Properties

Label 720.2.q.d.241.1
Level $720$
Weight $2$
Character 720.241
Analytic conductor $5.749$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.74922894553\)
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 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 241.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 720.241
Dual form 720.2.q.d.481.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.50000 + 2.59808i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.50000 + 2.59808i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{11} +(1.00000 + 1.73205i) q^{13} +(1.50000 + 0.866025i) q^{15} +4.00000 q^{17} +8.00000 q^{19} +5.19615i q^{21} +(1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.19615i q^{27} +(0.500000 - 0.866025i) q^{29} +3.46410i q^{33} -3.00000 q^{35} -4.00000 q^{37} +(3.00000 + 1.73205i) q^{39} +(-2.50000 - 4.33013i) q^{41} +(-4.00000 + 6.92820i) q^{43} +3.00000 q^{45} +(3.50000 - 6.06218i) q^{47} +(-1.00000 - 1.73205i) q^{49} +(6.00000 - 3.46410i) q^{51} -2.00000 q^{53} -2.00000 q^{55} +(12.0000 - 6.92820i) q^{57} +(-7.00000 - 12.1244i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(4.50000 + 7.79423i) q^{63} +(-1.00000 + 1.73205i) q^{65} +(-1.50000 - 2.59808i) q^{67} +(4.50000 + 2.59808i) q^{69} -2.00000 q^{71} +4.00000 q^{73} +1.73205i q^{75} +(-3.00000 - 5.19615i) q^{77} +(-3.00000 + 5.19615i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(4.50000 - 7.79423i) q^{83} +(2.00000 + 3.46410i) q^{85} -1.73205i q^{87} -15.0000 q^{89} -6.00000 q^{91} +(4.00000 + 6.92820i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{3} + q^{5} - 3 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{3} + q^{5} - 3 q^{7} + 3 q^{9} - 2 q^{11} + 2 q^{13} + 3 q^{15} + 8 q^{17} + 16 q^{19} + 3 q^{23} - q^{25} + q^{29} - 6 q^{35} - 8 q^{37} + 6 q^{39} - 5 q^{41} - 8 q^{43} + 6 q^{45} + 7 q^{47} - 2 q^{49} + 12 q^{51} - 4 q^{53} - 4 q^{55} + 24 q^{57} - 14 q^{59} - 7 q^{61} + 9 q^{63} - 2 q^{65} - 3 q^{67} + 9 q^{69} - 4 q^{71} + 8 q^{73} - 6 q^{77} - 6 q^{79} - 9 q^{81} + 9 q^{83} + 4 q^{85} - 30 q^{89} - 12 q^{91} + 8 q^{95} - 2 q^{97} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 1.50000 0.866025i 0.866025 0.500000i
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) −1.50000 + 2.59808i −0.566947 + 0.981981i 0.429919 + 0.902867i \(0.358542\pi\)
−0.996866 + 0.0791130i \(0.974791\pi\)
\(8\) 0 0
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 0 0
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 0 0
\(13\) 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i \(-0.0772105\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 1.50000 + 0.866025i 0.387298 + 0.223607i
\(16\) 0 0
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 0 0
\(19\) 8.00000 1.83533 0.917663 0.397360i \(-0.130073\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) 5.19615i 1.13389i
\(22\) 0 0
\(23\) 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 0.500000 0.866025i 0.0928477 0.160817i −0.815861 0.578249i \(-0.803736\pi\)
0.908708 + 0.417432i \(0.137070\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 0 0
\(33\) 3.46410i 0.603023i
\(34\) 0 0
\(35\) −3.00000 −0.507093
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 0 0
\(39\) 3.00000 + 1.73205i 0.480384 + 0.277350i
\(40\) 0 0
\(41\) −2.50000 4.33013i −0.390434 0.676252i 0.602072 0.798441i \(-0.294342\pi\)
−0.992507 + 0.122189i \(0.961009\pi\)
\(42\) 0 0
\(43\) −4.00000 + 6.92820i −0.609994 + 1.05654i 0.381246 + 0.924473i \(0.375495\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) 0 0
\(45\) 3.00000 0.447214
\(46\) 0 0
\(47\) 3.50000 6.06218i 0.510527 0.884260i −0.489398 0.872060i \(-0.662783\pi\)
0.999926 0.0121990i \(-0.00388317\pi\)
\(48\) 0 0
\(49\) −1.00000 1.73205i −0.142857 0.247436i
\(50\) 0 0
\(51\) 6.00000 3.46410i 0.840168 0.485071i
\(52\) 0 0
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) 12.0000 6.92820i 1.58944 0.917663i
\(58\) 0 0
\(59\) −7.00000 12.1244i −0.911322 1.57846i −0.812198 0.583382i \(-0.801729\pi\)
−0.0991242 0.995075i \(-0.531604\pi\)
\(60\) 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
\(63\) 4.50000 + 7.79423i 0.566947 + 0.981981i
\(64\) 0 0
\(65\) −1.00000 + 1.73205i −0.124035 + 0.214834i
\(66\) 0 0
\(67\) −1.50000 2.59808i −0.183254 0.317406i 0.759733 0.650236i \(-0.225330\pi\)
−0.942987 + 0.332830i \(0.891996\pi\)
\(68\) 0 0
\(69\) 4.50000 + 2.59808i 0.541736 + 0.312772i
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) 0 0
\(75\) 1.73205i 0.200000i
\(76\) 0 0
\(77\) −3.00000 5.19615i −0.341882 0.592157i
\(78\) 0 0
\(79\) −3.00000 + 5.19615i −0.337526 + 0.584613i −0.983967 0.178352i \(-0.942924\pi\)
0.646440 + 0.762964i \(0.276257\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) 4.50000 7.79423i 0.493939 0.855528i −0.506036 0.862512i \(-0.668890\pi\)
0.999976 + 0.00698436i \(0.00222321\pi\)
\(84\) 0 0
\(85\) 2.00000 + 3.46410i 0.216930 + 0.375735i
\(86\) 0 0
\(87\) 1.73205i 0.185695i
\(88\) 0 0
\(89\) −15.0000 −1.59000 −0.794998 0.606612i \(-0.792528\pi\)
−0.794998 + 0.606612i \(0.792528\pi\)
\(90\) 0 0
\(91\) −6.00000 −0.628971
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.00000 + 6.92820i 0.410391 + 0.710819i
\(96\) 0 0
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) 0 0
\(99\) 3.00000 + 5.19615i 0.301511 + 0.522233i
\(100\) 0 0
\(101\) 9.00000 15.5885i 0.895533 1.55111i 0.0623905 0.998052i \(-0.480128\pi\)
0.833143 0.553058i \(-0.186539\pi\)
\(102\) 0 0
\(103\) 4.00000 + 6.92820i 0.394132 + 0.682656i 0.992990 0.118199i \(-0.0377120\pi\)
−0.598858 + 0.800855i \(0.704379\pi\)
\(104\) 0 0
\(105\) −4.50000 + 2.59808i −0.439155 + 0.253546i
\(106\) 0 0
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 0 0
\(109\) 5.00000 0.478913 0.239457 0.970907i \(-0.423031\pi\)
0.239457 + 0.970907i \(0.423031\pi\)
\(110\) 0 0
\(111\) −6.00000 + 3.46410i −0.569495 + 0.328798i
\(112\) 0 0
\(113\) 4.00000 + 6.92820i 0.376288 + 0.651751i 0.990519 0.137376i \(-0.0438669\pi\)
−0.614231 + 0.789127i \(0.710534\pi\)
\(114\) 0 0
\(115\) −1.50000 + 2.59808i −0.139876 + 0.242272i
\(116\) 0 0
\(117\) 6.00000 0.554700
\(118\) 0 0
\(119\) −6.00000 + 10.3923i −0.550019 + 0.952661i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 0 0
\(123\) −7.50000 4.33013i −0.676252 0.390434i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) 0 0
\(129\) 13.8564i 1.21999i
\(130\) 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
\(133\) −12.0000 + 20.7846i −1.04053 + 1.80225i
\(134\) 0 0
\(135\) 4.50000 2.59808i 0.387298 0.223607i
\(136\) 0 0
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 0 0
\(139\) −8.00000 13.8564i −0.678551 1.17529i −0.975417 0.220366i \(-0.929275\pi\)
0.296866 0.954919i \(-0.404058\pi\)
\(140\) 0 0
\(141\) 12.1244i 1.02105i
\(142\) 0 0
\(143\) −4.00000 −0.334497
\(144\) 0 0
\(145\) 1.00000 0.0830455
\(146\) 0 0
\(147\) −3.00000 1.73205i −0.247436 0.142857i
\(148\) 0 0
\(149\) −8.50000 14.7224i −0.696347 1.20611i −0.969724 0.244202i \(-0.921474\pi\)
0.273377 0.961907i \(-0.411859\pi\)
\(150\) 0 0
\(151\) −1.00000 + 1.73205i −0.0813788 + 0.140952i −0.903842 0.427865i \(-0.859266\pi\)
0.822464 + 0.568818i \(0.192599\pi\)
\(152\) 0 0
\(153\) 6.00000 10.3923i 0.485071 0.840168i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −7.00000 12.1244i −0.558661 0.967629i −0.997609 0.0691164i \(-0.977982\pi\)
0.438948 0.898513i \(-0.355351\pi\)
\(158\) 0 0
\(159\) −3.00000 + 1.73205i −0.237915 + 0.137361i
\(160\) 0 0
\(161\) −9.00000 −0.709299
\(162\) 0 0
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 0 0
\(165\) −3.00000 + 1.73205i −0.233550 + 0.134840i
\(166\) 0 0
\(167\) −4.50000 7.79423i −0.348220 0.603136i 0.637713 0.770274i \(-0.279881\pi\)
−0.985933 + 0.167139i \(0.946547\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) 12.0000 20.7846i 0.917663 1.58944i
\(172\) 0 0
\(173\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 0 0
\(175\) −1.50000 2.59808i −0.113389 0.196396i
\(176\) 0 0
\(177\) −21.0000 12.1244i −1.57846 0.911322i
\(178\) 0 0
\(179\) 2.00000 0.149487 0.0747435 0.997203i \(-0.476186\pi\)
0.0747435 + 0.997203i \(0.476186\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) 12.1244i 0.896258i
\(184\) 0 0
\(185\) −2.00000 3.46410i −0.147043 0.254686i
\(186\) 0 0
\(187\) −4.00000 + 6.92820i −0.292509 + 0.506640i
\(188\) 0 0
\(189\) 13.5000 + 7.79423i 0.981981 + 0.566947i
\(190\) 0 0
\(191\) 4.00000 6.92820i 0.289430 0.501307i −0.684244 0.729253i \(-0.739868\pi\)
0.973674 + 0.227946i \(0.0732010\pi\)
\(192\) 0 0
\(193\) 5.00000 + 8.66025i 0.359908 + 0.623379i 0.987945 0.154805i \(-0.0494748\pi\)
−0.628037 + 0.778183i \(0.716141\pi\)
\(194\) 0 0
\(195\) 3.46410i 0.248069i
\(196\) 0 0
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 0 0
\(201\) −4.50000 2.59808i −0.317406 0.183254i
\(202\) 0 0
\(203\) 1.50000 + 2.59808i 0.105279 + 0.182349i
\(204\) 0 0
\(205\) 2.50000 4.33013i 0.174608 0.302429i
\(206\) 0 0
\(207\) 9.00000 0.625543
\(208\) 0 0
\(209\) −8.00000 + 13.8564i −0.553372 + 0.958468i
\(210\) 0 0
\(211\) −11.0000 19.0526i −0.757271 1.31163i −0.944237 0.329266i \(-0.893199\pi\)
0.186966 0.982366i \(-0.440135\pi\)
\(212\) 0 0
\(213\) −3.00000 + 1.73205i −0.205557 + 0.118678i
\(214\) 0 0
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 6.00000 3.46410i 0.405442 0.234082i
\(220\) 0 0
\(221\) 4.00000 + 6.92820i 0.269069 + 0.466041i
\(222\) 0 0
\(223\) −9.50000 + 16.4545i −0.636167 + 1.10187i 0.350100 + 0.936713i \(0.386148\pi\)
−0.986267 + 0.165161i \(0.947186\pi\)
\(224\) 0 0
\(225\) 1.50000 + 2.59808i 0.100000 + 0.173205i
\(226\) 0 0
\(227\) −2.00000 + 3.46410i −0.132745 + 0.229920i −0.924734 0.380615i \(-0.875712\pi\)
0.791989 + 0.610535i \(0.209046\pi\)
\(228\) 0 0
\(229\) −7.50000 12.9904i −0.495614 0.858429i 0.504373 0.863486i \(-0.331724\pi\)
−0.999987 + 0.00505719i \(0.998390\pi\)
\(230\) 0 0
\(231\) −9.00000 5.19615i −0.592157 0.341882i
\(232\) 0 0
\(233\) 24.0000 1.57229 0.786146 0.618041i \(-0.212073\pi\)
0.786146 + 0.618041i \(0.212073\pi\)
\(234\) 0 0
\(235\) 7.00000 0.456630
\(236\) 0 0
\(237\) 10.3923i 0.675053i
\(238\) 0 0
\(239\) −4.00000 6.92820i −0.258738 0.448148i 0.707166 0.707048i \(-0.249973\pi\)
−0.965904 + 0.258900i \(0.916640\pi\)
\(240\) 0 0
\(241\) 5.50000 9.52628i 0.354286 0.613642i −0.632709 0.774389i \(-0.718057\pi\)
0.986996 + 0.160748i \(0.0513906\pi\)
\(242\) 0 0
\(243\) −13.5000 7.79423i −0.866025 0.500000i
\(244\) 0 0
\(245\) 1.00000 1.73205i 0.0638877 0.110657i
\(246\) 0 0
\(247\) 8.00000 + 13.8564i 0.509028 + 0.881662i
\(248\) 0 0
\(249\) 15.5885i 0.987878i
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −6.00000 −0.377217
\(254\) 0 0
\(255\) 6.00000 + 3.46410i 0.375735 + 0.216930i
\(256\) 0 0
\(257\) 3.00000 + 5.19615i 0.187135 + 0.324127i 0.944294 0.329104i \(-0.106747\pi\)
−0.757159 + 0.653231i \(0.773413\pi\)
\(258\) 0 0
\(259\) 6.00000 10.3923i 0.372822 0.645746i
\(260\) 0 0
\(261\) −1.50000 2.59808i −0.0928477 0.160817i
\(262\) 0 0
\(263\) −8.00000 + 13.8564i −0.493301 + 0.854423i −0.999970 0.00771799i \(-0.997543\pi\)
0.506669 + 0.862141i \(0.330877\pi\)
\(264\) 0 0
\(265\) −1.00000 1.73205i −0.0614295 0.106399i
\(266\) 0 0
\(267\) −22.5000 + 12.9904i −1.37698 + 0.794998i
\(268\) 0 0
\(269\) 25.0000 1.52428 0.762138 0.647414i \(-0.224150\pi\)
0.762138 + 0.647414i \(0.224150\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 0 0
\(273\) −9.00000 + 5.19615i −0.544705 + 0.314485i
\(274\) 0 0
\(275\) −1.00000 1.73205i −0.0603023 0.104447i
\(276\) 0 0
\(277\) −6.00000 + 10.3923i −0.360505 + 0.624413i −0.988044 0.154172i \(-0.950729\pi\)
0.627539 + 0.778585i \(0.284062\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 7.50000 12.9904i 0.447412 0.774941i −0.550804 0.834634i \(-0.685679\pi\)
0.998217 + 0.0596933i \(0.0190123\pi\)
\(282\) 0 0
\(283\) 10.5000 + 18.1865i 0.624160 + 1.08108i 0.988703 + 0.149890i \(0.0478921\pi\)
−0.364542 + 0.931187i \(0.618775\pi\)
\(284\) 0 0
\(285\) 12.0000 + 6.92820i 0.710819 + 0.410391i
\(286\) 0 0
\(287\) 15.0000 0.885422
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 3.46410i 0.203069i
\(292\) 0 0
\(293\) −6.00000 10.3923i −0.350524 0.607125i 0.635818 0.771839i \(-0.280663\pi\)
−0.986341 + 0.164714i \(0.947330\pi\)
\(294\) 0 0
\(295\) 7.00000 12.1244i 0.407556 0.705907i
\(296\) 0 0
\(297\) 9.00000 + 5.19615i 0.522233 + 0.301511i
\(298\) 0 0
\(299\) −3.00000 + 5.19615i −0.173494 + 0.300501i
\(300\) 0 0
\(301\) −12.0000 20.7846i −0.691669 1.19800i
\(302\) 0 0
\(303\) 31.1769i 1.79107i
\(304\) 0 0
\(305\) −7.00000 −0.400819
\(306\) 0 0
\(307\) −7.00000 −0.399511 −0.199756 0.979846i \(-0.564015\pi\)
−0.199756 + 0.979846i \(0.564015\pi\)
\(308\) 0 0
\(309\) 12.0000 + 6.92820i 0.682656 + 0.394132i
\(310\) 0 0
\(311\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(312\) 0 0
\(313\) −7.00000 + 12.1244i −0.395663 + 0.685309i −0.993186 0.116543i \(-0.962819\pi\)
0.597522 + 0.801852i \(0.296152\pi\)
\(314\) 0 0
\(315\) −4.50000 + 7.79423i −0.253546 + 0.439155i
\(316\) 0 0
\(317\) 17.0000 29.4449i 0.954815 1.65379i 0.220024 0.975494i \(-0.429386\pi\)
0.734791 0.678294i \(-0.237280\pi\)
\(318\) 0 0
\(319\) 1.00000 + 1.73205i 0.0559893 + 0.0969762i
\(320\) 0 0
\(321\) −4.50000 + 2.59808i −0.251166 + 0.145010i
\(322\) 0 0
\(323\) 32.0000 1.78053
\(324\) 0 0
\(325\) −2.00000 −0.110940
\(326\) 0 0
\(327\) 7.50000 4.33013i 0.414751 0.239457i
\(328\) 0 0
\(329\) 10.5000 + 18.1865i 0.578884 + 1.00266i
\(330\) 0 0
\(331\) −3.00000 + 5.19615i −0.164895 + 0.285606i −0.936618 0.350352i \(-0.886062\pi\)
0.771723 + 0.635959i \(0.219395\pi\)
\(332\) 0 0
\(333\) −6.00000 + 10.3923i −0.328798 + 0.569495i
\(334\) 0 0
\(335\) 1.50000 2.59808i 0.0819538 0.141948i
\(336\) 0 0
\(337\) 4.00000 + 6.92820i 0.217894 + 0.377403i 0.954164 0.299285i \(-0.0967480\pi\)
−0.736270 + 0.676688i \(0.763415\pi\)
\(338\) 0 0
\(339\) 12.0000 + 6.92820i 0.651751 + 0.376288i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) 0 0
\(345\) 5.19615i 0.279751i
\(346\) 0 0
\(347\) 2.00000 + 3.46410i 0.107366 + 0.185963i 0.914702 0.404128i \(-0.132425\pi\)
−0.807337 + 0.590091i \(0.799092\pi\)
\(348\) 0 0
\(349\) 2.50000 4.33013i 0.133822 0.231786i −0.791325 0.611396i \(-0.790608\pi\)
0.925147 + 0.379610i \(0.123942\pi\)
\(350\) 0 0
\(351\) 9.00000 5.19615i 0.480384 0.277350i
\(352\) 0 0
\(353\) −12.0000 + 20.7846i −0.638696 + 1.10625i 0.347024 + 0.937856i \(0.387192\pi\)
−0.985719 + 0.168397i \(0.946141\pi\)
\(354\) 0 0
\(355\) −1.00000 1.73205i −0.0530745 0.0919277i
\(356\) 0 0
\(357\) 20.7846i 1.10004i
\(358\) 0 0
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) 45.0000 2.36842
\(362\) 0 0
\(363\) 10.5000 + 6.06218i 0.551107 + 0.318182i
\(364\) 0 0
\(365\) 2.00000 + 3.46410i 0.104685 + 0.181319i
\(366\) 0 0
\(367\) 12.0000 20.7846i 0.626395 1.08495i −0.361874 0.932227i \(-0.617863\pi\)
0.988269 0.152721i \(-0.0488036\pi\)
\(368\) 0 0
\(369\) −15.0000 −0.780869
\(370\) 0 0
\(371\) 3.00000 5.19615i 0.155752 0.269771i
\(372\) 0 0
\(373\) −5.00000 8.66025i −0.258890 0.448411i 0.707055 0.707159i \(-0.250023\pi\)
−0.965945 + 0.258748i \(0.916690\pi\)
\(374\) 0 0
\(375\) −1.50000 + 0.866025i −0.0774597 + 0.0447214i
\(376\) 0 0
\(377\) 2.00000 0.103005
\(378\) 0 0
\(379\) 26.0000 1.33553 0.667765 0.744372i \(-0.267251\pi\)
0.667765 + 0.744372i \(0.267251\pi\)
\(380\) 0 0
\(381\) 7.50000 4.33013i 0.384237 0.221839i
\(382\) 0 0
\(383\) 18.0000 + 31.1769i 0.919757 + 1.59307i 0.799783 + 0.600289i \(0.204948\pi\)
0.119974 + 0.992777i \(0.461719\pi\)
\(384\) 0 0
\(385\) 3.00000 5.19615i 0.152894 0.264820i
\(386\) 0 0
\(387\) 12.0000 + 20.7846i 0.609994 + 1.05654i
\(388\) 0 0
\(389\) −16.5000 + 28.5788i −0.836583 + 1.44900i 0.0561516 + 0.998422i \(0.482117\pi\)
−0.892735 + 0.450582i \(0.851216\pi\)
\(390\) 0 0
\(391\) 6.00000 + 10.3923i 0.303433 + 0.525561i
\(392\) 0 0
\(393\) −9.00000 5.19615i −0.453990 0.262111i
\(394\) 0 0
\(395\) −6.00000 −0.301893
\(396\) 0 0
\(397\) 34.0000 1.70641 0.853206 0.521575i \(-0.174655\pi\)
0.853206 + 0.521575i \(0.174655\pi\)
\(398\) 0 0
\(399\) 41.5692i 2.08106i
\(400\) 0 0
\(401\) 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 4.50000 7.79423i 0.223607 0.387298i
\(406\) 0 0
\(407\) 4.00000 6.92820i 0.198273 0.343418i
\(408\) 0 0
\(409\) −7.00000 12.1244i −0.346128 0.599511i 0.639430 0.768849i \(-0.279170\pi\)
−0.985558 + 0.169338i \(0.945837\pi\)
\(410\) 0 0
\(411\) 20.7846i 1.02523i
\(412\) 0 0
\(413\) 42.0000 2.06668
\(414\) 0 0
\(415\) 9.00000 0.441793
\(416\) 0 0
\(417\) −24.0000 13.8564i −1.17529 0.678551i
\(418\) 0 0
\(419\) 13.0000 + 22.5167i 0.635092 + 1.10001i 0.986496 + 0.163787i \(0.0523710\pi\)
−0.351404 + 0.936224i \(0.614296\pi\)
\(420\) 0 0
\(421\) −17.0000 + 29.4449i −0.828529 + 1.43505i 0.0706626 + 0.997500i \(0.477489\pi\)
−0.899192 + 0.437555i \(0.855845\pi\)
\(422\) 0 0
\(423\) −10.5000 18.1865i −0.510527 0.884260i
\(424\) 0 0
\(425\) −2.00000 + 3.46410i −0.0970143 + 0.168034i
\(426\) 0 0
\(427\) −10.5000 18.1865i −0.508131 0.880108i
\(428\) 0 0
\(429\) −6.00000 + 3.46410i −0.289683 + 0.167248i
\(430\) 0 0
\(431\) 30.0000 1.44505 0.722525 0.691345i \(-0.242982\pi\)
0.722525 + 0.691345i \(0.242982\pi\)
\(432\) 0 0
\(433\) 28.0000 1.34559 0.672797 0.739827i \(-0.265093\pi\)
0.672797 + 0.739827i \(0.265093\pi\)
\(434\) 0 0
\(435\) 1.50000 0.866025i 0.0719195 0.0415227i
\(436\) 0 0
\(437\) 12.0000 + 20.7846i 0.574038 + 0.994263i
\(438\) 0 0
\(439\) 14.0000 24.2487i 0.668184 1.15733i −0.310228 0.950662i \(-0.600405\pi\)
0.978412 0.206666i \(-0.0662612\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) 0 0
\(443\) 7.50000 12.9904i 0.356336 0.617192i −0.631010 0.775775i \(-0.717359\pi\)
0.987346 + 0.158583i \(0.0506926\pi\)
\(444\) 0 0
\(445\) −7.50000 12.9904i −0.355534 0.615803i
\(446\) 0 0
\(447\) −25.5000 14.7224i −1.20611 0.696347i
\(448\) 0 0
\(449\) −26.0000 −1.22702 −0.613508 0.789689i \(-0.710242\pi\)
−0.613508 + 0.789689i \(0.710242\pi\)
\(450\) 0 0
\(451\) 10.0000 0.470882
\(452\) 0 0
\(453\) 3.46410i 0.162758i
\(454\) 0 0
\(455\) −3.00000 5.19615i −0.140642 0.243599i
\(456\) 0 0
\(457\) 10.0000 17.3205i 0.467780 0.810219i −0.531542 0.847032i \(-0.678387\pi\)
0.999322 + 0.0368128i \(0.0117205\pi\)
\(458\) 0 0
\(459\) 20.7846i 0.970143i
\(460\) 0 0
\(461\) −4.50000 + 7.79423i −0.209586 + 0.363013i −0.951584 0.307388i \(-0.900545\pi\)
0.741998 + 0.670402i \(0.233878\pi\)
\(462\) 0 0
\(463\) −18.0000 31.1769i −0.836531 1.44891i −0.892778 0.450497i \(-0.851247\pi\)
0.0562469 0.998417i \(-0.482087\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −20.0000 −0.925490 −0.462745 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) 0 0
\(469\) 9.00000 0.415581
\(470\) 0 0
\(471\) −21.0000 12.1244i −0.967629 0.558661i
\(472\) 0 0
\(473\) −8.00000 13.8564i −0.367840 0.637118i
\(474\) 0 0
\(475\) −4.00000 + 6.92820i −0.183533 + 0.317888i
\(476\) 0 0
\(477\) −3.00000 + 5.19615i −0.137361 + 0.237915i
\(478\) 0 0
\(479\) −9.00000 + 15.5885i −0.411220 + 0.712255i −0.995023 0.0996406i \(-0.968231\pi\)
0.583803 + 0.811895i \(0.301564\pi\)
\(480\) 0 0
\(481\) −4.00000 6.92820i −0.182384 0.315899i
\(482\) 0 0
\(483\) −13.5000 + 7.79423i −0.614271 + 0.354650i
\(484\) 0 0
\(485\) −2.00000 −0.0908153
\(486\) 0 0
\(487\) 16.0000 0.725029 0.362515 0.931978i \(-0.381918\pi\)
0.362515 + 0.931978i \(0.381918\pi\)
\(488\) 0 0
\(489\) 6.00000 3.46410i 0.271329 0.156652i
\(490\) 0 0
\(491\) 10.0000 + 17.3205i 0.451294 + 0.781664i 0.998467 0.0553560i \(-0.0176294\pi\)
−0.547173 + 0.837020i \(0.684296\pi\)
\(492\) 0 0
\(493\) 2.00000 3.46410i 0.0900755 0.156015i
\(494\) 0 0
\(495\) −3.00000 + 5.19615i −0.134840 + 0.233550i
\(496\) 0 0
\(497\) 3.00000 5.19615i 0.134568 0.233079i
\(498\) 0 0
\(499\) −16.0000 27.7128i −0.716258 1.24060i −0.962472 0.271380i \(-0.912520\pi\)
0.246214 0.969216i \(-0.420813\pi\)
\(500\) 0 0
\(501\) −13.5000 7.79423i −0.603136 0.348220i
\(502\) 0 0
\(503\) 7.00000 0.312115 0.156057 0.987748i \(-0.450122\pi\)
0.156057 + 0.987748i \(0.450122\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 0 0
\(507\) 15.5885i 0.692308i
\(508\) 0 0
\(509\) −21.5000 37.2391i −0.952971 1.65059i −0.738945 0.673766i \(-0.764676\pi\)
−0.214026 0.976828i \(-0.568658\pi\)
\(510\) 0 0
\(511\) −6.00000 + 10.3923i −0.265424 + 0.459728i
\(512\) 0 0
\(513\) 41.5692i 1.83533i
\(514\) 0 0
\(515\) −4.00000 + 6.92820i −0.176261 + 0.305293i
\(516\) 0 0
\(517\) 7.00000 + 12.1244i 0.307860 + 0.533229i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 11.0000 0.481919 0.240959 0.970535i \(-0.422538\pi\)
0.240959 + 0.970535i \(0.422538\pi\)
\(522\) 0 0
\(523\) 29.0000 1.26808 0.634041 0.773300i \(-0.281395\pi\)
0.634041 + 0.773300i \(0.281395\pi\)
\(524\) 0 0
\(525\) −4.50000 2.59808i −0.196396 0.113389i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) −42.0000 −1.82264
\(532\) 0 0
\(533\) 5.00000 8.66025i 0.216574 0.375117i
\(534\) 0 0
\(535\) −1.50000 2.59808i −0.0648507 0.112325i
\(536\) 0 0
\(537\) 3.00000 1.73205i 0.129460 0.0747435i
\(538\) 0 0
\(539\) 4.00000 0.172292
\(540\) 0 0
\(541\) −39.0000 −1.67674 −0.838370 0.545101i \(-0.816491\pi\)
−0.838370 + 0.545101i \(0.816491\pi\)
\(542\) 0 0
\(543\) −10.5000 + 6.06218i −0.450598 + 0.260153i
\(544\) 0 0
\(545\) 2.50000 + 4.33013i 0.107088 + 0.185482i
\(546\) 0 0
\(547\) −14.5000 + 25.1147i −0.619975 + 1.07383i 0.369514 + 0.929225i \(0.379524\pi\)
−0.989490 + 0.144604i \(0.953809\pi\)
\(548\) 0 0
\(549\) 10.5000 + 18.1865i 0.448129 + 0.776182i
\(550\) 0 0
\(551\) 4.00000 6.92820i 0.170406 0.295151i
\(552\) 0 0
\(553\) −9.00000 15.5885i −0.382719 0.662889i
\(554\) 0 0
\(555\) −6.00000 3.46410i −0.254686 0.147043i
\(556\) 0 0
\(557\) −30.0000 −1.27114 −0.635570 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) 0 0
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) 13.8564i 0.585018i
\(562\) 0 0
\(563\) −10.5000 18.1865i −0.442522 0.766471i 0.555354 0.831614i \(-0.312583\pi\)
−0.997876 + 0.0651433i \(0.979250\pi\)
\(564\) 0 0
\(565\) −4.00000 + 6.92820i −0.168281 + 0.291472i
\(566\) 0 0
\(567\) 27.0000 1.13389
\(568\) 0 0
\(569\) 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) 0 0
\(571\) 16.0000 + 27.7128i 0.669579 + 1.15975i 0.978022 + 0.208502i \(0.0668588\pi\)
−0.308443 + 0.951243i \(0.599808\pi\)
\(572\) 0 0
\(573\) 13.8564i 0.578860i
\(574\) 0 0
\(575\) −3.00000 −0.125109
\(576\) 0 0
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) 0 0
\(579\) 15.0000 + 8.66025i 0.623379 + 0.359908i
\(580\) 0 0
\(581\) 13.5000 + 23.3827i 0.560074 + 0.970077i
\(582\) 0 0
\(583\) 2.00000 3.46410i 0.0828315 0.143468i
\(584\) 0 0
\(585\) 3.00000 + 5.19615i 0.124035 + 0.214834i
\(586\) 0 0
\(587\) −16.5000 + 28.5788i −0.681028 + 1.17957i 0.293640 + 0.955916i \(0.405133\pi\)
−0.974668 + 0.223659i \(0.928200\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) −18.0000 + 10.3923i −0.740421 + 0.427482i
\(592\) 0 0
\(593\) 20.0000 0.821302 0.410651 0.911793i \(-0.365302\pi\)
0.410651 + 0.911793i \(0.365302\pi\)
\(594\) 0 0
\(595\) −12.0000 −0.491952
\(596\) 0 0
\(597\) −6.00000 + 3.46410i −0.245564 + 0.141776i
\(598\) 0 0
\(599\) −5.00000 8.66025i −0.204294 0.353848i 0.745613 0.666379i \(-0.232157\pi\)
−0.949908 + 0.312531i \(0.898823\pi\)
\(600\) 0 0
\(601\) −1.00000 + 1.73205i −0.0407909 + 0.0706518i −0.885700 0.464258i \(-0.846321\pi\)
0.844909 + 0.534910i \(0.179654\pi\)
\(602\) 0 0
\(603\) −9.00000 −0.366508
\(604\) 0 0
\(605\) −3.50000 + 6.06218i −0.142295 + 0.246463i
\(606\) 0 0
\(607\) −20.5000 35.5070i −0.832069 1.44119i −0.896394 0.443257i \(-0.853823\pi\)
0.0643251 0.997929i \(-0.479511\pi\)
\(608\) 0 0
\(609\) 4.50000 + 2.59808i 0.182349 + 0.105279i
\(610\) 0 0
\(611\) 14.0000 0.566379
\(612\) 0 0
\(613\) −44.0000 −1.77714 −0.888572 0.458738i \(-0.848302\pi\)
−0.888572 + 0.458738i \(0.848302\pi\)
\(614\) 0 0
\(615\) 8.66025i 0.349215i
\(616\) 0 0
\(617\) 18.0000 + 31.1769i 0.724653 + 1.25514i 0.959117 + 0.283011i \(0.0913331\pi\)
−0.234464 + 0.972125i \(0.575334\pi\)
\(618\) 0 0
\(619\) −2.00000 + 3.46410i −0.0803868 + 0.139234i −0.903416 0.428765i \(-0.858949\pi\)
0.823029 + 0.567999i \(0.192282\pi\)
\(620\) 0 0
\(621\) 13.5000 7.79423i 0.541736 0.312772i
\(622\) 0 0
\(623\) 22.5000 38.9711i 0.901443 1.56135i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 27.7128i 1.10674i
\(628\) 0 0
\(629\) −16.0000 −0.637962
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) −33.0000 19.0526i −1.31163 0.757271i
\(634\) 0 0
\(635\) 2.50000 + 4.33013i 0.0992095 + 0.171836i
\(636\) 0 0
\(637\) 2.00000 3.46410i 0.0792429 0.137253i
\(638\) 0 0
\(639\) −3.00000 + 5.19615i −0.118678 + 0.205557i
\(640\) 0 0
\(641\) −16.5000 + 28.5788i −0.651711 + 1.12880i 0.330997 + 0.943632i \(0.392615\pi\)
−0.982708 + 0.185164i \(0.940718\pi\)
\(642\) 0 0
\(643\) −4.50000 7.79423i −0.177463 0.307374i 0.763548 0.645751i \(-0.223456\pi\)
−0.941011 + 0.338377i \(0.890122\pi\)
\(644\) 0 0
\(645\) −12.0000 + 6.92820i −0.472500 + 0.272798i
\(646\) 0 0
\(647\) 17.0000 0.668339 0.334169 0.942513i \(-0.391544\pi\)
0.334169 + 0.942513i \(0.391544\pi\)
\(648\) 0 0
\(649\) 28.0000 1.09910
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.00000 + 3.46410i 0.0782660 + 0.135561i 0.902502 0.430686i \(-0.141728\pi\)
−0.824236 + 0.566247i \(0.808395\pi\)
\(654\) 0 0
\(655\) 3.00000 5.19615i 0.117220 0.203030i
\(656\) 0 0
\(657\) 6.00000 10.3923i 0.234082 0.405442i
\(658\) 0 0
\(659\) −4.00000 + 6.92820i −0.155818 + 0.269884i −0.933357 0.358951i \(-0.883135\pi\)
0.777539 + 0.628835i \(0.216468\pi\)
\(660\) 0 0
\(661\) 7.00000 + 12.1244i 0.272268 + 0.471583i 0.969442 0.245319i \(-0.0788928\pi\)
−0.697174 + 0.716902i \(0.745559\pi\)
\(662\) 0 0
\(663\) 12.0000 + 6.92820i 0.466041 + 0.269069i
\(664\) 0 0
\(665\) −24.0000 −0.930680
\(666\) 0 0
\(667\) 3.00000 0.116160
\(668\) 0 0
\(669\) 32.9090i 1.27233i
\(670\) 0 0
\(671\) −7.00000 12.1244i −0.270232 0.468056i
\(672\) 0 0
\(673\) −3.00000 + 5.19615i −0.115642 + 0.200297i −0.918036 0.396497i \(-0.870226\pi\)
0.802395 + 0.596794i \(0.203559\pi\)
\(674\) 0 0
\(675\) 4.50000 + 2.59808i 0.173205 + 0.100000i
\(676\) 0 0
\(677\) 21.0000 36.3731i 0.807096 1.39793i −0.107772 0.994176i \(-0.534372\pi\)
0.914867 0.403755i \(-0.132295\pi\)
\(678\) 0 0
\(679\) −3.00000 5.19615i −0.115129 0.199410i
\(680\) 0 0
\(681\) 6.92820i 0.265489i
\(682\) 0 0
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) −22.5000 12.9904i −0.858429 0.495614i
\(688\) 0 0
\(689\) −2.00000 3.46410i −0.0761939 0.131972i
\(690\) 0 0
\(691\) −7.00000 + 12.1244i −0.266293 + 0.461232i −0.967901 0.251330i \(-0.919132\pi\)
0.701609 + 0.712562i \(0.252465\pi\)
\(692\) 0 0
\(693\) −18.0000 −0.683763
\(694\) 0 0
\(695\) 8.00000 13.8564i 0.303457 0.525603i
\(696\) 0 0
\(697\) −10.0000 17.3205i −0.378777 0.656061i
\(698\) 0 0
\(699\) 36.0000 20.7846i 1.36165 0.786146i
\(700\) 0 0
\(701\) 23.0000 0.868698 0.434349 0.900745i \(-0.356978\pi\)
0.434349 + 0.900745i \(0.356978\pi\)
\(702\) 0 0
\(703\) −32.0000 −1.20690
\(704\) 0 0
\(705\) 10.5000 6.06218i 0.395453 0.228315i
\(706\) 0 0
\(707\) 27.0000 + 46.7654i 1.01544 + 1.75879i
\(708\) 0 0
\(709\) 20.5000 35.5070i 0.769894 1.33349i −0.167727 0.985834i \(-0.553643\pi\)
0.937620 0.347661i \(-0.113024\pi\)
\(710\) 0 0
\(711\) 9.00000 + 15.5885i 0.337526 + 0.584613i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −2.00000 3.46410i −0.0747958 0.129550i
\(716\) 0 0
\(717\) −12.0000 6.92820i −0.448148 0.258738i
\(718\) 0 0
\(719\) −6.00000 −0.223762 −0.111881 0.993722i \(-0.535688\pi\)
−0.111881 + 0.993722i \(0.535688\pi\)
\(720\) 0 0
\(721\) −24.0000 −0.893807
\(722\) 0 0
\(723\) 19.0526i 0.708572i
\(724\) 0 0
\(725\) 0.500000 + 0.866025i 0.0185695 + 0.0321634i
\(726\) 0 0
\(727\) 11.5000 19.9186i 0.426511 0.738739i −0.570049 0.821611i \(-0.693076\pi\)
0.996560 + 0.0828714i \(0.0264091\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −16.0000 + 27.7128i −0.591781 + 1.02500i
\(732\) 0 0
\(733\) 17.0000 + 29.4449i 0.627909 + 1.08757i 0.987971 + 0.154642i \(0.0494225\pi\)
−0.360061 + 0.932929i \(0.617244\pi\)
\(734\) 0 0
\(735\) 3.46410i 0.127775i
\(736\) 0 0
\(737\) 6.00000 0.221013
\(738\) 0 0
\(739\) 2.00000 0.0735712 0.0367856 0.999323i \(-0.488288\pi\)
0.0367856 + 0.999323i \(0.488288\pi\)
\(740\) 0 0
\(741\) 24.0000 + 13.8564i 0.881662 + 0.509028i
\(742\) 0 0
\(743\) −14.5000 25.1147i −0.531953 0.921370i −0.999304 0.0372984i \(-0.988125\pi\)
0.467351 0.884072i \(-0.345209\pi\)
\(744\) 0 0
\(745\) 8.50000 14.7224i 0.311416 0.539388i
\(746\) 0 0
\(747\) −13.5000 23.3827i −0.493939 0.855528i
\(748\) 0 0
\(749\) 4.50000 7.79423i 0.164426 0.284795i
\(750\) 0 0
\(751\) 5.00000 + 8.66025i 0.182453 + 0.316017i 0.942715 0.333599i \(-0.108263\pi\)
−0.760263 + 0.649616i \(0.774930\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2.00000 −0.0727875
\(756\) 0 0
\(757\) −26.0000 −0.944986 −0.472493 0.881334i \(-0.656646\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(758\) 0 0
\(759\) −9.00000 + 5.19615i −0.326679 + 0.188608i
\(760\) 0 0
\(761\) −7.50000 12.9904i −0.271875 0.470901i 0.697467 0.716617i \(-0.254310\pi\)
−0.969342 + 0.245716i \(0.920977\pi\)
\(762\) 0 0
\(763\) −7.50000 + 12.9904i −0.271518 + 0.470283i
\(764\) 0 0
\(765\) 12.0000 0.433861
\(766\) 0 0
\(767\) 14.0000 24.2487i 0.505511 0.875570i
\(768\) 0 0
\(769\) −2.50000 4.33013i −0.0901523 0.156148i 0.817423 0.576038i \(-0.195402\pi\)
−0.907575 + 0.419890i \(0.862069\pi\)
\(770\) 0 0
\(771\) 9.00000 + 5.19615i 0.324127 + 0.187135i
\(772\) 0 0
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 20.7846i 0.745644i
\(778\) 0 0
\(779\) −20.0000 34.6410i −0.716574 1.24114i
\(780\) 0 0
\(781\) 2.00000 3.46410i 0.0715656 0.123955i
\(782\) 0 0
\(783\) −4.50000 2.59808i −0.160817 0.0928477i
\(784\) 0 0
\(785\) 7.00000 12.1244i 0.249841 0.432737i
\(786\) 0 0
\(787\) 14.0000 + 24.2487i 0.499046 + 0.864373i 0.999999 0.00110111i \(-0.000350496\pi\)
−0.500953 + 0.865474i \(0.667017\pi\)
\(788\) 0 0
\(789\) 27.7128i 0.986602i
\(790\) 0 0
\(791\) −24.0000 −0.853342
\(792\) 0 0
\(793\) −14.0000 −0.497155
\(794\) 0 0
\(795\) −3.00000 1.73205i −0.106399 0.0614295i