Properties

Label 105.2.d.a.64.2
Level 105
Weight 2
Character 105.64
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.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 64.2
Root \(1.00000i\)
Character \(\chi\) = 105.64
Dual form 105.2.d.a.64.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000i q^{3} +1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} -1.00000 q^{6} +1.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000i q^{3} +1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} -1.00000 q^{6} +1.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} +(2.00000 + 1.00000i) q^{10} -6.00000 q^{11} +1.00000i q^{12} -2.00000i q^{13} -1.00000 q^{14} +(2.00000 + 1.00000i) q^{15} -1.00000 q^{16} -4.00000i q^{17} -1.00000i q^{18} +6.00000 q^{19} +(1.00000 - 2.00000i) q^{20} -1.00000 q^{21} -6.00000i q^{22} -3.00000 q^{24} +(-3.00000 - 4.00000i) q^{25} +2.00000 q^{26} -1.00000i q^{27} +1.00000i q^{28} +2.00000 q^{29} +(-1.00000 + 2.00000i) q^{30} -10.0000 q^{31} +5.00000i q^{32} -6.00000i q^{33} +4.00000 q^{34} +(2.00000 + 1.00000i) q^{35} -1.00000 q^{36} +4.00000i q^{37} +6.00000i q^{38} +2.00000 q^{39} +(6.00000 + 3.00000i) q^{40} +2.00000 q^{41} -1.00000i q^{42} -4.00000i q^{43} -6.00000 q^{44} +(-1.00000 + 2.00000i) q^{45} -1.00000i q^{48} -1.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +4.00000 q^{51} -2.00000i q^{52} +6.00000i q^{53} +1.00000 q^{54} +(-6.00000 + 12.0000i) q^{55} -3.00000 q^{56} +6.00000i q^{57} +2.00000i q^{58} +8.00000 q^{59} +(2.00000 + 1.00000i) q^{60} -2.00000 q^{61} -10.0000i q^{62} -1.00000i q^{63} -7.00000 q^{64} +(-4.00000 - 2.00000i) q^{65} +6.00000 q^{66} +16.0000i q^{67} -4.00000i q^{68} +(-1.00000 + 2.00000i) q^{70} +10.0000 q^{71} -3.00000i q^{72} -6.00000i q^{73} -4.00000 q^{74} +(4.00000 - 3.00000i) q^{75} +6.00000 q^{76} -6.00000i q^{77} +2.00000i q^{78} -4.00000 q^{79} +(-1.00000 + 2.00000i) q^{80} +1.00000 q^{81} +2.00000i q^{82} +8.00000i q^{83} -1.00000 q^{84} +(-8.00000 - 4.00000i) q^{85} +4.00000 q^{86} +2.00000i q^{87} -18.0000i q^{88} -6.00000 q^{89} +(-2.00000 - 1.00000i) q^{90} +2.00000 q^{91} -10.0000i q^{93} +(6.00000 - 12.0000i) q^{95} -5.00000 q^{96} +2.00000i q^{97} -1.00000i q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{4} + 2q^{5} - 2q^{6} - 2q^{9} + O(q^{10}) \) \( 2q + 2q^{4} + 2q^{5} - 2q^{6} - 2q^{9} + 4q^{10} - 12q^{11} - 2q^{14} + 4q^{15} - 2q^{16} + 12q^{19} + 2q^{20} - 2q^{21} - 6q^{24} - 6q^{25} + 4q^{26} + 4q^{29} - 2q^{30} - 20q^{31} + 8q^{34} + 4q^{35} - 2q^{36} + 4q^{39} + 12q^{40} + 4q^{41} - 12q^{44} - 2q^{45} - 2q^{49} + 8q^{50} + 8q^{51} + 2q^{54} - 12q^{55} - 6q^{56} + 16q^{59} + 4q^{60} - 4q^{61} - 14q^{64} - 8q^{65} + 12q^{66} - 2q^{70} + 20q^{71} - 8q^{74} + 8q^{75} + 12q^{76} - 8q^{79} - 2q^{80} + 2q^{81} - 2q^{84} - 16q^{85} + 8q^{86} - 12q^{89} - 4q^{90} + 4q^{91} + 12q^{95} - 10q^{96} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i 0.935414 + 0.353553i \(0.115027\pi\)
−0.935414 + 0.353553i \(0.884973\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 1.00000 0.500000
\(5\) 1.00000 2.00000i 0.447214 0.894427i
\(6\) −1.00000 −0.408248
\(7\) 1.00000i 0.377964i
\(8\) 3.00000i 1.06066i
\(9\) −1.00000 −0.333333
\(10\) 2.00000 + 1.00000i 0.632456 + 0.316228i
\(11\) −6.00000 −1.80907 −0.904534 0.426401i \(-0.859781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 2.00000i 0.554700i −0.960769 0.277350i \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) −1.00000 −0.267261
\(15\) 2.00000 + 1.00000i 0.516398 + 0.258199i
\(16\) −1.00000 −0.250000
\(17\) 4.00000i 0.970143i −0.874475 0.485071i \(-0.838794\pi\)
0.874475 0.485071i \(-0.161206\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) 1.00000 2.00000i 0.223607 0.447214i
\(21\) −1.00000 −0.218218
\(22\) 6.00000i 1.27920i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) −3.00000 −0.612372
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 2.00000 0.392232
\(27\) 1.00000i 0.192450i
\(28\) 1.00000i 0.188982i
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) −1.00000 + 2.00000i −0.182574 + 0.365148i
\(31\) −10.0000 −1.79605 −0.898027 0.439941i \(-0.854999\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) 5.00000i 0.883883i
\(33\) 6.00000i 1.04447i
\(34\) 4.00000 0.685994
\(35\) 2.00000 + 1.00000i 0.338062 + 0.169031i
\(36\) −1.00000 −0.166667
\(37\) 4.00000i 0.657596i 0.944400 + 0.328798i \(0.106644\pi\)
−0.944400 + 0.328798i \(0.893356\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 2.00000 0.320256
\(40\) 6.00000 + 3.00000i 0.948683 + 0.474342i
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 1.00000i 0.154303i
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) −6.00000 −0.904534
\(45\) −1.00000 + 2.00000i −0.149071 + 0.298142i
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −1.00000 −0.142857
\(50\) 4.00000 3.00000i 0.565685 0.424264i
\(51\) 4.00000 0.560112
\(52\) 2.00000i 0.277350i
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 1.00000 0.136083
\(55\) −6.00000 + 12.0000i −0.809040 + 1.61808i
\(56\) −3.00000 −0.400892
\(57\) 6.00000i 0.794719i
\(58\) 2.00000i 0.262613i
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 2.00000 + 1.00000i 0.258199 + 0.129099i
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 10.0000i 1.27000i
\(63\) 1.00000i 0.125988i
\(64\) −7.00000 −0.875000
\(65\) −4.00000 2.00000i −0.496139 0.248069i
\(66\) 6.00000 0.738549
\(67\) 16.0000i 1.95471i 0.211604 + 0.977356i \(0.432131\pi\)
−0.211604 + 0.977356i \(0.567869\pi\)
\(68\) 4.00000i 0.485071i
\(69\) 0 0
\(70\) −1.00000 + 2.00000i −0.119523 + 0.239046i
\(71\) 10.0000 1.18678 0.593391 0.804914i \(-0.297789\pi\)
0.593391 + 0.804914i \(0.297789\pi\)
\(72\) 3.00000i 0.353553i
\(73\) 6.00000i 0.702247i −0.936329 0.351123i \(-0.885800\pi\)
0.936329 0.351123i \(-0.114200\pi\)
\(74\) −4.00000 −0.464991
\(75\) 4.00000 3.00000i 0.461880 0.346410i
\(76\) 6.00000 0.688247
\(77\) 6.00000i 0.683763i
\(78\) 2.00000i 0.226455i
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) −1.00000 + 2.00000i −0.111803 + 0.223607i
\(81\) 1.00000 0.111111
\(82\) 2.00000i 0.220863i
\(83\) 8.00000i 0.878114i 0.898459 + 0.439057i \(0.144687\pi\)
−0.898459 + 0.439057i \(0.855313\pi\)
\(84\) −1.00000 −0.109109
\(85\) −8.00000 4.00000i −0.867722 0.433861i
\(86\) 4.00000 0.431331
\(87\) 2.00000i 0.214423i
\(88\) 18.0000i 1.91881i
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) −2.00000 1.00000i −0.210819 0.105409i
\(91\) 2.00000 0.209657
\(92\) 0 0
\(93\) 10.0000i 1.03695i
\(94\) 0 0
\(95\) 6.00000 12.0000i 0.615587 1.23117i
\(96\) −5.00000 −0.510310
\(97\) 2.00000i 0.203069i 0.994832 + 0.101535i \(0.0323753\pi\)
−0.994832 + 0.101535i \(0.967625\pi\)
\(98\) 1.00000i 0.101015i
\(99\) 6.00000 0.603023
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 4.00000i 0.396059i
\(103\) 8.00000i 0.788263i 0.919054 + 0.394132i \(0.128955\pi\)
−0.919054 + 0.394132i \(0.871045\pi\)
\(104\) 6.00000 0.588348
\(105\) −1.00000 + 2.00000i −0.0975900 + 0.195180i
\(106\) −6.00000 −0.582772
\(107\) 4.00000i 0.386695i −0.981130 0.193347i \(-0.938066\pi\)
0.981130 0.193347i \(-0.0619344\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) −12.0000 6.00000i −1.14416 0.572078i
\(111\) −4.00000 −0.379663
\(112\) 1.00000i 0.0944911i
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) −6.00000 −0.561951
\(115\) 0 0
\(116\) 2.00000 0.185695
\(117\) 2.00000i 0.184900i
\(118\) 8.00000i 0.736460i
\(119\) 4.00000 0.366679
\(120\) −3.00000 + 6.00000i −0.273861 + 0.547723i
\(121\) 25.0000 2.27273
\(122\) 2.00000i 0.181071i
\(123\) 2.00000i 0.180334i
\(124\) −10.0000 −0.898027
\(125\) −11.0000 + 2.00000i −0.983870 + 0.178885i
\(126\) 1.00000 0.0890871
\(127\) 20.0000i 1.77471i −0.461084 0.887357i \(-0.652539\pi\)
0.461084 0.887357i \(-0.347461\pi\)
\(128\) 3.00000i 0.265165i
\(129\) 4.00000 0.352180
\(130\) 2.00000 4.00000i 0.175412 0.350823i
\(131\) 4.00000 0.349482 0.174741 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 6.00000i 0.522233i
\(133\) 6.00000i 0.520266i
\(134\) −16.0000 −1.38219
\(135\) −2.00000 1.00000i −0.172133 0.0860663i
\(136\) 12.0000 1.02899
\(137\) 6.00000i 0.512615i 0.966595 + 0.256307i \(0.0825059\pi\)
−0.966595 + 0.256307i \(0.917494\pi\)
\(138\) 0 0
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 2.00000 + 1.00000i 0.169031 + 0.0845154i
\(141\) 0 0
\(142\) 10.0000i 0.839181i
\(143\) 12.0000i 1.00349i
\(144\) 1.00000 0.0833333
\(145\) 2.00000 4.00000i 0.166091 0.332182i
\(146\) 6.00000 0.496564
\(147\) 1.00000i 0.0824786i
\(148\) 4.00000i 0.328798i
\(149\) 14.0000 1.14692 0.573462 0.819232i \(-0.305600\pi\)
0.573462 + 0.819232i \(0.305600\pi\)
\(150\) 3.00000 + 4.00000i 0.244949 + 0.326599i
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 18.0000i 1.45999i
\(153\) 4.00000i 0.323381i
\(154\) 6.00000 0.483494
\(155\) −10.0000 + 20.0000i −0.803219 + 1.60644i
\(156\) 2.00000 0.160128
\(157\) 18.0000i 1.43656i −0.695756 0.718278i \(-0.744931\pi\)
0.695756 0.718278i \(-0.255069\pi\)
\(158\) 4.00000i 0.318223i
\(159\) −6.00000 −0.475831
\(160\) 10.0000 + 5.00000i 0.790569 + 0.395285i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 4.00000i 0.313304i 0.987654 + 0.156652i \(0.0500701\pi\)
−0.987654 + 0.156652i \(0.949930\pi\)
\(164\) 2.00000 0.156174
\(165\) −12.0000 6.00000i −0.934199 0.467099i
\(166\) −8.00000 −0.620920
\(167\) 12.0000i 0.928588i −0.885681 0.464294i \(-0.846308\pi\)
0.885681 0.464294i \(-0.153692\pi\)
\(168\) 3.00000i 0.231455i
\(169\) 9.00000 0.692308
\(170\) 4.00000 8.00000i 0.306786 0.613572i
\(171\) −6.00000 −0.458831
\(172\) 4.00000i 0.304997i
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) −2.00000 −0.151620
\(175\) 4.00000 3.00000i 0.302372 0.226779i
\(176\) 6.00000 0.452267
\(177\) 8.00000i 0.601317i
\(178\) 6.00000i 0.449719i
\(179\) 14.0000 1.04641 0.523205 0.852207i \(-0.324736\pi\)
0.523205 + 0.852207i \(0.324736\pi\)
\(180\) −1.00000 + 2.00000i −0.0745356 + 0.149071i
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 2.00000i 0.148250i
\(183\) 2.00000i 0.147844i
\(184\) 0 0
\(185\) 8.00000 + 4.00000i 0.588172 + 0.294086i
\(186\) 10.0000 0.733236
\(187\) 24.0000i 1.75505i
\(188\) 0 0
\(189\) 1.00000 0.0727393
\(190\) 12.0000 + 6.00000i 0.870572 + 0.435286i
\(191\) −18.0000 −1.30243 −0.651217 0.758891i \(-0.725741\pi\)
−0.651217 + 0.758891i \(0.725741\pi\)
\(192\) 7.00000i 0.505181i
\(193\) 8.00000i 0.575853i −0.957653 0.287926i \(-0.907034\pi\)
0.957653 0.287926i \(-0.0929658\pi\)
\(194\) −2.00000 −0.143592
\(195\) 2.00000 4.00000i 0.143223 0.286446i
\(196\) −1.00000 −0.0714286
\(197\) 2.00000i 0.142494i −0.997459 0.0712470i \(-0.977302\pi\)
0.997459 0.0712470i \(-0.0226979\pi\)
\(198\) 6.00000i 0.426401i
\(199\) −14.0000 −0.992434 −0.496217 0.868199i \(-0.665278\pi\)
−0.496217 + 0.868199i \(0.665278\pi\)
\(200\) 12.0000 9.00000i 0.848528 0.636396i
\(201\) −16.0000 −1.12855
\(202\) 6.00000i 0.422159i
\(203\) 2.00000i 0.140372i
\(204\) 4.00000 0.280056
\(205\) 2.00000 4.00000i 0.139686 0.279372i
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) 2.00000i 0.138675i
\(209\) −36.0000 −2.49017
\(210\) −2.00000 1.00000i −0.138013 0.0690066i
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 10.0000i 0.685189i
\(214\) 4.00000 0.273434
\(215\) −8.00000 4.00000i −0.545595 0.272798i
\(216\) 3.00000 0.204124
\(217\) 10.0000i 0.678844i
\(218\) 2.00000i 0.135457i
\(219\) 6.00000 0.405442
\(220\) −6.00000 + 12.0000i −0.404520 + 0.809040i
\(221\) −8.00000 −0.538138
\(222\) 4.00000i 0.268462i
\(223\) 24.0000i 1.60716i −0.595198 0.803579i \(-0.702926\pi\)
0.595198 0.803579i \(-0.297074\pi\)
\(224\) −5.00000 −0.334077
\(225\) 3.00000 + 4.00000i 0.200000 + 0.266667i
\(226\) −6.00000 −0.399114
\(227\) 8.00000i 0.530979i −0.964114 0.265489i \(-0.914466\pi\)
0.964114 0.265489i \(-0.0855335\pi\)
\(228\) 6.00000i 0.397360i
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) 6.00000 0.394771
\(232\) 6.00000i 0.393919i
\(233\) 26.0000i 1.70332i −0.524097 0.851658i \(-0.675597\pi\)
0.524097 0.851658i \(-0.324403\pi\)
\(234\) −2.00000 −0.130744
\(235\) 0 0
\(236\) 8.00000 0.520756
\(237\) 4.00000i 0.259828i
\(238\) 4.00000i 0.259281i
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) −2.00000 1.00000i −0.129099 0.0645497i
\(241\) 22.0000 1.41714 0.708572 0.705638i \(-0.249340\pi\)
0.708572 + 0.705638i \(0.249340\pi\)
\(242\) 25.0000i 1.60706i
\(243\) 1.00000i 0.0641500i
\(244\) −2.00000 −0.128037
\(245\) −1.00000 + 2.00000i −0.0638877 + 0.127775i
\(246\) −2.00000 −0.127515
\(247\) 12.0000i 0.763542i
\(248\) 30.0000i 1.90500i
\(249\) −8.00000 −0.506979
\(250\) −2.00000 11.0000i −0.126491 0.695701i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) 0 0
\(254\) 20.0000 1.25491
\(255\) 4.00000 8.00000i 0.250490 0.500979i
\(256\) −17.0000 −1.06250
\(257\) 16.0000i 0.998053i −0.866587 0.499026i \(-0.833691\pi\)
0.866587 0.499026i \(-0.166309\pi\)
\(258\) 4.00000i 0.249029i
\(259\) −4.00000 −0.248548
\(260\) −4.00000 2.00000i −0.248069 0.124035i
\(261\) −2.00000 −0.123797
\(262\) 4.00000i 0.247121i
\(263\) 24.0000i 1.47990i −0.672660 0.739952i \(-0.734848\pi\)
0.672660 0.739952i \(-0.265152\pi\)
\(264\) 18.0000 1.10782
\(265\) 12.0000 + 6.00000i 0.737154 + 0.368577i
\(266\) −6.00000 −0.367884
\(267\) 6.00000i 0.367194i
\(268\) 16.0000i 0.977356i
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 1.00000 2.00000i 0.0608581 0.121716i
\(271\) −14.0000 −0.850439 −0.425220 0.905090i \(-0.639803\pi\)
−0.425220 + 0.905090i \(0.639803\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 2.00000i 0.121046i
\(274\) −6.00000 −0.362473
\(275\) 18.0000 + 24.0000i 1.08544 + 1.44725i
\(276\) 0 0
\(277\) 28.0000i 1.68236i 0.540758 + 0.841178i \(0.318138\pi\)
−0.540758 + 0.841178i \(0.681862\pi\)
\(278\) 2.00000i 0.119952i
\(279\) 10.0000 0.598684
\(280\) −3.00000 + 6.00000i −0.179284 + 0.358569i
\(281\) −2.00000 −0.119310 −0.0596550 0.998219i \(-0.519000\pi\)
−0.0596550 + 0.998219i \(0.519000\pi\)
\(282\) 0 0
\(283\) 20.0000i 1.18888i 0.804141 + 0.594438i \(0.202626\pi\)
−0.804141 + 0.594438i \(0.797374\pi\)
\(284\) 10.0000 0.593391
\(285\) 12.0000 + 6.00000i 0.710819 + 0.355409i
\(286\) −12.0000 −0.709575
\(287\) 2.00000i 0.118056i
\(288\) 5.00000i 0.294628i
\(289\) 1.00000 0.0588235
\(290\) 4.00000 + 2.00000i 0.234888 + 0.117444i
\(291\) −2.00000 −0.117242
\(292\) 6.00000i 0.351123i
\(293\) 24.0000i 1.40209i 0.713115 + 0.701047i \(0.247284\pi\)
−0.713115 + 0.701047i \(0.752716\pi\)
\(294\) 1.00000 0.0583212
\(295\) 8.00000 16.0000i 0.465778 0.931556i
\(296\) −12.0000 −0.697486
\(297\) 6.00000i 0.348155i
\(298\) 14.0000i 0.810998i
\(299\) 0 0
\(300\) 4.00000 3.00000i 0.230940 0.173205i
\(301\) 4.00000 0.230556
\(302\) 8.00000i 0.460348i
\(303\) 6.00000i 0.344691i
\(304\) −6.00000 −0.344124
\(305\) −2.00000 + 4.00000i −0.114520 + 0.229039i
\(306\) −4.00000 −0.228665
\(307\) 4.00000i 0.228292i −0.993464 0.114146i \(-0.963587\pi\)
0.993464 0.114146i \(-0.0364132\pi\)
\(308\) 6.00000i 0.341882i
\(309\) −8.00000 −0.455104
\(310\) −20.0000 10.0000i −1.13592 0.567962i
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 6.00000i 0.339683i
\(313\) 6.00000i 0.339140i 0.985518 + 0.169570i \(0.0542379\pi\)
−0.985518 + 0.169570i \(0.945762\pi\)
\(314\) 18.0000 1.01580
\(315\) −2.00000 1.00000i −0.112687 0.0563436i
\(316\) −4.00000 −0.225018
\(317\) 18.0000i 1.01098i 0.862832 + 0.505490i \(0.168688\pi\)
−0.862832 + 0.505490i \(0.831312\pi\)
\(318\) 6.00000i 0.336463i
\(319\) −12.0000 −0.671871
\(320\) −7.00000 + 14.0000i −0.391312 + 0.782624i
\(321\) 4.00000 0.223258
\(322\) 0 0
\(323\) 24.0000i 1.33540i
\(324\) 1.00000 0.0555556
\(325\) −8.00000 + 6.00000i −0.443760 + 0.332820i
\(326\) −4.00000 −0.221540
\(327\) 2.00000i 0.110600i
\(328\) 6.00000i 0.331295i
\(329\) 0 0
\(330\) 6.00000 12.0000i 0.330289 0.660578i
\(331\) −24.0000 −1.31916 −0.659580 0.751635i \(-0.729266\pi\)
−0.659580 + 0.751635i \(0.729266\pi\)
\(332\) 8.00000i 0.439057i
\(333\) 4.00000i 0.219199i
\(334\) 12.0000 0.656611
\(335\) 32.0000 + 16.0000i 1.74835 + 0.874173i
\(336\) 1.00000 0.0545545
\(337\) 24.0000i 1.30736i 0.756770 + 0.653682i \(0.226776\pi\)
−0.756770 + 0.653682i \(0.773224\pi\)
\(338\) 9.00000i 0.489535i
\(339\) −6.00000 −0.325875
\(340\) −8.00000 4.00000i −0.433861 0.216930i
\(341\) 60.0000 3.24918
\(342\) 6.00000i 0.324443i
\(343\) 1.00000i 0.0539949i
\(344\) 12.0000 0.646997
\(345\) 0 0
\(346\) 0 0
\(347\) 12.0000i 0.644194i −0.946707 0.322097i \(-0.895612\pi\)
0.946707 0.322097i \(-0.104388\pi\)
\(348\) 2.00000i 0.107211i
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 3.00000 + 4.00000i 0.160357 + 0.213809i
\(351\) −2.00000 −0.106752
\(352\) 30.0000i 1.59901i
\(353\) 20.0000i 1.06449i 0.846590 + 0.532246i \(0.178652\pi\)
−0.846590 + 0.532246i \(0.821348\pi\)
\(354\) −8.00000 −0.425195
\(355\) 10.0000 20.0000i 0.530745 1.06149i
\(356\) −6.00000 −0.317999
\(357\) 4.00000i 0.211702i
\(358\) 14.0000i 0.739923i
\(359\) −22.0000 −1.16112 −0.580558 0.814219i \(-0.697165\pi\)
−0.580558 + 0.814219i \(0.697165\pi\)
\(360\) −6.00000 3.00000i −0.316228 0.158114i
\(361\) 17.0000 0.894737
\(362\) 6.00000i 0.315353i
\(363\) 25.0000i 1.31216i
\(364\) 2.00000 0.104828
\(365\) −12.0000 6.00000i −0.628109 0.314054i
\(366\) 2.00000 0.104542
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) −2.00000 −0.104116
\(370\) −4.00000 + 8.00000i −0.207950 + 0.415900i
\(371\) −6.00000 −0.311504
\(372\) 10.0000i 0.518476i
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) −24.0000 −1.24101
\(375\) −2.00000 11.0000i −0.103280 0.568038i
\(376\) 0 0
\(377\) 4.00000i 0.206010i
\(378\) 1.00000i 0.0514344i
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) 6.00000 12.0000i 0.307794 0.615587i
\(381\) 20.0000 1.02463
\(382\) 18.0000i 0.920960i
\(383\) 20.0000i 1.02195i −0.859595 0.510976i \(-0.829284\pi\)
0.859595 0.510976i \(-0.170716\pi\)
\(384\) −3.00000 −0.153093
\(385\) −12.0000 6.00000i −0.611577 0.305788i
\(386\) 8.00000 0.407189
\(387\) 4.00000i 0.203331i
\(388\) 2.00000i 0.101535i
\(389\) −26.0000 −1.31825 −0.659126 0.752032i \(-0.729074\pi\)
−0.659126 + 0.752032i \(0.729074\pi\)
\(390\) 4.00000 + 2.00000i 0.202548 + 0.101274i
\(391\) 0 0
\(392\) 3.00000i 0.151523i
\(393\) 4.00000i 0.201773i
\(394\) 2.00000 0.100759
\(395\) −4.00000 + 8.00000i −0.201262 + 0.402524i
\(396\) 6.00000 0.301511
\(397\) 22.0000i 1.10415i −0.833795 0.552074i \(-0.813837\pi\)
0.833795 0.552074i \(-0.186163\pi\)
\(398\) 14.0000i 0.701757i
\(399\) −6.00000 −0.300376
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) −30.0000 −1.49813 −0.749064 0.662497i \(-0.769497\pi\)
−0.749064 + 0.662497i \(0.769497\pi\)
\(402\) 16.0000i 0.798007i
\(403\) 20.0000i 0.996271i
\(404\) −6.00000 −0.298511
\(405\) 1.00000 2.00000i 0.0496904 0.0993808i
\(406\) −2.00000 −0.0992583
\(407\) 24.0000i 1.18964i
\(408\) 12.0000i 0.594089i
\(409\) 22.0000 1.08783 0.543915 0.839140i \(-0.316941\pi\)
0.543915 + 0.839140i \(0.316941\pi\)
\(410\) 4.00000 + 2.00000i 0.197546 + 0.0987730i
\(411\) −6.00000 −0.295958
\(412\) 8.00000i 0.394132i
\(413\) 8.00000i 0.393654i
\(414\) 0 0
\(415\) 16.0000 + 8.00000i 0.785409 + 0.392705i
\(416\) 10.0000 0.490290
\(417\) 2.00000i 0.0979404i
\(418\) 36.0000i 1.76082i
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) −1.00000 + 2.00000i −0.0487950 + 0.0975900i
\(421\) 18.0000 0.877266 0.438633 0.898666i \(-0.355463\pi\)
0.438633 + 0.898666i \(0.355463\pi\)
\(422\) 16.0000i 0.778868i
\(423\) 0 0
\(424\) −18.0000 −0.874157
\(425\) −16.0000 + 12.0000i −0.776114 + 0.582086i
\(426\) −10.0000 −0.484502
\(427\) 2.00000i 0.0967868i
\(428\) 4.00000i 0.193347i
\(429\) −12.0000 −0.579365
\(430\) 4.00000 8.00000i 0.192897 0.385794i
\(431\) −14.0000 −0.674356 −0.337178 0.941441i \(-0.609472\pi\)
−0.337178 + 0.941441i \(0.609472\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 34.0000i 1.63394i −0.576683 0.816968i \(-0.695653\pi\)
0.576683 0.816968i \(-0.304347\pi\)
\(434\) 10.0000 0.480015
\(435\) 4.00000 + 2.00000i 0.191785 + 0.0958927i
\(436\) −2.00000 −0.0957826
\(437\) 0 0
\(438\) 6.00000i 0.286691i
\(439\) −6.00000 −0.286364 −0.143182 0.989696i \(-0.545733\pi\)
−0.143182 + 0.989696i \(0.545733\pi\)
\(440\) −36.0000 18.0000i −1.71623 0.858116i
\(441\) 1.00000 0.0476190
\(442\) 8.00000i 0.380521i
\(443\) 4.00000i 0.190046i −0.995475 0.0950229i \(-0.969708\pi\)
0.995475 0.0950229i \(-0.0302924\pi\)
\(444\) −4.00000 −0.189832
\(445\) −6.00000 + 12.0000i −0.284427 + 0.568855i
\(446\) 24.0000 1.13643
\(447\) 14.0000i 0.662177i
\(448\) 7.00000i 0.330719i
\(449\) −10.0000 −0.471929 −0.235965 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) −4.00000 + 3.00000i −0.188562 + 0.141421i
\(451\) −12.0000 −0.565058
\(452\) 6.00000i 0.282216i
\(453\) 8.00000i 0.375873i
\(454\) 8.00000 0.375459
\(455\) 2.00000 4.00000i 0.0937614 0.187523i
\(456\) −18.0000 −0.842927
\(457\) 20.0000i 0.935561i 0.883845 + 0.467780i \(0.154946\pi\)
−0.883845 + 0.467780i \(0.845054\pi\)
\(458\) 10.0000i 0.467269i
\(459\) −4.00000 −0.186704
\(460\) 0 0
\(461\) 30.0000 1.39724 0.698620 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) 6.00000i 0.279145i
\(463\) 36.0000i 1.67306i 0.547920 + 0.836531i \(0.315420\pi\)
−0.547920 + 0.836531i \(0.684580\pi\)
\(464\) −2.00000 −0.0928477
\(465\) −20.0000 10.0000i −0.927478 0.463739i
\(466\) 26.0000 1.20443
\(467\) 24.0000i 1.11059i 0.831654 + 0.555294i \(0.187394\pi\)
−0.831654 + 0.555294i \(0.812606\pi\)
\(468\) 2.00000i 0.0924500i
\(469\) −16.0000 −0.738811
\(470\) 0 0
\(471\) 18.0000 0.829396
\(472\) 24.0000i 1.10469i
\(473\) 24.0000i 1.10352i
\(474\) 4.00000 0.183726
\(475\) −18.0000 24.0000i −0.825897 1.10120i
\(476\) 4.00000 0.183340
\(477\) 6.00000i 0.274721i
\(478\) 6.00000i 0.274434i
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) −5.00000 + 10.0000i −0.228218 + 0.456435i
\(481\) 8.00000 0.364769
\(482\) 22.0000i 1.00207i
\(483\) 0 0
\(484\) 25.0000 1.13636
\(485\) 4.00000 + 2.00000i 0.181631 + 0.0908153i
\(486\) −1.00000 −0.0453609
\(487\) 12.0000i 0.543772i −0.962329 0.271886i \(-0.912353\pi\)
0.962329 0.271886i \(-0.0876473\pi\)
\(488\) 6.00000i 0.271607i
\(489\) −4.00000 −0.180886
\(490\) −2.00000 1.00000i −0.0903508 0.0451754i
\(491\) 10.0000 0.451294 0.225647 0.974209i \(-0.427550\pi\)
0.225647 + 0.974209i \(0.427550\pi\)
\(492\) 2.00000i 0.0901670i
\(493\) 8.00000i 0.360302i
\(494\) 12.0000 0.539906
\(495\) 6.00000 12.0000i 0.269680 0.539360i
\(496\) 10.0000 0.449013
\(497\) 10.0000i 0.448561i
\(498\) 8.00000i 0.358489i
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) −11.0000 + 2.00000i −0.491935 + 0.0894427i
\(501\) 12.0000 0.536120
\(502\) 0 0
\(503\) 36.0000i 1.60516i −0.596544 0.802580i \(-0.703460\pi\)
0.596544 0.802580i \(-0.296540\pi\)
\(504\) 3.00000 0.133631
\(505\) −6.00000 + 12.0000i −0.266996 + 0.533993i
\(506\) 0 0
\(507\) 9.00000i 0.399704i
\(508\) 20.0000i 0.887357i
\(509\) −30.0000 −1.32973 −0.664863 0.746965i \(-0.731510\pi\)
−0.664863 + 0.746965i \(0.731510\pi\)
\(510\) 8.00000 + 4.00000i 0.354246 + 0.177123i
\(511\) 6.00000 0.265424
\(512\) 11.0000i 0.486136i
\(513\) 6.00000i 0.264906i
\(514\) 16.0000 0.705730
\(515\) 16.0000 + 8.00000i 0.705044 + 0.352522i
\(516\) 4.00000 0.176090
\(517\) 0 0
\(518\) 4.00000i 0.175750i
\(519\) 0 0
\(520\) 6.00000 12.0000i 0.263117 0.526235i
\(521\) 38.0000 1.66481 0.832405 0.554168i \(-0.186963\pi\)
0.832405 + 0.554168i \(0.186963\pi\)
\(522\) 2.00000i 0.0875376i
\(523\) 20.0000i 0.874539i 0.899331 + 0.437269i \(0.144054\pi\)
−0.899331 + 0.437269i \(0.855946\pi\)
\(524\) 4.00000 0.174741
\(525\) 3.00000 + 4.00000i 0.130931 + 0.174574i
\(526\) 24.0000 1.04645
\(527\) 40.0000i 1.74243i
\(528\) 6.00000i 0.261116i
\(529\) 23.0000 1.00000
\(530\) −6.00000 + 12.0000i −0.260623 + 0.521247i
\(531\) −8.00000 −0.347170
\(532\) 6.00000i 0.260133i
\(533\) 4.00000i 0.173259i
\(534\) 6.00000 0.259645
\(535\) −8.00000 4.00000i −0.345870 0.172935i
\(536\) −48.0000 −2.07328
\(537\) 14.0000i 0.604145i
\(538\) 14.0000i 0.603583i
\(539\) 6.00000 0.258438
\(540\) −2.00000 1.00000i −0.0860663 0.0430331i
\(541\) 6.00000 0.257960 0.128980 0.991647i \(-0.458830\pi\)
0.128980 + 0.991647i \(0.458830\pi\)
\(542\) 14.0000i 0.601351i
\(543\) 6.00000i 0.257485i
\(544\) 20.0000 0.857493
\(545\) −2.00000 + 4.00000i −0.0856706 + 0.171341i
\(546\) −2.00000 −0.0855921
\(547\) 16.0000i 0.684111i 0.939680 + 0.342055i \(0.111123\pi\)
−0.939680 + 0.342055i \(0.888877\pi\)
\(548\) 6.00000i 0.256307i
\(549\) 2.00000 0.0853579
\(550\) −24.0000 + 18.0000i −1.02336 + 0.767523i
\(551\) 12.0000 0.511217
\(552\) 0 0
\(553\) 4.00000i 0.170097i
\(554\) −28.0000 −1.18961
\(555\) −4.00000 + 8.00000i −0.169791 + 0.339581i
\(556\) −2.00000 −0.0848189
\(557\) 38.0000i 1.61011i −0.593199 0.805056i \(-0.702135\pi\)
0.593199 0.805056i \(-0.297865\pi\)
\(558\) 10.0000i 0.423334i
\(559\) −8.00000 −0.338364
\(560\) −2.00000 1.00000i −0.0845154 0.0422577i
\(561\) −24.0000 −1.01328
\(562\) 2.00000i 0.0843649i
\(563\) 36.0000i 1.51722i −0.651546 0.758610i \(-0.725879\pi\)
0.651546 0.758610i \(-0.274121\pi\)
\(564\) 0 0
\(565\) 12.0000 + 6.00000i 0.504844 + 0.252422i
\(566\) −20.0000 −0.840663
\(567\) 1.00000i 0.0419961i
\(568\) 30.0000i 1.25877i
\(569\) 30.0000 1.25767 0.628833 0.777541i \(-0.283533\pi\)
0.628833 + 0.777541i \(0.283533\pi\)
\(570\) −6.00000 + 12.0000i −0.251312 + 0.502625i
\(571\) 36.0000 1.50655 0.753277 0.657704i \(-0.228472\pi\)
0.753277 + 0.657704i \(0.228472\pi\)
\(572\) 12.0000i 0.501745i
\(573\) 18.0000i 0.751961i
\(574\) −2.00000 −0.0834784
\(575\) 0 0
\(576\) 7.00000 0.291667
\(577\) 14.0000i 0.582828i −0.956597 0.291414i \(-0.905874\pi\)
0.956597 0.291414i \(-0.0941257\pi\)
\(578\) 1.00000i 0.0415945i
\(579\) 8.00000 0.332469
\(580\) 2.00000 4.00000i 0.0830455 0.166091i
\(581\) −8.00000 −0.331896
\(582\) 2.00000i 0.0829027i
\(583\) 36.0000i 1.49097i
\(584\) 18.0000 0.744845
\(585\) 4.00000 + 2.00000i 0.165380 + 0.0826898i
\(586\) −24.0000 −0.991431
\(587\) 12.0000i 0.495293i 0.968850 + 0.247647i \(0.0796572\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(588\) 1.00000i 0.0412393i
\(589\) −60.0000 −2.47226
\(590\) 16.0000 + 8.00000i 0.658710 + 0.329355i
\(591\) 2.00000 0.0822690
\(592\) 4.00000i 0.164399i
\(593\) 44.0000i 1.80686i 0.428732 + 0.903432i \(0.358960\pi\)
−0.428732 + 0.903432i \(0.641040\pi\)
\(594\) −6.00000 −0.246183
\(595\) 4.00000 8.00000i 0.163984 0.327968i
\(596\) 14.0000 0.573462
\(597\) 14.0000i 0.572982i
\(598\) 0 0
\(599\) 2.00000 0.0817178 0.0408589 0.999165i \(-0.486991\pi\)
0.0408589 + 0.999165i \(0.486991\pi\)
\(600\) 9.00000 + 12.0000i 0.367423 + 0.489898i
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 4.00000i 0.163028i
\(603\) 16.0000i 0.651570i
\(604\) 8.00000 0.325515
\(605\) 25.0000 50.0000i 1.01639 2.03279i
\(606\) 6.00000 0.243733
\(607\) 24.0000i 0.974130i −0.873366 0.487065i \(-0.838067\pi\)
0.873366 0.487065i \(-0.161933\pi\)
\(608\) 30.0000i 1.21666i
\(609\) −2.00000 −0.0810441
\(610\) −4.00000 2.00000i −0.161955 0.0809776i
\(611\) 0 0
\(612\) 4.00000i 0.161690i
\(613\) 4.00000i 0.161558i 0.996732 + 0.0807792i \(0.0257409\pi\)
−0.996732 + 0.0807792i \(0.974259\pi\)
\(614\) 4.00000 0.161427
\(615\) 4.00000 + 2.00000i 0.161296 + 0.0806478i
\(616\) 18.0000 0.725241
\(617\) 26.0000i 1.04672i 0.852111 + 0.523360i \(0.175322\pi\)
−0.852111 + 0.523360i \(0.824678\pi\)
\(618\) 8.00000i 0.321807i
\(619\) −10.0000 −0.401934 −0.200967 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) −10.0000 + 20.0000i −0.401610 + 0.803219i
\(621\) 0 0
\(622\) 24.0000i 0.962312i
\(623\) 6.00000i 0.240385i
\(624\) −2.00000 −0.0800641
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) −6.00000 −0.239808
\(627\) 36.0000i 1.43770i
\(628\) 18.0000i 0.718278i
\(629\) 16.0000 0.637962
\(630\) 1.00000 2.00000i 0.0398410 0.0796819i
\(631\) −20.0000 −0.796187 −0.398094 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) 12.0000i 0.477334i
\(633\) 16.0000i 0.635943i
\(634\) −18.0000 −0.714871
\(635\) −40.0000 20.0000i −1.58735 0.793676i
\(636\) −6.00000 −0.237915
\(637\) 2.00000i 0.0792429i
\(638\) 12.0000i 0.475085i
\(639\) −10.0000 −0.395594
\(640\) 6.00000 + 3.00000i 0.237171 + 0.118585i
\(641\) −2.00000 −0.0789953 −0.0394976 0.999220i \(-0.512576\pi\)
−0.0394976 + 0.999220i \(0.512576\pi\)
\(642\) 4.00000i 0.157867i
\(643\) 20.0000i 0.788723i −0.918955 0.394362i \(-0.870966\pi\)
0.918955 0.394362i \(-0.129034\pi\)
\(644\) 0 0
\(645\) 4.00000 8.00000i 0.157500 0.315000i
\(646\) 24.0000 0.944267
\(647\) 20.0000i 0.786281i 0.919478 + 0.393141i \(0.128611\pi\)
−0.919478 + 0.393141i \(0.871389\pi\)
\(648\) 3.00000i 0.117851i
\(649\) −48.0000 −1.88416
\(650\) −6.00000 8.00000i −0.235339 0.313786i
\(651\) 10.0000 0.391931
\(652\) 4.00000i 0.156652i
\(653\) 2.00000i 0.0782660i 0.999234 + 0.0391330i \(0.0124596\pi\)
−0.999234 + 0.0391330i \(0.987540\pi\)
\(654\) 2.00000 0.0782062
\(655\) 4.00000 8.00000i 0.156293 0.312586i
\(656\) −2.00000 −0.0780869
\(657\) 6.00000i 0.234082i
\(658\) 0 0
\(659\) 18.0000 0.701180 0.350590 0.936529i \(-0.385981\pi\)
0.350590 + 0.936529i \(0.385981\pi\)
\(660\) −12.0000 6.00000i −0.467099 0.233550i
\(661\) −18.0000 −0.700119 −0.350059 0.936727i \(-0.613839\pi\)
−0.350059 + 0.936727i \(0.613839\pi\)
\(662\) 24.0000i 0.932786i
\(663\) 8.00000i 0.310694i
\(664\) −24.0000 −0.931381
\(665\) 12.0000 + 6.00000i 0.465340 + 0.232670i
\(666\) 4.00000 0.154997
\(667\) 0 0
\(668\) 12.0000i 0.464294i
\(669\) 24.0000 0.927894
\(670\) −16.0000 + 32.0000i −0.618134 + 1.23627i
\(671\) 12.0000 0.463255
\(672\) 5.00000i 0.192879i
\(673\) 36.0000i 1.38770i −0.720121 0.693849i \(-0.755914\pi\)
0.720121 0.693849i \(-0.244086\pi\)
\(674\) −24.0000 −0.924445
\(675\) −4.00000 + 3.00000i −0.153960 + 0.115470i
\(676\) 9.00000 0.346154
\(677\) 32.0000i 1.22986i −0.788582 0.614930i \(-0.789184\pi\)
0.788582 0.614930i \(-0.210816\pi\)
\(678\) 6.00000i 0.230429i
\(679\) −2.00000 −0.0767530
\(680\) 12.0000 24.0000i 0.460179 0.920358i
\(681\) 8.00000 0.306561
\(682\) 60.0000i 2.29752i
\(683\) 28.0000i 1.07139i 0.844411 + 0.535695i \(0.179950\pi\)
−0.844411 + 0.535695i \(0.820050\pi\)
\(684\) −6.00000 −0.229416
\(685\) 12.0000 + 6.00000i 0.458496 + 0.229248i
\(686\) 1.00000 0.0381802
\(687\) 10.0000i 0.381524i
\(688\) 4.00000i 0.152499i
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) −50.0000 −1.90209 −0.951045 0.309053i \(-0.899988\pi\)
−0.951045 + 0.309053i \(0.899988\pi\)
\(692\) 0 0
\(693\) 6.00000i 0.227921i
\(694\) 12.0000 0.455514
\(695\) −2.00000 + 4.00000i −0.0758643 + 0.151729i
\(696\) −6.00000 −0.227429
\(697\) 8.00000i 0.303022i
\(698\) 2.00000i 0.0757011i
\(699\) 26.0000 0.983410
\(700\) 4.00000 3.00000i 0.151186 0.113389i
\(701\) −10.0000 −0.377695 −0.188847 0.982006i \(-0.560475\pi\)
−0.188847 + 0.982006i \(0.560475\pi\)
\(702\) 2.00000i 0.0754851i
\(703\) 24.0000i 0.905177i
\(704\) 42.0000 1.58293
\(705\) 0 0
\(706\) −20.0000 −0.752710
\(707\) 6.00000i 0.225653i
\(708\) 8.00000i 0.300658i
\(709\) −26.0000 −0.976450 −0.488225 0.872718i \(-0.662356\pi\)
−0.488225 + 0.872718i \(0.662356\pi\)
\(710\) 20.0000 + 10.0000i 0.750587 + 0.375293i
\(711\) 4.00000 0.150012
\(712\) 18.0000i 0.674579i
\(713\) 0 0
\(714\) −4.00000 −0.149696
\(715\) 24.0000 + 12.0000i 0.897549 + 0.448775i
\(716\) 14.0000 0.523205
\(717\) 6.00000i 0.224074i
\(718\) 22.0000i 0.821033i
\(719\) −12.0000 −0.447524 −0.223762 0.974644i \(-0.571834\pi\)
−0.223762 + 0.974644i \(0.571834\pi\)
\(720\) 1.00000 2.00000i 0.0372678 0.0745356i
\(721\) −8.00000 −0.297936
\(722\) 17.0000i 0.632674i
\(723\) 22.0000i 0.818189i
\(724\) −6.00000 −0.222988
\(725\) −6.00000 8.00000i −0.222834 0.297113i
\(726\) −25.0000 −0.927837
\(727\) 40.0000i 1.48352i 0.670667 + 0.741759i \(0.266008\pi\)
−0.670667 + 0.741759i \(0.733992\pi\)
\(728\) 6.00000i 0.222375i
\(729\) −1.00000 −0.0370370
\(730\) 6.00000 12.0000i 0.222070 0.444140i
\(731\) −16.0000 −0.591781
\(732\) 2.00000i 0.0739221i
\(733\) 22.0000i 0.812589i 0.913742 + 0.406294i \(0.133179\pi\)
−0.913742 + 0.406294i \(0.866821\pi\)
\(734\) 0 0
\(735\) −2.00000 1.00000i −0.0737711 0.0368856i
\(736\) 0 0
\(737\) 96.0000i 3.53621i
\(738\) 2.00000i 0.0736210i
\(739\) 44.0000 1.61857 0.809283 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(740\) 8.00000 + 4.00000i 0.294086 + 0.147043i
\(741\) 12.0000 0.440831
\(742\) 6.00000i 0.220267i
\(743\) 40.0000i 1.46746i 0.679442 + 0.733729i \(0.262222\pi\)
−0.679442 + 0.733729i \(0.737778\pi\)
\(744\) 30.0000 1.09985
\(745\) 14.0000 28.0000i 0.512920 1.02584i
\(746\) 0 0
\(747\) 8.00000i 0.292705i
\(748\) 24.0000i 0.877527i
\(749\) 4.00000 0.146157
\(750\) 11.0000 2.00000i 0.401663 0.0730297i
\(751\) −12.0000 −0.437886 −0.218943 0.975738i \(-0.570261\pi\)
−0.218943 + 0.975738i \(0.570261\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 4.00000 0.145671
\(755\) 8.00000 16.0000i 0.291150 0.582300i
\(756\) 1.00000 0.0363696
\(757\) 40.0000i 1.45382i 0.686730 + 0.726912i \(0.259045\pi\)
−0.686730 + 0.726912i \(0.740955\pi\)
\(758\) 28.0000i 1.01701i
\(759\) 0 0
\(760\) 36.0000 + 18.0000i 1.30586 + 0.652929i
\(761\) −22.0000 −0.797499 −0.398750 0.917060i \(-0.630556\pi\)
−0.398750 + 0.917060i \(0.630556\pi\)
\(762\) 20.0000i 0.724524i
\(763\) 2.00000i 0.0724049i
\(764\) −18.0000 −0.651217
\(765\) 8.00000 + 4.00000i 0.289241 + 0.144620i
\(766\) 20.0000 0.722629
\(767\) 16.0000i 0.577727i
\(768\) 17.0000i 0.613435i
\(769\) 18.0000 0.649097 0.324548 0.945869i \(-0.394788\pi\)
0.324548 + 0.945869i \(0.394788\pi\)
\(770\) 6.00000 12.0000i 0.216225 0.432450i
\(771\) 16.0000 0.576226
\(772\) 8.00000i 0.287926i
\(773\) 24.0000i 0.863220i 0.902060 + 0.431610i \(0.142054\pi\)
−0.902060 + 0.431610i \(0.857946\pi\)
\(774\) −4.00000 −0.143777
\(775\) 30.0000 + 40.0000i 1.07763 + 1.43684i
\(776\) −6.00000 −0.215387
\(777\) 4.00000i 0.143499i
\(778\) 26.0000i 0.932145i
\(779\) 12.0000 0.429945
\(780\) 2.00000 4.00000i 0.0716115 0.143223i
\(781\) −60.0000 −2.14697
\(782\) 0 0
\(783\) 2.00000i 0.0714742i
\(784\) 1.00000 0.0357143
\(785\) −36.0000 18.0000i −1.28490 0.642448i
\(786\) −4.00000 −0.142675
\(787\) 4.00000i 0.142585i 0.997455 + 0.0712923i \(0.0227123\pi\)
−0.997455 + 0.0712923i \(0.977288\pi\)
\(788\) 2.00000i 0.0712470i
\(789\) 24.0000 0.854423
\(790\) −8.00000 4.00000i −0.284627 0.142314i
\(791\) −6.00000 −0.213335
\(792\) 18.0000i 0.639602i
\(793\) 4.00000i 0.142044i
\(794\) 22.0000 0.780751
\(795\) −6.00000 + 12.0000i −0.212798 + 0.425596i
\(796\) −14.0000 −0.496217
\(797\) 16.0000i 0.566749i 0.959009 + 0.283375i \(0.0914540\pi\)
−0.959009 + 0.283375i \(0.908546\pi\)
\(798\) 6.00000i 0.212398i
\(799\) 0 0
\(800\) 20.0000 15.0000i 0.707107 0.530330i
\(801\) 6.00000 0.212000
\(802\) 30.0000i 1.05934i