Properties

Label 112.2.i.c.65.1
Level $112$
Weight $2$
Character 112.65
Analytic conductor $0.894$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 112.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.894324502638\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 65.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 112.65
Dual form 112.2.i.c.81.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 + 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\) \(q+(1.50000 + 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(-3.00000 + 5.19615i) q^{9} +(-0.500000 - 0.866025i) q^{11} +2.00000 q^{13} +3.00000 q^{15} +(-1.50000 - 2.59808i) q^{17} +(2.50000 - 4.33013i) q^{19} +(1.50000 - 7.79423i) q^{21} +(-1.50000 + 2.59808i) q^{23} +(2.00000 + 3.46410i) q^{25} -9.00000 q^{27} -6.00000 q^{29} +(-0.500000 - 0.866025i) q^{31} +(1.50000 - 2.59808i) q^{33} +(-2.50000 + 0.866025i) q^{35} +(2.50000 - 4.33013i) q^{37} +(3.00000 + 5.19615i) q^{39} -10.0000 q^{41} +4.00000 q^{43} +(3.00000 + 5.19615i) q^{45} +(0.500000 - 0.866025i) q^{47} +(1.00000 + 6.92820i) q^{49} +(4.50000 - 7.79423i) q^{51} +(4.50000 + 7.79423i) q^{53} -1.00000 q^{55} +15.0000 q^{57} +(1.50000 + 2.59808i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(15.0000 - 5.19615i) q^{63} +(1.00000 - 1.73205i) q^{65} +(5.50000 + 9.52628i) q^{67} -9.00000 q^{69} -16.0000 q^{71} +(-3.50000 - 6.06218i) q^{73} +(-6.00000 + 10.3923i) q^{75} +(-0.500000 + 2.59808i) q^{77} +(-5.50000 + 9.52628i) q^{79} +(-4.50000 - 7.79423i) q^{81} +4.00000 q^{83} -3.00000 q^{85} +(-9.00000 - 15.5885i) q^{87} +(4.50000 - 7.79423i) q^{89} +(-4.00000 - 3.46410i) q^{91} +(1.50000 - 2.59808i) q^{93} +(-2.50000 - 4.33013i) q^{95} +6.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{3} + q^{5} - 4q^{7} - 6q^{9} + O(q^{10}) \) \( 2q + 3q^{3} + q^{5} - 4q^{7} - 6q^{9} - q^{11} + 4q^{13} + 6q^{15} - 3q^{17} + 5q^{19} + 3q^{21} - 3q^{23} + 4q^{25} - 18q^{27} - 12q^{29} - q^{31} + 3q^{33} - 5q^{35} + 5q^{37} + 6q^{39} - 20q^{41} + 8q^{43} + 6q^{45} + q^{47} + 2q^{49} + 9q^{51} + 9q^{53} - 2q^{55} + 30q^{57} + 3q^{59} - 3q^{61} + 30q^{63} + 2q^{65} + 11q^{67} - 18q^{69} - 32q^{71} - 7q^{73} - 12q^{75} - q^{77} - 11q^{79} - 9q^{81} + 8q^{83} - 6q^{85} - 18q^{87} + 9q^{89} - 8q^{91} + 3q^{93} - 5q^{95} + 12q^{97} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\) \(85\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 1.50000 + 2.59808i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i −0.732294 0.680989i \(-0.761550\pi\)
0.955901 + 0.293691i \(0.0948835\pi\)
\(6\) 0 0
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) 0 0
\(9\) −3.00000 + 5.19615i −1.00000 + 1.73205i
\(10\) 0 0
\(11\) −0.500000 0.866025i −0.150756 0.261116i 0.780750 0.624844i \(-0.214837\pi\)
−0.931505 + 0.363727i \(0.881504\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 3.00000 0.774597
\(16\) 0 0
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0 0
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) 0 0
\(21\) 1.50000 7.79423i 0.327327 1.70084i
\(22\) 0 0
\(23\) −1.50000 + 2.59808i −0.312772 + 0.541736i −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 0 0
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) 0 0
\(27\) −9.00000 −1.73205
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −0.500000 0.866025i −0.0898027 0.155543i 0.817625 0.575751i \(-0.195290\pi\)
−0.907428 + 0.420208i \(0.861957\pi\)
\(32\) 0 0
\(33\) 1.50000 2.59808i 0.261116 0.452267i
\(34\) 0 0
\(35\) −2.50000 + 0.866025i −0.422577 + 0.146385i
\(36\) 0 0
\(37\) 2.50000 4.33013i 0.410997 0.711868i −0.584002 0.811752i \(-0.698514\pi\)
0.994999 + 0.0998840i \(0.0318472\pi\)
\(38\) 0 0
\(39\) 3.00000 + 5.19615i 0.480384 + 0.832050i
\(40\) 0 0
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 3.00000 + 5.19615i 0.447214 + 0.774597i
\(46\) 0 0
\(47\) 0.500000 0.866025i 0.0729325 0.126323i −0.827253 0.561830i \(-0.810098\pi\)
0.900185 + 0.435507i \(0.143431\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) 4.50000 7.79423i 0.630126 1.09141i
\(52\) 0 0
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) 0 0
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) 15.0000 1.98680
\(58\) 0 0
\(59\) 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i \(-0.104104\pi\)
−0.751710 + 0.659494i \(0.770771\pi\)
\(60\) 0 0
\(61\) −1.50000 + 2.59808i −0.192055 + 0.332650i −0.945931 0.324367i \(-0.894849\pi\)
0.753876 + 0.657017i \(0.228182\pi\)
\(62\) 0 0
\(63\) 15.0000 5.19615i 1.88982 0.654654i
\(64\) 0 0
\(65\) 1.00000 1.73205i 0.124035 0.214834i
\(66\) 0 0
\(67\) 5.50000 + 9.52628i 0.671932 + 1.16382i 0.977356 + 0.211604i \(0.0678686\pi\)
−0.305424 + 0.952217i \(0.598798\pi\)
\(68\) 0 0
\(69\) −9.00000 −1.08347
\(70\) 0 0
\(71\) −16.0000 −1.89885 −0.949425 0.313993i \(-0.898333\pi\)
−0.949425 + 0.313993i \(0.898333\pi\)
\(72\) 0 0
\(73\) −3.50000 6.06218i −0.409644 0.709524i 0.585206 0.810885i \(-0.301014\pi\)
−0.994850 + 0.101361i \(0.967680\pi\)
\(74\) 0 0
\(75\) −6.00000 + 10.3923i −0.692820 + 1.20000i
\(76\) 0 0
\(77\) −0.500000 + 2.59808i −0.0569803 + 0.296078i
\(78\) 0 0
\(79\) −5.50000 + 9.52628i −0.618798 + 1.07179i 0.370907 + 0.928670i \(0.379047\pi\)
−0.989705 + 0.143120i \(0.954286\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) −9.00000 15.5885i −0.964901 1.67126i
\(88\) 0 0
\(89\) 4.50000 7.79423i 0.476999 0.826187i −0.522654 0.852545i \(-0.675058\pi\)
0.999653 + 0.0263586i \(0.00839118\pi\)
\(90\) 0 0
\(91\) −4.00000 3.46410i −0.419314 0.363137i
\(92\) 0 0
\(93\) 1.50000 2.59808i 0.155543 0.269408i
\(94\) 0 0
\(95\) −2.50000 4.33013i −0.256495 0.444262i
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) 6.50000 + 11.2583i 0.646774 + 1.12025i 0.983889 + 0.178782i \(0.0572157\pi\)
−0.337115 + 0.941464i \(0.609451\pi\)
\(102\) 0 0
\(103\) 2.50000 4.33013i 0.246332 0.426660i −0.716173 0.697923i \(-0.754108\pi\)
0.962505 + 0.271263i \(0.0874412\pi\)
\(104\) 0 0
\(105\) −6.00000 5.19615i −0.585540 0.507093i
\(106\) 0 0
\(107\) −1.50000 + 2.59808i −0.145010 + 0.251166i −0.929377 0.369132i \(-0.879655\pi\)
0.784366 + 0.620298i \(0.212988\pi\)
\(108\) 0 0
\(109\) −5.50000 9.52628i −0.526804 0.912452i −0.999512 0.0312328i \(-0.990057\pi\)
0.472708 0.881219i \(-0.343277\pi\)
\(110\) 0 0
\(111\) 15.0000 1.42374
\(112\) 0 0
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) 1.50000 + 2.59808i 0.139876 + 0.242272i
\(116\) 0 0
\(117\) −6.00000 + 10.3923i −0.554700 + 0.960769i
\(118\) 0 0
\(119\) −1.50000 + 7.79423i −0.137505 + 0.714496i
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 0 0
\(123\) −15.0000 25.9808i −1.35250 2.34261i
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) 6.00000 + 10.3923i 0.528271 + 0.914991i
\(130\) 0 0
\(131\) 8.50000 14.7224i 0.742648 1.28630i −0.208637 0.977993i \(-0.566903\pi\)
0.951285 0.308312i \(-0.0997640\pi\)
\(132\) 0 0
\(133\) −12.5000 + 4.33013i −1.08389 + 0.375470i
\(134\) 0 0
\(135\) −4.50000 + 7.79423i −0.387298 + 0.670820i
\(136\) 0 0
\(137\) −1.50000 2.59808i −0.128154 0.221969i 0.794808 0.606861i \(-0.207572\pi\)
−0.922961 + 0.384893i \(0.874238\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 3.00000 0.252646
\(142\) 0 0
\(143\) −1.00000 1.73205i −0.0836242 0.144841i
\(144\) 0 0
\(145\) −3.00000 + 5.19615i −0.249136 + 0.431517i
\(146\) 0 0
\(147\) −16.5000 + 12.9904i −1.36090 + 1.07143i
\(148\) 0 0
\(149\) −7.50000 + 12.9904i −0.614424 + 1.06421i 0.376061 + 0.926595i \(0.377278\pi\)
−0.990485 + 0.137619i \(0.956055\pi\)
\(150\) 0 0
\(151\) 7.50000 + 12.9904i 0.610341 + 1.05714i 0.991183 + 0.132502i \(0.0423010\pi\)
−0.380841 + 0.924640i \(0.624366\pi\)
\(152\) 0 0
\(153\) 18.0000 1.45521
\(154\) 0 0
\(155\) −1.00000 −0.0803219
\(156\) 0 0
\(157\) −7.50000 12.9904i −0.598565 1.03675i −0.993033 0.117836i \(-0.962404\pi\)
0.394468 0.918910i \(-0.370929\pi\)
\(158\) 0 0
\(159\) −13.5000 + 23.3827i −1.07062 + 1.85437i
\(160\) 0 0
\(161\) 7.50000 2.59808i 0.591083 0.204757i
\(162\) 0 0
\(163\) 4.50000 7.79423i 0.352467 0.610491i −0.634214 0.773158i \(-0.718676\pi\)
0.986681 + 0.162667i \(0.0520095\pi\)
\(164\) 0 0
\(165\) −1.50000 2.59808i −0.116775 0.202260i
\(166\) 0 0
\(167\) 20.0000 1.54765 0.773823 0.633402i \(-0.218342\pi\)
0.773823 + 0.633402i \(0.218342\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 15.0000 + 25.9808i 1.14708 + 1.98680i
\(172\) 0 0
\(173\) 10.5000 18.1865i 0.798300 1.38270i −0.122422 0.992478i \(-0.539066\pi\)
0.920722 0.390218i \(-0.127601\pi\)
\(174\) 0 0
\(175\) 2.00000 10.3923i 0.151186 0.785584i
\(176\) 0 0
\(177\) −4.50000 + 7.79423i −0.338241 + 0.585850i
\(178\) 0 0
\(179\) −0.500000 0.866025i −0.0373718 0.0647298i 0.846735 0.532016i \(-0.178565\pi\)
−0.884106 + 0.467286i \(0.845232\pi\)
\(180\) 0 0
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 0 0
\(183\) −9.00000 −0.665299
\(184\) 0 0
\(185\) −2.50000 4.33013i −0.183804 0.318357i
\(186\) 0 0
\(187\) −1.50000 + 2.59808i −0.109691 + 0.189990i
\(188\) 0 0
\(189\) 18.0000 + 15.5885i 1.30931 + 1.13389i
\(190\) 0 0
\(191\) 8.50000 14.7224i 0.615038 1.06528i −0.375339 0.926887i \(-0.622474\pi\)
0.990378 0.138390i \(-0.0441928\pi\)
\(192\) 0 0
\(193\) 2.50000 + 4.33013i 0.179954 + 0.311689i 0.941865 0.335993i \(-0.109072\pi\)
−0.761911 + 0.647682i \(0.775738\pi\)
\(194\) 0 0
\(195\) 6.00000 0.429669
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −4.50000 7.79423i −0.318997 0.552518i 0.661282 0.750137i \(-0.270013\pi\)
−0.980279 + 0.197619i \(0.936679\pi\)
\(200\) 0 0
\(201\) −16.5000 + 28.5788i −1.16382 + 2.01580i
\(202\) 0 0
\(203\) 12.0000 + 10.3923i 0.842235 + 0.729397i
\(204\) 0 0
\(205\) −5.00000 + 8.66025i −0.349215 + 0.604858i
\(206\) 0 0
\(207\) −9.00000 15.5885i −0.625543 1.08347i
\(208\) 0 0
\(209\) −5.00000 −0.345857
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 0 0
\(213\) −24.0000 41.5692i −1.64445 2.84828i
\(214\) 0 0
\(215\) 2.00000 3.46410i 0.136399 0.236250i
\(216\) 0 0
\(217\) −0.500000 + 2.59808i −0.0339422 + 0.176369i
\(218\) 0 0
\(219\) 10.5000 18.1865i 0.709524 1.22893i
\(220\) 0 0
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) 0 0
\(223\) −24.0000 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) −24.0000 −1.60000
\(226\) 0 0
\(227\) 3.50000 + 6.06218i 0.232303 + 0.402361i 0.958485 0.285141i \(-0.0920405\pi\)
−0.726182 + 0.687502i \(0.758707\pi\)
\(228\) 0 0
\(229\) −3.50000 + 6.06218i −0.231287 + 0.400600i −0.958187 0.286143i \(-0.907627\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) −7.50000 + 2.59808i −0.493464 + 0.170941i
\(232\) 0 0
\(233\) 6.50000 11.2583i 0.425829 0.737558i −0.570668 0.821181i \(-0.693316\pi\)
0.996497 + 0.0836229i \(0.0266491\pi\)
\(234\) 0 0
\(235\) −0.500000 0.866025i −0.0326164 0.0564933i
\(236\) 0 0
\(237\) −33.0000 −2.14358
\(238\) 0 0
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 0 0
\(241\) 8.50000 + 14.7224i 0.547533 + 0.948355i 0.998443 + 0.0557856i \(0.0177663\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 6.50000 + 2.59808i 0.415270 + 0.165985i
\(246\) 0 0
\(247\) 5.00000 8.66025i 0.318142 0.551039i
\(248\) 0 0
\(249\) 6.00000 + 10.3923i 0.380235 + 0.658586i
\(250\) 0 0
\(251\) −24.0000 −1.51487 −0.757433 0.652913i \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) 0 0
\(253\) 3.00000 0.188608
\(254\) 0 0
\(255\) −4.50000 7.79423i −0.281801 0.488094i
\(256\) 0 0
\(257\) 6.50000 11.2583i 0.405459 0.702275i −0.588916 0.808194i \(-0.700445\pi\)
0.994375 + 0.105919i \(0.0337784\pi\)
\(258\) 0 0
\(259\) −12.5000 + 4.33013i −0.776712 + 0.269061i
\(260\) 0 0
\(261\) 18.0000 31.1769i 1.11417 1.92980i
\(262\) 0 0
\(263\) 1.50000 + 2.59808i 0.0924940 + 0.160204i 0.908560 0.417755i \(-0.137183\pi\)
−0.816066 + 0.577959i \(0.803849\pi\)
\(264\) 0 0
\(265\) 9.00000 0.552866
\(266\) 0 0
\(267\) 27.0000 1.65237
\(268\) 0 0
\(269\) 8.50000 + 14.7224i 0.518254 + 0.897643i 0.999775 + 0.0212079i \(0.00675120\pi\)
−0.481521 + 0.876435i \(0.659915\pi\)
\(270\) 0 0
\(271\) −1.50000 + 2.59808i −0.0911185 + 0.157822i −0.907982 0.419009i \(-0.862378\pi\)
0.816864 + 0.576831i \(0.195711\pi\)
\(272\) 0 0
\(273\) 3.00000 15.5885i 0.181568 0.943456i
\(274\) 0 0
\(275\) 2.00000 3.46410i 0.120605 0.208893i
\(276\) 0 0
\(277\) −3.50000 6.06218i −0.210295 0.364241i 0.741512 0.670940i \(-0.234109\pi\)
−0.951807 + 0.306699i \(0.900776\pi\)
\(278\) 0 0
\(279\) 6.00000 0.359211
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) −8.50000 14.7224i −0.505273 0.875158i −0.999981 0.00609896i \(-0.998059\pi\)
0.494709 0.869059i \(-0.335275\pi\)
\(284\) 0 0
\(285\) 7.50000 12.9904i 0.444262 0.769484i
\(286\) 0 0
\(287\) 20.0000 + 17.3205i 1.18056 + 1.02240i
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 9.00000 + 15.5885i 0.527589 + 0.913812i
\(292\) 0 0
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) 3.00000 0.174667
\(296\) 0 0
\(297\) 4.50000 + 7.79423i 0.261116 + 0.452267i
\(298\) 0 0
\(299\) −3.00000 + 5.19615i −0.173494 + 0.300501i
\(300\) 0 0
\(301\) −8.00000 6.92820i −0.461112 0.399335i
\(302\) 0 0
\(303\) −19.5000 + 33.7750i −1.12025 + 1.94032i
\(304\) 0 0
\(305\) 1.50000 + 2.59808i 0.0858898 + 0.148765i
\(306\) 0 0
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 0 0
\(309\) 15.0000 0.853320
\(310\) 0 0
\(311\) 5.50000 + 9.52628i 0.311876 + 0.540186i 0.978769 0.204968i \(-0.0657092\pi\)
−0.666892 + 0.745154i \(0.732376\pi\)
\(312\) 0 0
\(313\) −15.5000 + 26.8468i −0.876112 + 1.51747i −0.0205381 + 0.999789i \(0.506538\pi\)
−0.855574 + 0.517681i \(0.826795\pi\)
\(314\) 0 0
\(315\) 3.00000 15.5885i 0.169031 0.878310i
\(316\) 0 0
\(317\) −13.5000 + 23.3827i −0.758236 + 1.31330i 0.185514 + 0.982642i \(0.440605\pi\)
−0.943750 + 0.330661i \(0.892728\pi\)
\(318\) 0 0
\(319\) 3.00000 + 5.19615i 0.167968 + 0.290929i
\(320\) 0 0
\(321\) −9.00000 −0.502331
\(322\) 0 0
\(323\) −15.0000 −0.834622
\(324\) 0 0
\(325\) 4.00000 + 6.92820i 0.221880 + 0.384308i
\(326\) 0 0
\(327\) 16.5000 28.5788i 0.912452 1.58041i
\(328\) 0 0
\(329\) −2.50000 + 0.866025i −0.137829 + 0.0477455i
\(330\) 0 0
\(331\) −3.50000 + 6.06218i −0.192377 + 0.333207i −0.946038 0.324057i \(-0.894953\pi\)
0.753660 + 0.657264i \(0.228286\pi\)
\(332\) 0 0
\(333\) 15.0000 + 25.9808i 0.821995 + 1.42374i
\(334\) 0 0
\(335\) 11.0000 0.600994
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) −15.0000 25.9808i −0.814688 1.41108i
\(340\) 0 0
\(341\) −0.500000 + 0.866025i −0.0270765 + 0.0468979i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) −4.50000 + 7.79423i −0.242272 + 0.419627i
\(346\) 0 0
\(347\) 1.50000 + 2.59808i 0.0805242 + 0.139472i 0.903475 0.428640i \(-0.141007\pi\)
−0.822951 + 0.568112i \(0.807674\pi\)
\(348\) 0 0
\(349\) −6.00000 −0.321173 −0.160586 0.987022i \(-0.551338\pi\)
−0.160586 + 0.987022i \(0.551338\pi\)
\(350\) 0 0
\(351\) −18.0000 −0.960769
\(352\) 0 0
\(353\) 2.50000 + 4.33013i 0.133062 + 0.230469i 0.924855 0.380319i \(-0.124186\pi\)
−0.791794 + 0.610789i \(0.790853\pi\)
\(354\) 0 0
\(355\) −8.00000 + 13.8564i −0.424596 + 0.735422i
\(356\) 0 0
\(357\) −22.5000 + 7.79423i −1.19083 + 0.412514i
\(358\) 0 0
\(359\) −7.50000 + 12.9904i −0.395835 + 0.685606i −0.993207 0.116358i \(-0.962878\pi\)
0.597372 + 0.801964i \(0.296211\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 0 0
\(363\) 30.0000 1.57459
\(364\) 0 0
\(365\) −7.00000 −0.366397
\(366\) 0 0
\(367\) 9.50000 + 16.4545i 0.495896 + 0.858917i 0.999989 0.00473247i \(-0.00150640\pi\)
−0.504093 + 0.863649i \(0.668173\pi\)
\(368\) 0 0
\(369\) 30.0000 51.9615i 1.56174 2.70501i
\(370\) 0 0
\(371\) 4.50000 23.3827i 0.233628 1.21397i
\(372\) 0 0
\(373\) −9.50000 + 16.4545i −0.491891 + 0.851981i −0.999956 0.00933789i \(-0.997028\pi\)
0.508065 + 0.861319i \(0.330361\pi\)
\(374\) 0 0
\(375\) 13.5000 + 23.3827i 0.697137 + 1.20748i
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 0 0
\(381\) 12.0000 + 20.7846i 0.614779 + 1.06483i
\(382\) 0 0
\(383\) 4.50000 7.79423i 0.229939 0.398266i −0.727851 0.685736i \(-0.759481\pi\)
0.957790 + 0.287469i \(0.0928139\pi\)
\(384\) 0 0
\(385\) 2.00000 + 1.73205i 0.101929 + 0.0882735i
\(386\) 0 0
\(387\) −12.0000 + 20.7846i −0.609994 + 1.05654i
\(388\) 0 0
\(389\) −9.50000 16.4545i −0.481669 0.834275i 0.518110 0.855314i \(-0.326636\pi\)
−0.999779 + 0.0210389i \(0.993303\pi\)
\(390\) 0 0
\(391\) 9.00000 0.455150
\(392\) 0 0
\(393\) 51.0000 2.57261
\(394\) 0 0
\(395\) 5.50000 + 9.52628i 0.276735 + 0.479319i
\(396\) 0 0
\(397\) 8.50000 14.7224i 0.426603 0.738898i −0.569966 0.821668i \(-0.693044\pi\)
0.996569 + 0.0827707i \(0.0263769\pi\)
\(398\) 0 0
\(399\) −30.0000 25.9808i −1.50188 1.30066i
\(400\) 0 0
\(401\) −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i \(-0.857199\pi\)
0.826139 + 0.563466i \(0.190532\pi\)
\(402\) 0 0
\(403\) −1.00000 1.73205i −0.0498135 0.0862796i
\(404\) 0 0
\(405\) −9.00000 −0.447214
\(406\) 0 0
\(407\) −5.00000 −0.247841
\(408\) 0 0
\(409\) −9.50000 16.4545i −0.469745 0.813622i 0.529657 0.848212i \(-0.322321\pi\)
−0.999402 + 0.0345902i \(0.988987\pi\)
\(410\) 0 0
\(411\) 4.50000 7.79423i 0.221969 0.384461i
\(412\) 0 0
\(413\) 1.50000 7.79423i 0.0738102 0.383529i
\(414\) 0 0
\(415\) 2.00000 3.46410i 0.0981761 0.170046i
\(416\) 0 0
\(417\) −6.00000 10.3923i −0.293821 0.508913i
\(418\) 0 0
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 0 0
\(423\) 3.00000 + 5.19615i 0.145865 + 0.252646i
\(424\) 0 0
\(425\) 6.00000 10.3923i 0.291043 0.504101i
\(426\) 0 0
\(427\) 7.50000 2.59808i 0.362950 0.125730i
\(428\) 0 0
\(429\) 3.00000 5.19615i 0.144841 0.250873i
\(430\) 0 0
\(431\) −20.5000 35.5070i −0.987450 1.71031i −0.630497 0.776192i \(-0.717149\pi\)
−0.356953 0.934122i \(-0.616185\pi\)
\(432\) 0 0
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 0 0
\(435\) −18.0000 −0.863034
\(436\) 0 0
\(437\) 7.50000 + 12.9904i 0.358774 + 0.621414i
\(438\) 0 0
\(439\) −7.50000 + 12.9904i −0.357955 + 0.619997i −0.987619 0.156871i \(-0.949859\pi\)
0.629664 + 0.776868i \(0.283193\pi\)
\(440\) 0 0
\(441\) −39.0000 15.5885i −1.85714 0.742307i
\(442\) 0 0
\(443\) −13.5000 + 23.3827i −0.641404 + 1.11094i 0.343715 + 0.939074i \(0.388315\pi\)
−0.985119 + 0.171871i \(0.945019\pi\)
\(444\) 0 0
\(445\) −4.50000 7.79423i −0.213320 0.369482i
\(446\) 0 0
\(447\) −45.0000 −2.12843
\(448\) 0 0
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 0 0
\(451\) 5.00000 + 8.66025i 0.235441 + 0.407795i
\(452\) 0 0
\(453\) −22.5000 + 38.9711i −1.05714 + 1.83102i
\(454\) 0 0
\(455\) −5.00000 + 1.73205i −0.234404 + 0.0811998i
\(456\) 0 0
\(457\) 8.50000 14.7224i 0.397613 0.688686i −0.595818 0.803120i \(-0.703172\pi\)
0.993431 + 0.114433i \(0.0365053\pi\)
\(458\) 0 0
\(459\) 13.5000 + 23.3827i 0.630126 + 1.09141i
\(460\) 0 0
\(461\) −6.00000 −0.279448 −0.139724 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 0 0
\(465\) −1.50000 2.59808i −0.0695608 0.120483i
\(466\) 0 0
\(467\) 12.5000 21.6506i 0.578431 1.00187i −0.417229 0.908802i \(-0.636999\pi\)
0.995660 0.0930703i \(-0.0296681\pi\)
\(468\) 0 0
\(469\) 5.50000 28.5788i 0.253966 1.31965i
\(470\) 0 0
\(471\) 22.5000 38.9711i 1.03675 1.79570i
\(472\) 0 0
\(473\) −2.00000 3.46410i −0.0919601 0.159280i
\(474\) 0 0
\(475\) 20.0000 0.917663
\(476\) 0 0
\(477\) −54.0000 −2.47249
\(478\) 0 0
\(479\) −10.5000 18.1865i −0.479757 0.830964i 0.519973 0.854183i \(-0.325942\pi\)
−0.999730 + 0.0232187i \(0.992609\pi\)
\(480\) 0 0
\(481\) 5.00000 8.66025i 0.227980 0.394874i
\(482\) 0 0
\(483\) 18.0000 + 15.5885i 0.819028 + 0.709299i
\(484\) 0 0
\(485\) 3.00000 5.19615i 0.136223 0.235945i
\(486\) 0 0
\(487\) −6.50000 11.2583i −0.294543 0.510164i 0.680335 0.732901i \(-0.261834\pi\)
−0.974879 + 0.222737i \(0.928501\pi\)
\(488\) 0 0
\(489\) 27.0000 1.22098
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 9.00000 + 15.5885i 0.405340 + 0.702069i
\(494\) 0 0
\(495\) 3.00000 5.19615i 0.134840 0.233550i
\(496\) 0 0
\(497\) 32.0000 + 27.7128i 1.43540 + 1.24309i
\(498\) 0 0
\(499\) −3.50000 + 6.06218i −0.156682 + 0.271380i −0.933670 0.358134i \(-0.883413\pi\)
0.776989 + 0.629515i \(0.216746\pi\)
\(500\) 0 0
\(501\) 30.0000 + 51.9615i 1.34030 + 2.32147i
\(502\) 0 0
\(503\) −16.0000 −0.713405 −0.356702 0.934218i \(-0.616099\pi\)
−0.356702 + 0.934218i \(0.616099\pi\)
\(504\) 0 0
\(505\) 13.0000 0.578492
\(506\) 0 0
\(507\) −13.5000 23.3827i −0.599556 1.03846i
\(508\) 0 0
\(509\) −3.50000 + 6.06218i −0.155135 + 0.268701i −0.933108 0.359596i \(-0.882915\pi\)
0.777973 + 0.628297i \(0.216248\pi\)
\(510\) 0 0
\(511\) −3.50000 + 18.1865i −0.154831 + 0.804525i
\(512\) 0 0
\(513\) −22.5000 + 38.9711i −0.993399 + 1.72062i
\(514\) 0 0
\(515\) −2.50000 4.33013i −0.110163 0.190808i
\(516\) 0 0
\(517\) −1.00000 −0.0439799
\(518\) 0 0
\(519\) 63.0000 2.76539
\(520\) 0 0
\(521\) −7.50000 12.9904i −0.328581 0.569119i 0.653650 0.756797i \(-0.273237\pi\)
−0.982231 + 0.187678i \(0.939904\pi\)
\(522\) 0 0
\(523\) 6.50000 11.2583i 0.284225 0.492292i −0.688196 0.725525i \(-0.741597\pi\)
0.972421 + 0.233233i \(0.0749303\pi\)
\(524\) 0 0
\(525\) 30.0000 10.3923i 1.30931 0.453557i
\(526\) 0 0
\(527\) −1.50000 + 2.59808i −0.0653410 + 0.113174i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 0 0
\(531\) −18.0000 −0.781133
\(532\) 0 0
\(533\) −20.0000 −0.866296
\(534\) 0 0
\(535\) 1.50000 + 2.59808i 0.0648507 + 0.112325i
\(536\) 0 0
\(537\) 1.50000 2.59808i 0.0647298 0.112115i
\(538\) 0 0
\(539\) 5.50000 4.33013i 0.236902 0.186512i
\(540\) 0 0
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) 0 0
\(543\) 33.0000 + 57.1577i 1.41617 + 2.45287i
\(544\) 0 0
\(545\) −11.0000 −0.471188
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) −9.00000 15.5885i −0.384111 0.665299i
\(550\) 0 0
\(551\) −15.0000 + 25.9808i −0.639021 + 1.10682i
\(552\) 0 0
\(553\) 27.5000 9.52628i 1.16942 0.405099i
\(554\) 0 0
\(555\) 7.50000 12.9904i 0.318357 0.551411i
\(556\) 0 0
\(557\) −5.50000 9.52628i −0.233042 0.403641i 0.725660 0.688054i \(-0.241535\pi\)
−0.958702 + 0.284413i \(0.908201\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) −9.00000 −0.379980
\(562\) 0 0
\(563\) 5.50000 + 9.52628i 0.231797 + 0.401485i 0.958337 0.285640i \(-0.0922060\pi\)
−0.726540 + 0.687124i \(0.758873\pi\)
\(564\) 0 0
\(565\) −5.00000 + 8.66025i −0.210352 + 0.364340i
\(566\) 0 0
\(567\) −4.50000 + 23.3827i −0.188982 + 0.981981i
\(568\) 0 0
\(569\) 0.500000 0.866025i 0.0209611 0.0363057i −0.855355 0.518043i \(-0.826661\pi\)
0.876316 + 0.481737i \(0.159994\pi\)
\(570\) 0 0
\(571\) −8.50000 14.7224i −0.355714 0.616115i 0.631526 0.775355i \(-0.282429\pi\)
−0.987240 + 0.159240i \(0.949096\pi\)
\(572\) 0 0
\(573\) 51.0000 2.13056
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) −15.5000 26.8468i −0.645273 1.11765i −0.984238 0.176847i \(-0.943410\pi\)
0.338965 0.940799i \(-0.389923\pi\)
\(578\) 0 0
\(579\) −7.50000 + 12.9904i −0.311689 + 0.539862i
\(580\) 0 0
\(581\) −8.00000 6.92820i −0.331896 0.287430i
\(582\) 0 0
\(583\) 4.50000 7.79423i 0.186371 0.322804i
\(584\) 0 0
\(585\) 6.00000 + 10.3923i 0.248069 + 0.429669i
\(586\) 0 0
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) −5.00000 −0.206021
\(590\) 0 0
\(591\) 27.0000 + 46.7654i 1.11063 + 1.92367i
\(592\) 0 0
\(593\) −21.5000 + 37.2391i −0.882899 + 1.52923i −0.0347964 + 0.999394i \(0.511078\pi\)
−0.848103 + 0.529832i \(0.822255\pi\)
\(594\) 0 0
\(595\) 6.00000 + 5.19615i 0.245976 + 0.213021i
\(596\) 0 0
\(597\) 13.5000 23.3827i 0.552518 0.956990i
\(598\) 0 0
\(599\) −10.5000 18.1865i −0.429018 0.743082i 0.567768 0.823189i \(-0.307807\pi\)
−0.996786 + 0.0801071i \(0.974474\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) 0 0
\(603\) −66.0000 −2.68773
\(604\) 0 0
\(605\) −5.00000 8.66025i −0.203279 0.352089i
\(606\) 0 0
\(607\) −3.50000 + 6.06218i −0.142061 + 0.246056i −0.928272 0.371901i \(-0.878706\pi\)
0.786212 + 0.617957i \(0.212039\pi\)
\(608\) 0 0
\(609\) −9.00000 + 46.7654i −0.364698 + 1.89503i
\(610\) 0 0
\(611\) 1.00000 1.73205i 0.0404557 0.0700713i
\(612\) 0 0
\(613\) 10.5000 + 18.1865i 0.424091 + 0.734547i 0.996335 0.0855362i \(-0.0272603\pi\)
−0.572244 + 0.820083i \(0.693927\pi\)
\(614\) 0 0
\(615\) −30.0000 −1.20972
\(616\) 0 0
\(617\) 22.0000 0.885687 0.442843 0.896599i \(-0.353970\pi\)
0.442843 + 0.896599i \(0.353970\pi\)
\(618\) 0 0
\(619\) −2.50000 4.33013i −0.100483 0.174042i 0.811400 0.584491i \(-0.198706\pi\)
−0.911884 + 0.410448i \(0.865372\pi\)
\(620\) 0 0
\(621\) 13.5000 23.3827i 0.541736 0.938315i
\(622\) 0 0
\(623\) −22.5000 + 7.79423i −0.901443 + 0.312269i
\(624\) 0 0
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) 0 0
\(627\) −7.50000 12.9904i −0.299521 0.518786i
\(628\) 0 0
\(629\) −15.0000 −0.598089
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) −18.0000 31.1769i −0.715436 1.23917i
\(634\) 0 0
\(635\) 4.00000 6.92820i 0.158735 0.274937i
\(636\) 0 0
\(637\) 2.00000 + 13.8564i 0.0792429 + 0.549011i
\(638\) 0 0
\(639\) 48.0000 83.1384i 1.89885 3.28891i
\(640\) 0 0
\(641\) −7.50000 12.9904i −0.296232 0.513089i 0.679039 0.734103i \(-0.262397\pi\)
−0.975271 + 0.221013i \(0.929064\pi\)
\(642\) 0 0
\(643\) 44.0000 1.73519 0.867595 0.497271i \(-0.165665\pi\)
0.867595 + 0.497271i \(0.165665\pi\)
\(644\) 0 0
\(645\) 12.0000 0.472500
\(646\) 0 0
\(647\) 21.5000 + 37.2391i 0.845252 + 1.46402i 0.885402 + 0.464826i \(0.153883\pi\)
−0.0401498 + 0.999194i \(0.512784\pi\)
\(648\) 0 0
\(649\) 1.50000 2.59808i 0.0588802 0.101983i
\(650\) 0 0
\(651\) −7.50000 + 2.59808i −0.293948 + 0.101827i
\(652\) 0 0
\(653\) 2.50000 4.33013i 0.0978326 0.169451i −0.812955 0.582327i \(-0.802142\pi\)
0.910787 + 0.412876i \(0.135476\pi\)
\(654\) 0 0
\(655\) −8.50000 14.7224i −0.332122 0.575253i
\(656\) 0 0
\(657\) 42.0000 1.63858
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) 0.500000 + 0.866025i 0.0194477 + 0.0336845i 0.875585 0.483063i \(-0.160476\pi\)
−0.856138 + 0.516748i \(0.827143\pi\)
\(662\) 0 0
\(663\) 9.00000 15.5885i 0.349531 0.605406i
\(664\) 0 0
\(665\) −2.50000 + 12.9904i −0.0969458 + 0.503745i
\(666\) 0 0
\(667\) 9.00000 15.5885i 0.348481 0.603587i
\(668\) 0 0
\(669\) −36.0000 62.3538i −1.39184 2.41074i
\(670\) 0 0
\(671\) 3.00000 0.115814
\(672\) 0 0
\(673\) −2.00000 −0.0770943 −0.0385472 0.999257i \(-0.512273\pi\)
−0.0385472 + 0.999257i \(0.512273\pi\)
\(674\) 0 0
\(675\) −18.0000 31.1769i −0.692820 1.20000i
\(676\) 0 0
\(677\) 4.50000 7.79423i 0.172949 0.299557i −0.766501 0.642244i \(-0.778004\pi\)
0.939450 + 0.342687i \(0.111337\pi\)
\(678\) 0 0
\(679\) −12.0000 10.3923i −0.460518 0.398820i
\(680\) 0 0
\(681\) −10.5000 + 18.1865i −0.402361 + 0.696909i
\(682\) 0 0
\(683\) 19.5000 + 33.7750i 0.746147 + 1.29236i 0.949657 + 0.313291i \(0.101432\pi\)
−0.203510 + 0.979073i \(0.565235\pi\)
\(684\) 0 0
\(685\) −3.00000 −0.114624
\(686\) 0 0
\(687\) −21.0000 −0.801200
\(688\) 0 0
\(689\) 9.00000 + 15.5885i 0.342873 + 0.593873i
\(690\) 0 0
\(691\) −23.5000 + 40.7032i −0.893982 + 1.54842i −0.0589228 + 0.998263i \(0.518767\pi\)
−0.835059 + 0.550160i \(0.814567\pi\)
\(692\) 0 0
\(693\) −12.0000 10.3923i −0.455842 0.394771i
\(694\) 0 0
\(695\) −2.00000 + 3.46410i −0.0758643 + 0.131401i
\(696\) 0 0
\(697\) 15.0000 + 25.9808i 0.568166 + 0.984092i
\(698\) 0 0
\(699\) 39.0000 1.47512
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) −12.5000 21.6506i −0.471446 0.816569i
\(704\) 0 0
\(705\) 1.50000 2.59808i 0.0564933 0.0978492i
\(706\) 0 0
\(707\) 6.50000 33.7750i 0.244458 1.27024i
\(708\) 0 0
\(709\) −13.5000 + 23.3827i −0.507003 + 0.878155i 0.492964 + 0.870050i \(0.335913\pi\)
−0.999967 + 0.00810550i \(0.997420\pi\)
\(710\) 0 0
\(711\) −33.0000 57.1577i −1.23760 2.14358i
\(712\) 0 0
\(713\) 3.00000 0.112351
\(714\) 0 0
\(715\) −2.00000 −0.0747958
\(716\) 0 0
\(717\) 6.00000 + 10.3923i 0.224074 + 0.388108i
\(718\) 0 0
\(719\) 14.5000 25.1147i 0.540759 0.936622i −0.458102 0.888900i \(-0.651471\pi\)
0.998861 0.0477220i \(-0.0151961\pi\)
\(720\) 0 0
\(721\) −12.5000 + 4.33013i −0.465524 + 0.161262i
\(722\) 0 0
\(723\) −25.5000 + 44.1673i −0.948355 + 1.64260i
\(724\) 0 0
\(725\) −12.0000 20.7846i −0.445669 0.771921i
\(726\) 0 0
\(727\) −16.0000 −0.593407 −0.296704 0.954970i \(-0.595887\pi\)
−0.296704 + 0.954970i \(0.595887\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −6.00000 10.3923i −0.221918 0.384373i
\(732\) 0 0
\(733\) −5.50000 + 9.52628i −0.203147 + 0.351861i −0.949541 0.313644i \(-0.898450\pi\)
0.746394 + 0.665505i \(0.231784\pi\)
\(734\) 0 0
\(735\) 3.00000 + 20.7846i 0.110657 + 0.766652i
\(736\) 0 0
\(737\) 5.50000 9.52628i 0.202595 0.350905i
\(738\) 0 0
\(739\) −20.5000 35.5070i −0.754105 1.30615i −0.945818 0.324697i \(-0.894738\pi\)
0.191714 0.981451i \(-0.438596\pi\)
\(740\) 0 0
\(741\) 30.0000 1.10208
\(742\) 0 0
\(743\) −32.0000 −1.17397 −0.586983 0.809599i \(-0.699684\pi\)
−0.586983 + 0.809599i \(0.699684\pi\)
\(744\) 0 0
\(745\) 7.50000 + 12.9904i 0.274779 + 0.475931i
\(746\) 0 0
\(747\) −12.0000 + 20.7846i −0.439057 + 0.760469i
\(748\) 0 0
\(749\) 7.50000 2.59808i 0.274044 0.0949316i
\(750\) 0 0
\(751\) −23.5000 + 40.7032i −0.857527 + 1.48528i 0.0167534 + 0.999860i \(0.494667\pi\)
−0.874281 + 0.485421i \(0.838666\pi\)
\(752\) 0 0
\(753\) −36.0000 62.3538i −1.31191 2.27230i
\(754\) 0 0
\(755\) 15.0000 0.545906
\(756\) 0 0
\(757\) 34.0000 1.23575 0.617876 0.786276i \(-0.287994\pi\)
0.617876 + 0.786276i \(0.287994\pi\)
\(758\) 0 0
\(759\) 4.50000 + 7.79423i 0.163340 + 0.282913i
\(760\) 0 0
\(761\) −13.5000 + 23.3827i −0.489375 + 0.847622i −0.999925 0.0122260i \(-0.996108\pi\)
0.510551 + 0.859848i \(0.329442\pi\)
\(762\) 0 0
\(763\) −5.50000 + 28.5788i −0.199113 + 1.03462i
\(764\) 0 0
\(765\) 9.00000 15.5885i 0.325396 0.563602i
\(766\) 0 0
\(767\) 3.00000 + 5.19615i 0.108324 + 0.187622i
\(768\) 0 0
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) 39.0000 1.40455
\(772\) 0 0
\(773\) −17.5000 30.3109i −0.629431 1.09021i −0.987666 0.156575i \(-0.949955\pi\)
0.358235 0.933632i \(-0.383379\pi\)
\(774\) 0 0
\(775\) 2.00000 3.46410i 0.0718421 0.124434i
\(776\) 0 0
\(777\) −30.0000 25.9808i −1.07624 0.932055i
\(778\) 0 0
\(779\) −25.0000 + 43.3013i −0.895718 + 1.55143i
\(780\) 0 0
\(781\) 8.00000 + 13.8564i 0.286263 + 0.495821i
\(782\) 0 0
\(783\) 54.0000 1.92980
\(784\) 0 0
\(785\) −15.0000 −0.535373
\(786\) 0 0
\(787\) −6.50000 11.2583i −0.231700 0.401316i 0.726609 0.687052i \(-0.241095\pi\)
−0.958308 + 0.285736i \(0.907762\pi\)
\(788\) 0 0
\(789\) −4.50000 + 7.79423i −0.160204 + 0.277482i
\(790\) 0 0
\(791\) 20.0000 + 17.3205i 0.711118 + 0.615846i
\(792\) 0 0
\(793\) −3.00000 + 5.19615i −0.106533 + 0.184521i
\(794\) 0 0
\(795\) 13.5000 + 23.3827i 0.478796 + 0.829298i
\(796\) 0 0
\(797\)