Properties

Label 441.2.u.e.64.3
Level $441$
Weight $2$
Character 441.64
Analytic conductor $3.521$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(64,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.u (of order \(7\), degree \(6\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(10\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 64.3
Character \(\chi\) \(=\) 441.64
Dual form 441.2.u.e.379.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.418387 + 1.83307i) q^{2} +(-1.38317 - 0.666101i) q^{4} +(0.364972 - 0.457660i) q^{5} +(-1.75476 - 1.98010i) q^{7} +(-0.544876 + 0.683253i) q^{8} +O(q^{10})\) \(q+(-0.418387 + 1.83307i) q^{2} +(-1.38317 - 0.666101i) q^{4} +(0.364972 - 0.457660i) q^{5} +(-1.75476 - 1.98010i) q^{7} +(-0.544876 + 0.683253i) q^{8} +(0.686225 + 0.860499i) q^{10} +(-1.10244 + 4.83010i) q^{11} +(-0.595386 + 2.60856i) q^{13} +(4.36384 - 2.38816i) q^{14} +(-2.93885 - 3.68521i) q^{16} +(-5.69008 + 2.74020i) q^{17} -7.42404 q^{19} +(-0.809667 + 0.389915i) q^{20} +(-8.39268 - 4.04170i) q^{22} +(5.60040 + 2.69701i) q^{23} +(1.03636 + 4.54057i) q^{25} +(-4.53258 - 2.18277i) q^{26} +(1.10820 + 3.90767i) q^{28} +(-0.980927 + 0.472389i) q^{29} +4.19420 q^{31} +(6.41009 - 3.08694i) q^{32} +(-2.64233 - 11.5768i) q^{34} +(-1.54665 + 0.0804050i) q^{35} +(8.70021 - 4.18980i) q^{37} +(3.10612 - 13.6088i) q^{38} +(0.113833 + 0.498736i) q^{40} +(-4.33608 + 5.43727i) q^{41} +(-0.611376 - 0.766641i) q^{43} +(4.74219 - 5.94652i) q^{44} +(-7.28696 + 9.13756i) q^{46} +(2.49397 - 10.9268i) q^{47} +(-0.841600 + 6.94922i) q^{49} -8.75680 q^{50} +(2.56108 - 3.21150i) q^{52} +(-0.372613 - 0.179441i) q^{53} +(1.80818 + 2.26739i) q^{55} +(2.30904 - 0.120039i) q^{56} +(-0.455517 - 1.99575i) q^{58} +(-4.08380 - 5.12093i) q^{59} +(6.64278 - 3.19899i) q^{61} +(-1.75480 + 7.68828i) q^{62} +(0.878955 + 3.85095i) q^{64} +(0.976534 + 1.22453i) q^{65} +7.66017 q^{67} +9.69561 q^{68} +(0.499711 - 2.86877i) q^{70} +(-7.91463 - 3.81149i) q^{71} +(1.88441 + 8.25614i) q^{73} +(4.04016 + 17.7011i) q^{74} +(10.2687 + 4.94516i) q^{76} +(11.4986 - 6.29275i) q^{77} -0.434187 q^{79} -2.75917 q^{80} +(-8.15276 - 10.2232i) q^{82} +(0.936843 + 4.10458i) q^{83} +(-0.822640 + 3.60422i) q^{85} +(1.66110 - 0.799944i) q^{86} +(-2.69949 - 3.38505i) q^{88} +(-0.0408453 - 0.178955i) q^{89} +(6.20997 - 3.39848i) q^{91} +(-5.94984 - 7.46087i) q^{92} +(18.9862 + 9.14326i) q^{94} +(-2.70957 + 3.39769i) q^{95} +5.22181 q^{97} +(-12.3863 - 4.45018i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q - 12 q^{4} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 60 q - 12 q^{4} - 2 q^{7} + 12 q^{10} - 4 q^{13} - 48 q^{19} + 6 q^{22} - 22 q^{25} + 40 q^{28} - 76 q^{31} - 12 q^{34} + 34 q^{37} + 86 q^{40} + 4 q^{43} + 8 q^{46} + 26 q^{49} + 66 q^{52} + 10 q^{55} + 42 q^{58} + 62 q^{61} - 128 q^{64} + 8 q^{67} + 96 q^{70} - 70 q^{73} + 50 q^{76} - 24 q^{79} - 36 q^{82} + 72 q^{85} - 216 q^{88} + 52 q^{91} - 38 q^{94} - 252 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{7}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.418387 + 1.83307i −0.295844 + 1.29618i 0.580408 + 0.814326i \(0.302893\pi\)
−0.876252 + 0.481853i \(0.839964\pi\)
\(3\) 0 0
\(4\) −1.38317 0.666101i −0.691586 0.333050i
\(5\) 0.364972 0.457660i 0.163220 0.204672i −0.693495 0.720462i \(-0.743930\pi\)
0.856715 + 0.515790i \(0.172501\pi\)
\(6\) 0 0
\(7\) −1.75476 1.98010i −0.663239 0.748408i
\(8\) −0.544876 + 0.683253i −0.192643 + 0.241566i
\(9\) 0 0
\(10\) 0.686225 + 0.860499i 0.217003 + 0.272114i
\(11\) −1.10244 + 4.83010i −0.332398 + 1.45633i 0.482076 + 0.876129i \(0.339883\pi\)
−0.814474 + 0.580200i \(0.802974\pi\)
\(12\) 0 0
\(13\) −0.595386 + 2.60856i −0.165130 + 0.723484i 0.822767 + 0.568378i \(0.192429\pi\)
−0.987898 + 0.155106i \(0.950428\pi\)
\(14\) 4.36384 2.38816i 1.16629 0.638264i
\(15\) 0 0
\(16\) −2.93885 3.68521i −0.734713 0.921301i
\(17\) −5.69008 + 2.74020i −1.38005 + 0.664596i −0.969010 0.247022i \(-0.920548\pi\)
−0.411038 + 0.911618i \(0.634834\pi\)
\(18\) 0 0
\(19\) −7.42404 −1.70319 −0.851596 0.524199i \(-0.824365\pi\)
−0.851596 + 0.524199i \(0.824365\pi\)
\(20\) −0.809667 + 0.389915i −0.181047 + 0.0871876i
\(21\) 0 0
\(22\) −8.39268 4.04170i −1.78933 0.861694i
\(23\) 5.60040 + 2.69701i 1.16776 + 0.562366i 0.914323 0.404985i \(-0.132723\pi\)
0.253442 + 0.967351i \(0.418437\pi\)
\(24\) 0 0
\(25\) 1.03636 + 4.54057i 0.207271 + 0.908115i
\(26\) −4.53258 2.18277i −0.888911 0.428077i
\(27\) 0 0
\(28\) 1.10820 + 3.90767i 0.209429 + 0.738480i
\(29\) −0.980927 + 0.472389i −0.182154 + 0.0877205i −0.522738 0.852493i \(-0.675089\pi\)
0.340584 + 0.940214i \(0.389375\pi\)
\(30\) 0 0
\(31\) 4.19420 0.753301 0.376651 0.926355i \(-0.377076\pi\)
0.376651 + 0.926355i \(0.377076\pi\)
\(32\) 6.41009 3.08694i 1.13316 0.545699i
\(33\) 0 0
\(34\) −2.64233 11.5768i −0.453156 1.98540i
\(35\) −1.54665 + 0.0804050i −0.261432 + 0.0135909i
\(36\) 0 0
\(37\) 8.70021 4.18980i 1.43031 0.688799i 0.451251 0.892397i \(-0.350978\pi\)
0.979055 + 0.203598i \(0.0652635\pi\)
\(38\) 3.10612 13.6088i 0.503880 2.20764i
\(39\) 0 0
\(40\) 0.113833 + 0.498736i 0.0179986 + 0.0788571i
\(41\) −4.33608 + 5.43727i −0.677182 + 0.849159i −0.995091 0.0989620i \(-0.968448\pi\)
0.317909 + 0.948121i \(0.397019\pi\)
\(42\) 0 0
\(43\) −0.611376 0.766641i −0.0932339 0.116912i 0.733026 0.680200i \(-0.238107\pi\)
−0.826260 + 0.563289i \(0.809536\pi\)
\(44\) 4.74219 5.94652i 0.714913 0.896472i
\(45\) 0 0
\(46\) −7.28696 + 9.13756i −1.07440 + 1.34726i
\(47\) 2.49397 10.9268i 0.363783 1.59384i −0.379718 0.925102i \(-0.623979\pi\)
0.743501 0.668735i \(-0.233164\pi\)
\(48\) 0 0
\(49\) −0.841600 + 6.94922i −0.120229 + 0.992746i
\(50\) −8.75680 −1.23840
\(51\) 0 0
\(52\) 2.56108 3.21150i 0.355159 0.445355i
\(53\) −0.372613 0.179441i −0.0511824 0.0246481i 0.408117 0.912929i \(-0.366185\pi\)
−0.459300 + 0.888281i \(0.651900\pi\)
\(54\) 0 0
\(55\) 1.80818 + 2.26739i 0.243816 + 0.305735i
\(56\) 2.30904 0.120039i 0.308558 0.0160408i
\(57\) 0 0
\(58\) −0.455517 1.99575i −0.0598124 0.262055i
\(59\) −4.08380 5.12093i −0.531666 0.666688i 0.441374 0.897323i \(-0.354491\pi\)
−0.973040 + 0.230635i \(0.925920\pi\)
\(60\) 0 0
\(61\) 6.64278 3.19899i 0.850521 0.409589i 0.0427500 0.999086i \(-0.486388\pi\)
0.807771 + 0.589496i \(0.200674\pi\)
\(62\) −1.75480 + 7.68828i −0.222860 + 0.976413i
\(63\) 0 0
\(64\) 0.878955 + 3.85095i 0.109869 + 0.481369i
\(65\) 0.976534 + 1.22453i 0.121124 + 0.151885i
\(66\) 0 0
\(67\) 7.66017 0.935839 0.467919 0.883771i \(-0.345004\pi\)
0.467919 + 0.883771i \(0.345004\pi\)
\(68\) 9.69561 1.17577
\(69\) 0 0
\(70\) 0.499711 2.86877i 0.0597269 0.342883i
\(71\) −7.91463 3.81149i −0.939294 0.452340i −0.0993739 0.995050i \(-0.531684\pi\)
−0.839920 + 0.542710i \(0.817398\pi\)
\(72\) 0 0
\(73\) 1.88441 + 8.25614i 0.220554 + 0.966308i 0.957063 + 0.289881i \(0.0936157\pi\)
−0.736509 + 0.676428i \(0.763527\pi\)
\(74\) 4.04016 + 17.7011i 0.469659 + 2.05771i
\(75\) 0 0
\(76\) 10.2687 + 4.94516i 1.17790 + 0.567249i
\(77\) 11.4986 6.29275i 1.31039 0.717125i
\(78\) 0 0
\(79\) −0.434187 −0.0488499 −0.0244249 0.999702i \(-0.507775\pi\)
−0.0244249 + 0.999702i \(0.507775\pi\)
\(80\) −2.75917 −0.308485
\(81\) 0 0
\(82\) −8.15276 10.2232i −0.900321 1.12897i
\(83\) 0.936843 + 4.10458i 0.102832 + 0.450536i 0.999962 + 0.00876855i \(0.00279115\pi\)
−0.897130 + 0.441767i \(0.854352\pi\)
\(84\) 0 0
\(85\) −0.822640 + 3.60422i −0.0892278 + 0.390932i
\(86\) 1.66110 0.799944i 0.179121 0.0862601i
\(87\) 0 0
\(88\) −2.69949 3.38505i −0.287766 0.360848i
\(89\) −0.0408453 0.178955i −0.00432959 0.0189692i 0.972717 0.231995i \(-0.0745253\pi\)
−0.977047 + 0.213026i \(0.931668\pi\)
\(90\) 0 0
\(91\) 6.20997 3.39848i 0.650982 0.356258i
\(92\) −5.94984 7.46087i −0.620314 0.777849i
\(93\) 0 0
\(94\) 18.9862 + 9.14326i 1.95827 + 0.943055i
\(95\) −2.70957 + 3.39769i −0.277996 + 0.348595i
\(96\) 0 0
\(97\) 5.22181 0.530195 0.265097 0.964222i \(-0.414596\pi\)
0.265097 + 0.964222i \(0.414596\pi\)
\(98\) −12.3863 4.45018i −1.25121 0.449536i
\(99\) 0 0
\(100\) 1.59102 6.97071i 0.159102 0.697071i
\(101\) −5.04295 + 6.32366i −0.501792 + 0.629227i −0.966633 0.256167i \(-0.917540\pi\)
0.464840 + 0.885394i \(0.346112\pi\)
\(102\) 0 0
\(103\) −2.13439 + 2.67644i −0.210308 + 0.263718i −0.875786 0.482700i \(-0.839656\pi\)
0.665478 + 0.746417i \(0.268228\pi\)
\(104\) −1.45789 1.82814i −0.142958 0.179264i
\(105\) 0 0
\(106\) 0.484825 0.607952i 0.0470904 0.0590495i
\(107\) 2.94957 + 12.9229i 0.285145 + 1.24930i 0.891101 + 0.453805i \(0.149934\pi\)
−0.605956 + 0.795498i \(0.707209\pi\)
\(108\) 0 0
\(109\) −2.86185 + 12.5386i −0.274115 + 1.20098i 0.630991 + 0.775790i \(0.282649\pi\)
−0.905106 + 0.425186i \(0.860209\pi\)
\(110\) −4.91282 + 2.36589i −0.468419 + 0.225579i
\(111\) 0 0
\(112\) −2.14008 + 12.2859i −0.202219 + 1.16091i
\(113\) 3.30096 + 14.4625i 0.310528 + 1.36051i 0.853645 + 0.520856i \(0.174387\pi\)
−0.543116 + 0.839658i \(0.682756\pi\)
\(114\) 0 0
\(115\) 3.27830 1.57875i 0.305703 0.147219i
\(116\) 1.67145 0.155190
\(117\) 0 0
\(118\) 11.0956 5.34338i 1.02144 0.491898i
\(119\) 15.4106 + 6.45853i 1.41269 + 0.592053i
\(120\) 0 0
\(121\) −12.2038 5.87705i −1.10944 0.534278i
\(122\) 3.08474 + 13.5151i 0.279279 + 1.22360i
\(123\) 0 0
\(124\) −5.80131 2.79376i −0.520973 0.250887i
\(125\) 5.09328 + 2.45279i 0.455557 + 0.219385i
\(126\) 0 0
\(127\) −15.4030 + 7.41770i −1.36680 + 0.658214i −0.966141 0.258015i \(-0.916932\pi\)
−0.400655 + 0.916229i \(0.631217\pi\)
\(128\) 6.80251 0.601263
\(129\) 0 0
\(130\) −2.65323 + 1.27773i −0.232704 + 0.112064i
\(131\) −7.28531 9.13549i −0.636520 0.798171i 0.354043 0.935229i \(-0.384807\pi\)
−0.990563 + 0.137058i \(0.956235\pi\)
\(132\) 0 0
\(133\) 13.0274 + 14.7004i 1.12962 + 1.27468i
\(134\) −3.20492 + 14.0417i −0.276863 + 1.21301i
\(135\) 0 0
\(136\) 1.22814 5.38083i 0.105312 0.461403i
\(137\) −5.19256 6.51127i −0.443631 0.556295i 0.508865 0.860846i \(-0.330065\pi\)
−0.952496 + 0.304551i \(0.901494\pi\)
\(138\) 0 0
\(139\) 11.9526 14.9881i 1.01381 1.27127i 0.0516822 0.998664i \(-0.483542\pi\)
0.962125 0.272610i \(-0.0878868\pi\)
\(140\) 2.19285 + 0.919013i 0.185329 + 0.0776708i
\(141\) 0 0
\(142\) 10.2981 12.9134i 0.864198 1.08367i
\(143\) −11.9432 5.75155i −0.998742 0.480969i
\(144\) 0 0
\(145\) −0.141817 + 0.621340i −0.0117772 + 0.0515995i
\(146\) −15.9225 −1.31776
\(147\) 0 0
\(148\) −14.8247 −1.21858
\(149\) 1.47887 6.47935i 0.121154 0.530809i −0.877530 0.479522i \(-0.840810\pi\)
0.998684 0.0512879i \(-0.0163326\pi\)
\(150\) 0 0
\(151\) −4.95202 2.38477i −0.402990 0.194070i 0.221399 0.975183i \(-0.428938\pi\)
−0.624389 + 0.781114i \(0.714652\pi\)
\(152\) 4.04518 5.07250i 0.328108 0.411434i
\(153\) 0 0
\(154\) 6.72420 + 23.7106i 0.541852 + 1.91065i
\(155\) 1.53077 1.91952i 0.122954 0.154180i
\(156\) 0 0
\(157\) −5.57651 6.99272i −0.445054 0.558080i 0.507813 0.861467i \(-0.330454\pi\)
−0.952867 + 0.303387i \(0.901883\pi\)
\(158\) 0.181658 0.795897i 0.0144520 0.0633182i
\(159\) 0 0
\(160\) 0.926735 4.06029i 0.0732648 0.320994i
\(161\) −4.48704 15.8220i −0.353628 1.24695i
\(162\) 0 0
\(163\) 5.74180 + 7.19999i 0.449732 + 0.563946i 0.954079 0.299555i \(-0.0968381\pi\)
−0.504347 + 0.863501i \(0.668267\pi\)
\(164\) 9.61931 4.63242i 0.751142 0.361731i
\(165\) 0 0
\(166\) −7.91595 −0.614397
\(167\) 11.1422 5.36582i 0.862212 0.415220i 0.0501163 0.998743i \(-0.484041\pi\)
0.812096 + 0.583524i \(0.198327\pi\)
\(168\) 0 0
\(169\) 5.26250 + 2.53429i 0.404808 + 0.194945i
\(170\) −6.26262 3.01592i −0.480321 0.231310i
\(171\) 0 0
\(172\) 0.334978 + 1.46763i 0.0255418 + 0.111906i
\(173\) −0.575059 0.276934i −0.0437209 0.0210549i 0.411896 0.911231i \(-0.364867\pi\)
−0.455616 + 0.890176i \(0.650581\pi\)
\(174\) 0 0
\(175\) 7.17223 10.0197i 0.542170 0.757420i
\(176\) 21.0398 10.1322i 1.58594 0.763746i
\(177\) 0 0
\(178\) 0.345127 0.0258683
\(179\) −7.99421 + 3.84981i −0.597516 + 0.287748i −0.708093 0.706119i \(-0.750444\pi\)
0.110577 + 0.993868i \(0.464730\pi\)
\(180\) 0 0
\(181\) 3.33053 + 14.5920i 0.247557 + 1.08462i 0.933955 + 0.357391i \(0.116334\pi\)
−0.686398 + 0.727226i \(0.740809\pi\)
\(182\) 3.63149 + 12.8052i 0.269184 + 0.949186i
\(183\) 0 0
\(184\) −4.89427 + 2.35696i −0.360810 + 0.173757i
\(185\) 1.25783 5.51090i 0.0924773 0.405169i
\(186\) 0 0
\(187\) −6.96247 30.5046i −0.509146 2.23071i
\(188\) −10.7279 + 13.4524i −0.782415 + 0.981117i
\(189\) 0 0
\(190\) −5.09456 6.38838i −0.369598 0.463462i
\(191\) −5.75308 + 7.21414i −0.416278 + 0.521997i −0.945120 0.326724i \(-0.894055\pi\)
0.528841 + 0.848721i \(0.322627\pi\)
\(192\) 0 0
\(193\) −0.236017 + 0.295956i −0.0169889 + 0.0213034i −0.790253 0.612780i \(-0.790051\pi\)
0.773264 + 0.634084i \(0.218623\pi\)
\(194\) −2.18474 + 9.57197i −0.156855 + 0.687227i
\(195\) 0 0
\(196\) 5.79296 9.05138i 0.413783 0.646527i
\(197\) 20.7128 1.47573 0.737863 0.674950i \(-0.235835\pi\)
0.737863 + 0.674950i \(0.235835\pi\)
\(198\) 0 0
\(199\) −11.0362 + 13.8390i −0.782338 + 0.981021i 0.217650 + 0.976027i \(0.430161\pi\)
−0.999988 + 0.00499380i \(0.998410\pi\)
\(200\) −3.66705 1.76596i −0.259299 0.124872i
\(201\) 0 0
\(202\) −9.48182 11.8898i −0.667139 0.836565i
\(203\) 2.65667 + 1.11340i 0.186462 + 0.0781455i
\(204\) 0 0
\(205\) 0.905876 + 3.96890i 0.0632691 + 0.277200i
\(206\) −4.01311 5.03228i −0.279607 0.350616i
\(207\) 0 0
\(208\) 11.3628 5.47205i 0.787870 0.379418i
\(209\) 8.18455 35.8588i 0.566137 2.48041i
\(210\) 0 0
\(211\) −0.502270 2.20059i −0.0345777 0.151495i 0.954692 0.297596i \(-0.0961847\pi\)
−0.989270 + 0.146101i \(0.953328\pi\)
\(212\) 0.395862 + 0.496396i 0.0271879 + 0.0340926i
\(213\) 0 0
\(214\) −24.9227 −1.70368
\(215\) −0.573996 −0.0391462
\(216\) 0 0
\(217\) −7.35984 8.30495i −0.499619 0.563776i
\(218\) −21.7867 10.4919i −1.47558 0.710604i
\(219\) 0 0
\(220\) −0.990720 4.34063i −0.0667943 0.292645i
\(221\) −3.76017 16.4744i −0.252937 1.10819i
\(222\) 0 0
\(223\) 4.46249 + 2.14902i 0.298831 + 0.143909i 0.577291 0.816538i \(-0.304110\pi\)
−0.278460 + 0.960448i \(0.589824\pi\)
\(224\) −17.3607 7.27578i −1.15996 0.486134i
\(225\) 0 0
\(226\) −27.8918 −1.85534
\(227\) 29.9858 1.99023 0.995115 0.0987199i \(-0.0314748\pi\)
0.995115 + 0.0987199i \(0.0314748\pi\)
\(228\) 0 0
\(229\) 5.39112 + 6.76025i 0.356255 + 0.446730i 0.927373 0.374138i \(-0.122061\pi\)
−0.571118 + 0.820868i \(0.693490\pi\)
\(230\) 1.52236 + 6.66990i 0.100382 + 0.439800i
\(231\) 0 0
\(232\) 0.211722 0.927615i 0.0139002 0.0609009i
\(233\) −1.62661 + 0.783332i −0.106562 + 0.0513178i −0.486406 0.873733i \(-0.661692\pi\)
0.379843 + 0.925051i \(0.375978\pi\)
\(234\) 0 0
\(235\) −4.09053 5.12936i −0.266837 0.334603i
\(236\) 2.23755 + 9.80335i 0.145652 + 0.638144i
\(237\) 0 0
\(238\) −18.2866 + 25.5466i −1.18534 + 1.65594i
\(239\) −6.73112 8.44056i −0.435400 0.545974i 0.514924 0.857236i \(-0.327820\pi\)
−0.950324 + 0.311261i \(0.899249\pi\)
\(240\) 0 0
\(241\) −7.79797 3.75531i −0.502312 0.241901i 0.165529 0.986205i \(-0.447067\pi\)
−0.667841 + 0.744304i \(0.732781\pi\)
\(242\) 15.8790 19.9116i 1.02074 1.27997i
\(243\) 0 0
\(244\) −11.3190 −0.724622
\(245\) 2.87322 + 2.92144i 0.183563 + 0.186644i
\(246\) 0 0
\(247\) 4.42017 19.3660i 0.281249 1.23223i
\(248\) −2.28532 + 2.86570i −0.145118 + 0.181972i
\(249\) 0 0
\(250\) −6.62711 + 8.31014i −0.419135 + 0.525579i
\(251\) −9.49433 11.9055i −0.599277 0.751470i 0.385988 0.922504i \(-0.373861\pi\)
−0.985265 + 0.171034i \(0.945289\pi\)
\(252\) 0 0
\(253\) −19.2009 + 24.0772i −1.20715 + 1.51372i
\(254\) −7.15276 31.3383i −0.448804 1.96634i
\(255\) 0 0
\(256\) −4.60399 + 20.1714i −0.287750 + 1.26071i
\(257\) 0.538372 0.259266i 0.0335827 0.0161726i −0.417017 0.908899i \(-0.636924\pi\)
0.450600 + 0.892726i \(0.351210\pi\)
\(258\) 0 0
\(259\) −23.5631 9.87518i −1.46414 0.613614i
\(260\) −0.535051 2.34421i −0.0331825 0.145382i
\(261\) 0 0
\(262\) 19.7941 9.53234i 1.22288 0.588910i
\(263\) 9.69996 0.598125 0.299063 0.954233i \(-0.403326\pi\)
0.299063 + 0.954233i \(0.403326\pi\)
\(264\) 0 0
\(265\) −0.218116 + 0.105039i −0.0133988 + 0.00645251i
\(266\) −32.3973 + 17.7298i −1.98641 + 1.08709i
\(267\) 0 0
\(268\) −10.5953 5.10244i −0.647213 0.311681i
\(269\) 4.41807 + 19.3568i 0.269374 + 1.18021i 0.910743 + 0.412973i \(0.135510\pi\)
−0.641369 + 0.767233i \(0.721633\pi\)
\(270\) 0 0
\(271\) −2.56185 1.23372i −0.155621 0.0749433i 0.354452 0.935074i \(-0.384667\pi\)
−0.510073 + 0.860131i \(0.670382\pi\)
\(272\) 26.8205 + 12.9161i 1.62623 + 0.783152i
\(273\) 0 0
\(274\) 14.1081 6.79412i 0.852304 0.410448i
\(275\) −23.0739 −1.39141
\(276\) 0 0
\(277\) 9.83610 4.73681i 0.590994 0.284608i −0.114387 0.993436i \(-0.536490\pi\)
0.705381 + 0.708829i \(0.250776\pi\)
\(278\) 22.4735 + 28.1808i 1.34787 + 1.69017i
\(279\) 0 0
\(280\) 0.787797 1.10057i 0.0470799 0.0657714i
\(281\) −6.20706 + 27.1949i −0.370282 + 1.62231i 0.355702 + 0.934599i \(0.384242\pi\)
−0.725984 + 0.687712i \(0.758615\pi\)
\(282\) 0 0
\(283\) 1.44984 6.35214i 0.0861838 0.377596i −0.913381 0.407106i \(-0.866538\pi\)
0.999564 + 0.0295108i \(0.00939493\pi\)
\(284\) 8.40847 + 10.5439i 0.498951 + 0.625664i
\(285\) 0 0
\(286\) 15.5399 19.4864i 0.918894 1.15226i
\(287\) 18.3751 0.955258i 1.08465 0.0563871i
\(288\) 0 0
\(289\) 14.2690 17.8928i 0.839354 1.05252i
\(290\) −1.07963 0.519921i −0.0633979 0.0305308i
\(291\) 0 0
\(292\) 2.89296 12.6749i 0.169298 0.741741i
\(293\) 4.61665 0.269708 0.134854 0.990865i \(-0.456944\pi\)
0.134854 + 0.990865i \(0.456944\pi\)
\(294\) 0 0
\(295\) −3.83412 −0.223231
\(296\) −1.87784 + 8.22737i −0.109147 + 0.478206i
\(297\) 0 0
\(298\) 11.2584 + 5.42176i 0.652181 + 0.314074i
\(299\) −10.3697 + 13.0032i −0.599696 + 0.751995i
\(300\) 0 0
\(301\) −0.445206 + 2.55586i −0.0256612 + 0.147317i
\(302\) 6.44332 8.07967i 0.370771 0.464933i
\(303\) 0 0
\(304\) 21.8182 + 27.3591i 1.25136 + 1.56915i
\(305\) 0.960375 4.20768i 0.0549909 0.240931i
\(306\) 0 0
\(307\) −2.70168 + 11.8368i −0.154193 + 0.675563i 0.837446 + 0.546520i \(0.184048\pi\)
−0.991639 + 0.129043i \(0.958809\pi\)
\(308\) −20.0962 + 1.04473i −1.14508 + 0.0595288i
\(309\) 0 0
\(310\) 2.87817 + 3.60911i 0.163469 + 0.204984i
\(311\) −27.8125 + 13.3938i −1.57710 + 0.759492i −0.998427 0.0560673i \(-0.982144\pi\)
−0.578674 + 0.815559i \(0.696430\pi\)
\(312\) 0 0
\(313\) −35.2779 −1.99403 −0.997013 0.0772309i \(-0.975392\pi\)
−0.997013 + 0.0772309i \(0.975392\pi\)
\(314\) 15.1513 7.29649i 0.855038 0.411765i
\(315\) 0 0
\(316\) 0.600556 + 0.289212i 0.0337839 + 0.0162695i
\(317\) −20.0679 9.66418i −1.12712 0.542794i −0.225038 0.974350i \(-0.572250\pi\)
−0.902086 + 0.431556i \(0.857965\pi\)
\(318\) 0 0
\(319\) −1.20028 5.25875i −0.0672026 0.294434i
\(320\) 2.08322 + 1.00323i 0.116456 + 0.0560821i
\(321\) 0 0
\(322\) 30.8802 1.60535i 1.72089 0.0894627i
\(323\) 42.2434 20.3433i 2.35049 1.13193i
\(324\) 0 0
\(325\) −12.4614 −0.691233
\(326\) −15.6004 + 7.51276i −0.864026 + 0.416093i
\(327\) 0 0
\(328\) −1.35241 5.92528i −0.0746741 0.327169i
\(329\) −26.0125 + 14.2356i −1.43411 + 0.784836i
\(330\) 0 0
\(331\) 14.6596 7.05970i 0.805765 0.388036i 0.0147949 0.999891i \(-0.495290\pi\)
0.790970 + 0.611854i \(0.209576\pi\)
\(332\) 1.43825 6.30137i 0.0789340 0.345832i
\(333\) 0 0
\(334\) 5.17417 + 22.6695i 0.283118 + 1.24042i
\(335\) 2.79575 3.50575i 0.152748 0.191540i
\(336\) 0 0
\(337\) −1.28378 1.60981i −0.0699321 0.0876921i 0.745635 0.666355i \(-0.232146\pi\)
−0.815567 + 0.578663i \(0.803575\pi\)
\(338\) −6.84730 + 8.58624i −0.372444 + 0.467030i
\(339\) 0 0
\(340\) 3.53863 4.43730i 0.191909 0.240646i
\(341\) −4.62385 + 20.2584i −0.250396 + 1.09705i
\(342\) 0 0
\(343\) 15.2370 10.5278i 0.822719 0.568448i
\(344\) 0.856933 0.0462028
\(345\) 0 0
\(346\) 0.748237 0.938259i 0.0402255 0.0504411i
\(347\) −12.3714 5.95776i −0.664132 0.319829i 0.0712731 0.997457i \(-0.477294\pi\)
−0.735405 + 0.677628i \(0.763008\pi\)
\(348\) 0 0
\(349\) 5.49923 + 6.89581i 0.294367 + 0.369124i 0.906918 0.421306i \(-0.138428\pi\)
−0.612552 + 0.790431i \(0.709857\pi\)
\(350\) 15.3661 + 17.3394i 0.821354 + 0.926827i
\(351\) 0 0
\(352\) 7.84348 + 34.3645i 0.418059 + 1.83164i
\(353\) 15.9888 + 20.0493i 0.850999 + 1.06712i 0.996967 + 0.0778295i \(0.0247990\pi\)
−0.145968 + 0.989289i \(0.546630\pi\)
\(354\) 0 0
\(355\) −4.63298 + 2.23113i −0.245893 + 0.118416i
\(356\) −0.0627059 + 0.274733i −0.00332341 + 0.0145608i
\(357\) 0 0
\(358\) −3.71231 16.2647i −0.196202 0.859616i
\(359\) 11.2026 + 14.0476i 0.591250 + 0.741404i 0.983986 0.178248i \(-0.0570428\pi\)
−0.392736 + 0.919651i \(0.628471\pi\)
\(360\) 0 0
\(361\) 36.1164 1.90086
\(362\) −28.1417 −1.47909
\(363\) 0 0
\(364\) −10.8532 + 0.564219i −0.568862 + 0.0295731i
\(365\) 4.46626 + 2.15084i 0.233775 + 0.112580i
\(366\) 0 0
\(367\) 2.77955 + 12.1780i 0.145091 + 0.635687i 0.994207 + 0.107480i \(0.0342782\pi\)
−0.849116 + 0.528207i \(0.822865\pi\)
\(368\) −6.51972 28.5648i −0.339864 1.48904i
\(369\) 0 0
\(370\) 9.57562 + 4.61138i 0.497813 + 0.239734i
\(371\) 0.298537 + 1.05269i 0.0154993 + 0.0546529i
\(372\) 0 0
\(373\) 5.95573 0.308376 0.154188 0.988042i \(-0.450724\pi\)
0.154188 + 0.988042i \(0.450724\pi\)
\(374\) 58.8301 3.04203
\(375\) 0 0
\(376\) 6.10686 + 7.65776i 0.314937 + 0.394919i
\(377\) −0.648225 2.84006i −0.0333853 0.146270i
\(378\) 0 0
\(379\) 3.06768 13.4404i 0.157576 0.690386i −0.832983 0.553299i \(-0.813369\pi\)
0.990559 0.137087i \(-0.0437740\pi\)
\(380\) 6.01100 2.89474i 0.308358 0.148497i
\(381\) 0 0
\(382\) −10.8170 13.5641i −0.553447 0.694001i
\(383\) −3.36466 14.7415i −0.171926 0.753258i −0.985205 0.171383i \(-0.945177\pi\)
0.813278 0.581875i \(-0.197681\pi\)
\(384\) 0 0
\(385\) 1.31673 7.55913i 0.0671066 0.385249i
\(386\) −0.443763 0.556461i −0.0225869 0.0283231i
\(387\) 0 0
\(388\) −7.22267 3.47825i −0.366675 0.176582i
\(389\) −12.3222 + 15.4515i −0.624760 + 0.783424i −0.989005 0.147879i \(-0.952755\pi\)
0.364246 + 0.931303i \(0.381327\pi\)
\(390\) 0 0
\(391\) −39.2571 −1.98532
\(392\) −4.28951 4.36149i −0.216653 0.220289i
\(393\) 0 0
\(394\) −8.66597 + 37.9681i −0.436585 + 1.91281i
\(395\) −0.158466 + 0.198710i −0.00797330 + 0.00999820i
\(396\) 0 0
\(397\) 1.64310 2.06038i 0.0824649 0.103408i −0.738888 0.673829i \(-0.764649\pi\)
0.821352 + 0.570421i \(0.193220\pi\)
\(398\) −20.7505 26.0203i −1.04013 1.30428i
\(399\) 0 0
\(400\) 13.6872 17.1633i 0.684362 0.858163i
\(401\) 3.22570 + 14.1327i 0.161084 + 0.705754i 0.989367 + 0.145444i \(0.0464610\pi\)
−0.828283 + 0.560310i \(0.810682\pi\)
\(402\) 0 0
\(403\) −2.49717 + 10.9408i −0.124393 + 0.545001i
\(404\) 11.1875 5.38760i 0.556597 0.268043i
\(405\) 0 0
\(406\) −3.15246 + 4.40405i −0.156454 + 0.218569i
\(407\) 10.6457 + 46.6419i 0.527688 + 2.31195i
\(408\) 0 0
\(409\) 9.23464 4.44717i 0.456624 0.219898i −0.191410 0.981510i \(-0.561306\pi\)
0.648034 + 0.761612i \(0.275592\pi\)
\(410\) −7.65429 −0.378019
\(411\) 0 0
\(412\) 4.73501 2.28026i 0.233277 0.112340i
\(413\) −2.97384 + 17.0724i −0.146333 + 0.840076i
\(414\) 0 0
\(415\) 2.22042 + 1.06930i 0.108996 + 0.0524898i
\(416\) 4.23598 + 18.5590i 0.207686 + 0.909931i
\(417\) 0 0
\(418\) 62.3076 + 30.0058i 3.04756 + 1.46763i
\(419\) −13.0305 6.27517i −0.636583 0.306562i 0.0876149 0.996154i \(-0.472076\pi\)
−0.724198 + 0.689592i \(0.757790\pi\)
\(420\) 0 0
\(421\) 0.743425 0.358015i 0.0362323 0.0174486i −0.415680 0.909511i \(-0.636456\pi\)
0.451912 + 0.892062i \(0.350742\pi\)
\(422\) 4.24398 0.206594
\(423\) 0 0
\(424\) 0.325632 0.156816i 0.0158141 0.00761566i
\(425\) −18.3390 22.9964i −0.889573 1.11549i
\(426\) 0 0
\(427\) −17.9909 7.53989i −0.870638 0.364881i
\(428\) 4.52819 19.8393i 0.218878 0.958968i
\(429\) 0 0
\(430\) 0.240152 1.05218i 0.0115812 0.0507404i
\(431\) −18.4368 23.1191i −0.888072 1.11361i −0.992881 0.119114i \(-0.961995\pi\)
0.104809 0.994492i \(-0.466577\pi\)
\(432\) 0 0
\(433\) −14.8500 + 18.6213i −0.713644 + 0.894881i −0.997960 0.0638500i \(-0.979662\pi\)
0.284316 + 0.958731i \(0.408234\pi\)
\(434\) 18.3028 10.0164i 0.878564 0.480805i
\(435\) 0 0
\(436\) 12.3104 15.4367i 0.589560 0.739285i
\(437\) −41.5776 20.0227i −1.98893 0.957817i
\(438\) 0 0
\(439\) 1.33980 5.87003i 0.0639450 0.280161i −0.932839 0.360293i \(-0.882677\pi\)
0.996784 + 0.0801313i \(0.0255340\pi\)
\(440\) −2.53444 −0.120825
\(441\) 0 0
\(442\) 31.7720 1.51124
\(443\) 2.66998 11.6980i 0.126855 0.555787i −0.871056 0.491183i \(-0.836565\pi\)
0.997911 0.0646038i \(-0.0205783\pi\)
\(444\) 0 0
\(445\) −0.0968079 0.0466202i −0.00458913 0.00221001i
\(446\) −5.80637 + 7.28096i −0.274940 + 0.344763i
\(447\) 0 0
\(448\) 6.08292 8.49794i 0.287391 0.401490i
\(449\) 18.8010 23.5757i 0.887273 1.11260i −0.105716 0.994396i \(-0.533713\pi\)
0.992989 0.118209i \(-0.0377151\pi\)
\(450\) 0 0
\(451\) −21.4823 26.9379i −1.01156 1.26846i
\(452\) 5.06765 22.2028i 0.238362 1.04433i
\(453\) 0 0
\(454\) −12.5457 + 54.9663i −0.588798 + 2.57969i
\(455\) 0.711115 4.08241i 0.0333376 0.191386i
\(456\) 0 0
\(457\) −0.0104373 0.0130880i −0.000488239 0.000612232i 0.781587 0.623796i \(-0.214410\pi\)
−0.782076 + 0.623184i \(0.785839\pi\)
\(458\) −14.6476 + 7.05392i −0.684438 + 0.329608i
\(459\) 0 0
\(460\) −5.58607 −0.260452
\(461\) 34.0141 16.3803i 1.58420 0.762909i 0.585343 0.810786i \(-0.300960\pi\)
0.998853 + 0.0478771i \(0.0152456\pi\)
\(462\) 0 0
\(463\) 15.2684 + 7.35288i 0.709584 + 0.341718i 0.753618 0.657312i \(-0.228307\pi\)
−0.0440344 + 0.999030i \(0.514021\pi\)
\(464\) 4.62365 + 2.22663i 0.214648 + 0.103369i
\(465\) 0 0
\(466\) −0.755354 3.30942i −0.0349911 0.153306i
\(467\) 34.1764 + 16.4585i 1.58149 + 0.761608i 0.998698 0.0510107i \(-0.0162443\pi\)
0.582796 + 0.812618i \(0.301959\pi\)
\(468\) 0 0
\(469\) −13.4418 15.1679i −0.620684 0.700389i
\(470\) 11.1139 5.35218i 0.512647 0.246878i
\(471\) 0 0
\(472\) 5.72405 0.263471
\(473\) 4.37695 2.10783i 0.201253 0.0969181i
\(474\) 0 0
\(475\) −7.69395 33.7094i −0.353023 1.54669i
\(476\) −17.0135 19.1983i −0.779813 0.879952i
\(477\) 0 0
\(478\) 18.2884 8.80722i 0.836491 0.402833i
\(479\) 1.75901 7.70672i 0.0803711 0.352129i −0.918713 0.394927i \(-0.870770\pi\)
0.999084 + 0.0427978i \(0.0136271\pi\)
\(480\) 0 0
\(481\) 5.74935 + 25.1896i 0.262148 + 1.14855i
\(482\) 10.1463 12.7231i 0.462152 0.579521i
\(483\) 0 0
\(484\) 12.9653 + 16.2580i 0.589331 + 0.738998i
\(485\) 1.90582 2.38982i 0.0865386 0.108516i
\(486\) 0 0
\(487\) −18.4767 + 23.1691i −0.837260 + 1.04989i 0.160760 + 0.986993i \(0.448605\pi\)
−0.998020 + 0.0628969i \(0.979966\pi\)
\(488\) −1.43377 + 6.28176i −0.0649037 + 0.284362i
\(489\) 0 0
\(490\) −6.55733 + 4.04454i −0.296230 + 0.182714i
\(491\) −14.2486 −0.643030 −0.321515 0.946904i \(-0.604192\pi\)
−0.321515 + 0.946904i \(0.604192\pi\)
\(492\) 0 0
\(493\) 4.28711 5.37587i 0.193082 0.242117i
\(494\) 33.6500 + 16.2050i 1.51399 + 0.729098i
\(495\) 0 0
\(496\) −12.3261 15.4565i −0.553460 0.694017i
\(497\) 6.34119 + 22.3600i 0.284441 + 1.00298i
\(498\) 0 0
\(499\) −0.00130371 0.00571193i −5.83621e−5 0.000255701i 0.974899 0.222649i \(-0.0714703\pi\)
−0.974957 + 0.222393i \(0.928613\pi\)
\(500\) −5.41107 6.78527i −0.241991 0.303447i
\(501\) 0 0
\(502\) 25.7960 12.4227i 1.15133 0.554452i
\(503\) −0.706576 + 3.09571i −0.0315047 + 0.138031i −0.988234 0.152947i \(-0.951124\pi\)
0.956730 + 0.290978i \(0.0939807\pi\)
\(504\) 0 0
\(505\) 1.05355 + 4.61591i 0.0468824 + 0.205405i
\(506\) −36.1019 45.2703i −1.60492 2.01251i
\(507\) 0 0
\(508\) 26.2459 1.16448
\(509\) −10.2099 −0.452544 −0.226272 0.974064i \(-0.572654\pi\)
−0.226272 + 0.974064i \(0.572654\pi\)
\(510\) 0 0
\(511\) 13.0413 18.2189i 0.576913 0.805957i
\(512\) −22.7917 10.9759i −1.00726 0.485071i
\(513\) 0 0
\(514\) 0.250006 + 1.09535i 0.0110273 + 0.0483138i
\(515\) 0.445908 + 1.95365i 0.0196491 + 0.0860882i
\(516\) 0 0
\(517\) 50.0280 + 24.0922i 2.20023 + 1.05958i
\(518\) 27.9604 39.0612i 1.22851 1.71625i
\(519\) 0 0
\(520\) −1.36876 −0.0600240
\(521\) 18.4127 0.806674 0.403337 0.915052i \(-0.367850\pi\)
0.403337 + 0.915052i \(0.367850\pi\)
\(522\) 0 0
\(523\) −27.6293 34.6461i −1.20815 1.51497i −0.797667 0.603098i \(-0.793933\pi\)
−0.410480 0.911870i \(-0.634639\pi\)
\(524\) 3.99168 + 17.4887i 0.174377 + 0.763998i
\(525\) 0 0
\(526\) −4.05834 + 17.7807i −0.176952 + 0.775277i
\(527\) −23.8654 + 11.4930i −1.03959 + 0.500641i
\(528\) 0 0
\(529\) 9.75038 + 12.2266i 0.423930 + 0.531591i
\(530\) −0.101288 0.443770i −0.00439966 0.0192762i
\(531\) 0 0
\(532\) −8.22729 29.0107i −0.356698 1.25777i
\(533\) −11.6018 14.5482i −0.502530 0.630152i
\(534\) 0 0
\(535\) 6.99080 + 3.36659i 0.302239 + 0.145550i
\(536\) −4.17384 + 5.23383i −0.180283 + 0.226067i
\(537\) 0 0
\(538\) −37.3309 −1.60945
\(539\) −32.6376 11.7261i −1.40580 0.505079i
\(540\) 0 0
\(541\) −5.76287 + 25.2488i −0.247765 + 1.08553i 0.685988 + 0.727613i \(0.259370\pi\)
−0.933753 + 0.357918i \(0.883487\pi\)
\(542\) 3.33335 4.17989i 0.143180 0.179542i
\(543\) 0 0
\(544\) −28.0151 + 35.1299i −1.20114 + 1.50618i
\(545\) 4.69391 + 5.88597i 0.201065 + 0.252127i
\(546\) 0 0
\(547\) 20.4016 25.5828i 0.872310 1.09384i −0.122538 0.992464i \(-0.539103\pi\)
0.994848 0.101379i \(-0.0323254\pi\)
\(548\) 2.84505 + 12.4650i 0.121535 + 0.532477i
\(549\) 0 0
\(550\) 9.65384 42.2962i 0.411641 1.80352i
\(551\) 7.28244 3.50704i 0.310242 0.149405i
\(552\) 0 0
\(553\) 0.761897 + 0.859735i 0.0323991 + 0.0365596i
\(554\) 4.56763 + 20.0121i 0.194060 + 0.850233i
\(555\) 0 0
\(556\) −26.5161 + 12.7695i −1.12453 + 0.541546i
\(557\) −18.8113 −0.797061 −0.398531 0.917155i \(-0.630480\pi\)
−0.398531 + 0.917155i \(0.630480\pi\)
\(558\) 0 0
\(559\) 2.36383 1.13836i 0.0999794 0.0481476i
\(560\) 4.84170 + 5.46344i 0.204599 + 0.230872i
\(561\) 0 0
\(562\) −47.2533 22.7560i −1.99326 0.959903i
\(563\) 8.94916 + 39.2088i 0.377162 + 1.65246i 0.706106 + 0.708106i \(0.250450\pi\)
−0.328944 + 0.944349i \(0.606693\pi\)
\(564\) 0 0
\(565\) 7.82365 + 3.76767i 0.329143 + 0.158507i
\(566\) 11.0374 + 5.31531i 0.463934 + 0.223419i
\(567\) 0 0
\(568\) 6.91670 3.33091i 0.290218 0.139762i
\(569\) 18.1169 0.759501 0.379751 0.925089i \(-0.376010\pi\)
0.379751 + 0.925089i \(0.376010\pi\)
\(570\) 0 0
\(571\) 26.3563 12.6925i 1.10298 0.531165i 0.208383 0.978047i \(-0.433180\pi\)
0.894593 + 0.446882i \(0.147466\pi\)
\(572\) 12.6884 + 15.9108i 0.530529 + 0.665263i
\(573\) 0 0
\(574\) −5.93686 + 34.0827i −0.247800 + 1.42258i
\(575\) −6.44197 + 28.2241i −0.268649 + 1.17703i
\(576\) 0 0
\(577\) −5.11261 + 22.3998i −0.212841 + 0.932516i 0.749785 + 0.661681i \(0.230157\pi\)
−0.962626 + 0.270834i \(0.912700\pi\)
\(578\) 26.8288 + 33.6423i 1.11593 + 1.39933i
\(579\) 0 0
\(580\) 0.610032 0.764956i 0.0253302 0.0317631i
\(581\) 6.48354 9.05761i 0.268982 0.375773i
\(582\) 0 0
\(583\) 1.27750 1.60194i 0.0529087 0.0663454i
\(584\) −6.66780 3.21105i −0.275916 0.132874i
\(585\) 0 0
\(586\) −1.93155 + 8.46266i −0.0797915 + 0.349589i
\(587\) −12.2671 −0.506318 −0.253159 0.967425i \(-0.581470\pi\)
−0.253159 + 0.967425i \(0.581470\pi\)
\(588\) 0 0
\(589\) −31.1379 −1.28302
\(590\) 1.60414 7.02822i 0.0660416 0.289347i
\(591\) 0 0
\(592\) −41.0089 19.7489i −1.68546 0.811673i
\(593\) 20.4831 25.6850i 0.841139 1.05475i −0.156608 0.987661i \(-0.550056\pi\)
0.997747 0.0670940i \(-0.0213727\pi\)
\(594\) 0 0
\(595\) 8.58026 4.69565i 0.351756 0.192503i
\(596\) −6.36143 + 7.97699i −0.260575 + 0.326750i
\(597\) 0 0
\(598\) −19.4973 24.4488i −0.797304 0.999787i
\(599\) 3.36603 14.7475i 0.137532 0.602568i −0.858441 0.512913i \(-0.828566\pi\)
0.995973 0.0896552i \(-0.0285765\pi\)
\(600\) 0 0
\(601\) −4.71500 + 20.6578i −0.192329 + 0.842648i 0.783023 + 0.621993i \(0.213677\pi\)
−0.975352 + 0.220655i \(0.929181\pi\)
\(602\) −4.49881 1.88543i −0.183358 0.0768445i
\(603\) 0 0
\(604\) 5.26101 + 6.59709i 0.214067 + 0.268432i
\(605\) −7.14375 + 3.44025i −0.290435 + 0.139866i
\(606\) 0 0
\(607\) 16.3661 0.664278 0.332139 0.943230i \(-0.392230\pi\)
0.332139 + 0.943230i \(0.392230\pi\)
\(608\) −47.5888 + 22.9176i −1.92998 + 0.929430i
\(609\) 0 0
\(610\) 7.31118 + 3.52088i 0.296021 + 0.142556i
\(611\) 27.0183 + 13.0113i 1.09304 + 0.526382i
\(612\) 0 0
\(613\) −2.48613 10.8925i −0.100414 0.439942i −0.999995 0.00318830i \(-0.998985\pi\)
0.899581 0.436754i \(-0.143872\pi\)
\(614\) −20.5674 9.90475i −0.830033 0.399723i
\(615\) 0 0
\(616\) −1.96578 + 11.2852i −0.0792033 + 0.454695i
\(617\) −10.7960 + 5.19906i −0.434629 + 0.209306i −0.638388 0.769715i \(-0.720398\pi\)
0.203759 + 0.979021i \(0.434684\pi\)
\(618\) 0 0
\(619\) −38.2528 −1.53751 −0.768756 0.639542i \(-0.779124\pi\)
−0.768756 + 0.639542i \(0.779124\pi\)
\(620\) −3.39591 + 1.63538i −0.136383 + 0.0656785i
\(621\) 0 0
\(622\) −12.9154 56.5861i −0.517861 2.26890i
\(623\) −0.282675 + 0.394902i −0.0113251 + 0.0158214i
\(624\) 0 0
\(625\) −17.9992 + 8.66794i −0.719966 + 0.346717i
\(626\) 14.7598 64.6670i 0.589921 2.58461i
\(627\) 0 0
\(628\) 3.05542 + 13.3867i 0.121924 + 0.534186i
\(629\) −38.0240 + 47.6806i −1.51612 + 1.90115i
\(630\) 0 0
\(631\) 11.5784 + 14.5188i 0.460928 + 0.577986i 0.956924 0.290339i \(-0.0937681\pi\)
−0.495995 + 0.868325i \(0.665197\pi\)
\(632\) 0.236578 0.296660i 0.00941058 0.0118005i
\(633\) 0 0
\(634\) 26.1113 32.7425i 1.03701 1.30037i
\(635\) −2.22688 + 9.75659i −0.0883710 + 0.387179i
\(636\) 0 0
\(637\) −17.6264 6.33284i −0.698383 0.250916i
\(638\) 10.1419 0.401520
\(639\) 0 0
\(640\) 2.48273 3.11324i 0.0981383 0.123062i
\(641\) 26.4953 + 12.7595i 1.04650 + 0.503968i 0.876463 0.481469i \(-0.159897\pi\)
0.170038 + 0.985438i \(0.445611\pi\)
\(642\) 0 0
\(643\) 0.981532 + 1.23080i 0.0387079 + 0.0485381i 0.800809 0.598920i \(-0.204403\pi\)
−0.762101 + 0.647458i \(0.775832\pi\)
\(644\) −4.33269 + 24.8734i −0.170732 + 0.980147i
\(645\) 0 0
\(646\) 19.6168 + 85.9466i 0.771811 + 3.38153i
\(647\) −11.9418 14.9745i −0.469480 0.588710i 0.489563 0.871968i \(-0.337156\pi\)
−0.959044 + 0.283258i \(0.908585\pi\)
\(648\) 0 0
\(649\) 29.2367 14.0797i 1.14764 0.552675i
\(650\) 5.21368 22.8426i 0.204497 0.895962i
\(651\) 0 0
\(652\) −3.14598 13.7834i −0.123206 0.539801i
\(653\) 11.0850 + 13.9002i 0.433791 + 0.543957i 0.949895 0.312569i \(-0.101190\pi\)
−0.516104 + 0.856526i \(0.672618\pi\)
\(654\) 0 0
\(655\) −6.83988 −0.267256
\(656\) 32.7806 1.27987
\(657\) 0 0
\(658\) −15.2117 53.6388i −0.593013 2.09106i
\(659\) −39.2461 18.8999i −1.52881 0.736236i −0.534743 0.845015i \(-0.679592\pi\)
−0.994066 + 0.108779i \(0.965306\pi\)
\(660\) 0 0
\(661\) −4.99292 21.8754i −0.194202 0.850854i −0.974310 0.225210i \(-0.927693\pi\)
0.780108 0.625644i \(-0.215164\pi\)
\(662\) 6.80755 + 29.8258i 0.264583 + 1.15921i
\(663\) 0 0
\(664\) −3.31493 1.59638i −0.128644 0.0619517i
\(665\) 11.4824 0.596930i 0.445269 0.0231479i
\(666\) 0 0
\(667\) −6.76763 −0.262044
\(668\) −18.9858 −0.734583
\(669\) 0 0
\(670\) 5.25660 + 6.59157i 0.203080 + 0.254655i
\(671\) 8.12820 + 35.6120i 0.313786 + 1.37479i
\(672\) 0 0
\(673\) −2.57481 + 11.2810i −0.0992515 + 0.434849i 0.900748 + 0.434341i \(0.143019\pi\)
−1.00000 0.000507846i \(0.999838\pi\)
\(674\) 3.48802 1.67974i 0.134354 0.0647013i
\(675\) 0 0
\(676\) −5.59086 7.01071i −0.215033 0.269643i
\(677\) −2.87718 12.6057i −0.110579 0.484478i −0.999644 0.0266965i \(-0.991501\pi\)
0.889065 0.457782i \(-0.151356\pi\)
\(678\) 0 0
\(679\) −9.16306 10.3397i −0.351646 0.396802i
\(680\) −2.01436 2.52592i −0.0772471 0.0968648i
\(681\) 0 0
\(682\) −35.2006 16.9517i −1.34790 0.649115i
\(683\) −7.41818 + 9.30211i −0.283849 + 0.355935i −0.903231 0.429154i \(-0.858812\pi\)
0.619382 + 0.785090i \(0.287383\pi\)
\(684\) 0 0
\(685\) −4.87509 −0.186268
\(686\) 12.9233 + 32.3352i 0.493413 + 1.23456i
\(687\) 0 0
\(688\) −1.02849 + 4.50609i −0.0392106 + 0.171793i
\(689\) 0.689931 0.865147i 0.0262843 0.0329595i
\(690\) 0 0
\(691\) −11.6603 + 14.6216i −0.443580 + 0.556232i −0.952483 0.304592i \(-0.901480\pi\)
0.508903 + 0.860824i \(0.330051\pi\)
\(692\) 0.610940 + 0.766094i 0.0232244 + 0.0291225i
\(693\) 0 0
\(694\) 16.0970 20.1851i 0.611035 0.766214i
\(695\) −2.49709 10.9405i −0.0947200 0.414995i
\(696\) 0 0
\(697\) 9.77344 42.8202i 0.370195 1.62193i
\(698\) −14.9413 + 7.19537i −0.565538 + 0.272349i
\(699\) 0 0
\(700\) −16.5946 + 9.08158i −0.627216 + 0.343252i
\(701\) −6.95061 30.4526i −0.262521 1.15018i −0.918507 0.395406i \(-0.870604\pi\)
0.655986 0.754773i \(-0.272253\pi\)
\(702\) 0 0
\(703\) −64.5907 + 31.1053i −2.43609 + 1.17316i
\(704\) −19.5695 −0.737552
\(705\) 0 0
\(706\) −43.4414 + 20.9203i −1.63494 + 0.787345i
\(707\) 21.3707 1.11098i 0.803727 0.0417829i
\(708\) 0 0
\(709\) −8.33896 4.01583i −0.313176 0.150818i 0.270692 0.962666i \(-0.412747\pi\)
−0.583869 + 0.811848i \(0.698462\pi\)
\(710\) −2.15144 9.42607i −0.0807421 0.353754i
\(711\) 0 0
\(712\) 0.144527 + 0.0696006i 0.00541638 + 0.00260839i
\(713\) 23.4892 + 11.3118i 0.879679 + 0.423631i
\(714\) 0 0
\(715\) −6.99119 + 3.36678i −0.261456 + 0.125910i
\(716\) 13.6217 0.509068
\(717\) 0 0
\(718\) −30.4373 + 14.6578i −1.13591 + 0.547025i
\(719\) −11.4243 14.3256i −0.426055 0.534256i 0.521754 0.853096i \(-0.325278\pi\)
−0.947808 + 0.318841i \(0.896707\pi\)
\(720\) 0 0
\(721\) 9.04498 0.470216i 0.336853 0.0175118i
\(722\) −15.1106 + 66.2040i −0.562359 + 2.46386i
\(723\) 0 0
\(724\) 5.11305 22.4018i 0.190025 0.832555i
\(725\) −3.16151 3.96441i −0.117415 0.147234i
\(726\) 0 0
\(727\) −4.18507 + 5.24791i −0.155215 + 0.194634i −0.853359 0.521324i \(-0.825438\pi\)
0.698143 + 0.715958i \(0.254010\pi\)
\(728\) −1.06164 + 6.09473i −0.0393471 + 0.225886i
\(729\) 0 0
\(730\) −5.81127 + 7.28711i −0.215085 + 0.269708i
\(731\) 5.57952 + 2.68696i 0.206366 + 0.0993807i
\(732\) 0 0
\(733\) 6.95208 30.4590i 0.256781 1.12503i −0.667889 0.744261i \(-0.732802\pi\)
0.924670 0.380769i \(-0.124341\pi\)
\(734\) −23.4861 −0.866888
\(735\) 0 0
\(736\) 44.2246 1.63014
\(737\) −8.44487 + 36.9994i −0.311071 + 1.36289i
\(738\) 0 0
\(739\) 12.5936 + 6.06476i 0.463263 + 0.223096i 0.650931 0.759137i \(-0.274379\pi\)
−0.187668 + 0.982233i \(0.560093\pi\)
\(740\) −5.41061 + 6.78468i −0.198898 + 0.249410i
\(741\) 0 0
\(742\) −2.05456 + 0.106809i −0.0754253 + 0.00392109i
\(743\) −1.36708 + 1.71426i −0.0501533 + 0.0628902i −0.806276 0.591540i \(-0.798520\pi\)
0.756122 + 0.654430i \(0.227092\pi\)
\(744\) 0 0
\(745\) −2.42560 3.04160i −0.0888670 0.111436i
\(746\) −2.49180 + 10.9173i −0.0912313 + 0.399710i
\(747\) 0 0
\(748\) −10.6888 + 46.8308i −0.390822 + 1.71230i
\(749\) 20.4128 28.5171i 0.745869 1.04199i
\(750\) 0 0
\(751\) 14.8734 + 18.6506i 0.542737 + 0.680571i 0.975262 0.221051i \(-0.0709488\pi\)
−0.432525 + 0.901622i \(0.642377\pi\)
\(752\) −47.5969 + 22.9215i −1.73568 + 0.835859i
\(753\) 0 0
\(754\) 5.47724 0.199469
\(755\) −2.89876 + 1.39597i −0.105497 + 0.0508046i
\(756\) 0 0
\(757\) −25.3681 12.2166i −0.922018 0.444021i −0.0882269 0.996100i \(-0.528120\pi\)
−0.833791 + 0.552080i \(0.813834\pi\)
\(758\) 23.3537 + 11.2466i 0.848245 + 0.408493i
\(759\) 0 0
\(760\) −0.845103 3.70264i −0.0306551 0.134309i
\(761\) 6.36896 + 3.06713i 0.230875 + 0.111183i 0.545745 0.837951i \(-0.316247\pi\)
−0.314870 + 0.949135i \(0.601961\pi\)
\(762\) 0 0
\(763\) 29.8495 16.3355i 1.08062 0.591384i
\(764\) 12.7628 6.14626i 0.461743 0.222364i
\(765\) 0 0
\(766\) 28.4301 1.02722
\(767\) 15.7897 7.60391i 0.570132 0.274561i
\(768\) 0 0
\(769\) 8.54026 + 37.4173i 0.307970 + 1.34930i 0.857781 + 0.514015i \(0.171842\pi\)
−0.549812 + 0.835289i \(0.685300\pi\)
\(770\) 13.3055 + 5.57630i 0.479498 + 0.200956i
\(771\) 0 0
\(772\) 0.523589 0.252147i 0.0188444 0.00907497i
\(773\) 7.47824 32.7643i 0.268974 1.17845i −0.642236 0.766507i \(-0.721993\pi\)
0.911209 0.411943i \(-0.135150\pi\)
\(774\) 0 0
\(775\) 4.34669 + 19.0441i 0.156138 + 0.684084i
\(776\) −2.84524 + 3.56782i −0.102138 + 0.128077i
\(777\) 0 0
\(778\) −23.1683 29.0522i −0.830625 1.04157i
\(779\) 32.1912 40.3665i 1.15337 1.44628i
\(780\) 0 0
\(781\) 27.1353 34.0265i 0.970976 1.21756i
\(782\) 16.4247 71.9612i 0.587345 2.57333i
\(783\) 0 0
\(784\) 28.0827 17.3213i 1.00295 0.618617i
\(785\) −5.23556 −0.186865
\(786\) 0 0
\(787\) 12.6861 15.9079i 0.452212 0.567056i −0.502504 0.864575i \(-0.667588\pi\)
0.954716 + 0.297519i \(0.0961591\pi\)
\(788\) −28.6494 13.7968i −1.02059 0.491491i
\(789\) 0 0
\(790\) −0.297950 0.373618i −0.0106006 0.0132927i
\(791\) 22.8447 31.9144i 0.812265 1.13475i
\(792\) 0 0
\(793\) 4.38974 + 19.2327i 0.155884 + 0.682974i
\(794\) 3.08938 + 3.87396i 0.109638 + 0.137482i
\(795\) 0 0
\(796\) 24.4832 11.7905i 0.867783 0.417902i
\(797\) 5.93747 26.0138i 0.210316 0.921455i −0.754036 0.656833i \(-0.771896\pi\)
0.964352 0.264622i \(-0.0852472\pi\)
\(798\) 0 0
\(799\) 15.7507 + 69.0083i 0.557220 + 2.44134i
\(800\) 20.6596 + 25.9063i 0.730427 + 0.915927i
\(801\) 0 0
\(802\) −27.2559 −0.962439
\(803\) −41.9554 −1.48058
\(804\) 0 0
\(805\) −8.87874 3.72104i −0.312934 0.131150i
\(806\) −19.0105 9.15500i −0.669618 0.322471i
\(807\) 0 0
\(808\) −1.57288 6.89122i −0.0553336 0.242432i
\(809\) 3.61523 + 15.8394i 0.127105 + 0.556883i 0.997873 + 0.0651889i \(0.0207650\pi\)
−0.870768 + 0.491694i \(0.836378\pi\)
\(810\) 0 0
\(811\) 10.7645 + 5.18392i 0.377994 + 0.182032i 0.613227 0.789907i \(-0.289871\pi\)
−0.235233 + 0.971939i \(0.575585\pi\)
\(812\) −2.93300 3.30964i −0.102928 0.116146i
\(813\) 0 0
\(814\) −89.9520 −3.15282
\(815\) 5.39074 0.188829
\(816\) 0 0
\(817\) 4.53888 + 5.69157i 0.158795 + 0.199123i
\(818\) 4.28833 + 18.7884i 0.149938 + 0.656922i
\(819\) 0 0
\(820\) 1.39071 6.09308i 0.0485655 0.212780i
\(821\) 25.7405 12.3960i 0.898349 0.432622i 0.0730569 0.997328i \(-0.476725\pi\)
0.825292 + 0.564706i \(0.191010\pi\)
\(822\) 0 0
\(823\) 13.6348 + 17.0975i 0.475281 + 0.595983i 0.960455 0.278434i \(-0.0898154\pi\)
−0.485175 + 0.874417i \(0.661244\pi\)
\(824\) −0.665708 2.91666i −0.0231910 0.101607i
\(825\) 0 0
\(826\) −30.0507 12.5941i −1.04560 0.438205i
\(827\) −4.84209 6.07179i −0.168376 0.211137i 0.690483 0.723348i \(-0.257398\pi\)
−0.858859 + 0.512211i \(0.828826\pi\)
\(828\) 0 0
\(829\) 7.12896 + 3.43313i 0.247599 + 0.119237i 0.553568 0.832804i \(-0.313266\pi\)
−0.305969 + 0.952042i \(0.598980\pi\)
\(830\) −2.88910 + 3.62282i −0.100282 + 0.125750i
\(831\) 0 0
\(832\) −10.5688 −0.366406
\(833\) −14.2535 41.8478i −0.493854 1.44994i
\(834\) 0 0
\(835\) 1.61088 7.05773i 0.0557468 0.244243i
\(836\) −35.2062 + 44.1472i −1.21763 + 1.52686i
\(837\) 0 0
\(838\) 16.9547 21.2605i 0.585689 0.734431i
\(839\) −4.39444 5.51045i −0.151713 0.190242i 0.700167 0.713979i \(-0.253109\pi\)
−0.851880 + 0.523737i \(0.824537\pi\)
\(840\) 0 0
\(841\) −17.3421 + 21.7464i −0.598005 + 0.749874i
\(842\) 0.345228 + 1.51254i 0.0118973 + 0.0521256i
\(843\) 0 0
\(844\) −0.771087 + 3.37835i −0.0265419 + 0.116288i
\(845\) 3.08051 1.48349i 0.105973 0.0510338i
\(846\) 0 0
\(847\) 9.77769 + 34.4777i 0.335965 + 1.18467i
\(848\) 0.433778 + 1.90051i 0.0148960 + 0.0652637i
\(849\) 0 0
\(850\) 49.8269 23.9954i 1.70905 0.823035i
\(851\) 60.0246 2.05762
\(852\) 0 0
\(853\) 0.688830 0.331723i 0.0235851 0.0113580i −0.422054 0.906571i \(-0.638691\pi\)
0.445639 + 0.895213i \(0.352976\pi\)
\(854\) 21.3483 29.8240i 0.730524 1.02055i
\(855\) 0 0
\(856\) −10.4368 5.02607i −0.356721 0.171788i
\(857\) −11.0284 48.3187i −0.376724 1.65053i −0.707417 0.706797i \(-0.750140\pi\)
0.330693 0.943738i \(-0.392718\pi\)
\(858\) 0 0
\(859\) −3.51644 1.69343i −0.119980 0.0577791i 0.372931 0.927859i \(-0.378353\pi\)
−0.492911 + 0.870080i \(0.664067\pi\)
\(860\) 0.793935 + 0.382339i 0.0270730 + 0.0130376i
\(861\) 0 0
\(862\) 50.0927 24.1234i 1.70616 0.821645i
\(863\) −0.595925 −0.0202855 −0.0101428 0.999949i \(-0.503229\pi\)
−0.0101428 + 0.999949i \(0.503229\pi\)
\(864\) 0 0
\(865\) −0.336622 + 0.162108i −0.0114455 + 0.00551185i
\(866\) −27.9211 35.0120i −0.948798 1.18975i
\(867\) 0 0
\(868\) 4.64800 + 16.3896i 0.157763 + 0.556298i
\(869\) 0.478665 2.09717i 0.0162376 0.0711415i
\(870\) 0 0
\(871\) −4.56076 + 19.9820i −0.154535 + 0.677064i
\(872\) −7.00766 8.78733i −0.237309 0.297576i
\(873\) 0 0
\(874\) 54.0987 67.8376i 1.82991 2.29464i
\(875\) −4.08073 14.3893i −0.137954 0.486446i
\(876\) 0 0
\(877\) 35.5163 44.5360i 1.19930 1.50388i 0.385524 0.922698i \(-0.374021\pi\)
0.813777 0.581178i \(-0.197408\pi\)
\(878\) 10.1996 + 4.91189i 0.344221 + 0.165768i
\(879\) 0 0
\(880\) 3.04182 13.3271i 0.102540 0.449255i
\(881\) −48.3482 −1.62889 −0.814447 0.580238i \(-0.802959\pi\)
−0.814447 + 0.580238i \(0.802959\pi\)
\(882\) 0 0
\(883\) 37.6511 1.26706 0.633530 0.773718i \(-0.281605\pi\)
0.633530 + 0.773718i \(0.281605\pi\)
\(884\) −5.77264 + 25.2916i −0.194155 + 0.850648i
\(885\) 0 0
\(886\) 20.3261 + 9.78855i 0.682870 + 0.328853i
\(887\) 33.8241 42.4141i 1.13570 1.42412i 0.245008 0.969521i \(-0.421210\pi\)
0.890694 0.454604i \(-0.150219\pi\)
\(888\) 0 0
\(889\) 41.7164 + 17.4832i 1.39912 + 0.586368i
\(890\) 0.125961 0.157951i 0.00422224 0.00529452i
\(891\) 0 0
\(892\) −4.74093 5.94494i −0.158738 0.199051i
\(893\) −18.5153 + 81.1210i −0.619592 + 2.71461i
\(894\) 0 0
\(895\) −1.15576 + 5.06371i −0.0386327 + 0.169261i
\(896\) −11.9368 13.4697i −0.398781 0.449990i
\(897\) 0 0
\(898\) 35.3499 + 44.3273i 1.17964 + 1.47922i
\(899\) −4.11421 + 1.98130i −0.137216 + 0.0660800i
\(900\) 0 0
\(901\) 2.61190 0.0870151
\(902\) 58.3671 28.1081i 1.94341 0.935899i
\(903\) 0 0
\(904\) −11.6801 5.62485i −0.388475 0.187080i
\(905\) 7.89374 + 3.80142i 0.262397 + 0.126364i
\(906\) 0 0
\(907\) 3.40199 + 14.9051i 0.112961 + 0.494916i 0.999481 + 0.0322244i \(0.0102591\pi\)
−0.886519 + 0.462692i \(0.846884\pi\)
\(908\) −41.4756 19.9736i −1.37642 0.662847i
\(909\) 0 0
\(910\) 7.18583 + 3.01155i 0.238208 + 0.0998320i
\(911\) 24.5321 11.8140i 0.812784 0.391416i 0.0191539 0.999817i \(-0.493903\pi\)
0.793630 + 0.608400i \(0.208188\pi\)
\(912\) 0 0
\(913\) −20.8583 −0.690310
\(914\) 0.0283582 0.0136566i 0.000938004 0.000451719i
\(915\) 0 0
\(916\) −2.95384 12.9416i −0.0975976 0.427603i
\(917\) −5.30519 + 30.4563i −0.175193 + 1.00576i
\(918\) 0 0
\(919\) 32.2221 15.5174i 1.06291 0.511870i 0.181095 0.983466i \(-0.442036\pi\)
0.881815 + 0.471595i \(0.156322\pi\)
\(920\) −0.707585 + 3.10013i −0.0233284 + 0.102208i
\(921\) 0 0
\(922\) 15.7953 + 69.2037i 0.520190 + 2.27910i
\(923\) 14.6547 18.3765i 0.482367 0.604869i
\(924\) 0 0
\(925\) 28.0406 + 35.1618i 0.921970 + 1.15611i
\(926\) −19.8665 + 24.9118i −0.652853 + 0.818652i
\(927\) 0 0
\(928\) −4.82959 + 6.05612i −0.158539 + 0.198802i
\(929\) 0.0370105 0.162154i 0.00121428 0.00532009i −0.974317 0.225180i \(-0.927703\pi\)
0.975531 + 0.219860i \(0.0705601\pi\)
\(930\) 0 0
\(931\) 6.24807 51.5913i 0.204772 1.69084i
\(932\) 2.77165 0.0907885
\(933\) 0 0
\(934\) −44.4686 + 55.7618i −1.45506 + 1.82458i
\(935\) −16.5018 7.94686i −0.539667 0.259890i
\(936\) 0 0
\(937\) −12.7509 15.9891i −0.416554 0.522343i 0.528642 0.848845i \(-0.322701\pi\)
−0.945196 + 0.326502i \(0.894130\pi\)
\(938\) 33.4278 18.2937i 1.09146 0.597312i
\(939\) 0 0
\(940\) 2.24124 + 9.81950i 0.0731011 + 0.320277i
\(941\) −6.20557 7.78154i −0.202296 0.253671i 0.670327 0.742066i \(-0.266154\pi\)
−0.872623 + 0.488395i \(0.837583\pi\)
\(942\) 0 0
\(943\) −38.9482 + 18.7565i −1.26833 + 0.610794i
\(944\) −6.86997 + 30.0993i −0.223598 + 0.979649i
\(945\) 0 0
\(946\) 2.03255 + 8.90517i 0.0660838 + 0.289532i
\(947\) −14.1572 17.7525i −0.460047 0.576880i 0.496656 0.867948i \(-0.334561\pi\)
−0.956703 + 0.291067i \(0.905990\pi\)
\(948\) 0 0
\(949\) −22.6586 −0.735529
\(950\) 65.0109 2.10923
\(951\) 0 0
\(952\) −12.8097 + 7.01026i −0.415165 + 0.227204i
\(953\) −28.0017 13.4849i −0.907065 0.436820i −0.0786297 0.996904i \(-0.525054\pi\)
−0.828436 + 0.560084i \(0.810769\pi\)
\(954\) 0 0
\(955\) 1.20191 + 5.26591i 0.0388929 + 0.170401i
\(956\) 3.68804 + 16.1583i 0.119280 + 0.522598i
\(957\) 0 0
\(958\) 13.3910 + 6.44878i 0.432645 + 0.208351i
\(959\) −3.78124 + 21.7075i −0.122103 + 0.700973i
\(960\) 0 0
\(961\) −13.4087 −0.432537
\(962\) −48.5798 −1.56627
\(963\) 0 0
\(964\) 8.28453 + 10.3885i 0.266827 + 0.334590i
\(965\) 0.0493077 + 0.216031i 0.00158727 + 0.00695429i
\(966\) 0 0
\(967\) 8.51460 37.3049i 0.273811 1.19964i −0.631663 0.775243i \(-0.717627\pi\)
0.905474 0.424402i \(-0.139516\pi\)
\(968\) 10.6651 5.13604i 0.342789 0.165078i
\(969\) 0 0
\(970\) 3.58334 + 4.49337i 0.115054 + 0.144273i
\(971\) 7.74739 + 33.9435i 0.248626 + 1.08930i 0.932917 + 0.360092i \(0.117255\pi\)
−0.684291 + 0.729209i \(0.739888\pi\)
\(972\) 0 0
\(973\) −50.6520 + 2.63321i −1.62383 + 0.0844169i
\(974\) −34.7402 43.5628i −1.11315 1.39584i
\(975\) 0 0
\(976\) −31.3111 15.0786i −1.00224 0.482655i
\(977\) 4.75303 5.96011i 0.152063 0.190681i −0.699965 0.714177i \(-0.746801\pi\)
0.852028 + 0.523496i \(0.175373\pi\)
\(978\) 0 0
\(979\) 0.909399 0.0290645
\(980\) −2.02819 5.95471i −0.0647882 0.190216i
\(981\) 0 0
\(982\) 5.96143 26.1187i 0.190237 0.833482i
\(983\) 22.9342 28.7586i 0.731488 0.917257i −0.267439 0.963575i \(-0.586177\pi\)
0.998927 + 0.0463178i \(0.0147487\pi\)
\(984\) 0 0
\(985\) 7.55959 9.47943i 0.240869 0.302040i
\(986\) 8.06069 + 10.1078i 0.256705 + 0.321897i
\(987\) 0 0
\(988\) −19.0136 + 23.8423i −0.604903 + 0.758524i
\(989\) −1.35631 5.94238i −0.0431282 0.188957i
\(990\) 0 0
\(991\) 1.48428 6.50304i 0.0471496 0.206576i −0.945866 0.324557i \(-0.894785\pi\)
0.993016 + 0.117981i \(0.0376421\pi\)
\(992\) 26.8852 12.9472i 0.853607 0.411075i
\(993\) 0 0
\(994\) −43.6407 + 2.26872i −1.38420 + 0.0719595i
\(995\) 2.30564 + 10.1017i 0.0730939 + 0.320245i
\(996\) 0 0
\(997\) −11.5455 + 5.56001i −0.365649 + 0.176087i −0.607681 0.794181i \(-0.707900\pi\)
0.242033 + 0.970268i \(0.422186\pi\)
\(998\) 0.0110158 0.000348700
\(999\) 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 441.2.u.e.64.3 60
3.2 odd 2 inner 441.2.u.e.64.8 yes 60
49.36 even 7 inner 441.2.u.e.379.3 yes 60
147.134 odd 14 inner 441.2.u.e.379.8 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.u.e.64.3 60 1.1 even 1 trivial
441.2.u.e.64.8 yes 60 3.2 odd 2 inner
441.2.u.e.379.3 yes 60 49.36 even 7 inner
441.2.u.e.379.8 yes 60 147.134 odd 14 inner