Properties

Label 1386.2.k.w.793.2
Level $1386$
Weight $2$
Character 1386.793
Analytic conductor $11.067$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1156923.1
Defining polynomial: \(x^{6} - 3 x^{5} + 12 x^{4} - 19 x^{3} + 27 x^{2} - 18 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 462)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 793.2
Root \(0.500000 + 1.51496i\) of defining polynomial
Character \(\chi\) \(=\) 1386.793
Dual form 1386.2.k.w.991.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.227452 - 0.393958i) q^{5} +(-0.227452 + 2.63596i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.227452 - 0.393958i) q^{5} +(-0.227452 + 2.63596i) q^{7} -1.00000 q^{8} +(-0.227452 - 0.393958i) q^{10} +(0.500000 + 0.866025i) q^{11} +0.909808 q^{13} +(2.16908 + 1.51496i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{17} +(-1.94163 + 3.36300i) q^{19} -0.454904 q^{20} +1.00000 q^{22} +(4.16908 - 7.22106i) q^{23} +(2.39653 + 4.15091i) q^{25} +(0.454904 - 0.787917i) q^{26} +(2.39653 - 1.12100i) q^{28} +2.79306 q^{29} +(4.79306 + 8.30183i) q^{31} +(0.500000 + 0.866025i) q^{32} +1.00000 q^{34} +(0.986723 + 0.689160i) q^{35} +(-3.94163 + 6.82710i) q^{37} +(1.94163 + 3.36300i) q^{38} +(-0.227452 + 0.393958i) q^{40} +1.79306 q^{41} +7.88325 q^{43} +(0.500000 - 0.866025i) q^{44} +(-4.16908 - 7.22106i) q^{46} +(0.169079 - 0.292854i) q^{47} +(-6.89653 - 1.19911i) q^{49} +4.79306 q^{50} +(-0.454904 - 0.787917i) q^{52} +(0.454904 + 0.787917i) q^{53} +0.454904 q^{55} +(0.227452 - 2.63596i) q^{56} +(1.39653 - 2.41886i) q^{58} +(3.48672 + 6.03918i) q^{59} +(7.02051 - 12.1599i) q^{61} +9.58612 q^{62} +1.00000 q^{64} +(0.206938 - 0.358427i) q^{65} +(1.89653 + 3.28489i) q^{67} +(0.500000 - 0.866025i) q^{68} +(1.09019 - 0.509947i) q^{70} +4.79306 q^{71} +(-5.33816 - 9.24596i) q^{73} +(3.94163 + 6.82710i) q^{74} +3.88325 q^{76} +(-2.39653 + 1.12100i) q^{77} +(-2.68236 + 4.64598i) q^{79} +(0.227452 + 0.393958i) q^{80} +(0.896531 - 1.55284i) q^{82} -1.97345 q^{83} +0.454904 q^{85} +(3.94163 - 6.82710i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(-5.54510 + 9.60439i) q^{89} +(-0.206938 + 2.39821i) q^{91} -8.33816 q^{92} +(-0.169079 - 0.292854i) q^{94} +(0.883254 + 1.52984i) q^{95} +14.5861 q^{97} +(-4.48672 + 5.37302i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{2} - 3q^{4} - 6q^{8} + O(q^{10}) \) \( 6q + 3q^{2} - 3q^{4} - 6q^{8} + 3q^{11} - 3q^{14} - 3q^{16} + 3q^{17} + 3q^{19} + 6q^{22} + 9q^{23} - 3q^{25} - 3q^{28} - 18q^{29} - 6q^{31} + 3q^{32} + 6q^{34} - 6q^{35} - 9q^{37} - 3q^{38} - 24q^{41} + 18q^{43} + 3q^{44} - 9q^{46} - 15q^{47} - 24q^{49} - 6q^{50} - 9q^{58} + 9q^{59} + 6q^{61} - 12q^{62} + 6q^{64} + 36q^{65} - 6q^{67} + 3q^{68} + 12q^{70} - 6q^{71} + 9q^{74} - 6q^{76} + 3q^{77} - 12q^{79} - 12q^{82} + 12q^{83} + 9q^{86} - 3q^{88} - 36q^{89} - 36q^{91} - 18q^{92} + 15q^{94} - 24q^{95} + 18q^{97} - 15q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.227452 0.393958i 0.101720 0.176184i −0.810674 0.585498i \(-0.800899\pi\)
0.912393 + 0.409315i \(0.134232\pi\)
\(6\) 0 0
\(7\) −0.227452 + 2.63596i −0.0859688 + 0.996298i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −0.227452 0.393958i −0.0719267 0.124581i
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) 0 0
\(13\) 0.909808 0.252335 0.126168 0.992009i \(-0.459732\pi\)
0.126168 + 0.992009i \(0.459732\pi\)
\(14\) 2.16908 + 1.51496i 0.579711 + 0.404889i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i 0.920268 0.391289i \(-0.127971\pi\)
−0.799000 + 0.601331i \(0.794637\pi\)
\(18\) 0 0
\(19\) −1.94163 + 3.36300i −0.445440 + 0.771524i −0.998083 0.0618938i \(-0.980286\pi\)
0.552643 + 0.833418i \(0.313619\pi\)
\(20\) −0.454904 −0.101720
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 4.16908 7.22106i 0.869313 1.50569i 0.00661323 0.999978i \(-0.497895\pi\)
0.862700 0.505716i \(-0.168772\pi\)
\(24\) 0 0
\(25\) 2.39653 + 4.15091i 0.479306 + 0.830183i
\(26\) 0.454904 0.787917i 0.0892140 0.154523i
\(27\) 0 0
\(28\) 2.39653 1.12100i 0.452902 0.211849i
\(29\) 2.79306 0.518659 0.259329 0.965789i \(-0.416498\pi\)
0.259329 + 0.965789i \(0.416498\pi\)
\(30\) 0 0
\(31\) 4.79306 + 8.30183i 0.860859 + 1.49105i 0.871101 + 0.491105i \(0.163407\pi\)
−0.0102412 + 0.999948i \(0.503260\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 1.00000 0.171499
\(35\) 0.986723 + 0.689160i 0.166787 + 0.116489i
\(36\) 0 0
\(37\) −3.94163 + 6.82710i −0.647999 + 1.12237i 0.335601 + 0.942004i \(0.391061\pi\)
−0.983600 + 0.180364i \(0.942273\pi\)
\(38\) 1.94163 + 3.36300i 0.314973 + 0.545550i
\(39\) 0 0
\(40\) −0.227452 + 0.393958i −0.0359633 + 0.0622903i
\(41\) 1.79306 0.280029 0.140015 0.990149i \(-0.455285\pi\)
0.140015 + 0.990149i \(0.455285\pi\)
\(42\) 0 0
\(43\) 7.88325 1.20218 0.601092 0.799179i \(-0.294732\pi\)
0.601092 + 0.799179i \(0.294732\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) 0 0
\(46\) −4.16908 7.22106i −0.614697 1.06469i
\(47\) 0.169079 0.292854i 0.0246627 0.0427171i −0.853431 0.521206i \(-0.825482\pi\)
0.878093 + 0.478489i \(0.158815\pi\)
\(48\) 0 0
\(49\) −6.89653 1.19911i −0.985219 0.171301i
\(50\) 4.79306 0.677841
\(51\) 0 0
\(52\) −0.454904 0.787917i −0.0630838 0.109264i
\(53\) 0.454904 + 0.787917i 0.0624859 + 0.108229i 0.895576 0.444909i \(-0.146764\pi\)
−0.833090 + 0.553137i \(0.813430\pi\)
\(54\) 0 0
\(55\) 0.454904 0.0613393
\(56\) 0.227452 2.63596i 0.0303946 0.352244i
\(57\) 0 0
\(58\) 1.39653 2.41886i 0.183374 0.317612i
\(59\) 3.48672 + 6.03918i 0.453933 + 0.786234i 0.998626 0.0524008i \(-0.0166873\pi\)
−0.544693 + 0.838635i \(0.683354\pi\)
\(60\) 0 0
\(61\) 7.02051 12.1599i 0.898885 1.55691i 0.0699629 0.997550i \(-0.477712\pi\)
0.828922 0.559364i \(-0.188955\pi\)
\(62\) 9.58612 1.21744
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.206938 0.358427i 0.0256675 0.0444574i
\(66\) 0 0
\(67\) 1.89653 + 3.28489i 0.231698 + 0.401313i 0.958308 0.285737i \(-0.0922385\pi\)
−0.726610 + 0.687050i \(0.758905\pi\)
\(68\) 0.500000 0.866025i 0.0606339 0.105021i
\(69\) 0 0
\(70\) 1.09019 0.509947i 0.130303 0.0609503i
\(71\) 4.79306 0.568832 0.284416 0.958701i \(-0.408200\pi\)
0.284416 + 0.958701i \(0.408200\pi\)
\(72\) 0 0
\(73\) −5.33816 9.24596i −0.624784 1.08216i −0.988583 0.150680i \(-0.951854\pi\)
0.363798 0.931478i \(-0.381480\pi\)
\(74\) 3.94163 + 6.82710i 0.458205 + 0.793634i
\(75\) 0 0
\(76\) 3.88325 0.445440
\(77\) −2.39653 + 1.12100i −0.273110 + 0.127750i
\(78\) 0 0
\(79\) −2.68236 + 4.64598i −0.301789 + 0.522713i −0.976541 0.215331i \(-0.930917\pi\)
0.674753 + 0.738044i \(0.264250\pi\)
\(80\) 0.227452 + 0.393958i 0.0254299 + 0.0440459i
\(81\) 0 0
\(82\) 0.896531 1.55284i 0.0990053 0.171482i
\(83\) −1.97345 −0.216614 −0.108307 0.994118i \(-0.534543\pi\)
−0.108307 + 0.994118i \(0.534543\pi\)
\(84\) 0 0
\(85\) 0.454904 0.0493413
\(86\) 3.94163 6.82710i 0.425037 0.736185i
\(87\) 0 0
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) −5.54510 + 9.60439i −0.587779 + 1.01806i 0.406744 + 0.913542i \(0.366664\pi\)
−0.994523 + 0.104521i \(0.966669\pi\)
\(90\) 0 0
\(91\) −0.206938 + 2.39821i −0.0216930 + 0.251401i
\(92\) −8.33816 −0.869313
\(93\) 0 0
\(94\) −0.169079 0.292854i −0.0174392 0.0302055i
\(95\) 0.883254 + 1.52984i 0.0906200 + 0.156958i
\(96\) 0 0
\(97\) 14.5861 1.48100 0.740498 0.672058i \(-0.234590\pi\)
0.740498 + 0.672058i \(0.234590\pi\)
\(98\) −4.48672 + 5.37302i −0.453227 + 0.542757i
\(99\) 0 0
\(100\) 2.39653 4.15091i 0.239653 0.415091i
\(101\) −4.03182 6.98332i −0.401181 0.694866i 0.592688 0.805432i \(-0.298067\pi\)
−0.993869 + 0.110566i \(0.964733\pi\)
\(102\) 0 0
\(103\) −2.88325 + 4.99394i −0.284095 + 0.492068i −0.972389 0.233364i \(-0.925027\pi\)
0.688294 + 0.725432i \(0.258360\pi\)
\(104\) −0.909808 −0.0892140
\(105\) 0 0
\(106\) 0.909808 0.0883684
\(107\) 7.80634 13.5210i 0.754667 1.30712i −0.190872 0.981615i \(-0.561132\pi\)
0.945540 0.325507i \(-0.105535\pi\)
\(108\) 0 0
\(109\) −7.02051 12.1599i −0.672443 1.16471i −0.977209 0.212279i \(-0.931912\pi\)
0.304766 0.952427i \(-0.401422\pi\)
\(110\) 0.227452 0.393958i 0.0216867 0.0375625i
\(111\) 0 0
\(112\) −2.16908 1.51496i −0.204959 0.143150i
\(113\) −7.58612 −0.713643 −0.356821 0.934173i \(-0.616139\pi\)
−0.356821 + 0.934173i \(0.616139\pi\)
\(114\) 0 0
\(115\) −1.89653 3.28489i −0.176852 0.306317i
\(116\) −1.39653 2.41886i −0.129665 0.224586i
\(117\) 0 0
\(118\) 6.97345 0.641958
\(119\) −2.39653 + 1.12100i −0.219690 + 0.102762i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −7.02051 12.1599i −0.635608 1.10090i
\(123\) 0 0
\(124\) 4.79306 8.30183i 0.430430 0.745526i
\(125\) 4.45490 0.398459
\(126\) 0 0
\(127\) 7.42835 0.659159 0.329580 0.944128i \(-0.393093\pi\)
0.329580 + 0.944128i \(0.393093\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −0.206938 0.358427i −0.0181496 0.0314361i
\(131\) −9.70287 + 16.8059i −0.847744 + 1.46834i 0.0354732 + 0.999371i \(0.488706\pi\)
−0.883217 + 0.468965i \(0.844627\pi\)
\(132\) 0 0
\(133\) −8.42309 5.88296i −0.730374 0.510118i
\(134\) 3.79306 0.327671
\(135\) 0 0
\(136\) −0.500000 0.866025i −0.0428746 0.0742611i
\(137\) 0.454904 + 0.787917i 0.0388651 + 0.0673163i 0.884804 0.465964i \(-0.154292\pi\)
−0.845939 + 0.533280i \(0.820959\pi\)
\(138\) 0 0
\(139\) −8.37919 −0.710713 −0.355357 0.934731i \(-0.615641\pi\)
−0.355357 + 0.934731i \(0.615641\pi\)
\(140\) 0.103469 1.19911i 0.00874472 0.101343i
\(141\) 0 0
\(142\) 2.39653 4.15091i 0.201112 0.348337i
\(143\) 0.454904 + 0.787917i 0.0380410 + 0.0658889i
\(144\) 0 0
\(145\) 0.635288 1.10035i 0.0527578 0.0913791i
\(146\) −10.6763 −0.883578
\(147\) 0 0
\(148\) 7.88325 0.647999
\(149\) 2.05837 3.56521i 0.168628 0.292073i −0.769309 0.638876i \(-0.779400\pi\)
0.937938 + 0.346803i \(0.112733\pi\)
\(150\) 0 0
\(151\) 3.07889 + 5.33279i 0.250556 + 0.433976i 0.963679 0.267063i \(-0.0860531\pi\)
−0.713123 + 0.701039i \(0.752720\pi\)
\(152\) 1.94163 3.36300i 0.157487 0.272775i
\(153\) 0 0
\(154\) −0.227452 + 2.63596i −0.0183286 + 0.212411i
\(155\) 4.36077 0.350265
\(156\) 0 0
\(157\) 8.82488 + 15.2851i 0.704302 + 1.21989i 0.966943 + 0.254993i \(0.0820733\pi\)
−0.262641 + 0.964894i \(0.584593\pi\)
\(158\) 2.68236 + 4.64598i 0.213397 + 0.369614i
\(159\) 0 0
\(160\) 0.454904 0.0359633
\(161\) 18.0861 + 12.6320i 1.42539 + 0.995537i
\(162\) 0 0
\(163\) 5.80634 10.0569i 0.454788 0.787715i −0.543888 0.839158i \(-0.683049\pi\)
0.998676 + 0.0514424i \(0.0163818\pi\)
\(164\) −0.896531 1.55284i −0.0700073 0.121256i
\(165\) 0 0
\(166\) −0.986723 + 1.70905i −0.0765846 + 0.132648i
\(167\) 4.85670 0.375823 0.187911 0.982186i \(-0.439828\pi\)
0.187911 + 0.982186i \(0.439828\pi\)
\(168\) 0 0
\(169\) −12.1722 −0.936327
\(170\) 0.227452 0.393958i 0.0174448 0.0302152i
\(171\) 0 0
\(172\) −3.94163 6.82710i −0.300546 0.520561i
\(173\) −12.7931 + 22.1582i −0.972639 + 1.68466i −0.285121 + 0.958492i \(0.592034\pi\)
−0.687518 + 0.726168i \(0.741300\pi\)
\(174\) 0 0
\(175\) −11.4867 + 5.37302i −0.868315 + 0.406162i
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) 5.54510 + 9.60439i 0.415623 + 0.719879i
\(179\) −7.85144 13.5991i −0.586844 1.01644i −0.994643 0.103372i \(-0.967037\pi\)
0.407799 0.913072i \(-0.366296\pi\)
\(180\) 0 0
\(181\) −2.49593 −0.185521 −0.0927606 0.995688i \(-0.529569\pi\)
−0.0927606 + 0.995688i \(0.529569\pi\)
\(182\) 1.97345 + 1.37832i 0.146282 + 0.102168i
\(183\) 0 0
\(184\) −4.16908 + 7.22106i −0.307349 + 0.532343i
\(185\) 1.79306 + 3.10567i 0.131829 + 0.228334i
\(186\) 0 0
\(187\) −0.500000 + 0.866025i −0.0365636 + 0.0633300i
\(188\) −0.338158 −0.0246627
\(189\) 0 0
\(190\) 1.76651 0.128156
\(191\) 4.90981 8.50404i 0.355261 0.615331i −0.631901 0.775049i \(-0.717725\pi\)
0.987163 + 0.159718i \(0.0510586\pi\)
\(192\) 0 0
\(193\) −3.42835 5.93808i −0.246778 0.427432i 0.715852 0.698252i \(-0.246039\pi\)
−0.962630 + 0.270820i \(0.912705\pi\)
\(194\) 7.29306 12.6320i 0.523611 0.906921i
\(195\) 0 0
\(196\) 2.40981 + 6.57212i 0.172129 + 0.469437i
\(197\) −23.4694 −1.67212 −0.836062 0.548635i \(-0.815148\pi\)
−0.836062 + 0.548635i \(0.815148\pi\)
\(198\) 0 0
\(199\) 1.11675 + 1.93426i 0.0791640 + 0.137116i 0.902889 0.429873i \(-0.141442\pi\)
−0.823725 + 0.566989i \(0.808108\pi\)
\(200\) −2.39653 4.15091i −0.169460 0.293514i
\(201\) 0 0
\(202\) −8.06364 −0.567356
\(203\) −0.635288 + 7.36239i −0.0445885 + 0.516738i
\(204\) 0 0
\(205\) 0.407836 0.706392i 0.0284845 0.0493366i
\(206\) 2.88325 + 4.99394i 0.200886 + 0.347944i
\(207\) 0 0
\(208\) −0.454904 + 0.787917i −0.0315419 + 0.0546322i
\(209\) −3.88325 −0.268610
\(210\) 0 0
\(211\) −18.2624 −1.25724 −0.628619 0.777713i \(-0.716380\pi\)
−0.628619 + 0.777713i \(0.716380\pi\)
\(212\) 0.454904 0.787917i 0.0312429 0.0541144i
\(213\) 0 0
\(214\) −7.80634 13.5210i −0.533630 0.924275i
\(215\) 1.79306 3.10567i 0.122286 0.211805i
\(216\) 0 0
\(217\) −22.9734 + 10.7460i −1.55954 + 0.729488i
\(218\) −14.0410 −0.950978
\(219\) 0 0
\(220\) −0.227452 0.393958i −0.0153348 0.0265607i
\(221\) 0.454904 + 0.787917i 0.0306002 + 0.0530010i
\(222\) 0 0
\(223\) 12.4959 0.836790 0.418395 0.908265i \(-0.362593\pi\)
0.418395 + 0.908265i \(0.362593\pi\)
\(224\) −2.39653 + 1.12100i −0.160125 + 0.0748999i
\(225\) 0 0
\(226\) −3.79306 + 6.56978i −0.252311 + 0.437015i
\(227\) 4.89653 + 8.48104i 0.324994 + 0.562906i 0.981511 0.191405i \(-0.0613043\pi\)
−0.656517 + 0.754311i \(0.727971\pi\)
\(228\) 0 0
\(229\) −4.33816 + 7.51391i −0.286674 + 0.496533i −0.973014 0.230748i \(-0.925883\pi\)
0.686340 + 0.727281i \(0.259216\pi\)
\(230\) −3.79306 −0.250107
\(231\) 0 0
\(232\) −2.79306 −0.183374
\(233\) 8.38325 14.5202i 0.549205 0.951251i −0.449124 0.893469i \(-0.648264\pi\)
0.998329 0.0577819i \(-0.0184028\pi\)
\(234\) 0 0
\(235\) −0.0769148 0.133220i −0.00501737 0.00869033i
\(236\) 3.48672 6.03918i 0.226966 0.393117i
\(237\) 0 0
\(238\) −0.227452 + 2.63596i −0.0147435 + 0.170864i
\(239\) 26.2624 1.69878 0.849388 0.527769i \(-0.176971\pi\)
0.849388 + 0.527769i \(0.176971\pi\)
\(240\) 0 0
\(241\) −3.97345 6.88221i −0.255952 0.443322i 0.709202 0.705006i \(-0.249056\pi\)
−0.965154 + 0.261684i \(0.915722\pi\)
\(242\) 0.500000 + 0.866025i 0.0321412 + 0.0556702i
\(243\) 0 0
\(244\) −14.0410 −0.898885
\(245\) −2.04103 + 2.44421i −0.130397 + 0.156155i
\(246\) 0 0
\(247\) −1.76651 + 3.05968i −0.112400 + 0.194683i
\(248\) −4.79306 8.30183i −0.304360 0.527167i
\(249\) 0 0
\(250\) 2.22745 3.85806i 0.140876 0.244005i
\(251\) 3.93636 0.248461 0.124230 0.992253i \(-0.460354\pi\)
0.124230 + 0.992253i \(0.460354\pi\)
\(252\) 0 0
\(253\) 8.33816 0.524216
\(254\) 3.71417 6.43314i 0.233048 0.403651i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −7.54510 + 13.0685i −0.470650 + 0.815190i −0.999437 0.0335650i \(-0.989314\pi\)
0.528786 + 0.848755i \(0.322647\pi\)
\(258\) 0 0
\(259\) −17.0994 11.9428i −1.06251 0.742089i
\(260\) −0.413875 −0.0256675
\(261\) 0 0
\(262\) 9.70287 + 16.8059i 0.599445 + 1.03827i
\(263\) −14.3116 24.7884i −0.882491 1.52852i −0.848562 0.529096i \(-0.822531\pi\)
−0.0339291 0.999424i \(-0.510802\pi\)
\(264\) 0 0
\(265\) 0.413875 0.0254242
\(266\) −9.30634 + 4.35312i −0.570608 + 0.266907i
\(267\) 0 0
\(268\) 1.89653 3.28489i 0.115849 0.200656i
\(269\) −11.4754 19.8760i −0.699669 1.21186i −0.968581 0.248697i \(-0.919998\pi\)
0.268913 0.963165i \(-0.413336\pi\)
\(270\) 0 0
\(271\) −4.90981 + 8.50404i −0.298250 + 0.516583i −0.975736 0.218952i \(-0.929736\pi\)
0.677486 + 0.735536i \(0.263069\pi\)
\(272\) −1.00000 −0.0606339
\(273\) 0 0
\(274\) 0.909808 0.0549635
\(275\) −2.39653 + 4.15091i −0.144516 + 0.250310i
\(276\) 0 0
\(277\) −5.36471 9.29195i −0.322334 0.558299i 0.658635 0.752463i \(-0.271134\pi\)
−0.980969 + 0.194163i \(0.937801\pi\)
\(278\) −4.18959 + 7.25659i −0.251275 + 0.435221i
\(279\) 0 0
\(280\) −0.986723 0.689160i −0.0589680 0.0411852i
\(281\) −2.58612 −0.154275 −0.0771376 0.997020i \(-0.524578\pi\)
−0.0771376 + 0.997020i \(0.524578\pi\)
\(282\) 0 0
\(283\) 10.0410 + 17.3916i 0.596877 + 1.03382i 0.993279 + 0.115745i \(0.0369254\pi\)
−0.396402 + 0.918077i \(0.629741\pi\)
\(284\) −2.39653 4.15091i −0.142208 0.246311i
\(285\) 0 0
\(286\) 0.909808 0.0537981
\(287\) −0.407836 + 4.72643i −0.0240738 + 0.278993i
\(288\) 0 0
\(289\) 8.00000 13.8564i 0.470588 0.815083i
\(290\) −0.635288 1.10035i −0.0373054 0.0646148i
\(291\) 0 0
\(292\) −5.33816 + 9.24596i −0.312392 + 0.541079i
\(293\) −10.3792 −0.606359 −0.303179 0.952934i \(-0.598048\pi\)
−0.303179 + 0.952934i \(0.598048\pi\)
\(294\) 0 0
\(295\) 3.17225 0.184695
\(296\) 3.94163 6.82710i 0.229102 0.396817i
\(297\) 0 0
\(298\) −2.05837 3.56521i −0.119238 0.206527i
\(299\) 3.79306 6.56978i 0.219358 0.379940i
\(300\) 0 0
\(301\) −1.79306 + 20.7799i −0.103350 + 1.19773i
\(302\) 6.15777 0.354340
\(303\) 0 0
\(304\) −1.94163 3.36300i −0.111360 0.192881i
\(305\) −3.19366 5.53158i −0.182868 0.316737i
\(306\) 0 0
\(307\) 9.76651 0.557404 0.278702 0.960378i \(-0.410096\pi\)
0.278702 + 0.960378i \(0.410096\pi\)
\(308\) 2.16908 + 1.51496i 0.123595 + 0.0863227i
\(309\) 0 0
\(310\) 2.18038 3.77654i 0.123837 0.214493i
\(311\) −3.25927 5.64522i −0.184816 0.320111i 0.758698 0.651442i \(-0.225836\pi\)
−0.943515 + 0.331331i \(0.892502\pi\)
\(312\) 0 0
\(313\) −15.3965 + 26.6676i −0.870263 + 1.50734i −0.00853913 + 0.999964i \(0.502718\pi\)
−0.861724 + 0.507377i \(0.830615\pi\)
\(314\) 17.6498 0.996034
\(315\) 0 0
\(316\) 5.36471 0.301789
\(317\) −13.8136 + 23.9258i −0.775848 + 1.34381i 0.158469 + 0.987364i \(0.449344\pi\)
−0.934317 + 0.356444i \(0.883989\pi\)
\(318\) 0 0
\(319\) 1.39653 + 2.41886i 0.0781907 + 0.135430i
\(320\) 0.227452 0.393958i 0.0127150 0.0220229i
\(321\) 0 0
\(322\) 19.9827 9.34707i 1.11359 0.520892i
\(323\) −3.88325 −0.216070
\(324\) 0 0
\(325\) 2.18038 + 3.77654i 0.120946 + 0.209484i
\(326\) −5.80634 10.0569i −0.321583 0.556999i
\(327\) 0 0
\(328\) −1.79306 −0.0990053
\(329\) 0.733492 + 0.512295i 0.0404387 + 0.0282438i
\(330\) 0 0
\(331\) 14.4827 25.0847i 0.796039 1.37878i −0.126139 0.992013i \(-0.540258\pi\)
0.922177 0.386767i \(-0.126408\pi\)
\(332\) 0.986723 + 1.70905i 0.0541535 + 0.0937965i
\(333\) 0 0
\(334\) 2.42835 4.20603i 0.132873 0.230143i
\(335\) 1.72548 0.0942730
\(336\) 0 0
\(337\) −9.03708 −0.492281 −0.246141 0.969234i \(-0.579163\pi\)
−0.246141 + 0.969234i \(0.579163\pi\)
\(338\) −6.08612 + 10.5415i −0.331042 + 0.573381i
\(339\) 0 0
\(340\) −0.227452 0.393958i −0.0123353 0.0213654i
\(341\) −4.79306 + 8.30183i −0.259559 + 0.449569i
\(342\) 0 0
\(343\) 4.72942 17.9062i 0.255365 0.966845i
\(344\) −7.88325 −0.425037
\(345\) 0 0
\(346\) 12.7931 + 22.1582i 0.687759 + 1.19123i
\(347\) −10.8063 18.7171i −0.580115 1.00479i −0.995465 0.0951267i \(-0.969674\pi\)
0.415350 0.909661i \(-0.363659\pi\)
\(348\) 0 0
\(349\) 14.2745 0.764098 0.382049 0.924142i \(-0.375219\pi\)
0.382049 + 0.924142i \(0.375219\pi\)
\(350\) −1.09019 + 12.6343i −0.0582732 + 0.675332i
\(351\) 0 0
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) −14.2480 24.6782i −0.758343 1.31349i −0.943695 0.330816i \(-0.892676\pi\)
0.185353 0.982672i \(-0.440657\pi\)
\(354\) 0 0
\(355\) 1.09019 1.88827i 0.0578614 0.100219i
\(356\) 11.0902 0.587779
\(357\) 0 0
\(358\) −15.7029 −0.829922
\(359\) −6.81962 + 11.8119i −0.359926 + 0.623409i −0.987948 0.154786i \(-0.950531\pi\)
0.628022 + 0.778195i \(0.283865\pi\)
\(360\) 0 0
\(361\) 1.96017 + 3.39511i 0.103167 + 0.178690i
\(362\) −1.24797 + 2.16154i −0.0655917 + 0.113608i
\(363\) 0 0
\(364\) 2.18038 1.01989i 0.114283 0.0534570i
\(365\) −4.85670 −0.254211
\(366\) 0 0
\(367\) −11.3647 19.6843i −0.593233 1.02751i −0.993794 0.111240i \(-0.964518\pi\)
0.400560 0.916270i \(-0.368815\pi\)
\(368\) 4.16908 + 7.22106i 0.217328 + 0.376424i
\(369\) 0 0
\(370\) 3.58612 0.186434
\(371\) −2.18038 + 1.01989i −0.113200 + 0.0529503i
\(372\) 0 0
\(373\) −5.20090 + 9.00822i −0.269292 + 0.466428i −0.968679 0.248315i \(-0.920123\pi\)
0.699387 + 0.714743i \(0.253456\pi\)
\(374\) 0.500000 + 0.866025i 0.0258544 + 0.0447811i
\(375\) 0 0
\(376\) −0.169079 + 0.292854i −0.00871959 + 0.0151028i
\(377\) 2.54115 0.130876
\(378\) 0 0
\(379\) 7.61268 0.391037 0.195519 0.980700i \(-0.437361\pi\)
0.195519 + 0.980700i \(0.437361\pi\)
\(380\) 0.883254 1.52984i 0.0453100 0.0784792i
\(381\) 0 0
\(382\) −4.90981 8.50404i −0.251208 0.435104i
\(383\) −11.0728 + 19.1787i −0.565796 + 0.979988i 0.431179 + 0.902266i \(0.358098\pi\)
−0.996975 + 0.0777212i \(0.975236\pi\)
\(384\) 0 0
\(385\) −0.103469 + 1.19911i −0.00527326 + 0.0611122i
\(386\) −6.85670 −0.348997
\(387\) 0 0
\(388\) −7.29306 12.6320i −0.370249 0.641290i
\(389\) −1.77255 3.07014i −0.0898717 0.155662i 0.817585 0.575808i \(-0.195312\pi\)
−0.907457 + 0.420145i \(0.861979\pi\)
\(390\) 0 0
\(391\) 8.33816 0.421679
\(392\) 6.89653 + 1.19911i 0.348327 + 0.0605641i
\(393\) 0 0
\(394\) −11.7347 + 20.3251i −0.591185 + 1.02396i
\(395\) 1.22021 + 2.11347i 0.0613957 + 0.106340i
\(396\) 0 0
\(397\) 1.27979 2.21665i 0.0642306 0.111251i −0.832122 0.554593i \(-0.812874\pi\)
0.896352 + 0.443342i \(0.146207\pi\)
\(398\) 2.23349 0.111955
\(399\) 0 0
\(400\) −4.79306 −0.239653
\(401\) 5.24797 9.08974i 0.262071 0.453920i −0.704721 0.709484i \(-0.748928\pi\)
0.966792 + 0.255564i \(0.0822612\pi\)
\(402\) 0 0
\(403\) 4.36077 + 7.55307i 0.217225 + 0.376245i
\(404\) −4.03182 + 6.98332i −0.200590 + 0.347433i
\(405\) 0 0
\(406\) 6.05837 + 4.23137i 0.300672 + 0.209999i
\(407\) −7.88325 −0.390758
\(408\) 0 0
\(409\) −7.92428 13.7253i −0.391831 0.678670i 0.600860 0.799354i \(-0.294825\pi\)
−0.992691 + 0.120683i \(0.961491\pi\)
\(410\) −0.407836 0.706392i −0.0201416 0.0348862i
\(411\) 0 0
\(412\) 5.76651 0.284095
\(413\) −16.7121 + 7.81723i −0.822348 + 0.384661i
\(414\) 0 0
\(415\) −0.448864 + 0.777456i −0.0220339 + 0.0381638i
\(416\) 0.454904 + 0.787917i 0.0223035 + 0.0386308i
\(417\) 0 0
\(418\) −1.94163 + 3.36300i −0.0949681 + 0.164490i
\(419\) 9.52249 0.465204 0.232602 0.972572i \(-0.425276\pi\)
0.232602 + 0.972572i \(0.425276\pi\)
\(420\) 0 0
\(421\) −0.530621 −0.0258609 −0.0129305 0.999916i \(-0.504116\pi\)
−0.0129305 + 0.999916i \(0.504116\pi\)
\(422\) −9.13122 + 15.8157i −0.444501 + 0.769898i
\(423\) 0 0
\(424\) −0.454904 0.787917i −0.0220921 0.0382646i
\(425\) −2.39653 + 4.15091i −0.116249 + 0.201349i
\(426\) 0 0
\(427\) 30.4561 + 21.2716i 1.47387 + 1.02940i
\(428\) −15.6127 −0.754667
\(429\) 0 0
\(430\) −1.79306 3.10567i −0.0864691 0.149769i
\(431\) 10.4018 + 18.0164i 0.501037 + 0.867821i 0.999999 + 0.00119770i \(0.000381239\pi\)
−0.498962 + 0.866624i \(0.666285\pi\)
\(432\) 0 0
\(433\) −4.40574 −0.211726 −0.105863 0.994381i \(-0.533761\pi\)
−0.105863 + 0.994381i \(0.533761\pi\)
\(434\) −2.18038 + 25.2686i −0.104662 + 1.21293i
\(435\) 0 0
\(436\) −7.02051 + 12.1599i −0.336222 + 0.582353i
\(437\) 16.1896 + 28.0412i 0.774453 + 1.34139i
\(438\) 0 0
\(439\) 7.59743 13.1591i 0.362606 0.628051i −0.625783 0.779997i \(-0.715221\pi\)
0.988389 + 0.151946i \(0.0485539\pi\)
\(440\) −0.454904 −0.0216867
\(441\) 0 0
\(442\) 0.909808 0.0432752
\(443\) −5.69366 + 9.86171i −0.270514 + 0.468544i −0.968994 0.247086i \(-0.920527\pi\)
0.698480 + 0.715630i \(0.253860\pi\)
\(444\) 0 0
\(445\) 2.52249 + 4.36908i 0.119577 + 0.207114i
\(446\) 6.24797 10.8218i 0.295850 0.512427i
\(447\) 0 0
\(448\) −0.227452 + 2.63596i −0.0107461 + 0.124537i
\(449\) 24.0821 1.13650 0.568251 0.822855i \(-0.307620\pi\)
0.568251 + 0.822855i \(0.307620\pi\)
\(450\) 0 0
\(451\) 0.896531 + 1.55284i 0.0422160 + 0.0731203i
\(452\) 3.79306 + 6.56978i 0.178411 + 0.309016i
\(453\) 0 0
\(454\) 9.79306 0.459611
\(455\) 0.897729 + 0.627004i 0.0420862 + 0.0293944i
\(456\) 0 0
\(457\) 14.7665 25.5763i 0.690748 1.19641i −0.280845 0.959753i \(-0.590615\pi\)
0.971593 0.236658i \(-0.0760520\pi\)
\(458\) 4.33816 + 7.51391i 0.202709 + 0.351102i
\(459\) 0 0
\(460\) −1.89653 + 3.28489i −0.0884262 + 0.153159i
\(461\) −4.14569 −0.193084 −0.0965421 0.995329i \(-0.530778\pi\)
−0.0965421 + 0.995329i \(0.530778\pi\)
\(462\) 0 0
\(463\) −9.32368 −0.433308 −0.216654 0.976248i \(-0.569514\pi\)
−0.216654 + 0.976248i \(0.569514\pi\)
\(464\) −1.39653 + 2.41886i −0.0648323 + 0.112293i
\(465\) 0 0
\(466\) −8.38325 14.5202i −0.388347 0.672636i
\(467\) 18.2798 31.6615i 0.845888 1.46512i −0.0389606 0.999241i \(-0.512405\pi\)
0.884848 0.465880i \(-0.154262\pi\)
\(468\) 0 0
\(469\) −9.09019 + 4.25202i −0.419746 + 0.196340i
\(470\) −0.153830 −0.00709563
\(471\) 0 0
\(472\) −3.48672 6.03918i −0.160489 0.277976i
\(473\) 3.94163 + 6.82710i 0.181236 + 0.313910i
\(474\) 0 0
\(475\) −18.6127 −0.854008
\(476\) 2.16908 + 1.51496i 0.0994196 + 0.0694380i
\(477\) 0 0
\(478\) 13.1312 22.7439i 0.600608 1.04028i
\(479\) 0.364712 + 0.631700i 0.0166641 + 0.0288631i 0.874237 0.485499i \(-0.161362\pi\)
−0.857573 + 0.514362i \(0.828029\pi\)
\(480\) 0 0
\(481\) −3.58612 + 6.21135i −0.163513 + 0.283213i
\(482\) −7.94689 −0.361971
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 3.31764 5.74633i 0.150646 0.260927i
\(486\) 0 0
\(487\) 18.4283 + 31.9188i 0.835068 + 1.44638i 0.893975 + 0.448117i \(0.147905\pi\)
−0.0589066 + 0.998263i \(0.518761\pi\)
\(488\) −7.02051 + 12.1599i −0.317804 + 0.550452i
\(489\) 0 0
\(490\) 1.09623 + 2.98969i 0.0495227 + 0.135060i
\(491\) −25.5065 −1.15109 −0.575545 0.817770i \(-0.695210\pi\)
−0.575545 + 0.817770i \(0.695210\pi\)
\(492\) 0 0
\(493\) 1.39653 + 2.41886i 0.0628966 + 0.108940i
\(494\) 1.76651 + 3.05968i 0.0794790 + 0.137662i
\(495\) 0 0
\(496\) −9.58612 −0.430430
\(497\) −1.09019 + 12.6343i −0.0489018 + 0.566726i
\(498\) 0 0
\(499\) 2.06364 3.57433i 0.0923811 0.160009i −0.816131 0.577866i \(-0.803886\pi\)
0.908513 + 0.417857i \(0.137219\pi\)
\(500\) −2.22745 3.85806i −0.0996147 0.172538i
\(501\) 0 0
\(502\) 1.96818 3.40899i 0.0878442 0.152151i
\(503\) 6.85670 0.305725 0.152863 0.988247i \(-0.451151\pi\)
0.152863 + 0.988247i \(0.451151\pi\)
\(504\) 0 0
\(505\) −3.66818 −0.163232
\(506\) 4.16908 7.22106i 0.185338 0.321015i
\(507\) 0 0
\(508\) −3.71417 6.43314i −0.164790 0.285424i
\(509\) 8.22141 14.2399i 0.364408 0.631173i −0.624273 0.781206i \(-0.714605\pi\)
0.988681 + 0.150033i \(0.0479381\pi\)
\(510\) 0 0
\(511\) 25.5861 11.9681i 1.13186 0.529439i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 7.54510 + 13.0685i 0.332800 + 0.576426i
\(515\) 1.31160 + 2.27176i 0.0577962 + 0.100106i
\(516\) 0 0
\(517\) 0.338158 0.0148722
\(518\) −18.8925 + 8.83712i −0.830087 + 0.388281i
\(519\) 0 0
\(520\) −0.206938 + 0.358427i −0.00907482 + 0.0157180i
\(521\) −2.81962 4.88372i −0.123530 0.213960i 0.797628 0.603150i \(-0.206088\pi\)
−0.921157 + 0.389191i \(0.872755\pi\)
\(522\) 0 0
\(523\) 2.04103 3.53517i 0.0892480 0.154582i −0.817946 0.575296i \(-0.804887\pi\)
0.907193 + 0.420714i \(0.138220\pi\)
\(524\) 19.4057 0.847744
\(525\) 0 0
\(526\) −28.6232 −1.24803
\(527\) −4.79306 + 8.30183i −0.208789 + 0.361633i
\(528\) 0 0
\(529\) −23.2624 40.2917i −1.01141 1.75181i
\(530\) 0.206938 0.358427i 0.00898880 0.0155691i
\(531\) 0 0
\(532\) −0.883254 + 10.2361i −0.0382939 + 0.443791i
\(533\) 1.63134 0.0706613
\(534\) 0 0
\(535\) −3.55114 6.15075i −0.153529 0.265920i
\(536\) −1.89653 3.28489i −0.0819177 0.141886i
\(537\) 0 0
\(538\) −22.9508 −0.989481
\(539\) −2.40981 6.57212i −0.103798 0.283081i
\(540\) 0 0
\(541\) 2.44886 4.24156i 0.105285 0.182359i −0.808570 0.588400i \(-0.799758\pi\)
0.913855 + 0.406042i \(0.133091\pi\)
\(542\) 4.90981 + 8.50404i 0.210894 + 0.365280i
\(543\) 0 0
\(544\) −0.500000 + 0.866025i −0.0214373 + 0.0371305i
\(545\) −6.38732 −0.273603
\(546\) 0 0
\(547\) 21.4694 0.917964 0.458982 0.888445i \(-0.348214\pi\)
0.458982 + 0.888445i \(0.348214\pi\)
\(548\) 0.454904 0.787917i 0.0194325 0.0336581i
\(549\) 0 0
\(550\) 2.39653 + 4.15091i 0.102188 + 0.176996i
\(551\) −5.42309 + 9.39306i −0.231031 + 0.400158i
\(552\) 0 0
\(553\) −11.6365 8.12731i −0.494834 0.345608i
\(554\) −10.7294 −0.455850
\(555\) 0 0
\(556\) 4.18959 + 7.25659i 0.177678 + 0.307748i
\(557\) −19.7347 34.1815i −0.836186 1.44832i −0.893061 0.449935i \(-0.851447\pi\)
0.0568758 0.998381i \(-0.481886\pi\)
\(558\) 0 0
\(559\) 7.17225 0.303354
\(560\) −1.09019 + 0.509947i −0.0460690 + 0.0215492i
\(561\) 0 0
\(562\) −1.29306 + 2.23965i −0.0545445 + 0.0944739i
\(563\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) 0 0
\(565\) −1.72548 + 2.98862i −0.0725915 + 0.125732i
\(566\) 20.0821 0.844112
\(567\) 0 0
\(568\) −4.79306 −0.201112
\(569\) 17.0994 29.6170i 0.716844 1.24161i −0.245400 0.969422i \(-0.578919\pi\)
0.962244 0.272189i \(-0.0877475\pi\)
\(570\) 0 0
\(571\) −7.39653 12.8112i −0.309535 0.536131i 0.668726 0.743509i \(-0.266840\pi\)
−0.978261 + 0.207379i \(0.933507\pi\)
\(572\) 0.454904 0.787917i 0.0190205 0.0329445i
\(573\) 0 0
\(574\) 3.88929 + 2.71641i 0.162336 + 0.113381i
\(575\) 39.9653 1.66667
\(576\) 0 0
\(577\) 3.59940 + 6.23435i 0.149845 + 0.259539i 0.931170 0.364585i \(-0.118789\pi\)
−0.781325 + 0.624124i \(0.785456\pi\)
\(578\) −8.00000 13.8564i −0.332756 0.576351i
\(579\) 0 0
\(580\) −1.27058 −0.0527578
\(581\) 0.448864 5.20192i 0.0186220 0.215812i
\(582\) 0 0
\(583\) −0.454904 + 0.787917i −0.0188402 + 0.0326322i
\(584\) 5.33816 + 9.24596i 0.220895 + 0.382601i
\(585\) 0 0
\(586\) −5.18959 + 8.98864i −0.214380 + 0.371317i
\(587\) 44.4959 1.83654 0.918272 0.395951i \(-0.129585\pi\)
0.918272 + 0.395951i \(0.129585\pi\)
\(588\) 0 0
\(589\) −37.2254 −1.53384
\(590\) 1.58612 2.74725i 0.0652997 0.113102i
\(591\) 0 0
\(592\) −3.94163 6.82710i −0.162000 0.280592i
\(593\) 8.98266 15.5584i 0.368873 0.638908i −0.620516 0.784194i \(-0.713077\pi\)
0.989390 + 0.145286i \(0.0464102\pi\)
\(594\) 0 0
\(595\) −0.103469 + 1.19911i −0.00424181 + 0.0491586i
\(596\) −4.11675 −0.168628
\(597\) 0 0
\(598\) −3.79306 6.56978i −0.155110 0.268658i
\(599\) −12.9038 22.3500i −0.527234 0.913196i −0.999496 0.0317376i \(-0.989896\pi\)
0.472263 0.881458i \(-0.343437\pi\)
\(600\) 0 0
\(601\) 10.4139 0.424791 0.212395 0.977184i \(-0.431874\pi\)
0.212395 + 0.977184i \(0.431874\pi\)
\(602\) 17.0994 + 11.9428i 0.696920 + 0.486752i
\(603\) 0 0
\(604\) 3.07889 5.33279i 0.125278 0.216988i
\(605\) 0.227452 + 0.393958i 0.00924724 + 0.0160167i
\(606\) 0 0
\(607\) 4.44886 7.70566i 0.180574 0.312763i −0.761502 0.648162i \(-0.775538\pi\)
0.942076 + 0.335399i \(0.108871\pi\)
\(608\) −3.88325 −0.157487
\(609\) 0 0
\(610\) −6.38732 −0.258615
\(611\) 0.153830 0.266441i 0.00622328 0.0107790i
\(612\) 0 0
\(613\) 11.8136 + 20.4617i 0.477146 + 0.826441i 0.999657 0.0261916i \(-0.00833800\pi\)
−0.522511 + 0.852632i \(0.675005\pi\)
\(614\) 4.88325 8.45804i 0.197072 0.341339i
\(615\) 0 0
\(616\) 2.39653 1.12100i 0.0965590 0.0451663i
\(617\) 35.8486 1.44321 0.721604 0.692306i \(-0.243405\pi\)
0.721604 + 0.692306i \(0.243405\pi\)
\(618\) 0 0
\(619\) −13.9602 24.1797i −0.561107 0.971865i −0.997400 0.0720607i \(-0.977042\pi\)
0.436294 0.899804i \(-0.356291\pi\)
\(620\) −2.18038 3.77654i −0.0875663 0.151669i
\(621\) 0 0
\(622\) −6.51854 −0.261370
\(623\) −24.0555 16.8012i −0.963763 0.673125i
\(624\) 0 0
\(625\) −10.9694 + 18.9995i −0.438775 + 0.759981i
\(626\) 15.3965 + 26.6676i 0.615369 + 1.06585i
\(627\) 0 0
\(628\) 8.82488 15.2851i 0.352151 0.609944i
\(629\) −7.88325 −0.314326
\(630\) 0 0
\(631\) 43.6682 1.73840 0.869201 0.494458i \(-0.164633\pi\)
0.869201 + 0.494458i \(0.164633\pi\)
\(632\) 2.68236 4.64598i 0.106698 0.184807i
\(633\) 0 0
\(634\) 13.8136 + 23.9258i 0.548607 + 0.950216i
\(635\) 1.68959 2.92646i 0.0670495 0.116133i
\(636\) 0 0
\(637\) −6.27452 1.09096i −0.248606 0.0432253i
\(638\) 2.79306 0.110578
\(639\) 0 0
\(640\) −0.227452 0.393958i −0.00899083 0.0155726i
\(641\) −9.88325 17.1183i −0.390365 0.676132i 0.602133 0.798396i \(-0.294318\pi\)
−0.992498 + 0.122264i \(0.960985\pi\)
\(642\) 0 0
\(643\) 24.7584 0.976375 0.488187 0.872739i \(-0.337658\pi\)
0.488187 + 0.872739i \(0.337658\pi\)
\(644\) 1.89653 21.9790i 0.0747338 0.866095i
\(645\) 0 0
\(646\) −1.94163 + 3.36300i −0.0763923 + 0.132315i
\(647\) 15.5391 + 26.9144i 0.610903 + 1.05812i 0.991088 + 0.133205i \(0.0425269\pi\)
−0.380185 + 0.924910i \(0.624140\pi\)
\(648\) 0 0
\(649\) −3.48672 + 6.03918i −0.136866 + 0.237059i
\(650\) 4.36077 0.171043
\(651\) 0 0
\(652\) −11.6127 −0.454788
\(653\) 11.3587 19.6738i 0.444499 0.769895i −0.553518 0.832837i \(-0.686715\pi\)
0.998017 + 0.0629420i \(0.0200483\pi\)
\(654\) 0 0
\(655\) 4.41388 + 7.64506i 0.172464 + 0.298717i
\(656\) −0.896531 + 1.55284i −0.0350037 + 0.0606281i
\(657\) 0 0
\(658\) 0.810407 0.379075i 0.0315929 0.0147779i
\(659\) −43.6127 −1.69891 −0.849454 0.527662i \(-0.823069\pi\)
−0.849454 + 0.527662i \(0.823069\pi\)
\(660\) 0 0
\(661\) 3.96818 + 6.87309i 0.154344 + 0.267332i 0.932820 0.360342i \(-0.117340\pi\)
−0.778476 + 0.627675i \(0.784007\pi\)
\(662\) −14.4827 25.0847i −0.562884 0.974944i
\(663\) 0 0
\(664\) 1.97345 0.0765846
\(665\) −4.23349 + 1.98025i −0.164168 + 0.0767909i
\(666\) 0 0
\(667\) 11.6445 20.1689i 0.450877 0.780941i
\(668\) −2.42835 4.20603i −0.0939557 0.162736i
\(669\) 0 0
\(670\) 0.862740 1.49431i 0.0333305 0.0577302i
\(671\) 14.0410 0.542048
\(672\) 0 0
\(673\) 36.9388 1.42388 0.711942 0.702238i \(-0.247816\pi\)
0.711942 + 0.702238i \(0.247816\pi\)
\(674\) −4.51854 + 7.82634i −0.174048 + 0.301460i
\(675\) 0 0
\(676\) 6.08612 + 10.5415i 0.234082 + 0.405441i
\(677\) −19.8249 + 34.3377i −0.761932 + 1.31971i 0.179921 + 0.983681i \(0.442416\pi\)
−0.941853 + 0.336024i \(0.890918\pi\)
\(678\) 0 0
\(679\) −3.31764 + 38.4484i −0.127319 + 1.47551i
\(680\) −0.454904 −0.0174448
\(681\) 0 0
\(682\) 4.79306 + 8.30183i 0.183536 + 0.317893i
\(683\) −22.7757 39.4487i −0.871489 1.50946i −0.860457 0.509523i \(-0.829822\pi\)
−0.0110318 0.999939i \(-0.503512\pi\)
\(684\) 0 0
\(685\) 0.413875 0.0158134
\(686\) −13.1425 13.0489i −0.501784 0.498210i
\(687\) 0 0
\(688\) −3.94163 + 6.82710i −0.150273 + 0.260281i
\(689\) 0.413875 + 0.716853i 0.0157674 + 0.0273099i
\(690\) 0 0
\(691\) 9.59940 16.6267i 0.365178 0.632508i −0.623626 0.781723i \(-0.714341\pi\)
0.988805 + 0.149215i \(0.0476746\pi\)
\(692\) 25.5861 0.972639
\(693\) 0 0
\(694\) −21.6127 −0.820406
\(695\) −1.90586 + 3.30105i −0.0722935 + 0.125216i
\(696\) 0 0
\(697\) 0.896531 + 1.55284i 0.0339585 + 0.0588179i
\(698\) 7.13726 12.3621i 0.270149 0.467912i
\(699\) 0 0
\(700\) 10.3965 + 7.26129i 0.392952 + 0.274451i
\(701\) −23.2890 −0.879613 −0.439807 0.898093i \(-0.644953\pi\)
−0.439807 + 0.898093i \(0.644953\pi\)
\(702\) 0 0
\(703\) −15.3063 26.5114i −0.577290 0.999895i
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) −28.4959 −1.07246
\(707\) 19.3248 9.03933i 0.726782 0.339959i
\(708\) 0 0
\(709\) 10.3965 18.0073i 0.390450 0.676279i −0.602059 0.798452i \(-0.705653\pi\)
0.992509 + 0.122173i \(0.0389861\pi\)
\(710\) −1.09019 1.88827i −0.0409142 0.0708654i
\(711\) 0 0
\(712\) 5.54510 9.60439i 0.207811 0.359940i
\(713\) 79.9306 2.99343
\(714\) 0 0
\(715\) 0.413875 0.0154781
\(716\) −7.85144 + 13.5991i −0.293422 + 0.508222i
\(717\) 0 0
\(718\) 6.81962 + 11.8119i 0.254506 + 0.440817i
\(719\) −2.74073 + 4.74708i −0.102212 + 0.177036i −0.912596 0.408863i \(-0.865925\pi\)
0.810384 + 0.585899i \(0.199259\pi\)
\(720\) 0 0
\(721\) −12.5080 8.73601i −0.465823 0.325346i
\(722\) 3.92034 0.145900
\(723\) 0 0
\(724\) 1.24797 + 2.16154i 0.0463803 + 0.0803330i
\(725\) 6.69366 + 11.5938i 0.248596 + 0.430581i
\(726\) 0 0
\(727\) 25.5330 0.946967 0.473484 0.880803i \(-0.342996\pi\)
0.473484 + 0.880803i \(0.342996\pi\)
\(728\) 0.206938 2.39821i 0.00766962 0.0888837i
\(729\) 0 0
\(730\) −2.42835 + 4.20603i −0.0898773 + 0.155672i
\(731\) 3.94163 + 6.82710i 0.145786 + 0.252509i
\(732\) 0 0
\(733\) −8.11071 + 14.0482i −0.299576 + 0.518880i −0.976039 0.217596i \(-0.930178\pi\)
0.676463 + 0.736476i \(0.263512\pi\)
\(734\) −22.7294 −0.838958
\(735\) 0 0
\(736\) 8.33816 0.307349
\(737\) −1.89653 + 3.28489i −0.0698596 + 0.121000i
\(738\) 0 0
\(739\) −9.37919 16.2452i −0.345019 0.597590i 0.640338 0.768093i \(-0.278794\pi\)
−0.985357 + 0.170503i \(0.945461\pi\)
\(740\) 1.79306 3.10567i 0.0659143 0.114167i
\(741\) 0 0
\(742\) −0.206938 + 2.39821i −0.00759692 + 0.0880412i
\(743\) 44.6763 1.63902 0.819508 0.573068i \(-0.194247\pi\)
0.819508 + 0.573068i \(0.194247\pi\)
\(744\) 0 0
\(745\) −0.936362 1.62183i −0.0343057 0.0594191i
\(746\) 5.20090 + 9.00822i 0.190418 + 0.329814i
\(747\) 0 0
\(748\) 1.00000 0.0365636
\(749\) 33.8651 + 23.6525i 1.23741 + 0.864245i
\(750\) 0 0
\(751\) 1.48146 2.56596i 0.0540592 0.0936332i −0.837729 0.546085i \(-0.816117\pi\)
0.891789 + 0.452452i \(0.149451\pi\)
\(752\) 0.169079 + 0.292854i 0.00616568 + 0.0106793i
\(753\) 0 0
\(754\) 1.27058 2.20070i 0.0462716 0.0801448i
\(755\) 2.80120 0.101946
\(756\) 0 0
\(757\) 26.1988 0.952212 0.476106 0.879388i \(-0.342048\pi\)
0.476106 + 0.879388i \(0.342048\pi\)
\(758\) 3.80634 6.59277i 0.138252 0.239460i
\(759\) 0 0
\(760\) −0.883254 1.52984i −0.0320390 0.0554932i
\(761\) 12.8965 22.3374i 0.467499 0.809732i −0.531812 0.846863i \(-0.678489\pi\)
0.999310 + 0.0371309i \(0.0118219\pi\)
\(762\) 0 0
\(763\) 33.6498 15.7400i 1.21820 0.569825i
\(764\) −9.81962 −0.355261
\(765\) 0 0
\(766\) 11.0728 + 19.1787i 0.400078 + 0.692956i
\(767\) 3.17225 + 5.49450i 0.114543 + 0.198395i
\(768\) 0 0
\(769\) −37.2012 −1.34151 −0.670755 0.741679i \(-0.734030\pi\)
−0.670755 + 0.741679i \(0.734030\pi\)
\(770\) 0.986723 + 0.689160i 0.0355590 + 0.0248356i
\(771\) 0 0
\(772\) −3.42835 + 5.93808i −0.123389 + 0.213716i
\(773\) −20.3852 35.3082i −0.733206 1.26995i −0.955506 0.294971i \(-0.904690\pi\)
0.222300 0.974978i \(-0.428643\pi\)
\(774\) 0 0
\(775\) −22.9734 + 39.7912i −0.825231 + 1.42934i
\(776\) −14.5861 −0.523611
\(777\) 0 0
\(778\) −3.54510 −0.127098
\(779\) −3.48146 + 6.03006i −0.124736 + 0.216049i
\(780\) 0 0
\(781\) 2.39653 + 4.15091i 0.0857546 + 0.148531i
\(782\) 4.16908 7.22106i 0.149086 0.258224i
\(783\) 0 0
\(784\) 4.48672 5.37302i 0.160240 0.191893i
\(785\) 8.02895 0.286565
\(786\) 0 0
\(787\) −27.2943 47.2750i −0.972935 1.68517i −0.686587 0.727048i \(-0.740892\pi\)
−0.286348 0.958126i \(-0.592441\pi\)
\(788\) 11.7347 + 20.3251i 0.418031 + 0.724051i
\(789\) 0 0
\(790\) 2.44043 0.0868266
\(791\) 1.72548 19.9967i 0.0613510 0.711001i
\(792\) 0 0
\(793\) 6.38732 11.0632i 0.226820 0.392865i
\(794\) −1.27979 2.21665i −0.0454179 0.0786661i
\(795\) 0 0
\(796\) 1.11675 1.93426i 0.0395820