Properties

Label 1815.2.c.b.364.2
Level $1815$
Weight $2$
Character 1815.364
Analytic conductor $14.493$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1815.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.4928479669\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
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 364.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1815.364
Dual form 1815.2.c.b.364.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000i q^{3} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} +1.00000 q^{6} +4.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000i q^{3} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} +1.00000 q^{6} +4.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} +(-2.00000 - 1.00000i) q^{10} -1.00000i q^{12} -2.00000i q^{13} -4.00000 q^{14} +(2.00000 + 1.00000i) q^{15} -1.00000 q^{16} +2.00000i q^{17} -1.00000i q^{18} +8.00000 q^{19} +(-1.00000 + 2.00000i) q^{20} +4.00000 q^{21} +4.00000i q^{23} +3.00000 q^{24} +(-3.00000 - 4.00000i) q^{25} +2.00000 q^{26} +1.00000i q^{27} +4.00000i q^{28} +4.00000 q^{29} +(-1.00000 + 2.00000i) q^{30} -8.00000 q^{31} +5.00000i q^{32} -2.00000 q^{34} +(-8.00000 - 4.00000i) q^{35} -1.00000 q^{36} -8.00000i q^{37} +8.00000i q^{38} -2.00000 q^{39} +(-6.00000 - 3.00000i) q^{40} -12.0000 q^{41} +4.00000i q^{42} +8.00000i q^{43} +(1.00000 - 2.00000i) q^{45} -4.00000 q^{46} +4.00000i q^{47} +1.00000i q^{48} -9.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +2.00000 q^{51} -2.00000i q^{52} -4.00000i q^{53} -1.00000 q^{54} -12.0000 q^{56} -8.00000i q^{57} +4.00000i q^{58} +8.00000 q^{59} +(2.00000 + 1.00000i) q^{60} -8.00000i q^{62} -4.00000i q^{63} -7.00000 q^{64} +(4.00000 + 2.00000i) q^{65} +4.00000i q^{67} +2.00000i q^{68} +4.00000 q^{69} +(4.00000 - 8.00000i) q^{70} -12.0000 q^{71} -3.00000i q^{72} -2.00000i q^{73} +8.00000 q^{74} +(-4.00000 + 3.00000i) q^{75} +8.00000 q^{76} -2.00000i q^{78} +8.00000 q^{79} +(1.00000 - 2.00000i) q^{80} +1.00000 q^{81} -12.0000i q^{82} -4.00000i q^{83} +4.00000 q^{84} +(-4.00000 - 2.00000i) q^{85} -8.00000 q^{86} -4.00000i q^{87} -6.00000 q^{89} +(2.00000 + 1.00000i) q^{90} +8.00000 q^{91} +4.00000i q^{92} +8.00000i q^{93} -4.00000 q^{94} +(-8.00000 + 16.0000i) q^{95} +5.00000 q^{96} +8.00000i q^{97} -9.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{4} - 2q^{5} + 2q^{6} - 2q^{9} + O(q^{10}) \) \( 2q + 2q^{4} - 2q^{5} + 2q^{6} - 2q^{9} - 4q^{10} - 8q^{14} + 4q^{15} - 2q^{16} + 16q^{19} - 2q^{20} + 8q^{21} + 6q^{24} - 6q^{25} + 4q^{26} + 8q^{29} - 2q^{30} - 16q^{31} - 4q^{34} - 16q^{35} - 2q^{36} - 4q^{39} - 12q^{40} - 24q^{41} + 2q^{45} - 8q^{46} - 18q^{49} + 8q^{50} + 4q^{51} - 2q^{54} - 24q^{56} + 16q^{59} + 4q^{60} - 14q^{64} + 8q^{65} + 8q^{69} + 8q^{70} - 24q^{71} + 16q^{74} - 8q^{75} + 16q^{76} + 16q^{79} + 2q^{80} + 2q^{81} + 8q^{84} - 8q^{85} - 16q^{86} - 12q^{89} + 4q^{90} + 16q^{91} - 8q^{94} - 16q^{95} + 10q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times\).

\(n\) \(727\) \(1211\) \(1696\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(7\) 4.00000i 1.51186i 0.654654 + 0.755929i \(0.272814\pi\)
−0.654654 + 0.755929i \(0.727186\pi\)
\(8\) 3.00000i 1.06066i
\(9\) −1.00000 −0.333333
\(10\) −2.00000 1.00000i −0.632456 0.316228i
\(11\) 0 0
\(12\) 1.00000i 0.288675i
\(13\) 2.00000i 0.554700i −0.960769 0.277350i \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) −4.00000 −1.06904
\(15\) 2.00000 + 1.00000i 0.516398 + 0.258199i
\(16\) −1.00000 −0.250000
\(17\) 2.00000i 0.485071i 0.970143 + 0.242536i \(0.0779791\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 8.00000 1.83533 0.917663 0.397360i \(-0.130073\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) −1.00000 + 2.00000i −0.223607 + 0.447214i
\(21\) 4.00000 0.872872
\(22\) 0 0
\(23\) 4.00000i 0.834058i 0.908893 + 0.417029i \(0.136929\pi\)
−0.908893 + 0.417029i \(0.863071\pi\)
\(24\) 3.00000 0.612372
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 2.00000 0.392232
\(27\) 1.00000i 0.192450i
\(28\) 4.00000i 0.755929i
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) −1.00000 + 2.00000i −0.182574 + 0.365148i
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 5.00000i 0.883883i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) −8.00000 4.00000i −1.35225 0.676123i
\(36\) −1.00000 −0.166667
\(37\) 8.00000i 1.31519i −0.753371 0.657596i \(-0.771573\pi\)
0.753371 0.657596i \(-0.228427\pi\)
\(38\) 8.00000i 1.29777i
\(39\) −2.00000 −0.320256
\(40\) −6.00000 3.00000i −0.948683 0.474342i
\(41\) −12.0000 −1.87409 −0.937043 0.349215i \(-0.886448\pi\)
−0.937043 + 0.349215i \(0.886448\pi\)
\(42\) 4.00000i 0.617213i
\(43\) 8.00000i 1.21999i 0.792406 + 0.609994i \(0.208828\pi\)
−0.792406 + 0.609994i \(0.791172\pi\)
\(44\) 0 0
\(45\) 1.00000 2.00000i 0.149071 0.298142i
\(46\) −4.00000 −0.589768
\(47\) 4.00000i 0.583460i 0.956501 + 0.291730i \(0.0942309\pi\)
−0.956501 + 0.291730i \(0.905769\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −9.00000 −1.28571
\(50\) 4.00000 3.00000i 0.565685 0.424264i
\(51\) 2.00000 0.280056
\(52\) 2.00000i 0.277350i
\(53\) 4.00000i 0.549442i −0.961524 0.274721i \(-0.911414\pi\)
0.961524 0.274721i \(-0.0885855\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −12.0000 −1.60357
\(57\) 8.00000i 1.05963i
\(58\) 4.00000i 0.525226i
\(59\) 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
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 8.00000i 1.01600i
\(63\) 4.00000i 0.503953i
\(64\) −7.00000 −0.875000
\(65\) 4.00000 + 2.00000i 0.496139 + 0.248069i
\(66\) 0 0
\(67\) 4.00000i 0.488678i 0.969690 + 0.244339i \(0.0785709\pi\)
−0.969690 + 0.244339i \(0.921429\pi\)
\(68\) 2.00000i 0.242536i
\(69\) 4.00000 0.481543
\(70\) 4.00000 8.00000i 0.478091 0.956183i
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 3.00000i 0.353553i
\(73\) 2.00000i 0.234082i −0.993127 0.117041i \(-0.962659\pi\)
0.993127 0.117041i \(-0.0373409\pi\)
\(74\) 8.00000 0.929981
\(75\) −4.00000 + 3.00000i −0.461880 + 0.346410i
\(76\) 8.00000 0.917663
\(77\) 0 0
\(78\) 2.00000i 0.226455i
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 1.00000 2.00000i 0.111803 0.223607i
\(81\) 1.00000 0.111111
\(82\) 12.0000i 1.32518i
\(83\) 4.00000i 0.439057i −0.975606 0.219529i \(-0.929548\pi\)
0.975606 0.219529i \(-0.0704519\pi\)
\(84\) 4.00000 0.436436
\(85\) −4.00000 2.00000i −0.433861 0.216930i
\(86\) −8.00000 −0.862662
\(87\) 4.00000i 0.428845i
\(88\) 0 0
\(89\) −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
\(91\) 8.00000 0.838628
\(92\) 4.00000i 0.417029i
\(93\) 8.00000i 0.829561i
\(94\) −4.00000 −0.412568
\(95\) −8.00000 + 16.0000i −0.820783 + 1.64157i
\(96\) 5.00000 0.510310
\(97\) 8.00000i 0.812277i 0.913812 + 0.406138i \(0.133125\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) 9.00000i 0.909137i
\(99\) 0 0
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) 4.00000 0.398015 0.199007 0.979998i \(-0.436228\pi\)
0.199007 + 0.979998i \(0.436228\pi\)
\(102\) 2.00000i 0.198030i
\(103\) 12.0000i 1.18240i −0.806527 0.591198i \(-0.798655\pi\)
0.806527 0.591198i \(-0.201345\pi\)
\(104\) 6.00000 0.588348
\(105\) −4.00000 + 8.00000i −0.390360 + 0.780720i
\(106\) 4.00000 0.388514
\(107\) 12.0000i 1.16008i 0.814587 + 0.580042i \(0.196964\pi\)
−0.814587 + 0.580042i \(0.803036\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −8.00000 −0.766261 −0.383131 0.923694i \(-0.625154\pi\)
−0.383131 + 0.923694i \(0.625154\pi\)
\(110\) 0 0
\(111\) −8.00000 −0.759326
\(112\) 4.00000i 0.377964i
\(113\) 12.0000i 1.12887i 0.825479 + 0.564433i \(0.190905\pi\)
−0.825479 + 0.564433i \(0.809095\pi\)
\(114\) 8.00000 0.749269
\(115\) −8.00000 4.00000i −0.746004 0.373002i
\(116\) 4.00000 0.371391
\(117\) 2.00000i 0.184900i
\(118\) 8.00000i 0.736460i
\(119\) −8.00000 −0.733359
\(120\) −3.00000 + 6.00000i −0.273861 + 0.547723i
\(121\) 0 0
\(122\) 0 0
\(123\) 12.0000i 1.08200i
\(124\) −8.00000 −0.718421
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 4.00000 0.356348
\(127\) 4.00000i 0.354943i −0.984126 0.177471i \(-0.943208\pi\)
0.984126 0.177471i \(-0.0567917\pi\)
\(128\) 3.00000i 0.265165i
\(129\) 8.00000 0.704361
\(130\) −2.00000 + 4.00000i −0.175412 + 0.350823i
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 0 0
\(133\) 32.0000i 2.77475i
\(134\) −4.00000 −0.345547
\(135\) −2.00000 1.00000i −0.172133 0.0860663i
\(136\) −6.00000 −0.514496
\(137\) 4.00000i 0.341743i 0.985293 + 0.170872i \(0.0546583\pi\)
−0.985293 + 0.170872i \(0.945342\pi\)
\(138\) 4.00000i 0.340503i
\(139\) 16.0000 1.35710 0.678551 0.734553i \(-0.262608\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) −8.00000 4.00000i −0.676123 0.338062i
\(141\) 4.00000 0.336861
\(142\) 12.0000i 1.00702i
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −4.00000 + 8.00000i −0.332182 + 0.664364i
\(146\) 2.00000 0.165521
\(147\) 9.00000i 0.742307i
\(148\) 8.00000i 0.657596i
\(149\) 20.0000 1.63846 0.819232 0.573462i \(-0.194400\pi\)
0.819232 + 0.573462i \(0.194400\pi\)
\(150\) −3.00000 4.00000i −0.244949 0.326599i
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 24.0000i 1.94666i
\(153\) 2.00000i 0.161690i
\(154\) 0 0
\(155\) 8.00000 16.0000i 0.642575 1.28515i
\(156\) −2.00000 −0.160128
\(157\) 8.00000i 0.638470i −0.947676 0.319235i \(-0.896574\pi\)
0.947676 0.319235i \(-0.103426\pi\)
\(158\) 8.00000i 0.636446i
\(159\) −4.00000 −0.317221
\(160\) −10.0000 5.00000i −0.790569 0.395285i
\(161\) −16.0000 −1.26098
\(162\) 1.00000i 0.0785674i
\(163\) 20.0000i 1.56652i −0.621694 0.783260i \(-0.713555\pi\)
0.621694 0.783260i \(-0.286445\pi\)
\(164\) −12.0000 −0.937043
\(165\) 0 0
\(166\) 4.00000 0.310460
\(167\) 24.0000i 1.85718i 0.371113 + 0.928588i \(0.378976\pi\)
−0.371113 + 0.928588i \(0.621024\pi\)
\(168\) 12.0000i 0.925820i
\(169\) 9.00000 0.692308
\(170\) 2.00000 4.00000i 0.153393 0.306786i
\(171\) −8.00000 −0.611775
\(172\) 8.00000i 0.609994i
\(173\) 14.0000i 1.06440i −0.846619 0.532200i \(-0.821365\pi\)
0.846619 0.532200i \(-0.178635\pi\)
\(174\) 4.00000 0.303239
\(175\) 16.0000 12.0000i 1.20949 0.907115i
\(176\) 0 0
\(177\) 8.00000i 0.601317i
\(178\) 6.00000i 0.449719i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 1.00000 2.00000i 0.0745356 0.149071i
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 8.00000i 0.592999i
\(183\) 0 0
\(184\) −12.0000 −0.884652
\(185\) 16.0000 + 8.00000i 1.17634 + 0.588172i
\(186\) −8.00000 −0.586588
\(187\) 0 0
\(188\) 4.00000i 0.291730i
\(189\) −4.00000 −0.290957
\(190\) −16.0000 8.00000i −1.16076 0.580381i
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 7.00000i 0.505181i
\(193\) 6.00000i 0.431889i 0.976406 + 0.215945i \(0.0692831\pi\)
−0.976406 + 0.215945i \(0.930717\pi\)
\(194\) −8.00000 −0.574367
\(195\) 2.00000 4.00000i 0.143223 0.286446i
\(196\) −9.00000 −0.642857
\(197\) 6.00000i 0.427482i 0.976890 + 0.213741i \(0.0685649\pi\)
−0.976890 + 0.213741i \(0.931435\pi\)
\(198\) 0 0
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 12.0000 9.00000i 0.848528 0.636396i
\(201\) 4.00000 0.282138
\(202\) 4.00000i 0.281439i
\(203\) 16.0000i 1.12298i
\(204\) 2.00000 0.140028
\(205\) 12.0000 24.0000i 0.838116 1.67623i
\(206\) 12.0000 0.836080
\(207\) 4.00000i 0.278019i
\(208\) 2.00000i 0.138675i
\(209\) 0 0
\(210\) −8.00000 4.00000i −0.552052 0.276026i
\(211\) 16.0000 1.10149 0.550743 0.834675i \(-0.314345\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) 4.00000i 0.274721i
\(213\) 12.0000i 0.822226i
\(214\) −12.0000 −0.820303
\(215\) −16.0000 8.00000i −1.09119 0.545595i
\(216\) −3.00000 −0.204124
\(217\) 32.0000i 2.17230i
\(218\) 8.00000i 0.541828i
\(219\) −2.00000 −0.135147
\(220\) 0 0
\(221\) 4.00000 0.269069
\(222\) 8.00000i 0.536925i
\(223\) 4.00000i 0.267860i −0.990991 0.133930i \(-0.957240\pi\)
0.990991 0.133930i \(-0.0427597\pi\)
\(224\) −20.0000 −1.33631
\(225\) 3.00000 + 4.00000i 0.200000 + 0.266667i
\(226\) −12.0000 −0.798228
\(227\) 12.0000i 0.796468i −0.917284 0.398234i \(-0.869623\pi\)
0.917284 0.398234i \(-0.130377\pi\)
\(228\) 8.00000i 0.529813i
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 4.00000 8.00000i 0.263752 0.527504i
\(231\) 0 0
\(232\) 12.0000i 0.787839i
\(233\) 6.00000i 0.393073i −0.980497 0.196537i \(-0.937031\pi\)
0.980497 0.196537i \(-0.0629694\pi\)
\(234\) −2.00000 −0.130744
\(235\) −8.00000 4.00000i −0.521862 0.260931i
\(236\) 8.00000 0.520756
\(237\) 8.00000i 0.519656i
\(238\) 8.00000i 0.518563i
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) −2.00000 1.00000i −0.129099 0.0645497i
\(241\) −8.00000 −0.515325 −0.257663 0.966235i \(-0.582952\pi\)
−0.257663 + 0.966235i \(0.582952\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 9.00000 18.0000i 0.574989 1.14998i
\(246\) −12.0000 −0.765092
\(247\) 16.0000i 1.01806i
\(248\) 24.0000i 1.52400i
\(249\) −4.00000 −0.253490
\(250\) 2.00000 + 11.0000i 0.126491 + 0.695701i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 4.00000i 0.251976i
\(253\) 0 0
\(254\) 4.00000 0.250982
\(255\) −2.00000 + 4.00000i −0.125245 + 0.250490i
\(256\) −17.0000 −1.06250
\(257\) 4.00000i 0.249513i −0.992187 0.124757i \(-0.960185\pi\)
0.992187 0.124757i \(-0.0398150\pi\)
\(258\) 8.00000i 0.498058i
\(259\) 32.0000 1.98838
\(260\) 4.00000 + 2.00000i 0.248069 + 0.124035i
\(261\) −4.00000 −0.247594
\(262\) 8.00000i 0.494242i
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 8.00000 + 4.00000i 0.491436 + 0.245718i
\(266\) −32.0000 −1.96205
\(267\) 6.00000i 0.367194i
\(268\) 4.00000i 0.244339i
\(269\) 26.0000 1.58525 0.792624 0.609711i \(-0.208714\pi\)
0.792624 + 0.609711i \(0.208714\pi\)
\(270\) 1.00000 2.00000i 0.0608581 0.121716i
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 8.00000i 0.484182i
\(274\) −4.00000 −0.241649
\(275\) 0 0
\(276\) 4.00000 0.240772
\(277\) 10.0000i 0.600842i 0.953807 + 0.300421i \(0.0971271\pi\)
−0.953807 + 0.300421i \(0.902873\pi\)
\(278\) 16.0000i 0.959616i
\(279\) 8.00000 0.478947
\(280\) 12.0000 24.0000i 0.717137 1.43427i
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) 4.00000i 0.238197i
\(283\) 16.0000i 0.951101i 0.879688 + 0.475551i \(0.157751\pi\)
−0.879688 + 0.475551i \(0.842249\pi\)
\(284\) −12.0000 −0.712069
\(285\) 16.0000 + 8.00000i 0.947758 + 0.473879i
\(286\) 0 0
\(287\) 48.0000i 2.83335i
\(288\) 5.00000i 0.294628i
\(289\) 13.0000 0.764706
\(290\) −8.00000 4.00000i −0.469776 0.234888i
\(291\) 8.00000 0.468968
\(292\) 2.00000i 0.117041i
\(293\) 6.00000i 0.350524i 0.984522 + 0.175262i \(0.0560772\pi\)
−0.984522 + 0.175262i \(0.943923\pi\)
\(294\) −9.00000 −0.524891
\(295\) −8.00000 + 16.0000i −0.465778 + 0.931556i
\(296\) 24.0000 1.39497
\(297\) 0 0
\(298\) 20.0000i 1.15857i
\(299\) 8.00000 0.462652
\(300\) −4.00000 + 3.00000i −0.230940 + 0.173205i
\(301\) −32.0000 −1.84445
\(302\) 0 0
\(303\) 4.00000i 0.229794i
\(304\) −8.00000 −0.458831
\(305\) 0 0
\(306\) 2.00000 0.114332
\(307\) 24.0000i 1.36975i 0.728659 + 0.684876i \(0.240144\pi\)
−0.728659 + 0.684876i \(0.759856\pi\)
\(308\) 0 0
\(309\) −12.0000 −0.682656
\(310\) 16.0000 + 8.00000i 0.908739 + 0.454369i
\(311\) 28.0000 1.58773 0.793867 0.608091i \(-0.208065\pi\)
0.793867 + 0.608091i \(0.208065\pi\)
\(312\) 6.00000i 0.339683i
\(313\) 16.0000i 0.904373i 0.891923 + 0.452187i \(0.149356\pi\)
−0.891923 + 0.452187i \(0.850644\pi\)
\(314\) 8.00000 0.451466
\(315\) 8.00000 + 4.00000i 0.450749 + 0.225374i
\(316\) 8.00000 0.450035
\(317\) 20.0000i 1.12331i −0.827371 0.561656i \(-0.810164\pi\)
0.827371 0.561656i \(-0.189836\pi\)
\(318\) 4.00000i 0.224309i
\(319\) 0 0
\(320\) 7.00000 14.0000i 0.391312 0.782624i
\(321\) 12.0000 0.669775
\(322\) 16.0000i 0.891645i
\(323\) 16.0000i 0.890264i
\(324\) 1.00000 0.0555556
\(325\) −8.00000 + 6.00000i −0.443760 + 0.332820i
\(326\) 20.0000 1.10770
\(327\) 8.00000i 0.442401i
\(328\) 36.0000i 1.98777i
\(329\) −16.0000 −0.882109
\(330\) 0 0
\(331\) 4.00000 0.219860 0.109930 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(332\) 4.00000i 0.219529i
\(333\) 8.00000i 0.438397i
\(334\) −24.0000 −1.31322
\(335\) −8.00000 4.00000i −0.437087 0.218543i
\(336\) −4.00000 −0.218218
\(337\) 26.0000i 1.41631i 0.706057 + 0.708155i \(0.250472\pi\)
−0.706057 + 0.708155i \(0.749528\pi\)
\(338\) 9.00000i 0.489535i
\(339\) 12.0000 0.651751
\(340\) −4.00000 2.00000i −0.216930 0.108465i
\(341\) 0 0
\(342\) 8.00000i 0.432590i
\(343\) 8.00000i 0.431959i
\(344\) −24.0000 −1.29399
\(345\) −4.00000 + 8.00000i −0.215353 + 0.430706i
\(346\) 14.0000 0.752645
\(347\) 12.0000i 0.644194i 0.946707 + 0.322097i \(0.104388\pi\)
−0.946707 + 0.322097i \(0.895612\pi\)
\(348\) 4.00000i 0.214423i
\(349\) 16.0000 0.856460 0.428230 0.903670i \(-0.359137\pi\)
0.428230 + 0.903670i \(0.359137\pi\)
\(350\) 12.0000 + 16.0000i 0.641427 + 0.855236i
\(351\) 2.00000 0.106752
\(352\) 0 0
\(353\) 12.0000i 0.638696i 0.947638 + 0.319348i \(0.103464\pi\)
−0.947638 + 0.319348i \(0.896536\pi\)
\(354\) 8.00000 0.425195
\(355\) 12.0000 24.0000i 0.636894 1.27379i
\(356\) −6.00000 −0.317999
\(357\) 8.00000i 0.423405i
\(358\) 0 0
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 6.00000 + 3.00000i 0.316228 + 0.158114i
\(361\) 45.0000 2.36842
\(362\) 10.0000i 0.525588i
\(363\) 0 0
\(364\) 8.00000 0.419314
\(365\) 4.00000 + 2.00000i 0.209370 + 0.104685i
\(366\) 0 0
\(367\) 36.0000i 1.87918i −0.342296 0.939592i \(-0.611204\pi\)
0.342296 0.939592i \(-0.388796\pi\)
\(368\) 4.00000i 0.208514i
\(369\) 12.0000 0.624695
\(370\) −8.00000 + 16.0000i −0.415900 + 0.831800i
\(371\) 16.0000 0.830679
\(372\) 8.00000i 0.414781i
\(373\) 22.0000i 1.13912i −0.821951 0.569558i \(-0.807114\pi\)
0.821951 0.569558i \(-0.192886\pi\)
\(374\) 0 0
\(375\) −2.00000 11.0000i −0.103280 0.568038i
\(376\) −12.0000 −0.618853
\(377\) 8.00000i 0.412021i
\(378\) 4.00000i 0.205738i
\(379\) 4.00000 0.205466 0.102733 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(380\) −8.00000 + 16.0000i −0.410391 + 0.820783i
\(381\) −4.00000 −0.204926
\(382\) 12.0000i 0.613973i
\(383\) 36.0000i 1.83951i −0.392488 0.919757i \(-0.628386\pi\)
0.392488 0.919757i \(-0.371614\pi\)
\(384\) 3.00000 0.153093
\(385\) 0 0
\(386\) −6.00000 −0.305392
\(387\) 8.00000i 0.406663i
\(388\) 8.00000i 0.406138i
\(389\) −18.0000 −0.912636 −0.456318 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) 4.00000 + 2.00000i 0.202548 + 0.101274i
\(391\) −8.00000 −0.404577
\(392\) 27.0000i 1.36371i
\(393\) 8.00000i 0.403547i
\(394\) −6.00000 −0.302276
\(395\) −8.00000 + 16.0000i −0.402524 + 0.805047i
\(396\) 0 0
\(397\) 8.00000i 0.401508i −0.979642 0.200754i \(-0.935661\pi\)
0.979642 0.200754i \(-0.0643393\pi\)
\(398\) 16.0000i 0.802008i
\(399\) 32.0000 1.60200
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) −2.00000 −0.0998752 −0.0499376 0.998752i \(-0.515902\pi\)
−0.0499376 + 0.998752i \(0.515902\pi\)
\(402\) 4.00000i 0.199502i
\(403\) 16.0000i 0.797017i
\(404\) 4.00000 0.199007
\(405\) −1.00000 + 2.00000i −0.0496904 + 0.0993808i
\(406\) −16.0000 −0.794067
\(407\) 0 0
\(408\) 6.00000i 0.297044i
\(409\) −40.0000 −1.97787 −0.988936 0.148340i \(-0.952607\pi\)
−0.988936 + 0.148340i \(0.952607\pi\)
\(410\) 24.0000 + 12.0000i 1.18528 + 0.592638i
\(411\) 4.00000 0.197305
\(412\) 12.0000i 0.591198i
\(413\) 32.0000i 1.57462i
\(414\) 4.00000 0.196589
\(415\) 8.00000 + 4.00000i 0.392705 + 0.196352i
\(416\) 10.0000 0.490290
\(417\) 16.0000i 0.783523i
\(418\) 0 0
\(419\) −8.00000 −0.390826 −0.195413 0.980721i \(-0.562605\pi\)
−0.195413 + 0.980721i \(0.562605\pi\)
\(420\) −4.00000 + 8.00000i −0.195180 + 0.390360i
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 16.0000i 0.778868i
\(423\) 4.00000i 0.194487i
\(424\) 12.0000 0.582772
\(425\) 8.00000 6.00000i 0.388057 0.291043i
\(426\) −12.0000 −0.581402
\(427\) 0 0
\(428\) 12.0000i 0.580042i
\(429\) 0 0
\(430\) 8.00000 16.0000i 0.385794 0.771589i
\(431\) 24.0000 1.15604 0.578020 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 16.0000i 0.768911i 0.923144 + 0.384455i \(0.125611\pi\)
−0.923144 + 0.384455i \(0.874389\pi\)
\(434\) 32.0000 1.53605
\(435\) 8.00000 + 4.00000i 0.383571 + 0.191785i
\(436\) −8.00000 −0.383131
\(437\) 32.0000i 1.53077i
\(438\) 2.00000i 0.0955637i
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) 4.00000i 0.190261i
\(443\) 12.0000i 0.570137i 0.958507 + 0.285069i \(0.0920164\pi\)
−0.958507 + 0.285069i \(0.907984\pi\)
\(444\) −8.00000 −0.379663
\(445\) 6.00000 12.0000i 0.284427 0.568855i
\(446\) 4.00000 0.189405
\(447\) 20.0000i 0.945968i
\(448\) 28.0000i 1.32288i
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) −4.00000 + 3.00000i −0.188562 + 0.141421i
\(451\) 0 0
\(452\) 12.0000i 0.564433i
\(453\) 0 0
\(454\) 12.0000 0.563188
\(455\) −8.00000 + 16.0000i −0.375046 + 0.750092i
\(456\) 24.0000 1.12390
\(457\) 2.00000i 0.0935561i −0.998905 0.0467780i \(-0.985105\pi\)
0.998905 0.0467780i \(-0.0148953\pi\)
\(458\) 22.0000i 1.02799i
\(459\) −2.00000 −0.0933520
\(460\) −8.00000 4.00000i −0.373002 0.186501i
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) 28.0000i 1.30127i 0.759390 + 0.650635i \(0.225497\pi\)
−0.759390 + 0.650635i \(0.774503\pi\)
\(464\) −4.00000 −0.185695
\(465\) −16.0000 8.00000i −0.741982 0.370991i
\(466\) 6.00000 0.277945
\(467\) 12.0000i 0.555294i −0.960683 0.277647i \(-0.910445\pi\)
0.960683 0.277647i \(-0.0895545\pi\)
\(468\) 2.00000i 0.0924500i
\(469\) −16.0000 −0.738811
\(470\) 4.00000 8.00000i 0.184506 0.369012i
\(471\) −8.00000 −0.368621
\(472\) 24.0000i 1.10469i
\(473\) 0 0
\(474\) 8.00000 0.367452
\(475\) −24.0000 32.0000i −1.10120 1.46826i
\(476\) −8.00000 −0.366679
\(477\) 4.00000i 0.183147i
\(478\) 24.0000i 1.09773i
\(479\) −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
\(481\) −16.0000 −0.729537
\(482\) 8.00000i 0.364390i
\(483\) 16.0000i 0.728025i
\(484\) 0 0
\(485\) −16.0000 8.00000i −0.726523 0.363261i
\(486\) 1.00000 0.0453609
\(487\) 20.0000i 0.906287i −0.891438 0.453143i \(-0.850303\pi\)
0.891438 0.453143i \(-0.149697\pi\)
\(488\) 0 0
\(489\) −20.0000 −0.904431
\(490\) 18.0000 + 9.00000i 0.813157 + 0.406579i
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 12.0000i 0.541002i
\(493\) 8.00000i 0.360302i
\(494\) 16.0000 0.719874
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 48.0000i 2.15309i
\(498\) 4.00000i 0.179244i
\(499\) 12.0000 0.537194 0.268597 0.963253i \(-0.413440\pi\)
0.268597 + 0.963253i \(0.413440\pi\)
\(500\) 11.0000 2.00000i 0.491935 0.0894427i
\(501\) 24.0000 1.07224
\(502\) 0 0
\(503\) 24.0000i 1.07011i −0.844818 0.535054i \(-0.820291\pi\)
0.844818 0.535054i \(-0.179709\pi\)
\(504\) 12.0000 0.534522
\(505\) −4.00000 + 8.00000i −0.177998 + 0.355995i
\(506\) 0 0
\(507\) 9.00000i 0.399704i
\(508\) 4.00000i 0.177471i
\(509\) −26.0000 −1.15243 −0.576215 0.817298i \(-0.695471\pi\)
−0.576215 + 0.817298i \(0.695471\pi\)
\(510\) −4.00000 2.00000i −0.177123 0.0885615i
\(511\) 8.00000 0.353899
\(512\) 11.0000i 0.486136i
\(513\) 8.00000i 0.353209i
\(514\) 4.00000 0.176432
\(515\) 24.0000 + 12.0000i 1.05757 + 0.528783i
\(516\) 8.00000 0.352180
\(517\) 0 0
\(518\) 32.0000i 1.40600i
\(519\) −14.0000 −0.614532
\(520\) −6.00000 + 12.0000i −0.263117 + 0.526235i
\(521\) 22.0000 0.963837 0.481919 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) 4.00000i 0.175075i
\(523\) 24.0000i 1.04945i −0.851273 0.524723i \(-0.824169\pi\)
0.851273 0.524723i \(-0.175831\pi\)
\(524\) −8.00000 −0.349482
\(525\) −12.0000 16.0000i −0.523723 0.698297i
\(526\) 0 0
\(527\) 16.0000i 0.696971i
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) −4.00000 + 8.00000i −0.173749 + 0.347498i
\(531\) −8.00000 −0.347170
\(532\) 32.0000i 1.38738i
\(533\) 24.0000i 1.03956i
\(534\) −6.00000 −0.259645
\(535\) −24.0000 12.0000i −1.03761 0.518805i
\(536\) −12.0000 −0.518321
\(537\) 0 0
\(538\) 26.0000i 1.12094i
\(539\) 0 0
\(540\) −2.00000 1.00000i −0.0860663 0.0430331i
\(541\) −8.00000 −0.343947 −0.171973 0.985102i \(-0.555014\pi\)
−0.171973 + 0.985102i \(0.555014\pi\)
\(542\) 16.0000i 0.687259i
\(543\) 10.0000i 0.429141i
\(544\) −10.0000 −0.428746
\(545\) 8.00000 16.0000i 0.342682 0.685365i
\(546\) 8.00000 0.342368
\(547\) 8.00000i 0.342055i −0.985266 0.171028i \(-0.945291\pi\)
0.985266 0.171028i \(-0.0547087\pi\)
\(548\) 4.00000i 0.170872i
\(549\) 0 0
\(550\) 0 0
\(551\) 32.0000 1.36325
\(552\) 12.0000i 0.510754i
\(553\) 32.0000i 1.36078i
\(554\) −10.0000 −0.424859
\(555\) 8.00000 16.0000i 0.339581 0.679162i
\(556\) 16.0000 0.678551
\(557\) 14.0000i 0.593199i 0.955002 + 0.296600i \(0.0958526\pi\)
−0.955002 + 0.296600i \(0.904147\pi\)
\(558\) 8.00000i 0.338667i
\(559\) 16.0000 0.676728
\(560\) 8.00000 + 4.00000i 0.338062 + 0.169031i
\(561\) 0 0
\(562\) 12.0000i 0.506189i
\(563\) 36.0000i 1.51722i −0.651546 0.758610i \(-0.725879\pi\)
0.651546 0.758610i \(-0.274121\pi\)
\(564\) 4.00000 0.168430
\(565\) −24.0000 12.0000i −1.00969 0.504844i
\(566\) −16.0000 −0.672530
\(567\) 4.00000i 0.167984i
\(568\) 36.0000i 1.51053i
\(569\) 44.0000 1.84458 0.922288 0.386503i \(-0.126317\pi\)
0.922288 + 0.386503i \(0.126317\pi\)
\(570\) −8.00000 + 16.0000i −0.335083 + 0.670166i
\(571\) 40.0000 1.67395 0.836974 0.547243i \(-0.184323\pi\)
0.836974 + 0.547243i \(0.184323\pi\)
\(572\) 0 0
\(573\) 12.0000i 0.501307i
\(574\) 48.0000 2.00348
\(575\) 16.0000 12.0000i 0.667246 0.500435i
\(576\) 7.00000 0.291667
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 13.0000i 0.540729i
\(579\) 6.00000 0.249351
\(580\) −4.00000 + 8.00000i −0.166091 + 0.332182i
\(581\) 16.0000 0.663792
\(582\) 8.00000i 0.331611i
\(583\) 0 0
\(584\) 6.00000 0.248282
\(585\) −4.00000 2.00000i −0.165380 0.0826898i
\(586\) −6.00000 −0.247858
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 9.00000i 0.371154i
\(589\) −64.0000 −2.63707
\(590\) −16.0000 8.00000i −0.658710 0.329355i
\(591\) 6.00000 0.246807
\(592\) 8.00000i 0.328798i
\(593\) 14.0000i 0.574911i 0.957794 + 0.287456i \(0.0928094\pi\)
−0.957794 + 0.287456i \(0.907191\pi\)
\(594\) 0 0
\(595\) 8.00000 16.0000i 0.327968 0.655936i
\(596\) 20.0000 0.819232
\(597\) 16.0000i 0.654836i
\(598\) 8.00000i 0.327144i
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) −9.00000 12.0000i −0.367423 0.489898i
\(601\) 32.0000 1.30531 0.652654 0.757656i \(-0.273656\pi\)
0.652654 + 0.757656i \(0.273656\pi\)
\(602\) 32.0000i 1.30422i
\(603\) 4.00000i 0.162893i
\(604\) 0 0
\(605\) 0 0
\(606\) 4.00000 0.162489
\(607\) 20.0000i 0.811775i 0.913923 + 0.405887i \(0.133038\pi\)
−0.913923 + 0.405887i \(0.866962\pi\)
\(608\) 40.0000i 1.62221i
\(609\) 16.0000 0.648353
\(610\) 0 0
\(611\) 8.00000 0.323645
\(612\) 2.00000i 0.0808452i
\(613\) 42.0000i 1.69636i 0.529705 + 0.848182i \(0.322303\pi\)
−0.529705 + 0.848182i \(0.677697\pi\)
\(614\) −24.0000 −0.968561
\(615\) −24.0000 12.0000i −0.967773 0.483887i
\(616\) 0 0
\(617\) 28.0000i 1.12724i 0.826035 + 0.563619i \(0.190591\pi\)
−0.826035 + 0.563619i \(0.809409\pi\)
\(618\) 12.0000i 0.482711i
\(619\) 36.0000 1.44696 0.723481 0.690344i \(-0.242541\pi\)
0.723481 + 0.690344i \(0.242541\pi\)
\(620\) 8.00000 16.0000i 0.321288 0.642575i
\(621\) −4.00000 −0.160514
\(622\) 28.0000i 1.12270i
\(623\) 24.0000i 0.961540i
\(624\) 2.00000 0.0800641
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) −16.0000 −0.639489
\(627\) 0 0
\(628\) 8.00000i 0.319235i
\(629\) 16.0000 0.637962
\(630\) −4.00000 + 8.00000i −0.159364 + 0.318728i
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 24.0000i 0.954669i
\(633\) 16.0000i 0.635943i
\(634\) 20.0000 0.794301
\(635\) 8.00000 + 4.00000i 0.317470 + 0.158735i
\(636\) −4.00000 −0.158610
\(637\) 18.0000i 0.713186i
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) −6.00000 3.00000i −0.237171 0.118585i
\(641\) −2.00000 −0.0789953 −0.0394976 0.999220i \(-0.512576\pi\)
−0.0394976 + 0.999220i \(0.512576\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 12.0000i 0.473234i 0.971603 + 0.236617i \(0.0760386\pi\)
−0.971603 + 0.236617i \(0.923961\pi\)
\(644\) −16.0000 −0.630488
\(645\) −8.00000 + 16.0000i −0.315000 + 0.629999i
\(646\) −16.0000 −0.629512
\(647\) 28.0000i 1.10079i 0.834903 + 0.550397i \(0.185524\pi\)
−0.834903 + 0.550397i \(0.814476\pi\)
\(648\) 3.00000i 0.117851i
\(649\) 0 0
\(650\) −6.00000 8.00000i −0.235339 0.313786i
\(651\) −32.0000 −1.25418
\(652\) 20.0000i 0.783260i
\(653\) 28.0000i 1.09572i 0.836569 + 0.547862i \(0.184558\pi\)
−0.836569 + 0.547862i \(0.815442\pi\)
\(654\) −8.00000 −0.312825
\(655\) 8.00000 16.0000i 0.312586 0.625172i
\(656\) 12.0000 0.468521
\(657\) 2.00000i 0.0780274i
\(658\) 16.0000i 0.623745i
\(659\) 24.0000 0.934907 0.467454 0.884018i \(-0.345171\pi\)
0.467454 + 0.884018i \(0.345171\pi\)
\(660\) 0 0
\(661\) 6.00000 0.233373 0.116686 0.993169i \(-0.462773\pi\)
0.116686 + 0.993169i \(0.462773\pi\)
\(662\) 4.00000i 0.155464i
\(663\) 4.00000i 0.155347i
\(664\) 12.0000 0.465690
\(665\) −64.0000 32.0000i −2.48181 1.24091i
\(666\) −8.00000 −0.309994
\(667\) 16.0000i 0.619522i
\(668\) 24.0000i 0.928588i
\(669\) −4.00000 −0.154649
\(670\) 4.00000 8.00000i 0.154533 0.309067i
\(671\) 0 0
\(672\) 20.0000i 0.771517i
\(673\) 38.0000i 1.46479i 0.680879 + 0.732396i \(0.261598\pi\)
−0.680879 + 0.732396i \(0.738402\pi\)
\(674\) −26.0000 −1.00148
\(675\) 4.00000 3.00000i 0.153960 0.115470i
\(676\) 9.00000 0.346154
\(677\) 38.0000i 1.46046i −0.683202 0.730229i \(-0.739413\pi\)
0.683202 0.730229i \(-0.260587\pi\)
\(678\) 12.0000i 0.460857i
\(679\) −32.0000 −1.22805
\(680\) 6.00000 12.0000i 0.230089 0.460179i
\(681\) −12.0000 −0.459841
\(682\) 0 0
\(683\) 4.00000i 0.153056i 0.997067 + 0.0765279i \(0.0243834\pi\)
−0.997067 + 0.0765279i \(0.975617\pi\)
\(684\) −8.00000 −0.305888
\(685\) −8.00000 4.00000i −0.305664 0.152832i
\(686\) 8.00000 0.305441
\(687\) 22.0000i 0.839352i
\(688\) 8.00000i 0.304997i
\(689\) −8.00000 −0.304776
\(690\) −8.00000 4.00000i −0.304555 0.152277i
\(691\) −20.0000 −0.760836 −0.380418 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) 14.0000i 0.532200i
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −16.0000 + 32.0000i −0.606915 + 1.21383i
\(696\) 12.0000 0.454859
\(697\) 24.0000i 0.909065i
\(698\) 16.0000i 0.605609i
\(699\) −6.00000 −0.226941
\(700\) 16.0000 12.0000i 0.604743 0.453557i
\(701\) −12.0000 −0.453234 −0.226617 0.973984i \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) 2.00000i 0.0754851i
\(703\) 64.0000i 2.41381i
\(704\) 0 0
\(705\) −4.00000 + 8.00000i −0.150649 + 0.301297i
\(706\) −12.0000 −0.451626
\(707\) 16.0000i 0.601742i
\(708\) 8.00000i 0.300658i
\(709\) −26.0000 −0.976450 −0.488225 0.872718i \(-0.662356\pi\)
−0.488225 + 0.872718i \(0.662356\pi\)
\(710\) 24.0000 + 12.0000i 0.900704 + 0.450352i
\(711\) −8.00000 −0.300023
\(712\) 18.0000i 0.674579i
\(713\) 32.0000i 1.19841i
\(714\) −8.00000 −0.299392
\(715\) 0 0
\(716\) 0 0
\(717\) 24.0000i 0.896296i
\(718\) 24.0000i 0.895672i
\(719\) −36.0000 −1.34257 −0.671287 0.741198i \(-0.734258\pi\)
−0.671287 + 0.741198i \(0.734258\pi\)
\(720\) −1.00000 + 2.00000i −0.0372678 + 0.0745356i
\(721\) 48.0000 1.78761
\(722\) 45.0000i 1.67473i
\(723\) 8.00000i 0.297523i
\(724\) −10.0000 −0.371647
\(725\) −12.0000 16.0000i −0.445669 0.594225i
\(726\) 0 0
\(727\) 28.0000i 1.03846i −0.854634 0.519231i \(-0.826218\pi\)
0.854634 0.519231i \(-0.173782\pi\)
\(728\) 24.0000i 0.889499i
\(729\) −1.00000 −0.0370370
\(730\) −2.00000 + 4.00000i −0.0740233 + 0.148047i
\(731\) −16.0000 −0.591781
\(732\) 0 0
\(733\) 14.0000i 0.517102i −0.965998 0.258551i \(-0.916755\pi\)
0.965998 0.258551i \(-0.0832450\pi\)
\(734\) 36.0000 1.32878
\(735\) −18.0000 9.00000i −0.663940 0.331970i
\(736\) −20.0000 −0.737210
\(737\) 0 0
\(738\) 12.0000i 0.441726i
\(739\) 16.0000 0.588570 0.294285 0.955718i \(-0.404919\pi\)
0.294285 + 0.955718i \(0.404919\pi\)
\(740\) 16.0000 + 8.00000i 0.588172 + 0.294086i
\(741\) −16.0000 −0.587775
\(742\) 16.0000i 0.587378i
\(743\) 24.0000i 0.880475i 0.897881 + 0.440237i \(0.145106\pi\)
−0.897881 + 0.440237i \(0.854894\pi\)
\(744\) −24.0000 −0.879883
\(745\) −20.0000 + 40.0000i −0.732743 + 1.46549i
\(746\) 22.0000 0.805477
\(747\) 4.00000i 0.146352i
\(748\) 0 0
\(749\) −48.0000 −1.75388
\(750\) 11.0000 2.00000i 0.401663 0.0730297i
\(751\) −16.0000 −0.583848 −0.291924 0.956441i \(-0.594295\pi\)
−0.291924 + 0.956441i \(0.594295\pi\)
\(752\) 4.00000i 0.145865i
\(753\) 0 0
\(754\) 8.00000 0.291343
\(755\) 0 0
\(756\) −4.00000 −0.145479
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 4.00000i 0.145287i
\(759\) 0 0
\(760\) −48.0000 24.0000i −1.74114 0.870572i
\(761\) 36.0000 1.30500 0.652499 0.757789i \(-0.273720\pi\)
0.652499 + 0.757789i \(0.273720\pi\)
\(762\) 4.00000i 0.144905i
\(763\) 32.0000i 1.15848i
\(764\) 12.0000 0.434145
\(765\) 4.00000 + 2.00000i 0.144620 + 0.0723102i
\(766\) 36.0000 1.30073
\(767\) 16.0000i 0.577727i
\(768\) 17.0000i 0.613435i
\(769\) 16.0000 0.576975 0.288487 0.957484i \(-0.406848\pi\)
0.288487 + 0.957484i \(0.406848\pi\)
\(770\) 0 0
\(771\) −4.00000 −0.144056
\(772\) 6.00000i 0.215945i
\(773\) 36.0000i 1.29483i −0.762138 0.647415i \(-0.775850\pi\)
0.762138 0.647415i \(-0.224150\pi\)
\(774\) 8.00000 0.287554
\(775\) 24.0000 + 32.0000i 0.862105 + 1.14947i
\(776\) −24.0000 −0.861550
\(777\) 32.0000i 1.14799i
\(778\) 18.0000i 0.645331i
\(779\) −96.0000 −3.43956
\(780\) 2.00000 4.00000i 0.0716115 0.143223i
\(781\) 0 0
\(782\) 8.00000i 0.286079i
\(783\) 4.00000i 0.142948i
\(784\) 9.00000 0.321429
\(785\) 16.0000 + 8.00000i 0.571064 + 0.285532i
\(786\) −8.00000 −0.285351
\(787\) 32.0000i 1.14068i 0.821410 + 0.570338i \(0.193188\pi\)
−0.821410 + 0.570338i \(0.806812\pi\)
\(788\) 6.00000i 0.213741i
\(789\) 0 0
\(790\) −16.0000 8.00000i −0.569254 0.284627i
\(791\) −48.0000