Properties

Label 1110.2.d.c.889.1
Level $1110$
Weight $2$
Character 1110.889
Analytic conductor $8.863$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 889.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1110.889
Dual form 1110.2.d.c.889.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} +1.00000 q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} +1.00000 q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(2.00000 - 1.00000i) q^{10} +5.00000 q^{11} -1.00000i q^{12} -1.00000 q^{14} +(-2.00000 + 1.00000i) q^{15} +1.00000 q^{16} -1.00000i q^{17} +1.00000i q^{18} +(-1.00000 - 2.00000i) q^{20} +1.00000 q^{21} -5.00000i q^{22} +4.00000i q^{23} -1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} -1.00000i q^{27} +1.00000i q^{28} +3.00000 q^{29} +(1.00000 + 2.00000i) q^{30} +1.00000 q^{31} -1.00000i q^{32} +5.00000i q^{33} -1.00000 q^{34} +(2.00000 - 1.00000i) q^{35} +1.00000 q^{36} +1.00000i q^{37} +(-2.00000 + 1.00000i) q^{40} -1.00000 q^{41} -1.00000i q^{42} +7.00000i q^{43} -5.00000 q^{44} +(-1.00000 - 2.00000i) q^{45} +4.00000 q^{46} +4.00000i q^{47} +1.00000i q^{48} +6.00000 q^{49} +(4.00000 + 3.00000i) q^{50} +1.00000 q^{51} +3.00000i q^{53} -1.00000 q^{54} +(5.00000 + 10.0000i) q^{55} +1.00000 q^{56} -3.00000i q^{58} +8.00000 q^{59} +(2.00000 - 1.00000i) q^{60} +5.00000 q^{61} -1.00000i q^{62} +1.00000i q^{63} -1.00000 q^{64} +5.00000 q^{66} +4.00000i q^{67} +1.00000i q^{68} -4.00000 q^{69} +(-1.00000 - 2.00000i) q^{70} -6.00000 q^{71} -1.00000i q^{72} +10.0000i q^{73} +1.00000 q^{74} +(-4.00000 - 3.00000i) q^{75} -5.00000i q^{77} +(1.00000 + 2.00000i) q^{80} +1.00000 q^{81} +1.00000i q^{82} -8.00000i q^{83} -1.00000 q^{84} +(2.00000 - 1.00000i) q^{85} +7.00000 q^{86} +3.00000i q^{87} +5.00000i q^{88} -8.00000 q^{89} +(-2.00000 + 1.00000i) q^{90} -4.00000i q^{92} +1.00000i q^{93} +4.00000 q^{94} +1.00000 q^{96} +1.00000i q^{97} -6.00000i q^{98} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{4} + 2q^{5} + 2q^{6} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{4} + 2q^{5} + 2q^{6} - 2q^{9} + 4q^{10} + 10q^{11} - 2q^{14} - 4q^{15} + 2q^{16} - 2q^{20} + 2q^{21} - 2q^{24} - 6q^{25} + 6q^{29} + 2q^{30} + 2q^{31} - 2q^{34} + 4q^{35} + 2q^{36} - 4q^{40} - 2q^{41} - 10q^{44} - 2q^{45} + 8q^{46} + 12q^{49} + 8q^{50} + 2q^{51} - 2q^{54} + 10q^{55} + 2q^{56} + 16q^{59} + 4q^{60} + 10q^{61} - 2q^{64} + 10q^{66} - 8q^{69} - 2q^{70} - 12q^{71} + 2q^{74} - 8q^{75} + 2q^{80} + 2q^{81} - 2q^{84} + 4q^{85} + 14q^{86} - 16q^{89} - 4q^{90} + 8q^{94} + 2q^{96} - 10q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 1.00000 + 2.00000i 0.447214 + 0.894427i
\(6\) 1.00000 0.408248
\(7\) 1.00000i 0.377964i −0.981981 0.188982i \(-0.939481\pi\)
0.981981 0.188982i \(-0.0605189\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 2.00000 1.00000i 0.632456 0.316228i
\(11\) 5.00000 1.50756 0.753778 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −1.00000 −0.267261
\(15\) −2.00000 + 1.00000i −0.516398 + 0.258199i
\(16\) 1.00000 0.250000
\(17\) 1.00000i 0.242536i −0.992620 0.121268i \(-0.961304\pi\)
0.992620 0.121268i \(-0.0386960\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) −1.00000 2.00000i −0.223607 0.447214i
\(21\) 1.00000 0.218218
\(22\) 5.00000i 1.06600i
\(23\) 4.00000i 0.834058i 0.908893 + 0.417029i \(0.136929\pi\)
−0.908893 + 0.417029i \(0.863071\pi\)
\(24\) −1.00000 −0.204124
\(25\) −3.00000 + 4.00000i −0.600000 + 0.800000i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 1.00000i 0.188982i
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 1.00000 + 2.00000i 0.182574 + 0.365148i
\(31\) 1.00000 0.179605 0.0898027 0.995960i \(-0.471376\pi\)
0.0898027 + 0.995960i \(0.471376\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 5.00000i 0.870388i
\(34\) −1.00000 −0.171499
\(35\) 2.00000 1.00000i 0.338062 0.169031i
\(36\) 1.00000 0.166667
\(37\) 1.00000i 0.164399i
\(38\) 0 0
\(39\) 0 0
\(40\) −2.00000 + 1.00000i −0.316228 + 0.158114i
\(41\) −1.00000 −0.156174 −0.0780869 0.996947i \(-0.524881\pi\)
−0.0780869 + 0.996947i \(0.524881\pi\)
\(42\) 1.00000i 0.154303i
\(43\) 7.00000i 1.06749i 0.845645 + 0.533745i \(0.179216\pi\)
−0.845645 + 0.533745i \(0.820784\pi\)
\(44\) −5.00000 −0.753778
\(45\) −1.00000 2.00000i −0.149071 0.298142i
\(46\) 4.00000 0.589768
\(47\) 4.00000i 0.583460i 0.956501 + 0.291730i \(0.0942309\pi\)
−0.956501 + 0.291730i \(0.905769\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 6.00000 0.857143
\(50\) 4.00000 + 3.00000i 0.565685 + 0.424264i
\(51\) 1.00000 0.140028
\(52\) 0 0
\(53\) 3.00000i 0.412082i 0.978543 + 0.206041i \(0.0660580\pi\)
−0.978543 + 0.206041i \(0.933942\pi\)
\(54\) −1.00000 −0.136083
\(55\) 5.00000 + 10.0000i 0.674200 + 1.34840i
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) 3.00000i 0.393919i
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 2.00000 1.00000i 0.258199 0.129099i
\(61\) 5.00000 0.640184 0.320092 0.947386i \(-0.396286\pi\)
0.320092 + 0.947386i \(0.396286\pi\)
\(62\) 1.00000i 0.127000i
\(63\) 1.00000i 0.125988i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 5.00000 0.615457
\(67\) 4.00000i 0.488678i 0.969690 + 0.244339i \(0.0785709\pi\)
−0.969690 + 0.244339i \(0.921429\pi\)
\(68\) 1.00000i 0.121268i
\(69\) −4.00000 −0.481543
\(70\) −1.00000 2.00000i −0.119523 0.239046i
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 10.0000i 1.17041i 0.810885 + 0.585206i \(0.198986\pi\)
−0.810885 + 0.585206i \(0.801014\pi\)
\(74\) 1.00000 0.116248
\(75\) −4.00000 3.00000i −0.461880 0.346410i
\(76\) 0 0
\(77\) 5.00000i 0.569803i
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 1.00000 + 2.00000i 0.111803 + 0.223607i
\(81\) 1.00000 0.111111
\(82\) 1.00000i 0.110432i
\(83\) 8.00000i 0.878114i −0.898459 0.439057i \(-0.855313\pi\)
0.898459 0.439057i \(-0.144687\pi\)
\(84\) −1.00000 −0.109109
\(85\) 2.00000 1.00000i 0.216930 0.108465i
\(86\) 7.00000 0.754829
\(87\) 3.00000i 0.321634i
\(88\) 5.00000i 0.533002i
\(89\) −8.00000 −0.847998 −0.423999 0.905663i \(-0.639374\pi\)
−0.423999 + 0.905663i \(0.639374\pi\)
\(90\) −2.00000 + 1.00000i −0.210819 + 0.105409i
\(91\) 0 0
\(92\) 4.00000i 0.417029i
\(93\) 1.00000i 0.103695i
\(94\) 4.00000 0.412568
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 1.00000i 0.101535i 0.998711 + 0.0507673i \(0.0161667\pi\)
−0.998711 + 0.0507673i \(0.983833\pi\)
\(98\) 6.00000i 0.606092i
\(99\) −5.00000 −0.502519
\(100\) 3.00000 4.00000i 0.300000 0.400000i
\(101\) 10.0000 0.995037 0.497519 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 1.00000i 0.0990148i
\(103\) 8.00000i 0.788263i 0.919054 + 0.394132i \(0.128955\pi\)
−0.919054 + 0.394132i \(0.871045\pi\)
\(104\) 0 0
\(105\) 1.00000 + 2.00000i 0.0975900 + 0.195180i
\(106\) 3.00000 0.291386
\(107\) 6.00000i 0.580042i −0.957020 0.290021i \(-0.906338\pi\)
0.957020 0.290021i \(-0.0936623\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −1.00000 −0.0957826 −0.0478913 0.998853i \(-0.515250\pi\)
−0.0478913 + 0.998853i \(0.515250\pi\)
\(110\) 10.0000 5.00000i 0.953463 0.476731i
\(111\) −1.00000 −0.0949158
\(112\) 1.00000i 0.0944911i
\(113\) 21.0000i 1.97551i −0.156001 0.987757i \(-0.549860\pi\)
0.156001 0.987757i \(-0.450140\pi\)
\(114\) 0 0
\(115\) −8.00000 + 4.00000i −0.746004 + 0.373002i
\(116\) −3.00000 −0.278543
\(117\) 0 0
\(118\) 8.00000i 0.736460i
\(119\) −1.00000 −0.0916698
\(120\) −1.00000 2.00000i −0.0912871 0.182574i
\(121\) 14.0000 1.27273
\(122\) 5.00000i 0.452679i
\(123\) 1.00000i 0.0901670i
\(124\) −1.00000 −0.0898027
\(125\) −11.0000 2.00000i −0.983870 0.178885i
\(126\) 1.00000 0.0890871
\(127\) 8.00000i 0.709885i 0.934888 + 0.354943i \(0.115500\pi\)
−0.934888 + 0.354943i \(0.884500\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −7.00000 −0.616316
\(130\) 0 0
\(131\) −6.00000 −0.524222 −0.262111 0.965038i \(-0.584419\pi\)
−0.262111 + 0.965038i \(0.584419\pi\)
\(132\) 5.00000i 0.435194i
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 2.00000 1.00000i 0.172133 0.0860663i
\(136\) 1.00000 0.0857493
\(137\) 18.0000i 1.53784i −0.639343 0.768922i \(-0.720793\pi\)
0.639343 0.768922i \(-0.279207\pi\)
\(138\) 4.00000i 0.340503i
\(139\) 11.0000 0.933008 0.466504 0.884519i \(-0.345513\pi\)
0.466504 + 0.884519i \(0.345513\pi\)
\(140\) −2.00000 + 1.00000i −0.169031 + 0.0845154i
\(141\) −4.00000 −0.336861
\(142\) 6.00000i 0.503509i
\(143\) 0 0
\(144\) −1.00000 −0.0833333
\(145\) 3.00000 + 6.00000i 0.249136 + 0.498273i
\(146\) 10.0000 0.827606
\(147\) 6.00000i 0.494872i
\(148\) 1.00000i 0.0821995i
\(149\) −4.00000 −0.327693 −0.163846 0.986486i \(-0.552390\pi\)
−0.163846 + 0.986486i \(0.552390\pi\)
\(150\) −3.00000 + 4.00000i −0.244949 + 0.326599i
\(151\) −2.00000 −0.162758 −0.0813788 0.996683i \(-0.525932\pi\)
−0.0813788 + 0.996683i \(0.525932\pi\)
\(152\) 0 0
\(153\) 1.00000i 0.0808452i
\(154\) −5.00000 −0.402911
\(155\) 1.00000 + 2.00000i 0.0803219 + 0.160644i
\(156\) 0 0
\(157\) 23.0000i 1.83560i −0.397043 0.917800i \(-0.629964\pi\)
0.397043 0.917800i \(-0.370036\pi\)
\(158\) 0 0
\(159\) −3.00000 −0.237915
\(160\) 2.00000 1.00000i 0.158114 0.0790569i
\(161\) 4.00000 0.315244
\(162\) 1.00000i 0.0785674i
\(163\) 1.00000i 0.0783260i −0.999233 0.0391630i \(-0.987531\pi\)
0.999233 0.0391630i \(-0.0124692\pi\)
\(164\) 1.00000 0.0780869
\(165\) −10.0000 + 5.00000i −0.778499 + 0.389249i
\(166\) −8.00000 −0.620920
\(167\) 6.00000i 0.464294i 0.972681 + 0.232147i \(0.0745750\pi\)
−0.972681 + 0.232147i \(0.925425\pi\)
\(168\) 1.00000i 0.0771517i
\(169\) 13.0000 1.00000
\(170\) −1.00000 2.00000i −0.0766965 0.153393i
\(171\) 0 0
\(172\) 7.00000i 0.533745i
\(173\) 13.0000i 0.988372i −0.869356 0.494186i \(-0.835466\pi\)
0.869356 0.494186i \(-0.164534\pi\)
\(174\) 3.00000 0.227429
\(175\) 4.00000 + 3.00000i 0.302372 + 0.226779i
\(176\) 5.00000 0.376889
\(177\) 8.00000i 0.601317i
\(178\) 8.00000i 0.599625i
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) 1.00000 + 2.00000i 0.0745356 + 0.149071i
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 0 0
\(183\) 5.00000i 0.369611i
\(184\) −4.00000 −0.294884
\(185\) −2.00000 + 1.00000i −0.147043 + 0.0735215i
\(186\) 1.00000 0.0733236
\(187\) 5.00000i 0.365636i
\(188\) 4.00000i 0.291730i
\(189\) −1.00000 −0.0727393
\(190\) 0 0
\(191\) 3.00000 0.217072 0.108536 0.994092i \(-0.465384\pi\)
0.108536 + 0.994092i \(0.465384\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 10.0000i 0.719816i 0.932988 + 0.359908i \(0.117192\pi\)
−0.932988 + 0.359908i \(0.882808\pi\)
\(194\) 1.00000 0.0717958
\(195\) 0 0
\(196\) −6.00000 −0.428571
\(197\) 26.0000i 1.85242i −0.377004 0.926212i \(-0.623046\pi\)
0.377004 0.926212i \(-0.376954\pi\)
\(198\) 5.00000i 0.355335i
\(199\) −24.0000 −1.70131 −0.850657 0.525720i \(-0.823796\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) −4.00000 3.00000i −0.282843 0.212132i
\(201\) −4.00000 −0.282138
\(202\) 10.0000i 0.703598i
\(203\) 3.00000i 0.210559i
\(204\) −1.00000 −0.0700140
\(205\) −1.00000 2.00000i −0.0698430 0.139686i
\(206\) 8.00000 0.557386
\(207\) 4.00000i 0.278019i
\(208\) 0 0
\(209\) 0 0
\(210\) 2.00000 1.00000i 0.138013 0.0690066i
\(211\) −21.0000 −1.44570 −0.722850 0.691005i \(-0.757168\pi\)
−0.722850 + 0.691005i \(0.757168\pi\)
\(212\) 3.00000i 0.206041i
\(213\) 6.00000i 0.411113i
\(214\) −6.00000 −0.410152
\(215\) −14.0000 + 7.00000i −0.954792 + 0.477396i
\(216\) 1.00000 0.0680414
\(217\) 1.00000i 0.0678844i
\(218\) 1.00000i 0.0677285i
\(219\) −10.0000 −0.675737
\(220\) −5.00000 10.0000i −0.337100 0.674200i
\(221\) 0 0
\(222\) 1.00000i 0.0671156i
\(223\) 5.00000i 0.334825i −0.985887 0.167412i \(-0.946459\pi\)
0.985887 0.167412i \(-0.0535411\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 3.00000 4.00000i 0.200000 0.266667i
\(226\) −21.0000 −1.39690
\(227\) 1.00000i 0.0663723i −0.999449 0.0331862i \(-0.989435\pi\)
0.999449 0.0331862i \(-0.0105654\pi\)
\(228\) 0 0
\(229\) 16.0000 1.05731 0.528655 0.848837i \(-0.322697\pi\)
0.528655 + 0.848837i \(0.322697\pi\)
\(230\) 4.00000 + 8.00000i 0.263752 + 0.527504i
\(231\) 5.00000 0.328976
\(232\) 3.00000i 0.196960i
\(233\) 10.0000i 0.655122i −0.944830 0.327561i \(-0.893773\pi\)
0.944830 0.327561i \(-0.106227\pi\)
\(234\) 0 0
\(235\) −8.00000 + 4.00000i −0.521862 + 0.260931i
\(236\) −8.00000 −0.520756
\(237\) 0 0
\(238\) 1.00000i 0.0648204i
\(239\) −11.0000 −0.711531 −0.355765 0.934575i \(-0.615780\pi\)
−0.355765 + 0.934575i \(0.615780\pi\)
\(240\) −2.00000 + 1.00000i −0.129099 + 0.0645497i
\(241\) −2.00000 −0.128831 −0.0644157 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) 14.0000i 0.899954i
\(243\) 1.00000i 0.0641500i
\(244\) −5.00000 −0.320092
\(245\) 6.00000 + 12.0000i 0.383326 + 0.766652i
\(246\) −1.00000 −0.0637577
\(247\) 0 0
\(248\) 1.00000i 0.0635001i
\(249\) 8.00000 0.506979
\(250\) −2.00000 + 11.0000i −0.126491 + 0.695701i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) 20.0000i 1.25739i
\(254\) 8.00000 0.501965
\(255\) 1.00000 + 2.00000i 0.0626224 + 0.125245i
\(256\) 1.00000 0.0625000
\(257\) 6.00000i 0.374270i −0.982334 0.187135i \(-0.940080\pi\)
0.982334 0.187135i \(-0.0599201\pi\)
\(258\) 7.00000i 0.435801i
\(259\) 1.00000 0.0621370
\(260\) 0 0
\(261\) −3.00000 −0.185695
\(262\) 6.00000i 0.370681i
\(263\) 19.0000i 1.17159i 0.810459 + 0.585795i \(0.199218\pi\)
−0.810459 + 0.585795i \(0.800782\pi\)
\(264\) −5.00000 −0.307729
\(265\) −6.00000 + 3.00000i −0.368577 + 0.184289i
\(266\) 0 0
\(267\) 8.00000i 0.489592i
\(268\) 4.00000i 0.244339i
\(269\) 12.0000 0.731653 0.365826 0.930683i \(-0.380786\pi\)
0.365826 + 0.930683i \(0.380786\pi\)
\(270\) −1.00000 2.00000i −0.0608581 0.121716i
\(271\) −14.0000 −0.850439 −0.425220 0.905090i \(-0.639803\pi\)
−0.425220 + 0.905090i \(0.639803\pi\)
\(272\) 1.00000i 0.0606339i
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) −15.0000 + 20.0000i −0.904534 + 1.20605i
\(276\) 4.00000 0.240772
\(277\) 8.00000i 0.480673i 0.970690 + 0.240337i \(0.0772579\pi\)
−0.970690 + 0.240337i \(0.922742\pi\)
\(278\) 11.0000i 0.659736i
\(279\) −1.00000 −0.0598684
\(280\) 1.00000 + 2.00000i 0.0597614 + 0.119523i
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 4.00000i 0.238197i
\(283\) 16.0000i 0.951101i −0.879688 0.475551i \(-0.842249\pi\)
0.879688 0.475551i \(-0.157751\pi\)
\(284\) 6.00000 0.356034
\(285\) 0 0
\(286\) 0 0
\(287\) 1.00000i 0.0590281i
\(288\) 1.00000i 0.0589256i
\(289\) 16.0000 0.941176
\(290\) 6.00000 3.00000i 0.352332 0.176166i
\(291\) −1.00000 −0.0586210
\(292\) 10.0000i 0.585206i
\(293\) 9.00000i 0.525786i 0.964825 + 0.262893i \(0.0846766\pi\)
−0.964825 + 0.262893i \(0.915323\pi\)
\(294\) 6.00000 0.349927
\(295\) 8.00000 + 16.0000i 0.465778 + 0.931556i
\(296\) −1.00000 −0.0581238
\(297\) 5.00000i 0.290129i
\(298\) 4.00000i 0.231714i
\(299\) 0 0
\(300\) 4.00000 + 3.00000i 0.230940 + 0.173205i
\(301\) 7.00000 0.403473
\(302\) 2.00000i 0.115087i
\(303\) 10.0000i 0.574485i
\(304\) 0 0
\(305\) 5.00000 + 10.0000i 0.286299 + 0.572598i
\(306\) 1.00000 0.0571662
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 5.00000i 0.284901i
\(309\) −8.00000 −0.455104
\(310\) 2.00000 1.00000i 0.113592 0.0567962i
\(311\) 15.0000 0.850572 0.425286 0.905059i \(-0.360174\pi\)
0.425286 + 0.905059i \(0.360174\pi\)
\(312\) 0 0
\(313\) 10.0000i 0.565233i 0.959233 + 0.282617i \(0.0912024\pi\)
−0.959233 + 0.282617i \(0.908798\pi\)
\(314\) −23.0000 −1.29797
\(315\) −2.00000 + 1.00000i −0.112687 + 0.0563436i
\(316\) 0 0
\(317\) 5.00000i 0.280828i 0.990093 + 0.140414i \(0.0448433\pi\)
−0.990093 + 0.140414i \(0.955157\pi\)
\(318\) 3.00000i 0.168232i
\(319\) 15.0000 0.839839
\(320\) −1.00000 2.00000i −0.0559017 0.111803i
\(321\) 6.00000 0.334887
\(322\) 4.00000i 0.222911i
\(323\) 0 0
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −1.00000 −0.0553849
\(327\) 1.00000i 0.0553001i
\(328\) 1.00000i 0.0552158i
\(329\) 4.00000 0.220527
\(330\) 5.00000 + 10.0000i 0.275241 + 0.550482i
\(331\) −26.0000 −1.42909 −0.714545 0.699590i \(-0.753366\pi\)
−0.714545 + 0.699590i \(0.753366\pi\)
\(332\) 8.00000i 0.439057i
\(333\) 1.00000i 0.0547997i
\(334\) 6.00000 0.328305
\(335\) −8.00000 + 4.00000i −0.437087 + 0.218543i
\(336\) 1.00000 0.0545545
\(337\) 16.0000i 0.871576i −0.900049 0.435788i \(-0.856470\pi\)
0.900049 0.435788i \(-0.143530\pi\)
\(338\) 13.0000i 0.707107i
\(339\) 21.0000 1.14056
\(340\) −2.00000 + 1.00000i −0.108465 + 0.0542326i
\(341\) 5.00000 0.270765
\(342\) 0 0
\(343\) 13.0000i 0.701934i
\(344\) −7.00000 −0.377415
\(345\) −4.00000 8.00000i −0.215353 0.430706i
\(346\) −13.0000 −0.698884
\(347\) 12.0000i 0.644194i −0.946707 0.322097i \(-0.895612\pi\)
0.946707 0.322097i \(-0.104388\pi\)
\(348\) 3.00000i 0.160817i
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 3.00000 4.00000i 0.160357 0.213809i
\(351\) 0 0
\(352\) 5.00000i 0.266501i
\(353\) 31.0000i 1.64996i −0.565159 0.824982i \(-0.691185\pi\)
0.565159 0.824982i \(-0.308815\pi\)
\(354\) 8.00000 0.425195
\(355\) −6.00000 12.0000i −0.318447 0.636894i
\(356\) 8.00000 0.423999
\(357\) 1.00000i 0.0529256i
\(358\) 10.0000i 0.528516i
\(359\) −6.00000 −0.316668 −0.158334 0.987386i \(-0.550612\pi\)
−0.158334 + 0.987386i \(0.550612\pi\)
\(360\) 2.00000 1.00000i 0.105409 0.0527046i
\(361\) −19.0000 −1.00000
\(362\) 16.0000i 0.840941i
\(363\) 14.0000i 0.734809i
\(364\) 0 0
\(365\) −20.0000 + 10.0000i −1.04685 + 0.523424i
\(366\) 5.00000 0.261354
\(367\) 13.0000i 0.678594i −0.940679 0.339297i \(-0.889811\pi\)
0.940679 0.339297i \(-0.110189\pi\)
\(368\) 4.00000i 0.208514i
\(369\) 1.00000 0.0520579
\(370\) 1.00000 + 2.00000i 0.0519875 + 0.103975i
\(371\) 3.00000 0.155752
\(372\) 1.00000i 0.0518476i
\(373\) 6.00000i 0.310668i 0.987862 + 0.155334i \(0.0496454\pi\)
−0.987862 + 0.155334i \(0.950355\pi\)
\(374\) −5.00000 −0.258544
\(375\) 2.00000 11.0000i 0.103280 0.568038i
\(376\) −4.00000 −0.206284
\(377\) 0 0
\(378\) 1.00000i 0.0514344i
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) −8.00000 −0.409852
\(382\) 3.00000i 0.153493i
\(383\) 8.00000i 0.408781i 0.978889 + 0.204390i \(0.0655212\pi\)
−0.978889 + 0.204390i \(0.934479\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 10.0000 5.00000i 0.509647 0.254824i
\(386\) 10.0000 0.508987
\(387\) 7.00000i 0.355830i
\(388\) 1.00000i 0.0507673i
\(389\) −23.0000 −1.16615 −0.583073 0.812420i \(-0.698150\pi\)
−0.583073 + 0.812420i \(0.698150\pi\)
\(390\) 0 0
\(391\) 4.00000 0.202289
\(392\) 6.00000i 0.303046i
\(393\) 6.00000i 0.302660i
\(394\) −26.0000 −1.30986
\(395\) 0 0
\(396\) 5.00000 0.251259
\(397\) 22.0000i 1.10415i −0.833795 0.552074i \(-0.813837\pi\)
0.833795 0.552074i \(-0.186163\pi\)
\(398\) 24.0000i 1.20301i
\(399\) 0 0
\(400\) −3.00000 + 4.00000i −0.150000 + 0.200000i
\(401\) 10.0000 0.499376 0.249688 0.968326i \(-0.419672\pi\)
0.249688 + 0.968326i \(0.419672\pi\)
\(402\) 4.00000i 0.199502i
\(403\) 0 0
\(404\) −10.0000 −0.497519
\(405\) 1.00000 + 2.00000i 0.0496904 + 0.0993808i
\(406\) −3.00000 −0.148888
\(407\) 5.00000i 0.247841i
\(408\) 1.00000i 0.0495074i
\(409\) 40.0000 1.97787 0.988936 0.148340i \(-0.0473931\pi\)
0.988936 + 0.148340i \(0.0473931\pi\)
\(410\) −2.00000 + 1.00000i −0.0987730 + 0.0493865i
\(411\) 18.0000 0.887875
\(412\) 8.00000i 0.394132i
\(413\) 8.00000i 0.393654i
\(414\) −4.00000 −0.196589
\(415\) 16.0000 8.00000i 0.785409 0.392705i
\(416\) 0 0
\(417\) 11.0000i 0.538672i
\(418\) 0 0
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) −1.00000 2.00000i −0.0487950 0.0975900i
\(421\) −38.0000 −1.85201 −0.926003 0.377515i \(-0.876779\pi\)
−0.926003 + 0.377515i \(0.876779\pi\)
\(422\) 21.0000i 1.02226i
\(423\) 4.00000i 0.194487i
\(424\) −3.00000 −0.145693
\(425\) 4.00000 + 3.00000i 0.194029 + 0.145521i
\(426\) −6.00000 −0.290701
\(427\) 5.00000i 0.241967i
\(428\) 6.00000i 0.290021i
\(429\) 0 0
\(430\) 7.00000 + 14.0000i 0.337570 + 0.675140i
\(431\) −13.0000 −0.626188 −0.313094 0.949722i \(-0.601365\pi\)
−0.313094 + 0.949722i \(0.601365\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 20.0000i 0.961139i −0.876957 0.480569i \(-0.840430\pi\)
0.876957 0.480569i \(-0.159570\pi\)
\(434\) −1.00000 −0.0480015
\(435\) −6.00000 + 3.00000i −0.287678 + 0.143839i
\(436\) 1.00000 0.0478913
\(437\) 0 0
\(438\) 10.0000i 0.477818i
\(439\) 33.0000 1.57500 0.787502 0.616312i \(-0.211374\pi\)
0.787502 + 0.616312i \(0.211374\pi\)
\(440\) −10.0000 + 5.00000i −0.476731 + 0.238366i
\(441\) −6.00000 −0.285714
\(442\) 0 0
\(443\) 6.00000i 0.285069i −0.989790 0.142534i \(-0.954475\pi\)
0.989790 0.142534i \(-0.0455251\pi\)
\(444\) 1.00000 0.0474579
\(445\) −8.00000 16.0000i −0.379236 0.758473i
\(446\) −5.00000 −0.236757
\(447\) 4.00000i 0.189194i
\(448\) 1.00000i 0.0472456i
\(449\) 24.0000 1.13263 0.566315 0.824189i \(-0.308369\pi\)
0.566315 + 0.824189i \(0.308369\pi\)
\(450\) −4.00000 3.00000i −0.188562 0.141421i
\(451\) −5.00000 −0.235441
\(452\) 21.0000i 0.987757i
\(453\) 2.00000i 0.0939682i
\(454\) −1.00000 −0.0469323
\(455\) 0 0
\(456\) 0 0
\(457\) 19.0000i 0.888783i −0.895833 0.444391i \(-0.853420\pi\)
0.895833 0.444391i \(-0.146580\pi\)
\(458\) 16.0000i 0.747631i
\(459\) −1.00000 −0.0466760
\(460\) 8.00000 4.00000i 0.373002 0.186501i
\(461\) 3.00000 0.139724 0.0698620 0.997557i \(-0.477744\pi\)
0.0698620 + 0.997557i \(0.477744\pi\)
\(462\) 5.00000i 0.232621i
\(463\) 24.0000i 1.11537i −0.830051 0.557687i \(-0.811689\pi\)
0.830051 0.557687i \(-0.188311\pi\)
\(464\) 3.00000 0.139272
\(465\) −2.00000 + 1.00000i −0.0927478 + 0.0463739i
\(466\) −10.0000 −0.463241
\(467\) 27.0000i 1.24941i −0.780860 0.624705i \(-0.785219\pi\)
0.780860 0.624705i \(-0.214781\pi\)
\(468\) 0 0
\(469\) 4.00000 0.184703
\(470\) 4.00000 + 8.00000i 0.184506 + 0.369012i
\(471\) 23.0000 1.05978
\(472\) 8.00000i 0.368230i
\(473\) 35.0000i 1.60930i
\(474\) 0 0
\(475\) 0 0
\(476\) 1.00000 0.0458349
\(477\) 3.00000i 0.137361i
\(478\) 11.0000i 0.503128i
\(479\) 28.0000 1.27935 0.639676 0.768644i \(-0.279068\pi\)
0.639676 + 0.768644i \(0.279068\pi\)
\(480\) 1.00000 + 2.00000i 0.0456435 + 0.0912871i
\(481\) 0 0
\(482\) 2.00000i 0.0910975i
\(483\) 4.00000i 0.182006i
\(484\) −14.0000 −0.636364
\(485\) −2.00000 + 1.00000i −0.0908153 + 0.0454077i
\(486\) 1.00000 0.0453609
\(487\) 12.0000i 0.543772i 0.962329 + 0.271886i \(0.0876473\pi\)
−0.962329 + 0.271886i \(0.912353\pi\)
\(488\) 5.00000i 0.226339i
\(489\) 1.00000 0.0452216
\(490\) 12.0000 6.00000i 0.542105 0.271052i
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 1.00000i 0.0450835i
\(493\) 3.00000i 0.135113i
\(494\) 0 0
\(495\) −5.00000 10.0000i −0.224733 0.449467i
\(496\) 1.00000 0.0449013
\(497\) 6.00000i 0.269137i
\(498\) 8.00000i 0.358489i
\(499\) 30.0000 1.34298 0.671492 0.741012i \(-0.265654\pi\)
0.671492 + 0.741012i \(0.265654\pi\)
\(500\) 11.0000 + 2.00000i 0.491935 + 0.0894427i
\(501\) −6.00000 −0.268060
\(502\) 0 0
\(503\) 6.00000i 0.267527i 0.991013 + 0.133763i \(0.0427062\pi\)
−0.991013 + 0.133763i \(0.957294\pi\)
\(504\) −1.00000 −0.0445435
\(505\) 10.0000 + 20.0000i 0.444994 + 0.889988i
\(506\) 20.0000 0.889108
\(507\) 13.0000i 0.577350i
\(508\) 8.00000i 0.354943i
\(509\) 42.0000 1.86162 0.930809 0.365507i \(-0.119104\pi\)
0.930809 + 0.365507i \(0.119104\pi\)
\(510\) 2.00000 1.00000i 0.0885615 0.0442807i
\(511\) 10.0000 0.442374
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −6.00000 −0.264649
\(515\) −16.0000 + 8.00000i −0.705044 + 0.352522i
\(516\) 7.00000 0.308158
\(517\) 20.0000i 0.879599i
\(518\) 1.00000i 0.0439375i
\(519\) 13.0000 0.570637
\(520\) 0 0
\(521\) −35.0000 −1.53338 −0.766689 0.642019i \(-0.778097\pi\)
−0.766689 + 0.642019i \(0.778097\pi\)
\(522\) 3.00000i 0.131306i
\(523\) 20.0000i 0.874539i 0.899331 + 0.437269i \(0.144054\pi\)
−0.899331 + 0.437269i \(0.855946\pi\)
\(524\) 6.00000 0.262111
\(525\) −3.00000 + 4.00000i −0.130931 + 0.174574i
\(526\) 19.0000 0.828439
\(527\) 1.00000i 0.0435607i
\(528\) 5.00000i 0.217597i
\(529\) 7.00000 0.304348
\(530\) 3.00000 + 6.00000i 0.130312 + 0.260623i
\(531\) −8.00000 −0.347170
\(532\) 0 0
\(533\) 0 0
\(534\) −8.00000 −0.346194
\(535\) 12.0000 6.00000i 0.518805 0.259403i
\(536\) −4.00000 −0.172774
\(537\) 10.0000i 0.431532i
\(538\) 12.0000i 0.517357i
\(539\) 30.0000 1.29219
\(540\) −2.00000 + 1.00000i −0.0860663 + 0.0430331i
\(541\) 34.0000 1.46177 0.730887 0.682498i \(-0.239107\pi\)
0.730887 + 0.682498i \(0.239107\pi\)
\(542\) 14.0000i 0.601351i
\(543\) 16.0000i 0.686626i
\(544\) −1.00000 −0.0428746
\(545\) −1.00000 2.00000i −0.0428353 0.0856706i
\(546\) 0 0
\(547\) 41.0000i 1.75303i 0.481371 + 0.876517i \(0.340139\pi\)
−0.481371 + 0.876517i \(0.659861\pi\)
\(548\) 18.0000i 0.768922i
\(549\) −5.00000 −0.213395
\(550\) 20.0000 + 15.0000i 0.852803 + 0.639602i
\(551\) 0 0
\(552\) 4.00000i 0.170251i
\(553\) 0 0
\(554\) 8.00000 0.339887
\(555\) −1.00000 2.00000i −0.0424476 0.0848953i
\(556\) −11.0000 −0.466504
\(557\) 6.00000i 0.254228i −0.991888 0.127114i \(-0.959429\pi\)
0.991888 0.127114i \(-0.0405714\pi\)
\(558\) 1.00000i 0.0423334i
\(559\) 0 0
\(560\) 2.00000 1.00000i 0.0845154 0.0422577i
\(561\) 5.00000 0.211100
\(562\) 18.0000i 0.759284i
\(563\) 19.0000i 0.800755i −0.916350 0.400377i \(-0.868879\pi\)
0.916350 0.400377i \(-0.131121\pi\)
\(564\) 4.00000 0.168430
\(565\) 42.0000 21.0000i 1.76695 0.883477i
\(566\) −16.0000 −0.672530
\(567\) 1.00000i 0.0419961i
\(568\) 6.00000i 0.251754i
\(569\) 10.0000 0.419222 0.209611 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 0 0
\(571\) −29.0000 −1.21361 −0.606806 0.794850i \(-0.707550\pi\)
−0.606806 + 0.794850i \(0.707550\pi\)
\(572\) 0 0
\(573\) 3.00000i 0.125327i
\(574\) 1.00000 0.0417392
\(575\) −16.0000 12.0000i −0.667246 0.500435i
\(576\) 1.00000 0.0416667
\(577\) 22.0000i 0.915872i −0.888985 0.457936i \(-0.848589\pi\)
0.888985 0.457936i \(-0.151411\pi\)
\(578\) 16.0000i 0.665512i
\(579\) −10.0000 −0.415586
\(580\) −3.00000 6.00000i −0.124568 0.249136i
\(581\) −8.00000 −0.331896
\(582\) 1.00000i 0.0414513i
\(583\) 15.0000i 0.621237i
\(584\) −10.0000 −0.413803
\(585\) 0 0
\(586\) 9.00000 0.371787
\(587\) 33.0000i 1.36206i 0.732257 + 0.681028i \(0.238467\pi\)
−0.732257 + 0.681028i \(0.761533\pi\)
\(588\) 6.00000i 0.247436i
\(589\) 0 0
\(590\) 16.0000 8.00000i 0.658710 0.329355i
\(591\) 26.0000 1.06950
\(592\) 1.00000i 0.0410997i
\(593\) 24.0000i 0.985562i −0.870153 0.492781i \(-0.835980\pi\)
0.870153 0.492781i \(-0.164020\pi\)
\(594\) −5.00000 −0.205152
\(595\) −1.00000 2.00000i −0.0409960 0.0819920i
\(596\) 4.00000 0.163846
\(597\) 24.0000i 0.982255i
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 3.00000 4.00000i 0.122474 0.163299i
\(601\) −7.00000 −0.285536 −0.142768 0.989756i \(-0.545600\pi\)
−0.142768 + 0.989756i \(0.545600\pi\)
\(602\) 7.00000i 0.285299i
\(603\) 4.00000i 0.162893i
\(604\) 2.00000 0.0813788
\(605\) 14.0000 + 28.0000i 0.569181 + 1.13836i
\(606\) 10.0000 0.406222
\(607\) 10.0000i 0.405887i 0.979190 + 0.202944i \(0.0650509\pi\)
−0.979190 + 0.202944i \(0.934949\pi\)
\(608\) 0 0
\(609\) 3.00000 0.121566
\(610\) 10.0000 5.00000i 0.404888 0.202444i
\(611\) 0 0
\(612\) 1.00000i 0.0404226i
\(613\) 37.0000i 1.49442i 0.664590 + 0.747208i \(0.268606\pi\)
−0.664590 + 0.747208i \(0.731394\pi\)
\(614\) 0 0
\(615\) 2.00000 1.00000i 0.0806478 0.0403239i
\(616\) 5.00000 0.201456
\(617\) 34.0000i 1.36879i −0.729112 0.684394i \(-0.760067\pi\)
0.729112 0.684394i \(-0.239933\pi\)
\(618\) 8.00000i 0.321807i
\(619\) 31.0000 1.24600 0.622998 0.782224i \(-0.285915\pi\)
0.622998 + 0.782224i \(0.285915\pi\)
\(620\) −1.00000 2.00000i −0.0401610 0.0803219i
\(621\) 4.00000 0.160514
\(622\) 15.0000i 0.601445i
\(623\) 8.00000i 0.320513i
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 10.0000 0.399680
\(627\) 0 0
\(628\) 23.0000i 0.917800i
\(629\) 1.00000 0.0398726
\(630\) 1.00000 + 2.00000i 0.0398410 + 0.0796819i
\(631\) 5.00000 0.199047 0.0995234 0.995035i \(-0.468268\pi\)
0.0995234 + 0.995035i \(0.468268\pi\)
\(632\) 0 0
\(633\) 21.0000i 0.834675i
\(634\) 5.00000 0.198575
\(635\) −16.0000 + 8.00000i −0.634941 + 0.317470i
\(636\) 3.00000 0.118958
\(637\) 0 0
\(638\) 15.0000i 0.593856i
\(639\) 6.00000 0.237356
\(640\) −2.00000 + 1.00000i −0.0790569 + 0.0395285i
\(641\) −37.0000 −1.46141 −0.730706 0.682692i \(-0.760809\pi\)
−0.730706 + 0.682692i \(0.760809\pi\)
\(642\) 6.00000i 0.236801i
\(643\) 21.0000i 0.828159i −0.910241 0.414080i \(-0.864104\pi\)
0.910241 0.414080i \(-0.135896\pi\)
\(644\) −4.00000 −0.157622
\(645\) −7.00000 14.0000i −0.275625 0.551249i
\(646\) 0 0
\(647\) 42.0000i 1.65119i −0.564263 0.825595i \(-0.690840\pi\)
0.564263 0.825595i \(-0.309160\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 40.0000 1.57014
\(650\) 0 0
\(651\) 1.00000 0.0391931
\(652\) 1.00000i 0.0391630i
\(653\) 10.0000i 0.391330i 0.980671 + 0.195665i \(0.0626866\pi\)
−0.980671 + 0.195665i \(0.937313\pi\)
\(654\) −1.00000 −0.0391031
\(655\) −6.00000 12.0000i −0.234439 0.468879i
\(656\) −1.00000 −0.0390434
\(657\) 10.0000i 0.390137i
\(658\) 4.00000i 0.155936i
\(659\) 32.0000 1.24654 0.623272 0.782006i \(-0.285803\pi\)
0.623272 + 0.782006i \(0.285803\pi\)
\(660\) 10.0000 5.00000i 0.389249 0.194625i
\(661\) −13.0000 −0.505641 −0.252821 0.967513i \(-0.581358\pi\)
−0.252821 + 0.967513i \(0.581358\pi\)
\(662\) 26.0000i 1.01052i
\(663\) 0 0
\(664\) 8.00000 0.310460
\(665\) 0 0
\(666\) −1.00000 −0.0387492
\(667\) 12.0000i 0.464642i
\(668\) 6.00000i 0.232147i
\(669\) 5.00000 0.193311
\(670\) 4.00000 + 8.00000i 0.154533 + 0.309067i
\(671\) 25.0000 0.965114
\(672\) 1.00000i 0.0385758i
\(673\) 36.0000i 1.38770i 0.720121 + 0.693849i \(0.244086\pi\)
−0.720121 + 0.693849i \(0.755914\pi\)
\(674\) −16.0000 −0.616297
\(675\) 4.00000 + 3.00000i 0.153960 + 0.115470i
\(676\) −13.0000 −0.500000
\(677\) 2.00000i 0.0768662i 0.999261 + 0.0384331i \(0.0122367\pi\)
−0.999261 + 0.0384331i \(0.987763\pi\)
\(678\) 21.0000i 0.806500i
\(679\) 1.00000 0.0383765
\(680\) 1.00000 + 2.00000i 0.0383482 + 0.0766965i
\(681\) 1.00000 0.0383201
\(682\) 5.00000i 0.191460i
\(683\) 37.0000i 1.41577i 0.706330 + 0.707883i \(0.250350\pi\)
−0.706330 + 0.707883i \(0.749650\pi\)
\(684\) 0 0
\(685\) 36.0000 18.0000i 1.37549 0.687745i
\(686\) −13.0000 −0.496342
\(687\) 16.0000i 0.610438i
\(688\) 7.00000i 0.266872i
\(689\) 0 0
\(690\) −8.00000 + 4.00000i −0.304555 + 0.152277i
\(691\) −5.00000 −0.190209 −0.0951045 0.995467i \(-0.530319\pi\)
−0.0951045 + 0.995467i \(0.530319\pi\)
\(692\) 13.0000i 0.494186i
\(693\) 5.00000i 0.189934i
\(694\) −12.0000 −0.455514
\(695\) 11.0000 + 22.0000i 0.417254 + 0.834508i
\(696\) −3.00000 −0.113715
\(697\) 1.00000i 0.0378777i
\(698\) 2.00000i 0.0757011i
\(699\) 10.0000 0.378235
\(700\) −4.00000 3.00000i −0.151186 0.113389i
\(701\) 26.0000 0.982006 0.491003 0.871158i \(-0.336630\pi\)
0.491003 + 0.871158i \(0.336630\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −5.00000 −0.188445
\(705\) −4.00000 8.00000i −0.150649 0.301297i
\(706\) −31.0000 −1.16670
\(707\) 10.0000i 0.376089i
\(708\) 8.00000i 0.300658i
\(709\) −9.00000 −0.338002 −0.169001 0.985616i \(-0.554054\pi\)
−0.169001 + 0.985616i \(0.554054\pi\)
\(710\) −12.0000 + 6.00000i −0.450352 + 0.225176i
\(711\) 0 0
\(712\) 8.00000i 0.299813i
\(713\) 4.00000i 0.149801i
\(714\) −1.00000 −0.0374241
\(715\) 0 0
\(716\) 10.0000 0.373718
\(717\) 11.0000i 0.410803i
\(718\) 6.00000i 0.223918i
\(719\) 28.0000 1.04422 0.522112 0.852877i \(-0.325144\pi\)
0.522112 + 0.852877i \(0.325144\pi\)
\(720\) −1.00000 2.00000i −0.0372678 0.0745356i
\(721\) 8.00000 0.297936
\(722\) 19.0000i 0.707107i
\(723\) 2.00000i 0.0743808i
\(724\) 16.0000 0.594635
\(725\) −9.00000 + 12.0000i −0.334252 + 0.445669i
\(726\) 14.0000 0.519589
\(727\) 42.0000i 1.55769i 0.627214 + 0.778847i \(0.284195\pi\)
−0.627214 + 0.778847i \(0.715805\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 10.0000 + 20.0000i 0.370117 + 0.740233i
\(731\) 7.00000 0.258904
\(732\) 5.00000i 0.184805i
\(733\) 19.0000i 0.701781i −0.936416 0.350891i \(-0.885879\pi\)
0.936416 0.350891i \(-0.114121\pi\)
\(734\) −13.0000 −0.479839
\(735\) −12.0000 + 6.00000i −0.442627 + 0.221313i
\(736\) 4.00000 0.147442
\(737\) 20.0000i 0.736709i
\(738\) 1.00000i 0.0368105i
\(739\) −37.0000 −1.36107 −0.680534 0.732717i \(-0.738252\pi\)
−0.680534 + 0.732717i \(0.738252\pi\)
\(740\) 2.00000 1.00000i 0.0735215 0.0367607i
\(741\) 0 0
\(742\) 3.00000i 0.110133i
\(743\) 15.0000i 0.550297i 0.961402 + 0.275148i \(0.0887270\pi\)
−0.961402 + 0.275148i \(0.911273\pi\)
\(744\) −1.00000 −0.0366618
\(745\) −4.00000 8.00000i −0.146549 0.293097i
\(746\) 6.00000 0.219676
\(747\) 8.00000i 0.292705i
\(748\) 5.00000i 0.182818i
\(749\) −6.00000 −0.219235
\(750\) −11.0000 2.00000i −0.401663 0.0730297i
\(751\) 20.0000 0.729810 0.364905 0.931045i \(-0.381101\pi\)
0.364905 + 0.931045i \(0.381101\pi\)
\(752\) 4.00000i 0.145865i
\(753\) 0 0
\(754\) 0 0
\(755\) −2.00000 4.00000i −0.0727875 0.145575i
\(756\) 1.00000 0.0363696
\(757\) 20.0000i 0.726912i 0.931611 + 0.363456i \(0.118403\pi\)
−0.931611 + 0.363456i \(0.881597\pi\)
\(758\) 20.0000i 0.726433i
\(759\) −20.0000 −0.725954
\(760\) 0 0
\(761\) −21.0000 −0.761249 −0.380625 0.924730i \(-0.624291\pi\)
−0.380625 + 0.924730i \(0.624291\pi\)
\(762\) 8.00000i 0.289809i
\(763\) 1.00000i 0.0362024i
\(764\) −3.00000 −0.108536
\(765\) −2.00000 + 1.00000i −0.0723102 + 0.0361551i
\(766\) 8.00000 0.289052
\(767\) 0 0
\(768\) 1.00000i 0.0360844i
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) −5.00000 10.0000i −0.180187 0.360375i
\(771\) 6.00000 0.216085
\(772\) 10.0000i 0.359908i
\(773\) 27.0000i 0.971123i −0.874203 0.485561i \(-0.838615\pi\)
0.874203 0.485561i \(-0.161385\pi\)
\(774\) −7.00000 −0.251610
\(775\) −3.00000 + 4.00000i −0.107763 + 0.143684i
\(776\) −1.00000 −0.0358979
\(777\) 1.00000i 0.0358748i
\(778\) 23.0000i 0.824590i
\(779\) 0 0
\(780\) 0 0
\(781\) −30.0000 −1.07348
\(782\) 4.00000i 0.143040i
\(783\) 3.00000i 0.107211i
\(784\) 6.00000 0.214286
\(785\) 46.0000 23.0000i 1.64181 0.820905i
\(786\) −6.00000 −0.214013
\(787\) 10.0000i 0.356462i −0.983989 0.178231i \(-0.942963\pi\)
0.983989 0.178231i \(-0.0570374\pi\)
\(788\) 26.0000i 0.926212i
\(789\) −19.0000 −0.676418
\(790\) 0 0
\(791\) −21.0000 −0.746674