Properties

Label 912.2.bn.f.449.1
Level $912$
Weight $2$
Character 912.449
Analytic conductor $7.282$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bn (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 449.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 912.449
Dual form 912.2.bn.f.65.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 0.866025i) q^{3} +(3.00000 - 1.73205i) q^{5} -1.00000 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(1.50000 - 0.866025i) q^{3} +(3.00000 - 1.73205i) q^{5} -1.00000 q^{7} +(1.50000 - 2.59808i) q^{9} +3.46410i q^{11} +(4.50000 + 2.59808i) q^{13} +(3.00000 - 5.19615i) q^{15} +(-3.00000 + 1.73205i) q^{17} +(4.00000 - 1.73205i) q^{19} +(-1.50000 + 0.866025i) q^{21} +(3.50000 - 6.06218i) q^{25} -5.19615i q^{27} +(-3.00000 + 5.19615i) q^{29} -1.73205i q^{31} +(3.00000 + 5.19615i) q^{33} +(-3.00000 + 1.73205i) q^{35} -5.19615i q^{37} +9.00000 q^{39} +(-6.00000 - 10.3923i) q^{41} +(-0.500000 - 0.866025i) q^{43} -10.3923i q^{45} +(-6.00000 - 3.46410i) q^{47} -6.00000 q^{49} +(-3.00000 + 5.19615i) q^{51} +(-6.00000 + 10.3923i) q^{53} +(6.00000 + 10.3923i) q^{55} +(4.50000 - 6.06218i) q^{57} +(-3.50000 + 6.06218i) q^{61} +(-1.50000 + 2.59808i) q^{63} +18.0000 q^{65} +(-7.50000 - 4.33013i) q^{67} +(3.00000 + 5.19615i) q^{71} +(3.50000 + 6.06218i) q^{73} -12.1244i q^{75} -3.46410i q^{77} +(-4.50000 + 2.59808i) q^{79} +(-4.50000 - 7.79423i) q^{81} -10.3923i q^{83} +(-6.00000 + 10.3923i) q^{85} +10.3923i q^{87} +(-4.50000 - 2.59808i) q^{91} +(-1.50000 - 2.59808i) q^{93} +(9.00000 - 12.1244i) q^{95} +(6.00000 - 3.46410i) q^{97} +(9.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{3} + 6 q^{5} - 2 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{3} + 6 q^{5} - 2 q^{7} + 3 q^{9} + 9 q^{13} + 6 q^{15} - 6 q^{17} + 8 q^{19} - 3 q^{21} + 7 q^{25} - 6 q^{29} + 6 q^{33} - 6 q^{35} + 18 q^{39} - 12 q^{41} - q^{43} - 12 q^{47} - 12 q^{49} - 6 q^{51} - 12 q^{53} + 12 q^{55} + 9 q^{57} - 7 q^{61} - 3 q^{63} + 36 q^{65} - 15 q^{67} + 6 q^{71} + 7 q^{73} - 9 q^{79} - 9 q^{81} - 12 q^{85} - 9 q^{91} - 3 q^{93} + 18 q^{95} + 12 q^{97} + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(1\)

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
\(3\) 1.50000 0.866025i 0.866025 0.500000i
\(4\) 0 0
\(5\) 3.00000 1.73205i 1.34164 0.774597i 0.354593 0.935021i \(-0.384620\pi\)
0.987048 + 0.160424i \(0.0512862\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 0 0
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 0 0
\(11\) 3.46410i 1.04447i 0.852803 + 0.522233i \(0.174901\pi\)
−0.852803 + 0.522233i \(0.825099\pi\)
\(12\) 0 0
\(13\) 4.50000 + 2.59808i 1.24808 + 0.720577i 0.970725 0.240192i \(-0.0772105\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 3.00000 5.19615i 0.774597 1.34164i
\(16\) 0 0
\(17\) −3.00000 + 1.73205i −0.727607 + 0.420084i −0.817546 0.575863i \(-0.804666\pi\)
0.0899392 + 0.995947i \(0.471333\pi\)
\(18\) 0 0
\(19\) 4.00000 1.73205i 0.917663 0.397360i
\(20\) 0 0
\(21\) −1.50000 + 0.866025i −0.327327 + 0.188982i
\(22\) 0 0
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 0 0
\(25\) 3.50000 6.06218i 0.700000 1.21244i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 0 0
\(31\) 1.73205i 0.311086i −0.987829 0.155543i \(-0.950287\pi\)
0.987829 0.155543i \(-0.0497126\pi\)
\(32\) 0 0
\(33\) 3.00000 + 5.19615i 0.522233 + 0.904534i
\(34\) 0 0
\(35\) −3.00000 + 1.73205i −0.507093 + 0.292770i
\(36\) 0 0
\(37\) 5.19615i 0.854242i −0.904194 0.427121i \(-0.859528\pi\)
0.904194 0.427121i \(-0.140472\pi\)
\(38\) 0 0
\(39\) 9.00000 1.44115
\(40\) 0 0
\(41\) −6.00000 10.3923i −0.937043 1.62301i −0.770950 0.636895i \(-0.780218\pi\)
−0.166092 0.986110i \(-0.553115\pi\)
\(42\) 0 0
\(43\) −0.500000 0.866025i −0.0762493 0.132068i 0.825380 0.564578i \(-0.190961\pi\)
−0.901629 + 0.432511i \(0.857628\pi\)
\(44\) 0 0
\(45\) 10.3923i 1.54919i
\(46\) 0 0
\(47\) −6.00000 3.46410i −0.875190 0.505291i −0.00612051 0.999981i \(-0.501948\pi\)
−0.869069 + 0.494690i \(0.835282\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) −3.00000 + 5.19615i −0.420084 + 0.727607i
\(52\) 0 0
\(53\) −6.00000 + 10.3923i −0.824163 + 1.42749i 0.0783936 + 0.996922i \(0.475021\pi\)
−0.902557 + 0.430570i \(0.858312\pi\)
\(54\) 0 0
\(55\) 6.00000 + 10.3923i 0.809040 + 1.40130i
\(56\) 0 0
\(57\) 4.50000 6.06218i 0.596040 0.802955i
\(58\) 0 0
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) −3.50000 + 6.06218i −0.448129 + 0.776182i −0.998264 0.0588933i \(-0.981243\pi\)
0.550135 + 0.835076i \(0.314576\pi\)
\(62\) 0 0
\(63\) −1.50000 + 2.59808i −0.188982 + 0.327327i
\(64\) 0 0
\(65\) 18.0000 2.23263
\(66\) 0 0
\(67\) −7.50000 4.33013i −0.916271 0.529009i −0.0338274 0.999428i \(-0.510770\pi\)
−0.882443 + 0.470418i \(0.844103\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.00000 + 5.19615i 0.356034 + 0.616670i 0.987294 0.158901i \(-0.0507952\pi\)
−0.631260 + 0.775571i \(0.717462\pi\)
\(72\) 0 0
\(73\) 3.50000 + 6.06218i 0.409644 + 0.709524i 0.994850 0.101361i \(-0.0323196\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 0 0
\(75\) 12.1244i 1.40000i
\(76\) 0 0
\(77\) 3.46410i 0.394771i
\(78\) 0 0
\(79\) −4.50000 + 2.59808i −0.506290 + 0.292306i −0.731307 0.682048i \(-0.761089\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) 10.3923i 1.14070i −0.821401 0.570352i \(-0.806807\pi\)
0.821401 0.570352i \(-0.193193\pi\)
\(84\) 0 0
\(85\) −6.00000 + 10.3923i −0.650791 + 1.12720i
\(86\) 0 0
\(87\) 10.3923i 1.11417i
\(88\) 0 0
\(89\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 0 0
\(91\) −4.50000 2.59808i −0.471728 0.272352i
\(92\) 0 0
\(93\) −1.50000 2.59808i −0.155543 0.269408i
\(94\) 0 0
\(95\) 9.00000 12.1244i 0.923381 1.24393i
\(96\) 0 0
\(97\) 6.00000 3.46410i 0.609208 0.351726i −0.163448 0.986552i \(-0.552261\pi\)
0.772655 + 0.634826i \(0.218928\pi\)
\(98\) 0 0
\(99\) 9.00000 + 5.19615i 0.904534 + 0.522233i
\(100\) 0 0
\(101\) 9.00000 + 5.19615i 0.895533 + 0.517036i 0.875748 0.482768i \(-0.160368\pi\)
0.0197851 + 0.999804i \(0.493702\pi\)
\(102\) 0 0
\(103\) 8.66025i 0.853320i 0.904412 + 0.426660i \(0.140310\pi\)
−0.904412 + 0.426660i \(0.859690\pi\)
\(104\) 0 0
\(105\) −3.00000 + 5.19615i −0.292770 + 0.507093i
\(106\) 0 0
\(107\) 18.0000 1.74013 0.870063 0.492941i \(-0.164078\pi\)
0.870063 + 0.492941i \(0.164078\pi\)
\(108\) 0 0
\(109\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 0 0
\(111\) −4.50000 7.79423i −0.427121 0.739795i
\(112\) 0 0
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 13.5000 7.79423i 1.24808 0.720577i
\(118\) 0 0
\(119\) 3.00000 1.73205i 0.275010 0.158777i
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) 0 0
\(123\) −18.0000 10.3923i −1.62301 0.937043i
\(124\) 0 0
\(125\) 6.92820i 0.619677i
\(126\) 0 0
\(127\) 9.00000 + 5.19615i 0.798621 + 0.461084i 0.842989 0.537931i \(-0.180794\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) 0 0
\(129\) −1.50000 0.866025i −0.132068 0.0762493i
\(130\) 0 0
\(131\) −3.00000 + 1.73205i −0.262111 + 0.151330i −0.625297 0.780387i \(-0.715022\pi\)
0.363186 + 0.931717i \(0.381689\pi\)
\(132\) 0 0
\(133\) −4.00000 + 1.73205i −0.346844 + 0.150188i
\(134\) 0 0
\(135\) −9.00000 15.5885i −0.774597 1.34164i
\(136\) 0 0
\(137\) −3.00000 1.73205i −0.256307 0.147979i 0.366342 0.930480i \(-0.380610\pi\)
−0.622649 + 0.782501i \(0.713943\pi\)
\(138\) 0 0
\(139\) −2.50000 + 4.33013i −0.212047 + 0.367277i −0.952355 0.304991i \(-0.901346\pi\)
0.740308 + 0.672268i \(0.234680\pi\)
\(140\) 0 0
\(141\) −12.0000 −1.01058
\(142\) 0 0
\(143\) −9.00000 + 15.5885i −0.752618 + 1.30357i
\(144\) 0 0
\(145\) 20.7846i 1.72607i
\(146\) 0 0
\(147\) −9.00000 + 5.19615i −0.742307 + 0.428571i
\(148\) 0 0
\(149\) 15.0000 8.66025i 1.22885 0.709476i 0.262059 0.965052i \(-0.415599\pi\)
0.966789 + 0.255576i \(0.0822652\pi\)
\(150\) 0 0
\(151\) 3.46410i 0.281905i 0.990016 + 0.140952i \(0.0450164\pi\)
−0.990016 + 0.140952i \(0.954984\pi\)
\(152\) 0 0
\(153\) 10.3923i 0.840168i
\(154\) 0 0
\(155\) −3.00000 5.19615i −0.240966 0.417365i
\(156\) 0 0
\(157\) −3.50000 6.06218i −0.279330 0.483814i 0.691888 0.722005i \(-0.256779\pi\)
−0.971219 + 0.238190i \(0.923446\pi\)
\(158\) 0 0
\(159\) 20.7846i 1.64833i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 11.0000 0.861586 0.430793 0.902451i \(-0.358234\pi\)
0.430793 + 0.902451i \(0.358234\pi\)
\(164\) 0 0
\(165\) 18.0000 + 10.3923i 1.40130 + 0.809040i
\(166\) 0 0
\(167\) −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i \(-0.987025\pi\)
0.534875 + 0.844931i \(0.320359\pi\)
\(168\) 0 0
\(169\) 7.00000 + 12.1244i 0.538462 + 0.932643i
\(170\) 0 0
\(171\) 1.50000 12.9904i 0.114708 0.993399i
\(172\) 0 0
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 0 0
\(175\) −3.50000 + 6.06218i −0.264575 + 0.458258i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −6.00000 3.46410i −0.445976 0.257485i 0.260153 0.965567i \(-0.416227\pi\)
−0.706129 + 0.708083i \(0.749560\pi\)
\(182\) 0 0
\(183\) 12.1244i 0.896258i
\(184\) 0 0
\(185\) −9.00000 15.5885i −0.661693 1.14609i
\(186\) 0 0
\(187\) −6.00000 10.3923i −0.438763 0.759961i
\(188\) 0 0
\(189\) 5.19615i 0.377964i
\(190\) 0 0
\(191\) 17.3205i 1.25327i 0.779314 + 0.626634i \(0.215568\pi\)
−0.779314 + 0.626634i \(0.784432\pi\)
\(192\) 0 0
\(193\) −10.5000 + 6.06218i −0.755807 + 0.436365i −0.827788 0.561041i \(-0.810401\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) 0 0
\(195\) 27.0000 15.5885i 1.93351 1.11631i
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −12.5000 + 21.6506i −0.886102 + 1.53477i −0.0416556 + 0.999132i \(0.513263\pi\)
−0.844446 + 0.535641i \(0.820070\pi\)
\(200\) 0 0
\(201\) −15.0000 −1.05802
\(202\) 0 0
\(203\) 3.00000 5.19615i 0.210559 0.364698i
\(204\) 0 0
\(205\) −36.0000 20.7846i −2.51435 1.45166i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 6.00000 + 13.8564i 0.415029 + 0.958468i
\(210\) 0 0
\(211\) 19.5000 11.2583i 1.34244 0.775055i 0.355271 0.934763i \(-0.384389\pi\)
0.987164 + 0.159708i \(0.0510552\pi\)
\(212\) 0 0
\(213\) 9.00000 + 5.19615i 0.616670 + 0.356034i
\(214\) 0 0
\(215\) −3.00000 1.73205i −0.204598 0.118125i
\(216\) 0 0
\(217\) 1.73205i 0.117579i
\(218\) 0 0
\(219\) 10.5000 + 6.06218i 0.709524 + 0.409644i
\(220\) 0 0
\(221\) −18.0000 −1.21081
\(222\) 0 0
\(223\) −16.5000 + 9.52628i −1.10492 + 0.637927i −0.937509 0.347960i \(-0.886874\pi\)
−0.167412 + 0.985887i \(0.553541\pi\)
\(224\) 0 0
\(225\) −10.5000 18.1865i −0.700000 1.21244i
\(226\) 0 0
\(227\) −18.0000 −1.19470 −0.597351 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) 0 0
\(229\) 13.0000 0.859064 0.429532 0.903052i \(-0.358679\pi\)
0.429532 + 0.903052i \(0.358679\pi\)
\(230\) 0 0
\(231\) −3.00000 5.19615i −0.197386 0.341882i
\(232\) 0 0
\(233\) 15.0000 8.66025i 0.982683 0.567352i 0.0796037 0.996827i \(-0.474635\pi\)
0.903079 + 0.429474i \(0.141301\pi\)
\(234\) 0 0
\(235\) −24.0000 −1.56559
\(236\) 0 0
\(237\) −4.50000 + 7.79423i −0.292306 + 0.506290i
\(238\) 0 0
\(239\) 24.2487i 1.56852i −0.620433 0.784259i \(-0.713043\pi\)
0.620433 0.784259i \(-0.286957\pi\)
\(240\) 0 0
\(241\) −1.50000 0.866025i −0.0966235 0.0557856i 0.450910 0.892570i \(-0.351100\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 0 0
\(243\) −13.5000 7.79423i −0.866025 0.500000i
\(244\) 0 0
\(245\) −18.0000 + 10.3923i −1.14998 + 0.663940i
\(246\) 0 0
\(247\) 22.5000 + 2.59808i 1.43164 + 0.165312i
\(248\) 0 0
\(249\) −9.00000 15.5885i −0.570352 0.987878i
\(250\) 0 0
\(251\) 6.00000 + 3.46410i 0.378717 + 0.218652i 0.677260 0.735744i \(-0.263167\pi\)
−0.298543 + 0.954396i \(0.596501\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 20.7846i 1.30158i
\(256\) 0 0
\(257\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) 0 0
\(259\) 5.19615i 0.322873i
\(260\) 0 0
\(261\) 9.00000 + 15.5885i 0.557086 + 0.964901i
\(262\) 0 0
\(263\) 21.0000 12.1244i 1.29492 0.747620i 0.315394 0.948961i \(-0.397863\pi\)
0.979521 + 0.201341i \(0.0645299\pi\)
\(264\) 0 0
\(265\) 41.5692i 2.55358i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 0 0
\(271\) 4.00000 + 6.92820i 0.242983 + 0.420858i 0.961563 0.274586i \(-0.0885408\pi\)
−0.718580 + 0.695444i \(0.755208\pi\)
\(272\) 0 0
\(273\) −9.00000 −0.544705
\(274\) 0 0
\(275\) 21.0000 + 12.1244i 1.26635 + 0.731126i
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 0 0
\(279\) −4.50000 2.59808i −0.269408 0.155543i
\(280\) 0 0
\(281\) −3.00000 + 5.19615i −0.178965 + 0.309976i −0.941526 0.336939i \(-0.890608\pi\)
0.762561 + 0.646916i \(0.223942\pi\)
\(282\) 0 0
\(283\) −14.0000 24.2487i −0.832214 1.44144i −0.896279 0.443491i \(-0.853740\pi\)
0.0640654 0.997946i \(-0.479593\pi\)
\(284\) 0 0
\(285\) 3.00000 25.9808i 0.177705 1.53897i
\(286\) 0 0
\(287\) 6.00000 + 10.3923i 0.354169 + 0.613438i
\(288\) 0 0
\(289\) −2.50000 + 4.33013i −0.147059 + 0.254713i
\(290\) 0 0
\(291\) 6.00000 10.3923i 0.351726 0.609208i
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 18.0000 1.04447
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0.500000 + 0.866025i 0.0288195 + 0.0499169i
\(302\) 0 0
\(303\) 18.0000 1.03407
\(304\) 0 0
\(305\) 24.2487i 1.38848i
\(306\) 0 0
\(307\) −27.0000 + 15.5885i −1.54097 + 0.889680i −0.542194 + 0.840254i \(0.682406\pi\)
−0.998778 + 0.0494267i \(0.984261\pi\)
\(308\) 0 0
\(309\) 7.50000 + 12.9904i 0.426660 + 0.738997i
\(310\) 0 0
\(311\) 13.8564i 0.785725i −0.919597 0.392862i \(-0.871485\pi\)
0.919597 0.392862i \(-0.128515\pi\)
\(312\) 0 0
\(313\) 7.00000 12.1244i 0.395663 0.685309i −0.597522 0.801852i \(-0.703848\pi\)
0.993186 + 0.116543i \(0.0371814\pi\)
\(314\) 0 0
\(315\) 10.3923i 0.585540i
\(316\) 0 0
\(317\) 3.00000 5.19615i 0.168497 0.291845i −0.769395 0.638774i \(-0.779442\pi\)
0.937892 + 0.346929i \(0.112775\pi\)
\(318\) 0 0
\(319\) −18.0000 10.3923i −1.00781 0.581857i
\(320\) 0 0
\(321\) 27.0000 15.5885i 1.50699 0.870063i
\(322\) 0 0
\(323\) −9.00000 + 12.1244i −0.500773 + 0.674617i
\(324\) 0 0
\(325\) 31.5000 18.1865i 1.74731 1.00881i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6.00000 + 3.46410i 0.330791 + 0.190982i
\(330\) 0 0
\(331\) 5.19615i 0.285606i 0.989751 + 0.142803i \(0.0456116\pi\)
−0.989751 + 0.142803i \(0.954388\pi\)
\(332\) 0 0
\(333\) −13.5000 7.79423i −0.739795 0.427121i
\(334\) 0 0
\(335\) −30.0000 −1.63908
\(336\) 0 0
\(337\) 1.50000 0.866025i 0.0817102 0.0471754i −0.458588 0.888649i \(-0.651645\pi\)
0.540298 + 0.841473i \(0.318311\pi\)
\(338\) 0 0
\(339\) −18.0000 + 10.3923i −0.977626 + 0.564433i
\(340\) 0 0
\(341\) 6.00000 0.324918
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −21.0000 + 12.1244i −1.12734 + 0.650870i −0.943264 0.332043i \(-0.892262\pi\)
−0.184075 + 0.982912i \(0.558929\pi\)
\(348\) 0 0
\(349\) −7.00000 −0.374701 −0.187351 0.982293i \(-0.559990\pi\)
−0.187351 + 0.982293i \(0.559990\pi\)
\(350\) 0 0
\(351\) 13.5000 23.3827i 0.720577 1.24808i
\(352\) 0 0
\(353\) 10.3923i 0.553127i −0.960996 0.276563i \(-0.910804\pi\)
0.960996 0.276563i \(-0.0891955\pi\)
\(354\) 0 0
\(355\) 18.0000 + 10.3923i 0.955341 + 0.551566i
\(356\) 0 0
\(357\) 3.00000 5.19615i 0.158777 0.275010i
\(358\) 0 0
\(359\) 6.00000 3.46410i 0.316668 0.182828i −0.333238 0.942843i \(-0.608141\pi\)
0.649906 + 0.760014i \(0.274808\pi\)
\(360\) 0 0
\(361\) 13.0000 13.8564i 0.684211 0.729285i
\(362\) 0 0
\(363\) −1.50000 + 0.866025i −0.0787296 + 0.0454545i
\(364\) 0 0
\(365\) 21.0000 + 12.1244i 1.09919 + 0.634618i
\(366\) 0 0
\(367\) 8.50000 14.7224i 0.443696 0.768505i −0.554264 0.832341i \(-0.687000\pi\)
0.997960 + 0.0638362i \(0.0203335\pi\)
\(368\) 0 0
\(369\) −36.0000 −1.87409
\(370\) 0 0
\(371\) 6.00000 10.3923i 0.311504 0.539542i
\(372\) 0 0
\(373\) 6.92820i 0.358729i 0.983783 + 0.179364i \(0.0574041\pi\)
−0.983783 + 0.179364i \(0.942596\pi\)
\(374\) 0 0
\(375\) −6.00000 10.3923i −0.309839 0.536656i
\(376\) 0 0
\(377\) −27.0000 + 15.5885i −1.39057 + 0.802846i
\(378\) 0 0
\(379\) 12.1244i 0.622786i 0.950281 + 0.311393i \(0.100796\pi\)
−0.950281 + 0.311393i \(0.899204\pi\)
\(380\) 0 0
\(381\) 18.0000 0.922168
\(382\) 0 0
\(383\) −3.00000 5.19615i −0.153293 0.265511i 0.779143 0.626846i \(-0.215654\pi\)
−0.932436 + 0.361335i \(0.882321\pi\)
\(384\) 0 0
\(385\) −6.00000 10.3923i −0.305788 0.529641i
\(386\) 0 0
\(387\) −3.00000 −0.152499
\(388\) 0 0
\(389\) −24.0000 13.8564i −1.21685 0.702548i −0.252606 0.967569i \(-0.581288\pi\)
−0.964242 + 0.265022i \(0.914621\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −3.00000 + 5.19615i −0.151330 + 0.262111i
\(394\) 0 0
\(395\) −9.00000 + 15.5885i −0.452839 + 0.784340i
\(396\) 0 0
\(397\) −14.5000 25.1147i −0.727734 1.26047i −0.957839 0.287307i \(-0.907240\pi\)
0.230105 0.973166i \(-0.426093\pi\)
\(398\) 0 0
\(399\) −4.50000 + 6.06218i −0.225282 + 0.303488i
\(400\) 0 0
\(401\) −12.0000 20.7846i −0.599251 1.03793i −0.992932 0.118686i \(-0.962132\pi\)
0.393680 0.919247i \(-0.371202\pi\)
\(402\) 0 0
\(403\) 4.50000 7.79423i 0.224161 0.388258i
\(404\) 0 0
\(405\) −27.0000 15.5885i −1.34164 0.774597i
\(406\) 0 0
\(407\) 18.0000 0.892227
\(408\) 0 0
\(409\) 30.0000 + 17.3205i 1.48340 + 0.856444i 0.999822 0.0188549i \(-0.00600205\pi\)
0.483582 + 0.875299i \(0.339335\pi\)
\(410\) 0 0
\(411\) −6.00000 −0.295958
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −18.0000 31.1769i −0.883585 1.53041i
\(416\) 0 0
\(417\) 8.66025i 0.424094i
\(418\) 0 0
\(419\) 10.3923i 0.507697i −0.967244 0.253849i \(-0.918303\pi\)
0.967244 0.253849i \(-0.0816965\pi\)
\(420\) 0 0
\(421\) 12.0000 6.92820i 0.584844 0.337660i −0.178212 0.983992i \(-0.557031\pi\)
0.763056 + 0.646332i \(0.223698\pi\)
\(422\) 0 0
\(423\) −18.0000 + 10.3923i −0.875190 + 0.505291i
\(424\) 0 0
\(425\) 24.2487i 1.17624i
\(426\) 0 0
\(427\) 3.50000 6.06218i 0.169377 0.293369i
\(428\) 0 0
\(429\) 31.1769i 1.50524i
\(430\) 0 0
\(431\) 6.00000 10.3923i 0.289010 0.500580i −0.684564 0.728953i \(-0.740007\pi\)
0.973574 + 0.228373i \(0.0733406\pi\)
\(432\) 0 0
\(433\) −16.5000 9.52628i −0.792939 0.457804i 0.0480569 0.998845i \(-0.484697\pi\)
−0.840996 + 0.541041i \(0.818030\pi\)
\(434\) 0 0
\(435\) 18.0000 + 31.1769i 0.863034 + 1.49482i
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 7.50000 4.33013i 0.357955 0.206666i −0.310228 0.950662i \(-0.600405\pi\)
0.668184 + 0.743996i \(0.267072\pi\)
\(440\) 0 0
\(441\) −9.00000 + 15.5885i −0.428571 + 0.742307i
\(442\) 0 0
\(443\) 21.0000 + 12.1244i 0.997740 + 0.576046i 0.907579 0.419882i \(-0.137928\pi\)
0.0901612 + 0.995927i \(0.471262\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 15.0000 25.9808i 0.709476 1.22885i
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 0 0
\(451\) 36.0000 20.7846i 1.69517 0.978709i
\(452\) 0 0
\(453\) 3.00000 + 5.19615i 0.140952 + 0.244137i
\(454\) 0 0
\(455\) −18.0000 −0.843853
\(456\) 0 0
\(457\) 17.0000 0.795226 0.397613 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) 0 0
\(459\) 9.00000 + 15.5885i 0.420084 + 0.727607i
\(460\) 0 0
\(461\) 6.00000 3.46410i 0.279448 0.161339i −0.353726 0.935349i \(-0.615085\pi\)
0.633173 + 0.774010i \(0.281752\pi\)
\(462\) 0 0
\(463\) 19.0000 0.883005 0.441502 0.897260i \(-0.354446\pi\)
0.441502 + 0.897260i \(0.354446\pi\)
\(464\) 0 0
\(465\) −9.00000 5.19615i −0.417365 0.240966i
\(466\) 0 0
\(467\) 27.7128i 1.28240i −0.767375 0.641198i \(-0.778438\pi\)
0.767375 0.641198i \(-0.221562\pi\)
\(468\) 0 0
\(469\) 7.50000 + 4.33013i 0.346318 + 0.199947i
\(470\) 0 0
\(471\) −10.5000 6.06218i −0.483814 0.279330i
\(472\) 0 0
\(473\) 3.00000 1.73205i 0.137940 0.0796398i
\(474\) 0 0
\(475\) 3.50000 30.3109i 0.160591 1.39076i
\(476\) 0 0
\(477\) 18.0000 + 31.1769i 0.824163 + 1.42749i
\(478\) 0 0
\(479\) −9.00000 5.19615i −0.411220 0.237418i 0.280094 0.959973i \(-0.409635\pi\)
−0.691314 + 0.722554i \(0.742968\pi\)
\(480\) 0 0
\(481\) 13.5000 23.3827i 0.615547 1.06616i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 12.0000 20.7846i 0.544892 0.943781i
\(486\) 0 0
\(487\) 3.46410i 0.156973i 0.996915 + 0.0784867i \(0.0250088\pi\)
−0.996915 + 0.0784867i \(0.974991\pi\)
\(488\) 0 0
\(489\) 16.5000 9.52628i 0.746156 0.430793i
\(490\) 0 0
\(491\) 9.00000 5.19615i 0.406164 0.234499i −0.282976 0.959127i \(-0.591322\pi\)
0.689140 + 0.724628i \(0.257988\pi\)
\(492\) 0 0
\(493\) 20.7846i 0.936092i
\(494\) 0 0
\(495\) 36.0000 1.61808
\(496\) 0 0
\(497\) −3.00000 5.19615i −0.134568 0.233079i
\(498\) 0 0
\(499\) 15.5000 + 26.8468i 0.693875 + 1.20183i 0.970558 + 0.240866i \(0.0774314\pi\)
−0.276683 + 0.960961i \(0.589235\pi\)
\(500\) 0 0
\(501\) 20.7846i 0.928588i
\(502\) 0 0
\(503\) 27.0000 + 15.5885i 1.20387 + 0.695055i 0.961414 0.275107i \(-0.0887134\pi\)
0.242457 + 0.970162i \(0.422047\pi\)
\(504\) 0 0
\(505\) 36.0000 1.60198
\(506\) 0 0
\(507\) 21.0000 + 12.1244i 0.932643 + 0.538462i
\(508\) 0 0
\(509\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(510\) 0 0
\(511\) −3.50000 6.06218i −0.154831 0.268175i
\(512\) 0 0
\(513\) −9.00000 20.7846i −0.397360 0.917663i
\(514\) 0 0
\(515\) 15.0000 + 25.9808i 0.660979 + 1.14485i
\(516\) 0 0
\(517\) 12.0000 20.7846i 0.527759 0.914106i
\(518\) 0 0
\(519\) 9.00000 + 5.19615i 0.395056 + 0.228086i
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) 4.50000 + 2.59808i 0.196771 + 0.113606i 0.595149 0.803616i \(-0.297093\pi\)
−0.398377 + 0.917222i \(0.630427\pi\)
\(524\) 0 0
\(525\) 12.1244i 0.529150i
\(526\) 0 0
\(527\) 3.00000 + 5.19615i 0.130682 + 0.226348i
\(528\) 0 0
\(529\) −11.5000 19.9186i −0.500000 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 62.3538i 2.70084i
\(534\) 0 0
\(535\) 54.0000 31.1769i 2.33462 1.34790i
\(536\) 0 0
\(537\) −18.0000 + 10.3923i −0.776757 + 0.448461i
\(538\) 0 0
\(539\) 20.7846i 0.895257i
\(540\) 0 0
\(541\) 6.50000 11.2583i 0.279457 0.484033i −0.691793 0.722096i \(-0.743179\pi\)
0.971250 + 0.238062i \(0.0765123\pi\)
\(542\) 0 0
\(543\) −12.0000 −0.514969
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −22.5000 12.9904i −0.962031 0.555429i −0.0652331 0.997870i \(-0.520779\pi\)
−0.896797 + 0.442441i \(0.854112\pi\)
\(548\) 0 0
\(549\) 10.5000 + 18.1865i 0.448129 + 0.776182i
\(550\) 0 0
\(551\) −3.00000 + 25.9808i −0.127804 + 1.10682i
\(552\) 0 0
\(553\) 4.50000 2.59808i 0.191359 0.110481i
\(554\) 0 0
\(555\) −27.0000 15.5885i −1.14609 0.661693i
\(556\) 0 0
\(557\) −3.00000 1.73205i −0.127114 0.0733893i 0.435095 0.900385i \(-0.356715\pi\)
−0.562209 + 0.826995i \(0.690048\pi\)
\(558\) 0 0
\(559\) 5.19615i 0.219774i
\(560\) 0 0
\(561\) −18.0000 10.3923i −0.759961 0.438763i
\(562\) 0 0
\(563\) −18.0000 −0.758610 −0.379305 0.925272i \(-0.623837\pi\)
−0.379305 + 0.925272i \(0.623837\pi\)
\(564\) 0 0
\(565\) −36.0000 + 20.7846i −1.51453 + 0.874415i
\(566\) 0 0
\(567\) 4.50000 + 7.79423i 0.188982 + 0.327327i
\(568\) 0 0
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 0 0
\(571\) −5.00000 −0.209243 −0.104622 0.994512i \(-0.533363\pi\)
−0.104622 + 0.994512i \(0.533363\pi\)
\(572\) 0 0
\(573\) 15.0000 + 25.9808i 0.626634 + 1.08536i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −38.0000 −1.58196 −0.790980 0.611842i \(-0.790429\pi\)
−0.790980 + 0.611842i \(0.790429\pi\)
\(578\) 0 0
\(579\) −10.5000 + 18.1865i −0.436365 + 0.755807i
\(580\) 0 0
\(581\) 10.3923i 0.431145i
\(582\) 0 0
\(583\) −36.0000 20.7846i −1.49097 0.860811i
\(584\) 0 0
\(585\) 27.0000 46.7654i 1.11631 1.93351i
\(586\) 0 0
\(587\) −6.00000 + 3.46410i −0.247647 + 0.142979i −0.618686 0.785638i \(-0.712335\pi\)
0.371040 + 0.928617i \(0.379001\pi\)
\(588\) 0 0
\(589\) −3.00000 6.92820i −0.123613 0.285472i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −36.0000 20.7846i −1.47834 0.853522i −0.478643 0.878010i \(-0.658871\pi\)
−0.999700 + 0.0244882i \(0.992204\pi\)
\(594\) 0 0
\(595\) 6.00000 10.3923i 0.245976 0.426043i
\(596\) 0 0
\(597\) 43.3013i 1.77220i
\(598\) 0 0
\(599\) −15.0000 + 25.9808i −0.612883 + 1.06155i 0.377869 + 0.925859i \(0.376657\pi\)
−0.990752 + 0.135686i \(0.956676\pi\)
\(600\) 0 0
\(601\) 1.73205i 0.0706518i −0.999376 0.0353259i \(-0.988753\pi\)
0.999376 0.0353259i \(-0.0112469\pi\)
\(602\) 0 0
\(603\) −22.5000 + 12.9904i −0.916271 + 0.529009i
\(604\) 0 0
\(605\) −3.00000 + 1.73205i −0.121967 + 0.0704179i
\(606\) 0 0
\(607\) 32.9090i 1.33573i 0.744281 + 0.667867i \(0.232792\pi\)
−0.744281 + 0.667867i \(0.767208\pi\)
\(608\) 0 0
\(609\) 10.3923i 0.421117i
\(610\) 0 0
\(611\) −18.0000 31.1769i −0.728202 1.26128i
\(612\) 0 0
\(613\) 19.0000 + 32.9090i 0.767403 + 1.32918i 0.938967 + 0.344008i \(0.111785\pi\)
−0.171564 + 0.985173i \(0.554882\pi\)
\(614\) 0 0
\(615\) −72.0000 −2.90332
\(616\) 0 0
\(617\) 33.0000 + 19.0526i 1.32853 + 0.767027i 0.985072 0.172141i \(-0.0550685\pi\)
0.343458 + 0.939168i \(0.388402\pi\)
\(618\) 0 0
\(619\) 17.0000 0.683288 0.341644 0.939829i \(-0.389016\pi\)
0.341644 + 0.939829i \(0.389016\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) 0 0
\(627\) 21.0000 + 15.5885i 0.838659 + 0.622543i
\(628\) 0 0
\(629\) 9.00000 + 15.5885i 0.358854 + 0.621552i
\(630\) 0 0
\(631\) 6.50000 11.2583i 0.258761 0.448187i −0.707149 0.707064i \(-0.750019\pi\)
0.965910 + 0.258877i \(0.0833525\pi\)
\(632\) 0 0
\(633\) 19.5000 33.7750i 0.775055 1.34244i
\(634\) 0 0
\(635\) 36.0000 1.42862
\(636\) 0 0
\(637\) −27.0000 15.5885i −1.06978 0.617637i
\(638\) 0 0
\(639\) 18.0000 0.712069
\(640\) 0 0
\(641\) 12.0000 + 20.7846i 0.473972 + 0.820943i 0.999556 0.0297987i \(-0.00948663\pi\)
−0.525584 + 0.850741i \(0.676153\pi\)
\(642\) 0 0
\(643\) 2.50000 + 4.33013i 0.0985904 + 0.170764i 0.911101 0.412182i \(-0.135233\pi\)
−0.812511 + 0.582946i \(0.801900\pi\)
\(644\) 0 0
\(645\) −6.00000 −0.236250
\(646\) 0 0
\(647\) 38.1051i 1.49807i −0.662532 0.749033i \(-0.730518\pi\)
0.662532 0.749033i \(-0.269482\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 1.50000 + 2.59808i 0.0587896 + 0.101827i
\(652\) 0 0
\(653\) 17.3205i 0.677804i −0.940822 0.338902i \(-0.889945\pi\)
0.940822 0.338902i \(-0.110055\pi\)
\(654\) 0 0
\(655\) −6.00000 + 10.3923i −0.234439 + 0.406061i
\(656\) 0 0
\(657\) 21.0000 0.819288
\(658\) 0 0
\(659\) 3.00000 5.19615i 0.116863 0.202413i −0.801660 0.597781i \(-0.796049\pi\)
0.918523 + 0.395367i \(0.129383\pi\)
\(660\) 0 0
\(661\) −12.0000 6.92820i −0.466746 0.269476i 0.248131 0.968727i \(-0.420184\pi\)
−0.714877 + 0.699251i \(0.753517\pi\)
\(662\) 0 0
\(663\) −27.0000 + 15.5885i −1.04859 + 0.605406i
\(664\) 0 0
\(665\) −9.00000 + 12.1244i −0.349005 + 0.470162i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −16.5000 + 28.5788i −0.637927 + 1.10492i
\(670\) 0 0
\(671\) −21.0000 12.1244i −0.810696 0.468056i
\(672\) 0 0
\(673\) 12.1244i 0.467360i 0.972314 + 0.233680i \(0.0750767\pi\)
−0.972314 + 0.233680i \(0.924923\pi\)
\(674\) 0 0
\(675\) −31.5000 18.1865i −1.21244 0.700000i
\(676\) 0 0
\(677\) −36.0000 −1.38359 −0.691796 0.722093i \(-0.743180\pi\)
−0.691796 + 0.722093i \(0.743180\pi\)
\(678\) 0 0
\(679\) −6.00000 + 3.46410i −0.230259 + 0.132940i
\(680\) 0 0
\(681\) −27.0000 + 15.5885i −1.03464 + 0.597351i
\(682\) 0 0
\(683\) 30.0000 1.14792 0.573959 0.818884i \(-0.305407\pi\)
0.573959 + 0.818884i \(0.305407\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) 19.5000 11.2583i 0.743971 0.429532i
\(688\) 0 0
\(689\) −54.0000 + 31.1769i −2.05724 + 1.18775i
\(690\) 0 0
\(691\) −20.0000 −0.760836 −0.380418 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) 0 0
\(693\) −9.00000 5.19615i −0.341882 0.197386i
\(694\) 0 0
\(695\) 17.3205i 0.657004i
\(696\) 0 0
\(697\) 36.0000 + 20.7846i 1.36360 + 0.787273i
\(698\) 0 0
\(699\) 15.0000 25.9808i 0.567352 0.982683i
\(700\) 0 0
\(701\) −9.00000 + 5.19615i −0.339925 + 0.196256i −0.660239 0.751056i \(-0.729545\pi\)
0.320314 + 0.947312i \(0.396212\pi\)
\(702\) 0 0
\(703\) −9.00000 20.7846i −0.339441 0.783906i
\(704\) 0 0
\(705\) −36.0000 + 20.7846i −1.35584 + 0.782794i
\(706\) 0 0
\(707\) −9.00000 5.19615i −0.338480 0.195421i
\(708\) 0 0
\(709\) 6.50000 11.2583i 0.244113 0.422815i −0.717769 0.696281i \(-0.754837\pi\)
0.961882 + 0.273466i \(0.0881700\pi\)
\(710\) 0 0
\(711\) 15.5885i 0.584613i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 62.3538i 2.33190i
\(716\) 0 0
\(717\) −21.0000 36.3731i −0.784259 1.35838i
\(718\) 0 0
\(719\) −24.0000 + 13.8564i −0.895049 + 0.516757i −0.875591 0.483054i \(-0.839528\pi\)
−0.0194584 + 0.999811i \(0.506194\pi\)
\(720\) 0 0
\(721\) 8.66025i 0.322525i
\(722\) 0 0
\(723\) −3.00000 −0.111571
\(724\) 0 0
\(725\) 21.0000 + 36.3731i 0.779920 + 1.35086i
\(726\) 0 0
\(727\) −18.5000 32.0429i −0.686127 1.18841i −0.973081 0.230463i \(-0.925976\pi\)
0.286954 0.957944i \(-0.407357\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 3.00000 + 1.73205i 0.110959 + 0.0640622i
\(732\) 0 0
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) 0 0
\(735\) −18.0000 + 31.1769i −0.663940 + 1.14998i
\(736\) 0 0
\(737\) 15.0000 25.9808i 0.552532 0.957014i
\(738\) 0 0
\(739\) 12.5000 + 21.6506i 0.459820 + 0.796431i 0.998951 0.0457903i \(-0.0145806\pi\)
−0.539131 + 0.842222i \(0.681247\pi\)
\(740\) 0 0
\(741\) 36.0000 15.5885i 1.32249 0.572656i
\(742\) 0 0
\(743\) 3.00000 + 5.19615i 0.110059 + 0.190628i 0.915794 0.401648i \(-0.131563\pi\)
−0.805735 + 0.592277i \(0.798229\pi\)
\(744\) 0 0
\(745\) 30.0000 51.9615i 1.09911 1.90372i
\(746\) 0 0
\(747\) −27.0000 15.5885i −0.987878 0.570352i
\(748\) 0 0
\(749\) −18.0000 −0.657706
\(750\) 0 0
\(751\) −31.5000 18.1865i −1.14945 0.663636i −0.200698 0.979653i \(-0.564321\pi\)
−0.948753 + 0.316017i \(0.897654\pi\)
\(752\) 0 0
\(753\) 12.0000 0.437304
\(754\) 0 0
\(755\) 6.00000 + 10.3923i 0.218362 + 0.378215i
\(756\) 0 0
\(757\) −6.50000 11.2583i −0.236247 0.409191i 0.723388 0.690442i \(-0.242584\pi\)
−0.959634 + 0.281251i \(0.909251\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 27.7128i 1.00459i 0.864697 + 0.502294i \(0.167511\pi\)
−0.864697 + 0.502294i \(0.832489\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 18.0000 + 31.1769i 0.650791 + 1.12720i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −18.5000 + 32.0429i −0.667127 + 1.15550i 0.311577 + 0.950221i \(0.399143\pi\)
−0.978704 + 0.205277i \(0.934190\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −12.0000 + 20.7846i −0.431610 + 0.747570i −0.997012 0.0772449i \(-0.975388\pi\)
0.565402 + 0.824815i \(0.308721\pi\)
\(774\) 0 0
\(775\) −10.5000 6.06218i −0.377171 0.217760i
\(776\) 0 0
\(777\) 4.50000 + 7.79423i 0.161437 + 0.279616i
\(778\) 0 0
\(779\) −42.0000 31.1769i −1.50481 1.11703i
\(780\) 0 0
\(781\) −18.0000 + 10.3923i −0.644091 + 0.371866i
\(782\) 0 0
\(783\) 27.0000 + 15.5885i 0.964901 + 0.557086i
\(784\) 0 0
\(785\) −21.0000 12.1244i −0.749522 0.432737i
\(786\) 0 0
\(787\) 25.9808i 0.926114i −0.886328 0.463057i \(-0.846752\pi\)
0.886328 0.463057i \(-0.153248\pi\)
\(788\) 0 0
\(789\) 21.0000 36.3731i 0.747620 1.29492i
\(790\) 0 0
\(791\) 12.0000 0.426671
\(792\) 0 0
\(793\) −31.5000 + 18.1865i −1.11860 + 0.645823i
\(794\) 0 0
\(795\) 36.0000 + 62.3538i 1.27679