Properties

Label 2352.2.q.ba.1537.1
Level $2352$
Weight $2$
Character 2352.1537
Analytic conductor $18.781$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.7808145554\)
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: no (minimal twist has level 1176)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1537.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 2352.1537
Dual form 2352.2.q.ba.961.1

$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1471\) \(1765\) \(2257\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) −1.70711 2.95680i −0.763441 1.32232i −0.941067 0.338221i \(-0.890175\pi\)
0.177625 0.984098i \(-0.443158\pi\)
\(6\) 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 \(-0.793476\pi\)
0.921690 + 0.387927i \(0.126809\pi\)
\(12\) 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 −0.0704656 + 0.997514i \(0.522449\pi\)
−0.828640 + 0.559782i \(0.810885\pi\)
\(18\) 0 0
\(19\) 3.41421 + 5.91359i 0.783274 + 1.35667i 0.930025 + 0.367497i \(0.119785\pi\)
−0.146750 + 0.989174i \(0.546881\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.41421 4.18154i −0.503398 0.871911i −0.999992 0.00392850i \(-0.998750\pi\)
0.496594 0.867983i \(-0.334584\pi\)
\(24\) 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 \(-0.915080\pi\)
0.710623 + 0.703573i \(0.248413\pi\)
\(32\) 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 0.926052 0.377395i \(-0.123180\pi\)
−0.789860 + 0.613287i \(0.789847\pi\)
\(38\) 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 \(-0.168795\pi\)
0.862662 + 0.505781i \(0.168795\pi\)
\(44\) 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 \(-0.272746\pi\)
−0.981940 + 0.189194i \(0.939412\pi\)
\(48\) 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 −0.789136 0.614218i \(-0.789471\pi\)
0.926497 + 0.376303i \(0.122805\pi\)
\(54\) 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 −0.445760 0.895152i \(-0.647067\pi\)
0.998105 0.0615367i \(-0.0196001\pi\)
\(60\) 0 0
\(61\) −5.53553 9.58783i −0.708752 1.22760i −0.965320 0.261069i \(-0.915925\pi\)
0.256568 0.966526i \(-0.417408\pi\)
\(62\) 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 −0.280385 0.959888i \(-0.590462\pi\)
0.971480 0.237124i \(-0.0762046\pi\)
\(68\) 0 0
\(69\) 4.82843 0.581274
\(70\) 0 0
\(71\) 10.4853 1.24437 0.622187 0.782869i \(-0.286244\pi\)
0.622187 + 0.782869i \(0.286244\pi\)
\(72\) 0 0
\(73\) −3.87868 + 6.71807i −0.453965 + 0.786291i −0.998628 0.0523644i \(-0.983324\pi\)
0.544663 + 0.838655i \(0.316658\pi\)
\(74\) 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 0.938507 + 0.345261i \(0.112210\pi\)
−0.170249 + 0.985401i \(0.554457\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 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 0.672153 0.740412i \(-0.265370\pi\)
−0.977292 + 0.211895i \(0.932036\pi\)
\(90\) 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 −0.465489 0.885053i \(-0.654122\pi\)
0.999223 0.0394011i \(-0.0125450\pi\)
\(102\) 0 0
\(103\) 7.07107 + 12.2474i 0.696733 + 1.20678i 0.969593 + 0.244723i \(0.0786971\pi\)
−0.272860 + 0.962054i \(0.587970\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.41421 + 11.1097i 0.620085 + 1.07402i 0.989469 + 0.144743i \(0.0462354\pi\)
−0.369384 + 0.929277i \(0.620431\pi\)
\(108\) 0 0
\(109\) 1.65685 2.86976i 0.158698 0.274873i −0.775702 0.631100i \(-0.782604\pi\)
0.934399 + 0.356227i \(0.115937\pi\)
\(110\) 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 \(-0.847461\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) 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 \(-0.222575\pi\)
−0.940072 + 0.340977i \(0.889242\pi\)
\(132\) 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 −0.600896 0.799328i \(-0.705189\pi\)
0.992686 + 0.120727i \(0.0385226\pi\)
\(138\) 0 0
\(139\) 20.9706 1.77870 0.889350 0.457227i \(-0.151157\pi\)
0.889350 + 0.457227i \(0.151157\pi\)
\(140\) 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 0.837865 0.545878i \(-0.183804\pi\)
−0.891676 + 0.452673i \(0.850470\pi\)
\(150\) 0 0
\(151\) −4.82843 + 8.36308i −0.392932 + 0.680578i −0.992835 0.119495i \(-0.961872\pi\)
0.599903 + 0.800073i \(0.295206\pi\)
\(152\) 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 −0.870826 0.491591i \(-0.836415\pi\)
0.861144 + 0.508362i \(0.169749\pi\)
\(158\) 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 \(-0.0955585\pi\)
−0.733736 + 0.679435i \(0.762225\pi\)
\(164\) 0 0
\(165\) 1.41421 2.44949i 0.110096 0.190693i
\(166\) 0 0
\(167\) 14.8284 1.14746 0.573729 0.819045i \(-0.305496\pi\)
0.573729 + 0.819045i \(0.305496\pi\)
\(168\) 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 0.987450 + 0.157931i \(0.0504822\pi\)
−0.356953 + 0.934122i \(0.616184\pi\)
\(174\) 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 \(-0.911257\pi\)
0.719022 + 0.694988i \(0.244590\pi\)
\(180\) 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 \(-0.0218978\pi\)
−0.558348 + 0.829607i \(0.688564\pi\)
\(192\) 0 0
\(193\) −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i \(-0.856266\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) 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 \(-0.897591\pi\)
0.748188 + 0.663486i \(0.230924\pi\)
\(200\) 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 \(-0.518163\pi\)
−0.0570313 + 0.998372i \(0.518163\pi\)
\(212\) 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 \(-0.651171\pi\)
−0.457265 + 0.889330i \(0.651171\pi\)
\(224\) 0 0
\(225\) 6.65685 0.443790
\(226\) 0 0
\(227\) −2.58579 + 4.47871i −0.171625 + 0.297263i −0.938988 0.343950i \(-0.888235\pi\)
0.767363 + 0.641213i \(0.221568\pi\)
\(228\) 0 0
\(229\) 12.7071 + 22.0094i 0.839709 + 1.45442i 0.890138 + 0.455691i \(0.150608\pi\)
−0.0504286 + 0.998728i \(0.516059\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.41421 + 12.8418i 0.485721 + 0.841294i 0.999865 0.0164099i \(-0.00522367\pi\)
−0.514144 + 0.857704i \(0.671890\pi\)
\(234\) 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 \(-0.363816\pi\)
0.414901 + 0.909867i \(0.363816\pi\)
\(240\) 0 0
\(241\) −6.94975 + 12.0373i −0.447673 + 0.775392i −0.998234 0.0594029i \(-0.981080\pi\)
0.550561 + 0.834795i \(0.314414\pi\)
\(242\) 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 \(-0.437904\pi\)
0.193844 + 0.981032i \(0.437904\pi\)
\(252\) 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 0.914345 0.404937i \(-0.132707\pi\)
−0.807858 + 0.589377i \(0.799373\pi\)
\(258\) 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 0.368290 + 0.929711i \(0.379943\pi\)
−0.989298 + 0.145907i \(0.953390\pi\)
\(264\) 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 −0.864489 0.502651i \(-0.832358\pi\)
0.867553 + 0.497344i \(0.165691\pi\)
\(270\) 0 0
\(271\) 3.07107 + 5.31925i 0.186554 + 0.323121i 0.944099 0.329662i \(-0.106935\pi\)
−0.757545 + 0.652783i \(0.773601\pi\)
\(272\) 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 −0.0118739 0.999930i \(-0.503780\pi\)
0.871901 0.489682i \(-0.162887\pi\)
\(278\) 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 0.156672 + 0.987651i \(0.449923\pi\)
−0.933667 + 0.358143i \(0.883410\pi\)
\(284\) 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 \(-0.393427\pi\)
0.328590 + 0.944473i \(0.393427\pi\)
\(308\) 0 0
\(309\) −14.1421 −0.804518
\(310\) 0 0
\(311\) 11.8995 20.6105i 0.674758 1.16872i −0.301781 0.953377i \(-0.597581\pi\)
0.976539 0.215339i \(-0.0690855\pi\)
\(312\) 0 0
\(313\) −14.3640 24.8791i −0.811899 1.40625i −0.911533 0.411226i \(-0.865101\pi\)
0.0996342 0.995024i \(-0.468233\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 11.0000 + 19.0526i 0.617822 + 1.07010i 0.989882 + 0.141890i \(0.0453179\pi\)
−0.372061 + 0.928208i \(0.621349\pi\)
\(318\) 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 \(-0.102248\pi\)
−0.747852 + 0.663866i \(0.768915\pi\)
\(332\) 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 \(-0.854583\pi\)
0.830742 + 0.556657i \(0.187916\pi\)
\(348\) 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 −0.216666 0.976246i \(-0.569518\pi\)
0.953787 0.300485i \(-0.0971485\pi\)
\(354\) 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 0.942463 + 0.334311i \(0.108504\pi\)
−0.181710 + 0.983352i \(0.558163\pi\)
\(360\) 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 \(-0.794303\pi\)
0.920679 + 0.390321i \(0.127636\pi\)
\(368\) 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 0.789008 0.614383i \(-0.210595\pi\)
−0.926575 + 0.376110i \(0.877261\pi\)
\(374\) 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 \(-0.295655\pi\)
0.598772 + 0.800919i \(0.295655\pi\)
\(380\) 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 \(-0.240273\pi\)
−0.957567 + 0.288209i \(0.906940\pi\)
\(384\) 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 0.0900701 0.995935i \(-0.471291\pi\)
0.817470 0.575971i \(-0.195376\pi\)
\(390\) 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 0.994620 0.103591i \(-0.0330334\pi\)
−0.587023 + 0.809571i \(0.699700\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.585786 1.01461i −0.0292528 0.0506673i 0.851028 0.525120i \(-0.175979\pi\)
−0.880281 + 0.474452i \(0.842646\pi\)
\(402\) 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 −0.745959 0.665992i \(-0.768009\pi\)
0.949745 + 0.313024i \(0.101342\pi\)
\(410\) 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 \(-0.558762\pi\)
−0.183559 + 0.983009i \(0.558762\pi\)
\(420\) 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 \(-0.896160\pi\)
0.751163 + 0.660117i \(0.229493\pi\)
\(432\) 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 \(-0.0687647\pi\)
−0.674014 + 0.738718i \(0.735431\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5.58579 9.67487i −0.265389 0.459667i 0.702277 0.711904i \(-0.252167\pi\)
−0.967665 + 0.252237i \(0.918834\pi\)
\(444\) 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 0.995931 + 0.0901192i \(0.0287248\pi\)
−0.419920 + 0.907561i \(0.637942\pi\)
\(458\) 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 \(-0.512258\pi\)
−0.0385003 + 0.999259i \(0.512258\pi\)
\(464\) 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 \(-0.310144\pi\)
−0.997347 + 0.0727876i \(0.976810\pi\)
\(468\) 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 −0.478158 0.878274i \(-0.658695\pi\)
0.999686 0.0250403i \(-0.00797140\pi\)
\(480\) 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 \(-0.797409\pi\)
0.916825 + 0.399288i \(0.130743\pi\)
\(488\) 0 0
\(489\) −5.65685 −0.255812
\(490\) 0 0
\(491\) −19.1716 −0.865201 −0.432600 0.901586i \(-0.642404\pi\)
−0.432600 + 0.901586i \(0.642404\pi\)
\(492\) 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 −0.997587 0.0694257i \(-0.977883\pi\)
0.438669 0.898649i \(-0.355450\pi\)
\(500\) 0 0
\(501\) −7.41421 + 12.8418i −0.331243 + 0.573729i
\(502\) 0 0
\(503\) 19.3137 0.861156 0.430578 0.902553i \(-0.358310\pi\)
0.430578 + 0.902553i \(0.358310\pi\)
\(504\) 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 0.915367 + 0.402621i \(0.131901\pi\)
−0.109003 + 0.994041i \(0.534766\pi\)
\(510\) 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 −0.978793 0.204851i \(-0.934329\pi\)
0.666803 + 0.745234i \(0.267662\pi\)
\(522\) 0 0
\(523\) −2.48528 4.30463i −0.108674 0.188228i 0.806559 0.591153i \(-0.201327\pi\)
−0.915233 + 0.402924i \(0.867994\pi\)
\(524\) 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 0.992036 0.125952i \(-0.0401986\pi\)
−0.605096 + 0.796152i \(0.706865\pi\)
\(542\) 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 \(-0.479370\pi\)
0.0647647 + 0.997901i \(0.479370\pi\)
\(548\) 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 0.280200 + 0.959942i \(0.409599\pi\)
−0.971434 + 0.237311i \(0.923734\pi\)
\(558\) 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 \(-0.820868\pi\)
0.884936 + 0.465712i \(0.154202\pi\)
\(564\) 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 0.920866 0.389880i \(-0.127483\pi\)
−0.798079 + 0.602553i \(0.794150\pi\)
\(570\) 0 0
\(571\) −20.8284 + 36.0759i −0.871643 + 1.50973i −0.0113458 + 0.999936i \(0.503612\pi\)
−0.860297 + 0.509794i \(0.829722\pi\)
\(572\) 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 −0.970144 0.242528i \(-0.922023\pi\)
0.695108 + 0.718905i \(0.255357\pi\)
\(578\) 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 \(-0.235397\pi\)
0.738791 + 0.673934i \(0.235397\pi\)
\(588\) 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 −0.684690 0.728835i \(-0.740062\pi\)
−0.288844 0.957376i \(-0.593271\pi\)
\(594\) 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 \(-0.674264\pi\)
0.999715 + 0.0238650i \(0.00759718\pi\)
\(600\) 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 0.999969 + 0.00782569i \(0.00249102\pi\)
−0.493207 + 0.869912i \(0.664176\pi\)
\(608\) 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 −0.742483 0.669864i \(-0.766352\pi\)
0.951361 + 0.308077i \(0.0996856\pi\)
\(614\) 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 −0.299668 0.954043i \(-0.596876\pi\)
0.976060 0.217501i \(-0.0697906\pi\)
\(620\) 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 \(-0.480794\pi\)
0.0603000 + 0.998180i \(0.480794\pi\)
\(632\) 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 0.277272 + 0.960792i \(0.410570\pi\)
−0.970706 + 0.240272i \(0.922764\pi\)
\(642\) 0 0
\(643\) −31.7990 −1.25403 −0.627015 0.779007i \(-0.715723\pi\)
−0.627015 + 0.779007i \(0.715723\pi\)
\(644\) 0 0
\(645\) 38.6274 1.52095
\(646\) 0 0
\(647\) −0.100505 + 0.174080i −0.00395126 + 0.00684379i −0.867994 0.496574i \(-0.834591\pi\)
0.864043 + 0.503418i \(0.167924\pi\)
\(648\) 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 −0.823790 0.566895i \(-0.808144\pi\)
−0.0790508 0.996871i \(-0.525189\pi\)
\(654\) 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 \(-0.637636\pi\)
−0.419047 + 0.907964i \(0.637636\pi\)
\(660\) 0 0
\(661\) −2.46447 + 4.26858i −0.0958566 + 0.166029i −0.909966 0.414683i \(-0.863892\pi\)
0.814109 + 0.580712i \(0.197226\pi\)
\(662\) 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 −0.999290 0.0376716i \(-0.988006\pi\)
0.467021 0.884246i \(-0.345327\pi\)
\(678\) 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 \(-0.844291\pi\)
0.848303 + 0.529511i \(0.177624\pi\)
\(684\) 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 \(-0.113833\pi\)
−0.771513 + 0.636214i \(0.780500\pi\)
\(692\) 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 0.797068 0.603889i \(-0.206383\pi\)
−0.921517 + 0.388337i \(0.873050\pi\)
\(710\) 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 \(-0.206104\pi\)
−0.921177 + 0.389143i \(0.872771\pi\)
\(720\) 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 \(-0.441483\pi\)
0.182804 + 0.983149i \(0.441483\pi\)
\(728\) 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 0.930678 0.365840i \(-0.119218\pi\)
−0.782166 + 0.623071i \(0.785885\pi\)
\(734\) 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 −0.385404 0.922748i \(-0.625938\pi\)
0.991825 0.127604i \(-0.0407286\pi\)
\(740\) 0 0
\(741\) 28.9706 1.06426
\(742\) 0 0
\(743\) 4.82843 0.177138 0.0885689 0.996070i \(-0.471771\pi\)
0.0885689 + 0.996070i \(0.471771\pi\)
\(744\) 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 \(-0.0459929\pi\)
−0.619488 + 0.785006i \(0.712660\pi\)
\(752\) 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 0.995688 + 0.0927614i \(0.0295694\pi\)
−0.417510 + 0.908672i \(0.637097\pi\)
\(762\) 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 0.392988 + 0.919544i \(0.371441\pi\)
−0.992842 + 0.119434i \(0.961892\pi\)
\(774\) 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 \(-0.745338\pi\)
0.969613 + 0.244645i \(0.0786715\pi\)
\(788\) 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