Properties

Label 1008.2.r.a.673.1
Level 1008
Weight 2
Character 1008.673
Analytic conductor 8.049
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 673.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1008.673
Dual form 1008.2.r.a.337.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.50000 + 2.59808i) q^{9} +(0.500000 - 0.866025i) q^{11} +(3.00000 + 5.19615i) q^{13} +3.46410i q^{15} -5.00000 q^{17} +7.00000 q^{19} +(1.50000 - 0.866025i) q^{21} +(2.00000 + 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{25} -5.19615i q^{27} +(2.00000 - 3.46410i) q^{29} +(-3.00000 - 5.19615i) q^{31} +(-1.50000 + 0.866025i) q^{33} +2.00000 q^{35} +2.00000 q^{37} -10.3923i q^{39} +(-1.50000 - 2.59808i) q^{41} +(-0.500000 + 0.866025i) q^{43} +(3.00000 - 5.19615i) q^{45} +(-0.500000 - 0.866025i) q^{49} +(7.50000 + 4.33013i) q^{51} +12.0000 q^{53} -2.00000 q^{55} +(-10.5000 - 6.06218i) q^{57} +(-3.50000 - 6.06218i) q^{59} +(6.00000 - 10.3923i) q^{61} -3.00000 q^{63} +(6.00000 - 10.3923i) q^{65} +(6.50000 + 11.2583i) q^{67} -6.92820i q^{69} +8.00000 q^{71} +1.00000 q^{73} +(-1.50000 + 0.866025i) q^{75} +(0.500000 + 0.866025i) q^{77} +(-3.00000 + 5.19615i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(8.00000 - 13.8564i) q^{83} +(5.00000 + 8.66025i) q^{85} +(-6.00000 + 3.46410i) q^{87} -6.00000 q^{89} -6.00000 q^{91} +10.3923i q^{93} +(-7.00000 - 12.1244i) q^{95} +(2.50000 - 4.33013i) q^{97} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 3q^{3} - 2q^{5} - q^{7} + 3q^{9} + O(q^{10}) \) \( 2q - 3q^{3} - 2q^{5} - q^{7} + 3q^{9} + q^{11} + 6q^{13} - 10q^{17} + 14q^{19} + 3q^{21} + 4q^{23} + q^{25} + 4q^{29} - 6q^{31} - 3q^{33} + 4q^{35} + 4q^{37} - 3q^{41} - q^{43} + 6q^{45} - q^{49} + 15q^{51} + 24q^{53} - 4q^{55} - 21q^{57} - 7q^{59} + 12q^{61} - 6q^{63} + 12q^{65} + 13q^{67} + 16q^{71} + 2q^{73} - 3q^{75} + q^{77} - 6q^{79} - 9q^{81} + 16q^{83} + 10q^{85} - 12q^{87} - 12q^{89} - 12q^{91} - 14q^{95} + 5q^{97} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) 0.500000 0.866025i 0.150756 0.261116i −0.780750 0.624844i \(-0.785163\pi\)
0.931505 + 0.363727i \(0.118496\pi\)
\(12\) 0 0
\(13\) 3.00000 + 5.19615i 0.832050 + 1.44115i 0.896410 + 0.443227i \(0.146166\pi\)
−0.0643593 + 0.997927i \(0.520500\pi\)
\(14\) 0 0
\(15\) 3.46410i 0.894427i
\(16\) 0 0
\(17\) −5.00000 −1.21268 −0.606339 0.795206i \(-0.707363\pi\)
−0.606339 + 0.795206i \(0.707363\pi\)
\(18\) 0 0
\(19\) 7.00000 1.60591 0.802955 0.596040i \(-0.203260\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) 1.50000 0.866025i 0.327327 0.188982i
\(22\) 0 0
\(23\) 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) 0 0
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 2.00000 3.46410i 0.371391 0.643268i −0.618389 0.785872i \(-0.712214\pi\)
0.989780 + 0.142605i \(0.0455477\pi\)
\(30\) 0 0
\(31\) −3.00000 5.19615i −0.538816 0.933257i −0.998968 0.0454165i \(-0.985539\pi\)
0.460152 0.887840i \(-0.347795\pi\)
\(32\) 0 0
\(33\) −1.50000 + 0.866025i −0.261116 + 0.150756i
\(34\) 0 0
\(35\) 2.00000 0.338062
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 10.3923i 1.66410i
\(40\) 0 0
\(41\) −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i \(-0.241934\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(42\) 0 0
\(43\) −0.500000 + 0.866025i −0.0762493 + 0.132068i −0.901629 0.432511i \(-0.857628\pi\)
0.825380 + 0.564578i \(0.190961\pi\)
\(44\) 0 0
\(45\) 3.00000 5.19615i 0.447214 0.774597i
\(46\) 0 0
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) 7.50000 + 4.33013i 1.05021 + 0.606339i
\(52\) 0 0
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) −10.5000 6.06218i −1.39076 0.802955i
\(58\) 0 0
\(59\) −3.50000 6.06218i −0.455661 0.789228i 0.543065 0.839691i \(-0.317264\pi\)
−0.998726 + 0.0504625i \(0.983930\pi\)
\(60\) 0 0
\(61\) 6.00000 10.3923i 0.768221 1.33060i −0.170305 0.985391i \(-0.554475\pi\)
0.938527 0.345207i \(-0.112191\pi\)
\(62\) 0 0
\(63\) −3.00000 −0.377964
\(64\) 0 0
\(65\) 6.00000 10.3923i 0.744208 1.28901i
\(66\) 0 0
\(67\) 6.50000 + 11.2583i 0.794101 + 1.37542i 0.923408 + 0.383819i \(0.125391\pi\)
−0.129307 + 0.991605i \(0.541275\pi\)
\(68\) 0 0
\(69\) 6.92820i 0.834058i
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) 1.00000 0.117041 0.0585206 0.998286i \(-0.481362\pi\)
0.0585206 + 0.998286i \(0.481362\pi\)
\(74\) 0 0
\(75\) −1.50000 + 0.866025i −0.173205 + 0.100000i
\(76\) 0 0
\(77\) 0.500000 + 0.866025i 0.0569803 + 0.0986928i
\(78\) 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
\(83\) 8.00000 13.8564i 0.878114 1.52094i 0.0247060 0.999695i \(-0.492135\pi\)
0.853408 0.521243i \(-0.174532\pi\)
\(84\) 0 0
\(85\) 5.00000 + 8.66025i 0.542326 + 0.939336i
\(86\) 0 0
\(87\) −6.00000 + 3.46410i −0.643268 + 0.371391i
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) −6.00000 −0.628971
\(92\) 0 0
\(93\) 10.3923i 1.07763i
\(94\) 0 0
\(95\) −7.00000 12.1244i −0.718185 1.24393i
\(96\) 0 0
\(97\) 2.50000 4.33013i 0.253837 0.439658i −0.710742 0.703452i \(-0.751641\pi\)
0.964579 + 0.263795i \(0.0849741\pi\)
\(98\) 0 0
\(99\) 3.00000 0.301511
\(100\) 0 0
\(101\) 2.00000 3.46410i 0.199007 0.344691i −0.749199 0.662344i \(-0.769562\pi\)
0.948207 + 0.317653i \(0.102895\pi\)
\(102\) 0 0
\(103\) 7.00000 + 12.1244i 0.689730 + 1.19465i 0.971925 + 0.235291i \(0.0756043\pi\)
−0.282194 + 0.959357i \(0.591062\pi\)
\(104\) 0 0
\(105\) −3.00000 1.73205i −0.292770 0.169031i
\(106\) 0 0
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 0 0
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 0 0
\(111\) −3.00000 1.73205i −0.284747 0.164399i
\(112\) 0 0
\(113\) 5.00000 + 8.66025i 0.470360 + 0.814688i 0.999425 0.0338931i \(-0.0107906\pi\)
−0.529065 + 0.848581i \(0.677457\pi\)
\(114\) 0 0
\(115\) 4.00000 6.92820i 0.373002 0.646058i
\(116\) 0 0
\(117\) −9.00000 + 15.5885i −0.832050 + 1.44115i
\(118\) 0 0
\(119\) 2.50000 4.33013i 0.229175 0.396942i
\(120\) 0 0
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 0 0
\(123\) 5.19615i 0.468521i
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 12.0000 1.06483 0.532414 0.846484i \(-0.321285\pi\)
0.532414 + 0.846484i \(0.321285\pi\)
\(128\) 0 0
\(129\) 1.50000 0.866025i 0.132068 0.0762493i
\(130\) 0 0
\(131\) −2.00000 3.46410i −0.174741 0.302660i 0.765331 0.643637i \(-0.222575\pi\)
−0.940072 + 0.340977i \(0.889242\pi\)
\(132\) 0 0
\(133\) −3.50000 + 6.06218i −0.303488 + 0.525657i
\(134\) 0 0
\(135\) −9.00000 + 5.19615i −0.774597 + 0.447214i
\(136\) 0 0
\(137\) 9.50000 16.4545i 0.811640 1.40580i −0.100076 0.994980i \(-0.531909\pi\)
0.911716 0.410822i \(-0.134758\pi\)
\(138\) 0 0
\(139\) −2.50000 4.33013i −0.212047 0.367277i 0.740308 0.672268i \(-0.234680\pi\)
−0.952355 + 0.304991i \(0.901346\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 6.00000 0.501745
\(144\) 0 0
\(145\) −8.00000 −0.664364
\(146\) 0 0
\(147\) 1.73205i 0.142857i
\(148\) 0 0
\(149\) 12.0000 + 20.7846i 0.983078 + 1.70274i 0.650183 + 0.759778i \(0.274692\pi\)
0.332896 + 0.942964i \(0.391974\pi\)
\(150\) 0 0
\(151\) 5.00000 8.66025i 0.406894 0.704761i −0.587646 0.809118i \(-0.699945\pi\)
0.994540 + 0.104357i \(0.0332784\pi\)
\(152\) 0 0
\(153\) −7.50000 12.9904i −0.606339 1.05021i
\(154\) 0 0
\(155\) −6.00000 + 10.3923i −0.481932 + 0.834730i
\(156\) 0 0
\(157\) −1.00000 1.73205i −0.0798087 0.138233i 0.823359 0.567521i \(-0.192098\pi\)
−0.903167 + 0.429289i \(0.858764\pi\)
\(158\) 0 0
\(159\) −18.0000 10.3923i −1.42749 0.824163i
\(160\) 0 0
\(161\) −4.00000 −0.315244
\(162\) 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
\(167\) 10.0000 + 17.3205i 0.773823 + 1.34030i 0.935454 + 0.353450i \(0.114991\pi\)
−0.161630 + 0.986851i \(0.551675\pi\)
\(168\) 0 0
\(169\) −11.5000 + 19.9186i −0.884615 + 1.53220i
\(170\) 0 0
\(171\) 10.5000 + 18.1865i 0.802955 + 1.39076i
\(172\) 0 0
\(173\) −1.00000 + 1.73205i −0.0760286 + 0.131685i −0.901533 0.432710i \(-0.857557\pi\)
0.825505 + 0.564396i \(0.190891\pi\)
\(174\) 0 0
\(175\) 0.500000 + 0.866025i 0.0377964 + 0.0654654i
\(176\) 0 0
\(177\) 12.1244i 0.911322i
\(178\) 0 0
\(179\) −24.0000 −1.79384 −0.896922 0.442189i \(-0.854202\pi\)
−0.896922 + 0.442189i \(0.854202\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) −18.0000 + 10.3923i −1.33060 + 0.768221i
\(184\) 0 0
\(185\) −2.00000 3.46410i −0.147043 0.254686i
\(186\) 0 0
\(187\) −2.50000 + 4.33013i −0.182818 + 0.316650i
\(188\) 0 0
\(189\) 4.50000 + 2.59808i 0.327327 + 0.188982i
\(190\) 0 0
\(191\) 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i \(-0.690384\pi\)
0.997225 + 0.0744412i \(0.0237173\pi\)
\(192\) 0 0
\(193\) −8.50000 14.7224i −0.611843 1.05974i −0.990930 0.134382i \(-0.957095\pi\)
0.379086 0.925361i \(-0.376238\pi\)
\(194\) 0 0
\(195\) −18.0000 + 10.3923i −1.28901 + 0.744208i
\(196\) 0 0
\(197\) 10.0000 0.712470 0.356235 0.934396i \(-0.384060\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(198\) 0 0
\(199\) −14.0000 −0.992434 −0.496217 0.868199i \(-0.665278\pi\)
−0.496217 + 0.868199i \(0.665278\pi\)
\(200\) 0 0
\(201\) 22.5167i 1.58820i
\(202\) 0 0
\(203\) 2.00000 + 3.46410i 0.140372 + 0.243132i
\(204\) 0 0
\(205\) −3.00000 + 5.19615i −0.209529 + 0.362915i
\(206\) 0 0
\(207\) −6.00000 + 10.3923i −0.417029 + 0.722315i
\(208\) 0 0
\(209\) 3.50000 6.06218i 0.242100 0.419330i
\(210\) 0 0
\(211\) −8.00000 13.8564i −0.550743 0.953914i −0.998221 0.0596196i \(-0.981011\pi\)
0.447478 0.894295i \(-0.352322\pi\)
\(212\) 0 0
\(213\) −12.0000 6.92820i −0.822226 0.474713i
\(214\) 0 0
\(215\) 2.00000 0.136399
\(216\) 0 0
\(217\) 6.00000 0.407307
\(218\) 0 0
\(219\) −1.50000 0.866025i −0.101361 0.0585206i
\(220\) 0 0
\(221\) −15.0000 25.9808i −1.00901 1.74766i
\(222\) 0 0
\(223\) −2.00000 + 3.46410i −0.133930 + 0.231973i −0.925188 0.379509i \(-0.876093\pi\)
0.791258 + 0.611482i \(0.209426\pi\)
\(224\) 0 0
\(225\) 3.00000 0.200000
\(226\) 0 0
\(227\) 1.50000 2.59808i 0.0995585 0.172440i −0.811943 0.583736i \(-0.801590\pi\)
0.911502 + 0.411296i \(0.134924\pi\)
\(228\) 0 0
\(229\) 13.0000 + 22.5167i 0.859064 + 1.48794i 0.872823 + 0.488037i \(0.162287\pi\)
−0.0137585 + 0.999905i \(0.504380\pi\)
\(230\) 0 0
\(231\) 1.73205i 0.113961i
\(232\) 0 0
\(233\) −29.0000 −1.89985 −0.949927 0.312473i \(-0.898843\pi\)
−0.949927 + 0.312473i \(0.898843\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 9.00000 5.19615i 0.584613 0.337526i
\(238\) 0 0
\(239\) 3.00000 + 5.19615i 0.194054 + 0.336111i 0.946590 0.322440i \(-0.104503\pi\)
−0.752536 + 0.658551i \(0.771170\pi\)
\(240\) 0 0
\(241\) −11.5000 + 19.9186i −0.740780 + 1.28307i 0.211360 + 0.977408i \(0.432211\pi\)
−0.952141 + 0.305661i \(0.901123\pi\)
\(242\) 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
\(247\) 21.0000 + 36.3731i 1.33620 + 2.31436i
\(248\) 0 0
\(249\) −24.0000 + 13.8564i −1.52094 + 0.878114i
\(250\) 0 0
\(251\) −3.00000 −0.189358 −0.0946792 0.995508i \(-0.530183\pi\)
−0.0946792 + 0.995508i \(0.530183\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) 0 0
\(255\) 17.3205i 1.08465i
\(256\) 0 0
\(257\) 7.50000 + 12.9904i 0.467837 + 0.810318i 0.999325 0.0367485i \(-0.0117000\pi\)
−0.531487 + 0.847066i \(0.678367\pi\)
\(258\) 0 0
\(259\) −1.00000 + 1.73205i −0.0621370 + 0.107624i
\(260\) 0 0
\(261\) 12.0000 0.742781
\(262\) 0 0
\(263\) 9.00000 15.5885i 0.554964 0.961225i −0.442943 0.896550i \(-0.646065\pi\)
0.997906 0.0646755i \(-0.0206012\pi\)
\(264\) 0 0
\(265\) −12.0000 20.7846i −0.737154 1.27679i
\(266\) 0 0
\(267\) 9.00000 + 5.19615i 0.550791 + 0.317999i
\(268\) 0 0
\(269\) 20.0000 1.21942 0.609711 0.792624i \(-0.291286\pi\)
0.609711 + 0.792624i \(0.291286\pi\)
\(270\) 0 0
\(271\) 6.00000 0.364474 0.182237 0.983255i \(-0.441666\pi\)
0.182237 + 0.983255i \(0.441666\pi\)
\(272\) 0 0
\(273\) 9.00000 + 5.19615i 0.544705 + 0.314485i
\(274\) 0 0
\(275\) −0.500000 0.866025i −0.0301511 0.0522233i
\(276\) 0 0
\(277\) −1.00000 + 1.73205i −0.0600842 + 0.104069i −0.894503 0.447062i \(-0.852470\pi\)
0.834419 + 0.551131i \(0.185804\pi\)
\(278\) 0 0
\(279\) 9.00000 15.5885i 0.538816 0.933257i
\(280\) 0 0
\(281\) −11.0000 + 19.0526i −0.656205 + 1.13658i 0.325385 + 0.945582i \(0.394506\pi\)
−0.981590 + 0.190999i \(0.938827\pi\)
\(282\) 0 0
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) 0 0
\(285\) 24.2487i 1.43637i
\(286\) 0 0
\(287\) 3.00000 0.177084
\(288\) 0 0
\(289\) 8.00000 0.470588
\(290\) 0 0
\(291\) −7.50000 + 4.33013i −0.439658 + 0.253837i
\(292\) 0 0
\(293\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(294\) 0 0
\(295\) −7.00000 + 12.1244i −0.407556 + 0.705907i
\(296\) 0 0
\(297\) −4.50000 2.59808i −0.261116 0.150756i
\(298\) 0 0
\(299\) −12.0000 + 20.7846i −0.693978 + 1.20201i
\(300\) 0 0
\(301\) −0.500000 0.866025i −0.0288195 0.0499169i
\(302\) 0 0
\(303\) −6.00000 + 3.46410i −0.344691 + 0.199007i
\(304\) 0 0
\(305\) −24.0000 −1.37424
\(306\) 0 0
\(307\) −7.00000 −0.399511 −0.199756 0.979846i \(-0.564015\pi\)
−0.199756 + 0.979846i \(0.564015\pi\)
\(308\) 0 0
\(309\) 24.2487i 1.37946i
\(310\) 0 0
\(311\) 1.00000 + 1.73205i 0.0567048 + 0.0982156i 0.892984 0.450088i \(-0.148607\pi\)
−0.836280 + 0.548303i \(0.815274\pi\)
\(312\) 0 0
\(313\) 8.50000 14.7224i 0.480448 0.832161i −0.519300 0.854592i \(-0.673807\pi\)
0.999748 + 0.0224310i \(0.00714060\pi\)
\(314\) 0 0
\(315\) 3.00000 + 5.19615i 0.169031 + 0.292770i
\(316\) 0 0
\(317\) 3.00000 5.19615i 0.168497 0.291845i −0.769395 0.638774i \(-0.779442\pi\)
0.937892 + 0.346929i \(0.112775\pi\)
\(318\) 0 0
\(319\) −2.00000 3.46410i −0.111979 0.193952i
\(320\) 0 0
\(321\) 4.50000 + 2.59808i 0.251166 + 0.145010i
\(322\) 0 0
\(323\) −35.0000 −1.94745
\(324\) 0 0
\(325\) 6.00000 0.332820
\(326\) 0 0
\(327\) 3.00000 + 1.73205i 0.165900 + 0.0957826i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 4.00000 6.92820i 0.219860 0.380808i −0.734905 0.678170i \(-0.762773\pi\)
0.954765 + 0.297361i \(0.0961066\pi\)
\(332\) 0 0
\(333\) 3.00000 + 5.19615i 0.164399 + 0.284747i
\(334\) 0 0
\(335\) 13.0000 22.5167i 0.710266 1.23022i
\(336\) 0 0
\(337\) 4.50000 + 7.79423i 0.245131 + 0.424579i 0.962168 0.272456i \(-0.0878358\pi\)
−0.717038 + 0.697034i \(0.754502\pi\)
\(338\) 0 0
\(339\) 17.3205i 0.940721i
\(340\) 0 0
\(341\) −6.00000 −0.324918
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −12.0000 + 6.92820i −0.646058 + 0.373002i
\(346\) 0 0
\(347\) −1.50000 2.59808i −0.0805242 0.139472i 0.822951 0.568112i \(-0.192326\pi\)
−0.903475 + 0.428640i \(0.858993\pi\)
\(348\) 0 0
\(349\) 7.00000 12.1244i 0.374701 0.649002i −0.615581 0.788074i \(-0.711079\pi\)
0.990282 + 0.139072i \(0.0444119\pi\)
\(350\) 0 0
\(351\) 27.0000 15.5885i 1.44115 0.832050i
\(352\) 0 0
\(353\) 7.50000 12.9904i 0.399185 0.691408i −0.594441 0.804139i \(-0.702627\pi\)
0.993626 + 0.112731i \(0.0359599\pi\)
\(354\) 0 0
\(355\) −8.00000 13.8564i −0.424596 0.735422i
\(356\) 0 0
\(357\) −7.50000 + 4.33013i −0.396942 + 0.229175i
\(358\) 0 0
\(359\) −2.00000 −0.105556 −0.0527780 0.998606i \(-0.516808\pi\)
−0.0527780 + 0.998606i \(0.516808\pi\)
\(360\) 0 0
\(361\) 30.0000 1.57895
\(362\) 0 0
\(363\) 17.3205i 0.909091i
\(364\) 0 0
\(365\) −1.00000 1.73205i −0.0523424 0.0906597i
\(366\) 0 0
\(367\) −11.0000 + 19.0526i −0.574195 + 0.994535i 0.421933 + 0.906627i \(0.361352\pi\)
−0.996129 + 0.0879086i \(0.971982\pi\)
\(368\) 0 0
\(369\) 4.50000 7.79423i 0.234261 0.405751i
\(370\) 0 0
\(371\) −6.00000 + 10.3923i −0.311504 + 0.539542i
\(372\) 0 0
\(373\) −11.0000 19.0526i −0.569558 0.986504i −0.996610 0.0822766i \(-0.973781\pi\)
0.427051 0.904227i \(-0.359552\pi\)
\(374\) 0 0
\(375\) 18.0000 + 10.3923i 0.929516 + 0.536656i
\(376\) 0 0
\(377\) 24.0000 1.23606
\(378\) 0 0
\(379\) 17.0000 0.873231 0.436616 0.899648i \(-0.356177\pi\)
0.436616 + 0.899648i \(0.356177\pi\)
\(380\) 0 0
\(381\) −18.0000 10.3923i −0.922168 0.532414i
\(382\) 0 0
\(383\) 2.00000 + 3.46410i 0.102195 + 0.177007i 0.912589 0.408879i \(-0.134080\pi\)
−0.810394 + 0.585886i \(0.800747\pi\)
\(384\) 0 0
\(385\) 1.00000 1.73205i 0.0509647 0.0882735i
\(386\) 0 0
\(387\) −3.00000 −0.152499
\(388\) 0 0
\(389\) −4.00000 + 6.92820i −0.202808 + 0.351274i −0.949432 0.313972i \(-0.898340\pi\)
0.746624 + 0.665246i \(0.231673\pi\)
\(390\) 0 0
\(391\) −10.0000 17.3205i −0.505722 0.875936i
\(392\) 0 0
\(393\) 6.92820i 0.349482i
\(394\) 0 0
\(395\) 12.0000 0.603786
\(396\) 0 0
\(397\) 18.0000 0.903394 0.451697 0.892171i \(-0.350819\pi\)
0.451697 + 0.892171i \(0.350819\pi\)
\(398\) 0 0
\(399\) 10.5000 6.06218i 0.525657 0.303488i
\(400\) 0 0
\(401\) −4.50000 7.79423i −0.224719 0.389225i 0.731516 0.681824i \(-0.238813\pi\)
−0.956235 + 0.292599i \(0.905480\pi\)
\(402\) 0 0
\(403\) 18.0000 31.1769i 0.896644 1.55303i
\(404\) 0 0
\(405\) 18.0000 0.894427
\(406\) 0 0
\(407\) 1.00000 1.73205i 0.0495682 0.0858546i
\(408\) 0 0
\(409\) −5.50000 9.52628i −0.271957 0.471044i 0.697406 0.716677i \(-0.254338\pi\)
−0.969363 + 0.245633i \(0.921004\pi\)
\(410\) 0 0
\(411\) −28.5000 + 16.4545i −1.40580 + 0.811640i
\(412\) 0 0
\(413\) 7.00000 0.344447
\(414\) 0 0
\(415\) −32.0000 −1.57082
\(416\) 0 0
\(417\) 8.66025i 0.424094i
\(418\) 0 0
\(419\) −6.00000 10.3923i −0.293119 0.507697i 0.681426 0.731887i \(-0.261360\pi\)
−0.974546 + 0.224189i \(0.928027\pi\)
\(420\) 0 0
\(421\) 6.00000 10.3923i 0.292422 0.506490i −0.681960 0.731390i \(-0.738872\pi\)
0.974382 + 0.224900i \(0.0722054\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.50000 + 4.33013i −0.121268 + 0.210042i
\(426\) 0 0
\(427\) 6.00000 + 10.3923i 0.290360 + 0.502919i
\(428\) 0 0
\(429\) −9.00000 5.19615i −0.434524 0.250873i
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) −25.0000 −1.20142 −0.600712 0.799466i \(-0.705116\pi\)
−0.600712 + 0.799466i \(0.705116\pi\)
\(434\) 0 0
\(435\) 12.0000 + 6.92820i 0.575356 + 0.332182i
\(436\) 0 0
\(437\) 14.0000 + 24.2487i 0.669711 + 1.15997i
\(438\) 0 0
\(439\) −12.0000 + 20.7846i −0.572729 + 0.991995i 0.423556 + 0.905870i \(0.360782\pi\)
−0.996284 + 0.0861252i \(0.972552\pi\)
\(440\) 0 0
\(441\) 1.50000 2.59808i 0.0714286 0.123718i
\(442\) 0 0
\(443\) 3.50000 6.06218i 0.166290 0.288023i −0.770823 0.637050i \(-0.780155\pi\)
0.937113 + 0.349027i \(0.113488\pi\)
\(444\) 0 0
\(445\) 6.00000 + 10.3923i 0.284427 + 0.492642i
\(446\) 0 0
\(447\) 41.5692i 1.96616i
\(448\) 0 0
\(449\) 17.0000 0.802280 0.401140 0.916017i \(-0.368614\pi\)
0.401140 + 0.916017i \(0.368614\pi\)
\(450\) 0 0
\(451\) −3.00000 −0.141264
\(452\) 0 0
\(453\) −15.0000 + 8.66025i −0.704761 + 0.406894i
\(454\) 0 0
\(455\) 6.00000 + 10.3923i 0.281284 + 0.487199i
\(456\) 0 0
\(457\) −0.500000 + 0.866025i −0.0233890 + 0.0405110i −0.877483 0.479608i \(-0.840779\pi\)
0.854094 + 0.520119i \(0.174112\pi\)
\(458\) 0 0
\(459\) 25.9808i 1.21268i
\(460\) 0 0
\(461\) −7.00000 + 12.1244i −0.326023 + 0.564688i −0.981719 0.190337i \(-0.939042\pi\)
0.655696 + 0.755025i \(0.272375\pi\)
\(462\) 0 0
\(463\) −4.00000 6.92820i −0.185896 0.321981i 0.757982 0.652275i \(-0.226185\pi\)
−0.943878 + 0.330294i \(0.892852\pi\)
\(464\) 0 0
\(465\) 18.0000 10.3923i 0.834730 0.481932i
\(466\) 0 0
\(467\) 13.0000 0.601568 0.300784 0.953692i \(-0.402752\pi\)
0.300784 + 0.953692i \(0.402752\pi\)
\(468\) 0 0
\(469\) −13.0000 −0.600284
\(470\) 0 0
\(471\) 3.46410i 0.159617i
\(472\) 0 0
\(473\) 0.500000 + 0.866025i 0.0229900 + 0.0398199i
\(474\) 0 0
\(475\) 3.50000 6.06218i 0.160591 0.278152i
\(476\) 0 0
\(477\) 18.0000 + 31.1769i 0.824163 + 1.42749i
\(478\) 0 0
\(479\) −10.0000 + 17.3205i −0.456912 + 0.791394i −0.998796 0.0490589i \(-0.984378\pi\)
0.541884 + 0.840453i \(0.317711\pi\)
\(480\) 0 0
\(481\) 6.00000 + 10.3923i 0.273576 + 0.473848i
\(482\) 0 0
\(483\) 6.00000 + 3.46410i 0.273009 + 0.157622i
\(484\) 0 0
\(485\) −10.0000 −0.454077
\(486\) 0 0
\(487\) 10.0000 0.453143 0.226572 0.973995i \(-0.427248\pi\)
0.226572 + 0.973995i \(0.427248\pi\)
\(488\) 0 0
\(489\) −6.00000 3.46410i −0.271329 0.156652i
\(490\) 0 0
\(491\) 16.5000 + 28.5788i 0.744635 + 1.28974i 0.950365 + 0.311136i \(0.100710\pi\)
−0.205731 + 0.978609i \(0.565957\pi\)
\(492\) 0 0
\(493\) −10.0000 + 17.3205i −0.450377 + 0.780076i
\(494\) 0 0
\(495\) −3.00000 5.19615i −0.134840 0.233550i
\(496\) 0 0
\(497\) −4.00000 + 6.92820i −0.179425 + 0.310772i
\(498\) 0 0
\(499\) −14.5000 25.1147i −0.649109 1.12429i −0.983336 0.181797i \(-0.941809\pi\)
0.334227 0.942493i \(-0.391525\pi\)
\(500\) 0 0
\(501\) 34.6410i 1.54765i
\(502\) 0 0
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) 0 0
\(505\) −8.00000 −0.355995
\(506\) 0 0
\(507\) 34.5000 19.9186i 1.53220 0.884615i
\(508\) 0 0
\(509\) −15.0000 25.9808i −0.664863 1.15158i −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) 0 0
\(511\) −0.500000 + 0.866025i −0.0221187 + 0.0383107i
\(512\) 0 0
\(513\) 36.3731i 1.60591i
\(514\) 0 0
\(515\) 14.0000 24.2487i 0.616914 1.06853i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 3.00000 1.73205i 0.131685 0.0760286i
\(520\) 0 0
\(521\) −9.00000 −0.394297 −0.197149 0.980374i \(-0.563168\pi\)
−0.197149 + 0.980374i \(0.563168\pi\)
\(522\) 0 0
\(523\) 28.0000 1.22435 0.612177 0.790721i \(-0.290294\pi\)
0.612177 + 0.790721i \(0.290294\pi\)
\(524\) 0 0
\(525\) 1.73205i 0.0755929i
\(526\) 0 0
\(527\) 15.0000 + 25.9808i 0.653410 + 1.13174i
\(528\) 0 0
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) 10.5000 18.1865i 0.455661 0.789228i
\(532\) 0 0
\(533\) 9.00000 15.5885i 0.389833 0.675211i
\(534\) 0 0
\(535\) 3.00000 + 5.19615i 0.129701 + 0.224649i
\(536\) 0 0
\(537\) 36.0000 + 20.7846i 1.55351 + 0.896922i
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −24.0000 −1.03184 −0.515920 0.856637i \(-0.672550\pi\)
−0.515920 + 0.856637i \(0.672550\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.00000 + 3.46410i 0.0856706 + 0.148386i
\(546\) 0 0
\(547\) −10.5000 + 18.1865i −0.448948 + 0.777600i −0.998318 0.0579790i \(-0.981534\pi\)
0.549370 + 0.835579i \(0.314868\pi\)
\(548\) 0 0
\(549\) 36.0000 1.53644
\(550\) 0 0
\(551\) 14.0000 24.2487i 0.596420 1.03303i
\(552\) 0 0
\(553\) −3.00000 5.19615i −0.127573 0.220963i
\(554\) 0 0
\(555\) 6.92820i 0.294086i
\(556\) 0 0
\(557\) −28.0000 −1.18640 −0.593199 0.805056i \(-0.702135\pi\)
−0.593199 + 0.805056i \(0.702135\pi\)
\(558\) 0 0
\(559\) −6.00000 −0.253773
\(560\) 0 0
\(561\) 7.50000 4.33013i 0.316650 0.182818i
\(562\) 0 0
\(563\) 15.5000 + 26.8468i 0.653247 + 1.13146i 0.982330 + 0.187156i \(0.0599271\pi\)
−0.329083 + 0.944301i \(0.606740\pi\)
\(564\) 0 0
\(565\) 10.0000 17.3205i 0.420703 0.728679i
\(566\) 0 0
\(567\) −4.50000 7.79423i −0.188982 0.327327i
\(568\) 0 0
\(569\) 7.50000 12.9904i 0.314416 0.544585i −0.664897 0.746935i \(-0.731525\pi\)
0.979313 + 0.202350i \(0.0648579\pi\)
\(570\) 0 0
\(571\) −16.5000 28.5788i −0.690504 1.19599i −0.971673 0.236329i \(-0.924056\pi\)
0.281170 0.959658i \(-0.409278\pi\)
\(572\) 0 0
\(573\) −18.0000 + 10.3923i −0.751961 + 0.434145i
\(574\) 0 0
\(575\) 4.00000 0.166812
\(576\) 0 0
\(577\) −35.0000 −1.45707 −0.728535 0.685009i \(-0.759798\pi\)
−0.728535 + 0.685009i \(0.759798\pi\)
\(578\) 0 0
\(579\) 29.4449i 1.22369i
\(580\) 0 0
\(581\) 8.00000 + 13.8564i 0.331896 + 0.574861i
\(582\) 0 0
\(583\) 6.00000 10.3923i 0.248495 0.430405i
\(584\) 0 0
\(585\) 36.0000 1.48842
\(586\) 0 0
\(587\) −23.5000 + 40.7032i −0.969949 + 1.68000i −0.274263 + 0.961655i \(0.588434\pi\)
−0.695686 + 0.718346i \(0.744900\pi\)
\(588\) 0 0
\(589\) −21.0000 36.3731i −0.865290 1.49873i
\(590\) 0 0
\(591\) −15.0000 8.66025i −0.617018 0.356235i
\(592\) 0 0
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 0 0
\(595\) −10.0000 −0.409960
\(596\) 0 0
\(597\) 21.0000 + 12.1244i 0.859473 + 0.496217i
\(598\) 0 0
\(599\) 12.0000 + 20.7846i 0.490307 + 0.849236i 0.999938 0.0111569i \(-0.00355143\pi\)
−0.509631 + 0.860393i \(0.670218\pi\)
\(600\) 0 0
\(601\) 9.50000 16.4545i 0.387513 0.671192i −0.604601 0.796528i \(-0.706668\pi\)
0.992114 + 0.125336i \(0.0400009\pi\)
\(602\) 0 0
\(603\) −19.5000 + 33.7750i −0.794101 + 1.37542i
\(604\) 0 0
\(605\) 10.0000 17.3205i 0.406558 0.704179i
\(606\) 0 0
\(607\) −12.0000 20.7846i −0.487065 0.843621i 0.512824 0.858494i \(-0.328599\pi\)
−0.999889 + 0.0148722i \(0.995266\pi\)
\(608\) 0 0
\(609\) 6.92820i 0.280745i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 42.0000 1.69636 0.848182 0.529705i \(-0.177697\pi\)
0.848182 + 0.529705i \(0.177697\pi\)
\(614\) 0 0
\(615\) 9.00000 5.19615i 0.362915 0.209529i
\(616\) 0 0
\(617\) 8.50000 + 14.7224i 0.342197 + 0.592703i 0.984840 0.173463i \(-0.0554956\pi\)
−0.642643 + 0.766165i \(0.722162\pi\)
\(618\) 0 0
\(619\) 18.5000 32.0429i 0.743578 1.28791i −0.207279 0.978282i \(-0.566461\pi\)
0.950856 0.309633i \(-0.100206\pi\)
\(620\) 0 0
\(621\) 18.0000 10.3923i 0.722315 0.417029i
\(622\) 0 0
\(623\) 3.00000 5.19615i 0.120192 0.208179i
\(624\) 0 0
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 0 0
\(627\) −10.5000 + 6.06218i −0.419330 + 0.242100i
\(628\) 0 0
\(629\) −10.0000 −0.398726
\(630\) 0 0
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 0 0
\(633\) 27.7128i 1.10149i
\(634\) 0 0
\(635\) −12.0000 20.7846i −0.476205 0.824812i
\(636\) 0 0
\(637\) 3.00000 5.19615i 0.118864 0.205879i
\(638\) 0 0
\(639\) 12.0000 + 20.7846i 0.474713 + 0.822226i
\(640\) 0 0
\(641\) −0.500000 + 0.866025i −0.0197488 + 0.0342059i −0.875731 0.482800i \(-0.839620\pi\)
0.855982 + 0.517005i \(0.172953\pi\)
\(642\) 0 0
\(643\) −3.50000 6.06218i −0.138027 0.239069i 0.788723 0.614749i \(-0.210743\pi\)
−0.926750 + 0.375680i \(0.877409\pi\)
\(644\) 0 0
\(645\) −3.00000 1.73205i −0.118125 0.0681994i
\(646\) 0 0
\(647\) −12.0000 −0.471769 −0.235884 0.971781i \(-0.575799\pi\)
−0.235884 + 0.971781i \(0.575799\pi\)
\(648\) 0 0
\(649\) −7.00000 −0.274774
\(650\) 0 0
\(651\) −9.00000 5.19615i −0.352738 0.203653i
\(652\) 0 0
\(653\) 3.00000 + 5.19615i 0.117399 + 0.203341i 0.918736 0.394872i \(-0.129211\pi\)
−0.801337 + 0.598213i \(0.795878\pi\)
\(654\) 0 0
\(655\) −4.00000 + 6.92820i −0.156293 + 0.270707i
\(656\) 0 0
\(657\) 1.50000 + 2.59808i 0.0585206 + 0.101361i
\(658\) 0 0
\(659\) 8.00000 13.8564i 0.311636 0.539769i −0.667081 0.744985i \(-0.732456\pi\)
0.978717 + 0.205216i \(0.0657898\pi\)
\(660\) 0 0
\(661\) −14.0000 24.2487i −0.544537 0.943166i −0.998636 0.0522143i \(-0.983372\pi\)
0.454099 0.890951i \(-0.349961\pi\)
\(662\) 0 0
\(663\) 51.9615i 2.01802i
\(664\) 0 0
\(665\) 14.0000 0.542897
\(666\) 0 0
\(667\) 16.0000 0.619522
\(668\) 0 0
\(669\) 6.00000 3.46410i 0.231973 0.133930i
\(670\) 0 0
\(671\) −6.00000 10.3923i −0.231627 0.401190i
\(672\) 0 0
\(673\) −7.00000 + 12.1244i −0.269830 + 0.467360i −0.968818 0.247774i \(-0.920301\pi\)
0.698988 + 0.715134i \(0.253634\pi\)
\(674\) 0 0
\(675\) −4.50000 2.59808i −0.173205 0.100000i
\(676\) 0 0
\(677\) −15.0000 + 25.9808i −0.576497 + 0.998522i 0.419380 + 0.907811i \(0.362247\pi\)
−0.995877 + 0.0907112i \(0.971086\pi\)
\(678\) 0 0
\(679\) 2.50000 + 4.33013i 0.0959412 + 0.166175i
\(680\) 0 0
\(681\) −4.50000 + 2.59808i −0.172440 + 0.0995585i
\(682\) 0 0
\(683\) −39.0000 −1.49229 −0.746147 0.665782i \(-0.768098\pi\)
−0.746147 + 0.665782i \(0.768098\pi\)
\(684\) 0 0
\(685\) −38.0000 −1.45191
\(686\) 0 0
\(687\) 45.0333i 1.71813i
\(688\) 0 0
\(689\) 36.0000 + 62.3538i 1.37149 + 2.37549i
\(690\) 0 0
\(691\) 16.0000 27.7128i 0.608669 1.05425i −0.382791 0.923835i \(-0.625037\pi\)
0.991460 0.130410i \(-0.0416295\pi\)
\(692\) 0 0
\(693\) −1.50000 + 2.59808i −0.0569803 + 0.0986928i
\(694\) 0 0
\(695\) −5.00000 + 8.66025i −0.189661 + 0.328502i
\(696\) 0 0
\(697\) 7.50000 + 12.9904i 0.284083 + 0.492046i
\(698\) 0 0
\(699\) 43.5000 + 25.1147i 1.64532 + 0.949927i
\(700\) 0 0
\(701\) 8.00000 0.302156 0.151078 0.988522i \(-0.451726\pi\)
0.151078 + 0.988522i \(0.451726\pi\)
\(702\) 0 0
\(703\) 14.0000 0.528020
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.00000 + 3.46410i 0.0752177 + 0.130281i
\(708\) 0 0
\(709\) 2.00000 3.46410i 0.0751116 0.130097i −0.826023 0.563636i \(-0.809402\pi\)
0.901135 + 0.433539i \(0.142735\pi\)
\(710\) 0 0
\(711\) −18.0000 −0.675053
\(712\) 0 0
\(713\) 12.0000 20.7846i 0.449404 0.778390i
\(714\) 0 0
\(715\) −6.00000 10.3923i −0.224387 0.388650i
\(716\) 0 0
\(717\) 10.3923i 0.388108i
\(718\) 0 0
\(719\) −6.00000 −0.223762 −0.111881 0.993722i \(-0.535688\pi\)
−0.111881 + 0.993722i \(0.535688\pi\)
\(720\) 0 0
\(721\) −14.0000 −0.521387
\(722\) 0 0
\(723\) 34.5000 19.9186i 1.28307 0.740780i
\(724\) 0 0
\(725\) −2.00000 3.46410i −0.0742781 0.128654i
\(726\) 0 0
\(727\) −7.00000 + 12.1244i −0.259616 + 0.449667i −0.966139 0.258022i \(-0.916929\pi\)
0.706523 + 0.707690i \(0.250263\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 2.50000 4.33013i 0.0924658 0.160156i
\(732\) 0 0
\(733\) 9.00000 + 15.5885i 0.332423 + 0.575773i 0.982986 0.183679i \(-0.0588007\pi\)
−0.650564 + 0.759452i \(0.725467\pi\)
\(734\) 0 0
\(735\) 3.00000 1.73205i 0.110657 0.0638877i
\(736\) 0 0
\(737\) 13.0000 0.478861
\(738\) 0 0
\(739\) 33.0000 1.21392 0.606962 0.794731i \(-0.292388\pi\)
0.606962 + 0.794731i \(0.292388\pi\)
\(740\) 0 0
\(741\) 72.7461i 2.67240i
\(742\) 0 0
\(743\) −3.00000 5.19615i −0.110059 0.190628i 0.805735 0.592277i \(-0.201771\pi\)
−0.915794 + 0.401648i \(0.868437\pi\)
\(744\) 0 0
\(745\) 24.0000 41.5692i 0.879292 1.52298i
\(746\) 0 0
\(747\) 48.0000 1.75623
\(748\) 0 0
\(749\) 1.50000 2.59808i 0.0548088 0.0949316i
\(750\) 0 0
\(751\) −9.00000 15.5885i −0.328415 0.568831i 0.653783 0.756682i \(-0.273181\pi\)
−0.982197 + 0.187851i \(0.939848\pi\)
\(752\) 0 0
\(753\) 4.50000 + 2.59808i 0.163989 + 0.0946792i
\(754\) 0 0
\(755\) −20.0000 −0.727875
\(756\) 0 0
\(757\) −48.0000 −1.74459 −0.872295 0.488980i \(-0.837369\pi\)
−0.872295 + 0.488980i \(0.837369\pi\)
\(758\) 0 0
\(759\) −6.00000 3.46410i −0.217786 0.125739i
\(760\) 0 0
\(761\) −5.00000 8.66025i −0.181250 0.313934i 0.761057 0.648686i \(-0.224681\pi\)
−0.942306 + 0.334752i \(0.891348\pi\)
\(762\) 0 0
\(763\) 1.00000 1.73205i 0.0362024 0.0627044i
\(764\) 0 0
\(765\) −15.0000 + 25.9808i −0.542326 + 0.939336i
\(766\) 0 0
\(767\) 21.0000 36.3731i 0.758266 1.31336i
\(768\) 0 0
\(769\) −11.0000 19.0526i −0.396670 0.687053i 0.596643 0.802507i \(-0.296501\pi\)
−0.993313 + 0.115454i \(0.963168\pi\)
\(770\) 0 0
\(771\) 25.9808i 0.935674i
\(772\) 0 0
\(773\) −52.0000 −1.87031 −0.935155 0.354239i \(-0.884740\pi\)
−0.935155 + 0.354239i \(0.884740\pi\)
\(774\) 0 0
\(775\) −6.00000 −0.215526
\(776\) 0 0
\(777\) 3.00000 1.73205i 0.107624 0.0621370i
\(778\) 0 0
\(779\) −10.5000 18.1865i −0.376202 0.651600i
\(780\) 0 0
\(781\) 4.00000 6.92820i 0.143131 0.247911i
\(782\) 0 0
\(783\) −18.0000 10.3923i −0.643268 0.371391i
\(784\) 0 0
\(785\) −2.00000 + 3.46410i −0.0713831 + 0.123639i
\(786\) 0 0
\(787\) −6.00000 10.3923i −0.213877 0.370446i 0.739048 0.673653i \(-0.235276\pi\)
−0.952925 + 0.303207i \(0.901942\pi\)
\(788\) 0 0
\(789\) −27.0000 + 15.5885i −0.961225 + 0.554964i
\(790\) 0 0
\(791\) −10.0000 −0.355559
\(792\) 0 0
\(793\) 72.0000 2.55679
\(794\) 0 0
\(795\) 41.5692i 1.47431i
\(796\) 0 0
\(797\) 6.00000 + 10.3923i 0.212531 + 0.368114i 0.952506 0.304520i \(-0.0984960\pi\)
−0.739975 + 0.672634i \(0.765163\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −9.00000 15.5885i −0.317999 0.550791i
\(802\) 0 0
\(803\) 0.500000 0.866025i 0.0176446 0.0305614i
\(804\) 0 0
\(805\) 4.00000 + 6.92820i 0.140981 + 0.244187i
\(806\) 0 0
\(807\) −30.0000 17.3205i −1.05605 0.609711i
\(808\) 0 0
\(809\) −43.0000 −1.51180 −0.755900 0.654687i \(-0.772800\pi\)
−0.755900 + 0.654687i \(0.772800\pi\)