Properties

Label 45.2.f.a.8.1
Level $45$
Weight $2$
Character 45.8
Analytic conductor $0.359$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.359326809096\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 8.1
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 45.8
Dual form 45.2.f.a.17.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.12132 - 0.707107i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(-2.12132 + 2.12132i) q^{8} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.12132 - 0.707107i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(-2.00000 - 1.00000i) q^{10} +2.82843i q^{11} +(1.00000 + 1.00000i) q^{13} +2.82843 q^{14} +1.00000 q^{16} +(-2.82843 - 2.82843i) q^{17} +(-0.707107 - 2.12132i) q^{20} +(2.00000 - 2.00000i) q^{22} +(2.82843 - 2.82843i) q^{23} +(4.00000 - 3.00000i) q^{25} -1.41421i q^{26} +(2.00000 + 2.00000i) q^{28} -4.24264 q^{29} -4.00000 q^{31} +(3.53553 + 3.53553i) q^{32} +4.00000i q^{34} +(-2.82843 + 5.65685i) q^{35} +(1.00000 - 1.00000i) q^{37} +(-3.00000 + 6.00000i) q^{40} -1.41421i q^{41} +(-8.00000 - 8.00000i) q^{43} +2.82843 q^{44} -4.00000 q^{46} +(5.65685 + 5.65685i) q^{47} -1.00000i q^{49} +(-4.94975 - 0.707107i) q^{50} +(1.00000 - 1.00000i) q^{52} +(2.82843 - 2.82843i) q^{53} +(2.00000 + 6.00000i) q^{55} -8.48528i q^{56} +(3.00000 + 3.00000i) q^{58} -8.48528 q^{59} +8.00000 q^{61} +(2.82843 + 2.82843i) q^{62} -7.00000i q^{64} +(2.82843 + 1.41421i) q^{65} +(4.00000 - 4.00000i) q^{67} +(-2.82843 + 2.82843i) q^{68} +(6.00000 - 2.00000i) q^{70} -5.65685i q^{71} +(1.00000 + 1.00000i) q^{73} -1.41421 q^{74} +(-5.65685 - 5.65685i) q^{77} +12.0000i q^{79} +(2.12132 - 0.707107i) q^{80} +(-1.00000 + 1.00000i) q^{82} +(2.82843 - 2.82843i) q^{83} +(-8.00000 - 4.00000i) q^{85} +11.3137i q^{86} +(-6.00000 - 6.00000i) q^{88} +12.7279 q^{89} -4.00000 q^{91} +(-2.82843 - 2.82843i) q^{92} -8.00000i q^{94} +(-11.0000 + 11.0000i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{7} + O(q^{10}) \) \( 4 q - 8 q^{7} - 8 q^{10} + 4 q^{13} + 4 q^{16} + 8 q^{22} + 16 q^{25} + 8 q^{28} - 16 q^{31} + 4 q^{37} - 12 q^{40} - 32 q^{43} - 16 q^{46} + 4 q^{52} + 8 q^{55} + 12 q^{58} + 32 q^{61} + 16 q^{67} + 24 q^{70} + 4 q^{73} - 4 q^{82} - 32 q^{85} - 24 q^{88} - 16 q^{91} - 44 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i 0.411438 0.911438i \(-0.365027\pi\)
−0.911438 + 0.411438i \(0.865027\pi\)
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) 2.12132 0.707107i 0.948683 0.316228i
\(6\) 0 0
\(7\) −2.00000 + 2.00000i −0.755929 + 0.755929i −0.975579 0.219650i \(-0.929509\pi\)
0.219650 + 0.975579i \(0.429509\pi\)
\(8\) −2.12132 + 2.12132i −0.750000 + 0.750000i
\(9\) 0 0
\(10\) −2.00000 1.00000i −0.632456 0.316228i
\(11\) 2.82843i 0.852803i 0.904534 + 0.426401i \(0.140219\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 0 0
\(13\) 1.00000 + 1.00000i 0.277350 + 0.277350i 0.832050 0.554700i \(-0.187167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 2.82843 0.755929
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −2.82843 2.82843i −0.685994 0.685994i 0.275350 0.961344i \(-0.411206\pi\)
−0.961344 + 0.275350i \(0.911206\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −0.707107 2.12132i −0.158114 0.474342i
\(21\) 0 0
\(22\) 2.00000 2.00000i 0.426401 0.426401i
\(23\) 2.82843 2.82843i 0.589768 0.589768i −0.347801 0.937568i \(-0.613071\pi\)
0.937568 + 0.347801i \(0.113071\pi\)
\(24\) 0 0
\(25\) 4.00000 3.00000i 0.800000 0.600000i
\(26\) 1.41421i 0.277350i
\(27\) 0 0
\(28\) 2.00000 + 2.00000i 0.377964 + 0.377964i
\(29\) −4.24264 −0.787839 −0.393919 0.919145i \(-0.628881\pi\)
−0.393919 + 0.919145i \(0.628881\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 3.53553 + 3.53553i 0.625000 + 0.625000i
\(33\) 0 0
\(34\) 4.00000i 0.685994i
\(35\) −2.82843 + 5.65685i −0.478091 + 0.956183i
\(36\) 0 0
\(37\) 1.00000 1.00000i 0.164399 0.164399i −0.620113 0.784512i \(-0.712913\pi\)
0.784512 + 0.620113i \(0.212913\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −3.00000 + 6.00000i −0.474342 + 0.948683i
\(41\) 1.41421i 0.220863i −0.993884 0.110432i \(-0.964777\pi\)
0.993884 0.110432i \(-0.0352233\pi\)
\(42\) 0 0
\(43\) −8.00000 8.00000i −1.21999 1.21999i −0.967635 0.252353i \(-0.918795\pi\)
−0.252353 0.967635i \(-0.581205\pi\)
\(44\) 2.82843 0.426401
\(45\) 0 0
\(46\) −4.00000 −0.589768
\(47\) 5.65685 + 5.65685i 0.825137 + 0.825137i 0.986840 0.161703i \(-0.0516985\pi\)
−0.161703 + 0.986840i \(0.551699\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) −4.94975 0.707107i −0.700000 0.100000i
\(51\) 0 0
\(52\) 1.00000 1.00000i 0.138675 0.138675i
\(53\) 2.82843 2.82843i 0.388514 0.388514i −0.485643 0.874157i \(-0.661414\pi\)
0.874157 + 0.485643i \(0.161414\pi\)
\(54\) 0 0
\(55\) 2.00000 + 6.00000i 0.269680 + 0.809040i
\(56\) 8.48528i 1.13389i
\(57\) 0 0
\(58\) 3.00000 + 3.00000i 0.393919 + 0.393919i
\(59\) −8.48528 −1.10469 −0.552345 0.833616i \(-0.686267\pi\)
−0.552345 + 0.833616i \(0.686267\pi\)
\(60\) 0 0
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 2.82843 + 2.82843i 0.359211 + 0.359211i
\(63\) 0 0
\(64\) 7.00000i 0.875000i
\(65\) 2.82843 + 1.41421i 0.350823 + 0.175412i
\(66\) 0 0
\(67\) 4.00000 4.00000i 0.488678 0.488678i −0.419211 0.907889i \(-0.637693\pi\)
0.907889 + 0.419211i \(0.137693\pi\)
\(68\) −2.82843 + 2.82843i −0.342997 + 0.342997i
\(69\) 0 0
\(70\) 6.00000 2.00000i 0.717137 0.239046i
\(71\) 5.65685i 0.671345i −0.941979 0.335673i \(-0.891036\pi\)
0.941979 0.335673i \(-0.108964\pi\)
\(72\) 0 0
\(73\) 1.00000 + 1.00000i 0.117041 + 0.117041i 0.763202 0.646160i \(-0.223626\pi\)
−0.646160 + 0.763202i \(0.723626\pi\)
\(74\) −1.41421 −0.164399
\(75\) 0 0
\(76\) 0 0
\(77\) −5.65685 5.65685i −0.644658 0.644658i
\(78\) 0 0
\(79\) 12.0000i 1.35011i 0.737769 + 0.675053i \(0.235879\pi\)
−0.737769 + 0.675053i \(0.764121\pi\)
\(80\) 2.12132 0.707107i 0.237171 0.0790569i
\(81\) 0 0
\(82\) −1.00000 + 1.00000i −0.110432 + 0.110432i
\(83\) 2.82843 2.82843i 0.310460 0.310460i −0.534628 0.845088i \(-0.679548\pi\)
0.845088 + 0.534628i \(0.179548\pi\)
\(84\) 0 0
\(85\) −8.00000 4.00000i −0.867722 0.433861i
\(86\) 11.3137i 1.21999i
\(87\) 0 0
\(88\) −6.00000 6.00000i −0.639602 0.639602i
\(89\) 12.7279 1.34916 0.674579 0.738203i \(-0.264325\pi\)
0.674579 + 0.738203i \(0.264325\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) −2.82843 2.82843i −0.294884 0.294884i
\(93\) 0 0
\(94\) 8.00000i 0.825137i
\(95\) 0 0
\(96\) 0 0
\(97\) −11.0000 + 11.0000i −1.11688 + 1.11688i −0.124684 + 0.992196i \(0.539792\pi\)
−0.992196 + 0.124684i \(0.960208\pi\)
\(98\) −0.707107 + 0.707107i −0.0714286 + 0.0714286i
\(99\) 0 0
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) 15.5563i 1.54791i 0.633238 + 0.773957i \(0.281726\pi\)
−0.633238 + 0.773957i \(0.718274\pi\)
\(102\) 0 0
\(103\) 10.0000 + 10.0000i 0.985329 + 0.985329i 0.999894 0.0145647i \(-0.00463624\pi\)
−0.0145647 + 0.999894i \(0.504636\pi\)
\(104\) −4.24264 −0.416025
\(105\) 0 0
\(106\) −4.00000 −0.388514
\(107\) −2.82843 2.82843i −0.273434 0.273434i 0.557047 0.830481i \(-0.311934\pi\)
−0.830481 + 0.557047i \(0.811934\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 2.82843 5.65685i 0.269680 0.539360i
\(111\) 0 0
\(112\) −2.00000 + 2.00000i −0.188982 + 0.188982i
\(113\) −9.89949 + 9.89949i −0.931266 + 0.931266i −0.997785 0.0665190i \(-0.978811\pi\)
0.0665190 + 0.997785i \(0.478811\pi\)
\(114\) 0 0
\(115\) 4.00000 8.00000i 0.373002 0.746004i
\(116\) 4.24264i 0.393919i
\(117\) 0 0
\(118\) 6.00000 + 6.00000i 0.552345 + 0.552345i
\(119\) 11.3137 1.03713
\(120\) 0 0
\(121\) 3.00000 0.272727
\(122\) −5.65685 5.65685i −0.512148 0.512148i
\(123\) 0 0
\(124\) 4.00000i 0.359211i
\(125\) 6.36396 9.19239i 0.569210 0.822192i
\(126\) 0 0
\(127\) 10.0000 10.0000i 0.887357 0.887357i −0.106912 0.994268i \(-0.534096\pi\)
0.994268 + 0.106912i \(0.0340963\pi\)
\(128\) 2.12132 2.12132i 0.187500 0.187500i
\(129\) 0 0
\(130\) −1.00000 3.00000i −0.0877058 0.263117i
\(131\) 14.1421i 1.23560i −0.786334 0.617802i \(-0.788023\pi\)
0.786334 0.617802i \(-0.211977\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −5.65685 −0.488678
\(135\) 0 0
\(136\) 12.0000 1.02899
\(137\) −7.07107 7.07107i −0.604122 0.604122i 0.337282 0.941404i \(-0.390493\pi\)
−0.941404 + 0.337282i \(0.890493\pi\)
\(138\) 0 0
\(139\) 12.0000i 1.01783i −0.860818 0.508913i \(-0.830047\pi\)
0.860818 0.508913i \(-0.169953\pi\)
\(140\) 5.65685 + 2.82843i 0.478091 + 0.239046i
\(141\) 0 0
\(142\) −4.00000 + 4.00000i −0.335673 + 0.335673i
\(143\) −2.82843 + 2.82843i −0.236525 + 0.236525i
\(144\) 0 0
\(145\) −9.00000 + 3.00000i −0.747409 + 0.249136i
\(146\) 1.41421i 0.117041i
\(147\) 0 0
\(148\) −1.00000 1.00000i −0.0821995 0.0821995i
\(149\) 4.24264 0.347571 0.173785 0.984784i \(-0.444400\pi\)
0.173785 + 0.984784i \(0.444400\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 8.00000i 0.644658i
\(155\) −8.48528 + 2.82843i −0.681554 + 0.227185i
\(156\) 0 0
\(157\) −5.00000 + 5.00000i −0.399043 + 0.399043i −0.877896 0.478852i \(-0.841053\pi\)
0.478852 + 0.877896i \(0.341053\pi\)
\(158\) 8.48528 8.48528i 0.675053 0.675053i
\(159\) 0 0
\(160\) 10.0000 + 5.00000i 0.790569 + 0.395285i
\(161\) 11.3137i 0.891645i
\(162\) 0 0
\(163\) −8.00000 8.00000i −0.626608 0.626608i 0.320605 0.947213i \(-0.396114\pi\)
−0.947213 + 0.320605i \(0.896114\pi\)
\(164\) −1.41421 −0.110432
\(165\) 0 0
\(166\) −4.00000 −0.310460
\(167\) 14.1421 + 14.1421i 1.09435 + 1.09435i 0.995058 + 0.0992931i \(0.0316581\pi\)
0.0992931 + 0.995058i \(0.468342\pi\)
\(168\) 0 0
\(169\) 11.0000i 0.846154i
\(170\) 2.82843 + 8.48528i 0.216930 + 0.650791i
\(171\) 0 0
\(172\) −8.00000 + 8.00000i −0.609994 + 0.609994i
\(173\) −9.89949 + 9.89949i −0.752645 + 0.752645i −0.974972 0.222327i \(-0.928635\pi\)
0.222327 + 0.974972i \(0.428635\pi\)
\(174\) 0 0
\(175\) −2.00000 + 14.0000i −0.151186 + 1.05830i
\(176\) 2.82843i 0.213201i
\(177\) 0 0
\(178\) −9.00000 9.00000i −0.674579 0.674579i
\(179\) −25.4558 −1.90266 −0.951330 0.308175i \(-0.900282\pi\)
−0.951330 + 0.308175i \(0.900282\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 2.82843 + 2.82843i 0.209657 + 0.209657i
\(183\) 0 0
\(184\) 12.0000i 0.884652i
\(185\) 1.41421 2.82843i 0.103975 0.207950i
\(186\) 0 0
\(187\) 8.00000 8.00000i 0.585018 0.585018i
\(188\) 5.65685 5.65685i 0.412568 0.412568i
\(189\) 0 0
\(190\) 0 0
\(191\) 22.6274i 1.63726i −0.574320 0.818631i \(-0.694733\pi\)
0.574320 0.818631i \(-0.305267\pi\)
\(192\) 0 0
\(193\) 1.00000 + 1.00000i 0.0719816 + 0.0719816i 0.742181 0.670199i \(-0.233791\pi\)
−0.670199 + 0.742181i \(0.733791\pi\)
\(194\) 15.5563 1.11688
\(195\) 0 0
\(196\) −1.00000 −0.0714286
\(197\) 9.89949 + 9.89949i 0.705310 + 0.705310i 0.965545 0.260235i \(-0.0838002\pi\)
−0.260235 + 0.965545i \(0.583800\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −2.12132 + 14.8492i −0.150000 + 1.05000i
\(201\) 0 0
\(202\) 11.0000 11.0000i 0.773957 0.773957i
\(203\) 8.48528 8.48528i 0.595550 0.595550i
\(204\) 0 0
\(205\) −1.00000 3.00000i −0.0698430 0.209529i
\(206\) 14.1421i 0.985329i
\(207\) 0 0
\(208\) 1.00000 + 1.00000i 0.0693375 + 0.0693375i
\(209\) 0 0
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) −2.82843 2.82843i −0.194257 0.194257i
\(213\) 0 0
\(214\) 4.00000i 0.273434i
\(215\) −22.6274 11.3137i −1.54318 0.771589i
\(216\) 0 0
\(217\) 8.00000 8.00000i 0.543075 0.543075i
\(218\) 0 0
\(219\) 0 0
\(220\) 6.00000 2.00000i 0.404520 0.134840i
\(221\) 5.65685i 0.380521i
\(222\) 0 0
\(223\) 10.0000 + 10.0000i 0.669650 + 0.669650i 0.957635 0.287985i \(-0.0929854\pi\)
−0.287985 + 0.957635i \(0.592985\pi\)
\(224\) −14.1421 −0.944911
\(225\) 0 0
\(226\) 14.0000 0.931266
\(227\) 5.65685 + 5.65685i 0.375459 + 0.375459i 0.869461 0.494002i \(-0.164466\pi\)
−0.494002 + 0.869461i \(0.664466\pi\)
\(228\) 0 0
\(229\) 6.00000i 0.396491i 0.980152 + 0.198246i \(0.0635244\pi\)
−0.980152 + 0.198246i \(0.936476\pi\)
\(230\) −8.48528 + 2.82843i −0.559503 + 0.186501i
\(231\) 0 0
\(232\) 9.00000 9.00000i 0.590879 0.590879i
\(233\) 2.82843 2.82843i 0.185296 0.185296i −0.608363 0.793659i \(-0.708173\pi\)
0.793659 + 0.608363i \(0.208173\pi\)
\(234\) 0 0
\(235\) 16.0000 + 8.00000i 1.04372 + 0.521862i
\(236\) 8.48528i 0.552345i
\(237\) 0 0
\(238\) −8.00000 8.00000i −0.518563 0.518563i
\(239\) 16.9706 1.09773 0.548867 0.835910i \(-0.315059\pi\)
0.548867 + 0.835910i \(0.315059\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) −2.12132 2.12132i −0.136364 0.136364i
\(243\) 0 0
\(244\) 8.00000i 0.512148i
\(245\) −0.707107 2.12132i −0.0451754 0.135526i
\(246\) 0 0
\(247\) 0 0
\(248\) 8.48528 8.48528i 0.538816 0.538816i
\(249\) 0 0
\(250\) −11.0000 + 2.00000i −0.695701 + 0.126491i
\(251\) 19.7990i 1.24970i 0.780744 + 0.624851i \(0.214840\pi\)
−0.780744 + 0.624851i \(0.785160\pi\)
\(252\) 0 0
\(253\) 8.00000 + 8.00000i 0.502956 + 0.502956i
\(254\) −14.1421 −0.887357
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) 1.41421 + 1.41421i 0.0882162 + 0.0882162i 0.749838 0.661622i \(-0.230131\pi\)
−0.661622 + 0.749838i \(0.730131\pi\)
\(258\) 0 0
\(259\) 4.00000i 0.248548i
\(260\) 1.41421 2.82843i 0.0877058 0.175412i
\(261\) 0 0
\(262\) −10.0000 + 10.0000i −0.617802 + 0.617802i
\(263\) 2.82843 2.82843i 0.174408 0.174408i −0.614505 0.788913i \(-0.710644\pi\)
0.788913 + 0.614505i \(0.210644\pi\)
\(264\) 0 0
\(265\) 4.00000 8.00000i 0.245718 0.491436i
\(266\) 0 0
\(267\) 0 0
\(268\) −4.00000 4.00000i −0.244339 0.244339i
\(269\) 12.7279 0.776035 0.388018 0.921652i \(-0.373160\pi\)
0.388018 + 0.921652i \(0.373160\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) −2.82843 2.82843i −0.171499 0.171499i
\(273\) 0 0
\(274\) 10.0000i 0.604122i
\(275\) 8.48528 + 11.3137i 0.511682 + 0.682242i
\(276\) 0 0
\(277\) −11.0000 + 11.0000i −0.660926 + 0.660926i −0.955598 0.294672i \(-0.904789\pi\)
0.294672 + 0.955598i \(0.404789\pi\)
\(278\) −8.48528 + 8.48528i −0.508913 + 0.508913i
\(279\) 0 0
\(280\) −6.00000 18.0000i −0.358569 1.07571i
\(281\) 9.89949i 0.590554i −0.955412 0.295277i \(-0.904588\pi\)
0.955412 0.295277i \(-0.0954120\pi\)
\(282\) 0 0
\(283\) −8.00000 8.00000i −0.475551 0.475551i 0.428155 0.903705i \(-0.359164\pi\)
−0.903705 + 0.428155i \(0.859164\pi\)
\(284\) −5.65685 −0.335673
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) 2.82843 + 2.82843i 0.166957 + 0.166957i
\(288\) 0 0
\(289\) 1.00000i 0.0588235i
\(290\) 8.48528 + 4.24264i 0.498273 + 0.249136i
\(291\) 0 0
\(292\) 1.00000 1.00000i 0.0585206 0.0585206i
\(293\) −9.89949 + 9.89949i −0.578335 + 0.578335i −0.934444 0.356110i \(-0.884103\pi\)
0.356110 + 0.934444i \(0.384103\pi\)
\(294\) 0 0
\(295\) −18.0000 + 6.00000i −1.04800 + 0.349334i
\(296\) 4.24264i 0.246598i
\(297\) 0 0
\(298\) −3.00000 3.00000i −0.173785 0.173785i
\(299\) 5.65685 0.327144
\(300\) 0 0
\(301\) 32.0000 1.84445
\(302\) −5.65685 5.65685i −0.325515 0.325515i
\(303\) 0 0
\(304\) 0 0
\(305\) 16.9706 5.65685i 0.971732 0.323911i
\(306\) 0 0
\(307\) −8.00000 + 8.00000i −0.456584 + 0.456584i −0.897532 0.440948i \(-0.854642\pi\)
0.440948 + 0.897532i \(0.354642\pi\)
\(308\) −5.65685 + 5.65685i −0.322329 + 0.322329i
\(309\) 0 0
\(310\) 8.00000 + 4.00000i 0.454369 + 0.227185i
\(311\) 11.3137i 0.641542i 0.947157 + 0.320771i \(0.103942\pi\)
−0.947157 + 0.320771i \(0.896058\pi\)
\(312\) 0 0
\(313\) 19.0000 + 19.0000i 1.07394 + 1.07394i 0.997038 + 0.0769051i \(0.0245038\pi\)
0.0769051 + 0.997038i \(0.475496\pi\)
\(314\) 7.07107 0.399043
\(315\) 0 0
\(316\) 12.0000 0.675053
\(317\) −19.7990 19.7990i −1.11202 1.11202i −0.992877 0.119145i \(-0.961985\pi\)
−0.119145 0.992877i \(-0.538015\pi\)
\(318\) 0 0
\(319\) 12.0000i 0.671871i
\(320\) −4.94975 14.8492i −0.276699 0.830098i
\(321\) 0 0
\(322\) 8.00000 8.00000i 0.445823 0.445823i
\(323\) 0 0
\(324\) 0 0
\(325\) 7.00000 + 1.00000i 0.388290 + 0.0554700i
\(326\) 11.3137i 0.626608i
\(327\) 0 0
\(328\) 3.00000 + 3.00000i 0.165647 + 0.165647i
\(329\) −22.6274 −1.24749
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) −2.82843 2.82843i −0.155230 0.155230i
\(333\) 0 0
\(334\) 20.0000i 1.09435i
\(335\) 5.65685 11.3137i 0.309067 0.618134i
\(336\) 0 0
\(337\) −5.00000 + 5.00000i −0.272367 + 0.272367i −0.830053 0.557685i \(-0.811690\pi\)
0.557685 + 0.830053i \(0.311690\pi\)
\(338\) −7.77817 + 7.77817i −0.423077 + 0.423077i
\(339\) 0 0
\(340\) −4.00000 + 8.00000i −0.216930 + 0.433861i
\(341\) 11.3137i 0.612672i
\(342\) 0 0
\(343\) −12.0000 12.0000i −0.647939 0.647939i
\(344\) 33.9411 1.82998
\(345\) 0 0
\(346\) 14.0000 0.752645
\(347\) −11.3137 11.3137i −0.607352 0.607352i 0.334901 0.942253i \(-0.391297\pi\)
−0.942253 + 0.334901i \(0.891297\pi\)
\(348\) 0 0
\(349\) 24.0000i 1.28469i −0.766415 0.642345i \(-0.777962\pi\)
0.766415 0.642345i \(-0.222038\pi\)
\(350\) 11.3137 8.48528i 0.604743 0.453557i
\(351\) 0 0
\(352\) −10.0000 + 10.0000i −0.533002 + 0.533002i
\(353\) 2.82843 2.82843i 0.150542 0.150542i −0.627818 0.778360i \(-0.716052\pi\)
0.778360 + 0.627818i \(0.216052\pi\)
\(354\) 0 0
\(355\) −4.00000 12.0000i −0.212298 0.636894i
\(356\) 12.7279i 0.674579i
\(357\) 0 0
\(358\) 18.0000 + 18.0000i 0.951330 + 0.951330i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 11.3137 + 11.3137i 0.594635 + 0.594635i
\(363\) 0 0
\(364\) 4.00000i 0.209657i
\(365\) 2.82843 + 1.41421i 0.148047 + 0.0740233i
\(366\) 0 0
\(367\) −2.00000 + 2.00000i −0.104399 + 0.104399i −0.757377 0.652978i \(-0.773519\pi\)
0.652978 + 0.757377i \(0.273519\pi\)
\(368\) 2.82843 2.82843i 0.147442 0.147442i
\(369\) 0 0
\(370\) −3.00000 + 1.00000i −0.155963 + 0.0519875i
\(371\) 11.3137i 0.587378i
\(372\) 0 0
\(373\) −17.0000 17.0000i −0.880227 0.880227i 0.113331 0.993557i \(-0.463848\pi\)
−0.993557 + 0.113331i \(0.963848\pi\)
\(374\) −11.3137 −0.585018
\(375\) 0 0
\(376\) −24.0000 −1.23771
\(377\) −4.24264 4.24264i −0.218507 0.218507i
\(378\) 0 0
\(379\) 36.0000i 1.84920i 0.380945 + 0.924598i \(0.375599\pi\)
−0.380945 + 0.924598i \(0.624401\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −16.0000 + 16.0000i −0.818631 + 0.818631i
\(383\) −22.6274 + 22.6274i −1.15621 + 1.15621i −0.170923 + 0.985284i \(0.554675\pi\)
−0.985284 + 0.170923i \(0.945325\pi\)
\(384\) 0 0
\(385\) −16.0000 8.00000i −0.815436 0.407718i
\(386\) 1.41421i 0.0719816i
\(387\) 0 0
\(388\) 11.0000 + 11.0000i 0.558440 + 0.558440i
\(389\) −4.24264 −0.215110 −0.107555 0.994199i \(-0.534302\pi\)
−0.107555 + 0.994199i \(0.534302\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 2.12132 + 2.12132i 0.107143 + 0.107143i
\(393\) 0 0
\(394\) 14.0000i 0.705310i
\(395\) 8.48528 + 25.4558i 0.426941 + 1.28082i
\(396\) 0 0
\(397\) 19.0000 19.0000i 0.953583 0.953583i −0.0453868 0.998969i \(-0.514452\pi\)
0.998969 + 0.0453868i \(0.0144520\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 4.00000 3.00000i 0.200000 0.150000i
\(401\) 24.0416i 1.20058i 0.799782 + 0.600291i \(0.204949\pi\)
−0.799782 + 0.600291i \(0.795051\pi\)
\(402\) 0 0
\(403\) −4.00000 4.00000i −0.199254 0.199254i
\(404\) 15.5563 0.773957
\(405\) 0 0
\(406\) −12.0000 −0.595550
\(407\) 2.82843 + 2.82843i 0.140200 + 0.140200i
\(408\) 0 0
\(409\) 24.0000i 1.18672i 0.804936 + 0.593362i \(0.202200\pi\)
−0.804936 + 0.593362i \(0.797800\pi\)
\(410\) −1.41421 + 2.82843i −0.0698430 + 0.139686i
\(411\) 0 0
\(412\) 10.0000 10.0000i 0.492665 0.492665i
\(413\) 16.9706 16.9706i 0.835067 0.835067i
\(414\) 0 0
\(415\) 4.00000 8.00000i 0.196352 0.392705i
\(416\) 7.07107i 0.346688i
\(417\) 0 0
\(418\) 0 0
\(419\) −8.48528 −0.414533 −0.207267 0.978285i \(-0.566457\pi\)
−0.207267 + 0.978285i \(0.566457\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 2.82843 + 2.82843i 0.137686 + 0.137686i
\(423\) 0 0
\(424\) 12.0000i 0.582772i
\(425\) −19.7990 2.82843i −0.960392 0.137199i
\(426\) 0 0
\(427\) −16.0000 + 16.0000i −0.774294 + 0.774294i
\(428\) −2.82843 + 2.82843i −0.136717 + 0.136717i
\(429\) 0 0
\(430\) 8.00000 + 24.0000i 0.385794 + 1.15738i
\(431\) 5.65685i 0.272481i −0.990676 0.136241i \(-0.956498\pi\)
0.990676 0.136241i \(-0.0435020\pi\)
\(432\) 0 0
\(433\) −17.0000 17.0000i −0.816968 0.816968i 0.168700 0.985668i \(-0.446043\pi\)
−0.985668 + 0.168700i \(0.946043\pi\)
\(434\) −11.3137 −0.543075
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 24.0000i 1.14546i −0.819745 0.572729i \(-0.805885\pi\)
0.819745 0.572729i \(-0.194115\pi\)
\(440\) −16.9706 8.48528i −0.809040 0.404520i
\(441\) 0 0
\(442\) −4.00000 + 4.00000i −0.190261 + 0.190261i
\(443\) 28.2843 28.2843i 1.34383 1.34383i 0.451612 0.892215i \(-0.350849\pi\)
0.892215 0.451612i \(-0.149151\pi\)
\(444\) 0 0
\(445\) 27.0000 9.00000i 1.27992 0.426641i
\(446\) 14.1421i 0.669650i
\(447\) 0 0
\(448\) 14.0000 + 14.0000i 0.661438 + 0.661438i
\(449\) 12.7279 0.600668 0.300334 0.953834i \(-0.402902\pi\)
0.300334 + 0.953834i \(0.402902\pi\)
\(450\) 0 0
\(451\) 4.00000 0.188353
\(452\) 9.89949 + 9.89949i 0.465633 + 0.465633i
\(453\) 0 0
\(454\) 8.00000i 0.375459i
\(455\) −8.48528 + 2.82843i −0.397796 + 0.132599i
\(456\) 0 0
\(457\) 25.0000 25.0000i 1.16945 1.16945i 0.187112 0.982339i \(-0.440087\pi\)
0.982339 0.187112i \(-0.0599128\pi\)
\(458\) 4.24264 4.24264i 0.198246 0.198246i
\(459\) 0 0
\(460\) −8.00000 4.00000i −0.373002 0.186501i
\(461\) 9.89949i 0.461065i −0.973065 0.230533i \(-0.925953\pi\)
0.973065 0.230533i \(-0.0740469\pi\)
\(462\) 0 0
\(463\) 10.0000 + 10.0000i 0.464739 + 0.464739i 0.900205 0.435466i \(-0.143416\pi\)
−0.435466 + 0.900205i \(0.643416\pi\)
\(464\) −4.24264 −0.196960
\(465\) 0 0
\(466\) −4.00000 −0.185296
\(467\) −2.82843 2.82843i −0.130884 0.130884i 0.638630 0.769514i \(-0.279501\pi\)
−0.769514 + 0.638630i \(0.779501\pi\)
\(468\) 0 0
\(469\) 16.0000i 0.738811i
\(470\) −5.65685 16.9706i −0.260931 0.782794i
\(471\) 0 0
\(472\) 18.0000 18.0000i 0.828517 0.828517i
\(473\) 22.6274 22.6274i 1.04041 1.04041i
\(474\) 0 0
\(475\) 0 0
\(476\) 11.3137i 0.518563i
\(477\) 0 0
\(478\) −12.0000 12.0000i −0.548867 0.548867i
\(479\) −16.9706 −0.775405 −0.387702 0.921785i \(-0.626731\pi\)
−0.387702 + 0.921785i \(0.626731\pi\)
\(480\) 0 0
\(481\) 2.00000 0.0911922
\(482\) 7.07107 + 7.07107i 0.322078 + 0.322078i
\(483\) 0 0
\(484\) 3.00000i 0.136364i
\(485\) −15.5563 + 31.1127i −0.706377 + 1.41275i
\(486\) 0 0
\(487\) 10.0000 10.0000i 0.453143 0.453143i −0.443253 0.896396i \(-0.646176\pi\)
0.896396 + 0.443253i \(0.146176\pi\)
\(488\) −16.9706 + 16.9706i −0.768221 + 0.768221i
\(489\) 0 0
\(490\) −1.00000 + 2.00000i −0.0451754 + 0.0903508i
\(491\) 14.1421i 0.638226i −0.947717 0.319113i \(-0.896615\pi\)
0.947717 0.319113i \(-0.103385\pi\)
\(492\) 0 0
\(493\) 12.0000 + 12.0000i 0.540453 + 0.540453i
\(494\) 0 0
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 11.3137 + 11.3137i 0.507489 + 0.507489i
\(498\) 0 0
\(499\) 24.0000i 1.07439i 0.843459 + 0.537194i \(0.180516\pi\)
−0.843459 + 0.537194i \(0.819484\pi\)
\(500\) −9.19239 6.36396i −0.411096 0.284605i
\(501\) 0 0
\(502\) 14.0000 14.0000i 0.624851 0.624851i
\(503\) −22.6274 + 22.6274i −1.00891 + 1.00891i −0.00894668 + 0.999960i \(0.502848\pi\)
−0.999960 + 0.00894668i \(0.997152\pi\)
\(504\) 0 0
\(505\) 11.0000 + 33.0000i 0.489494 + 1.46848i
\(506\) 11.3137i 0.502956i
\(507\) 0 0
\(508\) −10.0000 10.0000i −0.443678 0.443678i
\(509\) 4.24264 0.188052 0.0940259 0.995570i \(-0.470026\pi\)
0.0940259 + 0.995570i \(0.470026\pi\)
\(510\) 0 0
\(511\) −4.00000 −0.176950
\(512\) 7.77817 + 7.77817i 0.343750 + 0.343750i
\(513\) 0 0
\(514\) 2.00000i 0.0882162i
\(515\) 28.2843 + 14.1421i 1.24635 + 0.623177i
\(516\) 0 0
\(517\) −16.0000 + 16.0000i −0.703679 + 0.703679i
\(518\) 2.82843 2.82843i 0.124274 0.124274i
\(519\) 0 0
\(520\) −9.00000 + 3.00000i −0.394676 + 0.131559i
\(521\) 18.3848i 0.805452i −0.915321 0.402726i \(-0.868063\pi\)
0.915321 0.402726i \(-0.131937\pi\)
\(522\) 0 0
\(523\) −8.00000 8.00000i −0.349816 0.349816i 0.510225 0.860041i \(-0.329562\pi\)
−0.860041 + 0.510225i \(0.829562\pi\)
\(524\) −14.1421 −0.617802
\(525\) 0 0
\(526\) −4.00000 −0.174408
\(527\) 11.3137 + 11.3137i 0.492833 + 0.492833i
\(528\) 0 0
\(529\) 7.00000i 0.304348i
\(530\) −8.48528 + 2.82843i −0.368577 + 0.122859i
\(531\) 0 0
\(532\) 0 0
\(533\) 1.41421 1.41421i 0.0612564 0.0612564i
\(534\) 0 0
\(535\) −8.00000 4.00000i −0.345870 0.172935i
\(536\) 16.9706i 0.733017i
\(537\) 0 0
\(538\) −9.00000 9.00000i −0.388018 0.388018i
\(539\) 2.82843 0.121829
\(540\) 0 0
\(541\) −16.0000 −0.687894 −0.343947 0.938989i \(-0.611764\pi\)
−0.343947 + 0.938989i \(0.611764\pi\)
\(542\) 11.3137 + 11.3137i 0.485965 + 0.485965i
\(543\) 0 0
\(544\) 20.0000i 0.857493i
\(545\) 0 0
\(546\) 0 0
\(547\) −20.0000 + 20.0000i −0.855138 + 0.855138i −0.990761 0.135622i \(-0.956697\pi\)
0.135622 + 0.990761i \(0.456697\pi\)
\(548\) −7.07107 + 7.07107i −0.302061 + 0.302061i
\(549\) 0 0
\(550\) 2.00000 14.0000i 0.0852803 0.596962i
\(551\) 0 0
\(552\) 0 0
\(553\) −24.0000 24.0000i −1.02058 1.02058i
\(554\) 15.5563 0.660926
\(555\) 0 0
\(556\) −12.0000 −0.508913
\(557\) −2.82843 2.82843i −0.119844 0.119844i 0.644641 0.764485i \(-0.277007\pi\)
−0.764485 + 0.644641i \(0.777007\pi\)
\(558\) 0 0
\(559\) 16.0000i 0.676728i
\(560\) −2.82843 + 5.65685i −0.119523 + 0.239046i
\(561\) 0 0
\(562\) −7.00000 + 7.00000i −0.295277 + 0.295277i
\(563\) 28.2843 28.2843i 1.19204 1.19204i 0.215546 0.976494i \(-0.430847\pi\)
0.976494 0.215546i \(-0.0691532\pi\)
\(564\) 0 0
\(565\) −14.0000 + 28.0000i −0.588984 + 1.17797i
\(566\) 11.3137i 0.475551i
\(567\) 0 0
\(568\) 12.0000 + 12.0000i 0.503509 + 0.503509i
\(569\) −29.6985 −1.24503 −0.622513 0.782610i \(-0.713888\pi\)
−0.622513 + 0.782610i \(0.713888\pi\)
\(570\) 0 0
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 2.82843 + 2.82843i 0.118262 + 0.118262i
\(573\) 0 0
\(574\) 4.00000i 0.166957i
\(575\) 2.82843 19.7990i 0.117954 0.825675i
\(576\) 0 0
\(577\) −17.0000 + 17.0000i −0.707719 + 0.707719i −0.966055 0.258336i \(-0.916826\pi\)
0.258336 + 0.966055i \(0.416826\pi\)
\(578\) −0.707107 + 0.707107i −0.0294118 + 0.0294118i
\(579\) 0 0
\(580\) 3.00000 + 9.00000i 0.124568 + 0.373705i
\(581\) 11.3137i 0.469372i
\(582\) 0 0
\(583\) 8.00000 + 8.00000i 0.331326 + 0.331326i
\(584\) −4.24264 −0.175562
\(585\) 0 0
\(586\) 14.0000 0.578335
\(587\) −19.7990 19.7990i −0.817192 0.817192i 0.168508 0.985700i \(-0.446105\pi\)
−0.985700 + 0.168508i \(0.946105\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 16.9706 + 8.48528i 0.698667 + 0.349334i
\(591\) 0 0
\(592\) 1.00000 1.00000i 0.0410997 0.0410997i
\(593\) −9.89949 + 9.89949i −0.406524 + 0.406524i −0.880524 0.474001i \(-0.842809\pi\)
0.474001 + 0.880524i \(0.342809\pi\)
\(594\) 0 0
\(595\) 24.0000 8.00000i 0.983904 0.327968i
\(596\) 4.24264i 0.173785i
\(597\) 0 0
\(598\) −4.00000 4.00000i −0.163572 0.163572i
\(599\) 16.9706 0.693398 0.346699 0.937976i \(-0.387302\pi\)
0.346699 + 0.937976i \(0.387302\pi\)
\(600\) 0 0
\(601\) 8.00000 0.326327 0.163163 0.986599i \(-0.447830\pi\)
0.163163 + 0.986599i \(0.447830\pi\)
\(602\) −22.6274 22.6274i −0.922225 0.922225i
\(603\) 0 0
\(604\) 8.00000i 0.325515i
\(605\) 6.36396 2.12132i 0.258732 0.0862439i
\(606\) 0 0
\(607\) 22.0000 22.0000i 0.892952 0.892952i −0.101848 0.994800i \(-0.532475\pi\)
0.994800 + 0.101848i \(0.0324754\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −16.0000 8.00000i −0.647821 0.323911i
\(611\) 11.3137i 0.457704i
\(612\) 0 0
\(613\) 1.00000 + 1.00000i 0.0403896 + 0.0403896i 0.727013 0.686624i \(-0.240908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) 11.3137 0.456584
\(615\) 0 0
\(616\) 24.0000 0.966988
\(617\) 14.1421 + 14.1421i 0.569341 + 0.569341i 0.931944 0.362603i \(-0.118112\pi\)
−0.362603 + 0.931944i \(0.618112\pi\)
\(618\) 0 0
\(619\) 12.0000i 0.482321i 0.970485 + 0.241160i \(0.0775280\pi\)
−0.970485 + 0.241160i \(0.922472\pi\)
\(620\) 2.82843 + 8.48528i 0.113592 + 0.340777i
\(621\) 0 0
\(622\) 8.00000 8.00000i 0.320771 0.320771i
\(623\) −25.4558 + 25.4558i −1.01987 + 1.01987i
\(624\) 0 0
\(625\) 7.00000 24.0000i 0.280000 0.960000i
\(626\) 26.8701i 1.07394i
\(627\) 0 0
\(628\) 5.00000 + 5.00000i 0.199522 + 0.199522i
\(629\) −5.65685 −0.225554
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) −25.4558 25.4558i −1.01258 1.01258i
\(633\) 0 0
\(634\) 28.0000i 1.11202i
\(635\) 14.1421 28.2843i 0.561214 1.12243i
\(636\) 0 0
\(637\) 1.00000 1.00000i 0.0396214 0.0396214i
\(638\) −8.48528 + 8.48528i −0.335936 + 0.335936i
\(639\) 0 0
\(640\) 3.00000 6.00000i 0.118585 0.237171i
\(641\) 15.5563i 0.614439i 0.951639 + 0.307219i \(0.0993986\pi\)
−0.951639 + 0.307219i \(0.900601\pi\)
\(642\) 0 0
\(643\) 28.0000 + 28.0000i 1.10421 + 1.10421i 0.993897 + 0.110316i \(0.0351862\pi\)
0.110316 + 0.993897i \(0.464814\pi\)
\(644\) 11.3137 0.445823
\(645\) 0 0
\(646\) 0 0
\(647\) −28.2843 28.2843i −1.11197 1.11197i −0.992884 0.119085i \(-0.962004\pi\)
−0.119085 0.992884i \(-0.537996\pi\)
\(648\) 0 0
\(649\) 24.0000i 0.942082i
\(650\) −4.24264 5.65685i −0.166410 0.221880i
\(651\) 0 0
\(652\) −8.00000 + 8.00000i −0.313304 + 0.313304i
\(653\) 2.82843 2.82843i 0.110685 0.110685i −0.649595 0.760280i \(-0.725062\pi\)
0.760280 + 0.649595i \(0.225062\pi\)
\(654\) 0 0
\(655\) −10.0000 30.0000i −0.390732 1.17220i
\(656\) 1.41421i 0.0552158i
\(657\) 0 0
\(658\) 16.0000 + 16.0000i 0.623745 + 0.623745i
\(659\) 8.48528 0.330540 0.165270 0.986248i \(-0.447151\pi\)
0.165270 + 0.986248i \(0.447151\pi\)
\(660\) 0 0
\(661\) −40.0000 −1.55582 −0.777910 0.628376i \(-0.783720\pi\)
−0.777910 + 0.628376i \(0.783720\pi\)
\(662\) −5.65685 5.65685i −0.219860 0.219860i
\(663\) 0 0
\(664\) 12.0000i 0.465690i
\(665\) 0 0
\(666\) 0 0
\(667\) −12.0000 + 12.0000i −0.464642 + 0.464642i
\(668\) 14.1421 14.1421i 0.547176 0.547176i
\(669\) 0 0
\(670\) −12.0000 + 4.00000i −0.463600 + 0.154533i
\(671\) 22.6274i 0.873522i
\(672\) 0 0
\(673\) 1.00000 + 1.00000i 0.0385472 + 0.0385472i 0.726118 0.687570i \(-0.241323\pi\)
−0.687570 + 0.726118i \(0.741323\pi\)
\(674\) 7.07107 0.272367
\(675\) 0 0
\(676\) −11.0000 −0.423077
\(677\) 31.1127 + 31.1127i 1.19576 + 1.19576i 0.975425 + 0.220334i \(0.0707146\pi\)
0.220334 + 0.975425i \(0.429285\pi\)
\(678\) 0 0
\(679\) 44.0000i 1.68857i
\(680\) 25.4558 8.48528i 0.976187 0.325396i
\(681\) 0 0
\(682\) −8.00000 + 8.00000i −0.306336 + 0.306336i
\(683\) 2.82843 2.82843i 0.108227 0.108227i −0.650920 0.759147i \(-0.725617\pi\)
0.759147 + 0.650920i \(0.225617\pi\)
\(684\) 0 0
\(685\) −20.0000 10.0000i −0.764161 0.382080i
\(686\) 16.9706i 0.647939i
\(687\) 0 0
\(688\) −8.00000 8.00000i −0.304997 0.304997i
\(689\) 5.65685 0.215509
\(690\) 0 0
\(691\) 8.00000 0.304334 0.152167 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) 9.89949 + 9.89949i 0.376322 + 0.376322i
\(693\) 0 0
\(694\) 16.0000i 0.607352i
\(695\) −8.48528 25.4558i −0.321865 0.965595i
\(696\) 0 0
\(697\) −4.00000 + 4.00000i −0.151511 + 0.151511i
\(698\) −16.9706 + 16.9706i −0.642345 + 0.642345i
\(699\) 0 0
\(700\) 14.0000 + 2.00000i 0.529150 + 0.0755929i
\(701\) 7.07107i 0.267071i 0.991044 + 0.133535i \(0.0426329\pi\)
−0.991044 + 0.133535i \(0.957367\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 19.7990 0.746203
\(705\) 0 0
\(706\) −4.00000 −0.150542
\(707\) −31.1127 31.1127i −1.17011 1.17011i
\(708\) 0 0
\(709\) 6.00000i 0.225335i −0.993633 0.112667i \(-0.964061\pi\)
0.993633 0.112667i \(-0.0359394\pi\)
\(710\) −5.65685 + 11.3137i −0.212298 + 0.424596i
\(711\) 0 0
\(712\) −27.0000 + 27.0000i −1.01187 + 1.01187i
\(713\) −11.3137 + 11.3137i −0.423702 + 0.423702i
\(714\) 0 0
\(715\) −4.00000 + 8.00000i −0.149592 + 0.299183i
\(716\) 25.4558i 0.951330i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) −40.0000 −1.48968
\(722\) −13.4350 13.4350i −0.500000 0.500000i
\(723\) 0 0
\(724\) 16.0000i 0.594635i
\(725\) −16.9706 + 12.7279i −0.630271 + 0.472703i
\(726\) 0 0
\(727\) −2.00000 + 2.00000i −0.0741759 + 0.0741759i −0.743221 0.669046i \(-0.766703\pi\)
0.669046 + 0.743221i \(0.266703\pi\)
\(728\) 8.48528 8.48528i 0.314485 0.314485i
\(729\) 0 0
\(730\) −1.00000 3.00000i −0.0370117 0.111035i
\(731\) 45.2548i 1.67381i
\(732\) 0 0
\(733\) 1.00000 + 1.00000i 0.0369358 + 0.0369358i 0.725333 0.688398i \(-0.241686\pi\)
−0.688398 + 0.725333i \(0.741686\pi\)
\(734\) 2.82843 0.104399
\(735\) 0 0
\(736\) 20.0000 0.737210
\(737\) 11.3137 + 11.3137i 0.416746 + 0.416746i
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) −2.82843 1.41421i −0.103975 0.0519875i
\(741\) 0 0
\(742\) 8.00000 8.00000i 0.293689 0.293689i
\(743\) −22.6274 + 22.6274i −0.830119 + 0.830119i −0.987533 0.157413i \(-0.949684\pi\)
0.157413 + 0.987533i \(0.449684\pi\)
\(744\) 0 0
\(745\) 9.00000 3.00000i 0.329734 0.109911i
\(746\) 24.0416i 0.880227i
\(747\) 0 0
\(748\) −8.00000 8.00000i −0.292509 0.292509i
\(749\) 11.3137 0.413394
\(750\) 0 0
\(751\) −4.00000 −0.145962 −0.0729810 0.997333i \(-0.523251\pi\)
−0.0729810 + 0.997333i \(0.523251\pi\)
\(752\) 5.65685 + 5.65685i 0.206284 + 0.206284i
\(753\) 0 0
\(754\) 6.00000i 0.218507i
\(755\) 16.9706 5.65685i 0.617622 0.205874i
\(756\) 0 0
\(757\) 19.0000 19.0000i 0.690567 0.690567i −0.271790 0.962357i \(-0.587616\pi\)
0.962357 + 0.271790i \(0.0876156\pi\)
\(758\) 25.4558 25.4558i 0.924598 0.924598i
\(759\) 0 0
\(760\) 0 0
\(761\) 52.3259i 1.89681i −0.317058 0.948406i \(-0.602695\pi\)
0.317058 0.948406i \(-0.397305\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −22.6274 −0.818631
\(765\) 0 0
\(766\) 32.0000 1.15621
\(767\) −8.48528 8.48528i −0.306386 0.306386i
\(768\) 0 0
\(769\) 24.0000i 0.865462i 0.901523 + 0.432731i \(0.142450\pi\)
−0.901523 + 0.432731i \(0.857550\pi\)
\(770\) 5.65685 + 16.9706i 0.203859 + 0.611577i
\(771\) 0 0
\(772\) 1.00000 1.00000i 0.0359908 0.0359908i
\(773\) 2.82843 2.82843i 0.101731 0.101731i −0.654409 0.756141i \(-0.727083\pi\)
0.756141 + 0.654409i \(0.227083\pi\)
\(774\) 0 0
\(775\) −16.0000 + 12.0000i −0.574737 + 0.431053i
\(776\) 46.6690i 1.67532i
\(777\) 0 0
\(778\) 3.00000 + 3.00000i 0.107555 + 0.107555i
\(779\) 0 0
\(780\) 0 0
\(781\) 16.0000 0.572525
\(782\) 11.3137 + 11.3137i 0.404577 + 0.404577i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) −7.07107 + 14.1421i −0.252377 + 0.504754i
\(786\) 0 0
\(787\) 4.00000 4.00000i 0.142585 0.142585i −0.632211 0.774796i \(-0.717853\pi\)
0.774796 + 0.632211i \(0.217853\pi\)
\(788\) 9.89949 9.89949i 0.352655 0.352655i
\(789\) 0 0
\(790\) 12.0000 24.0000i 0.426941 0.853882i
\(791\) 39.5980i 1.40794i
\(792\) 0 0