Properties

Label 144.2.k.a.109.1
Level $144$
Weight $2$
Character 144.109
Analytic conductor $1.150$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14984578911\)
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: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 109.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 144.109
Dual form 144.2.k.a.37.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(1.00000 - 1.00000i) q^{5} +2.00000i q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(1.00000 - 1.00000i) q^{5} +2.00000i q^{7} +(-2.00000 - 2.00000i) q^{8} -2.00000i q^{10} +(-1.00000 + 1.00000i) q^{11} +(-1.00000 - 1.00000i) q^{13} +(2.00000 + 2.00000i) q^{14} -4.00000 q^{16} +2.00000 q^{17} +(3.00000 + 3.00000i) q^{19} +(-2.00000 - 2.00000i) q^{20} +2.00000i q^{22} +6.00000i q^{23} +3.00000i q^{25} -2.00000 q^{26} +4.00000 q^{28} +(-3.00000 - 3.00000i) q^{29} -8.00000 q^{31} +(-4.00000 + 4.00000i) q^{32} +(2.00000 - 2.00000i) q^{34} +(2.00000 + 2.00000i) q^{35} +(3.00000 - 3.00000i) q^{37} +6.00000 q^{38} -4.00000 q^{40} +(5.00000 - 5.00000i) q^{43} +(2.00000 + 2.00000i) q^{44} +(6.00000 + 6.00000i) q^{46} -8.00000 q^{47} +3.00000 q^{49} +(3.00000 + 3.00000i) q^{50} +(-2.00000 + 2.00000i) q^{52} +(5.00000 - 5.00000i) q^{53} +2.00000i q^{55} +(4.00000 - 4.00000i) q^{56} -6.00000 q^{58} +(3.00000 - 3.00000i) q^{59} +(-9.00000 - 9.00000i) q^{61} +(-8.00000 + 8.00000i) q^{62} +8.00000i q^{64} -2.00000 q^{65} +(-5.00000 - 5.00000i) q^{67} -4.00000i q^{68} +4.00000 q^{70} -10.0000i q^{71} +4.00000i q^{73} -6.00000i q^{74} +(6.00000 - 6.00000i) q^{76} +(-2.00000 - 2.00000i) q^{77} +(-4.00000 + 4.00000i) q^{80} +(1.00000 + 1.00000i) q^{83} +(2.00000 - 2.00000i) q^{85} -10.0000i q^{86} +4.00000 q^{88} +4.00000i q^{89} +(2.00000 - 2.00000i) q^{91} +12.0000 q^{92} +(-8.00000 + 8.00000i) q^{94} +6.00000 q^{95} -2.00000 q^{97} +(3.00000 - 3.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + 2q^{5} - 4q^{8} + O(q^{10}) \) \( 2q + 2q^{2} + 2q^{5} - 4q^{8} - 2q^{11} - 2q^{13} + 4q^{14} - 8q^{16} + 4q^{17} + 6q^{19} - 4q^{20} - 4q^{26} + 8q^{28} - 6q^{29} - 16q^{31} - 8q^{32} + 4q^{34} + 4q^{35} + 6q^{37} + 12q^{38} - 8q^{40} + 10q^{43} + 4q^{44} + 12q^{46} - 16q^{47} + 6q^{49} + 6q^{50} - 4q^{52} + 10q^{53} + 8q^{56} - 12q^{58} + 6q^{59} - 18q^{61} - 16q^{62} - 4q^{65} - 10q^{67} + 8q^{70} + 12q^{76} - 4q^{77} - 8q^{80} + 2q^{83} + 4q^{85} + 8q^{88} + 4q^{91} + 24q^{92} - 16q^{94} + 12q^{95} - 4q^{97} + 6q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000i 0.707107 0.707107i
\(3\) 0 0
\(4\) 2.00000i 1.00000i
\(5\) 1.00000 1.00000i 0.447214 0.447214i −0.447214 0.894427i \(-0.647584\pi\)
0.894427 + 0.447214i \(0.147584\pi\)
\(6\) 0 0
\(7\) 2.00000i 0.755929i 0.925820 + 0.377964i \(0.123376\pi\)
−0.925820 + 0.377964i \(0.876624\pi\)
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) 0 0
\(10\) 2.00000i 0.632456i
\(11\) −1.00000 + 1.00000i −0.301511 + 0.301511i −0.841605 0.540094i \(-0.818389\pi\)
0.540094 + 0.841605i \(0.318389\pi\)
\(12\) 0 0
\(13\) −1.00000 1.00000i −0.277350 0.277350i 0.554700 0.832050i \(-0.312833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 2.00000 + 2.00000i 0.534522 + 0.534522i
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) 3.00000 + 3.00000i 0.688247 + 0.688247i 0.961844 0.273597i \(-0.0882135\pi\)
−0.273597 + 0.961844i \(0.588214\pi\)
\(20\) −2.00000 2.00000i −0.447214 0.447214i
\(21\) 0 0
\(22\) 2.00000i 0.426401i
\(23\) 6.00000i 1.25109i 0.780189 + 0.625543i \(0.215123\pi\)
−0.780189 + 0.625543i \(0.784877\pi\)
\(24\) 0 0
\(25\) 3.00000i 0.600000i
\(26\) −2.00000 −0.392232
\(27\) 0 0
\(28\) 4.00000 0.755929
\(29\) −3.00000 3.00000i −0.557086 0.557086i 0.371391 0.928477i \(-0.378881\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) 0 0
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) −4.00000 + 4.00000i −0.707107 + 0.707107i
\(33\) 0 0
\(34\) 2.00000 2.00000i 0.342997 0.342997i
\(35\) 2.00000 + 2.00000i 0.338062 + 0.338062i
\(36\) 0 0
\(37\) 3.00000 3.00000i 0.493197 0.493197i −0.416115 0.909312i \(-0.636609\pi\)
0.909312 + 0.416115i \(0.136609\pi\)
\(38\) 6.00000 0.973329
\(39\) 0 0
\(40\) −4.00000 −0.632456
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 5.00000 5.00000i 0.762493 0.762493i −0.214280 0.976772i \(-0.568740\pi\)
0.976772 + 0.214280i \(0.0687403\pi\)
\(44\) 2.00000 + 2.00000i 0.301511 + 0.301511i
\(45\) 0 0
\(46\) 6.00000 + 6.00000i 0.884652 + 0.884652i
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0 0
\(49\) 3.00000 0.428571
\(50\) 3.00000 + 3.00000i 0.424264 + 0.424264i
\(51\) 0 0
\(52\) −2.00000 + 2.00000i −0.277350 + 0.277350i
\(53\) 5.00000 5.00000i 0.686803 0.686803i −0.274721 0.961524i \(-0.588586\pi\)
0.961524 + 0.274721i \(0.0885855\pi\)
\(54\) 0 0
\(55\) 2.00000i 0.269680i
\(56\) 4.00000 4.00000i 0.534522 0.534522i
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) 3.00000 3.00000i 0.390567 0.390567i −0.484323 0.874889i \(-0.660934\pi\)
0.874889 + 0.484323i \(0.160934\pi\)
\(60\) 0 0
\(61\) −9.00000 9.00000i −1.15233 1.15233i −0.986084 0.166248i \(-0.946835\pi\)
−0.166248 0.986084i \(-0.553165\pi\)
\(62\) −8.00000 + 8.00000i −1.01600 + 1.01600i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) −2.00000 −0.248069
\(66\) 0 0
\(67\) −5.00000 5.00000i −0.610847 0.610847i 0.332320 0.943167i \(-0.392169\pi\)
−0.943167 + 0.332320i \(0.892169\pi\)
\(68\) 4.00000i 0.485071i
\(69\) 0 0
\(70\) 4.00000 0.478091
\(71\) 10.0000i 1.18678i −0.804914 0.593391i \(-0.797789\pi\)
0.804914 0.593391i \(-0.202211\pi\)
\(72\) 0 0
\(73\) 4.00000i 0.468165i 0.972217 + 0.234082i \(0.0752085\pi\)
−0.972217 + 0.234082i \(0.924791\pi\)
\(74\) 6.00000i 0.697486i
\(75\) 0 0
\(76\) 6.00000 6.00000i 0.688247 0.688247i
\(77\) −2.00000 2.00000i −0.227921 0.227921i
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −4.00000 + 4.00000i −0.447214 + 0.447214i
\(81\) 0 0
\(82\) 0 0
\(83\) 1.00000 + 1.00000i 0.109764 + 0.109764i 0.759856 0.650092i \(-0.225269\pi\)
−0.650092 + 0.759856i \(0.725269\pi\)
\(84\) 0 0
\(85\) 2.00000 2.00000i 0.216930 0.216930i
\(86\) 10.0000i 1.07833i
\(87\) 0 0
\(88\) 4.00000 0.426401
\(89\) 4.00000i 0.423999i 0.977270 + 0.212000i \(0.0679975\pi\)
−0.977270 + 0.212000i \(0.932002\pi\)
\(90\) 0 0
\(91\) 2.00000 2.00000i 0.209657 0.209657i
\(92\) 12.0000 1.25109
\(93\) 0 0
\(94\) −8.00000 + 8.00000i −0.825137 + 0.825137i
\(95\) 6.00000 0.615587
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 3.00000 3.00000i 0.303046 0.303046i
\(99\) 0 0
\(100\) 6.00000 0.600000
\(101\) −11.0000 + 11.0000i −1.09454 + 1.09454i −0.0995037 + 0.995037i \(0.531726\pi\)
−0.995037 + 0.0995037i \(0.968274\pi\)
\(102\) 0 0
\(103\) 6.00000i 0.591198i −0.955312 0.295599i \(-0.904481\pi\)
0.955312 0.295599i \(-0.0955191\pi\)
\(104\) 4.00000i 0.392232i
\(105\) 0 0
\(106\) 10.0000i 0.971286i
\(107\) 7.00000 7.00000i 0.676716 0.676716i −0.282540 0.959256i \(-0.591177\pi\)
0.959256 + 0.282540i \(0.0911770\pi\)
\(108\) 0 0
\(109\) 3.00000 + 3.00000i 0.287348 + 0.287348i 0.836031 0.548683i \(-0.184871\pi\)
−0.548683 + 0.836031i \(0.684871\pi\)
\(110\) 2.00000 + 2.00000i 0.190693 + 0.190693i
\(111\) 0 0
\(112\) 8.00000i 0.755929i
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 6.00000 + 6.00000i 0.559503 + 0.559503i
\(116\) −6.00000 + 6.00000i −0.557086 + 0.557086i
\(117\) 0 0
\(118\) 6.00000i 0.552345i
\(119\) 4.00000i 0.366679i
\(120\) 0 0
\(121\) 9.00000i 0.818182i
\(122\) −18.0000 −1.62964
\(123\) 0 0
\(124\) 16.0000i 1.43684i
\(125\) 8.00000 + 8.00000i 0.715542 + 0.715542i
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 8.00000 + 8.00000i 0.707107 + 0.707107i
\(129\) 0 0
\(130\) −2.00000 + 2.00000i −0.175412 + 0.175412i
\(131\) −11.0000 11.0000i −0.961074 0.961074i 0.0381958 0.999270i \(-0.487839\pi\)
−0.999270 + 0.0381958i \(0.987839\pi\)
\(132\) 0 0
\(133\) −6.00000 + 6.00000i −0.520266 + 0.520266i
\(134\) −10.0000 −0.863868
\(135\) 0 0
\(136\) −4.00000 4.00000i −0.342997 0.342997i
\(137\) 8.00000i 0.683486i 0.939793 + 0.341743i \(0.111017\pi\)
−0.939793 + 0.341743i \(0.888983\pi\)
\(138\) 0 0
\(139\) −3.00000 + 3.00000i −0.254457 + 0.254457i −0.822795 0.568338i \(-0.807586\pi\)
0.568338 + 0.822795i \(0.307586\pi\)
\(140\) 4.00000 4.00000i 0.338062 0.338062i
\(141\) 0 0
\(142\) −10.0000 10.0000i −0.839181 0.839181i
\(143\) 2.00000 0.167248
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) 4.00000 + 4.00000i 0.331042 + 0.331042i
\(147\) 0 0
\(148\) −6.00000 6.00000i −0.493197 0.493197i
\(149\) −7.00000 + 7.00000i −0.573462 + 0.573462i −0.933094 0.359632i \(-0.882902\pi\)
0.359632 + 0.933094i \(0.382902\pi\)
\(150\) 0 0
\(151\) 10.0000i 0.813788i 0.913475 + 0.406894i \(0.133388\pi\)
−0.913475 + 0.406894i \(0.866612\pi\)
\(152\) 12.0000i 0.973329i
\(153\) 0 0
\(154\) −4.00000 −0.322329
\(155\) −8.00000 + 8.00000i −0.642575 + 0.642575i
\(156\) 0 0
\(157\) 15.0000 + 15.0000i 1.19713 + 1.19713i 0.975022 + 0.222108i \(0.0712939\pi\)
0.222108 + 0.975022i \(0.428706\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 8.00000i 0.632456i
\(161\) −12.0000 −0.945732
\(162\) 0 0
\(163\) −1.00000 1.00000i −0.0783260 0.0783260i 0.666858 0.745184i \(-0.267639\pi\)
−0.745184 + 0.666858i \(0.767639\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 2.00000 0.155230
\(167\) 2.00000i 0.154765i −0.997001 0.0773823i \(-0.975344\pi\)
0.997001 0.0773823i \(-0.0246562\pi\)
\(168\) 0 0
\(169\) 11.0000i 0.846154i
\(170\) 4.00000i 0.306786i
\(171\) 0 0
\(172\) −10.0000 10.0000i −0.762493 0.762493i
\(173\) 1.00000 + 1.00000i 0.0760286 + 0.0760286i 0.744099 0.668070i \(-0.232879\pi\)
−0.668070 + 0.744099i \(0.732879\pi\)
\(174\) 0 0
\(175\) −6.00000 −0.453557
\(176\) 4.00000 4.00000i 0.301511 0.301511i
\(177\) 0 0
\(178\) 4.00000 + 4.00000i 0.299813 + 0.299813i
\(179\) 17.0000 + 17.0000i 1.27064 + 1.27064i 0.945753 + 0.324887i \(0.105326\pi\)
0.324887 + 0.945753i \(0.394674\pi\)
\(180\) 0 0
\(181\) −9.00000 + 9.00000i −0.668965 + 0.668965i −0.957476 0.288512i \(-0.906840\pi\)
0.288512 + 0.957476i \(0.406840\pi\)
\(182\) 4.00000i 0.296500i
\(183\) 0 0
\(184\) 12.0000 12.0000i 0.884652 0.884652i
\(185\) 6.00000i 0.441129i
\(186\) 0 0
\(187\) −2.00000 + 2.00000i −0.146254 + 0.146254i
\(188\) 16.0000i 1.16692i
\(189\) 0 0
\(190\) 6.00000 6.00000i 0.435286 0.435286i
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 0 0
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) −2.00000 + 2.00000i −0.143592 + 0.143592i
\(195\) 0 0
\(196\) 6.00000i 0.428571i
\(197\) 17.0000 17.0000i 1.21120 1.21120i 0.240567 0.970632i \(-0.422666\pi\)
0.970632 0.240567i \(-0.0773335\pi\)
\(198\) 0 0
\(199\) 14.0000i 0.992434i −0.868199 0.496217i \(-0.834722\pi\)
0.868199 0.496217i \(-0.165278\pi\)
\(200\) 6.00000 6.00000i 0.424264 0.424264i
\(201\) 0 0
\(202\) 22.0000i 1.54791i
\(203\) 6.00000 6.00000i 0.421117 0.421117i
\(204\) 0 0
\(205\) 0 0
\(206\) −6.00000 6.00000i −0.418040 0.418040i
\(207\) 0 0
\(208\) 4.00000 + 4.00000i 0.277350 + 0.277350i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) −9.00000 9.00000i −0.619586 0.619586i 0.325840 0.945425i \(-0.394353\pi\)
−0.945425 + 0.325840i \(0.894353\pi\)
\(212\) −10.0000 10.0000i −0.686803 0.686803i
\(213\) 0 0
\(214\) 14.0000i 0.957020i
\(215\) 10.0000i 0.681994i
\(216\) 0 0
\(217\) 16.0000i 1.08615i
\(218\) 6.00000 0.406371
\(219\) 0 0
\(220\) 4.00000 0.269680
\(221\) −2.00000 2.00000i −0.134535 0.134535i
\(222\) 0 0
\(223\) 24.0000 1.60716 0.803579 0.595198i \(-0.202926\pi\)
0.803579 + 0.595198i \(0.202926\pi\)
\(224\) −8.00000 8.00000i −0.534522 0.534522i
\(225\) 0 0
\(226\) 6.00000 6.00000i 0.399114 0.399114i
\(227\) −15.0000 15.0000i −0.995585 0.995585i 0.00440533 0.999990i \(-0.498598\pi\)
−0.999990 + 0.00440533i \(0.998598\pi\)
\(228\) 0 0
\(229\) 7.00000 7.00000i 0.462573 0.462573i −0.436925 0.899498i \(-0.643932\pi\)
0.899498 + 0.436925i \(0.143932\pi\)
\(230\) 12.0000 0.791257
\(231\) 0 0
\(232\) 12.0000i 0.787839i
\(233\) 4.00000i 0.262049i −0.991379 0.131024i \(-0.958173\pi\)
0.991379 0.131024i \(-0.0418266\pi\)
\(234\) 0 0
\(235\) −8.00000 + 8.00000i −0.521862 + 0.521862i
\(236\) −6.00000 6.00000i −0.390567 0.390567i
\(237\) 0 0
\(238\) 4.00000 + 4.00000i 0.259281 + 0.259281i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −18.0000 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 9.00000 + 9.00000i 0.578542 + 0.578542i
\(243\) 0 0
\(244\) −18.0000 + 18.0000i −1.15233 + 1.15233i
\(245\) 3.00000 3.00000i 0.191663 0.191663i
\(246\) 0 0
\(247\) 6.00000i 0.381771i
\(248\) 16.0000 + 16.0000i 1.01600 + 1.01600i
\(249\) 0 0
\(250\) 16.0000 1.01193
\(251\) −21.0000 + 21.0000i −1.32551 + 1.32551i −0.416265 + 0.909243i \(0.636661\pi\)
−0.909243 + 0.416265i \(0.863339\pi\)
\(252\) 0 0
\(253\) −6.00000 6.00000i −0.377217 0.377217i
\(254\) 8.00000 8.00000i 0.501965 0.501965i
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 22.0000 1.37232 0.686161 0.727450i \(-0.259294\pi\)
0.686161 + 0.727450i \(0.259294\pi\)
\(258\) 0 0
\(259\) 6.00000 + 6.00000i 0.372822 + 0.372822i
\(260\) 4.00000i 0.248069i
\(261\) 0 0
\(262\) −22.0000 −1.35916
\(263\) 6.00000i 0.369976i 0.982741 + 0.184988i \(0.0592246\pi\)
−0.982741 + 0.184988i \(0.940775\pi\)
\(264\) 0 0
\(265\) 10.0000i 0.614295i
\(266\) 12.0000i 0.735767i
\(267\) 0 0
\(268\) −10.0000 + 10.0000i −0.610847 + 0.610847i
\(269\) −3.00000 3.00000i −0.182913 0.182913i 0.609711 0.792624i \(-0.291286\pi\)
−0.792624 + 0.609711i \(0.791286\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) −8.00000 −0.485071
\(273\) 0 0
\(274\) 8.00000 + 8.00000i 0.483298 + 0.483298i
\(275\) −3.00000 3.00000i −0.180907 0.180907i
\(276\) 0 0
\(277\) 3.00000 3.00000i 0.180253 0.180253i −0.611213 0.791466i \(-0.709318\pi\)
0.791466 + 0.611213i \(0.209318\pi\)
\(278\) 6.00000i 0.359856i
\(279\) 0 0
\(280\) 8.00000i 0.478091i
\(281\) 20.0000i 1.19310i −0.802576 0.596550i \(-0.796538\pi\)
0.802576 0.596550i \(-0.203462\pi\)
\(282\) 0 0
\(283\) −15.0000 + 15.0000i −0.891657 + 0.891657i −0.994679 0.103022i \(-0.967149\pi\)
0.103022 + 0.994679i \(0.467149\pi\)
\(284\) −20.0000 −1.18678
\(285\) 0 0
\(286\) 2.00000 2.00000i 0.118262 0.118262i
\(287\) 0 0
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) −6.00000 + 6.00000i −0.352332 + 0.352332i
\(291\) 0 0
\(292\) 8.00000 0.468165
\(293\) −15.0000 + 15.0000i −0.876309 + 0.876309i −0.993151 0.116841i \(-0.962723\pi\)
0.116841 + 0.993151i \(0.462723\pi\)
\(294\) 0 0
\(295\) 6.00000i 0.349334i
\(296\) −12.0000 −0.697486
\(297\) 0 0
\(298\) 14.0000i 0.810998i
\(299\) 6.00000 6.00000i 0.346989 0.346989i
\(300\) 0 0
\(301\) 10.0000 + 10.0000i 0.576390 + 0.576390i
\(302\) 10.0000 + 10.0000i 0.575435 + 0.575435i
\(303\) 0 0
\(304\) −12.0000 12.0000i −0.688247 0.688247i
\(305\) −18.0000 −1.03068
\(306\) 0 0
\(307\) −5.00000 5.00000i −0.285365 0.285365i 0.549879 0.835244i \(-0.314674\pi\)
−0.835244 + 0.549879i \(0.814674\pi\)
\(308\) −4.00000 + 4.00000i −0.227921 + 0.227921i
\(309\) 0 0
\(310\) 16.0000i 0.908739i
\(311\) 30.0000i 1.70114i 0.525859 + 0.850572i \(0.323744\pi\)
−0.525859 + 0.850572i \(0.676256\pi\)
\(312\) 0 0
\(313\) 16.0000i 0.904373i −0.891923 0.452187i \(-0.850644\pi\)
0.891923 0.452187i \(-0.149356\pi\)
\(314\) 30.0000 1.69300
\(315\) 0 0
\(316\) 0 0
\(317\) 5.00000 + 5.00000i 0.280828 + 0.280828i 0.833439 0.552611i \(-0.186369\pi\)
−0.552611 + 0.833439i \(0.686369\pi\)
\(318\) 0 0
\(319\) 6.00000 0.335936
\(320\) 8.00000 + 8.00000i 0.447214 + 0.447214i
\(321\) 0 0
\(322\) −12.0000 + 12.0000i −0.668734 + 0.668734i
\(323\) 6.00000 + 6.00000i 0.333849 + 0.333849i
\(324\) 0 0
\(325\) 3.00000 3.00000i 0.166410 0.166410i
\(326\) −2.00000 −0.110770
\(327\) 0 0
\(328\) 0 0
\(329\) 16.0000i 0.882109i
\(330\) 0 0
\(331\) 1.00000 1.00000i 0.0549650 0.0549650i −0.679090 0.734055i \(-0.737625\pi\)
0.734055 + 0.679090i \(0.237625\pi\)
\(332\) 2.00000 2.00000i 0.109764 0.109764i
\(333\) 0 0
\(334\) −2.00000 2.00000i −0.109435 0.109435i
\(335\) −10.0000 −0.546358
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) −11.0000 11.0000i −0.598321 0.598321i
\(339\) 0 0
\(340\) −4.00000 4.00000i −0.216930 0.216930i
\(341\) 8.00000 8.00000i 0.433224 0.433224i
\(342\) 0 0
\(343\) 20.0000i 1.07990i
\(344\) −20.0000 −1.07833
\(345\) 0 0
\(346\) 2.00000 0.107521
\(347\) −13.0000 + 13.0000i −0.697877 + 0.697877i −0.963952 0.266076i \(-0.914273\pi\)
0.266076 + 0.963952i \(0.414273\pi\)
\(348\) 0 0
\(349\) 3.00000 + 3.00000i 0.160586 + 0.160586i 0.782826 0.622240i \(-0.213777\pi\)
−0.622240 + 0.782826i \(0.713777\pi\)
\(350\) −6.00000 + 6.00000i −0.320713 + 0.320713i
\(351\) 0 0
\(352\) 8.00000i 0.426401i
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) −10.0000 10.0000i −0.530745 0.530745i
\(356\) 8.00000 0.423999
\(357\) 0 0
\(358\) 34.0000 1.79696
\(359\) 26.0000i 1.37223i −0.727494 0.686114i \(-0.759315\pi\)
0.727494 0.686114i \(-0.240685\pi\)
\(360\) 0 0
\(361\) 1.00000i 0.0526316i
\(362\) 18.0000i 0.946059i
\(363\) 0 0
\(364\) −4.00000 4.00000i −0.209657 0.209657i
\(365\) 4.00000 + 4.00000i 0.209370 + 0.209370i
\(366\) 0 0
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 24.0000i 1.25109i
\(369\) 0 0
\(370\) −6.00000 6.00000i −0.311925 0.311925i
\(371\) 10.0000 + 10.0000i 0.519174 + 0.519174i
\(372\) 0 0
\(373\) −5.00000 + 5.00000i −0.258890 + 0.258890i −0.824603 0.565712i \(-0.808601\pi\)
0.565712 + 0.824603i \(0.308601\pi\)
\(374\) 4.00000i 0.206835i
\(375\) 0 0
\(376\) 16.0000 + 16.0000i 0.825137 + 0.825137i
\(377\) 6.00000i 0.309016i
\(378\) 0 0
\(379\) −3.00000 + 3.00000i −0.154100 + 0.154100i −0.779946 0.625847i \(-0.784754\pi\)
0.625847 + 0.779946i \(0.284754\pi\)
\(380\) 12.0000i 0.615587i
\(381\) 0 0
\(382\) 8.00000 8.00000i 0.409316 0.409316i
\(383\) 16.0000 0.817562 0.408781 0.912633i \(-0.365954\pi\)
0.408781 + 0.912633i \(0.365954\pi\)
\(384\) 0 0
\(385\) −4.00000 −0.203859
\(386\) 14.0000 14.0000i 0.712581 0.712581i
\(387\) 0 0
\(388\) 4.00000i 0.203069i
\(389\) 13.0000 13.0000i 0.659126 0.659126i −0.296047 0.955173i \(-0.595669\pi\)
0.955173 + 0.296047i \(0.0956686\pi\)
\(390\) 0 0
\(391\) 12.0000i 0.606866i
\(392\) −6.00000 6.00000i −0.303046 0.303046i
\(393\) 0 0
\(394\) 34.0000i 1.71290i
\(395\) 0 0
\(396\) 0 0
\(397\) −5.00000 5.00000i −0.250943 0.250943i 0.570414 0.821357i \(-0.306783\pi\)
−0.821357 + 0.570414i \(0.806783\pi\)
\(398\) −14.0000 14.0000i −0.701757 0.701757i
\(399\) 0 0
\(400\) 12.0000i 0.600000i
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) 8.00000 + 8.00000i 0.398508 + 0.398508i
\(404\) 22.0000 + 22.0000i 1.09454 + 1.09454i
\(405\) 0 0
\(406\) 12.0000i 0.595550i
\(407\) 6.00000i 0.297409i
\(408\) 0 0
\(409\) 16.0000i 0.791149i 0.918434 + 0.395575i \(0.129455\pi\)
−0.918434 + 0.395575i \(0.870545\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −12.0000 −0.591198
\(413\) 6.00000 + 6.00000i 0.295241 + 0.295241i
\(414\) 0 0
\(415\) 2.00000 0.0981761
\(416\) 8.00000 0.392232
\(417\) 0 0
\(418\) −6.00000 + 6.00000i −0.293470 + 0.293470i
\(419\) −3.00000 3.00000i −0.146560 0.146560i 0.630020 0.776579i \(-0.283047\pi\)
−0.776579 + 0.630020i \(0.783047\pi\)
\(420\) 0 0
\(421\) −9.00000 + 9.00000i −0.438633 + 0.438633i −0.891552 0.452919i \(-0.850383\pi\)
0.452919 + 0.891552i \(0.350383\pi\)
\(422\) −18.0000 −0.876226
\(423\) 0 0
\(424\) −20.0000 −0.971286
\(425\) 6.00000i 0.291043i
\(426\) 0 0
\(427\) 18.0000 18.0000i 0.871081 0.871081i
\(428\) −14.0000 14.0000i −0.676716 0.676716i
\(429\) 0 0
\(430\) −10.0000 10.0000i −0.482243 0.482243i
\(431\) −32.0000 −1.54139 −0.770693 0.637207i \(-0.780090\pi\)
−0.770693 + 0.637207i \(0.780090\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) −16.0000 16.0000i −0.768025 0.768025i
\(435\) 0 0
\(436\) 6.00000 6.00000i 0.287348 0.287348i
\(437\) −18.0000 + 18.0000i −0.861057 + 0.861057i
\(438\) 0 0
\(439\) 14.0000i 0.668184i −0.942541 0.334092i \(-0.891570\pi\)
0.942541 0.334092i \(-0.108430\pi\)
\(440\) 4.00000 4.00000i 0.190693 0.190693i
\(441\) 0 0
\(442\) −4.00000 −0.190261
\(443\) 15.0000 15.0000i 0.712672 0.712672i −0.254422 0.967093i \(-0.581885\pi\)
0.967093 + 0.254422i \(0.0818852\pi\)
\(444\) 0 0
\(445\) 4.00000 + 4.00000i 0.189618 + 0.189618i
\(446\) 24.0000 24.0000i 1.13643 1.13643i
\(447\) 0 0
\(448\) −16.0000 −0.755929
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 12.0000i 0.564433i
\(453\) 0 0
\(454\) −30.0000 −1.40797
\(455\) 4.00000i 0.187523i
\(456\) 0 0
\(457\) 32.0000i 1.49690i 0.663193 + 0.748448i \(0.269201\pi\)
−0.663193 + 0.748448i \(0.730799\pi\)
\(458\) 14.0000i 0.654177i
\(459\) 0 0
\(460\) 12.0000 12.0000i 0.559503 0.559503i
\(461\) −11.0000 11.0000i −0.512321 0.512321i 0.402916 0.915237i \(-0.367997\pi\)
−0.915237 + 0.402916i \(0.867997\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 12.0000 + 12.0000i 0.557086 + 0.557086i
\(465\) 0 0
\(466\) −4.00000 4.00000i −0.185296 0.185296i
\(467\) 5.00000 + 5.00000i 0.231372 + 0.231372i 0.813265 0.581893i \(-0.197688\pi\)
−0.581893 + 0.813265i \(0.697688\pi\)
\(468\) 0 0
\(469\) 10.0000 10.0000i 0.461757 0.461757i
\(470\) 16.0000i 0.738025i
\(471\) 0 0
\(472\) −12.0000 −0.552345
\(473\) 10.0000i 0.459800i
\(474\) 0 0
\(475\) −9.00000 + 9.00000i −0.412948 + 0.412948i
\(476\) 8.00000 0.366679
\(477\) 0 0
\(478\) 0 0
\(479\) 40.0000 1.82765 0.913823 0.406112i \(-0.133116\pi\)
0.913823 + 0.406112i \(0.133116\pi\)
\(480\) 0 0
\(481\) −6.00000 −0.273576
\(482\) −18.0000 + 18.0000i −0.819878 + 0.819878i
\(483\) 0 0
\(484\) 18.0000 0.818182
\(485\) −2.00000 + 2.00000i −0.0908153 + 0.0908153i
\(486\) 0 0
\(487\) 2.00000i 0.0906287i 0.998973 + 0.0453143i \(0.0144289\pi\)
−0.998973 + 0.0453143i \(0.985571\pi\)
\(488\) 36.0000i 1.62964i
\(489\) 0 0
\(490\) 6.00000i 0.271052i
\(491\) 19.0000 19.0000i 0.857458 0.857458i −0.133580 0.991038i \(-0.542647\pi\)
0.991038 + 0.133580i \(0.0426473\pi\)
\(492\) 0 0
\(493\) −6.00000 6.00000i −0.270226 0.270226i
\(494\) −6.00000 6.00000i −0.269953 0.269953i
\(495\) 0 0
\(496\) 32.0000 1.43684
\(497\) 20.0000 0.897123
\(498\) 0 0
\(499\) 23.0000 + 23.0000i 1.02962 + 1.02962i 0.999548 + 0.0300737i \(0.00957421\pi\)
0.0300737 + 0.999548i \(0.490426\pi\)
\(500\) 16.0000 16.0000i 0.715542 0.715542i
\(501\) 0 0
\(502\) 42.0000i 1.87455i
\(503\) 6.00000i 0.267527i 0.991013 + 0.133763i \(0.0427062\pi\)
−0.991013 + 0.133763i \(0.957294\pi\)
\(504\) 0 0
\(505\) 22.0000i 0.978987i
\(506\) −12.0000 −0.533465
\(507\) 0 0
\(508\) 16.0000i 0.709885i
\(509\) −23.0000 23.0000i −1.01946 1.01946i −0.999807 0.0196502i \(-0.993745\pi\)
−0.0196502 0.999807i \(-0.506255\pi\)
\(510\) 0 0
\(511\) −8.00000 −0.353899
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) 0 0
\(514\) 22.0000 22.0000i 0.970378 0.970378i
\(515\) −6.00000 6.00000i −0.264392 0.264392i
\(516\) 0 0
\(517\) 8.00000 8.00000i 0.351840 0.351840i
\(518\) 12.0000 0.527250
\(519\) 0 0
\(520\) 4.00000 + 4.00000i 0.175412 + 0.175412i
\(521\) 40.0000i 1.75243i 0.481919 + 0.876216i \(0.339940\pi\)
−0.481919 + 0.876216i \(0.660060\pi\)
\(522\) 0 0
\(523\) 25.0000 25.0000i 1.09317 1.09317i 0.0979859 0.995188i \(-0.468760\pi\)
0.995188 0.0979859i \(-0.0312400\pi\)
\(524\) −22.0000 + 22.0000i −0.961074 + 0.961074i
\(525\) 0 0
\(526\) 6.00000 + 6.00000i 0.261612 + 0.261612i
\(527\) −16.0000 −0.696971
\(528\) 0 0
\(529\) −13.0000 −0.565217
\(530\) −10.0000 10.0000i −0.434372 0.434372i
\(531\) 0 0
\(532\) 12.0000 + 12.0000i 0.520266 + 0.520266i
\(533\) 0 0
\(534\) 0 0
\(535\) 14.0000i 0.605273i
\(536\) 20.0000i 0.863868i
\(537\) 0 0
\(538\) −6.00000 −0.258678
\(539\) −3.00000 + 3.00000i −0.129219 + 0.129219i
\(540\) 0 0
\(541\) −9.00000 9.00000i −0.386940 0.386940i 0.486654 0.873595i \(-0.338217\pi\)
−0.873595 + 0.486654i \(0.838217\pi\)
\(542\) −8.00000 + 8.00000i −0.343629 + 0.343629i
\(543\) 0 0
\(544\) −8.00000 + 8.00000i −0.342997 + 0.342997i
\(545\) 6.00000 0.257012
\(546\) 0 0
\(547\) −5.00000 5.00000i −0.213785 0.213785i 0.592088 0.805873i \(-0.298304\pi\)
−0.805873 + 0.592088i \(0.798304\pi\)
\(548\) 16.0000 0.683486
\(549\) 0 0
\(550\) −6.00000 −0.255841
\(551\) 18.0000i 0.766826i
\(552\) 0 0
\(553\) 0 0
\(554\) 6.00000i 0.254916i
\(555\) 0 0
\(556\) 6.00000 + 6.00000i 0.254457 + 0.254457i
\(557\) 25.0000 + 25.0000i 1.05928 + 1.05928i 0.998128 + 0.0611558i \(0.0194786\pi\)
0.0611558 + 0.998128i \(0.480521\pi\)
\(558\) 0 0
\(559\) −10.0000 −0.422955
\(560\) −8.00000 8.00000i −0.338062 0.338062i
\(561\) 0 0
\(562\) −20.0000 20.0000i −0.843649 0.843649i
\(563\) −19.0000 19.0000i −0.800755 0.800755i 0.182459 0.983213i \(-0.441594\pi\)
−0.983213 + 0.182459i \(0.941594\pi\)
\(564\) 0 0
\(565\) 6.00000 6.00000i 0.252422 0.252422i
\(566\) 30.0000i 1.26099i
\(567\) 0 0
\(568\) −20.0000 + 20.0000i −0.839181 + 0.839181i
\(569\) 24.0000i 1.00613i 0.864248 + 0.503066i \(0.167795\pi\)
−0.864248 + 0.503066i \(0.832205\pi\)
\(570\) 0 0
\(571\) 1.00000 1.00000i 0.0418487 0.0418487i −0.685873 0.727721i \(-0.740579\pi\)
0.727721 + 0.685873i \(0.240579\pi\)
\(572\) 4.00000i 0.167248i
\(573\) 0 0
\(574\) 0 0
\(575\) −18.0000 −0.750652
\(576\) 0 0
\(577\) 18.0000 0.749350 0.374675 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) −13.0000 + 13.0000i −0.540729 + 0.540729i
\(579\) 0 0
\(580\) 12.0000i 0.498273i
\(581\) −2.00000 + 2.00000i −0.0829740 + 0.0829740i
\(582\) 0 0
\(583\) 10.0000i 0.414158i
\(584\) 8.00000 8.00000i 0.331042 0.331042i
\(585\) 0 0
\(586\) 30.0000i 1.23929i
\(587\) 7.00000 7.00000i 0.288921 0.288921i −0.547733 0.836653i \(-0.684509\pi\)
0.836653 + 0.547733i \(0.184509\pi\)
\(588\) 0 0
\(589\) −24.0000 24.0000i −0.988903 0.988903i
\(590\) −6.00000 6.00000i −0.247016 0.247016i
\(591\) 0 0
\(592\) −12.0000 + 12.0000i −0.493197 + 0.493197i
\(593\) −34.0000 −1.39621 −0.698106 0.715994i \(-0.745974\pi\)
−0.698106 + 0.715994i \(0.745974\pi\)
\(594\) 0 0
\(595\) 4.00000 + 4.00000i 0.163984 + 0.163984i
\(596\) 14.0000 + 14.0000i 0.573462 + 0.573462i
\(597\) 0 0
\(598\) 12.0000i 0.490716i
\(599\) 14.0000i 0.572024i 0.958226 + 0.286012i \(0.0923298\pi\)
−0.958226 + 0.286012i \(0.907670\pi\)
\(600\) 0 0
\(601\) 20.0000i 0.815817i −0.913023 0.407909i \(-0.866258\pi\)
0.913023 0.407909i \(-0.133742\pi\)
\(602\) 20.0000 0.815139
\(603\) 0 0
\(604\) 20.0000 0.813788
\(605\) 9.00000 + 9.00000i 0.365902 + 0.365902i
\(606\) 0 0
\(607\) −32.0000 −1.29884 −0.649420 0.760430i \(-0.724988\pi\)
−0.649420 + 0.760430i \(0.724988\pi\)
\(608\) −24.0000 −0.973329
\(609\) 0 0
\(610\) −18.0000 + 18.0000i −0.728799 + 0.728799i
\(611\) 8.00000 + 8.00000i 0.323645 + 0.323645i
\(612\) 0 0
\(613\) −25.0000 + 25.0000i −1.00974 + 1.00974i −0.00978840 + 0.999952i \(0.503116\pi\)
−0.999952 + 0.00978840i \(0.996884\pi\)
\(614\) −10.0000 −0.403567
\(615\) 0 0
\(616\) 8.00000i 0.322329i
\(617\) 12.0000i 0.483102i −0.970388 0.241551i \(-0.922344\pi\)
0.970388 0.241551i \(-0.0776561\pi\)
\(618\) 0 0
\(619\) 17.0000 17.0000i 0.683288 0.683288i −0.277452 0.960740i \(-0.589490\pi\)
0.960740 + 0.277452i \(0.0894899\pi\)
\(620\) 16.0000 + 16.0000i 0.642575 + 0.642575i
\(621\) 0 0
\(622\) 30.0000 + 30.0000i 1.20289 + 1.20289i
\(623\) −8.00000 −0.320513
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −16.0000 16.0000i −0.639489 0.639489i
\(627\) 0 0
\(628\) 30.0000 30.0000i 1.19713 1.19713i
\(629\) 6.00000 6.00000i 0.239236 0.239236i
\(630\) 0 0
\(631\) 10.0000i 0.398094i 0.979990 + 0.199047i \(0.0637846\pi\)
−0.979990 + 0.199047i \(0.936215\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 10.0000 0.397151
\(635\) 8.00000 8.00000i 0.317470 0.317470i
\(636\) 0 0
\(637\) −3.00000 3.00000i −0.118864 0.118864i
\(638\) 6.00000 6.00000i 0.237542 0.237542i
\(639\) 0 0
\(640\) 16.0000 0.632456
\(641\) 18.0000 0.710957 0.355479 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) 0 0
\(643\) −21.0000 21.0000i −0.828159 0.828159i 0.159103 0.987262i \(-0.449140\pi\)
−0.987262 + 0.159103i \(0.949140\pi\)
\(644\) 24.0000i 0.945732i
\(645\) 0 0
\(646\) 12.0000 0.472134
\(647\) 42.0000i 1.65119i −0.564263 0.825595i \(-0.690840\pi\)
0.564263 0.825595i \(-0.309160\pi\)
\(648\) 0 0
\(649\) 6.00000i 0.235521i
\(650\) 6.00000i 0.235339i
\(651\) 0 0
\(652\) −2.00000 + 2.00000i −0.0783260 + 0.0783260i
\(653\) −19.0000 19.0000i −0.743527 0.743527i 0.229728 0.973255i \(-0.426216\pi\)
−0.973255 + 0.229728i \(0.926216\pi\)
\(654\) 0 0
\(655\) −22.0000 −0.859611
\(656\) 0 0
\(657\) 0 0
\(658\) −16.0000 16.0000i −0.623745 0.623745i
\(659\) 17.0000 + 17.0000i 0.662226 + 0.662226i 0.955904 0.293678i \(-0.0948794\pi\)
−0.293678 + 0.955904i \(0.594879\pi\)
\(660\) 0 0
\(661\) −9.00000 + 9.00000i −0.350059 + 0.350059i −0.860132 0.510072i \(-0.829619\pi\)
0.510072 + 0.860132i \(0.329619\pi\)
\(662\) 2.00000i 0.0777322i
\(663\) 0 0
\(664\) 4.00000i 0.155230i
\(665\) 12.0000i 0.465340i
\(666\) 0 0
\(667\) 18.0000 18.0000i 0.696963 0.696963i
\(668\) −4.00000 −0.154765
\(669\) 0 0
\(670\) −10.0000 + 10.0000i −0.386334 + 0.386334i
\(671\) 18.0000 0.694882
\(672\) 0 0
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) 18.0000 18.0000i 0.693334 0.693334i
\(675\) 0 0
\(676\) −22.0000 −0.846154
\(677\) −3.00000 + 3.00000i −0.115299 + 0.115299i −0.762402 0.647103i \(-0.775980\pi\)
0.647103 + 0.762402i \(0.275980\pi\)
\(678\) 0 0
\(679\) 4.00000i 0.153506i
\(680\) −8.00000 −0.306786
\(681\) 0 0
\(682\) 16.0000i 0.612672i
\(683\) −5.00000 + 5.00000i −0.191320 + 0.191320i −0.796266 0.604946i \(-0.793195\pi\)
0.604946 + 0.796266i \(0.293195\pi\)
\(684\) 0 0
\(685\) 8.00000 + 8.00000i 0.305664 + 0.305664i
\(686\) 20.0000 + 20.0000i 0.763604 + 0.763604i
\(687\) 0 0
\(688\) −20.0000 + 20.0000i −0.762493 + 0.762493i
\(689\) −10.0000 −0.380970
\(690\) 0 0
\(691\) −9.00000 9.00000i −0.342376 0.342376i 0.514884 0.857260i \(-0.327835\pi\)
−0.857260 + 0.514884i \(0.827835\pi\)
\(692\) 2.00000 2.00000i 0.0760286 0.0760286i
\(693\) 0 0
\(694\) 26.0000i 0.986947i
\(695\) 6.00000i 0.227593i
\(696\) 0 0
\(697\) 0 0
\(698\) 6.00000 0.227103
\(699\) 0 0
\(700\) 12.0000i 0.453557i
\(701\) −31.0000 31.0000i −1.17085 1.17085i −0.982006 0.188847i \(-0.939525\pi\)
−0.188847 0.982006i \(-0.560475\pi\)
\(702\) 0 0
\(703\) 18.0000 0.678883
\(704\) −8.00000 8.00000i −0.301511 0.301511i
\(705\) 0 0
\(706\) 6.00000 6.00000i 0.225813 0.225813i
\(707\) −22.0000 22.0000i −0.827395 0.827395i
\(708\) 0 0
\(709\) 27.0000 27.0000i 1.01401 1.01401i 0.0141058 0.999901i \(-0.495510\pi\)
0.999901 0.0141058i \(-0.00449016\pi\)
\(710\) −20.0000 −0.750587
\(711\) 0 0
\(712\) 8.00000 8.00000i 0.299813 0.299813i
\(713\) 48.0000i 1.79761i
\(714\) 0 0
\(715\) 2.00000 2.00000i 0.0747958 0.0747958i
\(716\) 34.0000 34.0000i 1.27064 1.27064i
\(717\) 0 0
\(718\) −26.0000 26.0000i −0.970311 0.970311i
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 12.0000 0.446903
\(722\) −1.00000 1.00000i −0.0372161 0.0372161i
\(723\) 0 0
\(724\) 18.0000 + 18.0000i 0.668965 + 0.668965i
\(725\) 9.00000 9.00000i 0.334252 0.334252i
\(726\) 0 0
\(727\) 2.00000i 0.0741759i 0.999312 + 0.0370879i \(0.0118082\pi\)
−0.999312 + 0.0370879i \(0.988192\pi\)
\(728\) −8.00000 −0.296500
\(729\) 0 0
\(730\) 8.00000 0.296093
\(731\) 10.0000 10.0000i 0.369863 0.369863i
\(732\) 0 0
\(733\) −21.0000 21.0000i −0.775653 0.775653i 0.203436 0.979088i \(-0.434789\pi\)
−0.979088 + 0.203436i \(0.934789\pi\)
\(734\) 8.00000 8.00000i 0.295285 0.295285i
\(735\) 0 0
\(736\) −24.0000 24.0000i −0.884652 0.884652i
\(737\) 10.0000 0.368355
\(738\) 0 0
\(739\) 23.0000 + 23.0000i 0.846069 + 0.846069i 0.989640 0.143571i \(-0.0458586\pi\)
−0.143571 + 0.989640i \(0.545859\pi\)
\(740\) −12.0000 −0.441129
\(741\) 0 0
\(742\) 20.0000 0.734223
\(743\) 46.0000i 1.68758i 0.536676 + 0.843788i \(0.319680\pi\)
−0.536676 + 0.843788i \(0.680320\pi\)
\(744\) 0 0
\(745\) 14.0000i 0.512920i
\(746\) 10.0000i 0.366126i
\(747\) 0 0
\(748\) 4.00000 + 4.00000i 0.146254 + 0.146254i
\(749\) 14.0000 + 14.0000i 0.511549 + 0.511549i
\(750\) 0 0
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 32.0000 1.16692
\(753\) 0 0
\(754\) 6.00000 + 6.00000i 0.218507 + 0.218507i
\(755\) 10.0000 + 10.0000i 0.363937 + 0.363937i
\(756\) 0 0
\(757\) 23.0000 23.0000i 0.835949 0.835949i −0.152374 0.988323i \(-0.548692\pi\)
0.988323 + 0.152374i \(0.0486917\pi\)
\(758\) 6.00000i 0.217930i
\(759\) 0 0
\(760\) −12.0000 12.0000i −0.435286 0.435286i
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) −6.00000 + 6.00000i −0.217215 + 0.217215i
\(764\) 16.0000i 0.578860i
\(765\) 0 0
\(766\) 16.0000 16.0000i 0.578103 0.578103i
\(767\) −6.00000 −0.216647
\(768\) 0 0
\(769\) −50.0000 −1.80305 −0.901523 0.432731i \(-0.857550\pi\)
−0.901523 + 0.432731i \(0.857550\pi\)
\(770\) −4.00000 + 4.00000i −0.144150 + 0.144150i
\(771\) 0 0
\(772\) 28.0000i 1.00774i
\(773\) 5.00000 5.00000i 0.179838 0.179838i −0.611448 0.791285i \(-0.709412\pi\)
0.791285 + 0.611448i \(0.209412\pi\)
\(774\) 0 0
\(775\) 24.0000i 0.862105i
\(776\) 4.00000 + 4.00000i 0.143592 + 0.143592i
\(777\) 0 0
\(778\) 26.0000i 0.932145i
\(779\) 0 0
\(780\) 0 0
\(781\) 10.0000 + 10.0000i 0.357828 + 0.357828i
\(782\) 12.0000 + 12.0000i 0.429119 + 0.429119i
\(783\) 0 0
\(784\) −12.0000 −0.428571
\(785\) 30.0000 1.07075
\(786\) 0 0
\(787\) 15.0000 + 15.0000i 0.534692 + 0.534692i 0.921965 0.387273i \(-0.126583\pi\)
−0.387273 + 0.921965i \(0.626583\pi\)
\(788\) −34.0000 34.0000i −1.21120 1.21120i
\(789\) 0 0
\(790\) 0 0
\(791\) 12.0000i 0.426671i
\(792\) 0 0
\(793\) 18.0000i 0.639199i