Properties

Label 2646.2.h.s.667.2
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.3317760000.3
Defining polynomial: \(x^{8} - 4 x^{6} + 7 x^{4} - 36 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 882)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.2
Root \(-1.72286 + 0.178197i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.s.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -2.03151 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -2.03151 q^{5} -1.00000 q^{8} +(-1.01575 - 1.75934i) q^{10} -4.00000 q^{11} +(2.12132 + 3.67423i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(0.707107 + 1.22474i) q^{17} +(0.398461 - 0.690154i) q^{19} +(1.01575 - 1.75934i) q^{20} +(-2.00000 - 3.46410i) q^{22} -6.74597 q^{23} -0.872983 q^{25} +(-2.12132 + 3.67423i) q^{26} +(4.43649 - 7.68423i) q^{29} +(2.73861 - 4.74342i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.707107 + 1.22474i) q^{34} +(4.87298 - 8.44025i) q^{37} +0.796921 q^{38} +2.03151 q^{40} +(2.82843 + 4.89898i) q^{41} +(-4.43649 + 7.68423i) q^{43} +(2.00000 - 3.46410i) q^{44} +(-3.37298 - 5.84218i) q^{46} +(3.44572 + 5.96816i) q^{47} +(-0.436492 - 0.756026i) q^{50} -4.24264 q^{52} +(-5.30948 - 9.19628i) q^{53} +8.12602 q^{55} +8.87298 q^{58} +(1.32440 - 2.29393i) q^{59} +(-0.398461 - 0.690154i) q^{61} +5.47723 q^{62} +1.00000 q^{64} +(-4.30948 - 7.46423i) q^{65} +(-0.436492 + 0.756026i) q^{67} -1.41421 q^{68} +2.12702 q^{71} +(-7.68836 - 13.3166i) q^{73} +9.74597 q^{74} +(0.398461 + 0.690154i) q^{76} +(-2.93649 - 5.08615i) q^{79} +(1.01575 + 1.75934i) q^{80} +(-2.82843 + 4.89898i) q^{82} +(4.15283 - 7.19291i) q^{83} +(-1.43649 - 2.48808i) q^{85} -8.87298 q^{86} +4.00000 q^{88} +(3.53553 - 6.12372i) q^{89} +(3.37298 - 5.84218i) q^{92} +(-3.44572 + 5.96816i) q^{94} +(-0.809475 + 1.40205i) q^{95} +(8.92295 - 15.4550i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} + O(q^{10}) \) \( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 32 q^{11} - 4 q^{16} - 16 q^{22} + 8 q^{23} + 24 q^{25} + 20 q^{29} + 4 q^{32} + 8 q^{37} - 20 q^{43} + 16 q^{44} + 4 q^{46} + 12 q^{50} + 4 q^{53} + 40 q^{58} + 8 q^{64} + 12 q^{65} + 12 q^{67} + 48 q^{71} + 16 q^{74} - 8 q^{79} + 4 q^{85} - 40 q^{86} + 32 q^{88} - 4 q^{92} + 40 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −2.03151 −0.908517 −0.454259 0.890870i \(-0.650096\pi\)
−0.454259 + 0.890870i \(0.650096\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.01575 1.75934i −0.321209 0.556351i
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 0 0
\(13\) 2.12132 + 3.67423i 0.588348 + 1.01905i 0.994449 + 0.105221i \(0.0335550\pi\)
−0.406100 + 0.913828i \(0.633112\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.707107 + 1.22474i 0.171499 + 0.297044i 0.938944 0.344070i \(-0.111806\pi\)
−0.767445 + 0.641114i \(0.778472\pi\)
\(18\) 0 0
\(19\) 0.398461 0.690154i 0.0914131 0.158332i −0.816693 0.577073i \(-0.804195\pi\)
0.908106 + 0.418740i \(0.137528\pi\)
\(20\) 1.01575 1.75934i 0.227129 0.393399i
\(21\) 0 0
\(22\) −2.00000 3.46410i −0.426401 0.738549i
\(23\) −6.74597 −1.40663 −0.703316 0.710878i \(-0.748298\pi\)
−0.703316 + 0.710878i \(0.748298\pi\)
\(24\) 0 0
\(25\) −0.872983 −0.174597
\(26\) −2.12132 + 3.67423i −0.416025 + 0.720577i
\(27\) 0 0
\(28\) 0 0
\(29\) 4.43649 7.68423i 0.823836 1.42693i −0.0789700 0.996877i \(-0.525163\pi\)
0.902806 0.430049i \(-0.141504\pi\)
\(30\) 0 0
\(31\) 2.73861 4.74342i 0.491869 0.851943i −0.508087 0.861306i \(-0.669647\pi\)
0.999956 + 0.00936313i \(0.00298042\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −0.707107 + 1.22474i −0.121268 + 0.210042i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.87298 8.44025i 0.801114 1.38757i −0.117770 0.993041i \(-0.537575\pi\)
0.918884 0.394528i \(-0.129092\pi\)
\(38\) 0.796921 0.129278
\(39\) 0 0
\(40\) 2.03151 0.321209
\(41\) 2.82843 + 4.89898i 0.441726 + 0.765092i 0.997818 0.0660290i \(-0.0210330\pi\)
−0.556092 + 0.831121i \(0.687700\pi\)
\(42\) 0 0
\(43\) −4.43649 + 7.68423i −0.676559 + 1.17183i 0.299452 + 0.954111i \(0.403196\pi\)
−0.976011 + 0.217723i \(0.930137\pi\)
\(44\) 2.00000 3.46410i 0.301511 0.522233i
\(45\) 0 0
\(46\) −3.37298 5.84218i −0.497319 0.861382i
\(47\) 3.44572 + 5.96816i 0.502610 + 0.870546i 0.999995 + 0.00301623i \(0.000960097\pi\)
−0.497386 + 0.867530i \(0.665707\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −0.436492 0.756026i −0.0617292 0.106918i
\(51\) 0 0
\(52\) −4.24264 −0.588348
\(53\) −5.30948 9.19628i −0.729312 1.26321i −0.957174 0.289513i \(-0.906507\pi\)
0.227862 0.973694i \(-0.426827\pi\)
\(54\) 0 0
\(55\) 8.12602 1.09571
\(56\) 0 0
\(57\) 0 0
\(58\) 8.87298 1.16508
\(59\) 1.32440 2.29393i 0.172422 0.298644i −0.766844 0.641833i \(-0.778174\pi\)
0.939266 + 0.343190i \(0.111507\pi\)
\(60\) 0 0
\(61\) −0.398461 0.690154i −0.0510176 0.0883652i 0.839389 0.543531i \(-0.182913\pi\)
−0.890406 + 0.455166i \(0.849580\pi\)
\(62\) 5.47723 0.695608
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −4.30948 7.46423i −0.534525 0.925824i
\(66\) 0 0
\(67\) −0.436492 + 0.756026i −0.0533259 + 0.0923632i −0.891456 0.453107i \(-0.850316\pi\)
0.838130 + 0.545470i \(0.183649\pi\)
\(68\) −1.41421 −0.171499
\(69\) 0 0
\(70\) 0 0
\(71\) 2.12702 0.252430 0.126215 0.992003i \(-0.459717\pi\)
0.126215 + 0.992003i \(0.459717\pi\)
\(72\) 0 0
\(73\) −7.68836 13.3166i −0.899855 1.55859i −0.827679 0.561202i \(-0.810339\pi\)
−0.0721755 0.997392i \(-0.522994\pi\)
\(74\) 9.74597 1.13295
\(75\) 0 0
\(76\) 0.398461 + 0.690154i 0.0457066 + 0.0791661i
\(77\) 0 0
\(78\) 0 0
\(79\) −2.93649 5.08615i −0.330381 0.572237i 0.652205 0.758042i \(-0.273844\pi\)
−0.982587 + 0.185805i \(0.940511\pi\)
\(80\) 1.01575 + 1.75934i 0.113565 + 0.196700i
\(81\) 0 0
\(82\) −2.82843 + 4.89898i −0.312348 + 0.541002i
\(83\) 4.15283 7.19291i 0.455832 0.789524i −0.542904 0.839795i \(-0.682675\pi\)
0.998736 + 0.0502709i \(0.0160085\pi\)
\(84\) 0 0
\(85\) −1.43649 2.48808i −0.155809 0.269870i
\(86\) −8.87298 −0.956798
\(87\) 0 0
\(88\) 4.00000 0.426401
\(89\) 3.53553 6.12372i 0.374766 0.649113i −0.615526 0.788116i \(-0.711056\pi\)
0.990292 + 0.139003i \(0.0443898\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.37298 5.84218i 0.351658 0.609089i
\(93\) 0 0
\(94\) −3.44572 + 5.96816i −0.355399 + 0.615569i
\(95\) −0.809475 + 1.40205i −0.0830504 + 0.143847i
\(96\) 0 0
\(97\) 8.92295 15.4550i 0.905988 1.56922i 0.0864021 0.996260i \(-0.472463\pi\)
0.819586 0.572957i \(-0.194204\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.436492 0.756026i 0.0436492 0.0756026i
\(101\) 7.86799 0.782894 0.391447 0.920201i \(-0.371975\pi\)
0.391447 + 0.920201i \(0.371975\pi\)
\(102\) 0 0
\(103\) −18.0255 −1.77611 −0.888054 0.459740i \(-0.847943\pi\)
−0.888054 + 0.459740i \(0.847943\pi\)
\(104\) −2.12132 3.67423i −0.208013 0.360288i
\(105\) 0 0
\(106\) 5.30948 9.19628i 0.515702 0.893222i
\(107\) 7.87298 13.6364i 0.761110 1.31828i −0.181169 0.983452i \(-0.557988\pi\)
0.942279 0.334829i \(-0.108679\pi\)
\(108\) 0 0
\(109\) −4.56351 7.90423i −0.437105 0.757088i 0.560360 0.828249i \(-0.310663\pi\)
−0.997465 + 0.0711614i \(0.977329\pi\)
\(110\) 4.06301 + 7.03734i 0.387393 + 0.670984i
\(111\) 0 0
\(112\) 0 0
\(113\) −1.93649 3.35410i −0.182170 0.315527i 0.760449 0.649397i \(-0.224979\pi\)
−0.942619 + 0.333870i \(0.891645\pi\)
\(114\) 0 0
\(115\) 13.7045 1.27795
\(116\) 4.43649 + 7.68423i 0.411918 + 0.713463i
\(117\) 0 0
\(118\) 2.64880 0.243842
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0.398461 0.690154i 0.0360749 0.0624836i
\(123\) 0 0
\(124\) 2.73861 + 4.74342i 0.245935 + 0.425971i
\(125\) 11.9310 1.06714
\(126\) 0 0
\(127\) 14.7460 1.30849 0.654246 0.756281i \(-0.272986\pi\)
0.654246 + 0.756281i \(0.272986\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 4.30948 7.46423i 0.377966 0.654656i
\(131\) −7.86799 −0.687429 −0.343715 0.939074i \(-0.611685\pi\)
−0.343715 + 0.939074i \(0.611685\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.872983 −0.0754143
\(135\) 0 0
\(136\) −0.707107 1.22474i −0.0606339 0.105021i
\(137\) −15.4919 −1.32357 −0.661783 0.749696i \(-0.730200\pi\)
−0.661783 + 0.749696i \(0.730200\pi\)
\(138\) 0 0
\(139\) 9.23159 + 15.9896i 0.783013 + 1.35622i 0.930179 + 0.367107i \(0.119652\pi\)
−0.147165 + 0.989112i \(0.547015\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.06351 + 1.84205i 0.0892476 + 0.154581i
\(143\) −8.48528 14.6969i −0.709575 1.22902i
\(144\) 0 0
\(145\) −9.01276 + 15.6106i −0.748469 + 1.29639i
\(146\) 7.68836 13.3166i 0.636293 1.10209i
\(147\) 0 0
\(148\) 4.87298 + 8.44025i 0.400557 + 0.693785i
\(149\) 0.254033 0.0208112 0.0104056 0.999946i \(-0.496688\pi\)
0.0104056 + 0.999946i \(0.496688\pi\)
\(150\) 0 0
\(151\) 11.0000 0.895167 0.447584 0.894242i \(-0.352285\pi\)
0.447584 + 0.894242i \(0.352285\pi\)
\(152\) −0.398461 + 0.690154i −0.0323194 + 0.0559789i
\(153\) 0 0
\(154\) 0 0
\(155\) −5.56351 + 9.63628i −0.446872 + 0.774005i
\(156\) 0 0
\(157\) −3.22689 + 5.58913i −0.257534 + 0.446061i −0.965581 0.260104i \(-0.916243\pi\)
0.708047 + 0.706165i \(0.249576\pi\)
\(158\) 2.93649 5.08615i 0.233615 0.404633i
\(159\) 0 0
\(160\) −1.01575 + 1.75934i −0.0803023 + 0.139088i
\(161\) 0 0
\(162\) 0 0
\(163\) −5.00000 + 8.66025i −0.391630 + 0.678323i −0.992665 0.120900i \(-0.961422\pi\)
0.601035 + 0.799223i \(0.294755\pi\)
\(164\) −5.65685 −0.441726
\(165\) 0 0
\(166\) 8.30565 0.644644
\(167\) −6.18433 10.7116i −0.478558 0.828887i 0.521140 0.853471i \(-0.325507\pi\)
−0.999698 + 0.0245846i \(0.992174\pi\)
\(168\) 0 0
\(169\) −2.50000 + 4.33013i −0.192308 + 0.333087i
\(170\) 1.43649 2.48808i 0.110174 0.190827i
\(171\) 0 0
\(172\) −4.43649 7.68423i −0.338279 0.585917i
\(173\) 6.36396 + 11.0227i 0.483843 + 0.838041i 0.999828 0.0185571i \(-0.00590724\pi\)
−0.515985 + 0.856598i \(0.672574\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.00000 + 3.46410i 0.150756 + 0.261116i
\(177\) 0 0
\(178\) 7.07107 0.529999
\(179\) 0.436492 + 0.756026i 0.0326249 + 0.0565080i 0.881877 0.471480i \(-0.156280\pi\)
−0.849252 + 0.527988i \(0.822947\pi\)
\(180\) 0 0
\(181\) −7.86799 −0.584823 −0.292412 0.956293i \(-0.594458\pi\)
−0.292412 + 0.956293i \(0.594458\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 6.74597 0.497319
\(185\) −9.89949 + 17.1464i −0.727825 + 1.26063i
\(186\) 0 0
\(187\) −2.82843 4.89898i −0.206835 0.358249i
\(188\) −6.89144 −0.502610
\(189\) 0 0
\(190\) −1.61895 −0.117451
\(191\) −6.93649 12.0144i −0.501907 0.869328i −0.999998 0.00220333i \(-0.999299\pi\)
0.498091 0.867125i \(-0.334035\pi\)
\(192\) 0 0
\(193\) −8.06351 + 13.9664i −0.580424 + 1.00532i 0.415005 + 0.909819i \(0.363780\pi\)
−0.995429 + 0.0955048i \(0.969553\pi\)
\(194\) 17.8459 1.28126
\(195\) 0 0
\(196\) 0 0
\(197\) 6.61895 0.471581 0.235790 0.971804i \(-0.424232\pi\)
0.235790 + 0.971804i \(0.424232\pi\)
\(198\) 0 0
\(199\) 10.3372 + 17.9045i 0.732782 + 1.26922i 0.955690 + 0.294376i \(0.0951117\pi\)
−0.222908 + 0.974839i \(0.571555\pi\)
\(200\) 0.872983 0.0617292
\(201\) 0 0
\(202\) 3.93399 + 6.81388i 0.276795 + 0.479423i
\(203\) 0 0
\(204\) 0 0
\(205\) −5.74597 9.95231i −0.401316 0.695099i
\(206\) −9.01276 15.6106i −0.627949 1.08764i
\(207\) 0 0
\(208\) 2.12132 3.67423i 0.147087 0.254762i
\(209\) −1.59384 + 2.76062i −0.110248 + 0.190956i
\(210\) 0 0
\(211\) 1.30948 + 2.26808i 0.0901480 + 0.156141i 0.907573 0.419894i \(-0.137933\pi\)
−0.817425 + 0.576035i \(0.804599\pi\)
\(212\) 10.6190 0.729312
\(213\) 0 0
\(214\) 15.7460 1.07637
\(215\) 9.01276 15.6106i 0.614665 1.06463i
\(216\) 0 0
\(217\) 0 0
\(218\) 4.56351 7.90423i 0.309080 0.535342i
\(219\) 0 0
\(220\) −4.06301 + 7.03734i −0.273928 + 0.474458i
\(221\) −3.00000 + 5.19615i −0.201802 + 0.349531i
\(222\) 0 0
\(223\) 5.74667 9.95352i 0.384825 0.666537i −0.606920 0.794763i \(-0.707595\pi\)
0.991745 + 0.128226i \(0.0409283\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.93649 3.35410i 0.128814 0.223112i
\(227\) 6.09452 0.404507 0.202254 0.979333i \(-0.435173\pi\)
0.202254 + 0.979333i \(0.435173\pi\)
\(228\) 0 0
\(229\) 7.86799 0.519931 0.259966 0.965618i \(-0.416289\pi\)
0.259966 + 0.965618i \(0.416289\pi\)
\(230\) 6.85224 + 11.8684i 0.451823 + 0.782580i
\(231\) 0 0
\(232\) −4.43649 + 7.68423i −0.291270 + 0.504494i
\(233\) 11.3730 19.6986i 0.745069 1.29050i −0.205094 0.978742i \(-0.565750\pi\)
0.950163 0.311755i \(-0.100917\pi\)
\(234\) 0 0
\(235\) −7.00000 12.1244i −0.456630 0.790906i
\(236\) 1.32440 + 2.29393i 0.0862110 + 0.149322i
\(237\) 0 0
\(238\) 0 0
\(239\) −7.50000 12.9904i −0.485135 0.840278i 0.514719 0.857359i \(-0.327896\pi\)
−0.999854 + 0.0170808i \(0.994563\pi\)
\(240\) 0 0
\(241\) −1.77347 −0.114239 −0.0571197 0.998367i \(-0.518192\pi\)
−0.0571197 + 0.998367i \(0.518192\pi\)
\(242\) 2.50000 + 4.33013i 0.160706 + 0.278351i
\(243\) 0 0
\(244\) 0.796921 0.0510176
\(245\) 0 0
\(246\) 0 0
\(247\) 3.38105 0.215131
\(248\) −2.73861 + 4.74342i −0.173902 + 0.301207i
\(249\) 0 0
\(250\) 5.96550 + 10.3325i 0.377291 + 0.653488i
\(251\) −25.8935 −1.63438 −0.817192 0.576366i \(-0.804470\pi\)
−0.817192 + 0.576366i \(0.804470\pi\)
\(252\) 0 0
\(253\) 26.9839 1.69646
\(254\) 7.37298 + 12.7704i 0.462622 + 0.801285i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −13.9625 −0.870957 −0.435479 0.900199i \(-0.643421\pi\)
−0.435479 + 0.900199i \(0.643421\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 8.61895 0.534525
\(261\) 0 0
\(262\) −3.93399 6.81388i −0.243043 0.420963i
\(263\) −5.61895 −0.346479 −0.173240 0.984880i \(-0.555424\pi\)
−0.173240 + 0.984880i \(0.555424\pi\)
\(264\) 0 0
\(265\) 10.7862 + 18.6823i 0.662593 + 1.14764i
\(266\) 0 0
\(267\) 0 0
\(268\) −0.436492 0.756026i −0.0266630 0.0461816i
\(269\) 1.72286 + 2.98408i 0.105045 + 0.181943i 0.913756 0.406262i \(-0.133168\pi\)
−0.808712 + 0.588205i \(0.799835\pi\)
\(270\) 0 0
\(271\) −3.53553 + 6.12372i −0.214768 + 0.371990i −0.953201 0.302338i \(-0.902233\pi\)
0.738433 + 0.674327i \(0.235566\pi\)
\(272\) 0.707107 1.22474i 0.0428746 0.0742611i
\(273\) 0 0
\(274\) −7.74597 13.4164i −0.467951 0.810515i
\(275\) 3.49193 0.210572
\(276\) 0 0
\(277\) −24.3649 −1.46395 −0.731973 0.681334i \(-0.761400\pi\)
−0.731973 + 0.681334i \(0.761400\pi\)
\(278\) −9.23159 + 15.9896i −0.553674 + 0.958992i
\(279\) 0 0
\(280\) 0 0
\(281\) −3.37298 + 5.84218i −0.201215 + 0.348515i −0.948920 0.315516i \(-0.897822\pi\)
0.747705 + 0.664031i \(0.231156\pi\)
\(282\) 0 0
\(283\) −5.25839 + 9.10781i −0.312579 + 0.541403i −0.978920 0.204244i \(-0.934526\pi\)
0.666341 + 0.745647i \(0.267860\pi\)
\(284\) −1.06351 + 1.84205i −0.0631076 + 0.109306i
\(285\) 0 0
\(286\) 8.48528 14.6969i 0.501745 0.869048i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.50000 12.9904i 0.441176 0.764140i
\(290\) −18.0255 −1.05849
\(291\) 0 0
\(292\) 15.3767 0.899855
\(293\) −3.13707 5.43357i −0.183270 0.317433i 0.759722 0.650248i \(-0.225335\pi\)
−0.942992 + 0.332815i \(0.892002\pi\)
\(294\) 0 0
\(295\) −2.69052 + 4.66013i −0.156648 + 0.271323i
\(296\) −4.87298 + 8.44025i −0.283236 + 0.490580i
\(297\) 0 0
\(298\) 0.127017 + 0.219999i 0.00735788 + 0.0127442i
\(299\) −14.3104 24.7863i −0.827589 1.43343i
\(300\) 0 0
\(301\) 0 0
\(302\) 5.50000 + 9.52628i 0.316489 + 0.548176i
\(303\) 0 0
\(304\) −0.796921 −0.0457066
\(305\) 0.809475 + 1.40205i 0.0463504 + 0.0802813i
\(306\) 0 0
\(307\) −24.1200 −1.37660 −0.688302 0.725425i \(-0.741643\pi\)
−0.688302 + 0.725425i \(0.741643\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −11.1270 −0.631972
\(311\) −0.707107 + 1.22474i −0.0400963 + 0.0694489i −0.885377 0.464873i \(-0.846100\pi\)
0.845281 + 0.534322i \(0.179433\pi\)
\(312\) 0 0
\(313\) −13.3452 23.1146i −0.754316 1.30651i −0.945714 0.325001i \(-0.894635\pi\)
0.191397 0.981513i \(-0.438698\pi\)
\(314\) −6.45378 −0.364208
\(315\) 0 0
\(316\) 5.87298 0.330381
\(317\) 0.690525 + 1.19602i 0.0387837 + 0.0671754i 0.884766 0.466036i \(-0.154318\pi\)
−0.845982 + 0.533212i \(0.820985\pi\)
\(318\) 0 0
\(319\) −17.7460 + 30.7369i −0.993583 + 1.72094i
\(320\) −2.03151 −0.113565
\(321\) 0 0
\(322\) 0 0
\(323\) 1.12702 0.0627089
\(324\) 0 0
\(325\) −1.85188 3.20755i −0.102724 0.177923i
\(326\) −10.0000 −0.553849
\(327\) 0 0
\(328\) −2.82843 4.89898i −0.156174 0.270501i
\(329\) 0 0
\(330\) 0 0
\(331\) 9.18246 + 15.9045i 0.504714 + 0.874190i 0.999985 + 0.00545133i \(0.00173522\pi\)
−0.495272 + 0.868738i \(0.664931\pi\)
\(332\) 4.15283 + 7.19291i 0.227916 + 0.394762i
\(333\) 0 0
\(334\) 6.18433 10.7116i 0.338392 0.586111i
\(335\) 0.886735 1.53587i 0.0484475 0.0839136i
\(336\) 0 0
\(337\) −0.127017 0.219999i −0.00691904 0.0119841i 0.862545 0.505980i \(-0.168869\pi\)
−0.869464 + 0.493996i \(0.835536\pi\)
\(338\) −5.00000 −0.271964
\(339\) 0 0
\(340\) 2.87298 0.155809
\(341\) −10.9545 + 18.9737i −0.593217 + 1.02748i
\(342\) 0 0
\(343\) 0 0
\(344\) 4.43649 7.68423i 0.239200 0.414306i
\(345\) 0 0
\(346\) −6.36396 + 11.0227i −0.342129 + 0.592584i
\(347\) −3.87298 + 6.70820i −0.207913 + 0.360115i −0.951057 0.309016i \(-0.900000\pi\)
0.743144 + 0.669131i \(0.233334\pi\)
\(348\) 0 0
\(349\) −8.21584 + 14.2302i −0.439784 + 0.761728i −0.997672 0.0681880i \(-0.978278\pi\)
0.557889 + 0.829916i \(0.311612\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.00000 + 3.46410i −0.106600 + 0.184637i
\(353\) 18.0255 0.959402 0.479701 0.877432i \(-0.340745\pi\)
0.479701 + 0.877432i \(0.340745\pi\)
\(354\) 0 0
\(355\) −4.32105 −0.229337
\(356\) 3.53553 + 6.12372i 0.187383 + 0.324557i
\(357\) 0 0
\(358\) −0.436492 + 0.756026i −0.0230693 + 0.0399572i
\(359\) −14.1190 + 24.4547i −0.745170 + 1.29067i 0.204946 + 0.978773i \(0.434298\pi\)
−0.950115 + 0.311898i \(0.899035\pi\)
\(360\) 0 0
\(361\) 9.18246 + 15.9045i 0.483287 + 0.837078i
\(362\) −3.93399 6.81388i −0.206766 0.358129i
\(363\) 0 0
\(364\) 0 0
\(365\) 15.6190 + 27.0528i 0.817533 + 1.41601i
\(366\) 0 0
\(367\) −4.06301 −0.212088 −0.106044 0.994361i \(-0.533818\pi\)
−0.106044 + 0.994361i \(0.533818\pi\)
\(368\) 3.37298 + 5.84218i 0.175829 + 0.304545i
\(369\) 0 0
\(370\) −19.7990 −1.02930
\(371\) 0 0
\(372\) 0 0
\(373\) −8.87298 −0.459426 −0.229713 0.973258i \(-0.573779\pi\)
−0.229713 + 0.973258i \(0.573779\pi\)
\(374\) 2.82843 4.89898i 0.146254 0.253320i
\(375\) 0 0
\(376\) −3.44572 5.96816i −0.177699 0.307784i
\(377\) 37.6449 1.93881
\(378\) 0 0
\(379\) −12.3649 −0.635143 −0.317572 0.948234i \(-0.602867\pi\)
−0.317572 + 0.948234i \(0.602867\pi\)
\(380\) −0.809475 1.40205i −0.0415252 0.0719237i
\(381\) 0 0
\(382\) 6.93649 12.0144i 0.354902 0.614708i
\(383\) 23.8620 1.21929 0.609646 0.792674i \(-0.291312\pi\)
0.609646 + 0.792674i \(0.291312\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −16.1270 −0.820844
\(387\) 0 0
\(388\) 8.92295 + 15.4550i 0.452994 + 0.784608i
\(389\) −20.8730 −1.05830 −0.529151 0.848528i \(-0.677490\pi\)
−0.529151 + 0.848528i \(0.677490\pi\)
\(390\) 0 0
\(391\) −4.77012 8.26209i −0.241235 0.417832i
\(392\) 0 0
\(393\) 0 0
\(394\) 3.30948 + 5.73218i 0.166729 + 0.288783i
\(395\) 5.96550 + 10.3325i 0.300157 + 0.519887i
\(396\) 0 0
\(397\) −3.53553 + 6.12372i −0.177443 + 0.307341i −0.941004 0.338395i \(-0.890116\pi\)
0.763561 + 0.645736i \(0.223449\pi\)
\(398\) −10.3372 + 17.9045i −0.518155 + 0.897471i
\(399\) 0 0
\(400\) 0.436492 + 0.756026i 0.0218246 + 0.0378013i
\(401\) −3.87298 −0.193408 −0.0967038 0.995313i \(-0.530830\pi\)
−0.0967038 + 0.995313i \(0.530830\pi\)
\(402\) 0 0
\(403\) 23.2379 1.15756
\(404\) −3.93399 + 6.81388i −0.195724 + 0.339003i
\(405\) 0 0
\(406\) 0 0
\(407\) −19.4919 + 33.7610i −0.966179 + 1.67347i
\(408\) 0 0
\(409\) 15.8144 27.3913i 0.781971 1.35441i −0.148821 0.988864i \(-0.547548\pi\)
0.930792 0.365549i \(-0.119119\pi\)
\(410\) 5.74597 9.95231i 0.283773 0.491509i
\(411\) 0 0
\(412\) 9.01276 15.6106i 0.444027 0.769077i
\(413\) 0 0
\(414\) 0 0
\(415\) −8.43649 + 14.6124i −0.414131 + 0.717296i
\(416\) 4.24264 0.208013
\(417\) 0 0
\(418\) −3.18768 −0.155915
\(419\) −1.99230 3.45077i −0.0973304 0.168581i 0.813248 0.581917i \(-0.197697\pi\)
−0.910579 + 0.413335i \(0.864364\pi\)
\(420\) 0 0
\(421\) 2.56351 4.44013i 0.124938 0.216399i −0.796771 0.604282i \(-0.793460\pi\)
0.921709 + 0.387883i \(0.126794\pi\)
\(422\) −1.30948 + 2.26808i −0.0637442 + 0.110408i
\(423\) 0 0
\(424\) 5.30948 + 9.19628i 0.257851 + 0.446611i
\(425\) −0.617292 1.06918i −0.0299431 0.0518629i
\(426\) 0 0
\(427\) 0 0
\(428\) 7.87298 + 13.6364i 0.380555 + 0.659141i
\(429\) 0 0
\(430\) 18.0255 0.869268
\(431\) 4.74597 + 8.22026i 0.228605 + 0.395956i 0.957395 0.288782i \(-0.0932502\pi\)
−0.728790 + 0.684737i \(0.759917\pi\)
\(432\) 0 0
\(433\) −29.6985 −1.42722 −0.713609 0.700544i \(-0.752941\pi\)
−0.713609 + 0.700544i \(0.752941\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 9.12702 0.437105
\(437\) −2.68800 + 4.65576i −0.128585 + 0.222715i
\(438\) 0 0
\(439\) −5.47723 9.48683i −0.261414 0.452782i 0.705204 0.709004i \(-0.250855\pi\)
−0.966618 + 0.256223i \(0.917522\pi\)
\(440\) −8.12602 −0.387393
\(441\) 0 0
\(442\) −6.00000 −0.285391
\(443\) 12.1825 + 21.1006i 0.578806 + 1.00252i 0.995617 + 0.0935281i \(0.0298145\pi\)
−0.416811 + 0.908993i \(0.636852\pi\)
\(444\) 0 0
\(445\) −7.18246 + 12.4404i −0.340481 + 0.589731i
\(446\) 11.4933 0.544225
\(447\) 0 0
\(448\) 0 0
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 0 0
\(451\) −11.3137 19.5959i −0.532742 0.922736i
\(452\) 3.87298 0.182170
\(453\) 0 0
\(454\) 3.04726 + 5.27801i 0.143015 + 0.247709i
\(455\) 0 0
\(456\) 0 0
\(457\) −16.9365 29.3349i −0.792256 1.37223i −0.924567 0.381019i \(-0.875573\pi\)
0.132312 0.991208i \(-0.457760\pi\)
\(458\) 3.93399 + 6.81388i 0.183823 + 0.318392i
\(459\) 0 0
\(460\) −6.85224 + 11.8684i −0.319487 + 0.553368i
\(461\) −4.98895 + 8.64112i −0.232359 + 0.402457i −0.958502 0.285087i \(-0.907978\pi\)
0.726143 + 0.687544i \(0.241311\pi\)
\(462\) 0 0
\(463\) −10.8095 18.7226i −0.502359 0.870111i −0.999996 0.00272598i \(-0.999132\pi\)
0.497637 0.867385i \(-0.334201\pi\)
\(464\) −8.87298 −0.411918
\(465\) 0 0
\(466\) 22.7460 1.05369
\(467\) 19.5295 33.8262i 0.903720 1.56529i 0.0810929 0.996707i \(-0.474159\pi\)
0.822627 0.568582i \(-0.192508\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 7.00000 12.1244i 0.322886 0.559255i
\(471\) 0 0
\(472\) −1.32440 + 2.29393i −0.0609604 + 0.105587i
\(473\) 17.7460 30.7369i 0.815960 1.41328i
\(474\) 0 0
\(475\) −0.347849 + 0.602493i −0.0159604 + 0.0276443i
\(476\) 0 0
\(477\) 0 0
\(478\) 7.50000 12.9904i 0.343042 0.594166i
\(479\) 18.0255 0.823607 0.411803 0.911273i \(-0.364899\pi\)
0.411803 + 0.911273i \(0.364899\pi\)
\(480\) 0 0
\(481\) 41.3486 1.88534
\(482\) −0.886735 1.53587i −0.0403897 0.0699570i
\(483\) 0 0
\(484\) −2.50000 + 4.33013i −0.113636 + 0.196824i
\(485\) −18.1270 + 31.3969i −0.823105 + 1.42566i
\(486\) 0 0
\(487\) −15.2460 26.4068i −0.690861 1.19661i −0.971556 0.236809i \(-0.923898\pi\)
0.280696 0.959797i \(-0.409435\pi\)
\(488\) 0.398461 + 0.690154i 0.0180375 + 0.0312418i
\(489\) 0 0
\(490\) 0 0
\(491\) −6.87298 11.9044i −0.310173 0.537236i 0.668226 0.743958i \(-0.267054\pi\)
−0.978400 + 0.206722i \(0.933720\pi\)
\(492\) 0 0
\(493\) 12.5483 0.565147
\(494\) 1.69052 + 2.92808i 0.0760603 + 0.131740i
\(495\) 0 0
\(496\) −5.47723 −0.245935
\(497\) 0 0
\(498\) 0 0
\(499\) −14.2540 −0.638098 −0.319049 0.947738i \(-0.603363\pi\)
−0.319049 + 0.947738i \(0.603363\pi\)
\(500\) −5.96550 + 10.3325i −0.266785 + 0.462086i
\(501\) 0 0
\(502\) −12.9468 22.4244i −0.577842 1.00085i
\(503\) −18.0255 −0.803718 −0.401859 0.915702i \(-0.631636\pi\)
−0.401859 + 0.915702i \(0.631636\pi\)
\(504\) 0 0
\(505\) −15.9839 −0.711273
\(506\) 13.4919 + 23.3687i 0.599790 + 1.03887i
\(507\) 0 0
\(508\) −7.37298 + 12.7704i −0.327123 + 0.566594i
\(509\) −33.7615 −1.49645 −0.748226 0.663444i \(-0.769094\pi\)
−0.748226 + 0.663444i \(0.769094\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −6.98125 12.0919i −0.307930 0.533350i
\(515\) 36.6190 1.61362
\(516\) 0 0
\(517\) −13.7829 23.8726i −0.606170 1.04992i
\(518\) 0 0
\(519\) 0 0
\(520\) 4.30948 + 7.46423i 0.188983 + 0.327328i
\(521\) 0.707107 + 1.22474i 0.0309789 + 0.0536570i 0.881099 0.472931i \(-0.156804\pi\)
−0.850120 + 0.526589i \(0.823471\pi\)
\(522\) 0 0
\(523\) 15.5057 26.8567i 0.678019 1.17436i −0.297558 0.954704i \(-0.596172\pi\)
0.975577 0.219659i \(-0.0704945\pi\)
\(524\) 3.93399 6.81388i 0.171857 0.297666i
\(525\) 0 0
\(526\) −2.80948 4.86615i −0.122499 0.212174i
\(527\) 7.74597 0.337420
\(528\) 0 0
\(529\) 22.5081 0.978612
\(530\) −10.7862 + 18.6823i −0.468524 + 0.811507i
\(531\) 0 0
\(532\) 0 0
\(533\) −12.0000 + 20.7846i −0.519778 + 0.900281i
\(534\) 0 0
\(535\) −15.9940 + 27.7024i −0.691481 + 1.19768i
\(536\) 0.436492 0.756026i 0.0188536 0.0326553i
\(537\) 0 0
\(538\) −1.72286 + 2.98408i −0.0742778 + 0.128653i
\(539\) 0 0
\(540\) 0 0
\(541\) −8.05544 + 13.9524i −0.346330 + 0.599862i −0.985595 0.169125i \(-0.945906\pi\)
0.639264 + 0.768987i \(0.279239\pi\)
\(542\) −7.07107 −0.303728
\(543\) 0 0
\(544\) 1.41421 0.0606339
\(545\) 9.27079 + 16.0575i 0.397117 + 0.687827i
\(546\) 0 0
\(547\) −14.4919 + 25.1008i −0.619630 + 1.07323i 0.369923 + 0.929062i \(0.379384\pi\)
−0.989553 + 0.144169i \(0.953949\pi\)
\(548\) 7.74597 13.4164i 0.330891 0.573121i
\(549\) 0 0
\(550\) 1.74597 + 3.02410i 0.0744483 + 0.128948i
\(551\) −3.53553 6.12372i −0.150619 0.260879i
\(552\) 0 0
\(553\) 0 0
\(554\) −12.1825 21.1006i −0.517583 0.896480i
\(555\) 0 0
\(556\) −18.4632 −0.783013
\(557\) 1.69052 + 2.92808i 0.0716298 + 0.124067i 0.899616 0.436682i \(-0.143847\pi\)
−0.827986 + 0.560749i \(0.810513\pi\)
\(558\) 0 0
\(559\) −37.6449 −1.59221
\(560\) 0 0
\(561\) 0 0
\(562\) −6.74597 −0.284561
\(563\) −2.60960 + 4.51995i −0.109981 + 0.190493i −0.915762 0.401720i \(-0.868412\pi\)
0.805781 + 0.592213i \(0.201746\pi\)
\(564\) 0 0
\(565\) 3.93399 + 6.81388i 0.165504 + 0.286662i
\(566\) −10.5168 −0.442054
\(567\) 0 0
\(568\) −2.12702 −0.0892476
\(569\) 3.74597 + 6.48820i 0.157039 + 0.272000i 0.933800 0.357796i \(-0.116472\pi\)
−0.776761 + 0.629796i \(0.783138\pi\)
\(570\) 0 0
\(571\) −0.254033 + 0.439999i −0.0106310 + 0.0184134i −0.871292 0.490765i \(-0.836717\pi\)
0.860661 + 0.509178i \(0.170051\pi\)
\(572\) 16.9706 0.709575
\(573\) 0 0
\(574\) 0 0
\(575\) 5.88912 0.245593
\(576\) 0 0
\(577\) −17.5879 30.4631i −0.732192 1.26819i −0.955944 0.293548i \(-0.905164\pi\)
0.223752 0.974646i \(-0.428169\pi\)
\(578\) 15.0000 0.623918
\(579\) 0 0
\(580\) −9.01276 15.6106i −0.374234 0.648193i
\(581\) 0 0
\(582\) 0 0
\(583\) 21.2379 + 36.7851i 0.879584 + 1.52348i
\(584\) 7.68836 + 13.3166i 0.318147 + 0.551046i
\(585\) 0 0
\(586\) 3.13707 5.43357i 0.129591 0.224459i
\(587\) −14.8884 + 25.7875i −0.614512 + 1.06437i 0.375958 + 0.926637i \(0.377314\pi\)
−0.990470 + 0.137729i \(0.956020\pi\)
\(588\) 0 0
\(589\) −2.18246 3.78013i −0.0899266 0.155757i
\(590\) −5.38105 −0.221534
\(591\) 0 0
\(592\) −9.74597 −0.400557
\(593\) 11.4035 19.7515i 0.468287 0.811096i −0.531057 0.847336i \(-0.678205\pi\)
0.999343 + 0.0362403i \(0.0115382\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.127017 + 0.219999i −0.00520280 + 0.00901152i
\(597\) 0 0
\(598\) 14.3104 24.7863i 0.585194 1.01359i
\(599\) 0.618950 1.07205i 0.0252896 0.0438029i −0.853104 0.521742i \(-0.825283\pi\)
0.878393 + 0.477939i \(0.158616\pi\)
\(600\) 0 0
\(601\) 18.8224 32.6014i 0.767783 1.32984i −0.170979 0.985275i \(-0.554693\pi\)
0.938762 0.344565i \(-0.111974\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −5.50000 + 9.52628i −0.223792 + 0.387619i
\(605\) −10.1575 −0.412962
\(606\) 0 0
\(607\) 15.7360 0.638704 0.319352 0.947636i \(-0.396535\pi\)
0.319352 + 0.947636i \(0.396535\pi\)
\(608\) −0.398461 0.690154i −0.0161597 0.0279894i
\(609\) 0 0
\(610\) −0.809475 + 1.40205i −0.0327747 + 0.0567674i
\(611\) −14.6190 + 25.3208i −0.591419 + 1.02437i
\(612\) 0 0
\(613\) −1.69052 2.92808i −0.0682797 0.118264i 0.829864 0.557965i \(-0.188418\pi\)
−0.898144 + 0.439701i \(0.855084\pi\)
\(614\) −12.0600 20.8886i −0.486703 0.842994i
\(615\) 0 0
\(616\) 0 0
\(617\) −13.8730 24.0287i −0.558505 0.967360i −0.997622 0.0689293i \(-0.978042\pi\)
0.439116 0.898430i \(-0.355292\pi\)
\(618\) 0 0
\(619\) 22.3466 0.898184 0.449092 0.893485i \(-0.351747\pi\)
0.449092 + 0.893485i \(0.351747\pi\)
\(620\) −5.56351 9.63628i −0.223436 0.387002i
\(621\) 0 0
\(622\) −1.41421 −0.0567048
\(623\) 0 0
\(624\) 0 0
\(625\) −19.8730 −0.794919
\(626\) 13.3452 23.1146i 0.533382 0.923845i
\(627\) 0 0
\(628\) −3.22689 5.58913i −0.128767 0.223031i
\(629\) 13.7829 0.549559
\(630\) 0 0
\(631\) −27.6190 −1.09949 −0.549747 0.835332i \(-0.685276\pi\)
−0.549747 + 0.835332i \(0.685276\pi\)
\(632\) 2.93649 + 5.08615i 0.116807 + 0.202316i
\(633\) 0 0
\(634\) −0.690525 + 1.19602i −0.0274243 + 0.0475002i
\(635\) −29.9565 −1.18879
\(636\) 0 0
\(637\) 0 0
\(638\) −35.4919 −1.40514
\(639\) 0 0
\(640\) −1.01575 1.75934i −0.0401512 0.0695439i
\(641\) 37.1109 1.46579 0.732896 0.680341i \(-0.238168\pi\)
0.732896 + 0.680341i \(0.238168\pi\)
\(642\) 0 0
\(643\) 20.1468 + 34.8953i 0.794514 + 1.37614i 0.923147 + 0.384446i \(0.125608\pi\)
−0.128634 + 0.991692i \(0.541059\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.563508 + 0.976025i 0.0221709 + 0.0384012i
\(647\) 2.73861 + 4.74342i 0.107666 + 0.186483i 0.914824 0.403852i \(-0.132329\pi\)
−0.807158 + 0.590335i \(0.798996\pi\)
\(648\) 0 0
\(649\) −5.29760 + 9.17571i −0.207949 + 0.360178i
\(650\) 1.85188 3.20755i 0.0726366 0.125810i
\(651\) 0 0
\(652\) −5.00000 8.66025i −0.195815 0.339162i
\(653\) 45.4919 1.78024 0.890118 0.455729i \(-0.150621\pi\)
0.890118 + 0.455729i \(0.150621\pi\)
\(654\) 0 0
\(655\) 15.9839 0.624541
\(656\) 2.82843 4.89898i 0.110432 0.191273i
\(657\) 0 0
\(658\) 0 0
\(659\) 18.4365 31.9329i 0.718184 1.24393i −0.243535 0.969892i \(-0.578307\pi\)
0.961719 0.274039i \(-0.0883596\pi\)
\(660\) 0 0
\(661\) −12.4977 + 21.6466i −0.486104 + 0.841956i −0.999872 0.0159726i \(-0.994916\pi\)
0.513769 + 0.857929i \(0.328249\pi\)
\(662\) −9.18246 + 15.9045i −0.356886 + 0.618145i
\(663\) 0 0
\(664\) −4.15283 + 7.19291i −0.161161 + 0.279139i
\(665\) 0 0
\(666\) 0 0
\(667\) −29.9284 + 51.8376i −1.15883 + 2.00716i
\(668\) 12.3687 0.478558
\(669\) 0 0
\(670\) 1.77347 0.0685152
\(671\) 1.59384 + 2.76062i 0.0615296 + 0.106572i
\(672\) 0 0
\(673\) 16.1190 27.9188i 0.621340 1.07619i −0.367897 0.929867i \(-0.619922\pi\)
0.989236 0.146326i \(-0.0467447\pi\)
\(674\) 0.127017 0.219999i 0.00489250 0.00847406i
\(675\) 0 0
\(676\) −2.50000 4.33013i −0.0961538 0.166543i
\(677\) 6.36396 + 11.0227i 0.244587 + 0.423637i 0.962015 0.272995i \(-0.0880143\pi\)
−0.717428 + 0.696632i \(0.754681\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 1.43649 + 2.48808i 0.0550869 + 0.0954134i
\(681\) 0 0
\(682\) −21.9089 −0.838935
\(683\) −3.87298 6.70820i −0.148196 0.256682i 0.782365 0.622820i \(-0.214013\pi\)
−0.930561 + 0.366138i \(0.880680\pi\)
\(684\) 0 0
\(685\) 31.4720 1.20248
\(686\) 0 0
\(687\) 0 0
\(688\) 8.87298 0.338279
\(689\) 22.5262 39.0165i 0.858180 1.48641i
\(690\) 0 0
\(691\) 10.6458 + 18.4391i 0.404986 + 0.701455i 0.994320 0.106434i \(-0.0339432\pi\)
−0.589334 + 0.807889i \(0.700610\pi\)
\(692\) −12.7279 −0.483843
\(693\) 0 0
\(694\) −7.74597 −0.294033
\(695\) −18.7540 32.4829i −0.711381 1.23215i
\(696\) 0 0
\(697\) −4.00000 + 6.92820i −0.151511 + 0.262424i
\(698\) −16.4317 −0.621948
\(699\) 0 0
\(700\) 0 0
\(701\) 31.7460 1.19903 0.599514 0.800364i \(-0.295360\pi\)
0.599514 + 0.800364i \(0.295360\pi\)
\(702\) 0 0
\(703\) −3.88338 6.72622i −0.146465 0.253684i
\(704\) −4.00000 −0.150756
\(705\) 0 0
\(706\) 9.01276 + 15.6106i 0.339200 + 0.587511i
\(707\) 0 0
\(708\) 0 0
\(709\) −12.3649 21.4167i −0.464374 0.804320i 0.534799 0.844979i \(-0.320387\pi\)
−0.999173 + 0.0406597i \(0.987054\pi\)
\(710\) −2.16052 3.74214i −0.0810830 0.140440i
\(711\) 0 0
\(712\) −3.53553 + 6.12372i −0.132500 + 0.229496i
\(713\) −18.4746 + 31.9989i −0.691879 + 1.19837i
\(714\) 0 0
\(715\) 17.2379 + 29.8569i 0.644661 + 1.11659i
\(716\) −0.872983 −0.0326249
\(717\) 0 0
\(718\) −28.2379 −1.05383
\(719\) 4.68030 8.10653i 0.174546 0.302322i −0.765458 0.643486i \(-0.777488\pi\)
0.940004 + 0.341163i \(0.110821\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −9.18246 + 15.9045i −0.341736 + 0.591904i
\(723\) 0 0
\(724\) 3.93399 6.81388i 0.146206 0.253236i
\(725\) −3.87298 + 6.70820i −0.143839 + 0.249136i
\(726\) 0 0
\(727\) −18.1153 + 31.3767i −0.671861 + 1.16370i 0.305515 + 0.952187i \(0.401171\pi\)
−0.977376 + 0.211509i \(0.932162\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −15.6190 + 27.0528i −0.578083 + 1.00127i
\(731\) −12.5483 −0.464115
\(732\) 0 0
\(733\) −9.64146 −0.356115 −0.178058 0.984020i \(-0.556981\pi\)
−0.178058 + 0.984020i \(0.556981\pi\)
\(734\) −2.03151 3.51867i −0.0749843 0.129877i
\(735\) 0 0
\(736\) −3.37298 + 5.84218i −0.124330 + 0.215346i
\(737\) 1.74597 3.02410i 0.0643135 0.111394i
\(738\) 0 0
\(739\) 15.0000 + 25.9808i 0.551784 + 0.955718i 0.998146 + 0.0608653i \(0.0193860\pi\)
−0.446362 + 0.894852i \(0.647281\pi\)
\(740\) −9.89949 17.1464i −0.363913 0.630315i
\(741\) 0 0
\(742\) 0 0
\(743\) −13.8730 24.0287i −0.508950 0.881528i −0.999946 0.0103660i \(-0.996700\pi\)
0.490996 0.871162i \(-0.336633\pi\)
\(744\) 0 0
\(745\) −0.516070 −0.0189073
\(746\) −4.43649 7.68423i −0.162432 0.281340i
\(747\) 0 0
\(748\) 5.65685 0.206835
\(749\) 0 0
\(750\) 0 0
\(751\) −13.0000 −0.474377 −0.237188 0.971464i \(-0.576226\pi\)
−0.237188 + 0.971464i \(0.576226\pi\)
\(752\) 3.44572 5.96816i 0.125652 0.217636i
\(753\) 0 0
\(754\) 18.8224 + 32.6014i 0.685473 + 1.18727i
\(755\) −22.3466 −0.813275
\(756\) 0 0
\(757\) −15.2379 −0.553831 −0.276915 0.960894i \(-0.589312\pi\)
−0.276915 + 0.960894i \(0.589312\pi\)
\(758\) −6.18246 10.7083i −0.224557 0.388944i
\(759\) 0 0
\(760\) 0.809475 1.40205i 0.0293627 0.0508578i
\(761\) −2.28954 −0.0829958 −0.0414979 0.999139i \(-0.513213\pi\)
−0.0414979 + 0.999139i \(0.513213\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 13.8730 0.501907
\(765\) 0 0
\(766\) 11.9310 + 20.6651i 0.431085 + 0.746660i
\(767\) 11.2379 0.405777
\(768\) 0 0
\(769\) −4.85993 8.41765i −0.175254 0.303548i 0.764995 0.644036i \(-0.222741\pi\)
−0.940249 + 0.340488i \(0.889408\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −8.06351 13.9664i −0.290212 0.502662i
\(773\) 1.72286 + 2.98408i 0.0619670 + 0.107330i 0.895345 0.445374i \(-0.146929\pi\)
−0.833378 + 0.552704i \(0.813596\pi\)
\(774\) 0 0
\(775\) −2.39076 + 4.14092i −0.0858788 + 0.148746i
\(776\) −8.92295 + 15.4550i −0.320315 + 0.554802i
\(777\) 0 0
\(778\) −10.4365 18.0765i −0.374166 0.648075i
\(779\) 4.50807 0.161518
\(780\) 0 0
\(781\) −8.50807 −0.304443
\(782\) 4.77012 8.26209i 0.170579 0.295452i
\(783\) 0 0
\(784\) 0 0
\(785\) 6.55544 11.3544i 0.233974 0.405254i
\(786\) 0 0
\(787\) 4.77012 8.26209i 0.170036 0.294512i −0.768396 0.639975i \(-0.778945\pi\)
0.938432 + 0.345463i \(0.112278\pi\)
\(788\) −3.30948 + 5.73218i −0.117895 + 0.204200i
\(789\) 0 0
\(790\) −5.96550 + 10.3325i −0.212243 + 0.367616i
\(791\) 0 0
\(792\) 0 0
\(793\) 1.69052 2.92808i 0.0600323 0.103979i