Properties

Label 168.2.ba.a.101.2
Level $168$
Weight $2$
Character 168.101
Analytic conductor $1.341$
Analytic rank $0$
Dimension $4$
CM discriminant -24
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 168.ba (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.34148675396\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label 101.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 168.101
Dual form 168.2.ba.a.5.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(3.62132 - 2.09077i) q^{5} -2.44949i q^{6} +(1.62132 + 2.09077i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(3.62132 - 2.09077i) q^{5} -2.44949i q^{6} +(1.62132 + 2.09077i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(5.12132 + 2.95680i) q^{10} +(-0.0857864 + 0.148586i) q^{11} +(3.00000 - 1.73205i) q^{12} +(-1.41421 + 3.46410i) q^{14} -7.24264 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-2.12132 + 3.67423i) q^{18} +8.36308i q^{20} +(-0.621320 - 4.54026i) q^{21} -0.242641 q^{22} +(4.24264 + 2.44949i) q^{24} +(6.24264 - 10.8126i) q^{25} -5.19615i q^{27} +(-5.24264 + 0.717439i) q^{28} -10.4142 q^{29} +(-5.12132 - 8.87039i) q^{30} +(-5.37868 - 3.10538i) q^{31} +(2.82843 - 4.89898i) q^{32} +(0.257359 - 0.148586i) q^{33} +(10.2426 + 4.18154i) q^{35} -6.00000 q^{36} +(-10.2426 + 5.91359i) q^{40} +(5.12132 - 3.97141i) q^{42} +(-0.171573 - 0.297173i) q^{44} +(10.8640 + 6.27231i) q^{45} +6.92820i q^{48} +(-1.74264 + 6.77962i) q^{49} +17.6569 q^{50} +(-5.03553 + 8.72180i) q^{53} +(6.36396 - 3.67423i) q^{54} +0.717439i q^{55} +(-4.58579 - 5.91359i) q^{56} +(-7.36396 - 12.7548i) q^{58} +(-3.98528 - 2.30090i) q^{59} +(7.24264 - 12.5446i) q^{60} -8.78335i q^{62} +(-3.00000 + 7.34847i) q^{63} +8.00000 q^{64} +(0.363961 + 0.210133i) q^{66} +(2.12132 + 15.5014i) q^{70} +(-4.24264 - 7.34847i) q^{72} +(8.48528 + 4.89898i) q^{73} +(-18.7279 + 10.8126i) q^{75} +(-0.449747 + 0.0615465i) q^{77} +(-3.86396 - 6.69258i) q^{79} +(-14.4853 - 8.36308i) q^{80} +(-4.50000 + 7.79423i) q^{81} -3.76127i q^{83} +(8.48528 + 3.46410i) q^{84} +(15.6213 + 9.01897i) q^{87} +(0.242641 - 0.420266i) q^{88} +17.7408i q^{90} +(5.37868 + 9.31615i) q^{93} +(-8.48528 + 4.89898i) q^{96} -11.5300i q^{97} +(-9.53553 + 2.65962i) q^{98} -0.514719 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 6 q^{3} - 4 q^{4} + 6 q^{5} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 6 q^{3} - 4 q^{4} + 6 q^{5} - 2 q^{7} + 6 q^{9} + 12 q^{10} - 6 q^{11} + 12 q^{12} - 12 q^{15} - 8 q^{16} + 6 q^{21} + 16 q^{22} + 8 q^{25} - 4 q^{28} - 36 q^{29} - 12 q^{30} - 30 q^{31} + 18 q^{33} + 24 q^{35} - 24 q^{36} - 24 q^{40} + 12 q^{42} - 12 q^{44} + 18 q^{45} + 10 q^{49} + 48 q^{50} - 6 q^{53} - 24 q^{56} - 4 q^{58} + 18 q^{59} + 12 q^{60} - 12 q^{63} + 32 q^{64} - 24 q^{66} - 24 q^{75} + 18 q^{77} + 10 q^{79} - 24 q^{80} - 18 q^{81} + 54 q^{87} - 16 q^{88} + 30 q^{93} - 24 q^{98} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(85\) \(113\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 1.22474i 0.500000 + 0.866025i
\(3\) −1.50000 0.866025i −0.866025 0.500000i
\(4\) −1.00000 + 1.73205i −0.500000 + 0.866025i
\(5\) 3.62132 2.09077i 1.61950 0.935021i 0.632456 0.774597i \(-0.282047\pi\)
0.987048 0.160424i \(-0.0512862\pi\)
\(6\) 2.44949i 1.00000i
\(7\) 1.62132 + 2.09077i 0.612801 + 0.790237i
\(8\) −2.82843 −1.00000
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 5.12132 + 2.95680i 1.61950 + 0.935021i
\(11\) −0.0857864 + 0.148586i −0.0258656 + 0.0448005i −0.878668 0.477432i \(-0.841568\pi\)
0.852803 + 0.522233i \(0.174901\pi\)
\(12\) 3.00000 1.73205i 0.866025 0.500000i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −1.41421 + 3.46410i −0.377964 + 0.925820i
\(15\) −7.24264 −1.87004
\(16\) −2.00000 3.46410i −0.500000 0.866025i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) −2.12132 + 3.67423i −0.500000 + 0.866025i
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 8.36308i 1.87004i
\(21\) −0.621320 4.54026i −0.135583 0.990766i
\(22\) −0.242641 −0.0517312
\(23\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) 4.24264 + 2.44949i 0.866025 + 0.500000i
\(25\) 6.24264 10.8126i 1.24853 2.16251i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) −5.24264 + 0.717439i −0.990766 + 0.135583i
\(29\) −10.4142 −1.93387 −0.966935 0.255021i \(-0.917918\pi\)
−0.966935 + 0.255021i \(0.917918\pi\)
\(30\) −5.12132 8.87039i −0.935021 1.61950i
\(31\) −5.37868 3.10538i −0.966039 0.557743i −0.0680129 0.997684i \(-0.521666\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) 2.82843 4.89898i 0.500000 0.866025i
\(33\) 0.257359 0.148586i 0.0448005 0.0258656i
\(34\) 0 0
\(35\) 10.2426 + 4.18154i 1.73132 + 0.706809i
\(36\) −6.00000 −1.00000
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −10.2426 + 5.91359i −1.61950 + 0.935021i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 5.12132 3.97141i 0.790237 0.612801i
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −0.171573 0.297173i −0.0258656 0.0448005i
\(45\) 10.8640 + 6.27231i 1.61950 + 0.935021i
\(46\) 0 0
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 6.92820i 1.00000i
\(49\) −1.74264 + 6.77962i −0.248949 + 0.968517i
\(50\) 17.6569 2.49706
\(51\) 0 0
\(52\) 0 0
\(53\) −5.03553 + 8.72180i −0.691684 + 1.19803i 0.279602 + 0.960116i \(0.409797\pi\)
−0.971286 + 0.237915i \(0.923536\pi\)
\(54\) 6.36396 3.67423i 0.866025 0.500000i
\(55\) 0.717439i 0.0967394i
\(56\) −4.58579 5.91359i −0.612801 0.790237i
\(57\) 0 0
\(58\) −7.36396 12.7548i −0.966935 1.67478i
\(59\) −3.98528 2.30090i −0.518839 0.299552i 0.217620 0.976034i \(-0.430171\pi\)
−0.736460 + 0.676481i \(0.763504\pi\)
\(60\) 7.24264 12.5446i 0.935021 1.61950i
\(61\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(62\) 8.78335i 1.11549i
\(63\) −3.00000 + 7.34847i −0.377964 + 0.925820i
\(64\) 8.00000 1.00000
\(65\) 0 0
\(66\) 0.363961 + 0.210133i 0.0448005 + 0.0258656i
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 2.12132 + 15.5014i 0.253546 + 1.85277i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −4.24264 7.34847i −0.500000 0.866025i
\(73\) 8.48528 + 4.89898i 0.993127 + 0.573382i 0.906208 0.422833i \(-0.138964\pi\)
0.0869195 + 0.996215i \(0.472298\pi\)
\(74\) 0 0
\(75\) −18.7279 + 10.8126i −2.16251 + 1.24853i
\(76\) 0 0
\(77\) −0.449747 + 0.0615465i −0.0512535 + 0.00701388i
\(78\) 0 0
\(79\) −3.86396 6.69258i −0.434730 0.752974i 0.562544 0.826767i \(-0.309823\pi\)
−0.997274 + 0.0737937i \(0.976489\pi\)
\(80\) −14.4853 8.36308i −1.61950 0.935021i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 3.76127i 0.412854i −0.978462 0.206427i \(-0.933816\pi\)
0.978462 0.206427i \(-0.0661835\pi\)
\(84\) 8.48528 + 3.46410i 0.925820 + 0.377964i
\(85\) 0 0
\(86\) 0 0
\(87\) 15.6213 + 9.01897i 1.67478 + 0.966935i
\(88\) 0.242641 0.420266i 0.0258656 0.0448005i
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) 17.7408i 1.87004i
\(91\) 0 0
\(92\) 0 0
\(93\) 5.37868 + 9.31615i 0.557743 + 0.966039i
\(94\) 0 0
\(95\) 0 0
\(96\) −8.48528 + 4.89898i −0.866025 + 0.500000i
\(97\) 11.5300i 1.17070i −0.810782 0.585348i \(-0.800958\pi\)
0.810782 0.585348i \(-0.199042\pi\)
\(98\) −9.53553 + 2.65962i −0.963234 + 0.268662i
\(99\) −0.514719 −0.0517312
\(100\) 12.4853 + 21.6251i 1.24853 + 2.16251i
\(101\) −3.00000 1.73205i −0.298511 0.172345i 0.343263 0.939239i \(-0.388468\pi\)
−0.641774 + 0.766894i \(0.721801\pi\)
\(102\) 0 0
\(103\) 12.7279 7.34847i 1.25412 0.724066i 0.282194 0.959357i \(-0.408938\pi\)
0.971925 + 0.235291i \(0.0756043\pi\)
\(104\) 0 0
\(105\) −11.7426 15.1427i −1.14596 1.47778i
\(106\) −14.2426 −1.38337
\(107\) 10.3284 + 17.8894i 0.998487 + 1.72943i 0.546869 + 0.837218i \(0.315820\pi\)
0.451618 + 0.892211i \(0.350847\pi\)
\(108\) 9.00000 + 5.19615i 0.866025 + 0.500000i
\(109\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(110\) −0.878680 + 0.507306i −0.0837788 + 0.0483697i
\(111\) 0 0
\(112\) 4.00000 9.79796i 0.377964 0.925820i
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 10.4142 18.0379i 0.966935 1.67478i
\(117\) 0 0
\(118\) 6.50794i 0.599104i
\(119\) 0 0
\(120\) 20.4853 1.87004
\(121\) 5.48528 + 9.50079i 0.498662 + 0.863708i
\(122\) 0 0
\(123\) 0 0
\(124\) 10.7574 6.21076i 0.966039 0.557743i
\(125\) 31.3000i 2.79956i
\(126\) −11.1213 + 1.52192i −0.990766 + 0.135583i
\(127\) 6.75736 0.599619 0.299809 0.953999i \(-0.403077\pi\)
0.299809 + 0.953999i \(0.403077\pi\)
\(128\) 5.65685 + 9.79796i 0.500000 + 0.866025i
\(129\) 0 0
\(130\) 0 0
\(131\) 18.4706 10.6640i 1.61378 0.931717i 0.625297 0.780387i \(-0.284978\pi\)
0.988483 0.151330i \(-0.0483556\pi\)
\(132\) 0.594346i 0.0517312i
\(133\) 0 0
\(134\) 0 0
\(135\) −10.8640 18.8169i −0.935021 1.61950i
\(136\) 0 0
\(137\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) −17.4853 + 13.5592i −1.47778 + 1.14596i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 6.00000 10.3923i 0.500000 0.866025i
\(145\) −37.7132 + 21.7737i −3.13191 + 1.80821i
\(146\) 13.8564i 1.14676i
\(147\) 8.48528 8.66025i 0.699854 0.714286i
\(148\) 0 0
\(149\) 1.41421 + 2.44949i 0.115857 + 0.200670i 0.918122 0.396298i \(-0.129705\pi\)
−0.802265 + 0.596968i \(0.796372\pi\)
\(150\) −26.4853 15.2913i −2.16251 1.24853i
\(151\) −11.1066 + 19.2372i −0.903842 + 1.56550i −0.0813788 + 0.996683i \(0.525932\pi\)
−0.822464 + 0.568818i \(0.807401\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −0.393398 0.507306i −0.0317009 0.0408799i
\(155\) −25.9706 −2.08601
\(156\) 0 0
\(157\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(158\) 5.46447 9.46473i 0.434730 0.752974i
\(159\) 15.1066 8.72180i 1.19803 0.691684i
\(160\) 23.6544i 1.87004i
\(161\) 0 0
\(162\) −12.7279 −1.00000
\(163\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(164\) 0 0
\(165\) 0.621320 1.07616i 0.0483697 0.0837788i
\(166\) 4.60660 2.65962i 0.357542 0.206427i
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 1.75736 + 12.8418i 0.135583 + 0.990766i
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −15.0000 + 8.66025i −1.14043 + 0.658427i −0.946537 0.322596i \(-0.895445\pi\)
−0.193892 + 0.981023i \(0.562111\pi\)
\(174\) 25.5095i 1.93387i
\(175\) 32.7279 4.47871i 2.47400 0.338559i
\(176\) 0.686292 0.0517312
\(177\) 3.98528 + 6.90271i 0.299552 + 0.518839i
\(178\) 0 0
\(179\) 5.65685 9.79796i 0.422813 0.732334i −0.573400 0.819275i \(-0.694376\pi\)
0.996213 + 0.0869415i \(0.0277093\pi\)
\(180\) −21.7279 + 12.5446i −1.61950 + 0.935021i
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) −7.60660 + 13.1750i −0.557743 + 0.966039i
\(187\) 0 0
\(188\) 0 0
\(189\) 10.8640 8.42463i 0.790237 0.612801i
\(190\) 0 0
\(191\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) −12.0000 6.92820i −0.866025 0.500000i
\(193\) 10.7426 18.6068i 0.773272 1.33935i −0.162488 0.986710i \(-0.551952\pi\)
0.935760 0.352636i \(-0.114715\pi\)
\(194\) 14.1213 8.15295i 1.01385 0.585348i
\(195\) 0 0
\(196\) −10.0000 9.79796i −0.714286 0.699854i
\(197\) 14.1421 1.00759 0.503793 0.863825i \(-0.331938\pi\)
0.503793 + 0.863825i \(0.331938\pi\)
\(198\) −0.363961 0.630399i −0.0258656 0.0448005i
\(199\) −21.2132 12.2474i −1.50376 0.868199i −0.999990 0.00436292i \(-0.998611\pi\)
−0.503774 0.863836i \(-0.668055\pi\)
\(200\) −17.6569 + 30.5826i −1.24853 + 2.16251i
\(201\) 0 0
\(202\) 4.89898i 0.344691i
\(203\) −16.8848 21.7737i −1.18508 1.52822i
\(204\) 0 0
\(205\) 0 0
\(206\) 18.0000 + 10.3923i 1.25412 + 0.724066i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 10.2426 25.0892i 0.706809 1.73132i
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) −10.0711 17.4436i −0.691684 1.19803i
\(213\) 0 0
\(214\) −14.6066 + 25.2994i −0.998487 + 1.72943i
\(215\) 0 0
\(216\) 14.6969i 1.00000i
\(217\) −2.22792 16.2804i −0.151241 1.10519i
\(218\) 0 0
\(219\) −8.48528 14.6969i −0.573382 0.993127i
\(220\) −1.24264 0.717439i −0.0837788 0.0483697i
\(221\) 0 0
\(222\) 0 0
\(223\) 29.8651i 1.99992i 0.00910984 + 0.999959i \(0.497100\pi\)
−0.00910984 + 0.999959i \(0.502900\pi\)
\(224\) 14.8284 2.02922i 0.990766 0.135583i
\(225\) 37.4558 2.49706
\(226\) 0 0
\(227\) 25.7132 + 14.8455i 1.70665 + 0.985332i 0.938647 + 0.344881i \(0.112081\pi\)
0.767999 + 0.640451i \(0.221253\pi\)
\(228\) 0 0
\(229\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(230\) 0 0
\(231\) 0.727922 + 0.297173i 0.0478938 + 0.0195525i
\(232\) 29.4558 1.93387
\(233\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 7.97056 4.60181i 0.518839 0.299552i
\(237\) 13.3852i 0.869459i
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 14.4853 + 25.0892i 0.935021 + 1.61950i
\(241\) −20.2279 11.6786i −1.30300 0.752285i −0.322078 0.946713i \(-0.604381\pi\)
−0.980917 + 0.194429i \(0.937715\pi\)
\(242\) −7.75736 + 13.4361i −0.498662 + 0.863708i
\(243\) 13.5000 7.79423i 0.866025 0.500000i
\(244\) 0 0
\(245\) 7.86396 + 28.1946i 0.502410 + 1.80129i
\(246\) 0 0
\(247\) 0 0
\(248\) 15.2132 + 8.78335i 0.966039 + 0.557743i
\(249\) −3.25736 + 5.64191i −0.206427 + 0.357542i
\(250\) 38.3345 22.1324i 2.42449 1.39978i
\(251\) 20.4874i 1.29316i 0.762848 + 0.646578i \(0.223800\pi\)
−0.762848 + 0.646578i \(0.776200\pi\)
\(252\) −9.72792 12.5446i −0.612801 0.790237i
\(253\) 0 0
\(254\) 4.77817 + 8.27604i 0.299809 + 0.519285i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −15.6213 27.0569i −0.966935 1.67478i
\(262\) 26.1213 + 15.0812i 1.61378 + 0.931717i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) −0.727922 + 0.420266i −0.0448005 + 0.0258656i
\(265\) 42.1126i 2.58696i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −18.8345 10.8741i −1.14836 0.663007i −0.199874 0.979822i \(-0.564053\pi\)
−0.948487 + 0.316815i \(0.897387\pi\)
\(270\) 15.3640 26.6112i 0.935021 1.61950i
\(271\) −5.89340 + 3.40256i −0.357998 + 0.206691i −0.668202 0.743980i \(-0.732936\pi\)
0.310204 + 0.950670i \(0.399603\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.07107 + 1.85514i 0.0645878 + 0.111869i
\(276\) 0 0
\(277\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(278\) 0 0
\(279\) 18.6323i 1.11549i
\(280\) −28.9706 11.8272i −1.73132 0.706809i
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 16.9706 1.00000
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) −53.3345 30.7927i −3.13191 1.80821i
\(291\) −9.98528 + 17.2950i −0.585348 + 1.01385i
\(292\) −16.9706 + 9.79796i −0.993127 + 0.573382i
\(293\) 3.34101i 0.195184i 0.995227 + 0.0975919i \(0.0311140\pi\)
−0.995227 + 0.0975919i \(0.968886\pi\)
\(294\) 16.6066 + 4.26858i 0.968517 + 0.248949i
\(295\) −19.2426 −1.12035
\(296\) 0 0
\(297\) 0.772078 + 0.445759i 0.0448005 + 0.0258656i
\(298\) −2.00000 + 3.46410i −0.115857 + 0.200670i
\(299\) 0 0
\(300\) 43.2503i 2.49706i
\(301\) 0 0
\(302\) −31.4142 −1.80768
\(303\) 3.00000 + 5.19615i 0.172345 + 0.298511i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0.343146 0.840532i 0.0195525 0.0478938i
\(309\) −25.4558 −1.44813
\(310\) −18.3640 31.8073i −1.04300 1.80653i
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0 0
\(313\) 21.2574 12.2729i 1.20154 0.693708i 0.240640 0.970614i \(-0.422643\pi\)
0.960897 + 0.276907i \(0.0893093\pi\)
\(314\) 0 0
\(315\) 4.50000 + 32.8835i 0.253546 + 1.85277i
\(316\) 15.4558 0.869459
\(317\) 15.2782 + 26.4626i 0.858108 + 1.48629i 0.873732 + 0.486408i \(0.161693\pi\)
−0.0156238 + 0.999878i \(0.504973\pi\)
\(318\) 21.3640 + 12.3345i 1.19803 + 0.691684i
\(319\) 0.893398 1.54741i 0.0500207 0.0866384i
\(320\) 28.9706 16.7262i 1.61950 0.935021i
\(321\) 35.7787i 1.99697i
\(322\) 0 0
\(323\) 0 0
\(324\) −9.00000 15.5885i −0.500000 0.866025i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 1.75736 0.0967394
\(331\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) 6.51472 + 3.76127i 0.357542 + 0.206427i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −14.4853 + 11.2328i −0.790237 + 0.612801i
\(337\) 36.4558 1.98588 0.992938 0.118633i \(-0.0378512\pi\)
0.992938 + 0.118633i \(0.0378512\pi\)
\(338\) −9.19239 15.9217i −0.500000 0.866025i
\(339\) 0 0
\(340\) 0 0
\(341\) 0.922836 0.532799i 0.0499743 0.0288527i
\(342\) 0 0
\(343\) −17.0000 + 7.34847i −0.917914 + 0.396780i
\(344\) 0 0
\(345\) 0 0
\(346\) −21.2132 12.2474i −1.14043 0.658427i
\(347\) −14.1421 + 24.4949i −0.759190 + 1.31495i 0.184075 + 0.982912i \(0.441071\pi\)
−0.943264 + 0.332043i \(0.892262\pi\)
\(348\) −31.2426 + 18.0379i −1.67478 + 0.966935i
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 28.6274 + 36.9164i 1.53020 + 1.97327i
\(351\) 0 0
\(352\) 0.485281 + 0.840532i 0.0258656 + 0.0448005i
\(353\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(354\) −5.63604 + 9.76191i −0.299552 + 0.518839i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 16.0000 0.845626
\(359\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(360\) −30.7279 17.7408i −1.61950 0.935021i
\(361\) 9.50000 16.4545i 0.500000 0.866025i
\(362\) 0 0
\(363\) 19.0016i 0.997324i
\(364\) 0 0
\(365\) 40.9706 2.14450
\(366\) 0 0
\(367\) −26.3787 15.2297i −1.37696 0.794986i −0.385164 0.922848i \(-0.625855\pi\)
−0.991792 + 0.127862i \(0.959188\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −26.3995 + 3.61269i −1.37059 + 0.187561i
\(372\) −21.5147 −1.11549
\(373\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) 0 0
\(375\) −27.1066 + 46.9500i −1.39978 + 2.42449i
\(376\) 0 0
\(377\) 0 0
\(378\) 18.0000 + 7.34847i 0.925820 + 0.377964i
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) −10.1360 5.85204i −0.519285 0.299809i
\(382\) 0 0
\(383\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) 19.5959i 1.00000i
\(385\) −1.50000 + 1.16320i −0.0764471 + 0.0592821i
\(386\) 30.3848 1.54654
\(387\) 0 0
\(388\) 19.9706 + 11.5300i 1.01385 + 0.585348i
\(389\) 15.5563 26.9444i 0.788738 1.36613i −0.138002 0.990432i \(-0.544068\pi\)
0.926740 0.375703i \(-0.122599\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 4.92893 19.1757i 0.248949 0.968517i
\(393\) −36.9411 −1.86343
\(394\) 10.0000 + 17.3205i 0.503793 + 0.872595i
\(395\) −27.9853 16.1573i −1.40809 0.812962i
\(396\) 0.514719 0.891519i 0.0258656 0.0448005i
\(397\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(398\) 34.6410i 1.73640i
\(399\) 0 0
\(400\) −49.9411 −2.49706
\(401\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 6.00000 3.46410i 0.298511 0.172345i
\(405\) 37.6339i 1.87004i
\(406\) 14.7279 36.0759i 0.730934 1.79042i
\(407\) 0 0
\(408\) 0 0
\(409\) 9.47056 + 5.46783i 0.468289 + 0.270367i 0.715523 0.698589i \(-0.246188\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 29.3939i 1.44813i
\(413\) −1.65076 12.0628i −0.0812285 0.593572i
\(414\) 0 0
\(415\) −7.86396 13.6208i −0.386027 0.668618i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10.3923i 0.507697i −0.967244 0.253849i \(-0.918303\pi\)
0.967244 0.253849i \(-0.0816965\pi\)
\(420\) 37.9706 5.19615i 1.85277 0.253546i
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 14.2426 24.6690i 0.691684 1.19803i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −41.3137 −1.99697
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) −18.0000 + 10.3923i −0.866025 + 0.500000i
\(433\) 39.1918i 1.88344i −0.336399 0.941720i \(-0.609209\pi\)
0.336399 0.941720i \(-0.390791\pi\)
\(434\) 18.3640 14.2406i 0.881498 0.683572i
\(435\) 75.4264 3.61642
\(436\) 0 0
\(437\) 0 0
\(438\) 12.0000 20.7846i 0.573382 0.993127i
\(439\) 36.1066 20.8462i 1.72327 0.994933i 0.811366 0.584539i \(-0.198725\pi\)
0.911908 0.410394i \(-0.134609\pi\)
\(440\) 2.02922i 0.0967394i
\(441\) −20.2279 + 5.64191i −0.963234 + 0.268662i
\(442\) 0 0
\(443\) −20.5711 35.6301i −0.977361 1.69284i −0.671913 0.740630i \(-0.734527\pi\)
−0.305448 0.952209i \(-0.598806\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −36.5772 + 21.1178i −1.73198 + 0.999959i
\(447\) 4.89898i 0.231714i
\(448\) 12.9706 + 16.7262i 0.612801 + 0.790237i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 26.4853 + 45.8739i 1.24853 + 2.16251i
\(451\) 0 0
\(452\) 0 0
\(453\) 33.3198 19.2372i 1.56550 0.903842i
\(454\) 41.9895i 1.97066i
\(455\) 0 0
\(456\) 0 0
\(457\) 17.9853 + 31.1514i 0.841316 + 1.45720i 0.888783 + 0.458329i \(0.151552\pi\)
−0.0474665 + 0.998873i \(0.515115\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 38.1051i 1.77473i 0.461065 + 0.887366i \(0.347467\pi\)
−0.461065 + 0.887366i \(0.652533\pi\)
\(462\) 0.150758 + 1.10165i 0.00701388 + 0.0512535i
\(463\) −26.0000 −1.20832 −0.604161 0.796862i \(-0.706492\pi\)
−0.604161 + 0.796862i \(0.706492\pi\)
\(464\) 20.8284 + 36.0759i 0.966935 + 1.67478i
\(465\) 38.9558 + 22.4912i 1.80653 + 1.04300i
\(466\) 0 0
\(467\) −15.0000 + 8.66025i −0.694117 + 0.400749i −0.805153 0.593068i \(-0.797917\pi\)
0.111035 + 0.993816i \(0.464583\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 11.2721 + 6.50794i 0.518839 + 0.299552i
\(473\) 0 0
\(474\) −16.3934 + 9.46473i −0.752974 + 0.434730i
\(475\) 0 0
\(476\) 0 0
\(477\) −30.2132 −1.38337
\(478\) 0 0
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) −20.4853 + 35.4815i −0.935021 + 1.61950i
\(481\) 0 0
\(482\) 33.0321i 1.50457i
\(483\) 0 0
\(484\) −21.9411 −0.997324
\(485\) −24.1066 41.7539i −1.09462 1.89595i
\(486\) 19.0919 + 11.0227i 0.866025 + 0.500000i
\(487\) 18.5919 32.2021i 0.842479 1.45922i −0.0453143 0.998973i \(-0.514429\pi\)
0.887793 0.460243i \(-0.152238\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −28.9706 + 29.5680i −1.30876 + 1.33574i
\(491\) 21.6863 0.978689 0.489344 0.872091i \(-0.337236\pi\)
0.489344 + 0.872091i \(0.337236\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −1.86396 + 1.07616i −0.0837788 + 0.0483697i
\(496\) 24.8431i 1.11549i
\(497\) 0 0
\(498\) −9.21320 −0.412854
\(499\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(500\) 54.2132 + 31.3000i 2.42449 + 1.39978i
\(501\) 0 0
\(502\) −25.0919 + 14.4868i −1.11991 + 0.646578i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 8.48528 20.7846i 0.377964 0.925820i
\(505\) −14.4853 −0.644587
\(506\) 0 0
\(507\) 19.5000 + 11.2583i 0.866025 + 0.500000i
\(508\) −6.75736 + 11.7041i −0.299809 + 0.519285i
\(509\) −17.3787 + 10.0336i −0.770296 + 0.444731i −0.832980 0.553303i \(-0.813367\pi\)
0.0626839 + 0.998033i \(0.480034\pi\)
\(510\) 0 0
\(511\) 3.51472 + 25.6836i 0.155482 + 1.13618i
\(512\) −22.6274 −1.00000
\(513\) 0 0
\(514\) 0 0
\(515\) 30.7279 53.2223i 1.35403 2.34526i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 30.0000 1.31685
\(520\) 0 0
\(521\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(522\) 22.0919 38.2643i 0.966935 1.67478i
\(523\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(524\) 42.6559i 1.86343i
\(525\) −52.9706 21.6251i −2.31182 0.943799i
\(526\) 0 0
\(527\) 0 0
\(528\) −1.02944 0.594346i −0.0448005 0.0258656i
\(529\) −11.5000 + 19.9186i −0.500000 + 0.866025i
\(530\) −51.5772 + 29.7781i −2.24037 + 1.29348i
\(531\) 13.8054i 0.599104i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 74.8051 + 43.1887i 3.23411 + 1.86721i
\(536\) 0 0
\(537\) −16.9706 + 9.79796i −0.732334 + 0.422813i
\(538\) 30.7566i 1.32601i
\(539\) −0.857864 0.840532i −0.0369508 0.0362043i
\(540\) 43.4558 1.87004
\(541\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(542\) −8.33452 4.81194i −0.357998 0.206691i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) −1.51472 + 2.62357i −0.0645878 + 0.111869i
\(551\) 0 0
\(552\) 0 0
\(553\) 7.72792 18.9295i 0.328625 0.804963i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 15.9645 27.6513i 0.676436 1.17162i −0.299611 0.954062i \(-0.596857\pi\)
0.976047 0.217560i \(-0.0698099\pi\)
\(558\) 22.8198 13.1750i 0.966039 0.557743i
\(559\) 0 0
\(560\) −6.00000 43.8446i −0.253546 1.85277i
\(561\) 0 0
\(562\) 0 0
\(563\) 4.71320 + 2.72117i 0.198638 + 0.114684i 0.596020 0.802970i \(-0.296748\pi\)
−0.397382 + 0.917653i \(0.630081\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −23.5919 + 3.22848i −0.990766 + 0.135583i
\(568\) 0 0
\(569\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(570\) 0 0
\(571\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.500000 + 0.866025i
\(577\) −41.2279 23.8030i −1.71634 0.990930i −0.925361 0.379088i \(-0.876238\pi\)
−0.790980 0.611842i \(-0.790429\pi\)
\(578\) −12.0208 + 20.8207i −0.500000 + 0.866025i
\(579\) −32.2279 + 18.6068i −1.33935 + 0.773272i
\(580\) 87.0949i 3.61642i
\(581\) 7.86396 6.09823i 0.326252 0.252997i
\(582\) −28.2426 −1.17070
\(583\) −0.863961 1.49642i −0.0357816 0.0619756i
\(584\) −24.0000 13.8564i −0.993127 0.573382i
\(585\) 0 0
\(586\) −4.09188 + 2.36245i −0.169034 + 0.0975919i
\(587\) 30.5316i 1.26017i 0.776525 + 0.630087i \(0.216981\pi\)
−0.776525 + 0.630087i \(0.783019\pi\)
\(588\) 6.51472 + 23.3572i 0.268662 + 0.963234i
\(589\) 0 0
\(590\) −13.6066 23.5673i −0.560175 0.970251i
\(591\) −21.2132 12.2474i −0.872595 0.503793i
\(592\) 0 0
\(593\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(594\) 1.26080i 0.0517312i
\(595\) 0 0
\(596\) −5.65685 −0.231714
\(597\) 21.2132 + 36.7423i 0.868199 + 1.50376i
\(598\) 0 0
\(599\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 52.9706 30.5826i 2.16251 1.24853i
\(601\) 22.7628i 0.928516i 0.885700 + 0.464258i \(0.153679\pi\)
−0.885700 + 0.464258i \(0.846321\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −22.2132 38.4744i −0.903842 1.56550i
\(605\) 39.7279 + 22.9369i 1.61517 + 0.932519i
\(606\) −4.24264 + 7.34847i −0.172345 + 0.298511i
\(607\) −35.5919 + 20.5490i −1.44463 + 0.834058i −0.998154 0.0607380i \(-0.980655\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) 0 0
\(609\) 6.47056 + 47.2832i 0.262200 + 1.91601i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 1.27208 0.174080i 0.0512535 0.00701388i
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) −18.0000 31.1769i −0.724066 1.25412i
\(619\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(620\) 25.9706 44.9823i 1.04300 1.80653i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −34.2279 59.2845i −1.36912 2.37138i
\(626\) 30.0624 + 17.3566i 1.20154 + 0.693708i
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −37.0919 + 28.7635i −1.47778 + 1.14596i
\(631\) 20.7574 0.826337 0.413169 0.910654i \(-0.364422\pi\)
0.413169 + 0.910654i \(0.364422\pi\)
\(632\) 10.9289 + 18.9295i 0.434730 + 0.752974i
\(633\) 0 0
\(634\) −21.6066 + 37.4237i −0.858108 + 1.48629i
\(635\) 24.4706 14.1281i 0.971085 0.560656i
\(636\) 34.8872i 1.38337i
\(637\) 0 0
\(638\) 2.52691 0.100041
\(639\) 0 0
\(640\) 40.9706 + 23.6544i 1.61950 + 0.935021i
\(641\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 43.8198 25.2994i 1.72943 0.998487i
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(648\) 12.7279 22.0454i 0.500000 0.866025i
\(649\) 0.683766 0.394773i 0.0268402 0.0154962i
\(650\) 0 0
\(651\) −10.7574 + 26.3500i −0.421614 + 1.03274i
\(652\) 0 0
\(653\) −4.52082 7.83028i −0.176913 0.306423i 0.763909 0.645325i \(-0.223278\pi\)
−0.940822 + 0.338902i \(0.889945\pi\)
\(654\) 0 0
\(655\) 44.5919 77.2354i 1.74235 3.01784i
\(656\) 0 0
\(657\) 29.3939i 1.14676i
\(658\) 0 0
\(659\) −45.2548 −1.76288 −0.881439 0.472298i \(-0.843425\pi\)
−0.881439 + 0.472298i \(0.843425\pi\)
\(660\) 1.24264 + 2.15232i 0.0483697 + 0.0837788i
\(661\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 10.6385i 0.412854i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 25.8640 44.7977i 0.999959 1.73198i
\(670\) 0 0
\(671\) 0 0
\(672\) −24.0000 9.79796i −0.925820 0.377964i
\(673\) −50.9411 −1.96364 −0.981818 0.189824i \(-0.939208\pi\)
−0.981818 + 0.189824i \(0.939208\pi\)
\(674\) 25.7782 + 44.6491i 0.992938 + 1.71982i
\(675\) −56.1838 32.4377i −2.16251 1.24853i
\(676\) 13.0000 22.5167i 0.500000 0.866025i
\(677\) 24.6213 14.2151i 0.946274 0.546332i 0.0543526 0.998522i \(-0.482690\pi\)
0.891922 + 0.452190i \(0.149357\pi\)
\(678\) 0 0
\(679\) 24.1066 18.6938i 0.925126 0.717404i
\(680\) 0 0
\(681\) −25.7132 44.5366i −0.985332 1.70665i
\(682\) 1.30509 + 0.753492i 0.0499743 + 0.0288527i
\(683\) −21.0858 + 36.5217i −0.806825 + 1.39746i 0.108227 + 0.994126i \(0.465483\pi\)
−0.915052 + 0.403336i \(0.867851\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −21.0208 15.6245i −0.802578 0.596547i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(692\) 34.6410i 1.31685i
\(693\) −0.834524 1.07616i −0.0317009 0.0408799i
\(694\) −40.0000 −1.51838
\(695\) 0 0
\(696\) −44.1838 25.5095i −1.67478 0.966935i
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −24.9706 + 61.1651i −0.943799 + 2.31182i
\(701\) 51.3848 1.94078 0.970388 0.241551i \(-0.0776561\pi\)
0.970388 + 0.241551i \(0.0776561\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.686292 + 1.18869i −0.0258656 + 0.0448005i
\(705\) 0 0
\(706\) 0 0
\(707\) −1.24264 9.08052i −0.0467343 0.341508i
\(708\) −15.9411 −0.599104
\(709\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(710\) 0 0
\(711\) 11.5919 20.0777i 0.434730 0.752974i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 11.3137 + 19.5959i 0.422813 + 0.732334i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) 50.1785i 1.87004i
\(721\) 36.0000 + 14.6969i 1.34071 + 0.547343i
\(722\) 26.8701 1.00000
\(723\) 20.2279 + 35.0358i 0.752285 + 1.30300i
\(724\) 0 0
\(725\) −65.0122 + 112.604i −2.41449 + 4.18202i
\(726\) 23.2721 13.4361i 0.863708 0.498662i
\(727\) 28.6764i 1.06355i −0.846886 0.531775i \(-0.821525\pi\)
0.846886 0.531775i \(-0.178475\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 28.9706 + 50.1785i 1.07225 + 1.85719i
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(734\) 43.0762i 1.58997i
\(735\) 12.6213 49.1023i 0.465544 1.81117i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −23.0919 29.7781i −0.847730 1.09319i
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) −15.2132 26.3500i −0.557743 0.966039i
\(745\) 10.2426 + 5.91359i 0.375261 + 0.216657i
\(746\) 0 0
\(747\) 9.77208 5.64191i 0.357542 0.206427i
\(748\) 0 0
\(749\) −20.6569 + 50.5988i −0.754785 + 1.84884i
\(750\) −76.6690 −2.79956
\(751\) 25.8345 + 44.7467i 0.942715 + 1.63283i 0.760263 + 0.649616i \(0.225070\pi\)
0.182453 + 0.983215i \(0.441596\pi\)
\(752\) 0 0
\(753\) 17.7426 30.7312i 0.646578 1.11991i
\(754\) 0 0
\(755\) 92.8854i 3.38045i
\(756\) 3.72792 + 27.2416i 0.135583 + 0.990766i
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(762\) 16.5521i 0.599619i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 24.0000 13.8564i 0.866025 0.500000i
\(769\) 47.0116i 1.69528i 0.530572 + 0.847640i \(0.321977\pi\)
−0.530572 + 0.847640i \(0.678023\pi\)
\(770\) −2.48528 1.01461i −0.0895633 0.0365641i
\(771\) 0 0
\(772\) 21.4853 + 37.2136i 0.773272 + 1.33935i
\(773\) −45.0000 25.9808i −1.61854 0.934463i −0.987299 0.158874i \(-0.949213\pi\)
−0.631239 0.775589i \(-0.717453\pi\)
\(774\) 0 0
\(775\) −67.1543 + 38.7716i −2.41225 + 1.39272i
\(776\) 32.6118i 1.17070i
\(777\) 0 0
\(778\) 44.0000 1.57748
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 54.1138i 1.93387i
\(784\) 26.9706 7.52255i 0.963234 0.268662i
\(785\) 0 0
\(786\) −26.1213 45.2435i −0.931717 1.61378i
\(787\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(788\) −14.1421 + 24.4949i −0.503793 + 0.872595i
\(789\) 0 0
\(790\) 45.6998i 1.62592i
\(791\) 0 0