Properties

Label 882.2.f.r.295.2
Level $882$
Weight $2$
Character 882.295
Analytic conductor $7.043$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.31116960000.2
Defining polynomial: \( x^{8} + x^{6} - 8x^{4} + 9x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.2
Root \(1.62968 - 0.586627i\) of defining polynomial
Character \(\chi\) \(=\) 882.295
Dual form 882.2.f.r.589.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.306808 + 1.70466i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.62968 + 2.82269i) q^{5} +(1.32288 + 1.11803i) q^{6} -1.00000 q^{8} +(-2.81174 - 1.04601i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.306808 + 1.70466i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.62968 + 2.82269i) q^{5} +(1.32288 + 1.11803i) q^{6} -1.00000 q^{8} +(-2.81174 - 1.04601i) q^{9} +3.25937 q^{10} +(-2.81174 + 4.87007i) q^{11} +(1.62968 - 0.586627i) q^{12} +(0.613616 + 1.06281i) q^{13} +(-5.31174 + 1.91203i) q^{15} +(-0.500000 + 0.866025i) q^{16} -5.90512 q^{17} +(-2.31174 + 1.91203i) q^{18} +2.64575 q^{19} +(1.62968 - 2.82269i) q^{20} +(2.81174 + 4.87007i) q^{22} +(-3.31174 - 5.73610i) q^{23} +(0.306808 - 1.70466i) q^{24} +(-2.81174 + 4.87007i) q^{25} +1.22723 q^{26} +(2.64575 - 4.47214i) q^{27} +(2.00000 - 3.46410i) q^{29} +(-1.00000 + 5.55612i) q^{30} +(-0.613616 - 1.06281i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-7.43916 - 6.28724i) q^{33} +(-2.95256 + 5.11398i) q^{34} +(0.500000 + 2.95804i) q^{36} +6.00000 q^{37} +(1.32288 - 2.29129i) q^{38} +(-2.00000 + 0.719927i) q^{39} +(-1.62968 - 2.82269i) q^{40} +(2.95256 + 5.11398i) q^{41} +(-3.81174 + 6.60212i) q^{43} +5.62348 q^{44} +(-1.62968 - 9.64134i) q^{45} -6.62348 q^{46} +(-5.29150 + 9.16515i) q^{47} +(-1.32288 - 1.11803i) q^{48} +(2.81174 + 4.87007i) q^{50} +(1.81174 - 10.0662i) q^{51} +(0.613616 - 1.06281i) q^{52} -4.00000 q^{53} +(-2.55011 - 4.52736i) q^{54} -18.3290 q^{55} +(-0.811738 + 4.51011i) q^{57} +(-2.00000 - 3.46410i) q^{58} +(7.43916 + 12.8850i) q^{59} +(4.31174 + 3.64408i) q^{60} +(2.24330 - 3.88551i) q^{61} -1.22723 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(-9.16449 + 3.29888i) q^{66} +(2.81174 + 4.87007i) q^{67} +(2.95256 + 5.11398i) q^{68} +(10.7942 - 3.88551i) q^{69} -10.6235 q^{71} +(2.81174 + 1.04601i) q^{72} +11.1966 q^{73} +(3.00000 - 5.19615i) q^{74} +(-7.43916 - 6.28724i) q^{75} +(-1.32288 - 2.29129i) q^{76} +(-0.376525 + 2.09201i) q^{78} +(-1.68826 + 2.92416i) q^{79} -3.25937 q^{80} +(6.81174 + 5.88220i) q^{81} +5.90512 q^{82} +(3.87298 - 6.70820i) q^{83} +(-9.62348 - 16.6683i) q^{85} +(3.81174 + 6.60212i) q^{86} +(5.29150 + 4.47214i) q^{87} +(2.81174 - 4.87007i) q^{88} +8.97320 q^{89} +(-9.16449 - 3.40932i) q^{90} +(-3.31174 + 5.73610i) q^{92} +(2.00000 - 0.719927i) q^{93} +(5.29150 + 9.16515i) q^{94} +(4.31174 + 7.46815i) q^{95} +(-1.62968 + 0.586627i) q^{96} +(-1.53404 + 2.65704i) q^{97} +(13.0000 - 10.7523i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 2 q^{9} - 2 q^{11} - 22 q^{15} - 4 q^{16} + 2 q^{18} + 2 q^{22} - 6 q^{23} - 2 q^{25} + 16 q^{29} - 8 q^{30} + 4 q^{32} + 4 q^{36} + 48 q^{37} - 16 q^{39} - 10 q^{43} + 4 q^{44} - 12 q^{46} + 2 q^{50} - 6 q^{51} - 32 q^{53} + 14 q^{57} - 16 q^{58} + 14 q^{60} + 8 q^{64} - 16 q^{65} + 2 q^{67} - 44 q^{71} + 2 q^{72} + 24 q^{74} - 44 q^{78} - 34 q^{79} + 34 q^{81} - 36 q^{85} + 10 q^{86} + 2 q^{88} - 6 q^{92} + 16 q^{93} + 14 q^{95} + 104 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −0.306808 + 1.70466i −0.177136 + 0.984186i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.62968 + 2.82269i 0.728817 + 1.26235i 0.957384 + 0.288819i \(0.0932627\pi\)
−0.228567 + 0.973528i \(0.573404\pi\)
\(6\) 1.32288 + 1.11803i 0.540062 + 0.456435i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −2.81174 1.04601i −0.937246 0.348669i
\(10\) 3.25937 1.03070
\(11\) −2.81174 + 4.87007i −0.847771 + 1.46838i 0.0354222 + 0.999372i \(0.488722\pi\)
−0.883193 + 0.469010i \(0.844611\pi\)
\(12\) 1.62968 0.586627i 0.470449 0.169345i
\(13\) 0.613616 + 1.06281i 0.170186 + 0.294772i 0.938485 0.345320i \(-0.112230\pi\)
−0.768298 + 0.640092i \(0.778896\pi\)
\(14\) 0 0
\(15\) −5.31174 + 1.91203i −1.37148 + 0.493685i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −5.90512 −1.43220 −0.716101 0.697997i \(-0.754075\pi\)
−0.716101 + 0.697997i \(0.754075\pi\)
\(18\) −2.31174 + 1.91203i −0.544882 + 0.450670i
\(19\) 2.64575 0.606977 0.303488 0.952835i \(-0.401849\pi\)
0.303488 + 0.952835i \(0.401849\pi\)
\(20\) 1.62968 2.82269i 0.364408 0.631174i
\(21\) 0 0
\(22\) 2.81174 + 4.87007i 0.599464 + 1.03830i
\(23\) −3.31174 5.73610i −0.690545 1.19606i −0.971660 0.236385i \(-0.924037\pi\)
0.281114 0.959674i \(-0.409296\pi\)
\(24\) 0.306808 1.70466i 0.0626269 0.347962i
\(25\) −2.81174 + 4.87007i −0.562348 + 0.974015i
\(26\) 1.22723 0.240680
\(27\) 2.64575 4.47214i 0.509175 0.860663i
\(28\) 0 0
\(29\) 2.00000 3.46410i 0.371391 0.643268i −0.618389 0.785872i \(-0.712214\pi\)
0.989780 + 0.142605i \(0.0455477\pi\)
\(30\) −1.00000 + 5.55612i −0.182574 + 1.01440i
\(31\) −0.613616 1.06281i −0.110209 0.190887i 0.805646 0.592398i \(-0.201819\pi\)
−0.915854 + 0.401511i \(0.868485\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −7.43916 6.28724i −1.29499 1.09447i
\(34\) −2.95256 + 5.11398i −0.506360 + 0.877041i
\(35\) 0 0
\(36\) 0.500000 + 2.95804i 0.0833333 + 0.493007i
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 1.32288 2.29129i 0.214599 0.371696i
\(39\) −2.00000 + 0.719927i −0.320256 + 0.115281i
\(40\) −1.62968 2.82269i −0.257676 0.446307i
\(41\) 2.95256 + 5.11398i 0.461112 + 0.798670i 0.999017 0.0443359i \(-0.0141172\pi\)
−0.537904 + 0.843006i \(0.680784\pi\)
\(42\) 0 0
\(43\) −3.81174 + 6.60212i −0.581285 + 1.00681i 0.414043 + 0.910257i \(0.364116\pi\)
−0.995327 + 0.0965570i \(0.969217\pi\)
\(44\) 5.62348 0.847771
\(45\) −1.62968 9.64134i −0.242939 1.43725i
\(46\) −6.62348 −0.976578
\(47\) −5.29150 + 9.16515i −0.771845 + 1.33687i 0.164706 + 0.986343i \(0.447333\pi\)
−0.936551 + 0.350532i \(0.886001\pi\)
\(48\) −1.32288 1.11803i −0.190941 0.161374i
\(49\) 0 0
\(50\) 2.81174 + 4.87007i 0.397640 + 0.688732i
\(51\) 1.81174 10.0662i 0.253694 1.40955i
\(52\) 0.613616 1.06281i 0.0850932 0.147386i
\(53\) −4.00000 −0.549442 −0.274721 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) −2.55011 4.52736i −0.347026 0.616095i
\(55\) −18.3290 −2.47148
\(56\) 0 0
\(57\) −0.811738 + 4.51011i −0.107517 + 0.597379i
\(58\) −2.00000 3.46410i −0.262613 0.454859i
\(59\) 7.43916 + 12.8850i 0.968496 + 1.67748i 0.699914 + 0.714227i \(0.253222\pi\)
0.268582 + 0.963257i \(0.413445\pi\)
\(60\) 4.31174 + 3.64408i 0.556643 + 0.470449i
\(61\) 2.24330 3.88551i 0.287225 0.497488i −0.685921 0.727676i \(-0.740601\pi\)
0.973146 + 0.230187i \(0.0739339\pi\)
\(62\) −1.22723 −0.155859
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.00000 + 3.46410i −0.248069 + 0.429669i
\(66\) −9.16449 + 3.29888i −1.12807 + 0.406064i
\(67\) 2.81174 + 4.87007i 0.343508 + 0.594974i 0.985082 0.172088i \(-0.0550513\pi\)
−0.641573 + 0.767062i \(0.721718\pi\)
\(68\) 2.95256 + 5.11398i 0.358050 + 0.620162i
\(69\) 10.7942 3.88551i 1.29947 0.467760i
\(70\) 0 0
\(71\) −10.6235 −1.26077 −0.630387 0.776281i \(-0.717104\pi\)
−0.630387 + 0.776281i \(0.717104\pi\)
\(72\) 2.81174 + 1.04601i 0.331366 + 0.123273i
\(73\) 11.1966 1.31047 0.655233 0.755427i \(-0.272571\pi\)
0.655233 + 0.755427i \(0.272571\pi\)
\(74\) 3.00000 5.19615i 0.348743 0.604040i
\(75\) −7.43916 6.28724i −0.859000 0.725988i
\(76\) −1.32288 2.29129i −0.151744 0.262829i
\(77\) 0 0
\(78\) −0.376525 + 2.09201i −0.0426330 + 0.236874i
\(79\) −1.68826 + 2.92416i −0.189944 + 0.328993i −0.945231 0.326401i \(-0.894164\pi\)
0.755287 + 0.655394i \(0.227497\pi\)
\(80\) −3.25937 −0.364408
\(81\) 6.81174 + 5.88220i 0.756860 + 0.653577i
\(82\) 5.90512 0.652111
\(83\) 3.87298 6.70820i 0.425115 0.736321i −0.571316 0.820730i \(-0.693567\pi\)
0.996431 + 0.0844091i \(0.0269003\pi\)
\(84\) 0 0
\(85\) −9.62348 16.6683i −1.04381 1.80794i
\(86\) 3.81174 + 6.60212i 0.411030 + 0.711925i
\(87\) 5.29150 + 4.47214i 0.567309 + 0.479463i
\(88\) 2.81174 4.87007i 0.299732 0.519151i
\(89\) 8.97320 0.951157 0.475579 0.879673i \(-0.342239\pi\)
0.475579 + 0.879673i \(0.342239\pi\)
\(90\) −9.16449 3.40932i −0.966022 0.359374i
\(91\) 0 0
\(92\) −3.31174 + 5.73610i −0.345273 + 0.598030i
\(93\) 2.00000 0.719927i 0.207390 0.0746530i
\(94\) 5.29150 + 9.16515i 0.545777 + 0.945313i
\(95\) 4.31174 + 7.46815i 0.442375 + 0.766216i
\(96\) −1.62968 + 0.586627i −0.166329 + 0.0598724i
\(97\) −1.53404 + 2.65704i −0.155758 + 0.269781i −0.933335 0.359007i \(-0.883115\pi\)
0.777577 + 0.628788i \(0.216449\pi\)
\(98\) 0 0
\(99\) 13.0000 10.7523i 1.30655 1.08064i
\(100\) 5.62348 0.562348
\(101\) −6.30757 + 10.9250i −0.627627 + 1.08708i 0.360400 + 0.932798i \(0.382640\pi\)
−0.988027 + 0.154283i \(0.950693\pi\)
\(102\) −7.81174 6.60212i −0.773477 0.653708i
\(103\) 4.67789 + 8.10234i 0.460926 + 0.798347i 0.999007 0.0445458i \(-0.0141841\pi\)
−0.538081 + 0.842893i \(0.680851\pi\)
\(104\) −0.613616 1.06281i −0.0601700 0.104217i
\(105\) 0 0
\(106\) −2.00000 + 3.46410i −0.194257 + 0.336463i
\(107\) 0.376525 0.0364000 0.0182000 0.999834i \(-0.494206\pi\)
0.0182000 + 0.999834i \(0.494206\pi\)
\(108\) −5.19586 0.0552199i −0.499972 0.00531353i
\(109\) 11.2470 1.07726 0.538631 0.842542i \(-0.318942\pi\)
0.538631 + 0.842542i \(0.318942\pi\)
\(110\) −9.16449 + 15.8734i −0.873799 + 1.51347i
\(111\) −1.84085 + 10.2280i −0.174726 + 0.970796i
\(112\) 0 0
\(113\) 3.68826 + 6.38826i 0.346963 + 0.600957i 0.985708 0.168461i \(-0.0538798\pi\)
−0.638746 + 0.769418i \(0.720546\pi\)
\(114\) 3.50000 + 2.95804i 0.327805 + 0.277046i
\(115\) 10.7942 18.6961i 1.00656 1.74342i
\(116\) −4.00000 −0.371391
\(117\) −0.613616 3.63020i −0.0567288 0.335612i
\(118\) 14.8783 1.36966
\(119\) 0 0
\(120\) 5.31174 1.91203i 0.484893 0.174544i
\(121\) −10.3117 17.8605i −0.937431 1.62368i
\(122\) −2.24330 3.88551i −0.203099 0.351777i
\(123\) −9.62348 + 3.46410i −0.867720 + 0.312348i
\(124\) −0.613616 + 1.06281i −0.0551043 + 0.0954435i
\(125\) −2.03214 −0.181760
\(126\) 0 0
\(127\) 1.37652 0.122147 0.0610734 0.998133i \(-0.480548\pi\)
0.0610734 + 0.998133i \(0.480548\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −10.0849 8.52330i −0.887927 0.750435i
\(130\) 2.00000 + 3.46410i 0.175412 + 0.303822i
\(131\) 2.85692 + 4.94832i 0.249610 + 0.432337i 0.963418 0.268005i \(-0.0863643\pi\)
−0.713808 + 0.700342i \(0.753031\pi\)
\(132\) −1.72533 + 9.58612i −0.150170 + 0.834365i
\(133\) 0 0
\(134\) 5.62348 0.485794
\(135\) 16.9352 + 0.179982i 1.45755 + 0.0154904i
\(136\) 5.90512 0.506360
\(137\) 10.4352 18.0743i 0.891540 1.54419i 0.0535117 0.998567i \(-0.482959\pi\)
0.838029 0.545626i \(-0.183708\pi\)
\(138\) 2.03214 11.2908i 0.172987 0.961135i
\(139\) −3.96863 6.87386i −0.336615 0.583033i 0.647179 0.762338i \(-0.275949\pi\)
−0.983794 + 0.179305i \(0.942615\pi\)
\(140\) 0 0
\(141\) −14.0000 11.8322i −1.17901 0.996448i
\(142\) −5.31174 + 9.20020i −0.445751 + 0.772064i
\(143\) −6.90131 −0.577116
\(144\) 2.31174 1.91203i 0.192645 0.159336i
\(145\) 13.0375 1.08270
\(146\) 5.59831 9.69656i 0.463319 0.802493i
\(147\) 0 0
\(148\) −3.00000 5.19615i −0.246598 0.427121i
\(149\) 2.62348 + 4.54399i 0.214923 + 0.372258i 0.953249 0.302186i \(-0.0977165\pi\)
−0.738325 + 0.674445i \(0.764383\pi\)
\(150\) −9.16449 + 3.29888i −0.748277 + 0.269353i
\(151\) 4.31174 7.46815i 0.350884 0.607749i −0.635520 0.772084i \(-0.719214\pi\)
0.986405 + 0.164335i \(0.0525477\pi\)
\(152\) −2.64575 −0.214599
\(153\) 16.6036 + 6.17680i 1.34233 + 0.499364i
\(154\) 0 0
\(155\) 2.00000 3.46410i 0.160644 0.278243i
\(156\) 1.62348 + 1.37209i 0.129982 + 0.109855i
\(157\) −8.14842 14.1135i −0.650315 1.12638i −0.983046 0.183356i \(-0.941304\pi\)
0.332732 0.943021i \(-0.392030\pi\)
\(158\) 1.68826 + 2.92416i 0.134311 + 0.232633i
\(159\) 1.22723 6.81864i 0.0973258 0.540754i
\(160\) −1.62968 + 2.82269i −0.128838 + 0.223154i
\(161\) 0 0
\(162\) 8.50000 2.95804i 0.667823 0.232406i
\(163\) −1.24695 −0.0976687 −0.0488344 0.998807i \(-0.515551\pi\)
−0.0488344 + 0.998807i \(0.515551\pi\)
\(164\) 2.95256 5.11398i 0.230556 0.399335i
\(165\) 5.62348 31.2447i 0.437787 2.43240i
\(166\) −3.87298 6.70820i −0.300602 0.520658i
\(167\) 3.25937 + 5.64539i 0.252217 + 0.436853i 0.964136 0.265409i \(-0.0855069\pi\)
−0.711919 + 0.702262i \(0.752174\pi\)
\(168\) 0 0
\(169\) 5.74695 9.95401i 0.442073 0.765693i
\(170\) −19.2470 −1.47617
\(171\) −7.43916 2.76748i −0.568887 0.211634i
\(172\) 7.62348 0.581285
\(173\) −0.613616 + 1.06281i −0.0466524 + 0.0808043i −0.888409 0.459053i \(-0.848189\pi\)
0.841756 + 0.539858i \(0.181522\pi\)
\(174\) 6.51873 2.34651i 0.494184 0.177888i
\(175\) 0 0
\(176\) −2.81174 4.87007i −0.211943 0.367096i
\(177\) −24.2470 + 8.72802i −1.82251 + 0.656038i
\(178\) 4.48660 7.77102i 0.336285 0.582462i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) −7.53480 + 6.23202i −0.561611 + 0.464507i
\(181\) −4.48660 −0.333486 −0.166743 0.986000i \(-0.553325\pi\)
−0.166743 + 0.986000i \(0.553325\pi\)
\(182\) 0 0
\(183\) 5.93521 + 5.01617i 0.438744 + 0.370806i
\(184\) 3.31174 + 5.73610i 0.244145 + 0.422871i
\(185\) 9.77810 + 16.9362i 0.718900 + 1.24517i
\(186\) 0.376525 2.09201i 0.0276081 0.153394i
\(187\) 16.6036 28.7584i 1.21418 2.10302i
\(188\) 10.5830 0.771845
\(189\) 0 0
\(190\) 8.62348 0.625613
\(191\) −2.68826 + 4.65621i −0.194516 + 0.336911i −0.946742 0.321994i \(-0.895647\pi\)
0.752226 + 0.658905i \(0.228980\pi\)
\(192\) −0.306808 + 1.70466i −0.0221420 + 0.123023i
\(193\) −6.74695 11.6861i −0.485656 0.841181i 0.514208 0.857666i \(-0.328086\pi\)
−0.999864 + 0.0164844i \(0.994753\pi\)
\(194\) 1.53404 + 2.65704i 0.110138 + 0.190764i
\(195\) −5.29150 4.47214i −0.378932 0.320256i
\(196\) 0 0
\(197\) 7.24695 0.516324 0.258162 0.966102i \(-0.416883\pi\)
0.258162 + 0.966102i \(0.416883\pi\)
\(198\) −2.81174 16.6345i −0.199821 1.18216i
\(199\) −10.2004 −0.723089 −0.361545 0.932355i \(-0.617751\pi\)
−0.361545 + 0.932355i \(0.617751\pi\)
\(200\) 2.81174 4.87007i 0.198820 0.344366i
\(201\) −9.16449 + 3.29888i −0.646413 + 0.232685i
\(202\) 6.30757 + 10.9250i 0.443799 + 0.768683i
\(203\) 0 0
\(204\) −9.62348 + 3.46410i −0.673778 + 0.242536i
\(205\) −9.62348 + 16.6683i −0.672133 + 1.16417i
\(206\) 9.35577 0.651848
\(207\) 3.31174 + 19.5925i 0.230182 + 1.36177i
\(208\) −1.22723 −0.0850932
\(209\) −7.43916 + 12.8850i −0.514577 + 0.891274i
\(210\) 0 0
\(211\) 2.62348 + 4.54399i 0.180607 + 0.312821i 0.942088 0.335367i \(-0.108860\pi\)
−0.761480 + 0.648188i \(0.775527\pi\)
\(212\) 2.00000 + 3.46410i 0.137361 + 0.237915i
\(213\) 3.25937 18.1094i 0.223328 1.24084i
\(214\) 0.188262 0.326080i 0.0128693 0.0222904i
\(215\) −24.8477 −1.69460
\(216\) −2.64575 + 4.47214i −0.180021 + 0.304290i
\(217\) 0 0
\(218\) 5.62348 9.74015i 0.380870 0.659686i
\(219\) −3.43521 + 19.0864i −0.232130 + 1.28974i
\(220\) 9.16449 + 15.8734i 0.617870 + 1.07018i
\(221\) −3.62348 6.27604i −0.243741 0.422172i
\(222\) 7.93725 + 6.70820i 0.532714 + 0.450225i
\(223\) 3.25937 5.64539i 0.218263 0.378043i −0.736014 0.676967i \(-0.763294\pi\)
0.954277 + 0.298923i \(0.0966275\pi\)
\(224\) 0 0
\(225\) 13.0000 10.7523i 0.866667 0.716818i
\(226\) 7.37652 0.490679
\(227\) −14.3603 + 24.8728i −0.953130 + 1.65087i −0.214538 + 0.976716i \(0.568825\pi\)
−0.738592 + 0.674153i \(0.764509\pi\)
\(228\) 4.31174 1.55207i 0.285552 0.102788i
\(229\) 13.4399 + 23.2786i 0.888135 + 1.53829i 0.842078 + 0.539356i \(0.181332\pi\)
0.0460572 + 0.998939i \(0.485334\pi\)
\(230\) −10.7942 18.6961i −0.711746 1.23278i
\(231\) 0 0
\(232\) −2.00000 + 3.46410i −0.131306 + 0.227429i
\(233\) 17.0000 1.11371 0.556854 0.830611i \(-0.312008\pi\)
0.556854 + 0.830611i \(0.312008\pi\)
\(234\) −3.45065 1.28369i −0.225576 0.0839177i
\(235\) −34.4939 −2.25013
\(236\) 7.43916 12.8850i 0.484248 0.838742i
\(237\) −4.46672 3.77507i −0.290145 0.245217i
\(238\) 0 0
\(239\) −6.31174 10.9323i −0.408272 0.707148i 0.586424 0.810004i \(-0.300535\pi\)
−0.994696 + 0.102856i \(0.967202\pi\)
\(240\) 1.00000 5.55612i 0.0645497 0.358646i
\(241\) −13.3443 + 23.1130i −0.859580 + 1.48884i 0.0127491 + 0.999919i \(0.495942\pi\)
−0.872330 + 0.488918i \(0.837392\pi\)
\(242\) −20.6235 −1.32573
\(243\) −12.1170 + 9.80700i −0.777309 + 0.629119i
\(244\) −4.48660 −0.287225
\(245\) 0 0
\(246\) −1.81174 + 10.0662i −0.115512 + 0.641799i
\(247\) 1.62348 + 2.81194i 0.103299 + 0.178920i
\(248\) 0.613616 + 1.06281i 0.0389647 + 0.0674888i
\(249\) 10.2470 + 8.66025i 0.649374 + 0.548821i
\(250\) −1.01607 + 1.75988i −0.0642618 + 0.111305i
\(251\) −5.10022 −0.321923 −0.160961 0.986961i \(-0.551459\pi\)
−0.160961 + 0.986961i \(0.551459\pi\)
\(252\) 0 0
\(253\) 37.2470 2.34170
\(254\) 0.688262 1.19211i 0.0431854 0.0747993i
\(255\) 31.3664 11.2908i 1.96424 0.707056i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0.498095 + 0.862726i 0.0310703 + 0.0538154i 0.881142 0.472851i \(-0.156775\pi\)
−0.850072 + 0.526666i \(0.823442\pi\)
\(258\) −12.4239 + 4.47214i −0.773475 + 0.278423i
\(259\) 0 0
\(260\) 4.00000 0.248069
\(261\) −9.24695 + 7.64813i −0.572372 + 0.473407i
\(262\) 5.71383 0.353002
\(263\) 1.68826 2.92416i 0.104103 0.180311i −0.809269 0.587439i \(-0.800136\pi\)
0.913371 + 0.407128i \(0.133470\pi\)
\(264\) 7.43916 + 6.28724i 0.457849 + 0.386953i
\(265\) −6.51873 11.2908i −0.400443 0.693587i
\(266\) 0 0
\(267\) −2.75305 + 15.2963i −0.168484 + 0.936116i
\(268\) 2.81174 4.87007i 0.171754 0.297487i
\(269\) 24.0428 1.46592 0.732958 0.680274i \(-0.238139\pi\)
0.732958 + 0.680274i \(0.238139\pi\)
\(270\) 8.62348 14.5763i 0.524808 0.887087i
\(271\) 2.83704 0.172338 0.0861689 0.996281i \(-0.472538\pi\)
0.0861689 + 0.996281i \(0.472538\pi\)
\(272\) 2.95256 5.11398i 0.179025 0.310081i
\(273\) 0 0
\(274\) −10.4352 18.0743i −0.630414 1.09191i
\(275\) −15.8117 27.3867i −0.953484 1.65148i
\(276\) −8.76203 7.40527i −0.527412 0.445745i
\(277\) 14.2470 24.6764i 0.856016 1.48266i −0.0196827 0.999806i \(-0.506266\pi\)
0.875699 0.482857i \(-0.160401\pi\)
\(278\) −7.93725 −0.476045
\(279\) 0.613616 + 3.63020i 0.0367362 + 0.217334i
\(280\) 0 0
\(281\) 12.9352 22.4044i 0.771650 1.33654i −0.165008 0.986292i \(-0.552765\pi\)
0.936658 0.350245i \(-0.113902\pi\)
\(282\) −17.2470 + 6.20828i −1.02704 + 0.369697i
\(283\) −3.66182 6.34246i −0.217673 0.377020i 0.736423 0.676521i \(-0.236513\pi\)
−0.954096 + 0.299501i \(0.903180\pi\)
\(284\) 5.31174 + 9.20020i 0.315194 + 0.545931i
\(285\) −14.0535 + 5.05876i −0.832460 + 0.299655i
\(286\) −3.45065 + 5.97671i −0.204041 + 0.353410i
\(287\) 0 0
\(288\) −0.500000 2.95804i −0.0294628 0.174304i
\(289\) 17.8704 1.05120
\(290\) 6.51873 11.2908i 0.382793 0.663017i
\(291\) −4.05869 3.43022i −0.237925 0.201083i
\(292\) −5.59831 9.69656i −0.327616 0.567448i
\(293\) −12.8263 22.2158i −0.749321 1.29786i −0.948149 0.317827i \(-0.897047\pi\)
0.198828 0.980034i \(-0.436287\pi\)
\(294\) 0 0
\(295\) −24.2470 + 41.9970i −1.41171 + 2.44516i
\(296\) −6.00000 −0.348743
\(297\) 14.3405 + 25.4595i 0.832118 + 1.47731i
\(298\) 5.24695 0.303948
\(299\) 4.06427 7.03952i 0.235043 0.407106i
\(300\) −1.72533 + 9.58612i −0.0996118 + 0.553455i
\(301\) 0 0
\(302\) −4.31174 7.46815i −0.248113 0.429744i
\(303\) −16.6883 14.1042i −0.958716 0.810263i
\(304\) −1.32288 + 2.29129i −0.0758721 + 0.131414i
\(305\) 14.6235 0.837338
\(306\) 13.6511 11.2908i 0.780381 0.645451i
\(307\) 13.2288 0.755005 0.377503 0.926009i \(-0.376783\pi\)
0.377503 + 0.926009i \(0.376783\pi\)
\(308\) 0 0
\(309\) −15.2470 + 5.48835i −0.867369 + 0.312221i
\(310\) −2.00000 3.46410i −0.113592 0.196748i
\(311\) −10.3917 17.9990i −0.589260 1.02063i −0.994330 0.106343i \(-0.966086\pi\)
0.405069 0.914286i \(-0.367247\pi\)
\(312\) 2.00000 0.719927i 0.113228 0.0407579i
\(313\) −10.8898 + 18.8617i −0.615529 + 1.06613i 0.374763 + 0.927121i \(0.377724\pi\)
−0.990292 + 0.139006i \(0.955609\pi\)
\(314\) −16.2968 −0.919684
\(315\) 0 0
\(316\) 3.37652 0.189944
\(317\) −3.62348 + 6.27604i −0.203515 + 0.352498i −0.949658 0.313287i \(-0.898570\pi\)
0.746144 + 0.665785i \(0.231903\pi\)
\(318\) −5.29150 4.47214i −0.296733 0.250785i
\(319\) 11.2470 + 19.4803i 0.629708 + 1.09069i
\(320\) 1.62968 + 2.82269i 0.0911021 + 0.157793i
\(321\) −0.115521 + 0.641847i −0.00644774 + 0.0358244i
\(322\) 0 0
\(323\) −15.6235 −0.869313
\(324\) 1.68826 8.84024i 0.0937924 0.491124i
\(325\) −6.90131 −0.382816
\(326\) −0.623475 + 1.07989i −0.0345311 + 0.0598096i
\(327\) −3.45065 + 19.1722i −0.190822 + 1.06023i
\(328\) −2.95256 5.11398i −0.163028 0.282372i
\(329\) 0 0
\(330\) −24.2470 20.4924i −1.33475 1.12807i
\(331\) −4.00000 + 6.92820i −0.219860 + 0.380808i −0.954765 0.297361i \(-0.903893\pi\)
0.734905 + 0.678170i \(0.237227\pi\)
\(332\) −7.74597 −0.425115
\(333\) −16.8704 6.27604i −0.924494 0.343925i
\(334\) 6.51873 0.356689
\(335\) −9.16449 + 15.8734i −0.500709 + 0.867254i
\(336\) 0 0
\(337\) −1.56479 2.71029i −0.0852394 0.147639i 0.820254 0.572000i \(-0.193832\pi\)
−0.905493 + 0.424361i \(0.860499\pi\)
\(338\) −5.74695 9.95401i −0.312593 0.541427i
\(339\) −12.0214 + 4.32727i −0.652913 + 0.235025i
\(340\) −9.62348 + 16.6683i −0.521906 + 0.903968i
\(341\) 6.90131 0.373727
\(342\) −6.11628 + 5.05876i −0.330731 + 0.273547i
\(343\) 0 0
\(344\) 3.81174 6.60212i 0.205515 0.355963i
\(345\) 28.5587 + 24.1365i 1.53755 + 1.29947i
\(346\) 0.613616 + 1.06281i 0.0329882 + 0.0571372i
\(347\) 1.81174 + 3.13802i 0.0972592 + 0.168458i 0.910549 0.413401i \(-0.135659\pi\)
−0.813290 + 0.581858i \(0.802326\pi\)
\(348\) 1.22723 6.81864i 0.0657865 0.365518i
\(349\) 13.6511 23.6444i 0.730726 1.26565i −0.225848 0.974163i \(-0.572515\pi\)
0.956573 0.291492i \(-0.0941515\pi\)
\(350\) 0 0
\(351\) 6.37652 + 0.0677676i 0.340354 + 0.00361717i
\(352\) −5.62348 −0.299732
\(353\) 2.95256 5.11398i 0.157149 0.272190i −0.776691 0.629882i \(-0.783103\pi\)
0.933839 + 0.357693i \(0.116436\pi\)
\(354\) −4.56479 + 25.3625i −0.242616 + 1.34800i
\(355\) −17.3129 29.9868i −0.918874 1.59154i
\(356\) −4.48660 7.77102i −0.237789 0.411863i
\(357\) 0 0
\(358\) 0 0
\(359\) 31.1174 1.64231 0.821156 0.570704i \(-0.193329\pi\)
0.821156 + 0.570704i \(0.193329\pi\)
\(360\) 1.62968 + 9.64134i 0.0858919 + 0.508143i
\(361\) −12.0000 −0.631579
\(362\) −2.24330 + 3.88551i −0.117905 + 0.204218i
\(363\) 33.6097 12.0983i 1.76405 0.634995i
\(364\) 0 0
\(365\) 18.2470 + 31.6046i 0.955089 + 1.65426i
\(366\) 7.31174 2.63196i 0.382191 0.137575i
\(367\) 3.45065 5.97671i 0.180123 0.311982i −0.761799 0.647813i \(-0.775684\pi\)
0.941922 + 0.335831i \(0.109017\pi\)
\(368\) 6.62348 0.345273
\(369\) −2.95256 17.4676i −0.153704 0.909326i
\(370\) 19.5562 1.01668
\(371\) 0 0
\(372\) −1.62348 1.37209i −0.0841733 0.0711394i
\(373\) −5.62348 9.74015i −0.291173 0.504326i 0.682915 0.730498i \(-0.260712\pi\)
−0.974087 + 0.226172i \(0.927379\pi\)
\(374\) −16.6036 28.7584i −0.858554 1.48706i
\(375\) 0.623475 3.46410i 0.0321961 0.178885i
\(376\) 5.29150 9.16515i 0.272888 0.472657i
\(377\) 4.90893 0.252823
\(378\) 0 0
\(379\) 15.6235 0.802524 0.401262 0.915963i \(-0.368572\pi\)
0.401262 + 0.915963i \(0.368572\pi\)
\(380\) 4.31174 7.46815i 0.221187 0.383108i
\(381\) −0.422329 + 2.34651i −0.0216366 + 0.120215i
\(382\) 2.68826 + 4.65621i 0.137543 + 0.238232i
\(383\) −13.8424 23.9757i −0.707312 1.22510i −0.965851 0.259100i \(-0.916574\pi\)
0.258538 0.966001i \(-0.416759\pi\)
\(384\) 1.32288 + 1.11803i 0.0675077 + 0.0570544i
\(385\) 0 0
\(386\) −13.4939 −0.686822
\(387\) 17.6235 14.5763i 0.895852 0.740957i
\(388\) 3.06808 0.155758
\(389\) −18.6235 + 32.2568i −0.944248 + 1.63548i −0.186997 + 0.982360i \(0.559876\pi\)
−0.757251 + 0.653125i \(0.773458\pi\)
\(390\) −6.51873 + 2.34651i −0.330089 + 0.118820i
\(391\) 19.5562 + 33.8723i 0.989000 + 1.71300i
\(392\) 0 0
\(393\) −9.31174 + 3.35189i −0.469715 + 0.169080i
\(394\) 3.62348 6.27604i 0.182548 0.316183i
\(395\) −11.0053 −0.553738
\(396\) −15.8117 5.88220i −0.794570 0.295591i
\(397\) −9.35577 −0.469553 −0.234776 0.972049i \(-0.575436\pi\)
−0.234776 + 0.972049i \(0.575436\pi\)
\(398\) −5.10022 + 8.83383i −0.255651 + 0.442800i
\(399\) 0 0
\(400\) −2.81174 4.87007i −0.140587 0.243504i
\(401\) 7.50000 + 12.9904i 0.374532 + 0.648709i 0.990257 0.139253i \(-0.0444700\pi\)
−0.615725 + 0.787961i \(0.711137\pi\)
\(402\) −1.72533 + 9.58612i −0.0860515 + 0.478112i
\(403\) 0.753049 1.30432i 0.0375121 0.0649728i
\(404\) 12.6151 0.627627
\(405\) −5.50267 + 28.8136i −0.273430 + 1.43176i
\(406\) 0 0
\(407\) −16.8704 + 29.2204i −0.836236 + 1.44840i
\(408\) −1.81174 + 10.0662i −0.0896944 + 0.498352i
\(409\) −1.11171 1.92554i −0.0549706 0.0952118i 0.837231 0.546850i \(-0.184173\pi\)
−0.892201 + 0.451638i \(0.850840\pi\)
\(410\) 9.62348 + 16.6683i 0.475270 + 0.823191i
\(411\) 27.6090 + 23.3338i 1.36185 + 1.15097i
\(412\) 4.67789 8.10234i 0.230463 0.399174i
\(413\) 0 0
\(414\) 18.6235 + 6.92820i 0.915294 + 0.340503i
\(415\) 25.2470 1.23932
\(416\) −0.613616 + 1.06281i −0.0300850 + 0.0521087i
\(417\) 12.9352 4.65621i 0.633440 0.228015i
\(418\) 7.43916 + 12.8850i 0.363861 + 0.630226i
\(419\) −0.402452 0.697067i −0.0196610 0.0340539i 0.856027 0.516930i \(-0.172925\pi\)
−0.875689 + 0.482876i \(0.839592\pi\)
\(420\) 0 0
\(421\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(422\) 5.24695 0.255418
\(423\) 24.4651 20.2351i 1.18954 0.983862i
\(424\) 4.00000 0.194257
\(425\) 16.6036 28.7584i 0.805395 1.39499i
\(426\) −14.0535 11.8774i −0.680896 0.575462i
\(427\) 0 0
\(428\) −0.188262 0.326080i −0.00910000 0.0157617i
\(429\) 2.11738 11.7644i 0.102228 0.567990i
\(430\) −12.4239 + 21.5187i −0.599131 + 1.03773i
\(431\) −8.00000 −0.385346 −0.192673 0.981263i \(-0.561716\pi\)
−0.192673 + 0.981263i \(0.561716\pi\)
\(432\) 2.55011 + 4.52736i 0.122692 + 0.217823i
\(433\) −7.13235 −0.342759 −0.171379 0.985205i \(-0.554822\pi\)
−0.171379 + 0.985205i \(0.554822\pi\)
\(434\) 0 0
\(435\) −4.00000 + 22.2245i −0.191785 + 1.06558i
\(436\) −5.62348 9.74015i −0.269316 0.466468i
\(437\) −8.76203 15.1763i −0.419145 0.725980i
\(438\) 14.8117 + 12.5182i 0.707732 + 0.598143i
\(439\) −15.4919 + 26.8328i −0.739390 + 1.28066i 0.213381 + 0.976969i \(0.431552\pi\)
−0.952770 + 0.303691i \(0.901781\pi\)
\(440\) 18.3290 0.873799
\(441\) 0 0
\(442\) −7.24695 −0.344702
\(443\) −10.1883 + 17.6466i −0.484059 + 0.838415i −0.999832 0.0183103i \(-0.994171\pi\)
0.515773 + 0.856725i \(0.327505\pi\)
\(444\) 9.77810 3.51976i 0.464048 0.167040i
\(445\) 14.6235 + 25.3286i 0.693219 + 1.20069i
\(446\) −3.25937 5.64539i −0.154336 0.267317i
\(447\) −8.55087 + 3.07800i −0.404442 + 0.145585i
\(448\) 0 0
\(449\) −15.0000 −0.707894 −0.353947 0.935266i \(-0.615161\pi\)
−0.353947 + 0.935266i \(0.615161\pi\)
\(450\) −2.81174 16.6345i −0.132547 0.784156i
\(451\) −33.2073 −1.56367
\(452\) 3.68826 6.38826i 0.173481 0.300478i
\(453\) 11.4078 + 9.64134i 0.535985 + 0.452990i
\(454\) 14.3603 + 24.8728i 0.673964 + 1.16734i
\(455\) 0 0
\(456\) 0.811738 4.51011i 0.0380131 0.211205i
\(457\) −5.50000 + 9.52628i −0.257279 + 0.445621i −0.965512 0.260358i \(-0.916159\pi\)
0.708233 + 0.705979i \(0.249493\pi\)
\(458\) 26.8798 1.25601
\(459\) −15.6235 + 26.4085i −0.729241 + 1.23264i
\(460\) −21.5883 −1.00656
\(461\) −4.88905 + 8.46808i −0.227706 + 0.394398i −0.957128 0.289666i \(-0.906456\pi\)
0.729422 + 0.684064i \(0.239789\pi\)
\(462\) 0 0
\(463\) −12.6883 21.9767i −0.589674 1.02134i −0.994275 0.106851i \(-0.965923\pi\)
0.404601 0.914493i \(-0.367410\pi\)
\(464\) 2.00000 + 3.46410i 0.0928477 + 0.160817i
\(465\) 5.29150 + 4.47214i 0.245388 + 0.207390i
\(466\) 8.50000 14.7224i 0.393755 0.682003i
\(467\) 11.1966 0.518118 0.259059 0.965862i \(-0.416588\pi\)
0.259059 + 0.965862i \(0.416588\pi\)
\(468\) −2.83704 + 2.34651i −0.131142 + 0.108467i
\(469\) 0 0
\(470\) −17.2470 + 29.8726i −0.795543 + 1.37792i
\(471\) 26.5587 9.56016i 1.22376 0.440509i
\(472\) −7.43916 12.8850i −0.342415 0.593080i
\(473\) −21.4352 37.1269i −0.985592 1.70710i
\(474\) −5.50267 + 1.98076i −0.252746 + 0.0909793i
\(475\) −7.43916 + 12.8850i −0.341332 + 0.591204i
\(476\) 0 0
\(477\) 11.2470 + 4.18403i 0.514962 + 0.191574i
\(478\) −12.6235 −0.577384
\(479\) −7.74597 + 13.4164i −0.353922 + 0.613011i −0.986933 0.161132i \(-0.948486\pi\)
0.633011 + 0.774143i \(0.281819\pi\)
\(480\) −4.31174 3.64408i −0.196803 0.166329i
\(481\) 3.68170 + 6.37688i 0.167871 + 0.290761i
\(482\) 13.3443 + 23.1130i 0.607815 + 1.05277i
\(483\) 0 0
\(484\) −10.3117 + 17.8605i −0.468715 + 0.811839i
\(485\) −10.0000 −0.454077
\(486\) 2.43459 + 15.3972i 0.110435 + 0.698430i
\(487\) 4.62348 0.209510 0.104755 0.994498i \(-0.466594\pi\)
0.104755 + 0.994498i \(0.466594\pi\)
\(488\) −2.24330 + 3.88551i −0.101549 + 0.175889i
\(489\) 0.382574 2.12563i 0.0173006 0.0961242i
\(490\) 0 0
\(491\) 18.0587 + 31.2786i 0.814977 + 1.41158i 0.909344 + 0.416044i \(0.136584\pi\)
−0.0943671 + 0.995537i \(0.530083\pi\)
\(492\) 7.81174 + 6.60212i 0.352180 + 0.297647i
\(493\) −11.8102 + 20.4559i −0.531906 + 0.921289i
\(494\) 3.24695 0.146087
\(495\) 51.5363 + 19.1722i 2.31638 + 0.861728i
\(496\) 1.22723 0.0551043
\(497\) 0 0
\(498\) 12.6235 4.54399i 0.565671 0.203621i
\(499\) −4.18826 7.25428i −0.187492 0.324746i 0.756921 0.653506i \(-0.226703\pi\)
−0.944414 + 0.328760i \(0.893369\pi\)
\(500\) 1.01607 + 1.75988i 0.0454399 + 0.0787043i
\(501\) −10.6235 + 3.82407i −0.474622 + 0.170847i
\(502\) −2.55011 + 4.41692i −0.113817 + 0.197137i
\(503\) 20.7834 0.926688 0.463344 0.886179i \(-0.346650\pi\)
0.463344 + 0.886179i \(0.346650\pi\)
\(504\) 0 0
\(505\) −41.1174 −1.82970
\(506\) 18.6235 32.2568i 0.827914 1.43399i
\(507\) 15.2050 + 12.8506i 0.675278 + 0.570714i
\(508\) −0.688262 1.19211i −0.0305367 0.0528911i
\(509\) −8.35958 14.4792i −0.370532 0.641780i 0.619115 0.785300i \(-0.287491\pi\)
−0.989647 + 0.143520i \(0.954158\pi\)
\(510\) 5.90512 32.8095i 0.261483 1.45283i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 7.00000 11.8322i 0.309058 0.522403i
\(514\) 0.996190 0.0439401
\(515\) −15.2470 + 26.4085i −0.671861 + 1.16370i
\(516\) −2.33894 + 12.9954i −0.102966 + 0.572092i
\(517\) −29.7566 51.5400i −1.30870 2.26673i
\(518\) 0 0
\(519\) −1.62348 1.37209i −0.0712627 0.0602279i
\(520\) 2.00000 3.46410i 0.0877058 0.151911i
\(521\) 31.1354 1.36407 0.682033 0.731321i \(-0.261096\pi\)
0.682033 + 0.731321i \(0.261096\pi\)
\(522\) 2.00000 + 11.8322i 0.0875376 + 0.517880i
\(523\) 12.2326 0.534893 0.267446 0.963573i \(-0.413820\pi\)
0.267446 + 0.963573i \(0.413820\pi\)
\(524\) 2.85692 4.94832i 0.124805 0.216169i
\(525\) 0 0
\(526\) −1.68826 2.92416i −0.0736117 0.127499i
\(527\) 3.62348 + 6.27604i 0.157841 + 0.273389i
\(528\) 9.16449 3.29888i 0.398833 0.143565i
\(529\) −10.4352 + 18.0743i −0.453705 + 0.785840i
\(530\) −13.0375 −0.566311
\(531\) −7.43916 44.0107i −0.322832 1.90990i
\(532\) 0 0
\(533\) −3.62348 + 6.27604i −0.156950 + 0.271846i
\(534\) 11.8704 + 10.0323i 0.513684 + 0.434142i
\(535\) 0.613616 + 1.06281i 0.0265289 + 0.0459495i
\(536\) −2.81174 4.87007i −0.121449 0.210355i
\(537\) 0 0
\(538\) 12.0214 20.8217i 0.518279 0.897686i
\(539\) 0 0
\(540\) −8.31174 14.7563i −0.357680 0.635011i
\(541\) 4.00000 0.171973 0.0859867 0.996296i \(-0.472596\pi\)
0.0859867 + 0.996296i \(0.472596\pi\)
\(542\) 1.41852 2.45695i 0.0609306 0.105535i
\(543\) 1.37652 7.64813i 0.0590723 0.328213i
\(544\) −2.95256 5.11398i −0.126590 0.219260i
\(545\) 18.3290 + 31.7467i 0.785127 + 1.35988i
\(546\) 0 0
\(547\) −9.81174 + 16.9944i −0.419520 + 0.726629i −0.995891 0.0905585i \(-0.971135\pi\)
0.576372 + 0.817188i \(0.304468\pi\)
\(548\) −20.8704 −0.891540
\(549\) −10.3718 + 8.57852i −0.442659 + 0.366123i
\(550\) −31.6235 −1.34843
\(551\) 5.29150 9.16515i 0.225426 0.390449i
\(552\) −10.7942 + 3.88551i −0.459430 + 0.165378i
\(553\) 0 0
\(554\) −14.2470 24.6764i −0.605295 1.04840i
\(555\) −31.8704 + 11.4722i −1.35282 + 0.486968i
\(556\) −3.96863 + 6.87386i −0.168307 + 0.291517i
\(557\) 22.7530 0.964078 0.482039 0.876150i \(-0.339896\pi\)
0.482039 + 0.876150i \(0.339896\pi\)
\(558\) 3.45065 + 1.28369i 0.146078 + 0.0543431i
\(559\) −9.35577 −0.395707
\(560\) 0 0
\(561\) 43.9291 + 37.1269i 1.85469 + 1.56750i
\(562\) −12.9352 22.4044i −0.545639 0.945075i
\(563\) −2.74139 4.74824i −0.115536 0.200114i 0.802458 0.596709i \(-0.203525\pi\)
−0.917994 + 0.396595i \(0.870192\pi\)
\(564\) −3.24695 + 18.0404i −0.136721 + 0.759639i
\(565\) −12.0214 + 20.8217i −0.505744 + 0.875975i
\(566\) −7.32364 −0.307835
\(567\) 0 0
\(568\) 10.6235 0.445751
\(569\) −14.4352 + 25.0025i −0.605156 + 1.04816i 0.386871 + 0.922134i \(0.373556\pi\)
−0.992027 + 0.126027i \(0.959778\pi\)
\(570\) −2.64575 + 14.7001i −0.110818 + 0.615719i
\(571\) 4.18826 + 7.25428i 0.175273 + 0.303582i 0.940256 0.340469i \(-0.110586\pi\)
−0.764983 + 0.644051i \(0.777252\pi\)
\(572\) 3.45065 + 5.97671i 0.144279 + 0.249899i
\(573\) −7.11247 6.01114i −0.297128 0.251119i
\(574\) 0 0
\(575\) 37.2470 1.55331
\(576\) −2.81174 1.04601i −0.117156 0.0435836i
\(577\) −16.4881 −0.686410 −0.343205 0.939261i \(-0.611512\pi\)
−0.343205 + 0.939261i \(0.611512\pi\)
\(578\) 8.93521 15.4762i 0.371656 0.643727i
\(579\) 21.9908 7.91589i 0.913906 0.328973i
\(580\) −6.51873 11.2908i −0.270676 0.468824i
\(581\) 0 0
\(582\) −5.00000 + 1.79982i −0.207257 + 0.0746049i
\(583\) 11.2470 19.4803i 0.465801 0.806791i
\(584\) −11.1966 −0.463319
\(585\) 9.24695 7.64813i 0.382314 0.316211i
\(586\) −25.6526 −1.05970
\(587\) −1.51416 + 2.62261i −0.0624962 + 0.108247i −0.895581 0.444899i \(-0.853239\pi\)
0.833084 + 0.553146i \(0.186573\pi\)
\(588\) 0 0
\(589\) −1.62348 2.81194i −0.0668941 0.115864i
\(590\) 24.2470 + 41.9970i 0.998231 + 1.72899i
\(591\) −2.22342 + 12.3536i −0.0914594 + 0.508159i
\(592\) −3.00000 + 5.19615i −0.123299 + 0.213561i
\(593\) 12.1928 0.500699 0.250349 0.968156i \(-0.419455\pi\)
0.250349 + 0.968156i \(0.419455\pi\)
\(594\) 29.2188 + 0.310528i 1.19886 + 0.0127411i
\(595\) 0 0
\(596\) 2.62348 4.54399i 0.107462 0.186129i
\(597\) 3.12957 17.3883i 0.128085 0.711655i
\(598\) −4.06427 7.03952i −0.166200 0.287868i
\(599\) 1.24695 + 2.15978i 0.0509490 + 0.0882463i 0.890375 0.455227i \(-0.150442\pi\)
−0.839426 + 0.543474i \(0.817109\pi\)
\(600\) 7.43916 + 6.28724i 0.303702 + 0.256675i
\(601\) −19.8630 + 34.4037i −0.810229 + 1.40336i 0.102474 + 0.994736i \(0.467324\pi\)
−0.912704 + 0.408622i \(0.866009\pi\)
\(602\) 0 0
\(603\) −2.81174 16.6345i −0.114503 0.677408i
\(604\) −8.62348 −0.350884
\(605\) 33.6097 58.2138i 1.36643 2.36673i
\(606\) −20.5587 + 7.40038i −0.835140 + 0.300620i
\(607\) −13.8424 23.9757i −0.561845 0.973143i −0.997336 0.0729503i \(-0.976759\pi\)
0.435491 0.900193i \(-0.356575\pi\)
\(608\) 1.32288 + 2.29129i 0.0536497 + 0.0929240i
\(609\) 0 0
\(610\) 7.31174 12.6643i 0.296044 0.512763i
\(611\) −12.9878 −0.525430
\(612\) −2.95256 17.4676i −0.119350 0.706085i
\(613\) 2.00000 0.0807792 0.0403896 0.999184i \(-0.487140\pi\)
0.0403896 + 0.999184i \(0.487140\pi\)
\(614\) 6.61438 11.4564i 0.266935 0.462344i
\(615\) −25.4613 21.5187i −1.02670 0.867720i
\(616\) 0 0
\(617\) −20.0587 34.7427i −0.807532 1.39869i −0.914568 0.404432i \(-0.867469\pi\)
0.107036 0.994255i \(-0.465864\pi\)
\(618\) −2.87043 + 15.9484i −0.115465 + 0.641540i
\(619\) 17.0061 29.4554i 0.683533 1.18391i −0.290363 0.956917i \(-0.593776\pi\)
0.973896 0.226997i \(-0.0728907\pi\)
\(620\) −4.00000 −0.160644
\(621\) −34.4146 0.365747i −1.38101 0.0146769i
\(622\) −20.7834 −0.833340
\(623\) 0 0
\(624\) 0.376525 2.09201i 0.0150730 0.0837476i
\(625\) 10.7470 + 18.6143i 0.429878 + 0.744571i
\(626\) 10.8898 + 18.8617i 0.435244 + 0.753866i
\(627\) −19.6822 16.6345i −0.786030 0.664317i
\(628\) −8.14842 + 14.1135i −0.325157 + 0.563189i
\(629\) −35.4307 −1.41271
\(630\) 0 0
\(631\) 30.6235 1.21910 0.609551 0.792747i \(-0.291350\pi\)
0.609551 + 0.792747i \(0.291350\pi\)
\(632\) 1.68826 2.92416i 0.0671555 0.116317i
\(633\) −8.55087 + 3.07800i −0.339867 + 0.122340i
\(634\) 3.62348 + 6.27604i 0.143907 + 0.249254i
\(635\) 2.24330 + 3.88551i 0.0890226 + 0.154192i
\(636\) −6.51873 + 2.34651i −0.258485 + 0.0930451i
\(637\) 0 0
\(638\) 22.4939 0.890542
\(639\) 29.8704 + 11.1122i 1.18166 + 0.439593i
\(640\) 3.25937 0.128838
\(641\) 12.7470 22.0784i 0.503474 0.872043i −0.496518 0.868027i \(-0.665388\pi\)
0.999992 0.00401642i \(-0.00127847\pi\)
\(642\) 0.498095 + 0.420967i 0.0196583 + 0.0166143i
\(643\) 6.82554 + 11.8222i 0.269173 + 0.466222i 0.968649 0.248435i \(-0.0799163\pi\)
−0.699475 + 0.714657i \(0.746583\pi\)
\(644\) 0 0
\(645\) 7.62348 42.3569i 0.300174 1.66780i
\(646\) −7.81174 + 13.5303i −0.307349 + 0.532344i
\(647\) −35.0481 −1.37788 −0.688942 0.724816i \(-0.741925\pi\)
−0.688942 + 0.724816i \(0.741925\pi\)
\(648\) −6.81174 5.88220i −0.267590 0.231074i
\(649\) −83.6679 −3.28425
\(650\) −3.45065 + 5.97671i −0.135346 + 0.234426i
\(651\) 0 0
\(652\) 0.623475 + 1.07989i 0.0244172 + 0.0422918i
\(653\) −19.6235 33.9889i −0.767926 1.33009i −0.938686 0.344774i \(-0.887956\pi\)
0.170760 0.985313i \(-0.445378\pi\)
\(654\) 14.8783 + 12.5745i 0.581788 + 0.491701i
\(655\) −9.31174 + 16.1284i −0.363840 + 0.630189i
\(656\) −5.90512 −0.230556
\(657\) −31.4820 11.7117i −1.22823 0.456919i
\(658\) 0 0
\(659\) 5.24695 9.08799i 0.204392 0.354018i −0.745547 0.666453i \(-0.767812\pi\)
0.949939 + 0.312436i \(0.101145\pi\)
\(660\) −29.8704 + 10.7523i −1.16270 + 0.418531i
\(661\) 1.43840 + 2.49138i 0.0559471 + 0.0969033i 0.892643 0.450765i \(-0.148849\pi\)
−0.836695 + 0.547669i \(0.815516\pi\)
\(662\) 4.00000 + 6.92820i 0.155464 + 0.269272i
\(663\) 11.8102 4.25126i 0.458672 0.165105i
\(664\) −3.87298 + 6.70820i −0.150301 + 0.260329i
\(665\) 0 0
\(666\) −13.8704 + 11.4722i −0.537468 + 0.444539i
\(667\) −26.4939 −1.02585
\(668\) 3.25937 5.64539i 0.126109 0.218427i
\(669\) 8.62348 + 7.28817i 0.333403 + 0.281777i
\(670\) 9.16449 + 15.8734i 0.354055 + 0.613241i
\(671\) 12.6151 + 21.8501i 0.487002 + 0.843512i
\(672\) 0 0
\(673\) −9.68826 + 16.7806i −0.373455 + 0.646843i −0.990095 0.140403i \(-0.955160\pi\)
0.616639 + 0.787246i \(0.288494\pi\)
\(674\) −3.12957 −0.120547
\(675\) 14.3405 + 25.4595i 0.551965 + 0.979936i
\(676\) −11.4939 −0.442073
\(677\) 21.3971 37.0608i 0.822356 1.42436i −0.0815682 0.996668i \(-0.525993\pi\)
0.903924 0.427694i \(-0.140674\pi\)
\(678\) −2.26318 + 12.5745i −0.0869168 + 0.482920i
\(679\) 0 0
\(680\) 9.62348 + 16.6683i 0.369043 + 0.639202i
\(681\) −37.9939 32.1107i −1.45593 1.23048i
\(682\) 3.45065 5.97671i 0.132132 0.228860i
\(683\) −27.3643 −1.04707 −0.523533 0.852005i \(-0.675386\pi\)
−0.523533 + 0.852005i \(0.675386\pi\)
\(684\) 1.32288 + 7.82624i 0.0505814 + 0.299244i
\(685\) 68.0244 2.59908
\(686\) 0 0
\(687\) −43.8056 + 15.7684i −1.67129 + 0.601603i
\(688\) −3.81174 6.60212i −0.145321 0.251704i
\(689\) −2.45446 4.25126i −0.0935076 0.161960i
\(690\) 35.1822 12.6643i 1.33936 0.482122i
\(691\) −7.34352 + 12.7193i −0.279360 + 0.483867i −0.971226 0.238160i \(-0.923456\pi\)
0.691865 + 0.722026i \(0.256789\pi\)
\(692\) 1.22723 0.0466524
\(693\) 0 0
\(694\) 3.62348 0.137545
\(695\) 12.9352 22.4044i 0.490661 0.849849i
\(696\) −5.29150 4.47214i −0.200574 0.169516i
\(697\) −17.4352 30.1987i −0.660406 1.14386i
\(698\) −13.6511 23.6444i −0.516701 0.894953i
\(699\) −5.21574 + 28.9792i −0.197277 + 1.09610i
\(700\) 0 0
\(701\) −21.2470 −0.802486 −0.401243 0.915972i \(-0.631422\pi\)
−0.401243 + 0.915972i \(0.631422\pi\)
\(702\) 3.24695 5.48835i 0.122548 0.207144i
\(703\) 15.8745 0.598718
\(704\) −2.81174 + 4.87007i −0.105971 + 0.183548i
\(705\) 10.5830 58.8004i 0.398579 2.21455i
\(706\) −2.95256 5.11398i −0.111121 0.192467i
\(707\) 0 0
\(708\) 19.6822 + 16.6345i 0.739701 + 0.625161i
\(709\) −9.24695 + 16.0162i −0.347277 + 0.601501i −0.985765 0.168131i \(-0.946227\pi\)
0.638488 + 0.769632i \(0.279560\pi\)
\(710\) −34.6258 −1.29948
\(711\) 7.80564 6.45603i 0.292734 0.242120i
\(712\) −8.97320 −0.336285
\(713\) −4.06427 + 7.03952i −0.152208 + 0.263632i
\(714\) 0 0
\(715\) −11.2470 19.4803i −0.420612 0.728522i
\(716\) 0 0
\(717\) 20.5723 7.40527i 0.768286 0.276555i
\(718\) 15.5587 26.9484i 0.580645 1.00571i
\(719\) −11.8102 −0.440448 −0.220224 0.975449i \(-0.570679\pi\)
−0.220224 + 0.975449i \(0.570679\pi\)
\(720\) 9.16449 + 3.40932i 0.341540 + 0.127058i
\(721\) 0 0
\(722\) −6.00000 + 10.3923i −0.223297 + 0.386762i
\(723\) −35.3056 29.8387i −1.31303 1.10971i
\(724\) 2.24330 + 3.88551i 0.0833716 + 0.144404i
\(725\) 11.2470 + 19.4803i 0.417701 + 0.723480i
\(726\) 6.32745 35.1560i 0.234834 1.30476i
\(727\) 22.2020 38.4549i 0.823425 1.42621i −0.0796922 0.996820i \(-0.525394\pi\)
0.903117 0.429394i \(-0.141273\pi\)
\(728\) 0 0
\(729\) −13.0000 23.6643i −0.481481 0.876456i
\(730\) 36.4939 1.35070
\(731\) 22.5088 38.9863i 0.832517 1.44196i
\(732\) 1.37652 7.64813i 0.0508778 0.282683i
\(733\) 4.08415 + 7.07395i 0.150851 + 0.261282i 0.931541 0.363637i \(-0.118465\pi\)
−0.780689 + 0.624919i \(0.785132\pi\)
\(734\) −3.45065 5.97671i −0.127366 0.220604i
\(735\) 0 0
\(736\) 3.31174 5.73610i 0.122072 0.211435i
\(737\) −31.6235 −1.16487
\(738\) −16.6036 6.17680i −0.611189 0.227371i
\(739\) 20.8704 0.767731 0.383866 0.923389i \(-0.374593\pi\)
0.383866 + 0.923389i \(0.374593\pi\)
\(740\) 9.77810 16.9362i 0.359450 0.622586i
\(741\) −5.29150 + 1.90475i −0.194388 + 0.0699727i
\(742\) 0 0
\(743\) −15.6235 27.0607i −0.573170 0.992759i −0.996238 0.0866612i \(-0.972380\pi\)
0.423068 0.906098i \(-0.360953\pi\)
\(744\) −2.00000 + 0.719927i −0.0733236 + 0.0263938i
\(745\) −8.55087 + 14.8105i −0.313280 + 0.542616i
\(746\) −11.2470 −0.411780
\(747\) −17.9066 + 14.8105i −0.655170 + 0.541889i
\(748\) −33.2073 −1.21418
\(749\) 0 0
\(750\) −2.68826 2.27200i −0.0981615 0.0829616i
\(751\) 5.68826 + 9.85236i 0.207568 + 0.359518i 0.950948 0.309351i \(-0.100112\pi\)
−0.743380 + 0.668869i \(0.766779\pi\)
\(752\) −5.29150 9.16515i −0.192961 0.334219i
\(753\) 1.56479 8.69414i 0.0570240 0.316832i
\(754\) 2.45446 4.25126i 0.0893863 0.154822i
\(755\) 28.1071 1.02292
\(756\) 0 0
\(757\) 43.7409 1.58979 0.794894 0.606748i \(-0.207526\pi\)
0.794894 + 0.606748i \(0.207526\pi\)
\(758\) 7.81174 13.5303i 0.283735 0.491444i
\(759\) −11.4277 + 63.4934i −0.414798 + 2.30467i
\(760\) −4.31174 7.46815i −0.156403 0.270898i
\(761\) 2.83704 + 4.91389i 0.102843 + 0.178129i 0.912855 0.408285i \(-0.133873\pi\)
−0.810012 + 0.586413i \(0.800540\pi\)
\(762\) 1.82097 + 1.53900i 0.0659668 + 0.0557521i
\(763\) 0 0
\(764\) 5.37652 0.194516
\(765\) 9.62348 + 56.9332i 0.347937 + 2.05843i
\(766\) −27.6847 −1.00029
\(767\) −9.12957 + 15.8129i −0.329650 + 0.570970i
\(768\) 1.62968 0.586627i 0.0588061 0.0211681i
\(769\) 0.422329 + 0.731495i 0.0152296 + 0.0263784i 0.873540 0.486753i \(-0.161819\pi\)
−0.858310 + 0.513131i \(0.828485\pi\)
\(770\) 0 0
\(771\) −1.62348 + 0.584392i −0.0584680 + 0.0210464i
\(772\) −6.74695 + 11.6861i −0.242828 + 0.420591i
\(773\) −13.4598 −0.484115 −0.242058 0.970262i \(-0.577822\pi\)
−0.242058 + 0.970262i \(0.577822\pi\)
\(774\) −3.81174 22.5505i −0.137010 0.810563i
\(775\) 6.90131 0.247902
\(776\) 1.53404 2.65704i 0.0550688 0.0953820i
\(777\) 0 0
\(778\) 18.6235 + 32.2568i 0.667684 + 1.15646i
\(779\) 7.81174 + 13.5303i 0.279885 + 0.484774i
\(780\) −1.22723 + 6.81864i −0.0439420 + 0.244147i