Properties

Label 105.2.b.b.41.2
Level 105
Weight 2
Character 105.41
Analytic conductor 0.838
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 41.2
Root \(0.500000 - 0.866025i\)
Character \(\chi\) = 105.41
Dual form 105.2.b.b.41.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.73205i q^{2} -1.73205i q^{3} -1.00000 q^{4} +1.00000 q^{5} +3.00000 q^{6} +(2.00000 + 1.73205i) q^{7} +1.73205i q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+1.73205i q^{2} -1.73205i q^{3} -1.00000 q^{4} +1.00000 q^{5} +3.00000 q^{6} +(2.00000 + 1.73205i) q^{7} +1.73205i q^{8} -3.00000 q^{9} +1.73205i q^{10} -3.46410i q^{11} +1.73205i q^{12} +(-3.00000 + 3.46410i) q^{14} -1.73205i q^{15} -5.00000 q^{16} -6.00000 q^{17} -5.19615i q^{18} -3.46410i q^{19} -1.00000 q^{20} +(3.00000 - 3.46410i) q^{21} +6.00000 q^{22} +3.46410i q^{23} +3.00000 q^{24} +1.00000 q^{25} +5.19615i q^{27} +(-2.00000 - 1.73205i) q^{28} -6.92820i q^{29} +3.00000 q^{30} +3.46410i q^{31} -5.19615i q^{32} -6.00000 q^{33} -10.3923i q^{34} +(2.00000 + 1.73205i) q^{35} +3.00000 q^{36} -2.00000 q^{37} +6.00000 q^{38} +1.73205i q^{40} -6.00000 q^{41} +(6.00000 + 5.19615i) q^{42} -8.00000 q^{43} +3.46410i q^{44} -3.00000 q^{45} -6.00000 q^{46} +12.0000 q^{47} +8.66025i q^{48} +(1.00000 + 6.92820i) q^{49} +1.73205i q^{50} +10.3923i q^{51} -9.00000 q^{54} -3.46410i q^{55} +(-3.00000 + 3.46410i) q^{56} -6.00000 q^{57} +12.0000 q^{58} +12.0000 q^{59} +1.73205i q^{60} +6.92820i q^{61} -6.00000 q^{62} +(-6.00000 - 5.19615i) q^{63} -1.00000 q^{64} -10.3923i q^{66} +8.00000 q^{67} +6.00000 q^{68} +6.00000 q^{69} +(-3.00000 + 3.46410i) q^{70} +3.46410i q^{71} -5.19615i q^{72} -6.92820i q^{73} -3.46410i q^{74} -1.73205i q^{75} +3.46410i q^{76} +(6.00000 - 6.92820i) q^{77} +8.00000 q^{79} -5.00000 q^{80} +9.00000 q^{81} -10.3923i q^{82} +(-3.00000 + 3.46410i) q^{84} -6.00000 q^{85} -13.8564i q^{86} -12.0000 q^{87} +6.00000 q^{88} -6.00000 q^{89} -5.19615i q^{90} -3.46410i q^{92} +6.00000 q^{93} +20.7846i q^{94} -3.46410i q^{95} -9.00000 q^{96} -6.92820i q^{97} +(-12.0000 + 1.73205i) q^{98} +10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{4} + 2q^{5} + 6q^{6} + 4q^{7} - 6q^{9} + O(q^{10}) \) \( 2q - 2q^{4} + 2q^{5} + 6q^{6} + 4q^{7} - 6q^{9} - 6q^{14} - 10q^{16} - 12q^{17} - 2q^{20} + 6q^{21} + 12q^{22} + 6q^{24} + 2q^{25} - 4q^{28} + 6q^{30} - 12q^{33} + 4q^{35} + 6q^{36} - 4q^{37} + 12q^{38} - 12q^{41} + 12q^{42} - 16q^{43} - 6q^{45} - 12q^{46} + 24q^{47} + 2q^{49} - 18q^{54} - 6q^{56} - 12q^{57} + 24q^{58} + 24q^{59} - 12q^{62} - 12q^{63} - 2q^{64} + 16q^{67} + 12q^{68} + 12q^{69} - 6q^{70} + 12q^{77} + 16q^{79} - 10q^{80} + 18q^{81} - 6q^{84} - 12q^{85} - 24q^{87} + 12q^{88} - 12q^{89} + 12q^{93} - 18q^{96} - 24q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205i 1.22474i 0.790569 + 0.612372i \(0.209785\pi\)
−0.790569 + 0.612372i \(0.790215\pi\)
\(3\) 1.73205i 1.00000i
\(4\) −1.00000 −0.500000
\(5\) 1.00000 0.447214
\(6\) 3.00000 1.22474
\(7\) 2.00000 + 1.73205i 0.755929 + 0.654654i
\(8\) 1.73205i 0.612372i
\(9\) −3.00000 −1.00000
\(10\) 1.73205i 0.547723i
\(11\) 3.46410i 1.04447i −0.852803 0.522233i \(-0.825099\pi\)
0.852803 0.522233i \(-0.174901\pi\)
\(12\) 1.73205i 0.500000i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −3.00000 + 3.46410i −0.801784 + 0.925820i
\(15\) 1.73205i 0.447214i
\(16\) −5.00000 −1.25000
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 5.19615i 1.22474i
\(19\) 3.46410i 0.794719i −0.917663 0.397360i \(-0.869927\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) −1.00000 −0.223607
\(21\) 3.00000 3.46410i 0.654654 0.755929i
\(22\) 6.00000 1.27920
\(23\) 3.46410i 0.722315i 0.932505 + 0.361158i \(0.117618\pi\)
−0.932505 + 0.361158i \(0.882382\pi\)
\(24\) 3.00000 0.612372
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) −2.00000 1.73205i −0.377964 0.327327i
\(29\) 6.92820i 1.28654i −0.765641 0.643268i \(-0.777578\pi\)
0.765641 0.643268i \(-0.222422\pi\)
\(30\) 3.00000 0.547723
\(31\) 3.46410i 0.622171i 0.950382 + 0.311086i \(0.100693\pi\)
−0.950382 + 0.311086i \(0.899307\pi\)
\(32\) 5.19615i 0.918559i
\(33\) −6.00000 −1.04447
\(34\) 10.3923i 1.78227i
\(35\) 2.00000 + 1.73205i 0.338062 + 0.292770i
\(36\) 3.00000 0.500000
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 6.00000 0.973329
\(39\) 0 0
\(40\) 1.73205i 0.273861i
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 6.00000 + 5.19615i 0.925820 + 0.801784i
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 3.46410i 0.522233i
\(45\) −3.00000 −0.447214
\(46\) −6.00000 −0.884652
\(47\) 12.0000 1.75038 0.875190 0.483779i \(-0.160736\pi\)
0.875190 + 0.483779i \(0.160736\pi\)
\(48\) 8.66025i 1.25000i
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 1.73205i 0.244949i
\(51\) 10.3923i 1.45521i
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) −9.00000 −1.22474
\(55\) 3.46410i 0.467099i
\(56\) −3.00000 + 3.46410i −0.400892 + 0.462910i
\(57\) −6.00000 −0.794719
\(58\) 12.0000 1.57568
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 1.73205i 0.223607i
\(61\) 6.92820i 0.887066i 0.896258 + 0.443533i \(0.146275\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) −6.00000 −0.762001
\(63\) −6.00000 5.19615i −0.755929 0.654654i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 10.3923i 1.27920i
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) 6.00000 0.727607
\(69\) 6.00000 0.722315
\(70\) −3.00000 + 3.46410i −0.358569 + 0.414039i
\(71\) 3.46410i 0.411113i 0.978645 + 0.205557i \(0.0659005\pi\)
−0.978645 + 0.205557i \(0.934100\pi\)
\(72\) 5.19615i 0.612372i
\(73\) 6.92820i 0.810885i −0.914121 0.405442i \(-0.867117\pi\)
0.914121 0.405442i \(-0.132883\pi\)
\(74\) 3.46410i 0.402694i
\(75\) 1.73205i 0.200000i
\(76\) 3.46410i 0.397360i
\(77\) 6.00000 6.92820i 0.683763 0.789542i
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) −5.00000 −0.559017
\(81\) 9.00000 1.00000
\(82\) 10.3923i 1.14764i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) −3.00000 + 3.46410i −0.327327 + 0.377964i
\(85\) −6.00000 −0.650791
\(86\) 13.8564i 1.49417i
\(87\) −12.0000 −1.28654
\(88\) 6.00000 0.639602
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 5.19615i 0.547723i
\(91\) 0 0
\(92\) 3.46410i 0.361158i
\(93\) 6.00000 0.622171
\(94\) 20.7846i 2.14377i
\(95\) 3.46410i 0.355409i
\(96\) −9.00000 −0.918559
\(97\) 6.92820i 0.703452i −0.936103 0.351726i \(-0.885595\pi\)
0.936103 0.351726i \(-0.114405\pi\)
\(98\) −12.0000 + 1.73205i −1.21218 + 0.174964i
\(99\) 10.3923i 1.04447i
\(100\) −1.00000 −0.100000
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) −18.0000 −1.78227
\(103\) 3.46410i 0.341328i 0.985329 + 0.170664i \(0.0545913\pi\)
−0.985329 + 0.170664i \(0.945409\pi\)
\(104\) 0 0
\(105\) 3.00000 3.46410i 0.292770 0.338062i
\(106\) 0 0
\(107\) 10.3923i 1.00466i 0.864675 + 0.502331i \(0.167524\pi\)
−0.864675 + 0.502331i \(0.832476\pi\)
\(108\) 5.19615i 0.500000i
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 6.00000 0.572078
\(111\) 3.46410i 0.328798i
\(112\) −10.0000 8.66025i −0.944911 0.818317i
\(113\) 6.92820i 0.651751i −0.945413 0.325875i \(-0.894341\pi\)
0.945413 0.325875i \(-0.105659\pi\)
\(114\) 10.3923i 0.973329i
\(115\) 3.46410i 0.323029i
\(116\) 6.92820i 0.643268i
\(117\) 0 0
\(118\) 20.7846i 1.91338i
\(119\) −12.0000 10.3923i −1.10004 0.952661i
\(120\) 3.00000 0.273861
\(121\) −1.00000 −0.0909091
\(122\) −12.0000 −1.08643
\(123\) 10.3923i 0.937043i
\(124\) 3.46410i 0.311086i
\(125\) 1.00000 0.0894427
\(126\) 9.00000 10.3923i 0.801784 0.925820i
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 12.1244i 1.07165i
\(129\) 13.8564i 1.21999i
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 6.00000 0.522233
\(133\) 6.00000 6.92820i 0.520266 0.600751i
\(134\) 13.8564i 1.19701i
\(135\) 5.19615i 0.447214i
\(136\) 10.3923i 0.891133i
\(137\) 20.7846i 1.77575i 0.460086 + 0.887875i \(0.347819\pi\)
−0.460086 + 0.887875i \(0.652181\pi\)
\(138\) 10.3923i 0.884652i
\(139\) 17.3205i 1.46911i −0.678551 0.734553i \(-0.737392\pi\)
0.678551 0.734553i \(-0.262608\pi\)
\(140\) −2.00000 1.73205i −0.169031 0.146385i
\(141\) 20.7846i 1.75038i
\(142\) −6.00000 −0.503509
\(143\) 0 0
\(144\) 15.0000 1.25000
\(145\) 6.92820i 0.575356i
\(146\) 12.0000 0.993127
\(147\) 12.0000 1.73205i 0.989743 0.142857i
\(148\) 2.00000 0.164399
\(149\) 6.92820i 0.567581i 0.958886 + 0.283790i \(0.0915919\pi\)
−0.958886 + 0.283790i \(0.908408\pi\)
\(150\) 3.00000 0.244949
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 6.00000 0.486664
\(153\) 18.0000 1.45521
\(154\) 12.0000 + 10.3923i 0.966988 + 0.837436i
\(155\) 3.46410i 0.278243i
\(156\) 0 0
\(157\) 13.8564i 1.10586i −0.833227 0.552931i \(-0.813509\pi\)
0.833227 0.552931i \(-0.186491\pi\)
\(158\) 13.8564i 1.10236i
\(159\) 0 0
\(160\) 5.19615i 0.410792i
\(161\) −6.00000 + 6.92820i −0.472866 + 0.546019i
\(162\) 15.5885i 1.22474i
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 6.00000 0.468521
\(165\) −6.00000 −0.467099
\(166\) 0 0
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 6.00000 + 5.19615i 0.462910 + 0.400892i
\(169\) 13.0000 1.00000
\(170\) 10.3923i 0.797053i
\(171\) 10.3923i 0.794719i
\(172\) 8.00000 0.609994
\(173\) −18.0000 −1.36851 −0.684257 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 20.7846i 1.57568i
\(175\) 2.00000 + 1.73205i 0.151186 + 0.130931i
\(176\) 17.3205i 1.30558i
\(177\) 20.7846i 1.56227i
\(178\) 10.3923i 0.778936i
\(179\) 10.3923i 0.776757i 0.921500 + 0.388379i \(0.126965\pi\)
−0.921500 + 0.388379i \(0.873035\pi\)
\(180\) 3.00000 0.223607
\(181\) 20.7846i 1.54491i 0.635071 + 0.772454i \(0.280971\pi\)
−0.635071 + 0.772454i \(0.719029\pi\)
\(182\) 0 0
\(183\) 12.0000 0.887066
\(184\) −6.00000 −0.442326
\(185\) −2.00000 −0.147043
\(186\) 10.3923i 0.762001i
\(187\) 20.7846i 1.51992i
\(188\) −12.0000 −0.875190
\(189\) −9.00000 + 10.3923i −0.654654 + 0.755929i
\(190\) 6.00000 0.435286
\(191\) 10.3923i 0.751961i −0.926628 0.375980i \(-0.877306\pi\)
0.926628 0.375980i \(-0.122694\pi\)
\(192\) 1.73205i 0.125000i
\(193\) −14.0000 −1.00774 −0.503871 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) 12.0000 0.861550
\(195\) 0 0
\(196\) −1.00000 6.92820i −0.0714286 0.494872i
\(197\) 13.8564i 0.987228i −0.869681 0.493614i \(-0.835676\pi\)
0.869681 0.493614i \(-0.164324\pi\)
\(198\) −18.0000 −1.27920
\(199\) 10.3923i 0.736691i −0.929689 0.368345i \(-0.879924\pi\)
0.929689 0.368345i \(-0.120076\pi\)
\(200\) 1.73205i 0.122474i
\(201\) 13.8564i 0.977356i
\(202\) 10.3923i 0.731200i
\(203\) 12.0000 13.8564i 0.842235 0.972529i
\(204\) 10.3923i 0.727607i
\(205\) −6.00000 −0.419058
\(206\) −6.00000 −0.418040
\(207\) 10.3923i 0.722315i
\(208\) 0 0
\(209\) −12.0000 −0.830057
\(210\) 6.00000 + 5.19615i 0.414039 + 0.358569i
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) 6.00000 0.411113
\(214\) −18.0000 −1.23045
\(215\) −8.00000 −0.545595
\(216\) −9.00000 −0.612372
\(217\) −6.00000 + 6.92820i −0.407307 + 0.470317i
\(218\) 3.46410i 0.234619i
\(219\) −12.0000 −0.810885
\(220\) 3.46410i 0.233550i
\(221\) 0 0
\(222\) −6.00000 −0.402694
\(223\) 17.3205i 1.15987i 0.814664 + 0.579934i \(0.196921\pi\)
−0.814664 + 0.579934i \(0.803079\pi\)
\(224\) 9.00000 10.3923i 0.601338 0.694365i
\(225\) −3.00000 −0.200000
\(226\) 12.0000 0.798228
\(227\) 24.0000 1.59294 0.796468 0.604681i \(-0.206699\pi\)
0.796468 + 0.604681i \(0.206699\pi\)
\(228\) 6.00000 0.397360
\(229\) 6.92820i 0.457829i 0.973447 + 0.228914i \(0.0735176\pi\)
−0.973447 + 0.228914i \(0.926482\pi\)
\(230\) −6.00000 −0.395628
\(231\) −12.0000 10.3923i −0.789542 0.683763i
\(232\) 12.0000 0.787839
\(233\) 6.92820i 0.453882i 0.973909 + 0.226941i \(0.0728724\pi\)
−0.973909 + 0.226941i \(0.927128\pi\)
\(234\) 0 0
\(235\) 12.0000 0.782794
\(236\) −12.0000 −0.781133
\(237\) 13.8564i 0.900070i
\(238\) 18.0000 20.7846i 1.16677 1.34727i
\(239\) 10.3923i 0.672222i −0.941822 0.336111i \(-0.890888\pi\)
0.941822 0.336111i \(-0.109112\pi\)
\(240\) 8.66025i 0.559017i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 1.73205i 0.111340i
\(243\) 15.5885i 1.00000i
\(244\) 6.92820i 0.443533i
\(245\) 1.00000 + 6.92820i 0.0638877 + 0.442627i
\(246\) −18.0000 −1.14764
\(247\) 0 0
\(248\) −6.00000 −0.381000
\(249\) 0 0
\(250\) 1.73205i 0.109545i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 6.00000 + 5.19615i 0.377964 + 0.327327i
\(253\) 12.0000 0.754434
\(254\) 6.92820i 0.434714i
\(255\) 10.3923i 0.650791i
\(256\) 19.0000 1.18750
\(257\) −6.00000 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) −24.0000 −1.49417
\(259\) −4.00000 3.46410i −0.248548 0.215249i
\(260\) 0 0
\(261\) 20.7846i 1.28654i
\(262\) 20.7846i 1.28408i
\(263\) 24.2487i 1.49524i −0.664127 0.747620i \(-0.731197\pi\)
0.664127 0.747620i \(-0.268803\pi\)
\(264\) 10.3923i 0.639602i
\(265\) 0 0
\(266\) 12.0000 + 10.3923i 0.735767 + 0.637193i
\(267\) 10.3923i 0.635999i
\(268\) −8.00000 −0.488678
\(269\) −18.0000 −1.09748 −0.548740 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) −9.00000 −0.547723
\(271\) 24.2487i 1.47300i −0.676435 0.736502i \(-0.736476\pi\)
0.676435 0.736502i \(-0.263524\pi\)
\(272\) 30.0000 1.81902
\(273\) 0 0
\(274\) −36.0000 −2.17484
\(275\) 3.46410i 0.208893i
\(276\) −6.00000 −0.361158
\(277\) 14.0000 0.841178 0.420589 0.907251i \(-0.361823\pi\)
0.420589 + 0.907251i \(0.361823\pi\)
\(278\) 30.0000 1.79928
\(279\) 10.3923i 0.622171i
\(280\) −3.00000 + 3.46410i −0.179284 + 0.207020i
\(281\) 13.8564i 0.826604i 0.910594 + 0.413302i \(0.135625\pi\)
−0.910594 + 0.413302i \(0.864375\pi\)
\(282\) 36.0000 2.14377
\(283\) 17.3205i 1.02960i −0.857311 0.514799i \(-0.827867\pi\)
0.857311 0.514799i \(-0.172133\pi\)
\(284\) 3.46410i 0.205557i
\(285\) −6.00000 −0.355409
\(286\) 0 0
\(287\) −12.0000 10.3923i −0.708338 0.613438i
\(288\) 15.5885i 0.918559i
\(289\) 19.0000 1.11765
\(290\) 12.0000 0.704664
\(291\) −12.0000 −0.703452
\(292\) 6.92820i 0.405442i
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 3.00000 + 20.7846i 0.174964 + 1.21218i
\(295\) 12.0000 0.698667
\(296\) 3.46410i 0.201347i
\(297\) 18.0000 1.04447
\(298\) −12.0000 −0.695141
\(299\) 0 0
\(300\) 1.73205i 0.100000i
\(301\) −16.0000 13.8564i −0.922225 0.798670i
\(302\) 13.8564i 0.797347i
\(303\) 10.3923i 0.597022i
\(304\) 17.3205i 0.993399i
\(305\) 6.92820i 0.396708i
\(306\) 31.1769i 1.78227i
\(307\) 24.2487i 1.38395i 0.721923 + 0.691974i \(0.243259\pi\)
−0.721923 + 0.691974i \(0.756741\pi\)
\(308\) −6.00000 + 6.92820i −0.341882 + 0.394771i
\(309\) 6.00000 0.341328
\(310\) −6.00000 −0.340777
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 20.7846i 1.17482i 0.809291 + 0.587408i \(0.199852\pi\)
−0.809291 + 0.587408i \(0.800148\pi\)
\(314\) 24.0000 1.35440
\(315\) −6.00000 5.19615i −0.338062 0.292770i
\(316\) −8.00000 −0.450035
\(317\) 27.7128i 1.55651i 0.627950 + 0.778253i \(0.283894\pi\)
−0.627950 + 0.778253i \(0.716106\pi\)
\(318\) 0 0
\(319\) −24.0000 −1.34374
\(320\) −1.00000 −0.0559017
\(321\) 18.0000 1.00466
\(322\) −12.0000 10.3923i −0.668734 0.579141i
\(323\) 20.7846i 1.15649i
\(324\) −9.00000 −0.500000
\(325\) 0 0
\(326\) 27.7128i 1.53487i
\(327\) 3.46410i 0.191565i
\(328\) 10.3923i 0.573819i
\(329\) 24.0000 + 20.7846i 1.32316 + 1.14589i
\(330\) 10.3923i 0.572078i
\(331\) 28.0000 1.53902 0.769510 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 0 0
\(333\) 6.00000 0.328798
\(334\) 20.7846i 1.13728i
\(335\) 8.00000 0.437087
\(336\) −15.0000 + 17.3205i −0.818317 + 0.944911i
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) 22.5167i 1.22474i
\(339\) −12.0000 −0.651751
\(340\) 6.00000 0.325396
\(341\) 12.0000 0.649836
\(342\) −18.0000 −0.973329
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 13.8564i 0.747087i
\(345\) 6.00000 0.323029
\(346\) 31.1769i 1.67608i
\(347\) 17.3205i 0.929814i −0.885360 0.464907i \(-0.846088\pi\)
0.885360 0.464907i \(-0.153912\pi\)
\(348\) 12.0000 0.643268
\(349\) 6.92820i 0.370858i −0.982658 0.185429i \(-0.940632\pi\)
0.982658 0.185429i \(-0.0593675\pi\)
\(350\) −3.00000 + 3.46410i −0.160357 + 0.185164i
\(351\) 0 0
\(352\) −18.0000 −0.959403
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 36.0000 1.91338
\(355\) 3.46410i 0.183855i
\(356\) 6.00000 0.317999
\(357\) −18.0000 + 20.7846i −0.952661 + 1.10004i
\(358\) −18.0000 −0.951330
\(359\) 3.46410i 0.182828i 0.995813 + 0.0914141i \(0.0291387\pi\)
−0.995813 + 0.0914141i \(0.970861\pi\)
\(360\) 5.19615i 0.273861i
\(361\) 7.00000 0.368421
\(362\) −36.0000 −1.89212
\(363\) 1.73205i 0.0909091i
\(364\) 0 0
\(365\) 6.92820i 0.362639i
\(366\) 20.7846i 1.08643i
\(367\) 10.3923i 0.542474i −0.962513 0.271237i \(-0.912567\pi\)
0.962513 0.271237i \(-0.0874327\pi\)
\(368\) 17.3205i 0.902894i
\(369\) 18.0000 0.937043
\(370\) 3.46410i 0.180090i
\(371\) 0 0
\(372\) −6.00000 −0.311086
\(373\) 14.0000 0.724893 0.362446 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) −36.0000 −1.86152
\(375\) 1.73205i 0.0894427i
\(376\) 20.7846i 1.07188i
\(377\) 0 0
\(378\) −18.0000 15.5885i −0.925820 0.801784i
\(379\) 4.00000 0.205466 0.102733 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(380\) 3.46410i 0.177705i
\(381\) 6.92820i 0.354943i
\(382\) 18.0000 0.920960
\(383\) −12.0000 −0.613171 −0.306586 0.951843i \(-0.599187\pi\)
−0.306586 + 0.951843i \(0.599187\pi\)
\(384\) −21.0000 −1.07165
\(385\) 6.00000 6.92820i 0.305788 0.353094i
\(386\) 24.2487i 1.23423i
\(387\) 24.0000 1.21999
\(388\) 6.92820i 0.351726i
\(389\) 6.92820i 0.351274i 0.984455 + 0.175637i \(0.0561985\pi\)
−0.984455 + 0.175637i \(0.943802\pi\)
\(390\) 0 0
\(391\) 20.7846i 1.05112i
\(392\) −12.0000 + 1.73205i −0.606092 + 0.0874818i
\(393\) 20.7846i 1.04844i
\(394\) 24.0000 1.20910
\(395\) 8.00000 0.402524
\(396\) 10.3923i 0.522233i
\(397\) 13.8564i 0.695433i −0.937600 0.347717i \(-0.886957\pi\)
0.937600 0.347717i \(-0.113043\pi\)
\(398\) 18.0000 0.902258
\(399\) −12.0000 10.3923i −0.600751 0.520266i
\(400\) −5.00000 −0.250000
\(401\) 27.7128i 1.38391i −0.721940 0.691956i \(-0.756749\pi\)
0.721940 0.691956i \(-0.243251\pi\)
\(402\) 24.0000 1.19701
\(403\) 0 0
\(404\) −6.00000 −0.298511
\(405\) 9.00000 0.447214
\(406\) 24.0000 + 20.7846i 1.19110 + 1.03152i
\(407\) 6.92820i 0.343418i
\(408\) −18.0000 −0.891133
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 10.3923i 0.513239i
\(411\) 36.0000 1.77575
\(412\) 3.46410i 0.170664i
\(413\) 24.0000 + 20.7846i 1.18096 + 1.02274i
\(414\) 18.0000 0.884652
\(415\) 0 0
\(416\) 0 0
\(417\) −30.0000 −1.46911
\(418\) 20.7846i 1.01661i
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) −3.00000 + 3.46410i −0.146385 + 0.169031i
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 6.92820i 0.337260i
\(423\) −36.0000 −1.75038
\(424\) 0 0
\(425\) −6.00000 −0.291043
\(426\) 10.3923i 0.503509i
\(427\) −12.0000 + 13.8564i −0.580721 + 0.670559i
\(428\) 10.3923i 0.502331i
\(429\) 0 0
\(430\) 13.8564i 0.668215i
\(431\) 10.3923i 0.500580i −0.968171 0.250290i \(-0.919474\pi\)
0.968171 0.250290i \(-0.0805259\pi\)
\(432\) 25.9808i 1.25000i
\(433\) 6.92820i 0.332948i 0.986046 + 0.166474i \(0.0532382\pi\)
−0.986046 + 0.166474i \(0.946762\pi\)
\(434\) −12.0000 10.3923i −0.576018 0.498847i
\(435\) −12.0000 −0.575356
\(436\) 2.00000 0.0957826
\(437\) 12.0000 0.574038
\(438\) 20.7846i 0.993127i
\(439\) 17.3205i 0.826663i 0.910581 + 0.413331i \(0.135635\pi\)
−0.910581 + 0.413331i \(0.864365\pi\)
\(440\) 6.00000 0.286039
\(441\) −3.00000 20.7846i −0.142857 0.989743i
\(442\) 0 0
\(443\) 10.3923i 0.493753i 0.969047 + 0.246877i \(0.0794043\pi\)
−0.969047 + 0.246877i \(0.920596\pi\)
\(444\) 3.46410i 0.164399i
\(445\) −6.00000 −0.284427
\(446\) −30.0000 −1.42054
\(447\) 12.0000 0.567581
\(448\) −2.00000 1.73205i −0.0944911 0.0818317i
\(449\) 13.8564i 0.653924i −0.945037 0.326962i \(-0.893975\pi\)
0.945037 0.326962i \(-0.106025\pi\)
\(450\) 5.19615i 0.244949i
\(451\) 20.7846i 0.978709i
\(452\) 6.92820i 0.325875i
\(453\) 13.8564i 0.651031i
\(454\) 41.5692i 1.95094i
\(455\) 0 0
\(456\) 10.3923i 0.486664i
\(457\) −38.0000 −1.77757 −0.888783 0.458329i \(-0.848448\pi\)
−0.888783 + 0.458329i \(0.848448\pi\)
\(458\) −12.0000 −0.560723
\(459\) 31.1769i 1.45521i
\(460\) 3.46410i 0.161515i
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 18.0000 20.7846i 0.837436 0.966988i
\(463\) 20.0000 0.929479 0.464739 0.885448i \(-0.346148\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(464\) 34.6410i 1.60817i
\(465\) 6.00000 0.278243
\(466\) −12.0000 −0.555889
\(467\) −24.0000 −1.11059 −0.555294 0.831654i \(-0.687394\pi\)
−0.555294 + 0.831654i \(0.687394\pi\)
\(468\) 0 0
\(469\) 16.0000 + 13.8564i 0.738811 + 0.639829i
\(470\) 20.7846i 0.958723i
\(471\) −24.0000 −1.10586
\(472\) 20.7846i 0.956689i
\(473\) 27.7128i 1.27424i
\(474\) 24.0000 1.10236
\(475\) 3.46410i 0.158944i
\(476\) 12.0000 + 10.3923i 0.550019 + 0.476331i
\(477\) 0 0
\(478\) 18.0000 0.823301
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) −9.00000 −0.410792
\(481\) 0 0
\(482\) 0 0
\(483\) 12.0000 + 10.3923i 0.546019 + 0.472866i
\(484\) 1.00000 0.0454545
\(485\) 6.92820i 0.314594i
\(486\) 27.0000 1.22474
\(487\) 4.00000 0.181257 0.0906287 0.995885i \(-0.471112\pi\)
0.0906287 + 0.995885i \(0.471112\pi\)
\(488\) −12.0000 −0.543214
\(489\) 27.7128i 1.25322i
\(490\) −12.0000 + 1.73205i −0.542105 + 0.0782461i
\(491\) 24.2487i 1.09433i 0.837025 + 0.547165i \(0.184293\pi\)
−0.837025 + 0.547165i \(0.815707\pi\)
\(492\) 10.3923i 0.468521i
\(493\) 41.5692i 1.87218i
\(494\) 0 0
\(495\) 10.3923i 0.467099i
\(496\) 17.3205i 0.777714i
\(497\) −6.00000 + 6.92820i −0.269137 + 0.310772i
\(498\) 0 0
\(499\) −20.0000 −0.895323 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 20.7846i 0.928588i
\(502\) 20.7846i 0.927663i
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) 9.00000 10.3923i 0.400892 0.462910i
\(505\) 6.00000 0.266996
\(506\) 20.7846i 0.923989i
\(507\) 22.5167i 1.00000i
\(508\) 4.00000 0.177471
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) −18.0000 −0.797053
\(511\) 12.0000 13.8564i 0.530849 0.612971i
\(512\) 8.66025i 0.382733i
\(513\) 18.0000 0.794719
\(514\) 10.3923i 0.458385i
\(515\) 3.46410i 0.152647i
\(516\) 13.8564i 0.609994i
\(517\) 41.5692i 1.82821i
\(518\) 6.00000 6.92820i 0.263625 0.304408i
\(519\) 31.1769i 1.36851i
\(520\) 0 0
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) −36.0000 −1.57568
\(523\) 17.3205i 0.757373i −0.925525 0.378686i \(-0.876376\pi\)
0.925525 0.378686i \(-0.123624\pi\)
\(524\) −12.0000 −0.524222
\(525\) 3.00000 3.46410i 0.130931 0.151186i
\(526\) 42.0000 1.83129
\(527\) 20.7846i 0.905392i
\(528\) 30.0000 1.30558
\(529\) 11.0000 0.478261
\(530\) 0 0
\(531\) −36.0000 −1.56227
\(532\) −6.00000 + 6.92820i −0.260133 + 0.300376i
\(533\) 0 0
\(534\) −18.0000 −0.778936
\(535\) 10.3923i 0.449299i
\(536\) 13.8564i 0.598506i
\(537\) 18.0000 0.776757
\(538\) 31.1769i 1.34413i
\(539\) 24.0000 3.46410i 1.03375 0.149209i
\(540\) 5.19615i 0.223607i
\(541\) −34.0000 −1.46177 −0.730887 0.682498i \(-0.760893\pi\)
−0.730887 + 0.682498i \(0.760893\pi\)
\(542\) 42.0000 1.80405
\(543\) 36.0000 1.54491
\(544\) 31.1769i 1.33670i
\(545\) −2.00000 −0.0856706
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 20.7846i 0.887875i
\(549\) 20.7846i 0.887066i
\(550\) 6.00000 0.255841
\(551\) −24.0000 −1.02243
\(552\) 10.3923i 0.442326i
\(553\) 16.0000 + 13.8564i 0.680389 + 0.589234i
\(554\) 24.2487i 1.03023i
\(555\) 3.46410i 0.147043i
\(556\) 17.3205i 0.734553i
\(557\) 27.7128i 1.17423i −0.809504 0.587115i \(-0.800264\pi\)
0.809504 0.587115i \(-0.199736\pi\)
\(558\) 18.0000 0.762001
\(559\) 0 0
\(560\) −10.0000 8.66025i −0.422577 0.365963i
\(561\) 36.0000 1.51992
\(562\) −24.0000 −1.01238
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 20.7846i 0.875190i
\(565\) 6.92820i 0.291472i
\(566\) 30.0000 1.26099
\(567\) 18.0000 + 15.5885i 0.755929 + 0.654654i
\(568\) −6.00000 −0.251754
\(569\) 27.7128i 1.16178i −0.813982 0.580891i \(-0.802704\pi\)
0.813982 0.580891i \(-0.197296\pi\)
\(570\) 10.3923i 0.435286i
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) −18.0000 −0.751961
\(574\) 18.0000 20.7846i 0.751305 0.867533i
\(575\) 3.46410i 0.144463i
\(576\) 3.00000 0.125000
\(577\) 34.6410i 1.44212i −0.692870 0.721062i \(-0.743654\pi\)
0.692870 0.721062i \(-0.256346\pi\)
\(578\) 32.9090i 1.36883i
\(579\) 24.2487i 1.00774i
\(580\) 6.92820i 0.287678i
\(581\) 0 0
\(582\) 20.7846i 0.861550i
\(583\) 0 0
\(584\) 12.0000 0.496564
\(585\) 0 0
\(586\) 10.3923i 0.429302i
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) −12.0000 + 1.73205i −0.494872 + 0.0714286i
\(589\) 12.0000 0.494451
\(590\) 20.7846i 0.855689i
\(591\) −24.0000 −0.987228
\(592\) 10.0000 0.410997
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 31.1769i 1.27920i
\(595\) −12.0000 10.3923i −0.491952 0.426043i
\(596\) 6.92820i 0.283790i
\(597\) −18.0000 −0.736691
\(598\) 0 0
\(599\) 24.2487i 0.990775i −0.868672 0.495388i \(-0.835026\pi\)
0.868672 0.495388i \(-0.164974\pi\)
\(600\) 3.00000 0.122474
\(601\) 13.8564i 0.565215i −0.959236 0.282607i \(-0.908801\pi\)
0.959236 0.282607i \(-0.0911993\pi\)
\(602\) 24.0000 27.7128i 0.978167 1.12949i
\(603\) −24.0000 −0.977356
\(604\) 8.00000 0.325515
\(605\) −1.00000 −0.0406558
\(606\) 18.0000 0.731200
\(607\) 17.3205i 0.703018i 0.936185 + 0.351509i \(0.114331\pi\)
−0.936185 + 0.351509i \(0.885669\pi\)
\(608\) −18.0000 −0.729996
\(609\) −24.0000 20.7846i −0.972529 0.842235i
\(610\) −12.0000 −0.485866
\(611\) 0 0
\(612\) −18.0000 −0.727607
\(613\) −34.0000 −1.37325 −0.686624 0.727013i \(-0.740908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) −42.0000 −1.69498
\(615\) 10.3923i 0.419058i
\(616\) 12.0000 + 10.3923i 0.483494 + 0.418718i
\(617\) 6.92820i 0.278919i −0.990228 0.139459i \(-0.955464\pi\)
0.990228 0.139459i \(-0.0445365\pi\)
\(618\) 10.3923i 0.418040i
\(619\) 17.3205i 0.696170i −0.937463 0.348085i \(-0.886832\pi\)
0.937463 0.348085i \(-0.113168\pi\)
\(620\) 3.46410i 0.139122i
\(621\) −18.0000 −0.722315
\(622\) 0 0
\(623\) −12.0000 10.3923i −0.480770 0.416359i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −36.0000 −1.43885
\(627\) 20.7846i 0.830057i
\(628\) 13.8564i 0.552931i
\(629\) 12.0000 0.478471
\(630\) 9.00000 10.3923i 0.358569 0.414039i
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) 13.8564i 0.551178i
\(633\) 6.92820i 0.275371i
\(634\) −48.0000 −1.90632
\(635\) −4.00000 −0.158735
\(636\) 0 0
\(637\) 0 0
\(638\) 41.5692i 1.64574i
\(639\) 10.3923i 0.411113i
\(640\) 12.1244i 0.479257i
\(641\) 27.7128i 1.09459i 0.836940 + 0.547295i \(0.184342\pi\)
−0.836940 + 0.547295i \(0.815658\pi\)
\(642\) 31.1769i 1.23045i
\(643\) 31.1769i 1.22950i −0.788723 0.614749i \(-0.789257\pi\)
0.788723 0.614749i \(-0.210743\pi\)
\(644\) 6.00000 6.92820i 0.236433 0.273009i
\(645\) 13.8564i 0.545595i
\(646\) −36.0000 −1.41640
\(647\) −12.0000 −0.471769 −0.235884 0.971781i \(-0.575799\pi\)
−0.235884 + 0.971781i \(0.575799\pi\)
\(648\) 15.5885i 0.612372i
\(649\) 41.5692i 1.63173i
\(650\) 0 0
\(651\) 12.0000 + 10.3923i 0.470317 + 0.407307i
\(652\) 16.0000 0.626608
\(653\) 41.5692i 1.62673i −0.581754 0.813365i \(-0.697633\pi\)
0.581754 0.813365i \(-0.302367\pi\)
\(654\) −6.00000 −0.234619
\(655\) 12.0000 0.468879
\(656\) 30.0000 1.17130
\(657\) 20.7846i 0.810885i
\(658\) −36.0000 + 41.5692i −1.40343 + 1.62054i
\(659\) 10.3923i 0.404827i 0.979300 + 0.202413i \(0.0648785\pi\)
−0.979300 + 0.202413i \(0.935122\pi\)
\(660\) 6.00000 0.233550
\(661\) 48.4974i 1.88633i 0.332323 + 0.943166i \(0.392168\pi\)
−0.332323 + 0.943166i \(0.607832\pi\)
\(662\) 48.4974i 1.88491i
\(663\) 0 0
\(664\) 0 0
\(665\) 6.00000 6.92820i 0.232670 0.268664i
\(666\) 10.3923i 0.402694i
\(667\) 24.0000 0.929284
\(668\) 12.0000 0.464294
\(669\) 30.0000 1.15987
\(670\) 13.8564i 0.535320i
\(671\) 24.0000 0.926510
\(672\) −18.0000 15.5885i −0.694365 0.601338i
\(673\) −14.0000 −0.539660 −0.269830 0.962908i \(-0.586968\pi\)
−0.269830 + 0.962908i \(0.586968\pi\)
\(674\) 24.2487i 0.934025i
\(675\) 5.19615i 0.200000i
\(676\) −13.0000 −0.500000
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 20.7846i 0.798228i
\(679\) 12.0000 13.8564i 0.460518 0.531760i
\(680\) 10.3923i 0.398527i
\(681\) 41.5692i 1.59294i
\(682\) 20.7846i 0.795884i
\(683\) 17.3205i 0.662751i −0.943499 0.331375i \(-0.892487\pi\)
0.943499 0.331375i \(-0.107513\pi\)
\(684\) 10.3923i 0.397360i
\(685\) 20.7846i 0.794139i
\(686\) −27.0000 17.3205i −1.03086 0.661300i
\(687\) 12.0000 0.457829
\(688\) 40.0000 1.52499
\(689\) 0 0
\(690\) 10.3923i 0.395628i
\(691\) 31.1769i 1.18603i −0.805193 0.593013i \(-0.797938\pi\)
0.805193 0.593013i \(-0.202062\pi\)
\(692\) 18.0000 0.684257
\(693\) −18.0000 + 20.7846i −0.683763 + 0.789542i
\(694\) 30.0000 1.13878
\(695\) 17.3205i 0.657004i
\(696\) 20.7846i 0.787839i
\(697\) 36.0000 1.36360
\(698\) 12.0000 0.454207
\(699\) 12.0000 0.453882
\(700\) −2.00000 1.73205i −0.0755929 0.0654654i
\(701\) 20.7846i 0.785024i −0.919747 0.392512i \(-0.871606\pi\)
0.919747 0.392512i \(-0.128394\pi\)
\(702\) 0 0
\(703\) 6.92820i 0.261302i
\(704\) 3.46410i 0.130558i
\(705\) 20.7846i 0.782794i
\(706\) 10.3923i 0.391120i
\(707\) 12.0000 + 10.3923i 0.451306 + 0.390843i
\(708\) 20.7846i 0.781133i
\(709\) 22.0000 0.826227 0.413114 0.910679i \(-0.364441\pi\)
0.413114 + 0.910679i \(0.364441\pi\)
\(710\) −6.00000 −0.225176
\(711\) −24.0000 −0.900070
\(712\) 10.3923i 0.389468i
\(713\) −12.0000 −0.449404
\(714\) −36.0000 31.1769i −1.34727 1.16677i
\(715\) 0 0
\(716\) 10.3923i 0.388379i
\(717\) −18.0000 −0.672222
\(718\) −6.00000 −0.223918
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 15.0000 0.559017
\(721\) −6.00000 + 6.92820i −0.223452 + 0.258020i
\(722\) 12.1244i 0.451222i
\(723\) 0 0
\(724\) 20.7846i 0.772454i
\(725\) 6.92820i 0.257307i
\(726\) −3.00000 −0.111340
\(727\) 3.46410i 0.128476i 0.997935 + 0.0642382i \(0.0204617\pi\)
−0.997935 + 0.0642382i \(0.979538\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 12.0000 0.444140
\(731\) 48.0000 1.77534
\(732\) −12.0000 −0.443533
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 18.0000 0.664392
\(735\) 12.0000 1.73205i 0.442627 0.0638877i
\(736\) 18.0000 0.663489
\(737\) 27.7128i 1.02081i
\(738\) 31.1769i 1.14764i
\(739\) −4.00000 −0.147142 −0.0735712 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) 2.00000 0.0735215
\(741\) 0 0
\(742\) 0 0
\(743\) 31.1769i 1.14377i 0.820334 + 0.571885i \(0.193788\pi\)
−0.820334 + 0.571885i \(0.806212\pi\)
\(744\) 10.3923i 0.381000i
\(745\) 6.92820i 0.253830i
\(746\) 24.2487i 0.887808i
\(747\) 0 0
\(748\) 20.7846i 0.759961i
\(749\) −18.0000 + 20.7846i −0.657706 + 0.759453i
\(750\) 3.00000 0.109545
\(751\) 16.0000 0.583848 0.291924 0.956441i \(-0.405705\pi\)
0.291924 + 0.956441i \(0.405705\pi\)
\(752\) −60.0000 −2.18797
\(753\) 20.7846i 0.757433i
\(754\) 0 0
\(755\) −8.00000 −0.291150
\(756\) 9.00000 10.3923i 0.327327 0.377964i
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) 6.92820i 0.251644i
\(759\) 20.7846i 0.754434i
\(760\) 6.00000 0.217643
\(761\) 42.0000 1.52250 0.761249 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) −12.0000 −0.434714
\(763\) −4.00000 3.46410i −0.144810 0.125409i
\(764\) 10.3923i 0.375980i
\(765\) 18.0000 0.650791
\(766\) 20.7846i 0.750978i
\(767\) 0 0
\(768\) 32.9090i 1.18750i
\(769\) 41.5692i 1.49902i 0.661991 + 0.749512i \(0.269712\pi\)
−0.661991 + 0.749512i \(0.730288\pi\)
\(770\) 12.0000 + 10.3923i 0.432450 + 0.374513i
\(771\) 10.3923i 0.374270i
\(772\) 14.0000 0.503871
\(773\) 6.00000 0.215805 0.107903 0.994161i \(-0.465587\pi\)
0.107903 + 0.994161i \(0.465587\pi\)
\(774\) 41.5692i 1.49417i
\(775\) 3.46410i 0.124434i
\(776\) 12.0000 0.430775
\(777\) −6.00000 + 6.92820i −0.215249 + 0.248548i
\(778\) −12.0000 −0.430221
\(779\) 20.7846i 0.744686i
\(780\) 0 0
\(781\) 12.0000 0.429394
\(782\) 36.0000 1.28736
\(783\) 36.0000 1.28654
\(784\) −5.00000 34.6410i −0.178571 1.23718i
\(785\) 13.8564i 0.494556i
\(786\) 36.0000 1.28408
\(787\) 24.2487i 0.864373i 0.901784 + 0.432187i \(0.142258\pi\)
−0.901784 + 0.432187i \(0.857742\pi\)
\(788\) 13.8564i 0.493614i
\(789\) −42.0000 −1.49524
\(790\) 13.8564i 0.492989i
\(791\) 12.0000 13.8564i 0.426671 0.492677i
\(792\) −18.0000 −0.639602
\(793\) 0 0
\(794\) 24.0000 0.851728
\(795\) 0 0
\(796\) 10.3923i 0.368345i
\(797\) −18.0000 −0.637593 −0.318796 0.947823i \(-0.603279\pi\)
−0.318796 + 0.947823i \(0.603279\pi\)
\(798\) 18.0000 20.7846i 0.637193 0.735767i
\(799\) −72.0000 −2.54718
\(800\) 5.19615i 0.183712i
\(801\) 18.0000 0.635999
\(802\) 48.0000 1.69494
\(803\) −24.0000 −0.846942
\(804\) 13.8564i 0.488678i
\(805\)