Properties

Label 168.2.ba.a.101.1
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 101.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 168.101
Dual form 168.2.ba.a.5.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-0.621320 + 0.358719i) q^{5} +2.44949i q^{6} +(-2.62132 - 0.358719i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-0.621320 + 0.358719i) q^{5} +2.44949i q^{6} +(-2.62132 - 0.358719i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(0.878680 + 0.507306i) q^{10} +(-2.91421 + 5.04757i) q^{11} +(3.00000 - 1.73205i) q^{12} +(1.41421 + 3.46410i) q^{14} +1.24264 q^{15} +(-2.00000 - 3.46410i) q^{16} +(2.12132 - 3.67423i) q^{18} -1.43488i q^{20} +(3.62132 + 2.80821i) q^{21} +8.24264 q^{22} +(-4.24264 - 2.44949i) q^{24} +(-2.24264 + 3.88437i) q^{25} -5.19615i q^{27} +(3.24264 - 4.18154i) q^{28} -7.58579 q^{29} +(-0.878680 - 1.52192i) q^{30} +(-9.62132 - 5.55487i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(8.74264 - 5.04757i) q^{33} +(1.75736 - 0.717439i) q^{35} -6.00000 q^{36} +(-1.75736 + 1.01461i) q^{40} +(0.878680 - 6.42090i) q^{42} +(-5.82843 - 10.0951i) q^{44} +(-1.86396 - 1.07616i) q^{45} +6.92820i q^{48} +(6.74264 + 1.88064i) q^{49} +6.34315 q^{50} +(2.03553 - 3.52565i) q^{53} +(-6.36396 + 3.67423i) q^{54} -4.18154i q^{55} +(-7.41421 - 1.01461i) q^{56} +(5.36396 + 9.29065i) q^{58} +(12.9853 + 7.49706i) q^{59} +(-1.24264 + 2.15232i) q^{60} +15.7116i q^{62} +(-3.00000 - 7.34847i) q^{63} +8.00000 q^{64} +(-12.3640 - 7.13834i) q^{66} +(-2.12132 - 1.64501i) q^{70} +(4.24264 + 7.34847i) q^{72} +(-8.48528 - 4.89898i) q^{73} +(6.72792 - 3.88437i) q^{75} +(9.44975 - 12.1859i) q^{77} +(8.86396 + 15.3528i) q^{79} +(2.48528 + 1.43488i) q^{80} +(-4.50000 + 7.79423i) q^{81} -13.5592i q^{83} +(-8.48528 + 3.46410i) q^{84} +(11.3787 + 6.56948i) q^{87} +(-8.24264 + 14.2767i) q^{88} +3.04384i q^{90} +(9.62132 + 16.6646i) q^{93} +(8.48528 - 4.89898i) q^{96} +8.06591i q^{97} +(-2.46447 - 9.58783i) q^{98} -17.4853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 6 q^{3} - 4 q^{4} + 6 q^{5} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) 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
\(5\) −0.621320 + 0.358719i −0.277863 + 0.160424i −0.632456 0.774597i \(-0.717953\pi\)
0.354593 + 0.935021i \(0.384620\pi\)
\(6\) 2.44949i 1.00000i
\(7\) −2.62132 0.358719i −0.990766 0.135583i
\(8\) 2.82843 1.00000
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0.878680 + 0.507306i 0.277863 + 0.160424i
\(11\) −2.91421 + 5.04757i −0.878668 + 1.52190i −0.0258656 + 0.999665i \(0.508234\pi\)
−0.852803 + 0.522233i \(0.825099\pi\)
\(12\) 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
\(15\) 1.24264 0.320848
\(16\) −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 \(0.833333\pi\)
\(20\) 1.43488i 0.320848i
\(21\) 3.62132 + 2.80821i 0.790237 + 0.612801i
\(22\) 8.24264 1.75734
\(23\) 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
\(25\) −2.24264 + 3.88437i −0.448528 + 0.776874i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 3.24264 4.18154i 0.612801 0.790237i
\(29\) −7.58579 −1.40865 −0.704323 0.709880i \(-0.748749\pi\)
−0.704323 + 0.709880i \(0.748749\pi\)
\(30\) −0.878680 1.52192i −0.160424 0.277863i
\(31\) −9.62132 5.55487i −1.72804 0.997684i −0.898027 0.439941i \(-0.854999\pi\)
−0.830014 0.557743i \(-0.811667\pi\)
\(32\) −2.82843 + 4.89898i −0.500000 + 0.866025i
\(33\) 8.74264 5.04757i 1.52190 0.878668i
\(34\) 0 0
\(35\) 1.75736 0.717439i 0.297048 0.121269i
\(36\) −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
\(40\) −1.75736 + 1.01461i −0.277863 + 0.160424i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0.878680 6.42090i 0.135583 0.990766i
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −5.82843 10.0951i −0.878668 1.52190i
\(45\) −1.86396 1.07616i −0.277863 0.160424i
\(46\) 0 0
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 6.92820i 1.00000i
\(49\) 6.74264 + 1.88064i 0.963234 + 0.268662i
\(50\) 6.34315 0.897056
\(51\) 0 0
\(52\) 0 0
\(53\) 2.03553 3.52565i 0.279602 0.484285i −0.691684 0.722200i \(-0.743131\pi\)
0.971286 + 0.237915i \(0.0764641\pi\)
\(54\) −6.36396 + 3.67423i −0.866025 + 0.500000i
\(55\) 4.18154i 0.563839i
\(56\) −7.41421 1.01461i −0.990766 0.135583i
\(57\) 0 0
\(58\) 5.36396 + 9.29065i 0.704323 + 1.21992i
\(59\) 12.9853 + 7.49706i 1.69054 + 0.976034i 0.954080 + 0.299552i \(0.0968372\pi\)
0.736460 + 0.676481i \(0.236496\pi\)
\(60\) −1.24264 + 2.15232i −0.160424 + 0.277863i
\(61\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(62\) 15.7116i 1.99537i
\(63\) −3.00000 7.34847i −0.377964 0.925820i
\(64\) 8.00000 1.00000
\(65\) 0 0
\(66\) −12.3640 7.13834i −1.52190 0.878668i
\(67\) 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 1.64501i −0.253546 0.196616i
\(71\) 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 −0.0869195 0.996215i \(-0.527702\pi\)
−0.906208 + 0.422833i \(0.861036\pi\)
\(74\) 0 0
\(75\) 6.72792 3.88437i 0.776874 0.448528i
\(76\) 0 0
\(77\) 9.44975 12.1859i 1.07690 1.38871i
\(78\) 0 0
\(79\) 8.86396 + 15.3528i 0.997274 + 1.72733i 0.562544 + 0.826767i \(0.309823\pi\)
0.434730 + 0.900561i \(0.356844\pi\)
\(80\) 2.48528 + 1.43488i 0.277863 + 0.160424i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 13.5592i 1.48832i −0.668002 0.744160i \(-0.732850\pi\)
0.668002 0.744160i \(-0.267150\pi\)
\(84\) −8.48528 + 3.46410i −0.925820 + 0.377964i
\(85\) 0 0
\(86\) 0 0
\(87\) 11.3787 + 6.56948i 1.21992 + 0.704323i
\(88\) −8.24264 + 14.2767i −0.878668 + 1.52190i
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) 3.04384i 0.320848i
\(91\) 0 0
\(92\) 0 0
\(93\) 9.62132 + 16.6646i 0.997684 + 1.72804i
\(94\) 0 0
\(95\) 0 0
\(96\) 8.48528 4.89898i 0.866025 0.500000i
\(97\) 8.06591i 0.818969i 0.912317 + 0.409484i \(0.134291\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) −2.46447 9.58783i −0.248949 0.968517i
\(99\) −17.4853 −1.75734
\(100\) −4.48528 7.76874i −0.448528 0.776874i
\(101\) −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 −0.971925 0.235291i \(-0.924396\pi\)
−0.282194 + 0.959357i \(0.591062\pi\)
\(104\) 0 0
\(105\) −3.25736 0.445759i −0.317886 0.0435017i
\(106\) −5.75736 −0.559204
\(107\) 4.67157 + 8.09140i 0.451618 + 0.782225i 0.998487 0.0549930i \(-0.0175137\pi\)
−0.546869 + 0.837218i \(0.684180\pi\)
\(108\) 9.00000 + 5.19615i 0.866025 + 0.500000i
\(109\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(110\) −5.12132 + 2.95680i −0.488299 + 0.281919i
\(111\) 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
\(116\) 7.58579 13.1390i 0.704323 1.21992i
\(117\) 0 0
\(118\) 21.2049i 1.95207i
\(119\) 0 0
\(120\) 3.51472 0.320848
\(121\) −11.4853 19.8931i −1.04412 1.80846i
\(122\) 0 0
\(123\) 0 0
\(124\) 19.2426 11.1097i 1.72804 0.997684i
\(125\) 6.80511i 0.608668i
\(126\) −6.87868 + 8.87039i −0.612801 + 0.790237i
\(127\) 15.2426 1.35257 0.676283 0.736642i \(-0.263590\pi\)
0.676283 + 0.736642i \(0.263590\pi\)
\(128\) −5.65685 9.79796i −0.500000 0.866025i
\(129\) 0 0
\(130\) 0 0
\(131\) −15.4706 + 8.93193i −1.35167 + 0.780387i −0.988483 0.151330i \(-0.951644\pi\)
−0.363186 + 0.931717i \(0.618311\pi\)
\(132\) 20.1903i 1.75734i
\(133\) 0 0
\(134\) 0 0
\(135\) 1.86396 + 3.22848i 0.160424 + 0.277863i
\(136\) 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 \(0.5\pi\)
\(140\) −0.514719 + 3.76127i −0.0435017 + 0.317886i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 6.00000 10.3923i 0.500000 0.866025i
\(145\) 4.71320 2.72117i 0.391410 0.225981i
\(146\) 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 0.802265 0.596968i \(-0.203628\pi\)
−0.918122 + 0.396298i \(0.870295\pi\)
\(150\) −9.51472 5.49333i −0.776874 0.448528i
\(151\) 10.1066 17.5051i 0.822464 1.42455i −0.0813788 0.996683i \(-0.525932\pi\)
0.903842 0.427865i \(-0.140734\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −21.6066 2.95680i −1.74111 0.238265i
\(155\) 7.97056 0.640211
\(156\) 0 0
\(157\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(158\) 12.5355 21.7122i 0.997274 1.72733i
\(159\) −6.10660 + 3.52565i −0.484285 + 0.279602i
\(160\) 4.05845i 0.320848i
\(161\) 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
\(165\) −3.62132 + 6.27231i −0.281919 + 0.488299i
\(166\) −16.6066 + 9.58783i −1.28892 + 0.744160i
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 10.2426 + 7.94282i 0.790237 + 0.612801i
\(169\) −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 \(0.562111\pi\)
\(174\) 18.5813i 1.40865i
\(175\) 7.27208 9.37769i 0.549717 0.708887i
\(176\) 23.3137 1.75734
\(177\) −12.9853 22.4912i −0.976034 1.69054i
\(178\) 0 0
\(179\) −5.65685 + 9.79796i −0.422813 + 0.732334i −0.996213 0.0869415i \(-0.972291\pi\)
0.573400 + 0.819275i \(0.305624\pi\)
\(180\) 3.72792 2.15232i 0.277863 0.160424i
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 13.6066 23.5673i 0.997684 1.72804i
\(187\) 0 0
\(188\) 0 0
\(189\) −1.86396 + 13.6208i −0.135583 + 0.990766i
\(190\) 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
\(193\) 2.25736 3.90986i 0.162488 0.281438i −0.773272 0.634074i \(-0.781381\pi\)
0.935760 + 0.352636i \(0.114715\pi\)
\(194\) 9.87868 5.70346i 0.709248 0.409484i
\(195\) 0 0
\(196\) −10.0000 + 9.79796i −0.714286 + 0.699854i
\(197\) −14.1421 −1.00759 −0.503793 0.863825i \(-0.668062\pi\)
−0.503793 + 0.863825i \(0.668062\pi\)
\(198\) 12.3640 + 21.4150i 0.878668 + 1.52190i
\(199\) 21.2132 + 12.2474i 1.50376 + 0.868199i 0.999990 + 0.00436292i \(0.00138876\pi\)
0.503774 + 0.863836i \(0.331945\pi\)
\(200\) −6.34315 + 10.9867i −0.448528 + 0.776874i
\(201\) 0 0
\(202\) 4.89898i 0.344691i
\(203\) 19.8848 + 2.72117i 1.39564 + 0.190989i
\(204\) 0 0
\(205\) 0 0
\(206\) 18.0000 + 10.3923i 1.25412 + 0.724066i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 1.75736 + 4.30463i 0.121269 + 0.297048i
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 4.07107 + 7.05130i 0.279602 + 0.484285i
\(213\) 0 0
\(214\) 6.60660 11.4430i 0.451618 0.782225i
\(215\) 0 0
\(216\) 14.6969i 1.00000i
\(217\) 23.2279 + 18.0125i 1.57681 + 1.22277i
\(218\) 0 0
\(219\) 8.48528 + 14.6969i 0.573382 + 0.993127i
\(220\) 7.24264 + 4.18154i 0.488299 + 0.281919i
\(221\) 0 0
\(222\) 0 0
\(223\) 15.1682i 1.01574i 0.861435 + 0.507869i \(0.169566\pi\)
−0.861435 + 0.507869i \(0.830434\pi\)
\(224\) 9.17157 11.8272i 0.612801 0.790237i
\(225\) −13.4558 −0.897056
\(226\) 0 0
\(227\) −16.7132 9.64937i −1.10929 0.640451i −0.170648 0.985332i \(-0.554586\pi\)
−0.938647 + 0.344881i \(0.887919\pi\)
\(228\) 0 0
\(229\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(230\) 0 0
\(231\) −24.7279 + 10.0951i −1.62698 + 0.664211i
\(232\) −21.4558 −1.40865
\(233\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −25.9706 + 14.9941i −1.69054 + 0.976034i
\(237\) 30.7057i 1.99455i
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) −2.48528 4.30463i −0.160424 0.277863i
\(241\) 5.22792 + 3.01834i 0.336760 + 0.194429i 0.658838 0.752285i \(-0.271048\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) −16.2426 + 28.1331i −1.04412 + 1.80846i
\(243\) 13.5000 7.79423i 0.866025 0.500000i
\(244\) 0 0
\(245\) −4.86396 + 1.25024i −0.310747 + 0.0798748i
\(246\) 0 0
\(247\) 0 0
\(248\) −27.2132 15.7116i −1.72804 0.997684i
\(249\) −11.7426 + 20.3389i −0.744160 + 1.28892i
\(250\) −8.33452 + 4.81194i −0.527122 + 0.304334i
\(251\) 10.6895i 0.674714i 0.941377 + 0.337357i \(0.109533\pi\)
−0.941377 + 0.337357i \(0.890467\pi\)
\(252\) 15.7279 + 2.15232i 0.990766 + 0.135583i
\(253\) 0 0
\(254\) −10.7782 18.6683i −0.676283 1.17136i
\(255\) 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
\(261\) −11.3787 19.7085i −0.704323 1.21992i
\(262\) 21.8787 + 12.6317i 1.35167 + 0.780387i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 24.7279 14.2767i 1.52190 0.878668i
\(265\) 2.92074i 0.179420i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 27.8345 + 16.0703i 1.69710 + 0.979822i 0.948487 + 0.316815i \(0.102613\pi\)
0.748614 + 0.663007i \(0.230720\pi\)
\(270\) 2.63604 4.56575i 0.160424 0.277863i
\(271\) −27.1066 + 15.6500i −1.64661 + 0.950670i −0.668202 + 0.743980i \(0.732936\pi\)
−0.978406 + 0.206691i \(0.933731\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −13.0711 22.6398i −0.788215 1.36523i
\(276\) 0 0
\(277\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(278\) 0 0
\(279\) 33.3292i 1.99537i
\(280\) 4.97056 2.02922i 0.297048 0.121269i
\(281\) 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
\(290\) −6.66548 3.84831i −0.391410 0.225981i
\(291\) 6.98528 12.0989i 0.409484 0.709248i
\(292\) 16.9706 9.79796i 0.993127 0.573382i
\(293\) 27.8359i 1.62619i 0.582130 + 0.813095i \(0.302219\pi\)
−0.582130 + 0.813095i \(0.697781\pi\)
\(294\) −4.60660 + 16.5160i −0.268662 + 0.963234i
\(295\) −10.7574 −0.626318
\(296\) 0 0
\(297\) 26.2279 + 15.1427i 1.52190 + 0.878668i
\(298\) −2.00000 + 3.46410i −0.115857 + 0.200670i
\(299\) 0 0
\(300\) 15.5375i 0.897056i
\(301\) 0 0
\(302\) −28.5858 −1.64493
\(303\) 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 \(0.5\pi\)
\(308\) 11.6569 + 28.5533i 0.664211 + 1.62698i
\(309\) 25.4558 1.44813
\(310\) −5.63604 9.76191i −0.320106 0.554439i
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0 0
\(313\) 29.7426 17.1719i 1.68115 0.970614i 0.720257 0.693708i \(-0.244024\pi\)
0.960897 0.276907i \(-0.0893093\pi\)
\(314\) 0 0
\(315\) 4.50000 + 3.48960i 0.253546 + 0.196616i
\(316\) −35.4558 −1.99455
\(317\) −0.278175 0.481813i −0.0156238 0.0270613i 0.858108 0.513470i \(-0.171640\pi\)
−0.873732 + 0.486408i \(0.838307\pi\)
\(318\) 8.63604 + 4.98602i 0.484285 + 0.279602i
\(319\) 22.1066 38.2898i 1.23773 2.14381i
\(320\) −4.97056 + 2.86976i −0.277863 + 0.160424i
\(321\) 16.1828i 0.903236i
\(322\) 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
\(330\) 10.2426 0.563839
\(331\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) 23.4853 + 13.5592i 1.28892 + 0.744160i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 2.48528 18.1610i 0.135583 0.990766i
\(337\) −14.4558 −0.787460 −0.393730 0.919226i \(-0.628816\pi\)
−0.393730 + 0.919226i \(0.628816\pi\)
\(338\) 9.19239 + 15.9217i 0.500000 + 0.866025i
\(339\) 0 0
\(340\) 0 0
\(341\) 56.0772 32.3762i 3.03675 1.75327i
\(342\) 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 \(-0.558929\pi\)
0.943264 0.332043i \(-0.107738\pi\)
\(348\) −22.7574 + 13.1390i −1.21992 + 0.704323i
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) −16.6274 2.27541i −0.888773 0.121626i
\(351\) 0 0
\(352\) −16.4853 28.5533i −0.878668 1.52190i
\(353\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(354\) −18.3640 + 31.8073i −0.976034 + 1.69054i
\(355\) 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 \(0.333333\pi\)
\(360\) −5.27208 3.04384i −0.277863 0.160424i
\(361\) 9.50000 16.4545i 0.500000 0.866025i
\(362\) 0 0
\(363\) 39.7862i 2.08823i
\(364\) 0 0
\(365\) 7.02944 0.367938
\(366\) 0 0
\(367\) −30.6213 17.6792i −1.59842 0.922848i −0.991792 0.127862i \(-0.959188\pi\)
−0.606628 0.794986i \(-0.707478\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −6.60051 + 8.51167i −0.342681 + 0.441904i
\(372\) −38.4853 −1.99537
\(373\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) 0 0
\(375\) −5.89340 + 10.2077i −0.304334 + 0.527122i
\(376\) 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
\(381\) −22.8640 13.2005i −1.17136 0.676283i
\(382\) 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 + 10.9612i −0.0764471 + 0.558632i
\(386\) −6.38478 −0.324977
\(387\) 0 0
\(388\) −13.9706 8.06591i −0.709248 0.409484i
\(389\) −15.5563 + 26.9444i −0.788738 + 1.36613i 0.138002 + 0.990432i \(0.455932\pi\)
−0.926740 + 0.375703i \(0.877401\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 19.0711 + 5.31925i 0.963234 + 0.268662i
\(393\) 30.9411 1.56077
\(394\) 10.0000 + 17.3205i 0.503793 + 0.872595i
\(395\) −11.0147 6.35935i −0.554211 0.319974i
\(396\) 17.4853 30.2854i 0.878668 1.52190i
\(397\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(398\) 34.6410i 1.73640i
\(399\) 0 0
\(400\) 17.9411 0.897056
\(401\) 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
\(405\) 6.45695i 0.320848i
\(406\) −10.7279 26.2779i −0.532418 1.30415i
\(407\) 0 0
\(408\) 0 0
\(409\) −24.4706 14.1281i −1.20999 0.698589i −0.247234 0.968956i \(-0.579522\pi\)
−0.962757 + 0.270367i \(0.912855\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 29.3939i 1.44813i
\(413\) −31.3492 24.3103i −1.54260 1.19623i
\(414\) 0 0
\(415\) 4.86396 + 8.42463i 0.238762 + 0.413549i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10.3923i 0.507697i −0.967244 0.253849i \(-0.918303\pi\)
0.967244 0.253849i \(-0.0816965\pi\)
\(420\) 4.02944 5.19615i 0.196616 0.253546i
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 5.75736 9.97204i 0.279602 0.484285i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −18.6863 −0.903236
\(429\) 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 \(0.390791\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 5.63604 41.1850i 0.270539 1.97694i
\(435\) −9.42641 −0.451962
\(436\) 0 0
\(437\) 0 0
\(438\) 12.0000 20.7846i 0.573382 0.993127i
\(439\) 14.8934 8.59871i 0.710823 0.410394i −0.100543 0.994933i \(-0.532058\pi\)
0.811366 + 0.584539i \(0.198725\pi\)
\(440\) 11.8272i 0.563839i
\(441\) 5.22792 + 20.3389i 0.248949 + 0.968517i
\(442\) 0 0
\(443\) −6.42893 11.1352i −0.305448 0.529051i 0.671913 0.740630i \(-0.265473\pi\)
−0.977361 + 0.211579i \(0.932139\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 18.5772 10.7255i 0.879654 0.507869i
\(447\) 4.89898i 0.231714i
\(448\) −20.9706 2.86976i −0.990766 0.135583i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 9.51472 + 16.4800i 0.448528 + 0.776874i
\(451\) 0 0
\(452\) 0 0
\(453\) −30.3198 + 17.5051i −1.42455 + 0.822464i
\(454\) 27.2925i 1.28090i
\(455\) 0 0
\(456\) 0 0
\(457\) 1.01472 + 1.75754i 0.0474665 + 0.0822145i 0.888783 0.458329i \(-0.151552\pi\)
−0.841316 + 0.540544i \(0.818219\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 38.1051i 1.77473i 0.461065 + 0.887366i \(0.347467\pi\)
−0.461065 + 0.887366i \(0.652533\pi\)
\(462\) 29.8492 + 23.1471i 1.38871 + 1.07690i
\(463\) −26.0000 −1.20832 −0.604161 0.796862i \(-0.706492\pi\)
−0.604161 + 0.796862i \(0.706492\pi\)
\(464\) 15.1716 + 26.2779i 0.704323 + 1.21992i
\(465\) −11.9558 6.90271i −0.554439 0.320106i
\(466\) 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
\(472\) 36.7279 + 21.2049i 1.69054 + 0.976034i
\(473\) 0 0
\(474\) −37.6066 + 21.7122i −1.72733 + 0.997274i
\(475\) 0 0
\(476\) 0 0
\(477\) 12.2132 0.559204
\(478\) 0 0
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) −3.51472 + 6.08767i −0.160424 + 0.277863i
\(481\) 0 0
\(482\) 8.53716i 0.388857i
\(483\) 0 0
\(484\) 45.9411 2.08823
\(485\) −2.89340 5.01151i −0.131382 0.227561i
\(486\) −19.0919 11.0227i −0.866025 0.500000i
\(487\) −19.5919 + 33.9341i −0.887793 + 1.53770i −0.0453143 + 0.998973i \(0.514429\pi\)
−0.842479 + 0.538730i \(0.818904\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 4.97056 + 5.07306i 0.224547 + 0.229177i
\(491\) 44.3137 1.99985 0.999925 0.0122607i \(-0.00390281\pi\)
0.999925 + 0.0122607i \(0.00390281\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 10.8640 6.27231i 0.488299 0.281919i
\(496\) 44.4390i 1.99537i
\(497\) 0 0
\(498\) 33.2132 1.48832
\(499\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(500\) 11.7868 + 6.80511i 0.527122 + 0.304334i
\(501\) 0 0
\(502\) 13.0919 7.55860i 0.584319 0.337357i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) −8.48528 20.7846i −0.377964 0.925820i
\(505\) 2.48528 0.110594
\(506\) 0 0
\(507\) 19.5000 + 11.2583i 0.866025 + 0.500000i
\(508\) −15.2426 + 26.4010i −0.676283 + 1.17136i
\(509\) −21.6213 + 12.4831i −0.958348 + 0.553303i −0.895664 0.444731i \(-0.853299\pi\)
−0.0626839 + 0.998033i \(0.519966\pi\)
\(510\) 0 0
\(511\) 20.4853 + 15.8856i 0.906215 + 0.702739i
\(512\) 22.6274 1.00000
\(513\) 0 0
\(514\) 0 0
\(515\) 5.27208 9.13151i 0.232316 0.402382i
\(516\) 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 \(0.166667\pi\)
\(522\) −16.0919 + 27.8720i −0.704323 + 1.21992i
\(523\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(524\) 35.7277i 1.56077i
\(525\) −19.0294 + 7.76874i −0.830513 + 0.339055i
\(526\) 0 0
\(527\) 0 0
\(528\) −34.9706 20.1903i −1.52190 0.878668i
\(529\) −11.5000 + 19.9186i −0.500000 + 0.866025i
\(530\) 3.57716 2.06528i 0.155382 0.0897099i
\(531\) 44.9823i 1.95207i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −5.80509 3.35157i −0.250976 0.144901i
\(536\) 0 0
\(537\) 16.9706 9.79796i 0.732334 0.422813i
\(538\) 45.4536i 1.95964i
\(539\) −29.1421 + 28.5533i −1.25524 + 1.22988i
\(540\) −7.45584 −0.320848
\(541\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(542\) 38.3345 + 22.1324i 1.64661 + 0.950670i
\(543\) 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
\(550\) −18.4853 + 32.0174i −0.788215 + 1.36523i
\(551\) 0 0
\(552\) 0 0
\(553\) −17.7279 43.4244i −0.753868 1.84659i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 23.0355 39.8987i 0.976047 1.69056i 0.299611 0.954062i \(-0.403143\pi\)
0.676436 0.736501i \(-0.263523\pi\)
\(558\) −40.8198 + 23.5673i −1.72804 + 0.997684i
\(559\) 0 0
\(560\) −6.00000 4.65279i −0.253546 0.196616i
\(561\) 0 0
\(562\) 0 0
\(563\) −37.7132 21.7737i −1.58942 0.917653i −0.993402 0.114684i \(-0.963415\pi\)
−0.596020 0.802970i \(-0.703252\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 14.5919 18.8169i 0.612801 0.790237i
\(568\) 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
\(577\) −15.7721 9.10601i −0.656600 0.379088i 0.134380 0.990930i \(-0.457096\pi\)
−0.790980 + 0.611842i \(0.790429\pi\)
\(578\) 12.0208 20.8207i 0.500000 0.866025i
\(579\) −6.77208 + 3.90986i −0.281438 + 0.162488i
\(580\) 10.8847i 0.451962i
\(581\) −4.86396 + 35.5431i −0.201791 + 1.47458i
\(582\) −19.7574 −0.818969
\(583\) 11.8640 + 20.5490i 0.491355 + 0.851052i
\(584\) −24.0000 13.8564i −0.993127 0.573382i
\(585\) 0 0
\(586\) 34.0919 19.6830i 1.40832 0.813095i
\(587\) 47.8521i 1.97507i −0.157409 0.987534i \(-0.550314\pi\)
0.157409 0.987534i \(-0.449686\pi\)
\(588\) 23.4853 6.03668i 0.968517 0.248949i
\(589\) 0 0
\(590\) 7.60660 + 13.1750i 0.313159 + 0.542407i
\(591\) 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 \(0.833333\pi\)
\(594\) 42.8300i 1.75734i
\(595\) 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 \(0.666667\pi\)
\(600\) 19.0294 10.9867i 0.776874 0.448528i
\(601\) 26.2269i 1.06982i −0.844909 0.534910i \(-0.820346\pi\)
0.844909 0.534910i \(-0.179654\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 20.2132 + 35.0103i 0.822464 + 1.42455i
\(605\) 14.2721 + 8.23999i 0.580242 + 0.335003i
\(606\) 4.24264 7.34847i 0.172345 0.298511i
\(607\) 2.59188 1.49642i 0.105201 0.0607380i −0.446476 0.894795i \(-0.647321\pi\)
0.551678 + 0.834058i \(0.313988\pi\)
\(608\) 0 0
\(609\) −27.4706 21.3025i −1.11316 0.863220i
\(610\) 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
\(616\) 26.7279 34.4669i 1.07690 1.38871i
\(617\) 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 \(0.166667\pi\)
\(620\) −7.97056 + 13.8054i −0.320106 + 0.554439i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −8.77208 15.1937i −0.350883 0.607747i
\(626\) −42.0624 24.2848i −1.68115 0.970614i
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 1.09188 7.97887i 0.0435017 0.317886i
\(631\) 29.2426 1.16413 0.582066 0.813142i \(-0.302245\pi\)
0.582066 + 0.813142i \(0.302245\pi\)
\(632\) 25.0711 + 43.4244i 0.997274 + 1.72733i
\(633\) 0 0
\(634\) −0.393398 + 0.681386i −0.0156238 + 0.0270613i
\(635\) −9.47056 + 5.46783i −0.375828 + 0.216984i
\(636\) 14.1026i 0.559204i
\(637\) 0 0
\(638\) −62.5269 −2.47546
\(639\) 0 0
\(640\) 7.02944 + 4.05845i 0.277863 + 0.160424i
\(641\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) −19.8198 + 11.4430i −0.782225 + 0.451618i
\(643\) 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
\(649\) −75.6838 + 43.6960i −2.97085 + 1.71522i
\(650\) 0 0
\(651\) −19.2426 47.1347i −0.754179 1.84735i
\(652\) 0 0
\(653\) 19.5208 + 33.8110i 0.763909 + 1.32313i 0.940822 + 0.338902i \(0.110055\pi\)
−0.176913 + 0.984226i \(0.556611\pi\)
\(654\) 0 0
\(655\) 6.40812 11.0992i 0.250386 0.433681i
\(656\) 0 0
\(657\) 29.3939i 1.14676i
\(658\) 0 0
\(659\) 45.2548 1.76288 0.881439 0.472298i \(-0.156575\pi\)
0.881439 + 0.472298i \(0.156575\pi\)
\(660\) −7.24264 12.5446i −0.281919 0.488299i
\(661\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 38.3513i 1.48832i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 13.1360 22.7523i 0.507869 0.879654i
\(670\) 0 0
\(671\) 0 0
\(672\) −24.0000 + 9.79796i −0.925820 + 0.377964i
\(673\) 16.9411 0.653032 0.326516 0.945192i \(-0.394125\pi\)
0.326516 + 0.945192i \(0.394125\pi\)
\(674\) 10.2218 + 17.7047i 0.393730 + 0.681960i
\(675\) 20.1838 + 11.6531i 0.776874 + 0.448528i
\(676\) 13.0000 22.5167i 0.500000 0.866025i
\(677\) 20.3787 11.7656i 0.783216 0.452190i −0.0543526 0.998522i \(-0.517310\pi\)
0.837569 + 0.546332i \(0.183976\pi\)
\(678\) 0 0
\(679\) 2.89340 21.1433i 0.111038 0.811407i
\(680\) 0 0
\(681\) 16.7132 + 28.9481i 0.640451 + 1.10929i
\(682\) −79.3051 45.7868i −3.03675 1.75327i
\(683\) −23.9142 + 41.4206i −0.915052 + 1.58492i −0.108227 + 0.994126i \(0.534517\pi\)
−0.806825 + 0.590790i \(0.798816\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 3.02082 + 26.0168i 0.115335 + 0.993327i
\(687\) 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
\(693\) 45.8345 + 6.27231i 1.74111 + 0.238265i
\(694\) −40.0000 −1.51838
\(695\) 0 0
\(696\) 32.1838 + 18.5813i 1.21992 + 0.704323i
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 8.97056 + 21.9733i 0.339055 + 0.830513i
\(701\) 14.6152 0.552009 0.276005 0.961156i \(-0.410989\pi\)
0.276005 + 0.961156i \(0.410989\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −23.3137 + 40.3805i −0.878668 + 1.52190i
\(705\) 0 0
\(706\) 0 0
\(707\) 7.24264 + 5.61642i 0.272388 + 0.211227i
\(708\) 51.9411 1.95207
\(709\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(710\) 0 0
\(711\) −26.5919 + 46.0585i −0.997274 + 1.72733i
\(712\) 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 \(0.833333\pi\)
\(720\) 8.60927i 0.320848i
\(721\) 36.0000 14.6969i 1.34071 0.547343i
\(722\) −26.8701 −1.00000
\(723\) −5.22792 9.05503i −0.194429 0.336760i
\(724\) 0 0
\(725\) 17.0122 29.4660i 0.631817 1.09434i
\(726\) 48.7279 28.1331i 1.80846 1.04412i
\(727\) 25.2123i 0.935074i 0.883974 + 0.467537i \(0.154858\pi\)
−0.883974 + 0.467537i \(0.845142\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) −4.97056 8.60927i −0.183969 0.318643i
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(734\) 50.0044i 1.84570i
\(735\) 8.37868 + 2.33696i 0.309052 + 0.0861999i
\(736\) 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
\(742\) 15.0919 + 2.06528i 0.554040 + 0.0758187i
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 27.2132 + 47.1347i 0.997684 + 1.72804i
\(745\) 1.75736 + 1.01461i 0.0643847 + 0.0371725i
\(746\) 0 0
\(747\) 35.2279 20.3389i 1.28892 0.744160i
\(748\) 0 0
\(749\) −9.34315 22.8859i −0.341391 0.836234i
\(750\) 16.6690 0.608668
\(751\) −20.8345 36.0865i −0.760263 1.31681i −0.942715 0.333599i \(-0.891737\pi\)
0.182453 0.983215i \(-0.441596\pi\)
\(752\) 0 0
\(753\) 9.25736 16.0342i 0.337357 0.584319i
\(754\) 0 0
\(755\) 14.5017i 0.527772i
\(756\) −21.7279 16.8493i −0.790237 0.612801i
\(757\) 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 \(0.833333\pi\)
\(762\) 37.3367i 1.35257i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 24.0000 13.8564i 0.866025 0.500000i
\(769\) 1.97824i 0.0713370i −0.999364 0.0356685i \(-0.988644\pi\)
0.999364 0.0356685i \(-0.0113561\pi\)
\(770\) 14.4853 5.91359i 0.522013 0.213111i
\(771\) 0 0
\(772\) 4.51472 + 7.81972i 0.162488 + 0.281438i
\(773\) −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
\(775\) 43.1543 24.9152i 1.55015 0.894979i
\(776\) 22.8138i 0.818969i
\(777\) 0 0
\(778\) 44.0000 1.57748
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 39.4169i 1.40865i
\(784\) −6.97056 27.1185i −0.248949 0.968517i
\(785\) 0 0
\(786\) −21.8787 37.8950i −0.780387 1.35167i
\(787\) 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
\(790\) 17.9870i 0.639947i
\(791\) 0 0