Properties

Label 260.2.i.c.81.1
Level $260$
Weight $2$
Character 260.81
Analytic conductor $2.076$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07611045255\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 81.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 260.81
Dual form 260.2.i.c.61.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} -1.00000 q^{5} +(-2.50000 + 4.33013i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} -1.00000 q^{5} +(-2.50000 + 4.33013i) q^{7} +(1.00000 - 1.73205i) q^{9} +(2.50000 + 4.33013i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(-0.500000 - 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{17} +(1.50000 - 2.59808i) q^{19} -5.00000 q^{21} +(-1.50000 - 2.59808i) q^{23} +1.00000 q^{25} +5.00000 q^{27} +(0.500000 + 0.866025i) q^{29} +(-2.50000 + 4.33013i) q^{33} +(2.50000 - 4.33013i) q^{35} +(-3.50000 - 6.06218i) q^{37} +(-3.50000 + 0.866025i) q^{39} +(2.50000 + 4.33013i) q^{41} +(-2.50000 + 4.33013i) q^{43} +(-1.00000 + 1.73205i) q^{45} +12.0000 q^{47} +(-9.00000 - 15.5885i) q^{49} +1.00000 q^{51} +2.00000 q^{53} +(-2.50000 - 4.33013i) q^{55} +3.00000 q^{57} +(5.50000 - 9.52628i) q^{59} +(6.50000 - 11.2583i) q^{61} +(5.00000 + 8.66025i) q^{63} +(1.00000 - 3.46410i) q^{65} +(-1.50000 - 2.59808i) q^{67} +(1.50000 - 2.59808i) q^{69} +(-6.50000 + 11.2583i) q^{71} -2.00000 q^{73} +(0.500000 + 0.866025i) q^{75} -25.0000 q^{77} -4.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +(-0.500000 + 0.866025i) q^{85} +(-0.500000 + 0.866025i) q^{87} +(-3.50000 - 6.06218i) q^{89} +(-12.5000 - 12.9904i) q^{91} +(-1.50000 + 2.59808i) q^{95} +(-5.50000 + 9.52628i) q^{97} +10.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} - 2 q^{5} - 5 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{3} - 2 q^{5} - 5 q^{7} + 2 q^{9} + 5 q^{11} - 2 q^{13} - q^{15} + q^{17} + 3 q^{19} - 10 q^{21} - 3 q^{23} + 2 q^{25} + 10 q^{27} + q^{29} - 5 q^{33} + 5 q^{35} - 7 q^{37} - 7 q^{39} + 5 q^{41} - 5 q^{43} - 2 q^{45} + 24 q^{47} - 18 q^{49} + 2 q^{51} + 4 q^{53} - 5 q^{55} + 6 q^{57} + 11 q^{59} + 13 q^{61} + 10 q^{63} + 2 q^{65} - 3 q^{67} + 3 q^{69} - 13 q^{71} - 4 q^{73} + q^{75} - 50 q^{77} - 8 q^{79} - q^{81} + 24 q^{83} - q^{85} - q^{87} - 7 q^{89} - 25 q^{91} - 3 q^{95} - 11 q^{97} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i 0.973494 0.228714i \(-0.0734519\pi\)
−0.684819 + 0.728714i \(0.740119\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −2.50000 + 4.33013i −0.944911 + 1.63663i −0.188982 + 0.981981i \(0.560519\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 0 0
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) 0 0
\(11\) 2.50000 + 4.33013i 0.753778 + 1.30558i 0.945979 + 0.324227i \(0.105104\pi\)
−0.192201 + 0.981356i \(0.561563\pi\)
\(12\) 0 0
\(13\) −1.00000 + 3.46410i −0.277350 + 0.960769i
\(14\) 0 0
\(15\) −0.500000 0.866025i −0.129099 0.223607i
\(16\) 0 0
\(17\) 0.500000 0.866025i 0.121268 0.210042i −0.799000 0.601331i \(-0.794637\pi\)
0.920268 + 0.391289i \(0.127971\pi\)
\(18\) 0 0
\(19\) 1.50000 2.59808i 0.344124 0.596040i −0.641071 0.767482i \(-0.721509\pi\)
0.985194 + 0.171442i \(0.0548427\pi\)
\(20\) 0 0
\(21\) −5.00000 −1.09109
\(22\) 0 0
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) 0.500000 + 0.866025i 0.0928477 + 0.160817i 0.908708 0.417432i \(-0.137070\pi\)
−0.815861 + 0.578249i \(0.803736\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) −2.50000 + 4.33013i −0.435194 + 0.753778i
\(34\) 0 0
\(35\) 2.50000 4.33013i 0.422577 0.731925i
\(36\) 0 0
\(37\) −3.50000 6.06218i −0.575396 0.996616i −0.995998 0.0893706i \(-0.971514\pi\)
0.420602 0.907245i \(-0.361819\pi\)
\(38\) 0 0
\(39\) −3.50000 + 0.866025i −0.560449 + 0.138675i
\(40\) 0 0
\(41\) 2.50000 + 4.33013i 0.390434 + 0.676252i 0.992507 0.122189i \(-0.0389915\pi\)
−0.602072 + 0.798441i \(0.705658\pi\)
\(42\) 0 0
\(43\) −2.50000 + 4.33013i −0.381246 + 0.660338i −0.991241 0.132068i \(-0.957838\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) −1.00000 + 1.73205i −0.149071 + 0.258199i
\(46\) 0 0
\(47\) 12.0000 1.75038 0.875190 0.483779i \(-0.160736\pi\)
0.875190 + 0.483779i \(0.160736\pi\)
\(48\) 0 0
\(49\) −9.00000 15.5885i −1.28571 2.22692i
\(50\) 0 0
\(51\) 1.00000 0.140028
\(52\) 0 0
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) −2.50000 4.33013i −0.337100 0.583874i
\(56\) 0 0
\(57\) 3.00000 0.397360
\(58\) 0 0
\(59\) 5.50000 9.52628i 0.716039 1.24022i −0.246518 0.969138i \(-0.579287\pi\)
0.962557 0.271078i \(-0.0873801\pi\)
\(60\) 0 0
\(61\) 6.50000 11.2583i 0.832240 1.44148i −0.0640184 0.997949i \(-0.520392\pi\)
0.896258 0.443533i \(-0.146275\pi\)
\(62\) 0 0
\(63\) 5.00000 + 8.66025i 0.629941 + 1.09109i
\(64\) 0 0
\(65\) 1.00000 3.46410i 0.124035 0.429669i
\(66\) 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
\(69\) 1.50000 2.59808i 0.180579 0.312772i
\(70\) 0 0
\(71\) −6.50000 + 11.2583i −0.771408 + 1.33612i 0.165383 + 0.986229i \(0.447114\pi\)
−0.936791 + 0.349889i \(0.886219\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0 0
\(75\) 0.500000 + 0.866025i 0.0577350 + 0.100000i
\(76\) 0 0
\(77\) −25.0000 −2.84901
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) −0.500000 + 0.866025i −0.0542326 + 0.0939336i
\(86\) 0 0
\(87\) −0.500000 + 0.866025i −0.0536056 + 0.0928477i
\(88\) 0 0
\(89\) −3.50000 6.06218i −0.370999 0.642590i 0.618720 0.785611i \(-0.287651\pi\)
−0.989720 + 0.143022i \(0.954318\pi\)
\(90\) 0 0
\(91\) −12.5000 12.9904i −1.31036 1.36176i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.50000 + 2.59808i −0.153897 + 0.266557i
\(96\) 0 0
\(97\) −5.50000 + 9.52628i −0.558440 + 0.967247i 0.439187 + 0.898396i \(0.355267\pi\)
−0.997627 + 0.0688512i \(0.978067\pi\)
\(98\) 0 0
\(99\) 10.0000 1.00504
\(100\) 0 0
\(101\) 6.50000 + 11.2583i 0.646774 + 1.12025i 0.983889 + 0.178782i \(0.0572157\pi\)
−0.337115 + 0.941464i \(0.609451\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 5.00000 0.487950
\(106\) 0 0
\(107\) 4.50000 + 7.79423i 0.435031 + 0.753497i 0.997298 0.0734594i \(-0.0234039\pi\)
−0.562267 + 0.826956i \(0.690071\pi\)
\(108\) 0 0
\(109\) 18.0000 1.72409 0.862044 0.506834i \(-0.169184\pi\)
0.862044 + 0.506834i \(0.169184\pi\)
\(110\) 0 0
\(111\) 3.50000 6.06218i 0.332205 0.575396i
\(112\) 0 0
\(113\) 0.500000 0.866025i 0.0470360 0.0814688i −0.841549 0.540181i \(-0.818356\pi\)
0.888585 + 0.458712i \(0.151689\pi\)
\(114\) 0 0
\(115\) 1.50000 + 2.59808i 0.139876 + 0.242272i
\(116\) 0 0
\(117\) 5.00000 + 5.19615i 0.462250 + 0.480384i
\(118\) 0 0
\(119\) 2.50000 + 4.33013i 0.229175 + 0.396942i
\(120\) 0 0
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) 0 0
\(123\) −2.50000 + 4.33013i −0.225417 + 0.390434i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −3.50000 6.06218i −0.310575 0.537931i 0.667912 0.744240i \(-0.267188\pi\)
−0.978487 + 0.206309i \(0.933855\pi\)
\(128\) 0 0
\(129\) −5.00000 −0.440225
\(130\) 0 0
\(131\) 4.00000 0.349482 0.174741 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 0 0
\(133\) 7.50000 + 12.9904i 0.650332 + 1.12641i
\(134\) 0 0
\(135\) −5.00000 −0.430331
\(136\) 0 0
\(137\) −1.50000 + 2.59808i −0.128154 + 0.221969i −0.922961 0.384893i \(-0.874238\pi\)
0.794808 + 0.606861i \(0.207572\pi\)
\(138\) 0 0
\(139\) −6.50000 + 11.2583i −0.551323 + 0.954919i 0.446857 + 0.894606i \(0.352543\pi\)
−0.998179 + 0.0603135i \(0.980790\pi\)
\(140\) 0 0
\(141\) 6.00000 + 10.3923i 0.505291 + 0.875190i
\(142\) 0 0
\(143\) −17.5000 + 4.33013i −1.46342 + 0.362103i
\(144\) 0 0
\(145\) −0.500000 0.866025i −0.0415227 0.0719195i
\(146\) 0 0
\(147\) 9.00000 15.5885i 0.742307 1.28571i
\(148\) 0 0
\(149\) −5.50000 + 9.52628i −0.450578 + 0.780423i −0.998422 0.0561570i \(-0.982115\pi\)
0.547844 + 0.836580i \(0.315449\pi\)
\(150\) 0 0
\(151\) −24.0000 −1.95309 −0.976546 0.215308i \(-0.930924\pi\)
−0.976546 + 0.215308i \(0.930924\pi\)
\(152\) 0 0
\(153\) −1.00000 1.73205i −0.0808452 0.140028i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 10.0000 0.798087 0.399043 0.916932i \(-0.369342\pi\)
0.399043 + 0.916932i \(0.369342\pi\)
\(158\) 0 0
\(159\) 1.00000 + 1.73205i 0.0793052 + 0.137361i
\(160\) 0 0
\(161\) 15.0000 1.18217
\(162\) 0 0
\(163\) −2.50000 + 4.33013i −0.195815 + 0.339162i −0.947167 0.320740i \(-0.896069\pi\)
0.751352 + 0.659901i \(0.229402\pi\)
\(164\) 0 0
\(165\) 2.50000 4.33013i 0.194625 0.337100i
\(166\) 0 0
\(167\) 6.50000 + 11.2583i 0.502985 + 0.871196i 0.999994 + 0.00345033i \(0.00109828\pi\)
−0.497009 + 0.867745i \(0.665568\pi\)
\(168\) 0 0
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) 0 0
\(171\) −3.00000 5.19615i −0.229416 0.397360i
\(172\) 0 0
\(173\) 8.50000 14.7224i 0.646243 1.11933i −0.337770 0.941229i \(-0.609673\pi\)
0.984013 0.178097i \(-0.0569941\pi\)
\(174\) 0 0
\(175\) −2.50000 + 4.33013i −0.188982 + 0.327327i
\(176\) 0 0
\(177\) 11.0000 0.826811
\(178\) 0 0
\(179\) −5.50000 9.52628i −0.411089 0.712028i 0.583920 0.811811i \(-0.301518\pi\)
−0.995009 + 0.0997838i \(0.968185\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) 13.0000 0.960988
\(184\) 0 0
\(185\) 3.50000 + 6.06218i 0.257325 + 0.445700i
\(186\) 0 0
\(187\) 5.00000 0.365636
\(188\) 0 0
\(189\) −12.5000 + 21.6506i −0.909241 + 1.57485i
\(190\) 0 0
\(191\) 7.50000 12.9904i 0.542681 0.939951i −0.456068 0.889945i \(-0.650743\pi\)
0.998749 0.0500060i \(-0.0159241\pi\)
\(192\) 0 0
\(193\) −11.5000 19.9186i −0.827788 1.43377i −0.899770 0.436365i \(-0.856266\pi\)
0.0719816 0.997406i \(-0.477068\pi\)
\(194\) 0 0
\(195\) 3.50000 0.866025i 0.250640 0.0620174i
\(196\) 0 0
\(197\) −13.5000 23.3827i −0.961835 1.66595i −0.717888 0.696159i \(-0.754891\pi\)
−0.243947 0.969788i \(-0.578442\pi\)
\(198\) 0 0
\(199\) −10.5000 + 18.1865i −0.744325 + 1.28921i 0.206184 + 0.978513i \(0.433895\pi\)
−0.950509 + 0.310696i \(0.899438\pi\)
\(200\) 0 0
\(201\) 1.50000 2.59808i 0.105802 0.183254i
\(202\) 0 0
\(203\) −5.00000 −0.350931
\(204\) 0 0
\(205\) −2.50000 4.33013i −0.174608 0.302429i
\(206\) 0 0
\(207\) −6.00000 −0.417029
\(208\) 0 0
\(209\) 15.0000 1.03757
\(210\) 0 0
\(211\) 2.50000 + 4.33013i 0.172107 + 0.298098i 0.939156 0.343490i \(-0.111609\pi\)
−0.767049 + 0.641588i \(0.778276\pi\)
\(212\) 0 0
\(213\) −13.0000 −0.890745
\(214\) 0 0
\(215\) 2.50000 4.33013i 0.170499 0.295312i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1.00000 1.73205i −0.0675737 0.117041i
\(220\) 0 0
\(221\) 2.50000 + 2.59808i 0.168168 + 0.174766i
\(222\) 0 0
\(223\) −9.50000 16.4545i −0.636167 1.10187i −0.986267 0.165161i \(-0.947186\pi\)
0.350100 0.936713i \(-0.386148\pi\)
\(224\) 0 0
\(225\) 1.00000 1.73205i 0.0666667 0.115470i
\(226\) 0 0
\(227\) −8.50000 + 14.7224i −0.564165 + 0.977162i 0.432962 + 0.901412i \(0.357468\pi\)
−0.997127 + 0.0757500i \(0.975865\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) −12.5000 21.6506i −0.822440 1.42451i
\(232\) 0 0
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) −12.0000 −0.782794
\(236\) 0 0
\(237\) −2.00000 3.46410i −0.129914 0.225018i
\(238\) 0 0
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) 0 0
\(241\) −5.50000 + 9.52628i −0.354286 + 0.613642i −0.986996 0.160748i \(-0.948609\pi\)
0.632709 + 0.774389i \(0.281943\pi\)
\(242\) 0 0
\(243\) 8.00000 13.8564i 0.513200 0.888889i
\(244\) 0 0
\(245\) 9.00000 + 15.5885i 0.574989 + 0.995910i
\(246\) 0 0
\(247\) 7.50000 + 7.79423i 0.477214 + 0.495935i
\(248\) 0 0
\(249\) 6.00000 + 10.3923i 0.380235 + 0.658586i
\(250\) 0 0
\(251\) 7.50000 12.9904i 0.473396 0.819946i −0.526140 0.850398i \(-0.676361\pi\)
0.999536 + 0.0304521i \(0.00969471\pi\)
\(252\) 0 0
\(253\) 7.50000 12.9904i 0.471521 0.816698i
\(254\) 0 0
\(255\) −1.00000 −0.0626224
\(256\) 0 0
\(257\) −7.50000 12.9904i −0.467837 0.810318i 0.531487 0.847066i \(-0.321633\pi\)
−0.999325 + 0.0367485i \(0.988300\pi\)
\(258\) 0 0
\(259\) 35.0000 2.17479
\(260\) 0 0
\(261\) 2.00000 0.123797
\(262\) 0 0
\(263\) −5.50000 9.52628i −0.339145 0.587416i 0.645128 0.764075i \(-0.276804\pi\)
−0.984272 + 0.176659i \(0.943471\pi\)
\(264\) 0 0
\(265\) −2.00000 −0.122859
\(266\) 0 0
\(267\) 3.50000 6.06218i 0.214197 0.370999i
\(268\) 0 0
\(269\) 4.50000 7.79423i 0.274370 0.475223i −0.695606 0.718423i \(-0.744864\pi\)
0.969976 + 0.243201i \(0.0781974\pi\)
\(270\) 0 0
\(271\) −3.50000 6.06218i −0.212610 0.368251i 0.739921 0.672694i \(-0.234863\pi\)
−0.952531 + 0.304443i \(0.901530\pi\)
\(272\) 0 0
\(273\) 5.00000 17.3205i 0.302614 1.04828i
\(274\) 0 0
\(275\) 2.50000 + 4.33013i 0.150756 + 0.261116i
\(276\) 0 0
\(277\) 6.50000 11.2583i 0.390547 0.676448i −0.601975 0.798515i \(-0.705619\pi\)
0.992522 + 0.122068i \(0.0389525\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 0 0
\(283\) −11.5000 19.9186i −0.683604 1.18404i −0.973873 0.227092i \(-0.927078\pi\)
0.290269 0.956945i \(-0.406255\pi\)
\(284\) 0 0
\(285\) −3.00000 −0.177705
\(286\) 0 0
\(287\) −25.0000 −1.47570
\(288\) 0 0
\(289\) 8.00000 + 13.8564i 0.470588 + 0.815083i
\(290\) 0 0
\(291\) −11.0000 −0.644831
\(292\) 0 0
\(293\) −3.50000 + 6.06218i −0.204472 + 0.354156i −0.949964 0.312358i \(-0.898881\pi\)
0.745492 + 0.666514i \(0.232214\pi\)
\(294\) 0 0
\(295\) −5.50000 + 9.52628i −0.320222 + 0.554641i
\(296\) 0 0
\(297\) 12.5000 + 21.6506i 0.725324 + 1.25630i
\(298\) 0 0
\(299\) 10.5000 2.59808i 0.607231 0.150251i
\(300\) 0 0
\(301\) −12.5000 21.6506i −0.720488 1.24792i
\(302\) 0 0
\(303\) −6.50000 + 11.2583i −0.373415 + 0.646774i
\(304\) 0 0
\(305\) −6.50000 + 11.2583i −0.372189 + 0.644650i
\(306\) 0 0
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 0 0
\(315\) −5.00000 8.66025i −0.281718 0.487950i
\(316\) 0 0
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) 0 0
\(319\) −2.50000 + 4.33013i −0.139973 + 0.242441i
\(320\) 0 0
\(321\) −4.50000 + 7.79423i −0.251166 + 0.435031i
\(322\) 0 0
\(323\) −1.50000 2.59808i −0.0834622 0.144561i
\(324\) 0 0
\(325\) −1.00000 + 3.46410i −0.0554700 + 0.192154i
\(326\) 0 0
\(327\) 9.00000 + 15.5885i 0.497701 + 0.862044i
\(328\) 0 0
\(329\) −30.0000 + 51.9615i −1.65395 + 2.86473i
\(330\) 0 0
\(331\) −0.500000 + 0.866025i −0.0274825 + 0.0476011i −0.879440 0.476011i \(-0.842082\pi\)
0.851957 + 0.523612i \(0.175416\pi\)
\(332\) 0 0
\(333\) −14.0000 −0.767195
\(334\) 0 0
\(335\) 1.50000 + 2.59808i 0.0819538 + 0.141948i
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) 1.00000 0.0543125
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 55.0000 2.96972
\(344\) 0 0
\(345\) −1.50000 + 2.59808i −0.0807573 + 0.139876i
\(346\) 0 0
\(347\) 13.5000 23.3827i 0.724718 1.25525i −0.234372 0.972147i \(-0.575303\pi\)
0.959090 0.283101i \(-0.0913633\pi\)
\(348\) 0 0
\(349\) −17.5000 30.3109i −0.936754 1.62250i −0.771477 0.636257i \(-0.780482\pi\)
−0.165277 0.986247i \(-0.552852\pi\)
\(350\) 0 0
\(351\) −5.00000 + 17.3205i −0.266880 + 0.924500i
\(352\) 0 0
\(353\) 2.50000 + 4.33013i 0.133062 + 0.230469i 0.924855 0.380319i \(-0.124186\pi\)
−0.791794 + 0.610789i \(0.790853\pi\)
\(354\) 0 0
\(355\) 6.50000 11.2583i 0.344984 0.597530i
\(356\) 0 0
\(357\) −2.50000 + 4.33013i −0.132314 + 0.229175i
\(358\) 0 0
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) 5.00000 + 8.66025i 0.263158 + 0.455803i
\(362\) 0 0
\(363\) −14.0000 −0.734809
\(364\) 0 0
\(365\) 2.00000 0.104685
\(366\) 0 0
\(367\) −1.50000 2.59808i −0.0782994 0.135618i 0.824217 0.566274i \(-0.191616\pi\)
−0.902516 + 0.430656i \(0.858282\pi\)
\(368\) 0 0
\(369\) 10.0000 0.520579
\(370\) 0 0
\(371\) −5.00000 + 8.66025i −0.259587 + 0.449618i
\(372\) 0 0
\(373\) −9.50000 + 16.4545i −0.491891 + 0.851981i −0.999956 0.00933789i \(-0.997028\pi\)
0.508065 + 0.861319i \(0.330361\pi\)
\(374\) 0 0
\(375\) −0.500000 0.866025i −0.0258199 0.0447214i
\(376\) 0 0
\(377\) −3.50000 + 0.866025i −0.180259 + 0.0446026i
\(378\) 0 0
\(379\) 10.5000 + 18.1865i 0.539349 + 0.934179i 0.998939 + 0.0460485i \(0.0146629\pi\)
−0.459590 + 0.888131i \(0.652004\pi\)
\(380\) 0 0
\(381\) 3.50000 6.06218i 0.179310 0.310575i
\(382\) 0 0
\(383\) 1.50000 2.59808i 0.0766464 0.132755i −0.825155 0.564907i \(-0.808912\pi\)
0.901801 + 0.432151i \(0.142245\pi\)
\(384\) 0 0
\(385\) 25.0000 1.27412
\(386\) 0 0
\(387\) 5.00000 + 8.66025i 0.254164 + 0.440225i
\(388\) 0 0
\(389\) −10.0000 −0.507020 −0.253510 0.967333i \(-0.581585\pi\)
−0.253510 + 0.967333i \(0.581585\pi\)
\(390\) 0 0
\(391\) −3.00000 −0.151717
\(392\) 0 0
\(393\) 2.00000 + 3.46410i 0.100887 + 0.174741i
\(394\) 0 0
\(395\) 4.00000 0.201262
\(396\) 0 0
\(397\) 6.50000 11.2583i 0.326226 0.565039i −0.655534 0.755166i \(-0.727556\pi\)
0.981760 + 0.190126i \(0.0608897\pi\)
\(398\) 0 0
\(399\) −7.50000 + 12.9904i −0.375470 + 0.650332i
\(400\) 0 0
\(401\) −13.5000 23.3827i −0.674158 1.16768i −0.976714 0.214544i \(-0.931173\pi\)
0.302556 0.953131i \(-0.402160\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0.500000 + 0.866025i 0.0248452 + 0.0430331i
\(406\) 0 0
\(407\) 17.5000 30.3109i 0.867443 1.50245i
\(408\) 0 0
\(409\) −9.50000 + 16.4545i −0.469745 + 0.813622i −0.999402 0.0345902i \(-0.988987\pi\)
0.529657 + 0.848212i \(0.322321\pi\)
\(410\) 0 0
\(411\) −3.00000 −0.147979
\(412\) 0 0
\(413\) 27.5000 + 47.6314i 1.35319 + 2.34379i
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) 0 0
\(417\) −13.0000 −0.636613
\(418\) 0 0
\(419\) 8.50000 + 14.7224i 0.415252 + 0.719238i 0.995455 0.0952342i \(-0.0303600\pi\)
−0.580203 + 0.814472i \(0.697027\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 0 0
\(423\) 12.0000 20.7846i 0.583460 1.01058i
\(424\) 0 0
\(425\) 0.500000 0.866025i 0.0242536 0.0420084i
\(426\) 0 0
\(427\) 32.5000 + 56.2917i 1.57279 + 2.72414i
\(428\) 0 0
\(429\) −12.5000 12.9904i −0.603506 0.627182i
\(430\) 0 0
\(431\) 10.5000 + 18.1865i 0.505767 + 0.876014i 0.999978 + 0.00667224i \(0.00212386\pi\)
−0.494211 + 0.869342i \(0.664543\pi\)
\(432\) 0 0
\(433\) −3.50000 + 6.06218i −0.168199 + 0.291330i −0.937787 0.347212i \(-0.887129\pi\)
0.769588 + 0.638541i \(0.220462\pi\)
\(434\) 0 0
\(435\) 0.500000 0.866025i 0.0239732 0.0415227i
\(436\) 0 0
\(437\) −9.00000 −0.430528
\(438\) 0 0
\(439\) 14.5000 + 25.1147i 0.692047 + 1.19866i 0.971166 + 0.238404i \(0.0766244\pi\)
−0.279119 + 0.960257i \(0.590042\pi\)
\(440\) 0 0
\(441\) −36.0000 −1.71429
\(442\) 0 0
\(443\) −20.0000 −0.950229 −0.475114 0.879924i \(-0.657593\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(444\) 0 0
\(445\) 3.50000 + 6.06218i 0.165916 + 0.287375i
\(446\) 0 0
\(447\) −11.0000 −0.520282
\(448\) 0 0
\(449\) 10.5000 18.1865i 0.495526 0.858276i −0.504461 0.863434i \(-0.668309\pi\)
0.999987 + 0.00515887i \(0.00164213\pi\)
\(450\) 0 0
\(451\) −12.5000 + 21.6506i −0.588602 + 1.01949i
\(452\) 0 0
\(453\) −12.0000 20.7846i −0.563809 0.976546i
\(454\) 0 0
\(455\) 12.5000 + 12.9904i 0.586009 + 0.608998i
\(456\) 0 0
\(457\) −5.50000 9.52628i −0.257279 0.445621i 0.708233 0.705979i \(-0.249493\pi\)
−0.965512 + 0.260358i \(0.916159\pi\)
\(458\) 0 0
\(459\) 2.50000 4.33013i 0.116690 0.202113i
\(460\) 0 0
\(461\) 16.5000 28.5788i 0.768482 1.33105i −0.169904 0.985461i \(-0.554346\pi\)
0.938386 0.345589i \(-0.112321\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8.00000 −0.370196 −0.185098 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) 0 0
\(469\) 15.0000 0.692636
\(470\) 0 0
\(471\) 5.00000 + 8.66025i 0.230388 + 0.399043i
\(472\) 0 0
\(473\) −25.0000 −1.14950
\(474\) 0 0
\(475\) 1.50000 2.59808i 0.0688247 0.119208i
\(476\) 0 0
\(477\) 2.00000 3.46410i 0.0915737 0.158610i
\(478\) 0 0
\(479\) −5.50000 9.52628i −0.251301 0.435267i 0.712583 0.701588i \(-0.247525\pi\)
−0.963884 + 0.266321i \(0.914192\pi\)
\(480\) 0 0
\(481\) 24.5000 6.06218i 1.11710 0.276412i
\(482\) 0 0
\(483\) 7.50000 + 12.9904i 0.341262 + 0.591083i
\(484\) 0 0
\(485\) 5.50000 9.52628i 0.249742 0.432566i
\(486\) 0 0
\(487\) −8.50000 + 14.7224i −0.385172 + 0.667137i −0.991793 0.127854i \(-0.959191\pi\)
0.606621 + 0.794991i \(0.292524\pi\)
\(488\) 0 0
\(489\) −5.00000 −0.226108
\(490\) 0 0
\(491\) −7.50000 12.9904i −0.338470 0.586248i 0.645675 0.763612i \(-0.276576\pi\)
−0.984145 + 0.177365i \(0.943243\pi\)
\(492\) 0 0
\(493\) 1.00000 0.0450377
\(494\) 0 0
\(495\) −10.0000 −0.449467
\(496\) 0 0
\(497\) −32.5000 56.2917i −1.45782 2.52503i
\(498\) 0 0
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) −6.50000 + 11.2583i −0.290399 + 0.502985i
\(502\) 0 0
\(503\) 5.50000 9.52628i 0.245233 0.424756i −0.716964 0.697110i \(-0.754469\pi\)
0.962197 + 0.272354i \(0.0878022\pi\)
\(504\) 0 0
\(505\) −6.50000 11.2583i −0.289246 0.500989i
\(506\) 0 0
\(507\) 0.500000 12.9904i 0.0222058 0.576923i
\(508\) 0 0
\(509\) −1.50000 2.59808i −0.0664863 0.115158i 0.830866 0.556473i \(-0.187846\pi\)
−0.897352 + 0.441315i \(0.854512\pi\)
\(510\) 0 0
\(511\) 5.00000 8.66025i 0.221187 0.383107i
\(512\) 0 0
\(513\) 7.50000 12.9904i 0.331133 0.573539i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 30.0000 + 51.9615i 1.31940 + 2.28527i
\(518\) 0 0
\(519\) 17.0000 0.746217
\(520\) 0 0
\(521\) 22.0000 0.963837 0.481919 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) 0 0
\(523\) 10.5000 + 18.1865i 0.459133 + 0.795242i 0.998915 0.0465630i \(-0.0148268\pi\)
−0.539782 + 0.841805i \(0.681493\pi\)
\(524\) 0 0
\(525\) −5.00000 −0.218218
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) −11.0000 19.0526i −0.477359 0.826811i
\(532\) 0 0
\(533\) −17.5000 + 4.33013i −0.758009 + 0.187559i
\(534\) 0 0
\(535\) −4.50000 7.79423i −0.194552 0.336974i
\(536\) 0 0
\(537\) 5.50000 9.52628i 0.237343 0.411089i
\(538\) 0 0
\(539\) 45.0000 77.9423i 1.93829 3.35721i
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 0 0
\(543\) 5.00000 + 8.66025i 0.214571 + 0.371647i
\(544\) 0 0
\(545\) −18.0000 −0.771035
\(546\) 0 0
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) 0 0
\(549\) −13.0000 22.5167i −0.554826 0.960988i
\(550\) 0 0
\(551\) 3.00000 0.127804
\(552\) 0 0
\(553\) 10.0000 17.3205i 0.425243 0.736543i
\(554\) 0 0
\(555\) −3.50000 + 6.06218i −0.148567 + 0.257325i
\(556\) 0 0
\(557\) 6.50000 + 11.2583i 0.275414 + 0.477031i 0.970239 0.242147i \(-0.0778518\pi\)
−0.694826 + 0.719178i \(0.744518\pi\)
\(558\) 0 0
\(559\) −12.5000 12.9904i −0.528694 0.549435i
\(560\) 0 0
\(561\) 2.50000 + 4.33013i 0.105550 + 0.182818i
\(562\) 0 0
\(563\) −4.50000 + 7.79423i −0.189652 + 0.328488i −0.945134 0.326682i \(-0.894069\pi\)
0.755482 + 0.655169i \(0.227403\pi\)
\(564\) 0 0
\(565\) −0.500000 + 0.866025i −0.0210352 + 0.0364340i
\(566\) 0 0
\(567\) 5.00000 0.209980
\(568\) 0 0
\(569\) −19.5000 33.7750i −0.817483 1.41592i −0.907532 0.419984i \(-0.862036\pi\)
0.0900490 0.995937i \(-0.471298\pi\)
\(570\) 0 0
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 0 0
\(573\) 15.0000 0.626634
\(574\) 0 0
\(575\) −1.50000 2.59808i −0.0625543 0.108347i
\(576\) 0 0
\(577\) −42.0000 −1.74848 −0.874241 0.485491i \(-0.838641\pi\)
−0.874241 + 0.485491i \(0.838641\pi\)
\(578\) 0 0
\(579\) 11.5000 19.9186i 0.477924 0.827788i
\(580\) 0 0
\(581\) −30.0000 + 51.9615i −1.24461 + 2.15573i
\(582\) 0 0
\(583\) 5.00000 + 8.66025i 0.207079 + 0.358671i
\(584\) 0 0
\(585\) −5.00000 5.19615i −0.206725 0.214834i
\(586\) 0 0
\(587\) −1.50000 2.59808i −0.0619116 0.107234i 0.833408 0.552658i \(-0.186386\pi\)
−0.895320 + 0.445424i \(0.853053\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 13.5000 23.3827i 0.555316 0.961835i
\(592\) 0 0
\(593\) −2.00000 −0.0821302 −0.0410651 0.999156i \(-0.513075\pi\)
−0.0410651 + 0.999156i \(0.513075\pi\)
\(594\) 0 0
\(595\) −2.50000 4.33013i −0.102490 0.177518i
\(596\) 0 0
\(597\) −21.0000 −0.859473
\(598\) 0 0
\(599\) −36.0000 −1.47092 −0.735460 0.677568i \(-0.763034\pi\)
−0.735460 + 0.677568i \(0.763034\pi\)
\(600\) 0 0
\(601\) 2.50000 + 4.33013i 0.101977 + 0.176630i 0.912499 0.409079i \(-0.134150\pi\)
−0.810522 + 0.585708i \(0.800816\pi\)
\(602\) 0 0
\(603\) −6.00000 −0.244339
\(604\) 0 0
\(605\) 7.00000 12.1244i 0.284590 0.492925i
\(606\) 0 0
\(607\) 15.5000 26.8468i 0.629126 1.08968i −0.358602 0.933491i \(-0.616746\pi\)
0.987728 0.156187i \(-0.0499202\pi\)
\(608\) 0 0
\(609\) −2.50000 4.33013i −0.101305 0.175466i
\(610\) 0 0
\(611\) −12.0000 + 41.5692i −0.485468 + 1.68171i
\(612\) 0 0
\(613\) 12.5000 + 21.6506i 0.504870 + 0.874461i 0.999984 + 0.00563283i \(0.00179300\pi\)
−0.495114 + 0.868828i \(0.664874\pi\)
\(614\) 0 0
\(615\) 2.50000 4.33013i 0.100810 0.174608i
\(616\) 0 0
\(617\) −13.5000 + 23.3827i −0.543490 + 0.941351i 0.455211 + 0.890384i \(0.349564\pi\)
−0.998700 + 0.0509678i \(0.983769\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 0 0
\(621\) −7.50000 12.9904i −0.300965 0.521286i
\(622\) 0 0
\(623\) 35.0000 1.40225
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 7.50000 + 12.9904i 0.299521 + 0.518786i
\(628\) 0 0
\(629\) −7.00000 −0.279108
\(630\) 0 0
\(631\) 13.5000 23.3827i 0.537427 0.930850i −0.461615 0.887080i \(-0.652730\pi\)
0.999042 0.0437697i \(-0.0139368\pi\)
\(632\) 0 0
\(633\) −2.50000 + 4.33013i −0.0993661 + 0.172107i
\(634\) 0 0
\(635\) 3.50000 + 6.06218i 0.138893 + 0.240570i
\(636\) 0 0
\(637\) 63.0000 15.5885i 2.49615 0.617637i
\(638\) 0 0
\(639\) 13.0000 + 22.5167i 0.514272 + 0.890745i
\(640\) 0 0
\(641\) −13.5000 + 23.3827i −0.533218 + 0.923561i 0.466029 + 0.884769i \(0.345684\pi\)
−0.999247 + 0.0387913i \(0.987649\pi\)
\(642\) 0 0
\(643\) −2.50000 + 4.33013i −0.0985904 + 0.170764i −0.911101 0.412182i \(-0.864767\pi\)
0.812511 + 0.582946i \(0.198100\pi\)
\(644\) 0 0
\(645\) 5.00000 0.196875
\(646\) 0 0
\(647\) 4.50000 + 7.79423i 0.176913 + 0.306423i 0.940822 0.338902i \(-0.110055\pi\)
−0.763908 + 0.645325i \(0.776722\pi\)
\(648\) 0 0
\(649\) 55.0000 2.15894
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −19.5000 33.7750i −0.763094 1.32172i −0.941248 0.337715i \(-0.890346\pi\)
0.178154 0.984003i \(-0.442987\pi\)
\(654\) 0 0
\(655\) −4.00000 −0.156293
\(656\) 0 0
\(657\) −2.00000 + 3.46410i −0.0780274 + 0.135147i
\(658\) 0 0
\(659\) −8.50000 + 14.7224i −0.331113 + 0.573505i −0.982730 0.185043i \(-0.940757\pi\)
0.651617 + 0.758548i \(0.274091\pi\)
\(660\) 0 0
\(661\) −1.50000 2.59808i −0.0583432 0.101053i 0.835379 0.549675i \(-0.185248\pi\)
−0.893722 + 0.448622i \(0.851915\pi\)
\(662\) 0 0
\(663\) −1.00000 + 3.46410i −0.0388368 + 0.134535i
\(664\) 0 0
\(665\) −7.50000 12.9904i −0.290838 0.503745i
\(666\) 0 0
\(667\) 1.50000 2.59808i 0.0580802 0.100598i
\(668\) 0 0
\(669\) 9.50000 16.4545i 0.367291 0.636167i
\(670\) 0 0
\(671\) 65.0000 2.50930
\(672\) 0 0
\(673\) −5.50000 9.52628i −0.212009 0.367211i 0.740334 0.672239i \(-0.234667\pi\)
−0.952343 + 0.305028i \(0.901334\pi\)
\(674\) 0 0
\(675\) 5.00000 0.192450
\(676\) 0 0
\(677\) 42.0000 1.61419 0.807096 0.590421i \(-0.201038\pi\)
0.807096 + 0.590421i \(0.201038\pi\)
\(678\) 0 0
\(679\) −27.5000 47.6314i −1.05535 1.82793i
\(680\) 0 0
\(681\) −17.0000 −0.651441
\(682\) 0 0
\(683\) −24.5000 + 42.4352i −0.937466 + 1.62374i −0.167291 + 0.985908i \(0.553502\pi\)
−0.770176 + 0.637832i \(0.779831\pi\)
\(684\) 0 0
\(685\) 1.50000 2.59808i 0.0573121 0.0992674i
\(686\) 0 0
\(687\) 5.00000 + 8.66025i 0.190762 + 0.330409i
\(688\) 0 0
\(689\) −2.00000 + 6.92820i −0.0761939 + 0.263944i
\(690\) 0 0
\(691\) 2.50000 + 4.33013i 0.0951045 + 0.164726i 0.909652 0.415371i \(-0.136348\pi\)
−0.814548 + 0.580097i \(0.803015\pi\)
\(692\) 0 0
\(693\) −25.0000 + 43.3013i −0.949671 + 1.64488i
\(694\) 0 0
\(695\) 6.50000 11.2583i 0.246559 0.427053i
\(696\) 0 0
\(697\) 5.00000 0.189389
\(698\) 0 0
\(699\) 3.00000 + 5.19615i 0.113470 + 0.196537i
\(700\) 0 0
\(701\) 26.0000 0.982006 0.491003 0.871158i \(-0.336630\pi\)
0.491003 + 0.871158i \(0.336630\pi\)
\(702\) 0 0
\(703\) −21.0000 −0.792030
\(704\) 0 0
\(705\) −6.00000 10.3923i −0.225973 0.391397i
\(706\) 0 0
\(707\) −65.0000 −2.44458
\(708\) 0 0
\(709\) −11.5000 + 19.9186i −0.431892 + 0.748058i −0.997036 0.0769337i \(-0.975487\pi\)
0.565145 + 0.824992i \(0.308820\pi\)
\(710\) 0 0
\(711\) −4.00000 + 6.92820i −0.150012 + 0.259828i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 17.5000 4.33013i 0.654463 0.161938i
\(716\) 0 0
\(717\) −4.00000 6.92820i −0.149383 0.258738i
\(718\) 0 0
\(719\) −16.5000 + 28.5788i −0.615346 + 1.06581i 0.374978 + 0.927034i \(0.377650\pi\)
−0.990324 + 0.138777i \(0.955683\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −11.0000 −0.409094
\(724\) 0 0
\(725\) 0.500000 + 0.866025i 0.0185695 + 0.0321634i
\(726\) 0 0
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 2.50000 + 4.33013i 0.0924658 + 0.160156i
\(732\) 0 0
\(733\) −34.0000 −1.25582 −0.627909 0.778287i \(-0.716089\pi\)
−0.627909 + 0.778287i \(0.716089\pi\)
\(734\) 0 0
\(735\) −9.00000 + 15.5885i −0.331970 + 0.574989i
\(736\) 0 0
\(737\) 7.50000 12.9904i 0.276266 0.478507i
\(738\) 0 0
\(739\) −7.50000 12.9904i −0.275892 0.477859i 0.694468 0.719524i \(-0.255640\pi\)
−0.970360 + 0.241665i \(0.922307\pi\)
\(740\) 0 0
\(741\) −3.00000 + 10.3923i −0.110208 + 0.381771i
\(742\) 0 0
\(743\) 4.50000 + 7.79423i 0.165089 + 0.285943i 0.936687 0.350168i \(-0.113876\pi\)
−0.771598 + 0.636111i \(0.780542\pi\)
\(744\) 0 0
\(745\) 5.50000 9.52628i 0.201504 0.349016i
\(746\) 0 0
\(747\) 12.0000 20.7846i 0.439057 0.760469i
\(748\) 0 0
\(749\) −45.0000 −1.64426
\(750\) 0 0
\(751\) 12.5000 + 21.6506i 0.456131 + 0.790043i 0.998752 0.0499348i \(-0.0159013\pi\)
−0.542621 + 0.839978i \(0.682568\pi\)
\(752\) 0 0
\(753\) 15.0000 0.546630
\(754\) 0 0
\(755\) 24.0000 0.873449
\(756\) 0 0
\(757\) 4.50000 + 7.79423i 0.163555 + 0.283286i 0.936141 0.351624i \(-0.114370\pi\)
−0.772586 + 0.634910i \(0.781037\pi\)
\(758\) 0 0
\(759\) 15.0000 0.544466
\(760\) 0 0
\(761\) −9.50000 + 16.4545i −0.344375 + 0.596475i −0.985240 0.171179i \(-0.945242\pi\)
0.640865 + 0.767653i \(0.278576\pi\)
\(762\) 0 0
\(763\) −45.0000 + 77.9423i −1.62911 + 2.82170i
\(764\) 0 0
\(765\) 1.00000 + 1.73205i 0.0361551 + 0.0626224i
\(766\) 0 0
\(767\) 27.5000 + 28.5788i 0.992967 + 1.03192i
\(768\) 0 0
\(769\) −9.50000 16.4545i −0.342579 0.593364i 0.642332 0.766426i \(-0.277967\pi\)
−0.984911 + 0.173063i \(0.944634\pi\)
\(770\) 0 0
\(771\) 7.50000 12.9904i 0.270106 0.467837i
\(772\) 0 0
\(773\) 18.5000 32.0429i 0.665399 1.15250i −0.313778 0.949496i \(-0.601595\pi\)
0.979177 0.203008i \(-0.0650718\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 17.5000 + 30.3109i 0.627809 + 1.08740i
\(778\) 0 0
\(779\) 15.0000 0.537431
\(780\) 0 0
\(781\) −65.0000 −2.32588
\(782\) 0 0
\(783\) 2.50000 + 4.33013i 0.0893427 + 0.154746i
\(784\) 0 0
\(785\) −10.0000 −0.356915
\(786\) 0 0
\(787\) 5.50000 9.52628i 0.196054 0.339575i −0.751192 0.660084i \(-0.770521\pi\)
0.947245 + 0.320509i \(0.103854\pi\)
\(788\) 0 0
\(789\) 5.50000 9.52628i 0.195805 0.339145i
\(790\) 0 0
\(791\) 2.50000 + 4.33013i 0.0888898 + 0.153962i
\(792\) 0 0
\(793\) 32.5000 + 33.7750i 1.15411 + 1.19939i
\(794\) 0 0
\(795\) −1.00000 1.73205i −0.0354663 0.0614295i