Properties

Label 95.2.b.a.39.2
Level $95$
Weight $2$
Character 95.39
Analytic conductor $0.759$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.758578819202\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
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 39.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 95.39
Dual form 95.2.b.a.39.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -2.00000i q^{7} +3.00000i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -2.00000i q^{7} +3.00000i q^{8} +3.00000 q^{9} +(-2.00000 - 1.00000i) q^{10} -4.00000 q^{11} -2.00000i q^{13} +2.00000 q^{14} -1.00000 q^{16} -4.00000i q^{17} +3.00000i q^{18} -1.00000 q^{19} +(-1.00000 + 2.00000i) q^{20} -4.00000i q^{22} -6.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} +2.00000 q^{26} -2.00000i q^{28} +6.00000 q^{29} -4.00000 q^{31} +5.00000i q^{32} +4.00000 q^{34} +(4.00000 + 2.00000i) q^{35} +3.00000 q^{36} +10.0000i q^{37} -1.00000i q^{38} +(-6.00000 - 3.00000i) q^{40} -10.0000 q^{41} +2.00000i q^{43} -4.00000 q^{44} +(-3.00000 + 6.00000i) q^{45} +6.00000 q^{46} +6.00000i q^{47} +3.00000 q^{49} +(4.00000 - 3.00000i) q^{50} -2.00000i q^{52} +10.0000i q^{53} +(4.00000 - 8.00000i) q^{55} +6.00000 q^{56} +6.00000i q^{58} +2.00000 q^{61} -4.00000i q^{62} -6.00000i q^{63} -7.00000 q^{64} +(4.00000 + 2.00000i) q^{65} -8.00000i q^{67} -4.00000i q^{68} +(-2.00000 + 4.00000i) q^{70} +4.00000 q^{71} +9.00000i q^{72} +4.00000i q^{73} -10.0000 q^{74} -1.00000 q^{76} +8.00000i q^{77} -4.00000 q^{79} +(1.00000 - 2.00000i) q^{80} +9.00000 q^{81} -10.0000i q^{82} -18.0000i q^{83} +(8.00000 + 4.00000i) q^{85} -2.00000 q^{86} -12.0000i q^{88} +2.00000 q^{89} +(-6.00000 - 3.00000i) q^{90} -4.00000 q^{91} -6.00000i q^{92} -6.00000 q^{94} +(1.00000 - 2.00000i) q^{95} -6.00000i q^{97} +3.00000i q^{98} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{4} - 2 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{4} - 2 q^{5} + 6 q^{9} - 4 q^{10} - 8 q^{11} + 4 q^{14} - 2 q^{16} - 2 q^{19} - 2 q^{20} - 6 q^{25} + 4 q^{26} + 12 q^{29} - 8 q^{31} + 8 q^{34} + 8 q^{35} + 6 q^{36} - 12 q^{40} - 20 q^{41} - 8 q^{44} - 6 q^{45} + 12 q^{46} + 6 q^{49} + 8 q^{50} + 8 q^{55} + 12 q^{56} + 4 q^{61} - 14 q^{64} + 8 q^{65} - 4 q^{70} + 8 q^{71} - 20 q^{74} - 2 q^{76} - 8 q^{79} + 2 q^{80} + 18 q^{81} + 16 q^{85} - 4 q^{86} + 4 q^{89} - 12 q^{90} - 8 q^{91} - 12 q^{94} + 2 q^{95} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(1\) \(-1\)

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 \(0.884973\pi\)
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 + 2.00000i −0.447214 + 0.894427i
\(6\) 0 0
\(7\) 2.00000i 0.755929i −0.925820 0.377964i \(-0.876624\pi\)
0.925820 0.377964i \(-0.123376\pi\)
\(8\) 3.00000i 1.06066i
\(9\) 3.00000 1.00000
\(10\) −2.00000 1.00000i −0.632456 0.316228i
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 0 0
\(13\) 2.00000i 0.554700i −0.960769 0.277350i \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 4.00000i 0.970143i −0.874475 0.485071i \(-0.838794\pi\)
0.874475 0.485071i \(-0.161206\pi\)
\(18\) 3.00000i 0.707107i
\(19\) −1.00000 −0.229416
\(20\) −1.00000 + 2.00000i −0.223607 + 0.447214i
\(21\) 0 0
\(22\) 4.00000i 0.852803i
\(23\) 6.00000i 1.25109i −0.780189 0.625543i \(-0.784877\pi\)
0.780189 0.625543i \(-0.215123\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) 2.00000i 0.377964i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 5.00000i 0.883883i
\(33\) 0 0
\(34\) 4.00000 0.685994
\(35\) 4.00000 + 2.00000i 0.676123 + 0.338062i
\(36\) 3.00000 0.500000
\(37\) 10.0000i 1.64399i 0.569495 + 0.821995i \(0.307139\pi\)
−0.569495 + 0.821995i \(0.692861\pi\)
\(38\) 1.00000i 0.162221i
\(39\) 0 0
\(40\) −6.00000 3.00000i −0.948683 0.474342i
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i 0.988304 + 0.152499i \(0.0487319\pi\)
−0.988304 + 0.152499i \(0.951268\pi\)
\(44\) −4.00000 −0.603023
\(45\) −3.00000 + 6.00000i −0.447214 + 0.894427i
\(46\) 6.00000 0.884652
\(47\) 6.00000i 0.875190i 0.899172 + 0.437595i \(0.144170\pi\)
−0.899172 + 0.437595i \(0.855830\pi\)
\(48\) 0 0
\(49\) 3.00000 0.428571
\(50\) 4.00000 3.00000i 0.565685 0.424264i
\(51\) 0 0
\(52\) 2.00000i 0.277350i
\(53\) 10.0000i 1.37361i 0.726844 + 0.686803i \(0.240986\pi\)
−0.726844 + 0.686803i \(0.759014\pi\)
\(54\) 0 0
\(55\) 4.00000 8.00000i 0.539360 1.07872i
\(56\) 6.00000 0.801784
\(57\) 0 0
\(58\) 6.00000i 0.787839i
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 6.00000i 0.755929i
\(64\) −7.00000 −0.875000
\(65\) 4.00000 + 2.00000i 0.496139 + 0.248069i
\(66\) 0 0
\(67\) 8.00000i 0.977356i −0.872464 0.488678i \(-0.837479\pi\)
0.872464 0.488678i \(-0.162521\pi\)
\(68\) 4.00000i 0.485071i
\(69\) 0 0
\(70\) −2.00000 + 4.00000i −0.239046 + 0.478091i
\(71\) 4.00000 0.474713 0.237356 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(72\) 9.00000i 1.06066i
\(73\) 4.00000i 0.468165i 0.972217 + 0.234082i \(0.0752085\pi\)
−0.972217 + 0.234082i \(0.924791\pi\)
\(74\) −10.0000 −1.16248
\(75\) 0 0
\(76\) −1.00000 −0.114708
\(77\) 8.00000i 0.911685i
\(78\) 0 0
\(79\) −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
\(81\) 9.00000 1.00000
\(82\) 10.0000i 1.10432i
\(83\) 18.0000i 1.97576i −0.155230 0.987878i \(-0.549612\pi\)
0.155230 0.987878i \(-0.450388\pi\)
\(84\) 0 0
\(85\) 8.00000 + 4.00000i 0.867722 + 0.433861i
\(86\) −2.00000 −0.215666
\(87\) 0 0
\(88\) 12.0000i 1.27920i
\(89\) 2.00000 0.212000 0.106000 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) −6.00000 3.00000i −0.632456 0.316228i
\(91\) −4.00000 −0.419314
\(92\) 6.00000i 0.625543i
\(93\) 0 0
\(94\) −6.00000 −0.618853
\(95\) 1.00000 2.00000i 0.102598 0.205196i
\(96\) 0 0
\(97\) 6.00000i 0.609208i −0.952479 0.304604i \(-0.901476\pi\)
0.952479 0.304604i \(-0.0985241\pi\)
\(98\) 3.00000i 0.303046i
\(99\) −12.0000 −1.20605
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 0 0
\(103\) 16.0000i 1.57653i 0.615338 + 0.788263i \(0.289020\pi\)
−0.615338 + 0.788263i \(0.710980\pi\)
\(104\) 6.00000 0.588348
\(105\) 0 0
\(106\) −10.0000 −0.971286
\(107\) 4.00000i 0.386695i 0.981130 + 0.193347i \(0.0619344\pi\)
−0.981130 + 0.193347i \(0.938066\pi\)
\(108\) 0 0
\(109\) −6.00000 −0.574696 −0.287348 0.957826i \(-0.592774\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(110\) 8.00000 + 4.00000i 0.762770 + 0.381385i
\(111\) 0 0
\(112\) 2.00000i 0.188982i
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) 0 0
\(115\) 12.0000 + 6.00000i 1.11901 + 0.559503i
\(116\) 6.00000 0.557086
\(117\) 6.00000i 0.554700i
\(118\) 0 0
\(119\) −8.00000 −0.733359
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 2.00000i 0.181071i
\(123\) 0 0
\(124\) −4.00000 −0.359211
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 6.00000 0.534522
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 3.00000i 0.265165i
\(129\) 0 0
\(130\) −2.00000 + 4.00000i −0.175412 + 0.350823i
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) 2.00000i 0.173422i
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) 12.0000 1.02899
\(137\) 12.0000i 1.02523i −0.858619 0.512615i \(-0.828677\pi\)
0.858619 0.512615i \(-0.171323\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 4.00000 + 2.00000i 0.338062 + 0.169031i
\(141\) 0 0
\(142\) 4.00000i 0.335673i
\(143\) 8.00000i 0.668994i
\(144\) −3.00000 −0.250000
\(145\) −6.00000 + 12.0000i −0.498273 + 0.996546i
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) 10.0000i 0.821995i
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 0 0
\(151\) 24.0000 1.95309 0.976546 0.215308i \(-0.0690756\pi\)
0.976546 + 0.215308i \(0.0690756\pi\)
\(152\) 3.00000i 0.243332i
\(153\) 12.0000i 0.970143i
\(154\) −8.00000 −0.644658
\(155\) 4.00000 8.00000i 0.321288 0.642575i
\(156\) 0 0
\(157\) 8.00000i 0.638470i 0.947676 + 0.319235i \(0.103426\pi\)
−0.947676 + 0.319235i \(0.896574\pi\)
\(158\) 4.00000i 0.318223i
\(159\) 0 0
\(160\) −10.0000 5.00000i −0.790569 0.395285i
\(161\) −12.0000 −0.945732
\(162\) 9.00000i 0.707107i
\(163\) 10.0000i 0.783260i 0.920123 + 0.391630i \(0.128089\pi\)
−0.920123 + 0.391630i \(0.871911\pi\)
\(164\) −10.0000 −0.780869
\(165\) 0 0
\(166\) 18.0000 1.39707
\(167\) 12.0000i 0.928588i −0.885681 0.464294i \(-0.846308\pi\)
0.885681 0.464294i \(-0.153692\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) −4.00000 + 8.00000i −0.306786 + 0.613572i
\(171\) −3.00000 −0.229416
\(172\) 2.00000i 0.152499i
\(173\) 6.00000i 0.456172i −0.973641 0.228086i \(-0.926753\pi\)
0.973641 0.228086i \(-0.0732467\pi\)
\(174\) 0 0
\(175\) −8.00000 + 6.00000i −0.604743 + 0.453557i
\(176\) 4.00000 0.301511
\(177\) 0 0
\(178\) 2.00000i 0.149906i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) −3.00000 + 6.00000i −0.223607 + 0.447214i
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 4.00000i 0.296500i
\(183\) 0 0
\(184\) 18.0000 1.32698
\(185\) −20.0000 10.0000i −1.47043 0.735215i
\(186\) 0 0
\(187\) 16.0000i 1.17004i
\(188\) 6.00000i 0.437595i
\(189\) 0 0
\(190\) 2.00000 + 1.00000i 0.145095 + 0.0725476i
\(191\) −24.0000 −1.73658 −0.868290 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) 0 0
\(193\) 26.0000i 1.87152i −0.352636 0.935760i \(-0.614715\pi\)
0.352636 0.935760i \(-0.385285\pi\)
\(194\) 6.00000 0.430775
\(195\) 0 0
\(196\) 3.00000 0.214286
\(197\) 12.0000i 0.854965i 0.904024 + 0.427482i \(0.140599\pi\)
−0.904024 + 0.427482i \(0.859401\pi\)
\(198\) 12.0000i 0.852803i
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 12.0000 9.00000i 0.848528 0.636396i
\(201\) 0 0
\(202\) 6.00000i 0.422159i
\(203\) 12.0000i 0.842235i
\(204\) 0 0
\(205\) 10.0000 20.0000i 0.698430 1.39686i
\(206\) −16.0000 −1.11477
\(207\) 18.0000i 1.25109i
\(208\) 2.00000i 0.138675i
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 10.0000i 0.686803i
\(213\) 0 0
\(214\) −4.00000 −0.273434
\(215\) −4.00000 2.00000i −0.272798 0.136399i
\(216\) 0 0
\(217\) 8.00000i 0.543075i
\(218\) 6.00000i 0.406371i
\(219\) 0 0
\(220\) 4.00000 8.00000i 0.269680 0.539360i
\(221\) −8.00000 −0.538138
\(222\) 0 0
\(223\) 16.0000i 1.07144i 0.844396 + 0.535720i \(0.179960\pi\)
−0.844396 + 0.535720i \(0.820040\pi\)
\(224\) 10.0000 0.668153
\(225\) −9.00000 12.0000i −0.600000 0.800000i
\(226\) −6.00000 −0.399114
\(227\) 20.0000i 1.32745i −0.747978 0.663723i \(-0.768975\pi\)
0.747978 0.663723i \(-0.231025\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) −6.00000 + 12.0000i −0.395628 + 0.791257i
\(231\) 0 0
\(232\) 18.0000i 1.18176i
\(233\) 16.0000i 1.04819i 0.851658 + 0.524097i \(0.175597\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 6.00000 0.392232
\(235\) −12.0000 6.00000i −0.782794 0.391397i
\(236\) 0 0
\(237\) 0 0
\(238\) 8.00000i 0.518563i
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) −2.00000 −0.128831 −0.0644157 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) 5.00000i 0.321412i
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) −3.00000 + 6.00000i −0.191663 + 0.383326i
\(246\) 0 0
\(247\) 2.00000i 0.127257i
\(248\) 12.0000i 0.762001i
\(249\) 0 0
\(250\) 2.00000 + 11.0000i 0.126491 + 0.695701i
\(251\) 4.00000 0.252478 0.126239 0.992000i \(-0.459709\pi\)
0.126239 + 0.992000i \(0.459709\pi\)
\(252\) 6.00000i 0.377964i
\(253\) 24.0000i 1.50887i
\(254\) 0 0
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) 6.00000i 0.374270i 0.982334 + 0.187135i \(0.0599201\pi\)
−0.982334 + 0.187135i \(0.940080\pi\)
\(258\) 0 0
\(259\) 20.0000 1.24274
\(260\) 4.00000 + 2.00000i 0.248069 + 0.124035i
\(261\) 18.0000 1.11417
\(262\) 12.0000i 0.741362i
\(263\) 6.00000i 0.369976i −0.982741 0.184988i \(-0.940775\pi\)
0.982741 0.184988i \(-0.0592246\pi\)
\(264\) 0 0
\(265\) −20.0000 10.0000i −1.22859 0.614295i
\(266\) −2.00000 −0.122628
\(267\) 0 0
\(268\) 8.00000i 0.488678i
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 0 0
\(271\) 24.0000 1.45790 0.728948 0.684569i \(-0.240010\pi\)
0.728948 + 0.684569i \(0.240010\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 12.0000 + 16.0000i 0.723627 + 0.964836i
\(276\) 0 0
\(277\) 8.00000i 0.480673i −0.970690 0.240337i \(-0.922742\pi\)
0.970690 0.240337i \(-0.0772579\pi\)
\(278\) 4.00000i 0.239904i
\(279\) −12.0000 −0.718421
\(280\) −6.00000 + 12.0000i −0.358569 + 0.717137i
\(281\) −26.0000 −1.55103 −0.775515 0.631329i \(-0.782510\pi\)
−0.775515 + 0.631329i \(0.782510\pi\)
\(282\) 0 0
\(283\) 14.0000i 0.832214i 0.909316 + 0.416107i \(0.136606\pi\)
−0.909316 + 0.416107i \(0.863394\pi\)
\(284\) 4.00000 0.237356
\(285\) 0 0
\(286\) −8.00000 −0.473050
\(287\) 20.0000i 1.18056i
\(288\) 15.0000i 0.883883i
\(289\) 1.00000 0.0588235
\(290\) −12.0000 6.00000i −0.704664 0.352332i
\(291\) 0 0
\(292\) 4.00000i 0.234082i
\(293\) 14.0000i 0.817889i −0.912559 0.408944i \(-0.865897\pi\)
0.912559 0.408944i \(-0.134103\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −30.0000 −1.74371
\(297\) 0 0
\(298\) 10.0000i 0.579284i
\(299\) −12.0000 −0.693978
\(300\) 0 0
\(301\) 4.00000 0.230556
\(302\) 24.0000i 1.38104i
\(303\) 0 0
\(304\) 1.00000 0.0573539
\(305\) −2.00000 + 4.00000i −0.114520 + 0.229039i
\(306\) 12.0000 0.685994
\(307\) 20.0000i 1.14146i 0.821138 + 0.570730i \(0.193340\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(308\) 8.00000i 0.455842i
\(309\) 0 0
\(310\) 8.00000 + 4.00000i 0.454369 + 0.227185i
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 24.0000i 1.35656i −0.734803 0.678280i \(-0.762726\pi\)
0.734803 0.678280i \(-0.237274\pi\)
\(314\) −8.00000 −0.451466
\(315\) 12.0000 + 6.00000i 0.676123 + 0.338062i
\(316\) −4.00000 −0.225018
\(317\) 22.0000i 1.23564i −0.786318 0.617822i \(-0.788015\pi\)
0.786318 0.617822i \(-0.211985\pi\)
\(318\) 0 0
\(319\) −24.0000 −1.34374
\(320\) 7.00000 14.0000i 0.391312 0.782624i
\(321\) 0 0
\(322\) 12.0000i 0.668734i
\(323\) 4.00000i 0.222566i
\(324\) 9.00000 0.500000
\(325\) −8.00000 + 6.00000i −0.443760 + 0.332820i
\(326\) −10.0000 −0.553849
\(327\) 0 0
\(328\) 30.0000i 1.65647i
\(329\) 12.0000 0.661581
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 18.0000i 0.987878i
\(333\) 30.0000i 1.64399i
\(334\) 12.0000 0.656611
\(335\) 16.0000 + 8.00000i 0.874173 + 0.437087i
\(336\) 0 0
\(337\) 22.0000i 1.19842i −0.800593 0.599208i \(-0.795482\pi\)
0.800593 0.599208i \(-0.204518\pi\)
\(338\) 9.00000i 0.489535i
\(339\) 0 0
\(340\) 8.00000 + 4.00000i 0.433861 + 0.216930i
\(341\) 16.0000 0.866449
\(342\) 3.00000i 0.162221i
\(343\) 20.0000i 1.07990i
\(344\) −6.00000 −0.323498
\(345\) 0 0
\(346\) 6.00000 0.322562
\(347\) 6.00000i 0.322097i 0.986947 + 0.161048i \(0.0514875\pi\)
−0.986947 + 0.161048i \(0.948512\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) −6.00000 8.00000i −0.320713 0.427618i
\(351\) 0 0
\(352\) 20.0000i 1.06600i
\(353\) 4.00000i 0.212899i 0.994318 + 0.106449i \(0.0339482\pi\)
−0.994318 + 0.106449i \(0.966052\pi\)
\(354\) 0 0
\(355\) −4.00000 + 8.00000i −0.212298 + 0.424596i
\(356\) 2.00000 0.106000
\(357\) 0 0
\(358\) 0 0
\(359\) 8.00000 0.422224 0.211112 0.977462i \(-0.432292\pi\)
0.211112 + 0.977462i \(0.432292\pi\)
\(360\) −18.0000 9.00000i −0.948683 0.474342i
\(361\) 1.00000 0.0526316
\(362\) 18.0000i 0.946059i
\(363\) 0 0
\(364\) −4.00000 −0.209657
\(365\) −8.00000 4.00000i −0.418739 0.209370i
\(366\) 0 0
\(367\) 22.0000i 1.14839i 0.818718 + 0.574195i \(0.194685\pi\)
−0.818718 + 0.574195i \(0.805315\pi\)
\(368\) 6.00000i 0.312772i
\(369\) −30.0000 −1.56174
\(370\) 10.0000 20.0000i 0.519875 1.03975i
\(371\) 20.0000 1.03835
\(372\) 0 0
\(373\) 6.00000i 0.310668i −0.987862 0.155334i \(-0.950355\pi\)
0.987862 0.155334i \(-0.0496454\pi\)
\(374\) −16.0000 −0.827340
\(375\) 0 0
\(376\) −18.0000 −0.928279
\(377\) 12.0000i 0.618031i
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 1.00000 2.00000i 0.0512989 0.102598i
\(381\) 0 0
\(382\) 24.0000i 1.22795i
\(383\) 12.0000i 0.613171i 0.951843 + 0.306586i \(0.0991866\pi\)
−0.951843 + 0.306586i \(0.900813\pi\)
\(384\) 0 0
\(385\) −16.0000 8.00000i −0.815436 0.407718i
\(386\) 26.0000 1.32337
\(387\) 6.00000i 0.304997i
\(388\) 6.00000i 0.304604i
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) 0 0
\(391\) −24.0000 −1.21373
\(392\) 9.00000i 0.454569i
\(393\) 0 0
\(394\) −12.0000 −0.604551
\(395\) 4.00000 8.00000i 0.201262 0.402524i
\(396\) −12.0000 −0.603023
\(397\) 8.00000i 0.401508i 0.979642 + 0.200754i \(0.0643393\pi\)
−0.979642 + 0.200754i \(0.935661\pi\)
\(398\) 16.0000i 0.802008i
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) 8.00000i 0.398508i
\(404\) −6.00000 −0.298511
\(405\) −9.00000 + 18.0000i −0.447214 + 0.894427i
\(406\) 12.0000 0.595550
\(407\) 40.0000i 1.98273i
\(408\) 0 0
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) 20.0000 + 10.0000i 0.987730 + 0.493865i
\(411\) 0 0
\(412\) 16.0000i 0.788263i
\(413\) 0 0
\(414\) 18.0000 0.884652
\(415\) 36.0000 + 18.0000i 1.76717 + 0.883585i
\(416\) 10.0000 0.490290
\(417\) 0 0
\(418\) 4.00000i 0.195646i
\(419\) −36.0000 −1.75872 −0.879358 0.476162i \(-0.842028\pi\)
−0.879358 + 0.476162i \(0.842028\pi\)
\(420\) 0 0
\(421\) −30.0000 −1.46211 −0.731055 0.682318i \(-0.760972\pi\)
−0.731055 + 0.682318i \(0.760972\pi\)
\(422\) 20.0000i 0.973585i
\(423\) 18.0000i 0.875190i
\(424\) −30.0000 −1.45693
\(425\) −16.0000 + 12.0000i −0.776114 + 0.582086i
\(426\) 0 0
\(427\) 4.00000i 0.193574i
\(428\) 4.00000i 0.193347i
\(429\) 0 0
\(430\) 2.00000 4.00000i 0.0964486 0.192897i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 34.0000i 1.63394i −0.576683 0.816968i \(-0.695653\pi\)
0.576683 0.816968i \(-0.304347\pi\)
\(434\) −8.00000 −0.384012
\(435\) 0 0
\(436\) −6.00000 −0.287348
\(437\) 6.00000i 0.287019i
\(438\) 0 0
\(439\) −20.0000 −0.954548 −0.477274 0.878755i \(-0.658375\pi\)
−0.477274 + 0.878755i \(0.658375\pi\)
\(440\) 24.0000 + 12.0000i 1.14416 + 0.572078i
\(441\) 9.00000 0.428571
\(442\) 8.00000i 0.380521i
\(443\) 2.00000i 0.0950229i −0.998871 0.0475114i \(-0.984871\pi\)
0.998871 0.0475114i \(-0.0151291\pi\)
\(444\) 0 0
\(445\) −2.00000 + 4.00000i −0.0948091 + 0.189618i
\(446\) −16.0000 −0.757622
\(447\) 0 0
\(448\) 14.0000i 0.661438i
\(449\) −10.0000 −0.471929 −0.235965 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) 12.0000 9.00000i 0.565685 0.424264i
\(451\) 40.0000 1.88353
\(452\) 6.00000i 0.282216i
\(453\) 0 0
\(454\) 20.0000 0.938647
\(455\) 4.00000 8.00000i 0.187523 0.375046i
\(456\) 0 0
\(457\) 8.00000i 0.374224i 0.982339 + 0.187112i \(0.0599128\pi\)
−0.982339 + 0.187112i \(0.940087\pi\)
\(458\) 10.0000i 0.467269i
\(459\) 0 0
\(460\) 12.0000 + 6.00000i 0.559503 + 0.279751i
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 0 0
\(463\) 2.00000i 0.0929479i 0.998920 + 0.0464739i \(0.0147984\pi\)
−0.998920 + 0.0464739i \(0.985202\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) −16.0000 −0.741186
\(467\) 38.0000i 1.75843i 0.476425 + 0.879215i \(0.341932\pi\)
−0.476425 + 0.879215i \(0.658068\pi\)
\(468\) 6.00000i 0.277350i
\(469\) −16.0000 −0.738811
\(470\) 6.00000 12.0000i 0.276759 0.553519i
\(471\) 0 0
\(472\) 0 0
\(473\) 8.00000i 0.367840i
\(474\) 0 0
\(475\) 3.00000 + 4.00000i 0.137649 + 0.183533i
\(476\) −8.00000 −0.366679
\(477\) 30.0000i 1.37361i
\(478\) 16.0000i 0.731823i
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) 20.0000 0.911922
\(482\) 2.00000i 0.0910975i
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 12.0000 + 6.00000i 0.544892 + 0.272446i
\(486\) 0 0
\(487\) 20.0000i 0.906287i 0.891438 + 0.453143i \(0.149697\pi\)
−0.891438 + 0.453143i \(0.850303\pi\)
\(488\) 6.00000i 0.271607i
\(489\) 0 0
\(490\) −6.00000 3.00000i −0.271052 0.135526i
\(491\) −20.0000 −0.902587 −0.451294 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) 0 0
\(493\) 24.0000i 1.08091i
\(494\) −2.00000 −0.0899843
\(495\) 12.0000 24.0000i 0.539360 1.07872i
\(496\) 4.00000 0.179605
\(497\) 8.00000i 0.358849i
\(498\) 0 0
\(499\) −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
\(501\) 0 0
\(502\) 4.00000i 0.178529i
\(503\) 10.0000i 0.445878i 0.974832 + 0.222939i \(0.0715651\pi\)
−0.974832 + 0.222939i \(0.928435\pi\)
\(504\) 18.0000 0.801784
\(505\) 6.00000 12.0000i 0.266996 0.533993i
\(506\) −24.0000 −1.06693
\(507\) 0 0
\(508\) 0 0
\(509\) 6.00000 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 0 0
\(511\) 8.00000 0.353899
\(512\) 11.0000i 0.486136i
\(513\) 0 0
\(514\) −6.00000 −0.264649
\(515\) −32.0000 16.0000i −1.41009 0.705044i
\(516\) 0 0
\(517\) 24.0000i 1.05552i
\(518\) 20.0000i 0.878750i
\(519\) 0 0
\(520\) −6.00000 + 12.0000i −0.263117 + 0.526235i
\(521\) 42.0000 1.84005 0.920027 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) 18.0000i 0.787839i
\(523\) 44.0000i 1.92399i −0.273075 0.961993i \(-0.588041\pi\)
0.273075 0.961993i \(-0.411959\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 6.00000 0.261612
\(527\) 16.0000i 0.696971i
\(528\) 0 0
\(529\) −13.0000 −0.565217
\(530\) 10.0000 20.0000i 0.434372 0.868744i
\(531\) 0 0
\(532\) 2.00000i 0.0867110i
\(533\) 20.0000i 0.866296i
\(534\) 0 0
\(535\) −8.00000 4.00000i −0.345870 0.172935i
\(536\) 24.0000 1.03664
\(537\) 0 0
\(538\) 18.0000i 0.776035i
\(539\) −12.0000 −0.516877
\(540\) 0 0
\(541\) −22.0000 −0.945854 −0.472927 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) 24.0000i 1.03089i
\(543\) 0 0
\(544\) 20.0000 0.857493
\(545\) 6.00000 12.0000i 0.257012 0.514024i
\(546\) 0 0
\(547\) 28.0000i 1.19719i −0.801050 0.598597i \(-0.795725\pi\)
0.801050 0.598597i \(-0.204275\pi\)
\(548\) 12.0000i 0.512615i
\(549\) 6.00000 0.256074
\(550\) −16.0000 + 12.0000i −0.682242 + 0.511682i
\(551\) −6.00000 −0.255609
\(552\) 0 0
\(553\) 8.00000i 0.340195i
\(554\) 8.00000 0.339887
\(555\) 0 0
\(556\) 4.00000 0.169638
\(557\) 16.0000i 0.677942i 0.940797 + 0.338971i \(0.110079\pi\)
−0.940797 + 0.338971i \(0.889921\pi\)
\(558\) 12.0000i 0.508001i
\(559\) 4.00000 0.169182
\(560\) −4.00000 2.00000i −0.169031 0.0845154i
\(561\) 0 0
\(562\) 26.0000i 1.09674i
\(563\) 12.0000i 0.505740i 0.967500 + 0.252870i \(0.0813744\pi\)
−0.967500 + 0.252870i \(0.918626\pi\)
\(564\) 0 0
\(565\) −12.0000 6.00000i −0.504844 0.252422i
\(566\) −14.0000 −0.588464
\(567\) 18.0000i 0.755929i
\(568\) 12.0000i 0.503509i
\(569\) −42.0000 −1.76073 −0.880366 0.474295i \(-0.842703\pi\)
−0.880366 + 0.474295i \(0.842703\pi\)
\(570\) 0 0
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 8.00000i 0.334497i
\(573\) 0 0
\(574\) −20.0000 −0.834784
\(575\) −24.0000 + 18.0000i −1.00087 + 0.750652i
\(576\) −21.0000 −0.875000
\(577\) 24.0000i 0.999133i −0.866276 0.499567i \(-0.833493\pi\)
0.866276 0.499567i \(-0.166507\pi\)
\(578\) 1.00000i 0.0415945i
\(579\) 0 0
\(580\) −6.00000 + 12.0000i −0.249136 + 0.498273i
\(581\) −36.0000 −1.49353
\(582\) 0 0
\(583\) 40.0000i 1.65663i
\(584\) −12.0000 −0.496564
\(585\) 12.0000 + 6.00000i 0.496139 + 0.248069i
\(586\) 14.0000 0.578335
\(587\) 18.0000i 0.742940i −0.928445 0.371470i \(-0.878854\pi\)
0.928445 0.371470i \(-0.121146\pi\)
\(588\) 0 0
\(589\) 4.00000 0.164817
\(590\) 0 0
\(591\) 0 0
\(592\) 10.0000i 0.410997i
\(593\) 8.00000i 0.328521i −0.986417 0.164260i \(-0.947476\pi\)
0.986417 0.164260i \(-0.0525237\pi\)
\(594\) 0 0
\(595\) 8.00000 16.0000i 0.327968 0.655936i
\(596\) 10.0000 0.409616
\(597\) 0 0
\(598\) 12.0000i 0.490716i
\(599\) −12.0000 −0.490307 −0.245153 0.969484i \(-0.578838\pi\)
−0.245153 + 0.969484i \(0.578838\pi\)
\(600\) 0 0
\(601\) 14.0000 0.571072 0.285536 0.958368i \(-0.407828\pi\)
0.285536 + 0.958368i \(0.407828\pi\)
\(602\) 4.00000i 0.163028i
\(603\) 24.0000i 0.977356i
\(604\) 24.0000 0.976546
\(605\) −5.00000 + 10.0000i −0.203279 + 0.406558i
\(606\) 0 0
\(607\) 44.0000i 1.78590i 0.450151 + 0.892952i \(0.351370\pi\)
−0.450151 + 0.892952i \(0.648630\pi\)
\(608\) 5.00000i 0.202777i
\(609\) 0 0
\(610\) −4.00000 2.00000i −0.161955 0.0809776i
\(611\) 12.0000 0.485468
\(612\) 12.0000i 0.485071i
\(613\) 24.0000i 0.969351i −0.874694 0.484675i \(-0.838938\pi\)
0.874694 0.484675i \(-0.161062\pi\)
\(614\) −20.0000 −0.807134
\(615\) 0 0
\(616\) −24.0000 −0.966988
\(617\) 12.0000i 0.483102i −0.970388 0.241551i \(-0.922344\pi\)
0.970388 0.241551i \(-0.0776561\pi\)
\(618\) 0 0
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 4.00000 8.00000i 0.160644 0.321288i
\(621\) 0 0
\(622\) 24.0000i 0.962312i
\(623\) 4.00000i 0.160257i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 24.0000 0.959233
\(627\) 0 0
\(628\) 8.00000i 0.319235i
\(629\) 40.0000 1.59490
\(630\) −6.00000 + 12.0000i −0.239046 + 0.478091i
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 12.0000i 0.477334i
\(633\) 0 0
\(634\) 22.0000 0.873732
\(635\) 0 0
\(636\) 0 0
\(637\) 6.00000i 0.237729i
\(638\) 24.0000i 0.950169i
\(639\) 12.0000 0.474713
\(640\) −6.00000 3.00000i −0.237171 0.118585i
\(641\) 6.00000 0.236986 0.118493 0.992955i \(-0.462194\pi\)
0.118493 + 0.992955i \(0.462194\pi\)
\(642\) 0 0
\(643\) 38.0000i 1.49857i 0.662246 + 0.749287i \(0.269604\pi\)
−0.662246 + 0.749287i \(0.730396\pi\)
\(644\) −12.0000 −0.472866
\(645\) 0 0
\(646\) −4.00000 −0.157378
\(647\) 30.0000i 1.17942i −0.807614 0.589711i \(-0.799242\pi\)
0.807614 0.589711i \(-0.200758\pi\)
\(648\) 27.0000i 1.06066i
\(649\) 0 0
\(650\) −6.00000 8.00000i −0.235339 0.313786i
\(651\) 0 0
\(652\) 10.0000i 0.391630i
\(653\) 16.0000i 0.626128i 0.949732 + 0.313064i \(0.101356\pi\)
−0.949732 + 0.313064i \(0.898644\pi\)
\(654\) 0 0
\(655\) 12.0000 24.0000i 0.468879 0.937758i
\(656\) 10.0000 0.390434
\(657\) 12.0000i 0.468165i
\(658\) 12.0000i 0.467809i
\(659\) 16.0000 0.623272 0.311636 0.950202i \(-0.399123\pi\)
0.311636 + 0.950202i \(0.399123\pi\)
\(660\) 0 0
\(661\) −30.0000 −1.16686 −0.583432 0.812162i \(-0.698291\pi\)
−0.583432 + 0.812162i \(0.698291\pi\)
\(662\) 4.00000i 0.155464i
\(663\) 0 0
\(664\) 54.0000 2.09561
\(665\) −4.00000 2.00000i −0.155113 0.0775567i
\(666\) −30.0000 −1.16248
\(667\) 36.0000i 1.39393i
\(668\) 12.0000i 0.464294i
\(669\) 0 0
\(670\) −8.00000 + 16.0000i −0.309067 + 0.618134i
\(671\) −8.00000 −0.308837
\(672\) 0 0
\(673\) 34.0000i 1.31060i 0.755367 + 0.655302i \(0.227459\pi\)
−0.755367 + 0.655302i \(0.772541\pi\)
\(674\) 22.0000 0.847408
\(675\) 0 0
\(676\) 9.00000 0.346154
\(677\) 18.0000i 0.691796i −0.938272 0.345898i \(-0.887574\pi\)
0.938272 0.345898i \(-0.112426\pi\)
\(678\) 0 0
\(679\) −12.0000 −0.460518
\(680\) −12.0000 + 24.0000i −0.460179 + 0.920358i
\(681\) 0 0
\(682\) 16.0000i 0.612672i
\(683\) 12.0000i 0.459167i 0.973289 + 0.229584i \(0.0737364\pi\)
−0.973289 + 0.229584i \(0.926264\pi\)
\(684\) −3.00000 −0.114708
\(685\) 24.0000 + 12.0000i 0.916993 + 0.458496i
\(686\) 20.0000 0.763604
\(687\) 0 0
\(688\) 2.00000i 0.0762493i
\(689\) 20.0000 0.761939
\(690\) 0 0
\(691\) −12.0000 −0.456502 −0.228251 0.973602i \(-0.573301\pi\)
−0.228251 + 0.973602i \(0.573301\pi\)
\(692\) 6.00000i 0.228086i
\(693\) 24.0000i 0.911685i
\(694\) −6.00000 −0.227757
\(695\) −4.00000 + 8.00000i −0.151729 + 0.303457i
\(696\) 0 0
\(697\) 40.0000i 1.51511i
\(698\) 2.00000i 0.0757011i
\(699\) 0 0
\(700\) −8.00000 + 6.00000i −0.302372 + 0.226779i
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) 10.0000i 0.377157i
\(704\) 28.0000 1.05529
\(705\) 0 0
\(706\) −4.00000 −0.150542
\(707\) 12.0000i 0.451306i
\(708\) 0 0
\(709\) 38.0000 1.42712 0.713560 0.700594i \(-0.247082\pi\)
0.713560 + 0.700594i \(0.247082\pi\)
\(710\) −8.00000 4.00000i −0.300235 0.150117i
\(711\) −12.0000 −0.450035
\(712\) 6.00000i 0.224860i
\(713\) 24.0000i 0.898807i
\(714\) 0 0
\(715\) −16.0000 8.00000i −0.598366 0.299183i
\(716\) 0 0
\(717\) 0 0
\(718\) 8.00000i 0.298557i
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 3.00000 6.00000i 0.111803 0.223607i
\(721\) 32.0000 1.19174
\(722\) 1.00000i 0.0372161i
\(723\) 0 0
\(724\) −18.0000 −0.668965
\(725\) −18.0000 24.0000i −0.668503 0.891338i
\(726\) 0 0
\(727\) 2.00000i 0.0741759i −0.999312 0.0370879i \(-0.988192\pi\)
0.999312 0.0370879i \(-0.0118082\pi\)
\(728\) 12.0000i 0.444750i
\(729\) 27.0000 1.00000
\(730\) 4.00000 8.00000i 0.148047 0.296093i
\(731\) 8.00000 0.295891
\(732\) 0 0
\(733\) 12.0000i 0.443230i −0.975134 0.221615i \(-0.928867\pi\)
0.975134 0.221615i \(-0.0711328\pi\)
\(734\) −22.0000 −0.812035
\(735\) 0 0
\(736\) 30.0000 1.10581
\(737\) 32.0000i 1.17874i
\(738\) 30.0000i 1.10432i
\(739\) −4.00000 −0.147142 −0.0735712 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) −20.0000 10.0000i −0.735215 0.367607i
\(741\) 0 0
\(742\) 20.0000i 0.734223i
\(743\) 4.00000i 0.146746i −0.997305 0.0733729i \(-0.976624\pi\)
0.997305 0.0733729i \(-0.0233763\pi\)
\(744\) 0 0
\(745\) −10.0000 + 20.0000i −0.366372 + 0.732743i
\(746\) 6.00000 0.219676
\(747\) 54.0000i 1.97576i
\(748\) 16.0000i 0.585018i
\(749\) 8.00000 0.292314
\(750\) 0 0
\(751\) −40.0000 −1.45962 −0.729810 0.683650i \(-0.760392\pi\)
−0.729810 + 0.683650i \(0.760392\pi\)
\(752\) 6.00000i 0.218797i
\(753\) 0 0
\(754\) 12.0000 0.437014
\(755\) −24.0000 + 48.0000i −0.873449 + 1.74690i
\(756\) 0 0
\(757\) 4.00000i 0.145382i 0.997354 + 0.0726912i \(0.0231588\pi\)
−0.997354 + 0.0726912i \(0.976841\pi\)
\(758\) 28.0000i 1.01701i
\(759\) 0 0
\(760\) 6.00000 + 3.00000i 0.217643 + 0.108821i
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 0 0
\(763\) 12.0000i 0.434429i
\(764\) −24.0000 −0.868290
\(765\) 24.0000 + 12.0000i 0.867722 + 0.433861i
\(766\) −12.0000 −0.433578
\(767\) 0 0
\(768\) 0 0
\(769\) −26.0000 −0.937584 −0.468792 0.883309i \(-0.655311\pi\)
−0.468792 + 0.883309i \(0.655311\pi\)
\(770\) 8.00000 16.0000i 0.288300 0.576600i
\(771\) 0 0
\(772\) 26.0000i 0.935760i
\(773\) 46.0000i 1.65451i 0.561830 + 0.827253i \(0.310097\pi\)
−0.561830 + 0.827253i \(0.689903\pi\)
\(774\) −6.00000 −0.215666
\(775\) 12.0000 + 16.0000i 0.431053 + 0.574737i
\(776\) 18.0000 0.646162
\(777\) 0 0
\(778\) 30.0000i 1.07555i
\(779\) 10.0000 0.358287
\(780\) 0 0
\(781\) −16.0000 −0.572525
\(782\) 24.0000i 0.858238i
\(783\) 0 0
\(784\) −3.00000 −0.107143
\(785\) −16.0000 8.00000i −0.571064 0.285532i
\(786\) 0 0
\(787\) 44.0000i 1.56843i 0.620489 + 0.784215i \(0.286934\pi\)
−0.620489 + 0.784215i \(0.713066\pi\)
\(788\) 12.0000i 0.427482i
\(789\) 0 0
\(790\) 8.00000 + 4.00000i 0.284627 + 0.142314i
\(791\) 12.0000 0.426671
\(792\) 36.0000i 1.27920i
\(793\) 4.00000i 0.142044i