203024i
\(509\) −16.2442 28.1357i −0.720010 1.24709i −0.960995 0.276565i \(-0.910804\pi\)
0.240985 0.970529i \(-0.422529\pi\)
\(510\) 0 0
\(511\) −7.65797 + 1.18903i −0.338769 + 0.0525997i
\(512\) 14.6316 0.646630
\(513\) 0 0
\(514\) 7.80878 13.5252i 0.344431 0.596571i
\(515\) 13.9094 24.0919i 0.612923 1.06161i
\(516\) 0 0
\(517\) 17.6272 0.775243
\(518\) −17.2260 + 2.67463i −0.756866 + 0.117517i
\(519\) 0 0
\(520\) −20.2289 35.0375i −0.887096 1.53650i
\(521\) 16.4909 28.5631i 0.722479 1.25137i −0.237524 0.971382i \(-0.576336\pi\)
0.960003 0.279989i \(-0.0903308\pi\)
\(522\) 0 0
\(523\) −7.13133 12.3518i −0.311831 0.540108i 0.666928 0.745123i \(-0.267609\pi\)
−0.978759 + 0.205015i \(0.934276\pi\)
\(524\) −4.07348 −0.177951
\(525\) 0 0
\(526\) 13.9641 0.608863
\(527\) 5.73509 + 9.93347i 0.249825 + 0.432709i
\(528\) 0 0
\(529\) 0.440059 0.762205i 0.0191330 0.0331393i
\(530\) 30.5122 + 52.8487i 1.32537 + 2.29560i
\(531\) 0 0
\(532\) 2.26431 + 2.81364i 0.0981701 + 0.121987i
\(533\) 17.7424 0.768508
\(534\) 0 0
\(535\) −3.81768 + 6.61242i −0.165053 + 0.285880i
\(536\) 16.1312 27.9401i 0.696762 1.20683i
\(537\) 0 0
\(538\) −35.0277 −1.51015
\(539\) 18.8165 + 17.1509i 0.810484 + 0.738742i
\(540\) 0 0
\(541\) 7.99105 + 13.8409i 0.343562 + 0.595067i 0.985091 0.172032i \(-0.0550331\pi\)
−0.641529 + 0.767098i \(0.721700\pi\)
\(542\) −7.11796 + 12.3287i −0.305743 + 0.529562i
\(543\) 0 0
\(544\) 3.00670 + 5.20776i 0.128911 + 0.223281i
\(545\) 25.5899 1.09615
\(546\) 0 0
\(547\) −32.0570 −1.37066 −0.685330 0.728233i \(-0.740342\pi\)
−0.685330 + 0.728233i \(0.740342\pi\)
\(548\) 0.362714 + 0.628238i 0.0154944 + 0.0268370i
\(549\) 0 0
\(550\) −8.28784 + 14.3550i −0.353395 + 0.612098i
\(551\) 8.80583 + 15.2521i 0.375141 + 0.649763i
\(552\) 0 0
\(553\) 0.853910 2.20444i 0.0363120 0.0937425i
\(554\) −0.280142 −0.0119021
\(555\) 0 0
\(556\) 3.59657 6.22945i 0.152529 0.264187i
\(557\) −19.6474 + 34.0302i −0.832486 + 1.44191i 0.0635754 + 0.997977i \(0.479750\pi\)
−0.896061 + 0.443931i \(0.853584\pi\)
\(558\) 0 0
\(559\) 51.7496 2.18877
\(560\) −33.6691 + 5.22771i −1.42278 + 0.220911i
\(561\) 0 0
\(562\) −12.3797 21.4423i −0.522207 0.904489i
\(563\) 17.2532 29.8834i 0.727134 1.25943i −0.230955 0.972964i \(-0.574185\pi\)
0.958089 0.286469i \(-0.0924816\pi\)
\(564\) 0 0
\(565\) −0.657973 1.13964i −0.0276811 0.0479451i
\(566\) −31.6308 −1.32954
\(567\) 0 0
\(568\) 7.41332 0.311056
\(569\) −2.14203 3.71010i −0.0897985 0.155536i 0.817627 0.575748i \(-0.195289\pi\)
−0.907426 + 0.420212i \(0.861956\pi\)
\(570\) 0 0
\(571\) −12.5798 + 21.7888i −0.526447 + 0.911833i 0.473078 + 0.881021i \(0.343143\pi\)
−0.999525 + 0.0308128i \(0.990190\pi\)
\(572\) −3.43267 5.94555i −0.143527 0.248596i
\(573\) 0 0
\(574\) 4.60312 11.8834i 0.192131 0.496002i
\(575\) −14.0258 −0.584917
\(576\) 0 0
\(577\) 22.1281 38.3271i 0.921206 1.59558i 0.123655 0.992325i \(-0.460539\pi\)
0.797552 0.603251i \(-0.206128\pi\)
\(578\) −5.15447 + 8.92781i −0.214398 + 0.371348i
\(579\) 0 0
\(580\) 4.09861 0.170186
\(581\) −13.3508 16.5898i −0.553883 0.688259i
\(582\) 0 0
\(583\) −25.7040 44.5206i −1.06455 1.84385i
\(584\) −3.72573 + 6.45315i −0.154172 + 0.267033i
\(585\) 0 0
\(586\) 12.2433 + 21.2060i 0.505766 + 0.876012i
\(587\) 13.0046 0.536757 0.268378 0.963314i \(-0.413512\pi\)
0.268378 + 0.963314i \(0.413512\pi\)
\(588\) 0 0
\(589\) 14.5818 0.600831
\(590\) 3.24025 + 5.61228i 0.133399 + 0.231054i
\(591\) 0 0
\(592\) −9.82648 + 17.0200i −0.403866 + 0.699516i
\(593\) −14.1164 24.4503i −0.579691 1.00405i −0.995515 0.0946086i \(-0.969840\pi\)
0.415824 0.909445i \(-0.363493\pi\)
\(594\) 0 0
\(595\) 15.0070 + 18.6478i 0.615227 + 0.764486i
\(596\) 3.72116 0.152425
\(597\) 0 0
\(598\) 20.2289 35.0375i 0.827221 1.43279i
\(599\) 2.49768 4.32611i 0.102052 0.176760i −0.810478 0.585769i \(-0.800792\pi\)
0.912530 + 0.409010i \(0.134126\pi\)
\(600\) 0 0
\(601\) 8.15787 0.332766 0.166383 0.986061i \(-0.446791\pi\)
0.166383 + 0.986061i \(0.446791\pi\)
\(602\) 13.4260 34.6604i 0.547204 1.41265i
\(603\) 0 0
\(604\) −0.349925 0.606089i −0.0142383 0.0246614i
\(605\) 3.14856 5.45347i 0.128007 0.221715i
\(606\) 0 0
\(607\) −8.36385 14.4866i −0.339478 0.587993i 0.644857 0.764304i \(-0.276917\pi\)
−0.984335 + 0.176310i \(0.943584\pi\)
\(608\) 7.64469 0.310033
\(609\) 0 0
\(610\) 57.0133 2.30840
\(611\) −13.6405 23.6260i −0.551834 0.955805i
\(612\) 0 0
\(613\) 8.29381 14.3653i 0.334984 0.580209i −0.648498 0.761216i \(-0.724602\pi\)
0.983482 + 0.181007i \(0.0579358\pi\)
\(614\) −4.06729 7.04476i −0.164143 0.284303i
\(615\) 0 0
\(616\) 24.1903 3.75596i 0.974654 0.151332i
\(617\) −23.7085 −0.954470 −0.477235 0.878776i \(-0.658361\pi\)
−0.477235 + 0.878776i \(0.658361\pi\)
\(618\) 0 0
\(619\) 3.91206 6.77589i 0.157239 0.272346i −0.776633 0.629953i \(-0.783074\pi\)
0.933872 + 0.357607i \(0.116407\pi\)
\(620\) 1.69674 2.93885i 0.0681429 0.118027i
\(621\) 0 0
\(622\) −28.1581 −1.12904
\(623\) −5.40644 + 13.9572i −0.216604 + 0.559183i
\(624\) 0 0
\(625\) 15.5087 + 26.8619i 0.620350 + 1.07448i
\(626\) 3.55063 6.14986i 0.141912 0.245798i
\(627\) 0 0
\(628\) 3.62406 + 6.27706i 0.144616 + 0.250482i
\(629\) 13.8065 0.550500
\(630\) 0 0
\(631\) −2.54669 −0.101382 −0.0506911 0.998714i \(-0.516142\pi\)
−0.0506911 + 0.998714i \(0.516142\pi\)
\(632\) −1.13653 1.96853i −0.0452088 0.0783039i
\(633\) 0 0
\(634\) −8.00774 + 13.8698i −0.318028 + 0.550841i
\(635\) −22.2596 38.5547i −0.883344 1.53000i
\(636\) 0 0
\(637\) 8.42682 38.4919i 0.333883 1.52511i
\(638\) −24.0462 −0.951999
\(639\) 0 0
\(640\) −18.7906 + 32.5463i −0.742764 + 1.28651i
\(641\) −5.14269 + 8.90739i −0.203124 + 0.351821i −0.949533 0.313666i \(-0.898443\pi\)
0.746409 + 0.665487i \(0.231776\pi\)
\(642\) 0 0
\(643\) −4.92126 −0.194076 −0.0970378 0.995281i \(-0.530937\pi\)
−0.0970378 + 0.995281i \(0.530937\pi\)
\(644\) −2.61600 3.25067i −0.103085 0.128094i
\(645\) 0 0
\(646\) −9.96047 17.2520i −0.391890 0.678773i
\(647\) −4.39168 + 7.60661i −0.172655 + 0.299047i −0.939347 0.342968i \(-0.888568\pi\)
0.766692 + 0.642015i \(0.221901\pi\)
\(648\) 0 0
\(649\) −2.72964 4.72787i −0.107148 0.185585i
\(650\) 25.6536 1.00622
\(651\) 0 0
\(652\) −3.14614 −0.123212
\(653\) −0.887297 1.53684i −0.0347226 0.0601414i 0.848142 0.529769i \(-0.177721\pi\)
−0.882864 + 0.469628i \(0.844388\pi\)
\(654\) 0 0
\(655\) −17.1606 + 29.7231i −0.670522 + 1.16138i
\(656\) −7.18354 12.4423i −0.280470 0.485788i
\(657\) 0 0
\(658\) −19.3630 + 3.00643i −0.754846 + 0.117203i
\(659\) 2.34367 0.0912966 0.0456483 0.998958i \(-0.485465\pi\)
0.0456483 + 0.998958i \(0.485465\pi\)
\(660\) 0 0
\(661\) 11.4547 19.8401i 0.445537 0.771692i −0.552553 0.833478i \(-0.686346\pi\)
0.998089 + 0.0617856i \(0.0196795\pi\)
\(662\) 9.82124 17.0109i 0.381713 0.661147i
\(663\) 0 0
\(664\) −20.4751 −0.794587
\(665\) 30.0694 4.66880i 1.16604 0.181048i
\(666\) 0 0
\(667\) −10.1736 17.6212i −0.393922 0.682294i
\(668\) −2.91810 + 5.05429i −0.112905 + 0.195556i
\(669\) 0 0
\(670\) 27.3778 + 47.4197i 1.05770 + 1.83198i
\(671\) −48.0288 −1.85413
\(672\) 0 0
\(673\) −29.7349 −1.14620 −0.573098 0.819487i \(-0.694259\pi\)
−0.573098 + 0.819487i \(0.694259\pi\)
\(674\) 5.57187 + 9.65076i 0.214620 + 0.371733i
\(675\) 0 0
\(676\) −3.13301 + 5.42654i −0.120500 + 0.208713i
\(677\) −12.7480 22.0802i −0.489946 0.848611i 0.509987 0.860182i \(-0.329650\pi\)
−0.999933 + 0.0115711i \(0.996317\pi\)
\(678\) 0 0
\(679\) 8.51905 + 10.5858i 0.326931 + 0.406247i
\(680\) 23.0151 0.882590
\(681\) 0 0
\(682\) −9.95466 + 17.2420i −0.381184 + 0.660230i
\(683\) −5.69293 + 9.86044i −0.217834 + 0.377299i −0.954145 0.299343i \(-0.903232\pi\)
0.736312 + 0.676643i \(0.236566\pi\)
\(684\) 0 0
\(685\) 6.11212 0.233532
\(686\) −23.5946 15.6305i −0.900845 0.596775i
\(687\) 0 0
\(688\) −20.9524 36.2906i −0.798801 1.38356i
\(689\) −39.7811 + 68.9029i −1.51554 + 2.62499i
\(690\) 0 0
\(691\) 16.1261 + 27.9313i 0.613468 + 1.06256i 0.990651 + 0.136419i \(0.0435592\pi\)
−0.377184 + 0.926138i \(0.623107\pi\)
\(692\) −7.22539 −0.274668
\(693\) 0 0
\(694\) −26.8024 −1.01741
\(695\) −30.3031 52.4865i −1.14946 1.99093i
\(696\) 0 0
\(697\) −5.04653 + 8.74085i −0.191151 + 0.331083i
\(698\) 16.0581 + 27.8134i 0.607807 + 1.05275i
\(699\) 0 0
\(700\) 0.955663 2.46713i 0.0361207 0.0932486i
\(701\) 15.6291 0.590302 0.295151 0.955451i \(-0.404630\pi\)
0.295151 + 0.955451i \(0.404630\pi\)
\(702\) 0 0
\(703\) 8.77591 15.2003i 0.330990 0.573291i
\(704\) 11.3600 19.6761i 0.428146 0.741570i
\(705\) 0 0
\(706\) −7.72246 −0.290639
\(707\) 6.60002 1.02477i 0.248219 0.0385403i
\(708\) 0 0
\(709\) 5.90824 + 10.2334i 0.221888 + 0.384322i 0.955381 0.295375i \(-0.0954446\pi\)
−0.733493 + 0.679697i \(0.762111\pi\)
\(710\) −6.29092 + 10.8962i −0.236094 + 0.408927i
\(711\) 0 0
\(712\) 7.19582 + 12.4635i 0.269675 + 0.467090i
\(713\) −16.8466 −0.630912
\(714\) 0 0
\(715\) −57.8442 −2.16325
\(716\) −0.948505 1.64286i −0.0354473 0.0613965i
\(717\) 0 0
\(718\) −11.0610 + 19.1583i −0.412794 + 0.714980i
\(719\) 25.3616 + 43.9276i 0.945830 + 1.63822i 0.754082 + 0.656781i \(0.228082\pi\)
0.191748 + 0.981444i \(0.438584\pi\)
\(720\) 0 0
\(721\) 9.40985 24.2923i 0.350441 0.904694i
\(722\) 3.71036 0.138085
\(723\) 0 0
\(724\) −0.188497 + 0.326486i −0.00700543 + 0.0121338i
\(725\) 6.45088 11.1733i 0.239580 0.414964i
\(726\) 0 0
\(727\) 2.26602 0.0840422 0.0420211 0.999117i \(-0.486620\pi\)
0.0420211 + 0.999117i \(0.486620\pi\)
\(728\) −23.7534 29.5161i −0.880358 1.09394i
\(729\) 0 0
\(730\) −6.32328 10.9522i −0.234035 0.405361i
\(731\) −14.7193 + 25.4946i −0.544414 + 0.942952i
\(732\) 0 0
\(733\) 16.8262 + 29.1439i 0.621490 + 1.07645i 0.989208 + 0.146515i \(0.0468058\pi\)
−0.367718 + 0.929937i \(0.619861\pi\)
\(734\) −22.8047 −0.841738
\(735\) 0 0
\(736\) −8.83209 −0.325555
\(737\) −23.0634 39.9471i −0.849553 1.47147i
\(738\) 0 0
\(739\) −9.80187 + 16.9773i −0.360568 + 0.624521i −0.988054 0.154106i \(-0.950750\pi\)
0.627487 + 0.778627i \(0.284084\pi\)
\(740\) −2.04234 3.53744i −0.0750780 0.130039i
\(741\) 0 0
\(742\) 35.8284 + 44.5206i 1.31530 + 1.63440i
\(743\) 48.8390 1.79173 0.895865 0.444327i \(-0.146557\pi\)
0.895865 + 0.444327i \(0.146557\pi\)
\(744\) 0 0
\(745\) 15.6764 27.1523i 0.574339 0.994784i
\(746\) 5.97599 10.3507i 0.218796 0.378967i
\(747\) 0 0
\(748\) 3.90546 0.142798
\(749\) −2.58269 + 6.66745i −0.0943696 + 0.243623i
\(750\) 0 0
\(751\) −7.91269 13.7052i −0.288738 0.500109i 0.684771 0.728759i \(-0.259902\pi\)
−0.973509 + 0.228649i \(0.926569\pi\)
\(752\) −11.0455 + 19.1314i −0.402788 + 0.697650i
\(753\) 0 0
\(754\) 18.6077 + 32.2295i 0.677653 + 1.17373i
\(755\) −5.89663 −0.214600
\(756\) 0 0
\(757\) −2.18728 −0.0794982 −0.0397491 0.999210i \(-0.512656\pi\)
−0.0397491 + 0.999210i \(0.512656\pi\)
\(758\) 8.87084 + 15.3647i 0.322203 + 0.558073i
\(759\) 0 0
\(760\) 14.6293 25.3386i 0.530660 0.919129i
\(761\) 13.8781 + 24.0376i 0.503081 + 0.871361i 0.999994 + 0.00356072i \(0.00113341\pi\)
−0.496913 + 0.867800i \(0.665533\pi\)
\(762\) 0 0
\(763\) 23.6801 3.67674i 0.857276 0.133107i
\(764\) 1.32084 0.0477861
\(765\) 0 0
\(766\) 19.1606 33.1871i 0.692300 1.19910i
\(767\) −4.22456 + 7.31715i −0.152540 + 0.264207i
\(768\) 0 0
\(769\) 10.0206 0.361352 0.180676 0.983543i \(-0.442171\pi\)
0.180676 + 0.983543i \(0.442171\pi\)
\(770\) −15.0072 + 38.7425i −0.540823 + 1.39618i
\(771\) 0 0
\(772\) −3.03245 5.25236i −0.109140 0.189037i
\(773\) 21.7596 37.6887i 0.782639 1.35557i −0.147761 0.989023i \(-0.547207\pi\)
0.930400 0.366547i \(-0.119460\pi\)
\(774\) 0 0
\(775\) −5.34108 9.25102i −0.191857 0.332306i
\(776\) 13.0650 0.469007
\(777\) 0 0
\(778\) −35.9111 −1.28748
\(779\) 6.41553 + 11.1120i 0.229860 + 0.398130i
\(780\) 0 0
\(781\) 5.29957 9.17912i 0.189633 0.328455i
\(782\) 11.5076 + 19.9317i 0.411510 + 0.712756i
\(783\) 0 0
\(784\) −30.4052 + 9.67512i −1.08590 + 0.345540i
\(785\) 61.0694 2.17966
\(786\) 0 0
\(787\) 2.91819 5.05445i 0.104022 0.180172i −0.809316 0.587373i \(-0.800162\pi\)
0.913338 + 0.407202i \(0.133495\pi\)
\(788\) −4.27271 + 7.40055i −0.152209 + 0.263634i
\(789\) 0 0
\(790\) 3.85782 0.137255
\(791\) −0.772611 0.960053i −0.0274709 0.0341355i
\(792\) 0 0
\(793\) 37.1662 + 64.3738i 1.31981 + 2.28598i
\(794\) −15.0704 + 26.1027i −0.534829 + 0.926351i
\(795\) 0 0
\(796\) −2.11741 3.66746i −0.0750496 0.129990i
\(797\) 36.5800 1.29573 0.647865 0.761755i \(-0.275662\pi\)
0.647865 + 0.761755i \(0.275662\pi\)
\(798\) 0 0
\(799\) 15.5192 0.549031
\(800\) −2.80014 4.84998i −0.0989998 0.171473i
\(801\) 0 0
\(802\) 10.9873 19.0306i 0.387976 0.671994i
\(803\) 5.32683 + 9.22634i 0.187980 + 0.325590i
\(804\) 0 0
\(805\) −34.7399 + 5.39398i −1.22442 + 0.190113i
\(806\) 30.8129 1.08534
\(807\) 0 0
\(808\) 3.21102 5.56164i 0.112963 0.195658i
\(809\) 11.0249 19.0957i 0.387616 0.671370i −0.604513 0.796596i \(-0.706632\pi\)
0.992128 + 0.125225i \(0.0399654\pi\)
\(810\) 0 0
\(811\) −12.6451 −0.444029 −0.222015 0.975043i \(-0.571263\pi\)
−0.222015 + 0.975043i \(0.571263\pi\)
\(812\) 3.79273 0.588886i 0.133099 0.0206659i
\(813\) 0 0
\(814\) 11.9823 + 20.7539i 0.419978 + 0.727423i
\(815\) −13.2540 + 22.9566i −0.464267 + 0.804134i
\(816\) 0 0
\(817\) 18.7123 + 32.4107i 0.654660 + 1.13391i
\(818\) 17.6900 0.618517
\(819\) 0 0
\(820\) 2.98606 0.104278
\(821\) 15.5479 + 26.9298i 0.542625 + 0.939855i 0.998752 + 0.0499401i \(0.0159030\pi\)
−0.456127 + 0.889915i \(0.650764\pi\)
\(822\) 0 0
\(823\) 24.4819 42.4039i 0.853385 1.47811i −0.0247505 0.999694i \(-0.507879\pi\)
0.878135 0.478412i \(-0.158788\pi\)
\(824\) −12.5242 21.6926i −0.436303 0.755699i
\(825\) 0 0
\(826\) 3.80480 + 4.72787i 0.132386 + 0.164504i
\(827\) −36.3827 −1.26515 −0.632575 0.774499i \(-0.718002\pi\)
−0.632575 + 0.774499i \(0.718002\pi\)
\(828\) 0 0
\(829\) −22.8702 + 39.6124i −0.794316 + 1.37580i 0.128957 + 0.991650i \(0.458837\pi\)
−0.923273 + 0.384145i \(0.874496\pi\)
\(830\) 17.3751 30.0945i 0.603098 1.04460i
\(831\) 0 0
\(832\) −35.1629 −1.21905
\(833\) 16.5663 + 15.0999i 0.573989 + 0.523181i
\(834\) 0 0
\(835\) 24.5866 + 42.5852i 0.850853 + 1.47372i
\(836\) 2.48246 4.29974i 0.0858576 0.148710i
\(837\) 0 0
\(838\) 26.1105 + 45.2247i 0.901972 + 1.56226i
\(839\) −25.5348 −0.881559 −0.440779 0.897615i \(-0.645298\pi\)
−0.440779 + 0.897615i \(0.645298\pi\)
\(840\) 0 0
\(841\) −10.2835 −0.354604
\(842\) −7.80998 13.5273i −0.269150 0.466181i
\(843\) 0 0
\(844\) −0.387559 + 0.671271i −0.0133403 + 0.0231061i
\(845\) 26.3974 + 45.7216i 0.908097 + 1.57287i
\(846\) 0 0
\(847\) 2.13003 5.49885i 0.0731886 0.188943i
\(848\) 64.4263 2.21241
\(849\) 0 0
\(850\) −7.29674 + 12.6383i −0.250276 + 0.433491i
\(851\) −10.1390 + 17.5613i −0.347561 + 0.601993i
\(852\) 0 0
\(853\) −1.84673 −0.0632310 −0.0316155 0.999500i \(-0.510065\pi\)
−0.0316155 + 0.999500i \(0.510065\pi\)
\(854\) 52.7583 8.19164i 1.80535 0.280312i
\(855\) 0 0
\(856\) 3.43749 + 5.95391i 0.117491 + 0.203501i
\(857\) 11.2424 19.4724i 0.384033 0.665165i −0.607601 0.794242i \(-0.707868\pi\)
0.991635 + 0.129077i \(0.0412015\pi\)
\(858\) 0 0
\(859\) 0.573807 + 0.993864i 0.0195781 + 0.0339102i 0.875648 0.482949i \(-0.160434\pi\)
−0.856070 + 0.516859i \(0.827101\pi\)
\(860\) 8.70951 0.296992
\(861\) 0 0
\(862\) 0.116302 0.00396126
\(863\) −0.897635 1.55475i −0.0305558 0.0529243i 0.850343 0.526229i \(-0.176394\pi\)
−0.880899 + 0.473304i \(0.843061\pi\)
\(864\) 0 0
\(865\) −30.4390 + 52.7218i −1.03496 + 1.79260i
\(866\) −22.3646 38.7366i −0.759980 1.31632i
\(867\) 0 0
\(868\) 1.14786 2.96330i 0.0389610 0.100581i
\(869\) −3.24989 −0.110245
\(870\) 0 0
\(871\) −35.6944 + 61.8246i −1.20946 + 2.09485i
\(872\) 11.5207 19.9545i 0.390141 0.675745i
\(873\) 0 0
\(874\) 29.2585 0.989685
\(875\) 9.45634 + 11.7505i 0.319683 + 0.397240i
\(876\) 0 0
\(877\) −4.28998 7.43047i −0.144862 0.250909i 0.784459 0.620180i \(-0.212941\pi\)
−0.929322 + 0.369271i \(0.879607\pi\)
\(878\) −3.32016 + 5.75069i −0.112050 + 0.194076i
\(879\) 0 0
\(880\) 23.4200 + 40.5646i 0.789487 + 1.36743i
\(881\) −16.5346 −0.557066 −0.278533 0.960427i \(-0.589848\pi\)
−0.278533 + 0.960427i \(0.589848\pi\)
\(882\) 0 0
\(883\) −27.4948 −0.925273 −0.462636 0.886548i \(-0.653096\pi\)
−0.462636 + 0.886548i \(0.653096\pi\)
\(884\) −3.02217 5.23455i −0.101647 0.176057i
\(885\) 0 0
\(886\) −15.7053 + 27.2025i −0.527631 + 0.913885i
\(887\) 21.7210 + 37.6218i 0.729318 + 1.26322i 0.957172 + 0.289521i \(0.0934960\pi\)
−0.227853 + 0.973695i \(0.573171\pi\)
\(888\) 0 0
\(889\) −26.1378 32.4791i −0.876634 1.08931i
\(890\) −24.4254 −0.818741
\(891\) 0 0
\(892\) −1.55919 + 2.70059i −0.0522054 + 0.0904225i
\(893\) 9.86461 17.0860i 0.330107 0.571761i
\(894\) 0 0
\(895\) −15.9834 −0.534265
\(896\) −12.7120 + 32.8172i −0.424678 + 1.09634i
\(897\) 0 0
\(898\) −9.52968 16.5059i −0.318010 0.550809i
\(899\) 7.74826 13.4204i 0.258419 0.447595i
\(900\) 0 0
\(901\) −22.6302 39.1966i −0.753920 1.30583i
\(902\) −17.5190 −0.583319
\(903\) 0 0
\(904\) −1.18490 −0.0394091
\(905\) 1.58819 + 2.75083i 0.0527932 + 0.0914406i
\(906\) 0 0
\(907\) −5.64761 + 9.78196i −0.187526 + 0.324805i −0.944425 0.328728i \(-0.893380\pi\)
0.756899 + 0.653532i \(0.226714\pi\)
\(908\) 0.323282 + 0.559941i 0.0107285 + 0.0185823i
\(909\) 0 0
\(910\) 63.5402 9.86571i 2.10634 0.327045i
\(911\) 10.0338 0.332435 0.166217 0.986089i \(-0.446845\pi\)
0.166217 + 0.986089i \(0.446845\pi\)
\(912\) 0 0
\(913\) −14.6370 + 25.3521i −0.484415 + 0.839032i
\(914\) −23.6369 + 40.9403i −0.781839 + 1.35418i
\(915\) 0 0
\(916\) 1.12038 0.0370182
\(917\) −11.6093 + 29.9705i −0.383373 + 0.989712i
\(918\) 0 0
\(919\) 0.178967 + 0.309980i 0.00590358 + 0.0102253i 0.868962 0.494879i \(-0.164787\pi\)
−0.863059 + 0.505104i \(0.831454\pi\)
\(920\) −16.9015 + 29.2743i −0.557227 + 0.965146i
\(921\) 0 0
\(922\) 6.13013 + 10.6177i 0.201885 + 0.349675i
\(923\) −16.4039 −0.539941
\(924\) 0 0
\(925\) −12.8579 −0.422766
\(926\) −12.8537 22.2633i −0.422400 0.731619i
\(927\) 0 0
\(928\) 4.06214 7.03583i 0.133346 0.230962i
\(929\) −16.7632 29.0347i −0.549983 0.952599i −0.998275 0.0587116i \(-0.981301\pi\)
0.448292 0.893887i \(-0.352033\pi\)
\(930\) 0 0
\(931\) 27.1545 8.64073i 0.889953 0.283188i
\(932\) 7.09259 0.232326
\(933\) 0 0
\(934\) 0.734134 1.27156i 0.0240216 0.0416066i
\(935\) 16.4528 28.4972i 0.538065 0.931957i
\(936\) 0 0
\(937\) 12.8772 0.420680 0.210340 0.977628i \(-0.432543\pi\)
0.210340 + 0.977628i \(0.432543\pi\)
\(938\) 32.1478 + 39.9471i 1.04966 + 1.30432i
\(939\) 0 0
\(940\) −2.29571 3.97628i −0.0748777 0.129692i
\(941\) 16.0492 27.7980i 0.523189 0.906190i −0.476447 0.879203i \(-0.658075\pi\)
0.999636 0.0269868i \(-0.00859120\pi\)
\(942\) 0 0
\(943\) −7.41201 12.8380i −0.241368 0.418062i
\(944\) 6.84176 0.222680
\(945\) 0 0
\(946\) −51.0980 −1.66134
\(947\) 8.39928 + 14.5480i 0.272940 + 0.472746i 0.969613 0.244642i \(-0.0786706\pi\)
−0.696673 + 0.717389i \(0.745337\pi\)
\(948\) 0 0
\(949\) 8.24414 14.2793i 0.267616 0.463524i
\(950\) 9.27616 + 16.0668i 0.300958 + 0.521275i
\(951\) 0 0
\(952\) 21.2975 3.30680i 0.690255 0.107174i
\(953\) 2.69574 0.0873237 0.0436619 0.999046i \(-0.486098\pi\)
0.0436619 + 0.999046i \(0.486098\pi\)
\(954\) 0 0
\(955\) 5.56438 9.63780i 0.180059 0.311872i
\(956\) 4.04316 7.00297i 0.130765 0.226492i
\(957\) 0 0
\(958\) −36.8734 −1.19133
\(959\) 5.65597 0.878187i 0.182641 0.0283581i
\(960\) 0 0
\(961\) 9.08474 + 15.7352i 0.293056 + 0.507588i
\(962\) 18.5445 32.1200i 0.597898 1.03559i
\(963\) 0 0
\(964\) −1.54825 2.68165i −0.0498658 0.0863701i
\(965\) −51.1002 −1.64497
\(966\) 0 0
\(967\) 13.6775 0.439837 0.219919 0.975518i \(-0.429421\pi\)
0.219919 + 0.975518i \(0.429421\pi\)
\(968\) −2.83501 4.91038i −0.0911206 0.157826i
\(969\) 0 0
\(970\) −11.0869 + 19.2031i −0.355980 + 0.616576i
\(971\) 21.3133 + 36.9157i 0.683977 + 1.18468i 0.973757 + 0.227589i \(0.0730843\pi\)
−0.289781 + 0.957093i \(0.593582\pi\)
\(972\) 0 0
\(973\) −35.5828 44.2155i −1.14073 1.41748i
\(974\) −22.6153 −0.724641
\(975\) 0 0
\(976\) 30.0957 52.1273i 0.963341 1.66856i
\(977\) 2.52841 4.37934i 0.0808911 0.140108i −0.822742 0.568415i \(-0.807557\pi\)
0.903633 + 0.428308i \(0.140890\pi\)
\(978\) 0 0
\(979\) 20.5763 0.657622
\(980\) 1.41824 6.47823i 0.0453041 0.206940i
\(981\) 0 0
\(982\) 4.81668 + 8.34274i 0.153707 + 0.266227i
\(983\) 16.6442 28.8286i 0.530868 0.919490i −0.468483 0.883472i \(-0.655199\pi\)
0.999351 0.0360177i \(-0.0114673\pi\)
\(984\) 0 0
\(985\) 35.9999 + 62.3537i 1.14705 + 1.98675i
\(986\) −21.1707 −0.674211
\(987\) 0 0
\(988\) −7.68402 −0.244461
\(989\) −21.6188 37.4448i −0.687436 1.19067i
\(990\) 0 0
\(991\) −16.0440 + 27.7890i −0.509653 + 0.882746i 0.490284 + 0.871563i \(0.336893\pi\)
−0.999937 + 0.0111829i \(0.996440\pi\)
\(992\) −3.36329 5.82539i −0.106785 0.184956i
\(993\) 0 0
\(994\) −4.25586 + 10.9869i −0.134988 + 0.348482i
\(995\) −35.6807 −1.13115
\(996\) 0 0
\(997\) 21.6283 37.4613i 0.684975 1.18641i −0.288470 0.957489i \(-0.593146\pi\)
0.973445 0.228922i \(-0.0735202\pi\)
\(998\) −21.8507 + 37.8466i −0.691673 + 1.19801i
\(999\) 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.e.g.487.7 yes 16
3.2 odd 2 inner 567.2.e.g.487.2 yes 16
7.2 even 3 inner 567.2.e.g.163.7 yes 16
7.3 odd 6 3969.2.a.bf.1.2 8
7.4 even 3 3969.2.a.bg.1.2 8
9.2 odd 6 567.2.g.l.109.2 16
9.4 even 3 567.2.h.l.298.2 16
9.5 odd 6 567.2.h.l.298.7 16
9.7 even 3 567.2.g.l.109.7 16
21.2 odd 6 inner 567.2.e.g.163.2 16
21.11 odd 6 3969.2.a.bg.1.7 8
21.17 even 6 3969.2.a.bf.1.7 8
63.2 odd 6 567.2.h.l.352.7 16
63.16 even 3 567.2.h.l.352.2 16
63.23 odd 6 567.2.g.l.541.2 16
63.58 even 3 567.2.g.l.541.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
567.2.e.g.163.2 16 21.2 odd 6 inner
567.2.e.g.163.7 yes 16 7.2 even 3 inner
567.2.e.g.487.2 yes 16 3.2 odd 2 inner
567.2.e.g.487.7 yes 16 1.1 even 1 trivial
567.2.g.l.109.2 16 9.2 odd 6
567.2.g.l.109.7 16 9.7 even 3
567.2.g.l.541.2 16 63.23 odd 6
567.2.g.l.541.7 16 63.58 even 3
567.2.h.l.298.2 16 9.4 even 3
567.2.h.l.298.7 16 9.5 odd 6
567.2.h.l.352.2 16 63.16 even 3
567.2.h.l.352.7 16 63.2 odd 6
3969.2.a.bf.1.2 8 7.3 odd 6
3969.2.a.bf.1.7 8 21.17 even 6
3969.2.a.bg.1.2 8 7.4 even 3
3969.2.a.bg.1.7 8 21.11 odd 6