Properties

Label 1960.2.q.r.961.2
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 961.2
Root \(1.68614 + 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 1960.961
Dual form 1960.2.q.r.361.2

$q$-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 \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

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

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
\(3\) 1.18614 + 2.05446i 0.684819 + 1.18614i 0.973494 + 0.228714i \(0.0734519\pi\)
−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
\(9\) −1.31386 + 2.27567i −0.437953 + 0.758557i
\(10\) 0 0
\(11\) −3.18614 5.51856i −0.960658 1.66391i −0.720855 0.693086i \(-0.756251\pi\)
−0.239803 0.970822i \(-0.577083\pi\)
\(12\) 0 0
\(13\) −4.37228 −1.21265 −0.606326 0.795216i \(-0.707357\pi\)
−0.606326 + 0.795216i \(0.707357\pi\)
\(14\) 0 0
\(15\) −2.37228 −0.612520
\(16\) 0 0
\(17\) −0.186141 0.322405i −0.0451457 0.0781947i 0.842570 0.538588i \(-0.181042\pi\)
−0.887715 + 0.460393i \(0.847709\pi\)
\(18\) 0 0
\(19\) −2.37228 + 4.10891i −0.544239 + 0.942649i 0.454416 + 0.890790i \(0.349848\pi\)
−0.998654 + 0.0518593i \(0.983485\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.37228 4.10891i 0.494655 0.856767i −0.505326 0.862928i \(-0.668628\pi\)
0.999981 + 0.00616109i \(0.00196115\pi\)
\(24\) 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 −0.961625 0.274367i \(-0.911532\pi\)
0.243204 0.969975i \(-0.421802\pi\)
\(32\) 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 −0.772043 0.635571i \(-0.780765\pi\)
0.936442 + 0.350823i \(0.114098\pi\)
\(38\) 0 0
\(39\) −5.18614 8.98266i −0.830447 1.43838i
\(40\) 0 0
\(41\) −6.74456 −1.05332 −0.526662 0.850075i \(-0.676557\pi\)
−0.526662 + 0.850075i \(0.676557\pi\)
\(42\) 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 0.480706 + 0.876882i \(0.340381\pi\)
−0.999755 + 0.0221376i \(0.992953\pi\)
\(48\) 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 −0.953422 0.301641i \(-0.902466\pi\)
0.215482 0.976508i \(-0.430868\pi\)
\(54\) 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 0.999709 + 0.0241347i \(0.00768307\pi\)
−0.478953 + 0.877841i \(0.658984\pi\)
\(60\) 0 0
\(61\) −1.37228 + 2.37686i −0.175703 + 0.304326i −0.940404 0.340059i \(-0.889553\pi\)
0.764702 + 0.644385i \(0.222886\pi\)
\(62\) 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 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 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 \(-0.280867\pi\)
−0.986447 + 0.164083i \(0.947534\pi\)
\(74\) 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 0.0304688 + 0.999536i \(0.490300\pi\)
−0.880858 + 0.473381i \(0.843033\pi\)
\(80\) 0 0
\(81\) 4.98913 + 8.64142i 0.554347 + 0.960158i
\(82\) 0 0
\(83\) 9.48913 1.04157 0.520783 0.853689i \(-0.325640\pi\)
0.520783 + 0.853689i \(0.325640\pi\)
\(84\) 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 −0.149631 0.988742i \(-0.547808\pi\)
0.931091 0.364787i \(-0.118858\pi\)
\(90\) 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 \(-0.333099\pi\)
0.500637 + 0.865657i \(0.333099\pi\)
\(98\) 0 0
\(99\) 16.7446 1.68289
\(100\) 0 0
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 0 0
\(103\) −2.81386 + 4.87375i −0.277258 + 0.480225i −0.970702 0.240285i \(-0.922759\pi\)
0.693444 + 0.720510i \(0.256092\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.37228 + 7.57301i −0.422684 + 0.732111i −0.996201 0.0870831i \(-0.972245\pi\)
0.573517 + 0.819194i \(0.305579\pi\)
\(108\) 0 0
\(109\) −0.186141 0.322405i −0.0178290 0.0308808i 0.856973 0.515361i \(-0.172342\pi\)
−0.874802 + 0.484480i \(0.839009\pi\)
\(110\) 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 \(-0.899790\pi\)
0.743586 + 0.668641i \(0.233124\pi\)
\(132\) 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 −0.987580 0.157116i \(-0.949780\pi\)
0.357724 0.933827i \(-0.383553\pi\)
\(138\) 0 0
\(139\) 4.74456 0.402429 0.201214 0.979547i \(-0.435511\pi\)
0.201214 + 0.979547i \(0.435511\pi\)
\(140\) 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 0.352170 + 0.935936i \(0.385444\pi\)
−0.986629 + 0.162980i \(0.947889\pi\)
\(150\) 0 0
\(151\) −7.55842 13.0916i −0.615096 1.06538i −0.990368 0.138462i \(-0.955784\pi\)
0.375272 0.926915i \(-0.377549\pi\)
\(152\) 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 −0.989835 0.142220i \(-0.954576\pi\)
0.371752 0.928332i \(-0.378757\pi\)
\(158\) 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 −0.325933 0.945393i \(-0.605678\pi\)
0.981701 0.190430i \(-0.0609883\pi\)
\(164\) 0 0
\(165\) 7.55842 + 13.0916i 0.588422 + 1.01918i
\(166\) 0 0
\(167\) 5.62772 0.435486 0.217743 0.976006i \(-0.430131\pi\)
0.217743 + 0.976006i \(0.430131\pi\)
\(168\) 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 \(-0.837838\pi\)
0.858863 + 0.512206i \(0.171172\pi\)
\(174\) 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 0.873134 + 0.487481i \(0.162084\pi\)
−0.0143962 + 0.999896i \(0.504583\pi\)
\(180\) 0 0
\(181\) −16.2337 −1.20664 −0.603320 0.797499i \(-0.706156\pi\)
−0.603320 + 0.797499i \(0.706156\pi\)
\(182\) 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 −0.927383 0.374112i \(-0.877947\pi\)
0.787683 + 0.616081i \(0.211281\pi\)
\(192\) 0 0
\(193\) −3.37228 5.84096i −0.242742 0.420442i 0.718752 0.695266i \(-0.244714\pi\)
−0.961494 + 0.274825i \(0.911380\pi\)
\(194\) 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 −0.996850 0.0793045i \(-0.974730\pi\)
0.429745 0.902950i \(-0.358603\pi\)
\(200\) 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 \(-0.439660\pi\)
0.188430 + 0.982087i \(0.439660\pi\)
\(224\) 0 0
\(225\) 2.62772 0.175181
\(226\) 0 0
\(227\) 9.93070 + 17.2005i 0.659124 + 1.14164i 0.980843 + 0.194801i \(0.0624061\pi\)
−0.321719 + 0.946835i \(0.604261\pi\)
\(228\) 0 0
\(229\) −6.11684 + 10.5947i −0.404212 + 0.700116i −0.994229 0.107274i \(-0.965788\pi\)
0.590017 + 0.807391i \(0.299121\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.627719 1.08724i 0.0411232 0.0712275i −0.844731 0.535191i \(-0.820240\pi\)
0.885854 + 0.463963i \(0.153573\pi\)
\(234\) 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 0.892058 + 0.451920i \(0.149261\pi\)
−0.0546547 + 0.998505i \(0.517406\pi\)
\(242\) 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 \(-0.547843\pi\)
−0.149737 + 0.988726i \(0.547843\pi\)
\(252\) 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 0.223160 + 0.974782i \(0.428363\pi\)
−0.955766 + 0.294128i \(0.904971\pi\)
\(258\) 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 −0.973281 0.229616i \(-0.926253\pi\)
0.287787 0.957694i \(-0.407080\pi\)
\(264\) 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 \(-0.225219\pi\)
−0.942871 + 0.333157i \(0.891886\pi\)
\(270\) 0 0
\(271\) 4.74456 8.21782i 0.288212 0.499197i −0.685171 0.728382i \(-0.740273\pi\)
0.973383 + 0.229185i \(0.0736060\pi\)
\(272\) 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 −0.947630 0.319372i \(-0.896528\pi\)
0.197231 0.980357i \(-0.436805\pi\)
\(278\) 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 \(-0.251717\pi\)
−0.967308 + 0.253606i \(0.918383\pi\)
\(284\) 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 \(-0.762195\pi\)
−0.733671 + 0.679505i \(0.762195\pi\)
\(294\) 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 \(-0.847882\pi\)
−0.887966 + 0.459909i \(0.847882\pi\)
\(308\) 0 0
\(309\) −13.3505 −0.759485
\(310\) 0 0
\(311\) −6.37228 11.0371i −0.361339 0.625857i 0.626843 0.779146i \(-0.284347\pi\)
−0.988181 + 0.153289i \(0.951014\pi\)
\(312\) 0 0
\(313\) 1.44158 2.49689i 0.0814828 0.141132i −0.822404 0.568904i \(-0.807368\pi\)
0.903887 + 0.427771i \(0.140701\pi\)
\(314\) 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
\(319\) 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 −0.982470 0.186421i \(-0.940311\pi\)
0.652680 + 0.757634i \(0.273645\pi\)
\(332\) 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 0.979507 + 0.201409i \(0.0645520\pi\)
−0.315328 + 0.948983i \(0.602115\pi\)
\(348\) 0 0
\(349\) −19.4891 −1.04323 −0.521614 0.853181i \(-0.674670\pi\)
−0.521614 + 0.853181i \(0.674670\pi\)
\(350\) 0 0
\(351\) −3.86141 −0.206107
\(352\) 0 0
\(353\) −0.930703 1.61203i −0.0495363 0.0857995i 0.840194 0.542286i \(-0.182441\pi\)
−0.889730 + 0.456486i \(0.849108\pi\)
\(354\) 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
\(361\) −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 0.999772 + 0.0213533i \(0.00679748\pi\)
−0.481393 + 0.876505i \(0.659869\pi\)
\(368\) 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 −0.126290 0.991993i \(-0.540307\pi\)
0.922236 0.386626i \(-0.126360\pi\)
\(374\) 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 \(-0.980779\pi\)
0.551351 + 0.834273i \(0.314112\pi\)
\(384\) 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 0.545754 0.837945i \(-0.316243\pi\)
−0.998559 + 0.0536646i \(0.982910\pi\)
\(390\) 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 −0.130002 0.991514i \(-0.541498\pi\)
0.923677 0.383171i \(-0.125168\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 19.3030 33.4338i 0.963945 1.66960i 0.251522 0.967852i \(-0.419069\pi\)
0.712423 0.701750i \(-0.247598\pi\)
\(402\) 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 \(-0.0749884\pi\)
−0.688328 + 0.725399i \(0.741655\pi\)
\(410\) 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 \(-0.384668\pi\)
0.354451 + 0.935074i \(0.384668\pi\)
\(420\) 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 0.555392 0.831589i \(-0.312568\pi\)
−0.997873 + 0.0651893i \(0.979235\pi\)
\(432\) 0 0
\(433\) −28.9783 −1.39261 −0.696303 0.717748i \(-0.745173\pi\)
−0.696303 + 0.717748i \(0.745173\pi\)
\(434\) 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 \(-0.880861\pi\)
0.782010 + 0.623266i \(0.214194\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8.37228 14.5012i 0.397779 0.688974i −0.595673 0.803227i \(-0.703114\pi\)
0.993452 + 0.114254i \(0.0364477\pi\)
\(444\) 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 −0.920918 0.389757i \(-0.872559\pi\)
0.797998 + 0.602660i \(0.205892\pi\)
\(458\) 0 0
\(459\) −0.164391 0.284734i −0.00767313 0.0132902i
\(460\) 0 0
\(461\) 1.25544 0.0584715 0.0292358 0.999573i \(-0.490693\pi\)
0.0292358 + 0.999573i \(0.490693\pi\)
\(462\) 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 \(-0.769526\pi\)
0.948243 + 0.317546i \(0.102859\pi\)
\(468\) 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 0.999958 + 0.00919454i \(0.00292675\pi\)
−0.492016 + 0.870586i \(0.663740\pi\)
\(480\) 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 −0.973434 0.228969i \(-0.926465\pi\)
0.288424 0.957503i \(-0.406869\pi\)
\(488\) 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 0.250510 + 0.968114i \(0.419402\pi\)
−0.963666 + 0.267109i \(0.913932\pi\)
\(500\) 0 0
\(501\) 6.67527 + 11.5619i 0.298229 + 0.516548i
\(502\) 0 0
\(503\) 18.3723 0.819180 0.409590 0.912270i \(-0.365672\pi\)
0.409590 + 0.912270i \(0.365672\pi\)
\(504\) 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 −0.0915524 + 0.995800i \(0.529183\pi\)
−0.816612 + 0.577187i \(0.804150\pi\)
\(510\) 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 −0.981347 0.192244i \(-0.938423\pi\)
0.324185 0.945994i \(-0.394910\pi\)
\(522\) 0 0
\(523\) −18.2337 + 31.5817i −0.797304 + 1.38097i 0.124063 + 0.992274i \(0.460408\pi\)
−0.921366 + 0.388696i \(0.872926\pi\)
\(524\) 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 −0.302847 0.953039i \(-0.597937\pi\)
0.976780 0.214246i \(-0.0687294\pi\)
\(542\) 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 0.903160 0.429304i \(-0.141241\pi\)
−0.823368 + 0.567508i \(0.807908\pi\)
\(558\) 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 \(-0.0465246\pi\)
−0.620798 + 0.783971i \(0.713191\pi\)
\(564\) 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 −0.476052 0.879417i \(-0.657933\pi\)
0.999624 0.0274352i \(-0.00873399\pi\)
\(570\) 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
\(573\) −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 \(-0.322611\pi\)
−0.999433 + 0.0336791i \(0.989278\pi\)
\(578\) 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 \(-0.243290\pi\)
0.721853 + 0.692046i \(0.243290\pi\)
\(588\) 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 \(-0.965368\pi\)
0.591080 + 0.806613i \(0.298702\pi\)
\(594\) 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 0.978980 + 0.203957i \(0.0653803\pi\)
−0.312858 + 0.949800i \(0.601286\pi\)
\(600\) 0 0
\(601\) −16.5109 −0.673493 −0.336746 0.941595i \(-0.609326\pi\)
−0.336746 + 0.941595i \(0.609326\pi\)
\(602\) 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 \(-0.666901\pi\)
1.00000 0.000735686i \(0.000234176\pi\)
\(608\) 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 0.939076 0.343711i \(-0.111684\pi\)
−0.767200 + 0.641408i \(0.778351\pi\)
\(614\) 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 \(-0.249112\pi\)
−0.965200 + 0.261512i \(0.915779\pi\)
\(620\) 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 0.845601 0.533816i \(-0.179242\pi\)
−0.885098 + 0.465404i \(0.845909\pi\)
\(642\) 0 0
\(643\) −18.3723 −0.724532 −0.362266 0.932075i \(-0.617997\pi\)
−0.362266 + 0.932075i \(0.617997\pi\)
\(644\) 0 0
\(645\) 20.7446 0.816816
\(646\) 0 0
\(647\) −8.00000 13.8564i −0.314512 0.544752i 0.664821 0.747002i \(-0.268508\pi\)
−0.979334 + 0.202251i \(0.935174\pi\)
\(648\) 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 −0.918736 0.394872i \(-0.870789\pi\)
0.801337 + 0.598213i \(0.204122\pi\)
\(654\) 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 \(-0.0740923\pi\)
−0.686283 + 0.727334i \(0.740759\pi\)
\(662\) 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 \(-0.738019\pi\)
0.974981 + 0.222287i \(0.0713522\pi\)
\(678\) 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 −0.972242 0.233977i \(-0.924826\pi\)
0.283491 0.958975i \(-0.408507\pi\)
\(684\) 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 \(-0.891102\pi\)
0.761556 + 0.648099i \(0.224436\pi\)
\(692\) 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 −0.921360 0.388711i \(-0.872920\pi\)
0.797314 + 0.603565i \(0.206254\pi\)
\(710\) 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 \(-0.813999\pi\)
0.894780 + 0.446507i \(0.147332\pi\)
\(720\) 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 \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) 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 \(-0.893287\pi\)
0.757090 + 0.653311i \(0.226620\pi\)
\(734\) 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 0.990917 0.134473i \(-0.0429342\pi\)
−0.611916 + 0.790923i \(0.709601\pi\)
\(740\) 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 −0.989164 0.146818i \(-0.953097\pi\)
0.621730 + 0.783232i \(0.286430\pi\)
\(752\) 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 \(-0.804573\pi\)
0.907608 + 0.419818i \(0.137906\pi\)
\(762\) 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 \(-0.520038\pi\)
−0.0629105 + 0.998019i \(0.520038\pi\)
\(770\) 0 0
\(771\) −55.7228 −2.00681
\(772\) 0 0
\(773\) 2.18614 + 3.78651i 0.0786300 + 0.136191i 0.902659 0.430356i \(-0.141612\pi\)
−0.824029 + 0.566548i \(0.808279\pi\)
\(774\) 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 −0.997935 0.0642366i \(-0.979539\pi\)
0.443337 0.896355i \(-0.353795\pi\)
\(788\) 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 \(-0.589268\pi\)
−0.276781 + 0.960933i \(0.589268\pi\)
\(798\) 0 0