Properties

Label 1960.2.q.t.361.1
Level $1960$
Weight $2$
Character 1960.361
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 361.1
Root \(-1.18614 + 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 1960.361
Dual form 1960.2.q.t.961.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.18614 + 2.05446i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.31386 - 2.27567i) q^{9} +O(q^{10})\) \(q+(-1.18614 + 2.05446i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.31386 - 2.27567i) q^{9} +(-3.18614 + 5.51856i) q^{11} +4.37228 q^{13} -2.37228 q^{15} +(0.186141 - 0.322405i) q^{17} +(2.37228 + 4.10891i) q^{19} +(2.37228 + 4.10891i) q^{23} +(-0.500000 + 0.866025i) q^{25} -0.883156 q^{27} -4.37228 q^{29} +(4.00000 - 6.92820i) q^{31} +(-7.55842 - 13.0916i) q^{33} +(1.00000 + 1.73205i) q^{37} +(-5.18614 + 8.98266i) q^{39} +6.74456 q^{41} -8.74456 q^{43} +(1.31386 - 2.27567i) q^{45} +(3.55842 + 6.16337i) q^{47} +(0.441578 + 0.764836i) q^{51} +(-5.37228 + 9.30506i) q^{53} -6.37228 q^{55} -11.2554 q^{57} +(-4.00000 + 6.92820i) q^{59} +(1.37228 + 2.37686i) q^{61} +(2.18614 + 3.78651i) q^{65} +(2.00000 - 3.46410i) q^{67} -11.2554 q^{69} +8.00000 q^{71} +(3.00000 - 5.19615i) q^{73} +(-1.18614 - 2.05446i) q^{75} +(-7.55842 - 13.0916i) q^{79} +(4.98913 - 8.64142i) q^{81} -9.48913 q^{83} +0.372281 q^{85} +(5.18614 - 8.98266i) q^{87} +(-7.37228 - 12.7692i) q^{89} +(9.48913 + 16.4356i) q^{93} +(-2.37228 + 4.10891i) q^{95} -9.86141 q^{97} +16.7446 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + q^{3} + 2q^{5} - 11q^{9} + O(q^{10}) \) \( 4q + q^{3} + 2q^{5} - 11q^{9} - 7q^{11} + 6q^{13} + 2q^{15} - 5q^{17} - 2q^{19} - 2q^{23} - 2q^{25} - 38q^{27} - 6q^{29} + 16q^{31} - 13q^{33} + 4q^{37} - 15q^{39} + 4q^{41} - 12q^{43} + 11q^{45} - 3q^{47} + 19q^{51} - 10q^{53} - 14q^{55} - 68q^{57} - 16q^{59} - 6q^{61} + 3q^{65} + 8q^{67} - 68q^{69} + 32q^{71} + 12q^{73} + q^{75} - 13q^{79} - 26q^{81} + 8q^{83} - 10q^{85} + 15q^{87} - 18q^{89} - 8q^{93} + 2q^{95} + 18q^{97} + 44q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(3\) −1.18614 + 2.05446i −0.684819 + 1.18614i 0.288675 + 0.957427i \(0.406785\pi\)
−0.973494 + 0.228714i \(0.926548\pi\)
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −1.31386 2.27567i −0.437953 0.758557i
\(10\) 0 0
\(11\) −3.18614 + 5.51856i −0.960658 + 1.66391i −0.239803 + 0.970822i \(0.577083\pi\)
−0.720855 + 0.693086i \(0.756251\pi\)
\(12\) 0 0
\(13\) 4.37228 1.21265 0.606326 0.795216i \(-0.292643\pi\)
0.606326 + 0.795216i \(0.292643\pi\)
\(14\) 0 0
\(15\) −2.37228 −0.612520
\(16\) 0 0
\(17\) 0.186141 0.322405i 0.0451457 0.0781947i −0.842570 0.538588i \(-0.818958\pi\)
0.887715 + 0.460393i \(0.152291\pi\)
\(18\) 0 0
\(19\) 2.37228 + 4.10891i 0.544239 + 0.942649i 0.998654 + 0.0518593i \(0.0165147\pi\)
−0.454416 + 0.890790i \(0.650152\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.37228 + 4.10891i 0.494655 + 0.856767i 0.999981 0.00616109i \(-0.00196115\pi\)
−0.505326 + 0.862928i \(0.668628\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) −0.883156 −0.169963
\(28\) 0 0
\(29\) −4.37228 −0.811912 −0.405956 0.913893i \(-0.633061\pi\)
−0.405956 + 0.913893i \(0.633061\pi\)
\(30\) 0 0
\(31\) 4.00000 6.92820i 0.718421 1.24434i −0.243204 0.969975i \(-0.578198\pi\)
0.961625 0.274367i \(-0.0884683\pi\)
\(32\) 0 0
\(33\) −7.55842 13.0916i −1.31575 2.27895i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.00000 + 1.73205i 0.164399 + 0.284747i 0.936442 0.350823i \(-0.114098\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(38\) 0 0
\(39\) −5.18614 + 8.98266i −0.830447 + 1.43838i
\(40\) 0 0
\(41\) 6.74456 1.05332 0.526662 0.850075i \(-0.323443\pi\)
0.526662 + 0.850075i \(0.323443\pi\)
\(42\) 0 0
\(43\) −8.74456 −1.33353 −0.666767 0.745267i \(-0.732322\pi\)
−0.666767 + 0.745267i \(0.732322\pi\)
\(44\) 0 0
\(45\) 1.31386 2.27567i 0.195859 0.339237i
\(46\) 0 0
\(47\) 3.55842 + 6.16337i 0.519049 + 0.899020i 0.999755 + 0.0221376i \(0.00704719\pi\)
−0.480706 + 0.876882i \(0.659619\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0.441578 + 0.764836i 0.0618333 + 0.107098i
\(52\) 0 0
\(53\) −5.37228 + 9.30506i −0.737940 + 1.27815i 0.215482 + 0.976508i \(0.430868\pi\)
−0.953422 + 0.301641i \(0.902466\pi\)
\(54\) 0 0
\(55\) −6.37228 −0.859238
\(56\) 0 0
\(57\) −11.2554 −1.49082
\(58\) 0 0
\(59\) −4.00000 + 6.92820i −0.520756 + 0.901975i 0.478953 + 0.877841i \(0.341016\pi\)
−0.999709 + 0.0241347i \(0.992317\pi\)
\(60\) 0 0
\(61\) 1.37228 + 2.37686i 0.175703 + 0.304326i 0.940404 0.340059i \(-0.110447\pi\)
−0.764702 + 0.644385i \(0.777114\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.18614 + 3.78651i 0.271157 + 0.469658i
\(66\) 0 0
\(67\) 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) 0 0
\(69\) −11.2554 −1.35500
\(70\) 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 \(-0.719133\pi\)
0.986447 + 0.164083i \(0.0524664\pi\)
\(74\) 0 0
\(75\) −1.18614 2.05446i −0.136964 0.237228i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −7.55842 13.0916i −0.850389 1.47292i −0.880858 0.473381i \(-0.843033\pi\)
0.0304688 0.999536i \(-0.490300\pi\)
\(80\) 0 0
\(81\) 4.98913 8.64142i 0.554347 0.960158i
\(82\) 0 0
\(83\) −9.48913 −1.04157 −0.520783 0.853689i \(-0.674360\pi\)
−0.520783 + 0.853689i \(0.674360\pi\)
\(84\) 0 0
\(85\) 0.372281 0.0403796
\(86\) 0 0
\(87\) 5.18614 8.98266i 0.556013 0.963042i
\(88\) 0 0
\(89\) −7.37228 12.7692i −0.781460 1.35353i −0.931091 0.364787i \(-0.881142\pi\)
0.149631 0.988742i \(-0.452192\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 9.48913 + 16.4356i 0.983976 + 1.70430i
\(94\) 0 0
\(95\) −2.37228 + 4.10891i −0.243391 + 0.421565i
\(96\) 0 0
\(97\) −9.86141 −1.00127 −0.500637 0.865657i \(-0.666901\pi\)
−0.500637 + 0.865657i \(0.666901\pi\)
\(98\) 0 0
\(99\) 16.7446 1.68289
\(100\) 0 0
\(101\) 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i \(-0.736843\pi\)
0.975796 + 0.218685i \(0.0701767\pi\)
\(102\) 0 0
\(103\) 2.81386 + 4.87375i 0.277258 + 0.480225i 0.970702 0.240285i \(-0.0772411\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.37228 7.57301i −0.422684 0.732111i 0.573517 0.819194i \(-0.305579\pi\)
−0.996201 + 0.0870831i \(0.972245\pi\)
\(108\) 0 0
\(109\) −0.186141 + 0.322405i −0.0178290 + 0.0308808i −0.874802 0.484480i \(-0.839009\pi\)
0.856973 + 0.515361i \(0.172342\pi\)
\(110\) 0 0
\(111\) −4.74456 −0.450334
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) −2.37228 + 4.10891i −0.221216 + 0.383158i
\(116\) 0 0
\(117\) −5.74456 9.94987i −0.531085 0.919866i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −14.8030 25.6395i −1.34573 2.33087i
\(122\) 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
\(129\) 10.3723 17.9653i 0.913228 1.58176i
\(130\) 0 0
\(131\) 2.37228 + 4.10891i 0.207267 + 0.358997i 0.950853 0.309644i \(-0.100210\pi\)
−0.743586 + 0.668641i \(0.766876\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −0.441578 0.764836i −0.0380050 0.0658266i
\(136\) 0 0
\(137\) −7.37228 + 12.7692i −0.629857 + 1.09094i 0.357724 + 0.933827i \(0.383553\pi\)
−0.987580 + 0.157116i \(0.949780\pi\)
\(138\) 0 0
\(139\) −4.74456 −0.402429 −0.201214 0.979547i \(-0.564489\pi\)
−0.201214 + 0.979547i \(0.564489\pi\)
\(140\) 0 0
\(141\) −16.8832 −1.42182
\(142\) 0 0
\(143\) −13.9307 + 24.1287i −1.16494 + 2.01774i
\(144\) 0 0
\(145\) −2.18614 3.78651i −0.181549 0.314452i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.74456 13.4140i −0.634459 1.09892i −0.986629 0.162980i \(-0.947889\pi\)
0.352170 0.935936i \(-0.385444\pi\)
\(150\) 0 0
\(151\) −7.55842 + 13.0916i −0.615096 + 1.06538i 0.375272 + 0.926915i \(0.377549\pi\)
−0.990368 + 0.138462i \(0.955784\pi\)
\(152\) 0 0
\(153\) −0.978251 −0.0790869
\(154\) 0 0
\(155\) 8.00000 0.642575
\(156\) 0 0
\(157\) 7.74456 13.4140i 0.618083 1.07055i −0.371752 0.928332i \(-0.621243\pi\)
0.989835 0.142220i \(-0.0454239\pi\)
\(158\) 0 0
\(159\) −12.7446 22.0742i −1.01071 1.75060i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 8.37228 + 14.5012i 0.655768 + 1.13582i 0.981701 + 0.190430i \(0.0609883\pi\)
−0.325933 + 0.945393i \(0.605678\pi\)
\(164\) 0 0
\(165\) 7.55842 13.0916i 0.588422 1.01918i
\(166\) 0 0
\(167\) −5.62772 −0.435486 −0.217743 0.976006i \(-0.569869\pi\)
−0.217743 + 0.976006i \(0.569869\pi\)
\(168\) 0 0
\(169\) 6.11684 0.470526
\(170\) 0 0
\(171\) 6.23369 10.7971i 0.476702 0.825672i
\(172\) 0 0
\(173\) 0.186141 + 0.322405i 0.0141520 + 0.0245120i 0.873015 0.487694i \(-0.162162\pi\)
−0.858863 + 0.512206i \(0.828828\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −9.48913 16.4356i −0.713246 1.23538i
\(178\) 0 0
\(179\) 11.4891 19.8997i 0.858738 1.48738i −0.0143962 0.999896i \(-0.504583\pi\)
0.873134 0.487481i \(-0.162084\pi\)
\(180\) 0 0
\(181\) 16.2337 1.20664 0.603320 0.797499i \(-0.293844\pi\)
0.603320 + 0.797499i \(0.293844\pi\)
\(182\) 0 0
\(183\) −6.51087 −0.481298
\(184\) 0 0
\(185\) −1.00000 + 1.73205i −0.0735215 + 0.127343i
\(186\) 0 0
\(187\) 1.18614 + 2.05446i 0.0867392 + 0.150237i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.93070 3.34408i −0.139701 0.241969i 0.787683 0.616081i \(-0.211281\pi\)
−0.927383 + 0.374112i \(0.877947\pi\)
\(192\) 0 0
\(193\) −3.37228 + 5.84096i −0.242742 + 0.420442i −0.961494 0.274825i \(-0.911380\pi\)
0.718752 + 0.695266i \(0.244714\pi\)
\(194\) 0 0
\(195\) −10.3723 −0.742774
\(196\) 0 0
\(197\) −8.23369 −0.586626 −0.293313 0.956016i \(-0.594758\pi\)
−0.293313 + 0.956016i \(0.594758\pi\)
\(198\) 0 0
\(199\) 8.00000 13.8564i 0.567105 0.982255i −0.429745 0.902950i \(-0.641397\pi\)
0.996850 0.0793045i \(-0.0252700\pi\)
\(200\) 0 0
\(201\) 4.74456 + 8.21782i 0.334656 + 0.579641i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 3.37228 + 5.84096i 0.235530 + 0.407951i
\(206\) 0 0
\(207\) 6.23369 10.7971i 0.433271 0.750448i
\(208\) 0 0
\(209\) −30.2337 −2.09131
\(210\) 0 0
\(211\) −14.3723 −0.989429 −0.494714 0.869056i \(-0.664727\pi\)
−0.494714 + 0.869056i \(0.664727\pi\)
\(212\) 0 0
\(213\) −9.48913 + 16.4356i −0.650184 + 1.12615i
\(214\) 0 0
\(215\) −4.37228 7.57301i −0.298187 0.516475i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 7.11684 + 12.3267i 0.480912 + 0.832964i
\(220\) 0 0
\(221\) 0.813859 1.40965i 0.0547461 0.0948230i
\(222\) 0 0
\(223\) −5.62772 −0.376860 −0.188430 0.982087i \(-0.560340\pi\)
−0.188430 + 0.982087i \(0.560340\pi\)
\(224\) 0 0
\(225\) 2.62772 0.175181
\(226\) 0 0
\(227\) −9.93070 + 17.2005i −0.659124 + 1.14164i 0.321719 + 0.946835i \(0.395739\pi\)
−0.980843 + 0.194801i \(0.937594\pi\)
\(228\) 0 0
\(229\) 6.11684 + 10.5947i 0.404212 + 0.700116i 0.994229 0.107274i \(-0.0342123\pi\)
−0.590017 + 0.807391i \(0.700879\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.627719 + 1.08724i 0.0411232 + 0.0712275i 0.885854 0.463963i \(-0.153573\pi\)
−0.844731 + 0.535191i \(0.820240\pi\)
\(234\) 0 0
\(235\) −3.55842 + 6.16337i −0.232126 + 0.402054i
\(236\) 0 0
\(237\) 35.8614 2.32945
\(238\) 0 0
\(239\) 13.6277 0.881504 0.440752 0.897629i \(-0.354712\pi\)
0.440752 + 0.897629i \(0.354712\pi\)
\(240\) 0 0
\(241\) −13.0000 + 22.5167i −0.837404 + 1.45043i 0.0546547 + 0.998505i \(0.482594\pi\)
−0.892058 + 0.451920i \(0.850739\pi\)
\(242\) 0 0
\(243\) 10.5109 + 18.2054i 0.674273 + 1.16787i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 10.3723 + 17.9653i 0.659972 + 1.14311i
\(248\) 0 0
\(249\) 11.2554 19.4950i 0.713284 1.23544i
\(250\) 0 0
\(251\) 4.74456 0.299474 0.149737 0.988726i \(-0.452157\pi\)
0.149737 + 0.988726i \(0.452157\pi\)
\(252\) 0 0
\(253\) −30.2337 −1.90078
\(254\) 0 0
\(255\) −0.441578 + 0.764836i −0.0276527 + 0.0478959i
\(256\) 0 0
\(257\) 11.7446 + 20.3422i 0.732606 + 1.26891i 0.955766 + 0.294128i \(0.0950294\pi\)
−0.223160 + 0.974782i \(0.571637\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 5.74456 + 9.94987i 0.355580 + 0.615882i
\(262\) 0 0
\(263\) −11.1168 + 19.2549i −0.685494 + 1.18731i 0.287787 + 0.957694i \(0.407080\pi\)
−0.973281 + 0.229616i \(0.926253\pi\)
\(264\) 0 0
\(265\) −10.7446 −0.660033
\(266\) 0 0
\(267\) 34.9783 2.14063
\(268\) 0 0
\(269\) 3.00000 5.19615i 0.182913 0.316815i −0.759958 0.649972i \(-0.774781\pi\)
0.942871 + 0.333157i \(0.108114\pi\)
\(270\) 0 0
\(271\) −4.74456 8.21782i −0.288212 0.499197i 0.685171 0.728382i \(-0.259727\pi\)
−0.973383 + 0.229185i \(0.926394\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3.18614 5.51856i −0.192132 0.332782i
\(276\) 0 0
\(277\) −12.4891 + 21.6318i −0.750399 + 1.29973i 0.197231 + 0.980357i \(0.436805\pi\)
−0.947630 + 0.319372i \(0.896528\pi\)
\(278\) 0 0
\(279\) −21.0217 −1.25854
\(280\) 0 0
\(281\) 18.6060 1.10994 0.554970 0.831871i \(-0.312730\pi\)
0.554970 + 0.831871i \(0.312730\pi\)
\(282\) 0 0
\(283\) 4.44158 7.69304i 0.264024 0.457304i −0.703283 0.710910i \(-0.748283\pi\)
0.967308 + 0.253606i \(0.0816167\pi\)
\(284\) 0 0
\(285\) −5.62772 9.74749i −0.333357 0.577392i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 8.43070 + 14.6024i 0.495924 + 0.858965i
\(290\) 0 0
\(291\) 11.6970 20.2598i 0.685691 1.18765i
\(292\) 0 0
\(293\) 25.1168 1.46734 0.733671 0.679505i \(-0.237805\pi\)
0.733671 + 0.679505i \(0.237805\pi\)
\(294\) 0 0
\(295\) −8.00000 −0.465778
\(296\) 0 0
\(297\) 2.81386 4.87375i 0.163277 0.282804i
\(298\) 0 0
\(299\) 10.3723 + 17.9653i 0.599845 + 1.03896i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 7.11684 + 12.3267i 0.408852 + 0.708152i
\(304\) 0 0
\(305\) −1.37228 + 2.37686i −0.0785766 + 0.136099i
\(306\) 0 0
\(307\) 31.1168 1.77593 0.887966 0.459909i \(-0.152118\pi\)
0.887966 + 0.459909i \(0.152118\pi\)
\(308\) 0 0
\(309\) −13.3505 −0.759485
\(310\) 0 0
\(311\) 6.37228 11.0371i 0.361339 0.625857i −0.626843 0.779146i \(-0.715653\pi\)
0.988181 + 0.153289i \(0.0489864\pi\)
\(312\) 0 0
\(313\) −1.44158 2.49689i −0.0814828 0.141132i 0.822404 0.568904i \(-0.192632\pi\)
−0.903887 + 0.427771i \(0.859299\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7.00000 12.1244i −0.393159 0.680972i 0.599705 0.800221i \(-0.295285\pi\)
−0.992864 + 0.119249i \(0.961951\pi\)
\(318\) 0 0
\(319\) 13.9307 24.1287i 0.779970 1.35095i
\(320\) 0 0
\(321\) 20.7446 1.15785
\(322\) 0 0
\(323\) 1.76631 0.0982802
\(324\) 0 0
\(325\) −2.18614 + 3.78651i −0.121265 + 0.210038i
\(326\) 0 0
\(327\) −0.441578 0.764836i −0.0244193 0.0422955i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −6.00000 10.3923i −0.329790 0.571213i 0.652680 0.757634i \(-0.273645\pi\)
−0.982470 + 0.186421i \(0.940311\pi\)
\(332\) 0 0
\(333\) 2.62772 4.55134i 0.143998 0.249412i
\(334\) 0 0
\(335\) 4.00000 0.218543
\(336\) 0 0
\(337\) −7.48913 −0.407959 −0.203979 0.978975i \(-0.565388\pi\)
−0.203979 + 0.978975i \(0.565388\pi\)
\(338\) 0 0
\(339\) −2.37228 + 4.10891i −0.128845 + 0.223165i
\(340\) 0 0
\(341\) 25.4891 + 44.1485i 1.38031 + 2.39077i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −5.62772 9.74749i −0.302986 0.524787i
\(346\) 0 0
\(347\) 12.3723 21.4294i 0.664179 1.15039i −0.315328 0.948983i \(-0.602115\pi\)
0.979507 0.201409i \(-0.0645520\pi\)
\(348\) 0 0
\(349\) 19.4891 1.04323 0.521614 0.853181i \(-0.325330\pi\)
0.521614 + 0.853181i \(0.325330\pi\)
\(350\) 0 0
\(351\) −3.86141 −0.206107
\(352\) 0 0
\(353\) 0.930703 1.61203i 0.0495363 0.0857995i −0.840194 0.542286i \(-0.817559\pi\)
0.889730 + 0.456486i \(0.150892\pi\)
\(354\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(360\) 0 0
\(361\) −1.75544 + 3.04051i −0.0923914 + 0.160027i
\(362\) 0 0
\(363\) 70.2337 3.68631
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) 0 0
\(367\) −9.93070 + 17.2005i −0.518378 + 0.897858i 0.481393 + 0.876505i \(0.340131\pi\)
−0.999772 + 0.0213533i \(0.993203\pi\)
\(368\) 0 0
\(369\) −8.86141 15.3484i −0.461306 0.799006i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 15.3723 + 26.6256i 0.795947 + 1.37862i 0.922236 + 0.386626i \(0.126360\pi\)
−0.126290 + 0.991993i \(0.540307\pi\)
\(374\) 0 0
\(375\) 1.18614 2.05446i 0.0612520 0.106092i
\(376\) 0 0
\(377\) −19.1168 −0.984568
\(378\) 0 0
\(379\) 12.0000 0.616399 0.308199 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) 0 0
\(381\) −9.48913 + 16.4356i −0.486143 + 0.842024i
\(382\) 0 0
\(383\) 8.74456 + 15.1460i 0.446826 + 0.773926i 0.998177 0.0603475i \(-0.0192209\pi\)
−0.551351 + 0.834273i \(0.685888\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 11.4891 + 19.8997i 0.584025 + 1.01156i
\(388\) 0 0
\(389\) −8.93070 + 15.4684i −0.452805 + 0.784281i −0.998559 0.0536646i \(-0.982910\pi\)
0.545754 + 0.837945i \(0.316243\pi\)
\(390\) 0 0
\(391\) 1.76631 0.0893262
\(392\) 0 0
\(393\) −11.2554 −0.567762
\(394\) 0 0
\(395\) 7.55842 13.0916i 0.380305 0.658708i
\(396\) 0 0
\(397\) −15.8139 27.3904i −0.793675 1.37469i −0.923677 0.383171i \(-0.874832\pi\)
0.130002 0.991514i \(-0.458502\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 19.3030 + 33.4338i 0.963945 + 1.66960i 0.712423 + 0.701750i \(0.247598\pi\)
0.251522 + 0.967852i \(0.419069\pi\)
\(402\) 0 0
\(403\) 17.4891 30.2921i 0.871195 1.50895i
\(404\) 0 0
\(405\) 9.97825 0.495823
\(406\) 0 0
\(407\) −12.7446 −0.631725
\(408\) 0 0
\(409\) −5.74456 + 9.94987i −0.284050 + 0.491990i −0.972378 0.233410i \(-0.925012\pi\)
0.688328 + 0.725399i \(0.258345\pi\)
\(410\) 0 0
\(411\) −17.4891 30.2921i −0.862675 1.49420i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −4.74456 8.21782i −0.232901 0.403397i
\(416\) 0 0
\(417\) 5.62772 9.74749i 0.275591 0.477337i
\(418\) 0 0
\(419\) −14.5109 −0.708903 −0.354451 0.935074i \(-0.615332\pi\)
−0.354451 + 0.935074i \(0.615332\pi\)
\(420\) 0 0
\(421\) −18.6060 −0.906799 −0.453400 0.891307i \(-0.649789\pi\)
−0.453400 + 0.891307i \(0.649789\pi\)
\(422\) 0 0
\(423\) 9.35053 16.1956i 0.454638 0.787457i
\(424\) 0 0
\(425\) 0.186141 + 0.322405i 0.00902915 + 0.0156389i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −33.0475 57.2400i −1.59555 2.76357i
\(430\) 0 0
\(431\) −9.18614 + 15.9109i −0.442481 + 0.766399i −0.997873 0.0651893i \(-0.979235\pi\)
0.555392 + 0.831589i \(0.312568\pi\)
\(432\) 0 0
\(433\) 28.9783 1.39261 0.696303 0.717748i \(-0.254827\pi\)
0.696303 + 0.717748i \(0.254827\pi\)
\(434\) 0 0
\(435\) 10.3723 0.497313
\(436\) 0 0
\(437\) −11.2554 + 19.4950i −0.538421 + 0.932572i
\(438\) 0 0
\(439\) 3.11684 + 5.39853i 0.148759 + 0.257658i 0.930769 0.365608i \(-0.119139\pi\)
−0.782010 + 0.623266i \(0.785806\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8.37228 + 14.5012i 0.397779 + 0.688974i 0.993452 0.114254i \(-0.0364477\pi\)
−0.595673 + 0.803227i \(0.703114\pi\)
\(444\) 0 0
\(445\) 7.37228 12.7692i 0.349480 0.605317i
\(446\) 0 0
\(447\) 36.7446 1.73796
\(448\) 0 0
\(449\) 17.1168 0.807794 0.403897 0.914805i \(-0.367655\pi\)
0.403897 + 0.914805i \(0.367655\pi\)
\(450\) 0 0
\(451\) −21.4891 + 37.2203i −1.01188 + 1.75263i
\(452\) 0 0
\(453\) −17.9307 31.0569i −0.842458 1.45918i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −2.62772 4.55134i −0.122919 0.212903i 0.797998 0.602660i \(-0.205892\pi\)
−0.920918 + 0.389757i \(0.872559\pi\)
\(458\) 0 0
\(459\) −0.164391 + 0.284734i −0.00767313 + 0.0132902i
\(460\) 0 0
\(461\) −1.25544 −0.0584715 −0.0292358 0.999573i \(-0.509307\pi\)
−0.0292358 + 0.999573i \(0.509307\pi\)
\(462\) 0 0
\(463\) −6.51087 −0.302586 −0.151293 0.988489i \(-0.548344\pi\)
−0.151293 + 0.988489i \(0.548344\pi\)
\(464\) 0 0
\(465\) −9.48913 + 16.4356i −0.440048 + 0.762185i
\(466\) 0 0
\(467\) −4.30298 7.45299i −0.199118 0.344883i 0.749124 0.662429i \(-0.230474\pi\)
−0.948243 + 0.317546i \(0.897141\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 18.3723 + 31.8217i 0.846550 + 1.46627i
\(472\) 0 0
\(473\) 27.8614 48.2574i 1.28107 2.21888i
\(474\) 0 0
\(475\) −4.74456 −0.217695
\(476\) 0 0
\(477\) 28.2337 1.29273
\(478\) 0 0
\(479\) −11.1168 + 19.2549i −0.507942 + 0.879781i 0.492016 + 0.870586i \(0.336260\pi\)
−0.999958 + 0.00919454i \(0.997073\pi\)
\(480\) 0 0
\(481\) 4.37228 + 7.57301i 0.199359 + 0.345300i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.93070 8.54023i −0.223892 0.387792i
\(486\) 0 0
\(487\) −15.1168 + 26.1831i −0.685010 + 1.18647i 0.288424 + 0.957503i \(0.406869\pi\)
−0.973434 + 0.228969i \(0.926465\pi\)
\(488\) 0 0
\(489\) −39.7228 −1.79633
\(490\) 0 0
\(491\) 35.1168 1.58480 0.792400 0.610001i \(-0.208831\pi\)
0.792400 + 0.610001i \(0.208831\pi\)
\(492\) 0 0
\(493\) −0.813859 + 1.40965i −0.0366544 + 0.0634873i
\(494\) 0 0
\(495\) 8.37228 + 14.5012i 0.376306 + 0.651781i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −15.9307 27.5928i −0.713156 1.23522i −0.963666 0.267109i \(-0.913932\pi\)
0.250510 0.968114i \(-0.419402\pi\)
\(500\) 0 0
\(501\) 6.67527 11.5619i 0.298229 0.516548i
\(502\) 0 0
\(503\) −18.3723 −0.819180 −0.409590 0.912270i \(-0.634328\pi\)
−0.409590 + 0.912270i \(0.634328\pi\)
\(504\) 0 0
\(505\) 6.00000 0.266996
\(506\) 0 0
\(507\) −7.25544 + 12.5668i −0.322225 + 0.558111i
\(508\) 0 0
\(509\) 20.4891 + 35.4882i 0.908165 + 1.57299i 0.816612 + 0.577187i \(0.195850\pi\)
0.0915524 + 0.995800i \(0.470817\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −2.09509 3.62881i −0.0925007 0.160216i
\(514\) 0 0
\(515\) −2.81386 + 4.87375i −0.123993 + 0.214763i
\(516\) 0 0
\(517\) −45.3505 −1.99451
\(518\) 0 0
\(519\) −0.883156 −0.0387662
\(520\) 0 0
\(521\) 15.0000 25.9808i 0.657162 1.13824i −0.324185 0.945994i \(-0.605090\pi\)
0.981347 0.192244i \(-0.0615766\pi\)
\(522\) 0 0
\(523\) 18.2337 + 31.5817i 0.797304 + 1.38097i 0.921366 + 0.388696i \(0.127074\pi\)
−0.124063 + 0.992274i \(0.539592\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.48913 2.57924i −0.0648673 0.112353i
\(528\) 0 0
\(529\) 0.244563 0.423595i 0.0106332 0.0184172i
\(530\) 0 0
\(531\) 21.0217 0.912266
\(532\) 0 0
\(533\) 29.4891 1.27732
\(534\) 0 0
\(535\) 4.37228 7.57301i 0.189030 0.327410i
\(536\) 0 0
\(537\) 27.2554 + 47.2078i 1.17616 + 2.03717i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 15.6753 + 27.1504i 0.673932 + 1.16729i 0.976780 + 0.214246i \(0.0687294\pi\)
−0.302847 + 0.953039i \(0.597937\pi\)
\(542\) 0 0
\(543\) −19.2554 + 33.3514i −0.826330 + 1.43125i
\(544\) 0 0
\(545\) −0.372281 −0.0159468
\(546\) 0 0
\(547\) −30.9783 −1.32453 −0.662267 0.749268i \(-0.730406\pi\)
−0.662267 + 0.749268i \(0.730406\pi\)
\(548\) 0 0
\(549\) 3.60597 6.24572i 0.153899 0.266561i
\(550\) 0 0
\(551\) −10.3723 17.9653i −0.441874 0.765348i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −2.37228 4.10891i −0.100698 0.174414i
\(556\) 0 0
\(557\) 1.88316 3.26172i 0.0797919 0.138204i −0.823368 0.567508i \(-0.807908\pi\)
0.903160 + 0.429304i \(0.141241\pi\)
\(558\) 0 0
\(559\) −38.2337 −1.61711
\(560\) 0 0
\(561\) −5.62772 −0.237602
\(562\) 0 0
\(563\) −8.74456 + 15.1460i −0.368539 + 0.638329i −0.989337 0.145642i \(-0.953475\pi\)
0.620798 + 0.783971i \(0.286809\pi\)
\(564\) 0 0
\(565\) 1.00000 + 1.73205i 0.0420703 + 0.0728679i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 12.4891 + 21.6318i 0.523571 + 0.906852i 0.999624 + 0.0274352i \(0.00873399\pi\)
−0.476052 + 0.879417i \(0.657933\pi\)
\(570\) 0 0
\(571\) 10.0000 17.3205i 0.418487 0.724841i −0.577301 0.816532i \(-0.695894\pi\)
0.995788 + 0.0916910i \(0.0292272\pi\)
\(572\) 0 0
\(573\) 9.16034 0.382679
\(574\) 0 0
\(575\) −4.74456 −0.197862
\(576\) 0 0
\(577\) 11.3030 19.5773i 0.470549 0.815015i −0.528883 0.848695i \(-0.677389\pi\)
0.999433 + 0.0336791i \(0.0107224\pi\)
\(578\) 0 0
\(579\) −8.00000 13.8564i −0.332469 0.575853i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −34.2337 59.2945i −1.41781 2.45573i
\(584\) 0 0
\(585\) 5.74456 9.94987i 0.237508 0.411377i
\(586\) 0 0
\(587\) −34.9783 −1.44371 −0.721853 0.692046i \(-0.756710\pi\)
−0.721853 + 0.692046i \(0.756710\pi\)
\(588\) 0 0
\(589\) 37.9565 1.56397
\(590\) 0 0
\(591\) 9.76631 16.9157i 0.401732 0.695821i
\(592\) 0 0
\(593\) 9.81386 + 16.9981i 0.403007 + 0.698028i 0.994087 0.108584i \(-0.0346317\pi\)
−0.591080 + 0.806613i \(0.701298\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 18.9783 + 32.8713i 0.776728 + 1.34533i
\(598\) 0 0
\(599\) 16.3030 28.2376i 0.666122 1.15376i −0.312858 0.949800i \(-0.601286\pi\)
0.978980 0.203957i \(-0.0653803\pi\)
\(600\) 0 0
\(601\) 16.5109 0.673493 0.336746 0.941595i \(-0.390674\pi\)
0.336746 + 0.941595i \(0.390674\pi\)
\(602\) 0 0
\(603\) −10.5109 −0.428036
\(604\) 0 0
\(605\) 14.8030 25.6395i 0.601827 1.04239i
\(606\) 0 0
\(607\) −12.3030 21.3094i −0.499363 0.864922i 0.500637 0.865657i \(-0.333099\pi\)
−1.00000 0.000735686i \(0.999766\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 15.5584 + 26.9480i 0.629426 + 1.09020i
\(612\) 0 0
\(613\) 4.25544 7.37063i 0.171875 0.297697i −0.767200 0.641408i \(-0.778351\pi\)
0.939076 + 0.343711i \(0.111684\pi\)
\(614\) 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
\(619\) 6.37228 11.0371i 0.256124 0.443619i −0.709076 0.705132i \(-0.750888\pi\)
0.965200 + 0.261512i \(0.0842213\pi\)
\(620\) 0 0
\(621\) −2.09509 3.62881i −0.0840732 0.145619i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 35.8614 62.1138i 1.43217 2.48059i
\(628\) 0 0
\(629\) 0.744563 0.0296877
\(630\) 0 0
\(631\) 2.37228 0.0944390 0.0472195 0.998885i \(-0.484964\pi\)
0.0472195 + 0.998885i \(0.484964\pi\)
\(632\) 0 0
\(633\) 17.0475 29.5272i 0.677579 1.17360i
\(634\) 0 0
\(635\) 4.00000 + 6.92820i 0.158735 + 0.274937i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −10.5109 18.2054i −0.415804 0.720193i
\(640\) 0 0
\(641\) −1.00000 + 1.73205i −0.0394976 + 0.0684119i −0.885098 0.465404i \(-0.845909\pi\)
0.845601 + 0.533816i \(0.179242\pi\)
\(642\) 0 0
\(643\) 18.3723 0.724532 0.362266 0.932075i \(-0.382003\pi\)
0.362266 + 0.932075i \(0.382003\pi\)
\(644\) 0 0
\(645\) 20.7446 0.816816
\(646\) 0 0
\(647\) 8.00000 13.8564i 0.314512 0.544752i −0.664821 0.747002i \(-0.731492\pi\)
0.979334 + 0.202251i \(0.0648256\pi\)
\(648\) 0 0
\(649\) −25.4891 44.1485i −1.00054 1.73298i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.00000 5.19615i −0.117399 0.203341i 0.801337 0.598213i \(-0.204122\pi\)
−0.918736 + 0.394872i \(0.870789\pi\)
\(654\) 0 0
\(655\) −2.37228 + 4.10891i −0.0926927 + 0.160548i
\(656\) 0 0
\(657\) −15.7663 −0.615102
\(658\) 0 0
\(659\) −11.1168 −0.433051 −0.216525 0.976277i \(-0.569472\pi\)
−0.216525 + 0.976277i \(0.569472\pi\)
\(660\) 0 0
\(661\) −7.37228 + 12.7692i −0.286749 + 0.496663i −0.973032 0.230671i \(-0.925908\pi\)
0.686283 + 0.727334i \(0.259241\pi\)
\(662\) 0 0
\(663\) 1.93070 + 3.34408i 0.0749823 + 0.129873i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −10.3723 17.9653i −0.401616 0.695620i
\(668\) 0 0
\(669\) 6.67527 11.5619i 0.258081 0.447009i
\(670\) 0 0
\(671\) −17.4891 −0.675160
\(672\) 0 0
\(673\) 25.7228 0.991542 0.495771 0.868453i \(-0.334886\pi\)
0.495771 + 0.868453i \(0.334886\pi\)
\(674\) 0 0
\(675\) 0.441578 0.764836i 0.0169963 0.0294385i
\(676\) 0 0
\(677\) −7.67527 13.2940i −0.294984 0.510928i 0.679997 0.733215i \(-0.261981\pi\)
−0.974981 + 0.222287i \(0.928648\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −23.5584 40.8044i −0.902761 1.56363i
\(682\) 0 0
\(683\) −18.0000 + 31.1769i −0.688751 + 1.19295i 0.283491 + 0.958975i \(0.408507\pi\)
−0.972242 + 0.233977i \(0.924826\pi\)
\(684\) 0 0
\(685\) −14.7446 −0.563361
\(686\) 0 0
\(687\) −29.0217 −1.10725
\(688\) 0 0
\(689\) −23.4891 + 40.6844i −0.894864 + 1.54995i
\(690\) 0 0
\(691\) 4.74456 + 8.21782i 0.180492 + 0.312621i 0.942048 0.335478i \(-0.108898\pi\)
−0.761556 + 0.648099i \(0.775564\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.37228 4.10891i −0.0899858 0.155860i
\(696\) 0 0
\(697\) 1.25544 2.17448i 0.0475531 0.0823644i
\(698\) 0 0
\(699\) −2.97825 −0.112648
\(700\) 0 0
\(701\) 2.13859 0.0807736 0.0403868 0.999184i \(-0.487141\pi\)
0.0403868 + 0.999184i \(0.487141\pi\)
\(702\) 0 0
\(703\) −4.74456 + 8.21782i −0.178945 + 0.309941i
\(704\) 0 0
\(705\) −8.44158 14.6212i −0.317928 0.550668i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −3.30298 5.72094i −0.124046 0.214854i 0.797314 0.603565i \(-0.206254\pi\)
−0.921360 + 0.388711i \(0.872920\pi\)
\(710\) 0 0
\(711\) −19.8614 + 34.4010i −0.744861 + 1.29014i
\(712\) 0 0
\(713\) 37.9565 1.42148
\(714\) 0 0
\(715\) −27.8614 −1.04196
\(716\) 0 0
\(717\) −16.1644 + 27.9975i −0.603670 + 1.04559i
\(718\) 0 0
\(719\) −1.62772 2.81929i −0.0607037 0.105142i 0.834076 0.551649i \(-0.186001\pi\)
−0.894780 + 0.446507i \(0.852668\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −30.8397 53.4159i −1.14694 1.98656i
\(724\) 0 0
\(725\) 2.18614 3.78651i 0.0811912 0.140627i
\(726\) 0 0
\(727\) 32.0000 1.18681 0.593407 0.804902i \(-0.297782\pi\)
0.593407 + 0.804902i \(0.297782\pi\)
\(728\) 0 0
\(729\) −19.9348 −0.738324
\(730\) 0 0
\(731\) −1.62772 + 2.81929i −0.0602034 + 0.104275i
\(732\) 0 0
\(733\) 5.06930 + 8.78028i 0.187239 + 0.324307i 0.944329 0.329004i \(-0.106713\pi\)
−0.757090 + 0.653311i \(0.773380\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 12.7446 + 22.0742i 0.469452 + 0.813115i
\(738\) 0 0
\(739\) 10.3030 17.8453i 0.379001 0.656450i −0.611916 0.790923i \(-0.709601\pi\)
0.990917 + 0.134473i \(0.0429342\pi\)
\(740\) 0 0
\(741\) −49.2119 −1.80785
\(742\) 0 0
\(743\) −6.51087 −0.238861 −0.119430 0.992843i \(-0.538107\pi\)
−0.119430 + 0.992843i \(0.538107\pi\)
\(744\) 0 0
\(745\) 7.74456 13.4140i 0.283739 0.491450i
\(746\) 0 0
\(747\) 12.4674 + 21.5941i 0.456157 + 0.790088i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −10.0693 17.4405i −0.367434 0.636414i 0.621730 0.783232i \(-0.286430\pi\)
−0.989164 + 0.146818i \(0.953097\pi\)
\(752\) 0 0
\(753\) −5.62772 + 9.74749i −0.205085 + 0.355218i
\(754\) 0 0
\(755\) −15.1168 −0.550158
\(756\) 0 0
\(757\) −3.76631 −0.136889 −0.0684445 0.997655i \(-0.521804\pi\)
−0.0684445 + 0.997655i \(0.521804\pi\)
\(758\) 0 0
\(759\) 35.8614 62.1138i 1.30169 2.25459i
\(760\) 0 0
\(761\) −2.48913 4.31129i −0.0902307 0.156284i 0.817377 0.576103i \(-0.195427\pi\)
−0.907608 + 0.419818i \(0.862094\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −0.489125 0.847190i −0.0176844 0.0306302i
\(766\) 0 0
\(767\) −17.4891 + 30.2921i −0.631496 + 1.09378i
\(768\) 0 0
\(769\) 3.48913 0.125821 0.0629105 0.998019i \(-0.479962\pi\)
0.0629105 + 0.998019i \(0.479962\pi\)
\(770\) 0 0
\(771\) −55.7228 −2.00681
\(772\) 0 0
\(773\) −2.18614 + 3.78651i −0.0786300 + 0.136191i −0.902659 0.430356i \(-0.858388\pi\)
0.824029 + 0.566548i \(0.191721\pi\)
\(774\) 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
\(781\) −25.4891 + 44.1485i −0.912073 + 1.57976i
\(782\) 0 0
\(783\) 3.86141 0.137995
\(784\) 0 0
\(785\) 15.4891 0.552831
\(786\) 0 0
\(787\) 15.5584 26.9480i 0.554598 0.960592i −0.443337 0.896355i \(-0.646205\pi\)
0.997935 0.0642366i \(-0.0204612\pi\)
\(788\) 0 0
\(789\) −26.3723 45.6781i −0.938878 1.62618i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 6.00000 + 10.3923i 0.213066 + 0.369042i
\(794\) 0 0
\(795\) 12.7446 22.0742i 0.452003 0.782892i
\(796\) 0 0
\(797\) 15.6277 0.553562 0.276781 0.960933i \(-0.410732\pi\)
0.276781 + 0.960933i \(0.410732\pi\)
\(798\) 0 0
\(799\) 2.64947 0.0937314