Properties

Label 144.2.k.a.37.1
Level $144$
Weight $2$
Character 144.37
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 37.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 144.37
Dual form 144.2.k.a.109.1

$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

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

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 0.894427 0.447214i \(-0.147584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 0 0
\(7\) 2.00000i 0.755929i −0.925820 0.377964i \(-0.876624\pi\)
0.925820 0.377964i \(-0.123376\pi\)
\(8\) −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 0.540094 0.841605i \(-0.318389\pi\)
−0.841605 + 0.540094i \(0.818389\pi\)
\(12\) 0 0
\(13\) −1.00000 + 1.00000i −0.277350 + 0.277350i −0.832050 0.554700i \(-0.812833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 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 −0.273597 0.961844i \(-0.588214\pi\)
0.961844 + 0.273597i \(0.0882135\pi\)
\(20\) −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 \(-0.784877\pi\)
0.780189 0.625543i \(-0.215123\pi\)
\(24\) 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 −0.928477 0.371391i \(-0.878881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 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 0.909312 0.416115i \(-0.136609\pi\)
−0.416115 + 0.909312i \(0.636609\pi\)
\(38\) 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 0.976772 0.214280i \(-0.0687403\pi\)
−0.214280 + 0.976772i \(0.568740\pi\)
\(44\) 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 0.961524 0.274721i \(-0.0885855\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 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 0.874889 0.484323i \(-0.160934\pi\)
−0.484323 + 0.874889i \(0.660934\pi\)
\(60\) 0 0
\(61\) −9.00000 + 9.00000i −1.15233 + 1.15233i −0.166248 + 0.986084i \(0.553165\pi\)
−0.986084 + 0.166248i \(0.946835\pi\)
\(62\) −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 −0.943167 0.332320i \(-0.892169\pi\)
0.332320 + 0.943167i \(0.392169\pi\)
\(68\) 4.00000i 0.485071i
\(69\) 0 0
\(70\) 4.00000 0.478091
\(71\) 10.0000i 1.18678i 0.804914 + 0.593391i \(0.202211\pi\)
−0.804914 + 0.593391i \(0.797789\pi\)
\(72\) 0 0
\(73\) 4.00000i 0.468165i −0.972217 0.234082i \(-0.924791\pi\)
0.972217 0.234082i \(-0.0752085\pi\)
\(74\) 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 −0.650092 0.759856i \(-0.725269\pi\)
0.759856 + 0.650092i \(0.225269\pi\)
\(84\) 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 \(-0.932002\pi\)
0.977270 0.212000i \(-0.0679975\pi\)
\(90\) 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 −0.995037 0.0995037i \(-0.968274\pi\)
−0.0995037 0.995037i \(-0.531726\pi\)
\(102\) 0 0
\(103\) 6.00000i 0.591198i 0.955312 + 0.295599i \(0.0955191\pi\)
−0.955312 + 0.295599i \(0.904481\pi\)
\(104\) 4.00000i 0.392232i
\(105\) 0 0
\(106\) 10.0000i 0.971286i
\(107\) 7.00000 + 7.00000i 0.676716 + 0.676716i 0.959256 0.282540i \(-0.0911770\pi\)
−0.282540 + 0.959256i \(0.591177\pi\)
\(108\) 0 0
\(109\) 3.00000 3.00000i 0.287348 0.287348i −0.548683 0.836031i \(-0.684871\pi\)
0.836031 + 0.548683i \(0.184871\pi\)
\(110\) 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 −0.999270 0.0381958i \(-0.987839\pi\)
0.0381958 + 0.999270i \(0.487839\pi\)
\(132\) 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 \(-0.888983\pi\)
0.939793 0.341743i \(-0.111017\pi\)
\(138\) 0 0
\(139\) −3.00000 3.00000i −0.254457 0.254457i 0.568338 0.822795i \(-0.307586\pi\)
−0.822795 + 0.568338i \(0.807586\pi\)
\(140\) 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 0.359632 0.933094i \(-0.382902\pi\)
−0.933094 + 0.359632i \(0.882902\pi\)
\(150\) 0 0
\(151\) 10.0000i 0.813788i −0.913475 0.406894i \(-0.866612\pi\)
0.913475 0.406894i \(-0.133388\pi\)
\(152\) 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 0.222108 0.975022i \(-0.428706\pi\)
0.975022 0.222108i \(-0.0712939\pi\)
\(158\) 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 −0.745184 0.666858i \(-0.767639\pi\)
0.666858 + 0.745184i \(0.267639\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 2.00000 0.155230
\(167\) 2.00000i 0.154765i 0.997001 + 0.0773823i \(0.0246562\pi\)
−0.997001 + 0.0773823i \(0.975344\pi\)
\(168\) 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 −0.668070 0.744099i \(-0.732879\pi\)
0.744099 + 0.668070i \(0.232879\pi\)
\(174\) 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 0.324887 0.945753i \(-0.394674\pi\)
0.945753 0.324887i \(-0.105326\pi\)
\(180\) 0 0
\(181\) −9.00000 9.00000i −0.668965 0.668965i 0.288512 0.957476i \(-0.406840\pi\)
−0.957476 + 0.288512i \(0.906840\pi\)
\(182\) 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 0.970632 + 0.240567i \(0.0773335\pi\)
0.240567 + 0.970632i \(0.422666\pi\)
\(198\) 0 0
\(199\) 14.0000i 0.992434i 0.868199 + 0.496217i \(0.165278\pi\)
−0.868199 + 0.496217i \(0.834722\pi\)
\(200\) 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 −0.945425 0.325840i \(-0.894353\pi\)
0.325840 + 0.945425i \(0.394353\pi\)
\(212\) −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 −0.999990 0.00440533i \(-0.998598\pi\)
0.00440533 + 0.999990i \(0.498598\pi\)
\(228\) 0 0
\(229\) 7.00000 + 7.00000i 0.462573 + 0.462573i 0.899498 0.436925i \(-0.143932\pi\)
−0.436925 + 0.899498i \(0.643932\pi\)
\(230\) 12.0000 0.791257
\(231\) 0 0
\(232\) 12.0000i 0.787839i
\(233\) 4.00000i 0.262049i 0.991379 + 0.131024i \(0.0418266\pi\)
−0.991379 + 0.131024i \(0.958173\pi\)
\(234\) 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 −0.909243 0.416265i \(-0.863339\pi\)
−0.416265 0.909243i \(-0.636661\pi\)
\(252\) 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 \(-0.940775\pi\)
0.982741 0.184988i \(-0.0592246\pi\)
\(264\) 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 −0.792624 0.609711i \(-0.791286\pi\)
0.609711 + 0.792624i \(0.291286\pi\)
\(270\) 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 0.791466 0.611213i \(-0.209318\pi\)
−0.611213 + 0.791466i \(0.709318\pi\)
\(278\) 6.00000i 0.359856i
\(279\) 0 0
\(280\) 8.00000i 0.478091i
\(281\) 20.0000i 1.19310i 0.802576 + 0.596550i \(0.203462\pi\)
−0.802576 + 0.596550i \(0.796538\pi\)
\(282\) 0 0
\(283\) −15.0000 15.0000i −0.891657 0.891657i 0.103022 0.994679i \(-0.467149\pi\)
−0.994679 + 0.103022i \(0.967149\pi\)
\(284\) −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 0.116841 0.993151i \(-0.462723\pi\)
−0.993151 + 0.116841i \(0.962723\pi\)
\(294\) 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 −0.835244 0.549879i \(-0.814674\pi\)
0.549879 + 0.835244i \(0.314674\pi\)
\(308\) −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 \(-0.676256\pi\)
0.525859 0.850572i \(-0.323744\pi\)
\(312\) 0 0
\(313\) 16.0000i 0.904373i 0.891923 + 0.452187i \(0.149356\pi\)
−0.891923 + 0.452187i \(0.850644\pi\)
\(314\) 30.0000 1.69300
\(315\) 0 0
\(316\) 0 0
\(317\) 5.00000 5.00000i 0.280828 0.280828i −0.552611 0.833439i \(-0.686369\pi\)
0.833439 + 0.552611i \(0.186369\pi\)
\(318\) 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 0.734055 0.679090i \(-0.237625\pi\)
−0.679090 + 0.734055i \(0.737625\pi\)
\(332\) 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 0.266076 0.963952i \(-0.414273\pi\)
−0.963952 + 0.266076i \(0.914273\pi\)
\(348\) 0 0
\(349\) 3.00000 3.00000i 0.160586 0.160586i −0.622240 0.782826i \(-0.713777\pi\)
0.782826 + 0.622240i \(0.213777\pi\)
\(350\) −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 \(0.240685\pi\)
−0.727494 + 0.686114i \(0.759315\pi\)
\(360\) 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 0.565712 0.824603i \(-0.308601\pi\)
−0.824603 + 0.565712i \(0.808601\pi\)
\(374\) 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 0.625847 0.779946i \(-0.284754\pi\)
−0.779946 + 0.625847i \(0.784754\pi\)
\(380\) 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 0.955173 0.296047i \(-0.0956686\pi\)
−0.296047 + 0.955173i \(0.595669\pi\)
\(390\) 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 −0.821357 0.570414i \(-0.806783\pi\)
0.570414 + 0.821357i \(0.306783\pi\)
\(398\) −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 \(-0.870545\pi\)
0.918434 0.395575i \(-0.129455\pi\)
\(410\) 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 −0.776579 0.630020i \(-0.783047\pi\)
0.630020 + 0.776579i \(0.283047\pi\)
\(420\) 0 0
\(421\) −9.00000 9.00000i −0.438633 0.438633i 0.452919 0.891552i \(-0.350383\pi\)
−0.891552 + 0.452919i \(0.850383\pi\)
\(422\) −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 \(0.108430\pi\)
−0.942541 + 0.334092i \(0.891570\pi\)
\(440\) 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 0.967093 0.254422i \(-0.0818852\pi\)
−0.254422 + 0.967093i \(0.581885\pi\)
\(444\) 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 \(-0.730799\pi\)
0.663193 0.748448i \(-0.269201\pi\)
\(458\) 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 −0.915237 0.402916i \(-0.867997\pi\)
0.402916 + 0.915237i \(0.367997\pi\)
\(462\) 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 −0.581893 0.813265i \(-0.697688\pi\)
0.813265 + 0.581893i \(0.197688\pi\)
\(468\) 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 \(-0.985571\pi\)
0.998973 0.0453143i \(-0.0144289\pi\)
\(488\) 36.0000i 1.62964i
\(489\) 0 0
\(490\) 6.00000i 0.271052i
\(491\) 19.0000 + 19.0000i 0.857458 + 0.857458i 0.991038 0.133580i \(-0.0426473\pi\)
−0.133580 + 0.991038i \(0.542647\pi\)
\(492\) 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 0.0300737 0.999548i \(-0.490426\pi\)
0.999548 0.0300737i \(-0.00957421\pi\)
\(500\) 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 \(-0.957294\pi\)
0.991013 0.133763i \(-0.0427062\pi\)
\(504\) 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 −0.0196502 + 0.999807i \(0.506255\pi\)
−0.999807 + 0.0196502i \(0.993745\pi\)
\(510\) 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 \(-0.660060\pi\)
0.481919 0.876216i \(-0.339940\pi\)
\(522\) 0 0
\(523\) 25.0000 + 25.0000i 1.09317 + 1.09317i 0.995188 + 0.0979859i \(0.0312400\pi\)
0.0979859 + 0.995188i \(0.468760\pi\)
\(524\) −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 −0.873595 0.486654i \(-0.838217\pi\)
0.486654 + 0.873595i \(0.338217\pi\)
\(542\) −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 −0.805873 0.592088i \(-0.798304\pi\)
0.592088 + 0.805873i \(0.298304\pi\)
\(548\) 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 0.0611558 0.998128i \(-0.480521\pi\)
0.998128 0.0611558i \(-0.0194786\pi\)
\(558\) 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 −0.983213 0.182459i \(-0.941594\pi\)
0.182459 + 0.983213i \(0.441594\pi\)
\(564\) 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 \(-0.832205\pi\)
0.864248 0.503066i \(-0.167795\pi\)
\(570\) 0 0
\(571\) 1.00000 + 1.00000i 0.0418487 + 0.0418487i 0.727721 0.685873i \(-0.240579\pi\)
−0.685873 + 0.727721i \(0.740579\pi\)
\(572\) 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 0.836653 0.547733i \(-0.184509\pi\)
−0.547733 + 0.836653i \(0.684509\pi\)
\(588\) 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 \(-0.907670\pi\)
0.958226 0.286012i \(-0.0923298\pi\)
\(600\) 0 0
\(601\) 20.0000i 0.815817i 0.913023 + 0.407909i \(0.133742\pi\)
−0.913023 + 0.407909i \(0.866258\pi\)
\(602\) 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 −0.999952 0.00978840i \(-0.996884\pi\)
−0.00978840 0.999952i \(-0.503116\pi\)
\(614\) −10.0000 −0.403567
\(615\) 0 0
\(616\) 8.00000i 0.322329i
\(617\) 12.0000i 0.483102i 0.970388 + 0.241551i \(0.0776561\pi\)
−0.970388 + 0.241551i \(0.922344\pi\)
\(618\) 0 0
\(619\) 17.0000 + 17.0000i 0.683288 + 0.683288i 0.960740 0.277452i \(-0.0894899\pi\)
−0.277452 + 0.960740i \(0.589490\pi\)
\(620\) 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 \(-0.936215\pi\)
0.979990 0.199047i \(-0.0637846\pi\)
\(632\) 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 −0.987262 0.159103i \(-0.949140\pi\)
0.159103 + 0.987262i \(0.449140\pi\)
\(644\) 24.0000i 0.945732i
\(645\) 0 0
\(646\) 12.0000 0.472134
\(647\) 42.0000i 1.65119i 0.564263 + 0.825595i \(0.309160\pi\)
−0.564263 + 0.825595i \(0.690840\pi\)
\(648\) 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 −0.973255 0.229728i \(-0.926216\pi\)
0.229728 + 0.973255i \(0.426216\pi\)
\(654\) 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 −0.293678 0.955904i \(-0.594879\pi\)
0.955904 + 0.293678i \(0.0948794\pi\)
\(660\) 0 0
\(661\) −9.00000 9.00000i −0.350059 0.350059i 0.510072 0.860132i \(-0.329619\pi\)
−0.860132 + 0.510072i \(0.829619\pi\)
\(662\) 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 0.647103 0.762402i \(-0.275980\pi\)
−0.762402 + 0.647103i \(0.775980\pi\)
\(678\) 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 0.604946 0.796266i \(-0.293195\pi\)
−0.796266 + 0.604946i \(0.793195\pi\)
\(684\) 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 −0.857260 0.514884i \(-0.827835\pi\)
0.514884 + 0.857260i \(0.327835\pi\)
\(692\) 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 −0.188847 + 0.982006i \(0.560475\pi\)
−0.982006 + 0.188847i \(0.939525\pi\)
\(702\) 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 0.999901 + 0.0141058i \(0.00449016\pi\)
0.0141058 + 0.999901i \(0.495510\pi\)
\(710\) −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 \(-0.988192\pi\)
0.999312 0.0370879i \(-0.0118082\pi\)
\(728\) −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 −0.979088 0.203436i \(-0.934789\pi\)
0.203436 + 0.979088i \(0.434789\pi\)
\(734\) 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 −0.143571 0.989640i \(-0.545859\pi\)
0.989640 + 0.143571i \(0.0458586\pi\)
\(740\) −12.0000 −0.441129
\(741\) 0 0
\(742\) 20.0000 0.734223
\(743\) 46.0000i 1.68758i −0.536676 0.843788i \(-0.680320\pi\)
0.536676 0.843788i \(-0.319680\pi\)
\(744\) 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 0.988323 0.152374i \(-0.0486917\pi\)
−0.152374 + 0.988323i \(0.548692\pi\)
\(758\) 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 0.791285 0.611448i \(-0.209412\pi\)
−0.611448 + 0.791285i \(0.709412\pi\)
\(774\) 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 −0.387273 0.921965i \(-0.626583\pi\)
0.921965 + 0.387273i \(0.126583\pi\)
\(788\) −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