Properties

Label 280.2.q.e.121.3
Level $280$
Weight $2$
Character 280.121
Analytic conductor $2.236$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.11337408.1
Defining polynomial: \(x^{6} + 18 x^{4} + 81 x^{2} + 12\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.3
Root \(2.78499i\) of defining polynomial
Character \(\chi\) \(=\) 280.121
Dual form 280.2.q.e.81.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.64497 + 2.84918i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(2.64497 + 0.0641892i) q^{7} +(-3.91187 + 6.77556i) q^{9} +O(q^{10})\) \(q+(1.64497 + 2.84918i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(2.64497 + 0.0641892i) q^{7} +(-3.91187 + 6.77556i) q^{9} +(-2.91187 - 5.04351i) q^{11} +2.75615 q^{13} -3.28995 q^{15} +(-1.00000 - 1.73205i) q^{17} +(0.378076 - 0.654846i) q^{19} +(4.16802 + 7.64158i) q^{21} +(0.266897 - 0.462279i) q^{23} +(-0.500000 - 0.866025i) q^{25} -15.8698 q^{27} -0.823739 q^{29} +(1.28995 + 2.23425i) q^{31} +(9.57989 - 16.5929i) q^{33} +(-1.37808 + 2.25852i) q^{35} +(-2.37808 + 4.11895i) q^{37} +(4.53379 + 7.85276i) q^{39} +6.06759 q^{41} +0.710055 q^{43} +(-3.91187 - 6.77556i) q^{45} +(6.44566 - 11.1642i) q^{47} +(6.99176 + 0.339557i) q^{49} +(3.28995 - 5.69835i) q^{51} +(4.20181 + 7.27776i) q^{53} +5.82374 q^{55} +2.48770 q^{57} +(-4.00000 - 6.92820i) q^{59} +(-4.70181 + 8.14378i) q^{61} +(-10.7817 + 17.6701i) q^{63} +(-1.37808 + 2.38690i) q^{65} +(-5.93492 - 10.2796i) q^{67} +1.75615 q^{69} +(-1.75615 - 3.04174i) q^{73} +(1.64497 - 2.84918i) q^{75} +(-7.37808 - 13.5268i) q^{77} +(4.75615 - 8.23790i) q^{79} +(-14.3698 - 24.8893i) q^{81} -6.71005 q^{83} +2.00000 q^{85} +(-1.35503 - 2.34698i) q^{87} +(-0.878076 + 1.52087i) q^{89} +(7.28995 + 0.176915i) q^{91} +(-4.24385 + 7.35056i) q^{93} +(0.378076 + 0.654846i) q^{95} -2.00000 q^{97} +45.5634 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{5} + 6q^{7} - 9q^{9} + O(q^{10}) \) \( 6q - 3q^{5} + 6q^{7} - 9q^{9} - 3q^{11} + 6q^{13} - 6q^{17} - 3q^{19} - 3q^{23} - 3q^{25} - 36q^{27} + 24q^{29} - 12q^{31} + 18q^{33} - 3q^{35} - 9q^{37} + 18q^{39} + 18q^{41} + 24q^{43} - 9q^{45} + 15q^{47} - 12q^{49} - 9q^{53} + 6q^{55} + 36q^{57} - 24q^{59} + 6q^{61} + 9q^{63} - 3q^{65} - 6q^{67} - 39q^{77} + 18q^{79} - 27q^{81} - 60q^{83} + 12q^{85} - 18q^{87} + 24q^{91} - 36q^{93} - 3q^{95} - 12q^{97} + 126q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.64497 + 2.84918i 0.949725 + 1.64497i 0.746002 + 0.665944i \(0.231971\pi\)
0.203724 + 0.979028i \(0.434696\pi\)
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 2.64497 + 0.0641892i 0.999706 + 0.0242612i
\(8\) 0 0
\(9\) −3.91187 + 6.77556i −1.30396 + 2.25852i
\(10\) 0 0
\(11\) −2.91187 5.04351i −0.877962 1.52067i −0.853574 0.520972i \(-0.825570\pi\)
−0.0243876 0.999703i \(-0.507764\pi\)
\(12\) 0 0
\(13\) 2.75615 0.764419 0.382209 0.924076i \(-0.375163\pi\)
0.382209 + 0.924076i \(0.375163\pi\)
\(14\) 0 0
\(15\) −3.28995 −0.849460
\(16\) 0 0
\(17\) −1.00000 1.73205i −0.242536 0.420084i 0.718900 0.695113i \(-0.244646\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) 0 0
\(19\) 0.378076 0.654846i 0.0867365 0.150232i −0.819393 0.573232i \(-0.805690\pi\)
0.906130 + 0.423000i \(0.139023\pi\)
\(20\) 0 0
\(21\) 4.16802 + 7.64158i 0.909537 + 1.66753i
\(22\) 0 0
\(23\) 0.266897 0.462279i 0.0556518 0.0963918i −0.836857 0.547421i \(-0.815610\pi\)
0.892509 + 0.451029i \(0.148943\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −15.8698 −3.05415
\(28\) 0 0
\(29\) −0.823739 −0.152964 −0.0764822 0.997071i \(-0.524369\pi\)
−0.0764822 + 0.997071i \(0.524369\pi\)
\(30\) 0 0
\(31\) 1.28995 + 2.23425i 0.231681 + 0.401283i 0.958303 0.285754i \(-0.0922441\pi\)
−0.726622 + 0.687038i \(0.758911\pi\)
\(32\) 0 0
\(33\) 9.57989 16.5929i 1.66764 2.88845i
\(34\) 0 0
\(35\) −1.37808 + 2.25852i −0.232937 + 0.381759i
\(36\) 0 0
\(37\) −2.37808 + 4.11895i −0.390953 + 0.677151i −0.992576 0.121630i \(-0.961188\pi\)
0.601622 + 0.798781i \(0.294521\pi\)
\(38\) 0 0
\(39\) 4.53379 + 7.85276i 0.725988 + 1.25745i
\(40\) 0 0
\(41\) 6.06759 0.947598 0.473799 0.880633i \(-0.342882\pi\)
0.473799 + 0.880633i \(0.342882\pi\)
\(42\) 0 0
\(43\) 0.710055 0.108282 0.0541412 0.998533i \(-0.482758\pi\)
0.0541412 + 0.998533i \(0.482758\pi\)
\(44\) 0 0
\(45\) −3.91187 6.77556i −0.583147 1.01004i
\(46\) 0 0
\(47\) 6.44566 11.1642i 0.940197 1.62847i 0.175102 0.984550i \(-0.443974\pi\)
0.765095 0.643918i \(-0.222692\pi\)
\(48\) 0 0
\(49\) 6.99176 + 0.339557i 0.998823 + 0.0485082i
\(50\) 0 0
\(51\) 3.28995 5.69835i 0.460684 0.797929i
\(52\) 0 0
\(53\) 4.20181 + 7.27776i 0.577164 + 0.999677i 0.995803 + 0.0915241i \(0.0291738\pi\)
−0.418639 + 0.908153i \(0.637493\pi\)
\(54\) 0 0
\(55\) 5.82374 0.785273
\(56\) 0 0
\(57\) 2.48770 0.329504
\(58\) 0 0
\(59\) −4.00000 6.92820i −0.520756 0.901975i −0.999709 0.0241347i \(-0.992317\pi\)
0.478953 0.877841i \(-0.341016\pi\)
\(60\) 0 0
\(61\) −4.70181 + 8.14378i −0.602006 + 1.04270i 0.390511 + 0.920598i \(0.372298\pi\)
−0.992517 + 0.122106i \(0.961035\pi\)
\(62\) 0 0
\(63\) −10.7817 + 17.6701i −1.35837 + 2.22622i
\(64\) 0 0
\(65\) −1.37808 + 2.38690i −0.170929 + 0.296058i
\(66\) 0 0
\(67\) −5.93492 10.2796i −0.725066 1.25585i −0.958947 0.283585i \(-0.908476\pi\)
0.233881 0.972265i \(-0.424857\pi\)
\(68\) 0 0
\(69\) 1.75615 0.211416
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −1.75615 3.04174i −0.205542 0.356009i 0.744763 0.667329i \(-0.232562\pi\)
−0.950305 + 0.311320i \(0.899229\pi\)
\(74\) 0 0
\(75\) 1.64497 2.84918i 0.189945 0.328995i
\(76\) 0 0
\(77\) −7.37808 13.5268i −0.840810 1.54153i
\(78\) 0 0
\(79\) 4.75615 8.23790i 0.535109 0.926836i −0.464049 0.885809i \(-0.653604\pi\)
0.999158 0.0410263i \(-0.0130627\pi\)
\(80\) 0 0
\(81\) −14.3698 24.8893i −1.59665 2.76548i
\(82\) 0 0
\(83\) −6.71005 −0.736524 −0.368262 0.929722i \(-0.620047\pi\)
−0.368262 + 0.929722i \(0.620047\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) 0 0
\(87\) −1.35503 2.34698i −0.145274 0.251622i
\(88\) 0 0
\(89\) −0.878076 + 1.52087i −0.0930758 + 0.161212i −0.908804 0.417223i \(-0.863003\pi\)
0.815728 + 0.578436i \(0.196337\pi\)
\(90\) 0 0
\(91\) 7.28995 + 0.176915i 0.764194 + 0.0185458i
\(92\) 0 0
\(93\) −4.24385 + 7.35056i −0.440067 + 0.762218i
\(94\) 0 0
\(95\) 0.378076 + 0.654846i 0.0387898 + 0.0671858i
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) 45.5634 4.57929
\(100\) 0 0
\(101\) −1.16802 2.02307i −0.116222 0.201303i 0.802045 0.597263i \(-0.203745\pi\)
−0.918268 + 0.395960i \(0.870412\pi\)
\(102\) 0 0
\(103\) 1.11118 1.92462i 0.109488 0.189638i −0.806075 0.591813i \(-0.798412\pi\)
0.915563 + 0.402175i \(0.131746\pi\)
\(104\) 0 0
\(105\) −8.70181 0.211179i −0.849210 0.0206090i
\(106\) 0 0
\(107\) −7.93492 + 13.7437i −0.767097 + 1.32865i 0.172033 + 0.985091i \(0.444966\pi\)
−0.939131 + 0.343561i \(0.888367\pi\)
\(108\) 0 0
\(109\) 1.63423 + 2.83056i 0.156531 + 0.271119i 0.933615 0.358277i \(-0.116636\pi\)
−0.777085 + 0.629396i \(0.783302\pi\)
\(110\) 0 0
\(111\) −15.6475 −1.48519
\(112\) 0 0
\(113\) −13.1598 −1.23797 −0.618984 0.785404i \(-0.712455\pi\)
−0.618984 + 0.785404i \(0.712455\pi\)
\(114\) 0 0
\(115\) 0.266897 + 0.462279i 0.0248883 + 0.0431077i
\(116\) 0 0
\(117\) −10.7817 + 18.6745i −0.996769 + 1.72645i
\(118\) 0 0
\(119\) −2.53379 4.64542i −0.232272 0.425845i
\(120\) 0 0
\(121\) −11.4580 + 19.8458i −1.04163 + 1.80416i
\(122\) 0 0
\(123\) 9.98101 + 17.2876i 0.899958 + 1.55877i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 11.9159 1.05737 0.528684 0.848819i \(-0.322686\pi\)
0.528684 + 0.848819i \(0.322686\pi\)
\(128\) 0 0
\(129\) 1.16802 + 2.02307i 0.102839 + 0.178122i
\(130\) 0 0
\(131\) −10.7817 + 18.6745i −0.942002 + 1.63160i −0.180356 + 0.983601i \(0.557725\pi\)
−0.761646 + 0.647994i \(0.775608\pi\)
\(132\) 0 0
\(133\) 1.04203 1.70778i 0.0903558 0.148084i
\(134\) 0 0
\(135\) 7.93492 13.7437i 0.682929 1.18287i
\(136\) 0 0
\(137\) −2.00000 3.46410i −0.170872 0.295958i 0.767853 0.640626i \(-0.221325\pi\)
−0.938725 + 0.344668i \(0.887992\pi\)
\(138\) 0 0
\(139\) 6.57989 0.558099 0.279049 0.960277i \(-0.409981\pi\)
0.279049 + 0.960277i \(0.409981\pi\)
\(140\) 0 0
\(141\) 42.4118 3.57171
\(142\) 0 0
\(143\) −8.02555 13.9007i −0.671130 1.16243i
\(144\) 0 0
\(145\) 0.411869 0.713379i 0.0342039 0.0592429i
\(146\) 0 0
\(147\) 10.5338 + 20.4793i 0.868813 + 1.68911i
\(148\) 0 0
\(149\) −0.0543371 + 0.0941146i −0.00445147 + 0.00771017i −0.868243 0.496140i \(-0.834750\pi\)
0.863791 + 0.503850i \(0.168084\pi\)
\(150\) 0 0
\(151\) 6.53379 + 11.3169i 0.531713 + 0.920953i 0.999315 + 0.0370142i \(0.0117847\pi\)
−0.467602 + 0.883939i \(0.654882\pi\)
\(152\) 0 0
\(153\) 15.6475 1.26502
\(154\) 0 0
\(155\) −2.57989 −0.207222
\(156\) 0 0
\(157\) −4.44566 7.70011i −0.354803 0.614536i 0.632282 0.774739i \(-0.282119\pi\)
−0.987084 + 0.160203i \(0.948785\pi\)
\(158\) 0 0
\(159\) −13.8237 + 23.9434i −1.09629 + 1.89884i
\(160\) 0 0
\(161\) 0.735608 1.20558i 0.0579740 0.0950132i
\(162\) 0 0
\(163\) 5.75615 9.96995i 0.450857 0.780907i −0.547583 0.836751i \(-0.684452\pi\)
0.998439 + 0.0558449i \(0.0177853\pi\)
\(164\) 0 0
\(165\) 9.57989 + 16.5929i 0.745793 + 1.29175i
\(166\) 0 0
\(167\) 1.46621 0.113458 0.0567292 0.998390i \(-0.481933\pi\)
0.0567292 + 0.998390i \(0.481933\pi\)
\(168\) 0 0
\(169\) −5.40363 −0.415664
\(170\) 0 0
\(171\) 2.95797 + 5.12335i 0.226201 + 0.391792i
\(172\) 0 0
\(173\) 5.62192 9.73746i 0.427427 0.740325i −0.569217 0.822188i \(-0.692753\pi\)
0.996644 + 0.0818623i \(0.0260868\pi\)
\(174\) 0 0
\(175\) −1.26690 2.32271i −0.0957684 0.175580i
\(176\) 0 0
\(177\) 13.1598 22.7934i 0.989150 1.71326i
\(178\) 0 0
\(179\) −3.66802 6.35320i −0.274161 0.474860i 0.695762 0.718272i \(-0.255067\pi\)
−0.969923 + 0.243412i \(0.921733\pi\)
\(180\) 0 0
\(181\) −18.4712 −1.37295 −0.686477 0.727151i \(-0.740844\pi\)
−0.686477 + 0.727151i \(0.740844\pi\)
\(182\) 0 0
\(183\) −30.9374 −2.28696
\(184\) 0 0
\(185\) −2.37808 4.11895i −0.174840 0.302831i
\(186\) 0 0
\(187\) −5.82374 + 10.0870i −0.425874 + 0.737635i
\(188\) 0 0
\(189\) −41.9753 1.01867i −3.05325 0.0740975i
\(190\) 0 0
\(191\) −7.28995 + 12.6266i −0.527482 + 0.913625i 0.472005 + 0.881596i \(0.343530\pi\)
−0.999487 + 0.0320296i \(0.989803\pi\)
\(192\) 0 0
\(193\) 9.40363 + 16.2876i 0.676888 + 1.17240i 0.975913 + 0.218159i \(0.0700052\pi\)
−0.299025 + 0.954245i \(0.596661\pi\)
\(194\) 0 0
\(195\) −9.06759 −0.649343
\(196\) 0 0
\(197\) 2.75615 0.196368 0.0981838 0.995168i \(-0.468697\pi\)
0.0981838 + 0.995168i \(0.468697\pi\)
\(198\) 0 0
\(199\) −7.51230 13.0117i −0.532533 0.922374i −0.999278 0.0379825i \(-0.987907\pi\)
0.466745 0.884392i \(-0.345426\pi\)
\(200\) 0 0
\(201\) 19.5256 33.8192i 1.37723 2.38543i
\(202\) 0 0
\(203\) −2.17877 0.0528751i −0.152919 0.00371111i
\(204\) 0 0
\(205\) −3.03379 + 5.25468i −0.211889 + 0.367003i
\(206\) 0 0
\(207\) 2.08813 + 3.61675i 0.145135 + 0.251381i
\(208\) 0 0
\(209\) −4.40363 −0.304605
\(210\) 0 0
\(211\) −21.9159 −1.50875 −0.754377 0.656441i \(-0.772061\pi\)
−0.754377 + 0.656441i \(0.772061\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −0.355027 + 0.614926i −0.0242127 + 0.0419376i
\(216\) 0 0
\(217\) 3.26845 + 5.99233i 0.221877 + 0.406786i
\(218\) 0 0
\(219\) 5.77764 10.0072i 0.390417 0.676222i
\(220\) 0 0
\(221\) −2.75615 4.77379i −0.185399 0.321120i
\(222\) 0 0
\(223\) 18.8073 1.25943 0.629714 0.776827i \(-0.283172\pi\)
0.629714 + 0.776827i \(0.283172\pi\)
\(224\) 0 0
\(225\) 7.82374 0.521583
\(226\) 0 0
\(227\) −8.33604 14.4384i −0.553283 0.958313i −0.998035 0.0626599i \(-0.980042\pi\)
0.444752 0.895654i \(-0.353292\pi\)
\(228\) 0 0
\(229\) −9.75615 + 16.8982i −0.644705 + 1.11666i 0.339665 + 0.940546i \(0.389686\pi\)
−0.984370 + 0.176115i \(0.943647\pi\)
\(230\) 0 0
\(231\) 26.4036 43.2727i 1.73723 2.84714i
\(232\) 0 0
\(233\) −9.00000 + 15.5885i −0.589610 + 1.02123i 0.404674 + 0.914461i \(0.367385\pi\)
−0.994283 + 0.106773i \(0.965948\pi\)
\(234\) 0 0
\(235\) 6.44566 + 11.1642i 0.420469 + 0.728273i
\(236\) 0 0
\(237\) 31.2950 2.03283
\(238\) 0 0
\(239\) −16.0922 −1.04092 −0.520459 0.853887i \(-0.674239\pi\)
−0.520459 + 0.853887i \(0.674239\pi\)
\(240\) 0 0
\(241\) −0.445663 0.771911i −0.0287077 0.0497231i 0.851315 0.524655i \(-0.175806\pi\)
−0.880022 + 0.474932i \(0.842473\pi\)
\(242\) 0 0
\(243\) 23.4712 40.6533i 1.50568 2.60791i
\(244\) 0 0
\(245\) −3.78995 + 5.88526i −0.242131 + 0.375996i
\(246\) 0 0
\(247\) 1.04203 1.80486i 0.0663030 0.114840i
\(248\) 0 0
\(249\) −11.0379 19.1181i −0.699496 1.21156i
\(250\) 0 0
\(251\) 17.4712 1.10277 0.551387 0.834250i \(-0.314099\pi\)
0.551387 + 0.834250i \(0.314099\pi\)
\(252\) 0 0
\(253\) −3.10867 −0.195441
\(254\) 0 0
\(255\) 3.28995 + 5.69835i 0.206024 + 0.356845i
\(256\) 0 0
\(257\) 3.51230 6.08349i 0.219091 0.379478i −0.735439 0.677591i \(-0.763024\pi\)
0.954530 + 0.298113i \(0.0963574\pi\)
\(258\) 0 0
\(259\) −6.55434 + 10.7419i −0.407267 + 0.667467i
\(260\) 0 0
\(261\) 3.22236 5.58129i 0.199459 0.345473i
\(262\) 0 0
\(263\) −8.88882 15.3959i −0.548108 0.949351i −0.998404 0.0564719i \(-0.982015\pi\)
0.450296 0.892879i \(-0.351318\pi\)
\(264\) 0 0
\(265\) −8.40363 −0.516231
\(266\) 0 0
\(267\) −5.77764 −0.353586
\(268\) 0 0
\(269\) 4.70181 + 8.14378i 0.286675 + 0.496535i 0.973014 0.230746i \(-0.0741168\pi\)
−0.686339 + 0.727282i \(0.740783\pi\)
\(270\) 0 0
\(271\) −3.51230 + 6.08349i −0.213357 + 0.369546i −0.952763 0.303714i \(-0.901773\pi\)
0.739406 + 0.673260i \(0.235106\pi\)
\(272\) 0 0
\(273\) 11.4877 + 21.0614i 0.695267 + 1.27469i
\(274\) 0 0
\(275\) −2.91187 + 5.04351i −0.175592 + 0.304135i
\(276\) 0 0
\(277\) −13.5799 23.5211i −0.815937 1.41324i −0.908653 0.417551i \(-0.862889\pi\)
0.0927170 0.995693i \(-0.470445\pi\)
\(278\) 0 0
\(279\) −20.1844 −1.20841
\(280\) 0 0
\(281\) −0.620977 −0.0370444 −0.0185222 0.999828i \(-0.505896\pi\)
−0.0185222 + 0.999828i \(0.505896\pi\)
\(282\) 0 0
\(283\) −1.57989 2.73645i −0.0939147 0.162665i 0.815240 0.579123i \(-0.196605\pi\)
−0.909155 + 0.416458i \(0.863271\pi\)
\(284\) 0 0
\(285\) −1.24385 + 2.15441i −0.0736792 + 0.127616i
\(286\) 0 0
\(287\) 16.0486 + 0.389474i 0.947319 + 0.0229899i
\(288\) 0 0
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 0 0
\(291\) −3.28995 5.69835i −0.192860 0.334043i
\(292\) 0 0
\(293\) 11.2438 0.656873 0.328436 0.944526i \(-0.393478\pi\)
0.328436 + 0.944526i \(0.393478\pi\)
\(294\) 0 0
\(295\) 8.00000 0.465778
\(296\) 0 0
\(297\) 46.2109 + 80.0396i 2.68143 + 4.64437i
\(298\) 0 0
\(299\) 0.735608 1.27411i 0.0425413 0.0736837i
\(300\) 0 0
\(301\) 1.87808 + 0.0455779i 0.108250 + 0.00262706i
\(302\) 0 0
\(303\) 3.84272 6.65579i 0.220759 0.382365i
\(304\) 0 0
\(305\) −4.70181 8.14378i −0.269225 0.466312i
\(306\) 0 0
\(307\) 23.5173 1.34220 0.671102 0.741365i \(-0.265821\pi\)
0.671102 + 0.741365i \(0.265821\pi\)
\(308\) 0 0
\(309\) 7.31144 0.415933
\(310\) 0 0
\(311\) 14.5799 + 25.2531i 0.826750 + 1.43197i 0.900575 + 0.434701i \(0.143146\pi\)
−0.0738250 + 0.997271i \(0.523521\pi\)
\(312\) 0 0
\(313\) 12.0922 20.9443i 0.683491 1.18384i −0.290417 0.956900i \(-0.593794\pi\)
0.973908 0.226941i \(-0.0728726\pi\)
\(314\) 0 0
\(315\) −9.91187 18.1723i −0.558471 1.02389i
\(316\) 0 0
\(317\) −6.06759 + 10.5094i −0.340790 + 0.590265i −0.984580 0.174937i \(-0.944028\pi\)
0.643790 + 0.765202i \(0.277361\pi\)
\(318\) 0 0
\(319\) 2.39862 + 4.15453i 0.134297 + 0.232609i
\(320\) 0 0
\(321\) −52.2109 −2.91413
\(322\) 0 0
\(323\) −1.51230 −0.0841468
\(324\) 0 0
\(325\) −1.37808 2.38690i −0.0764419 0.132401i
\(326\) 0 0
\(327\) −5.37652 + 9.31240i −0.297322 + 0.514977i
\(328\) 0 0
\(329\) 17.7652 29.1153i 0.979428 1.60518i
\(330\) 0 0
\(331\) 0.911869 1.57940i 0.0501209 0.0868119i −0.839877 0.542778i \(-0.817373\pi\)
0.889997 + 0.455966i \(0.150706\pi\)
\(332\) 0 0
\(333\) −18.6054 32.2256i −1.01957 1.76595i
\(334\) 0 0
\(335\) 11.8698 0.648518
\(336\) 0 0
\(337\) −17.7827 −0.968683 −0.484341 0.874879i \(-0.660941\pi\)
−0.484341 + 0.874879i \(0.660941\pi\)
\(338\) 0 0
\(339\) −21.6475 37.4945i −1.17573 2.03642i
\(340\) 0 0
\(341\) 7.51230 13.0117i 0.406814 0.704623i
\(342\) 0 0
\(343\) 18.4712 + 1.34692i 0.997352 + 0.0727266i
\(344\) 0 0
\(345\) −0.878076 + 1.52087i −0.0472740 + 0.0818810i
\(346\) 0 0
\(347\) 0.644973 + 1.11713i 0.0346239 + 0.0599704i 0.882818 0.469715i \(-0.155643\pi\)
−0.848194 + 0.529685i \(0.822310\pi\)
\(348\) 0 0
\(349\) 1.31144 0.0701995 0.0350998 0.999384i \(-0.488825\pi\)
0.0350998 + 0.999384i \(0.488825\pi\)
\(350\) 0 0
\(351\) −43.7397 −2.33465
\(352\) 0 0
\(353\) 5.51230 + 9.54759i 0.293390 + 0.508167i 0.974609 0.223913i \(-0.0718831\pi\)
−0.681219 + 0.732080i \(0.738550\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 9.06759 14.8608i 0.479908 0.786517i
\(358\) 0 0
\(359\) −5.11368 + 8.85716i −0.269890 + 0.467463i −0.968833 0.247714i \(-0.920321\pi\)
0.698943 + 0.715177i \(0.253654\pi\)
\(360\) 0 0
\(361\) 9.21412 + 15.9593i 0.484954 + 0.839964i
\(362\) 0 0
\(363\) −75.3922 −3.95706
\(364\) 0 0
\(365\) 3.51230 0.183842
\(366\) 0 0
\(367\) −8.67053 15.0178i −0.452598 0.783922i 0.545949 0.837819i \(-0.316169\pi\)
−0.998547 + 0.0538962i \(0.982836\pi\)
\(368\) 0 0
\(369\) −23.7356 + 41.1113i −1.23563 + 2.14017i
\(370\) 0 0
\(371\) 10.6465 + 19.5192i 0.552740 + 1.01339i
\(372\) 0 0
\(373\) 8.89133 15.4002i 0.460375 0.797394i −0.538604 0.842559i \(-0.681048\pi\)
0.998980 + 0.0451654i \(0.0143815\pi\)
\(374\) 0 0
\(375\) 1.64497 + 2.84918i 0.0849460 + 0.147131i
\(376\) 0 0
\(377\) −2.27035 −0.116929
\(378\) 0 0
\(379\) −33.2109 −1.70593 −0.852964 0.521969i \(-0.825198\pi\)
−0.852964 + 0.521969i \(0.825198\pi\)
\(380\) 0 0
\(381\) 19.6014 + 33.9506i 1.00421 + 1.73934i
\(382\) 0 0
\(383\) −7.38058 + 12.7835i −0.377130 + 0.653208i −0.990643 0.136476i \(-0.956422\pi\)
0.613513 + 0.789684i \(0.289756\pi\)
\(384\) 0 0
\(385\) 15.4036 + 0.373821i 0.785042 + 0.0190517i
\(386\) 0 0
\(387\) −2.77764 + 4.81102i −0.141195 + 0.244558i
\(388\) 0 0
\(389\) 11.4036 + 19.7517i 0.578187 + 1.00145i 0.995687 + 0.0927724i \(0.0295729\pi\)
−0.417500 + 0.908677i \(0.637094\pi\)
\(390\) 0 0
\(391\) −1.06759 −0.0539902
\(392\) 0 0
\(393\) −70.9424 −3.57857
\(394\) 0 0
\(395\) 4.75615 + 8.23790i 0.239308 + 0.414494i
\(396\) 0 0
\(397\) 7.13517 12.3585i 0.358104 0.620255i −0.629540 0.776968i \(-0.716757\pi\)
0.987644 + 0.156714i \(0.0500899\pi\)
\(398\) 0 0
\(399\) 6.57989 + 0.159683i 0.329407 + 0.00799416i
\(400\) 0 0
\(401\) 5.74385 9.94864i 0.286834 0.496811i −0.686218 0.727396i \(-0.740730\pi\)
0.973052 + 0.230585i \(0.0740638\pi\)
\(402\) 0 0
\(403\) 3.55528 + 6.15793i 0.177101 + 0.306748i
\(404\) 0 0
\(405\) 28.7397 1.42809
\(406\) 0 0
\(407\) 27.6986 1.37297
\(408\) 0 0
\(409\) −0.899566 1.55809i −0.0444807 0.0770428i 0.842928 0.538027i \(-0.180830\pi\)
−0.887409 + 0.460984i \(0.847497\pi\)
\(410\) 0 0
\(411\) 6.57989 11.3967i 0.324562 0.562158i
\(412\) 0 0
\(413\) −10.1352 18.5817i −0.498719 0.914344i
\(414\) 0 0
\(415\) 3.35503 5.81108i 0.164692 0.285255i
\(416\) 0 0
\(417\) 10.8237 + 18.7473i 0.530041 + 0.918058i
\(418\) 0 0
\(419\) 27.4282 1.33996 0.669978 0.742381i \(-0.266303\pi\)
0.669978 + 0.742381i \(0.266303\pi\)
\(420\) 0 0
\(421\) 2.91593 0.142114 0.0710569 0.997472i \(-0.477363\pi\)
0.0710569 + 0.997472i \(0.477363\pi\)
\(422\) 0 0
\(423\) 50.4292 + 87.3459i 2.45195 + 4.24690i
\(424\) 0 0
\(425\) −1.00000 + 1.73205i −0.0485071 + 0.0840168i
\(426\) 0 0
\(427\) −12.9589 + 21.2383i −0.627126 + 1.02779i
\(428\) 0 0
\(429\) 26.4036 45.7324i 1.27478 2.20798i
\(430\) 0 0
\(431\) −7.28995 12.6266i −0.351144 0.608200i 0.635306 0.772261i \(-0.280874\pi\)
−0.986450 + 0.164061i \(0.947541\pi\)
\(432\) 0 0
\(433\) 21.1598 1.01687 0.508437 0.861099i \(-0.330223\pi\)
0.508437 + 0.861099i \(0.330223\pi\)
\(434\) 0 0
\(435\) 2.71005 0.129937
\(436\) 0 0
\(437\) −0.201814 0.349553i −0.00965409 0.0167214i
\(438\) 0 0
\(439\) 15.4712 26.7969i 0.738401 1.27895i −0.214814 0.976655i \(-0.568915\pi\)
0.953215 0.302293i \(-0.0977521\pi\)
\(440\) 0 0
\(441\) −29.6515 + 46.0448i −1.41198 + 2.19261i
\(442\) 0 0
\(443\) −18.7587 + 32.4909i −0.891251 + 1.54369i −0.0528732 + 0.998601i \(0.516838\pi\)
−0.838377 + 0.545090i \(0.816495\pi\)
\(444\) 0 0
\(445\) −0.878076 1.52087i −0.0416248 0.0720962i
\(446\) 0 0
\(447\) −0.357532 −0.0169107
\(448\) 0 0
\(449\) 31.0922 1.46733 0.733666 0.679511i \(-0.237808\pi\)
0.733666 + 0.679511i \(0.237808\pi\)
\(450\) 0 0
\(451\) −17.6680 30.6019i −0.831955 1.44099i
\(452\) 0 0
\(453\) −21.4958 + 37.2319i −1.00996 + 1.74931i
\(454\) 0 0
\(455\) −3.79819 + 6.22482i −0.178062 + 0.291824i
\(456\) 0 0
\(457\) 2.17626 3.76940i 0.101801 0.176325i −0.810626 0.585565i \(-0.800873\pi\)
0.912427 + 0.409240i \(0.134206\pi\)
\(458\) 0 0
\(459\) 15.8698 + 27.4874i 0.740740 + 1.28300i
\(460\) 0 0
\(461\) 37.2950 1.73700 0.868500 0.495690i \(-0.165085\pi\)
0.868500 + 0.495690i \(0.165085\pi\)
\(462\) 0 0
\(463\) −9.81873 −0.456315 −0.228158 0.973624i \(-0.573270\pi\)
−0.228158 + 0.973624i \(0.573270\pi\)
\(464\) 0 0
\(465\) −4.24385 7.35056i −0.196804 0.340874i
\(466\) 0 0
\(467\) 11.4011 19.7473i 0.527581 0.913797i −0.471902 0.881651i \(-0.656432\pi\)
0.999483 0.0321463i \(-0.0102342\pi\)
\(468\) 0 0
\(469\) −15.0379 27.5702i −0.694384 1.27307i
\(470\) 0 0
\(471\) 14.6260 25.3330i 0.673930 1.16728i
\(472\) 0 0
\(473\) −2.06759 3.58117i −0.0950678 0.164662i
\(474\) 0 0
\(475\) −0.756152 −0.0346946
\(476\) 0 0
\(477\) −65.7478 −3.01038
\(478\) 0 0
\(479\) 10.2224 + 17.7056i 0.467071 + 0.808991i 0.999292 0.0376140i \(-0.0119757\pi\)
−0.532221 + 0.846606i \(0.678642\pi\)
\(480\) 0 0
\(481\) −6.55434 + 11.3524i −0.298852 + 0.517627i
\(482\) 0 0
\(483\) 4.64497 + 0.112726i 0.211354 + 0.00512921i
\(484\) 0 0
\(485\) 1.00000 1.73205i 0.0454077 0.0786484i
\(486\) 0 0
\(487\) 21.4036 + 37.0722i 0.969891 + 1.67990i 0.695857 + 0.718181i \(0.255025\pi\)
0.274034 + 0.961720i \(0.411642\pi\)
\(488\) 0 0
\(489\) 37.8748 1.71276
\(490\) 0 0
\(491\) −18.8502 −0.850699 −0.425350 0.905029i \(-0.639849\pi\)
−0.425350 + 0.905029i \(0.639849\pi\)
\(492\) 0 0
\(493\) 0.823739 + 1.42676i 0.0370993 + 0.0642579i
\(494\) 0 0
\(495\) −22.7817 + 39.4591i −1.02396 + 1.77355i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −13.8698 + 24.0233i −0.620899 + 1.07543i 0.368420 + 0.929660i \(0.379899\pi\)
−0.989319 + 0.145769i \(0.953434\pi\)
\(500\) 0 0
\(501\) 2.41187 + 4.17748i 0.107754 + 0.186636i
\(502\) 0 0
\(503\) 14.7101 0.655889 0.327944 0.944697i \(-0.393644\pi\)
0.327944 + 0.944697i \(0.393644\pi\)
\(504\) 0 0
\(505\) 2.33604 0.103952
\(506\) 0 0
\(507\) −8.88882 15.3959i −0.394766 0.683755i
\(508\) 0 0
\(509\) 6.99176 12.1101i 0.309904 0.536770i −0.668437 0.743769i \(-0.733036\pi\)
0.978341 + 0.206999i \(0.0663697\pi\)
\(510\) 0 0
\(511\) −4.44973 8.15805i −0.196844 0.360891i
\(512\) 0 0
\(513\) −6.00000 + 10.3923i −0.264906 + 0.458831i
\(514\) 0 0
\(515\) 1.11118 + 1.92462i 0.0489644 + 0.0848088i
\(516\) 0 0
\(517\) −75.0757 −3.30183
\(518\) 0 0
\(519\) 36.9916 1.62375
\(520\) 0 0
\(521\) −10.3616 17.9468i −0.453950 0.786264i 0.544677 0.838646i \(-0.316652\pi\)
−0.998627 + 0.0523817i \(0.983319\pi\)
\(522\) 0 0
\(523\) 11.1763 19.3579i 0.488704 0.846460i −0.511212 0.859455i \(-0.670803\pi\)
0.999916 + 0.0129950i \(0.00413655\pi\)
\(524\) 0 0
\(525\) 4.53379 7.43040i 0.197871 0.324289i
\(526\) 0 0
\(527\) 2.57989 4.46850i 0.112382 0.194651i
\(528\) 0 0
\(529\) 11.3575 + 19.6718i 0.493806 + 0.855297i
\(530\) 0 0
\(531\) 62.5899 2.71617
\(532\) 0 0
\(533\) 16.7232 0.724362
\(534\) 0 0
\(535\) −7.93492 13.7437i −0.343056 0.594191i
\(536\) 0 0
\(537\) 12.0676 20.9017i 0.520755 0.901974i
\(538\) 0 0
\(539\) −18.6465 36.2517i −0.803163 1.56147i
\(540\) 0 0
\(541\) −16.3278 + 28.2806i −0.701987 + 1.21588i 0.265781 + 0.964033i \(0.414370\pi\)
−0.967768 + 0.251844i \(0.918963\pi\)
\(542\) 0 0
\(543\) −30.3846 52.6277i −1.30393 2.25847i
\(544\) 0 0
\(545\) −3.26845 −0.140005
\(546\) 0 0
\(547\) 31.1648 1.33251 0.666255 0.745724i \(-0.267896\pi\)
0.666255 + 0.745724i \(0.267896\pi\)
\(548\) 0 0
\(549\) −36.7858 63.7148i −1.56998 2.71928i
\(550\) 0 0
\(551\) −0.311436 + 0.539422i −0.0132676 + 0.0229802i
\(552\) 0 0
\(553\) 13.1087 21.4837i 0.557438 0.913581i
\(554\) 0 0
\(555\) 7.82374 13.5511i 0.332099 0.575213i
\(556\) 0 0
\(557\) 22.3616 + 38.7314i 0.947491 + 1.64110i 0.750685 + 0.660660i \(0.229724\pi\)
0.196806 + 0.980442i \(0.436943\pi\)
\(558\) 0 0
\(559\) 1.95702 0.0827731
\(560\) 0 0
\(561\) −38.3196 −1.61785
\(562\) 0 0
\(563\) 16.2464 + 28.1395i 0.684702 + 1.18594i 0.973530 + 0.228558i \(0.0734010\pi\)
−0.288828 + 0.957381i \(0.593266\pi\)
\(564\) 0 0
\(565\) 6.57989 11.3967i 0.276818 0.479463i
\(566\) 0 0
\(567\) −36.4102 66.7539i −1.52908 2.80340i
\(568\) 0 0
\(569\) −17.3370 + 30.0285i −0.726804 + 1.25886i 0.231423 + 0.972853i \(0.425662\pi\)
−0.958227 + 0.286009i \(0.907671\pi\)
\(570\) 0 0
\(571\) −1.55528 2.69383i −0.0650866 0.112733i 0.831646 0.555306i \(-0.187399\pi\)
−0.896732 + 0.442573i \(0.854066\pi\)
\(572\) 0 0
\(573\) −47.9670 −2.00385
\(574\) 0 0
\(575\) −0.533794 −0.0222607
\(576\) 0 0
\(577\) −0.336042 0.582041i −0.0139896 0.0242307i 0.858946 0.512066i \(-0.171120\pi\)
−0.872935 + 0.487836i \(0.837787\pi\)
\(578\) 0 0
\(579\) −30.9374 + 53.5852i −1.28572 + 2.22692i
\(580\) 0 0
\(581\) −17.7479 0.430713i −0.736307 0.0178690i
\(582\) 0 0
\(583\) 24.4703 42.3837i 1.01345 1.75536i
\(584\) 0 0
\(585\) −10.7817 18.6745i −0.445769 0.772094i
\(586\) 0 0
\(587\) −4.67208 −0.192838 −0.0964188 0.995341i \(-0.530739\pi\)
−0.0964188 + 0.995341i \(0.530739\pi\)
\(588\) 0 0
\(589\) 1.95079 0.0803808
\(590\) 0 0
\(591\) 4.53379 + 7.85276i 0.186495 + 0.323019i
\(592\) 0 0
\(593\) −10.0922 + 17.4802i −0.414437 + 0.717825i −0.995369 0.0961264i \(-0.969355\pi\)
0.580932 + 0.813952i \(0.302688\pi\)
\(594\) 0 0
\(595\) 5.28995 + 0.128378i 0.216867 + 0.00526300i
\(596\) 0 0
\(597\) 24.7151 42.8077i 1.01152 1.75200i
\(598\) 0 0
\(599\) −10.7562 18.6302i −0.439484 0.761209i 0.558165 0.829730i \(-0.311506\pi\)
−0.997650 + 0.0685204i \(0.978172\pi\)
\(600\) 0 0
\(601\) 5.29495 0.215986 0.107993 0.994152i \(-0.465558\pi\)
0.107993 + 0.994152i \(0.465558\pi\)
\(602\) 0 0
\(603\) 92.8665 3.78182
\(604\) 0 0
\(605\) −11.4580 19.8458i −0.465833 0.806846i
\(606\) 0 0
\(607\) −18.3591 + 31.7989i −0.745172 + 1.29068i 0.204942 + 0.978774i \(0.434300\pi\)
−0.950114 + 0.311902i \(0.899034\pi\)
\(608\) 0 0
\(609\) −3.43336 6.29467i −0.139127 0.255073i
\(610\) 0 0
\(611\) 17.7652 30.7703i 0.718704 1.24483i
\(612\) 0 0
\(613\) −20.3616 35.2673i −0.822397 1.42443i −0.903892 0.427760i \(-0.859303\pi\)
0.0814954 0.996674i \(-0.474030\pi\)
\(614\) 0 0
\(615\) −19.9620 −0.804947
\(616\) 0 0
\(617\) 16.8073 0.676635 0.338317 0.941032i \(-0.390142\pi\)
0.338317 + 0.941032i \(0.390142\pi\)
\(618\) 0 0
\(619\) 17.8954 + 30.9957i 0.719276 + 1.24582i 0.961287 + 0.275550i \(0.0888598\pi\)
−0.242010 + 0.970274i \(0.577807\pi\)
\(620\) 0 0
\(621\) −4.23561 + 7.33629i −0.169969 + 0.294395i
\(622\) 0 0
\(623\) −2.42011 + 3.96630i −0.0969597 + 0.158907i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −7.24385 12.5467i −0.289291 0.501067i
\(628\) 0 0
\(629\) 9.51230 0.379280
\(630\) 0 0
\(631\) −32.4447 −1.29160 −0.645802 0.763505i \(-0.723477\pi\)
−0.645802 + 0.763505i \(0.723477\pi\)
\(632\) 0 0
\(633\) −36.0511 62.4423i −1.43290 2.48186i
\(634\) 0 0
\(635\) −5.95797 + 10.3195i −0.236435 + 0.409517i
\(636\) 0 0
\(637\) 19.2703 + 0.935872i 0.763519 + 0.0370806i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −8.45390 14.6426i −0.333909 0.578348i 0.649366 0.760476i \(-0.275035\pi\)
−0.983275 + 0.182129i \(0.941701\pi\)
\(642\) 0 0
\(643\) 0.135174 0.00533075 0.00266538 0.999996i \(-0.499152\pi\)
0.00266538 + 0.999996i \(0.499152\pi\)
\(644\) 0 0
\(645\) −2.33604 −0.0919816
\(646\) 0 0
\(647\) 2.04454 + 3.54125i 0.0803791 + 0.139221i 0.903413 0.428772i \(-0.141054\pi\)
−0.823034 + 0.567993i \(0.807720\pi\)
\(648\) 0 0
\(649\) −23.2950 + 40.3480i −0.914407 + 1.58380i
\(650\) 0 0
\(651\) −11.6967 + 19.1696i −0.458429 + 0.751317i
\(652\) 0 0
\(653\) −15.9580 + 27.6400i −0.624483 + 1.08164i 0.364157 + 0.931338i \(0.381357\pi\)
−0.988641 + 0.150300i \(0.951976\pi\)
\(654\) 0 0
\(655\) −10.7817 18.6745i −0.421276 0.729672i
\(656\) 0 0
\(657\) 27.4793 1.07207
\(658\) 0 0
\(659\) 4.70505 0.183283 0.0916413 0.995792i \(-0.470789\pi\)
0.0916413 + 0.995792i \(0.470789\pi\)
\(660\) 0 0
\(661\) −2.25710 3.90941i −0.0877910 0.152058i 0.818786 0.574099i \(-0.194647\pi\)
−0.906577 + 0.422040i \(0.861314\pi\)
\(662\) 0 0
\(663\) 9.06759 15.7055i 0.352156 0.609952i
\(664\) 0 0
\(665\) 0.957966 + 1.75632i 0.0371483 + 0.0681071i
\(666\) 0 0
\(667\) −0.219853 + 0.380797i −0.00851275 + 0.0147445i
\(668\) 0 0
\(669\) 30.9374 + 53.5852i 1.19611 + 2.07172i
\(670\) 0 0
\(671\) 54.7643 2.11415
\(672\) 0 0
\(673\) 46.9424 1.80950 0.904749 0.425945i \(-0.140058\pi\)
0.904749 + 0.425945i \(0.140058\pi\)
\(674\) 0 0
\(675\) 7.93492 + 13.7437i 0.305415 + 0.528995i
\(676\) 0 0
\(677\) 5.20181 9.00981i 0.199922 0.346275i −0.748581 0.663043i \(-0.769264\pi\)
0.948503 + 0.316768i \(0.102598\pi\)
\(678\) 0 0
\(679\) −5.28995 0.128378i −0.203009 0.00492671i
\(680\) 0 0
\(681\) 27.4251 47.5017i 1.05093 1.82027i
\(682\) 0 0
\(683\) −2.53129 4.38432i −0.0968571 0.167761i 0.813525 0.581530i \(-0.197546\pi\)
−0.910382 + 0.413768i \(0.864212\pi\)
\(684\) 0 0
\(685\) 4.00000 0.152832
\(686\) 0 0
\(687\) −64.1944 −2.44917
\(688\) 0 0
\(689\) 11.5808 + 20.0586i 0.441195 + 0.764172i
\(690\) 0 0
\(691\) 2.22236 3.84924i 0.0845425 0.146432i −0.820654 0.571426i \(-0.806390\pi\)
0.905196 + 0.424994i \(0.139724\pi\)
\(692\) 0 0
\(693\) 120.514 + 2.92468i 4.57795 + 0.111099i
\(694\) 0 0
\(695\) −3.28995 + 5.69835i −0.124795 + 0.216151i
\(696\) 0 0
\(697\) −6.06759 10.5094i −0.229826 0.398071i
\(698\) 0 0
\(699\) −59.2190 −2.23987
\(700\) 0 0
\(701\) 21.7562 0.821719 0.410859 0.911699i \(-0.365229\pi\)
0.410859 + 0.911699i \(0.365229\pi\)
\(702\) 0 0
\(703\) 1.79819 + 3.11455i 0.0678199 + 0.117467i
\(704\) 0 0
\(705\) −21.2059 + 36.7297i −0.798660 + 1.38332i
\(706\) 0 0
\(707\) −2.95952 5.42594i −0.111304 0.204064i
\(708\) 0 0
\(709\) 20.5041 35.5141i 0.770046 1.33376i −0.167491 0.985874i \(-0.553566\pi\)
0.937537 0.347886i \(-0.113100\pi\)
\(710\) 0 0
\(711\) 37.2109 + 64.4511i 1.39552 + 2.41711i
\(712\) 0 0
\(713\) 1.37713 0.0515739
\(714\) 0 0
\(715\) 16.0511 0.600277
\(716\) 0 0
\(717\) −26.4712 45.8495i −0.988586 1.71228i
\(718\) 0 0
\(719\) −11.8698 + 20.5592i −0.442670 + 0.766727i −0.997887 0.0649787i \(-0.979302\pi\)
0.555216 + 0.831706i \(0.312635\pi\)
\(720\) 0 0
\(721\) 3.06258 5.01924i 0.114056 0.186926i
\(722\) 0 0
\(723\) 1.46621 2.53954i 0.0545288 0.0944467i
\(724\) 0 0
\(725\) 0.411869 + 0.713379i 0.0152964 + 0.0264942i
\(726\) 0 0
\(727\) −28.8534 −1.07011 −0.535056 0.844817i \(-0.679709\pi\)
−0.535056 + 0.844817i \(0.679709\pi\)
\(728\) 0 0
\(729\) 68.2190 2.52663
\(730\) 0 0
\(731\) −0.710055 1.22985i −0.0262623 0.0454877i
\(732\) 0 0
\(733\) −23.4292 + 40.5805i −0.865377 + 1.49888i 0.00129620 + 0.999999i \(0.499587\pi\)
−0.866673 + 0.498877i \(0.833746\pi\)
\(734\) 0 0
\(735\) −23.0025 1.11713i −0.848460 0.0412058i
\(736\) 0 0
\(737\) −34.5634 + 59.8656i −1.27316 + 2.20518i
\(738\) 0 0
\(739\) −8.07165 13.9805i −0.296920 0.514281i 0.678509 0.734592i \(-0.262626\pi\)
−0.975430 + 0.220310i \(0.929293\pi\)
\(740\) 0 0
\(741\) 6.85647 0.251879
\(742\) 0 0
\(743\) −16.2243 −0.595210 −0.297605 0.954689i \(-0.596188\pi\)
−0.297605 + 0.954689i \(0.596188\pi\)
\(744\) 0 0
\(745\) −0.0543371 0.0941146i −0.00199076 0.00344809i
\(746\) 0 0
\(747\) 26.2489 45.4644i 0.960395 1.66345i
\(748\) 0 0
\(749\) −21.8698 + 35.8423i −0.799106 + 1.30965i
\(750\) 0 0
\(751\) −10.7562 + 18.6302i −0.392498 + 0.679826i −0.992778 0.119964i \(-0.961722\pi\)
0.600281 + 0.799789i \(0.295056\pi\)
\(752\) 0 0
\(753\) 28.7397 + 49.7786i 1.04733 + 1.81403i
\(754\) 0 0
\(755\) −13.0676 −0.475578
\(756\) 0 0
\(757\) 0.840220 0.0305383 0.0152692 0.999883i \(-0.495139\pi\)
0.0152692 + 0.999883i \(0.495139\pi\)
\(758\) 0 0
\(759\) −5.11368 8.85716i −0.185615 0.321495i
\(760\) 0 0
\(761\) 14.4457 25.0206i 0.523655 0.906997i −0.475966 0.879464i \(-0.657901\pi\)
0.999621 0.0275332i \(-0.00876519\pi\)
\(762\) 0 0
\(763\) 4.14079 + 7.59167i 0.149907 + 0.274837i
\(764\) 0 0
\(765\) −7.82374 + 13.5511i −0.282868 + 0.489942i
\(766\) 0 0
\(767\) −11.0246 19.0952i −0.398075 0.689487i
\(768\) 0 0
\(769\) −27.3790 −0.987313 −0.493656 0.869657i \(-0.664340\pi\)
−0.493656 + 0.869657i \(0.664340\pi\)
\(770\) 0 0
\(771\) 23.1106 0.832307
\(772\) 0 0
\(773\) 19.1177 + 33.1129i 0.687618 + 1.19099i 0.972607 + 0.232458i \(0.0746767\pi\)
−0.284989 + 0.958531i \(0.591990\pi\)
\(774\) 0 0
\(775\) 1.28995 2.23425i 0.0463362 0.0802566i
\(776\) 0 0
\(777\) −41.3871 1.00440i −1.48476 0.0360326i
\(778\) 0 0
\(779\) 2.29401 3.97334i 0.0821914 0.142360i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 13.0726 0.467176
\(784\) 0 0
\(785\) 8.89133 0.317345
\(786\) 0 0
\(787\) −3.66646 6.35050i −0.130695 0.226371i 0.793249 0.608897i \(-0.208388\pi\)
−0.923945 + 0.382526i \(0.875054\pi\)
\(788\) 0 0
\(789\) 29.2437 50.6516i 1.04110 1.80325i
\(790\) 0 0
\(791\) −34.8073 0.844716i −1.23760 0.0300346i
\(792\) 0 0
\(793\) −12.9589 + 22.4455i −0.460184 + 0.797063i
\(794\) 0 0
\(795\) −13.8237 23.9434i −0.490277 0.849186i
\(796\) 0 0
\(797\) 14.4877 0.513181