Properties

Label 2646.2.h.m.361.1
Level $2646$
Weight $2$
Character 2646.361
Analytic conductor $21.128$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 2646.361
Dual form 2646.2.h.m.667.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.44949 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.44949 q^{5} -1.00000 q^{8} +(-1.72474 + 2.98735i) q^{10} -2.00000 q^{11} +(2.44949 - 4.24264i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-3.72474 - 6.45145i) q^{19} +(1.72474 + 2.98735i) q^{20} +(-1.00000 + 1.73205i) q^{22} +1.00000 q^{23} +6.89898 q^{25} +(-2.44949 - 4.24264i) q^{26} +(1.44949 + 2.51059i) q^{29} +(-3.00000 - 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{34} +(3.89898 + 6.75323i) q^{37} -7.44949 q^{38} +3.44949 q^{40} +(-4.89898 + 8.48528i) q^{41} +(1.44949 + 2.51059i) q^{43} +(1.00000 + 1.73205i) q^{44} +(0.500000 - 0.866025i) q^{46} +(-4.89898 + 8.48528i) q^{47} +(3.44949 - 5.97469i) q^{50} -4.89898 q^{52} +(-0.550510 + 0.953512i) q^{53} +6.89898 q^{55} +2.89898 q^{58} +(-1.00000 - 1.73205i) q^{59} +(-5.72474 + 9.91555i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(-8.44949 + 14.6349i) q^{65} +(1.55051 + 2.68556i) q^{67} -2.00000 q^{68} -9.89898 q^{71} +(-1.44949 + 2.51059i) q^{73} +7.79796 q^{74} +(-3.72474 + 6.45145i) q^{76} +(-3.94949 + 6.84072i) q^{79} +(1.72474 - 2.98735i) q^{80} +(4.89898 + 8.48528i) q^{82} +(1.00000 + 1.73205i) q^{83} +(-3.44949 + 5.97469i) q^{85} +2.89898 q^{86} +2.00000 q^{88} +(-3.55051 - 6.14966i) q^{89} +(-0.500000 - 0.866025i) q^{92} +(4.89898 + 8.48528i) q^{94} +(12.8485 + 22.2542i) q^{95} +(3.44949 + 5.97469i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 4 q^{8} - 2 q^{10} - 8 q^{11} - 2 q^{16} + 4 q^{17} - 10 q^{19} + 2 q^{20} - 4 q^{22} + 4 q^{23} + 8 q^{25} - 4 q^{29} - 12 q^{31} + 2 q^{32} - 4 q^{34} - 4 q^{37} - 20 q^{38} + 4 q^{40} - 4 q^{43} + 4 q^{44} + 2 q^{46} + 4 q^{50} - 12 q^{53} + 8 q^{55} - 8 q^{58} - 4 q^{59} - 18 q^{61} - 24 q^{62} + 4 q^{64} - 24 q^{65} + 16 q^{67} - 8 q^{68} - 20 q^{71} + 4 q^{73} - 8 q^{74} - 10 q^{76} - 6 q^{79} + 2 q^{80} + 4 q^{83} - 4 q^{85} - 8 q^{86} + 8 q^{88} - 24 q^{89} - 2 q^{92} + 22 q^{95} + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −3.44949 −1.54266 −0.771329 0.636436i \(-0.780408\pi\)
−0.771329 + 0.636436i \(0.780408\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.72474 + 2.98735i −0.545412 + 0.944682i
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 2.44949 4.24264i 0.679366 1.17670i −0.295806 0.955248i \(-0.595588\pi\)
0.975172 0.221449i \(-0.0710785\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) 0 0
\(19\) −3.72474 6.45145i −0.854515 1.48006i −0.877094 0.480318i \(-0.840521\pi\)
0.0225791 0.999745i \(-0.492812\pi\)
\(20\) 1.72474 + 2.98735i 0.385665 + 0.667991i
\(21\) 0 0
\(22\) −1.00000 + 1.73205i −0.213201 + 0.369274i
\(23\) 1.00000 0.208514 0.104257 0.994550i \(-0.466753\pi\)
0.104257 + 0.994550i \(0.466753\pi\)
\(24\) 0 0
\(25\) 6.89898 1.37980
\(26\) −2.44949 4.24264i −0.480384 0.832050i
\(27\) 0 0
\(28\) 0 0
\(29\) 1.44949 + 2.51059i 0.269163 + 0.466205i 0.968646 0.248445i \(-0.0799195\pi\)
−0.699483 + 0.714650i \(0.746586\pi\)
\(30\) 0 0
\(31\) −3.00000 5.19615i −0.538816 0.933257i −0.998968 0.0454165i \(-0.985539\pi\)
0.460152 0.887840i \(-0.347795\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −1.00000 1.73205i −0.171499 0.297044i
\(35\) 0 0
\(36\) 0 0
\(37\) 3.89898 + 6.75323i 0.640988 + 1.11022i 0.985213 + 0.171337i \(0.0548086\pi\)
−0.344224 + 0.938887i \(0.611858\pi\)
\(38\) −7.44949 −1.20847
\(39\) 0 0
\(40\) 3.44949 0.545412
\(41\) −4.89898 + 8.48528i −0.765092 + 1.32518i 0.175106 + 0.984550i \(0.443973\pi\)
−0.940198 + 0.340629i \(0.889360\pi\)
\(42\) 0 0
\(43\) 1.44949 + 2.51059i 0.221045 + 0.382861i 0.955126 0.296201i \(-0.0957199\pi\)
−0.734080 + 0.679062i \(0.762387\pi\)
\(44\) 1.00000 + 1.73205i 0.150756 + 0.261116i
\(45\) 0 0
\(46\) 0.500000 0.866025i 0.0737210 0.127688i
\(47\) −4.89898 + 8.48528i −0.714590 + 1.23771i 0.248528 + 0.968625i \(0.420053\pi\)
−0.963118 + 0.269081i \(0.913280\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 3.44949 5.97469i 0.487832 0.844949i
\(51\) 0 0
\(52\) −4.89898 −0.679366
\(53\) −0.550510 + 0.953512i −0.0756184 + 0.130975i −0.901355 0.433081i \(-0.857426\pi\)
0.825737 + 0.564056i \(0.190760\pi\)
\(54\) 0 0
\(55\) 6.89898 0.930258
\(56\) 0 0
\(57\) 0 0
\(58\) 2.89898 0.380655
\(59\) −1.00000 1.73205i −0.130189 0.225494i 0.793560 0.608492i \(-0.208225\pi\)
−0.923749 + 0.382998i \(0.874892\pi\)
\(60\) 0 0
\(61\) −5.72474 + 9.91555i −0.732978 + 1.26956i 0.222626 + 0.974904i \(0.428537\pi\)
−0.955605 + 0.294652i \(0.904796\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −8.44949 + 14.6349i −1.04803 + 1.81524i
\(66\) 0 0
\(67\) 1.55051 + 2.68556i 0.189425 + 0.328094i 0.945059 0.326901i \(-0.106004\pi\)
−0.755634 + 0.654994i \(0.772671\pi\)
\(68\) −2.00000 −0.242536
\(69\) 0 0
\(70\) 0 0
\(71\) −9.89898 −1.17479 −0.587396 0.809299i \(-0.699847\pi\)
−0.587396 + 0.809299i \(0.699847\pi\)
\(72\) 0 0
\(73\) −1.44949 + 2.51059i −0.169650 + 0.293842i −0.938297 0.345831i \(-0.887597\pi\)
0.768647 + 0.639673i \(0.220930\pi\)
\(74\) 7.79796 0.906494
\(75\) 0 0
\(76\) −3.72474 + 6.45145i −0.427258 + 0.740032i
\(77\) 0 0
\(78\) 0 0
\(79\) −3.94949 + 6.84072i −0.444352 + 0.769641i −0.998007 0.0631057i \(-0.979899\pi\)
0.553655 + 0.832746i \(0.313233\pi\)
\(80\) 1.72474 2.98735i 0.192832 0.333995i
\(81\) 0 0
\(82\) 4.89898 + 8.48528i 0.541002 + 0.937043i
\(83\) 1.00000 + 1.73205i 0.109764 + 0.190117i 0.915675 0.401920i \(-0.131657\pi\)
−0.805910 + 0.592037i \(0.798324\pi\)
\(84\) 0 0
\(85\) −3.44949 + 5.97469i −0.374150 + 0.648046i
\(86\) 2.89898 0.312605
\(87\) 0 0
\(88\) 2.00000 0.213201
\(89\) −3.55051 6.14966i −0.376353 0.651863i 0.614175 0.789170i \(-0.289489\pi\)
−0.990529 + 0.137307i \(0.956155\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.500000 0.866025i −0.0521286 0.0902894i
\(93\) 0 0
\(94\) 4.89898 + 8.48528i 0.505291 + 0.875190i
\(95\) 12.8485 + 22.2542i 1.31823 + 2.28323i
\(96\) 0 0
\(97\) 3.44949 + 5.97469i 0.350243 + 0.606638i 0.986292 0.165011i \(-0.0527658\pi\)
−0.636049 + 0.771649i \(0.719432\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.44949 5.97469i −0.344949 0.597469i
\(101\) −7.24745 −0.721148 −0.360574 0.932731i \(-0.617419\pi\)
−0.360574 + 0.932731i \(0.617419\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) −2.44949 + 4.24264i −0.240192 + 0.416025i
\(105\) 0 0
\(106\) 0.550510 + 0.953512i 0.0534703 + 0.0926132i
\(107\) −6.00000 10.3923i −0.580042 1.00466i −0.995474 0.0950377i \(-0.969703\pi\)
0.415432 0.909624i \(-0.363630\pi\)
\(108\) 0 0
\(109\) 8.34847 14.4600i 0.799638 1.38501i −0.120213 0.992748i \(-0.538358\pi\)
0.919852 0.392266i \(-0.128309\pi\)
\(110\) 3.44949 5.97469i 0.328896 0.569664i
\(111\) 0 0
\(112\) 0 0
\(113\) −7.94949 + 13.7689i −0.747825 + 1.29527i 0.201038 + 0.979583i \(0.435569\pi\)
−0.948863 + 0.315688i \(0.897765\pi\)
\(114\) 0 0
\(115\) −3.44949 −0.321667
\(116\) 1.44949 2.51059i 0.134582 0.233102i
\(117\) 0 0
\(118\) −2.00000 −0.184115
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 5.72474 + 9.91555i 0.518294 + 0.897712i
\(123\) 0 0
\(124\) −3.00000 + 5.19615i −0.269408 + 0.466628i
\(125\) −6.55051 −0.585895
\(126\) 0 0
\(127\) −3.00000 −0.266207 −0.133103 0.991102i \(-0.542494\pi\)
−0.133103 + 0.991102i \(0.542494\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 8.44949 + 14.6349i 0.741069 + 1.28357i
\(131\) 13.4495 1.17509 0.587544 0.809192i \(-0.300095\pi\)
0.587544 + 0.809192i \(0.300095\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 3.10102 0.267887
\(135\) 0 0
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) 11.7980 1.00797 0.503984 0.863713i \(-0.331867\pi\)
0.503984 + 0.863713i \(0.331867\pi\)
\(138\) 0 0
\(139\) −4.72474 + 8.18350i −0.400748 + 0.694115i −0.993816 0.111037i \(-0.964583\pi\)
0.593069 + 0.805152i \(0.297916\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.94949 + 8.57277i −0.415352 + 0.719411i
\(143\) −4.89898 + 8.48528i −0.409673 + 0.709575i
\(144\) 0 0
\(145\) −5.00000 8.66025i −0.415227 0.719195i
\(146\) 1.44949 + 2.51059i 0.119961 + 0.207778i
\(147\) 0 0
\(148\) 3.89898 6.75323i 0.320494 0.555112i
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 0 0
\(151\) −5.00000 −0.406894 −0.203447 0.979086i \(-0.565214\pi\)
−0.203447 + 0.979086i \(0.565214\pi\)
\(152\) 3.72474 + 6.45145i 0.302117 + 0.523281i
\(153\) 0 0
\(154\) 0 0
\(155\) 10.3485 + 17.9241i 0.831209 + 1.43970i
\(156\) 0 0
\(157\) −3.17423 5.49794i −0.253332 0.438783i 0.711109 0.703081i \(-0.248193\pi\)
−0.964441 + 0.264298i \(0.914860\pi\)
\(158\) 3.94949 + 6.84072i 0.314205 + 0.544218i
\(159\) 0 0
\(160\) −1.72474 2.98735i −0.136353 0.236170i
\(161\) 0 0
\(162\) 0 0
\(163\) 0.101021 + 0.174973i 0.00791254 + 0.0137049i 0.869955 0.493132i \(-0.164148\pi\)
−0.862042 + 0.506837i \(0.830815\pi\)
\(164\) 9.79796 0.765092
\(165\) 0 0
\(166\) 2.00000 0.155230
\(167\) 9.34847 16.1920i 0.723406 1.25298i −0.236220 0.971700i \(-0.575909\pi\)
0.959627 0.281277i \(-0.0907579\pi\)
\(168\) 0 0
\(169\) −5.50000 9.52628i −0.423077 0.732791i
\(170\) 3.44949 + 5.97469i 0.264564 + 0.458238i
\(171\) 0 0
\(172\) 1.44949 2.51059i 0.110523 0.191431i
\(173\) −6.44949 + 11.1708i −0.490346 + 0.849304i −0.999938 0.0111123i \(-0.996463\pi\)
0.509593 + 0.860416i \(0.329796\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.00000 1.73205i 0.0753778 0.130558i
\(177\) 0 0
\(178\) −7.10102 −0.532244
\(179\) −4.34847 + 7.53177i −0.325020 + 0.562951i −0.981516 0.191378i \(-0.938704\pi\)
0.656497 + 0.754329i \(0.272038\pi\)
\(180\) 0 0
\(181\) 4.34847 0.323219 0.161610 0.986855i \(-0.448331\pi\)
0.161610 + 0.986855i \(0.448331\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.00000 −0.0737210
\(185\) −13.4495 23.2952i −0.988826 1.71270i
\(186\) 0 0
\(187\) −2.00000 + 3.46410i −0.146254 + 0.253320i
\(188\) 9.79796 0.714590
\(189\) 0 0
\(190\) 25.6969 1.86425
\(191\) 6.94949 12.0369i 0.502847 0.870957i −0.497147 0.867666i \(-0.665619\pi\)
0.999995 0.00329106i \(-0.00104758\pi\)
\(192\) 0 0
\(193\) 4.05051 + 7.01569i 0.291562 + 0.505000i 0.974179 0.225776i \(-0.0724917\pi\)
−0.682617 + 0.730776i \(0.739158\pi\)
\(194\) 6.89898 0.495318
\(195\) 0 0
\(196\) 0 0
\(197\) 12.6969 0.904619 0.452310 0.891861i \(-0.350600\pi\)
0.452310 + 0.891861i \(0.350600\pi\)
\(198\) 0 0
\(199\) −3.44949 + 5.97469i −0.244528 + 0.423535i −0.961999 0.273054i \(-0.911966\pi\)
0.717471 + 0.696588i \(0.245300\pi\)
\(200\) −6.89898 −0.487832
\(201\) 0 0
\(202\) −3.62372 + 6.27647i −0.254964 + 0.441611i
\(203\) 0 0
\(204\) 0 0
\(205\) 16.8990 29.2699i 1.18028 2.04430i
\(206\) 7.00000 12.1244i 0.487713 0.844744i
\(207\) 0 0
\(208\) 2.44949 + 4.24264i 0.169842 + 0.294174i
\(209\) 7.44949 + 12.9029i 0.515292 + 0.892512i
\(210\) 0 0
\(211\) −1.55051 + 2.68556i −0.106742 + 0.184882i −0.914448 0.404703i \(-0.867375\pi\)
0.807707 + 0.589584i \(0.200708\pi\)
\(212\) 1.10102 0.0756184
\(213\) 0 0
\(214\) −12.0000 −0.820303
\(215\) −5.00000 8.66025i −0.340997 0.590624i
\(216\) 0 0
\(217\) 0 0
\(218\) −8.34847 14.4600i −0.565430 0.979353i
\(219\) 0 0
\(220\) −3.44949 5.97469i −0.232565 0.402814i
\(221\) −4.89898 8.48528i −0.329541 0.570782i
\(222\) 0 0
\(223\) 10.4495 + 18.0990i 0.699750 + 1.21200i 0.968553 + 0.248807i \(0.0800384\pi\)
−0.268804 + 0.963195i \(0.586628\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 7.94949 + 13.7689i 0.528792 + 0.915895i
\(227\) 0.550510 0.0365386 0.0182693 0.999833i \(-0.494184\pi\)
0.0182693 + 0.999833i \(0.494184\pi\)
\(228\) 0 0
\(229\) −23.2474 −1.53623 −0.768117 0.640309i \(-0.778806\pi\)
−0.768117 + 0.640309i \(0.778806\pi\)
\(230\) −1.72474 + 2.98735i −0.113726 + 0.196980i
\(231\) 0 0
\(232\) −1.44949 2.51059i −0.0951637 0.164828i
\(233\) −3.50000 6.06218i −0.229293 0.397146i 0.728306 0.685252i \(-0.240308\pi\)
−0.957599 + 0.288106i \(0.906975\pi\)
\(234\) 0 0
\(235\) 16.8990 29.2699i 1.10237 1.90936i
\(236\) −1.00000 + 1.73205i −0.0650945 + 0.112747i
\(237\) 0 0
\(238\) 0 0
\(239\) −6.39898 + 11.0834i −0.413916 + 0.716923i −0.995314 0.0966962i \(-0.969172\pi\)
0.581398 + 0.813619i \(0.302506\pi\)
\(240\) 0 0
\(241\) −8.89898 −0.573234 −0.286617 0.958045i \(-0.592531\pi\)
−0.286617 + 0.958045i \(0.592531\pi\)
\(242\) −3.50000 + 6.06218i −0.224989 + 0.389692i
\(243\) 0 0
\(244\) 11.4495 0.732978
\(245\) 0 0
\(246\) 0 0
\(247\) −36.4949 −2.32211
\(248\) 3.00000 + 5.19615i 0.190500 + 0.329956i
\(249\) 0 0
\(250\) −3.27526 + 5.67291i −0.207145 + 0.358786i
\(251\) −12.5505 −0.792181 −0.396091 0.918211i \(-0.629633\pi\)
−0.396091 + 0.918211i \(0.629633\pi\)
\(252\) 0 0
\(253\) −2.00000 −0.125739
\(254\) −1.50000 + 2.59808i −0.0941184 + 0.163018i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −27.7980 −1.73399 −0.866995 0.498318i \(-0.833951\pi\)
−0.866995 + 0.498318i \(0.833951\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 16.8990 1.04803
\(261\) 0 0
\(262\) 6.72474 11.6476i 0.415456 0.719591i
\(263\) −16.1010 −0.992831 −0.496416 0.868085i \(-0.665351\pi\)
−0.496416 + 0.868085i \(0.665351\pi\)
\(264\) 0 0
\(265\) 1.89898 3.28913i 0.116653 0.202050i
\(266\) 0 0
\(267\) 0 0
\(268\) 1.55051 2.68556i 0.0947125 0.164047i
\(269\) −1.82577 + 3.16232i −0.111319 + 0.192810i −0.916302 0.400487i \(-0.868841\pi\)
0.804983 + 0.593297i \(0.202174\pi\)
\(270\) 0 0
\(271\) −8.44949 14.6349i −0.513270 0.889010i −0.999882 0.0153912i \(-0.995101\pi\)
0.486612 0.873618i \(-0.338233\pi\)
\(272\) 1.00000 + 1.73205i 0.0606339 + 0.105021i
\(273\) 0 0
\(274\) 5.89898 10.2173i 0.356370 0.617252i
\(275\) −13.7980 −0.832048
\(276\) 0 0
\(277\) 10.6969 0.642717 0.321358 0.946958i \(-0.395861\pi\)
0.321358 + 0.946958i \(0.395861\pi\)
\(278\) 4.72474 + 8.18350i 0.283371 + 0.490814i
\(279\) 0 0
\(280\) 0 0
\(281\) −9.50000 16.4545i −0.566722 0.981592i −0.996887 0.0788417i \(-0.974878\pi\)
0.430165 0.902750i \(-0.358455\pi\)
\(282\) 0 0
\(283\) 10.2753 + 17.7973i 0.610801 + 1.05794i 0.991106 + 0.133077i \(0.0424856\pi\)
−0.380305 + 0.924861i \(0.624181\pi\)
\(284\) 4.94949 + 8.57277i 0.293698 + 0.508700i
\(285\) 0 0
\(286\) 4.89898 + 8.48528i 0.289683 + 0.501745i
\(287\) 0 0
\(288\) 0 0
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) −10.0000 −0.587220
\(291\) 0 0
\(292\) 2.89898 0.169650
\(293\) 13.6237 23.5970i 0.795906 1.37855i −0.126356 0.991985i \(-0.540328\pi\)
0.922262 0.386565i \(-0.126339\pi\)
\(294\) 0 0
\(295\) 3.44949 + 5.97469i 0.200837 + 0.347860i
\(296\) −3.89898 6.75323i −0.226624 0.392524i
\(297\) 0 0
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) 2.44949 4.24264i 0.141658 0.245358i
\(300\) 0 0
\(301\) 0 0
\(302\) −2.50000 + 4.33013i −0.143859 + 0.249171i
\(303\) 0 0
\(304\) 7.44949 0.427258
\(305\) 19.7474 34.2036i 1.13074 1.95849i
\(306\) 0 0
\(307\) 0.752551 0.0429504 0.0214752 0.999769i \(-0.493164\pi\)
0.0214752 + 0.999769i \(0.493164\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 20.6969 1.17551
\(311\) 0.651531 + 1.12848i 0.0369449 + 0.0639905i 0.883907 0.467663i \(-0.154904\pi\)
−0.846962 + 0.531654i \(0.821571\pi\)
\(312\) 0 0
\(313\) −12.3485 + 21.3882i −0.697977 + 1.20893i 0.271190 + 0.962526i \(0.412583\pi\)
−0.969167 + 0.246405i \(0.920751\pi\)
\(314\) −6.34847 −0.358265
\(315\) 0 0
\(316\) 7.89898 0.444352
\(317\) −4.34847 + 7.53177i −0.244234 + 0.423026i −0.961916 0.273345i \(-0.911870\pi\)
0.717682 + 0.696371i \(0.245203\pi\)
\(318\) 0 0
\(319\) −2.89898 5.02118i −0.162312 0.281132i
\(320\) −3.44949 −0.192832
\(321\) 0 0
\(322\) 0 0
\(323\) −14.8990 −0.829001
\(324\) 0 0
\(325\) 16.8990 29.2699i 0.937387 1.62360i
\(326\) 0.202041 0.0111900
\(327\) 0 0
\(328\) 4.89898 8.48528i 0.270501 0.468521i
\(329\) 0 0
\(330\) 0 0
\(331\) 12.3485 21.3882i 0.678733 1.17560i −0.296629 0.954993i \(-0.595863\pi\)
0.975363 0.220608i \(-0.0708041\pi\)
\(332\) 1.00000 1.73205i 0.0548821 0.0950586i
\(333\) 0 0
\(334\) −9.34847 16.1920i −0.511525 0.885988i
\(335\) −5.34847 9.26382i −0.292218 0.506137i
\(336\) 0 0
\(337\) −17.6969 + 30.6520i −0.964014 + 1.66972i −0.251772 + 0.967787i \(0.581013\pi\)
−0.712242 + 0.701934i \(0.752320\pi\)
\(338\) −11.0000 −0.598321
\(339\) 0 0
\(340\) 6.89898 0.374150
\(341\) 6.00000 + 10.3923i 0.324918 + 0.562775i
\(342\) 0 0
\(343\) 0 0
\(344\) −1.44949 2.51059i −0.0781512 0.135362i
\(345\) 0 0
\(346\) 6.44949 + 11.1708i 0.346727 + 0.600548i
\(347\) −9.79796 16.9706i −0.525982 0.911028i −0.999542 0.0302659i \(-0.990365\pi\)
0.473560 0.880762i \(-0.342969\pi\)
\(348\) 0 0
\(349\) −10.4495 18.0990i −0.559348 0.968820i −0.997551 0.0699435i \(-0.977718\pi\)
0.438203 0.898876i \(-0.355615\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.00000 1.73205i −0.0533002 0.0923186i
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) 34.1464 1.81230
\(356\) −3.55051 + 6.14966i −0.188177 + 0.325932i
\(357\) 0 0
\(358\) 4.34847 + 7.53177i 0.229824 + 0.398066i
\(359\) 5.39898 + 9.35131i 0.284947 + 0.493543i 0.972596 0.232500i \(-0.0746906\pi\)
−0.687649 + 0.726043i \(0.741357\pi\)
\(360\) 0 0
\(361\) −18.2474 + 31.6055i −0.960392 + 1.66345i
\(362\) 2.17423 3.76588i 0.114275 0.197931i
\(363\) 0 0
\(364\) 0 0
\(365\) 5.00000 8.66025i 0.261712 0.453298i
\(366\) 0 0
\(367\) 5.79796 0.302651 0.151325 0.988484i \(-0.451646\pi\)
0.151325 + 0.988484i \(0.451646\pi\)
\(368\) −0.500000 + 0.866025i −0.0260643 + 0.0451447i
\(369\) 0 0
\(370\) −26.8990 −1.39841
\(371\) 0 0
\(372\) 0 0
\(373\) 2.89898 0.150103 0.0750517 0.997180i \(-0.476088\pi\)
0.0750517 + 0.997180i \(0.476088\pi\)
\(374\) 2.00000 + 3.46410i 0.103418 + 0.179124i
\(375\) 0 0
\(376\) 4.89898 8.48528i 0.252646 0.437595i
\(377\) 14.2020 0.731442
\(378\) 0 0
\(379\) −26.4949 −1.36095 −0.680476 0.732771i \(-0.738227\pi\)
−0.680476 + 0.732771i \(0.738227\pi\)
\(380\) 12.8485 22.2542i 0.659113 1.14162i
\(381\) 0 0
\(382\) −6.94949 12.0369i −0.355567 0.615860i
\(383\) −6.89898 −0.352521 −0.176261 0.984344i \(-0.556400\pi\)
−0.176261 + 0.984344i \(0.556400\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 8.10102 0.412331
\(387\) 0 0
\(388\) 3.44949 5.97469i 0.175121 0.303319i
\(389\) 15.1010 0.765652 0.382826 0.923820i \(-0.374951\pi\)
0.382826 + 0.923820i \(0.374951\pi\)
\(390\) 0 0
\(391\) 1.00000 1.73205i 0.0505722 0.0875936i
\(392\) 0 0
\(393\) 0 0
\(394\) 6.34847 10.9959i 0.319831 0.553964i
\(395\) 13.6237 23.5970i 0.685484 1.18729i
\(396\) 0 0
\(397\) −4.65153 8.05669i −0.233454 0.404354i 0.725369 0.688361i \(-0.241669\pi\)
−0.958822 + 0.284007i \(0.908336\pi\)
\(398\) 3.44949 + 5.97469i 0.172907 + 0.299484i
\(399\) 0 0
\(400\) −3.44949 + 5.97469i −0.172474 + 0.298735i
\(401\) 10.1010 0.504421 0.252210 0.967672i \(-0.418842\pi\)
0.252210 + 0.967672i \(0.418842\pi\)
\(402\) 0 0
\(403\) −29.3939 −1.46421
\(404\) 3.62372 + 6.27647i 0.180287 + 0.312266i
\(405\) 0 0
\(406\) 0 0
\(407\) −7.79796 13.5065i −0.386530 0.669490i
\(408\) 0 0
\(409\) −2.89898 5.02118i −0.143345 0.248281i 0.785409 0.618977i \(-0.212453\pi\)
−0.928754 + 0.370696i \(0.879119\pi\)
\(410\) −16.8990 29.2699i −0.834581 1.44554i
\(411\) 0 0
\(412\) −7.00000 12.1244i −0.344865 0.597324i
\(413\) 0 0
\(414\) 0 0
\(415\) −3.44949 5.97469i −0.169329 0.293286i
\(416\) 4.89898 0.240192
\(417\) 0 0
\(418\) 14.8990 0.728733
\(419\) 12.2753 21.2614i 0.599685 1.03869i −0.393182 0.919461i \(-0.628626\pi\)
0.992867 0.119225i \(-0.0380410\pi\)
\(420\) 0 0
\(421\) −6.55051 11.3458i −0.319252 0.552961i 0.661080 0.750316i \(-0.270098\pi\)
−0.980332 + 0.197354i \(0.936765\pi\)
\(422\) 1.55051 + 2.68556i 0.0754777 + 0.130731i
\(423\) 0 0
\(424\) 0.550510 0.953512i 0.0267351 0.0463066i
\(425\) 6.89898 11.9494i 0.334650 0.579630i
\(426\) 0 0
\(427\) 0 0
\(428\) −6.00000 + 10.3923i −0.290021 + 0.502331i
\(429\) 0 0
\(430\) −10.0000 −0.482243
\(431\) −3.79796 + 6.57826i −0.182941 + 0.316864i −0.942881 0.333130i \(-0.891895\pi\)
0.759940 + 0.649994i \(0.225228\pi\)
\(432\) 0 0
\(433\) 11.7980 0.566974 0.283487 0.958976i \(-0.408509\pi\)
0.283487 + 0.958976i \(0.408509\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −16.6969 −0.799638
\(437\) −3.72474 6.45145i −0.178179 0.308615i
\(438\) 0 0
\(439\) −10.8990 + 18.8776i −0.520180 + 0.900978i 0.479545 + 0.877517i \(0.340802\pi\)
−0.999725 + 0.0234607i \(0.992532\pi\)
\(440\) −6.89898 −0.328896
\(441\) 0 0
\(442\) −9.79796 −0.466041
\(443\) −2.55051 + 4.41761i −0.121178 + 0.209887i −0.920233 0.391372i \(-0.872001\pi\)
0.799054 + 0.601259i \(0.205334\pi\)
\(444\) 0 0
\(445\) 12.2474 + 21.2132i 0.580585 + 1.00560i
\(446\) 20.8990 0.989595
\(447\) 0 0
\(448\) 0 0
\(449\) 18.5959 0.877596 0.438798 0.898586i \(-0.355404\pi\)
0.438798 + 0.898586i \(0.355404\pi\)
\(450\) 0 0
\(451\) 9.79796 16.9706i 0.461368 0.799113i
\(452\) 15.8990 0.747825
\(453\) 0 0
\(454\) 0.275255 0.476756i 0.0129184 0.0223753i
\(455\) 0 0
\(456\) 0 0
\(457\) −15.7474 + 27.2754i −0.736635 + 1.27589i 0.217368 + 0.976090i \(0.430253\pi\)
−0.954002 + 0.299799i \(0.903080\pi\)
\(458\) −11.6237 + 20.1329i −0.543141 + 0.940748i
\(459\) 0 0
\(460\) 1.72474 + 2.98735i 0.0804166 + 0.139286i
\(461\) 10.1742 + 17.6223i 0.473861 + 0.820752i 0.999552 0.0299238i \(-0.00952645\pi\)
−0.525691 + 0.850676i \(0.676193\pi\)
\(462\) 0 0
\(463\) 12.8485 22.2542i 0.597119 1.03424i −0.396125 0.918197i \(-0.629645\pi\)
0.993244 0.116044i \(-0.0370213\pi\)
\(464\) −2.89898 −0.134582
\(465\) 0 0
\(466\) −7.00000 −0.324269
\(467\) 5.00000 + 8.66025i 0.231372 + 0.400749i 0.958212 0.286058i \(-0.0923451\pi\)
−0.726840 + 0.686807i \(0.759012\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −16.8990 29.2699i −0.779492 1.35012i
\(471\) 0 0
\(472\) 1.00000 + 1.73205i 0.0460287 + 0.0797241i
\(473\) −2.89898 5.02118i −0.133295 0.230874i
\(474\) 0 0
\(475\) −25.6969 44.5084i −1.17906 2.04219i
\(476\) 0 0
\(477\) 0 0
\(478\) 6.39898 + 11.0834i 0.292683 + 0.506941i
\(479\) 29.5959 1.35227 0.676136 0.736777i \(-0.263653\pi\)
0.676136 + 0.736777i \(0.263653\pi\)
\(480\) 0 0
\(481\) 38.2020 1.74186
\(482\) −4.44949 + 7.70674i −0.202669 + 0.351032i
\(483\) 0 0
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) −11.8990 20.6096i −0.540305 0.935835i
\(486\) 0 0
\(487\) −11.1969 + 19.3937i −0.507382 + 0.878811i 0.492582 + 0.870266i \(0.336053\pi\)
−0.999963 + 0.00854475i \(0.997280\pi\)
\(488\) 5.72474 9.91555i 0.259147 0.448856i
\(489\) 0 0
\(490\) 0 0
\(491\) −1.89898 + 3.28913i −0.0856997 + 0.148436i −0.905689 0.423942i \(-0.860646\pi\)
0.819989 + 0.572379i \(0.193979\pi\)
\(492\) 0 0
\(493\) 5.79796 0.261127
\(494\) −18.2474 + 31.6055i −0.820992 + 1.42200i
\(495\) 0 0
\(496\) 6.00000 0.269408
\(497\) 0 0
\(498\) 0 0
\(499\) 33.3939 1.49492 0.747458 0.664309i \(-0.231274\pi\)
0.747458 + 0.664309i \(0.231274\pi\)
\(500\) 3.27526 + 5.67291i 0.146474 + 0.253700i
\(501\) 0 0
\(502\) −6.27526 + 10.8691i −0.280078 + 0.485110i
\(503\) −24.4949 −1.09217 −0.546087 0.837729i \(-0.683883\pi\)
−0.546087 + 0.837729i \(0.683883\pi\)
\(504\) 0 0
\(505\) 25.0000 1.11249
\(506\) −1.00000 + 1.73205i −0.0444554 + 0.0769991i
\(507\) 0 0
\(508\) 1.50000 + 2.59808i 0.0665517 + 0.115271i
\(509\) 16.8990 0.749034 0.374517 0.927220i \(-0.377809\pi\)
0.374517 + 0.927220i \(0.377809\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −13.8990 + 24.0737i −0.613058 + 1.06185i
\(515\) −48.2929 −2.12804
\(516\) 0 0
\(517\) 9.79796 16.9706i 0.430914 0.746364i
\(518\) 0 0
\(519\) 0 0
\(520\) 8.44949 14.6349i 0.370535 0.641785i
\(521\) −19.3485 + 33.5125i −0.847672 + 1.46821i 0.0356087 + 0.999366i \(0.488663\pi\)
−0.883281 + 0.468845i \(0.844670\pi\)
\(522\) 0 0
\(523\) −0.174235 0.301783i −0.00761875 0.0131961i 0.862191 0.506584i \(-0.169092\pi\)
−0.869810 + 0.493387i \(0.835758\pi\)
\(524\) −6.72474 11.6476i −0.293772 0.508828i
\(525\) 0 0
\(526\) −8.05051 + 13.9439i −0.351019 + 0.607983i
\(527\) −12.0000 −0.522728
\(528\) 0 0
\(529\) −22.0000 −0.956522
\(530\) −1.89898 3.28913i −0.0824864 0.142871i
\(531\) 0 0
\(532\) 0 0
\(533\) 24.0000 + 41.5692i 1.03956 + 1.80056i
\(534\) 0 0
\(535\) 20.6969 + 35.8481i 0.894807 + 1.54985i
\(536\) −1.55051 2.68556i −0.0669718 0.115999i
\(537\) 0 0
\(538\) 1.82577 + 3.16232i 0.0787143 + 0.136337i
\(539\) 0 0
\(540\) 0 0
\(541\) −15.2474 26.4094i −0.655539 1.13543i −0.981758 0.190133i \(-0.939108\pi\)
0.326219 0.945294i \(-0.394225\pi\)
\(542\) −16.8990 −0.725873
\(543\) 0 0
\(544\) 2.00000 0.0857493
\(545\) −28.7980 + 49.8795i −1.23357 + 2.13660i
\(546\) 0 0
\(547\) −15.7980 27.3629i −0.675472 1.16995i −0.976331 0.216283i \(-0.930607\pi\)
0.300859 0.953669i \(-0.402727\pi\)
\(548\) −5.89898 10.2173i −0.251992 0.436463i
\(549\) 0 0
\(550\) −6.89898 + 11.9494i −0.294173 + 0.509523i
\(551\) 10.7980 18.7026i 0.460009 0.796758i
\(552\) 0 0
\(553\) 0 0
\(554\) 5.34847 9.26382i 0.227235 0.393582i
\(555\) 0 0
\(556\) 9.44949 0.400748
\(557\) −1.55051 + 2.68556i −0.0656972 + 0.113791i −0.897003 0.442024i \(-0.854260\pi\)
0.831306 + 0.555815i \(0.187594\pi\)
\(558\) 0 0
\(559\) 14.2020 0.600682
\(560\) 0 0
\(561\) 0 0
\(562\) −19.0000 −0.801467
\(563\) 6.97219 + 12.0762i 0.293843 + 0.508951i 0.974715 0.223451i \(-0.0717324\pi\)
−0.680872 + 0.732402i \(0.738399\pi\)
\(564\) 0 0
\(565\) 27.4217 47.4957i 1.15364 1.99816i
\(566\) 20.5505 0.863802
\(567\) 0 0
\(568\) 9.89898 0.415352
\(569\) −15.0000 + 25.9808i −0.628833 + 1.08917i 0.358954 + 0.933355i \(0.383134\pi\)
−0.987786 + 0.155815i \(0.950200\pi\)
\(570\) 0 0
\(571\) −7.10102 12.2993i −0.297168 0.514711i 0.678319 0.734768i \(-0.262709\pi\)
−0.975487 + 0.220057i \(0.929376\pi\)
\(572\) 9.79796 0.409673
\(573\) 0 0
\(574\) 0 0
\(575\) 6.89898 0.287707
\(576\) 0 0
\(577\) −11.7980 + 20.4347i −0.491155 + 0.850706i −0.999948 0.0101829i \(-0.996759\pi\)
0.508793 + 0.860889i \(0.330092\pi\)
\(578\) 13.0000 0.540729
\(579\) 0 0
\(580\) −5.00000 + 8.66025i −0.207614 + 0.359597i
\(581\) 0 0
\(582\) 0 0
\(583\) 1.10102 1.90702i 0.0455996 0.0789808i
\(584\) 1.44949 2.51059i 0.0599803 0.103889i
\(585\) 0 0
\(586\) −13.6237 23.5970i −0.562791 0.974782i
\(587\) −9.07321 15.7153i −0.374492 0.648639i 0.615759 0.787934i \(-0.288849\pi\)
−0.990251 + 0.139296i \(0.955516\pi\)
\(588\) 0 0
\(589\) −22.3485 + 38.7087i −0.920853 + 1.59496i
\(590\) 6.89898 0.284026
\(591\) 0 0
\(592\) −7.79796 −0.320494
\(593\) −7.34847 12.7279i −0.301765 0.522673i 0.674770 0.738028i \(-0.264243\pi\)
−0.976536 + 0.215355i \(0.930909\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −3.00000 5.19615i −0.122885 0.212843i
\(597\) 0 0
\(598\) −2.44949 4.24264i −0.100167 0.173494i
\(599\) −7.10102 12.2993i −0.290140 0.502537i 0.683703 0.729761i \(-0.260368\pi\)
−0.973843 + 0.227224i \(0.927035\pi\)
\(600\) 0 0
\(601\) 6.34847 + 10.9959i 0.258959 + 0.448531i 0.965963 0.258679i \(-0.0832871\pi\)
−0.707004 + 0.707210i \(0.749954\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 2.50000 + 4.33013i 0.101724 + 0.176190i
\(605\) 24.1464 0.981692
\(606\) 0 0
\(607\) −8.69694 −0.352998 −0.176499 0.984301i \(-0.556477\pi\)
−0.176499 + 0.984301i \(0.556477\pi\)
\(608\) 3.72474 6.45145i 0.151058 0.261641i
\(609\) 0 0
\(610\) −19.7474 34.2036i −0.799551 1.38486i
\(611\) 24.0000 + 41.5692i 0.970936 + 1.68171i
\(612\) 0 0
\(613\) −7.34847 + 12.7279i −0.296802 + 0.514076i −0.975402 0.220432i \(-0.929253\pi\)
0.678601 + 0.734508i \(0.262587\pi\)
\(614\) 0.376276 0.651729i 0.0151852 0.0263016i
\(615\) 0 0
\(616\) 0 0
\(617\) 21.6969 37.5802i 0.873486 1.51292i 0.0151189 0.999886i \(-0.495187\pi\)
0.858367 0.513036i \(-0.171479\pi\)
\(618\) 0 0
\(619\) −4.14643 −0.166659 −0.0833295 0.996522i \(-0.526555\pi\)
−0.0833295 + 0.996522i \(0.526555\pi\)
\(620\) 10.3485 17.9241i 0.415605 0.719848i
\(621\) 0 0
\(622\) 1.30306 0.0522480
\(623\) 0 0
\(624\) 0 0
\(625\) −11.8990 −0.475959
\(626\) 12.3485 + 21.3882i 0.493544 + 0.854843i
\(627\) 0 0
\(628\) −3.17423 + 5.49794i −0.126666 + 0.219392i
\(629\) 15.5959 0.621850
\(630\) 0 0
\(631\) 18.1010 0.720590 0.360295 0.932838i \(-0.382676\pi\)
0.360295 + 0.932838i \(0.382676\pi\)
\(632\) 3.94949 6.84072i 0.157102 0.272109i
\(633\) 0 0
\(634\) 4.34847 + 7.53177i 0.172700 + 0.299125i
\(635\) 10.3485 0.410666
\(636\) 0 0
\(637\) 0 0
\(638\) −5.79796 −0.229543
\(639\) 0 0
\(640\) −1.72474 + 2.98735i −0.0681765 + 0.118085i
\(641\) −41.4949 −1.63895 −0.819475 0.573115i \(-0.805735\pi\)
−0.819475 + 0.573115i \(0.805735\pi\)
\(642\) 0 0
\(643\) −9.69694 + 16.7956i −0.382410 + 0.662353i −0.991406 0.130820i \(-0.958239\pi\)
0.608996 + 0.793173i \(0.291572\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −7.44949 + 12.9029i −0.293096 + 0.507658i
\(647\) −10.6515 + 18.4490i −0.418755 + 0.725305i −0.995815 0.0913973i \(-0.970867\pi\)
0.577060 + 0.816702i \(0.304200\pi\)
\(648\) 0 0
\(649\) 2.00000 + 3.46410i 0.0785069 + 0.135978i
\(650\) −16.8990 29.2699i −0.662833 1.14806i
\(651\) 0 0
\(652\) 0.101021 0.174973i 0.00395627 0.00685246i
\(653\) 9.79796 0.383424 0.191712 0.981451i \(-0.438596\pi\)
0.191712 + 0.981451i \(0.438596\pi\)
\(654\) 0 0
\(655\) −46.3939 −1.81276
\(656\) −4.89898 8.48528i −0.191273 0.331295i
\(657\) 0 0
\(658\) 0 0
\(659\) 2.34847 + 4.06767i 0.0914834 + 0.158454i 0.908136 0.418676i \(-0.137506\pi\)
−0.816652 + 0.577130i \(0.804172\pi\)
\(660\) 0 0
\(661\) −4.72474 8.18350i −0.183771 0.318301i 0.759391 0.650635i \(-0.225497\pi\)
−0.943162 + 0.332334i \(0.892164\pi\)
\(662\) −12.3485 21.3882i −0.479937 0.831275i
\(663\) 0 0
\(664\) −1.00000 1.73205i −0.0388075 0.0672166i
\(665\) 0 0
\(666\) 0 0
\(667\) 1.44949 + 2.51059i 0.0561245 + 0.0972104i
\(668\) −18.6969 −0.723406
\(669\) 0 0
\(670\) −10.6969 −0.413259
\(671\) 11.4495 19.8311i 0.442003 0.765571i
\(672\) 0 0
\(673\) −15.2980 26.4968i −0.589693 1.02138i −0.994272 0.106875i \(-0.965915\pi\)
0.404579 0.914503i \(-0.367418\pi\)
\(674\) 17.6969 + 30.6520i 0.681661 + 1.18067i
\(675\) 0 0
\(676\) −5.50000 + 9.52628i −0.211538 + 0.366395i
\(677\) −7.34847 + 12.7279i −0.282425 + 0.489174i −0.971981 0.235058i \(-0.924472\pi\)
0.689557 + 0.724232i \(0.257805\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 3.44949 5.97469i 0.132282 0.229119i
\(681\) 0 0
\(682\) 12.0000 0.459504
\(683\) 16.1010 27.8878i 0.616088 1.06710i −0.374104 0.927387i \(-0.622050\pi\)
0.990193 0.139710i \(-0.0446169\pi\)
\(684\) 0 0
\(685\) −40.6969 −1.55495
\(686\) 0 0
\(687\) 0 0
\(688\) −2.89898 −0.110523
\(689\) 2.69694 + 4.67123i 0.102745 + 0.177960i
\(690\) 0 0
\(691\) −3.47730 + 6.02285i −0.132283 + 0.229120i −0.924556 0.381046i \(-0.875564\pi\)
0.792274 + 0.610166i \(0.208897\pi\)
\(692\) 12.8990 0.490346
\(693\) 0 0
\(694\) −19.5959 −0.743851
\(695\) 16.2980 28.2289i 0.618217 1.07078i
\(696\) 0 0
\(697\) 9.79796 + 16.9706i 0.371124 + 0.642806i
\(698\) −20.8990 −0.791038
\(699\) 0 0
\(700\) 0 0
\(701\) −51.3939 −1.94112 −0.970560 0.240860i \(-0.922571\pi\)
−0.970560 + 0.240860i \(0.922571\pi\)
\(702\) 0 0
\(703\) 29.0454 50.3081i 1.09547 1.89741i
\(704\) −2.00000 −0.0753778
\(705\) 0 0
\(706\) 3.00000 5.19615i 0.112906 0.195560i
\(707\) 0 0
\(708\) 0 0
\(709\) 5.79796 10.0424i 0.217747 0.377149i −0.736372 0.676577i \(-0.763463\pi\)
0.954119 + 0.299428i \(0.0967959\pi\)
\(710\) 17.0732 29.5717i 0.640746 1.10981i
\(711\) 0 0
\(712\) 3.55051 + 6.14966i 0.133061 + 0.230468i
\(713\) −3.00000 5.19615i −0.112351 0.194597i
\(714\) 0 0
\(715\) 16.8990 29.2699i 0.631986 1.09463i
\(716\) 8.69694 0.325020
\(717\) 0 0
\(718\) 10.7980 0.402976
\(719\) −4.89898 8.48528i −0.182701 0.316448i 0.760098 0.649808i \(-0.225151\pi\)
−0.942799 + 0.333360i \(0.891817\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 18.2474 + 31.6055i 0.679100 + 1.17624i
\(723\) 0 0
\(724\) −2.17423 3.76588i −0.0808048 0.139958i
\(725\) 10.0000 + 17.3205i 0.371391 + 0.643268i
\(726\) 0 0
\(727\) −20.2474 35.0696i −0.750936 1.30066i −0.947369 0.320143i \(-0.896269\pi\)
0.196433 0.980517i \(-0.437064\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −5.00000 8.66025i −0.185058 0.320530i
\(731\) 5.79796 0.214445
\(732\) 0 0
\(733\) −12.5505 −0.463564 −0.231782 0.972768i \(-0.574456\pi\)
−0.231782 + 0.972768i \(0.574456\pi\)
\(734\) 2.89898 5.02118i 0.107003 0.185335i
\(735\) 0 0
\(736\) 0.500000 + 0.866025i 0.0184302 + 0.0319221i
\(737\) −3.10102 5.37113i −0.114228 0.197848i
\(738\) 0 0
\(739\) 12.7980 22.1667i 0.470781 0.815416i −0.528661 0.848833i \(-0.677306\pi\)
0.999441 + 0.0334173i \(0.0106390\pi\)
\(740\) −13.4495 + 23.2952i −0.494413 + 0.856349i
\(741\) 0 0
\(742\) 0 0
\(743\) 18.0000 31.1769i 0.660356 1.14377i −0.320166 0.947361i \(-0.603739\pi\)
0.980522 0.196409i \(-0.0629279\pi\)
\(744\) 0 0
\(745\) −20.6969 −0.758277
\(746\) 1.44949 2.51059i 0.0530696 0.0919192i
\(747\) 0 0
\(748\) 4.00000 0.146254
\(749\) 0 0
\(750\) 0 0
\(751\) 40.5959 1.48137 0.740683 0.671855i \(-0.234502\pi\)
0.740683 + 0.671855i \(0.234502\pi\)
\(752\) −4.89898 8.48528i −0.178647 0.309426i
\(753\) 0 0
\(754\) 7.10102 12.2993i 0.258604 0.447915i
\(755\) 17.2474 0.627699
\(756\) 0 0
\(757\) 23.3939 0.850265 0.425132 0.905131i \(-0.360228\pi\)
0.425132 + 0.905131i \(0.360228\pi\)
\(758\) −13.2474 + 22.9453i −0.481169 + 0.833409i
\(759\) 0 0
\(760\) −12.8485 22.2542i −0.466063 0.807245i
\(761\) −2.00000 −0.0724999 −0.0362500 0.999343i \(-0.511541\pi\)
−0.0362500 + 0.999343i \(0.511541\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −13.8990 −0.502847
\(765\) 0 0
\(766\) −3.44949 + 5.97469i −0.124635 + 0.215874i
\(767\) −9.79796 −0.353784
\(768\) 0 0
\(769\) −27.0454 + 46.8440i −0.975282 + 1.68924i −0.296282 + 0.955100i \(0.595747\pi\)
−0.679000 + 0.734138i \(0.737586\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 4.05051 7.01569i 0.145781 0.252500i
\(773\) −9.97219 + 17.2723i −0.358675 + 0.621243i −0.987740 0.156110i \(-0.950105\pi\)
0.629065 + 0.777353i \(0.283438\pi\)
\(774\) 0 0
\(775\) −20.6969 35.8481i −0.743456 1.28770i
\(776\) −3.44949 5.97469i −0.123829 0.214479i
\(777\) 0 0
\(778\) 7.55051 13.0779i 0.270699 0.468864i
\(779\) 72.9898 2.61513
\(780\) 0 0
\(781\) 19.7980 0.708427
\(782\) −1.00000 1.73205i −0.0357599 0.0619380i
\(783\) 0 0
\(784\) 0 0
\(785\) 10.9495 + 18.9651i 0.390804 + 0.676892i
\(786\) 0 0
\(787\) −23.6969 41.0443i −0.844705 1.46307i −0.885877 0.463919i \(-0.846443\pi\)
0.0411728 0.999152i \(-0.486891\pi\)
\(788\) −6.34847 10.9959i −0.226155 0.391712i
\(789\) 0 0
\(790\) −13.6237 23.5970i −0.484710 0.839543i
\(791\) 0 0
\(792\) 0 0