Properties

Label 2100.2.q.j.1201.2
Level 2100
Weight 2
Character 2100.1201
Analytic conductor 16.769
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(16.7685844245\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1201.2
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 2100.1201
Dual form 2100.2.q.j.1801.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(2.62132 + 0.358719i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(2.62132 + 0.358719i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-2.12132 + 3.67423i) q^{11} -5.00000 q^{13} +(2.12132 - 3.67423i) q^{17} +(2.62132 + 4.54026i) q^{19} +(1.62132 - 2.09077i) q^{21} +(3.00000 + 5.19615i) q^{23} -1.00000 q^{27} +8.48528 q^{29} +(2.00000 - 3.46410i) q^{31} +(2.12132 + 3.67423i) q^{33} +(2.50000 + 4.33013i) q^{37} +(-2.50000 + 4.33013i) q^{39} -10.2426 q^{41} +12.4853 q^{43} +(5.12132 + 8.87039i) q^{47} +(6.74264 + 1.88064i) q^{49} +(-2.12132 - 3.67423i) q^{51} +(2.12132 - 3.67423i) q^{53} +5.24264 q^{57} +(-5.12132 + 8.87039i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-1.00000 - 2.44949i) q^{63} +(5.86396 - 10.1567i) q^{67} +6.00000 q^{69} -8.48528 q^{71} +(-1.74264 + 3.01834i) q^{73} +(-6.87868 + 8.87039i) q^{77} +(-4.62132 - 8.00436i) q^{79} +(-0.500000 + 0.866025i) q^{81} -1.75736 q^{83} +(4.24264 - 7.34847i) q^{87} +(-3.87868 - 6.71807i) q^{89} +(-13.1066 - 1.79360i) q^{91} +(-2.00000 - 3.46410i) q^{93} +17.9706 q^{97} +4.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} + 2q^{7} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{3} + 2q^{7} - 2q^{9} - 20q^{13} + 2q^{19} - 2q^{21} + 12q^{23} - 4q^{27} + 8q^{31} + 10q^{37} - 10q^{39} - 24q^{41} + 16q^{43} + 12q^{47} + 10q^{49} + 4q^{57} - 12q^{59} + 2q^{61} - 4q^{63} - 2q^{67} + 24q^{69} + 10q^{73} - 36q^{77} - 10q^{79} - 2q^{81} - 24q^{83} - 24q^{89} - 10q^{91} - 8q^{93} + 4q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).

\(n\) \(701\) \(1051\) \(1177\) \(1501\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.62132 + 0.358719i 0.990766 + 0.135583i
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −2.12132 + 3.67423i −0.639602 + 1.10782i 0.345918 + 0.938265i \(0.387568\pi\)
−0.985520 + 0.169559i \(0.945766\pi\)
\(12\) 0 0
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.12132 3.67423i 0.514496 0.891133i −0.485363 0.874313i \(-0.661312\pi\)
0.999859 0.0168199i \(-0.00535420\pi\)
\(18\) 0 0
\(19\) 2.62132 + 4.54026i 0.601372 + 1.04161i 0.992614 + 0.121319i \(0.0387124\pi\)
−0.391241 + 0.920288i \(0.627954\pi\)
\(20\) 0 0
\(21\) 1.62132 2.09077i 0.353801 0.456243i
\(22\) 0 0
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 8.48528 1.57568 0.787839 0.615882i \(-0.211200\pi\)
0.787839 + 0.615882i \(0.211200\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) 0 0
\(33\) 2.12132 + 3.67423i 0.369274 + 0.639602i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.50000 + 4.33013i 0.410997 + 0.711868i 0.994999 0.0998840i \(-0.0318472\pi\)
−0.584002 + 0.811752i \(0.698514\pi\)
\(38\) 0 0
\(39\) −2.50000 + 4.33013i −0.400320 + 0.693375i
\(40\) 0 0
\(41\) −10.2426 −1.59963 −0.799816 0.600245i \(-0.795070\pi\)
−0.799816 + 0.600245i \(0.795070\pi\)
\(42\) 0 0
\(43\) 12.4853 1.90399 0.951994 0.306117i \(-0.0990300\pi\)
0.951994 + 0.306117i \(0.0990300\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.12132 + 8.87039i 0.747021 + 1.29388i 0.949244 + 0.314539i \(0.101850\pi\)
−0.202223 + 0.979339i \(0.564817\pi\)
\(48\) 0 0
\(49\) 6.74264 + 1.88064i 0.963234 + 0.268662i
\(50\) 0 0
\(51\) −2.12132 3.67423i −0.297044 0.514496i
\(52\) 0 0
\(53\) 2.12132 3.67423i 0.291386 0.504695i −0.682752 0.730650i \(-0.739217\pi\)
0.974138 + 0.225955i \(0.0725503\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 5.24264 0.694405
\(58\) 0 0
\(59\) −5.12132 + 8.87039i −0.666739 + 1.15483i 0.312072 + 0.950059i \(0.398977\pi\)
−0.978811 + 0.204767i \(0.934356\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 0 0
\(63\) −1.00000 2.44949i −0.125988 0.308607i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 5.86396 10.1567i 0.716397 1.24084i −0.246021 0.969264i \(-0.579123\pi\)
0.962418 0.271571i \(-0.0875433\pi\)
\(68\) 0 0
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) −8.48528 −1.00702 −0.503509 0.863990i \(-0.667958\pi\)
−0.503509 + 0.863990i \(0.667958\pi\)
\(72\) 0 0
\(73\) −1.74264 + 3.01834i −0.203961 + 0.353270i −0.949801 0.312854i \(-0.898715\pi\)
0.745840 + 0.666125i \(0.232048\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −6.87868 + 8.87039i −0.783898 + 1.01087i
\(78\) 0 0
\(79\) −4.62132 8.00436i −0.519939 0.900561i −0.999731 0.0231789i \(-0.992621\pi\)
0.479792 0.877382i \(-0.340712\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −1.75736 −0.192895 −0.0964476 0.995338i \(-0.530748\pi\)
−0.0964476 + 0.995338i \(0.530748\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 4.24264 7.34847i 0.454859 0.787839i
\(88\) 0 0
\(89\) −3.87868 6.71807i −0.411139 0.712114i 0.583875 0.811843i \(-0.301536\pi\)
−0.995015 + 0.0997293i \(0.968202\pi\)
\(90\) 0 0
\(91\) −13.1066 1.79360i −1.37395 0.188020i
\(92\) 0 0
\(93\) −2.00000 3.46410i −0.207390 0.359211i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 17.9706 1.82463 0.912317 0.409484i \(-0.134291\pi\)
0.912317 + 0.409484i \(0.134291\pi\)
\(98\) 0 0
\(99\) 4.24264 0.426401
\(100\) 0 0
\(101\) −3.36396 + 5.82655i −0.334727 + 0.579764i −0.983432 0.181276i \(-0.941977\pi\)
0.648706 + 0.761039i \(0.275311\pi\)
\(102\) 0 0
\(103\) 0.378680 + 0.655892i 0.0373124 + 0.0646270i 0.884079 0.467338i \(-0.154787\pi\)
−0.846766 + 0.531965i \(0.821454\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.36396 + 5.82655i 0.325206 + 0.563274i 0.981554 0.191185i \(-0.0612329\pi\)
−0.656348 + 0.754459i \(0.727900\pi\)
\(108\) 0 0
\(109\) −1.25736 + 2.17781i −0.120433 + 0.208596i −0.919939 0.392063i \(-0.871762\pi\)
0.799505 + 0.600659i \(0.205095\pi\)
\(110\) 0 0
\(111\) 5.00000 0.474579
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 2.50000 + 4.33013i 0.231125 + 0.400320i
\(118\) 0 0
\(119\) 6.87868 8.87039i 0.630568 0.813147i
\(120\) 0 0
\(121\) −3.50000 6.06218i −0.318182 0.551107i
\(122\) 0 0
\(123\) −5.12132 + 8.87039i −0.461774 + 0.799816i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −0.757359 −0.0672048 −0.0336024 0.999435i \(-0.510698\pi\)
−0.0336024 + 0.999435i \(0.510698\pi\)
\(128\) 0 0
\(129\) 6.24264 10.8126i 0.549634 0.951994i
\(130\) 0 0
\(131\) −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i \(-0.251085\pi\)
−0.966803 + 0.255524i \(0.917752\pi\)
\(132\) 0 0
\(133\) 5.24264 + 12.8418i 0.454595 + 1.11352i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.24264 + 2.15232i −0.106166 + 0.183885i −0.914214 0.405232i \(-0.867191\pi\)
0.808048 + 0.589117i \(0.200524\pi\)
\(138\) 0 0
\(139\) 11.7279 0.994749 0.497375 0.867536i \(-0.334297\pi\)
0.497375 + 0.867536i \(0.334297\pi\)
\(140\) 0 0
\(141\) 10.2426 0.862586
\(142\) 0 0
\(143\) 10.6066 18.3712i 0.886969 1.53627i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 5.00000 4.89898i 0.412393 0.404061i
\(148\) 0 0
\(149\) 11.1213 + 19.2627i 0.911094 + 1.57806i 0.812521 + 0.582931i \(0.198094\pi\)
0.0985727 + 0.995130i \(0.468572\pi\)
\(150\) 0 0
\(151\) 6.86396 11.8887i 0.558581 0.967491i −0.439034 0.898470i \(-0.644679\pi\)
0.997615 0.0690206i \(-0.0219874\pi\)
\(152\) 0 0
\(153\) −4.24264 −0.342997
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −7.74264 + 13.4106i −0.617930 + 1.07029i 0.371933 + 0.928260i \(0.378695\pi\)
−0.989863 + 0.142027i \(0.954638\pi\)
\(158\) 0 0
\(159\) −2.12132 3.67423i −0.168232 0.291386i
\(160\) 0 0
\(161\) 6.00000 + 14.6969i 0.472866 + 1.15828i
\(162\) 0 0
\(163\) −8.62132 14.9326i −0.675274 1.16961i −0.976389 0.216021i \(-0.930692\pi\)
0.301115 0.953588i \(-0.402641\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 10.2426 0.792599 0.396300 0.918121i \(-0.370294\pi\)
0.396300 + 0.918121i \(0.370294\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 2.62132 4.54026i 0.200457 0.347202i
\(172\) 0 0
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 5.12132 + 8.87039i 0.384942 + 0.666739i
\(178\) 0 0
\(179\) −10.2426 + 17.7408i −0.765571 + 1.32601i 0.174373 + 0.984680i \(0.444210\pi\)
−0.939944 + 0.341328i \(0.889123\pi\)
\(180\) 0 0
\(181\) −12.4853 −0.928024 −0.464012 0.885829i \(-0.653590\pi\)
−0.464012 + 0.885829i \(0.653590\pi\)
\(182\) 0 0
\(183\) 1.00000 0.0739221
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 9.00000 + 15.5885i 0.658145 + 1.13994i
\(188\) 0 0
\(189\) −2.62132 0.358719i −0.190673 0.0260930i
\(190\) 0 0
\(191\) −3.87868 6.71807i −0.280651 0.486103i 0.690894 0.722956i \(-0.257217\pi\)
−0.971545 + 0.236854i \(0.923884\pi\)
\(192\) 0 0
\(193\) −6.24264 + 10.8126i −0.449355 + 0.778306i −0.998344 0.0575237i \(-0.981680\pi\)
0.548989 + 0.835830i \(0.315013\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 8.48528 0.604551 0.302276 0.953221i \(-0.402254\pi\)
0.302276 + 0.953221i \(0.402254\pi\)
\(198\) 0 0
\(199\) 4.37868 7.58410i 0.310396 0.537622i −0.668052 0.744115i \(-0.732872\pi\)
0.978448 + 0.206492i \(0.0662049\pi\)
\(200\) 0 0
\(201\) −5.86396 10.1567i −0.413612 0.716397i
\(202\) 0 0
\(203\) 22.2426 + 3.04384i 1.56113 + 0.213635i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 3.00000 5.19615i 0.208514 0.361158i
\(208\) 0 0
\(209\) −22.2426 −1.53856
\(210\) 0 0
\(211\) 21.2426 1.46240 0.731202 0.682161i \(-0.238960\pi\)
0.731202 + 0.682161i \(0.238960\pi\)
\(212\) 0 0
\(213\) −4.24264 + 7.34847i −0.290701 + 0.503509i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 6.48528 8.36308i 0.440250 0.567723i
\(218\) 0 0
\(219\) 1.74264 + 3.01834i 0.117757 + 0.203961i
\(220\) 0 0
\(221\) −10.6066 + 18.3712i −0.713477 + 1.23578i
\(222\) 0 0
\(223\) −0.757359 −0.0507165 −0.0253583 0.999678i \(-0.508073\pi\)
−0.0253583 + 0.999678i \(0.508073\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −10.2426 + 17.7408i −0.679828 + 1.17750i 0.295205 + 0.955434i \(0.404612\pi\)
−0.975032 + 0.222062i \(0.928721\pi\)
\(228\) 0 0
\(229\) −13.9853 24.2232i −0.924173 1.60072i −0.792885 0.609371i \(-0.791422\pi\)
−0.131288 0.991344i \(-0.541911\pi\)
\(230\) 0 0
\(231\) 4.24264 + 10.3923i 0.279145 + 0.683763i
\(232\) 0 0
\(233\) −0.878680 1.52192i −0.0575642 0.0997042i 0.835807 0.549023i \(-0.185000\pi\)
−0.893371 + 0.449319i \(0.851667\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −9.24264 −0.600374
\(238\) 0 0
\(239\) −4.97056 −0.321519 −0.160759 0.986994i \(-0.551394\pi\)
−0.160759 + 0.986994i \(0.551394\pi\)
\(240\) 0 0
\(241\) 2.98528 5.17066i 0.192299 0.333071i −0.753713 0.657204i \(-0.771739\pi\)
0.946012 + 0.324132i \(0.105072\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −13.1066 22.7013i −0.833953 1.44445i
\(248\) 0 0
\(249\) −0.878680 + 1.52192i −0.0556841 + 0.0964476i
\(250\) 0 0
\(251\) −16.2426 −1.02523 −0.512613 0.858620i \(-0.671323\pi\)
−0.512613 + 0.858620i \(0.671323\pi\)
\(252\) 0 0
\(253\) −25.4558 −1.60040
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −11.1213 19.2627i −0.693729 1.20157i −0.970607 0.240669i \(-0.922633\pi\)
0.276878 0.960905i \(-0.410700\pi\)
\(258\) 0 0
\(259\) 5.00000 + 12.2474i 0.310685 + 0.761019i
\(260\) 0 0
\(261\) −4.24264 7.34847i −0.262613 0.454859i
\(262\) 0 0
\(263\) 14.4853 25.0892i 0.893201 1.54707i 0.0571849 0.998364i \(-0.481788\pi\)
0.836016 0.548705i \(-0.184879\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −7.75736 −0.474743
\(268\) 0 0
\(269\) 9.36396 16.2189i 0.570931 0.988881i −0.425540 0.904940i \(-0.639916\pi\)
0.996471 0.0839415i \(-0.0267509\pi\)
\(270\) 0 0
\(271\) −1.00000 1.73205i −0.0607457 0.105215i 0.834053 0.551684i \(-0.186015\pi\)
−0.894799 + 0.446469i \(0.852681\pi\)
\(272\) 0 0
\(273\) −8.10660 + 10.4539i −0.490634 + 0.632696i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 7.25736 12.5701i 0.436052 0.755265i −0.561328 0.827593i \(-0.689710\pi\)
0.997381 + 0.0723281i \(0.0230429\pi\)
\(278\) 0 0
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) −28.2426 −1.68481 −0.842407 0.538841i \(-0.818862\pi\)
−0.842407 + 0.538841i \(0.818862\pi\)
\(282\) 0 0
\(283\) −1.37868 + 2.38794i −0.0819540 + 0.141948i −0.904089 0.427344i \(-0.859449\pi\)
0.822135 + 0.569292i \(0.192783\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −26.8492 3.67423i −1.58486 0.216883i
\(288\) 0 0
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) 0 0
\(291\) 8.98528 15.5630i 0.526727 0.912317i
\(292\) 0 0
\(293\) −3.51472 −0.205332 −0.102666 0.994716i \(-0.532737\pi\)
−0.102666 + 0.994716i \(0.532737\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 2.12132 3.67423i 0.123091 0.213201i
\(298\) 0 0
\(299\) −15.0000 25.9808i −0.867472 1.50251i
\(300\) 0 0
\(301\) 32.7279 + 4.47871i 1.88641 + 0.258149i
\(302\) 0 0
\(303\) 3.36396 + 5.82655i 0.193255 + 0.334727i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −4.48528 −0.255989 −0.127994 0.991775i \(-0.540854\pi\)
−0.127994 + 0.991775i \(0.540854\pi\)
\(308\) 0 0
\(309\) 0.757359 0.0430847
\(310\) 0 0
\(311\) −7.24264 + 12.5446i −0.410692 + 0.711340i −0.994966 0.100217i \(-0.968046\pi\)
0.584273 + 0.811557i \(0.301380\pi\)
\(312\) 0 0
\(313\) 0.485281 + 0.840532i 0.0274297 + 0.0475097i 0.879414 0.476057i \(-0.157934\pi\)
−0.851985 + 0.523567i \(0.824601\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i \(-0.112775\pi\)
−0.769395 + 0.638774i \(0.779442\pi\)
\(318\) 0 0
\(319\) −18.0000 + 31.1769i −1.00781 + 1.74557i
\(320\) 0 0
\(321\) 6.72792 0.375516
\(322\) 0 0
\(323\) 22.2426 1.23761
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1.25736 + 2.17781i 0.0695321 + 0.120433i
\(328\) 0 0
\(329\) 10.2426 + 25.0892i 0.564695 + 1.38321i
\(330\) 0 0
\(331\) 8.62132 + 14.9326i 0.473871 + 0.820768i 0.999552 0.0299132i \(-0.00952310\pi\)
−0.525682 + 0.850681i \(0.676190\pi\)
\(332\) 0 0
\(333\) 2.50000 4.33013i 0.136999 0.237289i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −24.9706 −1.36023 −0.680117 0.733104i \(-0.738071\pi\)
−0.680117 + 0.733104i \(0.738071\pi\)
\(338\) 0 0
\(339\) 3.00000 5.19615i 0.162938 0.282216i
\(340\) 0 0
\(341\) 8.48528 + 14.6969i 0.459504 + 0.795884i
\(342\) 0 0
\(343\) 17.0000 + 7.34847i 0.917914 + 0.396780i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.63604 4.56575i 0.141510 0.245102i −0.786555 0.617520i \(-0.788138\pi\)
0.928065 + 0.372417i \(0.121471\pi\)
\(348\) 0 0
\(349\) 8.00000 0.428230 0.214115 0.976808i \(-0.431313\pi\)
0.214115 + 0.976808i \(0.431313\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) −9.36396 + 16.2189i −0.498393 + 0.863243i −0.999998 0.00185420i \(-0.999410\pi\)
0.501605 + 0.865097i \(0.332743\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −4.24264 10.3923i −0.224544 0.550019i
\(358\) 0 0
\(359\) −2.63604 4.56575i −0.139125 0.240971i 0.788041 0.615623i \(-0.211096\pi\)
−0.927166 + 0.374652i \(0.877762\pi\)
\(360\) 0 0
\(361\) −4.24264 + 7.34847i −0.223297 + 0.386762i
\(362\) 0 0
\(363\) −7.00000 −0.367405
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 7.00000 12.1244i 0.365397 0.632886i −0.623443 0.781869i \(-0.714267\pi\)
0.988840 + 0.148983i \(0.0475999\pi\)
\(368\) 0 0
\(369\) 5.12132 + 8.87039i 0.266605 + 0.461774i
\(370\) 0 0
\(371\) 6.87868 8.87039i 0.357123 0.460528i
\(372\) 0 0
\(373\) 0.742641 + 1.28629i 0.0384525 + 0.0666016i 0.884611 0.466329i \(-0.154424\pi\)
−0.846159 + 0.532931i \(0.821091\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −42.4264 −2.18507
\(378\) 0 0
\(379\) −13.7279 −0.705156 −0.352578 0.935782i \(-0.614695\pi\)
−0.352578 + 0.935782i \(0.614695\pi\)
\(380\) 0 0
\(381\) −0.378680 + 0.655892i −0.0194003 + 0.0336024i
\(382\) 0 0
\(383\) −15.7279 27.2416i −0.803659 1.39198i −0.917192 0.398444i \(-0.869550\pi\)
0.113533 0.993534i \(-0.463783\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −6.24264 10.8126i −0.317331 0.549634i
\(388\) 0 0
\(389\) −15.3640 + 26.6112i −0.778984 + 1.34924i 0.153544 + 0.988142i \(0.450931\pi\)
−0.932528 + 0.361098i \(0.882402\pi\)
\(390\) 0 0
\(391\) 25.4558 1.28736
\(392\) 0 0
\(393\) −6.00000 −0.302660
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 10.0000 + 17.3205i 0.501886 + 0.869291i 0.999998 + 0.00217869i \(0.000693499\pi\)
−0.498112 + 0.867113i \(0.665973\pi\)
\(398\) 0 0
\(399\) 13.7426 + 1.88064i 0.687993 + 0.0941496i
\(400\) 0 0
\(401\) 13.6066 + 23.5673i 0.679481 + 1.17690i 0.975137 + 0.221602i \(0.0711284\pi\)
−0.295656 + 0.955294i \(0.595538\pi\)
\(402\) 0 0
\(403\) −10.0000 + 17.3205i −0.498135 + 0.862796i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −21.2132 −1.05150
\(408\) 0 0
\(409\) 3.50000 6.06218i 0.173064 0.299755i −0.766426 0.642333i \(-0.777967\pi\)
0.939490 + 0.342578i \(0.111300\pi\)
\(410\) 0 0
\(411\) 1.24264 + 2.15232i 0.0612949 + 0.106166i
\(412\) 0 0
\(413\) −16.6066 + 21.4150i −0.817157 + 1.05376i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 5.86396 10.1567i 0.287159 0.497375i
\(418\) 0 0
\(419\) −12.7279 −0.621800 −0.310900 0.950443i \(-0.600630\pi\)
−0.310900 + 0.950443i \(0.600630\pi\)
\(420\) 0 0
\(421\) −1.00000 −0.0487370 −0.0243685 0.999703i \(-0.507758\pi\)
−0.0243685 + 0.999703i \(0.507758\pi\)
\(422\) 0 0
\(423\) 5.12132 8.87039i 0.249007 0.431293i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.00000 + 2.44949i 0.0483934 + 0.118539i
\(428\) 0 0
\(429\) −10.6066 18.3712i −0.512092 0.886969i
\(430\) 0 0
\(431\) −4.75736 + 8.23999i −0.229154 + 0.396906i −0.957558 0.288242i \(-0.906929\pi\)
0.728404 + 0.685148i \(0.240263\pi\)
\(432\) 0 0
\(433\) −24.9706 −1.20001 −0.600004 0.799997i \(-0.704834\pi\)
−0.600004 + 0.799997i \(0.704834\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −15.7279 + 27.2416i −0.752369 + 1.30314i
\(438\) 0 0
\(439\) −5.13604 8.89588i −0.245130 0.424577i 0.717038 0.697034i \(-0.245497\pi\)
−0.962168 + 0.272457i \(0.912164\pi\)
\(440\) 0 0
\(441\) −1.74264 6.77962i −0.0829829 0.322839i
\(442\) 0 0
\(443\) −9.72792 16.8493i −0.462188 0.800532i 0.536882 0.843657i \(-0.319602\pi\)
−0.999070 + 0.0431250i \(0.986269\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 22.2426 1.05204
\(448\) 0 0
\(449\) 11.2721 0.531962 0.265981 0.963978i \(-0.414304\pi\)
0.265981 + 0.963978i \(0.414304\pi\)
\(450\) 0 0
\(451\) 21.7279 37.6339i 1.02313 1.77211i
\(452\) 0 0
\(453\) −6.86396 11.8887i −0.322497 0.558581i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −4.74264 8.21449i −0.221851 0.384258i 0.733519 0.679669i \(-0.237877\pi\)
−0.955370 + 0.295411i \(0.904543\pi\)
\(458\) 0 0
\(459\) −2.12132 + 3.67423i −0.0990148 + 0.171499i
\(460\) 0 0
\(461\) −9.51472 −0.443145 −0.221572 0.975144i \(-0.571119\pi\)
−0.221572 + 0.975144i \(0.571119\pi\)
\(462\) 0 0
\(463\) 11.2426 0.522490 0.261245 0.965273i \(-0.415867\pi\)
0.261245 + 0.965273i \(0.415867\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 9.72792 + 16.8493i 0.450155 + 0.779691i 0.998395 0.0566301i \(-0.0180356\pi\)
−0.548241 + 0.836321i \(0.684702\pi\)
\(468\) 0 0
\(469\) 19.0147 24.5204i 0.878018 1.13225i
\(470\) 0 0
\(471\) 7.74264 + 13.4106i 0.356762 + 0.617930i
\(472\) 0 0
\(473\) −26.4853 + 45.8739i −1.21779 + 2.10928i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −4.24264 −0.194257
\(478\) 0 0
\(479\) −7.60660 + 13.1750i −0.347555 + 0.601982i −0.985814 0.167839i \(-0.946321\pi\)
0.638260 + 0.769821i \(0.279655\pi\)
\(480\) 0 0
\(481\) −12.5000 21.6506i −0.569951 0.987184i
\(482\) 0 0
\(483\) 15.7279 + 2.15232i 0.715645 + 0.0979338i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 14.2426 24.6690i 0.645396 1.11786i −0.338814 0.940853i \(-0.610026\pi\)
0.984210 0.177005i \(-0.0566408\pi\)
\(488\) 0 0
\(489\) −17.2426 −0.779739
\(490\) 0 0
\(491\) 38.4853 1.73682 0.868408 0.495850i \(-0.165143\pi\)
0.868408 + 0.495850i \(0.165143\pi\)
\(492\) 0 0
\(493\) 18.0000 31.1769i 0.810679 1.40414i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −22.2426 3.04384i −0.997719 0.136535i
\(498\) 0 0
\(499\) −1.62132 2.80821i −0.0725803 0.125713i 0.827451 0.561538i \(-0.189790\pi\)
−0.900031 + 0.435825i \(0.856457\pi\)
\(500\) 0 0
\(501\) 5.12132 8.87039i 0.228804 0.396300i
\(502\) 0 0
\(503\) −25.4558 −1.13502 −0.567510 0.823367i \(-0.692093\pi\)
−0.567510 + 0.823367i \(0.692093\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 6.00000 10.3923i 0.266469 0.461538i
\(508\) 0 0
\(509\) −13.7574 23.8284i −0.609784 1.05618i −0.991276 0.131805i \(-0.957923\pi\)
0.381491 0.924372i \(-0.375411\pi\)
\(510\) 0 0
\(511\) −5.65076 + 7.28692i −0.249975 + 0.322354i
\(512\) 0 0
\(513\) −2.62132 4.54026i −0.115734 0.200457i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −43.4558 −1.91119
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) −3.72792 + 6.45695i −0.163323 + 0.282884i −0.936059 0.351844i \(-0.885555\pi\)
0.772735 + 0.634728i \(0.218888\pi\)
\(522\) 0 0
\(523\) −12.2426 21.2049i −0.535333 0.927224i −0.999147 0.0412918i \(-0.986853\pi\)
0.463814 0.885933i \(-0.346481\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.48528 14.6969i −0.369625 0.640209i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) 10.2426 0.444493
\(532\) 0 0
\(533\) 51.2132 2.21829
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 10.2426 + 17.7408i 0.442003 + 0.765571i
\(538\) 0 0
\(539\) −21.2132 + 20.7846i −0.913717 + 0.895257i
\(540\) 0 0
\(541\) −0.742641 1.28629i −0.0319286 0.0553020i 0.849620 0.527396i \(-0.176832\pi\)
−0.881548 + 0.472094i \(0.843498\pi\)
\(542\) 0 0
\(543\) −6.24264 + 10.8126i −0.267897 + 0.464012i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −26.0000 −1.11168 −0.555840 0.831289i \(-0.687603\pi\)
−0.555840 + 0.831289i \(0.687603\pi\)
\(548\) 0 0
\(549\) 0.500000 0.866025i 0.0213395 0.0369611i
\(550\) 0 0
\(551\) 22.2426 + 38.5254i 0.947568 + 1.64124i
\(552\) 0 0
\(553\) −9.24264 22.6398i −0.393037 0.962740i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 13.7574 23.8284i 0.582918 1.00964i −0.412213 0.911087i \(-0.635244\pi\)
0.995131 0.0985563i \(-0.0314225\pi\)
\(558\) 0 0
\(559\) −62.4264 −2.64036
\(560\) 0 0
\(561\) 18.0000 0.759961
\(562\) 0 0
\(563\) 9.87868 17.1104i 0.416337 0.721116i −0.579231 0.815163i \(-0.696647\pi\)
0.995568 + 0.0940471i \(0.0299804\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −1.62132 + 2.09077i −0.0680891 + 0.0878041i
\(568\) 0 0
\(569\) −15.3640 26.6112i −0.644091 1.11560i −0.984511 0.175324i \(-0.943903\pi\)
0.340420 0.940273i \(-0.389431\pi\)
\(570\) 0 0
\(571\) −18.3787 + 31.8328i −0.769124 + 1.33216i 0.168915 + 0.985631i \(0.445974\pi\)
−0.938039 + 0.346531i \(0.887360\pi\)
\(572\) 0 0
\(573\) −7.75736 −0.324068
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 9.48528 16.4290i 0.394877 0.683948i −0.598208 0.801341i \(-0.704120\pi\)
0.993086 + 0.117393i \(0.0374537\pi\)
\(578\) 0 0
\(579\) 6.24264 + 10.8126i 0.259435 + 0.449355i
\(580\) 0 0
\(581\) −4.60660 0.630399i −0.191114 0.0261534i
\(582\) 0 0
\(583\) 9.00000 + 15.5885i 0.372742 + 0.645608i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 22.9706 0.948097 0.474048 0.880499i \(-0.342792\pi\)
0.474048 + 0.880499i \(0.342792\pi\)
\(588\) 0 0
\(589\) 20.9706 0.864077
\(590\) 0 0
\(591\) 4.24264 7.34847i 0.174519 0.302276i
\(592\) 0 0
\(593\) −0.514719 0.891519i −0.0211370 0.0366103i 0.855263 0.518193i \(-0.173395\pi\)
−0.876400 + 0.481583i \(0.840062\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −4.37868 7.58410i −0.179207 0.310396i
\(598\) 0 0
\(599\) 11.8492 20.5235i 0.484147 0.838567i −0.515687 0.856777i \(-0.672463\pi\)
0.999834 + 0.0182098i \(0.00579669\pi\)
\(600\) 0 0
\(601\) −9.48528 −0.386913 −0.193456 0.981109i \(-0.561970\pi\)
−0.193456 + 0.981109i \(0.561970\pi\)
\(602\) 0 0
\(603\) −11.7279 −0.477598
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −16.5919 28.7380i −0.673444 1.16644i −0.976921 0.213600i \(-0.931481\pi\)
0.303477 0.952839i \(-0.401852\pi\)
\(608\) 0 0
\(609\) 13.7574 17.7408i 0.557476 0.718892i
\(610\) 0 0
\(611\) −25.6066 44.3519i −1.03593 1.79429i
\(612\) 0 0
\(613\) −8.00000 + 13.8564i −0.323117 + 0.559655i −0.981129 0.193352i \(-0.938064\pi\)
0.658012 + 0.753007i \(0.271397\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −13.4558 −0.541712 −0.270856 0.962620i \(-0.587307\pi\)
−0.270856 + 0.962620i \(0.587307\pi\)
\(618\) 0 0
\(619\) 0.242641 0.420266i 0.00975255 0.0168919i −0.861108 0.508422i \(-0.830229\pi\)
0.870860 + 0.491530i \(0.163562\pi\)
\(620\) 0 0
\(621\) −3.00000 5.19615i −0.120386 0.208514i
\(622\) 0 0
\(623\) −7.75736 19.0016i −0.310792 0.761282i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −11.1213 + 19.2627i −0.444143 + 0.769278i
\(628\) 0 0
\(629\) 21.2132 0.845826
\(630\) 0 0
\(631\) 26.2132 1.04353 0.521766 0.853089i \(-0.325274\pi\)
0.521766 + 0.853089i \(0.325274\pi\)
\(632\) 0 0
\(633\) 10.6213 18.3967i 0.422160 0.731202i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −33.7132 9.40319i −1.33577 0.372568i
\(638\) 0 0
\(639\) 4.24264 + 7.34847i 0.167836 + 0.290701i
\(640\) 0 0
\(641\) −12.0000 + 20.7846i −0.473972 + 0.820943i −0.999556 0.0297987i \(-0.990513\pi\)
0.525584 + 0.850741i \(0.323847\pi\)
\(642\) 0 0
\(643\) 1.72792 0.0681426 0.0340713 0.999419i \(-0.489153\pi\)
0.0340713 + 0.999419i \(0.489153\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15.8787 + 27.5027i −0.624255 + 1.08124i 0.364429 + 0.931231i \(0.381264\pi\)
−0.988684 + 0.150011i \(0.952069\pi\)
\(648\) 0 0
\(649\) −21.7279 37.6339i −0.852896 1.47726i
\(650\) 0 0
\(651\) −4.00000 9.79796i −0.156772 0.384012i
\(652\) 0 0
\(653\) −6.87868 11.9142i −0.269184 0.466240i 0.699468 0.714664i \(-0.253420\pi\)
−0.968651 + 0.248425i \(0.920087\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 3.48528 0.135974
\(658\) 0 0
\(659\) 48.7279 1.89817 0.949085 0.315020i \(-0.102011\pi\)
0.949085 + 0.315020i \(0.102011\pi\)
\(660\) 0 0
\(661\) −16.9853 + 29.4194i −0.660651 + 1.14428i 0.319794 + 0.947487i \(0.396386\pi\)
−0.980445 + 0.196794i \(0.936947\pi\)
\(662\) 0 0
\(663\) 10.6066 + 18.3712i 0.411926 + 0.713477i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 25.4558 + 44.0908i 0.985654 + 1.70720i
\(668\) 0 0
\(669\) −0.378680 + 0.655892i −0.0146406 + 0.0253583i
\(670\) 0 0
\(671\) −4.24264 −0.163785
\(672\) 0 0
\(673\) 4.51472 0.174030 0.0870148 0.996207i \(-0.472267\pi\)
0.0870148 + 0.996207i \(0.472267\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −15.7279 27.2416i −0.604473 1.04698i −0.992135 0.125176i \(-0.960050\pi\)
0.387661 0.921802i \(-0.373283\pi\)
\(678\) 0 0
\(679\) 47.1066 + 6.44639i 1.80779 + 0.247390i
\(680\) 0 0
\(681\) 10.2426 + 17.7408i 0.392499 + 0.679828i
\(682\) 0 0
\(683\) 0.363961 0.630399i 0.0139266 0.0241215i −0.858978 0.512012i \(-0.828900\pi\)
0.872905 + 0.487891i \(0.162234\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −27.9706 −1.06714
\(688\) 0 0
\(689\) −10.6066 + 18.3712i −0.404079 + 0.699886i
\(690\) 0 0
\(691\) −14.3492 24.8536i −0.545871 0.945476i −0.998552 0.0538034i \(-0.982866\pi\)
0.452681 0.891673i \(-0.350468\pi\)
\(692\) 0 0
\(693\) 11.1213 + 1.52192i 0.422464 + 0.0578129i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −21.7279 + 37.6339i −0.823004 + 1.42548i
\(698\) 0 0
\(699\) −1.75736 −0.0664694
\(700\) 0 0
\(701\) −11.2721 −0.425741 −0.212870 0.977080i \(-0.568281\pi\)
−0.212870 + 0.977080i \(0.568281\pi\)
\(702\) 0 0
\(703\) −13.1066 + 22.7013i −0.494325 + 0.856196i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −10.9081 + 14.0665i −0.410242 + 0.529027i
\(708\) 0 0
\(709\) −3.74264 6.48244i −0.140558 0.243453i 0.787149 0.616763i \(-0.211556\pi\)
−0.927707 + 0.373310i \(0.878223\pi\)
\(710\) 0 0
\(711\) −4.62132 + 8.00436i −0.173313 + 0.300187i
\(712\) 0 0
\(713\) 24.0000 0.898807
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −2.48528 + 4.30463i −0.0928145 + 0.160759i
\(718\) 0 0
\(719\) −25.0919 43.4604i −0.935769 1.62080i −0.773256 0.634094i \(-0.781373\pi\)
−0.162513 0.986706i \(-0.551960\pi\)
\(720\) 0 0
\(721\) 0.757359 + 1.85514i 0.0282055 + 0.0690892i
\(722\) 0 0
\(723\) −2.98528 5.17066i −0.111024 0.192299i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 38.7574 1.43743 0.718715 0.695304i \(-0.244730\pi\)
0.718715 + 0.695304i \(0.244730\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 26.4853 45.8739i 0.979594 1.69671i
\(732\) 0 0
\(733\) 12.7426 + 22.0709i 0.470660 + 0.815207i 0.999437 0.0335536i \(-0.0106825\pi\)
−0.528777 + 0.848761i \(0.677349\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 24.8787 + 43.0911i 0.916418 + 1.58728i
\(738\) 0 0
\(739\) −25.8345 + 44.7467i −0.950338 + 1.64603i −0.205646 + 0.978626i \(0.565929\pi\)
−0.744692 + 0.667408i \(0.767404\pi\)
\(740\) 0 0
\(741\) −26.2132 −0.962966
\(742\) 0 0
\(743\) −10.9706 −0.402471 −0.201235 0.979543i \(-0.564496\pi\)
−0.201235 + 0.979543i \(0.564496\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.878680 + 1.52192i 0.0321492 + 0.0556841i
\(748\) 0 0
\(749\) 6.72792 + 16.4800i 0.245833 + 0.602165i
\(750\) 0 0
\(751\) −8.86396 15.3528i −0.323451 0.560233i 0.657747 0.753239i \(-0.271510\pi\)
−0.981198 + 0.193006i \(0.938176\pi\)
\(752\) 0 0
\(753\) −8.12132 + 14.0665i −0.295957 + 0.512613i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 14.4558 0.525407 0.262703 0.964877i \(-0.415386\pi\)
0.262703 + 0.964877i \(0.415386\pi\)
\(758\) 0 0
\(759\) −12.7279 + 22.0454i −0.461994 + 0.800198i
\(760\) 0 0
\(761\) −20.1213 34.8511i −0.729397 1.26335i −0.957138 0.289631i \(-0.906467\pi\)
0.227741 0.973722i \(-0.426866\pi\)
\(762\) 0 0
\(763\) −4.07716 + 5.25770i −0.147603 + 0.190341i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 25.6066 44.3519i 0.924601 1.60146i
\(768\) 0 0
\(769\) −31.5147 −1.13645 −0.568225 0.822873i \(-0.692370\pi\)
−0.568225 + 0.822873i \(0.692370\pi\)
\(770\) 0 0
\(771\) −22.2426 −0.801049
\(772\) 0 0
\(773\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 13.1066 + 1.79360i 0.470197 + 0.0643449i
\(778\) 0 0
\(779\) −26.8492 46.5043i −0.961974 1.66619i
\(780\) 0 0
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) 0 0
\(783\) −8.48528 −0.303239
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 8.86396 15.3528i 0.315966 0.547269i −0.663676 0.748020i \(-0.731005\pi\)
0.979642 + 0.200751i \(0.0643381\pi\)
\(788\) 0 0
\(789\) −14.4853 25.0892i −0.515690 0.893201i
\(790\) 0 0
\(791\) 15.7279 + 2.15232i 0.559221 + 0.0765276i
\(792\) 0 0
\(793\) −2.50000 4.33013i −0.0887776 0.153767i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 48.4264 1.71535 0.857676 0.514191i \(-0.171908\pi\)
0.857676 + 0.514191i \(0.171908\pi\)
\(798\) 0 0
\(799\) 43.4558 1.53736
\(800\) 0 0
\(801\) −3.87868 + 6.71807i −0.137046 + 0.237371i
\(802\) 0 0
\(803\) −7.39340 12.8057i −0.260907 0.451905i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −9.36396 16.2189i −0.329627 0.570931i
\(808\) 0 0
\(809\) −27.7279 + 48.0262i