Properties

Label 1960.2.q.r.961.1
Level $1960$
Weight $2$
Character 1960.961
Analytic conductor $15.651$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.6506787962\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
Defining polynomial: \(x^{4} - x^{3} - 2 x^{2} - 3 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(-1.18614 - 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 1960.961
Dual form 1960.2.q.r.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.68614 - 2.92048i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-4.18614 + 7.25061i) q^{9} +O(q^{10})\) \(q+(-1.68614 - 2.92048i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-4.18614 + 7.25061i) q^{9} +(-0.313859 - 0.543620i) q^{11} +1.37228 q^{13} +3.37228 q^{15} +(2.68614 + 4.65253i) q^{17} +(3.37228 - 5.84096i) q^{19} +(-3.37228 + 5.84096i) q^{23} +(-0.500000 - 0.866025i) q^{25} +18.1168 q^{27} +1.37228 q^{29} +(-4.00000 - 6.92820i) q^{31} +(-1.05842 + 1.83324i) q^{33} +(1.00000 - 1.73205i) q^{37} +(-2.31386 - 4.00772i) q^{39} +4.74456 q^{41} +2.74456 q^{43} +(-4.18614 - 7.25061i) q^{45} +(5.05842 - 8.76144i) q^{47} +(9.05842 - 15.6896i) q^{51} +(0.372281 + 0.644810i) q^{53} +0.627719 q^{55} -22.7446 q^{57} +(4.00000 + 6.92820i) q^{59} +(4.37228 - 7.57301i) q^{61} +(-0.686141 + 1.18843i) q^{65} +(2.00000 + 3.46410i) q^{67} +22.7446 q^{69} +8.00000 q^{71} +(-3.00000 - 5.19615i) q^{73} +(-1.68614 + 2.92048i) q^{75} +(1.05842 - 1.83324i) q^{79} +(-17.9891 - 31.1581i) q^{81} -13.4891 q^{83} -5.37228 q^{85} +(-2.31386 - 4.00772i) q^{87} +(1.62772 - 2.81929i) q^{89} +(-13.4891 + 23.3639i) q^{93} +(3.37228 + 5.84096i) q^{95} -18.8614 q^{97} +5.25544 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - q^{3} - 2q^{5} - 11q^{9} + O(q^{10}) \) \( 4q - q^{3} - 2q^{5} - 11q^{9} - 7q^{11} - 6q^{13} + 2q^{15} + 5q^{17} + 2q^{19} - 2q^{23} - 2q^{25} + 38q^{27} - 6q^{29} - 16q^{31} + 13q^{33} + 4q^{37} - 15q^{39} - 4q^{41} - 12q^{43} - 11q^{45} + 3q^{47} + 19q^{51} - 10q^{53} + 14q^{55} - 68q^{57} + 16q^{59} + 6q^{61} + 3q^{65} + 8q^{67} + 68q^{69} + 32q^{71} - 12q^{73} - q^{75} - 13q^{79} - 26q^{81} - 8q^{83} - 10q^{85} - 15q^{87} + 18q^{89} - 8q^{93} + 2q^{95} - 18q^{97} + 44q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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 0
\(3\) −1.68614 2.92048i −0.973494 1.68614i −0.684819 0.728714i \(-0.740119\pi\)
−0.288675 0.957427i \(-0.593215\pi\)
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −4.18614 + 7.25061i −1.39538 + 2.41687i
\(10\) 0 0
\(11\) −0.313859 0.543620i −0.0946322 0.163908i 0.814823 0.579710i \(-0.196834\pi\)
−0.909455 + 0.415802i \(0.863501\pi\)
\(12\) 0 0
\(13\) 1.37228 0.380602 0.190301 0.981726i \(-0.439054\pi\)
0.190301 + 0.981726i \(0.439054\pi\)
\(14\) 0 0
\(15\) 3.37228 0.870719
\(16\) 0 0
\(17\) 2.68614 + 4.65253i 0.651485 + 1.12840i 0.982763 + 0.184872i \(0.0591869\pi\)
−0.331278 + 0.943533i \(0.607480\pi\)
\(18\) 0 0
\(19\) 3.37228 5.84096i 0.773654 1.34001i −0.161893 0.986808i \(-0.551760\pi\)
0.935548 0.353200i \(-0.114907\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.37228 + 5.84096i −0.703169 + 1.21792i 0.264179 + 0.964474i \(0.414899\pi\)
−0.967348 + 0.253451i \(0.918434\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 18.1168 3.48659
\(28\) 0 0
\(29\) 1.37228 0.254826 0.127413 0.991850i \(-0.459333\pi\)
0.127413 + 0.991850i \(0.459333\pi\)
\(30\) 0 0
\(31\) −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i \(-0.911532\pi\)
0.243204 0.969975i \(-0.421802\pi\)
\(32\) 0 0
\(33\) −1.05842 + 1.83324i −0.184248 + 0.319126i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.00000 1.73205i 0.164399 0.284747i −0.772043 0.635571i \(-0.780765\pi\)
0.936442 + 0.350823i \(0.114098\pi\)
\(38\) 0 0
\(39\) −2.31386 4.00772i −0.370514 0.641749i
\(40\) 0 0
\(41\) 4.74456 0.740976 0.370488 0.928837i \(-0.379190\pi\)
0.370488 + 0.928837i \(0.379190\pi\)
\(42\) 0 0
\(43\) 2.74456 0.418542 0.209271 0.977858i \(-0.432891\pi\)
0.209271 + 0.977858i \(0.432891\pi\)
\(44\) 0 0
\(45\) −4.18614 7.25061i −0.624033 1.08086i
\(46\) 0 0
\(47\) 5.05842 8.76144i 0.737847 1.27799i −0.215616 0.976478i \(-0.569176\pi\)
0.953463 0.301510i \(-0.0974906\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 9.05842 15.6896i 1.26843 2.19699i
\(52\) 0 0
\(53\) 0.372281 + 0.644810i 0.0511368 + 0.0885715i 0.890461 0.455060i \(-0.150382\pi\)
−0.839324 + 0.543632i \(0.817049\pi\)
\(54\) 0 0
\(55\) 0.627719 0.0846416
\(56\) 0 0
\(57\) −22.7446 −3.01259
\(58\) 0 0
\(59\) 4.00000 + 6.92820i 0.520756 + 0.901975i 0.999709 + 0.0241347i \(0.00768307\pi\)
−0.478953 + 0.877841i \(0.658984\pi\)
\(60\) 0 0
\(61\) 4.37228 7.57301i 0.559813 0.969625i −0.437698 0.899122i \(-0.644206\pi\)
0.997512 0.0705031i \(-0.0224605\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.686141 + 1.18843i −0.0851053 + 0.147407i
\(66\) 0 0
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 0 0
\(69\) 22.7446 2.73812
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) −3.00000 5.19615i −0.351123 0.608164i 0.635323 0.772246i \(-0.280867\pi\)
−0.986447 + 0.164083i \(0.947534\pi\)
\(74\) 0 0
\(75\) −1.68614 + 2.92048i −0.194699 + 0.337228i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.05842 1.83324i 0.119082 0.206256i −0.800322 0.599570i \(-0.795338\pi\)
0.919404 + 0.393314i \(0.128672\pi\)
\(80\) 0 0
\(81\) −17.9891 31.1581i −1.99879 3.46201i
\(82\) 0 0
\(83\) −13.4891 −1.48062 −0.740312 0.672264i \(-0.765322\pi\)
−0.740312 + 0.672264i \(0.765322\pi\)
\(84\) 0 0
\(85\) −5.37228 −0.582706
\(86\) 0 0
\(87\) −2.31386 4.00772i −0.248072 0.429673i
\(88\) 0 0
\(89\) 1.62772 2.81929i 0.172538 0.298844i −0.766769 0.641924i \(-0.778137\pi\)
0.939306 + 0.343079i \(0.111470\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −13.4891 + 23.3639i −1.39876 + 2.42272i
\(94\) 0 0
\(95\) 3.37228 + 5.84096i 0.345989 + 0.599270i
\(96\) 0 0
\(97\) −18.8614 −1.91509 −0.957543 0.288291i \(-0.906913\pi\)
−0.957543 + 0.288291i \(0.906913\pi\)
\(98\) 0 0
\(99\) 5.25544 0.528191
\(100\) 0 0
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 0 0
\(103\) −5.68614 + 9.84868i −0.560272 + 0.970420i 0.437200 + 0.899364i \(0.355970\pi\)
−0.997472 + 0.0710555i \(0.977363\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.37228 2.37686i 0.132663 0.229780i −0.792039 0.610470i \(-0.790980\pi\)
0.924702 + 0.380691i \(0.124314\pi\)
\(108\) 0 0
\(109\) 2.68614 + 4.65253i 0.257286 + 0.445632i 0.965514 0.260352i \(-0.0838386\pi\)
−0.708228 + 0.705984i \(0.750505\pi\)
\(110\) 0 0
\(111\) −6.74456 −0.640166
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) −3.37228 5.84096i −0.314467 0.544673i
\(116\) 0 0
\(117\) −5.74456 + 9.94987i −0.531085 + 0.919866i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.30298 9.18504i 0.482090 0.835004i
\(122\) 0 0
\(123\) −8.00000 13.8564i −0.721336 1.24939i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) −4.62772 8.01544i −0.407448 0.705720i
\(130\) 0 0
\(131\) 3.37228 5.84096i 0.294638 0.510327i −0.680263 0.732968i \(-0.738134\pi\)
0.974901 + 0.222641i \(0.0714677\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −9.05842 + 15.6896i −0.779625 + 1.35035i
\(136\) 0 0
\(137\) −1.62772 2.81929i −0.139065 0.240868i 0.788078 0.615576i \(-0.211076\pi\)
−0.927143 + 0.374707i \(0.877743\pi\)
\(138\) 0 0
\(139\) −6.74456 −0.572066 −0.286033 0.958220i \(-0.592337\pi\)
−0.286033 + 0.958220i \(0.592337\pi\)
\(140\) 0 0
\(141\) −34.1168 −2.87316
\(142\) 0 0
\(143\) −0.430703 0.746000i −0.0360172 0.0623837i
\(144\) 0 0
\(145\) −0.686141 + 1.18843i −0.0569809 + 0.0986938i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.74456 6.48577i 0.306767 0.531335i −0.670887 0.741560i \(-0.734086\pi\)
0.977653 + 0.210225i \(0.0674196\pi\)
\(150\) 0 0
\(151\) 1.05842 + 1.83324i 0.0861332 + 0.149187i 0.905874 0.423548i \(-0.139216\pi\)
−0.819740 + 0.572735i \(0.805882\pi\)
\(152\) 0 0
\(153\) −44.9783 −3.63628
\(154\) 0 0
\(155\) 8.00000 0.642575
\(156\) 0 0
\(157\) 3.74456 + 6.48577i 0.298849 + 0.517621i 0.975873 0.218340i \(-0.0700641\pi\)
−0.677024 + 0.735961i \(0.736731\pi\)
\(158\) 0 0
\(159\) 1.25544 2.17448i 0.0995627 0.172448i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.62772 4.55134i 0.205819 0.356489i −0.744574 0.667539i \(-0.767348\pi\)
0.950393 + 0.311051i \(0.100681\pi\)
\(164\) 0 0
\(165\) −1.05842 1.83324i −0.0823980 0.142718i
\(166\) 0 0
\(167\) 11.3723 0.880014 0.440007 0.897994i \(-0.354976\pi\)
0.440007 + 0.897994i \(0.354976\pi\)
\(168\) 0 0
\(169\) −11.1168 −0.855142
\(170\) 0 0
\(171\) 28.2337 + 48.9022i 2.15908 + 3.73964i
\(172\) 0 0
\(173\) 2.68614 4.65253i 0.204223 0.353725i −0.745662 0.666325i \(-0.767866\pi\)
0.949885 + 0.312599i \(0.101200\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 13.4891 23.3639i 1.01390 1.75613i
\(178\) 0 0
\(179\) −11.4891 19.8997i −0.858738 1.48738i −0.873134 0.487481i \(-0.837916\pi\)
0.0143962 0.999896i \(-0.495417\pi\)
\(180\) 0 0
\(181\) 18.2337 1.35530 0.677650 0.735385i \(-0.262999\pi\)
0.677650 + 0.735385i \(0.262999\pi\)
\(182\) 0 0
\(183\) −29.4891 −2.17990
\(184\) 0 0
\(185\) 1.00000 + 1.73205i 0.0735215 + 0.127343i
\(186\) 0 0
\(187\) 1.68614 2.92048i 0.123303 0.213567i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 12.4307 21.5306i 0.899454 1.55790i 0.0712608 0.997458i \(-0.477298\pi\)
0.828193 0.560443i \(-0.189369\pi\)
\(192\) 0 0
\(193\) 2.37228 + 4.10891i 0.170761 + 0.295766i 0.938686 0.344773i \(-0.112044\pi\)
−0.767925 + 0.640539i \(0.778711\pi\)
\(194\) 0 0
\(195\) 4.62772 0.331398
\(196\) 0 0
\(197\) 26.2337 1.86907 0.934536 0.355867i \(-0.115815\pi\)
0.934536 + 0.355867i \(0.115815\pi\)
\(198\) 0 0
\(199\) −8.00000 13.8564i −0.567105 0.982255i −0.996850 0.0793045i \(-0.974730\pi\)
0.429745 0.902950i \(-0.358603\pi\)
\(200\) 0 0
\(201\) 6.74456 11.6819i 0.475725 0.823979i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −2.37228 + 4.10891i −0.165687 + 0.286979i
\(206\) 0 0
\(207\) −28.2337 48.9022i −1.96238 3.39894i
\(208\) 0 0
\(209\) −4.23369 −0.292850
\(210\) 0 0
\(211\) −8.62772 −0.593957 −0.296978 0.954884i \(-0.595979\pi\)
−0.296978 + 0.954884i \(0.595979\pi\)
\(212\) 0 0
\(213\) −13.4891 23.3639i −0.924260 1.60086i
\(214\) 0 0
\(215\) −1.37228 + 2.37686i −0.0935888 + 0.162101i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −10.1168 + 17.5229i −0.683633 + 1.18409i
\(220\) 0 0
\(221\) 3.68614 + 6.38458i 0.247957 + 0.429474i
\(222\) 0 0
\(223\) 11.3723 0.761544 0.380772 0.924669i \(-0.375658\pi\)
0.380772 + 0.924669i \(0.375658\pi\)
\(224\) 0 0
\(225\) 8.37228 0.558152
\(226\) 0 0
\(227\) −4.43070 7.67420i −0.294076 0.509355i 0.680693 0.732568i \(-0.261679\pi\)
−0.974770 + 0.223214i \(0.928345\pi\)
\(228\) 0 0
\(229\) 11.1168 19.2549i 0.734622 1.27240i −0.220267 0.975440i \(-0.570693\pi\)
0.954889 0.296963i \(-0.0959737\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.37228 11.0371i 0.417462 0.723065i −0.578221 0.815880i \(-0.696253\pi\)
0.995683 + 0.0928145i \(0.0295863\pi\)
\(234\) 0 0
\(235\) 5.05842 + 8.76144i 0.329975 + 0.571534i
\(236\) 0 0
\(237\) −7.13859 −0.463701
\(238\) 0 0
\(239\) 19.3723 1.25309 0.626544 0.779386i \(-0.284469\pi\)
0.626544 + 0.779386i \(0.284469\pi\)
\(240\) 0 0
\(241\) 13.0000 + 22.5167i 0.837404 + 1.45043i 0.892058 + 0.451920i \(0.149261\pi\)
−0.0546547 + 0.998505i \(0.517406\pi\)
\(242\) 0 0
\(243\) −33.4891 + 58.0049i −2.14833 + 3.72101i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 4.62772 8.01544i 0.294455 0.510010i
\(248\) 0 0
\(249\) 22.7446 + 39.3947i 1.44138 + 2.49654i
\(250\) 0 0
\(251\) 6.74456 0.425713 0.212857 0.977083i \(-0.431723\pi\)
0.212857 + 0.977083i \(0.431723\pi\)
\(252\) 0 0
\(253\) 4.23369 0.266170
\(254\) 0 0
\(255\) 9.05842 + 15.6896i 0.567260 + 0.982524i
\(256\) 0 0
\(257\) −0.255437 + 0.442430i −0.0159337 + 0.0275981i −0.873882 0.486137i \(-0.838405\pi\)
0.857949 + 0.513736i \(0.171739\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −5.74456 + 9.94987i −0.355580 + 0.615882i
\(262\) 0 0
\(263\) 6.11684 + 10.5947i 0.377181 + 0.653296i 0.990651 0.136422i \(-0.0435602\pi\)
−0.613470 + 0.789718i \(0.710227\pi\)
\(264\) 0 0
\(265\) −0.744563 −0.0457381
\(266\) 0 0
\(267\) −10.9783 −0.671858
\(268\) 0 0
\(269\) −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i \(-0.225219\pi\)
−0.942871 + 0.333157i \(0.891886\pi\)
\(270\) 0 0
\(271\) −6.74456 + 11.6819i −0.409703 + 0.709626i −0.994856 0.101296i \(-0.967701\pi\)
0.585153 + 0.810923i \(0.301034\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.313859 + 0.543620i −0.0189264 + 0.0327815i
\(276\) 0 0
\(277\) 10.4891 + 18.1677i 0.630230 + 1.09159i 0.987504 + 0.157592i \(0.0503729\pi\)
−0.357274 + 0.934000i \(0.616294\pi\)
\(278\) 0 0
\(279\) 66.9783 4.00988
\(280\) 0 0
\(281\) −21.6060 −1.28890 −0.644452 0.764645i \(-0.722914\pi\)
−0.644452 + 0.764645i \(0.722914\pi\)
\(282\) 0 0
\(283\) −13.0584 22.6179i −0.776243 1.34449i −0.934093 0.357029i \(-0.883790\pi\)
0.157851 0.987463i \(-0.449543\pi\)
\(284\) 0 0
\(285\) 11.3723 19.6974i 0.673636 1.16677i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −5.93070 + 10.2723i −0.348865 + 0.604252i
\(290\) 0 0
\(291\) 31.8030 + 55.0844i 1.86432 + 3.22910i
\(292\) 0 0
\(293\) −7.88316 −0.460539 −0.230269 0.973127i \(-0.573961\pi\)
−0.230269 + 0.973127i \(0.573961\pi\)
\(294\) 0 0
\(295\) −8.00000 −0.465778
\(296\) 0 0
\(297\) −5.68614 9.84868i −0.329943 0.571479i
\(298\) 0 0
\(299\) −4.62772 + 8.01544i −0.267628 + 0.463545i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −10.1168 + 17.5229i −0.581198 + 1.00666i
\(304\) 0 0
\(305\) 4.37228 + 7.57301i 0.250356 + 0.433629i
\(306\) 0 0
\(307\) −13.8832 −0.792354 −0.396177 0.918174i \(-0.629663\pi\)
−0.396177 + 0.918174i \(0.629663\pi\)
\(308\) 0 0
\(309\) 38.3505 2.18169
\(310\) 0 0
\(311\) −0.627719 1.08724i −0.0355947 0.0616518i 0.847679 0.530509i \(-0.177999\pi\)
−0.883274 + 0.468857i \(0.844666\pi\)
\(312\) 0 0
\(313\) 10.0584 17.4217i 0.568536 0.984733i −0.428175 0.903696i \(-0.640843\pi\)
0.996711 0.0810370i \(-0.0258232\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7.00000 + 12.1244i −0.393159 + 0.680972i −0.992864 0.119249i \(-0.961951\pi\)
0.599705 + 0.800221i \(0.295285\pi\)
\(318\) 0 0
\(319\) −0.430703 0.746000i −0.0241148 0.0417680i
\(320\) 0 0
\(321\) −9.25544 −0.516588
\(322\) 0 0
\(323\) 36.2337 2.01610
\(324\) 0 0
\(325\) −0.686141 1.18843i −0.0380602 0.0659223i
\(326\) 0 0
\(327\) 9.05842 15.6896i 0.500932 0.867639i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −6.00000 + 10.3923i −0.329790 + 0.571213i −0.982470 0.186421i \(-0.940311\pi\)
0.652680 + 0.757634i \(0.273645\pi\)
\(332\) 0 0
\(333\) 8.37228 + 14.5012i 0.458798 + 0.794662i
\(334\) 0 0
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) 15.4891 0.843746 0.421873 0.906655i \(-0.361373\pi\)
0.421873 + 0.906655i \(0.361373\pi\)
\(338\) 0 0
\(339\) −3.37228 5.84096i −0.183157 0.317238i
\(340\) 0 0
\(341\) −2.51087 + 4.34896i −0.135971 + 0.235510i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −11.3723 + 19.6974i −0.612263 + 1.06047i
\(346\) 0 0
\(347\) 6.62772 + 11.4795i 0.355795 + 0.616254i 0.987254 0.159155i \(-0.0508769\pi\)
−0.631459 + 0.775409i \(0.717544\pi\)
\(348\) 0 0
\(349\) 3.48913 0.186769 0.0933843 0.995630i \(-0.470231\pi\)
0.0933843 + 0.995630i \(0.470231\pi\)
\(350\) 0 0
\(351\) 24.8614 1.32700
\(352\) 0 0
\(353\) 13.4307 + 23.2627i 0.714844 + 1.23815i 0.963020 + 0.269431i \(0.0868357\pi\)
−0.248175 + 0.968715i \(0.579831\pi\)
\(354\) 0 0
\(355\) −4.00000 + 6.92820i −0.212298 + 0.367711i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(360\) 0 0
\(361\) −13.2446 22.9403i −0.697082 1.20738i
\(362\) 0 0
\(363\) −35.7663 −1.87724
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) 0 0
\(367\) −4.43070 7.67420i −0.231281 0.400590i 0.726904 0.686739i \(-0.240958\pi\)
−0.958185 + 0.286148i \(0.907625\pi\)
\(368\) 0 0
\(369\) −19.8614 + 34.4010i −1.03394 + 1.79084i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 9.62772 16.6757i 0.498504 0.863435i −0.501494 0.865161i \(-0.667216\pi\)
0.999999 + 0.00172614i \(0.000549447\pi\)
\(374\) 0 0
\(375\) −1.68614 2.92048i −0.0870719 0.150813i
\(376\) 0 0
\(377\) 1.88316 0.0969875
\(378\) 0 0
\(379\) 12.0000 0.616399 0.308199 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) 0 0
\(381\) −13.4891 23.3639i −0.691069 1.19697i
\(382\) 0 0
\(383\) 2.74456 4.75372i 0.140241 0.242904i −0.787347 0.616511i \(-0.788546\pi\)
0.927587 + 0.373607i \(0.121879\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −11.4891 + 19.8997i −0.584025 + 1.01156i
\(388\) 0 0
\(389\) 5.43070 + 9.40625i 0.275348 + 0.476916i 0.970223 0.242214i \(-0.0778737\pi\)
−0.694875 + 0.719130i \(0.744540\pi\)
\(390\) 0 0
\(391\) −36.2337 −1.83242
\(392\) 0 0
\(393\) −22.7446 −1.14731
\(394\) 0 0
\(395\) 1.05842 + 1.83324i 0.0532550 + 0.0922403i
\(396\) 0 0
\(397\) 18.6861 32.3653i 0.937831 1.62437i 0.168323 0.985732i \(-0.446165\pi\)
0.769507 0.638638i \(-0.220502\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.802985 + 1.39081i −0.0400991 + 0.0694537i −0.885378 0.464871i \(-0.846101\pi\)
0.845279 + 0.534325i \(0.179434\pi\)
\(402\) 0 0
\(403\) −5.48913 9.50744i −0.273433 0.473600i
\(404\) 0 0
\(405\) 35.9783 1.78777
\(406\) 0 0
\(407\) −1.25544 −0.0622297
\(408\) 0 0
\(409\) −5.74456 9.94987i −0.284050 0.491990i 0.688328 0.725399i \(-0.258345\pi\)
−0.972378 + 0.233410i \(0.925012\pi\)
\(410\) 0 0
\(411\) −5.48913 + 9.50744i −0.270759 + 0.468968i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 6.74456 11.6819i 0.331078 0.573443i
\(416\) 0 0
\(417\) 11.3723 + 19.6974i 0.556903 + 0.964584i
\(418\) 0 0
\(419\) 37.4891 1.83146 0.915732 0.401790i \(-0.131612\pi\)
0.915732 + 0.401790i \(0.131612\pi\)
\(420\) 0 0
\(421\) 21.6060 1.05301 0.526505 0.850172i \(-0.323502\pi\)
0.526505 + 0.850172i \(0.323502\pi\)
\(422\) 0 0
\(423\) 42.3505 + 73.3533i 2.05915 + 3.56656i
\(424\) 0 0
\(425\) 2.68614 4.65253i 0.130297 0.225681i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −1.45245 + 2.51572i −0.0701251 + 0.121460i
\(430\) 0 0
\(431\) −6.31386 10.9359i −0.304128 0.526765i 0.672939 0.739698i \(-0.265032\pi\)
−0.977067 + 0.212933i \(0.931698\pi\)
\(432\) 0 0
\(433\) 16.9783 0.815923 0.407961 0.912999i \(-0.366240\pi\)
0.407961 + 0.912999i \(0.366240\pi\)
\(434\) 0 0
\(435\) 4.62772 0.221882
\(436\) 0 0
\(437\) 22.7446 + 39.3947i 1.08802 + 1.88451i
\(438\) 0 0
\(439\) 14.1168 24.4511i 0.673760 1.16699i −0.303069 0.952968i \(-0.598011\pi\)
0.976830 0.214018i \(-0.0686553\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.62772 4.55134i 0.124847 0.216241i −0.796826 0.604208i \(-0.793489\pi\)
0.921673 + 0.387968i \(0.126823\pi\)
\(444\) 0 0
\(445\) 1.62772 + 2.81929i 0.0771613 + 0.133647i
\(446\) 0 0
\(447\) −25.2554 −1.19454
\(448\) 0 0
\(449\) −0.116844 −0.00551421 −0.00275710 0.999996i \(-0.500878\pi\)
−0.00275710 + 0.999996i \(0.500878\pi\)
\(450\) 0 0
\(451\) −1.48913 2.57924i −0.0701202 0.121452i
\(452\) 0 0
\(453\) 3.56930 6.18220i 0.167700 0.290465i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −8.37228 + 14.5012i −0.391639 + 0.678338i −0.992666 0.120890i \(-0.961425\pi\)
0.601027 + 0.799229i \(0.294758\pi\)
\(458\) 0 0
\(459\) 48.6644 + 84.2892i 2.27146 + 3.93428i
\(460\) 0 0
\(461\) 12.7446 0.593573 0.296787 0.954944i \(-0.404085\pi\)
0.296787 + 0.954944i \(0.404085\pi\)
\(462\) 0 0
\(463\) −29.4891 −1.37048 −0.685238 0.728319i \(-0.740302\pi\)
−0.685238 + 0.728319i \(0.740302\pi\)
\(464\) 0 0
\(465\) −13.4891 23.3639i −0.625543 1.08347i
\(466\) 0 0
\(467\) −15.8030 + 27.3716i −0.731275 + 1.26661i 0.225064 + 0.974344i \(0.427741\pi\)
−0.956339 + 0.292261i \(0.905592\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 12.6277 21.8719i 0.581855 1.00780i
\(472\) 0 0
\(473\) −0.861407 1.49200i −0.0396075 0.0686022i
\(474\) 0 0
\(475\) −6.74456 −0.309462
\(476\) 0 0
\(477\) −6.23369 −0.285421
\(478\) 0 0
\(479\) −6.11684 10.5947i −0.279486 0.484083i 0.691771 0.722117i \(-0.256831\pi\)
−0.971257 + 0.238033i \(0.923497\pi\)
\(480\) 0 0
\(481\) 1.37228 2.37686i 0.0625706 0.108376i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 9.43070 16.3345i 0.428226 0.741709i
\(486\) 0 0
\(487\) 2.11684 + 3.66648i 0.0959234 + 0.166144i 0.909994 0.414622i \(-0.136086\pi\)
−0.814070 + 0.580766i \(0.802753\pi\)
\(488\) 0 0
\(489\) −17.7228 −0.801453
\(490\) 0 0
\(491\) 17.8832 0.807056 0.403528 0.914967i \(-0.367784\pi\)
0.403528 + 0.914967i \(0.367784\pi\)
\(492\) 0 0
\(493\) 3.68614 + 6.38458i 0.166015 + 0.287547i
\(494\) 0 0
\(495\) −2.62772 + 4.55134i −0.118107 + 0.204568i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −1.56930 + 2.71810i −0.0702514 + 0.121679i −0.899011 0.437925i \(-0.855713\pi\)
0.828760 + 0.559604i \(0.189047\pi\)
\(500\) 0 0
\(501\) −19.1753 33.2125i −0.856688 1.48383i
\(502\) 0 0
\(503\) 12.6277 0.563042 0.281521 0.959555i \(-0.409161\pi\)
0.281521 + 0.959555i \(0.409161\pi\)
\(504\) 0 0
\(505\) 6.00000 0.266996
\(506\) 0 0
\(507\) 18.7446 + 32.4665i 0.832475 + 1.44189i
\(508\) 0 0
\(509\) 2.48913 4.31129i 0.110329 0.191095i −0.805574 0.592495i \(-0.798143\pi\)
0.915903 + 0.401400i \(0.131476\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 61.0951 105.820i 2.69741 4.67206i
\(514\) 0 0
\(515\) −5.68614 9.84868i −0.250561 0.433985i
\(516\) 0 0
\(517\) −6.35053 −0.279296
\(518\) 0 0
\(519\) −18.1168 −0.795241
\(520\) 0 0
\(521\) −15.0000 25.9808i −0.657162 1.13824i −0.981347 0.192244i \(-0.938423\pi\)
0.324185 0.945994i \(-0.394910\pi\)
\(522\) 0 0
\(523\) 16.2337 28.1176i 0.709850 1.22950i −0.255063 0.966924i \(-0.582096\pi\)
0.964913 0.262571i \(-0.0845704\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 21.4891 37.2203i 0.936081 1.62134i
\(528\) 0 0
\(529\) −11.2446 19.4762i −0.488894 0.846789i
\(530\) 0 0
\(531\) −66.9783 −2.90661
\(532\) 0 0
\(533\) 6.51087 0.282017
\(534\) 0 0
\(535\) 1.37228 + 2.37686i 0.0593289 + 0.102761i
\(536\) 0 0
\(537\) −38.7446 + 67.1076i −1.67195 + 2.89590i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −10.1753 + 17.6241i −0.437469 + 0.757718i −0.997494 0.0707576i \(-0.977458\pi\)
0.560025 + 0.828476i \(0.310792\pi\)
\(542\) 0 0
\(543\) −30.7446 53.2511i −1.31938 2.28523i
\(544\) 0 0
\(545\) −5.37228 −0.230123
\(546\) 0 0
\(547\) 14.9783 0.640424 0.320212 0.947346i \(-0.396246\pi\)
0.320212 + 0.947346i \(0.396246\pi\)
\(548\) 0 0
\(549\) 36.6060 + 63.4034i 1.56230 + 2.70599i
\(550\) 0 0
\(551\) 4.62772 8.01544i 0.197147 0.341469i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 3.37228 5.84096i 0.143145 0.247935i
\(556\) 0 0
\(557\) 19.1168 + 33.1113i 0.810007 + 1.40297i 0.912859 + 0.408276i \(0.133870\pi\)
−0.102852 + 0.994697i \(0.532797\pi\)
\(558\) 0 0
\(559\) 3.76631 0.159298
\(560\) 0 0
\(561\) −11.3723 −0.480138
\(562\) 0 0
\(563\) −2.74456 4.75372i −0.115670 0.200345i 0.802378 0.596817i \(-0.203568\pi\)
−0.918047 + 0.396471i \(0.870235\pi\)
\(564\) 0 0
\(565\) −1.00000 + 1.73205i −0.0420703 + 0.0728679i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −10.4891 + 18.1677i −0.439727 + 0.761630i −0.997668 0.0682510i \(-0.978258\pi\)
0.557941 + 0.829880i \(0.311591\pi\)
\(570\) 0 0
\(571\) 10.0000 + 17.3205i 0.418487 + 0.724841i 0.995788 0.0916910i \(-0.0292272\pi\)
−0.577301 + 0.816532i \(0.695894\pi\)
\(572\) 0 0
\(573\) −83.8397 −3.50245
\(574\) 0 0
\(575\) 6.74456 0.281268
\(576\) 0 0
\(577\) 8.80298 + 15.2472i 0.366473 + 0.634750i 0.989011 0.147839i \(-0.0472319\pi\)
−0.622538 + 0.782589i \(0.713899\pi\)
\(578\) 0 0
\(579\) 8.00000 13.8564i 0.332469 0.575853i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.233688 0.404759i 0.00967837 0.0167634i
\(584\) 0 0
\(585\) −5.74456 9.94987i −0.237508 0.411377i
\(586\) 0 0
\(587\) −10.9783 −0.453121 −0.226560 0.973997i \(-0.572748\pi\)
−0.226560 + 0.973997i \(0.572748\pi\)
\(588\) 0 0
\(589\) −53.9565 −2.22324
\(590\) 0 0
\(591\) −44.2337 76.6150i −1.81953 3.15152i
\(592\) 0 0
\(593\) −12.6861 + 21.9730i −0.520957 + 0.902325i 0.478746 + 0.877954i \(0.341092\pi\)
−0.999703 + 0.0243710i \(0.992242\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −26.9783 + 46.7277i −1.10415 + 1.91244i
\(598\) 0 0
\(599\) −3.80298 6.58696i −0.155386 0.269136i 0.777814 0.628495i \(-0.216329\pi\)
−0.933199 + 0.359359i \(0.882995\pi\)
\(600\) 0 0
\(601\) −39.4891 −1.61080 −0.805398 0.592735i \(-0.798048\pi\)
−0.805398 + 0.592735i \(0.798048\pi\)
\(602\) 0 0
\(603\) −33.4891 −1.36378
\(604\) 0 0
\(605\) 5.30298 + 9.18504i 0.215597 + 0.373425i
\(606\) 0 0
\(607\) −7.80298 + 13.5152i −0.316713 + 0.548564i −0.979800 0.199979i \(-0.935913\pi\)
0.663087 + 0.748542i \(0.269246\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.94158 12.0232i 0.280826 0.486405i
\(612\) 0 0
\(613\) 15.7446 + 27.2704i 0.635917 + 1.10144i 0.986320 + 0.164841i \(0.0527112\pi\)
−0.350403 + 0.936599i \(0.613955\pi\)
\(614\) 0 0
\(615\) 16.0000 0.645182
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 0 0
\(619\) −0.627719 1.08724i −0.0252301 0.0436999i 0.853135 0.521691i \(-0.174699\pi\)
−0.878365 + 0.477991i \(0.841365\pi\)
\(620\) 0 0
\(621\) −61.0951 + 105.820i −2.45166 + 4.24640i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 7.13859 + 12.3644i 0.285088 + 0.493787i
\(628\) 0 0
\(629\) 10.7446 0.428414
\(630\) 0 0
\(631\) −3.37228 −0.134248 −0.0671242 0.997745i \(-0.521382\pi\)
−0.0671242 + 0.997745i \(0.521382\pi\)
\(632\) 0 0
\(633\) 14.5475 + 25.1971i 0.578213 + 1.00149i
\(634\) 0 0
\(635\) −4.00000 + 6.92820i −0.158735 + 0.274937i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −33.4891 + 58.0049i −1.32481 + 2.29464i
\(640\) 0 0
\(641\) −1.00000 1.73205i −0.0394976 0.0684119i 0.845601 0.533816i \(-0.179242\pi\)
−0.885098 + 0.465404i \(0.845909\pi\)
\(642\) 0 0
\(643\) −12.6277 −0.497989 −0.248994 0.968505i \(-0.580100\pi\)
−0.248994 + 0.968505i \(0.580100\pi\)
\(644\) 0 0
\(645\) 9.25544 0.364432
\(646\) 0 0
\(647\) −8.00000 13.8564i −0.314512 0.544752i 0.664821 0.747002i \(-0.268508\pi\)
−0.979334 + 0.202251i \(0.935174\pi\)
\(648\) 0 0
\(649\) 2.51087 4.34896i 0.0985605 0.170712i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.00000 + 5.19615i −0.117399 + 0.203341i −0.918736 0.394872i \(-0.870789\pi\)
0.801337 + 0.598213i \(0.204122\pi\)
\(654\) 0 0
\(655\) 3.37228 + 5.84096i 0.131766 + 0.228225i
\(656\) 0 0
\(657\) 50.2337 1.95980
\(658\) 0 0
\(659\) 6.11684 0.238278 0.119139 0.992878i \(-0.461987\pi\)
0.119139 + 0.992878i \(0.461987\pi\)
\(660\) 0 0
\(661\) 1.62772 + 2.81929i 0.0633109 + 0.109658i 0.895943 0.444168i \(-0.146501\pi\)
−0.832633 + 0.553826i \(0.813167\pi\)
\(662\) 0 0
\(663\) 12.4307 21.5306i 0.482769 0.836180i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −4.62772 + 8.01544i −0.179186 + 0.310359i
\(668\) 0 0
\(669\) −19.1753 33.2125i −0.741359 1.28407i
\(670\) 0 0
\(671\) −5.48913 −0.211905
\(672\) 0 0
\(673\) −31.7228 −1.22282 −0.611412 0.791312i \(-0.709398\pi\)
−0.611412 + 0.791312i \(0.709398\pi\)
\(674\) 0 0
\(675\) −9.05842 15.6896i −0.348659 0.603895i
\(676\) 0 0
\(677\) −18.1753 + 31.4805i −0.698532 + 1.20989i 0.270443 + 0.962736i \(0.412830\pi\)
−0.968975 + 0.247157i \(0.920504\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −14.9416 + 25.8796i −0.572563 + 0.991707i
\(682\) 0 0
\(683\) −18.0000 31.1769i −0.688751 1.19295i −0.972242 0.233977i \(-0.924826\pi\)
0.283491 0.958975i \(-0.408507\pi\)
\(684\) 0 0
\(685\) 3.25544 0.124384
\(686\) 0 0
\(687\) −74.9783 −2.86060
\(688\) 0 0
\(689\) 0.510875 + 0.884861i 0.0194628 + 0.0337105i
\(690\) 0 0
\(691\) 6.74456 11.6819i 0.256575 0.444401i −0.708747 0.705463i \(-0.750739\pi\)
0.965322 + 0.261061i \(0.0840725\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.37228 5.84096i 0.127918 0.221560i
\(696\) 0 0
\(697\) 12.7446 + 22.0742i 0.482735 + 0.836121i
\(698\) 0 0
\(699\) −42.9783 −1.62559
\(700\) 0 0
\(701\) 30.8614 1.16562 0.582810 0.812609i \(-0.301953\pi\)
0.582810 + 0.812609i \(0.301953\pi\)
\(702\) 0 0
\(703\) −6.74456 11.6819i −0.254376 0.440592i
\(704\) 0 0
\(705\) 17.0584 29.5461i 0.642457 1.11277i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 16.8030 29.1036i 0.631049 1.09301i −0.356288 0.934376i \(-0.615958\pi\)
0.987338 0.158633i \(-0.0507088\pi\)
\(710\) 0 0
\(711\) 8.86141 + 15.3484i 0.332329 + 0.575610i
\(712\) 0 0
\(713\) 53.9565 2.02069
\(714\) 0 0
\(715\) 0.861407 0.0322148
\(716\) 0 0
\(717\) −32.6644 56.5764i −1.21987 2.11288i
\(718\) 0 0
\(719\) 7.37228 12.7692i 0.274940 0.476210i −0.695180 0.718836i \(-0.744675\pi\)
0.970120 + 0.242626i \(0.0780088\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 43.8397 75.9325i 1.63041 2.82396i
\(724\) 0 0
\(725\) −0.686141 1.18843i −0.0254826 0.0441372i
\(726\) 0 0
\(727\) −32.0000 −1.18681 −0.593407 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) 0 0
\(729\) 117.935 4.36795
\(730\) 0 0
\(731\) 7.37228 + 12.7692i 0.272674 + 0.472285i
\(732\) 0 0
\(733\) −19.4307 + 33.6550i −0.717689 + 1.24307i 0.244224 + 0.969719i \(0.421467\pi\)
−0.961913 + 0.273356i \(0.911866\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.25544 2.17448i 0.0462446 0.0800980i
\(738\) 0 0
\(739\) −9.80298 16.9793i −0.360609 0.624592i 0.627453 0.778655i \(-0.284098\pi\)
−0.988061 + 0.154062i \(0.950764\pi\)
\(740\) 0 0
\(741\) −31.2119 −1.14660
\(742\) 0 0
\(743\) −29.4891 −1.08185 −0.540926 0.841070i \(-0.681926\pi\)
−0.540926 + 0.841070i \(0.681926\pi\)
\(744\) 0 0
\(745\) 3.74456 + 6.48577i 0.137190 + 0.237620i
\(746\) 0 0
\(747\) 56.4674 97.8044i 2.06603 3.57847i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −24.4307 + 42.3152i −0.891489 + 1.54410i −0.0533984 + 0.998573i \(0.517005\pi\)
−0.838091 + 0.545531i \(0.816328\pi\)
\(752\) 0 0
\(753\) −11.3723 19.6974i −0.414429 0.717812i
\(754\) 0 0
\(755\) −2.11684 −0.0770398
\(756\) 0 0
\(757\) −38.2337 −1.38963 −0.694814 0.719190i \(-0.744513\pi\)
−0.694814 + 0.719190i \(0.744513\pi\)
\(758\) 0 0
\(759\) −7.13859 12.3644i −0.259115 0.448800i
\(760\) 0 0
\(761\) −20.4891 + 35.4882i −0.742730 + 1.28645i 0.208518 + 0.978019i \(0.433136\pi\)
−0.951248 + 0.308428i \(0.900197\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 22.4891 38.9523i 0.813096 1.40832i
\(766\) 0 0
\(767\) 5.48913 + 9.50744i 0.198201 + 0.343294i
\(768\) 0 0
\(769\) 19.4891 0.702796 0.351398 0.936226i \(-0.385706\pi\)
0.351398 + 0.936226i \(0.385706\pi\)
\(770\) 0 0
\(771\) 1.72281 0.0620456
\(772\) 0 0
\(773\) −0.686141 1.18843i −0.0246788 0.0427449i 0.853422 0.521220i \(-0.174523\pi\)
−0.878101 + 0.478475i \(0.841190\pi\)
\(774\) 0 0
\(775\) −4.00000 + 6.92820i −0.143684 + 0.248868i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 16.0000 27.7128i 0.573259 0.992915i
\(780\) 0 0
\(781\) −2.51087 4.34896i −0.0898462 0.155618i
\(782\) 0 0
\(783\) 24.8614 0.888474
\(784\) 0 0
\(785\) −7.48913 −0.267298
\(786\) 0 0
\(787\) −6.94158 12.0232i −0.247441 0.428580i 0.715374 0.698741i \(-0.246256\pi\)
−0.962815 + 0.270162i \(0.912923\pi\)
\(788\) 0 0
\(789\) 20.6277 35.7283i 0.734366 1.27196i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 6.00000 10.3923i 0.213066 0.369042i
\(794\) 0 0
\(795\) 1.25544 + 2.17448i 0.0445258 + 0.0771209i
\(796\) 0 0
\(797\) −21.3723 −0.757045 −0.378523 0.925592i \(-0.623568\pi\)
−0.378523 + 0.925592i \(0.623568\pi\)
\(798\) 0 0