Properties

Label 1176.2.q.n.961.1
Level $1176$
Weight $2$
Character 1176.961
Analytic conductor $9.390$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1176.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.39040727770\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1176.961
Dual form 1176.2.q.n.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(-1.70711 + 2.95680i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(-1.70711 + 2.95680i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(-0.414214 - 0.717439i) q^{11} -4.24264 q^{13} -3.41421 q^{15} +(-3.70711 - 6.42090i) q^{17} +(-3.41421 + 5.91359i) q^{19} +(2.41421 - 4.18154i) q^{23} +(-3.32843 - 5.76500i) q^{25} -1.00000 q^{27} +2.82843 q^{29} +(1.41421 + 2.44949i) q^{31} +(0.414214 - 0.717439i) q^{33} +(0.828427 - 1.43488i) q^{37} +(-2.12132 - 3.67423i) q^{39} +10.2426 q^{41} -11.3137 q^{43} +(-1.70711 - 2.95680i) q^{45} +(2.24264 - 3.88437i) q^{47} +(3.70711 - 6.42090i) q^{51} +(1.00000 + 1.73205i) q^{53} +2.82843 q^{55} -6.82843 q^{57} +(-4.24264 - 7.34847i) q^{59} +(-5.53553 + 9.58783i) q^{61} +(7.24264 - 12.5446i) q^{65} +(-5.65685 - 9.79796i) q^{67} +4.82843 q^{69} -10.4853 q^{71} +(-3.87868 - 6.71807i) q^{73} +(3.32843 - 5.76500i) q^{75} +(-6.82843 + 11.8272i) q^{79} +(-0.500000 - 0.866025i) q^{81} -4.00000 q^{83} +25.3137 q^{85} +(1.41421 + 2.44949i) q^{87} +(-2.87868 + 4.98602i) q^{89} +(-1.41421 + 2.44949i) q^{93} +(-11.6569 - 20.1903i) q^{95} -0.242641 q^{97} +0.828427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} - 4q^{5} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{3} - 4q^{5} - 2q^{9} + 4q^{11} - 8q^{15} - 12q^{17} - 8q^{19} + 4q^{23} - 2q^{25} - 4q^{27} - 4q^{33} - 8q^{37} + 24q^{41} - 4q^{45} - 8q^{47} + 12q^{51} + 4q^{53} - 16q^{57} - 8q^{61} + 12q^{65} + 8q^{69} - 8q^{71} - 24q^{73} + 2q^{75} - 16q^{79} - 2q^{81} - 16q^{83} + 56q^{85} - 20q^{89} - 24q^{95} + 16q^{97} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times\).

\(n\) \(295\) \(589\) \(785\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) −1.70711 + 2.95680i −0.763441 + 1.32232i 0.177625 + 0.984098i \(0.443158\pi\)
−0.941067 + 0.338221i \(0.890175\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −0.414214 0.717439i −0.124890 0.216316i 0.796800 0.604243i \(-0.206524\pi\)
−0.921690 + 0.387927i \(0.873191\pi\)
\(12\) 0 0
\(13\) −4.24264 −1.17670 −0.588348 0.808608i \(-0.700222\pi\)
−0.588348 + 0.808608i \(0.700222\pi\)
\(14\) 0 0
\(15\) −3.41421 −0.881546
\(16\) 0 0
\(17\) −3.70711 6.42090i −0.899105 1.55730i −0.828640 0.559782i \(-0.810885\pi\)
−0.0704656 0.997514i \(-0.522449\pi\)
\(18\) 0 0
\(19\) −3.41421 + 5.91359i −0.783274 + 1.35667i 0.146750 + 0.989174i \(0.453119\pi\)
−0.930025 + 0.367497i \(0.880215\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.41421 4.18154i 0.503398 0.871911i −0.496594 0.867983i \(-0.665416\pi\)
0.999992 0.00392850i \(-0.00125049\pi\)
\(24\) 0 0
\(25\) −3.32843 5.76500i −0.665685 1.15300i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 2.82843 0.525226 0.262613 0.964901i \(-0.415416\pi\)
0.262613 + 0.964901i \(0.415416\pi\)
\(30\) 0 0
\(31\) 1.41421 + 2.44949i 0.254000 + 0.439941i 0.964623 0.263631i \(-0.0849203\pi\)
−0.710623 + 0.703573i \(0.751587\pi\)
\(32\) 0 0
\(33\) 0.414214 0.717439i 0.0721053 0.124890i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0.828427 1.43488i 0.136193 0.235892i −0.789860 0.613287i \(-0.789847\pi\)
0.926052 + 0.377395i \(0.123180\pi\)
\(38\) 0 0
\(39\) −2.12132 3.67423i −0.339683 0.588348i
\(40\) 0 0
\(41\) 10.2426 1.59963 0.799816 0.600245i \(-0.204930\pi\)
0.799816 + 0.600245i \(0.204930\pi\)
\(42\) 0 0
\(43\) −11.3137 −1.72532 −0.862662 0.505781i \(-0.831205\pi\)
−0.862662 + 0.505781i \(0.831205\pi\)
\(44\) 0 0
\(45\) −1.70711 2.95680i −0.254480 0.440773i
\(46\) 0 0
\(47\) 2.24264 3.88437i 0.327123 0.566593i −0.654817 0.755788i \(-0.727254\pi\)
0.981940 + 0.189194i \(0.0605876\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 3.70711 6.42090i 0.519099 0.899105i
\(52\) 0 0
\(53\) 1.00000 + 1.73205i 0.137361 + 0.237915i 0.926497 0.376303i \(-0.122805\pi\)
−0.789136 + 0.614218i \(0.789471\pi\)
\(54\) 0 0
\(55\) 2.82843 0.381385
\(56\) 0 0
\(57\) −6.82843 −0.904447
\(58\) 0 0
\(59\) −4.24264 7.34847i −0.552345 0.956689i −0.998105 0.0615367i \(-0.980400\pi\)
0.445760 0.895152i \(-0.352933\pi\)
\(60\) 0 0
\(61\) −5.53553 + 9.58783i −0.708752 + 1.22760i 0.256568 + 0.966526i \(0.417408\pi\)
−0.965320 + 0.261069i \(0.915925\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 7.24264 12.5446i 0.898339 1.55597i
\(66\) 0 0
\(67\) −5.65685 9.79796i −0.691095 1.19701i −0.971480 0.237124i \(-0.923795\pi\)
0.280385 0.959888i \(-0.409538\pi\)
\(68\) 0 0
\(69\) 4.82843 0.581274
\(70\) 0 0
\(71\) −10.4853 −1.24437 −0.622187 0.782869i \(-0.713756\pi\)
−0.622187 + 0.782869i \(0.713756\pi\)
\(72\) 0 0
\(73\) −3.87868 6.71807i −0.453965 0.786291i 0.544663 0.838655i \(-0.316658\pi\)
−0.998628 + 0.0523644i \(0.983324\pi\)
\(74\) 0 0
\(75\) 3.32843 5.76500i 0.384334 0.665685i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −6.82843 + 11.8272i −0.768258 + 1.33066i 0.170249 + 0.985401i \(0.445543\pi\)
−0.938507 + 0.345261i \(0.887790\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) 25.3137 2.74566
\(86\) 0 0
\(87\) 1.41421 + 2.44949i 0.151620 + 0.262613i
\(88\) 0 0
\(89\) −2.87868 + 4.98602i −0.305139 + 0.528517i −0.977292 0.211895i \(-0.932036\pi\)
0.672153 + 0.740412i \(0.265370\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −1.41421 + 2.44949i −0.146647 + 0.254000i
\(94\) 0 0
\(95\) −11.6569 20.1903i −1.19597 2.07148i
\(96\) 0 0
\(97\) −0.242641 −0.0246364 −0.0123182 0.999924i \(-0.503921\pi\)
−0.0123182 + 0.999924i \(0.503921\pi\)
\(98\) 0 0
\(99\) 0.828427 0.0832601
\(100\) 0 0
\(101\) 5.36396 + 9.29065i 0.533734 + 0.924455i 0.999223 + 0.0394011i \(0.0125450\pi\)
−0.465489 + 0.885053i \(0.654122\pi\)
\(102\) 0 0
\(103\) −7.07107 + 12.2474i −0.696733 + 1.20678i 0.272860 + 0.962054i \(0.412030\pi\)
−0.969593 + 0.244723i \(0.921303\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.41421 + 11.1097i −0.620085 + 1.07402i 0.369384 + 0.929277i \(0.379569\pi\)
−0.989469 + 0.144743i \(0.953765\pi\)
\(108\) 0 0
\(109\) 1.65685 + 2.86976i 0.158698 + 0.274873i 0.934399 0.356227i \(-0.115937\pi\)
−0.775702 + 0.631100i \(0.782604\pi\)
\(110\) 0 0
\(111\) 1.65685 0.157262
\(112\) 0 0
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) 8.24264 + 14.2767i 0.768630 + 1.33131i
\(116\) 0 0
\(117\) 2.12132 3.67423i 0.196116 0.339683i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.15685 8.93193i 0.468805 0.811994i
\(122\) 0 0
\(123\) 5.12132 + 8.87039i 0.461774 + 0.799816i
\(124\) 0 0
\(125\) 5.65685 0.505964
\(126\) 0 0
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) 0 0
\(129\) −5.65685 9.79796i −0.498058 0.862662i
\(130\) 0 0
\(131\) 2.00000 3.46410i 0.174741 0.302660i −0.765331 0.643637i \(-0.777425\pi\)
0.940072 + 0.340977i \(0.110758\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.70711 2.95680i 0.146924 0.254480i
\(136\) 0 0
\(137\) 4.58579 + 7.94282i 0.391790 + 0.678600i 0.992686 0.120727i \(-0.0385226\pi\)
−0.600896 + 0.799328i \(0.705189\pi\)
\(138\) 0 0
\(139\) −20.9706 −1.77870 −0.889350 0.457227i \(-0.848843\pi\)
−0.889350 + 0.457227i \(0.848843\pi\)
\(140\) 0 0
\(141\) 4.48528 0.377729
\(142\) 0 0
\(143\) 1.75736 + 3.04384i 0.146958 + 0.254538i
\(144\) 0 0
\(145\) −4.82843 + 8.36308i −0.400979 + 0.694516i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −0.656854 + 1.13770i −0.0538116 + 0.0932044i −0.891676 0.452673i \(-0.850470\pi\)
0.837865 + 0.545878i \(0.183804\pi\)
\(150\) 0 0
\(151\) 4.82843 + 8.36308i 0.392932 + 0.680578i 0.992835 0.119495i \(-0.0381275\pi\)
−0.599903 + 0.800073i \(0.704794\pi\)
\(152\) 0 0
\(153\) 7.41421 0.599404
\(154\) 0 0
\(155\) −9.65685 −0.775657
\(156\) 0 0
\(157\) −0.121320 0.210133i −0.00968242 0.0167704i 0.861144 0.508362i \(-0.169749\pi\)
−0.870826 + 0.491591i \(0.836415\pi\)
\(158\) 0 0
\(159\) −1.00000 + 1.73205i −0.0793052 + 0.137361i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −2.82843 + 4.89898i −0.221540 + 0.383718i −0.955276 0.295717i \(-0.904442\pi\)
0.733736 + 0.679435i \(0.237775\pi\)
\(164\) 0 0
\(165\) 1.41421 + 2.44949i 0.110096 + 0.190693i
\(166\) 0 0
\(167\) −14.8284 −1.14746 −0.573729 0.819045i \(-0.694504\pi\)
−0.573729 + 0.819045i \(0.694504\pi\)
\(168\) 0 0
\(169\) 5.00000 0.384615
\(170\) 0 0
\(171\) −3.41421 5.91359i −0.261091 0.452224i
\(172\) 0 0
\(173\) 8.29289 14.3637i 0.630497 1.09205i −0.356953 0.934122i \(-0.616184\pi\)
0.987450 0.157931i \(-0.0504822\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 4.24264 7.34847i 0.318896 0.552345i
\(178\) 0 0
\(179\) 3.24264 + 5.61642i 0.242366 + 0.419791i 0.961388 0.275197i \(-0.0887431\pi\)
−0.719022 + 0.694988i \(0.755410\pi\)
\(180\) 0 0
\(181\) −7.07107 −0.525588 −0.262794 0.964852i \(-0.584644\pi\)
−0.262794 + 0.964852i \(0.584644\pi\)
\(182\) 0 0
\(183\) −11.0711 −0.818397
\(184\) 0 0
\(185\) 2.82843 + 4.89898i 0.207950 + 0.360180i
\(186\) 0 0
\(187\) −3.07107 + 5.31925i −0.224579 + 0.388982i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −6.07107 + 10.5154i −0.439287 + 0.760867i −0.997635 0.0687396i \(-0.978102\pi\)
0.558348 + 0.829607i \(0.311436\pi\)
\(192\) 0 0
\(193\) −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i \(-0.189599\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) 0 0
\(195\) 14.4853 1.03731
\(196\) 0 0
\(197\) −2.68629 −0.191390 −0.0956952 0.995411i \(-0.530507\pi\)
−0.0956952 + 0.995411i \(0.530507\pi\)
\(198\) 0 0
\(199\) 2.82843 + 4.89898i 0.200502 + 0.347279i 0.948690 0.316207i \(-0.102409\pi\)
−0.748188 + 0.663486i \(0.769076\pi\)
\(200\) 0 0
\(201\) 5.65685 9.79796i 0.399004 0.691095i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −17.4853 + 30.2854i −1.22123 + 2.11522i
\(206\) 0 0
\(207\) 2.41421 + 4.18154i 0.167799 + 0.290637i
\(208\) 0 0
\(209\) 5.65685 0.391293
\(210\) 0 0
\(211\) 1.65685 0.114063 0.0570313 0.998372i \(-0.481837\pi\)
0.0570313 + 0.998372i \(0.481837\pi\)
\(212\) 0 0
\(213\) −5.24264 9.08052i −0.359220 0.622187i
\(214\) 0 0
\(215\) 19.3137 33.4523i 1.31718 2.28143i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 3.87868 6.71807i 0.262097 0.453965i
\(220\) 0 0
\(221\) 15.7279 + 27.2416i 1.05797 + 1.83247i
\(222\) 0 0
\(223\) 13.6569 0.914531 0.457265 0.889330i \(-0.348829\pi\)
0.457265 + 0.889330i \(0.348829\pi\)
\(224\) 0 0
\(225\) 6.65685 0.443790
\(226\) 0 0
\(227\) 2.58579 + 4.47871i 0.171625 + 0.297263i 0.938988 0.343950i \(-0.111765\pi\)
−0.767363 + 0.641213i \(0.778432\pi\)
\(228\) 0 0
\(229\) 12.7071 22.0094i 0.839709 1.45442i −0.0504286 0.998728i \(-0.516059\pi\)
0.890138 0.455691i \(-0.150608\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.41421 12.8418i 0.485721 0.841294i −0.514144 0.857704i \(-0.671890\pi\)
0.999865 + 0.0164099i \(0.00522367\pi\)
\(234\) 0 0
\(235\) 7.65685 + 13.2621i 0.499478 + 0.865121i
\(236\) 0 0
\(237\) −13.6569 −0.887108
\(238\) 0 0
\(239\) −12.8284 −0.829802 −0.414901 0.909867i \(-0.636184\pi\)
−0.414901 + 0.909867i \(0.636184\pi\)
\(240\) 0 0
\(241\) −6.94975 12.0373i −0.447673 0.775392i 0.550561 0.834795i \(-0.314414\pi\)
−0.998234 + 0.0594029i \(0.981080\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 14.4853 25.0892i 0.921676 1.59639i
\(248\) 0 0
\(249\) −2.00000 3.46410i −0.126745 0.219529i
\(250\) 0 0
\(251\) −6.14214 −0.387688 −0.193844 0.981032i \(-0.562096\pi\)
−0.193844 + 0.981032i \(0.562096\pi\)
\(252\) 0 0
\(253\) −4.00000 −0.251478
\(254\) 0 0
\(255\) 12.6569 + 21.9223i 0.792603 + 1.37283i
\(256\) 0 0
\(257\) 1.70711 2.95680i 0.106486 0.184440i −0.807858 0.589377i \(-0.799373\pi\)
0.914345 + 0.404937i \(0.132707\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −1.41421 + 2.44949i −0.0875376 + 0.151620i
\(262\) 0 0
\(263\) 10.0711 + 17.4436i 0.621009 + 1.07562i 0.989298 + 0.145907i \(0.0466102\pi\)
−0.368290 + 0.929711i \(0.620057\pi\)
\(264\) 0 0
\(265\) −6.82843 −0.419467
\(266\) 0 0
\(267\) −5.75736 −0.352345
\(268\) 0 0
\(269\) 0.0502525 + 0.0870399i 0.00306395 + 0.00530692i 0.867553 0.497344i \(-0.165691\pi\)
−0.864489 + 0.502651i \(0.832358\pi\)
\(270\) 0 0
\(271\) −3.07107 + 5.31925i −0.186554 + 0.323121i −0.944099 0.329662i \(-0.893065\pi\)
0.757545 + 0.652783i \(0.226399\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.75736 + 4.77589i −0.166275 + 0.287997i
\(276\) 0 0
\(277\) 14.3137 + 24.7921i 0.860027 + 1.48961i 0.871901 + 0.489682i \(0.162887\pi\)
−0.0118739 + 0.999930i \(0.503780\pi\)
\(278\) 0 0
\(279\) −2.82843 −0.169334
\(280\) 0 0
\(281\) 1.17157 0.0698902 0.0349451 0.999389i \(-0.488874\pi\)
0.0349451 + 0.999389i \(0.488874\pi\)
\(282\) 0 0
\(283\) 13.0711 + 22.6398i 0.776994 + 1.34579i 0.933667 + 0.358143i \(0.116590\pi\)
−0.156672 + 0.987651i \(0.550077\pi\)
\(284\) 0 0
\(285\) 11.6569 20.1903i 0.690492 1.19597i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −18.9853 + 32.8835i −1.11678 + 1.93432i
\(290\) 0 0
\(291\) −0.121320 0.210133i −0.00711192 0.0123182i
\(292\) 0 0
\(293\) −1.75736 −0.102666 −0.0513330 0.998682i \(-0.516347\pi\)
−0.0513330 + 0.998682i \(0.516347\pi\)
\(294\) 0 0
\(295\) 28.9706 1.68673
\(296\) 0 0
\(297\) 0.414214 + 0.717439i 0.0240351 + 0.0416300i
\(298\) 0 0
\(299\) −10.2426 + 17.7408i −0.592347 + 1.02598i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −5.36396 + 9.29065i −0.308152 + 0.533734i
\(304\) 0 0
\(305\) −18.8995 32.7349i −1.08218 1.87439i
\(306\) 0 0
\(307\) −11.5147 −0.657180 −0.328590 0.944473i \(-0.606573\pi\)
−0.328590 + 0.944473i \(0.606573\pi\)
\(308\) 0 0
\(309\) −14.1421 −0.804518
\(310\) 0 0
\(311\) −11.8995 20.6105i −0.674758 1.16872i −0.976539 0.215339i \(-0.930914\pi\)
0.301781 0.953377i \(-0.402419\pi\)
\(312\) 0 0
\(313\) −14.3640 + 24.8791i −0.811899 + 1.40625i 0.0996342 + 0.995024i \(0.468233\pi\)
−0.911533 + 0.411226i \(0.865101\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 11.0000 19.0526i 0.617822 1.07010i −0.372061 0.928208i \(-0.621349\pi\)
0.989882 0.141890i \(-0.0453179\pi\)
\(318\) 0 0
\(319\) −1.17157 2.02922i −0.0655955 0.113615i
\(320\) 0 0
\(321\) −12.8284 −0.716013
\(322\) 0 0
\(323\) 50.6274 2.81698
\(324\) 0 0
\(325\) 14.1213 + 24.4588i 0.783310 + 1.35673i
\(326\) 0 0
\(327\) −1.65685 + 2.86976i −0.0916242 + 0.158698i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −3.65685 + 6.33386i −0.200999 + 0.348140i −0.948851 0.315726i \(-0.897752\pi\)
0.747852 + 0.663866i \(0.231085\pi\)
\(332\) 0 0
\(333\) 0.828427 + 1.43488i 0.0453975 + 0.0786308i
\(334\) 0 0
\(335\) 38.6274 2.11044
\(336\) 0 0
\(337\) 10.3431 0.563427 0.281714 0.959499i \(-0.409097\pi\)
0.281714 + 0.959499i \(0.409097\pi\)
\(338\) 0 0
\(339\) −5.00000 8.66025i −0.271563 0.470360i
\(340\) 0 0
\(341\) 1.17157 2.02922i 0.0634442 0.109889i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −8.24264 + 14.2767i −0.443769 + 0.768630i
\(346\) 0 0
\(347\) 1.24264 + 2.15232i 0.0667084 + 0.115542i 0.897451 0.441115i \(-0.145417\pi\)
−0.830742 + 0.556657i \(0.812084\pi\)
\(348\) 0 0
\(349\) 10.5858 0.566644 0.283322 0.959025i \(-0.408563\pi\)
0.283322 + 0.959025i \(0.408563\pi\)
\(350\) 0 0
\(351\) 4.24264 0.226455
\(352\) 0 0
\(353\) 13.8492 + 23.9876i 0.737121 + 1.27673i 0.953787 + 0.300485i \(0.0971485\pi\)
−0.216666 + 0.976246i \(0.569518\pi\)
\(354\) 0 0
\(355\) 17.8995 31.0028i 0.950007 1.64546i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −14.4142 + 24.9662i −0.760753 + 1.31766i 0.181710 + 0.983352i \(0.441837\pi\)
−0.942463 + 0.334311i \(0.891496\pi\)
\(360\) 0 0
\(361\) −13.8137 23.9260i −0.727037 1.25927i
\(362\) 0 0
\(363\) 10.3137 0.541329
\(364\) 0 0
\(365\) 26.4853 1.38630
\(366\) 0 0
\(367\) −2.34315 4.05845i −0.122311 0.211849i 0.798368 0.602171i \(-0.205697\pi\)
−0.920679 + 0.390321i \(0.872364\pi\)
\(368\) 0 0
\(369\) −5.12132 + 8.87039i −0.266605 + 0.461774i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −2.65685 + 4.60181i −0.137567 + 0.238273i −0.926575 0.376110i \(-0.877261\pi\)
0.789008 + 0.614383i \(0.210595\pi\)
\(374\) 0 0
\(375\) 2.82843 + 4.89898i 0.146059 + 0.252982i
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) −23.3137 −1.19754 −0.598772 0.800919i \(-0.704345\pi\)
−0.598772 + 0.800919i \(0.704345\pi\)
\(380\) 0 0
\(381\) 10.0000 + 17.3205i 0.512316 + 0.887357i
\(382\) 0 0
\(383\) 4.48528 7.76874i 0.229187 0.396964i −0.728380 0.685173i \(-0.759727\pi\)
0.957567 + 0.288209i \(0.0930599\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 5.65685 9.79796i 0.287554 0.498058i
\(388\) 0 0
\(389\) 17.8995 + 31.0028i 0.907540 + 1.57191i 0.817470 + 0.575971i \(0.195376\pi\)
0.0900701 + 0.995935i \(0.471291\pi\)
\(390\) 0 0
\(391\) −35.7990 −1.81043
\(392\) 0 0
\(393\) 4.00000 0.201773
\(394\) 0 0
\(395\) −23.3137 40.3805i −1.17304 2.03176i
\(396\) 0 0
\(397\) 8.12132 14.0665i 0.407597 0.705979i −0.587023 0.809571i \(-0.699700\pi\)
0.994620 + 0.103591i \(0.0330334\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.585786 + 1.01461i −0.0292528 + 0.0506673i −0.880281 0.474452i \(-0.842646\pi\)
0.851028 + 0.525120i \(0.175979\pi\)
\(402\) 0 0
\(403\) −6.00000 10.3923i −0.298881 0.517678i
\(404\) 0 0
\(405\) 3.41421 0.169654
\(406\) 0 0
\(407\) −1.37258 −0.0680364
\(408\) 0 0
\(409\) 4.12132 + 7.13834i 0.203786 + 0.352968i 0.949745 0.313024i \(-0.101342\pi\)
−0.745959 + 0.665992i \(0.768009\pi\)
\(410\) 0 0
\(411\) −4.58579 + 7.94282i −0.226200 + 0.391790i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 6.82843 11.8272i 0.335194 0.580574i
\(416\) 0 0
\(417\) −10.4853 18.1610i −0.513466 0.889350i
\(418\) 0 0
\(419\) 7.51472 0.367118 0.183559 0.983009i \(-0.441238\pi\)
0.183559 + 0.983009i \(0.441238\pi\)
\(420\) 0 0
\(421\) −25.3137 −1.23371 −0.616857 0.787075i \(-0.711594\pi\)
−0.616857 + 0.787075i \(0.711594\pi\)
\(422\) 0 0
\(423\) 2.24264 + 3.88437i 0.109041 + 0.188864i
\(424\) 0 0
\(425\) −24.6777 + 42.7430i −1.19704 + 2.07334i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −1.75736 + 3.04384i −0.0848461 + 0.146958i
\(430\) 0 0
\(431\) 4.07107 + 7.05130i 0.196096 + 0.339649i 0.947259 0.320468i \(-0.103840\pi\)
−0.751163 + 0.660117i \(0.770507\pi\)
\(432\) 0 0
\(433\) 0.928932 0.0446416 0.0223208 0.999751i \(-0.492894\pi\)
0.0223208 + 0.999751i \(0.492894\pi\)
\(434\) 0 0
\(435\) −9.65685 −0.463011
\(436\) 0 0
\(437\) 16.4853 + 28.5533i 0.788598 + 1.36589i
\(438\) 0 0
\(439\) −6.34315 + 10.9867i −0.302742 + 0.524364i −0.976756 0.214354i \(-0.931235\pi\)
0.674014 + 0.738718i \(0.264569\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.58579 9.67487i 0.265389 0.459667i −0.702277 0.711904i \(-0.747833\pi\)
0.967665 + 0.252237i \(0.0811664\pi\)
\(444\) 0 0
\(445\) −9.82843 17.0233i −0.465912 0.806983i
\(446\) 0 0
\(447\) −1.31371 −0.0621363
\(448\) 0 0
\(449\) −16.6274 −0.784696 −0.392348 0.919817i \(-0.628337\pi\)
−0.392348 + 0.919817i \(0.628337\pi\)
\(450\) 0 0
\(451\) −4.24264 7.34847i −0.199778 0.346026i
\(452\) 0 0
\(453\) −4.82843 + 8.36308i −0.226859 + 0.392932i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 12.3137 21.3280i 0.576011 0.997680i −0.419920 0.907561i \(-0.637942\pi\)
0.995931 0.0901192i \(-0.0287248\pi\)
\(458\) 0 0
\(459\) 3.70711 + 6.42090i 0.173033 + 0.299702i
\(460\) 0 0
\(461\) 16.3848 0.763115 0.381558 0.924345i \(-0.375388\pi\)
0.381558 + 0.924345i \(0.375388\pi\)
\(462\) 0 0
\(463\) 1.65685 0.0770005 0.0385003 0.999259i \(-0.487742\pi\)
0.0385003 + 0.999259i \(0.487742\pi\)
\(464\) 0 0
\(465\) −4.82843 8.36308i −0.223913 0.387829i
\(466\) 0 0
\(467\) 9.41421 16.3059i 0.435638 0.754547i −0.561710 0.827334i \(-0.689856\pi\)
0.997347 + 0.0727876i \(0.0231895\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0.121320 0.210133i 0.00559015 0.00968242i
\(472\) 0 0
\(473\) 4.68629 + 8.11689i 0.215476 + 0.373215i
\(474\) 0 0
\(475\) 45.4558 2.08566
\(476\) 0 0
\(477\) −2.00000 −0.0915737
\(478\) 0 0
\(479\) −11.4142 19.7700i −0.521529 0.903314i −0.999686 0.0250403i \(-0.992029\pi\)
0.478158 0.878274i \(-0.341305\pi\)
\(480\) 0 0
\(481\) −3.51472 + 6.08767i −0.160257 + 0.277574i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0.414214 0.717439i 0.0188085 0.0325772i
\(486\) 0 0
\(487\) −2.48528 4.30463i −0.112619 0.195062i 0.804207 0.594350i \(-0.202591\pi\)
−0.916825 + 0.399288i \(0.869257\pi\)
\(488\) 0 0
\(489\) −5.65685 −0.255812
\(490\) 0 0
\(491\) 19.1716 0.865201 0.432600 0.901586i \(-0.357596\pi\)
0.432600 + 0.901586i \(0.357596\pi\)
\(492\) 0 0
\(493\) −10.4853 18.1610i −0.472233 0.817932i
\(494\) 0 0
\(495\) −1.41421 + 2.44949i −0.0635642 + 0.110096i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 12.4853 21.6251i 0.558918 0.968074i −0.438669 0.898649i \(-0.644550\pi\)
0.997587 0.0694257i \(-0.0221167\pi\)
\(500\) 0 0
\(501\) −7.41421 12.8418i −0.331243 0.573729i
\(502\) 0 0
\(503\) −19.3137 −0.861156 −0.430578 0.902553i \(-0.641690\pi\)
−0.430578 + 0.902553i \(0.641690\pi\)
\(504\) 0 0
\(505\) −36.6274 −1.62990
\(506\) 0 0
\(507\) 2.50000 + 4.33013i 0.111029 + 0.192308i
\(508\) 0 0
\(509\) 18.1924 31.5101i 0.806363 1.39666i −0.109003 0.994041i \(-0.534766\pi\)
0.915367 0.402621i \(-0.131901\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 3.41421 5.91359i 0.150741 0.261091i
\(514\) 0 0
\(515\) −24.1421 41.8154i −1.06383 1.84261i
\(516\) 0 0
\(517\) −3.71573 −0.163418
\(518\) 0 0
\(519\) 16.5858 0.728035
\(520\) 0 0
\(521\) −7.12132 12.3345i −0.311991 0.540384i 0.666803 0.745234i \(-0.267662\pi\)
−0.978793 + 0.204851i \(0.934329\pi\)
\(522\) 0 0
\(523\) 2.48528 4.30463i 0.108674 0.188228i −0.806559 0.591153i \(-0.798673\pi\)
0.915233 + 0.402924i \(0.132006\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10.4853 18.1610i 0.456746 0.791107i
\(528\) 0 0
\(529\) −0.156854 0.271680i −0.00681975 0.0118122i
\(530\) 0 0
\(531\) 8.48528 0.368230
\(532\) 0 0
\(533\) −43.4558 −1.88228
\(534\) 0 0
\(535\) −21.8995 37.9310i −0.946798 1.63990i
\(536\) 0 0
\(537\) −3.24264 + 5.61642i −0.139930 + 0.242366i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 9.00000 15.5885i 0.386940 0.670200i −0.605096 0.796152i \(-0.706865\pi\)
0.992036 + 0.125952i \(0.0401986\pi\)
\(542\) 0 0
\(543\) −3.53553 6.12372i −0.151724 0.262794i
\(544\) 0 0
\(545\) −11.3137 −0.484626
\(546\) 0 0
\(547\) −3.02944 −0.129529 −0.0647647 0.997901i \(-0.520630\pi\)
−0.0647647 + 0.997901i \(0.520630\pi\)
\(548\) 0 0
\(549\) −5.53553 9.58783i −0.236251 0.409198i
\(550\) 0 0
\(551\) −9.65685 + 16.7262i −0.411396 + 0.712558i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −2.82843 + 4.89898i −0.120060 + 0.207950i
\(556\) 0 0
\(557\) −16.3137 28.2562i −0.691234 1.19725i −0.971434 0.237311i \(-0.923734\pi\)
0.280200 0.959942i \(-0.409599\pi\)
\(558\) 0 0
\(559\) 48.0000 2.03018
\(560\) 0 0
\(561\) −6.14214 −0.259321
\(562\) 0 0
\(563\) −0.928932 1.60896i −0.0391498 0.0678095i 0.845787 0.533521i \(-0.179132\pi\)
−0.884936 + 0.465712i \(0.845798\pi\)
\(564\) 0 0
\(565\) 17.0711 29.5680i 0.718185 1.24393i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2.92893 5.07306i 0.122787 0.212674i −0.798079 0.602553i \(-0.794150\pi\)
0.920866 + 0.389880i \(0.127483\pi\)
\(570\) 0 0
\(571\) 20.8284 + 36.0759i 0.871643 + 1.50973i 0.860297 + 0.509794i \(0.170278\pi\)
0.0113458 + 0.999936i \(0.496388\pi\)
\(572\) 0 0
\(573\) −12.1421 −0.507245
\(574\) 0 0
\(575\) −32.1421 −1.34042
\(576\) 0 0
\(577\) −6.60660 11.4430i −0.275036 0.476377i 0.695108 0.718905i \(-0.255357\pi\)
−0.970144 + 0.242528i \(0.922023\pi\)
\(578\) 0 0
\(579\) 1.00000 1.73205i 0.0415586 0.0719816i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.828427 1.43488i 0.0343099 0.0594266i
\(584\) 0 0
\(585\) 7.24264 + 12.5446i 0.299446 + 0.518656i
\(586\) 0 0
\(587\) −35.7990 −1.47758 −0.738791 0.673934i \(-0.764603\pi\)
−0.738791 + 0.673934i \(0.764603\pi\)
\(588\) 0 0
\(589\) −19.3137 −0.795807
\(590\) 0 0
\(591\) −1.34315 2.32640i −0.0552496 0.0956952i
\(592\) 0 0
\(593\) −23.7071 + 41.0619i −0.973534 + 1.68621i −0.288844 + 0.957376i \(0.593271\pi\)
−0.684690 + 0.728835i \(0.740062\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.82843 + 4.89898i −0.115760 + 0.200502i
\(598\) 0 0
\(599\) −11.7279 20.3134i −0.479190 0.829981i 0.520525 0.853846i \(-0.325736\pi\)
−0.999715 + 0.0238650i \(0.992403\pi\)
\(600\) 0 0
\(601\) −12.2426 −0.499388 −0.249694 0.968325i \(-0.580330\pi\)
−0.249694 + 0.968325i \(0.580330\pi\)
\(602\) 0 0
\(603\) 11.3137 0.460730
\(604\) 0 0
\(605\) 17.6066 + 30.4955i 0.715810 + 1.23982i
\(606\) 0 0
\(607\) −12.4853 + 21.6251i −0.506762 + 0.877737i 0.493207 + 0.869912i \(0.335824\pi\)
−0.999969 + 0.00782569i \(0.997509\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −9.51472 + 16.4800i −0.384924 + 0.666708i
\(612\) 0 0
\(613\) 5.17157 + 8.95743i 0.208878 + 0.361787i 0.951361 0.308077i \(-0.0996856\pi\)
−0.742483 + 0.669864i \(0.766352\pi\)
\(614\) 0 0
\(615\) −34.9706 −1.41015
\(616\) 0 0
\(617\) −4.48528 −0.180571 −0.0902853 0.995916i \(-0.528778\pi\)
−0.0902853 + 0.995916i \(0.528778\pi\)
\(618\) 0 0
\(619\) −16.8284 29.1477i −0.676392 1.17154i −0.976060 0.217501i \(-0.930209\pi\)
0.299668 0.954043i \(-0.403124\pi\)
\(620\) 0 0
\(621\) −2.41421 + 4.18154i −0.0968791 + 0.167799i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 6.98528 12.0989i 0.279411 0.483954i
\(626\) 0 0
\(627\) 2.82843 + 4.89898i 0.112956 + 0.195646i
\(628\) 0 0
\(629\) −12.2843 −0.489806
\(630\) 0 0
\(631\) −3.02944 −0.120600 −0.0603000 0.998180i \(-0.519206\pi\)
−0.0603000 + 0.998180i \(0.519206\pi\)
\(632\) 0 0
\(633\) 0.828427 + 1.43488i 0.0329270 + 0.0570313i
\(634\) 0 0
\(635\) −34.1421 + 59.1359i −1.35489 + 2.34674i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 5.24264 9.08052i 0.207396 0.359220i
\(640\) 0 0
\(641\) −17.5563 30.4085i −0.693434 1.20106i −0.970706 0.240272i \(-0.922764\pi\)
0.277272 0.960792i \(-0.410570\pi\)
\(642\) 0 0
\(643\) 31.7990 1.25403 0.627015 0.779007i \(-0.284277\pi\)
0.627015 + 0.779007i \(0.284277\pi\)
\(644\) 0 0
\(645\) 38.6274 1.52095
\(646\) 0 0
\(647\) 0.100505 + 0.174080i 0.00395126 + 0.00684379i 0.867994 0.496574i \(-0.165409\pi\)
−0.864043 + 0.503418i \(0.832076\pi\)
\(648\) 0 0
\(649\) −3.51472 + 6.08767i −0.137965 + 0.238962i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −23.0711 + 39.9603i −0.902841 + 1.56377i −0.0790508 + 0.996871i \(0.525189\pi\)
−0.823790 + 0.566895i \(0.808144\pi\)
\(654\) 0 0
\(655\) 6.82843 + 11.8272i 0.266809 + 0.462126i
\(656\) 0 0
\(657\) 7.75736 0.302643
\(658\) 0 0
\(659\) 21.5147 0.838094 0.419047 0.907964i \(-0.362364\pi\)
0.419047 + 0.907964i \(0.362364\pi\)
\(660\) 0 0
\(661\) −2.46447 4.26858i −0.0958566 0.166029i 0.814109 0.580712i \(-0.197226\pi\)
−0.909966 + 0.414683i \(0.863892\pi\)
\(662\) 0 0
\(663\) −15.7279 + 27.2416i −0.610822 + 1.05797i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 6.82843 11.8272i 0.264398 0.457950i
\(668\) 0 0
\(669\) 6.82843 + 11.8272i 0.264002 + 0.457265i
\(670\) 0 0
\(671\) 9.17157 0.354065
\(672\) 0 0
\(673\) −23.3137 −0.898677 −0.449339 0.893361i \(-0.648340\pi\)
−0.449339 + 0.893361i \(0.648340\pi\)
\(674\) 0 0
\(675\) 3.32843 + 5.76500i 0.128111 + 0.221895i
\(676\) 0 0
\(677\) −13.8492 + 23.9876i −0.532270 + 0.921918i 0.467021 + 0.884246i \(0.345327\pi\)
−0.999290 + 0.0376716i \(0.988006\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −2.58579 + 4.47871i −0.0990876 + 0.171625i
\(682\) 0 0
\(683\) 0.899495 + 1.55797i 0.0344182 + 0.0596141i 0.882721 0.469897i \(-0.155709\pi\)
−0.848303 + 0.529511i \(0.822376\pi\)
\(684\) 0 0
\(685\) −31.3137 −1.19644
\(686\) 0 0
\(687\) 25.4142 0.969613
\(688\) 0 0
\(689\) −4.24264 7.34847i −0.161632 0.279954i
\(690\) 0 0
\(691\) −4.34315 + 7.52255i −0.165221 + 0.286171i −0.936734 0.350043i \(-0.886167\pi\)
0.771513 + 0.636214i \(0.219500\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 35.7990 62.0057i 1.35793 2.35201i
\(696\) 0 0
\(697\) −37.9706 65.7669i −1.43824 2.49110i
\(698\) 0 0
\(699\) 14.8284 0.560863
\(700\) 0 0
\(701\) −6.14214 −0.231985 −0.115993 0.993250i \(-0.537005\pi\)
−0.115993 + 0.993250i \(0.537005\pi\)
\(702\) 0 0
\(703\) 5.65685 + 9.79796i 0.213352 + 0.369537i
\(704\) 0 0
\(705\) −7.65685 + 13.2621i −0.288374 + 0.499478i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −3.31371 + 5.73951i −0.124449 + 0.215552i −0.921517 0.388337i \(-0.873050\pi\)
0.797068 + 0.603889i \(0.206383\pi\)
\(710\) 0 0
\(711\) −6.82843 11.8272i −0.256086 0.443554i
\(712\) 0 0
\(713\) 13.6569 0.511453
\(714\) 0 0
\(715\) −12.0000 −0.448775
\(716\) 0 0
\(717\) −6.41421 11.1097i −0.239543 0.414901i
\(718\) 0 0
\(719\) 3.31371 5.73951i 0.123580 0.214048i −0.797597 0.603191i \(-0.793896\pi\)
0.921177 + 0.389143i \(0.127229\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 6.94975 12.0373i 0.258464 0.447673i
\(724\) 0 0
\(725\) −9.41421 16.3059i −0.349635 0.605586i
\(726\) 0 0
\(727\) −9.85786 −0.365608 −0.182804 0.983149i \(-0.558517\pi\)
−0.182804 + 0.983149i \(0.558517\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 41.9411 + 72.6442i 1.55125 + 2.68684i
\(732\) 0 0
\(733\) 4.02082 6.96426i 0.148512 0.257231i −0.782166 0.623071i \(-0.785885\pi\)
0.930678 + 0.365840i \(0.119218\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4.68629 + 8.11689i −0.172622 + 0.298990i
\(738\) 0 0
\(739\) −16.4853 28.5533i −0.606421 1.05035i −0.991825 0.127604i \(-0.959271\pi\)
0.385404 0.922748i \(-0.374062\pi\)
\(740\) 0 0
\(741\) 28.9706 1.06426
\(742\) 0 0
\(743\) −4.82843 −0.177138 −0.0885689 0.996070i \(-0.528229\pi\)
−0.0885689 + 0.996070i \(0.528229\pi\)
\(744\) 0 0
\(745\) −2.24264 3.88437i −0.0821640 0.142312i
\(746\) 0 0
\(747\) 2.00000 3.46410i 0.0731762 0.126745i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −10.1421 + 17.5667i −0.370092 + 0.641018i −0.989579 0.143989i \(-0.954007\pi\)
0.619488 + 0.785006i \(0.287340\pi\)
\(752\) 0 0
\(753\) −3.07107 5.31925i −0.111916 0.193844i
\(754\) 0 0
\(755\) −32.9706 −1.19992
\(756\) 0 0
\(757\) 41.9411 1.52438 0.762188 0.647356i \(-0.224125\pi\)
0.762188 + 0.647356i \(0.224125\pi\)
\(758\) 0 0
\(759\) −2.00000 3.46410i −0.0725954 0.125739i
\(760\) 0 0
\(761\) 15.9497 27.6258i 0.578178 1.00143i −0.417510 0.908672i \(-0.637097\pi\)
0.995688 0.0927614i \(-0.0295694\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −12.6569 + 21.9223i −0.457610 + 0.792603i
\(766\) 0 0
\(767\) 18.0000 + 31.1769i 0.649942 + 1.12573i
\(768\) 0 0
\(769\) 34.8701 1.25745 0.628723 0.777629i \(-0.283578\pi\)
0.628723 + 0.777629i \(0.283578\pi\)
\(770\) 0 0
\(771\) 3.41421 0.122960
\(772\) 0 0
\(773\) −16.6777 28.8866i −0.599854 1.03898i −0.992842 0.119434i \(-0.961892\pi\)
0.392988 0.919544i \(-0.371441\pi\)
\(774\) 0 0
\(775\) 9.41421 16.3059i 0.338169 0.585725i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −34.9706 + 60.5708i −1.25295 + 2.17017i
\(780\) 0 0
\(781\) 4.34315 + 7.52255i 0.155410 + 0.269178i
\(782\) 0 0
\(783\) −2.82843 −0.101080
\(784\) 0 0
\(785\) 0.828427 0.0295678
\(786\) 0 0
\(787\) −7.65685 13.2621i −0.272937 0.472741i 0.696675 0.717387i \(-0.254662\pi\)
−0.969613 + 0.244645i \(0.921329\pi\)
\(788\) 0 0
\(789\) −10.0711 + 17.4436i −0.358540 + 0.621009i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 23.4853 40.6777i 0.833987 1.44451i
\(794\) 0 0
\(795\) −3.41421 5.91359i −0.121090 0.209733i
\(796\) 0 0
\(797\) −39.4142 −1.39612 −0.698062 0.716038i \(-0.745954\pi\)
−0.698062 + 0.716038i \(0.745954\pi\)
\(798\) 0 0
\(799\) −33.2548 −1.17647