Properties

Label 42.2.d.a.41.1
Level $42$
Weight $2$
Character 42.41
Analytic conductor $0.335$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 42.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.335371688489\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \(x^{4} + 9\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 41.1
Root \(-1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 42.41
Dual form 42.2.d.a.41.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-1.22474 - 1.22474i) q^{3} -1.00000 q^{4} +2.44949 q^{5} +(-1.22474 + 1.22474i) q^{6} +(-1.00000 + 2.44949i) q^{7} +1.00000i q^{8} +3.00000i q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-1.22474 - 1.22474i) q^{3} -1.00000 q^{4} +2.44949 q^{5} +(-1.22474 + 1.22474i) q^{6} +(-1.00000 + 2.44949i) q^{7} +1.00000i q^{8} +3.00000i q^{9} -2.44949i q^{10} +(1.22474 + 1.22474i) q^{12} -2.44949i q^{13} +(2.44949 + 1.00000i) q^{14} +(-3.00000 - 3.00000i) q^{15} +1.00000 q^{16} -4.89898 q^{17} +3.00000 q^{18} +2.44949i q^{19} -2.44949 q^{20} +(4.22474 - 1.77526i) q^{21} -6.00000i q^{23} +(1.22474 - 1.22474i) q^{24} +1.00000 q^{25} -2.44949 q^{26} +(3.67423 - 3.67423i) q^{27} +(1.00000 - 2.44949i) q^{28} +6.00000i q^{29} +(-3.00000 + 3.00000i) q^{30} -1.00000i q^{32} +4.89898i q^{34} +(-2.44949 + 6.00000i) q^{35} -3.00000i q^{36} -2.00000 q^{37} +2.44949 q^{38} +(-3.00000 + 3.00000i) q^{39} +2.44949i q^{40} +4.89898 q^{41} +(-1.77526 - 4.22474i) q^{42} +4.00000 q^{43} +7.34847i q^{45} -6.00000 q^{46} -4.89898 q^{47} +(-1.22474 - 1.22474i) q^{48} +(-5.00000 - 4.89898i) q^{49} -1.00000i q^{50} +(6.00000 + 6.00000i) q^{51} +2.44949i q^{52} -6.00000i q^{53} +(-3.67423 - 3.67423i) q^{54} +(-2.44949 - 1.00000i) q^{56} +(3.00000 - 3.00000i) q^{57} +6.00000 q^{58} +12.2474 q^{59} +(3.00000 + 3.00000i) q^{60} -12.2474i q^{61} +(-7.34847 - 3.00000i) q^{63} -1.00000 q^{64} -6.00000i q^{65} +8.00000 q^{67} +4.89898 q^{68} +(-7.34847 + 7.34847i) q^{69} +(6.00000 + 2.44949i) q^{70} -3.00000 q^{72} +9.79796i q^{73} +2.00000i q^{74} +(-1.22474 - 1.22474i) q^{75} -2.44949i q^{76} +(3.00000 + 3.00000i) q^{78} -10.0000 q^{79} +2.44949 q^{80} -9.00000 q^{81} -4.89898i q^{82} -2.44949 q^{83} +(-4.22474 + 1.77526i) q^{84} -12.0000 q^{85} -4.00000i q^{86} +(7.34847 - 7.34847i) q^{87} +7.34847 q^{90} +(6.00000 + 2.44949i) q^{91} +6.00000i q^{92} +4.89898i q^{94} +6.00000i q^{95} +(-1.22474 + 1.22474i) q^{96} +4.89898i q^{97} +(-4.89898 + 5.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{4} - 4q^{7} + O(q^{10}) \) \( 4q - 4q^{4} - 4q^{7} - 12q^{15} + 4q^{16} + 12q^{18} + 12q^{21} + 4q^{25} + 4q^{28} - 12q^{30} - 8q^{37} - 12q^{39} - 12q^{42} + 16q^{43} - 24q^{46} - 20q^{49} + 24q^{51} + 12q^{57} + 24q^{58} + 12q^{60} - 4q^{64} + 32q^{67} + 24q^{70} - 12q^{72} + 12q^{78} - 40q^{79} - 36q^{81} - 12q^{84} - 48q^{85} + 24q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(31\)
\(\chi(n)\) \(-1\) \(-1\)

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
\(3\) −1.22474 1.22474i −0.707107 0.707107i
\(4\) −1.00000 −0.500000
\(5\) 2.44949 1.09545 0.547723 0.836660i \(-0.315495\pi\)
0.547723 + 0.836660i \(0.315495\pi\)
\(6\) −1.22474 + 1.22474i −0.500000 + 0.500000i
\(7\) −1.00000 + 2.44949i −0.377964 + 0.925820i
\(8\) 1.00000i 0.353553i
\(9\) 3.00000i 1.00000i
\(10\) 2.44949i 0.774597i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 1.22474 + 1.22474i 0.353553 + 0.353553i
\(13\) 2.44949i 0.679366i −0.940540 0.339683i \(-0.889680\pi\)
0.940540 0.339683i \(-0.110320\pi\)
\(14\) 2.44949 + 1.00000i 0.654654 + 0.267261i
\(15\) −3.00000 3.00000i −0.774597 0.774597i
\(16\) 1.00000 0.250000
\(17\) −4.89898 −1.18818 −0.594089 0.804400i \(-0.702487\pi\)
−0.594089 + 0.804400i \(0.702487\pi\)
\(18\) 3.00000 0.707107
\(19\) 2.44949i 0.561951i 0.959715 + 0.280976i \(0.0906580\pi\)
−0.959715 + 0.280976i \(0.909342\pi\)
\(20\) −2.44949 −0.547723
\(21\) 4.22474 1.77526i 0.921915 0.387392i
\(22\) 0 0
\(23\) 6.00000i 1.25109i −0.780189 0.625543i \(-0.784877\pi\)
0.780189 0.625543i \(-0.215123\pi\)
\(24\) 1.22474 1.22474i 0.250000 0.250000i
\(25\) 1.00000 0.200000
\(26\) −2.44949 −0.480384
\(27\) 3.67423 3.67423i 0.707107 0.707107i
\(28\) 1.00000 2.44949i 0.188982 0.462910i
\(29\) 6.00000i 1.11417i 0.830455 + 0.557086i \(0.188081\pi\)
−0.830455 + 0.557086i \(0.811919\pi\)
\(30\) −3.00000 + 3.00000i −0.547723 + 0.547723i
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 4.89898i 0.840168i
\(35\) −2.44949 + 6.00000i −0.414039 + 1.01419i
\(36\) 3.00000i 0.500000i
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 2.44949 0.397360
\(39\) −3.00000 + 3.00000i −0.480384 + 0.480384i
\(40\) 2.44949i 0.387298i
\(41\) 4.89898 0.765092 0.382546 0.923936i \(-0.375047\pi\)
0.382546 + 0.923936i \(0.375047\pi\)
\(42\) −1.77526 4.22474i −0.273928 0.651892i
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 7.34847i 1.09545i
\(46\) −6.00000 −0.884652
\(47\) −4.89898 −0.714590 −0.357295 0.933992i \(-0.616301\pi\)
−0.357295 + 0.933992i \(0.616301\pi\)
\(48\) −1.22474 1.22474i −0.176777 0.176777i
\(49\) −5.00000 4.89898i −0.714286 0.699854i
\(50\) 1.00000i 0.141421i
\(51\) 6.00000 + 6.00000i 0.840168 + 0.840168i
\(52\) 2.44949i 0.339683i
\(53\) 6.00000i 0.824163i −0.911147 0.412082i \(-0.864802\pi\)
0.911147 0.412082i \(-0.135198\pi\)
\(54\) −3.67423 3.67423i −0.500000 0.500000i
\(55\) 0 0
\(56\) −2.44949 1.00000i −0.327327 0.133631i
\(57\) 3.00000 3.00000i 0.397360 0.397360i
\(58\) 6.00000 0.787839
\(59\) 12.2474 1.59448 0.797241 0.603661i \(-0.206292\pi\)
0.797241 + 0.603661i \(0.206292\pi\)
\(60\) 3.00000 + 3.00000i 0.387298 + 0.387298i
\(61\) 12.2474i 1.56813i −0.620682 0.784063i \(-0.713144\pi\)
0.620682 0.784063i \(-0.286856\pi\)
\(62\) 0 0
\(63\) −7.34847 3.00000i −0.925820 0.377964i
\(64\) −1.00000 −0.125000
\(65\) 6.00000i 0.744208i
\(66\) 0 0
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) 4.89898 0.594089
\(69\) −7.34847 + 7.34847i −0.884652 + 0.884652i
\(70\) 6.00000 + 2.44949i 0.717137 + 0.292770i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −3.00000 −0.353553
\(73\) 9.79796i 1.14676i 0.819288 + 0.573382i \(0.194369\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 2.00000i 0.232495i
\(75\) −1.22474 1.22474i −0.141421 0.141421i
\(76\) 2.44949i 0.280976i
\(77\) 0 0
\(78\) 3.00000 + 3.00000i 0.339683 + 0.339683i
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 2.44949 0.273861
\(81\) −9.00000 −1.00000
\(82\) 4.89898i 0.541002i
\(83\) −2.44949 −0.268866 −0.134433 0.990923i \(-0.542921\pi\)
−0.134433 + 0.990923i \(0.542921\pi\)
\(84\) −4.22474 + 1.77526i −0.460957 + 0.193696i
\(85\) −12.0000 −1.30158
\(86\) 4.00000i 0.431331i
\(87\) 7.34847 7.34847i 0.787839 0.787839i
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 7.34847 0.774597
\(91\) 6.00000 + 2.44949i 0.628971 + 0.256776i
\(92\) 6.00000i 0.625543i
\(93\) 0 0
\(94\) 4.89898i 0.505291i
\(95\) 6.00000i 0.615587i
\(96\) −1.22474 + 1.22474i −0.125000 + 0.125000i
\(97\) 4.89898i 0.497416i 0.968579 + 0.248708i \(0.0800060\pi\)
−0.968579 + 0.248708i \(0.919994\pi\)
\(98\) −4.89898 + 5.00000i −0.494872 + 0.505076i
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) −7.34847 −0.731200 −0.365600 0.930772i \(-0.619136\pi\)
−0.365600 + 0.930772i \(0.619136\pi\)
\(102\) 6.00000 6.00000i 0.594089 0.594089i
\(103\) 9.79796i 0.965422i 0.875780 + 0.482711i \(0.160348\pi\)
−0.875780 + 0.482711i \(0.839652\pi\)
\(104\) 2.44949 0.240192
\(105\) 10.3485 4.34847i 1.00991 0.424367i
\(106\) −6.00000 −0.582772
\(107\) 12.0000i 1.16008i 0.814587 + 0.580042i \(0.196964\pi\)
−0.814587 + 0.580042i \(0.803036\pi\)
\(108\) −3.67423 + 3.67423i −0.353553 + 0.353553i
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 2.44949 + 2.44949i 0.232495 + 0.232495i
\(112\) −1.00000 + 2.44949i −0.0944911 + 0.231455i
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) −3.00000 3.00000i −0.280976 0.280976i
\(115\) 14.6969i 1.37050i
\(116\) 6.00000i 0.557086i
\(117\) 7.34847 0.679366
\(118\) 12.2474i 1.12747i
\(119\) 4.89898 12.0000i 0.449089 1.10004i
\(120\) 3.00000 3.00000i 0.273861 0.273861i
\(121\) 11.0000 1.00000
\(122\) −12.2474 −1.10883
\(123\) −6.00000 6.00000i −0.541002 0.541002i
\(124\) 0 0
\(125\) −9.79796 −0.876356
\(126\) −3.00000 + 7.34847i −0.267261 + 0.654654i
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −4.89898 4.89898i −0.431331 0.431331i
\(130\) −6.00000 −0.526235
\(131\) −7.34847 −0.642039 −0.321019 0.947073i \(-0.604025\pi\)
−0.321019 + 0.947073i \(0.604025\pi\)
\(132\) 0 0
\(133\) −6.00000 2.44949i −0.520266 0.212398i
\(134\) 8.00000i 0.691095i
\(135\) 9.00000 9.00000i 0.774597 0.774597i
\(136\) 4.89898i 0.420084i
\(137\) 12.0000i 1.02523i 0.858619 + 0.512615i \(0.171323\pi\)
−0.858619 + 0.512615i \(0.828677\pi\)
\(138\) 7.34847 + 7.34847i 0.625543 + 0.625543i
\(139\) 2.44949i 0.207763i 0.994590 + 0.103882i \(0.0331263\pi\)
−0.994590 + 0.103882i \(0.966874\pi\)
\(140\) 2.44949 6.00000i 0.207020 0.507093i
\(141\) 6.00000 + 6.00000i 0.505291 + 0.505291i
\(142\) 0 0
\(143\) 0 0
\(144\) 3.00000i 0.250000i
\(145\) 14.6969i 1.22051i
\(146\) 9.79796 0.810885
\(147\) 0.123724 + 12.1237i 0.0102046 + 0.999948i
\(148\) 2.00000 0.164399
\(149\) 6.00000i 0.491539i 0.969328 + 0.245770i \(0.0790407\pi\)
−0.969328 + 0.245770i \(0.920959\pi\)
\(150\) −1.22474 + 1.22474i −0.100000 + 0.100000i
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) −2.44949 −0.198680
\(153\) 14.6969i 1.18818i
\(154\) 0 0
\(155\) 0 0
\(156\) 3.00000 3.00000i 0.240192 0.240192i
\(157\) 7.34847i 0.586472i −0.956040 0.293236i \(-0.905268\pi\)
0.956040 0.293236i \(-0.0947321\pi\)
\(158\) 10.0000i 0.795557i
\(159\) −7.34847 + 7.34847i −0.582772 + 0.582772i
\(160\) 2.44949i 0.193649i
\(161\) 14.6969 + 6.00000i 1.15828 + 0.472866i
\(162\) 9.00000i 0.707107i
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) −4.89898 −0.382546
\(165\) 0 0
\(166\) 2.44949i 0.190117i
\(167\) −4.89898 −0.379094 −0.189547 0.981872i \(-0.560702\pi\)
−0.189547 + 0.981872i \(0.560702\pi\)
\(168\) 1.77526 + 4.22474i 0.136964 + 0.325946i
\(169\) 7.00000 0.538462
\(170\) 12.0000i 0.920358i
\(171\) −7.34847 −0.561951
\(172\) −4.00000 −0.304997
\(173\) 22.0454 1.67608 0.838041 0.545608i \(-0.183701\pi\)
0.838041 + 0.545608i \(0.183701\pi\)
\(174\) −7.34847 7.34847i −0.557086 0.557086i
\(175\) −1.00000 + 2.44949i −0.0755929 + 0.185164i
\(176\) 0 0
\(177\) −15.0000 15.0000i −1.12747 1.12747i
\(178\) 0 0
\(179\) 24.0000i 1.79384i −0.442189 0.896922i \(-0.645798\pi\)
0.442189 0.896922i \(-0.354202\pi\)
\(180\) 7.34847i 0.547723i
\(181\) 12.2474i 0.910346i 0.890403 + 0.455173i \(0.150423\pi\)
−0.890403 + 0.455173i \(0.849577\pi\)
\(182\) 2.44949 6.00000i 0.181568 0.444750i
\(183\) −15.0000 + 15.0000i −1.10883 + 1.10883i
\(184\) 6.00000 0.442326
\(185\) −4.89898 −0.360180
\(186\) 0 0
\(187\) 0 0
\(188\) 4.89898 0.357295
\(189\) 5.32577 + 12.6742i 0.387392 + 0.921915i
\(190\) 6.00000 0.435286
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 1.22474 + 1.22474i 0.0883883 + 0.0883883i
\(193\) 4.00000 0.287926 0.143963 0.989583i \(-0.454015\pi\)
0.143963 + 0.989583i \(0.454015\pi\)
\(194\) 4.89898 0.351726
\(195\) −7.34847 + 7.34847i −0.526235 + 0.526235i
\(196\) 5.00000 + 4.89898i 0.357143 + 0.349927i
\(197\) 18.0000i 1.28245i −0.767354 0.641223i \(-0.778427\pi\)
0.767354 0.641223i \(-0.221573\pi\)
\(198\) 0 0
\(199\) 9.79796i 0.694559i −0.937762 0.347279i \(-0.887106\pi\)
0.937762 0.347279i \(-0.112894\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) −9.79796 9.79796i −0.691095 0.691095i
\(202\) 7.34847i 0.517036i
\(203\) −14.6969 6.00000i −1.03152 0.421117i
\(204\) −6.00000 6.00000i −0.420084 0.420084i
\(205\) 12.0000 0.838116
\(206\) 9.79796 0.682656
\(207\) 18.0000 1.25109
\(208\) 2.44949i 0.169842i
\(209\) 0 0
\(210\) −4.34847 10.3485i −0.300073 0.714112i
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 0 0
\(214\) 12.0000 0.820303
\(215\) 9.79796 0.668215
\(216\) 3.67423 + 3.67423i 0.250000 + 0.250000i
\(217\) 0 0
\(218\) 10.0000i 0.677285i
\(219\) 12.0000 12.0000i 0.810885 0.810885i
\(220\) 0 0
\(221\) 12.0000i 0.807207i
\(222\) 2.44949 2.44949i 0.164399 0.164399i
\(223\) 14.6969i 0.984180i −0.870544 0.492090i \(-0.836233\pi\)
0.870544 0.492090i \(-0.163767\pi\)
\(224\) 2.44949 + 1.00000i 0.163663 + 0.0668153i
\(225\) 3.00000i 0.200000i
\(226\) −6.00000 −0.399114
\(227\) 7.34847 0.487735 0.243868 0.969809i \(-0.421584\pi\)
0.243868 + 0.969809i \(0.421584\pi\)
\(228\) −3.00000 + 3.00000i −0.198680 + 0.198680i
\(229\) 22.0454i 1.45680i −0.685151 0.728401i \(-0.740264\pi\)
0.685151 0.728401i \(-0.259736\pi\)
\(230\) −14.6969 −0.969087
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) 24.0000i 1.57229i 0.618041 + 0.786146i \(0.287927\pi\)
−0.618041 + 0.786146i \(0.712073\pi\)
\(234\) 7.34847i 0.480384i
\(235\) −12.0000 −0.782794
\(236\) −12.2474 −0.797241
\(237\) 12.2474 + 12.2474i 0.795557 + 0.795557i
\(238\) −12.0000 4.89898i −0.777844 0.317554i
\(239\) 6.00000i 0.388108i 0.980991 + 0.194054i \(0.0621637\pi\)
−0.980991 + 0.194054i \(0.937836\pi\)
\(240\) −3.00000 3.00000i −0.193649 0.193649i
\(241\) 24.4949i 1.57786i 0.614486 + 0.788928i \(0.289363\pi\)
−0.614486 + 0.788928i \(0.710637\pi\)
\(242\) 11.0000i 0.707107i
\(243\) 11.0227 + 11.0227i 0.707107 + 0.707107i
\(244\) 12.2474i 0.784063i
\(245\) −12.2474 12.0000i −0.782461 0.766652i
\(246\) −6.00000 + 6.00000i −0.382546 + 0.382546i
\(247\) 6.00000 0.381771
\(248\) 0 0
\(249\) 3.00000 + 3.00000i 0.190117 + 0.190117i
\(250\) 9.79796i 0.619677i
\(251\) 17.1464 1.08227 0.541136 0.840935i \(-0.317994\pi\)
0.541136 + 0.840935i \(0.317994\pi\)
\(252\) 7.34847 + 3.00000i 0.462910 + 0.188982i
\(253\) 0 0
\(254\) 8.00000i 0.501965i
\(255\) 14.6969 + 14.6969i 0.920358 + 0.920358i
\(256\) 1.00000 0.0625000
\(257\) −29.3939 −1.83354 −0.916770 0.399416i \(-0.869213\pi\)
−0.916770 + 0.399416i \(0.869213\pi\)
\(258\) −4.89898 + 4.89898i −0.304997 + 0.304997i
\(259\) 2.00000 4.89898i 0.124274 0.304408i
\(260\) 6.00000i 0.372104i
\(261\) −18.0000 −1.11417
\(262\) 7.34847i 0.453990i
\(263\) 24.0000i 1.47990i 0.672660 + 0.739952i \(0.265152\pi\)
−0.672660 + 0.739952i \(0.734848\pi\)
\(264\) 0 0
\(265\) 14.6969i 0.902826i
\(266\) −2.44949 + 6.00000i −0.150188 + 0.367884i
\(267\) 0 0
\(268\) −8.00000 −0.488678
\(269\) 12.2474 0.746740 0.373370 0.927682i \(-0.378202\pi\)
0.373370 + 0.927682i \(0.378202\pi\)
\(270\) −9.00000 9.00000i −0.547723 0.547723i
\(271\) 24.4949i 1.48796i −0.668202 0.743980i \(-0.732936\pi\)
0.668202 0.743980i \(-0.267064\pi\)
\(272\) −4.89898 −0.297044
\(273\) −4.34847 10.3485i −0.263181 0.626318i
\(274\) 12.0000 0.724947
\(275\) 0 0
\(276\) 7.34847 7.34847i 0.442326 0.442326i
\(277\) −22.0000 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) 2.44949 0.146911
\(279\) 0 0
\(280\) −6.00000 2.44949i −0.358569 0.146385i
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 6.00000 6.00000i 0.357295 0.357295i
\(283\) 22.0454i 1.31046i 0.755428 + 0.655232i \(0.227429\pi\)
−0.755428 + 0.655232i \(0.772571\pi\)
\(284\) 0 0
\(285\) 7.34847 7.34847i 0.435286 0.435286i
\(286\) 0 0
\(287\) −4.89898 + 12.0000i −0.289178 + 0.708338i
\(288\) 3.00000 0.176777
\(289\) 7.00000 0.411765
\(290\) 14.6969 0.863034
\(291\) 6.00000 6.00000i 0.351726 0.351726i
\(292\) 9.79796i 0.573382i
\(293\) −2.44949 −0.143101 −0.0715504 0.997437i \(-0.522795\pi\)
−0.0715504 + 0.997437i \(0.522795\pi\)
\(294\) 12.1237 0.123724i 0.707070 0.00721575i
\(295\) 30.0000 1.74667
\(296\) 2.00000i 0.116248i
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) −14.6969 −0.849946
\(300\) 1.22474 + 1.22474i 0.0707107 + 0.0707107i
\(301\) −4.00000 + 9.79796i −0.230556 + 0.564745i
\(302\) 8.00000i 0.460348i
\(303\) 9.00000 + 9.00000i 0.517036 + 0.517036i
\(304\) 2.44949i 0.140488i
\(305\) 30.0000i 1.71780i
\(306\) −14.6969 −0.840168
\(307\) 7.34847i 0.419399i −0.977766 0.209700i \(-0.932751\pi\)
0.977766 0.209700i \(-0.0672486\pi\)
\(308\) 0 0
\(309\) 12.0000 12.0000i 0.682656 0.682656i
\(310\) 0 0
\(311\) −19.5959 −1.11118 −0.555591 0.831456i \(-0.687508\pi\)
−0.555591 + 0.831456i \(0.687508\pi\)
\(312\) −3.00000 3.00000i −0.169842 0.169842i
\(313\) 34.2929i 1.93835i 0.246380 + 0.969173i \(0.420759\pi\)
−0.246380 + 0.969173i \(0.579241\pi\)
\(314\) −7.34847 −0.414698
\(315\) −18.0000 7.34847i −1.01419 0.414039i
\(316\) 10.0000 0.562544
\(317\) 18.0000i 1.01098i −0.862832 0.505490i \(-0.831312\pi\)
0.862832 0.505490i \(-0.168688\pi\)
\(318\) 7.34847 + 7.34847i 0.412082 + 0.412082i
\(319\) 0 0
\(320\) −2.44949 −0.136931
\(321\) 14.6969 14.6969i 0.820303 0.820303i
\(322\) 6.00000 14.6969i 0.334367 0.819028i
\(323\) 12.0000i 0.667698i
\(324\) 9.00000 0.500000
\(325\) 2.44949i 0.135873i
\(326\) 16.0000i 0.886158i
\(327\) −12.2474 12.2474i −0.677285 0.677285i
\(328\) 4.89898i 0.270501i
\(329\) 4.89898 12.0000i 0.270089 0.661581i
\(330\) 0 0
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 2.44949 0.134433
\(333\) 6.00000i 0.328798i
\(334\) 4.89898i 0.268060i
\(335\) 19.5959 1.07064
\(336\) 4.22474 1.77526i 0.230479 0.0968481i
\(337\) −32.0000 −1.74315 −0.871576 0.490261i \(-0.836901\pi\)
−0.871576 + 0.490261i \(0.836901\pi\)
\(338\) 7.00000i 0.380750i
\(339\) −7.34847 + 7.34847i −0.399114 + 0.399114i
\(340\) 12.0000 0.650791
\(341\) 0 0
\(342\) 7.34847i 0.397360i
\(343\) 17.0000 7.34847i 0.917914 0.396780i
\(344\) 4.00000i 0.215666i
\(345\) −18.0000 + 18.0000i −0.969087 + 0.969087i
\(346\) 22.0454i 1.18517i
\(347\) 12.0000i 0.644194i 0.946707 + 0.322097i \(0.104388\pi\)
−0.946707 + 0.322097i \(0.895612\pi\)
\(348\) −7.34847 + 7.34847i −0.393919 + 0.393919i
\(349\) 2.44949i 0.131118i 0.997849 + 0.0655591i \(0.0208831\pi\)
−0.997849 + 0.0655591i \(0.979117\pi\)
\(350\) 2.44949 + 1.00000i 0.130931 + 0.0534522i
\(351\) −9.00000 9.00000i −0.480384 0.480384i
\(352\) 0 0
\(353\) 9.79796 0.521493 0.260746 0.965407i \(-0.416031\pi\)
0.260746 + 0.965407i \(0.416031\pi\)
\(354\) −15.0000 + 15.0000i −0.797241 + 0.797241i
\(355\) 0 0
\(356\) 0 0
\(357\) −20.6969 + 8.69694i −1.09540 + 0.460291i
\(358\) −24.0000 −1.26844
\(359\) 6.00000i 0.316668i 0.987386 + 0.158334i \(0.0506123\pi\)
−0.987386 + 0.158334i \(0.949388\pi\)
\(360\) −7.34847 −0.387298
\(361\) 13.0000 0.684211
\(362\) 12.2474 0.643712
\(363\) −13.4722 13.4722i −0.707107 0.707107i
\(364\) −6.00000 2.44949i −0.314485 0.128388i
\(365\) 24.0000i 1.25622i
\(366\) 15.0000 + 15.0000i 0.784063 + 0.784063i
\(367\) 4.89898i 0.255725i 0.991792 + 0.127862i \(0.0408116\pi\)
−0.991792 + 0.127862i \(0.959188\pi\)
\(368\) 6.00000i 0.312772i
\(369\) 14.6969i 0.765092i
\(370\) 4.89898i 0.254686i
\(371\) 14.6969 + 6.00000i 0.763027 + 0.311504i
\(372\) 0 0
\(373\) 14.0000 0.724893 0.362446 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) 0 0
\(375\) 12.0000 + 12.0000i 0.619677 + 0.619677i
\(376\) 4.89898i 0.252646i
\(377\) 14.6969 0.756931
\(378\) 12.6742 5.32577i 0.651892 0.273928i
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 6.00000i 0.307794i
\(381\) −9.79796 9.79796i −0.501965 0.501965i
\(382\) 0 0
\(383\) 34.2929 1.75228 0.876142 0.482054i \(-0.160109\pi\)
0.876142 + 0.482054i \(0.160109\pi\)
\(384\) 1.22474 1.22474i 0.0625000 0.0625000i
\(385\) 0 0
\(386\) 4.00000i 0.203595i
\(387\) 12.0000i 0.609994i
\(388\) 4.89898i 0.248708i
\(389\) 6.00000i 0.304212i 0.988364 + 0.152106i \(0.0486055\pi\)
−0.988364 + 0.152106i \(0.951394\pi\)
\(390\) 7.34847 + 7.34847i 0.372104 + 0.372104i
\(391\) 29.3939i 1.48651i
\(392\) 4.89898 5.00000i 0.247436 0.252538i
\(393\) 9.00000 + 9.00000i 0.453990 + 0.453990i
\(394\) −18.0000 −0.906827
\(395\) −24.4949 −1.23247
\(396\) 0 0
\(397\) 7.34847i 0.368809i −0.982850 0.184405i \(-0.940964\pi\)
0.982850 0.184405i \(-0.0590357\pi\)
\(398\) −9.79796 −0.491127
\(399\) 4.34847 + 10.3485i 0.217696 + 0.518071i
\(400\) 1.00000 0.0500000
\(401\) 30.0000i 1.49813i −0.662497 0.749064i \(-0.730503\pi\)
0.662497 0.749064i \(-0.269497\pi\)
\(402\) −9.79796 + 9.79796i −0.488678 + 0.488678i
\(403\) 0 0
\(404\) 7.34847 0.365600
\(405\) −22.0454 −1.09545
\(406\) −6.00000 + 14.6969i −0.297775 + 0.729397i
\(407\) 0 0
\(408\) −6.00000 + 6.00000i −0.297044 + 0.297044i
\(409\) 34.2929i 1.69567i −0.530258 0.847836i \(-0.677905\pi\)
0.530258 0.847836i \(-0.322095\pi\)
\(410\) 12.0000i 0.592638i
\(411\) 14.6969 14.6969i 0.724947 0.724947i
\(412\) 9.79796i 0.482711i
\(413\) −12.2474 + 30.0000i −0.602658 + 1.47620i
\(414\) 18.0000i 0.884652i
\(415\) −6.00000 −0.294528
\(416\) −2.44949 −0.120096
\(417\) 3.00000 3.00000i 0.146911 0.146911i
\(418\) 0 0
\(419\) −12.2474 −0.598327 −0.299164 0.954202i \(-0.596708\pi\)
−0.299164 + 0.954202i \(0.596708\pi\)
\(420\) −10.3485 + 4.34847i −0.504954 + 0.212184i
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 8.00000i 0.389434i
\(423\) 14.6969i 0.714590i
\(424\) 6.00000 0.291386
\(425\) −4.89898 −0.237635
\(426\) 0 0
\(427\) 30.0000 + 12.2474i 1.45180 + 0.592696i
\(428\) 12.0000i 0.580042i
\(429\) 0 0
\(430\) 9.79796i 0.472500i
\(431\) 30.0000i 1.44505i −0.691345 0.722525i \(-0.742982\pi\)
0.691345 0.722525i \(-0.257018\pi\)
\(432\) 3.67423 3.67423i 0.176777 0.176777i
\(433\) 14.6969i 0.706290i −0.935569 0.353145i \(-0.885112\pi\)
0.935569 0.353145i \(-0.114888\pi\)
\(434\) 0 0
\(435\) 18.0000 18.0000i 0.863034 0.863034i
\(436\) −10.0000 −0.478913
\(437\) 14.6969 0.703050
\(438\) −12.0000 12.0000i −0.573382 0.573382i
\(439\) 14.6969i 0.701447i 0.936479 + 0.350723i \(0.114064\pi\)
−0.936479 + 0.350723i \(0.885936\pi\)
\(440\) 0 0
\(441\) 14.6969 15.0000i 0.699854 0.714286i
\(442\) 12.0000 0.570782
\(443\) 36.0000i 1.71041i −0.518289 0.855206i \(-0.673431\pi\)
0.518289 0.855206i \(-0.326569\pi\)
\(444\) −2.44949 2.44949i −0.116248 0.116248i
\(445\) 0 0
\(446\) −14.6969 −0.695920
\(447\) 7.34847 7.34847i 0.347571 0.347571i
\(448\) 1.00000 2.44949i 0.0472456 0.115728i
\(449\) 36.0000i 1.69895i 0.527633 + 0.849473i \(0.323080\pi\)
−0.527633 + 0.849473i \(0.676920\pi\)
\(450\) 3.00000 0.141421
\(451\) 0 0
\(452\) 6.00000i 0.282216i
\(453\) 9.79796 + 9.79796i 0.460348 + 0.460348i
\(454\) 7.34847i 0.344881i
\(455\) 14.6969 + 6.00000i 0.689003 + 0.281284i
\(456\) 3.00000 + 3.00000i 0.140488 + 0.140488i
\(457\) 28.0000 1.30978 0.654892 0.755722i \(-0.272714\pi\)
0.654892 + 0.755722i \(0.272714\pi\)
\(458\) −22.0454 −1.03011
\(459\) −18.0000 + 18.0000i −0.840168 + 0.840168i
\(460\) 14.6969i 0.685248i
\(461\) −31.8434 −1.48309 −0.741547 0.670901i \(-0.765907\pi\)
−0.741547 + 0.670901i \(0.765907\pi\)
\(462\) 0 0
\(463\) 14.0000 0.650635 0.325318 0.945605i \(-0.394529\pi\)
0.325318 + 0.945605i \(0.394529\pi\)
\(464\) 6.00000i 0.278543i
\(465\) 0 0
\(466\) 24.0000 1.11178
\(467\) 7.34847 0.340047 0.170023 0.985440i \(-0.445616\pi\)
0.170023 + 0.985440i \(0.445616\pi\)
\(468\) −7.34847 −0.339683
\(469\) −8.00000 + 19.5959i −0.369406 + 0.904855i
\(470\) 12.0000i 0.553519i
\(471\) −9.00000 + 9.00000i −0.414698 + 0.414698i
\(472\) 12.2474i 0.563735i
\(473\) 0 0
\(474\) 12.2474 12.2474i 0.562544 0.562544i
\(475\) 2.44949i 0.112390i
\(476\) −4.89898 + 12.0000i −0.224544 + 0.550019i
\(477\) 18.0000 0.824163
\(478\) 6.00000 0.274434
\(479\) −24.4949 −1.11920 −0.559600 0.828763i \(-0.689045\pi\)
−0.559600 + 0.828763i \(0.689045\pi\)
\(480\) −3.00000 + 3.00000i −0.136931 + 0.136931i
\(481\) 4.89898i 0.223374i
\(482\) 24.4949 1.11571
\(483\) −10.6515 25.3485i −0.484661 1.15340i
\(484\) −11.0000 −0.500000
\(485\) 12.0000i 0.544892i
\(486\) 11.0227 11.0227i 0.500000 0.500000i
\(487\) −32.0000 −1.45006 −0.725029 0.688718i \(-0.758174\pi\)
−0.725029 + 0.688718i \(0.758174\pi\)
\(488\) 12.2474 0.554416
\(489\) 19.5959 + 19.5959i 0.886158 + 0.886158i
\(490\) −12.0000 + 12.2474i −0.542105 + 0.553283i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 6.00000 + 6.00000i 0.270501 + 0.270501i
\(493\) 29.3939i 1.32383i
\(494\) 6.00000i 0.269953i
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 3.00000 3.00000i 0.134433 0.134433i
\(499\) −20.0000 −0.895323 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) 9.79796 0.438178
\(501\) 6.00000 + 6.00000i 0.268060 + 0.268060i
\(502\) 17.1464i 0.765283i
\(503\) −39.1918 −1.74748 −0.873739 0.486395i \(-0.838311\pi\)
−0.873739 + 0.486395i \(0.838311\pi\)
\(504\) 3.00000 7.34847i 0.133631 0.327327i
\(505\) −18.0000 −0.800989
\(506\) 0 0
\(507\) −8.57321 8.57321i −0.380750 0.380750i
\(508\) −8.00000 −0.354943
\(509\) 12.2474 0.542859 0.271429 0.962458i \(-0.412504\pi\)
0.271429 + 0.962458i \(0.412504\pi\)
\(510\) 14.6969 14.6969i 0.650791 0.650791i
\(511\) −24.0000 9.79796i −1.06170 0.433436i
\(512\) 1.00000i 0.0441942i
\(513\) 9.00000 + 9.00000i 0.397360 + 0.397360i
\(514\) 29.3939i 1.29651i
\(515\) 24.0000i 1.05757i
\(516\) 4.89898 + 4.89898i 0.215666 + 0.215666i
\(517\) 0 0
\(518\) −4.89898 2.00000i −0.215249 0.0878750i
\(519\) −27.0000 27.0000i −1.18517 1.18517i
\(520\) 6.00000 0.263117
\(521\) 4.89898 0.214628 0.107314 0.994225i \(-0.465775\pi\)
0.107314 + 0.994225i \(0.465775\pi\)
\(522\) 18.0000i 0.787839i
\(523\) 2.44949i 0.107109i −0.998565 0.0535544i \(-0.982945\pi\)
0.998565 0.0535544i \(-0.0170550\pi\)
\(524\) 7.34847 0.321019
\(525\) 4.22474 1.77526i 0.184383 0.0774785i
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) 0 0
\(529\) −13.0000 −0.565217
\(530\) −14.6969 −0.638394
\(531\) 36.7423i 1.59448i
\(532\) 6.00000 + 2.44949i 0.260133 + 0.106199i
\(533\) 12.0000i 0.519778i
\(534\) 0 0
\(535\) 29.3939i 1.27081i
\(536\) 8.00000i 0.345547i
\(537\) −29.3939 + 29.3939i −1.26844 + 1.26844i
\(538\) 12.2474i 0.528025i
\(539\) 0 0
\(540\) −9.00000 + 9.00000i −0.387298 + 0.387298i
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) −24.4949 −1.05215
\(543\) 15.0000 15.0000i 0.643712 0.643712i
\(544\) 4.89898i 0.210042i
\(545\) 24.4949 1.04925
\(546\) −10.3485 + 4.34847i −0.442874 + 0.186097i
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 12.0000i 0.512615i
\(549\) 36.7423 1.56813
\(550\) 0 0
\(551\) −14.6969 −0.626111
\(552\) −7.34847 7.34847i −0.312772 0.312772i
\(553\) 10.0000 24.4949i 0.425243 1.04163i
\(554\) 22.0000i 0.934690i
\(555\) 6.00000 + 6.00000i 0.254686 + 0.254686i
\(556\) 2.44949i 0.103882i
\(557\) 18.0000i 0.762684i −0.924434 0.381342i \(-0.875462\pi\)
0.924434 0.381342i \(-0.124538\pi\)
\(558\) 0 0
\(559\) 9.79796i 0.414410i
\(560\) −2.44949 + 6.00000i −0.103510 + 0.253546i
\(561\) 0 0
\(562\) 0 0
\(563\) 22.0454 0.929103 0.464552 0.885546i \(-0.346216\pi\)
0.464552 + 0.885546i \(0.346216\pi\)
\(564\) −6.00000 6.00000i −0.252646 0.252646i
\(565\) 14.6969i 0.618305i
\(566\) 22.0454 0.926638
\(567\) 9.00000 22.0454i 0.377964 0.925820i
\(568\) 0 0
\(569\) 6.00000i 0.251533i 0.992060 + 0.125767i \(0.0401390\pi\)
−0.992060 + 0.125767i \(0.959861\pi\)
\(570\) −7.34847 7.34847i −0.307794 0.307794i
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 12.0000 + 4.89898i 0.500870 + 0.204479i
\(575\) 6.00000i 0.250217i
\(576\) 3.00000i 0.125000i
\(577\) 19.5959i 0.815789i −0.913029 0.407894i \(-0.866263\pi\)
0.913029 0.407894i \(-0.133737\pi\)
\(578\) 7.00000i 0.291162i
\(579\) −4.89898 4.89898i −0.203595 0.203595i
\(580\) 14.6969i 0.610257i
\(581\) 2.44949 6.00000i 0.101622 0.248922i
\(582\) −6.00000 6.00000i −0.248708 0.248708i
\(583\) 0 0
\(584\) −9.79796 −0.405442
\(585\) 18.0000 0.744208
\(586\) 2.44949i 0.101187i
\(587\) 7.34847 0.303304 0.151652 0.988434i \(-0.451541\pi\)
0.151652 + 0.988434i \(0.451541\pi\)
\(588\) −0.123724 12.1237i −0.00510231 0.499974i
\(589\) 0 0
\(590\) 30.0000i 1.23508i
\(591\) −22.0454 + 22.0454i −0.906827 + 0.906827i
\(592\) −2.00000 −0.0821995
\(593\) −39.1918 −1.60942 −0.804708 0.593671i \(-0.797678\pi\)
−0.804708 + 0.593671i \(0.797678\pi\)
\(594\) 0 0
\(595\) 12.0000 29.3939i 0.491952 1.20503i
\(596\) 6.00000i 0.245770i
\(597\) −12.0000 + 12.0000i −0.491127 + 0.491127i
\(598\) 14.6969i 0.601003i
\(599\) 24.0000i 0.980613i −0.871550 0.490307i \(-0.836885\pi\)
0.871550 0.490307i \(-0.163115\pi\)
\(600\) 1.22474 1.22474i 0.0500000 0.0500000i
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 9.79796 + 4.00000i 0.399335 + 0.163028i
\(603\) 24.0000i 0.977356i
\(604\) 8.00000 0.325515
\(605\) 26.9444 1.09545
\(606\) 9.00000 9.00000i 0.365600 0.365600i
\(607\) 4.89898i 0.198843i 0.995045 + 0.0994217i \(0.0316993\pi\)
−0.995045 + 0.0994217i \(0.968301\pi\)
\(608\) 2.44949 0.0993399
\(609\) 10.6515 + 25.3485i 0.431622 + 1.02717i
\(610\) −30.0000 −1.21466
\(611\) 12.0000i 0.485468i
\(612\) 14.6969i 0.594089i
\(613\) 14.0000 0.565455 0.282727 0.959200i \(-0.408761\pi\)
0.282727 + 0.959200i \(0.408761\pi\)
\(614\) −7.34847 −0.296560
\(615\) −14.6969 14.6969i −0.592638 0.592638i
\(616\) 0 0
\(617\) 18.0000i 0.724653i −0.932051 0.362326i \(-0.881983\pi\)
0.932051 0.362326i \(-0.118017\pi\)
\(618\) −12.0000 12.0000i −0.482711 0.482711i
\(619\) 26.9444i 1.08299i 0.840705 + 0.541493i \(0.182141\pi\)
−0.840705 + 0.541493i \(0.817859\pi\)
\(620\) 0 0
\(621\) −22.0454 22.0454i −0.884652 0.884652i
\(622\) 19.5959i 0.785725i
\(623\) 0 0
\(624\) −3.00000 + 3.00000i −0.120096 + 0.120096i
\(625\) −29.0000 −1.16000
\(626\) 34.2929 1.37062
\(627\) 0 0
\(628\) 7.34847i 0.293236i
\(629\) 9.79796 0.390670
\(630\) −7.34847 + 18.0000i −0.292770 + 0.717137i
\(631\) 2.00000 0.0796187 0.0398094 0.999207i \(-0.487325\pi\)
0.0398094 + 0.999207i \(0.487325\pi\)
\(632\) 10.0000i 0.397779i
\(633\) 9.79796 + 9.79796i 0.389434 + 0.389434i
\(634\) −18.0000 −0.714871
\(635\) 19.5959 0.777640
\(636\) 7.34847 7.34847i 0.291386 0.291386i
\(637\) −12.0000 + 12.2474i −0.475457 + 0.485262i
\(638\) 0 0
\(639\) 0 0
\(640\) 2.44949i 0.0968246i
\(641\) 30.0000i 1.18493i 0.805597 + 0.592464i \(0.201845\pi\)
−0.805597 + 0.592464i \(0.798155\pi\)
\(642\) −14.6969 14.6969i −0.580042 0.580042i
\(643\) 22.0454i 0.869386i 0.900579 + 0.434693i \(0.143143\pi\)
−0.900579 + 0.434693i \(0.856857\pi\)
\(644\) −14.6969 6.00000i −0.579141 0.236433i
\(645\) −12.0000 12.0000i −0.472500 0.472500i
\(646\) −12.0000 −0.472134
\(647\) 44.0908 1.73339 0.866694 0.498839i \(-0.166240\pi\)
0.866694 + 0.498839i \(0.166240\pi\)
\(648\) 9.00000i 0.353553i
\(649\) 0 0
\(650\) −2.44949 −0.0960769
\(651\) 0 0
\(652\) 16.0000 0.626608
\(653\) 6.00000i 0.234798i −0.993085 0.117399i \(-0.962544\pi\)
0.993085 0.117399i \(-0.0374557\pi\)
\(654\) −12.2474 + 12.2474i −0.478913 + 0.478913i
\(655\) −18.0000 −0.703318
\(656\) 4.89898 0.191273
\(657\) −29.3939 −1.14676
\(658\) −12.0000 4.89898i −0.467809 0.190982i
\(659\) 36.0000i 1.40236i 0.712984 + 0.701180i \(0.247343\pi\)
−0.712984 + 0.701180i \(0.752657\pi\)
\(660\) 0 0
\(661\) 12.2474i 0.476371i 0.971220 + 0.238185i \(0.0765525\pi\)
−0.971220 + 0.238185i \(0.923447\pi\)
\(662\) 8.00000i 0.310929i
\(663\) 14.6969 14.6969i 0.570782 0.570782i
\(664\) 2.44949i 0.0950586i
\(665\) −14.6969 6.00000i −0.569923 0.232670i
\(666\) −6.00000 −0.232495
\(667\) 36.0000 1.39393
\(668\) 4.89898 0.189547
\(669\) −18.0000 + 18.0000i −0.695920 + 0.695920i
\(670\) 19.5959i 0.757056i
\(671\) 0 0
\(672\) −1.77526 4.22474i −0.0684820 0.162973i
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 32.0000i 1.23259i
\(675\) 3.67423 3.67423i 0.141421 0.141421i
\(676\) −7.00000 −0.269231
\(677\) 7.34847 0.282425 0.141212 0.989979i \(-0.454900\pi\)
0.141212 + 0.989979i \(0.454900\pi\)
\(678\) 7.34847 + 7.34847i 0.282216 + 0.282216i
\(679\) −12.0000 4.89898i −0.460518 0.188006i
\(680\) 12.0000i 0.460179i
\(681\) −9.00000 9.00000i −0.344881 0.344881i
\(682\) 0 0
\(683\) 24.0000i 0.918334i 0.888350 + 0.459167i \(0.151852\pi\)
−0.888350 + 0.459167i \(0.848148\pi\)
\(684\) 7.34847 0.280976
\(685\) 29.3939i 1.12308i
\(686\) −7.34847 17.0000i −0.280566 0.649063i
\(687\) −27.0000 + 27.0000i −1.03011 + 1.03011i
\(688\) 4.00000 0.152499
\(689\) −14.6969 −0.559909
\(690\) 18.0000 + 18.0000i 0.685248 + 0.685248i
\(691\) 36.7423i 1.39774i −0.715246 0.698872i \(-0.753686\pi\)
0.715246 0.698872i \(-0.246314\pi\)
\(692\) −22.0454 −0.838041
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 6.00000i 0.227593i
\(696\) 7.34847 + 7.34847i 0.278543 + 0.278543i
\(697\) −24.0000 −0.909065
\(698\) 2.44949 0.0927146
\(699\) 29.3939 29.3939i 1.11178 1.11178i
\(700\) 1.00000 2.44949i 0.0377964 0.0925820i
\(701\) 30.0000i 1.13308i −0.824033 0.566542i \(-0.808281\pi\)
0.824033 0.566542i \(-0.191719\pi\)
\(702\) −9.00000 + 9.00000i −0.339683 + 0.339683i
\(703\) 4.89898i 0.184769i
\(704\) 0 0
\(705\) 14.6969 + 14.6969i 0.553519 + 0.553519i
\(706\) 9.79796i 0.368751i
\(707\) 7.34847 18.0000i 0.276368 0.676960i
\(708\) 15.0000 + 15.0000i 0.563735 + 0.563735i
\(709\) 10.0000 0.375558 0.187779 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) 0 0
\(711\) 30.0000i 1.12509i
\(712\) 0 0
\(713\) 0 0
\(714\) 8.69694 + 20.6969i 0.325475 + 0.774563i
\(715\) 0 0
\(716\) 24.0000i 0.896922i
\(717\) 7.34847 7.34847i 0.274434 0.274434i
\(718\) 6.00000 0.223918
\(719\) −24.4949 −0.913506 −0.456753 0.889594i \(-0.650988\pi\)
−0.456753 + 0.889594i \(0.650988\pi\)
\(720\) 7.34847i 0.273861i
\(721\) −24.0000 9.79796i −0.893807 0.364895i
\(722\) 13.0000i 0.483810i
\(723\) 30.0000 30.0000i 1.11571 1.11571i
\(724\) 12.2474i 0.455173i
\(725\) 6.00000i 0.222834i
\(726\) −13.4722 + 13.4722i −0.500000 + 0.500000i
\(727\) 29.3939i 1.09016i 0.838385 + 0.545079i \(0.183500\pi\)
−0.838385 + 0.545079i \(0.816500\pi\)
\(728\) −2.44949 + 6.00000i −0.0907841 + 0.222375i
\(729\) 27.0000i 1.00000i
\(730\) 24.0000 0.888280
\(731\) −19.5959 −0.724781
\(732\) 15.0000 15.0000i 0.554416 0.554416i
\(733\) 22.0454i 0.814266i 0.913369 + 0.407133i \(0.133471\pi\)
−0.913369 + 0.407133i \(0.866529\pi\)
\(734\) 4.89898 0.180825
\(735\) 0.303062 + 29.6969i 0.0111786 + 1.09539i
\(736\) −6.00000 −0.221163
\(737\) 0 0
\(738\) 14.6969 0.541002
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 4.89898 0.180090
\(741\) −7.34847 7.34847i −0.269953 0.269953i
\(742\) 6.00000 14.6969i 0.220267 0.539542i
\(743\) 6.00000i 0.220119i −0.993925 0.110059i \(-0.964896\pi\)
0.993925 0.110059i \(-0.0351041\pi\)
\(744\) 0 0
\(745\) 14.6969i 0.538454i
\(746\) 14.0000i 0.512576i
\(747\) 7.34847i 0.268866i
\(748\) 0 0
\(749\) −29.3939 12.0000i −1.07403 0.438470i
\(750\) 12.0000 12.0000i 0.438178 0.438178i
\(751\) −8.00000 −0.291924 −0.145962 0.989290i \(-0.546628\pi\)
−0.145962 + 0.989290i \(0.546628\pi\)
\(752\) −4.89898 −0.178647
\(753\) −21.0000 21.0000i −0.765283 0.765283i
\(754\) 14.6969i 0.535231i
\(755\) −19.5959 −0.713168
\(756\) −5.32577 12.6742i −0.193696 0.460957i
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) 20.0000i 0.726433i
\(759\) 0 0
\(760\) −6.00000 −0.217643
\(761\) 4.89898 0.177588 0.0887939 0.996050i \(-0.471699\pi\)
0.0887939 + 0.996050i \(0.471699\pi\)
\(762\) −9.79796 + 9.79796i −0.354943 + 0.354943i
\(763\) −10.0000 + 24.4949i −0.362024 + 0.886775i
\(764\) 0 0
\(765\) 36.0000i 1.30158i
\(766\) 34.2929i 1.23905i
\(767\) 30.0000i 1.08324i
\(768\) −1.22474 1.22474i −0.0441942 0.0441942i
\(769\) 34.2929i 1.23663i −0.785930 0.618316i \(-0.787815\pi\)
0.785930 0.618316i \(-0.212185\pi\)
\(770\) 0 0
\(771\) 36.0000 + 36.0000i 1.29651 + 1.29651i
\(772\) −4.00000 −0.143963
\(773\) −26.9444 −0.969122 −0.484561 0.874757i \(-0.661021\pi\)
−0.484561 + 0.874757i \(0.661021\pi\)
\(774\) 12.0000 0.431331
\(775\) 0 0
\(776\) −4.89898 −0.175863
\(777\) −8.44949 + 3.55051i −0.303124 + 0.127374i
\(778\) 6.00000 0.215110
\(779\) 12.0000i 0.429945i
\(780\) 7.34847 7.34847i 0.263117 0.263117i
\(781\) 0 0
\(782\) 29.3939 1.05112
\(783\) 22.0454 + 22.0454i 0.787839 + 0.787839i
\(784\) −5.00000 4.89898i −0.178571 0.174964i
\(785\) 18.0000i 0.642448i
\(786\) 9.00000 9.00000i 0.321019 0.321019i
\(787\) 31.8434i 1.13509i −0.823341 0.567547i \(-0.807893\pi\)
0.823341 0.567547i \(-0.192107\pi\)
\(788\) 18.0000i 0.641223i
\(789\) 29.3939 29.3939i 1.04645 1.04645i
\(790\)